LMFDB - Embedded newform 392.6.i.h.361.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,6,Mod(177,392)] 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("392.177"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	392.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-14,0,42,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$62.8704573667$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-3.22311 + 5.58259i$ of defining polynomial
Character	$\chi$	$=$	392.361
Dual form			392.6.i.h.177.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.44622 - 5.96903i) q^{3} +(-24.2311 - 41.9695i) q^{5} +(97.7471 + 169.303i) q^{9} +(81.7529 - 141.600i) q^{11} +120.828 q^{13} -334.023 q^{15} +(39.0960 - 67.7162i) q^{17} +(-1132.50 - 1961.55i) q^{19} +(1225.98 + 2123.45i) q^{23} +(388.207 - 672.394i) q^{25} +3022.30 q^{27} +6985.27 q^{29} +(1397.02 - 2419.70i) q^{31} +(-563.477 - 975.971i) q^{33} +(-4729.72 - 8192.11i) q^{37} +(416.402 - 721.229i) q^{39} -10088.5 q^{41} -6934.29 q^{43} +(4737.04 - 8204.80i) q^{45} +(582.882 + 1009.58i) q^{47} +(-269.467 - 466.730i) q^{51} +(-4281.21 + 7415.27i) q^{53} -7923.85 q^{55} -15611.4 q^{57} +(3110.13 - 5386.90i) q^{59} +(-20964.4 - 36311.5i) q^{61} +(-2927.81 - 5071.11i) q^{65} +(-906.046 + 1569.32i) q^{67} +16900.0 q^{69} -56823.3 q^{71} +(-22149.7 + 38364.5i) q^{73} +(-2675.69 - 4634.44i) q^{75} +(-17456.2 - 30235.1i) q^{79} +(-13337.0 + 23100.4i) q^{81} +39652.9 q^{83} -3789.36 q^{85} +(24072.8 - 41695.3i) q^{87} +(-63149.7 - 109378. i) q^{89} +(-9628.85 - 16677.7i) q^{93} +(-54883.4 + 95060.8i) q^{95} +145513. q^{97} +31964.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 14 q^{3} + 42 q^{5} + 2 q^{9} + 716 q^{11} + 1428 q^{13} - 4448 q^{15} - 1344 q^{17} - 1946 q^{19} + 1792 q^{23} - 4282 q^{25} + 3976 q^{27} - 2400 q^{29} - 6804 q^{31} + 10416 q^{33} - 14640 q^{37}+ \cdots - 149880 q^{99}+O(q^{100}) $ 4 * q - 14 * q^3 + 42 * q^5 + 2 * q^9 + 716 * q^11 + 1428 * q^13 - 4448 * q^15 - 1344 * q^17 - 1946 * q^19 + 1792 * q^23 - 4282 * q^25 + 3976 * q^27 - 2400 * q^29 - 6804 * q^31 + 10416 * q^33 - 14640 * q^37 - 11560 * q^39 - 15792 * q^41 + 1048 * q^43 + 26978 * q^45 - 18396 * q^47 - 30252 * q^51 - 45132 * q^53 + 84112 * q^55 - 44552 * q^57 + 22582 * q^59 - 52822 * q^61 + 47804 * q^65 - 9848 * q^67 + 61376 * q^69 - 1680 * q^71 - 122052 * q^73 - 111034 * q^75 - 31704 * q^79 + 41954 * q^81 - 73948 * q^83 - 264888 * q^85 + 219156 * q^87 - 210588 * q^89 - 219784 * q^93 - 138624 * q^95 + 88480 * q^97 - 149880 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.44622	−	5.96903i	0.221075	−	0.382914i	−0.734060	−	0.679085i	$-0.762377\pi$
$3$	3.44622	−	5.96903i	0.221075	−	0.382914i	0.955135	+	0.296172i	$0.0957100\pi$
$4$		0			0
$5$	−24.2311	−	41.9695i	−0.433459	−	0.750773i	0.563709	−	0.825973i	$-0.309374\pi$
$5$	−24.2311	−	41.9695i	−0.433459	−	0.750773i	−0.997168	+	0.0751998i	$0.976041\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	97.7471	+	169.303i	0.402251	+	0.696720i
$10$		0			0
$11$	81.7529	−	141.600i	0.203714	−	0.352843i	−0.746008	−	0.665937i	$-0.768032\pi$
$11$	81.7529	−	141.600i	0.203714	−	0.352843i	0.949722	+	0.313093i	$0.101365\pi$
$12$		0			0
$13$	120.828			0.198295			0.0991473	−	0.995073i	$-0.468389\pi$
$13$	120.828			0.198295			0.0991473	+	0.995073i	$0.468389\pi$
$14$		0			0
$15$	−334.023			−0.383308
$16$		0			0
$17$	39.0960	−	67.7162i	0.0328103	−	0.0568291i	−0.849154	−	0.528145i	$-0.822888\pi$
$17$	39.0960	−	67.7162i	0.0328103	−	0.0568291i	0.881964	+	0.471316i	$0.156221\pi$
$18$		0			0
$19$	−1132.50	−	1961.55i	−0.719704	−	1.24656i	−0.961117	−	0.276141i	$-0.910944\pi$
$19$	−1132.50	−	1961.55i	−0.719704	−	1.24656i	0.241414	−	0.970422i	$-0.422389\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1225.98	+	2123.45i	0.483240	+	0.836996i	0.999815	−	0.0192461i	$-0.00612660\pi$
$23$	1225.98	+	2123.45i	0.483240	+	0.836996i	−0.516575	+	0.856242i	$0.672793\pi$
$24$		0			0
$25$	388.207	−	672.394i	0.124226	−	0.215166i
$26$		0			0
$27$	3022.30			0.797862
$28$		0			0
$29$	6985.27			1.54237			0.771185	−	0.636611i	$-0.219664\pi$
$29$	6985.27			1.54237			0.771185	+	0.636611i	$0.219664\pi$
$30$		0			0
$31$	1397.02	−	2419.70i	0.261094	−	0.452228i	−0.705439	−	0.708771i	$-0.749250\pi$
$31$	1397.02	−	2419.70i	0.261094	−	0.452228i	0.966533	+	0.256543i	$0.0825834\pi$
$32$		0			0
$33$	−563.477	−	975.971i	−0.0900724	−	0.156010i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4729.72	−	8192.11i	−0.567977	−	0.983765i	−0.996766	−	0.0803606i	$-0.974393\pi$
$37$	−4729.72	−	8192.11i	−0.567977	−	0.983765i	0.428789	−	0.903405i	$-0.358941\pi$
$38$		0			0
$39$	416.402	−	721.229i	0.0438380	−	0.0759297i
$40$		0			0
$41$	−10088.5			−0.937271			−0.468636	−	0.883392i	$-0.655254\pi$
$41$	−10088.5			−0.937271			−0.468636	+	0.883392i	$0.655254\pi$
$42$		0			0
$43$	−6934.29			−0.571914			−0.285957	−	0.958242i	$-0.592311\pi$
$43$	−6934.29			−0.571914			−0.285957	+	0.958242i	$0.592311\pi$
$44$		0			0
$45$	4737.04	−	8204.80i	0.348719	−	0.603999i
$46$		0			0
$47$	582.882	+	1009.58i	0.0384889	+	0.0666648i	0.884628	−	0.466297i	$-0.154412\pi$
$47$	582.882	+	1009.58i	0.0384889	+	0.0666648i	−0.846139	+	0.532962i	$0.821079\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−269.467	−	466.730i	−0.0145071	−	0.0251270i
$52$		0			0
$53$	−4281.21	+	7415.27i	−0.209352	+	0.362608i	−0.951511	−	0.307616i	$-0.900469\pi$
$53$	−4281.21	+	7415.27i	−0.209352	+	0.362608i	0.742159	+	0.670224i	$0.233802\pi$
$54$		0			0
$55$	−7923.85			−0.353207
$56$		0			0
$57$	−15611.4			−0.636435
$58$		0			0
$59$	3110.13	−	5386.90i	0.116318	−	0.201469i	−0.801988	−	0.597341i	$-0.796224\pi$
$59$	3110.13	−	5386.90i	0.116318	−	0.201469i	0.918306	+	0.395871i	$0.129557\pi$
$60$		0			0
$61$	−20964.4	−	36311.5i	−0.721371	−	1.24945i	−0.960451	−	0.278451i	$-0.910179\pi$
$61$	−20964.4	−	36311.5i	−0.721371	−	1.24945i	0.239080	−	0.971000i	$-0.423154\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2927.81	−	5071.11i	−0.0859526	−	0.148874i
$66$		0			0
$67$	−906.046	+	1569.32i	−0.0246583	+	0.0427095i	−0.878091	−	0.478493i	$-0.841183\pi$
$67$	−906.046	+	1569.32i	−0.0246583	+	0.0427095i	0.853433	+	0.521203i	$0.174516\pi$
$68$		0			0
$69$	16900.0			0.427329
$70$		0			0
$71$	−56823.3			−1.33777			−0.668884	−	0.743367i	$-0.733228\pi$
$71$	−56823.3			−1.33777			−0.668884	+	0.743367i	$0.733228\pi$
