LMFDB - Embedded newform 69.7.b.a.47.8

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			47.8
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.0694i q^{2} +(-6.47589 + 26.2119i) q^{3} -58.5309 q^{4} +94.9815i q^{5} +(290.149 + 71.6840i) q^{6} +96.5626 q^{7} -60.5391i q^{8} +(-645.126 - 339.491i) q^{9} +O(q^{10})$	\(q-11.0694i q^{2} +(-6.47589 + 26.2119i) q^{3} -58.5309 q^{4} +94.9815i q^{5} +(290.149 + 71.6840i) q^{6} +96.5626 q^{7} -60.5391i q^{8} +(-645.126 - 339.491i) q^{9} +1051.39 q^{10} -430.783i q^{11} +(379.040 - 1534.21i) q^{12} -1291.28 q^{13} -1068.89i q^{14} +(-2489.64 - 615.090i) q^{15} -4416.11 q^{16} -6185.48i q^{17} +(-3757.95 + 7141.13i) q^{18} -10485.4 q^{19} -5559.35i q^{20} +(-625.329 + 2531.09i) q^{21} -4768.49 q^{22} -2536.99i q^{23} +(1586.85 + 392.045i) q^{24} +6603.52 q^{25} +14293.7i q^{26} +(13076.4 - 14711.5i) q^{27} -5651.90 q^{28} -707.894i q^{29} +(-6808.65 + 27558.8i) q^{30} -21115.2 q^{31} +45009.0i q^{32} +(11291.6 + 2789.70i) q^{33} -68469.4 q^{34} +9171.66i q^{35} +(37759.8 + 19870.7i) q^{36} -80921.7 q^{37} +116066. i q^{38} +(8362.18 - 33846.9i) q^{39} +5750.10 q^{40} -2226.35i q^{41} +(28017.6 + 6922.00i) q^{42} +21242.9 q^{43} +25214.1i q^{44} +(32245.3 - 61275.0i) q^{45} -28082.9 q^{46} -132440. i q^{47} +(28598.2 - 115755. i) q^{48} -108325. q^{49} -73096.8i q^{50} +(162133. + 40056.5i) q^{51} +75579.8 q^{52} +38998.9i q^{53} +(-162847. - 144748. i) q^{54} +40916.4 q^{55} -5845.82i q^{56} +(67902.0 - 274841. i) q^{57} -7835.94 q^{58} -240069. i q^{59} +(145721. + 36001.8i) q^{60} -49199.8 q^{61} +233732. i q^{62} +(-62295.0 - 32782.1i) q^{63} +215591. q^{64} -122648. i q^{65} +(30880.2 - 124991. i) q^{66} +318800. q^{67} +362042. i q^{68} +(66499.4 + 16429.3i) q^{69} +101525. q^{70} +332895. i q^{71} +(-20552.5 + 39055.4i) q^{72} -176224. q^{73} +895753. i q^{74} +(-42763.6 + 173091. i) q^{75} +613717. q^{76} -41597.5i q^{77} +(-374664. - 92564.1i) q^{78} +106949. q^{79} -419449. i q^{80} +(300933. + 438028. i) q^{81} -24644.2 q^{82} +38736.0i q^{83} +(36601.1 - 148147. i) q^{84} +587507. q^{85} -235146. i q^{86} +(18555.2 + 4584.24i) q^{87} -26079.2 q^{88} +721125. i q^{89} +(-678276. - 356935. i) q^{90} -124689. q^{91} +148493. i q^{92} +(136740. - 553469. i) q^{93} -1.46603e6 q^{94} -995914. i q^{95} +(-1.17977e6 - 291474. i) q^{96} +749296. q^{97} +1.19909e6i q^{98} +(-146247. + 277909. 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 $

$2$		−	11.0694i		−	1.38367i	−0.722055	−	0.691836i	$-0.756802\pi$
$2$		−	11.0694i		−	1.38367i	0.722055	−	0.691836i	$-0.243198\pi$
$3$	−6.47589	+	26.2119i	−0.239848	+	0.970811i
$3$	−6.47589	+	26.2119i	−0.239848	+	0.970811i
$4$	−58.5309			−0.914546
$5$			94.9815i			0.759852i	0.925017	+	0.379926i	$0.124051\pi$
$5$			94.9815i			0.759852i	−0.925017	+	0.379926i	$0.875949\pi$
$6$	290.149	+	71.6840i	1.34328	+	0.331870i
$7$	96.5626			0.281524			0.140762	−	0.990043i	$-0.455045\pi$
$7$	96.5626			0.281524			0.140762	+	0.990043i	$0.455045\pi$
$8$		−	60.5391i		−	0.118241i
$9$	−645.126	−	339.491i	−0.884946	−	0.465693i
$10$	1051.39			1.05139
$11$		−	430.783i		−	0.323654i	−0.986819	−	0.161827i	$-0.948261\pi$
$11$		−	430.783i		−	0.323654i	0.986819	−	0.161827i	$-0.0517386\pi$
$12$	379.040	−	1534.21i	0.219352	−	0.887851i
$13$	−1291.28			−0.587747			−0.293873	−	0.955844i	$-0.594944\pi$
$13$	−1291.28			−0.587747			−0.293873	+	0.955844i	$0.594944\pi$
$14$		−	1068.89i		−	0.389536i
$15$	−2489.64	−	615.090i	−0.737672	−	0.182249i
$16$	−4416.11			−1.07815
$17$		−	6185.48i		−	1.25900i	−0.776999	−	0.629502i	$-0.783259\pi$
$17$		−	6185.48i		−	1.25900i	0.776999	−	0.629502i	$-0.216741\pi$
$18$	−3757.95	+	7141.13i	−0.644367	+	1.22447i
$19$	−10485.4			−1.52870			−0.764350	−	0.644802i	$-0.776940\pi$
$19$	−10485.4			−1.52870			−0.764350	+	0.644802i	$0.776940\pi$
$20$		−	5559.35i		−	0.694919i
$21$	−625.329	+	2531.09i	−0.0675228	+	0.273306i
$22$	−4768.49			−0.447830
$23$		−	2536.99i		−	0.208514i
$23$		−	2536.99i		−	0.208514i
$24$	1586.85	+	392.045i	0.114789	+	0.0283597i
$25$	6603.52			0.422625
$26$			14293.7i			0.813248i
$27$	13076.4	−	14711.5i	0.664352	−	0.747419i
$28$	−5651.90			−0.257466
$29$		−	707.894i		−	0.0290251i	−0.999895	−	0.0145126i	$-0.995380\pi$
$29$		−	707.894i		−	0.0290251i	0.999895	−	0.0145126i	$-0.00461966\pi$
$30$	−6808.65	+	27558.8i	−0.252172	+	1.02070i
$31$	−21115.2			−0.708777			−0.354389	−	0.935098i	$-0.615311\pi$
$31$	−21115.2			−0.708777			−0.354389	+	0.935098i	$0.615311\pi$
$32$			45009.0i			1.37357i
$33$	11291.6	+	2789.70i	0.314206	+	0.0776276i
$34$	−68469.4			−1.74205
$35$			9171.66i			0.213916i
$36$	37759.8	+	19870.7i	0.809324	+	0.425898i
$37$	−80921.7			−1.59757			−0.798785	−	0.601616i	$-0.794524\pi$
$37$	−80921.7			−1.59757			−0.798785	+	0.601616i	$0.794524\pi$
$38$			116066.i			2.11522i
$39$	8362.18	−	33846.9i	0.140970	−	0.570591i
$40$	5750.10			0.0898453
$41$		−	2226.35i		−	0.0323029i	−0.999870	−	0.0161514i	$-0.994859\pi$
$41$		−	2226.35i		−	0.0323029i	0.999870	−	0.0161514i	$-0.00514138\pi$
$42$	28017.6	+	6922.00i	0.378166	+	0.0934294i
$43$	21242.9			0.267183			0.133591	−	0.991036i	$-0.457349\pi$
$43$	21242.9			0.267183			0.133591	+	0.991036i	$0.457349\pi$
$44$			25214.1i			0.295996i
$45$	32245.3	−	61275.0i	0.353858	−	0.672428i
$46$	−28082.9			−0.288515
$47$		−	132440.i		−	1.27563i	−0.770188	−	0.637817i	$-0.779838\pi$
$47$		−	132440.i		−	1.27563i	0.770188	−	0.637817i	$-0.220162\pi$
$48$	28598.2	−	115755.i	0.258592	−	1.04668i
$49$	−108325.			−0.920744
$50$		−	73096.8i		−	0.584774i
$51$	162133.	+	40056.5i	1.22225	+	0.301969i
$52$	75579.8			0.537521
$53$			38998.9i			0.261954i	0.991385	+	0.130977i	$0.0418114\pi$
$53$			38998.9i			0.261954i	−0.991385	+	0.130977i	$0.958189\pi$
$54$	−162847.	−	144748.i	−1.03418	−	0.919245i
$55$	40916.4			0.245929
$56$		−	5845.82i		−	0.0332875i
$57$	67902.0	−	274841.i	0.366655	−	1.48408i
$58$	−7835.94			−0.0401612
$59$		−	240069.i		−	1.16891i	−0.811426	−	0.584455i	$-0.801308\pi$
$59$		−	240069.i		−	1.16891i	0.811426	−	0.584455i	$-0.198692\pi$
$60$	145721.	+	36001.8i	0.674635	+	0.166675i
$61$	−49199.8			−0.216758			−0.108379	−	0.994110i	$-0.534566\pi$
$61$	−49199.8			−0.216758			−0.108379	+	0.994110i	$0.534566\pi$
$62$			233732.i			0.980715i
$63$	−62295.0	−	32782.1i	−0.249133	−	0.131104i
$64$	215591.			0.822413
$65$		−	122648.i		−	0.446601i
$66$	30880.2	−	124991.i	0.107411	−	0.434758i
$67$	318800.			1.05997			0.529986	−	0.848006i	$-0.322197\pi$
$67$	318800.			1.05997			0.529986	+	0.848006i	$0.322197\pi$
$68$			362042.i			1.15142i
$69$	66499.4	+	16429.3i	0.202428	+	0.0500117i
$70$	101525.			0.295990
$71$			332895.i			0.930104i	0.885283	+	0.465052i	$0.153964\pi$
$71$			332895.i			0.930104i	−0.885283	+	0.465052i	$0.846036\pi$
$72$	−20552.5	+	39055.4i	−0.0550638	+	0.104636i
$73$	−176224.			−0.452999			−0.226499	−	0.974011i	$-0.572728\pi$
$73$	−176224.			−0.452999			−0.226499	+	0.974011i	$0.572728\pi$
$74$			895753.i			2.21051i
$75$	−42763.6	+	173091.i	−0.101366	+	0.410289i
$76$	613717.			1.39807
$77$		−	41597.5i		−	0.0911162i
$78$	−374664.	−	92564.1i	−0.789510	−	0.195056i
$79$	106949.			0.216918			0.108459	−	0.994101i	$-0.465408\pi$
$79$	106949.			0.216918			0.108459	+	0.994101i	$0.465408\pi$
$80$		−	419449.i		−	0.819236i
$81$	300933.	+	438028.i	0.566259	+	0.824227i
$82$	−24644.2			−0.0446965
$83$			38736.0i			0.0677455i	0.999426	+	0.0338727i	$0.0107841\pi$
$83$			38736.0i			0.0677455i	−0.999426	+	0.0338727i	$0.989216\pi$
