LMFDB - Embedded newform 69.7.b.a.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(47,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("69.47");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.20732i q^{2} +(17.8105 + 20.2925i) q^{3} +36.8838 q^{4} -125.797i q^{5} +(105.670 - 92.7449i) q^{6} -679.000 q^{7} -525.334i q^{8} +(-94.5737 + 722.839i) q^{9} +O(q^{10})$	\(q-5.20732i q^{2} +(17.8105 + 20.2925i) q^{3} +36.8838 q^{4} -125.797i q^{5} +(105.670 - 92.7449i) q^{6} -679.000 q^{7} -525.334i q^{8} +(-94.5737 + 722.839i) q^{9} -655.063 q^{10} -1924.82i q^{11} +(656.918 + 748.466i) q^{12} -1928.28 q^{13} +3535.77i q^{14} +(2552.73 - 2240.50i) q^{15} -375.020 q^{16} -4422.28i q^{17} +(3764.06 + 492.475i) q^{18} +6716.65 q^{19} -4639.86i q^{20} +(-12093.3 - 13778.6i) q^{21} -10023.2 q^{22} -2536.99i q^{23} +(10660.4 - 9356.46i) q^{24} -199.773 q^{25} +10041.2i q^{26} +(-16352.6 + 10955.0i) q^{27} -25044.1 q^{28} +11970.9i q^{29} +(-11667.0 - 13292.9i) q^{30} -23213.1 q^{31} -31668.5i q^{32} +(39059.5 - 34282.0i) q^{33} -23028.2 q^{34} +85415.8i q^{35} +(-3488.24 + 26661.1i) q^{36} -68465.9 q^{37} -34975.8i q^{38} +(-34343.6 - 39129.7i) q^{39} -66085.2 q^{40} -38306.2i q^{41} +(-71749.7 + 62973.7i) q^{42} +119575. q^{43} -70994.7i q^{44} +(90930.7 + 11897.0i) q^{45} -13210.9 q^{46} -38155.5i q^{47} +(-6679.28 - 7610.10i) q^{48} +343392. q^{49} +1040.28i q^{50} +(89739.2 - 78762.9i) q^{51} -71122.3 q^{52} -39821.6i q^{53} +(57046.1 + 85153.5i) q^{54} -242136. q^{55} +356702. i q^{56} +(119627. + 136298. i) q^{57} +62336.4 q^{58} +45777.4i q^{59} +(94154.4 - 82638.1i) q^{60} +143399. q^{61} +120878. i q^{62} +(64215.5 - 490808. i) q^{63} -188910. q^{64} +242571. i q^{65} +(-178517. - 203395. i) q^{66} -313543. q^{67} -163110. i q^{68} +(51482.0 - 45185.1i) q^{69} +444788. q^{70} +214612. i q^{71} +(379732. + 49682.8i) q^{72} +61451.6 q^{73} +356524. i q^{74} +(-3558.05 - 4053.89i) q^{75} +247736. q^{76} +1.30695e6i q^{77} +(-203761. + 178838. i) q^{78} +515901. q^{79} +47176.2i q^{80} +(-513553. - 136723. i) q^{81} -199473. q^{82} +55417.6i q^{83} +(-446047. - 508208. i) q^{84} -556307. q^{85} -622666. i q^{86} +(-242920. + 213208. i) q^{87} -1.01117e6 q^{88} +419701. i q^{89} +(61951.7 - 473505. i) q^{90} +1.30930e6 q^{91} -93574.1i q^{92} +(-413436. - 471052. i) q^{93} -198688. q^{94} -844932. i q^{95} +(642635. - 564032. i) q^{96} -424148. q^{97} -1.78815e6i q^{98} +(1.39134e6 + 182037. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	5.20732i		−	0.650915i	−0.945557	−	0.325458i	$-0.894482\pi$
$2$		−	5.20732i		−	0.650915i	0.945557	−	0.325458i	$-0.105518\pi$
$3$	17.8105	+	20.2925i	0.659647	+	0.751575i
$3$	17.8105	+	20.2925i	0.659647	+	0.751575i
$4$	36.8838			0.576310
$5$		−	125.797i		−	1.00637i	−0.864178	−	0.503186i	$-0.832161\pi$
$5$		−	125.797i		−	1.00637i	0.864178	−	0.503186i	$-0.167839\pi$
$6$	105.670	−	92.7449i	0.489212	−	0.429374i
$7$	−679.000			−1.97959			−0.989795	−	0.142496i	$-0.954487\pi$
$7$	−679.000			−1.97959			−0.989795	+	0.142496i	$0.954487\pi$
$8$		−	525.334i		−	1.02604i
$9$	−94.5737	+	722.839i	−0.129731	+	0.991549i
$10$	−655.063			−0.655063
$11$		−	1924.82i		−	1.44615i	−0.690772	−	0.723073i	$-0.742729\pi$
$11$		−	1924.82i		−	1.44615i	0.690772	−	0.723073i	$-0.257271\pi$
$12$	656.918	+	748.466i	0.380161	+	0.433140i
$13$	−1928.28			−0.877687			−0.438844	−	0.898563i	$-0.644612\pi$
$13$	−1928.28			−0.877687			−0.438844	+	0.898563i	$0.644612\pi$
$14$			3535.77i			1.28855i
$15$	2552.73	−	2240.50i	0.756365	−	0.663851i
$16$	−375.020			−0.0915576
$17$		−	4422.28i		−	0.900117i	−0.892999	−	0.450059i	$-0.851403\pi$
$17$		−	4422.28i		−	0.900117i	0.892999	−	0.450059i	$-0.148597\pi$
$18$	3764.06	+	492.475i	0.645414	+	0.0844436i
$19$	6716.65			0.979247			0.489623	−	0.871934i	$-0.337134\pi$
$19$	6716.65			0.979247			0.489623	+	0.871934i	$0.337134\pi$
$20$		−	4639.86i		−	0.579982i
$21$	−12093.3	−	13778.6i	−1.30583	−	1.48781i
$22$	−10023.2			−0.941318
$23$		−	2536.99i		−	0.208514i
$23$		−	2536.99i		−	0.208514i
$24$	10660.4	−	9356.46i	0.771149	−	0.676827i
$25$	−199.773			−0.0127854
$26$			10041.2i			0.571300i
$27$	−16352.6	+	10955.0i	−0.830800	+	0.556571i
$28$	−25044.1			−1.14086
$29$			11970.9i			0.490832i	0.969418	+	0.245416i	$0.0789246\pi$
$29$			11970.9i			0.490832i	−0.969418	+	0.245416i	$0.921075\pi$
$30$	−11667.0	−	13292.9i	−0.432111	−	0.492329i
$31$	−23213.1			−0.779197			−0.389599	−	0.920985i	$-0.627386\pi$
$31$	−23213.1			−0.779197			−0.389599	+	0.920985i	$0.627386\pi$
$32$		−	31668.5i		−	0.966447i
$33$	39059.5	−	34282.0i	1.08689	−	0.953946i
$34$	−23028.2			−0.585900
$35$			85415.8i			1.99221i
$36$	−3488.24	+	26661.1i	−0.0747650	+	0.571439i
$37$	−68465.9			−1.35167			−0.675833	−	0.737055i	$-0.736216\pi$
$37$	−68465.9			−1.35167			−0.675833	+	0.737055i	$0.736216\pi$
$38$		−	34975.8i		−	0.637406i
$39$	−34343.6	−	39129.7i	−0.578964	−	0.659648i
$40$	−66085.2			−1.03258
$41$		−	38306.2i		−	0.555799i	−0.960610	−	0.277899i	$-0.910362\pi$
$41$		−	38306.2i		−	0.555799i	0.960610	−	0.277899i	$-0.0896382\pi$
$42$	−71749.7	+	62973.7i	−0.968439	+	0.849986i
$43$	119575.			1.50396			0.751979	−	0.659187i	$-0.229100\pi$
$43$	119575.			1.50396			0.751979	+	0.659187i	$0.229100\pi$
$44$		−	70994.7i		−	0.833428i
$45$	90930.7	+	11897.0i	0.997868	+	0.130557i
$46$	−13210.9			−0.135725
$47$		−	38155.5i		−	0.367505i	−0.982973	−	0.183752i	$-0.941176\pi$
$47$		−	38155.5i		−	0.367505i	0.982973	−	0.183752i	$-0.0588245\pi$
$48$	−6679.28	−	7610.10i	−0.0603957	−	0.0688124i
$49$	343392.			2.91878
$50$			1040.28i			0.00832224i
$51$	89739.2	−	78762.9i	0.676506	−	0.593760i
$52$	−71122.3			−0.505820
$53$		−	39821.6i		−	0.267480i	−0.991016	−	0.133740i	$-0.957301\pi$
$53$		−	39821.6i		−	0.267480i	0.991016	−	0.133740i	$-0.0426987\pi$
$54$	57046.1	+	85153.5i	0.362280	+	0.540780i
$55$	−242136.			−1.45536
$56$			356702.i			2.03115i
$57$	119627.	+	136298.i	0.645957	+	0.735977i
$58$	62336.4			0.319490
$59$			45777.4i			0.222892i	0.993770	+	0.111446i	$0.0355482\pi$
$59$			45777.4i			0.222892i	−0.993770	+	0.111446i	$0.964452\pi$
$60$	94154.4	−	82638.1i	0.435900	−	0.382584i
$61$	143399.			0.631765			0.315883	−	0.948798i	$-0.397699\pi$
$61$	143399.			0.631765			0.315883	+	0.948798i	$0.397699\pi$
$62$			120878.i			0.507191i
$63$	64215.5	−	490808.i	0.256814	−	1.96286i
$64$	−188910.			−0.720633
$65$			242571.i			0.883280i
$66$	−178517.	−	203395.i	−0.620938	−	0.707471i
$67$	−313543.			−1.04249			−0.521246	−	0.853406i	$-0.674533\pi$
$67$	−313543.			−1.04249			−0.521246	+	0.853406i	$0.674533\pi$
$68$		−	163110.i		−	0.518746i
$69$	51482.0	−	45185.1i	0.156714	−	0.137546i
$70$	444788.			1.29676
$71$			214612.i			0.599623i	0.953999	+	0.299811i	$0.0969237\pi$
$71$			214612.i			0.599623i	−0.953999	+	0.299811i	$0.903076\pi$
$72$	379732.	+	49682.8i	1.01737	+	0.133109i
$73$	61451.6			0.157966			0.0789832	−	0.996876i	$-0.474833\pi$
$73$	61451.6			0.157966			0.0789832	+	0.996876i	$0.474833\pi$
$74$			356524.i			0.879819i
$75$	−3558.05	−	4053.89i	−0.00843389	−	0.00960923i
$76$	247736.			0.564349
$77$			1.30695e6i			2.86278i
$78$	−203761.	+	178838.i	−0.429375	+	0.376856i
$79$	515901.			1.04637			0.523184	−	0.852220i	$-0.324744\pi$
$79$	515901.			1.04637			0.523184	+	0.852220i	$0.324744\pi$
$80$			47176.2i			0.0921410i
$81$	−513553.	−	136723.i	−0.966340	−	0.257269i
$82$	−199473.			−0.361778
$83$			55417.6i			0.0969201i	0.998825	+	0.0484600i	$0.0154313\pi$
