LMFDB - Embedded newform 252.6.b.d.55.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,6,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	252.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$40.4167225929$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 674 x^{14} + 3404 x^{13} + 173721 x^{12} - 919512 x^{11} - 21981508 x^{10} + \cdots + 224266997486896 $ x^16 - 4x^15 - 674x^14 + 3404x^13 + 173721x^12 - 919512x^11 - 21981508x^10 + 94817024x^9 + 1652635052x^8 - 4373672096x^7 - 73339451096x^6 + 61523648112x^5 + 1688776741892x^4 + 257949039296x^3 - 14815785541168x^2 + 39188323305792*x + 224266997486896
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.7
Root			$-7.16085 - 2.48366i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.6.b.d.55.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70662 + 4.96731i) q^{2} +(-17.3484 - 26.8893i) q^{4} -28.3847i q^{5} +(-117.282 + 55.2436i) q^{7} +(180.523 - 13.3961i) q^{8} +O(q^{10})$	\(q+(-2.70662 + 4.96731i) q^{2} +(-17.3484 - 26.8893i) q^{4} -28.3847i q^{5} +(-117.282 + 55.2436i) q^{7} +(180.523 - 13.3961i) q^{8} +(140.996 + 76.8266i) q^{10} +271.548i q^{11} -180.279i q^{13} +(43.0265 - 732.102i) q^{14} +(-422.064 + 932.973i) q^{16} +2098.19i q^{17} -1445.92 q^{19} +(-763.243 + 492.430i) q^{20} +(-1348.86 - 734.977i) q^{22} -1665.96i q^{23} +2319.31 q^{25} +(895.504 + 487.948i) q^{26} +(3520.12 + 2195.25i) q^{28} +4202.58 q^{29} -1810.94 q^{31} +(-3492.00 - 4621.73i) q^{32} +(-10422.4 - 5679.00i) q^{34} +(1568.07 + 3329.02i) q^{35} -8532.29 q^{37} +(3913.55 - 7182.33i) q^{38} +(-380.244 - 5124.09i) q^{40} -20646.9i q^{41} -10894.2i q^{43} +(7301.72 - 4710.93i) q^{44} +(8275.37 + 4509.13i) q^{46} -15279.9 q^{47} +(10703.3 - 12958.2i) q^{49} +(-6277.49 + 11520.7i) q^{50} +(-4847.58 + 3127.56i) q^{52} +20297.1 q^{53} +7707.80 q^{55} +(-20432.1 + 11543.9i) q^{56} +(-11374.8 + 20875.5i) q^{58} +14318.9 q^{59} -18947.4i q^{61} +(4901.53 - 8995.51i) q^{62} +(32409.1 - 4836.61i) q^{64} -5117.17 q^{65} -58173.5i q^{67} +(56418.8 - 36400.3i) q^{68} +(-20780.5 - 1221.29i) q^{70} +45807.8i q^{71} -25714.9i q^{73} +(23093.7 - 42382.6i) q^{74} +(25084.4 + 38879.7i) q^{76} +(-15001.3 - 31847.8i) q^{77} +89207.5i q^{79} +(26482.1 + 11980.2i) q^{80} +(102560. + 55883.3i) q^{82} +68687.3 q^{83} +59556.5 q^{85} +(54114.8 + 29486.4i) q^{86} +(3637.68 + 49020.6i) q^{88} -31947.0i q^{89} +(9959.27 + 21143.6i) q^{91} +(-44796.5 + 28901.9i) q^{92} +(41356.9 - 75900.1i) q^{94} +41041.9i q^{95} -111178. i q^{97} +(35397.6 + 88239.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8	$ 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8} - 1176 q^{14} - 3008 q^{16} + 1552 q^{22} - 9776 q^{25} - 14672 q^{28} - 26592 q^{29} - 11648 q^{32} - 26272 q^{37} + 12256 q^{44} + 20208 q^{46} + 8848 q^{49} - 5992 q^{50} + 41888 q^{53} - 38304 q^{56} - 144400 q^{58} + 45312 q^{64} - 66688 q^{65} + 79296 q^{70} - 348464 q^{74} - 320992 q^{77} + 78080 q^{85} + 78448 q^{86} - 66112 q^{88} - 446944 q^{92} - 224840 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8 - 1176 * q^14 - 3008 * q^16 + 1552 * q^22 - 9776 * q^25 - 14672 * q^28 - 26592 * q^29 - 11648 * q^32 - 26272 * q^37 + 12256 * q^44 + 20208 * q^46 + 8848 * q^49 - 5992 * q^50 + 41888 * q^53 - 38304 * q^56 - 144400 * q^58 + 45312 * q^64 - 66688 * q^65 + 79296 * q^70 - 348464 * q^74 - 320992 * q^77 + 78080 * q^85 + 78448 * q^86 - 66112 * q^88 - 446944 * q^92 - 224840 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.70662	+	4.96731i	−0.478467	+	0.878105i
$2$	−2.70662	+	4.96731i	−0.478467	+	0.878105i
$3$		0			0
$3$		0			0
$4$	−17.3484	−	26.8893i	−0.542138	−	0.840289i
$5$		−	28.3847i		−	0.507761i	−0.967236	−	0.253880i	$-0.918293\pi$
$5$		−	28.3847i		−	0.507761i	0.967236	−	0.253880i	$-0.0817070\pi$
$6$		0			0
$7$	−117.282	+	55.2436i	−0.904665	+	0.426125i
$7$	−117.282	+	55.2436i	−0.904665	+	0.426125i
$8$	180.523	−	13.3961i	0.997258	−	0.0740037i
$9$		0			0
$10$	140.996	+	76.8266i	0.445868	+	0.242947i
$11$			271.548i			0.676651i	0.941029	+	0.338326i	$0.109861\pi$
$11$			271.548i			0.676651i	−0.941029	+	0.338326i	$0.890139\pi$
$12$		0			0
$13$		−	180.279i		−	0.295861i	−0.988998	−	0.147930i	$-0.952739\pi$
$13$		−	180.279i		−	0.295861i	0.988998	−	0.147930i	$-0.0472612\pi$
$14$	43.0265	−	732.102i	0.0586700	−	0.998277i
$15$		0			0
$16$	−422.064	+	932.973i	−0.412172	+	0.911106i
$17$			2098.19i			1.76085i	0.474185	+	0.880425i	$0.342743\pi$
$17$			2098.19i			1.76085i	−0.474185	+	0.880425i	$0.657257\pi$
$18$		0			0
$19$	−1445.92			−0.918882			−0.459441	−	0.888208i	$-0.651950\pi$
$19$	−1445.92			−0.918882			−0.459441	+	0.888208i	$0.651950\pi$
$20$	−763.243	+	492.430i	−0.426666	+	0.275277i
$21$		0			0
$22$	−1348.86	−	734.977i	−0.594171	−	0.323755i
$23$		−	1665.96i		−	0.656668i	−0.944562	−	0.328334i	$-0.893513\pi$
$23$		−	1665.96i		−	0.656668i	0.944562	−	0.328334i	$-0.106487\pi$
$24$		0			0
$25$	2319.31			0.742179
$26$	895.504	+	487.948i	0.259797	+	0.141560i
$27$		0			0
$28$	3520.12	+	2195.25i	0.848521	+	0.529161i
$29$	4202.58			0.927943			0.463971	−	0.885850i	$-0.346424\pi$
$29$	4202.58			0.927943			0.463971	+	0.885850i	$0.346424\pi$
$30$		0			0
$31$	−1810.94			−0.338454			−0.169227	−	0.985577i	$-0.554127\pi$
$31$	−1810.94			−0.338454			−0.169227	+	0.985577i	$0.554127\pi$
$32$	−3492.00	−	4621.73i	−0.602836	−	0.797865i
$33$		0			0
$34$	−10422.4	−	5679.00i	−1.54621	−	0.842509i
$35$	1568.07	+	3329.02i	0.216369	+	0.459353i
$36$		0			0
$37$	−8532.29			−1.02462			−0.512308	−	0.858802i	$-0.671209\pi$
$37$	−8532.29			−1.02462			−0.512308	+	0.858802i	$0.671209\pi$
$38$	3913.55	−	7182.33i	0.439655	−	0.806875i
$39$		0			0
$40$	−380.244	−	5124.09i	−0.0375762	−	0.506369i
$41$		−	20646.9i		−	1.91821i	−0.283058	−	0.959103i	$-0.591349\pi$
$41$		−	20646.9i		−	1.91821i	0.283058	−	0.959103i	$-0.408651\pi$
$42$		0			0
$43$		−	10894.2i		−	0.898511i	−0.893403	−	0.449256i	$-0.851689\pi$
$43$		−	10894.2i		−	0.898511i	0.893403	−	0.449256i	$-0.148311\pi$
$44$	7301.72	−	4710.93i	0.568583	−	0.366838i
$45$		0			0
$46$	8275.37	+	4509.13i	0.576624	+	0.314194i
$47$	−15279.9			−1.00897			−0.504483	−	0.863422i	$-0.668317\pi$
$47$	−15279.9			−1.00897			−0.504483	+	0.863422i	$0.668317\pi$
$48$		0			0
$49$	10703.3	−	12958.2i	0.636836	−	0.771000i
$50$	−6277.49	+	11520.7i	−0.355108	+	0.651711i
$51$		0			0
$52$	−4847.58	+	3127.56i	−0.248609	+	0.160398i
$53$	20297.1			0.992529			0.496265	−	0.868171i	$-0.334705\pi$
$53$	20297.1			0.992529			0.496265	+	0.868171i	$0.334705\pi$
$54$		0			0
$55$	7707.80			0.343577
$56$	−20432.1	+	11543.9i	−0.870649	+	0.491905i
$57$		0			0
$58$	−11374.8	+	20875.5i	−0.443990	+	0.814832i
$59$	14318.9			0.535523			0.267762	−	0.963485i	$-0.413716\pi$
$59$	14318.9			0.535523			0.267762	+	0.963485i	$0.413716\pi$
$60$		0			0
$61$		−	18947.4i		−	0.651968i	−0.945375	−	0.325984i	$-0.894305\pi$
$61$		−	18947.4i		−	0.651968i	0.945375	−	0.325984i	$-0.105695\pi$
$62$	4901.53	−	8995.51i	0.161939	−	0.297199i
$63$		0			0
$64$	32409.1	−	4836.61i	0.989047	−	0.147602i
