LMFDB - Embedded newform 28.6.e.b.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [28,6,Mod(9,28)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("28.9"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	28.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.49074695476$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{109})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 28x^{2} + 27x + 729 $ x^4 - x^3 + 28x^2 + 27x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$2.86008 - 4.95380i$ of defining polynomial
Character	$\chi$	$=$	28.9
Dual form			28.6.e.b.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.2202 - 21.1659i) q^{3} +(-41.8209 + 72.4360i) q^{5} +(28.0000 + 126.582i) q^{7} +(-177.164 + 306.858i) q^{9} +(-274.623 - 475.661i) q^{11} -823.135 q^{13} +2044.23 q^{15} +(-72.7837 - 126.065i) q^{17} +(-884.019 + 1531.17i) q^{19} +(2337.06 - 2139.50i) q^{21} +(761.363 - 1318.72i) q^{23} +(-1935.48 - 3352.35i) q^{25} +2720.90 q^{27} -741.943 q^{29} +(1602.09 + 2774.90i) q^{31} +(-6711.88 + 11625.3i) q^{33} +(-10340.1 - 3265.57i) q^{35} +(1774.77 - 3074.00i) q^{37} +(10058.8 + 17422.4i) q^{39} -6461.29 q^{41} +6716.00 q^{43} +(-14818.3 - 25666.1i) q^{45} +(9588.40 - 16607.6i) q^{47} +(-15239.0 + 7088.59i) q^{49} +(-1778.86 + 3081.07i) q^{51} +(10639.3 + 18427.8i) q^{53} +45940.0 q^{55} +43211.4 q^{57} +(-18264.3 - 31634.8i) q^{59} +(-21716.9 + 37614.7i) q^{61} +(-43803.2 - 13833.8i) q^{63} +(34424.3 - 59624.6i) q^{65} +(-2514.07 - 4354.50i) q^{67} -37215.9 q^{69} -6311.32 q^{71} +(21299.0 + 36890.9i) q^{73} +(-47303.7 + 81932.4i) q^{75} +(52520.7 - 48080.9i) q^{77} +(-47534.6 + 82332.3i) q^{79} +(9801.05 + 16975.9i) q^{81} -34978.2 q^{83} +12175.5 q^{85} +(9066.66 + 15703.9i) q^{87} +(-50276.7 + 87081.8i) q^{89} +(-23047.8 - 104194. i) q^{91} +(39155.5 - 67819.3i) q^{93} +(-73940.9 - 128069. i) q^{95} +76794.5 q^{97} +194614. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 28 q^{3} - 42 q^{5} + 112 q^{7} - 124 q^{9} - 660 q^{11} - 1288 q^{13} + 3792 q^{15} + 210 q^{17} - 3724 q^{19} + 3794 q^{21} - 24 q^{23} - 2480 q^{25} + 2072 q^{27} + 11064 q^{29} - 2800 q^{31} - 13818 q^{33}+ \cdots + 338208 q^{99}+O(q^{100}) $ 4 * q - 28 * q^3 - 42 * q^5 + 112 * q^7 - 124 * q^9 - 660 * q^11 - 1288 * q^13 + 3792 * q^15 + 210 * q^17 - 3724 * q^19 + 3794 * q^21 - 24 * q^23 - 2480 * q^25 + 2072 * q^27 + 11064 * q^29 - 2800 * q^31 - 13818 * q^33 - 28644 * q^35 + 13238 * q^37 + 19480 * q^39 + 8232 * q^41 + 26864 * q^43 - 39228 * q^45 - 8064 * q^47 - 60956 * q^49 - 2292 * q^51 + 53958 * q^53 + 82656 * q^55 + 100348 * q^57 - 36036 * q^59 - 83986 * q^61 - 131656 * q^63 + 76308 * q^65 + 2660 * q^67 - 63420 * q^69 + 143136 * q^71 - 31318 * q^73 - 89656 * q^75 + 77658 * q^77 - 51136 * q^79 - 30370 * q^81 + 12432 * q^83 + 53964 * q^85 - 4200 * q^87 - 166278 * q^89 - 36064 * q^91 + 56938 * q^93 - 66432 * q^95 + 16520 * q^97 + 338208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−12.2202	−	21.1659i	−0.783923	−	1.35779i	−0.929640	−	0.368468i	$-0.879882\pi$
$3$	−12.2202	−	21.1659i	−0.783923	−	1.35779i	0.145717	−	0.989326i	$-0.453451\pi$
$4$		0			0
$5$	−41.8209	+	72.4360i	−0.748115	+	1.29577i	0.200610	+	0.979671i	$0.435708\pi$
$5$	−41.8209	+	72.4360i	−0.748115	+	1.29577i	−0.948725	+	0.316103i	$0.897626\pi$
$6$		0			0
$7$	28.0000	+	126.582i	0.215980	+	0.976398i
$7$	28.0000	+	126.582i	0.215980	+	0.976398i
$8$		0			0
$9$	−177.164	+	306.858i	−0.729071	+	1.26279i
$10$		0			0
$11$	−274.623	−	475.661i	−0.684314	−	1.18527i	−0.973652	−	0.228040i	$-0.926768\pi$
$11$	−274.623	−	475.661i	−0.684314	−	1.18527i	0.289338	−	0.957227i	$-0.406565\pi$
$12$		0			0
$13$	−823.135			−1.35087			−0.675433	−	0.737421i	$-0.736043\pi$
$13$	−823.135			−1.35087			−0.675433	+	0.737421i	$0.736043\pi$
$14$		0			0
$15$	2044.23			2.34586
$16$		0			0
$17$	−72.7837	−	126.065i	−0.0610818	−	0.105797i	0.833867	−	0.551965i	$-0.186122\pi$
$17$	−72.7837	−	126.065i	−0.0610818	−	0.105797i	−0.894949	+	0.446168i	$0.852788\pi$
$18$		0			0
$19$	−884.019	+	1531.17i	−0.561794	+	0.973056i	0.435546	+	0.900167i	$0.356555\pi$
$19$	−884.019	+	1531.17i	−0.561794	+	0.973056i	−0.997340	+	0.0728898i	$0.976778\pi$
$20$		0			0
$21$	2337.06	−	2139.50i	1.15644	−	1.05868i
$22$		0			0
$23$	761.363	−	1318.72i	0.300104	−	0.519796i	−0.676055	−	0.736851i	$-0.736312\pi$
$23$	761.363	−	1318.72i	0.300104	−	0.519796i	0.976159	+	0.217055i	$0.0696453\pi$
$24$		0			0
$25$	−1935.48	−	3352.35i	−0.619353	−	1.07275i
$26$		0			0
$27$	2720.90			0.718297
$28$		0			0
$29$	−741.943			−0.163823			−0.0819116	−	0.996640i	$-0.526103\pi$
$29$	−741.943			−0.163823			−0.0819116	+	0.996640i	$0.526103\pi$
$30$		0			0
$31$	1602.09	+	2774.90i	0.299421	+	0.518612i	0.976004	−	0.217755i	$-0.0698732\pi$
$31$	1602.09	+	2774.90i	0.299421	+	0.518612i	−0.676583	+	0.736367i	$0.736540\pi$
$32$		0			0
$33$	−6711.88	+	11625.3i	−1.07290	+	1.85832i
$34$		0			0
$35$	−10340.1	−	3265.57i	−1.42677	−	0.450597i
$36$		0			0
$37$	1774.77	−	3074.00i	0.213127	−	0.369147i	−0.739564	−	0.673086i	$-0.764968\pi$
$37$	1774.77	−	3074.00i	0.213127	−	0.369147i	0.952692	+	0.303939i	$0.0983018\pi$
$38$		0			0
$39$	10058.8	+	17422.4i	1.05898	+	1.83420i
$40$		0			0
$41$	−6461.29			−0.600288			−0.300144	−	0.953894i	$-0.597035\pi$
$41$	−6461.29			−0.600288			−0.300144	+	0.953894i	$0.597035\pi$
$42$		0			0
$43$	6716.00			0.553910			0.276955	−	0.960883i	$-0.410675\pi$
$43$	6716.00			0.553910			0.276955	+	0.960883i	$0.410675\pi$
$44$		0			0
$45$	−14818.3	−	25666.1i	−1.09086	−	1.88942i
$46$		0			0
$47$	9588.40	−	16607.6i	0.633143	−	1.09664i	−0.353763	−	0.935335i	$-0.615098\pi$
$47$	9588.40	−	16607.6i	0.633143	−	1.09664i	0.986905	−	0.161300i	$-0.0515687\pi$
$48$		0			0
$49$	−15239.0	+	7088.59i	−0.906706	+	0.421764i
$50$		0			0
$51$	−1778.86	+	3081.07i	−0.0957669	+	0.165873i
$52$		0			0
$53$	10639.3	+	18427.8i	0.520263	+	0.901123i	0.999722	+	0.0235583i	$0.00749954\pi$
$53$	10639.3	+	18427.8i	0.520263	+	0.901123i	−0.479459	+	0.877564i	$0.659167\pi$
$54$		0			0
$55$	45940.0			2.04778
$56$		0			0
$57$	43211.4			1.76161
$58$		0			0
$59$	−18264.3	−	31634.8i	−0.683083	−	1.18314i	−0.974035	−	0.226397i	$-0.927305\pi$
$59$	−18264.3	−	31634.8i	−0.683083	−	1.18314i	0.290952	−	0.956738i	$-0.406028\pi$
$60$		0			0
$61$	−21716.9	+	37614.7i	−0.747262	+	1.29430i	0.201869	+	0.979413i	$0.435299\pi$
$61$	−21716.9	+	37614.7i	−0.747262	+	1.29430i	−0.949130	+	0.314883i	$0.898035\pi$
$62$		0			0
$63$	−43803.2	−	13833.8i	−1.39045	−	0.439127i
$64$		0			0
$65$	34424.3	−	59624.6i	1.01060	−	1.75042i
$66$		0			0
$67$	−2514.07	−	4354.50i	−0.0684212	−	0.118509i	0.829785	−	0.558083i	$-0.188463\pi$
$67$	−2514.07	−	4354.50i	−0.0684212	−	0.118509i	−0.898207	+	0.439574i	$0.855130\pi$
