LMFDB - Embedded newform 33.6.d.b.32.7

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			32.7
Root			$-6.72395 + 15.5879i$ of defining polynomial
Character	$\chi$	$=$	33.32
Dual form			33.6.d.b.32.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(-0.480974 + 55.9601i) q^{6} +150.804i q^{7} +183.491 q^{8} +(-242.964 - 4.17684i) q^{9} +O(q^{10})$	\(q-3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(-0.480974 + 55.9601i) q^{6} +150.804i q^{7} +183.491 q^{8} +(-242.964 - 4.17684i) q^{9} +42.6500i q^{10} +(-352.626 + 191.588i) q^{11} +(-2.56058 + 297.917i) q^{12} +778.957i q^{13} -541.384i q^{14} +(-185.188 - 1.59169i) q^{15} -47.1432 q^{16} -1255.02 q^{17} +(872.236 + 14.9947i) q^{18} -1214.37i q^{19} +227.057i q^{20} +(2350.72 + 20.2043i) q^{21} +(1265.92 - 687.798i) q^{22} -880.210i q^{23} +(24.5836 - 2860.24i) q^{24} +2983.86 q^{25} -2796.44i q^{26} +(-97.6596 + 3786.74i) q^{27} -2882.18i q^{28} -3201.27 q^{29} +(664.823 + 5.71411i) q^{30} -6446.10 q^{31} -5702.47 q^{32} +(2939.21 + 5522.36i) q^{33} +4505.50 q^{34} +1791.60 q^{35} +(4643.54 + 79.8279i) q^{36} -9311.53 q^{37} +4359.58i q^{38} +(12142.3 + 104.362i) q^{39} -2179.93i q^{40} -5398.38 q^{41} +(-8439.03 - 72.5330i) q^{42} +20867.6i q^{43} +(6739.40 - 3661.65i) q^{44} +(-49.6220 + 2886.48i) q^{45} +3159.93i q^{46} -11289.4i q^{47} +(-6.31611 + 734.863i) q^{48} -5934.91 q^{49} -10712.0 q^{50} +(-168.144 + 19563.1i) q^{51} -14887.5i q^{52} -23978.4i q^{53} +(350.596 - 13594.3i) q^{54} +(2276.12 + 4189.29i) q^{55} +27671.2i q^{56} +(-18929.5 - 162.698i) q^{57} +11492.5 q^{58} +22954.8i q^{59} +(3539.33 + 30.4204i) q^{60} -27244.5i q^{61} +23141.4 q^{62} +(629.884 - 36640.0i) q^{63} +21980.3 q^{64} +9254.23 q^{65} +(-10551.7 - 19825.1i) q^{66} +20257.5 q^{67} +23986.0 q^{68} +(-13720.6 - 117.928i) q^{69} -6431.79 q^{70} +56465.7i q^{71} +(-44581.8 - 766.412i) q^{72} -12025.4i q^{73} +33428.2 q^{74} +(399.768 - 46512.0i) q^{75} +23209.2i q^{76} +(-28892.3 - 53177.5i) q^{77} +(-43590.5 - 374.658i) q^{78} -11065.5i q^{79} +560.075i q^{80} +(59014.1 + 2029.64i) q^{81} +19380.1 q^{82} +51574.3 q^{83} +(-44927.1 - 386.146i) q^{84} +14910.0i q^{85} -74914.4i q^{86} +(-428.897 + 49901.1i) q^{87} +(-64703.7 + 35154.8i) q^{88} +84147.7i q^{89} +(178.142 - 10362.4i) q^{90} -117470. q^{91} +16822.6i q^{92} +(-863.629 + 100481. i) q^{93} +40528.8i q^{94} -14427.1 q^{95} +(-764.000 + 88889.5i) q^{96} +99342.9 q^{97} +21306.2 q^{98} +(86475.6 - 45076.2i) 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 $

$2$	−3.58998			−0.634624			−0.317312	−	0.948321i	$-0.602780\pi$
$2$	−3.58998			−0.634624			−0.317312	+	0.948321i	$0.602780\pi$
$3$	0.133977	−	15.5879i	0.00859463	−	0.999963i
$3$	0.133977	−	15.5879i	0.00859463	−	0.999963i
$4$	−19.1121			−0.597252
$5$		−	11.8803i		−	0.212521i	−0.994338	−	0.106261i	$-0.966112\pi$
$5$		−	11.8803i		−	0.212521i	0.994338	−	0.106261i	$-0.0338877\pi$
$6$	−0.480974	+	55.9601i	−0.00545436	+	0.634601i
$7$			150.804i			1.16324i	0.813461	+	0.581619i	$0.197580\pi$
$7$			150.804i			1.16324i	−0.813461	+	0.581619i	$0.802420\pi$
$8$	183.491			1.01365
$9$	−242.964	−	4.17684i	−0.999852	−	0.0171886i
$10$			42.6500i			0.134871i
$11$	−352.626	+	191.588i	−0.878683	+	0.477405i
$11$	−352.626	+	191.588i	−0.878683	+	0.477405i
$12$	−2.56058	+	297.917i	−0.00513316	+	0.597230i
$13$			778.957i			1.27837i	0.769055	+	0.639183i	$0.220727\pi$
$13$			778.957i			1.27837i	−0.769055	+	0.639183i	$0.779273\pi$
$14$		−	541.384i		−	0.738219i
$15$	−185.188	−	1.59169i	−0.212513	−	0.00182654i
$16$	−47.1432			−0.0460383
$17$	−1255.02			−1.05324			−0.526622	−	0.850100i	$-0.676542\pi$
$17$	−1255.02			−1.05324			−0.526622	+	0.850100i	$0.676542\pi$
$18$	872.236	+	14.9947i	0.634531	+	0.0109083i
$19$		−	1214.37i		−	0.771736i	−0.922554	−	0.385868i	$-0.873902\pi$
$19$		−	1214.37i		−	0.771736i	0.922554	−	0.385868i	$-0.126098\pi$
$20$			227.057i			0.126929i
$21$	2350.72	+	20.2043i	1.16319	+	0.00999759i
$22$	1265.92	−	687.798i	0.557634	−	0.302973i
$23$		−	880.210i		−	0.346950i	−0.984838	−	0.173475i	$-0.944500\pi$
$23$		−	880.210i		−	0.346950i	0.984838	−	0.173475i	$-0.0554996\pi$
$24$	24.5836	−	2860.24i	0.00871199	−	1.01362i
$25$	2983.86			0.954835
$26$		−	2796.44i		−	0.811282i
$27$	−97.6596	+	3786.74i	−0.0257813	+	0.999668i
$28$		−	2882.18i		−	0.694746i
$29$	−3201.27			−0.706851			−0.353425	−	0.935463i	$-0.614983\pi$
$29$	−3201.27			−0.706851			−0.353425	+	0.935463i	$0.614983\pi$
$30$	664.823	+	5.71411i	0.134866	+	0.00115917i
$31$	−6446.10			−1.20474			−0.602369	−	0.798218i	$-0.705777\pi$
$31$	−6446.10			−1.20474			−0.602369	+	0.798218i	$0.705777\pi$
$32$	−5702.47			−0.984438
$33$	2939.21	+	5522.36i	0.469836	+	0.882754i
$34$	4505.50			0.668414
$35$	1791.60			0.247212
$36$	4643.54	+	79.8279i	0.597164	+	0.0102659i
$37$	−9311.53			−1.11819			−0.559096	−	0.829103i	$-0.688852\pi$
$37$	−9311.53			−1.11819			−0.559096	+	0.829103i	$0.688852\pi$
$38$			4359.58i			0.489762i
$39$	12142.3	+	104.362i	1.27832	+	0.0109871i
$40$		−	2179.93i		−	0.215423i
$41$	−5398.38			−0.501538			−0.250769	−	0.968047i	$-0.580683\pi$
$41$	−5398.38			−0.501538			−0.250769	+	0.968047i	$0.580683\pi$
$42$	−8439.03	−	72.5330i	−0.738192	−	0.00634472i
$43$			20867.6i			1.72108i	0.509379	+	0.860542i	$0.329875\pi$
$43$			20867.6i			1.72108i	−0.509379	+	0.860542i	$0.670125\pi$
$44$	6739.40	−	3661.65i	0.524795	−	0.285131i
$45$	−49.6220	+	2886.48i	−0.00365294	+	0.212490i
$46$			3159.93i			0.220183i
$47$		−	11289.4i		−	0.745465i	−0.927939	−	0.372732i	$-0.878421\pi$
$47$		−	11289.4i		−	0.745465i	0.927939	−	0.372732i	$-0.121579\pi$
$48$	−6.31611	+	734.863i	−0.000395682	+	0.0460366i
$49$	−5934.91			−0.353122
$50$	−10712.0			−0.605961
$51$	−168.144	+	19563.1i	−0.00905223	+	1.05320i
$52$		−	14887.5i		−	0.763506i
$53$		−	23978.4i		−	1.17255i	−0.810113	−	0.586274i	$-0.800594\pi$
$53$		−	23978.4i		−	1.17255i	0.810113	−	0.586274i	$-0.199406\pi$
$54$	350.596	−	13594.3i	0.0163615	−	0.634413i
$55$	2276.12	+	4189.29i	0.101459	+	0.186739i
$56$			27671.2i			1.17912i
$57$	−18929.5	−	162.698i	−0.771707	−	0.00663278i
$58$	11492.5			0.448585
$59$			22954.8i			0.858507i	0.903184	+	0.429254i	$0.141223\pi$
$59$			22954.8i			0.858507i	−0.903184	+	0.429254i	$0.858777\pi$
$60$	3539.33	+	30.4204i	0.126924	+	0.00109090i
$61$		−	27244.5i		−	0.937462i	−0.883341	−	0.468731i	$-0.844711\pi$
$61$		−	27244.5i		−	0.937462i	0.883341	−	0.468731i	$-0.155289\pi$
$62$	23141.4			0.764557
$63$	629.884	−	36640.0i	0.0199945	−	1.16307i
$64$	21980.3			0.670787
$65$	9254.23			0.271680
$66$	−10551.7	−	19825.1i	−0.298169	−	0.560217i
$67$	20257.5			0.551312			0.275656	−	0.961256i	$-0.411105\pi$
$67$	20257.5			0.551312			0.275656	+	0.961256i	$0.411105\pi$
$68$	23986.0			0.629051
$69$	−13720.6	−	117.928i	−0.346937	−	0.00298191i
$70$	−6431.79			−0.156887
$71$			56465.7i			1.32935i	0.747133	+	0.664674i	$0.231430\pi$
$71$			56465.7i			1.32935i	−0.747133	+	0.664674i	$0.768570\pi$
$72$	−44581.8	−	766.412i	−1.01351	−	0.0174233i
$73$		−	12025.4i		−	0.264116i	−0.991242	−	0.132058i	$-0.957842\pi$
$73$		−	12025.4i		−	0.264116i	0.991242	−	0.132058i	$-0.0421585\pi$
$74$	33428.2			0.709632
$75$	399.768	−	46512.0i	0.00820645	−	0.954800i
$76$			23209.2i			0.460921i
$77$	−28892.3	−	53177.5i	−0.555336	−	1.02212i
$78$	−43590.5	−	374.658i	−0.811252	−	0.00697267i
$79$		−	11065.5i		−	0.199481i	−0.995013	−	0.0997407i	$-0.968199\pi$
$79$		−	11065.5i		−	0.199481i	0.995013	−	0.0997407i	$-0.0318013\pi$
$80$			560.075i			0.00978411i
$81$	59014.1	+	2029.64i	0.999409	+	0.0343722i
$82$	19380.1			0.318288
