LMFDB - Embedded newform 69.7.b.a.47.17

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			47.17
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.53332i q^{2} +(-0.406897 - 26.9969i) q^{3} +43.4490 q^{4} +169.748i q^{5} +(-122.386 + 1.84460i) q^{6} -134.238 q^{7} -487.101i q^{8} +(-728.669 + 21.9700i) q^{9} +O(q^{10})$	\(q-4.53332i q^{2} +(-0.406897 - 26.9969i) q^{3} +43.4490 q^{4} +169.748i q^{5} +(-122.386 + 1.84460i) q^{6} -134.238 q^{7} -487.101i q^{8} +(-728.669 + 21.9700i) q^{9} +769.522 q^{10} -2613.65i q^{11} +(-17.6793 - 1172.99i) q^{12} -3449.14 q^{13} +608.542i q^{14} +(4582.67 - 69.0700i) q^{15} +572.554 q^{16} -3824.51i q^{17} +(99.5969 + 3303.29i) q^{18} -6532.99 q^{19} +7375.38i q^{20} +(54.6209 + 3624.01i) q^{21} -11848.5 q^{22} +2536.99i q^{23} +(-13150.2 + 198.200i) q^{24} -13189.4 q^{25} +15636.1i q^{26} +(889.615 + 19662.9i) q^{27} -5832.49 q^{28} -29638.9i q^{29} +(-313.116 - 20774.7i) q^{30} +17438.5 q^{31} -33770.0i q^{32} +(-70560.6 + 1063.49i) q^{33} -17337.7 q^{34} -22786.6i q^{35} +(-31659.9 + 954.573i) q^{36} +25117.8 q^{37} +29616.2i q^{38} +(1403.45 + 93116.2i) q^{39} +82684.3 q^{40} +44919.6i q^{41} +(16428.8 - 247.614i) q^{42} +346.138 q^{43} -113561. i q^{44} +(-3729.36 - 123690. i) q^{45} +11501.0 q^{46} +163614. i q^{47} +(-232.971 - 15457.2i) q^{48} -99629.3 q^{49} +59791.6i q^{50} +(-103250. + 1556.18i) q^{51} -149862. q^{52} -190996. i q^{53} +(89138.1 - 4032.91i) q^{54} +443662. q^{55} +65387.3i q^{56} +(2658.26 + 176371. i) q^{57} -134363. q^{58} -17156.5i q^{59} +(199113. - 3001.02i) q^{60} +301351. q^{61} -79054.4i q^{62} +(97814.8 - 2949.20i) q^{63} -116447. q^{64} -585484. i q^{65} +(4821.13 + 319874. i) q^{66} +23407.9 q^{67} -166171. i q^{68} +(68491.1 - 1032.30i) q^{69} -103299. q^{70} -147413. i q^{71} +(10701.6 + 354935. i) q^{72} +546480. q^{73} -113867. i q^{74} +(5366.72 + 356073. i) q^{75} -283852. q^{76} +350850. i q^{77} +(422125. - 6362.27i) q^{78} -540217. q^{79} +97189.8i q^{80} +(530476. - 32017.7i) q^{81} +203635. q^{82} -11319.8i q^{83} +(2373.23 + 157459. i) q^{84} +649203. q^{85} -1569.15i q^{86} +(-800159. + 12060.0i) q^{87} -1.27311e6 q^{88} -530896. i q^{89} +(-560727. + 16906.4i) q^{90} +463004. q^{91} +110230. i q^{92} +(-7095.69 - 470787. i) q^{93} +741715. q^{94} -1.10896e6i q^{95} +(-911687. + 13740.9i) q^{96} -424344. q^{97} +451651. i q^{98} +(57421.8 + 1.90449e6i) 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 $

$2$		−	4.53332i		−	0.566665i	−0.959022	−	0.283332i	$-0.908560\pi$
$2$		−	4.53332i		−	0.566665i	0.959022	−	0.283332i	$-0.0914400\pi$
$3$	−0.406897	−	26.9969i	−0.0150703	−	0.999886i
$3$	−0.406897	−	26.9969i	−0.0150703	−	0.999886i
$4$	43.4490			0.678891
$5$			169.748i			1.35798i	0.734146	+	0.678992i	$0.237583\pi$
$5$			169.748i			1.35798i	−0.734146	+	0.678992i	$0.762417\pi$
$6$	−122.386	+	1.84460i	−0.566601	+	0.00853980i
$7$	−134.238			−0.391363			−0.195682	−	0.980667i	$-0.562692\pi$
$7$	−134.238			−0.391363			−0.195682	+	0.980667i	$0.562692\pi$
$8$		−	487.101i		−	0.951369i
$9$	−728.669	+	21.9700i	−0.999546	+	0.0301371i
$10$	769.522			0.769522
$11$		−	2613.65i		−	1.96368i	−0.189724	−	0.981838i	$-0.560759\pi$
$11$		−	2613.65i		−	1.96368i	0.189724	−	0.981838i	$-0.439241\pi$
$12$	−17.6793	−	1172.99i	−0.0102311	−	0.678814i
$13$	−3449.14			−1.56993			−0.784966	−	0.619539i	$-0.787319\pi$
$13$	−3449.14			−1.56993			−0.784966	+	0.619539i	$0.787319\pi$
$14$			608.542i			0.221772i
$15$	4582.67	−	69.0700i	1.35783	−	0.0204652i
$16$	572.554			0.139784
$17$		−	3824.51i		−	0.778447i	−0.921143	−	0.389224i	$-0.872743\pi$
$17$		−	3824.51i		−	0.778447i	0.921143	−	0.389224i	$-0.127257\pi$
$18$	99.5969	+	3303.29i	0.0170777	+	0.566408i
$19$	−6532.99			−0.952470			−0.476235	−	0.879318i	$-0.657999\pi$
$19$	−6532.99			−0.952470			−0.476235	+	0.879318i	$0.657999\pi$
$20$			7375.38i			0.921923i
$21$	54.6209	+	3624.01i	0.00589795	+	0.391319i
$22$	−11848.5			−1.11275
$23$			2536.99i			0.208514i
$23$			2536.99i			0.208514i
$24$	−13150.2	+	198.200i	−0.951261	+	0.0143374i
$25$	−13189.4			−0.844120
$26$			15636.1i			0.889625i
$27$	889.615	+	19662.9i	0.0451971	+	0.998978i
$28$	−5832.49			−0.265693
$29$		−	29638.9i		−	1.21526i	−0.794221	−	0.607628i	$-0.792121\pi$
$29$		−	29638.9i		−	1.21526i	0.794221	−	0.607628i	$-0.207879\pi$
$30$	−313.116	−	20774.7i	−0.0115969	−	0.769434i
$31$	17438.5			0.585362			0.292681	−	0.956210i	$-0.405453\pi$
$31$	17438.5			0.585362			0.292681	+	0.956210i	$0.405453\pi$
$32$		−	33770.0i		−	1.03058i
$33$	−70560.6	+	1063.49i	−1.96345	+	0.0295931i
$34$	−17337.7			−0.441119
$35$		−	22786.6i		−	0.531465i
$36$	−31659.9	+	954.573i	−0.678582	+	0.0204598i
$37$	25117.8			0.495879			0.247940	−	0.968776i	$-0.420247\pi$
$37$	25117.8			0.495879			0.247940	+	0.968776i	$0.420247\pi$
$38$			29616.2i			0.539732i
$39$	1403.45	+	93116.2i	0.0236593	+	1.56975i
$40$	82684.3			1.29194
$41$			44919.6i			0.651755i	0.945412	+	0.325878i	$0.105660\pi$
$41$			44919.6i			0.651755i	−0.945412	+	0.325878i	$0.894340\pi$
$42$	16428.8	−	247.614i	0.221747	−	0.00334216i
$43$	346.138			0.00435355			0.00217677	−	0.999998i	$-0.499307\pi$
$43$	346.138			0.00435355			0.00217677	+	0.999998i	$0.499307\pi$
$44$		−	113561.i		−	1.33312i
$45$	−3729.36	−	123690.i	−0.0409257	−	1.35737i
$46$	11501.0			0.118158
$47$			163614.i			1.57589i	0.615743	+	0.787947i	$0.288856\pi$
$47$			163614.i			1.57589i	−0.615743	+	0.787947i	$0.711144\pi$
$48$	−232.971	−	15457.2i	−0.00210658	−	0.139768i
$49$	−99629.3			−0.846835
$50$			59791.6i			0.478333i
$51$	−103250.	+	1556.18i	−0.778359	+	0.0117314i
$52$	−149862.			−1.06581
$53$		−	190996.i		−	1.28291i	−0.767160	−	0.641456i	$-0.778331\pi$
$53$		−	190996.i		−	1.28291i	0.767160	−	0.641456i	$-0.221669\pi$
$54$	89138.1	−	4032.91i	0.566086	−	0.0256116i
$55$	443662.			2.66664
$56$			65387.3i			0.372331i
$57$	2658.26	+	176371.i	0.0143540	+	0.952362i
$58$	−134363.			−0.688643
$59$		−	17156.5i		−	0.0835357i	−0.999127	−	0.0417678i	$-0.986701\pi$
$59$		−	17156.5i		−	0.0835357i	0.999127	−	0.0417678i	$-0.0132990\pi$
$60$	199113.	−	3001.02i	0.921818	−	0.0138936i
$61$	301351.			1.32765			0.663824	−	0.747889i	$-0.268932\pi$
$61$	301351.			1.32765			0.663824	+	0.747889i	$0.268932\pi$
$62$		−	79054.4i		−	0.331704i
$63$	97814.8	−	2949.20i	0.391186	−	0.0117946i
$64$	−116447.			−0.444209
$65$		−	585484.i		−	2.13194i
$66$	4821.13	+	319874.i	0.0167694	+	1.11262i
$67$	23407.9			0.0778284			0.0389142	−	0.999243i	$-0.487610\pi$
$67$	23407.9			0.0778284			0.0389142	+	0.999243i	$0.487610\pi$
$68$		−	166171.i		−	0.528481i
$69$	68491.1	−	1032.30i	0.208491	−	0.00314237i
$70$	−103299.			−0.301163
$71$		−	147413.i		−	0.411870i	−0.978566	−	0.205935i	$-0.933976\pi$
$71$		−	147413.i		−	0.411870i	0.978566	−	0.205935i	$-0.0660235\pi$
$72$	10701.6	+	354935.i	0.0286715	+	0.950936i
$73$	546480.			1.40477			0.702385	−	0.711797i	$-0.252118\pi$
$73$	546480.			1.40477			0.702385	+	0.711797i	$0.252118\pi$
$74$		−	113867.i		−	0.280997i
$75$	5366.72	+	356073.i	0.0127211	+	0.844024i
$76$	−283852.			−0.646623
$77$			350850.i			0.768511i
$78$	422125.	−	6362.27i	0.889524	−	0.0134069i
$79$	−540217.			−1.09569			−0.547844	−	0.836581i	$-0.684551\pi$
$79$	−540217.			−1.09569			−0.547844	+	0.836581i	$0.684551\pi$
$80$			97189.8i			0.189824i
$81$	530476.	−	32017.7i	0.998184	−	0.0602469i
$82$	203635.			0.369327
$83$		−	11319.8i		−	0.0197972i	−0.999951	−	0.00989858i	$-0.996849\pi$
