LMFDB - Embedded newform 72.7.b.c.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.b (of order $2$, degree $1$, 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 31 x^{10} - 1286 x^{9} + 7702 x^{8} - 174032 x^{7} + 1952056 x^{6} + \cdots + 767595744 $ x^12 - 2x^11 + 31x^10 - 1286x^9 + 7702x^8 - 174032x^7 + 1952056x^6 - 6345392x^5 + 7695616x^4 - 6850848x^3 - 19274256x^2 - 69390432*x + 767595744
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{11} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.12
Root			$3.47372 - 1.02840i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.c.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.49039 + 2.80965i) q^{2} +(48.2118 + 42.0907i) q^{4} -128.353i q^{5} -534.624i q^{7} +(242.865 + 450.734i) q^{8} +O(q^{10})$	\(q+(7.49039 + 2.80965i) q^{2} +(48.2118 + 42.0907i) q^{4} -128.353i q^{5} -534.624i q^{7} +(242.865 + 450.734i) q^{8} +(360.627 - 961.414i) q^{10} -1814.10 q^{11} -3118.64i q^{13} +(1502.10 - 4004.54i) q^{14} +(552.748 + 4058.53i) q^{16} +1243.01 q^{17} +9240.87 q^{19} +(5402.47 - 6188.13i) q^{20} +(-13588.3 - 5096.97i) q^{22} -403.201i q^{23} -849.496 q^{25} +(8762.27 - 23359.8i) q^{26} +(22502.7 - 25775.2i) q^{28} +13275.0i q^{29} -34011.5i q^{31} +(-7262.75 + 31953.0i) q^{32} +(9310.60 + 3492.41i) q^{34} -68620.6 q^{35} +38368.6i q^{37} +(69217.7 + 25963.6i) q^{38} +(57853.0 - 31172.4i) q^{40} +70448.5 q^{41} -9926.62 q^{43} +(-87460.8 - 76356.5i) q^{44} +(1132.85 - 3020.13i) q^{46} +99633.6i q^{47} -168174. q^{49} +(-6363.05 - 2386.78i) q^{50} +(131266. - 150355. i) q^{52} -115619. i q^{53} +232845. i q^{55} +(240973. - 129841. i) q^{56} +(-37298.1 + 99435.0i) q^{58} -173011. q^{59} -14422.9i q^{61} +(95560.3 - 254759. i) q^{62} +(-144177. + 218935. i) q^{64} -400287. q^{65} -311976. q^{67} +(59927.5 + 52319.0i) q^{68} +(-513995. - 192800. i) q^{70} +492884. i q^{71} +653588. q^{73} +(-107802. + 287396. i) q^{74} +(445519. + 388955. i) q^{76} +969859. i q^{77} +334398. i q^{79} +(520925. - 70946.9i) q^{80} +(527686. + 197935. i) q^{82} -418818. q^{83} -159544. i q^{85} +(-74354.2 - 27890.3i) q^{86} +(-440580. - 817674. i) q^{88} +197334. q^{89} -1.66730e6 q^{91} +(16971.0 - 19439.1i) q^{92} +(-279935. + 746294. i) q^{94} -1.18609e6i q^{95} +1.30640e6 q^{97} +(-1.25968e6 - 472508. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) $ 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8	$ 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8} + 2172 q^{10} - 2720 q^{11} + 6444 q^{14} + 11640 q^{16} + 4888 q^{17} + 3936 q^{19} + 31608 q^{20} - 60432 q^{22} - 27204 q^{25} - 53952 q^{26} - 57072 q^{28} - 109480 q^{32} + 47388 q^{34} - 162336 q^{35} + 89080 q^{38} + 72120 q^{40} + 54280 q^{41} - 49824 q^{43} - 229184 q^{44} + 171864 q^{46} - 304644 q^{49} + 500078 q^{50} + 256848 q^{52} + 699816 q^{56} - 409524 q^{58} + 886144 q^{59} - 691356 q^{62} - 500640 q^{64} - 473376 q^{65} + 1565952 q^{67} - 669104 q^{68} + 473784 q^{70} + 555480 q^{73} + 753720 q^{74} - 293136 q^{76} + 251616 q^{80} + 2317716 q^{82} - 2497760 q^{83} - 476024 q^{86} + 971424 q^{88} - 367400 q^{89} - 4475808 q^{91} + 377376 q^{92} - 2642568 q^{94} - 1165656 q^{97} - 182674 q^{98}+O(q^{100}) $ 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8 + 2172 * q^10 - 2720 * q^11 + 6444 * q^14 + 11640 * q^16 + 4888 * q^17 + 3936 * q^19 + 31608 * q^20 - 60432 * q^22 - 27204 * q^25 - 53952 * q^26 - 57072 * q^28 - 109480 * q^32 + 47388 * q^34 - 162336 * q^35 + 89080 * q^38 + 72120 * q^40 + 54280 * q^41 - 49824 * q^43 - 229184 * q^44 + 171864 * q^46 - 304644 * q^49 + 500078 * q^50 + 256848 * q^52 + 699816 * q^56 - 409524 * q^58 + 886144 * q^59 - 691356 * q^62 - 500640 * q^64 - 473376 * q^65 + 1565952 * q^67 - 669104 * q^68 + 473784 * q^70 + 555480 * q^73 + 753720 * q^74 - 293136 * q^76 + 251616 * q^80 + 2317716 * q^82 - 2497760 * q^83 - 476024 * q^86 + 971424 * q^88 - 367400 * q^89 - 4475808 * q^91 + 377376 * q^92 - 2642568 * q^94 - 1165656 * q^97 - 182674 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	7.49039	+	2.80965i	0.936298	+	0.351206i
$2$	7.49039	+	2.80965i	0.936298	+	0.351206i
$3$		0			0
$3$		0			0
$4$	48.2118	+	42.0907i	0.753309	+	0.657667i
$5$		−	128.353i		−	1.02682i	−0.858142	−	0.513412i	$-0.828381\pi$
$5$		−	128.353i		−	1.02682i	0.858142	−	0.513412i	$-0.171619\pi$
$6$		0			0
$7$		−	534.624i		−	1.55867i	−0.626608	−	0.779335i	$-0.715557\pi$
$7$		−	534.624i		−	1.55867i	0.626608	−	0.779335i	$-0.284443\pi$
$8$	242.865	+	450.734i	0.474345	+	0.880339i
$9$		0			0
$10$	360.627	−	961.414i	0.360627	−	0.961414i
$11$	−1814.10			−1.36296			−0.681478	−	0.731838i	$-0.738663\pi$
$11$	−1814.10			−1.36296			−0.681478	+	0.731838i	$0.738663\pi$
$12$		0			0
$13$		−	3118.64i		−	1.41950i	−0.704454	−	0.709749i	$-0.748808\pi$
$13$		−	3118.64i		−	1.41950i	0.704454	−	0.709749i	$-0.251192\pi$
$14$	1502.10	−	4004.54i	0.547414	−	1.45938i
$15$		0			0
$16$	552.748	+	4058.53i	0.134948	+	0.990853i
$17$	1243.01			0.253004			0.126502	−	0.991966i	$-0.459625\pi$
$17$	1243.01			0.253004			0.126502	+	0.991966i	$0.459625\pi$
$18$		0			0
$19$	9240.87			1.34726			0.673631	−	0.739068i	$-0.264734\pi$
$19$	9240.87			1.34726			0.673631	+	0.739068i	$0.264734\pi$
$20$	5402.47	−	6188.13i	0.675308	−	0.773516i
$21$		0			0
$22$	−13588.3	−	5096.97i	−1.27613	−	0.478679i
$23$		−	403.201i		−	0.0331389i	−0.999863	−	0.0165695i	$-0.994726\pi$
$23$		−	403.201i		−	0.0331389i	0.999863	−	0.0165695i	$-0.00527447\pi$
$24$		0			0
$25$	−849.496			−0.0543677
$26$	8762.27	−	23359.8i	0.498536	−	1.32907i
$27$		0			0
$28$	22502.7	−	25775.2i	1.02509	−	1.17416i
$29$			13275.0i			0.544303i	0.962254	+	0.272152i	$0.0877353\pi$
$29$			13275.0i			0.544303i	−0.962254	+	0.272152i	$0.912265\pi$
$30$		0			0
$31$		−	34011.5i		−	1.14167i	−0.821065	−	0.570835i	$-0.806619\pi$
$31$		−	34011.5i		−	1.14167i	0.821065	−	0.570835i	$-0.193381\pi$
$32$	−7262.75	+	31953.0i	−0.221641	+	0.975128i
$33$		0			0
$34$	9310.60	+	3492.41i	0.236887	+	0.0888563i
$35$	−68620.6			−1.60048
$36$		0			0
$37$			38368.6i			0.757479i	0.925503	+	0.378740i	$0.123642\pi$
$37$			38368.6i			0.757479i	−0.925503	+	0.378740i	$0.876358\pi$
$38$	69217.7	+	25963.6i	1.26144	+	0.473167i
$39$		0			0
$40$	57853.0	−	31172.4i	0.903953	−	0.487069i
$41$	70448.5			1.02216			0.511081	−	0.859532i	$-0.329245\pi$
$41$	70448.5			1.02216			0.511081	+	0.859532i	$0.329245\pi$
$42$		0			0
$43$	−9926.62			−0.124852			−0.0624261	−	0.998050i	$-0.519884\pi$
$43$	−9926.62			−0.124852			−0.0624261	+	0.998050i	$0.519884\pi$
$44$	−87460.8	−	76356.5i	−1.02673	−	0.896372i
$45$		0			0
$46$	1132.85	−	3020.13i	0.0116386	−	0.0310279i
$47$			99633.6i			0.959649i	0.877365	+	0.479824i	$0.159300\pi$
$47$			99633.6i			0.959649i	−0.877365	+	0.479824i	$0.840700\pi$
$48$		0			0
$49$	−168174.			−1.42945
$50$	−6363.05	−	2386.78i	−0.0509044	−	0.0190943i
$51$		0			0
$52$	131266.	−	150355.i	0.933557	−	1.06932i
$53$		−	115619.i		−	0.776611i	−0.921531	−	0.388305i	$-0.873061\pi$
$53$		−	115619.i		−	0.776611i	0.921531	−	0.388305i	$-0.126939\pi$
$54$		0			0
$55$			232845.i			1.39952i
$56$	240973.	−	129841.i	1.37216	−	0.739348i
