LMFDB - Embedded newform 336.7.bh.c.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 33x^{6} + 2x^{5} + 701x^{4} - 28x^{3} + 6468x^{2} + 5488x + 38416 $ x^8 - 2x^7 + 33x^6 + 2x^5 + 701x^4 - 28x^3 + 6468x^2 + 5488*x + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$-1.36222 - 2.35944i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.c.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 + 7.79423i) q^{3} +(41.1897 + 23.7809i) q^{5} +(138.771 + 313.674i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 + 7.79423i) q^{3} +(41.1897 + 23.7809i) q^{5} +(138.771 + 313.674i) q^{7} +(121.500 - 210.444i) q^{9} +(287.168 + 497.389i) q^{11} -2477.37i q^{13} -741.415 q^{15} +(6318.50 - 3647.99i) q^{17} +(-8325.02 - 4806.45i) q^{19} +(-4318.26 - 3152.99i) q^{21} +(-6998.35 + 12121.5i) q^{23} +(-6681.44 - 11572.6i) q^{25} +3788.00i q^{27} -7401.31 q^{29} +(43120.6 - 24895.7i) q^{31} +(-7753.53 - 4476.50i) q^{33} +(-1743.52 + 16220.3i) q^{35} +(-20228.6 + 35037.0i) q^{37} +(19309.2 + 33444.5i) q^{39} -36045.4i q^{41} -16173.6 q^{43} +(10009.1 - 5778.76i) q^{45} +(-57960.8 - 33463.7i) q^{47} +(-79134.2 + 87057.8i) q^{49} +(-56866.5 + 98495.7i) q^{51} +(-40003.9 - 69288.8i) q^{53} +27316.4i q^{55} +149850. q^{57} +(149123. - 86096.5i) q^{59} +(89903.0 + 51905.5i) q^{61} +(82871.6 + 8907.87i) q^{63} +(58914.1 - 102042. i) q^{65} +(-81131.3 - 140524. i) q^{67} -218187. i q^{69} -522124. q^{71} +(78658.7 - 45413.6i) q^{73} +(180399. + 104153. i) q^{75} +(-116168. + 159100. i) q^{77} +(235695. - 408235. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -361308. i q^{83} +347010. q^{85} +(99917.7 - 57687.5i) q^{87} +(706142. + 407691. i) q^{89} +(777088. - 343787. i) q^{91} +(-388086. + 672184. i) q^{93} +(-228603. - 395953. i) q^{95} -1.50721e6i q^{97} +139563. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9} - 2058 q^{11} - 3780 q^{15} - 11244 q^{17} - 21834 q^{19} - 4482 q^{21} - 15504 q^{23} - 6550 q^{25} + 35316 q^{29} + 51060 q^{31} + 55566 q^{33} - 71460 q^{35} + 20282 q^{37} + 101682 q^{39} - 387812 q^{43} + 51030 q^{45} + 55212 q^{47} - 277780 q^{49} + 101196 q^{51} - 336174 q^{53} + 393012 q^{57} + 560454 q^{59} + 850728 q^{61} - 26730 q^{63} + 826380 q^{65} + 947882 q^{67} - 147192 q^{71} - 533034 q^{73} + 176850 q^{75} - 1848102 q^{77} + 6260 q^{79} - 236196 q^{81} + 560040 q^{85} - 476766 q^{87} + 413460 q^{89} - 256074 q^{91} - 459540 q^{93} + 170880 q^{95} - 1000188 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9 - 2058 * q^11 - 3780 * q^15 - 11244 * q^17 - 21834 * q^19 - 4482 * q^21 - 15504 * q^23 - 6550 * q^25 + 35316 * q^29 + 51060 * q^31 + 55566 * q^33 - 71460 * q^35 + 20282 * q^37 + 101682 * q^39 - 387812 * q^43 + 51030 * q^45 + 55212 * q^47 - 277780 * q^49 + 101196 * q^51 - 336174 * q^53 + 393012 * q^57 + 560454 * q^59 + 850728 * q^61 - 26730 * q^63 + 826380 * q^65 + 947882 * q^67 - 147192 * q^71 - 533034 * q^73 + 176850 * q^75 - 1848102 * q^77 + 6260 * q^79 - 236196 * q^81 + 560040 * q^85 - 476766 * q^87 + 413460 * q^89 - 256074 * q^91 - 459540 * q^93 + 170880 * q^95 - 1000188 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$		0			0
$5$	41.1897	+	23.7809i	0.329518	+	0.190247i	0.655627	−	0.755085i	$-0.272404\pi$
$5$	41.1897	+	23.7809i	0.329518	+	0.190247i	−0.326109	+	0.945332i	$0.605738\pi$
$6$		0			0
$7$	138.771	+	313.674i	0.404580	+	0.914502i
$7$	138.771	+	313.674i	0.404580	+	0.914502i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	287.168	+	497.389i	0.215753	+	0.373696i	0.953505	−	0.301376i	$-0.0974460\pi$
$11$	287.168	+	497.389i	0.215753	+	0.373696i	−0.737752	+	0.675072i	$0.764113\pi$
$12$		0			0
$13$		−	2477.37i		−	1.12762i	−0.825906	−	0.563808i	$-0.809336\pi$
$13$		−	2477.37i		−	1.12762i	0.825906	−	0.563808i	$-0.190664\pi$
$14$		0			0
$15$	−741.415			−0.219678
$16$		0			0
$17$	6318.50	−	3647.99i	1.28608	−	0.742518i	0.308126	−	0.951346i	$-0.400298\pi$
$17$	6318.50	−	3647.99i	1.28608	−	0.742518i	0.977952	+	0.208828i	$0.0669649\pi$
$18$		0			0
$19$	−8325.02	−	4806.45i	−1.21374	−	0.700751i	−0.250165	−	0.968203i	$-0.580485\pi$
$19$	−8325.02	−	4806.45i	−1.21374	−	0.700751i	−0.963571	+	0.267452i	$0.913818\pi$
$20$		0			0
$21$	−4318.26	−	3152.99i	−0.466284	−	0.340459i
$22$		0			0
$23$	−6998.35	+	12121.5i	−0.575191	+	0.996261i	0.420829	+	0.907140i	$0.361739\pi$
$23$	−6998.35	+	12121.5i	−0.575191	+	0.996261i	−0.996021	+	0.0891209i	$0.971594\pi$
$24$		0			0
$25$	−6681.44	−	11572.6i	−0.427612	−	0.740646i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	−7401.31			−0.303469			−0.151735	−	0.988421i	$-0.548486\pi$
$29$	−7401.31			−0.303469			−0.151735	+	0.988421i	$0.548486\pi$
$30$		0			0
$31$	43120.6	−	24895.7i	1.44744	−	0.835679i	0.449110	−	0.893477i	$-0.351741\pi$
$31$	43120.6	−	24895.7i	1.44744	−	0.835679i	0.998328	+	0.0577978i	$0.0184079\pi$
$32$		0			0
$33$	−7753.53	−	4476.50i	−0.215753	−	0.124565i
$34$		0			0
$35$	−1743.52	+	16220.3i	−0.0406651	+	0.378315i
$36$		0			0
$37$	−20228.6	+	35037.0i	−0.399357	+	0.691707i	−0.993647	−	0.112544i	$-0.964100\pi$
$37$	−20228.6	+	35037.0i	−0.399357	+	0.691707i	0.594290	+	0.804251i	$0.297433\pi$
$38$		0			0
$39$	19309.2	+	33444.5i	0.325515	+	0.563808i
$40$		0			0
$41$		−	36045.4i		−	0.522996i	−0.965204	−	0.261498i	$-0.915784\pi$
$41$		−	36045.4i		−	0.522996i	0.965204	−	0.261498i	$-0.0842164\pi$
$42$		0			0
$43$	−16173.6			−0.203424			−0.101712	−	0.994814i	$-0.532432\pi$
$43$	−16173.6			−0.203424			−0.101712	+	0.994814i	$0.532432\pi$
$44$		0			0
$45$	10009.1	−	5778.76i	0.109839	−	0.0634157i
$46$		0			0
$47$	−57960.8	−	33463.7i	−0.558265	−	0.322315i	0.194184	−	0.980965i	$-0.437794\pi$
$47$	−57960.8	−	33463.7i	−0.558265	−	0.322315i	−0.752449	+	0.658651i	$0.771128\pi$
$48$		0			0
$49$	−79134.2	+	87057.8i	−0.672630	+	0.739979i
$50$		0			0
$51$	−56866.5	+	98495.7i	−0.428693	+	0.742518i
$52$		0			0
$53$	−40003.9	−	69288.8i	−0.268705	−	0.465410i	0.699823	−	0.714316i	$-0.253262\pi$
$53$	−40003.9	−	69288.8i	−0.268705	−	0.465410i	−0.968528	+	0.248906i	$0.919929\pi$
$54$		0			0
$55$			27316.4i			0.164186i
$56$		0			0
$57$	149850.			0.809158
$58$		0			0
$59$	149123.	−	86096.5i	0.726089	−	0.419208i	−0.0909006	−	0.995860i	$-0.528975\pi$
$59$	149123.	−	86096.5i	0.726089	−	0.419208i	0.816990	+	0.576652i	$0.195641\pi$
$60$		0			0
$61$	89903.0	+	51905.5i	0.396082	+	0.228678i	0.684792	−	0.728739i	$-0.259893\pi$
$61$	89903.0	+	51905.5i	0.396082	+	0.228678i	−0.288710	+	0.957417i	$0.593226\pi$
$62$		0			0
$63$	82871.6	+	8907.87i	0.331424	+	0.0356248i
$64$		0			0
$65$	58914.1	−	102042.i	0.214526	−	0.371569i
$66$		0			0
$67$	−81131.3	−	140524.i	−0.269752	−	0.467224i	0.699046	−	0.715077i	$-0.253608\pi$
$67$	−81131.3	−	140524.i	−0.269752	−	0.467224i	−0.968798	+	0.247853i	$0.920275\pi$
$68$		0			0
$69$		−	218187.i		−	0.664174i
$70$		0			0
$71$	−522124.			−1.45881			−0.729404	−	0.684083i	$-0.760203\pi$