$83$		−	11319.8i		−	0.0197972i	0.999951	−	0.00989858i	$-0.00315087\pi$
$84$	2373.23	+	157459.i	0.00400407	+	0.265663i
$85$	649203.			1.05712
$86$		−	1569.15i		−	0.00246700i
$87$	−800159.	+	12060.0i	−1.21512	+	0.0183143i
$88$	−1.27311e6			−1.86818
$89$		−	530896.i		−	0.753077i	−0.926401	−	0.376539i	$-0.877114\pi$
$89$		−	530896.i		−	0.753077i	0.926401	−	0.376539i	$-0.122886\pi$
$90$	−560727.	+	16906.4i	−0.769172	+	0.0231912i
$91$	463004.			0.614414
$92$			110230.i			0.141559i
$93$	−7095.69	−	470787.i	−0.00882156	−	0.585295i
$94$	741715.			0.893004
$95$		−	1.10896e6i		−	1.29344i
$96$	−911687.	+	13740.9i	−1.03046	+	0.0155311i
$97$	−424344.			−0.464946			−0.232473	−	0.972603i	$-0.574682\pi$
$97$	−424344.			−0.464946			−0.232473	+	0.972603i	$0.574682\pi$
$98$			451651.i			0.479872i
$99$	57421.8	+	1.90449e6i	0.0591795	+	1.96278i
$100$	−573065.			−0.573065
$101$		−	1.40686e6i		−	1.36548i	−0.730661	−	0.682740i	$-0.760788\pi$
$101$		−	1.40686e6i		−	1.36548i	0.730661	−	0.682740i	$-0.239212\pi$
$102$	7054.68	+	468066.i	0.00664778	+	0.441069i
$103$	−142007.			−0.129956			−0.0649781	−	0.997887i	$-0.520698\pi$
$103$	−142007.			−0.129956			−0.0649781	+	0.997887i	$0.520698\pi$
$104$			1.68008e6i			1.49358i
$105$	−615167.	+	9271.79i	−0.531405	+	0.00800932i
$106$	−865846.			−0.726981
$107$			433519.i			0.353881i	0.984222	+	0.176940i	$0.0566200\pi$
$107$			433519.i			0.353881i	−0.984222	+	0.176940i	$0.943380\pi$
$108$	38652.9	+	854333.i	0.0306839	+	0.678197i
$109$	−306091.			−0.236359			−0.118179	−	0.992992i	$-0.537706\pi$
$109$	−306091.			−0.236359			−0.118179	+	0.992992i	$0.537706\pi$
$110$		−	2.01126e6i		−	1.51109i
$111$	−10220.4	−	678103.i	−0.00747303	−	0.495823i
$112$	−76858.3			−0.0547062
$113$			568260.i			0.393832i	0.980420	+	0.196916i	$0.0630927\pi$
$113$			568260.i			0.393832i	−0.980420	+	0.196916i	$0.936907\pi$
$114$	799545.	−	12050.7i	0.539670	−	0.00813390i
$115$	−430650.			−0.283159
$116$		−	1.28778e6i		−	0.825027i
$117$	2.51328e6	−	75777.5i	1.56922	−	0.0473132i
$118$	−77775.8			−0.0473367
$119$			513394.i			0.304656i
$120$	−33644.0	−	2.23222e6i	−0.0194699	−	1.29180i
$121$	−5.05961e6			−2.85602
$122$		−	1.36612e6i		−	0.752332i
$123$	1.21269e6	−	18277.7i	0.651681	−	0.00982213i
$124$	757686.			0.397397
$125$			413444.i			0.211683i
$126$	−13369.6	−	443426.i	−0.00668357	−	0.221671i
$127$	3.48368e6			1.70070			0.850349	−	0.526219i	$-0.176391\pi$
$127$	3.48368e6			1.70070			0.850349	+	0.526219i	$0.176391\pi$
$128$		−	1.63339e6i		−	0.778861i
$129$	−140.842	−	9344.65i	−6.56092e−5	−	0.00435305i
$130$	−2.65419e6			−1.20810
$131$			844991.i			0.375871i	0.982181	+	0.187935i	$0.0601795\pi$
$131$			844991.i			0.375871i	−0.982181	+	0.187935i	$0.939820\pi$
$132$	−3.06579e6	+	46207.5i	−1.33297	+	0.0200905i
$133$	876974.			0.372762
$134$		−	106116.i		−	0.0441026i
$135$	−3.33773e6	+	151010.i	−1.35660	+	0.0613770i
$136$	−1.86292e6			−0.740590
$137$			2.49550e6i			0.970499i	0.874376	+	0.485250i	$0.161271\pi$
$137$			2.49550e6i			0.970499i	−0.874376	+	0.485250i	$0.838729\pi$
$138$	−4679.73	−	310492.i	−0.00178067	−	0.118144i
$139$	4.10229e6			1.52750			0.763752	−	0.645510i	$-0.223355\pi$
$139$	4.10229e6			1.52750			0.763752	+	0.645510i	$0.223355\pi$
$140$		−	990054.i		−	0.360807i
$141$	4.41708e6	−	66574.1i	1.57571	−	0.0237491i
$142$	−668269.			−0.233392
$143$			9.01485e6i			3.08283i
$144$	−417202.	+	12579.0i	−0.139720	+	0.00421268i
$145$	5.03114e6			1.65030
$146$		−	2.47737e6i		−	0.796034i
$147$	40538.9	+	2.68968e6i	0.0127620	+	0.846738i
$148$	1.09134e6			0.336648
$149$		−	5.78549e6i		−	1.74897i	−0.485056	−	0.874483i	$-0.661201\pi$
$149$		−	5.78549e6i		−	1.74897i	0.485056	−	0.874483i	$-0.338799\pi$
$150$	1.61419e6	−	24329.1i	0.478279	−	0.00720861i
$151$	2.16429e6			0.628615			0.314308	−	0.949321i	$-0.398228\pi$
$151$	2.16429e6			0.628615			0.314308	+	0.949321i	$0.398228\pi$
$152$			3.18223e6i			0.906150i
$153$	84024.4	+	2.78680e6i	0.0234602	+	0.778094i
$154$	1.59052e6			0.435488
$155$			2.96015e6i			0.794912i
$156$	60978.3	+	4.04581e6i	0.0160621	+	1.06569i
$157$	−6.88868e6			−1.78007			−0.890034	−	0.455894i	$-0.849320\pi$
$157$	−6.88868e6			−1.78007			−0.890034	+	0.455894i	$0.849320\pi$
$158$			2.44897e6i			0.620888i
$159$	−5.15631e6	+	77715.8i	−1.28277	+	0.0193338i
$160$	5.73239e6			1.39951
$161$		−	340560.i		−	0.0816049i
$162$	−145146.	−	2.40482e6i	−0.0341398	−	0.565636i
$163$	2.62152e6			0.605328			0.302664	−	0.953097i	$-0.402124\pi$
$163$	2.62152e6			0.605328			0.302664	+	0.953097i	$0.402124\pi$
$164$			1.95171e6i			0.442471i
$165$	−180525.	−	1.19775e7i	−0.0401870	−	2.66634i
$166$	−51316.1			−0.0112184
$167$		−	1.87915e6i		−	0.403471i	−0.979440	−	0.201736i	$-0.935342\pi$
$167$		−	1.87915e6i		−	0.403471i	0.979440	−	0.201736i	$-0.0646582\pi$
$168$	1.76526e6	−	26605.9i	0.372289	−	0.00561113i
$169$	7.06975e6			1.46468
$170$		−	2.94304e6i		−	0.599032i
$171$	4.76039e6	−	143530.i	0.952038	−	0.0287047i
$172$	15039.3			0.00295558
$173$		−	3.00075e6i		−	0.579551i	−0.957095	−	0.289775i	$-0.906419\pi$
$173$		−	3.00075e6i		−	0.579551i	0.957095	−	0.289775i	$-0.0935806\pi$
$174$	54671.8	+	3.62738e6i	0.0103780	+	0.688565i
$175$	1.77051e6			0.330358
$176$		−	1.49646e6i		−	0.274490i
$177$	−463172.	+	6980.92i	−0.0835262	+	0.00125891i
$178$	−2.40672e6			−0.426742
$179$		−	1.92332e6i		−	0.335345i	−0.985843	−	0.167672i	$-0.946375\pi$
$179$		−	1.92332e6i		−	0.335345i	0.985843	−	0.167672i	$-0.0536251\pi$
$180$	−162037.	−	5.37421e6i	−0.0277841	−	0.921504i
$181$	5.12632e6			0.864510			0.432255	−	0.901751i	$-0.357718\pi$
$181$	5.12632e6			0.864510			0.432255	+	0.901751i	$0.357718\pi$
$182$		−	2.09895e6i		−	0.348167i
$183$	−122619.	−	8.13555e6i	−0.0200080	−	1.32750i
$184$	1.23577e6			0.198374
$185$			4.26369e6i			0.673396i
$186$	−2.13423e6	+	32167.0i	−0.331666	+	0.00499887i
$187$	−9.99594e6			−1.52862
$188$			7.10887e6i			1.06986i
$189$	−119420.	−	2.63950e6i	−0.0176885	−	0.390963i
$190$	−5.02728e6			−0.732947
$191$		−	8.23738e6i		−	1.18220i	−0.806600	−	0.591098i	$-0.798695\pi$
$191$		−	8.23738e6i		−	1.18220i	0.806600	−	0.591098i	$-0.201305\pi$
$192$	47381.9	+	3.14371e6i	0.00669436	+	0.444159i
$193$	2.14568e6			0.298465			0.149232	−	0.988802i	$-0.452320\pi$
$193$	2.14568e6			0.298465			0.149232	+	0.988802i	$0.452320\pi$
$194$			1.92369e6i			0.263469i
$195$	−1.58063e7	+	238232.i	−2.13170	+	0.0321289i
$196$	−4.32879e6			−0.574908
$197$			4.11516e6i			0.538255i	0.963105	+	0.269127i	$0.0867352\pi$
$197$			4.11516e6i			0.538255i	−0.963105	+	0.269127i	$0.913265\pi$
$198$	8.63365e6	−	260311.i	1.11224	−	0.0335350i
$199$	3.87330e6			0.491498			0.245749	−	0.969334i	$-0.420966\pi$
$199$	3.87330e6			0.491498			0.245749	+	0.969334i	$0.420966\pi$
$200$			6.42455e6i			0.803069i
$201$	−9524.62	−	631942.i	−0.00117290	−	0.0778196i
$202$	−6.37773e6			−0.773770
$203$			3.97866e6i			0.475607i
$204$	−4.48611e6	+	67614.7i	−0.528421	+	0.00796435i
$205$	−7.62502e6			−0.885073
$206$			643762.i			0.0736417i
$207$	−55737.7	−	1.84863e6i	−0.00628402	−	0.208420i
$208$	−1.97482e6			−0.219451
$209$			1.70750e7i			1.87034i
$210$	42032.0	+	2.78875e6i	0.00453860	+	0.301128i
$211$	6.78113e6			0.721863			0.360931	−	0.932592i	$-0.382459\pi$
$211$	6.78113e6			0.721863			0.360931	+	0.932592i	$0.382459\pi$
$212$		−	8.29859e6i		−	0.870957i
$213$	−3.97969e6	+	59981.9i	−0.411823	+	0.00620699i
$214$	1.96528e6			0.200532
$215$			58756.1i			0.00591205i
$216$	9.57781e6	−	433332.i	0.950396	−	0.0429991i
$217$	−2.34091e6			−0.229089
$218$			1.38761e6i			0.133936i