$68$		0			0
$69$	−37215.9			−0.941034
$70$		0			0
$71$	−6311.32			−0.148585			−0.0742923	−	0.997237i	$-0.523670\pi$
$71$	−6311.32			−0.148585			−0.0742923	+	0.997237i	$0.523670\pi$
$72$		0			0
$73$	21299.0	+	36890.9i	0.467790	+	0.810236i	0.999323	−	0.0368015i	$-0.0117169\pi$
$73$	21299.0	+	36890.9i	0.467790	+	0.810236i	−0.531532	+	0.847038i	$0.678384\pi$
$74$		0			0
$75$	−47303.7	+	81932.4i	−0.971051	+	1.68191i
$76$		0			0
$77$	52520.7	−	48080.9i	1.00949	−	0.924156i
$78$		0			0
$79$	−47534.6	+	82332.3i	−0.856923	+	1.48423i	0.0179267	+	0.999839i	$0.494293\pi$
$79$	−47534.6	+	82332.3i	−0.856923	+	1.48423i	−0.874850	+	0.484395i	$0.839040\pi$
$80$		0			0
$81$	9801.05	+	16975.9i	0.165982	+	0.287489i
$82$		0			0
$83$	−34978.2			−0.557318			−0.278659	−	0.960390i	$-0.589890\pi$
$83$	−34978.2			−0.557318			−0.278659	+	0.960390i	$0.589890\pi$
$84$		0			0
$85$	12175.5			0.182785
$86$		0			0
$87$	9066.66	+	15703.9i	0.128425	+	0.222438i
$88$		0			0
$89$	−50276.7	+	87081.8i	−0.672809	+	1.16534i	0.304295	+	0.952578i	$0.401579\pi$
$89$	−50276.7	+	87081.8i	−0.672809	+	1.16534i	−0.977104	+	0.212762i	$0.931754\pi$
$90$		0			0
$91$	−23047.8	−	104194.i	−0.291760	−	1.31898i
$92$		0			0
$93$	39155.5	−	67819.3i	0.469446	−	0.813104i
$94$		0			0
$95$	−73940.9	−	128069.i	−0.840574	−	1.45592i
$96$		0			0
$97$	76794.5			0.828707			0.414353	−	0.910116i	$-0.364008\pi$
$97$	76794.5			0.828707			0.414353	+	0.910116i	$0.364008\pi$
$98$		0			0
$99$	194614.			1.99565
$100$		0			0
$101$	−57020.2	−	98761.9i	−0.556193	−	0.963355i	−0.997810	−	0.0661508i	$-0.978928\pi$
$101$	−57020.2	−	98761.9i	−0.556193	−	0.963355i	0.441617	−	0.897204i	$-0.354405\pi$
$102$		0			0
$103$	61818.5	−	107073.i	0.574150	−	0.994457i	−0.421983	−	0.906604i	$-0.638666\pi$
$103$	61818.5	−	107073.i	0.574150	−	0.994457i	0.996133	−	0.0878533i	$-0.0280007\pi$
$104$		0			0
$105$	57238.5	+	258763.i	0.506658	+	2.29049i
$106$		0			0
$107$	11670.1	−	20213.2i	0.0985404	−	0.170677i	−0.812540	−	0.582905i	$-0.801916\pi$
$107$	11670.1	−	20213.2i	0.0985404	−	0.170677i	0.911081	+	0.412228i	$0.135249\pi$
$108$		0			0
$109$	13601.6	+	23558.6i	0.109654	+	0.189926i	0.915630	−	0.402022i	$-0.131692\pi$
$109$	13601.6	+	23558.6i	0.109654	+	0.189926i	−0.805976	+	0.591948i	$0.798359\pi$
$110$		0			0
$111$	−86752.1			−0.668302
$112$		0			0
$113$	−157394.			−1.15955			−0.579777	−	0.814775i	$-0.696860\pi$
$113$	−157394.			−1.15955			−0.579777	+	0.814775i	$0.696860\pi$
$114$		0			0
$115$	63681.8	+	110300.i	0.449025	+	0.777734i
$116$		0			0
$117$	145830.	−	252585.i	0.984878	−	1.70586i
$118$		0			0
$119$	13919.6	−	12742.9i	0.0901073	−	0.0824901i
$120$		0			0
$121$	−70310.3	+	121781.i	−0.436572	+	0.756165i
$122$		0			0
$123$	78958.0	+	136759.i	0.470580	+	0.815068i
$124$		0			0
$125$	62393.2			0.357160
$126$		0			0
$127$	−253263.			−1.39336			−0.696679	−	0.717383i	$-0.745340\pi$
$127$	−253263.			−1.39336			−0.696679	+	0.717383i	$0.745340\pi$
$128$		0			0
$129$	−82070.5	−	142150.i	−0.434223	−	0.752097i
$130$		0			0
$131$	57772.6	−	100065.i	0.294133	−	0.509453i	−0.680650	−	0.732609i	$-0.738302\pi$
$131$	57772.6	−	100065.i	0.294133	−	0.509453i	0.974783	+	0.223156i	$0.0716358\pi$
$132$		0			0
$133$	−218570.	−	69028.2i	−1.07143	−	0.338374i
$134$		0			0
$135$	−113791.	+	197091.i	−0.537369	+	0.930750i
$136$		0			0
$137$	103904.	+	179967.i	0.472966	+	0.819202i	0.999521	−	0.0309393i	$-0.00984986\pi$
$137$	103904.	+	179967.i	0.472966	+	0.819202i	−0.526555	+	0.850141i	$0.676517\pi$
$138$		0			0
$139$	−28993.1			−0.127279			−0.0636395	−	0.997973i	$-0.520271\pi$
$139$	−28993.1			−0.127279			−0.0636395	+	0.997973i	$0.520271\pi$
$140$		0			0
$141$	−468687.			−1.98534
$142$		0			0
$143$	226052.	+	391533.i	0.924417	+	1.60114i
$144$		0			0
$145$	31028.7	−	53743.4i	0.122559	−	0.212278i
$146$		0			0
$147$	336260.	+	235924.i	1.28346	+	0.900489i
$148$		0			0
$149$	165490.	−	286637.i	0.610668	−	1.05771i	−0.380460	−	0.924798i	$-0.624234\pi$
$149$	165490.	−	286637.i	0.610668	−	1.05771i	0.991128	−	0.132911i	$-0.0424325\pi$
$150$		0			0
$151$	−54428.3	−	94272.6i	−0.194260	−	0.336468i	0.752398	−	0.658709i	$-0.228897\pi$
$151$	−54428.3	−	94272.6i	−0.194260	−	0.336468i	−0.946658	+	0.322241i	$0.895564\pi$
$152$		0			0
$153$	51578.7			0.178132
$154$		0			0
$155$	−268003.			−0.896005
$156$		0			0
$157$	248873.	+	431060.i	0.805801	+	1.39569i	0.915749	+	0.401752i	$0.131598\pi$
$157$	248873.	+	431060.i	0.805801	+	1.39569i	−0.109947	+	0.993937i	$0.535068\pi$
$158$		0			0
$159$	260028.	−	450381.i	0.815693	−	1.41282i
$160$		0			0
$161$	188244.	+	59450.7i	0.572344	+	0.180756i
$162$		0			0
$163$	179551.	−	310992.i	0.529321	−	0.916811i	−0.470094	−	0.882616i	$-0.655780\pi$
$163$	179551.	−	310992.i	0.529321	−	0.916811i	0.999415	−	0.0341950i	$-0.0108867\pi$
$164$		0			0
$165$	−561394.	−	972362.i	−1.60531	−	2.78047i
$166$		0			0
$167$	−50645.2			−0.140523			−0.0702614	−	0.997529i	$-0.522383\pi$
$167$	−50645.2			−0.140523			−0.0702614	+	0.997529i	$0.522383\pi$
$168$		0			0
$169$	306258.			0.824841
$170$		0			0
$171$	−313233.	−	542536.i	−0.819176	−	1.41885i
$172$		0			0
$173$	−151595.	+	262569.i	−0.385095	+	0.667005i	−0.991782	−	0.127936i	$-0.959165\pi$
$173$	−151595.	+	262569.i	−0.385095	+	0.667005i	0.606687	+	0.794941i	$0.292498\pi$
$174$		0			0
$175$	370153.	−	338862.i	0.913664	−	0.836428i
$176$		0			0
$177$	−446386.	+	773163.i	−1.07097	+	1.85497i
$178$		0			0
$179$	341272.	+	591100.i	0.796100	+	1.37889i	0.922138	+	0.386860i	$0.126440\pi$
$179$	341272.	+	591100.i	0.796100	+	1.37889i	−0.126039	+	0.992025i	$0.540226\pi$
$180$		0			0
$181$	182455.			0.413961			0.206980	−	0.978345i	$-0.433636\pi$
$181$	182455.			0.413961			0.206980	+	0.978345i	$0.433636\pi$
$182$		0			0
$183$	1.06153e6			2.34318
$184$		0			0
$185$	148445.	+	257115.i	0.318888	+	0.552329i
$186$		0			0
$187$	−39976.2	+	69240.8i	−0.0835983	+	0.144796i
$188$		0			0
$189$	76185.3	+	344418.i	0.155138	+	0.701343i
$190$		0			0
$191$	−341772.	+	591966.i	−0.677879	+	1.17412i	0.297739	+	0.954647i	$0.403768\pi$
$191$	−341772.	+	591966.i	−0.677879	+	1.17412i	−0.975618	+	0.219474i	$0.929566\pi$
$192$		0			0
$193$	−473251.	−	819696.i	−0.914532	−	1.58402i	−0.807586	−	0.589750i	$-0.799226\pi$
$193$	−473251.	−	819696.i	−0.914532	−	1.58402i	−0.106946	−	0.994265i	$-0.534107\pi$
$194$		0			0
$195$	−1.68268e6			−3.16894
$196$		0			0
$197$	−184209.			−0.338178			−0.169089	−	0.985601i	$-0.554082\pi$
$197$	−184209.			−0.338178			−0.169089	+	0.985601i	$0.554082\pi$
$198$		0			0
$199$	−34103.3	−	59068.6i	−0.0610469	−	0.105736i	0.833887	−	0.551936i	$-0.186111\pi$
$199$	−34103.3	−	59068.6i	−0.0610469	−	0.105736i	−0.894934	+	0.446199i	$0.852777\pi$
$200$		0			0
$201$	−61444.7	+	106425.i	−0.107274	+	0.185804i
$202$		0			0
