LMFDB - Embedded newform 72.7.m.a.41.5

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			41.5
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.5191 + 22.7639i) q^{3} +(26.1779 + 15.1138i) q^{5} +(301.407 + 522.052i) q^{7} +(-307.391 - 661.023i) q^{9} +O(q^{10})$	\(q+(-14.5191 + 22.7639i) q^{3} +(26.1779 + 15.1138i) q^{5} +(301.407 + 522.052i) q^{7} +(-307.391 - 661.023i) q^{9} +(1129.61 - 652.181i) q^{11} +(-1088.65 + 1885.60i) q^{13} +(-724.129 + 376.472i) q^{15} +4927.08i q^{17} -3405.62 q^{19} +(-16260.1 - 718.529i) q^{21} +(-11440.1 - 6604.95i) q^{23} +(-7355.64 - 12740.4i) q^{25} +(19510.5 + 2600.04i) q^{27} +(-31812.2 + 18366.8i) q^{29} +(-17765.5 + 30770.8i) q^{31} +(-1554.75 + 35183.4i) q^{33} +18221.6i q^{35} -8571.62 q^{37} +(-27117.3 - 52159.1i) q^{39} +(67439.9 + 38936.4i) q^{41} +(-31474.2 - 54514.9i) q^{43} +(1943.73 - 21950.1i) q^{45} +(100507. - 58027.8i) q^{47} +(-122868. + 212813. i) q^{49} +(-112160. - 71536.8i) q^{51} -48474.0i q^{53} +39427.8 q^{55} +(49446.5 - 77525.2i) q^{57} +(176147. + 101699. i) q^{59} +(-13962.8 - 24184.3i) q^{61} +(252439. - 359711. i) q^{63} +(-56997.1 + 32907.3i) q^{65} +(233296. - 404080. i) q^{67} +(316455. - 164524. i) q^{69} +328264. i q^{71} -606671. q^{73} +(396818. + 17535.3i) q^{75} +(680944. + 393143. i) q^{77} +(283582. + 491178. i) q^{79} +(-342462. + 406385. i) q^{81} +(556799. - 321468. i) q^{83} +(-74467.0 + 128981. i) q^{85} +(43784.9 - 990840. i) q^{87} +220044. i q^{89} -1.31251e6 q^{91} +(-442524. - 851177. i) q^{93} +(-89152.0 - 51471.9i) q^{95} +(114375. + 198104. i) q^{97} +(-778339. - 546224. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−14.5191	+	22.7639i	−0.537745	+	0.843108i
$3$	−14.5191	+	22.7639i	−0.537745	+	0.843108i
$4$		0			0
$5$	26.1779	+	15.1138i	0.209423	+	0.120911i	0.601043	−	0.799216i	$-0.294752\pi$
$5$	26.1779	+	15.1138i	0.209423	+	0.120911i	−0.391620	+	0.920127i	$0.628085\pi$
$6$		0			0
$7$	301.407	+	522.052i	0.878737	+	1.52202i	0.852728	+	0.522355i	$0.174946\pi$
$7$	301.407	+	522.052i	0.878737	+	1.52202i	0.0260087	+	0.999662i	$0.491720\pi$
$8$		0			0
$9$	−307.391	−	661.023i	−0.421661	−	0.906753i
$10$		0			0
$11$	1129.61	−	652.181i	0.848693	−	0.489993i	−0.0115166	−	0.999934i	$-0.503666\pi$
$11$	1129.61	−	652.181i	0.848693	−	0.489993i	0.860210	+	0.509941i	$0.170333\pi$
$12$		0			0
$13$	−1088.65	+	1885.60i	−0.495516	+	0.858260i	−0.999987	−	0.00516953i	$-0.998354\pi$
$13$	−1088.65	+	1885.60i	−0.495516	+	0.858260i	0.504470	+	0.863429i	$0.331688\pi$
$14$		0			0
$15$	−724.129	+	376.472i	−0.214557	+	0.111547i
$16$		0			0
$17$			4927.08i			1.00287i	0.865197	+	0.501433i	$0.167193\pi$
$17$			4927.08i			1.00287i	−0.865197	+	0.501433i	$0.832807\pi$
$18$		0			0
$19$	−3405.62			−0.496518			−0.248259	−	0.968694i	$-0.579858\pi$
$19$	−3405.62			−0.496518			−0.248259	+	0.968694i	$0.579858\pi$
$20$		0			0
$21$	−16260.1	−	718.529i	−1.75576	−	0.0775865i
$22$		0			0
$23$	−11440.1	−	6604.95i	−0.940258	−	0.542858i	−0.0502165	−	0.998738i	$-0.515991\pi$
$23$	−11440.1	−	6604.95i	−0.940258	−	0.542858i	−0.890041	+	0.455880i	$0.849324\pi$
$24$		0			0
$25$	−7355.64	−	12740.4i	−0.470761	−	0.815382i
$26$		0			0
$27$	19510.5	+	2600.04i	0.991237	+	0.132096i
$28$		0			0
$29$	−31812.2	+	18366.8i	−1.30437	+	0.753077i	−0.981150	−	0.193248i	$-0.938098\pi$
$29$	−31812.2	+	18366.8i	−1.30437	+	0.753077i	−0.323218	+	0.946325i	$0.604765\pi$
$30$		0			0
$31$	−17765.5	+	30770.8i	−0.596338	+	1.03289i	0.397018	+	0.917811i	$0.370045\pi$
$31$	−17765.5	+	30770.8i	−0.596338	+	1.03289i	−0.993357	+	0.115077i	$0.963288\pi$
$32$		0			0
$33$	−1554.75	+	35183.4i	−0.0432631	+	0.979031i
$34$		0			0
$35$			18221.6i			0.424994i
$36$		0			0
$37$	−8571.62			−0.169222			−0.0846112	−	0.996414i	$-0.526965\pi$
$37$	−8571.62			−0.169222			−0.0846112	+	0.996414i	$0.526965\pi$
$38$		0			0
$39$	−27117.3	−	52159.1i	−0.457144	−	0.879298i
$40$		0			0
$41$	67439.9	+	38936.4i	0.978509	+	0.564943i	0.901820	−	0.432112i	$-0.142232\pi$
$41$	67439.9	+	38936.4i	0.978509	+	0.564943i	0.0766897	+	0.997055i	$0.475565\pi$
$42$		0			0
$43$	−31474.2	−	54514.9i	−0.395867	−	0.685662i	0.597344	−	0.801985i	$-0.296223\pi$
$43$	−31474.2	−	54514.9i	−0.395867	−	0.685662i	−0.993211	+	0.116323i	$0.962889\pi$
$44$		0			0
$45$	1943.73	−	21950.1i	0.0213304	−	0.240879i
$46$		0			0
$47$	100507.	−	58027.8i	0.968062	−	0.558911i	0.0694169	−	0.997588i	$-0.477886\pi$
$47$	100507.	−	58027.8i	0.968062	−	0.558911i	0.898645	+	0.438677i	$0.144553\pi$
$48$		0			0
$49$	−122868.	+	212813.i	−1.04436	+	1.80888i
$50$		0			0
$51$	−112160.	−	71536.8i	−0.845524	−	0.539285i
$52$		0			0
$53$		−	48474.0i		−	0.325598i	−0.986659	−	0.162799i	$-0.947948\pi$
$53$		−	48474.0i		−	0.325598i	0.986659	−	0.162799i	$-0.0520522\pi$
$54$		0			0
$55$	39427.8			0.236981
$56$		0			0
$57$	49446.5	−	77525.2i	0.267000	−	0.418619i
$58$		0			0
$59$	176147.	+	101699.i	0.857670	+	0.495176i	0.863231	−	0.504808i	$-0.168437\pi$
$59$	176147.	+	101699.i	0.857670	+	0.495176i	−0.00556114	+	0.999985i	$0.501770\pi$
$60$		0			0
$61$	−13962.8	−	24184.3i	−0.0615154	−	0.106548i	0.833628	−	0.552327i	$-0.186260\pi$
$61$	−13962.8	−	24184.3i	−0.0615154	−	0.106548i	−0.895143	+	0.445779i	$0.852927\pi$
$62$		0			0
$63$	252439.	−	359711.i	1.00956	−	1.43857i
$64$		0			0
$65$	−56997.1	+	32907.3i	−0.207545	+	0.119826i
$66$		0			0
$67$	233296.	−	404080.i	0.775680	−	1.34352i	−0.158731	−	0.987322i	$-0.550740\pi$
$67$	233296.	−	404080.i	0.775680	−	1.34352i	0.934411	−	0.356196i	$-0.115926\pi$
$68$		0			0
$69$	316455.	−	164524.i	0.963306	−	0.500820i
$70$		0			0
$71$			328264.i			0.917167i	0.888651	+	0.458583i	$0.151643\pi$
$71$			328264.i			0.917167i	−0.888651	+	0.458583i	$0.848357\pi$
$72$		0			0
$73$	−606671.			−1.55950			−0.779749	−	0.626092i	$-0.784653\pi$
$73$	−606671.			−1.55950			−0.779749	+	0.626092i	$0.784653\pi$
$74$		0			0
$75$	396818.	+	17535.3i	0.940605	+	0.0415650i
$76$		0			0
$77$	680944.	+	393143.i	1.49156	+	0.861150i
$78$		0			0
$79$	283582.	+	491178.i	0.575171	+	0.996225i	0.996023	+	0.0890957i	$0.0283977\pi$
$79$	283582.	+	491178.i	0.575171	+	0.996225i	−0.420852	+	0.907129i	$0.638269\pi$
$80$		0			0
$81$	−342462.	+	406385.i	−0.644403	+	0.764686i
$82$		0			0
$83$	556799.	−	321468.i	0.973787	−	0.562216i	0.0733984	−	0.997303i	$-0.476616\pi$
$83$	556799.	−	321468.i	0.973787	−	0.562216i	0.900389	+	0.435086i	$0.143282\pi$
$84$		0			0
$85$	−74467.0	+	128981.i	−0.121257	+	0.210023i
$86$		0			0
$87$	43784.9	−	990840.i	0.0664916	−	1.50469i
$88$		0			0
$89$			220044.i			0.312133i	0.987747	+	0.156066i	$0.0498814\pi$
$89$			220044.i			0.312133i	−0.987747	+	0.156066i	$0.950119\pi$
$90$		0			0
$91$	−1.31251e6			−1.74171
