LMFDB - Embedded newform 33.6.d.b.32.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(32,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("33.32");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.d (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:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} + \cdots + 92\!\cdots\!40 $ x^16 - 6x^15 - 195x^14 - 642x^13 + 89670x^12 + 53946x^11 + 91115757x^10 - 2121785838x^9 + 37710373995x^8 - 835758339660x^7 + 12972600642204x^6 - 129499271268696x^5 + 2168293345395660x^4 - 17336133272224368x^3 + 169639595563975056x^2 - 1075523563426213440*x + 9241272870780234240
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.6
Root			$6.80653 - 6.27606i$ of defining polynomial
Character	$\chi$	$=$	33.32
Dual form			33.6.d.b.32.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.46270 q^{2} +(-14.2692 + 6.27606i) q^{3} -12.0843 q^{4} -59.8956i q^{5} +(63.6794 - 28.0082i) q^{6} +169.425i q^{7} +196.735 q^{8} +(164.222 - 179.109i) q^{9} +O(q^{10})$	\(q-4.46270 q^{2} +(-14.2692 + 6.27606i) q^{3} -12.0843 q^{4} -59.8956i q^{5} +(63.6794 - 28.0082i) q^{6} +169.425i q^{7} +196.735 q^{8} +(164.222 - 179.109i) q^{9} +267.296i q^{10} +(358.129 + 181.093i) q^{11} +(172.433 - 75.8416i) q^{12} -838.100i q^{13} -756.094i q^{14} +(375.908 + 854.664i) q^{15} -491.273 q^{16} +512.592 q^{17} +(-732.875 + 799.311i) q^{18} +1878.22i q^{19} +723.795i q^{20} +(-1063.32 - 2417.57i) q^{21} +(-1598.22 - 808.163i) q^{22} -3339.01i q^{23} +(-2807.26 + 1234.72i) q^{24} -462.483 q^{25} +3740.19i q^{26} +(-1219.22 + 3586.42i) q^{27} -2047.38i q^{28} +1329.42 q^{29} +(-1677.57 - 3814.11i) q^{30} +6737.49 q^{31} -4103.11 q^{32} +(-6246.78 - 336.413i) q^{33} -2287.55 q^{34} +10147.8 q^{35} +(-1984.51 + 2164.40i) q^{36} +4959.19 q^{37} -8381.92i q^{38} +(5259.96 + 11959.0i) q^{39} -11783.6i q^{40} +17769.0 q^{41} +(4745.29 + 10788.9i) q^{42} +7851.09i q^{43} +(-4327.73 - 2188.37i) q^{44} +(-10727.8 - 9836.18i) q^{45} +14901.0i q^{46} -20190.6i q^{47} +(7010.10 - 3083.26i) q^{48} -11897.8 q^{49} +2063.92 q^{50} +(-7314.30 + 3217.06i) q^{51} +10127.8i q^{52} +18738.7i q^{53} +(5441.04 - 16005.1i) q^{54} +(10846.7 - 21450.4i) q^{55} +33331.8i q^{56} +(-11787.8 - 26800.7i) q^{57} -5932.81 q^{58} -5842.82i q^{59} +(-4542.58 - 10328.0i) q^{60} -1703.10i q^{61} -30067.4 q^{62} +(30345.6 + 27823.3i) q^{63} +34031.7 q^{64} -50198.5 q^{65} +(27877.5 + 1501.31i) q^{66} -29337.8 q^{67} -6194.30 q^{68} +(20955.8 + 47645.1i) q^{69} -45286.7 q^{70} -17330.8i q^{71} +(32308.3 - 35237.0i) q^{72} +16626.5i q^{73} -22131.4 q^{74} +(6599.28 - 2902.57i) q^{75} -22696.9i q^{76} +(-30681.6 + 60676.0i) q^{77} +(-23473.7 - 53369.7i) q^{78} -2586.42i q^{79} +29425.1i q^{80} +(-5111.17 - 58827.4i) q^{81} -79297.6 q^{82} +31993.8 q^{83} +(12849.5 + 29214.5i) q^{84} -30702.0i q^{85} -35037.1i q^{86} +(-18969.8 + 8343.52i) q^{87} +(70456.6 + 35627.3i) q^{88} -63768.5i q^{89} +(47875.2 + 43896.0i) q^{90} +141995. q^{91} +40349.5i q^{92} +(-96138.9 + 42284.9i) q^{93} +90104.9i q^{94} +112497. q^{95} +(58548.3 - 25751.4i) q^{96} +103785. q^{97} +53096.5 q^{98} +(91248.1 - 34404.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 54 q^{3} + 316 q^{4} - 222 q^{9}+O(q^{10}) $ 16 * q - 54 * q^3 + 316 * q^4 - 222 * q^9	$ 16 q - 54 q^{3} + 316 q^{4} - 222 q^{9} - 552 q^{12} - 1674 q^{15} + 1684 q^{16} + 7932 q^{22} - 1356 q^{25} - 3240 q^{27} - 11980 q^{31} - 5106 q^{33} - 34032 q^{34} + 14016 q^{36} + 9356 q^{37} + 45912 q^{42} + 77430 q^{45} - 78012 q^{48} - 1136 q^{49} + 117308 q^{55} + 31848 q^{58} - 220548 q^{60} + 5860 q^{64} - 164796 q^{66} - 364132 q^{67} + 113790 q^{69} + 231144 q^{70} + 320364 q^{75} + 296088 q^{78} - 251334 q^{81} + 4824 q^{82} + 586836 q^{88} - 209184 q^{91} - 521046 q^{93} + 119852 q^{97} - 243894 q^{99}+O(q^{100}) $ 16 * q - 54 * q^3 + 316 * q^4 - 222 * q^9 - 552 * q^12 - 1674 * q^15 + 1684 * q^16 + 7932 * q^22 - 1356 * q^25 - 3240 * q^27 - 11980 * q^31 - 5106 * q^33 - 34032 * q^34 + 14016 * q^36 + 9356 * q^37 + 45912 * q^42 + 77430 * q^45 - 78012 * q^48 - 1136 * q^49 + 117308 * q^55 + 31848 * q^58 - 220548 * q^60 + 5860 * q^64 - 164796 * q^66 - 364132 * q^67 + 113790 * q^69 + 231144 * q^70 + 320364 * q^75 + 296088 * q^78 - 251334 * q^81 + 4824 * q^82 + 586836 * q^88 - 209184 * q^91 - 521046 * q^93 + 119852 * q^97 - 243894 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.46270			−0.788902			−0.394451	−	0.918917i	$-0.629065\pi$
$2$	−4.46270			−0.788902			−0.394451	+	0.918917i	$0.629065\pi$
$3$	−14.2692	+	6.27606i	−0.915372	+	0.402609i
$3$	−14.2692	+	6.27606i	−0.915372	+	0.402609i
$4$	−12.0843			−0.377634
$5$		−	59.8956i		−	1.07145i	−0.844394	−	0.535723i	$-0.820039\pi$
$5$		−	59.8956i		−	1.07145i	0.844394	−	0.535723i	$-0.179961\pi$
$6$	63.6794	−	28.0082i	0.722139	−	0.317619i
$7$			169.425i			1.30687i	0.756983	+	0.653435i	$0.226673\pi$
$7$			169.425i			1.30687i	−0.756983	+	0.653435i	$0.773327\pi$
$8$	196.735			1.08682
$9$	164.222	−	179.109i	0.675811	−	0.737075i
$10$			267.296i			0.845265i
$11$	358.129	+	181.093i	0.892397	+	0.451252i
$11$	358.129	+	181.093i	0.892397	+	0.451252i
$12$	172.433	−	75.8416i	0.345675	−	0.152039i
$13$		−	838.100i		−	1.37543i	−0.725983	−	0.687713i	$-0.758615\pi$
$13$		−	838.100i		−	1.37543i	0.725983	−	0.687713i	$-0.241385\pi$
$14$		−	756.094i		−	1.03099i
$15$	375.908	+	854.664i	0.431374	+	0.980771i
$16$	−491.273			−0.479759
$17$	512.592			0.430179			0.215090	−	0.976594i	$-0.430996\pi$
$17$	512.592			0.430179			0.215090	+	0.976594i	$0.430996\pi$
$18$	−732.875	+	799.311i	−0.533149	+	0.581480i
$19$			1878.22i			1.19361i	0.802387	+	0.596804i	$0.203563\pi$
$19$			1878.22i			1.19361i	−0.802387	+	0.596804i	$0.796437\pi$
$20$			723.795i			0.404614i
$21$	−1063.32	−	2417.57i	−0.526158	−	1.19627i
$22$	−1598.22	−	808.163i	−0.704013	−	0.355994i
$23$		−	3339.01i		−	1.31613i	−0.752963	−	0.658063i	$-0.771376\pi$
$23$		−	3339.01i		−	1.31613i	0.752963	−	0.658063i	$-0.228624\pi$
$24$	−2807.26	+	1234.72i	−0.994843	+	0.437563i
$25$	−462.483			−0.147995
$26$			3740.19i			1.08508i
$27$	−1219.22	+	3586.42i	−0.321865	+	0.946785i
$28$		−	2047.38i		−	0.493518i
$29$	1329.42			0.293540			0.146770	−	0.989171i	$-0.453112\pi$
$29$	1329.42			0.293540			0.146770	+	0.989171i	$0.453112\pi$
$30$	−1677.57	−	3814.11i	−0.340312	−	0.773732i
$31$	6737.49			1.25920			0.629599	−	0.776920i	$-0.283219\pi$
$31$	6737.49			1.25920			0.629599	+	0.776920i	$0.283219\pi$
$32$	−4103.11			−0.708335
$33$	−6246.78	−	336.413i	−0.998553	−	0.0537760i
$34$	−2287.55			−0.339369
$35$	10147.8			1.40024
$36$	−1984.51	+	2164.40i	−0.255209	+	0.278344i
$37$	4959.19			0.595534			0.297767	−	0.954639i	$-0.403758\pi$
$37$	4959.19			0.595534			0.297767	+	0.954639i	$0.403758\pi$
$38$		−	8381.92i		−	0.941639i
$39$	5259.96	+	11959.0i	0.553759	+	1.25903i
$40$		−	11783.6i		−	1.16447i
$41$	17769.0			1.65083			0.825415	−	0.564527i	$-0.190941\pi$
$41$	17769.0			1.65083			0.825415	+	0.564527i	$0.190941\pi$
$42$	4745.29	+	10788.9i	0.415087	+	0.943741i
$43$			7851.09i			0.647528i	0.946138	+	0.323764i	$0.104948\pi$
$43$			7851.09i			0.647528i	−0.946138	+	0.323764i	$0.895052\pi$
$44$	−4327.73	−	2188.37i	−0.336999	−	0.170408i
$45$	−10727.8	−	9836.18i	−0.789735	−	0.724095i
$46$			14901.0i			1.03829i
$47$		−	20190.6i		−	1.33323i	−0.745402	−	0.666616i	$-0.767742\pi$
$47$		−	20190.6i		−	1.33323i	0.745402	−	0.666616i	$-0.232258\pi$
$48$	7010.10	−	3083.26i	0.439158	−	0.193156i
$49$	−11897.8			−0.707909
$50$	2063.92			0.116753
$51$	−7314.30	+	3217.06i	−0.393774	+	0.173194i
$52$			10127.8i			0.519407i
$53$			18738.7i			0.916325i	0.888868	+	0.458163i	$0.151492\pi$
$53$			18738.7i			0.916325i	−0.888868	+	0.458163i	$0.848508\pi$
$54$	5441.04	−	16005.1i	0.253920	−	0.746921i
$55$	10846.7	−	21450.4i	0.483492	−	0.956154i
$56$			33331.8i			1.42033i
$57$	−11787.8	−	26800.7i	−0.480557	−	1.09259i
$58$	−5932.81			−0.231574
