LMFDB - Embedded newform 336.7.bh.h.145.9

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.9
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.h.241.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(76.6020 + 44.2262i) q^{5} +(298.004 + 169.831i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(76.6020 + 44.2262i) q^{5} +(298.004 + 169.831i) q^{7} +(121.500 - 210.444i) q^{9} +(-194.919 - 337.610i) q^{11} +157.546i q^{13} +1378.84 q^{15} +(4444.14 - 2565.83i) q^{17} +(-6.75175 - 3.89813i) q^{19} +(5346.76 - 29.9981i) q^{21} +(-80.9415 + 140.195i) q^{23} +(-3900.59 - 6756.02i) q^{25} -3788.00i q^{27} +26655.6 q^{29} +(36851.7 - 21276.4i) q^{31} +(-5262.82 - 3038.49i) q^{33} +(15316.7 + 26189.0i) q^{35} +(-4858.97 + 8415.98i) q^{37} +(1227.95 + 2126.87i) q^{39} +46553.8i q^{41} -42532.9 q^{43} +(18614.3 - 10747.0i) q^{45} +(-142328. - 82172.9i) q^{47} +(59964.0 + 101221. i) q^{49} +(39997.3 - 69277.3i) q^{51} +(117706. + 203874. i) q^{53} -34482.1i q^{55} -121.532 q^{57} +(-59549.9 + 34381.2i) q^{59} +(323494. + 186769. i) q^{61} +(71947.4 - 42078.8i) q^{63} +(-6967.64 + 12068.3i) q^{65} +(-149388. - 258747. i) q^{67} +2523.51i q^{69} +429798. q^{71} +(38726.1 - 22358.5i) q^{73} +(-105316. - 60804.2i) q^{75} +(-750.197 - 133712. i) q^{77} +(-86568.2 + 149940. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -423270. i q^{83} +453907. q^{85} +(359851. - 207760. i) q^{87} +(291346. + 168209. i) q^{89} +(-26756.1 + 46949.3i) q^{91} +(331666. - 574462. i) q^{93} +(-344.798 - 597.208i) q^{95} +415502. i q^{97} -94730.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * 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
$5$	76.6020	+	44.2262i	0.612816	+	0.353809i	0.774067	−	0.633104i	$-0.218219\pi$
$5$	76.6020	+	44.2262i	0.612816	+	0.353809i	−0.161251	+	0.986913i	$0.551553\pi$
$6$		0			0
$7$	298.004	+	169.831i	0.868817	+	0.495133i
$7$	298.004	+	169.831i	0.868817	+	0.495133i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−194.919	−	337.610i	−0.146446	−	0.253651i	0.783466	−	0.621435i	$-0.213450\pi$
$11$	−194.919	−	337.610i	−0.146446	−	0.253651i	−0.929911	+	0.367784i	$0.880117\pi$
$12$		0			0
$13$			157.546i			0.0717095i	0.999357	+	0.0358547i	$0.0114154\pi$
$13$			157.546i			0.0717095i	−0.999357	+	0.0358547i	$0.988585\pi$
$14$		0			0
$15$	1378.84			0.408544
$16$		0			0
$17$	4444.14	−	2565.83i	0.904568	−	0.522253i	0.0258887	−	0.999665i	$-0.491758\pi$
$17$	4444.14	−	2565.83i	0.904568	−	0.522253i	0.878680	+	0.477412i	$0.158425\pi$
$18$		0			0
$19$	−6.75175	−	3.89813i	−0.000984364	−	0.000568323i	0.499508	−	0.866309i	$-0.333514\pi$
$19$	−6.75175	−	3.89813i	−0.000984364	−	0.000568323i	−0.500492	+	0.865741i	$0.666848\pi$
$20$		0			0
$21$	5346.76	−	29.9981i	0.577341	−	0.00323919i
$22$		0			0
$23$	−80.9415	+	140.195i	−0.00665255	+	0.0115225i	−0.869333	−	0.494228i	$-0.835451\pi$
$23$	−80.9415	+	140.195i	−0.00665255	+	0.0115225i	0.862680	+	0.505750i	$0.168784\pi$
$24$		0			0
$25$	−3900.59	−	6756.02i	−0.249638	−	0.432385i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	26655.6			1.09294			0.546468	−	0.837480i	$-0.315972\pi$
$29$	26655.6			1.09294			0.546468	+	0.837480i	$0.315972\pi$
$30$		0			0
$31$	36851.7	−	21276.4i	1.23701	−	0.714188i	0.268528	−	0.963272i	$-0.413463\pi$
$31$	36851.7	−	21276.4i	1.23701	−	0.714188i	0.968482	+	0.249084i	$0.0801296\pi$
$32$		0			0
$33$	−5262.82	−	3038.49i	−0.146446	−	0.0845504i
$34$		0			0
$35$	15316.7	+	26189.0i	0.357242	+	0.610821i
$36$		0			0
$37$	−4858.97	+	8415.98i	−0.0959266	+	0.166150i	−0.909995	−	0.414619i	$-0.863915\pi$
$37$	−4858.97	+	8415.98i	−0.0959266	+	0.166150i	0.814068	+	0.580769i	$0.197248\pi$
$38$		0			0
$39$	1227.95	+	2126.87i	0.0207007	+	0.0358547i
$40$		0			0
$41$			46553.8i			0.675467i	0.941242	+	0.337733i	$0.109660\pi$
$41$			46553.8i			0.675467i	−0.941242	+	0.337733i	$0.890340\pi$
$42$		0			0
$43$	−42532.9			−0.534958			−0.267479	−	0.963564i	$-0.586191\pi$
$43$	−42532.9			−0.534958			−0.267479	+	0.963564i	$0.586191\pi$
$44$		0			0
$45$	18614.3	−	10747.0i	0.204272	−	0.117936i
$46$		0			0
$47$	−142328.	−	82172.9i	−1.37087	−	0.791472i	−0.379831	−	0.925056i	$-0.624018\pi$
$47$	−142328.	−	82172.9i	−1.37087	−	0.791472i	−0.991037	+	0.133584i	$0.957351\pi$
$48$		0			0
$49$	59964.0	+	101221.i	0.509686	+	0.860361i
$50$		0			0
$51$	39997.3	−	69277.3i	0.301523	−	0.522253i
$52$		0			0
$53$	117706.	+	203874.i	0.790629	+	1.36941i	0.925578	+	0.378557i	$0.123580\pi$
$53$	117706.	+	203874.i	0.790629	+	1.36941i	−0.134949	+	0.990853i	$0.543087\pi$
$54$		0			0
$55$		−	34482.1i		−	0.207255i
$56$		0			0
$57$	−121.532			−0.000656242
$58$		0			0
$59$	−59549.9	+	34381.2i	−0.289951	+	0.167404i	−0.637920	−	0.770103i	$-0.720205\pi$
$59$	−59549.9	+	34381.2i	−0.289951	+	0.167404i	0.347969	+	0.937506i	$0.386872\pi$
$60$		0			0
$61$	323494.	+	186769.i	1.42520	+	0.822840i	0.996737	−	0.0807182i	$-0.0257214\pi$
$61$	323494.	+	186769.i	1.42520	+	0.822840i	0.428464	+	0.903559i	$0.359055\pi$
$62$		0			0
$63$	71947.4	−	42078.8i	0.287736	−	0.168284i
$64$		0			0
$65$	−6967.64	+	12068.3i	−0.0253715	+	0.0439447i
$66$		0			0
$67$	−149388.	−	258747.i	−0.496695	−	0.860302i	0.503297	−	0.864113i	$-0.332120\pi$
$67$	−149388.	−	258747.i	−0.496695	−	0.860302i	−0.999993	+	0.00381168i	$0.998787\pi$
$68$		0			0
$69$			2523.51i			0.00768170i
$70$		0			0
$71$	429798.			1.20085			0.600425	−	0.799681i	$-0.294998\pi$
$71$	429798.			1.20085			0.600425	+	0.799681i	$0.294998\pi$
$72$		0			0
$73$	38726.1	−	22358.5i	0.0995485	−	0.0574744i	−0.449399	−	0.893331i	$-0.648362\pi$
$73$	38726.1	−	22358.5i	0.0995485	−	0.0574744i	0.548948	+	0.835857i	$0.315029\pi$
$74$		0			0
$75$	−105316.	−	60804.2i	−0.249638	−	0.144128i
$76$		0			0
$77$	−750.197	−	133712.i	−0.00164325	−	0.292887i
$78$		0			0
$79$	−86568.2	+	149940.i	−0.175581	+	0.304115i	−0.940362	−	0.340175i	$-0.889514\pi$
$79$	−86568.2	+	149940.i	−0.175581	+	0.304115i	0.764781	+	0.644290i	$0.222847\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	423270.i		−	0.740258i	−0.928980	−	0.370129i	$-0.879313\pi$
$83$		−	423270.i		−	0.740258i	0.928980	−	0.370129i	$-0.120687\pi$
$84$		0			0
$85$	453907.			0.739112
$86$		0			0
$87$	359851.	−	207760.i	0.546468	−	0.315503i
$88$		0			0
$89$	291346.	+	168209.i	0.413275	+	0.238605i	0.692196	−	0.721710i	$-0.256643\pi$
$89$	291346.	+	168209.i	0.413275	+	0.238605i	−0.278921	+	0.960314i	$0.589977\pi$
$90$		0			0
$91$	−26756.1	+	46949.3i	−0.0355058	+	0.0623024i
$92$		0			0
$93$	331666.	−	574462.i	0.412336	−	0.714188i