$92$		0			0
$93$	−442524.	−	851177.i	−0.550158	−	1.05821i
$94$		0			0
$95$	−89152.0	−	51471.9i	−0.103982	−	0.0600343i
$96$		0			0
$97$	114375.	+	198104.i	0.125319	+	0.217059i	0.921858	−	0.387529i	$-0.126671\pi$
$97$	114375.	+	198104.i	0.125319	+	0.217059i	−0.796539	+	0.604588i	$0.793338\pi$
$98$		0			0
$99$	−778339.	−	546224.i	−0.802164	−	0.562944i
$100$		0			0
$101$	683187.	−	394438.i	0.663095	−	0.382838i	−0.130360	−	0.991467i	$-0.541613\pi$
$101$	683187.	−	394438.i	0.663095	−	0.382838i	0.793455	+	0.608629i	$0.208280\pi$
$102$		0			0
$103$	−957556.	+	1.65854e6i	−0.876300	+	1.51780i	−0.0209280	+	0.999781i	$0.506662\pi$
$103$	−957556.	+	1.65854e6i	−0.876300	+	1.51780i	−0.855372	+	0.518015i	$0.826671\pi$
$104$		0			0
$105$	−414796.	−	264562.i	−0.358316	−	0.228538i
$106$		0			0
$107$			1.55760e6i			1.27146i	0.771910	+	0.635731i	$0.219301\pi$
$107$			1.55760e6i			1.27146i	−0.771910	+	0.635731i	$0.780699\pi$
$108$		0			0
$109$	−2.15378e6			−1.66311			−0.831555	−	0.555443i	$-0.812549\pi$
$109$	−2.15378e6			−1.66311			−0.831555	+	0.555443i	$0.812549\pi$
$110$		0			0
$111$	124452.	−	195124.i	0.0909984	−	0.142673i
$112$		0			0
$113$	706126.	+	407682.i	0.489381	+	0.282544i	0.724318	−	0.689466i	$-0.242155\pi$
$113$	706126.	+	407682.i	0.489381	+	0.282544i	−0.234937	+	0.972011i	$0.575488\pi$
$114$		0			0
$115$	−199652.	−	345808.i	−0.131275	−	0.227374i
$116$		0			0
$117$	1.58106e6	+	140007.i	0.987170	+	0.0874162i
$118$		0			0
$119$	−2.57219e6	+	1.48505e6i	−1.52638	+	0.881255i
$120$		0			0
$121$	−35100.7	+	60796.2i	−0.0198134	+	0.0343179i
$122$		0			0
$123$	−1.86551e6	+	969873.i	−1.00250	+	0.521194i
$124$		0			0
$125$		−	916995.i		−	0.469501i
$126$		0			0
$127$	2.09013e6			1.02038			0.510189	−	0.860062i	$-0.329575\pi$
$127$	2.09013e6			1.02038			0.510189	+	0.860062i	$0.329575\pi$
$128$		0			0
$129$	1.69795e6	+	75031.9i	0.790962	+	0.0349524i
$130$		0			0
$131$	489044.	+	282350.i	0.217537	+	0.125595i	0.604810	−	0.796370i	$-0.293249\pi$
$131$	489044.	+	282350.i	0.217537	+	0.125595i	−0.387272	+	0.921965i	$0.626583\pi$
$132$		0			0
$133$	−1.02648e6	−	1.77791e6i	−0.436309	−	0.755709i
$134$		0			0
$135$	471448.	+	362942.i	0.191616	+	0.147515i
$136$		0			0
$137$	2.13254e6	−	1.23122e6i	0.829345	−	0.478823i	−0.0242833	−	0.999705i	$-0.507730\pi$
$137$	2.13254e6	−	1.23122e6i	0.829345	−	0.478823i	0.853628	+	0.520882i	$0.174397\pi$
$138$		0			0
$139$	919096.	−	1.59192e6i	0.342229	−	0.592757i	−0.642618	−	0.766187i	$-0.722152\pi$
$139$	919096.	−	1.59192e6i	0.342229	−	0.592757i	0.984846	+	0.173430i	$0.0554849\pi$
$140$		0			0
$141$	−138333.	+	3.13045e6i	−0.0493480	+	1.11673i
$142$		0			0
$143$			2.83999e6i			0.971199i
$144$		0			0
$145$	−1.11037e6			−0.364220
$146$		0			0
$147$	−3.06052e6	−	5.88680e6i	−0.963483	−	1.85322i
$148$		0			0
$149$	−2.13710e6	−	1.23386e6i	−0.646050	−	0.372997i	0.140891	−	0.990025i	$-0.455003\pi$
$149$	−2.13710e6	−	1.23386e6i	−0.646050	−	0.372997i	−0.786941	+	0.617028i	$0.788337\pi$
$150$		0			0
$151$	2.42550e6	+	4.20109e6i	0.704483	+	1.22020i	0.966878	+	0.255239i	$0.0821543\pi$
$151$	2.42550e6	+	4.20109e6i	0.704483	+	1.22020i	−0.262395	+	0.964961i	$0.584512\pi$
$152$		0			0
$153$	3.25691e6	−	1.51454e6i	0.909351	−	0.422870i
$154$		0			0
$155$	−930128.	+	537010.i	−0.249774	+	0.144207i
$156$		0			0
$157$	−35796.3	+	62000.9i	−0.00924994	+	0.0160214i	−0.870613	−	0.491968i	$-0.836278\pi$
$157$	−35796.3	+	62000.9i	−0.00924994	+	0.0160214i	0.861363	+	0.507989i	$0.169611\pi$
$158$		0			0
$159$	1.10346e6	+	703800.i	0.274514	+	0.175089i
$160$		0			0
$161$		−	7.96311e6i		−	1.90812i
$162$		0			0
$163$	2.68015e6			0.618866			0.309433	−	0.950921i	$-0.399861\pi$
$163$	2.68015e6			0.618866			0.309433	+	0.950921i	$0.399861\pi$
$164$		0			0
$165$	−572456.	+	897531.i	−0.127435	+	0.199801i
$166$		0			0
$167$	1.86267e6	+	1.07541e6i	0.399933	+	0.230901i	0.686455	−	0.727172i	$-0.259166\pi$
$167$	1.86267e6	+	1.07541e6i	0.399933	+	0.230901i	−0.286522	+	0.958074i	$0.592499\pi$
$168$		0			0
$169$	43089.1	+	74632.5i	0.00892704	+	0.0154621i
$170$		0			0
$171$	1.04686e6	+	2.25119e6i	0.209363	+	0.450220i
$172$		0			0
$173$	5.26951e6	−	3.04236e6i	1.01773	−	0.587586i	0.104284	−	0.994548i	$-0.466745\pi$
$173$	5.26951e6	−	3.04236e6i	1.01773	−	0.587586i	0.913445	+	0.406961i	$0.133412\pi$
$174$		0			0
$175$	4.43408e6	−	7.68005e6i	0.827350	−	1.43301i
$176$		0			0
$177$	−4.87257e6	+	2.53323e6i	−0.878694	+	0.456830i
$178$		0			0
$179$		−	4.23553e6i		−	0.738497i	−0.929331	−	0.369249i	$-0.879615\pi$
$179$		−	4.23553e6i		−	0.738497i	0.929331	−	0.369249i	$-0.120385\pi$
$180$		0			0
$181$	2.62571e6			0.442803			0.221402	−	0.975183i	$-0.428937\pi$
$181$	2.62571e6			0.442803			0.221402	+	0.975183i	$0.428937\pi$
$182$		0			0
$183$	753258.	+	33286.2i	0.122911	+	0.00543140i
$184$		0			0
$185$	−224387.	−	129550.i	−0.0354391	−	0.0204608i
$186$		0			0
$187$	3.21335e6	+	5.56568e6i	0.491397	+	0.851125i
$188$		0			0
$189$	4.52325e6	+	1.09692e7i	0.669984	+	1.62476i
$190$		0			0
$191$	−6.11550e6	+	3.53079e6i	−0.877672	+	0.506724i	−0.869890	−	0.493246i	$-0.835810\pi$
$191$	−6.11550e6	+	3.53079e6i	−0.877672	+	0.506724i	−0.00778159	+	0.999970i	$0.502477\pi$
$192$		0			0
$193$	5.29477e6	−	9.17080e6i	0.736503	−	1.27566i	−0.217557	−	0.976048i	$-0.569809\pi$
$193$	5.29477e6	−	9.17080e6i	0.736503	−	1.27566i	0.954061	−	0.299614i	$-0.0968578\pi$
$194$		0			0
$195$	78448.3	−	1.77526e6i	0.0105799	−	0.239419i
$196$		0			0
$197$			8.69292e6i			1.13702i	0.822677	+	0.568509i	$0.192480\pi$
$197$			8.69292e6i			1.13702i	−0.822677	+	0.568509i	$0.807520\pi$
$198$		0			0
$199$	1.55617e6			0.197469			0.0987345	−	0.995114i	$-0.468521\pi$
$199$	1.55617e6			0.197469			0.0987345	+	0.995114i	$0.468521\pi$
$200$		0			0
$201$	5.81120e6	+	1.11776e7i	0.715612	+	1.37645i
$202$		0			0
$203$	−1.91768e7	−	1.10718e7i	−2.29239	−	1.32351i
$204$		0			0
$205$	1.17696e6	+	2.03855e6i	0.136615	+	0.236624i
$206$		0			0
$207$	−849437.	+	9.59248e6i	−0.0957679	+	1.08148i
$208$		0			0
$209$	−3.84702e6	+	2.22108e6i	−0.421392	+	0.243291i
$210$		0			0
$211$	7.39607e6	−	1.28104e7i	0.787324	−	1.36369i	−0.140277	−	0.990112i	$-0.544799\pi$
$211$	7.39607e6	−	1.28104e7i	0.787324	−	1.36369i	0.927601	−	0.373573i	$-0.121867\pi$
$212$		0			0
$213$	−7.47258e6	−	4.76610e6i	−0.773271	−	0.493202i
$214$		0			0
$215$		−	1.90278e6i		−	0.191458i
$216$		0			0
$217$	−2.14186e7			−2.09610
$218$		0			0
$219$	8.80833e6	−	1.38102e7i	0.838612	−	1.31483i
$220$		0			0
$221$	−9.29048e6	−	5.36386e6i	−0.860719	−	0.496936i
$222$		0			0
$223$	5.70510e6	+	9.88151e6i	0.514456	+	0.891064i	0.999859	+	0.0167737i	$0.00533947\pi$
$223$	5.70510e6	+	9.88151e6i	0.514456	+	0.891064i	−0.485403	+	0.874290i	$0.661327\pi$
