LMFDB - Embedded newform 99.7.k.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,7,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$22.7753542784$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.1
Root			$13.3023i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.7.k.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.7693 - 4.47392i) q^{2} +(117.801 + 85.5872i) q^{4} +(50.2998 + 154.807i) q^{5} +(218.726 - 301.051i) q^{7} +(-694.490 - 955.883i) q^{8} +O(q^{10})$	\(q+(-13.7693 - 4.47392i) q^{2} +(117.801 + 85.5872i) q^{4} +(50.2998 + 154.807i) q^{5} +(218.726 - 301.051i) q^{7} +(-694.490 - 955.883i) q^{8} -2356.62i q^{10} +(1173.78 - 627.535i) q^{11} +(-676.019 - 219.652i) q^{13} +(-4358.59 + 3166.70i) q^{14} +(2406.36 + 7406.03i) q^{16} +(2700.07 - 877.307i) q^{17} +(3595.40 + 4948.64i) q^{19} +(-7324.14 + 22541.4i) q^{20} +(-18969.7 + 3389.32i) q^{22} -16105.1 q^{23} +(-8794.25 + 6389.39i) q^{25} +(8325.60 + 6048.91i) q^{26} +(51532.2 - 16743.8i) q^{28} +(13310.6 - 18320.5i) q^{29} +(6434.78 - 19804.2i) q^{31} -37123.4i q^{32} -41103.2 q^{34} +(57606.7 + 18717.5i) q^{35} +(14970.9 + 10877.0i) q^{37} +(-27366.3 - 84224.8i) q^{38} +(113045. - 155593. i) q^{40} +(8208.64 + 11298.2i) q^{41} -42621.5i q^{43} +(191981. + 26536.5i) q^{44} +(221755. + 72052.7i) q^{46} +(-18833.6 + 13683.4i) q^{47} +(-6434.91 - 19804.6i) q^{49} +(149676. - 48632.8i) q^{50} +(-60836.1 - 83733.7i) q^{52} +(72638.0 - 223557. i) q^{53} +(156188. + 150145. i) q^{55} -439673. q^{56} +(-265243. + 192710. i) q^{58} +(6115.84 + 4443.42i) q^{59} +(178688. - 58059.2i) q^{61} +(-177205. + 243902. i) q^{62} +(-12079.6 + 37177.0i) q^{64} -115701. i q^{65} -148760. q^{67} +(393157. + 127744. i) q^{68} +(-709463. - 515455. i) q^{70} +(189186. + 582255. i) q^{71} +(116805. - 160768. i) q^{73} +(-157476. - 216747. i) q^{74} +890673. i q^{76} +(67816.6 - 490626. i) q^{77} +(450118. + 146252. i) q^{79} +(-1.02547e6 + 745044. i) q^{80} +(-62479.9 - 192293. i) q^{82} +(-36790.9 + 11954.1i) q^{83} +(271627. + 373862. i) q^{85} +(-190685. + 586869. i) q^{86} +(-1.41503e6 - 686181. i) q^{88} +974721. q^{89} +(-213989. + 155472. i) q^{91} +(-1.89719e6 - 1.37839e6i) q^{92} +(320544. - 104151. i) q^{94} +(-585236. + 805508. i) q^{95} +(-174460. + 536933. i) q^{97} +301485. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} + 215 q^{4} - 181 q^{5} - 365 q^{7} - 1595 q^{8}+O(q^{10}) $ 20 * q + 5 * q^2 + 215 * q^4 - 181 * q^5 - 365 * q^7 - 1595 * q^8	$ 20 q + 5 q^{2} + 215 q^{4} - 181 q^{5} - 365 q^{7} - 1595 q^{8} + 3498 q^{11} - 1805 q^{13} - 7170 q^{14} - 2185 q^{16} - 3635 q^{17} + 23845 q^{19} - 5144 q^{20} - 2915 q^{22} - 7816 q^{23} - 30416 q^{25} + 131310 q^{26} + 226540 q^{28} - 134595 q^{29} - 71211 q^{31} - 228190 q^{34} + 377445 q^{35} - 205731 q^{37} - 127220 q^{38} + 704340 q^{40} - 490975 q^{41} + 537812 q^{44} - 714610 q^{46} - 25329 q^{47} + 304010 q^{49} - 417855 q^{50} + 1468510 q^{52} + 110919 q^{53} - 5511 q^{55} + 862620 q^{56} - 667940 q^{58} + 581009 q^{59} + 892675 q^{61} - 2337360 q^{62} + 124615 q^{64} - 960956 q^{67} + 1822680 q^{68} - 1987140 q^{70} + 288895 q^{71} - 806585 q^{73} + 404170 q^{74} - 623095 q^{77} + 1662955 q^{79} - 1190956 q^{80} - 282095 q^{82} - 14645 q^{83} - 33365 q^{85} - 735635 q^{86} - 1860485 q^{88} - 1111620 q^{89} + 650935 q^{91} - 4407784 q^{92} - 5913080 q^{94} + 4329525 q^{95} - 1189281 q^{97}+O(q^{100}) $ 20 * q + 5 * q^2 + 215 * q^4 - 181 * q^5 - 365 * q^7 - 1595 * q^8 + 3498 * q^11 - 1805 * q^13 - 7170 * q^14 - 2185 * q^16 - 3635 * q^17 + 23845 * q^19 - 5144 * q^20 - 2915 * q^22 - 7816 * q^23 - 30416 * q^25 + 131310 * q^26 + 226540 * q^28 - 134595 * q^29 - 71211 * q^31 - 228190 * q^34 + 377445 * q^35 - 205731 * q^37 - 127220 * q^38 + 704340 * q^40 - 490975 * q^41 + 537812 * q^44 - 714610 * q^46 - 25329 * q^47 + 304010 * q^49 - 417855 * q^50 + 1468510 * q^52 + 110919 * q^53 - 5511 * q^55 + 862620 * q^56 - 667940 * q^58 + 581009 * q^59 + 892675 * q^61 - 2337360 * q^62 + 124615 * q^64 - 960956 * q^67 + 1822680 * q^68 - 1987140 * q^70 + 288895 * q^71 - 806585 * q^73 + 404170 * q^74 - 623095 * q^77 + 1662955 * q^79 - 1190956 * q^80 - 282095 * q^82 - 14645 * q^83 - 33365 * q^85 - 735635 * q^86 - 1860485 * q^88 - 1111620 * q^89 + 650935 * q^91 - 4407784 * q^92 - 5913080 * q^94 + 4329525 * q^95 - 1189281 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−13.7693	−	4.47392i	−1.72116	−	0.559240i	−0.729036	−	0.684475i	$-0.760031\pi$
$2$	−13.7693	−	4.47392i	−1.72116	−	0.559240i	−0.992127	+	0.125236i	$0.960031\pi$
$3$		0			0
$3$		0			0
$4$	117.801	+	85.5872i	1.84064	+	1.33730i
$5$	50.2998	+	154.807i	0.402399	+	1.23846i	0.923048	+	0.384685i	$0.125690\pi$
$5$	50.2998	+	154.807i	0.402399	+	1.23846i	−0.520649	+	0.853771i	$0.674310\pi$
$6$		0			0
$7$	218.726	−	301.051i	0.637686	−	0.877699i	−0.360804	−	0.932642i	$-0.617498\pi$
$7$	218.726	−	301.051i	0.637686	−	0.877699i	0.998490	+	0.0549425i	$0.0174975\pi$
$8$	−694.490	−	955.883i	−1.35643	−	1.86696i
$9$		0			0
$10$		−	2356.62i		−	2.35662i
$11$	1173.78	−	627.535i	0.881879	−	0.471476i
$11$	1173.78	−	627.535i	0.881879	−	0.471476i
$12$		0			0
$13$	−676.019	−	219.652i	−0.307701	−	0.0999781i	0.151096	−	0.988519i	$-0.451720\pi$
$13$	−676.019	−	219.652i	−0.307701	−	0.0999781i	−0.458797	+	0.888541i	$0.651720\pi$
$14$	−4358.59	+	3166.70i	−1.58841	+	1.15404i
$15$		0			0
$16$	2406.36	+	7406.03i	0.587491	+	1.80811i
$17$	2700.07	−	877.307i	0.549578	−	0.178569i	−0.0210487	−	0.999778i	$-0.506700\pi$
$17$	2700.07	−	877.307i	0.549578	−	0.178569i	0.570626	+	0.821210i	$0.306700\pi$
$18$		0			0
$19$	3595.40	+	4948.64i	0.524187	+	0.721481i	0.986231	−	0.165376i	$-0.0528838\pi$
$19$	3595.40	+	4948.64i	0.524187	+	0.721481i	−0.462044	+	0.886857i	$0.652884\pi$
$20$	−7324.14	+	22541.4i	−0.915518	+	2.81767i
$21$		0			0
$22$	−18969.7	+	3389.32i	−1.78153	+	0.318306i
$23$	−16105.1			−1.32367			−0.661833	−	0.749651i	$-0.730221\pi$
$23$	−16105.1			−1.32367			−0.661833	+	0.749651i	$0.730221\pi$
$24$		0			0
$25$	−8794.25	+	6389.39i	−0.562832	+	0.408921i
$26$	8325.60	+	6048.91i	0.473692	+	0.344157i
$27$		0			0
$28$	51532.2	−	16743.8i	2.34750	−	0.762747i
$29$	13310.6	−	18320.5i	0.545764	−	0.751179i	−0.443666	−	0.896192i	$-0.646322\pi$
$29$	13310.6	−	18320.5i	0.545764	−	0.751179i	0.989430	+	0.145013i	$0.0463223\pi$
$30$		0			0
$31$	6434.78	−	19804.2i	0.215998	−	0.664772i	−0.783084	−	0.621916i	$-0.786354\pi$
$31$	6434.78	−	19804.2i	0.215998	−	0.664772i	0.999081	−	0.0428559i	$-0.0136456\pi$
$32$		−	37123.4i		−	1.13292i
$33$		0			0
$34$	−41103.2			−1.04578
$35$	57606.7	+	18717.5i	1.34360	+	0.436561i
$36$		0			0
$37$	14970.9	+	10877.0i	0.295557	+	0.214735i	0.725675	−	0.688038i	$-0.241528\pi$
$37$	14970.9	+	10877.0i	0.295557	+	0.214735i	−0.430117	+	0.902773i	$0.641528\pi$
$38$	−27366.3	−	84224.8i	−0.498730	−	1.53493i
$39$		0			0
$40$	113045.	−	155593.i	1.76632	−	2.43114i
$41$	8208.64	+	11298.2i	0.119102	+	0.163930i	0.864405	−	0.502796i	$-0.167695\pi$
$41$	8208.64	+	11298.2i	0.119102	+	0.163930i	−0.745303	+	0.666726i	$0.767695\pi$
$42$		0			0
$43$		−	42621.5i		−	0.536073i	−0.963409	−	0.268036i	$-0.913625\pi$
$43$		−	42621.5i		−	0.536073i	0.963409	−	0.268036i	$-0.0863747\pi$
$44$	191981.	+	26536.5i	2.25372	+	0.311520i
$45$		0			0
$46$	221755.	+	72052.7i	2.27825	+	0.740247i
$47$	−18833.6	+	13683.4i	−0.181401	+	0.131796i	−0.674780	−	0.738019i	$-0.735762\pi$
$47$	−18833.6	+	13683.4i	−0.181401	+	0.131796i	0.493379	+	0.869814i	$0.335762\pi$
$48$		0			0
$49$	−6434.91	−	19804.6i	−0.0546958	−	0.168336i
$50$	149676.	−	48632.8i	1.19741	−	0.389062i
$51$		0			0
$52$	−60836.1	−	83733.7i	−0.432665	−	0.595512i
$53$	72638.0	−	223557.i	0.487906	−	1.50162i	−0.339821	−	0.940490i	$-0.610367\pi$
$53$	72638.0	−	223557.i	0.487906	−	1.50162i	0.827727	−	0.561131i	$-0.189633\pi$
$54$		0			0
$55$	156188.	+	150145.i	0.938770	+	0.902447i
$56$	−439673.			−2.50360
$57$		0			0
$58$	−265243.	+	192710.i	−1.35944	+	0.987690i
$59$	6115.84	+	4443.42i	0.0297783	+	0.0216352i	0.602575	−	0.798062i	$-0.294141\pi$