$65$	−5117.17			−0.150227
$66$		0			0
$67$		−	58173.5i		−	1.58321i	−0.611035	−	0.791604i	$-0.709246\pi$
$67$		−	58173.5i		−	1.58321i	0.611035	−	0.791604i	$-0.290754\pi$
$68$	56418.8	−	36400.3i	1.47962	−	0.954624i
$69$		0			0
$70$	−20780.5	−	1221.29i	−0.506886	−	0.0297903i
$71$			45807.8i			1.07843i	0.842167	+	0.539216i	$0.181280\pi$
$71$			45807.8i			1.07843i	−0.842167	+	0.539216i	$0.818720\pi$
$72$		0			0
$73$		−	25714.9i		−	0.564777i	−0.959300	−	0.282389i	$-0.908873\pi$
$73$		−	25714.9i		−	0.564777i	0.959300	−	0.282389i	$-0.0911268\pi$
$74$	23093.7	−	42382.6i	0.490245	−	0.899721i
$75$		0			0
$76$	25084.4	+	38879.7i	0.498161	+	0.772126i
$77$	−15001.3	−	31847.8i	−0.288338	−	0.612142i
$78$		0			0
$79$			89207.5i			1.60818i	0.594510	+	0.804088i	$0.297346\pi$
$79$			89207.5i			1.60818i	−0.594510	+	0.804088i	$0.702654\pi$
$80$	26482.1	+	11980.2i	0.462624	+	0.209285i
$81$		0			0
$82$	102560.	+	55883.3i	1.68439	+	0.917799i
$83$	68687.3			1.09441			0.547206	−	0.836998i	$-0.315691\pi$
$83$	68687.3			1.09441			0.547206	+	0.836998i	$0.315691\pi$
$84$		0			0
$85$	59556.5			0.894091
$86$	54114.8	+	29486.4i	0.788988	+	0.429908i
$87$		0			0
$88$	3637.68	+	49020.6i	0.0500747	+	0.674796i
$89$		−	31947.0i		−	0.427519i	−0.976886	−	0.213759i	$-0.931429\pi$
$89$		−	31947.0i		−	0.427519i	0.976886	−	0.213759i	$-0.0685709\pi$
$90$		0			0
$91$	9959.27	+	21143.6i	0.126074	+	0.267655i
$92$	−44796.5	+	28901.9i	−0.551791	+	0.356005i
$93$		0			0
$94$	41356.9	−	75900.1i	0.482757	−	0.885978i
$95$			41041.9i			0.466572i
$96$		0			0
$97$		−	111178.i		−	1.19975i	−0.800095	−	0.599874i	$-0.795218\pi$
$97$		−	111178.i		−	1.19975i	0.800095	−	0.599874i	$-0.204782\pi$
$98$	35397.6	+	88239.5i	0.372314	+	0.928107i
$99$		0			0
$100$	−40236.4	−	62364.5i	−0.402364	−	0.623645i
$101$		−	90187.0i		−	0.879712i	−0.898068	−	0.439856i	$-0.855029\pi$
$101$		−	90187.0i		−	0.879712i	0.898068	−	0.439856i	$-0.144971\pi$
$102$		0			0
$103$	26036.4			0.241817			0.120909	−	0.992664i	$-0.461419\pi$
$103$	26036.4			0.241817			0.120909	+	0.992664i	$0.461419\pi$
$104$	−2415.04	−	32544.6i	−0.0218948	−	0.295050i
$105$		0			0
$106$	−54936.4	+	100822.i	−0.474893	+	0.871545i
$107$		−	27241.7i		−	0.230025i	−0.993364	−	0.115012i	$-0.963309\pi$
$107$		−	27241.7i		−	0.230025i	0.993364	−	0.115012i	$-0.0366908\pi$
$108$		0			0
$109$	−48187.3			−0.388478			−0.194239	−	0.980954i	$-0.562224\pi$
$109$	−48187.3			−0.388478			−0.194239	+	0.980954i	$0.562224\pi$
$110$	−20862.1	+	38287.1i	−0.164390	+	0.301697i
$111$		0			0
$112$	−2040.03	−	132738.i	−0.0153671	−	0.999882i
$113$	218602.			1.61049			0.805245	−	0.592942i	$-0.202034\pi$
$113$	218602.			1.61049			0.805245	+	0.592942i	$0.202034\pi$
$114$		0			0
$115$	−47287.9			−0.333430
$116$	−72908.2	−	113004.i	−0.503073	−	0.779741i
$117$		0			0
$118$	−38755.7	+	71126.3i	−0.256230	+	0.470246i
$119$	−115911.	−	246081.i	−0.750342	−	1.59298i
$120$		0			0
$121$	87312.7			0.542143
$122$	94117.9	+	51283.5i	0.572496	+	0.311945i
$123$		0			0
$124$	31417.0	+	48694.9i	0.183489	+	0.284400i
$125$		−	154535.i		−	0.884610i
$126$		0			0
$127$			70206.5i			0.386250i	0.981174	+	0.193125i	$0.0618622\pi$
$127$			70206.5i			0.386250i	−0.981174	+	0.193125i	$0.938138\pi$
$128$	−63694.1	+	174077.i	−0.343617	+	0.939110i
$129$		0			0
$130$	13850.2	−	25418.6i	0.0718785	−	0.131915i
$131$	63299.6			0.322272			0.161136	−	0.986932i	$-0.448484\pi$
$131$	63299.6			0.322272			0.161136	+	0.986932i	$0.448484\pi$
$132$		0			0
$133$	169581.	−	79877.6i	0.831280	−	0.391558i
$134$	288966.	+	157453.i	1.39022	+	0.757513i
$135$		0			0
$136$	28107.6	+	378771.i	0.130309	+	1.75602i
$137$	749.523			0.00341180			0.00170590	−	0.999999i	$-0.499457\pi$
$137$	749.523			0.00341180			0.00170590	+	0.999999i	$0.499457\pi$
$138$		0			0
$139$	−338690.			−1.48685			−0.743423	−	0.668822i	$-0.766799\pi$
$139$	−338690.			−1.48685			−0.743423	+	0.668822i	$0.766799\pi$
$140$	62311.4	−	99917.6i	0.268687	−	0.430846i
$141$		0			0
$142$	−227542.	−	123984.i	−0.946978	−	0.515995i
$143$	48954.5			0.200195
$144$		0			0
$145$		−	119289.i		−	0.471173i
$146$	127734.	+	69600.4i	0.495934	+	0.270228i
$147$		0			0
$148$	148022.	+	229427.i	0.555484	+	0.860974i
$149$	−339997.			−1.25461			−0.627305	−	0.778773i	$-0.715842\pi$
$149$	−339997.			−1.25461			−0.627305	+	0.778773i	$0.715842\pi$
$150$		0			0
$151$		−	338495.i		−	1.20812i	−0.796938	−	0.604061i	$-0.793548\pi$
$151$		−	338495.i		−	1.20812i	0.796938	−	0.604061i	$-0.206452\pi$
$152$	−261021.	+	19369.7i	−0.916362	+	0.0680006i
$153$		0			0
$154$	198801.	+	11683.8i	0.675486	+	0.0396991i
$155$			51403.0i			0.171854i
$156$		0			0
$157$		−	592002.i		−	1.91679i	−0.285449	−	0.958394i	$-0.592143\pi$
$157$		−	592002.i		−	1.91679i	0.285449	−	0.958394i	$-0.407857\pi$
$158$	−443122.	−	241451.i	−1.41215	−	0.769459i
$159$		0			0
$160$	−131186.	+	99119.4i	−0.405125	+	0.306097i
$161$	92033.8	+	195388.i	0.279822	+	0.594064i
$162$		0			0
$163$		−	255977.i		−	0.754625i	−0.926086	−	0.377313i	$-0.876848\pi$
$163$		−	255977.i		−	0.754625i	0.926086	−	0.377313i	$-0.123152\pi$
$164$	−555180.	+	358191.i	−1.61185	+	1.03993i
$165$		0			0
$166$	−185910.	+	341191.i	−0.523641	+	0.961010i
$167$	−515543.			−1.43045			−0.715227	−	0.698892i	$-0.753677\pi$
$167$	−515543.			−1.43045			−0.715227	+	0.698892i	$0.753677\pi$
$168$		0			0
$169$	338792.			0.912466
$170$	−161197.	+	295836.i	−0.427793	+	0.785106i
$171$		0			0
$172$	−292937.	+	188997.i	−0.755010	+	0.487117i
$173$			37150.1i			0.0943723i	0.998886	+	0.0471861i	$0.0150254\pi$
$173$			37150.1i			0.0943723i	−0.998886	+	0.0471861i	$0.984975\pi$
$174$		0			0
$175$	−272014.	+	128127.i	−0.671423	+	0.316261i
$176$	−253347.	−	114611.i	−0.616501	−	0.278897i
$177$		0			0
$178$	158691.	+	86468.4i	0.375407	+	0.204554i
$179$		−	143168.i		−	0.333975i	−0.985959	−	0.166987i	$-0.946596\pi$
$179$		−	143168.i		−	0.333975i	0.985959	−	0.166987i	$-0.0534039\pi$
$180$		0			0
$181$			470966.i			1.06855i	0.845312	+	0.534273i	$0.179415\pi$
$181$			470966.i			1.06855i	−0.845312	+	0.534273i	$0.820585\pi$
$182$	−131983.	−	7756.80i	−0.295351	−	0.0173582i
$183$		0			0
$184$	−22317.4	−	300745.i	−0.0485959	−	0.654868i
$185$			242186.i			0.520260i
$186$		0			0
$187$	−569759.			−1.19148
$188$	265082.	+	410865.i	0.546999	+	0.847823i
$189$		0			0
$190$	−203868.	−	111085.i	−0.409699	−	0.223239i
$191$		−	22686.0i		−	0.0449961i	−0.999747	−	0.0224981i	$-0.992838\pi$
$191$		−	22686.0i		−	0.0449961i	0.999747	−	0.0224981i	$-0.00716196\pi$
$192$		0			0
$193$	−191865.			−0.370768			−0.185384	−	0.982666i	$-0.559353\pi$
$193$	−191865.			−0.370768			−0.185384	+	0.982666i	$0.559353\pi$
$194$	552256.	+	300917.i	1.05350	+	0.574040i
$195$		0			0
$196$	−534121.	−	62999.6i	−0.993116	−	0.117138i
$197$	−126782.			−0.232751			−0.116376	−	0.993205i	$-0.537128\pi$
$197$	−126782.			−0.232751			−0.116376	+	0.993205i	$0.537128\pi$
$198$		0			0
$199$	47757.2			0.0854881			0.0427441	−	0.999086i	$-0.486390\pi$
$199$	47757.2			0.0854881			0.0427441	+	0.999086i	$0.486390\pi$
$200$	418689.	−	31069.7i	0.740144	−	0.0549240i
$201$		0			0