$224$		0			0
$225$	−6.16061e6	+	8.77852e6i	−0.540849	+	0.770680i
$226$		0			0
$227$	−1.03199e7	+	5.95820e6i	−0.882263	+	0.509374i	−0.871404	−	0.490567i	$-0.836790\pi$
$227$	−1.03199e7	+	5.95820e6i	−0.882263	+	0.509374i	−0.0108588	+	0.999941i	$0.503457\pi$
$228$		0			0
$229$	−268740.	+	465471.i	−0.0223782	+	0.0387602i	−0.876998	−	0.480495i	$-0.840457\pi$
$229$	−268740.	+	465471.i	−0.0223782	+	0.0387602i	0.854619	+	0.519255i	$0.173790\pi$
$230$		0			0
$231$	−1.88362e7	+	9.79287e6i	−1.52812	+	0.794463i
$232$		0			0
$233$		−	1.79820e7i		−	1.42158i	−0.703405	−	0.710790i	$-0.748338\pi$
$233$		−	1.79820e7i		−	1.42158i	0.703405	−	0.710790i	$-0.251662\pi$
$234$		0			0
$235$	3.50809e6			0.270313
$236$		0			0
$237$	−1.52985e7	−	676035.i	−1.14922	−	0.0507837i
$238$		0			0
$239$	1.89055e7	+	1.09151e7i	1.38483	+	0.799529i	0.992726	−	0.120394i	$-0.0384157\pi$
$239$	1.89055e7	+	1.09151e7i	1.38483	+	0.799529i	0.392099	+	0.919923i	$0.371749\pi$
$240$		0			0
$241$	1.18018e7	+	2.04413e7i	0.843135	+	1.46035i	0.887231	+	0.461326i	$0.152626\pi$
$241$	1.18018e7	+	2.04413e7i	0.843135	+	1.46035i	−0.0440955	+	0.999027i	$0.514041\pi$
$242$		0			0
$243$	−4.27867e6	−	1.36961e7i	−0.298188	−	0.954507i
$244$		0			0
$245$	−6.43283e6	+	3.71400e6i	−0.437425	+	0.252548i
$246$		0			0
$247$	3.70753e6	−	6.42162e6i	0.246033	−	0.426142i
$248$		0			0
$249$	−766353.	+	1.73423e7i	−0.0496399	+	1.12334i
$250$		0			0
$251$			5.11888e6i			0.323709i	0.986815	+	0.161854i	$0.0517475\pi$
$251$			5.11888e6i			0.323709i	−0.986815	+	0.161854i	$0.948253\pi$
$252$		0			0
$253$	−1.72305e7			−1.06399
$254$		0			0
$255$	−1.85491e6	−	3.56784e6i	−0.111867	−	0.215172i
$256$		0			0
$257$	7.46731e6	+	4.31125e6i	0.439911	+	0.253983i	0.703560	−	0.710636i	$-0.251593\pi$
$257$	7.46731e6	+	4.31125e6i	0.439911	+	0.253983i	−0.263649	+	0.964619i	$0.584926\pi$
$258$		0			0
$259$	−2.58354e6	−	4.47483e6i	−0.148702	−	0.257559i
$260$		0			0
$261$	2.19197e7	+	1.53828e7i	1.23286	+	0.865196i
$262$		0			0
$263$	2.41185e7	−	1.39248e7i	1.32582	−	0.765461i	0.341167	−	0.940003i	$-0.389178\pi$
$263$	2.41185e7	−	1.39248e7i	1.32582	−	0.765461i	0.984650	+	0.174542i	$0.0558444\pi$
$264$		0			0
$265$	732628.	−	1.26895e6i	0.0393682	−	0.0681878i
$266$		0			0
$267$	−5.00906e6	−	3.19484e6i	−0.263161	−	0.167848i
$268$		0			0
$269$		−	1.34743e7i		−	0.692230i	−0.938192	−	0.346115i	$-0.887501\pi$
$269$		−	1.34743e7i		−	0.692230i	0.938192	−	0.346115i	$-0.112499\pi$
$270$		0			0
$271$	6.69932e6			0.336607			0.168303	−	0.985735i	$-0.446171\pi$
$271$	6.69932e6			0.336607			0.168303	+	0.985735i	$0.446171\pi$
$272$		0			0
$273$	1.90564e7	−	2.98777e7i	0.936597	−	1.46845i
$274$		0			0
$275$	−1.66180e7	−	9.59442e6i	−0.799064	−	0.461340i
$276$		0			0
$277$	−2.73670e6	−	4.74010e6i	−0.128762	−	0.223022i	0.794435	−	0.607349i	$-0.207767\pi$
$277$	−2.73670e6	−	4.74010e6i	−0.128762	−	0.223022i	−0.923197	+	0.384327i	$0.874434\pi$
$278$		0			0
$279$	2.58012e7	+	2.28475e6i	1.18803	+	0.105203i
$280$		0			0
$281$	−2.07990e7	+	1.20083e7i	−0.937398	+	0.541207i	−0.889144	−	0.457628i	$-0.848699\pi$
$281$	−2.07990e7	+	1.20083e7i	−0.937398	+	0.541207i	−0.0482541	+	0.998835i	$0.515366\pi$
$282$		0			0
$283$	2.37222e6	−	4.10880e6i	0.104664	−	0.181283i	−0.808937	−	0.587895i	$-0.799957\pi$
$283$	2.37222e6	−	4.10880e6i	0.104664	−	0.181283i	0.913601	+	0.406613i	$0.133290\pi$
$284$		0			0
$285$	2.46611e6	−	1.28212e6i	0.106531	−	0.0553853i
$286$		0			0
$287$			4.69428e7i			1.98574i
$288$		0			0
$289$	−138522.			−0.00573884
$290$		0			0
$291$	−6.17023e6	−	272661.i	−0.250393	−	0.0110648i
$292$		0			0
$293$	2.55470e7	+	1.47496e7i	1.01563	+	0.586376i	0.912836	−	0.408327i	$-0.133888\pi$
$293$	2.55470e7	+	1.47496e7i	1.01563	+	0.586376i	0.102797	+	0.994702i	$0.467221\pi$
$294$		0			0
$295$	3.07411e6	+	5.32452e6i	0.119744	+	0.207403i
$296$		0			0
$297$	2.37350e7	−	9.78735e6i	0.905982	−	0.373591i
$298$		0			0
$299$	2.49085e7	−	1.43810e7i	0.931826	−	0.537990i
$300$		0			0
$301$	1.89731e7	−	3.28623e7i	0.695726	−	1.20503i
$302$		0			0
$303$	−940308.	+	2.12789e7i	−0.0338020	+	0.764929i
$304$		0			0
$305$		−	844127.i		−	0.0297515i
$306$		0			0
$307$	−4.47192e7			−1.54554			−0.772768	−	0.634689i	$-0.781128\pi$
$307$	−4.47192e7			−1.54554			−0.772768	+	0.634689i	$0.781128\pi$
$308$		0			0
$309$	−2.38519e7	−	4.58782e7i	−0.808440	−	1.55500i
$310$		0			0
$311$	−3.24613e7	−	1.87416e7i	−1.07916	−	0.623053i	−0.148489	−	0.988914i	$-0.547441\pi$
$311$	−3.24613e7	−	1.87416e7i	−1.07916	−	0.623053i	−0.930669	+	0.365861i	$0.880774\pi$
$312$		0			0
$313$	−6.13998e6	−	1.06348e7i	−0.200232	−	0.346812i	0.748371	−	0.663280i	$-0.230836\pi$
$313$	−6.13998e6	−	1.06348e7i	−0.200232	−	0.346812i	−0.948603	+	0.316468i	$0.897503\pi$
$314$		0			0
$315$	1.20449e7	−	5.60117e6i	0.385365	−	0.179204i
$316$		0			0
$317$	5.14483e7	−	2.97037e7i	1.61508	−	0.932464i	0.626907	−	0.779094i	$-0.284321\pi$
$317$	5.14483e7	−	2.97037e7i	1.61508	−	0.932464i	0.988169	−	0.153370i	$-0.0490127\pi$
$318$		0			0
$319$	−2.39569e7	+	4.14947e7i	−0.738005	+	1.27826i
$320$		0			0
$321$	−3.54570e7	−	2.26149e7i	−1.07198	−	0.683722i
$322$		0			0
$323$		−	1.67798e7i		−	0.497941i
$324$		0			0
$325$	3.20309e7			0.933080
$326$		0			0
$327$	3.12709e7	−	4.90283e7i	0.894328	−	1.40218i
$328$		0			0
$329$	6.05870e7	+	3.49799e7i	1.70134	+	0.982271i
$330$		0			0
$331$	5.29163e6	+	9.16537e6i	0.145917	+	0.252735i	0.929715	−	0.368281i	$-0.120053\pi$
$331$	5.29163e6	+	9.16537e6i	0.145917	+	0.252735i	−0.783798	+	0.621016i	$0.786720\pi$
$332$		0			0
$333$	2.63484e6	+	5.66604e6i	0.0713545	+	0.153443i
$334$		0			0
$335$	1.22144e7	−	7.05199e6i	0.324891	−	0.187576i
$336$		0			0
$337$	−1.88528e7	+	3.26540e7i	−0.492590	+	0.853191i	−0.999964	−	0.00853516i	$-0.997283\pi$
$337$	−1.88528e7	+	3.26540e7i	−0.492590	+	0.853191i	0.507373	+	0.861726i	$0.330616\pi$
$338$		0			0
$339$	−1.95328e7	+	1.01550e7i	−0.501377	+	0.260664i
$340$		0			0
$341$			4.63453e7i			1.16881i
$342$		0			0
$343$	−7.72120e7			−1.91339
$344$		0			0
$345$	1.07707e7	+	475954.i	0.262293	+	0.0115907i
$346$		0			0
$347$	6.36319e7	+	3.67379e7i	1.52295	+	0.879278i	0.999632	+	0.0271424i	$0.00864074\pi$
$347$	6.36319e7	+	3.67379e7i	1.52295	+	0.879278i	0.523322	+	0.852135i	$0.324693\pi$
$348$		0			0
$349$	2.10990e7	+	3.65446e7i	0.496348	+	0.859700i	0.999991	−	0.00421214i	$-0.00134077\pi$
$349$	2.10990e7	+	3.65446e7i	0.496348	+	0.859700i	−0.503643	+	0.863912i	$0.668007\pi$
$350$		0			0
$351$	−2.61427e7	+	3.39584e7i	−0.604547	+	0.785283i
$352$		0			0
$353$	−6.99832e7	+	4.04048e7i	−1.59100	+	0.918563i	−0.597861	+	0.801600i	$0.703982\pi$
$353$	−6.99832e7	+	4.04048e7i	−1.59100	+	0.918563i	−0.993136	+	0.116963i	$0.962684\pi$