$94$		0			0
$95$	−344.798	−	597.208i	−0.000402156	−	0.000696554i
$96$		0			0
$97$			415502.i			0.455258i	0.973748	+	0.227629i	$0.0730974\pi$
$97$			415502.i			0.455258i	−0.973748	+	0.227629i	$0.926903\pi$
$98$		0			0
$99$	−94730.7			−0.0976304
$100$		0			0
$101$	151792.	−	87637.3i	0.147328	−	0.0850599i	−0.424524	−	0.905417i	$-0.639559\pi$
$101$	151792.	−	87637.3i	0.147328	−	0.0850599i	0.571852	+	0.820357i	$0.306225\pi$
$102$		0			0
$103$	−637239.	−	367910.i	−0.583164	−	0.336690i	0.179226	−	0.983808i	$-0.442641\pi$
$103$	−637239.	−	367910.i	−0.583164	−	0.336690i	−0.762390	+	0.647118i	$0.775974\pi$
$104$		0			0
$105$	410899.	+	234169.i	0.354950	+	0.202284i
$106$		0			0
$107$	230675.	−	399541.i	0.188300	−	0.326145i	−0.756384	−	0.654128i	$-0.773036\pi$
$107$	230675.	−	399541.i	0.188300	−	0.326145i	0.944683	+	0.327983i	$0.106369\pi$
$108$		0			0
$109$	622799.	+	1.07872e6i	0.480915	+	0.832970i	0.999760	−	0.0218986i	$-0.00697110\pi$
$109$	622799.	+	1.07872e6i	0.480915	+	0.832970i	−0.518845	+	0.854868i	$0.673638\pi$
$110$		0			0
$111$			151488.i			0.110766i
$112$		0			0
$113$	128848.			0.0892978			0.0446489	−	0.999003i	$-0.485783\pi$
$113$	128848.			0.0892978			0.0446489	+	0.999003i	$0.485783\pi$
$114$		0			0
$115$	−12400.6	+	7159.47i	−0.00815357	+	0.00470747i
$116$		0			0
$117$	33154.6	+	19141.8i	0.0207007	+	0.0119516i
$118$		0			0
$119$	1.76013e6	−	9875.25i	1.04449	−	0.00586013i
$120$		0			0
$121$	809794.	−	1.40260e6i	0.457107	−	0.791733i
$122$		0			0
$123$	362851.	+	628477.i	0.194990	+	0.337733i
$124$		0			0
$125$		−	2.07210e6i		−	1.06092i
$126$		0			0
$127$	2.45474e6			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$127$	2.45474e6			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$128$		0			0
$129$	−574194.	+	331511.i	−0.267479	+	0.154429i
$130$		0			0
$131$	1.21767e6	+	703021.i	0.541645	+	0.312719i	0.745746	−	0.666231i	$-0.232093\pi$
$131$	1.21767e6	+	703021.i	0.541645	+	0.312719i	−0.204100	+	0.978950i	$0.565427\pi$
$132$		0			0
$133$	−1350.03	−	2308.31i	−0.000573836	−	0.000981160i
$134$		0			0
$135$	167529.	−	290168.i	0.0680906	−	0.117936i
$136$		0			0
$137$	−130690.	−	226361.i	−0.0508253	−	0.0880320i	0.839493	−	0.543370i	$-0.182852\pi$
$137$	−130690.	−	226361.i	−0.0508253	−	0.0880320i	−0.890319	+	0.455338i	$0.849519\pi$
$138$		0			0
$139$		−	560728.i		−	0.208789i	−0.994536	−	0.104395i	$-0.966710\pi$
$139$		−	560728.i		−	0.208789i	0.994536	−	0.104395i	$-0.0332905\pi$
$140$		0			0
$141$	−2.56190e6			−0.913913
$142$		0			0
$143$	53189.0	−	30708.7i	0.0181892	−	0.0105015i
$144$		0			0
$145$	2.04187e6	+	1.17888e6i	0.669768	+	0.386691i
$146$		0			0
$147$	1.59845e6	+	899104.i	0.503208	+	0.283047i
$148$		0			0
$149$	790969.	−	1.37000e6i	0.239111	−	0.414153i	−0.721348	−	0.692573i	$-0.756477\pi$
$149$	790969.	−	1.37000e6i	0.239111	−	0.414153i	0.960460	+	0.278419i	$0.0898105\pi$
$150$		0			0
$151$	684080.	+	1.18486e6i	0.198690	+	0.344141i	0.948104	−	0.317961i	$-0.102998\pi$
$151$	684080.	+	1.18486e6i	0.198690	+	0.344141i	−0.749414	+	0.662102i	$0.769665\pi$
$152$		0			0
$153$		−	1.24699e6i		−	0.348168i
$154$		0			0
$155$	3.76389e6			1.01075
$156$		0			0
$157$	3.90800e6	−	2.25628e6i	1.00985	−	0.583035i	0.0986996	−	0.995117i	$-0.468532\pi$
$157$	3.90800e6	−	2.25628e6i	1.00985	−	0.583035i	0.911147	+	0.412082i	$0.135198\pi$
$158$		0			0
$159$	3.17807e6	+	1.83486e6i	0.790629	+	0.456470i
$160$		0			0
$161$	−47930.3	+	28032.3i	−0.0114850	+	0.00671709i
$162$		0			0
$163$	−33001.2	+	57159.8i	−0.00762022	+	0.0131986i	−0.869810	−	0.493386i	$-0.835759\pi$
$163$	−33001.2	+	57159.8i	−0.00762022	+	0.0131986i	0.862190	+	0.506585i	$0.169092\pi$
$164$		0			0
$165$	−268761.	−	465509.i	−0.0598295	−	0.103628i
$166$		0			0
$167$			5.70215e6i			1.22430i	0.790740	+	0.612152i	$0.209696\pi$
$167$			5.70215e6i			1.22430i	−0.790740	+	0.612152i	$0.790304\pi$
$168$		0			0
$169$	4.80199e6			0.994858
$170$		0			0
$171$	−1640.68	+	947.244i	−0.000328121	+	0.000189441i
$172$		0			0
$173$	−1.34595e6	−	777086.i	−0.259951	−	0.150083i	0.364361	−	0.931258i	$-0.381287\pi$
$173$	−1.34595e6	−	777086.i	−0.259951	−	0.150083i	−0.624312	+	0.781175i	$0.714621\pi$
$174$		0			0
$175$	−15012.4	−	2.67576e6i	−0.00280115	−	0.499268i
$176$		0			0
$177$	−535949.	+	928292.i	−0.0966505	+	0.167404i
$178$		0			0
$179$	2.42355e6	+	4.19771e6i	0.422564	+	0.731902i	0.996189	−	0.0872156i	$-0.0277969\pi$
$179$	2.42355e6	+	4.19771e6i	0.422564	+	0.731902i	−0.573626	+	0.819118i	$0.694464\pi$
$180$		0			0
$181$		−	8.81838e6i		−	1.48714i	−0.668655	−	0.743572i	$-0.733130\pi$
$181$		−	8.81838e6i		−	1.48714i	0.668655	−	0.743572i	$-0.266870\pi$
$182$		0			0
$183$	5.82289e6			0.950134
$184$		0			0
$185$	−744413.	+	429787.i	−0.117571	+	0.0678794i
$186$		0			0
$187$	−1.73250e6	−	1.00026e6i	−0.264940	−	0.152963i
$188$		0			0
$189$	643318.	−	1.12884e6i	0.0952885	−	0.167204i
$190$		0			0
$191$	839748.	−	1.45449e6i	0.120517	−	0.208742i	−0.799455	−	0.600727i	$-0.794878\pi$
$191$	839748.	−	1.45449e6i	0.120517	−	0.208742i	0.919972	+	0.391985i	$0.128211\pi$
$192$		0			0
$193$	4.71767e6	+	8.17124e6i	0.656229	+	1.13662i	0.981584	+	0.191030i	$0.0611828\pi$
$193$	4.71767e6	+	8.17124e6i	0.656229	+	1.13662i	−0.325355	+	0.945592i	$0.605484\pi$
$194$		0			0
$195$			217230.i			0.0292965i
$196$		0			0
$197$	−6.75404e6			−0.883416			−0.441708	−	0.897159i	$-0.645627\pi$
$197$	−6.75404e6			−0.883416			−0.441708	+	0.897159i	$0.645627\pi$
$198$		0			0
$199$	−5.28284e6	+	3.05005e6i	−0.670360	+	0.387033i	−0.796213	−	0.605016i	$-0.793167\pi$
$199$	−5.28284e6	+	3.05005e6i	−0.670360	+	0.387033i	0.125853	+	0.992049i	$0.459833\pi$
$200$		0			0
$201$	−4.03346e6	−	2.32872e6i	−0.496695	−	0.286767i
$202$		0			0
$203$	7.94348e6	+	4.52694e6i	0.949561	+	0.541149i
$204$		0			0
$205$	−2.05890e6	+	3.56612e6i	−0.238986	+	0.413937i
$206$		0			0
$207$	19668.8	+	34067.4i	0.00221752	+	0.00384085i
$208$		0			0
$209$			3039.28i			0.000332914i
$210$		0			0
$211$	2.93269e6			0.312190			0.156095	−	0.987742i	$-0.450109\pi$
$211$	2.93269e6			0.312190			0.156095	+	0.987742i	$0.450109\pi$
$212$		0			0
$213$	5.80227e6	−	3.34994e6i	0.600425	−	0.346656i
$214$		0			0
$215$	−3.25810e6	−	1.88107e6i	−0.327831	−	0.189273i
$216$		0			0
$217$	1.45954e7	−	81887.6i	1.42835	−	0.00801381i
$218$		0			0
$219$	348535.	−	603680.i	0.0331828	−	0.0574744i
$220$		0			0
$221$	404235.	+	700156.i	0.0374505	+	0.0648661i
$222$		0			0
$223$		−	1.93119e7i		−	1.74144i	−0.491775	−	0.870722i	$-0.663652\pi$
$223$		−	1.93119e7i		−	1.74144i	0.491775	−	0.870722i	$-0.336348\pi$