$71$	−522124.			−1.45881			−0.729404	+	0.684083i	$0.760203\pi$
$72$		0			0
$73$	78658.7	−	45413.6i	0.202199	−	0.116739i	−0.395482	−	0.918474i	$-0.629422\pi$
$73$	78658.7	−	45413.6i	0.202199	−	0.116739i	0.597681	+	0.801734i	$0.296089\pi$
$74$		0			0
$75$	180399.	+	104153.i	0.427612	+	0.246882i
$76$		0			0
$77$	−116168.	+	159100.i	−0.254456	+	0.348497i
$78$		0			0
$79$	235695.	−	408235.i	0.478045	−	0.827998i	−0.521638	−	0.853167i	$-0.674679\pi$
$79$	235695.	−	408235.i	0.478045	−	0.827998i	0.999683	+	0.0251685i	$0.00801223\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	361308.i		−	0.631893i	−0.948777	−	0.315946i	$-0.897678\pi$
$83$		−	361308.i		−	0.631893i	0.948777	−	0.315946i	$-0.102322\pi$
$84$		0			0
$85$	347010.			0.565047
$86$		0			0
$87$	99917.7	−	57687.5i	0.151735	−	0.0876040i
$88$		0			0
$89$	706142.	+	407691.i	1.00166	+	0.578311i	0.908740	−	0.417362i	$-0.137045\pi$
$89$	706142.	+	407691.i	1.00166	+	0.578311i	0.0929238	+	0.995673i	$0.470379\pi$
$90$		0			0
$91$	777088.	−	343787.i	1.03121	−	0.456211i
$92$		0			0
$93$	−388086.	+	672184.i	−0.482479	+	0.835679i
$94$		0			0
$95$	−228603.	−	395953.i	−0.266632	−	0.461820i
$96$		0			0
$97$		−	1.50721e6i		−	1.65142i	−0.564096	−	0.825709i	$-0.690775\pi$
$97$		−	1.50721e6i		−	1.65142i	0.564096	−	0.825709i	$-0.309225\pi$
$98$		0			0
$99$	139563.			0.143836
$100$		0			0
$101$	−846.700	+	488.842i	−0.000821799	+	0.000474466i	−0.500411	−	0.865788i	$-0.666818\pi$
$101$	−846.700	+	488.842i	−0.000821799	+	0.000474466i	0.499589	+	0.866263i	$0.333484\pi$
$102$		0			0
$103$	1.19079e6	+	687505.i	1.08975	+	0.629165i	0.933509	−	0.358555i	$-0.116730\pi$
$103$	1.19079e6	+	687505.i	1.08975	+	0.629165i	0.156236	+	0.987720i	$0.450064\pi$
$104$		0			0
$105$	−102887.	−	232563.i	−0.0888776	−	0.200897i
$106$		0			0
$107$	1.21858e6	−	2.11065e6i	0.994728	−	1.72292i	0.408555	−	0.912734i	$-0.366033\pi$
$107$	1.21858e6	−	2.11065e6i	0.994728	−	1.72292i	0.586173	−	0.810186i	$-0.300634\pi$
$108$		0			0
$109$	47120.8	+	81615.5i	0.0363859	+	0.0630222i	0.883645	−	0.468158i	$-0.155082\pi$
$109$	47120.8	+	81615.5i	0.0363859	+	0.0630222i	−0.847259	+	0.531180i	$0.821749\pi$
$110$		0			0
$111$		−	630666.i		−	0.461138i
$112$		0			0
$113$	2.32811e6			1.61350			0.806749	−	0.590895i	$-0.201225\pi$
$113$	2.32811e6			1.61350			0.806749	+	0.590895i	$0.201225\pi$
$114$		0			0
$115$	−576520.	+	332854.i	−0.379072	+	0.218857i
$116$		0			0
$117$	−521348.	−	301001.i	−0.325515	−	0.187936i
$118$		0			0
$119$	2.02111e6	+	1.47572e6i	1.19936	+	0.875714i
$120$		0			0
$121$	720850.	−	1.24855e6i	0.406901	−	0.704773i
$122$		0			0
$123$	280946.	+	486613.i	0.150976	+	0.261498i
$124$		0			0
$125$		−	1.37872e6i		−	0.705902i
$126$		0			0
$127$	−1.05302e6			−0.514072			−0.257036	−	0.966402i	$-0.582746\pi$
$127$	−1.05302e6			−0.514072			−0.257036	+	0.966402i	$0.582746\pi$
$128$		0			0
$129$	218344.	−	126061.i	0.101712	−	0.0587234i
$130$		0			0
$131$	−1.04088e6	−	600955.i	−0.463008	−	0.267318i	0.250300	−	0.968168i	$-0.419471\pi$
$131$	−1.04088e6	−	600955.i	−0.463008	−	0.267318i	−0.713308	+	0.700850i	$0.752804\pi$
$132$		0			0
$133$	352389.	−	3.27834e6i	0.149785	−	1.39348i
$134$		0			0
$135$	−90081.9	+	156026.i	−0.0366131	+	0.0634157i
$136$		0			0
$137$	1.91465e6	+	3.31626e6i	0.744607	+	1.28970i	0.950378	+	0.311096i	$0.100696\pi$
$137$	1.91465e6	+	3.31626e6i	0.744607	+	1.28970i	−0.205772	+	0.978600i	$0.565970\pi$
$138$		0			0
$139$			4.72037e6i			1.75765i	0.477146	+	0.878824i	$0.341671\pi$
$139$			4.72037e6i			1.75765i	−0.477146	+	0.878824i	$0.658329\pi$
$140$		0			0
$141$	1.04329e6			0.372177
$142$		0			0
$143$	1.23222e6	−	711421.i	0.421385	−	0.243287i
$144$		0			0
$145$	−304858.	−	176010.i	−0.0999985	−	0.0577341i
$146$		0			0
$147$	389763.	−	1.79207e6i	0.122701	−	0.564161i
$148$		0			0
$149$	2.84892e6	−	4.93448e6i	0.861235	−	1.49170i	−0.00950308	−	0.999955i	$-0.503025\pi$
$149$	2.84892e6	−	4.93448e6i	0.861235	−	1.49170i	0.870738	−	0.491748i	$-0.163642\pi$
$150$		0			0
$151$	−2.07120e6	−	3.58742e6i	−0.601576	−	1.04196i	−0.992583	−	0.121572i	$-0.961207\pi$
$151$	−2.07120e6	−	3.58742e6i	−0.601576	−	1.04196i	0.391007	−	0.920388i	$-0.372127\pi$
$152$		0			0
$153$		−	1.77292e6i		−	0.495012i
$154$		0			0
$155$	2.36817e6			0.635942
$156$		0			0
$157$	−105149.	+	60707.7i	−0.0271710	+	0.0156872i	−0.513524	−	0.858075i	$-0.671660\pi$
$157$	−105149.	+	60707.7i	−0.0271710	+	0.0156872i	0.486353	+	0.873762i	$0.338327\pi$
$158$		0			0
$159$	1.08011e6	+	623599.i	0.268705	+	0.155137i
$160$		0			0
$161$	−4.77337e6	−	513090.i	−1.14379	−	0.122946i
$162$		0			0
$163$	2.68974e6	−	4.65876e6i	0.621079	−	1.07574i	−0.368206	−	0.929744i	$-0.620028\pi$
$163$	2.68974e6	−	4.65876e6i	0.621079	−	1.07574i	0.989285	−	0.145996i	$-0.0466387\pi$
$164$		0			0
$165$	−212910.	−	368772.i	−0.0473964	−	0.0820929i
$166$		0			0
$167$		−	4.10978e6i		−	0.882407i	−0.897407	−	0.441203i	$-0.854552\pi$
$167$		−	4.10978e6i		−	0.882407i	0.897407	−	0.441203i	$-0.145448\pi$
$168$		0			0
$169$	−1.31056e6			−0.271517
$170$		0			0
$171$	−2.02298e6	+	1.16797e6i	−0.404579	+	0.233584i
$172$		0			0
$173$	−2.23786e6	−	1.29203e6i	−0.432210	−	0.249537i	0.268078	−	0.963397i	$-0.413612\pi$
$173$	−2.23786e6	−	1.29203e6i	−0.432210	−	0.249537i	−0.700288	+	0.713861i	$0.746945\pi$
$174$		0			0
$175$	2.70283e6	−	3.70174e6i	0.504319	−	0.690703i
$176$		0			0
$177$	−1.34211e6	+	2.32460e6i	−0.242030	+	0.419208i
$178$		0			0
$179$	−1.63925e6	−	2.83926e6i	−0.285815	−	0.495047i	0.686991	−	0.726666i	$-0.258931\pi$
$179$	−1.63925e6	−	2.83926e6i	−0.285815	−	0.495047i	−0.972807	+	0.231619i	$0.925598\pi$
$180$		0			0
$181$			7.21340e6i			1.21648i	0.793754	+	0.608239i	$0.208124\pi$
$181$			7.21340e6i			1.21648i	−0.793754	+	0.608239i	$0.791876\pi$
$182$		0			0
$183$	−1.61825e6			−0.264054
$184$		0			0
$185$	−1.66642e6	+	962110.i	−0.263190	+	0.151953i
$186$		0			0
$187$	3.62894e6	+	2.09517e6i	0.554951	+	0.320401i
$188$		0			0
$189$	−1.18820e6	+	525664.i	−0.175996	+	0.0778615i
$190$		0			0
$191$	−3.01747e6	+	5.22641e6i	−0.433055	+	0.750073i	−0.997135	−	0.0756472i	$-0.975898\pi$
$191$	−3.01747e6	+	5.22641e6i	−0.433055	+	0.750073i	0.564080	+	0.825720i	$0.309231\pi$
$192$		0			0
$193$	4.97380e6	+	8.61488e6i	0.691858	+	1.19833i	0.971229	+	0.238149i	$0.0765407\pi$
$193$	4.97380e6	+	8.61488e6i	0.691858	+	1.19833i	−0.279371	+	0.960183i	$0.590126\pi$
$194$		0			0
$195$			1.83676e6i			0.247713i
$196$		0			0
$197$	8.61270e6			1.12652			0.563262	−	0.826278i	$-0.309546\pi$
$197$	8.61270e6			1.12652			0.563262	+	0.826278i	$0.309546\pi$
$198$		0			0
$199$	7.41392e6	−	4.28043e6i	0.940781	−	0.543160i	0.0505761	−	0.998720i	$-0.483894\pi$
$199$	7.41392e6	−	4.28043e6i	0.940781	−	0.543160i	0.890205	+	0.455560i	$0.150561\pi$
$200$		0			0
$201$	2.19055e6	+	1.26471e6i	0.269752	+	0.155741i
$202$		0			0
$203$	−1.02709e6	−	2.32160e6i	−0.122778	−	0.277523i
$204$		0			0
$205$	857191.	−	1.48470e6i	0.0994984	−	0.172336i