$84$	36601.1	−	148147.i	0.0617527	−	0.249951i
$85$	587507.			0.956656
$86$		−	235146.i		−	0.369693i
$87$	18555.2	+	4584.24i	0.0281779	+	0.00696161i
$88$	−26079.2			−0.0382690
$89$			721125.i			1.02292i	0.859308	+	0.511459i	$0.170895\pi$
$89$			721125.i			1.02292i	−0.859308	+	0.511459i	$0.829105\pi$
$90$	−678276.	−	356935.i	−0.930419	−	0.489623i
$91$	−124689.			−0.165465
$92$			148493.i			0.190696i
$93$	136740.	−	553469.i	0.169999	−	0.688088i
$94$	−1.46603e6			−1.76506
$95$		−	995914.i		−	1.16159i
$96$	−1.17977e6	−	291474.i	−1.33347	−	0.329447i
$97$	749296.			0.820990			0.410495	−	0.911863i	$-0.365356\pi$
$97$	749296.			0.820990			0.410495	+	0.911863i	$0.365356\pi$
$98$			1.19909e6i			1.27401i
$99$	−146247.	+	277909.i	−0.150723	+	0.286416i
$100$	−386510.			−0.386510
$101$		−	865444.i		−	0.839991i	−0.907526	−	0.419996i	$-0.862032\pi$
$101$		−	865444.i		−	0.839991i	0.907526	−	0.419996i	$-0.137968\pi$
$102$	443400.	−	1.79471e6i	0.417826	−	1.69120i
$103$	−1.24786e6			−1.14197			−0.570986	−	0.820960i	$-0.693439\pi$
$103$	−1.24786e6			−1.14197			−0.570986	+	0.820960i	$0.693439\pi$
$104$			78173.0i			0.0694955i
$105$	−240407.	−	59394.7i	−0.207672	−	0.0513074i
$106$	431694.			0.362458
$107$			1.59582e6i			1.30266i	0.758794	+	0.651330i	$0.225789\pi$
$107$			1.59582e6i			1.30266i	−0.758794	+	0.651330i	$0.774211\pi$
$108$	−765377.	+	861075.i	−0.607581	+	0.683549i
$109$	882345.			0.681332			0.340666	−	0.940184i	$-0.389347\pi$
$109$	882345.			0.681332			0.340666	+	0.940184i	$0.389347\pi$
$110$		−	452919.i		−	0.340285i
$111$	524040.	−	2.12111e6i	0.383174	−	1.55094i
$112$	−426431.			−0.303525
$113$			595850.i			0.412954i	0.978451	+	0.206477i	$0.0661999\pi$
$113$			595850.i			0.412954i	−0.978451	+	0.206477i	$0.933800\pi$
$114$	−3.04231e6	−	751632.i	−2.05348	−	0.507330i
$115$	240968.			0.158440
$116$			41433.7i			0.0265448i
$117$	833038.	+	438377.i	0.520124	+	0.273710i
$118$	−2.65742e6			−1.61739
$119$		−	597287.i		−	0.354439i
$120$	−37237.0	+	150721.i	−0.0215492	+	0.0872227i
$121$	1.58599e6			0.895248
$122$			544611.i			0.299921i
$123$	58356.7	+	14417.6i	0.0313600	+	0.00774777i
$124$	1.23589e6			0.648209
$125$			2.11130e6i			1.08098i
$126$	−362877.	+	689567.i	−0.181404	+	0.344719i
$127$	857488.			0.418617			0.209309	−	0.977850i	$-0.432879\pi$
$127$	857488.			0.418617			0.209309	+	0.977850i	$0.432879\pi$
$128$			494126.i			0.235618i
$129$	−137567.	+	556816.i	−0.0640832	+	0.259384i
$130$	−1.35763e6			−0.617948
$131$			3.86820e6i			1.72066i	0.509737	+	0.860330i	$0.329743\pi$
$131$			3.86820e6i			1.72066i	−0.509737	+	0.860330i	$0.670257\pi$
$132$	−660910.	−	163284.i	−0.287356	−	0.0709940i
$133$	−1.01249e6			−0.430365
$134$		−	3.52892e6i		−	1.46665i
$135$	1.39732e6	+	1.24202e6i	0.567928	+	0.504809i
$136$	−374464.			−0.148865
$137$		−	3.88882e6i		−	1.51236i	−0.654361	−	0.756182i	$-0.727062\pi$
$137$		−	3.88882e6i		−	1.51236i	0.654361	−	0.756182i	$-0.272938\pi$
$138$	181862.	−	736107.i	0.0691998	−	0.280094i
$139$	−461614.			−0.171884			−0.0859419	−	0.996300i	$-0.527390\pi$
$139$	−461614.			−0.171884			−0.0859419	+	0.996300i	$0.527390\pi$
$140$		−	536826.i		−	0.195636i
$141$	3.47150e6	+	857667.i	1.23840	+	0.305958i
$142$	3.68493e6			1.28696
$143$			556261.i			0.190226i
$144$	2.84895e6	+	1.49923e6i	0.954106	+	0.502088i
$145$	67236.8			0.0220548
$146$			1.95069e6i			0.626802i
$147$	701498.	−	2.83939e6i	0.220838	−	0.893868i
$148$	4.73643e6			1.46105
$149$			873004.i			0.263911i	0.991256	+	0.131956i	$0.0421256\pi$
$149$			873004.i			0.263911i	−0.991256	+	0.131956i	$0.957874\pi$
$150$	1.91600e6	+	473367.i	0.567705	+	0.140257i
$151$	756939.			0.219852			0.109926	−	0.993940i	$-0.464939\pi$
$151$	756939.			0.219852			0.109926	+	0.993940i	$0.464939\pi$
$152$			634774.i			0.180754i
$153$	−2.09991e6	+	3.99042e6i	−0.586310	+	1.11415i
$154$	−460458.			−0.126075
$155$		−	2.00555e6i		−	0.538566i
$156$	−489446.	+	1.98109e6i	−0.128923	+	0.521831i
$157$	−1.33233e6			−0.344280			−0.172140	−	0.985072i	$-0.555068\pi$
$157$	−1.33233e6			−0.344280			−0.172140	+	0.985072i	$0.555068\pi$
$158$		−	1.18386e6i		−	0.300143i
$159$	−1.02224e6	−	252553.i	−0.254308	−	0.0628291i
$160$	−4.27503e6			−1.04371
$161$		−	244979.i		−	0.0587018i
$162$	4.84869e6	−	3.33114e6i	1.14046	−	0.783517i
$163$	−8.19540e6			−1.89237			−0.946187	−	0.323619i	$-0.895100\pi$
$163$	−8.19540e6			−1.89237			−0.946187	+	0.323619i	$0.895100\pi$
$164$			130310.i			0.0295424i
$165$	−264970.	+	1.07250e6i	−0.0589855	+	0.238750i
$166$	428783.			0.0937374
$167$		−	3.03467e6i		−	0.651571i	−0.945444	−	0.325785i	$-0.894371\pi$
$167$		−	3.03467e6i		−	0.651571i	0.945444	−	0.325785i	$-0.105629\pi$
$168$	153230.	+	37856.9i	0.0323159	+	0.00798394i
$169$	−3.15941e6			−0.654554
$170$		−	6.50333e6i		−	1.32370i
$171$	6.76437e6	+	3.55968e6i	1.35282	+	0.711905i
$172$	−1.24337e6			−0.244351
$173$			97726.8i			0.0188745i	0.999955	+	0.00943725i	$0.00300402\pi$
$173$			97726.8i			0.0188745i	−0.999955	+	0.00943725i	$0.996996\pi$
$174$	50744.7	−	205395.i	0.00963258	−	0.0389890i
$175$	637653.			0.118979
$176$			1.90238e6i			0.348948i
$177$	6.29267e6	+	1.55466e6i	1.13479	+	0.280360i
$178$	7.98240e6			1.41538
$179$		−	1.00569e7i		−	1.75350i	−0.480947	−	0.876750i	$-0.659707\pi$
$179$		−	1.00569e7i		−	1.75350i	0.480947	−	0.876750i	$-0.340293\pi$
$180$	−1.88735e6	+	3.58648e6i	−0.323619	+	0.614966i
$181$	7.00816e6			1.18187			0.590933	−	0.806720i	$-0.298760\pi$
$181$	7.00816e6			1.18187			0.590933	+	0.806720i	$0.298760\pi$
$182$			1.38023e6i			0.228949i
$183$	318613.	−	1.28962e6i	0.0519888	−	0.210430i
$184$	−153588.			−0.0246549
$185$		−	7.68607e6i		−	1.21392i
$186$	−6.12655e6	−	1.51362e6i	−0.952088	−	0.235222i
$187$	−2.66460e6			−0.407481
$188$			7.75184e6i			1.16663i
$189$	1.26270e6	−	1.42058e6i	0.187031	−	0.210416i
$190$	−1.10241e7			−1.60725
$191$		−	1.14167e7i		−	1.63847i	−0.573456	−	0.819236i	$-0.694398\pi$
$191$		−	1.14167e7i		−	1.63847i	0.573456	−	0.819236i	$-0.305602\pi$
$192$	−1.39614e6	+	5.65104e6i	−0.197254	+	0.798407i
$193$	1.06679e7			1.48391			0.741956	−	0.670448i	$-0.233898\pi$
$193$	1.06679e7			1.48391			0.741956	+	0.670448i	$0.233898\pi$
$194$		−	8.29423e6i		−	1.13598i
$195$	3.21483e6	+	794253.i	0.433565	+	0.107116i
$196$	6.34034e6			0.842063
$197$			4.24320e6i			0.555002i	0.960725	+	0.277501i	$0.0895062\pi$
$197$			4.24320e6i			0.555002i	−0.960725	+	0.277501i	$0.910494\pi$
$198$	3.07628e6	+	1.61886e6i	0.396305	+	0.208552i
$199$	−1.11584e7			−1.41594			−0.707970	−	0.706243i	$-0.750389\pi$
$199$	−1.11584e7			−1.41594			−0.707970	+	0.706243i	$0.750389\pi$
$200$		−	399771.i		−	0.0499714i
$201$	−2.06452e6	+	8.35636e6i	−0.254232	+	1.02903i
$202$	−9.57992e6			−1.16227
$203$		−	68356.1i		−	0.00817127i
$204$	−9.48981e6	−	2.34455e6i	−1.11781	−	0.276165i
$205$	211462.			0.0245454
$206$			1.38131e7i			1.58011i
$207$	−861286.	+	1.63668e6i	−0.0971038	+	0.184524i
$208$	5.70243e6			0.633680
$209$			4.51691e6i			0.494769i
$210$	−657462.	+	2.66115e6i	−0.0709925	+	0.287350i
$211$	−1.54269e7			−1.64222			−0.821111	−	0.570769i	$-0.806645\pi$
$211$	−1.54269e7			−1.64222			−0.821111	+	0.570769i	$0.806645\pi$
$212$		−	2.28264e6i		−	0.239569i
$213$	−8.72580e6	−	2.15579e6i	−0.902955	−	0.223083i
$214$	1.76647e7			1.80245
$215$			2.01768e6i			0.203019i
$216$	−890619.	−	791637.i	−0.0883753	−	0.0785534i
$217$	−2.03894e6			−0.199538
$218$		−	9.76700e6i		−	0.942740i
$219$	1.14121e6	−	4.61917e6i	0.108651	−	0.439776i
