LMFDB - Embedded newform 336.7.bh.c.145.2

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			145.2
Root			$2.56933 + 4.45021i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.c.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 + 7.79423i) q^{3} +(-52.3293 - 30.2124i) q^{5} +(17.4716 - 342.555i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 + 7.79423i) q^{3} +(-52.3293 - 30.2124i) q^{5} +(17.4716 - 342.555i) q^{7} +(121.500 - 210.444i) q^{9} +(-1191.99 - 2064.59i) q^{11} +195.716i q^{13} +941.928 q^{15} +(-8378.55 + 4837.36i) q^{17} +(-7489.77 - 4324.22i) q^{19} +(2434.08 + 4760.67i) q^{21} +(7454.09 - 12910.9i) q^{23} +(-5986.93 - 10369.7i) q^{25} +3788.00i q^{27} +27549.7 q^{29} +(4633.43 - 2675.11i) q^{31} +(32183.7 + 18581.3i) q^{33} +(-11263.7 + 17397.8i) q^{35} +(45298.9 - 78460.1i) q^{37} +(-1525.46 - 2642.17i) q^{39} +65147.4i q^{41} -36138.3 q^{43} +(-12716.0 + 7341.60i) q^{45} +(169.222 + 97.7002i) q^{47} +(-117038. - 11970.0i) q^{49} +(75407.0 - 130609. i) q^{51} +(410.570 + 711.129i) q^{53} +144051. i q^{55} +134816. q^{57} +(105860. - 61118.0i) q^{59} +(85494.7 + 49360.4i) q^{61} +(-69965.8 - 45297.2i) q^{63} +(5913.04 - 10241.7i) q^{65} +(129826. + 224866. i) q^{67} +232396. i q^{69} -248100. q^{71} +(-239698. + 138390. i) q^{73} +(161647. + 93327.0i) q^{75} +(-728060. + 372250. i) q^{77} +(29342.4 - 50822.5i) q^{79} +(-29524.5 - 51137.9i) q^{81} +871615. i q^{83} +584592. q^{85} +(-371921. + 214728. i) q^{87} +(-629506. - 363445. i) q^{89} +(67043.5 + 3419.47i) q^{91} +(-41700.9 + 72228.0i) q^{93} +(261290. + 452567. i) q^{95} -1.22489e6i q^{97} -579307. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	−52.3293	−	30.2124i	−0.418635	−	0.241699i	0.275858	−	0.961198i	$-0.411038\pi$
$5$	−52.3293	−	30.2124i	−0.418635	−	0.241699i	−0.694493	+	0.719499i	$0.744371\pi$
$6$		0			0
$7$	17.4716	−	342.555i	0.0509376	−	0.998702i
$7$	17.4716	−	342.555i	0.0509376	−	0.998702i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−1191.99	−	2064.59i	−0.895560	−	1.55116i	−0.833110	−	0.553108i	$-0.813442\pi$
$11$	−1191.99	−	2064.59i	−0.895560	−	1.55116i	−0.0624504	−	0.998048i	$-0.519892\pi$
$12$		0			0
$13$			195.716i			0.0890833i	0.999008	+	0.0445417i	$0.0141827\pi$
$13$			195.716i			0.0890833i	−0.999008	+	0.0445417i	$0.985817\pi$
$14$		0			0
$15$	941.928			0.279090
$16$		0			0
$17$	−8378.55	+	4837.36i	−1.70538	+	0.984604i	−0.765293	+	0.643682i	$0.777406\pi$
$17$	−8378.55	+	4837.36i	−1.70538	+	0.984604i	−0.940091	+	0.340922i	$0.889261\pi$
$18$		0			0
$19$	−7489.77	−	4324.22i	−1.09196	−	0.630444i	−0.157864	−	0.987461i	$-0.550461\pi$
$19$	−7489.77	−	4324.22i	−1.09196	−	0.630444i	−0.934098	+	0.357016i	$0.883794\pi$
$20$		0			0
$21$	2434.08	+	4760.67i	0.262832	+	0.514055i
$22$		0			0
$23$	7454.09	−	12910.9i	0.612648	−	1.06114i	−0.378144	−	0.925747i	$-0.623438\pi$
$23$	7454.09	−	12910.9i	0.612648	−	1.06114i	0.990792	−	0.135391i	$-0.0432290\pi$
$24$		0			0
$25$	−5986.93	−	10369.7i	−0.383163	−	0.663658i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	27549.7			1.12959			0.564797	−	0.825230i	$-0.308954\pi$
$29$	27549.7			1.12959			0.564797	+	0.825230i	$0.308954\pi$
$30$		0			0
$31$	4633.43	−	2675.11i	0.155531	−	0.0897960i	−0.420215	−	0.907425i	$-0.638045\pi$
$31$	4633.43	−	2675.11i	0.155531	−	0.0897960i	0.575746	+	0.817629i	$0.304712\pi$
$32$		0			0
$33$	32183.7	+	18581.3i	0.895560	+	0.517052i
$34$		0			0
$35$	−11263.7	+	17397.8i	−0.262709	+	0.405780i
$36$		0			0
$37$	45298.9	−	78460.1i	0.894299	−	1.54897i	0.0596298	−	0.998221i	$-0.481008\pi$
$37$	45298.9	−	78460.1i	0.894299	−	1.54897i	0.834669	−	0.550751i	$-0.185659\pi$
$38$		0			0
$39$	−1525.46	−	2642.17i	−0.0257161	−	0.0445417i
$40$		0			0
$41$			65147.4i			0.945248i	0.881264	+	0.472624i	$0.156693\pi$
$41$			65147.4i			0.945248i	−0.881264	+	0.472624i	$0.843307\pi$
$42$		0			0
$43$	−36138.3			−0.454530			−0.227265	−	0.973833i	$-0.572978\pi$
$43$	−36138.3			−0.454530			−0.227265	+	0.973833i	$0.572978\pi$
$44$		0			0
$45$	−12716.0	+	7341.60i	−0.139545	+	0.0805663i
$46$		0			0
$47$	169.222	+	97.7002i	0.00162991	+	0.000941026i	0.500815	−	0.865555i	$-0.333034\pi$
$47$	169.222	+	97.7002i	0.00162991	+	0.000941026i	−0.499185	+	0.866496i	$0.666367\pi$
$48$		0			0
$49$	−117038.	−	11970.0i	−0.994811	−	0.101743i
$50$		0			0
$51$	75407.0	−	130609.i	0.568462	−	0.984604i
$52$		0			0
$53$	410.570	+	711.129i	0.00275778	+	0.00477662i	0.867401	−	0.497610i	$-0.165789\pi$
$53$	410.570	+	711.129i	0.00275778	+	0.00477662i	−0.864643	+	0.502386i	$0.832456\pi$
$54$		0			0
$55$			144051.i			0.865823i
$56$		0			0
$57$	134816.			0.727975
$58$		0			0
$59$	105860.	−	61118.0i	0.515435	−	0.297587i	−0.219630	−	0.975583i	$-0.570485\pi$
$59$	105860.	−	61118.0i	0.515435	−	0.297587i	0.735065	+	0.677997i	$0.237152\pi$
$60$		0			0
$61$	85494.7	+	49360.4i	0.376660	+	0.217465i	0.676364	−	0.736567i	$-0.263555\pi$
$61$	85494.7	+	49360.4i	0.376660	+	0.217465i	−0.299704	+	0.954032i	$0.596888\pi$
$62$		0			0
$63$	−69965.8	−	45297.2i	−0.279811	−	0.181155i
$64$		0			0
$65$	5913.04	−	10241.7i	0.0215313	−	0.0372934i
$66$		0			0
$67$	129826.	+	224866.i	0.431656	+	0.747650i	0.997016	−	0.0771940i	$-0.0245961\pi$
$67$	129826.	+	224866.i	0.431656	+	0.747650i	−0.565360	+	0.824844i	$0.691263\pi$
$68$		0			0
$69$			232396.i			0.707425i
$70$		0			0
$71$	−248100.			−0.693188			−0.346594	−	0.938015i	$-0.612662\pi$
$71$	−248100.			−0.693188			−0.346594	+	0.938015i	$0.612662\pi$
$72$		0			0
$73$	−239698.	+	138390.i	−0.616163	+	0.355742i	−0.775374	−	0.631503i	$-0.782439\pi$
$73$	−239698.	+	138390.i	−0.616163	+	0.355742i	0.159210	+	0.987245i	$0.449105\pi$
$74$		0			0
$75$	161647.	+	93327.0i	0.383163	+	0.221219i
$76$		0			0
$77$	−728060.	+	372250.i	−1.59476	+	0.815385i
$78$		0			0
$79$	29342.4	−	50822.5i	0.0595133	−	0.103080i	−0.834734	−	0.550654i	$-0.814378\pi$
$79$	29342.4	−	50822.5i	0.0595133	−	0.103080i	0.894247	+	0.447574i	$0.147712\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			871615.i			1.52437i	0.647359	+	0.762185i	$0.275873\pi$
$83$			871615.i			1.52437i	−0.647359	+	0.762185i	$0.724127\pi$
$84$		0			0
$85$	584592.			0.951911
$86$		0			0
$87$	−371921.	+	214728.i	−0.564797	+	0.326086i
$88$		0			0
$89$	−629506.	−	363445.i	−0.892955	−	0.515548i	−0.0180472	−	0.999837i	$-0.505745\pi$
$89$	−629506.	−	363445.i	−0.892955	−	0.515548i	−0.874908	+	0.484289i	$0.839078\pi$
$90$		0			0
$91$	67043.5	+	3419.47i	0.0889677	+	0.00453769i
$92$		0			0
$93$	−41700.9	+	72228.0i	−0.0518437	+	0.0897960i
$94$		0			0
$95$	261290.	+	452567.i	0.304755	+	0.527852i
