LMFDB - Embedded newform 400.3.i.b.93.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(93,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.i (of order $4$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.9
Character	$\chi$	$=$	400.93
Dual form			400.3.i.b.357.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.634321 - 1.89674i) q^{2} -2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(5.39242 + 5.39242i) q^{7} +(6.59094 + 4.53426i) q^{8} +1.30888 q^{9} +O(q^{10})$	\(q+(-0.634321 - 1.89674i) q^{2} -2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(5.39242 + 5.39242i) q^{7} +(6.59094 + 4.53426i) q^{8} +1.30888 q^{9} +(2.98007 - 2.98007i) q^{11} +(6.67333 + 8.86141i) q^{12} -21.2000i q^{13} +(6.80752 - 13.6486i) q^{14} +(4.41955 - 15.3775i) q^{16} +(-6.66924 + 6.66924i) q^{17} +(-0.830250 - 2.48261i) q^{18} +(14.3102 - 14.3102i) q^{19} +(14.9547 - 14.9547i) q^{21} +(-7.54275 - 3.76211i) q^{22} +(-2.07267 + 2.07267i) q^{23} +(12.5748 - 18.2786i) q^{24} +(-40.2109 + 13.4476i) q^{26} -28.5895i q^{27} +(-30.2060 - 4.25454i) q^{28} +(17.5413 - 17.5413i) q^{29} -23.6474 q^{31} +(-31.9706 + 1.37153i) q^{32} +(-8.26459 - 8.26459i) q^{33} +(16.8803 + 8.41940i) q^{34} +(-4.18223 + 3.14954i) q^{36} +65.3234i q^{37} +(-36.2201 - 18.0655i) q^{38} -58.7936 q^{39} -1.18249i q^{41} +(-37.8514 - 18.8792i) q^{42} -9.57434 q^{43} +(-2.35123 + 16.6930i) q^{44} +(5.24607 + 2.61659i) q^{46} +(47.2286 - 47.2286i) q^{47} +(-42.6462 - 12.2567i) q^{48} +9.15649i q^{49} +(18.4957 + 18.4957i) q^{51} +(51.0133 + 67.7397i) q^{52} +99.2178 q^{53} +(-54.2269 + 18.1349i) q^{54} +(11.0905 + 59.9918i) q^{56} +(-39.6863 - 39.6863i) q^{57} +(-44.3981 - 22.1445i) q^{58} +(-54.7400 - 54.7400i) q^{59} +(-12.1054 - 12.1054i) q^{61} +(15.0000 + 44.8531i) q^{62} +(7.05803 + 7.05803i) q^{63} +(22.8811 + 59.7700i) q^{64} +(-10.4334 + 20.9182i) q^{66} -109.074 q^{67} +(5.26193 - 37.3582i) q^{68} +(5.74812 + 5.74812i) q^{69} -73.1674i q^{71} +(8.62675 + 5.93479i) q^{72} +(-17.0166 + 17.0166i) q^{73} +(123.902 - 41.4360i) q^{74} +(-11.2905 + 80.1595i) q^{76} +32.1396 q^{77} +(37.2940 + 111.516i) q^{78} -2.15129i q^{79} -67.5069 q^{81} +(-2.24289 + 0.750081i) q^{82} -76.4850i q^{83} +(-11.7991 + 83.7699i) q^{84} +(6.07320 + 18.1601i) q^{86} +(-48.6470 - 48.6470i) q^{87} +(33.1539 - 6.12907i) q^{88} -38.7296 q^{89} +(114.319 - 114.319i) q^{91} +(1.63531 - 11.6102i) q^{92} +65.5810i q^{93} +(-119.539 - 59.6224i) q^{94} +(3.80365 + 88.6636i) q^{96} +(-8.53929 + 8.53929i) q^{97} +(17.3675 - 5.80816i) q^{98} +(3.90055 - 3.90055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9	$ 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9} - 4 q^{11} + 8 q^{12} + 24 q^{16} + 4 q^{17} - 22 q^{18} + 32 q^{19} - 4 q^{21} - 92 q^{22} + 36 q^{24} - 52 q^{26} - 36 q^{28} - 8 q^{31} + 132 q^{32} + 4 q^{33} - 88 q^{34} - 116 q^{36} + 216 q^{38} + 72 q^{39} - 16 q^{42} - 124 q^{43} - 168 q^{44} + 108 q^{46} + 4 q^{47} - 340 q^{48} - 100 q^{51} - 48 q^{52} + 4 q^{53} + 228 q^{54} - 172 q^{56} - 36 q^{57} - 16 q^{58} + 64 q^{59} - 36 q^{61} + 356 q^{62} + 200 q^{63} - 176 q^{64} + 276 q^{66} + 292 q^{67} + 72 q^{68} - 60 q^{69} - 448 q^{72} - 48 q^{73} + 284 q^{74} + 252 q^{76} - 192 q^{77} - 620 q^{78} + 100 q^{81} + 240 q^{82} + 288 q^{84} + 20 q^{86} - 36 q^{87} + 624 q^{88} + 188 q^{91} + 412 