$202$	447987.	+	244102.i	0.772480	+	0.420913i
$203$	−492889.	+	232166.i	−0.839477	+	0.395419i
$204$		0			0
$205$	−586056.			−0.973990
$206$	−70470.5	+	129331.i	−0.115702	+	0.212341i
$207$		0			0
$208$	168196.	+	76089.5i	0.269561	+	0.121946i
$209$		−	392636.i		−	0.621762i
$210$		0			0
$211$		−	317222.i		−	0.490521i	−0.969457	−	0.245261i	$-0.921126\pi$
$211$		−	317222.i		−	0.490521i	0.969457	−	0.245261i	$-0.0788735\pi$
$212$	−352122.	−	545773.i	−0.538088	−	0.834012i
$213$		0			0
$214$	135318.	+	73732.9i	0.201986	+	0.110059i
$215$	−309228.			−0.456229
$216$		0			0
$217$	212391.	−	100043.i	0.306188	−	0.144224i
$218$	130425.	−	239361.i	0.185874	−	0.341124i
$219$		0			0
$220$	−133718.	−	207257.i	−0.186266	−	0.288704i
$221$	378260.			0.520967
$222$		0			0
$223$	422350.			0.568736			0.284368	−	0.958715i	$-0.408216\pi$
$223$	422350.			0.568736			0.284368	+	0.958715i	$0.408216\pi$
$224$	664871.	+	349137.i	0.885354	+	0.464917i
$225$		0			0
$226$	−591672.	+	1.08586e6i	−0.770567	+	1.41418i
$227$	−383018.			−0.493349			−0.246675	−	0.969098i	$-0.579338\pi$
$227$	−383018.			−0.493349			−0.246675	+	0.969098i	$0.579338\pi$
$228$		0			0
$229$		−	856224.i		−	1.07894i	−0.842004	−	0.539472i	$-0.818624\pi$
$229$		−	856224.i		−	1.07894i	0.842004	−	0.539472i	$-0.181376\pi$
$230$	127990.	−	234894.i	0.159536	−	0.292787i
$231$		0			0
$232$	758663.	−	56298.2i	0.925398	−	0.0686712i
$233$	324537.			0.391629			0.195814	−	0.980641i	$-0.437265\pi$
$233$	324537.			0.391629			0.195814	+	0.980641i	$0.437265\pi$
$234$		0			0
$235$			433716.i			0.512313i
$236$	−248410.	−	385023.i	−0.290328	−	0.449994i
$237$		0			0
$238$	1.53609e6	+	90277.8i	1.75782	+	0.103309i
$239$			214134.i			0.242489i	0.992623	+	0.121244i	$0.0386885\pi$
$239$			214134.i			0.242489i	−0.992623	+	0.121244i	$0.961312\pi$
$240$		0			0
$241$			437254.i			0.484944i	0.970158	+	0.242472i	$0.0779582\pi$
$241$			437254.i			0.484944i	−0.970158	+	0.242472i	$0.922042\pi$
$242$	−236322.	+	433710.i	−0.259398	+	0.476059i
$243$		0			0
$244$	−509483.	+	328708.i	−0.547841	+	0.353457i
$245$	−367814.	−	303810.i	−0.391483	−	0.323360i
$246$		0			0
$247$			260669.i			0.271861i
$248$	−326916.	+	24259.5i	−0.337526	+	0.0250469i
$249$		0			0
$250$	767624.	+	418268.i	0.776781	+	0.423257i
$251$	1.50647e6			1.50930			0.754650	−	0.656128i	$-0.227807\pi$
$251$	1.50647e6			1.50930			0.754650	+	0.656128i	$0.227807\pi$
$252$		0			0
$253$	452389.			0.444335
$254$	−348738.	−	190022.i	−0.339168	−	0.184808i
$255$		0			0
$256$	−692299.	−	787549.i	−0.660228	−	0.751065i
$257$			1.17493e6i			1.10963i	0.831973	+	0.554817i	$0.187212\pi$
$257$			1.17493e6i			1.10963i	−0.831973	+	0.554817i	$0.812788\pi$
$258$		0			0
$259$	1.00069e6	−	471354.i	0.926934	−	0.436614i
$260$	88774.9	+	137597.i	0.0814436	+	0.126234i
$261$		0			0
$262$	−171328.	+	314429.i	−0.154197	+	0.282989i
$263$		−	1.59797e6i		−	1.42456i	−0.701897	−	0.712278i	$-0.747663\pi$
$263$		−	1.59797e6i		−	1.42456i	0.701897	−	0.712278i	$-0.252337\pi$
$264$		0			0
$265$		−	576126.i		−	0.503967i
$266$	−62212.8	+	1.05856e6i	−0.0539108	+	0.917299i
$267$		0			0
$268$	−1.56424e6	+	1.00922e6i	−1.33035	+	0.858318i
$269$		−	201541.i		−	0.169818i	−0.996389	−	0.0849090i	$-0.972940\pi$
$269$		−	201541.i		−	0.169818i	0.996389	−	0.0849090i	$-0.0270599\pi$
$270$		0			0
$271$	−988629.			−0.817730			−0.408865	−	0.912595i	$-0.634075\pi$
$271$	−988629.			−0.817730			−0.408865	+	0.912595i	$0.634075\pi$
$272$	−1.95755e6	−	885571.i	−1.60432	−	0.725774i
$273$		0			0
$274$	−2028.67	+	3723.12i	−0.00163244	+	0.00299592i
$275$			629804.i			0.502196i
$276$		0			0
$277$	1.53035e6			1.19837			0.599187	−	0.800609i	$-0.295491\pi$
$277$	1.53035e6			1.19837			0.599187	+	0.800609i	$0.295491\pi$
$278$	916706.	−	1.68238e6i	0.711407	−	1.30561i
$279$		0			0
$280$	327669.	+	579959.i	0.249770	+	0.442081i
$281$	456987.			0.345253			0.172627	−	0.984987i	$-0.444775\pi$
$281$	456987.			0.345253			0.172627	+	0.984987i	$0.444775\pi$
$282$		0			0
$283$	1.62201e6			1.20389			0.601946	−	0.798537i	$-0.294392\pi$
$283$	1.62201e6			1.20389			0.601946	+	0.798537i	$0.294392\pi$
$284$	1.23174e6	−	794692.i	0.906196	−	0.584660i
$285$		0			0
$286$	−132501.	+	243172.i	−0.0957866	+	0.175792i
$287$	1.14061e6	+	2.42152e6i	0.817395	+	1.73533i
$288$		0			0
$289$	−2.98254e6			−2.10059
$290$	592546.	+	322870.i	0.413740	+	0.225441i
$291$		0			0
$292$	−691454.	+	446113.i	−0.474576	+	0.306187i
$293$		−	543908.i		−	0.370132i	−0.982726	−	0.185066i	$-0.940750\pi$
$293$		−	543908.i		−	0.370132i	0.982726	−	0.185066i	$-0.0592499\pi$
$294$		0			0
$295$		−	406436.i		−	0.271918i
$296$	−1.54027e6	+	114299.i	−1.02181	+	0.0758254i
$297$		0			0
$298$	920242.	−	1.68887e6i	0.600290	−	1.10168i
$299$	−300339.			−0.194283
$300$		0			0
$301$	601834.	+	1.27770e6i	0.382878	+	0.812851i
$302$	1.68141e6	+	916178.i	1.06086	+	0.578046i
$303$		0			0
$304$	610270.	−	1.34900e6i	0.378737	−	0.837199i
$305$	−537817.			−0.331044
$306$		0			0
$307$	483324.			0.292680			0.146340	−	0.989234i	$-0.453251\pi$
$307$	483324.			0.292680			0.146340	+	0.989234i	$0.453251\pi$
$308$	−596115.	+	955882.i	−0.358058	+	0.574153i
$309$		0			0
$310$	−255335.	−	139128.i	−0.150906	−	0.0822264i
$311$	1.48235e6			0.869059			0.434529	−	0.900658i	$-0.356915\pi$
$311$	1.48235e6			0.869059			0.434529	+	0.900658i	$0.356915\pi$
$312$		0			0
$313$			874317.i			0.504438i	0.967670	+	0.252219i	$0.0811604\pi$
$313$			874317.i			0.504438i	−0.967670	+	0.252219i	$0.918840\pi$
$314$	2.94066e6	+	1.60232e6i	1.68314	+	0.917120i
$315$		0			0
$316$	2.39872e6	−	1.54761e6i	1.35133	−	0.871854i
$317$	−1.32505e6			−0.740598			−0.370299	−	0.928913i	$-0.620745\pi$
$317$	−1.32505e6			−0.740598			−0.370299	+	0.928913i	$0.620745\pi$
$318$		0			0
$319$			1.14120e6i			0.627894i
$320$	−137286.	−	919922.i	−0.0749463	−	0.502199i
$321$		0			0
$322$	−1.21965e6	−	71680.6i	−0.655537	−	0.0385267i
$323$		−	3.03381e6i		−	1.61801i
$324$		0			0
$325$		−	418124.i		−	0.219582i
$326$	1.27152e6	+	692831.i	0.662640	+	0.361063i
$327$		0			0
$328$	−276588.	−	3.72724e6i	−0.141954	−	1.91295i
$329$	1.79206e6	−	844117.i	0.912775	−	0.429945i
$330$		0			0
$331$		−	26134.3i		−	0.0131112i	−0.999979	−	0.00655558i	$-0.997913\pi$
$331$		−	26134.3i		−	0.0131112i	0.999979	−	0.00655558i	$-0.00208672\pi$
$332$	−1.19162e6	−	1.84695e6i	−0.593323	−	0.919623i
$333$		0			0
$334$	1.39538e6	−	2.56087e6i	0.684425	−	1.25609i
$335$	−1.65124e6			−0.803891
$336$		0			0
$337$	1.18182e6			0.566863			0.283431	−	0.958993i	$-0.408527\pi$
$337$	1.18182e6			0.566863			0.283431	+	0.958993i	$0.408527\pi$
$338$	−916982.	+	1.68289e6i	−0.436585	+	0.801242i
$339$		0			0
$340$	−1.03321e6	−	1.60143e6i	−0.484721	−	0.751295i
$341$		−	491757.i		−	0.229015i
$342$		0			0
$343$	−539451.	+	2.11106e6i	−0.247581	+	0.968867i
$344$	−145940.	−	1.96665e6i	−0.0664932	−	0.896048i
$345$		0			0
$346$	−184536.	−	100551.i	−0.0828688	−	0.0451540i
$347$		−	541674.i		−	0.241499i	−0.992683	−	0.120749i	$-0.961470\pi$
$347$		−	541674.i		−	0.241499i	0.992683	−	0.120749i	$-0.0385297\pi$
$348$		0			0
$349$			3.74079e6i			1.64399i	0.569494	+	0.821996i	$0.307139\pi$