$59$		−	5842.82i		−	0.218520i	−0.994013	−	0.109260i	$-0.965152\pi$
$59$		−	5842.82i		−	0.218520i	0.994013	−	0.109260i	$-0.0348482\pi$
$60$	−4542.58	−	10328.0i	−0.162901	−	0.370372i
$61$		−	1703.10i		−	0.0586026i	−0.999571	−	0.0293013i	$-0.990672\pi$
$61$		−	1703.10i		−	0.0586026i	0.999571	−	0.0293013i	$-0.00932822\pi$
$62$	−30067.4			−0.993384
$63$	30345.6	+	27823.3i	0.963261	+	0.883198i
$64$	34031.7			1.03857
$65$	−50198.5			−1.47369
$66$	27877.5	+	1501.31i	0.787760	+	0.0424240i
$67$	−29337.8			−0.798437			−0.399218	−	0.916856i	$-0.630718\pi$
$67$	−29337.8			−0.798437			−0.399218	+	0.916856i	$0.630718\pi$
$68$	−6194.30			−0.162450
$69$	20955.8	+	47645.1i	0.529885	+	1.20475i
$70$	−45286.7			−1.10465
$71$		−	17330.8i		−	0.408011i	−0.978970	−	0.204006i	$-0.934604\pi$
$71$		−	17330.8i		−	0.408011i	0.978970	−	0.204006i	$-0.0653961\pi$
$72$	32308.3	−	35237.0i	0.734484	−	0.801066i
$73$			16626.5i			0.365168i	0.983190	+	0.182584i	$0.0584462\pi$
$73$			16626.5i			0.365168i	−0.983190	+	0.182584i	$0.941554\pi$
$74$	−22131.4			−0.469818
$75$	6599.28	−	2902.57i	0.135470	−	0.0595840i
$76$		−	22696.9i		−	0.450746i
$77$	−30681.6	+	60676.0i	−0.589728	+	1.16625i
$78$	−23473.7	−	53369.7i	−0.436862	−	0.993248i
$79$		−	2586.42i		−	0.0466263i	−0.999728	−	0.0233132i	$-0.992579\pi$
$79$		−	2586.42i		−	0.0466263i	0.999728	−	0.0233132i	$-0.00742148\pi$
$80$			29425.1i			0.514036i
$81$	−5111.17	−	58827.4i	−0.0865581	−	0.996247i
$82$	−79297.6			−1.30234
$83$	31993.8			0.509766			0.254883	−	0.966972i	$-0.417963\pi$
$83$	31993.8			0.509766			0.254883	+	0.966972i	$0.417963\pi$
$84$	12849.5	+	29214.5i	0.198695	+	0.451753i
$85$		−	30702.0i		−	0.460913i
$86$		−	35037.1i		−	0.510836i
$87$	−18969.8	+	8343.52i	−0.268698	+	0.118182i
$88$	70456.6	+	35627.3i	0.969873	+	0.490429i
$89$		−	63768.5i		−	0.853357i	−0.904403	−	0.426679i	$-0.859684\pi$
$89$		−	63768.5i		−	0.853357i	0.904403	−	0.426679i	$-0.140316\pi$
$90$	47875.2	+	43896.0i	0.623024	+	0.571240i
$91$	141995.			1.79750
$92$			40349.5i			0.497014i
$93$	−96138.9	+	42284.9i	−1.15263	+	0.506965i
$94$			90104.9i			1.05179i
$95$	112497.			1.27888
$96$	58548.3	−	25751.4i	0.648390	−	0.285182i
$97$	103785.			1.11997			0.559984	−	0.828503i	$-0.310807\pi$
$97$	103785.			1.11997			0.559984	+	0.828503i	$0.310807\pi$
$98$	53096.5			0.558471
$99$	91248.1	−	34404.8i	0.935698	−	0.352802i
$100$	5588.77			0.0558877
$101$	24287.2			0.236905			0.118453	−	0.992960i	$-0.462207\pi$
$101$	24287.2			0.236905			0.118453	+	0.992960i	$0.462207\pi$
$102$	32641.5	−	14356.8i	0.310649	−	0.136633i
$103$	−108341.			−1.00624			−0.503119	−	0.864217i	$-0.667814\pi$
$103$	−108341.			−1.00624			−0.503119	+	0.864217i	$0.667814\pi$
$104$		−	164884.i		−	1.49484i
$105$	−144802.	+	63688.3i	−1.28174	+	0.563750i
$106$		−	83625.2i		−	0.722891i
$107$	−115625.			−0.976317			−0.488158	−	0.872755i	$-0.662331\pi$
$107$	−115625.			−0.976317			−0.488158	+	0.872755i	$0.662331\pi$
$108$	14733.4	−	43339.3i	0.121547	−	0.357538i
$109$		−	33180.5i		−	0.267496i	−0.991015	−	0.133748i	$-0.957299\pi$
$109$		−	33180.5i		−	0.267496i	0.991015	−	0.133748i	$-0.0427012\pi$
$110$	−48405.4	+	95726.6i	−0.381427	+	0.754312i
$111$	−70763.8	+	31124.2i	−0.545135	+	0.239767i
$112$		−	83234.0i		−	0.626983i
$113$			75910.6i			0.559250i	0.960109	+	0.279625i	$0.0902102\pi$
$113$			75910.6i			0.559250i	−0.960109	+	0.279625i	$0.909790\pi$
$114$	52605.4	+	119604.i	0.379113	+	0.861950i
$115$	−199992.			−1.41016
$116$	−16065.1			−0.110851
$117$	−150111.	−	137635.i	−1.01379	−	0.929529i
$118$			26074.8i			0.172391i
$119$			86845.9i			0.562188i
$120$	73954.4	+	168142.i	0.468825	+	1.06592i
$121$	95461.9	+	129709.i	0.592743	+	0.805391i
$122$			7600.45i			0.0462317i
$123$	−253549.	+	111519.i	−1.51112	+	0.664640i
$124$	−81417.7			−0.475515
$125$		−	159473.i		−	0.912877i
$126$	−135423.	−	124167.i	−0.759918	−	0.696756i
$127$		−	258255.i		−	1.42082i	−0.703787	−	0.710411i	$-0.748509\pi$
$127$		−	258255.i		−	1.42082i	0.703787	−	0.710411i	$-0.251491\pi$
$128$	−20573.9			−0.110992
$129$	−49273.9	−	112029.i	−0.260701	−	0.592729i
$130$	224021.			1.16260
$131$	185955.			0.946736			0.473368	−	0.880865i	$-0.343038\pi$
$131$	185955.			0.946736			0.473368	+	0.880865i	$0.343038\pi$
$132$	75487.8	+	4065.31i	0.377087	+	0.0203076i
$133$	−318217.			−1.55989
$134$	130926.			0.629888
$135$	214811.	+	73026.2i	1.01443	+	0.344861i
$136$	100845.			0.467527
$137$			79544.3i			0.362083i	0.983475	+	0.181041i	$0.0579468\pi$
$137$			79544.3i			0.362083i	−0.983475	+	0.181041i	$0.942053\pi$
$138$	−93519.5	−	212626.i	−0.418027	−	0.950426i
$139$			419383.i			1.84109i	0.390642	+	0.920543i	$0.372253\pi$
$139$			419383.i			1.84109i	−0.390642	+	0.920543i	$0.627747\pi$
$140$	−122629.			−0.528777
$141$	126718.	+	288105.i	0.536772	+	1.22040i
$142$			77342.1i			0.321881i
$143$	151774.	−	300148.i	0.620664	−	1.22743i
$144$	−80678.0	+	87991.6i	−0.324227	+	0.353618i
$145$		−	79626.5i		−	0.314512i
$146$		−	74199.1i		−	0.288082i
$147$	169773.	−	74671.5i	0.648000	−	0.285011i
$148$	−59928.2			−0.224894
$149$	61974.2			0.228689			0.114344	−	0.993441i	$-0.463523\pi$
$149$	61974.2			0.228689			0.114344	+	0.993441i	$0.463523\pi$
$150$	−29450.6	+	12953.3i	−0.106873	+	0.0470059i
$151$			36038.3i			0.128624i	0.997930	+	0.0643121i	$0.0204853\pi$
$151$			36038.3i			0.128624i	−0.997930	+	0.0643121i	$0.979515\pi$
$152$			369511.i			1.29723i
$153$	84179.0	−	91809.9i	0.290720	−	0.317074i
$154$	136923.	−	270779.i	0.465237	−	0.920054i
$155$		−	403546.i		−	1.34916i
$156$	−63562.8	−	144516.i	−0.209118	−	0.475451i
$157$	−65185.9			−0.211059			−0.105530	−	0.994416i	$-0.533654\pi$
$157$	−65185.9			−0.211059			−0.105530	+	0.994416i	$0.533654\pi$
$158$			11542.4i			0.0367836i
$159$	−117605.	−	267387.i	−0.368921	−	0.838778i
$160$			245758.i			0.758942i
$161$	565711.			1.72001
$162$	22809.6	+	262529.i	0.0682859	+	0.785941i
$163$	304117.			0.896543			0.448272	−	0.893897i	$-0.352040\pi$
$163$	304117.			0.896543			0.448272	+	0.893897i	$0.352040\pi$
$164$	−214725.			−0.623409
$165$	−20149.7	+	374154.i	−0.0576180	+	1.06989i
$166$	−142779.			−0.402155
$167$	452837.			1.25647			0.628233	−	0.778025i	$-0.283778\pi$
$167$	452837.			1.25647			0.628233	+	0.778025i	$0.283778\pi$
$168$	−209193.	−	475620.i	−0.571838	−	1.30013i
$169$	−331118.			−0.891797
$170$			137014.i			0.363616i
$171$	336406.	+	308445.i	0.879778	+	0.806653i
$172$		−	94874.7i		−	0.244528i
$173$	−573310.			−1.45638			−0.728189	−	0.685376i	$-0.759638\pi$
$173$	−573310.			−1.45638			−0.728189	+	0.685376i	$0.759638\pi$
$174$	84656.7	−	37234.7i	0.211977	−	0.0932340i
$175$		−	78356.2i		−	0.193410i
$176$	−175939.	−	88966.0i	−0.428136	−	0.216492i
$177$	36669.9	+	83372.5i	0.0879784	+	0.200028i
$178$			284580.i			0.673215i
$179$			331246.i			0.772713i	0.922349	+	0.386357i	$0.126267\pi$
$179$			331246.i			0.772713i	−0.922349	+	0.386357i	$0.873733\pi$
$180$	129638.	+	118863.i	0.298230	+	0.273443i
$181$	593309.			1.34612			0.673061	−	0.739587i	$-0.264979\pi$
$181$	593309.			1.34612			0.673061	+	0.739587i	$0.264979\pi$
$182$	−633682.			−1.41805
$183$	10688.8	+	24302.0i	0.0235939	+	0.0536431i
$184$		−	656900.i		−	1.43039i
$185$		−	297034.i		−	0.638082i
$186$	429039.	−	188705.i	0.909316	−	0.399946i
$187$	183574.	+	92826.6i	0.383891	+	0.194119i
$188$			243989.i			0.503473i
$189$	−607629.	−	206567.i	−1.23733	−	0.420636i
$190$	−502040.			−1.00891
$191$			434454.i			0.861709i	0.902421	+	0.430855i	$0.141788\pi$
$191$			434454.i			0.861709i	−0.902421	+	0.430855i	$0.858212\pi$
$192$	−485607.	+	213585.i	−0.950674	+	0.418136i
$193$		−	71460.4i		−	0.138093i	−0.997613	−	0.0690466i	$-0.978004\pi$
$193$		−	71460.4i		−	0.138093i	0.997613	−	0.0690466i	$-0.0219957\pi$
$194$	−463162.			−0.883545
$195$	716294.	−	315049.i	1.34898	−	0.593323i
$196$	143777.			0.267330
$197$	−909746.			−1.67015			−0.835073	−	0.550139i	$-0.814575\pi$
$197$	−909746.			−1.67015			−0.835073	+	0.550139i	$0.814575\pi$