$83$			55417.6i			0.0969201i	−0.998825	+	0.0484600i	$0.984569\pi$
$84$	−446047.	−	508208.i	−0.752564	−	0.857440i
$85$	−556307.			−0.905853
$86$		−	622666.i		−	0.978949i
$87$	−242920.	+	213208.i	−0.368898	+	0.323776i
$88$	−1.01117e6			−1.48381
$89$			419701.i			0.595346i	0.954668	+	0.297673i	$0.0962106\pi$
$89$			419701.i			0.595346i	−0.954668	+	0.297673i	$0.903789\pi$
$90$	61951.7	−	473505.i	0.0849818	−	0.649527i
$91$	1.30930e6			1.73746
$92$		−	93574.1i		−	0.120169i
$93$	−413436.	−	471052.i	−0.513995	−	0.585625i
$94$	−198688.			−0.239214
$95$		−	844932.i		−	0.985487i
$96$	642635.	−	564032.i	0.726358	−	0.637515i
$97$	−424148.			−0.464732			−0.232366	−	0.972628i	$-0.574647\pi$
$97$	−424148.			−0.464732			−0.232366	+	0.972628i	$0.574647\pi$
$98$		−	1.78815e6i		−	1.89988i
$99$	1.39134e6	+	182037.i	1.43392	+	0.187609i
$100$	−7368.38			−0.00736838
$101$			1.31621e6i			1.27750i	0.769414	+	0.638751i	$0.220549\pi$
$101$			1.31621e6i			1.27750i	−0.769414	+	0.638751i	$0.779451\pi$
$102$	−410143.	−	467301.i	−0.386487	−	0.440348i
$103$	989957.			0.905951			0.452975	−	0.891523i	$-0.350363\pi$
$103$	989957.			0.905951			0.452975	+	0.891523i	$0.350363\pi$
$104$			1.01299e6i			0.900545i
$105$	−1.73330e6	+	1.52130e6i	−1.49729	+	1.31415i
$106$	−207364.			−0.174107
$107$		−	2.09288e6i		−	1.70841i	−0.519933	−	0.854207i	$-0.674043\pi$
$107$		−	2.09288e6i		−	1.70841i	0.519933	−	0.854207i	$-0.325957\pi$
$108$	−603148.	+	404061.i	−0.478798	+	0.320757i
$109$	1.47515e6			1.13909			0.569543	−	0.821961i	$-0.307120\pi$
$109$	1.47515e6			1.13909			0.569543	+	0.821961i	$0.307120\pi$
$110$			1.26088e6i			0.947317i
$111$	−1.21941e6	−	1.38935e6i	−0.891623	−	1.01588i
$112$	254638.			0.181247
$113$		−	858892.i		−	0.595255i	−0.954682	−	0.297628i	$-0.903805\pi$
$113$		−	858892.i		−	0.595255i	0.954682	−	0.297628i	$-0.0961954\pi$
$114$	709747.	−	622935.i	0.479059	−	0.420463i
$115$	−319145.			−0.209843
$116$			441533.i			0.282871i
$117$	182364.	−	1.39384e6i	0.113863	−	0.870270i
$118$	238377.			0.145084
$119$			3.00272e6i			1.78186i
$120$	−1.17701e6	−	1.34104e6i	−0.681140	−	0.776063i
$121$	−1.93337e6			−1.09134
$122$		−	746723.i		−	0.411225i
$123$	777330.	−	682252.i	0.417725	−	0.366631i
$124$	−856187.			−0.449059
$125$		−	1.94044e6i		−	0.993505i
$126$	−2.55579e6	−	334391.i	−1.27766	−	0.167164i
$127$	−1.37412e6			−0.670832			−0.335416	−	0.942070i	$-0.608877\pi$
$127$	−1.37412e6			−0.670832			−0.335416	+	0.942070i	$0.608877\pi$
$128$		−	1.04307e6i		−	0.497377i
$129$	2.12969e6	+	2.42648e6i	0.992082	+	1.13034i
$130$	1.26314e6			0.574940
$131$		−	1.48497e6i		−	0.660547i	−0.943885	−	0.330274i	$-0.892859\pi$
$131$		−	1.48497e6i		−	0.660547i	0.943885	−	0.330274i	$-0.107141\pi$
$132$	1.44066e6	−	1.26445e6i	0.626384	−	0.549769i
$133$	−4.56060e6			−1.93851
$134$			1.63272e6i			0.678574i
$135$	1.37810e6	+	2.05711e6i	0.560117	+	0.836095i
$136$	−2.32317e6			−0.923560
$137$			1.63158e6i			0.634524i	0.948338	+	0.317262i	$0.102763\pi$
$137$			1.63158e6i			0.634524i	−0.948338	+	0.317262i	$0.897237\pi$
$138$	−235293.	−	268084.i	−0.0895307	−	0.102008i
$139$	1.25229e6			0.466296			0.233148	−	0.972441i	$-0.425097\pi$
$139$	1.25229e6			0.466296			0.233148	+	0.972441i	$0.425097\pi$
$140$			3.15046e6i			1.14813i
$141$	774271.	−	679567.i	0.276208	−	0.242424i
$142$	1.11755e6			0.390303
$143$			3.71159e6i			1.26926i
$144$	35467.0	−	271079.i	0.0118778	−	0.0907838i
$145$	1.50590e6			0.493960
$146$		−	319998.i		−	0.102823i
$147$	6.11597e6	+	6.96828e6i	1.92537	+	2.19368i
$148$	−2.52528e6			−0.778978
$149$		−	3.39715e6i		−	1.02696i	−0.858100	−	0.513482i	$-0.828355\pi$
$149$		−	3.39715e6i		−	1.02696i	0.858100	−	0.513482i	$-0.171645\pi$
$150$	−21109.9	+	18527.9i	−0.00625479	+	0.00548974i
$151$	3.11288e6			0.904132			0.452066	−	0.891985i	$-0.350687\pi$
$151$	3.11288e6			0.904132			0.452066	+	0.891985i	$0.350687\pi$
$152$		−	3.52849e6i		−	1.00475i
$153$	3.19660e6	+	418231.i	0.892511	+	0.116773i
$154$	6.80572e6			1.86342
$155$			2.92012e6i			0.784163i
$156$	−1.26672e6	−	1.44325e6i	−0.333663	−	0.380161i
$157$	1.03424e6			0.267252			0.133626	−	0.991032i	$-0.457338\pi$
$157$	1.03424e6			0.267252			0.133626	+	0.991032i	$0.457338\pi$
$158$		−	2.68646e6i		−	0.681097i
$159$	808081.	−	709242.i	0.201031	−	0.176442i
$160$	−3.98379e6			−0.972606
$161$			1.72262e6i			0.412773i
$162$	−711961.	+	2.67423e6i	−0.167460	+	0.629005i
$163$	4.94434e6			1.14168			0.570842	−	0.821060i	$-0.306617\pi$
$163$	4.94434e6			1.14168			0.570842	+	0.821060i	$0.306617\pi$
$164$		−	1.41288e6i		−	0.320312i
$165$	−4.31255e6	−	4.91355e6i	−0.960025	−	1.09381i
$166$	288577.			0.0630867
$167$		−	7.40064e6i		−	1.58898i	−0.607274	−	0.794492i	$-0.707737\pi$
$167$		−	7.40064e6i		−	1.58898i	0.607274	−	0.794492i	$-0.292263\pi$
$168$	−7.23838e6	+	6.35303e6i	−1.52656	+	1.33984i
$169$	−1.10855e6			−0.229665
$170$			2.89687e6i			0.589634i
$171$	−635218.	+	4.85506e6i	−0.127038	+	0.970971i
$172$	4.41039e6			0.866745
$173$			6.54271e6i			1.26363i	0.775120	+	0.631814i	$0.217689\pi$
$173$			6.54271e6i			1.26363i	−0.775120	+	0.631814i	$0.782311\pi$
$174$	1.11024e6	+	1.26496e6i	0.210751	+	0.240121i
$175$	135646.			0.0253100
$176$			721846.i			0.132406i
$177$	−928938.	+	815317.i	−0.167520	+	0.147030i
$178$	2.18552e6			0.387520
$179$		−	9.57003e6i		−	1.66861i	−0.551304	−	0.834304i	$-0.685870\pi$
$179$		−	9.57003e6i		−	1.66861i	0.551304	−	0.834304i	$-0.314130\pi$
$180$	3.35387e6	+	438808.i	0.575081	+	0.0752415i
$181$	−2.01207e6			−0.339319			−0.169660	−	0.985503i	$-0.554267\pi$
$181$	−2.01207e6			−0.339319			−0.169660	+	0.985503i	$0.554267\pi$
$182$		−	6.81795e6i		−	1.13094i
$183$	2.55400e6	+	2.90992e6i	0.416742	+	0.474819i
$184$	−1.33277e6			−0.213945
$185$			8.61278e6i			1.36028i
$186$	−2.45292e6	+	2.15289e6i	−0.381192	+	0.334567i
$187$	−8.51209e6			−1.30170
$188$		−	1.40732e6i		−	0.211797i
$189$	1.11034e7	−	7.43843e6i	1.64464	−	1.10178i
$190$	−4.39983e6			−0.641468
$191$			8.10201e6i			1.16277i	0.813629	+	0.581384i	$0.197488\pi$
$191$			8.10201e6i			1.16277i	−0.813629	+	0.581384i	$0.802512\pi$
$192$	−3.36457e6	−	3.83345e6i	−0.475363	−	0.541610i
$193$	−605071.			−0.0841656			−0.0420828	−	0.999114i	$-0.513399\pi$
$193$	−605071.			−0.0841656			−0.0420828	+	0.999114i	$0.513399\pi$
$194$			2.20868e6i			0.302501i
$195$	−4.92238e6	+	4.32030e6i	−0.663852	+	0.582653i
$196$	1.26656e7			1.68212
$197$		−	5.22675e6i		−	0.683649i	−0.939764	−	0.341825i	$-0.888955\pi$
$197$		−	5.22675e6i		−	0.683649i	0.939764	−	0.341825i	$-0.111045\pi$
$198$	947926.	−	7.24513e6i	0.122118	−	0.933363i
$199$	−1.31363e7			−1.66691			−0.833456	−	0.552586i	$-0.813641\pi$
$199$	−1.31363e7			−1.66691			−0.833456	+	0.552586i	$0.813641\pi$
$200$			104947.i			0.0131184i
$201$	−5.58435e6	−	6.36258e6i	−0.687677	−	0.783511i
$202$	6.85393e6			0.831545
$203$		−	8.12825e6i		−	0.971648i
$204$	3.30992e6	−	2.90508e6i	0.389877	−	0.342190i
$205$	−4.81879e6			−0.559341
$206$		−	5.15502e6i		−	0.589697i
$207$	1.83384e6	+	239933.i	0.206752	+	0.0270507i
$208$	723143.			0.0803589
$209$		−	1.29283e7i		−	1.41613i
$210$	7.92188e6	+	9.02586e6i	0.855402	+	0.974610i
$211$	−8.78236e6			−0.934898			−0.467449	−	0.884020i	$-0.654827\pi$
$211$	−8.78236e6			−0.934898			−0.467449	+	0.884020i	$0.654827\pi$
$212$		−	1.46877e6i		−	0.154151i
$213$	−4.35501e6	+	3.82233e6i	−0.450662	+	0.395539i
$214$	−1.08983e7			−1.11203
$215$		−	1.50421e7i		−	1.51354i
$216$	5.75503e6	+	8.59061e6i	0.571066	+	0.852437i
