LMFDB - Embedded newform 72.7.m.a.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("72.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, 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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.12
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.6322 + 23.8627i) q^{3} +(152.846 + 88.2455i) q^{5} +(152.534 + 264.197i) q^{7} +(-409.853 + 602.878i) q^{9} +O(q^{10})$	\(q+(12.6322 + 23.8627i) q^{3} +(152.846 + 88.2455i) q^{5} +(152.534 + 264.197i) q^{7} +(-409.853 + 602.878i) q^{9} +(458.300 - 264.600i) q^{11} +(1607.05 - 2783.49i) q^{13} +(-174.989 + 4762.04i) q^{15} +2535.45i q^{17} -9079.88 q^{19} +(-4377.59 + 6977.27i) q^{21} +(9311.16 + 5375.80i) q^{23} +(7762.03 + 13444.2i) q^{25} +(-19563.6 - 2164.50i) q^{27} +(-559.710 + 323.149i) q^{29} +(-15344.6 + 26577.6i) q^{31} +(12103.4 + 7593.78i) q^{33} +53841.8i q^{35} +32532.3 q^{37} +(86722.0 + 3186.75i) q^{39} +(-113396. - 65469.3i) q^{41} +(76167.3 + 131926. i) q^{43} +(-115845. + 55979.5i) q^{45} +(82469.8 - 47614.0i) q^{47} +(12291.1 - 21288.9i) q^{49} +(-60502.6 + 32028.4i) q^{51} -153021. i q^{53} +93399.0 q^{55} +(-114699. - 216670. i) q^{57} +(-127927. - 73858.9i) q^{59} +(-146956. - 254535. i) q^{61} +(-221795. - 16322.5i) q^{63} +(491260. - 283629. i) q^{65} +(108022. - 187099. i) q^{67} +(-10660.1 + 290097. i) q^{69} -232297. i q^{71} +292835. q^{73} +(-222763. + 355053. i) q^{75} +(139813. + 80721.1i) q^{77} +(379763. + 657769. i) q^{79} +(-195482. - 494183. i) q^{81} +(354469. - 204653. i) q^{83} +(-223742. + 387533. i) q^{85} +(-14781.6 - 9274.07i) q^{87} -1.05651e6i q^{89} +980519. q^{91} +(-828049. - 30428.1i) q^{93} +(-1.38782e6 - 801258. i) q^{95} +(209235. + 362405. i) q^{97} +(-28314.6 + 384746. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	12.6322	+	23.8627i	0.467861	+	0.883802i
$3$	12.6322	+	23.8627i	0.467861	+	0.883802i
$4$		0			0
$5$	152.846	+	88.2455i	1.22277	+	0.705964i	0.965507	−	0.260379i	$-0.0838475\pi$
$5$	152.846	+	88.2455i	1.22277	+	0.705964i	0.257259	+	0.966343i	$0.417181\pi$
$6$		0			0
$7$	152.534	+	264.197i	0.444706	+	0.770254i	0.998032	−	0.0627115i	$-0.0199748\pi$
$7$	152.534	+	264.197i	0.444706	+	0.770254i	−0.553326	+	0.832965i	$0.686641\pi$
$8$		0			0
$9$	−409.853	+	602.878i	−0.562213	+	0.826993i
$10$		0			0
$11$	458.300	−	264.600i	0.344328	−	0.198798i	−0.317856	−	0.948139i	$-0.602963\pi$
$11$	458.300	−	264.600i	0.344328	−	0.198798i	0.662184	+	0.749341i	$0.269630\pi$
$12$		0			0
$13$	1607.05	−	2783.49i	0.731473	−	1.26695i	−0.224780	−	0.974410i	$-0.572166\pi$
$13$	1607.05	−	2783.49i	0.731473	−	1.26695i	0.956253	−	0.292540i	$-0.0945003\pi$
$14$		0			0
$15$	−174.989	+	4762.04i	−0.0518487	+	1.41098i
$16$		0			0
$17$			2535.45i			0.516070i	0.966136	+	0.258035i	$0.0830750\pi$
$17$			2535.45i			0.516070i	−0.966136	+	0.258035i	$0.916925\pi$
$18$		0			0
$19$	−9079.88			−1.32379			−0.661895	−	0.749596i	$-0.730248\pi$
$19$	−9079.88			−1.32379			−0.661895	+	0.749596i	$0.730248\pi$
$20$		0			0
$21$	−4377.59	+	6977.27i	−0.472691	+	0.753404i
$22$		0			0
$23$	9311.16	+	5375.80i	0.765280	+	0.441834i	0.831188	−	0.555991i	$-0.187661\pi$
$23$	9311.16	+	5375.80i	0.765280	+	0.441834i	−0.0659084	+	0.997826i	$0.520995\pi$
$24$		0			0
$25$	7762.03	+	13444.2i	0.496770	+	0.860430i
$26$		0			0
$27$	−19563.6	−	2164.50i	−0.993935	−	0.109968i
$28$		0			0
$29$	−559.710	+	323.149i	−0.0229493	+	0.0132498i	−0.511431	−	0.859324i	$-0.670884\pi$
$29$	−559.710	+	323.149i	−0.0229493	+	0.0132498i	0.488481	+	0.872574i	$0.337551\pi$
$30$		0			0
$31$	−15344.6	+	26577.6i	−0.515075	+	0.892136i	0.484772	+	0.874640i	$0.338903\pi$
$31$	−15344.6	+	26577.6i	−0.515075	+	0.892136i	−0.999847	+	0.0174953i	$0.994431\pi$
$32$		0			0
$33$	12103.4	+	7593.78i	0.336795	+	0.211308i
$34$		0			0
$35$			53841.8i			1.25579i
$36$		0			0
$37$	32532.3			0.642259			0.321129	−	0.947035i	$-0.395938\pi$
$37$	32532.3			0.642259			0.321129	+	0.947035i	$0.395938\pi$
$38$		0			0
$39$	86722.0	+	3186.75i	1.46196	+	0.0537223i
$40$		0			0
$41$	−113396.	−	65469.3i	−1.64531	−	0.949917i	−0.978903	−	0.204325i	$-0.934500\pi$
$41$	−113396.	−	65469.3i	−1.64531	−	0.949917i	−0.666402	−	0.745593i	$-0.732167\pi$
$42$		0			0
$43$	76167.3	+	131926.i	0.957995	+	1.65930i	0.727362	+	0.686254i	$0.240746\pi$
$43$	76167.3	+	131926.i	0.957995	+	1.65930i	0.230633	+	0.973041i	$0.425920\pi$
$44$		0			0
$45$	−115845.	+	55979.5i	−1.27128	+	0.614316i
$46$		0			0
$47$	82469.8	−	47614.0i	0.794331	−	0.458607i	−0.0471543	−	0.998888i	$-0.515015\pi$
$47$	82469.8	−	47614.0i	0.794331	−	0.458607i	0.841485	+	0.540281i	$0.181682\pi$
$48$		0			0
$49$	12291.1	−	21288.9i	0.104473	−	0.180953i
$50$		0			0
$51$	−60502.6	+	32028.4i	−0.456104	+	0.241449i
$52$		0			0
$53$		−	153021.i		−	1.02784i	−0.857839	−	0.513918i	$-0.828193\pi$
$53$		−	153021.i		−	1.02784i	0.857839	−	0.513918i	$-0.171807\pi$
$54$		0			0
$55$	93399.0			0.561376
$56$		0			0
$57$	−114699.	−	216670.i	−0.619349	−	1.16997i
$58$		0			0
$59$	−127927.	−	73858.9i	−0.622885	−	0.359623i	0.155107	−	0.987898i	$-0.450428\pi$
$59$	−127927.	−	73858.9i	−0.622885	−	0.359623i	−0.777991	+	0.628275i	$0.783761\pi$
$60$		0			0
$61$	−146956.	−	254535.i	−0.647437	−	1.12139i	−0.983733	−	0.179637i	$-0.942508\pi$
$61$	−146956.	−	254535.i	−0.647437	−	1.12139i	0.336296	−	0.941756i	$-0.390826\pi$
$62$		0			0
$63$	−221795.	−	16322.5i	−0.887013	−	0.0652778i
$64$		0			0
$65$	491260.	−	283629.i	1.78884	−	1.03279i
$66$		0			0
$67$	108022.	−	187099.i	0.359159	−	0.622082i	−0.628661	−	0.777679i	$-0.716397\pi$
$67$	108022.	−	187099.i	0.359159	−	0.622082i	0.987821	+	0.155597i	$0.0497301\pi$
$68$		0			0
$69$	−10660.1	+	290097.i	−0.0324500	+	0.883073i
$70$		0			0
$71$		−	232297.i		−	0.649036i	−0.945880	−	0.324518i	$-0.894798\pi$
$71$		−	232297.i		−	0.649036i	0.945880	−	0.324518i	$-0.105202\pi$
$72$		0			0
$73$	292835.			0.752756			0.376378	−	0.926466i	$-0.377169\pi$
$73$	292835.			0.752756			0.376378	+	0.926466i	$0.377169\pi$
$74$		0			0
$75$	−222763.	+	355053.i	−0.528031	+	0.841608i
$76$		0			0
$77$	139813.	+	80721.1i	0.306249	+	0.176813i
$78$		0			0
$79$	379763.	+	657769.i	0.770250	+	1.33411i	0.937426	+	0.348185i	$0.113202\pi$
$79$	379763.	+	657769.i	0.770250	+	1.33411i	−0.167176	+	0.985927i	$0.553465\pi$
$80$		0			0
$81$	−195482.	−	494183.i	−0.367833	−	0.929892i
$82$		0			0
$83$	354469.	−	204653.i	0.619931	−	0.357918i	−0.156911	−	0.987613i	$-0.550154\pi$
$83$	354469.	−	204653.i	0.619931	−	0.357918i	0.776842	+	0.629695i	$0.216820\pi$
$84$		0			0
$85$	−223742.	+	387533.i	−0.364327	+	0.631032i
$86$		0			0
$87$	−14781.6	−	9274.07i	−0.0224472	−	0.0140836i
$88$		0			0
$89$		−	1.05651e6i		−	1.49866i	−0.662195	−	0.749331i	$-0.730375\pi$