$59$	6115.84	+	4443.42i	0.0297783	+	0.0216352i	−0.572797	+	0.819698i	$0.694141\pi$
$60$		0			0
$61$	178688.	−	58059.2i	0.787237	−	0.255789i	0.112310	−	0.993673i	$-0.464175\pi$
$61$	178688.	−	58059.2i	0.787237	−	0.255789i	0.674927	+	0.737885i	$0.264175\pi$
$62$	−177205.	+	243902.i	−0.743534	+	1.02339i
$63$		0			0
$64$	−12079.6	+	37177.0i	−0.0460798	+	0.141819i
$65$		−	115701.i		−	0.421305i
$66$		0			0
$67$	−148760.			−0.494610			−0.247305	−	0.968938i	$-0.579545\pi$
$67$	−148760.			−0.494610			−0.247305	+	0.968938i	$0.579545\pi$
$68$	393157.	+	127744.i	1.25037	+	0.406271i
$69$		0			0
$70$	−709463.	−	515455.i	−2.06841	−	1.50278i
$71$	189186.	+	582255.i	0.528584	+	1.62682i	0.757117	+	0.653279i	$0.226607\pi$
$71$	189186.	+	582255.i	0.528584	+	1.62682i	−0.228533	+	0.973536i	$0.573393\pi$
$72$		0			0
$73$	116805.	−	160768.i	0.300256	−	0.413267i	−0.632056	−	0.774923i	$-0.717789\pi$
$73$	116805.	−	160768.i	0.300256	−	0.413267i	0.932311	+	0.361656i	$0.117789\pi$
$74$	−157476.	−	216747.i	−0.388614	−	0.534881i
$75$		0			0
$76$			890673.i			2.02898i
$77$	67816.6	−	490626.i	0.148547	−	1.07468i
$78$		0			0
$79$	450118.	+	146252.i	0.912946	+	0.296634i	0.727570	−	0.686034i	$-0.240650\pi$
$79$	450118.	+	146252.i	0.912946	+	0.296634i	0.185376	+	0.982668i	$0.440650\pi$
$80$	−1.02547e6	+	745044.i	−2.00286	+	1.45516i
$81$		0			0
$82$	−62479.9	−	192293.i	−0.113318	−	0.348757i
$83$	−36790.9	+	11954.1i	−0.0643437	+	0.0209065i	−0.341012	−	0.940059i	$-0.610770\pi$
$83$	−36790.9	+	11954.1i	−0.0643437	+	0.0209065i	0.276668	+	0.960965i	$0.410770\pi$
$84$		0			0
$85$	271627.	+	373862.i	0.442299	+	0.608772i
$86$	−190685.	+	586869.i	−0.299793	+	0.922669i
$87$		0			0
$88$	−1.41503e6	−	686181.i	−2.07643	−	1.00691i
$89$	974721.			1.38264			0.691322	−	0.722547i	$-0.257029\pi$
$89$	974721.			1.38264			0.691322	+	0.722547i	$0.257029\pi$
$90$		0			0
$91$	−213989.	+	155472.i	−0.283967	+	0.206314i
$92$	−1.89719e6	−	1.37839e6i	−2.43639	−	1.77014i
$93$		0			0
$94$	320544.	−	104151.i	0.385926	−	0.125395i
$95$	−585236.	+	805508.i	−0.682591	+	0.939505i
$96$		0			0
$97$	−174460.	+	536933.i	−0.191153	+	0.588308i	0.808847	+	0.588019i	$0.200092\pi$
$97$	−174460.	+	536933.i	−0.191153	+	0.588308i	−1.00000		0.000289079i	$0.999908\pi$
$98$			301485.i			0.320323i
$99$		0			0
$100$	−1.58282e6			−1.58282
$101$	1.83888e6	+	597487.i	1.78479	+	0.579915i	0.999244	−	0.0388830i	$-0.0123800\pi$
$101$	1.83888e6	+	597487.i	1.78479	+	0.579915i	0.785550	+	0.618798i	$0.212380\pi$
$102$		0			0
$103$	1.38897e6	+	1.00914e6i	1.27110	+	0.923510i	0.999246	−	0.0388278i	$-0.0123624\pi$
$103$	1.38897e6	+	1.00914e6i	1.27110	+	0.923510i	0.271857	+	0.962338i	$0.412362\pi$
$104$	259527.	+	798741.i	0.230718	+	0.710078i
$105$		0			0
$106$	−2.00035e6	+	2.75325e6i	−1.67953	+	2.31168i
$107$	−4361.85	−	6003.57i	−0.00356057	−	0.00490070i	0.807233	−	0.590233i	$-0.200964\pi$
$107$	−4361.85	−	6003.57i	−0.00356057	−	0.00490070i	−0.810794	+	0.585332i	$0.800964\pi$
$108$		0			0
$109$		−	1.90513e6i		−	1.47111i	−0.677465	−	0.735555i	$-0.736922\pi$
$109$		−	1.90513e6i		−	1.47111i	0.677465	−	0.735555i	$-0.263078\pi$
$110$	−1.47886e6	−	2.76616e6i	−1.11109	−	2.07825i
$111$		0			0
$112$	2.75593e6	+	895455.i	1.96161	+	0.637367i
$113$	1.24377e6	−	903649.i	0.861992	−	0.626274i	−0.0664341	−	0.997791i	$-0.521162\pi$
$113$	1.24377e6	−	903649.i	0.861992	−	0.626274i	0.928426	+	0.371517i	$0.121162\pi$
$114$		0			0
$115$	−810082.	−	2.49318e6i	−0.532642	−	1.63930i
$116$	3.13600e6	−	1.01895e6i	2.00911	−	0.652798i
$117$		0			0
$118$	−64331.3	−	88544.5i	−0.0391540	−	0.0538909i
$119$	326463.	−	1.00475e6i	0.193728	−	0.596235i
$120$		0			0
$121$	983960.	−	1.47318e6i	0.555420	−	0.831570i
$122$	−2.72016e6			−1.49801
$123$		0			0
$124$	2.45301e6	−	1.78222e6i	1.28657	−	0.934750i
$125$	626133.	+	454912.i	0.320580	+	0.232915i
$126$		0			0
$127$	235602.	−	76551.8i	0.115019	−	0.0373718i	−0.250942	−	0.968002i	$-0.580740\pi$
$127$	235602.	−	76551.8i	0.115019	−	0.0373718i	0.365961	+	0.930630i	$0.380740\pi$
$128$	−1.06386e6	+	1.46428e6i	−0.507289	+	0.698223i
$129$		0			0
$130$	−517636.	+	1.59312e6i	−0.235611	+	0.725135i
$131$		−	2.12748e6i		−	0.946348i	−0.880969	−	0.473174i	$-0.843108\pi$
$131$		−	2.12748e6i		−	0.946348i	0.880969	−	0.473174i	$-0.156892\pi$
$132$		0			0
$133$	2.27620e6			0.967510
$134$	2.04833e6	+	665542.i	0.851304	+	0.276606i
$135$		0			0
$136$	−2.71378e6	−	1.97168e6i	−1.07884	−	0.783824i
$137$	−416520.	−	1.28192e6i	−0.161985	−	0.498538i	0.836817	−	0.547483i	$-0.184414\pi$
$137$	−416520.	−	1.28192e6i	−0.161985	−	0.498538i	−0.998801	+	0.0489455i	$0.984414\pi$
$138$		0			0
$139$	−2.64897e6	+	3.64599e6i	−0.986353	+	1.35760i	−0.0530173	+	0.998594i	$0.516884\pi$
$139$	−2.64897e6	+	3.64599e6i	−0.986353	+	1.35760i	−0.933336	+	0.359005i	$0.883116\pi$
$140$	5.18413e6	+	7.13534e6i	1.88926	+	2.60034i
$141$		0			0
$142$		−	8.86365e6i		−	3.09562i
$143$	−931337.	+	166402.i	−0.318492	+	0.0569052i
$144$		0			0
$145$	3.50567e6	+	1.13906e6i	1.14992	+	0.373631i
$146$	−2.32758e6	+	1.69109e6i	−0.747904	+	0.543384i
$147$		0			0
$148$	832649.	+	2.56263e6i	0.256848	+	0.790498i
$149$	−3.50882e6	+	1.14008e6i	−1.06072	+	0.344650i	−0.786868	−	0.617121i	$-0.788299\pi$
$149$	−3.50882e6	+	1.14008e6i	−1.06072	+	0.344650i	−0.273855	+	0.961771i	$0.588299\pi$
$150$		0			0
$151$	1.28293e6	+	1.76580e6i	0.372625	+	0.512875i	0.953612	−	0.301038i	$-0.0973332\pi$
$151$	1.28293e6	+	1.76580e6i	0.372625	+	0.512875i	−0.580987	+	0.813913i	$0.697333\pi$
$152$	2.23336e6	−	6.87356e6i	0.635956	−	1.95727i
$153$		0			0
$154$	−3.12881e6	+	6.45217e6i	−0.856677	+	1.76662i
$155$	3.38950e6			0.910208
$156$		0			0
$157$	−1.73332e6	+	1.25933e6i	−0.447899	+	0.325418i	−0.788766	−	0.614694i	$-0.789279\pi$
$157$	−1.73332e6	+	1.25933e6i	−0.447899	+	0.325418i	0.340867	+	0.940112i	$0.389279\pi$
$158$	−5.54349e6	−	4.02758e6i	−1.40544	−	1.02111i
$159$		0			0
$160$	5.74696e6	−	1.86730e6i	1.40307	−	0.455884i
$161$	−3.52260e6	+	4.84844e6i	−0.844084	+	1.16178i
$162$		0			0
$163$	−251083.	+	772754.i	−0.0579768	+	0.178434i	−0.975851	−	0.218437i	$-0.929904\pi$
$163$	−251083.	+	772754.i	−0.0579768	+	0.178434i	0.917874	+	0.396871i	$0.129904\pi$
$164$			2.03349e6i			0.461011i
$165$		0			0
$166$	560066.			0.122438
$167$	−4.66915e6	−	1.51710e6i	−1.00251	−	0.325735i	−0.238641	−	0.971108i	$-0.576702\pi$
$167$	−4.66915e6	−	1.51710e6i	−1.00251	−	0.325735i	−0.763868	+	0.645373i	$0.776702\pi$
$168$		0			0
$169$	−3.49622e6	−	2.54015e6i	−0.724333	−	0.526259i
$170$	−2.06748e6	−	6.36306e6i	−0.420819	−	1.29515i
$171$		0			0
$172$	3.64786e6	−	5.02085e6i	0.716890	−	0.986715i
$173$	4.79610e6	+	6.60127e6i	0.926297	+	1.27494i	0.961286	+	0.275551i	$0.0888603\pi$
$173$	4.79610e6	+	6.60127e6i	0.926297	+	1.27494i	−0.0349894	+	0.999388i	$0.511140\pi$
$174$		0			0
$175$			4.04504e6i			0.754760i
$176$	7.47209e6	+	7.18297e6i	1.37058	+	1.31755i
$177$		0			0
$178$	−1.34212e7	−	4.36082e6i	−2.37975	−	0.773229i
$179$	−5.45824e6	+	3.96565e6i	−0.951686	+	0.691440i	−0.951205	−	0.308559i	$-0.900153\pi$
$179$	−5.45824e6	+	3.96565e6i	−0.951686	+	0.691440i	−0.000481115		1.00000i	$0.500153\pi$
$180$		0			0
$181$	485921.	+	1.49551e6i	0.0819465	+	0.252205i	0.983633	−	0.180186i	$-0.0576699\pi$
$181$	485921.	+	1.49551e6i	0.0819465	+	0.252205i	−0.901686	+	0.432391i	$0.857670\pi$
$182$	3.64206e6	−	1.18338e6i	0.604133	−	0.196295i
$183$		0			0
$184$	1.11848e7	+	1.53946e7i	1.79546	+	2.47123i
$185$	−930799.	+	2.86470e6i	−0.147008	+	0.452444i
$186$		0			0
$187$	2.61875e6	−	2.72416e6i	0.400470	−	0.416589i
$188$	−3.38974e6			−0.510144
$189$		0			0
$190$	1.16621e7	−	8.47299e6i	1.70026	−	1.23531i
$191$	−205329.	−	149181.i	−0.0294680	−	0.0214098i	0.572954	−	0.819588i	$-0.305797\pi$
$191$	−205329.	−	149181.i	−0.0294680	−	0.0214098i	−0.602422	+	0.798178i	$0.705797\pi$
$192$		0			0
$193$	1.20143e7	−	3.90369e6i	1.67120	−	0.543005i	0.688024	−	0.725688i	$-0.258478\pi$
$193$	1.20143e7	−	3.90369e6i	1.67120	−	0.543005i	0.983172	+	0.182683i	$0.0584782\pi$
$194$	4.80439e6	−	6.61267e6i	0.658011	−	0.905674i
$195$		0			0
$196$	936985.	−	2.88374e6i	0.124441	−	0.382991i
$197$		−	9.97446e6i		−	1.30464i	−0.757943	−	0.652320i	$-0.773796\pi$