$57$		0			0
$58$	−37298.1	+	99435.0i	−0.191163	+	0.509630i
$59$	−173011.			−0.842400			−0.421200	−	0.906968i	$-0.638391\pi$
$59$	−173011.			−0.842400			−0.421200	+	0.906968i	$0.638391\pi$
$60$		0			0
$61$		−	14422.9i		−	0.0635423i	−0.999495	−	0.0317712i	$-0.989885\pi$
$61$		−	14422.9i		−	0.0635423i	0.999495	−	0.0317712i	$-0.0101148\pi$
$62$	95560.3	−	254759.i	0.400961	−	1.06894i
$63$		0			0
$64$	−144177.	+	218935.i	−0.549993	+	0.835169i
$65$	−400287.			−1.45758
$66$		0			0
$67$	−311976.			−1.03728			−0.518641	−	0.854992i	$-0.673562\pi$
$67$	−311976.			−1.03728			−0.518641	+	0.854992i	$0.673562\pi$
$68$	59927.5	+	52319.0i	0.190590	+	0.166392i
$69$		0			0
$70$	−513995.	−	192800.i	−1.49853	−	0.562098i
$71$			492884.i			1.37711i	0.725182	+	0.688557i	$0.241755\pi$
$71$			492884.i			1.37711i	−0.725182	+	0.688557i	$0.758245\pi$
$72$		0			0
$73$	653588.			1.68010			0.840051	−	0.542508i	$-0.182525\pi$
$73$	653588.			1.68010			0.840051	+	0.542508i	$0.182525\pi$
$74$	−107802.	+	287396.i	−0.266031	+	0.709227i
$75$		0			0
$76$	445519.	+	388955.i	1.01490	+	0.886050i
$77$			969859.i			2.12440i
$78$		0			0
$79$			334398.i			0.678239i	0.940743	+	0.339120i	$0.110129\pi$
$79$			334398.i			0.678239i	−0.940743	+	0.339120i	$0.889871\pi$
$80$	520925.	−	70946.9i	1.01743	−	0.138568i
$81$		0			0
$82$	527686.	+	197935.i	0.957049	+	0.358990i
$83$	−418818.			−0.732472			−0.366236	−	0.930522i	$-0.619354\pi$
$83$	−418818.			−0.732472			−0.366236	+	0.930522i	$0.619354\pi$
$84$		0			0
$85$		−	159544.i		−	0.259790i
$86$	−74354.2	−	27890.3i	−0.116899	−	0.0438488i
$87$		0			0
$88$	−440580.	−	817674.i	−0.646512	−	1.19986i
$89$	197334.			0.279919			0.139960	−	0.990157i	$-0.455303\pi$
$89$	197334.			0.279919			0.139960	+	0.990157i	$0.455303\pi$
$90$		0			0
$91$	−1.66730e6			−2.21253
$92$	16971.0	−	19439.1i	0.0217944	−	0.0249639i
$93$		0			0
$94$	−279935.	+	746294.i	−0.337034	+	0.898517i
$95$		−	1.18609e6i		−	1.38340i
$96$		0			0
$97$	1.30640e6			1.43140			0.715701	−	0.698407i	$-0.246107\pi$
$97$	1.30640e6			1.43140			0.715701	+	0.698407i	$0.246107\pi$
$98$	−1.25968e6	−	472508.i	−1.33839	−	0.502032i
$99$		0			0
$100$	−40955.7	−	35755.9i	−0.0409557	−	0.0357559i
$101$		−	1.34757e6i		−	1.30794i	−0.756521	−	0.653970i	$-0.773102\pi$
$101$		−	1.34757e6i		−	1.30794i	0.756521	−	0.653970i	$-0.226898\pi$
$102$		0			0
$103$		−	866380.i		−	0.792860i	−0.918065	−	0.396430i	$-0.870249\pi$
$103$		−	866380.i		−	0.792860i	0.918065	−	0.396430i	$-0.129751\pi$
$104$	1.40567e6	−	757407.i	1.24964	−	0.673332i
$105$		0			0
$106$	324850.	−	866034.i	0.272750	−	0.727139i
$107$	1.29097e6			1.05382			0.526909	−	0.849922i	$-0.323351\pi$
$107$	1.29097e6			1.05382			0.526909	+	0.849922i	$0.323351\pi$
$108$		0			0
$109$		−	366934.i		−	0.283340i	−0.989914	−	0.141670i	$-0.954753\pi$
$109$		−	366934.i		−	0.283340i	0.989914	−	0.141670i	$-0.0452472\pi$
$110$	−654211.	+	1.74410e6i	−0.491519	+	1.31037i
$111$		0			0
$112$	2.16979e6	−	295512.i	1.54441	−	0.210340i
$113$	1.61378e6			1.11843			0.559216	−	0.829022i	$-0.311102\pi$
$113$	1.61378e6			1.11843			0.559216	+	0.829022i	$0.311102\pi$
$114$		0			0
$115$	−51752.1			−0.0340279
$116$	−558755.	+	640012.i	−0.357970	+	0.410029i
$117$		0			0
$118$	−1.29592e6	−	486101.i	−0.788737	−	0.295856i
$119$		−	664541.i		−	0.394349i
$120$		0			0
$121$	1.51938e6			0.857652
$122$	40523.3	−	108033.i	0.0223164	−	0.0594946i
$123$		0			0
$124$	1.43157e6	−	1.63975e6i	0.750839	−	0.860031i
$125$		−	1.89648e6i		−	0.970998i
$126$		0			0
$127$			2.63199e6i			1.28491i	0.766323	+	0.642456i	$0.222084\pi$
$127$			2.63199e6i			1.28491i	−0.766323	+	0.642456i	$0.777916\pi$
$128$	−1.69507e6	+	1.23482e6i	−0.808274	+	0.588806i
$129$		0			0
$130$	−2.99830e6	−	1.12466e6i	−1.36473	−	0.511909i
$131$	−1.01394e6			−0.451023			−0.225512	−	0.974240i	$-0.572405\pi$
$131$	−1.01394e6			−0.451023			−0.225512	+	0.974240i	$0.572405\pi$
$132$		0			0
$133$		−	4.94039e6i		−	2.09994i
$134$	−2.33682e6	−	876542.i	−0.971204	−	0.364299i
$135$		0			0
$136$	301882.	+	560265.i	0.120011	+	0.222729i
$137$	3.34920e6			1.30250			0.651252	−	0.758861i	$-0.274244\pi$
$137$	3.34920e6			1.30250			0.651252	+	0.758861i	$0.274244\pi$
$138$		0			0
$139$	432357.			0.160990			0.0804949	−	0.996755i	$-0.474350\pi$
$139$	432357.			0.160990			0.0804949	+	0.996755i	$0.474350\pi$
$140$	−3.30832e6	−	2.88829e6i	−1.20566	−	1.05258i
$141$		0			0
$142$	−1.38483e6	+	3.69189e6i	−0.483651	+	1.28939i
$143$			5.65751e6i			1.93472i
$144$		0			0
$145$	1.70389e6			0.558904
$146$	4.89563e6	+	1.83635e6i	1.57308	+	0.590062i
$147$		0			0
$148$	−1.61496e6	+	1.84982e6i	−0.498169	+	0.570616i
$149$		−	2.75420e6i		−	0.832600i	−0.909227	−	0.416300i	$-0.863327\pi$
$149$		−	2.75420e6i		−	0.832600i	0.909227	−	0.416300i	$-0.136673\pi$
$150$		0			0
$151$		−	2.81277e6i		−	0.816966i	−0.912766	−	0.408483i	$-0.866058\pi$
$151$		−	2.81277e6i		−	0.816966i	0.912766	−	0.408483i	$-0.133942\pi$
$152$	2.24428e6	+	4.16517e6i	0.639068	+	1.18605i
$153$		0			0
$154$	−2.72496e6	+	7.26462e6i	−0.746102	+	1.98907i
$155$	−4.36548e6			−1.17229
$156$		0			0
$157$			6.04418e6i			1.56185i	0.624626	+	0.780924i	$0.285251\pi$
$157$			6.04418e6i			1.56185i	−0.624626	+	0.780924i	$0.714749\pi$
$158$	−939542.	+	2.50477e6i	−0.238202	+	0.635034i
$159$		0			0
$160$	4.10126e6	+	932195.i	1.00129	+	0.227587i
$161$	−215561.			−0.0516527
$162$		0			0
$163$	−429524.			−0.0991802			−0.0495901	−	0.998770i	$-0.515791\pi$
$163$	−429524.			−0.0991802			−0.0495901	+	0.998770i	$0.515791\pi$
$164$	3.39645e6	+	2.96522e6i	0.770004	+	0.672243i
$165$		0			0
$166$	−3.13711e6	−	1.17673e6i	−0.685812	−	0.257248i
$167$		−	7.49437e6i		−	1.60911i	−0.593878	−	0.804555i	$-0.702404\pi$
$167$		−	7.49437e6i		−	1.60911i	0.593878	−	0.804555i	$-0.297596\pi$
$168$		0			0
$169$	−4.89909e6			−1.01498
$170$	448261.	−	1.19504e6i	0.0912398	−	0.243241i
$171$		0			0
$172$	−478580.	−	417818.i	−0.0940522	−	0.0821112i
$173$			8.63756e6i			1.66822i	0.551599	+	0.834109i	$0.314018\pi$
$173$			8.63756e6i			1.66822i	−0.551599	+	0.834109i	$0.685982\pi$
$174$		0			0
$175$			454161.i			0.0847413i
$176$	−1.00274e6	−	7.36257e6i	−0.183929	−	1.35049i
$177$		0			0
$178$	1.47811e6	+	554440.i	0.262088	+	0.0983092i
$179$	−579391.			−0.101021			−0.0505106	−	0.998724i	$-0.516085\pi$
$179$	−579391.			−0.101021			−0.0505106	+	0.998724i	$0.516085\pi$
$180$		0			0
$181$			4.42377e6i			0.746031i	0.927825	+	0.373015i	$0.121676\pi$
$181$			4.42377e6i			0.746031i	−0.927825	+	0.373015i	$0.878324\pi$
$182$	−1.24887e7	−	4.68452e6i	−2.07159	−	0.777053i
$183$		0			0
$184$	181736.	−	97923.4i	0.0291735	−	0.0157193i
$185$	4.92473e6			0.777798
$186$		0			0
$187$	−2.25493e6			−0.344833
$188$	−4.19365e6	+	4.80351e6i	−0.631129	+	0.722912i
$189$		0			0
$190$	3.33251e6	−	8.88430e6i	0.485859	−	1.29528i
$191$			2.73990e6i			0.393219i	0.980482	+	0.196609i	$0.0629931\pi$
$191$			2.73990e6i			0.393219i	−0.980482	+	0.196609i	$0.937007\pi$
$192$		0			0
$193$	1.02386e7			1.42419			0.712097	−	0.702081i	$-0.247746\pi$
$193$	1.02386e7			1.42419			0.712097	+	0.702081i	$0.247746\pi$
$194$	9.78545e6	+	3.67053e6i	1.34022	+	0.502717i
$195$		0			0
