LMFDB - Embedded newform 40.4.d.a.21.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,4,Mod(21,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.21"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.2
Root			$-1.86176 + 0.730647i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.4.d.a.21.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59241 + 1.13111i) q^{2} +6.25785i q^{3} +(5.44116 - 5.86462i) q^{4} +5.00000i q^{5} +(-7.07834 - 16.2229i) q^{6} -34.6280 q^{7} +(-7.47214 + 21.3581i) q^{8} -12.1606 q^{9} +(-5.65557 - 12.9620i) q^{10} +7.91595i q^{11} +(36.6999 + 34.0499i) q^{12} +11.0346i q^{13} +(89.7698 - 39.1682i) q^{14} -31.2892 q^{15} +(-4.78760 - 63.8207i) q^{16} +57.6152 q^{17} +(31.5253 - 13.7551i) q^{18} +141.133i q^{19} +(29.3231 + 27.2058i) q^{20} -216.696i q^{21} +(-8.95385 - 20.5214i) q^{22} +129.328 q^{23} +(-133.655 - 46.7595i) q^{24} -25.0000 q^{25} +(-12.4814 - 28.6062i) q^{26} +92.8625i q^{27} +(-188.416 + 203.080i) q^{28} +89.1664i q^{29} +(81.1144 - 35.3917i) q^{30} -78.3307 q^{31} +(84.5999 + 160.034i) q^{32} -49.5368 q^{33} +(-149.362 + 65.1694i) q^{34} -173.140i q^{35} +(-66.1679 + 71.3175i) q^{36} -249.332i q^{37} +(-159.637 - 365.874i) q^{38} -69.0530 q^{39} +(-106.790 - 37.3607i) q^{40} +91.8705 q^{41} +(245.109 + 561.766i) q^{42} -194.184i q^{43} +(46.4240 + 43.0719i) q^{44} -60.8031i q^{45} +(-335.270 + 146.285i) q^{46} -72.6149 q^{47} +(399.380 - 29.9600i) q^{48} +856.096 q^{49} +(64.8102 - 28.2779i) q^{50} +360.547i q^{51} +(64.7139 + 60.0411i) q^{52} +456.782i q^{53} +(-105.038 - 240.737i) q^{54} -39.5797 q^{55} +(258.745 - 739.586i) q^{56} -883.187 q^{57} +(-100.857 - 231.156i) q^{58} -341.098i q^{59} +(-170.250 + 183.500i) q^{60} +217.067i q^{61} +(203.065 - 88.6011i) q^{62} +421.098 q^{63} +(-400.334 - 319.181i) q^{64} -55.1731 q^{65} +(128.420 - 56.0318i) q^{66} -529.237i q^{67} +(313.494 - 337.892i) q^{68} +809.314i q^{69} +(195.841 + 448.849i) q^{70} +381.540 q^{71} +(90.8659 - 259.728i) q^{72} -876.902 q^{73} +(282.023 + 646.370i) q^{74} -156.446i q^{75} +(827.690 + 767.926i) q^{76} -274.113i q^{77} +(179.013 - 78.1069i) q^{78} -203.950 q^{79} +(319.103 - 23.9380i) q^{80} -909.456 q^{81} +(-238.166 + 103.916i) q^{82} +996.654i q^{83} +(-1270.84 - 1179.08i) q^{84} +288.076i q^{85} +(219.644 + 503.403i) q^{86} -557.989 q^{87} +(-169.069 - 59.1491i) q^{88} +172.456 q^{89} +(68.7753 + 157.627i) q^{90} -382.107i q^{91} +(703.693 - 758.459i) q^{92} -490.182i q^{93} +(188.247 - 82.1358i) q^{94} -705.664 q^{95} +(-1001.47 + 529.413i) q^{96} +1058.49 q^{97} +(-2219.35 + 968.343i) q^{98} -96.2629i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.59241	+	1.13111i	−0.916555	+	0.399910i
$2$	−2.59241	+	1.13111i	−0.916555	+	0.399910i
$3$			6.25785i			1.20432i	0.798374	+	0.602161i	$0.205694\pi$
$3$			6.25785i			1.20432i	−0.798374	+	0.602161i	$0.794306\pi$
$4$	5.44116	−	5.86462i	0.680145	−	0.733078i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	−7.07834	−	16.2229i	−0.481620	−	1.10383i
$7$	−34.6280			−1.86973			−0.934867	−	0.354998i	$-0.884482\pi$
$7$	−34.6280			−1.86973			−0.934867	+	0.354998i	$0.884482\pi$
$8$	−7.47214	+	21.3581i	−0.330225	+	0.943902i
$9$	−12.1606			−0.450394
$10$	−5.65557	−	12.9620i	−0.178845	−	0.409896i
$11$			7.91595i			0.216977i	0.994098	+	0.108489i	$0.0346011\pi$
$11$			7.91595i			0.216977i	−0.994098	+	0.108489i	$0.965399\pi$
$12$	36.6999	+	34.0499i	0.882862	+	0.819114i
$13$			11.0346i			0.235420i	0.993048	+	0.117710i	$0.0375553\pi$
$13$			11.0346i			0.235420i	−0.993048	+	0.117710i	$0.962445\pi$
$14$	89.7698	−	39.1682i	1.71371	−	0.747725i
$15$	−31.2892			−0.538590
$16$	−4.78760	−	63.8207i	−0.0748062	−	0.997198i
$17$	57.6152			0.821985			0.410992	−	0.911639i	$-0.365182\pi$
$17$	57.6152			0.821985			0.410992	+	0.911639i	$0.365182\pi$
$18$	31.5253	−	13.7551i	0.412810	−	0.180117i
$19$			141.133i			1.70411i	0.523453	+	0.852055i	$0.324644\pi$
$19$			141.133i			1.70411i	−0.523453	+	0.852055i	$0.675356\pi$
$20$	29.3231	+	27.2058i	0.327842	+	0.304170i
$21$		−	216.696i		−	2.25176i
$22$	−8.95385	−	20.5214i	−0.0867712	−	0.198871i
$23$	129.328			1.17247			0.586233	−	0.810143i	$-0.300610\pi$
$23$	129.328			1.17247			0.586233	+	0.810143i	$0.300610\pi$
$24$	−133.655	−	46.7595i	−1.13676	−	0.397698i
$25$	−25.0000			−0.200000
$26$	−12.4814	−	28.6062i	−0.0941465	−	0.215775i
$27$			92.8625i			0.661903i
$28$	−188.416	+	203.080i	−1.27169	+	1.37066i
$29$			89.1664i			0.570958i	0.958385	+	0.285479i	$0.0921527\pi$
$29$			89.1664i			0.570958i	−0.958385	+	0.285479i	$0.907847\pi$
$30$	81.1144	−	35.3917i	0.493647	−	0.215387i
$31$	−78.3307			−0.453826			−0.226913	−	0.973915i	$-0.572863\pi$
$31$	−78.3307			−0.453826			−0.226913	+	0.973915i	$0.572863\pi$
$32$	84.5999	+	160.034i	0.467353	+	0.884071i
$33$	−49.5368			−0.261310
$34$	−149.362	+	65.1694i	−0.753394	+	0.328720i
$35$		−	173.140i		−	0.836171i
$36$	−66.1679	+	71.3175i	−0.306333	+	0.330174i
$37$		−	249.332i		−	1.10783i	−0.832572	−	0.553917i	$-0.813132\pi$
$37$		−	249.332i		−	1.10783i	0.832572	−	0.553917i	$-0.186868\pi$
$38$	−159.637	−	365.874i	−0.681489	−	1.56191i
$39$	−69.0530			−0.283521
$40$	−106.790	−	37.3607i	−0.422126	−	0.147681i
$41$	91.8705			0.349946			0.174973	−	0.984573i	$-0.444016\pi$
$41$	91.8705			0.349946			0.174973	+	0.984573i	$0.444016\pi$
$42$	245.109	+	561.766i	0.900502	+	2.06386i
$43$		−	194.184i		−	0.688668i	−0.938847	−	0.344334i	$-0.888105\pi$
$43$		−	194.184i		−	0.688668i	0.938847	−	0.344334i	$-0.111895\pi$
$44$	46.4240	+	43.0719i	0.159061	+	0.147576i
$45$		−	60.8031i		−	0.201422i
$46$	−335.270	+	146.285i	−1.07463	+	0.468880i
$47$	−72.6149			−0.225361			−0.112680	−	0.993631i	$-0.535944\pi$
$47$	−72.6149			−0.225361			−0.112680	+	0.993631i	$0.535944\pi$
$48$	399.380	−	29.9600i	1.20095	−	0.0900908i
$49$	856.096			2.49591
$50$	64.8102	−	28.2779i	0.183311	−	0.0799819i
$51$			360.547i			0.989935i
$52$	64.7139	+	60.0411i	0.172581	+	0.160119i
$53$			456.782i			1.18385i	0.805995	+	0.591923i	$0.201631\pi$
$53$			456.782i			1.18385i	−0.805995	+	0.591923i	$0.798369\pi$
$54$	−105.038	−	240.737i	−0.264701	−	0.606671i
$55$	−39.5797			−0.0970351
$56$	258.745	−	739.586i	0.617433	−	1.76485i
$57$	−883.187			−2.05230
$58$	−100.857	−	231.156i	−0.228331	−	0.523314i
$59$		−	341.098i		−	0.752664i	−0.926485	−	0.376332i	$-0.877185\pi$
$59$		−	341.098i		−	0.752664i	0.926485	−	0.376332i	$-0.122815\pi$
$60$	−170.250	+	183.500i	−0.366319	+	0.394828i
$61$			217.067i			0.455616i	0.973706	+	0.227808i	$0.0731559\pi$
$61$			217.067i			0.455616i	−0.973706	+	0.227808i	$0.926844\pi$
$62$	203.065	−	88.6011i	0.415957	−	0.181489i
$63$	421.098			0.842117
$64$	−400.334	−	319.181i	−0.781903	−	0.623400i
$65$	−55.1731			−0.105283
$66$	128.420	−	56.0318i	0.239505	−	0.104501i
$67$		−	529.237i		−	0.965024i	−0.875889	−	0.482512i	$-0.839724\pi$
$67$		−	529.237i		−	0.965024i	0.875889	−	0.482512i	$-0.160276\pi$
$68$	313.494	−	337.892i	0.559069	−	0.602579i
$69$			809.314i			1.41203i
$70$	195.841	+	448.849i	0.334393	+	0.766396i
$71$	381.540			0.637754			0.318877	−	0.947796i	$-0.396694\pi$
$71$	381.540			0.637754			0.318877	+	0.947796i	$0.396694\pi$
$72$	90.8659	−	259.728i	0.148731	−	0.425128i
$73$	−876.902			−1.40594			−0.702970	−	0.711220i	$-0.748143\pi$
$73$	−876.902			−1.40594			−0.702970	+	0.711220i	$0.748143\pi$
$74$	282.023	+	646.370i	0.443034	+	1.01539i
$75$		−	156.446i		−	0.240865i
$76$	827.690	+	767.926i	1.24924	+	1.15904i
$77$		−	274.113i		−	0.405690i
$78$	179.013	−	78.1069i	0.259863	−	0.113383i
$79$	−203.950			−0.290458			−0.145229	−	0.989398i	$-0.546392\pi$
$79$	−203.950			−0.290458			−0.145229	+	0.989398i	$0.546392\pi$
$80$	319.103	−	23.9380i	0.445961	−	0.0334543i
$81$	−909.456			−1.24754