$197$		−	9.97446e6i		−	1.30464i	0.757943	−	0.652320i	$-0.226204\pi$
$198$		0			0
$199$	−9.29580e6			−1.17958			−0.589790	−	0.807557i	$-0.700789\pi$
$199$	−9.29580e6			−1.17958			−0.589790	+	0.807557i	$0.700789\pi$
$200$	1.22150e7	+	3.96890e6i	1.52688	+	0.496113i
$201$		0			0
$202$	−2.26469e7	−	1.64540e7i	−2.74761	−	1.99626i
$203$	−2.60402e6	−	8.01436e6i	−0.311284	−	0.958033i
$204$		0			0
$205$	−1.33615e6	+	1.83905e6i	−0.155094	+	0.213468i
$206$	−1.46103e7	−	2.01093e7i	−1.67131	−	2.30036i
$207$		0			0
$208$		−	5.53518e6i		−	0.615094i
$209$	7.32565e6	+	3.55238e6i	0.802430	+	0.389117i
$210$		0			0
$211$	7.75347e6	+	2.51926e6i	0.825371	+	0.268179i	0.691094	−	0.722765i	$-0.257129\pi$
$211$	7.75347e6	+	2.51926e6i	0.825371	+	0.268179i	0.134276	+	0.990944i	$0.457129\pi$
$212$	2.76904e7	−	2.01183e7i	2.90618	−	2.11146i
$213$		0			0
$214$	33200.2	+	102180.i	0.00338765	+	0.0104261i
$215$	6.59811e6	−	2.14386e6i	0.663903	−	0.215715i
$216$		0			0
$217$	−4.55462e6	−	6.26890e6i	−0.445732	−	0.613497i
$218$	−8.52339e6	+	2.62323e7i	−0.822703	+	2.53202i
$219$		0			0
$220$	5.54858e6	+	3.10548e7i	0.521091	+	2.91649i
$221$	−2.01800e6			−0.186958
$222$		0			0
$223$	8.44501e6	−	6.13566e6i	0.761527	−	0.553282i	−0.137851	−	0.990453i	$-0.544020\pi$
$223$	8.44501e6	−	6.13566e6i	0.761527	−	0.553282i	0.899378	+	0.437171i	$0.144020\pi$
$224$	−1.11760e7	−	8.11985e6i	−0.994359	−	0.722444i
$225$		0			0
$226$	−2.11686e7	+	6.87811e6i	−1.83387	+	0.595859i
$227$	−2.89743e6	+	3.98797e6i	−0.247705	+	0.340937i	−0.914706	−	0.404120i	$-0.867578\pi$
$227$	−2.89743e6	+	3.98797e6i	−0.247705	+	0.340937i	0.667001	+	0.745057i	$0.267578\pi$
$228$		0			0
$229$	−5.44106e6	+	1.67459e7i	−0.453083	+	1.39444i	0.420289	+	0.907390i	$0.361929\pi$
$229$	−5.44106e6	+	1.67459e7i	−0.453083	+	1.39444i	−0.873372	+	0.487054i	$0.838071\pi$
$230$			3.79535e7i			3.11938i
$231$		0			0
$232$	−2.67564e7			−2.14271
$233$	−1.87903e7	−	6.10535e6i	−1.48548	−	0.482661i	−0.549734	−	0.835340i	$-0.685271\pi$
$233$	−1.87903e7	−	6.10535e6i	−1.48548	−	0.482661i	−0.935745	+	0.352678i	$0.885271\pi$
$234$		0			0
$235$	−3.06562e6	−	2.22730e6i	−0.236219	−	0.171623i
$236$	340150.	+	1.04687e6i	0.0258782	+	0.0796451i
$237$		0			0
$238$	−8.99034e6	+	1.23741e7i	−0.666876	+	0.917876i
$239$	6.70660e6	+	9.23085e6i	0.491257	+	0.676157i	0.980619	−	0.195923i	$-0.0627703\pi$
$239$	6.70660e6	+	9.23085e6i	0.491257	+	0.676157i	−0.489362	+	0.872081i	$0.662770\pi$
$240$		0			0
$241$		−	5.25355e6i		−	0.375320i	−0.982234	−	0.187660i	$-0.939910\pi$
$241$		−	5.25355e6i		−	0.375320i	0.982234	−	0.187660i	$-0.0600904\pi$
$242$	−2.01393e7	+	1.58825e7i	−1.42102	+	1.12065i
$243$		0			0
$244$	2.60187e7	+	8.45398e6i	1.79108	+	0.581958i
$245$	2.74222e6	−	1.99234e6i	0.186468	−	0.135477i
$246$		0			0
$247$	−1.34358e6	−	4.13511e6i	−0.0891604	−	0.274408i
$248$	−2.33994e7	+	7.60294e6i	−1.53409	+	0.498455i
$249$		0			0
$250$	−6.58617e6	−	9.06509e6i	−0.421515	−	0.580166i
$251$	5.01611e6	−	1.54380e7i	0.317209	−	0.976270i	−0.657626	−	0.753344i	$-0.728439\pi$
$251$	5.01611e6	−	1.54380e7i	0.317209	−	0.976270i	0.974835	−	0.222925i	$-0.0715606\pi$
$252$		0			0
$253$	−1.89038e7	+	1.01065e7i	−1.16731	+	0.624078i
$254$	−3.58656e6			−0.218866
$255$		0			0
$256$	2.32237e7	−	1.68730e7i	1.38424	−	1.00571i
$257$	4.94612e6	+	3.59357e6i	0.291384	+	0.211703i	0.723868	−	0.689939i	$-0.242363\pi$
$257$	4.94612e6	+	3.59357e6i	0.291384	+	0.211703i	−0.432484	+	0.901642i	$0.642363\pi$
$258$		0			0
$259$	6.54904e6	−	2.12791e6i	0.376945	−	0.122477i
$260$	9.90252e6	−	1.36296e7i	0.563411	−	0.775469i
$261$		0			0
$262$	−9.51815e6	+	2.92939e7i	−0.529235	+	1.62882i
$263$		−	1.50722e7i		−	0.828535i	−0.910155	−	0.414267i	$-0.864038\pi$
$263$		−	1.50722e7i		−	0.828535i	0.910155	−	0.414267i	$-0.135962\pi$
$264$		0			0
$265$	3.82618e7			2.05602
$266$	−3.13417e7	−	1.01835e7i	−1.66524	−	0.541070i
$267$		0			0
$268$	−1.75241e7	−	1.27320e7i	−0.910397	−	0.661442i
$269$	4.88930e6	+	1.50477e7i	0.251183	+	0.773061i	0.994558	+	0.104186i	$0.0332238\pi$
$269$	4.88930e6	+	1.50477e7i	0.251183	+	0.773061i	−0.743375	+	0.668875i	$0.766776\pi$
$270$		0			0
$271$	5.77278e6	−	7.94555e6i	0.290053	−	0.399224i	−0.638978	−	0.769225i	$-0.720643\pi$
$271$	5.77278e6	−	7.94555e6i	0.290053	−	0.399224i	0.929031	+	0.370001i	$0.120643\pi$
$272$	1.29947e7	+	1.78857e7i	0.645744	+	0.888791i
$273$		0			0
$274$			1.95146e7i			0.948653i
$275$	−6.31295e6	+	1.30184e7i	−0.303553	+	0.625981i
$276$		0			0
$277$	−1.35351e7	−	4.39781e6i	−0.636826	−	0.206917i	−0.0272297	−	0.999629i	$-0.508669\pi$
$277$	−1.35351e7	−	4.39781e6i	−0.636826	−	0.206917i	−0.609597	+	0.792712i	$0.708669\pi$
$278$	5.27863e7	−	3.83515e7i	2.45690	−	1.78504i
$279$		0			0
$280$	−2.21155e7	−	6.80644e7i	−1.00745	−	3.10060i
$281$	375125.	−	121886.i	0.0169066	−	0.00549330i	−0.300551	−	0.953766i	$-0.597171\pi$
$281$	375125.	−	121886.i	0.0169066	−	0.00549330i	0.317458	+	0.948272i	$0.397171\pi$
$282$		0			0
$283$	7.98367e6	+	1.09886e7i	0.352244	+	0.484822i	0.947967	−	0.318367i	$-0.103135\pi$
$283$	7.98367e6	+	1.09886e7i	0.352244	+	0.484822i	−0.595723	+	0.803190i	$0.703135\pi$
$284$	−2.75473e7	+	8.47820e7i	−1.20261	+	3.70125i
$285$		0			0
$286$	1.35683e7	+	1.87548e6i	0.580001	+	0.0801704i
$287$	5.19678e6			0.219831
$288$		0			0
$289$	−1.30070e7	+	9.45012e6i	−0.538868	+	0.391511i
$290$	−4.31745e7	−	3.13681e7i	−1.77025	−	1.28616i
$291$		0			0
$292$	2.75193e7	−	8.94157e6i	1.10532	−	0.359141i
$293$	1.53510e7	−	2.11289e7i	0.610288	−	0.839990i	−0.386313	−	0.922368i	$-0.626251\pi$
$293$	1.53510e7	−	2.11289e7i	0.610288	−	0.839990i	0.996601	+	0.0823779i	$0.0262514\pi$
$294$		0			0
$295$	−380246.	+	1.17028e6i	−0.0148115	+	0.0455851i
$296$		−	2.18643e7i		−	0.843066i
$297$		0			0
$298$	5.34146e7			2.01842
$299$	1.08873e7	+	3.53750e6i	0.407293	+	0.132338i
$300$		0			0
$301$	−1.28313e7	−	9.32245e6i	−0.470511	−	0.341846i
$302$	−9.76501e6	−	3.00536e7i	−0.354529	−	1.09113i
$303$		0			0
$304$	−2.79979e7	+	3.85358e7i	−0.996564	+	1.37165i
$305$	1.79759e7	+	2.47418e7i	0.633566	+	0.872029i
$306$		0			0
$307$		−	3.16482e7i		−	1.09379i	−0.837201	−	0.546895i	$-0.815810\pi$
$307$		−	3.16482e7i		−	1.09379i	0.837201	−	0.546895i	$-0.184190\pi$
$308$	4.99802e7	−	5.19919e7i	1.71059	−	1.77944i
$309$		0			0
$310$	−4.66711e7	−	1.51644e7i	−1.56662	−	0.509025i
$311$	5.84392e6	−	4.24586e6i	0.194278	−	0.141151i	−0.486394	−	0.873740i	$-0.661688\pi$
$311$	5.84392e6	−	4.24586e6i	0.194278	−	0.141151i	0.680672	+	0.732589i	$0.261688\pi$
$312$		0			0
$313$	8.18170e6	+	2.51807e7i	0.266815	+	0.821172i	0.991270	+	0.131850i	$0.0420917\pi$
$313$	8.18170e6	+	2.51807e7i	0.266815	+	0.821172i	−0.724455	+	0.689323i	$0.757908\pi$
$314$	2.95008e7	−	9.58538e6i	0.952893	−	0.309614i
$315$		0			0
$316$	4.05069e7	+	5.57530e7i	1.28371	+	1.76688i
$317$	−5.12592e6	+	1.57760e7i	−0.160914	+	0.495243i	−0.998712	−	0.0507378i	$-0.983843\pi$
$317$	−5.12592e6	+	1.57760e7i	−0.160914	+	0.495243i	0.837798	+	0.545980i	$0.183843\pi$
$318$		0			0
$319$	4.12700e6	−	2.98572e7i	0.127134	−	0.919764i
$320$	−6.36287e6			−0.194179
$321$		0			0
$322$	7.01953e7	−	5.09998e7i	2.10252	−	1.52757i
$323$	1.40493e7	+	1.02074e7i	0.416915	+	0.302907i
$324$		0			0
$325$	7.34852e6	−	2.38768e6i	0.214067	−	0.0695546i
$326$	6.91448e6	−	9.51696e6i	0.199575	−	0.274692i
$327$		0			0
$328$	5.09896e6	−	1.56930e7i	0.144498	−	0.444718i
$329$			8.66279e6i			0.243260i
$330$		0			0
$331$	−4.76366e7			−1.31358			−0.656791	−	0.754073i	$-0.728086\pi$
$331$	−4.76366e7			−1.31358			−0.656791	+	0.754073i	$0.728086\pi$
$332$	−5.35711e6	−	1.74063e6i	−0.146392	−	0.0475655i
$333$		0			0
$334$	5.75036e7	+	4.17788e7i	1.54332	+	1.12129i
$335$	−7.48262e6	−	2.30292e7i	−0.199030	−	0.612553i
$336$		0			0
$337$	340443.	−	468579.i	0.00889518	−	0.0122432i	−0.804546	−	0.593890i	$-0.797591\pi$
$337$	340443.	−	468579.i	0.00889518	−	0.0122432i	0.813441	+	0.581647i	$0.197591\pi$
$338$	3.67760e7	+	5.06179e7i	0.952390	+	1.31085i
$339$		0			0
$340$			6.72890e7i			1.71201i
$341$	−4.87482e6	−	2.72839e7i	−0.122941	−	0.688086i
$342$		0			0
$343$	3.42671e7	+	1.11340e7i	0.849170	+	0.275912i