$217$	1.57617e7			1.54249
$218$		−	7.68158e6i		−	0.741449i
$219$	1.09448e6	+	1.24701e6i	0.104202	+	0.118724i
$220$	−8.93089e6			−0.838739
$221$			8.52738e6i			0.790022i
$222$	−7.23477e6	+	6.34986e6i	−0.661250	+	0.580371i
$223$	9.23686e6			0.832933			0.416466	−	0.909151i	$-0.363268\pi$
$223$	9.23686e6			0.832933			0.416466	+	0.909151i	$0.363268\pi$
$224$			2.15029e7i			1.91317i
$225$	18893.2	−	144404.i	0.00165866	−	0.0126774i
$226$	−4.47253e6			−0.387461
$227$		−	2.27454e7i		−	1.94453i	−0.233873	−	0.972267i	$-0.575140\pi$
$227$		−	2.27454e7i		−	1.94453i	0.233873	−	0.972267i	$-0.424860\pi$
$228$	4.41229e6	+	5.02719e6i	0.372271	+	0.424151i
$229$	−1.92118e7			−1.59978			−0.799891	−	0.600145i	$-0.795110\pi$
$229$	−1.92118e7			−1.59978			−0.799891	+	0.600145i	$0.795110\pi$
$230$			1.66189e6i			0.136590i
$231$	−2.65214e7	+	2.32774e7i	−2.15159	+	1.88842i
$232$	6.28873e6			0.503616
$233$			1.41041e7i			1.11500i	0.830176	+	0.557502i	$0.188240\pi$
$233$			1.41041e7i			1.11500i	−0.830176	+	0.557502i	$0.811760\pi$
$234$	−7.25815e6	−	949630.i	−0.566472	−	0.0741151i
$235$	−4.79982e6			−0.369847
$236$			1.68844e6i			0.128455i
$237$	9.18844e6	+	1.04689e7i	0.690234	+	0.786425i
$238$	1.56361e7			1.15984
$239$		−	1.28904e7i		−	0.944218i	−0.881540	−	0.472109i	$-0.843493\pi$
$239$		−	1.28904e7i		−	0.944218i	0.881540	−	0.472109i	$-0.156507\pi$
$240$	−957325.	+	840231.i	−0.0692509	+	0.0607806i
$241$	2.03708e7			1.45532			0.727658	−	0.685940i	$-0.240609\pi$
$241$	2.03708e7			1.45532			0.727658	+	0.685940i	$0.240609\pi$
$242$			1.00677e7i			0.710368i
$243$	−6.37216e6	−	1.28564e7i	−0.444087	−	0.895984i
$244$	5.28909e6			0.364092
$245$		−	4.31975e7i		−	2.93738i
$246$	−3.55270e6	−	4.04781e6i	−0.238646	−	0.271903i
$247$	−1.29516e7			−0.859472
$248$			1.21946e7i			0.799490i
$249$	−1.12456e6	+	987014.i	−0.0728427	+	0.0639331i
$250$	−1.01045e7			−0.646688
$251$		−	2.64953e7i		−	1.67551i	−0.546043	−	0.837757i	$-0.683866\pi$
$251$		−	2.64953e7i		−	1.67551i	0.546043	−	0.837757i	$-0.316134\pi$
$252$	2.36851e6	−	1.81029e7i	0.148004	−	1.13122i
$253$	−4.88326e6			−0.301542
$254$			7.15549e6i			0.436655i
$255$	−9.90810e6	−	1.12889e7i	−0.597544	−	0.680817i
$256$	−1.75218e7			−1.04438
$257$			1.81309e7i			1.06812i	0.845446	+	0.534061i	$0.179335\pi$
$257$			1.81309e7i			1.06812i	−0.845446	+	0.534061i	$0.820665\pi$
$258$	1.26355e7	−	1.10900e7i	0.735754	−	0.645761i
$259$	4.64883e7			2.67574
$260$			8.94694e6i			0.509043i
$261$	−8.65305e6	−	1.13213e6i	−0.486685	−	0.0636760i
$262$	−7.73272e6			−0.429960
$263$			2.22863e7i			1.22510i	0.790432	+	0.612550i	$0.209856\pi$
$263$			2.22863e7i			1.22510i	−0.790432	+	0.612550i	$0.790144\pi$
$264$	−1.80095e7	−	2.05193e7i	−0.978791	−	1.11519i
$265$	−5.00942e6			−0.269184
$266$			2.37485e7i			1.26180i
$267$	−8.51679e6	+	7.47507e6i	−0.447448	+	0.392719i
$268$	−1.15647e7			−0.600798
$269$			1.05053e7i			0.539698i	0.962903	+	0.269849i	$0.0869737\pi$
$269$			1.05053e7i			0.539698i	−0.962903	+	0.269849i	$0.913026\pi$
$270$	1.07120e7	−	7.17620e6i	0.544227	−	0.364589i
$271$	−1.20264e7			−0.604266			−0.302133	−	0.953266i	$-0.597699\pi$
$271$	−1.20264e7			−0.604266			−0.302133	+	0.953266i	$0.597699\pi$
$272$			1.65844e6i			0.0824126i
$273$	2.33193e7	+	2.65690e7i	1.14611	+	1.30583i
$274$	8.49618e6			0.413021
$275$			384526.i			0.0184896i
$276$	1.89885e6	−	1.66660e6i	0.0903159	−	0.0792691i
$277$	3.21622e7			1.51324			0.756619	−	0.653856i	$-0.226850\pi$
$277$	3.21622e7			1.51324			0.756619	+	0.653856i	$0.226850\pi$
$278$		−	6.52109e6i		−	0.303519i
$279$	2.19534e6	−	1.67793e7i	0.101086	−	0.772613i
$280$	4.48719e7			2.04409
$281$			2.75824e7i			1.24312i	0.783367	+	0.621560i	$0.213501\pi$
$281$			2.75824e7i			1.24312i	−0.783367	+	0.621560i	$0.786499\pi$
$282$	−3.53872e6	−	4.03188e6i	−0.157797	−	0.179788i
$283$	1.53183e7			0.675852			0.337926	−	0.941173i	$-0.390275\pi$
$283$	1.53183e7			0.675852			0.337926	+	0.941173i	$0.390275\pi$
$284$			7.91569e6i			0.345568i
$285$	1.71458e7	−	1.50486e7i	0.740667	−	0.650074i
$286$	1.93274e7			0.826183
$287$			2.60099e7i			1.10025i
$288$	2.28913e7	+	2.99501e6i	0.958280	+	0.125378i
$289$	4.58104e6			0.189789
$290$		−	7.84170e6i		−	0.321526i
$291$	−7.55429e6	−	8.60704e6i	−0.306559	−	0.349281i
$292$	2.26657e6			0.0910375
$293$		−	3.98134e6i		−	0.158280i	−0.996864	−	0.0791401i	$-0.974783\pi$
$293$		−	3.98134e6i		−	0.158280i	0.996864	−	0.0791401i	$-0.0252175\pi$
$294$	3.62861e7	−	3.18478e7i	1.42790	−	1.25325i
$295$	5.75863e6			0.224312
$296$			3.59675e7i			1.38687i
$297$	2.10864e7	+	3.14759e7i	0.804882	+	1.20146i
$298$	−1.76900e7			−0.668467
$299$			4.89203e6i			0.183010i
$300$	−131234.	−	149523.i	−0.00486053	−	0.00553789i
$301$	−8.11915e7			−2.97722
$302$		−	1.62098e7i		−	0.588513i
$303$	−2.67093e7	+	2.34424e7i	−0.960139	+	0.842701i
$304$	−2.51888e6			−0.0896574
$305$		−	1.80391e7i		−	0.635791i
$306$	2.17786e6	−	1.66457e7i	0.0760092	−	0.580949i
$307$	−1.00571e7			−0.347583			−0.173792	−	0.984782i	$-0.555602\pi$
$307$	−1.00571e7			−0.347583			−0.173792	+	0.984782i	$0.555602\pi$
$308$			4.82054e7i			1.64985i
$309$	1.76316e7	+	2.00887e7i	0.597608	+	0.680890i
$310$	1.52060e7			0.510423
$311$		−	3.88238e7i		−	1.29068i	−0.763898	−	0.645338i	$-0.776717\pi$
$311$		−	3.88238e7i		−	1.29068i	0.763898	−	0.645338i	$-0.223283\pi$
$312$	−2.05562e7	+	1.80419e7i	−0.676828	+	0.594042i
$313$	−2.25731e7			−0.736136			−0.368068	−	0.929799i	$-0.619981\pi$
$313$	−2.25731e7			−0.736136			−0.368068	+	0.929799i	$0.619981\pi$
$314$		−	5.38561e6i		−	0.173959i
$315$	−6.17419e7	−	8.07809e6i	−1.97537	−	0.258450i
$316$	1.90284e7			0.603032
$317$		−	9.96057e6i		−	0.312684i	−0.987703	−	0.156342i	$-0.950030\pi$
$317$		−	9.96057e6i		−	0.312684i	0.987703	−	0.156342i	$-0.0499703\pi$
$318$	−3.69325e6	−	4.20794e6i	−0.114849	−	0.130854i
$319$	2.30419e7			0.709815
$320$			2.37642e7i			0.725225i
$321$	4.24699e7	−	3.72752e7i	1.28400	−	1.12695i
$322$	8.97023e6			0.268680
$323$		−	2.97029e7i		−	0.881437i
$324$	−1.89418e7	−	5.04287e6i	−0.556911	−	0.148266i
$325$	385217.			0.0112216
$326$		−	2.57468e7i		−	0.743139i
$327$	2.62731e7	+	2.99345e7i	0.751396	+	0.856109i
$328$	−2.01236e7			−0.570274
$329$			2.59075e7i			0.727509i
$330$	−2.55864e7	+	2.24568e7i	−0.711980	+	0.624895i
$331$	−4.51454e6			−0.124489			−0.0622443	−	0.998061i	$-0.519826\pi$
$331$	−4.51454e6			−0.124489			−0.0622443	+	0.998061i	$0.519826\pi$
$332$			2.04401e6i			0.0558560i
$333$	6.47507e6	−	4.94899e7i	0.175352	−	1.34024i
$334$	−3.85375e7			−1.03429
$335$			3.94426e7i			1.04914i
$336$	4.53523e6	+	5.16726e6i	0.119559	+	0.136220i
$337$	6.54603e7			1.71036			0.855181	−	0.518329i	$-0.173446\pi$
$337$	6.54603e7			1.71036			0.855181	+	0.518329i	$0.173446\pi$
$338$			5.77257e6i			0.149492i
$339$	1.74291e7	−	1.52973e7i	0.447379	−	0.392659i
$340$	−2.05187e7			−0.522052
$341$			4.46810e7i			1.12683i
$342$	2.52819e7	+	3.30779e6i	0.632020	+	0.0826911i
$343$	−1.53279e8			−3.79840
$344$		−	6.28169e7i		−	1.54313i
$345$	−5.68413e6	−	6.47626e6i	−0.138422	−	0.157713i
$346$	3.40700e7			0.822515
$347$		−	5.12884e7i		−	1.22753i	−0.789491	−	0.613763i	$-0.789655\pi$
$347$		−	5.12884e7i		−	1.22753i	0.789491	−	0.613763i	$-0.210345\pi$
$348$	−8.95982e6	+	7.86391e6i	−0.212599	+	0.186595i
$349$	−259368.			−0.00610156			−0.00305078	−	0.999995i	$-0.500971\pi$
$349$	−259368.			−0.00610156			−0.00305078	+	0.999995i	$0.500971\pi$
$350$		−	706350.i		−	0.0164746i
$351$	3.15325e7	−	2.11243e7i	0.729183	−	0.488495i
