LMFDB - Embedded newform 315.4.j.b.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, 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:	$18.5856016518$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.4.j.b.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +(-7.50000 - 12.9904i) q^{10} +(-22.5000 - 38.9711i) q^{11} +59.0000 q^{13} +(10.5000 + 54.5596i) q^{14} +(35.5000 - 61.4878i) q^{16} +(-27.0000 - 46.7654i) q^{17} +(60.5000 - 104.789i) q^{19} -5.00000 q^{20} -135.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(88.5000 - 153.286i) q^{26} +(17.5000 + 6.06218i) q^{28} +162.000 q^{29} +(44.0000 + 76.2102i) q^{31} +(-22.5000 - 38.9711i) q^{32} -162.000 q^{34} +(17.5000 + 90.9327i) q^{35} +(129.500 - 224.301i) q^{37} +(-181.500 - 314.367i) q^{38} +(52.5000 - 90.9327i) q^{40} -195.000 q^{41} -286.000 q^{43} +(-22.5000 + 38.9711i) q^{44} +(-103.500 - 179.267i) q^{46} +(22.5000 - 38.9711i) q^{47} +(49.0000 - 339.482i) q^{49} -75.0000 q^{50} +(-29.5000 - 51.0955i) q^{52} +(298.500 + 517.017i) q^{53} -225.000 q^{55} +(-294.000 + 254.611i) q^{56} +(243.000 - 420.888i) q^{58} +(-180.000 - 311.769i) q^{59} +(-196.000 + 339.482i) q^{61} +264.000 q^{62} +433.000 q^{64} +(147.500 - 255.477i) q^{65} +(140.000 + 242.487i) q^{67} +(-27.0000 + 46.7654i) q^{68} +(262.500 + 90.9327i) q^{70} -48.0000 q^{71} +(-334.000 - 578.505i) q^{73} +(-388.500 - 672.902i) q^{74} -121.000 q^{76} +(787.500 + 272.798i) q^{77} +(-391.000 + 677.232i) q^{79} +(-177.500 - 307.439i) q^{80} +(-292.500 + 506.625i) q^{82} -768.000 q^{83} -270.000 q^{85} +(-429.000 + 743.050i) q^{86} +(-472.500 - 818.394i) q^{88} +(-597.000 + 1034.03i) q^{89} +(-826.000 + 715.337i) q^{91} -69.0000 q^{92} +(-67.5000 - 116.913i) q^{94} +(-302.500 - 523.945i) q^{95} +902.000 q^{97} +(-808.500 - 636.529i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - q^{4} + 5 q^{5} - 28 q^{7} + 42 q^{8}+O(q^{10}) $ 2 * q + 3 * q^2 - q^4 + 5 * q^5 - 28 * q^7 + 42 * q^8	$ 2 q + 3 q^{2} - q^{4} + 5 q^{5} - 28 q^{7} + 42 q^{8} - 15 q^{10} - 45 q^{11} + 118 q^{13} + 21 q^{14} + 71 q^{16} - 54 q^{17} + 121 q^{19} - 10 q^{20} - 270 q^{22} + 69 q^{23} - 25 q^{25} + 177 q^{26} + 35 q^{28} + 324 q^{29} + 88 q^{31} - 45 q^{32} - 324 q^{34} + 35 q^{35} + 259 q^{37} - 363 q^{38} + 105 q^{40} - 390 q^{41} - 572 q^{43} - 45 q^{44} - 207 q^{46} + 45 q^{47} + 98 q^{49} - 150 q^{50} - 59 q^{52} + 597 q^{53} - 450 q^{55} - 588 q^{56} + 486 q^{58} - 360 q^{59} - 392 q^{61} + 528 q^{62} + 866 q^{64} + 295 q^{65} + 280 q^{67} - 54 q^{68} + 525 q^{70} - 96 q^{71} - 668 q^{73} - 777 q^{74} - 242 q^{76} + 1575 q^{77} - 782 q^{79} - 355 q^{80} - 585 q^{82} - 1536 q^{83} - 540 q^{85} - 858 q^{86} - 945 q^{88} - 1194 q^{89} - 1652 q^{91} - 138 q^{92} - 135 q^{94} - 605 q^{95} + 1804 q^{97} - 1617 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 - q^4 + 5 * q^5 - 28 * q^7 + 42 * q^8 - 15 * q^10 - 45 * q^11 + 118 * q^13 + 21 * q^14 + 71 * q^16 - 54 * q^17 + 121 * q^19 - 10 * q^20 - 270 * q^22 + 69 * q^23 - 25 * q^25 + 177 * q^26 + 35 * q^28 + 324 * q^29 + 88 * q^31 - 45 * q^32 - 324 * q^34 + 35 * q^35 + 259 * q^37 - 363 * q^38 + 105 * q^40 - 390 * q^41 - 572 * q^43 - 45 * q^44 - 207 * q^46 + 45 * q^47 + 98 * q^49 - 150 * q^50 - 59 * q^52 + 597 * q^53 - 450 * q^55 - 588 * q^56 + 486 * q^58 - 360 * q^59 - 392 * q^61 + 528 * q^62 + 866 * q^64 + 295 * q^65 + 280 * q^67 - 54 * q^68 + 525 * q^70 - 96 * q^71 - 668 * q^73 - 777 * q^74 - 242 * q^76 + 1575 * q^77 - 782 * q^79 - 355 * q^80 - 585 * q^82 - 1536 * q^83 - 540 * q^85 - 858 * q^86 - 945 * q^88 - 1194 * q^89 - 1652 * q^91 - 138 * q^92 - 135 * q^94 - 605 * q^95 + 1804 * q^97 - 1617 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	−14.0000	+	12.1244i	−0.755929	+	0.654654i
$7$	−14.0000	+	12.1244i	−0.755929	+	0.654654i
$8$	21.0000			0.928078
$9$		0			0
$10$	−7.50000	−	12.9904i	−0.237171	−	0.410792i
$11$	−22.5000	−	38.9711i	−0.616728	−	1.06820i	−0.990079	−	0.140514i	$-0.955125\pi$
$11$	−22.5000	−	38.9711i	−0.616728	−	1.06820i	0.373351	−	0.927690i	$-0.378209\pi$
$12$		0			0
$13$	59.0000			1.25874			0.629371	−	0.777105i	$-0.283312\pi$
$13$	59.0000			1.25874			0.629371	+	0.777105i	$0.283312\pi$
$14$	10.5000	+	54.5596i	0.200446	+	1.04155i
$15$		0			0
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	−27.0000	−	46.7654i	−0.385204	−	0.667192i	0.606594	−	0.795012i	$-0.292535\pi$
$17$	−27.0000	−	46.7654i	−0.385204	−	0.667192i	−0.991797	+	0.127820i	$0.959202\pi$
$18$		0			0
$19$	60.5000	−	104.789i	0.730508	−	1.26528i	−0.226158	−	0.974091i	$-0.572617\pi$
$19$	60.5000	−	104.789i	0.730508	−	1.26528i	0.956666	−	0.291186i	$-0.0940500\pi$
$20$	−5.00000			−0.0559017
$21$		0			0
$22$	−135.000			−1.30828
$23$	34.5000	−	59.7558i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	34.5000	−	59.7558i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	88.5000	−	153.286i	0.667549	−	1.15623i
$27$		0			0
$28$	17.5000	+	6.06218i	0.118114	+	0.0409159i
$29$	162.000			1.03733			0.518666	−	0.854977i	$-0.326429\pi$
$29$	162.000			1.03733			0.518666	+	0.854977i	$0.326429\pi$
$30$		0			0
$31$	44.0000	+	76.2102i	0.254924	+	0.441541i	0.964875	−	0.262710i	$-0.0846163\pi$
$31$	44.0000	+	76.2102i	0.254924	+	0.441541i	−0.709951	+	0.704251i	$0.751283\pi$
$32$	−22.5000	−	38.9711i	−0.124296	−	0.215287i
$33$		0			0
$34$	−162.000			−0.817140
$35$	17.5000	+	90.9327i	0.0845154	+	0.439155i
$36$		0			0
$37$	129.500	−	224.301i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	129.500	−	224.301i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−181.500	−	314.367i	−0.774821	−	1.34203i
$39$		0			0
$40$	52.5000	−	90.9327i	0.207524	−	0.359443i
$41$	−195.000			−0.742778			−0.371389	−	0.928477i	$-0.621118\pi$
$41$	−195.000			−0.742778			−0.371389	+	0.928477i	$0.621118\pi$
$42$		0			0
$43$	−286.000			−1.01429			−0.507146	−	0.861860i	$-0.669300\pi$
$43$	−286.000			−1.01429			−0.507146	+	0.861860i	$0.669300\pi$