$96$		0			0
$97$		−	1.22489e6i		−	1.34209i	−0.741418	−	0.671044i	$-0.765846\pi$
$97$		−	1.22489e6i		−	1.34209i	0.741418	−	0.671044i	$-0.234154\pi$
$98$		0			0
$99$	−579307.			−0.597040
$100$		0			0
$101$	−329592.	+	190290.i	−0.319899	+	0.184694i	−0.651348	−	0.758780i	$-0.725796\pi$
$101$	−329592.	+	190290.i	−0.319899	+	0.184694i	0.331449	+	0.943473i	$0.392463\pi$
$102$		0			0
$103$	−994554.	−	574206.i	−0.910157	−	0.525480i	−0.0296756	−	0.999560i	$-0.509447\pi$
$103$	−994554.	−	574206.i	−0.910157	−	0.525480i	−0.880482	+	0.474080i	$0.842781\pi$
$104$		0			0
$105$	16457.0	−	322662.i	0.0142162	−	0.278727i
$106$		0			0
$107$	283009.	−	490185.i	0.231019	−	0.400137i	−0.727089	−	0.686543i	$-0.759127\pi$
$107$	283009.	−	490185.i	0.231019	−	0.400137i	0.958108	+	0.286406i	$0.0924606\pi$
$108$		0			0
$109$	1.12047e6	+	1.94071e6i	0.865209	+	1.49859i	0.866840	+	0.498587i	$0.166148\pi$
$109$	1.12047e6	+	1.94071e6i	0.865209	+	1.49859i	−0.00163094	+	0.999999i	$0.500519\pi$
$110$		0			0
$111$			1.41228e6i			1.03265i
$112$		0			0
$113$	436932.			0.302816			0.151408	−	0.988471i	$-0.451619\pi$
$113$	436932.			0.302816			0.151408	+	0.988471i	$0.451619\pi$
$114$		0			0
$115$	−780135.	+	450411.i	−0.512951	+	0.296153i
$116$		0			0
$117$	41187.3	+	23779.5i	0.0257161	+	0.0148472i
$118$		0			0
$119$	1.51067e6	+	2.95463e6i	0.896458	+	1.75332i
$120$		0			0
$121$	−1.95590e6	+	3.38772e6i	−1.10406	+	1.91228i
$122$		0			0
$123$	−507774.	−	879490.i	−0.272870	−	0.472624i
$124$		0			0
$125$			1.66765e6i			0.853838i
$126$		0			0
$127$	−1.35247e6			−0.660264			−0.330132	−	0.943935i	$-0.607093\pi$
$127$	−1.35247e6			−0.660264			−0.330132	+	0.943935i	$0.607093\pi$
$128$		0			0
$129$	487867.	−	281670.i	0.227265	−	0.131211i
$130$		0			0
$131$	−415449.	−	239860.i	−0.184801	−	0.106695i	0.404745	−	0.914429i	$-0.367360\pi$
$131$	−415449.	−	239860.i	−0.184801	−	0.106695i	−0.589546	+	0.807735i	$0.700693\pi$
$132$		0			0
$133$	−1.61214e6	+	2.49010e6i	−0.685248	+	1.05843i
$134$		0			0
$135$	114444.	−	198223.i	0.0465150	−	0.0805663i
$136$		0			0
$137$	1.49050e6	+	2.58162e6i	0.579655	+	1.00399i	0.995519	+	0.0945655i	$0.0301462\pi$
$137$	1.49050e6	+	2.58162e6i	0.579655	+	1.00399i	−0.415863	+	0.909427i	$0.636520\pi$
$138$		0			0
$139$		−	79622.7i		−	0.0296478i	−0.999890	−	0.0148239i	$-0.995281\pi$
$139$		−	79622.7i		−	0.0296478i	0.999890	−	0.0148239i	$-0.00471877\pi$
$140$		0			0
$141$	−3045.99			−0.00108660
$142$		0			0
$143$	404073.	−	233292.i	0.138182	−	0.0797795i
$144$		0			0
$145$	−1.44166e6	−	832340.i	−0.472887	−	0.273022i
$146$		0			0
$147$	1.67332e6	−	750630.i	0.526776	−	0.236306i
$148$		0			0
$149$	959789.	−	1.66240e6i	0.290146	−	0.502548i	−0.683698	−	0.729765i	$-0.739629\pi$
$149$	959789.	−	1.66240e6i	0.290146	−	0.502548i	0.973844	+	0.227217i	$0.0729628\pi$
$150$		0			0
$151$	−1.94418e6	−	3.36742e6i	−0.564684	−	0.978062i	−0.997079	−	0.0763775i	$-0.975665\pi$
$151$	−1.94418e6	−	3.36742e6i	−0.564684	−	0.978062i	0.432395	−	0.901684i	$-0.357669\pi$
$152$		0			0
$153$			2.35096e6i			0.656403i
$154$		0			0
$155$	−323286.			−0.0868143
$156$		0			0
$157$	−909997.	+	525387.i	−0.235148	+	0.135763i	−0.612945	−	0.790126i	$-0.710015\pi$
$157$	−909997.	+	525387.i	−0.235148	+	0.135763i	0.377797	+	0.925889i	$0.376682\pi$
$158$		0			0
$159$	−11085.4	−	6400.16i	−0.00275778	−	0.00159221i
$160$		0			0
$161$	−4.29244e6	−	2.77901e6i	−1.02855	−	0.665905i
$162$		0			0
$163$	−3.34452e6	+	5.79288e6i	−0.772274	+	1.33762i	0.164040	+	0.986454i	$0.447547\pi$
$163$	−3.34452e6	+	5.79288e6i	−0.772274	+	1.33762i	−0.936314	+	0.351164i	$0.885786\pi$
$164$		0			0
$165$	−1.12277e6	−	1.94469e6i	−0.249942	−	0.432912i
$166$		0			0
$167$			6.42044e6i			1.37853i	0.724511	+	0.689264i	$0.242066\pi$
$167$			6.42044e6i			1.37853i	−0.724511	+	0.689264i	$0.757934\pi$
$168$		0			0
$169$	4.78850e6			0.992064
$170$		0			0
$171$	−1.82001e6	+	1.05079e6i	−0.363987	+	0.210148i
$172$		0			0
$173$	5.91967e6	+	3.41772e6i	1.14330	+	0.660083i	0.947245	−	0.320510i	$-0.103854\pi$
$173$	5.91967e6	+	3.41772e6i	1.14330	+	0.660083i	0.196052	+	0.980593i	$0.437188\pi$
$174$		0			0
$175$	−3.65678e6	+	1.86968e6i	−0.682314	+	0.348861i
$176$		0			0
$177$	−952736.	+	1.65019e6i	−0.171812	+	0.297587i
$178$		0			0
$179$	−1.28948e6	−	2.23344e6i	−0.224830	−	0.389417i	0.731438	−	0.681908i	$-0.238849\pi$
$179$	−1.28948e6	−	2.23344e6i	−0.224830	−	0.389417i	−0.956268	+	0.292490i	$0.905516\pi$
$180$		0			0
$181$		−	9.12904e6i		−	1.53953i	−0.638325	−	0.769767i	$-0.720372\pi$
$181$		−	9.12904e6i		−	1.53953i	0.638325	−	0.769767i	$-0.279628\pi$
$182$		0			0
$183$	−1.53890e6			−0.251107
$184$		0			0
$185$	−4.74093e6	+	2.73718e6i	−0.748769	+	0.432302i
$186$		0			0
$187$	1.99743e7	+	1.15322e7i	3.05455	+	1.76354i
$188$		0			0
$189$	1.29760e6	+	66182.3i	0.192200	+	0.00980294i
$190$		0			0
$191$	−2.45660e6	+	4.25495e6i	−0.352561	+	0.610653i	−0.986697	−	0.162568i	$-0.948022\pi$
$191$	−2.45660e6	+	4.25495e6i	−0.352561	+	0.610653i	0.634136	+	0.773221i	$0.281356\pi$
$192$		0			0
$193$	−856442.	−	1.48340e6i	−0.119131	−	0.206341i	0.800292	−	0.599610i	$-0.204678\pi$
$193$	−856442.	−	1.48340e6i	−0.119131	−	0.206341i	−0.919424	+	0.393269i	$0.871344\pi$
$194$		0			0
$195$			184350.i			0.0248622i
$196$		0			0
$197$	−2.91906e6			−0.381807			−0.190904	−	0.981609i	$-0.561142\pi$
$197$	−2.91906e6			−0.381807			−0.190904	+	0.981609i	$0.561142\pi$
$198$		0			0
$199$	6.46624e6	−	3.73328e6i	0.820526	−	0.473731i	−0.0300719	−	0.999548i	$-0.509574\pi$
$199$	6.46624e6	−	3.73328e6i	0.820526	−	0.473731i	0.850598	+	0.525817i	$0.176240\pi$
$200$		0			0
$201$	−3.50531e6	−	2.02379e6i	−0.431656	−	0.249217i
$202$		0			0
$203$	481337.	−	9.43727e6i	0.0575388	−	1.12813i
$204$		0			0
$205$	1.96826e6	−	3.40912e6i	0.228465	−	0.395713i
$206$		0			0
$207$	−1.81134e6	−	3.13734e6i	−0.204216	−	0.353713i
$208$		0			0
$209$			2.06177e7i			2.25840i
$210$		0			0
$211$	−3.43606e6			−0.365774			−0.182887	−	0.983134i	$-0.558544\pi$
$211$	−3.43606e6			−0.365774			−0.182887	+	0.983134i	$0.558544\pi$
$212$		0			0
$213$	3.34934e6	−	1.93374e6i	0.346594	−	0.200106i
$214$		0			0
$215$	1.89109e6	+	1.09182e6i	0.190282	+	0.109859i
$216$		0			0
$217$	−835419.	−	1.63394e6i	−0.0817570	−	0.159903i
$218$		0			0
$219$	2.15728e6	−	3.73652e6i	0.205388	−	0.355742i
$220$		0			0
$221$	−946749.	−	1.63982e6i	−0.0877118	−	0.151921i
$222$		0			0
$223$		−	3.63065e6i		−	0.327393i	−0.986511	−	0.163697i	$-0.947658\pi$
$223$		−	3.63065e6i		−	0.327393i	0.986511	−	0.163697i	$-0.0523419\pi$
$224$		0			0
$225$	−2.90965e6			−0.255442
$226$		0			0