$224$		0			0
$225$	−1.89569e6			−0.166425
$226$		0			0
$227$	−865111.	+	499472.i	−0.0739596	+	0.0427006i	−0.536524	−	0.843885i	$-0.680263\pi$
$227$	−865111.	+	499472.i	−0.0739596	+	0.0427006i	0.462564	+	0.886586i	$0.346929\pi$
$228$		0			0
$229$	291459.	+	168274.i	0.0242700	+	0.0140123i	0.512086	−	0.858934i	$-0.328873\pi$
$229$	291459.	+	168274.i	0.0242700	+	0.0140123i	−0.487816	+	0.872947i	$0.662206\pi$
$230$		0			0
$231$	−1.05231e6	−	1.79927e6i	−0.0853707	−	0.145969i
$232$		0			0
$233$	−1.08773e7	+	1.88400e7i	−0.859907	+	1.48940i	0.0121099	+	0.999927i	$0.496145\pi$
$233$	−1.08773e7	+	1.88400e7i	−0.859907	+	1.48940i	−0.872017	+	0.489476i	$0.837188\pi$
$234$		0			0
$235$	−7.26839e6	−	1.25892e7i	−0.560060	−	0.970053i
$236$		0			0
$237$			2.69893e6i			0.202743i
$238$		0			0
$239$	−2.24920e7			−1.64754			−0.823768	−	0.566927i	$-0.808132\pi$
$239$	−2.24920e7			−1.64754			−0.823768	+	0.566927i	$0.808132\pi$
$240$		0			0
$241$	1.14893e7	−	6.63338e6i	0.820813	−	0.473897i	−0.0298837	−	0.999553i	$-0.509514\pi$
$241$	1.14893e7	−	6.63338e6i	0.820813	−	0.473897i	0.850697	+	0.525657i	$0.176180\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	116766.	+	1.04057e7i	0.00793997	+	0.707574i
$246$		0			0
$247$	614.133	−	1063.71i	4.07541e−5	−	7.05882e-5i
$248$		0			0
$249$	−3.29906e6	−	5.71414e6i	−0.213694	−	0.370129i
$250$		0			0
$251$			9.69221e6i			0.612917i	0.951884	+	0.306458i	$0.0991440\pi$
$251$			9.69221e6i			0.612917i	−0.951884	+	0.306458i	$0.900856\pi$
$252$		0			0
$253$	63108.2			0.00389695
$254$		0			0
$255$	6.12774e6	−	3.53785e6i	0.369556	−	0.213363i
$256$		0			0
$257$	−1.60589e7	−	9.27160e6i	−0.946054	−	0.546204i	−0.0542009	−	0.998530i	$-0.517261\pi$
$257$	−1.60589e7	−	9.27160e6i	−0.946054	−	0.546204i	−0.891853	+	0.452326i	$0.850594\pi$
$258$		0			0
$259$	−2.87729e6	+	1.68280e6i	−0.165609	+	0.0968572i
$260$		0			0
$261$	3.23866e6	−	5.60952e6i	0.182156	−	0.315503i
$262$		0			0
$263$	−1.08191e7	−	1.87393e7i	−0.594737	−	1.03011i	−0.993584	−	0.113097i	$-0.963923\pi$
$263$	−1.08191e7	−	1.87393e7i	−0.594737	−	1.03011i	0.398847	−	0.917017i	$-0.369410\pi$
$264$		0			0
$265$			2.08228e7i			1.11893i
$266$		0			0
$267$	5.24423e6			0.275517
$268$		0			0
$269$	−3.90283e6	+	2.25330e6i	−0.200504	+	0.115761i	−0.596891	−	0.802323i	$-0.703597\pi$
$269$	−3.90283e6	+	2.25330e6i	−0.200504	+	0.115761i	0.396387	+	0.918084i	$0.370264\pi$
$270$		0			0
$271$	−3.21517e7	−	1.85628e7i	−1.61546	−	0.932686i	−0.988075	−	0.153976i	$-0.950792\pi$
$271$	−3.21517e7	−	1.85628e7i	−1.61546	−	0.932686i	−0.627385	−	0.778710i	$-0.715875\pi$
$272$		0			0
$273$	4726.07	+	842359.i	0.000232280	+	0.0414008i
$274$		0			0
$275$	−1.52060e6	+	2.63376e6i	−0.0731168	+	0.126642i
$276$		0			0
$277$	9.68158e6	+	1.67690e7i	0.455520	+	0.788983i	0.998718	−	0.0506213i	$-0.0161201\pi$
$277$	9.68158e6	+	1.67690e7i	0.455520	+	0.788983i	−0.543198	+	0.839604i	$0.682787\pi$
$278$		0			0
$279$		−	1.03403e7i		−	0.476125i
$280$		0			0
$281$	−2.51513e7			−1.13355			−0.566775	−	0.823873i	$-0.691809\pi$
$281$	−2.51513e7			−1.13355			−0.566775	+	0.823873i	$0.691809\pi$
$282$		0			0
$283$	−2.44850e7	+	1.41364e7i	−1.08029	+	0.623706i	−0.930975	−	0.365084i	$-0.881040\pi$
$283$	−2.44850e7	+	1.41364e7i	−1.08029	+	0.623706i	−0.149315	+	0.988790i	$0.547707\pi$
$284$		0			0
$285$	−9309.55	−	5374.87i	−0.000402156	−	0.000232185i
$286$		0			0
$287$	−7.90627e6	+	1.38732e7i	−0.334446	+	0.586857i
$288$		0			0
$289$	1.09816e6	−	1.90207e6i	0.0454958	−	0.0788011i
$290$		0			0
$291$	3.23852e6	+	5.60928e6i	0.131422	+	0.227629i
$292$		0			0
$293$		−	6.73401e6i		−	0.267714i	−0.991001	−	0.133857i	$-0.957264\pi$
$293$		−	6.73401e6i		−	0.267714i	0.991001	−	0.133857i	$-0.0427363\pi$
$294$		0			0
$295$	−6.08219e6			−0.236916
$296$		0			0
$297$	−1.27886e6	+	738353.i	−0.0488152	+	0.0281835i
$298$		0			0
$299$	−22087.1	−	12752.0i	−0.000826276	−	0.000477051i
$300$		0			0
$301$	−1.26750e7	−	7.22339e6i	−0.464781	−	0.264876i
$302$		0			0
$303$	1.36613e6	−	2.36621e6i	0.0491093	−	0.0850599i
$304$		0			0
$305$	1.65202e7	+	2.86138e7i	0.582257	+	1.00850i
$306$		0			0
$307$			1.93416e7i			0.668463i	0.942491	+	0.334231i	$0.108477\pi$
$307$			1.93416e7i			0.668463i	−0.942491	+	0.334231i	$0.891523\pi$
$308$		0			0
$309$	−1.14703e7			−0.388776
$310$		0			0
$311$	−4.03371e7	+	2.32886e7i	−1.34098	+	0.774217i	−0.986952	−	0.161017i	$-0.948523\pi$
$311$	−4.03371e7	+	2.32886e7i	−1.34098	+	0.774217i	−0.354031	+	0.935234i	$0.615189\pi$
$312$		0			0
$313$	−2.05199e7	−	1.18472e7i	−0.669179	−	0.386351i	0.126586	−	0.991956i	$-0.459598\pi$
$313$	−2.05199e7	−	1.18472e7i	−0.669179	−	0.386351i	−0.795765	+	0.605605i	$0.792931\pi$
$314$		0			0
$315$	7.37230e6	−	41362.4i	0.235869	−	0.00132335i
$316$		0			0
$317$	−1.48496e7	+	2.57203e7i	−0.466163	+	0.807418i	−0.999253	−	0.0386402i	$-0.987697\pi$
$317$	−1.48496e7	+	2.57203e7i	−0.466163	+	0.807418i	0.533090	+	0.846059i	$0.321031\pi$
$318$		0			0
$319$	−5.19569e6	−	8.99920e6i	−0.160056	−	0.277225i
$320$		0			0
$321$		−	7.19174e6i		−	0.217430i
$322$		0			0
$323$	−40007.7			−0.00118723
$324$		0			0
$325$	1.06438e6	−	614521.i	0.0310061	−	0.0179014i
$326$		0			0
$327$	1.68156e7	+	9.70848e6i	0.480915	+	0.277657i
$328$		0			0
$329$	−2.84588e7	−	4.86595e7i	−0.799150	−	1.36641i
$330$		0			0
$331$	4.07155e6	−	7.05214e6i	0.112273	−	0.194463i	−0.804413	−	0.594070i	$-0.797520\pi$
$331$	4.07155e6	−	7.05214e6i	0.112273	−	0.194463i	0.916686	+	0.399607i	$0.130853\pi$
$332$		0			0
$333$	1.18073e6	+	2.04508e6i	0.0319755	+	0.0553832i
$334$		0			0
$335$		−	2.64274e7i		−	0.702942i
$336$		0			0
$337$	−1.26594e7			−0.330767			−0.165384	−	0.986229i	$-0.552886\pi$
$337$	−1.26594e7			−0.330767			−0.165384	+	0.986229i	$0.552886\pi$
$338$		0			0
$339$	1.73944e6	−	1.00427e6i	0.0446489	−	0.0257781i
$340$		0			0
$341$	−1.43662e7	−	8.29434e6i	−0.362309	−	0.209179i
$342$		0			0
$343$	679175.	+	4.03479e7i	0.0168306	+	0.999858i
$344$		0			0
$345$	−111605.	+	193306.i	−0.00271786	+	0.00470747i
$346$		0			0
$347$	−1.55462e7	−	2.69268e7i	−0.372079	−	0.644461i	0.617806	−	0.786331i	$-0.288022\pi$
$347$	−1.55462e7	−	2.69268e7i	−0.372079	−	0.644461i	−0.989885	+	0.141870i	$0.954688\pi$
$348$		0			0
$349$			5.52908e7i			1.30070i	0.759635	+	0.650349i	$0.225378\pi$
$349$			5.52908e7i			1.30070i	−0.759635	+	0.650349i	$0.774622\pi$
$350$		0			0
$351$	596782.			0.0138005
$352$		0			0
$353$	−2.32099e6	+	1.34002e6i	−0.0527654	+	0.0304641i	−0.526151	−	0.850391i	$-0.676365\pi$