$82$	−238.166	+	103.916i	−0.320744	+	0.139947i
$83$			996.654i			1.31804i	0.752127	+	0.659018i	$0.229028\pi$
$83$			996.654i			1.31804i	−0.752127	+	0.659018i	$0.770972\pi$
$84$	−1270.84	−	1179.08i	−1.65072	−	1.53153i
$85$			288.076i			0.367603i
$86$	219.644	+	503.403i	0.275405	+	0.631202i
$87$	−557.989			−0.687618
$88$	−169.069	−	59.1491i	−0.204805	−	0.0716513i
$89$	172.456			0.205396			0.102698	−	0.994713i	$-0.467252\pi$
$89$	172.456			0.205396			0.102698	+	0.994713i	$0.467252\pi$
$90$	68.7753	+	157.627i	0.0805506	+	0.184614i
$91$		−	382.107i		−	0.440172i
$92$	703.693	−	758.459i	0.797447	−	0.859509i
$93$		−	490.182i		−	0.546553i
$94$	188.247	−	82.1358i	0.206556	−	0.0901240i
$95$	−705.664			−0.762101
$96$	−1001.47	+	529.413i	−1.06471	+	0.562844i
$97$	1058.49			1.10797			0.553984	−	0.832527i	$-0.313107\pi$
$97$	1058.49			1.10797			0.553984	+	0.832527i	$0.313107\pi$
$98$	−2219.35	+	968.343i	−2.28763	+	0.998137i
$99$		−	96.2629i		−	0.0977251i
$100$	−136.029	+	146.616i	−0.136029	+	0.146616i
$101$			689.992i			0.679770i	0.940467	+	0.339885i	$0.110388\pi$
$101$			689.992i			0.679770i	−0.940467	+	0.339885i	$0.889612\pi$
$102$	−407.820	−	934.685i	−0.395885	−	0.907330i
$103$	1289.96			1.23402			0.617009	−	0.786956i	$-0.288344\pi$
$103$	1289.96			1.23402			0.617009	+	0.786956i	$0.288344\pi$
$104$	−235.678	−	82.4523i	−0.222213	−	0.0777414i
$105$	1083.48			1.00702
$106$	−516.673	−	1184.16i	−0.473431	−	1.08506i
$107$		−	1843.74i		−	1.66580i	−0.553420	−	0.832902i	$-0.686678\pi$
$107$		−	1843.74i		−	1.66580i	0.553420	−	0.832902i	$-0.313322\pi$
$108$	544.603	+	505.279i	0.485227	+	0.450190i
$109$		−	340.598i		−	0.299297i	−0.988739	−	0.149648i	$-0.952186\pi$
$109$		−	340.598i		−	0.299297i	0.988739	−	0.149648i	$-0.0478142\pi$
$110$	102.607	−	44.7692i	0.0889380	−	0.0388053i
$111$	1560.28			1.33419
$112$	165.785	+	2209.98i	0.139868	+	1.86450i
$113$	157.831			0.131393			0.0656967	−	0.997840i	$-0.479073\pi$
$113$	157.831			0.131393			0.0656967	+	0.997840i	$0.479073\pi$
$114$	2289.58	−	998.986i	1.88104	−	0.820733i
$115$			646.639i			0.524343i
$116$	522.927	+	485.168i	0.418557	+	0.388334i
$117$		−	134.188i		−	0.106031i
$118$	385.821	+	884.265i	0.300997	+	0.689858i
$119$	−1995.10			−1.53689
$120$	233.797	−	668.277i	0.177856	−	0.508376i
$121$	1268.34			0.952921
$122$	−245.528	−	562.727i	−0.182205	−	0.417597i
$123$			574.912i			0.421447i
$124$	−426.210	+	459.380i	−0.308668	+	0.332690i
$125$		−	125.000i		−	0.0894427i
$126$	−1091.66	+	476.310i	−0.771846	+	0.336770i
$127$	494.704			0.345652			0.172826	−	0.984952i	$-0.444710\pi$
$127$	494.704			0.345652			0.172826	+	0.984952i	$0.444710\pi$
$128$	1398.86	+	374.623i	0.965960	+	0.258690i
$129$	1215.17			0.829379
$130$	143.031	−	62.4071i	0.0964975	−	0.0421036i
$131$			488.783i			0.325993i	0.986627	+	0.162997i	$0.0521160\pi$
$131$			488.783i			0.325993i	−0.986627	+	0.162997i	$0.947884\pi$
$132$	−269.537	+	290.514i	−0.177729	+	0.191561i
$133$		−	4887.14i		−	3.18623i
$134$	598.628	+	1372.00i	0.385922	+	0.884498i
$135$	−464.312			−0.296012
$136$	−430.509	+	1230.55i	−0.271440	+	0.775873i
$137$	−1532.13			−0.955464			−0.477732	−	0.878506i	$-0.658541\pi$
$137$	−1532.13			−0.955464			−0.477732	+	0.878506i	$0.658541\pi$
$138$	−915.427	−	2098.07i	−0.564683	−	1.29420i
$139$		−	755.095i		−	0.460765i	−0.973100	−	0.230382i	$-0.926002\pi$
$139$		−	755.095i		−	0.460765i	0.973100	−	0.230382i	$-0.0739977\pi$
$140$	−1015.40	−	942.081i	−0.612978	−	0.568717i
$141$		−	454.413i		−	0.271407i
$142$	−989.108	+	431.566i	−0.584536	+	0.255044i
$143$	−87.3495			−0.0510807
$144$	58.2202	+	776.100i	0.0336922	+	0.449132i
$145$	−445.832			−0.255340
$146$	2273.29	−	991.877i	1.28862	−	0.562249i
$147$			5357.32i			3.00588i
$148$	−1462.24	−	1356.65i	−0.812129	−	0.753488i
$149$			1446.67i			0.795410i	0.917513	+	0.397705i	$0.130193\pi$
$149$			1446.67i			0.795410i	−0.917513	+	0.397705i	$0.869807\pi$
$150$	176.959	+	405.572i	0.0963240	+	0.220766i
$151$	−1230.20			−0.662998			−0.331499	−	0.943456i	$-0.607554\pi$
$151$	−1230.20			−0.662998			−0.331499	+	0.943456i	$0.607554\pi$
$152$	−3014.32	−	1054.56i	−1.60851	−	0.562739i
$153$	−700.637			−0.370217
$154$	310.053	+	710.613i	0.162239	+	0.371837i
$155$		−	391.654i		−	0.202957i
$156$	−375.728	+	404.970i	−0.192835	+	0.207843i
$157$			1773.74i			0.901657i	0.892611	+	0.450828i	$0.148871\pi$
$157$			1773.74i			0.901657i	−0.892611	+	0.450828i	$0.851129\pi$
$158$	528.722	−	230.691i	0.266221	−	0.116157i
$159$	−2858.47			−1.42573
$160$	−800.170	+	423.000i	−0.395368	+	0.209007i
$161$	−4478.36			−2.19220
$162$	2357.68	−	1028.70i	1.14344	−	0.498903i
$163$			1711.28i			0.822319i	0.911563	+	0.411159i	$0.134876\pi$
$163$			1711.28i			0.822319i	−0.911563	+	0.411159i	$0.865124\pi$
$164$	499.882	−	538.786i	0.238014	−	0.256537i
$165$		−	247.684i		−	0.116862i
$166$	−1127.33	−	2583.73i	−0.527095	−	1.20805i
$167$	3913.26			1.81328			0.906638	−	0.421909i	$-0.138640\pi$
$167$	3913.26			1.81328			0.906638	+	0.421909i	$0.138640\pi$
$168$	4628.22	+	1619.19i	2.12544	+	0.743589i
$169$	2075.24			0.944578
$170$	−325.847	−	746.811i	−0.147008	−	0.336928i
$171$		−	1716.26i		−	0.767520i
$172$	−1138.81	−	1056.58i	−0.504847	−	0.468394i
$173$			3985.34i			1.75144i	0.482815	+	0.875722i	$0.339614\pi$
$173$			3985.34i			1.75144i	−0.482815	+	0.875722i	$0.660386\pi$
$174$	1446.54	−	631.150i	0.630239	−	0.274985i
$175$	865.699			0.373947
$176$	505.201	−	37.8984i	0.216369	−	0.0162312i
$177$	2134.54			0.906450
$178$	−447.076	+	195.067i	−0.188257	+	0.0821400i
$179$		−	884.734i		−	0.369431i	−0.982792	−	0.184715i	$-0.940864\pi$
$179$		−	884.734i		−	0.369431i	0.982792	−	0.184715i	$-0.0591363\pi$
$180$	−356.588	−	330.840i	−0.147658	−	0.136996i
$181$		−	2810.77i		−	1.15427i	−0.816649	−	0.577134i	$-0.804171\pi$
$181$		−	2810.77i		−	1.15427i	0.816649	−	0.577134i	$-0.195829\pi$
$182$	432.206	+	990.576i	0.176029	+	0.403442i
$183$	−1358.37			−0.548709
$184$	−966.356	+	2762.19i	−0.387178	+	1.10669i
$185$	1246.66			0.495439
$186$	554.452	+	1270.75i	0.218572	+	0.500946i
$187$			456.079i			0.178352i
$188$	−395.109	+	425.859i	−0.153278	+	0.165207i
$189$		−	3215.64i		−	1.23758i
$190$	1829.37	−	798.187i	0.698507	−	0.304771i
$191$	−749.321			−0.283869			−0.141935	−	0.989876i	$-0.545332\pi$
$191$	−749.321			−0.283869			−0.141935	+	0.989876i	$0.545332\pi$
$192$	1997.39	−	2505.23i	0.750775	−	0.941663i
$193$	−3969.83			−1.48060			−0.740298	−	0.672279i	$-0.765315\pi$
$193$	−3969.83			−1.48060			−0.740298	+	0.672279i	$0.765315\pi$
$194$	−2744.03	+	1197.27i	−1.01551	+	0.443087i
$195$		−	345.265i		−	0.126795i
$196$	4658.15	−	5020.68i	1.69758	−	1.82969i
$197$			2243.20i			0.811275i	0.914034	+	0.405638i	$0.132951\pi$
$197$			2243.20i			0.811275i	−0.914034	+	0.405638i	$0.867049\pi$
$198$	108.884	+	249.553i	0.0390812	+	0.0895704i
$199$	−672.030			−0.239392			−0.119696	−	0.992811i	$-0.538192\pi$
$199$	−672.030			−0.239392			−0.119696	+	0.992811i	$0.538192\pi$
$200$	186.803	−	533.952i	0.0660450	−	0.188780i
$201$	3311.89			1.16220
$202$	−780.460	−	1788.74i	−0.271846	−	0.623046i
$203$		−	3087.65i		−	1.06754i
$204$	2114.47	+	1961.79i	0.725700	+	0.673299i
$205$			459.353i			0.156500i
$206$	−3344.11	+	1459.10i	−1.13104	+	0.493495i
$207$	−1572.71			−0.528071
$208$	704.237	−	52.8293i	0.234760	−	0.0176108i
$209$	−1117.20			−0.369753
$210$	−2808.83	+	1225.54i	−0.922988	+	0.402717i
$211$			1935.07i			0.631356i	0.948866	+	0.315678i	$0.102232\pi$
$211$			1935.07i			0.631356i	−0.948866	+	0.315678i	$0.897768\pi$
$212$	2678.85	+	2485.42i	0.867851	+	0.805186i
$213$			2387.62i			0.768061i
$214$	2085.48	+	4779.73i	0.666171	+	1.52680i
$215$	970.918			0.307982
$216$	−1983.36	−	693.882i	−0.624772	−	0.218577i
$217$	2712.43			0.848535