$198$	−407213.	+	153538.i	−0.738174	+	0.278326i
$199$	177806.			0.318283			0.159142	−	0.987256i	$-0.449127\pi$
$199$	177806.			0.318283			0.159142	+	0.987256i	$0.449127\pi$
$200$	−90986.6			−0.160843
$201$	418628.	−	184126.i	0.730866	−	0.321458i
$202$	−108387.			−0.186895
$203$			225237.i			0.383619i
$204$	88388.0	−	38875.8i	0.148702	−	0.0654040i
$205$		−	1.06428e6i		−	1.76877i
$206$	483495.			0.793823
$207$	−598047.	−	548339.i	−0.970084	−	0.889453i
$208$			411736.i			0.659873i
$209$	−340131.	+	672644.i	−0.538617	+	1.06517i
$210$	646206.	−	284222.i	1.01117	−	0.444743i
$211$			323638.i			0.500442i	0.968189	+	0.250221i	$0.0805032\pi$
$211$			323638.i			0.500442i	−0.968189	+	0.250221i	$0.919497\pi$
$212$		−	226444.i		−	0.346035i
$213$	108769.	+	247297.i	0.164269	+	0.373482i
$214$	515998.			0.770218
$215$	470246.			0.693791
$216$	−239864.	+	705574.i	−0.349809	+	1.02898i
$217$			1.14150e6i			1.64561i
$218$			148075.i			0.211028i
$219$	−104349.	−	237247.i	−0.147020	−	0.334265i
$220$	−131074.	+	259212.i	−0.182583	+	0.361076i
$221$		−	429603.i		−	0.591680i
$222$	315798.	−	138898.i	0.430058	−	0.189153i
$223$	13271.8			0.0178718			0.00893588	−	0.999960i	$-0.497156\pi$
$223$	13271.8			0.0178718			0.00893588	+	0.999960i	$0.497156\pi$
$224$		−	695170.i		−	0.925702i
$225$	−75949.9	+	82834.9i	−0.100016	+	0.109083i
$226$		−	338766.i		−	0.441194i
$227$	−281859.			−0.363051			−0.181525	−	0.983386i	$-0.558103\pi$
$227$	−281859.			−0.363051			−0.181525	+	0.983386i	$0.558103\pi$
$228$	142447.	+	323867.i	0.181475	+	0.412600i
$229$	−1.35791e6			−1.71113			−0.855566	−	0.517693i	$-0.826791\pi$
$229$	−1.35791e6			−1.71113			−0.855566	+	0.517693i	$0.826791\pi$
$230$	892504.			1.11248
$231$	56996.8	−	1.05836e6i	0.0702782	−	1.30498i
$232$	261544.			0.319025
$233$	66995.0			0.0808449			0.0404224	−	0.999183i	$-0.487130\pi$
$233$	66995.0			0.0808449			0.0404224	+	0.999183i	$0.487130\pi$
$234$	669902.	+	614222.i	0.799782	+	0.733307i
$235$	−1.20933e6			−1.42848
$236$			70606.2i			0.0825207i
$237$	16232.5	+	36906.2i	0.0187722	+	0.0426804i
$238$		−	387567.i		−	0.443512i
$239$	383601.			0.434395			0.217198	−	0.976128i	$-0.430308\pi$
$239$	383601.			0.434395			0.217198	+	0.976128i	$0.430308\pi$
$240$	−184674.	−	419874.i	−0.206956	−	0.470534i
$241$			23367.5i			0.0259161i	0.999916	+	0.0129581i	$0.00412480\pi$
$241$			23367.5i			0.0259161i	−0.999916	+	0.0129581i	$0.995875\pi$
$242$	−426018.	−	578853.i	−0.467617	−	0.635375i
$243$	442137.	+	807344.i	0.480331	+	0.877087i
$244$			20580.8i			0.0221303i
$245$			712628.i			0.758486i
$246$	1.13152e6	−	497676.i	1.19213	−	0.524336i
$247$	1.57413e6			1.64172
$248$	1.32550e6			1.36852
$249$	−456527.	+	200795.i	−0.466626	+	0.205237i
$250$			711681.i			0.720171i
$251$		−	1.73283e6i		−	1.73608i	−0.496491	−	0.868042i	$-0.665378\pi$
$251$		−	1.73283e6i		−	1.73608i	0.496491	−	0.868042i	$-0.334622\pi$
$252$	−366704.	−	336225.i	−0.363760	−	0.333525i
$253$	604669.	−	1.19580e6i	0.593905	−	1.17451i
$254$			1.15252e6i			1.12089i
$255$	192688.	+	438094.i	0.185568	+	0.421907i
$256$	−997200.			−0.951004
$257$			83741.8i			0.0790878i	0.999218	+	0.0395439i	$0.0125905\pi$
$257$			83741.8i			0.0790878i	−0.999218	+	0.0395439i	$0.987410\pi$
$258$	219895.	+	499952.i	0.205668	+	0.467605i
$259$			840210.i			0.778285i
$260$	606612.			0.556516
$261$	218320.	−	238111.i	0.198378	−	0.216361i
$262$	−829860.			−0.746882
$263$	−1.45210e6			−1.29451			−0.647256	−	0.762272i	$-0.724084\pi$
$263$	−1.45210e6			−1.29451			−0.647256	+	0.762272i	$0.724084\pi$
$264$	−1.22896e6	−	66184.3i	−1.08525	−	0.0584447i
$265$	1.12237e6			0.981792
$266$	1.42011e6			1.23060
$267$	400215.	+	909927.i	0.343570	+	0.781139i
$268$	354526.			0.301517
$269$		−	335334.i		−	0.282551i	−0.989970	−	0.141275i	$-0.954880\pi$
$269$		−	335334.i		−	0.282551i	0.989970	−	0.141275i	$-0.0451203\pi$
$270$	−958636.	−	325894.i	−0.800285	−	0.272062i
$271$			2.35862e6i			1.95090i	0.220227	+	0.975449i	$0.429320\pi$
$271$			2.35862e6i			1.95090i	−0.220227	+	0.975449i	$0.570680\pi$
$272$	−251823.			−0.206382
$273$	−2.02616e6	+	891169.i	−1.64538	+	0.723692i
$274$		−	354983.i		−	0.285648i
$275$	−165629.	−	83752.2i	−0.132070	−	0.0667828i
$276$	−253236.	−	575756.i	−0.200102	−	0.454952i
$277$		−	1.98229e6i		−	1.55227i	−0.630564	−	0.776137i	$-0.717176\pi$
$277$		−	1.98229e6i		−	1.55227i	0.630564	−	0.776137i	$-0.282824\pi$
$278$		−	1.87158e6i		−	1.45244i
$279$	1.10645e6	−	1.20675e6i	0.850980	−	0.928123i
$280$	1.99643e6			1.52181
$281$	119166.			0.0900299			0.0450150	−	0.998986i	$-0.485666\pi$
$281$	119166.			0.0900299			0.0450150	+	0.998986i	$0.485666\pi$
$282$	−565504.	−	1.28573e6i	−0.423460	−	0.962778i
$283$		−	2.04647e6i		−	1.51894i	−0.650544	−	0.759468i	$-0.725459\pi$
$283$		−	2.04647e6i		−	1.51894i	0.650544	−	0.759468i	$-0.274541\pi$
$284$			209430.i			0.154079i
$285$	−1.60524e6	+	706037.i	−1.17065	+	0.514891i
$286$	−677321.	+	1.33947e6i	−0.489643	+	0.968319i
$287$			3.01051e6i			2.15742i
$288$	−673822.	+	734905.i	−0.478701	+	0.522096i
$289$	−1.15711e6			−0.814946
$290$			355349.i			0.248119i
$291$	−1.48093e6	+	651362.i	−1.02519	+	0.450910i
$292$		−	200919.i		−	0.137900i
$293$	874404.			0.595036			0.297518	−	0.954716i	$-0.403841\pi$
$293$	874404.			0.595036			0.297518	+	0.954716i	$0.403841\pi$
$294$	−757646.	+	333237.i	−0.511209	+	0.224846i
$295$	−349959.			−0.234133
$296$	975646.			0.647237
$297$	−1.08611e6	+	1.06361e6i	−0.714470	+	0.699666i
$298$	−276572.			−0.180413
$299$	−2.79842e6			−1.81023
$300$	−79747.5	+	35075.5i	−0.0511580	+	0.0225009i
$301$	−1.33017e6			−0.846235
$302$		−	160828.i		−	0.101472i
$303$	−346560.	+	152428.i	−0.216856	+	0.0953803i
$304$		−	922717.i		−	0.572644i
$305$	−102008.			−0.0627894
$306$	−375666.	+	409720.i	−0.229350	+	0.250141i
$307$		−	2.22344e6i		−	1.34642i	−0.739452	−	0.673209i	$-0.764915\pi$
$307$		−	2.22344e6i		−	1.34642i	0.739452	−	0.673209i	$-0.235085\pi$
$308$	370765.	−	733226.i	0.222701	−	0.440414i
$309$	1.54595e6	−	679956.i	0.921082	−	0.405121i
$310$			1.80091e6i			1.06436i
$311$		−	2.04294e6i		−	1.19772i	−0.800854	−	0.598860i	$-0.795621\pi$
$311$		−	2.04294e6i		−	1.19772i	0.800854	−	0.598860i	$-0.204379\pi$
$312$	1.03482e6	+	2.35276e6i	0.601836	+	1.36833i
$313$	2.46189e6			1.42039			0.710195	−	0.704005i	$-0.248607\pi$
$313$	2.46189e6			1.42039			0.710195	+	0.704005i	$0.248607\pi$
$314$	290905.			0.166505
$315$	1.66650e6	−	1.81757e6i	0.946298	−	1.03208i
$316$			31255.0i			0.0176077i
$317$			59333.5i			0.0331628i	0.999863	+	0.0165814i	$0.00527827\pi$
$317$			59333.5i			0.0331628i	−0.999863	+	0.0165814i	$0.994722\pi$
$318$	524837.	+	1.19327e6i	0.291043	+	0.661714i
$319$	476104.	+	240748.i	0.261954	+	0.132461i
$320$		−	2.03835e6i		−	1.11277i
$321$	1.64987e6	−	725667.i	0.893693	−	0.393074i
$322$	−2.52460e6			−1.35692
$323$			962758.i			0.513465i
$324$	61764.8	+	710886.i	0.0326872	+	0.376216i
$325$			387607.i			0.203556i
$326$	−1.35718e6			−0.707285
$327$	208243.	+	473461.i	0.107696	+	0.244858i
$328$	3.49578e6			1.79415
$329$	3.42080e6			1.74236
$330$	89922.1	−	1.66974e6i	0.0454550	−	0.844042i
$331$	1.38194e6			0.693297			0.346648	−	0.937995i	$-0.387320\pi$
$331$	1.38194e6			0.693297			0.346648	+	0.937995i	$0.387320\pi$
$332$	−386622.			−0.192505
$333$	814409.	−	888236.i	0.402468	−	0.438953i
$334$	−2.02088e6			−0.991229
$335$			1.75720e6i			0.855481i
$336$	522382.	+	1.18769e6i	0.252429	+	0.573923i
$337$			1.39179e6i			0.667572i	0.942649	+	0.333786i	$0.108326\pi$
$337$			1.39179e6i			0.667572i	−0.942649	+	0.333786i	$0.891674\pi$
$338$	1.47768e6			0.703540
$339$	−476419.	−	1.08319e6i	−0.225159	−	0.511922i
$340$			371011.i			0.174056i
$341$	2.41289e6	+	1.22011e6i	1.12370	+	0.568215i
$342$	−1.50128e6	−	1.37650e6i	−0.694058	−	0.636370i
$343$			831736.i			0.381725i
$344$			1.54458e6i			0.703745i
$345$	2.85373e6	−	1.25516e6i	1.29082	−	0.567743i
$346$	2.55851e6			1.14894
