LMFDB - Embedded newform 72.7.b.c.19.1

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			19.1
Root			$8.16014 - 0.886446i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.97364 - 0.648923i) q^{2} +(63.1578 + 10.3486i) q^{4} +232.265i q^{5} +483.645i q^{7} +(-496.882 - 123.500i) q^{8} +O(q^{10})$	\(q+(-7.97364 - 0.648923i) q^{2} +(63.1578 + 10.3486i) q^{4} +232.265i q^{5} +483.645i q^{7} +(-496.882 - 123.500i) q^{8} +(150.722 - 1852.00i) q^{10} +538.354 q^{11} +764.025i q^{13} +(313.849 - 3856.41i) q^{14} +(3881.81 + 1307.18i) q^{16} +4272.59 q^{17} -5001.25 q^{19} +(-2403.61 + 14669.4i) q^{20} +(-4292.64 - 349.350i) q^{22} -12638.4i q^{23} -38322.2 q^{25} +(495.793 - 6092.06i) q^{26} +(-5005.03 + 30546.0i) q^{28} +26153.1i q^{29} -16328.0i q^{31} +(-30103.9 - 12942.0i) q^{32} +(-34068.1 - 2772.58i) q^{34} -112334. q^{35} +46087.7i q^{37} +(39878.1 + 3245.43i) q^{38} +(28684.8 - 115409. i) q^{40} -53120.7 q^{41} +84385.9 q^{43} +(34001.2 + 5571.19i) q^{44} +(-8201.37 + 100774. i) q^{46} +115895. i q^{47} -116264. q^{49} +(305568. + 24868.2i) q^{50} +(-7906.55 + 48254.1i) q^{52} -158403. i q^{53} +125041. i q^{55} +(59730.3 - 240315. i) q^{56} +(16971.4 - 208535. i) q^{58} +2208.17 q^{59} -304462. i q^{61} +(-10595.6 + 130194. i) q^{62} +(231639. + 122730. i) q^{64} -177457. q^{65} +144392. q^{67} +(269847. + 44215.1i) q^{68} +(895712. + 72896.2i) q^{70} -15941.7i q^{71} -261094. q^{73} +(29907.4 - 367487. i) q^{74} +(-315868. - 51755.7i) q^{76} +260372. i q^{77} -337398. i q^{79} +(-303614. + 901611. i) q^{80} +(423565. + 34471.2i) q^{82} +461158. q^{83} +992374. i q^{85} +(-672862. - 54760.0i) q^{86} +(-267498. - 66486.8i) q^{88} -1.14120e6 q^{89} -369517. q^{91} +(130790. - 798216. i) q^{92} +(75206.8 - 924103. i) q^{94} -1.16162e6i q^{95} -288877. q^{97} +(927046. + 75446.3i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.97364	−	0.648923i	−0.996705	−	0.0811154i
$2$	−7.97364	−	0.648923i	−0.996705	−	0.0811154i
$3$		0			0
$3$		0			0
$4$	63.1578	+	10.3486i	0.986841	+	0.161696i
$5$			232.265i			1.85812i	0.369925	+	0.929062i	$0.379384\pi$
$5$			232.265i			1.85812i	−0.369925	+	0.929062i	$0.620616\pi$
$6$		0			0
$7$			483.645i			1.41004i	0.709185	+	0.705022i	$0.249063\pi$
$7$			483.645i			1.41004i	−0.709185	+	0.705022i	$0.750937\pi$
$8$	−496.882	−	123.500i	−0.970473	−	0.241211i
$9$		0			0
$10$	150.722	−	1852.00i	0.150722	−	1.85200i
$11$	538.354			0.404473			0.202237	−	0.979337i	$-0.435179\pi$
$11$	538.354			0.404473			0.202237	+	0.979337i	$0.435179\pi$
$12$		0			0
$13$			764.025i			0.347758i	0.984767	+	0.173879i	$0.0556302\pi$
$13$			764.025i			0.347758i	−0.984767	+	0.173879i	$0.944370\pi$
$14$	313.849	−	3856.41i	0.114376	−	1.40540i
$15$		0			0
$16$	3881.81	+	1307.18i	0.947709	+	0.319137i
$17$	4272.59			0.869649			0.434825	−	0.900515i	$-0.356810\pi$
$17$	4272.59			0.869649			0.434825	+	0.900515i	$0.356810\pi$
$18$		0			0
$19$	−5001.25			−0.729151			−0.364576	−	0.931174i	$-0.618786\pi$
$19$	−5001.25			−0.729151			−0.364576	+	0.931174i	$0.618786\pi$
$20$	−2403.61	+	14669.4i	−0.300452	+	1.83367i
$21$		0			0
$22$	−4292.64	−	349.350i	−0.403140	−	0.0328090i
$23$		−	12638.4i		−	1.03875i	−0.854547	−	0.519373i	$-0.826165\pi$
$23$		−	12638.4i		−	1.03875i	0.854547	−	0.519373i	$-0.173835\pi$
$24$		0			0
$25$	−38322.2			−2.45262
$26$	495.793	−	6092.06i	0.0282085	−	0.346612i
$27$		0			0
$28$	−5005.03	+	30546.0i	−0.227999	+	1.39149i
$29$			26153.1i			1.07233i	0.844113	+	0.536166i	$0.180128\pi$
$29$			26153.1i			1.07233i	−0.844113	+	0.536166i	$0.819872\pi$
$30$		0			0
$31$		−	16328.0i		−	0.548085i	−0.961718	−	0.274042i	$-0.911639\pi$
$31$		−	16328.0i		−	0.548085i	0.961718	−	0.274042i	$-0.0883609\pi$
$32$	−30103.9	−	12942.0i	−0.918699	−	0.394959i
$33$		0			0
$34$	−34068.1	−	2772.58i	−0.866784	−	0.0705420i
$35$	−112334.			−2.62004
$36$		0			0
$37$			46087.7i			0.909871i	0.890524	+	0.454936i	$0.150338\pi$
$37$			46087.7i			0.909871i	−0.890524	+	0.454936i	$0.849662\pi$
$38$	39878.1	+	3245.43i	0.726748	+	0.0591454i
$39$		0			0
$40$	28684.8	−	115409.i	0.448201	−	1.80326i
$41$	−53120.7			−0.770747			−0.385374	−	0.922761i	$-0.625927\pi$
$41$	−53120.7			−0.770747			−0.385374	+	0.922761i	$0.625927\pi$
$42$		0			0
$43$	84385.9			1.06136			0.530682	−	0.847571i	$-0.321936\pi$
$43$	84385.9			1.06136			0.530682	+	0.847571i	$0.321936\pi$
$44$	34001.2	+	5571.19i	0.399151	+	0.0654018i
$45$		0			0
$46$	−8201.37	+	100774.i	−0.0842584	+	1.03532i
$47$			115895.i			1.11627i	0.829749	+	0.558136i	$0.188483\pi$
$47$			115895.i			1.11627i	−0.829749	+	0.558136i	$0.811517\pi$
$48$		0			0
$49$	−116264.			−0.988227
$50$	305568.	+	24868.2i	2.44454	+	0.198946i
$51$		0			0
$52$	−7906.55	+	48254.1i	−0.0562312	+	0.343182i
$53$		−	158403.i		−	1.06398i	−0.846750	−	0.531992i	$-0.821444\pi$
$53$		−	158403.i		−	1.06398i	0.846750	−	0.531992i	$-0.178556\pi$
$54$		0			0
$55$			125041.i			0.751561i
$56$	59730.3	−	240315.i	0.340119	−	1.36841i
$57$		0			0
$58$	16971.4	−	208535.i	0.0869826	−	1.06880i
$59$	2208.17			0.0107517			0.00537583	−	0.999986i	$-0.498289\pi$
$59$	2208.17			0.0107517			0.00537583	+	0.999986i	$0.498289\pi$
$60$		0			0
$61$		−	304462.i		−	1.34135i	−0.741750	−	0.670676i	$-0.766004\pi$
$61$		−	304462.i		−	1.34135i	0.741750	−	0.670676i	$-0.233996\pi$
$62$	−10595.6	+	130194.i	−0.0444581	+	0.546279i
$63$		0			0
$64$	231639.	+	122730.i	0.883634	+	0.468178i
$65$	−177457.			−0.646178
$66$		0			0
$67$	144392.			0.480085			0.240043	−	0.970762i	$-0.422839\pi$
$67$	144392.			0.480085			0.240043	+	0.970762i	$0.422839\pi$
$68$	269847.	+	44215.1i	0.858205	+	0.140619i
$69$		0			0
$70$	895712.	+	72896.2i	2.61140	+	0.212525i
$71$		−	15941.7i		−	0.0445410i	−0.999752	−	0.0222705i	$-0.992910\pi$
$71$		−	15941.7i		−	0.0445410i	0.999752	−	0.0222705i	$-0.00708951\pi$
$72$		0			0
$73$	−261094.			−0.671165			−0.335582	−	0.942011i	$-0.608933\pi$
$73$	−261094.			−0.671165			−0.335582	+	0.942011i	$0.608933\pi$
$74$	29907.4	−	367487.i	0.0738046	−	0.906873i
$75$		0			0
$76$	−315868.	−	51755.7i	−0.719556	−	0.117901i
$77$			260372.i			0.570325i
$78$		0			0
$79$		−	337398.i		−	0.684322i	−0.939641	−	0.342161i	$-0.888841\pi$
$79$		−	337398.i		−	0.684322i	0.939641	−	0.342161i	$-0.111159\pi$
$80$	−303614.	+	901611.i	−0.592996	+	1.76096i
$81$		0			0
$82$	423565.	+	34471.2i	0.768207	+	0.0625195i
$83$	461158.			0.806521			0.403261	−	0.915085i	$-0.367877\pi$
$83$	461158.			0.806521			0.403261	+	0.915085i	$0.367877\pi$
$84$		0			0
$85$			992374.i			1.61592i
$86$	−672862.	−	54760.0i	−1.05787	−	0.0860930i
$87$		0			0
$88$	−267498.	−	66486.8i	−0.392530	−	0.0975636i
$89$	−1.14120e6			−1.61879			−0.809397	−	0.587262i	$-0.800206\pi$