$227$	−8.55780e6	+	4.94085e6i	−0.731618	+	0.422400i	−0.819014	−	0.573774i	$-0.805479\pi$
$227$	−8.55780e6	+	4.94085e6i	−0.731618	+	0.422400i	0.0873958	+	0.996174i	$0.472146\pi$
$228$		0			0
$229$	9.48752e6	+	5.47762e6i	0.790035	+	0.456127i	0.839975	−	0.542625i	$-0.182570\pi$
$229$	9.48752e6	+	5.47762e6i	0.790035	+	0.456127i	−0.0499399	+	0.998752i	$0.515903\pi$
$230$		0			0
$231$	6.92741e6	−	1.07000e7i	0.561998	−	0.868060i
$232$		0			0
$233$	5.09331e6	−	8.82187e6i	0.402654	−	0.697417i	−0.591391	−	0.806385i	$-0.701421\pi$
$233$	5.09331e6	−	8.82187e6i	0.402654	−	0.697417i	0.994045	+	0.108967i	$0.0347544\pi$
$234$		0			0
$235$	−5903.51	−	10225.2i	−0.000454890	−	0.000787893i
$236$		0			0
$237$			914805.i			0.0687200i
$238$		0			0
$239$	−1.30448e7			−0.955530			−0.477765	−	0.878488i	$-0.658553\pi$
$239$	−1.30448e7			−0.955530			−0.477765	+	0.878488i	$0.658553\pi$
$240$		0			0
$241$	−2.45893e6	+	1.41966e6i	−0.175669	+	0.101423i	−0.585256	−	0.810848i	$-0.699006\pi$
$241$	−2.45893e6	+	1.41966e6i	−0.175669	+	0.101423i	0.409587	+	0.912271i	$0.365673\pi$
$242$		0			0
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$		0			0
$245$	5.76290e6	+	4.16239e6i	0.391871	+	0.283038i
$246$		0			0
$247$	846319.	−	1.46587e6i	0.0561621	−	0.0972756i
$248$		0			0
$249$	−6.79357e6	−	1.17668e7i	−0.440048	−	0.762185i
$250$		0			0
$251$		−	8.47048e6i		−	0.535657i	−0.963467	−	0.267829i	$-0.913694\pi$
$251$		−	8.47048e6i		−	0.535657i	0.963467	−	0.267829i	$-0.0863061\pi$
$252$		0			0
$253$	−3.55408e7			−2.19465
$254$		0			0
$255$	−7.89199e6	+	4.55644e6i	−0.475955	+	0.274793i
$256$		0			0
$257$	−8.72072e6	−	5.03491e6i	−0.513751	−	0.296615i	0.220623	−	0.975359i	$-0.429191\pi$
$257$	−8.72072e6	−	5.03491e6i	−0.513751	−	0.296615i	−0.734374	+	0.678745i	$0.762524\pi$
$258$		0			0
$259$	−2.60854e7	−	1.68882e7i	−1.50141	−	0.972039i
$260$		0			0
$261$	3.34729e6	−	5.79767e6i	0.188266	−	0.326086i
$262$		0			0
$263$	3.72677e6	+	6.45495e6i	0.204864	+	0.354834i	0.950089	−	0.311978i	$-0.100992\pi$
$263$	3.72677e6	+	6.45495e6i	0.204864	+	0.354834i	−0.745226	+	0.666812i	$0.767658\pi$
$264$		0			0
$265$		−	49617.2i		−	0.00266621i
$266$		0			0
$267$	1.13311e7			0.595303
$268$		0			0
$269$	1.61693e7	−	9.33534e6i	0.830681	−	0.479594i	−0.0234050	−	0.999726i	$-0.507451\pi$
$269$	1.61693e7	−	9.33534e6i	0.830681	−	0.479594i	0.854086	+	0.520132i	$0.174117\pi$
$270$		0			0
$271$	−1.01263e6	−	584640.i	−0.0508793	−	0.0293752i	0.474345	−	0.880339i	$-0.342685\pi$
$271$	−1.01263e6	−	584640.i	−0.0508793	−	0.0293752i	−0.525224	+	0.850964i	$0.676018\pi$
$272$		0			0
$273$	−931739.	+	476389.i	−0.0457938	+	0.0234139i
$274$		0			0
$275$	−1.42727e7	+	2.47211e7i	−0.686292	+	1.18869i
$276$		0			0
$277$	1.54720e7	+	2.67983e7i	0.727960	+	1.26086i	0.957744	+	0.287622i	$0.0928646\pi$
$277$	1.54720e7	+	2.67983e7i	0.727960	+	1.26086i	−0.229784	+	0.973242i	$0.573802\pi$
$278$		0			0
$279$		−	1.30010e6i		−	0.0598640i
$280$		0			0
$281$	2.59728e7			1.17058			0.585289	−	0.810825i	$-0.300981\pi$
$281$	2.59728e7			1.17058			0.585289	+	0.810825i	$0.300981\pi$
$282$		0			0
$283$	2.17425e7	−	1.25530e7i	0.959289	−	0.553846i	0.0633347	−	0.997992i	$-0.479826\pi$
$283$	2.17425e7	−	1.25530e7i	0.959289	−	0.553846i	0.895954	+	0.444147i	$0.146493\pi$
$284$		0			0
$285$	−7.05482e6	−	4.07310e6i	−0.304755	−	0.175951i
$286$		0			0
$287$	2.23166e7	+	1.13823e6i	0.944021	+	0.0481486i
$288$		0			0
$289$	3.47313e7	−	6.01564e7i	1.43889	−	2.49223i
$290$		0			0
$291$	9.54705e6	+	1.65360e7i	0.387427	+	0.671044i
$292$		0			0
$293$			3.47279e7i			1.38062i	0.723512	+	0.690312i	$0.242527\pi$
$293$			3.47279e7i			1.38062i	−0.723512	+	0.690312i	$0.757473\pi$
$294$		0			0
$295$	−7.38608e6			−0.287705
$296$		0			0
$297$	7.82065e6	−	4.51525e6i	0.298520	−	0.172351i
$298$		0			0
$299$	2.52686e6	+	1.45889e6i	0.0945297	+	0.0545767i
$300$		0			0
$301$	−631394.	+	1.23793e7i	−0.0231527	+	0.453940i
$302$		0			0
$303$	2.96633e6	−	5.13783e6i	0.106633	−	0.184694i
$304$		0			0
$305$	−2.98259e6	−	5.16599e6i	−0.105122	−	0.182077i
$306$		0			0
$307$		−	3.52859e7i		−	1.21951i	−0.792589	−	0.609756i	$-0.791267\pi$
$307$		−	3.52859e7i		−	1.21951i	0.792589	−	0.609756i	$-0.208733\pi$
$308$		0			0
$309$	1.79020e7			0.606772
$310$		0			0
$311$	−1.51845e7	+	8.76676e6i	−0.504799	+	0.291446i	−0.730693	−	0.682706i	$-0.760803\pi$
$311$	−1.51845e7	+	8.76676e6i	−0.504799	+	0.291446i	0.225894	+	0.974152i	$0.427470\pi$
$312$		0			0
$313$	−3.47168e7	−	2.00437e7i	−1.13216	−	0.653650i	−0.187679	−	0.982230i	$-0.560097\pi$
$313$	−3.47168e7	−	2.00437e7i	−1.13216	−	0.653650i	−0.944476	+	0.328580i	$0.893430\pi$
$314$		0			0
$315$	2.29273e6	+	4.48420e6i	0.0733536	+	0.143468i
$316$		0			0
$317$	−1.06761e6	+	1.84915e6i	−0.0335145	+	0.0580489i	−0.882296	−	0.470695i	$-0.844003\pi$
$317$	−1.06761e6	+	1.84915e6i	−0.0335145	+	0.0580489i	0.848782	+	0.528744i	$0.177337\pi$
$318$		0			0
$319$	−3.28390e7	−	5.68787e7i	−1.01162	−	1.75218i
$320$		0			0
$321$			8.82333e6i			0.266758i
$322$		0			0
$323$	8.36712e7			2.48295
$324$		0			0
$325$	2.02951e6	−	1.17174e6i	0.0591209	−	0.0341335i
$326$		0			0
$327$	−3.02527e7	−	1.74664e7i	−0.865209	−	0.499529i
$328$		0			0
$329$	36424.2	−	56260.7i	0.00102283	−	0.00157986i
$330$		0			0
$331$	3.13110e7	−	5.42323e7i	0.863402	−	1.49546i	−0.00522312	−	0.999986i	$-0.501663\pi$
$331$	3.13110e7	−	5.42323e7i	0.863402	−	1.49546i	0.868625	−	0.495470i	$-0.165004\pi$
$332$		0			0
$333$	−1.10076e7	−	1.90658e7i	−0.298100	−	0.516324i
$334$		0			0
$335$		−	1.56894e7i		−	0.417323i
$336$		0			0
$337$	−2.94208e7			−0.768713			−0.384356	−	0.923185i	$-0.625577\pi$
$337$	−2.94208e7			−0.768713			−0.384356	+	0.923185i	$0.625577\pi$
$338$		0			0
$339$	−5.89859e6	+	3.40555e6i	−0.151408	+	0.0874155i
$340$		0			0
$341$	−1.10460e7	−	6.37742e6i	−0.278575	−	0.160835i
$342$		0			0
$343$	−6.14521e6	+	3.98830e7i	−0.152284	+	0.988337i
$344$		0			0
$345$	7.02122e6	−	1.21611e7i	0.170984	−	0.296153i
$346$		0			0
$347$	1.69149e7	+	2.92974e7i	0.404837	+	0.701199i	0.994303	−	0.106595i	$-0.0339948\pi$
$347$	1.69149e7	+	2.92974e7i	0.404837	+	0.701199i	−0.589465	+	0.807794i	$0.700661\pi$
$348$		0			0
$349$		−	6.53452e7i		−	1.53723i	−0.639714	−	0.768613i	$-0.720947\pi$
$349$		−	6.53452e7i		−	1.53723i	0.639714	−	0.768613i	$-0.279053\pi$
$350$		0			0
$351$	−741372.			−0.0171441
$352$		0			0
$353$	1.51432e7	−	8.74294e6i	0.344266	−	0.198762i	−0.317891	−	0.948127i	$-0.602975\pi$
$353$	1.51432e7	−	8.74294e6i	0.344266	−	0.198762i	0.662157	+	0.749365i	$0.269641\pi$
$354$		0			0
$355$	1.29829e7	+	7.49567e6i	0.290192	+	0.167543i
$356$		0			0