q^{92} - 340 q^{94} - 24 q^{96} + 4 q^{97} + 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9 - 4 * q^11 + 8 * q^12 + 24 * q^16 + 4 * q^17 - 22 * q^18 + 32 * q^19 - 4 * q^21 - 92 * q^22 + 36 * q^24 - 52 * q^26 - 36 * q^28 - 8 * q^31 + 132 * q^32 + 4 * q^33 - 88 * q^34 - 116 * q^36 + 216 * q^38 + 72 * q^39 - 16 * q^42 - 124 * q^43 - 168 * q^44 + 108 * q^46 + 4 * q^47 - 340 * q^48 - 100 * q^51 - 48 * q^52 + 4 * q^53 + 228 * q^54 - 172 * q^56 - 36 * q^57 - 16 * q^58 + 64 * q^59 - 36 * q^61 + 356 * q^62 + 200 * q^63 - 176 * q^64 + 276 * q^66 + 292 * q^67 + 72 * q^68 - 60 * q^69 - 448 * q^72 - 48 * q^73 + 284 * q^74 + 252 * q^76 - 192 * q^77 - 620 * q^78 + 100 * q^81 + 240 * q^82 + 288 * q^84 + 20 * q^86 - 36 * q^87 + 624 * q^88 + 188 * q^91 + 412 * q^92 - 340 * q^94 - 24 * q^96 + 4 * q^97 + 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.634321	−	1.89674i	−0.317161	−	0.948372i
$2$	−0.634321	−	1.89674i	−0.317161	−	0.948372i
$3$		−	2.77329i		−	0.924429i	−0.886768	−	0.462215i	$-0.847055\pi$
$3$		−	2.77329i		−	0.924429i	0.886768	−	0.462215i	$-0.152945\pi$
$4$	−3.19527	+	2.40629i	−0.798818	+	0.601572i
$5$		0			0
$5$		0			0
$6$	−5.26021	+	1.75915i	−0.876702	+	0.293192i
$7$	5.39242	+	5.39242i	0.770346	+	0.770346i	0.978167	−	0.207821i	$-0.0666370\pi$
$7$	5.39242	+	5.39242i	0.770346	+	0.770346i	−0.207821	+	0.978167i	$0.566637\pi$
$8$	6.59094	+	4.53426i	0.823868	+	0.566782i
$9$	1.30888			0.145431
$10$		0			0
$11$	2.98007	−	2.98007i	0.270915	−	0.270915i	−0.558553	−	0.829469i	$-0.688643\pi$
$11$	2.98007	−	2.98007i	0.270915	−	0.270915i	0.829469	+	0.558553i	$0.188643\pi$
$12$	6.67333	+	8.86141i	0.556111	+	0.738451i
$13$		−	21.2000i		−	1.63077i	−0.578921	−	0.815383i	$-0.696526\pi$
$13$		−	21.2000i		−	1.63077i	0.578921	−	0.815383i	$-0.303474\pi$
$14$	6.80752	−	13.6486i	0.486251	−	0.974898i
$15$		0			0
$16$	4.41955	−	15.3775i	0.276222	−	0.961094i
$17$	−6.66924	+	6.66924i	−0.392308	+	0.392308i	−0.875509	−	0.483201i	$-0.839474\pi$
$17$	−6.66924	+	6.66924i	−0.392308	+	0.392308i	0.483201	+	0.875509i	$0.339474\pi$
$18$	−0.830250	−	2.48261i	−0.0461250	−	0.137923i
$19$	14.3102	−	14.3102i	0.753169	−	0.753169i	−0.221901	−	0.975069i	$-0.571226\pi$
$19$	14.3102	−	14.3102i	0.753169	−	0.753169i	0.975069	+	0.221901i	$0.0712261\pi$
$20$		0			0
$21$	14.9547	−	14.9547i	0.712131	−	0.712131i
$22$	−7.54275	−	3.76211i	−0.342852	−	0.171005i
$23$	−2.07267	+	2.07267i	−0.0901163	+	0.0901163i	−0.750728	−	0.660612i	$-0.770297\pi$
$23$	−2.07267	+	2.07267i	−0.0901163	+	0.0901163i	0.660612	+	0.750728i	$0.270297\pi$
$24$	12.5748	−	18.2786i	0.523950	−	0.761607i
$25$		0			0
$26$	−40.2109	+	13.4476i	−1.54657	+	0.517215i
$27$		−	28.5895i		−	1.05887i
$28$	−30.2060	−	4.25454i	−1.07879	−	0.151948i
$29$	17.5413	−	17.5413i	0.604872	−	0.604872i	−0.336730	−	0.941601i	$-0.609321\pi$
$29$	17.5413	−	17.5413i	0.604872	−	0.604872i	0.941601	+	0.336730i	$0.109321\pi$
$30$		0			0
$31$	−23.6474			−0.762819			−0.381410	−	0.924406i	$-0.624561\pi$
$31$	−23.6474			−0.762819			−0.381410	+	0.924406i	$0.624561\pi$
$32$	−31.9706	+	1.37153i	−0.999081	+	0.0428603i
$33$	−8.26459	−	8.26459i	−0.250442	−	0.250442i
$34$	16.8803	+	8.41940i	0.496479	+	0.247629i
$35$		0			0
$36$	−4.18223	+	3.14954i	−0.116173	+	0.0874873i
$37$			65.3234i			1.76550i	0.469845	+	0.882749i	$0.344310\pi$
$37$			65.3234i			1.76550i	−0.469845	+	0.882749i	$0.655690\pi$