$203$	−20774.4	−	93916.6i	−0.0353825	−	0.159957i
$204$		0			0
$205$	270217.	−	468030.i	0.449085	−	0.777837i
$206$		0			0
$207$	269773.	+	467260.i	0.437594	+	0.757936i
$208$		0			0
$209$	971088.			1.53778
$210$		0			0
$211$	−1.19270e6			−1.84427			−0.922134	−	0.386871i	$-0.873556\pi$
$211$	−1.19270e6			−1.84427			−0.922134	+	0.386871i	$0.873556\pi$
$212$		0			0
$213$	77125.2	+	133585.i	0.116479	+	0.201748i
$214$		0			0
$215$	−280869.	+	486480.i	−0.414389	+	0.717743i
$216$		0			0
$217$	−306394.	+	280493.i	−0.441703	+	0.404364i
$218$		0			0
$219$	520553.	−	901624.i	0.733423	−	1.27033i
$220$		0			0
$221$	59910.8	+	103769.i	0.0825134	+	0.142917i
$222$		0			0
$223$	200502.			0.269995			0.134998	−	0.990846i	$-0.456897\pi$
$223$	200502.			0.269995			0.134998	+	0.990846i	$0.456897\pi$
$224$		0			0
$225$	1.37159e6			1.80621
$226$		0			0
$227$	−145384.	−	251813.i	−0.187264	−	0.324350i	0.757073	−	0.653330i	$-0.226629\pi$
$227$	−145384.	−	251813.i	−0.187264	−	0.324350i	−0.944337	+	0.328980i	$0.893295\pi$
$228$		0			0
$229$	−472471.	+	818344.i	−0.595369	+	1.03121i	0.398125	+	0.917331i	$0.369661\pi$
$229$	−472471.	+	818344.i	−0.595369	+	1.03121i	−0.993495	+	0.113879i	$0.963672\pi$
$230$		0			0
$231$	−1.65949e6	−	524094.i	−2.04618	−	0.646218i
$232$		0			0
$233$	−108192.	+	187394.i	−0.130558	+	0.226134i	−0.923892	−	0.382653i	$-0.875010\pi$
$233$	−108192.	+	187394.i	−0.130558	+	0.226134i	0.793334	+	0.608787i	$0.208344\pi$
$234$		0			0
$235$	801991.	+	1.38909e6i	0.947327	+	1.64082i
$236$		0			0
$237$	2.32352e6			2.68705
$238$		0			0
$239$	−668807.			−0.757366			−0.378683	−	0.925526i	$-0.623623\pi$
$239$	−668807.			−0.757366			−0.378683	+	0.925526i	$0.623623\pi$
$240$		0			0
$241$	−578006.	−	1.00114e6i	−0.641047	−	1.11033i	−0.985199	−	0.171413i	$-0.945167\pi$
$241$	−578006.	−	1.00114e6i	−0.641047	−	1.11033i	0.344152	−	0.938914i	$-0.388166\pi$
$242$		0			0
$243$	570131.	−	987495.i	0.619382	−	1.07280i
$244$		0			0
$245$	123840.	−	1.40030e6i	0.131809	−	1.49041i
$246$		0			0
$247$	727666.	−	1.26036e6i	0.758909	−	1.31447i
$248$		0			0
$249$	427439.	+	740347.i	0.436894	+	0.756723i
$250$		0			0
$251$	−77574.9			−0.0777207			−0.0388604	−	0.999245i	$-0.512373\pi$
$251$	−77574.9			−0.0777207			−0.0388604	+	0.999245i	$0.512373\pi$
$252$		0			0
$253$	−836351.			−0.821462
$254$		0			0
$255$	−148787.	−	257706.i	−0.143289	−	0.248184i
$256$		0			0
$257$	140101.	−	242662.i	0.132315	−	0.229176i	−0.792254	−	0.610192i	$-0.791092\pi$
$257$	140101.	−	242662.i	0.132315	−	0.229176i	0.924569	+	0.381016i	$0.124426\pi$
$258$		0			0
$259$	438807.	+	138583.i	0.406466	+	0.128369i
$260$		0			0
$261$	131446.	−	227671.i	0.119439	−	0.206874i
$262$		0			0
$263$	134983.	+	233797.i	0.120334	+	0.208425i	0.919900	−	0.392154i	$-0.128270\pi$
$263$	134983.	+	233797.i	0.120334	+	0.208425i	−0.799565	+	0.600579i	$0.794937\pi$
$264$		0			0
$265$	−1.77978e6			−1.55687
$266$		0			0
$267$	2.45756e6			2.10972
$268$		0			0
$269$	−445133.	−	770994.i	−0.375068	−	0.649636i	0.615270	−	0.788317i	$-0.289047\pi$
$269$	−445133.	−	770994.i	−0.375068	−	0.649636i	−0.990337	+	0.138681i	$0.955714\pi$
$270$		0			0
$271$	−192140.	+	332796.i	−0.158926	+	0.275267i	−0.934482	−	0.356012i	$-0.884136\pi$
$271$	−192140.	+	332796.i	−0.158926	+	0.275267i	0.775556	+	0.631279i	$0.217470\pi$
$272$		0			0
$273$	−1.92372e6	+	1.76109e6i	−1.56219	+	1.43013i
$274$		0			0
$275$	−1.06305e6	+	1.84126e6i	−0.847664	+	1.46820i
$276$		0			0
$277$	545967.	+	945642.i	0.427530	+	0.740504i	0.996653	−	0.0817484i	$-0.0260504\pi$
$277$	545967.	+	945642.i	0.427530	+	0.740504i	−0.569123	+	0.822253i	$0.692717\pi$
$278$		0			0
$279$	−1.13533e6			−0.873196
$280$		0			0
$281$	771640.			0.582974			0.291487	−	0.956575i	$-0.405850\pi$
$281$	771640.			0.582974			0.291487	+	0.956575i	$0.405850\pi$
$282$		0			0
$283$	270902.	+	469217.i	0.201070	+	0.348263i	0.948873	−	0.315657i	$-0.102225\pi$
$283$	270902.	+	469217.i	0.201070	+	0.348263i	−0.747804	+	0.663920i	$0.768892\pi$
$284$		0			0
$285$	−1.80714e6	+	3.13006e6i	−1.31789	+	2.28265i
$286$		0			0
$287$	−180916.	−	817883.i	−0.129650	−	0.586120i
$288$		0			0
$289$	699334.	−	1.21128e6i	0.492538	−	0.853101i
$290$		0			0
$291$	−938441.	−	1.62543e6i	−0.649643	−	1.12521i
$292$		0			0
$293$	1.69804e6			1.15552			0.577762	−	0.816205i	$-0.303926\pi$
$293$	1.69804e6			1.15552			0.577762	+	0.816205i	$0.303926\pi$
$294$		0			0
$295$	3.05532e6			2.04410
$296$		0			0
$297$	−747224.	−	1.29423e6i	−0.491541	−	0.851373i
$298$		0			0
$299$	−626704.	+	1.08548e6i	−0.405401	+	0.702175i
$300$		0			0
$301$	188048.	+	850125.i	0.119633	+	0.540837i
$302$		0			0
$303$	−1.39359e6	+	2.41377e6i	−0.872025	+	1.51039i
$304$		0			0
$305$	−1.81644e6	−	3.14617e6i	−1.11808	−	1.93656i
$306$		0			0
$307$	−288376.			−0.174627			−0.0873137	−	0.996181i	$-0.527828\pi$
$307$	−288376.			−0.174627			−0.0873137	+	0.996181i	$0.527828\pi$
$308$		0			0
$309$	−3.02173e6			−1.80036
$310$		0			0
$311$	−173801.	−	301032.i	−0.101894	−	0.176486i	0.810571	−	0.585641i	$-0.199157\pi$
$311$	−173801.	−	301032.i	−0.101894	−	0.176486i	−0.912465	+	0.409154i	$0.865824\pi$
$312$		0			0
$313$	385201.	−	667188.i	0.222242	−	0.384935i	−0.733246	−	0.679963i	$-0.761996\pi$
$313$	385201.	−	667188.i	0.222242	−	0.384935i	0.955489	+	0.295028i	$0.0953290\pi$
$314$		0			0
$315$	2.83396e6	−	2.59439e6i	1.60922	−	1.47319i
$316$		0			0
$317$	1.00876e6	−	1.74722e6i	0.563819	−	0.976564i	−0.433339	−	0.901231i	$-0.642665\pi$
$317$	1.00876e6	−	1.74722e6i	0.563819	−	0.976564i	0.997158	−	0.0753328i	$-0.0240019\pi$
$318$		0			0
$319$	203755.	+	352914.i	0.112107	+	0.194174i
$320$		0			0
$321$	−570441.			−0.308993
$322$		0			0
$323$	257369.			0.137262
$324$		0			0
$325$	1.59316e6	+	2.75943e6i	0.836664	+	1.44914i
$326$		0			0
$327$	332427.	−	575780.i	0.171920	−	0.297775i
$328$		0			0
$329$	2.37070e6	+	748706.i	1.20750	+	0.381348i
$330$		0			0
$331$	−212966.	+	368868.i	−0.106842	+	0.185055i	−0.914489	−	0.404610i	$-0.867407\pi$
$331$	−212966.	+	368868.i	−0.106842	+	0.185055i	0.807648	+	0.589666i	$0.200740\pi$
$332$		0			0
$333$	628853.	+	1.08921e6i	0.310770	+	0.538269i
$334$		0			0
$335$	420563.			0.204748
$336$		0			0
$337$	1.15035e6			0.551767			0.275884	−	0.961191i	$-0.411030\pi$
$337$	1.15035e6			0.551767			0.275884	+	0.961191i	$0.411030\pi$
$338$		0			0
$339$	1.92338e6	+	3.33138e6i	0.909002	+	1.57444i
$340$		0			0
$341$	879941.	−	1.52410e6i	0.409796	−	0.709787i
$342$		0			0
$343$	−1.32398e6	−	1.73050e6i	−0.607640	−	0.794213i
$344$		0			0
$345$	1.55640e6	−	2.69577e6i	0.704002	−	1.21937i
$346$		0			0
$347$	156568.	+	271184.i	0.0698039	+	0.120904i	0.898815	−	0.438328i	$-0.144429\pi$
$347$	156568.	+	271184.i	0.0698039	+	0.120904i	−0.829011	+	0.559232i	$0.811096\pi$
$348$		0			0