$83$	51574.3			0.821747			0.410873	−	0.911692i	$-0.365224\pi$
$83$	51574.3			0.821747			0.410873	+	0.911692i	$0.365224\pi$
$84$	−44927.1	−	386.146i	−0.694720	−	0.00597108i
$85$			14910.0i			0.223836i
$86$		−	74914.4i		−	1.09224i
$87$	−428.897	+	49901.1i	−0.00607512	+	0.706825i
$88$	−64703.7	+	35154.8i	−0.890682	+	0.483924i
$89$			84147.7i			1.12608i	0.826431	+	0.563038i	$0.190367\pi$
$89$			84147.7i			1.12608i	−0.826431	+	0.563038i	$0.809633\pi$
$90$	178.142	−	10362.4i	0.00231825	−	0.134851i
$91$	−117470.			−1.48704
$92$			16822.6i			0.207216i
$93$	−863.629	+	100481.i	−0.0103543	+	1.20469i
$94$			40528.8i			0.473090i
$95$	−14427.1			−0.164010
$96$	−764.000	+	88889.5i	−0.00846088	+	0.984402i
$97$	99342.9			1.07203			0.536016	−	0.844208i	$-0.319929\pi$
$97$	99342.9			1.07203			0.536016	+	0.844208i	$0.319929\pi$
$98$	21306.2			0.224100
$99$	86475.6	−	45076.2i	0.886759	−	0.462231i
$100$	−57027.7			−0.570277
$101$	8413.56			0.0820685			0.0410343	−	0.999158i	$-0.486935\pi$
$101$	8413.56			0.0820685			0.0410343	+	0.999158i	$0.486935\pi$
$102$	603.633	−	70231.1i	0.00574477	−	0.668389i
$103$	11603.9			0.107773			0.0538864	−	0.998547i	$-0.482839\pi$
$103$	11603.9			0.107773			0.0538864	+	0.998547i	$0.482839\pi$
$104$			142932.i			1.29582i
$105$	240.033	−	27927.2i	0.00212470	−	0.247203i
$106$			86082.0i			0.744128i
$107$	−181478.			−1.53238			−0.766188	−	0.642616i	$-0.777849\pi$
$107$	−181478.			−1.53238			−0.766188	+	0.642616i	$0.777849\pi$
$108$	1866.48	−	72372.3i	0.0153980	−	0.597053i
$109$		−	153350.i		−	1.23628i	−0.786067	−	0.618141i	$-0.787886\pi$
$109$		−	153350.i		−	1.23628i	0.786067	−	0.618141i	$-0.212114\pi$
$110$	−8171.23	−	15039.5i	−0.0643881	−	0.118509i
$111$	−1247.53	+	145147.i	−0.00961045	+	1.11815i
$112$		−	7109.40i		−	0.0535535i
$113$		−	209395.i		−	1.54266i	−0.636435	−	0.771330i	$-0.719592\pi$
$113$		−	209395.i		−	1.54266i	0.636435	−	0.771330i	$-0.280408\pi$
$114$	67956.6	+	584.083i	0.489744	+	0.00420933i
$115$	−10457.1			−0.0737341
$116$	61182.9			0.422168
$117$	3253.57	−	189259.i	0.0219733	−	1.27818i
$118$		−	82407.3i		−	0.544830i
$119$		−	189262.i		−	1.22517i
$120$	−33980.5	−	292.060i	−0.215415	−	0.00185148i
$121$	87638.8	−	135118.i	0.544168	−	0.838976i
$122$			97807.0i			0.594936i
$123$	−723.259	+	84149.3i	−0.00431053	+	0.501519i
$124$	123198.			0.719532
$125$		−	72575.0i		−	0.415443i
$126$	−2261.27	+	131537.i	−0.0126890	+	0.738110i
$127$			117065.i			0.644046i	0.946732	+	0.322023i	$0.104363\pi$
$127$			117065.i			0.644046i	−0.946732	+	0.322023i	$0.895637\pi$
$128$	103570.			0.558740
$129$	325282.	+	2795.78i	1.72102	+	0.0147921i
$130$	−33222.5			−0.172414
$131$	−176896.			−0.900614			−0.450307	−	0.892874i	$-0.648686\pi$
$131$	−176896.			−0.900614			−0.450307	+	0.892874i	$0.648686\pi$
$132$	−56174.4	−	105544.i	−0.280610	−	0.527226i
$133$	183133.			0.897712
$134$	−72723.8			−0.349876
$135$	44987.5	+	1160.22i	0.212450	+	0.00547908i
$136$	−230285.			−1.06763
$137$			347712.i			1.58277i	0.611318	+	0.791385i	$0.290640\pi$
$137$			347712.i			1.58277i	−0.611318	+	0.791385i	$0.709360\pi$
$138$	49256.7	+	423.359i	0.220175	+	0.00189239i
$139$			8720.60i			0.0382833i	0.999817	+	0.0191417i	$0.00609335\pi$
$139$			8720.60i			0.0382833i	−0.999817	+	0.0191417i	$0.993907\pi$
$140$	−34241.1			−0.147648
$141$	−175978.	−	1512.52i	−0.745437	−	0.00640699i
$142$		−	202711.i		−	0.843637i
$143$	−149239.	−	274680.i	−0.610299	−	1.12328i
$144$	11454.1	+	196.909i	0.0460315	+	0.000791335i
$145$			38032.0i			0.150221i
$146$			43171.1i			0.167614i
$147$	−795.142	+	92512.7i	−0.00303495	+	0.353109i
$148$	177962.			0.667843
$149$	−354108.			−1.30668			−0.653342	−	0.757063i	$-0.726634\pi$
$149$	−354108.			−1.30668			−0.653342	+	0.757063i	$0.726634\pi$
$150$	−1435.16	+	166977.i	−0.00520801	+	0.605939i
$151$			493279.i			1.76056i	0.474457	+	0.880278i	$0.342644\pi$
$151$			493279.i			1.76056i	−0.474457	+	0.880278i	$0.657356\pi$
$152$		−	222827.i		−	0.782274i
$153$	304925.	+	5242.02i	1.05309	+	0.0181038i
$154$	103723.	+	190906.i	0.352430	+	0.648661i
$155$			76581.5i			0.256032i
$156$	−232064.	−	1994.58i	−0.763478	−	0.00656205i
$157$	−94457.3			−0.305834			−0.152917	−	0.988239i	$-0.548867\pi$
$157$	−94457.3			−0.305834			−0.152917	+	0.988239i	$0.548867\pi$
$158$			39724.8i			0.126596i
$159$	−373773.	−	3212.56i	−1.17251	−	0.0100776i
$160$			67747.0i			0.209214i
$161$	132739.			0.403585
$162$	−211859.	−	7286.37i	−0.634249	−	0.0218134i
$163$	−296304.			−0.873510			−0.436755	−	0.899580i	$-0.643872\pi$
$163$	−296304.			−0.873510			−0.436755	+	0.899580i	$0.643872\pi$
$164$	103174.			0.299544
$165$	65607.2	−	34918.7i	0.187604	−	0.0998500i
$166$	−185151.			−0.521501
$167$	571023.			1.58439			0.792196	−	0.610267i	$-0.208938\pi$
$167$	571023.			1.58439			0.792196	+	0.610267i	$0.208938\pi$
$168$	431336.	+	3707.31i	1.17908	+	0.0101341i
$169$	−235481.			−0.634219
$170$		−	53526.6i		−	0.142052i
$171$	−5072.24	+	295049.i	−0.0132651	+	0.771622i
$172$		−	398824.i		−	1.02792i
$173$	12657.7			0.0321545			0.0160772	−	0.999871i	$-0.494882\pi$
$173$	12657.7			0.0321545			0.0160772	+	0.999871i	$0.494882\pi$
$174$	1539.73	−	179144.i	0.00385542	−	0.448568i
$175$			449979.i			1.11070i
$176$	16623.9	−	9032.09i	0.0404531	−	0.0219789i
$177$	357817.	+	3075.42i	0.858476	+	0.00737855i
$178$		−	302089.i		−	0.714635i
$179$			46770.9i			0.109105i	0.998511	+	0.0545523i	$0.0173732\pi$
$179$			46770.9i			0.109105i	−0.998511	+	0.0545523i	$0.982627\pi$
$180$	948.379	−	55166.6i	0.00218173	−	0.126910i
$181$	118107.			0.267965			0.133983	−	0.990984i	$-0.457223\pi$
$181$	118107.			0.267965			0.133983	+	0.990984i	$0.457223\pi$
$182$	421715.			0.943714
$183$	−424683.	−	3650.13i	−0.937427	−	0.00805714i
$184$		−	161511.i		−	0.351688i
$185$			110624.i			0.237639i
$186$	3100.41	−	360725.i	0.00657108	−	0.764528i
$187$	442553.	−	240447.i	0.925467	−	0.502824i
$188$			215764.i			0.445230i
$189$	−571056.	−	14727.5i	−1.16285	−	0.0299898i
$190$	51793.0			0.104085
$191$			540991.i			1.07302i	0.843895	+	0.536509i	$0.180257\pi$
$191$			540991.i			1.07302i	−0.843895	+	0.536509i	$0.819743\pi$
$192$	2944.86	−	342627.i	0.00576516	−	0.670762i
$193$		−	610969.i		−	1.18066i	−0.807161	−	0.590331i	$-0.798997\pi$
$193$		−	610969.i		−	1.18066i	0.807161	−	0.590331i	$-0.201003\pi$
$194$	−356639.			−0.680337
$195$	1239.85	−	144254.i	0.00233498	−	0.271670i
$196$	113428.			0.210903
$197$	−365903.			−0.671739			−0.335869	−	0.941909i	$-0.609030\pi$
$197$	−365903.			−0.671739			−0.335869	+	0.941909i	$0.609030\pi$
$198$	−310446.	+	161823.i	−0.562759	+	0.293343i
$199$	−218381.			−0.390915			−0.195457	−	0.980712i	$-0.562619\pi$
$199$	−218381.			−0.390915			−0.195457	+	0.980712i	$0.562619\pi$
$200$	547512.			0.967873
$201$	2714.03	−	315771.i	0.00473833	−	0.551292i
$202$	−30204.5			−0.0520827
$203$		−	482765.i		−	0.822235i
$204$	3213.58	−	373891.i	0.00540646	−	0.629028i
$205$			64134.3i			0.106587i
$206$	−41657.6			−0.0683953
$207$	−3676.49	+	213859.i	−0.00596359	+	0.346899i
$208$		−	36722.5i		−	0.0588538i
$209$	232660.	+	428220.i	0.368431	+	0.678111i
$210$	−861.713	+	100258.i	−0.00134839	+	0.156881i
$211$			697135.i			1.07798i	0.842312	+	0.538990i	$0.181194\pi$
$211$			697135.i			1.07798i	−0.842312	+	0.538990i	$0.818806\pi$
$212$			458277.i			0.700307i
$213$	880181.	+	7565.11i	1.32930	+	0.0114253i
$214$	651503.			0.972483
$215$	247914.			0.365767
$216$	−17919.7	+	694833.i	−0.0261334	+	1.01332i
$217$		−	972099.i		−	1.40140i
$218$			550523.i			0.784575i
$219$	−187451.	−	1611.13i	−0.264106	−	0.00226998i