$352$	−6.09563e7			−1.39762
$353$			2.87355e7i			0.653272i	0.945150	+	0.326636i	$0.105915\pi$
$353$			2.87355e7i			0.653272i	−0.945150	+	0.326636i	$0.894085\pi$
$354$	4.24562e6	+	4.83728e6i	0.0957042	+	0.109041i
$355$	2.69974e7			0.603444
$356$			1.54802e7i			0.343104i
$357$	−6.09329e7	+	5.34800e7i	−1.33921	+	1.17540i
$358$	−4.98342e7			−1.08612
$359$			9.68217e6i			0.209261i	0.994511	+	0.104631i	$0.0333661\pi$
$359$			9.68217e6i			0.209261i	−0.994511	+	0.104631i	$0.966634\pi$
$360$	6.24992e6	−	4.77690e7i	0.133958	−	1.02386i
$361$	−1.93247e6			−0.0410763
$362$			1.04775e7i			0.220868i
$363$	−3.44343e7	−	3.92330e7i	−0.719898	−	0.820223i
$364$	4.82920e7			1.00132
$365$		−	7.73040e6i		−	0.158973i
$366$	1.51529e7	−	1.32995e7i	0.309067	−	0.271264i
$367$	−2.86013e7			−0.578613			−0.289306	−	0.957237i	$-0.593425\pi$
$367$	−2.86013e7			−0.578613			−0.289306	+	0.957237i	$0.593425\pi$
$368$			951423.i			0.0190911i
$369$	2.76892e7	+	3.62276e6i	0.551102	+	0.0721041i
$370$	4.48495e7			0.885426
$371$			2.70389e7i			0.529501i
$372$	−1.52491e7	−	1.73742e7i	−0.296221	−	0.337502i
$373$	−7.08841e7			−1.36591			−0.682956	−	0.730460i	$-0.739306\pi$
$373$	−7.08841e7			−1.36591			−0.682956	+	0.730460i	$0.739306\pi$
$374$			4.43252e7i			0.847297i
$375$	3.93764e7	−	3.45602e7i	0.746694	−	0.655363i
$376$	−2.00444e7			−0.377076
$377$		−	2.30833e7i		−	0.430797i
$378$	−3.87343e7	−	5.78192e7i	−0.717166	−	1.07052i
$379$	7.01714e7			1.28897			0.644485	−	0.764617i	$-0.277072\pi$
$379$	7.01714e7			1.28897			0.644485	+	0.764617i	$0.277072\pi$
$380$		−	3.11643e7i		−	0.567945i
$381$	−2.44737e7	−	2.78844e7i	−0.442512	−	0.504181i
$382$	4.21898e7			0.756863
$383$		−	1.12726e7i		−	0.200645i	−0.994955	−	0.100323i	$-0.968013\pi$
$383$		−	1.12726e7i		−	0.200645i	0.994955	−	0.100323i	$-0.0319875\pi$
$384$	2.11666e7	−	1.85777e7i	0.373816	−	0.328093i
$385$	1.64410e8			2.88102
$386$			3.15080e6i			0.0547847i
$387$	−1.13087e7	+	8.64336e7i	−0.195109	+	1.49125i
$388$	−1.56442e7			−0.267830
$389$			2.37555e7i			0.403566i	0.979430	+	0.201783i	$0.0646736\pi$
$389$			2.37555e7i			0.403566i	−0.979430	+	0.201783i	$0.935326\pi$
$390$	2.24972e7	+	2.56324e7i	0.379258	+	0.432111i
$391$	−1.12193e7			−0.187687
$392$		−	1.80395e8i		−	2.99480i
$393$	3.01338e7	−	2.64480e7i	0.496451	−	0.435728i
$394$	−2.72174e7			−0.444997
$395$		−	6.48985e7i		−	1.05304i
$396$	5.13178e7	+	6.71423e6i	0.826385	+	0.108121i
$397$	1.56547e6			0.0250192			0.0125096	−	0.999922i	$-0.496018\pi$
$397$	1.56547e6			0.0250192			0.0125096	+	0.999922i	$0.496018\pi$
$398$			6.84047e7i			1.08502i
$399$	−8.12266e7	−	9.25462e7i	−1.27873	−	1.45693i
$400$	74918.7			0.00117060
$401$		−	1.15393e8i		−	1.78957i	−0.446502	−	0.894783i	$-0.647330\pi$
$401$		−	1.15393e8i		−	1.78957i	0.446502	−	0.894783i	$-0.352670\pi$
$402$	−3.31320e7	+	2.90795e7i	−0.509999	+	0.447620i
$403$	4.47613e7			0.683892
$404$			4.85469e7i			0.736237i
$405$	−1.71993e7	+	6.46032e7i	−0.258908	+	0.972498i
$406$	−4.23264e7			−0.632460
$407$			1.31785e8i			1.95471i
$408$	−4.13768e7	−	4.71431e7i	−0.609224	−	0.694125i
$409$	6.10607e7			0.892467			0.446233	−	0.894917i	$-0.352765\pi$
$409$	6.10607e7			0.892467			0.446233	+	0.894917i	$0.352765\pi$
$410$			2.50930e7i			0.364083i
$411$	−3.31090e7	+	2.90593e7i	−0.476892	+	0.418562i
$412$	3.65134e7			0.522108
$413$		−	3.10828e7i		−	0.441235i
$414$	1.24941e6	−	9.54939e6i	0.0176077	−	0.134578i
$415$	6.97135e6			0.0975377
$416$			6.10658e7i			0.848239i
$417$	2.23039e7	+	2.54122e7i	0.307591	+	0.350457i
$418$	−6.73220e7			−0.921783
$419$			9.31816e7i			1.26674i	0.773849	+	0.633371i	$0.218329\pi$
$419$			9.31816e7i			1.26674i	−0.773849	+	0.633371i	$0.781671\pi$
$420$	−6.39308e7	+	5.61112e7i	−0.862904	+	0.757359i
$421$	4.55162e7			0.609985			0.304993	−	0.952355i	$-0.401346\pi$
$421$	4.55162e7			0.609985			0.304993	+	0.952355i	$0.401346\pi$
$422$			4.57326e7i			0.608539i
$423$	2.75803e7	+	3.60850e6i	0.364399	+	0.0476766i
$424$	−2.09197e7			−0.274446
$425$			883450.i			0.0115084i
$426$	1.99041e7	+	2.26779e7i	0.257463	+	0.293342i
$427$	−9.73676e7			−1.25064
$428$		−	7.71934e7i		−	0.984576i
$429$	−7.53176e7	+	6.61052e7i	−0.953947	+	0.837267i
$430$	−7.83293e7			−0.985187
$431$		−	1.10032e6i		−	0.0137432i	−0.999976	−	0.00687159i	$-0.997813\pi$
$431$		−	1.10032e6i		−	0.0137432i	0.999976	−	0.00687159i	$-0.00218731\pi$
$432$	6.13257e6	−	4.10833e6i	0.0760661	−	0.0509582i
$433$	−4.60122e7			−0.566773			−0.283387	−	0.959006i	$-0.591458\pi$
$433$	−4.60122e7			−0.566773			−0.283387	+	0.959006i	$0.591458\pi$
$434$		−	8.20760e7i		−	1.00403i
$435$	2.68208e7	+	3.05585e7i	0.325840	+	0.371248i
$436$	5.44092e7			0.656467
$437$		−	1.70401e7i		−	0.204187i
$438$	6.49357e6	−	5.69932e6i	0.0772790	−	0.0678267i
$439$	4.04212e7			0.477766			0.238883	−	0.971048i	$-0.423219\pi$
$439$	4.04212e7			0.477766			0.238883	+	0.971048i	$0.423219\pi$
$440$			1.27202e8i			1.49326i
$441$	−3.24758e7	+	2.48217e8i	−0.378655	+	2.89411i
$442$	4.44048e7			0.514237
$443$		−	6.84955e7i		−	0.787863i	−0.919140	−	0.393931i	$-0.871115\pi$
$443$		−	6.84955e7i		−	0.787863i	0.919140	−	0.393931i	$-0.128885\pi$
$444$	−4.49765e7	−	5.12444e7i	−0.513851	−	0.585460i
$445$	5.27969e7			0.599140
$446$		−	4.80993e7i		−	0.542168i
$447$	6.89367e7	−	6.05048e7i	0.771841	−	0.677435i
$448$	1.28270e8			1.42656
$449$		−	2.23727e7i		−	0.247160i	−0.992335	−	0.123580i	$-0.960562\pi$
$449$		−	2.23727e7i		−	0.247160i	0.992335	−	0.123580i	$-0.0394376\pi$
$450$	−751955.	−	98383.1i	−0.00825191	−	0.00107965i
$451$	−7.37326e7			−0.803766
$452$		−	3.16792e7i		−	0.343051i
$453$	5.54419e7	+	6.31682e7i	0.596408	+	0.679523i
$454$	−1.18442e8			−1.26573
$455$		−	1.64706e8i		−	1.74853i
$456$	7.16020e7	−	6.28441e7i	0.755145	−	0.662780i
$457$	4.95658e6			0.0519318			0.0259659	−	0.999663i	$-0.491734\pi$
$457$	4.95658e6			0.0519318			0.0259659	+	0.999663i	$0.491734\pi$
$458$			1.00042e8i			1.04132i
$459$	4.84459e7	+	7.23159e7i	0.500979	+	0.747818i
$460$	−1.17713e7			−0.120935
$461$			1.92281e8i			1.96261i	0.192456	+	0.981306i	$0.438355\pi$
$461$			1.92281e8i			1.96261i	−0.192456	+	0.981306i	$0.561645\pi$
$462$	1.21213e8	+	1.38105e8i	1.22920	+	1.40050i
$463$	4.25674e7			0.428879			0.214439	−	0.976737i	$-0.431208\pi$
$463$	4.25674e7			0.428879			0.214439	+	0.976737i	$0.431208\pi$
$464$		−	4.48933e6i		−	0.0449394i
$465$	−5.92567e7	+	5.20088e7i	−0.589357	+	0.517271i
$466$	7.34444e7			0.725773
$467$			3.54195e7i			0.347769i	0.984766	+	0.173885i	$0.0556320\pi$
$467$			3.54195e7i			0.347769i	−0.984766	+	0.173885i	$0.944368\pi$
$468$	6.72629e6	−	5.14100e7i	0.0656203	−	0.501545i
$469$	2.12896e8			2.06371
$470$			2.49942e7i			0.240739i
$471$	1.84203e7	+	2.09873e7i	0.176292	+	0.200860i
$472$	2.40484e7			0.228697
$473$		−	2.30161e8i		−	2.17494i
$474$	5.45151e7	−	4.78471e7i	0.511896	−	0.449284i
$475$	−1.34180e6			−0.0125201
$476$			1.10752e8i			1.02691i
$477$	2.87846e7	+	3.76608e6i	0.265220	+	0.0347004i
$478$	−6.71244e7			−0.614606
$479$		−	1.20742e8i		−	1.09863i	−0.835615	−	0.549316i	$-0.814888\pi$
$479$		−	1.20742e8i		−	1.09863i	0.835615	−	0.549316i	$-0.185112\pi$
$480$	−7.09533e7	−	8.08413e7i	−0.641577	−	0.730987i
$481$	1.32021e8			1.18634
$482$		−	1.06077e8i		−	0.947287i
$483$	−3.49563e7	+	3.06807e7i	−0.310230	+	0.272285i
$484$	−7.13101e7			−0.628949
$485$			5.33564e7i			0.467693i
$486$	−6.69473e7	+	3.31819e7i	−0.583209	+	0.289063i
$487$	−1.22134e7			−0.105742			−0.0528712	−	0.998601i	$-0.516837\pi$