$349$	−3.01459e6			−1.32484			−0.662422	−	0.749131i	$-0.730471\pi$
$349$	−3.01459e6			−1.32484			−0.662422	+	0.749131i	$0.730471\pi$
$350$		0			0
$351$	−2.23967e6			−0.970323
$352$		0			0
$353$	−2.19230e6	−	3.79717e6i	−0.936404	−	1.62190i	−0.772111	−	0.635487i	$-0.780799\pi$
$353$	−2.19230e6	−	3.79717e6i	−0.936404	−	1.62190i	−0.164292	−	0.986412i	$-0.552534\pi$
$354$		0			0
$355$	263945.	−	457166.i	0.111158	−	0.192532i
$356$		0			0
$357$	−439816.	−	138901.i	−0.182642	−	0.0576813i
$358$		0			0
$359$	96327.8	−	166845.i	0.0394471	−	0.0683244i	−0.845628	−	0.533773i	$-0.820774\pi$
$359$	96327.8	−	166845.i	0.0394471	−	0.0683244i	0.885075	+	0.465449i	$0.154107\pi$
$360$		0			0
$361$	−324928.	−	562792.i	−0.131226	−	0.227290i
$362$		0			0
$363$	3.43681e6			1.36896
$364$		0			0
$365$	−3.56297e6			−1.39984
$366$		0			0
$367$	1.16991e6	+	2.02634e6i	0.453405	+	0.785320i	0.998595	−	0.0529924i	$-0.0168759\pi$
$367$	1.16991e6	+	2.02634e6i	0.453405	+	0.785320i	−0.545190	+	0.838312i	$0.683543\pi$
$368$		0			0
$369$	1.14471e6	−	1.98270e6i	0.437653	−	0.758037i
$370$		0			0
$371$	−2.03473e6	+	1.86272e6i	−0.767488	+	0.702608i
$372$		0			0
$373$	−1.96217e6	+	3.39857e6i	−0.730237	+	1.26481i	0.226545	+	0.974001i	$0.427257\pi$
$373$	−1.96217e6	+	3.39857e6i	−0.730237	+	1.26481i	−0.956782	+	0.290806i	$0.906077\pi$
$374$		0			0
$375$	−762455.	−	1.32061e6i	−0.279986	−	0.484950i
$376$		0			0
$377$	610719.			0.221303
$378$		0			0
$379$	−3.26556e6			−1.16778			−0.583889	−	0.811834i	$-0.698470\pi$
$379$	−3.26556e6			−1.16778			−0.583889	+	0.811834i	$0.698470\pi$
$380$		0			0
$381$	3.09492e6	+	5.36055e6i	1.09229	+	1.89190i
$382$		0			0
$383$	2.21488e6	−	3.83628e6i	0.771529	−	1.33633i	−0.165195	−	0.986261i	$-0.552825\pi$
$383$	2.21488e6	−	3.83628e6i	0.771529	−	1.33633i	0.936725	−	0.350067i	$-0.113841\pi$
$384$		0			0
$385$	1.28632e6	+	5.81517e6i	0.442280	+	1.99945i
$386$		0			0
$387$	−1.18984e6	+	2.06086e6i	−0.403840	+	0.699472i
$388$		0			0
$389$	2.55733e6	+	4.42943e6i	0.856867	+	1.48414i	0.874902	+	0.484300i	$0.160926\pi$
$389$	2.55733e6	+	4.42943e6i	0.856867	+	1.48414i	−0.0180345	+	0.999837i	$0.505741\pi$
$390$		0			0
$391$	−221659.			−0.0733236
$392$		0			0
$393$	−2.82396e6			−0.922311
$394$		0			0
$395$	−3.97588e6	−	6.88642e6i	−1.28215	−	2.22076i
$396$		0			0
$397$	770944.	−	1.33531e6i	0.245497	−	0.425214i	−0.716774	−	0.697306i	$-0.754382\pi$
$397$	770944.	−	1.33531e6i	0.245497	−	0.425214i	0.962271	+	0.272092i	$0.0877154\pi$
$398$		0			0
$399$	1.20992e6	+	5.46978e6i	0.380473	+	1.72004i
$400$		0			0
$401$	−2.72114e6	+	4.71315e6i	−0.845064	+	1.46369i	0.0405025	+	0.999179i	$0.487104\pi$
$401$	−2.72114e6	+	4.71315e6i	−0.845064	+	1.46369i	−0.885566	+	0.464514i	$0.846229\pi$
$402$		0			0
$403$	−1.31873e6	−	2.28411e6i	−0.404478	−	0.700576i
$404$		0			0
$405$	−1.63956e6			−0.496694
$406$		0			0
$407$	−1.94958e6			−0.583384
$408$		0			0
$409$	−2.59241e6	−	4.49019e6i	−0.766294	−	1.32726i	−0.939560	−	0.342385i	$-0.888765\pi$
$409$	−2.59241e6	−	4.49019e6i	−0.766294	−	1.32726i	0.173265	−	0.984875i	$-0.444568\pi$
$410$		0			0
$411$	2.53944e6	−	4.39844e6i	0.741539	−	1.28438i
$412$		0			0
$413$	3.49299e6	−	3.19771e6i	1.00768	−	0.922494i
$414$		0			0
$415$	1.46282e6	−	2.53368e6i	0.416938	−	0.722157i
$416$		0			0
$417$	354300.	+	613665.i	0.0997770	+	0.172819i
$418$		0			0
$419$	−2.17093e6			−0.604102			−0.302051	−	0.953292i	$-0.597671\pi$
$419$	−2.17093e6			−0.604102			−0.302051	+	0.953292i	$0.597671\pi$
$420$		0			0
$421$	6.61967e6			1.82025			0.910125	−	0.414334i	$-0.135986\pi$
$421$	6.61967e6			1.82025			0.910125	+	0.414334i	$0.135986\pi$
$422$		0			0
$423$	3.39744e6	+	5.88455e6i	0.923212	+	1.59905i
$424$		0			0
$425$	−281743.	+	487992.i	−0.0756624	+	0.131051i
$426$		0			0
$427$	−5.36942e6	−	1.69575e6i	−1.42514	−	0.450083i
$428$		0			0
$429$	5.52478e6	−	9.56920e6i	1.44934	−	2.51034i
$430$		0			0
$431$	1.44992e6	+	2.51134e6i	0.375968	+	0.651196i	0.990471	−	0.137718i	$-0.0439768\pi$
$431$	1.44992e6	+	2.51134e6i	0.375968	+	0.651196i	−0.614503	+	0.788914i	$0.710643\pi$
$432$		0			0
$433$	4.71803e6			1.20932			0.604659	−	0.796484i	$-0.293309\pi$
$433$	4.71803e6			1.20932			0.604659	+	0.796484i	$0.293309\pi$
$434$		0			0
$435$	−1.51670e6			−0.384306
$436$		0			0
$437$	1.34612e6	+	2.33154e6i	0.337194	+	0.584036i
$438$		0			0
$439$	1.73850e6	−	3.01117e6i	0.430540	−	0.745718i	−0.566379	−	0.824145i	$-0.691656\pi$
$439$	1.73850e6	−	3.01117e6i	0.430540	−	0.745718i	0.996920	+	0.0784267i	$0.0249896\pi$
$440$		0			0
$441$	524619.	−	5.93205e6i	0.128454	−	1.45247i
$442$		0			0
$443$	−3.64829e6	+	6.31902e6i	−0.883243	+	1.52982i	−0.0355278	+	0.999369i	$0.511311\pi$
$443$	−3.64829e6	+	6.31902e6i	−0.883243	+	1.52982i	−0.847715	+	0.530452i	$0.822022\pi$
$444$		0			0
$445$	−4.20524e6	−	7.28368e6i	−1.00668	−	1.74362i
$446$		0			0
$447$	−8.08924e6			−1.91487
$448$		0			0
$449$	3.65867e6			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$449$	3.65867e6			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$450$		0			0
$451$	1.77442e6	+	3.07339e6i	0.410786	+	0.711501i
$452$		0			0
$453$	−1.33025e6	+	2.30405e6i	−0.304569	+	0.527530i
$454$		0			0
$455$	8.51127e6	+	2.68800e6i	1.92737	+	0.608697i
$456$		0			0
$457$	−3.22031e6	+	5.57774e6i	−0.721286	+	1.24930i	0.239199	+	0.970971i	$0.423115\pi$
$457$	−3.22031e6	+	5.57774e6i	−0.721286	+	1.24930i	−0.960485	+	0.278333i	$0.910218\pi$
$458$		0			0
$459$	−198037.	−	343011.i	−0.0438748	−	0.0759935i
$460$		0			0
$461$	4.47898e6			0.981583			0.490791	−	0.871277i	$-0.336708\pi$
$461$	4.47898e6			0.981583			0.490791	+	0.871277i	$0.336708\pi$
$462$		0			0
$463$	−2.11214e6			−0.457899			−0.228949	−	0.973438i	$-0.573529\pi$
$463$	−2.11214e6			−0.457899			−0.228949	+	0.973438i	$0.573529\pi$
$464$		0			0
$465$	3.27504e6	+	5.67253e6i	0.702399	+	1.21659i
$466$		0			0
$467$	−3.92919e6	+	6.80556e6i	−0.833702	+	1.44401i	0.0613806	+	0.998114i	$0.480450\pi$
$467$	−3.92919e6	+	6.80556e6i	−0.833702	+	1.44401i	−0.895083	+	0.445900i	$0.852884\pi$
$468$		0			0
$469$	480808.	−	440162.i	0.100934	−	0.0924019i
$470$		0			0
$471$	6.08252e6	−	1.05352e7i	1.26337	−	2.18823i
$472$		0			0
$473$	−1.84437e6	−	3.19454e6i	−0.379049	−	0.656532i
$474$		0			0
$475$	6.84400e6			1.39180
$476$		0			0
$477$	−7.53961e6			−1.51724
$478$		0			0
$479$	−4.24373e6	−	7.35035e6i	−0.845101	−	1.46376i	−0.885533	−	0.464576i	$-0.846207\pi$
$479$	−4.24373e6	−	7.35035e6i	−0.845101	−	1.46376i	0.0404324	−	0.999182i	$-0.487126\pi$
$480$		0			0
$481$	−1.46088e6	+	2.53032e6i	−0.287907	+	0.498669i
$482$		0			0
$483$	−1.04204e6	−	4.71086e6i	−0.203244	−	0.918824i
$484$		0			0
$485$	−3.21162e6	+	5.56269e6i	−0.619968	+	1.07382i
$486$		0			0
$487$	−1.37808e6	−	2.38691e6i	−0.263301	−	0.456051i	0.703816	−	0.710382i	$-0.251478\pi$