$196$	−8.10794e6	−	7.07854e6i	−1.07682	−	0.940103i
$197$		−	3.26749e6i		−	0.427382i	−0.976901	−	0.213691i	$-0.931451\pi$
$197$		−	3.26749e6i		−	0.427382i	0.976901	−	0.213691i	$-0.0685485\pi$
$198$		0			0
$199$			1.32582e6i			0.168238i	0.996456	+	0.0841191i	$0.0268076\pi$
$199$			1.32582e6i			0.168238i	−0.996456	+	0.0841191i	$0.973192\pi$
$200$	−206313.	−	382896.i	−0.0257891	−	0.0478620i
$201$		0			0
$202$	3.78620e6	−	1.00938e7i	0.459356	−	1.22462i
$203$	7.09714e6			0.848389
$204$		0			0
$205$		−	9.04227e6i		−	1.04958i
$206$	2.43422e6	−	6.48952e6i	0.278457	−	0.742354i
$207$		0			0
$208$	1.26571e7	−	1.72382e6i	1.40651	−	0.191559i
$209$	−1.67638e7			−1.83626
$210$		0			0
$211$	−8.07379e6			−0.859468			−0.429734	−	0.902955i	$-0.641393\pi$
$211$	−8.07379e6			−0.859468			−0.429734	+	0.902955i	$0.641393\pi$
$212$	4.86650e6	−	5.57422e6i	0.510751	−	0.585028i
$213$		0			0
$214$	9.66987e6	+	3.62717e6i	0.986687	+	0.370107i
$215$			1.27411e6i			0.128201i
$216$		0			0
$217$	−1.81834e7			−1.77949
$218$	1.03095e6	−	2.74848e6i	0.0995108	−	0.265291i
$219$		0			0
$220$	−9.80059e6	+	1.12259e7i	−0.920416	+	1.05427i
$221$		−	3.87649e6i		−	0.359138i
$222$		0			0
$223$			1.48782e7i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$223$			1.48782e7i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$224$	1.70828e7	+	3.88284e6i	1.51990	+	0.345466i
$225$		0			0
$226$	1.20878e7	+	4.53416e6i	1.04719	+	0.392800i
$227$	5.89044e6			0.503582			0.251791	−	0.967782i	$-0.418980\pi$
$227$	5.89044e6			0.503582			0.251791	+	0.967782i	$0.418980\pi$
$228$		0			0
$229$		−	897265.i		−	0.0747161i	−0.999302	−	0.0373581i	$-0.988106\pi$
$229$		−	897265.i		−	0.0747161i	0.999302	−	0.0373581i	$-0.0118942\pi$
$230$	−387643.	−	145405.i	−0.0318602	−	0.0119508i
$231$		0			0
$232$	−5.98350e6	+	3.22403e6i	−0.479172	+	0.258188i
$233$	−1.39643e7			−1.10395			−0.551977	−	0.833859i	$-0.686127\pi$
$233$	−1.39643e7			−1.10395			−0.551977	+	0.833859i	$0.686127\pi$
$234$		0			0
$235$	1.27883e7			0.985390
$236$	−8.34118e6	−	7.28216e6i	−0.634587	−	0.554018i
$237$		0			0
$238$	1.86713e6	−	4.97767e6i	0.138498	−	0.369228i
$239$		−	107737.i		−	0.00789168i	−0.999992	−	0.00394584i	$-0.998744\pi$
$239$		−	107737.i		−	0.00789168i	0.999992	−	0.00394584i	$-0.00125600\pi$
$240$		0			0
$241$	7.55599e6			0.539809			0.269905	−	0.962887i	$-0.413008\pi$
$241$	7.55599e6			0.539809			0.269905	+	0.962887i	$0.413008\pi$
$242$	1.13808e7	+	4.26893e6i	0.803018	+	0.301212i
$243$		0			0
$244$	607070.	−	695353.i	0.0417897	−	0.0478670i
$245$			2.15856e7i			1.46780i
$246$		0			0
$247$		−	2.88189e7i		−	1.91244i
$248$	1.53301e7	−	8.26020e6i	1.00506	−	0.541546i
$249$		0			0
$250$	5.32844e6	−	1.42054e7i	0.341020	−	0.909144i
$251$	−5.44971e6			−0.344629			−0.172315	−	0.985042i	$-0.555125\pi$
$251$	−5.44971e6			−0.344629			−0.172315	+	0.985042i	$0.555125\pi$
$252$		0			0
$253$			731446.i			0.0451669i
$254$	−7.39496e6	+	1.97146e7i	−0.451268	+	1.20306i
$255$		0			0
$256$	−1.61662e7	+	4.48669e6i	−0.963578	+	0.267428i
$257$	−1.61338e7			−0.950466			−0.475233	−	0.879860i	$-0.657636\pi$
$257$	−1.61338e7			−0.950466			−0.475233	+	0.879860i	$0.657636\pi$
$258$		0			0
$259$	2.05128e7			1.18066
$260$	−1.92985e7	−	1.68483e7i	−1.09800	−	0.958599i
$261$		0			0
$262$	−7.59481e6	−	2.84882e6i	−0.422292	−	0.158402i
$263$			2.41483e7i			1.32746i	0.747974	+	0.663728i	$0.231027\pi$
$263$			2.41483e7i			1.32746i	−0.747974	+	0.663728i	$0.768973\pi$
$264$		0			0
$265$	−1.48401e7			−0.797442
$266$	1.38808e7	−	3.70054e7i	0.737511	−	1.96617i
$267$		0			0
$268$	−1.50409e7	−	1.31313e7i	−0.781393	−	0.682185i
$269$			545214.i			0.0280098i	0.999902	+	0.0140049i	$0.00445804\pi$
$269$			545214.i			0.0280098i	−0.999902	+	0.0140049i	$0.995542\pi$
$270$		0			0
$271$		−	8.73496e6i		−	0.438887i	−0.975625	−	0.219444i	$-0.929576\pi$
$271$		−	8.73496e6i		−	0.438887i	0.975625	−	0.219444i	$-0.0704242\pi$
$272$	687070.	+	5.04478e6i	0.0341424	+	0.250689i
$273$		0			0
$274$	2.50868e7	+	9.41007e6i	1.21953	+	0.457447i
$275$	1.54107e6			0.0741009
$276$		0			0
$277$			3.08819e7i			1.45300i	0.687168	+	0.726499i	$0.258854\pi$
$277$			3.08819e7i			1.45300i	−0.687168	+	0.726499i	$0.741146\pi$
$278$	3.23852e6	+	1.21477e6i	0.150734	+	0.0565406i
$279$		0			0
$280$	−1.66655e7	−	3.09296e7i	−0.759180	−	1.40896i
$281$	3.32381e7			1.49802			0.749010	−	0.662558i	$-0.230529\pi$
$281$	3.32381e7			1.49802			0.749010	+	0.662558i	$0.230529\pi$
$282$		0			0
$283$	1.94804e7			0.859485			0.429742	−	0.902952i	$-0.358604\pi$
$283$	1.94804e7			0.859485			0.429742	+	0.902952i	$0.358604\pi$
$284$	−2.07458e7	+	2.37628e7i	−0.905682	+	1.03739i
$285$		0			0
$286$	−1.58956e7	+	4.23769e7i	−0.679483	+	1.81147i
$287$		−	3.76634e7i		−	1.59321i
$288$		0			0
$289$	−2.25925e7			−0.935989
$290$	1.27628e7	+	4.78733e6i	0.523301	+	0.196290i
$291$		0			0
$292$	3.15106e7	+	2.75100e7i	1.26564	+	1.10495i
$293$		−	1.29157e7i		−	0.513468i	−0.966482	−	0.256734i	$-0.917354\pi$
$293$		−	1.29157e7i		−	0.513468i	0.966482	−	0.256734i	$-0.0826465\pi$
$294$		0			0
$295$			2.22065e7i			0.864996i
$296$	−1.72940e7	+	9.31838e6i	−0.666839	+	0.359307i
$297$		0			0
$298$	7.73832e6	−	2.06300e7i	0.292414	−	0.779562i
$299$	−1.25744e6			−0.0470407
$300$		0			0
$301$			5.30701e6i			0.194603i
$302$	7.90290e6	−	2.10688e7i	0.286923	−	0.764924i
$303$		0			0
$304$	5.10788e6	+	3.75044e7i	0.181811	+	1.33494i
$305$	−1.85122e6			−0.0652468
$306$		0			0
$307$	−1.24854e7			−0.431508			−0.215754	−	0.976448i	$-0.569221\pi$
$307$	−1.24854e7			−0.431508			−0.215754	+	0.976448i	$0.569221\pi$
$308$	−4.08220e7	+	4.67586e7i	−1.39715	+	1.60033i
$309$		0			0
$310$	−3.26991e7	−	1.22655e7i	−1.09762	−	0.411717i
$311$		−	3.11044e7i		−	1.03405i	−0.855971	−	0.517025i	$-0.827040\pi$
$311$		−	3.11044e7i		−	1.03405i	0.855971	−	0.517025i	$-0.172960\pi$
$312$		0			0
$313$	−5.15327e7			−1.68054			−0.840271	−	0.542166i	$-0.817604\pi$
$313$	−5.15327e7			−1.68054			−0.840271	+	0.542166i	$0.817604\pi$
$314$	−1.69820e7	+	4.52733e7i	−0.548530	+	1.46236i
$315$		0			0
$316$	−1.40751e7	+	1.61219e7i	−0.446056	+	0.510924i
$317$		−	3.45703e7i		−	1.08524i	−0.839978	−	0.542620i	$-0.817432\pi$
$317$		−	3.45703e7i		−	1.08524i	0.839978	−	0.542620i	$-0.182568\pi$
$318$		0			0
$319$		−	2.40822e7i		−	0.741862i
$320$	2.81009e7	+	1.85056e7i	0.857572	+	0.564746i
$321$		0			0
$322$	−1.61464e6	−	605651.i	−0.0483623	−	0.0181407i
$323$	1.14865e7			0.340862
$324$		0			0
$325$			2.64927e6i			0.0771749i
$326$	−3.21730e6	−	1.20681e6i	−0.0928623	−	0.0348327i
$327$		0			0
$328$	1.71095e7	+	3.17535e7i	0.484858	+	0.899850i
$329$	5.32665e7			1.49578
$330$		0			0
$331$	3.03750e7			0.837592			0.418796	−	0.908080i	$-0.362452\pi$
$331$	3.03750e7			0.837592			0.418796	+	0.908080i	$0.362452\pi$
$332$	−2.01920e7	−	1.76283e7i	−0.551778	−	0.481723i
$333$		0			0
$334$	2.10565e7	−	5.61357e7i	0.565129	−	1.50661i
$335$			4.00430e7i			1.06511i
$336$		0			0
$337$	2.02730e7			0.529698			0.264849	−	0.964290i	$-0.414678\pi$
$337$	2.02730e7			0.529698			0.264849	+	0.964290i	$0.414678\pi$
$338$	−3.66961e7	−	1.37647e7i	−0.950320	−	0.356465i
$339$		0			0
$340$	6.71530e6	−	7.69188e6i	0.170855	−	0.195702i