$220$	−43501.4	−	80066.1i	−0.0605964	−	0.111530i
$221$		−	977607.i		−	1.34643i
$222$	4478.61	−	521075.i	0.00609903	−	0.709606i
$223$	−1.13148e6			−1.52365			−0.761826	−	0.647781i	$-0.775697\pi$
$223$	−1.13148e6			−1.52365			−0.761826	+	0.647781i	$0.775697\pi$
$224$		−	859957.i		−	1.14514i
$225$	−724971.	−	12463.1i	−0.954694	−	0.0164123i
$226$			751724.i			0.979010i
$227$	1.33675e6			1.72181			0.860904	−	0.508767i	$-0.169899\pi$
$227$	1.33675e6			1.72181			0.860904	+	0.508767i	$0.169899\pi$
$228$	361782.	+	3109.50i	0.460904	+	0.00396144i
$229$	936509.			1.18011			0.590056	−	0.807362i	$-0.299106\pi$
$229$	936509.			1.18011			0.590056	+	0.807362i	$0.299106\pi$
$230$	37540.9			0.0467935
$231$	−832795.	+	443246.i	−1.02685	+	0.546531i
$232$	−587405.			−0.716503
$233$	−675682.			−0.815366			−0.407683	−	0.913124i	$-0.633663\pi$
$233$	−675682.			−0.815366			−0.407683	+	0.913124i	$0.633663\pi$
$234$	−11680.3	+	679434.i	−0.0139448	+	0.811162i
$235$	−134122.			−0.158427
$236$		−	438714.i		−	0.512745i
$237$	−172487.	−	1482.52i	−0.199474	−	0.00171447i
$238$			679448.i			0.777524i
$239$	−596353.			−0.675319			−0.337659	−	0.941268i	$-0.609635\pi$
$239$	−596353.			−0.675319			−0.337659	+	0.941268i	$0.609635\pi$
$240$	8730.38	+	75.0372i	0.00978374	+	8.40908e-5i
$241$			1.24321e6i			1.37880i	0.724381	+	0.689400i	$0.242126\pi$
$241$			1.24321e6i			1.37880i	−0.724381	+	0.689400i	$0.757874\pi$
$242$	−314621.	+	485070.i	−0.345342	+	0.532435i
$243$	39544.4	−	919633.i	0.0429604	−	0.999077i
$244$			520698.i			0.559901i
$245$			70508.5i			0.0750458i
$246$	2596.48	−	302094.i	0.00273557	−	0.318276i
$247$	945945.			0.986560
$248$	−1.18280e6			−1.22119
$249$	6909.77	−	803934.i	0.00706261	−	0.821716i
$250$			260543.i			0.263651i
$251$			1.76567e6i			1.76899i	0.466551	+	0.884494i	$0.345496\pi$
$251$			1.76567e6i			1.76899i	−0.466551	+	0.884494i	$0.654504\pi$
$252$	−12038.4	+	700266.i	−0.0119417	+	0.694643i
$253$	168638.	+	310385.i	0.165636	+	0.304859i
$254$		−	420260.i		−	0.408727i
$255$	232415.	+	1997.60i	0.223828	+	0.00192379i
$256$	−1.07519e6			−1.02538
$257$		−	347788.i		−	0.328459i	−0.986422	−	0.164230i	$-0.947486\pi$
$257$		−	347788.i		−	0.328459i	0.986422	−	0.164230i	$-0.0525138\pi$
$258$	−1.16776e6	−	10036.8i	−1.09220	−	0.00938742i
$259$		−	1.40422e6i		−	1.30072i
$260$	−176867.			−0.162261
$261$	777794.	+	13371.2i	0.706746	+	0.0121498i
$262$	635051.			0.571552
$263$	985521.			0.878570			0.439285	−	0.898348i	$-0.355232\pi$
$263$	985521.			0.878570			0.439285	+	0.898348i	$0.355232\pi$
$264$	539319.	+	1.01330e6i	0.476251	+	0.894808i
$265$	−284871.			−0.249191
$266$	−657443.			−0.569710
$267$	1.31169e6	+	11273.9i	1.12603	+	0.00967820i
$268$	−387162.			−0.329272
$269$		−	1.36787e6i		−	1.15257i	−0.817250	−	0.576283i	$-0.804503\pi$
$269$		−	1.36787e6i		−	1.15257i	0.817250	−	0.576283i	$-0.195497\pi$
$270$	−161504.	−	4165.18i	−0.134826	−	0.00347716i
$271$		−	346976.i		−	0.286996i	−0.989651	−	0.143498i	$-0.954165\pi$
$271$		−	346976.i		−	0.286996i	0.989651	−	0.143498i	$-0.0458351\pi$
$272$	59165.7			0.0484895
$273$	−15738.3	+	1.83111e6i	−0.0127806	+	1.48699i
$274$		−	1.24828e6i		−	1.00446i
$275$	−1.05219e6	+	571672.i	−0.838997	+	0.455843i
$276$	262229.	+	2253.85i	0.207209	+	0.00178095i
$277$		−	1.92307e6i		−	1.50590i	−0.658079	−	0.752949i	$-0.728631\pi$
$277$		−	1.92307e6i		−	1.50590i	0.658079	−	0.752949i	$-0.271369\pi$
$278$		−	31306.8i		−	0.0242955i
$279$	1.56617e6	+	26924.3i	1.20456	+	0.0207078i
$280$	328742.			0.250588
$281$	1.51815e6			1.14696			0.573482	−	0.819218i	$-0.305592\pi$
$281$	1.51815e6			1.14696			0.573482	+	0.819218i	$0.305592\pi$
$282$	631758.	+	5429.93i	0.473073	+	0.00406603i
$283$		−	195988.i		−	0.145466i	−0.997351	−	0.0727332i	$-0.976828\pi$
$283$		−	195988.i		−	0.145466i	0.997351	−	0.0727332i	$-0.0231721\pi$
$284$		−	1.07918e6i		−	0.793956i
$285$	−1932.90	+	224888.i	−0.00140961	+	0.164004i
$286$	535765.	+	986096.i	0.387310	+	0.712860i
$287$		−	814098.i		−	0.583408i
$288$	1.38550e6	+	23818.3i	0.984293	+	0.0169211i
$289$	155220.			0.109321
$290$		−	136534.i		−	0.0953337i
$291$	13309.7	−	1.54855e6i	0.00921371	−	1.07199i
$292$			229831.i			0.157744i
$293$	−2.75485e6			−1.87469			−0.937345	−	0.348403i	$-0.886724\pi$
$293$	−2.75485e6			−1.87469			−0.937345	+	0.348403i	$0.886724\pi$
$294$	2854.54	−	332119.i	0.00192605	−	0.224091i
$295$	272710.			0.182451
$296$	−1.70858e6			−1.13346
$297$	−691057.	−	1.35401e6i	−0.454593	−	0.890699i
$298$	1.27124e6			0.829254
$299$	685646.			0.443529
$300$	−7640.40	+	888941.i	−0.00490132	+	0.570256i
$301$	−3.14693e6			−2.00203
$302$		−	1.77086e6i		−	1.11729i
$303$	1127.22	−	131150.i	0.000705348	−	0.0820655i
$304$			57249.5i			0.0355294i
$305$	−323672.			−0.199230
$306$	−1.09467e6	−	18818.7i	−0.668315	−	0.0114891i
$307$		−	684538.i		−	0.414526i	−0.978285	−	0.207263i	$-0.933544\pi$
$307$		−	684538.i		−	0.414526i	0.978285	−	0.207263i	$-0.0664556\pi$
$308$	552192.	+	1.01633e6i	0.331675	+	0.610461i
$309$	1554.65	−	180880.i	0.000926268	−	0.107769i
$310$		−	274926.i		−	0.162484i
$311$		−	414984.i		−	0.243294i	−0.992573	−	0.121647i	$-0.961182\pi$
$311$		−	414984.i		−	0.243294i	0.992573	−	0.121647i	$-0.0388175\pi$
$312$	2.22800e6	+	19149.6i	1.29577	+	0.0111371i
$313$	1.28268e6			0.740043			0.370022	−	0.929023i	$-0.379350\pi$
$313$	1.28268e6			0.740043			0.370022	+	0.929023i	$0.379350\pi$
$314$	339099.			0.194090
$315$	−435294.	−	7483.21i	−0.247176	−	0.00424924i
$316$			211484.i			0.119141i
$317$			2.70836e6i			1.51376i	0.653553	+	0.756881i	$0.273278\pi$
$317$			2.70836e6i			1.51376i	−0.653553	+	0.756881i	$0.726722\pi$
$318$	1.34184e6	+	11533.0i	0.744101	+	0.00639550i
$319$	1.12885e6	−	613326.i	0.621098	−	0.337454i
$320$		−	261133.i		−	0.142556i
$321$	−24313.9	+	2.82886e6i	−0.0131702	+	1.53232i
$322$	−476532.			−0.256125
$323$			1.52407e6i			0.812825i
$324$	−1.12788e6	−	38790.6i	−0.596899	−	0.0205288i
$325$			2.32430e6i			1.22063i
$326$	1.06372e6			0.554351
$327$	−2.39040e6	−	20545.4i	−1.23624	−	0.0106254i
$328$	−990555.			−0.508386
$329$	1.70249e6			0.867153
$330$	−235528.	+	125357.i	−0.119058	+	0.0633672i
$331$	−1.10525e6			−0.554486			−0.277243	−	0.960800i	$-0.589421\pi$
$331$	−1.10525e6			−0.554486			−0.277243	+	0.960800i	$0.589421\pi$
$332$	−985691.			−0.490790
$333$	2.26237e6	+	38892.7i	1.11803	+	0.0192202i
$334$	−2.04996e6			−1.00549
$335$		−	240664.i		−	0.117165i
$336$	−110820.	−	952.496i	−0.0535515	−	0.000460272i
$337$			1.20295e6i			0.576996i	0.957480	+	0.288498i	$0.0931559\pi$
$337$			1.20295e6i			0.576996i	−0.957480	+	0.288498i	$0.906844\pi$
$338$	845371.			0.402491
$339$	−3.26403e6	−	28054.1i	−1.54260	−	0.0132586i
$340$		−	284961.i		−	0.133687i
$341$	2.27306e6	−	1.23500e6i	1.05858	−	0.575149i
$342$	18209.2	−	1.05922e6i	0.00841834	−	0.489690i
$343$			1.63956e6i			0.752473i
$344$			3.82903e6i			1.74459i
$345$	−1401.02	+	163005.i	−0.000633718	+	0.0737314i
$346$	−45441.0			−0.0204060
$347$	−1.61441e6			−0.719765			−0.359882	−	0.932998i	$-0.617183\pi$
$347$	−1.61441e6			−0.719765			−0.359882	+	0.932998i	$0.617183\pi$
$348$	8197.10	−	953712.i	0.00362838	−	0.422152i
$349$			3.17188e6i			1.39397i	0.717085	+	0.696986i	$0.245476\pi$
$349$			3.17188e6i			1.39397i	−0.717085	+	0.696986i	$0.754524\pi$
$350$		−	1.61541e6i		−	0.704877i
$351$	−2.94970e6	−	76072.6i	−1.27794	−	0.0329580i
$352$	2.01084e6	−	1.09253e6i	0.865009	−	0.469976i
$353$		−	675430.i		−	0.288499i	−0.989541	−	0.144249i	$-0.953923\pi$
$353$		−	675430.i		−	0.288499i	0.989541	−	0.144249i	$-0.0460767\pi$
$354$	−1.28456e6	−	11040.7i	−0.544810	−	0.00468261i