$38$	−36.2201	−	18.0655i	−0.953159	−	0.475409i
$39$	−58.7936			−1.50753
$40$		0			0
$41$		−	1.18249i		−	0.0288413i	−0.999896	−	0.0144207i	$-0.995410\pi$
$41$		−	1.18249i		−	0.0288413i	0.999896	−	0.0144207i	$-0.00459040\pi$
$42$	−37.8514	−	18.8792i	−0.901224	−	0.449505i
$43$	−9.57434			−0.222659			−0.111330	−	0.993784i	$-0.535511\pi$
$43$	−9.57434			−0.222659			−0.111330	+	0.993784i	$0.535511\pi$
$44$	−2.35123	+	16.6930i	−0.0534370	+	0.379387i
$45$		0			0
$46$	5.24607	+	2.61659i	0.114045	+	0.0568824i
$47$	47.2286	−	47.2286i	1.00486	−	1.00486i	0.00487524	−	0.999988i	$-0.498448\pi$
$47$	47.2286	−	47.2286i	1.00486	−	1.00486i	0.999988	−	0.00487524i	$-0.00155184\pi$
$48$	−42.6462	−	12.2567i	−0.888463	−	0.255347i
$49$			9.15649i			0.186867i
$50$		0			0
$51$	18.4957	+	18.4957i	0.362661	+	0.362661i
$52$	51.0133	+	67.7397i	0.981024	+	1.30269i
$53$	99.2178			1.87203			0.936017	−	0.351955i	$-0.114483\pi$
$53$	99.2178			1.87203			0.936017	+	0.351955i	$0.114483\pi$
$54$	−54.2269	+	18.1349i	−1.00420	+	0.335832i
$55$		0			0
$56$	11.0905	+	59.9918i	0.198045	+	1.07128i
$57$	−39.6863	−	39.6863i	−0.696251	−	0.696251i
$58$	−44.3981	−	22.1445i	−0.765485	−	0.381802i
$59$	−54.7400	−	54.7400i	−0.927796	−	0.927796i	0.0697673	−	0.997563i	$-0.477774\pi$
$59$	−54.7400	−	54.7400i	−0.927796	−	0.927796i	−0.997563	+	0.0697673i	$0.977774\pi$
$60$		0			0
$61$	−12.1054	−	12.1054i	−0.198449	−	0.198449i	0.600886	−	0.799335i	$-0.294815\pi$
$61$	−12.1054	−	12.1054i	−0.198449	−	0.198449i	−0.799335	+	0.600886i	$0.794815\pi$
$62$	15.0000	+	44.8531i	0.241936	+	0.723436i
$63$	7.05803	+	7.05803i	0.112032	+	0.112032i
$64$	22.8811	+	59.7700i	0.357517	+	0.933907i
$65$		0			0
$66$	−10.4334	+	20.9182i	−0.158082	+	0.316942i
$67$	−109.074			−1.62798			−0.813988	−	0.580882i	$-0.802708\pi$
$67$	−109.074			−1.62798			−0.813988	+	0.580882i	$0.802708\pi$
$68$	5.26193	−	37.3582i	0.0773813	−	0.549385i
$69$	5.74812	+	5.74812i	0.0833061	+	0.0833061i
$70$		0			0
$71$		−	73.1674i		−	1.03053i	−0.857032	−	0.515263i	$-0.827694\pi$
$71$		−	73.1674i		−	1.03053i	0.857032	−	0.515263i	$-0.172306\pi$
$72$	8.62675	+	5.93479i	0.119816	+	0.0824277i
$73$	−17.0166	+	17.0166i	−0.233103	+	0.233103i	−0.813987	−	0.580883i	$-0.802707\pi$
$73$	−17.0166	+	17.0166i	−0.233103	+	0.233103i	0.580883	+	0.813987i	$0.302707\pi$
$74$	123.902	−	41.4360i	1.67435	−	0.559946i
$75$		0			0
$76$	−11.2905	+	80.1595i	−0.148560	+	1.05473i
$77$	32.1396			0.417397
$78$	37.2940	+	111.516i	0.478129	+	1.42970i
$79$		−	2.15129i		−	0.0272315i	−0.999907	−	0.0136157i	$-0.995666\pi$
$79$		−	2.15129i		−	0.0272315i	0.999907	−	0.0136157i	$-0.00433416\pi$
$80$		0			0
$81$	−67.5069			−0.833419
$82$	−2.24289	+	0.750081i	−0.0273523	+	0.00914732i
$83$		−	76.4850i		−	0.921506i	−0.887528	−	0.460753i	$-0.847579\pi$
$83$		−	76.4850i		−	0.921506i	0.887528	−	0.460753i	$-0.152421\pi$
$84$	−11.7991	+	83.7699i	−0.140465	+	0.997261i
$85$		0			0
$86$	6.07320	+	18.1601i	0.0706187	+	0.211164i
$87$	−48.6470	−	48.6470i	−0.559161	−	0.559161i
$88$	33.1539	−	6.12907i	0.376748	−	0.0696485i
$89$	−38.7296			−0.435164			−0.217582	−	0.976042i	$-0.569817\pi$
$89$	−38.7296			−0.435164			−0.217582	+	0.976042i	$0.569817\pi$
$90$		0			0
$91$	114.319	−	114.319i	1.25626	−	1.25626i
$92$	1.63531	−	11.6102i	0.0177751	−	0.126198i
$93$			65.5810i			0.705172i
$94$	−119.539	−	59.6224i	−1.27169	−	0.634281i
