LMFDB - Embedded newform 63.7.m.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,7,Mod(10,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("63.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	63.m (of order $6$, degree $2$, 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:	$14.4934072681$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.10
Dual form			63.7.m.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.00000 - 10.3923i) q^{2} +(-40.0000 + 69.2820i) q^{4} +(-157.500 + 90.9327i) q^{5} -343.000 q^{7} +192.000 q^{8} +O(q^{10})$	\(q+(-6.00000 - 10.3923i) q^{2} +(-40.0000 + 69.2820i) q^{4} +(-157.500 + 90.9327i) q^{5} -343.000 q^{7} +192.000 q^{8} +(1890.00 + 1091.19i) q^{10} +(739.500 - 1280.85i) q^{11} +484.974i q^{13} +(2058.00 + 3564.56i) q^{14} +(1408.00 + 2438.73i) q^{16} +(2614.50 + 1509.48i) q^{17} +(5953.50 - 3437.25i) q^{19} -14549.2i q^{20} -17748.0 q^{22} +(-2956.50 - 5120.81i) q^{23} +(8725.00 - 15112.1i) q^{25} +(5040.00 - 2909.85i) q^{26} +(13720.0 - 23763.7i) q^{28} -3978.00 q^{29} +(-11098.5 - 6407.72i) q^{31} +(23040.0 - 39906.5i) q^{32} -36227.6i q^{34} +(54022.5 - 31189.9i) q^{35} +(30788.5 + 53327.2i) q^{37} +(-71442.0 - 41247.1i) q^{38} +(-30240.0 + 17459.1i) q^{40} +110574. i q^{41} -17414.0 q^{43} +(59160.0 + 102468. i) q^{44} +(-35478.0 + 61449.7i) q^{46} +(26554.5 - 15331.2i) q^{47} +117649. q^{49} -209400. q^{50} +(-33600.0 - 19399.0i) q^{52} +(-30256.5 + 52405.8i) q^{53} +268979. i q^{55} -65856.0 q^{56} +(23868.0 + 41340.6i) q^{58} +(186826. + 107864. i) q^{59} +(140942. - 81372.6i) q^{61} +153785. i q^{62} -372736. q^{64} +(-44100.0 - 76383.4i) q^{65} +(134388. - 232768. i) q^{67} +(-209160. + 120759. i) q^{68} +(-648270. - 374279. i) q^{70} -101922. q^{71} +(275090. + 158823. i) q^{73} +(369462. - 639927. i) q^{74} +549961. i q^{76} +(-253648. + 439332. i) q^{77} +(-181116. - 313701. i) q^{79} +(-443520. - 256066. i) q^{80} +(1.14912e6 - 663445. i) q^{82} -216783. i q^{83} -549045. q^{85} +(104484. + 180972. i) q^{86} +(141984. - 245924. i) q^{88} +(1.15577e6 - 667282. i) q^{89} -166346. i q^{91} +473040. q^{92} +(-318654. - 183975. i) q^{94} +(-625118. + 1.08274e6i) q^{95} +1.51409e6i q^{97} +(-705894. - 1.22264e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 12 q^{2} - 80 q^{4} - 315 q^{5} - 686 q^{7} + 384 q^{8}+O(q^{10}) $ 2 * q - 12 * q^2 - 80 * q^4 - 315 * q^5 - 686 * q^7 + 384 * q^8	$ 2 q - 12 q^{2} - 80 q^{4} - 315 q^{5} - 686 q^{7} + 384 q^{8} + 3780 q^{10} + 1479 q^{11} + 4116 q^{14} + 2816 q^{16} + 5229 q^{17} + 11907 q^{19} - 35496 q^{22} - 5913 q^{23} + 17450 q^{25} + 10080 q^{26} + 27440 q^{28} - 7956 q^{29} - 22197 q^{31} + 46080 q^{32} + 108045 q^{35} + 61577 q^{37} - 142884 q^{38} - 60480 q^{40} - 34828 q^{43} + 118320 q^{44} - 70956 q^{46} + 53109 q^{47} + 235298 q^{49} - 418800 q^{50} - 67200 q^{52} - 60513 q^{53} - 131712 q^{56} + 47736 q^{58} + 373653 q^{59} + 281883 q^{61} - 745472 q^{64} - 88200 q^{65} + 268777 q^{67} - 418320 q^{68} - 1296540 q^{70} - 203844 q^{71} + 550179 q^{73} + 738924 q^{74} - 507297 q^{77} - 362231 q^{79} - 887040 q^{80} + 2298240 q^{82} - 1098090 q^{85} + 208968 q^{86} + 283968 q^{88} + 2311533 q^{89} + 946080 q^{92} - 637308 q^{94} - 1250235 q^{95} - 1411788 q^{98}+O(q^{100}) $ 2 * q - 12 * q^2 - 80 * q^4 - 315 * q^5 - 686 * q^7 + 384 * q^8 + 3780 * q^10 + 1479 * q^11 + 4116 * q^14 + 2816 * q^16 + 5229 * q^17 + 11907 * q^19 - 35496 * q^22 - 5913 * q^23 + 17450 * q^25 + 10080 * q^26 + 27440 * q^28 - 7956 * q^29 - 22197 * q^31 + 46080 * q^32 + 108045 * q^35 + 61577 * q^37 - 142884 * q^38 - 60480 * q^40 - 34828 * q^43 + 118320 * q^44 - 70956 * q^46 + 53109 * q^47 + 235298 * q^49 - 418800 * q^50 - 67200 * q^52 - 60513 * q^53 - 131712 * q^56 + 47736 * q^58 + 373653 * q^59 + 281883 * q^61 - 745472 * q^64 - 88200 * q^65 + 268777 * q^67 - 418320 * q^68 - 1296540 * q^70 - 203844 * q^71 + 550179 * q^73 + 738924 * q^74 - 507297 * q^77 - 362231 * q^79 - 887040 * q^80 + 2298240 * q^82 - 1098090 * q^85 + 208968 * q^86 + 283968 * q^88 + 2311533 * q^89 + 946080 * q^92 - 637308 * q^94 - 1250235 * q^95 - 1411788 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−6.00000	−	10.3923i	−0.750000	−	1.29904i	−0.947822	−	0.318800i	$-0.896720\pi$
$2$	−6.00000	−	10.3923i	−0.750000	−	1.29904i	0.197822	−	0.980238i	$-0.436613\pi$
$3$		0			0
$3$		0			0
$4$	−40.0000	+	69.2820i	−0.625000	+	1.08253i
$5$	−157.500	+	90.9327i	−1.26000	+	0.727461i	−0.973074	−	0.230492i	$-0.925967\pi$
$5$	−157.500	+	90.9327i	−1.26000	+	0.727461i	−0.286926	+	0.957953i	$0.592633\pi$
$6$		0			0
$7$	−343.000			−1.00000
$7$	−343.000			−1.00000
$8$	192.000			0.375000
$9$		0			0
$10$	1890.00	+	1091.19i	1.89000	+	1.09119i
$11$	739.500	−	1280.85i	0.555597	−	0.962323i	−0.442259	−	0.896887i	$-0.645823\pi$
$11$	739.500	−	1280.85i	0.555597	−	0.962323i	0.997857	−	0.0654356i	$-0.0208437\pi$
$12$		0			0
$13$			484.974i			0.220744i	0.993890	+	0.110372i	$0.0352042\pi$
$13$			484.974i			0.220744i	−0.993890	+	0.110372i	$0.964796\pi$
$14$	2058.00	+	3564.56i	0.750000	+	1.29904i
$15$		0			0
$16$	1408.00	+	2438.73i	0.343750	+	0.595392i
$17$	2614.50	+	1509.48i	0.532160	+	0.307242i	0.741895	−	0.670516i	$-0.233927\pi$
$17$	2614.50	+	1509.48i	0.532160	+	0.307242i	−0.209736	+	0.977758i	$0.567260\pi$
$18$		0			0
$19$	5953.50	−	3437.25i	0.867984	−	0.501131i	0.00130600	−	0.999999i	$-0.499584\pi$
$19$	5953.50	−	3437.25i	0.867984	−	0.501131i	0.866678	+	0.498869i	$0.166251\pi$
$20$		−	14549.2i		−	1.81865i
$21$		0			0
$22$	−17748.0			−1.66679
$23$	−2956.50	−	5120.81i	−0.242993	−	0.420877i	0.718572	−	0.695452i	$-0.244796\pi$
$23$	−2956.50	−	5120.81i	−0.242993	−	0.420877i	−0.961566	+	0.274576i	$0.911463\pi$
$24$		0			0
$25$	8725.00	−	15112.1i	0.558400	−	0.967177i
$26$	5040.00	−	2909.85i	0.286755	−	0.165558i
$27$		0			0
$28$	13720.0	−	23763.7i	0.625000	−	1.08253i
$29$	−3978.00			−0.163106			−0.0815532	−	0.996669i	$-0.525988\pi$
$29$	−3978.00			−0.163106			−0.0815532	+	0.996669i	$0.525988\pi$
$30$		0			0
$31$	−11098.5	−	6407.72i	−0.372545	−	0.215089i	0.302025	−	0.953300i	$-0.402338\pi$
$31$	−11098.5	−	6407.72i	−0.372545	−	0.215089i	−0.674570	+	0.738211i	$0.735671\pi$
$32$	23040.0	−	39906.5i	0.703125	−	1.21785i
$33$		0			0
$34$		−	36227.6i		−	0.921727i
$35$	54022.5	−	31189.9i	1.26000	−	0.727461i
$36$		0			0
$37$	30788.5	+	53327.2i	0.607832	+	1.05280i	0.991597	+	0.129365i	$0.0412938\pi$
$37$	30788.5	+	53327.2i	0.607832	+	1.05280i	−0.383765	+	0.923431i	$0.625373\pi$
$38$	−71442.0	−	41247.1i	−1.30198	−	0.751696i
$39$		0			0
$40$	−30240.0	+	17459.1i	−0.472500	+	0.272798i
$41$			110574.i			1.60436i	0.597082	+	0.802180i	$0.296327\pi$
$41$			110574.i			1.60436i	−0.597082	+	0.802180i	$0.703673\pi$
$42$		0			0
$43$	−17414.0			−0.219025			−0.109512	−	0.993985i	$-0.534929\pi$
$43$	−17414.0			−0.219025			−0.109512	+	0.993985i	$0.534929\pi$
$44$	59160.0	+	102468.i	0.694497	+	1.20290i
$45$		0			0
$46$	−35478.0	+	61449.7i	−0.364490	+	0.631315i
$47$	26554.5	−	15331.2i	0.255767	−	0.147667i	−0.366635	−	0.930365i	$-0.619490\pi$
$47$	26554.5	−	15331.2i	0.255767	−	0.147667i	0.622402	+	0.782698i	$0.286157\pi$
$48$		0			0
$49$	117649.			1.00000
$50$	−209400.			−1.67520
$51$		0			0
$52$	−33600.0	−	19399.0i	−0.238962	−	0.137965i
$53$	−30256.5	+	52405.8i	−0.203232	+	0.352007i	−0.949568	−	0.313562i	$-0.898478\pi$
$53$	−30256.5	+	52405.8i	−0.203232	+	0.352007i	0.746336	+	0.665569i	$0.231811\pi$
$54$		0			0
$55$			268979.i			1.61670i
$56$	−65856.0			−0.375000
$57$		0			0
$58$	23868.0	+	41340.6i	0.122330	+	0.211881i
$59$	186826.	+	107864.i	0.909667	+	0.525196i	0.880324	−	0.474373i	$-0.157325\pi$
$59$	186826.	+	107864.i	0.909667	+	0.525196i	0.0293430	+	0.999569i	$0.490658\pi$
$60$		0			0