$219$	−222361.	−	1.47533e7i	−0.0211703	−	1.40461i
$220$	1.92767e7			1.81036
$221$			1.31913e7i			1.22211i
$222$	−3.07406e6	+	46332.1i	−0.280965	+	0.00423471i
$223$	−2.10690e7			−1.89989			−0.949947	−	0.312411i	$-0.898864\pi$
$223$	−2.10690e7			−1.89989			−0.949947	+	0.312411i	$0.898864\pi$
$224$			4.53321e6i			0.403331i
$225$	9.61068e6	−	289770.i	0.843736	−	0.0254393i
$226$	2.57610e6			0.223171
$227$			6.90559e6i			0.590369i	0.955440	+	0.295184i	$0.0953811\pi$
$227$			6.90559e6i			0.590369i	−0.955440	+	0.295184i	$0.904619\pi$
$228$	115499.	+	7.66314e6i	0.00974479	+	0.646550i
$229$	−1.43017e7			−1.19091			−0.595457	−	0.803387i	$-0.703029\pi$
$229$	−1.43017e7			−1.19091			−0.595457	+	0.803387i	$0.703029\pi$
$230$			1.95227e6i			0.160456i
$231$	9.47189e6	−	142760.i	0.768423	−	0.0115817i
$232$	−1.44371e7			−1.15616
$233$		−	1.36973e7i		−	1.08285i	−0.840749	−	0.541425i	$-0.817885\pi$
$233$		−	1.36973e7i		−	1.08285i	0.840749	−	0.541425i	$-0.182115\pi$
$234$	−343523.	−	1.13935e7i	−0.0268107	−	0.889221i
$235$	−2.77731e7			−2.14004
$236$		−	745432.i		−	0.0567116i
$237$	219813.	+	1.45842e7i	0.0165123	+	1.09556i
$238$	2.32738e6			0.172638
$239$		−	5.06271e6i		−	0.370842i	−0.982659	−	0.185421i	$-0.940635\pi$
$239$		−	5.06271e6i		−	0.370842i	0.982659	−	0.185421i	$-0.0593649\pi$
$240$	2.62383e6	−	39546.3i	0.189802	−	0.00286070i
$241$	−2.58963e7			−1.85006			−0.925032	−	0.379889i	$-0.875962\pi$
$241$	−2.58963e7			−1.85006			−0.925032	+	0.379889i	$0.875962\pi$
$242$			2.29368e7i			1.61841i
$243$	−1.08023e6	−	1.43082e7i	−0.0752829	−	0.997162i
$244$	1.30934e7			0.901328
$245$		−	1.69119e7i		−	1.14999i
$246$	−82858.6	−	5.49752e6i	−0.00556586	−	0.369285i
$247$	2.25332e7			1.49531
$248$		−	8.49431e6i		−	0.556895i
$249$	−305599.	+	4605.98i	−0.0197949	+	0.000298349i
$250$	1.87427e6			0.119953
$251$		−	8.69995e6i		−	0.550168i	−0.961420	−	0.275084i	$-0.911294\pi$
$251$		−	8.69995e6i		−	0.550168i	0.961420	−	0.275084i	$-0.0887057\pi$
$252$	4.24996e6	−	128140.i	0.265572	−	0.00800722i
$253$	6.63082e6			0.409455
$254$		−	1.57926e7i		−	0.963726i
$255$	−264159.	−	1.75265e7i	−0.0159311	−	1.05700i
$256$	−1.48573e7			−0.885563
$257$			1.92474e7i			1.13389i	0.823754	+	0.566947i	$0.191876\pi$
$257$			1.92474e7i			1.13389i	−0.823754	+	0.566947i	$0.808124\pi$
$258$	−42362.3	+	638.484i	−0.00246672	+	3.71784e-5i
$259$	−3.37175e6			−0.194069
$260$		−	2.54387e7i		−	1.44736i
$261$	651165.	+	2.15969e7i	0.0366243	+	1.21470i
$262$	3.83062e6			0.212993
$263$			2.62596e7i			1.44351i	0.692146	+	0.721757i	$0.256665\pi$
$263$			2.62596e7i			1.44351i	−0.692146	+	0.721757i	$0.743335\pi$
$264$	518026.	+	3.43701e7i	0.0281540	+	1.86797i
$265$	3.24212e7			1.74217
$266$		−	3.97560e6i		−	0.211231i
$267$	−1.43326e7	+	216020.i	−0.752992	+	0.0113491i
$268$	1.01705e6			0.0528370
$269$		−	2.58401e7i		−	1.32751i	−0.747950	−	0.663755i	$-0.768962\pi$
$269$		−	2.58401e7i		−	1.32751i	0.747950	−	0.663755i	$-0.231038\pi$
$270$	684578.	+	1.51310e7i	0.0347802	+	0.768735i
$271$	2.59722e7			1.30497			0.652485	−	0.757802i	$-0.273727\pi$
$271$	2.59722e7			1.30497			0.652485	+	0.757802i	$0.273727\pi$
$272$		−	2.18974e6i		−	0.108814i
$273$	−188395.	−	1.24997e7i	−0.00925938	−	0.614344i
$274$	1.13129e7			0.549948
$275$			3.44724e7i			1.65758i
$276$	2.97587e6	−	44852.3i	0.141542	−	0.00213333i
$277$	2.33029e7			1.09640			0.548201	−	0.836346i	$-0.315313\pi$
$277$	2.33029e7			1.09640			0.548201	+	0.836346i	$0.315313\pi$
$278$		−	1.85970e7i		−	0.865583i
$279$	−1.27069e7	+	383124.i	−0.585096	+	0.0176411i
$280$	−1.10994e7			−0.505619
$281$		−	2.38846e7i		−	1.07646i	−0.842797	−	0.538232i	$-0.819093\pi$
$281$		−	2.38846e7i		−	1.07646i	0.842797	−	0.538232i	$-0.180907\pi$
$282$	−301802.	−	2.00240e7i	−0.0134578	−	0.892902i
$283$	−1.16364e6			−0.0513403			−0.0256701	−	0.999670i	$-0.508172\pi$
$283$	−1.16364e6			−0.0513403			−0.0256701	+	0.999670i	$0.508172\pi$
$284$		−	6.40494e6i		−	0.279615i
$285$	−2.99386e7	+	451234.i	−1.29329	+	0.0194925i
$286$	4.08672e7			1.74693
$287$		−	6.02991e6i		−	0.255073i
$288$	741926.	+	2.46072e7i	0.0310587	+	1.03011i
$289$	9.51068e6			0.394020
$290$		−	2.28078e7i		−	0.935167i
$291$	172664.	+	1.14560e7i	0.00700686	+	0.464893i
$292$	2.37440e7			0.953686
$293$		−	1.03655e6i		−	0.0412087i	−0.999788	−	0.0206043i	$-0.993441\pi$
$293$		−	1.03655e6i		−	0.0412087i	0.999788	−	0.0206043i	$-0.00655903\pi$
$294$	1.21932e7	−	183776.i	0.479817	−	0.00723179i
$295$	2.91228e6			0.113440
$296$		−	1.22349e7i		−	0.471764i
$297$	5.13919e7	−	2.32514e6i	1.96167	−	0.0887525i
$298$	−2.62275e7			−0.991078
$299$		−	8.75045e6i		−	0.327353i
$300$	233179.	+	1.54710e7i	0.00863625	+	0.573000i
$301$	−46464.7			−0.00170382
$302$		−	9.81143e6i		−	0.356214i
$303$	−3.79808e7	+	572446.i	−1.36533	+	0.0205782i
$304$	−3.74049e6			−0.133140
$305$			5.11537e7i			1.80292i
$306$	1.26335e7	−	380909.i	0.440918	−	0.0132941i
$307$	−2.16038e7			−0.746647			−0.373324	−	0.927701i	$-0.621782\pi$
$307$	−2.16038e7			−0.746647			−0.373324	+	0.927701i	$0.621782\pi$
$308$			1.52441e7i			0.521735i
$309$	57782.2	+	3.83375e6i	0.00195848	+	0.129942i
$310$	1.34193e7			0.450449
$311$		−	2.23224e7i		−	0.742095i	−0.928614	−	0.371048i	$-0.878999\pi$
$311$		−	2.23224e7i		−	0.742095i	0.928614	−	0.371048i	$-0.121001\pi$
$312$	4.53570e7	−	683619.i	1.49341	−	0.0225087i
$313$	−2.11620e6			−0.0690119			−0.0345059	−	0.999404i	$-0.510986\pi$
$313$	−2.11620e6			−0.0690119			−0.0345059	+	0.999404i	$0.510986\pi$
$314$			3.12286e7i			1.00870i
$315$	500620.	+	1.66039e7i	0.0160168	+	0.531224i
$316$	−2.34719e7			−0.743852
$317$			2.18386e7i			0.685562i	0.939415	+	0.342781i	$0.111369\pi$
$317$			2.18386e7i			0.685562i	−0.939415	+	0.342781i	$0.888631\pi$
$318$	352311.	+	2.33752e7i	0.0109558	+	0.726899i
$319$	−7.74657e7			−2.38637
$320$		−	1.97666e7i		−	0.603229i
$321$	1.17037e7	−	176398.i	0.353841	−	0.00533308i
$322$	−1.54387e6			−0.0462426
$323$			2.49855e7i			0.741448i
$324$	2.30486e7	−	1.39114e6i	0.677658	−	0.0409010i
$325$	4.54920e7			1.32521
$326$		−	1.18842e7i		−	0.343018i
$327$	124548.	+	8.26353e6i	0.00356199	+	0.236332i
$328$	2.18804e7			0.620060
$329$		−	2.19632e7i		−	0.616747i
$330$	−5.42979e7	+	818377.i	−1.51092	+	0.0227725i
$331$	−5.82897e7			−1.60734			−0.803670	−	0.595075i	$-0.797122\pi$
$331$	−5.82897e7			−1.60734			−0.803670	+	0.595075i	$0.797122\pi$
$332$		−	491833.i		−	0.0134401i
$333$	−1.83025e7	+	551836.i	−0.495654	+	0.0149444i
$334$	−8.51880e6			−0.228633
$335$			3.97344e6i			0.105690i
$336$	31273.4	+	2.07494e6i	0.000824437	+	0.0547000i
$337$	1.58693e7			0.414636			0.207318	−	0.978274i	$-0.433527\pi$
$337$	1.58693e7			0.414636			0.207318	+	0.978274i	$0.433527\pi$
$338$		−	3.20494e7i		−	0.829985i
$339$	1.53413e7	−	231223.i	0.393788	−	0.00593516i
$340$	2.82072e7			0.717668
$341$		−	4.55782e7i		−	1.14946i
$342$	−650666.	−	2.15804e7i	−0.0162660	−	0.539486i
$343$	2.91669e7			0.722784
$344$		−	168604.i		−	0.00414183i
$345$	175230.	+	1.16262e7i	0.00426729	+	0.283127i
$346$	−1.36034e7			−0.328411
$347$			1.73415e7i			0.415048i	0.978230	+	0.207524i	$0.0665406\pi$
$347$			1.73415e7i			0.415048i	−0.978230	+	0.207524i	$0.933459\pi$
$348$	−3.47661e7	+	523995.i	−0.824933	+	0.0124334i
$349$	3.76317e6			0.0885274			0.0442637	−	0.999020i	$-0.485906\pi$
$349$	3.76317e6			0.0885274			0.0442637	+	0.999020i	$0.485906\pi$
$350$		−	8.02629e6i		−	0.187202i
$351$	−3.06841e6	−	6.78200e7i	−0.0709564	−	1.56833i
$352$	−8.82630e7			−2.02372
$353$		−	4.89432e7i		−	1.11267i	−0.830957	−	0.556337i	$-0.812206\pi$