$206$		0			0
$207$	1.70060e6	+	2.94553e6i	0.191730	+	0.332087i
$208$		0			0
$209$		−	5.52103e6i		−	0.604757i
$210$		0			0
$211$	−8.79482e6			−0.936224			−0.468112	−	0.883669i	$-0.655066\pi$
$211$	−8.79482e6			−0.936224			−0.468112	+	0.883669i	$0.655066\pi$
$212$		0			0
$213$	7.04867e6	−	4.06955e6i	0.729404	−	0.421122i
$214$		0			0
$215$	−666187.	−	384623.i	−0.0670318	−	0.0387008i
$216$		0			0
$217$	1.37930e7	+	1.00710e7i	1.34984	+	0.985587i
$218$		0			0
$219$	−707929.	+	1.22617e6i	−0.0673996	+	0.116739i
$220$		0			0
$221$	−9.03742e6	−	1.56533e7i	−0.837275	−	1.45020i
$222$		0			0
$223$			3.42876e6i			0.309188i	0.987978	+	0.154594i	$0.0494070\pi$
$223$			3.42876e6i			0.309188i	−0.987978	+	0.154594i	$0.950593\pi$
$224$		0			0
$225$	−3.24718e6			−0.285075
$226$		0			0
$227$	−4.37261e6	+	2.52453e6i	−0.373820	+	0.215825i	−0.675126	−	0.737702i	$-0.735911\pi$
$227$	−4.37261e6	+	2.52453e6i	−0.373820	+	0.215825i	0.301306	+	0.953528i	$0.402577\pi$
$228$		0			0
$229$	−1.39393e7	−	8.04784e6i	−1.16074	−	0.670151i	−0.209256	−	0.977861i	$-0.567104\pi$
$229$	−1.39393e7	−	8.04784e6i	−1.16074	−	0.670151i	−0.951480	+	0.307710i	$0.900437\pi$
$230$		0			0
$231$	328198.	−	3.05329e6i	0.0266257	−	0.247704i
$232$		0			0
$233$	9.05777e6	−	1.56885e7i	0.716067	−	1.24026i	−0.246480	−	0.969148i	$-0.579274\pi$
$233$	9.05777e6	−	1.56885e7i	0.716067	−	1.24026i	0.962547	−	0.271116i	$-0.0873928\pi$
$234$		0			0
$235$	−1.59159e6	−	2.75672e6i	−0.122639	−	0.212417i
$236$		0			0
$237$			7.34824e6i			0.551999i
$238$		0			0
$239$	1.71766e7			1.25819			0.629093	−	0.777330i	$-0.283427\pi$
$239$	1.71766e7			1.25819			0.629093	+	0.777330i	$0.283427\pi$
$240$		0			0
$241$	−8.14385e6	+	4.70185e6i	−0.581806	+	0.335906i	−0.761851	−	0.647752i	$-0.775709\pi$
$241$	−8.14385e6	+	4.70185e6i	−0.581806	+	0.335906i	0.180045	+	0.983658i	$0.442376\pi$
$242$		0			0
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−5.32983e6	+	1.70401e6i	−0.362422	+	0.115870i
$246$		0			0
$247$	−1.19074e7	+	2.06242e7i	−0.790178	+	1.36863i
$248$		0			0
$249$	2.81612e6	+	4.87766e6i	0.182412	+	0.315946i
$250$		0			0
$251$		−	2.41058e7i		−	1.52440i	−0.647339	−	0.762202i	$-0.724118\pi$
$251$		−	2.41058e7i		−	1.52440i	0.647339	−	0.762202i	$-0.275882\pi$
$252$		0			0
$253$	−8.03880e6			−0.496398
$254$		0			0
$255$	−4.68463e6	+	2.70467e6i	−0.282524	+	0.163115i
$256$		0			0
$257$	−1.04626e6	−	604056.i	−0.0616366	−	0.0355859i	0.468865	−	0.883270i	$-0.344663\pi$
$257$	−1.04626e6	−	604056.i	−0.0616366	−	0.0355859i	−0.530502	+	0.847684i	$0.677996\pi$
$258$		0			0
$259$	−1.37974e7	−	1.48308e6i	−0.794140	−	0.0853621i
$260$		0			0
$261$	−899259.	+	1.55756e6i	−0.0505782	+	0.0876040i
$262$		0			0
$263$	8.70733e6	+	1.50815e7i	0.478650	+	0.829045i	0.999700	−	0.0244804i	$-0.00779312\pi$
$263$	8.70733e6	+	1.50815e7i	0.478650	+	0.829045i	−0.521051	+	0.853526i	$0.674460\pi$
$264$		0			0
$265$		−	3.80532e6i		−	0.204481i
$266$		0			0
$267$	−1.27106e7			−0.667776
$268$		0			0
$269$	−4.64217e6	+	2.68016e6i	−0.238487	+	0.137690i	−0.614481	−	0.788932i	$-0.710635\pi$
$269$	−4.64217e6	+	2.68016e6i	−0.238487	+	0.137690i	0.375994	+	0.926622i	$0.377301\pi$
$270$		0			0
$271$	1.67010e7	+	9.64234e6i	0.839142	+	0.484479i	0.856972	−	0.515362i	$-0.172343\pi$
$271$	1.67010e7	+	9.64234e6i	0.839142	+	0.484479i	−0.0178306	+	0.999841i	$0.505676\pi$
$272$		0			0
$273$	−7.81113e6	+	1.06979e7i	−0.383907	+	0.525790i
$274$		0			0
$275$	3.83739e6	−	6.64655e6i	0.184517	−	0.319594i
$276$		0			0
$277$	1.01507e7	+	1.75815e7i	0.477591	+	0.827212i	0.999670	−	0.0256854i	$-0.00817681\pi$
$277$	1.01507e7	+	1.75815e7i	0.477591	+	0.827212i	−0.522079	+	0.852897i	$0.674843\pi$
$278$		0			0
$279$		−	1.20993e7i		−	0.557119i
$280$		0			0
$281$	−2.59249e7			−1.16842			−0.584209	−	0.811603i	$-0.698595\pi$
$281$	−2.59249e7			−1.16842			−0.584209	+	0.811603i	$0.698595\pi$
$282$		0			0
$283$	−1.79342e7	+	1.03543e7i	−0.791268	+	0.456839i	−0.840409	−	0.541953i	$-0.817685\pi$
$283$	−1.79342e7	+	1.03543e7i	−0.791268	+	0.456839i	0.0491410	+	0.998792i	$0.484352\pi$
$284$		0			0
$285$	6.17229e6	+	3.56358e6i	0.266632	+	0.153940i
$286$		0			0
$287$	1.13065e7	−	5.00205e6i	0.478281	−	0.211594i
$288$		0			0
$289$	1.45469e7	−	2.51959e7i	0.602665	−	1.04385i
$290$		0			0
$291$	1.17475e7	+	2.03473e7i	0.476724	+	0.825709i
$292$		0			0
$293$			4.25891e7i			1.69315i	0.532269	+	0.846576i	$0.321340\pi$
$293$			4.25891e7i			1.69315i	−0.532269	+	0.846576i	$0.678660\pi$
$294$		0			0
$295$	8.18980e6			0.319012
$296$		0			0
$297$	−1.88411e6	+	1.08779e6i	−0.0719178	+	0.0415217i
$298$		0			0
$299$	3.00295e7	+	1.73375e7i	1.12340	+	0.648595i
$300$		0			0
$301$	−2.24443e6	−	5.07325e6i	−0.0823013	−	0.186032i
$302$		0			0
$303$	7620.30	−	13198.7i	0.000273933	−	0.000474466i
$304$		0			0
$305$	2.46872e6	+	4.27595e6i	0.0870106	+	0.150707i
$306$		0			0
$307$			1.60335e7i			0.554134i	0.960851	+	0.277067i	$0.0893623\pi$
$307$			1.60335e7i			0.554134i	−0.960851	+	0.277067i	$0.910638\pi$
$308$		0			0
$309$	−2.14343e7			−0.726497
$310$		0			0
$311$	−3.79477e7	+	2.19091e7i	−1.26155	+	0.728356i	−0.973374	−	0.229222i	$-0.926382\pi$
$311$	−3.79477e7	+	2.19091e7i	−1.26155	+	0.728356i	−0.288175	+	0.957578i	$0.593048\pi$
$312$		0			0
$313$	−1.78881e6	−	1.03277e6i	−0.0583351	−	0.0336798i	0.470549	−	0.882374i	$-0.344056\pi$
$313$	−1.78881e6	−	1.03277e6i	−0.0583351	−	0.0336798i	−0.528884	+	0.848694i	$0.677389\pi$
$314$		0			0
$315$	3.20162e6	+	2.33767e6i	0.102433	+	0.0747915i
$316$		0			0
$317$	1.18406e7	−	2.05086e7i	0.371704	−	0.643810i	−0.618124	−	0.786081i	$-0.712107\pi$
$317$	1.18406e7	−	2.05086e7i	0.371704	−	0.643810i	0.989828	+	0.142271i	$0.0454404\pi$
$318$		0			0
$319$	−2.12542e6	−	3.68133e6i	−0.0654745	−	0.113405i
$320$		0			0
$321$			3.79917e7i			1.14861i
$322$		0			0
$323$	−7.01355e7			−2.08128
$324$		0			0
$325$	−2.86696e7	+	1.65524e7i	−0.835164	+	0.482182i
$326$		0			0
$327$	−1.27226e6	−	734540.i	−0.0363859	−	0.0210074i
$328$		0			0
$329$	2.45342e6	−	2.28246e7i	0.0688944	−	0.640937i
$330$		0			0
$331$	−2.68675e7	+	4.65358e7i	−0.740871	+	1.28323i	0.211228	+	0.977437i	$0.432254\pi$
$331$	−2.68675e7	+	4.65358e7i	−0.740871	+	1.28323i	−0.952099	+	0.305789i	$0.901080\pi$
$332$		0			0
$333$	4.91556e6	+	8.51400e6i	0.133119	+	0.230569i
$334$		0			0
$335$		−	7.71750e6i		−	0.205278i
$336$		0			0
$337$	−5.15056e7			−1.34575			−0.672876	−	0.739755i	$-0.734941\pi$
$337$	−5.15056e7			−1.34575			−0.672876	+	0.739755i	$0.734941\pi$
$338$		0			0
$339$	−3.14295e7	+	1.81458e7i	−0.806749	+	0.465777i
$340$		0			0
$341$	2.47657e7	+	1.42985e7i	0.624579	+	0.360601i
$342$		0			0
$343$	−3.82893e7	−	1.27413e7i	−0.948846	−	0.315740i
$344$		0			0
$345$	5.18868e6	−	8.98706e6i	0.126357	−	0.218857i
$346$		0			0
$347$	−3.00817e7	−	5.21030e7i	−0.719968	−	1.24702i	−0.961012	−	0.276508i	$-0.910823\pi$
$347$	−3.00817e7	−	5.21030e7i	−0.719968	−	1.24702i	0.241043	−	0.970514i	$-0.422510\pi$
$348$		0			0
