LMFDB - Embedded newform 112.6.i.f.81.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,6,Mod(65,112)] 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("112.65"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	112.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$17.9629878191$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 200 x^{8} - 198 x^{7} + 34197 x^{6} - 16185 x^{5} + 1170401 x^{4} + 2020497 x^{3} + \cdots + 13068225 $ x^10 + 200x^8 - 198x^7 + 34197x^6 - 16185x^5 + 1170401x^4 + 2020497x^3 + 33316924x^2 + 20977845x + 13068225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.5
Root			$-6.63412 + 11.4906i$ of defining polynomial
Character	$\chi$	$=$	112.81
Dual form			112.6.i.f.65.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(13.7682 - 23.8473i) q^{3} +(39.9714 + 69.2326i) q^{5} +(-113.410 - 62.8111i) q^{7} +(-257.629 - 446.226i) q^{9} +(227.576 - 394.173i) q^{11} -581.059 q^{13} +2201.35 q^{15} +(1187.69 - 2057.15i) q^{17} +(-366.096 - 634.097i) q^{19} +(-3059.33 + 1839.72i) q^{21} +(-296.582 - 513.695i) q^{23} +(-1632.93 + 2828.32i) q^{25} -7497.01 q^{27} -930.360 q^{29} +(-312.116 + 540.601i) q^{31} +(-6266.64 - 10854.1i) q^{33} +(-184.578 - 10362.3i) q^{35} +(2038.91 + 3531.50i) q^{37} +(-8000.16 + 13856.7i) q^{39} +6674.36 q^{41} +8956.88 q^{43} +(20595.6 - 35672.6i) q^{45} +(-5140.47 - 8903.56i) q^{47} +(8916.54 + 14246.8i) q^{49} +(-32704.9 - 56646.6i) q^{51} +(-6921.96 + 11989.2i) q^{53} +36386.1 q^{55} -20162.0 q^{57} +(-5361.58 + 9286.53i) q^{59} +(11075.5 + 19183.3i) q^{61} +(1189.67 + 66788.3i) q^{63} +(-23225.8 - 40228.2i) q^{65} +(-10021.2 + 17357.2i) q^{67} -16333.6 q^{69} +35780.7 q^{71} +(-27929.3 + 48374.9i) q^{73} +(44965.2 + 77882.0i) q^{75} +(-50567.8 + 30408.8i) q^{77} +(-27558.3 - 47732.4i) q^{79} +(-40616.8 + 70350.4i) q^{81} +87650.6 q^{83} +189896. q^{85} +(-12809.4 + 22186.6i) q^{87} +(37881.5 + 65612.6i) q^{89} +(65897.8 + 36497.0i) q^{91} +(8594.58 + 14886.3i) q^{93} +(29266.8 - 50691.6i) q^{95} +32072.1 q^{97} -234520. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} + 81 q^{5} - 116 q^{7} - 390 q^{9} + 361 q^{11} - 684 q^{13} + 2098 q^{15} + 1809 q^{17} - 1277 q^{19} - 5253 q^{21} + 911 q^{23} - 3940 q^{25} - 9502 q^{27} + 10884 q^{29} - 2187 q^{31}+ \cdots - 499596 q^{99}+O(q^{100}) $ 10 * q + 5 * q^3 + 81 * q^5 - 116 * q^7 - 390 * q^9 + 361 * q^11 - 684 * q^13 + 2098 * q^15 + 1809 * q^17 - 1277 * q^19 - 5253 * q^21 + 911 * q^23 - 3940 * q^25 - 9502 * q^27 + 10884 * q^29 - 2187 * q^31 - 5553 * q^33 + 16845 * q^35 + 8181 * q^37 - 3422 * q^39 - 33156 * q^41 - 12664 * q^43 + 41310 * q^45 - 16101 * q^47 - 10070 * q^49 - 67865 * q^51 - 16047 * q^53 + 91258 * q^55 + 44694 * q^57 - 71027 * q^59 + 31093 * q^61 + 127978 * q^63 + 64370 * q^65 + 47981 * q^67 - 274498 * q^69 - 45024 * q^71 + 123333 * q^73 + 45460 * q^75 - 245825 * q^77 - 212481 * q^79 - 52917 * q^81 + 174920 * q^83 + 444282 * q^85 - 318070 * q^87 + 129045 * q^89 + 526488 * q^91 + 252835 * q^93 + 300417 * q^95 - 656548 * q^97 - 499596 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	13.7682	−	23.8473i	0.883233	−	1.52980i	0.0355070	−	0.999369i	$-0.488695\pi$
$3$	13.7682	−	23.8473i	0.883233	−	1.52980i	0.847726	−	0.530435i	$-0.177971\pi$
$4$		0			0
$5$	39.9714	+	69.2326i	0.715031	+	1.23847i	0.962948	+	0.269688i	$0.0869207\pi$
$5$	39.9714	+	69.2326i	0.715031	+	1.23847i	−0.247917	+	0.968781i	$0.579746\pi$
$6$		0			0
$7$	−113.410	−	62.8111i	−0.874793	−	0.484497i
$7$	−113.410	−	62.8111i	−0.874793	−	0.484497i
$8$		0			0
$9$	−257.629	−	446.226i	−1.06020	−	1.83632i
$10$		0			0
$11$	227.576	−	394.173i	0.567080	−	0.982212i	−0.429773	−	0.902937i	$-0.641406\pi$
$11$	227.576	−	394.173i	0.567080	−	0.982212i	0.996853	−	0.0792747i	$-0.0252604\pi$
$12$		0			0
$13$	−581.059			−0.953591			−0.476795	−	0.879014i	$-0.658202\pi$
$13$	−581.059			−0.953591			−0.476795	+	0.879014i	$0.658202\pi$
$14$		0			0
$15$	2201.35			2.52615
$16$		0			0
$17$	1187.69	−	2057.15i	0.996742	−	1.72641i	0.428517	−	0.903534i	$-0.359036\pi$
$17$	1187.69	−	2057.15i	0.996742	−	1.72641i	0.568224	−	0.822874i	$-0.307631\pi$
$18$		0			0
$19$	−366.096	−	634.097i	−0.232654	−	0.402969i	0.725934	−	0.687764i	$-0.241408\pi$
$19$	−366.096	−	634.097i	−0.232654	−	0.402969i	−0.958588	+	0.284795i	$0.908074\pi$
$20$		0			0
$21$	−3059.33	+	1839.72i	−1.51383	+	0.910338i
$22$		0			0
$23$	−296.582	−	513.695i	−0.116903	−	0.202482i	0.801636	−	0.597813i	$-0.203963\pi$
$23$	−296.582	−	513.695i	−0.116903	−	0.202482i	−0.918539	+	0.395331i	$0.870630\pi$
$24$		0			0
$25$	−1632.93	+	2828.32i	−0.522538	+	0.905063i
$26$		0			0
$27$	−7497.01			−1.97915
$28$		0			0
$29$	−930.360			−0.205426			−0.102713	−	0.994711i	$-0.532752\pi$
$29$	−930.360			−0.205426			−0.102713	+	0.994711i	$0.532752\pi$
$30$		0			0
$31$	−312.116	+	540.601i	−0.0583327	+	0.101035i	−0.893717	−	0.448631i	$-0.851912\pi$
$31$	−312.116	+	540.601i	−0.0583327	+	0.101035i	0.835384	+	0.549666i	$0.185245\pi$
$32$		0			0
$33$	−6266.64	−	10854.1i	−1.00173	−	1.73504i
$34$		0			0
$35$	−184.578	−	10362.3i	−0.0254689	−	1.42983i
$36$		0			0
$37$	2038.91	+	3531.50i	0.244847	+	0.424087i	0.962088	−	0.272737i	$-0.0879290\pi$
$37$	2038.91	+	3531.50i	0.244847	+	0.424087i	−0.717242	+	0.696824i	$0.754596\pi$
$38$		0			0
$39$	−8000.16	+	13856.7i	−0.842243	+	1.45881i
$40$		0			0
$41$	6674.36			0.620083			0.310042	−	0.950723i	$-0.399657\pi$
$41$	6674.36			0.620083			0.310042	+	0.950723i	$0.399657\pi$
$42$		0			0
$43$	8956.88			0.738730			0.369365	−	0.929284i	$-0.379575\pi$
$43$	8956.88			0.738730			0.369365	+	0.929284i	$0.379575\pi$
$44$		0			0
$45$	20595.6	−	35672.6i	1.51615	−	2.62605i
$46$		0			0
$47$	−5140.47	−	8903.56i	−0.339436	−	0.587921i	0.644891	−	0.764275i	$-0.276903\pi$
$47$	−5140.47	−	8903.56i	−0.339436	−	0.587921i	−0.984327	+	0.176354i	$0.943570\pi$
$48$		0			0
$49$	8916.54	+	14246.8i	0.530525	+	0.847669i
$50$		0			0
$51$	−32704.9	−	56646.6i	−1.76071	−	3.04964i
$52$		0			0
$53$	−6921.96	+	11989.2i	−0.338485	+	0.586273i	−0.984148	−	0.177349i	$-0.943248\pi$
$53$	−6921.96	+	11989.2i	−0.338485	+	0.586273i	0.645663	+	0.763622i	$0.276581\pi$
$54$		0			0
$55$	36386.1			1.62192
$56$		0			0
$57$	−20162.0			−0.821952
$58$		0			0
$59$	−5361.58	+	9286.53i	−0.200522	+	0.347315i	−0.948697	−	0.316187i	$-0.897597\pi$
$59$	−5361.58	+	9286.53i	−0.200522	+	0.347315i	0.748174	+	0.663502i	$0.230931\pi$
$60$		0			0
$61$	11075.5	+	19183.3i	0.381099	+	0.660083i	0.991220	−	0.132225i	$-0.0422123\pi$
$61$	11075.5	+	19183.3i	0.381099	+	0.660083i	−0.610120	+	0.792309i	$0.708879\pi$
$62$		0			0
$63$	1189.67	+	66788.3i	0.0377636	+	2.12006i
$64$		0			0
$65$	−23225.8	−	40228.2i	−0.681847	−	1.18099i
$66$		0			0
$67$	−10021.2	+	17357.2i	−0.272730	+	0.472382i	−0.969560	−	0.244854i	$-0.921260\pi$