$220$	−2.39487e6			−0.224913
$221$			7.98719e6i			0.739975i
$222$	−2.34794e7	−	5.80079e6i	−2.14599	−	0.530186i
$223$	−4.61851e6			−0.416474			−0.208237	−	0.978078i	$-0.566772\pi$
$223$	−4.61851e6			−0.416474			−0.208237	+	0.978078i	$0.566772\pi$
$224$			4.34619e6i			0.386692i
$225$	−4.26010e6	−	2.24183e6i	−0.374000	−	0.196814i
$226$	6.59569e6			0.571393
$227$			3.94980e6i			0.337674i	0.985644	+	0.168837i	$0.0540011\pi$
$227$			3.94980e6i			0.337674i	−0.985644	+	0.168837i	$0.945999\pi$
$228$	−3.97437e6	+	1.60867e7i	−0.335323	+	1.35726i
$229$	−1.50062e7			−1.24958			−0.624792	−	0.780791i	$-0.714816\pi$
$229$	−1.50062e7			−1.24958			−0.624792	+	0.780791i	$0.714816\pi$
$230$		−	2.66736e6i		−	0.219229i
$231$	1.09035e6	+	269381.i	0.0884565	+	0.0218540i
$232$	−42855.3			−0.00343195
$233$			2.05975e7i			1.62835i	0.580621	+	0.814174i	$0.302810\pi$
$233$			2.05975e7i			1.62835i	−0.580621	+	0.814174i	$0.697190\pi$
$234$	4.85256e6	−	9.22120e6i	0.378724	−	0.719681i
$235$	1.25794e7			0.969292
$236$			1.40515e7i			1.06902i
$237$	−692590.	+	2.80334e6i	−0.0520273	+	0.210586i
$238$	−6.61159e6			−0.490428
$239$		−	8.39984e6i		−	0.615286i	−0.951502	−	0.307643i	$-0.900460\pi$
$239$		−	8.39984e6i		−	0.615286i	0.951502	−	0.307643i	$-0.0995403\pi$
$240$	1.09945e7	+	2.71630e6i	0.795323	+	0.196492i
$241$	7.21157e6			0.515203			0.257602	−	0.966251i	$-0.417068\pi$
$241$	7.21157e6			0.515203			0.257602	+	0.966251i	$0.417068\pi$
$242$		−	1.75559e7i		−	1.23873i
$243$	−1.34304e7	+	5.05141e6i	−0.935984	+	0.352041i
$244$	2.87971e6			0.198235
$245$		−	1.02888e7i		−	0.699629i
$246$	159593.	−	645972.i	0.0107204	−	0.0433919i
$247$	1.35395e7			0.898488
$248$			1.27830e6i			0.0838062i
$249$	−1.01534e6	−	250850.i	−0.0657680	−	0.0162486i
$250$	2.33707e7			1.49573
$251$			1.82388e7i			1.15339i	0.816961	+	0.576693i	$0.195657\pi$
$251$			1.82388e7i			1.15339i	−0.816961	+	0.576693i	$0.804343\pi$
$252$	3.64619e6	+	1.91877e6i	0.227844	+	0.119900i
$253$	−1.09289e6			−0.0674864
$254$		−	9.49186e6i		−	0.579229i
$255$	−3.80463e6	+	1.53997e7i	−0.229452	+	0.928732i
$256$	1.92675e7			1.14843
$257$		−	2.14734e7i		−	1.26503i	−0.774546	−	0.632517i	$-0.782022\pi$
$257$		−	2.14734e7i		−	1.26503i	0.774546	−	0.632517i	$-0.217978\pi$
$258$	6.16361e6	+	1.52278e6i	0.358902	+	0.0886701i
$259$	−7.81402e6			−0.449754
$260$			7.17868e6i			0.408437i
$261$	−240323.	+	456681.i	−0.0135168	+	0.0256857i
$262$	4.28185e7			2.38083
$263$		−	1.85495e7i		−	1.01968i	−0.860269	−	0.509841i	$-0.829704\pi$
$263$		−	1.85495e7i		−	1.01968i	0.860269	−	0.509841i	$-0.170296\pi$
$264$	168886.	−	683586.i	0.00917872	−	0.0371519i
$265$	−3.70418e6			−0.199046
$266$			1.12077e7i			0.595484i
$267$	−1.89021e7	−	4.66993e6i	−0.993059	−	0.245345i
$268$	−1.86597e7			−0.969393
$269$		−	2.30751e7i		−	1.18546i	−0.805401	−	0.592730i	$-0.798050\pi$
$269$		−	2.30751e7i		−	1.18546i	0.805401	−	0.592730i	$-0.201950\pi$
$270$	1.37484e7	−	1.54674e7i	0.698490	−	0.785826i
$271$	−3.71861e7			−1.86841			−0.934205	−	0.356736i	$-0.883890\pi$
$271$	−3.71861e7			−1.86841			−0.934205	+	0.356736i	$0.883890\pi$
$272$			2.73158e7i			1.35740i
$273$	807475.	−	3.26834e6i	0.0396863	−	0.160635i
$274$	−4.30468e7			−2.09262
$275$		−	2.84468e6i		−	0.136784i
$276$	−3.89227e6	−	961622.i	−0.185130	−	0.0457380i
$277$	1.86805e7			0.878919			0.439459	−	0.898262i	$-0.355170\pi$
$277$	1.86805e7			0.878919			0.439459	+	0.898262i	$0.355170\pi$
$278$			5.10978e6i			0.237831i
$279$	1.36219e7	+	7.16840e6i	0.627230	+	0.330073i
$280$	555245.			0.0252936
$281$		−	2.45838e7i		−	1.10797i	−0.832525	−	0.553987i	$-0.813106\pi$
$281$		−	2.45838e7i		−	1.10797i	0.832525	−	0.553987i	$-0.186894\pi$
$282$	9.49384e6	−	3.84274e7i	0.423345	−	1.71354i
$283$	−7.26158e6			−0.320385			−0.160192	−	0.987086i	$-0.551211\pi$
$283$	−7.26158e6			−0.320385			−0.160192	+	0.987086i	$0.551211\pi$
$284$		−	1.94846e7i		−	0.850623i
$285$	2.61048e7	+	6.44943e6i	1.12768	+	0.278604i
$286$	6.15746e6			0.263211
$287$		−	214982.i		−	0.00909402i
$288$	1.52801e7	−	2.90365e7i	0.639661	−	1.21553i
$289$	−1.41227e7			−0.585090
$290$		−	744269.i		−	0.0305166i
$291$	−4.85236e6	+	1.96405e7i	−0.196913	+	0.797026i
$292$	1.03146e7			0.414288
$293$			1.34925e6i			0.0536403i	0.999640	+	0.0268201i	$0.00853814\pi$
$293$			1.34925e6i			0.0536403i	−0.999640	+	0.0268201i	$0.991462\pi$
$294$	−3.14303e7	−	7.76515e6i	−1.23682	−	0.305568i
$295$	2.28022e7			0.888198
$296$			4.89893e6i			0.188898i
$297$	−6.33744e6	−	5.63311e6i	−0.241905	−	0.215020i
$298$	9.66361e6			0.365166
$299$			3.27597e6i			0.122554i
$300$	2.50300e6	−	1.01312e7i	0.0927036	−	0.375228i
$301$	2.05127e6			0.0752183
$302$		−	8.37884e6i		−	0.304203i
$303$	2.26849e7	+	5.60452e6i	0.815472	+	0.201470i
$304$	4.63045e7			1.64817
$305$		−	4.67307e6i		−	0.164704i
$306$	4.41714e7	+	2.32447e7i	1.54162	+	0.811260i
$307$	−4.04776e7			−1.39894			−0.699472	−	0.714660i	$-0.746581\pi$
$307$	−4.04776e7			−1.39894			−0.699472	+	0.714660i	$0.746581\pi$
$308$			2.43474e6i			0.0833299i
$309$	8.08102e6	−	3.27088e7i	0.273899	−	1.10864i
$310$	−2.22002e7			−0.745198
$311$			8.13934e6i			0.270588i	0.990806	+	0.135294i	$0.0431978\pi$
$311$			8.13934e6i			0.270588i	−0.990806	+	0.135294i	$0.956802\pi$
$312$	−2.04906e6	−	506240.i	−0.0674670	−	0.0166683i
$313$	4.72064e7			1.53946			0.769729	−	0.638371i	$-0.220391\pi$
$313$	4.72064e7			1.53946			0.769729	+	0.638371i	$0.220391\pi$
$314$			1.47480e7i			0.476370i
$315$	3.11369e6	−	5.91688e6i	0.0996194	−	0.189304i
$316$	−6.25983e6			−0.198381
$317$			3.71830e7i			1.16726i	0.812020	+	0.583629i	$0.198368\pi$
$317$			3.71830e7i			1.16726i	−0.812020	+	0.583629i	$0.801632\pi$
$318$	−2.79560e6	+	1.13155e7i	−0.0869348	+	0.351878i
$319$	−304949.			−0.00939409
$320$			2.04771e7i			0.624912i
$321$	−4.18293e7	−	1.03343e7i	−1.26464	−	0.312440i
$322$	−2.71176e6			−0.0812239
$323$			6.48570e7i			1.92464i
$324$	−1.76139e7	−	2.56382e7i	−0.517870	−	0.753793i
$325$	−8.52699e6			−0.248397
$326$			9.07179e7i			2.61842i
$327$	−5.71397e6	+	2.31279e7i	−0.163416	+	0.661445i
$328$	−134781.			−0.00381951
$329$		−	1.27888e7i		−	0.359121i
$330$	1.18719e7	+	2.93305e6i	0.330352	+	0.0816165i
$331$	5.58798e7			1.54089			0.770444	−	0.637508i	$-0.220035\pi$
$331$	5.58798e7			1.54089			0.770444	+	0.637508i	$0.220035\pi$
$332$		−	2.26725e6i		−	0.0619563i
$333$	5.22047e7	+	2.74722e7i	1.41376	+	0.743978i
$334$	−3.35919e7			−0.901560
$335$			3.02801e7i			0.805422i
$336$	2.76152e6	−	1.11776e7i	0.0727999	−	0.294666i
$337$	−6.36594e7			−1.66331			−0.831655	−	0.555293i	$-0.812606\pi$
$337$	−6.36594e7			−1.66331			−0.831655	+	0.555293i	$0.812606\pi$
$338$			3.49726e7i			0.905687i
$339$	−1.56184e7	−	3.85866e6i	−0.400900	−	0.0990461i
$340$	−3.43873e7			−0.874906
$341$			9.09606e6i			0.229398i
$342$	3.94034e7	−	7.48773e7i	0.985043	−	1.87185i
$343$	−2.18206e7			−0.540735
$344$		−	1.28603e6i		−	0.0315918i
$345$	−1.56048e6	+	6.31621e6i	−0.0380015	+	0.153815i
$346$	1.08177e6			0.0261161
$347$			3.40444e7i			0.814811i	0.913247	+	0.407405i	$0.133566\pi$
$347$			3.40444e7i			0.814811i	−0.913247	+	0.407405i	$0.866434\pi$
$348$	−1.08606e6	−	268320.i	−0.0257700	−	0.00636672i
$349$	2.18425e6			0.0513838			0.0256919	−	0.999670i	$-0.491821\pi$
$349$	2.18425e6			0.0513838			0.0256919	+	0.999670i	$0.491821\pi$
$350$		−	7.05842e6i		−	0.164628i
$351$	−1.68854e7	+	1.89966e7i	−0.390471	+	0.439293i
$352$	1.93891e7			0.444560
$353$		−	1.30861e7i		−	0.297500i	−0.988875	−	0.148750i	$-0.952475\pi$