$353$	−2.32099e6	+	1.34002e6i	−0.0527654	+	0.0304641i	0.473385	+	0.880856i	$0.343032\pi$
$354$		0			0
$355$	3.29234e7	+	1.90083e7i	0.735900	+	0.424872i
$356$		0			0
$357$	2.36848e7	−	1.38522e7i	0.520553	−	0.304448i
$358$		0			0
$359$	−1.53031e7	+	2.65058e7i	−0.330748	+	0.572872i	−0.982659	−	0.185423i	$-0.940634\pi$
$359$	−1.53031e7	+	2.65058e7i	−0.330748	+	0.572872i	0.651911	+	0.758296i	$0.273968\pi$
$360$		0			0
$361$	−2.35229e7	−	4.07429e7i	−0.499999	−	0.866024i
$362$		0			0
$363$		−	2.52469e7i		−	0.527822i
$364$		0			0
$365$	3.95532e6			0.0813399
$366$		0			0
$367$	6.38805e7	−	3.68814e7i	1.29232	−	0.746121i	0.313255	−	0.949669i	$-0.398581\pi$
$367$	6.38805e7	−	3.68814e7i	1.29232	−	0.746121i	0.979065	+	0.203548i	$0.0652472\pi$
$368$		0			0
$369$	9.79698e6	+	5.65629e6i	0.194990	+	0.112578i
$370$		0			0
$371$	453024.	+	8.07453e7i	0.00887154	+	1.58123i
$372$		0			0
$373$	1.91718e7	−	3.32065e7i	0.369433	−	0.639876i	−0.620044	−	0.784567i	$-0.712885\pi$
$373$	1.91718e7	−	3.32065e7i	0.369433	−	0.639876i	0.989477	+	0.144691i	$0.0462187\pi$
$374$		0			0
$375$	−1.61504e7	−	2.79734e7i	−0.306260	−	0.530458i
$376$		0			0
$377$			4.19948e6i			0.0783738i
$378$		0			0
$379$	5.28278e7			0.970388			0.485194	−	0.874407i	$-0.338749\pi$
$379$	5.28278e7			0.970388			0.485194	+	0.874407i	$0.338749\pi$
$380$		0			0
$381$	3.31390e7	−	1.91328e7i	0.599189	−	0.345942i
$382$		0			0
$383$	−1.99396e7	−	1.15121e7i	−0.354912	−	0.204909i	0.311935	−	0.950104i	$-0.399023\pi$
$383$	−1.99396e7	−	1.15121e7i	−0.354912	−	0.204909i	−0.666847	+	0.745195i	$0.732356\pi$
$384$		0			0
$385$	5.85612e6	−	1.02758e7i	0.102619	−	0.180067i
$386$		0			0
$387$	−5.16775e6	+	8.95080e6i	−0.0891597	+	0.154429i
$388$		0			0
$389$	−3.83227e6	−	6.63768e6i	−0.0651039	−	0.112763i	0.831636	−	0.555321i	$-0.187405\pi$
$389$	−3.83227e6	−	6.63768e6i	−0.0651039	−	0.112763i	−0.896740	+	0.442558i	$0.854071\pi$
$390$		0			0
$391$			830728.i			0.0138972i
$392$		0			0
$393$	2.19180e7			0.361097
$394$		0			0
$395$	−1.32626e7	+	7.65716e6i	−0.215197	+	0.124244i
$396$		0			0
$397$	−6.94404e7	−	4.00914e7i	−1.10979	−	0.640737i	−0.171015	−	0.985268i	$-0.554705\pi$
$397$	−6.94404e7	−	4.00914e7i	−1.10979	−	0.640737i	−0.938775	+	0.344531i	$0.888038\pi$
$398$		0			0
$399$	−36216.9	−	20639.8i	−0.000570155	−	0.000324928i
$400$		0			0
$401$	−4.72206e7	+	8.17885e7i	−0.732316	+	1.26841i	0.223575	+	0.974687i	$0.428227\pi$
$401$	−4.72206e7	+	8.17885e7i	−0.732316	+	1.26841i	−0.955891	+	0.293722i	$0.905106\pi$
$402$		0			0
$403$	3.35200e6	+	5.80584e6i	0.0512140	+	0.0887053i
$404$		0			0
$405$		−	5.22302e6i		−	0.0786243i
$406$		0			0
$407$	3.78842e6			0.0561921
$408$		0			0
$409$	9.27394e7	−	5.35431e7i	1.35548	−	0.782589i	0.366472	−	0.930429i	$-0.380566\pi$
$409$	9.27394e7	−	5.35431e7i	1.35548	−	0.782589i	0.989011	+	0.147841i	$0.0472322\pi$
$410$		0			0
$411$	−3.52863e6	−	2.03725e6i	−0.0508253	−	0.0293440i
$412$		0			0
$413$	−2.35851e7	+	132325.i	−0.334802	+	0.00187841i
$414$		0			0
$415$	1.87196e7	−	3.24233e7i	0.261910	−	0.453642i
$416$		0			0
$417$	−4.37044e6	−	7.56983e6i	−0.0602723	−	0.104395i
$418$		0			0
$419$			9.80625e7i			1.33309i	0.745463	+	0.666547i	$0.232228\pi$
$419$			9.80625e7i			1.33309i	−0.745463	+	0.666547i	$0.767772\pi$
$420$		0			0
$421$	−1.23780e8			−1.65883			−0.829416	−	0.558631i	$-0.811327\pi$
$421$	−1.23780e8			−1.65883			−0.829416	+	0.558631i	$0.811327\pi$
$422$		0			0
$423$	−3.45856e7	+	1.99680e7i	−0.456956	+	0.263824i
$424$		0			0
$425$	−3.46696e7	−	2.00165e7i	−0.451629	−	0.260748i
$426$		0			0
$427$	6.46833e7	+	1.10597e8i	0.830823	+	1.42056i
$428$		0			0
$429$	478701.	−	829134.i	0.00606307	−	0.0105015i
$430$		0			0
$431$	−3.31282e7	−	5.73798e7i	−0.413777	−	0.716683i	0.581522	−	0.813531i	$-0.302457\pi$
$431$	−3.31282e7	−	5.73798e7i	−0.413777	−	0.716683i	−0.995299	+	0.0968474i	$0.969124\pi$
$432$		0			0
$433$		−	5.59770e7i		−	0.689519i	−0.938691	−	0.344759i	$-0.887960\pi$
$433$		−	5.59770e7i		−	0.689519i	0.938691	−	0.344759i	$-0.112040\pi$
$434$		0			0
$435$	3.67537e7			0.446512
$436$		0			0
$437$	1092.99	−	631.040i	1.30971e−5	−	7.56159e-6i
$438$		0			0
$439$	6.01488e6	+	3.47269e6i	0.0710940	+	0.0410462i	0.535126	−	0.844772i	$-0.320264\pi$
$439$	6.01488e6	+	3.47269e6i	0.0710940	+	0.0410462i	−0.464032	+	0.885819i	$0.653598\pi$
$440$		0			0
$441$	2.85869e7	−	320785.i	0.333312	−	0.00374023i
$442$		0			0
$443$	−3.99434e7	+	6.91839e7i	−0.459445	+	0.795782i	−0.998932	−	0.0462122i	$-0.985285\pi$
$443$	−3.99434e7	+	6.91839e7i	−0.459445	+	0.795782i	0.539487	+	0.841994i	$0.318618\pi$
$444$		0			0
$445$	1.48785e7	+	2.57703e7i	0.168841	+	0.292441i
$446$		0			0
$447$		−	2.46600e7i		−	0.276102i
$448$		0			0
$449$	−9.31648e7			−1.02923			−0.514616	−	0.857421i	$-0.672065\pi$
$449$	−9.31648e7			−1.02923			−0.514616	+	0.857421i	$0.672065\pi$
$450$		0			0
$451$	1.57170e7	−	9.07424e6i	0.171333	−	0.0989192i
$452$		0			0
$453$	1.84702e7	+	1.06638e7i	0.198690	+	0.114714i
$454$		0			0
$455$	−4.12596e6	+	2.41309e6i	−0.0438017	+	0.0256176i
$456$		0			0
$457$	1.43952e7	−	2.49332e7i	0.150824	−	0.261234i	−0.780707	−	0.624897i	$-0.785141\pi$
$457$	1.43952e7	−	2.49332e7i	0.150824	−	0.261234i	0.931530	+	0.363663i	$0.118474\pi$
$458$		0			0
$459$	−9.71934e6	−	1.68344e7i	−0.100508	−	0.174084i
$460$		0			0
$461$			1.65056e8i			1.68472i	0.538914	+	0.842361i	$0.318835\pi$
$461$			1.65056e8i			1.68472i	−0.538914	+	0.842361i	$0.681165\pi$
$462$		0			0
$463$	9.22058e7			0.928999			0.464499	−	0.885573i	$-0.346234\pi$
$463$	9.22058e7			0.928999			0.464499	+	0.885573i	$0.346234\pi$
$464$		0			0
$465$	5.08125e7	−	2.93366e7i	0.505373	−	0.291777i
$466$		0			0
$467$	2.49224e7	+	1.43890e7i	0.244703	+	0.141280i	0.617337	−	0.786699i	$-0.288212\pi$
$467$	2.49224e7	+	1.43890e7i	0.244703	+	0.141280i	−0.372633	+	0.927979i	$0.621545\pi$
$468$		0			0
$469$	−574957.	−	1.02478e8i	−0.00557335	−	0.993375i
$470$		0			0
$471$	3.51720e7	−	6.09196e7i	0.336615	−	0.583035i
$472$		0			0
$473$	8.29048e6	+	1.43595e7i	0.0783423	+	0.135693i
$474$		0			0
$475$			60820.0i			0.000567499i
$476$		0			0
$477$	5.72053e7			0.527086
$478$		0			0
$479$	−1.33128e8	+	7.68615e7i	−1.21133	+	0.699362i	−0.963049	−	0.269325i	$-0.913199\pi$
$479$	−1.33128e8	+	7.68615e7i	−1.21133	+	0.699362i	−0.248282	+	0.968688i	$0.579866\pi$
$480$		0			0
$481$	−1.32590e6	−	765510.i	−0.0119145	−	0.00687884i
$482$		0			0
$483$	−428569.	+	752016.i	−0.00380347	+	0.00667399i
$484$		0			0
$485$	−1.83761e7	+	3.18283e7i	−0.161075	+	0.278989i
$486$		0			0
$487$	−1.05594e8	−	1.82893e8i	−0.914220	−	1.58347i	−0.808040	−	0.589128i	$-0.799471\pi$