$344$	−4.07412e7	+	2.96002e7i	−1.00083	+	0.727143i
$345$		0			0
$346$	−3.65055e7	−	1.12352e8i	−0.881312	−	2.71240i
$347$	4.34119e7	−	1.41054e7i	1.03901	−	0.337595i	0.260664	−	0.965429i	$-0.416058\pi$
$347$	4.34119e7	−	1.41054e7i	1.03901	−	0.337595i	0.778347	+	0.627834i	$0.216058\pi$
$348$		0			0
$349$	1.19240e6	+	1.64120e6i	0.0280508	+	0.0386087i	0.822812	−	0.568314i	$-0.192404\pi$
$349$	1.19240e6	+	1.64120e6i	0.0280508	+	0.0386087i	−0.794761	+	0.606922i	$0.792404\pi$
$350$	1.80972e7	−	5.56974e7i	0.422092	−	1.29907i
$351$		0			0
$352$	−2.32962e7	−	4.35747e7i	−0.534143	−	0.999094i
$353$	−4.45069e7			−1.01182			−0.505910	−	0.862586i	$-0.668843\pi$
$353$	−4.45069e7			−1.01182			−0.505910	+	0.862586i	$0.668843\pi$
$354$		0			0
$355$	−8.06211e7	+	5.85747e7i	−1.80204	+	1.30926i
$356$	1.14823e8	+	8.34236e7i	2.54494	+	1.84901i
$357$		0			0
$358$	9.28982e7	−	3.01844e7i	2.02469	−	0.657861i
$359$	−2.76622e7	+	3.80738e7i	−0.597866	+	0.822892i	−0.995511	−	0.0946475i	$-0.969828\pi$
$359$	−2.76622e7	+	3.80738e7i	−0.597866	+	0.822892i	0.397645	+	0.917539i	$0.369828\pi$
$360$		0			0
$361$	2.97583e6	−	9.15865e6i	0.0632537	−	0.194675i
$362$		−	2.27661e7i		−	0.479914i
$363$		0			0
$364$	−3.85146e7			−0.798584
$365$	3.07632e7	+	9.99558e6i	0.632635	+	0.205556i
$366$		0			0
$367$	−3.04950e7	−	2.21559e7i	−0.616922	−	0.448220i	0.234923	−	0.972014i	$-0.424516\pi$
$367$	−3.04950e7	−	2.21559e7i	−0.616922	−	0.448220i	−0.851845	+	0.523794i	$0.824516\pi$
$368$	−3.87546e7	−	1.19274e8i	−0.777643	−	2.39334i
$369$		0			0
$370$	2.56329e7	−	3.52807e7i	0.506049	−	0.696517i
$371$	−5.14141e7	−	7.07655e7i	−1.00684	−	1.38580i
$372$		0			0
$373$		−	3.76414e7i		−	0.725336i	−0.931918	−	0.362668i	$-0.881866\pi$
$373$		−	3.76414e7i		−	0.725336i	0.931918	−	0.362668i	$-0.118134\pi$
$374$	−4.82461e7	+	2.57937e7i	−0.922247	+	0.493058i
$375$		0			0
$376$	2.61595e7	+	8.49974e6i	0.492114	+	0.159898i
$377$	−1.30224e7	+	9.46131e6i	−0.243033	+	0.176574i
$378$		0			0
$379$	8.50517e6	+	2.61762e7i	0.156230	+	0.480827i	0.998283	−	0.0585671i	$-0.0186532\pi$
$379$	8.50517e6	+	2.61762e7i	0.156230	+	0.480827i	−0.842053	+	0.539394i	$0.818653\pi$
$380$	−1.37882e8	+	4.48007e7i	−2.51280	+	0.816459i
$381$		0			0
$382$	2.15982e6	+	2.97274e6i	0.0387461	+	0.0533294i
$383$	1.73806e7	−	5.34919e7i	0.309362	−	0.952120i	−0.668651	−	0.743577i	$-0.733128\pi$
$383$	1.73806e7	−	5.34919e7i	0.309362	−	0.952120i	0.978013	−	0.208543i	$-0.0668722\pi$
$384$		0			0
$385$	7.93635e7	−	1.41799e7i	1.39072	−	0.248480i
$386$	−1.82894e8			−3.18007
$387$		0			0
$388$	−6.65061e7	+	4.83195e7i	−1.13859	+	0.827232i
$389$	−4.70617e7	−	3.41923e7i	−0.799501	−	0.580871i	0.111267	−	0.993791i	$-0.464509\pi$
$389$	−4.70617e7	−	3.41923e7i	−0.799501	−	0.580871i	−0.910768	+	0.412919i	$0.864509\pi$
$390$		0			0
$391$	−4.34849e7	+	1.41291e7i	−0.727458	+	0.236365i
$392$	−1.44619e7	+	1.99051e7i	−0.240087	+	0.330451i
$393$		0			0
$394$	−4.46249e7	+	1.37341e8i	−0.729607	+	2.24550i
$395$			7.70379e7i			1.25001i
$396$		0			0
$397$	−7.35626e7			−1.17567			−0.587835	−	0.808981i	$-0.700020\pi$
$397$	−7.35626e7			−1.17567			−0.587835	+	0.808981i	$0.700020\pi$
$398$	1.27997e8	+	4.15886e7i	2.03025	+	0.659668i
$399$		0			0
$400$	−6.84822e7	−	4.97552e7i	−1.07003	−	0.777425i
$401$	3.67310e7	+	1.13046e8i	0.569639	+	1.75317i	0.653749	+	0.756711i	$0.273195\pi$
$401$	3.67310e7	+	1.13046e8i	0.569639	+	1.75317i	−0.0841108	+	0.996456i	$0.526805\pi$
$402$		0			0
$403$	−8.70007e6	+	1.19746e7i	−0.132925	+	0.182956i
$404$	1.65484e8	+	2.27769e8i	2.50964	+	3.45422i
$405$		0			0
$406$			1.22002e8i			1.82301i
$407$	2.43982e7	+	3.37243e6i	0.361888	+	0.0500219i
$408$		0			0
$409$	−1.68902e6	−	548795.i	−0.0246868	−	0.00802121i	0.296648	−	0.954987i	$-0.404131\pi$
$409$	−1.68902e6	−	548795.i	−0.0246868	−	0.00802121i	−0.321334	+	0.946966i	$0.604131\pi$
$410$	2.66256e7	−	1.93447e7i	0.386321	−	0.280679i
$411$		0			0
$412$	7.72515e7	+	2.37756e8i	1.10463	+	3.39969i
$413$	2.67539e6	−	869286.i	0.0379784	−	0.0123399i
$414$		0			0
$415$	−3.70115e6	−	5.09420e6i	−0.0517836	−	0.0712740i
$416$	−8.15421e6	+	2.50961e7i	−0.113267	+	0.348599i
$417$		0			0
$418$	−8.49761e7	−	8.16881e7i	−1.16350	−	1.11848i
$419$	−8.72576e7			−1.18621			−0.593104	−	0.805126i	$-0.702098\pi$
$419$	−8.72576e7			−1.18621			−0.593104	+	0.805126i	$0.702098\pi$
$420$		0			0
$421$	1.73278e7	−	1.25894e7i	0.232218	−	0.168717i	−0.465591	−	0.885000i	$-0.654158\pi$
$421$	1.73278e7	−	1.25894e7i	0.232218	−	0.168717i	0.697809	+	0.716283i	$0.254158\pi$
$422$	−9.54890e7	−	6.93768e7i	−1.27062	−	0.923160i
$423$		0			0
$424$	−2.64141e8	+	8.58245e7i	−3.46527	+	1.12594i
$425$	−1.81397e7	+	2.49671e7i	−0.236299	+	0.325238i
$426$		0			0
$427$	2.16049e7	−	6.64932e7i	0.277504	−	0.854070i
$428$		−	1.08054e6i		−	0.0137820i
$429$		0			0
$430$	−1.00443e8			−1.26332
$431$	−1.44203e7	−	4.68543e6i	−0.180112	−	0.0585218i	0.217573	−	0.976044i	$-0.430186\pi$
$431$	−1.44203e7	−	4.68543e6i	−0.180112	−	0.0585218i	−0.397684	+	0.917522i	$0.630186\pi$
$432$		0			0
$433$	−2.58070e7	−	1.87499e7i	−0.317888	−	0.230959i	0.417386	−	0.908729i	$-0.362946\pi$
$433$	−2.58070e7	−	1.87499e7i	−0.317888	−	0.230959i	−0.735274	+	0.677770i	$0.762946\pi$
$434$	3.46675e7	+	1.06695e8i	0.424085	+	1.30520i
$435$		0			0
$436$	1.63055e8	−	2.24426e8i	1.96732	−	2.70778i
$437$	−5.79041e7	−	7.96981e7i	−0.693849	−	0.955001i
$438$		0			0
$439$		−	7.17575e7i		−	0.848152i	−0.905626	−	0.424076i	$-0.860599\pi$
$439$		−	7.17575e7i		−	0.848152i	0.905626	−	0.424076i	$-0.139401\pi$
$440$	3.50498e7	−	2.53571e8i	0.411460	−	2.97675i
$441$		0			0
$442$	2.77865e7	+	9.02838e6i	0.321786	+	0.104555i
$443$	−3.61066e7	+	2.62330e7i	−0.415313	+	0.301743i	−0.775749	−	0.631041i	$-0.782628\pi$
$443$	−3.61066e7	+	2.62330e7i	−0.415313	+	0.301743i	0.360436	+	0.932784i	$0.382628\pi$
$444$		0			0
$445$	4.90283e7	+	1.50894e8i	0.556374	+	1.71234i
$446$	−1.43732e8	+	4.67014e7i	−1.62013	+	0.526412i
$447$		0			0
$448$	8.55006e6	+	1.17682e7i	0.0950901	+	0.130880i
$449$	5.12810e7	−	1.57827e8i	0.566522	−	1.74358i	−0.0968618	−	0.995298i	$-0.530880\pi$
$449$	5.12810e7	−	1.57827e8i	0.566522	−	1.74358i	0.663384	−	0.748279i	$-0.269120\pi$
$450$		0			0
$451$	1.67252e7	+	8.11042e6i	0.182323	+	0.0884125i
$452$	2.23857e8			2.42413
$453$		0			0
$454$	5.77375e7	−	4.19487e7i	0.617007	−	0.448282i
$455$	−3.48319e7	−	2.53068e7i	−0.369779	−	0.268660i
$456$		0			0
$457$	3.75882e7	−	1.22131e7i	0.393825	−	0.127961i	−0.105409	−	0.994429i	$-0.533615\pi$
$457$	3.75882e7	−	1.22131e7i	0.393825	−	0.127961i	0.499233	+	0.866468i	$0.333615\pi$
$458$	1.49839e8	−	2.06236e8i	1.55966	−	2.14668i
$459$		0			0
$460$	1.17956e8	−	3.63030e8i	1.21184	−	3.72966i
$461$			2.68720e7i			0.274282i	0.990552	+	0.137141i	$0.0437914\pi$
$461$			2.68720e7i			0.274282i	−0.990552	+	0.137141i	$0.956209\pi$
$462$		0			0
$463$	−6.14457e7			−0.619082			−0.309541	−	0.950886i	$-0.600175\pi$
$463$	−6.14457e7			−0.619082			−0.309541	+	0.950886i	$0.600175\pi$
$464$	1.67712e8	+	5.44931e7i	1.67885	+	0.545491i
$465$		0			0
$466$	2.31415e8	+	1.68133e8i	2.28683	+	1.66148i
$467$	−2.77764e7	−	8.54869e7i	−0.272725	−	0.839361i	−0.989812	−	0.142378i	$-0.954525\pi$
$467$	−2.77764e7	−	8.54869e7i	−0.272725	−	0.839361i	0.717087	−	0.696983i	$-0.245475\pi$
$468$		0			0
$469$	−3.25378e7	+	4.47844e7i	−0.315406	+	0.434119i
$470$	3.22466e7	+	4.43837e7i	0.310592	+	0.427494i
$471$		0			0
$472$		−	8.93194e6i		−	0.0849414i
$473$	−2.67465e7	−	5.00283e7i	−0.252746	−	0.472751i
$474$		0			0
$475$	−6.32376e7	−	2.05471e7i	−0.590058	−	0.191721i
$476$	1.24451e8	−	9.04192e7i	1.15393	−	0.838378i
$477$		0			0
$478$	−5.10472e7	−	1.57107e8i	−0.467400	−	1.43851i
$479$	−1.02575e8	+	3.33285e7i	−0.933325	+	0.303256i	−0.735922	−	0.677067i	$-0.763251\pi$
$479$	−1.02575e8	+	3.33285e7i	−0.933325	+	0.303256i	−0.197403	+	0.980322i	$0.563251\pi$
$480$		0			0
$481$	−7.73144e6	−	1.06414e7i	−0.0694745	−	0.0956234i
$482$	−2.35040e7	+	7.23378e7i	−0.209894	+	0.645988i
$483$		0			0
$484$	2.41996e8	−	8.93268e7i	2.13438	−	0.787854i
$485$	−9.18963e7			−0.805514
$486$		0			0
$487$	−1.25418e6	+	911215.i	−0.0108586	+	0.00788922i	−0.593201	−	0.805054i	$-0.702136\pi$