$357$	−4.34232e7	−	2.81130e7i	−0.954370	−	0.617877i
$358$		0			0
$359$	1.81799e7	−	3.14885e7i	0.392923	−	0.680563i	−0.599910	−	0.800067i	$-0.704797\pi$
$359$	1.81799e7	−	3.14885e7i	0.392923	−	0.680563i	0.992834	+	0.119504i	$0.0381305\pi$
$360$		0			0
$361$	1.38748e7	+	2.40318e7i	0.294920	+	0.510817i
$362$		0			0
$363$		−	6.09790e7i		−	1.27485i
$364$		0			0
$365$	1.67243e7			0.343930
$366$		0			0
$367$	−8.10145e6	+	4.67738e6i	−0.163895	+	0.0946246i	−0.579704	−	0.814827i	$-0.696832\pi$
$367$	−8.10145e6	+	4.67738e6i	−0.163895	+	0.0946246i	0.415809	+	0.909452i	$0.363498\pi$
$368$		0			0
$369$	1.37099e7	+	7.91541e6i	0.272870	+	0.157541i
$370$		0			0
$371$	250774.	−	128218.i	0.00491089	−	0.00251089i
$372$		0			0
$373$	4.29004e7	−	7.43056e7i	0.826675	−	1.43184i	−0.0739582	−	0.997261i	$-0.523563\pi$
$373$	4.29004e7	−	7.43056e7i	0.826675	−	1.43184i	0.900633	−	0.434581i	$-0.143104\pi$
$374$		0			0
$375$	−1.29981e7	−	2.25133e7i	−0.246482	−	0.426919i
$376$		0			0
$377$			5.39191e6i			0.100628i
$378$		0			0
$379$	4.41722e6			0.0811393			0.0405696	−	0.999177i	$-0.487083\pi$
$379$	4.41722e6			0.0811393			0.0405696	+	0.999177i	$0.487083\pi$
$380$		0			0
$381$	1.82584e7	−	1.05415e7i	0.330132	−	0.190602i
$382$		0			0
$383$	7.80978e7	+	4.50898e7i	1.39009	+	0.802568i	0.993325	−	0.115353i	$-0.0368001\pi$
$383$	7.80978e7	+	4.50898e7i	1.39009	+	0.802568i	0.396763	+	0.917921i	$0.370133\pi$
$384$		0			0
$385$	4.93455e7	+	2.51681e6i	0.864699	+	0.0441029i
$386$		0			0
$387$	−4.39080e6	+	7.60510e6i	−0.0757550	+	0.131211i
$388$		0			0
$389$	−1.36992e7	−	2.37277e7i	−0.232726	−	0.403094i	0.725883	−	0.687818i	$-0.241431\pi$
$389$	−1.36992e7	−	2.37277e7i	−0.232726	−	0.403094i	−0.958609	+	0.284724i	$0.908098\pi$
$390$		0			0
$391$			1.44232e8i			2.41286i
$392$		0			0
$393$	7.47809e6			0.123201
$394$		0			0
$395$	−3.07093e6	+	1.77300e6i	−0.0498286	+	0.0287686i
$396$		0			0
$397$	−8.23970e6	−	4.75719e6i	−0.131686	−	0.0760289i	0.432710	−	0.901533i	$-0.357557\pi$
$397$	−8.23970e6	−	4.75719e6i	−0.131686	−	0.0760289i	−0.564396	+	0.825504i	$0.690891\pi$
$398$		0			0
$399$	2.35545e6	−	4.61818e7i	0.0370813	−	0.727030i
$400$		0			0
$401$	−5.25388e7	+	9.09999e7i	−0.814793	+	1.41126i	0.0946832	+	0.995507i	$0.469816\pi$
$401$	−5.25388e7	+	9.09999e7i	−0.814793	+	1.41126i	−0.909476	+	0.415756i	$0.863517\pi$
$402$		0			0
$403$	523562.	+	906837.i	0.00799932	+	0.0138552i
$404$		0			0
$405$			3.56802e6i			0.0537108i
$406$		0			0
$407$	−2.15984e8			−3.20360
$408$		0			0
$409$	−1.94205e7	+	1.12124e7i	−0.283851	+	0.163882i	−0.635166	−	0.772376i	$-0.719068\pi$
$409$	−1.94205e7	+	1.12124e7i	−0.283851	+	0.163882i	0.351314	+	0.936258i	$0.385735\pi$
$410$		0			0
$411$	−4.02435e7	−	2.32346e7i	−0.579655	−	0.334664i
$412$		0			0
$413$	−1.90867e7	−	3.73305e7i	−0.270945	−	0.529924i
$414$		0			0
$415$	2.63335e7	−	4.56110e7i	0.368439	−	0.638154i
$416$		0			0
$417$	620597.	+	1.07491e6i	0.00855858	+	0.0148239i
$418$		0			0
$419$			6.33360e7i			0.861011i	0.902588	+	0.430505i	$0.141665\pi$
$419$			6.33360e7i			0.861011i	−0.902588	+	0.430505i	$0.858335\pi$
$420$		0			0
$421$	−1.77837e7			−0.238328			−0.119164	−	0.992875i	$-0.538021\pi$
$421$	−1.77837e7			−0.238328			−0.119164	+	0.992875i	$0.538021\pi$
$422$		0			0
$423$	41120.9	−	23741.1i	0.000543302	−	0.000313675i
$424$		0			0
$425$	1.00324e8	+	5.79219e7i	1.30688	+	0.754529i
$426$		0			0
$427$	1.84024e7	−	2.84242e7i	0.236369	−	0.365094i
$428$		0			0
$429$	−3.63666e6	+	6.29888e6i	−0.0460607	+	0.0797795i
$430$		0			0
$431$	4.99304e7	+	8.64820e7i	0.623639	+	1.08017i	0.988802	+	0.149231i	$0.0476798\pi$
$431$	4.99304e7	+	8.64820e7i	0.623639	+	1.08017i	−0.365163	+	0.930943i	$0.618987\pi$
$432$		0			0
$433$		−	6.77284e6i		−	0.0834271i	−0.999130	−	0.0417135i	$-0.986718\pi$
$433$		−	6.77284e6i		−	0.0834271i	0.999130	−	0.0417135i	$-0.0132817\pi$
$434$		0			0
$435$	2.59498e7			0.315258
$436$		0			0
$437$	−1.11659e8	+	6.44662e7i	−1.33798	+	0.772481i
$438$		0			0
$439$	−8.79243e7	−	5.07631e7i	−1.03924	−	0.600005i	−0.119621	−	0.992820i	$-0.538168\pi$
$439$	−8.79243e7	−	5.07631e7i	−1.03924	−	0.600005i	−0.919617	+	0.392815i	$0.871501\pi$
$440$		0			0
$441$	−1.67392e7	+	2.31757e7i	−0.195172	+	0.270220i
$442$		0			0
$443$	3.97205e7	−	6.87979e7i	0.456882	−	0.791342i	−0.541913	−	0.840435i	$-0.682300\pi$
$443$	3.97205e7	−	6.87979e7i	0.456882	−	0.791342i	0.998794	+	0.0490927i	$0.0156330\pi$
$444$		0			0
$445$	2.19611e7	+	3.80377e7i	0.249215	+	0.431652i
$446$		0			0
$447$			2.99232e7i			0.335032i
$448$		0			0
$449$	−1.91759e7			−0.211844			−0.105922	−	0.994374i	$-0.533779\pi$
$449$	−1.91759e7			−0.211844			−0.105922	+	0.994374i	$0.533779\pi$
$450$		0			0
$451$	1.34503e8	−	7.76551e7i	1.46623	−	0.846526i
$452$		0			0
$453$	5.24929e7	+	3.03068e7i	0.564684	+	0.326021i
$454$		0			0
$455$	−3.40503e6	−	2.20448e6i	−0.0361482	−	0.0234030i
$456$		0			0
$457$	−1.42233e7	+	2.46355e7i	−0.149022	+	0.258114i	−0.930866	−	0.365360i	$-0.880946\pi$
$457$	−1.42233e7	+	2.46355e7i	−0.149022	+	0.258114i	0.781844	+	0.623474i	$0.214279\pi$
$458$		0			0
$459$	−1.83239e7	−	3.17379e7i	−0.189487	−	0.328201i
$460$		0			0
$461$			1.15190e8i			1.17575i	0.808953	+	0.587873i	$0.200034\pi$
$461$			1.15190e8i			1.17575i	−0.808953	+	0.587873i	$0.799966\pi$
$462$		0			0
$463$	−1.15681e8			−1.16551			−0.582757	−	0.812647i	$-0.698026\pi$
$463$	−1.15681e8			−1.16551			−0.582757	+	0.812647i	$0.698026\pi$
$464$		0			0
$465$	4.36436e6	−	2.51976e6i	0.0434072	−	0.0250611i
$466$		0			0
$467$	1.24191e8	+	7.17015e7i	1.21938	+	0.704008i	0.964785	−	0.263041i	$-0.0847254\pi$
$467$	1.24191e8	+	7.17015e7i	1.21938	+	0.704008i	0.254592	+	0.967049i	$0.418059\pi$
$468$		0			0
$469$	7.92970e7	−	4.05438e7i	0.768667	−	0.393012i
$470$		0			0
$471$	8.18997e6	−	1.41854e7i	0.0783826	−	0.135763i
$472$		0			0
$473$	4.30765e7	+	7.46107e7i	0.407059	+	0.705047i
$474$		0			0
$475$			1.03555e8i			0.966253i
$476$		0			0
$477$	199537.			0.00183852
$478$		0			0
$479$	−1.70589e8	+	9.84899e7i	−1.55219	+	0.896159i	−0.554229	+	0.832364i	$0.686987\pi$
$479$	−1.70589e8	+	9.84899e7i	−1.55219	+	0.896159i	−0.997963	+	0.0637949i	$0.979680\pi$
$480$		0			0
$481$	1.53559e7	+	8.86573e6i	0.137988	+	0.0796672i
$482$		0			0
$483$	7.96082e7	+	4.06032e6i	0.706507	+	0.0360345i
$484$		0			0
$485$	−3.70067e7	+	6.40975e7i	−0.324381	+	0.561844i
$486$		0			0
$487$	−9.13374e7	−	1.58201e8i	−0.790791	−	1.36969i	−0.925478	−	0.378802i	$-0.876336\pi$
$487$	−9.13374e7	−	1.58201e8i	−0.790791	−	1.36969i	0.134687	−	0.990888i	$-0.456997\pi$
$488$		0			0
$489$		−	1.04272e8i		−	0.891745i
$490$		0			0