$72$		0			0
$73$	−22149.7	+	38364.5i	−0.486476	+	0.842602i	−0.999879	−	0.0155461i	$-0.995051\pi$
$73$	−22149.7	+	38364.5i	−0.486476	+	0.842602i	0.513403	+	0.858148i	$0.328385\pi$
$74$		0			0
$75$	−2675.69	−	4634.44i	−0.0549266	−	0.0951357i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−17456.2	−	30235.1i	−0.314690	−	0.545058i	0.664682	−	0.747127i	$-0.268567\pi$
$79$	−17456.2	−	30235.1i	−0.314690	−	0.545058i	−0.979371	+	0.202068i	$0.935234\pi$
$80$		0			0
$81$	−13337.0	+	23100.4i	−0.225864	+	0.391208i
$82$		0			0
$83$	39652.9			0.631800			0.315900	−	0.948793i	$-0.397694\pi$
$83$	39652.9			0.631800			0.315900	+	0.948793i	$0.397694\pi$
$84$		0			0
$85$	−3789.36			−0.0568877
$86$		0			0
$87$	24072.8	−	41695.3i	0.340980	−	0.590594i
$88$		0			0
$89$	−63149.7	−	109378.i	−0.845077	−	1.46372i	−0.885554	−	0.464536i	$-0.846221\pi$
$89$	−63149.7	−	109378.i	−0.845077	−	1.46372i	0.0404777	−	0.999180i	$-0.487112\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9628.85	−	16677.7i	−0.115443	−	0.199953i
$94$		0			0
$95$	−54883.4	+	95060.8i	−0.623924	+	1.08067i
$96$		0			0
$97$	145513.			1.57026			0.785130	−	0.619331i	$-0.212596\pi$
$97$	145513.			1.57026			0.785130	+	0.619331i	$0.212596\pi$
$98$		0			0
$99$	31964.4			0.327777
$100$		0			0
$101$	49772.7	−	86208.9i	0.485499	−	0.840909i	−0.514362	−	0.857573i	$-0.671971\pi$
$101$	49772.7	−	86208.9i	0.485499	−	0.840909i	0.999861	+	0.0166644i	$0.00530468\pi$
$102$		0			0
$103$	−64895.6	−	112402.i	−0.602729	−	1.04396i	−0.992406	−	0.123005i	$-0.960747\pi$
$103$	−64895.6	−	112402.i	−0.602729	−	1.04396i	0.389677	−	0.920952i	$-0.372587\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−109406.	−	189496.i	−0.923804	−	1.60008i	−0.793473	−	0.608606i	$-0.791729\pi$
$107$	−109406.	−	189496.i	−0.923804	−	1.60008i	−0.130332	−	0.991470i	$-0.541604\pi$
$108$		0			0
$109$	−100814.	+	174614.i	−0.812743	+	1.40771i	0.0981950	+	0.995167i	$0.468693\pi$
$109$	−100814.	+	174614.i	−0.812743	+	1.40771i	−0.910938	+	0.412544i	$0.864640\pi$
$110$		0			0
$111$	−65198.6			−0.502263
$112$		0			0
$113$	31803.9			0.234306			0.117153	−	0.993114i	$-0.462623\pi$
$113$	31803.9			0.234306			0.117153	+	0.993114i	$0.462623\pi$
$114$		0			0
$115$	59413.6	−	102907.i	0.418930	−	0.725607i
$116$		0			0
$117$	11810.6	+	20456.6i	0.0797643	+	0.138156i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	67158.4	+	116322.i	0.417001	+	0.722267i
$122$		0			0
$123$	−34767.1	+	60218.3i	−0.207207	+	0.358894i
$124$		0			0
$125$	−189071.			−1.08231
$126$		0			0
$127$	−318115.			−1.75015			−0.875075	−	0.483988i	$-0.839188\pi$
$127$	−318115.			−1.75015			−0.875075	+	0.483988i	$0.839188\pi$
$128$		0			0
$129$	−23897.1	+	41391.0i	−0.126436	+	0.218994i
$130$		0			0
$131$	−152597.	−	264306.i	−0.776905	−	1.34564i	−0.933717	−	0.358011i	$-0.883455\pi$
$131$	−152597.	−	264306.i	−0.776905	−	1.34564i	0.156812	−	0.987628i	$-0.449878\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−73233.6	−	126844.i	−0.345841	−	0.599014i
$136$		0			0
$137$	−90022.3	+	155923.i	−0.409778	+	0.709757i	−0.994865	−	0.101214i	$-0.967727\pi$
$137$	−90022.3	+	155923.i	−0.409778	+	0.709757i	0.585086	+	0.810971i	$0.301061\pi$
$138$		0			0
$139$	323204.			1.41886			0.709430	−	0.704776i	$-0.248953\pi$
$139$	323204.			1.41886			0.709430	+	0.704776i	$0.248953\pi$
$140$		0			0
$141$	8034.96			0.0340358
$142$		0			0
$143$	9878.08	−	17109.3i	0.0403954	−	0.0699669i
$144$		0			0
$145$	−169261.	−	293169.i	−0.668554	−	1.15797i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−147079.	−	254749.i	−0.542733	−	0.940041i	−0.998746	−	0.0500677i	$-0.984056\pi$
$149$	−147079.	−	254749.i	−0.542733	−	0.940041i	0.456013	−	0.889973i	$-0.349277\pi$
$150$		0			0
$151$	167481.	−	290085.i	0.597754	−	1.03534i	−0.395397	−	0.918510i	$-0.629393\pi$
$151$	167481.	−	290085.i	0.597754	−	1.03534i	0.993152	−	0.116831i	$-0.0372736\pi$
$152$		0			0
$153$	15286.1			0.0527919
$154$		0			0
$155$	−135405.			−0.452694
$156$		0			0
$157$	−72574.9	+	125703.i	−0.234984	+	0.407003i	−0.959268	−	0.282498i	$-0.908837\pi$
$157$	−72574.9	+	125703.i	−0.234984	+	0.407003i	0.724284	+	0.689501i	$0.242170\pi$
$158$		0			0
$159$	29508.0	+	51109.3i	0.0925650	+	0.160327i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	88110.6	+	152612.i	0.259752	+	0.449904i	0.966175	−	0.257886i	$-0.0830258\pi$
$163$	88110.6	+	152612.i	0.259752	+	0.449904i	−0.706423	+	0.707790i	$0.749692\pi$
$164$		0			0
$165$	−27307.4	+	47297.7i	−0.0780854	+	0.135248i
$166$		0			0
$167$	45460.7			0.126138			0.0630689	−	0.998009i	$-0.479911\pi$
$167$	45460.7			0.126138			0.0630689	+	0.998009i	$0.479911\pi$
$168$		0			0
$169$	−356693.			−0.960679
$170$		0			0
$171$	221397.	−	383471.i	0.579004	−	1.00286i
$172$		0			0
$173$	−102921.	−	178264.i	−0.261450	−	0.452844i	0.705178	−	0.709031i	$-0.250867\pi$
$173$	−102921.	−	178264.i	−0.261450	−	0.452844i	−0.966627	+	0.256186i	$0.917534\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−21436.4	−	37128.9i	−0.0514302	−	0.0890798i
$178$		0			0
$179$	99602.6	−	172517.i	0.232348	−	0.402438i	−0.726151	−	0.687535i	$-0.758693\pi$
$179$	99602.6	−	172517.i	0.232348	−	0.402438i	0.958499	+	0.285097i	$0.0920260\pi$
$180$		0			0
$181$	−198411.			−0.450162			−0.225081	−	0.974340i	$-0.572265\pi$
$181$	−198411.			−0.450162			−0.225081	+	0.974340i	$0.572265\pi$
$182$		0			0
$183$	−288992.			−0.637909
$184$		0			0
$185$	−229213.	+	397008.i	−0.492390	+	0.852845i
$186$		0			0
$187$	−6392.42	−	11072.0i	−0.0133678	−	0.0231538i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−186474.	−	322982.i	−0.369857	−	0.640611i	0.619686	−	0.784850i	$-0.287260\pi$
$191$	−186474.	−	322982.i	−0.369857	−	0.640611i	−0.989543	+	0.144239i	$0.953927\pi$
$192$		0			0
$193$	−87509.8	+	151571.i	−0.169108	+	0.292903i	−0.938106	−	0.346347i	$-0.887422\pi$
$193$	−87509.8	+	151571.i	−0.169108	+	0.292903i	0.768999	+	0.639250i	$0.220755\pi$
$194$		0			0
$195$	−40359.5			−0.0760080
$196$		0			0
$197$	883770.			1.62246			0.811229	−	0.584728i	$-0.198799\pi$
$197$	883770.			1.62246			0.811229	+	0.584728i	$0.198799\pi$
$198$		0			0
$199$	392921.	−	680560.i	0.703353	−	1.21824i	−0.263930	−	0.964542i	$-0.585019\pi$
$199$	392921.	−	680560.i	0.703353	−	1.21824i	0.967283	−	0.253701i	$-0.0816478\pi$
$200$		0			0
$201$	6244.87	+	10816.4i	0.0109027	+	0.0188840i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	244455.	+	423408.i	0.406269	+	0.703678i