$487$	−1.25418e6	+	911215.i	−0.0108586	+	0.00788922i	0.582343	+	0.812943i	$0.302136\pi$
$488$	−1.79595e8	−	1.30483e8i	−1.54538	−	1.12278i
$489$		0			0
$490$	−4.66720e7	+	1.51647e7i	−0.396706	+	0.128897i
$491$	−2.25359e7	+	3.10180e7i	−0.190384	+	0.262041i	−0.893529	−	0.449005i	$-0.851778\pi$
$491$	−2.25359e7	+	3.10180e7i	−0.190384	+	0.262041i	0.703145	+	0.711047i	$0.251778\pi$
$492$		0			0
$493$	1.98670e7	−	6.11443e7i	0.165803	−	0.510288i
$494$			6.29486e7i			0.522162i
$495$		0			0
$496$	1.62155e8			1.32888
$497$	2.16668e8	+	7.03998e7i	1.76493	+	0.573459i
$498$		0			0
$499$	−4.66237e7	−	3.38741e7i	−0.375236	−	0.272625i	0.384143	−	0.923274i	$-0.374497\pi$
$499$	−4.66237e7	−	3.38741e7i	−0.375236	−	0.272625i	−0.759379	+	0.650649i	$0.774497\pi$
$500$	3.48242e7	+	1.07178e8i	0.278594	+	0.857423i
$501$		0			0
$502$	−1.38137e8	+	1.90129e8i	−1.09194	+	1.50292i
$503$	3.67507e7	+	5.05829e7i	0.288776	+	0.397466i	0.928616	−	0.371042i	$-0.120999\pi$
$503$	3.67507e7	+	5.05829e7i	0.288776	+	0.397466i	−0.639840	+	0.768508i	$0.720999\pi$
$504$		0			0
$505$			3.14724e8i			2.44375i
$506$	3.05508e8	−	5.45852e7i	2.35815	−	0.421331i
$507$		0			0
$508$	3.43060e7	+	1.11467e7i	0.261685	+	0.0850265i
$509$	−1.03548e8	+	7.52318e7i	−0.785212	+	0.570490i	−0.906539	−	0.422123i	$-0.861285\pi$
$509$	−1.03548e8	+	7.52318e7i	−0.785212	+	0.570490i	0.121327	+	0.992613i	$0.461285\pi$
$510$		0			0
$511$	−2.28510e7	−	7.03282e7i	−0.171255	−	0.527068i
$512$	−2.85095e8	+	9.26330e7i	−2.12412	+	0.690170i
$513$		0			0
$514$	−5.20273e7	−	7.16095e7i	−0.383127	−	0.527328i
$515$	−8.63577e7	+	2.65782e8i	−0.632237	+	1.94582i
$516$		0			0
$517$	−1.35197e7	+	2.78801e7i	−0.0978352	+	0.201754i
$518$	−9.96959e7			−0.717279
$519$		0			0
$520$	−1.10597e8	+	8.03531e7i	−0.786560	+	0.571469i
$521$	1.67266e8	+	1.21526e8i	1.18275	+	0.859321i	0.992480	−	0.122410i	$-0.0390624\pi$
$521$	1.67266e8	+	1.21526e8i	1.18275	+	0.859321i	0.190274	+	0.981731i	$0.439062\pi$
$522$		0			0
$523$	−1.12640e8	+	3.65988e7i	−0.787383	+	0.255836i	−0.674989	−	0.737828i	$-0.735852\pi$
$523$	−1.12640e8	+	3.65988e7i	−0.787383	+	0.255836i	−0.112393	+	0.993664i	$0.535852\pi$
$524$	1.82085e8	−	2.50618e8i	1.26555	−	1.74188i
$525$		0			0
$526$	−6.74320e7	+	2.07534e8i	−0.463350	+	1.42604i
$527$		−	5.91182e7i		−	0.403914i
$528$		0			0
$529$	1.11337e8			0.752094
$530$	−5.26839e8	−	1.71180e8i	−3.53875	−	1.14981i
$531$		0			0
$532$	2.68138e8	+	1.94814e8i	1.78083	+	1.29385i
$533$	−3.06752e6	−	9.44085e6i	−0.0202584	−	0.0623490i
$534$		0			0
$535$	709995.	−	977224.i	0.00463654	−	0.00638165i
$536$	1.03313e8	+	1.42198e8i	0.670902	+	0.923417i
$537$		0			0
$538$		−	2.29071e8i		−	1.47104i
$539$	−1.99813e7	−	1.92081e7i	−0.127602	−	0.122665i
$540$		0			0
$541$	−2.74218e7	−	8.90989e6i	−0.173183	−	0.0562705i	0.221142	−	0.975242i	$-0.429022\pi$
$541$	−2.74218e7	−	8.90989e6i	−0.173183	−	0.0562705i	−0.394325	+	0.918971i	$0.629022\pi$
$542$	−1.15035e8	+	8.35778e7i	−0.722490	+	0.524920i
$543$		0			0
$544$	−3.25686e7	−	1.00236e8i	−0.202303	−	0.622625i
$545$	2.94927e8	−	9.58277e7i	1.82190	−	0.591973i
$546$		0			0
$547$	−1.16621e8	−	1.60516e8i	−0.712552	−	0.980744i	−0.999738	−	0.0228690i	$-0.992720\pi$
$547$	−1.16621e8	−	1.60516e8i	−0.712552	−	0.980744i	0.287187	−	0.957875i	$-0.407280\pi$
$548$	6.06493e7	−	1.86659e8i	0.368540	−	1.13425i
$549$		0			0
$550$	1.45168e8	−	1.51011e8i	0.872537	−	0.907656i
$551$	1.38519e8			0.828044
$552$		0			0
$553$	1.42482e8	−	1.03519e8i	0.842528	−	0.612133i
$554$	1.66693e8	+	1.21110e8i	0.980365	+	0.712277i
$555$		0			0
$556$	−6.24101e8	+	2.02783e8i	−3.63103	+	1.17979i
$557$	−1.21517e8	+	1.67254e8i	−0.703190	+	0.967858i	0.296727	+	0.954962i	$0.404105\pi$
$557$	−1.21517e8	+	1.67254e8i	−0.703190	+	0.967858i	−0.999917	+	0.0128958i	$0.995895\pi$
$558$		0			0
$559$	−9.36190e6	+	2.88130e7i	−0.0535955	+	0.164950i
$560$			4.71678e8i			2.68585i
$561$		0			0
$562$	−5.71052e6			−0.0321712
$563$	−2.74301e8	−	8.91257e7i	−1.53710	−	0.499434i	−0.586525	−	0.809931i	$-0.699504\pi$
$563$	−2.74301e8	−	8.91257e7i	−1.53710	−	0.499434i	−0.950574	+	0.310497i	$0.899504\pi$
$564$		0			0
$565$	2.02452e8	+	1.47090e8i	1.12248	+	0.815528i
$566$	−6.07676e7	−	1.87023e8i	−0.335137	−	1.03145i
$567$		0			0
$568$	4.25180e8	−	5.85210e8i	2.32021	−	3.19350i
$569$	−5.83545e7	−	8.03181e7i	−0.316765	−	0.435990i	0.620711	−	0.784040i	$-0.286844\pi$
$569$	−5.83545e7	−	8.03181e7i	−0.316765	−	0.435990i	−0.937476	+	0.348049i	$0.886844\pi$
$570$		0			0
$571$		−	3.34829e8i		−	1.79852i	−0.437416	−	0.899259i	$-0.644106\pi$
$571$		−	3.34829e8i		−	1.79852i	0.437416	−	0.899259i	$-0.355894\pi$
$572$	−1.23954e8	−	6.01082e7i	−0.662327	−	0.321178i
$573$		0			0
$574$	−7.15561e7	−	2.32500e7i	−0.378365	−	0.122938i
$575$	1.41632e8	−	1.02902e8i	0.745002	−	0.541275i
$576$		0			0
$577$	8.02142e7	+	2.46874e8i	0.417565	+	1.28513i	0.909937	+	0.414747i	$0.136130\pi$
$577$	8.02142e7	+	2.46874e8i	0.417565	+	1.28513i	−0.492372	+	0.870385i	$0.663870\pi$
$578$	2.21376e8	−	7.19294e7i	1.14643	−	0.372497i
$579$		0			0
$580$	3.15481e8	+	4.34222e8i	1.61692	+	2.22550i
$581$	−4.44834e6	+	1.36906e7i	−0.0226814	+	0.0698062i
$582$		0			0
$583$	−5.50287e7	−	3.07990e8i	−0.277705	−	1.55428i
$584$	−2.34795e8			−1.17883
$585$		0			0
$586$	−3.05902e8	+	2.22251e8i	−1.52016	+	1.10446i
$587$	8.37662e7	+	6.08597e7i	0.414147	+	0.300896i	0.775279	−	0.631619i	$-0.217609\pi$
$587$	8.37662e7	+	6.08597e7i	0.414147	+	0.300896i	−0.361131	+	0.932515i	$0.617609\pi$
$588$		0			0
$589$	1.21140e8	−	3.93606e7i	0.592844	−	0.192627i
$590$	1.04715e7	−	1.44127e7i	0.0509860	−	0.0701762i
$591$		0			0
$592$	−4.45298e7	+	1.37049e8i	−0.214628	+	0.660556i
$593$		−	2.40665e8i		−	1.15412i	−0.816703	−	0.577058i	$-0.804201\pi$
$593$		−	2.40665e8i		−	1.15412i	0.816703	−	0.577058i	$-0.195799\pi$
$594$		0			0
$595$	1.71963e8			0.816366
$596$	−5.10918e8	−	1.66007e8i	−2.41331	−	0.784131i
$597$		0			0
$598$	−1.34084e8	−	9.74180e7i	−0.627010	−	0.455549i
$599$	−1.00131e7	−	3.08173e7i	−0.0465897	−	0.143388i	0.925056	−	0.379832i	$-0.124018\pi$
$599$	−1.00131e7	−	3.08173e7i	−0.0465897	−	0.143388i	−0.971645	+	0.236444i	$0.924018\pi$
$600$		0			0
$601$	4.54073e7	−	6.24977e7i	0.209171	−	0.287899i	−0.691522	−	0.722356i	$-0.743059\pi$
$601$	4.54073e7	−	6.24977e7i	0.209171	−	0.287899i	0.900693	+	0.434456i	$0.143059\pi$
$602$	1.34970e8	+	1.85770e8i	0.618652	+	0.851501i
$603$		0			0
$604$			3.17815e8i			1.44233i
$605$	2.77551e8	+	7.82234e7i	1.25336	+	0.353241i
$606$		0			0
$607$	−1.20893e8	−	3.92805e7i	−0.540549	−	0.175635i	0.0260017	−	0.999662i	$-0.491722\pi$
$607$	−1.20893e8	−	3.92805e7i	−0.540549	−	0.175635i	−0.566551	+	0.824027i	$0.691722\pi$
$608$	1.83710e8	−	1.33473e8i	0.817377	−	0.593859i
$609$		0			0
$610$	−1.36824e8	−	4.21100e8i	−0.602797	−	1.85522i
$611$	1.57375e7	−	5.11341e6i	0.0689939	−	0.0224175i
$612$		0			0
$613$	1.22607e8	+	1.68754e8i	0.532271	+	0.732608i	0.987474	−	0.157779i	$-0.0504334\pi$
$613$	1.22607e8	+	1.68754e8i	0.532271	+	0.732608i	−0.455203	+	0.890388i	$0.650433\pi$
$614$	−1.41591e8	+	4.35774e8i	−0.611691	+	1.88259i
$615$		0			0
$616$	−5.16079e8	+	2.75910e8i	−2.20787	+	1.18039i
$617$	1.61919e8			0.689353			0.344677	−	0.938721i	$-0.387989\pi$
$617$	1.61919e8			0.689353			0.344677	+	0.938721i	$0.387989\pi$
$618$		0			0
$619$	2.62657e8	−	1.90831e8i	1.10743	−	0.804596i	0.125174	−	0.992135i	$-0.460051\pi$
$619$	2.62657e8	−	1.90831e8i	1.10743	−	0.804596i	0.982257	+	0.187539i	$0.0600510\pi$
$620$	3.99286e8	+	2.90098e8i	1.67536	+	1.21722i
$621$		0			0
$622$	−9.94623e7	+	3.23173e7i	−0.413321	+	0.134296i
$623$	2.13197e8	−	2.93440e8i	0.881692	−	1.21354i
$624$		0			0
$625$	−9.14152e7	+	2.81347e8i	−0.374437	+	1.15240i
$626$		−	3.83325e8i		−	1.56259i
$627$		0			0
$628$	−3.11969e8			−1.25960
$629$	4.99649e7	+	1.62346e7i	0.200777	+	0.0652363i
$630$		0			0
$631$	1.36522e8	+	9.91894e7i	0.543396	+	0.394800i	0.825345	−	0.564629i	$-0.190981\pi$
$631$	1.36522e8	+	9.91894e7i	0.543396	+	0.394800i	−0.281949	+	0.959429i	$0.590981\pi$
$632$	−1.72802e8	−	5.31831e8i	−0.684539	−	2.10680i
$633$		0			0
