LMFDB - Embedded newform 336.7.bh.e.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 82x^{6} - 165x^{5} + 5606x^{4} - 7807x^{3} + 102447x^{2} + 132594x + 1162084 $ x^8 - x^7 + 82x^6 - 165x^5 + 5606x^4 - 7807x^3 + 102447x^2 + 132594x + 1162084
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-1.59227 - 2.75789i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.e.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(-181.505 - 104.792i) q^{5} +(223.761 - 259.961i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(-181.505 - 104.792i) q^{5} +(223.761 - 259.961i) q^{7} +(121.500 - 210.444i) q^{9} +(460.778 + 798.091i) q^{11} +1794.79i q^{13} -3267.10 q^{15} +(7212.40 - 4164.08i) q^{17} +(1718.83 + 992.368i) q^{19} +(994.580 - 5253.52i) q^{21} +(5343.69 - 9255.54i) q^{23} +(14150.3 + 24509.1i) q^{25} -3788.00i q^{27} +39717.2 q^{29} +(15848.6 - 9150.17i) q^{31} +(12441.0 + 7182.82i) q^{33} +(-67855.8 + 23736.0i) q^{35} +(29140.0 - 50471.9i) q^{37} +(13989.0 + 24229.6i) q^{39} +73309.8i q^{41} -136517. q^{43} +(-44105.8 + 25464.5i) q^{45} +(20926.0 + 12081.6i) q^{47} +(-17510.7 - 116339. i) q^{49} +(64911.6 - 112430. i) q^{51} +(-12255.9 - 21227.9i) q^{53} -193144. i q^{55} +30939.0 q^{57} +(50090.5 - 28919.8i) q^{59} +(-329986. - 190517. i) q^{61} +(-27520.3 - 78674.6i) q^{63} +(188080. - 325763. i) q^{65} +(-97520.4 - 168910. i) q^{67} -166600. i q^{69} -226460. q^{71} +(-280254. + 161805. i) q^{73} +(382059. + 220582. i) q^{75} +(310577. + 58797.5i) q^{77} +(277989. - 481492. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +529636. i q^{83} -1.74545e6 q^{85} +(536182. - 309565. i) q^{87} +(-41162.6 - 23765.2i) q^{89} +(466575. + 401604. i) q^{91} +(142637. - 247055. i) q^{93} +(-207985. - 360240. i) q^{95} -1.02234e6i q^{97} +223938. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q + 108 * q^3 - 42 * q^5 + 92 * q^7 + 972 * q^9	$ 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9} - 126 q^{11} - 756 q^{15} - 2532 q^{17} - 19998 q^{19} - 5886 q^{21} + 15648 q^{23} + 42698 q^{25} + 129468 q^{29} + 42096 q^{31} - 3402 q^{33} - 73524 q^{35} + 9866 q^{37} - 29106 q^{39} + 71764 q^{43} - 10206 q^{45} - 86988 q^{47} + 314588 q^{49} - 22788 q^{51} + 391710 q^{53} - 359964 q^{57} + 553434 q^{59} - 1009104 q^{61} - 181278 q^{63} + 589452 q^{65} - 229762 q^{67} - 208488 q^{71} - 1249290 q^{73} + 1152846 q^{75} + 1009566 q^{77} - 693808 q^{79} - 236196 q^{81} - 1302600 q^{85} + 1747818 q^{87} - 1414692 q^{89} + 766410 q^{91} + 378864 q^{93} - 3047568 q^{95} - 61236 q^{99}+O(q^{100}) $ 8 * q + 108 * q^3 - 42 * q^5 + 92 * q^7 + 972 * q^9 - 126 * q^11 - 756 * q^15 - 2532 * q^17 - 19998 * q^19 - 5886 * q^21 + 15648 * q^23 + 42698 * q^25 + 129468 * q^29 + 42096 * q^31 - 3402 * q^33 - 73524 * q^35 + 9866 * q^37 - 29106 * q^39 + 71764 * q^43 - 10206 * q^45 - 86988 * q^47 + 314588 * q^49 - 22788 * q^51 + 391710 * q^53 - 359964 * q^57 + 553434 * q^59 - 1009104 * q^61 - 181278 * q^63 + 589452 * q^65 - 229762 * q^67 - 208488 * q^71 - 1249290 * q^73 + 1152846 * q^75 + 1009566 * q^77 - 693808 * q^79 - 236196 * q^81 - 1302600 * q^85 + 1747818 * q^87 - 1414692 * q^89 + 766410 * q^91 + 378864 * q^93 - 3047568 * q^95 - 61236 * 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
$5$	−181.505	−	104.792i	−1.45204	−	0.838338i	−0.453446	−	0.891284i	$-0.649806\pi$
$5$	−181.505	−	104.792i	−1.45204	−	0.838338i	−0.998597	+	0.0529456i	$0.983139\pi$
$6$		0			0
$7$	223.761	−	259.961i	0.652365	−	0.757905i
$7$	223.761	−	259.961i	0.652365	−	0.757905i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	460.778	+	798.091i	0.346189	+	0.599618i	0.985569	−	0.169273i	$-0.0541421\pi$
$11$	460.778	+	798.091i	0.346189	+	0.599618i	−0.639380	+	0.768891i	$0.720809\pi$
$12$		0			0
$13$			1794.79i			0.816926i	0.912775	+	0.408463i	$0.133935\pi$
$13$			1794.79i			0.816926i	−0.912775	+	0.408463i	$0.866065\pi$
$14$		0			0
$15$	−3267.10			−0.968029
$16$		0			0
$17$	7212.40	−	4164.08i	1.46802	−	0.847564i	0.468666	−	0.883376i	$-0.344735\pi$
$17$	7212.40	−	4164.08i	1.46802	−	0.847564i	0.999359	+	0.0358113i	$0.0114015\pi$
$18$		0			0
$19$	1718.83	+	992.368i	0.250595	+	0.144681i	0.620037	−	0.784573i	$-0.287118\pi$
$19$	1718.83	+	992.368i	0.250595	+	0.144681i	−0.369442	+	0.929254i	$0.620451\pi$
$20$		0			0
$21$	994.580	−	5253.52i	0.107394	−	0.567274i
$22$		0			0
$23$	5343.69	−	9255.54i	0.439195	−	0.760708i	−0.558432	−	0.829550i	$-0.688597\pi$
$23$	5343.69	−	9255.54i	0.439195	−	0.760708i	0.997628	+	0.0688416i	$0.0219303\pi$
$24$		0			0
$25$	14150.3	+	24509.1i	0.905621	+	1.56858i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	39717.2			1.62849			0.814244	−	0.580523i	$-0.197152\pi$
$29$	39717.2			1.62849			0.814244	+	0.580523i	$0.197152\pi$
$30$		0			0
$31$	15848.6	−	9150.17i	0.531992	−	0.307145i	−0.209835	−	0.977737i	$-0.567293\pi$
$31$	15848.6	−	9150.17i	0.531992	−	0.307145i	0.741827	+	0.670591i	$0.233960\pi$
$32$		0			0
$33$	12441.0	+	7182.82i	0.346189	+	0.199873i
$34$		0			0
$35$	−67855.8	+	23736.0i	−1.58264	+	0.553608i
$36$		0			0
$37$	29140.0	−	50471.9i	0.575286	−	0.996424i	−0.420725	−	0.907188i	$-0.638224\pi$
$37$	29140.0	−	50471.9i	0.575286	−	0.996424i	0.996011	−	0.0892359i	$-0.0284425\pi$
$38$		0			0
$39$	13989.0	+	24229.6i	0.235826	+	0.408463i
$40$		0			0
$41$			73309.8i			1.06368i	0.846845	+	0.531839i	$0.178499\pi$
$41$			73309.8i			1.06368i	−0.846845	+	0.531839i	$0.821501\pi$
$42$		0			0
$43$	−136517.			−1.71704			−0.858522	−	0.512777i	$-0.828617\pi$
$43$	−136517.			−1.71704			−0.858522	+	0.512777i	$0.828617\pi$
$44$		0			0
$45$	−44105.8	+	25464.5i	−0.484015	+	0.279446i
$46$		0			0
$47$	20926.0	+	12081.6i	0.201554	+	0.116367i	0.597380	−	0.801958i	$-0.296208\pi$
$47$	20926.0	+	12081.6i	0.201554	+	0.116367i	−0.395826	+	0.918326i	$0.629542\pi$
$48$		0			0
$49$	−17510.7	−	116339.i	−0.148839	−	0.988861i
$50$		0			0
$51$	64911.6	−	112430.i	0.489341	−	0.847564i
$52$		0			0
$53$	−12255.9	−	21227.9i	−0.0823225	−	0.142587i	0.821925	−	0.569596i	$-0.192900\pi$
$53$	−12255.9	−	21227.9i	−0.0823225	−	0.142587i	−0.904247	+	0.427010i	$0.859567\pi$
$54$		0			0
$55$		−	193144.i		−	1.16090i
$56$		0			0
$57$	30939.0			0.167063
$58$		0			0
$59$	50090.5	−	28919.8i	0.243893	−	0.140812i	−0.373072	−	0.927803i	$-0.621695\pi$
$59$	50090.5	−	28919.8i	0.243893	−	0.140812i	0.616965	+	0.786991i	$0.288362\pi$
$60$		0			0
$61$	−329986.	−	190517.i	−1.45380	−	0.839354i	−0.455109	−	0.890436i	$-0.650400\pi$
$61$	−329986.	−	190517.i	−1.45380	−	0.839354i	−0.998694	+	0.0510816i	$0.983733\pi$
$62$		0			0
$63$	−27520.3	−	78674.6i	−0.110061	−	0.314639i
$64$		0			0
$65$	188080.	−	325763.i	0.684860	−	1.18621i
$66$		0			0
$67$	−97520.4	−	168910.i	−0.324243	−	0.561606i	0.657116	−	0.753790i	$-0.271776\pi$
$67$	−97520.4	−	168910.i	−0.324243	−	0.561606i	−0.981359	+	0.192184i	$0.938443\pi$
$68$		0			0
$69$		−	166600.i		−	0.507139i
$70$		0			0