$349$			3.74079e6i			1.64399i	−0.569494	+	0.821996i	$0.692861\pi$
$350$	99791.8	−	1.69797e6i	0.0435437	−	0.740901i
$351$		0			0
$352$	1.25502e6	−	948245.i	0.539876	−	0.407910i
$353$		−	416451.i		−	0.177880i	−0.996037	−	0.0889399i	$-0.971652\pi$
$353$		−	416451.i		−	0.177880i	0.996037	−	0.0889399i	$-0.0283479\pi$
$354$		0			0
$355$	1.30024e6			0.547586
$356$	−859032.	+	554230.i	−0.359240	+	0.231774i
$357$		0			0
$358$	711161.	+	387501.i	0.293265	+	0.159796i
$359$			2.78304e6i			1.13968i	0.821755	+	0.569840i	$0.192995\pi$
$359$			2.78304e6i			1.13968i	−0.821755	+	0.569840i	$0.807005\pi$
$360$		0			0
$361$	−385421.			−0.155656
$362$	−2.33944e6	−	1.27473e6i	−0.938297	−	0.511265i
$363$		0			0
$364$	395758.	−	634605.i	0.156558	−	0.251044i
$365$	−729909.			−0.286772
$366$		0			0
$367$	−4.80251e6			−1.86124			−0.930622	−	0.365982i	$-0.880733\pi$
$367$	−4.80251e6			−1.86124			−0.930622	+	0.365982i	$0.880733\pi$
$368$	1.55430e6	+	703144.i	0.598294	+	0.270660i
$369$		0			0
$370$	−1.20302e6	−	655507.i	−0.456843	−	0.248927i
$371$	−2.38049e6	+	1.12128e6i	−0.897906	+	0.422941i
$372$		0			0
$373$	−285751.			−0.106345			−0.0531723	−	0.998585i	$-0.516933\pi$
$373$	−285751.			−0.106345			−0.0531723	+	0.998585i	$0.516933\pi$
$374$	1.54212e6	−	2.83017e6i	0.570085	−	1.04625i
$375$		0			0
$376$	−2.75838e6	+	204691.i	−1.00620	+	0.0746671i
$377$		−	757639.i		−	0.274542i
$378$		0			0
$379$			220006.i			0.0786749i	0.999226	+	0.0393374i	$0.0125247\pi$
$379$			220006.i			0.0786749i	−0.999226	+	0.0393374i	$0.987475\pi$
$380$	1.10359e6	−	712013.i	0.392056	−	0.252947i
$381$		0			0
$382$	112689.	+	61402.5i	0.0395113	+	0.0215292i
$383$	3.72820e6			1.29868			0.649341	−	0.760498i	$-0.275045\pi$
$383$	3.72820e6			1.29868			0.649341	+	0.760498i	$0.275045\pi$
$384$		0			0
$385$	−903989.	+	425807.i	−0.310822	+	0.146407i
$386$	519305.	−	953053.i	0.177400	−	0.325573i
$387$		0			0
$388$	−2.98950e6	+	1.92876e6i	−1.00813	+	0.650429i
$389$	2.84417e6			0.952975			0.476488	−	0.879181i	$-0.341910\pi$
$389$	2.84417e6			0.952975			0.476488	+	0.879181i	$0.341910\pi$
$390$		0			0
$391$	3.49551e6			1.15629
$392$	1.75860e6	−	2.48263e6i	0.578033	−	0.816014i
$393$		0			0
$394$	343151.	−	629766.i	0.111364	−	0.204380i
$395$	2.53213e6			0.816569
$396$		0			0
$397$		−	1.69596e6i		−	0.540056i	−0.962852	−	0.270028i	$-0.912967\pi$
$397$		−	1.69596e6i		−	0.540056i	0.962852	−	0.270028i	$-0.0870330\pi$
$398$	−129260.	+	237225.i	−0.0409033	+	0.0750676i
$399$		0			0
$400$	−978898.	+	2.16385e6i	−0.305906	+	0.676204i
$401$	−4.51541e6			−1.40229			−0.701143	−	0.713021i	$-0.747326\pi$
$401$	−4.51541e6			−1.40229			−0.701143	+	0.713021i	$0.747326\pi$
$402$		0			0
$403$			326475.i			0.100135i
$404$	−2.42506e6	+	1.56460e6i	−0.739213	+	0.476926i
$405$		0			0
$406$	180823.	−	3.07672e6i	0.0544424	−	0.926344i
$407$		−	2.31693e6i		−	0.693308i
$408$		0			0
$409$			911330.i			0.269381i	0.990888	+	0.134691i	$0.0430041\pi$
$409$			911330.i			0.269381i	−0.990888	+	0.134691i	$0.956996\pi$
$410$	1.58623e6	−	2.91112e6i	0.466022	−	0.855266i
$411$		0			0
$412$	−451690.	−	700098.i	−0.131098	−	0.203196i
$413$	−1.67935e6	+	791025.i	−0.484469	+	0.228200i
$414$		0			0
$415$		−	1.94967e6i		−	0.555700i
$416$	−833202.	+	629536.i	−0.236057	+	0.178356i
$417$		0			0
$418$	1.95035e6	+	1.06272e6i	0.545973	+	0.297493i
$419$	69632.2			0.0193765			0.00968824	−	0.999953i	$-0.496916\pi$
$419$	69632.2			0.0193765			0.00968824	+	0.999953i	$0.496916\pi$
$420$		0			0
$421$	−3.62044e6			−0.995533			−0.497767	−	0.867311i	$-0.665846\pi$
$421$	−3.62044e6			−0.995533			−0.497767	+	0.867311i	$0.665846\pi$
$422$	1.57574e6	+	858600.i	0.430729	+	0.234698i
$423$		0			0
$424$	3.66408e6	−	271901.i	0.989808	−	0.0734508i
$425$			4.86635e6i			1.30687i
$426$		0			0
$427$	1.04672e6	+	2.22220e6i	0.277819	+	0.589812i
$428$	−732509.	+	472600.i	−0.193287	+	0.124705i
$429$		0			0
$430$	836963.	−	1.53603e6i	0.218291	−	0.400617i
$431$		−	791654.i		−	0.205278i	−0.994719	−	0.102639i	$-0.967271\pi$
$431$		−	791654.i		−	0.205278i	0.994719	−	0.102639i	$-0.0327286\pi$
$432$		0			0
$433$		−	329131.i		−	0.0843625i	−0.999110	−	0.0421812i	$-0.986569\pi$
$433$		−	329131.i		−	0.0843625i	0.999110	−	0.0421812i	$-0.0134307\pi$
$434$	−77918.5	+	1.32579e6i	−0.0198571	+	0.337871i
$435$		0			0
$436$	835973.	+	1.29572e6i	0.210609	+	0.326434i
$437$			2.40885e6i			0.603400i
$438$		0			0
$439$	4.71306e6			1.16719			0.583595	−	0.812045i	$-0.301646\pi$
$439$	4.71306e6			1.16719			0.583595	+	0.812045i	$0.301646\pi$
$440$	1.39144e6	−	103255.i	0.342635	−	0.0254260i
$441$		0			0
$442$	−1.02381e6	+	1.87894e6i	−0.249266	+	0.457464i
$443$			2.41380e6i			0.584377i	0.956361	+	0.292188i	$0.0943834\pi$
$443$			2.41380e6i			0.584377i	−0.956361	+	0.292188i	$0.905617\pi$
$444$		0			0
$445$	−906806.			−0.217077
$446$	−1.14314e6	+	2.09795e6i	−0.272122	+	0.499410i
$447$		0			0
$448$	−3.53382e6	+	2.35764e6i	−0.831859	+	0.554987i
$449$	2.88865e6			0.676205			0.338103	−	0.941109i	$-0.390215\pi$
$449$	2.88865e6			0.676205			0.338103	+	0.941109i	$0.390215\pi$
$450$		0			0
$451$	5.60662e6			1.29796
$452$	−3.79240e6	−	5.87805e6i	−0.873108	−	1.35328i
$453$		0			0
$454$	1.03668e6	−	1.90257e6i	0.236051	−	0.433213i
$455$	600154.	−	282691.i	0.135905	−	0.0640152i
$456$		0			0
$457$	−3.81000e6			−0.853365			−0.426682	−	0.904402i	$-0.640318\pi$
$457$	−3.81000e6			−0.853365			−0.426682	+	0.904402i	$0.640318\pi$
$458$	4.25313e6	+	2.31747e6i	0.947426	+	0.516239i
$459$		0			0
$460$	820370.	+	1.27154e6i	0.180765	+	0.280178i
$461$			5.30428e6i			1.16245i	0.813743	+	0.581224i	$0.197426\pi$
$461$			5.30428e6i			1.16245i	−0.813743	+	0.581224i	$0.802574\pi$
$462$		0			0
$463$		−	4.63705e6i		−	1.00529i	−0.864494	−	0.502643i	$-0.832361\pi$
$463$		−	4.63705e6i		−	1.00529i	0.864494	−	0.502643i	$-0.167639\pi$
$464$	−1.77376e6	+	3.92089e6i	−0.382472	+	0.845454i
$465$		0			0
$466$	−878398.	+	1.61208e6i	−0.187381	+	0.343891i
$467$	1.92138e6			0.407682			0.203841	−	0.979004i	$-0.434658\pi$
$467$	1.92138e6			0.407682			0.203841	+	0.979004i	$0.434658\pi$
$468$		0			0
$469$	3.21371e6	+	6.82272e6i	0.674644	+	1.43227i
$470$	−2.15440e6	−	1.17390e6i	−0.449865	−	0.245125i
$471$		0			0
$472$	2.58488e6	−	191817.i	0.534055	−	0.0396307i
$473$	2.95829e6			0.607979
$474$		0			0
$475$	−3.35353e6			−0.681975
$476$	−4.60604e6	+	7.38588e6i	−0.931774	+	1.49412i
$477$		0			0
$478$	−1.06367e6	−	579580.i	−0.212931	−	0.116023i
$479$	−5.23498e6			−1.04250			−0.521250	−	0.853404i	$-0.674534\pi$
$479$	−5.23498e6			−1.04250			−0.521250	+	0.853404i	$0.674534\pi$
$480$		0			0
$481$			1.53820e6i			0.303144i
$482$	−2.17198e6	−	1.18348e6i	−0.425832	−	0.232030i
$483$		0			0
$484$	−1.51474e6	−	2.34777e6i	−0.293917	−	0.455557i
$485$	−3.15576e6			−0.609185
$486$		0			0
$487$		−	4.98270e6i		−	0.952012i	−0.879442	−	0.476006i	$-0.842084\pi$
$487$		−	4.98270e6i		−	0.952012i	0.879442	−	0.476006i	$-0.157916\pi$
$488$	−253822.	−	3.42045e6i	−0.0482480	−	0.650180i
$489$		0			0
$490$	2.50465e6	−	1.00475e6i	0.471256	−	0.189046i
$491$			4.48170e6i			0.838956i	0.907766	+	0.419478i	$0.137787\pi$