$89$		−	1.05651e6i		−	1.49866i	0.662195	−	0.749331i	$-0.269625\pi$
$90$		0			0
$91$	980519.			1.30116
$92$		0			0
$93$	−828049.	−	30428.1i	−1.02945	−	0.0378291i
$94$		0			0
$95$	−1.38782e6	−	801258.i	−1.61868	−	0.934548i
$96$		0			0
$97$	209235.	+	362405.i	0.229255	+	0.397081i	0.957587	−	0.288143i	$-0.0930378\pi$
$97$	209235.	+	362405.i	0.229255	+	0.397081i	−0.728333	+	0.685224i	$0.759704\pi$
$98$		0			0
$99$	−28314.6	+	384746.i	−0.0291813	+	0.396523i
$100$		0			0
$101$	−1.11139e6	+	641662.i	−1.07871	+	0.622791i	−0.930547	−	0.366173i	$-0.880668\pi$
$101$	−1.11139e6	+	641662.i	−1.07871	+	0.622791i	−0.148158	+	0.988964i	$0.547335\pi$
$102$		0			0
$103$	−603557.	+	1.04539e6i	−0.552341	+	0.956682i	0.445765	+	0.895150i	$0.352932\pi$
$103$	−603557.	+	1.04539e6i	−0.552341	+	0.956682i	−0.998105	+	0.0615316i	$0.980401\pi$
$104$		0			0
$105$	−1.28481e6	+	680142.i	−1.10987	+	0.587533i
$106$		0			0
$107$		−	847174.i		−	0.691547i	−0.938318	−	0.345773i	$-0.887617\pi$
$107$		−	847174.i		−	0.691547i	0.938318	−	0.345773i	$-0.112383\pi$
$108$		0			0
$109$	1.87372e6			1.44685			0.723426	−	0.690402i	$-0.242566\pi$
$109$	1.87372e6			1.44685			0.723426	+	0.690402i	$0.242566\pi$
$110$		0			0
$111$	410956.	+	776308.i	0.300488	+	0.567630i
$112$		0			0
$113$	2.04561e6	+	1.18103e6i	1.41771	+	0.818516i	0.996098	−	0.0882594i	$-0.0281304\pi$
$113$	2.04561e6	+	1.18103e6i	1.41771	+	0.818516i	0.421614	+	0.906775i	$0.361464\pi$
$114$		0			0
$115$	948780.	+	1.64334e6i	0.623838	+	1.08052i
$116$		0			0
$117$	1.01945e6	+	2.10967e6i	0.636514	+	1.31722i
$118$		0			0
$119$	−669859.	+	386743.i	−0.397505	+	0.229499i
$120$		0			0
$121$	−745754.	+	1.29168e6i	−0.420959	+	0.729122i
$122$		0			0
$123$	129825.	−	3.53296e6i	0.0697656	−	1.89855i
$124$		0			0
$125$		−	17816.3i		−	0.00912192i
$126$		0			0
$127$	−1.19607e6			−0.583909			−0.291955	−	0.956432i	$-0.594306\pi$
$127$	−1.19607e6			−0.583909			−0.291955	+	0.956432i	$0.594306\pi$
$128$		0			0
$129$	−2.18593e6	+	3.48407e6i	−1.01828	+	1.62300i
$130$		0			0
$131$	1.83912e6	+	1.06182e6i	0.818083	+	0.472320i	0.849755	−	0.527178i	$-0.176750\pi$
$131$	1.83912e6	+	1.06182e6i	0.818083	+	0.472320i	−0.0316720	+	0.999498i	$0.510083\pi$
$132$		0			0
$133$	−1.38499e6	−	2.39888e6i	−0.588698	−	1.01965i
$134$		0			0
$135$	−2.79921e6	−	2.05724e6i	−1.13772	−	0.836147i
$136$		0			0
$137$	3.45588e6	−	1.99526e6i	1.34399	−	0.775956i	0.356603	−	0.934256i	$-0.383935\pi$
$137$	3.45588e6	−	1.99526e6i	1.34399	−	0.775956i	0.987391	+	0.158300i	$0.0506014\pi$
$138$		0			0
$139$	507765.	−	879474.i	0.189068	−	0.327475i	−0.755872	−	0.654720i	$-0.772787\pi$
$139$	507765.	−	879474.i	0.189068	−	0.327475i	0.944940	+	0.327244i	$0.106120\pi$
$140$		0			0
$141$	2.17797e6	+	1.36648e6i	0.776954	+	0.487467i
$142$		0			0
$143$		−	1.70090e6i		−	0.581661i
$144$		0			0
$145$	−114066.			−0.0374154
$146$		0			0
$147$	663274.	+	24373.2i	0.208805	+	0.00767290i
$148$		0			0
$149$	−647143.	−	373628.i	−0.195633	−	0.112949i	0.398984	−	0.916958i	$-0.369363\pi$
$149$	−647143.	−	373628.i	−0.195633	−	0.112949i	−0.594617	+	0.804009i	$0.702696\pi$
$150$		0			0
$151$	−973822.	−	1.68671e6i	−0.282845	−	0.489902i	0.689239	−	0.724534i	$-0.257945\pi$
$151$	−973822.	−	1.68671e6i	−0.282845	−	0.489902i	−0.972084	+	0.234632i	$0.924612\pi$
$152$		0			0
$153$	−1.52857e6	−	1.03916e6i	−0.426786	−	0.290141i
$154$		0			0
$155$	−4.69071e6	+	2.70818e6i	−1.25963	+	0.727248i
$156$		0			0
$157$	2.56557e6	−	4.44369e6i	0.662956	−	1.14827i	−0.316879	−	0.948466i	$-0.602635\pi$
$157$	2.56557e6	−	4.44369e6i	0.662956	−	1.14827i	0.979835	−	0.199807i	$-0.0640317\pi$
$158$		0			0
$159$	3.65149e6	−	1.93300e6i	0.908404	−	0.480884i
$160$		0			0
$161$			3.27997e6i			0.785946i
$162$		0			0
$163$	601118.			0.138802			0.0694012	−	0.997589i	$-0.477891\pi$
$163$	601118.			0.138802			0.0694012	+	0.997589i	$0.477891\pi$
$164$		0			0
$165$	1.17984e6	+	2.22875e6i	0.262646	+	0.496146i
$166$		0			0
$167$	−6.61143e6	−	3.81711e6i	−1.41953	−	0.819569i	−0.423277	−	0.906000i	$-0.639120\pi$
$167$	−6.61143e6	−	3.81711e6i	−1.41953	−	0.819569i	−0.996258	+	0.0864315i	$0.972454\pi$
$168$		0			0
$169$	−2.75180e6	−	4.76625e6i	−0.570107	−	0.987454i
$170$		0			0
$171$	3.72142e6	−	5.47406e6i	0.744252	−	1.09476i
$172$		0			0
$173$	2.61931e6	−	1.51226e6i	0.505881	−	0.292071i	−0.225258	−	0.974299i	$-0.572322\pi$
$173$	2.61931e6	−	1.51226e6i	0.505881	−	0.292071i	0.731139	+	0.682229i	$0.238989\pi$
$174$		0			0
$175$	−2.36795e6	+	4.10141e6i	−0.441833	+	0.765277i
$176$		0			0
$177$	146461.	−	3.98569e6i	0.0264121	−	0.718760i
$178$		0			0
$179$		−	1.64844e6i		−	0.287419i	−0.989620	−	0.143709i	$-0.954097\pi$
$179$		−	1.64844e6i		−	0.287419i	0.989620	−	0.143709i	$-0.0459031\pi$
$180$		0			0
$181$	−2.10547e6			−0.355069			−0.177535	−	0.984115i	$-0.556812\pi$
$181$	−2.10547e6			−0.355069			−0.177535	+	0.984115i	$0.556812\pi$
$182$		0			0
$183$	4.21750e6	−	6.72211e6i	0.688180	−	1.09686i
$184$		0			0
$185$	4.97242e6	+	2.87083e6i	0.785332	+	0.453411i
$186$		0			0
$187$	670880.	+	1.16200e6i	0.102594	+	0.177697i
$188$		0			0
$189$	−2.41227e6	−	5.49881e6i	−0.357306	−	0.814485i
$190$		0			0
$191$	−2.87616e6	+	1.66055e6i	−0.412775	+	0.238316i	−0.691981	−	0.721916i	$-0.743262\pi$
$191$	−2.87616e6	+	1.66055e6i	−0.412775	+	0.238316i	0.279207	+	0.960231i	$0.409929\pi$
$192$		0			0
$193$	−3.89928e6	+	6.75375e6i	−0.542391	+	0.939449i	0.456375	+	0.889788i	$0.349148\pi$
$193$	−3.89928e6	+	6.75375e6i	−0.542391	+	0.939449i	−0.998766	+	0.0496616i	$0.984186\pi$
$194$		0			0
$195$	1.29739e7	+	8.13991e6i	1.74971	+	1.09778i
$196$		0			0
$197$			1.17590e7i			1.53805i	0.639217	+	0.769026i	$0.279258\pi$
$197$			1.17590e7i			1.53805i	−0.639217	+	0.769026i	$0.720742\pi$
$198$		0			0
$199$	9.07325e6			1.15134			0.575670	−	0.817682i	$-0.304741\pi$
$199$	9.07325e6			1.15134			0.575670	+	0.817682i	$0.304741\pi$
$200$		0			0
$201$	5.82925e6	+	214206.i	0.717834	+	0.0263781i
$202$		0			0
$203$	−170750.	−	98582.4i	−0.0204114	−	0.0117845i
$204$		0			0
$205$	−1.15547e7	−	2.00134e7i	−1.34121	−	2.32305i
$206$		0			0
$207$	−7.05716e6	+	3.41020e6i	−0.795644	+	0.384476i
$208$		0			0
$209$	−4.16131e6	+	2.40253e6i	−0.455818	+	0.263167i
$210$		0			0
$211$	−5.96405e6	+	1.03300e7i	−0.634883	+	1.09965i	0.351657	+	0.936129i	$0.385618\pi$
$211$	−5.96405e6	+	1.03300e7i	−0.634883	+	1.09965i	−0.986540	+	0.163521i	$0.947715\pi$
$212$		0			0
$213$	5.54323e6	−	2.93443e6i	0.573619	−	0.303658i
$214$		0			0
$215$			2.68857e7i			2.70524i
$216$		0			0
$217$	−9.36230e6			−0.916228
$218$		0			0
$219$	3.69916e6	+	6.98782e6i	0.352185	+	0.665288i
$220$		0			0
$221$	7.05740e6	+	4.07459e6i	0.653834	+	0.377492i
$222$		0			0