$353$		−	4.89432e7i		−	1.11267i	0.830957	−	0.556337i	$-0.187794\pi$
$354$	31646.8	+	2.09971e6i	0.000713378	+	0.0473314i
$355$	2.50230e7			0.559313
$356$		−	2.30669e7i		−	0.511257i
$357$	1.38601e7	−	208898.i	0.304621	−	0.00459125i
$358$	−8.71901e6			−0.190028
$359$		−	5.79027e7i		−	1.25146i	−0.780041	−	0.625728i	$-0.784802\pi$
$359$		−	5.79027e7i		−	1.25146i	0.780041	−	0.625728i	$-0.215198\pi$
$360$	−6.02495e7	+	1.81657e6i	−1.29136	+	0.0389354i
$361$	−4.36586e6			−0.0928000
$362$		−	2.32393e7i		−	0.489888i
$363$	2.05874e6	+	1.36594e8i	0.0430410	+	2.85570i
$364$	2.01171e7			0.417120
$365$			9.27638e7i			1.90766i
$366$	−3.68810e7	+	555871.i	−0.752246	+	0.0113378i
$367$	4.02106e7			0.813471			0.406736	−	0.913546i	$-0.366667\pi$
$367$	4.02106e7			0.813471			0.406736	+	0.913546i	$0.366667\pi$
$368$			1.45257e6i			0.0291469i
$369$	−986883.	−	3.27315e7i	−0.0196420	−	0.651459i
$370$	1.93287e7			0.381590
$371$			2.56389e7i			0.502085i
$372$	−308301.	−	2.04552e7i	−0.00598888	−	0.397352i
$373$	−7.28534e7			−1.40386			−0.701929	−	0.712247i	$-0.747678\pi$
$373$	−7.28534e7			−1.40386			−0.701929	+	0.712247i	$0.747678\pi$
$374$			4.53148e7i			0.866214i
$375$	1.11617e7	−	168229.i	0.211659	−	0.00319012i
$376$	7.96965e7			1.49926
$377$			1.02229e8i			1.90787i
$378$	−1.19657e7	+	541368.i	−0.221545	+	0.0100235i
$379$	−2.42618e7			−0.445662			−0.222831	−	0.974857i	$-0.571530\pi$
$379$	−2.42618e7			−0.445662			−0.222831	+	0.974857i	$0.571530\pi$
$380$		−	4.81833e7i		−	0.878104i
$381$	−1.41750e6	−	9.40487e7i	−0.0256300	−	1.70050i
$382$	−3.73427e7			−0.669909
$383$			2.36613e6i			0.0421155i	0.999778	+	0.0210577i	$0.00670338\pi$
$383$			2.36613e6i			0.0421155i	−0.999778	+	0.0210577i	$0.993297\pi$
$384$	−4.40965e7	+	664622.i	−0.778773	+	0.0117377i
$385$	−5.95561e7			−1.04362
$386$		−	9.72706e6i		−	0.169130i
$387$	−252220.	+	7604.63i	−0.00435157	+	0.000131203i
$388$	−1.84373e7			−0.315648
$389$		−	4.52137e7i		−	0.768105i	−0.923311	−	0.384053i	$-0.874528\pi$
$389$		−	4.52137e7i		−	0.768105i	0.923311	−	0.384053i	$-0.125472\pi$
$390$	1.07998e6	+	7.16549e7i	0.0182063	+	1.20796i
$391$	9.70277e6			0.162317
$392$			4.85295e7i			0.805652i
$393$	2.28122e7	−	343825.i	0.375828	−	0.00566447i
$394$	1.86553e7			0.305010
$395$		−	9.17006e7i		−	1.48793i
$396$	2.49492e6	+	8.27481e7i	0.0401764	+	1.33252i
$397$	5.99525e7			0.958156			0.479078	−	0.877772i	$-0.340971\pi$
$397$	5.99525e7			0.958156			0.479078	+	0.877772i	$0.340971\pi$
$398$		−	1.75589e7i		−	0.278514i
$399$	−356838.	−	2.36756e7i	−0.00561763	−	0.372720i
$400$	−7.55162e6			−0.117994
$401$			7.63325e6i			0.118379i	0.998247	+	0.0591897i	$0.0188517\pi$
$401$			7.63325e6i			0.118379i	−0.998247	+	0.0591897i	$0.981148\pi$
$402$	−2.86479e6	+	43178.1i	−0.0440976	+	0.000664639i
$403$	−6.01479e7			−0.918978
$404$		−	6.11265e7i		−	0.927012i
$405$	5.43493e6	+	9.00472e7i	0.0818143	+	1.35552i
$406$	1.80365e7			0.269510
$407$		−	6.56491e7i		−	0.973745i
$408$	758018.	+	5.02932e7i	0.0111609	+	0.740506i
$409$	−8.30683e6			−0.121413			−0.0607066	−	0.998156i	$-0.519335\pi$
$409$	−8.30683e6			−0.121413			−0.0607066	+	0.998156i	$0.519335\pi$
$410$			3.45666e7i			0.501540i
$411$	6.73707e7	−	1.01541e6i	0.970389	−	0.0146257i
$412$	−6.17005e6			−0.0882261
$413$			2.30304e6i			0.0326928i
$414$	−8.38043e6	+	252677.i	−0.118104	+	0.00356094i
$415$	1.92151e6			0.0268842
$416$			1.16477e8i			1.61794i
$417$	−1.66921e6	−	1.10749e8i	−0.0230199	−	1.52733i
$418$	7.74063e7			1.05986
$419$		−	430161.i		−	0.00584775i	−0.999996	−	0.00292388i	$-0.999069\pi$
$419$		−	430161.i		−	0.00584775i	0.999996	−	0.00292388i	$-0.000930700\pi$
$420$	−2.67284e7	+	402850.i	−0.360766	+	0.00543746i
$421$	7.34160e7			0.983885			0.491943	−	0.870628i	$-0.336287\pi$
$421$	7.34160e7			0.983885			0.491943	+	0.870628i	$0.336287\pi$
$422$		−	3.07410e7i		−	0.409054i
$423$	−3.59459e6	−	1.19220e8i	−0.0474929	−	1.57518i
$424$	−9.30343e7			−1.22052
$425$			5.04429e7i			0.657103i
$426$	271917.	+	1.80412e7i	0.00351729	+	0.233366i
$427$	−4.04526e7			−0.519593
$428$			1.88360e7i			0.240246i
$429$	2.43373e8	−	3.66812e6i	3.08248	−	0.0464592i
$430$	266360.			0.00335015
$431$		−	4.77108e7i		−	0.595915i	−0.954579	−	0.297958i	$-0.903695\pi$
$431$		−	4.77108e7i		−	0.595915i	0.954579	−	0.297958i	$-0.0963054\pi$
$432$	509352.	+	1.12581e7i	0.00631782	+	0.139641i
$433$	−1.04269e8			−1.28437			−0.642185	−	0.766550i	$-0.721972\pi$
$433$	−1.04269e8			−1.28437			−0.642185	+	0.766550i	$0.721972\pi$
$434$			1.06121e7i			0.129817i
$435$	−2.04716e6	−	1.35825e8i	−0.0248705	−	1.65011i
$436$	−1.32994e7			−0.160462
$437$		−	1.65742e7i		−	0.198604i
$438$	−6.68813e7	+	1.00803e6i	−0.795944	+	0.0119965i
$439$	−1.16395e7			−0.137575			−0.0687875	−	0.997631i	$-0.521913\pi$
$439$	−1.16395e7			−0.137575			−0.0687875	+	0.997631i	$0.521913\pi$
$440$		−	2.16108e8i		−	2.53696i
$441$	7.25967e7	−	2.18885e6i	0.846450	−	0.0255212i
$442$	5.98003e7			0.692526
$443$			1.63171e8i			1.87687i	0.345462	+	0.938433i	$0.387722\pi$
$443$			1.63171e8i			1.87687i	−0.345462	+	0.938433i	$0.612278\pi$
$444$	−444064.	−	2.94629e7i	−0.00507337	−	0.336610i
$445$	9.01185e7			1.02267
$446$			9.55125e7i			1.07660i
$447$	−1.56191e8	+	2.35410e6i	−1.74877	+	0.0263574i
$448$	1.56315e7			0.173847
$449$			1.36644e8i			1.50957i	0.655974	+	0.754784i	$0.272258\pi$
$449$			1.36644e8i			1.50957i	−0.655974	+	0.754784i	$0.727742\pi$
$450$	−1.31362e6	−	4.35683e7i	−0.0144156	−	0.478116i
$451$	1.17404e8			1.27984
$452$			2.46903e7i			0.267369i
$453$	−880645.	−	5.84293e7i	−0.00947341	−	0.628544i
$454$	3.13053e7			0.334541
$455$			7.85940e7i			0.834364i
$456$	8.59104e7	−	1.29484e6i	0.906048	−	0.0136559i
$457$	1.13481e8			1.18898			0.594489	−	0.804104i	$-0.297354\pi$
$457$	1.13481e8			1.18898			0.594489	+	0.804104i	$0.297354\pi$
$458$			6.48341e7i			0.674849i
$459$	7.52009e7	−	3.40234e6i	0.777652	−	0.0351836i
$460$	−1.87113e7			−0.192234
$461$			9.62347e7i			0.982266i	0.871085	+	0.491133i	$0.163417\pi$
$461$			9.62347e7i			0.982266i	−0.871085	+	0.491133i	$0.836583\pi$
$462$	−647177.	−	4.29391e7i	−0.00656292	−	0.435439i
$463$	2.85176e7			0.287323			0.143662	−	0.989627i	$-0.454112\pi$
$463$	2.85176e7			0.287323			0.143662	+	0.989627i	$0.454112\pi$
$464$		−	1.69699e7i		−	0.169873i
$465$	7.99150e7	−	1.20448e6i	0.794822	−	0.0119795i
$466$	−6.20944e7			−0.613613
$467$		−	9.20520e7i		−	0.903821i	−0.892063	−	0.451911i	$-0.850743\pi$
$467$		−	9.20520e7i		−	0.903821i	0.892063	−	0.451911i	$-0.149257\pi$
$468$	1.09200e8	−	3.29246e6i	1.06533	−	0.0321205i
$469$	−3.14222e6			−0.0304592
$470$			1.25905e8i			1.21268i
$471$	2.80298e6	+	1.85973e8i	0.0268261	+	1.77987i
$472$	−8.35693e6			−0.0794732
$473$		−	904683.i		−	0.00854895i
$474$	6.61148e7	−	996481.i	0.620817	−	0.00935694i
$475$	8.61661e7			0.803999
$476$			2.23064e7i			0.206828i
$477$	4.19618e6	+	1.39173e8i	0.0386633	+	1.28233i
$478$	−2.29509e7			−0.210143
$479$		−	9.65232e7i		−	0.878265i	−0.898422	−	0.439132i	$-0.855286\pi$
$479$		−	9.65232e7i		−	0.878265i	0.898422	−	0.439132i	$-0.144714\pi$
$480$	−2.33249e6	−	1.54757e8i	−0.0210910	−	1.39935i
$481$	−8.66347e7			−0.778496
$482$			1.17396e8i			1.04837i
$483$	−9.19408e6	+	138573.i	−0.0815957	+	0.00122981i
$484$	−2.19835e8			−1.93893
$485$		−	7.20315e7i		−	0.631389i
$486$	−6.48636e7	+	4.89702e6i	−0.565057	+	0.0426602i
$487$	−2.04861e7			−0.177367			−0.0886833	−	0.996060i	$-0.528266\pi$
$487$	−2.04861e7			−0.177367			−0.0886833	+	0.996060i	$0.528266\pi$