$61$	140942.	−	81372.6i	0.620940	−	0.358500i	−0.156295	−	0.987710i	$-0.549955\pi$
$61$	140942.	−	81372.6i	0.620940	−	0.358500i	0.777235	+	0.629211i	$0.216622\pi$
$62$			153785.i			0.645268i
$63$		0			0
$64$	−372736.			−1.42188
$65$	−44100.0	−	76383.4i	−0.160583	−	0.278137i
$66$		0			0
$67$	134388.	−	232768.i	0.446825	−	0.773924i	−0.551352	−	0.834273i	$-0.685888\pi$
$67$	134388.	−	232768.i	0.446825	−	0.773924i	0.998177	+	0.0603486i	$0.0192212\pi$
$68$	−209160.	+	120759.i	−0.665199	+	0.384053i
$69$		0			0
$70$	−648270.	−	374279.i	−1.89000	−	1.09119i
$71$	−101922.			−0.284769			−0.142385	−	0.989811i	$-0.545477\pi$
$71$	−101922.			−0.284769			−0.142385	+	0.989811i	$0.545477\pi$
$72$		0			0
$73$	275090.	+	158823.i	0.707140	+	0.408267i	0.810001	−	0.586428i	$-0.199466\pi$
$73$	275090.	+	158823.i	0.707140	+	0.408267i	−0.102861	+	0.994696i	$0.532800\pi$
$74$	369462.	−	639927.i	0.911748	−	1.57919i
$75$		0			0
$76$			549961.i			1.25283i
$77$	−253648.	+	439332.i	−0.555597	+	0.962323i
$78$		0			0
$79$	−181116.	−	313701.i	−0.367345	−	0.636261i	0.621804	−	0.783173i	$-0.286400\pi$
$79$	−181116.	−	313701.i	−0.367345	−	0.636261i	−0.989150	+	0.146912i	$0.953067\pi$
$80$	−443520.	−	256066.i	−0.866250	−	0.500130i
$81$		0			0
$82$	1.14912e6	−	663445.i	2.08413	−	1.20327i
$83$		−	216783.i		−	0.379133i	−0.981868	−	0.189567i	$-0.939292\pi$
$83$		−	216783.i		−	0.379133i	0.981868	−	0.189567i	$-0.0607083\pi$
$84$		0			0
$85$	−549045.			−0.894028
$86$	104484.	+	180972.i	0.164269	+	0.284521i
$87$		0			0
$88$	141984.	−	245924.i	0.208349	−	0.360871i
$89$	1.15577e6	−	667282.i	1.63946	−	0.946541i	0.658437	−	0.752636i	$-0.271218\pi$
$89$	1.15577e6	−	667282.i	1.63946	−	0.946541i	0.981020	−	0.193905i	$-0.0621154\pi$
$90$		0			0
$91$		−	166346.i		−	0.220744i
$92$	473040.			0.607483
$93$		0			0
$94$	−318654.	−	183975.i	−0.383651	−	0.221501i
$95$	−625118.	+	1.08274e6i	−0.729106	+	1.26285i
$96$		0			0
$97$			1.51409e6i			1.65896i	0.558535	+	0.829481i	$0.311364\pi$
$97$			1.51409e6i			1.65896i	−0.558535	+	0.829481i	$0.688636\pi$
$98$	−705894.	−	1.22264e6i	−0.750000	−	1.29904i
$99$		0			0
$100$	698000.	+	1.20897e6i	0.698000	+	1.20897i
$101$	1.14720e6	+	662335.i	1.11346	+	0.642856i	0.939723	−	0.341936i	$-0.111083\pi$
$101$	1.14720e6	+	662335.i	1.11346	+	0.642856i	0.173736	+	0.984792i	$0.444416\pi$
$102$		0			0
$103$	55429.5	−	32002.2i	0.0507258	−	0.0292866i	−0.474423	−	0.880297i	$-0.657343\pi$
$103$	55429.5	−	32002.2i	0.0507258	−	0.0292866i	0.525148	+	0.851011i	$0.324010\pi$
$104$			93115.1i			0.0827789i
$105$		0			0
$106$	726156.			0.609695
$107$	330272.	+	572047.i	0.269600	+	0.466961i	0.968759	−	0.248006i	$-0.0797752\pi$
$107$	330272.	+	572047.i	0.269600	+	0.466961i	−0.699159	+	0.714967i	$0.746442\pi$
$108$		0			0
$109$	36584.5	−	63366.2i	0.0282499	−	0.0489303i	−0.851555	−	0.524266i	$-0.824340\pi$
$109$	36584.5	−	63366.2i	0.0282499	−	0.0489303i	0.879805	+	0.475335i	$0.157673\pi$
$110$	2.79531e6	−	1.61387e6i	2.10016	−	1.21253i
$111$		0			0
$112$	−482944.	−	836484.i	−0.343750	−	0.595392i
$113$	−1.60351e6			−1.11131			−0.555655	−	0.831413i	$-0.687532\pi$
$113$	−1.60351e6			−1.11131			−0.555655	+	0.831413i	$0.687532\pi$
$114$		0			0
$115$	931298.	+	537685.i	0.612343	+	0.353537i
$116$	159120.	−	275604.i	0.101941	−	0.176568i
$117$		0			0
$118$		−	2.58874e6i		−	1.57559i
$119$	−896774.	−	517752.i	−0.532160	−	0.307242i
$120$		0			0
$121$	−207940.	−	360163.i	−0.117377	−	0.203302i
$122$	−1.69130e6	−	976471.i	−0.931409	−	0.537750i
$123$		0			0
$124$	887880.	−	512618.i	0.465682	−	0.268861i
$125$			331904.i			0.169935i
$126$		0			0
$127$	−3.22997e6			−1.57684			−0.788418	−	0.615139i	$-0.789100\pi$
$127$	−3.22997e6			−1.57684			−0.788418	+	0.615139i	$0.789100\pi$
$128$	761856.	+	1.31957e6i	0.363281	+	0.629222i
$129$		0			0
$130$	−529200.	+	916601.i	−0.240874	+	0.417206i
$131$	−1.72812e6	+	997731.i	−0.768706	+	0.443813i	−0.832413	−	0.554156i	$-0.813041\pi$
$131$	−1.72812e6	+	997731.i	−0.768706	+	0.443813i	0.0637067	+	0.997969i	$0.479708\pi$
$132$		0			0
$133$	−2.04205e6	+	1.17898e6i	−0.867984	+	0.501131i
$134$	−3.22532e6			−1.34048
$135$		0			0
$136$	501984.	+	289821.i	0.199560	+	0.115216i
$137$	710792.	−	1.23113e6i	0.276427	−	0.478786i	−0.694067	−	0.719910i	$-0.744183\pi$
$137$	710792.	−	1.23113e6i	0.276427	−	0.478786i	0.970494	+	0.241125i	$0.0775163\pi$
$138$		0			0
$139$		−	2.43603e6i		−	0.907063i	−0.891240	−	0.453531i	$-0.850164\pi$
$139$		−	2.43603e6i		−	0.907063i	0.891240	−	0.453531i	$-0.149836\pi$
$140$			4.99038e6i			1.81865i
$141$		0			0
$142$	611532.	+	1.05920e6i	0.213577	+	0.369926i
$143$	621180.	+	358638.i	0.212427	+	0.122645i
$144$		0			0
$145$	626535.	−	361730.i	0.205514	−	0.118654i
$146$		−	3.81175e6i		−	1.22480i
$147$		0			0
$148$	−4.92616e6			−1.51958
$149$	1.57188e6	+	2.72257e6i	0.475181	+	0.823038i	0.999596	−	0.0284249i	$-0.00904914\pi$
$149$	1.57188e6	+	2.72257e6i	0.475181	+	0.823038i	−0.524415	+	0.851463i	$0.675716\pi$
$150$		0			0
$151$	1.14110e6	−	1.97644e6i	0.331431	−	0.574055i	−0.651362	−	0.758767i	$-0.725802\pi$
$151$	1.14110e6	−	1.97644e6i	0.331431	−	0.574055i	0.982793	+	0.184712i	$0.0591353\pi$
$152$	1.14307e6	−	659953.i	0.325494	−	0.187924i
$153$		0			0
$154$	6.08756e6			1.66679
$155$	2.33068e6			0.625876
$156$		0			0
$157$	−128614.	−	74255.6i	−0.0332346	−	0.0191880i	0.483291	−	0.875460i	$-0.339441\pi$
$157$	−128614.	−	74255.6i	−0.0332346	−	0.0191880i	−0.516525	+	0.856272i	$0.672775\pi$
$158$	−2.17339e6	+	3.76441e6i	−0.551018	+	0.954391i
$159$		0			0
$160$			8.38035e6i			2.04599i
$161$	1.01408e6	+	1.75644e6i	0.242993	+	0.420877i
$162$		0			0
$163$	3.54874e6	+	6.14659e6i	0.819428	+	1.41929i	0.906104	+	0.423055i	$0.139042\pi$
$163$	3.54874e6	+	6.14659e6i	0.819428	+	1.41929i	−0.0866758	+	0.996237i	$0.527624\pi$
$164$	−7.66080e6	−	4.42296e6i	−1.73677	−	1.00273i
$165$		0			0
$166$	−2.25288e6	+	1.30070e6i	−0.492509	+	0.284350i
$167$			645986.i			0.138699i	0.997592	+	0.0693495i	$0.0220924\pi$
$167$			645986.i			0.138699i	−0.997592	+	0.0693495i	$0.977908\pi$
$168$		0			0
$169$	4.59161e6			0.951272
$170$	3.29427e6	+	5.70584e6i	0.670521	+	1.16138i
$171$		0			0
$172$	696560.	−	1.20648e6i	0.136890	−	0.237101i
$173$	−2.71571e6	+	1.56792e6i	−0.524499	+	0.302820i	−0.738774	−	0.673954i	$-0.764595\pi$
$173$	−2.71571e6	+	1.56792e6i	−0.524499	+	0.302820i	0.214274	+	0.976774i	$0.431261\pi$
$174$		0			0
$175$	−2.99268e6	+	5.18347e6i	−0.558400	+	0.967177i
$176$	4.16486e6			0.763946
$177$		0			0
$178$	−1.38692e7	−	8.00739e6i	−2.45919	−	1.41981i
$179$	5.08140e6	−	8.80124e6i	0.885980	−	1.53456i	0.0413937	−	0.999143i	$-0.486820\pi$
$179$	5.08140e6	−	8.80124e6i	0.885980	−	1.53456i	0.844586	−	0.535419i	$-0.179846\pi$
$180$		0			0
$181$		−	8.72517e6i		−	1.47143i	−0.677294	−	0.735713i	$-0.736847\pi$
$181$		−	8.72517e6i		−	1.47143i	0.677294	−	0.735713i	$-0.263153\pi$
$182$	−1.72872e6	+	998077.i	−0.286755	+	0.165558i
$183$		0			0
$184$	−567648.	−	983195.i	−0.0911225	−	0.157829i
$185$	−9.69838e6	−	5.59936e6i	−1.53174	−	0.884348i
$186$		0			0
$187$	3.86685e6	−	2.23252e6i	0.591333	−	0.341406i
$188$			2.45300e6i			0.369168i
$189$		0			0
$190$	1.50028e7			2.18732
$191$	2.11922e6	+	3.67060e6i	0.304142	+	0.526789i	0.977070	−	0.212919i	$-0.0682971\pi$
$191$	2.11922e6	+	3.67060e6i	0.304142	+	0.526789i	−0.672928	+	0.739708i	$0.734964\pi$
$192$		0			0
$193$	−3.07410e6	+	5.32450e6i	−0.427609	+	0.740640i	−0.996660	−	0.0816619i	$-0.973977\pi$
$193$	−3.07410e6	+	5.32450e6i	−0.427609	+	0.740640i	0.569051	+	0.822302i	$0.307311\pi$
$194$	1.57349e7	−	9.08454e6i	2.15505	−	1.24422i
$195$		0			0
$196$	−4.70596e6	+	8.15096e6i	−0.625000	+	1.08253i
$197$	−790554.			−0.103403			−0.0517015	−	0.998663i	$-0.516464\pi$
$197$	−790554.			−0.103403			−0.0517015	+	0.998663i	$0.516464\pi$
$198$		0			0