$89$	−1.14120e6			−1.61879			−0.809397	+	0.587262i	$0.800206\pi$
$90$		0			0
$91$	−369517.			−0.490355
$92$	130790.	−	798216.i	0.167961	−	1.02508i
$93$		0			0
$94$	75206.8	−	924103.i	0.0905469	−	1.11259i
$95$		−	1.16162e6i		−	1.35485i
$96$		0			0
$97$	−288877.			−0.316518			−0.158259	−	0.987398i	$-0.550588\pi$
$97$	−288877.			−0.316518			−0.158259	+	0.987398i	$0.550588\pi$
$98$	927046.	+	75446.3i	0.984970	+	0.0801604i
$99$		0			0
$100$	−2.42035e6	−	396580.i	−2.42035	−	0.396580i
$101$			1.56920e6i			1.52305i	0.648135	+	0.761525i	$0.275549\pi$
$101$			1.56920e6i			1.52305i	−0.648135	+	0.761525i	$0.724451\pi$
$102$		0			0
$103$			76467.5i			0.0699786i	0.999388	+	0.0349893i	$0.0111397\pi$
$103$			76467.5i			0.0699786i	−0.999388	+	0.0349893i	$0.988860\pi$
$104$	94357.2	−	379630.i	0.0838832	−	0.337490i
$105$		0			0
$106$	−102791.	+	1.26305e6i	−0.0863055	+	1.06048i
$107$	1.43813e6			1.17394			0.586970	−	0.809609i	$-0.300321\pi$
$107$	1.43813e6			1.17394			0.586970	+	0.809609i	$0.300321\pi$
$108$		0			0
$109$		−	543912.i		−	0.420000i	−0.977701	−	0.210000i	$-0.932654\pi$
$109$		−	543912.i		−	0.420000i	0.977701	−	0.210000i	$-0.0673464\pi$
$110$	81142.0	−	997032.i	0.0609632	−	0.749085i
$111$		0			0
$112$	−632214.	+	1.87742e6i	−0.449997	+	1.33631i
$113$	−460059.			−0.318844			−0.159422	−	0.987211i	$-0.550963\pi$
$113$	−460059.			−0.318844			−0.159422	+	0.987211i	$0.550963\pi$
$114$		0			0
$115$	2.93547e6			1.93012
$116$	−270647.	+	1.65177e6i	−0.173392	+	1.05822i
$117$		0			0
$118$	−17607.1	−	1432.93i	−0.0107162	−	0.000872126i
$119$			2.06642e6i			1.22624i
$120$		0			0
$121$	−1.48174e6			−0.836401
$122$	−197572.	+	2.42767e6i	−0.108804	+	1.33693i
$123$		0			0
$124$	168971.	−	1.03124e6i	0.0886233	−	0.540873i
$125$		−	5.27178e6i		−	2.69915i
$126$		0			0
$127$		−	722384.i		−	0.352660i	−0.984331	−	0.176330i	$-0.943577\pi$
$127$		−	722384.i		−	0.352660i	0.984331	−	0.176330i	$-0.0564227\pi$
$128$	−1.76737e6	−	1.12892e6i	−0.842746	−	0.538312i
$129$		0			0
$130$	1.41497e6	+	115156.i	0.644048	+	0.0524150i
$131$	−8824.80			−0.00392546			−0.00196273	−	0.999998i	$-0.500625\pi$
$131$	−8824.80			−0.00392546			−0.00196273	+	0.999998i	$0.500625\pi$
$132$		0			0
$133$		−	2.41883e6i		−	1.02814i
$134$	−1.15133e6	−	93699.2i	−0.478503	−	0.0389423i
$135$		0			0
$136$	−2.12297e6	−	527665.i	−0.843971	−	0.209769i
$137$	2.68929e6			1.04586			0.522932	−	0.852374i	$-0.324838\pi$
$137$	2.68929e6			1.04586			0.522932	+	0.852374i	$0.324838\pi$
$138$		0			0
$139$	3.79511e6			1.41312			0.706562	−	0.707651i	$-0.250245\pi$
$139$	3.79511e6			1.41312			0.706562	+	0.707651i	$0.250245\pi$
$140$	−7.09478e6	−	1.16250e6i	−2.58556	−	0.423650i
$141$		0			0
$142$	−10345.0	+	127114.i	−0.00361297	+	0.0443943i
$143$			411316.i			0.140659i
$144$		0			0
$145$	−6.07446e6			−1.99253
$146$	2.08187e6	+	169430.i	0.668953	+	0.0544418i
$147$		0			0
$148$	−476941.	+	2.91080e6i	−0.147123	+	0.897898i
$149$			4.11786e6i			1.24484i	0.782684	+	0.622420i	$0.213850\pi$
$149$			4.11786e6i			1.24484i	−0.782684	+	0.622420i	$0.786150\pi$
$150$		0			0
$151$			6.35829e6i			1.84676i	0.383891	+	0.923379i	$0.374584\pi$
$151$			6.35829e6i			1.84676i	−0.383891	+	0.923379i	$0.625416\pi$
$152$	2.48503e6	+	617655.i	0.707621	+	0.175880i
$153$		0			0
$154$	168962.	−	2.07612e6i	0.0462622	−	0.568446i
$155$	3.79243e6			1.01841
$156$		0			0
$157$			4.68450e6i			1.21050i	0.796036	+	0.605249i	$0.206926\pi$
$157$			4.68450e6i			1.21050i	−0.796036	+	0.605249i	$0.793074\pi$
$158$	−218945.	+	2.69029e6i	−0.0555091	+	0.682067i
$159$		0			0
$160$	3.00598e6	−	6.99210e6i	0.733883	−	1.70706i
$161$	6.11252e6			1.46468
$162$		0			0
$163$	2.93670e6			0.678104			0.339052	−	0.940768i	$-0.389894\pi$
$163$	2.93670e6			0.678104			0.339052	+	0.940768i	$0.389894\pi$
$164$	−3.35498e6	−	549722.i	−0.760605	−	0.124627i
$165$		0			0
$166$	−3.67711e6	−	299256.i	−0.803864	−	0.0654213i
$167$		−	2.44641e6i		−	0.525267i	−0.964896	−	0.262634i	$-0.915409\pi$
$167$		−	2.44641e6i		−	0.525267i	0.964896	−	0.262634i	$-0.0845911\pi$
$168$		0			0
$169$	4.24308e6			0.879064
$170$	643975.	−	7.91283e6i	0.131076	−	1.61059i
$171$		0			0
$172$	5.32963e6	+	873272.i	1.04740	+	0.171619i
$173$			686911.i			0.132667i	0.997798	+	0.0663334i	$0.0211301\pi$
$173$			686911.i			0.132667i	−0.997798	+	0.0663334i	$0.978870\pi$
$174$		0			0
$175$		−	1.85344e7i		−	3.45831i
$176$	2.08979e6	+	703728.i	0.383323	+	0.129082i
$177$		0			0
$178$	9.09951e6	+	740551.i	1.61346	+	0.131309i
$179$	−166953.			−0.0291096			−0.0145548	−	0.999894i	$-0.504633\pi$
$179$	−166953.			−0.0291096			−0.0145548	+	0.999894i	$0.504633\pi$
$180$		0			0
$181$			2.04866e6i			0.345489i	0.984967	+	0.172745i	$0.0552635\pi$
$181$			2.04866e6i			0.345489i	−0.984967	+	0.172745i	$0.944736\pi$
$182$	2.94639e6	+	239788.i	0.488739	+	0.0397753i
$183$		0			0
$184$	−1.56085e6	+	6.27981e6i	−0.250558	+	1.00808i
$185$	−1.07046e7			−1.69065
$186$		0			0
$187$	2.30016e6			0.351750
$188$	−1.19934e6	+	7.31966e6i	−0.180497	+	1.10158i
$189$		0			0
$190$	−753800.	+	9.26231e6i	−0.109899	+	1.35039i
$191$		−	1.08350e7i		−	1.55499i	−0.628886	−	0.777497i	$-0.716489\pi$
$191$		−	1.08350e7i		−	1.55499i	0.628886	−	0.777497i	$-0.283511\pi$
$192$		0			0
$193$	2.59024e6			0.360303			0.180152	−	0.983639i	$-0.442341\pi$
$193$	2.59024e6			0.360303			0.180152	+	0.983639i	$0.442341\pi$
$194$	2.30340e6	+	187459.i	0.315475	+	0.0256745i
$195$		0			0
$196$	−7.34297e6	−	1.20316e6i	−0.975222	−	0.159793i
$197$			2.14817e6i			0.280977i	0.990082	+	0.140488i	$0.0448672\pi$
$197$			2.14817e6i			0.280977i	−0.990082	+	0.140488i	$0.955133\pi$
$198$		0			0
$199$			1.31512e7i			1.66880i	0.551157	+	0.834401i	$0.314186\pi$
$199$			1.31512e7i			1.66880i	−0.551157	+	0.834401i	$0.685814\pi$
$200$	1.90416e7	+	4.73281e6i	2.38020	+	0.591601i
$201$		0			0
$202$	1.01829e6	−	1.25122e7i	0.123543	−	1.51803i
$203$	−1.26488e7			−1.51204
$204$		0			0
$205$		−	1.23381e7i		−	1.43214i
$206$	49621.5	−	609724.i	0.00567634	−	0.0697480i
$207$		0			0
$208$	−998721.	+	2.96580e6i	−0.110982	+	0.329573i
$209$	−2.69244e6			−0.294922
$210$		0			0
$211$	−1.68096e7			−1.78941			−0.894706	−	0.446655i	$-0.852615\pi$
$211$	−1.68096e7			−1.78941			−0.894706	+	0.446655i	$0.852615\pi$
$212$	1.63924e6	−	1.00044e7i	0.172042	−	1.04998i
$213$		0			0
$214$	−1.14671e7	−	933234.i	−1.17007	−	0.0952246i
$215$			1.95999e7i			1.97215i
$216$		0			0
$217$	7.89696e6			0.772824
$218$	−352957.	+	4.33696e6i	−0.0340685	+	0.418616i
$219$		0			0
$220$	−1.29399e6	+	7.89732e6i	−0.121525	+	0.741671i
$221$			3.26436e6i			0.302428i
$222$		0			0
$223$			1.39327e7i			1.25638i	0.778060	+	0.628190i	$0.216204\pi$
$223$			1.39327e7i			1.25638i	−0.778060	+	0.628190i	$0.783796\pi$