$347$	−4.18029e6			−1.86373			−0.931865	−	0.362806i	$-0.881819\pi$
$347$	−4.18029e6			−1.86373			−0.931865	+	0.362806i	$0.881819\pi$
$348$	229237.	−	100825.i	0.101470	−	0.0446295i
$349$			1.74185e6i			0.765506i	0.923851	+	0.382753i	$0.125024\pi$
$349$			1.74185e6i			0.765506i	−0.923851	+	0.382753i	$0.874976\pi$
$350$			349680.i			0.152581i
$351$	3.00578e6	+	1.02183e6i	1.30223	+	0.442702i
$352$	−1.46944e6	−	743044.i	−0.632116	−	0.319637i
$353$		−	2.80701e6i		−	1.19897i	−0.800387	−	0.599483i	$-0.795373\pi$
$353$		−	2.80701e6i		−	1.19897i	0.800387	−	0.599483i	$-0.204627\pi$
$354$	−163647.	−	372067.i	−0.0694063	−	0.157802i
$355$	−1.03804e6			−0.437162
$356$			770596.i			0.322256i
$357$	−545050.	−	1.23922e6i	−0.226342	−	0.514611i
$358$		−	1.47825e6i		−	0.609595i
$359$	−596226.			−0.244160			−0.122080	−	0.992520i	$-0.538956\pi$
$359$	−596226.			−0.244160			−0.122080	+	0.992520i	$0.538956\pi$
$360$	−2.11054e6	−	1.93512e6i	−0.858298	−	0.786959i
$361$	−1.05159e6			−0.424698
$362$	−2.64776e6			−1.06196
$363$	−2.17623e6	−	1.25172e6i	−0.866839	−	0.498588i
$364$	−1.71591e6			−0.678798
$365$	995853.			0.391258
$366$	−47700.9	−	108453.i	−0.0186133	−	0.0423192i
$367$	−3.46674e6			−1.34356			−0.671779	−	0.740752i	$-0.734470\pi$
$367$	−3.46674e6			−1.34356			−0.671779	+	0.740752i	$0.734470\pi$
$368$			1.64037e6i			0.631424i
$369$	2.91806e6	−	3.18258e6i	1.11565	−	1.21678i
$370$			1.32557e6i			0.503384i
$371$	−3.17480e6			−1.19752
$372$	1.16177e6	−	510982.i	0.435273	−	0.191447i
$373$			4.41525e6i			1.64317i	0.570085	+	0.821586i	$0.306910\pi$
$373$			4.41525e6i			1.64317i	−0.570085	+	0.821586i	$0.693090\pi$
$374$	−819237.	−	414258.i	−0.302852	−	0.153141i
$375$	1.00086e6	+	2.27556e6i	0.367533	+	0.835622i
$376$		−	3.97221e6i		−	1.44898i
$377$		−	1.11419e6i		−	0.403743i
$378$	2.71167e6	+	921848.i	0.976129	+	0.331841i
$379$	−2.65164e6			−0.948236			−0.474118	−	0.880461i	$-0.657233\pi$
$379$	−2.65164e6			−0.948236			−0.474118	+	0.880461i	$0.657233\pi$
$380$	−1.35944e6			−0.482950
$381$	1.62083e6	+	3.68510e6i	0.572036	+	1.30058i
$382$		−	1.93884e6i		−	0.679804i
$383$			1.60664e6i			0.559656i	0.960050	+	0.279828i	$0.0902774\pi$
$383$			1.60664e6i			0.559656i	−0.960050	+	0.279828i	$0.909723\pi$
$384$	293574.	−	129123.i	0.101599	−	0.0446864i
$385$	3.63423e6	+	1.83769e6i	1.24957	+	0.631861i
$386$			318907.i			0.108942i
$387$	1.40620e6	+	1.28932e6i	0.477277	+	0.437607i
$388$	−1.25417e6			−0.422938
$389$			243726.i			0.0816634i	0.999166	+	0.0408317i	$0.0130008\pi$
$389$			243726.i			0.0816634i	−0.999166	+	0.0408317i	$0.986999\pi$
$390$	−3.19661e6	+	1.40597e6i	−1.06421	+	0.468074i
$391$		−	1.71155e6i		−	0.566170i
$392$	−2.34072e6			−0.769368
$393$	−2.65343e6	+	1.16706e6i	−0.866615	+	0.381165i
$394$	4.05993e6			1.31758
$395$	−154915.			−0.0499576
$396$	−1.10267e6	+	415757.i	−0.353351	+	0.133230i
$397$	181651.			0.0578445			0.0289223	−	0.999582i	$-0.490792\pi$
$397$	181651.			0.0578445			0.0289223	+	0.999582i	$0.490792\pi$
$398$	−793496.			−0.251094
$399$	4.54071e6	−	1.99715e6i	1.42788	−	0.628026i
$400$	227206.			0.0710017
$401$		−	3.23285e6i		−	1.00398i	−0.864874	−	0.501989i	$-0.832602\pi$
$401$		−	3.23285e6i		−	1.00398i	0.864874	−	0.501989i	$-0.167398\pi$
$402$	−1.86821e6	+	821699.i	−0.576582	+	0.253599i
$403$		−	5.64669e6i		−	1.73193i
$404$	−293494.			−0.0894634
$405$	−3.52350e6	+	306137.i	−1.06742	+	0.0927423i
$406$		−	1.00517e6i		−	0.302638i
$407$	1.77603e6	+	898072.i	0.531452	+	0.268736i
$408$	−1.43898e6	+	632908.i	−0.427961	+	0.188231i
$409$			2.73058e6i			0.807135i	0.914950	+	0.403567i	$0.132230\pi$
$409$			2.73058e6i			0.807135i	−0.914950	+	0.403567i	$0.867770\pi$
$410$			4.74958e6i			1.39539i
$411$	−499225.	−	1.13504e6i	−0.145778	−	0.331440i
$412$	1.30923e6			0.379989
$413$	989919.			0.285578
$414$	2.66890e6	+	2.44707e6i	0.765301	+	0.701691i
$415$		−	1.91629e6i		−	0.546186i
$416$			3.43882e6i			0.974262i
$417$	−2.63207e6	−	5.98428e6i	−0.741238	−	1.68528i
$418$	1.51790e6	−	3.00181e6i	0.424916	−	0.840316i
$419$			2.32728e6i			0.647611i	0.946124	+	0.323805i	$0.104962\pi$
$419$			2.32728e6i			0.647611i	−0.946124	+	0.323805i	$0.895038\pi$
$420$	1.74982e6	−	769627.i	0.484028	−	0.212891i
$421$	2.07600e6			0.570851			0.285425	−	0.958401i	$-0.407865\pi$
$421$	2.07600e6			0.570851			0.285425	+	0.958401i	$0.407865\pi$
$422$		−	1.44430e6i		−	0.394799i
$423$	−3.61633e6	−	3.31575e6i	−0.982691	−	0.901013i
$424$			3.68656e6i			0.995879i
$425$	−237065.			−0.0636642
$426$	−485404.	−	1.10361e6i	−0.129592	−	0.294641i
$427$	288548.			0.0765859
$428$	1.39724e6			0.368690
$429$	−281948.	+	5.23542e6i	−0.0739649	+	1.37344i
$430$	−2.09857e6			−0.547333
$431$	−4.32285e6			−1.12092			−0.560462	−	0.828180i	$-0.689377\pi$
$431$	−4.32285e6			−1.12092			−0.560462	+	0.828180i	$0.689377\pi$
$432$	598973.	−	1.76191e6i	0.154418	−	0.454229i
$433$	−2.24130e6			−0.574488			−0.287244	−	0.957857i	$-0.592739\pi$
$433$	−2.24130e6			−0.574488			−0.287244	+	0.957857i	$0.592739\pi$
$434$		−	5.09417e6i		−	1.29822i
$435$	499740.	+	1.13621e6i	0.126626	+	0.287896i
$436$			400963.i			0.101015i
$437$	6.27137e6			1.57094
$438$	465678.	+	1.05876e6i	0.115985	+	0.263702i
$439$			771175.i			0.190982i	0.995430	+	0.0954908i	$0.0304421\pi$
$439$			771175.i			0.190982i	−0.995430	+	0.0954908i	$0.969558\pi$
$440$	2.13392e6	−	4.22004e6i	0.525467	−	1.03917i
$441$	−1.95389e6	+	2.13101e6i	−0.478413	+	0.521782i
$442$			1.91719e6i			0.466777i
$443$			4.38448e6i			1.06147i	0.847537	+	0.530737i	$0.178085\pi$
$443$			4.38448e6i			1.06147i	−0.847537	+	0.530737i	$0.821915\pi$
$444$	855130.	−	376113.i	0.205861	−	0.0905442i
$445$	−3.81945e6			−0.914325
$446$	−59228.0			−0.0140991
$447$	−884324.	+	388954.i	−0.209335	+	0.0920723i
$448$			5.76583e6i			1.35727i
$449$		−	6.62600e6i		−	1.55108i	−0.631295	−	0.775542i	$-0.717476\pi$
$449$		−	6.62600e6i		−	1.55108i	0.631295	−	0.775542i	$-0.282524\pi$
$450$	338942.	−	369668.i	0.0789031	−	0.0860558i
$451$	6.36358e6	+	3.21783e6i	1.47319	+	0.744940i
$452$		−	917324.i		−	0.211192i
$453$	−226179.	−	514240.i	−0.0517853	−	0.117739i
$454$	1.25785e6			0.286412
$455$		−	8.50488e6i		−	1.92593i
$456$	−2.31907e6	−	5.27264e6i	−0.522278	−	1.18745i
$457$			1.04547e6i			0.234164i	0.993122	+	0.117082i	$0.0373540\pi$
$457$			1.04547e6i			0.234164i	−0.993122	+	0.117082i	$0.962646\pi$
$458$	6.05997e6			1.34992
$459$	−624965.	+	1.83837e6i	−0.138460	+	0.407287i
$460$	2.41676e6			0.532523
$461$	4.96719e6			1.08857			0.544287	−	0.838899i	$-0.316800\pi$
$461$	4.96719e6			1.08857			0.544287	+	0.838899i	$0.316800\pi$
$462$	−254360.	+	4.72315e6i	−0.0554426	+	1.02950i
$463$	−3.13080e6			−0.678739			−0.339370	−	0.940653i	$-0.610214\pi$
$463$	−3.13080e6			−0.678739			−0.339370	+	0.940653i	$0.610214\pi$
$464$	−653109.			−0.140829
$465$	2.53268e6	+	5.75829e6i	0.543185	+	1.23498i
$466$	−298979.			−0.0637787
$467$			6.97533e6i			1.48004i	0.672587	+	0.740018i	$0.265183\pi$
$467$			6.97533e6i			1.48004i	−0.672587	+	0.740018i	$0.734817\pi$
$468$	1.81399e6	+	1.66321e6i	0.382842	+	0.351021i
$469$		−	4.97056e6i		−	1.04345i
$470$	5.39688e6			1.12693
$471$	930153.	−	409110.i	0.193198	−	0.0849744i
$472$		−	1.14949e6i		−	0.237492i
$473$	−1.42177e6	+	2.81170e6i	−0.292198	+	0.577852i
$474$	−72440.9	−	164702.i	−0.0148094	−	0.0336707i
$475$		−	868643.i		−	0.176647i
$476$		−	1.04947e6i		−	0.212301i
$477$	3.35627e6	+	3.07731e6i	0.675400	+	0.619263i
$478$	−1.71190e6			−0.342695
$479$	5.09382e6			1.01439			0.507194	−	0.861832i	$-0.330683\pi$
$479$	5.09382e6			1.01439			0.507194	+	0.861832i	$0.330683\pi$
$480$	−1.54239e6	−	3.50679e6i	−0.305557	−	0.694714i
$481$		−	4.15629e6i		−	0.819112i
$482$		−	104282.i		−	0.0204453i
$483$	−8.07226e6	+	3.55044e6i	−1.57445	+	0.692491i
$484$	−1.15359e6	−	1.56744e6i	−0.223840	−	0.304143i
$485$		−	6.21627e6i		−	1.19998i
$486$	−1.97312e6	−	3.60294e6i	−0.378934	−	0.691936i
$487$	7.86781e6			1.50325			0.751625	−	0.659590i	$-0.229270\pi$