$199$	7.03717e6	+	4.06291e6i	0.892974	+	0.515559i	0.874914	−	0.484278i	$-0.160918\pi$
$199$	7.03717e6	+	4.06291e6i	0.892974	+	0.515559i	0.0180602	+	0.999837i	$0.494251\pi$
$200$	1.67520e6	−	2.90153e6i	0.209400	−	0.362691i
$201$		0			0
$202$		−	1.58960e7i		−	1.92857i
$203$	1.36445e6			0.163106
$204$		0			0
$205$	−1.00548e7	−	1.74154e7i	−1.16711	−	2.02149i
$206$	−665154.	−	384027.i	−0.0760888	−	0.0439299i
$207$		0			0
$208$	−1.18272e6	+	682844.i	−0.131429	+	0.0758807i
$209$		−	1.01674e7i		−	1.11371i
$210$		0			0
$211$	1.16724e7			1.24254			0.621271	−	0.783595i	$-0.286616\pi$
$211$	1.16724e7			1.24254			0.621271	+	0.783595i	$0.286616\pi$
$212$	−2.42052e6	−	4.19246e6i	−0.254039	−	0.440009i
$213$		0			0
$214$	3.96326e6	−	6.86456e6i	0.404400	−	0.700441i
$215$	2.74270e6	−	1.58350e6i	0.275971	−	0.159332i
$216$		0			0
$217$	3.80679e6	+	2.19785e6i	0.372545	+	0.215089i
$218$	−878028.			−0.0847498
$219$		0			0
$220$	−1.86354e7	−	1.07592e7i	−1.75013	−	1.01044i
$221$	−732060.	+	1.26797e6i	−0.0678219	+	0.117471i
$222$		0			0
$223$		−	2.89821e6i		−	0.261345i	−0.991426	−	0.130673i	$-0.958286\pi$
$223$		−	2.89821e6i		−	0.261345i	0.991426	−	0.130673i	$-0.0417137\pi$
$224$	−7.90272e6	+	1.36879e7i	−0.703125	+	1.21785i
$225$		0			0
$226$	9.62104e6	+	1.66641e7i	0.833483	+	1.44363i
$227$	1.45241e7	+	8.38550e6i	1.24169	+	0.716888i	0.969437	−	0.245338i	$-0.0788991\pi$
$227$	1.45241e7	+	8.38550e6i	1.24169	+	0.716888i	0.272249	+	0.962227i	$0.412232\pi$
$228$		0			0
$229$	−1.51363e7	+	8.73895e6i	−1.26041	+	0.727701i	−0.973155	−	0.230152i	$-0.926078\pi$
$229$	−1.51363e7	+	8.73895e6i	−1.26041	+	0.727701i	−0.287260	+	0.957853i	$0.592744\pi$
$230$		−	1.29044e7i		−	1.06061i
$231$		0			0
$232$	−763776.			−0.0611649
$233$	−5.10218e6	−	8.83723e6i	−0.403355	−	0.698632i	0.590773	−	0.806838i	$-0.298823\pi$
$233$	−5.10218e6	−	8.83723e6i	−0.403355	−	0.698632i	−0.994129	+	0.108206i	$0.965489\pi$
$234$		0			0
$235$	−2.78822e6	+	4.82934e6i	−0.214844	+	0.372121i
$236$	−1.49461e7	+	8.62915e6i	−1.13708	+	0.656496i
$237$		0			0
$238$			1.24261e7i			0.921727i
$239$	−1.43114e6			−0.104831			−0.0524153	−	0.998625i	$-0.516692\pi$
$239$	−1.43114e6			−0.104831			−0.0524153	+	0.998625i	$0.516692\pi$
$240$		0			0
$241$	1.34268e7	+	7.75197e6i	0.959227	+	0.553810i	0.895935	−	0.444185i	$-0.146507\pi$
$241$	1.34268e7	+	7.75197e6i	0.959227	+	0.553810i	0.0632920	+	0.997995i	$0.479840\pi$
$242$	−2.49528e6	+	4.32195e6i	−0.176065	+	0.304954i
$243$		0			0
$244$			1.30196e7i			0.896249i
$245$	−1.85297e7	+	1.06981e7i	−1.26000	+	0.727461i
$246$		0			0
$247$	1.66698e6	+	2.88729e6i	0.110621	+	0.191602i
$248$	−2.13091e6	−	1.23028e6i	−0.139705	−	0.0806584i
$249$		0			0
$250$	3.44925e6	−	1.99143e6i	0.220752	−	0.127451i
$251$		−	3.44089e6i		−	0.217595i	−0.994064	−	0.108798i	$-0.965300\pi$
$251$		−	3.44089e6i		−	0.217595i	0.994064	−	0.108798i	$-0.0347001\pi$
$252$		0			0
$253$	−8.74533e6			−0.540026
$254$	1.93798e7	+	3.35668e7i	1.18263	+	2.04837i
$255$		0			0
$256$	−2.78528e6	+	4.82425e6i	−0.166016	+	0.287547i
$257$	2.01374e7	−	1.16263e7i	1.18633	−	0.684926i	0.228857	−	0.973460i	$-0.426501\pi$
$257$	2.01374e7	−	1.16263e7i	1.18633	−	0.684926i	0.957470	+	0.288534i	$0.0931678\pi$
$258$		0			0
$259$	−1.05605e7	−	1.82912e7i	−0.607832	−	1.05280i
$260$	7.05600e6			0.401457
$261$		0			0
$262$	2.07375e7	+	1.19728e7i	1.15306	+	0.665719i
$263$	−1.41309e7	+	2.44755e7i	−0.776789	+	1.34544i	0.156994	+	0.987599i	$0.449820\pi$
$263$	−1.41309e7	+	2.44755e7i	−0.776789	+	1.34544i	−0.933783	+	0.357839i	$0.883514\pi$
$264$		0			0
$265$		−	1.10052e7i		−	0.591372i
$266$	2.45046e7	+	1.41477e7i	1.30198	+	0.751696i
$267$		0			0
$268$	1.07511e7	+	1.86214e7i	0.558532	+	0.967405i
$269$	−1.36921e7	−	7.90512e6i	−0.703416	−	0.406118i	0.105202	−	0.994451i	$-0.466451\pi$
$269$	−1.36921e7	−	7.90512e6i	−0.703416	−	0.406118i	−0.808619	+	0.588333i	$0.799784\pi$
$270$		0			0
$271$	3.16124e7	−	1.82514e7i	1.58836	−	0.917041i	0.594784	−	0.803885i	$-0.297238\pi$
$271$	3.16124e7	−	1.82514e7i	1.58836	−	0.917041i	0.993577	−	0.113155i	$-0.0360958\pi$
$272$			8.50140e6i			0.422458i
$273$		0			0
$274$	−1.70590e7			−0.829281
$275$	−1.29043e7	−	2.23509e7i	−0.620491	−	1.07472i
$276$		0			0
$277$	−1.57404e7	+	2.72631e7i	−0.740585	+	1.28273i	0.211644	+	0.977347i	$0.432118\pi$
$277$	−1.57404e7	+	2.72631e7i	−0.740585	+	1.28273i	−0.952229	+	0.305385i	$0.901215\pi$
$278$	−2.53159e7	+	1.46162e7i	−1.17831	+	0.680297i
$279$		0			0
$280$	1.03723e7	−	5.98846e6i	0.472500	−	0.272798i
$281$	−6.62368e6			−0.298525			−0.149262	−	0.988798i	$-0.547690\pi$
$281$	−6.62368e6			−0.298525			−0.149262	+	0.988798i	$0.547690\pi$
$282$		0			0
$283$	−3.48558e7	−	2.01240e7i	−1.53786	−	0.887882i	−0.998964	−	0.0455076i	$-0.985509\pi$
$283$	−3.48558e7	−	2.01240e7i	−1.53786	−	0.887882i	−0.538893	−	0.842374i	$-0.681157\pi$
$284$	4.07688e6	−	7.06136e6i	0.177981	−	0.308272i
$285$		0			0
$286$		−	8.60732e6i		−	0.367934i
$287$		−	3.79269e7i		−	1.60436i
$288$		0			0
$289$	−7.51171e6	−	1.30107e7i	−0.311204	−	0.539021i
$290$	−7.51842e6	−	4.34076e6i	−0.308271	−	0.177980i
$291$		0			0
$292$	−2.20072e7	+	1.27058e7i	−0.883925	+	0.510334i
$293$		−	1.26797e7i		−	0.504086i	−0.967716	−	0.252043i	$-0.918898\pi$
$293$		−	1.26797e7i		−	0.504086i	0.967716	−	0.252043i	$-0.0811024\pi$
$294$		0			0
$295$	−3.92336e7			−1.52824
$296$	5.91139e6	+	1.02388e7i	0.227937	+	0.394798i
$297$		0			0
$298$	1.88625e7	−	3.26708e7i	0.712772	−	1.23456i
$299$	2.48346e6	−	1.43383e6i	0.0929060	−	0.0536393i
$300$		0			0
$301$	5.97300e6			0.219025
$302$	−2.73864e7			−0.994293
$303$		0			0
$304$	1.67651e7	+	9.67931e6i	0.596739	+	0.344527i
$305$	−1.47989e7	+	2.56324e7i	−0.521589	+	0.903419i
$306$		0			0
$307$			1.77258e6i			0.0612620i	0.999531	+	0.0306310i	$0.00975167\pi$
$307$			1.77258e6i			0.0612620i	−0.999531	+	0.0306310i	$0.990248\pi$
$308$	−2.02919e7	−	3.51466e7i	−0.694497	−	1.20290i
$309$		0			0
$310$	−1.39841e7	−	2.42212e7i	−0.469407	−	0.813037i
$311$	3.16329e7	+	1.82633e7i	1.05162	+	0.607152i	0.923102	−	0.384556i	$-0.125645\pi$
$311$	3.16329e7	+	1.82633e7i	1.05162	+	0.607152i	0.128516	+	0.991707i	$0.458979\pi$
$312$		0			0
$313$	1.00502e7	−	5.80247e6i	0.327748	−	0.189226i	−0.327093	−	0.944992i	$-0.606069\pi$
$313$	1.00502e7	−	5.80247e6i	0.327748	−	0.189226i	0.654841	+	0.755767i	$0.272736\pi$
$314$			1.78213e6i			0.0575641i
$315$		0			0
$316$	2.89785e7			0.918363
$317$	1.05821e7	+	1.83287e7i	0.332194	+	0.575377i	0.982942	−	0.183917i	$-0.0588777\pi$
$317$	1.05821e7	+	1.83287e7i	0.332194	+	0.575377i	−0.650748	+	0.759294i	$0.725544\pi$
$318$		0			0
$319$	−2.94173e6	+	5.09523e6i	−0.0906214	+	0.156961i
$320$	5.87059e7	−	3.38939e7i	1.79156	−	1.03436i
$321$		0			0
$322$	1.21690e7	−	2.10772e7i	0.364490	−	0.631315i
$323$	2.07539e7			0.615874
$324$		0			0
$325$	7.32900e6	+	4.23140e6i	0.213498	+	0.123263i
$326$	4.25848e7	−	7.37591e7i	1.22914	−	2.12894i
$327$		0			0
$328$			2.12302e7i			0.601635i
$329$	−9.10819e6	+	5.25862e6i	−0.255767	+	0.147667i
$330$		0			0
$331$	2.96100e7	+	5.12860e7i	0.816496	+	1.41421i	0.908249	+	0.418430i	$0.137420\pi$
$331$	2.96100e7	+	5.12860e7i	0.816496	+	1.41421i	−0.0917534	+	0.995782i	$0.529247\pi$
$332$	1.50192e7	+	8.67134e6i	0.410424	+	0.236958i
$333$		0			0
$334$	6.71328e6	−	3.87591e6i	0.180175	−	0.104024i
$335$			4.88812e7i			1.30019i
$336$		0			0
$337$	3.67798e7			0.960992			0.480496	−	0.876997i	$-0.340457\pi$
$337$	3.67798e7			0.960992			0.480496	+	0.876997i	$0.340457\pi$
$338$	−2.75497e7	−	4.77174e7i	−0.713454	−	1.23574i
$339$		0			0
$340$	2.19618e7	−	3.80390e7i	0.558768	−	0.967814i
$341$	−1.64147e7	+	9.47702e6i	−0.413970	+	0.239006i
$342$		0			0
$343$	−4.03536e7			−1.00000
$344$	−3.34349e6			−0.0821343
$345$		0			0
$346$	3.25885e7	+	1.88150e7i	0.786749	+	0.454230i