$223$	−8.52936e6	−	1.47733e7i	−0.769134	−	1.33218i	−0.938033	−	0.346546i	$-0.887354\pi$
$223$	−8.52936e6	−	1.47733e7i	−0.769134	−	1.33218i	0.168899	−	0.985633i	$-0.445979\pi$
$224$		0			0
$225$	−1.12865e7	−	830607.i	−0.990860	−	0.0729202i
$226$		0			0
$227$	5.55823e6	−	3.20904e6i	0.475181	−	0.274346i	−0.243225	−	0.969970i	$-0.578205\pi$
$227$	5.55823e6	−	3.20904e6i	0.475181	−	0.274346i	0.718406	+	0.695624i	$0.244872\pi$
$228$		0			0
$229$	404953.	−	701400.i	0.0337209	−	0.0584062i	−0.848672	−	0.528919i	$-0.822598\pi$
$229$	404953.	−	701400.i	0.0337209	−	0.0584062i	0.882393	+	0.470513i	$0.155931\pi$
$230$		0			0
$231$	−160069.	+	4.35600e6i	−0.0129859	+	0.353388i
$232$		0			0
$233$		−	1.05567e7i		−	0.834565i	−0.908777	−	0.417283i	$-0.862983\pi$
$233$		−	1.05567e7i		−	0.834565i	0.908777	−	0.417283i	$-0.137017\pi$
$234$		0			0
$235$	1.68069e7			1.29504
$236$		0			0
$237$	−1.08989e7	+	1.73713e7i	−0.818721	+	1.30493i
$238$		0			0
$239$	−1.00585e7	−	5.80725e6i	−0.736780	−	0.425380i	0.0841176	−	0.996456i	$-0.473193\pi$
$239$	−1.00585e7	−	5.80725e6i	−0.736780	−	0.425380i	−0.820897	+	0.571076i	$0.806526\pi$
$240$		0			0
$241$	−4.14105e6	−	7.17251e6i	−0.295842	−	0.512413i	0.679339	−	0.733825i	$-0.262267\pi$
$241$	−4.14105e6	−	7.17251e6i	−0.295842	−	0.512413i	−0.975180	+	0.221412i	$0.928933\pi$
$242$		0			0
$243$	9.32314e6	−	1.09073e7i	0.649746	−	0.760152i
$244$		0			0
$245$	3.75729e6	−	2.16928e6i	0.255492	−	0.147508i
$246$		0			0
$247$	−1.45918e7	+	2.52737e7i	−0.968318	+	1.67718i
$248$		0			0
$249$	9.36129e6	+	5.87335e6i	0.606370	+	0.380441i
$250$		0			0
$251$			1.08466e7i			0.685921i	0.939350	+	0.342960i	$0.111430\pi$
$251$			1.08466e7i			0.685921i	−0.939350	+	0.342960i	$0.888570\pi$
$252$		0			0
$253$	5.68974e6			0.351343
$254$		0			0
$255$	−1.20739e7	−	443677.i	−0.728162	−	0.0267576i
$256$		0			0
$257$	9.47369e6	+	5.46964e6i	0.558110	+	0.322225i	0.752387	−	0.658722i	$-0.228903\pi$
$257$	9.47369e6	+	5.46964e6i	0.558110	+	0.322225i	−0.194277	+	0.980947i	$0.562236\pi$
$258$		0			0
$259$	4.96229e6	+	8.59494e6i	0.285616	+	0.494702i
$260$		0			0
$261$	34579.8	−	469880.i	0.00194492	−	0.0264281i
$262$		0			0
$263$	−1.47766e7	+	8.53127e6i	−0.812282	+	0.468971i	−0.847748	−	0.530400i	$-0.822042\pi$
$263$	−1.47766e7	+	8.53127e6i	−0.812282	+	0.468971i	0.0354656	+	0.999371i	$0.488709\pi$
$264$		0			0
$265$	1.35034e7	−	2.33886e7i	0.725615	−	1.25680i
$266$		0			0
$267$	2.52112e7	−	1.33461e7i	1.32452	−	0.701165i
$268$		0			0
$269$		−	1.08090e7i		−	0.555303i	−0.960682	−	0.277651i	$-0.910444\pi$
$269$		−	1.08090e7i		−	0.555303i	0.960682	−	0.277651i	$-0.0895560\pi$
$270$		0			0
$271$	−8.37302e6			−0.420702			−0.210351	−	0.977626i	$-0.567461\pi$
$271$	−8.37302e6			−0.420702			−0.210351	+	0.977626i	$0.567461\pi$
$272$		0			0
$273$	1.23861e7	+	2.33978e7i	0.608763	+	1.14997i
$274$		0			0
$275$	7.11468e6	+	4.10766e6i	0.342103	+	0.197513i
$276$		0			0
$277$	1.68349e7	+	2.91589e7i	0.792083	+	1.37193i	0.924675	+	0.380757i	$0.124337\pi$
$277$	1.68349e7	+	2.91589e7i	0.792083	+	1.37193i	−0.132592	+	0.991171i	$0.542330\pi$
$278$		0			0
$279$	−9.73402e6	−	2.01438e7i	−0.448208	−	0.927533i
$280$		0			0
$281$	−1.78319e7	+	1.02953e7i	−0.803672	+	0.464000i	−0.844753	−	0.535156i	$-0.820253\pi$
$281$	−1.78319e7	+	1.02953e7i	−0.803672	+	0.464000i	0.0410817	+	0.999156i	$0.486920\pi$
$282$		0			0
$283$	2.94310e6	−	5.09759e6i	0.129851	−	0.224908i	−0.793768	−	0.608221i	$-0.791883\pi$
$283$	2.94310e6	−	5.09759e6i	0.129851	−	0.224908i	0.923619	+	0.383313i	$0.125217\pi$
$284$		0			0
$285$	1.58888e6	−	4.32388e7i	0.0686369	−	1.86784i
$286$		0			0
$287$		−	3.99452e7i		−	1.68974i
$288$		0			0
$289$	1.77091e7			0.733672
$290$		0			0
$291$	−6.00485e6	+	9.57088e6i	−0.243682	+	0.388395i
$292$		0			0
$293$	−2.11892e7	−	1.22336e7i	−0.842387	−	0.486352i	0.0156879	−	0.999877i	$-0.495006\pi$
$293$	−2.11892e7	−	1.22336e7i	−0.842387	−	0.486352i	−0.858075	+	0.513525i	$0.828340\pi$
$294$		0			0
$295$	−1.30354e7	−	2.25780e7i	−0.507761	−	0.879468i
$296$		0			0
$297$	−9.53874e6	+	4.18454e6i	−0.364101	+	0.159727i
$298$		0			0
$299$	2.99269e7	−	1.72783e7i	1.11956	−	0.646380i
$300$		0			0
$301$	−2.32362e7	+	4.02463e7i	−0.852052	+	1.47580i
$302$		0			0
$303$	−2.93511e7	−	1.84151e7i	−1.05511	−	0.661983i
$304$		0			0
$305$		−	5.18728e7i		−	1.82827i
$306$		0			0
$307$	3.18476e7			1.10068			0.550340	−	0.834941i	$-0.314498\pi$
$307$	3.18476e7			1.10068			0.550340	+	0.834941i	$0.314498\pi$
$308$		0			0
$309$	−3.25701e7	−	1.19685e6i	−1.10394	−	0.0405660i
$310$		0			0
$311$	5.00795e6	+	2.89134e6i	0.166486	+	0.0961209i	0.580928	−	0.813955i	$-0.302690\pi$
$311$	5.00795e6	+	2.89134e6i	0.166486	+	0.0961209i	−0.414442	+	0.910076i	$0.636023\pi$
$312$		0			0
$313$	−1.73591e7	−	3.00669e7i	−0.566102	−	0.980518i	−0.996946	−	0.0780914i	$-0.975117\pi$
$313$	−1.73591e7	−	3.00669e7i	−0.566102	−	0.980518i	0.430844	−	0.902426i	$-0.358216\pi$
$314$		0			0
$315$	−3.24600e7	−	2.20672e7i	−1.03853	−	0.706019i
$316$		0			0
$317$	−5.46245e6	+	3.15374e6i	−0.171478	+	0.0990031i	−0.583283	−	0.812269i	$-0.698232\pi$
$317$	−5.46245e6	+	3.15374e6i	−0.171478	+	0.0990031i	0.411804	+	0.911272i	$0.364899\pi$
$318$		0			0
$319$	−171010.	+	296198.i	−0.00526805	+	0.00912453i
$320$		0			0
$321$	2.02158e7	−	1.07017e7i	0.611190	−	0.323547i
$322$		0			0
$323$		−	2.30216e7i		−	0.683169i
$324$		0			0
$325$	4.98958e7			1.45350
$326$		0			0
$327$	2.36692e7	+	4.47119e7i	0.676925	+	1.27873i
$328$		0			0
$329$	2.51589e7	+	1.45255e7i	0.706487	+	0.407891i
$330$		0			0
$331$	−1.24610e7	−	2.15831e7i	−0.343612	−	0.595154i	0.641488	−	0.767133i	$-0.278317\pi$
$331$	−1.24610e7	−	2.15831e7i	−0.343612	−	0.595154i	−0.985101	+	0.171979i	$0.944984\pi$
$332$		0			0
$333$	−1.33335e7	+	1.96130e7i	−0.361086	+	0.531143i
$334$		0			0
$335$	3.30213e7	−	1.90649e7i	0.878335	−	0.507107i
$336$		0			0
$337$	−1.37907e7	+	2.38863e7i	−0.360328	+	0.624106i	−0.988015	−	0.154360i	$-0.950669\pi$
$337$	−1.37907e7	+	2.38863e7i	−0.360328	+	0.624106i	0.627687	+	0.778466i	$0.284002\pi$
$338$		0			0
$339$	−2.34197e6	+	6.37328e7i	−0.0601150	+	1.63593i
$340$		0			0
$341$			1.62407e7i			0.409583i
$342$		0			0
$343$	4.33903e7			1.07525
$344$		0			0
$345$	−2.72291e7	+	4.33994e7i	−0.663096	+	1.05688i
$346$		0			0
$347$	−3.46464e7	−	2.00031e7i	−0.829221	−	0.478751i	0.0243650	−	0.999703i	$-0.492244\pi$
$347$	−3.46464e7	−	2.00031e7i	−0.829221	−	0.478751i	−0.853586	+	0.520952i	$0.825577\pi$
$348$		0			0
$349$	3.51133e7	+	6.08181e7i	0.826030	+	1.43073i	0.901130	+	0.433550i	$0.142739\pi$
$349$	3.51133e7	+	6.08181e7i	0.826030	+	1.43073i	−0.0750996	+	0.997176i	$0.523927\pi$
$350$		0			0
$351$	−3.74645e7	+	5.09767e7i	−0.866361	+	1.17883i
$352$		0			0