$634$	1.41161e8	−	1.94291e8i	0.553919	−	0.762404i
$635$	2.37015e7	+	3.26223e7i	0.0925667	+	0.127407i
$636$		0			0
$637$			1.48017e7i			0.0572657i
$638$	−1.90404e8	+	3.92648e8i	−0.733187	+	1.51197i
$639$		0			0
$640$	−2.80193e8	−	9.10402e7i	−1.06885	−	0.347291i
$641$	2.81093e8	−	2.04226e8i	1.06727	−	0.775419i	0.0918530	−	0.995773i	$-0.470721\pi$
$641$	2.81093e8	−	2.04226e8i	1.06727	−	0.775419i	0.975420	+	0.220353i	$0.0707210\pi$
$642$		0			0
$643$	1.58622e8	+	4.88188e8i	0.596665	+	1.83635i	0.546257	+	0.837618i	$0.316052\pi$
$643$	1.58622e8	+	4.88188e8i	0.596665	+	1.83635i	0.0504079	+	0.998729i	$0.483948\pi$
$644$	−8.29929e8	+	2.69660e8i	−3.10730	+	1.00962i
$645$		0			0
$646$	−1.47782e8	−	2.03405e8i	−0.548182	−	0.754507i
$647$	−8.77759e6	+	2.70146e7i	−0.0324088	+	0.0997439i	−0.965952	−	0.258720i	$-0.916699\pi$
$647$	−8.77759e6	+	2.70146e7i	−0.0324088	+	0.0997439i	0.933544	+	0.358464i	$0.116699\pi$
$648$		0			0
$649$	9.96705e6	+	1.37769e6i	0.0364613	+	0.00503986i
$650$	−1.11866e8			−0.407342
$651$		0			0
$652$	−9.57156e7	+	6.95415e7i	−0.345335	+	0.250900i
$653$	−1.06927e8	−	7.76873e7i	−0.384016	−	0.279004i	0.378983	−	0.925404i	$-0.376274\pi$
$653$	−1.06927e8	−	7.76873e7i	−0.384016	−	0.279004i	−0.762999	+	0.646400i	$0.776274\pi$
$654$		0			0
$655$	3.29348e8	−	1.07012e8i	1.17201	−	0.380809i
$656$	−6.39219e7	+	8.79810e7i	−0.226432	+	0.311657i
$657$		0			0
$658$	3.87566e7	−	1.19281e8i	0.136041	−	0.418690i
$659$			2.85200e8i			0.996536i	0.867023	+	0.498268i	$0.166030\pi$
$659$			2.85200e8i			0.996536i	−0.867023	+	0.498268i	$0.833970\pi$
$660$		0			0
$661$	9.10777e7			0.315361			0.157680	−	0.987490i	$-0.449598\pi$
$661$	9.10777e7			0.315361			0.157680	+	0.987490i	$0.449598\pi$
$662$	6.55923e8	+	2.13122e8i	2.26089	+	0.734607i
$663$		0			0
$664$	3.69776e7	+	2.68658e7i	0.126309	+	0.0917689i
$665$	1.14492e8	+	3.52372e8i	0.389325	+	1.19822i
$666$		0			0
$667$	−2.14369e8	+	2.95053e8i	−0.722410	+	0.994311i
$668$	−4.20185e8	−	5.78335e8i	−1.40965	−	1.94021i
$669$		0			0
$670$			3.50572e8i			1.16561i
$671$	1.73306e8	−	1.80282e8i	0.573649	−	0.596738i
$672$		0			0
$673$	−2.21522e8	−	7.19768e7i	−0.726727	−	0.236128i	−0.0777898	−	0.996970i	$-0.524786\pi$
$673$	−2.21522e8	−	7.19768e7i	−0.726727	−	0.236128i	−0.648937	+	0.760842i	$0.724786\pi$
$674$	−6.78405e6	+	4.92890e6i	−0.0221569	+	0.0160979i
$675$		0			0
$676$	−1.94452e8	−	5.98463e8i	−0.629467	−	1.93730i
$677$	−3.02743e8	+	9.83670e7i	−0.975680	+	0.317018i	−0.753107	−	0.657898i	$-0.771446\pi$
$677$	−3.02743e8	+	9.83670e7i	−0.975680	+	0.317018i	−0.222573	+	0.974916i	$0.571446\pi$
$678$		0			0
$679$	1.23485e8	+	1.69963e8i	0.394462	+	0.542931i
$680$	1.68727e8	−	5.19287e8i	0.536607	−	1.65151i
$681$		0			0
$682$	−5.49429e7	+	3.97489e8i	−0.173204	+	1.25306i
$683$	4.29254e8			1.34726			0.673631	−	0.739067i	$-0.264734\pi$
$683$	4.29254e8			1.34726			0.673631	+	0.739067i	$0.264734\pi$
$684$		0			0
$685$	1.77499e8	−	1.28960e8i	0.552234	−	0.401222i
$686$	−4.22021e8	−	3.06616e8i	−1.30726	−	0.949779i
$687$		0			0
$688$	3.15656e8	−	1.02563e8i	0.969280	−	0.314938i
$689$	−9.82093e7	+	1.35174e8i	−0.300258	+	0.413270i
$690$		0			0
$691$	9.14232e7	−	2.81372e8i	0.277091	−	0.852798i	−0.711568	−	0.702617i	$-0.752015\pi$
$691$	9.14232e7	−	2.81372e8i	0.277091	−	0.852798i	0.988659	−	0.150180i	$-0.0479855\pi$
$692$			1.18812e9i			3.58544i
$693$		0			0
$694$	−6.60858e8			−1.97710
$695$	−6.97668e8	−	2.26686e8i	−2.07823	−	0.675259i
$696$		0			0
$697$	3.20759e7	+	2.33045e7i	0.0947286	+	0.0688243i
$698$	−9.07594e6	−	2.79329e7i	−0.0266886	−	0.0821390i
$699$		0			0
$700$	−3.46204e8	+	4.76509e8i	−1.00934	+	1.38924i
$701$	−1.24633e8	−	1.71542e8i	−0.361807	−	0.497985i	0.588844	−	0.808247i	$-0.299583\pi$
$701$	−1.24633e8	−	1.71542e8i	−0.361807	−	0.497985i	−0.950651	+	0.310262i	$0.899583\pi$
$702$		0			0
$703$			1.13192e8i			0.325800i
$704$	9.15115e6	+	5.12180e7i	0.0262276	+	0.146793i
$705$		0			0
$706$	6.12829e8	+	1.99120e8i	1.74151	+	0.565850i
$707$	5.82084e8	−	4.22909e8i	1.64713	−	1.19671i
$708$		0			0
$709$	−7.27897e7	−	2.24024e8i	−0.204235	−	0.628572i	−0.999744	−	0.0226296i	$-0.992796\pi$
$709$	−7.27897e7	−	2.24024e8i	−0.204235	−	0.628572i	0.795508	−	0.605942i	$-0.207204\pi$
$710$	1.37216e9	−	4.45840e8i	3.83379	−	1.24567i
$711$		0			0
$712$	−6.76934e8	−	9.31719e8i	−1.87545	−	2.58134i
$713$	−1.03633e8	+	3.18948e8i	−0.285909	+	0.879937i
$714$		0			0
$715$	−7.26064e7	−	1.35807e8i	−0.198635	−	0.371540i
$716$	−9.82393e8			−2.67637
$717$		0			0
$718$	5.51229e8	−	4.00491e8i	1.48922	−	1.08198i
$719$	−2.53099e6	−	1.83887e6i	−0.00680932	−	0.00494726i	0.584375	−	0.811483i	$-0.301340\pi$
$719$	−2.53099e6	−	1.83887e6i	−0.00680932	−	0.00494726i	−0.591185	+	0.806536i	$0.701340\pi$
$720$		0			0
$721$	6.07608e8	−	1.97424e8i	1.62113	−	0.526737i
$722$	−8.19501e7	+	1.12795e8i	−0.217740	+	0.299693i
$723$		0			0
$724$	−7.07548e7	+	2.17761e8i	−0.186441	+	0.573805i
$725$			2.46162e8i			0.645962i
$726$		0			0
$727$	−5.03036e8			−1.30917			−0.654584	−	0.755989i	$-0.727156\pi$
$727$	−5.03036e8			−1.30917			−0.654584	+	0.755989i	$0.727156\pi$
$728$	2.97227e8	+	9.65749e7i	0.770361	+	0.250305i
$729$		0			0
$730$	−3.78869e8	−	2.75264e8i	−0.973913	−	0.707589i
$731$	−3.73922e7	−	1.15081e8i	−0.0957258	−	0.294614i
$732$		0			0
$733$	3.92704e8	−	5.40511e8i	0.997134	−	1.37244i	0.0700675	−	0.997542i	$-0.477679\pi$
$733$	3.92704e8	−	5.40511e8i	0.997134	−	1.37244i	0.927067	−	0.374896i	$-0.122321\pi$
$734$	3.20771e8	+	4.41504e8i	0.811161	+	1.11647i
$735$		0			0
$736$			5.97874e8i			1.49960i
$737$	−1.74612e8	+	9.33524e7i	−0.436186	+	0.233197i
$738$		0			0
$739$	−5.58670e8	−	1.81523e8i	−1.38427	−	0.449778i	−0.480202	−	0.877158i	$-0.659437\pi$
$739$	−5.58670e8	−	1.81523e8i	−1.38427	−	0.449778i	−0.904072	+	0.427380i	$0.859437\pi$
$740$	−3.54831e8	+	2.57800e8i	−0.875641	+	0.636191i
$741$		0			0
$742$	3.91338e8	+	1.20441e9i	0.957944	+	2.94825i
$743$	−3.19311e8	+	1.03751e8i	−0.778481	+	0.252944i	−0.671191	−	0.741284i	$-0.734217\pi$
$743$	−3.19311e8	+	1.03751e8i	−0.778481	+	0.252944i	−0.107289	+	0.994228i	$0.534217\pi$
$744$		0			0
$745$	−3.52986e8	−	4.85844e8i	−0.853667	−	1.17497i
$746$	−1.68404e8	+	5.18296e8i	−0.405637	+	1.24842i
$747$		0			0
$748$	5.41644e8	−	9.67759e7i	1.29422	−	0.231240i
$749$	−2.76143e6			−0.00657187
$750$		0			0
$751$	−6.33745e8	+	4.60442e8i	−1.49622	+	1.08706i	−0.524358	+	0.851498i	$0.675695\pi$
$751$	−6.33745e8	+	4.60442e8i	−1.49622	+	1.08706i	−0.971858	+	0.235567i	$0.924305\pi$
$752$	−1.46660e8	−	1.06555e8i	−0.344873	−	0.250565i
$753$		0			0
$754$	2.21638e8	−	7.20146e7i	0.517048	−	0.167999i
$755$	−2.08827e8	+	2.87426e8i	−0.485229	+	0.667860i
$756$		0			0
$757$	−2.22239e8	+	6.83980e8i	−0.512309	+	1.57672i	0.275817	+	0.961210i	$0.411052\pi$
$757$	−2.22239e8	+	6.83980e8i	−0.512309	+	1.57672i	−0.788126	+	0.615514i	$0.788948\pi$
$758$		−	3.98480e8i		−	0.914952i
$759$		0			0
$760$	1.17641e9			2.67990
$761$	4.77743e8	+	1.55228e8i	1.08403	+	0.352222i	0.795936	−	0.605380i	$-0.206979\pi$
$761$	4.77743e8	+	1.55228e8i	1.08403	+	0.352222i	0.288092	+	0.957603i	$0.406979\pi$
$762$		0			0
$763$	−5.73541e8	−	4.16702e8i	−1.29119	−	0.938106i
$764$	−1.14200e7	−	3.51472e7i	−0.0256086	−	0.0788152i
$765$		0			0
$766$	−4.78637e8	+	6.58787e8i	−1.06493	+	1.46575i
$767$	−3.15842e6	−	4.34719e6i	−0.00699976	−	0.00963435i
$768$		0			0
$769$			2.81032e8i			0.617984i	0.951065	+	0.308992i	$0.0999916\pi$
$769$			2.81032e8i			0.617984i	−0.951065	+	0.308992i	$0.900008\pi$
$770$	−1.15622e9	−	1.59818e8i	−2.53261	−	0.350069i
$771$		0			0
$772$	1.74940e9	+	5.68415e8i	3.80222	+	1.23542i
$773$	−6.57818e8	+	4.77933e8i	−1.42419	+	1.03473i	−0.433126	+	0.901333i	$0.642590\pi$
$773$	−6.57818e8	+	4.77933e8i	−1.42419	+	1.03473i	−0.991062	+	0.133400i	$0.957410\pi$
$774$		0			0
$775$	6.99479e7	+	2.15278e8i	0.150269	+	0.462481i
$776$	6.34406e8	−	2.06131e8i	1.35763	−	0.441122i
$777$		0			0
$778$	4.95033e8	+	6.81355e8i	1.05122	+	1.44689i
$779$	−2.63975e7	+	8.12431e7i	−0.0558406	+	0.171860i
$780$		0			0
$781$	5.87448e8	+	5.64719e8i	1.23315	+	1.18544i
$782$	6.61969e8			1.38426
$783$		0			0
$784$	1.31189e8	−	9.53143e7i	0.272238	−	0.197792i