$218$	385.255	+	882.968i	0.119692	+	0.274322i
$219$		−	5487.52i		−	1.69321i
$220$	−215.360	+	232.120i	−0.0659979	+	0.0711343i
$221$			635.762i			0.193511i
$222$	−4044.88	+	1764.86i	−1.22286	+	0.533556i
$223$	2492.56			0.748494			0.374247	−	0.927329i	$-0.377901\pi$
$223$	2492.56			0.748494			0.374247	+	0.927329i	$0.377901\pi$
$224$	−2929.52	−	5541.65i	−0.873826	−	1.65298i
$225$	304.016			0.0900787
$226$	−409.161	+	178.524i	−0.120429	+	0.0525455i
$227$		−	3155.27i		−	0.922567i	−0.887253	−	0.461283i	$-0.847389\pi$
$227$		−	3155.27i		−	0.922567i	0.887253	−	0.461283i	$-0.152611\pi$
$228$	−4805.56	+	5179.56i	−1.39586	+	1.50449i
$229$			2299.43i			0.663539i	0.943360	+	0.331770i	$0.107646\pi$
$229$			2299.43i			0.663539i	−0.943360	+	0.331770i	$0.892354\pi$
$230$	−731.423	−	1676.35i	−0.209690	−	0.480589i
$231$	1715.36			0.488581
$232$	−1904.42	−	666.264i	−0.538928	−	0.188545i
$233$	741.991			0.208624			0.104312	−	0.994545i	$-0.466736\pi$
$233$	741.991			0.208624			0.104312	+	0.994545i	$0.466736\pi$
$234$	151.782	+	347.870i	0.0424030	+	0.0971836i
$235$		−	363.074i		−	0.100785i
$236$	−2000.41	−	1855.97i	−0.551761	−	0.511920i
$237$		−	1276.29i		−	0.349806i
$238$	5172.11	−	2256.68i	1.40865	−	0.614618i
$239$	5786.01			1.56597			0.782984	−	0.622042i	$-0.213697\pi$
$239$	5786.01			1.56597			0.782984	+	0.622042i	$0.213697\pi$
$240$	149.800	+	1996.90i	0.0402898	+	0.537081i
$241$	265.054			0.0708449			0.0354224	−	0.999372i	$-0.488722\pi$
$241$	265.054			0.0708449			0.0354224	+	0.999372i	$0.488722\pi$
$242$	−3288.05	+	1434.64i	−0.873404	+	0.381082i
$243$		−	3183.95i		−	0.840537i
$244$	1273.02	+	1181.10i	0.334002	+	0.309885i
$245$			4280.48i			1.11620i
$246$	−650.291	−	1490.41i	−0.168541	−	0.386280i
$247$	−1557.35			−0.401181
$248$	585.298	−	1672.99i	0.149865	−	0.428368i
$249$	−6236.91			−1.58734
$250$	141.389	+	324.051i	0.0357690	+	0.0819791i
$251$		−	1762.02i		−	0.443098i	−0.975149	−	0.221549i	$-0.928889\pi$
$251$		−	1762.02i		−	0.443098i	0.975149	−	0.221549i	$-0.0711113\pi$
$252$	2291.26	−	2469.58i	0.572761	−	0.617337i
$253$			1023.75i			0.254398i
$254$	−1282.47	+	559.567i	−0.316809	+	0.138230i
$255$	−1802.74			−0.442713
$256$	−4050.16	+	611.095i	−0.988808	+	0.149193i
$257$	−1507.84			−0.365980			−0.182990	−	0.983115i	$-0.558578\pi$
$257$	−1507.84			−0.365980			−0.182990	+	0.983115i	$0.558578\pi$
$258$	−3150.22	+	1374.50i	−0.760171	+	0.331677i
$259$			8633.85i			2.07136i
$260$	−300.206	+	323.570i	−0.0716076	+	0.0771805i
$261$		−	1084.32i		−	0.257156i
$262$	−552.869	−	1267.12i	−0.130368	−	0.298791i
$263$	2772.54			0.650046			0.325023	−	0.945706i	$-0.394628\pi$
$263$	2772.54			0.650046			0.325023	+	0.945706i	$0.394628\pi$
$264$	370.146	−	1058.01i	0.0862913	−	0.246652i
$265$	−2283.91			−0.529432
$266$	5527.92	+	12669.5i	1.27420	+	2.92035i
$267$			1079.20i			0.247364i
$268$	−3103.78	−	2879.66i	−0.707438	−	0.656356i
$269$		−	5166.61i		−	1.17106i	−0.810652	−	0.585528i	$-0.800887\pi$
$269$		−	5166.61i		−	1.17106i	0.810652	−	0.585528i	$-0.199113\pi$
$270$	1203.69	−	525.191i	0.271311	−	0.118378i
$271$	−1458.79			−0.326994			−0.163497	−	0.986544i	$-0.552277\pi$
$271$	−1458.79			−0.326994			−0.163497	+	0.986544i	$0.552277\pi$
$272$	−275.838	−	3677.04i	−0.0614896	−	0.819682i
$273$	2391.16			0.530109
$274$	3971.90	−	1733.01i	0.875735	−	0.382099i
$275$		−	197.899i		−	0.0433954i
$276$	4746.32	+	4403.60i	1.03513	+	0.960383i
$277$		−	1994.60i		−	0.432650i	−0.976321	−	0.216325i	$-0.930593\pi$
$277$		−	1994.60i		−	0.432650i	0.976321	−	0.216325i	$-0.0694070\pi$
$278$	854.099	+	1957.51i	0.184264	+	0.422316i
$279$	952.551			0.204400
$280$	3697.93	+	1293.72i	0.789263	+	0.276124i
$281$	−311.583			−0.0661477			−0.0330739	−	0.999453i	$-0.510530\pi$
$281$	−311.583			−0.0661477			−0.0330739	+	0.999453i	$0.510530\pi$
$282$	513.993	+	1178.02i	0.108538	+	0.248760i
$283$		−	6072.33i		−	1.27549i	−0.770249	−	0.637743i	$-0.779868\pi$
$283$		−	6072.33i		−	1.27549i	0.770249	−	0.637743i	$-0.220132\pi$
$284$	2076.02	−	2237.59i	0.433765	−	0.467523i
$285$		−	4415.93i		−	0.917815i
$286$	226.446	−	98.8023i	0.0468182	−	0.0204276i
$287$	−3181.29			−0.654305
$288$	−1028.79	−	1946.11i	−0.210493	−	0.398180i
$289$	−1593.49			−0.324341
$290$	1155.78	−	504.287i	0.234033	−	0.102113i
$291$			6623.84i			1.33435i
$292$	−4771.36	+	5142.70i	−0.956243	+	1.03066i
$293$		−	2321.06i		−	0.462791i	−0.972860	−	0.231395i	$-0.925671\pi$
$293$		−	2321.06i		−	0.462791i	0.972860	−	0.231395i	$-0.0743291\pi$
$294$	−6059.74	−	13888.3i	−1.20208	−	2.75505i
$295$	1705.49			0.336602
$296$	5325.24	+	1863.04i	1.04569	+	0.365835i
$297$	−735.095			−0.143618
$298$	−1636.35	−	3750.37i	−0.318092	−	0.729037i
$299$			1427.08i			0.276021i
$300$	−917.498	−	851.248i	−0.176572	−	0.163823i
$301$			6724.19i			1.28763i
$302$	3189.19	−	1391.50i	0.607674	−	0.265139i
$303$	−4317.86			−0.818662
$304$	9007.19	−	675.686i	1.69933	−	0.127478i
$305$	−1085.34			−0.203758
$306$	1816.34	−	792.501i	0.339324	−	0.148053i
$307$		−	2499.43i		−	0.464658i	−0.972637	−	0.232329i	$-0.925365\pi$
$307$		−	2499.43i		−	0.464658i	0.972637	−	0.232329i	$-0.0746347\pi$
$308$	−1607.57	−	1491.49i	−0.297402	−	0.275928i
$309$			8072.39i			1.48616i
$310$	443.005	+	1015.33i	0.0811645	+	0.186021i
$311$	−3052.83			−0.556624			−0.278312	−	0.960491i	$-0.589775\pi$
$311$	−3052.83			−0.556624			−0.278312	+	0.960491i	$0.589775\pi$
$312$	515.974	−	1474.84i	0.0936258	−	0.267616i
$313$	6179.23			1.11588			0.557941	−	0.829881i	$-0.311592\pi$
$313$	6179.23			1.11588			0.557941	+	0.829881i	$0.311592\pi$
$314$	−2006.31	−	4598.27i	−0.360581	−	0.826418i
$315$			2105.49i			0.376606i
$316$	−1109.73	+	1196.09i	−0.197554	+	0.212929i
$317$		−	3116.20i		−	0.552124i	−0.961140	−	0.276062i	$-0.910971\pi$
$317$		−	3116.20i		−	0.552124i	0.961140	−	0.276062i	$-0.0890295\pi$
$318$	7410.32	−	3233.26i	1.30676	−	0.570164i
$319$	−705.836			−0.123885
$320$	1595.90	−	2001.67i	0.278793	−	0.349678i
$321$	11537.8			2.00617
$322$	11609.7	−	5065.54i	2.00927	−	0.876682i
$323$			8131.39i			1.40075i
$324$	−4948.49	+	5333.62i	−0.848507	+	0.914543i
$325$		−	275.866i		−	0.0470839i
$326$	−1935.66	−	4436.34i	−0.328853	−	0.753700i
$327$	2131.41			0.360450
$328$	−686.469	+	1962.18i	−0.115561	+	0.330314i
$329$	2514.51			0.421365
$330$	280.159	+	642.098i	0.0467341	+	0.107110i
$331$			4157.26i			0.690343i	0.938540	+	0.345171i	$0.112179\pi$
$331$			4157.26i			0.690343i	−0.938540	+	0.345171i	$0.887821\pi$
$332$	5845.00	+	5422.95i	0.966223	+	0.896455i
$333$			3032.03i			0.498962i
$334$	−10144.8	+	4426.35i	−1.66197	+	0.725146i
$335$	2646.19			0.431572
$336$	−13829.7	+	1037.45i	−2.24545	+	0.168446i
$337$	−8123.42			−1.31309			−0.656544	−	0.754287i	$-0.727983\pi$
$337$	−8123.42			−1.31309			−0.656544	+	0.754287i	$0.727983\pi$
$338$	−5379.86	+	2347.33i	−0.865757	+	0.377746i
$339$			987.679i			0.158240i
$340$	1689.46	+	1567.47i	0.269481	+	0.250023i
$341$		−	620.062i		−	0.0984699i
$342$	1941.29	+	4449.25i	0.306939	+	0.703474i
$343$	−17767.5			−2.79695
$344$	4147.39	+	1450.97i	0.650035	+	0.227416i
$345$	−4046.57			−0.631478
$346$	−4507.88	−	10331.6i	−0.700419	−	1.60529i
$347$		−	4620.55i		−	0.714824i	−0.933947	−	0.357412i	$-0.883659\pi$
$347$		−	4620.55i		−	0.714824i	0.933947	−	0.357412i	$-0.116341\pi$
$348$	−3036.11	+	3272.40i	−0.467680	+	0.504077i
$349$		−	5560.98i		−	0.852929i	−0.904504	−	0.426465i	$-0.859759\pi$
$349$		−	5560.98i		−	0.852929i	0.904504	−	0.426465i	$-0.140241\pi$
$350$	−2244.25	+	979.205i	−0.342743	+	0.149545i
$351$	−1024.70			−0.155825
$352$	−1266.82	+	669.689i	−0.191823	+	0.101405i
$353$	12031.8			1.81413			0.907066	−	0.420989i	$-0.138317\pi$
$353$	12031.8			1.81413			0.907066	+	0.420989i	$0.138317\pi$
$354$	−5533.59	+	2414.41i	−0.830811	+	0.362498i