$353$	−1.07056e7	+	6.18087e6i	−0.243381	+	0.140516i	−0.616729	−	0.787175i	$-0.711543\pi$
$353$	−1.07056e7	+	6.18087e6i	−0.243381	+	0.140516i	0.373349	+	0.927691i	$0.378209\pi$
$354$		0			0
$355$	2.04992e7	−	3.55056e7i	0.458196	−	0.793618i
$356$		0			0
$357$	−1.76905e7	−	1.10992e7i	−0.388809	−	0.243942i
$358$		0			0
$359$		−	1.77807e7i		−	0.384296i	−0.981366	−	0.192148i	$-0.938455\pi$
$359$		−	1.77807e7i		−	0.384296i	0.981366	−	0.192148i	$-0.0615454\pi$
$360$		0			0
$361$	3.53983e7			0.752421
$362$		0			0
$363$	−4.02436e7	−	1.47882e6i	−0.841350	−	0.0309169i
$364$		0			0
$365$	4.47586e7	+	2.58414e7i	0.920444	+	0.531419i
$366$		0			0
$367$	−4.61099e6	−	7.98646e6i	−0.0932815	−	0.161568i	0.815609	−	0.578604i	$-0.196402\pi$
$367$	−4.61099e6	−	7.98646e6i	−0.0932815	−	0.161568i	−0.908890	+	0.417036i	$0.863069\pi$
$368$		0			0
$369$	8.59457e7	−	4.15312e7i	1.71059	−	0.826599i
$370$		0			0
$371$	4.04277e7	−	2.33410e7i	0.791695	−	0.457085i
$372$		0			0
$373$	−3.22734e7	+	5.58991e7i	−0.621896	+	1.07716i	0.367236	+	0.930128i	$0.380304\pi$
$373$	−3.22734e7	+	5.58991e7i	−0.621896	+	1.07716i	−0.989132	+	0.147028i	$0.953029\pi$
$374$		0			0
$375$	425143.	−	225059.i	0.00806198	−	0.00426779i
$376$		0			0
$377$			2.07726e6i			0.0387674i
$378$		0			0
$379$	−9.87904e7			−1.81467			−0.907334	−	0.420410i	$-0.861886\pi$
$379$	−9.87904e7			−1.81467			−0.907334	+	0.420410i	$0.861886\pi$
$380$		0			0
$381$	−1.51090e7	−	2.85414e7i	−0.273188	−	0.516060i
$382$		0			0
$383$	−4.13770e7	−	2.38890e7i	−0.736483	−	0.425209i	0.0843059	−	0.996440i	$-0.473133\pi$
$383$	−4.13770e7	−	2.38890e7i	−0.736483	−	0.425209i	−0.820789	+	0.571231i	$0.806466\pi$
$384$		0			0
$385$	1.42465e7	+	2.46757e7i	0.249647	+	0.432402i
$386$		0			0
$387$	−1.10752e8	−	8.15058e6i	−1.91082	−	0.140623i
$388$		0			0
$389$	−1.82940e7	+	1.05620e7i	−0.310785	+	0.179432i	−0.647278	−	0.762254i	$-0.724093\pi$
$389$	−1.82940e7	+	1.05620e7i	−0.310785	+	0.179432i	0.336493	+	0.941686i	$0.390759\pi$
$390$		0			0
$391$	−1.36301e7	+	2.36080e7i	−0.228018	+	0.394938i
$392$		0			0
$393$	−2.10557e6	+	5.72996e7i	−0.0346891	+	0.944004i
$394$		0			0
$395$			1.34050e8i			2.17507i
$396$		0			0
$397$	4.42027e7			0.706443			0.353222	−	0.935540i	$-0.385086\pi$
$397$	4.42027e7			0.706443			0.353222	+	0.935540i	$0.385086\pi$
$398$		0			0
$399$	3.97480e7	−	6.33528e7i	0.625744	−	0.997348i
$400$		0			0
$401$	−9.50260e7	−	5.48633e7i	−1.47370	−	0.850842i	−0.474139	−	0.880450i	$-0.657241\pi$
$401$	−9.50260e7	−	5.48633e7i	−1.47370	−	0.850842i	−0.999562	+	0.0296082i	$0.990574\pi$
$402$		0			0
$403$	4.93190e7	+	8.54230e7i	0.753527	+	1.30515i
$404$		0			0
$405$	1.37308e7	−	9.27840e7i	0.206696	−	1.39672i
$406$		0			0
$407$	1.49096e7	−	8.60805e6i	0.221148	−	0.127680i
$408$		0			0
$409$	−6.26959e7	+	1.08593e8i	−0.916367	+	1.58719i	−0.111480	+	0.993767i	$0.535559\pi$
$409$	−6.26959e7	+	1.08593e8i	−0.916367	+	1.58719i	−0.804887	+	0.593428i	$0.797774\pi$
$410$		0			0
$411$	9.12677e7	+	5.72621e7i	1.31459	+	0.824786i
$412$		0			0
$413$		−	4.50640e7i		−	0.639705i
$414$		0			0
$415$	7.22387e7			1.01071
$416$		0			0
$417$	2.74008e7	+	1.00689e6i	0.377881	+	0.0138859i
$418$		0			0
$419$	3.37497e7	+	1.94854e7i	0.458804	+	0.264891i	0.711541	−	0.702644i	$-0.247997\pi$
$419$	3.37497e7	+	1.94854e7i	0.458804	+	0.264891i	−0.252737	+	0.967535i	$0.581331\pi$
$420$		0			0
$421$	−3.84468e7	−	6.65917e7i	−0.515245	−	0.892430i	−0.999843	−	0.0176934i	$-0.994368\pi$
$421$	−3.84468e7	−	6.65917e7i	−0.515245	−	0.892430i	0.484599	−	0.874737i	$-0.338966\pi$
$422$		0			0
$423$	−5.09512e6	+	6.92339e7i	−0.0673183	+	0.914740i
$424$		0			0
$425$	−3.40872e7	+	1.96802e7i	−0.444042	+	0.256368i
$426$		0			0
$427$	4.48316e7	−	7.76506e7i	0.575838	−	0.997381i
$428$		0			0
$429$	4.05879e7	−	2.14861e7i	0.514073	−	0.272136i
$430$		0			0
$431$			6.73782e7i			0.841565i	0.907162	+	0.420782i	$0.138244\pi$
$431$			6.73782e7i			0.841565i	−0.907162	+	0.420782i	$0.861756\pi$
$432$		0			0
$433$	−6.68372e7			−0.823293			−0.411647	−	0.911344i	$-0.635046\pi$
$433$	−6.68372e7			−0.823293			−0.411647	+	0.911344i	$0.635046\pi$
$434$		0			0
$435$	−1.44090e6	−	2.72191e6i	−0.0175052	−	0.0330678i
$436$		0			0
$437$	−8.45442e7	−	4.88116e7i	−1.01307	−	0.584896i
$438$		0			0
$439$	−5.72889e7	−	9.92273e7i	−0.677138	−	1.17284i	−0.975839	−	0.218490i	$-0.929887\pi$
$439$	−5.72889e7	−	9.92273e7i	−0.677138	−	1.17284i	0.298702	−	0.954347i	$-0.403446\pi$
$440$		0			0
$441$	7.79703e6	+	1.61354e7i	0.0909103	+	0.188132i
$442$		0			0
$443$	6.01363e7	−	3.47197e7i	0.691712	−	0.399360i	−0.112541	−	0.993647i	$-0.535899\pi$
$443$	6.01363e7	−	3.47197e7i	0.691712	−	0.399360i	0.804253	+	0.594287i	$0.202566\pi$
$444$		0			0
$445$	9.32323e7	−	1.61483e8i	1.05800	−	1.83251i
$446$		0			0
$447$	740900.	−	2.01623e7i	0.00829539	−	0.225745i
$448$		0			0
$449$		−	6.62259e7i		−	0.731625i	−0.930689	−	0.365813i	$-0.880791\pi$
$449$		−	6.62259e7i		−	0.731625i	0.930689	−	0.365813i	$-0.119209\pi$
$450$		0			0
$451$	−6.92926e7			−0.755366
$452$		0			0
$453$	2.79478e7	−	4.45449e7i	0.300645	−	0.479185i
$454$		0			0
$455$	1.49868e8	+	8.65263e7i	1.59102	+	0.918574i
$456$		0			0
$457$	−1.01848e7	−	1.76406e7i	−0.106710	−	0.184827i	0.807726	−	0.589559i	$-0.200698\pi$
$457$	−1.01848e7	−	1.76406e7i	−0.106710	−	0.184827i	−0.914436	+	0.404732i	$0.867365\pi$
$458$		0			0
$459$	5.48798e6	−	4.96026e7i	0.0567511	−	0.512940i
$460$		0			0
$461$	−1.15890e8	+	6.69090e7i	−1.18288	+	0.682938i	−0.956680	−	0.291142i	$-0.905965\pi$
$461$	−1.15890e8	+	6.69090e7i	−1.18288	+	0.682938i	−0.226204	+	0.974080i	$0.572632\pi$
$462$		0			0
$463$	−2.87620e7	+	4.98172e7i	−0.289785	+	0.501922i	−0.973758	−	0.227585i	$-0.926917\pi$
$463$	−2.87620e7	+	4.98172e7i	−0.289785	+	0.501922i	0.683973	+	0.729507i	$0.260250\pi$
$464$		0			0
$465$	−1.23879e8	−	7.77224e7i	−1.23208	−	0.773014i
$466$		0			0
$467$		−	976346.i		−	0.00958635i	−0.999989	−	0.00479317i	$-0.998474\pi$
$467$		−	976346.i		−	0.00958635i	0.999989	−	0.00479317i	$-0.00152572\pi$
$468$		0			0
$469$	6.59081e7			0.638882
$470$		0			0
$471$	1.38447e8	+	5.08748e6i	1.32502	+	0.0486901i
$472$		0			0
$473$	6.98150e7	+	4.03077e7i	0.659728	+	0.380894i
$474$		0			0
$475$	−7.04783e7	−	1.22072e8i	−0.657619	−	1.13903i
$476$		0			0
$477$	9.22531e7	+	6.27162e7i	0.850013	+	0.577863i
$478$		0			0
$479$	1.14205e8	−	6.59365e7i	1.03915	−	0.599956i	0.119561	−	0.992827i	$-0.461851\pi$
$479$	1.14205e8	−	6.59365e7i	1.03915	−	0.599956i	0.919594	+	0.392871i	$0.128518\pi$
$480$		0			0
$481$	5.22810e7	−	9.05533e7i	0.469795	−	0.813709i
$482$		0			0
$483$	−7.82689e7	+	4.14334e7i	−0.694621	+	0.367713i
$484$		0			0
$485$			7.38561e7i			0.647382i
$486$		0			0
$487$	−2.08780e8			−1.80760			−0.903800	−	0.427955i	$-0.859234\pi$