$488$		−	1.46788e8i		−	1.26308i
$489$	−1.06669e6	−	7.07731e7i	−0.00912246	−	0.605260i
$490$	−7.66669e7			−0.651658
$491$			1.99701e8i			1.68708i	0.537063	+	0.843542i	$0.319534\pi$
$491$			1.99701e8i			1.68708i	−0.537063	+	0.843542i	$0.680466\pi$
$492$	5.26903e7	−	794147.i	0.442420	−	0.00666815i
$493$	−1.13354e8			−0.946013
$494$		−	1.02150e8i		−	0.847342i
$495$	−3.23283e8	+	9.74724e6i	−2.66543	+	0.0803648i
$496$	9.98449e6			0.0818240
$497$			1.97884e7i			0.161191i
$498$	20880.4	+	1.38538e6i	0.000169064	+	0.0112171i
$499$	−6.46534e6			−0.0520343			−0.0260171	−	0.999661i	$-0.508282\pi$
$499$	−6.46534e6			−0.0520343			−0.0260171	+	0.999661i	$0.508282\pi$
$500$			1.79637e7i			0.143710i
$501$	−5.07313e7	+	764622.i	−0.403425	+	0.00608042i
$502$	−3.94396e7			−0.311761
$503$			3.27665e7i			0.257470i	0.991679	+	0.128735i	$0.0410916\pi$
$503$			3.27665e7i			0.257470i	−0.991679	+	0.128735i	$0.958908\pi$
$504$	−1.43656e6	−	4.76457e7i	−0.0112210	−	0.372162i
$505$	2.38811e8			1.85430
$506$		−	3.00596e7i		−	0.232024i
$507$	−2.87666e6	−	1.90862e8i	−0.0220732	−	1.46452i
$508$	1.51363e8			1.15459
$509$		−	5.02033e7i		−	0.380696i	−0.981717	−	0.190348i	$-0.939038\pi$
$509$		−	5.02033e7i		−	0.380696i	0.981717	−	0.190348i	$-0.0609617\pi$
$510$	−7.94532e7	+	1.19752e6i	−0.598964	+	0.00902758i
$511$	−7.33582e7			−0.549776
$512$		−	3.71842e7i		−	0.277044i
$513$	−5.81185e6	−	1.28458e8i	−0.0430489	−	0.951497i
$514$	8.72546e7			0.642539
$515$		−	2.41054e7i		−	0.176479i
$516$	−6119.47	−	406016.i	−4.45415e−5	−	0.00295525i
$517$	4.27630e8			3.09454
$518$			1.52852e7i			0.109972i
$519$	−8.10110e7	+	1.22100e6i	−0.579485	+	0.00873399i
$520$	−2.85190e8			−2.02826
$521$			1.80370e8i			1.27541i	0.770280	+	0.637706i	$0.220117\pi$
$521$			1.80370e8i			1.27541i	−0.770280	+	0.637706i	$0.779883\pi$
$522$	9.79058e7	−	2.95194e6i	0.688331	−	0.0207537i
$523$	−1.62459e8			−1.13564			−0.567818	−	0.823154i	$-0.692212\pi$
$523$	−1.62459e8			−1.13564			−0.567818	+	0.823154i	$0.692212\pi$
$524$			3.67140e7i			0.255175i
$525$	−720416.	−	4.77983e7i	−0.00497858	−	0.330320i
$526$	1.19043e8			0.817989
$527$		−	6.66938e7i		−	0.455673i
$528$	−4.03997e7	+	608904.i	−0.274458	+	0.00413663i
$529$	−6.43634e6			−0.0434783
$530$		−	1.46976e8i		−	0.987228i
$531$	376927.	+	1.25014e7i	0.00251752	+	0.0834977i
$532$	3.81037e7			0.253065
$533$		−	1.54934e8i		−	1.02321i
$534$	979289.	+	6.49741e7i	0.00643113	+	0.426694i
$535$	−7.35890e7			−0.480564
$536$		−	1.14020e7i		−	0.0740435i
$537$	−5.19237e7	+	782593.i	−0.335307	+	0.00505374i
$538$	−1.17142e8			−0.752253
$539$			2.60396e8i			1.66291i
$540$	−1.45021e8	+	6.56125e6i	−0.920981	+	0.0416683i
$541$	6.12842e7			0.387041			0.193520	−	0.981096i	$-0.438009\pi$
$541$	6.12842e7			0.387041			0.193520	+	0.981096i	$0.438009\pi$
$542$		−	1.17740e8i		−	0.739481i
$543$	−2.08589e6	−	1.38395e8i	−0.0130284	−	0.864412i
$544$	−1.29154e8			−0.802252
$545$		−	5.19584e7i		−	0.320971i
$546$	−5.66651e7	+	854056.i	−0.348127	+	0.00524697i
$547$	−1.06218e8			−0.648989			−0.324495	−	0.945888i	$-0.605194\pi$
$547$	−1.06218e8			−0.648989			−0.324495	+	0.945888i	$0.605194\pi$
$548$			1.08427e8i			0.658863i
$549$	−2.19585e8	+	6.62067e6i	−1.32704	+	0.0400115i
$550$	1.56274e8			0.939290
$551$			1.93631e8i			1.15750i
$552$	−502832.	−	3.33621e7i	−0.00298955	−	0.198352i
$553$	7.25174e7			0.428812
$554$		−	1.05639e8i		−	0.621293i
$555$	1.15107e8	−	1.73488e6i	0.673319	−	0.0101483i
$556$	1.78241e8			1.03701
$557$		−	2.33514e8i		−	1.35128i	−0.737230	−	0.675642i	$-0.763867\pi$
$557$		−	2.33514e8i		−	1.35128i	0.737230	−	0.675642i	$-0.236133\pi$
$558$	1.73682e6	+	5.76045e7i	0.00999661	+	0.331553i
$559$	−1.19388e6			−0.00683477
$560$		−	1.30465e7i		−	0.0742901i
$561$	4.06732e6	+	2.69860e8i	0.0230367	+	1.52844i
$562$	−1.08277e8			−0.609994
$563$			9.60018e7i			0.537965i	0.963145	+	0.268983i	$0.0866874\pi$
$563$			9.60018e7i			0.537965i	−0.963145	+	0.268983i	$0.913313\pi$
$564$	1.91918e8	−	2.89258e6i	1.06974	−	0.0161231i
$565$	−9.64609e7			−0.534818
$566$			5.27514e6i			0.0290927i
$567$	−7.12098e7	+	4.29798e6i	−0.390653	+	0.0235784i
$568$	−7.18049e7			−0.391840
$569$			1.54770e8i			0.840136i	0.907493	+	0.420068i	$0.137994\pi$
$569$			1.54770e8i			0.840136i	−0.907493	+	0.420068i	$0.862006\pi$
$570$	2.04559e6	+	1.35721e8i	0.0110457	+	0.732863i
$571$	−1.85555e8			−0.996700			−0.498350	−	0.866976i	$-0.666060\pi$
$571$	−1.85555e8			−0.996700			−0.498350	+	0.866976i	$0.666060\pi$
$572$			3.91686e8i			2.09291i
$573$	−2.22384e8	+	3.35177e6i	−1.18206	+	0.0178160i
$574$	−2.73355e7			−0.144541
$575$		−	3.34614e7i		−	0.176011i
$576$	8.48512e7	−	2.55833e6i	0.444008	−	0.0133872i
$577$	1.55843e6			0.00811257			0.00405629	−	0.999992i	$-0.498709\pi$
$577$	1.55843e6			0.00811257			0.00405629	+	0.999992i	$0.498709\pi$
$578$		−	4.31149e7i		−	0.223277i
$579$	−873072.	−	5.79268e7i	−0.00449795	−	0.298431i
$580$	2.18598e8			1.12037
$581$			1.51954e6i			0.00774789i
$582$	5.19336e7	−	782743.i	0.263439	−	0.00397054i
$583$	−4.99197e8			−2.51922
$584$		−	2.66191e8i		−	1.33645i
$585$	1.28631e7	+	4.26624e8i	0.0642506	+	2.13097i
$586$	−4.69903e6			−0.0233515
$587$			6.08182e7i			0.300690i	0.988634	+	0.150345i	$0.0480384\pi$
$587$			6.08182e7i			0.300690i	−0.988634	+	0.150345i	$0.951962\pi$
$588$	1.76137e6	+	1.16864e8i	0.00866402	+	0.574843i
$589$	−1.13926e8			−0.557540
$590$		−	1.32023e7i		−	0.0642825i
$591$	1.11097e8	−	1.67445e6i	0.538193	−	0.00811164i
$592$	1.43813e7			0.0693158
$593$			8.57497e7i			0.411214i	0.978635	+	0.205607i	$0.0659169\pi$
$593$			8.57497e7i			0.411214i	−0.978635	+	0.205607i	$0.934083\pi$
$594$	−1.05406e7	−	2.32976e8i	−0.0502929	−	1.11161i
$595$	−8.71475e7			−0.413718
$596$		−	2.51374e8i		−	1.18736i
$597$	−1.57603e6	−	1.04567e8i	−0.00740700	−	0.491442i
$598$	−3.96686e7			−0.185500
$599$			2.05419e8i			0.955783i	0.878419	+	0.477891i	$0.158599\pi$
$599$			2.05419e8i			0.955783i	−0.878419	+	0.477891i	$0.841401\pi$
$600$	1.73443e8	−	2.61413e6i	0.802978	−	0.0121025i
$601$	1.49556e8			0.688938			0.344469	−	0.938798i	$-0.388059\pi$
$601$	1.49556e8			0.688938			0.344469	+	0.938798i	$0.388059\pi$
$602$			210639.i			0.000965495i
$603$	−1.70566e7	+	514271.i	−0.0777931	+	0.00234552i
$604$	9.40364e7			0.426761
$605$		−	8.58859e8i		−	3.87843i
$606$	2.59508e6	+	1.72179e8i	0.0116609	+	0.773682i
$607$	−7.54118e7			−0.337189			−0.168594	−	0.985686i	$-0.553923\pi$
$607$	−7.54118e7			−0.337189			−0.168594	+	0.985686i	$0.553923\pi$
$608$			2.20619e8i			0.981596i
$609$	1.07412e8	−	1.61890e6i	0.475553	−	0.00716753i
$610$	2.31896e8			1.02165
$611$		−	5.64328e8i		−	2.47405i
$612$	3.65078e6	+	1.21084e8i	0.0159269	+	0.528241i
$613$	1.11658e8			0.484739			0.242369	−	0.970184i	$-0.422075\pi$
$613$	1.11658e8			0.484739			0.242369	+	0.970184i	$0.422075\pi$
$614$			9.79370e7i			0.423099i
$615$	3.10260e6	+	2.05852e8i	0.0133383	+	0.884973i
$616$	1.70900e8			0.731137
$617$		−	2.95889e8i		−	1.25972i	−0.776710	−	0.629858i	$-0.783113\pi$
$617$		−	2.95889e8i		−	1.25972i	0.776710	−	0.629858i	$-0.216887\pi$
$618$	1.73796e7	−	261945.i	0.0736333	−	0.00110980i
$619$	3.60810e8			1.52127			0.760636	−	0.649179i	$-0.224887\pi$
$619$	3.60810e8			1.52127			0.760636	+	0.649179i	$0.224887\pi$
$620$			1.28616e8i			0.539658i
$621$	−4.98846e7	+	2.25695e6i	−0.208301	+	0.00942425i
$622$	−1.01195e8			−0.420519
$623$			7.12663e7i			0.294727i
$624$	803548.	+	5.33140e7i	0.00330718	+	0.219426i
$625$	−2.76265e8			−1.13158
$626$			9.59342e6i			0.0391066i