$491$	1.47298e7			0.124438			0.0622188	−	0.998063i	$-0.480182\pi$
$491$	1.47298e7			0.124438			0.0622188	+	0.998063i	$0.480182\pi$
$492$		0			0
$493$	−2.30826e8	+	1.33268e8i	−1.92639	+	1.11220i
$494$		0			0
$495$	3.03148e7	+	1.75022e7i	0.249942	+	0.144304i
$496$		0			0
$497$	−4.33469e6	+	8.49877e7i	−0.0353093	+	0.692288i
$498$		0			0
$499$	−4.67447e7	+	8.09643e7i	−0.376211	+	0.651616i	−0.990507	−	0.137459i	$-0.956106\pi$
$499$	−4.67447e7	+	8.09643e7i	−0.376211	+	0.651616i	0.614297	+	0.789075i	$0.289440\pi$
$500$		0			0
$501$	−5.00424e7	−	8.66759e7i	−0.397946	−	0.689264i
$502$		0			0
$503$			1.42465e8i			1.11945i	0.828679	+	0.559724i	$0.189093\pi$
$503$			1.42465e8i			1.11945i	−0.828679	+	0.559724i	$0.810907\pi$
$504$		0			0
$505$	2.29965e7			0.178561
$506$		0			0
$507$	−6.46448e7	+	3.73227e7i	−0.496032	+	0.286384i
$508$		0			0
$509$	4.23180e7	+	2.44323e7i	0.320902	+	0.185273i	0.651794	−	0.758396i	$-0.274017\pi$
$509$	4.23180e7	+	2.44323e7i	0.320902	+	0.185273i	−0.330893	+	0.943668i	$0.607350\pi$
$510$		0			0
$511$	4.32182e7	+	8.45276e7i	0.323894	+	0.633484i
$512$		0			0
$513$	1.63801e7	−	2.83712e7i	0.121329	−	0.210148i
$514$		0			0
$515$	3.46962e7	+	6.00956e7i	0.254016	+	0.439968i
$516$		0			0
$517$		−	465831.i		−	0.00337098i
$518$		0			0
$519$	−1.06554e8			−0.762198
$520$		0			0
$521$	−1.21658e7	+	7.02396e6i	−0.0860259	+	0.0496671i	−0.542396	−	0.840123i	$-0.682483\pi$
$521$	−1.21658e7	+	7.02396e6i	−0.0860259	+	0.0496671i	0.456370	+	0.889790i	$0.349149\pi$
$522$		0			0
$523$	−1.14237e8	−	6.59548e7i	−0.798549	−	0.461043i	0.0444143	−	0.999013i	$-0.485858\pi$
$523$	−1.14237e8	−	6.59548e7i	−0.798549	−	0.461043i	−0.842964	+	0.537970i	$0.819191\pi$
$524$		0			0
$525$	3.47938e7	−	5.37424e7i	0.240450	−	0.371398i
$526$		0			0
$527$	−2.58810e7	+	4.48271e7i	−0.176827	+	0.306273i
$528$		0			0
$529$	−3.71090e7	−	6.42746e7i	−0.250676	−	0.434183i
$530$		0			0
$531$		−	2.97034e7i		−	0.198391i
$532$		0			0
$533$	−1.27504e7			−0.0842058
$534$		0			0
$535$	−2.96193e7	+	1.71007e7i	−0.193425	+	0.111674i
$536$		0			0
$537$	3.48159e7	+	2.01010e7i	0.224830	+	0.129806i
$538$		0			0
$539$	1.14796e8	+	2.55904e8i	0.733094	+	1.63422i
$540$		0			0
$541$	−7.91333e7	+	1.37063e8i	−0.499767	+	0.865622i	−1.00000		0.000269212i	$-0.999914\pi$
$541$	−7.91333e7	+	1.37063e8i	−0.499767	+	0.865622i	0.500233	+	0.865891i	$0.333248\pi$
$542$		0			0
$543$	7.11538e7	+	1.23242e8i	0.444425	+	0.769767i
$544$		0			0
$545$		−	1.35408e8i		−	0.836480i
$546$		0			0
$547$	1.56549e8			0.956505			0.478252	−	0.878222i	$-0.341270\pi$
$547$	1.56549e8			0.956505			0.478252	+	0.878222i	$0.341270\pi$
$548$		0			0
$549$	2.07752e7	−	1.19946e7i	0.125553	−	0.0724883i
$550$		0			0
$551$	−2.06341e8	−	1.19131e8i	−1.23347	−	0.712146i
$552$		0			0
$553$	−1.68968e7	−	1.09393e7i	−0.0999148	−	0.0646867i
$554$		0			0
$555$	4.26683e7	−	7.39037e7i	0.249590	−	0.432302i
$556$		0			0
$557$	−4.64886e7	−	8.05206e7i	−0.269018	−	0.465952i	0.699591	−	0.714544i	$-0.253366\pi$
$557$	−4.64886e7	−	8.05206e7i	−0.269018	−	0.465952i	−0.968608	+	0.248592i	$0.920032\pi$
$558$		0			0
$559$		−	7.07285e6i		−	0.0404910i
$560$		0			0
$561$	−3.59538e8			−2.03637
$562$		0			0
$563$	1.21496e8	−	7.01460e7i	0.680829	−	0.393077i	−0.119338	−	0.992854i	$-0.538077\pi$
$563$	1.21496e8	−	7.01460e7i	0.680829	−	0.393077i	0.800167	+	0.599777i	$0.204744\pi$
$564$		0			0
$565$	−2.28644e7	−	1.32008e7i	−0.126769	−	0.0731903i
$566$		0			0
$567$	−1.80334e7	+	9.22030e6i	−0.0989300	+	0.0505820i
$568$		0			0
$569$	−2.66689e7	+	4.61919e7i	−0.144767	+	0.250743i	−0.929286	−	0.369361i	$-0.879576\pi$
$569$	−2.66689e7	+	4.61919e7i	−0.144767	+	0.250743i	0.784519	+	0.620104i	$0.212910\pi$
$570$		0			0
$571$	1.17332e8	+	2.03224e8i	0.630241	+	1.09161i	0.987502	+	0.157604i	$0.0503771\pi$
$571$	1.17332e8	+	2.03224e8i	0.630241	+	1.09161i	−0.357262	+	0.934004i	$0.616290\pi$
$572$		0			0
$573$		−	7.65892e7i		−	0.407102i
$574$		0			0
$575$	−1.78508e8			−0.938977
$576$		0			0
$577$	2.35850e8	−	1.36168e8i	1.22775	−	0.708839i	0.261187	−	0.965288i	$-0.415886\pi$
$577$	2.35850e8	−	1.36168e8i	1.22775	−	0.708839i	0.966558	+	0.256449i	$0.0825526\pi$
$578$		0			0
$579$	2.31239e7	+	1.33506e7i	0.119131	+	0.0687805i
$580$		0			0
$581$	2.98576e8	+	1.52285e7i	1.52239	+	0.0776477i
$582$		0			0
$583$	978792.	−	1.69532e6i	0.00493952	−	0.00855550i
$584$		0			0
$585$	−1.43687e6	−	2.48873e6i	−0.00717711	−	0.0124311i
$586$		0			0
$587$		−	1.61881e8i		−	0.800355i	−0.916438	−	0.400177i	$-0.868949\pi$
$587$		−	1.61881e8i		−	0.800355i	0.916438	−	0.400177i	$-0.131051\pi$
$588$		0			0
$589$	−4.62711e7			−0.226445
$590$		0			0
$591$	3.94073e7	−	2.27518e7i	0.190904	−	0.110218i
$592$		0			0
$593$	−1.26937e8	−	7.32870e7i	−0.608728	−	0.351449i	0.163739	−	0.986504i	$-0.447644\pi$
$593$	−1.26937e8	−	7.32870e7i	−0.608728	−	0.351449i	−0.772467	+	0.635054i	$0.780978\pi$
$594$		0			0
$595$	1.02138e7	−	2.00255e8i	0.0484880	−	0.950675i
$596$		0			0
$597$	−5.81961e7	+	1.00799e8i	−0.273509	+	0.473731i
$598$		0			0
$599$	2.20452e7	+	3.81834e7i	0.102573	+	0.177662i	0.912744	−	0.408532i	$-0.133959\pi$
$599$	2.20452e7	+	3.81834e7i	0.102573	+	0.177662i	−0.810171	+	0.586194i	$0.800626\pi$
$600$		0			0
$601$			2.90178e8i			1.33672i	0.743836	+	0.668362i	$0.233004\pi$
$601$			2.90178e8i			1.33672i	−0.743836	+	0.668362i	$0.766996\pi$
$602$		0			0
$603$	6.30955e7			0.287771
$604$		0			0
$605$	2.04702e8	−	1.18185e8i	0.924392	−	0.533698i
$606$		0			0
$607$	−8.58670e7	−	4.95753e7i	−0.383937	−	0.221666i	0.295593	−	0.955314i	$-0.404483\pi$
$607$	−8.58670e7	−	4.95753e7i	−0.383937	−	0.221666i	−0.679530	+	0.733648i	$0.737816\pi$
$608$		0			0
$609$	6.70582e7	+	1.31155e8i	0.296893	+	0.580674i
$610$		0			0
$611$	−19121.5	+	33119.4i	−8.38298e−5	+	0.000145197i
$612$		0			0
$613$	−3.76738e7	−	6.52530e7i	−0.163553	−	0.283282i	0.772588	−	0.634908i	$-0.218962\pi$
$613$	−3.76738e7	−	6.52530e7i	−0.163553	−	0.283282i	−0.936140	+	0.351626i	$0.885629\pi$
$614$		0			0
$615$			6.13642e7i			0.263809i
$616$		0			0
$617$	5.15170e7			0.219329			0.109664	−	0.993969i	$-0.465022\pi$
$617$	5.15170e7			0.219329			0.109664	+	0.993969i	$0.465022\pi$
$618$		0			0
$619$	2.65799e6	−	1.53459e6i	0.0112068	−	0.00647026i	−0.494386	−	0.869242i	$-0.664607\pi$
$619$	2.65799e6	−	1.53459e6i	0.0112068	−	0.00647026i	0.505593	+	0.862772i	$0.331274\pi$
$620$		0			0
$621$	4.89063e7	+	2.82361e7i	0.204216	+	0.117904i
$622$		0			0
$623$	−1.35498e8	+	2.09290e8i	−0.560364	+	0.865535i
$624$		0			0
$625$	−4.31620e7	+	7.47588e7i	−0.176792	+	0.306212i
$626$		0			0
$627$	−1.60699e8	−	2.78339e8i	−0.651945	−	1.12920i
