LMFDB - Embedded newform 336.7.bh.c.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not 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:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 33x^{6} + 2x^{5} + 701x^{4} - 28x^{3} + 6468x^{2} + 5488x + 38416 $ x^8 - 2x^7 + 33x^6 + 2x^5 + 701x^4 - 28x^3 + 6468x^2 + 5488*x + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$1.77014 - 3.06597i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.c.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 - 7.79423i) q^{3} +(-65.9934 + 38.1013i) q^{5} +(334.046 - 77.8600i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 - 7.79423i) q^{3} +(-65.9934 + 38.1013i) q^{5} +(334.046 - 77.8600i) q^{7} +(121.500 + 210.444i) q^{9} +(361.792 - 626.642i) q^{11} +681.463i q^{13} +1187.88 q^{15} +(-645.081 - 372.438i) q^{17} +(3276.22 - 1891.53i) q^{19} +(-5116.48 - 1552.52i) q^{21} +(1734.53 + 3004.30i) q^{23} +(-4909.08 + 8502.78i) q^{25} -3788.00i q^{27} +16206.6 q^{29} +(-39852.0 - 23008.6i) q^{31} +(-9768.39 + 5639.78i) q^{33} +(-19078.3 + 17865.8i) q^{35} +(29917.2 + 51818.1i) q^{37} +(5311.48 - 9199.75i) q^{39} -22221.2i q^{41} -137706. q^{43} +(-16036.4 - 9258.61i) q^{45} +(17491.0 - 10098.5i) q^{47} +(105525. - 52017.6i) q^{49} +(5805.73 + 10055.8i) q^{51} +(-74637.4 + 129276. i) q^{53} +55139.0i q^{55} -58972.0 q^{57} +(238196. + 137523. i) q^{59} +(-24595.1 + 14200.0i) q^{61} +(56971.8 + 60838.1i) q^{63} +(-25964.6 - 44972.0i) q^{65} +(183124. - 317181. i) q^{67} -54077.3i q^{69} +627339. q^{71} +(36263.1 + 20936.5i) q^{73} +(132545. - 76525.0i) q^{75} +(72064.9 - 237497. i) q^{77} +(-170439. - 295210. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +997103. i q^{83} +56761.5 q^{85} +(-218790. - 126318. i) q^{87} +(1.11190e6 - 641958. i) q^{89} +(53058.7 + 227640. i) q^{91} +(358668. + 621231. i) q^{93} +(-144139. + 249657. i) q^{95} -1.34466e6i q^{97} +175831. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9} - 2058 q^{11} - 3780 q^{15} - 11244 q^{17} - 21834 q^{19} - 4482 q^{21} - 15504 q^{23} - 6550 q^{25} + 35316 q^{29} + 51060 q^{31} + 55566 q^{33} - 71460 q^{35} + 20282 q^{37} + 101682 q^{39} - 387812 q^{43} + 51030 q^{45} + 55212 q^{47} - 277780 q^{49} + 101196 q^{51} - 336174 q^{53} + 393012 q^{57} + 560454 q^{59} + 850728 q^{61} - 26730 q^{63} + 826380 q^{65} + 947882 q^{67} - 147192 q^{71} - 533034 q^{73} + 176850 q^{75} - 1848102 q^{77} + 6260 q^{79} - 236196 q^{81} + 560040 q^{85} - 476766 q^{87} + 413460 q^{89} - 256074 q^{91} - 459540 q^{93} + 170880 q^{95} - 1000188 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9 - 2058 * q^11 - 3780 * q^15 - 11244 * q^17 - 21834 * q^19 - 4482 * q^21 - 15504 * q^23 - 6550 * q^25 + 35316 * q^29 + 51060 * q^31 + 55566 * q^33 - 71460 * q^35 + 20282 * q^37 + 101682 * q^39 - 387812 * q^43 + 51030 * q^45 + 55212 * q^47 - 277780 * q^49 + 101196 * q^51 - 336174 * q^53 + 393012 * q^57 + 560454 * q^59 + 850728 * q^61 - 26730 * q^63 + 826380 * q^65 + 947882 * q^67 - 147192 * q^71 - 533034 * q^73 + 176850 * q^75 - 1848102 * q^77 + 6260 * q^79 - 236196 * q^81 + 560040 * q^85 - 476766 * q^87 + 413460 * q^89 - 256074 * q^91 - 459540 * q^93 + 170880 * q^95 - 1000188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$4$		0			0
$5$	−65.9934	+	38.1013i	−0.527947	+	0.304810i	−0.740180	−	0.672409i	$-0.765260\pi$
$5$	−65.9934	+	38.1013i	−0.527947	+	0.304810i	0.212233	+	0.977219i	$0.431926\pi$
$6$		0			0
$7$	334.046	−	77.8600i	0.973895	−	0.226997i
$7$	334.046	−	77.8600i	0.973895	−	0.226997i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	361.792	−	626.642i	0.271820	−	0.470806i	−0.697508	−	0.716577i	$-0.745708\pi$
$11$	361.792	−	626.642i	0.271820	−	0.470806i	0.969328	+	0.245771i	$0.0790412\pi$
$12$		0			0
$13$			681.463i			0.310179i	0.987900	+	0.155089i	$0.0495666\pi$
$13$			681.463i			0.310179i	−0.987900	+	0.155089i	$0.950433\pi$
$14$		0			0
$15$	1187.88			0.351965
$16$		0			0
$17$	−645.081	−	372.438i	−0.131301	−	0.0758066i	0.432911	−	0.901437i	$-0.357486\pi$
$17$	−645.081	−	372.438i	−0.131301	−	0.0758066i	−0.564212	+	0.825630i	$0.690820\pi$
$18$		0			0
$19$	3276.22	−	1891.53i	0.477653	−	0.275773i	−0.241785	−	0.970330i	$-0.577733\pi$
$19$	3276.22	−	1891.53i	0.477653	−	0.275773i	0.719438	+	0.694557i	$0.244399\pi$
$20$		0			0
$21$	−5116.48	−	1552.52i	−0.552476	−	0.167641i
$22$		0			0
$23$	1734.53	+	3004.30i	0.142560	+	0.246922i	0.928460	−	0.371432i	$-0.121133\pi$
$23$	1734.53	+	3004.30i	0.142560	+	0.246922i	−0.785900	+	0.618354i	$0.787800\pi$
$24$		0			0
$25$	−4909.08	+	8502.78i	−0.314181	+	0.544178i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	16206.6			0.664506			0.332253	−	0.943190i	$-0.392191\pi$
$29$	16206.6			0.664506			0.332253	+	0.943190i	$0.392191\pi$
$30$		0			0
$31$	−39852.0	−	23008.6i	−1.33772	−	0.772333i	−0.351251	−	0.936281i	$-0.614244\pi$
$31$	−39852.0	−	23008.6i	−1.33772	−	0.772333i	−0.986469	+	0.163948i	$0.947577\pi$
$32$		0			0
$33$	−9768.39	+	5639.78i	−0.271820	+	0.156935i
$34$		0			0
$35$	−19078.3	+	17865.8i	−0.444974	+	0.416696i
$36$		0			0
$37$	29917.2	+	51818.1i	0.590630	+	1.02300i	0.994148	+	0.108030i	$0.0344542\pi$
$37$	29917.2	+	51818.1i	0.590630	+	1.02300i	−0.403517	+	0.914972i	$0.632212\pi$
$38$		0			0
$39$	5311.48	−	9199.75i	0.0895409	−	0.155089i
$40$		0			0
$41$		−	22221.2i		−	0.322415i	−0.986921	−	0.161207i	$-0.948461\pi$
$41$		−	22221.2i		−	0.322415i	0.986921	−	0.161207i	$-0.0515388\pi$
$42$		0			0
$43$	−137706.			−1.73200			−0.866002	−	0.500040i	$-0.833319\pi$
$43$	−137706.			−1.73200			−0.866002	+	0.500040i	$0.833319\pi$
$44$		0			0
$45$	−16036.4	−	9258.61i	−0.175982	−	0.101603i
$46$		0			0
$47$	17491.0	−	10098.5i	0.168470	−	0.0972661i	−0.413394	−	0.910552i	$-0.635657\pi$
$47$	17491.0	−	10098.5i	0.168470	−	0.0972661i	0.581864	+	0.813286i	$0.302324\pi$
$48$		0			0
$49$	105525.	−	52017.6i	0.896945	−	0.442143i
$50$		0			0
$51$	5805.73	+	10055.8i	0.0437670	+	0.0758066i
$52$		0			0
$53$	−74637.4	+	129276.i	−0.501336	+	0.868340i	0.498663	+	0.866796i	$0.333825\pi$
$53$	−74637.4	+	129276.i	−0.501336	+	0.868340i	−0.999999	+	0.00154361i	$0.999509\pi$
$54$		0			0
$55$			55139.0i			0.331414i
$56$		0			0
$57$	−58972.0			−0.318436
$58$		0			0
$59$	238196.	+	137523.i	1.15979	+	0.669605i	0.951254	−	0.308410i	$-0.0997969\pi$
$59$	238196.	+	137523.i	1.15979	+	0.669605i	0.208536	+	0.978015i	$0.433130\pi$
$60$		0			0
$61$	−24595.1	+	14200.0i	−0.108357	+	0.0625602i	−0.553199	−	0.833049i	$-0.686593\pi$
$61$	−24595.1	+	14200.0i	−0.108357	+	0.0625602i	0.444842	+	0.895609i	$0.353260\pi$
$62$		0			0
$63$	56971.8	+	60838.1i	0.227844	+	0.243307i
$64$		0			0
$65$	−25964.6	−	44972.0i	−0.0945457	−	0.163758i
$66$		0			0
$67$	183124.	−	317181.i	0.608866	−	1.05459i	−0.382561	−	0.923930i	$-0.624958\pi$
$67$	183124.	−	317181.i	0.608866	−	1.05459i	0.991428	−	0.130657i	$-0.0417088\pi$
$68$		0			0
$69$		−	54077.3i		−	0.164614i