$487$	−1.22134e7			−0.105742			−0.0528712	+	0.998601i	$0.516837\pi$
$488$		−	7.53322e7i		−	0.648218i
$489$	8.80611e7	+	1.00333e8i	0.753108	+	0.858061i
$490$	−2.24943e8			−1.91198
$491$			2.37699e7i			0.200809i	0.994947	+	0.100405i	$0.0320137\pi$
$491$			2.37699e7i			0.200809i	−0.994947	+	0.100405i	$0.967986\pi$
$492$	2.86709e7	−	2.51641e7i	0.240739	−	0.211293i
$493$	5.29387e7			0.441807
$494$			6.74430e7i			0.559443i
$495$	2.28997e7	−	1.75025e8i	0.188805	−	1.44306i
$496$	8.70536e6			0.0713414
$497$		−	1.45721e8i		−	1.18701i
$498$	5.13970e6	+	5.85596e6i	0.0416150	+	0.0474144i
$499$	−9.91624e6			−0.0798078			−0.0399039	−	0.999204i	$-0.512705\pi$
$499$	−9.91624e6			−0.0798078			−0.0399039	+	0.999204i	$0.512705\pi$
$500$		−	7.15708e7i		−	0.572567i
$501$	1.50178e8	−	1.31809e8i	1.19424	−	1.04817i
$502$	−1.37970e8			−1.09062
$503$		−	4.84727e6i		−	0.0380884i	−0.999819	−	0.0190442i	$-0.993938\pi$
$503$		−	4.84727e6i		−	0.0380884i	0.999819	−	0.0190442i	$-0.00606233\pi$
$504$	−2.57838e8	−	3.37346e7i	−2.01398	−	0.263502i
$505$	1.65575e8			1.28564
$506$			2.54287e7i			0.196278i
$507$	−1.97438e7	−	2.24953e7i	−0.151498	−	0.172611i
$508$	−5.06828e7			−0.386607
$509$			1.80501e8i			1.36876i	0.729127	+	0.684379i	$0.239926\pi$
$509$			1.80501e8i			1.36876i	−0.729127	+	0.684379i	$0.760074\pi$
$510$	−5.87848e7	+	5.15946e7i	−0.443154	+	0.388950i
$511$	−4.17256e7			−0.312709
$512$			2.44850e7i			0.182428i
$513$	−1.09835e8	+	7.35808e7i	−0.813558	+	0.545020i
$514$	9.44136e7			0.695257
$515$		−	1.24533e8i		−	0.911724i
$516$	7.85511e7	+	8.94979e7i	0.571746	+	0.651424i
$517$	−7.34424e7			−0.531466
$518$		−	2.42080e8i		−	1.74168i
$519$	−1.32768e8	+	1.16529e8i	−0.949712	+	0.833549i
$520$	1.27431e8			0.906284
$521$			1.85727e8i			1.31329i	0.754199	+	0.656646i	$0.228026\pi$
$521$			1.85727e8i			1.31329i	−0.754199	+	0.656646i	$0.771974\pi$
$522$	−5.89538e6	+	4.50592e7i	−0.0414477	+	0.316790i
$523$	−1.04169e8			−0.728169			−0.364084	−	0.931366i	$-0.618618\pi$
$523$	−1.04169e8			−0.728169			−0.364084	+	0.931366i	$0.618618\pi$
$524$		−	5.47714e7i		−	0.380680i
$525$	2.41591e6	+	2.75259e6i	0.0166956	+	0.0190223i
$526$	1.16052e8			0.797436
$527$			1.02655e8i			0.701369i
$528$	−1.46481e7	+	1.28564e7i	−0.0995128	+	0.0873410i
$529$	−6.43634e6			−0.0434783
$530$			2.60857e7i			0.175216i
$531$	−3.30897e7	−	4.32933e6i	−0.221009	−	0.0289159i
$532$	−1.68212e8			−1.11718
$533$			7.38650e7i			0.487817i
$534$	3.89251e7	+	4.43497e7i	0.255626	+	0.291250i
$535$	−2.63277e8			−1.71930
$536$			1.64715e8i			1.06964i
$537$	1.94200e8	−	1.70447e8i	1.25408	−	1.10069i
$538$	5.47043e7			0.351297
$539$		−	6.60967e8i		−	4.22098i
$540$	5.08295e7	+	7.58739e7i	0.322801	+	0.481849i
$541$	2.01826e8			1.27463			0.637315	−	0.770603i	$-0.280045\pi$
$541$	2.01826e8			1.27463			0.637315	+	0.770603i	$0.280045\pi$
$542$			6.26253e7i			0.393326i
$543$	−3.58360e7	−	4.08301e7i	−0.223831	−	0.255024i
$544$	−1.40047e8			−0.869916
$545$		−	1.85569e8i		−	1.14635i
$546$	1.38353e8	−	1.21431e8i	0.849986	−	0.746022i
$547$	4.51725e7			0.276002			0.138001	−	0.990432i	$-0.455932\pi$
$547$	4.51725e7			0.276002			0.138001	+	0.990432i	$0.455932\pi$
$548$			6.01791e7i			0.365682i
$549$	−1.35617e7	+	1.03654e8i	−0.0819593	+	0.626426i
$550$	2.00235e6			0.0120352
$551$			8.04045e7i			0.480646i
$552$	−2.37373e7	−	2.70453e7i	−0.141128	−	0.160796i
$553$	−3.50296e8			−2.07138
$554$		−	1.67479e8i		−	0.984989i
$555$	−1.74775e8	+	1.53398e8i	−1.02235	+	0.897304i
$556$	4.61894e7			0.268731
$557$		−	6.06232e7i		−	0.350811i	−0.984496	−	0.175406i	$-0.943876\pi$
$557$		−	6.06232e7i		−	0.350811i	0.984496	−	0.175406i	$-0.0561237\pi$
$558$	−8.73753e7	−	1.14319e7i	−0.502905	−	0.0657983i
$559$	−2.30574e8			−1.32000
$560$		−	3.20326e7i		−	0.182402i
$561$	−1.51604e8	−	1.72732e8i	−0.858664	−	0.978326i
$562$	1.43630e8			0.809165
$563$			1.99056e8i			1.11545i	0.830026	+	0.557724i	$0.188325\pi$
$563$			1.99056e8i			1.11545i	−0.830026	+	0.557724i	$0.811675\pi$
$564$	2.85581e7	−	2.50650e7i	0.159181	−	0.139711i
$565$	−1.08046e8			−0.599048
$566$		−	7.97673e7i		−	0.439922i
$567$	3.48702e8	+	9.28350e7i	1.91296	+	0.509287i
$568$	1.12743e8			0.615239
$569$			2.12025e7i			0.115093i	0.998343	+	0.0575467i	$0.0183278\pi$
$569$			2.12025e7i			0.115093i	−0.998343	+	0.0575467i	$0.981672\pi$
$570$	−7.83631e7	−	8.92837e7i	−0.423143	−	0.482112i
$571$	−2.48164e8			−1.33300			−0.666499	−	0.745506i	$-0.732208\pi$
$571$	−2.48164e8			−1.33300			−0.666499	+	0.745506i	$0.732208\pi$
$572$			1.36898e8i			0.731489i
$573$	−1.64410e8	+	1.44301e8i	−0.873907	+	0.767017i
$574$	1.35442e8			0.716172
$575$			506822.i			0.00266595i
$576$	1.78659e7	−	1.36551e8i	0.0934882	−	0.714543i
$577$	−7.41368e7			−0.385928			−0.192964	−	0.981206i	$-0.561810\pi$
$577$	−7.41368e7			−0.385928			−0.192964	+	0.981206i	$0.561810\pi$
$578$		−	2.38549e7i		−	0.123536i
$579$	−1.07766e7	−	1.22784e7i	−0.0555196	−	0.0632568i
$580$	5.55433e7			0.284674
$581$		−	3.76285e7i		−	0.191862i
$582$	−4.48196e7	+	3.93376e7i	−0.227352	+	0.199544i
$583$	−7.66495e7			−0.386815
$584$		−	3.22826e7i		−	0.162080i
$585$	−1.75340e8	−	2.29408e7i	−0.875816	−	0.114589i
$586$	−2.07321e7			−0.103027
$587$			2.78891e8i			1.37886i	0.724352	+	0.689431i	$0.242139\pi$
$587$			2.78891e8i			1.37886i	−0.724352	+	0.689431i	$0.757861\pi$
$588$	2.25580e8	+	2.57017e8i	1.10961	+	1.26424i
$589$	−1.55914e8			−0.763026
$590$		−	2.99871e7i		−	0.146008i
$591$	1.06064e8	−	9.30910e7i	0.513814	−	0.450967i
$592$	2.56761e7			0.123755
$593$			1.37159e8i			0.657751i	0.944373	+	0.328876i	$0.106670\pi$
$593$			1.37159e8i			0.657751i	−0.944373	+	0.328876i	$0.893330\pi$
$594$	1.63905e8	−	1.09803e8i	0.782047	−	0.523910i
$595$	3.77732e8			1.79322
$596$		−	1.25300e8i		−	0.591850i
$597$	−2.33963e8	−	2.66568e8i	−1.09957	−	1.25281i
$598$	2.54744e7			0.119124
$599$			1.11634e8i			0.519418i	0.965687	+	0.259709i	$0.0836266\pi$
$599$			1.11634e8i			0.519418i	−0.965687	+	0.259709i	$0.916373\pi$
$600$	−2.12965e6	+	1.86916e6i	−0.00985948	+	0.00865354i
$601$	−4.98564e7			−0.229666			−0.114833	−	0.993385i	$-0.536633\pi$
$601$	−4.98564e7			−0.229666			−0.114833	+	0.993385i	$0.536633\pi$
$602$			4.22790e8i			1.93792i
$603$	2.96529e7	−	2.26641e8i	0.135243	−	1.03368i
$604$	1.14815e8			0.521060
$605$			2.43212e8i			1.09829i
$606$	1.22072e8	+	1.39084e8i	0.548527	+	0.624969i
$607$	−1.09208e8			−0.488301			−0.244151	−	0.969737i	$-0.578509\pi$
$607$	−1.09208e8			−0.488301			−0.244151	+	0.969737i	$0.578509\pi$
$608$		−	2.12707e8i		−	0.946390i
$609$	1.64943e8	−	1.44768e8i	0.730266	−	0.640945i
$610$	−9.39351e7			−0.413846
$611$			7.35744e7i			0.322554i
$612$	1.17903e8	+	1.54260e7i	0.514363	+	0.0672973i
$613$	2.94815e8			1.27988			0.639938	−	0.768427i	$-0.278960\pi$
$613$	2.94815e8			1.27988			0.639938	+	0.768427i	$0.278960\pi$
$614$			5.23707e7i			0.226247i
$615$	−8.58249e7	−	9.77854e7i	−0.368968	−	0.420386i
$616$	6.86587e8			2.93733
$617$			2.73359e8i			1.16380i	0.813260	+	0.581900i	$0.197691\pi$
$617$			2.73359e8i			1.16380i	−0.813260	+	0.581900i	$0.802309\pi$
$618$	1.04608e8	−	9.18134e7i	0.443202	−	0.388992i
$619$	−4.11811e7			−0.173631			−0.0868153	−	0.996224i	$-0.527669\pi$
$619$	−4.11811e7			−0.173631			−0.0868153	+	0.996224i	$0.527669\pi$
$620$			1.07705e8i			0.451921i
$621$	2.77927e7	+	4.14866e7i	0.116053	+	0.173234i
$622$	−2.02168e8			−0.840120
$623$		−	2.84977e8i		−	1.17854i
$624$	1.28795e7	+	1.46744e7i	0.0530085	+	0.0603958i
$625$	−2.47222e8			−1.01262
$626$			1.17545e8i			0.479162i