$487$	−1.05594e8	−	1.82893e8i	−0.914220	−	1.58347i	−0.106180	−	0.994347i	$-0.533862\pi$
$488$		0			0
$489$			1.02888e6i			0.00879907i
$490$		0			0
$491$	−1.14369e8			−0.966195			−0.483098	−	0.875566i	$-0.660488\pi$
$491$	−1.14369e8			−0.966195			−0.483098	+	0.875566i	$0.660488\pi$
$492$		0			0
$493$	1.18461e8	−	6.83937e7i	0.988635	−	0.570789i
$494$		0			0
$495$	−7.25656e6	−	4.18958e6i	−0.0598295	−	0.0345426i
$496$		0			0
$497$	1.28082e8	+	7.29929e7i	1.04332	+	0.594581i
$498$		0			0
$499$	1.04355e8	−	1.80748e8i	0.839867	−	1.45469i	−0.0501375	−	0.998742i	$-0.515966\pi$
$499$	1.04355e8	−	1.80748e8i	0.839867	−	1.45469i	0.890005	−	0.455951i	$-0.150701\pi$
$500$		0			0
$501$	4.44439e7	+	7.69791e7i	0.353426	+	0.612152i
$502$		0			0
$503$		−	4.42650e7i		−	0.347822i	−0.984761	−	0.173911i	$-0.944360\pi$
$503$		−	4.42650e7i		−	0.347822i	0.984761	−	0.173911i	$-0.0556405\pi$
$504$		0			0
$505$	1.55034e7			0.120380
$506$		0			0
$507$	6.48268e7	−	3.74278e7i	0.497429	−	0.287191i
$508$		0			0
$509$	9.42539e7	+	5.44175e7i	0.714736	+	0.412653i	0.812812	−	0.582526i	$-0.197935\pi$
$509$	9.42539e7	+	5.44175e7i	0.714736	+	0.412653i	−0.0980760	+	0.995179i	$0.531269\pi$
$510$		0			0
$511$	1.53377e7	−	86052.5i	0.114947	−	0.000644912i
$512$		0			0
$513$	−14766.1	+	25575.6i	−0.000109374	+	0.000189441i
$514$		0			0
$515$	−3.25425e7	−	5.63652e7i	−0.238248	−	0.412658i
$516$		0			0
$517$			6.40683e7i			0.463630i
$518$		0			0
$519$	−2.42271e7			−0.173301
$520$		0			0
$521$	2.26960e8	−	1.31036e8i	1.60486	−	0.926565i	0.614361	−	0.789025i	$-0.289414\pi$
$521$	2.26960e8	−	1.31036e8i	1.60486	−	0.926565i	0.990496	−	0.137540i	$-0.0439196\pi$
$522$		0			0
$523$	1.47810e8	+	8.53379e7i	1.03323	+	0.596537i	0.917909	−	0.396791i	$-0.129876\pi$
$523$	1.47810e8	+	8.53379e7i	1.03323	+	0.596537i	0.115323	+	0.993328i	$0.463210\pi$
$524$		0			0
$525$	−2.10582e7	−	3.60058e7i	−0.145527	−	0.248825i
$526$		0			0
$527$	1.09183e8	−	1.89110e8i	0.745973	−	1.29206i
$528$		0			0
$529$	7.40048e7	+	1.28180e8i	0.499911	+	0.865872i
$530$		0			0
$531$			1.67092e7i			0.111602i
$532$		0			0
$533$	−7.33436e6			−0.0484374
$534$		0			0
$535$	3.53404e7	−	2.04038e7i	0.230786	−	0.133244i
$536$		0			0
$537$	6.54358e7	+	3.77794e7i	0.422564	+	0.243967i
$538$		0			0
$539$	2.24849e7	−	3.99743e7i	0.143590	−	0.255279i
$540$		0			0
$541$	4.33041e7	−	7.50049e7i	0.273487	−	0.473694i	−0.696265	−	0.717785i	$-0.745156\pi$
$541$	4.33041e7	−	7.50049e7i	0.273487	−	0.473694i	0.969752	+	0.244091i	$0.0784895\pi$
$542$		0			0
$543$	−6.87325e7	−	1.19048e8i	−0.429302	−	0.743572i
$544$		0			0
$545$			1.10176e8i			0.680609i
$546$		0			0
$547$	2.94906e8			1.80186			0.900931	−	0.433963i	$-0.142885\pi$
$547$	2.94906e8			1.80186			0.900931	+	0.433963i	$0.142885\pi$
$548$		0			0
$549$	7.86090e7	−	4.53849e7i	0.475067	−	0.274280i
$550$		0			0
$551$	−179972.	−	103907.i	−0.00107585	−	0.000621140i
$552$		0			0
$553$	−5.12622e7	+	2.99810e7i	−0.303125	+	0.177284i
$554$		0			0
$555$	−6.69972e6	+	1.16043e7i	−0.0391902	+	0.0678794i
$556$		0			0
$557$	8.54052e7	+	1.47926e8i	0.494218	+	0.856011i	0.999978	−	0.00666324i	$-0.00212099\pi$
$557$	8.54052e7	+	1.47926e8i	0.494218	+	0.856011i	−0.505759	+	0.862675i	$0.668788\pi$
$558$		0			0
$559$		−	6.70088e6i		−	0.0383616i
$560$		0			0
$561$	−3.11850e7			−0.176627
$562$		0			0
$563$	−6.05824e7	+	3.49772e7i	−0.339485	+	0.196002i	−0.660044	−	0.751227i	$-0.729463\pi$
$563$	−6.05824e7	+	3.49772e7i	−0.339485	+	0.196002i	0.320559	+	0.947229i	$0.396129\pi$
$564$		0			0
$565$	9.86998e6	+	5.69844e6i	0.0547231	+	0.0315944i
$566$		0			0
$567$	−113633.	−	2.02535e7i	−0.000623382	−	0.111109i
$568$		0			0
$569$	922020.	−	1.59699e6i	0.00500499	−	0.00866890i	−0.863512	−	0.504328i	$-0.831740\pi$
$569$	922020.	−	1.59699e6i	0.00500499	−	0.00866890i	0.868517	+	0.495659i	$0.165074\pi$
$570$		0			0
$571$	9.98929e7	+	1.73020e8i	0.536570	+	0.929366i	0.999086	+	0.0427552i	$0.0136136\pi$
$571$	9.98929e7	+	1.73020e8i	0.536570	+	0.929366i	−0.462516	+	0.886611i	$0.653053\pi$
$572$		0			0
$573$		−	2.61808e7i		−	0.139161i
$574$		0			0
$575$	1.26288e6			0.00664291
$576$		0			0
$577$	−1.36179e7	+	7.86229e6i	−0.0708895	+	0.0409281i	−0.535026	−	0.844836i	$-0.679698\pi$
$577$	−1.36179e7	+	7.86229e6i	−0.0708895	+	0.0409281i	0.464136	+	0.885764i	$0.346365\pi$
$578$		0			0
$579$	1.27377e8	+	7.35411e7i	0.656229	+	0.378874i
$580$		0			0
$581$	7.18843e7	−	1.26136e8i	0.366526	−	0.643149i
$582$		0			0
$583$	4.58865e7	−	7.94777e7i	0.231568	−	0.401088i
$584$		0			0
$585$	1.69314e6	+	2.93260e6i	0.00845716	+	0.0146482i
$586$		0			0
$587$			2.39993e8i			1.18654i	0.805002	+	0.593272i	$0.202164\pi$
$587$			2.39993e8i			1.18654i	−0.805002	+	0.593272i	$0.797836\pi$
$588$		0			0
$589$	−331752.			−0.00162356
$590$		0			0
$591$	−9.11796e7	+	5.26426e7i	−0.441708	+	0.255020i
$592$		0			0
$593$	−3.98158e7	−	2.29877e7i	−0.190938	−	0.110238i	0.401484	−	0.915866i	$-0.368495\pi$
$593$	−3.98158e7	−	2.29877e7i	−0.190938	−	0.110238i	−0.592421	+	0.805628i	$0.701828\pi$
$594$		0			0
$595$	1.35266e8	+	7.70874e7i	0.642153	+	0.365959i
$596$		0			0
$597$	−4.75456e7	+	8.23513e7i	−0.223453	+	0.387033i
$598$		0			0
$599$	−1.64605e8	−	2.85105e8i	−0.765884	−	1.32655i	−0.939778	−	0.341786i	$-0.888968\pi$
$599$	−1.64605e8	−	2.85105e8i	−0.765884	−	1.32655i	0.173894	−	0.984764i	$-0.444365\pi$
$600$		0			0
$601$			2.05844e7i			0.0948234i	0.998875	+	0.0474117i	$0.0150973\pi$
$601$			2.05844e7i			0.0948234i	−0.998875	+	0.0474117i	$0.984903\pi$
$602$		0			0
$603$	−7.26024e7			−0.331130
$604$		0			0
$605$	1.24064e8	−	7.16281e7i	0.560245	−	0.323458i
$606$		0			0
$607$	−2.42769e8	−	1.40163e8i	−1.08549	−	0.626709i	−0.153120	−	0.988208i	$-0.548932\pi$
$607$	−2.42769e8	−	1.40163e8i	−1.08549	−	0.626709i	−0.932373	+	0.361498i	$0.882265\pi$
$608$		0			0
$609$	1.42521e8	−	799618.i	0.630997	−	0.00354022i
$610$		0			0
$611$	1.29460e7	−	2.24231e7i	0.0567560	−	0.0983043i
$612$		0			0
$613$	9.35420e7	+	1.62020e8i	0.406093	+	0.703373i	0.994448	−	0.105229i	$-0.0335576\pi$
$613$	9.35420e7	+	1.62020e8i	0.406093	+	0.703373i	−0.588355	+	0.808603i	$0.700224\pi$
$614$		0			0
$615$			6.41901e7i			0.275958i
$616$		0			0
$617$	−4.35566e8			−1.85438			−0.927189	−	0.374595i	$-0.877782\pi$
$617$	−4.35566e8			−1.85438			−0.927189	+	0.374595i	$0.877782\pi$
$618$		0			0
$619$	−1.88531e8	+	1.08848e8i	−0.794896	+	0.458933i	−0.841683	−	0.539972i	$-0.818435\pi$
$619$	−1.88531e8	+	1.08848e8i	−0.794896	+	0.458933i	0.0467875	+	0.998905i	$0.485102\pi$