$95$		0			0
$96$	3.80365	+	88.6636i	0.0396213	+	0.923580i
$97$	−8.53929	+	8.53929i	−0.0880339	+	0.0880339i	−0.749752	−	0.661718i	$-0.769827\pi$
$97$	−8.53929	+	8.53929i	−0.0880339	+	0.0880339i	0.661718	+	0.749752i	$0.269827\pi$
$98$	17.3675	−	5.80816i	0.177220	−	0.0592669i
$99$	3.90055	−	3.90055i	0.0393995	−	0.0393995i
$100$		0			0
$101$	65.0118	−	65.0118i	0.643681	−	0.643681i	−0.307777	−	0.951458i	$-0.599585\pi$
$101$	65.0118	−	65.0118i	0.643681	−	0.643681i	0.951458	+	0.307777i	$0.0995852\pi$
$102$	23.3494	−	46.8138i	0.228916	−	0.458959i
$103$	−32.9039	+	32.9039i	−0.319456	+	0.319456i	−0.848558	−	0.529102i	$-0.822529\pi$
$103$	−32.9039	+	32.9039i	−0.319456	+	0.319456i	0.529102	+	0.848558i	$0.322529\pi$
$104$	96.1261	−	139.728i	0.924289	−	1.34354i
$105$		0			0
$106$	−62.9359	−	188.191i	−0.593735	−	1.77538i
$107$		−	19.9537i		−	0.186484i	−0.995643	−	0.0932418i	$-0.970277\pi$
$107$		−	19.9537i		−	0.186484i	0.995643	−	0.0932418i	$-0.0297230\pi$
$108$	68.7946	+	91.3512i	0.636987	+	0.845845i
$109$	−31.4162	+	31.4162i	−0.288222	+	0.288222i	−0.836377	−	0.548155i	$-0.815330\pi$
$109$	−31.4162	+	31.4162i	−0.288222	+	0.288222i	0.548155	+	0.836377i	$0.315330\pi$
$110$		0			0
$111$	181.161			1.63208
$112$	106.754	−	59.0900i	0.953162	−	0.527589i
$113$	48.1807	+	48.1807i	0.426378	+	0.426378i	0.887393	−	0.461014i	$-0.152514\pi$
$113$	48.1807	+	48.1807i	0.426378	+	0.426378i	−0.461014	+	0.887393i	$0.652514\pi$
$114$	−50.1009	+	100.449i	−0.439481	+	0.881128i
$115$		0			0
$116$	−13.8398	+	98.2586i	−0.119309	+	0.847057i
$117$		−	27.7482i		−	0.237164i
$118$	−69.1050	+	138.550i	−0.585635	+	1.17416i
$119$	−71.9267			−0.604426
$120$		0			0
$121$			103.238i			0.853210i
$122$	−15.2821	+	30.6395i	−0.125263	+	0.251144i
$123$	−3.27939			−0.0266617
$124$	75.5599	−	56.9025i	0.609354	−	0.458891i
$125$		0			0
$126$	8.91022	−	17.8643i	0.0707160	−	0.141780i
$127$	165.164	−	165.164i	1.30051	−	1.30051i	0.372456	−	0.928050i	$-0.378516\pi$
$127$	165.164	−	165.164i	1.30051	−	1.30051i	0.928050	−	0.372456i	$-0.121484\pi$
$128$	98.8545	−	81.3129i	0.772301	−	0.635257i
$129$			26.5524i			0.205832i
$130$		0			0
$131$	10.9705	+	10.9705i	0.0837444	+	0.0837444i	0.747738	−	0.663994i	$-0.231140\pi$
$131$	10.9705	+	10.9705i	0.0837444	+	0.0837444i	−0.663994	+	0.747738i	$0.731140\pi$
$132$	46.2946	+	6.52063i	0.350717	+	0.0493987i
$133$	154.333			1.16040
$134$	69.1882	+	206.886i	0.516330	+	1.54393i
$135$		0			0
$136$	−74.1966	+	13.7165i	−0.545563	+	0.100857i
$137$	122.401	+	122.401i	0.893436	+	0.893436i	0.994845	−	0.101408i	$-0.0323349\pi$
$137$	122.401	+	122.401i	0.893436	+	0.893436i	−0.101408	+	0.994845i	$0.532335\pi$
$138$	7.25656	−	14.5489i	0.0525837	−	0.105427i
$139$	163.514	+	163.514i	1.17636	+	1.17636i	0.980665	+	0.195693i	$0.0626955\pi$
$139$	163.514	+	163.514i	1.17636	+	1.17636i	0.195693	+	0.980665i	$0.437305\pi$
$140$		0			0
$141$	−130.978	−	130.978i	−0.928925	−	0.928925i
$142$	−138.780	+	46.4116i	−0.977322	+	0.326842i
$143$	−63.1774	−	63.1774i	−0.441800	−	0.441800i
$144$	5.78465	−	20.1273i	0.0401712	−	0.139773i
$145$		0			0
$146$	43.0700	+	21.4821i	0.295000	+	0.147138i
$147$	25.3936			0.172745
$148$	−157.187	−	208.726i	−1.06207	−	1.41031i
$149$	182.956	+	182.956i	1.22789	+	1.22789i	0.964759	+	0.263134i	$0.0847562\pi$
$149$	182.956	+	182.956i	1.22789	+	1.22789i	0.263134	+	0.964759i	$0.415244\pi$