$224$	6.25935e6	−	1.45596e7i	0.556910	−	1.29541i
$225$		0			0
$226$	3.66834e6	+	298543.i	0.317793	+	0.0258632i
$227$	3.05829e6			0.261458			0.130729	−	0.991418i	$-0.458268\pi$
$227$	3.05829e6			0.261458			0.130729	+	0.991418i	$0.458268\pi$
$228$		0			0
$229$			1.32328e7i			1.10191i	0.834536	+	0.550953i	$0.185736\pi$
$229$			1.32328e7i			1.10191i	−0.834536	+	0.550953i	$0.814264\pi$
$230$	−2.34064e7	−	1.90490e6i	−1.92376	−	0.156563i
$231$		0			0
$232$	3.22991e6	−	1.29950e7i	0.258659	−	1.04067i
$233$	−1.86949e7			−1.47794			−0.738969	−	0.673739i	$-0.764687\pi$
$233$	−1.86949e7			−1.47794			−0.738969	+	0.673739i	$0.764687\pi$
$234$		0			0
$235$	−2.69183e7			−2.07417
$236$	139463.	+	22851.3i	0.0106102	+	0.00173850i
$237$		0			0
$238$	1.34095e6	−	1.64769e7i	0.0994673	−	1.22220i
$239$			9.85321e6i			0.721745i	0.932615	+	0.360873i	$0.117521\pi$
$239$			9.85321e6i			0.721745i	−0.932615	+	0.360873i	$0.882479\pi$
$240$		0			0
$241$	−1.31011e7			−0.935957			−0.467979	−	0.883740i	$-0.655018\pi$
$241$	−1.31011e7			−0.935957			−0.467979	+	0.883740i	$0.655018\pi$
$242$	1.18148e7	+	961533.i	0.833645	+	0.0678450i
$243$		0			0
$244$	3.15074e6	−	1.92291e7i	0.216892	−	1.32370i
$245$		−	2.70041e7i		−	1.83625i
$246$		0			0
$247$		−	3.82108e6i		−	0.253568i
$248$	−2.01651e6	+	8.11309e6i	−0.132204	+	0.531901i
$249$		0			0
$250$	−3.42098e6	+	4.20353e7i	−0.218943	+	2.69026i
$251$	−3.11163e6			−0.196774			−0.0983869	−	0.995148i	$-0.531368\pi$
$251$	−3.11163e6			−0.196774			−0.0983869	+	0.995148i	$0.531368\pi$
$252$		0			0
$253$		−	6.80395e6i		−	0.420145i
$254$	−468772.	+	5.76003e6i	−0.0286062	+	0.351498i
$255$		0			0
$256$	1.33598e7	+	1.01485e7i	0.796303	+	0.604897i
$257$	1.22031e7			0.718903			0.359451	−	0.933164i	$-0.382964\pi$
$257$	1.22031e7			0.718903			0.359451	+	0.933164i	$0.382964\pi$
$258$		0			0
$259$	−2.22901e7			−1.28296
$260$	−1.12078e7	−	1.83642e6i	−0.637674	−	0.104484i
$261$		0			0
$262$	70365.7	+	5726.62i	0.00391253	+	0.000318416i
$263$		−	1.25288e7i		−	0.688721i	−0.938837	−	0.344361i	$-0.888096\pi$
$263$		−	1.25288e7i		−	0.688721i	0.938837	−	0.344361i	$-0.111904\pi$
$264$		0			0
$265$	3.67915e7			1.97701
$266$	−1.56964e6	+	1.92869e7i	−0.0833977	+	1.02475i
$267$		0			0
$268$	9.11947e6	+	1.49425e6i	0.473767	+	0.0776279i
$269$			2.56365e7i			1.31705i	0.752559	+	0.658525i	$0.228819\pi$
$269$			2.56365e7i			1.31705i	−0.752559	+	0.658525i	$0.771181\pi$
$270$		0			0
$271$		−	2.07798e7i		−	1.04408i	−0.852921	−	0.522040i	$-0.825171\pi$
$271$		−	2.07798e7i		−	1.04408i	0.852921	−	0.522040i	$-0.174829\pi$
$272$	1.65854e7	+	5.58506e6i	0.824174	+	0.277537i
$273$		0			0
$274$	−2.14434e7	−	1.74514e6i	−1.04242	−	0.0848357i
$275$	−2.06309e7			−0.992021
$276$		0			0
$277$		−	1.52965e7i		−	0.719702i	−0.933010	−	0.359851i	$-0.882828\pi$
$277$		−	1.52965e7i		−	0.719702i	0.933010	−	0.359851i	$-0.117172\pi$
$278$	−3.02608e7	−	2.46274e6i	−1.40847	−	0.114626i
$279$		0			0
$280$	5.58168e7	+	1.38733e7i	2.54267	+	0.631983i
$281$	3.18478e7			1.43536			0.717679	−	0.696374i	$-0.245204\pi$
$281$	3.18478e7			1.43536			0.717679	+	0.696374i	$0.245204\pi$
$282$		0			0
$283$	3.43882e7			1.51723			0.758614	−	0.651541i	$-0.225877\pi$
$283$	3.43882e7			1.51723			0.758614	+	0.651541i	$0.225877\pi$
$284$	164974.	−	1.00684e6i	0.00720212	−	0.0439549i
$285$		0			0
$286$	266912.	−	3.27968e6i	0.0114096	−	0.140195i
$287$		−	2.56916e7i		−	1.08679i
$288$		0			0
$289$	−5.88257e6			−0.243710
$290$	4.84356e7	+	3.94186e6i	1.98596	+	0.161625i
$291$		0			0
$292$	−1.64902e7	−	2.70195e6i	−0.662333	−	0.108525i
$293$		−	846373.i		−	0.0336480i	−0.999858	−	0.0168240i	$-0.994645\pi$
$293$		−	846373.i		−	0.0336480i	0.999858	−	0.0168240i	$-0.00535550\pi$
$294$		0			0
$295$			512881.i			0.0199779i
$296$	5.69184e6	−	2.29002e7i	0.219471	−	0.883005i
$297$		0			0
$298$	2.67218e6	−	3.28344e7i	0.100976	−	1.24074i
$299$	9.65607e6			0.361233
$300$		0			0
$301$			4.08128e7i			1.49657i
$302$	4.12605e6	−	5.06987e7i	0.149800	−	1.84067i
$303$		0			0
$304$	−1.94139e7	−	6.53755e6i	−0.691023	−	0.232699i
$305$	7.07159e7			2.49240
$306$		0			0
$307$	2.68661e7			0.928517			0.464258	−	0.885700i	$-0.346321\pi$
$307$	2.68661e7			0.928517			0.464258	+	0.885700i	$0.346321\pi$
$308$	−2.69448e6	+	1.64445e7i	−0.0922195	+	0.562820i
$309$		0			0
$310$	−3.02395e7	−	2.46100e6i	−1.01505	−	0.0826087i
$311$			8.05278e6i			0.267710i	0.991001	+	0.133855i	$0.0427356\pi$
$311$			8.05278e6i			0.267710i	−0.991001	+	0.133855i	$0.957264\pi$
$312$		0			0
$313$	3.46861e7			1.13116			0.565578	−	0.824695i	$-0.308653\pi$
$313$	3.46861e7			1.13116			0.565578	+	0.824695i	$0.308653\pi$
$314$	3.03988e6	−	3.73525e7i	0.0981900	−	1.20651i
$315$		0			0
$316$	3.49158e6	−	2.13093e7i	0.110652	−	0.675317i
$317$			1.24867e7i			0.391985i	0.980605	+	0.195992i	$0.0627928\pi$
$317$			1.24867e7i			0.391985i	−0.980605	+	0.195992i	$0.937207\pi$
$318$		0			0
$319$			1.40796e7i			0.433730i
$320$	−2.85060e7	+	5.38018e7i	−0.869933	+	1.64190i
$321$		0			0
$322$	−4.87390e7	−	3.96656e6i	−1.45985	−	0.118808i
$323$	−2.13683e7			−0.634106
$324$		0			0
$325$		−	2.92791e7i		−	0.852920i
$326$	−2.34162e7	−	1.90569e6i	−0.675870	−	0.0550047i
$327$		0			0
$328$	2.63947e7	+	6.56041e6i	0.747989	+	0.185913i
$329$	−5.60519e7			−1.57399
$330$		0			0
$331$	−619532.			−0.0170836			−0.00854181	−	0.999964i	$-0.502719\pi$
$331$	−619532.			−0.0170836			−0.00854181	+	0.999964i	$0.502719\pi$
$332$	2.91258e7	+	4.77233e6i	0.795908	+	0.130411i
$333$		0			0
$334$	−1.58753e6	+	1.95068e7i	−0.0426073	+	0.523536i
$335$			3.35372e7i			0.892057i
$336$		0			0
$337$	2.24155e6			0.0585676			0.0292838	−	0.999571i	$-0.490677\pi$
$337$	2.24155e6			0.0585676			0.0292838	+	0.999571i	$0.490677\pi$
$338$	−3.38327e7	−	2.75343e6i	−0.876168	−	0.0713057i
$339$		0			0
$340$	−1.02696e7	+	6.26762e7i	−0.261288	+	1.59465i
$341$		−	8.79024e6i		−	0.221686i
$342$		0			0
$343$			669909.i			0.0166010i
$344$	−4.19298e7	−	1.04217e7i	−1.03002	−	0.256013i
$345$		0			0
$346$	445753.	−	5.47718e6i	0.0107613	−	0.132230i
$347$	1.03912e7			0.248702			0.124351	−	0.992238i	$-0.460315\pi$
$347$	1.03912e7			0.248702			0.124351	+	0.992238i	$0.460315\pi$
$348$		0			0
$349$		−	1.11263e6i		−	0.0261742i	−0.999914	−	0.0130871i	$-0.995834\pi$
$349$		−	1.11263e6i		−	0.0261742i	0.999914	−	0.0130871i	$-0.00416587\pi$
$350$	−1.20274e7	+	1.47786e8i	−0.280522	+	3.44691i
$351$		0			0
$352$	−1.62066e7	−	6.96738e6i	−0.371589	−	0.159750i
$353$	2.30608e7			0.524265			0.262132	−	0.965032i	$-0.415574\pi$
$353$	2.30608e7			0.524265			0.262132	+	0.965032i	$0.415574\pi$
$354$		0			0
$355$	3.70271e6			0.0827628
$356$	−7.20756e7	−	1.18098e7i	−1.59749	−	0.261753i
$357$		0			0