$355$			1907.70i			0.285212i
$356$	938.359	−	1011.39i	0.139699	−	0.150572i
$357$		−	12485.0i		−	1.85092i
$358$	1000.74	+	2293.59i	0.147739	+	0.338603i
$359$	1533.24			0.225408			0.112704	−	0.993629i	$-0.464049\pi$
$359$	1533.24			0.225408			0.112704	+	0.993629i	$0.464049\pi$
$360$	1298.64	+	454.330i	0.190123	+	0.0665146i
$361$	−13059.5			−1.90399
$362$	3179.30	+	7286.66i	0.461603	+	1.05795i
$363$			7937.06i			1.14762i
$364$	−2240.91	−	2079.10i	−0.322680	−	0.299381i
$365$		−	4384.51i		−	0.628755i
$366$	3521.46	−	1536.48i	0.502922	−	0.219434i
$367$	−5480.04			−0.779444			−0.389722	−	0.920933i	$-0.627429\pi$
$367$	−5480.04			−0.779444			−0.389722	+	0.920933i	$0.627429\pi$
$368$	−619.169	−	8253.79i	−0.0877077	−	1.16918i
$369$	−1117.20			−0.157613
$370$	−3231.85	+	1410.11i	−0.454097	+	0.198131i
$371$		−	15817.4i		−	2.21348i
$372$	−2874.73	−	2667.16i	−0.400666	−	0.371735i
$373$		−	6225.70i		−	0.864221i	−0.901821	−	0.432111i	$-0.857769\pi$
$373$		−	6225.70i		−	0.864221i	0.901821	−	0.432111i	$-0.142231\pi$
$374$	−515.878	−	1182.34i	−0.0713246	−	0.163469i
$375$	782.231			0.107718
$376$	542.588	−	1550.91i	0.0744198	−	0.212719i
$377$	−983.917			−0.134415
$378$	3637.26	+	8336.25i	0.494921	+	1.13431i
$379$			11172.0i			1.51416i	0.653325	+	0.757078i	$0.273374\pi$
$379$			11172.0i			1.51416i	−0.653325	+	0.757078i	$0.726626\pi$
$380$	−3839.63	+	4138.45i	−0.518339	+	0.558679i
$381$			3095.78i			0.416277i
$382$	1942.55	−	847.569i	0.260182	−	0.113522i
$383$	7621.03			1.01675			0.508376	−	0.861135i	$-0.330246\pi$
$383$	7621.03			1.01675			0.508376	+	0.861135i	$0.330246\pi$
$384$	−2344.33	+	8753.85i	−0.311546	+	1.16333i
$385$	1370.57			0.181430
$386$	10291.4	−	4490.34i	1.35705	−	0.592104i
$387$			2361.40i			0.310172i
$388$	5759.39	−	6207.62i	0.753579	−	0.812227i
$389$		−	5546.31i		−	0.722903i	−0.932391	−	0.361451i	$-0.882281\pi$
$389$		−	5546.31i		−	0.722903i	0.932391	−	0.361451i	$-0.117719\pi$
$390$	390.534	+	895.067i	0.0507063	+	0.116214i
$391$	7451.25			0.963749
$392$	−6396.87	+	18284.6i	−0.824211	+	2.35589i
$393$	−3058.73			−0.392601
$394$	−2537.31	−	5815.28i	−0.324437	−	0.743578i
$395$		−	1019.75i		−	0.129897i
$396$	−564.546	−	523.782i	−0.0716401	−	0.0664672i
$397$			11025.2i			1.39380i	0.717169	+	0.696900i	$0.245438\pi$
$397$			11025.2i			1.39380i	−0.717169	+	0.696900i	$0.754562\pi$
$398$	1742.18	−	760.143i	0.219416	−	0.0957350i
$399$	30583.0			3.83725
$400$	119.690	+	1595.52i	0.0149612	+	0.199440i
$401$	10522.3			1.31037			0.655186	−	0.755467i	$-0.272590\pi$
$401$	10522.3			1.31037			0.655186	+	0.755467i	$0.272590\pi$
$402$	−8585.76	+	3746.12i	−1.06522	+	0.464775i
$403$		−	864.350i		−	0.106840i
$404$	4046.54	+	3754.35i	0.498324	+	0.462342i
$405$		−	4547.28i		−	0.557916i
$406$	3492.49	+	8004.45i	0.426919	+	0.978458i
$407$	1973.70			0.240375
$408$	−7700.59	−	2694.06i	−0.934402	−	0.326901i
$409$	2320.17			0.280502			0.140251	−	0.990116i	$-0.455209\pi$
$409$	2320.17			0.280502			0.140251	+	0.990116i	$0.455209\pi$
$410$	−519.581	−	1190.83i	−0.0625860	−	0.143441i
$411$		−	9587.82i		−	1.15069i
$412$	7018.89	−	7565.14i	0.839310	−	0.904631i
$413$			11811.5i			1.40728i
$414$	4077.10	−	1778.91i	0.484006	−	0.211181i
$415$	−4983.27			−0.589444
$416$	−1765.91	+	933.528i	−0.208128	+	0.110024i
$417$	4725.27			0.554910
$418$	2896.24	−	1263.68i	0.338898	−	0.147868i
$419$		−	9212.17i		−	1.07409i	−0.843554	−	0.537045i	$-0.819541\pi$
$419$		−	9212.17i		−	1.07409i	0.843554	−	0.537045i	$-0.180459\pi$
$420$	5895.40	−	6354.21i	0.684919	−	0.738224i
$421$		−	6967.70i		−	0.806615i	−0.915064	−	0.403308i	$-0.867860\pi$
$421$		−	6967.70i		−	0.806615i	0.915064	−	0.403308i	$-0.132140\pi$
$422$	−2188.79	−	5016.50i	−0.252485	−	0.578672i
$423$	883.042			0.101501
$424$	−9755.98	−	3413.14i	−1.11743	−	0.390935i
$425$	−1440.38			−0.164397
$426$	−2700.67	−	6189.69i	−0.307155	−	0.703970i
$427$		−	7516.59i		−	0.851882i
$428$	−10812.8	−	10032.1i	−1.22116	−	1.13299i
$429$		−	546.620i		−	0.0615176i
$430$	−2517.02	+	1098.22i	−0.282282	+	0.123165i
$431$	−11247.1			−1.25697			−0.628486	−	0.777821i	$-0.716325\pi$
$431$	−11247.1			−1.25697			−0.628486	+	0.777821i	$0.716325\pi$
$432$	5926.55	−	444.588i	0.660049	−	0.0495145i
$433$	2589.27			0.287372			0.143686	−	0.989623i	$-0.454104\pi$
$433$	2589.27			0.287372			0.143686	+	0.989623i	$0.454104\pi$
$434$	−7031.74	+	3068.07i	−0.777728	+	0.339337i
$435$		−	2789.95i		−	0.307512i
$436$	−1997.48	−	1853.25i	−0.219408	−	0.203565i
$437$			18252.4i			1.99801i
$438$	6207.01	+	14225.9i	0.677129	+	1.55192i
$439$	4220.01			0.458793			0.229396	−	0.973333i	$-0.426325\pi$
$439$	4220.01			0.458793			0.229396	+	0.973333i	$0.426325\pi$
$440$	295.745	−	845.347i	0.0320434	−	0.0915917i
$441$	−10410.7			−1.12414
$442$	−719.120	−	1648.16i	−0.0773870	−	0.177364i
$443$			9764.04i			1.04719i	0.851969	+	0.523593i	$0.175409\pi$
$443$			9764.04i			1.04719i	−0.851969	+	0.523593i	$0.824591\pi$
$444$	8489.73	−	9150.45i	0.907443	−	0.978066i
$445$			862.279i			0.0918560i
$446$	−6461.73	+	2819.37i	−0.686035	+	0.299330i
$447$	−9053.06			−0.957931
$448$	13862.8	+	11052.6i	1.46195	+	1.16559i
$449$	−17159.3			−1.80355			−0.901777	−	0.432202i	$-0.857737\pi$
$449$	−17159.3			−1.80355			−0.901777	+	0.432202i	$0.857737\pi$
$450$	−788.133	+	343.877i	−0.0825621	+	0.0360233i
$451$			727.242i			0.0759302i
$452$	858.781	−	925.617i	0.0893665	−	0.0963216i
$453$		−	7698.43i		−	0.798463i
$454$	3568.97	+	8179.75i	0.368943	+	0.845583i
$455$	1910.53			0.196851
$456$	6599.30	−	18863.2i	0.677720	−	1.93717i
$457$	13027.3			1.33346			0.666730	−	0.745299i	$-0.267693\pi$
$457$	13027.3			1.33346			0.666730	+	0.745299i	$0.267693\pi$
$458$	−2600.92	−	5961.05i	−0.265356	−	0.608170i
$459$			5350.29i			0.544075i
$460$	3792.29	+	3518.47i	0.384384	+	0.356629i
$461$			313.396i			0.0316623i	0.999875	+	0.0158312i	$0.00503943\pi$
$461$			313.396i			0.0316623i	−0.999875	+	0.0158312i	$0.994961\pi$
$462$	−4446.91	+	1940.27i	−0.447811	+	0.195388i
$463$	−12166.5			−1.22123			−0.610613	−	0.791930i	$-0.709077\pi$
$463$	−12166.5			−1.22123			−0.610613	+	0.791930i	$0.709077\pi$
$464$	5690.66	−	426.892i	0.569358	−	0.0427112i
$465$	2450.91			0.244426
$466$	−1923.54	+	839.277i	−0.191216	+	0.0834308i
$467$			1844.42i			0.182761i	0.995816	+	0.0913806i	$0.0291280\pi$
$467$			1844.42i			0.182761i	−0.995816	+	0.0913806i	$0.970872\pi$
$468$	−786.962	−	730.138i	−0.0777293	−	0.0721168i
$469$			18326.4i			1.80434i
$470$	410.679	+	941.237i	0.0403047	+	0.0923745i
$471$	−11099.8			−1.08589
$472$	7285.19	+	2548.73i	0.710441	+	0.248548i
$473$	1537.15			0.149425
$474$	1443.63	+	3308.66i	0.139891	+	0.320616i
$475$		−	3528.32i		−	0.340822i
$476$	−10855.6	+	11700.5i	−1.04531	+	1.12666i
$477$		−	5554.75i		−	0.533196i
$478$	−14999.7	+	6544.65i	−1.43529	+	0.626245i
$479$	−16355.9			−1.56017			−0.780084	−	0.625675i	$-0.784824\pi$
$479$	−16355.9			−1.56017			−0.780084	+	0.625675i	$0.784824\pi$
$480$	−2647.07	−	5007.34i	−0.251711	−	0.476151i
$481$	2751.28			0.260806
$482$	−687.128	+	299.806i	−0.0649332	+	0.0283315i
$483$		−	28024.9i		−	2.64012i
$484$	6901.23	−	7438.32i	0.648124	−	0.698565i
$485$			5292.43i			0.495499i
$486$	3601.41	+	8254.09i	0.336139	+	0.770398i
$487$	11824.6			1.10025			0.550126	−	0.835082i	$-0.314580\pi$
$487$	11824.6			1.10025			0.550126	+	0.835082i	$0.314580\pi$
$488$	−4636.13	−	1621.96i	−0.430057	−	0.150456i
$489$	−10708.9			−0.990337
$490$	−4841.71	−	11096.7i	−0.446380	−	1.02306i
$491$			7931.40i			0.729000i	0.931203	+	0.364500i	$0.118760\pi$
$491$			7931.40i			0.729000i	−0.931203	+	0.364500i	$0.881240\pi$
$492$	3371.64	+	3128.18i	0.308954	+	0.286645i
$493$			5137.34i			0.469319i
$494$	4037.28	−	1761.54i	0.367704	−	0.160436i
$495$	481.315			0.0437040