$71$	−226460.			−0.632726			−0.316363	−	0.948638i	$-0.602462\pi$
$71$	−226460.			−0.632726			−0.316363	+	0.948638i	$0.602462\pi$
$72$		0			0
$73$	−280254.	+	161805.i	−0.720416	+	0.415933i	−0.814906	−	0.579593i	$-0.803211\pi$
$73$	−280254.	+	161805.i	−0.720416	+	0.415933i	0.0944896	+	0.995526i	$0.469878\pi$
$74$		0			0
$75$	382059.	+	220582.i	0.905621	+	0.522860i
$76$		0			0
$77$	310577.	+	58797.5i	0.680295	+	0.128791i
$78$		0			0
$79$	277989.	−	481492.i	0.563828	−	0.976579i	−0.433329	−	0.901236i	$-0.642661\pi$
$79$	277989.	−	481492.i	0.563828	−	0.976579i	0.997158	−	0.0753436i	$-0.0240053\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			529636.i			0.926281i	0.886285	+	0.463141i	$0.153278\pi$
$83$			529636.i			0.926281i	−0.886285	+	0.463141i	$0.846722\pi$
$84$		0			0
$85$	−1.74545e6			−2.84218
$86$		0			0
$87$	536182.	−	309565.i	0.814244	−	0.470104i
$88$		0			0
$89$	−41162.6	−	23765.2i	−0.0583892	−	0.0337110i	0.470521	−	0.882389i	$-0.344066\pi$
$89$	−41162.6	−	23765.2i	−0.0583892	−	0.0337110i	−0.528910	+	0.848678i	$0.677399\pi$
$90$		0			0
$91$	466575.	+	401604.i	0.619152	+	0.532934i
$92$		0			0
$93$	142637.	−	247055.i	0.177331	−	0.307145i
$94$		0			0
$95$	−207985.	−	360240.i	−0.242583	−	0.420167i
$96$		0			0
$97$		−	1.02234e6i		−	1.12017i	−0.828437	−	0.560083i	$-0.810769\pi$
$97$		−	1.02234e6i		−	1.12017i	0.828437	−	0.560083i	$-0.189231\pi$
$98$		0			0
$99$	223938.			0.230793
$100$		0			0
$101$	543849.	−	313991.i	0.527854	−	0.304757i	−0.212288	−	0.977207i	$-0.568092\pi$
$101$	543849.	−	313991.i	0.527854	−	0.304757i	0.740142	+	0.672450i	$0.234758\pi$
$102$		0			0
$103$	−743176.	−	429073.i	−0.680112	−	0.392663i	0.119785	−	0.992800i	$-0.461779\pi$
$103$	−743176.	−	429073.i	−0.680112	−	0.392663i	−0.799897	+	0.600137i	$0.795113\pi$
$104$		0			0
$105$	−731050.	+	849319.i	−0.631509	+	0.733674i
$106$		0			0
$107$	−755399.	+	1.30839e6i	−0.616630	+	1.06804i	0.373466	+	0.927644i	$0.378169\pi$
$107$	−755399.	+	1.30839e6i	−0.616630	+	1.06804i	−0.990096	+	0.140391i	$0.955164\pi$
$108$		0			0
$109$	1.10063e6	+	1.90635e6i	0.849891	+	1.47205i	0.881305	+	0.472548i	$0.156666\pi$
$109$	1.10063e6	+	1.90635e6i	0.849891	+	1.47205i	−0.0314137	+	0.999506i	$0.510001\pi$
$110$		0			0
$111$		−	908494.i		−	0.664283i
$112$		0			0
$113$	2.31425e6			1.60389			0.801946	−	0.597397i	$-0.203798\pi$
$113$	2.31425e6			1.60389			0.801946	+	0.597397i	$0.203798\pi$
$114$		0			0
$115$	−1.93982e6	+	1.11995e6i	−1.27546	+	0.736388i
$116$		0			0
$117$	377702.	+	218066.i	0.235826	+	0.136154i
$118$		0			0
$119$	531356.	−	2.80671e6i	0.315315	−	1.66554i
$120$		0			0
$121$	461147.	−	798731.i	0.260306	−	0.450863i
$122$		0			0
$123$	571393.	+	989682.i	0.307057	+	0.531839i
$124$		0			0
$125$		−	2.65662e6i		−	1.36019i
$126$		0			0
$127$	1.08748e6			0.530898			0.265449	−	0.964125i	$-0.414480\pi$
$127$	1.08748e6			0.530898			0.265449	+	0.964125i	$0.414480\pi$
$128$		0			0
$129$	−1.84298e6	+	1.06404e6i	−0.858522	+	0.495668i
$130$		0			0
$131$	−2.58564e6	−	1.49282e6i	−1.15015	−	0.664039i	−0.201225	−	0.979545i	$-0.564492\pi$
$131$	−2.58564e6	−	1.49282e6i	−1.15015	−	0.664039i	−0.948923	+	0.315506i	$0.897826\pi$
$132$		0			0
$133$	642585.	−	224776.i	0.273134	−	0.0955422i
$134$		0			0
$135$	−396952.	+	687542.i	−0.161338	+	0.279446i
$136$		0			0
$137$	833850.	+	1.44427e6i	0.324285	+	0.561678i	0.981367	−	0.192141i	$-0.0615431\pi$
$137$	833850.	+	1.44427e6i	0.324285	+	0.561678i	−0.657083	+	0.753819i	$0.728210\pi$
$138$		0			0
$139$		−	3.54942e6i		−	1.32164i	−0.750544	−	0.660820i	$-0.770209\pi$
$139$		−	3.54942e6i		−	1.32164i	0.750544	−	0.660820i	$-0.229791\pi$
$140$		0			0
$141$	376667.			0.134369
$142$		0			0
$143$	−1.43240e6	+	826998.i	−0.489843	+	0.282811i
$144$		0			0
$145$	−7.20888e6	−	4.16205e6i	−2.36463	−	1.36522i
$146$		0			0
$147$	−1.14316e6	−	1.43409e6i	−0.359879	−	0.451465i
$148$		0			0
$149$	2.02935e6	−	3.51494e6i	0.613477	−	1.06257i	−0.377173	−	0.926143i	$-0.623104\pi$
$149$	2.02935e6	−	3.51494e6i	0.613477	−	1.06257i	0.990650	−	0.136430i	$-0.0435630\pi$
$150$		0			0
$151$	−2.76232e6	−	4.78447e6i	−0.802310	−	1.38964i	−0.918092	−	0.396368i	$-0.870271\pi$
$151$	−2.76232e6	−	4.78447e6i	−0.802310	−	1.38964i	0.115782	−	0.993275i	$-0.463063\pi$
$152$		0			0
$153$		−	2.02374e6i		−	0.565043i
$154$		0			0
$155$	−3.83547e6			−1.02997
$156$		0			0
$157$	4.69617e6	−	2.71134e6i	1.21351	−	0.700623i	0.249991	−	0.968248i	$-0.419572\pi$
$157$	4.69617e6	−	2.71134e6i	1.21351	−	0.700623i	0.963523	+	0.267625i	$0.0862390\pi$
$158$		0			0
$159$	−330910.	−	191051.i	−0.0823225	−	0.0475289i
$160$		0			0
$161$	−1.21037e6	−	3.46018e6i	−0.290029	−	0.829128i
$162$		0			0
$163$	1.70824e6	−	2.95875e6i	0.394444	−	0.683197i	−0.598586	−	0.801058i	$-0.704271\pi$
$163$	1.70824e6	−	2.95875e6i	0.394444	−	0.683197i	0.993030	+	0.117862i	$0.0376039\pi$
$164$		0			0
$165$	−1.50541e6	−	2.60744e6i	−0.335122	−	0.580448i
$166$		0			0
$167$		−	8.61704e6i		−	1.85016i	−0.379777	−	0.925078i	$-0.623999\pi$
$167$		−	8.61704e6i		−	1.85016i	0.379777	−	0.925078i	$-0.376001\pi$
$168$		0			0
$169$	1.60555e6			0.332632
$170$		0			0
$171$	417676.	−	241145.i	0.0835317	−	0.0482270i
$172$		0			0
$173$	−4.46734e6	−	2.57922e6i	−0.862801	−	0.498138i	0.00214848	−	0.999998i	$-0.499316\pi$
$173$	−4.46734e6	−	2.57922e6i	−0.862801	−	0.498138i	−0.864949	+	0.501859i	$0.832649\pi$
$174$		0			0
$175$	9.53771e6	+	1.80565e6i	1.77963	+	0.336914i
$176$		0			0
$177$	450815.	−	780834.i	0.0812977	−	0.140812i
$178$		0			0
$179$	4.41115e6	+	7.64034e6i	0.769118	+	1.33215i	0.938042	+	0.346522i	$0.112637\pi$
$179$	4.41115e6	+	7.64034e6i	0.769118	+	1.33215i	−0.168924	+	0.985629i	$0.554029\pi$
$180$		0			0
$181$			6.71665e6i			1.13270i	0.824163	+	0.566352i	$0.191646\pi$
$181$			6.71665e6i			1.13270i	−0.824163	+	0.566352i	$0.808354\pi$
$182$		0			0
$183$	−5.93974e6			−0.969203
$184$		0			0
$185$	−1.05781e7	+	6.10728e6i	−1.67068	+	0.964568i
$186$		0			0
$187$	6.64664e6	+	3.83744e6i	1.01643	+	0.586836i
$188$		0			0
$189$	−984732.	−	847607.i	−0.145859	−	0.125548i
$190$		0			0
$191$	−686211.	+	1.18855e6i	−0.0984822	+	0.170576i	−0.911057	−	0.412281i	$-0.864732\pi$
$191$	−686211.	+	1.18855e6i	−0.0984822	+	0.170576i	0.812574	+	0.582858i	$0.198065\pi$
$192$		0			0
$193$	1.36111e6	+	2.35751e6i	0.189331	+	0.327931i	0.945027	−	0.326991i	$-0.106035\pi$
$193$	1.36111e6	+	2.35751e6i	0.189331	+	0.327931i	−0.755696	+	0.654922i	$0.772701\pi$
$194$		0			0
$195$		−	5.86374e6i		−	0.790808i
$196$		0			0
$197$	−3.38161e6			−0.442308			−0.221154	−	0.975239i	$-0.570982\pi$
$197$	−3.38161e6			−0.442308			−0.221154	+	0.975239i	$0.570982\pi$
$198$		0			0
$199$	−8.34464e6	+	4.81778e6i	−1.05888	+	0.611347i	−0.925123	−	0.379667i	$-0.876039\pi$
$199$	−8.34464e6	+	4.81778e6i	−1.05888	+	0.611347i	−0.133760	+	0.991014i	$0.542705\pi$
$200$		0			0
$201$	−2.63305e6	−	1.52019e6i	−0.324243	−	0.187202i
$202$		0			0
$203$	8.88717e6	−	1.03249e7i	1.06237	−	1.23424i