$353$		−	1.30861e7i		−	0.297500i	0.988875	−	0.148750i	$-0.0475250\pi$
$354$	1.72091e7	−	6.96559e7i	0.387926	−	1.57018i
$355$	−3.16188e7			−0.706742
$356$		−	4.22081e7i		−	0.935505i
$357$	1.56560e7	+	3.86796e6i	0.344094	+	0.0850115i
$358$	−1.11324e8			−2.42627
$359$		−	7.05483e7i		−	1.52477i	−0.647126	−	0.762383i	$-0.724029\pi$
$359$		−	7.05483e7i		−	1.52477i	0.647126	−	0.762383i	$-0.275971\pi$
$360$	−3.70954e6	−	1.95210e6i	−0.0795082	−	0.0418404i
$361$	6.28967e7			1.33692
$362$		−	7.75760e7i		−	1.63531i
$363$	−1.02707e7	+	4.15717e7i	−0.214723	+	0.869117i
$364$	7.29819e6			0.151325
$365$		−	1.67380e7i		−	0.344212i
$366$	−1.42753e7	−	3.52684e6i	−0.291167	−	0.0719354i
$367$	−5.69390e7			−1.15189			−0.575946	−	0.817488i	$-0.695366\pi$
$367$	−5.69390e7			−1.15189			−0.575946	+	0.817488i	$0.695366\pi$
$368$			1.12036e7i			0.224810i
$369$	−755823.	+	1.43627e6i	−0.0150432	+	0.0285863i
$370$	−8.50799e7			−1.67966
$371$			3.76584e6i			0.0737463i
$372$	−8.00349e6	+	3.23950e7i	−0.155472	+	0.629288i
$373$	8.01787e7			1.54502			0.772508	−	0.635005i	$-0.219002\pi$
$373$	8.01787e7			1.54502			0.772508	+	0.635005i	$0.219002\pi$
$374$			2.94955e7i			0.563820i
$375$	−5.53411e7	−	1.36725e7i	−1.04943	−	0.259272i
$376$	−8.01781e6			−0.150832
$377$			914089.i			0.0170594i
$378$	−1.57249e7	−	1.39773e7i	−0.291147	−	0.258789i
$379$	7.51845e7			1.38105			0.690527	−	0.723307i	$-0.257379\pi$
$379$	7.51845e7			1.38105			0.690527	+	0.723307i	$0.257379\pi$
$380$			5.82918e7i			1.06232i
$381$	−5.55300e6	+	2.24764e7i	−0.100404	+	0.406398i
$382$	−1.26375e8			−2.26711
$383$		−	8.51378e6i		−	0.151540i	−0.997125	−	0.0757698i	$-0.975859\pi$
$383$		−	8.51378e6i		−	0.151540i	0.997125	−	0.0757698i	$-0.0241414\pi$
$384$	−1.29520e7	−	3.19990e6i	−0.228740	−	0.0565124i
$385$	3.95100e6			0.0692348
$386$		−	1.18087e8i		−	2.05325i
$387$	−1.37043e7	−	7.21176e6i	−0.236442	−	0.124425i
$388$	−4.38570e7			−0.750833
$389$		−	7.79422e7i		−	1.32411i	−0.749456	−	0.662055i	$-0.769685\pi$
$389$		−	7.79422e7i		−	1.32411i	0.749456	−	0.662055i	$-0.230315\pi$
$390$	8.79188e6	−	3.55861e7i	0.148213	−	0.599911i
$391$	−1.56925e7			−0.262520
$392$			6.55788e6i			0.108869i
$393$	−1.01393e8	−	2.50500e7i	−1.67043	−	0.412696i
$394$	4.69695e7			0.767940
$395$			1.01582e7i			0.164826i
$396$	8.55995e6	−	1.62663e7i	0.137843	−	0.261940i
$397$	5.11087e7			0.816815			0.408407	−	0.912800i	$-0.366084\pi$
$397$	5.11087e7			0.816815			0.408407	+	0.912800i	$0.366084\pi$
$398$			1.23517e8i			1.95919i
$399$	6.55679e6	−	2.65394e7i	0.103222	−	0.417803i
$400$	−2.91619e7			−0.455654
$401$		−	7.24862e7i		−	1.12415i	−0.827088	−	0.562073i	$-0.810004\pi$
$401$		−	7.24862e7i		−	1.12415i	0.827088	−	0.562073i	$-0.189996\pi$
$402$	9.24996e7	+	2.28529e7i	1.42384	+	0.351773i
$403$	2.72656e7			0.416582
$404$			5.06552e7i			0.768210i
$405$	−4.16046e7	+	2.85831e7i	−0.626291	+	0.430273i
$406$	−756659.			−0.0113063
$407$			3.48597e7i			0.517059i
$408$	2.42499e6	−	9.81541e6i	0.0357050	−	0.144520i
$409$	3.10118e7			0.453270			0.226635	−	0.973980i	$-0.427228\pi$
$409$	3.10118e7			0.453270			0.226635	+	0.973980i	$0.427228\pi$
$410$		−	2.34075e6i		−	0.0339627i
$411$	1.01933e8	+	2.51836e7i	1.46822	+	0.362737i
$412$	7.30386e7			1.04438
$413$		−	2.31817e7i		−	0.329076i
$414$	1.81170e7	+	9.53389e6i	0.255321	+	0.134360i
$415$	−3.67920e6			−0.0514765
$416$		−	5.81193e7i		−	0.807310i
$417$	2.98936e6	−	1.20998e7i	0.0412259	−	0.166867i
$418$	4.99993e7			0.684598
$419$		−	3.11759e7i		−	0.423815i	−0.977290	−	0.211908i	$-0.932032\pi$
$419$		−	3.11759e7i		−	0.423815i	0.977290	−	0.211908i	$-0.0679676\pi$
$420$	1.40712e7	+	3.47643e6i	0.189926	+	0.0469229i
$421$	1.31996e8			1.76894			0.884470	−	0.466597i	$-0.154520\pi$
$421$	1.31996e8			1.76894			0.884470	+	0.466597i	$0.154520\pi$
$422$			1.70766e8i			2.27229i
$423$	−4.49622e7	+	8.54405e7i	−0.594054	+	1.12887i
$424$	2.36096e6			0.0309736
$425$		−	4.08460e7i		−	0.532087i
$426$	−2.38632e7	+	9.65890e7i	−0.308674	+	1.24939i
$427$	−4.75087e6			−0.0610224
$428$		−	9.34046e7i		−	1.19134i
$429$	−1.45807e7	−	3.60229e6i	−0.184674	−	0.0456254i
$430$	2.23345e7			0.280912
$431$		−	1.51428e8i		−	1.89136i	−0.325093	−	0.945682i	$-0.605395\pi$
$431$		−	1.51428e8i		−	1.89136i	0.325093	−	0.945682i	$-0.394605\pi$
$432$	−5.77470e7	+	6.49674e7i	−0.716273	+	0.805832i
$433$	5.99368e7			0.738295			0.369147	−	0.929371i	$-0.379650\pi$
$433$	5.99368e7			0.738295			0.369147	+	0.929371i	$0.379650\pi$
$434$			2.25698e7i			0.276094i
$435$	−435418.	+	1.76240e6i	−0.00528980	+	0.0214110i
$436$	−5.16445e7			−0.623110
$437$			2.66013e7i			0.318756i
$438$	−5.11313e7	−	1.26325e7i	−0.608506	−	0.150337i
$439$	1.21227e8			1.43286			0.716432	−	0.697657i	$-0.245774\pi$
$439$	1.21227e8			1.43286			0.716432	+	0.697657i	$0.245774\pi$
$440$		−	2.47704e6i		−	0.0290787i
$441$	6.98830e7	+	3.67752e7i	0.814809	+	0.428785i
$442$	8.84132e7			1.02388
$443$			9.24263e7i			1.06313i	0.847019	+	0.531563i	$0.178395\pi$
$443$			9.24263e7i			1.06313i	−0.847019	+	0.531563i	$0.821605\pi$
$444$	−3.06726e7	+	1.24151e8i	−0.350430	+	1.41840i
$445$	−6.84935e7			−0.777266
$446$			5.11240e7i			0.576263i
$447$	−2.28831e7	−	5.65348e6i	−0.256208	−	0.0632985i
$448$	2.08180e7			0.231529
$449$		−	1.12975e8i		−	1.24809i	−0.781390	−	0.624043i	$-0.785489\pi$
$449$		−	1.12975e8i		−	1.24809i	0.781390	−	0.624043i	$-0.214511\pi$
$450$	−2.48157e7	+	4.71566e7i	−0.272325	+	0.517494i
$451$	−959071.			−0.0104549
$452$		−	3.48757e7i		−	0.377666i
$453$	−4.90185e6	+	1.98408e7i	−0.0527310	+	0.213435i
$454$	4.37218e7			0.467229
$455$		−	1.18432e7i		−	0.125729i
$456$	−1.66386e7	−	4.11073e6i	−0.175478	−	0.0433535i
$457$	7.09247e7			0.743103			0.371552	−	0.928412i	$-0.378826\pi$
$457$	7.09247e7			0.743103			0.371552	+	0.928412i	$0.378826\pi$
$458$			1.66110e8i			1.72901i
$459$	−9.09975e7	−	8.08842e7i	−0.941004	−	0.836422i
$460$	−1.41041e7			−0.144901
$461$			4.29939e7i			0.438837i	0.975631	+	0.219419i	$0.0704161\pi$
$461$			4.29939e7i			0.438837i	−0.975631	+	0.219419i	$0.929584\pi$
$462$	2.98188e6	−	1.20695e7i	0.0302388	−	0.122395i
$463$	−5.21679e7			−0.525606			−0.262803	−	0.964850i	$-0.584647\pi$
$463$	−5.21679e7			−0.525606			−0.262803	+	0.964850i	$0.584647\pi$
$464$			3.12614e6i			0.0312935i
$465$	5.25693e7	+	1.29877e7i	0.522845	+	0.129174i
$466$	2.28002e8			2.25310
$467$			1.10904e7i			0.108892i	0.998517	+	0.0544460i	$0.0173393\pi$
$467$			1.10904e7i			0.108892i	−0.998517	+	0.0544460i	$0.982661\pi$
$468$	−4.87585e7	−	2.56586e7i	−0.475677	−	0.250320i
$469$	3.07842e7			0.298407
$470$		−	1.39246e8i		−	1.34118i
$471$	8.62800e6	−	3.49228e7i	0.0825748	−	0.334231i
$472$	−1.45336e7			−0.138212
$473$		−	9.15108e6i		−	0.0864746i
$474$	3.10312e7	+	7.66653e6i	0.291382	+	0.0719887i
$475$	−6.92402e7			−0.646067
$476$			3.49598e7i			0.324151i
$477$	1.32398e7	−	2.51592e7i	0.121990	−	0.231815i
$478$	−9.29809e7			−0.851354
$479$		−	7.12025e7i		−	0.647871i	−0.946079	−	0.323936i	$-0.894994\pi$
$479$		−	7.12025e7i		−	0.647871i	0.946079	−	0.323936i	$-0.105006\pi$
$480$	2.76846e7	−	1.12056e8i	0.250331	−	1.01324i
$481$	1.04493e8			0.938967
$482$		−	7.98275e7i		−	0.712872i
$483$	6.42136e6	+	1.58646e6i	0.0569883	+	0.0140795i
$484$	−9.28293e7			−0.818746
$485$			7.11692e7i			0.623831i
$486$	5.59159e7	+	1.48666e8i	0.487110	+	1.29509i
$487$	−1.92406e8			−1.66583			−0.832915	−	0.553400i	$-0.813330\pi$
$487$	−1.92406e8			−1.66583			−0.832915	+	0.553400i	$0.813330\pi$
$488$			2.97852e6i			0.0256295i