$627$	4.60972e8	−	6.94776e6i	1.87013	−	0.0281866i
$628$	−2.99306e8			−1.20847
$629$		−	9.60632e7i		−	0.386016i
$630$	7.52706e7	−	2.26947e6i	0.301026	−	0.00907618i
$631$	3.89749e8			1.55130			0.775652	−	0.631161i	$-0.217421\pi$
$631$	3.89749e8			1.55130			0.775652	+	0.631161i	$0.217421\pi$
$632$			2.63140e8i			1.04240i
$633$	−2.75922e6	−	1.83070e8i	−0.0108787	−	0.721781i
$634$	9.90013e7			0.388484
$635$			5.91348e8i			2.30952i
$636$	−2.24036e8	+	3.37667e6i	−0.870858	+	0.0131256i
$637$	3.43635e8			1.32947
$638$			3.51177e8i			1.35227i
$639$	3.23865e6	+	1.07415e8i	0.0124126	+	0.411683i
$640$	2.77265e8			1.05768
$641$		−	3.87378e7i		−	0.147083i	−0.997292	−	0.0735413i	$-0.976570\pi$
$641$		−	3.87378e7i		−	0.147083i	0.997292	−	0.0735413i	$-0.0234301\pi$
$642$	−799668.	−	5.30566e7i	−0.00302207	−	0.200509i
$643$	−3.51846e8			−1.32349			−0.661743	−	0.749731i	$-0.730183\pi$
$643$	−3.51846e8			−1.32349			−0.661743	+	0.749731i	$0.730183\pi$
$644$		−	1.47970e7i		−	0.0554008i
$645$	1.58624e6	−	23907.7i	0.00591138	−	8.90962e-5i
$646$	1.13267e8			0.420153
$647$		−	2.30514e8i		−	0.851108i	−0.904933	−	0.425554i	$-0.860079\pi$
$647$		−	2.30514e8i		−	0.851108i	0.904933	−	0.425554i	$-0.139921\pi$
$648$	−1.55958e7	−	2.58395e8i	−0.0573170	−	0.949640i
$649$	−4.48410e7			−0.164037
$650$		−	2.06230e8i		−	0.750950i
$651$	952508.	+	6.31973e7i	0.00345244	+	0.229063i
$652$	1.13903e8			0.410952
$653$			2.13933e7i			0.0768312i	0.999262	+	0.0384156i	$0.0122311\pi$
$653$			2.13933e7i			0.0768312i	−0.999262	+	0.0384156i	$0.987769\pi$
$654$	3.74612e7	−	564615.i	0.133921	−	0.00201845i
$655$	−1.43436e8			−0.510426
$656$			2.57189e7i			0.0911047i
$657$	−3.98203e8	+	1.20061e7i	−1.40413	+	0.0423357i
$658$	−9.95660e7			−0.349489
$659$		−	2.82771e8i		−	0.988049i	−0.869448	−	0.494024i	$-0.835525\pi$
$659$		−	2.82771e8i		−	0.988049i	0.869448	−	0.494024i	$-0.164475\pi$
$660$	−7.84363e6	−	5.20411e8i	−0.0272826	−	1.81015i
$661$	1.95209e8			0.675920			0.337960	−	0.941160i	$-0.390263\pi$
$661$	1.95209e8			0.675920			0.337960	+	0.941160i	$0.390263\pi$
$662$			2.64246e8i			0.910823i
$663$	3.56124e8	−	5.36749e6i	1.22197	−	0.0184175i
$664$	−5.51386e6			−0.0188344
$665$			1.48865e8i			0.506205i
$666$	2.50165e6	+	8.29712e7i	0.00846845	+	0.280870i
$667$	7.51937e7			0.253399
$668$		−	8.16473e7i		−	0.273913i
$669$	8.57292e6	+	5.68799e8i	0.0286319	+	1.89968i
$670$	1.80129e7			0.0598907
$671$		−	7.87626e8i		−	2.60707i
$672$	1.22383e8	−	1.84455e6i	0.403285	−	0.00607831i
$673$	−1.44132e8			−0.472840			−0.236420	−	0.971651i	$-0.575974\pi$
$673$	−1.44132e8			−0.472840			−0.236420	+	0.971651i	$0.575974\pi$
$674$		−	7.19404e7i		−	0.234960i
$675$	−1.17335e7	−	2.59341e8i	−0.0381518	−	0.843257i
$676$	3.07174e8			0.994361
$677$		−	4.66018e8i		−	1.50189i	−0.660367	−	0.750943i	$-0.729599\pi$
$677$		−	4.66018e8i		−	1.50189i	0.660367	−	0.750943i	$-0.270401\pi$
$678$	−1.04821e6	−	6.95469e7i	−0.00336325	−	0.223146i
$679$	5.69629e7			0.181963
$680$		−	3.16227e8i		−	1.00571i
$681$	1.86430e8	−	2.80987e6i	0.590302	−	0.00889702i
$682$	−2.06621e8			−0.651359
$683$		−	3.20070e8i		−	1.00458i	−0.864700	−	0.502288i	$-0.832492\pi$
$683$		−	3.20070e8i		−	1.00458i	0.864700	−	0.502288i	$-0.167508\pi$
$684$	2.06834e8	−	6.23622e6i	0.646330	−	0.0194874i
$685$	−4.23605e8			−1.31792
$686$		−	1.32223e8i		−	0.409576i
$687$	5.81932e6	+	3.86101e8i	0.0179474	+	1.19078i
$688$	198182.			0.000608555
$689$			6.58772e8i			2.01408i
$690$	5.27054e7	−	794375.i	0.160438	−	0.00241812i
$691$	4.11499e8			1.24720			0.623598	−	0.781745i	$-0.285670\pi$
$691$	4.11499e8			1.24720			0.623598	+	0.781745i	$0.285670\pi$
$692$		−	1.30380e8i		−	0.393452i
$693$	−7.70817e6	−	2.55654e8i	−0.0231607	−	0.768162i
$694$	7.86147e7			0.235193
$695$			6.96356e8i			2.07432i
$696$	5.87443e6	+	3.89758e8i	0.0174236	+	1.15603i
$697$	1.71796e8			0.507357
$698$		−	1.70597e7i		−	0.0501654i
$699$	−3.69786e8	+	5.57341e6i	−1.08273	+	0.0163188i
$700$	7.69269e7			0.224277
$701$		−	3.16021e8i		−	0.917408i	−0.888589	−	0.458704i	$-0.848314\pi$
$701$		−	3.16021e8i		−	0.917408i	0.888589	−	0.458704i	$-0.151686\pi$
$702$	−3.07450e8	+	1.39101e7i	−0.888716	+	0.0402085i
$703$	−1.64094e8			−0.472310
$704$			3.04351e8i			0.872283i
$705$	1.13008e7	+	7.49790e8i	0.0322510	+	2.13979i
$706$	−2.21875e8			−0.630513
$707$			1.88853e8i			0.534399i
$708$	−2.01244e7	+	303314.i	−0.0567052	+	0.000854659i
$709$	1.02656e8			0.288034			0.144017	−	0.989575i	$-0.453998\pi$
$709$	1.02656e8			0.288034			0.144017	+	0.989575i	$0.453998\pi$
$710$		−	1.13437e8i		−	0.316943i
$711$	3.93639e8	−	1.18685e7i	1.09519	−	0.0330209i
$712$	−2.58600e8			−0.716454
$713$			4.42414e7i			0.122056i
$714$	−947004.	−	6.28320e7i	−0.00260170	−	0.172618i
$715$	−1.53025e9			−4.18644
$716$		−	8.35662e7i		−	0.227663i
$717$	−1.36678e8	+	2.06000e6i	−0.370800	+	0.00558870i
$718$	−2.62491e8			−0.709156
$719$			1.53471e8i			0.412894i	0.978458	+	0.206447i	$0.0661902\pi$
$719$			1.53471e8i			0.412894i	−0.978458	+	0.206447i	$0.933810\pi$
$720$	−2.13526e6	−	7.08192e7i	−0.00572075	−	0.189738i
$721$	1.90627e7			0.0508601
$722$			1.97918e7i			0.0525865i
$723$	1.05371e7	+	6.99121e8i	0.0278810	+	1.84985i
$724$	2.22734e8			0.586908
$725$			3.90918e8i			1.02582i
$726$	6.19224e8	−	9.33294e6i	1.61822	−	0.0243898i
$727$	4.14620e8			1.07906			0.539531	−	0.841966i	$-0.318602\pi$
$727$	4.14620e8			1.07906			0.539531	+	0.841966i	$0.318602\pi$
$728$		−	2.25530e8i		−	0.584534i
$729$	−3.85838e8	+	3.49848e7i	−0.995914	+	0.0903019i
$730$	4.20528e8			1.08100
$731$		−	1.32381e6i		−	0.00338901i
$732$	−5.32767e6	−	3.53482e8i	−0.0135833	−	0.901226i
$733$	2.31612e8			0.588098			0.294049	−	0.955790i	$-0.404997\pi$
$733$	2.31612e8			0.588098			0.294049	+	0.955790i	$0.404997\pi$
$734$		−	1.82287e8i		−	0.460966i
$735$	−4.56568e8	+	6.88139e6i	−1.14986	+	0.0173306i
$736$	8.56744e7			0.214891
$737$		−	6.11801e7i		−	0.152830i
$738$	−1.48383e8	+	4.47385e6i	−0.369159	+	0.0111305i
$739$	−2.21737e8			−0.549421			−0.274711	−	0.961527i	$-0.588582\pi$
$739$	−2.21737e8			−0.549421			−0.274711	+	0.961527i	$0.588582\pi$
$740$			1.85253e8i			0.457162i
$741$	−9.16870e6	−	6.08328e8i	−0.0225348	−	1.49514i
$742$	1.16229e8			0.284514
$743$			2.05127e8i			0.500100i	0.968233	+	0.250050i	$0.0804470\pi$
$743$			2.05127e8i			0.500100i	−0.968233	+	0.250050i	$0.919553\pi$
$744$	−2.29320e8	+	3.45631e6i	−0.556832	+	0.00839256i
$745$	9.82075e8			2.37507
$746$			3.30268e8i			0.795517i
$747$	248695.	+	8.24836e6i	0.000596630	+	0.0197882i
$748$	−4.34314e8			−1.03776
$749$		−	5.81946e7i		−	0.138496i
$750$	−762636.	−	5.05996e7i	−0.00180773	−	0.119940i
$751$	−1.97141e8			−0.465432			−0.232716	−	0.972545i	$-0.574761\pi$
$751$	−1.97141e8			−0.465432			−0.232716	+	0.972545i	$0.574761\pi$
$752$			9.36778e7i			0.220284i
$753$	−2.34872e8	+	3.53999e6i	−0.550106	+	0.00829118i
$754$	4.63435e8			1.08112
$755$			3.67384e8i			0.853650i
$756$	−5.18867e6	−	1.14684e8i	−0.0120086	−	0.265422i
$757$	−4.96512e8			−1.14457			−0.572285	−	0.820055i	$-0.693943\pi$
$757$	−4.96512e8			−1.14457			−0.572285	+	0.820055i	$0.693943\pi$
$758$			1.09987e8i			0.252541i
$759$	−2.69806e6	−	1.79012e8i	−0.00617059	−	0.409408i
$760$	−5.40176e8			−1.23054
$761$		−	2.10266e8i		−	0.477107i	−0.971129	−	0.238553i	$-0.923327\pi$
$761$		−	2.10266e8i		−	0.477107i	0.971129	−	0.238553i	$-0.0766732\pi$
$762$	−4.26353e8	+	6.42598e6i	−0.963616	+	0.0145236i
$763$	4.10890e7			0.0925021
$764$		−	3.57906e8i		−	0.802582i
$765$	−4.73054e8	+	1.42630e7i	−1.05664	+	0.0318585i