$347$	1.69887e7	−	2.94253e7i	0.406605	−	0.704260i	−0.587902	−	0.808932i	$-0.700046\pi$
$347$	1.69887e7	−	2.94253e7i	0.406605	−	0.704260i	0.994507	+	0.104672i	$0.0333793\pi$
$348$		0			0
$349$			5.48045e7i			1.28926i	0.764495	+	0.644629i	$0.222988\pi$
$349$			5.48045e7i			1.28926i	−0.764495	+	0.644629i	$0.777012\pi$
$350$	7.18242e7			1.67520
$351$		0			0
$352$	−3.40762e7	−	5.90216e7i	−0.781309	−	1.35327i
$353$	4.12231e6	+	2.38002e6i	0.0937166	+	0.0541073i	0.546126	−	0.837703i	$-0.316102\pi$
$353$	4.12231e6	+	2.38002e6i	0.0937166	+	0.0541073i	−0.452409	+	0.891810i	$0.649435\pi$
$354$		0			0
$355$	1.60527e7	−	9.26804e6i	0.358809	−	0.207159i
$356$			1.06765e8i			2.36635i
$357$		0			0
$358$	−1.21953e8			−2.65794
$359$	−2.65584e6	−	4.60006e6i	−0.0574010	−	0.0994214i	0.835897	−	0.548886i	$-0.184948\pi$
$359$	−2.65584e6	−	4.60006e6i	−0.0574010	−	0.0994214i	−0.893298	+	0.449465i	$0.851615\pi$
$360$		0			0
$361$	106501.	−	184465.i	0.00226377	−	0.00392096i
$362$	−9.06746e7	+	5.23510e7i	−1.91144	+	1.10357i
$363$		0			0
$364$	1.15248e7	+	6.65385e6i	0.238962	+	0.137965i
$365$	−5.77688e7			−1.18800
$366$		0			0
$367$	6.91399e7	+	3.99179e7i	1.39872	+	0.807551i	0.994259	−	0.107005i	$-0.0341260\pi$
$367$	6.91399e7	+	3.99179e7i	1.39872	+	0.807551i	0.404460	+	0.914555i	$0.367459\pi$
$368$	8.32550e6	−	1.44202e7i	0.167058	−	0.289353i
$369$		0			0
$370$			1.34385e8i			2.65304i
$371$	1.03780e7	−	1.79752e7i	0.203232	−	0.352007i
$372$		0			0
$373$	−2.11300e7	−	3.65983e7i	−0.407168	−	0.705236i	0.587403	−	0.809295i	$-0.300150\pi$
$373$	−2.11300e7	−	3.65983e7i	−0.407168	−	0.705236i	−0.994571	+	0.104059i	$0.966817\pi$
$374$	−4.64021e7	−	2.67903e7i	−0.886999	−	0.512109i
$375$		0			0
$376$	5.09846e6	−	2.94360e6i	0.0959126	−	0.0553752i
$377$		−	1.92923e6i		−	0.0360047i
$378$		0			0
$379$	1.28840e7			0.236664			0.118332	−	0.992974i	$-0.462245\pi$
$379$	1.28840e7			0.236664			0.118332	+	0.992974i	$0.462245\pi$
$380$	−5.00094e7	−	8.66188e7i	−0.911383	−	1.57856i
$381$		0			0
$382$	2.54306e7	−	4.40472e7i	0.456212	−	0.790183i
$383$	2.31723e7	−	1.33785e7i	0.412451	−	0.238128i	−0.279392	−	0.960177i	$-0.590133\pi$
$383$	2.31723e7	−	1.33785e7i	0.412451	−	0.238128i	0.691842	+	0.722049i	$0.256799\pi$
$384$		0			0
$385$		−	9.22597e7i		−	1.61670i
$386$	7.37785e7			1.28283
$387$		0			0
$388$	−1.04899e8	−	6.05636e7i	−1.79588	−	1.03685i
$389$	−5.37786e6	+	9.31473e6i	−0.0913610	+	0.158242i	−0.908084	−	0.418788i	$-0.862455\pi$
$389$	−5.37786e6	+	9.31473e6i	−0.0913610	+	0.158242i	0.816723	+	0.577030i	$0.195788\pi$
$390$		0			0
$391$		−	1.78511e7i		−	0.298632i
$392$	2.25886e7			0.375000
$393$		0			0
$394$	4.74332e6	+	8.21568e6i	0.0775522	+	0.134324i
$395$	5.70514e7	+	3.29386e7i	0.925710	+	0.534459i
$396$		0			0
$397$	8.24745e6	−	4.76166e6i	0.131810	−	0.0761005i	−0.432645	−	0.901564i	$-0.642420\pi$
$397$	8.24745e6	−	4.76166e6i	0.131810	−	0.0761005i	0.564455	+	0.825464i	$0.309086\pi$
$398$		−	9.75099e7i		−	1.54668i
$399$		0			0
$400$	4.91392e7			0.767800
$401$	3.83942e7	+	6.65007e7i	0.595432	+	1.03132i	0.993486	+	0.113957i	$0.0363526\pi$
$401$	3.83942e7	+	6.65007e7i	0.595432	+	1.03132i	−0.398053	+	0.917362i	$0.630314\pi$
$402$		0			0
$403$	3.10758e6	−	5.38249e6i	0.0474796	−	0.0822371i
$404$	−9.17759e7	+	5.29868e7i	−1.39182	+	0.803570i
$405$		0			0
$406$	−8.18672e6	−	1.41798e7i	−0.122330	−	0.211881i
$407$	9.10724e7			1.35084
$408$		0			0
$409$	2.60317e7	+	1.50294e7i	0.380480	+	0.219670i	0.678027	−	0.735037i	$-0.262835\pi$
$409$	2.60317e7	+	1.50294e7i	0.380480	+	0.219670i	−0.297547	+	0.954707i	$0.596168\pi$
$410$	−1.20658e8	+	2.08985e8i	−1.75067	+	3.03224i
$411$		0			0
$412$			5.12036e6i			0.0732165i
$413$	−6.40815e7	−	3.69975e7i	−0.909667	−	0.525196i
$414$		0			0
$415$	1.97127e7	+	3.41434e7i	0.275805	+	0.477708i
$416$	1.93536e7	+	1.11738e7i	0.268832	+	0.155211i
$417$		0			0
$418$	−1.05663e8	+	6.10044e7i	−1.44675	+	0.835280i
$419$			4.76385e7i			0.647614i	0.946123	+	0.323807i	$0.104963\pi$
$419$			4.76385e7i			0.647614i	−0.946123	+	0.323807i	$0.895037\pi$
$420$		0			0
$421$	−2.79191e7			−0.374158			−0.187079	−	0.982345i	$-0.559902\pi$
$421$	−2.79191e7			−0.374158			−0.187079	+	0.982345i	$0.559902\pi$
$422$	−7.00342e7	−	1.21303e8i	−0.931907	−	1.61411i
$423$		0			0
$424$	−5.80925e6	+	1.00619e7i	−0.0762118	+	0.132003i
$425$	4.56230e7	−	2.63405e7i	0.594316	−	0.343128i
$426$		0			0
$427$	−4.83429e7	+	2.79108e7i	−0.620940	+	0.358500i
$428$	−5.28434e7			−0.674000
$429$		0			0
$430$	−3.29125e7	−	1.90020e7i	−0.413957	−	0.238998i
$431$	1.65722e6	−	2.87039e6i	0.0206989	−	0.0358516i	−0.855490	−	0.517819i	$-0.826744\pi$
$431$	1.65722e6	−	2.87039e6i	0.0206989	−	0.0358516i	0.876189	+	0.481967i	$0.160078\pi$
$432$		0			0
$433$		−	4.59746e7i		−	0.566310i	−0.959074	−	0.283155i	$-0.908619\pi$
$433$		−	4.59746e7i		−	0.566310i	0.959074	−	0.283155i	$-0.0913811\pi$
$434$		−	5.27484e7i		−	0.645268i
$435$		0			0
$436$	2.92676e6	+	5.06930e6i	0.0353124	+	0.0611629i
$437$	−3.52030e7	−	2.03245e7i	−0.421829	−	0.243543i
$438$		0			0
$439$	4.71463e7	−	2.72199e7i	0.557255	−	0.321732i	−0.194788	−	0.980845i	$-0.562402\pi$
$439$	4.71463e7	−	2.72199e7i	0.557255	−	0.321732i	0.752043	+	0.659114i	$0.229068\pi$
$440$			5.16439e7i			0.606263i
$441$		0			0
$442$	1.75694e7			0.203466
$443$	5.29435e7	+	9.17008e7i	0.608978	+	1.05478i	0.991409	+	0.130797i	$0.0417535\pi$
$443$	5.29435e7	+	9.17008e7i	0.608978	+	1.05478i	−0.382431	+	0.923984i	$0.624913\pi$
$444$		0			0
$445$	−1.21355e8	+	2.10194e8i	−1.37714	+	2.38528i
$446$	−3.01190e7	+	1.73892e7i	−0.339497	+	0.196009i
$447$		0			0
$448$	1.27848e8			1.42188
$449$	−1.14053e8			−1.26000			−0.629998	−	0.776597i	$-0.716944\pi$
$449$	−1.14053e8			−1.26000			−0.629998	+	0.776597i	$0.716944\pi$
$450$		0			0
$451$	1.41629e8	+	8.17696e7i	1.54391	+	0.891378i
$452$	6.41402e7	−	1.11094e8i	0.694569	−	1.20303i
$453$		0			0
$454$		−	2.01252e8i		−	2.15066i
$455$	1.51263e7	+	2.61995e7i	0.160583	+	0.278137i
$456$		0			0
$457$	−4.92365e7	−	8.52801e7i	−0.515868	−	0.893509i	−0.999830	−	0.0184204i	$-0.994136\pi$
$457$	−4.92365e7	−	8.52801e7i	−0.515868	−	0.893509i	0.483963	−	0.875089i	$-0.339197\pi$
$458$	1.81636e8	+	1.04867e8i	1.89062	+	1.09155i
$459$		0			0
$460$	−7.45038e7	+	4.30148e7i	−0.765429	+	0.441921i
$461$			3.58333e7i			0.365750i	0.983136	+	0.182875i	$0.0585403\pi$
$461$			3.58333e7i			0.365750i	−0.983136	+	0.182875i	$0.941460\pi$
$462$		0			0
$463$	1.81000e8			1.82362			0.911810	−	0.410612i	$-0.134685\pi$
$463$	1.81000e8			1.82362			0.911810	+	0.410612i	$0.134685\pi$
$464$	−5.60102e6	−	9.70126e6i	−0.0560678	−	0.0971123i
$465$		0			0
$466$	−6.12261e7	+	1.06047e8i	−0.605033	+	1.04795i
$467$	−7.34856e7	+	4.24269e7i	−0.721526	+	0.416573i	−0.815314	−	0.579019i	$-0.803436\pi$
$467$	−7.34856e7	+	4.24269e7i	−0.721526	+	0.416573i	0.0937883	+	0.995592i	$0.470102\pi$
$468$		0			0
$469$	−4.60953e7	+	7.98393e7i	−0.446825	+	0.773924i
$470$	6.69173e7			0.644533
$471$		0			0
$472$	3.58707e7	+	2.07100e7i	0.341125	+	0.196949i
$473$	−1.28777e7	+	2.23047e7i	−0.121690	+	0.210772i
$474$		0			0
$475$		−	1.19960e8i		−	1.11933i
$476$	7.17419e7	−	4.14202e7i	0.665199	−	0.384053i
$477$		0			0
$478$	8.58683e6	+	1.48728e7i	0.0786229	+	0.136179i
$479$	1.37892e8	+	7.96121e7i	1.25468	+	0.724390i	0.972035	−	0.234834i	$-0.0754547\pi$
$479$	1.37892e8	+	7.96121e7i	1.25468	+	0.724390i	0.282645	+	0.959224i	$0.408788\pi$
$480$		0			0
$481$	−2.58623e7	+	1.49316e7i	−0.232398	+	0.134175i
$482$		−	1.86047e8i		−	1.66143i
$483$		0			0
$484$	3.32704e7			0.293442
$485$	−1.37680e8	−	2.38469e8i	−1.20683	−	2.09029i
$486$		0			0
$487$	4.03071e7	−	6.98140e7i	0.348975	−	0.604443i	−0.637092	−	0.770787i	$-0.719863\pi$
$487$	4.03071e7	−	6.98140e7i	0.348975	−	0.604443i	0.986068	+	0.166344i	$0.0531964\pi$