$67$	−10021.2	+	17357.2i	−0.272730	+	0.472382i	0.696830	+	0.717237i	$0.254593\pi$
$68$		0			0
$69$	−16333.6			−0.413010
$70$		0			0
$71$	35780.7			0.842370			0.421185	−	0.906975i	$-0.361614\pi$
$71$	35780.7			0.842370			0.421185	+	0.906975i	$0.361614\pi$
$72$		0			0
$73$	−27929.3	+	48374.9i	−0.613413	+	1.06246i	0.377248	+	0.926112i	$0.376870\pi$
$73$	−27929.3	+	48374.9i	−0.613413	+	1.06246i	−0.990661	+	0.136350i	$0.956463\pi$
$74$		0			0
$75$	44965.2	+	77882.0i	0.923046	+	1.59876i
$76$		0			0
$77$	−50567.8	+	30408.8i	−0.971957	+	0.584483i
$78$		0			0
$79$	−27558.3	−	47732.4i	−0.496804	−	0.860490i	0.503189	−	0.864176i	$-0.332160\pi$
$79$	−27558.3	−	47732.4i	−0.496804	−	0.860490i	−0.999993	+	0.00368633i	$0.998827\pi$
$80$		0			0
$81$	−40616.8	+	70350.4i	−0.687849	+	1.19139i
$82$		0			0
$83$	87650.6			1.39656			0.698280	−	0.715825i	$-0.253949\pi$
$83$	87650.6			1.39656			0.698280	+	0.715825i	$0.253949\pi$
$84$		0			0
$85$	189896.			2.85080
$86$		0			0
$87$	−12809.4	+	22186.6i	−0.181439	+	0.314262i
$88$		0			0
$89$	37881.5	+	65612.6i	0.506935	+	0.878036i	0.999968	+	0.00802590i	$0.00255475\pi$
$89$	37881.5	+	65612.6i	0.506935	+	0.878036i	−0.493033	+	0.870010i	$0.664112\pi$
$90$		0			0
$91$	65897.8	+	36497.0i	0.834194	+	0.462012i
$92$		0			0
$93$	8594.58	+	14886.3i	0.103043	+	0.178475i
$94$		0			0
$95$	29266.8	−	50691.6i	0.332710	−	0.576271i
$96$		0			0
$97$	32072.1			0.346097			0.173048	−	0.984913i	$-0.444638\pi$
$97$	32072.1			0.346097			0.173048	+	0.984913i	$0.444638\pi$
$98$		0			0
$99$	−234520.			−2.40487
$100$		0			0
$101$	93930.1	−	162692.i	0.916223	−	1.58694i	0.111122	−	0.993807i	$-0.464555\pi$
$101$	93930.1	−	162692.i	0.916223	−	1.58694i	0.805101	−	0.593138i	$-0.202111\pi$
$102$		0			0
$103$	−80497.3	−	139425.i	−0.747633	−	1.29494i	−0.948954	−	0.315413i	$-0.897857\pi$
$103$	−80497.3	−	139425.i	−0.747633	−	1.29494i	0.201321	−	0.979525i	$-0.435476\pi$
$104$		0			0
$105$	−249654.	−	138269.i	−2.20986	−	1.22391i
$106$		0			0
$107$	76668.2	+	132793.i	0.647375	+	1.12129i	0.983748	+	0.179557i	$0.0574663\pi$
$107$	76668.2	+	132793.i	0.647375	+	1.12129i	−0.336373	+	0.941729i	$0.609200\pi$
$108$		0			0
$109$	21031.5	−	36427.6i	0.169552	−	0.293673i	−0.768710	−	0.639597i	$-0.779101\pi$
$109$	21031.5	−	36427.6i	0.169552	−	0.293673i	0.938263	+	0.345924i	$0.112434\pi$
$110$		0			0
$111$	112289.			0.865026
$112$		0			0
$113$	92809.7			0.683750			0.341875	−	0.939745i	$-0.388938\pi$
$113$	92809.7			0.683750			0.341875	+	0.939745i	$0.388938\pi$
$114$		0			0
$115$	23709.6	−	41066.3i	0.167178	−	0.289561i
$116$		0			0
$117$	149698.	+	259284.i	1.01100	+	1.75110i
$118$		0			0
$119$	−263908.	+	158700.i	−1.70838	+	1.02733i
$120$		0			0
$121$	−23056.1	−	39934.3i	−0.143160	−	0.247961i
$122$		0			0
$123$	91894.2	−	159165.i	0.547678	−	0.948606i
$124$		0			0
$125$	−11261.1			−0.0644622
$126$		0			0
$127$	59778.1			0.328877			0.164438	−	0.986387i	$-0.447419\pi$
$127$	59778.1			0.328877			0.164438	+	0.986387i	$0.447419\pi$
$128$		0			0
$129$	123320.	−	213597.i	0.652470	−	1.13011i
$130$		0			0
$131$	130861.	+	226658.i	0.666243	+	1.15397i	0.978947	+	0.204116i	$0.0654321\pi$
$131$	130861.	+	226658.i	0.666243	+	1.15397i	−0.312703	+	0.949851i	$0.601235\pi$
$132$		0			0
$133$	1690.54	+	94907.7i	0.00828699	+	0.465235i
$134$		0			0
$135$	−299666.	−	519037.i	−1.41515	−	2.45112i
$136$		0			0
$137$	−25937.8	+	44925.5i	−0.118068	+	0.204499i	−0.919002	−	0.394253i	$-0.871003\pi$
$137$	−25937.8	+	44925.5i	−0.118068	+	0.204499i	0.800934	+	0.598752i	$0.204337\pi$
$138$		0			0
$139$	−299390.			−1.31432			−0.657159	−	0.753752i	$-0.728242\pi$
$139$	−299390.			−1.31432			−0.657159	+	0.753752i	$0.728242\pi$
$140$		0			0
$141$	−283101.			−1.19920
$142$		0			0
$143$	−132235.	+	229038.i	−0.540762	+	0.936628i
$144$		0			0
$145$	−37187.8	−	64411.2i	−0.146886	−	0.254414i
$146$		0			0
$147$	462512.	−	16482.2i	1.76535	−	0.0629103i
$148$		0			0
$149$	140841.	+	243944.i	0.519713	+	0.900170i	0.999737	+	0.0229145i	$0.00729454\pi$
$149$	140841.	+	243944.i	0.519713	+	0.900170i	−0.480024	+	0.877255i	$0.659372\pi$
$150$		0			0
$151$	111199.	−	192603.i	0.396881	−	0.687417i	−0.596459	−	0.802644i	$-0.703426\pi$
$151$	111199.	−	192603.i	0.396881	−	0.687417i	0.993339	+	0.115226i	$0.0367593\pi$
$152$		0			0
$153$	−1.22394e6			−4.22698
$154$		0			0
$155$	−49902.9			−0.166839
$156$		0			0
$157$	29837.4	−	51680.0i	0.0966078	−	0.167330i	−0.813671	−	0.581326i	$-0.802534\pi$
$157$	29837.4	−	51680.0i	0.0966078	−	0.167330i	0.910279	+	0.413996i	$0.135867\pi$
$158$		0			0
$159$	190606.	+	330140.i	0.597922	+	1.03563i
$160$		0			0
$161$	1369.54	+	76886.6i	0.00416400	+	0.233769i
$162$		0			0
$163$	−189494.	−	328212.i	−0.558631	−	0.967578i	−0.997611	−	0.0690809i	$-0.977993\pi$
$163$	−189494.	−	328212.i	−0.558631	−	0.967578i	0.438980	−	0.898497i	$-0.355340\pi$
$164$		0			0
$165$	500973.	−	867711.i	1.43253	−	2.48122i
$166$		0			0
$167$	143609.			0.398465			0.199233	−	0.979952i	$-0.436155\pi$
$167$	143609.			0.398465			0.199233	+	0.979952i	$0.436155\pi$
$168$		0			0
$169$	−33663.2			−0.0906648
$170$		0			0
$171$	−188634.	+	326723.i	−0.493321	+	0.854456i
$172$		0			0
$173$	−387067.	−	670419.i	−0.983265	−	1.70307i	−0.649406	−	0.760442i	$-0.724982\pi$
$173$	−387067.	−	670419.i	−0.983265	−	1.70307i	−0.333859	−	0.942623i	$-0.608351\pi$
$174$		0			0
$175$	362840.	−	218193.i	0.895613	−	0.538574i
$176$		0			0
$177$	147639.	+	255718.i	0.354216	+	0.613520i
$178$		0			0
$179$	233276.	−	404046.i	0.544173	−	0.942536i	−0.454485	−	0.890754i	$-0.650177\pi$
$179$	233276.	−	404046.i	0.544173	−	0.942536i	0.998658	−	0.0517815i	$-0.0164899\pi$
$180$		0			0
$181$	575239.			1.30512			0.652562	−	0.757736i	$-0.273694\pi$
$181$	575239.			1.30512			0.652562	+	0.757736i	$0.273694\pi$
$182$		0			0
$183$	609960.			1.34640
$184$		0			0
$185$	−162997.	+	282318.i	−0.350146	+	0.606470i
$186$		0			0
$187$	−540581.	−	936315.i	−1.13047	−	1.95802i
$188$		0			0
$189$	850234.	+	470895.i	1.73135	+	0.958892i
$190$		0			0
$191$	140023.	+	242527.i	0.277726	+	0.481035i	0.970819	−	0.239813i	$-0.0770861\pi$
$191$	140023.	+	242527.i	0.277726	+	0.481035i	−0.693094	+	0.720848i	$0.743753\pi$
$192$		0			0
$193$	−14380.9	+	24908.4i	−0.0277902	+	0.0481341i	−0.879586	−	0.475740i	$-0.842180\pi$
$193$	−14380.9	+	24908.4i	−0.0277902	+	0.0481341i	0.851796	+	0.523874i	$0.175514\pi$
$194$		0			0
$195$	−1.27911e6			−2.40892
$196$		0			0
$197$	−174264.			−0.319921			−0.159960	−	0.987123i	$-0.551137\pi$
$197$	−174264.			−0.319921			−0.159960	+	0.987123i	$0.551137\pi$
$198$		0			0
$199$	−327203.	+	566732.i	−0.585713	+	1.01448i	0.409073	+	0.912502i	$0.365852\pi$
$199$	−327203.	+	566732.i	−0.585713	+	1.01448i	−0.994786	+	0.101983i	$0.967481\pi$
$200$		0			0