$487$	−2.08780e8			−1.80760			−0.903800	+	0.427955i	$0.859234\pi$
$488$		0			0
$489$	7.59347e6	+	1.43443e7i	0.0649402	+	0.122674i
$490$		0			0
$491$	−4.51505e7	−	2.60676e7i	−0.381433	−	0.220220i	0.297009	−	0.954875i	$-0.404011\pi$
$491$	−4.51505e7	−	2.60676e7i	−0.381433	−	0.220220i	−0.678441	+	0.734655i	$0.737344\pi$
$492$		0			0
$493$	−819328.	−	1.41912e6i	−0.00683781	−	0.0118434i
$494$		0			0
$495$	−3.82799e7	+	5.63081e7i	−0.315613	+	0.464254i
$496$		0			0
$497$	6.13722e7	−	3.54332e7i	0.499922	−	0.288630i
$498$		0			0
$499$	5.40972e7	−	9.36991e7i	0.435385	−	0.754108i	−0.561942	−	0.827176i	$-0.689946\pi$
$499$	5.40972e7	−	9.36991e7i	0.435385	−	0.754108i	0.997327	+	0.0730680i	$0.0232790\pi$
$500$		0			0
$501$	7.56928e6	−	2.05985e8i	0.0601923	−	1.63803i
$502$		0			0
$503$			1.56779e8i			1.23193i	0.787775	+	0.615964i	$0.211233\pi$
$503$			1.56779e8i			1.23193i	−0.787775	+	0.615964i	$0.788767\pi$
$504$		0			0
$505$	−2.26495e8			−1.75867
$506$		0			0
$507$	7.89741e7	−	1.25874e8i	0.605983	−	0.965852i
$508$		0			0
$509$	6.48207e7	+	3.74243e7i	0.491542	+	0.283792i	0.725214	−	0.688524i	$-0.241741\pi$
$509$	6.48207e7	+	3.74243e7i	0.491542	+	0.283792i	−0.233672	+	0.972315i	$0.575074\pi$
$510$		0			0
$511$	4.46674e7	+	7.73661e7i	0.334755	+	0.579813i
$512$		0			0
$513$	1.77635e8	+	1.96534e7i	1.31576	+	0.145574i
$514$		0			0
$515$	−1.84502e8	+	1.06522e8i	−1.35077	+	0.779865i
$516$		0			0
$517$	2.51973e7	−	4.36430e7i	0.182340	−	0.315822i
$518$		0			0
$519$	6.91742e7	+	4.34005e7i	0.494814	+	0.310450i
$520$		0			0
$521$		−	1.33396e8i		−	0.943253i	−0.881799	−	0.471626i	$-0.843667\pi$
$521$		−	1.33396e8i		−	0.943253i	0.881799	−	0.471626i	$-0.156333\pi$
$522$		0			0
$523$	−2.15497e8			−1.50639			−0.753194	−	0.657798i	$-0.771488\pi$
$523$	−2.15497e8			−1.50639			−0.753194	+	0.657798i	$0.771488\pi$
$524$		0			0
$525$	−1.27783e8	−	4.69561e6i	−0.883070	−	0.0324499i
$526$		0			0
$527$	−6.73863e7	−	3.89055e7i	−0.460405	−	0.265815i
$528$		0			0
$529$	−1.62195e7	−	2.80930e7i	−0.109565	−	0.189771i
$530$		0			0
$531$	9.69593e7	−	4.68532e7i	0.647599	−	0.312936i
$532$		0			0
$533$	−3.64466e8	+	2.10424e8i	−2.40699	+	1.38968i
$534$		0			0
$535$	7.47593e7	−	1.29487e8i	0.488207	−	0.845599i
$536$		0			0
$537$	3.93363e7	−	2.08235e7i	0.254021	−	0.134472i
$538$		0			0
$539$		−	1.30089e7i		−	0.0830760i
$540$		0			0
$541$	−8.48143e7			−0.535645			−0.267823	−	0.963468i	$-0.586304\pi$
$541$	−8.48143e7			−0.535645			−0.267823	+	0.963468i	$0.586304\pi$
$542$		0			0
$543$	−2.65968e7	−	5.02421e7i	−0.166123	−	0.313811i
$544$		0			0
$545$	2.86389e8	+	1.65347e8i	1.76916	+	1.02143i
$546$		0			0
$547$	1.06096e8	+	1.83764e8i	0.648243	+	1.12279i	0.983542	+	0.180678i	$0.0578291\pi$
$547$	1.06096e8	+	1.83764e8i	0.648243	+	1.12279i	−0.335300	+	0.942112i	$0.608838\pi$
$548$		0			0
$549$	2.13684e8	+	1.57256e7i	1.29138	+	0.0950364i
$550$		0			0
$551$	5.08210e6	−	2.93415e6i	0.0303800	−	0.0175399i
$552$		0			0
$553$	−1.15854e8	+	2.00665e8i	−0.685070	+	1.18658i
$554$		0			0
$555$	−5.69282e6	+	1.54920e8i	−0.0333003	+	0.906211i
$556$		0			0
$557$			1.34140e8i			0.776231i	0.921611	+	0.388116i	$0.126874\pi$
$557$			1.34140e8i			0.776231i	−0.921611	+	0.388116i	$0.873126\pi$
$558$		0			0
$559$	4.89618e8			2.80299
$560$		0			0
$561$	−1.92537e7	+	3.06876e7i	−0.109050	+	0.173810i
$562$		0			0
$563$	−1.69990e8	−	9.81437e7i	−0.952573	−	0.549968i	−0.0586934	−	0.998276i	$-0.518693\pi$
$563$	−1.69990e8	−	9.81437e7i	−0.952573	−	0.549968i	−0.893879	+	0.448308i	$0.852027\pi$
$564$		0			0
$565$	2.08442e8	+	3.61032e8i	1.15569	+	2.00171i
$566$		0			0
$567$	1.00744e8	−	1.27025e8i	0.552675	−	0.696853i
$568$		0			0
$569$	2.21527e8	−	1.27898e8i	1.20251	−	0.694270i	0.241398	−	0.970426i	$-0.422394\pi$
$569$	2.21527e8	−	1.27898e8i	1.20251	−	0.694270i	0.961113	+	0.276156i	$0.0890607\pi$
$570$		0			0
$571$	−1.08013e8	+	1.87084e8i	−0.580188	+	1.00492i	0.415269	+	0.909699i	$0.363688\pi$
$571$	−1.08013e8	+	1.87084e8i	−0.580188	+	1.00492i	−0.995457	+	0.0952163i	$0.969646\pi$
$572$		0			0
$573$	−7.59575e7	−	4.76564e7i	−0.403745	−	0.253313i
$574$		0			0
$575$			1.66908e8i			0.877960i
$576$		0			0
$577$	−2.21020e8			−1.15055			−0.575273	−	0.817962i	$-0.695104\pi$
$577$	−2.21020e8			−1.15055			−0.575273	+	0.817962i	$0.695104\pi$
$578$		0			0
$579$	−2.10419e8	−	7.73222e6i	−1.08405	−	0.0398353i
$580$		0			0
$581$	1.08137e8	+	6.24330e7i	0.551374	+	0.318336i
$582$		0			0
$583$	−4.04894e7	−	7.01297e7i	−0.204332	−	0.353913i
$584$		0			0
$585$	−3.03509e7	+	4.12416e8i	−0.151602	+	2.06000i
$586$		0			0
$587$	−1.04364e8	+	6.02544e7i	−0.515982	+	0.297903i	−0.735289	−	0.677753i	$-0.762954\pi$
$587$	−1.04364e8	+	6.02544e7i	−0.515982	+	0.297903i	0.219307	+	0.975656i	$0.429620\pi$
$588$		0			0
$589$	1.39327e8	−	2.41322e8i	0.681851	−	1.18100i
$590$		0			0
$591$	−2.80601e8	+	1.48542e8i	−1.35933	+	0.719594i
$592$		0			0
$593$		−	1.53231e8i		−	0.734824i	−0.930058	−	0.367412i	$-0.880244\pi$
$593$		−	1.53231e8i		−	0.734824i	0.930058	−	0.367412i	$-0.119756\pi$
$594$		0			0
$595$	−1.36513e8			−0.648073
$596$		0			0
$597$	1.14615e8	+	2.16512e8i	0.538667	+	1.01756i
$598$		0			0
$599$	−2.13874e8	−	1.23480e8i	−0.995125	−	0.574536i	−0.0883229	−	0.996092i	$-0.528151\pi$
$599$	−2.13874e8	−	1.23480e8i	−0.995125	−	0.574536i	−0.906802	+	0.421556i	$0.861484\pi$
$600$		0			0
$601$	−4.47088e7	−	7.74379e7i	−0.205954	−	0.356722i	0.744483	−	0.667642i	$-0.232696\pi$
$601$	−4.47088e7	−	7.74379e7i	−0.205954	−	0.356722i	−0.950436	+	0.310920i	$0.899363\pi$
$602$		0			0
$603$	6.85249e7	+	1.41807e8i	0.312533	+	0.646765i
$604$		0			0
$605$	−2.27971e8	+	1.31619e8i	−1.02947	+	0.594363i
$606$		0			0
$607$	3.70421e7	−	6.41588e7i	0.165626	−	0.286873i	−0.771251	−	0.636531i	$-0.780369\pi$
$607$	3.70421e7	−	6.41588e7i	0.165626	−	0.286873i	0.936878	+	0.349658i	$0.113702\pi$
$608$		0			0
$609$	195487.	−	5.31986e6i	0.000865500	−	0.0235531i
$610$		0			0
$611$		−	3.06071e8i		−	1.34184i
$612$		0			0
$613$	−6.52980e7			−0.283478			−0.141739	−	0.989904i	$-0.545269\pi$
$613$	−6.52980e7			−0.283478			−0.141739	+	0.989904i	$0.545269\pi$
$614$		0			0
$615$	3.31610e8	−	5.28540e8i	1.42562	−	2.27223i
$616$		0			0
$617$	2.02104e8	+	1.16685e8i	0.860439	+	0.496775i	0.864159	−	0.503218i	$-0.167851\pi$
$617$	2.02104e8	+	1.16685e8i	0.860439	+	0.496775i	−0.00372032	+	0.999993i	$0.501184\pi$
$618$		0			0
$619$	−4.40897e7	−	7.63656e7i	−0.185894	−	0.321978i	0.757983	−	0.652274i	$-0.226185\pi$
$619$	−4.40897e7	−	7.63656e7i	−0.185894	−	0.321978i	−0.943877	+	0.330296i	$0.892851\pi$
$620$		0			0
$621$	−1.70524e8	−	1.25324e8i	−0.712051	−	0.523311i
$622$		0			0
$623$	2.79127e8	−	1.61154e8i	1.15435	−	0.666465i
$624$		0			0
$625$	1.22854e8	−	2.12789e8i	0.503209	−	0.871584i