$204$		0			0
$205$	7.68229e6	−	1.33061e7i	0.891722	−	1.54451i
$206$		0			0
$207$	−1.29852e6	−	2.24910e6i	−0.146398	−	0.253569i
$208$		0			0
$209$			1.82905e6i			0.200348i
$210$		0			0
$211$	−6.59114e6			−0.701638			−0.350819	−	0.936443i	$-0.614097\pi$
$211$	−6.59114e6			−0.701638			−0.350819	+	0.936443i	$0.614097\pi$
$212$		0			0
$213$	−3.05721e6	+	1.76508e6i	−0.316363	+	0.182652i
$214$		0			0
$215$	2.47786e7	+	1.43059e7i	2.49322	+	1.43946i
$216$		0			0
$217$	1.16760e6	−	6.16747e6i	0.114266	−	0.603570i
$218$		0			0
$219$	−2.52229e6	+	4.36873e6i	−0.240139	+	0.415933i
$220$		0			0
$221$	7.47364e6	+	1.29447e7i	0.692397	+	1.19927i
$222$		0			0
$223$			6.24541e6i			0.563178i	0.959535	+	0.281589i	$0.0908615\pi$
$223$			6.24541e6i			0.563178i	−0.959535	+	0.281589i	$0.909138\pi$
$224$		0			0
$225$	6.87706e6			0.603747
$226$		0			0
$227$	−7.03151e6	+	4.05964e6i	−0.601134	+	0.347065i	−0.769487	−	0.638662i	$-0.779488\pi$
$227$	−7.03151e6	+	4.05964e6i	−0.601134	+	0.347065i	0.168354	+	0.985727i	$0.446155\pi$
$228$		0			0
$229$	2.91787e6	+	1.68463e6i	0.242974	+	0.140281i	0.616543	−	0.787321i	$-0.288533\pi$
$229$	2.91787e6	+	1.68463e6i	0.242974	+	0.140281i	−0.373569	+	0.927602i	$0.621866\pi$
$230$		0			0
$231$	4.65107e6	−	1.62694e6i	0.377326	−	0.131989i
$232$		0			0
$233$	821960.	−	1.42368e6i	0.0649805	−	0.112550i	−0.831705	−	0.555218i	$-0.812635\pi$
$233$	821960.	−	1.42368e6i	0.0649805	−	0.112550i	0.896685	+	0.442668i	$0.145968\pi$
$234$		0			0
$235$	−2.53212e6	−	4.38576e6i	−0.195110	−	0.337941i
$236$		0			0
$237$		−	8.66685e6i		−	0.651053i
$238$		0			0
$239$	5.10928e6			0.374254			0.187127	−	0.982336i	$-0.440082\pi$
$239$	5.10928e6			0.374254			0.187127	+	0.982336i	$0.440082\pi$
$240$		0			0
$241$	−1.49250e7	+	8.61698e6i	−1.06626	+	0.615607i	−0.927158	−	0.374670i	$-0.877756\pi$
$241$	−1.49250e7	+	8.61698e6i	−1.06626	+	0.615607i	−0.139105	+	0.990278i	$0.544423\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−9.01308e6	+	2.29511e7i	−0.612879	+	1.56065i
$246$		0			0
$247$	−1.78109e6	+	3.08493e6i	−0.118194	+	0.204718i
$248$		0			0
$249$	4.12810e6	+	7.15008e6i	0.267394	+	0.463141i
$250$		0			0
$251$			576684.i			0.0364684i	0.999834	+	0.0182342i	$0.00580445\pi$
$251$			576684.i			0.0364684i	−0.999834	+	0.0182342i	$0.994196\pi$
$252$		0			0
$253$	9.84902e6			0.608179
$254$		0			0
$255$	−2.35636e7	+	1.36045e7i	−1.42109	+	0.820467i
$256$		0			0
$257$	1.27238e7	+	7.34607e6i	0.749577	+	0.432769i	0.825541	−	0.564342i	$-0.190870\pi$
$257$	1.27238e7	+	7.34607e6i	0.749577	+	0.432769i	−0.0759639	+	0.997111i	$0.524203\pi$
$258$		0			0
$259$	−6.60034e6	−	1.88689e7i	−0.379898	−	1.08604i
$260$		0			0
$261$	4.82564e6	−	8.35825e6i	0.271415	−	0.470104i
$262$		0			0
$263$	−4.02385e6	−	6.96951e6i	−0.221195	−	0.383120i	0.733976	−	0.679175i	$-0.237662\pi$
$263$	−4.02385e6	−	6.96951e6i	−0.221195	−	0.383120i	−0.955171	+	0.296055i	$0.904329\pi$
$264$		0			0
$265$			5.13730e6i			0.276056i
$266$		0			0
$267$	−740926.			−0.0389261
$268$		0			0
$269$	1.85745e7	−	1.07240e7i	0.954246	−	0.550934i	0.0598484	−	0.998207i	$-0.480938\pi$
$269$	1.85745e7	−	1.07240e7i	0.954246	−	0.550934i	0.894397	+	0.447274i	$0.147605\pi$
$270$		0			0
$271$	−1.50184e7	−	8.67088e6i	−0.754598	−	0.435667i	0.0727548	−	0.997350i	$-0.476821\pi$
$271$	−1.50184e7	−	8.67088e6i	−0.754598	−	0.435667i	−0.827353	+	0.561682i	$0.810154\pi$
$272$		0			0
$273$	9.42895e6	+	1.78506e6i	0.463421	+	0.0877333i
$274$		0			0
$275$	−1.30403e7	+	2.25865e7i	−0.627033	+	1.08605i
$276$		0			0
$277$	1.11394e7	+	1.92941e7i	0.524112	+	0.907788i	0.999606	+	0.0280691i	$0.00893583\pi$
$277$	1.11394e7	+	1.92941e7i	0.524112	+	0.907788i	−0.475494	+	0.879719i	$0.657731\pi$
$278$		0			0
$279$		−	4.44698e6i		−	0.204764i
$280$		0			0
$281$	−2.42003e7			−1.09069			−0.545346	−	0.838211i	$-0.683602\pi$
$281$	−2.42003e7			−1.09069			−0.545346	+	0.838211i	$0.683602\pi$
$282$		0			0
$283$	−1.31661e7	+	7.60147e6i	−0.580896	+	0.335381i	−0.761490	−	0.648177i	$-0.775532\pi$
$283$	−1.31661e7	+	7.60147e6i	−0.580896	+	0.335381i	0.180593	+	0.983558i	$0.442198\pi$
$284$		0			0
$285$	−5.61559e6	−	3.24216e6i	−0.242583	−	0.140056i
$286$		0			0
$287$	1.90577e7	+	1.64039e7i	0.806167	+	0.693907i
$288$		0			0
$289$	2.26104e7	−	3.91623e7i	0.936730	−	1.62246i
$290$		0			0
$291$	−7.96839e6	−	1.38017e7i	−0.323364	−	0.560083i
$292$		0			0
$293$		−	1.75547e7i		−	0.697894i	−0.937142	−	0.348947i	$-0.886539\pi$
$293$		−	1.75547e7i		−	0.697894i	0.937142	−	0.348947i	$-0.113461\pi$
$294$		0			0
$295$	−1.21223e7			−0.472191
$296$		0			0
$297$	3.02317e6	−	1.74543e6i	0.115396	−	0.0666242i
$298$		0			0
$299$	1.66117e7	+	9.59078e6i	0.621442	+	0.358790i
$300$		0			0
$301$	−3.05472e7	+	3.54891e7i	−1.12014	+	1.30136i
$302$		0			0
$303$	4.89464e6	−	8.47776e6i	0.175951	−	0.304757i
$304$		0			0
$305$	3.99295e7	+	6.91599e7i	1.40732	+	2.43756i
$306$		0			0
$307$			1.15281e7i			0.398420i	0.979957	+	0.199210i	$0.0638375\pi$
$307$			1.15281e7i			0.398420i	−0.979957	+	0.199210i	$0.936162\pi$
$308$		0			0
$309$	−1.33772e7			−0.453408
$310$		0			0
$311$	2.90011e7	−	1.67438e7i	0.964124	−	0.556637i	0.0666840	−	0.997774i	$-0.478758\pi$
$311$	2.90011e7	−	1.67438e7i	0.964124	−	0.556637i	0.897440	+	0.441137i	$0.145425\pi$
$312$		0			0
$313$	−5.17516e7	−	2.98788e7i	−1.68768	−	0.974385i	−0.956286	−	0.292435i	$-0.905535\pi$
$313$	−5.17516e7	−	2.98788e7i	−1.68768	−	0.974385i	−0.731399	−	0.681950i	$-0.761132\pi$
$314$		0			0
$315$	−3.24939e6	+	1.71638e7i	−0.103961	+	0.549138i
$316$		0			0
$317$	−3.57873e6	+	6.19855e6i	−0.112344	+	0.194586i	−0.916715	−	0.399541i	$-0.869169\pi$
$317$	−3.57873e6	+	6.19855e6i	−0.112344	+	0.194586i	0.804371	+	0.594128i	$0.202503\pi$
$318$		0			0
$319$	1.83008e7	+	3.16979e7i	0.563765	+	0.976470i
$320$		0			0
$321$			2.35510e7i			0.712024i
$322$		0			0
$323$	1.65292e7			0.490506
$324$		0			0
$325$	−4.39886e7	+	2.53968e7i	−1.28141	+	0.739825i
$326$		0			0
$327$	2.97171e7	+	1.71572e7i	0.849891	+	0.490685i
$328$		0			0
$329$	7.82317e6	−	2.73654e6i	0.219682	−	0.0768448i
$330$		0			0
$331$	−1.98576e7	+	3.43944e7i	−0.547574	+	0.948427i	0.450866	+	0.892592i	$0.351115\pi$
$331$	−1.98576e7	+	3.43944e7i	−0.547574	+	0.948427i	−0.998440	+	0.0558348i	$0.982218\pi$
$332$		0			0
$333$	−7.08101e6	−	1.22647e7i	−0.191762	−	0.332141i
$334$		0			0
$335$			4.08775e7i			1.08730i
$336$		0			0
$337$	5.87064e7			1.53390			0.766948	−	0.641710i	$-0.221775\pi$
$337$	5.87064e7			1.53390			0.766948	+	0.641710i	$0.221775\pi$
$338$		0			0
$339$	3.12424e7	−	1.80378e7i	0.801946	−	0.463004i
$340$		0			0
$341$	1.46053e7	+	8.43240e6i	0.368340	+	0.212661i
$342$		0			0
$343$	−3.41618e7	−	2.14800e7i	−0.846560	−	0.532293i
$344$		0			0
$345$	−1.74584e7	+	3.02388e7i	−0.425154	+	0.736388i
$346$		0			0
$347$	1.62185e7	+	2.80912e7i	0.388170	+	0.672330i	0.992203	−	0.124629i	$-0.0397741\pi$
$347$	1.62185e7	+	2.80912e7i	0.388170	+	0.672330i	−0.604034	+	0.796959i	$0.706441\pi$