$354$		0			0
$355$	−4.96133e6	+	8.59327e6i	−0.110895	+	0.192076i
$356$		0			0
$357$	3.54025e6	−	8.01147e7i	0.0778088	−	1.76079i
$358$		0			0
$359$			3.34817e7i			0.723642i	0.932248	+	0.361821i	$0.117845\pi$
$359$			3.34817e7i			0.723642i	−0.932248	+	0.361821i	$0.882155\pi$
$360$		0			0
$361$	−3.54476e7			−0.753469
$362$		0			0
$363$	−874328.	−	1.68173e6i	−0.0182791	−	0.0351591i
$364$		0			0
$365$	−1.58814e7	−	9.16912e6i	−0.326595	−	0.188560i
$366$		0			0
$367$	2.04848e7	+	3.54808e7i	0.414414	+	0.717786i	0.995367	−	0.0961511i	$-0.0306532\pi$
$367$	2.04848e7	+	3.54808e7i	0.414414	+	0.717786i	−0.580953	+	0.813937i	$0.697320\pi$
$368$		0			0
$369$	5.00746e6	−	5.65480e7i	0.0996640	−	1.12548i
$370$		0			0
$371$	2.53060e7	−	1.46104e7i	0.495565	−	0.286115i
$372$		0			0
$373$	2.54633e7	−	4.41037e7i	0.490668	−	0.849862i	−0.509274	−	0.860604i	$-0.670086\pi$
$373$	2.54633e7	−	4.41037e7i	0.490668	−	0.849862i	0.999942	+	0.0107421i	$0.00341937\pi$
$374$		0			0
$375$	2.08744e7	+	1.33139e7i	0.395840	+	0.252472i
$376$		0			0
$377$		−	7.99800e7i		−	1.49265i
$378$		0			0
$379$	−8.46556e7			−1.55503			−0.777513	−	0.628866i	$-0.783519\pi$
$379$	−8.46556e7			−1.55503			−0.777513	+	0.628866i	$0.783519\pi$
$380$		0			0
$381$	−3.03468e7	+	4.75794e7i	−0.548703	+	0.860289i
$382$		0			0
$383$	−2.92560e7	−	1.68910e7i	−0.520737	−	0.300648i	0.216499	−	0.976283i	$-0.430536\pi$
$383$	−2.92560e7	−	1.68910e7i	−0.520737	−	0.300648i	−0.737236	+	0.675635i	$0.763870\pi$
$384$		0			0
$385$	1.18838e7	+	2.05833e7i	0.208244	+	0.360690i
$386$		0			0
$387$	−2.63607e7	+	3.75626e7i	−0.454804	+	0.648071i
$388$		0			0
$389$	−8.41523e7	+	4.85854e7i	−1.42961	+	0.825385i	−0.997090	−	0.0762392i	$-0.975709\pi$
$389$	−8.41523e7	+	4.85854e7i	−1.42961	+	0.825385i	−0.432520	+	0.901625i	$0.642375\pi$
$390$		0			0
$391$	3.25431e7	−	5.63663e7i	0.544413	−	0.942952i
$392$		0			0
$393$	−1.35279e7	+	7.03309e6i	−0.222870	+	0.115869i
$394$		0			0
$395$			1.71440e7i			0.278177i
$396$		0			0
$397$	−7.73396e7			−1.23603			−0.618017	−	0.786165i	$-0.712064\pi$
$397$	−7.73396e7			−1.23603			−0.618017	+	0.786165i	$0.712064\pi$
$398$		0			0
$399$	5.53757e7	+	2.44704e6i	0.871767	+	0.0385231i
$400$		0			0
$401$	−4.22049e7	−	2.43670e7i	−0.654530	−	0.377893i	0.135660	−	0.990755i	$-0.456685\pi$
$401$	−4.22049e7	−	2.43670e7i	−0.654530	−	0.377893i	−0.790190	+	0.612863i	$0.790018\pi$
$402$		0			0
$403$	−3.86808e7	−	6.69972e7i	−0.590991	−	1.02363i
$404$		0			0
$405$	−1.51070e7	+	5.46240e6i	−0.227412	+	0.0822278i
$406$		0			0
$407$	−9.68259e6	+	5.59025e6i	−0.143618	+	0.0829178i
$408$		0			0
$409$	−1.30392e7	+	2.25845e7i	−0.190582	+	0.330097i	−0.945443	−	0.325787i	$-0.894371\pi$
$409$	−1.30392e7	+	2.25845e7i	−0.190582	+	0.330097i	0.754862	+	0.655884i	$0.227704\pi$
$410$		0			0
$411$	−2.93513e6	+	6.64212e7i	−0.0422768	+	0.956712i
$412$		0			0
$413$			1.22611e8i			1.74052i
$414$		0			0
$415$	1.94344e7			0.271912
$416$		0			0
$417$	2.28939e7	+	4.40355e7i	0.315727	+	0.607288i
$418$		0			0
$419$	2.07013e7	+	1.19519e7i	0.281420	+	0.162478i	0.634066	−	0.773279i	$-0.281385\pi$
$419$	2.07013e7	+	1.19519e7i	0.281420	+	0.162478i	−0.352646	+	0.935757i	$0.614718\pi$
$420$		0			0
$421$	2.65906e7	+	4.60562e7i	0.356354	+	0.617223i	0.987349	−	0.158564i	$-0.0506865\pi$
$421$	2.65906e7	+	4.60562e7i	0.356354	+	0.617223i	−0.630995	+	0.775787i	$0.717353\pi$
$422$		0			0
$423$	−6.92527e7	−	4.86003e7i	−0.914988	−	0.642122i
$424$		0			0
$425$	6.27727e7	−	3.62418e7i	0.817719	−	0.472110i
$426$		0			0
$427$	8.41698e6	−	1.45786e7i	0.108112	−	0.187255i
$428$		0			0
$429$	−6.46492e7	−	4.12340e7i	−0.818825	−	0.522257i
$430$		0			0
$431$		−	1.42759e8i		−	1.78308i	−0.452941	−	0.891541i	$-0.649625\pi$
$431$		−	1.42759e8i		−	1.78308i	0.452941	−	0.891541i	$-0.350375\pi$
$432$		0			0
$433$	1.12881e8			1.39045			0.695226	−	0.718791i	$-0.255304\pi$
$433$	1.12881e8			1.39045			0.695226	+	0.718791i	$0.255304\pi$
$434$		0			0
$435$	1.61216e7	−	2.52764e7i	0.195857	−	0.307077i
$436$		0			0
$437$	3.89607e7	+	2.24940e7i	0.466855	+	0.269539i
$438$		0			0
$439$	−1.04402e7	−	1.80829e7i	−0.123400	−	0.213734i	0.797707	−	0.603046i	$-0.206046\pi$
$439$	−1.04402e7	−	1.80829e7i	−0.123400	−	0.213734i	−0.921106	+	0.389311i	$0.872713\pi$
$440$		0			0
$441$	1.78443e8	+	1.58015e7i	2.08057	+	0.184240i
$442$		0			0
$443$	7.97602e7	−	4.60496e7i	0.917435	−	0.529681i	0.0346192	−	0.999401i	$-0.488978\pi$
$443$	7.97602e7	−	4.60496e7i	0.917435	−	0.529681i	0.882816	+	0.469719i	$0.155645\pi$
$444$		0			0
$445$	−3.32570e6	+	5.76029e6i	−0.0377401	+	0.0653678i
$446$		0			0
$447$	5.91162e7	−	3.07343e7i	0.661887	−	0.344113i
$448$		0			0
$449$		−	1.80082e7i		−	0.198944i	−0.995040	−	0.0994718i	$-0.968285\pi$
$449$		−	1.80082e7i		−	0.198944i	0.995040	−	0.0994718i	$-0.0317153\pi$
$450$		0			0
$451$	1.01574e8			1.10727
$452$		0			0
$453$	−1.30849e8	−	5.78219e6i	−1.40759	−	0.0622011i
$454$		0			0
$455$	−3.43586e7	−	1.98370e7i	−0.364755	−	0.210592i
$456$		0			0
$457$	5.30724e6	+	9.19241e6i	0.0556058	+	0.0963120i	0.892488	−	0.451070i	$-0.148958\pi$
$457$	5.30724e6	+	9.19241e6i	0.0556058	+	0.0963120i	−0.836883	+	0.547382i	$0.815624\pi$
$458$		0			0
$459$	−1.28106e7	+	9.61298e7i	−0.132474	+	0.994077i
$460$		0			0
$461$	−5.58492e7	+	3.22446e7i	−0.570052	+	0.329120i	−0.757170	−	0.653218i	$-0.773419\pi$
$461$	−5.58492e7	+	3.22446e7i	−0.570052	+	0.329120i	0.187118	+	0.982337i	$0.440085\pi$
$462$		0			0
$463$	−3.44061e7	+	5.95931e7i	−0.346651	+	0.600417i	−0.985652	−	0.168789i	$-0.946014\pi$
$463$	−3.44061e7	+	5.95931e7i	−0.346651	+	0.600417i	0.639001	+	0.769206i	$0.279348\pi$
$464$		0			0
$465$	1.28019e6	−	2.89702e7i	0.0127325	−	0.288133i
$466$		0			0
$467$		−	6.30877e7i		−	0.619432i	−0.950829	−	0.309716i	$-0.899766\pi$
$467$		−	6.30877e7i		−	0.619432i	0.950829	−	0.309716i	$-0.100234\pi$
$468$		0			0
$469$	2.81268e8			2.72648
$470$		0			0
$471$	−891654.	−	1.71506e6i	−0.00853363	−	0.0164141i
$472$		0			0
$473$	−7.11072e7	−	4.10538e7i	−0.671939	−	0.387944i
$474$		0			0
$475$	2.50505e7	+	4.33888e7i	0.233742	+	0.404852i
$476$		0			0
$477$	−3.20425e7	+	1.49005e7i	−0.295237	+	0.137292i
$478$		0			0
$479$	1.21741e8	−	7.02873e7i	1.10772	−	0.639544i	0.169484	−	0.985533i	$-0.445790\pi$
$479$	1.21741e8	−	7.02873e7i	1.10772	−	0.639544i	0.938239	+	0.345989i	$0.112457\pi$
$480$		0			0
$481$	9.33149e6	−	1.61626e7i	0.0838524	−	0.145237i
$482$		0			0
$483$	1.81271e8	+	1.15617e8i	1.60875	+	1.02608i
$484$		0			0
$485$			6.91458e6i			0.0606095i
$486$		0			0
$487$	8.13729e7			0.704520			0.352260	−	0.935902i	$-0.385413\pi$
$487$	8.13729e7			0.704520			0.352260	+	0.935902i	$0.385413\pi$
$488$		0			0
$489$	−3.89134e7	+	6.10107e7i	−0.332792	+	0.521770i