$766$	1.07264e7			0.0238654
$767$			5.91751e7i			0.131145i
$768$	6.04539e6	+	4.01101e8i	0.0133457	+	0.885462i
$769$	1.21018e7			0.0266117			0.0133058	−	0.999911i	$-0.495764\pi$
$769$	1.21018e7			0.0266117			0.0133058	+	0.999911i	$0.495764\pi$
$770$			2.69987e8i			0.591386i
$771$	5.19621e8	−	7.83172e6i	1.13377	−	0.0170881i
$772$	9.32277e7			0.202625
$773$		−	6.90900e8i		−	1.49581i	−0.663806	−	0.747905i	$-0.731060\pi$
$773$		−	6.90900e8i		−	1.49581i	0.663806	−	0.747905i	$-0.268940\pi$
$774$	34474.2	+	1.14339e6i	7.43484e−5	+	0.00246588i
$775$	−2.30003e8			−0.494115
$776$			2.06698e8i			0.442335i
$777$	1.37196e6	+	9.10269e7i	0.00292467	+	0.194047i
$778$	−2.04968e8			−0.435258
$779$		−	2.93460e8i		−	0.620778i
$780$	−6.86767e8	+	1.03509e7i	−1.44719	+	0.0218120i
$781$	−3.85286e8			−0.808779
$782$		−	4.39857e7i		−	0.0919796i
$783$	5.82786e8	−	2.63672e7i	1.21401	−	0.0549261i
$784$	−5.70431e7			−0.118374
$785$		−	1.16934e9i		−	2.41730i
$786$	−1.55867e6	−	1.03415e8i	−0.00320986	−	0.212968i
$787$	1.19101e8			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$787$	1.19101e8			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$788$			1.78799e8i			0.365416i
$789$	7.08929e8	−	1.06850e7i	1.44335	−	0.0217542i
$790$	−4.15708e8			−0.843155
$791$		−	7.62819e7i		−	0.154132i
$792$	9.27677e8	−	2.79702e7i	1.86733	−	0.0563015i
$793$	−1.03940e9			−2.08432
$794$		−	2.71784e8i		−	0.542953i
$795$	−1.31921e7	−	8.75273e8i	−0.0262550	−	1.74198i
$796$	1.68291e8			0.333673
$797$			6.91478e8i			1.36585i	0.730488	+	0.682926i	$0.239293\pi$
$797$			6.91478e8i			1.36585i	−0.730488	+	0.682926i	$0.760707\pi$
$798$	−1.07329e8	+	1.61766e6i	−0.211207	+	0.00318331i
$799$	6.25744e8			1.22675
$800$			4.45405e8i			0.869932i
$801$	1.16638e7	+	3.86847e8i	0.0226956	+	0.752735i
$802$	3.46040e7			0.0670815
$803$		−	1.42831e9i		−	2.75851i
$804$	−413835.	−	2.74572e7i	−0.000796268	−	0.0528310i
$805$	5.78094e7			0.110818
$806$			2.72670e8i			0.520753i
$807$	−6.97604e8	+	1.05143e7i	−1.32736	+	0.0200059i
$808$	−6.85280e8			−1.29908
$809$		−	7.26455e8i		−	1.37203i	−0.727588	−	0.686014i	$-0.759359\pi$
$809$		−	7.26455e8i		−	1.37203i	0.727588	−	0.686014i	$-0.240641\pi$
$810$	4.08213e8	−	2.46383e7i	0.768124	−	0.0463613i
$811$	4.54245e8			0.851585			0.425792	−	0.904821i	$-0.359995\pi$
$811$	4.54245e8			0.851585			0.425792	+	0.904821i	$0.359995\pi$
$812$			1.72869e8i			0.322885i
$813$	−1.05680e7	−	7.01169e8i	−0.0196663	−	1.30482i
$814$	−2.97608e8			−0.551787
$815$			4.44998e8i			0.822026i
$816$	−5.91162e7	+	890999.i	−0.108802	+	0.00163986i
$817$	−2.26131e6			−0.00414663
$818$			3.76575e7i			0.0688006i
$819$	−3.37377e8	+	1.01722e7i	−0.614135	+	0.0185167i
$820$	−3.31299e8			−0.600868
$821$			5.55621e8i			1.00404i	0.864857	+	0.502018i	$0.167409\pi$
$821$			5.55621e8i			1.00404i	−0.864857	+	0.502018i	$0.832591\pi$
$822$	−4.60318e6	−	3.05413e8i	−0.00828786	−	0.549885i
$823$	−1.65277e7			−0.0296492			−0.0148246	−	0.999890i	$-0.504719\pi$
$823$	−1.65277e7			−0.0296492			−0.0148246	+	0.999890i	$0.504719\pi$
$824$			6.91716e7i			0.123636i
$825$	9.30649e8	−	1.40267e7i	1.65739	−	0.0249801i
$826$	1.04404e7			0.0185259
$827$			2.69586e8i			0.476630i	0.971188	+	0.238315i	$0.0765950\pi$
$827$			2.69586e8i			0.476630i	−0.971188	+	0.238315i	$0.923405\pi$
$828$	−2.42175e6	−	8.03211e7i	−0.00426617	−	0.141494i
$829$	5.44163e8			0.955136			0.477568	−	0.878595i	$-0.341518\pi$
$829$	5.44163e8			0.955136			0.477568	+	0.878595i	$0.341518\pi$
$830$		−	8.71080e6i		−	0.0152344i
$831$	−9.48187e6	−	6.29106e8i	−0.0165231	−	1.09628i
$832$	4.01641e8			0.697378
$833$			3.81033e8i			0.659216i
$834$	−5.02062e8	+	7.56707e6i	−0.865484	+	0.0130446i
$835$	3.18982e8			0.547907
$836$			7.41891e8i			1.26976i
$837$	1.55136e7	+	3.42892e8i	0.0264567	+	0.584764i
$838$	−1.95006e6			−0.00331372
$839$			6.52958e8i			1.10560i	0.833313	+	0.552802i	$0.186441\pi$
$839$			6.52958e8i			1.10560i	−0.833313	+	0.552802i	$0.813559\pi$
$840$	4.51630e6	+	2.99649e8i	0.00761982	+	0.505562i
$841$	−2.83641e8			−0.476849
$842$		−	3.32818e8i		−	0.557533i
$843$	−6.44811e8	+	9.71859e6i	−1.07634	+	0.0162226i
$844$	2.94633e8			0.490066
$845$			1.20008e9i			1.98902i
$846$	−5.40464e8	+	1.62954e7i	−0.892598	+	0.0269126i
$847$	6.79191e8			1.11774
$848$		−	1.09356e8i		−	0.179330i
$849$	473481.	+	3.14146e7i	0.000773712	+	0.0513344i
$850$	2.28674e8			0.372357
$851$			6.37236e7i			0.103398i
$852$	−1.72914e8	+	2.60615e6i	−0.279583	+	0.00421387i
$853$	9.08209e8			1.46332			0.731659	−	0.681670i	$-0.238746\pi$
$853$	9.08209e8			1.46332			0.731659	+	0.681670i	$0.238746\pi$
$854$			1.83385e8i			0.294435i
$855$	2.43639e7	+	8.08066e8i	0.0389805	+	1.29285i
$856$	2.11168e8			0.336671
$857$			2.10284e8i			0.334091i	0.985949	+	0.167045i	$0.0534227\pi$
$857$			2.10284e8i			0.334091i	−0.985949	+	0.167045i	$0.946577\pi$
$858$	−1.66287e7	−	1.10329e9i	−0.0263268	−	1.74674i
$859$	9.64448e8			1.52160			0.760798	−	0.648989i	$-0.224808\pi$
$859$	9.64448e8			1.52160			0.760798	+	0.648989i	$0.224808\pi$
$860$			2.55290e6i			0.00401363i
$861$	−1.62789e8	+	2.45355e6i	−0.255044	+	0.00384402i
$862$	−2.16288e8			−0.337684
$863$			3.46769e8i			0.539521i	0.962927	+	0.269761i	$0.0869446\pi$
$863$			3.46769e8i			0.539521i	−0.962927	+	0.269761i	$0.913055\pi$
$864$	6.64016e8	−	3.00423e7i	1.02953	−	0.0465792i
$865$	5.09371e8			0.787020
$866$			4.72683e8i			0.727807i
$867$	−3.86987e6	−	2.56759e8i	−0.00593798	−	0.393975i
$868$	−1.01710e8			−0.155527
$869$			1.41194e9i			2.15157i
$870$	−6.15740e8	+	9.28042e6i	−0.935060	+	0.0140932i
$871$	−8.07371e7			−0.122185
$872$			1.49097e8i			0.224864i
$873$	3.09206e8	−	9.32281e6i	0.464735	−	0.0140121i
$874$	−7.51360e7			−0.112542
$875$		−	5.54997e7i		−	0.0828450i
$876$	−9.66137e6	−	6.41015e8i	−0.0143723	−	0.953578i
$877$	1.04938e9			1.55572			0.777862	−	0.628435i	$-0.216304\pi$
$877$	1.04938e9			1.55572			0.777862	+	0.628435i	$0.216304\pi$
$878$			5.27654e7i			0.0779589i
$879$	−2.79838e7	+	421771.i	−0.0412040	+	0.000621026i
$880$	2.54020e8			0.372752
$881$		−	7.52464e8i		−	1.10042i	−0.835027	−	0.550209i	$-0.814548\pi$
$881$		−	7.52464e8i		−	1.10042i	0.835027	−	0.550209i	$-0.185452\pi$
$882$	−9.92276e6	−	3.29104e8i	−0.0144619	−	0.479654i
$883$	3.22748e8			0.468793			0.234397	−	0.972141i	$-0.424689\pi$
$883$	3.22748e8			0.468793			0.234397	+	0.972141i	$0.424689\pi$
$884$			5.73148e8i			0.829679i
$885$	−1.18500e6	−	7.86225e7i	−0.00170957	−	0.113427i
$886$	7.39708e8			1.06355
$887$			5.15412e6i			0.00738557i	0.999993	+	0.00369278i	$0.00117545\pi$
$887$			5.15412e6i			0.00738557i	−0.999993	+	0.00369278i	$0.998825\pi$
$888$	−3.30304e8	+	4.97834e6i	−0.471710	+	0.00710961i
$889$	−4.67641e8			−0.665591
$890$		−	4.08536e8i		−	0.579509i
$891$	−8.36830e7	−	1.38648e9i	−0.118305	−	1.96011i
$892$	−9.15428e8			−1.28982
$893$		−	1.06889e9i		−	1.50099i
$894$	1.06719e7	+	7.08062e8i	0.0149358	+	0.990965i
$895$	3.26479e8			0.455393
$896$			2.19262e8i			0.304818i
$897$	−2.36235e8	+	3.56053e6i	−0.327316	+	0.00493330i
$898$	6.19452e8			0.855419
$899$		−	5.16858e8i		−	0.711365i
$900$	4.17575e8	−	1.25902e7i	0.572805	−	0.0172705i
$901$	−7.30467e8			−0.998679
$902$		−	5.32231e8i		−	0.725238i
$903$	18906.4	+	1.25440e6i	2.56770e−5	+	0.00170363i
$904$	2.76800e8			0.374680
$905$			8.70183e8i			1.17399i
$906$	−2.64878e8	+	3.99224e6i	−0.356174	+	0.00536825i
$907$	7.83830e8			1.05051			0.525255	−	0.850945i	$-0.323970\pi$
$907$	7.83830e8			1.05051			0.525255	+	0.850945i	$0.323970\pi$