$349$			5.11761e6i			0.120390i	0.998187	+	0.0601950i	$0.0191723\pi$
$349$			5.11761e6i			0.120390i	−0.998187	+	0.0601950i	$0.980828\pi$
$350$		0			0
$351$	9.38427e6			0.217010
$352$		0			0
$353$	3.23279e7	−	1.86645e7i	0.734943	−	0.424320i	−0.0852846	−	0.996357i	$-0.527180\pi$
$353$	3.23279e7	−	1.86645e7i	0.734943	−	0.424320i	0.820228	+	0.572037i	$0.193847\pi$
$354$		0			0
$355$	−2.15061e7	−	1.24166e7i	−0.480703	−	0.277534i
$356$		0			0
$357$	−3.87870e7	−	4.16922e6i	−0.852475	−	0.0916325i
$358$		0			0
$359$	3.70476e7	−	6.41684e7i	0.800714	−	1.38688i	−0.118433	−	0.992962i	$-0.537787\pi$
$359$	3.70476e7	−	6.41684e7i	0.800714	−	1.38688i	0.919147	−	0.393915i	$-0.128879\pi$
$360$		0			0
$361$	2.26810e7	+	3.92847e7i	0.482104	+	0.835029i
$362$		0			0
$363$			2.24739e7i			0.469849i
$364$		0			0
$365$	4.31991e6			0.0888374
$366$		0			0
$367$	4.04084e7	−	2.33298e7i	0.817473	−	0.471968i	−0.0320713	−	0.999486i	$-0.510210\pi$
$367$	4.04084e7	−	2.33298e7i	0.817473	−	0.471968i	0.849544	+	0.527517i	$0.176877\pi$
$368$		0			0
$369$	−7.58554e6	−	4.37951e6i	−0.150976	−	0.0871659i
$370$		0			0
$371$	1.61827e7	−	2.21635e7i	0.316906	−	0.434027i
$372$		0			0
$373$	−3.75062e7	+	6.49626e7i	−0.722730	+	1.25181i	0.237172	+	0.971468i	$0.423780\pi$
$373$	−3.75062e7	+	6.49626e7i	−0.722730	+	1.25181i	−0.959902	+	0.280337i	$0.909554\pi$
$374$		0			0
$375$	1.07460e7	+	1.86127e7i	0.203776	+	0.352951i
$376$		0			0
$377$			1.83358e7i			0.342197i
$378$		0			0
$379$	3.87162e7			0.711173			0.355587	−	0.934643i	$-0.384281\pi$
$379$	3.87162e7			0.711173			0.355587	+	0.934643i	$0.384281\pi$
$380$		0			0
$381$	1.42157e7	−	8.20746e6i	0.257036	−	0.148400i
$382$		0			0
$383$	2.09918e7	+	1.21196e7i	0.373641	+	0.215722i	0.675048	−	0.737774i	$-0.264123\pi$
$383$	2.09918e7	+	1.21196e7i	0.373641	+	0.215722i	−0.301407	+	0.953496i	$0.597456\pi$
$384$		0			0
$385$	−8.56846e6	+	3.79073e6i	−0.150148	+	0.0664263i
$386$		0			0
$387$	−1.96510e6	+	3.40364e6i	−0.0339040	+	0.0587234i
$388$		0			0
$389$	−5.54024e7	−	9.59598e7i	−0.941196	−	1.63020i	−0.763194	−	0.646169i	$-0.776370\pi$
$389$	−5.54024e7	−	9.59598e7i	−0.941196	−	1.63020i	−0.178002	−	0.984030i	$-0.556963\pi$
$390$		0			0
$391$			1.02120e8i			1.70836i
$392$		0			0
$393$	1.87359e7			0.308672
$394$		0			0
$395$	1.94164e7	−	1.12101e7i	0.315049	−	0.181893i
$396$		0			0
$397$	2.24475e7	+	1.29601e7i	0.358754	+	0.207127i	0.668534	−	0.743682i	$-0.266922\pi$
$397$	2.24475e7	+	1.29601e7i	0.358754	+	0.207127i	−0.309780	+	0.950808i	$0.600255\pi$
$398$		0			0
$399$	2.07949e7	+	4.70042e7i	0.327369	+	0.739977i
$400$		0			0
$401$	−1.98930e7	+	3.44557e7i	−0.308509	+	0.534353i	−0.978036	−	0.208434i	$-0.933163\pi$
$401$	−1.98930e7	+	3.44557e7i	−0.308509	+	0.534353i	0.669527	+	0.742787i	$0.266497\pi$
$402$		0			0
$403$	−6.16759e7	−	1.06826e8i	−0.942325	−	1.63215i
$404$		0			0
$405$		−	2.80848e6i		−	0.0422771i
$406$		0			0
$407$	−2.32360e7			−0.344650
$408$		0			0
$409$	−1.07571e8	+	6.21064e7i	−1.57227	+	0.907750i	−0.576379	+	0.817183i	$0.695535\pi$
$409$	−1.07571e8	+	6.21064e7i	−1.57227	+	0.907750i	−0.995890	+	0.0905676i	$0.971132\pi$
$410$		0			0
$411$	−5.16954e7	−	2.98464e7i	−0.744607	−	0.429899i
$412$		0			0
$413$	4.77003e7	+	3.48285e7i	0.677128	+	0.494407i
$414$		0			0
$415$	8.59223e6	−	1.48822e7i	0.120216	−	0.208220i
$416$		0			0
$417$	−3.67917e7	−	6.37250e7i	−0.507389	−	0.878824i
$418$		0			0
$419$			6.77769e6i			0.0921381i	0.998938	+	0.0460691i	$0.0146694\pi$
$419$			6.77769e6i			0.0921381i	−0.998938	+	0.0460691i	$0.985331\pi$
$420$		0			0
$421$	8.10777e7			1.08656			0.543282	−	0.839550i	$-0.317181\pi$
$421$	8.10777e7			1.08656			0.543282	+	0.839550i	$0.317181\pi$
$422$		0			0
$423$	−1.40845e7	+	8.13167e6i	−0.186088	+	0.107438i
$424$		0			0
$425$	−8.44334e7	−	4.87476e7i	−1.09988	−	0.635019i
$426$		0			0
$427$	−3.80550e6	+	3.54032e7i	−0.0488796	+	0.454736i
$428$		0			0
$429$	−1.10900e7	+	1.92084e7i	−0.140462	+	0.243287i
$430$		0			0
$431$	1.04209e7	+	1.80495e7i	0.130159	+	0.225442i	0.923738	−	0.383026i	$-0.125118\pi$
$431$	1.04209e7	+	1.80495e7i	0.130159	+	0.225442i	−0.793579	+	0.608467i	$0.791785\pi$
$432$		0			0
$433$		−	7.20710e7i		−	0.887763i	−0.896086	−	0.443881i	$-0.853601\pi$
$433$		−	7.20710e7i		−	0.887763i	0.896086	−	0.443881i	$-0.146399\pi$
$434$		0			0
$435$	5.48744e6			0.0666656
$436$		0			0
$437$	1.16523e8	−	6.72745e7i	1.39626	−	0.806132i
$438$		0			0
$439$	1.03361e8	+	5.96757e7i	1.22170	+	0.705349i	0.965280	−	0.261217i	$-0.0841238\pi$
$439$	1.03361e8	+	5.96757e7i	1.22170	+	0.705349i	0.256420	+	0.966566i	$0.417457\pi$
$440$		0			0
$441$	8.70601e6	+	2.72309e7i	0.101509	+	0.317501i
$442$		0			0
$443$	3.25766e7	−	5.64243e7i	0.374709	−	0.649016i	−0.615574	−	0.788079i	$-0.711076\pi$
$443$	3.25766e7	−	5.64243e7i	0.374709	−	0.649016i	0.990283	+	0.139063i	$0.0444092\pi$
$444$		0			0
$445$	1.93905e7	+	3.35854e7i	0.220044	+	0.381127i
$446$		0			0
$447$			8.88206e7i			0.994468i
$448$		0			0
$449$	1.38728e8			1.53258			0.766292	−	0.642492i	$-0.222100\pi$
$449$	1.38728e8			1.53258			0.766292	+	0.642492i	$0.222100\pi$
$450$		0			0
$451$	1.79286e7	−	1.03511e7i	0.195441	−	0.112838i
$452$		0			0
$453$	5.59223e7	+	3.22867e7i	0.601576	+	0.347320i
$454$		0			0
$455$	4.01836e7	+	4.31934e6i	0.426594	+	0.0458546i
$456$		0			0
$457$	4.57738e7	−	7.92825e7i	0.479588	−	0.830670i	−0.520138	−	0.854082i	$-0.674120\pi$
$457$	4.57738e7	−	7.92825e7i	0.479588	−	0.830670i	0.999726	+	0.0234119i	$0.00745292\pi$
$458$		0			0
$459$	1.38186e7	+	2.39345e7i	0.142898	+	0.247506i
$460$		0			0
$461$		−	1.07178e8i		−	1.09397i	−0.837143	−	0.546984i	$-0.815776\pi$
$461$		−	1.07178e8i		−	1.09397i	0.837143	−	0.546984i	$-0.184224\pi$
$462$		0			0
$463$	−1.45128e7			−0.146221			−0.0731103	−	0.997324i	$-0.523293\pi$
$463$	−1.45128e7			−0.146221			−0.0731103	+	0.997324i	$0.523293\pi$
$464$		0			0
$465$	−3.19703e7	+	1.84580e7i	−0.317971	+	0.183581i
$466$		0			0
$467$	−1.32921e8	−	7.67420e7i	−1.30510	−	0.753498i	−0.323824	−	0.946117i	$-0.604968\pi$
$467$	−1.32921e8	−	7.67420e7i	−1.30510	−	0.753498i	−0.981274	+	0.192619i	$0.938302\pi$
$468$		0			0
$469$	3.28200e7	−	4.49494e7i	0.318141	−	0.435718i
$470$		0			0
$471$	946340.	−	1.63911e6i	0.00905700	−	0.0156872i
$472$		0			0
$473$	−4.64454e6	−	8.04458e6i	−0.0438894	−	0.0760186i
$474$		0			0
$475$			1.28456e8i			1.19860i
$476$		0			0
$477$	−1.94419e7			−0.179136
$478$		0			0
$479$	1.63512e8	−	9.44035e7i	1.48779	−	0.858977i	0.487888	−	0.872906i	$-0.337767\pi$
$479$	1.63512e8	−	9.44035e7i	1.48779	−	0.858977i	0.999903	+	0.0139293i	$0.00443397\pi$
$480$		0			0
$481$	8.67997e7	+	5.01138e7i	0.779979	+	0.450321i
$482$		0			0
$483$	6.84397e7	−	3.02781e7i	0.607389	−	0.268712i
$484$		0			0
$485$	3.58427e7	−	6.20814e7i	0.314178	−	0.544172i
$486$		0			0
$487$	5.30859e7	+	9.19474e7i	0.459613	+	0.796072i	0.998940	−	0.0460235i	$-0.0146549\pi$
$487$	5.30859e7	+	9.19474e7i	0.459613	+	0.796072i	−0.539328	+	0.842096i	$0.681322\pi$