$358$	1.33123e6	+	108340.i	0.0290137	+	0.00236124i
$359$		−	5.61370e7i		−	1.21329i	−0.794972	−	0.606647i	$-0.792514\pi$
$359$		−	5.61370e7i		−	1.21329i	0.794972	−	0.606647i	$-0.207486\pi$
$360$		0			0
$361$	−2.20334e7			−0.468338
$362$	1.32942e6	−	1.63353e7i	0.0280245	−	0.344351i
$363$		0			0
$364$	−2.33379e7	−	3.82397e6i	−0.483902	−	0.0792885i
$365$		−	6.06432e7i		−	1.24711i
$366$		0			0
$367$			1.22476e7i			0.247772i	0.992296	+	0.123886i	$0.0395357\pi$
$367$			1.22476e7i			0.247772i	−0.992296	+	0.123886i	$0.960464\pi$
$368$	1.65208e7	−	4.90601e7i	0.331502	−	0.984429i
$369$		0			0
$370$	8.53545e7	+	6.94645e6i	1.68508	+	0.137138i
$371$	7.66107e7			1.50026
$372$		0			0
$373$		−	6.52783e7i		−	1.25789i	−0.777450	−	0.628944i	$-0.783487\pi$
$373$		−	6.52783e7i		−	1.25789i	0.777450	−	0.628944i	$-0.216513\pi$
$374$	−1.83407e7	−	1.49263e6i	−0.350591	−	0.0285323i
$375$		0			0
$376$	1.43130e7	−	5.75860e7i	0.269258	−	1.08331i
$377$	−1.99816e7			−0.372912
$378$		0			0
$379$	−9.94190e7			−1.82621			−0.913107	−	0.407719i	$-0.866324\pi$
$379$	−9.94190e7			−1.82621			−0.913107	+	0.407719i	$0.866324\pi$
$380$	1.20211e7	−	7.33652e7i	0.219075	−	1.33702i
$381$		0			0
$382$	−7.03109e6	+	8.63944e7i	−0.126134	+	1.54987i
$383$			6.77081e7i			1.20516i	0.798059	+	0.602579i	$0.205860\pi$
$383$			6.77081e7i			1.20516i	−0.798059	+	0.602579i	$0.794140\pi$
$384$		0			0
$385$	−6.04755e7			−1.05974
$386$	−2.06536e7	−	1.68087e6i	−0.359116	−	0.0292261i
$387$		0			0
$388$	−1.82448e7	−	2.98946e6i	−0.312352	−	0.0511797i
$389$			2.32668e7i			0.395264i	0.980276	+	0.197632i	$0.0633251\pi$
$389$			2.32668e7i			0.395264i	−0.980276	+	0.197632i	$0.936675\pi$
$390$		0			0
$391$		−	5.39988e7i		−	0.903346i
$392$	5.77694e7	+	1.43586e7i	0.959047	+	0.238372i
$393$		0			0
$394$	1.39400e6	−	1.71287e7i	0.0227915	−	0.280051i
$395$	7.83658e7			1.27156
$396$		0			0
$397$			9.30870e7i			1.48771i	0.668342	+	0.743854i	$0.267004\pi$
$397$			9.30870e7i			1.48771i	−0.668342	+	0.743854i	$0.732996\pi$
$398$	8.53410e6	−	1.04863e8i	0.135366	−	1.66330i
$399$		0			0
$400$	−1.48760e8	−	5.00942e7i	−2.32437	−	0.782722i
$401$	1.32398e6			0.0205328			0.0102664	−	0.999947i	$-0.496732\pi$
$401$	1.32398e6			0.0205328			0.0102664	+	0.999947i	$0.496732\pi$
$402$		0			0
$403$	1.24750e7			0.190601
$404$	−1.62390e7	+	9.91073e7i	−0.246272	+	1.50301i
$405$		0			0
$406$	1.00857e8	+	8.20812e6i	1.50705	+	0.122649i
$407$			2.48115e7i			0.368019i
$408$		0			0
$409$	3.00825e7			0.439687			0.219844	−	0.975535i	$-0.429445\pi$
$409$	3.00825e7			0.439687			0.219844	+	0.975535i	$0.429445\pi$
$410$	−8.00648e6	+	9.83795e7i	−0.116169	+	1.42742i
$411$		0			0
$412$	−791328.	+	4.82952e6i	−0.0113153	+	0.0690577i
$413$			1.06797e6i			0.0151603i
$414$		0			0
$415$			1.07111e8i			1.49862i
$416$	9.88802e6	−	2.30001e7i	0.137350	−	0.319485i
$417$		0			0
$418$	2.14686e7	+	1.74719e6i	0.293950	+	0.0239227i
$419$	−7.44264e7			−1.01178			−0.505888	−	0.862599i	$-0.668835\pi$
$419$	−7.44264e7			−1.01178			−0.505888	+	0.862599i	$0.668835\pi$
$420$		0			0
$421$			1.27370e8i			1.70695i	0.521133	+	0.853476i	$0.325510\pi$
$421$			1.27370e8i			1.70695i	−0.521133	+	0.853476i	$0.674490\pi$
$422$	1.34034e8	+	1.09082e7i	1.78352	+	0.145149i
$423$		0			0
$424$	−1.95628e7	+	7.87074e7i	−0.256645	+	1.03257i
$425$	−1.63735e8			−2.13292
$426$		0			0
$427$	1.47251e8			1.89137
$428$	9.08289e7	+	1.48825e7i	1.15849	+	0.189822i
$429$		0			0
$430$	1.27188e7	−	1.56283e8i	0.159971	−	1.96565i
$431$		−	6.99576e7i		−	0.873782i	−0.899514	−	0.436891i	$-0.856080\pi$
$431$		−	6.99576e7i		−	0.873782i	0.899514	−	0.436891i	$-0.143920\pi$
$432$		0			0
$433$	−1.17963e8			−1.45305			−0.726527	−	0.687137i	$-0.758867\pi$
$433$	−1.17963e8			−1.45305			−0.726527	+	0.687137i	$0.758867\pi$
$434$	−6.29675e7	−	5.12452e6i	−0.770278	−	0.0626880i
$435$		0			0
$436$	5.62871e6	−	3.43523e7i	0.0679124	−	0.414473i
$437$			6.32079e7i			0.757404i
$438$		0			0
$439$		−	1.28777e8i		−	1.52211i	−0.648688	−	0.761054i	$-0.724682\pi$
$439$		−	1.28777e8i		−	1.52211i	0.648688	−	0.761054i	$-0.275318\pi$
$440$	1.54426e7	−	6.21306e7i	0.181285	−	0.729370i
$441$		0			0
$442$	2.11832e6	−	2.60288e7i	0.0245315	−	0.301431i
$443$	2.43763e6			0.0280386			0.0140193	−	0.999902i	$-0.495537\pi$
$443$	2.43763e6			0.0280386			0.0140193	+	0.999902i	$0.495537\pi$
$444$		0			0
$445$		−	2.65061e8i		−	3.00792i
$446$	9.04126e6	−	1.11094e8i	0.101912	−	1.25224i
$447$		0			0
$448$	−5.93578e7	+	1.12031e8i	−0.660152	+	1.24596i
$449$	−1.16849e8			−1.29088			−0.645442	−	0.763809i	$-0.723327\pi$
$449$	−1.16849e8			−1.29088			−0.645442	+	0.763809i	$0.723327\pi$
$450$		0			0
$451$	−2.85977e7			−0.311747
$452$	−2.90563e7	−	4.76095e6i	−0.314648	−	0.0515559i
$453$		0			0
$454$	−2.43857e7	−	1.98460e6i	−0.260596	−	0.0212083i
$455$		−	8.58260e7i		−	0.911139i
$456$		0			0
$457$	7.71566e7			0.808396			0.404198	−	0.914671i	$-0.367551\pi$
$457$	7.71566e7			0.808396			0.404198	+	0.914671i	$0.367551\pi$
$458$	8.58705e6	−	1.05513e8i	0.0893815	−	1.09827i
$459$		0			0
$460$	1.85398e8	+	3.03779e7i	1.90472	+	0.312093i
$461$			1.03556e8i			1.05699i	0.848935	+	0.528497i	$0.177244\pi$
$461$			1.03556e8i			1.05699i	−0.848935	+	0.528497i	$0.822756\pi$
$462$		0			0
$463$			1.46124e8i			1.47224i	0.676853	+	0.736118i	$0.263343\pi$
$463$			1.46124e8i			1.47224i	−0.676853	+	0.736118i	$0.736657\pi$
$464$	−3.41869e7	+	1.01521e8i	−0.342221	+	1.01626i
$465$		0			0
$466$	1.49067e8	+	1.21316e7i	1.47307	+	0.119884i
$467$	−1.85335e8			−1.81973			−0.909864	−	0.414907i	$-0.863814\pi$
$467$	−1.85335e8			−1.81973			−0.909864	+	0.414907i	$0.863814\pi$
$468$		0			0
$469$			6.98344e7i			0.676941i
$470$	2.14637e8	+	1.74679e7i	2.06734	+	0.168247i
$471$		0			0
$472$	−1.09720e6	−	272709.i	−0.0104342	−	0.00259342i
$473$	4.54295e7			0.429293
$474$		0			0
$475$	1.91659e8			1.78833
$476$	−2.13844e7	+	1.30510e8i	−0.198279	+	1.21011i
$477$		0			0
$478$	6.39398e6	−	7.85659e7i	0.0585447	−	0.719367i
$479$			4.87900e7i			0.443940i	0.975054	+	0.221970i	$0.0712487\pi$
$479$			4.87900e7i			0.443940i	−0.975054	+	0.221970i	$0.928751\pi$
$480$		0			0
$481$	−3.52121e7			−0.316415
$482$	1.04463e8	+	8.50159e6i	0.932873	+	0.0759205i
$483$		0			0
$484$	−9.35832e7	−	1.53338e7i	−0.825395	−	0.135243i
$485$		−	6.70962e7i		−	0.588129i
$486$		0			0
$487$		−	1.86223e8i		−	1.61230i	−0.591712	−	0.806150i	$-0.701548\pi$
$487$		−	1.86223e8i		−	1.61230i	0.591712	−	0.806150i	$-0.298452\pi$
$488$	−3.76011e7	+	1.51281e8i	−0.323550	+	1.30175i
$489$		0			0
$490$	−1.75236e7	+	2.15321e8i	−0.148948	+	1.83020i
$491$	1.49162e8			1.26012			0.630061	−	0.776545i	$-0.283030\pi$
$491$	1.49162e8			1.26012			0.630061	+	0.776545i	$0.283030\pi$
$492$		0			0