$206$		0			0
$207$	−239671.	+	415123.i	−0.388768	+	0.673366i
$208$		0			0
$209$	−370340.			−0.586456
$210$		0			0
$211$	763861.			1.18116			0.590579	−	0.806980i	$-0.298899\pi$
$211$	763861.			1.18116			0.590579	+	0.806980i	$0.298899\pi$
$212$		0			0
$213$	−195826.	+	339180.i	−0.295747	+	0.512249i
$214$		0			0
$215$	168025.	+	291029.i	0.247901	+	0.429378i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	152666.	+	264425.i	0.215096	+	0.372557i
$220$		0			0
$221$	4723.91	−	8182.05i	0.00650610	−	0.0112689i
$222$		0			0
$223$	204400.			0.275245			0.137623	−	0.990485i	$-0.456054\pi$
$223$	204400.			0.275245			0.137623	+	0.990485i	$0.456054\pi$
$224$		0			0
$225$	151784.			0.199881
$226$		0			0
$227$	504028.	−	873003.i	0.649218	−	1.12448i	−0.334093	−	0.942540i	$-0.608430\pi$
$227$	504028.	−	873003.i	0.649218	−	1.12448i	0.983310	−	0.181938i	$-0.0582369\pi$
$228$		0			0
$229$	−122162.	−	211591.i	−0.153938	−	0.266629i	0.778734	−	0.627355i	$-0.215862\pi$
$229$	−122162.	−	211591.i	−0.153938	−	0.266629i	−0.932672	+	0.360726i	$0.882529\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10411.4	−	18033.1i	−0.0125638	−	0.0217611i	0.859675	−	0.510841i	$-0.170666\pi$
$233$	−10411.4	−	18033.1i	−0.0125638	−	0.0217611i	−0.872239	+	0.489080i	$0.837333\pi$
$234$		0			0
$235$	28247.7	−	48926.5i	0.0333668	−	0.0577929i
$236$		0			0
$237$	−240632.			−0.278280
$238$		0			0
$239$	−474033.			−0.536801			−0.268401	−	0.963307i	$-0.586495\pi$
$239$	−474033.			−0.536801			−0.268401	+	0.963307i	$0.586495\pi$
$240$		0			0
$241$	−851950.	+	1.47562e6i	−0.944869	+	1.63656i	−0.188854	+	0.982005i	$0.560477\pi$
$241$	−851950.	+	1.47562e6i	−0.944869	+	1.63656i	−0.756014	+	0.654555i	$0.772856\pi$
$242$		0			0
$243$	459134.	+	795243.i	0.498797	+	0.863941i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−136838.	−	237010.i	−0.142713	−	0.247187i
$248$		0			0
$249$	136653.	−	236689.i	0.139675	−	0.241925i
$250$		0			0
$251$	810918.			0.812442			0.406221	−	0.913775i	$-0.366846\pi$
$251$	810918.			0.812442			0.406221	+	0.913775i	$0.366846\pi$
$252$		0			0
$253$	400909.			0.393771
$254$		0			0
$255$	−13059.0	+	22618.8i	−0.0125765	+	0.0217831i
$256$		0			0
$257$	633283.	+	1.09688e6i	0.598088	+	1.03592i	0.993103	+	0.117244i	$0.0374058\pi$
$257$	633283.	+	1.09688e6i	0.598088	+	1.03592i	−0.395016	+	0.918674i	$0.629261\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	682790.	+	1.18263e6i	0.620420	+	1.07460i
$262$		0			0
$263$	980241.	−	1.69783e6i	0.873863	−	1.51358i	0.0158947	−	0.999874i	$-0.494940\pi$
$263$	980241.	−	1.69783e6i	0.873863	−	1.51358i	0.857969	−	0.513702i	$-0.171726\pi$
$264$		0			0
$265$	414954.			0.362982
$266$		0			0
$267$	−870511.			−0.747302
$268$		0			0
$269$	−746790.	+	1.29348e6i	−0.629242	+	1.08988i	0.358462	+	0.933544i	$0.383301\pi$
$269$	−746790.	+	1.29348e6i	−0.629242	+	1.08988i	−0.987704	+	0.156335i	$0.950032\pi$
$270$		0			0
$271$	618128.	+	1.07063e6i	0.511275	+	0.885555i	0.999915	+	0.0130691i	$0.00416013\pi$
$271$	618128.	+	1.07063e6i	0.511275	+	0.885555i	−0.488639	+	0.872486i	$0.662507\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−63474.0	−	109940.i	−0.0506133	−	0.0876647i
$276$		0			0
$277$	85075.0	−	147354.i	0.0666197	−	0.115389i	−0.830792	−	0.556584i	$-0.812112\pi$
$277$	85075.0	−	147354.i	0.0666197	−	0.115389i	0.897411	+	0.441195i	$0.145445\pi$
$278$		0			0
$279$	546217.			0.420102
$280$		0			0
$281$	1.29957e6			0.981824			0.490912	−	0.871209i	$-0.336664\pi$
$281$	1.29957e6			0.981824			0.490912	+	0.871209i	$0.336664\pi$
$282$		0			0
$283$	−187016.	+	323921.i	−0.138807	+	0.240422i	−0.927045	−	0.374949i	$-0.877660\pi$
$283$	−187016.	+	323921.i	−0.138807	+	0.240422i	0.788238	+	0.615370i	$0.210994\pi$
$284$		0			0
$285$	378281.	+	655201.i	0.275868	+	0.477818i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	706872.	+	1.22434e6i	0.497847	+	0.862296i
$290$		0			0
$291$	501469.	−	868570.i	0.347146	−	0.601274i
$292$		0			0
$293$	−1.15022e6			−0.782728			−0.391364	−	0.920236i	$-0.627997\pi$
$293$	−1.15022e6			−0.782728			−0.391364	+	0.920236i	$0.627997\pi$
$294$		0			0
$295$	−301448.			−0.201677
$296$		0			0
$297$	247082.	−	427958.i	0.162536	−	0.281520i
$298$		0			0
$299$	148133.	+	256574.i	0.0958238	+	0.165972i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−343056.	−	594190.i	−0.214664	−	0.371808i
$304$		0			0
$305$	−1.01598e6	+	1.75973e6i	−0.625370	+	1.08317i
$306$		0			0
$307$	−2.61214e6			−1.58179			−0.790897	−	0.611949i	$-0.790386\pi$
$307$	−2.61214e6			−1.58179			−0.790897	+	0.611949i	$0.790386\pi$
$308$		0			0
$309$	−894578.			−0.532994
$310$		0			0
$311$	−703229.	+	1.21803e6i	−0.412283	+	0.714095i	−0.995139	−	0.0984801i	$-0.968602\pi$
$311$	−703229.	+	1.21803e6i	−0.412283	+	0.714095i	0.582856	+	0.812576i	$0.301935\pi$
$312$		0			0
$313$	1.18965e6	+	2.06053e6i	0.686369	+	1.18883i	0.973004	+	0.230786i	$0.0741298\pi$
$313$	1.18965e6	+	2.06053e6i	0.686369	+	1.18883i	−0.286635	+	0.958040i	$0.592537\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	281600.	+	487745.i	0.157393	+	0.272612i	0.933928	−	0.357462i	$-0.116358\pi$
$317$	281600.	+	487745.i	0.157393	+	0.272612i	−0.776535	+	0.630074i	$0.783025\pi$
$318$		0			0
$319$	571066.	−	989116.i	0.314203	−	0.544215i
$320$		0			0
$321$	−1.50814e6			−0.816921
$322$		0			0
$323$	−177105.			−0.0944547
$324$		0			0
$325$	46906.4	−	81244.3i	0.0246334	−	0.0426662i
$326$		0			0
$327$	694852.	+	1.20352e6i	0.359355	+	0.622420i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	425324.	+	736683.i	0.213378	+	0.369582i	0.952770	−	0.303694i	$-0.0982200\pi$
$331$	425324.	+	736683.i	0.213378	+	0.369582i	−0.739391	+	0.673276i	$0.764887\pi$
$332$		0			0
$333$	924633.	−	1.60151e6i	0.456939	−	0.791442i
$334$		0			0
$335$	87818.0			0.0427535
$336$		0			0
$337$	4.01506e6			1.92582			0.962912	−	0.269814i	$-0.0869623\pi$
$337$	4.01506e6			1.92582			0.962912	+	0.269814i	$0.0869623\pi$
$338$		0			0
$339$	109603.	−	189838.i	0.0517993	−	0.0897191i
$340$		0			0
$341$	−228420.	−	395635.i	−0.106377	−	0.184251i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−409505.	−	709283.i	−0.185230	−	0.320828i
$346$		0			0
$347$	1.19980e6	−	2.07812e6i	0.534918	−	0.926505i	−0.464250	−	0.885704i	$-0.653676\pi$
$347$	1.19980e6	−	2.07812e6i	0.534918	−	0.926505i	0.999167	−	0.0408002i	$-0.0129907\pi$
$348$		0			0