$348$		0			0
$349$			1.54009e7i			0.362302i	0.983455	+	0.181151i	$0.0579823\pi$
$349$			1.54009e7i			0.362302i	−0.983455	+	0.181151i	$0.942018\pi$
$350$		0			0
$351$	6.79864e6			0.157217
$352$		0			0
$353$	4.08353e7	−	2.35763e7i	0.928350	−	0.535983i	0.0420604	−	0.999115i	$-0.486608\pi$
$353$	4.08353e7	−	2.35763e7i	0.928350	−	0.535983i	0.886289	+	0.463132i	$0.153274\pi$
$354$		0			0
$355$	4.11037e7	+	2.37312e7i	0.918746	+	0.530438i
$356$		0			0
$357$	−1.47028e7	−	4.20321e7i	−0.323143	−	0.923796i
$358$		0			0
$359$	6.82935e6	−	1.18288e7i	0.147603	−	0.255656i	−0.782738	−	0.622351i	$-0.786177\pi$
$359$	6.82935e6	−	1.18288e7i	0.147603	−	0.255656i	0.930341	+	0.366695i	$0.119511\pi$
$360$		0			0
$361$	−2.15534e7	−	3.73315e7i	−0.458135	−	0.793513i
$362$		0			0
$363$		−	1.43772e7i		−	0.300575i
$364$		0			0
$365$	6.78236e7			1.39477
$366$		0			0
$367$	6.56532e7	−	3.79049e7i	1.32818	−	0.766826i	0.343163	−	0.939276i	$-0.388502\pi$
$367$	6.56532e7	−	3.79049e7i	1.32818	−	0.766826i	0.985018	+	0.172450i	$0.0551682\pi$
$368$		0			0
$369$	1.54276e7	+	8.90714e6i	0.307057	+	0.177280i
$370$		0			0
$371$	−8.26083e6	−	1.56391e6i	−0.161771	−	0.0306260i
$372$		0			0
$373$	−3.25829e7	+	5.64352e7i	−0.627860	+	1.08749i	0.360120	+	0.932906i	$0.382736\pi$
$373$	−3.25829e7	+	5.64352e7i	−0.627860	+	1.08749i	−0.987980	+	0.154580i	$0.950598\pi$
$374$		0			0
$375$	−2.07063e7	−	3.58644e7i	−0.392653	−	0.680095i
$376$		0			0
$377$			7.12838e7i			1.33035i
$378$		0			0
$379$	4.57899e6			0.0841109			0.0420555	−	0.999115i	$-0.486609\pi$
$379$	4.57899e6			0.0841109			0.0420555	+	0.999115i	$0.486609\pi$
$380$		0			0
$381$	1.46810e7	−	8.47609e6i	0.265449	−	0.153257i
$382$		0			0
$383$	5.46037e7	+	3.15254e7i	0.971909	+	0.561132i	0.899818	−	0.436266i	$-0.143699\pi$
$383$	5.46037e7	+	3.15254e7i	0.971909	+	0.561132i	0.0720912	+	0.997398i	$0.477033\pi$
$384$		0			0
$385$	−5.02099e7	−	4.32181e7i	−0.879848	−	0.757328i
$386$		0			0
$387$	−1.65868e7	+	2.87292e7i	−0.286174	+	0.495668i
$388$		0			0
$389$	−2.11662e7	−	3.66610e7i	−0.359580	−	0.622810i	0.628311	−	0.777962i	$-0.283747\pi$
$389$	−2.11662e7	−	3.66610e7i	−0.359580	−	0.622810i	−0.987891	+	0.155152i	$0.950413\pi$
$390$		0			0
$391$		−	8.90062e7i		−	1.48898i
$392$		0			0
$393$	−4.65415e7			−0.766766
$394$		0			0
$395$	−1.00913e8	+	5.82622e7i	−1.63741	+	0.945357i
$396$		0			0
$397$	−1.22475e7	−	7.07107e6i	−0.195738	−	0.113009i	0.398928	−	0.916982i	$-0.369382\pi$
$397$	−1.22475e7	−	7.07107e6i	−0.195738	−	0.113009i	−0.594666	+	0.803973i	$0.702716\pi$
$398$		0			0
$399$	6.92294e6	−	8.04293e6i	0.108986	−	0.126618i
$400$		0			0
$401$	3.00770e7	−	5.20949e7i	0.466446	−	0.807908i	−0.532819	−	0.846229i	$-0.678868\pi$
$401$	3.00770e7	−	5.20949e7i	0.466446	−	0.807908i	0.999265	+	0.0383207i	$0.0122008\pi$
$402$		0			0
$403$	1.64226e7	+	2.84448e7i	0.250915	+	0.434598i
$404$		0			0
$405$			1.23758e7i			0.186297i
$406$		0			0
$407$	5.37082e7			0.796632
$408$		0			0
$409$	−3.29559e7	+	1.90271e7i	−0.481685	+	0.278101i	−0.721118	−	0.692812i	$-0.756372\pi$
$409$	−3.29559e7	+	1.90271e7i	−0.481685	+	0.278101i	0.239434	+	0.970913i	$0.423038\pi$
$410$		0			0
$411$	2.25140e7	+	1.29984e7i	0.324285	+	0.187226i
$412$		0			0
$413$	3.69030e6	−	1.94927e7i	0.0523855	−	0.276708i
$414$		0			0
$415$	5.55017e7	−	9.61318e7i	0.776537	−	1.34500i
$416$		0			0
$417$	−2.76650e7	−	4.79172e7i	−0.381525	−	0.660820i
$418$		0			0
$419$			1.11966e8i			1.52211i	0.648690	+	0.761053i	$0.275317\pi$
$419$			1.11966e8i			1.52211i	−0.648690	+	0.761053i	$0.724683\pi$
$420$		0			0
$421$	6.22296e7			0.833970			0.416985	−	0.908913i	$-0.363087\pi$
$421$	6.22296e7			0.833970			0.416985	+	0.908913i	$0.363087\pi$
$422$		0			0
$423$	5.08501e6	−	2.93583e6i	0.0671847	−	0.0387891i
$424$		0			0
$425$	2.04116e8	+	1.17846e8i	2.65895	+	1.53514i
$426$		0			0
$427$	−1.23365e8	+	4.31531e7i	−1.58456	+	0.554279i
$428$		0			0
$429$	−1.28916e7	+	2.23290e7i	−0.163281	+	0.282811i
$430$		0			0
$431$	−6.79249e7	−	1.17649e8i	−0.848394	−	1.46946i	−0.882641	−	0.470047i	$-0.844237\pi$
$431$	−6.79249e7	−	1.17649e8i	−0.848394	−	1.46946i	0.0342477	−	0.999413i	$-0.489096\pi$
$432$		0			0
$433$		−	4.12757e7i		−	0.508430i	−0.967148	−	0.254215i	$-0.918183\pi$
$433$		−	4.12757e7i		−	0.508430i	0.967148	−	0.254215i	$-0.0818171\pi$
$434$		0			0
$435$	−1.29760e8			−1.57642
$436$		0			0
$437$	1.83698e7	−	1.06058e7i	0.220120	−	0.127087i
$438$		0			0
$439$	−9.91802e7	−	5.72617e7i	−1.17228	−	0.676816i	−0.218064	−	0.975934i	$-0.569974\pi$
$439$	−9.91802e7	−	5.72617e7i	−1.17228	−	0.676816i	−0.954216	+	0.299118i	$0.903308\pi$
$440$		0			0
$441$	−2.66103e7	−	1.04501e7i	−0.310266	−	0.121844i
$442$		0			0
$443$	−6.30057e7	+	1.09129e8i	−0.724717	+	1.25525i	0.234373	+	0.972147i	$0.424696\pi$
$443$	−6.30057e7	+	1.09129e8i	−0.724717	+	1.25525i	−0.959090	+	0.283100i	$0.908637\pi$
$444$		0			0
$445$	4.98082e6	+	8.62703e6i	0.0565224	+	0.0978997i
$446$		0			0
$447$		−	6.32689e7i		−	0.708382i
$448$		0			0
$449$	−4.74196e7			−0.523864			−0.261932	−	0.965086i	$-0.584360\pi$
$449$	−4.74196e7			−0.523864			−0.261932	+	0.965086i	$0.584360\pi$
$450$		0			0
$451$	−5.85079e7	+	3.37795e7i	−0.637800	+	0.368234i
$452$		0			0
$453$	−7.45825e7	−	4.30602e7i	−0.802310	−	0.463214i
$454$		0			0
$455$	−4.26009e7	−	1.21787e8i	−0.452257	−	1.29290i
$456$		0			0
$457$	2.42944e7	−	4.20792e7i	0.254541	−	0.440878i	−0.710230	−	0.703970i	$-0.751409\pi$
$457$	2.42944e7	−	4.20792e7i	0.254541	−	0.440878i	0.964771	+	0.263092i	$0.0847422\pi$
$458$		0			0
$459$	−1.57735e7	−	2.73205e7i	−0.163114	−	0.282521i
$460$		0			0
$461$			1.47655e7i			0.150712i	0.997157	+	0.0753558i	$0.0240092\pi$
$461$			1.47655e7i			0.150712i	−0.997157	+	0.0753558i	$0.975991\pi$
$462$		0			0
$463$	1.02866e8			1.03640			0.518200	−	0.855259i	$-0.326602\pi$
$463$	1.02866e8			1.03640			0.518200	+	0.855259i	$0.326602\pi$
$464$		0			0
$465$	−5.17788e7	+	2.98945e7i	−0.514983	+	0.297326i
$466$		0			0
$467$	−1.19585e8	−	6.90423e7i	−1.17415	−	0.677899i	−0.219500	−	0.975613i	$-0.570443\pi$
$467$	−1.19585e8	−	6.90423e7i	−1.17415	−	0.677899i	−0.954655	+	0.297714i	$0.903776\pi$
$468$		0			0
$469$	−6.57314e7	−	1.24441e7i	−0.637169	−	0.120627i
$470$		0			0
$471$	4.22655e7	−	7.32060e7i	0.404505	−	0.700623i
$472$		0			0
$473$	−6.29041e7	−	1.08953e8i	−0.594423	−	1.02957i
$474$		0			0
$475$			5.61693e7i			0.524105i
$476$		0			0
$477$	−5.95638e6			−0.0548816
$478$		0			0
$479$	5.88901e6	−	3.40002e6i	0.0535841	−	0.0309368i	−0.472969	−	0.881079i	$-0.656818\pi$
$479$	5.88901e6	−	3.40002e6i	0.0535841	−	0.0309368i	0.526553	+	0.850142i	$0.323484\pi$
$480$		0			0
$481$	9.05862e7	+	5.23000e7i	0.814005	+	0.469966i
$482$		0			0
$483$	−4.33095e7	−	3.72786e7i	−0.384363	−	0.330840i
$484$		0			0
$485$	−1.07134e8	+	1.85561e8i	−0.939077	+	1.62653i
$486$		0			0
$487$	3.76363e7	+	6.51879e7i	0.325851	+	0.564391i	0.981684	−	0.190515i	$-0.0610157\pi$