$626$		0			0
$627$	−1.09898e8	−	6.89506e7i	−0.445847	−	0.279728i
$628$		0			0
$629$			8.24842e7i			0.331450i
$630$		0			0
$631$	5.84922e7			0.232815			0.116407	−	0.993202i	$-0.462862\pi$
$631$	5.84922e7			0.232815			0.116407	+	0.993202i	$0.462862\pi$
$632$		0			0
$633$	−3.21841e8	−	1.18266e7i	−1.26891	−	0.0466283i
$634$		0			0
$635$	−1.82814e8	−	1.05548e8i	−0.713984	−	0.412219i
$636$		0			0
$637$	−3.95049e7	−	6.84245e7i	−0.152838	−	0.264724i
$638$		0			0
$639$	1.40047e8	+	9.52077e7i	0.536748	+	0.364896i
$640$		0			0
$641$	3.71576e8	−	2.14529e8i	1.41082	−	0.814540i	0.415358	−	0.909658i	$-0.363656\pi$
$641$	3.71576e8	−	2.14529e8i	1.41082	−	0.814540i	0.995466	+	0.0951179i	$0.0303228\pi$
$642$		0			0
$643$	−2.98358e7	+	5.16772e7i	−0.112229	+	0.194386i	−0.916669	−	0.399648i	$-0.869132\pi$
$643$	−2.98358e7	+	5.16772e7i	−0.112229	+	0.194386i	0.804440	+	0.594034i	$0.202466\pi$
$644$		0			0
$645$	−6.41564e8	+	3.39626e8i	−2.39090	+	1.26567i
$646$		0			0
$647$			1.04569e7i			0.0386092i	0.999814	+	0.0193046i	$0.00614523\pi$
$647$			1.04569e7i			0.0386092i	−0.999814	+	0.0193046i	$0.993855\pi$
$648$		0			0
$649$	−7.81722e7			−0.285969
$650$		0			0
$651$	−1.18267e8	−	2.23409e8i	−0.428667	−	0.809764i
$652$		0			0
$653$	1.35417e8	+	7.81829e7i	0.486332	+	0.280784i	0.723051	−	0.690794i	$-0.242739\pi$
$653$	1.35417e8	+	7.81829e7i	0.486332	+	0.280784i	−0.236720	+	0.971578i	$0.576072\pi$
$654$		0			0
$655$	1.87401e8	+	3.24589e8i	0.666882	+	1.15507i
$656$		0			0
$657$	−1.20019e8	+	1.76544e8i	−0.423209	+	0.622524i
$658$		0			0
$659$	3.38006e8	−	1.95148e8i	1.18105	−	0.681879i	0.224792	−	0.974407i	$-0.427830\pi$
$659$	3.38006e8	−	1.95148e8i	1.18105	−	0.681879i	0.956257	+	0.292528i	$0.0944966\pi$
$660$		0			0
$661$	6.47807e7	−	1.12203e8i	0.224306	−	0.388510i	−0.731805	−	0.681514i	$-0.761322\pi$
$661$	6.47807e7	−	1.12203e8i	0.224306	−	0.388510i	0.956111	+	0.293005i	$0.0946551\pi$
$662$		0			0
$663$	−8.07985e6	+	2.19880e8i	−0.0277245	+	0.754474i
$664$		0			0
$665$		−	4.88877e8i		−	1.66240i
$666$		0			0
$667$	−6.94873e6			−0.0234168
$668$		0			0
$669$	2.44785e8	−	3.90153e8i	0.817536	−	1.30304i
$670$		0			0
$671$	−1.34700e8	−	7.77690e7i	−0.445861	−	0.257418i
$672$		0			0
$673$	9.71328e7	+	1.68239e8i	0.318655	+	0.551927i	0.980208	−	0.197972i	$-0.0634355\pi$
$673$	9.71328e7	+	1.68239e8i	0.318655	+	0.551927i	−0.661553	+	0.749899i	$0.730102\pi$
$674$		0			0
$675$	−1.22753e8	−	2.79819e8i	−0.399137	−	0.909841i
$676$		0			0
$677$	1.88506e8	−	1.08834e8i	0.607518	−	0.350751i	−0.164475	−	0.986381i	$-0.552593\pi$
$677$	1.88506e8	−	1.08834e8i	0.607518	−	0.350751i	0.771994	+	0.635630i	$0.219260\pi$
$678$		0			0
$679$	−6.38309e7	+	1.10558e8i	−0.203902	+	0.353169i
$680$		0			0
$681$	1.46789e8	+	9.20967e7i	0.464786	+	0.291610i
$682$		0			0
$683$			4.76916e8i			1.49685i	0.663217	+	0.748427i	$0.269191\pi$
$683$			4.76916e8i			1.49685i	−0.663217	+	0.748427i	$0.730809\pi$
$684$		0			0
$685$	7.04289e8			2.19119
$686$		0			0
$687$	2.18527e7	+	803017.i	0.0673962	+	0.00247659i
$688$		0			0
$689$	−4.25933e8	−	2.45912e8i	−1.30222	−	0.751835i
$690$		0			0
$691$	2.20738e8	+	3.82329e8i	0.669025	+	1.15878i	0.978177	+	0.207772i	$0.0666213\pi$
$691$	2.20738e8	+	3.82329e8i	0.669025	+	1.15878i	−0.309152	+	0.951013i	$0.600045\pi$
$692$		0			0
$693$	−1.05968e8	+	5.12063e7i	−0.318401	+	0.153859i
$694$		0			0
$695$	1.55219e8	−	8.96158e7i	0.462371	−	0.266950i
$696$		0			0
$697$	1.65994e8	−	2.87510e8i	0.490224	−	0.849093i
$698$		0			0
$699$	2.51911e8	−	1.33355e8i	0.737591	−	0.390460i
$700$		0			0
$701$		−	3.89659e8i		−	1.13118i	−0.824687	−	0.565589i	$-0.808649\pi$
$701$		−	3.89659e8i		−	1.13118i	0.824687	−	0.565589i	$-0.191351\pi$
$702$		0			0
$703$	−2.95390e8			−0.850216
$704$		0			0
$705$	2.12308e8	+	4.01056e8i	0.605898	+	1.14456i
$706$		0			0
$707$	−3.39050e8	−	1.95751e8i	−0.959414	−	0.553918i
$708$		0			0
$709$	7.45822e7	+	1.29180e8i	0.209265	+	0.362458i	0.951483	−	0.307701i	$-0.0995595\pi$
$709$	7.45822e7	+	1.29180e8i	0.209265	+	0.362458i	−0.742218	+	0.670158i	$0.766226\pi$
$710$		0			0
$711$	−5.52201e8	−	4.06381e7i	−1.53634	−	0.113064i
$712$		0			0
$713$	−2.85752e8	+	1.64979e8i	−0.788353	+	0.455156i
$714$		0			0
$715$	1.50097e8	−	2.59975e8i	0.410632	−	0.711235i
$716$		0			0
$717$	1.15157e7	−	3.13380e8i	0.0312416	−	0.850186i
$718$		0			0
$719$		−	3.85971e8i		−	1.03841i	−0.854650	−	0.519204i	$-0.826229\pi$
$719$		−	3.85971e8i		−	1.03841i	0.854650	−	0.519204i	$-0.173771\pi$
$720$		0			0
$721$	−3.68253e8			−0.982517
$722$		0			0
$723$	1.18844e8	−	1.89421e8i	0.314459	−	0.501204i
$724$		0			0
$725$	−8.68896e6	−	5.01658e6i	−0.0228010	−	0.0131642i
$726$		0			0
$727$	2.28630e8	+	3.95999e8i	0.595017	+	1.03060i	0.993544	+	0.113444i	$0.0361882\pi$
$727$	2.28630e8	+	3.95999e8i	0.595017	+	1.03060i	−0.398527	+	0.917157i	$0.630478\pi$
$728$		0			0
$729$	3.78050e8	+	8.46908e7i	0.975814	+	0.218602i
$730$		0			0
$731$	−3.34491e8	+	1.93118e8i	−0.856313	+	0.494392i
$732$		0			0
$733$	6.13711e7	−	1.06298e8i	0.155830	−	0.269906i	−0.777531	−	0.628845i	$-0.783528\pi$
$733$	6.13711e7	−	1.06298e8i	0.155830	−	0.269906i	0.933361	+	0.358939i	$0.116861\pi$
$734$		0			0
$735$	9.92277e7	+	6.22563e7i	0.249903	+	0.156791i
$736$		0			0
$737$		−	1.14330e8i		−	0.285600i
$738$		0			0
$739$	4.40901e8			1.09246			0.546232	−	0.837634i	$-0.316062\pi$
$739$	4.40901e8			1.09246			0.546232	+	0.837634i	$0.316062\pi$
$740$		0			0
$741$	−7.87425e8	−	2.89353e7i	−1.93533	−	0.0711170i
$742$		0			0
$743$	−3.93131e8	−	2.26974e8i	−0.958453	−	0.553363i	−0.0627562	−	0.998029i	$-0.519989\pi$
$743$	−3.93131e8	−	2.26974e8i	−0.958453	−	0.553363i	−0.895696	+	0.444666i	$0.853322\pi$
$744$		0			0
$745$	−6.59420e7	−	1.14215e8i	−0.159475	−	0.276219i
$746$		0			0
$747$	−2.18997e7	+	2.97579e8i	−0.0525383	+	0.713904i
$748$		0			0
$749$	2.23821e8	−	1.29223e8i	0.532666	−	0.307535i
$750$		0			0
$751$	−1.47000e8	+	2.54612e8i	−0.347054	+	0.601116i	−0.985725	−	0.168364i	$-0.946151\pi$
$751$	−1.47000e8	+	2.54612e8i	−0.347054	+	0.601116i	0.638670	+	0.769480i	$0.279485\pi$
$752$		0			0
$753$	−2.58830e8	+	1.37017e8i	−0.606218	+	0.320915i
$754$		0			0
$755$		−	3.43742e8i		−	0.798714i
$756$		0			0
$757$	−1.07641e8			−0.248136			−0.124068	−	0.992274i	$-0.539594\pi$
$757$	−1.07641e8			−0.248136			−0.124068	+	0.992274i	$0.539594\pi$
$758$		0			0
$759$	7.18742e7	+	1.35772e8i	0.164379	+	0.310518i
$760$		0			0
$761$	1.03995e8	+	6.00417e7i	0.235972	+	0.136238i	0.613324	−	0.789832i	$-0.289832\pi$
$761$	1.03995e8	+	6.00417e7i	0.235972	+	0.136238i	−0.377352	+	0.926070i	$0.623165\pi$
$762$		0			0
$763$	2.85806e8	+	4.95030e8i	0.643424	+	1.11444i
$764$		0			0
$765$	−1.41933e8	−	2.93721e8i	−0.317030	−	0.656070i
$766$		0			0