$349$	919171.			0.403955			0.201977	−	0.979390i	$-0.435263\pi$
$349$	919171.			0.403955			0.201977	+	0.979390i	$0.435263\pi$
$350$		0			0
$351$	365179.			0.158212
$352$		0			0
$353$	538418.	−	932568.i	0.229976	−	0.398331i	−0.727825	−	0.685763i	$-0.759468\pi$
$353$	538418.	−	932568.i	0.229976	−	0.398331i	0.957801	+	0.287433i	$0.0928018\pi$
$354$		0			0
$355$	1.37689e6	+	2.38485e6i	0.579868	+	1.00436i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	621095.	+	1.07577e6i	0.254344	+	0.440537i	0.964717	−	0.263288i	$-0.0848071\pi$
$359$	621095.	+	1.07577e6i	0.254344	+	0.440537i	−0.710373	+	0.703825i	$0.751474\pi$
$360$		0			0
$361$	−1.32706e6	+	2.29853e6i	−0.535947	+	0.928287i
$362$		0			0
$363$	925771.			0.368754
$364$		0			0
$365$	2.14685e6			0.843471
$366$		0			0
$367$	2.08647e6	−	3.61387e6i	0.808624	−	1.40058i	−0.105194	−	0.994452i	$-0.533546\pi$
$367$	2.08647e6	−	3.61387e6i	0.808624	−	1.40058i	0.913817	−	0.406125i	$-0.133120\pi$
$368$		0			0
$369$	−986118.	−	1.70801e6i	−0.377019	−	0.653016i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	861191.	+	1.49163e6i	0.320500	+	0.555121i	0.980591	−	0.196064i	$-0.0628159\pi$
$373$	861191.	+	1.49163e6i	0.320500	+	0.555121i	−0.660092	+	0.751185i	$0.729483\pi$
$374$		0			0
$375$	−651581.	+	1.12857e6i	−0.239271	+	0.414430i
$376$		0			0
$377$	844020.			0.305844
$378$		0			0
$379$	1.72998e6			0.618647			0.309324	−	0.950957i	$-0.399897\pi$
$379$	1.72998e6			0.618647			0.309324	+	0.950957i	$0.399897\pi$
$380$		0			0
$381$	−1.09630e6	+	1.89884e6i	−0.386915	+	0.670156i
$382$		0			0
$383$	−1.67441e6	−	2.90016e6i	−0.583262	−	1.01024i	−0.995090	−	0.0989781i	$-0.968443\pi$
$383$	−1.67441e6	−	2.90016e6i	−0.583262	−	1.01024i	0.411827	−	0.911262i	$-0.364891\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−677806.	−	1.17400e6i	−0.230053	−	0.398464i
$388$		0			0
$389$	2.59346e6	−	4.49200e6i	0.868970	−	1.50510i	0.00592035	−	0.999982i	$-0.498115\pi$
$389$	2.59346e6	−	4.49200e6i	0.868970	−	1.50510i	0.863050	−	0.505118i	$-0.168551\pi$
$390$		0			0
$391$	191723.			0.0634209
$392$		0			0
$393$	−2.10353e6			−0.687018
$394$		0			0
$395$	−845967.	+	1.46526e6i	−0.272810	+	0.472521i
$396$		0			0
$397$	−651353.	−	1.12818e6i	−0.207415	−	0.359254i	0.743484	−	0.668753i	$-0.233172\pi$
$397$	−651353.	−	1.12818e6i	−0.207415	−	0.359254i	−0.950900	+	0.309500i	$0.899838\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	765180.	+	1.32533e6i	0.237631	+	0.411588i	0.960034	−	0.279884i	$-0.0902959\pi$
$401$	765180.	+	1.32533e6i	0.237631	+	0.411588i	−0.722403	+	0.691472i	$0.756963\pi$
$402$		0			0
$403$	168799.	−	292369.i	0.0517735	−	0.0896744i
$404$		0			0
$405$	1.29269e6			0.391611
$406$		0			0
$407$	−1.54667e6			−0.462820
$408$		0			0
$409$	−1.46845e6	+	2.54343e6i	−0.434062	+	0.751817i	−0.997219	−	0.0745332i	$-0.976253\pi$
$409$	−1.46845e6	+	2.54343e6i	−0.434062	+	0.751817i	0.563157	+	0.826350i	$0.309587\pi$
$410$		0			0
$411$	620474.	+	1.07469e6i	0.181184	+	0.313819i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−960833.	−	1.66421e6i	−0.273859	−	0.474339i
$416$		0			0
$417$	1.11383e6	−	1.92921e6i	0.313675	−	0.543301i
$418$		0			0
$419$	1.16465e6			0.324085			0.162043	−	0.986784i	$-0.448192\pi$
$419$	1.16465e6			0.324085			0.162043	+	0.986784i	$0.448192\pi$
$420$		0			0
$421$	−1.58204e6			−0.435022			−0.217511	−	0.976058i	$-0.569794\pi$
$421$	−1.58204e6			−0.435022			−0.217511	+	0.976058i	$0.569794\pi$
$422$		0			0
$423$	−113950.	+	197367.i	−0.0309644	+	0.0536320i
$424$		0			0
$425$	−30354.6	−	52575.8i	−0.00815179	−	0.0141193i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−68084.1	−	117925.i	−0.0178609	−	0.0309359i
$430$		0			0
$431$	−3.05116e6	+	5.28477e6i	−0.791174	+	1.37035i	0.134066	+	0.990972i	$0.457197\pi$
$431$	−3.05116e6	+	5.28477e6i	−0.791174	+	1.37035i	−0.925240	+	0.379382i	$0.876137\pi$
$432$		0			0
$433$	−1.08115e6			−0.277118			−0.138559	−	0.990354i	$-0.544247\pi$
$433$	−1.08115e6			−0.277118			−0.138559	+	0.990354i	$0.544247\pi$
$434$		0			0
$435$	−2.33324e6			−0.591203
$436$		0			0
$437$	2.77683e6	−	4.80962e6i	0.695579	−	1.20478i
$438$		0			0
$439$	−3.52403e6	−	6.10381e6i	−0.872728	−	1.51161i	−0.859164	−	0.511701i	$-0.829016\pi$
$439$	−3.52403e6	−	6.10381e6i	−0.872728	−	1.51161i	−0.0135639	−	0.999908i	$-0.504318\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.16016e6	+	2.00945e6i	0.280871	+	0.486483i	0.971599	−	0.236631i	$-0.0760434\pi$
$443$	1.16016e6	+	2.00945e6i	0.280871	+	0.486483i	−0.690729	+	0.723114i	$0.742710\pi$
$444$		0			0
$445$	−3.06037e6	+	5.30072e6i	−0.732613	+	1.26892i
$446$		0			0
$447$	−2.02747e6			−0.479939
$448$		0			0
$449$	−5.45039e6			−1.27589			−0.637943	−	0.770084i	$-0.720214\pi$
$449$	−5.45039e6			−1.27589			−0.637943	+	0.770084i	$0.720214\pi$
$450$		0			0
$451$	−824761.	+	1.42853e6i	−0.190935	+	0.330710i
$452$		0			0
$453$	−1.15435e6	−	1.99940e6i	−0.264297	−	0.457777i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.31338e6	−	5.73895e6i	−0.742132	−	1.28541i	−0.951523	−	0.307578i	$-0.900482\pi$
$457$	−3.31338e6	−	5.73895e6i	−0.742132	−	1.28541i	0.209391	−	0.977832i	$-0.432852\pi$
$458$		0			0
$459$	118160.	−	204659.i	0.0261781	−	0.0453417i
$460$		0			0
$461$	−606397.			−0.132894			−0.0664469	−	0.997790i	$-0.521166\pi$
$461$	−606397.			−0.132894			−0.0664469	+	0.997790i	$0.521166\pi$
$462$		0			0
$463$	3.65855e6			0.793153			0.396576	−	0.918002i	$-0.370198\pi$
$463$	3.65855e6			0.793153			0.396576	+	0.918002i	$0.370198\pi$
$464$		0			0
$465$	−466635.	+	808236.i	−0.100080	+	0.173343i
$466$		0			0
$467$	2.81356e6	+	4.87323e6i	0.596986	+	1.03401i	0.993263	+	0.115879i	$0.0369686\pi$
$467$	2.81356e6	+	4.87323e6i	0.596986	+	1.03401i	−0.396277	+	0.918131i	$0.629698\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	500219.	+	866404.i	0.103898	+	0.179957i
$472$		0			0
$473$	−566898.	+	981896.i	−0.116507	+	0.201796i
$474$		0			0
$475$	−1.75857e6			−0.357624
$476$		0			0
$477$	−1.67390e6			−0.336848
$478$		0			0
$479$	2.12553e6	−	3.68153e6i	0.423281	−	0.733145i	−0.572977	−	0.819571i	$-0.694212\pi$
$479$	2.12553e6	−	3.68153e6i	0.423281	−	0.733145i	0.996258	+	0.0864268i	$0.0275449\pi$
$480$		0			0
$481$	−571485.	−	989840.i	−0.112627	−	0.195075i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.52593e6	−	6.10710e6i	−0.680644	−	1.17891i
$486$		0			0
$487$	−2.64378e6	+	4.57916e6i	−0.505130	+	0.874911i	0.494852	+	0.868977i	$0.335222\pi$