$488$	2.70608e7	−	1.56235e7i	0.232852	−	0.134437i
$489$		0			0
$490$	2.22357e8	+	1.28378e8i	1.89000	+	1.09119i
$491$	1.46544e7			0.123800			0.0619002	−	0.998082i	$-0.480284\pi$
$491$	1.46544e7			0.123800			0.0619002	+	0.998082i	$0.480284\pi$
$492$		0			0
$493$	−1.04005e7	−	6.00472e6i	−0.0867986	−	0.0501132i
$494$	2.00038e7	−	3.46475e7i	0.165932	−	0.287403i
$495$		0			0
$496$		−	3.60883e7i		−	0.295748i
$497$	3.49592e7			0.284769
$498$		0			0
$499$	1.56278e7	+	2.70682e7i	0.125776	+	0.217850i	0.922036	−	0.387104i	$-0.126525\pi$
$499$	1.56278e7	+	2.70682e7i	0.125776	+	0.217850i	−0.796260	+	0.604954i	$0.793191\pi$
$500$	−2.29950e7	−	1.32762e7i	−0.183960	−	0.106209i
$501$		0			0
$502$	−3.57588e7	+	2.06454e7i	−0.282665	+	0.163197i
$503$		−	1.42620e8i		−	1.12067i	−0.828267	−	0.560334i	$-0.810673\pi$
$503$		−	1.42620e8i		−	1.12067i	0.828267	−	0.560334i	$-0.189327\pi$
$504$		0			0
$505$	−2.40912e8			−1.87061
$506$	5.24720e7	+	9.08841e7i	0.405019	+	0.701514i
$507$		0			0
$508$	1.29199e8	−	2.23779e8i	0.985523	−	1.70698i
$509$	9.05219e6	−	5.22628e6i	0.0686436	−	0.0396314i	−0.465285	−	0.885161i	$-0.654048\pi$
$509$	9.05219e6	−	5.22628e6i	0.0686436	−	0.0396314i	0.533929	+	0.845529i	$0.320715\pi$
$510$		0			0
$511$	−9.43557e7	−	5.44763e7i	−0.707140	−	0.408267i
$512$	1.64364e8			1.22461
$513$		0			0
$514$	−2.41649e8	−	1.39516e8i	−1.77949	−	1.02739i
$515$	−5.82010e6	+	1.00807e7i	−0.0426097	+	0.0738022i
$516$		0			0
$517$		−	4.53498e7i		−	0.328174i
$518$	−1.26725e8	+	2.19495e8i	−0.911748	+	1.57919i
$519$		0			0
$520$	−8.46720e6	−	1.46656e7i	−0.0602185	−	0.104301i
$521$	−2.35560e6	−	1.36001e6i	−0.0166567	−	0.00961674i	0.491649	−	0.870794i	$-0.336394\pi$
$521$	−2.35560e6	−	1.36001e6i	−0.0166567	−	0.00961674i	−0.508305	+	0.861177i	$0.669728\pi$
$522$		0			0
$523$	−1.98382e8	+	1.14536e8i	−1.38675	+	0.800640i	−0.992947	−	0.118555i	$-0.962174\pi$
$523$	−1.98382e8	+	1.14536e8i	−1.38675	+	0.800640i	−0.393802	+	0.919195i	$0.628840\pi$
$524$		−	1.59637e8i		−	1.10953i
$525$		0			0
$526$	3.39142e8			2.33037
$527$	−1.93447e7	−	3.35060e7i	−0.132169	−	0.228924i
$528$		0			0
$529$	5.65362e7	−	9.79235e7i	0.381908	−	0.661485i
$530$	−1.14370e8	+	6.60313e7i	−0.768215	+	0.443529i
$531$		0			0
$532$		−	1.88637e8i		−	1.25283i
$533$	−5.36256e7			−0.354153
$534$		0			0
$535$	−1.04036e8	−	6.00649e7i	−0.679392	−	0.392247i
$536$	2.58026e7	−	4.46914e7i	0.167559	−	0.290222i
$537$		0			0
$538$			1.89723e8i			1.21835i
$539$	8.70014e7	−	1.50691e8i	0.555597	−	0.962323i
$540$		0			0
$541$	−1.14695e8	−	1.98657e8i	−0.724355	−	1.25462i	−0.959239	−	0.282596i	$-0.908805\pi$
$541$	−1.14695e8	−	1.98657e8i	−0.724355	−	1.25462i	0.234884	−	0.972023i	$-0.424529\pi$
$542$	−3.79349e8	−	2.19017e8i	−2.38254	−	1.37556i
$543$		0			0
$544$	1.20476e8	−	6.95569e7i	0.748349	−	0.432060i
$545$			1.33069e7i			0.0822030i
$546$		0			0
$547$	7.87986e7			0.481456			0.240728	−	0.970593i	$-0.422614\pi$
$547$	7.87986e7			0.481456			0.240728	+	0.970593i	$0.422614\pi$
$548$	5.68633e7	+	9.84902e7i	0.345534	+	0.598482i
$549$		0			0
$550$	−1.54851e8	+	2.68210e8i	−0.930737	+	1.61208i
$551$	−2.36830e7	+	1.36734e7i	−0.141574	+	0.0817376i
$552$		0			0
$553$	6.21226e7	+	1.07600e8i	0.367345	+	0.636261i
$554$	3.77768e8			2.22176
$555$		0			0
$556$	1.68773e8	+	9.74410e7i	0.981924	+	0.566914i
$557$	−5.36775e7	+	9.29722e7i	−0.310618	+	0.538007i	−0.978496	−	0.206264i	$-0.933869\pi$
$557$	−5.36775e7	+	9.29722e7i	−0.310618	+	0.538007i	0.667878	+	0.744271i	$0.267203\pi$
$558$		0			0
$559$		−	8.44534e6i		−	0.0483484i
$560$	1.52127e8	+	8.78308e7i	0.866250	+	0.500130i
$561$		0			0
$562$	3.97421e7	+	6.88353e7i	0.223894	+	0.387795i
$563$	−1.98593e8	−	1.14658e8i	−1.11285	−	0.642507i	−0.173287	−	0.984871i	$-0.555439\pi$
$563$	−1.98593e8	−	1.14658e8i	−1.11285	−	0.642507i	−0.939567	+	0.342365i	$0.888772\pi$
$564$		0			0
$565$	2.52552e8	−	1.45811e8i	1.40025	−	0.808435i
$566$			4.82976e8i			2.66365i
$567$		0			0
$568$	−1.95690e7			−0.106788
$569$	−7.35523e7	−	1.27396e8i	−0.399263	−	0.691544i	0.594372	−	0.804190i	$-0.297401\pi$
$569$	−7.35523e7	−	1.27396e8i	−0.399263	−	0.691544i	−0.993635	+	0.112646i	$0.964067\pi$
$570$		0			0
$571$	−1.37778e6	+	2.38638e6i	−0.00740068	+	0.0128183i	−0.869702	−	0.493577i	$-0.835689\pi$
$571$	−1.37778e6	+	2.38638e6i	−0.00740068	+	0.0128183i	0.862301	+	0.506395i	$0.169022\pi$
$572$	−4.96944e7	+	2.86911e7i	−0.265534	+	0.153306i
$573$		0			0
$574$	−3.94148e8	+	2.27562e8i	−2.08413	+	1.20327i
$575$	−1.03182e8			−0.542750
$576$		0			0
$577$	−2.77041e6	−	1.59950e6i	−0.0144217	−	0.00832639i	0.492772	−	0.870159i	$-0.335984\pi$
$577$	−2.77041e6	−	1.59950e6i	−0.0144217	−	0.00832639i	−0.507194	+	0.861832i	$0.669317\pi$
$578$	−9.01405e7	+	1.56128e8i	−0.466806	+	0.808532i
$579$		0			0
$580$			5.78768e7i			0.296634i
$581$			7.43567e7i			0.379133i
$582$		0			0
$583$	4.47494e7	+	7.75082e7i	0.225830	+	0.391149i
$584$	5.28172e7	+	3.04940e7i	0.265178	+	0.153100i
$585$		0			0
$586$	−1.31771e8	+	7.60779e7i	−0.654827	+	0.378064i
$587$			2.39854e8i			1.18586i	0.805254	+	0.592929i	$0.202029\pi$
$587$			2.39854e8i			1.18586i	−0.805254	+	0.592929i	$0.797971\pi$
$588$		0			0
$589$	−8.80999e7			−0.431151
$590$	2.35401e8	+	4.07727e8i	1.14618	+	1.98524i
$591$		0			0
$592$	−8.67004e7	+	1.50170e8i	−0.417884	+	0.723797i
$593$	1.64470e8	−	9.49567e7i	0.788719	−	0.455367i	−0.0507923	−	0.998709i	$-0.516175\pi$
$593$	1.64470e8	−	9.49567e7i	0.788719	−	0.455367i	0.839511	+	0.543342i	$0.182841\pi$
$594$		0			0
$595$	1.88322e8			0.894028
$596$	−2.51500e8			−1.18795
$597$		0			0
$598$	−2.98015e7	−	1.72059e7i	−0.139359	−	0.0804589i
$599$	1.92575e8	−	3.33550e8i	0.896025	−	1.55196i	0.0634938	−	0.997982i	$-0.479776\pi$
$599$	1.92575e8	−	3.33550e8i	0.896025	−	1.55196i	0.832531	−	0.553978i	$-0.186891\pi$
$600$		0			0
$601$			2.97376e8i			1.36988i	0.728598	+	0.684941i	$0.240172\pi$
$601$			2.97376e8i			1.36988i	−0.728598	+	0.684941i	$0.759828\pi$
$602$	−3.58380e7	−	6.20733e7i	−0.164269	−	0.284521i
$603$		0			0
$604$	9.12880e7	+	1.58116e8i	0.414289	+	0.717569i
$605$	6.55011e7	+	3.78171e7i	0.295789	+	0.170774i
$606$		0			0
$607$	−2.55751e8	+	1.47658e8i	−1.14354	+	0.660223i	−0.947305	−	0.320334i	$-0.896205\pi$
$607$	−2.55751e8	+	1.47658e8i	−1.14354	+	0.660223i	−0.196235	+	0.980557i	$0.562872\pi$
$608$		−	3.16777e8i		−	1.40943i
$609$		0			0
$610$	3.55173e8			1.56477
$611$	7.43526e6	+	1.28782e7i	0.0325966	+	0.0564590i
$612$		0			0
$613$	1.68606e8	−	2.92035e8i	0.731968	−	1.26781i	−0.224073	−	0.974572i	$-0.571935\pi$
$613$	1.68606e8	−	2.92035e8i	0.731968	−	1.26781i	0.956041	−	0.293234i	$-0.0947313\pi$
$614$	1.84212e7	−	1.06355e7i	0.0795816	−	0.0459465i
$615$		0			0
$616$	−4.87005e7	+	8.43518e7i	−0.208349	+	0.360871i
$617$	−3.68150e8			−1.56736			−0.783682	−	0.621163i	$-0.786661\pi$
$617$	−3.68150e8			−1.56736			−0.783682	+	0.621163i	$0.786661\pi$
$618$		0			0
$619$	−2.69156e7	−	1.55397e7i	−0.113483	−	0.0655197i	0.442184	−	0.896924i	$-0.354204\pi$
$619$	−2.69156e7	−	1.55397e7i	−0.113483	−	0.0655197i	−0.555667	+	0.831405i	$0.687537\pi$
$620$	−9.32274e7	+	1.61475e8i	−0.391173	+	0.677531i
$621$		0			0
$622$		−	4.38318e8i		−	1.82146i
$623$	−3.96428e8	+	2.28878e8i	−1.63946	+	0.946541i
$624$		0			0
$625$	1.06147e8	+	1.83852e8i	0.434779	+	0.753059i
$626$	−1.20602e8	−	6.96296e7i	−0.491622	−	0.283838i
$627$		0			0
$628$	1.02892e7	−	5.94045e6i	0.0415433	−	0.0239850i
$629$			1.85899e8i			0.747007i
$630$		0			0
$631$	−3.25406e8			−1.29520			−0.647601	−	0.761980i	$-0.724228\pi$
$631$	−3.25406e8			−1.29520			−0.647601	+	0.761980i	$0.724228\pi$
$632$	−3.47742e7	−	6.02306e7i	−0.137754	−	0.238598i
$633$		0			0
$634$	1.26985e8	−	2.19944e8i	0.498291	−	0.863066i
$635$	5.08720e8	−	2.93709e8i	1.98681	−	1.14709i
$636$		0			0
$637$			5.70567e7i			0.220744i