$620$		0			0
$621$	531057.	+	306606.i	0.00221752	+	0.00128028i
$622$		0			0
$623$	5.82554e7	+	9.96065e7i	0.240919	+	0.411930i
$624$		0			0
$625$	3.06943e7	−	5.31642e7i	0.125724	−	0.217760i
$626$		0			0
$627$	23688.8	+	41030.2i	9.61039e−5	+	0.000166457i
$628$		0			0
$629$			4.98691e7i			0.200392i
$630$		0			0
$631$	−3.69130e8			−1.46924			−0.734618	−	0.678481i	$-0.762638\pi$
$631$	−3.69130e8			−1.46924			−0.734618	+	0.678481i	$0.762638\pi$
$632$		0			0
$633$	3.95914e7	−	2.28581e7i	0.156095	−	0.0901216i
$634$		0			0
$635$	1.88038e8	+	1.08564e8i	0.734385	+	0.423997i
$636$		0			0
$637$	−1.59469e7	+	9.44708e6i	−0.0616960	+	0.0365493i
$638$		0			0
$639$	5.22204e7	−	9.04484e7i	0.200142	−	0.346656i
$640$		0			0
$641$	−5.61574e7	−	9.72675e7i	−0.213223	−	0.369312i	0.739499	−	0.673158i	$-0.235063\pi$
$641$	−5.61574e7	−	9.72675e7i	−0.213223	−	0.369312i	−0.952721	+	0.303846i	$0.901729\pi$
$642$		0			0
$643$			3.30263e8i			1.24230i	0.783692	+	0.621150i	$0.213334\pi$
$643$			3.30263e8i			1.24230i	−0.783692	+	0.621150i	$0.786666\pi$
$644$		0			0
$645$	−5.86459e7			−0.218554
$646$		0			0
$647$	−4.52482e7	+	2.61241e7i	−0.167066	+	0.0964558i	−0.581202	−	0.813759i	$-0.697417\pi$
$647$	−4.52482e7	+	2.61241e7i	−0.167066	+	0.0964558i	0.414135	+	0.910215i	$0.364084\pi$
$648$		0			0
$649$	2.32148e7	+	1.34031e7i	0.0849242	+	0.0490310i
$650$		0			0
$651$	1.96399e8	−	1.14865e8i	0.711863	−	0.416337i
$652$		0			0
$653$	1.43990e8	−	2.49399e8i	0.517123	−	0.895683i	−0.482679	−	0.875797i	$-0.660336\pi$
$653$	1.43990e8	−	2.49399e8i	0.517123	−	0.895683i	0.999802	−	0.0198859i	$-0.00633030\pi$
$654$		0			0
$655$	6.21839e7	+	1.07706e8i	0.221286	+	0.383278i
$656$		0			0
$657$		−	1.08662e7i		−	0.0383162i
$658$		0			0
$659$	4.28596e8			1.49759			0.748794	−	0.662803i	$-0.230633\pi$
$659$	4.28596e8			1.49759			0.748794	+	0.662803i	$0.230633\pi$
$660$		0			0
$661$	−1.16549e8	+	6.72895e7i	−0.403556	+	0.232993i	−0.688017	−	0.725695i	$-0.741519\pi$
$661$	−1.16549e8	+	6.72895e7i	−0.403556	+	0.232993i	0.284461	+	0.958688i	$0.408185\pi$
$662$		0			0
$663$	1.09143e7	+	6.30140e6i	0.0374505	+	0.0216220i
$664$		0			0
$665$	−1327.05	−	236528.i	−4.51254e−6	−	0.000804299i
$666$		0			0
$667$	−2.15755e6	+	3.73698e6i	−0.00727081	+	0.0125934i
$668$		0			0
$669$	−1.50521e8	−	2.60710e8i	−0.502712	−	0.870722i
$670$		0			0
$671$		−	1.45620e8i		−	0.482006i
$672$		0			0
$673$	−3.44995e8			−1.13179			−0.565897	−	0.824476i	$-0.691470\pi$
$673$	−3.44995e8			−1.13179			−0.565897	+	0.824476i	$0.691470\pi$
$674$		0			0
$675$	−2.55918e7	+	1.47754e7i	−0.0832126	+	0.0480428i
$676$		0			0
$677$	−8.96363e7	−	5.17515e7i	−0.288880	−	0.166785i	0.348556	−	0.937288i	$-0.386672\pi$
$677$	−8.96363e7	−	5.17515e7i	−0.288880	−	0.166785i	−0.637437	+	0.770503i	$0.720005\pi$
$678$		0			0
$679$	−7.05650e7	+	1.23821e8i	−0.225414	+	0.395536i
$680$		0			0
$681$	−7.78600e6	+	1.34858e7i	−0.0246532	+	0.0427006i
$682$		0			0
$683$	1.42279e8	+	2.46435e8i	0.446560	+	0.773464i	0.998159	−	0.0606448i	$-0.0193157\pi$
$683$	1.42279e8	+	2.46435e8i	0.446560	+	0.773464i	−0.551600	+	0.834109i	$0.685982\pi$
$684$		0			0
$685$		−	2.31196e7i		−	0.0719299i
$686$		0			0
$687$	5.24625e6			0.0161800
$688$		0			0
$689$	−3.21194e7	+	1.85441e7i	−0.0981996	+	0.0566956i
$690$		0			0
$691$	−2.86318e8	−	1.65306e8i	−0.867790	−	0.501019i	−0.00117669	−	0.999999i	$-0.500375\pi$
$691$	−2.86318e8	−	1.65306e8i	−0.867790	−	0.501019i	−0.866613	+	0.498981i	$0.833708\pi$
$692$		0			0
$693$	−2.82302e7	−	1.60882e7i	−0.0848230	−	0.0483401i
$694$		0			0
$695$	2.47989e7	−	4.29529e7i	0.0738716	−	0.127949i
$696$		0			0
$697$	1.19449e8	+	2.06892e8i	0.352764	+	0.611006i
$698$		0			0
$699$			3.39119e8i			0.992935i
$700$		0			0
$701$	−6.32139e8			−1.83509			−0.917547	−	0.397626i	$-0.869834\pi$
$701$	−6.32139e8			−1.83509			−0.917547	+	0.397626i	$0.869834\pi$
$702$		0			0
$703$	65613.1	−	37881.7i	0.000188853	−	0.000109034i
$704$		0			0
$705$	−1.96247e8	−	1.13303e8i	−0.560060	−	0.323351i
$706$		0			0
$707$	6.01182e7	−	337295.i	0.170117	−	0.000954446i
$708$		0			0
$709$	2.89569e8	−	5.01548e8i	0.812481	−	1.40726i	−0.0986411	−	0.995123i	$-0.531450\pi$
$709$	2.89569e8	−	5.01548e8i	0.812481	−	1.40726i	0.911122	−	0.412136i	$-0.135217\pi$
$710$		0			0
$711$	2.10361e7	+	3.64355e7i	0.0585269	+	0.101372i
$712$		0			0
$713$			6.88857e6i			0.0190047i
$714$		0			0
$715$	5.43251e6			0.0148622
$716$		0			0
$717$	−3.03642e8	+	1.75308e8i	−0.823768	+	0.475603i
$718$		0			0
$719$	9.29210e7	+	5.36480e7i	0.249993	+	0.144333i	0.619761	−	0.784791i	$-0.287230\pi$
$719$	9.29210e7	+	5.36480e7i	0.249993	+	0.144333i	−0.369768	+	0.929124i	$0.620563\pi$
$720$		0			0
$721$	−1.27417e8	−	2.17861e8i	−0.339956	−	0.581265i
$722$		0			0
$723$	1.03404e8	−	1.79101e8i	0.273604	−	0.473897i
$724$		0			0
$725$	−1.03973e8	−	1.80086e8i	−0.272838	−	0.472570i
$726$		0			0
$727$		−	1.96684e8i		−	0.511877i	−0.966693	−	0.255938i	$-0.917616\pi$
$727$		−	1.96684e8i		−	0.511877i	0.966693	−	0.255938i	$-0.0823844\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−1.89022e8	+	1.09132e8i	−0.483906	+	0.279383i
$732$		0			0
$733$	1.68852e8	+	9.74870e7i	0.428741	+	0.247534i	0.698810	−	0.715307i	$-0.253713\pi$
$733$	1.68852e8	+	9.74870e7i	0.428741	+	0.247534i	−0.270069	+	0.962841i	$0.587047\pi$
$734$		0			0
$735$	8.26806e7	+	1.39567e8i	0.208229	+	0.351495i
$736$		0			0
$737$	−5.82370e7	+	1.00869e8i	−0.145478	+	0.251975i
$738$		0			0
$739$	−2.79444e8	−	4.84010e8i	−0.692406	−	1.19928i	−0.971047	−	0.238887i	$-0.923217\pi$
$739$	−2.79444e8	−	4.84010e8i	−0.692406	−	1.19928i	0.278641	−	0.960395i	$-0.410116\pi$
$740$		0			0
$741$		−	19146.8i		−	4.70588e-5i
$742$		0			0
$743$	−4.53243e8			−1.10501			−0.552504	−	0.833511i	$-0.686327\pi$
$743$	−4.53243e8			−1.10501			−0.552504	+	0.833511i	$0.686327\pi$
$744$		0			0
$745$	1.21180e8	−	6.99630e7i	0.293063	−	0.169200i
$746$		0			0
$747$	−8.90747e7	−	5.14273e7i	−0.213694	−	0.123376i
$748$		0			0
$749$	1.36597e8	−	7.98892e7i	0.325083	−	0.190127i
$750$		0			0
$751$	4.43835e7	−	7.68745e7i	0.104786	−	0.181494i	−0.808865	−	0.587994i	$-0.799918\pi$
$751$	4.43835e7	−	7.68745e7i	0.104786	−	0.181494i	0.913651	+	0.406500i	$0.133251\pi$
$752$		0			0
$753$	7.55433e7	+	1.30845e8i	0.176934	+	0.306458i
$754$		0			0
$755$			1.21017e8i			0.281194i
$756$		0			0
$757$	−2.65118e8			−0.611156			−0.305578	−	0.952167i	$-0.598850\pi$
$757$	−2.65118e8			−0.611156			−0.305578	+	0.952167i	$0.598850\pi$
$758$		0			0
$759$	851961.	−	491880.i	0.00194847	−	0.00112495i
$760$		0			0