$493$			1.11741e8i			0.932553i
$494$	−2.47959e6	+	3.04679e7i	−0.0205683	+	0.252733i
$495$		0			0
$496$	2.13437e7	−	6.33823e7i	0.174914	−	0.519425i
$497$	7.71014e6			0.0628049
$498$		0			0
$499$	6.57207e7			0.528933			0.264466	−	0.964395i	$-0.414804\pi$
$499$	6.57207e7			0.528933			0.264466	+	0.964395i	$0.414804\pi$
$500$	5.45554e7	−	3.32954e8i	0.436443	−	2.66363i
$501$		0			0
$502$	2.48110e7	+	2.01921e6i	0.196125	+	0.0159614i
$503$			1.22782e8i			0.964782i	0.875956	+	0.482391i	$0.160232\pi$
$503$			1.22782e8i			0.964782i	−0.875956	+	0.482391i	$0.839768\pi$
$504$		0			0
$505$	−3.64471e8			−2.83002
$506$	−4.41524e6	+	5.42522e7i	−0.0340803	+	0.418761i
$507$		0			0
$508$	7.47563e6	−	4.56242e7i	0.0570239	−	0.348020i
$509$		−	1.01090e8i		−	0.766577i	−0.923629	−	0.383288i	$-0.874792\pi$
$509$		−	1.01090e8i		−	0.766577i	0.923629	−	0.383288i	$-0.125208\pi$
$510$		0			0
$511$		−	1.26277e8i		−	0.946372i
$512$	−9.99402e7	−	8.95899e7i	−0.744613	−	0.667497i
$513$		0			0
$514$	−9.73029e7	−	7.91886e6i	−0.716534	−	0.0583141i
$515$	−1.77608e7			−0.130029
$516$		0			0
$517$			6.23924e7i			0.451502i
$518$	1.77733e8	+	1.44646e7i	1.27873	+	0.104068i
$519$		0			0
$520$	8.81749e7	+	2.19159e7i	0.627098	+	0.155865i
$521$	2.72972e8			1.93021			0.965107	−	0.261856i	$-0.0843344\pi$
$521$	2.72972e8			1.93021			0.965107	+	0.261856i	$0.0843344\pi$
$522$		0			0
$523$	−1.30965e8			−0.915481			−0.457741	−	0.889086i	$-0.651341\pi$
$523$	−1.30965e8			−0.915481			−0.457741	+	0.889086i	$0.651341\pi$
$524$	−557355.	−	91323.9i	−0.00387381	−	0.000634733i
$525$		0			0
$526$	−8.13026e6	+	9.99004e7i	−0.0558659	+	0.686452i
$527$		−	6.97628e7i		−	0.476642i
$528$		0			0
$529$	−1.16941e7			−0.0789952
$530$	−2.93362e8	−	2.38748e7i	−1.97050	−	0.160366i
$531$		0			0
$532$	2.50314e7	−	1.52768e8i	0.166246	−	1.01461i
$533$		−	4.05855e7i		−	0.268034i
$534$		0			0
$535$			3.34027e8i			2.18133i
$536$	−7.17457e7	−	1.78324e7i	−0.465909	−	0.115802i
$537$		0			0
$538$	1.66361e7	−	2.04416e8i	0.106833	−	1.31271i
$539$	−6.25911e7			−0.399711
$540$		0			0
$541$		−	8.91062e7i		−	0.562751i	−0.959598	−	0.281375i	$-0.909209\pi$
$541$		−	8.91062e7i		−	0.562751i	0.959598	−	0.281375i	$-0.0907906\pi$
$542$	−1.34845e7	+	1.65691e8i	−0.0846909	+	1.04064i
$543$		0			0
$544$	−1.28622e8	−	5.52959e7i	−0.798946	−	0.343476i
$545$	1.26332e8			0.780412
$546$		0			0
$547$	5.56270e7			0.339879			0.169939	−	0.985455i	$-0.445643\pi$
$547$	5.56270e7			0.339879			0.169939	+	0.985455i	$0.445643\pi$
$548$	1.69849e8	+	2.78302e7i	1.03210	+	0.169112i
$549$		0			0
$550$	1.64504e8	+	1.33879e7i	0.988752	+	0.0804682i
$551$		−	1.30798e8i		−	0.781892i
$552$		0			0
$553$	1.63181e8			0.964925
$554$	−9.92625e6	+	1.21969e8i	−0.0583789	+	0.717330i
$555$		0			0
$556$	2.39691e8	+	3.92739e7i	1.39453	+	0.228497i
$557$		−	5.81040e7i		−	0.336233i	−0.985767	−	0.168117i	$-0.946231\pi$
$557$		−	5.81040e7i		−	0.336233i	0.985767	−	0.168117i	$-0.0537685\pi$
$558$		0			0
$559$			6.44729e7i			0.369098i
$560$	−4.36060e8	−	1.46841e8i	−2.48303	−	0.836150i
$561$		0			0
$562$	−2.53943e8	−	2.06668e7i	−1.43063	−	0.116430i
$563$	1.34691e8			0.754766			0.377383	−	0.926057i	$-0.376824\pi$
$563$	1.34691e8			0.754766			0.377383	+	0.926057i	$0.376824\pi$
$564$		0			0
$565$		−	1.06856e8i		−	0.592451i
$566$	−2.74199e8	−	2.23153e7i	−1.51223	−	0.123071i
$567$		0			0
$568$	−1.96881e6	+	7.92116e6i	−0.0107438	+	0.0432259i
$569$	−2.74122e8			−1.48802			−0.744008	−	0.668171i	$-0.767077\pi$
$569$	−2.74122e8			−1.48802			−0.744008	+	0.668171i	$0.767077\pi$
$570$		0			0
$571$	1.23049e8			0.660950			0.330475	−	0.943815i	$-0.392791\pi$
$571$	1.23049e8			0.660950			0.330475	+	0.943815i	$0.392791\pi$
$572$	−4.25652e6	+	2.59778e7i	−0.0227440	+	0.138808i
$573$		0			0
$574$	−1.66719e7	+	2.04855e8i	−0.0881553	+	1.08321i
$575$			4.84333e8i			2.54766i
$576$		0			0
$577$	7.55002e7			0.393025			0.196513	−	0.980501i	$-0.437038\pi$
$577$	7.55002e7			0.393025			0.196513	+	0.980501i	$0.437038\pi$
$578$	4.69055e7	+	3.81734e6i	0.242907	+	0.0197686i
$579$		0			0
$580$	−3.83650e8	−	6.28619e7i	−1.96630	−	0.322184i
$581$			2.23037e8i			1.13723i
$582$		0			0
$583$		−	8.52767e7i		−	0.430353i
$584$	1.29733e8	+	3.22452e7i	0.651347	+	0.161893i
$585$		0			0
$586$	−549231.	+	6.74867e6i	−0.00272937	+	0.0335371i
$587$	4.36553e7			0.215836			0.107918	−	0.994160i	$-0.465582\pi$
$587$	4.36553e7			0.215836			0.107918	+	0.994160i	$0.465582\pi$
$588$		0			0
$589$			8.16604e7i			0.399637i
$590$	332820.	−	4.08952e6i	0.00162052	−	0.0199121i
$591$		0			0
$592$	−6.02451e7	+	1.78904e8i	−0.290373	+	0.862293i
$593$	−1.17686e8			−0.564367			−0.282183	−	0.959360i	$-0.591059\pi$
$593$	−1.17686e8			−0.564367			−0.282183	+	0.959360i	$0.591059\pi$
$594$		0			0
$595$	−4.79957e8			−2.27851
$596$	−4.26140e7	+	2.60075e8i	−0.201286	+	1.22846i
$597$		0			0
$598$	−7.69940e7	−	6.26605e6i	−0.360042	−	0.0293015i
$599$		−	1.02190e8i		−	0.475478i	−0.971329	−	0.237739i	$-0.923594\pi$
$599$		−	1.02190e8i		−	0.475478i	0.971329	−	0.237739i	$-0.0764062\pi$
$600$		0			0
$601$	1.75403e8			0.808003			0.404001	−	0.914758i	$-0.367619\pi$
$601$	1.75403e8			0.808003			0.404001	+	0.914758i	$0.367619\pi$
$602$	2.64844e7	−	3.25427e8i	0.121395	−	1.49164i
$603$		0			0
$604$	−6.57992e7	+	4.01576e8i	−0.298614	+	1.82245i
$605$		−	3.44156e8i		−	1.55414i
$606$		0			0
$607$		−	2.69263e8i		−	1.20395i	−0.798513	−	0.601977i	$-0.794380\pi$
$607$		−	2.69263e8i		−	1.20395i	0.798513	−	0.601977i	$-0.205620\pi$
$608$	1.50557e8	+	6.47262e7i	0.669870	+	0.287985i
$609$		0			0
$610$	−5.63863e8	−	4.58892e7i	−2.48419	−	0.202172i
$611$	−8.85464e7			−0.388193
$612$		0			0
$613$		−	9.71769e7i		−	0.421873i	−0.977500	−	0.210936i	$-0.932349\pi$
$613$		−	9.71769e7i		−	0.421873i	0.977500	−	0.210936i	$-0.0676513\pi$
$614$	−2.14221e8	−	1.74340e7i	−0.925457	−	0.0753170i
$615$		0			0
$616$	3.21561e7	−	1.29374e8i	0.137569	−	0.553485i
$617$	3.18248e8			1.35491			0.677454	−	0.735565i	$-0.263083\pi$
$617$	3.18248e8			1.35491			0.677454	+	0.735565i	$0.263083\pi$
$618$		0			0
$619$	−2.55972e8			−1.07925			−0.539623	−	0.841907i	$-0.681433\pi$
$619$	−2.55972e8			−1.07925			−0.539623	+	0.841907i	$0.681433\pi$
$620$	2.39522e8	+	3.92462e7i	1.00501	+	0.164673i
$621$		0			0
$622$	5.22564e6	−	6.42099e7i	0.0217154	−	0.266828i
$623$		−	5.51936e8i		−	2.28257i
$624$		0			0
$625$	6.25668e8			2.56274
$626$	−2.76574e8	−	2.25086e7i	−1.12743	−	0.0917542i
$627$		0			0
$628$	−4.84778e7	+	2.95863e8i	−0.195733	+	1.19457i
$629$			1.96914e8i			0.791269i
$630$		0			0
$631$			2.21386e8i			0.881174i	0.897710	+	0.440587i	$0.145230\pi$
$631$			2.21386e8i			0.881174i	−0.897710	+	0.440587i	$0.854770\pi$
$632$	−4.16687e7	+	1.67647e8i	−0.165066	+	0.664116i