$487$	−1.37808e6	−	2.38691e6i	−0.263301	−	0.456051i	−0.967117	+	0.254331i	$0.918145\pi$
$488$		0			0
$489$	−8.77658e6			−1.65979
$490$		0			0
$491$	2.45533e6			0.459628			0.229814	−	0.973235i	$-0.426188\pi$
$491$	2.45533e6			0.459628			0.229814	+	0.973235i	$0.426188\pi$
$492$		0			0
$493$	54001.3	+	93533.1i	0.0100066	+	0.0173320i
$494$		0			0
$495$	−8.13892e6	+	1.40970e7i	−1.49298	+	2.58592i
$496$		0			0
$497$	−176717.	−	798899.i	−0.0320913	−	0.145078i
$498$		0			0
$499$	2.22925e6	−	3.86117e6i	0.400781	−	0.694172i	−0.593040	−	0.805173i	$-0.702072\pi$
$499$	2.22925e6	−	3.86117e6i	0.400781	−	0.694172i	0.993820	+	0.111001i	$0.0354056\pi$
$500$		0			0
$501$	618892.	+	1.07195e6i	0.110159	+	0.190801i
$502$		0			0
$503$	2.64080e6			0.465389			0.232694	−	0.972550i	$-0.425246\pi$
$503$	2.64080e6			0.465389			0.232694	+	0.972550i	$0.425246\pi$
$504$		0			0
$505$	9.53856e6			1.66439
$506$		0			0
$507$	−3.74252e6	−	6.48223e6i	−0.646612	−	1.11997i
$508$		0			0
$509$	−2.35520e6	+	4.07933e6i	−0.402934	+	0.697902i	−0.994079	−	0.108663i	$-0.965343\pi$
$509$	−2.35520e6	+	4.07933e6i	−0.402934	+	0.697902i	0.591145	+	0.806566i	$0.298676\pi$
$510$		0			0
$511$	−4.07335e6	+	3.72901e6i	−0.690080	+	0.631744i
$512$		0			0
$513$	−2.40533e6	+	4.16615e6i	−0.403535	+	0.698943i
$514$		0			0
$515$	5.17061e6	+	8.95576e6i	0.859061	+	1.48794i
$516$		0			0
$517$	−1.05328e7			−1.73307
$518$		0			0
$519$	7.41003e6			1.20754
$520$		0			0
$521$	1.40134e6	+	2.42720e6i	0.226178	+	0.391752i	0.956672	−	0.291167i	$-0.0940436\pi$
$521$	1.40134e6	+	2.42720e6i	0.226178	+	0.391752i	−0.730494	+	0.682919i	$0.760710\pi$
$522$		0			0
$523$	1.49878e6	−	2.59596e6i	0.239598	−	0.414995i	−0.721001	−	0.692934i	$-0.756318\pi$
$523$	1.49878e6	−	2.59596e6i	0.239598	−	0.414995i	0.960599	+	0.277939i	$0.0896512\pi$
$524$		0			0
$525$	−1.16957e7	−	3.69369e6i	−1.85194	−	0.584874i
$526$		0			0
$527$	233212.	−	403934.i	0.0365783	−	0.0633555i
$528$		0			0
$529$	2.05883e6	+	3.56599e6i	0.319875	+	0.554040i
$530$		0			0
$531$	1.29431e7			1.99207
$532$		0			0
$533$	5.31851e6			0.810909
$534$		0			0
$535$	976107.	+	1.69067e6i	0.147439	+	0.255372i
$536$		0			0
$537$	8.34078e6	−	1.44467e7i	1.24816	−	2.16188i
$538$		0			0
$539$	7.55675e6	+	5.30191e6i	1.12037	+	0.786069i
$540$		0			0
$541$	−1.65252e6	+	2.86225e6i	−0.242747	+	0.420450i	−0.961496	−	0.274820i	$-0.911382\pi$
$541$	−1.65252e6	+	2.86225e6i	−0.242747	+	0.420450i	0.718749	+	0.695270i	$0.244715\pi$
$542$		0			0
$543$	−2.22963e6	−	3.86183e6i	−0.324514	−	0.562074i
$544$		0			0
$545$	−2.27532e6			−0.328135
$546$		0			0
$547$	3.51435e6			0.502201			0.251100	−	0.967961i	$-0.419208\pi$
$547$	3.51435e6			0.502201			0.251100	+	0.967961i	$0.419208\pi$
$548$		0			0
$549$	−7.69491e6	−	1.33280e7i	−1.08961	−	1.88727i
$550$		0			0
$551$	655891.	−	1.13604e6i	0.0920350	−	0.159409i
$552$		0			0
$553$	−1.17528e7	−	3.71172e6i	−1.63428	−	0.516133i
$554$		0			0
$555$	3.62805e6	−	6.28397e6i	0.499967	−	0.865968i
$556$		0			0
$557$	2.99093e6	+	5.18045e6i	0.408478	+	0.707505i	0.994719	−	0.102632i	$-0.0327263\pi$
$557$	2.99093e6	+	5.18045e6i	0.408478	+	0.707505i	−0.586241	+	0.810137i	$0.699393\pi$
$558$		0			0
$559$	−5.52817e6			−0.748259
$560$		0			0
$561$	1.95406e6			0.262138
$562$		0			0
$563$	−5.36921e6	−	9.29974e6i	−0.713903	−	1.23652i	−0.963381	−	0.268136i	$-0.913592\pi$
$563$	−5.36921e6	−	9.29974e6i	−0.713903	−	1.23652i	0.249478	−	0.968380i	$-0.419741\pi$
$564$		0			0
$565$	6.58235e6	−	1.14010e7i	0.867481	−	1.50252i
$566$		0			0
$567$	−1.87442e6	+	1.71596e6i	−0.244855	+	0.224156i
$568$		0			0
$569$	3.29774e6	−	5.71186e6i	0.427008	−	0.739600i	−0.569598	−	0.821924i	$-0.692901\pi$
$569$	3.29774e6	−	5.71186e6i	0.427008	−	0.739600i	0.996606	+	0.0823241i	$0.0262343\pi$
$570$		0			0
$571$	1.30789e6	+	2.26533e6i	0.167873	+	0.290764i	0.937672	−	0.347522i	$-0.112977\pi$
$571$	1.30789e6	+	2.26533e6i	0.167873	+	0.290764i	−0.769799	+	0.638286i	$0.779644\pi$
$572$		0			0
$573$	1.67060e7			2.12562
$574$		0			0
$575$	−5.89440e6			−0.743482
$576$		0			0
$577$	619490.	+	1.07299e6i	0.0774630	+	0.134170i	0.902155	−	0.431413i	$-0.141985\pi$
$577$	619490.	+	1.07299e6i	0.0774630	+	0.134170i	−0.824692	+	0.565583i	$0.808651\pi$
$578$		0			0
$579$	−1.15664e7	+	2.00336e7i	−1.43385	+	2.48349i
$580$		0			0
$581$	−979391.	−	4.42761e6i	−0.120369	−	0.544164i
$582$		0			0
$583$	5.84360e6	−	1.01214e7i	0.712047	−	1.23330i
$584$		0			0
$585$	1.21975e7	+	2.11267e7i	1.47360	+	2.55236i
$586$		0			0
$587$	1.02896e7			1.23254			0.616270	−	0.787535i	$-0.288643\pi$
$587$	1.02896e7			1.23254			0.616270	+	0.787535i	$0.288643\pi$
$588$		0			0
$589$	−5.66510e6			−0.672852
$590$		0			0
$591$	2.25106e6	+	3.89895e6i	0.265105	+	0.459176i
$592$		0			0
$593$	−7.65889e6	+	1.32656e7i	−0.894394	+	1.54914i	−0.0598415	+	0.998208i	$0.519060\pi$
$593$	−7.65889e6	+	1.32656e7i	−0.894394	+	1.54914i	−0.834553	+	0.550928i	$0.814274\pi$
$594$		0			0
$595$	340915.	+	1.54120e6i	0.0394778	+	0.178471i
$596$		0			0
$597$	−833495.	+	1.44366e6i	−0.0957122	+	0.165778i
$598$		0			0
$599$	−1.34748e6	−	2.33391e6i	−0.153446	−	0.265776i	0.779046	−	0.626967i	$-0.215704\pi$
$599$	−1.34748e6	−	2.33391e6i	−0.153446	−	0.265776i	−0.932492	+	0.361190i	$0.882370\pi$
$600$		0			0
$601$	1.54704e6			0.174709			0.0873547	−	0.996177i	$-0.472159\pi$
$601$	1.54704e6			0.174709			0.0873547	+	0.996177i	$0.472159\pi$
$602$		0			0
$603$	1.78162e6			0.199536
$604$		0			0
$605$	−5.88088e6	−	1.01860e7i	−0.653212	−	1.13140i
$606$		0			0
$607$	−1.89569e6	+	3.28343e6i	−0.208831	+	0.361706i	−0.951347	−	0.308123i	$-0.900299\pi$
$607$	−1.89569e6	+	3.28343e6i	−0.208831	+	0.361706i	0.742516	+	0.669829i	$0.233633\pi$
$608$		0			0
$609$	−1.73397e6	+	1.58738e6i	−0.189451	+	0.173436i
$610$		0			0
$611$	−7.89255e6	+	1.36703e7i	−0.855291	+	1.48141i
$612$		0			0
$613$	−3.09603e6	−	5.36249e6i	−0.332778	−	0.576388i	0.650277	−	0.759697i	$-0.274653\pi$
$613$	−3.09603e6	−	5.36249e6i	−0.332778	−	0.576388i	−0.983055	+	0.183308i	$0.941319\pi$
$614$		0			0
$615$	−1.32084e7			−1.40819
$616$		0			0
$617$	−1.59349e7			−1.68514			−0.842571	−	0.538585i	$-0.818959\pi$
$617$	−1.59349e7			−1.68514			−0.842571	+	0.538585i	$0.818959\pi$
$618$		0			0
$619$	5.78660e6	+	1.00227e7i	0.607011	+	1.05137i	0.991730	+	0.128341i	$0.0409651\pi$
$619$	5.78660e6	+	1.00227e7i	0.607011	+	1.05137i	−0.384719	+	0.923034i	$0.625702\pi$
$620$		0			0
$621$	2.07159e6	−	3.58811e6i	0.215564	−	0.373367i
$622$		0			0
$623$	−1.24307e7	−	3.92584e6i	−1.28315	−	0.405240i
$624$		0			0
$625$	3.43903e6	−	5.95657e6i	0.352156	−	0.609953i
$626$		0			0
$627$	−1.18668e7	−	2.05540e7i	−1.20550	−	2.08798i
$628$		0			0
$629$	−516699.			−0.0520728
$630$		0			0
$631$	900933.			0.0900781			0.0450390	−	0.998985i	$-0.485659\pi$