$44$	−22.5000	+	38.9711i	−0.0770910	+	0.133525i
$45$		0			0
$46$	−103.500	−	179.267i	−0.331744	−	0.574598i
$47$	22.5000	−	38.9711i	0.0698290	−	0.120947i	−0.828997	−	0.559253i	$-0.811088\pi$
$47$	22.5000	−	38.9711i	0.0698290	−	0.120947i	0.898826	+	0.438306i	$0.144421\pi$
$48$		0			0
$49$	49.0000	−	339.482i	0.142857	−	0.989743i
$50$	−75.0000			−0.212132
$51$		0			0
$52$	−29.5000	−	51.0955i	−0.0786714	−	0.136263i
$53$	298.500	+	517.017i	0.773625	+	1.33996i	0.935564	+	0.353157i	$0.114892\pi$
$53$	298.500	+	517.017i	0.773625	+	1.33996i	−0.161939	+	0.986801i	$0.551775\pi$
$54$		0			0
$55$	−225.000			−0.551618
$56$	−294.000	+	254.611i	−0.701561	+	0.607569i
$57$		0			0
$58$	243.000	−	420.888i	0.550129	−	0.952851i
$59$	−180.000	−	311.769i	−0.397187	−	0.687947i	0.596191	−	0.802843i	$-0.296680\pi$
$59$	−180.000	−	311.769i	−0.397187	−	0.687947i	−0.993378	+	0.114895i	$0.963347\pi$
$60$		0			0
$61$	−196.000	+	339.482i	−0.411397	+	0.712561i	−0.995043	−	0.0994477i	$-0.968292\pi$
$61$	−196.000	+	339.482i	−0.411397	+	0.712561i	0.583646	+	0.812009i	$0.301626\pi$
$62$	264.000			0.540775
$63$		0			0
$64$	433.000			0.845703
$65$	147.500	−	255.477i	0.281463	−	0.487509i
$66$		0			0
$67$	140.000	+	242.487i	0.255279	+	0.442157i	0.964971	−	0.262355i	$-0.0844992\pi$
$67$	140.000	+	242.487i	0.255279	+	0.442157i	−0.709692	+	0.704512i	$0.751166\pi$
$68$	−27.0000	+	46.7654i	−0.0481505	+	0.0833990i
$69$		0			0
$70$	262.500	+	90.9327i	0.448211	+	0.155265i
$71$	−48.0000			−0.0802331			−0.0401166	−	0.999195i	$-0.512773\pi$
$71$	−48.0000			−0.0802331			−0.0401166	+	0.999195i	$0.512773\pi$
$72$		0			0
$73$	−334.000	−	578.505i	−0.535503	−	0.927519i	−0.999139	−	0.0414929i	$-0.986789\pi$
$73$	−334.000	−	578.505i	−0.535503	−	0.927519i	0.463635	−	0.886026i	$-0.346545\pi$
$74$	−388.500	−	672.902i	−0.610300	−	1.05707i
$75$		0			0
$76$	−121.000			−0.182627
$77$	787.500	+	272.798i	1.16551	+	0.403743i
$78$		0			0
$79$	−391.000	+	677.232i	−0.556847	+	0.964488i	0.440910	+	0.897551i	$0.354656\pi$
$79$	−391.000	+	677.232i	−0.556847	+	0.964488i	−0.997757	+	0.0669365i	$0.978678\pi$
$80$	−177.500	−	307.439i	−0.248064	−	0.429659i
$81$		0			0
$82$	−292.500	+	506.625i	−0.393917	+	0.682285i
$83$	−768.000			−1.01565			−0.507825	−	0.861460i	$-0.669550\pi$
$83$	−768.000			−1.01565			−0.507825	+	0.861460i	$0.669550\pi$
$84$		0			0
$85$	−270.000			−0.344537
$86$	−429.000	+	743.050i	−0.537910	+	0.931687i
$87$		0			0
$88$	−472.500	−	818.394i	−0.572371	−	0.991376i
$89$	−597.000	+	1034.03i	−0.711032	+	1.23154i	0.253438	+	0.967352i	$0.418439\pi$
$89$	−597.000	+	1034.03i	−0.711032	+	1.23154i	−0.964470	+	0.264192i	$0.914895\pi$
$90$		0			0
$91$	−826.000	+	715.337i	−0.951520	+	0.824041i
$92$	−69.0000			−0.0781929
$93$		0			0
$94$	−67.5000	−	116.913i	−0.0740648	−	0.128284i
$95$	−302.500	−	523.945i	−0.326693	−	0.565849i
$96$		0			0
$97$	902.000			0.944167			0.472084	−	0.881554i	$-0.343502\pi$
$97$	902.000			0.944167			0.472084	+	0.881554i	$0.343502\pi$
$98$	−808.500	−	636.529i	−0.833376	−	0.656113i
$99$		0			0
$100$	−12.5000	+	21.6506i	−0.0125000	+	0.0216506i
$101$	342.000	+	592.361i	0.336933	+	0.583586i	0.983854	−	0.178971i	$-0.0572769\pi$
$101$	342.000	+	592.361i	0.336933	+	0.583586i	−0.646921	+	0.762557i	$0.723944\pi$
$102$		0			0
$103$	758.000	−	1312.89i	0.725126	−	1.25595i	−0.233796	−	0.972286i	$-0.575115\pi$
$103$	758.000	−	1312.89i	0.725126	−	1.25595i	0.958922	−	0.283669i	$-0.0915518\pi$
$104$	1239.00			1.16821
$105$		0			0
$106$	1791.00			1.64111
$107$	−366.000	+	633.931i	−0.330678	+	0.572751i	−0.982645	−	0.185496i	$-0.940611\pi$
$107$	−366.000	+	633.931i	−0.330678	+	0.572751i	0.651967	+	0.758247i	$0.273944\pi$
$108$		0			0
$109$	800.000	+	1385.64i	0.702992	+	1.21762i	0.967411	+	0.253210i	$0.0814863\pi$
$109$	800.000	+	1385.64i	0.702992	+	1.21762i	−0.264420	+	0.964408i	$0.585180\pi$
$110$	−337.500	+	584.567i	−0.292540	+	0.506694i
$111$		0			0
$112$	248.500	+	1291.24i	0.209652	+	1.08938i
$113$	1392.00			1.15883			0.579417	−	0.815031i	$-0.303280\pi$
$113$	1392.00			1.15883			0.579417	+	0.815031i	$0.303280\pi$
$114$		0			0
$115$	−172.500	−	298.779i	−0.139876	−	0.242272i
$116$	−81.0000	−	140.296i	−0.0648333	−	0.112295i
$117$		0			0
$118$	−1080.00			−0.842560
$119$	945.000	+	327.358i	0.727966	+	0.252175i
$120$		0			0
$121$	−347.000	+	601.022i	−0.260706	+	0.451556i
$122$	588.000	+	1018.45i	0.436353	+	0.755785i
$123$		0			0
$124$	44.0000	−	76.2102i	0.0318655	−	0.0551926i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	803.000			0.561061			0.280530	−	0.959845i	$-0.409490\pi$
$127$	803.000			0.561061			0.280530	+	0.959845i	$0.409490\pi$
$128$	829.500	−	1436.74i	0.572798	−	0.992115i
$129$		0			0
$130$	−442.500	−	766.432i	−0.298537	−	0.517081i
$131$	1009.50	−	1748.51i	0.673286	−	1.16617i	−0.303681	−	0.952774i	$-0.598216\pi$
$131$	1009.50	−	1748.51i	0.673286	−	1.16617i	0.976967	−	0.213391i	$-0.0684509\pi$
$132$		0			0
$133$	423.500	+	2200.57i	0.276106	+	1.43469i
$134$	840.000			0.541529
$135$		0			0
$136$	−567.000	−	982.073i	−0.357499	−	0.619206i
$137$	30.0000	+	51.9615i	0.0187086	+	0.0324042i	0.875228	−	0.483710i	$-0.160711\pi$
$137$	30.0000	+	51.9615i	0.0187086	+	0.0324042i	−0.856520	+	0.516115i	$0.827378\pi$
$138$		0			0
$139$	−1708.00			−1.04224			−0.521118	−	0.853485i	$-0.674485\pi$
$139$	−1708.00			−1.04224			−0.521118	+	0.853485i	$0.674485\pi$
$140$	70.0000	−	60.6218i	0.0422577	−	0.0365963i
$141$		0			0
$142$	−72.0000	+	124.708i	−0.0425500	+	0.0736988i
$143$	−1327.50	−	2299.30i	−0.776302	−	1.34459i
$144$		0			0
$145$	405.000	−	701.481i	0.231955	−	0.401757i
$146$	−2004.00			−1.13597
$147$		0			0
$148$	−259.000			−0.143849
$149$	−543.000	+	940.504i	−0.298552	+	0.517108i	−0.975805	−	0.218643i	$-0.929837\pi$
$149$	−543.000	+	940.504i	−0.298552	+	0.517108i	0.677253	+	0.735751i	$0.263170\pi$
$150$		0			0
$151$	1433.00	+	2482.03i	0.772291	+	1.33765i	0.936305	+	0.351189i	$0.114222\pi$