$70$		0			0
$71$	627339.			1.75278			0.876389	−	0.481603i	$-0.159945\pi$
$71$	627339.			1.75278			0.876389	+	0.481603i	$0.159945\pi$
$72$		0			0
$73$	36263.1	+	20936.5i	0.0932172	+	0.0538190i	0.545884	−	0.837861i	$-0.316194\pi$
$73$	36263.1	+	20936.5i	0.0932172	+	0.0538190i	−0.452667	+	0.891680i	$0.649527\pi$
$74$		0			0
$75$	132545.	−	76525.0i	0.314181	−	0.181393i
$76$		0			0
$77$	72064.9	−	237497.i	0.157853	−	0.520218i
$78$		0			0
$79$	−170439.	−	295210.i	−0.345691	−	0.598755i	0.639788	−	0.768552i	$-0.279022\pi$
$79$	−170439.	−	295210.i	−0.345691	−	0.598755i	−0.985479	+	0.169797i	$0.945689\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			997103.i			1.74384i	0.489651	+	0.871918i	$0.337124\pi$
$83$			997103.i			1.74384i	−0.489651	+	0.871918i	$0.662876\pi$
$84$		0			0
$85$	56761.5			0.0924266
$86$		0			0
$87$	−218790.	−	126318.i	−0.332253	−	0.191826i
$88$		0			0
$89$	1.11190e6	−	641958.i	1.57724	−	0.910619i	0.581995	−	0.813192i	$-0.302272\pi$
$89$	1.11190e6	−	641958.i	1.57724	−	0.910619i	0.995243	−	0.0974262i	$-0.0310610\pi$
$90$		0			0
$91$	53058.7	+	227640.i	0.0704097	+	0.302082i
$92$		0			0
$93$	358668.	+	621231.i	0.445907	+	0.772333i
$94$		0			0
$95$	−144139.	+	249657.i	−0.168117	+	0.291187i
$96$		0			0
$97$		−	1.34466e6i		−	1.47332i	−0.676264	−	0.736660i	$-0.736402\pi$
$97$		−	1.34466e6i		−	1.47332i	0.676264	−	0.736660i	$-0.263598\pi$
$98$		0			0
$99$	175831.			0.181213
$100$		0			0
$101$	685157.	+	395576.i	0.665007	+	0.383942i	0.794182	−	0.607680i	$-0.207900\pi$
$101$	685157.	+	395576.i	0.665007	+	0.383942i	−0.129175	+	0.991622i	$0.541233\pi$
$102$		0			0
$103$	1.13941e6	−	657837.i	1.04272	−	0.602014i	0.122116	−	0.992516i	$-0.461032\pi$
$103$	1.13941e6	−	657837.i	1.04272	−	0.602014i	0.920602	+	0.390502i	$0.127699\pi$
$104$		0			0
$105$	396807.	−	92488.3i	0.342777	−	0.0798949i
$106$		0			0
$107$	−617172.	−	1.06897e6i	−0.503796	−	0.872601i	−0.999990	−	0.00438924i	$-0.998603\pi$
$107$	−617172.	−	1.06897e6i	−0.503796	−	0.872601i	0.496194	−	0.868212i	$-0.334730\pi$
$108$		0			0
$109$	−394741.	+	683711.i	−0.304812	+	0.527950i	−0.977220	−	0.212231i	$-0.931927\pi$
$109$	−394741.	+	683711.i	−0.304812	+	0.527950i	0.672407	+	0.740181i	$0.265260\pi$
$110$		0			0
$111$		−	932726.i		−	0.682001i
$112$		0			0
$113$	−601721.			−0.417023			−0.208511	−	0.978020i	$-0.566862\pi$
$113$	−601721.			−0.417023			−0.208511	+	0.978020i	$0.566862\pi$
$114$		0			0
$115$	−228935.	−	132176.i	−0.150529	−	0.0869077i
$116$		0			0
$117$	−143410.	+	82797.8i	−0.0895409	+	0.0516965i
$118$		0			0
$119$	−244485.	−	74185.4i	−0.145081	−	0.0440228i
$120$		0			0
$121$	623993.	+	1.08079e6i	0.352228	+	0.610077i
$122$		0			0
$123$	−173197.	+	299986.i	−0.0930732	+	0.161207i
$124$		0			0
$125$		−	1.93883e6i		−	0.992684i
$126$		0			0
$127$	3.57343e6			1.74451			0.872256	−	0.489049i	$-0.162656\pi$
$127$	3.57343e6			1.74451			0.872256	+	0.489049i	$0.162656\pi$
$128$		0			0
$129$	1.85904e6	+	1.07332e6i	0.866002	+	0.499987i
$130$		0			0
$131$	2.59310e6	−	1.49713e6i	1.15347	−	0.665956i	0.203739	−	0.979025i	$-0.434690\pi$
$131$	2.59310e6	−	1.49713e6i	1.15347	−	0.665956i	0.949730	+	0.313069i	$0.101357\pi$
$132$		0			0
$133$	947136.	−	886945.i	0.402585	−	0.377000i
$134$		0			0
$135$	144328.	+	249983.i	0.0586608	+	0.101603i
$136$		0			0
$137$	1.27777e6	−	2.21316e6i	0.496924	−	0.860697i	−0.503070	−	0.864246i	$-0.667796\pi$
$137$	1.27777e6	−	2.21316e6i	0.496924	−	0.860697i	0.999994	+	0.00354867i	$0.00112958\pi$
$138$		0			0
$139$			1.02313e6i			0.380968i	0.981690	+	0.190484i	$0.0610057\pi$
$139$			1.02313e6i			0.380968i	−0.981690	+	0.190484i	$0.938994\pi$
$140$		0			0
$141$	−314839.			−0.112313
$142$		0			0
$143$	427034.	+	246548.i	0.146034	+	0.0843128i
$144$		0			0
$145$	−1.06953e6	+	617494.i	−0.350824	+	0.202548i
$146$		0			0
$147$	−1.83002e6	−	120245.i	−0.576108	−	0.0378543i
$148$		0			0
$149$	2.52985e6	+	4.38183e6i	0.764780	+	1.32464i	0.940363	+	0.340173i	$0.110486\pi$
$149$	2.52985e6	+	4.38183e6i	0.764780	+	1.32464i	−0.175583	+	0.984465i	$0.556181\pi$
$150$		0			0
$151$	784536.	−	1.35886e6i	0.227867	−	0.394678i	−0.729309	−	0.684185i	$-0.760158\pi$
$151$	784536.	−	1.35886e6i	0.227867	−	0.394678i	0.957176	+	0.289507i	$0.0934914\pi$
$152$		0			0
$153$		−	181005.i		−	0.0505377i
$154$		0			0
$155$	3.50662e6			0.941660
$156$		0			0
$157$	4.57450e6	+	2.64109e6i	1.18207	+	0.682470i	0.956493	−	0.291755i	$-0.0942391\pi$
$157$	4.57450e6	+	2.64109e6i	1.18207	+	0.682470i	0.225580	+	0.974225i	$0.427572\pi$
$158$		0			0
$159$	2.01521e6	−	1.16348e6i	0.501336	−	0.289447i
$160$		0			0
$161$	813328.	+	868523.i	0.194889	+	0.208115i
$162$		0			0
$163$	−5009.33	−	8676.41i	−0.00115669	−	0.00200345i	0.865446	−	0.501001i	$-0.167035\pi$
$163$	−5009.33	−	8676.41i	−0.00115669	−	0.00200345i	−0.866603	+	0.498998i	$0.833702\pi$
$164$		0			0
$165$	429766.	−	744377.i	0.0956710	−	0.165707i
$166$		0			0
$167$			1.89890e6i			0.407711i	0.979001	+	0.203855i	$0.0653472\pi$
$167$			1.89890e6i			0.407711i	−0.979001	+	0.203855i	$0.934653\pi$
$168$		0			0
$169$	4.36242e6			0.903789
$170$		0			0
$171$	796123.	+	459642.i	0.159218	+	0.0919244i
$172$		0			0
$173$	1.08312e6	−	625341.i	0.209189	−	0.120775i	−0.391745	−	0.920074i	$-0.628129\pi$
$173$	1.08312e6	−	625341.i	0.209189	−	0.120775i	0.600934	+	0.799298i	$0.294795\pi$
$174$		0			0
$175$	−977834.	+	3.22254e6i	−0.182453	+	0.601291i
$176$		0			0
$177$	−2.14377e6	−	3.71311e6i	−0.386596	−	0.669605i
$178$		0			0
$179$	−2.40750e6	+	4.16992e6i	−0.419766	+	0.727057i	−0.995916	−	0.0902877i	$-0.971221\pi$
$179$	−2.40750e6	+	4.16992e6i	−0.419766	+	0.727057i	0.576149	+	0.817344i	$0.304555\pi$
$180$		0			0
$181$		−	3.51401e6i		−	0.592608i	−0.955094	−	0.296304i	$-0.904246\pi$
$181$		−	3.51401e6i		−	0.592608i	0.955094	−	0.296304i	$-0.0957542\pi$
$182$		0			0
$183$	442711.			0.0722383
$184$		0			0
$185$	−3.94867e6	−	2.27977e6i	−0.623643	−	0.360060i
$186$		0			0
$187$	−466771.	+	269490.i	−0.0713804	+	0.0412115i
$188$		0			0
$189$	−294933.	−	1.26537e6i	−0.0436856	−	0.187426i
$190$		0			0
$191$	−1.12447e6	−	1.94763e6i	−0.161379	−	0.279516i	0.773985	−	0.633204i	$-0.218261\pi$
$191$	−1.12447e6	−	1.94763e6i	−0.161379	−	0.279516i	−0.935363	+	0.353688i	$0.884927\pi$
$192$		0			0
$193$	−313767.	+	543460.i	−0.0436450	+	0.0755954i	−0.887023	−	0.461726i	$-0.847230\pi$
$193$	−313767.	+	543460.i	−0.0436450	+	0.0755954i	0.843378	+	0.537321i	$0.180564\pi$
$194$		0			0
$195$			809497.i			0.109172i
$196$		0			0
$197$	2.58174e6			0.337687			0.168843	−	0.985643i	$-0.445997\pi$
$197$	2.58174e6			0.337687			0.168843	+	0.985643i	$0.445997\pi$
$198$		0			0
$199$	−1.26866e6	−	732460.i	−0.160985	−	0.0929447i	0.417343	−	0.908749i	$-0.362961\pi$
$199$	−1.26866e6	−	732460.i	−0.160985	−	0.0929447i	−0.578328	+	0.815804i	$0.696295\pi$
$200$		0			0
$201$	−4.94436e6	+	2.85463e6i	−0.608866	+	0.351529i
$202$		0			0
$203$	5.41376e6	−	1.26185e6i	0.647159	−	0.150841i
$204$		0			0