$488$		0			0
$489$			8.38577e7i			0.717160i
$490$		0			0
$491$	−1.29373e8			−1.09295			−0.546475	−	0.837475i	$-0.684031\pi$
$491$	−1.29373e8			−1.09295			−0.546475	+	0.837475i	$0.684031\pi$
$492$		0			0
$493$	−4.67652e7	+	2.69999e7i	−0.390285	+	0.225331i
$494$		0			0
$495$	5.74858e6	+	3.31894e6i	0.0473964	+	0.0273643i
$496$		0			0
$497$	−7.24557e7	−	1.63777e8i	−0.590205	−	1.33408i
$498$		0			0
$499$	5.70783e7	−	9.88626e7i	0.459378	−	0.795665i	−0.539551	−	0.841953i	$-0.681406\pi$
$499$	5.70783e7	−	9.88626e7i	0.459378	−	0.795665i	0.998928	+	0.0462880i	$0.0147392\pi$
$500$		0			0
$501$	3.20325e7	+	5.54820e7i	0.254729	+	0.441203i
$502$		0			0
$503$		−	1.41676e8i		−	1.11325i	−0.830765	−	0.556623i	$-0.812097\pi$
$503$		−	1.41676e8i		−	1.11325i	0.830765	−	0.556623i	$-0.187903\pi$
$504$		0			0
$505$	−46500.4			−0.000361063
$506$		0			0
$507$	1.76926e7	−	1.02148e7i	0.135759	−	0.0783803i
$508$		0			0
$509$	−3.69362e6	−	2.13251e6i	−0.0280091	−	0.0161711i	0.485930	−	0.873998i	$-0.338481\pi$
$509$	−3.69362e6	−	2.13251e6i	−0.0280091	−	0.0161711i	−0.513939	+	0.857827i	$0.671814\pi$
$510$		0			0
$511$	2.51607e7	+	1.83711e7i	0.188564	+	0.137681i
$512$		0			0
$513$	1.82068e7	−	3.15351e7i	0.134860	−	0.233584i
$514$		0			0
$515$	3.26990e7	+	5.66363e7i	0.239394	+	0.414642i
$516$		0			0
$517$		−	3.84387e7i		−	0.278162i
$518$		0			0
$519$	4.02815e7			0.288140
$520$		0			0
$521$	2.05008e6	−	1.18362e6i	0.0144963	−	0.00836946i	−0.492734	−	0.870180i	$-0.664003\pi$
$521$	2.05008e6	−	1.18362e6i	0.0144963	−	0.00836946i	0.507231	+	0.861810i	$0.330669\pi$
$522$		0			0
$523$	−1.12872e8	−	6.51664e7i	−0.789004	−	0.455532i	0.0506075	−	0.998719i	$-0.483884\pi$
$523$	−1.12872e8	−	6.51664e7i	−0.789004	−	0.455532i	−0.839612	+	0.543187i	$0.817218\pi$
$524$		0			0
$525$	−7.63609e6	+	7.10399e7i	−0.0527707	+	0.490936i
$526$		0			0
$527$	1.81639e8	−	3.14607e8i	1.24101	−	2.14950i
$528$		0			0
$529$	−2.39360e7	−	4.14583e7i	−0.161690	−	0.280056i
$530$		0			0
$531$		−	4.18429e7i		−	0.279472i
$532$		0			0
$533$	−8.92978e7			−0.589738
$534$		0			0
$535$	1.00386e8	−	5.79581e7i	0.655561	−	0.378488i
$536$		0			0
$537$	4.42597e7	+	2.55534e7i	0.285815	+	0.165016i
$538$		0			0
$539$	−6.60264e7	−	1.43603e7i	−0.421649	−	0.0917057i
$540$		0			0
$541$	8.73133e6	−	1.51231e7i	0.0551428	−	0.0955101i	−0.837136	−	0.546994i	$-0.815772\pi$
$541$	8.73133e6	−	1.51231e7i	0.0551428	−	0.0955101i	0.892279	+	0.451484i	$0.149105\pi$
$542$		0			0
$543$	−5.62229e7	−	9.73808e7i	−0.351167	−	0.608239i
$544$		0			0
$545$			4.48229e6i			0.0276892i
$546$		0			0
$547$	−1.31922e8			−0.806038			−0.403019	−	0.915192i	$-0.632039\pi$
$547$	−1.31922e8			−0.806038			−0.403019	+	0.915192i	$0.632039\pi$
$548$		0			0
$549$	2.18464e7	−	1.26130e7i	0.132027	−	0.0762259i
$550$		0			0
$551$	6.16160e7	+	3.55740e7i	0.368332	+	0.212656i
$552$		0			0
$553$	1.60761e8	+	1.72802e7i	0.950614	+	0.102182i
$554$		0			0
$555$	1.49978e7	−	2.59770e7i	0.0877302	−	0.151953i
$556$		0			0
$557$	3.13827e7	+	5.43564e7i	0.181604	+	0.314547i	0.942427	−	0.334413i	$-0.108538\pi$
$557$	3.13827e7	+	5.43564e7i	0.181604	+	0.314547i	−0.760823	+	0.648959i	$0.775205\pi$
$558$		0			0
$559$			4.00681e7i			0.229384i
$560$		0			0
$561$	−6.53209e7			−0.369967
$562$		0			0
$563$	1.25354e8	−	7.23729e7i	0.702444	−	0.405556i	−0.105813	−	0.994386i	$-0.533745\pi$
$563$	1.25354e8	−	7.23729e7i	0.702444	−	0.405556i	0.808257	+	0.588830i	$0.200411\pi$
$564$		0			0
$565$	9.58942e7	+	5.53646e7i	0.531676	+	0.306963i
$566$		0			0
$567$	1.19435e7	−	1.63575e7i	0.0655214	−	0.0897365i
$568$		0			0
$569$	4.87489e6	−	8.44355e6i	0.0264623	−	0.0458340i	−0.852491	−	0.522742i	$-0.824909\pi$
$569$	4.87489e6	−	8.44355e6i	0.0264623	−	0.0458340i	0.878953	+	0.476908i	$0.158242\pi$
$570$		0			0
$571$	−1.13999e8	−	1.97452e8i	−0.612340	−	1.06060i	−0.990845	−	0.135005i	$-0.956895\pi$
$571$	−1.13999e8	−	1.97452e8i	−0.612340	−	1.06060i	0.378505	−	0.925599i	$-0.376438\pi$
$572$		0			0
$573$		−	9.40754e7i		−	0.500049i
$574$		0			0
$575$	1.87036e8			0.983835
$576$		0			0
$577$	2.36302e8	−	1.36429e8i	1.23010	−	0.710199i	0.263050	−	0.964782i	$-0.415272\pi$
$577$	2.36302e8	−	1.36429e8i	1.23010	−	0.710199i	0.967051	+	0.254583i	$0.0819384\pi$
$578$		0			0
$579$	−1.34293e8	−	7.75339e7i	−0.691858	−	0.399444i
$580$		0			0
$581$	1.13333e8	−	5.01391e7i	0.577867	−	0.255651i
$582$		0			0
$583$	2.29757e7	−	3.97950e7i	0.115948	−	0.200827i
$584$		0			0
$585$	−1.43161e7	−	2.47963e7i	−0.0715086	−	0.123856i
$586$		0			0
$587$			5.81852e7i			0.287672i	0.989602	+	0.143836i	$0.0459438\pi$
$587$			5.81852e7i			0.287672i	−0.989602	+	0.143836i	$0.954056\pi$
$588$		0			0
$589$	−4.78640e8			−2.34241
$590$		0			0
$591$	−1.16271e8	+	6.71294e7i	−0.563262	+	0.325200i
$592$		0			0
$593$	1.57599e7	+	9.09900e6i	0.0755771	+	0.0436344i	0.537312	−	0.843383i	$-0.319440\pi$
$593$	1.57599e7	+	9.09900e6i	0.0755771	+	0.0436344i	−0.461735	+	0.887018i	$0.652773\pi$
$594$		0			0
$595$	4.81549e7	+	1.08848e8i	0.228607	+	0.516737i
$596$		0			0
$597$	−6.67253e7	+	1.15572e8i	−0.313594	+	0.543160i
$598$		0			0
$599$	1.50805e8	+	2.61203e8i	0.701675	+	1.21534i	0.967878	+	0.251420i	$0.0808977\pi$
$599$	1.50805e8	+	2.61203e8i	0.701675	+	1.21534i	−0.266202	+	0.963917i	$0.585769\pi$
$600$		0			0
$601$			1.70533e8i			0.785570i	0.919630	+	0.392785i	$0.128488\pi$
$601$			1.70533e8i			0.785570i	−0.919630	+	0.392785i	$0.871512\pi$
$602$		0			0
$603$	−3.94298e7			−0.179834
$604$		0			0
$605$	5.93832e7	−	3.42849e7i	0.268162	−	0.154824i
$606$		0			0
$607$	1.11945e8	+	6.46316e7i	0.500540	+	0.288987i	0.728937	−	0.684581i	$-0.240015\pi$
$607$	1.11945e8	+	6.46316e7i	0.500540	+	0.288987i	−0.228396	+	0.973568i	$0.573348\pi$
$608$		0			0
$609$	3.19608e7	+	2.33363e7i	0.141503	+	0.103319i
$610$		0			0
$611$	−8.29020e7	+	1.43590e8i	−0.363447	+	0.629509i
$612$		0			0
$613$	−1.17875e8	−	2.04166e8i	−0.511731	−	0.886344i	−0.999908	−	0.0135993i	$-0.995671\pi$
$613$	−1.17875e8	−	2.04166e8i	−0.511731	−	0.886344i	0.488176	−	0.872745i	$-0.337662\pi$
$614$		0			0
$615$			2.67246e7i			0.114891i
$616$		0			0
$617$	7.43296e7			0.316451			0.158226	−	0.987403i	$-0.449423\pi$
$617$	7.43296e7			0.316451			0.158226	+	0.987403i	$0.449423\pi$
$618$		0			0
$619$	−3.32320e8	+	1.91865e8i	−1.40115	+	0.808955i	−0.994511	−	0.104634i	$-0.966633\pi$
$619$	−3.32320e8	+	1.91865e8i	−1.40115	+	0.808955i	−0.406640	+	0.913589i	$0.633300\pi$
$620$		0			0
$621$	−4.59162e7	−	2.65097e7i	−0.191730	−	0.110696i
$622$		0			0
$623$	−2.98902e7	+	2.78074e8i	−0.123613	+	1.15000i
$624$		0			0
$625$	−7.16104e7	+	1.24033e8i	−0.293316	+	0.508038i
$626$		0			0
$627$	4.30322e7	+	7.45339e7i	0.174578	+	0.302379i
$628$		0			0
$629$			2.95175e8i			1.18612i
$630$		0			0
$631$	−3.38487e7			−0.134727			−0.0673633	−	0.997729i	$-0.521459\pi$
$631$	−3.38487e7			−0.134727			−0.0673633	+	0.997729i	$0.521459\pi$
$632$		0			0