$487$	3.76363e7	+	6.51879e7i	0.325851	+	0.564391i	−0.655833	+	0.754906i	$0.727682\pi$
$488$		0			0
$489$		−	5.32575e7i		−	0.455465i
$490$		0			0
$491$	1.92123e8			1.62306			0.811532	−	0.584308i	$-0.198634\pi$
$491$	1.92123e8			1.62306			0.811532	+	0.584308i	$0.198634\pi$
$492$		0			0
$493$	2.86456e8	−	1.65386e8i	2.39066	−	1.38025i
$494$		0			0
$495$	−4.06460e7	−	2.34670e7i	−0.335122	−	0.193483i
$496$		0			0
$497$	−5.06729e7	+	5.88707e7i	−0.412769	+	0.479546i
$498$		0			0
$499$	7.28568e7	−	1.26192e8i	0.586366	−	1.01561i	−0.408338	−	0.912831i	$-0.633892\pi$
$499$	7.28568e7	−	1.26192e8i	0.586366	−	1.01561i	0.994704	−	0.102784i	$-0.0327751\pi$
$500$		0			0
$501$	−6.71631e7	−	1.16330e8i	−0.534094	−	0.925078i
$502$		0			0
$503$			1.82561e8i			1.43451i	0.696812	+	0.717254i	$0.254601\pi$
$503$			1.82561e8i			1.43451i	−0.696812	+	0.717254i	$0.745399\pi$
$504$		0			0
$505$	−1.31615e8			−1.02196
$506$		0			0
$507$	2.16750e7	−	1.25140e7i	0.166316	−	0.0960227i
$508$		0			0
$509$	1.05246e8	+	6.07636e7i	0.798088	+	0.460776i	0.842802	−	0.538224i	$-0.180904\pi$
$509$	1.05246e8	+	6.07636e7i	0.798088	+	0.460776i	−0.0447143	+	0.999000i	$0.514238\pi$
$510$		0			0
$511$	−2.06471e7	+	1.09061e8i	−0.154737	+	0.817347i
$512$		0			0
$513$	3.75908e6	−	6.51093e6i	0.0278439	−	0.0482270i
$514$		0			0
$515$	8.99271e7	+	1.55758e8i	0.658368	+	1.14033i
$516$		0			0
$517$			2.22678e7i			0.161141i
$518$		0			0
$519$	−8.04121e7			−0.575200
$520$		0			0
$521$	−6.06815e7	+	3.50345e7i	−0.429085	+	0.247732i	−0.698957	−	0.715164i	$-0.746352\pi$
$521$	−6.06815e7	+	3.50345e7i	−0.429085	+	0.247732i	0.269872	+	0.962896i	$0.413019\pi$
$522$		0			0
$523$	−1.09457e8	−	6.31947e7i	−0.765132	−	0.441749i	0.0660031	−	0.997819i	$-0.478975\pi$
$523$	−1.09457e8	−	6.31947e7i	−0.765132	−	0.441749i	−0.831135	+	0.556070i	$0.812309\pi$
$524$		0			0
$525$	1.42833e8	−	4.99628e7i	0.987074	−	0.345278i
$526$		0			0
$527$	7.62041e7	−	1.31989e8i	0.520651	−	0.901794i
$528$		0			0
$529$	1.69079e7	+	2.92854e7i	0.114215	+	0.197826i
$530$		0			0
$531$		−	1.40550e7i		−	0.0938745i
$532$		0			0
$533$	−1.31575e8			−0.868946
$534$		0			0
$535$	2.74218e8	−	1.58320e8i	1.79075	−	1.03389i
$536$		0			0
$537$	1.19101e8	+	6.87630e7i	0.769118	+	0.444050i
$538$		0			0
$539$	8.47802e7	−	6.75814e7i	0.541412	−	0.431580i
$540$		0			0
$541$	−1.47236e7	+	2.55020e7i	−0.0929869	+	0.161058i	−0.908767	−	0.417305i	$-0.862975\pi$
$541$	−1.47236e7	+	2.55020e7i	−0.0929869	+	0.161058i	0.815780	+	0.578363i	$0.196308\pi$
$542$		0			0
$543$	5.23511e7	+	9.06747e7i	0.326984	+	0.566352i
$544$		0			0
$545$		−	4.61351e8i		−	2.84998i
$546$		0			0
$547$	2.00583e7			0.122555			0.0612777	−	0.998121i	$-0.480482\pi$
$547$	2.00583e7			0.122555			0.0612777	+	0.998121i	$0.480482\pi$
$548$		0			0
$549$	−8.01866e7	+	4.62957e7i	−0.484601	+	0.279785i
$550$		0			0
$551$	6.82671e7	+	3.94140e7i	0.408091	+	0.235611i
$552$		0			0
$553$	−6.29659e7	−	1.80006e8i	−0.372332	−	1.06441i
$554$		0			0
$555$	−9.52031e7	+	1.64897e8i	−0.556893	+	0.964568i
$556$		0			0
$557$	−6.02294e7	−	1.04320e8i	−0.348532	−	0.603676i	0.637457	−	0.770486i	$-0.279987\pi$
$557$	−6.02294e7	−	1.04320e8i	−0.348532	−	0.603676i	−0.985989	+	0.166810i	$0.946653\pi$
$558$		0			0
$559$		−	2.45019e8i		−	1.40270i
$560$		0			0
$561$	1.19639e8			0.677619
$562$		0			0
$563$	1.59791e8	−	9.22556e7i	0.895423	−	0.516973i	0.0197104	−	0.999806i	$-0.493726\pi$
$563$	1.59791e8	−	9.22556e7i	0.895423	−	0.516973i	0.875712	+	0.482833i	$0.160392\pi$
$564$		0			0
$565$	−4.20049e8	−	2.42516e8i	−2.32892	−	1.34460i
$566$		0			0
$567$	−1.99003e7	−	3.76746e6i	−0.109172	−	0.0206681i
$568$		0			0
$569$	−9.00390e7	+	1.55952e8i	−0.488758	+	0.846554i	−0.999916	−	0.0129327i	$-0.995883\pi$
$569$	−9.00390e7	+	1.55952e8i	−0.488758	+	0.846554i	0.511158	+	0.859487i	$0.329217\pi$
$570$		0			0
$571$	−1.50724e8	−	2.61062e8i	−0.809609	−	1.40228i	−0.913135	−	0.407657i	$-0.866346\pi$
$571$	−1.50724e8	−	2.61062e8i	−0.809609	−	1.40228i	0.103527	−	0.994627i	$-0.466987\pi$
$572$		0			0
$573$			2.13940e7i			0.113717i
$574$		0			0
$575$	3.02460e8			1.59098
$576$		0			0
$577$	−3.88168e7	+	2.24109e7i	−0.202066	+	0.116663i	−0.597619	−	0.801780i	$-0.703886\pi$
$577$	−3.88168e7	+	2.24109e7i	−0.202066	+	0.116663i	0.395553	+	0.918443i	$0.370553\pi$
$578$		0			0
$579$	3.67500e7	+	2.12176e7i	0.189331	+	0.109310i
$580$		0			0
$581$	1.37685e8	+	1.18512e8i	0.702033	+	0.604274i
$582$		0			0
$583$	1.12945e7	−	1.95627e7i	0.0569983	−	0.0987240i
$584$		0			0
$585$	−4.57033e7	−	7.91605e7i	−0.228287	−	0.395404i
$586$		0			0
$587$		−	2.88473e8i		−	1.42623i	−0.701045	−	0.713117i	$-0.747283\pi$
$587$		−	2.88473e8i		−	1.42623i	0.701045	−	0.713117i	$-0.252717\pi$
$588$		0			0
$589$	3.63213e7			0.177753
$590$		0			0
$591$	−4.56517e7	+	2.63570e7i	−0.221154	+	0.127683i
$592$		0			0
$593$	2.25115e8	+	1.29970e8i	1.07954	+	0.623275i	0.930773	−	0.365597i	$-0.119135\pi$
$593$	2.25115e8	+	1.29970e8i	1.07954	+	0.623275i	0.148770	+	0.988872i	$0.452468\pi$
$594$		0			0
$595$	−3.90565e8	+	4.53751e8i	−1.85414	+	2.15410i
$596$		0			0
$597$	−7.51017e7	+	1.30080e8i	−0.352961	+	0.611347i
$598$		0			0
$599$	−4.84290e7	−	8.38815e7i	−0.225333	−	0.390289i	0.731086	−	0.682285i	$-0.239014\pi$
$599$	−4.84290e7	−	8.38815e7i	−0.225333	−	0.390289i	−0.956419	+	0.291997i	$0.905680\pi$
$600$		0			0
$601$			9.67065e7i			0.445484i	0.974877	+	0.222742i	$0.0715008\pi$
$601$			9.67065e7i			0.445484i	−0.974877	+	0.222742i	$0.928499\pi$
$602$		0			0
$603$	−4.73949e7			−0.216162
$604$		0			0
$605$	−1.67402e8	+	9.66493e7i	−0.755951	+	0.436448i
$606$		0			0
$607$	−1.33896e8	−	7.73047e7i	−0.598688	−	0.345652i	0.169837	−	0.985472i	$-0.445676\pi$
$607$	−1.33896e8	−	7.73047e7i	−0.598688	−	0.345652i	−0.768525	+	0.639820i	$0.779009\pi$
$608$		0			0
$609$	3.95019e7	−	2.08655e8i	0.174890	−	0.923798i
$610$		0			0
$611$	−2.16839e7	+	3.75576e7i	−0.0950635	+	0.164655i
$612$		0			0
$613$	−3.80409e7	−	6.58887e7i	−0.165146	−	0.286042i	0.771561	−	0.636155i	$-0.219476\pi$
$613$	−3.80409e7	−	6.58887e7i	−0.165146	−	0.286042i	−0.936707	+	0.350114i	$0.886143\pi$
$614$		0			0
$615$		−	2.39510e8i		−	1.02967i
$616$		0			0
$617$	−1.44709e7			−0.0616085			−0.0308043	−	0.999525i	$-0.509807\pi$
$617$	−1.44709e7			−0.0616085			−0.0308043	+	0.999525i	$0.509807\pi$
$618$		0			0
$619$	−3.92476e8	+	2.26596e8i	−1.65478	+	0.955389i	−0.679717	+	0.733475i	$0.737897\pi$
$619$	−3.92476e8	+	2.26596e8i	−1.65478	+	0.955389i	−0.975066	+	0.221914i	$0.928769\pi$
$620$		0			0
$621$	−3.50599e7	−	2.02419e7i	−0.146398	−	0.0845232i
$622$		0			0
$623$	−1.53886e7	+	5.38294e6i	−0.0636408	+	0.0222615i
$624$		0			0
$625$	−5.72943e7	+	9.92366e7i	−0.234677	+	0.406473i
$626$		0			0
$627$	1.42560e7	+	2.46921e7i	0.0578356	+	0.100174i
$628$		0			0
$629$		−	4.85365e8i		−	1.95037i
$630$		0			0
$631$	−2.83654e8			−1.12902			−0.564508	−	0.825428i	$-0.690934\pi$
$631$	−2.83654e8			−1.12902			−0.564508	+	0.825428i	$0.690934\pi$