$487$	−2.64378e6	+	4.57916e6i	−0.505130	+	0.874911i	−0.999982	+	0.00593382i	$0.998111\pi$
$488$		0			0
$489$	1.21459e6			0.229699
$490$		0			0
$491$	−3.33842e6			−0.624939			−0.312469	−	0.949928i	$-0.601156\pi$
$491$	−3.33842e6			−0.624939			−0.312469	+	0.949928i	$0.601156\pi$
$492$		0			0
$493$	273096.	−	473016.i	0.0506056	−	0.0876514i
$494$		0			0
$495$	−774534.	−	1.34153e6i	−0.142078	−	0.246087i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.26424e6	−	2.18972e6i	−0.227288	−	0.393675i	0.729715	−	0.683751i	$-0.239653\pi$
$499$	−1.26424e6	−	2.18972e6i	−0.227288	−	0.393675i	−0.957003	+	0.290076i	$0.906319\pi$
$500$		0			0
$501$	156668.	−	271356.i	0.0278859	−	0.0482999i
$502$		0			0
$503$	5.94498e6			1.04768			0.523842	−	0.851815i	$-0.324498\pi$
$503$	5.94498e6			1.04768			0.523842	+	0.851815i	$0.324498\pi$
$504$		0			0
$505$	−4.82420e6			−0.841776
$506$		0			0
$507$	−1.22924e6	+	2.12911e6i	−0.212382	+	0.367857i
$508$		0			0
$509$	−301762.	−	522668.i	−0.0516263	−	0.0894193i	0.839057	−	0.544043i	$-0.183107\pi$
$509$	−301762.	−	522668.i	−0.0516263	−	0.0894193i	−0.890684	+	0.454624i	$0.849774\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3.42275e6	−	5.92837e6i	−0.574224	−	0.994585i
$514$		0			0
$515$	−3.14498e6	+	5.44727e6i	−0.522517	+	0.905026i
$516$		0			0
$517$	190609.			0.0313630
$518$		0			0
$519$	−1.41875e6			−0.231200
$520$		0			0
$521$	5.16943e6	−	8.95371e6i	0.834350	−	1.44514i	−0.0602088	−	0.998186i	$-0.519177\pi$
$521$	5.16943e6	−	8.95371e6i	0.834350	−	1.44514i	0.894559	−	0.446951i	$-0.147490\pi$
$522$		0			0
$523$	−4.41155e6	−	7.64103e6i	−0.705240	−	1.22151i	−0.966605	−	0.256272i	$-0.917506\pi$
$523$	−4.41155e6	−	7.64103e6i	−0.705240	−	1.22151i	0.261364	−	0.965240i	$-0.415828\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−109235.	−	189201.i	−0.0171331	−	0.0296755i
$528$		0			0
$529$	212133.	−	367425.i	0.0329586	−	0.0570860i
$530$		0			0
$531$	1.21602e6			0.187157
$532$		0			0
$533$	−1.21897e6			−0.185856
$534$		0			0
$535$	−5.30204e6	+	9.18340e6i	−0.800863	+	1.38714i
$536$		0			0
$537$	−686505.	−	1.18906e6i	−0.102733	−	0.177938i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−584056.	−	1.01161e6i	−0.0857949	−	0.148601i	0.819935	−	0.572457i	$-0.194010\pi$
$541$	−584056.	−	1.01161e6i	−0.0857949	−	0.148601i	−0.905730	+	0.423856i	$0.860676\pi$
$542$		0			0
$543$	−683767.	+	1.18432e6i	−0.0995196	+	0.172373i
$544$		0			0
$545$	9.77130e6			1.40916
$546$		0			0
$547$	9.17075e6			1.31050			0.655249	−	0.755413i	$-0.272564\pi$
$547$	9.17075e6			1.31050			0.655249	+	0.755413i	$0.272564\pi$
$548$		0			0
$549$	4.09842e6	−	7.09868e6i	0.580345	−	1.00519i
$550$		0			0
$551$	−7.91081e6	−	1.37019e7i	−1.11005	−	1.92266i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.57984e6	+	2.73636e6i	0.217710	+	0.377086i
$556$		0			0
$557$	−3.11211e6	+	5.39033e6i	−0.425027	+	0.736168i	−0.996423	−	0.0845062i	$-0.973069\pi$
$557$	−3.11211e6	+	5.39033e6i	−0.425027	+	0.736168i	0.571396	+	0.820674i	$0.306402\pi$
$558$		0			0
$559$	−837859.			−0.113407
$560$		0			0
$561$	−88118.8			−0.0118212
$562$		0			0
$563$	−2.82021e6	+	4.88475e6i	−0.374982	+	0.649488i	−0.990324	−	0.138772i	$-0.955684\pi$
$563$	−2.82021e6	+	4.88475e6i	−0.374982	+	0.649488i	0.615342	+	0.788260i	$0.289018\pi$
$564$		0			0
$565$	−770643.	−	1.33479e6i	−0.101562	−	0.175911i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.26432e6	+	9.11807e6i	0.681650	+	1.18065i	0.974477	+	0.224487i	$0.0720707\pi$
$569$	5.26432e6	+	9.11807e6i	0.681650	+	1.18065i	−0.292827	+	0.956165i	$0.594596\pi$
$570$		0			0
$571$	3.65698e6	−	6.33407e6i	0.469388	−	0.813004i	−0.530000	−	0.847998i	$-0.677808\pi$
$571$	3.65698e6	−	6.33407e6i	0.469388	−	0.813004i	0.999388	+	0.0349941i	$0.0111413\pi$
$572$		0			0
$573$	−2.57052e6			−0.327065
$574$		0			0
$575$	1.90373e6			0.240124
$576$		0			0
$577$	1.33267e6	−	2.30825e6i	0.166641	−	0.288631i	−0.770596	−	0.637324i	$-0.780041\pi$
$577$	1.33267e6	−	2.30825e6i	0.166641	−	0.288631i	0.937237	+	0.348693i	$0.113375\pi$
$578$		0			0
$579$	603156.	+	1.04470e6i	0.0747710	+	0.129507i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	700002.	+	1.21244e6i	0.0852959	+	0.147737i
$584$		0			0
$585$	572369.	−	991373.i	0.0691491	−	0.119770i
$586$		0			0
$587$	−4.92431e6			−0.589861			−0.294931	−	0.955519i	$-0.595297\pi$
$587$	−4.92431e6			−0.589861			−0.294931	+	0.955519i	$0.595297\pi$
$588$		0			0
$589$	−6.32847e6			−0.751641
$590$		0			0
$591$	3.04567e6	−	5.27525e6i	0.358685	−	0.621261i
$592$		0			0
$593$	−2.54368e6	−	4.40578e6i	−0.297047	−	0.514501i	0.678412	−	0.734682i	$-0.262668\pi$
$593$	−2.54368e6	−	4.40578e6i	−0.297047	−	0.514501i	−0.975459	+	0.220181i	$0.929335\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.70819e6	−	4.69072e6i	−0.310988	−	0.538646i
$598$		0			0
$599$	−2.32339e6	+	4.02423e6i	−0.264579	+	0.458263i	−0.967453	−	0.253050i	$-0.918566\pi$
$599$	−2.32339e6	+	4.02423e6i	−0.264579	+	0.458263i	0.702875	+	0.711314i	$0.251900\pi$
$600$		0			0
$601$	4.35424e6			0.491730			0.245865	−	0.969304i	$-0.420928\pi$
$601$	4.35424e6			0.491730			0.245865	+	0.969304i	$0.420928\pi$
$602$		0			0
$603$	−354254.			−0.0396754
$604$		0			0
$605$	3.25465e6	−	5.63721e6i	0.361506	−	0.626147i
$606$		0			0
$607$	−6.27303e6	−	1.08652e7i	−0.691043	−	1.19692i	−0.971496	−	0.237054i	$-0.923818\pi$
$607$	−6.27303e6	−	1.08652e7i	−0.691043	−	1.19692i	0.280453	−	0.959868i	$-0.409515\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	70428.7	+	121986.i	0.00763214	+	0.0132193i
$612$		0			0
$613$	2.03818e6	−	3.53024e6i	0.219075	−	0.379448i	−0.735451	−	0.677578i	$-0.763030\pi$
$613$	2.03818e6	−	3.53024e6i	0.219075	−	0.379448i	0.954525	+	0.298130i	$0.0963629\pi$
$614$		0			0
$615$	3.36978e6			0.359264
$616$		0			0
$617$	−8.88533e6			−0.939639			−0.469819	−	0.882763i	$-0.655681\pi$
$617$	−8.88533e6			−0.939639			−0.469819	+	0.882763i	$0.655681\pi$
$618$		0			0
$619$	−6.42650e6	+	1.11310e7i	−0.674136	+	1.16764i	0.302584	+	0.953123i	$0.402151\pi$
$619$	−6.42650e6	+	1.11310e7i	−0.674136	+	1.16764i	−0.976721	+	0.214516i	$0.931183\pi$
$620$		0			0
$621$	3.70527e6	+	6.41771e6i	0.385559	+	0.667807i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	3.36826e6	+	5.83399e6i	0.344910	+	0.597401i
$626$		0			0
$627$	−1.27627e6	+	2.21057e6i	−0.129651	+	0.224562i
$628$		0			0
$629$	−739652.			−0.0745420
$630$		0			0