$205$	846655.	+	1.46645e6i	0.0982754	+	0.170218i
$206$		0			0
$207$	−421491.	+	730044.i	−0.0475201	+	0.0823072i
$208$		0			0
$209$		−	2.73736e6i		−	0.299843i
$210$		0			0
$211$	−9.66376e6			−1.02872			−0.514362	−	0.857573i	$-0.671971\pi$
$211$	−9.66376e6			−1.02872			−0.514362	+	0.857573i	$0.671971\pi$
$212$		0			0
$213$	−8.46907e6	−	4.88962e6i	−0.876389	−	0.505984i
$214$		0			0
$215$	9.08771e6	−	5.24679e6i	0.914406	−	0.527933i
$216$		0			0
$217$	−1.51039e7	−	4.58305e6i	−1.47812	−	0.448513i
$218$		0			0
$219$	−326368.	−	565286.i	−0.0310724	−	0.0538190i
$220$		0			0
$221$	253803.	−	439599.i	0.0235136	−	0.0407268i
$222$		0			0
$223$		−	8.68374e6i		−	0.783055i	−0.920166	−	0.391527i	$-0.871947\pi$
$223$		−	8.68374e6i		−	0.783055i	0.920166	−	0.391527i	$-0.128053\pi$
$224$		0			0
$225$	−2.38581e6			−0.209454
$226$		0			0
$227$	1.62883e7	+	9.40408e6i	1.39251	+	0.803968i	0.993593	−	0.113018i	$-0.0360519\pi$
$227$	1.62883e7	+	9.40408e6i	1.39251	+	0.803968i	0.398920	+	0.916986i	$0.369385\pi$
$228$		0			0
$229$	2.96505e6	−	1.71187e6i	0.246903	−	0.142549i	−0.371442	−	0.928456i	$-0.621137\pi$
$229$	2.96505e6	−	1.71187e6i	0.246903	−	0.142549i	0.618345	+	0.785907i	$0.287803\pi$
$230$		0			0
$231$	−2.82398e6	+	2.64451e6i	−0.229100	+	0.214541i
$232$		0			0
$233$	1.18982e7	+	2.06083e7i	0.940619	+	1.62920i	0.764294	+	0.644867i	$0.223087\pi$
$233$	1.18982e7	+	2.06083e7i	0.940619	+	1.62920i	0.176324	+	0.984332i	$0.443579\pi$
$234$		0			0
$235$	−769529.	+	1.33286e6i	−0.0592954	+	0.102703i
$236$		0			0
$237$			5.31377e6i			0.399170i
$238$		0			0
$239$	−1.46940e7			−1.07634			−0.538168	−	0.842838i	$-0.680883\pi$
$239$	−1.46940e7			−1.07634			−0.538168	+	0.842838i	$0.680883\pi$
$240$		0			0
$241$	2.07831e6	+	1.19992e6i	0.148477	+	0.0857234i	0.572398	−	0.819976i	$-0.306013\pi$
$241$	2.07831e6	+	1.19992e6i	0.148477	+	0.0857234i	−0.423921	+	0.905699i	$0.639347\pi$
$242$		0			0
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−4.98199e6	+	7.45344e6i	−0.338770	+	0.506826i
$246$		0			0
$247$	1.28901e6	+	2.23263e6i	0.0855391	+	0.148158i
$248$		0			0
$249$	7.77165e6	−	1.34609e7i	0.503402	−	0.871918i
$250$		0			0
$251$		−	2.42524e7i		−	1.53368i	−0.641839	−	0.766839i	$-0.721828\pi$
$251$		−	2.42524e7i		−	1.53368i	0.641839	−	0.766839i	$-0.278172\pi$
$252$		0			0
$253$	2.51016e6			0.155003
$254$		0			0
$255$	−766280.	−	442412.i	−0.0462133	−	0.0266812i
$256$		0			0
$257$	5.49412e6	−	3.17203e6i	0.323667	−	0.186869i	−0.329359	−	0.944205i	$-0.606833\pi$
$257$	5.49412e6	−	3.17203e6i	0.323667	−	0.186869i	0.653026	+	0.757336i	$0.273499\pi$
$258$		0			0
$259$	1.40283e7	+	1.49803e7i	0.807431	+	0.862226i
$260$		0			0
$261$	1.96911e6	+	3.41059e6i	0.110751	+	0.191826i
$262$		0			0
$263$	−4.83709e6	+	8.37809e6i	−0.265899	+	0.460551i	−0.967799	−	0.251725i	$-0.919002\pi$
$263$	−4.83709e6	+	8.37809e6i	−0.265899	+	0.460551i	0.701900	+	0.712276i	$0.252336\pi$
$264$		0			0
$265$		−	1.13751e7i		−	0.611250i
$266$		0			0
$267$	−2.00143e7			−1.05149
$268$		0			0
$269$	9.92469e6	+	5.73002e6i	0.509871	+	0.294374i	0.732780	−	0.680465i	$-0.238222\pi$
$269$	9.92469e6	+	5.73002e6i	0.509871	+	0.294374i	−0.222910	+	0.974839i	$0.571556\pi$
$270$		0			0
$271$	310180.	−	179082.i	0.0155849	−	0.00899797i	−0.492187	−	0.870489i	$-0.663802\pi$
$271$	310180.	−	179082.i	0.0155849	−	0.00899797i	0.507772	+	0.861491i	$0.330469\pi$
$272$		0			0
$273$	1.05799e6	−	3.48669e6i	0.0519987	−	0.171366i
$274$		0			0
$275$	3.55214e6	+	6.15248e6i	0.170801	+	0.295837i
$276$		0			0
$277$	−3.75013e6	+	6.49542e6i	−0.176444	+	0.305610i	−0.940660	−	0.339350i	$-0.889793\pi$
$277$	−3.75013e6	+	6.49542e6i	−0.176444	+	0.305610i	0.764216	+	0.644960i	$0.223126\pi$
$278$		0			0
$279$		−	1.11822e7i		−	0.514889i
$280$		0			0
$281$	2.16443e7			0.975494			0.487747	−	0.872985i	$-0.337819\pi$
$281$	2.16443e7			0.975494			0.487747	+	0.872985i	$0.337819\pi$
$282$		0			0
$283$	−3.29465e7	−	1.90216e7i	−1.45361	−	0.839245i	−0.454931	−	0.890527i	$-0.650336\pi$
$283$	−3.29465e7	−	1.90216e7i	−1.45361	−	0.839245i	−0.998684	+	0.0512820i	$0.983669\pi$
$284$		0			0
$285$	3.89176e6	−	2.24691e6i	0.168117	−	0.0970624i
$286$		0			0
$287$	−1.73014e6	−	7.42289e6i	−0.0731872	−	0.313998i
$288$		0			0
$289$	−1.17914e7	−	2.04232e7i	−0.488507	−	0.846118i
$290$		0			0
$291$	−1.04806e7	+	1.81529e7i	−0.425311	+	0.736660i
$292$		0			0
$293$			2.83379e7i			1.12659i	0.826257	+	0.563293i	$0.190466\pi$
$293$			2.83379e7i			1.12659i	−0.826257	+	0.563293i	$0.809534\pi$
$294$		0			0
$295$	−2.09592e7			−0.816410
$296$		0			0
$297$	−2.37372e6	−	1.37047e6i	−0.0906066	−	0.0523118i
$298$		0			0
$299$	−2.04732e6	+	1.18202e6i	−0.0765899	+	0.0442192i
$300$		0			0
$301$	−4.60003e7	+	1.07218e7i	−1.68679	+	0.393160i
$302$		0			0
$303$	−6.16642e6	−	1.06805e7i	−0.221669	−	0.383942i
$304$		0			0
$305$	1.08207e6	−	1.87421e6i	0.0381380	−	0.0660569i
$306$		0			0
$307$			1.32974e7i			0.459569i	0.973242	+	0.229785i	$0.0738022\pi$
$307$			1.32974e7i			0.459569i	−0.973242	+	0.229785i	$0.926198\pi$
$308$		0			0
$309$	−2.05093e7			−0.695145
$310$		0			0
$311$	−4.11104e6	−	2.37351e6i	−0.136669	−	0.0789060i	0.430106	−	0.902778i	$-0.358476\pi$
$311$	−4.11104e6	−	2.37351e6i	−0.136669	−	0.0789060i	−0.566776	+	0.823872i	$0.691809\pi$
$312$		0			0
$313$	−2.95277e7	+	1.70478e7i	−0.962934	+	0.555950i	−0.897075	−	0.441878i	$-0.854312\pi$
$313$	−2.95277e7	+	1.70478e7i	−0.962934	+	0.555950i	−0.0658595	+	0.997829i	$0.520979\pi$
$314$		0			0
$315$	−6.07777e6	−	1.84421e6i	−0.194452	−	0.0590037i
$316$		0			0
$317$	−1.58965e7	−	2.75335e7i	−0.499025	−	0.864337i	0.500974	−	0.865462i	$-0.332975\pi$
$317$	−1.58965e7	−	2.75335e7i	−0.499025	−	0.864337i	−0.999999	+	0.00112521i	$0.999642\pi$
$318$		0			0
$319$	5.86343e6	−	1.01558e7i	0.180626	−	0.312853i
$320$		0			0
$321$			1.92415e7i			0.581734i
$322$		0			0
$323$	−2.81791e6			−0.0836218
$324$		0			0
$325$	−5.79433e6	−	3.34536e6i	−0.168793	−	0.0974524i
$326$		0			0
$327$	1.06580e7	−	6.15340e6i	0.304812	−	0.175983i
$328$		0			0
$329$	5.05655e6	−	4.73520e6i	0.141993	−	0.132969i
$330$		0			0
$331$	1.72553e7	+	2.98871e7i	0.475816	+	0.824138i	0.999616	−	0.0277036i	$-0.00881946\pi$
$331$	1.72553e7	+	2.98871e7i	0.475816	+	0.824138i	−0.523800	+	0.851841i	$0.675486\pi$
$332$		0			0
$333$	−7.26988e6	+	1.25918e7i	−0.196877	+	0.341001i
$334$		0			0
$335$			2.79091e7i			0.742355i
$336$		0			0
$337$	−3.51575e7			−0.918604			−0.459302	−	0.888280i	$-0.651900\pi$
$337$	−3.51575e7			−0.918604			−0.459302	+	0.888280i	$0.651900\pi$
$338$		0			0
$339$	8.12323e6	+	4.68995e6i	0.208511	+	0.120384i
$340$		0			0
$341$	−2.88363e7	+	1.66486e7i	−0.727238	+	0.419871i
$342$		0			0
$343$	3.12000e7	−	2.55924e7i	0.773165	−	0.634204i
$344$		0			0
$345$	2.06042e6	+	3.56874e6i	0.0501762	+	0.0869077i
$346$		0			0
$347$	−2.50882e7	+	4.34541e7i	−0.600456	+	1.04002i	0.392296	+	0.919839i	$0.371681\pi$
$347$	−2.50882e7	+	4.34541e7i	−0.600456	+	1.04002i	−0.992752	+	0.120181i	$0.961652\pi$