$908$			3.00041e8i			0.400796i
$909$	3.09086e7	+	1.02513e9i	0.0411516	+	1.36486i
$910$	3.56292e8			0.472805
$911$		−	5.30687e8i		−	0.701914i	−0.936392	−	0.350957i	$-0.885856\pi$
$911$		−	5.30687e8i		−	0.701914i	0.936392	−	0.350957i	$-0.114144\pi$
$912$	1.52200e6	+	1.00982e8i	0.00200645	+	0.133125i
$913$	−2.95859e7			−0.0388752
$914$		−	5.14444e8i		−	0.673752i
$915$	1.38099e9	−	2.08143e7i	1.80272	−	0.0271706i
$916$	−6.21394e8			−0.808501
$917$		−	1.13430e8i		−	0.147102i
$918$	−1.54239e7	−	3.40910e8i	−0.0199373	−	0.440668i
$919$	−4.67057e8			−0.601760			−0.300880	−	0.953662i	$-0.597280\pi$
$919$	−4.67057e8			−0.601760			−0.300880	+	0.953662i	$0.597280\pi$
$920$			2.09770e8i			0.269389i
$921$	8.79054e6	+	5.83237e8i	0.0112522	+	0.746562i
$922$	4.36263e8			0.556616
$923$			5.08447e8i			0.646608i
$924$	4.11544e8	−	6.20279e6i	0.521676	−	0.00786269i
$925$	−3.31287e8			−0.418581
$926$		−	1.29280e8i		−	0.162816i
$927$	1.03476e8	−	3.11988e6i	0.129897	−	0.00391651i
$928$	−1.00091e9			−1.25242
$929$			7.88359e8i			0.983280i	0.870799	+	0.491640i	$0.163602\pi$
$929$			7.88359e8i			0.983280i	−0.870799	+	0.491640i	$0.836398\pi$
$930$	−5.46029e6	−	3.62280e8i	−0.00678839	−	0.450398i
$931$	6.50877e8			0.806585
$932$		−	5.95135e8i		−	0.735137i
$933$	−6.02636e8	+	9.08292e6i	−0.742011	+	0.0111836i
$934$	−4.17301e8			−0.512164
$935$		−	1.69679e9i		−	2.07584i
$936$	−3.69113e7	−	1.22422e9i	−0.0450123	−	1.49290i
$937$	−1.36672e9			−1.66135			−0.830676	−	0.556757i	$-0.812046\pi$
$937$	−1.36672e9			−1.66135			−0.830676	+	0.556757i	$0.812046\pi$
$938$			1.42447e7i			0.0172602i
$939$	861077.	+	5.71309e7i	0.00104003	+	0.0690041i
$940$	−1.20672e9			−1.45285
$941$			5.73908e8i			0.688769i	0.938829	+	0.344384i	$0.111912\pi$
$941$			5.73908e8i			0.688769i	−0.938829	+	0.344384i	$0.888088\pi$
$942$	8.43076e8	−	1.27068e7i	1.00859	−	0.0152014i
$943$	−1.13961e8			−0.135900
$944$		−	9.82300e6i		−	0.0116769i
$945$	4.48050e8	−	2.02713e7i	0.530922	−	0.0240207i
$946$	−4.10122e6			−0.00484439
$947$		−	3.56439e8i		−	0.419696i	−0.977734	−	0.209848i	$-0.932703\pi$
$947$		−	3.56439e8i		−	0.419696i	0.977734	−	0.209848i	$-0.0672970\pi$
$948$	9.55064e6	+	6.33669e8i	0.0112101	+	0.743768i
$949$	−1.88488e9			−2.20539
$950$		−	3.90618e8i		−	0.455598i
$951$	5.89575e8	−	8.88606e6i	0.685484	−	0.0103316i
$952$	2.50074e8			0.289840
$953$		−	1.16121e9i		−	1.34162i	−0.741628	−	0.670811i	$-0.765946\pi$
$953$		−	1.16121e9i		−	1.34162i	0.741628	−	0.670811i	$-0.234054\pi$
$954$	6.30915e8	−	1.90226e7i	0.726651	−	0.0219091i
$955$	1.39828e9			1.60540
$956$		−	2.19970e8i		−	0.251762i
$957$	3.15206e7	+	2.09134e9i	0.0359632	+	2.38610i
$958$	−4.37571e8			−0.497682
$959$		−	3.34990e8i		−	0.379818i
$960$	−5.33638e8	+	8.04298e6i	−0.603161	+	0.00909083i
$961$	−5.83402e8			−0.657351
$962$			3.92743e8i			0.441146i
$963$	−9.52440e6	−	3.15892e8i	−0.0106650	−	0.353720i
$964$	−1.12517e9			−1.25599
$965$			3.64225e8i			0.405311i
$966$	628196.	+	4.16797e7i	0.000696889	+	0.0462374i
$967$	3.16833e8			0.350389			0.175195	−	0.984534i	$-0.443945\pi$
$967$	3.16833e8			0.350389			0.175195	+	0.984534i	$0.443945\pi$
$968$			2.46454e9i			2.71713i
$969$	6.74532e8	−	1.01665e7i	0.741364	−	0.0111738i
$970$	−3.26542e8			−0.357786
$971$		−	8.62988e7i		−	0.0942642i	−0.998889	−	0.0471321i	$-0.984992\pi$
$971$		−	8.62988e7i		−	0.0942642i	0.998889	−	0.0471321i	$-0.0150082\pi$
$972$	−4.69348e7	−	6.21677e8i	−0.0511089	−	0.676964i
$973$	−5.50682e8			−0.597809
$974$			9.28699e7i			0.100507i
$975$	−1.85106e7	−	1.22814e9i	−0.0199713	−	1.32506i
$976$	1.72540e8			0.185583
$977$			9.57957e8i			1.02722i	0.858024	+	0.513609i	$0.171692\pi$
$977$			9.57957e8i			1.02722i	−0.858024	+	0.513609i	$0.828308\pi$
$978$	−3.20837e8	+	4.83565e6i	−0.342979	+	0.00516938i
$979$	−1.38758e9			−1.47880
$980$		−	7.34804e8i		−	0.780716i
$981$	2.23039e8	−	6.72481e6i	0.236251	−	0.00712317i
$982$	9.05310e8			0.956011
$983$			4.65724e7i			0.0490307i	0.999699	+	0.0245153i	$0.00780425\pi$
$983$			4.65724e7i			0.0490307i	−0.999699	+	0.0245153i	$0.992196\pi$
$984$	−8.90307e6	−	5.90703e8i	−0.00934447	−	0.619989i
$985$	−6.98539e8			−0.730941
$986$			5.13871e8i			0.536073i
$987$	−5.92938e8	+	8.93675e6i	−0.616677	+	0.00929455i
$988$	9.79046e8			1.01515
$989$			878149.i			0.000907777i
$990$	4.41873e7	+	1.46554e9i	0.0455399	+	1.51040i
$991$	1.30464e9			1.34051			0.670257	−	0.742129i	$-0.266184\pi$
$991$	1.30464e9			1.34051			0.670257	+	0.742129i	$0.266184\pi$
$992$		−	5.88899e8i		−	0.603262i
$993$	2.37179e7	+	1.57364e9i	0.0242231	+	1.60716i
$994$	8.97069e7			0.0913412
$995$			6.57484e8i			0.667446i
$996$	−1.32780e7	+	200125.i	−0.0134386	+	0.000202546i
$997$	−2.74891e8			−0.277380			−0.138690	−	0.990336i	$-0.544289\pi$
$997$	−2.74891e8			−0.277380			−0.138690	+	0.990336i	$0.544289\pi$
$998$			2.93094e7i			0.0294860i
$999$	2.23451e7	+	4.93888e8i	0.0224123	+	0.495372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.17	✓	44
3.2	odd	2	inner	69.7.b.a.47.28	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.17	✓	44	1.1	even	1	trivial
69.7.b.a.47.28	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)

\(f(q)\)	\(=\)	\(q-4.53332i q^{2} +(-0.406897 - 26.9969i) q^{3} +43.4490 q^{4} +169.748i q^{5} +(-122.386 + 1.84460i) q^{6} -134.238 q^{7} -487.101i q^{8} +(-728.669 + 21.9700i) q^{9} +O(q^{10})\)	\(q-4.53332i q^{2} +(-0.406897 - 26.9969i) q^{3} +43.4490 q^{4} +169.748i q^{5} +(-122.386 + 1.84460i) q^{6} -134.238 q^{7} -487.101i q^{8} +(-728.669 + 21.9700i) q^{9} +769.522 q^{10} -2613.65i q^{11} +(-17.6793 - 1172.99i) q^{12} -3449.14 q^{13} +608.542i q^{14} +(4582.67 - 69.0700i) q^{15} +572.554 q^{16} -3824.51i q^{17} +(99.5969 + 3303.29i) q^{18} -6532.99 q^{19} +7375.38i q^{20} +(54.6209 + 3624.01i) q^{21} -11848.5 q^{22} +2536.99i q^{23} +(-13150.2 + 198.200i) q^{24} -13189.4 q^{25} +15636.1i q^{26} +(889.615 + 19662.9i) q^{27} -5832.49 q^{28} -29638.9i q^{29} +(-313.116 - 20774.7i) q^{30} +17438.5 q^{31} -33770.0i q^{32} +(-70560.6 + 1063.49i) q^{33} -17337.7 q^{34} -22786.6i q^{35} +(-31659.9 + 954.573i) q^{36} +25117.8 q^{37} +29616.2i q^{38} +(1403.45 + 93116.2i) q^{39} +82684.3 q^{40} +44919.6i q^{41} +(16428.8 - 247.614i) q^{42} +346.138 q^{43} -113561. i q^{44} +(-3729.36 - 123690. i) q^{45} +11501.0 q^{46} +163614. i q^{47} +(-232.971 - 15457.2i) q^{48} -99629.3 q^{49} +59791.6i q^{50} +(-103250. + 1556.18i) q^{51} -149862. q^{52} -190996. i q^{53} +(89138.1 - 4032.91i) q^{54} +443662. q^{55} +65387.3i q^{56} +(2658.26 + 176371. i) q^{57} -134363. q^{58} -17156.5i q^{59} +(199113. - 3001.02i) q^{60} +301351. q^{61} -79054.4i q^{62} +(97814.8 - 2949.20i) q^{63} -116447. q^{64} -585484. i q^{65} +(4821.13 + 319874. i) q^{66} +23407.9 q^{67} -166171. i q^{68} +(68491.1 - 1032.30i) q^{69} -103299. q^{70} -147413. i q^{71} +(10701.6 + 354935. i) q^{72} +546480. q^{73} -113867. i q^{74} +(5366.72 + 356073. i) q^{75} -283852. q^{76} +350850. i q^{77} +(422125. - 6362.27i) q^{78} -540217. q^{79} +97189.8i q^{80} +(530476. - 32017.7i) q^{81} +203635. q^{82} -11319.8i q^{83} +(2373.23 + 157459. i) q^{84} +649203. q^{85} -1569.15i q^{86} +(-800159. + 12060.0i) q^{87} -1.27311e6 q^{88} -530896. i q^{89} +(-560727. + 16906.4i) q^{90} +463004. q^{91} +110230. i q^{92} +(-7095.69 - 470787. i) q^{93} +741715. q^{94} -1.10896e6i q^{95} +(-911687. + 13740.9i) q^{96} -424344. q^{97} +451651. i q^{98} +(57421.8 + 1.90449e6i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more