$491$			4.48170e6i			0.838956i	−0.907766	+	0.419478i	$0.862213\pi$
$492$		0			0
$493$			8.81782e6i			1.63397i
$494$	−1.29483e6	−	705532.i	−0.238723	−	0.130077i
$495$		0			0
$496$	764334.	−	1.68956e6i	0.139501	−	0.308368i
$497$	−2.53058e6	−	5.37244e6i	−0.459547	−	0.975620i
$498$		0			0
$499$			8.74642e6i			1.57246i	0.617935	+	0.786229i	$0.287969\pi$
$499$			8.74642e6i			1.57246i	−0.617935	+	0.786229i	$0.712031\pi$
$500$	−4.15533e6	+	2.68094e6i	−0.743328	+	0.479581i
$501$		0			0
$502$	−4.07743e6	+	7.48310e6i	−0.722150	+	1.32532i
$503$	−7.16489e6			−1.26267			−0.631335	−	0.775511i	$-0.717493\pi$
$503$	−7.16489e6			−1.26267			−0.631335	+	0.775511i	$0.717493\pi$
$504$		0			0
$505$	−2.55993e6			−0.446683
$506$	−1.22445e6	+	2.24716e6i	−0.212600	+	0.390173i
$507$		0			0
$508$	1.88780e6	−	1.21797e6i	0.324562	−	0.209401i
$509$			509493.i			0.0871654i	0.999050	+	0.0435827i	$0.0138772\pi$
$509$			509493.i			0.0871654i	−0.999050	+	0.0435827i	$0.986123\pi$
$510$		0			0
$511$	1.42058e6	+	3.01590e6i	0.240666	+	0.510934i
$512$	5.78579e6	−	1.30727e6i	0.975412	−	0.220390i
$513$		0			0
$514$	−5.83625e6	−	3.18009e6i	−0.974375	−	0.530923i
$515$		−	739034.i		−	0.122785i
$516$		0			0
$517$		−	4.14923e6i		−	0.682717i
$518$	−367115.	+	6.24650e6i	−0.0601143	+	1.02285i
$519$		0			0
$520$	−923768.	+	68550.2i	−0.149815	+	0.0111173i
$521$			2.24559e6i			0.362441i	0.983443	+	0.181220i	$0.0580047\pi$
$521$			2.24559e6i			0.362441i	−0.983443	+	0.181220i	$0.941995\pi$
$522$		0			0
$523$	−6.67986e6			−1.06786			−0.533929	−	0.845529i	$-0.679285\pi$
$523$	−6.67986e6			−1.06786			−0.533929	+	0.845529i	$0.679285\pi$
$524$	−1.09815e6	−	1.70208e6i	−0.174716	−	0.270802i
$525$		0			0
$526$	7.93763e6	+	4.32510e6i	1.25091	+	0.681604i
$527$		−	3.79970e6i		−	0.595967i
$528$		0			0
$529$	3.66091e6			0.568787
$530$	2.86180e6	+	1.55935e6i	0.442537	+	0.241132i
$531$		0			0
$532$	−5.08981e6	−	3.17415e6i	−0.779691	−	0.486237i
$533$	−3.72221e6			−0.567522
$534$		0			0
$535$	−773247.			−0.116798
$536$	−779297.	−	1.05016e7i	−0.117163	−	1.57887i
$537$		0			0
$538$	1.00112e6	+	545496.i	0.149118	+	0.0812523i
$539$	3.51877e6	+	2.90646e6i	0.521698	+	0.430916i
$540$		0			0
$541$	8.39309e6			1.23290			0.616451	−	0.787393i	$-0.288570\pi$
$541$	8.39309e6			1.23290			0.616451	+	0.787393i	$0.288570\pi$
$542$	2.67584e6	−	4.91083e6i	0.391257	−	0.718053i
$543$		0			0
$544$	9.69726e6	−	7.32688e6i	1.40492	−	1.06150i
$545$			1.36778e6i			0.197254i
$546$		0			0
$547$		−	9.21277e6i		−	1.31650i	−0.752798	−	0.658251i	$-0.771296\pi$
$547$		−	9.21277e6i		−	1.31650i	0.752798	−	0.658251i	$-0.228704\pi$
$548$	−13003.1	−	20154.1i	−0.00184967	−	0.00286690i
$549$		0			0
$550$	−3.12843e6	−	1.70464e6i	−0.440981	−	0.240284i
$551$	−6.07659e6			−0.852670
$552$		0			0
$553$	−4.92814e6	−	1.04625e7i	−0.685283	−	1.45486i
$554$	−4.14208e6	+	7.60175e6i	−0.573383	+	1.05230i
$555$		0			0
$556$	5.87574e6	+	9.10713e6i	0.806076	+	1.24938i
$557$	7.30468e6			0.997616			0.498808	−	0.866713i	$-0.333771\pi$
$557$	7.30468e6			0.997616			0.498808	+	0.866713i	$0.333771\pi$
$558$		0			0
$559$	−1.96400e6			−0.265834
$560$	−3.76771e6	+	57905.6i	−0.507701	+	0.00780279i
$561$		0			0
$562$	−1.23689e6	+	2.27000e6i	−0.165192	+	0.303169i
$563$	−41121.0			−0.00546754			−0.00273377	−	0.999996i	$-0.500870\pi$
$563$	−41121.0			−0.00546754			−0.00273377	+	0.999996i	$0.500870\pi$
$564$		0			0
$565$		−	6.20495e6i		−	0.817744i
$566$	−4.39016e6	+	8.05703e6i	−0.576023	+	1.05714i
$567$		0			0
$568$	613645.	+	8.26935e6i	0.0798080	+	1.07548i
$569$	5.94994e6			0.770428			0.385214	−	0.922827i	$-0.374128\pi$
$569$	5.94994e6			0.770428			0.385214	+	0.922827i	$0.374128\pi$
$570$		0			0
$571$		−	4.93009e6i		−	0.632797i	−0.948626	−	0.316399i	$-0.897526\pi$
$571$		−	4.93009e6i		−	0.632797i	0.948626	−	0.316399i	$-0.102474\pi$
$572$	−849283.	−	1.31635e6i	−0.108533	−	0.168221i
$573$		0			0
$574$	−1.51156e7	−	888364.i	−1.91490	−	0.112541i
$575$		−	3.86389e6i		−	0.487365i
$576$		0			0
$577$		−	7.17226e6i		−	0.896843i	−0.893822	−	0.448422i	$-0.851986\pi$
$577$		−	7.17226e6i		−	0.896843i	0.893822	−	0.448422i	$-0.148014\pi$
$578$	8.07261e6	−	1.48152e7i	1.00507	−	1.84454i
$579$		0			0
$580$	−3.20759e6	+	2.06948e6i	−0.395922	+	0.255441i
$581$	−8.05581e6	+	3.79453e6i	−0.990076	+	0.466356i
$582$		0			0
$583$			5.51162e6i			0.671596i
$584$	−344479.	−	4.64213e6i	−0.0417956	−	0.563229i
$585$		0			0
$586$	2.70176e6	+	1.47215e6i	0.325015	+	0.177096i
$587$	6.02358e6			0.721538			0.360769	−	0.932655i	$-0.382514\pi$
$587$	6.02358e6			0.721538			0.360769	+	0.932655i	$0.382514\pi$
$588$		0			0
$589$	2.61847e6			0.310999
$590$	2.01890e6	+	1.10007e6i	0.238772	+	0.130104i
$591$		0			0
$592$	3.60118e6	−	7.96039e6i	0.422318	−	0.933534i
$593$		−	1.29430e6i		−	0.151146i	−0.997140	−	0.0755731i	$-0.975921\pi$
$593$		−	1.29430e6i		−	0.151146i	0.997140	−	0.0755731i	$-0.0240786\pi$
$594$		0			0
$595$	−6.98492e6	+	3.29011e6i	−0.808852	+	0.380994i
$596$	5.89841e6	+	9.14226e6i	0.680172	+	1.05424i
$597$		0			0
$598$	812903.	−	1.49188e6i	0.0929578	−	0.170601i
$599$		−	1.32740e7i		−	1.51159i	−0.654810	−	0.755794i	$-0.727251\pi$
$599$		−	1.32740e7i		−	1.51159i	0.654810	−	0.755794i	$-0.272749\pi$
$600$		0			0
$601$			2.50249e6i			0.282609i	0.989966	+	0.141304i	$0.0451297\pi$
$601$			2.50249e6i			0.282609i	−0.989966	+	0.141304i	$0.954870\pi$
$602$	−7.97565e6	−	468739.i	−0.896964	−	0.0527157i
$603$		0			0
$604$	−9.10189e6	+	5.87236e6i	−1.01517	+	0.654969i
$605$		−	2.47834e6i		−	0.275279i
$606$		0			0
$607$	−7.09850e6			−0.781978			−0.390989	−	0.920395i	$-0.627867\pi$
$607$	−7.09850e6			−0.781978			−0.390989	+	0.920395i	$0.627867\pi$
$608$	5.04915e6	+	6.68264e6i	0.553935	+	0.733144i
$609$		0			0
$610$	1.45567e6	−	2.67151e6i	0.158394	−	0.290691i
$611$			2.75465e6i			0.298513i
$612$		0			0
$613$	11324.6			0.00121722			0.000608612	−	1.00000i	$-0.499806\pi$
$613$	11324.6			0.00121722			0.000608612		1.00000i	$0.499806\pi$
$614$	−1.30818e6	+	2.40082e6i	−0.140038	+	0.257004i
$615$		0			0
$616$	−3.13471e6	−	5.54830e6i	−0.332848	−	0.589126i
$617$	−6.35901e6			−0.672476			−0.336238	−	0.941777i	$-0.609155\pi$
$617$	−6.35901e6			−0.672476			−0.336238	+	0.941777i	$0.609155\pi$
$618$		0			0
$619$	−1.53359e7			−1.60873			−0.804365	−	0.594135i	$-0.797494\pi$
$619$	−1.53359e7			−1.60873			−0.804365	+	0.594135i	$0.797494\pi$
$620$	1.38219e6	−	891761.i	0.144407	−	0.0931685i
$621$		0			0
$622$	−4.01215e6	+	7.36329e6i	−0.415816	+	0.763125i
$623$	1.76487e6	+	3.74682e6i	0.182176	+	0.386761i
$624$		0			0
$625$	2.86141e6			0.293009
$626$	−4.34301e6	−	2.36644e6i	−0.442950	−	0.241357i
$627$		0			0
$628$	−1.59185e7	+	1.02703e7i	−1.61066	+	1.03916i
$629$		−	1.79024e7i		−	1.80420i
$630$		0			0
$631$		−	2.80461e6i		−	0.280413i	−0.990122	−	0.140207i	$-0.955223\pi$
$631$		−	2.80461e6i		−	0.280413i	0.990122	−	0.140207i	$-0.0447767\pi$
$632$	1.19503e6	+	1.61040e7i	0.119011	+	1.60377i
$633$		0			0
$634$	3.58639e6	−	6.58192e6i	0.354352	−	0.650324i
$635$	1.99279e6			0.196122
$636$		0			0