$348$		0			0
$349$		−	6.33704e7i		−	1.49077i	−0.666635	−	0.745384i	$-0.732266\pi$
$349$		−	6.33704e7i		−	1.49077i	0.666635	−	0.745384i	$-0.267734\pi$
$350$		0			0
$351$	2.58138e6			0.0596940
$352$		0			0
$353$	−3.54979e7	−	2.04947e7i	−0.807010	−	0.465928i	0.0389063	−	0.999243i	$-0.487613\pi$
$353$	−3.54979e7	−	2.04947e7i	−0.807010	−	0.465928i	−0.845917	+	0.533315i	$0.820946\pi$
$354$		0			0
$355$	−4.14002e7	+	2.39024e7i	−0.925374	+	0.534265i
$356$		0			0
$357$	2.72233e6	+	2.90707e6i	0.0598323	+	0.0638927i
$358$		0			0
$359$	1.49127e7	+	2.58295e7i	0.322308	+	0.558255i	0.980964	−	0.194190i	$-0.0622078\pi$
$359$	1.49127e7	+	2.58295e7i	0.322308	+	0.558255i	−0.658655	+	0.752445i	$0.728875\pi$
$360$		0			0
$361$	−1.63672e7	+	2.83488e7i	−0.347898	+	0.602577i
$362$		0			0
$363$		−	1.94542e7i		−	0.406718i
$364$		0			0
$365$	−3.19083e6			−0.0656183
$366$		0			0
$367$	−7.82009e7	−	4.51493e7i	−1.58203	−	0.913383i	−0.994564	−	0.104131i	$-0.966794\pi$
$367$	−7.82009e7	−	4.51493e7i	−1.58203	−	0.913383i	−0.587462	−	0.809252i	$-0.699873\pi$
$368$		0			0
$369$	4.67631e6	−	2.69987e6i	0.0930732	−	0.0537358i
$370$		0			0
$371$	−1.48669e7	+	4.89954e7i	−0.291139	+	0.959474i
$372$		0			0
$373$	2.81899e7	+	4.88264e7i	0.543210	+	0.940867i	0.998717	+	0.0506352i	$0.0161246\pi$
$373$	2.81899e7	+	4.88264e7i	0.543210	+	0.940867i	−0.455507	+	0.890232i	$0.650542\pi$
$374$		0			0
$375$	−1.51117e7	+	2.61743e7i	−0.286563	+	0.496342i
$376$		0			0
$377$			1.10442e7i			0.206116i
$378$		0			0
$379$	−6.23208e7			−1.14476			−0.572381	−	0.819988i	$-0.693980\pi$
$379$	−6.23208e7			−1.14476			−0.572381	+	0.819988i	$0.693980\pi$
$380$		0			0
$381$	−4.82413e7	−	2.78521e7i	−0.872256	−	0.503597i
$382$		0			0
$383$	9.47736e7	−	5.47175e7i	1.68691	−	0.973936i	0.730041	−	0.683403i	$-0.239501\pi$
$383$	9.47736e7	−	5.47175e7i	1.68691	−	0.973936i	0.956865	−	0.290532i	$-0.0938324\pi$
$384$		0			0
$385$	4.29312e6	+	1.84190e7i	0.0752300	+	0.322763i
$386$		0			0
$387$	−1.67313e7	−	2.89795e7i	−0.288667	−	0.499987i
$388$		0			0
$389$	4.36370e7	−	7.55815e7i	0.741321	−	1.28401i	−0.210573	−	0.977578i	$-0.567533\pi$
$389$	4.36370e7	−	7.55815e7i	0.741321	−	1.28401i	0.951894	−	0.306427i	$-0.0991336\pi$
$390$		0			0
$391$		−	2.58402e6i		−	0.0432280i
$392$		0			0
$393$	−4.66759e7			−0.768980
$394$		0			0
$395$	2.24957e7	+	1.29879e7i	0.365013	+	0.210741i
$396$		0			0
$397$	6.70522e7	−	3.87126e7i	1.07162	−	0.618701i	0.142997	−	0.989723i	$-0.454326\pi$
$397$	6.70522e7	−	3.87126e7i	1.07162	−	0.618701i	0.928624	+	0.371022i	$0.120993\pi$
$398$		0			0
$399$	−1.96994e7	+	4.59156e6i	−0.310123	+	0.0722839i
$400$		0			0
$401$	4.14946e7	+	7.18708e7i	0.643515	+	1.11460i	0.984642	+	0.174584i	$0.0558580\pi$
$401$	4.14946e7	+	7.18708e7i	0.643515	+	1.11460i	−0.341127	+	0.940017i	$0.610809\pi$
$402$		0			0
$403$	1.56795e7	−	2.71577e7i	0.239561	−	0.414932i
$404$		0			0
$405$		−	4.49969e6i		−	0.0677356i
$406$		0			0
$407$	4.32952e7			0.642180
$408$		0			0
$409$	3.88077e7	+	2.24056e7i	0.567215	+	0.327482i	0.756036	−	0.654530i	$-0.227133\pi$
$409$	3.88077e7	+	2.24056e7i	0.567215	+	0.327482i	−0.188821	+	0.982011i	$0.560467\pi$
$410$		0			0
$411$	−3.44997e7	+	1.99184e7i	−0.496924	+	0.286899i
$412$		0			0
$413$	9.02761e7	+	2.73930e7i	1.28151	+	0.388856i
$414$		0			0
$415$	−3.79909e7	−	6.58022e7i	−0.531540	−	0.920653i
$416$		0			0
$417$	7.97454e6	−	1.38123e7i	0.109976	−	0.190484i
$418$		0			0
$419$			7.57914e7i			1.03033i	0.857090	+	0.515166i	$0.172270\pi$
$419$			7.57914e7i			1.03033i	−0.857090	+	0.515166i	$0.827730\pi$
$420$		0			0
$421$	−2.76960e7			−0.371169			−0.185584	−	0.982628i	$-0.559418\pi$
$421$	−2.76960e7			−0.371169			−0.185584	+	0.982628i	$0.559418\pi$
$422$		0			0
$423$	4.25032e6	+	2.45393e6i	0.0561566	+	0.0324220i
$424$		0			0
$425$	6.33352e6	−	3.65666e6i	0.0825046	−	0.0476340i
$426$		0			0
$427$	−7.11028e6	+	6.65842e6i	−0.0913278	+	0.0855239i
$428$		0			0
$429$	−3.84330e6	−	6.65680e6i	−0.0486780	−	0.0843128i
$430$		0			0
$431$	6.68429e7	−	1.15775e8i	0.834879	−	1.44605i	−0.0592499	−	0.998243i	$-0.518871\pi$
$431$	6.68429e7	−	1.15775e8i	0.834879	−	1.44605i	0.894129	−	0.447810i	$-0.147796\pi$
$432$		0			0
$433$		−	3.41335e7i		−	0.420452i	−0.977653	−	0.210226i	$-0.932580\pi$
$433$		−	3.41335e7i		−	0.420452i	0.977653	−	0.210226i	$-0.0674200\pi$
$434$		0			0
$435$	1.92516e7			0.233883
$436$		0			0
$437$	1.13654e7	+	6.56183e6i	0.136189	+	0.0786286i
$438$		0			0
$439$	−7.30681e7	+	4.21859e7i	−0.863643	+	0.498625i	−0.865231	−	0.501374i	$-0.832828\pi$
$439$	−7.30681e7	+	4.21859e7i	−0.863643	+	0.498625i	0.00158753	+	0.999999i	$0.499495\pi$
$440$		0			0
$441$	2.37681e7	+	1.58869e7i	0.277126	+	0.185235i
$442$		0			0
$443$	6.26713e7	+	1.08550e8i	0.720871	+	1.24859i	0.960651	+	0.277758i	$0.0895914\pi$
$443$	6.26713e7	+	1.08550e8i	0.720871	+	1.24859i	−0.239780	+	0.970827i	$0.577075\pi$
$444$		0			0
$445$	−4.89188e7	+	8.47299e7i	−0.555132	+	0.961517i
$446$		0			0
$447$		−	7.88730e7i		−	0.883092i
$448$		0			0
$449$	3.18813e7			0.352206			0.176103	−	0.984372i	$-0.443651\pi$
$449$	3.18813e7			0.352206			0.176103	+	0.984372i	$0.443651\pi$
$450$		0			0
$451$	−1.39247e7	−	8.03944e6i	−0.151795	−	0.0876388i
$452$		0			0
$453$	−2.11825e7	+	1.22297e7i	−0.227867	+	0.131559i
$454$		0			0
$455$	−1.21749e7	−	1.30011e7i	−0.129250	−	0.138022i
$456$		0			0
$457$	2.89026e7	+	5.00608e7i	0.302823	+	0.524504i	0.976774	−	0.214271i	$-0.0687376\pi$
$457$	2.89026e7	+	5.00608e7i	0.302823	+	0.524504i	−0.673951	+	0.738776i	$0.735404\pi$
$458$		0			0
$459$	−1.41079e6	+	2.44356e6i	−0.0145890	+	0.0252689i
$460$		0			0
$461$		−	9.98429e7i		−	1.01909i	−0.860443	−	0.509547i	$-0.829813\pi$
$461$		−	9.98429e7i		−	1.01909i	0.860443	−	0.509547i	$-0.170187\pi$
$462$		0			0
$463$	1.62275e8			1.63496			0.817481	−	0.575956i	$-0.195370\pi$
$463$	1.62275e8			1.63496			0.817481	+	0.575956i	$0.195370\pi$
$464$		0			0
$465$	−4.73394e7	−	2.73314e7i	−0.470830	−	0.271834i
$466$		0			0
$467$	6.02487e7	−	3.47846e7i	0.591558	−	0.341536i	−0.174155	−	0.984718i	$-0.555720\pi$
$467$	6.02487e7	−	3.47846e7i	0.591558	−	0.341536i	0.765713	+	0.643182i	$0.222386\pi$
$468$		0			0
$469$	3.64763e7	−	1.20211e8i	0.353584	−	1.16527i
$470$		0			0
$471$	−4.11705e7	−	7.13093e7i	−0.394024	−	0.682470i
$472$		0			0
$473$	−4.98211e7	+	8.62927e7i	−0.470793	+	0.815438i
$474$		0			0
$475$			3.71427e7i			0.346571i
$476$		0			0
$477$	−3.62738e7			−0.334224
$478$		0			0
$479$	1.15779e8	+	6.68451e7i	1.05347	+	0.608223i	0.923620	−	0.383310i	$-0.125216\pi$
$479$	1.15779e8	+	6.68451e7i	1.05347	+	0.608223i	0.129854	+	0.991533i	$0.458549\pi$
$480$		0			0
$481$	−3.53121e7	+	2.03875e7i	−0.317314	+	0.183201i
$482$		0			0
$483$	−4.21046e6	−	1.80643e7i	−0.0373670	−	0.160317i
$484$		0			0
$485$	5.12332e7	+	8.87386e7i	0.449083	+	0.777835i
$486$		0			0
$487$	1.13719e8	−	1.96968e8i	0.984573	−	1.70533i	0.340752	−	0.940153i	$-0.389318\pi$