$633$		0			0
$634$	8.10290e6	−	9.95643e7i	0.0317960	−	0.390693i
$635$	1.67785e8			0.655287
$636$		0			0
$637$		−	8.88285e7i		−	0.343664i
$638$	9.13660e6	−	1.12266e8i	0.0351822	−	0.432300i
$639$		0			0
$640$	2.62209e8	−	4.10498e8i	1.00025	−	1.56593i
$641$	−2.40330e8			−0.912503			−0.456252	−	0.889851i	$-0.650808\pi$
$641$	−2.40330e8			−0.912503			−0.456252	+	0.889851i	$0.650808\pi$
$642$		0			0
$643$	2.69614e7			0.101417			0.0507084	−	0.998714i	$-0.483852\pi$
$643$	2.69614e7			0.101417			0.0507084	+	0.998714i	$0.483852\pi$
$644$	3.86053e8	+	6.32558e7i	1.44541	+	0.236833i
$645$		0			0
$646$	1.70383e8	+	1.38664e7i	0.632016	+	0.0514358i
$647$		−	8.38452e7i		−	0.309575i	−0.987948	−	0.154787i	$-0.950531\pi$
$647$		−	8.38452e7i		−	0.309575i	0.987948	−	0.154787i	$-0.0494692\pi$
$648$		0			0
$649$	1.18877e6			0.00434876
$650$	−1.89999e7	+	2.33461e8i	−0.0691849	+	0.850109i
$651$		0			0
$652$	1.85475e8	+	3.03906e7i	0.669181	+	0.109647i
$653$			3.90251e8i			1.40154i	0.713389	+	0.700769i	$0.247159\pi$
$653$			3.90251e8i			1.40154i	−0.713389	+	0.700769i	$0.752841\pi$
$654$		0			0
$655$		−	2.04970e6i		−	0.00729400i
$656$	−2.06205e8	−	6.94385e7i	−0.730444	−	0.245974i
$657$		0			0
$658$	4.46938e8	+	3.63734e7i	1.56881	+	0.127675i
$659$	4.69468e7			0.164040			0.0820200	−	0.996631i	$-0.473863\pi$
$659$	4.69468e7			0.164040			0.0820200	+	0.996631i	$0.473863\pi$
$660$		0			0
$661$			6.80969e6i			0.0235789i	0.999931	+	0.0117894i	$0.00375278\pi$
$661$			6.80969e6i			0.0235789i	−0.999931	+	0.0117894i	$0.996247\pi$
$662$	4.93992e6	+	402029.i	0.0170273	+	0.00138574i
$663$		0			0
$664$	−2.29141e8	−	5.69532e7i	−0.782707	−	0.194542i
$665$	5.61811e8			1.91040
$666$		0			0
$667$	3.30534e8			1.11388
$668$	2.53168e7	−	1.54510e8i	0.0849337	−	0.518355i
$669$		0			0
$670$	2.17631e7	−	2.67414e8i	0.0723596	−	0.889118i
$671$		−	1.63908e8i		−	0.542541i
$672$		0			0
$673$	4.93288e8			1.61829			0.809143	−	0.587611i	$-0.199932\pi$
$673$	4.93288e8			1.61829			0.809143	+	0.587611i	$0.199932\pi$
$674$	−1.78733e7	−	1.45459e6i	−0.0583747	−	0.00475074i
$675$		0			0
$676$	2.67983e8	+	4.39097e7i	0.867496	+	0.142141i
$677$			1.16729e8i			0.376194i	0.982151	+	0.188097i	$0.0602319\pi$
$677$			1.16729e8i			0.376194i	−0.982151	+	0.188097i	$0.939768\pi$
$678$		0			0
$679$		−	1.39714e8i		−	0.446304i
$680$	1.22558e8	−	4.93093e8i	0.389777	−	1.56820i
$681$		0			0
$682$	−5.70419e6	+	7.00902e7i	−0.0179821	+	0.220955i
$683$	2.76782e8			0.868712			0.434356	−	0.900741i	$-0.356976\pi$
$683$	2.76782e8			0.868712			0.434356	+	0.900741i	$0.356976\pi$
$684$		0			0
$685$			6.24628e8i			1.94335i
$686$	434719.	−	5.34161e6i	0.00134659	−	0.0165463i
$687$		0			0
$688$	3.27570e8	+	1.10308e8i	1.00586	+	0.338720i
$689$	1.21024e8			0.370009
$690$		0			0
$691$	−3.85019e8			−1.16694			−0.583470	−	0.812135i	$-0.698305\pi$
$691$	−3.85019e8			−1.16694			−0.583470	+	0.812135i	$0.698305\pi$
$692$	−7.10854e6	+	4.33838e7i	−0.0214517	+	0.130921i
$693$		0			0
$694$	−8.28559e7	−	6.74311e6i	−0.247882	−	0.0201735i
$695$			8.81473e8i			2.62576i
$696$		0			0
$697$	−2.26963e8			−0.670280
$698$	−722009.	+	8.87168e6i	−0.00212313	+	0.0260879i
$699$		0			0
$700$	1.91804e8	−	1.17059e9i	0.559196	−	3.41280i
$701$		−	3.23184e8i		−	0.938200i	−0.883145	−	0.469100i	$-0.844578\pi$
$701$		−	3.23184e8i		−	0.938200i	0.883145	−	0.469100i	$-0.155422\pi$
$702$		0			0
$703$		−	2.30496e8i		−	0.663434i
$704$	1.24704e8	+	6.60722e7i	0.357406	+	0.189366i
$705$		0			0
$706$	−1.83879e8	−	1.49647e7i	−0.522537	−	0.0425259i
$707$	−7.58937e8			−2.14757
$708$		0			0
$709$		−	1.48892e8i		−	0.417765i	−0.977941	−	0.208882i	$-0.933017\pi$
$709$		−	1.48892e8i		−	0.417765i	0.977941	−	0.208882i	$-0.0669826\pi$
$710$	−2.95241e7	−	2.40278e6i	−0.0824900	−	0.00671334i
$711$		0			0
$712$	5.67041e8	+	1.40938e8i	1.57099	+	0.390471i
$713$	−2.06360e8			−0.569322
$714$		0			0
$715$	−9.55344e7			−0.261362
$716$	−1.05444e7	−	1.72773e6i	−0.0287265	−	0.00470691i
$717$		0			0
$718$	−3.64286e7	+	4.47616e8i	−0.0984168	+	1.20930i
$719$		−	2.48577e8i		−	0.668765i	−0.942437	−	0.334383i	$-0.891472\pi$
$719$		−	2.48577e8i		−	0.668765i	0.942437	−	0.334383i	$-0.108528\pi$
$720$		0			0
$721$	−3.69831e7			−0.0986729
$722$	1.75686e8	+	1.42980e7i	0.466795	+	0.0379895i
$723$		0			0
$724$	−2.12007e7	+	1.29389e8i	−0.0558643	+	0.340943i
$725$		−	1.00225e9i		−	2.63003i
$726$		0			0
$727$			7.18736e8i			1.87054i	0.353939	+	0.935269i	$0.384842\pi$
$727$			7.18736e8i			1.87054i	−0.353939	+	0.935269i	$0.615158\pi$
$728$	1.83606e8	+	4.56354e7i	0.475876	+	0.118279i
$729$		0			0
$730$	−3.93528e7	+	4.83547e8i	−0.101160	+	1.24300i
$731$	3.60546e8			0.923015
$732$		0			0
$733$		−	4.51009e8i		−	1.14518i	−0.819842	−	0.572590i	$-0.805939\pi$
$733$		−	4.51009e8i		−	1.14518i	0.819842	−	0.572590i	$-0.194061\pi$
$734$	7.94774e6	−	9.76578e7i	0.0200981	−	0.246956i
$735$		0			0
$736$	−1.63567e8	+	3.80466e8i	−0.410262	+	0.954296i
$737$	7.77339e7			0.194182
$738$		0			0
$739$	−5.53465e8			−1.37138			−0.685688	−	0.727896i	$-0.740499\pi$
$739$	−5.53465e8			−1.37138			−0.685688	+	0.727896i	$0.740499\pi$
$740$	−6.76078e8	−	1.10777e8i	−1.66841	−	0.273372i
$741$		0			0
$742$	−6.10866e8	−	4.97145e7i	−1.49532	−	0.121695i
$743$			2.47667e8i			0.603813i	0.953338	+	0.301906i	$0.0976230\pi$
$743$			2.47667e8i			0.603813i	−0.953338	+	0.301906i	$0.902377\pi$
$744$		0			0
$745$	−9.56438e8			−2.31307
$746$	−4.23606e7	+	5.20505e8i	−0.102034	+	1.25374i
$747$		0			0
$748$	1.45273e8	+	2.38034e7i	0.347121	+	0.0568766i
$749$			6.95543e8i			1.65531i
$750$		0			0
$751$		−	5.96096e8i		−	1.40733i	−0.710531	−	0.703666i	$-0.751545\pi$
$751$		−	5.96096e8i		−	1.40733i	0.710531	−	0.703666i	$-0.248455\pi$
$752$	−1.51496e8	+	4.49882e8i	−0.356244	+	1.05790i
$753$		0			0
$754$	1.59326e8	+	1.29665e7i	0.371683	+	0.0302489i
$755$	−1.47681e9			−3.43150
$756$		0			0
$757$		−	6.85494e8i		−	1.58021i	−0.612969	−	0.790107i	$-0.710025\pi$
$757$		−	6.85494e8i		−	1.58021i	0.612969	−	0.790107i	$-0.289975\pi$
$758$	7.92731e8	+	6.45153e7i	1.82020	+	0.148134i
$759$		0			0
$760$	−1.43460e8	+	5.77187e8i	−0.326806	+	1.31485i
$761$	1.08194e8			0.245498			0.122749	−	0.992438i	$-0.460829\pi$
$761$	1.08194e8			0.245498			0.122749	+	0.992438i	$0.460829\pi$
$762$		0			0
$763$	2.63061e8			0.592219
$764$	1.12127e8	−	6.84315e8i	0.251437	−	1.53453i
$765$		0			0
$766$	4.39373e7	−	5.39880e8i	0.0977569	−	1.20119i
$767$			1.68709e6i			0.00373898i
$768$		0			0
$769$	−5.79262e7			−0.127378			−0.0636892	−	0.997970i	$-0.520287\pi$
$769$	−5.79262e7			−0.127378			−0.0636892	+	0.997970i	$0.520287\pi$
$770$	4.82210e8	+	3.92440e7i	1.05624	+	0.0859609i
$771$		0			0
$772$	1.63594e8	+	2.68053e7i	0.355562	+	0.0582597i