$487$	7.86781e6			1.50325			0.751625	+	0.659590i	$0.229270\pi$
$488$		−	335060.i		−	0.0636903i
$489$	−4.33951e6	+	1.90865e6i	−0.820670	+	0.360957i
$490$		−	3.18025e6i		−	0.598371i
$491$	−8.05135e6			−1.50718			−0.753590	−	0.657345i	$-0.771680\pi$
$491$	−8.05135e6			−1.50718			−0.753590	+	0.657345i	$0.771680\pi$
$492$	3.06396e6	−	1.34763e6i	0.570651	−	0.250990i
$493$	681450.			0.126275
$494$	−7.02488e6			−1.29515
$495$	−2.06070e6	−	5.46536e6i	−0.378008	−	1.00255i
$496$	−3.30995e6			−0.604112
$497$	2.93627e6			0.533218
$498$	2.03735e6	−	896089.i	0.368122	−	0.161912i
$499$	−9.10103e6			−1.63621			−0.818106	−	0.575068i	$-0.804976\pi$
$499$	−9.10103e6			−1.63621			−0.818106	+	0.575068i	$0.804976\pi$
$500$			1.92712e6i			0.344733i
$501$	−6.46164e6	+	2.84203e6i	−1.15013	+	0.505865i
$502$			7.73309e6i			1.36960i
$503$	1.00620e6			0.177323			0.0886615	−	0.996062i	$-0.471741\pi$
$503$	1.00620e6			0.177323			0.0886615	+	0.996062i	$0.471741\pi$
$504$	5.97004e6	+	5.47383e6i	1.04689	+	0.959875i
$505$		−	1.45470e6i		−	0.253831i
$506$	−2.69846e6	+	5.33648e6i	−0.468533	+	0.926571i
$507$	4.72480e6	−	2.07812e6i	0.816326	−	0.359046i
$508$			3.12083e6i			0.536550i
$509$			2.93973e6i			0.502936i	0.967866	+	0.251468i	$0.0809134\pi$
$509$			2.93973e6i			0.502936i	−0.967866	+	0.251468i	$0.919087\pi$
$510$	−859908.	−	1.95508e6i	−0.146395	−	0.332843i
$511$	−2.81694e6			−0.477228
$512$	5.10857e6			0.861241
$513$	−6.73607e6	−	2.28997e6i	−1.13009	−	0.384181i
$514$		−	373715.i		−	0.0623925i
$515$			6.48916e6i			1.07813i
$516$	595439.	+	1.35379e6i	0.0984495	+	0.223834i
$517$	3.65638e6	−	7.23086e6i	0.601623	−	1.18977i
$518$		−	3.74961e6i		−	0.613991i
$519$	8.18069e6	−	3.59813e6i	1.33313	−	0.586352i
$520$	−9.87580e6			−1.60164
$521$			9.05577e6i			1.46161i	0.682587	+	0.730804i	$0.260855\pi$
$521$			9.05577e6i			1.46161i	−0.682587	+	0.730804i	$0.739145\pi$
$522$	−974299.	+	1.06262e6i	−0.156501	+	0.170688i
$523$		−	912191.i		−	0.145825i	−0.997338	−	0.0729124i	$-0.976771\pi$
$523$		−	912191.i		−	0.145825i	0.997338	−	0.0729124i	$-0.0232294\pi$
$524$	−2.24713e6			−0.357519
$525$	491768.	+	1.11808e6i	0.0778685	+	0.177042i
$526$	6.48028e6			1.02124
$527$	3.45358e6			0.541681
$528$	3.06888e6	+	165271.i	0.479065	+	0.0257995i
$529$	−4.71262e6			−0.732189
$530$	−5.00878e6			−0.774538
$531$	−1.04650e6	−	959520.i	−0.161066	−	0.147679i
$532$	3.84542e6			0.589067
$533$		−	1.48922e7i		−	2.27059i
$534$	−1.78604e6	−	4.06074e6i	−0.271043	−	0.616242i
$535$			6.92540e6i			1.04607i
$536$	−5.77177e6			−0.867755
$537$	−2.07892e6	−	4.72663e6i	−0.311102	−	0.707320i
$538$			1.49649e6i			0.222905i
$539$	−4.26096e6	−	2.15461e6i	−0.631736	−	0.319445i
$540$	−2.59583e6	−	882469.i	−0.383082	−	0.130231i
$541$			2.77036e6i			0.406952i	0.979080	+	0.203476i	$0.0652238\pi$
$541$			2.77036e6i			0.406952i	−0.979080	+	0.203476i	$0.934776\pi$
$542$		−	1.05258e7i		−	1.53907i
$543$	−8.46606e6	+	3.72364e6i	−1.23220	+	0.541961i
$544$	−2.10322e6			−0.304711
$545$	−1.98737e6			−0.286607
$546$	9.04215e6	−	3.97702e6i	1.29805	−	0.570922i
$547$			9.31603e6i			1.33126i	0.746282	+	0.665630i	$0.231837\pi$
$547$			9.31603e6i			1.33126i	−0.746282	+	0.665630i	$0.768163\pi$
$548$		−	961236.i		−	0.136735i
$549$	−305041.	−	279687.i	−0.0431945	−	0.0396043i
$550$	739151.	+	373761.i	0.104190	+	0.0526851i
$551$			2.49694e6i			0.350372i
$552$	4.12274e6	+	9.37345e6i	0.575888	+	1.30934i
$553$	438204.			0.0609346
$554$			8.84639e6i			1.22459i
$555$	1.86420e6	+	4.23844e6i	0.256898	+	0.584082i
$556$		−	5.06794e6i		−	0.695256i
$557$	109865.			0.0150045			0.00750225	−	0.999972i	$-0.497612\pi$
$557$	109865.			0.0150045			0.00750225	+	0.999972i	$0.497612\pi$
$558$	−4.93774e6	+	5.38535e6i	−0.671340	+	0.732198i
$559$	6.57999e6			0.890627
$560$	−4.98535e6			−0.671778
$561$	−3.20205e6	−	172443.i	−0.429557	−	0.0231333i
$562$	−531803.			−0.0710248
$563$	4.75207e6			0.631847			0.315924	−	0.948785i	$-0.397686\pi$
$563$	4.75207e6			0.631847			0.315924	+	0.948785i	$0.397686\pi$
$564$	−1.53129e6	−	3.48154e6i	−0.202703	−	0.460865i
$565$	4.54671e6			0.599206
$566$			9.13279e6i			1.19829i
$567$	9.96683e6	−	865960.i	1.30197	−	0.113120i
$568$		−	3.40957e6i		−	0.443434i
$569$	76851.0			0.00995105			0.00497552	−	0.999988i	$-0.498416\pi$
$569$	76851.0			0.00995105			0.00497552	+	0.999988i	$0.498416\pi$
$570$	7.16373e6	−	3.15083e6i	0.923532	−	0.406199i
$571$		−	9.51570e6i		−	1.22138i	−0.791870	−	0.610689i	$-0.790892\pi$
$571$		−	9.51570e6i		−	1.22138i	0.791870	−	0.610689i	$-0.209108\pi$
$572$	−1.83407e6	+	3.62707e6i	−0.234383	+	0.463517i
$573$	−2.72666e6	−	6.19933e6i	−0.346932	−	0.788784i
$574$		−	1.34350e7i		−	1.70199i
$575$			1.54423e6i			0.194780i
$576$	5.58876e6	−	6.09539e6i	0.701875	−	0.765501i
$577$	3.79444e6			0.474470			0.237235	−	0.971452i	$-0.423759\pi$
$577$	3.79444e6			0.474470			0.237235	+	0.971452i	$0.423759\pi$
$578$	5.16382e6			0.642912
$579$	448490.	+	1.01969e6i	0.0555976	+	0.126407i
$580$			962228.i			0.118770i
$581$			5.42055e6i			0.666198i
$582$	6.60897e6	−	2.90683e6i	0.808772	−	0.355724i
$583$	−3.39344e6	+	6.71087e6i	−0.413493	+	0.817726i
$584$			3.27101e6i			0.396872i
$585$	−8.24370e6	+	8.99101e6i	−0.995939	+	1.08622i
$586$	−3.90221e6			−0.469425
$587$		−	1.06797e7i		−	1.27927i	−0.768679	−	0.639635i	$-0.779085\pi$
$587$		−	1.06797e7i		−	1.27927i	0.768679	−	0.639635i	$-0.220915\pi$
$588$	−2.05158e6	+	902351.i	−0.244707	+	0.107630i
$589$			1.26545e7i			1.50299i
$590$	1.56176e6			0.184708
$591$	1.29814e7	−	5.70962e6i	1.52880	−	0.672417i
$592$	−2.43632e6			−0.285713
$593$	1.56261e6			0.182480			0.0912400	−	0.995829i	$-0.470917\pi$
$593$	1.56261e6			0.182480			0.0912400	+	0.995829i	$0.470917\pi$
$594$	4.84700e6	−	4.74657e6i	0.563647	−	0.551968i
$595$	5.20169e6			0.602354
$596$	−748913.			−0.0863606
$597$	−2.53716e6	+	1.11592e6i	−0.291348	+	0.128144i
$598$	1.24885e7			1.42810
$599$		−	8.24346e6i		−	0.938734i	−0.883003	−	0.469367i	$-0.844482\pi$
$599$		−	8.24346e6i		−	0.938734i	0.883003	−	0.469367i	$-0.155518\pi$
$600$	1.29831e6	−	571037.i	0.147231	−	0.0647569i
$601$		−	3.24701e6i		−	0.366689i	−0.983049	−	0.183344i	$-0.941308\pi$
$601$		−	3.24701e6i		−	0.366689i	0.983049	−	0.183344i	$-0.0586923\pi$
$602$	5.93616e6			0.667597
$603$	−4.81792e6	+	5.25467e6i	−0.539593	+	0.588507i
$604$		−	435497.i		−	0.0485728i
$605$	7.76900e6	−	5.71775e6i	0.862933	−	0.635092i
$606$	1.54660e6	−	680242.i	0.171078	−	0.0752457i
$607$		−	4.58595e6i		−	0.505194i	−0.967572	−	0.252597i	$-0.918715\pi$
$607$		−	4.58595e6i		−	0.505194i	0.967572	−	0.252597i	$-0.0812846\pi$
$608$		−	7.70653e6i		−	0.845474i
$609$	−1.41360e6	−	3.21396e6i	−0.154449	−	0.351154i
$610$	455233.			0.0495347
$611$	−1.69218e7			−1.83376
$612$	−1.01724e6	+	1.10946e6i	−0.109786	+	0.119738i
$613$		−	1.50334e7i		−	1.61587i	−0.589274	−	0.807933i	$-0.700586\pi$
$613$		−	1.50334e7i		−	1.61587i	0.589274	−	0.807933i	$-0.299414\pi$
$614$			9.92257e6i			1.06219i
$615$	6.67950e6	+	1.51865e7i	0.712125	+	1.61909i
$616$	−6.03615e6	+	1.19371e7i	−0.640926	+	1.26750i
$617$			1.03976e7i			1.09956i	0.835308	+	0.549782i	$0.185289\pi$
$617$			1.03976e7i			1.09956i	−0.835308	+	0.549782i	$0.814711\pi$
$618$	−6.89910e6	+	3.03444e6i	−0.726643	+	0.319601i
$619$	7.96319e6			0.835335			0.417667	−	0.908600i	$-0.362848\pi$
$619$	7.96319e6			0.835335			0.417667	+	0.908600i	$0.362848\pi$
$620$			4.87656e6i			0.509489i
$621$	1.19751e7	+	4.07100e6i	1.24609	+	0.423616i
$622$			9.11704e6i			0.944883i
$623$	1.08040e7			1.11523
$624$	−2.58408e6	−	5.87516e6i	−0.265671	−	0.604030i
$625$	−1.09970e7			−1.12609
$626$	−1.09867e7			−1.12055
$627$	631857.	−	1.17328e7i	0.0641874	−	1.19188i
$628$	787724.			0.0797031
$629$	2.54204e6			0.256186
$630$	−7.43708e6	+	8.11126e6i	−0.746536	+	0.814211i
$631$	−3.40838e6			−0.340780			−0.170390	−	0.985377i	$-0.554503\pi$
$631$	−3.40838e6			−0.340780			−0.170390	+	0.985377i	$0.554503\pi$
$632$		−	508839.i		−	0.0506743i
$633$	−2.03117e6	−	4.61807e6i	−0.201483	−	0.458090i