$201$	275949.	+	477957.i	0.481768	+	0.834447i
$202$		0			0
$203$	105512.	+	58436.9i	0.179705	+	0.0995284i
$204$		0			0
$205$	266784.	+	462083.i	0.443379	+	0.767954i
$206$		0			0
$207$	−152816.	+	264685.i	−0.247881	+	0.429342i
$208$		0			0
$209$	−333259.			−0.527735
$210$		0			0
$211$	610071.			0.943354			0.471677	−	0.881771i	$-0.343649\pi$
$211$	610071.			0.943354			0.471677	+	0.881771i	$0.343649\pi$
$212$		0			0
$213$	492637.	−	853272.i	0.744009	−	1.28866i
$214$		0			0
$215$	358019.	+	620108.i	0.528215	+	0.914894i
$216$		0			0
$217$	69352.8	−	41705.1i	0.0999803	−	0.0601229i
$218$		0			0
$219$	769074.	+	1.33208e6i	1.08357	+	1.87680i
$220$		0			0
$221$	−690121.	+	1.19532e6i	−0.950484	+	1.64629i
$222$		0			0
$223$	−862752.			−1.16178			−0.580890	−	0.813982i	$-0.697295\pi$
$223$	−862752.			−1.16178			−0.580890	+	0.813982i	$0.697295\pi$
$224$		0			0
$225$	1.68276e6			2.21598
$226$		0			0
$227$	−13389.2	+	23190.9i	−0.0172461	+	0.0298712i	−0.874520	−	0.484990i	$-0.838823\pi$
$227$	−13389.2	+	23190.9i	−0.0172461	+	0.0298712i	0.857274	+	0.514861i	$0.172157\pi$
$228$		0			0
$229$	406277.	+	703692.i	0.511957	+	0.886736i	0.999904	+	0.0138624i	$0.00441266\pi$
$229$	406277.	+	703692.i	0.511957	+	0.886736i	−0.487947	+	0.872873i	$0.662254\pi$
$230$		0			0
$231$	28937.8	+	1.62458e6i	0.0356809	+	2.00314i
$232$		0			0
$233$	−625018.	−	1.08256e6i	−0.754228	−	1.30636i	−0.945757	−	0.324875i	$-0.894678\pi$
$233$	−625018.	−	1.08256e6i	−0.754228	−	1.30636i	0.191529	−	0.981487i	$-0.438655\pi$
$234$		0			0
$235$	410944.	−	711776.i	0.485415	−	0.840763i
$236$		0			0
$237$	−1.51772e6			−1.75517
$238$		0			0
$239$	−1.59397e6			−1.80504			−0.902518	−	0.430653i	$-0.858283\pi$
$239$	−1.59397e6			−1.80504			−0.902518	+	0.430653i	$0.858283\pi$
$240$		0			0
$241$	−789579.	+	1.36759e6i	−0.875696	+	1.51675i	−0.0196757	+	0.999806i	$0.506263\pi$
$241$	−789579.	+	1.36759e6i	−0.875696	+	1.51675i	−0.856020	+	0.516943i	$0.827070\pi$
$242$		0			0
$243$	207557.	+	359500.i	0.225487	+	0.390556i
$244$		0			0
$245$	−629934.	+	1.18678e6i	−0.670471	+	1.26315i
$246$		0			0
$247$	212724.	+	368448.i	0.221857	+	0.384268i
$248$		0			0
$249$	1.20679e6	−	2.09023e6i	1.23349	−	2.13646i
$250$		0			0
$251$	−1.47838e6			−1.48116			−0.740581	−	0.671967i	$-0.765450\pi$
$251$	−1.47838e6			−1.48116			−0.740581	+	0.671967i	$0.765450\pi$
$252$		0			0
$253$	−269980.			−0.265173
$254$		0			0
$255$	2.61453e6	−	4.52849e6i	2.51792	−	4.36117i
$256$		0			0
$257$	524809.	+	908997.i	0.495643	+	0.858478i	0.999987	−	0.00502401i	$-0.00159920\pi$
$257$	524809.	+	908997.i	0.495643	+	0.858478i	−0.504345	+	0.863502i	$0.668266\pi$
$258$		0			0
$259$	−9415.19	−	528573.i	−0.00872127	−	0.489616i
$260$		0			0
$261$	239687.	+	415151.i	0.217793	+	0.377228i
$262$		0			0
$263$	79923.1	−	138431.i	0.0712497	−	0.123408i	−0.828200	−	0.560433i	$-0.810635\pi$
$263$	79923.1	−	138431.i	0.0712497	−	0.123408i	0.899449	+	0.437025i	$0.143968\pi$
$264$		0			0
$265$	−1.10672e6			−0.968109
$266$		0			0
$267$	2.08624e6			1.79096
$268$		0			0
$269$	−113255.	+	196163.i	−0.0954280	+	0.165286i	−0.909787	−	0.415075i	$-0.863755\pi$
$269$	−113255.	+	196163.i	−0.0954280	+	0.165286i	0.814359	+	0.580361i	$0.197089\pi$
$270$		0			0
$271$	753214.	+	1.30461e6i	0.623011	+	1.07909i	0.988922	+	0.148436i	$0.0474240\pi$
$271$	753214.	+	1.30461e6i	0.623011	+	1.07909i	−0.365911	+	0.930650i	$0.619243\pi$
$272$		0			0
$273$	1.77765e6	−	1.06898e6i	1.44358	−	0.868090i
$274$		0			0
$275$	743232.	+	1.28732e6i	0.592642	+	1.02649i
$276$		0			0
$277$	955820.	−	1.65553e6i	0.748474	−	1.29639i	−0.200080	−	0.979780i	$-0.564120\pi$
$277$	955820.	−	1.65553e6i	0.748474	−	1.29639i	0.948554	−	0.316615i	$-0.102546\pi$
$278$		0			0
$279$	321640.			0.247377
$280$		0			0
$281$	1.17933e6			0.890987			0.445493	−	0.895285i	$-0.353028\pi$
$281$	1.17933e6			0.890987			0.445493	+	0.895285i	$0.353028\pi$
$282$		0			0
$283$	−176772.	+	306178.i	−0.131204	+	0.227252i	−0.924141	−	0.382052i	$-0.875218\pi$
$283$	−176772.	+	306178.i	−0.131204	+	0.227252i	0.792937	+	0.609304i	$0.208551\pi$
$284$		0			0
$285$	−805904.	−	1.39587e6i	−0.587721	−	1.01796i
$286$		0			0
$287$	−756937.	−	419224.i	−0.542444	−	0.300428i
$288$		0			0
$289$	−2.11131e6	−	3.65690e6i	−1.48699	−	2.57554i
$290$		0			0
$291$	441576.	−	764831.i	0.305684	−	0.529460i
$292$		0			0
$293$	61933.0			0.0421457			0.0210728	−	0.999778i	$-0.493292\pi$
$293$	61933.0			0.0421457			0.0210728	+	0.999778i	$0.493292\pi$
$294$		0			0
$295$	−857240.			−0.573519
$296$		0			0
$297$	−1.70614e6	+	2.95512e6i	−1.12234	+	1.94394i
$298$		0			0
$299$	172332.	+	298487.i	0.111477	+	0.193085i
$300$		0			0
$301$	−1.01580e6	−	562591.i	−0.646235	−	0.357912i
$302$		0			0
$303$	−2.58650e6	−	4.47995e6i	−1.61848	−	2.80328i
$304$		0			0
$305$	−885406.	+	1.53357e6i	−0.544996	+	0.943960i
$306$		0			0
$307$	1.90020e6			1.15068			0.575338	−	0.817915i	$-0.304870\pi$
$307$	1.90020e6			1.15068			0.575338	+	0.817915i	$0.304870\pi$
$308$		0			0
$309$	−4.43323e6			−2.64134
$310$		0			0
$311$	−1.31531e6	+	2.27819e6i	−0.771131	+	1.33564i	0.165812	+	0.986157i	$0.446976\pi$
$311$	−1.31531e6	+	2.27819e6i	−0.771131	+	1.33564i	−0.936943	+	0.349481i	$0.886358\pi$
$312$		0			0
$313$	1.38022e6	+	2.39061e6i	0.796319	+	1.37926i	0.921998	+	0.387194i	$0.126556\pi$
$313$	1.38022e6	+	2.39061e6i	0.796319	+	1.37926i	−0.125680	+	0.992071i	$0.540111\pi$
$314$		0			0
$315$	−4.57637e6	+	2.75199e6i	−2.59863	+	1.56268i
$316$		0			0
$317$	−310702.	−	538151.i	−0.173658	−	0.300785i	0.766038	−	0.642795i	$-0.222225\pi$
$317$	−310702.	−	538151.i	−0.173658	−	0.300785i	−0.939696	+	0.342010i	$0.888892\pi$
$318$		0			0
$319$	−211727.	+	366723.i	−0.116493	+	0.201772i
$320$		0			0
$321$	4.22234e6			2.28713
$322$		0			0
$323$	−1.73924e6			−0.927586
$324$		0			0
$325$	948830.	−	1.64342e6i	0.498288	−	0.863059i
$326$		0			0
$327$	−579133.	−	1.00309e6i	−0.299509	−	0.518764i
$328$		0			0
$329$	23737.4	+	1.33263e6i	0.0120905	+	0.678765i
$330$		0			0
$331$	−439158.	−	760644.i	−0.220318	−	0.381603i	0.734586	−	0.678515i	$-0.237376\pi$
$331$	−439158.	−	760644.i	−0.220318	−	0.381603i	−0.954905	+	0.296913i	$0.904043\pi$
$332$		0			0
$333$	1.05056e6	−	1.81963e6i	0.519173	−	0.899234i
$334$		0			0
$335$	−1.60225e6			−0.780042
$336$		0			0
$337$	1.72499e6			0.827392			0.413696	−	0.910415i	$-0.364238\pi$
$337$	1.72499e6			0.827392			0.413696	+	0.910415i	$0.364238\pi$
$338$		0			0
$339$	1.27783e6	−	2.21326e6i	0.603911	−	1.04600i
$340$		0			0
$341$	142060.	+	246056.i	0.0661587	+	0.114590i
$342$		0			0
$343$	−116367.	−	2.17578e6i	−0.0534064	−	0.998573i
$344$		0			0
$345$	−652879.	−	1.13082e6i	−0.295315	−	0.511500i
$346$		0			0
$347$	−462787.	+	801571.i	−0.206328	+	0.357370i	−0.950555	−	0.310556i	$-0.899485\pi$