$773$		−	2.28429e8i		−	0.494553i	−0.968945	−	0.247276i	$-0.920464\pi$
$773$		−	2.28429e8i		−	0.494553i	0.968945	−	0.247276i	$-0.0795356\pi$
$774$		0			0
$775$			6.25726e8i			1.34425i
$776$	1.43538e8	+	3.56764e7i	0.307172	+	0.0763477i
$777$		0			0
$778$	1.50983e7	−	1.85521e8i	0.0320620	−	0.393961i
$779$	2.65670e8			0.561991
$780$		0			0
$781$		−	8.58229e6i		−	0.0180157i
$782$	−3.50411e7	+	4.30567e8i	−0.0732752	+	0.900369i
$783$		0			0
$784$	−4.51315e8	−	1.51978e8i	−0.936551	−	0.315379i
$785$	−1.08805e9			−2.24925
$786$		0			0
$787$	3.74734e8			0.768773			0.384387	−	0.923172i	$-0.374413\pi$
$787$	3.74734e8			0.768773			0.384387	+	0.923172i	$0.374413\pi$
$788$	−2.22305e7	+	1.35674e8i	−0.0454329	+	0.277279i
$789$		0			0
$790$	−6.24861e8	−	5.08534e7i	−1.26737	−	0.103143i
$791$		−	2.22505e8i		−	0.449584i
$792$		0			0
$793$	2.32616e8			0.466466
$794$	6.04064e7	−	7.42242e8i	0.120676	−	1.48281i
$795$		0			0
$796$	−1.36096e8	+	8.30598e8i	−0.269839	+	1.64684i
$797$			3.19465e8i			0.631028i	0.948921	+	0.315514i	$0.102177\pi$
$797$			3.19465e8i			0.631028i	−0.948921	+	0.315514i	$0.897823\pi$
$798$		0			0
$799$			4.95170e8i			0.970765i
$800$	1.15365e9	+	4.95967e8i	2.25322	+	0.968686i
$801$		0			0
$802$	−1.05569e7	−	859160.i	−0.0204651	−	0.00166552i
$803$	−1.40561e8			−0.271468
$804$		0			0
$805$			1.41973e9i			2.72156i
$806$	−9.94711e7	−	8.09531e6i	−0.189973	−	0.0154607i
$807$		0			0
$808$	1.93797e8	−	7.79708e8i	0.367377	−	1.47808i
$809$	2.64298e8			0.499170			0.249585	−	0.968353i	$-0.419706\pi$
$809$	2.64298e8			0.499170			0.249585	+	0.968353i	$0.419706\pi$
$810$		0			0
$811$	3.16399e8			0.593161			0.296580	−	0.955008i	$-0.404154\pi$
$811$	3.16399e8			0.593161			0.296580	+	0.955008i	$0.404154\pi$
$812$	−7.98872e8	−	1.30897e8i	−1.49214	−	0.244491i
$813$		0			0
$814$	1.61008e7	−	1.97838e8i	0.0298520	−	0.366806i
$815$			6.82094e8i			1.26000i
$816$		0			0
$817$	−4.22035e8			−0.773895
$818$	−2.39867e8	−	1.95212e7i	−0.438238	−	0.0356654i
$819$		0			0
$820$	1.27682e8	−	7.79247e8i	0.231572	−	1.41330i
$821$			1.43420e8i			0.259167i	0.991568	+	0.129584i	$0.0413641\pi$
$821$			1.43420e8i			0.259167i	−0.991568	+	0.129584i	$0.958636\pi$
$822$		0			0
$823$		−	7.95672e8i		−	1.42736i	−0.700470	−	0.713682i	$-0.747026\pi$
$823$		−	7.95672e8i		−	1.42736i	0.700470	−	0.713682i	$-0.252974\pi$
$824$	9.44375e6	−	3.79953e7i	0.0168796	−	0.0679123i
$825$		0			0
$826$	693030.	−	8.51560e6i	0.00122974	−	0.0151104i
$827$	−6.01860e8			−1.06409			−0.532045	−	0.846716i	$-0.678576\pi$
$827$	−6.01860e8			−1.06409			−0.532045	+	0.846716i	$0.678576\pi$
$828$		0			0
$829$		−	1.82458e8i		−	0.320258i	−0.987096	−	0.160129i	$-0.948809\pi$
$829$		−	1.82458e8i		−	0.320258i	0.987096	−	0.160129i	$-0.0511910\pi$
$830$	6.95069e7	−	8.54066e8i	0.121561	−	1.49368i
$831$		0			0
$832$	−9.37688e7	+	1.76978e8i	−0.162813	+	0.307291i
$833$	−4.96748e8			−0.859411
$834$		0			0
$835$	5.68217e8			0.976011
$836$	−1.70049e8	−	2.78629e7i	−0.291041	−	0.0476878i
$837$		0			0
$838$	5.93449e8	+	4.82970e7i	1.00844	+	0.0820707i
$839$		−	4.37621e8i		−	0.740990i	−0.928835	−	0.370495i	$-0.879188\pi$
$839$		−	4.37621e8i		−	0.740990i	0.928835	−	0.370495i	$-0.120812\pi$
$840$		0			0
$841$	−8.91615e7			−0.149896
$842$	8.26534e7	−	1.01560e9i	0.138460	−	1.70133i
$843$		0			0
$844$	−1.06166e9	−	1.73955e8i	−1.76587	−	0.289341i
$845$			9.85520e8i			1.63341i
$846$		0			0
$847$		−	7.16635e8i		−	1.17936i
$848$	2.07062e8	−	6.14890e8i	0.339556	−	1.00835i
$849$		0			0
$850$	1.30556e9	+	1.06252e8i	2.12589	+	0.173013i
$851$	5.82477e8			0.945126
$852$		0			0
$853$		−	5.45023e6i		−	0.00878149i	−0.999990	−	0.00439074i	$-0.998602\pi$
$853$		−	5.45023e6i		−	0.00878149i	0.999990	−	0.00439074i	$-0.00139762\pi$
$854$	−1.17413e9	−	9.55549e7i	−1.88513	−	0.153419i
$855$		0			0
$856$	−7.14579e8	−	1.77609e8i	−1.13928	−	0.283168i
$857$	4.02235e8			0.639053			0.319527	−	0.947577i	$-0.396476\pi$
$857$	4.02235e8			0.639053			0.319527	+	0.947577i	$0.396476\pi$
$858$		0			0
$859$	−3.45909e8			−0.545735			−0.272868	−	0.962052i	$-0.587972\pi$
$859$	−3.45909e8			−0.545735			−0.272868	+	0.962052i	$0.587972\pi$
$860$	−2.02831e8	+	1.23789e9i	−0.318889	+	1.94619i
$861$		0			0
$862$	−4.53971e7	+	5.57817e8i	−0.0708772	+	0.870903i
$863$		−	1.27610e9i		−	1.98542i	−0.120511	−	0.992712i	$-0.538453\pi$
$863$		−	1.27610e9i		−	1.98542i	0.120511	−	0.992712i	$-0.461547\pi$
$864$		0			0
$865$	−1.59546e8			−0.246511
$866$	9.40594e8	+	7.65489e7i	1.44827	+	0.117865i
$867$		0			0
$868$	4.98755e8	+	8.17222e7i	0.762655	+	0.124963i
$869$		−	1.81639e8i		−	0.276790i
$870$		0			0
$871$			1.10319e8i			0.166953i
$872$	−6.71733e7	+	2.70260e8i	−0.101309	+	0.407599i
$873$		0			0
$874$	4.10171e7	−	5.03997e8i	0.0614371	−	0.754908i
$875$	2.54967e9			3.80593
$876$		0			0
$877$			7.80308e8i			1.15682i	0.815745	+	0.578412i	$0.196327\pi$
$877$			7.80308e8i			1.15682i	−0.815745	+	0.578412i	$0.803673\pi$
$878$	−8.35666e7	+	1.02682e9i	−0.123466	+	1.51709i
$879$		0			0
$880$	−1.63452e8	+	4.85386e8i	−0.239851	+	0.712261i
$881$	7.47208e8			1.09273			0.546366	−	0.837546i	$-0.316011\pi$
$881$	7.47208e8			1.09273			0.546366	+	0.837546i	$0.316011\pi$
$882$		0			0
$883$	−3.70806e8			−0.538598			−0.269299	−	0.963057i	$-0.586792\pi$
$883$	−3.70806e8			−0.538598			−0.269299	+	0.963057i	$0.586792\pi$
$884$	−3.37814e7	+	2.06170e8i	−0.0489014	+	0.298448i
$885$		0			0
$886$	−1.94367e7	−	1.58183e6i	−0.0279462	−	0.00227436i
$887$		−	6.49315e8i		−	0.930432i	−0.885197	−	0.465216i	$-0.845977\pi$
$887$		−	6.49315e8i		−	0.930432i	0.885197	−	0.465216i	$-0.154023\pi$
$888$		0			0
$889$	3.49378e8			0.497267
$890$	−1.72004e8	+	2.11350e9i	−0.243989	+	2.99801i
$891$		0			0
$892$	−1.44183e8	+	8.79959e8i	−0.203152	+	1.23985i
$893$		−	5.79618e8i		−	0.813931i
$894$		0			0
$895$		−	3.87775e7i		−	0.0540892i
$896$	5.45998e8	−	8.54779e8i	0.759044	−	1.18831i
$897$		0			0
$898$	9.31715e8	+	7.58263e7i	1.28663	+	0.104711i
$899$	4.27028e8			0.587729
$900$		0			0
$901$		−	6.76789e8i		−	0.925293i
$902$	2.28028e8	+	1.85577e7i	0.310719	+	0.0252875i
$903$		0			0
$904$	2.28595e8	+	5.68174e7i	0.309429	+	0.0769088i
$905$	−4.75833e8			−0.641962
$906$		0			0
$907$	−1.96033e7			−0.0262728			−0.0131364	−	0.999914i	$-0.504182\pi$
$907$	−1.96033e7			−0.0262728			−0.0131364	+	0.999914i	$0.504182\pi$
$908$	1.93155e8	+	3.16489e7i	0.258017	+	0.0422767i
$909$		0			0
$910$	−5.56945e7	+	6.84346e8i	−0.0739074	+	0.908137i
$911$			7.97758e8i			1.05515i	0.849507	+	0.527577i	$0.176899\pi$
$911$			7.97758e8i			1.05515i	−0.849507	+	0.527577i	$0.823101\pi$
$912$		0			0
$913$	2.48266e8			0.326216
$914$	−6.15218e8	−	5.00687e7i	−0.805732	−	0.0655734i
$915$		0			0