$150$		0			0
$151$			100.104i			0.662938i	0.943466	+	0.331469i	$0.107544\pi$
$151$			100.104i			0.662938i	−0.943466	+	0.331469i	$0.892456\pi$
$152$	159.204	−	29.4316i	1.04739	−	0.193629i
$153$	−8.72923	+	8.72923i	−0.0570538	+	0.0570538i
$154$	−20.3868	−	60.9606i	−0.132382	−	0.395848i
$155$		0			0
$156$	187.862	−	141.474i	1.20424	−	0.906887i
$157$	−27.8875			−0.177627			−0.0888136	−	0.996048i	$-0.528308\pi$
$157$	−27.8875			−0.177627			−0.0888136	+	0.996048i	$0.528308\pi$
$158$	−4.08044	+	1.36461i	−0.0258256	+	0.00863675i
$159$		−	275.159i		−	1.73056i
$160$		0			0
$161$	−22.3535			−0.138841
$162$	42.8211	+	128.043i	0.264328	+	0.790391i
$163$			122.177i			0.749552i	0.927115	+	0.374776i	$0.122280\pi$
$163$			122.177i			0.749552i	−0.927115	+	0.374776i	$0.877720\pi$
$164$	2.84542	+	3.77839i	0.0173501	+	0.0230390i
$165$		0			0
$166$	−145.072	+	48.5160i	−0.873930	+	0.292265i
$167$	102.217	+	102.217i	0.612078	+	0.612078i	0.943487	−	0.331409i	$-0.107524\pi$
$167$	102.217	+	102.217i	0.612078	+	0.612078i	−0.331409	+	0.943487i	$0.607524\pi$
$168$	166.374	−	30.7572i	0.990324	−	0.183079i
$169$	−280.439			−1.65940
$170$		0			0
$171$	18.7303	−	18.7303i	0.109534	−	0.109534i
$172$	30.5926	−	23.0386i	0.177864	−	0.133945i
$173$		−	144.968i		−	0.837968i	−0.907994	−	0.418984i	$-0.862386\pi$
$173$		−	144.968i		−	0.837968i	0.907994	−	0.418984i	$-0.137614\pi$
$174$	−61.4131	+	123.129i	−0.352949	+	0.707636i
$175$		0			0
$176$	−32.6555	−	58.9966i	−0.185542	−	0.335208i
$177$	−151.810	+	151.810i	−0.857682	+	0.857682i
$178$	24.5670	+	73.4602i	0.138017	+	0.412698i
$179$	−71.1438	+	71.1438i	−0.397451	+	0.397451i	−0.877333	−	0.479882i	$-0.840680\pi$
$179$	−71.1438	+	71.1438i	−0.397451	+	0.397451i	0.479882	+	0.877333i	$0.340680\pi$
$180$		0			0
$181$	−192.954	+	192.954i	−1.06604	+	1.06604i	−0.0683832	+	0.997659i	$0.521784\pi$
$181$	−192.954	+	192.954i	−1.06604	+	1.06604i	−0.997659	+	0.0683832i	$0.978216\pi$
$182$	−289.349	−	144.319i	−1.58983	−	0.792963i
$183$	−33.5717	+	33.5717i	−0.183452	+	0.183452i
$184$	−23.0589	+	4.26284i	−0.125320	+	0.0231676i
$185$		0			0
$186$	124.390	−	41.5994i	0.668765	−	0.223653i
$187$			39.7496i			0.212565i
$188$	−37.2626	+	264.554i	−0.198205	+	1.40720i
$189$	154.167	−	154.167i	0.815696	−	0.815696i
$190$		0			0
$191$	−209.558			−1.09716			−0.548581	−	0.836097i	$-0.684832\pi$
$191$	−209.558			−1.09716			−0.548581	+	0.836097i	$0.684832\pi$
$192$	165.759	−	63.4558i	0.863331	−	0.330499i
$193$	90.2693	+	90.2693i	0.467717	+	0.467717i	0.901174	−	0.433457i	$-0.142707\pi$
$193$	90.2693	+	90.2693i	0.467717	+	0.467717i	−0.433457	+	0.901174i	$0.642707\pi$
$194$	21.6135	+	10.7802i	0.111410	+	0.0555680i
$195$		0			0
$196$	−22.0332	−	29.2575i	−0.112414	−	0.149273i
$197$			67.8338i			0.344334i	0.985068	+	0.172167i	$0.0550768\pi$
$197$			67.8338i			0.344334i	−0.985068	+	0.172167i	$0.944923\pi$
$198$	−9.87254	−	4.92414i	−0.0498613	−	0.0248694i
$199$	278.771			1.40086			0.700430	−	0.713721i	$-0.252991\pi$
$199$	278.771			1.40086			0.700430	+	0.713721i	$0.252991\pi$
$200$		0			0
$201$			302.495i			1.50495i
$202$	−164.549	−	82.0723i	−0.814599	−	0.406299i
$203$	189.180			0.931922
$204$	−103.605	−	14.5928i	−0.507867	−	0.0715335i
$205$		0			0
$206$	83.2820	+	41.5387i	0.404281	+	0.201644i
$207$	−2.71288	+	2.71288i	−0.0131057	+	0.0131057i
$208$	−326.003	−	93.6942i	−1.56732	−	0.450453i