$355$	670829.			0.282515
$356$		−	1.60824e6i		−	0.672551i
$357$	−2.95020e6	−	25356.8i	−1.22513	−	0.0105299i
$358$		−	167906.i		−	0.0692404i
$359$	2.48053e6			1.01580			0.507900	−	0.861416i	$-0.330422\pi$
$359$	2.48053e6			1.01580			0.507900	+	0.861416i	$0.330422\pi$
$360$	−9105.20	+	529644.i	−0.00370282	+	0.215391i
$361$	1.00139e6			0.404424
$362$	−424001.			−0.170057
$363$	−2.09446e6	−	1.38421e6i	−0.834268	−	0.551359i
$364$	2.24509e6			0.888139
$365$	−142866.			−0.0561301
$366$	1.52460e6	+	13103.9i	0.594914	+	0.00511326i
$367$	−2.46844e6			−0.956659			−0.478329	−	0.878181i	$-0.658757\pi$
$367$	−2.46844e6			−0.956659			−0.478329	+	0.878181i	$0.658757\pi$
$368$			41495.9i			0.0159730i
$369$	1.31161e6	+	22548.1i	0.501464	+	0.00862075i
$370$		−	397136.i		−	0.150812i
$371$	3.61605e6			1.36395
$372$	16505.7	−	1.92040e6i	0.00618411	−	0.719506i
$373$		−	2.16792e6i		−	0.806809i	−0.915022	−	0.403405i	$-0.867827\pi$
$373$		−	2.16792e6i		−	0.806809i	0.915022	−	0.403405i	$-0.132173\pi$
$374$	−1.58875e6	+	863201.i	−0.587324	+	0.319104i
$375$	−1.13129e6	−	9723.38i	−0.415428	−	0.00357058i
$376$		−	2.07151e6i		−	0.755644i
$377$		−	2.49365e6i		−	0.903614i
$378$	2.05008e6	+	52871.3i	0.737974	+	0.0190323i
$379$	3.73283e6			1.33487			0.667437	−	0.744666i	$-0.267391\pi$
$379$	3.73283e6			1.33487			0.667437	+	0.744666i	$0.267391\pi$
$380$	275732.			0.0979553
$381$	1.82479e6	+	15684.0i	0.644022	+	0.00553534i
$382$		−	1.94215e6i		−	0.680963i
$383$			2.18000e6i			0.759382i	0.925113	+	0.379691i	$0.123970\pi$
$383$			2.18000e6i			0.759382i	−0.925113	+	0.379691i	$0.876030\pi$
$384$	13876.0	−	1.61444e6i	0.00480217	−	0.558720i
$385$	−631763.	+	343249.i	−0.217221	+	0.118021i
$386$			2.19336e6i			0.749277i
$387$	87160.7	−	5.07009e6i	0.0295831	−	1.72083i
$388$	−1.89865e6			−0.640273
$389$			2.48481e6i			0.832567i	0.909235	+	0.416284i	$0.136668\pi$
$389$			2.48481e6i			0.832567i	−0.909235	+	0.416284i	$0.863332\pi$
$390$	−4451.05	+	517868.i	−0.00148184	+	0.172408i
$391$			1.10468e6i			0.365423i
$392$	−1.08900e6			−0.357943
$393$	−23699.9	+	2.75743e6i	−0.00774045	+	0.900581i
$394$	1.31358e6			0.426302
$395$	−131461.			−0.0423940
$396$	−1.65273e6	+	861499.i	−0.529619	+	0.276069i
$397$	−54162.3			−0.0172473			−0.00862364	−	0.999963i	$-0.502745\pi$
$397$	−54162.3			−0.0172473			−0.00862364	+	0.999963i	$0.502745\pi$
$398$	783983.			0.248084
$399$	24535.6	−	2.85465e6i	0.00771550	−	0.897679i
$400$	−140669.			−0.0439590
$401$			3.15932e6i			0.981144i	0.871401	+	0.490572i	$0.163212\pi$
$401$			3.15932e6i			0.981144i	−0.871401	+	0.490572i	$0.836788\pi$
$402$	−9743.32	+	1.13361e6i	−0.00300706	+	0.349863i
$403$		−	5.02123e6i		−	1.54010i
$404$	−160801.			−0.0490156
$405$	24112.7	−	701105.i	0.00730481	−	0.212395i
$406$			1.73312e6i			0.521811i
$407$	3.28348e6	−	1.78398e6i	0.982537	−	0.533831i
$408$	−30852.9	+	3.58966e6i	−0.00917584	+	1.06759i
$409$			3.24246e6i			0.958444i	0.877694	+	0.479222i	$0.159081\pi$
$409$			3.24246e6i			0.958444i	−0.877694	+	0.479222i	$0.840919\pi$
$410$		−	230241.i		−	0.0676429i
$411$	5.42009e6	+	46585.4i	1.58271	+	0.0136033i
$412$	−221774.			−0.0643675
$413$	−3.46168e6			−0.998648
$414$	13198.5	−	767751.i	0.00378464	−	0.220150i
$415$		−	612717.i		−	0.174638i
$416$		−	4.44198e6i		−	1.25847i
$417$	135936.	+	1168.36i	0.0382819	+	0.000329031i
$418$	−835244.	−	1.53730e6i	−0.233815	−	0.430346i
$419$			540226.i			0.150328i	0.997171	+	0.0751642i	$0.0239481\pi$
$419$			540226.i			0.150328i	−0.997171	+	0.0751642i	$0.976052\pi$
$420$	−4587.52	+	533746.i	−0.00126898	+	0.147643i
$421$	−3.05118e6			−0.839003			−0.419501	−	0.907755i	$-0.637795\pi$
$421$	−3.05118e6			−0.839003			−0.419501	+	0.907755i	$0.637795\pi$
$422$		−	2.50270e6i		−	0.684112i
$423$	−47154.1	+	2.74293e6i	−0.0128135	+	0.745355i
$424$		−	4.39983e6i		−	1.18856i
$425$	−3.74480e6			−1.00567
$426$	−3.15983e6	−	27158.6i	−0.843606	−	0.00725075i
$427$	4.10858e6			1.09049
$428$	3.46843e6			0.915215
$429$	−4.30168e6	+	2.28952e6i	−1.12848	+	0.600622i
$430$	−890004.			−0.232124
$431$	−2.10023e6			−0.544596			−0.272298	−	0.962213i	$-0.587784\pi$
$431$	−2.10023e6			−0.544596			−0.272298	+	0.962213i	$0.587784\pi$
$432$	4603.99	−	178519.i	0.00118693	−	0.0460230i
$433$	−3.92143e6			−1.00514			−0.502568	−	0.864538i	$-0.667611\pi$
$433$	−3.92143e6			−1.00514			−0.502568	+	0.864538i	$0.667611\pi$
$434$			3.48981e6i			0.889361i
$435$	592839.	+	5095.42i	0.150215	+	0.00129109i
$436$			2.93084e6i			0.738372i
$437$	−1.06890e6			−0.267754
$438$	672946.	+	5783.93i	0.167608	+	0.00144058i
$439$			1.31281e6i			0.325118i	0.986699	+	0.162559i	$0.0519748\pi$
$439$			1.31281e6i			0.325118i	−0.986699	+	0.162559i	$0.948025\pi$
$440$	417649.	+	768699.i	0.102844	+	0.189289i
$441$	1.44197e6	+	24789.2i	0.353069	+	0.00606967i
$442$			3.50959e6i			0.854477i
$443$		−	6.39479e6i		−	1.54816i	−0.633086	−	0.774082i	$-0.718212\pi$
$443$		−	6.39479e6i		−	1.54816i	0.633086	−	0.774082i	$-0.281788\pi$
$444$	23842.9	−	2.77406e6i	0.00573986	−	0.667818i
$445$	999699.			0.239315
$446$	4.06200e6			0.966947
$447$	−47442.4	+	5.51980e6i	−0.0112305	+	1.30664i
$448$			3.31473e6i			0.780284i
$449$		−	4.54884e6i		−	1.06484i	−0.846480	−	0.532420i	$-0.821283\pi$
$449$		−	4.54884e6i		−	1.06484i	0.846480	−	0.532420i	$-0.178717\pi$
$450$	2.60263e6	+	44742.2i	0.605872	+	0.0104156i
$451$	1.90361e6	−	1.03427e6i	0.440693	−	0.239437i
$452$			4.00197e6i			0.921357i
$453$	7.68917e6	+	66088.0i	1.76049	+	0.0151313i
$454$	−4.79889e6			−1.09270
$455$			1.39558e6i			0.316028i
$456$	−3.47340e6	−	29853.7i	−0.782245	−	0.00672335i
$457$			2.25014e6i			0.503987i	0.967729	+	0.251993i	$0.0810861\pi$
$457$			2.25014e6i			0.503987i	−0.967729	+	0.251993i	$0.918914\pi$
$458$	−3.36205e6			−0.748928
$459$	122565.	−	4.75243e6i	0.0271540	−	1.05289i
$460$	199858.			0.0440379
$461$	−3.13541e6			−0.687136			−0.343568	−	0.939128i	$-0.611636\pi$
$461$	−3.13541e6			−0.687136			−0.343568	+	0.939128i	$0.611636\pi$
$462$	2.98971e6	−	1.59124e6i	0.651666	−	0.346842i
$463$	−5.47459e6			−1.18686			−0.593429	−	0.804886i	$-0.702226\pi$
$463$	−5.47459e6			−1.18686			−0.593429	+	0.804886i	$0.702226\pi$
$464$	150918.			0.0325422
$465$	1.19374e6	+	10260.2i	0.256023	+	0.00220050i
$466$	2.42568e6			0.517451
$467$			8.52104e6i			1.80801i	0.427524	+	0.904004i	$0.359386\pi$
$467$			8.52104e6i			1.80801i	−0.427524	+	0.904004i	$0.640614\pi$
$468$	−62182.5	+	3.61712e6i	−0.0131236	+	0.763393i
$469$			3.05491e6i			0.641307i
$470$	481494.			0.100542
$471$	−12655.1	+	1.47239e6i	−0.00262853	+	0.305823i
$472$			4.21201e6i			0.870230i
$473$	−3.99800e6	−	7.35847e6i	−0.821655	−	1.51229i
$474$	619226.	+	5322.21i	0.126591	+	0.00108804i
$475$		−	3.62352e6i		−	0.736880i
$476$			3.61720e6i			0.731736i
$477$	−100154.	+	5.82590e6i	−0.0201545	+	1.17238i
$478$	2.14089e6			0.428574
$479$	−8568.59			−0.00170636			−0.000853180	−	1.00000i	$-0.500272\pi$
$479$	−8568.59			−0.00170636			−0.000853180		1.00000i	$0.500272\pi$
$480$	1.05603e6	+	9076.54i	0.209206	+	0.00179811i
$481$		−	7.25328e6i		−	1.42946i
$482$		−	4.46309e6i		−	0.875020i
$483$	17784.0	−	2.06913e6i	0.00346866	−	0.403570i
$484$	−1.67496e6	+	2.58238e6i	−0.325006	+	0.501080i
$485$		−	1.18022e6i		−	0.227829i
$486$	−141963.	+	3.30146e6i	−0.0272637	+	0.634038i
$487$	440964.			0.0842520			0.0421260	−	0.999112i	$-0.486587\pi$
$487$	440964.			0.0842520			0.0421260	+	0.999112i	$0.486587\pi$
$488$		−	4.99912e6i		−	0.950263i
$489$	−39697.9	+	4.61875e6i	−0.00750750	+	0.873478i
$490$		−	253124.i		−	0.0476259i
$491$	179754.			0.0336493			0.0168246	−	0.999858i	$-0.494644\pi$