$341$			6.17001e7i			1.55605i
$342$		0			0
$343$			2.70116e7i			0.669373i
$344$	−2.41083e6	−	4.47426e6i	−0.0592230	−	0.109912i
$345$		0			0
$346$	−2.42685e7	+	6.46987e7i	−0.585888	+	1.56195i
$347$	5.28864e7			1.26577			0.632886	−	0.774245i	$-0.281870\pi$
$347$	5.28864e7			1.26577			0.632886	+	0.774245i	$0.281870\pi$
$348$		0			0
$349$		−	1.86020e7i		−	0.437607i	−0.975769	−	0.218804i	$-0.929785\pi$
$349$		−	1.86020e7i		−	0.437607i	0.975769	−	0.218804i	$-0.0702154\pi$
$350$	−1.27603e6	+	3.40184e6i	−0.0297617	+	0.0793432i
$351$		0			0
$352$	1.31753e7	−	5.79658e7i	0.302088	−	1.32906i
$353$	−5.51181e7			−1.25306			−0.626528	−	0.779399i	$-0.715524\pi$
$353$	−5.51181e7			−1.25306			−0.626528	+	0.779399i	$0.715524\pi$
$354$		0			0
$355$	6.32632e7			1.41405
$356$	9.51383e6	+	8.30594e6i	0.210866	+	0.184094i
$357$		0			0
$358$	−4.33986e6	−	1.62788e6i	−0.0945860	−	0.0354792i
$359$			6.49139e6i			0.140299i	0.997536	+	0.0701495i	$0.0223476\pi$
$359$			6.49139e6i			0.140299i	−0.997536	+	0.0701495i	$0.977652\pi$
$360$		0			0
$361$	3.83479e7			0.815117
$362$	−1.24292e7	+	3.31357e7i	−0.262010	+	0.698507i
$363$		0			0
$364$	−8.03834e7	−	7.01777e7i	−1.66672	−	1.45511i
$365$		−	8.38900e7i		−	1.72517i
$366$		0			0
$367$		−	5.39218e7i		−	1.09085i	−0.838159	−	0.545426i	$-0.816368\pi$
$367$		−	5.39218e7i		−	1.09085i	0.838159	−	0.545426i	$-0.183632\pi$
$368$	1.63641e6	−	222869.i	0.0328358	−	0.00447204i
$369$		0			0
$370$	3.68881e7	+	1.38367e7i	0.728251	+	0.273167i
$371$	−6.18129e7			−1.21048
$372$		0			0
$373$		−	7.08636e7i		−	1.36552i	−0.730645	−	0.682758i	$-0.760780\pi$
$373$		−	7.08636e7i		−	1.36552i	0.730645	−	0.682758i	$-0.239220\pi$
$374$	−1.68903e7	−	6.33557e6i	−0.322866	−	0.121107i
$375$		0			0
$376$	−4.49082e7	+	2.41975e7i	−0.844816	+	0.455205i
$377$	4.14000e7			0.772638
$378$		0			0
$379$	−9.85646e7			−1.81052			−0.905260	−	0.424858i	$-0.860324\pi$
$379$	−9.85646e7			−1.81052			−0.905260	+	0.424858i	$0.860324\pi$
$380$	4.99235e7	−	5.71837e7i	0.909818	−	1.04213i
$381$		0			0
$382$	−7.69815e6	+	2.05229e7i	−0.138101	+	0.368170i
$383$		−	1.01711e7i		−	0.181039i	−0.995895	−	0.0905196i	$-0.971147\pi$
$383$		−	1.01711e7i		−	0.181039i	0.995895	−	0.0905196i	$-0.0288528\pi$
$384$		0			0
$385$	1.24484e8			2.18139
$386$	7.66912e7	+	2.87669e7i	1.33347	+	0.500185i
$387$		0			0
$388$	6.29839e7	+	5.49873e7i	1.07829	+	0.941386i
$389$		−	1.78320e7i		−	0.302936i	−0.988462	−	0.151468i	$-0.951600\pi$
$389$		−	1.78320e7i		−	0.302936i	0.988462	−	0.151468i	$-0.0484000\pi$
$390$		0			0
$391$		−	501182.i		−	0.00838427i
$392$	−4.08434e7	−	7.58015e7i	−0.678054	−	1.25840i
$393$		0			0
$394$	9.18050e6	−	2.44748e7i	0.150099	−	0.400157i
$395$	4.29210e7			0.696432
$396$		0			0
$397$			9.25929e6i			0.147981i	0.997259	+	0.0739906i	$0.0235735\pi$
$397$			9.25929e6i			0.147981i	−0.997259	+	0.0739906i	$0.976427\pi$
$398$	−3.72508e6	+	9.93089e6i	−0.0590863	+	0.157521i
$399$		0			0
$400$	−469557.	−	3.44771e6i	−0.00733683	−	0.0538704i
$401$	−7.07125e7			−1.09664			−0.548318	−	0.836270i	$-0.684732\pi$
$401$	−7.07125e7			−1.09664			−0.548318	+	0.836270i	$0.684732\pi$
$402$		0			0
$403$	−1.06070e8			−1.62060
$404$	5.67202e7	−	6.49688e7i	0.860188	−	0.985282i
$405$		0			0
$406$	5.31603e7	+	1.99405e7i	0.794346	+	0.297959i
$407$		−	6.96043e7i		−	1.03241i
$408$		0			0
$409$	3.84535e7			0.562039			0.281019	−	0.959702i	$-0.409328\pi$
$409$	3.84535e7			0.562039			0.281019	+	0.959702i	$0.409328\pi$
$410$	2.54056e7	−	6.77301e7i	0.368619	−	0.982721i
$411$		0			0
$412$	3.64665e7	−	4.17697e7i	0.521438	−	0.597269i
$413$			9.24959e7i			1.31302i
$414$		0			0
$415$			5.37565e7i			0.752120i
$416$	9.96498e7	+	2.26499e7i	1.38419	+	0.314620i
$417$		0			0
$418$	−1.25568e8	−	4.71005e7i	−1.71929	−	0.644906i
$419$	−9.37498e6			−0.127447			−0.0637233	−	0.997968i	$-0.520298\pi$
$419$	−9.37498e6			−0.127447			−0.0637233	+	0.997968i	$0.520298\pi$
$420$		0			0
$421$		−	9.30388e6i		−	0.124686i	−0.998055	−	0.0623430i	$-0.980143\pi$
$421$		−	9.30388e6i		−	0.124686i	0.998055	−	0.0623430i	$-0.0198573\pi$
$422$	−6.04758e7	−	2.26845e7i	−0.804719	−	0.301850i
$423$		0			0
$424$	5.21136e7	−	2.80799e7i	0.683680	−	0.368381i
$425$	−1.05593e6			−0.0137552
$426$		0			0
$427$	−7.71082e6			−0.0990415
$428$	6.22400e7	+	5.43379e7i	0.793850	+	0.693061i
$429$		0			0
$430$	−3.57981e6	+	9.54359e6i	−0.0450250	+	0.120035i
$431$			2.00343e7i			0.250232i	0.992142	+	0.125116i	$0.0399303\pi$
$431$			2.00343e7i			0.250232i	−0.992142	+	0.125116i	$0.960070\pi$
$432$		0			0
$433$	−3.26354e7			−0.402000			−0.201000	−	0.979591i	$-0.564419\pi$
$433$	−3.26354e7			−0.402000			−0.201000	+	0.979591i	$0.564419\pi$
$434$	−1.36200e8	−	5.10888e7i	−1.66613	−	0.624967i
$435$		0			0
$436$	1.54445e7	−	1.76905e7i	0.186344	−	0.213443i
$437$		−	3.72593e6i		−	0.0446468i
$438$		0			0
$439$			2.21673e7i			0.262010i	0.991382	+	0.131005i	$0.0418204\pi$
$439$			2.21673e7i			0.262010i	−0.991382	+	0.131005i	$0.958180\pi$
$440$	−1.04951e8	+	5.65498e7i	−1.23205	+	0.663854i
$441$		0			0
$442$	1.08916e7	−	2.90364e7i	0.126131	−	0.336260i
$443$	−2.33644e7			−0.268747			−0.134373	−	0.990931i	$-0.542902\pi$
$443$	−2.33644e7			−0.268747			−0.134373	+	0.990931i	$0.542902\pi$
$444$		0			0
$445$		−	2.53285e7i		−	0.287428i
$446$	−4.18025e7	+	1.11443e8i	−0.471192	+	1.25617i
$447$		0			0
$448$	1.17048e8	+	7.70807e7i	1.30175	+	0.857258i
$449$	8.43083e6			0.0931390			0.0465695	−	0.998915i	$-0.485171\pi$
$449$	8.43083e6			0.0931390			0.0465695	+	0.998915i	$0.485171\pi$
$450$		0			0
$451$	−1.27800e8			−1.39316
$452$	7.78032e7	+	6.79251e7i	0.842524	+	0.735555i
$453$		0			0
$454$	4.41217e7	+	1.65501e7i	0.471503	+	0.176861i
$455$			2.14003e8i			2.27188i
$456$		0			0
$457$	−7.63494e7			−0.799939			−0.399970	−	0.916528i	$-0.630979\pi$
$457$	−7.63494e7			−0.799939			−0.399970	+	0.916528i	$0.630979\pi$
$458$	2.52100e6	−	6.72086e6i	0.0262408	−	0.0699566i
$459$		0			0
$460$	−2.49506e6	−	2.17828e6i	−0.0256335	−	0.0223790i
$461$			9.40919e7i			0.960394i	0.877161	+	0.480197i	$0.159435\pi$
$461$			9.40919e7i			0.960394i	−0.877161	+	0.480197i	$0.840565\pi$
$462$		0			0
$463$			1.56936e8i			1.58118i	0.612349	+	0.790588i	$0.290225\pi$
$463$			1.56936e8i			1.58118i	−0.612349	+	0.790588i	$0.709775\pi$
$464$	−5.38771e7	+	7.33774e6i	−0.539325	+	0.0734528i
$465$		0			0
$466$	−1.04598e8	−	3.92347e7i	−1.03363	−	0.387715i
$467$	−1.52288e8			−1.49525			−0.747627	−	0.664119i	$-0.768807\pi$
$467$	−1.52288e8			−1.49525			−0.747627	+	0.664119i	$0.768807\pi$
$468$		0			0
$469$			1.66790e8i			1.61678i
$470$	9.57891e7	+	3.59305e7i	0.922619	+	0.346075i
$471$		0			0
$472$	−4.20183e7	−	7.79820e7i	−0.399588	−	0.741597i
$473$	1.80078e7			0.170168
$474$		0			0
$475$	−7.85008e6			−0.0732476
$476$	2.79710e7	−	3.20387e7i	0.259350	−	0.297067i
$477$		0			0
$478$	302702.	−	806989.i	0.00277161	−	0.00738897i
$479$		−	3.90685e7i		−	0.355484i	−0.984077	−	0.177742i	$-0.943121\pi$
$479$		−	3.90685e7i		−	0.355484i	0.984077	−	0.177742i	$-0.0568792\pi$
$480$		0			0
$481$	1.19658e8			1.07524
$482$	5.65973e7	+	2.12297e7i	0.505422	+	0.189584i
$483$		0			0
$484$	7.32521e7	+	6.39518e7i	0.646077	+	0.564049i
$485$		−	1.67681e8i		−	1.46980i