$151$	1433.00	+	2482.03i	0.772291	+	1.33765i	−0.164014	+	0.986458i	$0.552444\pi$
$152$	1270.50	−	2200.57i	0.677968	−	1.17428i
$153$		0			0
$154$	1890.00	−	1636.79i	0.988965	−	0.856468i
$155$	440.000			0.228011
$156$		0			0
$157$	114.500	+	198.320i	0.0582044	+	0.100813i	0.893659	−	0.448746i	$-0.148129\pi$
$157$	114.500	+	198.320i	0.0582044	+	0.100813i	−0.835455	+	0.549559i	$0.814796\pi$
$158$	1173.00	+	2031.70i	0.590626	+	1.02299i
$159$		0			0
$160$	−225.000			−0.111174
$161$	241.500	+	1254.87i	0.118217	+	0.614271i
$162$		0			0
$163$	614.000	−	1063.48i	0.295044	−	0.511031i	−0.679951	−	0.733258i	$-0.737999\pi$
$163$	614.000	−	1063.48i	0.295044	−	0.511031i	0.974995	+	0.222226i	$0.0713323\pi$
$164$	97.5000	+	168.875i	0.0464236	+	0.0804080i
$165$		0			0
$166$	−1152.00	+	1995.32i	−0.538630	+	0.932934i
$167$	1929.00			0.893835			0.446918	−	0.894575i	$-0.352522\pi$
$167$	1929.00			0.893835			0.446918	+	0.894575i	$0.352522\pi$
$168$		0			0
$169$	1284.00			0.584433
$170$	−405.000	+	701.481i	−0.182718	+	0.316477i
$171$		0			0
$172$	143.000	+	247.683i	0.0633933	+	0.109800i
$173$	−349.500	+	605.352i	−0.153595	+	0.266035i	−0.932547	−	0.361049i	$-0.882419\pi$
$173$	−349.500	+	605.352i	−0.153595	+	0.266035i	0.778951	+	0.627084i	$0.215752\pi$
$174$		0			0
$175$	437.500	+	151.554i	0.188982	+	0.0654654i
$176$	−3195.00			−1.36836
$177$		0			0
$178$	1791.00	+	3102.10i	0.754164	+	1.30625i
$179$	1558.50	+	2699.40i	0.650770	+	1.12717i	0.982936	+	0.183945i	$0.0588870\pi$
$179$	1558.50	+	2699.40i	0.650770	+	1.12717i	−0.332167	+	0.943221i	$0.607780\pi$
$180$		0			0
$181$	−1798.00			−0.738366			−0.369183	−	0.929357i	$-0.620362\pi$
$181$	−1798.00			−0.738366			−0.369183	+	0.929357i	$0.620362\pi$
$182$	619.500	+	3219.02i	0.252310	+	1.31104i
$183$		0			0
$184$	724.500	−	1254.87i	0.290276	−	0.502773i
$185$	−647.500	−	1121.50i	−0.257325	−	0.445700i
$186$		0			0
$187$	−1215.00	+	2104.44i	−0.475132	+	0.822952i
$188$	−45.0000			−0.0174572
$189$		0			0
$190$	−1815.00			−0.693021
$191$	−1194.00	+	2068.07i	−0.452329	+	0.783457i	−0.998530	−	0.0541974i	$-0.982740\pi$
$191$	−1194.00	+	2068.07i	−0.452329	+	0.783457i	0.546201	+	0.837654i	$0.316073\pi$
$192$		0			0
$193$	−136.000	−	235.559i	−0.0507228	−	0.0878544i	0.839549	−	0.543284i	$-0.182819\pi$
$193$	−136.000	−	235.559i	−0.0507228	−	0.0878544i	−0.890272	+	0.455429i	$0.849486\pi$
$194$	1353.00	−	2343.46i	0.500720	−	0.867273i
$195$		0			0
$196$	−318.500	+	127.306i	−0.116071	+	0.0463942i
$197$	2109.00			0.762741			0.381371	−	0.924422i	$-0.375452\pi$
$197$	2109.00			0.762741			0.381371	+	0.924422i	$0.375452\pi$
$198$		0			0
$199$	−712.000	−	1233.22i	−0.253630	−	0.439300i	0.710893	−	0.703301i	$-0.248291\pi$
$199$	−712.000	−	1233.22i	−0.253630	−	0.439300i	−0.964522	+	0.264001i	$0.914958\pi$
$200$	−262.500	−	454.663i	−0.0928078	−	0.160748i
$201$		0			0
$202$	2052.00			0.714744
$203$	−2268.00	+	1964.15i	−0.784150	+	0.679094i
$204$		0			0
$205$	−487.500	+	844.375i	−0.166090	+	0.287677i
$206$	−2274.00	−	3938.68i	−0.769112	−	1.33214i
$207$		0			0
$208$	2094.50	−	3627.78i	0.698209	−	1.20933i
$209$	−5445.00			−1.80210
$210$		0			0
$211$	−3625.00			−1.18273			−0.591363	−	0.806405i	$-0.701410\pi$
$211$	−3625.00			−1.18273			−0.591363	+	0.806405i	$0.701410\pi$
$212$	298.500	−	517.017i	0.0967031	−	0.167495i
$213$		0			0
$214$	1098.00	+	1901.79i	0.350737	+	0.607494i
$215$	−715.000	+	1238.42i	−0.226803	+	0.392834i
$216$		0			0
$217$	−1540.00	−	533.472i	−0.481760	−	0.166887i
$218$	4800.00			1.49127
$219$		0			0
$220$	112.500	+	194.856i	0.0344761	+	0.0597144i
$221$	−1593.00	−	2759.16i	−0.484872	−	0.839823i
$222$		0			0
$223$	−4960.00			−1.48944			−0.744722	−	0.667374i	$-0.767418\pi$
$223$	−4960.00			−1.48944			−0.744722	+	0.667374i	$0.767418\pi$
$224$	787.500	+	272.798i	0.234898	+	0.0813709i
$225$		0			0
$226$	2088.00	−	3616.52i	0.614565	−	1.06446i
$227$	−750.000	−	1299.04i	−0.219292	−	0.379825i	0.735300	−	0.677742i	$-0.237041\pi$
$227$	−750.000	−	1299.04i	−0.219292	−	0.379825i	−0.954592	+	0.297917i	$0.903708\pi$
$228$		0			0
$229$	−3046.00	+	5275.83i	−0.878975	+	1.52243i	−0.0265085	+	0.999649i	$0.508439\pi$
$229$	−3046.00	+	5275.83i	−0.878975	+	1.52243i	−0.852467	+	0.522781i	$0.824894\pi$
$230$	−1035.00			−0.296721
$231$		0			0
$232$	3402.00			0.962725
$233$	69.0000	−	119.512i	0.0194006	−	0.0336028i	−0.856162	−	0.516707i	$-0.827158\pi$
$233$	69.0000	−	119.512i	0.0194006	−	0.0336028i	0.875563	+	0.483104i	$0.160491\pi$
$234$		0			0
$235$	−112.500	−	194.856i	−0.0312285	−	0.0540893i
$236$	−180.000	+	311.769i	−0.0496483	+	0.0859934i
$237$		0			0
$238$	2268.00	−	1964.15i	0.617700	−	0.534944i
$239$	5502.00			1.48910			0.744550	−	0.667567i	$-0.232664\pi$
$239$	5502.00			1.48910			0.744550	+	0.667567i	$0.232664\pi$
$240$		0			0
$241$	−1775.50	−	3075.26i	−0.474564	−	0.821970i	0.525011	−	0.851095i	$-0.324061\pi$
$241$	−1775.50	−	3075.26i	−0.474564	−	0.821970i	−0.999576	+	0.0291256i	$0.990728\pi$
$242$	1041.00	+	1803.06i	0.276521	+	0.478948i
$243$		0			0
$244$	392.000			0.102849
$245$	−1347.50	−	1060.88i	−0.351382	−	0.276642i
$246$		0			0
$247$	3569.50	−	6182.56i	0.919522	−	1.59266i
$248$	924.000	+	1600.41i	0.236589	+	0.409784i
$249$		0			0
$250$	−187.500	+	324.760i	−0.0474342	+	0.0821584i
$251$	−7065.00			−1.77665			−0.888324	−	0.459216i	$-0.848130\pi$
$251$	−7065.00			−1.77665			−0.888324	+	0.459216i	$0.848130\pi$
$252$		0			0
$253$	−3105.00			−0.771580
$254$	1204.50	−	2086.26i	0.297547	−	0.515367i
$255$		0			0
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	−2040.00	+	3533.38i	−0.495143	+	0.857613i	−0.999984	−	0.00559954i	$-0.998218\pi$
$257$	−2040.00	+	3533.38i	−0.495143	+	0.857613i	0.504842	+	0.863212i	$0.331551\pi$
$258$		0			0
$259$	906.500	+	4710.31i	0.217479	+	1.13006i
$260$	−295.000			−0.0703659
$261$		0			0
$262$	−3028.50	−	5245.52i	−0.714127	−	1.23690i