$631$	−288616.			−0.0288567			−0.0144283	−	0.999896i	$-0.504593\pi$
$631$	−288616.			−0.0288567			−0.0144283	+	0.999896i	$0.504593\pi$
$632$		0			0
$633$	2.63243e6	−	4.55951e6i	0.261125	−	0.452282i
$634$		0			0
$635$	7.70829e6	+	1.33511e7i	0.758619	+	1.31397i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.55432e6	−	9.62036e6i	−0.538119	−	0.932050i
$640$		0			0
$641$	9.72953e6	−	1.68520e7i	0.935291	−	1.61997i	0.161177	−	0.986926i	$-0.448471\pi$
$641$	9.72953e6	−	1.68520e7i	0.935291	−	1.61997i	0.774114	−	0.633046i	$-0.218196\pi$
$642$		0			0
$643$	−1.30171e7			−1.24161			−0.620805	−	0.783965i	$-0.713194\pi$
$643$	−1.30171e7			−1.24161			−0.620805	+	0.783965i	$0.713194\pi$
$644$		0			0
$645$	2.31621e6			0.219219
$646$		0			0
$647$	3.21432e6	−	5.56736e6i	0.301876	−	0.522864i	−0.674685	−	0.738106i	$-0.735721\pi$
$647$	3.21432e6	−	5.56736e6i	0.301876	−	0.522864i	0.976561	+	0.215242i	$0.0690539\pi$
$648$		0			0
$649$	−508524.	−	880790.i	−0.0473914	−	0.0820844i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.01012e6	−	8.67778e6i	−0.459796	−	0.796390i	0.539154	−	0.842207i	$-0.318744\pi$
$653$	−5.01012e6	−	8.67778e6i	−0.459796	−	0.796390i	−0.998950	+	0.0458174i	$0.985411\pi$
$654$		0			0
$655$	−7.39519e6	+	1.28089e7i	−0.673514	+	1.16656i
$656$		0			0
$657$	−8.66030e6			−0.782743
$658$		0			0
$659$	1.49356e7			1.33971			0.669854	−	0.742493i	$-0.266357\pi$
$659$	1.49356e7			1.33971			0.669854	+	0.742493i	$0.266357\pi$
$660$		0			0
$661$	−675276.	+	1.16961e6i	−0.0601143	+	0.104121i	−0.894516	−	0.447035i	$-0.852480\pi$
$661$	−675276.	+	1.16961e6i	−0.0601143	+	0.104121i	0.834402	+	0.551156i	$0.185813\pi$
$662$		0			0
$663$	−32559.3	−	56394.3i	−0.00287668	−	0.00498255i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.56378e6	+	1.48329e7i	0.745334	+	1.29096i
$668$		0			0
$669$	704409.	−	1.22007e6i	0.0608499	−	0.105395i
$670$		0			0
$671$	−6.85561e6			−0.587814
$672$		0			0
$673$	6.59401e6			0.561193			0.280596	−	0.959826i	$-0.409468\pi$
$673$	6.59401e6			0.561193			0.280596	+	0.959826i	$0.409468\pi$
$674$		0			0
$675$	1.17328e6	−	2.03217e6i	0.0991153	−	0.171673i
$676$		0			0
$677$	7.12586e6	+	1.23424e7i	0.597538	+	1.03497i	0.993183	+	0.116563i	$0.0371878\pi$
$677$	7.12586e6	+	1.23424e7i	0.597538	+	1.03497i	−0.395645	+	0.918404i	$0.629479\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.47399e6	−	6.01712e6i	−0.287052	−	0.497188i
$682$		0			0
$683$	3.82503e6	−	6.62515e6i	0.313749	−	0.543430i	−0.665421	−	0.746468i	$-0.731748\pi$
$683$	3.82503e6	−	6.62515e6i	0.313749	−	0.543430i	0.979171	+	0.203038i	$0.0650815\pi$
$684$		0			0
$685$	8.72536e6			0.710489
$686$		0			0
$687$	−1.68399e6			−0.136128
$688$		0			0
$689$	−517292.	+	895976.i	−0.0415133	+	0.0719032i
$690$		0			0
$691$	6.93274e6	+	1.20079e7i	0.552344	+	0.956688i	0.998105	+	0.0615362i	$0.0196000\pi$
$691$	6.93274e6	+	1.20079e7i	0.552344	+	0.956688i	−0.445761	+	0.895152i	$0.647067\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.83159e6	−	1.35647e7i	−0.615018	−	1.06524i
$696$		0			0
$697$	−394418.	+	683153.i	−0.0307521	+	0.0532642i
$698$		0			0
$699$	−143521.			−0.0111102
$700$		0			0
$701$	−2.38825e6			−0.183563			−0.0917814	−	0.995779i	$-0.529256\pi$
$701$	−2.38825e6			−0.183563			−0.0917814	+	0.995779i	$0.529256\pi$
$702$		0			0
$703$	−1.07128e7	+	1.85551e7i	−0.817551	+	1.41604i
$704$		0			0
$705$	−194696.	−	337223.i	−0.0147531	−	0.0255532i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.78204e6	+	1.34789e7i	0.581404	+	1.00702i	0.995313	+	0.0967032i	$0.0308298\pi$
$709$	7.78204e6	+	1.34789e7i	0.581404	+	1.00702i	−0.413909	+	0.910318i	$0.635837\pi$
$710$		0			0
$711$	3.41259e6	−	5.91078e6i	0.253169	−	0.438501i
$712$		0			0
$713$	6.85083e6			0.504684
$714$		0			0
$715$	−957427.			−0.0700391
$716$		0			0
$717$	−1.63362e6	+	2.82952e6i	−0.118673	+	0.205548i
$718$		0			0
$719$	9.12775e6	+	1.58097e7i	0.658478	+	1.14052i	0.981010	+	0.193959i	$0.0621329\pi$
$719$	9.12775e6	+	1.58097e7i	0.658478	+	1.14052i	−0.322531	+	0.946559i	$0.604534\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.87202e6	+	1.01706e7i	0.417774	+	0.723606i
$724$		0			0
$725$	2.71173e6	−	4.69685e6i	0.191603	−	0.331865i
$726$		0			0
$727$	2.11427e6			0.148362			0.0741812	−	0.997245i	$-0.476366\pi$
$727$	2.11427e6			0.148362			0.0741812	+	0.997245i	$0.476366\pi$
$728$		0			0
$729$	−152693.			−0.0106414
$730$		0			0
$731$	−271103.	+	469564.i	−0.0187647	+	0.0325013i
$732$		0			0
$733$	1.06466e6	+	1.84404e6i	0.0731898	+	0.126768i	0.900298	−	0.435275i	$-0.143349\pi$
$733$	1.06466e6	+	1.84404e6i	0.0731898	+	0.126768i	−0.827108	+	0.562043i	$0.810015\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	148144.	+	256593.i	0.0100465	+	0.0174010i
$738$		0			0
$739$	4.04335e6	−	7.00329e6i	0.272352	−	0.471728i	−0.697112	−	0.716963i	$-0.745532\pi$
$739$	4.04335e6	−	7.00329e6i	0.272352	−	0.471728i	0.969464	+	0.245235i	$0.0788651\pi$
$740$		0			0
$741$	−1.88630e6			−0.126202
$742$		0			0
$743$	−1.18944e7			−0.790442			−0.395221	−	0.918586i	$-0.629332\pi$
$743$	−1.18944e7			−0.790442			−0.395221	+	0.918586i	$0.629332\pi$
$744$		0			0
$745$	−7.12779e6	+	1.23457e7i	−0.470505	+	0.814939i
$746$		0			0
$747$	3.87595e6	+	6.71335e6i	0.254142	+	0.440188i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9.27692e6	+	1.60681e7i	0.600211	+	1.03960i	0.992789	+	0.119877i	$0.0382500\pi$
$751$	9.27692e6	+	1.60681e7i	0.600211	+	1.03960i	−0.392578	+	0.919719i	$0.628417\pi$
$752$		0			0
$753$	2.79460e6	−	4.84039e6i	0.179611	−	0.311095i
$754$		0			0
$755$	−1.62330e7			−1.03641
$756$		0			0
$757$	9.32534e6			0.591459			0.295730	−	0.955272i	$-0.404437\pi$
$757$	9.32534e6			0.591459			0.295730	+	0.955272i	$0.404437\pi$
$758$		0			0
$759$	1.38162e6	−	2.39304e6i	0.0870531	−	0.150780i
$760$		0			0
$761$	4.00378e6	+	6.93475e6i	0.250616	+	0.434079i	0.963696	−	0.267004i	$-0.0860336\pi$
$761$	4.00378e6	+	6.93475e6i	0.250616	+	0.434079i	−0.713080	+	0.701083i	$0.752700\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−370399.	−	641549.i	−0.0228832	−	0.0396348i
$766$		0			0
$767$	375792.	−	650891.i	0.0230653	−	0.0399503i
$768$		0			0
$769$	−2.02720e7			−1.23618			−0.618089	−	0.786108i	$-0.712093\pi$
$769$	−2.02720e7			−1.23618			−0.618089	+	0.786108i	$0.712093\pi$
$770$		0			0
$771$	8.72973e6			0.528889
$772$		0			0
$773$	1.43940e6	−	2.49312e6i	0.0866431	−	0.150070i	−0.819447	−	0.573155i	$-0.805719\pi$