$209$		−	85.2908i		−	0.408090i
$210$		0			0
$211$	−26.5489	−	26.5489i	−0.125824	−	0.125824i	0.641391	−	0.767215i	$-0.278358\pi$
$211$	−26.5489	−	26.5489i	−0.125824	−	0.125824i	−0.767215	+	0.641391i	$0.778358\pi$
$212$	−317.028	+	238.747i	−1.49542	+	1.12616i
$213$	−202.914			−0.952648
$214$	−37.8471	+	12.6571i	−0.176856	+	0.0591452i
$215$		0			0
$216$	129.632	−	188.432i	0.600148	−	0.872369i
$217$	−127.517	−	127.517i	−0.587635	−	0.587635i
$218$	79.5164	+	39.6605i	0.364754	+	0.181929i
$219$	47.1918	+	47.1918i	0.215488	+	0.215488i
$220$		0			0
$221$	141.388	+	141.388i	0.639763	+	0.639763i
$222$	−114.914	−	343.615i	−0.517631	−	1.54782i
$223$	−90.1705	−	90.1705i	−0.404352	−	0.404352i	0.475412	−	0.879764i	$-0.342299\pi$
$223$	−90.1705	−	90.1705i	−0.404352	−	0.404352i	−0.879764	+	0.475412i	$0.842299\pi$
$224$	−179.795	−	165.003i	−0.802656	−	0.736621i
$225$		0			0
$226$	60.8244	−	121.949i	0.269135	−	0.539595i
$227$	346.057			1.52448			0.762240	−	0.647294i	$-0.224100\pi$
$227$	346.057			1.52448			0.762240	+	0.647294i	$0.224100\pi$
$228$	222.305	+	31.3119i	0.975023	+	0.137333i
$229$	73.4761	+	73.4761i	0.320856	+	0.320856i	0.849096	−	0.528239i	$-0.177148\pi$
$229$	73.4761	+	73.4761i	0.320856	+	0.320856i	−0.528239	+	0.849096i	$0.677148\pi$
$230$		0			0
$231$		−	89.1323i		−	0.385854i
$232$	195.150	−	36.0770i	0.841165	−	0.155504i
$233$	−86.7985	+	86.7985i	−0.372526	+	0.372526i	−0.868396	−	0.495871i	$-0.834849\pi$
$233$	−86.7985	+	86.7985i	−0.372526	+	0.372526i	0.495871	+	0.868396i	$0.334849\pi$
$234$	−52.6312	+	17.6013i	−0.224920	+	0.0752191i
$235$		0			0
$236$	306.629	+	43.1890i	1.29928	+	0.183004i
$237$	−5.96613			−0.0251736
$238$	45.6246	+	136.427i	0.191700	+	0.573221i
$239$		−	204.791i		−	0.856868i	−0.903573	−	0.428434i	$-0.859065\pi$
$239$		−	204.791i		−	0.856868i	0.903573	−	0.428434i	$-0.140935\pi$
$240$		0			0
$241$	98.8804			0.410292			0.205146	−	0.978731i	$-0.434233\pi$
$241$	98.8804			0.410292			0.205146	+	0.978731i	$0.434233\pi$
$242$	195.817	−	65.4863i	0.809160	−	0.270604i
$243$		−	70.0893i		−	0.288433i
$244$	67.8091	+	9.55097i	0.277906	+	0.0391433i
$245$		0			0
$246$	2.08019	+	6.22017i	0.00845605	+	0.0252852i
$247$	−303.376	−	303.376i	−1.22824	−	1.22824i
$248$	−155.859	−	107.223i	−0.628462	−	0.432352i
$249$	−212.115			−0.851867
$250$		0			0
$251$	−38.3371	+	38.3371i	−0.152737	+	0.152737i	−0.779339	−	0.626602i	$-0.784445\pi$
$251$	−38.3371	+	38.3371i	−0.152737	+	0.152737i	0.626602	+	0.779339i	$0.284445\pi$
$252$	−39.5360	−	5.56868i	−0.156889	−	0.0220979i
$253$			12.3534i			0.0488277i
$254$	−418.041	−	208.507i	−1.64583	−	0.820894i
$255$		0			0
$256$	−216.935	−	135.923i	−0.847403	−	0.530950i
$257$	−166.481	+	166.481i	−0.647785	+	0.647785i	−0.952457	−	0.304672i	$-0.901453\pi$
$257$	−166.481	+	166.481i	−0.647785	+	0.647785i	0.304672	+	0.952457i	$0.401453\pi$
$258$	50.3631	−	16.8427i	0.195206	−	0.0652819i
$259$	−352.252	+	352.252i	−1.36005	+	1.36005i
$260$		0			0
$261$	22.9594	−	22.9594i	0.0879671	−	0.0879671i
$262$	13.8494	−	27.7671i	0.0528604	−	0.105981i
$263$	−78.7097	+	78.7097i	−0.299276	+	0.299276i	−0.840730	−	0.541454i	$-0.817874\pi$
$263$	−78.7097	+	78.7097i	−0.299276	+	0.299276i	0.541454	+	0.840730i	$0.317874\pi$
$264$	−16.9977	−	91.9452i	−0.0643851	−	0.348277i
$265$		0			0
$266$	−97.8969	−	292.731i	−0.368034	−	1.10049i
$267$			107.408i			0.402279i