$637$	−2.33609e6	−	1.92958e6i	−0.228109	−	0.188415i
$638$	−5.66871e6	−	3.08880e6i	−0.551357	−	0.300427i
$639$		0			0
$640$	4.94112e6	+	1.80794e6i	0.476843	+	0.174475i
$641$	6.37046e6			0.612386			0.306193	−	0.951969i	$-0.400945\pi$
$641$	6.37046e6			0.612386			0.306193	+	0.951969i	$0.400945\pi$
$642$		0			0
$643$	1.01925e7			0.972198			0.486099	−	0.873904i	$-0.338419\pi$
$643$	1.01925e7			0.972198			0.486099	+	0.873904i	$0.338419\pi$
$644$	3.65720e6	−	5.86440e6i	0.347484	−	0.557197i
$645$		0			0
$646$	1.50699e7	+	8.21137e6i	1.42079	+	0.774166i
$647$	−1.45811e7			−1.36940			−0.684698	−	0.728827i	$-0.740066\pi$
$647$	−1.45811e7			−1.36940			−0.684698	+	0.728827i	$0.740066\pi$
$648$		0			0
$649$			3.88826e6i			0.362362i
$650$	2.07695e6	+	1.13170e6i	0.192816	+	0.105063i
$651$		0			0
$652$	−6.88302e6	+	4.44079e6i	−0.634103	+	0.409111i
$653$	−1.59522e6			−0.146399			−0.0731996	−	0.997317i	$-0.523321\pi$
$653$	−1.59522e6			−0.146399			−0.0731996	+	0.997317i	$0.523321\pi$
$654$		0			0
$655$		−	1.79674e6i		−	0.163637i
$656$	1.92630e7	+	8.71432e6i	1.74769	+	0.790631i
$657$		0			0
$658$	−657442.	+	1.11864e7i	−0.0591960	+	1.00723i
$659$		−	5.66808e6i		−	0.508419i	−0.967149	−	0.254210i	$-0.918185\pi$
$659$		−	5.66808e6i		−	0.508419i	0.967149	−	0.254210i	$-0.0818154\pi$
$660$		0			0
$661$		−	2.08220e7i		−	1.85361i	−0.375541	−	0.926806i	$-0.622543\pi$
$661$		−	2.08220e7i		−	1.85361i	0.375541	−	0.926806i	$-0.377457\pi$
$662$	129817.	+	70735.6i	0.0115130	+	0.00627326i
$663$		0			0
$664$	1.23996e7	−	920142.i	1.09141	−	0.0809906i
$665$	−2.26730e6	−	4.81349e6i	−0.198818	−	0.422091i
$666$		0			0
$667$		−	7.00135e6i		−	0.609351i
$668$	8.94386e6	+	1.38626e7i	0.775504	+	1.20200i
$669$		0			0
$670$	4.46927e6	−	8.20221e6i	0.384635	−	0.705901i
$671$	5.14514e6			0.441155
$672$		0			0
$673$	−1.63494e7			−1.39144			−0.695720	−	0.718313i	$-0.744915\pi$
$673$	−1.63494e7			−1.39144			−0.695720	+	0.718313i	$0.744915\pi$
$674$	−3.19875e6	+	5.87049e6i	−0.271225	+	0.497765i
$675$		0			0
$676$	−5.87751e6	−	9.10987e6i	−0.494683	−	0.766736i
$677$		−	1.27172e7i		−	1.06640i	−0.845991	−	0.533198i	$-0.820990\pi$
$677$		−	1.27172e7i		−	1.06640i	0.845991	−	0.533198i	$-0.179010\pi$
$678$		0			0
$679$	6.14187e6	+	1.30392e7i	0.511242	+	1.08537i
$680$	1.07513e7	−	797824.i	0.891639	−	0.0661660i
$681$		0			0
$682$	2.44271e6	+	1.33100e6i	0.201100	+	0.109576i
$683$		−	5.60180e6i		−	0.459490i	−0.973251	−	0.229745i	$-0.926211\pi$
$683$		−	5.60180e6i		−	0.459490i	0.973251	−	0.229745i	$-0.0737891\pi$
$684$		0			0
$685$		−	21275.0i		−	0.00173238i
$686$	−9.02618e6	−	8.39345e6i	−0.732308	−	0.680973i
$687$		0			0
$688$	1.01640e7	+	4.59805e6i	0.818639	+	0.370341i
$689$		−	3.65914e6i		−	0.293651i
$690$		0			0
$691$	7.62765e6			0.607709			0.303855	−	0.952718i	$-0.401726\pi$
$691$	7.62765e6			0.607709			0.303855	+	0.952718i	$0.401726\pi$
$692$	998938.	−	644495.i	0.0793000	−	0.0511628i
$693$		0			0
$694$	2.69067e6	+	1.46611e6i	0.212061	+	0.115549i
$695$			9.61362e6i			0.754962i
$696$		0			0
$697$	4.33211e7			3.37767
$698$	−1.85817e7	−	1.01249e7i	−1.44360	−	0.786596i
$699$		0			0
$700$	8.16425e6	+	5.09146e6i	0.629755	+	0.392733i
$701$	1.48602e7			1.14217			0.571083	−	0.820893i	$-0.306524\pi$
$701$	1.48602e7			1.14217			0.571083	+	0.820893i	$0.306524\pi$
$702$		0			0
$703$	1.23370e7			0.941501
$704$	1.31337e6	+	8.80062e6i	0.0998747	+	0.669240i
$705$		0			0
$706$	2.06864e6	+	1.12717e6i	0.156197	+	0.0851097i
$707$	4.98225e6	+	1.05773e7i	0.374867	+	0.795844i
$708$		0			0
$709$	1.36416e7			1.01917			0.509587	−	0.860419i	$-0.329798\pi$
$709$	1.36416e7			1.01917			0.509587	+	0.860419i	$0.329798\pi$
$710$	−3.51925e6	+	6.45870e6i	−0.262002	+	0.480838i
$711$		0			0
$712$	−427965.	−	5.76717e6i	−0.0316380	−	0.426347i
$713$			3.01696e6i			0.222252i
$714$		0			0
$715$		−	1.38956e6i		−	0.101651i
$716$	−3.84968e6	+	2.48374e6i	−0.280635	+	0.181060i
$717$		0			0
$718$	−1.38242e7	−	7.53263e6i	−1.00076	−	0.545300i
$719$	2.34845e6			0.169418			0.0847088	−	0.996406i	$-0.473004\pi$
$719$	2.34845e6			0.169418			0.0847088	+	0.996406i	$0.473004\pi$
$720$		0			0
$721$	−3.05361e6	+	1.43834e6i	−0.218763	+	0.103044i
$722$	1.04319e6	−	1.91451e6i	0.0744765	−	0.136683i
$723$		0			0
$724$	1.26639e7	−	8.17053e6i	0.897888	−	0.579300i
$725$	9.74709e6			0.688700
$726$		0			0
$727$	−2.45752e7			−1.72449			−0.862246	−	0.506490i	$-0.830943\pi$
$727$	−2.45752e7			−1.72449			−0.862246	+	0.506490i	$0.830943\pi$
$728$	2.08112e6	+	3.68349e6i	0.145535	+	0.257591i
$729$		0			0
$730$	1.97559e6	−	3.62569e6i	0.137211	−	0.251816i
$731$	2.28581e7			1.58214
$732$		0			0
$733$		−	1.80954e7i		−	1.24396i	−0.783032	−	0.621982i	$-0.786328\pi$
$733$		−	1.80954e7i		−	1.24396i	0.783032	−	0.621982i	$-0.213672\pi$
$734$	1.29986e7	−	2.38556e7i	0.890544	−	1.63437i
$735$		0			0
$736$	−7.69963e6	+	5.81755e6i	−0.523933	+	0.395863i
$737$	1.57969e7			1.07128
$738$		0			0
$739$			2.37056e7i			1.59676i	0.602151	+	0.798382i	$0.294310\pi$
$739$			2.37056e7i			1.59676i	−0.602151	+	0.798382i	$0.705690\pi$
$740$	6.51221e6	−	4.20155e6i	0.437169	−	0.282053i
$741$		0			0
$742$	873312.	−	1.48595e7i	0.0582317	−	0.990819i
$743$		−	7.66583e6i		−	0.509433i	−0.967016	−	0.254717i	$-0.918018\pi$
$743$		−	7.66583e6i		−	0.509433i	0.967016	−	0.254717i	$-0.0819822\pi$
$744$		0			0
$745$			9.65070e6i			0.637042i
$746$	773419.	−	1.41941e6i	0.0508824	−	0.0933818i
$747$		0			0
$748$	9.88442e6	+	1.53204e7i	0.645948	+	1.00119i
$749$	1.50493e6	+	3.19497e6i	0.0980192	+	0.208095i
$750$		0			0
$751$		−	2.68186e7i		−	1.73515i	−0.497310	−	0.867573i	$-0.665679\pi$
$751$		−	2.68186e7i		−	1.73515i	0.497310	−	0.867573i	$-0.334321\pi$
$752$	6.44911e6	−	1.42557e7i	0.415867	−	0.919274i
$753$		0			0
$754$	3.76343e6	+	2.05064e6i	0.241077	+	0.131359i
$755$	−9.60809e6			−0.613437
$756$		0			0
$757$	−1.38220e7			−0.876661			−0.438330	−	0.898814i	$-0.644430\pi$
$757$	−1.38220e7			−0.876661			−0.438330	+	0.898814i	$0.644430\pi$
$758$	−1.09284e6	−	595472.i	−0.0690848	−	0.0376433i
$759$		0			0
$760$	549802.	+	7.40901e6i	0.0345281	+	0.465293i
$761$		−	8.75585e6i		−	0.548071i	−0.961720	−	0.274035i	$-0.911641\pi$
$761$		−	8.75585e6i		−	0.548071i	0.961720	−	0.274035i	$-0.0883585\pi$
$762$		0			0
$763$	5.65152e6	−	2.66204e6i	0.351442	−	0.165540i
$764$	−610011.	+	393567.i	−0.0378098	+	0.0243941i
$765$		0			0
$766$	−1.00908e7	+	1.85192e7i	−0.621376	+	1.14038i
$767$		−	2.58139e6i		−	0.158440i
$768$		0			0
$769$		−	2.57987e7i		−	1.57319i	−0.617466	−	0.786597i	$-0.711841\pi$
$769$		−	2.57987e7i		−	1.57319i	0.617466	−	0.786597i	$-0.288159\pi$
$770$	331640.	−	5.64290e6i	0.0201577	−	0.342985i
$771$		0			0
$772$	3.32855e6	+	5.15910e6i	0.201007	+	0.311552i
$773$		−	1.88397e7i		−	1.13403i	−0.823706	−	0.567017i	$-0.808097\pi$
$773$		−	1.88397e7i		−	1.13403i	0.823706	−	0.567017i	$-0.191903\pi$
$774$		0			0
$775$	−4.20013e6			−0.251194
$776$	−1.48935e6	−	2.00702e7i	−0.0887857	−	1.19646i
$777$		0			0
$778$	−7.69809e6	+	1.41279e7i	−0.455967	+	0.836813i
$779$			2.98537e7i			1.76260i
$780$		0			0
$781$	−1.24390e7			−0.729723
$782$	−9.46101e6	+	1.73633e7i	−0.553249	+	1.01535i