$487$	1.13719e8	−	1.96968e8i	0.984573	−	1.70533i	0.643820	−	0.765177i	$-0.277348\pi$
$488$		0			0
$489$			156175.i			0.00133563i
$490$		0			0
$491$	−3.14613e7			−0.265786			−0.132893	−	0.991130i	$-0.542427\pi$
$491$	−3.14613e7			−0.265786			−0.132893	+	0.991130i	$0.542427\pi$
$492$		0			0
$493$	−1.04546e7	−	6.03597e6i	−0.0872502	−	0.0503739i
$494$		0			0
$495$	−1.16037e7	+	6.69939e6i	−0.0956710	+	0.0552357i
$496$		0			0
$497$	2.09560e8	−	4.88446e7i	1.70702	−	0.397875i
$498$		0			0
$499$	9.70894e7	+	1.68164e8i	0.781395	+	1.35342i	0.931129	+	0.364689i	$0.118825\pi$
$499$	9.70894e7	+	1.68164e8i	0.781395	+	1.35342i	−0.149735	+	0.988726i	$0.547842\pi$
$500$		0			0
$501$	1.48004e7	−	2.56351e7i	0.117696	−	0.203855i
$502$		0			0
$503$		−	1.63737e8i		−	1.28659i	−0.765616	−	0.643297i	$-0.777566\pi$
$503$		−	1.63737e8i		−	1.28659i	0.765616	−	0.643297i	$-0.222434\pi$
$504$		0			0
$505$	−6.02878e7			−0.468118
$506$		0			0
$507$	−5.88926e7	−	3.40017e7i	−0.451895	−	0.260901i
$508$		0			0
$509$	1.33445e8	−	7.70448e7i	1.01193	−	0.584238i	0.100174	−	0.994970i	$-0.468060\pi$
$509$	1.33445e8	−	7.70448e7i	1.01193	−	0.584238i	0.911756	+	0.410732i	$0.134727\pi$
$510$		0			0
$511$	1.37437e7	+	4.17032e6i	0.103001	+	0.0312540i
$512$		0			0
$513$	−7.16510e6	−	1.24103e7i	−0.0530726	−	0.0919244i
$514$		0			0
$515$	−5.01288e7	+	8.68257e7i	−0.367000	+	0.635663i
$516$		0			0
$517$		−	1.46142e7i		−	0.105755i
$518$		0			0
$519$	−1.94962e7			−0.139459
$520$		0			0
$521$	1.80521e8	+	1.04224e8i	1.27648	+	0.736976i	0.976199	−	0.216875i	$-0.0695864\pi$
$521$	1.80521e8	+	1.04224e8i	1.27648	+	0.736976i	0.300280	+	0.953851i	$0.402920\pi$
$522$		0			0
$523$	−9.10980e7	+	5.25954e7i	−0.636801	+	0.367657i	−0.783381	−	0.621542i	$-0.786507\pi$
$523$	−9.10980e7	+	5.25954e7i	−0.636801	+	0.367657i	0.146580	+	0.989199i	$0.453173\pi$
$524$		0			0
$525$	3.83180e7	−	3.58829e7i	0.264804	−	0.247976i
$526$		0			0
$527$	1.71385e7	+	2.96848e7i	0.117096	+	0.202816i
$528$		0			0
$529$	6.80008e7	−	1.17781e8i	0.459353	−	0.795623i
$530$		0			0
$531$			6.68361e7i			0.446403i
$532$		0			0
$533$	1.51429e7			0.100006
$534$		0			0
$535$	8.14586e7	+	4.70301e7i	0.531956	+	0.307125i
$536$		0			0
$537$	6.50026e7	−	3.75293e7i	0.419766	−	0.242352i
$538$		0			0
$539$	5.58154e6	−	8.49458e7i	0.0356441	−	0.542470i
$540$		0			0
$541$	−2.49087e7	−	4.31432e7i	−0.157311	−	0.272471i	0.776587	−	0.630010i	$-0.216949\pi$
$541$	−2.49087e7	−	4.31432e7i	−0.157311	−	0.272471i	−0.933898	+	0.357539i	$0.883616\pi$
$542$		0			0
$543$	−2.73890e7	+	4.74392e7i	−0.171071	+	0.296304i
$544$		0			0
$545$		−	6.01605e7i		−	0.371640i
$546$		0			0
$547$	5.33785e7			0.326140			0.163070	−	0.986614i	$-0.447860\pi$
$547$	5.33785e7			0.326140			0.163070	+	0.986614i	$0.447860\pi$
$548$		0			0
$549$	−5.97660e6	−	3.45059e6i	−0.0361191	−	0.0208534i
$550$		0			0
$551$	5.30966e7	−	3.06553e7i	0.317403	−	0.183253i
$552$		0			0
$553$	−7.99196e7	−	8.53432e7i	−0.472583	−	0.504654i
$554$		0			0
$555$	3.55381e7	+	6.15537e7i	0.207881	+	0.360060i
$556$		0			0
$557$	−3.88698e7	+	6.73244e7i	−0.224929	+	0.389589i	−0.956298	−	0.292393i	$-0.905548\pi$
$557$	−3.88698e7	+	6.73244e7i	−0.224929	+	0.389589i	0.731369	+	0.681982i	$0.238882\pi$
$558$		0			0
$559$		−	9.38419e7i		−	0.537231i
$560$		0			0
$561$	8.40187e6			0.0475869
$562$		0			0
$563$	1.04386e8	+	6.02676e7i	0.584950	+	0.337721i	0.763098	−	0.646282i	$-0.223677\pi$
$563$	1.04386e8	+	6.02676e7i	0.584950	+	0.337721i	−0.178148	+	0.984004i	$0.557011\pi$
$564$		0			0
$565$	3.97096e7	−	2.29263e7i	0.220166	−	0.127113i
$566$		0			0
$567$	−5.88095e6	+	1.93812e7i	−0.0322625	+	0.106324i
$568$		0			0
$569$	−8.57413e7	−	1.48508e8i	−0.465429	−	0.806147i	0.533792	−	0.845616i	$-0.320767\pi$
$569$	−8.57413e7	−	1.48508e8i	−0.465429	−	0.806147i	−0.999221	+	0.0394692i	$0.987433\pi$
$570$		0			0
$571$	−4.46484e7	+	7.73332e7i	−0.239827	+	0.415392i	−0.960664	−	0.277712i	$-0.910424\pi$
$571$	−4.46484e7	+	7.73332e7i	−0.239827	+	0.415392i	0.720838	+	0.693104i	$0.243757\pi$
$572$		0			0
$573$			3.50574e7i			0.186344i
$574$		0			0
$575$	−3.40598e7			−0.179159
$576$		0			0
$577$	7.37929e7	+	4.26043e7i	0.384138	+	0.221782i	0.679617	−	0.733567i	$-0.262146\pi$
$577$	7.37929e7	+	4.26043e7i	0.384138	+	0.221782i	−0.295479	+	0.955349i	$0.595479\pi$
$578$		0			0
$579$	8.47170e6	−	4.89114e6i	0.0436450	−	0.0251985i
$580$		0			0
$581$	7.76344e7	+	3.33079e8i	0.395846	+	1.69831i
$582$		0			0
$583$	5.40065e7	+	9.35420e7i	0.272546	+	0.472064i
$584$		0			0
$585$	6.30940e6	−	1.09282e7i	0.0315152	−	0.0545860i
$586$		0			0
$587$			9.06904e7i			0.448381i	0.974545	+	0.224190i	$0.0719737\pi$
$587$			9.06904e7i			0.448381i	−0.974545	+	0.224190i	$0.928026\pi$
$588$		0			0
$589$	−1.74085e8			−0.851955
$590$		0			0
$591$	−3.48535e7	−	2.01227e7i	−0.168843	−	0.0974818i
$592$		0			0
$593$	−1.78253e8	+	1.02915e8i	−0.854818	+	0.493529i	−0.862273	−	0.506443i	$-0.830960\pi$
$593$	−1.78253e8	+	1.02915e8i	−0.854818	+	0.493529i	0.00745579	+	0.999972i	$0.497627\pi$
$594$		0			0
$595$	1.89609e7	−	4.41944e6i	0.0900138	−	0.0209805i
$596$		0			0
$597$	1.14179e7	+	1.97764e7i	0.0536616	+	0.0929447i
$598$		0			0
$599$	9.63962e7	−	1.66963e8i	0.448517	−	0.776855i	−0.549772	−	0.835315i	$-0.685286\pi$
$599$	9.63962e7	−	1.66963e8i	0.448517	−	0.776855i	0.998290	+	0.0584595i	$0.0186189\pi$
$600$		0			0
$601$		−	4.06788e7i		−	0.187389i	−0.995601	−	0.0936946i	$-0.970132\pi$
$601$		−	4.06788e7i		−	0.187389i	0.995601	−	0.0936946i	$-0.0298677\pi$
$602$		0			0
$603$	8.89985e7			0.405911
$604$		0			0
$605$	−8.23588e7	−	4.75499e7i	−0.371915	−	0.214725i
$606$		0			0
$607$	7.44718e7	−	4.29963e7i	0.332986	−	0.192250i	−0.324180	−	0.945995i	$-0.605088\pi$
$607$	7.44718e7	−	4.29963e7i	0.332986	−	0.192250i	0.657166	+	0.753746i	$0.271755\pi$
$608$		0			0
$609$	−8.29209e7	−	2.51612e7i	−0.367124	−	0.111398i
$610$		0			0
$611$	6.88173e6	+	1.19195e7i	0.0301699	+	0.0522558i
$612$		0			0
$613$	−2.44629e7	+	4.23711e7i	−0.106201	+	0.183945i	−0.914228	−	0.405200i	$-0.867202\pi$
$613$	−2.44629e7	+	4.23711e7i	−0.106201	+	0.183945i	0.808027	+	0.589145i	$0.200535\pi$
$614$		0			0
$615$		−	2.63961e7i		−	0.113479i
$616$		0			0
$617$	−1.86601e7			−0.0794434			−0.0397217	−	0.999211i	$-0.512647\pi$
$617$	−1.86601e7			−0.0794434			−0.0397217	+	0.999211i	$0.512647\pi$
$618$		0			0
$619$	4.36267e7	+	2.51879e7i	0.183942	+	0.106199i	0.589143	−	0.808029i	$-0.299465\pi$
$619$	4.36267e7	+	2.51879e7i	0.183942	+	0.106199i	−0.405202	+	0.914227i	$0.632799\pi$
$620$		0			0
$621$	1.13803e7	−	6.57039e6i	0.0475201	−	0.0274357i
$622$		0			0
$623$	3.21444e8	−	3.01016e8i	1.32936	−	1.24488i
$624$		0			0
$625$	−2.83231e6	−	4.90570e6i	−0.0116011	−	0.0200938i
$626$		0			0
$627$	−2.13356e7	+	3.69544e7i	−0.0865571	+	0.149921i
$628$		0			0
$629$		−	4.45692e7i		−	0.179095i
$630$		0			0
$631$	−4.47446e8			−1.78096			−0.890478	−	0.455027i	$-0.849630\pi$
$631$	−4.47446e8			−1.78096			−0.890478	+	0.455027i	$0.849630\pi$