$347$	−462787.	+	801571.i	−0.206328	+	0.357370i	0.744227	+	0.667926i	$0.232818\pi$
$348$		0			0
$349$	3.27452e6			1.43908			0.719539	−	0.694452i	$-0.244353\pi$
$349$	3.27452e6			1.43908			0.719539	+	0.694452i	$0.244353\pi$
$350$		0			0
$351$	4.35621e6			1.88730
$352$		0			0
$353$	954155.	−	1.65265e6i	0.407551	−	0.705900i	−0.587063	−	0.809541i	$-0.699716\pi$
$353$	954155.	−	1.65265e6i	0.407551	−	0.705900i	0.994615	+	0.103641i	$0.0330494\pi$
$354$		0			0
$355$	1.43021e6	+	2.47719e6i	0.602320	+	1.04325i
$356$		0			0
$357$	151023.	+	8.47851e6i	0.0627153	+	3.52086i
$358$		0			0
$359$	724500.	+	1.25487e6i	0.296690	+	0.513882i	0.975377	−	0.220546i	$-0.0707840\pi$
$359$	724500.	+	1.25487e6i	0.296690	+	0.513882i	−0.678687	+	0.734428i	$0.737451\pi$
$360$		0			0
$361$	969996.	−	1.68008e6i	0.391744	−	0.678520i
$362$		0			0
$363$	−1.26977e6			−0.505775
$364$		0			0
$365$	−4.46550e6			−1.75444
$366$		0			0
$367$	−939895.	+	1.62795e6i	−0.364262	+	0.630921i	−0.988657	−	0.150188i	$-0.952012\pi$
$367$	−939895.	+	1.62795e6i	−0.364262	+	0.630921i	0.624395	+	0.781109i	$0.285345\pi$
$368$		0			0
$369$	−1.71951e6	−	2.97827e6i	−0.657412	−	1.13867i
$370$		0			0
$371$	1.53807e6	−	924914.i	0.580152	−	0.348873i
$372$		0			0
$373$	−2.25431e6	−	3.90457e6i	−0.838959	−	1.45312i	−0.890766	−	0.454463i	$-0.849831\pi$
$373$	−2.25431e6	−	3.90457e6i	−0.838959	−	1.45312i	0.0518065	−	0.998657i	$-0.483502\pi$
$374$		0			0
$375$	−155045.	+	268546.i	−0.0569352	+	0.0986146i
$376$		0			0
$377$	540594.			0.195893
$378$		0			0
$379$	2.33971e6			0.836688			0.418344	−	0.908289i	$-0.362611\pi$
$379$	2.33971e6			0.836688			0.418344	+	0.908289i	$0.362611\pi$
$380$		0			0
$381$	823039.	−	1.42555e6i	0.290475	−	0.503117i
$382$		0			0
$383$	855907.	+	1.48247e6i	0.298146	+	0.516405i	0.975712	−	0.219058i	$-0.0702983\pi$
$383$	855907.	+	1.48247e6i	0.298146	+	0.516405i	−0.677566	+	0.735462i	$0.736965\pi$
$384$		0			0
$385$	−4.12654e6	−	2.28545e6i	−1.41884	−	0.785815i
$386$		0			0
$387$	−2.30755e6	−	3.99679e6i	−0.783201	−	1.35654i
$388$		0			0
$389$	−538866.	+	933344.i	−0.180554	+	0.312729i	−0.942069	−	0.335418i	$-0.891122\pi$
$389$	−538866.	+	933344.i	−0.180554	+	0.312729i	0.761515	+	0.648147i	$0.224456\pi$
$390$		0			0
$391$	−1.40900e6			−0.466088
$392$		0			0
$393$	7.20691e6			2.35379
$394$		0			0
$395$	2.20309e6	−	3.81587e6i	0.710461	−	1.23055i
$396$		0			0
$397$	144041.	+	249487.i	0.0458682	+	0.0794460i	0.888048	−	0.459751i	$-0.152061\pi$
$397$	144041.	+	249487.i	0.0458682	+	0.0794460i	−0.842180	+	0.539197i	$0.818728\pi$
$398$		0			0
$399$	2.28657e6	+	1.26640e6i	0.719038	+	0.398233i
$400$		0			0
$401$	2.73215e6	+	4.73223e6i	0.848485	+	1.46962i	0.882560	+	0.470200i	$0.155818\pi$
$401$	2.73215e6	+	4.73223e6i	0.848485	+	1.46962i	−0.0340752	+	0.999419i	$0.510849\pi$
$402$		0			0
$403$	181358.	−	314121.i	0.0556255	−	0.0963462i
$404$		0			0
$405$	−6.49405e6			−1.96733
$406$		0			0
$407$	1.85603e6			0.555391
$408$		0			0
$409$	1.22838e6	−	2.12761e6i	0.363098	−	0.628904i	−0.625371	−	0.780327i	$-0.715052\pi$
$409$	1.22838e6	−	2.12761e6i	0.363098	−	0.628904i	0.988469	+	0.151424i	$0.0483858\pi$
$410$		0			0
$411$	714234.	+	1.23709e6i	0.208563	+	0.361241i
$412$		0			0
$413$	1.19135e6	−	716416.i	0.343689	−	0.206676i
$414$		0			0
$415$	3.50352e6	+	6.06827e6i	0.998583	+	1.72960i
$416$		0			0
$417$	−4.12207e6	+	7.13964e6i	−1.16085	+	2.01065i
$418$		0			0
$419$	−267685.			−0.0744884			−0.0372442	−	0.999306i	$-0.511858\pi$
$419$	−267685.			−0.0744884			−0.0372442	+	0.999306i	$0.511858\pi$
$420$		0			0
$421$	−1.11613e6			−0.306908			−0.153454	−	0.988156i	$-0.549040\pi$
$421$	−1.11613e6			−0.306908			−0.153454	+	0.988156i	$0.549040\pi$
$422$		0			0
$423$	−2.64867e6	+	4.58762e6i	−0.719741	+	1.24663i
$424$		0			0
$425$	3.87885e6	+	6.71837e6i	1.04167	+	1.80423i
$426$		0			0
$427$	−51143.9	−	2.87124e6i	−0.0135745	−	0.762078i
$428$		0			0
$429$	3.64129e6	+	6.30689e6i	0.955238	+	1.65452i
$430$		0			0
$431$	780225.	−	1.35139e6i	0.202314	−	0.350419i	−0.746959	−	0.664870i	$-0.768487\pi$
$431$	780225.	−	1.35139e6i	0.202314	−	0.350419i	0.949274	+	0.314451i	$0.101820\pi$
$432$		0			0
$433$	−2.91249e6			−0.746525			−0.373263	−	0.927726i	$-0.621761\pi$
$433$	−2.91249e6			−0.746525			−0.373263	+	0.927726i	$0.621761\pi$
$434$		0			0
$435$	−2.04804e6			−0.518938
$436$		0			0
$437$	−217155.	+	376124.i	−0.0543959	+	0.0942165i
$438$		0			0
$439$	−552704.	−	957311.i	−0.136877	−	0.237078i	0.789436	−	0.613833i	$-0.210373\pi$
$439$	−552704.	−	957311.i	−0.136877	−	0.237078i	−0.926313	+	0.376755i	$0.877040\pi$
$440$		0			0
$441$	4.06013e6	−	7.64917e6i	0.994130	−	1.87291i
$442$		0			0
$443$	894031.	+	1.54851e6i	0.216443	+	0.374890i	0.953718	−	0.300703i	$-0.0972212\pi$
$443$	894031.	+	1.54851e6i	0.216443	+	0.374890i	−0.737275	+	0.675593i	$0.763888\pi$
$444$		0			0
$445$	−3.02835e6	+	5.24526e6i	−0.724948	+	1.25565i
$446$		0			0
$447$	7.75654e6			1.83611
$448$		0			0
$449$	−4.24314e6			−0.993279			−0.496639	−	0.867957i	$-0.665433\pi$
$449$	−4.24314e6			−0.993279			−0.496639	+	0.867957i	$0.665433\pi$
$450$		0			0
$451$	1.51892e6	−	2.63085e6i	0.351637	−	0.609053i
$452$		0			0
$453$	−3.06204e6	−	5.30361e6i	−0.701076	−	1.21430i
$454$		0			0
$455$	107251.	+	6.02111e6i	0.0242869	+	1.36348i
$456$		0			0
$457$	−829873.	−	1.43738e6i	−0.185875	−	0.321945i	0.757996	−	0.652259i	$-0.226179\pi$
$457$	−829873.	−	1.43738e6i	−0.185875	−	0.321945i	−0.943871	+	0.330314i	$0.892845\pi$
$458$		0			0
$459$	−8.90416e6	+	1.54225e7i	−1.97270	+	3.41682i
$460$		0			0
$461$	8.34155e6			1.82808			0.914038	−	0.405628i	$-0.132947\pi$
$461$	8.34155e6			1.82808			0.914038	+	0.405628i	$0.132947\pi$
$462$		0			0
$463$	−487990.			−0.105793			−0.0528967	−	0.998600i	$-0.516845\pi$
$463$	−487990.			−0.105793			−0.0528967	+	0.998600i	$0.516845\pi$
$464$		0			0
$465$	−687076.	+	1.19005e6i	−0.147357	+	0.255231i
$466$		0			0
$467$	−2.99457e6	−	5.18674e6i	−0.635392	−	1.10053i	−0.986432	−	0.164171i	$-0.947505\pi$
$467$	−2.99457e6	−	5.18674e6i	−0.635392	−	1.10053i	0.351040	−	0.936360i	$-0.385828\pi$
$468$		0			0
$469$	2.22673e6	−	1.33904e6i	0.467450	−	0.281100i
$470$		0			0
$471$	−821618.	−	1.42308e6i	−0.170654	−	0.295582i
$472$		0			0
$473$	2.03837e6	−	3.53056e6i	0.418919	−	0.725589i
$474$		0			0
$475$	2.39124e6			0.486283
$476$		0			0
$477$	7.13318e6			1.43545
$478$		0			0
$479$	−1.98540e6	+	3.43882e6i	−0.395375	+	0.684810i	−0.993149	−	0.116855i	$-0.962719\pi$
$479$	−1.98540e6	+	3.43882e6i	−0.395375	+	0.684810i	0.597774	+	0.801665i	$0.296052\pi$
$480$		0			0
$481$	−1.18473e6	−	2.05201e6i	−0.233483	−	0.404405i
$482$		0			0
$483$	1.85239e6	+	1.02593e6i	0.361298	+	0.200102i
$484$		0			0
$485$	1.28197e6	+	2.22043e6i	0.247470	+	0.428630i
$486$		0			0
$487$	3.81911e6	−	6.61489e6i	0.729692	−	1.26386i	−0.227321	−	0.973820i	$-0.572997\pi$