$491$	179754.			0.0336493			0.0168246	+	0.999858i	$0.494644\pi$
$492$	13823.0	−	1.60827e6i	0.00257447	−	0.299533i
$493$	4.01766e6			0.744486
$494$	−3.39592e6			−0.626095
$495$	−535518.	−	1.02736e6i	−0.0982339	−	0.188455i
$496$	303890.			0.0554641
$497$	−8.51527e6			−1.54635
$498$	−24805.9	+	2.88610e6i	−0.00448210	+	0.521481i
$499$	4.77108e6			0.857759			0.428879	−	0.903362i	$-0.358908\pi$
$499$	4.77108e6			0.857759			0.428879	+	0.903362i	$0.358908\pi$
$500$			1.38706e6i			0.248124i
$501$	76504.0	−	8.90105e6i	0.0136173	−	1.58433i
$502$		−	6.33871e6i		−	1.12264i
$503$	−270590.			−0.0476860			−0.0238430	−	0.999716i	$-0.507590\pi$
$503$	−270590.			−0.0476860			−0.0238430	+	0.999716i	$0.507590\pi$
$504$	115578.	−	6.72312e6i	0.0202675	−	1.17895i
$505$		−	99955.6i		−	0.0174413i
$506$	−605407.	−	1.11427e6i	−0.105116	−	0.193471i
$507$	−31549.0	+	3.67065e6i	−0.00545087	+	0.634195i
$508$		−	2.23735e6i		−	0.384658i
$509$		−	3.74567e6i		−	0.640819i	−0.947279	−	0.320410i	$-0.896179\pi$
$509$		−	3.74567e6i		−	0.640819i	0.947279	−	0.320410i	$-0.103821\pi$
$510$	−834366.	−	7171.33i	−0.142047	−	0.00122088i
$511$	1.81349e6			0.307229
$512$	545645.			0.0919888
$513$	4.59852e6	+	118595.i	0.771479	+	0.0198964i
$514$			1.24855e6i			0.208448i
$515$		−	137857.i		−	0.0229040i
$516$	−6.21682e6	−	53433.2i	−1.02788	−	0.00883460i
$517$	2.16292e6	+	3.98094e6i	0.355889	+	0.655027i
$518$			5.04111e6i			0.825471i
$519$	1695.85	−	197307.i	0.000276356	−	0.0321533i
$520$	1.69807e6			0.275389
$521$			6.27808e6i			1.01329i	0.862156	+	0.506644i	$0.169114\pi$
$521$			6.27808e6i			1.01329i	−0.862156	+	0.506644i	$0.830886\pi$
$522$	−2.79226e6	−	48002.3i	−0.448518	−	0.00771055i
$523$		−	5.76389e6i		−	0.921428i	−0.887549	−	0.460714i	$-0.847593\pi$
$523$		−	5.76389e6i		−	0.921428i	0.887549	−	0.460714i	$-0.152407\pi$
$524$	3.38084e6			0.537894
$525$	7.01421e6	+	60286.8i	1.11066	+	0.00954605i
$526$	−3.53800e6			−0.557562
$527$	8.08999e6			1.26888
$528$	−138564.	−	260342.i	−0.0216304	−	0.0406405i
$529$	5.66157e6			0.879626
$530$	1.02268e6			0.158143
$531$	95878.5	−	5.57720e6i	0.0147566	−	0.858380i
$532$	−3.50005e6			−0.536160
$533$		−	4.20510e6i		−	0.641149i
$534$	−4.70892e6	−	40472.9i	−0.714609	−	0.00614202i
$535$			2.15601e6i			0.325662i
$536$	3.71706e6			0.558841
$537$	729059.	+	6266.22i	0.109101	+	0.000937713i
$538$			4.91064e6i			0.731446i
$539$	2.09280e6	−	1.13706e6i	0.310282	−	0.168582i
$540$	−859804.	−	22174.3i	−0.126886	−	0.00327239i
$541$		−	7.90557e6i		−	1.16129i	−0.814157	−	0.580644i	$-0.802801\pi$
$541$		−	7.90557e6i		−	1.16129i	0.814157	−	0.580644i	$-0.197199\pi$
$542$			1.24564e6i			0.182135i
$543$	15823.6	−	1.84104e6i	0.00230306	−	0.267955i
$544$	7.15672e6			1.03685
$545$	−1.82184e6			−0.262736
$546$	56500.1	−	6.57364e6i	0.00811087	−	0.943679i
$547$			721261.i			0.103068i	0.998671	+	0.0515341i	$0.0164111\pi$
$547$			721261.i			0.103068i	−0.998671	+	0.0515341i	$0.983589\pi$
$548$		−	6.64549e6i		−	0.945312i
$549$	−113796.	+	6.61943e6i	−0.0161137	+	0.937323i
$550$	3.77732e6	−	2.05229e6i	0.532448	−	0.289289i
$551$			3.88754e6i			0.545502i
$552$	−2.51761e6	−	21638.7i	−0.351675	−	0.00302262i
$553$	1.66872e6			0.232044
$554$			6.90377e6i			0.955679i
$555$	1.72439e6	+	14821.0i	0.237631	+	0.00204242i
$556$		−	166669.i		−	0.0228648i
$557$	8.49710e6			1.16047			0.580233	−	0.814450i	$-0.302961\pi$
$557$	8.49710e6			1.16047			0.580233	+	0.814450i	$0.302961\pi$
$558$	−5.62252e6	−	96657.6i	−0.764444	−	0.0131417i
$559$	−1.62550e7			−2.20018
$560$	−84461.7			−0.0113812
$561$	−3.68877e6	−	6.93067e6i	−0.494851	−	0.929754i
$562$	−5.45013e6			−0.727891
$563$	1.78249e6			0.237005			0.118502	−	0.992954i	$-0.462191\pi$
$563$	1.78249e6			0.237005			0.118502	+	0.992954i	$0.462191\pi$
$564$	3.36331e6	+	28907.4i	0.445214	+	0.00382659i
$565$	−2.48767e6			−0.327848
$566$			703591.i			0.0923165i
$567$	−306079.	+	8.89958e6i	−0.0399830	+	1.16255i
$568$			1.03610e7i			1.34750i
$569$	−1.16476e7			−1.50819			−0.754094	−	0.656767i	$-0.771924\pi$
$569$	−1.16476e7			−1.50819			−0.754094	+	0.656767i	$0.771924\pi$
$570$	6939.07	−	807344.i	0.000894570	−	0.104081i
$571$		−	7.50760e6i		−	0.963632i	−0.876272	−	0.481816i	$-0.839977\pi$
$571$		−	7.50760e6i		−	0.963632i	0.876272	−	0.481816i	$-0.160023\pi$
$572$	2.85227e6	+	5.24971e6i	0.364502	+	0.670880i
$573$	8.43291e6	+	72480.4i	1.07298	+	0.00922219i
$574$			2.92260e6i			0.370245i
$575$		−	2.62642e6i		−	0.331280i
$576$	−5.34043e6	−	91808.2i	−0.670688	−	0.0115299i
$577$	−1.53192e7			−1.91557			−0.957784	−	0.287488i	$-0.907180\pi$
$577$	−1.53192e7			−1.91557			−0.957784	+	0.287488i	$0.907180\pi$
$578$	−557237.			−0.0693778
$579$	−9.52371e6	−	81855.7i	−1.18062	−	0.0101474i
$580$		−	726871.i		−	0.0897196i
$581$			7.77762e6i			0.955887i
$582$	−47781.4	+	5.55924e6i	−0.00584725	+	0.680312i
$583$	4.59399e6	+	8.45541e6i	0.559781	+	1.03030i
$584$		−	2.20656e6i		−	0.267722i
$585$	−2.24845e6	−	38653.4i	−0.271639	−	0.00466980i
$586$	9.88986e6			1.18972
$587$		−	2.66999e6i		−	0.319826i	−0.987131	−	0.159913i	$-0.948879\pi$
$587$		−	2.66999e6i		−	0.319826i	0.987131	−	0.159913i	$-0.0511214\pi$
$588$	15196.8	−	1.76811e6i	0.00181263	−	0.210895i
$589$			7.82798e6i			0.929740i
$590$	−979022.			−0.115788
$591$	−49022.6	+	5.70365e6i	−0.00577334	+	0.671714i
$592$	438975.			0.0514797
$593$	814291.			0.0950918			0.0475459	−	0.998869i	$-0.484860\pi$
$593$	814291.			0.0950918			0.0475459	+	0.998869i	$0.484860\pi$
$594$	2.48088e6	+	4.86087e6i	0.288496	+	0.565259i
$595$	−2.24849e6			−0.260375
$596$	6.76774e6			0.780419
$597$	−29258.0	+	3.40410e6i	−0.00335977	+	0.390900i
$598$	−2.46145e6			−0.281474
$599$		−	1.21744e6i		−	0.138637i	−0.997595	−	0.0693187i	$-0.977917\pi$
$599$		−	1.21744e6i		−	0.138637i	0.997595	−	0.0693187i	$-0.0220825\pi$
$600$	73354.0	−	8.53455e6i	0.00831851	−	0.967837i
$601$			3.13293e6i			0.353806i	0.984228	+	0.176903i	$0.0566078\pi$
$601$			3.13293e6i			0.353806i	−0.984228	+	0.176903i	$0.943392\pi$
$602$	1.12974e7			1.27054
$603$	−4.92183e6	−	84612.0i	−0.551231	−	0.00947630i
$604$		−	9.42757e6i		−	1.05150i
$605$	−1.60524e6	−	1.04117e6i	−0.178300	−	0.115647i
$606$	−4046.71	+	470824.i	−0.000447631	+	0.0520808i
$607$			1.32997e7i			1.46511i	0.680707	+	0.732556i	$0.261673\pi$
$607$			1.32997e7i			1.46511i	−0.680707	+	0.732556i	$0.738327\pi$
$608$			6.92494e6i			0.759726i
$609$	−7.52529e6	−	64679.5i	−0.822205	−	0.00706681i
$610$	1.16198e6			0.126436
$611$	8.79398e6			0.952977
$612$	−5.82775e6	−	100186.i	−0.628959	−	0.0108125i
$613$		−	2.10731e6i		−	0.226504i	−0.993566	−	0.113252i	$-0.963873\pi$
$613$		−	2.10731e6i		−	0.226504i	0.993566	−	0.113252i	$-0.0361268\pi$
$614$			2.45748e6i			0.263068i
$615$	999718.	+	8592.52i	0.106583	+	0.000916079i
$616$	−5.30149e6	−	9.75759e6i	−0.562919	−	1.03607i
$617$		−	4.13947e6i		−	0.437756i	−0.975752	−	0.218878i	$-0.929760\pi$
$617$		−	4.13947e6i		−	0.437756i	0.975752	−	0.218878i	$-0.0702397\pi$
$618$	−5581.16	+	649354.i	−0.000587832	+	0.0683928i
$619$	−5.30546e6			−0.556540			−0.278270	−	0.960503i	$-0.589761\pi$
$619$	−5.30546e6			−0.556540			−0.278270	+	0.960503i	$0.589761\pi$
$620$		−	1.46363e6i		−	0.152916i
$621$	3.33312e6	+	85961.0i	0.346835	+	0.00894484i
$622$			1.48978e6i			0.154400i
$623$	−1.26898e7			−1.30989
$624$	−572426.	−	4919.97i	−0.0588516	−	0.000505826i
$625$	8.46235e6			0.866544
$626$	−4.60479e6			−0.469649
$627$	6.70621e6	−	3.56930e6i	0.681253	−	0.362589i
$628$	1.80527e6			0.182660
$629$	1.16862e7			1.17773
$630$	1.56270e6	+	26864.5i	0.156864	+	0.00269667i