$773$	1.43940e6	−	2.49312e6i	0.0866431	−	0.150070i	0.906090	+	0.423085i	$0.139053\pi$
$774$		0			0
$775$	−1.08466e6	−	1.87869e6i	−0.0648694	−	0.112357i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.14252e7	+	1.97890e7i	0.674557	+	1.16837i
$780$		0			0
$781$	−4.64547e6	+	8.04619e6i	−0.272522	+	0.472023i
$782$		0			0
$783$	2.11116e7			1.23060
$784$		0			0
$785$	7.03428e6			0.407423
$786$		0			0
$787$	−1.01754e7	+	1.76243e7i	−0.585618	+	1.01432i	0.409180	+	0.912454i	$0.365815\pi$
$787$	−1.01754e7	+	1.76243e7i	−0.585618	+	1.01432i	−0.994798	+	0.101867i	$0.967518\pi$
$788$		0			0
$789$	−6.75626e6	−	1.17022e7i	−0.386379	−	0.669228i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.53310e6	−	4.38746e6i	−0.143044	−	0.247759i
$794$		0			0
$795$	1.43002e6	−	2.47687e6i	0.0802463	−	0.138991i
$796$		0			0
$797$	2.24765e7			1.25338			0.626689	−	0.779269i	$-0.284410\pi$
$797$	2.24765e7			1.25338			0.626689	+	0.779269i	$0.284410\pi$
$798$		0			0
$799$	91153.3			0.00505133
$800$		0			0
$801$	1.23454e7	−	2.13829e7i	0.679867	−	1.17756i
$802$		0			0
$803$	3.62161e6	+	6.27282e6i	0.198204	+	0.343300i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.14721e6	+	8.91523e6i	0.278220	+	0.481891i
$808$		0			0
$809$	577134.	−	999625.i	0.0310031	−	0.0536990i	−0.850108	−	0.526609i	$-0.823463\pi$
$809$	577134.	−	999625.i	0.0310031	−	0.0536990i	0.881111	+	0.472910i	$0.156796\pi$
$810$		0			0
$811$	2.26698e7			1.21031			0.605154	−	0.796108i	$-0.293112\pi$
$811$	2.26698e7			1.21031			0.605154	+	0.796108i	$0.293112\pi$
$812$		0			0
$813$	8.52082e6			0.452121
$814$		0			0
$815$	4.27003e6	−	7.39592e6i	0.225184	−	0.390030i
$816$		0			0
$817$	7.85307e6	+	1.36019e7i	0.411608	+	0.712927i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.20829e6	+	2.09281e6i	0.0625622	+	0.108361i	0.895610	−	0.444840i	$-0.146739\pi$
$821$	1.20829e6	+	2.09281e6i	0.0625622	+	0.108361i	−0.833048	+	0.553201i	$0.813406\pi$
$822$		0			0
$823$	1.05085e6	−	1.82012e6i	0.0540804	−	0.0936699i	−0.837718	−	0.546103i	$-0.816111\pi$
$823$	1.05085e6	−	1.82012e6i	0.0540804	−	0.0936699i	0.891798	+	0.452433i	$0.149444\pi$
$824$		0			0
$825$	−874982.			−0.0447574
$826$		0			0
$827$	1.53997e7			0.782977			0.391489	−	0.920183i	$-0.371960\pi$
$827$	1.53997e7			0.782977			0.391489	+	0.920183i	$0.371960\pi$
$828$		0			0
$829$	−1.16920e7	+	2.02511e7i	−0.590883	+	1.02344i	0.403231	+	0.915098i	$0.367887\pi$
$829$	−1.16920e7	+	2.02511e7i	−0.590883	+	1.02344i	−0.994114	+	0.108341i	$0.965446\pi$
$830$		0			0
$831$	−586375.	−	1.01563e6i	−0.0294559	−	0.0510192i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.10156e6	−	1.90796e6i	−0.0546756	−	0.0947009i
$836$		0			0
$837$	4.22219e6	−	7.31305e6i	0.208317	−	0.360815i
$838$		0			0
$839$	−2.03016e7			−0.995695			−0.497848	−	0.867265i	$-0.665876\pi$
$839$	−2.03016e7			−0.995695			−0.497848	+	0.867265i	$0.665876\pi$
$840$		0			0
$841$	2.82829e7			1.37890
$842$		0			0
$843$	4.47860e6	−	7.75717e6i	0.217057	−	0.375954i
$844$		0			0
$845$	8.64308e6	+	1.49703e7i	0.416415	+	0.721253i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.28900e6	+	2.23261e6i	0.0613738	+	0.106303i
$850$		0			0
$851$	1.15971e7	−	2.00867e7i	0.548938	−	0.950789i
$852$		0			0
$853$	−3.35163e7			−1.57719			−0.788594	−	0.614914i	$-0.789191\pi$
$853$	−3.35163e7			−1.57719			−0.788594	+	0.614914i	$0.789191\pi$
$854$		0			0
$855$	−2.14588e7			−1.00390
$856$		0			0
$857$	−1.15331e7	+	1.99759e7i	−0.536405	+	0.929081i	0.462689	+	0.886521i	$0.346885\pi$
$857$	−1.15331e7	+	1.99759e7i	−0.536405	+	0.929081i	−0.999094	+	0.0425602i	$0.986449\pi$
$858$		0			0
$859$	1.92805e7	+	3.33947e7i	0.891527	+	1.54417i	0.838045	+	0.545601i	$0.183699\pi$
$859$	1.92805e7	+	3.33947e7i	0.891527	+	1.54417i	0.0534819	+	0.998569i	$0.482968\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.93446e7	−	3.35058e7i	−0.884163	−	1.53142i	−0.846670	−	0.532118i	$-0.821396\pi$
$863$	−1.93446e7	−	3.35058e7i	−0.884163	−	1.53142i	−0.0374930	−	0.999297i	$-0.511937\pi$
$864$		0			0
$865$	−4.98778e6	+	8.63908e6i	−0.226656	+	0.392579i
$866$		0			0
$867$	9.74414e6			0.440247
$868$		0			0
$869$	−5.70838e6			−0.256427
$870$		0			0
$871$	−109476.	+	189618.i	−0.00488961	+	0.00846905i
$872$		0			0
$873$	1.42234e7	+	2.46357e7i	0.631639	+	1.09403i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.08685e7	+	1.88247e7i	0.477166	+	0.826476i	0.999658	−	0.0261687i	$-0.00833072\pi$
$877$	1.08685e7	+	1.88247e7i	0.477166	+	0.826476i	−0.522492	+	0.852644i	$0.674997\pi$
$878$		0			0
$879$	−3.96390e6	+	6.86568e6i	−0.173042	+	0.299717i
$880$		0			0
$881$	−8.42086e6			−0.365525			−0.182762	−	0.983157i	$-0.558504\pi$
$881$	−8.42086e6			−0.365525			−0.182762	+	0.983157i	$0.558504\pi$
$882$		0			0
$883$	3.22954e7			1.39392			0.696962	−	0.717108i	$-0.254535\pi$
$883$	3.22954e7			1.39392			0.696962	+	0.717108i	$0.254535\pi$
$884$		0			0
$885$	−1.03886e6	+	1.79935e6i	−0.0445858	+	0.0772249i
$886$		0			0
$887$	−2.10900e7	−	3.65290e7i	−0.900052	−	1.55894i	−0.827424	−	0.561577i	$-0.810195\pi$
$887$	−2.10900e7	−	3.65290e7i	−0.900052	−	1.55894i	−0.0726278	−	0.997359i	$-0.523139\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.18068e6	+	3.77705e6i	0.0920234	+	0.159389i
$892$		0			0
$893$	1.32023e6	−	2.28670e6i	0.0554012	−	0.0959577i
$894$		0			0
$895$	−9.65393e6			−0.402853
$896$		0			0
$897$	2.04200e6			0.0847371
$898$		0			0
$899$	9.75853e6	−	1.69023e7i	0.402703	−	0.697503i
$900$		0			0
$901$	334756.	+	579815.i	0.0137378	+	0.0237945i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.80771e6	+	8.32720e6i	0.195127	+	0.337970i
$906$		0			0
$907$	3.82259e6	−	6.62092e6i	0.154291	−	0.267239i	−0.778510	−	0.627632i	$-0.784024\pi$
$907$	3.82259e6	−	6.62092e6i	0.154291	−	0.267239i	0.932800	+	0.360393i	$0.117357\pi$
$908$		0			0
$909$	1.94606e7			0.781170
$910$		0			0
$911$	−3.93310e7			−1.57014			−0.785072	−	0.619405i	$-0.787374\pi$
$911$	−3.93310e7			−1.57014			−0.785072	+	0.619405i	$0.787374\pi$
$912$		0			0
$913$	3.24174e6	−	5.61485e6i	0.128707	−	0.222926i
$914$		0			0
$915$	7.00260e6	+	1.21289e7i	0.276507	+	0.478925i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.76102e7	−	3.05018e7i	−0.687822	−	1.19134i	−0.972541	−	0.232731i	$-0.925234\pi$
$919$	−1.76102e7	−	3.05018e7i	−0.687822	−	1.19134i	0.284720	−	0.958611i	$-0.408100\pi$
$920$		0			0
$921$	−9.00201e6	+	1.55919e7i	−0.349696	+	0.605691i