$634$		−	264788.i		−	0.0261622i
$635$	−1.54684e7			−1.52233
$636$	1.42117e6	+	3.23118e6i	0.139317	+	0.316751i
$637$			9.97156e6i			0.973677i
$638$	−2.12471e6	−	1.07439e6i	−0.206656	−	0.104498i
$639$	−3.10410e6	−	2.84610e6i	−0.300735	−	0.275739i
$640$			1.23229e6i			0.118922i
$641$			3.31964e6i			0.319114i	0.987189	+	0.159557i	$0.0510066\pi$
$641$			3.31964e6i			0.319114i	−0.987189	+	0.159557i	$0.948993\pi$
$642$	−7.36290e6	+	3.23844e6i	−0.705036	+	0.310097i
$643$	1.41646e6			0.135107			0.0675534	−	0.997716i	$-0.478481\pi$
$643$	1.41646e6			0.135107			0.0675534	+	0.997716i	$0.478481\pi$
$644$	−6.83621e6			−0.649532
$645$	−6.71005e6	+	2.95129e6i	−0.635077	+	0.279327i
$646$		−	4.29650e6i		−	0.405074i
$647$		−	1.40678e7i		−	1.32119i	−0.750742	−	0.660596i	$-0.770304\pi$
$647$		−	1.40678e7i		−	1.32119i	0.750742	−	0.660596i	$-0.229696\pi$
$648$	−1.00555e6	−	1.15734e7i	−0.0940729	−	1.08274i
$649$	1.05809e6	−	2.09248e6i	0.0986078	−	0.195007i
$650$		−	1.72977e6i		−	0.160585i
$651$	−7.16412e6	−	1.62883e7i	−0.662537	−	1.50634i
$652$	−3.67503e6			−0.338565
$653$			1.38283e6i			0.126907i	0.997985	+	0.0634535i	$0.0202114\pi$
$653$			1.38283e6i			0.126907i	−0.997985	+	0.0634535i	$0.979789\pi$
$654$	−929326.	−	2.11291e6i	−0.0849618	−	0.193169i
$655$		−	1.11379e7i		−	1.01438i
$656$	−8.72942e6			−0.792001
$657$	2.97795e6	+	2.73044e6i	0.269156	+	0.246785i
$658$	−1.52660e7			−1.37455
$659$	9.61639e6			0.862578			0.431289	−	0.902214i	$-0.358059\pi$
$659$	9.61639e6			0.862578			0.431289	+	0.902214i	$0.358059\pi$
$660$	243494.	−	4.52139e6i	0.0217585	−	0.404028i
$661$	−3.17414e6			−0.282568			−0.141284	−	0.989969i	$-0.545123\pi$
$661$	−3.17414e6			−0.282568			−0.141284	+	0.989969i	$0.545123\pi$
$662$	−6.16719e6			−0.546943
$663$	2.69621e6	+	6.13011e6i	0.238216	+	0.541607i
$664$	6.29431e6			0.554023
$665$			1.90598e7i			1.67134i
$666$	−3.63446e6	+	3.96393e6i	−0.317508	+	0.346291i
$667$		−	4.43894e6i		−	0.386336i
$668$	−5.47221e6			−0.474484
$669$	−189378.	+	83294.5i	−0.0163593	+	0.00719534i
$670$		−	7.84188e6i		−	0.674891i
$671$	308420.	−	609931.i	0.0264445	−	0.0522967i
$672$	4.36293e6	+	9.91955e6i	0.372696	+	0.847361i
$673$			6.37989e6i			0.542969i	0.962443	+	0.271485i	$0.0875146\pi$
$673$			6.37989e6i			0.542969i	−0.962443	+	0.271485i	$0.912485\pi$
$674$		−	6.21113e6i		−	0.526649i
$675$	563871.	−	1.65866e6i	0.0476343	−	0.140119i
$676$	4.00132e6			0.336772
$677$	2.33822e6			0.196071			0.0980356	−	0.995183i	$-0.468744\pi$
$677$	2.33822e6			0.196071			0.0980356	+	0.995183i	$0.468744\pi$
$678$	2.12612e6	+	4.83394e6i	0.177629	+	0.403856i
$679$			1.75838e7i			1.46365i
$680$		−	6.04016e6i		−	0.500929i
$681$	4.02191e6	−	1.76896e6i	0.332327	−	0.146168i
$682$	−1.07680e7	−	5.44499e6i	−0.886492	−	0.448266i
$683$			1.64219e7i			1.34701i	0.739183	+	0.673505i	$0.235212\pi$
$683$			1.64219e7i			1.34701i	−0.739183	+	0.673505i	$0.764788\pi$
$684$	−4.06522e6	−	3.72733e6i	−0.332234	−	0.304619i
$685$	4.76435e6			0.387952
$686$		−	3.71179e6i		−	0.301143i
$687$	1.93764e7	−	8.52235e6i	1.56632	−	0.688918i
$688$		−	3.85703e6i		−	0.310658i
$689$	1.57049e7			1.26034
$690$	−1.27354e7	+	5.60141e6i	−1.01833	+	0.447893i
$691$	−8.80612e6			−0.701600			−0.350800	−	0.936450i	$-0.614090\pi$
$691$	−8.80612e6			−0.701600			−0.350800	+	0.936450i	$0.614090\pi$
$692$	6.92803e6			0.549977
$693$	5.82903e6	+	1.54597e7i	0.461066	+	1.22284i
$694$	1.86554e7			1.47030
$695$	2.51192e7			1.97262
$696$	−3.73203e6	+	1.64146e6i	−0.292026	+	0.128442i
$697$	9.10823e6			0.710153
$698$		−	7.77338e6i		−	0.603909i
$699$	−955967.	+	420464.i	−0.0740031	+	0.0325489i
$700$			946877.i			0.0730380i
$701$	−1.86560e7			−1.43392			−0.716958	−	0.697117i	$-0.754466\pi$
$701$	−1.86560e7			−1.43392			−0.716958	+	0.697117i	$0.754466\pi$
$702$	−1.34139e7	−	4.56013e6i	−1.02733	−	0.349249i
$703$			9.31442e6i			0.710833i
$704$	1.21878e7	+	6.16290e6i	0.926813	+	0.468655i
$705$	1.72562e7	−	7.58983e6i	1.30759	−	0.575121i
$706$			1.25268e7i			0.945867i
$707$			4.11486e6i			0.309604i
$708$	−443129.	−	1.00750e6i	−0.0332236	−	0.0755371i
$709$	−1.00665e7			−0.752076			−0.376038	−	0.926604i	$-0.622714\pi$
$709$	−1.00665e7			−0.752076			−0.376038	+	0.926604i	$0.622714\pi$
$710$	4.63245e6			0.344878
$711$	−463251.	−	424747.i	−0.0343671	−	0.0315106i
$712$		−	1.25455e7i		−	0.927444i
$713$		−	2.24965e7i		−	1.65726i
$714$	2.43240e6	+	5.53029e6i	0.178562	+	0.405978i
$715$	−1.79775e7	−	9.09057e6i	−1.31512	−	0.665007i
$716$		−	4.00287e6i		−	0.291803i
$717$	−5.47369e6	+	2.40750e6i	−0.397633	+	0.174892i
$718$	2.66078e6			0.192618
$719$		−	8.33326e6i		−	0.601164i	−0.953756	−	0.300582i	$-0.902819\pi$
$719$		−	8.33326e6i		−	0.601164i	0.953756	−	0.300582i	$-0.0971809\pi$
$720$	5.27031e6	+	4.83226e6i	0.378883	+	0.347391i
$721$		−	1.83557e7i		−	1.31502i
$722$	4.69296e6			0.335045
$723$	−146656.	−	333437.i	−0.0104341	−	0.0237229i
$724$	−7.16971e6			−0.508341
$725$	−614834.			−0.0434423
$726$	9.71187e6	+	5.58608e6i	0.683851	+	0.393337i
$727$	1.38279e7			0.970333			0.485167	−	0.874422i	$-0.338759\pi$
$727$	1.38279e7			0.970333			0.485167	+	0.874422i	$0.338759\pi$
$728$	2.79354e7			1.95356
$729$	−1.13759e7	−	8.74530e6i	−0.792805	−	0.609475i
$730$	−4.44420e6			−0.308664
$731$			4.02440e6i			0.278553i
$732$	−129166.	−	293672.i	−0.00890987	−	0.0202574i
$733$			1.35485e7i			0.931390i	0.884945	+	0.465695i	$0.154196\pi$
$733$			1.35485e7i			0.931390i	−0.884945	+	0.465695i	$0.845804\pi$
$734$	1.54710e7			1.05994
$735$	−4.47249e6	−	1.01687e7i	−0.305373	−	0.694296i
$736$			1.37003e7i			0.932258i
$737$	−1.05067e7	−	5.31286e6i	−0.712522	−	0.360296i
$738$	−1.30224e7	+	1.42029e7i	−0.880138	+	0.959924i
$739$			1.17902e7i			0.794164i	0.917783	+	0.397082i	$0.129977\pi$
$739$			1.17902e7i			0.794164i	−0.917783	+	0.397082i	$0.870023\pi$
$740$			3.58944e6i			0.240961i
$741$	−2.24617e7	+	9.87934e6i	−1.50278	+	0.660971i
$742$	1.41682e7			0.944724
$743$	1.50901e6			0.100281			0.0501407	−	0.998742i	$-0.484033\pi$
$743$	1.50901e6			0.100281			0.0501407	+	0.998742i	$0.484033\pi$
$744$	−1.89139e7	+	8.31892e6i	−1.25270	+	0.550979i
$745$		−	3.71198e6i		−	0.245028i
$746$		−	1.97039e7i		−	1.29630i
$747$	5.25409e6	−	5.73039e6i	0.344506	−	0.375736i
$748$	−2.21836e6	−	1.12174e6i	−0.144970	−	0.0733059i
$749$		−	1.95897e7i		−	1.27592i
$750$	−4.46655e6	−	1.01551e7i	−0.289947	−	0.659224i
$751$	1.29385e7			0.837112			0.418556	−	0.908191i	$-0.362536\pi$
$751$	1.29385e7			0.837112			0.418556	+	0.908191i	$0.362536\pi$
$752$			9.91913e6i			0.639630i
$753$	1.08753e7	+	2.47261e7i	0.698964	+	1.58916i
$754$			4.97229e6i			0.318513i
$755$	2.15854e6			0.137814
$756$	7.34276e6	+	2.49621e6i	0.467256	+	0.158846i
$757$	−2.29160e7			−1.45345			−0.726724	−	0.686929i	$-0.758958\pi$
$757$	−2.29160e7			−1.45345			−0.726724	+	0.686929i	$0.758958\pi$
$758$	1.18335e7			0.748065
$759$	−1.12329e6	+	2.08580e7i	−0.0707760	+	1.31422i
$760$	2.21321e7			1.38991
$761$	−2.50919e7			−1.57062			−0.785311	−	0.619101i	$-0.787497\pi$
$761$	−2.50919e7			−1.57062			−0.785311	+	0.619101i	$0.787497\pi$
$762$	−7.23326e6	−	1.64455e7i	−0.451281	−	1.02603i
$763$	5.62161e6			0.349582
$764$		−	5.25007e6i		−	0.325410i
$765$	−5.49901e6	−	5.04195e6i	−0.339728	−	0.311491i
$766$		−	7.16995e6i		−	0.441513i
$767$	−4.89686e6			−0.300559
$768$	1.42293e7	−	6.25849e6i	0.870523	−	0.382883i
$769$		−	4.73793e6i		−	0.288917i	−0.989511	−	0.144458i	$-0.953856\pi$
$769$		−	4.73793e6i		−	0.288917i	0.989511	−	0.144458i	$-0.0461440\pi$
$770$	−1.62185e7	−	8.20108e6i	−0.985787	−	0.498476i
$771$	−525568.	−	1.19493e6i	−0.0318415	−	0.0723947i
$772$			863548.i			0.0521487i
$773$		−	2.64966e6i		−	0.159493i	−0.996815	−	0.0797466i	$-0.974589\pi$
$773$		−	2.64966e6i		−	0.159493i	0.996815	−	0.0797466i	$-0.0254111\pi$
$774$	−6.27546e6	−	5.75386e6i	−0.376525	−	0.345229i
$775$	−3.11597e6			−0.186354
$776$	2.04182e7			1.21720
$777$	−5.27321e6	−	1.19892e7i	−0.313345	−	0.712420i
$778$		−	1.08768e6i		−	0.0644245i