$631$	8.10190e6			0.810053			0.405027	−	0.914305i	$-0.367262\pi$
$631$	8.10190e6			0.810053			0.405027	+	0.914305i	$0.367262\pi$
$632$		−	2.03042e6i		−	0.202205i
$633$	1.08669e7	+	93400.0i	1.07794	+	0.00926483i
$634$		−	9.72293e6i		−	0.960670i
$635$	1.39076e6			0.136873
$636$	7.14357e6	+	61398.6i	0.700281	+	0.00601888i
$637$		−	4.62304e6i		−	0.451418i
$638$	−4.05255e6	+	2.20183e6i	−0.394164	+	0.214157i
$639$	235848.	−	1.37191e7i	0.0228497	−	1.32915i
$640$		−	1.23044e6i		−	0.118744i
$641$			1.82583e6i			0.175515i	0.996142	+	0.0877576i	$0.0279701\pi$
$641$			1.82583e6i			0.175515i	−0.996142	+	0.0877576i	$0.972030\pi$
$642$	87286.5	−	1.01556e7i	0.00835813	−	0.972447i
$643$	−3.69890e6			−0.352813			−0.176407	−	0.984317i	$-0.556447\pi$
$643$	−3.69890e6			−0.352813			−0.176407	+	0.984317i	$0.556447\pi$
$644$	−2.53692e6			−0.241042
$645$	33214.7	−	3.86445e6i	0.00314363	−	0.365753i
$646$		−	5.47136e6i		−	0.515839i
$647$			1.07732e7i			1.01178i	0.862599	+	0.505888i	$0.168835\pi$
$647$			1.07732e7i			1.01178i	−0.862599	+	0.505888i	$0.831165\pi$
$648$	1.08286e7	+	372421.i	1.01306	+	0.0348415i
$649$	−4.39788e6	−	8.09446e6i	−0.409856	−	0.754356i
$650$		−	8.34418e6i		−	0.774640i
$651$	−1.51530e7	−	130239.i	−1.40135	−	0.0120445i
$652$	5.66297e6			0.521706
$653$		−	1.06326e7i		−	0.975791i	−0.872902	−	0.487896i	$-0.837765\pi$
$653$		−	1.06326e7i		−	0.975791i	0.872902	−	0.487896i	$-0.162235\pi$
$654$	8.58149e6	+	73757.4i	0.784546	+	0.00674313i
$655$			2.10157e6i			0.191400i
$656$	254497.			0.0230899
$657$	−50228.3	+	2.92175e6i	−0.00453978	+	0.264077i
$658$	−6.11191e6			−0.550316
$659$	−6.09424e6			−0.546645			−0.273323	−	0.961922i	$-0.588123\pi$
$659$	−6.09424e6			−0.546645			−0.273323	+	0.961922i	$0.588123\pi$
$660$	−1.25389e6	+	667368.i	−0.112047	+	0.0596356i
$661$	1.01212e7			0.901004			0.450502	−	0.892775i	$-0.351245\pi$
$661$	1.01212e7			0.901004			0.450502	+	0.892775i	$0.351245\pi$
$662$	3.96782e6			0.351890
$663$	−1.52388e7	−	130977.i	−1.34638	−	0.0115721i
$664$	9.46342e6			0.832968
$665$		−	2.17567e6i		−	0.190783i
$666$	−8.12185e6	−	139624.i	−0.709528	−	0.0121976i
$667$			2.81779e6i			0.245242i
$668$	−1.09134e7			−0.946281
$669$	−151593.	+	1.76374e7i	−0.0130952	+	1.52360i
$670$			863980.i			0.0743561i
$671$	5.21972e6	+	9.60710e6i	0.447549	+	0.823732i
$672$	−1.34049e7	−	115214.i	−1.14509	−	0.00984201i
$673$		−	1.28100e7i		−	1.09022i	−0.838366	−	0.545108i	$-0.816489\pi$
$673$		−	1.28100e7i		−	1.09022i	0.838366	−	0.545108i	$-0.183511\pi$
$674$		−	4.31857e6i		−	0.366176i
$675$	−291403.	+	1.12991e7i	−0.0246169	+	0.954517i
$676$	4.50053e6			0.378788
$677$	−1.11938e7			−0.938656			−0.469328	−	0.883024i	$-0.655504\pi$
$677$	−1.11938e7			−0.938656			−0.469328	+	0.883024i	$0.655504\pi$
$678$	1.17178e7	+	100714.i	0.978974	+	0.00841423i
$679$			1.49813e7i			1.24703i
$680$			2.73585e6i			0.226893i
$681$	179093.	−	2.08371e7i	0.0147983	−	1.72174i
$682$	−8.16024e6	+	4.43361e6i	−0.671803	+	0.365003i
$683$			577600.i			0.0473779i	0.999719	+	0.0236889i	$0.00754113\pi$
$683$			577600.i			0.0473779i	−0.999719	+	0.0236889i	$0.992459\pi$
$684$	96941.0	−	5.63900e6i	0.00792259	−	0.460853i
$685$	4.13091e6			0.336372
$686$		−	5.88597e6i		−	0.477538i
$687$	125471.	−	1.45982e7i	0.0101426	−	1.18007i
$688$		−	983768.i		−	0.0792358i
$689$	1.86782e7			1.49895
$690$	5029.62	−	585184.i	0.000402173	−	0.0467918i
$691$	7.05063e6			0.561737			0.280868	−	0.959746i	$-0.409378\pi$
$691$	7.05063e6			0.561737			0.280868	+	0.959746i	$0.409378\pi$
$692$	−241916.			−0.0192043
$693$	6.79768e6	+	1.30409e7i	0.537685	+	1.03151i
$694$	5.79570e6			0.456780
$695$	103603.			0.00813601
$696$	−78698.8	+	9.15640e6i	−0.00615808	+	0.716476i
$697$	6.77508e6			0.528241
$698$		−	1.13870e7i		−	0.884648i
$699$	−90525.8	+	1.05324e7i	−0.00700777	+	0.815336i
$700$		−	8.60002e6i		−	0.663367i
$701$	−5.52192e6			−0.424419			−0.212209	−	0.977224i	$-0.568066\pi$
$701$	−5.52192e6			−0.424419			−0.212209	+	0.977224i	$0.568066\pi$
$702$	1.05894e7	+	273099.i	0.811012	+	0.0209159i
$703$			1.13077e7i			0.862949i
$704$	−7.75083e6	+	4.21118e6i	−0.589409	+	0.320237i
$705$	−17969.2	+	2.09067e6i	−0.00136162	+	0.158421i
$706$			2.42478e6i			0.183088i
$707$			1.26880e6i			0.0954652i
$708$	−6.83862e6	−	58777.6i	−0.512726	−	0.00440685i
$709$	−9.02213e6			−0.674052			−0.337026	−	0.941495i	$-0.609421\pi$
$709$	−9.02213e6			−0.674052			−0.337026	+	0.941495i	$0.609421\pi$
$710$	−2.40826e6			−0.179291
$711$	−46218.7	+	2.68851e6i	−0.00342881	+	0.199452i
$712$			1.54404e7i			1.14145i
$713$			5.67392e6i			0.417984i
$714$	1.05912e7	+	91030.4i	0.777495	+	0.00668253i
$715$	−3.26328e6	+	1.77300e6i	−0.238720	+	0.129701i
$716$		−	893888.i		−	0.0651629i
$717$	−79897.6	+	9.29588e6i	−0.00580411	+	0.675294i
$718$	−8.90505e6			−0.644652
$719$			1.01462e7i			0.731949i	0.930625	+	0.365974i	$0.119264\pi$
$719$			1.01462e7i			0.731949i	−0.930625	+	0.365974i	$0.880736\pi$
$720$	2339.34	−	136078.i	0.000168175	−	0.00978266i
$721$			1.74991e6i			0.125365i
$722$	−3.59498e6			−0.256657
$723$	1.93790e7	+	166561.i	1.37875	+	0.0118503i
$724$	−2.25726e6			−0.160043
$725$	−9.55215e6			−0.674926
$726$	7.51907e6	+	4.96927e6i	0.529447	+	0.349906i
$727$	−1.92374e7			−1.34993			−0.674965	−	0.737850i	$-0.735841\pi$
$727$	−1.92374e7			−1.34993			−0.674965	+	0.737850i	$0.735841\pi$
$728$	−2.15547e7			−1.50735
$729$	−1.43298e7	−	739622.i	−0.998671	−	0.0515456i
$730$	512885.			0.0356215
$731$		−	2.61893e7i		−	1.81272i
$732$	8.11658e6	+	69761.5i	0.559880	+	0.00481214i
$733$		−	1.22590e7i		−	0.842743i	−0.906888	−	0.421371i	$-0.861549\pi$
$733$		−	1.22590e7i		−	0.842743i	0.906888	−	0.421371i	$-0.138451\pi$
$734$	8.86164e6			0.607119
$735$	1.09908e6	+	9446.52i	0.0750430	+	0.000644990i
$736$			5.01938e6i			0.341551i
$737$	−7.14330e6	+	3.88109e6i	−0.484429	+	0.263200i
$738$	−4.70866e6	−	80947.3i	−0.318241	−	0.00547094i
$739$			1.89627e6i			0.127729i	0.997959	+	0.0638645i	$0.0203425\pi$
$739$			1.89627e6i			0.127729i	−0.997959	+	0.0638645i	$0.979657\pi$
$740$		−	2.11425e6i		−	0.141931i
$741$	126735.	−	1.47453e7i	0.00847912	−	0.986524i
$742$	−1.29815e7			−0.865598
$743$	−6.60277e6			−0.438787			−0.219394	−	0.975636i	$-0.570408\pi$
$743$	−6.60277e6			−0.438787			−0.219394	+	0.975636i	$0.570408\pi$
$744$	−158468.	+	1.84374e7i	−0.0104957	+	1.22114i
$745$			4.20691e6i			0.277698i
$746$			7.78278e6i			0.512021i
$747$	−1.25307e7	−	215417.i	−0.821625	−	0.0141247i
$748$	−8.45809e6	+	4.59544e6i	−0.552737	+	0.300313i
$749$		−	2.73677e7i		−	1.78252i
$750$	4.06131e6	+	34906.7i	0.263641	+	0.00226598i
$751$	3.98388e6			0.257754			0.128877	−	0.991661i	$-0.458863\pi$
$751$	3.98388e6			0.257754			0.128877	+	0.991661i	$0.458863\pi$
$752$			532220.i			0.0343199i
$753$	2.75230e7	+	236559.i	1.76892	+	0.0152038i
$754$			8.95216e6i			0.573455i
$755$	5.86029e6			0.374155
$756$	1.09141e7	+	281473.i	0.694515	+	0.0179115i
$757$	1.21560e7			0.770994			0.385497	−	0.922709i	$-0.374030\pi$
$757$	1.21560e7			0.770994			0.385497	+	0.922709i	$0.374030\pi$
$758$	−1.34008e7			−0.847143
$759$	4.86083e6	−	2.58712e6i	0.306271	−	0.163009i
$760$	−2.64725e6			−0.166250
$761$	1.46323e7			0.915904			0.457952	−	0.888977i	$-0.348583\pi$
$761$	1.46323e7			0.915904			0.457952	+	0.888977i	$0.348583\pi$
$762$	−6.55096e6	−	56305.2i	−0.408712	−	0.00351286i
$763$	2.31258e7			1.43809
$764$		−	1.03395e7i		−	0.640862i
$765$	62276.6	−	3.62260e6i	0.00384744	−	0.223803i
$766$		−	7.82616e6i		−	0.481922i
$767$	−1.78808e7			−1.09749
$768$	−144050.	+	1.67599e7i	−0.00881273	+	1.02534i
$769$			6.23273e6i			0.380069i	0.981777	+	0.190034i	$0.0608600\pi$