$633$	1.18730e8	−	6.85489e7i	0.468112	−	0.270265i
$634$		0			0
$635$	−4.33735e7	−	2.50417e7i	−0.169396	−	0.0978008i
$636$		0			0
$637$	2.15675e8	+	1.96045e8i	0.834412	+	0.758468i
$638$		0			0
$639$	−6.34380e7	+	1.09878e8i	−0.243135	+	0.421122i
$640$		0			0
$641$	−1.30222e8	−	2.25551e8i	−0.494437	−	0.856390i	0.505543	−	0.862802i	$-0.331292\pi$
$641$	−1.30222e8	−	2.25551e8i	−0.494437	−	0.856390i	−0.999979	+	0.00641187i	$0.997959\pi$
$642$		0			0
$643$		−	2.53839e8i		−	0.954830i	−0.878678	−	0.477415i	$-0.841574\pi$
$643$		−	2.53839e8i		−	0.954830i	0.878678	−	0.477415i	$-0.158426\pi$
$644$		0			0
$645$	1.19914e7			0.0446879
$646$		0			0
$647$	1.39147e7	−	8.03365e6i	0.0513760	−	0.0296620i	−0.474092	−	0.880475i	$-0.657224\pi$
$647$	1.39147e7	−	8.03365e6i	0.0513760	−	0.0296620i	0.525468	+	0.850813i	$0.323890\pi$
$648$		0			0
$649$	8.56469e7	+	4.94482e7i	0.313312	+	0.180891i
$650$		0			0
$651$	−2.64702e8	−	2.84528e7i	−0.959432	−	0.103129i
$652$		0			0
$653$	1.64338e8	−	2.84642e8i	0.590200	−	1.02226i	−0.404005	−	0.914757i	$-0.632382\pi$
$653$	1.64338e8	−	2.84642e8i	0.590200	−	1.02226i	0.994205	−	0.107499i	$-0.0342844\pi$
$654$		0			0
$655$	−2.85825e7	−	4.95063e7i	−0.101713	−	0.176172i
$656$		0			0
$657$		−	2.20710e7i		−	0.0778263i
$658$		0			0
$659$	−9.62135e7			−0.336186			−0.168093	−	0.985771i	$-0.553761\pi$
$659$	−9.62135e7			−0.336186			−0.168093	+	0.985771i	$0.553761\pi$
$660$		0			0
$661$	2.27344e8	−	1.31257e8i	0.787188	−	0.454483i	−0.0517839	−	0.998658i	$-0.516491\pi$
$661$	2.27344e8	−	1.31257e8i	0.787188	−	0.454483i	0.838972	+	0.544175i	$0.183157\pi$
$662$		0			0
$663$	2.44010e8	+	1.40880e8i	0.837275	+	0.483401i
$664$		0			0
$665$	9.24767e7	−	1.26654e8i	0.314461	−	0.430679i
$666$		0			0
$667$	5.17970e7	−	8.97150e7i	0.174553	−	0.302334i
$668$		0			0
$669$	−2.67246e7	−	4.62883e7i	−0.0892550	−	0.154594i
$670$		0			0
$671$			5.96223e7i			0.197352i
$672$		0			0
$673$	−4.60742e8			−1.51151			−0.755757	−	0.654852i	$-0.772731\pi$
$673$	−4.60742e8			−1.51151			−0.755757	+	0.654852i	$0.772731\pi$
$674$		0			0
$675$	4.38369e7	−	2.53093e7i	0.142537	−	0.0822940i
$676$		0			0
$677$	−3.62937e8	−	2.09542e8i	−1.16967	−	0.675312i	−0.216071	−	0.976378i	$-0.569324\pi$
$677$	−3.62937e8	−	2.09542e8i	−1.16967	−	0.675312i	−0.953603	+	0.301066i	$0.902658\pi$
$678$		0			0
$679$	4.72772e8	−	2.09156e8i	1.51023	−	0.668132i
$680$		0			0
$681$	3.93535e7	−	6.81622e7i	0.124607	−	0.215825i
$682$		0			0
$683$	−9.77014e7	−	1.69224e8i	−0.306647	−	0.531128i	0.670980	−	0.741476i	$-0.265874\pi$
$683$	−9.77014e7	−	1.69224e8i	−0.306647	−	0.531128i	−0.977627	+	0.210348i	$0.932540\pi$
$684$		0			0
$685$			1.82128e8i			0.566637i
$686$		0			0
$687$	2.50907e8			0.773824
$688$		0			0
$689$	−1.71654e8	+	9.91046e7i	−0.524804	+	0.302995i
$690$		0			0
$691$	−2.54815e8	−	1.47118e8i	−0.772309	−	0.445893i	0.0613884	−	0.998114i	$-0.480447\pi$
$691$	−2.54815e8	−	1.47118e8i	−0.772309	−	0.445893i	−0.833698	+	0.552221i	$0.813781\pi$
$692$		0			0
$693$	1.93674e7	+	4.37775e7i	0.0581930	+	0.131538i
$694$		0			0
$695$	−1.12255e8	+	1.94431e8i	−0.334388	+	0.579176i
$696$		0			0
$697$	−1.31493e8	−	2.27753e8i	−0.388333	−	0.672613i
$698$		0			0
$699$			2.82393e8i			0.826843i
$700$		0			0
$701$	−2.78761e8			−0.809242			−0.404621	−	0.914485i	$-0.632597\pi$
$701$	−2.78761e8			−0.809242			−0.404621	+	0.914485i	$0.632597\pi$
$702$		0			0
$703$	3.36808e8	−	1.94456e8i	0.969429	−	0.559700i
$704$		0			0
$705$	4.29730e7	+	2.48105e7i	0.122639	+	0.0708056i
$706$		0			0
$707$	−270835.	−	197751.i	−0.000766384	−	0.000559577i
$708$		0			0
$709$	−3.12423e7	+	5.41133e7i	−0.0876606	+	0.151833i	−0.906522	−	0.422159i	$-0.861272\pi$
$709$	−3.12423e7	+	5.41133e7i	−0.0876606	+	0.151833i	0.818861	+	0.573992i	$0.194606\pi$
$710$		0			0
$711$	−5.72738e7	−	9.92012e7i	−0.159348	−	0.275999i
$712$		0			0
$713$			6.96916e8i			1.92270i
$714$		0			0
$715$	6.76729e7			0.185138
$716$		0			0
$717$	−2.31885e8	+	1.33879e8i	−0.629093	+	0.363207i
$718$		0			0
$719$	−1.92789e8	−	1.11307e8i	−0.518675	−	0.299457i	0.217718	−	0.976012i	$-0.430139\pi$
$719$	−1.92789e8	−	1.11307e8i	−0.518675	−	0.299457i	−0.736392	+	0.676555i	$0.763472\pi$
$720$		0			0
$721$	−5.04050e7	+	4.68927e8i	−0.134483	+	1.25112i
$722$		0			0
$723$	7.32946e7	−	1.26950e8i	0.193935	−	0.335906i
$724$		0			0
$725$	4.94514e7	+	8.56523e7i	0.129767	+	0.224763i
$726$		0			0
$727$			2.97797e8i			0.775029i	0.921864	+	0.387514i	$0.126666\pi$
$727$			2.97797e8i			0.775029i	−0.921864	+	0.387514i	$0.873334\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−1.02193e8	+	5.90012e7i	−0.261619	+	0.151046i
$732$		0			0
$733$	−3.38948e8	−	1.95692e8i	−0.860640	−	0.496891i	0.00358682	−	0.999994i	$-0.498858\pi$
$733$	−3.38948e8	−	1.95692e8i	−0.860640	−	0.496891i	−0.864226	+	0.503103i	$0.832192\pi$
$734$		0			0
$735$	5.86713e7	−	6.45460e7i	0.147762	−	0.162558i
$736$		0			0
$737$	4.65966e7	−	8.07077e7i	0.116400	−	0.201610i
$738$		0			0
$739$	1.93125e8	+	3.34503e8i	0.478526	+	0.828831i	0.999697	−	0.0246210i	$-0.00783789\pi$
$739$	1.93125e8	+	3.34503e8i	0.478526	+	0.828831i	−0.521171	+	0.853452i	$0.674505\pi$
$740$		0			0
$741$		−	3.71235e8i		−	0.912419i
$742$		0			0
$743$	−3.06725e8			−0.747796			−0.373898	−	0.927470i	$-0.621979\pi$
$743$	−3.06725e8			−0.747796			−0.373898	+	0.927470i	$0.621979\pi$
$744$		0			0
$745$	2.34692e8	−	1.35500e8i	0.567584	−	0.327695i
$746$		0			0
$747$	−7.60352e7	−	4.38989e7i	−0.182412	−	0.105315i
$748$		0			0
$749$	8.31161e8	+	8.93415e7i	1.97806	+	0.212622i
$750$		0			0
$751$	−2.30227e8	+	3.98765e8i	−0.543546	+	0.941449i	0.455151	+	0.890414i	$0.349585\pi$
$751$	−2.30227e8	+	3.98765e8i	−0.543546	+	0.941449i	−0.998697	+	0.0510350i	$0.983748\pi$
$752$		0			0
$753$	1.87886e8	+	3.25428e8i	0.440058	+	0.762202i
$754$		0			0
$755$		−	1.97020e8i		−	0.457792i
$756$		0			0
$757$	4.12811e8			0.951620			0.475810	−	0.879548i	$-0.342155\pi$
$757$	4.12811e8			0.951620			0.475810	+	0.879548i	$0.342155\pi$
$758$		0			0
$759$	1.08524e8	−	6.26563e7i	0.248199	−	0.143298i
$760$		0			0
$761$	−1.95630e8	−	1.12947e8i	−0.443897	−	0.256284i	0.261352	−	0.965244i	$-0.415832\pi$
$761$	−1.95630e8	−	1.12947e8i	−0.443897	−	0.256284i	−0.705249	+	0.708959i	$0.749165\pi$
$762$		0			0
$763$	−1.90617e7	+	2.61064e7i	−0.0429129	+	0.0587725i
$764$		0			0
$765$	4.21617e7	−	7.30262e7i	0.0941746	−	0.163115i
$766$		0			0
$767$	−2.13293e8	−	3.69434e8i	−0.472705	−	0.818750i
$768$		0			0
$769$			3.17891e8i			0.699036i	0.936930	+	0.349518i	$0.113655\pi$
$769$			3.17891e8i			0.699036i	−0.936930	+	0.349518i	$0.886345\pi$
$770$		0			0
$771$	1.88326e7			0.0410911
$772$		0			0
$773$	−6.38425e8	+	3.68595e8i	−1.38220	+	0.798014i	−0.992420	−	0.122894i	$-0.960783\pi$
$773$	−6.38425e8	+	3.68595e8i	−1.38220	+	0.798014i	−0.389781	+	0.920908i	$0.627449\pi$
$774$		0			0
$775$	−5.76216e8	−	3.32678e8i	−1.23788	−	0.714693i
$776$		0			0
$777$	1.97824e8	−	8.75182e7i	0.421712	−	0.186567i
$778$		0			0