$767$	−4.11171e8	+	2.37390e8i	−0.911247	+	0.526109i
$768$		0			0
$769$	−3.34926e7	+	5.80109e7i	−0.0736495	+	0.127565i	−0.900498	−	0.434860i	$-0.856798\pi$
$769$	−3.34926e7	+	5.80109e7i	−0.0736495	+	0.127565i	0.826849	+	0.562424i	$0.190131\pi$
$770$		0			0
$771$	−1.08462e7	+	2.95161e8i	−0.0236655	+	0.644015i
$772$		0			0
$773$			8.23234e8i			1.78232i	0.453693	+	0.891158i	$0.350106\pi$
$773$			8.23234e8i			1.78232i	−0.453693	+	0.891158i	$0.649894\pi$
$774$		0			0
$775$	−4.76421e8			−1.02349
$776$		0			0
$777$	−1.42413e8	+	2.26987e8i	−0.303590	+	0.483880i
$778$		0			0
$779$	1.02962e9	+	5.94453e8i	2.17804	+	1.25749i
$780$		0			0
$781$	−6.14658e7	−	1.06462e8i	−0.129027	−	0.223481i
$782$		0			0
$783$	1.16494e7	−	5.11047e6i	0.0242671	−	0.0106457i
$784$		0			0
$785$	7.84272e8	−	4.52800e8i	1.62128	−	0.936046i
$786$		0			0
$787$	−4.02636e7	+	6.97386e7i	−0.0826015	+	0.143070i	−0.904367	−	0.426756i	$-0.859656\pi$
$787$	−4.02636e7	+	6.97386e7i	−0.0826015	+	0.143070i	0.821765	+	0.569826i	$0.192990\pi$
$788$		0			0
$789$	−3.90240e8	−	2.44840e8i	−0.794513	−	0.498484i
$790$		0			0
$791$			7.20592e8i			1.45600i
$792$		0			0
$793$	−9.44660e8			−1.89433
$794$		0			0
$795$	7.28693e8	+	2.67771e7i	1.45025	+	0.0532920i
$796$		0			0
$797$	2.86152e8	+	1.65210e8i	0.565226	+	0.326334i	0.755240	−	0.655448i	$-0.227520\pi$
$797$	2.86152e8	+	1.65210e8i	0.565226	+	0.326334i	−0.190014	+	0.981781i	$0.560853\pi$
$798$		0			0
$799$	1.20723e8	+	2.09098e8i	0.236673	+	0.409930i
$800$		0			0
$801$	6.36947e8	+	4.33014e8i	1.23938	+	0.842568i
$802$		0			0
$803$	1.34206e8	−	7.74841e7i	0.259195	−	0.149646i
$804$		0			0
$805$	−2.89443e8	+	5.01330e8i	−0.554849	+	0.961027i
$806$		0			0
$807$	2.57932e8	−	1.36542e8i	0.490778	−	0.259804i
$808$		0			0
$809$			3.53108e8i			0.666902i	0.942767	+	0.333451i	$0.108213\pi$
$809$			3.53108e8i			0.666902i	−0.942767	+	0.333451i	$0.891787\pi$
$810$		0			0
$811$	9.49554e8			1.78015			0.890076	−	0.455812i	$-0.150651\pi$
$811$	9.49554e8			1.78015			0.890076	+	0.455812i	$0.150651\pi$
$812$		0			0
$813$	−1.05770e8	−	1.99803e8i	−0.196830	−	0.371817i
$814$		0			0
$815$	9.18783e7	+	5.30460e7i	0.169723	+	0.0979895i
$816$		0			0
$817$	−6.91590e8	−	1.19787e9i	−1.26818	−	2.19656i
$818$		0			0
$819$	−4.01869e8	+	5.91133e8i	−0.731530	+	1.07605i
$820$		0			0
$821$	−5.57652e8	+	3.21961e8i	−1.00771	+	0.581800i	−0.910519	−	0.413467i	$-0.864318\pi$
$821$	−5.57652e8	+	3.21961e8i	−1.00771	+	0.581800i	−0.0971871	+	0.995266i	$0.530985\pi$
$822$		0			0
$823$	2.41019e8	−	4.17457e8i	0.432366	−	0.748879i	−0.564711	−	0.825289i	$-0.691012\pi$
$823$	2.41019e8	−	4.17457e8i	0.432366	−	0.748879i	0.997077	+	0.0764095i	$0.0243456\pi$
$824$		0			0
$825$	−8.14543e6	+	2.21664e8i	−0.0145062	+	0.394760i
$826$		0			0
$827$			1.59470e8i			0.281945i	0.990014	+	0.140972i	$0.0450228\pi$
$827$			1.59470e8i			0.281945i	−0.990014	+	0.140972i	$0.954977\pi$
$828$		0			0
$829$	7.53389e8			1.32238			0.661189	−	0.750219i	$-0.270052\pi$
$829$	7.53389e8			1.32238			0.661189	+	0.750219i	$0.270052\pi$
$830$		0			0
$831$	−4.83146e8	+	7.70067e8i	−0.841928	+	1.34192i
$832$		0			0
$833$	5.39769e7	+	3.11636e7i	0.0933842	+	0.0539154i
$834$		0			0
$835$	−6.73686e8	−	1.16686e9i	−1.15717	−	2.00428i
$836$		0			0
$837$	3.57723e8	−	4.86741e8i	0.610057	−	0.830083i
$838$		0			0
$839$	−5.44085e8	+	3.14128e8i	−0.921257	+	0.531888i	−0.884036	−	0.467419i	$-0.845184\pi$
$839$	−5.44085e8	+	3.14128e8i	−0.921257	+	0.531888i	−0.0372211	+	0.999307i	$0.511851\pi$
$840$		0			0
$841$	−2.97203e8	+	5.14770e8i	−0.499649	+	0.865417i
$842$		0			0
$843$	−4.70929e8	−	2.95465e8i	−0.786091	−	0.493200i
$844$		0			0
$845$		−	9.71334e8i		−	1.60990i
$846$		0			0
$847$	−4.55012e8			−0.748812
$848$		0			0
$849$	1.58820e8	+	5.83612e6i	0.259527	+	0.00953676i
$850$		0			0
$851$	3.02914e8	+	1.74887e8i	0.491508	+	0.283772i
$852$		0			0
$853$	2.24374e8	+	3.88627e8i	0.361514	+	0.626161i	0.988210	−	0.153103i	$-0.0489265\pi$
$853$	2.24374e8	+	3.88627e8i	0.361514	+	0.626161i	−0.626696	+	0.779264i	$0.715593\pi$
$854$		0			0
$855$	1.05186e9	−	5.08287e8i	1.68291	−	0.813225i
$856$		0			0
$857$	−8.75366e8	+	5.05393e8i	−1.39074	+	0.802947i	−0.993398	−	0.114722i	$-0.963402\pi$
$857$	−8.75366e8	+	5.05393e8i	−1.39074	+	0.802947i	−0.397347	+	0.917669i	$0.630069\pi$
$858$		0			0
$859$	−1.05546e8	+	1.82811e8i	−0.166518	+	0.288418i	−0.937193	−	0.348810i	$-0.886586\pi$
$859$	−1.05546e8	+	1.82811e8i	−0.166518	+	0.288418i	0.770675	+	0.637228i	$0.219919\pi$
$860$		0			0
$861$	9.53199e8	−	5.04597e8i	1.49339	−	0.790561i
$862$		0			0
$863$		−	7.44386e8i		−	1.15815i	−0.815273	−	0.579076i	$-0.803413\pi$
$863$		−	7.44386e8i		−	1.15815i	0.815273	−	0.579076i	$-0.196587\pi$
$864$		0			0
$865$	5.33800e8			0.824765
$866$		0			0
$867$	2.23705e8	+	4.22585e8i	0.343256	+	0.648421i
$868$		0			0
$869$	3.48091e8	+	2.00971e8i	0.530437	+	0.306248i
$870$		0			0
$871$	−3.47193e8	−	6.01355e8i	−0.525431	−	0.910074i
$872$		0			0
$873$	−3.04241e8	−	2.23900e7i	−0.457273	−	0.0336520i
$874$		0			0
$875$	4.70700e6	−	2.71759e6i	0.00702619	−	0.00405658i
$876$		0			0
$877$	−2.48646e8	+	4.30667e8i	−0.368623	+	0.638473i	−0.989350	−	0.145553i	$-0.953504\pi$
$877$	−2.48646e8	+	4.30667e8i	−0.368623	+	0.638473i	0.620728	+	0.784026i	$0.286837\pi$
$878$		0			0
$879$	2.42590e7	−	6.60168e8i	0.0357196	−	0.972049i
$880$		0			0
$881$			5.48601e8i			0.802286i	0.916016	+	0.401143i	$0.131387\pi$
$881$			5.48601e8i			0.802286i	−0.916016	+	0.401143i	$0.868613\pi$
$882$		0			0
$883$	−5.30017e8			−0.769852			−0.384926	−	0.922947i	$-0.625773\pi$
$883$	−5.30017e8			−0.769852			−0.384926	+	0.922947i	$0.625773\pi$
$884$		0			0
$885$	3.74105e8	−	5.96271e8i	0.539714	−	0.860229i
$886$		0			0
$887$	−1.43927e8	−	8.30965e7i	−0.206240	−	0.119073i	0.393323	−	0.919400i	$-0.371325\pi$
$887$	−1.43927e8	−	8.30965e7i	−0.206240	−	0.119073i	−0.599563	+	0.800328i	$0.704659\pi$
$888$		0			0
$889$	−1.82442e8	−	3.15998e8i	−0.259668	−	0.449758i
$890$		0			0
$891$	−2.20350e8	−	1.74760e8i	−0.311516	−	0.247063i
$892$		0			0
$893$	−7.48816e8	+	4.32329e8i	−1.05153	+	0.607100i
$894$		0			0
$895$	1.45468e8	−	2.51957e8i	0.202907	−	0.351446i
$896$		0			0
$897$	7.90351e8	+	4.95873e8i	1.09507	+	0.687057i
$898$		0			0
$899$		−	1.98343e7i		−	0.0272985i
$900$		0			0
$901$	3.87978e8			0.530436
$902$		0			0
$903$	−1.25391e9	−	4.60771e7i	−1.70295	−	0.0625780i
$904$		0			0
$905$	−3.21812e8	−	1.85798e8i	−0.434166	−	0.250666i
$906$		0			0
$907$	−2.40421e8	−	4.16421e8i	−0.322218	−	0.558099i	0.658727	−	0.752382i	$-0.271095\pi$
$907$	−2.40421e8	−	4.16421e8i	−0.322218	−	0.558099i	−0.980945	+	0.194283i	$0.937762\pi$
$908$		0			0
$909$	6.86636e7	−	9.33020e8i	0.0914187	−	1.24222i
$910$		0			0