$487$	3.81911e6	−	6.61489e6i	0.729692	−	1.26386i	0.957013	−	0.290045i	$-0.0936701\pi$
$488$		0			0
$489$	−1.04360e7			−1.97361
$490$		0			0
$491$	−8.30768e6			−1.55516			−0.777581	−	0.628782i	$-0.783554\pi$
$491$	−8.30768e6			−1.55516			−0.777581	+	0.628782i	$0.783554\pi$
$492$		0			0
$493$	−1.10498e6	+	1.91389e6i	−0.204757	+	0.354649i
$494$		0			0
$495$	−9.37411e6	−	1.62364e7i	−1.71956	−	2.97836i
$496$		0			0
$497$	−4.05788e6	−	2.24742e6i	−0.736899	−	0.408126i
$498$		0			0
$499$	−2.85191e6	−	4.93966e6i	−0.512725	−	0.888066i	−0.999891	−	0.0147567i	$-0.995303\pi$
$499$	−2.85191e6	−	4.93966e6i	−0.512725	−	0.888066i	0.487166	−	0.873309i	$-0.338031\pi$
$500$		0			0
$501$	1.97724e6	−	3.42468e6i	0.351937	−	0.609573i
$502$		0			0
$503$	−58117.5			−0.0102421			−0.00512103	−	0.999987i	$-0.501630\pi$
$503$	−58117.5			−0.0102421			−0.00512103	+	0.999987i	$0.501630\pi$
$504$		0			0
$505$	1.50181e7			2.62051
$506$		0			0
$507$	−463483.	+	802776.i	−0.0800781	+	0.138699i
$508$		0			0
$509$	−884060.	−	1.53124e6i	−0.151247	−	0.261968i	0.780439	−	0.625232i	$-0.214996\pi$
$509$	−884060.	−	1.53124e6i	−0.151247	−	0.261968i	−0.931686	+	0.363264i	$0.881662\pi$
$510$		0			0
$511$	6.20594e6	−	3.73192e6i	1.05137	−	0.632237i
$512$		0			0
$513$	2.74463e6	+	4.75383e6i	0.460458	+	0.797536i
$514$		0			0
$515$	6.43519e6	−	1.11461e7i	1.06916	−	1.85184i
$516$		0			0
$517$	−4.67939e6			−0.769950
$518$		0			0
$519$	−2.13169e7			−3.47381
$520$		0			0
$521$	−3.97041e6	+	6.87695e6i	−0.640827	+	1.10994i	0.344422	+	0.938815i	$0.388075\pi$
$521$	−3.97041e6	+	6.87695e6i	−0.640827	+	1.10994i	−0.985248	+	0.171130i	$0.945258\pi$
$522$		0			0
$523$	3.88419e6	+	6.72762e6i	0.620936	+	1.07549i	0.989312	+	0.145815i	$0.0465805\pi$
$523$	3.88419e6	+	6.72762e6i	0.620936	+	1.07549i	−0.368376	+	0.929677i	$0.620086\pi$
$524$		0			0
$525$	−207638.	−	1.16569e7i	−0.0328783	−	1.84580i
$526$		0			0
$527$	741398.	+	1.28414e6i	0.116285	+	0.201412i
$528$		0			0
$529$	3.04225e6	−	5.26933e6i	0.472667	−	0.818684i
$530$		0			0
$531$	5.52519e6			0.850376
$532$		0			0
$533$	−3.87820e6			−0.591306
$534$		0			0
$535$	−6.12907e6	+	1.06159e7i	−0.925785	+	1.60351i
$536$		0			0
$537$	−6.42359e6	−	1.11260e7i	−0.961263	−	1.66496i
$538$		0			0
$539$	7.64488e6	−	272435.i	1.13344	−	0.0403916i
$540$		0			0
$541$	2.44250e6	+	4.23053e6i	0.358791	+	0.621444i	0.987759	−	0.155987i	$-0.0498558\pi$
$541$	2.44250e6	+	4.23053e6i	0.358791	+	0.621444i	−0.628968	+	0.777431i	$0.716522\pi$
$542$		0			0
$543$	7.92002e6	−	1.37179e7i	1.15273	−	1.99658i
$544$		0			0
$545$	3.36264e6			0.484941
$546$		0			0
$547$	8.12743e6			1.16141			0.580704	−	0.814115i	$-0.302777\pi$
$547$	8.12743e6			1.16141			0.580704	+	0.814115i	$0.302777\pi$
$548$		0			0
$549$	5.70673e6	−	9.88434e6i	0.808083	−	1.39964i
$550$		0			0
$551$	340601.	+	589939.i	0.0477933	+	0.0827805i
$552$		0			0
$553$	127258.	+	7.14429e6i	0.0176958	+	0.993451i
$554$		0			0
$555$	4.48835e6	+	7.77405e6i	0.618521	+	1.07131i
$556$		0			0
$557$	3.04614e6	−	5.27608e6i	0.416018	−	0.720565i	−0.579516	−	0.814961i	$-0.696759\pi$
$557$	3.04614e6	−	5.27608e6i	0.416018	−	0.720565i	0.995535	+	0.0943956i	$0.0300919\pi$
$558$		0			0
$559$	−5.20448e6			−0.704446
$560$		0			0
$561$	−2.97714e7			−3.99386
$562$		0			0
$563$	−1.67191e6	+	2.89583e6i	−0.222301	+	0.385037i	−0.955506	−	0.294971i	$-0.904690\pi$
$563$	−1.67191e6	+	2.89583e6i	−0.222301	+	0.385037i	0.733205	+	0.680007i	$0.238023\pi$
$564$		0			0
$565$	3.70974e6	+	6.42546e6i	0.488903	+	0.846804i
$566$		0			0
$567$	9.02513e6	−	5.42723e6i	1.17895	−	0.708958i
$568$		0			0
$569$	−3.96694e6	−	6.87094e6i	−0.513659	−	0.889683i	−0.999874	−	0.0158445i	$-0.994956\pi$
$569$	−3.96694e6	−	6.87094e6i	−0.513659	−	0.889683i	0.486215	−	0.873839i	$-0.338377\pi$
$570$		0			0
$571$	−2.99931e6	+	5.19496e6i	−0.384974	+	0.666794i	−0.991766	−	0.128067i	$-0.959123\pi$
$571$	−2.99931e6	+	5.19496e6i	−0.384974	+	0.666794i	0.606792	+	0.794861i	$0.292456\pi$
$572$		0			0
$573$	7.71148e6			0.981185
$574$		0			0
$575$	1.93719e6			0.244345
$576$		0			0
$577$	−1.71465e6	+	2.96985e6i	−0.214405	+	0.371360i	−0.953088	−	0.302692i	$-0.902115\pi$
$577$	−1.71465e6	+	2.96985e6i	−0.214405	+	0.371360i	0.738683	+	0.674053i	$0.235448\pi$
$578$		0			0
$579$	395999.	+	685890.i	0.0490905	+	0.0850272i
$580$		0			0
$581$	−9.94043e6	−	5.50543e6i	−1.22170	−	0.676629i
$582$		0			0
$583$	3.15054e6	+	5.45690e6i	0.383896	+	0.664928i
$584$		0			0
$585$	−1.19673e7	+	2.07279e7i	−1.44579	+	2.50418i
$586$		0			0
$587$	−4.04291e6			−0.484282			−0.242141	−	0.970241i	$-0.577850\pi$
$587$	−4.04291e6			−0.484282			−0.242141	+	0.970241i	$0.577850\pi$
$588$		0			0
$589$	457058.			0.0542855
$590$		0			0
$591$	−2.39931e6	+	4.15573e6i	−0.282565	+	0.489416i
$592$		0			0
$593$	734686.	+	1.27251e6i	0.0857956	+	0.148602i	0.905730	−	0.423855i	$-0.139323\pi$
$593$	734686.	+	1.27251e6i	0.0857956	+	0.148602i	−0.819934	+	0.572458i	$0.805990\pi$
$594$		0			0
$595$	−2.15360e7	−	1.19275e7i	−2.49386	−	1.38121i
$596$		0			0
$597$	9.01002e6	+	1.56058e7i	1.03464	+	1.79205i
$598$		0			0
$599$	−4.67617e6	+	8.09936e6i	−0.532504	+	0.922324i	0.466776	+	0.884376i	$0.345416\pi$
$599$	−4.67617e6	+	8.09936e6i	−0.532504	+	0.922324i	−0.999280	+	0.0379483i	$0.987918\pi$
$600$		0			0
$601$	−4.19824e6			−0.474112			−0.237056	−	0.971496i	$-0.576182\pi$
$601$	−4.19824e6			−0.474112			−0.237056	+	0.971496i	$0.576182\pi$
$602$		0			0
$603$	1.03270e7			1.15659
$604$		0			0
$605$	1.84317e6	−	3.19246e6i	0.204728	−	0.354599i
$606$		0			0
$607$	−6.07004e6	−	1.05136e7i	−0.668683	−	1.15819i	−0.978273	−	0.207322i	$-0.933525\pi$
$607$	−6.07004e6	−	1.05136e7i	−0.668683	−	1.15819i	0.309590	−	0.950870i	$-0.399808\pi$
$608$		0			0
$609$	2.84627e6	−	1.71160e6i	0.310981	−	0.187007i
$610$		0			0
$611$	2.98692e6	+	5.17349e6i	0.323683	+	0.560636i
$612$		0			0
$613$	−3.49542e6	+	6.05425e6i	−0.375706	+	0.650742i	−0.990432	−	0.137998i	$-0.955933\pi$
$613$	−3.49542e6	+	6.05425e6i	−0.375706	+	0.650742i	0.614726	+	0.788741i	$0.289266\pi$
$614$		0			0
$615$	1.46926e7			1.56643
$616$		0			0
$617$	−9.72855e6			−1.02881			−0.514405	−	0.857547i	$-0.671987\pi$
$617$	−9.72855e6			−1.02881			−0.514405	+	0.857547i	$0.671987\pi$
$618$		0			0
$619$	−4.33404e6	+	7.50678e6i	−0.454639	+	0.787457i	−0.998667	−	0.0516095i	$-0.983565\pi$
$619$	−4.33404e6	+	7.50678e6i	−0.454639	+	0.787457i	0.544029	+	0.839067i	$0.316898\pi$
$620$		0			0
$621$	2.22348e6	+	3.85118e6i	0.231368	+	0.400742i
$622$		0			0
$623$	−174927.	−	9.82049e6i	−0.0180567	−	1.01371i
$624$		0			0
$625$	4.65279e6	+	8.05887e6i	0.476446	+	0.825228i
$626$		0			0
$627$	−4.58839e6	+	7.94732e6i	−0.466113	+	0.807331i
$628$		0			0
$629$	9.68642e6			0.976195
$630$		0			0
$631$	−4.83557e6			−0.483476			−0.241738	−	0.970342i	$-0.577717\pi$