$632$		0			0
$633$	−8.89804e7	+	5.13728e7i	−0.350819	+	0.202545i
$634$		0			0
$635$	−1.97384e8	−	1.13960e8i	−0.770887	−	0.445072i
$636$		0			0
$637$	2.08803e8	−	3.14280e7i	0.807826	−	0.121590i
$638$		0			0
$639$	−2.75148e7	+	4.76571e7i	−0.105454	+	0.182652i
$640$		0			0
$641$	1.86195e7	+	3.22500e7i	0.0706960	+	0.122449i	0.899207	−	0.437524i	$-0.144145\pi$
$641$	1.86195e7	+	3.22500e7i	0.0706960	+	0.122449i	−0.828511	+	0.559973i	$0.810811\pi$
$642$		0			0
$643$		−	1.57727e7i		−	0.0593297i	−0.999560	−	0.0296648i	$-0.990556\pi$
$643$		−	1.57727e7i		−	0.0593297i	0.999560	−	0.0296648i	$-0.00944399\pi$
$644$		0			0
$645$	4.46015e8			1.66215
$646$		0			0
$647$	4.25974e7	−	2.45936e7i	0.157279	−	0.0908049i	−0.419295	−	0.907850i	$-0.637723\pi$
$647$	4.25974e7	−	2.45936e7i	0.157279	−	0.0908049i	0.576574	+	0.817045i	$0.304389\pi$
$648$		0			0
$649$	4.61613e7	+	2.66512e7i	0.168867	+	0.0974951i
$650$		0			0
$651$	−3.23080e7	−	9.23614e7i	−0.117103	−	0.334771i
$652$		0			0
$653$	−9.52792e7	+	1.65028e8i	−0.342183	+	0.592678i	−0.984838	−	0.173477i	$-0.944500\pi$
$653$	−9.52792e7	+	1.65028e8i	−0.342183	+	0.592678i	0.642655	+	0.766156i	$0.277833\pi$
$654$		0			0
$655$	3.12872e8	+	5.41910e8i	1.11338	+	1.92843i
$656$		0			0
$657$			7.86372e7i			0.277288i
$658$		0			0
$659$	2.19319e8			0.766338			0.383169	−	0.923678i	$-0.374833\pi$
$659$	2.19319e8			0.766338			0.383169	+	0.923678i	$0.374833\pi$
$660$		0			0
$661$	−1.48603e8	+	8.57963e7i	−0.514547	+	0.297074i	−0.734701	−	0.678392i	$-0.762677\pi$
$661$	−1.48603e8	+	8.57963e7i	−0.514547	+	0.297074i	0.220154	+	0.975465i	$0.429344\pi$
$662$		0			0
$663$	2.01788e8	+	1.16502e8i	0.692397	+	0.399756i
$664$		0			0
$665$	−1.40188e8	−	2.65398e7i	−0.476699	−	0.0902471i
$666$		0			0
$667$	2.12236e8	−	3.67604e8i	0.715224	−	1.23880i
$668$		0			0
$669$	4.86781e7	+	8.43130e7i	0.162576	+	0.281589i
$670$		0			0
$671$		−	3.51145e8i		−	1.16230i
$672$		0			0
$673$	3.97407e8			1.30374			0.651869	−	0.758332i	$-0.273985\pi$
$673$	3.97407e8			1.30374			0.651869	+	0.758332i	$0.273985\pi$
$674$		0			0
$675$	9.28403e7	−	5.36014e7i	0.301874	−	0.174287i
$676$		0			0
$677$	1.13243e8	+	6.53809e7i	0.364960	+	0.210710i	0.671254	−	0.741227i	$-0.265756\pi$
$677$	1.13243e8	+	6.53809e7i	0.364960	+	0.210710i	−0.306294	+	0.951937i	$0.599089\pi$
$678$		0			0
$679$	−2.65770e8	−	2.28761e8i	−0.848979	−	0.730757i
$680$		0			0
$681$	−6.32836e7	+	1.09610e8i	−0.200378	+	0.347065i
$682$		0			0
$683$	1.22907e8	+	2.12882e8i	0.385759	+	0.668154i	0.991874	−	0.127223i	$-0.0406063\pi$
$683$	1.22907e8	+	2.12882e8i	0.385759	+	0.668154i	−0.606115	+	0.795377i	$0.707273\pi$
$684$		0			0
$685$		−	3.49524e8i		−	1.08744i
$686$		0			0
$687$	5.25216e7			0.161983
$688$		0			0
$689$	3.80995e7	−	2.19968e7i	0.116483	−	0.0672513i
$690$		0			0
$691$	−2.21758e8	−	1.28032e8i	−0.672116	−	0.388046i	0.124762	−	0.992187i	$-0.460183\pi$
$691$	−2.21758e8	−	1.28032e8i	−0.672116	−	0.388046i	−0.796878	+	0.604140i	$0.793517\pi$
$692$		0			0
$693$	5.01087e7	−	5.82153e7i	0.150561	−	0.174919i
$694$		0			0
$695$	−3.71952e8	+	6.44240e8i	−1.10798	+	1.91908i
$696$		0			0
$697$	3.05268e8	+	5.28740e8i	0.901536	+	1.56151i
$698$		0			0
$699$		−	2.56262e7i		−	0.0750330i
$700$		0			0
$701$	3.67117e7			0.106574			0.0532869	−	0.998579i	$-0.483030\pi$
$701$	3.67117e7			0.106574			0.0532869	+	0.998579i	$0.483030\pi$
$702$		0			0
$703$	1.00173e8	−	5.78351e7i	0.288328	−	0.166466i
$704$		0			0
$705$	−6.83672e7	−	3.94718e7i	−0.195110	−	0.112647i
$706$		0			0
$707$	4.00667e7	−	2.11639e8i	0.113377	−	0.598876i
$708$		0			0
$709$	5.84664e7	−	1.01267e8i	0.164047	−	0.284137i	−0.772270	−	0.635295i	$-0.780879\pi$
$709$	5.84664e7	−	1.01267e8i	0.164047	−	0.284137i	0.936316	+	0.351158i	$0.114212\pi$
$710$		0			0
$711$	−6.75514e7	−	1.17002e8i	−0.187943	−	0.325526i
$712$		0			0
$713$		−	1.95583e8i		−	0.539587i
$714$		0			0
$715$	3.46652e8			0.948365
$716$		0			0
$717$	6.89753e7	−	3.98229e7i	0.187127	−	0.108038i
$718$		0			0
$719$	−2.27783e8	−	1.31511e8i	−0.612823	−	0.353813i	0.161247	−	0.986914i	$-0.448449\pi$
$719$	−2.27783e8	−	1.31511e8i	−0.612823	−	0.353813i	−0.774069	+	0.633101i	$0.781782\pi$
$720$		0			0
$721$	−2.77837e8	+	9.71871e7i	−0.741282	+	0.259300i
$722$		0			0
$723$	−1.34325e8	+	2.32658e8i	−0.355421	+	0.615607i
$724$		0			0
$725$	5.62011e8	+	9.73432e8i	1.47479	+	2.55441i
$726$		0			0
$727$		−	4.25452e7i		−	0.110726i	−0.998466	−	0.0553628i	$-0.982368\pi$
$727$		−	4.25452e7i		−	0.110726i	0.998466	−	0.0553628i	$-0.0176315\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−9.84616e8	+	5.68468e8i	−2.52066	+	1.45531i
$732$		0			0
$733$	−2.07737e8	−	1.19937e8i	−0.527475	−	0.304538i	0.212513	−	0.977158i	$-0.431835\pi$
$733$	−2.07737e8	−	1.19937e8i	−0.527475	−	0.304538i	−0.739988	+	0.672621i	$0.765169\pi$
$734$		0			0
$735$	5.72093e7	+	3.80090e8i	0.144080	+	0.957247i
$736$		0			0
$737$	8.98705e7	−	1.55660e8i	0.224499	−	0.388844i
$738$		0			0
$739$	3.43587e8	+	5.95110e8i	0.851340	+	1.47456i	0.879999	+	0.474975i	$0.157543\pi$
$739$	3.43587e8	+	5.95110e8i	0.851340	+	1.47456i	−0.0286595	+	0.999589i	$0.509124\pi$
$740$		0			0
$741$			5.55288e7i			0.136478i
$742$		0			0
$743$	7.22022e8			1.76029			0.880145	−	0.474705i	$-0.157445\pi$
$743$	7.22022e8			1.76029			0.880145	+	0.474705i	$0.157445\pi$
$744$		0			0
$745$	−7.36676e8	+	4.25320e8i	−1.78159	+	1.02860i
$746$		0			0
$747$	1.11459e8	+	6.43507e7i	0.267394	+	0.154380i
$748$		0			0
$749$	1.71102e8	+	4.89141e8i	0.407201	+	1.16410i
$750$		0			0
$751$	1.18653e8	−	2.05513e8i	0.280129	−	0.485198i	−0.691287	−	0.722580i	$-0.742956\pi$
$751$	1.18653e8	−	2.05513e8i	0.280129	−	0.485198i	0.971416	+	0.237382i	$0.0762894\pi$
$752$		0			0
$753$	4.49481e6	+	7.78523e6i	0.0105275	+	0.0182342i
$754$		0			0
$755$			1.15788e9i			2.69043i
$756$		0			0
$757$	4.51958e8			1.04186			0.520931	−	0.853599i	$-0.325585\pi$
$757$	4.51958e8			1.04186			0.520931	+	0.853599i	$0.325585\pi$
$758$		0			0
$759$	1.32962e8	−	7.67655e7i	0.304090	−	0.175566i
$760$		0			0
$761$	2.47772e8	+	1.43051e8i	0.562210	+	0.324592i	0.754032	−	0.656837i	$-0.228106\pi$
$761$	2.47772e8	+	1.43051e8i	0.562210	+	0.324592i	−0.191822	+	0.981430i	$0.561440\pi$
$762$		0			0
$763$	7.41857e8	+	1.40446e8i	1.67012	+	0.316181i
$764$		0			0
$765$	−2.12073e8	+	3.67321e8i	−0.473697	+	0.820467i
$766$		0			0
$767$	5.19048e7	+	8.99018e7i	0.115033	+	0.199243i
$768$		0			0
$769$			8.53791e8i			1.87747i	0.344642	+	0.938734i	$0.388000\pi$
$769$			8.53791e8i			1.87747i	−0.344642	+	0.938734i	$0.612000\pi$
$770$		0			0
$771$	2.29028e8			0.499718
$772$		0			0
$773$	3.74548e8	−	2.16245e8i	0.810902	−	0.468175i	−0.0363669	−	0.999339i	$-0.511578\pi$
$773$	3.74548e8	−	2.16245e8i	0.810902	−	0.468175i	0.847269	+	0.531164i	$0.178245\pi$
$774$		0			0
$775$	4.48525e8	+	2.58956e8i	0.963565	+	0.556315i
$776$		0			0
$777$	−2.36173e8	−	2.03286e8i	−0.503463	−	0.433355i
$778$		0			0