$783$		0			0
$784$	7.57215e6	+	1.54551e7i	0.439976	+	0.898009i
$785$	−1.68038e7			−0.973270
$786$		0			0
$787$	9.08065e6			0.522613			0.261306	−	0.965256i	$-0.415847\pi$
$787$	9.08065e6			0.522613			0.261306	+	0.965256i	$0.415847\pi$
$788$	2.19947e6	+	3.40907e6i	0.126183	+	0.195578i
$789$		0			0
$790$	−6.85350e6	+	1.25779e7i	−0.390701	+	0.717033i
$791$	−2.56382e7	+	1.20764e7i	−1.45695	+	0.686269i
$792$		0			0
$793$	−3.41583e6			−0.192892
$794$	8.42436e6	+	4.59031e6i	0.474226	+	0.258399i
$795$		0			0
$796$	−828512.	−	1.28415e6i	−0.0463464	−	0.0718348i
$797$			1.78683e7i			0.996409i	0.867060	+	0.498204i	$0.166007\pi$
$797$			1.78683e7i			0.996409i	−0.867060	+	0.498204i	$0.833993\pi$
$798$		0			0
$799$		−	3.20602e7i		−	1.77664i
$800$	−8.09903e6	−	1.07192e7i	−0.447412	−	0.592159i
$801$		0			0
$802$	1.22215e7	−	2.24295e7i	0.670948	−	1.23135i
$803$	6.98282e6			0.382157
$804$		0			0
$805$	5.54603e6	−	2.61235e6i	0.301643	−	0.142083i
$806$	−1.62171e6	−	883644.i	−0.0879294	−	0.0479115i
$807$		0			0
$808$	−1.20815e6	−	1.62808e7i	−0.0651019	−	0.877300i
$809$	−7.98209e6			−0.428790			−0.214395	−	0.976747i	$-0.568778\pi$
$809$	−7.98209e6			−0.428790			−0.214395	+	0.976747i	$0.568778\pi$
$810$		0			0
$811$	7.67840e6			0.409939			0.204969	−	0.978768i	$-0.434291\pi$
$811$	7.67840e6			0.409939			0.204969	+	0.978768i	$0.434291\pi$
$812$	1.47936e7	+	9.22570e6i	0.787379	+	0.491032i
$813$		0			0
$814$	1.15089e7	+	6.27104e6i	0.608797	+	0.331725i
$815$	−7.26582e6			−0.383169
$816$		0			0
$817$			1.57521e7i			0.825626i
$818$	−4.52686e6	−	2.46662e6i	−0.236545	−	0.128890i
$819$		0			0
$820$	1.01671e7	+	1.57586e7i	0.528037	+	0.818433i
$821$	−2.51595e7			−1.30270			−0.651350	−	0.758778i	$-0.725797\pi$
$821$	−2.51595e7			−1.30270			−0.651350	+	0.758778i	$0.725797\pi$
$822$		0			0
$823$			2.68144e7i			1.37997i	0.723826	+	0.689983i	$0.242382\pi$
$823$			2.68144e7i			1.37997i	−0.723826	+	0.689983i	$0.757618\pi$
$824$	4.70016e6	−	348786.i	0.241154	−	0.0178954i
$825$		0			0
$826$	616091.	−	1.04829e7i	0.0314192	−	0.534601i
$827$		−	3.63867e7i		−	1.85003i	−0.379932	−	0.925014i	$-0.624053\pi$
$827$		−	3.63867e7i		−	1.85003i	0.379932	−	0.925014i	$-0.375947\pi$
$828$		0			0
$829$		−	1.21755e6i		−	0.0615318i	−0.999527	−	0.0307659i	$-0.990205\pi$
$829$		−	1.21755e6i		−	0.0615318i	0.999527	−	0.0307659i	$-0.00979464\pi$
$830$	9.68461e6	+	5.27701e6i	0.487963	+	0.265884i
$831$		0			0
$832$	−871940.	−	5.84269e6i	−0.0436695	−	0.292620i
$833$	2.71887e7	+	2.24576e7i	1.35761	+	1.12137i
$834$		0			0
$835$			1.46335e7i			0.726329i
$836$	−1.05577e7	+	6.81162e6i	−0.522460	+	0.337081i
$837$		0			0
$838$	−188468.	+	345885.i	−0.00927101	+	0.0170146i
$839$	2.09675e7			1.02835			0.514176	−	0.857684i	$-0.328098\pi$
$839$	2.09675e7			1.02835			0.514176	+	0.857684i	$0.328098\pi$
$840$		0			0
$841$	−2.84945e6			−0.138922
$842$	9.79915e6	−	1.79839e7i	0.476330	−	0.874183i
$843$		0			0
$844$	−8.52987e6	+	5.50331e6i	−0.412180	+	0.265930i
$845$		−	9.61652e6i		−	0.463315i
$846$		0			0
$847$	−1.02402e7	+	4.82347e6i	−0.490458	+	0.231021i
$848$	−8.56666e6	+	1.89366e7i	−0.409093	+	0.904299i
$849$		0			0
$850$	−2.41727e7	−	1.31714e7i	−1.14757	−	0.625293i
$851$			1.42145e7i			0.672833i
$852$		0			0
$853$			1.70557e7i			0.802598i	0.915947	+	0.401299i	$0.131441\pi$
$853$			1.70557e7i			0.802598i	−0.915947	+	0.401299i	$0.868559\pi$
$854$	−1.38715e7	−	815243.i	−0.650845	−	0.0382510i
$855$		0			0
$856$	−364932.	−	4.91775e6i	−0.0170227	−	0.229394i
$857$			2.25388e7i			1.04828i	0.851631	+	0.524142i	$0.175614\pi$
$857$			2.25388e7i			1.04828i	−0.851631	+	0.524142i	$0.824386\pi$
$858$		0			0
$859$	3.25330e7			1.50433			0.752163	−	0.658977i	$-0.229011\pi$
$859$	3.25330e7			1.50433			0.752163	+	0.658977i	$0.229011\pi$
$860$	5.36462e6	+	8.31491e6i	0.247339	+	0.383364i
$861$		0			0
$862$	3.93239e6	+	2.14271e6i	0.180256	+	0.0982187i
$863$		−	2.91580e7i		−	1.33270i	−0.745641	−	0.666348i	$-0.767857\pi$
$863$		−	2.91580e7i		−	1.33270i	0.745641	−	0.666348i	$-0.232143\pi$
$864$		0			0
$865$	1.05449e6			0.0479185
$866$	1.63490e6	+	890833.i	0.0740792	+	0.0403647i
$867$		0			0
$868$	−6.37473e6	−	3.97546e6i	−0.287186	−	0.179097i
$869$	−2.42241e7			−1.08817
$870$		0			0
$871$	−1.04875e7			−0.468409
$872$	−8.69891e6	+	645522.i	−0.387413	+	0.0287488i
$873$		0			0
$874$	−1.19655e7	−	6.51983e6i	−0.529849	−	0.288707i
$875$	8.53707e6	+	1.81242e7i	0.376954	+	0.800275i
$876$		0			0
$877$	−2.01593e7			−0.885068			−0.442534	−	0.896752i	$-0.645920\pi$
$877$	−2.01593e7			−0.885068			−0.442534	+	0.896752i	$0.645920\pi$
$878$	−1.27565e7	+	2.34113e7i	−0.558462	+	1.02492i
$879$		0			0
$880$	−3.25319e6	+	7.19117e6i	−0.141613	+	0.313035i
$881$		−	1.13630e7i		−	0.493235i	−0.969113	−	0.246618i	$-0.920681\pi$
$881$		−	1.13630e7i		−	0.493235i	0.969113	−	0.246618i	$-0.0793192\pi$
$882$		0			0
$883$		−	3.80949e7i		−	1.64424i	−0.569314	−	0.822120i	$-0.692791\pi$
$883$		−	3.80949e7i		−	1.64424i	0.569314	−	0.822120i	$-0.307209\pi$
$884$	−6.56222e6	−	1.01711e7i	−0.282436	−	0.437763i
$885$		0			0
$886$	−1.19901e7	−	6.53325e6i	−0.513144	−	0.279605i
$887$	−2.78544e7			−1.18873			−0.594366	−	0.804195i	$-0.702597\pi$
$887$	−2.78544e7			−1.18873			−0.594366	+	0.804195i	$0.702597\pi$
$888$		0			0
$889$	−3.87846e6	−	8.23399e6i	−0.164590	−	0.349426i
$890$	2.45438e6	−	4.50439e6i	0.103864	−	0.190617i
$891$		0			0
$892$	−7.32712e6	−	1.13567e7i	−0.308334	−	0.477903i
$893$	2.20935e7			0.927120
$894$		0			0
$895$	−4.06378e6			−0.169579
$896$	−2.14644e6	−	2.39348e7i	−0.0893199	−	0.996003i
$897$		0			0
$898$	−7.81846e6	+	1.43488e7i	−0.323542	+	0.593779i
$899$	−7.61063e6			−0.314066
$900$		0			0
$901$			4.25871e7i			1.74770i
$902$	−1.51750e7	+	2.78499e7i	−0.621029	+	1.13974i
$903$		0			0
$904$	3.94627e7	−	2.92841e6i	1.60607	−	0.119182i
$905$	1.33682e7			0.542566
$906$		0			0
$907$			2.46521e7i			0.995028i	0.867456	+	0.497514i	$0.165754\pi$
$907$			2.46521e7i			0.995028i	−0.867456	+	0.497514i	$0.834246\pi$
$908$	6.64476e6	+	1.02991e7i	0.267463	+	0.414556i
$909$		0			0
$910$	−220174.	+	3.74629e6i	−0.00881380	+	0.149968i
$911$		−	7.97197e6i		−	0.318251i	−0.987258	−	0.159125i	$-0.949133\pi$
$911$		−	7.97197e6i		−	0.318251i	0.987258	−	0.159125i	$-0.0508674\pi$
$912$		0			0
$913$			1.86519e7i			0.740536i
$914$	1.03122e7	−	1.89255e7i	0.408307	−	0.749344i
$915$		0			0
$916$	−2.30232e7	+	1.48541e7i	−0.906625	+	0.584937i
$917$	−7.42392e6	+	3.49689e6i	−0.291548	+	0.137328i
$918$		0			0
$919$		−	2.11031e7i		−	0.824248i	−0.911128	−	0.412124i	$-0.864787\pi$
$919$		−	2.11031e7i		−	0.824248i	0.911128	−	0.412124i	$-0.135213\pi$
$920$	−8.53655e6	+	633473.i	−0.332516	+	0.0246751i
$921$		0			0
$922$	−2.63480e7	−	1.43567e7i	−1.02075	−	0.556194i
$923$	8.25819e6			0.319066
$924$		0			0
$925$	−1.97890e7			−0.760449
$926$	2.30337e7	+	1.25507e7i	0.882746	+	0.480996i
$927$		0			0
$928$	−1.46754e7	−	1.94232e7i	−0.559398	−	0.740373i
$929$			8.47045e6i			0.322009i	0.986954	+	0.161004i	$0.0514733\pi$
$929$			8.47045e6i			0.322009i	−0.986954	+	0.161004i	$0.948527\pi$
$930$		0			0