$486$		0			0
$487$			1.62449e8i			1.40647i	0.710957	+	0.703235i	$0.248262\pi$
$487$			1.62449e8i			1.40647i	−0.710957	+	0.703235i	$0.751738\pi$
$488$	6.50088e6	−	3.50281e6i	0.0559388	−	0.0301410i
$489$		0			0
$490$	−6.06479e7	+	1.61684e8i	−0.515498	+	1.37429i
$491$	−1.49105e8			−1.25965			−0.629823	−	0.776739i	$-0.716873\pi$
$491$	−1.49105e8			−1.25965			−0.629823	+	0.776739i	$0.716873\pi$
$492$		0			0
$493$			1.65009e7i			0.137711i
$494$	8.09711e7	−	2.15865e8i	0.671659	−	1.79061i
$495$		0			0
$496$	1.38037e8	−	1.87998e7i	1.13123	−	0.154067i
$497$	2.63508e8			2.14647
$498$		0			0
$499$	4.10958e7			0.330747			0.165373	−	0.986231i	$-0.447117\pi$
$499$	4.10958e7			0.330747			0.165373	+	0.986231i	$0.447117\pi$
$500$	7.98242e7	−	9.14327e7i	0.638593	−	0.731461i
$501$		0			0
$502$	−4.08204e7	−	1.53118e7i	−0.322676	−	0.121036i
$503$		−	2.11225e7i		−	0.165975i	−0.996551	−	0.0829874i	$-0.973554\pi$
$503$		−	2.11225e7i		−	0.165975i	0.996551	−	0.0829874i	$-0.0264461\pi$
$504$		0			0
$505$	−1.72965e8			−1.34302
$506$	−2.05511e6	+	5.47881e6i	−0.0158629	+	0.0422897i
$507$		0			0
$508$	−1.10782e8	+	1.26893e8i	−0.845044	+	0.967935i
$509$			2.26464e8i			1.71730i	0.512564	+	0.858649i	$0.328696\pi$
$509$			2.26464e8i			1.71730i	−0.512564	+	0.858649i	$0.671304\pi$
$510$		0			0
$511$		−	3.49424e8i		−	2.61872i
$512$	−1.33697e8	−	1.18141e7i	−0.996119	−	0.0880221i
$513$		0			0
$514$	−1.20848e8	−	4.53302e7i	−0.889919	−	0.333809i
$515$	−1.11202e8			−0.814128
$516$		0			0
$517$		−	1.80745e8i		−	1.30796i
$518$	1.53649e8	+	5.76336e7i	1.10545	+	0.414655i
$519$		0			0
$520$	−9.72155e7	−	1.80423e8i	−0.691394	−	1.28316i
$521$	−2.11544e8			−1.49585			−0.747924	−	0.663784i	$-0.768949\pi$
$521$	−2.11544e8			−1.49585			−0.747924	+	0.663784i	$0.768949\pi$
$522$		0			0
$523$	4.47306e7			0.312680			0.156340	−	0.987703i	$-0.450030\pi$
$523$	4.47306e7			0.312680			0.156340	+	0.987703i	$0.450030\pi$
$524$	−4.88839e7	−	4.26775e7i	−0.339760	−	0.296623i
$525$		0			0
$526$	−6.78483e7	+	1.80880e8i	−0.466210	+	1.24289i
$527$		−	4.22765e7i		−	0.288847i
$528$		0			0
$529$	1.47873e8			0.998902
$530$	−1.11158e8	−	4.16955e7i	−0.746644	−	0.280066i
$531$		0			0
$532$	2.07944e8	−	2.38185e8i	1.38106	−	1.58190i
$533$		−	2.19703e8i		−	1.45096i
$534$		0			0
$535$		−	1.65700e8i		−	1.08208i
$536$	−7.57679e7	−	1.40618e8i	−0.492029	−	0.913159i
$537$		0			0
$538$	−1.53186e6	+	4.08386e6i	−0.00983721	+	0.0262255i
$539$	3.05083e8			1.94828
$540$		0			0
$541$			1.59390e8i			1.00663i	0.864103	+	0.503314i	$0.167886\pi$
$541$			1.59390e8i			1.00663i	−0.864103	+	0.503314i	$0.832114\pi$
$542$	2.45421e7	−	6.54282e7i	0.154140	−	0.410929i
$543$		0			0
$544$	−9.02764e6	+	3.97178e7i	−0.0560761	+	0.246711i
$545$	−4.70971e7			−0.290941
$546$		0			0
$547$	4.77047e7			0.291474			0.145737	−	0.989323i	$-0.453445\pi$
$547$	4.77047e7			0.291474			0.145737	+	0.989323i	$0.453445\pi$
$548$	1.61471e8	+	1.40970e8i	0.981188	+	0.856614i
$549$		0			0
$550$	1.15432e7	+	4.32985e6i	0.0693805	+	0.0260247i
$551$			1.22673e8i			0.733320i
$552$		0			0
$553$	1.78777e8			1.05715
$554$	−8.67673e7	+	2.31317e8i	−0.510301	+	1.36044i
$555$		0			0
$556$	2.08447e7	+	1.81982e7i	0.121275	+	0.105878i
$557$		−	2.05366e8i		−	1.18840i	−0.804317	−	0.594200i	$-0.797469\pi$
$557$		−	2.05366e8i		−	1.18840i	0.804317	−	0.594200i	$-0.202531\pi$
$558$		0			0
$559$			3.09575e7i			0.177227i
$560$	−3.79299e7	−	2.78499e8i	−0.215982	−	1.58584i
$561$		0			0
$562$	2.48967e8	+	9.33875e7i	1.40259	+	0.526114i
$563$	−1.08550e7			−0.0608283			−0.0304142	−	0.999537i	$-0.509683\pi$
$563$	−1.08550e7			−0.0608283			−0.0304142	+	0.999537i	$0.509683\pi$
$564$		0			0
$565$		−	2.07134e8i		−	1.14843i
$566$	1.45916e8	+	5.47330e7i	0.804734	+	0.301856i
$567$		0			0
$568$	−2.22159e8	+	1.19704e8i	−1.21233	+	0.653227i
$569$	1.56945e8			0.851943			0.425971	−	0.904737i	$-0.359932\pi$
$569$	1.56945e8			0.851943			0.425971	+	0.904737i	$0.359932\pi$
$570$		0			0
$571$	2.35542e8			1.26520			0.632602	−	0.774477i	$-0.281987\pi$
$571$	2.35542e8			1.26520			0.632602	+	0.774477i	$0.281987\pi$
$572$	−2.38128e8	+	2.72758e8i	−1.27240	+	1.45744i
$573$		0			0
$574$	1.05821e8	−	2.82114e8i	0.559546	−	1.49172i
$575$			342518.i			0.00180169i
$576$		0			0
$577$	−3.66090e8			−1.90572			−0.952862	−	0.303403i	$-0.901877\pi$
$577$	−3.66090e8			−1.90572			−0.952862	+	0.303403i	$0.901877\pi$
$578$	−1.69227e8	−	6.34770e7i	−0.876365	−	0.328725i
$579$		0			0
$580$	8.21475e7	+	7.17178e7i	0.421027	+	0.367573i
$581$			2.23910e8i			1.14168i
$582$		0			0
$583$			2.09745e8i			1.05849i
$584$	1.58733e8	+	2.94594e8i	0.796948	+	1.47906i
$585$		0			0
$586$	3.62884e7	−	9.67433e7i	0.180333	−	0.480760i
$587$	9.07755e7			0.448801			0.224401	−	0.974497i	$-0.427958\pi$
$587$	9.07755e7			0.448801			0.224401	+	0.974497i	$0.427958\pi$
$588$		0			0
$589$		−	3.14296e8i		−	1.53813i
$590$	−6.23925e7	+	1.66335e8i	−0.303792	+	0.809895i
$591$		0			0
$592$	−1.55720e8	+	2.12082e7i	−0.750551	+	0.102221i
$593$	−5.81061e7			−0.278649			−0.139324	−	0.990247i	$-0.544493\pi$
$593$	−5.81061e7			−0.278649			−0.139324	+	0.990247i	$0.544493\pi$
$594$		0			0
$595$	−8.52958e7			−0.404927
$596$	1.15926e8	−	1.32785e8i	0.547573	−	0.627205i
$597$		0			0
$598$	−9.41871e6	−	3.53296e6i	−0.0440441	−	0.0165210i
$599$		−	4.18560e8i		−	1.94750i	−0.227625	−	0.973749i	$-0.573096\pi$
$599$		−	4.18560e8i		−	1.94750i	0.227625	−	0.973749i	$-0.426904\pi$
$600$		0			0
$601$	2.19397e8			1.01067			0.505334	−	0.862924i	$-0.331369\pi$
$601$	2.19397e8			1.01067			0.505334	+	0.862924i	$0.331369\pi$
$602$	−1.49108e7	+	3.97515e7i	−0.0683458	+	0.182207i
$603$		0			0
$604$	1.18392e8	−	1.35609e8i	0.537292	−	0.615428i
$605$		−	1.95017e8i		−	0.880657i
$606$		0			0
$607$		−	3.13531e6i		−	0.0140189i	−0.999975	−	0.00700946i	$-0.997769\pi$
$607$		−	3.13531e6i		−	0.0140189i	0.999975	−	0.00700946i	$-0.00223120\pi$
$608$	−6.71141e7	+	2.95274e8i	−0.298609	+	1.31375i
$609$		0			0
$610$	−1.38664e7	−	5.20128e6i	−0.0610904	−	0.0229151i
$611$	3.10721e8			1.36222
$612$		0			0
$613$			2.22085e8i			0.964133i	0.876135	+	0.482067i	$0.160114\pi$
$613$			2.22085e8i			0.964133i	−0.876135	+	0.482067i	$0.839886\pi$
$614$	−9.35208e7	−	3.50797e7i	−0.404020	−	0.151548i
$615$		0			0
$616$	−4.37148e8	+	2.35544e8i	−1.87019	+	1.00770i
$617$	6.82919e7			0.290746			0.145373	−	0.989377i	$-0.453562\pi$
$617$	6.82919e7			0.290746			0.145373	+	0.989377i	$0.453562\pi$
$618$		0			0
$619$	1.54874e8			0.652992			0.326496	−	0.945199i	$-0.394132\pi$
$619$	1.54874e8			0.652992			0.326496	+	0.945199i	$0.394132\pi$
$620$	−2.10467e8	−	1.83746e8i	−0.883100	−	0.770980i
$621$		0			0
$622$	8.73925e7	−	2.32984e8i	0.363164	−	0.968179i
$623$		−	1.05500e8i		−	0.436301i
$624$		0			0
$625$	−2.56692e8			−1.05141
$626$	−3.86000e8	−	1.44789e8i	−1.57349	−	0.590217i
$627$		0			0
$628$	−2.54404e8	+	2.91401e8i	−1.02718	+	1.17655i
$629$			4.76924e7i			0.191645i
$630$		0			0
$631$		−	9.28270e7i		−	0.369476i	−0.982788	−	0.184738i	$-0.940856\pi$
$631$		−	9.28270e7i		−	0.369476i	0.982788	−	0.184738i	$-0.0591436\pi$
$632$	−1.50725e8	+	8.12136e7i	−0.597080	+	0.321720i
$633$		0			0
$634$	9.71304e7	−	2.58945e8i	0.381143	−	1.01611i