$490$		0			0
$491$	−1.33726e8	−	7.72069e7i	−1.12972	−	0.652246i	−0.185858	−	0.982577i	$-0.559507\pi$
$491$	−1.33726e8	−	7.72069e7i	−1.12972	−	0.652246i	−0.943865	+	0.330330i	$0.892840\pi$
$492$		0			0
$493$	−9.04946e7	−	1.56741e8i	−0.755235	−	1.30811i
$494$		0			0
$495$	−1.21198e7	−	2.60627e7i	−0.0999259	−	0.214884i
$496$		0			0
$497$	−1.71371e8	+	9.89410e7i	−1.39594	+	0.805948i
$498$		0			0
$499$	2.59211e7	−	4.48967e7i	0.208618	−	0.361337i	−0.742661	−	0.669667i	$-0.766437\pi$
$499$	2.59211e7	−	4.48967e7i	0.208618	−	0.361337i	0.951280	+	0.308330i	$0.0997701\pi$
$500$		0			0
$501$	−5.15250e7	+	2.67876e7i	−0.409736	+	0.213020i
$502$		0			0
$503$		−	1.23007e7i		−	0.0966552i	−0.998832	−	0.0483276i	$-0.984611\pi$
$503$		−	1.23007e7i		−	0.0966552i	0.998832	−	0.0483276i	$-0.0153892\pi$
$504$		0			0
$505$	2.38459e7			0.185157
$506$		0			0
$507$	−2.32454e6	−	102721.i	−0.0178367	−	0.000788197i
$508$		0			0
$509$	8.40111e7	+	4.85038e7i	0.637064	+	0.367809i	0.783483	−	0.621413i	$-0.213441\pi$
$509$	8.40111e7	+	4.85038e7i	0.637064	+	0.367809i	−0.146418	+	0.989223i	$0.546775\pi$
$510$		0			0
$511$	−1.82855e8	−	3.16714e8i	−1.37039	−	2.37358i
$512$		0			0
$513$	−6.64454e7	−	8.85475e6i	−0.492167	−	0.0655880i
$514$		0			0
$515$	−5.01336e7	+	2.89447e7i	−0.367035	+	0.211908i
$516$		0			0
$517$	7.56892e7	−	1.31098e8i	0.547725	−	0.948687i
$518$		0			0
$519$	−7.25272e6	+	1.64127e8i	−0.0518799	+	1.17403i
$520$		0			0
$521$		−	1.97622e8i		−	1.39740i	−0.715413	−	0.698702i	$-0.753761\pi$
$521$		−	1.97622e8i		−	1.39740i	0.715413	−	0.698702i	$-0.246239\pi$
$522$		0			0
$523$	1.25072e8			0.874286			0.437143	−	0.899392i	$-0.355990\pi$
$523$	1.25072e8			0.874286			0.437143	+	0.899392i	$0.355990\pi$
$524$		0			0
$525$	1.10449e8	+	2.12445e8i	0.763281	+	1.46814i
$526$		0			0
$527$	−1.51610e8	−	8.75321e7i	−1.03585	−	0.598047i
$528$		0			0
$529$	1.32329e7	+	2.29200e7i	0.0893895	+	0.154827i
$530$		0			0
$531$	1.30791e7	−	1.47699e8i	0.0873562	−	0.986492i
$532$		0			0
$533$	−1.46837e8	+	8.47762e7i	−0.969735	+	0.559877i
$534$		0			0
$535$	−2.35412e7	+	4.07746e7i	−0.153733	+	0.266274i
$536$		0			0
$537$	9.64172e7	+	6.14961e7i	0.622633	+	0.397123i
$538$		0			0
$539$			3.20527e8i			2.04691i
$540$		0			0
$541$	−7.32707e6			−0.0462742			−0.0231371	−	0.999732i	$-0.507365\pi$
$541$	−7.32707e6			−0.0462742			−0.0231371	+	0.999732i	$0.507365\pi$
$542$		0			0
$543$	−3.81229e7	+	5.97714e7i	−0.238115	+	0.373331i
$544$		0			0
$545$	−5.63813e7	−	3.25518e7i	−0.348294	−	0.201088i
$546$		0			0
$547$	1.53059e8	+	2.65106e8i	0.935184	+	1.61979i	0.774305	+	0.632812i	$0.218100\pi$
$547$	1.53059e8	+	2.65106e8i	0.935184	+	1.61979i	0.160879	+	0.986974i	$0.448567\pi$
$548$		0			0
$549$	−1.16944e7	+	1.66638e7i	−0.0706739	+	0.100706i
$550$		0			0
$551$	1.08340e8	−	6.25503e7i	0.647643	−	0.373917i
$552$		0			0
$553$	−1.70947e8	+	2.96089e8i	−1.01085	+	1.75084i
$554$		0			0
$555$	6.20696e6	−	3.22698e6i	0.0363078	−	0.0188763i
$556$		0			0
$557$		−	2.71494e8i		−	1.57107i	−0.618819	−	0.785534i	$-0.712388\pi$
$557$		−	2.71494e8i		−	1.57107i	0.618819	−	0.785534i	$-0.287612\pi$
$558$		0			0
$559$	1.37058e8			0.784635
$560$		0			0
$561$	−1.73351e8	−	7.66035e6i	−0.981836	−	0.0433871i
$562$		0			0
$563$	−1.48864e8	−	8.59468e7i	−0.834191	−	0.481620i	0.0210947	−	0.999777i	$-0.493285\pi$
$563$	−1.48864e8	−	8.59468e7i	−0.834191	−	0.481620i	−0.855285	+	0.518157i	$0.826618\pi$
$564$		0			0
$565$	1.23233e7	+	2.13445e7i	0.0683252	+	0.118343i
$566$		0			0
$567$	−3.15375e8	−	5.62958e7i	−1.73013	−	0.308835i
$568$		0			0
$569$	1.42180e8	−	8.20879e7i	0.771797	−	0.445597i	−0.0617184	−	0.998094i	$-0.519658\pi$
$569$	1.42180e8	−	8.20879e7i	0.771797	−	0.445597i	0.833515	+	0.552496i	$0.186325\pi$
$570$		0			0
$571$	−9.96859e7	+	1.72661e8i	−0.535458	+	0.927441i	0.463683	+	0.886001i	$0.346528\pi$
$571$	−9.96859e7	+	1.72661e8i	−0.535458	+	0.927441i	−0.999141	+	0.0414394i	$0.986806\pi$
$572$		0			0
$573$	8.41711e6	−	1.90477e8i	0.0447403	−	1.01246i
$574$		0			0
$575$			1.94335e8i			1.02223i
$576$		0			0
$577$	−2.97359e8			−1.54794			−0.773969	−	0.633224i	$-0.781731\pi$
$577$	−2.97359e8			−1.54794			−0.773969	+	0.633224i	$0.781731\pi$
$578$		0			0
$579$	1.31888e8	+	2.53681e8i	0.679469	+	1.30693i
$580$		0			0
$581$	3.35646e8	+	1.93785e8i	1.71141	+	0.988080i
$582$		0			0
$583$	−3.16138e7	−	5.47568e7i	−0.159541	−	0.276333i
$584$		0			0
$585$	3.92729e7	+	2.75610e7i	0.196167	+	0.137666i
$586$		0			0
$587$	−1.19090e8	+	6.87566e7i	−0.588791	+	0.339939i	−0.764619	−	0.644482i	$-0.777073\pi$
$587$	−1.19090e8	+	6.87566e7i	−0.588791	+	0.339939i	0.175828	+	0.984421i	$0.443740\pi$
$588$		0			0
$589$	6.05026e7	−	1.04794e8i	0.296093	−	0.512848i
$590$		0			0
$591$	−1.97885e8	−	1.26213e8i	−0.958629	−	0.611425i
$592$		0			0
$593$		−	1.99904e8i		−	0.958646i	−0.877638	−	0.479323i	$-0.840882\pi$
$593$		−	1.99904e8i		−	0.958646i	0.877638	−	0.479323i	$-0.159118\pi$
$594$		0			0
$595$	−8.97794e7			−0.426212
$596$		0			0
$597$	−2.25943e7	+	3.54246e7i	−0.106188	+	0.166488i
$598$		0			0
$599$	2.63502e7	+	1.52133e7i	0.122604	+	0.0707852i	0.560048	−	0.828460i	$-0.310783\pi$
$599$	2.63502e7	+	1.52133e7i	0.122604	+	0.0707852i	−0.437444	+	0.899246i	$0.644116\pi$
$600$		0			0
$601$	−1.29224e6	−	2.23822e6i	−0.00595276	−	0.0103105i	0.863034	−	0.505146i	$-0.168561\pi$
$601$	−1.29224e6	−	2.23822e6i	−0.00595276	−	0.0103105i	−0.868986	+	0.494836i	$0.835228\pi$
$602$		0			0
$603$	−3.38820e8	−	3.00033e7i	−1.54531	−	0.136841i
$604$		0			0
$605$	−1.83772e6	+	1.06101e6i	−0.00829878	+	0.00479130i
$606$		0			0
$607$	1.02054e8	−	1.76762e8i	0.456313	−	0.790357i	−0.542450	−	0.840088i	$-0.682503\pi$
$607$	1.02054e8	−	1.76762e8i	0.456313	−	0.790357i	0.998763	+	0.0497312i	$0.0158365\pi$
$608$		0			0
$609$	5.30467e8	−	2.75788e8i	2.34859	−	1.22102i
$610$		0			0
$611$			2.52688e8i			1.10780i
$612$		0			0
$613$	3.85516e7			0.167363			0.0836817	−	0.996493i	$-0.473332\pi$
$613$	3.85516e7			0.167363			0.0836817	+	0.996493i	$0.473332\pi$
$614$		0			0
$615$	−6.34937e7	−	2.80577e6i	−0.272964	−	0.0120622i
$616$		0			0
$617$	−9.74233e7	−	5.62473e7i	−0.414770	−	0.239467i	0.278067	−	0.960562i	$-0.410306\pi$
$617$	−9.74233e7	−	5.62473e7i	−0.414770	−	0.239467i	−0.692837	+	0.721094i	$0.743640\pi$
$618$		0			0
$619$	−3.32184e7	−	5.75359e7i	−0.140057	−	0.242587i	0.787461	−	0.616365i	$-0.211395\pi$
$619$	−3.32184e7	−	5.75359e7i	−0.140057	−	0.242587i	−0.927518	+	0.373778i	$0.878062\pi$
$620$		0			0
$621$	−2.06029e8	−	1.58611e8i	−0.860309	−	0.662305i
$622$		0			0
$623$	−1.14874e8	+	6.63227e7i	−0.475071	+	0.274282i
$624$		0			0
$625$	−1.01073e8	+	1.75063e8i	−0.413994	+	0.717058i
$626$		0			0