$631$	900933.			0.0900781			0.0450390	+	0.998985i	$0.485659\pi$
$632$		0			0
$633$	1.45749e7	+	2.52445e7i	1.44576	+	2.50414i
$634$		0			0
$635$	1.05917e7	−	1.83454e7i	1.04239	−	1.80548i
$636$		0			0
$637$	1.25437e7	−	5.83487e6i	1.22484	−	0.569747i
$638$		0			0
$639$	1.11814e6	−	1.93667e6i	0.108329	−	0.187631i
$640$		0			0
$641$	424385.	+	735057.i	0.0407958	+	0.0706604i	0.885702	−	0.464254i	$-0.153677\pi$
$641$	424385.	+	735057.i	0.0407958	+	0.0706604i	−0.844907	+	0.534914i	$0.820344\pi$
$642$		0			0
$643$	−1.37977e7			−1.31607			−0.658036	−	0.752986i	$-0.728613\pi$
$643$	−1.37977e7			−1.31607			−0.658036	+	0.752986i	$0.728613\pi$
$644$		0			0
$645$	1.37291e7			1.29940
$646$		0			0
$647$	1.82675e6	+	3.16402e6i	0.171561	+	0.297152i	0.938966	−	0.344011i	$-0.111786\pi$
$647$	1.82675e6	+	3.16402e6i	0.171561	+	0.297152i	−0.767405	+	0.641163i	$0.778452\pi$
$648$		0			0
$649$	−1.00316e7	+	1.73753e7i	−0.934887	+	1.61927i
$650$		0			0
$651$	9.68106e6	+	3.05744e6i	0.895304	+	0.282752i
$652$		0			0
$653$	−5.89558e6	+	1.02115e7i	−0.541058	+	0.937140i	0.457786	+	0.889063i	$0.348643\pi$
$653$	−5.89558e6	+	1.02115e7i	−0.541058	+	0.937140i	−0.998844	+	0.0480774i	$0.984691\pi$
$654$		0			0
$655$	4.83221e6	+	8.36963e6i	0.440091	+	0.762260i
$656$		0			0
$657$	−1.50937e7			−1.36421
$658$		0			0
$659$	−1.15208e7			−1.03340			−0.516700	−	0.856166i	$-0.672840\pi$
$659$	−1.15208e7			−1.03340			−0.516700	+	0.856166i	$0.672840\pi$
$660$		0			0
$661$	−2.68607e6	−	4.65241e6i	−0.239119	−	0.414166i	0.721343	−	0.692578i	$-0.243525\pi$
$661$	−2.68607e6	−	4.65241e6i	−0.239119	−	0.414166i	−0.960462	+	0.278412i	$0.910192\pi$
$662$		0			0
$663$	1.46424e6	−	2.53613e6i	0.129368	−	0.224072i
$664$		0			0
$665$	1.41409e7	−	1.29455e7i	1.24001	−	1.13518i
$666$		0			0
$667$	−564888.	+	978414.i	−0.0491640	+	0.0851546i
$668$		0			0
$669$	−2.45016e6	−	4.24381e6i	−0.211655	−	0.366598i
$670$		0			0
$671$	2.38558e7			2.04545
$672$		0			0
$673$	1.48042e7			1.25993			0.629966	−	0.776623i	$-0.283069\pi$
$673$	1.48042e7			1.25993			0.629966	+	0.776623i	$0.283069\pi$
$674$		0			0
$675$	−5.26625e6	−	9.12142e6i	−0.444879	−	0.770554i
$676$		0			0
$677$	2.95353e6	−	5.11567e6i	0.247668	−	0.428974i	−0.715210	−	0.698909i	$-0.753669\pi$
$677$	2.95353e6	−	5.11567e6i	0.247668	−	0.428974i	0.962878	+	0.269935i	$0.0870024\pi$
$678$		0			0
$679$	2.15025e6	+	9.72080e6i	0.178984	+	0.809148i
$680$		0			0
$681$	−3.55324e6	+	6.15439e6i	−0.293601	+	0.508531i
$682$		0			0
$683$	−1.10080e7	−	1.90663e7i	−0.902932	−	1.56392i	−0.823670	−	0.567070i	$-0.808077\pi$
$683$	−1.10080e7	−	1.90663e7i	−0.902932	−	1.56392i	−0.0792618	−	0.996854i	$-0.525256\pi$
$684$		0			0
$685$	−1.73814e7			−1.41533
$686$		0			0
$687$	2.30947e7			1.86690
$688$		0			0
$689$	−8.75757e6	−	1.51686e7i	−0.702806	−	1.21730i
$690$		0			0
$691$	−6.53254e6	+	1.13147e7i	−0.520460	+	0.901463i	0.479257	+	0.877674i	$0.340906\pi$
$691$	−6.53254e6	+	1.13147e7i	−0.520460	+	0.901463i	−0.999717	+	0.0237881i	$0.992427\pi$
$692$		0			0
$693$	5.44918e6	+	2.46346e7i	0.431021	+	1.94855i
$694$		0			0
$695$	1.21252e6	−	2.10014e6i	0.0952194	−	0.164925i
$696$		0			0
$697$	470276.	+	814543.i	0.0366667	+	0.0635085i
$698$		0			0
$699$	5.28848e6			0.409391
$700$		0			0
$701$	1.20043e7			0.922658			0.461329	−	0.887229i	$-0.347373\pi$
$701$	1.20043e7			0.922658			0.461329	+	0.887229i	$0.347373\pi$
$702$		0			0
$703$	3.13787e6	+	5.43495e6i	0.239467	+	0.414770i
$704$		0			0
$705$	1.96009e7	−	3.39498e7i	1.48526	−	2.57255i
$706$		0			0
$707$	1.09049e7	−	9.98307e6i	0.820491	−	0.751131i
$708$		0			0
$709$	8.23972e6	−	1.42716e7i	0.615597	−	1.06625i	−0.374682	−	0.927153i	$-0.622248\pi$
$709$	8.23972e6	−	1.42716e7i	0.615597	−	1.06625i	0.990279	−	0.139093i	$-0.0444185\pi$
$710$		0			0
$711$	−1.68429e7	−	2.91727e7i	−1.24952	−	2.16422i
$712$		0			0
$713$	4.87908e6			0.359430
$714$		0			0
$715$	−3.78148e7			−2.76628
$716$		0			0
$717$	8.17292e6	+	1.41559e7i	0.593717	+	1.02835i
$718$		0			0
$719$	3.66177e6	−	6.34237e6i	0.264161	−	0.457540i	−0.703183	−	0.711009i	$-0.748238\pi$
$719$	3.66177e6	−	6.34237e6i	0.264161	−	0.457540i	0.967343	+	0.253469i	$0.0815717\pi$
$720$		0			0
$721$	1.52844e7	+	4.82707e6i	1.09499	+	0.345816i
$722$		0			0
$723$	−1.41267e7	+	2.44681e7i	−1.00506	+	1.74082i
$724$		0			0
$725$	1.43601e6	+	2.48725e6i	0.101464	+	0.175742i
$726$		0			0
$727$	1.83777e7			1.28960			0.644798	−	0.764353i	$-0.276941\pi$
$727$	1.83777e7			1.28960			0.644798	+	0.764353i	$0.276941\pi$
$728$		0			0
$729$	−2.31050e7			−1.61023
$730$		0			0
$731$	−488815.	−	846653.i	−0.0338338	−	0.0586019i
$732$		0			0
$733$	5.92488e6	−	1.02622e7i	0.407305	−	0.705472i	−0.587282	−	0.809382i	$-0.699802\pi$
$733$	5.92488e6	−	1.02622e7i	0.407305	−	0.705472i	0.994587	+	0.103910i	$0.0331354\pi$
$734$		0			0
$735$	−3.11521e7	+	1.44907e7i	−2.12700	+	0.989400i
$736$		0			0
$737$	−1.38085e6	+	2.39170e6i	−0.0936432	+	0.162195i
$738$		0			0
$739$	1.04756e7	+	1.81442e7i	0.705613	+	1.22216i	0.966470	+	0.256780i	$0.0826616\pi$
$739$	1.04756e7	+	1.81442e7i	0.705613	+	1.22216i	−0.260857	+	0.965377i	$0.584005\pi$
$740$		0			0
$741$	−3.55688e7			−2.37971
$742$		0			0
$743$	−1.42524e7			−0.947141			−0.473570	−	0.880756i	$-0.657035\pi$
$743$	−1.42524e7			−0.947141			−0.473570	+	0.880756i	$0.657035\pi$
$744$		0			0
$745$	1.38419e7	+	2.39748e7i	0.913701	+	1.58258i
$746$		0			0
$747$	6.19689e6	−	1.07333e7i	0.406324	−	0.703774i
$748$		0			0
$749$	2.88539e6	+	911253.i	0.187931	+	0.0593519i
$750$		0			0
$751$	−659846.	+	1.14289e6i	−0.0426916	+	0.0739441i	−0.886582	−	0.462572i	$-0.846927\pi$
$751$	−659846.	+	1.14289e6i	−0.0426916	+	0.0739441i	0.843890	+	0.536516i	$0.180260\pi$
$752$		0			0
$753$	947977.	+	1.64194e6i	0.0609271	+	0.105529i
$754$		0			0
$755$	9.10497e6			0.581315
$756$		0			0
$757$	102138.			0.00647812			0.00323906	−	0.999995i	$-0.498969\pi$
$757$	102138.			0.00647812			0.00323906	+	0.999995i	$0.498969\pi$
$758$		0			0
$759$	1.02203e7	+	1.77022e7i	0.643963	+	1.11538i
$760$		0			0
$761$	−1.09596e7	+	1.89826e7i	−0.686016	+	1.18821i	0.287100	+	0.957901i	$0.407309\pi$
$761$	−1.09596e7	+	1.89826e7i	−0.686016	+	1.18821i	−0.973116	+	0.230314i	$0.926025\pi$
$762$		0			0
$763$	−2.60126e6	+	2.38136e6i	−0.161760	+	0.148086i
$764$		0			0
$765$	−2.15707e6	+	3.73615e6i	−0.133263	+	0.230819i
$766$		0			0
$767$	1.50340e7	+	2.60397e7i	0.922755	+	1.59826i
$768$		0			0
$769$	6.44098e6			0.392768			0.196384	−	0.980527i	$-0.437080\pi$
$769$	6.44098e6			0.392768			0.196384	+	0.980527i	$0.437080\pi$
$770$		0			0
$771$	−6.84823e6			−0.414899
$772$		0			0
$773$	−1.45580e6	−	2.52152e6i	−0.0876302	−	0.151780i	0.818879	−	0.573966i	$-0.194596\pi$
$773$	−1.45580e6	−	2.52152e6i	−0.0876302	−	0.151780i	−0.906509	+	0.422187i	$0.861263\pi$
$774$		0			0