$263$	−1644.00	−	2847.49i	−0.385450	−	0.667619i	0.606381	−	0.795174i	$-0.292620\pi$
$263$	−1644.00	−	2847.49i	−0.385450	−	0.667619i	−0.991832	+	0.127555i	$0.959287\pi$
$264$		0			0
$265$	2985.00			0.691951
$266$	6352.50	+	2200.57i	1.46427	+	0.507239i
$267$		0			0
$268$	140.000	−	242.487i	0.0319099	−	0.0552696i
$269$	−1632.00	−	2826.71i	−0.369906	−	0.640697i	0.619644	−	0.784883i	$-0.287277\pi$
$269$	−1632.00	−	2826.71i	−0.369906	−	0.640697i	−0.989551	+	0.144186i	$0.953944\pi$
$270$		0			0
$271$	1376.00	−	2383.30i	0.308436	−	0.534226i	−0.669585	−	0.742736i	$-0.733528\pi$
$271$	1376.00	−	2383.30i	0.308436	−	0.534226i	0.978020	+	0.208510i	$0.0668612\pi$
$272$	−3834.00			−0.854671
$273$		0			0
$274$	180.000			0.0396869
$275$	−562.500	+	974.279i	−0.123346	+	0.213641i
$276$		0			0
$277$	2345.00	+	4061.66i	0.508655	+	0.881016i	0.999950	+	0.0100228i	$0.00319040\pi$
$277$	2345.00	+	4061.66i	0.508655	+	0.881016i	−0.491295	+	0.870993i	$0.663476\pi$
$278$	−2562.00	+	4437.51i	−0.552729	+	0.957354i
$279$		0			0
$280$	367.500	+	1909.59i	0.0784369	+	0.407570i
$281$	−7821.00			−1.66036			−0.830181	−	0.557494i	$-0.811763\pi$
$281$	−7821.00			−1.66036			−0.830181	+	0.557494i	$0.811763\pi$
$282$		0			0
$283$	329.000	+	569.845i	0.0691061	+	0.119695i	0.898508	−	0.438957i	$-0.144652\pi$
$283$	329.000	+	569.845i	0.0691061	+	0.119695i	−0.829402	+	0.558652i	$0.811319\pi$
$284$	24.0000	+	41.5692i	0.00501457	+	0.00868549i
$285$		0			0
$286$	−7965.00			−1.64678
$287$	2730.00	−	2364.25i	0.561487	−	0.486262i
$288$		0			0
$289$	998.500	−	1729.45i	0.203236	−	0.352016i
$290$	−1215.00	−	2104.44i	−0.246025	−	0.426128i
$291$		0			0
$292$	−334.000	+	578.505i	−0.0669379	+	0.115940i
$293$	5997.00			1.19573			0.597864	−	0.801597i	$-0.296016\pi$
$293$	5997.00			1.19573			0.597864	+	0.801597i	$0.296016\pi$
$294$		0			0
$295$	−1800.00			−0.355254
$296$	2719.50	−	4710.31i	0.534013	−	0.924937i
$297$		0			0
$298$	1629.00	+	2821.51i	0.316663	+	0.548476i
$299$	2035.50	−	3525.59i	0.393699	−	0.681907i
$300$		0			0
$301$	4004.00	−	3467.57i	0.766733	−	0.664011i
$302$	8598.00			1.63828
$303$		0			0
$304$	−4295.50	−	7440.02i	−0.810407	−	1.40367i
$305$	980.000	+	1697.41i	0.183982	+	0.318667i
$306$		0			0
$307$	−6226.00			−1.15745			−0.578724	−	0.815523i	$-0.696449\pi$
$307$	−6226.00			−1.15745			−0.578724	+	0.815523i	$0.696449\pi$
$308$	−157.500	−	818.394i	−0.0291376	−	0.151404i
$309$		0			0
$310$	660.000	−	1143.15i	0.120921	−	0.209441i
$311$	2340.00	+	4053.00i	0.426653	+	0.738985i	0.996573	−	0.0827149i	$-0.0263591\pi$
$311$	2340.00	+	4053.00i	0.426653	+	0.738985i	−0.569920	+	0.821700i	$0.693026\pi$
$312$		0			0
$313$	−514.000	+	890.274i	−0.0928211	+	0.160771i	−0.908697	−	0.417456i	$-0.862922\pi$
$313$	−514.000	+	890.274i	−0.0928211	+	0.160771i	0.815876	+	0.578227i	$0.196255\pi$
$314$	687.000			0.123470
$315$		0			0
$316$	782.000			0.139212
$317$	4311.00	−	7466.87i	0.763817	−	1.32297i	−0.177053	−	0.984201i	$-0.556656\pi$
$317$	4311.00	−	7466.87i	0.763817	−	1.32297i	0.940870	−	0.338768i	$-0.110010\pi$
$318$		0			0
$319$	−3645.00	−	6313.33i	−0.639752	−	1.10808i
$320$	1082.50	−	1874.94i	0.189105	−	0.327539i
$321$		0			0
$322$	3622.50	+	1254.87i	0.626938	+	0.217178i
$323$	−6534.00			−1.12558
$324$		0			0
$325$	−737.500	−	1277.39i	−0.125874	−	0.218021i
$326$	−1842.00	−	3190.44i	−0.312942	−	0.542031i
$327$		0			0
$328$	−4095.00			−0.689355
$329$	157.500	+	818.394i	0.0263929	+	0.137141i
$330$		0			0
$331$	999.500	−	1731.18i	0.165974	−	0.287476i	−0.771027	−	0.636803i	$-0.780256\pi$
$331$	999.500	−	1731.18i	0.165974	−	0.287476i	0.937001	+	0.349327i	$0.113590\pi$
$332$	384.000	+	665.108i	0.0634781	+	0.109947i
$333$		0			0
$334$	2893.50	−	5011.69i	0.474028	−	0.821040i
$335$	1400.00			0.228329
$336$		0			0
$337$	5114.00			0.826639			0.413319	−	0.910586i	$-0.364369\pi$
$337$	5114.00			0.826639			0.413319	+	0.910586i	$0.364369\pi$
$338$	1926.00	−	3335.93i	0.309943	−	0.536836i
$339$		0			0
$340$	135.000	+	233.827i	0.0215335	+	0.0372972i
$341$	1980.00	−	3429.46i	0.314437	−	0.544621i
$342$		0			0
$343$	3430.00	+	5346.84i	0.539949	+	0.841698i
$344$	−6006.00			−0.941342
$345$		0			0
$346$	1048.50	+	1816.06i	0.162912	+	0.282173i
$347$	2160.00	+	3741.23i	0.334164	+	0.578789i	0.983324	−	0.181863i	$-0.0582128\pi$
$347$	2160.00	+	3741.23i	0.334164	+	0.578789i	−0.649160	+	0.760652i	$0.724879\pi$
$348$		0			0
$349$	7922.00			1.21506			0.607529	−	0.794298i	$-0.292161\pi$
$349$	7922.00			1.21506			0.607529	+	0.794298i	$0.292161\pi$
$350$	1050.00	−	909.327i	0.160357	−	0.138873i
$351$		0			0
$352$	−1012.50	+	1753.70i	−0.153314	+	0.265547i
$353$	414.000	+	717.069i	0.0624221	+	0.108118i	0.895548	−	0.444966i	$-0.146784\pi$
$353$	414.000	+	717.069i	0.0624221	+	0.108118i	−0.833125	+	0.553084i	$0.813451\pi$
$354$		0			0
$355$	−120.000	+	207.846i	−0.0179407	+	0.0310742i
$356$	1194.00			0.177758
$357$		0			0
$358$	9351.00			1.38049
$359$	−675.000	+	1169.13i	−0.0992344	+	0.171879i	−0.911368	−	0.411593i	$-0.864973\pi$
$359$	−675.000	+	1169.13i	−0.0992344	+	0.171879i	0.812134	+	0.583472i	$0.198306\pi$
$360$		0			0
$361$	−3891.00	−	6739.41i	−0.567284	−	0.982564i
$362$	−2697.00	+	4671.34i	−0.391578	+	0.678233i
$363$		0			0
$364$	1032.50	+	357.668i	0.148675	+	0.0515025i
$365$	−3340.00			−0.478969
$366$		0			0
$367$	−1400.50	−	2425.74i	−0.199198	−	0.345020i	0.749071	−	0.662490i	$-0.230500\pi$
$367$	−1400.50	−	2425.74i	−0.199198	−	0.345020i	−0.948268	+	0.317470i	$0.897167\pi$
$368$	−2449.50	−	4242.66i	−0.346981	−	0.600989i
$369$		0			0
$370$	−3885.00			−0.545869
$371$	−10447.5	−	3619.12i	−1.46201	−	0.506456i
$372$		0			0
$373$	−3301.00	+	5717.50i	−0.458229	+	0.793675i	−0.998867	−	0.0475795i	$-0.984849\pi$
$373$	−3301.00	+	5717.50i	−0.458229	+	0.793675i	0.540639	+	0.841255i	$0.318183\pi$
$374$	3645.00	+	6313.33i	0.503953	+	0.872872i
$375$		0			0
$376$	472.500	−	818.394i	0.0648067	−	0.112249i
$377$	9558.00			1.30573
$378$		0			0