$922$		0			0
$923$	−6.86587e6			−0.265272
$924$		0			0
$925$	−7.34443e6			−0.282230
$926$		0			0
$927$	1.26867e7	−	2.19740e7i	0.484897	−	0.839866i
$928$		0			0
$929$	−8.31501e6	−	1.44020e7i	−0.316099	−	0.547500i	0.663571	−	0.748113i	$-0.269040\pi$
$929$	−8.31501e6	−	1.44020e7i	−0.316099	−	0.547500i	−0.979671	+	0.200613i	$0.935707\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	4.84696e6	+	8.39519e6i	0.182291	+	0.315738i
$934$		0			0
$935$	−309791.	+	536574.i	−0.0115888	+	0.0200724i
$936$		0			0
$937$	−2.07121e7			−0.770681			−0.385341	−	0.922774i	$-0.625916\pi$
$937$	−2.07121e7			−0.770681			−0.385341	+	0.922774i	$0.625916\pi$
$938$		0			0
$939$	1.63992e7			0.606957
$940$		0			0
$941$	−5.48985e6	+	9.50871e6i	−0.202110	+	0.350064i	−0.949208	−	0.314649i	$-0.898113\pi$
$941$	−5.48985e6	+	9.50871e6i	−0.202110	+	0.350064i	0.747098	+	0.664713i	$0.231446\pi$
$942$		0			0
$943$	−1.23682e7	−	2.14224e7i	−0.452927	−	0.784492i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.35861e6	−	2.35319e6i	−0.0492290	−	0.0852672i	0.840361	−	0.542027i	$-0.182343\pi$
$947$	−1.35861e6	−	2.35319e6i	−0.0492290	−	0.0852672i	−0.889590	+	0.456760i	$0.849010\pi$
$948$		0			0
$949$	−2.67632e6	+	4.63552e6i	−0.0964656	+	0.167083i
$950$		0			0
$951$	3.88182e6			0.139182
$952$		0			0
$953$	−9.24083e6			−0.329594			−0.164797	−	0.986328i	$-0.552697\pi$
$953$	−9.24083e6			−0.329594			−0.164797	+	0.986328i	$0.552697\pi$
$954$		0			0
$955$	−9.03693e6	+	1.56524e7i	−0.320636	+	0.555358i
$956$		0			0
$957$	−3.93604e6	−	6.81743e6i	−0.138925	−	0.240625i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.04113e7	+	1.80329e7i	0.363660	+	0.629877i
$962$		0			0
$963$	2.13882e7	−	3.70454e7i	0.743203	−	1.28727i
$964$		0			0
$965$	8.48183e6			0.293205
$966$		0			0
$967$	−1.50444e7			−0.517379			−0.258690	−	0.965960i	$-0.583291\pi$
$967$	−1.50444e7			−0.517379			−0.258690	+	0.965960i	$0.583291\pi$
$968$		0			0
$969$	−610342.	+	1.05714e6i	−0.0208816	+	0.0361680i
$970$		0			0
$971$	1.13947e7	+	1.97362e7i	0.387842	+	0.671763i	0.992159	−	0.124981i	$-0.0398871\pi$
$971$	1.13947e7	+	1.97362e7i	0.387842	+	0.671763i	−0.604317	+	0.796744i	$0.706554\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−323300.	−	559972.i	−0.0108917	−	0.0188649i
$976$		0			0
$977$	1.98341e7	−	3.43537e7i	0.664777	−	1.15143i	−0.314568	−	0.949235i	$-0.601860\pi$
$977$	1.98341e7	−	3.43537e7i	0.664777	−	1.15143i	0.979346	−	0.202193i	$-0.0648069\pi$
$978$		0			0
$979$	−2.06507e7			−0.688617
$980$		0			0
$981$	−3.94170e7			−1.30771
$982$		0			0
$983$	1.38546e7	−	2.39969e7i	0.457310	−	0.792085i	−0.541507	−	0.840696i	$-0.682146\pi$
$983$	1.38546e7	−	2.39969e7i	0.457310	−	0.792085i	0.998818	+	0.0486112i	$0.0154795\pi$
$984$		0			0
$985$	−2.14147e7	−	3.70914e7i	−0.703270	−	1.21810i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.50127e6	−	1.47246e7i	−0.276372	−	0.478690i
$990$		0			0
$991$	−2.39267e7	+	4.14423e7i	−0.773926	+	1.34048i	0.161470	+	0.986878i	$0.448376\pi$
$991$	−2.39267e7	+	4.14423e7i	−0.773926	+	1.34048i	−0.935396	+	0.353601i	$0.884957\pi$
$992$		0			0
$993$	5.86305e6			0.188691
$994$		0			0
$995$	−3.80837e7			−1.21950
$996$		0			0
$997$	−2.74144e7	+	4.74832e7i	−0.873457	+	1.51287i	−0.0150590	+	0.999887i	$0.504794\pi$
$997$	−2.74144e7	+	4.74832e7i	−0.873457	+	1.51287i	−0.858398	+	0.512985i	$0.828540\pi$
$998$		0			0
$999$	−1.42946e7	−	2.47590e7i	−0.453167	−	0.784909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.6.i.h.361.2		4
7.2	even	3	inner	392.6.i.h.177.2		4
7.3	odd	6		56.6.a.d.1.2	✓	2
7.4	even	3		392.6.a.e.1.1		2
7.5	odd	6		392.6.i.k.177.1		4
7.6	odd	2		392.6.i.k.361.1		4
21.17	even	6		504.6.a.m.1.2		2
28.3	even	6		112.6.a.j.1.1		2
28.11	odd	6		784.6.a.q.1.2		2
56.3	even	6		448.6.a.r.1.2		2
56.45	odd	6		448.6.a.x.1.1		2
84.59	odd	6		1008.6.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.a.d.1.2	✓	2	7.3	odd	6
112.6.a.j.1.1		2	28.3	even	6
392.6.a.e.1.1		2	7.4	even	3
392.6.i.h.177.2		4	7.2	even	3	inner
392.6.i.h.361.2		4	1.1	even	1	trivial
392.6.i.k.177.1		4	7.5	odd	6
392.6.i.k.361.1		4	7.6	odd	2
448.6.a.r.1.2		2	56.3	even	6
448.6.a.x.1.1		2	56.45	odd	6
504.6.a.m.1.2		2	21.17	even	6
784.6.a.q.1.2		2	28.11	odd	6
1008.6.a.bi.1.2		2	84.59	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	392.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.44622 - 5.96903i) q^{3} +(-24.2311 - 41.9695i) q^{5} +(97.7471 + 169.303i) q^{9} +(81.7529 - 141.600i) q^{11} +120.828 q^{13} -334.023 q^{15} +(39.0960 - 67.7162i) q^{17} +(-1132.50 - 1961.55i) q^{19} +(1225.98 + 2123.45i) q^{23} +(388.207 - 672.394i) q^{25} +3022.30 q^{27} +6985.27 q^{29} +(1397.02 - 2419.70i) q^{31} +(-563.477 - 975.971i) q^{33} +(-4729.72 - 8192.11i) q^{37} +(416.402 - 721.229i) q^{39} -10088.5 q^{41} -6934.29 q^{43} +(4737.04 - 8204.80i) q^{45} +(582.882 + 1009.58i) q^{47} +(-269.467 - 466.730i) q^{51} +(-4281.21 + 7415.27i) q^{53} -7923.85 q^{55} -15611.4 q^{57} +(3110.13 - 5386.90i) q^{59} +(-20964.4 - 36311.5i) q^{61} +(-2927.81 - 5071.11i) q^{65} +(-906.046 + 1569.32i) q^{67} +16900.0 q^{69} -56823.3 q^{71} +(-22149.7 + 38364.5i) q^{73} +(-2675.69 - 4634.44i) q^{75} +(-17456.2 - 30235.1i) q^{79} +(-13337.0 + 23100.4i) q^{81} +39652.9 q^{83} -3789.36 q^{85} +(24072.8 - 41695.3i) q^{87} +(-63149.7 - 109378. i) q^{89} +(-9628.85 - 16677.7i) q^{93} +(-54883.4 + 95060.8i) q^{95} +145513. q^{97} +31964.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 14 q^{3} + 42 q^{5} + 2 q^{9} + 716 q^{11} + 1428 q^{13} - 4448 q^{15} - 1344 q^{17} - 1946 q^{19} + 1792 q^{23} - 4282 q^{25} + 3976 q^{27} - 2400 q^{29} - 6804 q^{31} + 10416 q^{33} - 14640 q^{37}+ \cdots - 149880 q^{99}+O(q^{100}) \) 4 * q - 14 * q^3 + 42 * q^5 + 2 * q^9 + 716 * q^11 + 1428 * q^13 - 4448 * q^15 - 1344 * q^17 - 1946 * q^19 + 1792 * q^23 - 4282 * q^25 + 3976 * q^27 - 2400 * q^29 - 6804 * q^31 + 10416 * q^33 - 14640 * q^37 - 11560 * q^39 - 15792 * q^41 + 1048 * q^43 + 26978 * q^45 - 18396 * q^47 - 30252 * q^51 - 45132 * q^53 + 84112 * q^55 - 44552 * q^57 + 22582 * q^59 - 52822 * q^61 + 47804 * q^65 - 9848 * q^67 + 61376 * q^69 - 1680 * q^71 - 122052 * q^73 - 111034 * q^75 - 31704 * q^79 + 41954 * q^81 - 73948 * q^83 - 264888 * q^85 + 219156 * q^87 - 210588 * q^89 - 219784 * q^93 - 138624 * q^95 + 88480 * q^97 - 149880 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more