$496$	375.016	+	4999.12i	0.0339490	+	0.452555i
$497$	−13212.0			−1.19243
$498$	16168.6	−	7054.66i	1.45488	−	0.634793i
$499$		−	2734.69i		−	0.245333i	−0.992448	−	0.122667i	$-0.960855\pi$
$499$		−	2734.69i		−	0.245333i	0.992448	−	0.122667i	$-0.0391446\pi$
$500$	−733.078	−	680.145i	−0.0655685	−	0.0608340i
$501$			24488.6i			2.18377i
$502$	1993.05	+	4567.87i	0.177199	+	0.406124i
$503$	7297.64			0.646890			0.323445	−	0.946247i	$-0.395159\pi$
$503$	7297.64			0.646890			0.323445	+	0.946247i	$0.395159\pi$
$504$	−3146.50	+	8993.84i	−0.278088	+	0.794876i
$505$	−3449.96			−0.304002
$506$	−1157.98	−	2653.98i	−0.101736	−	0.233170i
$507$			12986.5i			1.13758i
$508$	2691.76	−	2901.25i	0.235094	−	0.253390i
$509$		−	10972.4i		−	0.955486i	−0.878500	−	0.477743i	$-0.841455\pi$
$509$		−	10972.4i		−	0.955486i	0.878500	−	0.477743i	$-0.158545\pi$
$510$	4673.43	−	2039.10i	0.405770	−	0.177045i
$511$	30365.3			2.62873
$512$	9808.44	−	6165.40i	0.846633	−	0.532177i
$513$	−13105.9			−1.12796
$514$	3908.95	−	1705.55i	0.335440	−	0.146359i
$515$			6449.81i			0.551869i
$516$	6611.94	−	7126.52i	0.564098	−	0.607999i
$517$		−	574.815i		−	0.0488982i
$518$	−9765.88	−	22382.5i	−0.828355	−	1.89851i
$519$	−24939.7			−2.10931
$520$	412.261	−	1178.39i	0.0347670	−	0.0993767i
$521$	7693.43			0.646939			0.323470	−	0.946239i	$-0.395151\pi$
$521$	7693.43			0.646939			0.323470	+	0.946239i	$0.395151\pi$
$522$	1226.49	+	2811.00i	0.102839	+	0.235697i
$523$		−	14535.3i		−	1.21527i	−0.794217	−	0.607634i	$-0.792119\pi$
$523$		−	14535.3i		−	1.21527i	0.794217	−	0.607634i	$-0.207881\pi$
$524$	2866.53	+	2659.54i	0.238979	+	0.221723i
$525$			5417.41i			0.450353i
$526$	−7187.55	+	3136.06i	−0.595802	+	0.259959i
$527$	−4513.04			−0.373038
$528$	237.162	+	3161.47i	0.0195476	+	0.260578i
$529$	4558.69			0.374676
$530$	5920.82	−	2583.36i	0.485253	−	0.211725i
$531$			4147.97i			0.338995i
$532$	−28661.2	−	26591.7i	−2.33576	−	2.16710i
$533$			1013.76i			0.0823840i
$534$	−1220.70	−	2797.73i	−0.0989230	−	0.226722i
$535$	9218.70			0.744970
$536$	11303.5	+	3954.54i	0.910889	+	0.318675i
$537$	5536.53			0.444914
$538$	5844.03	+	13394.0i	0.468316	+	1.07334i
$539$			6776.81i			0.541555i
$540$	−2526.40	+	2723.02i	−0.201331	+	0.217000i
$541$		−	19131.8i		−	1.52040i	−0.649686	−	0.760202i	$-0.725100\pi$
$541$		−	19131.8i		−	1.52040i	0.649686	−	0.760202i	$-0.274900\pi$
$542$	3781.78	−	1650.06i	0.299708	−	0.130768i
$543$	17589.3			1.39011
$544$	4874.24	+	9220.39i	0.384157	+	0.726693i
$545$	1702.99			0.133850
$546$	−6198.87	+	2704.68i	−0.485874	+	0.211996i
$547$		−	7142.78i		−	0.558324i	−0.960244	−	0.279162i	$-0.909943\pi$
$547$		−	7142.78i		−	0.558324i	0.960244	−	0.279162i	$-0.0900566\pi$
$548$	−8336.55	+	8985.36i	−0.649854	+	0.700430i
$549$		−	2639.67i		−	0.205207i
$550$	223.846	+	513.034i	0.0173542	+	0.0397743i
$551$	−12584.3			−0.972974
$552$	−17285.4	−	6047.30i	−1.33282	−	0.466287i
$553$	7062.39			0.543080
$554$	2256.12	+	5170.82i	0.173021	+	0.396547i
$555$			7801.40i			0.596668i
$556$	−4428.35	−	4108.59i	−0.337777	−	0.313387i
$557$		−	11347.8i		−	0.863236i	−0.902057	−	0.431618i	$-0.857943\pi$
$557$		−	11347.8i		−	0.863236i	0.902057	−	0.431618i	$-0.142057\pi$
$558$	−2469.40	+	1077.44i	−0.187344	+	0.0817417i
$559$	2142.74			0.162126
$560$	−11049.9	+	828.923i	−0.833828	+	0.0625507i
$561$	−2854.07			−0.214793
$562$	807.751	−	352.437i	0.0606280	−	0.0264531i
$563$			8802.19i			0.658913i	0.944171	+	0.329456i	$0.106865\pi$
$563$			8802.19i			0.658913i	−0.944171	+	0.329456i	$0.893135\pi$
$564$	−2664.96	−	2472.53i	−0.198963	−	0.184596i
$565$			789.153i			0.0587609i
$566$	6868.51	+	15742.0i	0.510079	+	1.16905i
$567$	31492.6			2.33257
$568$	−2850.92	+	8148.96i	−0.210602	+	0.601977i
$569$	16714.7			1.23149			0.615744	−	0.787946i	$-0.288855\pi$
$569$	16714.7			1.23149			0.615744	+	0.787946i	$0.288855\pi$
$570$	4994.93	+	11447.9i	0.367043	+	0.841228i
$571$			17386.8i			1.27428i	0.770746	+	0.637142i	$0.219884\pi$
$571$			17386.8i			1.27428i	−0.770746	+	0.637142i	$0.780116\pi$
$572$	−475.283	+	512.272i	−0.0347422	+	0.0374461i
$573$		−	4689.14i		−	0.341870i
$574$	8247.20	−	3598.40i	0.599706	−	0.261663i
$575$	−3233.20			−0.234493
$576$	4868.32	+	3881.44i	0.352164	+	0.280776i
$577$	2260.52			0.163097			0.0815483	−	0.996669i	$-0.474014\pi$
$577$	2260.52			0.163097			0.0815483	+	0.996669i	$0.474014\pi$
$578$	4130.97	−	1802.42i	0.297276	−	0.129707i
$579$		−	24842.6i		−	1.78311i
$580$	−2425.84	+	2614.64i	−0.173668	+	0.187184i
$581$		−	34512.1i		−	2.46438i
$582$	−7492.32	−	17171.7i	−0.533620	−	1.22301i
$583$	−3615.86			−0.256867
$584$	6552.33	−	18728.9i	0.464276	−	1.32707i
$585$	670.940			0.0474187
$586$	2625.38	+	6017.13i	0.185074	+	0.424173i
$587$			25591.0i			1.79941i	0.436498	+	0.899705i	$0.356219\pi$
$587$			25591.0i			1.79941i	−0.436498	+	0.899705i	$0.643781\pi$
$588$	31418.6	+	29150.0i	2.20354	+	2.04443i
$589$		−	11055.0i		−	0.773369i
$590$	−4421.33	+	1929.10i	−0.308514	+	0.134610i
$591$	−14037.6			−0.977037
$592$	−15912.5	+	1193.70i	−1.10473	+	0.0828729i
$593$	−10053.7			−0.696218			−0.348109	−	0.937454i	$-0.613176\pi$
$593$	−10053.7			−0.696218			−0.348109	+	0.937454i	$0.613176\pi$
$594$	1905.67	−	831.476i	0.131634	−	0.0574342i
$595$		−	9975.49i		−	0.687320i
$596$	8484.20	+	7871.58i	0.583098	+	0.540994i
$597$		−	4205.46i		−	0.288305i
$598$	−1614.20	−	3699.58i	−0.110384	−	0.252989i
$599$	−7086.68			−0.483395			−0.241698	−	0.970352i	$-0.577704\pi$
$599$	−7086.68			−0.483395			−0.241698	+	0.970352i	$0.577704\pi$
$600$	3341.39	+	1168.99i	0.227353	+	0.0795395i
$601$	6673.11			0.452915			0.226458	−	0.974021i	$-0.427286\pi$
$601$	6673.11			0.452915			0.226458	+	0.974021i	$0.427286\pi$
$602$	−7605.83	−	17431.8i	−0.514934	−	1.18018i
$603$			6435.86i			0.434641i
$604$	−6693.74	+	7214.69i	−0.450934	+	0.486029i
$605$			6341.69i			0.426159i
$606$	11193.7	−	4884.00i	0.750348	−	0.327391i
$607$	−15205.6			−1.01677			−0.508383	−	0.861131i	$-0.669757\pi$
$607$	−15205.6			−1.01677			−0.508383	+	0.861131i	$0.669757\pi$
$608$	−22586.0	+	11939.8i	−1.50655	+	0.796420i
$609$	19322.0			1.28566
$610$	2813.63	−	1227.64i	0.186755	−	0.0814847i
$611$		−	801.278i		−	0.0530544i
$612$	−3812.28	+	4108.97i	−0.251801	+	0.271398i
$613$			8147.64i			0.536836i	0.963303	+	0.268418i	$0.0865008\pi$
$613$			8147.64i			0.536836i	−0.963303	+	0.268418i	$0.913499\pi$
$614$	2827.14	+	6479.55i	0.185821	+	0.425885i
$615$	−2874.56			−0.188477
$616$	5854.53	+	2048.21i	0.382931	+	0.133969i
$617$	449.110			0.0293039			0.0146519	−	0.999893i	$-0.495336\pi$
$617$	449.110			0.0293039			0.0146519	+	0.999893i	$0.495336\pi$
$618$	−9130.80	−	20926.9i	−0.594328	−	1.36214i
$619$		−	27800.4i		−	1.80516i	−0.430524	−	0.902579i	$-0.641671\pi$
$619$		−	27800.4i		−	1.80516i	0.430524	−	0.902579i	$-0.358329\pi$
$620$	−2296.90	−	2131.05i	−0.148783	−	0.138040i
$621$			12009.7i			0.776059i
$622$	7914.18	−	3453.10i	0.510176	−	0.222599i
$623$	−5971.79			−0.384037
$624$	330.598	+	4407.01i	0.0212091	+	0.282727i
$625$	625.000			0.0400000
$626$	−16019.1	+	6989.42i	−1.02277	+	0.446252i
$627$		−	6991.26i		−	0.445302i
$628$	10402.3	+	9651.22i	0.660984	+	0.613257i
$629$		−	14365.3i		−	0.910623i
$630$	−2381.55	−	5458.29i	−0.150608	−	0.345180i
$631$	14793.5			0.933315			0.466657	−	0.884438i	$-0.345458\pi$
$631$	14793.5			0.933315			0.466657	+	0.884438i	$0.345458\pi$
$632$	1523.95	−	4355.99i	0.0959166	−	0.274164i
$633$	−12109.4			−0.760356
$634$	3524.78	+	8078.46i	0.220800	+	0.506052i
$635$			2473.52i			0.154580i
$636$	−15553.4	+	16763.8i	−0.969704	+	1.04517i
$637$			9446.70i			0.587585i
$638$	1829.82	−	798.382i	0.113547	−	0.0495427i
$639$	−4639.77			−0.287240
$640$	−1873.12	+	6994.30i	−0.115690	+	0.431991i
$641$	−13853.8			−0.853655			−0.426828	−	0.904333i	$-0.640369\pi$