$379$	−8305.00			−1.12559			−0.562796	−	0.826596i	$-0.690274\pi$
$379$	−8305.00			−1.12559			−0.562796	+	0.826596i	$0.690274\pi$
$380$	−302.500	+	523.945i	−0.0408366	+	0.0707311i
$381$		0			0
$382$	3582.00	+	6204.21i	0.479767	+	0.830981i
$383$	472.500	−	818.394i	0.0630382	−	0.109185i	−0.832784	−	0.553598i	$-0.813254\pi$
$383$	472.500	−	818.394i	0.0630382	−	0.109185i	0.895822	+	0.444413i	$0.146588\pi$
$384$		0			0
$385$	3150.00	−	2727.98i	0.416984	−	0.361119i
$386$	−816.000			−0.107599
$387$		0			0
$388$	−451.000	−	781.155i	−0.0590105	−	0.102209i
$389$	6018.00	+	10423.5i	0.784382	+	1.35859i	0.929367	+	0.369156i	$0.120353\pi$
$389$	6018.00	+	10423.5i	0.784382	+	1.35859i	−0.144985	+	0.989434i	$0.546313\pi$
$390$		0			0
$391$	−3726.00			−0.481923
$392$	1029.00	−	7129.12i	0.132583	−	0.918559i
$393$		0			0
$394$	3163.50	−	5479.34i	0.404505	−	0.700623i
$395$	1955.00	+	3386.16i	0.249030	+	0.431332i
$396$		0			0
$397$	1349.00	−	2336.54i	0.170540	−	0.295384i	−0.768069	−	0.640367i	$-0.778782\pi$
$397$	1349.00	−	2336.54i	0.170540	−	0.295384i	0.938609	+	0.344983i	$0.112115\pi$
$398$	−4272.00			−0.538030
$399$		0			0
$400$	−1775.00			−0.221875
$401$	3526.50	−	6108.08i	0.439165	−	0.760655i	−0.558461	−	0.829531i	$-0.688608\pi$
$401$	3526.50	−	6108.08i	0.439165	−	0.760655i	0.997625	+	0.0688756i	$0.0219412\pi$
$402$		0			0
$403$	2596.00	+	4496.40i	0.320883	+	0.555786i
$404$	342.000	−	592.361i	0.0421167	−	0.0729482i
$405$		0			0
$406$	1701.00	+	8838.66i	0.207929	+	1.08043i
$407$	−11655.0			−1.41945
$408$		0			0
$409$	5435.00	+	9413.70i	0.657074	+	1.13809i	0.981369	+	0.192130i	$0.0615396\pi$
$409$	5435.00	+	9413.70i	0.657074	+	1.13809i	−0.324295	+	0.945956i	$0.605127\pi$
$410$	1462.50	+	2533.12i	0.176165	+	0.305127i
$411$		0			0
$412$	−1516.00			−0.181281
$413$	6300.00	+	2182.38i	0.750612	+	0.260020i
$414$		0			0
$415$	−1920.00	+	3325.54i	−0.227106	+	0.393360i
$416$	−1327.50	−	2299.30i	−0.156457	−	0.270991i
$417$		0			0
$418$	−8167.50	+	14146.5i	−0.955707	+	1.65533i
$419$	9729.00			1.13435			0.567175	−	0.823597i	$-0.308036\pi$
$419$	9729.00			1.13435			0.567175	+	0.823597i	$0.308036\pi$
$420$		0			0
$421$	−12550.0			−1.45285			−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0			−1.45285			−0.726425	+	0.687246i	$0.758819\pi$
$422$	−5437.50	+	9418.03i	−0.627235	+	1.08640i
$423$		0			0
$424$	6268.50	+	10857.4i	0.717984	+	1.24358i
$425$	−675.000	+	1169.13i	−0.0770407	+	0.133438i
$426$		0			0
$427$	−1372.00	−	7129.12i	−0.155494	−	0.807968i
$428$	732.000			0.0826695
$429$		0			0
$430$	2145.00	+	3715.25i	0.240561	+	0.416663i
$431$	1494.00	+	2587.68i	0.166969	+	0.289198i	0.937353	−	0.348382i	$-0.113269\pi$
$431$	1494.00	+	2587.68i	0.166969	+	0.289198i	−0.770384	+	0.637580i	$0.779935\pi$
$432$		0			0
$433$	16616.0			1.84414			0.922072	−	0.387019i	$-0.126495\pi$
$433$	16616.0			1.84414			0.922072	+	0.387019i	$0.126495\pi$
$434$	−3696.00	+	3200.83i	−0.408787	+	0.354020i
$435$		0			0
$436$	800.000	−	1385.64i	0.0878740	−	0.152202i
$437$	−4174.50	−	7230.45i	−0.456964	−	0.791485i
$438$		0			0
$439$	−3673.00	+	6361.82i	−0.399323	+	0.691647i	−0.993642	−	0.112581i	$-0.964088\pi$
$439$	−3673.00	+	6361.82i	−0.399323	+	0.691647i	0.594320	+	0.804229i	$0.297421\pi$
$440$	−4725.00			−0.511944
$441$		0			0
$442$	−9558.00			−1.02857
$443$	6.00000	−	10.3923i	0.000643496	−	0.00111457i	−0.865703	−	0.500557i	$-0.833129\pi$
$443$	6.00000	−	10.3923i	0.000643496	−	0.00111457i	0.866347	+	0.499443i	$0.166462\pi$
$444$		0			0
$445$	2985.00	+	5170.17i	0.317983	+	0.550763i
$446$	−7440.00	+	12886.5i	−0.789897	+	1.36814i
$447$		0			0
$448$	−6062.00	+	5249.85i	−0.639291	+	0.553643i
$449$	−9669.00			−1.01628			−0.508138	−	0.861275i	$-0.669666\pi$
$449$	−9669.00			−1.01628			−0.508138	+	0.861275i	$0.669666\pi$
$450$		0			0
$451$	4387.50	+	7599.37i	0.458092	+	0.793438i
$452$	−696.000	−	1205.51i	−0.0724272	−	0.125448i
$453$		0			0
$454$	−4500.00			−0.465188
$455$	1032.50	+	5365.03i	0.106383	+	0.552783i
$456$		0			0
$457$	4817.00	−	8343.29i	0.493063	−	0.854010i	−0.506905	−	0.862002i	$-0.669211\pi$
$457$	4817.00	−	8343.29i	0.493063	−	0.854010i	0.999968	+	0.00799181i	$0.00254390\pi$
$458$	9138.00	+	15827.5i	0.932294	+	1.61478i
$459$		0			0
$460$	−172.500	+	298.779i	−0.0174845	+	0.0302840i
$461$	342.000			0.0345521			0.0172761	−	0.999851i	$-0.494501\pi$
$461$	342.000			0.0345521			0.0172761	+	0.999851i	$0.494501\pi$
$462$		0			0
$463$	2411.00			0.242006			0.121003	−	0.992652i	$-0.461389\pi$
$463$	2411.00			0.242006			0.121003	+	0.992652i	$0.461389\pi$
$464$	5751.00	−	9961.02i	0.575395	−	0.996614i
$465$		0			0
$466$	−207.000	−	358.535i	−0.0205774	−	0.0356412i
$467$	−603.000	+	1044.43i	−0.0597506	+	0.103491i	−0.894353	−	0.447361i	$-0.852364\pi$
$467$	−603.000	+	1044.43i	−0.0597506	+	0.103491i	0.834603	+	0.550852i	$0.185697\pi$
$468$		0			0
$469$	−4900.00	−	1697.41i	−0.482433	−	0.167120i
$470$	−675.000			−0.0662456
$471$		0			0
$472$	−3780.00	−	6547.15i	−0.368620	−	0.638468i
$473$	6435.00	+	11145.7i	0.625543	+	1.08347i
$474$		0			0
$475$	−3025.00			−0.292203
$476$	−189.000	−	982.073i	−0.0181992	−	0.0945656i
$477$		0			0
$478$	8253.00	−	14294.6i	0.789714	−	1.36783i
$479$	−216.000	−	374.123i	−0.0206039	−	0.0356871i	0.855540	−	0.517737i	$-0.173226\pi$
$479$	−216.000	−	374.123i	−0.0206039	−	0.0356871i	−0.876144	+	0.482050i	$0.839892\pi$
$480$		0			0
$481$	7640.50	−	13233.7i	0.724276	−	1.25448i
$482$	−10653.0			−1.00670
$483$		0			0
$484$	694.000			0.0651766
$485$	2255.00	−	3905.77i	0.211122	−	0.365674i
$486$		0			0
$487$	5948.00	+	10302.2i	0.553449	+	0.958602i	0.998022	+	0.0628592i	$0.0200219\pi$
$487$	5948.00	+	10302.2i	0.553449	+	0.958602i	−0.444574	+	0.895742i	$0.646645\pi$
$488$	−4116.00	+	7129.12i	−0.381809	+	0.661312i
$489$		0			0
$490$	−4777.50	+	1909.59i	−0.440460	+	0.176054i
$491$	12276.0			1.12833			0.564163	−	0.825663i	$-0.309199\pi$
$491$	12276.0			1.12833			0.564163	+	0.825663i	$0.309199\pi$