$931$	−1.54761e7	+	1.87365e7i	−0.585177	+	0.708457i
$932$	−5.63020e6	−	8.72656e6i	−0.212317	−	0.329081i
$933$		0			0
$934$	−5.20044e6	+	9.54410e6i	−0.195062	+	0.357987i
$935$			1.61724e7i			0.604988i
$936$		0			0
$937$			2.95834e7i			1.10077i	0.834909	+	0.550387i	$0.185520\pi$
$937$			2.95834e7i			1.10077i	−0.834909	+	0.550387i	$0.814480\pi$
$938$	−4.25889e7	−	2.50300e6i	−1.58048	−	0.0928868i
$939$		0			0
$940$	1.16623e7	−	7.52428e6i	0.430491	−	0.277744i
$941$			3.62480e7i			1.33447i	0.744846	+	0.667237i	$0.232523\pi$
$941$			3.62480e7i			1.33447i	−0.744846	+	0.667237i	$0.767477\pi$
$942$		0			0
$943$	−3.43970e7			−1.25962
$944$	−6.04348e6	+	1.33591e7i	−0.220728	+	0.487918i
$945$		0			0
$946$	−8.00697e6	+	1.46948e7i	−0.290898	+	0.533869i
$947$		−	2.19768e7i		−	0.796322i	−0.917316	−	0.398161i	$-0.869649\pi$
$947$		−	2.19768e7i		−	0.796322i	0.917316	−	0.398161i	$-0.130351\pi$
$948$		0			0
$949$	−4.63586e6			−0.167096
$950$	9.07673e6	−	1.66580e7i	0.326303	−	0.598846i
$951$		0			0
$952$	−2.42212e7	−	4.28704e7i	−0.866170	−	1.53308i
$953$	−2.02983e7			−0.723982			−0.361991	−	0.932182i	$-0.617903\pi$
$953$	−2.02983e7			−0.723982			−0.361991	+	0.932182i	$0.617903\pi$
$954$		0			0
$955$	−643936.			−0.0228473
$956$	5.75792e6	−	3.71489e6i	0.203761	−	0.131462i
$957$		0			0
$958$	1.41691e7	−	2.60038e7i	0.498802	−	0.915425i
$959$	−87905.9	+	41406.3i	−0.00308654	+	0.00145385i
$960$		0			0
$961$	−2.53496e7			−0.885449
$962$	−7.64070e6	−	4.16331e6i	−0.266192	−	0.145044i
$963$		0			0
$964$	1.17574e7	−	7.58567e6i	0.407493	−	0.262906i
$965$			5.44602e6i			0.188261i
$966$		0			0
$967$		−	8.30270e6i		−	0.285531i	−0.989757	−	0.142765i	$-0.954401\pi$
$967$		−	8.30270e6i		−	0.285531i	0.989757	−	0.142765i	$-0.0455995\pi$
$968$	1.57620e7	−	1.16965e6i	0.540657	−	0.0401206i
$969$		0			0
$970$	8.54143e6	−	1.56756e7i	0.291475	−	0.534928i
$971$	−3.20554e7			−1.09107			−0.545536	−	0.838088i	$-0.683674\pi$
$971$	−3.20554e7			−1.09107			−0.545536	+	0.838088i	$0.683674\pi$
$972$		0			0
$973$	3.97224e7	−	1.87105e7i	1.34510	−	0.633581i
$974$	2.47506e7	+	1.34863e7i	0.835967	+	0.455507i
$975$		0			0
$976$	1.76774e7	+	7.99704e6i	0.594012	+	0.268723i
$977$	−5.73398e7			−1.92185			−0.960926	−	0.276806i	$-0.910724\pi$
$977$	−5.73398e7			−1.92185			−0.960926	+	0.276806i	$0.910724\pi$
$978$		0			0
$979$	8.67515e6			0.289281
$980$	−1.78822e6	+	1.51609e7i	−0.0594780	+	0.504265i
$981$		0			0
$982$	−2.22620e7	−	1.21303e7i	−0.736692	−	0.401413i
$983$	2.32471e7			0.767335			0.383668	−	0.923471i	$-0.374661\pi$
$983$	2.32471e7			0.767335			0.383668	+	0.923471i	$0.374661\pi$
$984$		0			0
$985$			3.59867e6i			0.118182i
$986$	−4.38009e7	−	2.38665e7i	−1.43480	−	0.781800i
$987$		0			0
$988$	7.00920e6	−	4.52220e6i	0.228442	−	0.147386i
$989$	−1.81493e7			−0.590024
$990$		0			0
$991$			1.54996e7i			0.501343i	0.968072	+	0.250672i	$0.0806515\pi$
$991$			1.54996e7i			0.501343i	−0.968072	+	0.250672i	$0.919349\pi$
$992$	6.32381e6	+	8.36968e6i	0.204033	+	0.270041i
$993$		0			0
$994$	3.35359e7	+	1.97095e6i	1.07658	+	0.0632717i
$995$		−	1.35557e6i		−	0.0434075i
$996$		0			0
$997$			1.02461e7i			0.326452i	0.986589	+	0.163226i	$0.0521900\pi$
$997$			1.02461e7i			0.326452i	−0.986589	+	0.163226i	$0.947810\pi$
$998$	−4.34462e7	−	2.36732e7i	−1.38078	−	0.752370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.6.b.d.55.7		16
3.2	odd	2		28.6.d.b.27.9	✓	16
4.3	odd	2	inner	252.6.b.d.55.5		16
7.6	odd	2	inner	252.6.b.d.55.8		16
12.11	even	2		28.6.d.b.27.12	yes	16
21.20	even	2		28.6.d.b.27.10	yes	16
24.5	odd	2		448.6.f.d.447.13		16
24.11	even	2		448.6.f.d.447.3		16
28.27	even	2	inner	252.6.b.d.55.6		16
84.83	odd	2		28.6.d.b.27.11	yes	16
168.83	odd	2		448.6.f.d.447.14		16
168.125	even	2		448.6.f.d.447.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.d.b.27.9	✓	16	3.2	odd	2
28.6.d.b.27.10	yes	16	21.20	even	2
28.6.d.b.27.11	yes	16	84.83	odd	2
28.6.d.b.27.12	yes	16	12.11	even	2
252.6.b.d.55.5		16	4.3	odd	2	inner
252.6.b.d.55.6		16	28.27	even	2	inner
252.6.b.d.55.7		16	1.1	even	1	trivial
252.6.b.d.55.8		16	7.6	odd	2	inner
448.6.f.d.447.3		16	24.11	even	2
448.6.f.d.447.4		16	168.125	even	2
448.6.f.d.447.13		16	24.5	odd	2
448.6.f.d.447.14		16	168.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70662 + 4.96731i) q^{2} +(-17.3484 - 26.8893i) q^{4} -28.3847i q^{5} +(-117.282 + 55.2436i) q^{7} +(180.523 - 13.3961i) q^{8} +O(q^{10})\)	\(q+(-2.70662 + 4.96731i) q^{2} +(-17.3484 - 26.8893i) q^{4} -28.3847i q^{5} +(-117.282 + 55.2436i) q^{7} +(180.523 - 13.3961i) q^{8} +(140.996 + 76.8266i) q^{10} +271.548i q^{11} -180.279i q^{13} +(43.0265 - 732.102i) q^{14} +(-422.064 + 932.973i) q^{16} +2098.19i q^{17} -1445.92 q^{19} +(-763.243 + 492.430i) q^{20} +(-1348.86 - 734.977i) q^{22} -1665.96i q^{23} +2319.31 q^{25} +(895.504 + 487.948i) q^{26} +(3520.12 + 2195.25i) q^{28} +4202.58 q^{29} -1810.94 q^{31} +(-3492.00 - 4621.73i) q^{32} +(-10422.4 - 5679.00i) q^{34} +(1568.07 + 3329.02i) q^{35} -8532.29 q^{37} +(3913.55 - 7182.33i) q^{38} +(-380.244 - 5124.09i) q^{40} -20646.9i q^{41} -10894.2i q^{43} +(7301.72 - 4710.93i) q^{44} +(8275.37 + 4509.13i) q^{46} -15279.9 q^{47} +(10703.3 - 12958.2i) q^{49} +(-6277.49 + 11520.7i) q^{50} +(-4847.58 + 3127.56i) q^{52} +20297.1 q^{53} +7707.80 q^{55} +(-20432.1 + 11543.9i) q^{56} +(-11374.8 + 20875.5i) q^{58} +14318.9 q^{59} -18947.4i q^{61} +(4901.53 - 8995.51i) q^{62} +(32409.1 - 4836.61i) q^{64} -5117.17 q^{65} -58173.5i q^{67} +(56418.8 - 36400.3i) q^{68} +(-20780.5 - 1221.29i) q^{70} +45807.8i q^{71} -25714.9i q^{73} +(23093.7 - 42382.6i) q^{74} +(25084.4 + 38879.7i) q^{76} +(-15001.3 - 31847.8i) q^{77} +89207.5i q^{79} +(26482.1 + 11980.2i) q^{80} +(102560. + 55883.3i) q^{82} +68687.3 q^{83} +59556.5 q^{85} +(54114.8 + 29486.4i) q^{86} +(3637.68 + 49020.6i) q^{88} -31947.0i q^{89} +(9959.27 + 21143.6i) q^{91} +(-44796.5 + 28901.9i) q^{92} +(41356.9 - 75900.1i) q^{94} +41041.9i q^{95} -111178. i q^{97} +(35397.6 + 88239.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8	\( 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8} - 1176 q^{14} - 3008 q^{16} + 1552 q^{22} - 9776 q^{25} - 14672 q^{28} - 26592 q^{29} - 11648 q^{32} - 26272 q^{37} + 12256 q^{44} + 20208 q^{46} + 8848 q^{49} - 5992 q^{50} + 41888 q^{53} - 38304 q^{56} - 144400 q^{58} + 45312 q^{64} - 66688 q^{65} + 79296 q^{70} - 348464 q^{74} - 320992 q^{77} + 78080 q^{85} + 78448 q^{86} - 66112 q^{88} - 446944 q^{92} - 224840 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8 - 1176 * q^14 - 3008 * q^16 + 1552 * q^22 - 9776 * q^25 - 14672 * q^28 - 26592 * q^29 - 11648 * q^32 - 26272 * q^37 + 12256 * q^44 + 20208 * q^46 + 8848 * q^49 - 5992 * q^50 + 41888 * q^53 - 38304 * q^56 - 144400 * q^58 + 45312 * q^64 - 66688 * q^65 + 79296 * q^70 - 348464 * q^74 - 320992 * q^77 + 78080 * q^85 + 78448 * q^86 - 66112 * q^88 - 446944 * q^92 - 224840 * q^98

Introduction

L-functions

Modular forms

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Database

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