$632$		0			0
$633$	1.30461e8	+	7.53216e7i	0.514362	+	0.296967i
$634$		0			0
$635$	−2.35823e8	+	1.36152e8i	−0.921010	+	0.531745i
$636$		0			0
$637$	3.54481e7	+	7.19111e7i	0.137143	+	0.278213i
$638$		0			0
$639$	7.62217e7	+	1.32020e8i	0.292130	+	0.505984i
$640$		0			0
$641$	−4.49199e7	+	7.78036e7i	−0.170555	+	0.295410i	−0.938614	−	0.344969i	$-0.887889\pi$
$641$	−4.49199e7	+	7.78036e7i	−0.170555	+	0.295410i	0.768059	+	0.640379i	$0.221223\pi$
$642$		0			0
$643$		−	3.49931e8i		−	1.31628i	−0.752894	−	0.658141i	$-0.771343\pi$
$643$		−	3.49931e8i		−	1.31628i	0.752894	−	0.658141i	$-0.228657\pi$
$644$		0			0
$645$	−1.63579e8			−0.609604
$646$		0			0
$647$	−2.97868e7	−	1.71974e7i	−0.109979	−	0.0634967i	0.444001	−	0.896026i	$-0.353559\pi$
$647$	−2.97868e7	−	1.71974e7i	−0.109979	−	0.0634967i	−0.553981	+	0.832529i	$0.686892\pi$
$648$		0			0
$649$	1.72355e8	−	9.95093e7i	0.630508	−	0.364024i
$650$		0			0
$651$	1.68181e8	+	1.79594e8i	0.609584	+	0.650952i
$652$		0			0
$653$	−7.25161e6	−	1.25602e7i	−0.0260432	−	0.0451082i	0.852710	−	0.522385i	$-0.174957\pi$
$653$	−7.25161e6	−	1.25602e7i	−0.0260432	−	0.0451082i	−0.878753	+	0.477276i	$0.841624\pi$
$654$		0			0
$655$	−1.14085e8	+	1.97601e8i	−0.405981	+	0.703179i
$656$		0			0
$657$			1.01751e7i			0.0358793i
$658$		0			0
$659$	−2.92809e8			−1.02312			−0.511562	−	0.859246i	$-0.670933\pi$
$659$	−2.92809e8			−1.02312			−0.511562	+	0.859246i	$0.670933\pi$
$660$		0			0
$661$	1.81797e8	+	1.04961e8i	0.629481	+	0.363431i	0.780551	−	0.625092i	$-0.214939\pi$
$661$	1.81797e8	+	1.04961e8i	0.629481	+	0.363431i	−0.151070	+	0.988523i	$0.548272\pi$
$662$		0			0
$663$	−6.85267e6	+	3.95639e6i	−0.0235136	+	0.0135756i
$664$		0			0
$665$	−2.87109e7	+	9.46196e7i	−0.0976298	+	0.321748i
$666$		0			0
$667$	2.81109e7	+	4.86895e7i	0.0947321	+	0.164081i
$668$		0			0
$669$	−6.76830e7	+	1.17230e8i	−0.226048	+	0.391527i
$670$		0			0
$671$			2.05498e7i			0.0680204i
$672$		0			0
$673$	1.84729e8			0.606023			0.303012	−	0.952987i	$-0.402008\pi$
$673$	1.84729e8			0.606023			0.303012	+	0.952987i	$0.402008\pi$
$674$		0			0
$675$	3.22085e7	+	1.85956e7i	0.104727	+	0.0604642i
$676$		0			0
$677$	1.96552e8	−	1.13479e8i	0.633448	−	0.365722i	−0.148638	−	0.988892i	$-0.547489\pi$
$677$	1.96552e8	−	1.13479e8i	0.633448	−	0.365722i	0.782086	+	0.623170i	$0.214156\pi$
$678$		0			0
$679$	−1.04695e8	−	4.49178e8i	−0.334439	−	1.43486i
$680$		0			0
$681$	−1.46595e8	−	2.53910e8i	−0.464171	−	0.803968i
$682$		0			0
$683$	−1.20978e8	+	2.09539e8i	−0.379702	+	0.657664i	−0.991019	−	0.133723i	$-0.957307\pi$
$683$	−1.20978e8	+	2.09539e8i	−0.379702	+	0.657664i	0.611317	+	0.791386i	$0.290640\pi$
$684$		0			0
$685$			1.94738e8i			0.605870i
$686$		0			0
$687$	−5.33709e7			−0.164602
$688$		0			0
$689$	−8.80967e7	−	5.08626e7i	−0.269341	−	0.155504i
$690$		0			0
$691$	−3.94294e8	+	2.27646e8i	−1.19505	+	0.689963i	−0.959448	−	0.281887i	$-0.909040\pi$
$691$	−3.94294e8	+	2.27646e8i	−1.19505	+	0.689963i	−0.235603	+	0.971849i	$0.575706\pi$
$692$		0			0
$693$	5.87357e7	−	1.36902e7i	0.176483	−	0.0411349i
$694$		0			0
$695$	−3.89827e7	−	6.75201e7i	−0.116123	−	0.201131i
$696$		0			0
$697$	−8.27600e6	+	1.43345e7i	−0.0244412	+	0.0423334i
$698$		0			0
$699$		−	3.70949e8i		−	1.08613i
$700$		0			0
$701$	3.09324e8			0.897965			0.448983	−	0.893541i	$-0.351787\pi$
$701$	3.09324e8			0.897965			0.448983	+	0.893541i	$0.351787\pi$
$702$		0			0
$703$	1.96031e8	+	1.13179e8i	0.564233	+	0.325760i
$704$		0			0
$705$	2.07773e7	−	1.19958e7i	0.0592954	−	0.0342342i
$706$		0			0
$707$	2.59674e8	+	7.87942e7i	0.734801	+	0.222965i
$708$		0			0
$709$	6.03636e7	+	1.04553e8i	0.169370	+	0.293358i	0.938199	−	0.346097i	$-0.112493\pi$
$709$	6.03636e7	+	1.04553e8i	0.169370	+	0.293358i	−0.768828	+	0.639455i	$0.779160\pi$
$710$		0			0
$711$	4.14168e7	−	7.17359e7i	0.115230	−	0.199585i
$712$		0			0
$713$		−	1.59636e8i		−	0.440416i
$714$		0			0
$715$	−3.75752e7			−0.102798
$716$		0			0
$717$	1.98370e8	+	1.14529e8i	0.538168	+	0.310711i
$718$		0			0
$719$	−6.51894e7	+	3.76371e7i	−0.175384	+	0.101258i	−0.585122	−	0.810945i	$-0.698953\pi$
$719$	−6.51894e7	+	3.76371e7i	−0.175384	+	0.101258i	0.409738	+	0.912203i	$0.365620\pi$
$720$		0			0
$721$	3.29395e8	−	3.08462e8i	0.878843	−	0.822992i
$722$		0			0
$723$	−1.87048e7	−	3.23977e7i	−0.0494924	−	0.0857234i
$724$		0			0
$725$	−7.95597e7	+	1.37801e8i	−0.208775	+	0.361610i
$726$		0			0
$727$		−	6.43074e8i		−	1.67362i	−0.547492	−	0.836811i	$-0.684417\pi$
$727$		−	6.43074e8i		−	1.67362i	0.547492	−	0.836811i	$-0.315583\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	8.88319e7	+	5.12871e7i	0.227414	+	0.131297i
$732$		0			0
$733$	−5.69522e8	+	3.28814e8i	−1.44610	+	0.834906i	−0.998246	−	0.0592002i	$-0.981145\pi$
$733$	−5.69522e8	+	3.28814e8i	−1.44610	+	0.834906i	−0.447854	+	0.894107i	$0.647812\pi$
$734$		0			0
$735$	1.25351e8	−	6.17907e7i	0.315693	−	0.155619i
$736$		0			0
$737$	−1.32506e8	−	2.29507e8i	−0.331004	−	0.573316i
$738$		0			0
$739$	−1.97820e8	+	3.42635e8i	−0.490160	+	0.848982i	−0.999936	−	0.0113252i	$-0.996395\pi$
$739$	−1.97820e8	+	3.42635e8i	−0.490160	+	0.848982i	0.509776	+	0.860307i	$0.329728\pi$
$740$		0			0
$741$		−	4.01873e7i		−	0.0987720i
$742$		0			0
$743$	−4.72543e8			−1.15206			−0.576030	−	0.817429i	$-0.695399\pi$
$743$	−4.72543e8			−1.15206			−0.576030	+	0.817429i	$0.695399\pi$
$744$		0			0
$745$	−3.33907e8	−	1.92781e8i	−0.807526	−	0.466226i
$746$		0			0
$747$	−2.09835e8	+	1.21148e8i	−0.503402	+	0.290639i
$748$		0			0
$749$	−2.89394e8	−	3.09034e8i	−0.688723	−	0.735462i
$750$		0			0
$751$	1.06470e8	+	1.84412e8i	0.251367	+	0.435381i	0.963902	−	0.266256i	$-0.0857865\pi$
$751$	1.06470e8	+	1.84412e8i	0.251367	+	0.435381i	−0.712535	+	0.701636i	$0.752453\pi$
$752$		0			0
$753$	−1.89029e8	+	3.27408e8i	−0.442735	+	0.766839i
$754$		0			0
$755$			1.19567e8i			0.277825i
$756$		0			0
$757$	−5.51303e8			−1.27088			−0.635438	−	0.772152i	$-0.719180\pi$
$757$	−5.51303e8			−1.27088			−0.635438	+	0.772152i	$0.719180\pi$
$758$		0			0
$759$	−3.38871e7	−	1.95648e7i	−0.0775014	−	0.0447455i
$760$		0			0
$761$	−4.46288e8	+	2.57664e8i	−1.01265	+	0.584656i	−0.911968	−	0.410262i	$-0.865437\pi$
$761$	−4.46288e8	+	2.57664e8i	−1.01265	+	0.584656i	−0.100687	+	0.994918i	$0.532104\pi$
$762$		0			0
$763$	−7.86279e7	+	2.59126e8i	−0.177012	+	0.583360i
$764$		0			0
$765$	6.89652e6	+	1.19451e7i	0.0154044	+	0.0266812i
$766$		0			0
$767$	−9.37167e7	+	1.62322e8i	−0.207697	+	0.359742i
$768$		0			0
$769$			3.34981e8i			0.736617i	0.929704	+	0.368308i	$0.120063\pi$
$769$			3.34981e8i			0.736617i	−0.929704	+	0.368308i	$0.879937\pi$
$770$		0			0
$771$	−9.88941e7			−0.215778
$772$		0			0
$773$	−3.32077e8	−	1.91725e8i	−0.718954	−	0.415088i	0.0954138	−	0.995438i	$-0.469583\pi$
$773$	−3.32077e8	−	1.91725e8i	−0.718954	−	0.415088i	−0.814367	+	0.580350i	$0.802916\pi$
$774$		0			0
$775$	3.91274e8	−	2.25902e8i	0.840573	−	0.485305i
$776$		0			0