$631$	−4.83557e6			−0.483476			−0.241738	+	0.970342i	$0.577717\pi$
$632$		0			0
$633$	8.39961e6	−	1.45485e7i	0.833201	−	1.44315i
$634$		0			0
$635$	2.38942e6	+	4.13859e6i	0.235157	+	0.407304i
$636$		0			0
$637$	−5.18104e6	−	8.27822e6i	−0.505904	−	0.808329i
$638$		0			0
$639$	−9.21813e6	−	1.59663e7i	−0.893081	−	1.54686i
$640$		0			0
$641$	8.91094e6	−	1.54342e7i	0.856601	−	1.48368i	−0.0185516	−	0.999828i	$-0.505906\pi$
$641$	8.91094e6	−	1.54342e7i	0.856601	−	1.48368i	0.875152	−	0.483848i	$-0.160761\pi$
$642$		0			0
$643$	1.58095e7			1.50796			0.753980	−	0.656897i	$-0.228132\pi$
$643$	1.58095e7			1.50796			0.753980	+	0.656897i	$0.228132\pi$
$644$		0			0
$645$	1.97172e7			1.86615
$646$		0			0
$647$	393188.	−	681021.i	0.0369266	−	0.0639587i	−0.846971	−	0.531638i	$-0.821577\pi$
$647$	393188.	−	681021.i	0.0369266	−	0.0639587i	0.883898	+	0.467680i	$0.154910\pi$
$648$		0			0
$649$	2.44033e6	+	4.22678e6i	0.227425	+	0.393911i
$650$		0			0
$651$	−39687.7	−	2.22808e6i	−0.00367031	−	0.206053i
$652$		0			0
$653$	−592559.	−	1.02634e6i	−0.0543812	−	0.0941910i	0.837553	−	0.546356i	$-0.183985\pi$
$653$	−592559.	−	1.02634e6i	−0.0543812	−	0.0941910i	−0.891934	+	0.452165i	$0.850652\pi$
$654$		0			0
$655$	−1.04614e7	+	1.81197e7i	−0.952769	+	1.65024i
$656$		0			0
$657$	2.87815e7			2.60136
$658$		0			0
$659$	2.81475e6			0.252479			0.126240	−	0.992000i	$-0.459709\pi$
$659$	2.81475e6			0.252479			0.126240	+	0.992000i	$0.459709\pi$
$660$		0			0
$661$	−147788.	+	255976.i	−0.0131564	+	0.0227875i	−0.872529	−	0.488563i	$-0.837521\pi$
$661$	−147788.	+	255976.i	−0.0131564	+	0.0227875i	0.859372	+	0.511350i	$0.170855\pi$
$662$		0			0
$663$	1.90035e7	+	3.29150e7i	1.67900	+	2.90811i
$664$		0			0
$665$	−6.50313e6	+	3.91064e6i	−0.570254	+	0.342921i
$666$		0			0
$667$	275928.	+	477921.i	0.0240149	+	0.0415950i
$668$		0			0
$669$	−1.18786e7	+	2.05743e7i	−1.02612	+	1.77729i
$670$		0			0
$671$	1.00821e7			0.864456
$672$		0			0
$673$	−3.29325e6			−0.280277			−0.140138	−	0.990132i	$-0.544755\pi$
$673$	−3.29325e6			−0.280277			−0.140138	+	0.990132i	$0.544755\pi$
$674$		0			0
$675$	1.22421e7	−	2.12039e7i	1.03418	−	1.79125i
$676$		0			0
$677$	−7.49208e6	−	1.29767e7i	−0.628248	−	1.08816i	−0.987903	−	0.155072i	$-0.950439\pi$
$677$	−7.49208e6	−	1.29767e7i	−0.628248	−	1.08816i	0.359656	−	0.933085i	$-0.382894\pi$
$678$		0			0
$679$	−3.63728e6	−	2.01448e6i	−0.302763	−	0.167683i
$680$		0			0
$681$	368693.	+	638594.i	0.0304647	+	0.0527664i
$682$		0			0
$683$	1.37102e6	−	2.37467e6i	0.112458	−	0.194783i	−0.804303	−	0.594220i	$-0.797461\pi$
$683$	1.37102e6	−	2.37467e6i	0.112458	−	0.194783i	0.916761	+	0.399436i	$0.130794\pi$
$684$		0			0
$685$	−4.14708e6			−0.337688
$686$		0			0
$687$	2.23749e7			1.80871
$688$		0			0
$689$	4.02207e6	−	6.96643e6i	0.322776	−	0.559065i
$690$		0			0
$691$	−9.76449e6	−	1.69126e7i	−0.777955	−	1.34746i	−0.933119	−	0.359568i	$-0.882924\pi$
$691$	−9.76449e6	−	1.69126e7i	−0.777955	−	1.34746i	0.155164	−	0.987889i	$-0.450409\pi$
$692$		0			0
$693$	2.65969e7	+	1.47305e7i	2.10377	+	1.16515i
$694$		0			0
$695$	−1.19670e7	−	2.07275e7i	−0.939777	−	1.62774i
$696$		0			0
$697$	7.92710e6	−	1.37301e7i	0.618063	−	1.07052i
$698$		0			0
$699$	−3.44216e7			−2.66464
$700$		0			0
$701$	7.97976e6			0.613331			0.306665	−	0.951817i	$-0.400787\pi$
$701$	7.97976e6			0.613331			0.306665	+	0.951817i	$0.400787\pi$
$702$		0			0
$703$	1.49288e6	−	2.58574e6i	0.113929	−	0.197331i
$704$		0			0
$705$	−1.13159e7	−	1.95998e7i	−0.857469	−	1.48518i
$706$		0			0
$707$	−2.08714e7	+	1.25510e7i	−1.57038	+	0.944341i
$708$		0			0
$709$	−4.10494e6	−	7.10996e6i	−0.306684	−	0.531192i	0.670951	−	0.741502i	$-0.265886\pi$
$709$	−4.10494e6	−	7.10996e6i	−0.306684	−	0.531192i	−0.977635	+	0.210310i	$0.932553\pi$
$710$		0			0
$711$	−1.41996e7	+	2.45945e7i	−1.05342	+	1.82458i
$712$		0			0
$713$	370272.			0.0272770
$714$		0			0
$715$	−2.11425e7			−1.54665
$716$		0			0
$717$	−2.19462e7	+	3.80119e7i	−1.59427	+	2.76135i
$718$		0			0
$719$	4.94472e6	+	8.56451e6i	0.356714	+	0.617846i	0.987410	−	0.158184i	$-0.0505639\pi$
$719$	4.94472e6	+	8.56451e6i	0.356714	+	0.617846i	−0.630696	+	0.776030i	$0.717231\pi$
$720$		0			0
$721$	371717.	+	2.08683e7i	0.0266302	+	1.49503i
$722$		0			0
$723$	2.17422e7	+	3.76586e7i	1.54689	+	2.67929i
$724$		0			0
$725$	1.51921e6	−	2.63136e6i	0.107343	−	0.185924i
$726$		0			0
$727$	1.40610e7			0.986691			0.493345	−	0.869834i	$-0.335774\pi$
$727$	1.40610e7			0.986691			0.493345	+	0.869834i	$0.335774\pi$
$728$		0			0
$729$	−8.30898e6			−0.579067
$730$		0			0
$731$	1.06380e7	−	1.84256e7i	0.736323	−	1.27535i
$732$		0			0
$733$	1.13209e7	+	1.96085e7i	0.778257	+	1.34798i	0.932946	+	0.360017i	$0.117229\pi$
$733$	1.13209e7	+	1.96085e7i	0.778257	+	1.34798i	−0.154689	+	0.987963i	$0.549438\pi$
$734$		0			0
$735$	1.96284e7	+	3.13621e7i	1.34019	+	2.14134i
$736$		0			0
$737$	4.56117e6	+	7.90018e6i	0.309320	+	0.535758i
$738$		0			0
$739$	9.71787e6	−	1.68318e7i	0.654576	−	1.13376i	−0.327424	−	0.944877i	$-0.606181\pi$
$739$	9.71787e6	−	1.68318e7i	0.654576	−	1.13376i	0.982000	−	0.188881i	$-0.0604861\pi$
$740$		0			0
$741$	1.17153e7			0.783806
$742$		0			0
$743$	−6.54899e6			−0.435214			−0.217607	−	0.976037i	$-0.569825\pi$
$743$	−6.54899e6			−0.435214			−0.217607	+	0.976037i	$0.569825\pi$
$744$		0			0
$745$	−1.12592e7	+	1.95016e7i	−0.743222	+	1.28730i
$746$		0			0
$747$	−2.25813e7	−	3.91120e7i	−1.48063	−	2.56453i
$748$		0			0
$749$	−354035.	−	1.98756e7i	−0.0230590	−	1.29454i
$750$		0			0
$751$	−5.07859e6	−	8.79638e6i	−0.328582	−	0.569120i	0.653649	−	0.756798i	$-0.273237\pi$
$751$	−5.07859e6	−	8.79638e6i	−0.328582	−	0.569120i	−0.982231	+	0.187678i	$0.939904\pi$
$752$		0			0
$753$	−2.03547e7	+	3.52554e7i	−1.30821	+	2.26589i
$754$		0			0
$755$	1.77792e7			1.13513
$756$		0			0
$757$	−8.02731e6			−0.509132			−0.254566	−	0.967055i	$-0.581933\pi$
$757$	−8.02731e6			−0.509132			−0.254566	+	0.967055i	$0.581933\pi$
$758$		0			0
$759$	−3.71714e6	+	6.43828e6i	−0.234210	+	0.405663i
$760$		0			0
$761$	2.65668e6	+	4.60150e6i	0.166294	+	0.288030i	0.937114	−	0.349023i	$-0.113487\pi$
$761$	2.65668e6	+	4.60150e6i	0.166294	+	0.288030i	−0.770820	+	0.637053i	$0.780153\pi$
$762$		0			0
$763$	−4.67324e6	+	2.81024e6i	−0.290607	+	0.174756i
$764$		0			0
$765$	−4.89225e7	−	8.47363e7i	−3.02242	−	5.23499i
$766$		0			0
$767$	3.11540e6	−	5.39602e6i	0.191216	−	0.331196i
$768$		0			0
$769$	−6.32376e6			−0.385620			−0.192810	−	0.981236i	$-0.561760\pi$
$769$	−6.32376e6			−0.385620			−0.192810	+	0.981236i	$0.561760\pi$
$770$		0			0
$771$	2.89028e7			1.75107
$772$		0			0
$773$	−1.51512e6	+	2.62427e6i	−0.0912009	+	0.157965i	−0.908017	−	0.418934i	$-0.862404\pi$
$773$	−1.51512e6	+	2.62427e6i	−0.0912009	+	0.157965i	0.816816	+	0.576899i	$0.195737\pi$