$489$	5.30725e7	−	2.14817e8i	0.453882	−	1.83714i
$490$	−1.13891e8			−0.968057
$491$		−	1.75484e8i		−	1.48250i	−0.671231	−	0.741248i	$-0.734234\pi$
$491$		−	1.75484e8i		−	1.48250i	0.671231	−	0.741248i	$-0.265766\pi$
$492$	−3.41567e6	−	843874.i	−0.0286801	−	0.00708569i
$493$	−4.37867e6			−0.0365428
$494$		−	1.49874e8i		−	1.24321i
$495$	−2.63962e7	−	1.38907e7i	−0.217634	−	0.114527i
$496$	9.32470e7			0.764169
$497$			3.21452e7i			0.261847i
$498$	−2.77675e6	+	1.12392e7i	−0.0224827	+	0.0910013i
$499$	−713500.			−0.00574239			−0.00287119	−	0.999996i	$-0.500914\pi$
$499$	−713500.			−0.00574239			−0.00287119	+	0.999996i	$0.500914\pi$
$500$		−	1.23576e8i		−	0.988610i
$501$	7.95444e7	+	1.96522e7i	0.632552	+	0.156278i
$502$	2.01892e8			1.59591
$503$			4.06241e7i			0.319212i	0.987181	+	0.159606i	$0.0510224\pi$
$503$			4.06241e7i			0.319212i	−0.987181	+	0.159606i	$0.948978\pi$
$504$	−1.98460e6	+	3.77129e6i	−0.0155018	+	0.0294577i
$505$	8.22011e7			0.638269
$506$			1.20976e7i			0.0933790i
$507$	2.04600e7	−	8.28140e7i	0.156993	−	0.635448i
$508$	−5.01896e7			−0.382845
$509$			1.51329e8i			1.14754i	0.819015	+	0.573772i	$0.194520\pi$
$509$			1.51329e8i			1.14754i	−0.819015	+	0.573772i	$0.805480\pi$
$510$	1.70464e8	+	4.21148e7i	1.28506	+	0.317486i
$511$	−1.70167e7			−0.127530
$512$		−	1.81655e8i		−	1.35343i
$513$	−1.37111e8	+	1.54255e8i	−1.01560	+	1.14258i
$514$	−2.37697e8			−1.75039
$515$		−	1.18524e8i		−	0.867729i
$516$	8.05191e6	−	3.25910e7i	0.0586070	−	0.237218i
$517$	−5.70529e7			−0.412863
$518$			8.64962e7i			0.622312i
$519$	−2.56160e6	−	632868.i	−0.0183236	−	0.00452701i
$520$	−7.42499e6			−0.0528063
$521$		−	1.68339e8i		−	1.19034i	−0.803598	−	0.595172i	$-0.797084\pi$
$521$		−	1.68339e8i		−	1.19034i	0.803598	−	0.595172i	$-0.202916\pi$
$522$	5.05517e6	+	2.66023e6i	0.0355405	+	0.0187028i
$523$	−2.23068e8			−1.55931			−0.779656	−	0.626208i	$-0.784606\pi$
$523$	−2.23068e8			−1.55931			−0.779656	+	0.626208i	$0.784606\pi$
$524$		−	2.26409e8i		−	1.57362i
$525$	−4.12937e6	+	1.67141e7i	−0.0285368	+	0.115506i
$526$	−2.05331e8			−1.41090
$527$			1.30608e8i			0.892353i
$528$	−4.98651e7	−	1.23196e7i	−0.338762	−	0.0836943i
$529$	−6.43634e6			−0.0434783
$530$			4.10029e7i			0.275415i
$531$	−8.15013e7	+	1.54875e8i	−0.544353	+	1.03442i
$532$	5.92622e7			0.393589
$533$			2.87483e6i			0.0189859i
$534$	−5.16931e7	+	2.09234e8i	−0.339476	+	1.37407i
$535$	−1.51573e8			−0.989829
$536$		−	1.92999e7i		−	0.125332i
$537$	2.63611e8	+	6.51275e7i	1.70232	+	0.420573i
$538$	−2.55427e8			−1.64029
$539$			4.66644e7i			0.298002i
$540$	−8.17862e7	−	7.26966e7i	−0.519396	−	0.461671i
$541$	−1.86151e8			−1.17564			−0.587818	−	0.808993i	$-0.700013\pi$
$541$	−1.86151e8			−1.17564			−0.587818	+	0.808993i	$0.700013\pi$
$542$			4.11626e8i			2.58527i
$543$	−4.53841e7	+	1.83697e8i	−0.283468	+	1.14737i
$544$	2.78403e8			1.72933
$545$			8.38065e7i			0.517712i
$546$	−3.61785e7	−	8.93824e6i	−0.222266	−	0.0549128i
$547$	−4.46273e7			−0.272671			−0.136335	−	0.990663i	$-0.543532\pi$
$547$	−4.46273e7			−0.272671			−0.136335	+	0.990663i	$0.543532\pi$
$548$			2.27616e8i			1.38313i
$549$	3.17401e7	+	1.67029e7i	0.191819	+	0.100943i
$550$	−3.14888e7			−0.189264
$551$			7.42252e6i			0.0443707i
$552$	994616.	−	4.02582e6i	0.00591341	−	0.0239352i
$553$	1.03273e7			0.0610676
$554$		−	2.06781e8i		−	1.21613i
$555$	2.01466e8	+	4.97741e7i	1.17848	+	0.291155i
$556$	2.70187e7			0.157196
$557$			2.10827e8i			1.22000i	0.792401	+	0.610000i	$0.208831\pi$
$557$			2.10827e8i			1.22000i	−0.792401	+	0.610000i	$0.791169\pi$
$558$	7.93497e7	−	1.50786e8i	0.456712	−	0.867880i
$559$	−2.74305e7			−0.157036
$560$		−	4.05031e7i		−	0.230634i
$561$	1.72557e7	−	6.98442e7i	0.0977334	−	0.395587i
$562$	−2.72127e8			−1.53307
$563$		−	2.33140e8i		−	1.30644i	−0.757166	−	0.653222i	$-0.773417\pi$
$563$		−	2.33140e8i		−	1.30644i	0.757166	−	0.653222i	$-0.226583\pi$
$564$	−2.03190e8	−	5.02001e7i	−1.13257	−	0.279812i
$565$	−5.65948e7			−0.313784
$566$			8.03811e7i			0.443307i
$567$	2.90589e7	+	4.22972e7i	0.159415	+	0.232040i
$568$	2.01532e7			0.109976
$569$			3.64508e8i			1.97865i	0.145712	+	0.989327i	$0.453453\pi$
$569$			3.64508e8i			1.97865i	−0.145712	+	0.989327i	$0.546547\pi$
$570$	7.13911e7	−	2.88964e8i	0.385496	−	1.56034i
$571$	1.58314e8			0.850376			0.425188	−	0.905105i	$-0.360208\pi$
$571$	1.58314e8			0.850376			0.425188	+	0.905105i	$0.360208\pi$
$572$		−	3.25585e7i		−	0.173971i
$573$	2.99252e8	+	7.39330e7i	1.59065	+	0.392984i
$574$	−2.37971e6			−0.0125831
$575$		−	1.67531e7i		−	0.0881234i
$576$	−1.39083e8	−	7.31910e7i	−0.727791	−	0.382992i
$577$	4.35164e7			0.226530			0.113265	−	0.993565i	$-0.463869\pi$
$577$	4.35164e7			0.226530			0.113265	+	0.993565i	$0.463869\pi$
$578$			1.56329e8i			0.809572i
$579$	−6.90844e7	+	2.79627e8i	−0.355913	+	1.44060i
$580$	−3.93543e6			−0.0201701
$581$			3.74045e6i			0.0190720i
$582$	2.17407e8	+	5.37125e7i	1.10282	+	0.272462i
$583$	1.68001e7			0.0847823
$584$			1.06685e7i			0.0535628i
$585$	−4.16377e7	+	7.91232e7i	−0.207979	+	0.395217i
$586$	1.49354e7			0.0742205
$587$		−	1.25815e8i		−	0.622039i	−0.950404	−	0.311019i	$-0.899330\pi$
$587$		−	1.25815e8i		−	0.622039i	0.950404	−	0.311019i	$-0.100670\pi$
$588$	−4.10594e7	+	1.66192e8i	−0.201967	+	0.817484i
$589$	2.21400e8			1.08351
$590$		−	2.52405e8i		−	1.22897i
$591$	−1.11222e8	−	2.74785e7i	−0.538802	−	0.133116i
$592$	3.57359e8			1.72242
$593$		−	2.35119e8i		−	1.12752i	−0.825939	−	0.563759i	$-0.809355\pi$
$593$		−	2.35119e8i		−	1.12752i	0.825939	−	0.563759i	$-0.190645\pi$
$594$	−6.23550e7	+	7.01515e7i	−0.297517	+	0.334717i
$595$	5.67312e7			0.269321
$596$		−	5.10978e7i		−	0.241359i
$597$	7.22609e7	−	2.92484e8i	0.339610	−	1.37461i
$598$	3.62629e7			0.169574
$599$			5.30028e7i			0.246614i	0.992369	+	0.123307i	$0.0393500\pi$
$599$			5.30028e7i			0.246614i	−0.992369	+	0.123307i	$0.960650\pi$
$600$	1.04788e7	+	2.58887e6i	0.0485128	+	0.0119855i
$601$	−2.30442e8			−1.06154			−0.530772	−	0.847515i	$-0.678098\pi$
$601$	−2.30442e8			−1.06154			−0.530772	+	0.847515i	$0.678098\pi$
$602$		−	2.27063e7i		−	0.104077i
$603$	−2.05666e8	−	1.08230e8i	−0.938018	−	0.493622i
$604$	−4.43044e7			−0.201065
$605$			1.50639e8i			0.680256i
$606$	6.20385e7	−	2.51108e8i	0.278768	−	1.12835i
$607$	−2.14920e8			−0.960971			−0.480485	−	0.877003i	$-0.659540\pi$
$607$	−2.14920e8			−0.960971			−0.480485	+	0.877003i	$0.659540\pi$
$608$		−	4.71936e8i		−	2.09977i
$609$	1.79174e6	+	442667.i	0.00793275	+	0.00195986i
$610$	−5.17280e7			−0.227896
$611$			1.71017e8i			0.749750i
$612$	1.22910e8	−	2.33563e8i	0.536207	−	1.01894i
$613$	4.42056e7			0.191909			0.0959546	−	0.995386i	$-0.469410\pi$
$613$	4.42056e7			0.191909			0.0959546	+	0.995386i	$0.469410\pi$
$614$			4.48062e8i			1.93568i
$615$	−1.36940e6	+	5.54281e6i	−0.00588716	+	0.0238289i
$616$	−2.51828e6			−0.0107736
$617$		−	1.76054e7i		−	0.0749531i	−0.999298	−	0.0374765i	$-0.988068\pi$
$617$		−	1.76054e7i		−	0.0749531i	0.999298	−	0.0374765i	$-0.0119319\pi$
$618$	−3.62066e8	−	8.94518e7i	−1.53399	−	0.378986i
$619$	1.84020e8			0.775879			0.387939	−	0.921685i	$-0.373187\pi$
$619$	1.84020e8			0.775879			0.387939	+	0.921685i	$0.373187\pi$
$620$			1.17387e8i			0.492543i
$621$	−3.73229e7	−	3.31749e7i	−0.155848	−	0.138527i
$622$	9.00973e7			0.374404
$623$			6.96338e7i			0.287976i
$624$	−3.69283e7	+	1.49472e8i	−0.151987	+	0.615184i
$625$	−9.73542e7			−0.398763
$626$		−	5.22545e8i		−	2.13010i
$627$	−1.18397e8	−	2.92510e7i	−0.480327	−	0.118669i