$627$	2.62349e8	−	2.30260e8i	1.06433	−	0.934149i
$628$	3.81466e7			0.154020
$629$			3.02775e8i			1.21666i
$630$	−4.20652e7	+	3.21510e8i	−0.168229	+	1.28580i
$631$	2.65482e8			1.05669			0.528345	−	0.849030i	$-0.322813\pi$
$631$	2.65482e8			1.05669			0.528345	+	0.849030i	$0.322813\pi$
$632$		−	2.71020e8i		−	1.07362i
$633$	−1.56418e8	−	1.78216e8i	−0.616703	−	0.702646i
$634$	−5.18679e7			−0.203531
$635$			1.72860e8i			0.675107i
$636$	2.98051e7	−	2.61596e7i	0.115856	−	0.101685i
$637$	−6.62155e8			−2.56178
$638$		−	1.19986e8i		−	0.462030i
$639$	−1.55130e8	−	2.02966e7i	−0.594555	−	0.0777894i
$640$	−1.31215e8			−0.500546
$641$		−	2.07844e7i		−	0.0789157i	−0.999221	−	0.0394578i	$-0.987437\pi$
$641$		−	2.07844e7i		−	0.0789157i	0.999221	−	0.0394578i	$-0.0125631\pi$
$642$	−1.94104e8	−	2.21154e8i	−0.733549	−	0.835776i
$643$	2.18756e8			0.822862			0.411431	−	0.911441i	$-0.365029\pi$
$643$	2.18756e8			0.822862			0.411431	+	0.911441i	$0.365029\pi$
$644$			6.35368e7i			0.237885i
$645$	3.05243e8	−	2.67908e8i	1.13754	−	0.998404i
$646$	−1.54672e8			−0.573740
$647$			3.19841e8i			1.18092i	0.807066	+	0.590461i	$0.201054\pi$
$647$			3.19841e8i			1.18092i	−0.807066	+	0.590461i	$0.798946\pi$
$648$	−7.18254e7	+	2.69787e8i	−0.263969	+	0.991507i
$649$	8.81132e7			0.322335
$650$		−	2.00595e6i		−	0.00730432i
$651$	2.80723e8	+	3.19844e8i	1.01750	+	1.15930i
$652$	1.82366e8			0.657963
$653$		−	4.17032e8i		−	1.49772i	−0.662731	−	0.748858i	$-0.730603\pi$
$653$		−	4.17032e8i		−	1.49772i	0.662731	−	0.748858i	$-0.269397\pi$
$654$	1.55879e8	−	1.36813e8i	0.557254	−	0.489095i
$655$	−1.86804e8			−0.664757
$656$			1.43656e7i			0.0508876i
$657$	−5.81170e6	+	4.44196e7i	−0.0204931	+	0.156631i
$658$	1.34909e8			0.473547
$659$		−	1.62947e8i		−	0.569365i	−0.958622	−	0.284683i	$-0.908112\pi$
$659$		−	1.62947e8i		−	0.569365i	0.958622	−	0.284683i	$-0.0918882\pi$
$660$	−1.59063e8	−	1.81230e8i	−0.553272	−	0.630375i
$661$	4.93340e8			1.70821			0.854106	−	0.520100i	$-0.174105\pi$
$661$	4.93340e8			1.70821			0.854106	+	0.520100i	$0.174105\pi$
$662$			2.35087e7i			0.0810315i
$663$	−1.73042e8	+	1.51877e8i	−0.593761	+	0.521136i
$664$	2.91128e7			0.0994442
$665$			5.73708e8i			1.95086i
$666$	−2.57710e8	−	3.37178e7i	−0.872384	−	0.114140i
$667$	3.03701e7			0.102346
$668$		−	2.72964e8i		−	0.915747i
$669$	1.64513e8	+	1.87439e8i	0.549442	+	0.626011i
$670$	2.05390e8			0.682898
$671$		−	2.76017e8i		−	0.913624i
$672$	−4.36349e8	+	3.82978e8i	−1.43789	+	1.26202i
$673$	3.04346e8			0.998440			0.499220	−	0.866475i	$-0.333620\pi$
$673$	3.04346e8			0.998440			0.499220	+	0.866475i	$0.333620\pi$
$674$		−	3.40873e8i		−	1.11330i
$675$	3.26681e6	−	2.18850e6i	0.0106222	−	0.00711600i
$676$	−4.08875e7			−0.132358
$677$			8.51438e7i			0.274402i	0.990543	+	0.137201i	$0.0438106\pi$
$677$			8.51438e7i			0.274402i	−0.990543	+	0.137201i	$0.956189\pi$
$678$	−7.96578e7	−	9.07589e7i	−0.255587	−	0.291206i
$679$	2.87997e8			0.919979
$680$			2.92247e8i			0.929445i
$681$	4.61561e8	−	4.05106e8i	1.46146	−	1.28271i
$682$	2.32668e8			0.733473
$683$			5.29148e8i			1.66079i	0.557174	+	0.830396i	$0.311886\pi$
$683$			5.29148e8i			1.66079i	−0.557174	+	0.830396i	$0.688114\pi$
$684$	−2.34293e7	+	1.79073e8i	−0.0732134	+	0.559580i
$685$	2.05248e8			0.638567
$686$			7.98173e8i			2.47244i
$687$	−3.42171e8	−	3.89856e8i	−1.05529	−	1.20236i
$688$	−4.48431e7			−0.137699
$689$			7.67872e7i			0.234764i
$690$	−3.37240e7	+	2.95991e7i	−0.102658	+	0.0901013i
$691$	5.98229e8			1.81315			0.906574	−	0.422046i	$-0.138688\pi$
$691$	5.98229e8			1.81315			0.906574	+	0.422046i	$0.138688\pi$
$692$			2.41320e8i			0.728241i
$693$	−9.44717e8	−	1.23603e8i	−2.83858	−	0.371390i
$694$	−2.67075e8			−0.799015
$695$		−	1.57534e8i		−	0.469268i
$696$	1.12005e8	+	1.27614e8i	0.332209	+	0.378505i
$697$	−1.69401e8			−0.500284
$698$			1.35061e6i			0.00397160i
$699$	−2.86207e8	+	2.51200e8i	−0.838010	+	0.735510i
$700$	5.00313e6			0.0145864
$701$		−	6.17811e8i		−	1.79350i	−0.442538	−	0.896750i	$-0.645922\pi$
$701$		−	6.17811e8i		−	1.79350i	0.442538	−	0.896750i	$-0.354078\pi$
$702$	−1.10001e8	−	1.64200e8i	−0.317969	−	0.474636i
$703$	−4.59862e8			−1.32361
$704$			3.63617e8i			1.04214i
$705$	−8.54872e7	−	9.74006e7i	−0.243968	−	0.277968i
$706$	1.49635e8			0.425225
$707$		−	8.93707e8i		−	2.52893i
$708$	−3.42628e7	+	3.00720e7i	−0.0965435	+	0.0847349i
$709$	−3.69962e8			−1.03805			−0.519025	−	0.854759i	$-0.673705\pi$
$709$	−3.69962e8			−1.03805			−0.519025	+	0.854759i	$0.673705\pi$
$710$		−	1.40584e8i		−	0.392791i
$711$	−4.87906e7	+	3.72913e8i	−0.135746	+	1.03753i
$712$	2.20483e8			0.610851
$713$			5.88914e7i			0.162474i
$714$	2.78487e8	+	3.17297e8i	0.765087	+	0.871709i
$715$	4.66905e8			1.27735
$716$		−	3.52979e8i		−	0.961635i
$717$	2.61579e8	−	2.29584e8i	0.709651	−	0.622851i
$718$	5.04181e7			0.136211
$719$		−	3.62384e7i		−	0.0974949i	−0.998811	−	0.0487475i	$-0.984477\pi$
$719$		−	3.62384e7i		−	0.0974949i	0.998811	−	0.0487475i	$-0.0155229\pi$
$720$	−3.41008e7	−	4.46163e6i	−0.0913624	−	0.0119535i
$721$	−6.72180e8			−1.79341
$722$			1.00630e7i			0.0267371i
$723$	3.62814e8	+	4.13376e8i	0.959996	+	1.09378i
$724$	−7.42130e7			−0.195553
$725$		−	2.39146e6i		−	0.00627551i
$726$	−2.04299e8	+	1.79310e8i	−0.533895	+	0.468593i
$727$	2.15237e7			0.0560162			0.0280081	−	0.999608i	$-0.491084\pi$
$727$	2.15237e7			0.0560162			0.0280081	+	0.999608i	$0.491084\pi$
$728$		−	6.87821e8i		−	1.78271i
$729$	1.47397e8	−	3.58286e8i	0.380459	−	0.924798i
$730$	−4.02547e7			−0.103478
$731$		−	5.28794e8i		−	1.35374i
$732$	9.42012e7	+	1.07329e8i	0.240173	+	0.273643i
$733$	−6.74313e8			−1.71218			−0.856090	−	0.516826i	$-0.827113\pi$
$733$	−6.74313e8			−1.71218			−0.856090	+	0.516826i	$0.827113\pi$
$734$			1.48936e8i			0.376628i
$735$	8.76586e8	−	7.69368e8i	2.20766	−	1.93763i
$736$	−8.03429e7			−0.201518
$737$			6.03514e8i			1.50760i
$738$	1.88649e7	−	1.44187e8i	0.0469337	−	0.358720i
$739$	−1.12755e8			−0.279384			−0.139692	−	0.990195i	$-0.544611\pi$
$739$	−1.12755e8			−0.279384			−0.139692	+	0.990195i	$0.544611\pi$
$740$			3.17672e8i			0.783942i
$741$	−2.30674e8	−	2.62820e8i	−0.566949	−	0.645958i
$742$	1.40800e8			0.344660
$743$			2.16978e8i			0.528992i	0.964387	+	0.264496i	$0.0852055\pi$
$743$			2.16978e8i			0.528992i	−0.964387	+	0.264496i	$0.914794\pi$
$744$	−2.47460e8	+	2.17192e8i	−0.600877	+	0.527382i
$745$	−4.27349e8			−1.03351
$746$			3.69116e8i			0.889092i
$747$	−4.00580e7	−	5.24105e6i	−0.0961010	−	0.0125735i
$748$	−3.13958e8			−0.750183
$749$			1.42107e9i			3.38196i
$750$	−1.79966e8	−	2.05046e8i	−0.426586	−	0.486034i
$751$	3.78929e7			0.0894619			0.0447309	−	0.998999i	$-0.485757\pi$
$751$	3.78929e7			0.0894619			0.0447309	+	0.998999i	$0.485757\pi$
$752$			1.43091e7i			0.0336478i
$753$	5.37657e8	−	4.71895e8i	1.25928	−	1.10525i
$754$	−1.20202e8			−0.280412
$755$		−	3.91590e8i		−	0.909893i
$756$	4.09537e8	−	2.74358e8i	0.947825	−	0.634968i
$757$	7.18721e8			1.65681			0.828405	−	0.560130i	$-0.189249\pi$
$757$	7.18721e8			1.65681			0.828405	+	0.560130i	$0.189249\pi$
$758$		−	3.65405e8i		−	0.839009i
$759$	−8.69732e7	−	9.90937e7i	−0.198912	−	0.226632i
$760$	−4.43872e8			−1.01115
$761$			1.30190e8i			0.295409i	0.989032	+	0.147704i	$0.0471884\pi$
$761$			1.30190e8i			0.295409i	−0.989032	+	0.147704i	$0.952812\pi$
$762$	−1.45203e8	+	1.27443e8i	−0.328179	+	0.288038i
$763$	−1.00163e9			−2.25493
$764$			2.98833e8i			0.670114i
$765$	5.26120e7	−	4.02121e8i	0.117517	−	0.898198i