$774$		0			0
$775$	−1.01933e6	−	1.76553e6i	−0.0609621	−	0.105590i
$776$		0			0
$777$	−1.27347e7	−	7.05299e6i	−0.756719	−	0.419103i
$778$		0			0
$779$	−2.44346e6	−	4.23219e6i	−0.144265	−	0.249874i
$780$		0			0
$781$	8.14282e6	−	1.41038e7i	0.477691	−	0.827386i
$782$		0			0
$783$	6.97491e6			0.406569
$784$		0			0
$785$	4.77058e6			0.276310
$786$		0			0
$787$	−1.22311e6	+	2.11849e6i	−0.0703930	+	0.121924i	−0.899074	−	0.437798i	$-0.855759\pi$
$787$	−1.22311e6	+	2.11849e6i	−0.0703930	+	0.121924i	0.828681	+	0.559722i	$0.189092\pi$
$788$		0			0
$789$	−2.20080e6	−	3.81190e6i	−0.125860	−	0.217996i
$790$		0			0
$791$	−1.05255e7	−	5.82948e6i	−0.598140	−	0.331275i
$792$		0			0
$793$	−6.43551e6	−	1.11466e7i	−0.363413	−	0.629449i
$794$		0			0
$795$	−1.52376e7	+	2.63923e7i	−0.855065	+	1.48102i
$796$		0			0
$797$	−6.16846e6			−0.343978			−0.171989	−	0.985099i	$-0.555019\pi$
$797$	−6.16846e6			−0.343978			−0.171989	+	0.985099i	$0.555019\pi$
$798$		0			0
$799$	−2.44212e7			−1.35332
$800$		0			0
$801$	1.95187e7	−	3.38074e7i	1.07490	−	1.86179i
$802$		0			0
$803$	1.27121e7	+	2.20179e7i	0.695708	+	1.20500i
$804$		0			0
$805$	−5.26832e6	+	3.16809e6i	−0.286538	+	0.172309i
$806$		0			0
$807$	3.11864e6	+	5.40164e6i	0.168570	+	0.291972i
$808$		0			0
$809$	−1.54494e7	+	2.67592e7i	−0.829930	+	1.43748i	0.0681631	+	0.997674i	$0.478286\pi$
$809$	−1.54494e7	+	2.67592e7i	−0.829930	+	1.43748i	−0.898093	+	0.439806i	$0.855047\pi$
$810$		0			0
$811$	8.16479e6			0.435906			0.217953	−	0.975959i	$-0.430062\pi$
$811$	8.16479e6			0.435906			0.217953	+	0.975959i	$0.430062\pi$
$812$		0			0
$813$	4.14817e7			2.20105
$814$		0			0
$815$	1.51487e7	−	2.62382e7i	0.798877	−	1.38370i
$816$		0			0
$817$	−3.27908e6	−	5.67953e6i	−0.171869	−	0.297685i
$818$		0			0
$819$	−691266.	−	3.88080e7i	−0.0360110	−	2.02167i
$820$		0			0
$821$	−8.89643e6	−	1.54091e7i	−0.460636	−	0.797845i	0.538357	−	0.842717i	$-0.319045\pi$
$821$	−8.89643e6	−	1.54091e7i	−0.460636	−	0.797845i	−0.998993	+	0.0448721i	$0.985712\pi$
$822$		0			0
$823$	1.04562e7	−	1.81107e7i	0.538116	−	0.932044i	−0.460890	−	0.887457i	$-0.652470\pi$
$823$	1.04562e7	−	1.81107e7i	0.538116	−	0.932044i	0.999006	−	0.0445863i	$-0.0141970\pi$
$824$		0			0
$825$	4.09320e7			2.09376
$826$		0			0
$827$	2.17379e7			1.10523			0.552617	−	0.833435i	$-0.313629\pi$
$827$	2.17379e7			1.10523			0.552617	+	0.833435i	$0.313629\pi$
$828$		0			0
$829$	−1.75768e7	+	3.04439e7i	−0.888287	+	1.53856i	−0.0463888	+	0.998923i	$0.514771\pi$
$829$	−1.75768e7	+	3.04439e7i	−0.888287	+	1.53856i	−0.841899	+	0.539636i	$0.818562\pi$
$830$		0			0
$831$	−2.63199e7	−	4.55874e7i	−1.32215	−	2.29004i
$832$		0			0
$833$	3.98979e7	−	1.42181e6i	1.99222	−	0.0709953i
$834$		0			0
$835$	5.74025e6	+	9.94241e6i	0.284915	+	0.493487i
$836$		0			0
$837$	2.33994e6	−	4.05289e6i	0.115449	−	0.199964i
$838$		0			0
$839$	−8.68616e6			−0.426013			−0.213007	−	0.977051i	$-0.568326\pi$
$839$	−8.68616e6			−0.426013			−0.213007	+	0.977051i	$0.568326\pi$
$840$		0			0
$841$	−1.96456e7			−0.957800
$842$		0			0
$843$	1.62374e7	−	2.81239e7i	0.786949	−	1.36303i
$844$		0			0
$845$	−1.34557e6	−	2.33059e6i	−0.0648281	−	0.112286i
$846$		0			0
$847$	106467.	+	5.97711e6i	0.00509926	+	0.286275i
$848$		0			0
$849$	4.86768e6	+	8.43107e6i	0.231768	+	0.401433i
$850$		0			0
$851$	1.20941e6	−	2.09476e6i	0.0572465	−	0.0991539i
$852$		0			0
$853$	125857.			0.00592247			0.00296124	−	0.999996i	$-0.499057\pi$
$853$	125857.			0.00592247			0.00296124	+	0.999996i	$0.499057\pi$
$854$		0			0
$855$	−3.01599e7			−1.41096
$856$		0			0
$857$	7.45717e6	−	1.29162e7i	0.346834	−	0.600735i	−0.638851	−	0.769331i	$-0.720590\pi$
$857$	7.45717e6	−	1.29162e7i	0.346834	−	0.600735i	0.985685	+	0.168596i	$0.0539232\pi$
$858$		0			0
$859$	2.03433e7	+	3.52356e7i	0.940672	+	1.62929i	0.764193	+	0.644988i	$0.223137\pi$
$859$	2.03433e7	+	3.52356e7i	0.940672	+	1.62929i	0.176479	+	0.984304i	$0.443529\pi$
$860$		0			0
$861$	−2.04190e7	+	1.22789e7i	−0.938701	+	0.564485i
$862$		0			0
$863$	−1.57204e7	−	2.72286e7i	−0.718518	−	1.24451i	−0.961587	−	0.274501i	$-0.911487\pi$
$863$	−1.57204e7	−	2.72286e7i	−0.718518	−	1.24451i	0.243069	−	0.970009i	$-0.421846\pi$
$864$		0			0
$865$	3.09432e7	−	5.35952e7i	1.40613	−	2.43549i
$866$		0			0
$867$	−1.16276e8			−5.25343
$868$		0			0
$869$	−2.50864e7			−1.12691
$870$		0			0
$871$	5.82292e6	−	1.00856e7i	0.260073	−	0.450459i
$872$		0			0
$873$	−8.26268e6	−	1.43114e7i	−0.366932	−	0.635545i
$874$		0			0
$875$	1.27712e6	+	707321.i	0.0563911	+	0.0312318i
$876$		0			0
$877$	1.35823e7	+	2.35253e7i	0.596315	+	1.03285i	0.993360	+	0.115049i	$0.0367024\pi$
$877$	1.35823e7	+	2.35253e7i	0.596315	+	1.03285i	−0.397045	+	0.917799i	$0.629964\pi$
$878$		0			0
$879$	852708.	−	1.47693e6i	0.0372244	−	0.0644746i
$880$		0			0
$881$	1.03892e6			0.0450966			0.0225483	−	0.999746i	$-0.492822\pi$
$881$	1.03892e6			0.0450966			0.0225483	+	0.999746i	$0.492822\pi$
$882$		0			0
$883$	−2.29747e7			−0.991625			−0.495812	−	0.868430i	$-0.665130\pi$
$883$	−2.29747e7			−0.991625			−0.495812	+	0.868430i	$0.665130\pi$
$884$		0			0
$885$	−1.18027e7	+	2.04429e7i	−0.506551	+	0.877371i
$886$		0			0
$887$	1.71339e7	+	2.96767e7i	0.731217	+	1.26651i	0.956363	+	0.292180i	$0.0943807\pi$
$887$	1.71339e7	+	2.96767e7i	0.731217	+	1.26651i	−0.225146	+	0.974325i	$0.572286\pi$
$888$		0			0
$889$	−6.77942e6	−	3.75473e6i	−0.287699	−	0.159340i
$890$		0			0
$891$	1.84868e7	+	3.20201e7i	0.780132	+	1.35123i
$892$		0			0
$893$	−3.76381e6	+	6.51912e6i	−0.157943	+	0.273565i
$894$		0			0
$895$	3.72975e7			1.55640
$896$		0			0
$897$	9.49081e6			0.393842
$898$		0			0
$899$	290380.	−	502953.i	0.0119831	−	0.0207553i
$900$		0			0
$901$	1.64423e7	+	2.84790e7i	0.674764	+	1.16873i
$902$		0			0
$903$	−2.74020e7	+	1.64781e7i	−1.11831	+	0.672494i
$904$		0			0
$905$	2.29931e7	+	3.98252e7i	0.933204	+	1.61636i
$906$		0			0
$907$	−1.64911e7	+	2.85635e7i	−0.665630	+	1.15290i	0.313485	+	0.949593i	$0.398504\pi$
$907$	−1.64911e7	+	2.85635e7i	−0.665630	+	1.15290i	−0.979114	+	0.203311i	$0.934830\pi$
$908$		0			0
$909$	−9.67963e7			−3.88552
$910$		0			0
$911$	1.04563e7			0.417429			0.208714	−	0.977977i	$-0.433072\pi$
$911$	1.04563e7			0.417429			0.208714	+	0.977977i	$0.433072\pi$
$912$		0			0
$913$	1.99472e7	−	3.45495e7i	0.791961	−	1.37172i
$914$		0			0
$915$	2.43810e7	+	4.22291e7i	0.962716	+	1.66747i
$916$		0			0
$917$	−604285.	−	3.39248e7i	−0.0237311	−	1.33228i
$918$		0			0
$919$	3.03257e6	+	5.25257e6i	0.118446	+	0.205155i	0.919152	−	0.393903i	$-0.128875\pi$
$919$	3.03257e6	+	5.25257e6i	0.118446	+	0.205155i	−0.800706	+	0.599058i	$0.795542\pi$
$920$		0			0
$921$	2.61624e7	−	4.53146e7i	1.01632	−	1.76031i
$922$		0			0
$923$	−2.07907e7			−0.803276
$924$		0			0
$925$	−1.33176e7			−0.511767
$926$		0			0