$628$	7.79824e7			0.314860
$629$			5.00540e8i			2.01135i
$630$	−6.54961e7	−	3.44666e7i	−0.261935	−	0.137841i
$631$	−2.52213e8			−1.00388			−0.501938	−	0.864904i	$-0.667379\pi$
$631$	−2.52213e8			−1.00388			−0.501938	+	0.864904i	$0.667379\pi$
$632$		−	6.47460e6i		−	0.0256485i
$633$	9.99030e7	−	4.04369e8i	0.393883	−	1.59429i
$634$	4.11593e8			1.61510
$635$			8.14455e7i			0.318087i
$636$	5.98324e7	+	1.47821e7i	0.232576	+	0.0574601i
$637$	1.39877e8			0.541165
$638$			3.37559e6i			0.0129983i
$639$	1.13015e8	−	2.14759e8i	0.433144	−	0.823092i
$640$	−4.69328e7			−0.179034
$641$			6.47408e7i			0.245813i	0.992418	+	0.122906i	$0.0392214\pi$
$641$			6.47408e7i			0.245813i	−0.992418	+	0.122906i	$0.960779\pi$
$642$	−1.14394e8	+	4.63024e8i	−0.432315	+	1.74984i
$643$	7.48343e7			0.281493			0.140747	−	0.990046i	$-0.455050\pi$
$643$	7.48343e7			0.281493			0.140747	+	0.990046i	$0.455050\pi$
$644$			1.43388e7i			0.0536854i
$645$	−5.28873e7	−	1.30663e7i	−0.197093	−	0.0486937i
$646$	7.17926e8			2.66307
$647$			3.14596e8i			1.16156i	0.814062	+	0.580778i	$0.197251\pi$
$647$			3.14596e8i			1.16156i	−0.814062	+	0.580778i	$0.802749\pi$
$648$	2.65178e7	−	1.82183e7i	0.0974571	−	0.0669548i
$649$	−1.03418e8			−0.378322
$650$			9.43884e7i			0.343699i
$651$	1.32039e7	−	5.34444e7i	0.0478586	−	0.193713i
$652$	4.79684e8			1.73066
$653$		−	1.10410e8i		−	0.396522i	−0.980149	−	0.198261i	$-0.936471\pi$
$653$		−	1.10410e8i		−	0.396522i	0.980149	−	0.198261i	$-0.0635294\pi$
$654$	2.56012e8	+	6.32500e7i	0.915222	+	0.226114i
$655$	−3.67407e8			−1.30745
$656$			9.83179e6i			0.0348274i
$657$	1.13687e8	+	5.98265e7i	0.400880	+	0.210959i
$658$	−1.41564e8			−0.496906
$659$		−	4.56886e8i		−	1.59644i	−0.602368	−	0.798218i	$-0.705776\pi$
$659$		−	4.56886e8i		−	1.59644i	0.602368	−	0.798218i	$-0.294224\pi$
$660$	1.55089e7	−	6.27742e7i	0.0539449	−	0.218348i
$661$	1.81270e7			0.0627657			0.0313829	−	0.999507i	$-0.490009\pi$
$661$	1.81270e7			0.0627657			0.0313829	+	0.999507i	$0.490009\pi$
$662$		−	6.18554e8i		−	2.13208i
$663$	−2.09359e8	−	5.17242e7i	−0.718376	−	0.177481i
$664$	2.34504e6			0.00801026
$665$		−	9.61681e7i		−	0.327014i
$666$	3.04100e8	−	5.77873e8i	1.02942	−	1.95618i
$667$	−1.79592e6			−0.00605216
$668$			1.77622e8i			0.595891i
$669$	2.99090e7	−	1.21060e8i	0.0998903	−	0.404317i
$670$	3.35182e8			1.11444
$671$			2.11944e7i			0.0701543i
$672$	−1.13922e8	−	2.81455e7i	−0.375404	−	0.0927471i
$673$	−4.96238e8			−1.62796			−0.813982	−	0.580890i	$-0.802705\pi$
$673$	−4.96238e8			−1.62796			−0.813982	+	0.580890i	$0.802705\pi$
$674$			7.04670e8i			2.30147i
$675$	8.63506e7	−	9.71474e7i	0.280772	−	0.315878i
$676$	1.84923e8			0.598619
$677$		−	1.67885e7i		−	0.0541060i	−0.999634	−	0.0270530i	$-0.991388\pi$
$677$		−	1.67885e7i		−	0.0541060i	0.999634	−	0.0270530i	$-0.00861229\pi$
$678$	−4.27129e7	+	1.72885e8i	−0.137047	+	0.554714i
$679$	7.23540e7			0.231128
$680$		−	3.55671e7i		−	0.113116i
$681$	−1.03532e8	−	2.55784e7i	−0.327817	−	0.0809903i
$682$	1.00688e8			0.317412
$683$			3.72836e8i			1.17019i	0.810966	+	0.585094i	$0.198942\pi$
$683$			3.72836e8i			1.17019i	−0.810966	+	0.585094i	$0.801058\pi$
$684$	−3.95925e8	−	2.08351e8i	−1.23721	−	0.651070i
$685$	3.69366e8			1.14917
$686$			2.41540e8i			0.748200i
$687$	9.71787e7	−	3.93342e8i	0.299710	−	1.21311i
$688$	−9.38110e7			−0.288064
$689$		−	5.03585e7i		−	0.153963i
$690$	6.99165e7	+	1.72735e7i	0.212830	+	0.0525816i
$691$	4.35470e7			0.131985			0.0659924	−	0.997820i	$-0.478979\pi$
$691$	4.35470e7			0.131985			0.0659924	+	0.997820i	$0.478979\pi$
$692$		−	5.72004e6i		−	0.0172616i
$693$	−1.41220e7	+	2.68356e7i	−0.0424322	+	0.0806329i
$694$	3.76850e8			1.12743
$695$		−	4.38448e7i		−	0.130606i
$696$	277526.	−	1.12332e6i	0.000823145	−	0.00333177i
$697$	−1.37710e7			−0.0406694
$698$		−	2.41783e7i		−	0.0710983i
$699$	−5.39900e8	−	1.33387e8i	−1.58082	−	0.390556i
$700$	−3.73224e7			−0.108812
$701$			1.03884e8i			0.301573i	0.988566	+	0.150787i	$0.0481806\pi$
$701$			1.03884e8i			0.301573i	−0.988566	+	0.150787i	$0.951819\pi$
$702$	2.10280e8	+	1.86910e8i	0.607838	+	0.540283i
$703$	8.48493e8			2.44221
$704$		−	9.28728e7i		−	0.266177i
$705$	−8.14625e7	+	3.29729e8i	−0.232483	+	0.940999i
$706$	−1.44855e8			−0.411642
$707$		−	8.35695e7i		−	0.236477i
$708$	−3.68316e8	−	9.09959e7i	−1.03782	−	0.256402i
$709$	−5.58193e8			−1.56619			−0.783097	−	0.621899i	$-0.786361\pi$
$709$	−5.58193e8			−1.56619			−0.783097	+	0.621899i	$0.786361\pi$
$710$			3.50000e8i			0.977898i
$711$	−6.89956e7	−	3.63082e7i	−0.191961	−	0.101017i
$712$	4.36563e7			0.120950
$713$			5.35691e7i			0.147790i
$714$	4.28159e7	−	1.73302e8i	0.117628	−	0.476112i
$715$	−5.28345e7			−0.144544
$716$			5.88641e8i			1.60366i
$717$	2.20176e8	+	5.43964e7i	0.597326	+	0.147575i
$718$	−7.80925e8			−2.10977
$719$			3.37942e8i			0.909193i	0.890698	+	0.454596i	$0.150216\pi$
$719$			3.37942e8i			0.909193i	−0.890698	+	0.454596i	$0.849784\pi$
$720$	−1.42399e8	+	2.70597e8i	−0.381513	+	0.724979i
$721$	−1.20497e8			−0.321492
$722$		−	6.96227e8i		−	1.84986i
$723$	−4.67013e7	+	1.89029e8i	−0.123570	+	0.500165i
$724$	−4.10194e8			−1.08087
$725$		−	4.67459e6i		−	0.0122668i
$726$	4.60173e8	+	1.13690e8i	1.20257	+	0.297106i
$727$	−2.21325e7			−0.0576007			−0.0288004	−	0.999585i	$-0.509169\pi$
$727$	−2.21325e7			−0.0576007			−0.0288004	+	0.999585i	$0.509169\pi$
$728$			7.54859e6i			0.0195646i
$729$	−4.54335e7	−	3.84747e8i	−0.117272	−	0.993100i
$730$	−1.85280e8			−0.476276
$731$		−	1.31398e8i		−	0.336384i
$732$	−1.86487e7	+	7.54827e7i	−0.0475461	+	0.192448i
$733$	−1.65504e8			−0.420240			−0.210120	−	0.977676i	$-0.567386\pi$
$733$	−1.65504e8			−0.420240			−0.210120	+	0.977676i	$0.567386\pi$
$734$			6.30279e8i			1.59384i
$735$	2.69690e8	+	6.66294e7i	0.679208	+	0.167805i
$736$	1.14188e8			0.286409
$737$		−	1.37334e8i		−	0.343064i
$738$	1.58986e7	+	8.36648e6i	0.0395540	+	0.0208149i
$739$	−4.69632e8			−1.16366			−0.581828	−	0.813312i	$-0.697662\pi$
$739$	−4.69632e8			−1.16366			−0.581828	+	0.813312i	$0.697662\pi$
$740$			4.49873e8i			1.11018i
$741$	−8.76804e7	+	3.54896e8i	−0.215500	+	0.872262i
$742$	4.16855e7			0.102041
$743$		−	2.62771e8i		−	0.640636i	−0.947310	−	0.320318i	$-0.896210\pi$
$743$		−	2.62771e8i		−	0.640636i	0.947310	−	0.320318i	$-0.103790\pi$
$744$	−3.35065e7	−	8.27810e6i	−0.0813599	−	0.0201007i
$745$	−8.29192e7			−0.200533
$746$		−	8.87528e8i		−	2.13779i
$747$	1.31505e7	−	2.49896e7i	0.0315486	−	0.0599511i
$748$	1.55962e8			0.372660
$749$			1.54096e8i			0.366730i
$750$	−1.51346e8	+	6.12591e8i	−0.358747	+	1.45207i
$751$	6.03709e8			1.42530			0.712652	−	0.701517i	$-0.247494\pi$
$751$	6.03709e8			1.42530			0.712652	+	0.701517i	$0.247494\pi$
$752$			5.84870e8i			1.37533i
$753$	−4.78073e8	−	1.18112e8i	−1.11972	−	0.276637i
$754$	1.01184e7			0.0236046
$755$			7.18952e7i			0.167055i
$756$	−7.39068e7	+	8.31477e7i	−0.171048	+	0.192435i
$757$	2.54276e8			0.586163			0.293081	−	0.956087i	$-0.405319\pi$
$757$	2.54276e8			0.586163			0.293081	+	0.956087i	$0.405319\pi$
$758$		−	8.32245e8i		−	1.91092i
$759$	7.07746e6	−	2.86468e7i	0.0161865	−	0.0655165i
$760$	−6.02918e7			−0.137346
$761$		−	7.88570e8i		−	1.78931i	−0.446754	−	0.894657i	$-0.647420\pi$
$761$		−	7.88570e8i		−	1.78931i	0.446754	−	0.894657i	$-0.352580\pi$
$762$	2.48799e8	+	6.14682e7i	0.562321	+	0.138927i
$763$	8.52016e7			0.191811
$764$			6.68228e8i			1.49846i
$765$	−3.79016e8	−	1.99453e8i	−0.846589	−	0.445509i
$766$	−9.42422e7			−0.209681