$641$	−13853.8			−0.853655			−0.426828	+	0.904333i	$0.640369\pi$
$642$	−29910.8	+	13050.6i	−1.83876	+	0.802285i
$643$			4978.60i			0.305345i	0.988277	+	0.152672i	$0.0487880\pi$
$643$			4978.60i			0.305345i	−0.988277	+	0.152672i	$0.951212\pi$
$644$	−24367.5	+	26263.9i	−1.49101	+	1.60705i
$645$			6075.86i			0.370910i
$646$	−9197.54	−	21079.9i	−0.560174	−	1.28387i
$647$	−1903.39			−0.115657			−0.0578284	−	0.998327i	$-0.518418\pi$
$647$	−1903.39			−0.115657			−0.0578284	+	0.998327i	$0.518418\pi$
$648$	6795.58	−	19424.2i	0.411969	−	1.17756i
$649$	2700.11			0.163311
$650$	312.036	+	715.156i	0.0188293	+	0.0431550i
$651$			16974.0i			1.02191i
$652$	10036.0	+	9311.36i	0.602824	+	0.559296i
$653$		−	10877.0i		−	0.651839i	−0.945397	−	0.325920i	$-0.894326\pi$
$653$		−	10877.0i		−	0.651839i	0.945397	−	0.325920i	$-0.105674\pi$
$654$	−5525.48	+	2410.87i	−0.330372	+	0.144147i
$655$	−2443.91			−0.145789
$656$	−439.839	−	5863.24i	−0.0261781	−	0.348965i
$657$	10663.7			0.633226
$658$	−6518.62	+	2844.19i	−0.386204	+	0.168508i
$659$			30611.3i			1.80948i	0.425965	+	0.904739i	$0.359935\pi$
$659$			30611.3i			1.80948i	−0.425965	+	0.904739i	$0.640065\pi$
$660$	−1452.57	−	1347.69i	−0.0856686	−	0.0794828i
$661$			16098.8i			0.947310i	0.880710	+	0.473655i	$0.157066\pi$
$661$			16098.8i			0.947310i	−0.880710	+	0.473655i	$0.842934\pi$
$662$	−4702.34	−	10777.3i	−0.276075	−	0.632737i
$663$	−3978.50			−0.233050
$664$	−21286.6	−	7447.14i	−1.24410	−	0.435249i
$665$	24435.7			1.42493
$666$	−3429.57	−	7860.26i	−0.199540	−	0.457326i
$667$			11531.7i			0.669429i
$668$	21292.7	−	22949.8i	1.23329	−	1.32927i
$669$			15598.0i			0.901428i
$670$	−6860.00	+	2993.14i	−0.395559	+	0.172590i
$671$	−1718.29			−0.0988583
$672$	34678.8	−	18332.5i	1.99072	−	1.05237i
$673$	−23837.8			−1.36535			−0.682673	−	0.730724i	$-0.739183\pi$
$673$	−23837.8			−1.36535			−0.682673	+	0.730724i	$0.739183\pi$
$674$	21059.2	−	9188.52i	1.20352	−	0.525117i
$675$		−	2321.56i		−	0.132381i
$676$	11291.7	−	12170.5i	0.642450	−	0.692449i
$677$		−	25235.3i		−	1.43260i	−0.697791	−	0.716302i	$-0.745833\pi$
$677$		−	25235.3i		−	1.43260i	0.697791	−	0.716302i	$-0.254167\pi$
$678$	−1117.18	−	2560.47i	−0.0632817	−	0.145036i
$679$	−36653.2			−2.07161
$680$	−6152.75	−	2152.55i	−0.346981	−	0.121392i
$681$	19745.2			1.11107
$682$	701.361	+	1607.45i	0.0393791	+	0.0902531i
$683$			19975.3i			1.11909i	0.828802	+	0.559543i	$0.189023\pi$
$683$			19975.3i			1.11909i	−0.828802	+	0.559543i	$0.810977\pi$
$684$	−10065.2	−	9338.46i	−0.562652	−	0.522025i
$685$		−	7660.64i		−	0.427297i
$686$	46060.5	−	20097.0i	2.56356	−	1.11853i
$687$	−14389.5			−0.799115
$688$	−12392.9	+	929.673i	−0.686739	+	0.0515166i
$689$	−5040.42			−0.278700
$690$	10490.4	−	4577.13i	0.578784	−	0.252534i
$691$		−	13772.3i		−	0.758209i	−0.925354	−	0.379104i	$-0.876232\pi$
$691$		−	13772.3i		−	0.758209i	0.925354	−	0.379104i	$-0.123768\pi$
$692$	23372.5	+	21684.9i	1.28395	+	1.19124i
$693$			3333.39i			0.182720i
$694$	5226.37	+	11978.3i	0.285865	+	0.655175i
$695$	3775.48			0.206060
$696$	4169.37	−	11917.6i	0.227069	−	0.649044i
$697$	5293.14			0.287650
$698$	6290.10	+	14416.3i	0.341095	+	0.781756i
$699$			4643.26i			0.251251i
$700$	4710.41	−	5077.00i	0.254338	−	0.274132i
$701$			6347.90i			0.342021i	0.985269	+	0.171011i	$0.0547032\pi$
$701$			6347.90i			0.342021i	−0.985269	+	0.171011i	$0.945297\pi$
$702$	2656.45	−	1159.06i	0.142822	−	0.0623159i
$703$	35188.9			1.88787
$704$	2526.62	−	3169.02i	0.135264	−	0.169655i
$705$	2272.06			0.121377
$706$	−31191.4	+	13609.4i	−1.66275	+	0.725488i
$707$		−	23893.0i		−	1.27099i
$708$	11614.4	−	12518.3i	0.616517	−	0.664499i
$709$		−	17910.5i		−	0.948719i	−0.880331	−	0.474360i	$-0.842680\pi$
$709$		−	17910.5i		−	0.948719i	0.880331	−	0.474360i	$-0.157320\pi$
$710$	−2157.83	−	4945.54i	−0.114059	−	0.261412i
$711$	2480.16			0.130821
$712$	−1288.61	+	3683.32i	−0.0678270	+	0.193874i
$713$	−10130.3			−0.532096
$714$	14122.0	+	32366.3i	0.740199	+	1.69647i
$715$		−	436.748i		−	0.0228440i
$716$	−5188.63	−	4813.98i	−0.270821	−	0.251266i
$717$			36208.0i			1.88593i
$718$	−3974.78	+	1734.27i	−0.206598	+	0.0901426i
$719$	36601.6			1.89849			0.949243	−	0.314545i	$-0.101852\pi$
$719$	36601.6			1.89849			0.949243	+	0.314545i	$0.101852\pi$
$720$	−3880.50	+	291.101i	−0.200858	+	0.0150676i
$721$	−44668.8			−2.30728
$722$	33855.4	−	14771.7i	1.74511	−	0.761423i
$723$			1658.67i			0.0853201i
$724$	−16484.1	−	15293.8i	−0.846169	−	0.785070i
$725$		−	2229.16i		−	0.114192i
$726$	−8977.73	−	20576.1i	−0.458946	−	1.05186i
$727$	2644.18			0.134893			0.0674466	−	0.997723i	$-0.478515\pi$
$727$	2644.18			0.134893			0.0674466	+	0.997723i	$0.478515\pi$
$728$	8161.06	+	2855.15i	0.415479	+	0.145356i
$729$	−4630.66			−0.235262
$730$	4959.38	+	11366.4i	0.251445	+	0.576289i
$731$		−	11187.9i		−	0.566075i
$732$	−7391.12	+	7966.34i	−0.373202	+	0.402247i
$733$		−	33452.1i		−	1.68565i	−0.538188	−	0.842825i	$-0.680891\pi$
$733$		−	33452.1i		−	1.68565i	0.538188	−	0.842825i	$-0.319109\pi$
$734$	14206.5	−	6198.56i	0.714403	−	0.311707i
$735$	−26786.6			−1.34427
$736$	10941.1	+	20696.8i	0.547955	+	1.03654i
$737$	4189.42			0.209388
$738$	2896.25	−	1263.69i	0.144461	−	0.0630310i
$739$		−	25834.9i		−	1.28600i	−0.765867	−	0.642999i	$-0.777690\pi$
$739$		−	25834.9i		−	1.28600i	0.765867	−	0.642999i	$-0.222310\pi$
$740$	6783.27	−	7311.18i	0.336970	−	0.363195i
$741$		−	9745.64i		−	0.483151i
$742$	17891.3	+	41005.2i	0.885190	+	2.02877i
$743$	7625.09			0.376497			0.188249	−	0.982121i	$-0.439719\pi$
$743$	7625.09			0.376497			0.188249	+	0.982121i	$0.439719\pi$
$744$	10469.3	+	3662.71i	0.515893	+	0.180486i
$745$	−7233.37			−0.355718
$746$	7041.98	+	16139.6i	0.345610	+	0.792106i
$747$		−	12119.9i		−	0.593635i
$748$	2674.73	+	2481.60i	0.130746	+	0.121305i
$749$			63845.0i			3.11461i
$750$	−2027.86	+	884.793i	−0.0987294	+	0.0430774i
$751$	25362.7			1.23235			0.616177	−	0.787607i	$-0.288680\pi$
$751$	25362.7			1.23235			0.616177	+	0.787607i	$0.288680\pi$
$752$	347.651	+	4634.33i	0.0168584	+	0.224730i
$753$	11026.4			0.533633
$754$	2550.72	−	1112.92i	0.123198	−	0.0537537i
$755$		−	6151.02i		−	0.296502i
$756$	−18858.5	−	17496.8i	−0.907245	−	0.841736i
$757$			38948.0i			1.87000i	0.354648	+	0.935000i	$0.384601\pi$
$757$			38948.0i			1.87000i	−0.354648	+	0.935000i	$0.615399\pi$
$758$	−12636.8	−	28962.3i	−0.605525	−	1.38781i
$759$	−6406.48			−0.306378
$760$	5272.82	−	15071.6i	0.251665	−	0.719349i
$761$	−13722.2			−0.653654			−0.326827	−	0.945084i	$-0.605979\pi$
$761$	−13722.2			−0.653654			−0.326827	+	0.945084i	$0.605979\pi$
$762$	−3501.68	−	8025.52i	−0.166473	−	0.381541i
$763$			11794.2i			0.559606i
$764$	−4077.18	+	4394.49i	−0.193072	+	0.208098i
$765$		−	3503.19i		−	0.165566i
$766$	−19756.8	+	8620.26i	−0.931909	+	0.406609i
$767$	3763.89			0.177192
$768$	−3824.14	−	25345.3i	−0.179677	−	1.19084i
$769$	18689.5			0.876414			0.438207	−	0.898874i	$-0.355614\pi$
$769$	18689.5			0.876414			0.438207	+	0.898874i	$0.355614\pi$
$770$	−3553.07	+	1550.27i	−0.166290	+	0.0725555i
$771$		−	9435.86i		−	0.440758i
$772$	−21600.5	+	23281.6i	−1.00702	+	1.08539i
$773$		−	6386.49i		−	0.297162i	−0.988900	−	0.148581i	$-0.952529\pi$
$773$		−	6386.49i		−	0.297162i	0.988900	−	0.148581i	$-0.0474705\pi$
$774$	−2671.01	−	6121.70i	−0.124041	−	0.284289i
$775$	1958.27			0.0907653
$776$	−7909.15	+	22607.2i	−0.365879	+	1.04581i
$777$	−54029.3			−2.49458
$778$	6273.52	+	14378.3i	0.289096	+	0.662580i
$779$			12965.9i			0.596345i
$780$	−2024.85	−	1878.64i	−0.0929503	−	0.0862386i
$781$			3020.25i			0.138378i
$782$	−19316.7	+	8428.22i	−0.883329	+	0.385413i
$783$	−8280.21			−0.377919
$784$	−4098.64	−	54636.6i	−0.186709	−	2.48891i
$785$	−8868.71			−0.403233