$769$			6.23273e6i			0.380069i	−0.981777	+	0.190034i	$0.939140\pi$
$770$	2.26802e6	−	1.23226e6i	0.137854	−	0.0748987i
$771$	−5.42128e6	−	46595.6i	−0.328447	−	0.00282299i
$772$			1.16769e7i			0.705153i
$773$			2.38906e7i			1.43806i	0.694978	+	0.719031i	$0.255414\pi$
$773$			2.38906e7i			1.43806i	−0.694978	+	0.719031i	$0.744586\pi$
$774$	−312905.	+	1.82015e7i	−0.0187741	+	1.09208i
$775$	−1.92343e7			−1.15033
$776$	1.82285e7			1.08667
$777$	−2.18888e7	−	188133.i	−1.30068	−	0.0111792i
$778$		−	8.92041e6i		−	0.528367i
$779$			6.55565e6i			0.387055i
$780$	−23696.2	+	2.75699e6i	−0.00139457	+	0.162255i
$781$	−1.08182e7	−	1.99113e7i	−0.634638	−	1.16808i
$782$		−	3.96578e6i		−	0.231906i
$783$	312635.	−	1.21224e7i	0.0182236	−	0.706616i
$784$	279791.			0.0162571
$785$			1.12218e6i			0.0649962i
$786$	85082.3	−	9.89911e6i	0.00491228	−	0.571531i
$787$		−	2.81984e7i		−	1.62288i	−0.584433	−	0.811442i	$-0.698683\pi$
$787$		−	2.81984e7i		−	1.62288i	0.584433	−	0.811442i	$-0.301317\pi$
$788$	6.99316e6			0.401197
$789$	132037.	−	1.53622e7i	0.00755098	−	0.878537i
$790$	471942.			0.0269043
$791$	3.15777e7			1.79448
$792$	1.58675e7	−	8.27109e6i	0.898868	−	0.468543i
$793$	2.12223e7			1.19842
$794$	194441.			0.0109455
$795$	−38166.1	+	4.44053e6i	−0.00214171	+	0.249182i
$796$	4.17371e6			0.233475
$797$			3.41343e6i			0.190347i	0.995461	+	0.0951733i	$0.0303405\pi$
$797$			3.41343e6i			0.190347i	−0.995461	+	0.0951733i	$0.969659\pi$
$798$	−88082.2	+	1.02481e7i	−0.00489645	+	0.569689i
$799$			1.41685e7i			0.785156i
$800$	−1.70154e7			−0.939976
$801$	351471.	−	2.04449e7i	0.0193557	−	1.12591i
$802$		−	1.13419e7i		−	0.622658i
$803$	2.30394e6	+	4.24048e6i	0.126090	+	0.232074i
$804$	−51870.8	+	6.03503e6i	−0.00282997	+	0.329260i
$805$		−	1.57698e6i		−	0.0857703i
$806$			1.80261e7i			0.977383i
$807$	−2.13223e7	−	183264.i	−1.15252	−	0.00990587i
$808$	1.54381e6			0.0831892
$809$	7.67008e6			0.412030			0.206015	−	0.978549i	$-0.433950\pi$
$809$	7.67008e6			0.412030			0.206015	+	0.978549i	$0.433950\pi$
$810$	−86564.2	+	2.51695e6i	−0.00463581	+	0.134791i
$811$		−	2.38944e7i		−	1.27569i	−0.770166	−	0.637843i	$-0.779827\pi$
$811$		−	2.38944e7i		−	1.27569i	0.770166	−	0.637843i	$-0.220173\pi$
$812$			9.22664e6i			0.491082i
$813$	−5.40862e6	−	46486.8i	−0.286986	−	0.00246663i
$814$	−1.17876e7	+	6.40445e6i	−0.623542	+	0.338782i
$815$			3.52017e6i			0.185639i
$816$	7926.85	−	922268.i	0.000416749	−	0.0484877i
$817$	2.53411e7			1.32822
$818$		−	1.16404e7i		−	0.608252i
$819$	2.85410e7	+	490653.i	1.48682	+	0.0255602i
$820$		−	1.22574e6i		−	0.0636595i
$821$	−2.14968e7			−1.11305			−0.556527	−	0.830830i	$-0.687866\pi$
$821$	−2.14968e7			−1.11305			−0.556527	+	0.830830i	$0.687866\pi$
$822$	−1.94580e7	−	167240.i	−1.00443	−	0.00863300i
$823$	−1.39033e7			−0.715512			−0.357756	−	0.933815i	$-0.616458\pi$
$823$	−1.39033e7			−0.715512			−0.357756	+	0.933815i	$0.616458\pi$
$824$	2.12921e6			0.109245
$825$	8.77019e6	+	1.64779e7i	0.448616	+	0.842884i
$826$	1.24274e7			0.633766
$827$	1.82513e7			0.927964			0.463982	−	0.885845i	$-0.346420\pi$
$827$	1.82513e7			0.927964			0.463982	+	0.885845i	$0.346420\pi$
$828$	70265.4	−	4.08729e6i	0.00356177	−	0.207186i
$829$	−1.05826e7			−0.534819			−0.267410	−	0.963583i	$-0.586168\pi$
$829$	−1.05826e7			−0.534819			−0.267410	+	0.963583i	$0.586168\pi$
$830$			2.19964e6i			0.110830i
$831$	−2.99766e7	−	257647.i	−1.50584	−	0.0129426i
$832$			1.71217e7i			0.857511i
$833$	7.44844e6			0.371923
$834$	−488006.	−	4194.39i	−0.0242946	−	0.000208811i
$835$		−	6.78392e6i		−	0.336717i
$836$	−4.44661e6	−	8.18416e6i	−0.220046	−	0.405003i
$837$	629524.	−	2.44097e7i	0.0310598	−	1.20434i
$838$		−	1.93940e6i		−	0.0954020i
$839$		−	3.34860e6i		−	0.164232i	−0.996623	−	0.0821160i	$-0.973832\pi$
$839$		−	3.34860e6i		−	0.164232i	0.996623	−	0.0821160i	$-0.0261678\pi$
$840$	44043.9	−	5.12440e6i	0.00215371	−	0.250579i
$841$	−1.02630e7			−0.500362
$842$	1.09537e7			0.532451
$843$	203397.	−	2.36648e7i	0.00985772	−	1.14692i
$844$		−	1.33237e7i		−	0.643825i
$845$			2.79758e6i			0.134785i
$846$	169282.	−	9.84704e6i	0.00813177	−	0.473020i
$847$	2.03764e7	+	1.32163e7i	0.975929	+	0.632997i
$848$			1.13042e6i			0.0539821i
$849$	−3.05503e6	−	26257.8i	−0.145461	−	0.00125023i
$850$	1.34438e7			0.638225
$851$			8.19610e6i			0.387957i
$852$	−1.68221e7	−	144585.i	−0.793927	−	0.00682376i
$853$		−	5.72242e6i		−	0.269282i	−0.990894	−	0.134641i	$-0.957012\pi$
$853$		−	5.72242e6i		−	0.269282i	0.990894	−	0.134641i	$-0.0429881\pi$
$854$	−1.47497e7			−0.692052
$855$	3.50527e6	+	60259.7i	0.163986	+	0.00281911i
$856$	−3.32997e7			−1.55330
$857$	1.32490e7			0.616215			0.308107	−	0.951352i	$-0.400304\pi$
$857$	1.32490e7			0.616215			0.308107	+	0.951352i	$0.400304\pi$
$858$	1.54429e7	−	8.21932e6i	0.716162	−	0.381169i
$859$	−2.07212e6			−0.0958145			−0.0479072	−	0.998852i	$-0.515255\pi$
$859$	−2.07212e6			−0.0958145			−0.0479072	+	0.998852i	$0.515255\pi$
$860$	−4.73814e6			−0.218455
$861$	−1.26901e7	−	109070.i	−0.583386	−	0.00501417i
$862$	7.53979e6			0.345614
$863$		−	1.16792e6i		−	0.0533808i	−0.999644	−	0.0266904i	$-0.991503\pi$
$863$		−	1.16792e6i		−	0.0533808i	0.999644	−	0.0266904i	$-0.00849682\pi$
$864$	556901.	−	2.15938e7i	0.0253801	−	0.984111i
$865$		−	150378.i		−	0.00683350i
$866$	1.40778e7			0.637884
$867$	20796.0	−	2.41956e6i	0.000939574	−	0.109317i
$868$			1.85788e7i			0.836987i
$869$	2.12002e6	+	3.90197e6i	0.0952335	+	0.175281i
$870$	−2.12828e6	−	18292.4i	−0.0953302	−	0.000819358i
$871$			1.57797e7i			0.704779i
$872$		−	2.81384e7i		−	1.25316i
$873$	−2.41368e7	−	414939.i	−1.07187	−	0.0184267i
$874$	3.83734e6			0.169923
$875$	1.09446e7			0.483259
$876$	3.58258e6	+	30792.1i	0.157738	+	0.00135575i
$877$			4.06658e6i			0.178538i	0.996008	+	0.0892690i	$0.0284531\pi$
$877$			4.06658e6i			0.178538i	−0.996008	+	0.0892690i	$0.971547\pi$
$878$		−	4.71296e6i		−	0.206328i
$879$	−369087.	+	4.29423e7i	−0.0161123	+	1.87462i
$880$	−107304.	−	197497.i	−0.00467098	−	0.00859713i
$881$			2.68824e7i			1.16689i	0.812154	+	0.583443i	$0.198295\pi$
$881$			2.68824e7i			1.16689i	−0.812154	+	0.583443i	$0.801705\pi$
$882$	−5.17664e6	−	88992.5i	−0.224066	−	0.00385196i
$883$	3.29324e7			1.42142			0.710709	−	0.703486i	$-0.248374\pi$
$883$	3.29324e7			1.42142			0.710709	+	0.703486i	$0.248374\pi$
$884$			1.86841e7i			0.804158i
$885$	36536.9	−	4.25097e6i	0.00156810	−	0.182444i
$886$			2.29571e7i			0.982502i
$887$	4.53827e7			1.93678			0.968392	−	0.249435i	$-0.0802447\pi$
$887$	4.53827e7			1.93678			0.968392	+	0.249435i	$0.0802447\pi$
$888$	−228911.	+	2.66332e7i	−0.00974168	+	1.13342i
$889$	−1.76539e7			−0.749179
$890$	−3.58890e6			−0.151875
$891$	−2.11987e7	+	1.05907e7i	−0.894573	+	0.446921i
$892$	2.16250e7			0.910004
$893$	−1.37096e7			−0.575302
$894$	170317.	−	1.98160e7i	0.00712713	−	0.829223i
$895$	555651.			0.0231870
$896$			1.56188e7i			0.649948i
$897$	91860.8	−	1.06878e7i	0.00381197	−	0.443512i
$898$			1.63302e7i			0.675774i
$899$	2.06357e7			0.851570
$900$	1.38557e7	+	238195.i	0.570193	+	0.00980227i
$901$			3.00934e7i			1.23498i
$902$	−6.83391e6	+	3.71299e6i	−0.279674	+	0.151952i
$903$	−421616.	+	4.90539e7i	−0.0172067	+	2.00196i
$904$		−	3.84221e7i		−	1.56373i
$905$		−	1.40314e6i		−	0.0569483i
$906$	−2.76040e7	−	237254.i	−1.11725	−	0.00960271i
$907$	−3.29518e7			−1.33003			−0.665014	−	0.746831i	$-0.731574\pi$
$907$	−3.29518e7			−1.33003			−0.665014	+	0.746831i	$0.731574\pi$
$908$	−2.55480e7			−1.02835
$909$	−2.04419e6	−	35142.1i	−0.0820564	−	0.00141064i
$910$		−	5.01009e6i		−	0.200559i