$779$			3.33739e7i			1.97044i
$780$	−8.65589e6	+	3.80713e6i	−0.509419	+	0.224059i
$781$	3.13848e6	−	6.20666e6i	0.184116	−	0.364108i
$782$			7.63813e6i			0.446653i
$783$	−1.62086e6	+	4.76786e6i	−0.0944804	+	0.277920i
$784$	5.84509e6			0.339626
$785$			3.90435e6i			0.226138i
$786$	1.18415e7	−	5.20825e6i	0.683675	−	0.300702i
$787$			6.36462e6i			0.366299i	0.983085	+	0.183150i	$0.0586292\pi$
$787$			6.36462e6i			0.366299i	−0.983085	+	0.183150i	$0.941371\pi$
$788$	1.09936e7			0.630703
$789$	2.07203e7	−	9.11345e6i	1.18496	−	0.521183i
$790$	691340.			0.0394116
$791$	−1.28611e7			−0.730867
$792$	1.79517e7	−	6.76863e6i	1.01693	−	0.383431i
$793$	−1.42737e6			−0.0806035
$794$	−810656.			−0.0456337
$795$	−1.60153e7	+	7.04403e6i	−0.898705	+	0.395279i
$796$	−2.14866e6			−0.120195
$797$			2.74248e7i			1.52932i	0.644436	+	0.764658i	$0.277092\pi$
$797$			2.74248e7i			1.52932i	−0.644436	+	0.764658i	$0.722908\pi$
$798$	−2.02638e7	+	8.91267e6i	−1.12646	+	0.495451i
$799$		−	1.03496e7i		−	0.573529i
$800$	1.89762e6			0.104830
$801$	−1.14215e7	−	1.04722e7i	−0.628988	−	0.576709i
$802$			1.44272e7i			0.792040i
$803$	−3.01093e6	+	5.95443e6i	−0.164783	+	0.325875i
$804$	−5.05881e6	+	2.22503e6i	−0.276000	+	0.121393i
$805$		−	3.38836e7i		−	1.84289i
$806$			2.51995e7i			1.36633i
$807$	2.10457e6	+	4.78495e6i	0.113758	+	0.258639i
$808$	4.77815e6			0.257473
$809$	−8.49113e6			−0.456136			−0.228068	−	0.973645i	$-0.573241\pi$
$809$	−8.49113e6			−0.456136			−0.228068	+	0.973645i	$0.573241\pi$
$810$	1.57243e7	−	1.36620e6i	0.842093	−	0.0731646i
$811$			1.66787e7i			0.890452i	0.895418	+	0.445226i	$0.146877\pi$
$811$			1.66787e7i			0.890452i	−0.895418	+	0.445226i	$0.853123\pi$
$812$		−	2.72183e6i		−	0.144867i
$813$	−1.48028e7	−	3.36557e7i	−0.785450	−	1.78580i
$814$	−7.92589e6	−	4.00783e6i	−0.419264	−	0.212006i
$815$		−	1.82153e7i		−	0.960597i
$816$	3.59332e6	−	1.58046e6i	0.188917	−	0.0830915i
$817$	−1.47460e7			−0.772894
$818$		−	1.21858e7i		−	0.636750i
$819$	2.33187e7	−	2.54326e7i	1.21477	−	1.32489i
$820$			1.28611e7i			0.667948i
$821$	−2.77497e7			−1.43681			−0.718406	−	0.695625i	$-0.755128\pi$
$821$	−2.77497e7			−1.43681			−0.718406	+	0.695625i	$0.755128\pi$
$822$	2.22789e6	+	5.06533e6i	0.115004	+	0.261474i
$823$	1.20865e7			0.622018			0.311009	−	0.950407i	$-0.399333\pi$
$823$	1.20865e7			0.622018			0.311009	+	0.950407i	$0.399333\pi$
$824$	−2.13145e7			−1.09360
$825$	2.88903e6	+	155585.i	0.147780	+	0.00795855i
$826$	−4.41772e6			−0.225293
$827$	−2.83484e7			−1.44133			−0.720667	−	0.693281i	$-0.756164\pi$
$827$	−2.83484e7			−1.44133			−0.720667	+	0.693281i	$0.756164\pi$
$828$	7.22696e6	+	6.62628e6i	0.366336	+	0.335887i
$829$	3.06974e7			1.55137			0.775685	−	0.631120i	$-0.217404\pi$
$829$	3.06974e7			1.55137			0.775685	+	0.631120i	$0.217404\pi$
$830$			8.55183e6i			0.430887i
$831$	1.24410e7	+	2.82858e7i	0.624960	+	1.42091i
$832$		−	2.85220e7i		−	1.42847i
$833$	−6.09873e6			−0.304528
$834$	1.17462e7	+	2.67061e7i	0.584764	+	1.32952i
$835$		−	2.71230e7i		−	1.34624i
$836$	4.11024e6	−	8.12841e6i	0.203400	−	0.402244i
$837$	−8.21452e6	+	2.41635e7i	−0.405292	+	1.19219i
$838$		−	1.03860e7i		−	0.510901i
$839$			150471.i			0.00737987i	0.999993	+	0.00368993i	$0.00117454\pi$
$839$			150471.i			0.00737987i	−0.999993	+	0.00368993i	$0.998825\pi$
$840$	−2.84875e7	+	1.25297e7i	−1.39302	+	0.612693i
$841$	−1.87438e7			−0.913834
$842$	−9.26458e6			−0.450345
$843$	−1.70041e6	+	747893.i	−0.0824108	+	0.0362469i
$844$		−	3.91093e6i		−	0.188984i
$845$			1.98325e7i			0.955511i
$846$	1.61386e7	+	1.47972e7i	0.775247	+	0.710811i
$847$	−2.19760e7	+	1.61736e7i	−1.05254	+	0.774639i
$848$		−	9.20582e6i		−	0.439615i
$849$	1.28438e7	+	2.92016e7i	0.611538	+	1.39039i
$850$	1.05795e6			0.0502248
$851$		−	1.65588e7i		−	0.783798i
$852$	−1.31439e6	−	2.98840e6i	−0.0620336	−	0.141039i
$853$			1.36865e7i			0.644048i	0.946731	+	0.322024i	$0.104363\pi$
$853$			1.36865e7i			0.644048i	−0.946731	+	0.322024i	$0.895637\pi$
$854$	−1.28771e6			−0.0604188
$855$	1.84745e7	−	2.01492e7i	0.864285	−	0.942633i
$856$	−2.27474e7			−1.06108
$857$	−1.37392e7			−0.639013			−0.319507	−	0.947584i	$-0.603517\pi$
$857$	−1.37392e7			−0.639013			−0.319507	+	0.947584i	$0.603517\pi$
$858$	1.25825e6	−	2.33641e7i	0.0583511	−	1.08351i
$859$	−2.18827e7			−1.01186			−0.505928	−	0.862576i	$-0.668850\pi$
$859$	−2.18827e7			−1.01186			−0.505928	+	0.862576i	$0.668850\pi$
$860$	−5.68258e6			−0.261999
$861$	−1.88941e7	−	4.29576e7i	−0.868598	−	1.97484i
$862$	1.92916e7			0.884300
$863$		−	8.18461e6i		−	0.374086i	−0.982352	−	0.187043i	$-0.940110\pi$
$863$		−	8.18461e6i		−	0.374086i	0.982352	−	0.187043i	$-0.0598903\pi$
$864$	5.00262e6	−	1.47155e7i	0.227989	−	0.670641i
$865$			3.43387e7i			1.56043i
$866$	1.00023e7			0.453215
$867$	1.65110e7	−	7.26207e6i	0.745978	−	0.328105i
$868$		−	1.37942e7i		−	0.621437i
$869$	468381.	−	926272.i	0.0210402	−	0.0416092i
$870$	−2.23019e6	−	5.07056e6i	−0.0998951	−	0.227121i
$871$			2.45880e7i			1.09819i
$872$		−	6.52777e6i		−	0.290719i
$873$	1.70438e7	−	1.85889e7i	0.756887	−	0.825500i
$874$	−2.79873e7			−1.23932
$875$	2.70187e7			1.19301
$876$	1.26098e6	+	2.86696e6i	0.0555198	+	0.126230i
$877$			1.11241e7i			0.488387i	0.969727	+	0.244194i	$0.0785232\pi$
$877$			1.11241e7i			0.488387i	−0.969727	+	0.244194i	$0.921477\pi$
$878$		−	3.44153e6i		−	0.150666i
$879$	−1.24771e7	+	5.48781e6i	−0.544679	+	0.239567i
$880$	−5.32867e6	+	1.05380e7i	−0.231960	+	0.458724i
$881$			4.13547e7i			1.79509i	0.440926	+	0.897544i	$0.354650\pi$
$881$			4.13547e7i			1.79509i	−0.440926	+	0.897544i	$0.645350\pi$
$882$	8.71962e6	−	9.51007e6i	0.377421	−	0.411635i
$883$	6.49069e6			0.280149			0.140074	−	0.990141i	$-0.455266\pi$
$883$	6.49069e6			0.280149			0.140074	+	0.990141i	$0.455266\pi$
$884$			5.19144e6i			0.223438i
$885$	4.99365e6	−	2.19636e6i	0.214318	−	0.0942640i
$886$		−	1.95667e7i		−	0.837399i
$887$	2.55265e7			1.08939			0.544693	−	0.838636i	$-0.316646\pi$
$887$	2.55265e7			1.08939			0.544693	+	0.838636i	$0.316646\pi$
$888$	−1.39217e7	+	6.12321e6i	−0.592462	+	0.260584i
$889$	4.37549e7			1.85683
$890$	1.70451e7			0.721313
$891$	8.82274e6	−	2.19934e7i	0.372314	−	0.928107i
$892$	−160380.			−0.00674898
$893$	3.79224e7			1.59135
$894$	3.94648e6	−	1.73579e6i	0.165145	−	0.0726361i
$895$	1.98402e7			0.827920
$896$		−	3.48573e6i		−	0.145052i
$897$	3.99313e7	−	1.75630e7i	1.65704	−	0.728818i
$898$			2.95699e7i			1.22365i
$899$	8.95696e6			0.369625
$900$	917800.	−	1.00100e6i	0.0377695	−	0.0411934i
$901$			9.60530e6i			0.394184i
$902$	−2.83988e7	−	1.43602e7i	−1.16221	−	0.587685i
$903$	1.89805e7	−	8.34823e6i	0.774620	−	0.340702i
$904$			1.49343e7i			0.607803i
$905$		−	3.55366e7i		−	1.44230i
$906$	1.00937e6	+	2.29490e6i	0.0408535	+	0.0928845i
$907$	−2.07306e7			−0.836748			−0.418374	−	0.908275i	$-0.637400\pi$
$907$	−2.07306e7			−0.836748			−0.418374	+	0.908275i	$0.637400\pi$
$908$	3.40606e6			0.137100
$909$	3.98850e6	−	4.35007e6i	0.160103	−	0.174617i
$910$			3.79547e7i			1.51937i
$911$			2.89435e7i			1.15546i	0.816228	+	0.577730i	$0.196061\pi$
$911$			2.89435e7i			1.15546i	−0.816228	+	0.577730i	$0.803939\pi$
$912$	5.79103e6	+	1.31665e7i	0.230552	+	0.524182i
$913$	1.14579e7	+	5.79385e6i	0.454914	+	0.230033i
$914$		−	4.66561e6i		−	0.184732i
$915$	1.45558e6	−	640211.i	0.0574757	−	0.0252796i
$916$	1.64094e7			0.646181
$917$			3.15054e7i			1.23726i
$918$	2.78903e6	−	8.20410e6i	0.109231	−	0.321310i
$919$		−	2.28240e7i		−	0.891462i	−0.895167	−	0.445731i	$-0.852944\pi$
$919$		−	2.28240e7i		−	0.891462i	0.895167	−	0.445731i	$-0.147056\pi$
$920$	−3.93454e7			−1.53258
$921$	1.39545e7	+	3.17268e7i	0.542081	+	1.23247i
$922$	−2.21671e7			−0.858779
$923$	−1.45249e7			−0.561189
$924$	−688765.	+	1.27895e7i	−0.0265394	+	0.492804i
$925$	−2.29354e6			−0.0881357
$926$	1.39718e7			0.535459
$927$	−1.77920e7	+	1.94049e7i	−0.680027	+	0.741673i
$928$	−5.45477e6			−0.207925