$628$		0			0
$629$			8.76509e8i			3.52212i
$630$		0			0
$631$	3.72207e8			1.48148			0.740741	−	0.671790i	$-0.234474\pi$
$631$	3.72207e8			1.48148			0.740741	+	0.671790i	$0.234474\pi$
$632$		0			0
$633$	4.63868e7	−	2.67814e7i	0.182887	−	0.105590i
$634$		0			0
$635$	7.07741e7	+	4.08614e7i	0.276409	+	0.159585i
$636$		0			0
$637$	2.34271e6	−	2.29063e7i	0.00906360	−	0.0886211i
$638$		0			0
$639$	−3.01441e7	+	5.22111e7i	−0.115531	+	0.200106i
$640$		0			0
$641$	8.93251e7	+	1.54716e8i	0.339156	+	0.587436i	0.984274	−	0.176647i	$-0.0565252\pi$
$641$	8.93251e7	+	1.54716e8i	0.339156	+	0.587436i	−0.645118	+	0.764083i	$0.723192\pi$
$642$		0			0
$643$			4.07067e8i			1.53120i	0.643314	+	0.765602i	$0.277559\pi$
$643$			4.07067e8i			1.53120i	−0.643314	+	0.765602i	$0.722441\pi$
$644$		0			0
$645$	−3.40397e7			−0.126855
$646$		0			0
$647$	3.66757e8	−	2.11747e8i	1.35415	−	0.781818i	0.365320	−	0.930882i	$-0.380959\pi$
$647$	3.66757e8	−	2.11747e8i	1.35415	−	0.781818i	0.988827	+	0.149064i	$0.0476262\pi$
$648$		0			0
$649$	−2.52367e8	−	1.45704e8i	−0.923206	−	0.533013i
$650$		0			0
$651$	2.40135e7	+	1.55468e7i	0.0870386	+	0.0563504i
$652$		0			0
$653$	1.27959e8	−	2.21632e8i	0.459549	−	0.795962i	−0.539388	−	0.842057i	$-0.681344\pi$
$653$	1.27959e8	−	2.21632e8i	0.459549	−	0.795962i	0.998937	+	0.0460953i	$0.0146778\pi$
$654$		0			0
$655$	1.44935e7	+	2.51034e7i	0.0515760	+	0.0893323i
$656$		0			0
$657$			6.72574e7i			0.237161i
$658$		0			0
$659$	−9.39048e7			−0.328119			−0.164060	−	0.986450i	$-0.552459\pi$
$659$	−9.39048e7			−0.328119			−0.164060	+	0.986450i	$0.552459\pi$
$660$		0			0
$661$	3.82558e8	−	2.20870e8i	1.32462	−	0.764772i	0.340162	−	0.940367i	$-0.389518\pi$
$661$	3.82558e8	−	2.20870e8i	1.32462	−	0.764772i	0.984463	+	0.175595i	$0.0561848\pi$
$662$		0			0
$663$	2.55622e7	+	1.47584e7i	0.0877118	+	0.0506404i
$664$		0			0
$665$	1.59594e8	−	8.15989e7i	0.542690	−	0.277472i
$666$		0			0
$667$	2.05358e8	−	3.55690e8i	0.692044	−	1.19866i
$668$		0			0
$669$	2.82981e7	+	4.90138e7i	0.0945104	+	0.163697i
$670$		0			0
$671$		−	2.35348e8i		−	0.779011i
$672$		0			0
$673$	−1.30593e8			−0.428424			−0.214212	−	0.976787i	$-0.568718\pi$
$673$	−1.30593e8			−0.428424			−0.214212	+	0.976787i	$0.568718\pi$
$674$		0			0
$675$	3.92802e7	−	2.26785e7i	0.127721	−	0.0737398i
$676$		0			0
$677$	−7.37455e7	−	4.25770e7i	−0.237667	−	0.137217i	0.376437	−	0.926442i	$-0.377149\pi$
$677$	−7.37455e7	−	4.25770e7i	−0.237667	−	0.137217i	−0.614104	+	0.789225i	$0.710483\pi$
$678$		0			0
$679$	−4.19591e8	−	2.14007e7i	−1.34034	−	0.0683627i
$680$		0			0
$681$	7.70202e7	−	1.33403e8i	0.243873	−	0.422400i
$682$		0			0
$683$	−1.08327e8	−	1.87629e8i	−0.339998	−	0.588894i	0.644434	−	0.764660i	$-0.277093\pi$
$683$	−1.08327e8	−	1.87629e8i	−0.339998	−	0.588894i	−0.984432	+	0.175766i	$0.943760\pi$
$684$		0			0
$685$		−	1.80126e8i		−	0.560408i
$686$		0			0
$687$	−1.70775e8			−0.526690
$688$		0			0
$689$	−139179.	+	80355.2i	−0.000425517	+	0.000245672i
$690$		0			0
$691$	−1.68185e8	−	9.71016e7i	−0.509745	−	0.294301i	0.222984	−	0.974822i	$-0.428420\pi$
$691$	−1.68185e8	−	9.71016e7i	−0.509745	−	0.294301i	−0.732729	+	0.680521i	$0.761754\pi$
$692$		0			0
$693$	−1.01214e7	+	1.98444e8i	−0.0304118	+	0.596265i
$694$		0			0
$695$	−2.40559e6	+	4.16660e6i	−0.00716584	+	0.0124116i
$696$		0			0
$697$	−3.15142e8	−	5.45841e8i	−0.930695	−	1.61201i
$698$		0			0
$699$			1.58794e8i			0.464945i
$700$		0			0
$701$	−5.00094e8			−1.45177			−0.725884	−	0.687817i	$-0.758569\pi$
$701$	−5.00094e8			−1.45177			−0.725884	+	0.687817i	$0.758569\pi$
$702$		0			0
$703$	−6.78557e8	+	3.91765e8i	−1.95308	+	1.12761i
$704$		0			0
$705$	159395.	+	92026.5i	0.000454890	+	0.000262631i
$706$		0			0
$707$	5.94263e7	+	1.16228e8i	0.168159	+	0.328892i
$708$		0			0
$709$	3.29158e8	−	5.70118e8i	0.923561	−	1.59966i	0.129703	−	0.991553i	$-0.458598\pi$
$709$	3.29158e8	−	5.70118e8i	0.923561	−	1.59966i	0.793859	−	0.608102i	$-0.208069\pi$
$710$		0			0
$711$	−7.13020e6	−	1.23499e7i	−0.0198378	−	0.0343600i
$712$		0			0
$713$		−	7.97621e7i		−	0.220053i
$714$		0			0
$715$	−2.81932e7			−0.0771304
$716$		0			0
$717$	1.76105e8	−	1.01674e8i	0.477765	−	0.275838i
$718$		0			0
$719$	−3.80204e8	−	2.19511e8i	−1.02289	−	0.590568i	−0.107953	−	0.994156i	$-0.534429\pi$
$719$	−3.80204e8	−	2.19511e8i	−1.02289	−	0.590568i	−0.914941	+	0.403588i	$0.867763\pi$
$720$		0			0
$721$	−2.14073e8	+	3.30657e8i	−0.571159	+	0.882209i
$722$		0			0
$723$	2.21304e7	−	3.83309e7i	0.0585564	−	0.101423i
$724$		0			0
$725$	−1.64938e8	−	2.85681e8i	−0.432819	−	0.749665i
$726$		0			0
$727$		−	4.37292e8i		−	1.13807i	−0.822314	−	0.569035i	$-0.807317\pi$
$727$		−	4.37292e8i		−	1.13807i	0.822314	−	0.569035i	$-0.192683\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	3.02787e8	−	1.74814e8i	0.775148	−	0.447532i
$732$		0			0
$733$	1.38075e8	+	7.97174e7i	0.350592	+	0.202414i	0.664946	−	0.746891i	$-0.268455\pi$
$733$	1.38075e8	+	7.97174e7i	0.350592	+	0.202414i	−0.314354	+	0.949306i	$0.601788\pi$
$734$		0			0
$735$	−1.10242e8	−	1.12748e7i	−0.277641	−	0.0283954i
$736$		0			0
$737$	3.09503e8	−	5.36075e8i	0.773148	−	1.33913i
$738$		0			0
$739$	1.28391e8	+	2.22379e8i	0.318127	+	0.551012i	0.980097	−	0.198518i	$-0.0636128\pi$
$739$	1.28391e8	+	2.22379e8i	0.318127	+	0.551012i	−0.661970	+	0.749530i	$0.730279\pi$
$740$		0			0
$741$			2.63856e7i			0.0648504i
$742$		0			0
$743$	−8.42386e7			−0.205374			−0.102687	−	0.994714i	$-0.532744\pi$
$743$	−8.42386e7			−0.205374			−0.102687	+	0.994714i	$0.532744\pi$
$744$		0			0
$745$	−1.00450e8	+	5.79949e7i	−0.242930	+	0.140256i
$746$		0			0
$747$	1.83426e8	+	1.05901e8i	0.440048	+	0.254062i
$748$		0			0
$749$	−1.62971e8	−	1.05510e8i	−0.387850	−	0.251101i
$750$		0			0
$751$	−5.34068e7	+	9.25033e7i	−0.126089	+	0.218392i	−0.922158	−	0.386813i	$-0.873576\pi$
$751$	−5.34068e7	+	9.25033e7i	−0.126089	+	0.218392i	0.796069	+	0.605206i	$0.206909\pi$
$752$		0			0
$753$	6.60209e7	+	1.14352e8i	0.154631	+	0.267829i
$754$		0			0
$755$			2.34953e8i			0.545934i
$756$		0			0
$757$	3.11489e7			0.0718051			0.0359025	−	0.999355i	$-0.488569\pi$
$757$	3.11489e7			0.0718051			0.0359025	+	0.999355i	$0.488569\pi$
$758$		0			0
$759$	4.79801e8	−	2.77013e8i	1.09733	−	0.633542i
$760$		0			0
$761$	−2.92562e8	−	1.68911e8i	−0.663840	−	0.383268i	0.129899	−	0.991527i	$-0.458535\pi$
$761$	−2.92562e8	−	1.68911e8i	−0.663840	−	0.383268i	−0.793739	+	0.608259i	$0.791868\pi$
$762$		0			0
$763$	6.84376e8	−	3.49915e8i	1.54071	−	0.787751i
$764$		0			0
$765$	7.10279e7	−	1.23024e8i	0.158652	−	0.274793i
$766$		0			0