$638$	7.06015e7			0.271864
$639$		0			0
$640$	−2.39985e8	−	1.38555e8i	−0.915469	−	0.528546i
$641$	−2.77818e7	+	4.81196e7i	−0.105484	+	0.182704i	−0.913936	−	0.405859i	$-0.866973\pi$
$641$	−2.77818e7	+	4.81196e7i	−0.105484	+	0.182704i	0.808452	+	0.588562i	$0.200306\pi$
$642$		0			0
$643$			9.33357e7i			0.351087i	0.984472	+	0.175544i	$0.0561683\pi$
$643$			9.33357e7i			0.351087i	−0.984472	+	0.175544i	$0.943832\pi$
$644$	−1.62253e8			−0.607483
$645$		0			0
$646$	−1.24523e8	−	2.15681e8i	−0.461906	−	0.800044i
$647$	1.67312e8	+	9.65975e7i	0.617751	+	0.356659i	0.775993	−	0.630742i	$-0.217249\pi$
$647$	1.67312e8	+	9.65975e7i	0.617751	+	0.356659i	−0.158242	+	0.987400i	$0.550583\pi$
$648$		0			0
$649$	2.76316e8	−	1.59531e8i	1.01082	−	0.583595i
$650$		−	1.01554e8i		−	0.369790i
$651$		0			0
$652$	−5.67798e8			−2.04857
$653$	1.81224e8	+	3.13889e8i	0.650842	+	1.12729i	0.982919	+	0.184039i	$0.0589172\pi$
$653$	1.81224e8	+	3.13889e8i	0.650842	+	1.12729i	−0.332077	+	0.943252i	$0.607749\pi$
$654$		0			0
$655$	1.81453e8	−	3.14285e8i	0.645713	−	1.11841i
$656$	−2.69660e8	+	1.55688e8i	−0.955224	+	0.551499i
$657$		0			0
$658$	1.09298e8	+	6.31034e7i	0.383651	+	0.221501i
$659$	−2.39985e8			−0.838549			−0.419274	−	0.907860i	$-0.637715\pi$
$659$	−2.39985e8			−0.838549			−0.419274	+	0.907860i	$0.637715\pi$
$660$		0			0
$661$	−1.67334e7	−	9.66103e6i	−0.0579402	−	0.0334518i	0.470750	−	0.882267i	$-0.343983\pi$
$661$	−1.67334e7	−	9.66103e6i	−0.0579402	−	0.0334518i	−0.528690	+	0.848815i	$0.677317\pi$
$662$	3.55320e8	−	6.15431e8i	1.22474	−	2.12132i
$663$		0			0
$664$		−	4.16224e7i		−	0.142175i
$665$	2.14415e8	−	3.71378e8i	0.729106	−	1.26285i
$666$		0			0
$667$	1.17610e7	+	2.03706e7i	0.0396337	+	0.0686477i
$668$	−4.47552e7	−	2.58394e7i	−0.150146	−	0.0866869i
$669$		0			0
$670$	5.07989e8	−	2.93287e8i	1.68900	−	0.975144i
$671$		−	2.40700e8i		−	0.796726i
$672$		0			0
$673$	−4.27171e7			−0.140138			−0.0700692	−	0.997542i	$-0.522322\pi$
$673$	−4.27171e7			−0.140138			−0.0700692	+	0.997542i	$0.522322\pi$
$674$	−2.20679e8	−	3.82227e8i	−0.720744	−	1.24836i
$675$		0			0
$676$	−1.83664e8	+	3.18116e8i	−0.594545	+	1.02978i
$677$	2.51797e8	−	1.45375e8i	0.811493	−	0.468516i	−0.0359809	−	0.999352i	$-0.511456\pi$
$677$	2.51797e8	−	1.45375e8i	0.811493	−	0.468516i	0.847474	+	0.530837i	$0.178122\pi$
$678$		0			0
$679$		−	5.19333e8i		−	1.65896i
$680$	−1.05417e8			−0.335261
$681$		0			0
$682$	1.96976e8	+	1.13724e8i	0.620956	+	0.358509i
$683$	4.10966e7	−	7.11813e7i	0.128986	−	0.223411i	−0.794298	−	0.607529i	$-0.792161\pi$
$683$	4.10966e7	−	7.11813e7i	0.128986	−	0.223411i	0.923284	+	0.384118i	$0.125494\pi$
$684$		0			0
$685$			2.58537e8i			0.804360i
$686$	2.42122e8	+	4.19367e8i	0.750000	+	1.29904i
$687$		0			0
$688$	−2.45189e7	−	4.24680e7i	−0.0752898	−	0.130406i
$689$	−2.54155e7	−	1.46736e7i	−0.0777035	−	0.0448621i
$690$		0			0
$691$	3.00664e7	−	1.73588e7i	0.0911269	−	0.0526122i	−0.453744	−	0.891132i	$-0.649912\pi$
$691$	3.00664e7	−	1.73588e7i	0.0911269	−	0.0526122i	0.544871	+	0.838520i	$0.316579\pi$
$692$		−	2.50866e8i		−	0.757050i
$693$		0			0
$694$	−4.07730e8			−1.21981
$695$	2.21514e8	+	3.83674e8i	0.659853	+	1.14290i
$696$		0			0
$697$	−1.66910e8	+	2.89096e8i	−0.492928	+	0.853776i
$698$	5.69545e8	−	3.28827e8i	1.67480	−	0.966944i
$699$		0			0
$700$	−2.39414e8	−	4.14677e8i	−0.698000	−	1.20897i
$701$	3.04543e8			0.884087			0.442044	−	0.896994i	$-0.354254\pi$
$701$	3.04543e8			0.884087			0.442044	+	0.896994i	$0.354254\pi$
$702$		0			0
$703$	3.66599e8	+	2.11656e8i	1.05518	+	0.609206i
$704$	−2.75638e8	+	4.77419e8i	−0.789990	+	1.36830i
$705$		0			0
$706$		−	5.71204e7i		−	0.162322i
$707$	−3.93489e8	−	2.27181e8i	−1.11346	−	0.642856i
$708$		0			0
$709$	1.14446e8	+	1.98226e8i	0.321116	+	0.556188i	0.980718	−	0.195426i	$-0.0626089\pi$
$709$	1.14446e8	+	1.98226e8i	0.321116	+	0.556188i	−0.659603	+	0.751614i	$0.729276\pi$
$710$	−1.92633e8	−	1.11216e8i	−0.538214	−	0.310738i
$711$		0			0
$712$	2.21907e8	−	1.28118e8i	0.614796	−	0.354953i
$713$			7.57777e7i			0.209061i
$714$		0			0
$715$	−1.30448e8			−0.356877
$716$	4.06512e8	+	7.04099e8i	1.10747	+	1.91820i
$717$		0			0
$718$	−3.18701e7	+	5.52007e7i	−0.0861015	+	0.149132i
$719$	−3.87891e8	+	2.23949e8i	−1.04357	+	0.602507i	−0.920843	−	0.389933i	$-0.872498\pi$
$719$	−3.87891e8	+	2.23949e8i	−1.04357	+	0.602507i	−0.122729	+	0.992440i	$0.539165\pi$
$720$		0			0
$721$	−1.90123e7	+	1.09768e7i	−0.0507258	+	0.0292866i
$722$	−2.55602e6			−0.00679131
$723$		0			0
$724$	6.04498e8	+	3.49007e8i	1.59286	+	0.919641i
$725$	−3.47080e7	+	6.01161e7i	−0.0910786	+	0.157753i
$726$		0			0
$727$		−	3.71752e7i		−	0.0967498i	−0.998829	−	0.0483749i	$-0.984596\pi$
$727$		−	3.71752e7i		−	0.0967498i	0.998829	−	0.0483749i	$-0.0154042\pi$
$728$		−	3.19385e7i		−	0.0827789i
$729$		0			0
$730$	3.46613e8	+	6.00351e8i	0.890996	+	1.54325i
$731$	−4.55289e7	−	2.62861e7i	−0.116556	−	0.0672937i
$732$		0			0
$733$	5.24092e8	−	3.02585e8i	1.33075	−	0.768307i	0.345333	−	0.938480i	$-0.387766\pi$
$733$	5.24092e8	−	3.02585e8i	1.33075	−	0.768307i	0.985414	+	0.170173i	$0.0544326\pi$
$734$		−	9.58030e8i		−	2.42265i
$735$		0			0
$736$	−2.72471e8			−0.683419
$737$	−1.98761e8	−	3.44263e8i	−0.496510	−	0.859980i
$738$		0			0
$739$	1.00894e8	−	1.74753e8i	0.249994	−	0.433003i	−0.713530	−	0.700625i	$-0.752905\pi$
$739$	1.00894e8	−	1.74753e8i	0.249994	−	0.433003i	0.963524	+	0.267622i	$0.0862379\pi$
$740$	7.75870e8	−	4.47949e8i	1.91467	−	1.10544i
$741$		0			0
$742$	−2.49072e8			−0.609695
$743$	9.81196e7			0.239216			0.119608	−	0.992821i	$-0.461836\pi$
$743$	9.81196e7			0.239216			0.119608	+	0.992821i	$0.461836\pi$
$744$		0			0
$745$	−4.95141e8	−	2.85870e8i	−1.19746	−	0.691352i
$746$	−2.53561e8	+	4.39180e8i	−0.610752	+	1.05785i
$747$		0			0
$748$			3.57204e8i			0.853515i
$749$	−1.13283e8	−	1.96212e8i	−0.269600	−	0.466961i
$750$		0			0
$751$	2.12914e8	+	3.68777e8i	0.502670	+	0.870651i	0.999995	+	0.00308636i	$0.000982422\pi$
$751$	2.12914e8	+	3.68777e8i	0.502670	+	0.870651i	−0.497325	+	0.867564i	$0.665684\pi$
$752$	7.47775e7	+	4.31728e7i	0.175840	+	0.101521i
$753$		0			0
$754$	−2.00491e7	+	1.15754e7i	−0.0467715	+	0.0270035i
$755$			4.15053e8i			0.964413i
$756$		0			0
$757$	3.07427e7			0.0708687			0.0354344	−	0.999372i	$-0.488719\pi$
$757$	3.07427e7			0.0708687			0.0354344	+	0.999372i	$0.488719\pi$
$758$	−7.73039e7	−	1.33894e8i	−0.177498	−	0.307436i
$759$		0			0
$760$	−1.20023e8	+	2.07885e8i	−0.273415	+	0.473568i
$761$	−3.21493e8	+	1.85614e8i	−0.729488	+	0.421170i	−0.818235	−	0.574884i	$-0.805047\pi$
$761$	−3.21493e8	+	1.85614e8i	−0.729488	+	0.421170i	0.0887468	+	0.996054i	$0.471714\pi$
$762$		0			0
$763$	−1.25485e7	+	2.17346e7i	−0.0282499	+	0.0489303i
$764$	−3.39075e8			−0.760354
$765$		0			0
$766$	−2.78067e8	−	1.60542e8i	−0.618676	−	0.357193i
$767$	−5.23114e7	+	9.06060e7i	−0.115934	+	0.200803i
$768$		0			0
$769$			4.59933e8i			1.01138i	0.862714	+	0.505691i	$0.168763\pi$
$769$			4.59933e8i			1.01138i	−0.862714	+	0.505691i	$0.831237\pi$
$770$	−9.58791e8	+	5.53558e8i	−2.10016	+	1.21253i
$771$		0			0
$772$	−2.45928e8	−	4.25960e8i	−0.534511	−	0.925800i
$773$	5.94294e8	+	3.43116e8i	1.28666	+	0.742852i	0.978056	−	0.208340i	$-0.0668062\pi$
$773$	5.94294e8	+	3.43116e8i	1.28666	+	0.742852i	0.308600	+	0.951192i	$0.400139\pi$
$774$		0			0
$775$	−1.93669e8	+	1.11815e8i	−0.416059	+	0.240212i
$776$			2.90705e8i			0.622111i
$777$		0			0
$778$	1.29069e8			0.274083
$779$	3.80071e8	+	6.58303e8i	0.803994	+	1.39256i
$780$		0			0
$781$	−7.53713e7	+	1.30547e8i	−0.158217	+	0.274040i
$782$	−1.85514e8	+	1.07107e8i	−0.387934	+	0.223974i
$783$		0			0
$784$	1.65650e8	+	2.86914e8i	0.343750	+	0.595392i
$785$	2.70090e7			0.0558342
$786$		0			0
$787$	−4.87045e8	−	2.81196e8i	−0.999183	−	0.576879i	−0.0911765	−	0.995835i	$-0.529063\pi$