$929$		−	3.70762e7i		−	1.40947i	−0.709470	−	0.704736i	$-0.751066\pi$
$929$		−	3.70762e7i		−	1.40947i	0.709470	−	0.704736i	$-0.248934\pi$
$930$	−1.13026e7	−	2.56976e7i	−0.428520	−	0.974282i
$931$		−	2.23467e7i		−	0.844965i
$932$	−809586.			−0.0305297
$933$	1.28216e7	+	2.91512e7i	0.482213	+	1.09636i
$934$		−	3.11288e7i		−	1.16760i
$935$	5.55991e6	−	1.09953e7i	0.207988	−	0.411318i
$936$	−2.95322e7	−	2.70775e7i	−1.10181	−	1.01023i
$937$		−	4.38476e7i		−	1.63154i	−0.578379	−	0.815768i	$-0.696315\pi$
$937$		−	4.38476e7i		−	1.63154i	0.578379	−	0.815768i	$-0.303685\pi$
$938$			2.21821e7i			0.823182i
$939$	−3.51293e7	+	1.54510e7i	−1.30018	+	0.571862i
$940$	1.46139e7			0.539444
$941$	1.41203e6			0.0519841			0.0259920	−	0.999662i	$-0.491726\pi$
$941$	1.41203e6			0.0519841			0.0259920	+	0.999662i	$0.491726\pi$
$942$	−4.15100e6	+	1.82574e6i	−0.152414	+	0.0670365i
$943$		−	5.93307e7i		−	2.17270i
$944$			2.87042e6i			0.104837i
$945$	−1.23725e7	+	3.63943e7i	−0.450689	+	1.32573i
$946$	6.34496e6	−	1.25478e7i	0.230516	−	0.455869i
$947$		−	2.01772e7i		−	0.731115i	−0.930789	−	0.365557i	$-0.880878\pi$
$947$		−	2.01772e7i		−	0.731115i	0.930789	−	0.365557i	$-0.119122\pi$
$948$	−196158.	−	445985.i	−0.00708901	−	0.0161176i
$949$	1.39346e7			0.502262
$950$			3.87649e6i			0.139357i
$951$	−372381.	−	846644.i	−0.0133517	−	0.0303563i
$952$			1.70856e7i			0.610996i
$953$	1.48197e6			0.0528577			0.0264289	−	0.999651i	$-0.491586\pi$
$953$	1.48197e6			0.0528577			0.0264289	+	0.999651i	$0.491586\pi$
$954$	−1.49780e7	−	1.37331e7i	−0.532824	−	0.488538i
$955$	2.60219e7			0.923274
$956$	−4.63554e6			−0.164042
$957$	−8.30459e6	−	447235.i	−0.293115	−	0.0157854i
$958$	−2.27322e7			−0.800253
$959$	−1.34768e7			−0.473195
$960$	1.27928e7	+	2.90857e7i	0.448010	+	1.01860i
$961$	1.67646e7			0.585580
$962$			1.85483e7i			0.646199i
$963$	−1.89881e7	+	2.07094e7i	−0.659806	+	0.719618i
$964$		−	282380.i		−	0.00978681i
$965$	−4.28017e6			−0.147959
$966$	3.60241e7	−	1.58445e7i	1.24208	−	0.546307i
$967$			3.24697e7i			1.11664i	0.829626	+	0.558319i	$0.188553\pi$
$967$			3.24697e7i			1.11664i	−0.829626	+	0.558319i	$0.811447\pi$
$968$	1.87807e7	+	2.55183e7i	0.644204	+	0.875314i
$969$	−6.04233e6	−	1.37378e7i	−0.206726	−	0.470012i
$970$			2.77414e7i			0.946670i
$971$		−	4.12664e6i		−	0.140459i	−0.997531	−	0.0702293i	$-0.977627\pi$
$971$		−	4.12664e6i		−	0.140459i	0.997531	−	0.0702293i	$-0.0223731\pi$
$972$	−5.34290e6	−	9.75616e6i	−0.181389	−	0.331218i
$973$	−7.10540e7			−2.40606
$974$	−3.51117e7			−1.18592
$975$	−2.43264e6	−	5.53085e6i	−0.0819534	−	0.186329i
$976$			836690.i			0.0281151i
$977$		−	5.18080e7i		−	1.73644i	−0.496177	−	0.868221i	$-0.665263\pi$
$977$		−	5.18080e7i		−	1.73644i	0.496177	−	0.868221i	$-0.334737\pi$
$978$	1.93660e7	−	8.51776e6i	0.647429	−	0.284759i
$979$	1.15480e7	−	2.28373e7i	0.385079	−	0.761533i
$980$		−	8.61159e6i		−	0.286430i
$981$	−5.94293e6	−	5.44898e6i	−0.197164	−	0.180777i
$982$	3.59308e7			1.18902
$983$			1.81166e7i			0.597990i	0.954255	+	0.298995i	$0.0966514\pi$
$983$			1.81166e7i			0.597990i	−0.954255	+	0.298995i	$0.903349\pi$
$984$	−4.98821e7	+	2.19397e7i	−1.64232	+	0.722342i
$985$			5.44898e7i			1.78947i
$986$	−3.04111e6			−0.0996185
$987$	−4.88122e7	+	2.14691e7i	−1.59491	+	0.701491i
$988$	−1.90222e7			−0.619968
$989$	2.62148e7			0.852229
$990$	9.19627e6	+	2.43903e7i	0.298211	+	0.790913i
$991$	−1.89585e7			−0.613224			−0.306612	−	0.951835i	$-0.599195\pi$
$991$	−1.89585e7			−0.613224			−0.306612	+	0.951835i	$0.599195\pi$
$992$	−2.76447e7			−0.891934
$993$	−1.97192e7	+	8.67314e6i	−0.634624	+	0.279128i
$994$	−1.31037e7			−0.420656
$995$		−	1.06498e7i		−	0.341023i
$996$	5.51680e6	−	2.42646e6i	0.176213	−	0.0775042i
$997$		−	3.68727e6i		−	0.117481i	−0.998273	−	0.0587405i	$-0.981292\pi$
$997$		−	3.68727e6i		−	0.117481i	0.998273	−	0.0587405i	$-0.0187084\pi$
$998$	4.06152e7			1.29081
$999$	−6.04637e6	+	1.77857e7i	−0.191682	+	0.563843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.d.b.32.6	yes	16
3.2	odd	2	inner	33.6.d.b.32.11	yes	16
11.10	odd	2	inner	33.6.d.b.32.12	yes	16
33.32	even	2	inner	33.6.d.b.32.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.d.b.32.5	✓	16	33.32	even	2	inner
33.6.d.b.32.6	yes	16	1.1	even	1	trivial
33.6.d.b.32.11	yes	16	3.2	odd	2	inner
33.6.d.b.32.12	yes	16	11.10	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.46270 q^{2} +(-14.2692 + 6.27606i) q^{3} -12.0843 q^{4} -59.8956i q^{5} +(63.6794 - 28.0082i) q^{6} +169.425i q^{7} +196.735 q^{8} +(164.222 - 179.109i) q^{9} +O(q^{10})\)	\(q-4.46270 q^{2} +(-14.2692 + 6.27606i) q^{3} -12.0843 q^{4} -59.8956i q^{5} +(63.6794 - 28.0082i) q^{6} +169.425i q^{7} +196.735 q^{8} +(164.222 - 179.109i) q^{9} +267.296i q^{10} +(358.129 + 181.093i) q^{11} +(172.433 - 75.8416i) q^{12} -838.100i q^{13} -756.094i q^{14} +(375.908 + 854.664i) q^{15} -491.273 q^{16} +512.592 q^{17} +(-732.875 + 799.311i) q^{18} +1878.22i q^{19} +723.795i q^{20} +(-1063.32 - 2417.57i) q^{21} +(-1598.22 - 808.163i) q^{22} -3339.01i q^{23} +(-2807.26 + 1234.72i) q^{24} -462.483 q^{25} +3740.19i q^{26} +(-1219.22 + 3586.42i) q^{27} -2047.38i q^{28} +1329.42 q^{29} +(-1677.57 - 3814.11i) q^{30} +6737.49 q^{31} -4103.11 q^{32} +(-6246.78 - 336.413i) q^{33} -2287.55 q^{34} +10147.8 q^{35} +(-1984.51 + 2164.40i) q^{36} +4959.19 q^{37} -8381.92i q^{38} +(5259.96 + 11959.0i) q^{39} -11783.6i q^{40} +17769.0 q^{41} +(4745.29 + 10788.9i) q^{42} +7851.09i q^{43} +(-4327.73 - 2188.37i) q^{44} +(-10727.8 - 9836.18i) q^{45} +14901.0i q^{46} -20190.6i q^{47} +(7010.10 - 3083.26i) q^{48} -11897.8 q^{49} +2063.92 q^{50} +(-7314.30 + 3217.06i) q^{51} +10127.8i q^{52} +18738.7i q^{53} +(5441.04 - 16005.1i) q^{54} +(10846.7 - 21450.4i) q^{55} +33331.8i q^{56} +(-11787.8 - 26800.7i) q^{57} -5932.81 q^{58} -5842.82i q^{59} +(-4542.58 - 10328.0i) q^{60} -1703.10i q^{61} -30067.4 q^{62} +(30345.6 + 27823.3i) q^{63} +34031.7 q^{64} -50198.5 q^{65} +(27877.5 + 1501.31i) q^{66} -29337.8 q^{67} -6194.30 q^{68} +(20955.8 + 47645.1i) q^{69} -45286.7 q^{70} -17330.8i q^{71} +(32308.3 - 35237.0i) q^{72} +16626.5i q^{73} -22131.4 q^{74} +(6599.28 - 2902.57i) q^{75} -22696.9i q^{76} +(-30681.6 + 60676.0i) q^{77} +(-23473.7 - 53369.7i) q^{78} -2586.42i q^{79} +29425.1i q^{80} +(-5111.17 - 58827.4i) q^{81} -79297.6 q^{82} +31993.8 q^{83} +(12849.5 + 29214.5i) q^{84} -30702.0i q^{85} -35037.1i q^{86} +(-18969.8 + 8343.52i) q^{87} +(70456.6 + 35627.3i) q^{88} -63768.5i q^{89} +(47875.2 + 43896.0i) q^{90} +141995. q^{91} +40349.5i q^{92} +(-96138.9 + 42284.9i) q^{93} +90104.9i q^{94} +112497. q^{95} +(58548.3 - 25751.4i) q^{96} +103785. q^{97} +53096.5 q^{98} +(91248.1 - 34404.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 54 q^{3} + 316 q^{4} - 222 q^{9}+O(q^{10}) \) 16 * q - 54 * q^3 + 316 * q^4 - 222 * q^9	\( 16 q - 54 q^{3} + 316 q^{4} - 222 q^{9} - 552 q^{12} - 1674 q^{15} + 1684 q^{16} + 7932 q^{22} - 1356 q^{25} - 3240 q^{27} - 11980 q^{31} - 5106 q^{33} - 34032 q^{34} + 14016 q^{36} + 9356 q^{37} + 45912 q^{42} + 77430 q^{45} - 78012 q^{48} - 1136 q^{49} + 117308 q^{55} + 31848 q^{58} - 220548 q^{60} + 5860 q^{64} - 164796 q^{66} - 364132 q^{67} + 113790 q^{69} + 231144 q^{70} + 320364 q^{75} + 296088 q^{78} - 251334 q^{81} + 4824 q^{82} + 586836 q^{88} - 209184 q^{91} - 521046 q^{93} + 119852 q^{97} - 243894 q^{99}+O(q^{100}) \) 16 * q - 54 * q^3 + 316 * q^4 - 222 * q^9 - 552 * q^12 - 1674 * q^15 + 1684 * q^16 + 7932 * q^22 - 1356 * q^25 - 3240 * q^27 - 11980 * q^31 - 5106 * q^33 - 34032 * q^34 + 14016 * q^36 + 9356 * q^37 + 45912 * q^42 + 77430 * q^45 - 78012 * q^48 - 1136 * q^49 + 117308 * q^55 + 31848 * q^58 - 220548 * q^60 + 5860 * q^64 - 164796 * q^66 - 364132 * q^67 + 113790 * q^69 + 231144 * q^70 + 320364 * q^75 + 296088 * q^78 - 251334 * q^81 + 4824 * q^82 + 586836 * q^88 - 209184 * q^91 - 521046 * q^93 + 119852 * q^97 - 243894 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more