$767$	1.19618e7	+	2.07184e7i	0.0265100	+	0.0459167i
$768$		0			0
$769$			7.59710e8i			1.67059i	0.549805	+	0.835293i	$0.314702\pi$
$769$			7.59710e8i			1.67059i	−0.549805	+	0.835293i	$0.685298\pi$
$770$		0			0
$771$	1.56973e8			0.342501
$772$		0			0
$773$	−3.89950e8	+	2.25138e8i	−0.844249	+	0.487427i	−0.858706	−	0.512468i	$-0.828731\pi$
$773$	−3.89950e8	+	2.25138e8i	−0.844249	+	0.487427i	0.0144574	+	0.999895i	$0.495398\pi$
$774$		0			0
$775$	−5.54800e7	−	3.20314e7i	−0.119188	−	0.0688130i
$776$		0			0
$777$	4.83784e8	+	2.46748e7i	1.03131	+	0.0526006i
$778$		0			0
$779$	2.81712e8	−	4.87939e8i	0.595926	−	1.03217i
$780$		0			0
$781$	2.95732e8	+	5.12223e8i	0.620791	+	1.07524i
$782$		0			0
$783$			1.04358e8i			0.217391i
$784$		0			0
$785$	6.34927e7			0.131255
$786$		0			0
$787$	4.86012e8	−	2.80599e8i	0.997063	−	0.575655i	0.0896854	−	0.995970i	$-0.471414\pi$
$787$	4.86012e8	−	2.80599e8i	0.997063	−	0.575655i	0.907378	+	0.420315i	$0.138081\pi$
$788$		0			0
$789$	−1.00623e8	−	5.80945e7i	−0.204864	−	0.118278i
$790$		0			0
$791$	7.63390e6	−	1.49673e8i	0.0154247	−	0.302423i
$792$		0			0
$793$	−9.66062e6	+	1.67327e7i	−0.0193725	+	0.0335541i
$794$		0			0
$795$	386728.	+	669832.i	0.000769669	+	0.00133311i
$796$		0			0
$797$		−	4.63186e8i		−	0.914915i	−0.889232	−	0.457457i	$-0.848760\pi$
$797$		−	4.63186e8i		−	0.914915i	0.889232	−	0.457457i	$-0.151240\pi$
$798$		0			0
$799$	−1.89044e6			−0.00370615
$800$		0			0
$801$	−1.52970e8	+	8.83172e7i	−0.297652	+	0.171849i
$802$		0			0
$803$	5.71436e8	+	3.29919e8i	1.10362	+	0.637177i
$804$		0			0
$805$	1.40660e8	+	2.75108e8i	0.269640	+	0.527371i
$806$		0			0
$807$	−1.45524e8	+	2.52054e8i	−0.276894	+	0.479594i
$808$		0			0
$809$	−4.81979e8	−	8.34812e8i	−0.910295	−	1.57668i	−0.813647	−	0.581359i	$-0.802521\pi$
$809$	−4.81979e8	−	8.34812e8i	−0.910295	−	1.57668i	−0.0966484	−	0.995319i	$-0.530812\pi$
$810$		0			0
$811$			1.34804e8i			0.252720i	0.991984	+	0.126360i	$0.0403295\pi$
$811$			1.34804e8i			0.252720i	−0.991984	+	0.126360i	$0.959670\pi$
$812$		0			0
$813$	1.82273e7			0.0339195
$814$		0			0
$815$	3.50033e8	−	2.02092e8i	0.646601	−	0.373315i
$816$		0			0
$817$	2.70668e8	+	1.56270e8i	0.496329	+	0.286556i
$818$		0			0
$819$	8.86539e6	−	1.36934e7i	0.0161379	−	0.0249265i
$820$		0			0
$821$	1.52751e8	−	2.64572e8i	0.276029	−	0.478095i	−0.694366	−	0.719622i	$-0.744315\pi$
$821$	1.52751e8	−	2.64572e8i	0.276029	−	0.478095i	0.970394	+	0.241527i	$0.0776482\pi$
$822$		0			0
$823$	−1.23955e8	−	2.14696e8i	−0.222364	−	0.385146i	0.733161	−	0.680055i	$-0.238044\pi$
$823$	−1.23955e8	−	2.14696e8i	−0.222364	−	0.385146i	−0.955525	+	0.294909i	$0.904711\pi$
$824$		0			0
$825$		−	4.44979e8i		−	0.792461i
$826$		0			0
$827$	−6.70206e8			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$827$	−6.70206e8			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$828$		0			0
$829$	3.94536e8	−	2.27785e8i	0.692505	−	0.399818i	−0.112045	−	0.993703i	$-0.535740\pi$
$829$	3.94536e8	−	2.27785e8i	0.692505	−	0.399818i	0.804550	+	0.593885i	$0.202407\pi$
$830$		0			0
$831$	−4.17744e8	−	2.41185e8i	−0.727960	−	0.420288i
$832$		0			0
$833$	1.03852e9	−	4.65866e8i	1.79671	−	0.805984i
$834$		0			0
$835$	1.93977e8	−	3.35977e8i	0.333188	−	0.577099i
$836$		0			0
$837$	1.01333e7	+	1.75514e7i	0.0172812	+	0.0299320i
$838$		0			0
$839$		−	2.23237e8i		−	0.377991i	−0.981978	−	0.188995i	$-0.939477\pi$
$839$		−	2.23237e8i		−	0.377991i	0.981978	−	0.188995i	$-0.0605231\pi$
$840$		0			0
$841$	1.64161e8			0.275983
$842$		0			0
$843$	−3.50633e8	+	2.02438e8i	−0.585289	+	0.337917i
$844$		0			0
$845$	−2.50579e8	−	1.44672e8i	−0.415312	−	0.239781i
$846$		0			0
$847$	1.12631e9	+	7.29193e8i	1.85356	+	1.20003i
$848$		0			0
$849$	−1.95682e8	+	3.38931e8i	−0.319763	+	0.553846i
$850$		0			0
$851$	−6.75325e8	−	1.16970e9i	−1.09578	−	1.89795i
$852$		0			0
$853$		−	5.46519e7i		−	0.0880559i	−0.999030	−	0.0440280i	$-0.985981\pi$
$853$		−	5.46519e7i		−	0.0880559i	0.999030	−	0.0440280i	$-0.0140191\pi$
$854$		0			0
$855$	1.26987e8			0.203170
$856$		0			0
$857$	−2.83165e8	+	1.63486e8i	−0.449881	+	0.259739i	−0.707780	−	0.706433i	$-0.750303\pi$
$857$	−2.83165e8	+	1.63486e8i	−0.449881	+	0.259739i	0.257899	+	0.966172i	$0.416970\pi$
$858$		0			0
$859$	−5.83512e8	−	3.36891e8i	−0.920598	−	0.531507i	−0.0367721	−	0.999324i	$-0.511708\pi$
$859$	−5.83512e8	−	3.36891e8i	−0.920598	−	0.531507i	−0.883826	+	0.467816i	$0.845041\pi$
$860$		0			0
$861$	−3.10145e8	+	1.58574e8i	−0.485910	+	0.248441i
$862$		0			0
$863$	−3.46795e8	+	6.00666e8i	−0.539560	+	0.934546i	0.459367	+	0.888246i	$0.348076\pi$
$863$	−3.46795e8	+	6.00666e8i	−0.539560	+	0.934546i	−0.998928	+	0.0462995i	$0.985257\pi$
$864$		0			0
$865$	−2.06515e8	−	3.57694e8i	−0.319083	−	0.552667i
$866$		0			0
$867$			1.08282e9i			1.66149i
$868$		0			0
$869$	−1.39903e8			−0.213191
$870$		0			0
$871$	−4.40098e7	+	2.54091e7i	−0.0666032	+	0.0384534i
$872$		0			0
$873$	−2.57770e8	−	1.48824e8i	−0.387427	−	0.223681i
$874$		0			0
$875$	5.71262e8	+	2.91365e7i	0.852730	+	0.0434924i
$876$		0			0
$877$	8.20766e7	−	1.42161e8i	0.121680	−	0.210757i	−0.798750	−	0.601663i	$-0.794505\pi$
$877$	8.20766e7	−	1.42161e8i	0.121680	−	0.210757i	0.920430	+	0.390906i	$0.127838\pi$
$878$		0			0
$879$	−2.70677e8	−	4.68826e8i	−0.398552	−	0.690312i
$880$		0			0
$881$		−	3.51783e8i		−	0.514454i	−0.966351	−	0.257227i	$-0.917191\pi$
$881$		−	3.51783e8i		−	0.514454i	0.966351	−	0.257227i	$-0.0828089\pi$
$882$		0			0
$883$	−1.28307e9			−1.86367			−0.931835	−	0.362883i	$-0.881793\pi$
$883$	−1.28307e9			−1.86367			−0.931835	+	0.362883i	$0.881793\pi$
$884$		0			0
$885$	9.97120e7	−	5.75688e7i	0.143853	−	0.0830533i
$886$		0			0
$887$	1.14526e9	+	6.61216e8i	1.64109	+	0.947485i	0.980446	+	0.196789i	$0.0630513\pi$
$887$	1.14526e9	+	6.61216e8i	1.64109	+	0.947485i	0.660647	+	0.750697i	$0.270282\pi$
$888$		0			0
$889$	−2.36299e7	+	4.63296e8i	−0.0336323	+	0.659407i
$890$		0			0
$891$	−7.03859e7	+	1.21912e8i	−0.0995067	+	0.172351i
$892$		0			0
$893$	−844954.	−	1.46350e6i	−0.00118653	−	0.00205513i
$894$		0			0
$895$			1.55833e8i			0.217365i
$896$		0			0
$897$	−4.54835e7			−0.0630198
$898$		0			0
$899$	1.27649e8	−	7.36984e7i	0.175687	−	0.101433i
$900$		0			0
$901$	−6.87997e6	−	3.97215e6i	−0.00940616	−	0.00543065i
$902$		0			0
$903$	−8.79637e7	−	1.72042e8i	−0.119465	−	0.233654i
$904$		0			0
$905$	−2.75810e8	+	4.77716e8i	−0.372104	+	0.644502i
$906$		0			0
$907$	−2.66115e8	−	4.60924e8i	−0.356654	−	0.617743i	0.630746	−	0.775990i	$-0.282749\pi$
$907$	−2.66115e8	−	4.60924e8i	−0.356654	−	0.617743i	−0.987400	+	0.158247i	$0.949416\pi$
$908$		0			0