$492$		0			0
$493$	−4374.00	−	7575.99i	−0.399584	−	0.692100i
$494$	−10708.5	−	18547.7i	−0.975300	−	1.68927i
$495$		0			0
$496$	6248.00			0.565612
$497$	672.000	−	581.969i	0.0606505	−	0.0525249i
$498$		0			0
$499$	5438.00	−	9418.89i	0.487852	−	0.844985i	−0.512050	−	0.858956i	$-0.671114\pi$
$499$	5438.00	−	9418.89i	0.487852	−	0.844985i	0.999902	+	0.0139706i	$0.00444712\pi$
$500$	62.5000	+	108.253i	0.00559017	+	0.00968246i
$501$		0			0
$502$	−10597.5	+	18355.4i	−0.942210	+	1.63196i
$503$	−12000.0			−1.06372			−0.531862	−	0.846831i	$-0.678508\pi$
$503$	−12000.0			−1.06372			−0.531862	+	0.846831i	$0.678508\pi$
$504$		0			0
$505$	3420.00			0.301362
$506$	−4657.50	+	8067.03i	−0.409192	+	0.708741i
$507$		0			0
$508$	−401.500	−	695.418i	−0.0350663	−	0.0607366i
$509$	−5841.00	+	10116.9i	−0.508640	+	0.880990i	0.491310	+	0.870985i	$0.336518\pi$
$509$	−5841.00	+	10116.9i	−0.508640	+	0.880990i	−0.999950	+	0.0100055i	$0.996815\pi$
$510$		0			0
$511$	11690.0	+	4049.53i	1.01201	+	0.350569i
$512$	8733.00			0.753804
$513$		0			0
$514$	6120.00	+	10600.2i	0.525178	+	0.909635i
$515$	−3790.00	−	6564.47i	−0.324286	−	0.561680i
$516$		0			0
$517$	−2025.00			−0.172262
$518$	13597.5	+	4710.31i	1.15336	+	0.399535i
$519$		0			0
$520$	3097.50	−	5365.03i	0.261220	−	0.452446i
$521$	4804.50	+	8321.64i	0.404010	+	0.699765i	0.994206	−	0.107495i	$-0.0342829\pi$
$521$	4804.50	+	8321.64i	0.404010	+	0.699765i	−0.590196	+	0.807260i	$0.700950\pi$
$522$		0			0
$523$	−10594.0	+	18349.3i	−0.885742	+	1.53415i	−0.0408820	+	0.999164i	$0.513017\pi$
$523$	−10594.0	+	18349.3i	−0.885742	+	1.53415i	−0.844860	+	0.534987i	$0.820317\pi$
$524$	−2019.00			−0.168321
$525$		0			0
$526$	−9864.00			−0.817663
$527$	2376.00	−	4115.35i	0.196395	−	0.340166i
$528$		0			0
$529$	3703.00	+	6413.78i	0.304348	+	0.527146i
$530$	4477.50	−	7755.26i	0.366963	−	0.635598i
$531$		0			0
$532$	1694.00	−	1467.05i	0.138053	−	0.119557i
$533$	−11505.0			−0.934966
$534$		0			0
$535$	1830.00	+	3169.65i	0.147884	+	0.256142i
$536$	2940.00	+	5092.23i	0.236919	+	0.410356i
$537$		0			0
$538$	−9792.00			−0.784690
$539$	−14332.5	+	5728.76i	−1.14535	+	0.457802i
$540$		0			0
$541$	−4036.00	+	6990.56i	−0.320742	+	0.555541i	−0.980641	−	0.195813i	$-0.937265\pi$
$541$	−4036.00	+	6990.56i	−0.320742	+	0.555541i	0.659900	+	0.751354i	$0.270599\pi$
$542$	−4128.00	−	7149.91i	−0.327145	−	0.566632i
$543$		0			0
$544$	−1215.00	+	2104.44i	−0.0957586	+	0.165859i
$545$	8000.00			0.628775
$546$		0			0
$547$	344.000			0.0268892			0.0134446	−	0.999910i	$-0.495720\pi$
$547$	344.000			0.0268892			0.0134446	+	0.999910i	$0.495720\pi$
$548$	30.0000	−	51.9615i	0.00233857	−	0.00405052i
$549$		0			0
$550$	1687.50	+	2922.84i	0.130828	+	0.226600i
$551$	9801.00	−	16975.8i	0.757780	−	1.31251i
$552$		0			0
$553$	−2737.00	−	14221.9i	−0.210468	−	1.09363i
$554$	14070.0			1.07902
$555$		0			0
$556$	854.000	+	1479.17i	0.0651397	+	0.112825i
$557$	9181.50	+	15902.8i	0.698443	+	1.20974i	0.969006	+	0.247036i	$0.0794567\pi$
$557$	9181.50	+	15902.8i	0.698443	+	1.20974i	−0.270563	+	0.962702i	$0.587210\pi$
$558$		0			0
$559$	−16874.0			−1.27673
$560$	6212.50	+	2152.07i	0.468797	+	0.162396i
$561$		0			0
$562$	−11731.5	+	20319.6i	−0.880540	+	1.52514i
$563$	−3147.00	−	5450.76i	−0.235578	−	0.408033i	0.723863	−	0.689944i	$-0.242365\pi$
$563$	−3147.00	−	5450.76i	−0.235578	−	0.408033i	−0.959440	+	0.281912i	$0.909032\pi$
$564$		0			0
$565$	3480.00	−	6027.54i	0.259123	−	0.448815i
$566$	1974.00			0.146596
$567$		0			0
$568$	−1008.00			−0.0744626
$569$	5866.50	−	10161.1i	0.432226	−	0.748637i	−0.564839	−	0.825201i	$-0.691062\pi$
$569$	5866.50	−	10161.1i	0.432226	−	0.748637i	0.997065	+	0.0765642i	$0.0243950\pi$
$570$		0			0
$571$	−526.000	−	911.059i	−0.0385506	−	0.0667717i	0.846106	−	0.533014i	$-0.178941\pi$
$571$	−526.000	−	911.059i	−0.0385506	−	0.0667717i	−0.884657	+	0.466242i	$0.845607\pi$
$572$	−1327.50	+	2299.30i	−0.0970377	+	0.168074i
$573$		0			0
$574$	−2047.50	−	10639.1i	−0.148887	−	0.773638i
$575$	−1725.00			−0.125109
$576$		0			0
$577$	6578.00	+	11393.4i	0.474603	+	0.822036i	0.999577	−	0.0290821i	$-0.00925844\pi$
$577$	6578.00	+	11393.4i	0.474603	+	0.822036i	−0.524974	+	0.851118i	$0.675925\pi$
$578$	−2995.50	−	5188.36i	−0.215565	−	0.373369i
$579$		0			0
$580$	−810.000			−0.0579887
$581$	10752.0	−	9311.51i	0.767759	−	0.664899i
$582$		0			0
$583$	13432.5	−	23265.8i	0.954232	−	1.65278i
$584$	−7014.00	−	12148.6i	−0.496989	−	0.860810i
$585$		0			0
$586$	8995.50	−	15580.7i	0.634131	−	1.09835i
$587$	13368.0			0.939960			0.469980	−	0.882677i	$-0.344261\pi$
$587$	13368.0			0.939960			0.469980	+	0.882677i	$0.344261\pi$
$588$		0			0
$589$	10648.0			0.744895
$590$	−2700.00	+	4676.54i	−0.188402	+	0.326322i
$591$		0			0
$592$	−9194.50	−	15925.3i	−0.638330	−	1.10562i
$593$	13332.0	−	23091.7i	0.923237	−	1.59909i	0.128865	−	0.991662i	$-0.458867\pi$
$593$	13332.0	−	23091.7i	0.923237	−	1.59909i	0.794372	−	0.607431i	$-0.207800\pi$
$594$		0			0
$595$	3780.00	−	3273.58i	0.260445	−	0.225552i
$596$	1086.00			0.0746381
$597$		0			0
$598$	−6106.50	−	10576.8i	−0.417581	−	0.723271i
$599$	3807.00	+	6593.92i	0.259682	+	0.449783i	0.966157	−	0.257955i	$-0.0830488\pi$
$599$	3807.00	+	6593.92i	0.259682	+	0.449783i	−0.706474	+	0.707739i	$0.749715\pi$
$600$		0			0
$601$	6410.00			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$601$	6410.00			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$602$	−3003.00	−	15604.0i	−0.203311	−	1.05643i
$603$		0			0
$604$	1433.00	−	2482.03i	0.0965363	−	0.167206i
$605$	1735.00	+	3005.11i	0.116591	+	0.201942i
$606$		0			0
$607$	10734.5	−	18592.7i	0.717792	−	1.24325i	−0.244080	−	0.969755i	$-0.578486\pi$
$607$	10734.5	−	18592.7i	0.717792	−	1.24325i	0.961873	−	0.273498i	$-0.0881806\pi$
$608$	−5445.00			−0.363197
$609$		0			0
$610$	5880.00			0.390286
$611$	1327.50	−	2299.30i	0.0878967	−	0.152242i
$612$		0			0