$766$	−5.87001e7			−0.130603
$767$		−	8.82715e7i		−	0.195630i
$768$	−3.12072e8	−	3.55562e8i	−0.688924	−	0.784932i
$769$	4.87575e8			1.07217			0.536084	−	0.844165i	$-0.319903\pi$
$769$	4.87575e8			1.07217			0.536084	+	0.844165i	$0.319903\pi$
$770$		−	8.56136e8i		−	1.87530i
$771$	−3.67923e8	+	3.22921e8i	−0.802774	+	0.704584i
$772$	−2.23173e7			−0.0485055
$773$		−	4.51279e7i		−	0.0977028i	−0.998806	−	0.0488514i	$-0.984444\pi$
$773$		−	4.51279e7i		−	0.0977028i	0.998806	−	0.0488514i	$-0.0155561\pi$
$774$	4.50088e8	+	5.88878e7i	0.970676	+	0.127000i
$775$	4.63734e6			0.00996239
$776$			2.22820e8i			0.476835i
$777$	8.27979e8	+	9.43366e8i	1.76505	+	2.01102i
$778$	1.23702e8			0.262687
$779$		−	2.57289e8i		−	0.544264i
$780$	−1.81556e8	+	1.59349e8i	−0.382584	+	0.335789i
$781$	4.13089e8			0.867142
$782$			5.84225e7i			0.122169i
$783$	−1.31141e8	−	1.95756e8i	−0.273183	−	0.407784i
$784$	−1.28779e8			−0.267236
$785$		−	1.30104e8i		−	0.268955i
$786$	−1.37723e8	−	1.56916e8i	−0.283622	−	0.323147i
$787$	−3.57995e8			−0.734434			−0.367217	−	0.930135i	$-0.619689\pi$
$787$	−3.57995e8			−0.734434			−0.367217	+	0.930135i	$0.619689\pi$
$788$		−	1.92783e8i		−	0.393994i
$789$	−4.52246e8	+	3.96930e8i	−0.920754	+	0.808134i
$790$	−3.37947e8			−0.685437
$791$			5.83187e8i			1.17836i
$792$	9.56304e7	−	7.30917e8i	0.192496	−	1.47127i
$793$	−2.76513e8			−0.554492
$794$		−	8.15191e6i		−	0.0162854i
$795$	−8.92202e7	−	1.01654e8i	−0.177567	−	0.202312i
$796$	−4.84516e8			−0.960657
$797$		−	7.25178e8i		−	1.43242i	−0.697886	−	0.716209i	$-0.745876\pi$
$797$		−	7.25178e8i		−	1.43242i	0.697886	−	0.716209i	$-0.254124\pi$
$798$	−4.81918e8	+	4.22973e8i	−0.948340	+	0.832345i
$799$	−1.68734e8			−0.330797
$800$			6.32651e6i			0.0123565i
$801$	−3.03376e8	−	3.96926e7i	−0.590315	−	0.0772347i
$802$	−6.00890e8			−1.16486
$803$		−	1.18283e8i		−	0.228442i
$804$	−2.05972e8	−	2.34676e8i	−0.396315	−	0.451545i
$805$	2.16699e8			0.415404
$806$		−	2.33086e8i		−	0.445155i
$807$	−2.13179e8	+	1.87104e8i	−0.405623	+	0.356010i
$808$	6.91451e8			1.31077
$809$		−	1.16751e7i		−	0.0220503i	−0.999939	−	0.0110252i	$-0.996491\pi$
$809$		−	1.16751e7i		−	0.0220503i	0.999939	−	0.0110252i	$-0.00350949\pi$
$810$	3.36409e8	+	8.95623e7i	0.633013	+	0.168527i
$811$	−4.97333e8			−0.932362			−0.466181	−	0.884689i	$-0.654370\pi$
$811$	−4.97333e8			−0.932362			−0.466181	+	0.884689i	$0.654370\pi$
$812$		−	2.99801e8i		−	0.559970i
$813$	−2.14196e8	−	2.44046e8i	−0.398602	−	0.454151i
$814$	6.86244e8			1.27235
$815$		−	6.21981e8i		−	1.14896i
$816$	−3.36540e7	+	2.95376e7i	−0.0619392	+	0.0543632i
$817$	8.03145e8			1.47275
$818$		−	3.17963e8i		−	0.580920i
$819$	−1.23825e8	+	9.46414e8i	−0.225402	+	1.72278i
$820$	−1.77735e8			−0.322353
$821$			8.39678e8i			1.51734i	0.651475	+	0.758670i	$0.274151\pi$
$821$			8.39678e8i			1.51734i	−0.651475	+	0.758670i	$0.725849\pi$
$822$	1.51321e8	+	1.72409e8i	0.272448	+	0.310416i
$823$	2.32950e8			0.417892			0.208946	−	0.977927i	$-0.432997\pi$
$823$	2.32950e8			0.417892			0.208946	+	0.977927i	$0.432997\pi$
$824$		−	5.20058e8i		−	0.929545i
$825$	−7.80301e6	+	6.84860e6i	−0.0138963	+	0.0121966i
$826$	−1.61858e8			−0.287207
$827$		−	1.49021e8i		−	0.263470i	−0.991285	−	0.131735i	$-0.957945\pi$
$827$		−	1.49021e8i		−	0.263470i	0.991285	−	0.131735i	$-0.0420548\pi$
$828$	6.76390e7	+	8.84964e6i	0.119153	+	0.0155896i
$829$	4.10442e8			0.720424			0.360212	−	0.932870i	$-0.382704\pi$
$829$	4.10442e8			0.720424			0.360212	+	0.932870i	$0.382704\pi$
$830$		−	3.63020e7i		−	0.0634887i
$831$	5.72825e8	+	6.52653e8i	0.998203	+	1.13731i
$832$	3.64270e8			0.632490
$833$		−	1.51857e9i		−	2.62724i
$834$	1.32329e8	−	1.16144e8i	0.228117	−	0.200216i
$835$	−9.30974e8			−1.59911
$836$		−	4.76847e8i		−	0.816131i
$837$	3.79595e8	−	2.54299e8i	0.647357	−	0.433678i
$838$	4.85226e8			0.824541
$839$			4.27351e8i			0.723600i	0.932256	+	0.361800i	$0.117838\pi$
$839$			4.27351e8i			0.723600i	−0.932256	+	0.361800i	$0.882162\pi$
$840$	7.99189e8	+	9.10564e8i	1.34838	+	1.53629i
$841$	4.51521e8			0.759083
$842$		−	2.37017e8i		−	0.397049i
$843$	−5.59716e8	+	4.91256e8i	−0.934298	+	0.820021i
$844$	−3.23927e8			−0.538791
$845$			1.39452e8i			0.231129i
$846$	1.87906e7	−	1.43619e8i	0.0310334	−	0.237193i
$847$	1.31276e9			2.16040
$848$			1.49339e7i			0.0244898i
$849$	2.72826e8	+	3.10847e8i	0.445824	+	0.507953i
$850$	4.60041e6			0.00749099
$851$			1.73698e8i			0.281842i
$852$	−1.60629e8	+	1.40982e8i	−0.259721	+	0.227953i
$853$	1.09518e8			0.176457			0.0882286	−	0.996100i	$-0.471879\pi$
$853$	1.09518e8			0.176457			0.0882286	+	0.996100i	$0.471879\pi$
$854$			5.07025e8i			0.814058i
$855$	6.10750e8	+	7.99083e7i	0.977159	+	0.127848i
$856$	−1.09946e9			−1.75291
$857$			3.72947e8i			0.592522i	0.955107	+	0.296261i	$0.0957398\pi$
$857$			3.72947e8i			0.592522i	−0.955107	+	0.296261i	$0.904260\pi$
$858$	3.44231e8	+	3.92203e8i	0.544989	+	0.620939i
$859$	4.30194e8			0.678712			0.339356	−	0.940658i	$-0.389791\pi$
$859$	4.30194e8			0.678712			0.339356	+	0.940658i	$0.389791\pi$
$860$		−	5.54812e8i		−	0.872269i
$861$	−5.27807e8	+	4.63249e8i	−0.826924	+	0.725780i
$862$	−5.72972e6			−0.00894564
$863$			2.77770e8i			0.432168i	0.976375	+	0.216084i	$0.0693286\pi$
$863$			2.77770e8i			0.432168i	−0.976375	+	0.216084i	$0.930671\pi$
$864$	3.46928e8	+	5.17865e8i	0.537896	+	0.802925i
$865$	8.23050e8			1.27168
$866$			2.39600e8i			0.368921i
$867$	8.15905e7	+	9.29608e7i	0.125194	+	0.142640i
$868$	5.81350e8			0.888953
$869$		−	9.93016e8i		−	1.51320i
$870$	1.59128e8	−	1.39664e8i	0.241651	−	0.212094i
$871$	6.04599e8			0.914982
$872$		−	7.74947e8i		−	1.16875i
$873$	4.01133e7	−	3.06591e8i	0.0602900	−	0.460805i
$874$	−8.87333e7			−0.132908
$875$			1.31756e9i			1.96673i
$876$	4.03687e7	+	4.59944e7i	0.0600527	+	0.0684215i
$877$	−1.04363e9			−1.54721			−0.773603	−	0.633670i	$-0.781548\pi$
$877$	−1.04363e9			−1.54721			−0.773603	+	0.633670i	$0.781548\pi$
$878$		−	2.10486e8i		−	0.310985i
$879$	8.07915e7	−	7.09096e7i	0.118960	−	0.104409i
$880$	9.08057e7			0.133249
$881$			1.00183e9i			1.46510i	0.680712	+	0.732551i	$0.261671\pi$
$881$			1.00183e9i			1.46510i	−0.680712	+	0.732551i	$0.738329\pi$
$882$	1.29255e9	+	1.69112e8i	1.88382	+	0.246472i
$883$	5.15872e7			0.0749307			0.0374654	−	0.999298i	$-0.488072\pi$
$883$	5.15872e7			0.0749307			0.0374654	+	0.999298i	$0.488072\pi$
$884$			3.14522e8i			0.455297i
$885$	1.02564e8	+	1.16857e8i	0.147967	+	0.168588i
$886$	−3.56678e8			−0.512832
$887$			8.88957e8i			1.27383i	0.770936	+	0.636913i	$0.219789\pi$
$887$			8.88957e8i			1.27383i	−0.770936	+	0.636913i	$0.780211\pi$
$888$	−7.29871e8	+	6.40598e8i	−1.04234	+	0.914844i
$889$	9.33027e8			1.32797
$890$		−	2.74930e8i		−	0.389989i
$891$	−2.63167e8	+	9.88497e8i	−0.372048	+	1.39747i
$892$	3.40691e8			0.480027
$893$		−	2.56277e8i		−	0.359878i
$894$	−3.15068e8	−	3.58975e8i	−0.440952	−	0.502403i
$895$	−1.20388e9			−1.67924
$896$			7.08247e8i			0.984603i
$897$	−9.92717e7	+	8.71295e7i	−0.137546	+	0.120722i
$898$	−1.16502e8			−0.160880
$899$		−	2.77882e8i		−	0.382455i
$900$	696854.	−	5.32615e6i	0.000955904	−	0.00730611i
$901$	−1.76102e8			−0.240763
$902$			3.83949e8i			0.523183i
$903$	−1.44606e9	−	1.64758e9i	−1.96392	−	2.23761i
$904$	−4.51205e8			−0.610758
$905$			2.53112e8i			0.341481i
$906$	3.28937e8	−	2.88704e8i	0.442312	−	0.388211i
$907$	−9.05588e8			−1.21369			−0.606846	−	0.794819i	$-0.707566\pi$
$907$	−9.05588e8			−1.21369			−0.606846	+	0.794819i	$0.707566\pi$
$908$		−	8.38936e8i		−	1.12065i