$761$	−3.81404e8	−	2.20204e8i	−0.865430	−	0.499656i	0.000397044	−	1.00000i	$-0.499874\pi$
$761$	−3.81404e8	−	2.20204e8i	−0.865430	−	0.499656i	−0.865827	+	0.500344i	$0.833207\pi$
$762$		0			0
$763$	2.39700e6	+	4.27234e8i	0.00539629	+	0.961816i
$764$		0			0
$765$	5.51497e7	−	9.55221e7i	0.123185	−	0.213363i
$766$		0			0
$767$	−5.41661e6	−	9.38184e6i	−0.0120044	−	0.0207923i
$768$		0			0
$769$			5.68157e8i			1.24936i	0.780879	+	0.624682i	$0.214772\pi$
$769$			5.68157e8i			1.24936i	−0.780879	+	0.624682i	$0.785228\pi$
$770$		0			0
$771$	−2.89060e8			−0.630702
$772$		0			0
$773$	−2.90405e8	+	1.67665e8i	−0.628732	+	0.362998i	−0.780261	−	0.625454i	$-0.784914\pi$
$773$	−2.90405e8	+	1.67665e8i	−0.628732	+	0.362998i	0.151529	+	0.988453i	$0.451580\pi$
$774$		0			0
$775$	−2.87487e8	−	1.65981e8i	−0.617609	−	0.356577i
$776$		0			0
$777$	−2.57273e7	+	4.51440e7i	−0.0548442	+	0.0962358i
$778$		0			0
$779$	181473.	−	314320.i	0.000383883	−	0.000664905i
$780$		0			0
$781$	−8.37758e7	−	1.45104e8i	−0.175859	−	0.304597i
$782$		0			0
$783$		−	1.00971e8i		−	0.210336i
$784$		0			0
$785$	3.99147e8			0.825133
$786$		0			0
$787$	6.53582e7	−	3.77346e7i	0.134084	−	0.0774132i	−0.431458	−	0.902133i	$-0.642001\pi$
$787$	6.53582e7	−	3.77346e7i	0.134084	−	0.0774132i	0.565541	+	0.824720i	$0.308667\pi$
$788$		0			0
$789$	−2.92116e8	−	1.68653e8i	−0.594737	−	0.343372i
$790$		0			0
$791$	3.83971e7	+	2.18823e7i	0.0775835	+	0.0442143i
$792$		0			0
$793$	−2.94247e7	+	5.09650e7i	−0.0590055	+	0.102200i
$794$		0			0
$795$	1.62298e8	+	2.81108e8i	0.323007	+	0.559464i
$796$		0			0
$797$			1.42558e8i			0.281589i	0.990039	+	0.140794i	$0.0449657\pi$
$797$			1.42558e8i			0.281589i	−0.990039	+	0.140794i	$0.955034\pi$
$798$		0			0
$799$	−8.43366e8			−1.65339
$800$		0			0
$801$	7.07971e7	−	4.08747e7i	0.137758	−	0.0795348i
$802$		0			0
$803$	−1.50969e7	−	8.71620e6i	−0.0291569	−	0.0168337i
$804$		0			0
$805$	−4.91132e6	+	27555.1i	−0.00941479	+	5.28219e-5i
$806$		0			0
$807$	−3.51255e7	+	6.08391e7i	−0.0668346	+	0.115761i
$808$		0			0
$809$	−1.79970e8	−	3.11717e8i	−0.339902	−	0.588728i	0.644512	−	0.764594i	$-0.277061\pi$
$809$	−1.79970e8	−	3.11717e8i	−0.339902	−	0.588728i	−0.984414	+	0.175866i	$0.943727\pi$
$810$		0			0
$811$			1.32004e8i			0.247471i	0.992315	+	0.123735i	$0.0394874\pi$
$811$			1.32004e8i			0.247471i	−0.992315	+	0.123735i	$0.960513\pi$
$812$		0			0
$813$	−5.78730e8			−1.07697
$814$		0			0
$815$	−5.05592e6	+	2.91904e6i	−0.00933958	+	0.00539221i
$816$		0			0
$817$	287172.	+	165799.i	0.000526593	+	0.000304029i
$818$		0			0
$819$	6.62934e6	+	1.13350e7i	0.0120675	+	0.0206334i
$820$		0			0
$821$	1.81008e8	−	3.13514e8i	0.327090	−	0.566537i	−0.654843	−	0.755765i	$-0.727265\pi$
$821$	1.81008e8	−	3.13514e8i	0.327090	−	0.566537i	0.981933	+	0.189228i	$0.0605986\pi$
$822$		0			0
$823$	−1.43400e8	−	2.48376e8i	−0.257247	−	0.445564i	0.708257	−	0.705955i	$-0.249482\pi$
$823$	−1.43400e8	−	2.48376e8i	−0.257247	−	0.445564i	−0.965503	+	0.260391i	$0.916149\pi$
$824$		0			0
$825$			4.74076e7i			0.0844280i
$826$		0			0
$827$	−3.69600e8			−0.653454			−0.326727	−	0.945119i	$-0.605946\pi$
$827$	−3.69600e8			−0.653454			−0.326727	+	0.945119i	$0.605946\pi$
$828$		0			0
$829$	−6.65461e8	+	3.84204e8i	−1.16804	+	0.674370i	−0.953218	−	0.302282i	$-0.902251\pi$
$829$	−6.65461e8	+	3.84204e8i	−1.16804	+	0.674370i	−0.214825	+	0.976653i	$0.568918\pi$
$830$		0			0
$831$	2.61403e8	+	1.50921e8i	0.455520	+	0.262994i
$832$		0			0
$833$	5.26203e8	+	2.95981e8i	0.910371	+	0.512070i
$834$		0			0
$835$	−2.52184e8	+	4.36796e8i	−0.433170	+	0.750273i
$836$		0			0
$837$	−8.05948e7	−	1.39594e8i	−0.137445	−	0.238063i
$838$		0			0
$839$			5.21850e8i			0.883608i	0.897112	+	0.441804i	$0.145661\pi$
$839$			5.21850e8i			0.883608i	−0.897112	+	0.441804i	$0.854339\pi$
$840$		0			0
$841$	1.15698e8			0.194508
$842$		0			0
$843$	−3.39542e8	+	1.96035e8i	−0.566775	+	0.327228i
$844$		0			0
$845$	3.67842e8	+	2.12374e8i	0.609665	+	0.351990i
$846$		0			0
$847$	4.79527e8	−	2.80454e8i	0.789156	−	0.461542i
$848$		0			0
$849$	−2.20365e8	+	3.81683e8i	−0.360097	+	0.623706i
$850$		0			0
$851$	−786585.	−	1.36240e6i	−0.00127631	−	0.00221064i
$852$		0			0
$853$			7.64693e8i			1.23208i	0.787713	+	0.616042i	$0.211265\pi$
$853$			7.64693e8i			1.23208i	−0.787713	+	0.616042i	$0.788735\pi$
$854$		0			0
$855$	−167572.			−0.000268104
$856$		0			0
$857$	−3.01924e8	+	1.74316e8i	−0.479684	+	0.276946i	−0.720285	−	0.693679i	$-0.755989\pi$
$857$	−3.01924e8	+	1.74316e8i	−0.479684	+	0.276946i	0.240601	+	0.970624i	$0.422656\pi$
$858$		0			0
$859$	−7.88817e8	−	4.55424e8i	−1.24451	−	0.718516i	−0.274498	−	0.961588i	$-0.588512\pi$
$859$	−7.88817e8	−	4.55424e8i	−1.24451	−	0.718516i	−0.970008	+	0.243072i	$0.921845\pi$
$860$		0			0
$861$	1.39653e6	+	2.48912e8i	0.00218796	+	0.389975i
$862$		0			0
$863$	4.74227e8	−	8.21385e8i	0.737826	−	1.27795i	−0.215646	−	0.976472i	$-0.569186\pi$
$863$	4.74227e8	−	8.21385e8i	0.737826	−	1.27795i	0.953472	−	0.301481i	$-0.0974809\pi$
$864$		0			0
$865$	−6.87351e7	−	1.19053e8i	−0.106201	−	0.183946i
$866$		0			0
$867$		−	3.42372e7i		−	0.0525340i
$868$		0			0
$869$	6.74952e7			0.102852
$870$		0			0
$871$	4.07645e7	−	2.35354e7i	0.0616918	−	0.0356178i
$872$		0			0
$873$	8.74400e7	+	5.04835e7i	0.131422	+	0.0758764i
$874$		0			0
$875$	3.51906e8	−	6.17495e8i	0.525295	−	0.921741i
$876$		0			0
$877$	4.32336e8	−	7.48828e8i	0.640948	−	1.11015i	−0.344274	−	0.938869i	$-0.611875\pi$
$877$	4.32336e8	−	7.48828e8i	0.640948	−	1.11015i	0.985222	−	0.171285i	$-0.0547918\pi$
$878$		0			0
$879$	−5.24864e7	−	9.09091e7i	−0.0772823	−	0.133857i
$880$		0			0
$881$			2.24787e8i			0.328734i	0.986399	+	0.164367i	$0.0525581\pi$
$881$			2.24787e8i			0.328734i	−0.986399	+	0.164367i	$0.947442\pi$
$882$		0			0
$883$	−9.22033e8			−1.33926			−0.669629	−	0.742696i	$-0.733547\pi$
$883$	−9.22033e8			−1.33926			−0.669629	+	0.742696i	$0.733547\pi$
$884$		0			0
$885$	−8.21096e7	+	4.74060e7i	−0.118458	+	0.0683917i
$886$		0			0
$887$	3.21829e8	+	1.85808e8i	0.461163	+	0.266252i	0.712533	−	0.701639i	$-0.247548\pi$
$887$	3.21829e8	+	1.85808e8i	0.461163	+	0.266252i	−0.251370	+	0.967891i	$0.580881\pi$
$888$		0			0
$889$	7.31522e8	+	4.16890e8i	1.04117	+	0.593357i
$890$		0			0
$891$	−1.15098e7	+	1.99355e7i	−0.0162717	+	0.0281835i
$892$		0			0
$893$	640641.	+	1.10962e6i	0.000899622	+	0.00155819i
$894$		0			0
$895$			4.28737e8i			0.598028i
$896$		0			0
$897$	−397568.			−0.000550851
$898$		0			0
$899$	9.82306e8	−	5.67135e8i	1.35197	−	0.780561i
$900$		0			0
$901$	1.04621e9	+	6.04029e8i	1.43036	+	0.825816i