$767$			3.09997e8i			0.687023i
$768$	−1.24774e8	+	5.05037e8i	−0.275448	+	1.11491i
$769$	−6.43796e7			−0.141569			−0.0707847	−	0.997492i	$-0.522550\pi$
$769$	−6.43796e7			−0.141569			−0.0707847	+	0.997492i	$0.522550\pi$
$770$		−	4.37350e7i		−	0.0957982i
$771$	5.62859e8	+	1.39060e8i	1.22811	+	0.303416i
$772$	−6.24404e8			−1.35711
$773$		−	5.22489e8i		−	1.13120i	−0.824680	−	0.565599i	$-0.808645\pi$
$773$		−	5.22489e8i		−	1.13120i	0.824680	−	0.565599i	$-0.191355\pi$
$774$	−7.98297e7	+	1.51698e8i	−0.172164	+	0.327158i
$775$	−1.39434e8			−0.299547
$776$		−	4.53617e7i		−	0.0970743i
$777$	5.06027e7	−	2.04820e8i	0.107872	−	0.436626i
$778$	−8.62771e8			−1.83213
$779$			2.33440e7i			0.0493814i
$780$	−1.88167e8	−	4.64884e7i	−0.396515	−	0.0979626i
$781$	1.43405e8			0.301032
$782$			1.73707e8i			0.363242i
$783$	−1.04142e7	−	9.25674e6i	−0.0216940	−	0.0192829i
$784$	4.78374e8			0.992702
$785$		−	1.26546e8i		−	0.261602i
$786$	−2.77288e8	+	1.12235e9i	−0.571036	+	2.31133i
$787$	−4.42575e8			−0.907952			−0.453976	−	0.891014i	$-0.649995\pi$
$787$	−4.42575e8			−0.907952			−0.453976	+	0.891014i	$0.649995\pi$
$788$		−	2.48358e8i		−	0.507575i
$789$	4.86217e8	+	1.20124e8i	0.989917	+	0.244568i
$790$	1.12445e8			0.228064
$791$			5.75369e7i			0.116256i
$792$	1.68244e7	+	8.85365e6i	0.0338660	+	0.0178216i
$793$	6.35308e7			0.127399
$794$		−	5.65741e8i		−	1.13020i
$795$	2.39878e7	−	9.70934e7i	0.0477408	−	0.193236i
$796$	6.53114e8			1.29494
$797$		−	3.54170e8i		−	0.699579i	−0.936828	−	0.349790i	$-0.886253\pi$
$797$		−	3.54170e8i		−	0.699579i	0.936828	−	0.349790i	$-0.113747\pi$
$798$	−2.93774e8	−	7.25796e7i	−0.578102	−	0.142825i
$799$	−8.19206e8			−1.60603
$800$			2.97218e8i			0.580504i
$801$	2.44815e8	−	4.65216e8i	0.476366	−	0.905227i
$802$	−8.02377e8			−1.55545
$803$			7.59144e7i			0.146615i
$804$	1.20838e8	−	4.89106e8i	0.232507	−	0.941097i
$805$	2.32685e7			0.0446046
$806$		−	3.01813e8i		−	0.576412i
$807$	6.04842e8	+	1.49432e8i	1.15086	+	0.284330i
$808$	−5.23932e7			−0.0993210
$809$			5.92745e7i			0.111950i	0.998432	+	0.0559748i	$0.0178267\pi$
$809$			5.92745e7i			0.111950i	−0.998432	+	0.0559748i	$0.982173\pi$
$810$	3.16397e8	+	4.60536e8i	0.595357	+	0.866580i
$811$	−3.35057e8			−0.628139			−0.314070	−	0.949400i	$-0.601693\pi$
$811$	−3.35057e8			−0.628139			−0.314070	+	0.949400i	$0.601693\pi$
$812$			4.00095e6i			0.00747300i
$813$	2.40813e8	−	9.74717e8i	0.448134	−	1.81387i
$814$	3.85875e8			0.715440
$815$		−	7.78411e8i		−	1.43792i
$816$	−7.15998e8	−	1.76894e8i	−1.31778	−	0.325569i
$817$	−2.22739e8			−0.408442
$818$		−	3.43281e8i		−	0.627176i
$819$	8.04403e7	+	4.23309e7i	0.146427	+	0.0770558i
$820$	−1.23770e7			−0.0224479
$821$			1.42386e8i			0.257299i	0.991690	+	0.128650i	$0.0410642\pi$
$821$			1.42386e8i			0.257299i	−0.991690	+	0.128650i	$0.958936\pi$
$822$	2.78766e8	−	1.12834e9i	0.501909	−	2.03153i
$823$	4.02097e8			0.721325			0.360662	−	0.932696i	$-0.382551\pi$
$823$	4.02097e8			0.721325			0.360662	+	0.932696i	$0.382551\pi$
$824$			7.55445e7i			0.135027i
$825$	7.45645e7	+	1.84218e7i	0.132791	+	0.0328074i
$826$	−2.56607e8			−0.455333
$827$			6.56933e8i			1.16146i	0.814096	+	0.580730i	$0.197233\pi$
$827$			6.56933e8i			1.16146i	−0.814096	+	0.580730i	$0.802767\pi$
$828$	5.04119e7	−	9.57964e7i	0.0888059	−	0.168756i
$829$	7.85239e8			1.37828			0.689142	−	0.724627i	$-0.257988\pi$
$829$	7.85239e8			1.37828			0.689142	+	0.724627i	$0.257988\pi$
$830$			4.07264e7i			0.0712266i
$831$	−1.20973e8	+	4.89651e8i	−0.210807	+	0.853264i
$832$	−2.78388e8			−0.483371
$833$			6.70041e8i			1.15922i
$834$	−1.33937e8	−	3.30904e7i	−0.230888	−	0.0570431i
$835$	2.88237e8			0.495097
$836$		−	2.64379e8i		−	0.452489i
$837$	−2.76112e8	+	3.10635e8i	−0.470878	+	0.529754i
$838$	−3.45097e8			−0.586421
$839$		−	8.16709e7i		−	0.138287i	−0.997607	−	0.0691435i	$-0.977973\pi$
$839$		−	8.16709e7i		−	0.138287i	0.997607	−	0.0691435i	$-0.0220266\pi$
$840$	−3.59570e6	+	1.45540e7i	−0.00606661	+	0.0245553i
$841$	5.94322e8			0.999158
$842$		−	1.46111e9i		−	2.44763i
$843$	6.44387e8	+	1.59202e8i	1.07563	+	0.265745i
$844$	9.02952e8			1.50189
$845$		−	3.00085e8i		−	0.497364i
$846$	9.45773e8	+	4.97703e8i	1.56198	+	0.821976i
$847$	1.53147e8			0.252034
$848$		−	1.72224e8i		−	0.282426i
$849$	4.70252e7	−	1.90340e8i	0.0768436	−	0.311033i
$850$	−4.52139e8			−0.736233
$851$			2.05298e8i			0.333117i
$852$	5.10729e8	+	1.26180e8i	0.825794	+	0.204020i
$853$	−9.54185e8			−1.53739			−0.768697	−	0.639613i	$-0.779095\pi$
$853$	−9.54185e8			−1.53739			−0.768697	+	0.639613i	$0.779095\pi$
$854$			5.25891e7i			0.0844349i
$855$	−3.38103e8	+	6.42490e8i	−0.540943	+	1.02794i
$856$	9.66093e7			0.154027
$857$			9.60999e8i			1.52679i	0.645930	+	0.763397i	$0.276470\pi$
$857$			9.60999e8i			1.52679i	−0.645930	+	0.763397i	$0.723530\pi$
$858$	−3.98750e7	+	1.61399e8i	−0.0631305	+	0.255528i
$859$	5.94092e8			0.937290			0.468645	−	0.883387i	$-0.344742\pi$
$859$	5.94092e8			0.937290			0.468645	+	0.883387i	$0.344742\pi$
$860$		−	1.18097e8i		−	0.185670i
$861$	5.63508e6	+	1.39220e6i	0.00882857	+	0.00218118i
$862$	−1.67622e9			−2.61703
$863$			5.36267e8i			0.834351i	0.908826	+	0.417175i	$0.136980\pi$
$863$			5.36267e8i			0.834351i	−0.908826	+	0.417175i	$0.863020\pi$
$864$	6.62149e8	+	5.88558e8i	1.02663	+	0.912533i
$865$	−9.28224e6			−0.0143418
$866$		−	6.63463e8i		−	1.02156i
$867$	9.14567e7	−	3.70181e8i	0.140333	−	0.568012i
$868$	1.19341e8			0.182486
$869$		−	4.60718e7i		−	0.0702063i
$870$	1.95087e7	+	4.81981e6i	0.0296258	+	0.00731934i
$871$	−4.11661e8			−0.622995
$872$		−	5.34164e7i		−	0.0805611i
$873$	−4.83390e8	−	2.54379e8i	−0.726532	−	0.382330i
$874$	2.94459e8			0.441053
$875$			2.03872e8i			0.304323i
$876$	−6.67960e7	+	2.70364e8i	−0.0993661	+	0.402195i
$877$	−1.74162e7			−0.0258198			−0.0129099	−	0.999917i	$-0.504109\pi$
$877$	−1.74162e7			−0.0258198			−0.0129099	+	0.999917i	$0.504109\pi$
$878$		−	1.34190e9i		−	1.98261i
$879$	−3.53665e7	−	8.73763e6i	−0.0520746	−	0.0128655i
$880$	−1.80691e8			−0.265149
$881$			5.62757e8i			0.822987i	0.911413	+	0.411493i	$0.134993\pi$
$881$			5.62757e8i			0.822987i	−0.911413	+	0.411493i	$0.865007\pi$
$882$	4.07078e8	−	7.73561e8i	0.593297	−	1.12743i
$883$	3.81844e8			0.554631			0.277315	−	0.960779i	$-0.410555\pi$
$883$	3.81844e8			0.554631			0.277315	+	0.960779i	$0.410555\pi$
$884$		−	4.67498e8i		−	0.676741i
$885$	−1.47664e8	+	5.97687e8i	−0.213032	+	0.862272i
$886$	1.02310e9			1.47102
$887$			4.78834e7i			0.0686143i	0.999411	+	0.0343071i	$0.0109224\pi$
$887$			4.78834e7i			0.0686143i	−0.999411	+	0.0343071i	$0.989078\pi$
$888$	−1.28410e8	−	3.17250e7i	−0.183384	−	0.0453067i
$889$	8.28013e7			0.117851
$890$			7.58180e8i			1.07548i
$891$	1.88695e8	−	1.29637e8i	0.266764	−	0.183272i
$892$	2.70326e8			0.380884
$893$			1.38868e9i			1.95006i
$894$	−6.25804e7	+	2.53301e8i	−0.0875843	+	0.354507i
$895$	9.55221e8			1.33240
$896$			4.77141e7i			0.0663320i
$897$	−8.58694e7	−	2.12148e7i	−0.118976	−	0.0293942i
$898$	−1.25057e9			−1.72694
$899$			1.49473e7i			0.0205724i
$900$	2.49348e8	+	1.31216e8i	0.342041	+	0.179995i
$901$	2.41227e8			0.329801
$902$			1.06163e7i			0.0144662i
$903$	−1.32838e7	+	5.37677e7i	−0.0180409	+	0.0730227i
$904$	3.60723e7			0.0488279
$905$			6.65646e8i			0.898044i
$906$	2.19625e8	+	5.42604e7i	0.295323	+	0.0729623i
$907$	7.00725e8			0.939130			0.469565	−	0.882898i	$-0.344411\pi$
$907$	7.00725e8			0.939130			0.469565	+	0.882898i	$0.344411\pi$
$908$		−	2.31185e8i		−	0.308818i