$909$	−9.51409e8	−	1.24479e8i	−1.26671	−	0.165731i
$910$	−8.57674e8			−1.13815
$911$		−	9.99510e8i		−	1.32200i	−0.750385	−	0.661001i	$-0.770132\pi$
$911$		−	9.99510e8i		−	1.32200i	0.750385	−	0.661001i	$-0.229868\pi$
$912$	−4.48624e7	−	5.11144e7i	−0.0591423	−	0.0673843i
$913$	1.06669e8			0.140161
$914$		−	2.58105e7i		−	0.0338032i
$915$	3.66058e8	−	3.21284e8i	0.477845	−	0.419398i
$916$	−7.08604e8			−0.921970
$917$			1.00829e9i			1.30761i
$918$	3.76572e8	−	2.52274e8i	0.486766	−	0.326095i
$919$	−1.52324e8			−0.196255			−0.0981277	−	0.995174i	$-0.531285\pi$
$919$	−1.52324e8			−0.196255			−0.0981277	+	0.995174i	$0.531285\pi$
$920$			1.67658e8i			0.215308i
$921$	−1.79122e8	−	2.04085e8i	−0.229282	−	0.261235i
$922$	1.00127e9			1.27749
$923$		−	4.13831e8i		−	0.526281i
$924$	−9.78209e8	+	8.58561e8i	−1.23998	+	1.08832i
$925$	1.36776e7			0.0172816
$926$		−	2.21662e8i		−	0.279164i
$927$	−9.36239e7	+	7.15580e8i	−0.117530	+	0.898295i
$928$	3.79101e8			0.474364
$929$			3.68890e8i			0.460097i	0.973179	+	0.230048i	$0.0738885\pi$
$929$			3.68890e8i			0.460097i	−0.973179	+	0.230048i	$0.926112\pi$
$930$	2.70827e8	+	3.08569e8i	0.336699	+	0.383622i
$931$	2.30644e9			2.85821
$932$			5.20212e8i			0.642588i
$933$	7.87833e8	−	6.91471e8i	0.970039	−	0.851390i
$934$	1.84441e8			0.226368
$935$			1.07079e9i			1.31000i
$936$	−7.32230e8	−	9.58023e7i	−0.892935	−	0.116828i
$937$	−1.60844e8			−0.195517			−0.0977586	−	0.995210i	$-0.531167\pi$
$937$	−1.60844e8			−0.195517			−0.0977586	+	0.995210i	$0.531167\pi$
$938$		−	1.10862e9i		−	1.34330i
$939$	−4.02038e8	−	4.58065e8i	−0.485590	−	0.553262i
$940$	−1.77036e8			−0.213146
$941$			4.82049e8i			0.578525i	0.957250	+	0.289262i	$0.0934100\pi$
$941$			4.82049e8i			0.578525i	−0.957250	+	0.289262i	$0.906590\pi$
$942$	1.09288e8	−	9.59203e7i	0.130743	−	0.114751i
$943$	−9.71826e7			−0.115892
$944$		−	1.71674e7i		−	0.0204075i
$945$	−9.35728e8	−	1.39677e9i	−1.10880	−	1.65513i
$946$	−1.19852e9			−1.41570
$947$			3.43627e8i			0.404610i	0.979323	+	0.202305i	$0.0648433\pi$
$947$			3.43627e8i			0.404610i	−0.979323	+	0.202305i	$0.935157\pi$
$948$	3.38905e8	+	3.86134e8i	0.397789	+	0.453224i
$949$	−1.18496e8			−0.138645
$950$			6.98720e6i			0.00814952i
$951$	2.02125e8	−	1.77402e8i	0.235006	−	0.206261i
$952$	1.57743e9			1.82827
$953$			1.26246e8i			0.145860i	0.997337	+	0.0729302i	$0.0232350\pi$
$953$			1.26246e8i			0.145860i	−0.997337	+	0.0729302i	$0.976765\pi$
$954$	1.96112e7	−	1.49891e8i	0.0225870	−	0.172635i
$955$	1.01921e9			1.17018
$956$		−	4.75447e8i		−	0.544162i
$957$	4.10387e8	+	4.67578e8i	0.468228	+	0.533480i
$958$	−6.28743e8			−0.715116
$959$		−	1.10785e9i		−	1.25610i
$960$	−4.82235e8	+	4.23251e8i	−0.545061	+	0.478393i
$961$	−3.48657e8			−0.392852
$962$		−	6.87478e8i		−	0.772206i
$963$	1.51282e9	+	1.97931e8i	1.69398	+	0.221634i
$964$	7.51354e8			0.838713
$965$			7.61159e7i			0.0847019i
$966$	1.59764e8	+	1.82029e8i	0.177234	+	0.201933i
$967$	−7.16479e8			−0.792362			−0.396181	−	0.918172i	$-0.629665\pi$
$967$	−7.16479e8			−0.792362			−0.396181	+	0.918172i	$0.629665\pi$
$968$			1.01567e9i			1.11976i
$969$	6.02747e8	−	5.29023e8i	0.662466	−	0.581438i
$970$	2.77844e8			0.304429
$971$			2.71057e8i			0.296076i	0.988982	+	0.148038i	$0.0472958\pi$
$971$			2.71057e8i			0.296076i	−0.988982	+	0.148038i	$0.952704\pi$
$972$	−2.35030e8	−	4.74193e8i	−0.255932	−	0.516364i
$973$	−8.50307e8			−0.923075
$974$			6.35990e7i			0.0688293i
$975$	6.86090e6	+	7.81703e6i	0.00740231	+	0.00843389i
$976$	−5.37773e7			−0.0578429
$977$		−	9.53980e8i		−	1.02295i	−0.859297	−	0.511476i	$-0.829099\pi$
$977$		−	9.53980e8i		−	1.02295i	0.859297	−	0.511476i	$-0.170901\pi$
$978$	5.22467e8	−	4.58562e8i	0.558525	−	0.490210i
$979$	8.07849e8			0.860958
$980$		−	1.59329e9i		−	1.69284i
$981$	−1.39510e8	+	1.06630e9i	−0.147774	+	1.12946i
$982$	1.23778e8			0.130710
$983$			5.18945e8i			0.546337i	0.961966	+	0.273169i	$0.0880717\pi$
$983$			5.18945e8i			0.546337i	−0.961966	+	0.273169i	$0.911928\pi$
$984$	−3.58410e8	−	4.08358e8i	−0.376180	−	0.428604i
$985$	−6.57507e8			−0.688006
$986$		−	2.75669e8i		−	0.287579i
$987$	−5.25730e8	+	4.61426e8i	−0.546778	+	0.479900i
$988$	−4.77704e8			−0.495322
$989$		−	3.03362e8i		−	0.313597i
$990$	−9.11413e8	−	1.19246e8i	−0.939311	−	0.122896i
$991$	7.82290e8			0.803798			0.401899	−	0.915684i	$-0.368350\pi$
$991$	7.82290e8			0.803798			0.401899	+	0.915684i	$0.368350\pi$
$992$			7.35124e8i			0.753053i
$993$	−8.04061e7	−	9.16115e7i	−0.0821186	−	0.0935625i
$994$	−7.58817e8			−0.772641
$995$			1.65250e9i			1.67753i
$996$	−4.14782e7	+	3.64049e7i	−0.0419800	+	0.0368452i
$997$	7.75428e8			0.782448			0.391224	−	0.920295i	$-0.372052\pi$
$997$	7.75428e8			0.782448			0.391224	+	0.920295i	$0.372052\pi$
$998$			5.16370e7i			0.0519481i
$999$	1.11960e9	−	7.50043e8i	1.12296	−	0.752297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.16	✓	44
3.2	odd	2	inner	69.7.b.a.47.29	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.16	✓	44	1.1	even	1	trivial
69.7.b.a.47.29	yes	44	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.20732i q^{2} +(17.8105 + 20.2925i) q^{3} +36.8838 q^{4} -125.797i q^{5} +(105.670 - 92.7449i) q^{6} -679.000 q^{7} -525.334i q^{8} +(-94.5737 + 722.839i) q^{9} +O(q^{10})\)	\(q-5.20732i q^{2} +(17.8105 + 20.2925i) q^{3} +36.8838 q^{4} -125.797i q^{5} +(105.670 - 92.7449i) q^{6} -679.000 q^{7} -525.334i q^{8} +(-94.5737 + 722.839i) q^{9} -655.063 q^{10} -1924.82i q^{11} +(656.918 + 748.466i) q^{12} -1928.28 q^{13} +3535.77i q^{14} +(2552.73 - 2240.50i) q^{15} -375.020 q^{16} -4422.28i q^{17} +(3764.06 + 492.475i) q^{18} +6716.65 q^{19} -4639.86i q^{20} +(-12093.3 - 13778.6i) q^{21} -10023.2 q^{22} -2536.99i q^{23} +(10660.4 - 9356.46i) q^{24} -199.773 q^{25} +10041.2i q^{26} +(-16352.6 + 10955.0i) q^{27} -25044.1 q^{28} +11970.9i q^{29} +(-11667.0 - 13292.9i) q^{30} -23213.1 q^{31} -31668.5i q^{32} +(39059.5 - 34282.0i) q^{33} -23028.2 q^{34} +85415.8i q^{35} +(-3488.24 + 26661.1i) q^{36} -68465.9 q^{37} -34975.8i q^{38} +(-34343.6 - 39129.7i) q^{39} -66085.2 q^{40} -38306.2i q^{41} +(-71749.7 + 62973.7i) q^{42} +119575. q^{43} -70994.7i q^{44} +(90930.7 + 11897.0i) q^{45} -13210.9 q^{46} -38155.5i q^{47} +(-6679.28 - 7610.10i) q^{48} +343392. q^{49} +1040.28i q^{50} +(89739.2 - 78762.9i) q^{51} -71122.3 q^{52} -39821.6i q^{53} +(57046.1 + 85153.5i) q^{54} -242136. q^{55} +356702. i q^{56} +(119627. + 136298. i) q^{57} +62336.4 q^{58} +45777.4i q^{59} +(94154.4 - 82638.1i) q^{60} +143399. q^{61} +120878. i q^{62} +(64215.5 - 490808. i) q^{63} -188910. q^{64} +242571. i q^{65} +(-178517. - 203395. i) q^{66} -313543. q^{67} -163110. i q^{68} +(51482.0 - 45185.1i) q^{69} +444788. q^{70} +214612. i q^{71} +(379732. + 49682.8i) q^{72} +61451.6 q^{73} +356524. i q^{74} +(-3558.05 - 4053.89i) q^{75} +247736. q^{76} +1.30695e6i q^{77} +(-203761. + 178838. i) q^{78} +515901. q^{79} +47176.2i q^{80} +(-513553. - 136723. i) q^{81} -199473. q^{82} +55417.6i q^{83} +(-446047. - 508208. i) q^{84} -556307. q^{85} -622666. i q^{86} +(-242920. + 213208. i) q^{87} -1.01117e6 q^{88} +419701. i q^{89} +(61951.7 - 473505. i) q^{90} +1.30930e6 q^{91} -93574.1i q^{92} +(-413436. - 471052. i) q^{93} -198688. q^{94} -844932. i q^{95} +(642635. - 564032. i) q^{96} -424148. q^{97} -1.78815e6i q^{98} +(1.39134e6 + 182037. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Introduction

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