$613$	−1868.50	−	3236.34i	−0.123113	−	0.213237i	0.797881	−	0.602815i	$-0.205954\pi$
$613$	−1868.50	−	3236.34i	−0.123113	−	0.213237i	−0.920994	+	0.389578i	$0.872621\pi$
$614$	−9339.00	+	16175.6i	−0.613830	+	1.06318i
$615$		0			0
$616$	16537.5	+	5728.76i	1.08168	+	0.374705i
$617$	−18078.0			−1.17957			−0.589784	−	0.807561i	$-0.700787\pi$
$617$	−18078.0			−1.17957			−0.589784	+	0.807561i	$0.700787\pi$
$618$		0			0
$619$	−6143.50	−	10640.9i	−0.398915	−	0.690940i	0.594678	−	0.803964i	$-0.297280\pi$
$619$	−6143.50	−	10640.9i	−0.398915	−	0.690940i	−0.993592	+	0.113024i	$0.963946\pi$
$620$	−220.000	−	381.051i	−0.0142507	−	0.0246829i
$621$		0			0
$622$	14040.0			0.905069
$623$	−4179.00	−	21714.7i	−0.268745	−	1.39644i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	1542.00	+	2670.82i	0.0984516	+	0.170523i
$627$		0			0
$628$	114.500	−	198.320i	0.00727555	−	0.0126016i
$629$	−13986.0			−0.886579
$630$		0			0
$631$	−9580.00			−0.604396			−0.302198	−	0.953245i	$-0.597720\pi$
$631$	−9580.00			−0.604396			−0.302198	+	0.953245i	$0.597720\pi$
$632$	−8211.00	+	14221.9i	−0.516798	+	0.895120i
$633$		0			0
$634$	−12933.0	−	22400.6i	−0.810150	−	1.40322i
$635$	2007.50	−	3477.09i	0.125457	−	0.217298i
$636$		0			0
$637$	2891.00	−	20029.4i	0.179820	−	1.24583i
$638$	−21870.0			−1.35712
$639$		0			0
$640$	−4147.50	−	7183.68i	−0.256163	−	0.443687i
$641$	5389.50	+	9334.89i	0.332094	+	0.575204i	0.982922	−	0.184021i	$-0.0589114\pi$
$641$	5389.50	+	9334.89i	0.332094	+	0.575204i	−0.650828	+	0.759225i	$0.725578\pi$
$642$		0			0
$643$	8882.00			0.544746			0.272373	−	0.962192i	$-0.412191\pi$
$643$	8882.00			0.544746			0.272373	+	0.962192i	$0.412191\pi$
$644$	966.000	−	836.581i	0.0591083	−	0.0511893i
$645$		0			0
$646$	−9801.00	+	16975.8i	−0.596928	+	1.03391i
$647$	−5509.50	−	9542.73i	−0.334777	−	0.579851i	0.648665	−	0.761074i	$-0.275328\pi$
$647$	−5509.50	−	9542.73i	−0.334777	−	0.579851i	−0.983442	+	0.181223i	$0.941994\pi$
$648$		0			0
$649$	−8100.00	+	14029.6i	−0.489912	+	0.848552i
$650$	−4425.00			−0.267020
$651$		0			0
$652$	−1228.00			−0.0737610
$653$	11161.5	−	19332.3i	0.668887	−	1.15855i	−0.309329	−	0.950955i	$-0.600104\pi$
$653$	11161.5	−	19332.3i	0.668887	−	1.15855i	0.978216	−	0.207591i	$-0.0665624\pi$
$654$		0			0
$655$	−5047.50	−	8742.53i	−0.301103	−	0.521525i
$656$	−6922.50	+	11990.1i	−0.412009	+	0.713621i
$657$		0			0
$658$	2362.50	+	818.394i	0.139969	+	0.0484868i
$659$	11856.0			0.700826			0.350413	−	0.936595i	$-0.386041\pi$
$659$	11856.0			0.700826			0.350413	+	0.936595i	$0.386041\pi$
$660$		0			0
$661$	16622.0	+	28790.1i	0.978095	+	1.69411i	0.669318	+	0.742976i	$0.266586\pi$
$661$	16622.0	+	28790.1i	0.978095	+	1.69411i	0.308777	+	0.951134i	$0.400080\pi$
$662$	−2998.50	−	5193.55i	−0.176042	−	0.304914i
$663$		0			0
$664$	−16128.0			−0.942602
$665$	10587.5	+	3667.62i	0.617392	+	0.213871i
$666$		0			0
$667$	5589.00	−	9680.43i	0.324448	−	0.561961i
$668$	−964.500	−	1670.56i	−0.0558647	−	0.0967605i
$669$		0			0
$670$	2100.00	−	3637.31i	0.121090	−	0.209733i
$671$	17640.0			1.01488
$672$		0			0
$673$	−12322.0			−0.705763			−0.352881	−	0.935668i	$-0.614798\pi$
$673$	−12322.0			−0.705763			−0.352881	+	0.935668i	$0.614798\pi$
$674$	7671.00	−	13286.6i	0.438392	−	0.759316i
$675$		0			0
$676$	−642.000	−	1111.98i	−0.0365271	−	0.0632668i
$677$	−6298.50	+	10909.3i	−0.357564	+	0.619320i	−0.987553	−	0.157285i	$-0.949726\pi$
$677$	−6298.50	+	10909.3i	−0.357564	+	0.619320i	0.629989	+	0.776604i	$0.283059\pi$
$678$		0			0
$679$	−12628.0	+	10936.2i	−0.713723	+	0.618103i
$680$	−5670.00			−0.319757
$681$		0			0
$682$	−5940.00	−	10288.4i	−0.333511	−	0.577658i
$683$	−4170.00	−	7222.65i	−0.233617	−	0.404637i	0.725253	−	0.688483i	$-0.241723\pi$
$683$	−4170.00	−	7222.65i	−0.233617	−	0.404637i	−0.958870	+	0.283846i	$0.908390\pi$
$684$		0			0
$685$	300.000			0.0167334
$686$	19036.5	−	891.140i	1.05950	−	0.0495975i
$687$		0			0
$688$	−10153.0	+	17585.5i	−0.562616	+	0.974479i
$689$	17611.5	+	30504.0i	0.973795	+	1.68666i
$690$		0			0
$691$	10100.0	−	17493.7i	0.556038	−	0.963086i	−0.441784	−	0.897121i	$-0.645654\pi$
$691$	10100.0	−	17493.7i	0.556038	−	0.963086i	0.997822	−	0.0659643i	$-0.0210124\pi$
$692$	699.000			0.0383988
$693$		0			0
$694$	12960.0			0.708869
$695$	−4270.00	+	7395.86i	−0.233051	+	0.403656i
$696$		0			0
$697$	5265.00	+	9119.25i	0.286121	+	0.495576i
$698$	11883.0	−	20582.0i	0.644381	−	1.11610i
$699$		0			0
$700$	−87.5000	−	454.663i	−0.00472456	−	0.0245495i
$701$	−474.000			−0.0255388			−0.0127694	−	0.999918i	$-0.504065\pi$
$701$	−474.000			−0.0255388			−0.0127694	+	0.999918i	$0.504065\pi$
$702$		0			0
$703$	−15669.5	−	27140.4i	−0.840663	−	1.45607i
$704$	−9742.50	−	16874.5i	−0.521569	−	0.903383i
$705$		0			0
$706$	2484.00			0.132417
$707$	−11970.0	−	4146.53i	−0.636744	−	0.220575i
$708$		0			0
$709$	12563.0	−	21759.8i	0.665463	−	1.15262i	−0.313696	−	0.949523i	$-0.601567\pi$
$709$	12563.0	−	21759.8i	0.665463	−	1.15262i	0.979160	−	0.203093i	$-0.0650993\pi$
$710$	360.000	+	623.538i	0.0190290	+	0.0329591i
$711$		0			0
$712$	−12537.0	+	21714.7i	−0.659893	+	1.14297i
$713$	6072.00			0.318932
$714$		0			0
$715$	−13275.0			−0.694345
$716$	1558.50	−	2699.40i	0.0813462	−	0.140896i
$717$		0			0
$718$	2025.00	+	3507.40i	0.105254	+	0.182305i
$719$	−3648.00	+	6318.52i	−0.189218	+	0.327734i	−0.944990	−	0.327100i	$-0.893928\pi$
$719$	−3648.00	+	6318.52i	−0.189218	+	0.327734i	0.755772	+	0.654835i	$0.227262\pi$
$720$		0			0
$721$	5306.00	+	27570.8i	0.274072	+	1.42412i
$722$	−23346.0			−1.20339
$723$		0			0
$724$	899.000	+	1557.11i	0.0461479	+	0.0799305i
$725$	−2025.00	−	3507.40i	−0.103733	−	0.179671i
$726$		0			0
$727$	−15421.0			−0.786703			−0.393352	−	0.919388i	$-0.628684\pi$
$727$	−15421.0			−0.786703			−0.393352	+	0.919388i	$0.628684\pi$
$728$	−17346.0	+	15022.1i	−0.883085	+	0.764774i
$729$		0			0
$730$	−5010.00	+	8677.57i	−0.254012	+	0.439961i
$731$	7722.00	+	13374.9i	0.390709	+	0.676728i
$732$		0			0