$785$	−2.82139e8	−	2.04986e8i	−0.583249	−	0.423755i
$786$		0			0
$787$	7.07771e8	−	2.29969e8i	1.45201	−	0.471785i	0.526388	−	0.850244i	$-0.323546\pi$
$787$	7.07771e8	−	2.29969e8i	1.45201	−	0.471785i	0.925618	+	0.378459i	$0.123546\pi$
$788$	8.53687e8	−	1.17500e9i	1.74470	−	2.40137i
$789$		0			0
$790$	3.44661e8	−	1.06076e9i	0.699055	−	2.15147i
$791$		−	5.72089e8i		−	1.15594i
$792$		0			0
$793$	−1.33549e8			−0.267807
$794$	1.01291e9	+	3.29113e8i	2.02352	+	0.657482i
$795$		0			0
$796$	−1.09505e9	−	7.95601e8i	−2.17118	−	1.57745i
$797$	6.16903e7	+	1.89863e8i	0.121855	+	0.375030i	0.993315	−	0.115436i	$-0.0368266\pi$
$797$	6.16903e7	+	1.89863e8i	0.121855	+	0.375030i	−0.871460	+	0.490466i	$0.836827\pi$
$798$		0			0
$799$	−3.88476e7	+	5.34691e7i	−0.0761594	+	0.104824i
$800$	2.37196e8	+	3.26472e8i	0.463273	+	0.637641i
$801$		0			0
$802$		−	1.72090e9i		−	3.33605i
$803$	3.62156e7	−	2.62005e8i	0.0699437	−	0.506014i
$804$		0			0
$805$	−9.27759e8	−	3.01447e8i	−1.77847	−	0.577861i
$806$	1.73367e8	−	1.25959e8i	0.331102	−	0.240560i
$807$		0			0
$808$	−7.05953e8	−	2.17270e9i	−1.33826	−	4.11875i
$809$	1.14776e7	−	3.72930e6i	0.0216773	−	0.00704339i	−0.298158	−	0.954516i	$-0.596372\pi$
$809$	1.14776e7	−	3.72930e6i	0.0216773	−	0.00704339i	0.319836	+	0.947473i	$0.396372\pi$
$810$		0			0
$811$	4.24994e8	+	5.84954e8i	0.796746	+	1.09663i	0.993235	+	0.116121i	$0.0370460\pi$
$811$	4.24994e8	+	5.84954e8i	0.796746	+	1.09663i	−0.196489	+	0.980506i	$0.562954\pi$
$812$	3.79171e8	−	1.16697e9i	0.708218	−	2.17967i
$813$		0			0
$814$	−3.20858e8	−	1.55592e8i	−0.594894	−	0.288478i
$815$	−1.32257e8			−0.244313
$816$		0			0
$817$	2.10919e8	−	1.53241e8i	0.386766	−	0.281002i
$818$	2.08013e7	+	1.51130e7i	0.0380042	+	0.0276116i
$819$		0			0
$820$	−3.14799e8	+	1.02284e8i	−0.570941	+	0.185510i
$821$	−1.75859e8	+	2.42049e8i	−0.317786	+	0.437394i	−0.937790	−	0.347204i	$-0.887131\pi$
$821$	−1.75859e8	+	2.42049e8i	−0.317786	+	0.437394i	0.620004	+	0.784599i	$0.287131\pi$
$822$		0			0
$823$	−2.40878e8	+	7.41345e8i	−0.432113	+	1.32991i	0.463904	+	0.885885i	$0.346448\pi$
$823$	−2.40878e8	+	7.41345e8i	−0.432113	+	1.32991i	−0.896017	+	0.444020i	$0.853552\pi$
$824$		−	2.02853e9i		−	3.62577i
$825$		0			0
$826$	−4.07274e7			−0.0722680
$827$	−4.22018e8	−	1.37122e8i	−0.746129	−	0.242432i	−0.0888144	−	0.996048i	$-0.528308\pi$
$827$	−4.22018e8	−	1.37122e8i	−0.746129	−	0.242432i	−0.657315	+	0.753616i	$0.728308\pi$
$828$		0			0
$829$	6.18089e8	+	4.49068e8i	1.08489	+	0.788221i	0.978530	−	0.206106i	$-0.0660792\pi$
$829$	6.18089e8	+	4.49068e8i	1.08489	+	0.788221i	0.106364	+	0.994327i	$0.466079\pi$
$830$	2.81712e7	+	8.67022e7i	0.0492688	+	0.151634i
$831$		0			0
$832$	1.63320e7	−	2.24791e7i	0.0283576	−	0.0390309i
$833$	−3.47495e7	−	4.78286e7i	−0.0601192	−	0.0827470i
$834$		0			0
$835$		−	7.99127e8i		−	1.37264i
$836$	5.58929e8	+	1.04545e9i	0.956616	+	1.78931i
$837$		0			0
$838$	1.20148e9	+	3.90383e8i	2.04166	+	0.663375i
$839$	−5.07966e7	+	3.69059e7i	−0.0860099	+	0.0624899i	−0.629959	−	0.776628i	$-0.716928\pi$
$839$	−5.07966e7	+	3.69059e7i	−0.0860099	+	0.0624899i	0.543949	+	0.839118i	$0.316928\pi$
$840$		0			0
$841$	2.53422e7	+	7.79952e7i	0.0426045	+	0.131123i
$842$	−2.94915e8	+	9.58238e7i	−0.494039	+	0.160523i
$843$		0			0
$844$	6.97749e8	+	9.60369e8i	1.16057	+	1.59739i
$845$	2.17374e8	−	6.69008e8i	0.360278	−	1.10882i
$846$		0			0
$847$	−2.28283e8	−	6.18445e8i	−0.375685	−	1.01777i
$848$	1.83046e9			3.00174
$849$		0			0
$850$	3.61471e8	−	2.62624e8i	0.588596	−	0.427640i
$851$	−2.41107e8	−	1.75174e8i	−0.391219	−	0.284238i
$852$		0			0
$853$	−2.24699e8	+	7.30092e7i	−0.362038	+	0.117633i	−0.484387	−	0.874854i	$-0.660957\pi$
$853$	−2.24699e8	+	7.30092e7i	−0.362038	+	0.117633i	0.122349	+	0.992487i	$0.460957\pi$
$854$	−5.94970e8	+	8.18906e8i	−0.955260	+	1.31480i
$855$		0			0
$856$	−2.70945e6	+	8.33884e6i	−0.00431977	+	0.0132949i
$857$		−	4.83150e7i		−	0.0767609i	−0.999263	−	0.0383804i	$-0.987780\pi$
$857$		−	4.83150e7i		−	0.0767609i	0.999263	−	0.0383804i	$-0.0122199\pi$
$858$		0			0
$859$	−4.09758e8			−0.646469			−0.323235	−	0.946319i	$-0.604770\pi$
$859$	−4.09758e8			−0.646469			−0.323235	+	0.946319i	$0.604770\pi$
$860$	9.60749e8	+	3.12166e8i	1.51048	+	0.490784i
$861$		0			0
$862$	1.77595e8	+	1.29030e8i	0.277274	+	0.201451i
$863$	1.48301e8	+	4.56423e8i	0.230734	+	0.710125i	0.997659	+	0.0683887i	$0.0217858\pi$
$863$	1.48301e8	+	4.56423e8i	0.230734	+	0.710125i	−0.766925	+	0.641737i	$0.778214\pi$
$864$		0			0
$865$	−7.80680e8	+	1.07451e9i	−1.20621	+	1.66021i
$866$	2.71459e8	+	3.73631e8i	0.417975	+	0.575294i
$867$		0			0
$868$		−	1.12830e9i		−	1.72530i
$869$	6.20118e8	−	1.10797e8i	0.944964	−	0.168837i
$870$		0			0
$871$	1.00565e8	+	3.26755e7i	0.152192	+	0.0494502i
$872$	−1.82108e9	+	1.32309e9i	−2.74650	+	1.99545i
$873$		0			0
$874$	4.40736e8	+	1.35645e9i	0.660152	+	2.03174i
$875$	2.73903e8	−	8.89966e7i	0.408859	−	0.132846i
$876$		0			0
$877$	−3.54069e8	−	4.87334e8i	−0.524915	−	0.722483i	0.461430	−	0.887177i	$-0.347336\pi$
$877$	−3.54069e8	−	4.87334e8i	−0.524915	−	0.722483i	−0.986345	+	0.164694i	$0.947336\pi$
$878$	−3.21037e8	+	9.88051e8i	−0.474321	+	1.45981i
$879$		0			0
$880$	−7.36130e8	+	1.51803e9i	−1.08021	+	2.22758i
$881$	−6.92476e8			−1.01269			−0.506346	−	0.862331i	$-0.669004\pi$
$881$	−6.92476e8			−1.01269			−0.506346	+	0.862331i	$0.669004\pi$
$882$		0			0
$883$	7.43278e8	−	5.40023e8i	1.07962	−	0.784387i	0.102000	−	0.994784i	$-0.467476\pi$
$883$	7.43278e8	−	5.40023e8i	1.07962	−	0.784387i	0.977616	+	0.210397i	$0.0674757\pi$
$884$	−2.37722e8	−	1.72715e8i	−0.344122	−	0.250020i
$885$		0			0
$886$	6.14527e8	−	1.99672e8i	0.883568	−	0.287089i
$887$	−5.04692e8	+	6.94649e8i	−0.723195	+	0.995393i	0.276216	+	0.961095i	$0.410919\pi$
$887$	−5.04692e8	+	6.94649e8i	−0.723195	+	0.995393i	−0.999412	+	0.0342973i	$0.989081\pi$
$888$		0			0
$889$	2.84864e7	−	8.76721e7i	0.0405445	−	0.124783i
$890$		−	2.29705e9i		−	3.25837i
$891$		0			0
$892$	1.51996e9			2.14160
$893$	−1.35429e8	−	4.40034e7i	−0.190176	−	0.0617919i
$894$		0			0
$895$	−8.88459e8	−	6.45503e8i	−1.23928	−	0.900387i
$896$	2.08128e8	+	6.40553e8i	0.289339	+	0.890494i
$897$		0			0
$898$	−1.41221e9	+	1.94374e9i	−1.95015	+	2.68416i
$899$	−2.77173e8	−	3.81495e8i	−0.381480	−	0.525062i
$900$		0			0
$901$		−	6.67346e8i		−	0.912382i
$902$	−1.94009e8	−	1.86502e8i	−0.264363	−	0.254134i
$903$		0			0
$904$	−1.72757e9	−	5.61320e8i	−2.33846	−	0.759811i
$905$	−2.07074e8	+	1.50448e8i	−0.279370	+	0.202974i
$906$		0			0
$907$	−2.03336e8	−	6.25803e8i	−0.272516	−	0.838718i	−0.989866	−	0.142005i	$-0.954645\pi$
$907$	−2.03336e8	−	6.25803e8i	−0.272516	−	0.838718i	0.717350	−	0.696713i	$-0.245355\pi$
$908$	−6.82639e8	+	2.21803e8i	−0.911871	+	0.296285i
$909$		0			0
$910$	3.66390e8	+	5.04292e8i	0.486205	+	0.669203i
$911$	−1.65736e8	+	5.10082e8i	−0.219210	+	0.674660i	0.779617	+	0.626256i	$0.215414\pi$
$911$	−1.65736e8	+	5.10082e8i	−0.219210	+	0.674660i	−0.998828	+	0.0484041i	$0.984586\pi$
$912$		0			0
$913$	−3.56828e7	+	3.71190e7i	−0.0468864	+	0.0487735i
$914$	−5.72204e8			−0.749397
$915$		0			0
$916$	−2.07419e9	+	1.50699e9i	−2.69875	+	1.96076i
$917$	−6.40478e8	−	4.65335e8i	−0.830609	−	0.603472i
$918$		0			0
$919$	−5.43956e8	+	1.76742e8i	−0.700838	+	0.227716i	−0.637696	−	0.770289i	$-0.720112\pi$
$919$	−5.43956e8	+	1.76742e8i	−0.700838	+	0.227716i	−0.0631423	+	0.998005i	$0.520112\pi$
$920$	−1.82059e9	+	2.50583e9i	−2.33802	+	3.21801i
$921$		0			0
$922$	1.20223e8	−	3.70009e8i	0.153390	−	0.472085i
$923$		−	4.35170e8i		−	0.553419i
$924$		0			0
$925$	−2.01155e8			−0.254159
$926$	8.46064e8	+	2.74903e8i	1.06554	+	0.346215i
$927$		0			0
$928$	−6.80119e8	−	4.94135e8i	−0.851023	−	0.618304i
$929$	1.13618e8	+	3.49681e8i	0.141710	+	0.436139i	0.996573	−	0.0827148i	$-0.0263591\pi$
$929$	1.13618e8	+	3.49681e8i	0.141710	+	0.436139i	−0.854863	+	0.518853i	$0.826359\pi$
$930$		0			0
$931$	7.48699e7	−	1.03050e8i	0.0927808	−	0.127702i
$932$	−1.69097e9	−	2.32743e9i	−2.08876	−	2.87494i
$933$		0			0
$934$			1.30136e9i			1.59720i
$935$	5.53442e8	+	2.68377e8i	0.677075	+	0.328330i
$936$		0			0