$911$		−	3.28702e7i		−	1.31222i	−0.754666	−	0.656110i	$-0.772201\pi$
$911$		−	3.28702e7i		−	1.31222i	0.754666	−	0.656110i	$-0.227799\pi$
$912$	892399.	+	7670.12i	0.0355281	+	0.000305362i
$913$	−1.81864e7	+	9.88103e6i	−0.722055	+	0.392306i
$914$		−	8.07795e6i		−	0.319842i
$915$	−43364.6	+	5.04536e6i	−0.00171231	+	0.199223i
$916$	−1.78986e7			−0.704824
$917$		−	2.66766e7i		−	1.04763i
$918$	−440005.	+	1.70611e7i	−0.0172326	+	0.668192i
$919$			1.54186e7i			0.602220i	0.953589	+	0.301110i	$0.0973571\pi$
$919$			1.54186e7i			0.602220i	−0.953589	+	0.301110i	$0.902643\pi$
$920$	−1.91879e6			−0.0747410
$921$	−1.06705e7	−	91712.3i	−0.414510	−	0.00356270i
$922$	1.12561e7			0.436073
$923$	−4.39844e7			−1.69939
$924$	1.59164e7	−	8.47134e6i	0.613290	−	0.326416i
$925$	−2.77843e7			−1.06769
$926$	1.96536e7			0.753209
$927$	−2.81932e6	−	48467.4i	−0.107757	−	0.00185247i
$928$	1.82552e7			0.695851
$929$			4.64429e7i			1.76555i	0.469798	+	0.882774i	$0.344327\pi$
$929$			4.64429e7i			1.76555i	−0.469798	+	0.882774i	$0.655673\pi$
$930$	−4.28551e6	−	36833.8i	−0.162478	−	0.00139649i
$931$			7.20721e6i			0.272517i
$932$	1.29137e7			0.486979
$933$	−6.46873e6	−	55598.4i	−0.243285	−	0.00209102i
$934$		−	3.05903e7i		−	1.14741i
$935$	−2.85658e6	−	5.25765e6i	−0.106861	−	0.196681i
$936$	597002.	−	3.47273e7i	0.0222734	−	1.29563i
$937$			273623.i			0.0101813i	0.999987	+	0.00509066i	$0.00162041\pi$
$937$			273623.i			0.0101813i	−0.999987	+	0.00509066i	$0.998380\pi$
$938$		−	1.09671e7i		−	0.406989i
$939$	171849.	−	1.99942e7i	0.00636040	−	0.740016i
$940$	2.56334e6			0.0946208
$941$	−1.06577e7			−0.392363			−0.196182	−	0.980568i	$-0.562854\pi$
$941$	−1.06577e7			−0.392363			−0.196182	+	0.980568i	$0.562854\pi$
$942$	45431.5	−	5.28584e6i	0.00166813	−	0.194083i
$943$			4.75171e6i			0.174009i
$944$		−	1.08216e6i		−	0.0395242i
$945$	−174967.	+	6.78431e6i	−0.00637347	+	0.247130i
$946$	1.43527e7	+	2.64167e7i	0.521442	+	0.959735i
$947$			2.94592e7i			1.06745i	0.845659	+	0.533723i	$0.179208\pi$
$947$			2.94592e7i			1.06745i	−0.845659	+	0.533723i	$0.820792\pi$
$948$	3.29659e6	+	28334.0i	0.119136	+	0.00102397i
$949$	9.36731e6			0.337636
$950$			1.30084e7i			0.467642i
$951$	4.22175e7	+	362857.i	1.51371	+	0.0130102i
$952$		−	3.47280e7i		−	1.24190i
$953$	6.69811e6			0.238902			0.119451	−	0.992840i	$-0.461887\pi$
$953$	6.69811e6			0.238902			0.119451	+	0.992840i	$0.461887\pi$
$954$	359550.	−	2.09148e7i	0.0127905	−	0.744018i
$955$	6.42713e6			0.228039
$956$	1.13975e7			0.403335
$957$	−9.40922e6	−	1.76786e7i	−0.332104	−	0.623975i
$958$	30761.1			0.00108290
$959$	−5.24364e7			−1.84114
$960$	−4.07051e6	−	34985.8i	−0.142551	−	0.00122522i
$961$	1.29231e7			0.451395
$962$			2.60391e7i			0.907170i
$963$	4.40927e7	+	758005.i	1.53215	+	0.0263394i
$964$		−	2.37603e7i		−	0.823491i
$965$	−7.25848e6			−0.250916
$966$	−63844.3	+	7.42812e6i	−0.00220130	+	0.256116i
$967$		−	3.37513e7i		−	1.16071i	−0.814363	−	0.580356i	$-0.802913\pi$
$967$		−	3.37513e7i		−	1.16071i	0.814363	−	0.580356i	$-0.197087\pi$
$968$	1.60810e7	−	2.47929e7i	0.551599	−	0.850432i
$969$	2.37570e7	+	204190.i	0.812795	+	0.00698593i
$970$			4.23697e6i			0.144586i
$971$		−	9.80791e6i		−	0.333832i	−0.985971	−	0.166916i	$-0.946619\pi$
$971$		−	9.80791e6i		−	0.333832i	0.985971	−	0.166916i	$-0.0533809\pi$
$972$	−755774.	+	1.75761e7i	−0.0256582	+	0.596700i
$973$	−1.31510e6			−0.0445326
$974$	−1.58305e6			−0.0534684
$975$	3.62309e7	+	311402.i	1.22058	+	0.0104908i
$976$			1.28439e6i			0.0431591i
$977$		−	3.44181e7i		−	1.15359i	−0.816890	−	0.576793i	$-0.804304\pi$
$977$		−	3.44181e7i		−	1.15359i	0.816890	−	0.576793i	$-0.195696\pi$
$978$	142514.	−	1.65812e7i	0.00476444	−	0.554330i
$979$	−1.61217e7	−	2.96727e7i	−0.537594	−	0.989463i
$980$		−	1.34756e6i		−	0.0448212i
$981$	−640518.	+	3.72586e7i	−0.0212500	+	1.23610i
$982$	−645314.			−0.0213547
$983$		−	1.57313e7i		−	0.519254i	−0.965709	−	0.259627i	$-0.916400\pi$
$983$		−	1.57313e7i		−	0.519254i	0.965709	−	0.259627i	$-0.0835995\pi$
$984$	−132712.	+	1.54407e7i	−0.00436939	+	0.508368i
$985$			4.34703e6i			0.142759i
$986$	−1.44233e7			−0.472469
$987$	228095.	−	2.65383e7i	0.00745286	−	0.867121i
$988$	−1.80790e7			−0.589225
$989$	1.83679e7			0.597130
$990$	1.92250e6	+	3.68818e6i	0.0623416	+	0.119598i
$991$	−2.38014e7			−0.769870			−0.384935	−	0.922944i	$-0.625776\pi$
$991$	−2.38014e7			−0.769870			−0.384935	+	0.922944i	$0.625776\pi$
$992$	3.67587e7			1.18599
$993$	−148078.	+	1.72285e7i	−0.00476560	+	0.554466i
$994$	3.05696e7			0.981350
$995$			2.59443e6i			0.0830776i
$996$	−132060.	+	1.53648e7i	−0.00421816	+	0.490772i
$997$			7.04150e6i			0.224351i	0.993688	+	0.112175i	$0.0357818\pi$
$997$			7.04150e6i			0.224351i	−0.993688	+	0.112175i	$0.964218\pi$
$998$	−1.71281e7			−0.544355
$999$	909360.	−	3.52603e7i	0.0288285	−	1.11782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.d.b.32.7	✓	16
3.2	odd	2	inner	33.6.d.b.32.10	yes	16
11.10	odd	2	inner	33.6.d.b.32.9	yes	16
33.32	even	2	inner	33.6.d.b.32.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.d.b.32.7	✓	16	1.1	even	1	trivial
33.6.d.b.32.8	yes	16	33.32	even	2	inner
33.6.d.b.32.9	yes	16	11.10	odd	2	inner
33.6.d.b.32.10	yes	16	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(-0.480974 + 55.9601i) q^{6} +150.804i q^{7} +183.491 q^{8} +(-242.964 - 4.17684i) q^{9} +O(q^{10})\)	\(q-3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(-0.480974 + 55.9601i) q^{6} +150.804i q^{7} +183.491 q^{8} +(-242.964 - 4.17684i) q^{9} +42.6500i q^{10} +(-352.626 + 191.588i) q^{11} +(-2.56058 + 297.917i) q^{12} +778.957i q^{13} -541.384i q^{14} +(-185.188 - 1.59169i) q^{15} -47.1432 q^{16} -1255.02 q^{17} +(872.236 + 14.9947i) q^{18} -1214.37i q^{19} +227.057i q^{20} +(2350.72 + 20.2043i) q^{21} +(1265.92 - 687.798i) q^{22} -880.210i q^{23} +(24.5836 - 2860.24i) q^{24} +2983.86 q^{25} -2796.44i q^{26} +(-97.6596 + 3786.74i) q^{27} -2882.18i q^{28} -3201.27 q^{29} +(664.823 + 5.71411i) q^{30} -6446.10 q^{31} -5702.47 q^{32} +(2939.21 + 5522.36i) q^{33} +4505.50 q^{34} +1791.60 q^{35} +(4643.54 + 79.8279i) q^{36} -9311.53 q^{37} +4359.58i q^{38} +(12142.3 + 104.362i) q^{39} -2179.93i q^{40} -5398.38 q^{41} +(-8439.03 - 72.5330i) q^{42} +20867.6i q^{43} +(6739.40 - 3661.65i) q^{44} +(-49.6220 + 2886.48i) q^{45} +3159.93i q^{46} -11289.4i q^{47} +(-6.31611 + 734.863i) q^{48} -5934.91 q^{49} -10712.0 q^{50} +(-168.144 + 19563.1i) q^{51} -14887.5i q^{52} -23978.4i q^{53} +(350.596 - 13594.3i) q^{54} +(2276.12 + 4189.29i) q^{55} +27671.2i q^{56} +(-18929.5 - 162.698i) q^{57} +11492.5 q^{58} +22954.8i q^{59} +(3539.33 + 30.4204i) q^{60} -27244.5i q^{61} +23141.4 q^{62} +(629.884 - 36640.0i) q^{63} +21980.3 q^{64} +9254.23 q^{65} +(-10551.7 - 19825.1i) q^{66} +20257.5 q^{67} +23986.0 q^{68} +(-13720.6 - 117.928i) q^{69} -6431.79 q^{70} +56465.7i q^{71} +(-44581.8 - 766.412i) q^{72} -12025.4i q^{73} +33428.2 q^{74} +(399.768 - 46512.0i) q^{75} +23209.2i q^{76} +(-28892.3 - 53177.5i) q^{77} +(-43590.5 - 374.658i) q^{78} -11065.5i q^{79} +560.075i q^{80} +(59014.1 + 2029.64i) q^{81} +19380.1 q^{82} +51574.3 q^{83} +(-44927.1 - 386.146i) q^{84} +14910.0i q^{85} -74914.4i q^{86} +(-428.897 + 49901.1i) q^{87} +(-64703.7 + 35154.8i) q^{88} +84147.7i q^{89} +(178.142 - 10362.4i) q^{90} -117470. q^{91} +16822.6i q^{92} +(-863.629 + 100481. i) q^{93} +40528.8i q^{94} -14427.1 q^{95} +(-764.000 + 88889.5i) q^{96} +99342.9 q^{97} +21306.2 q^{98} +(86475.6 - 45076.2i) 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

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