$775$	6.20161e6	−	1.07415e7i	0.370894	−	0.642408i
$776$		0			0
$777$	−2.42906e6	−	1.09813e7i	−0.144340	−	0.652528i
$778$		0			0
$779$	5.71190e6	−	9.89330e6i	0.337238	−	0.584114i
$780$		0			0
$781$	1.73323e6	+	3.00205e6i	0.101679	+	0.176113i
$782$		0			0
$783$	−2.01876e6			−0.117674
$784$		0			0
$785$	−4.16323e7			−2.41133
$786$		0			0
$787$	−1.27290e7	−	2.20472e7i	−0.732582	−	1.26887i	−0.955776	−	0.294095i	$-0.904982\pi$
$787$	−1.27290e7	−	2.20472e7i	−0.732582	−	1.26887i	0.223195	−	0.974774i	$-0.428351\pi$
$788$		0			0
$789$	3.29902e6	−	5.71408e6i	0.188666	−	0.326779i
$790$		0			0
$791$	−4.40702e6	−	1.99232e7i	−0.250440	−	1.13219i
$792$		0			0
$793$	1.78759e7	−	3.09620e7i	1.00945	−	1.74842i
$794$		0			0
$795$	2.17492e7	+	3.76707e7i	1.22046	+	2.11391i
$796$		0			0
$797$	−2.04344e7			−1.13950			−0.569752	−	0.821817i	$-0.692961\pi$
$797$	−2.04344e7			−1.13950			−0.569752	+	0.821817i	$0.692961\pi$
$798$		0			0
$799$	−2.79152e6			−0.154694
$800$		0			0
$801$	−1.78145e7	−	3.08556e7i	−0.981051	−	1.69923i
$802$		0			0
$803$	1.16984e7	−	2.02622e7i	0.640231	−	1.10891i
$804$		0			0
$805$	−1.21789e7	+	1.11494e7i	−0.662398	+	0.606402i
$806$		0			0
$807$	−1.08792e7	+	1.88433e7i	−0.588048	+	1.01853i
$808$		0			0
$809$	−1.41416e7	−	2.44939e7i	−0.759672	−	1.31579i	−0.943018	−	0.332743i	$-0.892026\pi$
$809$	−1.41416e7	−	2.44939e7i	−0.759672	−	1.31579i	0.183345	−	0.983049i	$-0.441307\pi$
$810$		0			0
$811$	1.58852e7			0.848087			0.424043	−	0.905642i	$-0.360610\pi$
$811$	1.58852e7			0.848087			0.424043	+	0.905642i	$0.360610\pi$
$812$		0			0
$813$	9.39191e6			0.498342
$814$		0			0
$815$	1.50180e7	+	2.60119e7i	0.791987	+	1.37176i
$816$		0			0
$817$	−5.93707e6	+	1.02833e7i	−0.311184	+	0.538986i
$818$		0			0
$819$	3.60560e7	+	1.13871e7i	1.87831	+	0.593202i
$820$		0			0
$821$	−7.72198e6	+	1.33749e7i	−0.399826	+	0.692519i	−0.993704	−	0.112036i	$-0.964263\pi$
$821$	−7.72198e6	+	1.33749e7i	−0.399826	+	0.692519i	0.593878	+	0.804555i	$0.297596\pi$
$822$		0			0
$823$	−1.48943e7	−	2.57977e7i	−0.766516	−	1.32764i	−0.939441	−	0.342710i	$-0.888655\pi$
$823$	−1.48943e7	−	2.57977e7i	−0.766516	−	1.32764i	0.172926	−	0.984935i	$-0.444678\pi$
$824$		0			0
$825$	5.19628e7			2.65801
$826$		0			0
$827$	1.66831e7			0.848230			0.424115	−	0.905608i	$-0.360585\pi$
$827$	1.66831e7			0.848230			0.424115	+	0.905608i	$0.360585\pi$
$828$		0			0
$829$	1.10568e7	+	1.91510e7i	0.558785	+	0.967844i	0.997598	+	0.0692656i	$0.0220656\pi$
$829$	1.10568e7	+	1.91510e7i	0.558785	+	0.967844i	−0.438813	+	0.898578i	$0.644601\pi$
$830$		0			0
$831$	1.33436e7	−	2.31118e7i	0.670302	−	1.16100i
$832$		0			0
$833$	2.00277e6	+	1.40517e6i	0.100004	+	0.0701644i
$834$		0			0
$835$	2.11803e6	−	3.66853e6i	0.105127	−	0.182086i
$836$		0			0
$837$	4.35913e6	+	7.55023e6i	0.215073	+	0.372517i
$838$		0			0
$839$	539166.			0.0264434			0.0132217	−	0.999913i	$-0.495791\pi$
$839$	539166.			0.0264434			0.0132217	+	0.999913i	$0.495791\pi$
$840$		0			0
$841$	−1.99607e7			−0.973162
$842$		0			0
$843$	−9.42956e6	−	1.63325e7i	−0.457007	−	0.791559i
$844$		0			0
$845$	−1.28080e7	+	2.21841e7i	−0.617076	+	1.06881i
$846$		0			0
$847$	−1.73840e7	−	5.49015e6i	−0.832608	−	0.262952i
$848$		0			0
$849$	6.62094e6	−	1.14678e7i	0.315247	−	0.546023i
$850$		0			0
$851$	−2.70249e6	−	4.68086e6i	−0.127921	−	0.221565i
$852$		0			0
$853$	2.55452e6			0.120209			0.0601044	−	0.998192i	$-0.480857\pi$
$853$	2.55452e6			0.120209			0.0601044	+	0.998192i	$0.480857\pi$
$854$		0			0
$855$	5.23988e7			2.45135
$856$		0			0
$857$	−120039.	−	207913.i	−0.00558303	−	0.00967008i	0.863220	−	0.504827i	$-0.168444\pi$
$857$	−120039.	−	207913.i	−0.00558303	−	0.00967008i	−0.868803	+	0.495157i	$0.835110\pi$
$858$		0			0
$859$	−3.33955e6	+	5.78428e6i	−0.154421	+	0.267464i	−0.932848	−	0.360270i	$-0.882684\pi$
$859$	−3.33955e6	+	5.78428e6i	−0.154421	+	0.267464i	0.778427	+	0.627735i	$0.216018\pi$
$860$		0			0
$861$	−1.51004e7	+	1.38239e7i	−0.694195	+	0.635511i
$862$		0			0
$863$	1.02530e7	−	1.77587e7i	0.468622	−	0.811678i	−0.530734	−	0.847538i	$-0.678084\pi$
$863$	1.02530e7	−	1.77587e7i	0.468622	−	0.811678i	0.999357	+	0.0358604i	$0.0114172\pi$
$864$		0			0
$865$	−1.26796e7	−	2.19618e7i	−0.576192	−	0.997993i
$866$		0			0
$867$	−3.41839e7			−1.54445
$868$		0			0
$869$	5.22164e7			2.34562
$870$		0			0
$871$	2.06942e6	+	3.58434e6i	0.0924280	+	0.160090i
$872$		0			0
$873$	−1.36052e7	+	2.35650e7i	−0.604186	+	1.04648i
$874$		0			0
$875$	1.74701e6	+	7.89786e6i	0.0771392	+	0.348730i
$876$		0			0
$877$	−1.26387e7	+	2.18909e7i	−0.554888	+	0.961093i	0.443025	+	0.896509i	$0.353905\pi$
$877$	−1.26387e7	+	2.18909e7i	−0.554888	+	0.961093i	−0.997912	+	0.0645840i	$0.979428\pi$
$878$		0			0
$879$	−2.07503e7	−	3.59406e7i	−0.905842	−	1.56896i
$880$		0			0
$881$	−2.45932e7			−1.06752			−0.533759	−	0.845637i	$-0.679221\pi$
$881$	−2.45932e7			−1.06752			−0.533759	+	0.845637i	$0.679221\pi$
$882$		0			0
$883$	2.78301e7			1.20120			0.600598	−	0.799551i	$-0.294929\pi$
$883$	2.78301e7			1.20120			0.600598	+	0.799551i	$0.294929\pi$
$884$		0			0
$885$	−3.73365e7	−	6.46688e7i	−1.60242	−	2.77547i
$886$		0			0
$887$	−1.74928e7	+	3.02984e7i	−0.746534	+	1.29304i	0.202940	+	0.979191i	$0.434950\pi$
$887$	−1.74928e7	+	3.02984e7i	−0.746534	+	1.29304i	−0.949474	+	0.313844i	$0.898383\pi$
$888$		0			0
$889$	−7.09137e6	−	3.20586e7i	−0.300937	−	1.36047i
$890$		0			0
$891$	5.38319e6	−	9.32396e6i	0.227167	−	0.393465i
$892$		0			0
$893$	1.69526e7	+	2.93629e7i	0.711392	+	1.23217i
$894$		0			0
$895$	−5.70892e7			−2.38230
$896$		0			0
$897$	3.06337e7			1.27121
$898$		0			0
$899$	−1.18866e6	−	2.05882e6i	−0.0490521	−	0.0849607i
$900$		0			0
$901$	1.54873e6	−	2.68249e6i	0.0635572	−	0.110084i
$902$		0			0
$903$	1.56957e7	−	1.43689e7i	0.640562	−	0.586412i
$904$		0			0
$905$	−7.63044e6	+	1.32163e7i	−0.309691	+	0.536400i
$906$		0			0
$907$	2.03300e7	+	3.52127e7i	0.820578	+	1.42128i	0.905252	+	0.424874i	$0.139682\pi$
$907$	2.03300e7	+	3.52127e7i	0.820578	+	1.42128i	−0.0846741	+	0.996409i	$0.526985\pi$
$908$		0			0
$909$	4.04078e7			1.62202
$910$		0			0
$911$	−2.87014e7			−1.14579			−0.572897	−	0.819627i	$-0.694180\pi$
$911$	−2.87014e7			−1.14579			−0.572897	+	0.819627i	$0.694180\pi$
$912$		0			0
$913$	9.60584e6	+	1.66378e7i	0.381380	+	0.660570i
$914$		0			0
$915$	−4.43943e7	+	7.68933e7i	−1.75297	+	3.03624i
$916$		0			0
$917$	1.42841e7	+	4.51115e6i	0.560956	+	0.177159i
$918$		0			0
$919$	−1.47415e7	+	2.55330e7i	−0.575773	+	0.997269i	0.420184	+	0.907439i	$0.361966\pi$
$919$	−1.47415e7	+	2.55330e7i	−0.575773	+	0.997269i	−0.995957	+	0.0898297i	$0.971368\pi$
$920$		0			0
$921$	3.52399e6	+	6.10374e6i	0.136895	+	0.237108i
$922$		0			0
$923$	5.19506e6			0.200718
$924$		0			0
$925$	−1.37402e7			−0.528004
$926$		0			0