$916$	−1.36940e8	+	8.35753e8i	−0.178174	+	1.08740i
$917$		−	4.26807e6i		−	0.00553508i
$918$		0			0
$919$		−	2.56112e8i		−	0.329977i	−0.986296	−	0.164988i	$-0.947241\pi$
$919$		−	2.56112e8i		−	0.329977i	0.986296	−	0.164988i	$-0.0527586\pi$
$920$	−1.45858e9	−	3.62531e8i	−1.87313	−	0.465567i
$921$		0			0
$922$	6.71999e7	−	8.25718e8i	0.0857385	−	1.05351i
$923$	1.21799e7			0.0154895
$924$		0			0
$925$		−	1.76618e9i		−	2.23157i
$926$	9.48231e7	−	1.16514e9i	0.119421	−	1.46739i
$927$		0			0
$928$	3.38474e8	−	7.87311e8i	0.423527	−	0.985150i
$929$	−7.85064e8			−0.979170			−0.489585	−	0.871956i	$-0.662852\pi$
$929$	−7.85064e8			−0.979170			−0.489585	+	0.871956i	$0.662852\pi$
$930$		0			0
$931$	5.81465e8			0.720567
$932$	−1.18073e9	−	1.93466e8i	−1.45849	−	0.238977i
$933$		0			0
$934$	1.47779e9	+	1.20268e8i	1.81373	+	0.147608i
$935$			5.34249e8i			0.653595i
$936$		0			0
$937$	−5.64983e8			−0.686778			−0.343389	−	0.939193i	$-0.611575\pi$
$937$	−5.64983e8			−0.686778			−0.343389	+	0.939193i	$0.611575\pi$
$938$	4.53172e7	−	5.56835e8i	0.0549104	−	0.674711i
$939$		0			0
$940$	−1.70010e9	−	2.78566e8i	−2.04688	−	0.335386i
$941$		−	1.40879e9i		−	1.69074i	−0.534180	−	0.845371i	$-0.679379\pi$
$941$		−	1.40879e9i		−	1.69074i	0.534180	−	0.845371i	$-0.320621\pi$
$942$		0			0
$943$			6.71362e8i			0.800611i
$944$	8.57169e6	+	2.88648e6i	0.0101894	+	0.00343125i
$945$		0			0
$946$	−3.62238e8	−	2.94802e7i	−0.427879	−	0.0348223i
$947$	7.71784e8			0.908753			0.454377	−	0.890810i	$-0.349862\pi$
$947$	7.71784e8			0.908753			0.454377	+	0.890810i	$0.349862\pi$
$948$		0			0
$949$		−	1.99483e8i		−	0.233403i
$950$	−1.52822e9	−	1.24372e8i	−1.78244	−	0.145061i
$951$		0			0
$952$	2.55203e8	−	1.02677e9i	0.295784	−	1.19004i
$953$	−3.82045e8			−0.441404			−0.220702	−	0.975341i	$-0.570835\pi$
$953$	−3.82045e8			−0.441404			−0.220702	+	0.975341i	$0.570835\pi$
$954$		0			0
$955$	2.51660e9			2.88937
$956$	−1.01967e8	+	6.22307e8i	−0.116703	+	0.712248i
$957$		0			0
$958$	3.16610e7	−	3.89034e8i	0.0360104	−	0.442477i
$959$			1.30066e9i			1.47472i
$960$		0			0
$961$	6.20900e8			0.699603
$962$	2.80769e8	+	2.28500e7i	0.315372	+	0.0256661i
$963$		0			0
$964$	−8.27435e8	−	1.35577e8i	−0.923640	−	0.151341i
$965$			6.01623e8i			0.669488i
$966$		0			0
$967$			7.92497e8i			0.876432i	0.898870	+	0.438216i	$0.144390\pi$
$967$			7.92497e8i			0.876432i	−0.898870	+	0.438216i	$0.855610\pi$
$968$	7.36248e8	+	1.82995e8i	0.811705	+	0.201750i
$969$		0			0
$970$	−4.35403e7	+	5.35001e8i	−0.0477063	+	0.586191i
$971$	1.07047e9			1.16928			0.584639	−	0.811293i	$-0.301236\pi$
$971$	1.07047e9			1.16928			0.584639	+	0.811293i	$0.301236\pi$
$972$		0			0
$973$			1.83549e9i			1.99257i
$974$	−1.20844e8	+	1.48487e9i	−0.130782	+	1.60699i
$975$		0			0
$976$	3.97987e8	−	1.18186e9i	0.428075	−	1.27121i
$977$	9.03996e8			0.969355			0.484677	−	0.874693i	$-0.338937\pi$
$977$	9.03996e8			0.969355			0.484677	+	0.874693i	$0.338937\pi$
$978$		0			0
$979$	−6.14369e8			−0.654759
$980$	2.79453e8	−	1.70552e9i	0.296914	−	1.81208i
$981$		0			0
$982$	−1.18936e9	−	9.67945e7i	−1.25597	−	0.102215i
$983$			1.84218e8i			0.193942i	0.995287	+	0.0969709i	$0.0309154\pi$
$983$			1.84218e8i			0.193942i	−0.995287	+	0.0969709i	$0.969085\pi$
$984$		0			0
$985$	−4.98946e8			−0.522089
$986$	7.25116e7	−	8.90986e8i	0.0756444	−	0.929480i
$987$		0			0
$988$	3.95426e7	−	2.41331e8i	0.0410010	−	0.250231i
$989$		−	1.06651e9i		−	1.10249i
$990$		0			0
$991$			1.70881e9i			1.75579i	0.478850	+	0.877897i	$0.341054\pi$
$991$			1.70881e9i			1.75579i	−0.478850	+	0.877897i	$0.658946\pi$
$992$	−2.11317e8	+	4.91537e8i	−0.216471	+	0.503525i
$993$		0			0
$994$	−6.14779e7	−	5.00329e6i	−0.0625979	−	0.00509444i
$995$	−3.05456e9			−3.10084
$996$		0			0
$997$			2.93187e8i			0.295842i	0.988999	+	0.147921i	$0.0472582\pi$
$997$			2.93187e8i			0.295842i	−0.988999	+	0.147921i	$0.952742\pi$
$998$	−5.24033e8	−	4.26477e7i	−0.527190	−	0.0429046i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.c.19.1		12
3.2	odd	2		24.7.b.a.19.12	yes	12
4.3	odd	2		288.7.b.d.271.12		12
8.3	odd	2	inner	72.7.b.c.19.2		12
8.5	even	2		288.7.b.d.271.1		12
12.11	even	2		96.7.b.a.79.1		12
24.5	odd	2		96.7.b.a.79.6		12
24.11	even	2		24.7.b.a.19.11	✓	12
48.5	odd	4		768.7.g.l.511.18		24
48.11	even	4		768.7.g.l.511.20		24
48.29	odd	4		768.7.g.l.511.19		24
48.35	even	4		768.7.g.l.511.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.b.a.19.11	✓	12	24.11	even	2
24.7.b.a.19.12	yes	12	3.2	odd	2
72.7.b.c.19.1		12	1.1	even	1	trivial
72.7.b.c.19.2		12	8.3	odd	2	inner
96.7.b.a.79.1		12	12.11	even	2
96.7.b.a.79.6		12	24.5	odd	2
288.7.b.d.271.1		12	8.5	even	2
288.7.b.d.271.12		12	4.3	odd	2
768.7.g.l.511.17		24	48.35	even	4
768.7.g.l.511.18		24	48.5	odd	4
768.7.g.l.511.19		24	48.29	odd	4
768.7.g.l.511.20		24	48.11	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)

\(f(q)\)	\(=\)	\(q+(-7.97364 - 0.648923i) q^{2} +(63.1578 + 10.3486i) q^{4} +232.265i q^{5} +483.645i q^{7} +(-496.882 - 123.500i) q^{8} +O(q^{10})\)	\(q+(-7.97364 - 0.648923i) q^{2} +(63.1578 + 10.3486i) q^{4} +232.265i q^{5} +483.645i q^{7} +(-496.882 - 123.500i) q^{8} +(150.722 - 1852.00i) q^{10} +538.354 q^{11} +764.025i q^{13} +(313.849 - 3856.41i) q^{14} +(3881.81 + 1307.18i) q^{16} +4272.59 q^{17} -5001.25 q^{19} +(-2403.61 + 14669.4i) q^{20} +(-4292.64 - 349.350i) q^{22} -12638.4i q^{23} -38322.2 q^{25} +(495.793 - 6092.06i) q^{26} +(-5005.03 + 30546.0i) q^{28} +26153.1i q^{29} -16328.0i q^{31} +(-30103.9 - 12942.0i) q^{32} +(-34068.1 - 2772.58i) q^{34} -112334. q^{35} +46087.7i q^{37} +(39878.1 + 3245.43i) q^{38} +(28684.8 - 115409. i) q^{40} -53120.7 q^{41} +84385.9 q^{43} +(34001.2 + 5571.19i) q^{44} +(-8201.37 + 100774. i) q^{46} +115895. i q^{47} -116264. q^{49} +(305568. + 24868.2i) q^{50} +(-7906.55 + 48254.1i) q^{52} -158403. i q^{53} +125041. i q^{55} +(59730.3 - 240315. i) q^{56} +(16971.4 - 208535. i) q^{58} +2208.17 q^{59} -304462. i q^{61} +(-10595.6 + 130194. i) q^{62} +(231639. + 122730. i) q^{64} -177457. q^{65} +144392. q^{67} +(269847. + 44215.1i) q^{68} +(895712. + 72896.2i) q^{70} -15941.7i q^{71} -261094. q^{73} +(29907.4 - 367487. i) q^{74} +(-315868. - 51755.7i) q^{76} +260372. i q^{77} -337398. i q^{79} +(-303614. + 901611. i) q^{80} +(423565. + 34471.2i) q^{82} +461158. q^{83} +992374. i q^{85} +(-672862. - 54760.0i) q^{86} +(-267498. - 66486.8i) q^{88} -1.14120e6 q^{89} -369517. q^{91} +(130790. - 798216. i) q^{92} +(75206.8 - 924103. i) q^{94} -1.16162e6i q^{95} -288877. q^{97} +(927046. + 75446.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) \) 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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