$927$	−4.14769e7	+	7.18400e7i	−1.58528	+	2.74579i
$928$		0			0
$929$	1.71630e7	+	2.97271e7i	0.652459	+	1.13009i	0.982524	+	0.186134i	$0.0595959\pi$
$929$	1.71630e7	+	2.97271e7i	0.652459	+	1.13009i	−0.330065	+	0.943958i	$0.607071\pi$
$930$		0			0
$931$	5.76953e6	−	1.08696e7i	0.218156	−	0.410999i
$932$		0			0
$933$	3.62191e7	+	6.27333e7i	1.36218	+	2.35936i
$934$		0			0
$935$	4.32156e7	−	7.48517e7i	1.61663	−	2.80009i
$936$		0			0
$937$	−1.21642e7			−0.452621			−0.226310	−	0.974055i	$-0.572666\pi$
$937$	−1.21642e7			−0.452621			−0.226310	+	0.974055i	$0.572666\pi$
$938$		0			0
$939$	7.60127e7			2.81334
$940$		0			0
$941$	1.14188e7	−	1.97780e7i	0.420385	−	0.728128i	−0.575592	−	0.817737i	$-0.695228\pi$
$941$	1.14188e7	−	1.97780e7i	0.420385	−	0.728128i	0.995977	+	0.0896089i	$0.0285617\pi$
$942$		0			0
$943$	−1.97949e6	−	3.42859e6i	−0.0724895	−	0.125555i
$944$		0			0
$945$	1.38378e6	+	7.76862e7i	0.0504068	+	2.82986i
$946$		0			0
$947$	9.24007e6	+	1.60043e7i	0.334811	+	0.579910i	0.983449	−	0.181187i	$-0.0579941\pi$
$947$	9.24007e6	+	1.60043e7i	0.334811	+	0.579910i	−0.648637	+	0.761098i	$0.724661\pi$
$948$		0			0
$949$	1.62286e7	−	2.81087e7i	0.584945	−	1.01315i
$950$		0			0
$951$	−1.71113e7			−0.613523
$952$		0			0
$953$	−1.03848e7			−0.370394			−0.185197	−	0.982701i	$-0.559292\pi$
$953$	−1.03848e7			−0.370394			−0.185197	+	0.982701i	$0.559292\pi$
$954$		0			0
$955$	−1.11938e7	+	1.93883e7i	−0.397165	+	0.687909i
$956$		0			0
$957$	5.83023e6	+	1.00982e7i	0.205781	+	0.356423i
$958$		0			0
$959$	5.76342e6	−	3.46581e6i	0.202364	−	0.121691i
$960$		0			0
$961$	1.41197e7	+	2.44561e7i	0.493195	+	0.854238i
$962$		0			0
$963$	3.95038e7	−	6.84226e7i	1.37269	−	2.37757i
$964$		0			0
$965$	−2.29930e6			−0.0794835
$966$		0			0
$967$	5.47893e7			1.88421			0.942105	−	0.335318i	$-0.108844\pi$
$967$	5.47893e7			1.88421			0.942105	+	0.335318i	$0.108844\pi$
$968$		0			0
$969$	−2.39463e7	+	4.14762e7i	−0.819274	+	1.41902i
$970$		0			0
$971$	−8.34954e6	−	1.44618e7i	−0.284194	−	0.492238i	0.688220	−	0.725502i	$-0.258393\pi$
$971$	−8.34954e6	−	1.44618e7i	−0.284194	−	0.492238i	−0.972413	+	0.233264i	$0.925059\pi$
$972$		0			0
$973$	3.39537e7	+	1.88050e7i	1.14976	+	0.636783i
$974$		0			0
$975$	−2.61274e7	−	4.52541e7i	−0.880208	−	1.52456i
$976$		0			0
$977$	1.49764e7	−	2.59398e7i	0.501961	−	0.869422i	−0.498036	−	0.867156i	$-0.665945\pi$
$977$	1.49764e7	−	2.59398e7i	0.501961	−	0.869422i	0.999997	−	0.00226593i	$-0.000721267\pi$
$978$		0			0
$979$	3.44836e7			1.14989
$980$		0			0
$981$	−2.16733e7			−0.719038
$982$		0			0
$983$	−2.71288e7	+	4.69884e7i	−0.895460	+	1.55098i	−0.0622265	+	0.998062i	$0.519820\pi$
$983$	−2.71288e7	+	4.69884e7i	−0.895460	+	1.55098i	−0.833234	+	0.552921i	$0.813513\pi$
$984$		0			0
$985$	−6.96559e6	−	1.20648e7i	−0.228753	−	0.396212i
$986$		0			0
$987$	3.21064e7	+	1.77819e7i	1.04906	+	0.581011i
$988$		0			0
$989$	−2.65645e6	−	4.60110e6i	−0.0863596	−	0.149579i
$990$		0			0
$991$	−2.96948e7	+	5.14329e7i	−0.960497	+	1.66363i	−0.239242	+	0.970960i	$0.576899\pi$
$991$	−2.96948e7	+	5.14329e7i	−0.960497	+	1.66363i	−0.721255	+	0.692670i	$0.756434\pi$
$992$		0			0
$993$	−2.41857e7			−0.778370
$994$		0			0
$995$	−5.23151e7			−1.67521
$996$		0			0
$997$	1.33985e7	−	2.32069e7i	0.426893	−	0.739401i	−0.569702	−	0.821851i	$-0.692941\pi$
$997$	1.33985e7	−	2.32069e7i	0.426893	−	0.739401i	0.996595	+	0.0824508i	$0.0262747\pi$
$998$		0			0
$999$	−1.52857e7	−	2.64757e7i	−0.484588	−	0.839331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.6.i.f.81.5		10
4.3	odd	2		56.6.i.b.25.1	yes	10
7.2	even	3	inner	112.6.i.f.65.5		10
7.3	odd	6		784.6.a.bl.1.5		5
7.4	even	3		784.6.a.bk.1.1		5
12.11	even	2		504.6.s.b.361.2		10
28.3	even	6		392.6.a.j.1.1		5
28.11	odd	6		392.6.a.k.1.5		5
28.19	even	6		392.6.i.o.177.5		10
28.23	odd	6		56.6.i.b.9.1	✓	10
28.27	even	2		392.6.i.o.361.5		10
84.23	even	6		504.6.s.b.289.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.i.b.9.1	✓	10	28.23	odd	6
56.6.i.b.25.1	yes	10	4.3	odd	2
112.6.i.f.65.5		10	7.2	even	3	inner
112.6.i.f.81.5		10	1.1	even	1	trivial
392.6.a.j.1.1		5	28.3	even	6
392.6.a.k.1.5		5	28.11	odd	6
392.6.i.o.177.5		10	28.19	even	6
392.6.i.o.361.5		10	28.27	even	2
504.6.s.b.289.2		10	84.23	even	6
504.6.s.b.361.2		10	12.11	even	2
784.6.a.bk.1.1		5	7.4	even	3
784.6.a.bl.1.5		5	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(13.7682 - 23.8473i) q^{3} +(39.9714 + 69.2326i) q^{5} +(-113.410 - 62.8111i) q^{7} +(-257.629 - 446.226i) q^{9} +(227.576 - 394.173i) q^{11} -581.059 q^{13} +2201.35 q^{15} +(1187.69 - 2057.15i) q^{17} +(-366.096 - 634.097i) q^{19} +(-3059.33 + 1839.72i) q^{21} +(-296.582 - 513.695i) q^{23} +(-1632.93 + 2828.32i) q^{25} -7497.01 q^{27} -930.360 q^{29} +(-312.116 + 540.601i) q^{31} +(-6266.64 - 10854.1i) q^{33} +(-184.578 - 10362.3i) q^{35} +(2038.91 + 3531.50i) q^{37} +(-8000.16 + 13856.7i) q^{39} +6674.36 q^{41} +8956.88 q^{43} +(20595.6 - 35672.6i) q^{45} +(-5140.47 - 8903.56i) q^{47} +(8916.54 + 14246.8i) q^{49} +(-32704.9 - 56646.6i) q^{51} +(-6921.96 + 11989.2i) q^{53} +36386.1 q^{55} -20162.0 q^{57} +(-5361.58 + 9286.53i) q^{59} +(11075.5 + 19183.3i) q^{61} +(1189.67 + 66788.3i) q^{63} +(-23225.8 - 40228.2i) q^{65} +(-10021.2 + 17357.2i) q^{67} -16333.6 q^{69} +35780.7 q^{71} +(-27929.3 + 48374.9i) q^{73} +(44965.2 + 77882.0i) q^{75} +(-50567.8 + 30408.8i) q^{77} +(-27558.3 - 47732.4i) q^{79} +(-40616.8 + 70350.4i) q^{81} +87650.6 q^{83} +189896. q^{85} +(-12809.4 + 22186.6i) q^{87} +(37881.5 + 65612.6i) q^{89} +(65897.8 + 36497.0i) q^{91} +(8594.58 + 14886.3i) q^{93} +(29266.8 - 50691.6i) q^{95} +32072.1 q^{97} -234520. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} + 81 q^{5} - 116 q^{7} - 390 q^{9} + 361 q^{11} - 684 q^{13} + 2098 q^{15} + 1809 q^{17} - 1277 q^{19} - 5253 q^{21} + 911 q^{23} - 3940 q^{25} - 9502 q^{27} + 10884 q^{29} - 2187 q^{31}+ \cdots - 499596 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 + 81 * q^5 - 116 * q^7 - 390 * q^9 + 361 * q^11 - 684 * q^13 + 2098 * q^15 + 1809 * q^17 - 1277 * q^19 - 5253 * q^21 + 911 * q^23 - 3940 * q^25 - 9502 * q^27 + 10884 * q^29 - 2187 * q^31 - 5553 * q^33 + 16845 * q^35 + 8181 * q^37 - 3422 * q^39 - 33156 * q^41 - 12664 * q^43 + 41310 * q^45 - 16101 * q^47 - 10070 * q^49 - 67865 * q^51 - 16047 * q^53 + 91258 * q^55 + 44694 * q^57 - 71027 * q^59 + 31093 * q^61 + 127978 * q^63 + 64370 * q^65 + 47981 * q^67 - 274498 * q^69 - 45024 * q^71 + 123333 * q^73 + 45460 * q^75 - 245825 * q^77 - 212481 * q^79 - 52917 * q^81 + 174920 * q^83 + 444282 * q^85 - 318070 * q^87 + 129045 * q^89 + 526488 * q^91 + 252835 * q^93 + 300417 * q^95 - 656548 * q^97 - 499596 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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