$635$	3.37824e8			1.31938
$636$		0			0
$637$			5.24472e8i			2.02910i
$638$	6.76624e7	−	1.80385e8i	0.260546	−	0.694604i
$639$		0			0
$640$	1.58492e8	+	2.17568e8i	0.604601	+	0.829955i
$641$	1.42897e8			0.542561			0.271280	−	0.962500i	$-0.412553\pi$
$641$	1.42897e8			0.542561			0.271280	+	0.962500i	$0.412553\pi$
$642$		0			0
$643$	−2.74682e8			−1.03323			−0.516615	−	0.856218i	$-0.672808\pi$
$643$	−2.74682e8			−1.03323			−0.516615	+	0.856218i	$0.672808\pi$
$644$	−1.03926e7	−	9.07311e6i	−0.0389104	−	0.0339702i
$645$		0			0
$646$	8.60381e7	+	3.22729e7i	0.319149	+	0.119713i
$647$		−	3.25441e7i		−	0.120160i	−0.998194	−	0.0600799i	$-0.980864\pi$
$647$		−	3.25441e7i		−	0.120160i	0.998194	−	0.0600799i	$-0.0191356\pi$
$648$		0			0
$649$	3.13859e8			1.14815
$650$	−7.44351e6	+	1.98440e7i	−0.0271043	+	0.0722587i
$651$		0			0
$652$	−2.07081e7	−	1.80790e7i	−0.0747133	−	0.0652276i
$653$			2.15133e8i			0.772623i	0.922368	+	0.386311i	$0.126251\pi$
$653$			2.15133e8i			0.772623i	−0.922368	+	0.386311i	$0.873749\pi$
$654$		0			0
$655$			1.30142e8i			0.463122i
$656$	3.89403e7	+	2.85917e8i	0.137939	+	1.01281i
$657$		0			0
$658$	3.98987e8	+	1.49660e8i	1.40049	+	0.525325i
$659$	−9.93128e7			−0.347016			−0.173508	−	0.984832i	$-0.555510\pi$
$659$	−9.93128e7			−0.347016			−0.173508	+	0.984832i	$0.555510\pi$
$660$		0			0
$661$			7.32197e7i			0.253527i	0.991933	+	0.126763i	$0.0404589\pi$
$661$			7.32197e7i			0.253527i	−0.991933	+	0.126763i	$0.959541\pi$
$662$	2.27520e8	+	8.53430e7i	0.784235	+	0.294167i
$663$		0			0
$664$	−1.01716e8	−	1.88775e8i	−0.347445	−	0.644824i
$665$	−6.34114e8			−2.15627
$666$		0			0
$667$	5.35251e6			0.0180376
$668$	3.15443e8	−	3.61317e8i	1.05826	−	1.21216i
$669$		0			0
$670$	−1.12507e8	+	2.99938e8i	−0.374071	+	0.997256i
$671$			2.61645e7i			0.0866054i
$672$		0			0
$673$	−4.98189e8			−1.63437			−0.817183	−	0.576378i	$-0.804465\pi$
$673$	−4.98189e8			−1.63437			−0.817183	+	0.576378i	$0.804465\pi$
$674$	1.51852e8	+	5.69599e7i	0.495955	+	0.186033i
$675$		0			0
$676$	−2.36194e8	−	2.06206e8i	−0.764590	−	0.667516i
$677$			2.50535e8i			0.807425i	0.914886	+	0.403712i	$0.132280\pi$
$677$			2.50535e8i			0.807425i	−0.914886	+	0.403712i	$0.867720\pi$
$678$		0			0
$679$		−	6.98433e8i		−	2.23108i
$680$	7.19117e7	−	3.87475e7i	0.228703	−	0.123230i
$681$		0			0
$682$	−1.73356e8	+	4.62158e8i	−0.546493	+	1.45692i
$683$	1.62121e8			0.508836			0.254418	−	0.967094i	$-0.418116\pi$
$683$	1.62121e8			0.508836			0.254418	+	0.967094i	$0.418116\pi$
$684$		0			0
$685$		−	4.29880e8i		−	1.33744i
$686$	−7.58932e7	+	2.02328e8i	−0.235088	+	0.626733i
$687$		0			0
$688$	−5.48692e6	−	4.02875e7i	−0.0168486	−	0.123710i
$689$	−3.60575e8			−1.10240
$690$		0			0
$691$	3.44697e8			1.04473			0.522365	−	0.852722i	$-0.325050\pi$
$691$	3.44697e8			1.04473			0.522365	+	0.852722i	$0.325050\pi$
$692$	−3.63561e8	+	4.16432e8i	−1.09713	+	1.25668i
$693$		0			0
$694$	3.96140e8	+	1.48592e8i	1.18514	+	0.444547i
$695$		−	5.54943e7i		−	0.165308i
$696$		0			0
$697$	8.75679e7			0.258611
$698$	5.22652e7	−	1.39336e8i	0.153690	−	0.409731i
$699$		0			0
$700$	−1.91159e7	+	2.18959e7i	−0.0557316	+	0.0638364i
$701$			7.35414e7i			0.213490i	0.994286	+	0.106745i	$0.0340429\pi$
$701$			7.35414e7i			0.213490i	−0.994286	+	0.106745i	$0.965957\pi$
$702$		0			0
$703$			3.54559e8i			1.02052i
$704$	2.61552e8	−	3.97168e8i	0.749617	−	1.13830i
$705$		0			0
$706$	−4.12856e8	−	1.54862e8i	−1.17323	−	0.440080i
$707$	−7.20444e8			−2.03865
$708$		0			0
$709$		−	1.05459e8i		−	0.295899i	−0.988995	−	0.147950i	$-0.952733\pi$
$709$		−	1.05459e8i		−	0.295899i	0.988995	−	0.147950i	$-0.0472673\pi$
$710$	4.73866e8	+	1.77747e8i	1.32398	+	0.496624i
$711$		0			0
$712$	4.79255e7	+	8.89452e7i	0.132778	+	0.246424i
$713$	−1.37135e7			−0.0378337
$714$		0			0
$715$	7.26158e8			1.98661
$716$	−2.79335e7	−	2.43870e7i	−0.0761002	−	0.0664383i
$717$		0			0
$718$	−1.82385e7	+	4.86230e7i	−0.0492738	+	0.131362i
$719$			2.61169e8i			0.702644i	0.936255	+	0.351322i	$0.114268\pi$
$719$			2.61169e8i			0.702644i	−0.936255	+	0.351322i	$0.885732\pi$
$720$		0			0
$721$	−4.63187e8			−1.23581
$722$	2.87240e8	+	1.07744e8i	0.763192	+	0.286274i
$723$		0			0
$724$	−1.86200e8	+	2.13278e8i	−0.490640	+	0.561992i
$725$		−	1.12771e7i		−	0.0295925i
$726$		0			0
$727$		−	4.28633e7i		−	0.111553i	−0.998443	−	0.0557766i	$-0.982237\pi$
$727$		−	4.28633e7i		−	0.111553i	0.998443	−	0.0557766i	$-0.0177635\pi$
$728$	−4.04928e8	−	7.51507e8i	−1.04950	−	1.94778i
$729$		0			0
$730$	2.35701e8	−	6.28368e8i	0.605890	−	1.61527i
$731$	−1.23389e7			−0.0315880
$732$		0			0
$733$			6.67447e8i			1.69475i	0.530998	+	0.847373i	$0.321817\pi$
$733$			6.67447e8i			1.69475i	−0.530998	+	0.847373i	$0.678183\pi$
$734$	1.51501e8	−	4.03895e8i	0.383114	−	1.02136i
$735$		0			0
$736$	1.28835e7	+	2.92835e6i	0.0323147	+	0.00734496i
$737$	5.65954e8			1.41377
$738$		0			0
$739$	−3.30289e8			−0.818390			−0.409195	−	0.912447i	$-0.634190\pi$
$739$	−3.30289e8			−0.818390			−0.409195	+	0.912447i	$0.634190\pi$
$740$	2.37430e8	+	2.07285e8i	0.585922	+	0.511532i
$741$		0			0
$742$	−4.63003e8	−	1.73672e8i	−1.13337	−	0.425128i
$743$			7.39513e8i			1.80293i	0.432849	+	0.901466i	$0.357508\pi$
$743$			7.39513e8i			1.80293i	−0.432849	+	0.901466i	$0.642492\pi$
$744$		0			0
$745$	−3.53510e8			−0.854934
$746$	1.99102e8	−	5.30796e8i	0.479577	−	1.27853i
$747$		0			0
$748$	−1.08714e8	−	9.49117e7i	−0.259766	−	0.226785i
$749$		−	6.90184e8i		−	1.64255i
$750$		0			0
$751$			3.89748e8i			0.920161i	0.887877	+	0.460080i	$0.152179\pi$
$751$			3.89748e8i			0.920161i	−0.887877	+	0.460080i	$0.847821\pi$
$752$	−4.04366e8	+	5.50723e7i	−0.950870	+	0.129503i
$753$		0			0
$754$	3.10102e8	+	1.16319e8i	0.723420	+	0.271355i
$755$	−3.61028e8			−0.838881
$756$		0			0
$757$			4.94872e8i			1.14079i	0.821371	+	0.570395i	$0.193210\pi$
$757$			4.94872e8i			1.14079i	−0.821371	+	0.570395i	$0.806790\pi$
$758$	−7.38287e8	−	2.76932e8i	−1.69519	−	0.635865i
$759$		0			0
$760$	5.34612e8	−	2.88060e8i	1.21786	−	0.656210i
$761$	−1.74687e8			−0.396376			−0.198188	−	0.980164i	$-0.563506\pi$
$761$	−1.74687e8			−0.396376			−0.198188	+	0.980164i	$0.563506\pi$
$762$		0			0
$763$	−1.96172e8			−0.441634
$764$	−1.15324e8	+	1.32095e8i	−0.258607	+	0.296215i
$765$		0			0
$766$	2.85773e7	−	7.61857e7i	0.0635820	−	0.169507i
$767$			5.39559e8i			1.19579i
$768$		0			0
$769$	3.88007e7			0.0853219			0.0426610	−	0.999090i	$-0.486416\pi$
$769$	3.88007e7			0.0853219			0.0426610	+	0.999090i	$0.486416\pi$
$770$	9.32435e8	+	3.49757e8i	2.04243	+	0.766115i
$771$		0			0
$772$	4.93622e8	+	4.30950e8i	1.07286	+	0.936645i
$773$			6.59639e8i			1.42813i	0.700079	+	0.714065i	$0.253148\pi$
$773$			6.59639e8i			1.42813i	−0.700079	+	0.714065i	$0.746852\pi$
$774$		0			0
$775$			2.88926e7i			0.0620700i
$776$	3.17279e8	+	5.88839e8i	0.678978	+	1.26012i
$777$		0			0
$778$	5.01015e7	−	1.33568e8i	0.106393	−	0.283638i
$779$	6.51006e8			1.37712
$780$		0			0
$781$		−	8.94139e8i		−	1.87695i
$782$	1.40814e6	−	3.75405e6i	0.00294460	−	0.00785017i
$783$		0			0
$784$	−9.29576e7	−	6.82538e8i	−0.192902	−	1.41638i
$785$	7.75789e8			1.60374
$786$		0			0