$627$	5.29487e6	−	1.19821e8i	0.0214809	−	0.486107i
$628$		0			0
$629$		−	4.22330e7i		−	0.169707i
$630$		0			0
$631$	−1.71175e8			−0.681323			−0.340661	−	0.940186i	$-0.610651\pi$
$631$	−1.71175e8			−0.681323			−0.340661	+	0.940186i	$0.610651\pi$
$632$		0			0
$633$	1.84230e8	+	3.54358e8i	0.726354	+	1.39711i
$634$		0			0
$635$	5.47151e7	+	3.15898e7i	0.213691	+	0.123375i
$636$		0			0
$637$	−2.67519e8	−	4.63357e8i	−1.03499	−	1.79266i
$638$		0			0
$639$	2.16990e8	−	1.00906e8i	0.831644	−	0.386734i
$640$		0			0
$641$	3.36697e7	−	1.94392e7i	0.127839	−	0.0738082i	−0.434716	−	0.900567i	$-0.643151\pi$
$641$	3.36697e7	−	1.94392e7i	0.127839	−	0.0738082i	0.562556	+	0.826759i	$0.309818\pi$
$642$		0			0
$643$	−1.75228e8	+	3.03504e8i	−0.659130	+	1.14165i	0.321711	+	0.946838i	$0.395742\pi$
$643$	−1.75228e8	+	3.03504e8i	−0.659130	+	1.14165i	−0.980841	+	0.194809i	$0.937591\pi$
$644$		0			0
$645$	4.33148e7	+	2.76267e7i	0.161420	+	0.102956i
$646$		0			0
$647$			2.37058e8i			0.875269i	0.899153	+	0.437634i	$0.144184\pi$
$647$			2.37058e8i			0.875269i	−0.899153	+	0.437634i	$0.855816\pi$
$648$		0			0
$649$	2.65304e8			0.970532
$650$		0			0
$651$	3.10979e8	−	4.87571e8i	1.12717	−	1.76724i
$652$		0			0
$653$	3.07731e8	+	1.77669e8i	1.10518	+	0.638074i	0.937576	−	0.347781i	$-0.113065\pi$
$653$	3.07731e8	+	1.77669e8i	1.10518	+	0.638074i	0.167601	+	0.985855i	$0.446398\pi$
$654$		0			0
$655$	8.53477e6	+	1.47826e7i	0.0303716	+	0.0526052i
$656$		0			0
$657$	1.86485e8	+	4.01024e8i	0.657580	+	1.41408i
$658$		0			0
$659$	1.76643e8	−	1.01985e8i	0.617221	−	0.356353i	−0.158565	−	0.987349i	$-0.550687\pi$
$659$	1.76643e8	−	1.01985e8i	0.617221	−	0.356353i	0.775786	+	0.630996i	$0.217353\pi$
$660$		0			0
$661$	2.85662e6	−	4.94780e6i	0.00989116	−	0.0171320i	−0.861037	−	0.508542i	$-0.830185\pi$
$661$	2.85662e6	−	4.94780e6i	0.00989116	−	0.0171320i	0.870929	+	0.491410i	$0.163518\pi$
$662$		0			0
$663$	2.56992e8	−	1.33609e8i	0.881818	−	0.458454i
$664$		0			0
$665$		−	6.20559e7i		−	0.211017i
$666$		0			0
$667$	4.85247e8			1.63526
$668$		0			0
$669$	−3.07775e8	−	1.36005e7i	−1.02791	−	0.0454230i
$670$		0			0
$671$	−3.15451e7	−	1.82126e7i	−0.104415	−	0.0602843i
$672$		0			0
$673$	−5.57546e7	−	9.65697e7i	−0.182909	−	0.316808i	0.759961	−	0.649969i	$-0.225218\pi$
$673$	−5.57546e7	−	9.65697e7i	−0.182909	−	0.316808i	−0.942870	+	0.333161i	$0.891885\pi$
$674$		0			0
$675$	−1.10387e8	−	2.67696e8i	−0.358927	−	0.870423i
$676$		0			0
$677$	2.89143e8	−	1.66937e8i	0.931851	−	0.538004i	0.0444543	−	0.999011i	$-0.485845\pi$
$677$	2.89143e8	−	1.66937e8i	0.931851	−	0.538004i	0.887396	+	0.461007i	$0.152512\pi$
$678$		0			0
$679$	−6.89469e7	+	1.19419e8i	−0.220245	+	0.381475i
$680$		0			0
$681$	1.42038e7	−	3.21429e8i	0.0449743	−	1.01776i
$682$		0			0
$683$		−	5.54231e7i		−	0.173952i	−0.996210	−	0.0869759i	$-0.972280\pi$
$683$		−	5.54231e7i		−	0.173952i	0.996210	−	0.0869759i	$-0.0277203\pi$
$684$		0			0
$685$	7.44339e7			0.231579
$686$		0			0
$687$	−6.69408e6	−	1.28758e7i	−0.0206453	−	0.0397103i
$688$		0			0
$689$	9.14025e7	+	5.27712e7i	0.279448	+	0.161339i
$690$		0			0
$691$	5.91997e7	+	1.02537e8i	0.179426	+	0.310775i	0.941684	−	0.336498i	$-0.109243\pi$
$691$	5.91997e7	+	1.02537e8i	0.179426	+	0.310775i	−0.762258	+	0.647273i	$0.775909\pi$
$692$		0			0
$693$	5.05606e7	−	5.70969e8i	0.151919	−	1.71559i
$694$		0			0
$695$	4.81200e7	−	2.77821e7i	0.143341	−	0.0827581i
$696$		0			0
$697$	−1.91843e8	+	3.32281e8i	−0.566561	+	0.981313i
$698$		0			0
$699$	4.09342e8	+	2.61083e8i	1.19854	+	0.764447i
$700$		0			0
$701$			5.67279e8i			1.64681i	0.567457	+	0.823403i	$0.307927\pi$
$701$			5.67279e8i			1.64681i	−0.567457	+	0.823403i	$0.692073\pi$
$702$		0			0
$703$	2.91917e7			0.0840220
$704$		0			0
$705$	−5.09343e7	+	7.98578e7i	−0.145359	+	0.227903i
$706$		0			0
$707$	4.11834e8	+	2.37773e8i	1.16537	+	0.672827i
$708$		0			0
$709$	−8.41924e7	−	1.45825e8i	−0.236229	−	0.409161i	0.723400	−	0.690429i	$-0.242578\pi$
$709$	−8.41924e7	−	1.45825e8i	−0.236229	−	0.409161i	−0.959629	+	0.281268i	$0.909245\pi$
$710$		0			0
$711$	2.37509e8	−	3.38438e8i	0.660803	−	0.941608i
$712$		0			0
$713$	4.06479e8	−	2.34681e8i	1.12142	−	0.647454i
$714$		0			0
$715$	−4.29230e7	+	7.43449e7i	−0.117428	+	0.203392i
$716$		0			0
$717$	−5.22962e8	+	2.71886e8i	−1.41877	+	0.737614i
$718$		0			0
$719$		−	1.46968e8i		−	0.395398i	−0.980263	−	0.197699i	$-0.936653\pi$
$719$		−	1.46968e8i		−	0.395398i	0.980263	−	0.197699i	$-0.0633469\pi$
$720$		0			0
$721$	−1.15446e9			−3.08015
$722$		0			0
$723$	−6.36676e8	−	2.81345e7i	−1.68463	−	0.0744432i
$724$		0			0
$725$	4.67999e8	+	2.70199e8i	1.22809	+	0.709039i
$726$		0			0
$727$	1.36289e8	+	2.36060e8i	0.354697	+	0.614354i	0.987066	−	0.160314i	$-0.0512505\pi$
$727$	1.36289e8	+	2.36060e8i	0.354697	+	0.614354i	−0.632369	+	0.774668i	$0.717917\pi$
$728$		0			0
$729$	3.73900e8	+	1.01456e8i	0.965101	+	0.261876i
$730$		0			0
$731$	2.68599e8	−	1.55076e8i	0.687627	−	0.397001i
$732$		0			0
$733$	−1.06813e8	+	1.85006e8i	−0.271215	+	0.469759i	−0.969173	−	0.246380i	$-0.920759\pi$
$733$	−1.06813e8	+	1.85006e8i	−0.271215	+	0.469759i	0.697958	+	0.716139i	$0.254092\pi$
$734$		0			0
$735$	8.85386e6	−	2.00360e8i	0.0222982	−	0.504603i
$736$		0			0
$737$		−	6.08605e8i		−	1.52031i
$738$		0			0
$739$	1.56931e8			0.388844			0.194422	−	0.980918i	$-0.437717\pi$
$739$	1.56931e8			0.388844			0.194422	+	0.980918i	$0.437717\pi$
$740$		0			0
$741$	9.23513e7	+	1.77634e8i	0.226980	+	0.436588i
$742$		0			0
$743$	−6.54901e7	−	3.78107e7i	−0.159665	−	0.0921825i	0.418039	−	0.908429i	$-0.362718\pi$
$743$	−6.54901e7	−	3.78107e7i	−0.159665	−	0.0921825i	−0.577703	+	0.816247i	$0.696051\pi$
$744$		0			0
$745$	−3.72965e7	−	6.45995e7i	−0.0901986	−	0.156229i
$746$		0			0
$747$	−3.83653e8	−	2.69241e8i	−0.920400	−	0.645920i
$748$		0			0
$749$	−8.13146e8	+	4.69470e8i	−1.93519	+	1.11728i
$750$		0			0
$751$	−8.96351e7	+	1.55253e8i	−0.211621	+	0.366538i	−0.952222	−	0.305407i	$-0.901208\pi$
$751$	−8.96351e7	+	1.55253e8i	−0.211621	+	0.366538i	0.740601	+	0.671945i	$0.234541\pi$
$752$		0			0
$753$	−1.16526e8	−	7.43216e7i	−0.272921	−	0.174073i
$754$		0			0
$755$			1.46634e8i			0.340718i
$756$		0			0
$757$	2.83759e8			0.654126			0.327063	−	0.945003i	$-0.393941\pi$
$757$	2.83759e8			0.654126			0.327063	+	0.945003i	$0.393941\pi$
$758$		0			0
$759$	2.50171e8	−	3.92233e8i	0.572153	−	0.897055i
$760$		0			0
$761$	−3.76249e8	−	2.17228e8i	−0.853732	−	0.492903i	0.00817604	−	0.999967i	$-0.497397\pi$
$761$	−3.76249e8	−	2.17228e8i	−0.853732	−	0.492903i	−0.861908	+	0.507064i	$0.830731\pi$
$762$		0			0
$763$	−6.49162e8	−	1.12438e9i	−1.46144	−	2.53128i
$764$		0			0
$765$	1.08150e8	+	9.57690e6i	0.241569	+	0.0213915i
$766$		0			0