$779$	−1.73250e8	+	3.00078e8i	−0.366490	+	0.634779i
$780$		0			0
$781$	−1.49937e8	−	2.59699e8i	−0.314743	−	0.545151i
$782$		0			0
$783$		−	2.80361e7i		−	0.0584027i
$784$		0			0
$785$	−5.77474e6			−0.0119378
$786$		0			0
$787$	−3.34619e8	+	1.93192e8i	−0.686478	+	0.396338i	−0.802291	−	0.596933i	$-0.796386\pi$
$787$	−3.34619e8	+	1.93192e8i	−0.686478	+	0.396338i	0.115813	+	0.993271i	$0.463053\pi$
$788$		0			0
$789$	−2.35098e8	−	1.35734e8i	−0.478650	−	0.276348i
$790$		0			0
$791$	3.23074e8	+	7.30269e8i	0.652789	+	1.47555i
$792$		0			0
$793$	1.28589e8	−	2.22723e8i	0.257861	−	0.446628i
$794$		0			0
$795$	2.96595e7	+	5.13718e7i	0.0590286	+	0.102241i
$796$		0			0
$797$			5.52760e8i			1.09185i	0.837835	+	0.545923i	$0.183821\pi$
$797$			5.52760e8i			1.09185i	−0.837835	+	0.545923i	$0.816179\pi$
$798$		0			0
$799$	−4.88300e8			−0.957297
$800$		0			0
$801$	1.71593e8	−	9.90690e7i	0.333888	−	0.192770i
$802$		0			0
$803$	4.51765e7	+	2.60827e7i	0.0872501	+	0.0503739i
$804$		0			0
$805$	−1.84412e8	−	1.34649e8i	−0.353510	−	0.258117i
$806$		0			0
$807$	4.17795e7	−	7.23643e7i	0.0794956	−	0.137690i
$808$		0			0
$809$	1.45018e8	+	2.51178e8i	0.273889	+	0.474390i	0.969854	−	0.243686i	$-0.0783565\pi$
$809$	1.45018e8	+	2.51178e8i	0.273889	+	0.474390i	−0.695965	+	0.718076i	$0.745023\pi$
$810$		0			0
$811$			3.78427e8i			0.709446i	0.934971	+	0.354723i	$0.115425\pi$
$811$			3.78427e8i			0.709446i	−0.934971	+	0.354723i	$0.884575\pi$
$812$		0			0
$813$	−3.00619e8			−0.559428
$814$		0			0
$815$	2.21579e8	−	1.27929e8i	0.409313	−	0.236317i
$816$		0			0
$817$	1.34646e8	+	7.77377e7i	0.246903	+	0.142550i
$818$		0			0
$819$	2.20681e7	−	2.05304e8i	0.0401711	−	0.373719i
$820$		0			0
$821$	−1.78686e8	+	3.09493e8i	−0.322894	+	0.559269i	−0.981084	−	0.193583i	$-0.937989\pi$
$821$	−1.78686e8	+	3.09493e8i	−0.322894	+	0.559269i	0.658190	+	0.752852i	$0.271322\pi$
$822$		0			0
$823$	3.64584e8	+	6.31478e8i	0.654031	+	1.13281i	0.982136	+	0.188174i	$0.0602567\pi$
$823$	3.64584e8	+	6.31478e8i	0.654031	+	1.13281i	−0.328105	+	0.944641i	$0.606410\pi$
$824$		0			0
$825$			1.19638e8i			0.213062i
$826$		0			0
$827$	−9.96247e8			−1.76137			−0.880685	−	0.473702i	$-0.842917\pi$
$827$	−9.96247e8			−1.76137			−0.880685	+	0.473702i	$0.842917\pi$
$828$		0			0
$829$	2.92363e8	−	1.68796e8i	0.513167	−	0.296277i	−0.220968	−	0.975281i	$-0.570922\pi$
$829$	2.92363e8	−	1.68796e8i	0.513167	−	0.296277i	0.734134	+	0.679004i	$0.237588\pi$
$830$		0			0
$831$	−2.74068e8	−	1.58234e8i	−0.477591	−	0.275737i
$832$		0			0
$833$	−1.82424e8	+	8.38756e8i	−0.315606	+	1.45111i
$834$		0			0
$835$	9.77342e7	−	1.69281e8i	0.167875	−	0.290769i
$836$		0			0
$837$	9.43048e7	+	1.63341e8i	0.160826	+	0.278560i
$838$		0			0
$839$			3.43350e8i			0.581368i	0.956819	+	0.290684i	$0.0938829\pi$
$839$			3.43350e8i			0.581368i	−0.956819	+	0.290684i	$0.906117\pi$
$840$		0			0
$841$	−5.40044e8			−0.907906
$842$		0			0
$843$	3.49986e8	−	2.02065e8i	0.584209	−	0.337293i
$844$		0			0
$845$	−5.39817e7	−	3.11663e7i	−0.0894698	−	0.0516554i
$846$		0			0
$847$	4.91671e8	+	5.28497e7i	0.809141	+	0.0869746i
$848$		0			0
$849$	1.61408e8	−	2.79567e8i	0.263756	−	0.456839i
$850$		0			0
$851$	−2.83134e8	−	4.90403e8i	−0.459414	−	0.795728i
$852$		0			0
$853$		−	8.07895e6i		−	0.0130169i	−0.999979	−	0.00650845i	$-0.997928\pi$
$853$		−	8.07895e6i		−	0.0130169i	0.999979	−	0.00650845i	$-0.00207172\pi$
$854$		0			0
$855$	−1.11101e8			−0.177755
$856$		0			0
$857$	−9.47559e8	+	5.47073e8i	−1.50544	+	0.869167i	−0.505461	+	0.862850i	$0.668677\pi$
$857$	−9.47559e8	+	5.47073e8i	−1.50544	+	0.869167i	−0.999980	+	0.00631697i	$0.997989\pi$
$858$		0			0
$859$	2.23289e8	+	1.28916e8i	0.352279	+	0.203389i	0.665689	−	0.746230i	$-0.268138\pi$
$859$	2.23289e8	+	1.28916e8i	0.352279	+	0.203389i	−0.313409	+	0.949618i	$0.601471\pi$
$860$		0			0
$861$	−1.13651e8	+	1.55653e8i	−0.178059	+	0.243865i
$862$		0			0
$863$	1.34633e8	−	2.33191e8i	0.209469	−	0.362811i	−0.742078	−	0.670313i	$-0.766160\pi$
$863$	1.34633e8	−	2.33191e8i	0.209469	−	0.362811i	0.951547	+	0.307502i	$0.0994932\pi$
$864$		0			0
$865$	−6.14512e7	−	1.06437e8i	−0.0949472	−	0.164453i
$866$		0			0
$867$			4.53526e8i			0.695897i
$868$		0			0
$869$	2.70736e8			0.412559
$870$		0			0
$871$	−3.48129e8	+	2.00993e8i	−0.526849	+	0.304176i
$872$		0			0
$873$	−3.17183e8	−	1.83125e8i	−0.476724	−	0.275236i
$874$		0			0
$875$	4.32468e8	−	1.91326e8i	0.645549	−	0.285594i
$876$		0			0
$877$	−7.45536e7	+	1.29131e8i	−0.110527	+	0.191439i	−0.915983	−	0.401217i	$-0.868587\pi$
$877$	−7.45536e7	+	1.29131e8i	−0.110527	+	0.191439i	0.805456	+	0.592656i	$0.201921\pi$
$878$		0			0
$879$	−3.31949e8	−	5.74953e8i	−0.488771	−	0.846576i
$880$		0			0
$881$		−	8.53209e8i		−	1.24775i	−0.781524	−	0.623875i	$-0.785557\pi$
$881$		−	8.53209e8i		−	1.24775i	0.781524	−	0.623875i	$-0.214443\pi$
$882$		0			0
$883$	2.32614e7			0.0337874			0.0168937	−	0.999857i	$-0.494622\pi$
$883$	2.32614e7			0.0337874			0.0168937	+	0.999857i	$0.494622\pi$
$884$		0			0
$885$	−1.10562e8	+	6.38332e7i	−0.159506	+	0.0920909i
$886$		0			0
$887$	7.09684e8	+	4.09736e8i	1.01694	+	0.587129i	0.913215	−	0.407477i	$-0.133591\pi$
$887$	7.09684e8	+	4.09736e8i	1.01694	+	0.587129i	0.103722	+	0.994606i	$0.466925\pi$
$888$		0			0
$889$	−1.46128e8	−	3.30304e8i	−0.207984	−	0.470120i
$890$		0			0
$891$	1.69570e7	−	2.93703e7i	0.0239726	−	0.0415217i
$892$		0			0
$893$	3.21683e8	+	5.57171e8i	0.451725	+	0.782410i
$894$		0			0
$895$		−	1.55931e8i		−	0.217502i
$896$		0			0
$897$	−5.40531e8			−0.748933
$898$		0			0
$899$	−3.19149e8	+	1.84261e8i	−0.439253	+	0.253603i
$900$		0			0
$901$	−5.05530e8	−	2.91868e8i	−0.691150	−	0.399036i
$902$		0			0
$903$	6.98419e7	+	5.09953e7i	0.0948534	+	0.0692575i
$904$		0			0
$905$	−1.71541e8	+	2.97118e8i	−0.231431	+	0.400851i
$906$		0			0
$907$	−5.08221e8	−	8.80264e8i	−0.681131	−	1.17975i	−0.974636	−	0.223796i	$-0.928155\pi$
$907$	−5.08221e8	−	8.80264e8i	−0.681131	−	1.17975i	0.293505	−	0.955958i	$-0.405178\pi$
$908$		0			0
$909$			237577.i			0.000316310i
$910$		0			0
$911$	−1.03700e9			−1.37158			−0.685791	−	0.727799i	$-0.740543\pi$
$911$	−1.03700e9			−1.37158			−0.685791	+	0.727799i	$0.740543\pi$
$912$		0			0
$913$	1.79711e8	−	1.03756e8i	0.236136	−	0.136333i
$914$		0			0
$915$	−6.66554e7	−	3.84835e7i	−0.0870106	−	0.0502356i
$916$		0			0
$917$	4.40595e7	−	4.09894e8i	0.0571389	−	0.531574i
$918$		0			0
$919$	4.83007e8	−	8.36592e8i	0.622310	−	1.07787i	−0.366744	−	0.930322i	$-0.619528\pi$
$919$	4.83007e8	−	8.36592e8i	0.622310	−	1.07787i	0.989054	−	0.147551i	$-0.0471390\pi$
$920$		0			0
$921$	−1.24969e8	−	2.16453e8i	−0.159965	−	0.277067i
$922$		0			0
$923$			1.29349e9i			1.64498i
$924$		0			0
$925$	5.40625e8			0.683080
$926$		0			0
$927$	2.89363e8	−	1.67064e8i	0.363248	−	0.209722i
$928$		0			0
$929$	3.72170e8	+	2.14872e8i	0.464188	+	0.267999i	0.713804	−	0.700346i	$-0.246971\pi$
$929$	3.72170e8	+	2.14872e8i	0.464188	+	0.267999i	−0.249616	+	0.968345i	$0.580304\pi$