$787$	5.49020e8			1.12633			0.563163	−	0.826346i	$-0.309584\pi$
$787$	5.49020e8			1.12633			0.563163	+	0.826346i	$0.309584\pi$
$788$	1.37531e8	−	1.57532e8i	0.281075	−	0.321950i
$789$		0			0
$790$	3.21495e8	+	1.20593e8i	0.652068	+	0.244591i
$791$		−	8.62766e8i		−	1.74326i
$792$		0			0
$793$	−4.49798e7			−0.0901982
$794$	−2.60154e7	+	6.93557e7i	−0.0519718	+	0.138554i
$795$		0			0
$796$	−5.58046e7	+	6.39200e7i	−0.110645	+	0.126735i
$797$		−	3.09650e8i		−	0.611640i	−0.952089	−	0.305820i	$-0.901069\pi$
$797$		−	3.09650e8i		−	0.611640i	0.952089	−	0.305820i	$-0.0989306\pi$
$798$		0			0
$799$			1.23845e8i			0.242794i
$800$	6.16967e6	−	2.71439e7i	0.0120501	−	0.0530155i
$801$		0			0
$802$	−5.29664e8	−	1.98677e8i	−1.02678	−	0.385145i
$803$	−1.18567e9			−2.28991
$804$		0			0
$805$			2.76679e7i			0.0530382i
$806$	−7.94502e8	−	2.98018e8i	−1.51736	−	0.569164i
$807$		0			0
$808$	6.07396e8	−	3.27277e8i	1.15143	−	0.620415i
$809$	−8.65850e8			−1.63530			−0.817649	−	0.575716i	$-0.804723\pi$
$809$	−8.65850e8			−1.63530			−0.817649	+	0.575716i	$0.804723\pi$
$810$		0			0
$811$	−3.60771e7			−0.0676345			−0.0338173	−	0.999428i	$-0.510766\pi$
$811$	−3.60771e7			−0.0676345			−0.0338173	+	0.999428i	$0.510766\pi$
$812$	3.42166e8	+	2.98723e8i	0.639099	+	0.557958i
$813$		0			0
$814$	1.95564e8	−	5.21363e8i	0.362589	−	0.966645i
$815$			5.51308e7i			0.101841i
$816$		0			0
$817$	−9.17307e7			−0.168209
$818$	2.88032e8	+	1.08041e8i	0.526236	+	0.197391i
$819$		0			0
$820$	3.80596e8	−	4.35944e8i	0.690275	−	0.790659i
$821$		−	2.35164e8i		−	0.424954i	−0.977166	−	0.212477i	$-0.931847\pi$
$821$		−	2.35164e8i		−	0.424954i	0.977166	−	0.212477i	$-0.0681530\pi$
$822$		0			0
$823$		−	4.98780e8i		−	0.894766i	−0.894343	−	0.447383i	$-0.852356\pi$
$823$		−	4.98780e8i		−	0.894766i	0.894343	−	0.447383i	$-0.147644\pi$
$824$	3.90506e8	−	2.10413e8i	0.697986	−	0.376089i
$825$		0			0
$826$	−2.59881e8	+	6.92830e8i	−0.461141	+	1.22938i
$827$	9.72527e8			1.71943			0.859716	−	0.510772i	$-0.170640\pi$
$827$	9.72527e8			1.71943			0.859716	+	0.510772i	$0.170640\pi$
$828$		0			0
$829$		−	7.45706e8i		−	1.30889i	−0.756109	−	0.654446i	$-0.772902\pi$
$829$		−	7.45706e8i		−	1.30889i	0.756109	−	0.654446i	$-0.227098\pi$
$830$	−1.51037e8	+	4.02657e8i	−0.264149	+	0.704209i
$831$		0			0
$832$	6.82778e8	+	4.49637e8i	1.18552	+	0.780715i
$833$	−2.09041e8			−0.361656
$834$		0			0
$835$	−9.61925e8			−1.65227
$836$	−8.08214e8	−	7.05601e8i	−1.38327	−	1.20765i
$837$		0			0
$838$	−7.02222e7	−	2.63404e7i	−0.119328	−	0.0447600i
$839$		−	8.19173e8i		−	1.38704i	−0.720436	−	0.693521i	$-0.756058\pi$
$839$		−	8.19173e8i		−	1.38704i	0.720436	−	0.693521i	$-0.243942\pi$
$840$		0			0
$841$	4.18597e8			0.703734
$842$	2.61406e7	−	6.96897e7i	0.0437905	−	0.116743i
$843$		0			0
$844$	−3.89252e8	−	3.39831e8i	−0.647445	−	0.565244i
$845$			6.28813e8i			1.04220i
$846$		0			0
$847$		−	8.12298e8i		−	1.33680i
$848$	4.69245e8	−	6.39084e7i	0.769507	−	0.104802i
$849$		0			0
$850$	−7.90931e6	−	2.96679e6i	−0.0128790	−	0.00483092i
$851$	1.54703e7			0.0251021
$852$		0			0
$853$			4.85520e8i			0.782276i	0.920332	+	0.391138i	$0.127918\pi$
$853$			4.85520e8i			0.782276i	−0.920332	+	0.391138i	$0.872082\pi$
$854$	−5.77570e7	−	2.16647e7i	−0.0927324	−	0.0347840i
$855$		0			0
$856$	3.13531e8	+	5.81884e8i	0.499873	+	0.927716i
$857$	4.92557e8			0.782553			0.391276	−	0.920273i	$-0.372034\pi$
$857$	4.92557e8			0.782553			0.391276	+	0.920273i	$0.372034\pi$
$858$		0			0
$859$	−1.14628e9			−1.80847			−0.904236	−	0.427032i	$-0.859559\pi$
$859$	−1.14628e9			−1.80847			−0.904236	+	0.427032i	$0.859559\pi$
$860$	−5.36282e7	+	6.14272e7i	−0.0843137	+	0.0965751i
$861$		0			0
$862$	−5.62893e7	+	1.50065e8i	−0.0878829	+	0.234292i
$863$		−	7.40770e8i		−	1.15253i	−0.817264	−	0.576264i	$-0.804510\pi$
$863$		−	7.40770e8i		−	1.15253i	0.817264	−	0.576264i	$-0.195490\pi$
$864$		0			0
$865$	1.10866e9			1.71297
$866$	−2.44452e8	−	9.16940e7i	−0.376392	−	0.141185i
$867$		0			0
$868$	−8.76652e8	−	7.65350e8i	−1.34050	−	1.17031i
$869$		−	6.06631e8i		−	0.924411i
$870$		0			0
$871$			9.72939e8i			1.47242i
$872$	1.65389e8	−	8.91153e7i	0.249435	−	0.134401i
$873$		0			0
$874$	1.04686e7	−	2.79087e7i	0.0156802	−	0.0418028i
$875$	−1.01390e9			−1.51347
$876$		0			0
$877$			6.92196e8i			1.02620i	0.858330	+	0.513098i	$0.171502\pi$
$877$			6.92196e8i			1.02620i	−0.858330	+	0.513098i	$0.828498\pi$
$878$	−6.22822e7	+	1.66041e8i	−0.0920196	+	0.245320i
$879$		0			0
$880$	−9.45008e8	+	1.28704e8i	−1.38672	+	0.188862i
$881$	4.49473e8			0.657319			0.328660	−	0.944448i	$-0.393403\pi$
$881$	4.49473e8			0.657319			0.328660	+	0.944448i	$0.393403\pi$
$882$		0			0
$883$	−2.87114e8			−0.417035			−0.208518	−	0.978019i	$-0.566864\pi$
$883$	−2.87114e8			−0.417035			−0.208518	+	0.978019i	$0.566864\pi$
$884$	1.63164e8	−	1.86892e8i	0.236193	−	0.270542i
$885$		0			0
$886$	−1.75008e8	−	6.56457e7i	−0.251627	−	0.0943855i
$887$			9.92257e8i			1.42185i	0.703268	+	0.710924i	$0.251723\pi$
$887$			9.92257e8i			1.42185i	−0.703268	+	0.710924i	$0.748277\pi$
$888$		0			0
$889$	1.40712e9			2.00275
$890$	7.11640e7	−	1.89720e8i	0.100946	−	0.269118i
$891$		0			0
$892$	−6.26234e8	+	7.17304e8i	−0.882352	+	1.01067i
$893$			9.20702e8i			1.29290i
$894$		0			0
$895$			7.43666e7i			0.103731i
$896$	6.60162e8	+	9.06227e8i	0.917755	+	1.25983i
$897$		0			0
$898$	6.31502e7	+	2.36877e7i	0.0872059	+	0.0327110i
$899$	4.51503e8			0.621415
$900$		0			0
$901$		−	1.43716e8i		−	0.196485i
$902$	−9.57274e8	−	3.59074e8i	−1.30442	−	0.489287i
$903$		0			0
$904$	3.91930e8	+	7.27385e8i	0.530522	+	0.984598i
$905$	5.67804e8			0.766043
$906$		0			0
$907$	1.15315e9			1.54548			0.772742	−	0.634721i	$-0.218885\pi$
$907$	1.15315e9			1.54548			0.772742	+	0.634721i	$0.218885\pi$
$908$	2.83989e8	+	2.47933e8i	0.379353	+	0.331189i
$909$		0			0
$910$	−6.01272e8	+	1.60296e9i	−0.797897	+	2.12716i
$911$			1.01431e9i			1.34157i	0.741651	+	0.670786i	$0.234043\pi$
$911$			1.01431e9i			1.34157i	−0.741651	+	0.670786i	$0.765957\pi$
$912$		0			0
$913$	7.59776e8			0.998328
$914$	−5.71886e8	−	2.14515e8i	−0.748982	−	0.280943i
$915$		0			0
$916$	3.77665e7	−	4.32587e7i	0.0491383	−	0.0562843i
$917$			5.42077e8i			0.702996i
$918$		0			0
$919$			9.26580e8i			1.19381i	0.802311	+	0.596906i	$0.203604\pi$
$919$			9.26580e8i			1.19381i	−0.802311	+	0.596906i	$0.796396\pi$
$920$	−1.25688e7	−	2.33264e7i	−0.0161409	−	0.0299560i
$921$		0			0
$922$	−2.64365e8	+	7.04784e8i	−0.337296	+	0.899215i
$923$	1.53713e9			1.95481
$924$		0			0
$925$		−	3.25940e7i		−	0.0411824i
$926$	−4.40935e8	+	1.17551e9i	−0.555318	+	1.48045i
$927$		0			0
$928$	−4.24177e8	−	9.64131e7i	−0.530766	−	0.120640i
$929$	−2.42163e8			−0.302037			−0.151019	−	0.988531i	$-0.548255\pi$
$929$	−2.42163e8			−0.302037			−0.151019	+	0.988531i	$0.548255\pi$
$930$		0			0
$931$	−1.55407e9			−1.92585
$932$	−6.73243e8	−	5.87767e8i	−0.831619	−	0.726035i
$933$		0			0
$934$	−1.14070e9	−	4.27876e8i	−1.40000	−	0.525142i
$935$			2.89427e8i			0.354083i
$936$		0			0
$937$	−7.79217e8			−0.947196			−0.473598	−	0.880741i	$-0.657045\pi$
$937$	−7.79217e8			−0.947196			−0.473598	+	0.880741i	$0.657045\pi$
$938$	−4.68620e8	+	1.24932e9i	−0.567822	+	1.51379i