$787$	−4.87045e8	−	2.81196e8i	−0.999183	−	0.576879i	−0.908006	+	0.418956i	$0.862396\pi$
$788$	3.16222e7	−	5.47712e7i	0.0646268	−	0.111937i
$789$		0			0
$790$		−	7.90527e8i		−	1.60338i
$791$	5.50003e8			1.11131
$792$		0			0
$793$	3.94636e7	+	6.83530e7i	0.0791366	+	0.137069i
$794$	−9.89693e7	−	5.71400e7i	−0.197715	−	0.114151i
$795$		0			0
$796$	−5.62974e8	+	3.25033e8i	−1.11622	+	0.644449i
$797$			9.95198e8i			1.96578i	0.184200	+	0.982889i	$0.441031\pi$
$797$			9.95198e8i			1.96578i	−0.184200	+	0.982889i	$0.558969\pi$
$798$		0			0
$799$	9.25690e7			0.181478
$800$	−4.02048e8	−	6.96368e8i	−0.785250	−	1.36009i
$801$		0			0
$802$	4.60730e8	−	7.98008e8i	0.893149	−	1.54698i
$803$	4.06857e8	−	2.34899e8i	0.785770	−	0.453665i
$804$		0			0
$805$	−3.19435e8	−	1.84426e8i	−0.612343	−	0.353537i
$806$	−7.45819e7			−0.142439
$807$		0			0
$808$	2.20262e8	+	1.27168e8i	0.417547	+	0.241071i
$809$	3.57584e8	−	6.19353e8i	0.675355	−	1.16975i	−0.301010	−	0.953621i	$-0.597324\pi$
$809$	3.57584e8	−	6.19353e8i	0.675355	−	1.16975i	0.976365	−	0.216128i	$-0.0693429\pi$
$810$		0			0
$811$			3.33892e8i			0.625955i	0.949761	+	0.312977i	$0.101326\pi$
$811$			3.33892e8i			0.625955i	−0.949761	+	0.312977i	$0.898674\pi$
$812$	−5.45782e7	+	9.45321e7i	−0.101941	+	0.176568i
$813$		0			0
$814$	−5.46434e8	−	9.46452e8i	−1.01313	−	1.75479i
$815$	−1.11785e9	−	6.45392e8i	−2.06496	−	1.19220i
$816$		0			0
$817$	−1.03674e8	+	5.98564e7i	−0.190110	+	0.109760i
$818$		−	3.60705e8i		−	0.659011i
$819$		0			0
$820$	1.60877e9			2.91778
$821$	−2.41980e8	−	4.19121e8i	−0.437270	−	0.757374i	0.560208	−	0.828352i	$-0.310721\pi$
$821$	−2.41980e8	−	4.19121e8i	−0.437270	−	0.757374i	−0.997478	+	0.0709784i	$0.977388\pi$
$822$		0			0
$823$	−7.85037e7	+	1.35972e8i	−0.140829	+	0.243922i	−0.927809	−	0.373056i	$-0.878310\pi$
$823$	−7.85037e7	+	1.35972e8i	−0.140829	+	0.243922i	0.786980	+	0.616978i	$0.211643\pi$
$824$	1.06425e7	−	6.14443e6i	0.0190222	−	0.0109825i
$825$		0			0
$826$			8.87939e8i			1.57559i
$827$	−8.84716e8			−1.56418			−0.782091	−	0.623164i	$-0.785847\pi$
$827$	−8.84716e8			−1.56418			−0.782091	+	0.623164i	$0.785847\pi$
$828$		0			0
$829$	−7.05137e7	−	4.07111e7i	−0.123768	−	0.0714578i	0.436838	−	0.899540i	$-0.356098\pi$
$829$	−7.05137e7	−	4.07111e7i	−0.123768	−	0.0714578i	−0.560606	+	0.828083i	$0.689432\pi$
$830$	2.36552e8	−	4.09721e8i	0.413707	−	0.716562i
$831$		0			0
$832$		−	1.80767e8i		−	0.313870i
$833$	3.07593e8	+	1.77589e8i	0.532160	+	0.307242i
$834$		0			0
$835$	−5.87412e7	−	1.01743e8i	−0.100898	−	0.174761i
$836$	7.04418e8	+	4.06696e8i	1.20562	+	0.696067i
$837$		0			0
$838$	4.95074e8	−	2.85831e8i	0.841275	−	0.485711i
$839$			4.66806e8i			0.790407i	0.918594	+	0.395203i	$0.129326\pi$
$839$			4.66806e8i			0.790407i	−0.918594	+	0.395203i	$0.870674\pi$
$840$		0			0
$841$	−5.78999e8			−0.973396
$842$	1.67514e8	+	2.90144e8i	0.280618	+	0.486045i
$843$		0			0
$844$	−4.66894e8	+	8.08685e8i	−0.776589	+	1.34509i
$845$	−7.23178e8	+	4.17527e8i	−1.19860	+	0.692014i
$846$		0			0
$847$	7.13234e7	+	1.23536e8i	0.117377	+	0.203302i
$848$	−1.70405e8			−0.279443
$849$		0			0
$850$	−5.47476e8	−	3.16086e8i	−0.891474	−	0.514693i
$851$	1.82052e8	−	3.15324e8i	0.295398	−	0.511645i
$852$		0			0
$853$		−	8.80430e8i		−	1.41856i	−0.704926	−	0.709280i	$-0.749020\pi$
$853$		−	8.80430e8i		−	1.41856i	0.704926	−	0.709280i	$-0.250980\pi$
$854$	5.80115e8	+	3.34930e8i	0.931409	+	0.537750i
$855$		0			0
$856$	6.34121e7	+	1.09833e8i	0.101100	+	0.175110i
$857$	−1.55796e8	−	8.99491e7i	−0.247523	−	0.142907i	0.371107	−	0.928590i	$-0.378978\pi$
$857$	−1.55796e8	−	8.99491e7i	−0.247523	−	0.142907i	−0.618629	+	0.785683i	$0.712312\pi$
$858$		0			0
$859$	−7.85361e8	+	4.53429e8i	−1.23905	+	0.715368i	−0.968901	−	0.247450i	$-0.920407\pi$
$859$	−7.85361e8	+	4.53429e8i	−1.23905	+	0.715368i	−0.270153	+	0.962818i	$0.587074\pi$
$860$			2.53360e8i			0.398330i
$861$		0			0
$862$	−3.97733e7			−0.0620968
$863$	2.72072e7	+	4.71242e7i	0.0423303	+	0.0733182i	0.886414	−	0.462893i	$-0.153189\pi$
$863$	2.72072e7	+	4.71242e7i	0.0423303	+	0.0733182i	−0.844084	+	0.536211i	$0.819855\pi$
$864$		0			0
$865$	2.85149e8	−	4.93893e8i	0.440580	−	0.763106i
$866$	−4.77782e8	+	2.75848e8i	−0.735658	+	0.424732i
$867$		0			0
$868$	−3.04543e8	+	1.75828e8i	−0.465682	+	0.268861i
$869$	−5.35740e8			−0.816384
$870$		0			0
$871$	1.12886e8	+	6.51750e7i	0.170839	+	0.0986339i
$872$	7.02422e6	−	1.21663e7i	0.0105937	−	0.0183489i
$873$		0			0
$874$			4.87788e8i			0.730628i
$875$		−	1.13843e8i		−	0.169935i
$876$		0			0
$877$	6.30185e7	+	1.09151e8i	0.0934263	+	0.161819i	0.908951	−	0.416904i	$-0.136885\pi$
$877$	6.30185e7	+	1.09151e8i	0.0934263	+	0.161819i	−0.815524	+	0.578723i	$0.803551\pi$
$878$	−5.65756e8	−	3.26639e8i	−0.835883	−	0.482597i
$879$		0			0
$880$	−6.55966e8	+	3.78722e8i	−0.962572	+	0.555741i
$881$			1.37857e8i			0.201605i	0.994906	+	0.100802i	$0.0321410\pi$
$881$			1.37857e8i			0.201605i	−0.994906	+	0.100802i	$0.967859\pi$
$882$		0			0
$883$	7.41288e8			1.07672			0.538362	−	0.842713i	$-0.319043\pi$
$883$	7.41288e8			1.07672			0.538362	+	0.842713i	$0.319043\pi$
$884$	−5.85648e7	−	1.01437e8i	−0.0847774	−	0.146839i
$885$		0			0
$886$	6.35322e8	−	1.10041e9i	0.913467	−	1.58217i
$887$	3.02999e8	−	1.74936e8i	0.434180	−	0.250674i	−0.266946	−	0.963712i	$-0.586014\pi$
$887$	3.02999e8	−	1.74936e8i	0.434180	−	0.250674i	0.701126	+	0.713038i	$0.252681\pi$
$888$		0			0
$889$	1.10788e9			1.57684
$890$	2.91253e9			4.13143
$891$		0			0
$892$	2.00794e8	+	1.15928e8i	0.282915	+	0.163341i
$893$	1.05395e8	−	1.82549e8i	0.148001	−	0.256345i
$894$		0			0
$895$			1.84826e9i			2.57806i
$896$	−2.61317e8	−	4.52614e8i	−0.363281	−	0.629222i
$897$		0			0
$898$	6.84320e8	+	1.18528e9i	0.944996	+	1.63678i
$899$	4.41498e7	+	2.54899e7i	0.0607645	+	0.0350824i
$900$		0			0
$901$	−1.58211e8	+	9.13433e7i	−0.216303	+	0.124883i
$902$		−	1.96247e9i		−	2.67413i
$903$		0			0
$904$	−3.07873e8			−0.416741
$905$	7.93403e8	+	1.37421e9i	1.07041	+	1.85400i
$906$		0			0
$907$	−3.66171e8	+	6.34226e8i	−0.490751	+	0.850006i	−0.999943	−	0.0106466i	$-0.996611\pi$
$907$	−3.66171e8	+	6.34226e8i	−0.490751	+	0.850006i	0.509192	+	0.860653i	$0.329944\pi$
$908$	−1.16193e9	+	6.70840e8i	−1.55211	+	0.896110i
$909$		0			0
$910$	1.81516e8	−	3.14394e8i	0.240874	−	0.417206i
$911$	8.09031e8			1.07007			0.535033	−	0.844831i	$-0.320299\pi$
$911$	8.09031e8			1.07007			0.535033	+	0.844831i	$0.320299\pi$
$912$		0			0
$913$	−2.77667e8	−	1.60311e8i	−0.364849	−	0.210645i
$914$	−5.90838e8	+	1.02336e9i	−0.773802	+	1.34026i
$915$		0			0
$916$		−	1.39823e9i		−	1.81925i
$917$	5.92746e8	−	3.42222e8i	0.768706	−	0.443813i
$918$		0			0
$919$	−6.19741e8	−	1.07342e9i	−0.798479	−	1.38301i	−0.920606	−	0.390492i	$-0.872305\pi$
$919$	−6.19741e8	−	1.07342e9i	−0.798479	−	1.38301i	0.122127	−	0.992515i	$-0.461029\pi$
$920$	1.78809e8	+	1.03235e8i	0.229629	+	0.132576i
$921$		0			0
$922$	3.72390e8	−	2.15000e8i	0.475123	−	0.274312i
$923$		−	4.94295e7i		−	0.0628610i
$924$		0			0
$925$	1.07452e9			1.35765
$926$	−1.08600e9	−	1.88100e9i	−1.36772	−	2.36895i
$927$		0			0
$928$	−9.16531e7	+	1.58748e8i	−0.114684	+	0.198639i
$929$	1.04924e9	−	6.05780e8i	1.30866	−	0.755558i	0.326791	−	0.945097i	$-0.394033\pi$
$929$	1.04924e9	−	6.05780e8i	1.30866	−	0.755558i	0.981873	+	0.189539i	$0.0606993\pi$
$930$		0			0
$931$	7.00423e8	−	4.04390e8i	0.867984	−	0.501131i
$932$	8.16348e8			1.00839
$933$		0			0
$934$	8.81828e8	+	5.09123e8i	1.08229	+	0.624860i
$935$	−4.06019e8	+	7.03245e8i	−0.496720	+	0.860344i
$936$		0			0
$937$		−	1.26862e8i		−	0.154211i	−0.997023	−	0.0771053i	$-0.975432\pi$
$937$		−	1.26862e8i		−	0.154211i	0.997023	−	0.0771053i	$-0.0245678\pi$
$938$	1.10629e9			1.34048
$939$		0			0
$940$	−2.23058e8	−	3.86347e8i	−0.268555	−	0.465152i