$909$	−2.93810e8	+	5.58320e8i	−0.391178	+	0.743347i
$910$	−1.31097e8			−0.173967
$911$		−	1.00195e9i		−	1.32523i	−0.748962	−	0.662613i	$-0.769448\pi$
$911$		−	1.00195e9i		−	1.32523i	0.748962	−	0.662613i	$-0.230552\pi$
$912$	−2.99863e8	+	1.21373e9i	−0.395310	+	1.60006i
$913$	1.66868e7			0.0219261
$914$		−	7.85092e8i		−	1.02821i
$915$	1.22490e8	+	3.02623e7i	0.159896	+	0.0395038i
$916$	8.78329e8			1.14280
$917$			3.73524e8i			0.484407i
$918$	−8.95337e8	+	1.00728e9i	−1.15733	+	1.30204i
$919$	7.98055e8			1.02822			0.514110	−	0.857724i	$-0.328122\pi$
$919$	7.98055e8			1.02822			0.514110	+	0.857724i	$0.328122\pi$
$920$		−	1.45880e7i		−	0.0187340i
$921$	2.62129e8	−	1.06100e9i	0.335533	−	1.35811i
$922$	4.75915e8			0.607207
$923$		−	4.29860e8i		−	0.546666i
$924$	−6.38192e7	−	1.57671e7i	−0.0808975	−	0.0199865i
$925$	−5.34368e8			−0.675173
$926$			5.77465e8i			0.727265i
$927$	8.05028e8	+	4.23638e8i	1.01058	+	0.531808i
$928$	3.18616e7			0.0398680
$929$			7.61265e8i			0.949486i	0.880125	+	0.474743i	$0.157459\pi$
$929$			7.61265e8i			0.949486i	−0.880125	+	0.474743i	$0.842541\pi$
$930$	1.43766e8	−	5.81909e8i	0.178734	−	0.723446i
$931$	1.13582e9			1.40754
$932$		−	1.20559e9i		−	1.48920i
$933$	−2.13347e8	−	5.27094e7i	−0.262689	−	0.0648998i
$934$	1.22764e8			0.150671
$935$		−	2.53088e8i		−	0.309625i
$936$	2.65390e7	−	5.04314e7i	0.0323636	−	0.0614998i
$937$	6.92042e8			0.841228			0.420614	−	0.907240i	$-0.361815\pi$
$937$	6.92042e8			0.841228			0.420614	+	0.907240i	$0.361815\pi$
$938$		−	3.40762e8i		−	0.412898i
$939$	−3.05703e8	+	1.23737e9i	−0.369235	+	1.49452i
$940$	−7.36281e8			−0.886462
$941$		−	4.50844e8i		−	0.541075i	−0.962709	−	0.270538i	$-0.912799\pi$
$941$		−	4.50844e8i		−	0.541075i	0.962709	−	0.270538i	$-0.0872014\pi$
$942$	−3.86573e8	−	9.55066e7i	−0.462465	−	0.114256i
$943$	−5.64823e6			−0.00673561
$944$			1.06017e9i			1.26026i
$945$	1.34929e8	+	1.19933e8i	0.159885	+	0.142116i
$946$	−1.01297e8			−0.119652
$947$		−	5.75842e8i		−	0.678037i	−0.940780	−	0.339018i	$-0.889905\pi$
$947$		−	5.75842e8i		−	0.678037i	0.940780	−	0.339018i	$-0.110095\pi$
$948$	4.05379e7	−	1.64082e8i	0.0475813	−	0.192591i
$949$	2.27555e8			0.266249
$950$			7.66445e8i			0.893944i
$951$	−9.74637e8	−	2.40793e8i	−1.13319	−	0.279964i
$952$	−3.61592e7			−0.0419091
$953$		−	1.50058e9i		−	1.73372i	−0.498550	−	0.866861i	$-0.666134\pi$
$953$		−	1.50058e9i		−	1.73372i	0.498550	−	0.866861i	$-0.333866\pi$
$954$	−2.78497e8	−	1.46556e8i	−0.320756	−	0.168794i
$955$	1.08437e9			1.24500
$956$			4.91650e8i			0.562707i
$957$	1.97481e6	−	7.99328e6i	0.00225315	−	0.00911988i
$958$	−7.88167e8			−0.896441
$959$		−	3.75515e8i		−	0.425767i
$960$	−5.36744e8	−	1.32608e8i	−0.606671	−	0.149884i
$961$	−4.41653e8			−0.497635
$962$		−	1.15667e9i		−	1.29922i
$963$	5.41764e8	−	1.02950e9i	0.606641	−	1.15278i
$964$	−4.22100e8			−0.471177
$965$			1.01326e9i			1.12755i
$966$	1.75611e7	−	7.10804e7i	0.0194814	−	0.0788530i
$967$	5.92729e8			0.655506			0.327753	−	0.944763i	$-0.393709\pi$
$967$	5.92729e8			0.655506			0.327753	+	0.944763i	$0.393709\pi$
$968$		−	9.60143e7i		−	0.105855i
$969$	−1.70002e9	−	4.20007e8i	−1.86846	−	0.461620i
$970$	7.87798e8			0.863177
$971$		−	1.35421e9i		−	1.47921i	−0.673044	−	0.739603i	$-0.735013\pi$
$971$		−	1.35421e9i		−	1.47921i	0.673044	−	0.739603i	$-0.264987\pi$
$972$	7.86091e8	−	2.95664e8i	0.856001	−	0.321958i
$973$	−4.45747e7			−0.0483893
$974$			2.12981e9i			2.30496i
$975$	5.52198e7	−	2.23508e8i	0.0595774	−	0.241146i
$976$	2.17272e8			0.233697
$977$		−	4.82287e8i		−	0.517156i	−0.965990	−	0.258578i	$-0.916746\pi$
$977$		−	4.82287e8i		−	0.517156i	0.965990	−	0.258578i	$-0.0832540\pi$
$978$	−2.37789e9	−	5.87479e8i	−2.54199	−	0.628023i
$979$	3.10648e8			0.331071
$980$			6.02215e8i			0.639843i
$981$	−5.69224e8	−	2.99548e8i	−0.602942	−	0.317292i
$982$	−1.94250e9			−2.05129
$983$			8.47472e8i			0.892205i	0.894982	+	0.446103i	$0.147188\pi$
$983$			8.47472e8i			0.892205i	−0.894982	+	0.446103i	$0.852812\pi$
$984$	872827.	−	3.53287e6i	0.000916100	−	0.00370802i
$985$	−4.03025e8			−0.421719
$986$			4.84691e7i			0.0505632i
$987$	3.35218e8	+	8.28186e7i	0.348639	+	0.0861344i
$988$	−7.92481e8			−0.821709
$989$		−	5.38931e7i		−	0.0557115i
$990$	−1.53762e8	+	2.92189e8i	−0.158468	+	0.301133i
$991$	−2.21205e8			−0.227287			−0.113643	−	0.993522i	$-0.536252\pi$
$991$	−2.21205e8			−0.227287			−0.113643	+	0.993522i	$0.536252\pi$
$992$		−	9.50374e8i		−	0.973553i
$993$	−3.61871e8	+	1.46471e9i	−0.369578	+	1.49591i
$994$	3.55827e8			0.362309
$995$		−	1.05985e9i		−	1.07590i
$996$	5.94290e7	+	1.46825e7i	0.0601478	+	0.0148601i
$997$	−1.80142e9			−1.81773			−0.908865	−	0.417091i	$-0.863050\pi$
$997$	−1.80142e9			−1.81773			−0.908865	+	0.417091i	$0.863050\pi$
$998$			7.89800e6i			0.00794557i
$999$	−1.05817e9	+	1.19048e9i	−1.06135	+	1.19406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.8	✓	44
3.2	odd	2	inner	69.7.b.a.47.37	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.8	✓	44	1.1	even	1	trivial
69.7.b.a.47.37	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)

\(f(q)\)	\(=\)	\(q-11.0694i q^{2} +(-6.47589 + 26.2119i) q^{3} -58.5309 q^{4} +94.9815i q^{5} +(290.149 + 71.6840i) q^{6} +96.5626 q^{7} -60.5391i q^{8} +(-645.126 - 339.491i) q^{9} +O(q^{10})\)	\(q-11.0694i q^{2} +(-6.47589 + 26.2119i) q^{3} -58.5309 q^{4} +94.9815i q^{5} +(290.149 + 71.6840i) q^{6} +96.5626 q^{7} -60.5391i q^{8} +(-645.126 - 339.491i) q^{9} +1051.39 q^{10} -430.783i q^{11} +(379.040 - 1534.21i) q^{12} -1291.28 q^{13} -1068.89i q^{14} +(-2489.64 - 615.090i) q^{15} -4416.11 q^{16} -6185.48i q^{17} +(-3757.95 + 7141.13i) q^{18} -10485.4 q^{19} -5559.35i q^{20} +(-625.329 + 2531.09i) q^{21} -4768.49 q^{22} -2536.99i q^{23} +(1586.85 + 392.045i) q^{24} +6603.52 q^{25} +14293.7i q^{26} +(13076.4 - 14711.5i) q^{27} -5651.90 q^{28} -707.894i q^{29} +(-6808.65 + 27558.8i) q^{30} -21115.2 q^{31} +45009.0i q^{32} +(11291.6 + 2789.70i) q^{33} -68469.4 q^{34} +9171.66i q^{35} +(37759.8 + 19870.7i) q^{36} -80921.7 q^{37} +116066. i q^{38} +(8362.18 - 33846.9i) q^{39} +5750.10 q^{40} -2226.35i q^{41} +(28017.6 + 6922.00i) q^{42} +21242.9 q^{43} +25214.1i q^{44} +(32245.3 - 61275.0i) q^{45} -28082.9 q^{46} -132440. i q^{47} +(28598.2 - 115755. i) q^{48} -108325. q^{49} -73096.8i q^{50} +(162133. + 40056.5i) q^{51} +75579.8 q^{52} +38998.9i q^{53} +(-162847. - 144748. i) q^{54} +40916.4 q^{55} -5845.82i q^{56} +(67902.0 - 274841. i) q^{57} -7835.94 q^{58} -240069. i q^{59} +(145721. + 36001.8i) q^{60} -49199.8 q^{61} +233732. i q^{62} +(-62295.0 - 32782.1i) q^{63} +215591. q^{64} -122648. i q^{65} +(30880.2 - 124991. i) q^{66} +318800. q^{67} +362042. i q^{68} +(66499.4 + 16429.3i) q^{69} +101525. q^{70} +332895. i q^{71} +(-20552.5 + 39055.4i) q^{72} -176224. q^{73} +895753. i q^{74} +(-42763.6 + 173091. i) q^{75} +613717. q^{76} -41597.5i q^{77} +(-374664. - 92564.1i) q^{78} +106949. q^{79} -419449. i q^{80} +(300933. + 438028. i) q^{81} -24644.2 q^{82} +38736.0i q^{83} +(36601.1 - 148147. i) q^{84} +587507. q^{85} -235146. i q^{86} +(18555.2 + 4584.24i) q^{87} -26079.2 q^{88} +721125. i q^{89} +(-678276. - 356935. i) q^{90} -124689. q^{91} +148493. i q^{92} +(136740. - 553469. i) q^{93} -1.46603e6 q^{94} -995914. i q^{95} +(-1.17977e6 - 291474. i) q^{96} +749296. q^{97} +1.19909e6i q^{98} +(-146247. + 277909. 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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