$937$	−5.92174e8	−	1.92409e8i	−0.719831	−	0.233887i	−0.0738809	−	0.997267i	$-0.523538\pi$
$937$	−5.92174e8	−	1.92409e8i	−0.719831	−	0.233887i	−0.645950	+	0.763380i	$0.723538\pi$
$938$	6.48385e8	−	4.71079e8i	0.785641	−	0.570802i
$939$		0			0
$940$	−1.70503e8	−	5.24755e8i	−0.205281	−	0.631790i
$941$	1.24933e9	−	4.05933e8i	1.49937	−	0.487175i	0.559536	−	0.828806i	$-0.310979\pi$
$941$	1.24933e9	−	4.05933e8i	1.49937	−	0.487175i	0.939834	+	0.341631i	$0.110979\pi$
$942$		0			0
$943$	−1.32201e8	−	1.81958e8i	−0.157651	−	0.216989i
$944$	−1.81911e7	+	5.59865e7i	−0.0216244	+	0.0665530i
$945$		0			0
$946$	1.44458e8	+	8.08517e8i	0.170635	+	0.955027i
$947$	−1.01794e9			−1.19859			−0.599297	−	0.800527i	$-0.704553\pi$
$947$	−1.01794e9			−1.19859			−0.599297	+	0.800527i	$0.704553\pi$
$948$		0			0
$949$	−1.14275e8	+	8.30257e7i	−0.133707	+	0.0971435i
$950$	7.78812e8	+	5.65840e8i	0.908367	+	0.659968i
$951$		0			0
$952$	−1.18715e9	+	3.85728e8i	−1.37592	+	0.447065i
$953$	2.86452e8	−	3.94267e8i	0.330958	−	0.455524i	−0.610815	−	0.791773i	$-0.709158\pi$
$953$	2.86452e8	−	3.94267e8i	0.330958	−	0.455524i	0.941773	+	0.336249i	$0.109158\pi$
$954$		0			0
$955$	1.27662e7	−	3.92902e7i	0.0146572	−	0.0451101i
$956$			1.66140e9i			1.90152i
$957$		0			0
$958$	1.56149e9			1.77600
$959$	−4.77026e8	−	1.54995e8i	−0.540861	−	0.175737i
$960$		0			0
$961$	3.67205e8	+	2.66790e8i	0.413750	+	0.300607i
$962$	5.88477e7	+	1.81115e8i	0.0661005	+	0.203436i
$963$		0			0
$964$	4.49637e8	−	6.18872e8i	0.501916	−	0.690828i
$965$	1.20864e9	+	1.66355e9i	1.34497	+	1.85120i
$966$		0			0
$967$			8.21587e8i			0.908602i	0.890848	+	0.454301i	$0.150111\pi$
$967$			8.21587e8i			0.908602i	−0.890848	+	0.454301i	$0.849889\pi$
$968$	−2.09154e9	+	8.25551e7i	−2.30589	+	0.0910160i
$969$		0			0
$970$	1.26535e9	+	4.11137e8i	1.38642	+	0.450475i
$971$	−3.00122e8	+	2.18051e8i	−0.327823	+	0.238177i	−0.739506	−	0.673150i	$-0.764941\pi$
$971$	−3.00122e8	+	2.18051e8i	−0.327823	+	0.238177i	0.411683	+	0.911327i	$0.364941\pi$
$972$		0			0
$973$	5.18230e8	+	1.59495e9i	0.562580	+	1.73144i
$974$	2.13459e7	−	6.93570e6i	0.0231014	−	0.00750609i
$975$		0			0
$976$	8.59976e8	+	1.18366e9i	0.924989	+	1.27314i
$977$	2.16170e8	−	6.65301e8i	0.231799	−	0.713403i	−0.765731	−	0.643161i	$-0.777623\pi$
$977$	2.16170e8	−	6.65301e8i	0.231799	−	0.713403i	0.997530	−	0.0702422i	$-0.0223772\pi$
$978$		0			0
$979$	1.14411e9	−	6.11671e8i	1.21932	−	0.651884i
$980$	4.93554e8			0.524393
$981$		0			0
$982$	4.49076e8	−	3.26273e8i	0.474226	−	0.344546i
$983$	4.48636e8	+	3.25953e8i	0.472317	+	0.343158i	0.798344	−	0.602202i	$-0.205710\pi$
$983$	4.48636e8	+	3.25953e8i	0.472317	+	0.343158i	−0.326027	+	0.945361i	$0.605710\pi$
$984$		0			0
$985$	1.54412e9	−	5.01714e8i	1.61574	−	0.524986i
$986$	−5.47109e8	+	7.53031e8i	−0.570746	+	0.785565i
$987$		0			0
$988$	1.95638e8	−	6.02112e8i	0.202853	−	0.624319i
$989$			6.86422e8i			0.709582i
$990$		0			0
$991$	−1.59329e9			−1.63710			−0.818549	−	0.574437i	$-0.805221\pi$
$991$	−1.59329e9			−1.63710			−0.818549	+	0.574437i	$0.805221\pi$
$992$	−7.35200e8	−	2.38881e8i	−0.753130	−	0.244707i
$993$		0			0
$994$	−2.66841e9	−	1.93871e9i	−2.71702	−	1.97403i
$995$	−4.67577e8	−	1.43905e9i	−0.474662	−	1.46086i
$996$		0			0
$997$	−9.43669e7	+	1.29885e8i	−0.0952214	+	0.131061i	−0.853969	−	0.520323i	$-0.825811\pi$
$997$	−9.43669e7	+	1.29885e8i	−0.0952214	+	0.131061i	0.758748	+	0.651384i	$0.225811\pi$
$998$	4.90426e8	+	6.75013e8i	0.493380	+	0.679080i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.7.k.a.46.1		20
3.2	odd	2		11.7.d.a.2.5	✓	20
11.6	odd	10	inner	99.7.k.a.28.1		20
33.17	even	10		11.7.d.a.6.5	yes	20
33.26	odd	10		121.7.b.c.120.20		20
33.29	even	10		121.7.b.c.120.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.2.5	✓	20	3.2	odd	2
11.7.d.a.6.5	yes	20	33.17	even	10
99.7.k.a.28.1		20	11.6	odd	10	inner
99.7.k.a.46.1		20	1.1	even	1	trivial
121.7.b.c.120.1		20	33.29	even	10
121.7.b.c.120.20		20	33.26	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.7693 - 4.47392i) q^{2} +(117.801 + 85.5872i) q^{4} +(50.2998 + 154.807i) q^{5} +(218.726 - 301.051i) q^{7} +(-694.490 - 955.883i) q^{8} +O(q^{10})\)	\(q+(-13.7693 - 4.47392i) q^{2} +(117.801 + 85.5872i) q^{4} +(50.2998 + 154.807i) q^{5} +(218.726 - 301.051i) q^{7} +(-694.490 - 955.883i) q^{8} -2356.62i q^{10} +(1173.78 - 627.535i) q^{11} +(-676.019 - 219.652i) q^{13} +(-4358.59 + 3166.70i) q^{14} +(2406.36 + 7406.03i) q^{16} +(2700.07 - 877.307i) q^{17} +(3595.40 + 4948.64i) q^{19} +(-7324.14 + 22541.4i) q^{20} +(-18969.7 + 3389.32i) q^{22} -16105.1 q^{23} +(-8794.25 + 6389.39i) q^{25} +(8325.60 + 6048.91i) q^{26} +(51532.2 - 16743.8i) q^{28} +(13310.6 - 18320.5i) q^{29} +(6434.78 - 19804.2i) q^{31} -37123.4i q^{32} -41103.2 q^{34} +(57606.7 + 18717.5i) q^{35} +(14970.9 + 10877.0i) q^{37} +(-27366.3 - 84224.8i) q^{38} +(113045. - 155593. i) q^{40} +(8208.64 + 11298.2i) q^{41} -42621.5i q^{43} +(191981. + 26536.5i) q^{44} +(221755. + 72052.7i) q^{46} +(-18833.6 + 13683.4i) q^{47} +(-6434.91 - 19804.6i) q^{49} +(149676. - 48632.8i) q^{50} +(-60836.1 - 83733.7i) q^{52} +(72638.0 - 223557. i) q^{53} +(156188. + 150145. i) q^{55} -439673. q^{56} +(-265243. + 192710. i) q^{58} +(6115.84 + 4443.42i) q^{59} +(178688. - 58059.2i) q^{61} +(-177205. + 243902. i) q^{62} +(-12079.6 + 37177.0i) q^{64} -115701. i q^{65} -148760. q^{67} +(393157. + 127744. i) q^{68} +(-709463. - 515455. i) q^{70} +(189186. + 582255. i) q^{71} +(116805. - 160768. i) q^{73} +(-157476. - 216747. i) q^{74} +890673. i q^{76} +(67816.6 - 490626. i) q^{77} +(450118. + 146252. i) q^{79} +(-1.02547e6 + 745044. i) q^{80} +(-62479.9 - 192293. i) q^{82} +(-36790.9 + 11954.1i) q^{83} +(271627. + 373862. i) q^{85} +(-190685. + 586869. i) q^{86} +(-1.41503e6 - 686181. i) q^{88} +974721. q^{89} +(-213989. + 155472. i) q^{91} +(-1.89719e6 - 1.37839e6i) q^{92} +(320544. - 104151. i) q^{94} +(-585236. + 805508. i) q^{95} +(-174460. + 536933. i) q^{97} +301485. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} + 215 q^{4} - 181 q^{5} - 365 q^{7} - 1595 q^{8}+O(q^{10}) \) 20 * q + 5 * q^2 + 215 * q^4 - 181 * q^5 - 365 * q^7 - 1595 * q^8	\( 20 q + 5 q^{2} + 215 q^{4} - 181 q^{5} - 365 q^{7} - 1595 q^{8} + 3498 q^{11} - 1805 q^{13} - 7170 q^{14} - 2185 q^{16} - 3635 q^{17} + 23845 q^{19} - 5144 q^{20} - 2915 q^{22} - 7816 q^{23} - 30416 q^{25} + 131310 q^{26} + 226540 q^{28} - 134595 q^{29} - 71211 q^{31} - 228190 q^{34} + 377445 q^{35} - 205731 q^{37} - 127220 q^{38} + 704340 q^{40} - 490975 q^{41} + 537812 q^{44} - 714610 q^{46} - 25329 q^{47} + 304010 q^{49} - 417855 q^{50} + 1468510 q^{52} + 110919 q^{53} - 5511 q^{55} + 862620 q^{56} - 667940 q^{58} + 581009 q^{59} + 892675 q^{61} - 2337360 q^{62} + 124615 q^{64} - 960956 q^{67} + 1822680 q^{68} - 1987140 q^{70} + 288895 q^{71} - 806585 q^{73} + 404170 q^{74} - 623095 q^{77} + 1662955 q^{79} - 1190956 q^{80} - 282095 q^{82} - 14645 q^{83} - 33365 q^{85} - 735635 q^{86} - 1860485 q^{88} - 1111620 q^{89} + 650935 q^{91} - 4407784 q^{92} - 5913080 q^{94} + 4329525 q^{95} - 1189281 q^{97}+O(q^{100}) \) 20 * q + 5 * q^2 + 215 * q^4 - 181 * q^5 - 365 * q^7 - 1595 * q^8 + 3498 * q^11 - 1805 * q^13 - 7170 * q^14 - 2185 * q^16 - 3635 * q^17 + 23845 * q^19 - 5144 * q^20 - 2915 * q^22 - 7816 * q^23 - 30416 * q^25 + 131310 * q^26 + 226540 * q^28 - 134595 * q^29 - 71211 * q^31 - 228190 * q^34 + 377445 * q^35 - 205731 * q^37 - 127220 * q^38 + 704340 * q^40 - 490975 * q^41 + 537812 * q^44 - 714610 * q^46 - 25329 * q^47 + 304010 * q^49 - 417855 * q^50 + 1468510 * q^52 + 110919 * q^53 - 5511 * q^55 + 862620 * q^56 - 667940 * q^58 + 581009 * q^59 + 892675 * q^61 - 2337360 * q^62 + 124615 * q^64 - 960956 * q^67 + 1822680 * q^68 - 1987140 * q^70 + 288895 * q^71 - 806585 * q^73 + 404170 * q^74 - 623095 * q^77 + 1662955 * q^79 - 1190956 * q^80 - 282095 * q^82 - 14645 * q^83 - 33365 * q^85 - 735635 * q^86 - 1860485 * q^88 - 1111620 * q^89 + 650935 * q^91 - 4407784 * q^92 - 5913080 * q^94 + 4329525 * q^95 - 1189281 * q^97

Introduction

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