$268$	348.522	−	262.464i	1.30046	−	0.979345i
$269$	98.2650	−	98.2650i	0.365297	−	0.365297i	−0.500461	−	0.865759i	$-0.666836\pi$
$269$	98.2650	−	98.2650i	0.365297	−	0.365297i	0.865759	+	0.500461i	$0.166836\pi$
$270$		0			0
$271$	−115.967			−0.427922			−0.213961	−	0.976842i	$-0.568637\pi$
$271$	−115.967			−0.427922			−0.213961	+	0.976842i	$0.568637\pi$
$272$	73.0812	+	132.031i	0.268681	+	0.485409i
$273$	−317.040	−	317.040i	−1.16132	−	1.16132i
$274$	154.522	−	309.804i	0.563947	−	1.13067i
$275$		0			0
$276$	−32.1984	−	4.53518i	−0.116661	−	0.0164318i
$277$			340.610i			1.22964i	0.788668	+	0.614819i	$0.210771\pi$
$277$			340.610i			1.22964i	−0.788668	+	0.614819i	$0.789229\pi$
$278$	206.423	−	413.864i	0.742530	−	1.48872i
$279$	−30.9516			−0.110938
$280$		0			0
$281$		−	103.541i		−	0.368474i	−0.982882	−	0.184237i	$-0.941019\pi$
$281$		−	103.541i		−	0.368474i	0.982882	−	0.184237i	$-0.0589814\pi$
$282$	−165.350	+	331.515i	−0.586348	+	1.17558i
$283$	−561.986			−1.98582			−0.992908	−	0.118887i	$-0.962068\pi$
$283$	−561.986			−1.98582			−0.992908	+	0.118887i	$0.962068\pi$
$284$	176.062	+	233.790i	0.619936	+	0.823203i
$285$		0			0
$286$	−79.7565	+	159.906i	−0.278869	+	0.559112i
$287$	6.37651	−	6.37651i	0.0222178	−	0.0222178i
$288$	−41.8456	+	1.79517i	−0.145297	+	0.00623322i
$289$			200.043i			0.692189i
$290$		0			0
$291$	23.6819	+	23.6819i	0.0813811	+	0.0813811i
$292$	13.4258	−	95.3193i	0.0459787	−	0.326436i
$293$	−1.90920			−0.00651604			−0.00325802	−	0.999995i	$-0.501037\pi$
$293$	−1.90920			−0.00651604			−0.00325802	+	0.999995i	$0.501037\pi$
$294$	−16.1077	−	48.1651i	−0.0547880	−	0.163827i
$295$		0			0
$296$	−296.193	+	430.543i	−1.00065	+	1.45454i
$297$	−85.1986	−	85.1986i	−0.286864	−	0.286864i
$298$	230.968	−	463.074i	0.775060	−	1.55394i
$299$	43.9406	+	43.9406i	0.146959	+	0.146959i
$300$		0			0
$301$	−51.6289	−	51.6289i	−0.171525	−	0.171525i
$302$	189.871	−	63.4978i	0.628712	−	0.210258i
$303$	−180.296	−	180.296i	−0.595037	−	0.595037i
$304$	−156.811	−	283.300i	−0.515824	−	0.931907i
$305$		0			0
$306$	22.0942	+	11.0200i	0.0722034	+	0.0360130i
$307$	−465.516			−1.51634			−0.758169	−	0.652058i	$-0.773906\pi$
$307$	−465.516			−1.51634			−0.758169	+	0.652058i	$0.773906\pi$
$308$	−102.695	+	77.3372i	−0.333425	+	0.251095i
$309$	91.2520	+	91.2520i	0.295314	+	0.295314i
$310$		0			0
$311$			212.375i			0.682879i	0.939904	+	0.341439i	$0.110914\pi$
$311$			212.375i			0.682879i	−0.939904	+	0.341439i	$0.889086\pi$
$312$	−387.505	−	266.585i	−1.24200	−	0.854440i
$313$	−46.0307	+	46.0307i	−0.147063	+	0.147063i	−0.776805	−	0.629742i	$-0.783161\pi$
$313$	−46.0307	+	46.0307i	−0.147063	+	0.147063i	0.629742	+	0.776805i	$0.283161\pi$
$314$	17.6896	+	52.8954i	0.0563364	+	0.168457i
$315$		0			0
$316$	5.17661	+	6.87395i	0.0163817	+	0.0217530i
$317$	430.649			1.35851			0.679257	−	0.733901i	$-0.262302\pi$
$317$	430.649			1.35851			0.679257	+	0.733901i	$0.262302\pi$
$318$	−521.907	+	174.539i	−1.64122	+	0.548866i
$319$		−	104.548i		−	0.327738i
$320$		0			0
$321$	−55.3375			−0.172391
$322$	14.1793	+	42.3988i	0.0440350	+	0.131673i
$323$			190.876i			0.590948i
$324$	215.703	−	162.441i	0.665750	−	0.501362i
$325$		0			0
$326$	231.738	−	77.4994i	0.710854	−	0.237728i
$327$	87.1261	+	87.1261i	0.266441	+	0.266441i
$328$	5.36173	−	7.79375i	0.0163467	−	0.0237614i
$329$	509.353			1.54819