$930$		0			0
$931$	1.07723e9	−	3.44403e8i	1.33494	−	0.426794i
$932$		0			0
$933$	3.41529e8	−	5.91546e8i	0.420516	−	0.728356i
$934$		0			0
$935$	9.96500e7	+	1.72599e8i	0.121911	+	0.211156i
$936$		0			0
$937$			4.05634e8i			0.493078i	0.969133	+	0.246539i	$0.0792933\pi$
$937$			4.05634e8i			0.493078i	−0.969133	+	0.246539i	$0.920707\pi$
$938$		0			0
$939$	3.21985e7			0.0388901
$940$		0			0
$941$	1.33972e9	−	7.73486e8i	1.60785	−	0.928290i	0.617994	−	0.786183i	$-0.287946\pi$
$941$	1.33972e9	−	7.73486e8i	1.60785	−	0.928290i	0.989851	−	0.142107i	$-0.0453876\pi$
$942$		0			0
$943$	4.36924e8	+	2.52258e8i	0.521040	+	0.300823i
$944$		0			0
$945$	−6.14423e7	−	6.60443e6i	−0.0728068	−	0.00782600i
$946$		0			0
$947$	4.46007e7	−	7.72508e7i	0.0525161	−	0.0909605i	−0.838572	−	0.544790i	$-0.816609\pi$
$947$	4.46007e7	−	7.72508e7i	0.0525161	−	0.0909605i	0.891088	+	0.453830i	$0.149943\pi$
$948$		0			0
$949$	−1.12506e8	−	1.94867e8i	−0.131637	−	0.228002i
$950$		0			0
$951$			3.69154e8i			0.429207i
$952$		0			0
$953$	−7.23811e8			−0.836270			−0.418135	−	0.908385i	$-0.637316\pi$
$953$	−7.23811e8			−0.836270			−0.418135	+	0.908385i	$0.637316\pi$
$954$		0			0
$955$	−2.48578e8	+	1.43516e8i	−0.285399	+	0.164775i
$956$		0			0
$957$	5.73862e7	+	3.31320e7i	0.0654745	+	0.0378017i
$958$		0			0
$959$	−7.74530e8	+	1.06078e9i	−0.878177	+	1.20273i
$960$		0			0
$961$	7.95841e8	−	1.37844e9i	0.896718	−	1.55316i
$962$		0			0
$963$	−2.96116e8	−	5.12888e8i	−0.331576	−	0.574306i
$964$		0			0
$965$			4.73126e8i			0.526496i
$966$		0			0
$967$	−1.40918e9			−1.55843			−0.779216	−	0.626755i	$-0.784383\pi$
$967$	−1.40918e9			−1.55843			−0.779216	+	0.626755i	$0.784383\pi$
$968$		0			0
$969$	9.46830e8	−	5.46652e8i	1.04064	−	0.600814i
$970$		0			0
$971$	1.43083e9	+	8.26092e8i	1.56290	+	0.902342i	0.996962	+	0.0778951i	$0.0248199\pi$
$971$	1.43083e9	+	8.26092e8i	1.56290	+	0.902342i	0.565940	+	0.824446i	$0.308513\pi$
$972$		0			0
$973$	−1.48066e9	+	6.55051e8i	−1.60737	+	0.711110i
$974$		0			0
$975$	2.58026e8	−	4.46915e8i	0.278388	−	0.482182i
$976$		0			0
$977$	−2.43889e8	−	4.22428e8i	−0.261522	−	0.452970i	0.705124	−	0.709084i	$-0.250891\pi$
$977$	−2.43889e8	−	4.22428e8i	−0.261522	−	0.452970i	−0.966647	+	0.256114i	$0.917558\pi$
$978$		0			0
$979$			4.68303e8i			0.499090i
$980$		0			0
$981$	2.29007e7			0.0242572
$982$		0			0
$983$	−3.32429e8	+	1.91928e8i	−0.349976	+	0.202059i	−0.664675	−	0.747133i	$-0.731430\pi$
$983$	−3.32429e8	+	1.91928e8i	−0.349976	+	0.202059i	0.314698	+	0.949192i	$0.398097\pi$
$984$		0			0
$985$	3.54755e8	+	2.04818e8i	0.371210	+	0.214318i
$986$		0			0
$987$	1.44779e8	+	3.27255e8i	0.150575	+	0.340357i
$988$		0			0
$989$	1.13189e8	−	1.96049e8i	0.117008	−	0.202663i
$990$		0			0
$991$	−5.39106e8	−	9.33759e8i	−0.553928	−	0.959432i	−0.997986	−	0.0634336i	$-0.979795\pi$
$991$	−5.39106e8	−	9.33759e8i	−0.553928	−	0.959432i	0.444058	−	0.895998i	$-0.353538\pi$
$992$		0			0
$993$		−	8.37644e8i		−	0.855484i
$994$		0			0
$995$	4.07170e8			0.413339
$996$		0			0
$997$	4.11289e8	−	2.37458e8i	0.415013	−	0.239608i	−0.277929	−	0.960602i	$-0.589648\pi$
$997$	4.11289e8	−	2.37458e8i	0.415013	−	0.239608i	0.692941	+	0.720994i	$0.256315\pi$
$998$		0			0
$999$	−1.32720e8	−	7.66260e7i	−0.133119	−	0.0768563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.c.145.3		8
4.3	odd	2		42.7.g.b.19.2	✓	8
7.3	odd	6	inner	336.7.bh.c.241.3		8
12.11	even	2		126.7.n.b.19.3		8
28.3	even	6		42.7.g.b.31.2	yes	8
28.11	odd	6		294.7.g.b.31.1		8
28.19	even	6		294.7.c.a.97.6		8
28.23	odd	6		294.7.c.a.97.7		8
28.27	even	2		294.7.g.b.19.1		8
84.59	odd	6		126.7.n.b.73.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.7.g.b.19.2	✓	8	4.3	odd	2
42.7.g.b.31.2	yes	8	28.3	even	6
126.7.n.b.19.3		8	12.11	even	2
126.7.n.b.73.3		8	84.59	odd	6
294.7.c.a.97.6		8	28.19	even	6
294.7.c.a.97.7		8	28.23	odd	6
294.7.g.b.19.1		8	28.27	even	2
294.7.g.b.31.1		8	28.11	odd	6
336.7.bh.c.145.3		8	1.1	even	1	trivial
336.7.bh.c.241.3		8	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-13.5000 + 7.79423i) q^{3} +(41.1897 + 23.7809i) q^{5} +(138.771 + 313.674i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 + 7.79423i) q^{3} +(41.1897 + 23.7809i) q^{5} +(138.771 + 313.674i) q^{7} +(121.500 - 210.444i) q^{9} +(287.168 + 497.389i) q^{11} -2477.37i q^{13} -741.415 q^{15} +(6318.50 - 3647.99i) q^{17} +(-8325.02 - 4806.45i) q^{19} +(-4318.26 - 3152.99i) q^{21} +(-6998.35 + 12121.5i) q^{23} +(-6681.44 - 11572.6i) q^{25} +3788.00i q^{27} -7401.31 q^{29} +(43120.6 - 24895.7i) q^{31} +(-7753.53 - 4476.50i) q^{33} +(-1743.52 + 16220.3i) q^{35} +(-20228.6 + 35037.0i) q^{37} +(19309.2 + 33444.5i) q^{39} -36045.4i q^{41} -16173.6 q^{43} +(10009.1 - 5778.76i) q^{45} +(-57960.8 - 33463.7i) q^{47} +(-79134.2 + 87057.8i) q^{49} +(-56866.5 + 98495.7i) q^{51} +(-40003.9 - 69288.8i) q^{53} +27316.4i q^{55} +149850. q^{57} +(149123. - 86096.5i) q^{59} +(89903.0 + 51905.5i) q^{61} +(82871.6 + 8907.87i) q^{63} +(58914.1 - 102042. i) q^{65} +(-81131.3 - 140524. i) q^{67} -218187. i q^{69} -522124. q^{71} +(78658.7 - 45413.6i) q^{73} +(180399. + 104153. i) q^{75} +(-116168. + 159100. i) q^{77} +(235695. - 408235. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -361308. i q^{83} +347010. q^{85} +(99917.7 - 57687.5i) q^{87} +(706142. + 407691. i) q^{89} +(777088. - 343787. i) q^{91} +(-388086. + 672184. i) q^{93} +(-228603. - 395953. i) q^{95} -1.50721e6i q^{97} +139563. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} + 210 q^{5} + 608 q^{7} + 972 q^{9} - 2058 q^{11} - 3780 q^{15} - 11244 q^{17} - 21834 q^{19} - 4482 q^{21} - 15504 q^{23} - 6550 q^{25} + 35316 q^{29} + 51060 q^{31} + 55566 q^{33} - 71460 q^{35} + 20282 q^{37} + 101682 q^{39} - 387812 q^{43} + 51030 q^{45} + 55212 q^{47} - 277780 q^{49} + 101196 q^{51} - 336174 q^{53} + 393012 q^{57} + 560454 q^{59} + 850728 q^{61} - 26730 q^{63} + 826380 q^{65} + 947882 q^{67} - 147192 q^{71} - 533034 q^{73} + 176850 q^{75} - 1848102 q^{77} + 6260 q^{79} - 236196 q^{81} + 560040 q^{85} - 476766 q^{87} + 413460 q^{89} - 256074 q^{91} - 459540 q^{93} + 170880 q^{95} - 1000188 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 + 210 * q^5 + 608 * q^7 + 972 * q^9 - 2058 * q^11 - 3780 * q^15 - 11244 * q^17 - 21834 * q^19 - 4482 * q^21 - 15504 * q^23 - 6550 * q^25 + 35316 * q^29 + 51060 * q^31 + 55566 * q^33 - 71460 * q^35 + 20282 * q^37 + 101682 * q^39 - 387812 * q^43 + 51030 * q^45 + 55212 * q^47 - 277780 * q^49 + 101196 * q^51 - 336174 * q^53 + 393012 * q^57 + 560454 * q^59 + 850728 * q^61 - 26730 * q^63 + 826380 * q^65 + 947882 * q^67 - 147192 * q^71 - 533034 * q^73 + 176850 * q^75 - 1848102 * q^77 + 6260 * q^79 - 236196 * q^81 + 560040 * q^85 - 476766 * q^87 + 413460 * q^89 - 256074 * q^91 - 459540 * q^93 + 170880 * q^95 - 1000188 * q^99

Introduction

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