$911$	1.86236e8	−	1.07524e8i	0.246325	−	0.142216i	−0.371755	−	0.928331i	$-0.621244\pi$
$911$	1.86236e8	−	1.07524e8i	0.246325	−	0.142216i	0.618080	+	0.786115i	$0.287911\pi$
$912$		0			0
$913$	1.08302e8	−	1.87585e8i	0.142306	−	0.246482i
$914$		0			0
$915$	1.23782e9	−	6.55269e8i	1.61583	−	0.855375i
$916$		0			0
$917$			6.47855e8i			0.840175i
$918$		0			0
$919$	−6.54865e8			−0.843733			−0.421866	−	0.906658i	$-0.638625\pi$
$919$	−6.54865e8			−0.843733			−0.421866	+	0.906658i	$0.638625\pi$
$920$		0			0
$921$	4.02306e8	+	7.59968e8i	0.514965	+	0.972784i
$922$		0			0
$923$	−6.46596e8	−	3.73312e8i	−0.822295	−	0.474752i
$924$		0			0
$925$	2.52517e8	+	4.37372e8i	0.319055	+	0.552619i
$926$		0			0
$927$	−3.82874e8	−	7.92329e8i	−0.480636	−	0.994640i
$928$		0			0
$929$	8.70883e8	−	5.02804e8i	1.08621	−	0.627122i	0.153643	−	0.988126i	$-0.450900\pi$
$929$	8.70883e8	−	5.02804e8i	1.08621	−	0.627122i	0.932564	+	0.361005i	$0.117566\pi$
$930$		0			0
$931$	−1.11602e8	+	1.93300e8i	−0.138300	+	0.239543i
$932$		0			0
$933$	−5.73348e6	+	1.56027e8i	−0.00705950	+	0.192112i
$934$		0			0
$935$			2.36809e8i			0.289709i
$936$		0			0
$937$	6.04407e8			0.734701			0.367350	−	0.930083i	$-0.380265\pi$
$937$	6.04407e8			0.734701			0.367350	+	0.930083i	$0.380265\pi$
$938$		0			0
$939$	4.98191e8	−	7.94047e8i	0.601727	−	0.959068i
$940$		0			0
$941$	−6.30311e8	−	3.63910e8i	−0.756461	−	0.436743i	0.0715630	−	0.997436i	$-0.477201\pi$
$941$	−6.30311e8	−	3.63910e8i	−0.756461	−	0.436743i	−0.828024	+	0.560693i	$0.810535\pi$
$942$		0			0
$943$	−7.03899e8	−	1.21919e9i	−0.839413	−	1.45391i
$944$		0			0
$945$	1.16540e8	−	1.05334e9i	0.138096	−	1.24817i
$946$		0			0
$947$	1.84595e8	−	1.06576e8i	0.217355	−	0.125490i	−0.387370	−	0.921924i	$-0.626616\pi$
$947$	1.84595e8	−	1.06576e8i	0.217355	−	0.125490i	0.604725	+	0.796434i	$0.293283\pi$
$948$		0			0
$949$	4.70600e8	−	8.15103e8i	0.550621	−	0.953704i
$950$		0			0
$951$	−1.44260e8	−	9.05097e7i	−0.167727	−	0.105233i
$952$		0			0
$953$		−	2.78643e8i		−	0.321936i	−0.986960	−	0.160968i	$-0.948538\pi$
$953$		−	2.78643e8i		−	0.321936i	0.986960	−	0.160968i	$-0.0514617\pi$
$954$		0			0
$955$	−5.86145e8			−0.672969
$956$		0			0
$957$	−9.22832e6	−	339111.i	−0.0105290	−	0.000386906i
$958$		0			0
$959$	1.05428e9	+	6.08689e8i	1.19537	+	0.690144i
$960$		0			0
$961$	−2.71613e7	−	4.70447e7i	−0.0306041	−	0.0530079i
$962$		0			0
$963$	5.10742e8	+	3.47217e8i	0.571904	+	0.388796i
$964$		0			0
$965$	−1.19198e9	+	6.88188e8i	−1.32643	+	0.765817i
$966$		0			0
$967$	4.43506e7	−	7.68176e7i	0.0490479	−	0.0849535i	−0.840459	−	0.541875i	$-0.817715\pi$
$967$	4.43506e7	−	7.68176e7i	0.0490479	−	0.0849535i	0.889507	+	0.456921i	$0.151048\pi$
$968$		0			0
$969$	5.49357e8	−	2.90814e8i	0.603786	−	0.319628i
$970$		0			0
$971$			5.74421e8i			0.627441i	0.949515	+	0.313720i	$0.101575\pi$
$971$			5.74421e8i			0.627441i	−0.949515	+	0.313720i	$0.898425\pi$
$972$		0			0
$973$	3.09806e8			0.336319
$974$		0			0
$975$	6.30295e8	+	1.19065e9i	0.680033	+	1.28460i
$976$		0			0
$977$	−1.52300e8	−	8.79306e7i	−0.163312	−	0.0942880i	0.416117	−	0.909311i	$-0.363391\pi$
$977$	−1.52300e8	−	8.79306e7i	−0.163312	−	0.0942880i	−0.579428	+	0.815023i	$0.696724\pi$
$978$		0			0
$979$	−2.79553e8	−	4.84199e8i	−0.297931	−	0.516031i
$980$		0			0
$981$	−7.67949e8	+	1.12962e9i	−0.813439	+	1.19654i
$982$		0			0
$983$	1.34373e9	−	7.75804e8i	1.41466	−	0.816755i	0.418837	−	0.908061i	$-0.362438\pi$
$983$	1.34373e9	−	7.75804e8i	1.41466	−	0.816755i	0.995823	+	0.0913067i	$0.0291044\pi$
$984$		0			0
$985$	−1.03768e9	+	1.79731e9i	−1.08581	+	1.88068i
$986$		0			0
$987$	−2.88039e7	+	7.83849e8i	−0.0299571	+	0.815231i
$988$		0			0
$989$			1.63784e9i			1.69310i
$990$		0			0
$991$	−2.56929e8			−0.263993			−0.131997	−	0.991250i	$-0.542139\pi$
$991$	−2.56929e8			−0.263993			−0.131997	+	0.991250i	$0.542139\pi$
$992$		0			0
$993$	3.57619e8	−	5.69995e8i	0.365236	−	0.582135i
$994$		0			0
$995$	1.38681e9	+	8.00673e8i	1.40782	+	0.812805i
$996$		0			0
$997$	−2.38204e8	−	4.12582e8i	−0.240361	−	0.416318i	0.720456	−	0.693501i	$-0.243933\pi$
$997$	−2.38204e8	−	4.12582e8i	−0.240361	−	0.416318i	−0.960817	+	0.277183i	$0.910599\pi$
$998$		0			0
$999$	−6.36450e8	−	7.04161e7i	−0.638364	−	0.0706278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.12	✓	36
3.2	odd	2		216.7.m.a.17.4		36
4.3	odd	2		144.7.q.d.113.7		36
9.2	odd	6	inner	72.7.m.a.65.12	yes	36
9.4	even	3		648.7.e.c.161.6		36
9.5	odd	6		648.7.e.c.161.31		36
9.7	even	3		216.7.m.a.89.4		36
12.11	even	2		432.7.q.d.17.4		36
36.7	odd	6		432.7.q.d.305.4		36
36.11	even	6		144.7.q.d.65.7		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.12	✓	36	1.1	even	1	trivial
72.7.m.a.65.12	yes	36	9.2	odd	6	inner
144.7.q.d.65.7		36	36.11	even	6
144.7.q.d.113.7		36	4.3	odd	2
216.7.m.a.17.4		36	3.2	odd	2
216.7.m.a.89.4		36	9.7	even	3
432.7.q.d.17.4		36	12.11	even	2
432.7.q.d.305.4		36	36.7	odd	6
648.7.e.c.161.6		36	9.4	even	3
648.7.e.c.161.31		36	9.5	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.6322 + 23.8627i) q^{3} +(152.846 + 88.2455i) q^{5} +(152.534 + 264.197i) q^{7} +(-409.853 + 602.878i) q^{9} +O(q^{10})\)	\(q+(12.6322 + 23.8627i) q^{3} +(152.846 + 88.2455i) q^{5} +(152.534 + 264.197i) q^{7} +(-409.853 + 602.878i) q^{9} +(458.300 - 264.600i) q^{11} +(1607.05 - 2783.49i) q^{13} +(-174.989 + 4762.04i) q^{15} +2535.45i q^{17} -9079.88 q^{19} +(-4377.59 + 6977.27i) q^{21} +(9311.16 + 5375.80i) q^{23} +(7762.03 + 13444.2i) q^{25} +(-19563.6 - 2164.50i) q^{27} +(-559.710 + 323.149i) q^{29} +(-15344.6 + 26577.6i) q^{31} +(12103.4 + 7593.78i) q^{33} +53841.8i q^{35} +32532.3 q^{37} +(86722.0 + 3186.75i) q^{39} +(-113396. - 65469.3i) q^{41} +(76167.3 + 131926. i) q^{43} +(-115845. + 55979.5i) q^{45} +(82469.8 - 47614.0i) q^{47} +(12291.1 - 21288.9i) q^{49} +(-60502.6 + 32028.4i) q^{51} -153021. i q^{53} +93399.0 q^{55} +(-114699. - 216670. i) q^{57} +(-127927. - 73858.9i) q^{59} +(-146956. - 254535. i) q^{61} +(-221795. - 16322.5i) q^{63} +(491260. - 283629. i) q^{65} +(108022. - 187099. i) q^{67} +(-10660.1 + 290097. i) q^{69} -232297. i q^{71} +292835. q^{73} +(-222763. + 355053. i) q^{75} +(139813. + 80721.1i) q^{77} +(379763. + 657769. i) q^{79} +(-195482. - 494183. i) q^{81} +(354469. - 204653. i) q^{83} +(-223742. + 387533. i) q^{85} +(-14781.6 - 9274.07i) q^{87} -1.05651e6i q^{89} +980519. q^{91} +(-828049. - 30428.1i) q^{93} +(-1.38782e6 - 801258. i) q^{95} +(209235. + 362405. i) q^{97} +(-28314.6 + 384746. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 36 * q + 10 * q^3 + 74 * q^9	\( 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) \) 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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