$909$			9.24810e7i			0.123129i
$910$		0			0
$911$	−8.93658e8			−1.18200			−0.590998	−	0.806673i	$-0.701266\pi$
$911$	−8.93658e8			−1.18200			−0.590998	+	0.806673i	$0.701266\pi$
$912$		0			0
$913$	1.79953e9	−	1.03896e9i	2.36454	−	1.36517i
$914$		0			0
$915$	8.05298e7	+	4.64939e7i	0.105122	+	0.0606922i
$916$		0			0
$917$	−8.94236e7	+	1.38123e8i	−0.115970	+	0.179126i
$918$		0			0
$919$	1.58354e8	−	2.74277e8i	0.204025	−	0.353381i	−0.745797	−	0.666173i	$-0.767931\pi$
$919$	1.58354e8	−	2.74277e8i	0.204025	−	0.353381i	0.949822	+	0.312792i	$0.101264\pi$
$920$		0			0
$921$	2.75026e8	+	4.76360e8i	0.352043	+	0.609756i
$922$		0			0
$923$		−	4.85571e7i		−	0.0617515i
$924$		0			0
$925$	−1.08481e9			−1.37065
$926$		0			0
$927$	−2.41677e8	+	1.39532e8i	−0.303386	+	0.175160i
$928$		0			0
$929$	−1.02372e9	−	5.91047e8i	−1.27684	−	0.737183i	−0.300572	−	0.953759i	$-0.597178\pi$
$929$	−1.02372e9	−	5.91047e8i	−1.27684	−	0.737183i	−0.976266	+	0.216576i	$0.930511\pi$
$930$		0			0
$931$	8.24830e8	+	5.95752e8i	1.02215	+	0.738272i
$932$		0			0
$933$	1.36660e8	−	2.36702e8i	0.168266	−	0.291446i
$934$		0			0
$935$	−6.96828e8	−	1.20694e9i	−0.852493	−	1.47656i
$936$		0			0
$937$			1.27161e9i			1.54573i	0.634569	+	0.772866i	$0.281178\pi$
$937$			1.27161e9i			1.54573i	−0.634569	+	0.772866i	$0.718822\pi$
$938$		0			0
$939$	6.24902e8			0.754770
$940$		0			0
$941$	6.86035e8	−	3.96083e8i	0.823337	−	0.475354i	−0.0282288	−	0.999601i	$-0.508987\pi$
$941$	6.86035e8	−	3.96083e8i	0.823337	−	0.475354i	0.851566	+	0.524248i	$0.175653\pi$
$942$		0			0
$943$	8.41110e8	+	4.85615e8i	1.00304	+	0.579104i
$944$		0			0
$945$	−6.59028e7	−	4.26667e7i	−0.0780923	−	0.0505584i
$946$		0			0
$947$	6.15314e8	−	1.06575e9i	0.724514	−	1.25489i	−0.234660	−	0.972077i	$-0.575398\pi$
$947$	6.15314e8	−	1.06575e9i	0.724514	−	1.25489i	0.959174	−	0.282817i	$-0.0912689\pi$
$948$		0			0
$949$	−2.70851e7	−	4.69128e7i	−0.0316907	−	0.0548899i
$950$		0			0
$951$		−	3.32846e7i		−	0.0386992i
$952$		0			0
$953$	1.46481e9			1.69240			0.846198	−	0.532869i	$-0.178886\pi$
$953$	1.46481e9			1.69240			0.846198	+	0.532869i	$0.178886\pi$
$954$		0			0
$955$	2.57104e8	−	1.48439e8i	0.295188	−	0.170427i
$956$		0			0
$957$	8.86652e8	+	5.11909e8i	1.01162	+	0.584059i
$958$		0			0
$959$	9.10387e8	−	4.65472e8i	1.03222	−	0.527762i
$960$		0			0
$961$	−4.29439e8	+	7.43811e8i	−0.483873	+	0.838093i
$962$		0			0
$963$	−6.87711e7	−	1.19115e8i	−0.0770064	−	0.133379i
$964$		0			0
$965$			1.03500e8i			0.115176i
$966$		0			0
$967$	−1.57261e9			−1.73917			−0.869585	−	0.493783i	$-0.835614\pi$
$967$	−1.57261e9			−1.73917			−0.869585	+	0.493783i	$0.835614\pi$
$968$		0			0
$969$	−1.12956e9	+	6.52153e8i	−1.24148	+	0.716767i
$970$		0			0
$971$	−1.30961e9	−	7.56105e8i	−1.43049	−	0.825895i	−0.433333	−	0.901234i	$-0.642663\pi$
$971$	−1.30961e9	−	7.56105e8i	−1.43049	−	0.825895i	−0.997158	+	0.0753392i	$0.975996\pi$
$972$		0			0
$973$	−2.72751e7	−	1.39113e6i	−0.0296093	−	0.00151019i
$974$		0			0
$975$	−1.82656e7	+	3.16369e7i	−0.0197070	+	0.0341335i
$976$		0			0
$977$	6.37066e8	+	1.10343e9i	0.683125	+	1.18321i	0.974022	+	0.226453i	$0.0727131\pi$
$977$	6.37066e8	+	1.10343e9i	0.683125	+	1.18321i	−0.290897	+	0.956755i	$0.593954\pi$
$978$		0			0
$979$			1.73289e9i			1.84682i
$980$		0			0
$981$	5.44549e8			0.576806
$982$		0			0
$983$	2.09154e8	−	1.20755e8i	0.220195	−	0.127129i	−0.385846	−	0.922563i	$-0.626090\pi$
$983$	2.09154e8	−	1.20755e8i	0.220195	−	0.127129i	0.606040	+	0.795434i	$0.292757\pi$
$984$		0			0
$985$	1.52752e8	+	8.81916e7i	0.159838	+	0.0922824i
$986$		0			0
$987$	−53218.3	+	1.04342e6i	−5.53490e−5	+	0.00108519i
$988$		0			0
$989$	−2.69378e8	+	4.66577e8i	−0.278467	+	0.482319i
$990$		0			0
$991$	3.69371e8	+	6.39769e8i	0.379526	+	0.657359i	0.990993	−	0.133911i	$-0.0427536\pi$
$991$	3.69371e8	+	6.39769e8i	0.379526	+	0.657359i	−0.611467	+	0.791270i	$0.709420\pi$
$992$		0			0
$993$			9.76181e8i			0.996971i
$994$		0			0
$995$	−4.51165e8			−0.458001
$996$		0			0
$997$	−1.32231e9	+	7.63436e8i	−1.33428	+	0.770348i	−0.985953	−	0.167024i	$-0.946584\pi$
$997$	−1.32231e9	+	7.63436e8i	−1.33428	+	0.770348i	−0.348330	+	0.937372i	$0.613251\pi$
$998$		0			0
$999$	2.97206e8	+	1.71592e8i	0.298100	+	0.172108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.c.145.2		8
4.3	odd	2		42.7.g.b.19.1	✓	8
7.3	odd	6	inner	336.7.bh.c.241.2		8
12.11	even	2		126.7.n.b.19.4		8
28.3	even	6		42.7.g.b.31.1	yes	8
28.11	odd	6		294.7.g.b.31.2		8
28.19	even	6		294.7.c.a.97.5		8
28.23	odd	6		294.7.c.a.97.8		8
28.27	even	2		294.7.g.b.19.2		8
84.59	odd	6		126.7.n.b.73.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.7.g.b.19.1	✓	8	4.3	odd	2
42.7.g.b.31.1	yes	8	28.3	even	6
126.7.n.b.19.4		8	12.11	even	2
126.7.n.b.73.4		8	84.59	odd	6
294.7.c.a.97.5		8	28.19	even	6
294.7.c.a.97.8		8	28.23	odd	6
294.7.g.b.19.2		8	28.27	even	2
294.7.g.b.31.2		8	28.11	odd	6
336.7.bh.c.145.2		8	1.1	even	1	trivial
336.7.bh.c.241.2		8	7.3	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-13.5000 + 7.79423i) q^{3} +(-52.3293 - 30.2124i) q^{5} +(17.4716 - 342.555i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 + 7.79423i) q^{3} +(-52.3293 - 30.2124i) q^{5} +(17.4716 - 342.555i) q^{7} +(121.500 - 210.444i) q^{9} +(-1191.99 - 2064.59i) q^{11} +195.716i q^{13} +941.928 q^{15} +(-8378.55 + 4837.36i) q^{17} +(-7489.77 - 4324.22i) q^{19} +(2434.08 + 4760.67i) q^{21} +(7454.09 - 12910.9i) q^{23} +(-5986.93 - 10369.7i) q^{25} +3788.00i q^{27} +27549.7 q^{29} +(4633.43 - 2675.11i) q^{31} +(32183.7 + 18581.3i) q^{33} +(-11263.7 + 17397.8i) q^{35} +(45298.9 - 78460.1i) q^{37} +(-1525.46 - 2642.17i) q^{39} +65147.4i q^{41} -36138.3 q^{43} +(-12716.0 + 7341.60i) q^{45} +(169.222 + 97.7002i) q^{47} +(-117038. - 11970.0i) q^{49} +(75407.0 - 130609. i) q^{51} +(410.570 + 711.129i) q^{53} +144051. i q^{55} +134816. q^{57} +(105860. - 61118.0i) q^{59} +(85494.7 + 49360.4i) q^{61} +(-69965.8 - 45297.2i) q^{63} +(5913.04 - 10241.7i) q^{65} +(129826. + 224866. i) q^{67} +232396. i q^{69} -248100. q^{71} +(-239698. + 138390. i) q^{73} +(161647. + 93327.0i) q^{75} +(-728060. + 372250. i) q^{77} +(29342.4 - 50822.5i) q^{79} +(-29524.5 - 51137.9i) q^{81} +871615. i q^{83} +584592. q^{85} +(-371921. + 214728. i) q^{87} +(-629506. - 363445. i) q^{89} +(67043.5 + 3419.47i) q^{91} +(-41700.9 + 72228.0i) q^{93} +(261290. + 452567. i) q^{95} -1.22489e6i q^{97} -579307. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9}+O(q^{10}) \) 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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