$786$	7929.47	−	3459.77i	0.359841	−	0.157005i
$787$			19410.3i			0.879167i	0.898202	+	0.439583i	$0.144874\pi$
$787$			19410.3i			0.879167i	−0.898202	+	0.439583i	$0.855126\pi$
$788$	13155.5	+	12205.6i	0.594728	+	0.551785i
$789$			17350.1i			0.782865i
$790$	1153.46	+	2643.61i	0.0519470	+	0.119058i
$791$	−5465.35			−0.245671
$792$	2055.99	+	719.290i	0.0922429	+	0.0322713i
$793$	−2395.25			−0.107261
$794$	−12470.8	−	28581.8i	−0.557394	−	1.27749i
$795$		−	14292.3i		−	0.637607i
$796$	−3656.62	+	3941.20i	−0.162821	+	0.175493i
$797$		−	30740.8i		−	1.36624i	−0.730305	−	0.683121i	$-0.760622\pi$
$797$		−	30740.8i		−	1.36624i	0.730305	−	0.683121i	$-0.239378\pi$
$798$	−79283.5	+	34592.8i	−3.51705	+	1.53455i
$799$	−4183.72			−0.185243
$800$	−2115.00	−	4000.85i	−0.0934706	−	0.176814i
$801$	−2097.17			−0.0925092
$802$	−27278.1	+	11902.0i	−1.20103	+	0.524031i
$803$		−	6941.51i		−	0.305057i
$804$	18020.5	−	19423.0i	0.790465	−	0.851984i
$805$		−	22391.8i		−	0.980382i
$806$	977.679	+	2240.75i	0.0427262	+	0.0979243i
$807$	32331.9			1.41033
$808$	−14736.9	−	5155.71i	−0.641636	−	0.224477i
$809$	31805.5			1.38223			0.691114	−	0.722746i	$-0.257120\pi$
$809$	31805.5			1.38223			0.691114	+	0.722746i	$0.257120\pi$
$810$	5143.50	+	11788.4i	0.223116	+	0.511361i
$811$		−	31014.7i		−	1.34288i	−0.741060	−	0.671439i	$-0.765677\pi$
$811$		−	31014.7i		−	1.34288i	0.741060	−	0.671439i	$-0.234323\pi$
$812$	−18107.9	−	16800.4i	−0.782590	−	0.726081i
$813$		−	9128.90i		−	0.393806i
$814$	−5116.63	+	2232.48i	−0.220317	+	0.0961281i
$815$	−8556.41			−0.367752
$816$	23010.4	−	1726.15i	0.987162	−	0.0740533i
$817$	27405.7			1.17357
$818$	−6014.84	+	2624.38i	−0.257095	+	0.112175i
$819$			4646.66i			0.198251i
$820$	2693.93	+	2499.41i	0.114727	+	0.106443i
$821$			12021.4i			0.511021i	0.966806	+	0.255511i	$0.0822436\pi$
$821$			12021.4i			0.511021i	−0.966806	+	0.255511i	$0.917756\pi$
$822$	10844.9	+	24855.6i	0.460171	+	1.05467i
$823$	15489.0			0.656032			0.328016	−	0.944672i	$-0.393620\pi$
$823$	15489.0			0.656032			0.328016	+	0.944672i	$0.393620\pi$
$824$	−9638.78	+	27551.1i	−0.407503	+	1.16479i
$825$	1238.42			0.0522621
$826$	−13360.2	−	30620.3i	−0.562785	−	1.28985i
$827$		−	17097.2i		−	0.718898i	−0.933165	−	0.359449i	$-0.882965\pi$
$827$		−	17097.2i		−	0.718898i	0.933165	−	0.359449i	$-0.117035\pi$
$828$	−8557.35	+	9223.34i	−0.359165	+	0.387117i
$829$			9885.97i			0.414178i	0.978322	+	0.207089i	$0.0663990\pi$
$829$			9885.97i			0.414178i	−0.978322	+	0.207089i	$0.933601\pi$
$830$	12918.7	−	5636.65i	0.540257	−	0.235724i
$831$	12481.9			0.521050
$832$	3522.04	−	4417.54i	0.146761	−	0.184075i
$833$	49324.2			2.05160
$834$	−12249.8	+	5344.82i	−0.508605	+	0.221914i
$835$			19566.3i			0.810922i
$836$	−6078.86	+	6551.95i	−0.251485	+	0.271057i
$837$		−	7273.99i		−	0.300389i
$838$	10420.0	+	23881.7i	0.429539	+	0.984462i
$839$	−39204.3			−1.61321			−0.806606	−	0.591090i	$-0.798698\pi$
$839$	−39204.3			−1.61321			−0.806606	+	0.591090i	$0.798698\pi$
$840$	−8095.93	+	23141.1i	−0.332543	+	0.950528i
$841$	16438.4			0.674007
$842$	7881.27	+	18063.1i	0.322573	+	0.739307i
$843$		−	1949.84i		−	0.0796632i
$844$	11348.5	+	10529.0i	0.462833	+	0.429413i
$845$			10376.2i			0.422428i
$846$	−2289.21	+	998.822i	−0.0930314	+	0.0405913i
$847$	−43920.0			−1.78171
$848$	29152.1	−	2186.89i	1.18053	−	0.0885589i
$849$	37999.7			1.53610
$850$	3734.05	−	1629.24i	0.150679	−	0.0657439i
$851$		−	32245.5i		−	1.29890i
$852$	14002.5	+	12991.4i	0.563049	+	0.522393i
$853$			45054.1i			1.80847i	0.427038	+	0.904234i	$0.359557\pi$
$853$			45054.1i			1.80847i	−0.427038	+	0.904234i	$0.640443\pi$
$854$	8502.13	+	19486.1i	0.340676	+	0.780796i
$855$	8581.31			0.343245
$856$	39378.7	+	13776.7i	1.57236	+	0.550090i
$857$	−48464.2			−1.93174			−0.965872	−	0.259021i	$-0.916600\pi$
$857$	−48464.2			−1.93174			−0.965872	+	0.259021i	$0.916600\pi$
$858$	618.290	+	1417.06i	0.0246015	+	0.0563842i
$859$		−	1000.76i		−	0.0397503i	−0.999802	−	0.0198751i	$-0.993673\pi$
$859$		−	1000.76i		−	0.0397503i	0.999802	−	0.0198751i	$-0.00632687\pi$
$860$	5282.92	−	5694.07i	0.209472	−	0.225775i
$861$		−	19908.0i		−	0.787995i
$862$	29157.1	−	12721.8i	1.15208	−	0.502675i
$863$	22485.5			0.886922			0.443461	−	0.896294i	$-0.353750\pi$
$863$	22485.5			0.886922			0.443461	+	0.896294i	$0.353750\pi$
$864$	−14861.1	+	7856.16i	−0.585170	+	0.309343i
$865$	−19926.7			−0.783270
$866$	−6712.44	+	2928.76i	−0.263392	+	0.114923i
$867$		−	9971.79i		−	0.390611i
$868$	14758.8	−	15907.4i	0.577126	−	0.622042i
$869$		−	1614.46i		−	0.0630228i
$870$	3155.75	+	7232.68i	0.122977	+	0.281851i
$871$	5839.94			0.227186
$872$	7274.51	+	2544.99i	0.282507	+	0.0988353i
$873$	−12871.9			−0.499022
$874$	−20645.6	−	47317.6i	−0.799023	−	1.83129i
$875$			4328.50i			0.167234i
$876$	−32182.2	−	29858.4i	−1.24125	−	1.15162i
$877$		−	43726.2i		−	1.68361i	−0.539780	−	0.841806i	$-0.681493\pi$
$877$		−	43726.2i		−	1.68361i	0.539780	−	0.841806i	$-0.318507\pi$
$878$	−10940.0	+	4773.32i	−0.420509	+	0.183476i
$879$	14524.8			0.557349
$880$	189.492	+	2526.01i	0.00725883	+	0.0967632i
$881$	20290.0			0.775923			0.387962	−	0.921675i	$-0.373179\pi$
$881$	20290.0			0.775923			0.387962	+	0.921675i	$0.373179\pi$
$882$	26988.7	−	11775.7i	1.03034	−	0.449554i
$883$			14887.3i			0.567382i	0.958916	+	0.283691i	$0.0915590\pi$
$883$			14887.3i			0.567382i	−0.958916	+	0.283691i	$0.908441\pi$
$884$	3728.51	+	3459.28i	0.141859	+	0.131616i
$885$			10672.7i			0.405377i
$886$	−11044.2	−	25312.4i	−0.418780	−	0.959803i
$887$	34359.3			1.30065			0.650323	−	0.759658i	$-0.274633\pi$
$887$	34359.3			1.30065			0.650323	+	0.759658i	$0.274633\pi$
$888$	−11658.6	+	33324.6i	−0.440583	+	1.25935i
$889$	−17130.6			−0.646278
$890$	−975.337	−	2235.38i	−0.0367341	−	0.0841911i
$891$		−	7199.21i		−	0.270687i
$892$	13562.4	−	14617.9i	0.509084	−	0.548704i
$893$		−	10248.3i		−	0.384040i
$894$	23469.2	−	10240.1i	0.877996	−	0.383086i
$895$	4423.67			0.165214
$896$	−48439.7	−	12972.4i	−1.80609	−	0.483682i
$897$	−8930.47			−0.332419
$898$	44483.8	−	19409.1i	1.65306	−	0.721258i
$899$		−	6984.47i		−	0.259116i
$900$	1654.20	−	1782.94i	0.0612666	−	0.0660347i
$901$			26317.6i			0.973103i
$902$	−822.595	−	1885.31i	−0.0303652	−	0.0695941i
$903$	−42078.9			−1.55072
$904$	−1179.33	+	3370.96i	−0.0433894	+	0.124022i
$905$	14053.8			0.516205
$906$	8707.81	+	19957.5i	0.319313	+	0.731835i
$907$		−	53363.9i		−	1.95360i	−0.214144	−	0.976802i	$-0.568696\pi$
$907$		−	53363.9i		−	1.95360i	0.214144	−	0.976802i	$-0.431304\pi$
$908$	−18504.5	−	17168.3i	−0.676313	−	0.627479i
$909$		−	8390.73i		−	0.306164i
$910$	−4952.88	+	2161.03i	−0.180425	+	0.0787226i
$911$	−25213.9			−0.916984			−0.458492	−	0.888699i	$-0.651610\pi$
$911$	−25213.9			−0.916984			−0.458492	+	0.888699i	$0.651610\pi$
$912$	4228.34	+	56365.6i	0.153525	+	2.04655i
$913$	−7889.46			−0.285984
$914$	−33772.1	+	14735.4i	−1.22219	+	0.533264i
$915$		−	6791.86i		−	0.245390i
$916$	13485.3	+	12511.6i	0.486426	+	0.451303i
$917$		−	16925.5i		−	0.609521i
$918$	−6051.80	−	13870.1i	−0.217581	−	0.498674i
$919$	3747.02			0.134497			0.0672485	−	0.997736i	$-0.478578\pi$
$919$	3747.02			0.134497			0.0672485	+	0.997736i	$0.478578\pi$
$920$	−13811.0	−	4831.78i	−0.494928	−	0.173151i
$921$	15641.1			0.559599
$922$	−354.487	−	812.452i	−0.0126621	−	0.0290202i
$923$			4210.15i			0.150140i
$924$	9333.53	−	10059.9i	0.332306	−	0.358168i
$925$			6233.29i			0.221567i
$926$	31540.6	−	13761.8i	1.11932	−	0.488380i
$927$	−15686.8			−0.555794
$928$	−14269.6	+	7543.47i	−0.504767	+	0.266839i
$929$	−27726.7			−0.979209			−0.489604	−	0.871945i	$-0.662859\pi$
$929$	−27726.7			−0.979209			−0.489604	+	0.871945i	$0.662859\pi$
$930$	−6353.75	+	2772.26i	−0.224030	+	0.0977483i