$767$	−3.83526e8	+	2.21429e8i	−0.849979	+	0.490736i
$768$		0			0
$769$	−3.67476e8	+	6.36488e8i	−0.808073	+	1.39962i	0.106125	+	0.994353i	$0.466156\pi$
$769$	−3.67476e8	+	6.36488e8i	−0.808073	+	1.39962i	−0.914197	+	0.405270i	$0.867178\pi$
$770$		0			0
$771$	−2.06560e8	+	1.07390e8i	−0.450694	+	0.234314i
$772$		0			0
$773$		−	2.07227e8i		−	0.448650i	−0.974514	−	0.224325i	$-0.927982\pi$
$773$		−	2.07227e8i		−	0.448650i	0.974514	−	0.224325i	$-0.0720177\pi$
$774$		0			0
$775$	5.22707e8			1.12293
$776$		0			0
$777$	1.39375e8	+	6.15896e6i	0.297114	+	0.0131294i
$778$		0			0
$779$	−2.29674e8	−	1.32603e8i	−0.485848	−	0.280504i
$780$		0			0
$781$	2.14088e8	+	3.70811e8i	0.449406	+	0.778393i
$782$		0			0
$783$	−6.68427e8	+	2.75633e8i	−1.39242	+	0.574176i
$784$		0			0
$785$	−1.87414e6	+	1.08204e6i	−0.00387430	+	0.00223683i
$786$		0			0
$787$	3.71331e8	−	6.43165e8i	0.761794	−	1.31947i	−0.180131	−	0.983643i	$-0.557652\pi$
$787$	3.71331e8	−	6.43165e8i	0.761794	−	1.31947i	0.941925	−	0.335823i	$-0.109014\pi$
$788$		0			0
$789$	−3.31957e7	+	7.51208e8i	−0.0675850	+	1.52943i
$790$		0			0
$791$			4.91513e8i			0.993128i
$792$		0			0
$793$	6.08025e7			0.121928
$794$		0			0
$795$	1.82491e7	+	3.51015e7i	0.0363196	+	0.0698593i
$796$		0			0
$797$	−1.61133e8	−	9.30303e7i	−0.318281	−	0.183759i	0.332345	−	0.943158i	$-0.392160\pi$
$797$	−1.61133e8	−	9.30303e7i	−0.318281	−	0.183759i	−0.650626	+	0.759398i	$0.725493\pi$
$798$		0			0
$799$	2.85907e8	+	4.95206e8i	0.560512	+	0.970835i
$800$		0			0
$801$	1.45454e8	−	6.76395e7i	0.283027	−	0.131614i
$802$		0			0
$803$	−6.85302e8	+	3.95659e8i	−1.32354	+	0.764144i
$804$		0			0
$805$	1.20353e8	−	2.08458e8i	0.230712	−	0.399604i
$806$		0			0
$807$	3.06728e8	+	1.95635e8i	0.583624	+	0.372243i
$808$		0			0
$809$			7.22902e8i			1.36532i	0.730737	+	0.682659i	$0.239177\pi$
$809$			7.22902e8i			1.36532i	−0.730737	+	0.682659i	$0.760823\pi$
$810$		0			0
$811$	−6.33240e8			−1.18715			−0.593576	−	0.804778i	$-0.702284\pi$
$811$	−6.33240e8			−1.18715			−0.593576	+	0.804778i	$0.702284\pi$
$812$		0			0
$813$	−9.72681e7	+	1.52503e8i	−0.181008	+	0.283796i
$814$		0			0
$815$	7.01607e7	+	4.05073e7i	0.129605	+	0.0748274i
$816$		0			0
$817$	1.07189e8	+	1.85657e8i	0.196555	+	0.340444i
$818$		0			0
$819$	4.03452e8	+	8.67596e8i	0.734414	+	1.57930i
$820$		0			0
$821$	2.22637e8	−	1.28540e8i	0.402317	−	0.232278i	−0.285166	−	0.958478i	$-0.592049\pi$
$821$	2.22637e8	−	1.28540e8i	0.402317	−	0.232278i	0.687483	+	0.726200i	$0.258716\pi$
$822$		0			0
$823$	−2.65155e7	+	4.59262e7i	−0.0475664	+	0.0823874i	−0.888828	−	0.458240i	$-0.848480\pi$
$823$	−2.65155e7	+	4.59262e7i	−0.0475664	+	0.0823874i	0.841262	+	0.540628i	$0.181813\pi$
$824$		0			0
$825$	4.59685e8	−	2.38989e8i	0.818651	−	0.425614i
$826$		0			0
$827$		−	5.98063e8i		−	1.05738i	−0.848815	−	0.528689i	$-0.822684\pi$
$827$		−	5.98063e8i		−	1.05738i	0.848815	−	0.528689i	$-0.177316\pi$
$828$		0			0
$829$	9.83498e7			0.172628			0.0863138	−	0.996268i	$-0.472491\pi$
$829$	9.83498e7			0.172628			0.0863138	+	0.996268i	$0.472491\pi$
$830$		0			0
$831$	1.47638e8	+	6.52406e6i	0.257273	+	0.0113688i
$832$		0			0
$833$	−1.04855e9	−	6.05378e8i	−1.81406	−	1.04735i
$834$		0			0
$835$	3.25072e7	+	5.63042e7i	0.0558368	+	0.0967122i
$836$		0			0
$837$	−4.26620e8	+	5.54163e8i	−0.727553	+	0.945063i
$838$		0			0
$839$	3.85765e8	−	2.22721e8i	0.653186	−	0.377117i	−0.136490	−	0.990641i	$-0.543582\pi$
$839$	3.85765e8	−	2.22721e8i	0.653186	−	0.377117i	0.789676	+	0.613525i	$0.210249\pi$
$840$		0			0
$841$	3.77267e8	−	6.53445e8i	0.634250	−	1.09855i
$842$		0			0
$843$	2.86268e7	−	6.47817e8i	0.0477849	−	1.08136i
$844$		0			0
$845$			2.60496e6i			0.00431749i
$846$		0			0
$847$	−4.23183e7			−0.0696431
$848$		0			0
$849$	5.90900e7	+	1.13657e8i	0.0965585	+	0.185726i
$850$		0			0
$851$	9.80603e7	+	5.66151e7i	0.159113	+	0.0918637i
$852$		0			0
$853$	−2.15506e8	−	3.73267e8i	−0.347225	−	0.601412i	0.638530	−	0.769597i	$-0.279543\pi$
$853$	−2.15506e8	−	3.73267e8i	−0.347225	−	0.601412i	−0.985755	+	0.168185i	$0.946209\pi$
$854$		0			0
$855$	−6.61960e6	+	7.47536e7i	−0.0105909	+	0.119601i
$856$		0			0
$857$	3.07511e8	−	1.77542e8i	0.488561	−	0.282071i	−0.235417	−	0.971895i	$-0.575645\pi$
$857$	3.07511e8	−	1.77542e8i	0.488561	−	0.282071i	0.723977	+	0.689824i	$0.242312\pi$
$858$		0			0
$859$	1.86985e8	−	3.23867e8i	0.295004	−	0.510961i	−0.679982	−	0.733229i	$-0.738013\pi$
$859$	1.86985e8	−	3.23867e8i	0.295004	−	0.510961i	0.974986	+	0.222268i	$0.0713458\pi$
$860$		0			0
$861$	−1.06860e9	−	6.81567e8i	−1.67420	−	1.06782i
$862$		0			0
$863$		−	1.06627e8i		−	0.165895i	−0.996554	−	0.0829476i	$-0.973567\pi$
$863$		−	1.06627e8i		−	0.165895i	0.996554	−	0.0829476i	$-0.0264334\pi$
$864$		0			0
$865$	1.83926e8			0.284182
$866$		0			0
$867$	2.01121e6	−	3.15330e6i	0.00308603	−	0.00483846i
$868$		0			0
$869$	6.40673e8	+	3.69893e8i	0.976287	+	0.563659i
$870$		0			0
$871$	5.07955e8	+	8.79804e8i	0.768725	+	1.33147i
$872$		0			0
$873$	9.57931e7	−	1.36500e8i	0.143976	−	0.205159i
$874$		0			0
$875$	4.78719e8	−	2.76388e8i	0.714589	−	0.412568i
$876$		0			0
$877$	5.08182e8	−	8.80197e8i	0.753391	−	1.30491i	−0.192779	−	0.981242i	$-0.561750\pi$
$877$	5.08182e8	−	8.80197e8i	0.753391	−	1.30491i	0.946170	−	0.323670i	$-0.104917\pi$
$878$		0			0
$879$	−7.06677e8	+	3.67399e8i	−1.04053	+	0.540967i
$880$		0			0
$881$		−	4.30149e8i		−	0.629058i	−0.949248	−	0.314529i	$-0.898153\pi$
$881$		−	4.30149e8i		−	0.629058i	0.949248	−	0.314529i	$-0.101847\pi$
$882$		0			0
$883$	−2.90705e8			−0.422251			−0.211125	−	0.977459i	$-0.567713\pi$
$883$	−2.90705e8			−0.422251			−0.211125	+	0.977459i	$0.567713\pi$
$884$		0			0
$885$	−1.65840e8	−	7.32844e6i	−0.239255	−	0.0105726i
$886$		0			0
$887$	−8.95081e8	−	5.16775e8i	−1.28260	−	0.740510i	−0.305278	−	0.952263i	$-0.598749\pi$
$887$	−8.95081e8	−	5.16775e8i	−1.28260	−	0.740510i	−0.977323	+	0.211753i	$0.932083\pi$
$888$		0			0
$889$	6.29978e8	+	1.09115e9i	0.896644	+	1.55303i
$890$		0			0
$891$	−1.21812e8	+	6.82405e8i	−0.172210	+	0.964737i
$892$		0			0
$893$	−3.42289e8	+	1.97621e8i	−0.480660	+	0.277509i
$894$		0			0
$895$	6.40151e7	−	1.10877e8i	0.0892921	−	0.154658i
$896$		0			0
$897$	−3.42830e7	+	7.75815e8i	−0.0475009	+	1.07493i
$898$		0			0
$899$		−	1.30518e9i		−	1.79635i
$900$		0			0
$901$	2.38835e8			0.326531
$902$		0			0
$903$	4.72603e8	+	9.09033e8i	0.641850	+	1.23457i
$904$		0			0
$905$	6.87355e7	+	3.96845e7i	0.0927333	+	0.0535396i
$906$		0			0
$907$	4.16894e8	+	7.22081e8i	0.558732	+	0.967752i	0.997603	+	0.0692017i	$0.0220452\pi$
$907$	4.16894e8	+	7.22081e8i	0.558732	+	0.967752i	−0.438871	+	0.898550i	$0.644621\pi$
$908$		0			0
$909$	−4.70739e8	−	3.30356e8i	−0.626741	−	0.439835i