$777$	−7.26220e7	−	3.11574e8i	−0.154812	−	0.664198i
$778$		0			0
$779$	−4.20320e7	−	7.28015e7i	−0.0889134	−	0.154003i
$780$		0			0
$781$	2.26966e8	−	3.93117e8i	0.476440	−	0.825218i
$782$		0			0
$783$		−	6.13907e7i		−	0.127884i
$784$		0			0
$785$	−4.02515e8			−0.832096
$786$		0			0
$787$	4.22755e8	+	2.44078e8i	0.867290	+	0.500730i	0.866447	−	0.499270i	$-0.166398\pi$
$787$	4.22755e8	+	2.44078e8i	0.867290	+	0.500730i	0.000843106		1.00000i	$0.499732\pi$
$788$		0			0
$789$	1.30602e8	−	7.54028e7i	0.265899	−	0.153517i
$790$		0			0
$791$	−2.01003e8	+	4.68500e7i	−0.406137	+	0.0946629i
$792$		0			0
$793$	−9.67676e6	−	1.67606e7i	−0.0194049	−	0.0336102i
$794$		0			0
$795$	−8.86604e7	+	1.53564e8i	−0.176453	+	0.305625i
$796$		0			0
$797$		−	8.78831e8i		−	1.73592i	−0.496631	−	0.867962i	$-0.665430\pi$
$797$		−	8.78831e8i		−	1.73592i	0.496631	−	0.867962i	$-0.334570\pi$
$798$		0			0
$799$	−1.50442e7			−0.0294937
$800$		0			0
$801$	2.70193e8	+	1.55996e8i	0.525746	+	0.303540i
$802$		0			0
$803$	2.62394e7	−	1.51493e7i	0.0506766	−	0.0292581i
$804$		0			0
$805$	−8.67661e7	−	2.63279e7i	−0.166327	−	0.0504695i
$806$		0			0
$807$	−8.93222e7	−	1.54711e8i	−0.169957	−	0.294374i
$808$		0			0
$809$	−3.43339e8	+	5.94681e8i	−0.648452	+	1.12315i	0.335040	+	0.942204i	$0.391250\pi$
$809$	−3.43339e8	+	5.94681e8i	−0.648452	+	1.12315i	−0.983493	+	0.180948i	$0.942083\pi$
$810$		0			0
$811$		−	9.75268e7i		−	0.182836i	−0.995813	−	0.0914180i	$-0.970860\pi$
$811$		−	9.75268e7i		−	0.182836i	0.995813	−	0.0914180i	$-0.0291399\pi$
$812$		0			0
$813$	−5.58323e6			−0.0103900
$814$		0			0
$815$	661165.	+	381724.i	0.00122134	+	0.000705142i
$816$		0			0
$817$	−4.51157e8	+	2.60476e8i	−0.827298	+	0.477641i
$818$		0			0
$819$	−4.14589e7	+	3.88242e7i	−0.0754686	+	0.0706725i
$820$		0			0
$821$	2.55819e8	+	4.43091e8i	0.462278	+	0.800689i	0.999074	−	0.0430230i	$-0.0136989\pi$
$821$	2.55819e8	+	4.43091e8i	0.462278	+	0.800689i	−0.536796	+	0.843712i	$0.680366\pi$
$822$		0			0
$823$	−2.22948e8	+	3.86157e8i	−0.399948	+	0.692730i	−0.993719	−	0.111904i	$-0.964305\pi$
$823$	−2.22948e8	+	3.86157e8i	−0.399948	+	0.692730i	0.593771	+	0.804634i	$0.297638\pi$
$824$		0			0
$825$		−	1.10745e8i		−	0.197225i
$826$		0			0
$827$	−6.01667e8			−1.06375			−0.531875	−	0.846823i	$-0.678512\pi$
$827$	−6.01667e8			−1.06375			−0.531875	+	0.846823i	$0.678512\pi$
$828$		0			0
$829$	−7.47622e7	−	4.31640e7i	−0.131226	−	0.0757631i	0.432950	−	0.901418i	$-0.357473\pi$
$829$	−7.47622e7	−	4.31640e7i	−0.131226	−	0.0757631i	−0.564176	+	0.825655i	$0.690806\pi$
$830$		0			0
$831$	1.01254e8	−	5.84588e7i	0.176444	−	0.101870i
$832$		0			0
$833$	−8.74453e7	−	5.74577e6i	−0.151287	−	0.00994062i
$834$		0			0
$835$	−7.23505e7	−	1.25315e8i	−0.124274	−	0.215250i
$836$		0			0
$837$	−8.71563e7	+	1.50959e8i	−0.148636	+	0.257444i
$838$		0			0
$839$		−	1.50849e8i		−	0.255421i	−0.991811	−	0.127711i	$-0.959237\pi$
$839$		−	1.50849e8i		−	0.255421i	0.991811	−	0.127711i	$-0.0407629\pi$
$840$		0			0
$841$	−3.32168e8			−0.558432
$842$		0			0
$843$	−2.92198e8	−	1.68701e8i	−0.487747	−	0.281601i
$844$		0			0
$845$	−2.87891e8	+	1.66214e8i	−0.477153	+	0.275484i
$846$		0			0
$847$	2.92593e8	+	3.12449e8i	0.481519	+	0.514196i
$848$		0			0
$849$	2.96518e8	+	5.13584e8i	0.484538	+	0.839245i
$850$		0			0
$851$	−1.03785e8	+	1.79760e8i	−0.168401	+	0.291679i
$852$		0			0
$853$		−	3.76022e8i		−	0.605851i	−0.953014	−	0.302926i	$-0.902037\pi$
$853$		−	3.76022e8i		−	0.605851i	0.953014	−	0.302926i	$-0.0979634\pi$
$854$		0			0
$855$	−7.00517e7			−0.112078
$856$		0			0
$857$	2.36459e8	+	1.36520e8i	0.375677	+	0.216897i	0.675936	−	0.736961i	$-0.263740\pi$
$857$	2.36459e8	+	1.36520e8i	0.375677	+	0.216897i	−0.300259	+	0.953858i	$0.597073\pi$
$858$		0			0
$859$	−1.00244e8	+	5.78760e7i	−0.158154	+	0.0913101i	−0.576988	−	0.816753i	$-0.695772\pi$
$859$	−1.00244e8	+	5.78760e7i	−0.158154	+	0.0913101i	0.418834	+	0.908063i	$0.362439\pi$
$860$		0			0
$861$	−3.44988e7	+	1.13694e8i	−0.0540499	+	0.178127i
$862$		0			0
$863$	1.26569e8	+	2.19224e8i	0.196922	+	0.341079i	0.947529	−	0.319670i	$-0.103572\pi$
$863$	1.26569e8	+	2.19224e8i	0.196922	+	0.341079i	−0.750607	+	0.660749i	$0.770239\pi$
$864$		0			0
$865$	−4.76526e7	+	8.25367e7i	−0.0736272	+	0.127526i
$866$		0			0
$867$			3.67618e8i			0.564079i
$868$		0			0
$869$	−2.46654e8			−0.375863
$870$		0			0
$871$	2.16147e8	+	1.24793e8i	0.327111	+	0.188858i
$872$		0			0
$873$	2.82976e8	−	1.63376e8i	0.425311	−	0.245553i
$874$		0			0
$875$	−1.50958e8	−	6.47660e8i	−0.225336	−	0.966770i
$876$		0			0
$877$	6.36894e8	+	1.10313e9i	0.944210	+	1.63542i	0.757326	+	0.653037i	$0.226506\pi$
$877$	6.36894e8	+	1.10313e9i	0.944210	+	1.63542i	0.186884	+	0.982382i	$0.440161\pi$
$878$		0			0
$879$	2.20872e8	−	3.82562e8i	0.325218	−	0.563293i
$880$		0			0
$881$		−	1.28152e9i		−	1.87412i	−0.349164	−	0.937062i	$-0.613534\pi$
$881$		−	1.28152e9i		−	1.87412i	0.349164	−	0.937062i	$-0.386466\pi$
$882$		0			0
$883$	5.52027e8			0.801822			0.400911	−	0.916117i	$-0.368694\pi$
$883$	5.52027e8			0.801822			0.400911	+	0.916117i	$0.368694\pi$
$884$		0			0
$885$	2.82949e8	+	1.63361e8i	0.408205	+	0.235677i
$886$		0			0
$887$	−4.15256e8	+	2.39748e8i	−0.595038	+	0.343545i	−0.767087	−	0.641543i	$-0.778295\pi$
$887$	−4.15256e8	+	2.39748e8i	−0.595038	+	0.343545i	0.172049	+	0.985088i	$0.444961\pi$
$888$		0			0
$889$	1.19369e9	−	2.78227e8i	1.69897	−	0.395999i
$890$		0			0
$891$	2.13635e7	+	3.70026e7i	0.0302022	+	0.0523118i
$892$		0			0
$893$	3.82031e7	−	6.61696e7i	0.0536468	−	0.0929190i
$894$		0			0
$895$		−	3.66916e8i		−	0.511797i
$896$		0			0
$897$	3.68517e7			0.0510599
$898$		0			0
$899$	−6.45867e8	−	3.72892e8i	−0.888923	−	0.513220i
$900$		0			0
$901$	9.62944e7	−	5.55956e7i	0.131652	−	0.0760092i
$902$		0			0
$903$	7.04573e8	+	2.13792e8i	0.956891	+	0.290355i
$904$		0			0
$905$	1.33888e8	+	2.31902e8i	0.180633	+	0.312866i
$906$		0			0
$907$	−4.57281e8	+	7.92034e8i	−0.612860	+	1.06151i	0.377896	+	0.925848i	$0.376648\pi$
$907$	−4.57281e8	+	7.92034e8i	−0.612860	+	1.06151i	−0.990756	+	0.135657i	$0.956686\pi$
$908$		0			0
$909$			1.92250e8i			0.255961i
$910$		0			0
$911$	−1.36518e9			−1.80565			−0.902827	−	0.430005i	$-0.858512\pi$
$911$	−1.36518e9			−1.80565			−0.902827	+	0.430005i	$0.858512\pi$
$912$		0			0
$913$	6.24827e8	+	3.60744e8i	0.821008	+	0.474009i
$914$		0			0
$915$	−2.92160e7	+	1.68679e7i	−0.0381380	+	0.0220190i
$916$		0			0
$917$	7.49650e8	−	7.02009e8i	0.972189	−	0.910406i
$918$		0			0
$919$	−2.34689e8	−	4.06493e8i	−0.302375	−	0.523729i	0.674298	−	0.738459i	$-0.264446\pi$
$919$	−2.34689e8	−	4.06493e8i	−0.302375	−	0.523729i	−0.976674	+	0.214730i	$0.931113\pi$
$920$		0			0
$921$	1.03643e8	−	1.79515e8i	0.132666	−	0.229785i
$922$		0			0
$923$			4.27508e8i			0.543675i
$924$		0			0
$925$	−5.87464e8			−0.742260
$926$		0			0
$927$	2.76876e8	+	1.59854e8i	0.347573	+	0.200671i
$928$		0			0
$929$	−7.93579e8	+	4.58173e8i	−0.989790	+	0.571455i	−0.905211	−	0.424962i	$-0.860288\pi$