$902$		0			0
$903$	−2.27413e8	+	1.27591e6i	−0.308853	+	0.00173283i
$904$		0			0
$905$	3.90003e8	−	6.75506e8i	0.526166	−	0.911346i
$906$		0			0
$907$	−2.18476e8	−	3.78412e8i	−0.292808	−	0.507158i	0.681665	−	0.731665i	$-0.261256\pi$
$907$	−2.18476e8	−	3.78412e8i	−0.292808	−	0.507158i	−0.974473	+	0.224507i	$0.927923\pi$
$908$		0			0
$909$		−	4.25917e7i		−	0.0567066i
$910$		0			0
$911$	−4.99739e8			−0.660979			−0.330490	−	0.943810i	$-0.607214\pi$
$911$	−4.99739e8			−0.660979			−0.330490	+	0.943810i	$0.607214\pi$
$912$		0			0
$913$	−1.42900e8	+	8.25034e7i	−0.187767	+	0.108408i
$914$		0			0
$915$	4.46045e8	+	2.57524e8i	0.582257	+	0.336166i
$916$		0			0
$917$	2.43476e8	+	4.16301e8i	0.315753	+	0.539882i
$918$		0			0
$919$	2.65148e8	−	4.59250e8i	0.341619	−	0.591701i	−0.643115	−	0.765770i	$-0.722358\pi$
$919$	2.65148e8	−	4.59250e8i	0.341619	−	0.591701i	0.984734	+	0.174069i	$0.0556915\pi$
$920$		0			0
$921$	1.50753e8	+	2.61112e8i	0.192969	+	0.334231i
$922$		0			0
$923$			6.77128e7i			0.0861124i
$924$		0			0
$925$	7.58114e7			0.0957876
$926$		0			0
$927$	−1.54849e8	+	8.94021e7i	−0.194388	+	0.112230i
$928$		0			0
$929$	−3.69889e8	−	2.13555e8i	−0.461343	−	0.266357i	0.251266	−	0.967918i	$-0.419153\pi$
$929$	−3.69889e8	−	2.13555e8i	−0.461343	−	0.266357i	−0.712609	+	0.701562i	$0.752487\pi$
$930$		0			0
$931$	−10291.9	−	917163.i	−1.27539e−5	−	0.00113657i
$932$		0			0
$933$	−3.63034e8	+	6.28793e8i	−0.446994	+	0.774217i
$934$		0			0
$935$	−8.84752e7	−	1.53243e8i	−0.108240	−	0.187477i
$936$		0			0
$937$			1.25555e9i			1.52622i	0.646270	+	0.763108i	$0.276328\pi$
$937$			1.25555e9i			1.52622i	−0.646270	+	0.763108i	$0.723672\pi$
$938$		0			0
$939$	−3.69358e8			−0.446119
$940$		0			0
$941$	1.43136e9	−	8.26398e8i	1.71783	−	0.991791i	0.794983	−	0.606631i	$-0.207480\pi$
$941$	1.43136e9	−	8.26398e8i	1.71783	−	0.991791i	0.922850	−	0.385160i	$-0.125854\pi$
$942$		0			0
$943$	−6.52661e6	−	3.76814e6i	−0.00778310	−	0.00449357i
$944$		0			0
$945$	9.92036e7	−	5.80198e7i	0.117553	−	0.0687512i
$946$		0			0
$947$	8.28343e8	−	1.43473e9i	0.975349	−	1.68935i	0.296572	−	0.955011i	$-0.404157\pi$
$947$	8.28343e8	−	1.43473e9i	0.975349	−	1.68935i	0.678777	−	0.734344i	$-0.262510\pi$
$948$		0			0
$949$	3.52249e6	+	6.10113e6i	0.00412146	+	0.00713857i
$950$		0			0
$951$			4.62966e8i			0.538279i
$952$		0			0
$953$	3.24494e8			0.374911			0.187455	−	0.982273i	$-0.439976\pi$
$953$	3.24494e8			0.374911			0.187455	+	0.982273i	$0.439976\pi$
$954$		0			0
$955$	1.28653e8	−	7.42777e7i	0.147710	−	0.0852802i
$956$		0			0
$957$	−1.40284e8	−	8.09928e7i	−0.160056	−	0.0924082i
$958$		0			0
$959$	−502994.	−	8.96518e7i	−0.000570304	−	0.101649i
$960$		0			0
$961$	4.61616e8	−	7.99542e8i	0.520128	−	0.900889i
$962$		0			0
$963$	−5.60541e7	−	9.70885e7i	−0.0627666	−	0.108715i
$964$		0			0
$965$			8.34577e8i			0.928720i
$966$		0			0
$967$	−6.15365e8			−0.680539			−0.340270	−	0.940328i	$-0.610518\pi$
$967$	−6.15365e8			−0.680539			−0.340270	+	0.940328i	$0.610518\pi$
$968$		0			0
$969$	−540104.	+	311829.i	−0.000593616	+	0.000342724i
$970$		0			0
$971$	5.35519e8	+	3.09182e8i	0.584948	+	0.337720i	0.763097	−	0.646284i	$-0.223678\pi$
$971$	5.35519e8	+	3.09182e8i	0.584948	+	0.337720i	−0.178149	+	0.984003i	$0.557011\pi$
$972$		0			0
$973$	9.52289e7	−	1.67099e8i	0.103379	−	0.181400i
$974$		0			0
$975$	9.57944e6	−	1.65921e7i	0.0103354	−	0.0179014i
$976$		0			0
$977$	−8.44910e8	−	1.46343e9i	−0.905997	−	1.56923i	−0.819573	−	0.572975i	$-0.805789\pi$
$977$	−8.44910e8	−	1.46343e9i	−0.905997	−	1.56923i	−0.0864245	−	0.996258i	$-0.527544\pi$
$978$		0			0
$979$		−	1.31148e8i		−	0.139770i
$980$		0			0
$981$	3.02680e8			0.320610
$982$		0			0
$983$	1.32267e9	−	7.63645e8i	1.39249	−	0.803954i	0.398899	−	0.916995i	$-0.369392\pi$
$983$	1.32267e9	−	7.63645e8i	1.39249	−	0.803954i	0.993590	+	0.113041i	$0.0360591\pi$
$984$		0			0
$985$	−5.17373e8	−	2.98705e8i	−0.541371	−	0.312561i
$986$		0			0
$987$	−7.63457e8	−	4.35089e8i	−0.794023	−	0.452509i
$988$		0			0
$989$	3.44268e6	−	5.96289e6i	0.00355883	−	0.00616408i
$990$		0			0
$991$	8.96688e8	+	1.55311e9i	0.921341	+	1.59581i	0.797343	+	0.603526i	$0.206238\pi$
$991$	8.96688e8	+	1.55311e9i	0.921341	+	1.59581i	0.123998	+	0.992282i	$0.460428\pi$
$992$		0			0
$993$		−	1.26938e8i		−	0.129642i
$994$		0			0
$995$	−5.39568e8			−0.547743
$996$		0			0
$997$	−1.01314e9	+	5.84934e8i	−1.02231	+	0.590230i	−0.914772	−	0.403971i	$-0.867630\pi$
$997$	−1.01314e9	+	5.84934e8i	−1.02231	+	0.590230i	−0.107537	+	0.994201i	$0.534296\pi$
$998$		0			0
$999$	3.18797e7	+	1.84058e7i	0.0319755	+	0.0184611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.h.145.9		24
4.3	odd	2		168.7.z.a.145.9	yes	24
7.3	odd	6	inner	336.7.bh.h.241.9		24
28.3	even	6		168.7.z.a.73.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.7.z.a.73.9	✓	24	28.3	even	6
168.7.z.a.145.9	yes	24	4.3	odd	2
336.7.bh.h.145.9		24	1.1	even	1	trivial
336.7.bh.h.241.9		24	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)

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(76.6020 + 44.2262i) q^{5} +(298.004 + 169.831i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(76.6020 + 44.2262i) q^{5} +(298.004 + 169.831i) q^{7} +(121.500 - 210.444i) q^{9} +(-194.919 - 337.610i) q^{11} +157.546i q^{13} +1378.84 q^{15} +(4444.14 - 2565.83i) q^{17} +(-6.75175 - 3.89813i) q^{19} +(5346.76 - 29.9981i) q^{21} +(-80.9415 + 140.195i) q^{23} +(-3900.59 - 6756.02i) q^{25} -3788.00i q^{27} +26655.6 q^{29} +(36851.7 - 21276.4i) q^{31} +(-5262.82 - 3038.49i) q^{33} +(15316.7 + 26189.0i) q^{35} +(-4858.97 + 8415.98i) q^{37} +(1227.95 + 2126.87i) q^{39} +46553.8i q^{41} -42532.9 q^{43} +(18614.3 - 10747.0i) q^{45} +(-142328. - 82172.9i) q^{47} +(59964.0 + 101221. i) q^{49} +(39997.3 - 69277.3i) q^{51} +(117706. + 203874. i) q^{53} -34482.1i q^{55} -121.532 q^{57} +(-59549.9 + 34381.2i) q^{59} +(323494. + 186769. i) q^{61} +(71947.4 - 42078.8i) q^{63} +(-6967.64 + 12068.3i) q^{65} +(-149388. - 258747. i) q^{67} +2523.51i q^{69} +429798. q^{71} +(38726.1 - 22358.5i) q^{73} +(-105316. - 60804.2i) q^{75} +(-750.197 - 133712. i) q^{77} +(-86568.2 + 149940. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -423270. i q^{83} +453907. q^{85} +(359851. - 207760. i) q^{87} +(291346. + 168209. i) q^{89} +(-26756.1 + 46949.3i) q^{91} +(331666. - 574462. i) q^{93} +(-344.798 - 597.208i) q^{95} +415502. i q^{97} -94730.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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