$910$		0			0
$911$	5.06826e8	−	2.92616e8i	0.670354	−	0.387029i	−0.125857	−	0.992048i	$-0.540168\pi$
$911$	5.06826e8	−	2.92616e8i	0.670354	−	0.387029i	0.796211	+	0.605019i	$0.206835\pi$
$912$		0			0
$913$	4.19311e8	−	7.26267e8i	0.550964	−	0.954298i
$914$		0			0
$915$	1.92156e7	+	1.22560e7i	0.0250837	+	0.0159987i
$916$		0			0
$917$			3.40408e8i			0.441461i
$918$		0			0
$919$	−5.45286e8			−0.702551			−0.351276	−	0.936272i	$-0.614252\pi$
$919$	−5.45286e8			−0.702551			−0.351276	+	0.936272i	$0.614252\pi$
$920$		0			0
$921$	6.49283e8	−	1.01798e9i	0.831103	−	1.30305i
$922$		0			0
$923$	−6.18974e8	−	3.57365e8i	−0.787167	−	0.454471i
$924$		0			0
$925$	6.30498e7	+	1.09205e8i	0.0796633	+	0.137981i
$926$		0			0
$927$	1.39068e9	+	1.23148e8i	1.74577	+	0.154592i
$928$		0			0
$929$	−2.87655e8	+	1.66078e8i	−0.358777	+	0.207140i	−0.668544	−	0.743672i	$-0.733082\pi$
$929$	−2.87655e8	+	1.66078e8i	−0.358777	+	0.207140i	0.309767	+	0.950812i	$0.399749\pi$
$930$		0			0
$931$	4.18440e8	−	7.24759e8i	0.518542	−	0.898142i
$932$		0			0
$933$	8.97941e8	−	4.66836e8i	1.10561	−	0.574804i
$934$		0			0
$935$			1.94264e8i			0.237660i
$936$		0			0
$937$	9.47822e8			1.15215			0.576073	−	0.817398i	$-0.304584\pi$
$937$	9.47822e8			1.15215			0.576073	+	0.817398i	$0.304584\pi$
$938$		0			0
$939$	3.31236e8	+	1.46372e7i	0.400074	+	0.0176792i
$940$		0			0
$941$	−7.30615e8	−	4.21821e8i	−0.876839	−	0.506243i	−0.00722422	−	0.999974i	$-0.502300\pi$
$941$	−7.30615e8	−	4.21821e8i	−0.876839	−	0.506243i	−0.869615	+	0.493731i	$0.835633\pi$
$942$		0			0
$943$	−5.14346e8	−	8.90874e8i	−0.613367	−	1.06238i
$944$		0			0
$945$	−4.73770e7	+	3.55513e8i	−0.0561399	+	0.421270i
$946$		0			0
$947$	−7.29154e8	+	4.20977e8i	−0.858557	+	0.495688i	−0.863529	−	0.504299i	$-0.831751\pi$
$947$	−7.29154e8	+	4.20977e8i	−0.858557	+	0.495688i	0.00497159	+	0.999988i	$0.498417\pi$
$948$		0			0
$949$	6.60452e8	−	1.14394e9i	0.772757	−	1.33845i
$950$		0			0
$951$	−7.08111e7	+	1.60243e9i	−0.0823303	+	1.86311i
$952$		0			0
$953$		−	5.57885e8i		−	0.644564i	−0.946644	−	0.322282i	$-0.895550\pi$
$953$		−	5.57885e8i		−	0.644564i	0.946644	−	0.322282i	$-0.104450\pi$
$954$		0			0
$955$	−2.13455e8			−0.245073
$956$		0			0
$957$	−5.96747e8	−	1.14782e9i	−0.680855	−	1.30960i
$958$		0			0
$959$	1.28552e9	+	7.42197e8i	1.45755	+	0.841518i
$960$		0			0
$961$	−1.87475e8	−	3.24716e8i	−0.211239	−	0.365876i
$962$		0			0
$963$	1.02961e9	−	4.78791e8i	1.15290	−	0.536127i
$964$		0			0
$965$	2.77212e8	−	1.60048e8i	0.308482	−	0.178102i
$966$		0			0
$967$	1.96067e7	−	3.39598e7i	0.0216833	−	0.0375565i	−0.854980	−	0.518661i	$-0.826431\pi$
$967$	1.96067e7	−	3.39598e7i	0.0216833	−	0.0375565i	0.876663	+	0.481104i	$0.159764\pi$
$968$		0			0
$969$	3.81973e8	+	2.43627e8i	0.419818	+	0.267765i
$970$		0			0
$971$			1.73271e8i			0.189264i	0.995512	+	0.0946320i	$0.0301675\pi$
$971$			1.73271e8i			0.189264i	−0.995512	+	0.0946320i	$0.969833\pi$
$972$		0			0
$973$	1.10809e9			1.20292
$974$		0			0
$975$	−4.65060e8	+	7.29148e8i	−0.501759	+	0.786687i
$976$		0			0
$977$	−4.07843e7	−	2.35468e7i	−0.0437330	−	0.0252493i	0.477974	−	0.878374i	$-0.341371\pi$
$977$	−4.07843e7	−	2.35468e7i	−0.0437330	−	0.0252493i	−0.521707	+	0.853125i	$0.674705\pi$
$978$		0			0
$979$	1.43508e8	+	2.48564e8i	0.152943	+	0.264905i
$980$		0			0
$981$	6.62051e8	+	1.42370e9i	0.701269	+	1.50803i
$982$		0			0
$983$	−1.55792e8	+	8.99464e7i	−0.164015	+	0.0946941i	−0.579761	−	0.814787i	$-0.696854\pi$
$983$	−1.55792e8	+	8.99464e7i	−0.164015	+	0.0946941i	0.415746	+	0.909481i	$0.363521\pi$
$984$		0			0
$985$	−1.31383e8	+	2.27563e8i	−0.137477	+	0.238118i
$986$		0			0
$987$	−1.67595e9	+	8.71320e8i	−1.74305	+	0.906205i
$988$		0			0
$989$			8.31543e8i			0.859599i
$990$		0			0
$991$	−3.12914e8			−0.321517			−0.160759	−	0.986994i	$-0.551394\pi$
$991$	−3.12914e8			−0.321517			−0.160759	+	0.986994i	$0.551394\pi$
$992$		0			0
$993$	−2.85469e8	−	1.26148e7i	−0.291549	−	0.0128835i
$994$		0			0
$995$	4.07374e7	+	2.35197e7i	0.0413546	+	0.0238761i
$996$		0			0
$997$	2.73193e8	+	4.73184e8i	0.275666	+	0.477468i	0.970303	−	0.241893i	$-0.0777682\pi$
$997$	2.73193e8	+	4.73184e8i	0.275666	+	0.477468i	−0.694637	+	0.719361i	$0.744435\pi$
$998$		0			0
$999$	−1.67237e8	−	2.22866e7i	−0.167739	−	0.0223535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.5	✓	36
3.2	odd	2		216.7.m.a.17.9		36
4.3	odd	2		144.7.q.d.113.14		36
9.2	odd	6	inner	72.7.m.a.65.5	yes	36
9.4	even	3		648.7.e.c.161.16		36
9.5	odd	6		648.7.e.c.161.21		36
9.7	even	3		216.7.m.a.89.9		36
12.11	even	2		432.7.q.d.17.9		36
36.7	odd	6		432.7.q.d.305.9		36
36.11	even	6		144.7.q.d.65.14		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.5	✓	36	1.1	even	1	trivial
72.7.m.a.65.5	yes	36	9.2	odd	6	inner
144.7.q.d.65.14		36	36.11	even	6
144.7.q.d.113.14		36	4.3	odd	2
216.7.m.a.17.9		36	3.2	odd	2
216.7.m.a.89.9		36	9.7	even	3
432.7.q.d.17.9		36	12.11	even	2
432.7.q.d.305.9		36	36.7	odd	6
648.7.e.c.161.16		36	9.4	even	3
648.7.e.c.161.21		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)

\(f(q)\)	\(=\)	\(q+(-14.5191 + 22.7639i) q^{3} +(26.1779 + 15.1138i) q^{5} +(301.407 + 522.052i) q^{7} +(-307.391 - 661.023i) q^{9} +O(q^{10})\)	\(q+(-14.5191 + 22.7639i) q^{3} +(26.1779 + 15.1138i) q^{5} +(301.407 + 522.052i) q^{7} +(-307.391 - 661.023i) q^{9} +(1129.61 - 652.181i) q^{11} +(-1088.65 + 1885.60i) q^{13} +(-724.129 + 376.472i) q^{15} +4927.08i q^{17} -3405.62 q^{19} +(-16260.1 - 718.529i) q^{21} +(-11440.1 - 6604.95i) q^{23} +(-7355.64 - 12740.4i) q^{25} +(19510.5 + 2600.04i) q^{27} +(-31812.2 + 18366.8i) q^{29} +(-17765.5 + 30770.8i) q^{31} +(-1554.75 + 35183.4i) q^{33} +18221.6i q^{35} -8571.62 q^{37} +(-27117.3 - 52159.1i) q^{39} +(67439.9 + 38936.4i) q^{41} +(-31474.2 - 54514.9i) q^{43} +(1943.73 - 21950.1i) q^{45} +(100507. - 58027.8i) q^{47} +(-122868. + 212813. i) q^{49} +(-112160. - 71536.8i) q^{51} -48474.0i q^{53} +39427.8 q^{55} +(49446.5 - 77525.2i) q^{57} +(176147. + 101699. i) q^{59} +(-13962.8 - 24184.3i) q^{61} +(252439. - 359711. i) q^{63} +(-56997.1 + 32907.3i) q^{65} +(233296. - 404080. i) q^{67} +(316455. - 164524. i) q^{69} +328264. i q^{71} -606671. q^{73} +(396818. + 17535.3i) q^{75} +(680944. + 393143. i) q^{77} +(283582. + 491178. i) q^{79} +(-342462. + 406385. i) q^{81} +(556799. - 321468. i) q^{83} +(-74467.0 + 128981. i) q^{85} +(43784.9 - 990840. i) q^{87} +220044. i q^{89} -1.31251e6 q^{91} +(-442524. - 851177. i) q^{93} +(-89152.0 - 51471.9i) q^{95} +(114375. + 198104. i) q^{97} +(-778339. - 546224. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 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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