$931$			120823.i			4.25330i
$932$	4037.29	−	4351.50i	0.141895	−	0.152938i
$933$		−	19104.1i		−	0.670355i
$934$	−2086.25	−	4781.48i	−0.0730879	−	0.167511i
$935$	−2280.40			−0.0797614
$936$	2866.00	+	1002.67i	0.100083	+	0.0350143i
$937$	29333.2			1.02270			0.511352	−	0.859371i	$-0.329145\pi$
$937$	29333.2			1.02270			0.511352	+	0.859371i	$0.329145\pi$
$938$	−20729.3	−	47509.5i	−0.721572	−	1.65378i
$939$			38668.7i			1.34388i
$940$	−2129.29	−	1975.54i	−0.0738829	−	0.0685481i
$941$		−	24218.4i		−	0.838998i	−0.907756	−	0.419499i	$-0.862206\pi$
$941$		−	24218.4i		−	0.838998i	0.907756	−	0.419499i	$-0.137794\pi$
$942$	28775.2	−	12555.2i	0.995274	−	0.434256i
$943$	11881.4			0.410299
$944$	−21769.1	+	1633.04i	−0.750555	+	0.0563039i
$945$	16078.2			0.553464
$946$	−3984.91	+	1738.69i	−0.136956	+	0.0597566i
$947$			50824.6i			1.74401i	0.489497	+	0.872005i	$0.337180\pi$
$947$			50824.6i			1.74401i	−0.489497	+	0.872005i	$0.662820\pi$
$948$	−7484.96	−	6944.49i	−0.256435	−	0.237918i
$949$		−	9676.28i		−	0.330986i
$950$	3990.93	+	9146.84i	0.136298	+	0.312382i
$951$	19500.7			0.664935
$952$	14907.7	−	42611.4i	0.507521	−	1.45068i
$953$	−10155.1			−0.345180			−0.172590	−	0.984994i	$-0.555214\pi$
$953$	−10155.1			−0.345180			−0.172590	+	0.984994i	$0.555214\pi$
$954$	6283.06	+	14400.2i	0.213230	+	0.488704i
$955$		−	3746.61i		−	0.126950i
$956$	31482.6	−	33932.8i	1.06508	−	1.14798i
$957$		−	4417.01i		−	0.149197i
$958$	42401.2	−	18500.4i	1.42998	−	0.623926i
$959$	53054.5			1.78646
$960$	12526.1	+	9986.93i	0.421125	+	0.335757i
$961$	−23655.3			−0.794042
$962$	−7132.45	+	3112.02i	−0.239043	+	0.104299i
$963$			22421.0i			0.750268i
$964$	1442.20	−	1554.44i	0.0481848	−	0.0519348i
$965$		−	19849.2i		−	0.662142i
$966$	31699.4	+	72651.9i	1.05581	+	2.41981i
$967$	−28225.7			−0.938652			−0.469326	−	0.883025i	$-0.655503\pi$
$967$	−28225.7			−0.938652			−0.469326	+	0.883025i	$0.655503\pi$
$968$	−9477.20	+	27089.2i	−0.314678	+	0.899464i
$969$	−50885.0			−1.68696
$970$	−5986.34	−	13720.1i	−0.198155	−	0.454151i
$971$			47631.4i			1.57422i	0.616814	+	0.787109i	$0.288423\pi$
$971$			47631.4i			1.57422i	−0.616814	+	0.787109i	$0.711577\pi$
$972$	−18672.7	−	17324.4i	−0.616179	−	0.571687i
$973$			26147.4i			0.861508i
$974$	−30654.1	+	13375.0i	−1.00844	+	0.440001i
$975$	1726.32			0.0567042
$976$	13853.4	−	1039.23i	0.454340	−	0.0340829i
$977$	13542.4			0.443460			0.221730	−	0.975108i	$-0.428830\pi$
$977$	13542.4			0.443460			0.221730	+	0.975108i	$0.428830\pi$
$978$	27761.9	−	12113.0i	0.907698	−	0.396045i
$979$			1365.15i			0.0445663i
$980$	25103.4	+	23290.8i	0.818264	+	0.759180i
$981$			4141.88i			0.134801i
$982$	−8971.32	−	20561.4i	−0.291534	−	0.668168i
$983$	−35108.5			−1.13915			−0.569576	−	0.821938i	$-0.692893\pi$
$983$	−35108.5			−1.13915			−0.569576	+	0.821938i	$0.692893\pi$
$984$	−12279.0	−	4295.82i	−0.397805	−	0.139172i
$985$	−11216.0			−0.362813
$986$	−5810.92	−	13318.1i	−0.187685	−	0.430156i
$987$			15735.4i			0.507460i
$988$	−8473.77	+	9133.25i	−0.272861	+	0.294097i
$989$		−	25113.4i		−	0.807440i
$990$	−1247.76	+	544.422i	−0.0400571	+	0.0174776i
$991$	−42816.1			−1.37245			−0.686225	−	0.727390i	$-0.740733\pi$
$991$	−42816.1			−1.37245			−0.686225	+	0.727390i	$0.740733\pi$
$992$	−6626.77	−	12535.6i	−0.212097	−	0.401215i
$993$	−26015.5			−0.831396
$994$	34250.8	−	14944.2i	1.09293	−	0.476864i
$995$		−	3360.15i		−	0.107059i
$996$	−33936.0	+	36577.1i	−1.07962	+	1.16364i
$997$			13029.0i			0.413873i	0.978354	+	0.206936i	$0.0663493\pi$
$997$			13029.0i			0.413873i	−0.978354	+	0.206936i	$0.933651\pi$
$998$	3093.24	+	7089.42i	0.0981111	+	0.224861i
$999$	23153.6			0.733280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.d.a.21.2	yes	12
3.2	odd	2		360.4.k.c.181.11		12
4.3	odd	2		160.4.d.a.81.3		12
5.2	odd	4		200.4.f.c.149.3		12
5.3	odd	4		200.4.f.b.149.10		12
5.4	even	2		200.4.d.b.101.11		12
8.3	odd	2		160.4.d.a.81.10		12
8.5	even	2	inner	40.4.d.a.21.1	✓	12
12.11	even	2		1440.4.k.c.721.6		12
16.3	odd	4		1280.4.a.bd.1.5		6
16.5	even	4		1280.4.a.bc.1.5		6
16.11	odd	4		1280.4.a.ba.1.2		6
16.13	even	4		1280.4.a.bb.1.2		6
20.3	even	4		800.4.f.c.49.9		12
20.7	even	4		800.4.f.b.49.4		12
20.19	odd	2		800.4.d.d.401.10		12
24.5	odd	2		360.4.k.c.181.12		12
24.11	even	2		1440.4.k.c.721.12		12
40.3	even	4		800.4.f.b.49.3		12
40.13	odd	4		200.4.f.c.149.4		12
40.19	odd	2		800.4.d.d.401.3		12
40.27	even	4		800.4.f.c.49.10		12
40.29	even	2		200.4.d.b.101.12		12
40.37	odd	4		200.4.f.b.149.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.1	✓	12	8.5	even	2	inner
40.4.d.a.21.2	yes	12	1.1	even	1	trivial
160.4.d.a.81.3		12	4.3	odd	2
160.4.d.a.81.10		12	8.3	odd	2
200.4.d.b.101.11		12	5.4	even	2
200.4.d.b.101.12		12	40.29	even	2
200.4.f.b.149.9		12	40.37	odd	4
200.4.f.b.149.10		12	5.3	odd	4
200.4.f.c.149.3		12	5.2	odd	4
200.4.f.c.149.4		12	40.13	odd	4
360.4.k.c.181.11		12	3.2	odd	2
360.4.k.c.181.12		12	24.5	odd	2
800.4.d.d.401.3		12	40.19	odd	2
800.4.d.d.401.10		12	20.19	odd	2
800.4.f.b.49.3		12	40.3	even	4
800.4.f.b.49.4		12	20.7	even	4
800.4.f.c.49.9		12	20.3	even	4
800.4.f.c.49.10		12	40.27	even	4
1280.4.a.ba.1.2		6	16.11	odd	4
1280.4.a.bb.1.2		6	16.13	even	4
1280.4.a.bc.1.5		6	16.5	even	4
1280.4.a.bd.1.5		6	16.3	odd	4
1440.4.k.c.721.6		12	12.11	even	2
1440.4.k.c.721.12		12	24.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59241 + 1.13111i) q^{2} +6.25785i q^{3} +(5.44116 - 5.86462i) q^{4} +5.00000i q^{5} +(-7.07834 - 16.2229i) q^{6} -34.6280 q^{7} +(-7.47214 + 21.3581i) q^{8} -12.1606 q^{9} +(-5.65557 - 12.9620i) q^{10} +7.91595i q^{11} +(36.6999 + 34.0499i) q^{12} +11.0346i q^{13} +(89.7698 - 39.1682i) q^{14} -31.2892 q^{15} +(-4.78760 - 63.8207i) q^{16} +57.6152 q^{17} +(31.5253 - 13.7551i) q^{18} +141.133i q^{19} +(29.3231 + 27.2058i) q^{20} -216.696i q^{21} +(-8.95385 - 20.5214i) q^{22} +129.328 q^{23} +(-133.655 - 46.7595i) q^{24} -25.0000 q^{25} +(-12.4814 - 28.6062i) q^{26} +92.8625i q^{27} +(-188.416 + 203.080i) q^{28} +89.1664i q^{29} +(81.1144 - 35.3917i) q^{30} -78.3307 q^{31} +(84.5999 + 160.034i) q^{32} -49.5368 q^{33} +(-149.362 + 65.1694i) q^{34} -173.140i q^{35} +(-66.1679 + 71.3175i) q^{36} -249.332i q^{37} +(-159.637 - 365.874i) q^{38} -69.0530 q^{39} +(-106.790 - 37.3607i) q^{40} +91.8705 q^{41} +(245.109 + 561.766i) q^{42} -194.184i q^{43} +(46.4240 + 43.0719i) q^{44} -60.8031i q^{45} +(-335.270 + 146.285i) q^{46} -72.6149 q^{47} +(399.380 - 29.9600i) q^{48} +856.096 q^{49} +(64.8102 - 28.2779i) q^{50} +360.547i q^{51} +(64.7139 + 60.0411i) q^{52} +456.782i q^{53} +(-105.038 - 240.737i) q^{54} -39.5797 q^{55} +(258.745 - 739.586i) q^{56} -883.187 q^{57} +(-100.857 - 231.156i) q^{58} -341.098i q^{59} +(-170.250 + 183.500i) q^{60} +217.067i q^{61} +(203.065 - 88.6011i) q^{62} +421.098 q^{63} +(-400.334 - 319.181i) q^{64} -55.1731 q^{65} +(128.420 - 56.0318i) q^{66} -529.237i q^{67} +(313.494 - 337.892i) q^{68} +809.314i q^{69} +(195.841 + 448.849i) q^{70} +381.540 q^{71} +(90.8659 - 259.728i) q^{72} -876.902 q^{73} +(282.023 + 646.370i) q^{74} -156.446i q^{75} +(827.690 + 767.926i) q^{76} -274.113i q^{77} +(179.013 - 78.1069i) q^{78} -203.950 q^{79} +(319.103 - 23.9380i) q^{80} -909.456 q^{81} +(-238.166 + 103.916i) q^{82} +996.654i q^{83} +(-1270.84 - 1179.08i) q^{84} +288.076i q^{85} +(219.644 + 503.403i) q^{86} -557.989 q^{87} +(-169.069 - 59.1491i) q^{88} +172.456 q^{89} +(68.7753 + 157.627i) q^{90} -382.107i q^{91} +(703.693 - 758.459i) q^{92} -490.182i q^{93} +(188.247 - 82.1358i) q^{94} -705.664 q^{95} +(-1001.47 + 529.413i) q^{96} +1058.49 q^{97} +(-2219.35 + 968.343i) q^{98} -96.2629i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

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