$939$		0			0
$940$	6.16545e8	+	5.38267e8i	0.742303	+	0.648059i
$941$		−	1.51961e9i		−	1.82375i	−0.410474	−	0.911873i	$-0.634637\pi$
$941$		−	1.51961e9i		−	1.82375i	0.410474	−	0.911873i	$-0.365363\pi$
$942$		0			0
$943$		−	2.84049e7i		−	0.0338734i
$944$	−9.56316e7	−	7.02172e8i	−0.113680	−	0.834694i
$945$		0			0
$946$	1.34886e8	+	5.05957e7i	0.159328	+	0.0597641i
$947$	−1.64620e9			−1.93836			−0.969178	−	0.246363i	$-0.920764\pi$
$947$	−1.64620e9			−1.93836			−0.969178	+	0.246363i	$0.920764\pi$
$948$		0			0
$949$		−	2.03830e9i		−	2.38490i
$950$	−5.88001e7	−	2.20560e7i	−0.0685816	−	0.0257250i
$951$		0			0
$952$	2.99531e8	−	1.61394e8i	0.347161	−	0.187058i
$953$	−1.51426e9			−1.74953			−0.874766	−	0.484545i	$-0.838985\pi$
$953$	−1.51426e9			−1.74953			−0.874766	+	0.484545i	$0.838985\pi$
$954$		0			0
$955$	3.51674e8			0.403767
$956$	4.53471e6	−	5.19417e6i	0.00519010	−	0.00594487i
$957$		0			0
$958$	1.09769e8	−	2.92638e8i	0.124848	−	0.332839i
$959$		−	1.79056e9i		−	2.03017i
$960$		0			0
$961$	−2.69279e8			−0.303412
$962$	8.96283e8	+	3.36196e8i	1.00675	+	0.377631i
$963$		0			0
$964$	3.64288e8	+	3.18037e8i	0.406643	+	0.355015i
$965$		−	1.31416e9i		−	1.46240i
$966$		0			0
$967$			5.59324e8i			0.618563i	0.950971	+	0.309282i	$0.100089\pi$
$967$			5.59324e8i			0.618563i	−0.950971	+	0.309282i	$0.899911\pi$
$968$	3.69004e8	+	6.84837e8i	0.406823	+	0.755024i
$969$		0			0
$970$	4.71123e8	−	1.25599e9i	0.516202	−	1.37617i
$971$	1.02653e9			1.12128			0.560640	−	0.828059i	$-0.310555\pi$
$971$	1.02653e9			1.12128			0.560640	+	0.828059i	$0.310555\pi$
$972$		0			0
$973$		−	2.31148e8i		−	0.250930i
$974$	−4.56425e8	+	1.21681e9i	−0.493961	+	1.31688i
$975$		0			0
$976$	5.85358e7	−	7.97223e6i	0.0629611	−	0.00857493i
$977$	−6.10029e7			−0.0654135			−0.0327067	−	0.999465i	$-0.510413\pi$
$977$	−6.10029e7			−0.0654135			−0.0327067	+	0.999465i	$0.510413\pi$
$978$		0			0
$979$	−3.57983e8			−0.381518
$980$	−9.08552e8	+	1.04068e9i	−0.965321	+	1.10570i
$981$		0			0
$982$	−1.11686e9	−	4.18933e8i	−1.17940	−	0.442395i
$983$			1.82313e9i			1.91936i	0.281093	+	0.959681i	$0.409303\pi$
$983$			1.82313e9i			1.91936i	−0.281093	+	0.959681i	$0.590697\pi$
$984$		0			0
$985$	−4.19393e8			−0.438846
$986$	−4.63618e7	+	1.23598e8i	−0.0483648	+	0.128938i
$987$		0			0
$988$	1.21301e9	−	1.38941e9i	1.25775	−	1.44066i
$989$			4.00243e6i			0.00413747i
$990$		0			0
$991$			2.67481e8i			0.274835i	0.990513	+	0.137417i	$0.0438802\pi$
$991$			2.67481e8i			0.274835i	−0.990513	+	0.137417i	$0.956120\pi$
$992$	1.08677e9	+	2.47017e8i	1.11328	+	0.253042i
$993$		0			0
$994$	1.97377e9	+	7.40363e8i	2.00973	+	0.753851i
$995$	1.70173e8			0.172751
$996$		0			0
$997$		−	9.95073e8i		−	1.00408i	−0.864844	−	0.502041i	$-0.832583\pi$
$997$		−	9.95073e8i		−	1.00408i	0.864844	−	0.502041i	$-0.167417\pi$
$998$	3.07823e8	+	1.15465e8i	0.309678	+	0.116160i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.c.19.12		12
3.2	odd	2		24.7.b.a.19.1	✓	12
4.3	odd	2		288.7.b.d.271.2		12
8.3	odd	2	inner	72.7.b.c.19.11		12
8.5	even	2		288.7.b.d.271.11		12
12.11	even	2		96.7.b.a.79.12		12
24.5	odd	2		96.7.b.a.79.7		12
24.11	even	2		24.7.b.a.19.2	yes	12
48.5	odd	4		768.7.g.l.511.23		24
48.11	even	4		768.7.g.l.511.21		24
48.29	odd	4		768.7.g.l.511.22		24
48.35	even	4		768.7.g.l.511.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.b.a.19.1	✓	12	3.2	odd	2
24.7.b.a.19.2	yes	12	24.11	even	2
72.7.b.c.19.11		12	8.3	odd	2	inner
72.7.b.c.19.12		12	1.1	even	1	trivial
96.7.b.a.79.7		12	24.5	odd	2
96.7.b.a.79.12		12	12.11	even	2
288.7.b.d.271.2		12	4.3	odd	2
288.7.b.d.271.11		12	8.5	even	2
768.7.g.l.511.21		24	48.11	even	4
768.7.g.l.511.22		24	48.29	odd	4
768.7.g.l.511.23		24	48.5	odd	4
768.7.g.l.511.24		24	48.35	even	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(7.49039 + 2.80965i) q^{2} +(48.2118 + 42.0907i) q^{4} -128.353i q^{5} -534.624i q^{7} +(242.865 + 450.734i) q^{8} +O(q^{10})\)	\(q+(7.49039 + 2.80965i) q^{2} +(48.2118 + 42.0907i) q^{4} -128.353i q^{5} -534.624i q^{7} +(242.865 + 450.734i) q^{8} +(360.627 - 961.414i) q^{10} -1814.10 q^{11} -3118.64i q^{13} +(1502.10 - 4004.54i) q^{14} +(552.748 + 4058.53i) q^{16} +1243.01 q^{17} +9240.87 q^{19} +(5402.47 - 6188.13i) q^{20} +(-13588.3 - 5096.97i) q^{22} -403.201i q^{23} -849.496 q^{25} +(8762.27 - 23359.8i) q^{26} +(22502.7 - 25775.2i) q^{28} +13275.0i q^{29} -34011.5i q^{31} +(-7262.75 + 31953.0i) q^{32} +(9310.60 + 3492.41i) q^{34} -68620.6 q^{35} +38368.6i q^{37} +(69217.7 + 25963.6i) q^{38} +(57853.0 - 31172.4i) q^{40} +70448.5 q^{41} -9926.62 q^{43} +(-87460.8 - 76356.5i) q^{44} +(1132.85 - 3020.13i) q^{46} +99633.6i q^{47} -168174. q^{49} +(-6363.05 - 2386.78i) q^{50} +(131266. - 150355. i) q^{52} -115619. i q^{53} +232845. i q^{55} +(240973. - 129841. i) q^{56} +(-37298.1 + 99435.0i) q^{58} -173011. q^{59} -14422.9i q^{61} +(95560.3 - 254759. i) q^{62} +(-144177. + 218935. i) q^{64} -400287. q^{65} -311976. q^{67} +(59927.5 + 52319.0i) q^{68} +(-513995. - 192800. i) q^{70} +492884. i q^{71} +653588. q^{73} +(-107802. + 287396. i) q^{74} +(445519. + 388955. i) q^{76} +969859. i q^{77} +334398. i q^{79} +(520925. - 70946.9i) q^{80} +(527686. + 197935. i) q^{82} -418818. q^{83} -159544. i q^{85} +(-74354.2 - 27890.3i) q^{86} +(-440580. - 817674. i) q^{88} +197334. q^{89} -1.66730e6 q^{91} +(16971.0 - 19439.1i) q^{92} +(-279935. + 746294. i) q^{94} -1.18609e6i q^{95} +1.30640e6 q^{97} +(-1.25968e6 - 472508. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) \) 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8} + 2172 q^{10} - 2720 q^{11} + 6444 q^{14} + 11640 q^{16} + 4888 q^{17} + 3936 q^{19} + 31608 q^{20} - 60432 q^{22} - 27204 q^{25} - 53952 q^{26} - 57072 q^{28} - 109480 q^{32} + 47388 q^{34} - 162336 q^{35} + 89080 q^{38} + 72120 q^{40} + 54280 q^{41} - 49824 q^{43} - 229184 q^{44} + 171864 q^{46} - 304644 q^{49} + 500078 q^{50} + 256848 q^{52} + 699816 q^{56} - 409524 q^{58} + 886144 q^{59} - 691356 q^{62} - 500640 q^{64} - 473376 q^{65} + 1565952 q^{67} - 669104 q^{68} + 473784 q^{70} + 555480 q^{73} + 753720 q^{74} - 293136 q^{76} + 251616 q^{80} + 2317716 q^{82} - 2497760 q^{83} - 476024 q^{86} + 971424 q^{88} - 367400 q^{89} - 4475808 q^{91} + 377376 q^{92} - 2642568 q^{94} - 1165656 q^{97} - 182674 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8 + 2172 * q^10 - 2720 * q^11 + 6444 * q^14 + 11640 * q^16 + 4888 * q^17 + 3936 * q^19 + 31608 * q^20 - 60432 * q^22 - 27204 * q^25 - 53952 * q^26 - 57072 * q^28 - 109480 * q^32 + 47388 * q^34 - 162336 * q^35 + 89080 * q^38 + 72120 * q^40 + 54280 * q^41 - 49824 * q^43 - 229184 * q^44 + 171864 * q^46 - 304644 * q^49 + 500078 * q^50 + 256848 * q^52 + 699816 * q^56 - 409524 * q^58 + 886144 * q^59 - 691356 * q^62 - 500640 * q^64 - 473376 * q^65 + 1565952 * q^67 - 669104 * q^68 + 473784 * q^70 + 555480 * q^73 + 753720 * q^74 - 293136 * q^76 + 251616 * q^80 + 2317716 * q^82 - 2497760 * q^83 - 476024 * q^86 + 971424 * q^88 - 367400 * q^89 - 4475808 * q^91 + 377376 * q^92 - 2642568 * q^94 - 1165656 * q^97 - 182674 * q^98

Introduction

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