$733$	14583.5	−	25259.4i	0.734862	−	1.27282i	−0.219922	−	0.975517i	$-0.570580\pi$
$733$	14583.5	−	25259.4i	0.734862	−	1.27282i	0.954784	−	0.297301i	$-0.0960864\pi$
$734$	−8403.00			−0.422562
$735$		0			0
$736$	−3105.00			−0.155505
$737$	6300.00	−	10911.9i	0.314876	−	0.545381i
$738$		0			0
$739$	6690.50	+	11588.3i	0.333037	+	0.576836i	0.983106	−	0.183039i	$-0.0585934\pi$
$739$	6690.50	+	11588.3i	0.333037	+	0.576836i	−0.650069	+	0.759875i	$0.725260\pi$
$740$	−647.500	+	1121.50i	−0.0321656	+	0.0557125i
$741$		0			0
$742$	−25074.0	+	21714.7i	−1.24056	+	1.07436i
$743$	−5487.00			−0.270927			−0.135463	−	0.990782i	$-0.543252\pi$
$743$	−5487.00			−0.270927			−0.135463	+	0.990782i	$0.543252\pi$
$744$		0			0
$745$	2715.00	+	4702.52i	0.133517	+	0.231258i
$746$	9903.00	+	17152.5i	0.486025	+	0.841820i
$747$		0			0
$748$	2430.00			0.118783
$749$	−2562.00	−	13312.5i	−0.124985	−	0.649439i
$750$		0			0
$751$	−3319.00	+	5748.68i	−0.161268	+	0.279324i	−0.935324	−	0.353793i	$-0.884892\pi$
$751$	−3319.00	+	5748.68i	−0.161268	+	0.279324i	0.774056	+	0.633117i	$0.218225\pi$
$752$	−1597.50	−	2766.95i	−0.0774665	−	0.134176i
$753$		0			0
$754$	14337.0	−	24832.4i	0.692470	−	1.19939i
$755$	14330.0			0.690758
$756$		0			0
$757$	14846.0			0.712797			0.356398	−	0.934334i	$-0.384005\pi$
$757$	14846.0			0.712797			0.356398	+	0.934334i	$0.384005\pi$
$758$	−12457.5	+	21577.0i	−0.596935	+	1.03392i
$759$		0			0
$760$	−6352.50	−	11002.9i	−0.303197	−	0.525152i
$761$	−1825.50	+	3161.86i	−0.0869571	+	0.150614i	−0.906223	−	0.422799i	$-0.861048\pi$
$761$	−1825.50	+	3161.86i	−0.0869571	+	0.150614i	0.819266	+	0.573413i	$0.194381\pi$
$762$		0			0
$763$	−28000.0	−	9699.48i	−1.32853	−	0.460216i
$764$	2388.00			0.113082
$765$		0			0
$766$	−1417.50	−	2455.18i	−0.0668621	−	0.115809i
$767$	−10620.0	−	18394.4i	−0.499956	−	0.865949i
$768$		0			0
$769$	29855.0			1.40000			0.699999	−	0.714144i	$-0.253184\pi$
$769$	29855.0			1.40000			0.699999	+	0.714144i	$0.253184\pi$
$770$	−2362.50	−	12275.9i	−0.110570	−	0.574536i
$771$		0			0
$772$	−136.000	+	235.559i	−0.00634035	+	0.0109818i
$773$	−3259.50	−	5645.62i	−0.151664	−	0.262689i	0.780175	−	0.625561i	$-0.215130\pi$
$773$	−3259.50	−	5645.62i	−0.151664	−	0.262689i	−0.931839	+	0.362871i	$0.881796\pi$
$774$		0			0
$775$	1100.00	−	1905.26i	0.0509847	−	0.0883081i
$776$	18942.0			0.876261
$777$		0			0
$778$	36108.0			1.66393

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +(-7.50000 - 12.9904i) q^{10} +(-22.5000 - 38.9711i) q^{11} +59.0000 q^{13} +(10.5000 + 54.5596i) q^{14} +(35.5000 - 61.4878i) q^{16} +(-27.0000 - 46.7654i) q^{17} +(60.5000 - 104.789i) q^{19} -5.00000 q^{20} -135.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(88.5000 - 153.286i) q^{26} +(17.5000 + 6.06218i) q^{28} +162.000 q^{29} +(44.0000 + 76.2102i) q^{31} +(-22.5000 - 38.9711i) q^{32} -162.000 q^{34} +(17.5000 + 90.9327i) q^{35} +(129.500 - 224.301i) q^{37} +(-181.500 - 314.367i) q^{38} +(52.5000 - 90.9327i) q^{40} -195.000 q^{41} -286.000 q^{43} +(-22.5000 + 38.9711i) q^{44} +(-103.500 - 179.267i) q^{46} +(22.5000 - 38.9711i) q^{47} +(49.0000 - 339.482i) q^{49} -75.0000 q^{50} +(-29.5000 - 51.0955i) q^{52} +(298.500 + 517.017i) q^{53} -225.000 q^{55} +(-294.000 + 254.611i) q^{56} +(243.000 - 420.888i) q^{58} +(-180.000 - 311.769i) q^{59} +(-196.000 + 339.482i) q^{61} +264.000 q^{62} +433.000 q^{64} +(147.500 - 255.477i) q^{65} +(140.000 + 242.487i) q^{67} +(-27.0000 + 46.7654i) q^{68} +(262.500 + 90.9327i) q^{70} -48.0000 q^{71} +(-334.000 - 578.505i) q^{73} +(-388.500 - 672.902i) q^{74} -121.000 q^{76} +(787.500 + 272.798i) q^{77} +(-391.000 + 677.232i) q^{79} +(-177.500 - 307.439i) q^{80} +(-292.500 + 506.625i) q^{82} -768.000 q^{83} -270.000 q^{85} +(-429.000 + 743.050i) q^{86} +(-472.500 - 818.394i) q^{88} +(-597.000 + 1034.03i) q^{89} +(-826.000 + 715.337i) q^{91} -69.0000 q^{92} +(-67.5000 - 116.913i) q^{94} +(-302.500 - 523.945i) q^{95} +902.000 q^{97} +(-808.500 - 636.529i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - q^{4} + 5 q^{5} - 28 q^{7} + 42 q^{8}+O(q^{10}) \) 2 * q + 3 * q^2 - q^4 + 5 * q^5 - 28 * q^7 + 42 * q^8	\( 2 q + 3 q^{2} - q^{4} + 5 q^{5} - 28 q^{7} + 42 q^{8} - 15 q^{10} - 45 q^{11} + 118 q^{13} + 21 q^{14} + 71 q^{16} - 54 q^{17} + 121 q^{19} - 10 q^{20} - 270 q^{22} + 69 q^{23} - 25 q^{25} + 177 q^{26} + 35 q^{28} + 324 q^{29} + 88 q^{31} - 45 q^{32} - 324 q^{34} + 35 q^{35} + 259 q^{37} - 363 q^{38} + 105 q^{40} - 390 q^{41} - 572 q^{43} - 45 q^{44} - 207 q^{46} + 45 q^{47} + 98 q^{49} - 150 q^{50} - 59 q^{52} + 597 q^{53} - 450 q^{55} - 588 q^{56} + 486 q^{58} - 360 q^{59} - 392 q^{61} + 528 q^{62} + 866 q^{64} + 295 q^{65} + 280 q^{67} - 54 q^{68} + 525 q^{70} - 96 q^{71} - 668 q^{73} - 777 q^{74} - 242 q^{76} + 1575 q^{77} - 782 q^{79} - 355 q^{80} - 585 q^{82} - 1536 q^{83} - 540 q^{85} - 858 q^{86} - 945 q^{88} - 1194 q^{89} - 1652 q^{91} - 138 q^{92} - 135 q^{94} - 605 q^{95} + 1804 q^{97} - 1617 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - q^4 + 5 * q^5 - 28 * q^7 + 42 * q^8 - 15 * q^10 - 45 * q^11 + 118 * q^13 + 21 * q^14 + 71 * q^16 - 54 * q^17 + 121 * q^19 - 10 * q^20 - 270 * q^22 + 69 * q^23 - 25 * q^25 + 177 * q^26 + 35 * q^28 + 324 * q^29 + 88 * q^31 - 45 * q^32 - 324 * q^34 + 35 * q^35 + 259 * q^37 - 363 * q^38 + 105 * q^40 - 390 * q^41 - 572 * q^43 - 45 * q^44 - 207 * q^46 + 45 * q^47 + 98 * q^49 - 150 * q^50 - 59 * q^52 + 597 * q^53 - 450 * q^55 - 588 * q^56 + 486 * q^58 - 360 * q^59 - 392 * q^61 + 528 * q^62 + 866 * q^64 + 295 * q^65 + 280 * q^67 - 54 * q^68 + 525 * q^70 - 96 * q^71 - 668 * q^73 - 777 * q^74 - 242 * q^76 + 1575 * q^77 - 782 * q^79 - 355 * q^80 - 585 * q^82 - 1536 * q^83 - 540 * q^85 - 858 * q^86 - 945 * q^88 - 1194 * q^89 - 1652 * q^91 - 138 * q^92 - 135 * q^94 - 605 * q^95 + 1804 * q^97 - 1617 * q^98

Introduction

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