$779$	−7.27502e7	+	1.26007e8i	−0.153894	+	0.266552i
$780$		0			0
$781$	−1.04348e8	−	1.80735e8i	−0.219043	−	0.379394i
$782$		0			0
$783$		−	1.50448e8i		−	0.313403i
$784$		0			0
$785$	−1.13651e9			−2.34943
$786$		0			0
$787$	2.78457e8	−	1.60767e8i	0.571260	−	0.329817i	−0.186392	−	0.982475i	$-0.559680\pi$
$787$	2.78457e8	−	1.60767e8i	0.571260	−	0.329817i	0.757653	+	0.652658i	$0.226346\pi$
$788$		0			0
$789$	−1.08644e8	−	6.27256e7i	−0.221195	−	0.127707i
$790$		0			0
$791$	5.17840e8	−	6.01616e8i	1.04632	−	1.21560i
$792$		0			0
$793$	3.41938e8	−	5.92254e8i	0.685690	−	1.18765i
$794$		0			0
$795$	4.00413e7	+	6.93536e7i	0.0796906	+	0.138028i
$796$		0			0
$797$		−	7.05947e8i		−	1.39443i	−0.716861	−	0.697216i	$-0.754422\pi$
$797$		−	7.05947e8i		−	1.39443i	0.716861	−	0.697216i	$-0.245578\pi$
$798$		0			0
$799$	2.01235e8			0.394515
$800$		0			0
$801$	−1.00025e7	+	5.77495e6i	−0.0194631	+	0.0112370i
$802$		0			0
$803$	−2.58270e8	−	1.49112e8i	−0.498801	−	0.287983i
$804$		0			0
$805$	−1.42911e8	+	7.54880e8i	−0.273955	+	1.44707i
$806$		0			0
$807$	1.67170e8	−	2.89548e8i	0.318082	−	0.550934i
$808$		0			0
$809$	−7.67123e7	−	1.32870e8i	−0.144884	−	0.250946i	0.784446	−	0.620197i	$-0.212947\pi$
$809$	−7.67123e7	−	1.32870e8i	−0.144884	−	0.250946i	−0.929330	+	0.369251i	$0.879614\pi$
$810$		0			0
$811$		−	3.23998e8i		−	0.607407i	−0.952767	−	0.303704i	$-0.901777\pi$
$811$		−	3.23998e8i		−	0.607407i	0.952767	−	0.303704i	$-0.0982233\pi$
$812$		0			0
$813$	−2.70331e8			−0.503065
$814$		0			0
$815$	−6.20109e8	+	3.58020e8i	−1.14550	+	0.661355i
$816$		0			0
$817$	−2.34650e8	−	1.35475e8i	−0.430283	−	0.248424i
$818$		0			0
$819$	1.41204e8	−	4.93931e7i	0.257037	−	0.0899114i
$820$		0			0
$821$	−3.54738e8	+	6.14424e8i	−0.641030	+	1.11030i	0.344174	+	0.938906i	$0.388159\pi$
$821$	−3.54738e8	+	6.14424e8i	−0.641030	+	1.11030i	−0.985203	+	0.171390i	$0.945174\pi$
$822$		0			0
$823$	3.37680e8	+	5.84879e8i	0.605768	+	1.04922i	0.991930	+	0.126789i	$0.0404672\pi$
$823$	3.37680e8	+	5.84879e8i	0.605768	+	1.04922i	−0.386162	+	0.922431i	$0.626199\pi$
$824$		0			0
$825$			4.06557e8i			0.724035i
$826$		0			0
$827$	−6.68754e8			−1.18236			−0.591180	−	0.806540i	$-0.701338\pi$
$827$	−6.68754e8			−1.18236			−0.591180	+	0.806540i	$0.701338\pi$
$828$		0			0
$829$	1.58225e8	−	9.13510e7i	0.277722	−	0.160343i	−0.354670	−	0.934992i	$-0.615407\pi$
$829$	1.58225e8	−	9.13510e7i	0.277722	−	0.160343i	0.632392	+	0.774649i	$0.282073\pi$
$830$		0			0
$831$	3.00765e8	+	1.73647e8i	0.524112	+	0.302596i
$832$		0			0
$833$	−6.10738e8	−	7.66164e8i	−1.05662	−	1.32552i
$834$		0			0
$835$	−9.02998e8	+	1.56404e9i	−1.55106	+	2.68651i
$836$		0			0
$837$	−3.46608e7	−	6.00343e7i	−0.0591102	−	0.102382i
$838$		0			0
$839$		−	8.94089e8i		−	1.51389i	−0.653477	−	0.756946i	$-0.726690\pi$
$839$		−	8.94089e8i		−	1.51389i	0.653477	−	0.756946i	$-0.273310\pi$
$840$		0			0
$841$	9.82631e8			1.65197
$842$		0			0
$843$	−3.26704e8	+	1.88623e8i	−0.545346	+	0.314856i
$844$		0			0
$845$	−2.91417e8	−	1.68250e8i	−0.482997	−	0.278858i
$846$		0			0
$847$	−1.04452e8	−	2.98606e8i	−0.171897	−	0.491414i
$848$		0			0
$849$	−1.18495e8	+	2.05240e8i	−0.193632	+	0.335381i
$850$		0			0
$851$	−3.11430e8	−	5.39412e8i	−0.505326	−	0.875250i
$852$		0			0
$853$		−	1.10048e9i		−	1.77311i	−0.462621	−	0.886556i	$-0.653091\pi$
$853$		−	1.10048e9i		−	1.77311i	0.462621	−	0.886556i	$-0.346909\pi$
$854$		0			0
$855$	−1.01081e8			−0.161722
$856$		0			0
$857$	4.37624e8	−	2.52663e8i	0.695279	−	0.401419i	−0.110308	−	0.993897i	$-0.535184\pi$
$857$	4.37624e8	−	2.52663e8i	0.695279	−	0.401419i	0.805587	+	0.592478i	$0.201850\pi$
$858$		0			0
$859$	4.38236e8	+	2.53016e8i	0.691399	+	0.399179i	0.804136	−	0.594445i	$-0.202628\pi$
$859$	4.38236e8	+	2.53016e8i	0.691399	+	0.399179i	−0.112737	+	0.993625i	$0.535962\pi$
$860$		0			0
$861$	3.85135e8	+	7.29124e7i	0.603397	+	0.114233i
$862$		0			0
$863$	−2.25163e8	+	3.89994e8i	−0.350320	+	0.606771i	−0.986305	−	0.164929i	$-0.947260\pi$
$863$	−2.25163e8	+	3.89994e8i	−0.350320	+	0.606771i	0.635986	+	0.771701i	$0.280594\pi$
$864$		0			0
$865$	5.40564e8	+	9.36285e8i	0.835216	+	1.44664i
$866$		0			0
$867$		−	7.04922e8i		−	1.08164i
$868$		0			0
$869$	5.12366e8			0.780766
$870$		0			0
$871$	3.03158e8	−	1.75028e8i	0.458790	−	0.264883i
$872$		0			0
$873$	−2.15147e8	−	1.24215e8i	−0.323364	−	0.186694i
$874$		0			0
$875$	−6.90618e8	−	5.94449e8i	−1.03089	−	0.887340i
$876$		0			0
$877$	−5.79576e8	+	1.00386e9i	−0.859235	+	1.48824i	0.0134246	+	0.999910i	$0.495727\pi$
$877$	−5.79576e8	+	1.00386e9i	−0.859235	+	1.48824i	−0.872660	+	0.488329i	$0.837607\pi$
$878$		0			0
$879$	−1.36825e8	−	2.36988e8i	−0.201465	−	0.348947i
$880$		0			0
$881$		−	3.06547e8i		−	0.448300i	−0.974555	−	0.224150i	$-0.928039\pi$
$881$		−	3.06547e8i		−	0.448300i	0.974555	−	0.224150i	$-0.0719606\pi$
$882$		0			0
$883$	−1.52518e8			−0.221533			−0.110767	−	0.993846i	$-0.535331\pi$
$883$	−1.52518e8			−0.221533			−0.110767	+	0.993846i	$0.535331\pi$
$884$		0			0
$885$	−1.63651e8	+	9.44838e7i	−0.236096	+	0.136310i
$886$		0			0
$887$	−3.21672e8	−	1.85717e8i	−0.460938	−	0.266122i	0.251501	−	0.967857i	$-0.419076\pi$
$887$	−3.21672e8	−	1.85717e8i	−0.460938	−	0.266122i	−0.712438	+	0.701735i	$0.752409\pi$
$888$		0			0
$889$	2.43337e8	−	2.82703e8i	0.346340	−	0.402370i
$890$		0			0
$891$	2.72085e7	−	4.71265e7i	0.0384655	−	0.0666242i
$892$		0			0
$893$	2.39788e7	+	4.15325e7i	0.0336723	+	0.0583222i
$894$		0			0
$895$		−	1.84902e9i		−	2.57912i
$896$		0			0
$897$	2.99011e8			0.414295
$898$		0			0
$899$	6.29460e8	−	3.63419e8i	0.866342	−	0.500183i
$900$		0			0
$901$	−1.76789e8	−	1.02069e8i	−0.241703	−	0.139547i
$902$		0			0
$903$	−1.35777e8	+	7.17195e8i	−0.184401	+	0.974034i
$904$		0			0
$905$	7.03852e8	−	1.21911e9i	0.949589	−	1.64474i
$906$		0			0
$907$	−1.42050e7	−	2.46038e7i	−0.0190379	−	0.0329746i	0.856349	−	0.516397i	$-0.172727\pi$
$907$	−1.42050e7	−	2.46038e7i	−0.0190379	−	0.0329746i	−0.875387	+	0.483422i	$0.839394\pi$
$908$		0			0
$909$		−	1.52600e8i		−	0.203171i
$910$		0			0
$911$	−6.83478e6			−0.00904002			−0.00452001	−	0.999990i	$-0.501439\pi$
$911$	−6.83478e6			−0.00904002			−0.00452001	+	0.999990i	$0.501439\pi$
$912$		0			0
$913$	−4.22698e8	+	2.44045e8i	−0.555415	+	0.320669i
$914$		0			0
$915$	1.07810e9	+	6.22439e8i	1.40732	+	0.812519i
$916$		0			0
$917$	−9.66641e8	+	3.38131e8i	−1.25360	+	0.438507i
$918$		0			0
$919$	−4.42907e8	+	7.67138e8i	−0.570646	+	0.988387i	0.425854	+	0.904792i	$0.359974\pi$
$919$	−4.42907e8	+	7.67138e8i	−0.570646	+	0.988387i	−0.996500	+	0.0835954i	$0.973360\pi$
$920$		0			0
$921$	8.98523e7	+	1.55629e8i	0.115014	+	0.199210i
$922$		0			0
$923$		−	4.06447e8i		−	0.516890i
$924$		0			0
$925$	1.64936e9			2.08396
$926$		0			0
$927$	−1.80592e8	+	1.04265e8i	−0.226704	+	0.130888i
$928$		0			0
$929$	−5.94674e8	−	3.43335e8i	−0.741706	−	0.428224i	0.0809836	−	0.996715i	$-0.474194\pi$
$929$	−5.94674e8	−	3.43335e8i	−0.741706	−	0.428224i	−0.822689	+	0.568492i	$0.807527\pi$