$929$	−7.93579e8	+	4.58173e8i	−0.989790	+	0.571455i	−0.0845782	+	0.996417i	$0.526954\pi$
$930$		0			0
$931$	2.47330e8	−	3.70024e8i	0.306498	−	0.458544i
$932$		0			0
$933$	3.69994e7	+	6.40848e7i	0.0455564	+	0.0789060i
$934$		0			0
$935$	2.05359e7	−	3.55691e7i	0.0251234	−	0.0435150i
$936$		0			0
$937$		−	2.88725e8i		−	0.350966i	−0.984482	−	0.175483i	$-0.943851\pi$
$937$		−	2.88725e8i		−	0.350966i	0.984482	−	0.175483i	$-0.0561487\pi$
$938$		0			0
$939$	5.31499e8			0.641956
$940$		0			0
$941$	−7.85378e7	−	4.53438e7i	−0.0942562	−	0.0544188i	0.452131	−	0.891952i	$-0.350664\pi$
$941$	−7.85378e7	−	4.53438e7i	−0.0942562	−	0.0544188i	−0.546387	+	0.837533i	$0.683997\pi$
$942$		0			0
$943$	6.67589e7	−	3.85433e7i	0.0796112	−	0.0459636i
$944$		0			0
$945$	6.76757e7	+	7.22684e7i	0.0801931	+	0.0856353i
$946$		0			0
$947$	−9.38337e7	−	1.62525e8i	−0.110486	−	0.191368i	0.805480	−	0.592623i	$-0.201908\pi$
$947$	−9.38337e7	−	1.62525e8i	−0.110486	−	0.191368i	−0.915966	+	0.401255i	$0.868574\pi$
$948$		0			0
$949$	−1.42675e7	+	2.47120e7i	−0.0166935	+	0.0289140i
$950$		0			0
$951$			4.95602e8i			0.576225i
$952$		0			0
$953$	−1.56716e9			−1.81065			−0.905326	−	0.424716i	$-0.860374\pi$
$953$	−1.56716e9			−1.81065			−0.905326	+	0.424716i	$0.860374\pi$
$954$		0			0
$955$	1.48415e8	+	8.56872e7i	0.170399	+	0.0983798i
$956$		0			0
$957$	−1.58313e8	+	9.14019e7i	−0.180626	+	0.104284i
$958$		0			0
$959$	2.54517e8	−	8.38783e8i	0.288576	−	0.951029i
$960$		0			0
$961$	6.15037e8	+	1.06527e9i	0.692996	+	1.20030i
$962$		0			0
$963$	1.49973e8	−	2.59761e8i	0.167932	−	0.290867i
$964$		0			0
$965$		−	4.78196e7i		−	0.0532138i
$966$		0			0
$967$	7.19327e8			0.795512			0.397756	−	0.917491i	$-0.369789\pi$
$967$	7.19327e8			0.795512			0.397756	+	0.917491i	$0.369789\pi$
$968$		0			0
$969$	3.80418e7	+	2.19634e7i	0.0418109	+	0.0241395i
$970$		0			0
$971$	7.27775e8	−	4.20181e8i	0.794949	−	0.458964i	−0.0467528	−	0.998906i	$-0.514887\pi$
$971$	7.27775e8	−	4.20181e8i	0.794949	−	0.458964i	0.841702	+	0.539942i	$0.181554\pi$
$972$		0			0
$973$	7.96612e7	+	3.41774e8i	0.0864785	+	0.371023i
$974$		0			0
$975$	5.21490e7	+	9.03247e7i	0.0562642	+	0.0974524i
$976$		0			0
$977$	−2.32392e8	+	4.02515e8i	−0.249194	+	0.431617i	−0.963302	−	0.268419i	$-0.913499\pi$
$977$	−2.32392e8	+	4.02515e8i	−0.249194	+	0.431617i	0.714108	+	0.700035i	$0.246832\pi$
$978$		0			0
$979$		−	9.29021e8i		−	0.990097i
$980$		0			0
$981$	−1.91844e8			−0.203208
$982$		0			0
$983$	−5.95203e8	−	3.43641e8i	−0.626621	−	0.361780i	0.152822	−	0.988254i	$-0.451164\pi$
$983$	−5.95203e8	−	3.43641e8i	−0.626621	−	0.361780i	−0.779442	+	0.626474i	$0.784497\pi$
$984$		0			0
$985$	−1.70378e8	+	9.83677e7i	−0.178281	+	0.102930i
$986$		0			0
$987$	−1.05171e8	+	2.45133e7i	−0.109381	+	0.0254948i
$988$		0			0
$989$	−2.38856e8	−	4.13711e8i	−0.246915	−	0.427669i
$990$		0			0
$991$	−2.09353e8	+	3.62611e8i	−0.215109	+	0.372580i	−0.953306	−	0.302005i	$-0.902344\pi$
$991$	−2.09353e8	+	3.62611e8i	−0.215109	+	0.372580i	0.738197	+	0.674585i	$0.235677\pi$
$992$		0			0
$993$		−	5.37968e8i		−	0.549425i
$994$		0			0
$995$	1.11631e8			0.113322
$996$		0			0
$997$	4.38552e8	+	2.53198e8i	0.442523	+	0.255491i	0.704667	−	0.709538i	$-0.251096\pi$
$997$	4.38552e8	+	2.53198e8i	0.442523	+	0.255491i	−0.262144	+	0.965029i	$0.584430\pi$
$998$		0			0
$999$	1.96287e8	−	1.13326e8i	0.196877	−	0.113667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.c.241.1		8
4.3	odd	2		42.7.g.b.31.3	yes	8
7.5	odd	6	inner	336.7.bh.c.145.1		8
12.11	even	2		126.7.n.b.73.2		8
28.3	even	6		294.7.c.a.97.4		8
28.11	odd	6		294.7.c.a.97.1		8
28.19	even	6		42.7.g.b.19.3	✓	8
28.23	odd	6		294.7.g.b.19.4		8
28.27	even	2		294.7.g.b.31.4		8
84.47	odd	6		126.7.n.b.19.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.7.g.b.19.3	✓	8	28.19	even	6
42.7.g.b.31.3	yes	8	4.3	odd	2
126.7.n.b.19.2		8	84.47	odd	6
126.7.n.b.73.2		8	12.11	even	2
294.7.c.a.97.1		8	28.11	odd	6
294.7.c.a.97.4		8	28.3	even	6
294.7.g.b.19.4		8	28.23	odd	6
294.7.g.b.31.4		8	28.27	even	2
336.7.bh.c.145.1		8	7.5	odd	6	inner
336.7.bh.c.241.1		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.5000 - 7.79423i) q^{3} +(-65.9934 + 38.1013i) q^{5} +(334.046 - 77.8600i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 - 7.79423i) q^{3} +(-65.9934 + 38.1013i) q^{5} +(334.046 - 77.8600i) q^{7} +(121.500 + 210.444i) q^{9} +(361.792 - 626.642i) q^{11} +681.463i q^{13} +1187.88 q^{15} +(-645.081 - 372.438i) q^{17} +(3276.22 - 1891.53i) q^{19} +(-5116.48 - 1552.52i) q^{21} +(1734.53 + 3004.30i) q^{23} +(-4909.08 + 8502.78i) q^{25} -3788.00i q^{27} +16206.6 q^{29} +(-39852.0 - 23008.6i) q^{31} +(-9768.39 + 5639.78i) q^{33} +(-19078.3 + 17865.8i) q^{35} +(29917.2 + 51818.1i) q^{37} +(5311.48 - 9199.75i) q^{39} -22221.2i q^{41} -137706. q^{43} +(-16036.4 - 9258.61i) q^{45} +(17491.0 - 10098.5i) q^{47} +(105525. - 52017.6i) q^{49} +(5805.73 + 10055.8i) q^{51} +(-74637.4 + 129276. i) q^{53} +55139.0i q^{55} -58972.0 q^{57} +(238196. + 137523. i) q^{59} +(-24595.1 + 14200.0i) q^{61} +(56971.8 + 60838.1i) q^{63} +(-25964.6 - 44972.0i) q^{65} +(183124. - 317181. i) q^{67} -54077.3i q^{69} +627339. q^{71} +(36263.1 + 20936.5i) q^{73} +(132545. - 76525.0i) q^{75} +(72064.9 - 237497. i) q^{77} +(-170439. - 295210. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +997103. i q^{83} +56761.5 q^{85} +(-218790. - 126318. i) q^{87} +(1.11190e6 - 641958. i) q^{89} +(53058.7 + 227640. i) q^{91} +(358668. + 621231. i) q^{93} +(-144139. + 249657. i) q^{95} -1.34466e6i q^{97} +175831. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9} - 2058 q^{11} - 3780 q^{15} - 11244 q^{17} - 21834 q^{19} - 4482 q^{21} - 15504 q^{23} - 6550 q^{25} + 35316 q^{29} + 51060 q^{31} + 55566 q^{33} - 71460 q^{35} + 20282 q^{37} + 101682 q^{39} - 387812 q^{43} + 51030 q^{45} + 55212 q^{47} - 277780 q^{49} + 101196 q^{51} - 336174 q^{53} + 393012 q^{57} + 560454 q^{59} + 850728 q^{61} - 26730 q^{63} + 826380 q^{65} + 947882 q^{67} - 147192 q^{71} - 533034 q^{73} + 176850 q^{75} - 1848102 q^{77} + 6260 q^{79} - 236196 q^{81} + 560040 q^{85} - 476766 q^{87} + 413460 q^{89} - 256074 q^{91} - 459540 q^{93} + 170880 q^{95} - 1000188 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9 - 2058 * q^11 - 3780 * q^15 - 11244 * q^17 - 21834 * q^19 - 4482 * q^21 - 15504 * q^23 - 6550 * q^25 + 35316 * q^29 + 51060 * q^31 + 55566 * q^33 - 71460 * q^35 + 20282 * q^37 + 101682 * q^39 - 387812 * q^43 + 51030 * q^45 + 55212 * q^47 - 277780 * q^49 + 101196 * q^51 - 336174 * q^53 + 393012 * q^57 + 560454 * q^59 + 850728 * q^61 - 26730 * q^63 + 826380 * q^65 + 947882 * q^67 - 147192 * q^71 - 533034 * q^73 + 176850 * q^75 - 1848102 * q^77 + 6260 * q^79 - 236196 * q^81 + 560040 * q^85 - 476766 * q^87 + 413460 * q^89 - 256074 * q^91 - 459540 * q^93 + 170880 * q^95 - 1000188 * q^99

Introduction

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