$927$	2.19041e7	+	3.79389e7i	0.837192	+	1.45006i
$928$		0			0
$929$	7.94112e6	−	1.37544e7i	0.301886	−	0.522881i	−0.674677	−	0.738113i	$-0.735717\pi$
$929$	7.94112e6	−	1.37544e7i	0.301886	−	0.522881i	0.976563	+	0.215231i	$0.0690505\pi$
$930$		0			0
$931$	2.61776e6	−	2.95999e7i	0.0989817	−	1.11922i
$932$		0			0
$933$	−4.24774e6	+	7.35731e6i	−0.159755	+	0.276704i
$934$		0			0
$935$	−3.34368e6	−	5.79143e6i	−0.125082	−	0.216649i
$936$		0			0
$937$	1.04452e7			0.388656			0.194328	−	0.980937i	$-0.437747\pi$
$937$	1.04452e7			0.388656			0.194328	+	0.980937i	$0.437747\pi$
$938$		0			0
$939$	−1.88289e7			−0.696884
$940$		0			0
$941$	1.34241e7	+	2.32513e7i	0.494211	+	0.855998i	0.999978	−	0.00667223i	$-0.00212385\pi$
$941$	1.34241e7	+	2.32513e7i	0.494211	+	0.855998i	−0.505767	+	0.862670i	$0.668791\pi$
$942$		0			0
$943$	−4.91938e6	+	8.52062e6i	−0.180149	+	0.312027i
$944$		0			0
$945$	−2.81344e7	−	8.88530e6i	−1.02484	−	0.323663i
$946$		0			0
$947$	7.62047e6	−	1.31990e7i	0.276126	−	0.478264i	−0.694293	−	0.719693i	$-0.744283\pi$
$947$	7.62047e6	−	1.31990e7i	0.276126	−	0.478264i	0.970418	+	0.241429i	$0.0776161\pi$
$948$		0			0
$949$	−1.75319e7	−	3.03662e7i	−0.631922	−	1.09452i
$950$		0			0
$951$	−4.93088e7			−1.76796
$952$		0			0
$953$	−1.29112e7			−0.460504			−0.230252	−	0.973131i	$-0.573955\pi$
$953$	−1.29112e7			−0.460504			−0.230252	+	0.973131i	$0.573955\pi$
$954$		0			0
$955$	−2.85864e7	−	4.95131e7i	−1.01426	−	1.75676i
$956$		0			0
$957$	4.97983e6	−	8.62532e6i	0.175766	−	0.304435i
$958$		0			0
$959$	−1.98712e7	+	1.81914e7i	−0.697716	+	0.638734i
$960$		0			0
$961$	9.18121e6	−	1.59023e7i	0.320694	−	0.555459i
$962$		0			0
$963$	4.13504e6	+	7.16211e6i	0.143686	+	0.248871i
$964$		0			0
$965$	7.91672e7			2.73670
$966$		0			0
$967$	4.60406e7			1.58334			0.791671	−	0.610948i	$-0.209211\pi$
$967$	4.60406e7			1.58334			0.791671	+	0.610948i	$0.209211\pi$
$968$		0			0
$969$	−3.14508e6	−	5.44744e6i	−0.107603	−	0.186373i
$970$		0			0
$971$	−9.36580e6	+	1.62220e7i	−0.318784	+	0.552150i	−0.980235	−	0.197839i	$-0.936608\pi$
$971$	−9.36580e6	+	1.62220e7i	−0.318784	+	0.552150i	0.661451	+	0.749989i	$0.269941\pi$
$972$		0			0
$973$	−811806.	−	3.67000e6i	−0.0274897	−	0.124275i
$974$		0			0
$975$	3.89373e7	−	6.74414e7i	1.31176	−	2.27204i
$976$		0			0
$977$	1.44602e7	+	2.50458e7i	0.484660	+	0.839456i	0.999845	−	0.0176231i	$-0.00560991\pi$
$977$	1.44602e7	+	2.50458e7i	0.484660	+	0.839456i	−0.515184	+	0.857079i	$0.672277\pi$
$978$		0			0
$979$	5.52286e7			1.84165
$980$		0			0
$981$	−9.63886e6			−0.319781
$982$		0			0
$983$	−1.08834e7	−	1.88505e7i	−0.359235	−	0.622214i	0.628598	−	0.777730i	$-0.283629\pi$
$983$	−1.08834e7	−	1.88505e7i	−0.359235	−	0.622214i	−0.987833	+	0.155517i	$0.950296\pi$
$984$		0			0
$985$	7.70379e6	−	1.33433e7i	0.252996	−	0.438202i
$986$		0			0
$987$	−1.31232e7	−	5.93273e7i	−0.428793	−	1.93848i
$988$		0			0
$989$	5.11331e6	−	8.85651e6i	0.166231	−	0.287920i
$990$		0			0
$991$	9.39333e6	+	1.62697e7i	0.303833	+	0.526255i	0.977001	−	0.213235i	$-0.0684001\pi$
$991$	9.39333e6	+	1.62697e7i	0.303833	+	0.526255i	−0.673168	+	0.739490i	$0.735067\pi$
$992$		0			0
$993$	1.04099e7			0.335023
$994$		0			0
$995$	5.70492e6			0.182680
$996$		0			0
$997$	7.38382e6	+	1.27891e7i	0.235257	+	0.407477i	0.959347	−	0.282228i	$-0.0910734\pi$
$997$	7.38382e6	+	1.27891e7i	0.235257	+	0.407477i	−0.724090	+	0.689705i	$0.757740\pi$
$998$		0			0
$999$	4.82899e6	−	8.36406e6i	0.153089	−	0.265157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.6.e.b.9.1	✓	4
3.2	odd	2		252.6.k.d.37.2		4
4.3	odd	2		112.6.i.e.65.2		4
7.2	even	3		196.6.a.j.1.2		2
7.3	odd	6		196.6.e.k.165.2		4
7.4	even	3	inner	28.6.e.b.25.1	yes	4
7.5	odd	6		196.6.a.h.1.1		2
7.6	odd	2		196.6.e.k.177.2		4
21.11	odd	6		252.6.k.d.109.2		4
28.11	odd	6		112.6.i.e.81.2		4
28.19	even	6		784.6.a.bd.1.2		2
28.23	odd	6		784.6.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.e.b.9.1	✓	4	1.1	even	1	trivial
28.6.e.b.25.1	yes	4	7.4	even	3	inner
112.6.i.e.65.2		4	4.3	odd	2
112.6.i.e.81.2		4	28.11	odd	6
196.6.a.h.1.1		2	7.5	odd	6
196.6.a.j.1.2		2	7.2	even	3
196.6.e.k.165.2		4	7.3	odd	6
196.6.e.k.177.2		4	7.6	odd	2
252.6.k.d.37.2		4	3.2	odd	2
252.6.k.d.109.2		4	21.11	odd	6
784.6.a.o.1.1		2	28.23	odd	6
784.6.a.bd.1.2		2	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	28.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.2202 - 21.1659i) q^{3} +(-41.8209 + 72.4360i) q^{5} +(28.0000 + 126.582i) q^{7} +(-177.164 + 306.858i) q^{9} +(-274.623 - 475.661i) q^{11} -823.135 q^{13} +2044.23 q^{15} +(-72.7837 - 126.065i) q^{17} +(-884.019 + 1531.17i) q^{19} +(2337.06 - 2139.50i) q^{21} +(761.363 - 1318.72i) q^{23} +(-1935.48 - 3352.35i) q^{25} +2720.90 q^{27} -741.943 q^{29} +(1602.09 + 2774.90i) q^{31} +(-6711.88 + 11625.3i) q^{33} +(-10340.1 - 3265.57i) q^{35} +(1774.77 - 3074.00i) q^{37} +(10058.8 + 17422.4i) q^{39} -6461.29 q^{41} +6716.00 q^{43} +(-14818.3 - 25666.1i) q^{45} +(9588.40 - 16607.6i) q^{47} +(-15239.0 + 7088.59i) q^{49} +(-1778.86 + 3081.07i) q^{51} +(10639.3 + 18427.8i) q^{53} +45940.0 q^{55} +43211.4 q^{57} +(-18264.3 - 31634.8i) q^{59} +(-21716.9 + 37614.7i) q^{61} +(-43803.2 - 13833.8i) q^{63} +(34424.3 - 59624.6i) q^{65} +(-2514.07 - 4354.50i) q^{67} -37215.9 q^{69} -6311.32 q^{71} +(21299.0 + 36890.9i) q^{73} +(-47303.7 + 81932.4i) q^{75} +(52520.7 - 48080.9i) q^{77} +(-47534.6 + 82332.3i) q^{79} +(9801.05 + 16975.9i) q^{81} -34978.2 q^{83} +12175.5 q^{85} +(9066.66 + 15703.9i) q^{87} +(-50276.7 + 87081.8i) q^{89} +(-23047.8 - 104194. i) q^{91} +(39155.5 - 67819.3i) q^{93} +(-73940.9 - 128069. i) q^{95} +76794.5 q^{97} +194614. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 28 q^{3} - 42 q^{5} + 112 q^{7} - 124 q^{9} - 660 q^{11} - 1288 q^{13} + 3792 q^{15} + 210 q^{17} - 3724 q^{19} + 3794 q^{21} - 24 q^{23} - 2480 q^{25} + 2072 q^{27} + 11064 q^{29} - 2800 q^{31} - 13818 q^{33}+ \cdots + 338208 q^{99}+O(q^{100}) \) 4 * q - 28 * q^3 - 42 * q^5 + 112 * q^7 - 124 * q^9 - 660 * q^11 - 1288 * q^13 + 3792 * q^15 + 210 * q^17 - 3724 * q^19 + 3794 * q^21 - 24 * q^23 - 2480 * q^25 + 2072 * q^27 + 11064 * q^29 - 2800 * q^31 - 13818 * q^33 - 28644 * q^35 + 13238 * q^37 + 19480 * q^39 + 8232 * q^41 + 26864 * q^43 - 39228 * q^45 - 8064 * q^47 - 60956 * q^49 - 2292 * q^51 + 53958 * q^53 + 82656 * q^55 + 100348 * q^57 - 36036 * q^59 - 83986 * q^61 - 131656 * q^63 + 76308 * q^65 + 2660 * q^67 - 63420 * q^69 + 143136 * q^71 - 31318 * q^73 - 89656 * q^75 + 77658 * q^77 - 51136 * q^79 - 30370 * q^81 + 12432 * q^83 + 53964 * q^85 - 4200 * q^87 - 166278 * q^89 - 36064 * q^91 + 56938 * q^93 - 66432 * q^95 + 16520 * q^97 + 338208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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