$930$		0			0
$931$	8.53526e7	−	2.17343e8i	0.105771	−	0.269338i
$932$		0			0
$933$	2.61010e8	−	4.52082e8i	0.321375	−	0.556637i
$934$		0			0
$935$	−8.04267e8	−	1.39303e9i	−0.983933	−	1.70422i
$936$		0			0
$937$			3.64827e8i			0.443474i	0.975107	+	0.221737i	$0.0711727\pi$
$937$			3.64827e8i			0.443474i	−0.975107	+	0.221737i	$0.928827\pi$
$938$		0			0
$939$	−9.31530e8			−1.12512
$940$		0			0
$941$	2.72677e8	−	1.57430e8i	0.327250	−	0.188938i	−0.327369	−	0.944896i	$-0.606162\pi$
$941$	2.72677e8	−	1.57430e8i	0.327250	−	0.188938i	0.654620	+	0.755958i	$0.272829\pi$
$942$		0			0
$943$	6.78521e8	+	3.91745e8i	0.809149	+	0.467162i
$944$		0			0
$945$	8.99117e7	+	2.57038e8i	0.106542	+	0.304580i
$946$		0			0
$947$	−6.59511e8	+	1.14231e9i	−0.776555	+	1.34503i	0.157362	+	0.987541i	$0.449701\pi$
$947$	−6.59511e8	+	1.14231e9i	−0.776555	+	1.34503i	−0.933917	+	0.357491i	$0.883632\pi$
$948$		0			0
$949$	−2.90405e8	−	5.02996e8i	−0.339786	−	0.588527i
$950$		0			0
$951$			1.11574e8i			0.129724i
$952$		0			0
$953$	1.45853e9			1.68514			0.842570	−	0.538587i	$-0.181042\pi$
$953$	1.45853e9			1.68514			0.842570	+	0.538587i	$0.181042\pi$
$954$		0			0
$955$	2.49102e8	−	1.43819e8i	0.286001	−	0.165123i
$956$		0			0
$957$	4.94122e8	+	2.85281e8i	0.563765	+	0.325490i
$958$		0			0
$959$	5.62038e8	+	1.06403e8i	0.637250	+	0.120642i
$960$		0			0
$961$	−2.76301e8	+	4.78567e8i	−0.311323	+	0.539228i
$962$		0			0
$963$	1.83562e8	+	3.17939e8i	0.205543	+	0.356012i
$964$		0			0
$965$		−	5.70536e8i		−	0.634893i
$966$		0			0
$967$	1.14158e8			0.126249			0.0631243	−	0.998006i	$-0.479894\pi$
$967$	1.14158e8			0.126249			0.0631243	+	0.998006i	$0.479894\pi$
$968$		0			0
$969$	2.23144e8	−	1.28832e8i	0.245253	−	0.141597i
$970$		0			0
$971$	−2.39718e8	−	1.38401e8i	−0.261844	−	0.151176i	0.363331	−	0.931660i	$-0.381639\pi$
$971$	−2.39718e8	−	1.38401e8i	−0.261844	−	0.151176i	−0.625176	+	0.780484i	$0.714973\pi$
$972$		0			0
$973$	−9.22712e8	−	7.94223e8i	−1.00168	−	0.862192i
$974$		0			0
$975$	−3.95897e8	+	6.85714e8i	−0.427138	+	0.739825i
$976$		0			0
$977$	1.28667e8	+	2.22858e8i	0.137970	+	0.238970i	0.926728	−	0.375733i	$-0.122609\pi$
$977$	1.28667e8	+	2.22858e8i	0.137970	+	0.238970i	−0.788758	+	0.614703i	$0.789276\pi$
$978$		0			0
$979$		−	4.38020e7i		−	0.0466816i
$980$		0			0
$981$	5.34908e8			0.566594
$982$		0			0
$983$	−4.69243e8	+	2.70917e8i	−0.494012	+	0.285218i	−0.726237	−	0.687444i	$-0.758733\pi$
$983$	−4.69243e8	+	2.70917e8i	−0.494012	+	0.285218i	0.232226	+	0.972662i	$0.425399\pi$
$984$		0			0
$985$	6.13781e8	+	3.54366e8i	0.642250	+	0.370803i
$986$		0			0
$987$	8.42836e7	−	9.79189e7i	0.0876580	−	0.101839i
$988$		0			0
$989$	−7.29504e8	+	1.26354e9i	−0.754117	+	1.30617i
$990$		0			0
$991$	−3.53479e8	−	6.12243e8i	−0.363197	−	0.629076i	0.625288	−	0.780394i	$-0.284982\pi$
$991$	−3.53479e8	−	6.12243e8i	−0.363197	−	0.629076i	−0.988485	+	0.151318i	$0.951648\pi$
$992$		0			0
$993$			6.19099e8i			0.632284i
$994$		0			0
$995$	2.01946e9			2.05006
$996$		0			0
$997$	1.41068e9	−	8.14455e8i	1.42345	−	0.821829i	0.426858	−	0.904319i	$-0.359620\pi$
$997$	1.41068e9	−	8.14455e8i	1.42345	−	0.821829i	0.996592	+	0.0824896i	$0.0262871\pi$
$998$		0			0
$999$	−1.91187e8	−	1.10382e8i	−0.191762	−	0.110714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.e.145.1		8
4.3	odd	2		84.7.m.a.61.1	✓	8
7.3	odd	6	inner	336.7.bh.e.241.1		8
12.11	even	2		252.7.z.d.145.4		8
28.3	even	6		84.7.m.a.73.1	yes	8
28.11	odd	6		588.7.m.c.325.4		8
28.19	even	6		588.7.d.b.97.5		8
28.23	odd	6		588.7.d.b.97.4		8
28.27	even	2		588.7.m.c.313.4		8
84.59	odd	6		252.7.z.d.73.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.7.m.a.61.1	✓	8	4.3	odd	2
84.7.m.a.73.1	yes	8	28.3	even	6
252.7.z.d.73.4		8	84.59	odd	6
252.7.z.d.145.4		8	12.11	even	2
336.7.bh.e.145.1		8	1.1	even	1	trivial
336.7.bh.e.241.1		8	7.3	odd	6	inner
588.7.d.b.97.4		8	28.23	odd	6
588.7.d.b.97.5		8	28.19	even	6
588.7.m.c.313.4		8	28.27	even	2
588.7.m.c.325.4		8	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(-181.505 - 104.792i) q^{5} +(223.761 - 259.961i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(-181.505 - 104.792i) q^{5} +(223.761 - 259.961i) q^{7} +(121.500 - 210.444i) q^{9} +(460.778 + 798.091i) q^{11} +1794.79i q^{13} -3267.10 q^{15} +(7212.40 - 4164.08i) q^{17} +(1718.83 + 992.368i) q^{19} +(994.580 - 5253.52i) q^{21} +(5343.69 - 9255.54i) q^{23} +(14150.3 + 24509.1i) q^{25} -3788.00i q^{27} +39717.2 q^{29} +(15848.6 - 9150.17i) q^{31} +(12441.0 + 7182.82i) q^{33} +(-67855.8 + 23736.0i) q^{35} +(29140.0 - 50471.9i) q^{37} +(13989.0 + 24229.6i) q^{39} +73309.8i q^{41} -136517. q^{43} +(-44105.8 + 25464.5i) q^{45} +(20926.0 + 12081.6i) q^{47} +(-17510.7 - 116339. i) q^{49} +(64911.6 - 112430. i) q^{51} +(-12255.9 - 21227.9i) q^{53} -193144. i q^{55} +30939.0 q^{57} +(50090.5 - 28919.8i) q^{59} +(-329986. - 190517. i) q^{61} +(-27520.3 - 78674.6i) q^{63} +(188080. - 325763. i) q^{65} +(-97520.4 - 168910. i) q^{67} -166600. i q^{69} -226460. q^{71} +(-280254. + 161805. i) q^{73} +(382059. + 220582. i) q^{75} +(310577. + 58797.5i) q^{77} +(277989. - 481492. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +529636. i q^{83} -1.74545e6 q^{85} +(536182. - 309565. i) q^{87} +(-41162.6 - 23765.2i) q^{89} +(466575. + 401604. i) q^{91} +(142637. - 247055. i) q^{93} +(-207985. - 360240. i) q^{95} -1.02234e6i q^{97} +223938. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q + 108 * q^3 - 42 * q^5 + 92 * q^7 + 972 * q^9	\( 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9} - 126 q^{11} - 756 q^{15} - 2532 q^{17} - 19998 q^{19} - 5886 q^{21} + 15648 q^{23} + 42698 q^{25} + 129468 q^{29} + 42096 q^{31} - 3402 q^{33} - 73524 q^{35} + 9866 q^{37} - 29106 q^{39} + 71764 q^{43} - 10206 q^{45} - 86988 q^{47} + 314588 q^{49} - 22788 q^{51} + 391710 q^{53} - 359964 q^{57} + 553434 q^{59} - 1009104 q^{61} - 181278 q^{63} + 589452 q^{65} - 229762 q^{67} - 208488 q^{71} - 1249290 q^{73} + 1152846 q^{75} + 1009566 q^{77} - 693808 q^{79} - 236196 q^{81} - 1302600 q^{85} + 1747818 q^{87} - 1414692 q^{89} + 766410 q^{91} + 378864 q^{93} - 3047568 q^{95} - 61236 q^{99}+O(q^{100}) \) 8 * q + 108 * q^3 - 42 * q^5 + 92 * q^7 + 972 * q^9 - 126 * q^11 - 756 * q^15 - 2532 * q^17 - 19998 * q^19 - 5886 * q^21 + 15648 * q^23 + 42698 * q^25 + 129468 * q^29 + 42096 * q^31 - 3402 * q^33 - 73524 * q^35 + 9866 * q^37 - 29106 * q^39 + 71764 * q^43 - 10206 * q^45 - 86988 * q^47 + 314588 * q^49 - 22788 * q^51 + 391710 * q^53 - 359964 * q^57 + 553434 * q^59 - 1009104 * q^61 - 181278 * q^63 + 589452 * q^65 - 229762 * q^67 - 208488 * q^71 - 1249290 * q^73 + 1152846 * q^75 + 1009566 * q^77 - 693808 * q^79 - 236196 * q^81 - 1302600 * q^85 + 1747818 * q^87 - 1414692 * q^89 + 766410 * q^91 + 378864 * q^93 - 3047568 * q^95 - 61236 * q^99

Introduction

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