$941$	3.66610e8	+	2.11662e8i	0.439983	+	0.254024i	0.703590	−	0.710606i	$-0.251579\pi$
$941$	3.66610e8	+	2.11662e8i	0.439983	+	0.254024i	−0.263608	+	0.964630i	$0.584912\pi$
$942$		0			0
$943$	5.66229e8	−	3.26912e8i	0.675238	−	0.389849i
$944$			6.07492e8i			0.722145i
$945$		0			0
$946$	3.09064e8			0.365069
$947$	−7.97747e8	−	1.38174e9i	−0.939324	−	1.62696i	−0.766736	−	0.641962i	$-0.778121\pi$
$947$	−7.97747e8	−	1.38174e9i	−0.939324	−	1.62696i	−0.172587	−	0.984994i	$-0.555213\pi$
$948$		0			0
$949$	−7.70251e7	+	1.33411e8i	−0.0901225	+	0.156097i
$950$	−1.24666e9	+	7.19761e8i	−1.45405	+	0.839494i
$951$		0			0
$952$	−1.72181e8	−	9.94085e7i	−0.199560	−	0.115216i
$953$	3.42254e8			0.395430			0.197715	−	0.980260i	$-0.436648\pi$
$953$	3.42254e8			0.395430			0.197715	+	0.980260i	$0.436648\pi$
$954$		0			0
$955$	−6.67554e8	−	3.85413e8i	−0.766437	−	0.442503i
$956$	5.72455e7	−	9.91521e7i	0.0655191	−	0.113482i
$957$		0			0
$958$		−	1.91069e9i		−	2.17317i
$959$	−2.43801e8	+	4.22277e8i	−0.276427	+	0.478786i
$960$		0			0
$961$	−3.61634e8	−	6.26369e8i	−0.407473	−	0.705764i
$962$	3.10348e8	+	1.79180e8i	0.348597	+	0.201263i
$963$		0			0
$964$	−1.07414e9	+	6.20157e8i	−1.19903	+	0.692263i
$965$		−	1.11815e9i		−	1.24428i
$966$		0			0
$967$	−1.56835e9			−1.73445			−0.867227	−	0.497914i	$-0.834100\pi$
$967$	−1.56835e9			−1.73445			−0.867227	+	0.497914i	$0.834100\pi$
$968$	−3.99245e7	−	6.91512e7i	−0.0440163	−	0.0762384i
$969$		0			0
$970$	−1.65216e9	+	2.86163e9i	−1.81025	+	3.13544i
$971$	−5.20251e8	+	3.00367e8i	−0.568271	+	0.328091i	−0.756458	−	0.654042i	$-0.773072\pi$
$971$	−5.20251e8	+	3.00367e8i	−0.568271	+	0.328091i	0.188188	+	0.982133i	$0.439739\pi$
$972$		0			0
$973$			8.35557e8i			0.907063i
$974$	−9.67371e8			−1.04693
$975$		0			0
$976$	3.96891e8	+	2.29145e8i	0.426896	+	0.246469i
$977$	−5.89510e7	+	1.02106e8i	−0.0632132	+	0.109488i	−0.895900	−	0.444256i	$-0.853468\pi$
$977$	−5.89510e7	+	1.02106e8i	−0.0632132	+	0.109488i	0.832687	+	0.553744i	$0.186801\pi$
$978$		0			0
$979$		−	1.97382e9i		−	2.10358i
$980$		−	1.71170e9i		−	1.81865i
$981$		0			0
$982$	−8.79261e7	−	1.52293e8i	−0.0928504	−	0.160822i
$983$	−9.01345e8	−	5.20392e8i	−0.948922	−	0.547860i	−0.0561762	−	0.998421i	$-0.517891\pi$
$983$	−9.01345e8	−	5.20392e8i	−0.948922	−	0.547860i	−0.892746	+	0.450560i	$0.851224\pi$
$984$		0			0
$985$	1.24512e8	−	7.18872e7i	0.130288	−	0.0752216i
$986$			1.44113e8i			0.150340i
$987$		0			0
$988$	−2.66717e8			−0.276554
$989$	5.14845e7	+	8.91738e7i	0.0532216	+	0.0921824i
$990$		0			0
$991$	7.09380e8	−	1.22868e9i	0.728883	−	1.26246i	−0.228473	−	0.973550i	$-0.573373\pi$
$991$	7.09380e8	−	1.22868e9i	0.728883	−	1.26246i	0.957356	−	0.288912i	$-0.0932934\pi$
$992$	−5.11419e8	+	2.95268e8i	−0.523892	+	0.302469i
$993$		0			0
$994$	−2.09755e8	−	3.63307e8i	−0.213577	−	0.369926i
$995$	−1.47781e9			−1.50020
$996$		0			0
$997$	7.05186e8	+	4.07139e8i	0.711571	+	0.410826i	0.811642	−	0.584155i	$-0.198574\pi$
$997$	7.05186e8	+	4.07139e8i	0.711571	+	0.410826i	−0.100072	+	0.994980i	$0.531907\pi$
$998$	1.87534e8	−	3.24818e8i	0.188664	−	0.326775i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.7.m.a.10.1		2
3.2	odd	2		7.7.d.a.3.1	✓	2
7.3	odd	6		441.7.d.a.244.2		2
7.4	even	3		441.7.d.a.244.1		2
7.5	odd	6	inner	63.7.m.a.19.1		2
12.11	even	2		112.7.s.a.17.1		2
21.2	odd	6		49.7.d.b.19.1		2
21.5	even	6		7.7.d.a.5.1	yes	2
21.11	odd	6		49.7.b.a.48.2		2
21.17	even	6		49.7.b.a.48.1		2
21.20	even	2		49.7.d.b.31.1		2
84.47	odd	6		112.7.s.a.33.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.7.d.a.3.1	✓	2	3.2	odd	2
7.7.d.a.5.1	yes	2	21.5	even	6
49.7.b.a.48.1		2	21.17	even	6
49.7.b.a.48.2		2	21.11	odd	6
49.7.d.b.19.1		2	21.2	odd	6
49.7.d.b.31.1		2	21.20	even	2
63.7.m.a.10.1		2	1.1	even	1	trivial
63.7.m.a.19.1		2	7.5	odd	6	inner
112.7.s.a.17.1		2	12.11	even	2
112.7.s.a.33.1		2	84.47	odd	6
441.7.d.a.244.1		2	7.4	even	3
441.7.d.a.244.2		2	7.3	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.00000 - 10.3923i) q^{2} +(-40.0000 + 69.2820i) q^{4} +(-157.500 + 90.9327i) q^{5} -343.000 q^{7} +192.000 q^{8} +O(q^{10})\)	\(q+(-6.00000 - 10.3923i) q^{2} +(-40.0000 + 69.2820i) q^{4} +(-157.500 + 90.9327i) q^{5} -343.000 q^{7} +192.000 q^{8} +(1890.00 + 1091.19i) q^{10} +(739.500 - 1280.85i) q^{11} +484.974i q^{13} +(2058.00 + 3564.56i) q^{14} +(1408.00 + 2438.73i) q^{16} +(2614.50 + 1509.48i) q^{17} +(5953.50 - 3437.25i) q^{19} -14549.2i q^{20} -17748.0 q^{22} +(-2956.50 - 5120.81i) q^{23} +(8725.00 - 15112.1i) q^{25} +(5040.00 - 2909.85i) q^{26} +(13720.0 - 23763.7i) q^{28} -3978.00 q^{29} +(-11098.5 - 6407.72i) q^{31} +(23040.0 - 39906.5i) q^{32} -36227.6i q^{34} +(54022.5 - 31189.9i) q^{35} +(30788.5 + 53327.2i) q^{37} +(-71442.0 - 41247.1i) q^{38} +(-30240.0 + 17459.1i) q^{40} +110574. i q^{41} -17414.0 q^{43} +(59160.0 + 102468. i) q^{44} +(-35478.0 + 61449.7i) q^{46} +(26554.5 - 15331.2i) q^{47} +117649. q^{49} -209400. q^{50} +(-33600.0 - 19399.0i) q^{52} +(-30256.5 + 52405.8i) q^{53} +268979. i q^{55} -65856.0 q^{56} +(23868.0 + 41340.6i) q^{58} +(186826. + 107864. i) q^{59} +(140942. - 81372.6i) q^{61} +153785. i q^{62} -372736. q^{64} +(-44100.0 - 76383.4i) q^{65} +(134388. - 232768. i) q^{67} +(-209160. + 120759. i) q^{68} +(-648270. - 374279. i) q^{70} -101922. q^{71} +(275090. + 158823. i) q^{73} +(369462. - 639927. i) q^{74} +549961. i q^{76} +(-253648. + 439332. i) q^{77} +(-181116. - 313701. i) q^{79} +(-443520. - 256066. i) q^{80} +(1.14912e6 - 663445. i) q^{82} -216783. i q^{83} -549045. q^{85} +(104484. + 180972. i) q^{86} +(141984. - 245924. i) q^{88} +(1.15577e6 - 667282. i) q^{89} -166346. i q^{91} +473040. q^{92} +(-318654. - 183975. i) q^{94} +(-625118. + 1.08274e6i) q^{95} +1.51409e6i q^{97} +(-705894. - 1.22264e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 12 q^{2} - 80 q^{4} - 315 q^{5} - 686 q^{7} + 384 q^{8}+O(q^{10}) \) 2 * q - 12 * q^2 - 80 * q^4 - 315 * q^5 - 686 * q^7 + 384 * q^8	\( 2 q - 12 q^{2} - 80 q^{4} - 315 q^{5} - 686 q^{7} + 384 q^{8} + 3780 q^{10} + 1479 q^{11} + 4116 q^{14} + 2816 q^{16} + 5229 q^{17} + 11907 q^{19} - 35496 q^{22} - 5913 q^{23} + 17450 q^{25} + 10080 q^{26} + 27440 q^{28} - 7956 q^{29} - 22197 q^{31} + 46080 q^{32} + 108045 q^{35} + 61577 q^{37} - 142884 q^{38} - 60480 q^{40} - 34828 q^{43} + 118320 q^{44} - 70956 q^{46} + 53109 q^{47} + 235298 q^{49} - 418800 q^{50} - 67200 q^{52} - 60513 q^{53} - 131712 q^{56} + 47736 q^{58} + 373653 q^{59} + 281883 q^{61} - 745472 q^{64} - 88200 q^{65} + 268777 q^{67} - 418320 q^{68} - 1296540 q^{70} - 203844 q^{71} + 550179 q^{73} + 738924 q^{74} - 507297 q^{77} - 362231 q^{79} - 887040 q^{80} + 2298240 q^{82} - 1098090 q^{85} + 208968 q^{86} + 283968 q^{88} + 2311533 q^{89} + 946080 q^{92} - 637308 q^{94} - 1250235 q^{95} - 1411788 q^{98}+O(q^{100}) \) 2 * q - 12 * q^2 - 80 * q^4 - 315 * q^5 - 686 * q^7 + 384 * q^8 + 3780 * q^10 + 1479 * q^11 + 4116 * q^14 + 2816 * q^16 + 5229 * q^17 + 11907 * q^19 - 35496 * q^22 - 5913 * q^23 + 17450 * q^25 + 10080 * q^26 + 27440 * q^28 - 7956 * q^29 - 22197 * q^31 + 46080 * q^32 + 108045 * q^35 + 61577 * q^37 - 142884 * q^38 - 60480 * q^40 - 34828 * q^43 + 118320 * q^44 - 70956 * q^46 + 53109 * q^47 + 235298 * q^49 - 418800 * q^50 - 67200 * q^52 - 60513 * q^53 - 131712 * q^56 + 47736 * q^58 + 373653 * q^59 + 281883 * q^61 - 745472 * q^64 - 88200 * q^65 + 268777 * q^67 - 418320 * q^68 - 1296540 * q^70 - 203844 * q^71 + 550179 * q^73 + 738924 * q^74 - 507297 * q^77 - 362231 * q^79 - 887040 * q^80 + 2298240 * q^82 - 1098090 * q^85 + 208968 * q^86 + 283968 * q^88 + 2311533 * q^89 + 946080 * q^92 - 637308 * q^94 - 1250235 * q^95 - 1411788 * q^98

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