$330$		0			0
$331$	3.70469	−	3.70469i	0.0111924	−	0.0111924i	−0.701488	−	0.712681i	$-0.747481\pi$
$331$	3.70469	−	3.70469i	0.0111924	−	0.0111924i	0.712681	+	0.701488i	$0.247481\pi$
$332$	184.045	+	244.390i	0.554352	+	0.736116i
$333$			85.5005i			0.256758i
$334$	129.041	−	258.718i	0.386351	−	0.774605i
$335$		0			0
$336$	−163.873	−	296.060i	−0.487719	−	0.881130i
$337$	226.237	−	226.237i	0.671327	−	0.671327i	−0.286695	−	0.958022i	$-0.592557\pi$
$337$	226.237	−	226.237i	0.671327	−	0.671327i	0.958022	+	0.286695i	$0.0925567\pi$
$338$	177.888	+	531.920i	0.526297	+	1.57373i
$339$	133.619	−	133.619i	0.394156	−	0.394156i
$340$		0			0
$341$	−70.4709	+	70.4709i	−0.206659	+	0.206659i
$342$	−47.4077	−	23.6456i	−0.138619	−	0.0691391i
$343$	214.853	−	214.853i	0.626394	−	0.626394i
$344$	−63.1039	−	43.4125i	−0.183442	−	0.126199i
$345$		0			0
$346$	−274.968	+	91.9566i	−0.794705	+	0.265770i
$347$			231.886i			0.668259i	0.942527	+	0.334130i	$0.108442\pi$
$347$			231.886i			0.668259i	−0.942527	+	0.334130i	$0.891558\pi$
$348$	272.499	+	38.3817i	0.783044	+	0.110292i
$349$	205.898	−	205.898i	0.589965	−	0.589965i	−0.347657	−	0.937622i	$-0.613022\pi$
$349$	205.898	−	205.898i	0.589965	−	0.589965i	0.937622	+	0.347657i	$0.113022\pi$
$350$		0			0
$351$	−606.096			−1.72677
$352$	−91.1873	+	99.3618i	−0.259055	+	0.282278i
$353$	299.539	+	299.539i	0.848551	+	0.848551i	0.989952	−	0.141401i	$-0.0451607\pi$
$353$	299.539	+	299.539i	0.848551	+	0.848551i	−0.141401	+	0.989952i	$0.545161\pi$
$354$	384.240	+	191.648i	1.08542	+	0.541378i
$355$		0			0
$356$	123.752	−	93.1947i	0.347617	−	0.261783i
$357$			199.473i			0.558749i
$358$	180.070	+	89.8135i	0.502987	+	0.250876i
$359$	−108.844			−0.303187			−0.151593	−	0.988443i	$-0.548440\pi$
$359$	−108.844			−0.303187			−0.151593	+	0.988443i	$0.548440\pi$
$360$		0			0
$361$		−	48.5638i		−	0.134526i
$362$	488.378	+	243.589i	1.34911	+	0.672898i
$363$	286.310			0.788732
$364$	−90.1961	+	640.366i	−0.247791	+	1.75925i
$365$		0			0
$366$	84.9722	+	42.3817i	0.232165	+	0.115797i
$367$	−271.565	+	271.565i	−0.739960	+	0.739960i	−0.972570	−	0.232610i	$-0.925274\pi$
$367$	−271.565	+	271.565i	−0.739960	+	0.739960i	0.232610	+	0.972570i	$0.425274\pi$
$368$	22.7123	+	41.0328i	0.0617181	+	0.111502i
$369$		−	1.54774i		−	0.00419442i
$370$		0			0
$371$	535.025	+	535.025i	1.44211	+	1.44211i
$372$	−157.807	−	209.549i	−0.424212	−	0.563305i
$373$	−205.735			−0.551569			−0.275784	−	0.961220i	$-0.588938\pi$
$373$	−205.735			−0.551569			−0.275784	+	0.961220i	$0.588938\pi$
$374$	75.3948	−	25.2140i	0.201590	−	0.0674171i
$375$		0			0
$376$	525.427	−	97.1345i	1.39741	−	0.258336i
$377$	−371.875	−	371.875i	−0.986405	−	0.986405i
$378$	−390.206	−	194.623i	−1.03229	−	0.514877i
$379$	146.474	+	146.474i	0.386475	+	0.386475i	0.873428	−	0.486953i	$-0.161892\pi$
$379$	146.474	+	146.474i	0.386475	+	0.386475i	−0.486953	+	0.873428i	$0.661892\pi$
$380$		0			0
$381$	−458.048	−	458.048i	−1.20223	−	1.20223i
$382$	132.927	+	397.478i	0.347977	+	1.04052i
$383$	−77.8502	−	77.8502i	−0.203264	−	0.203264i	0.598133	−	0.801397i	$-0.295910\pi$
$383$	−77.8502	−	77.8502i	−0.203264	−	0.203264i	−0.801397	+	0.598133i	$0.795910\pi$
$384$	−225.504	−	274.152i	−0.587250	−	0.713937i
$385$		0			0
$386$	113.958	−	228.477i	0.295228	−	0.591910i
$387$	−12.5317			−0.0323815
$388$	6.73737	−	47.8334i	0.0173643	−	0.123282i
$389$	91.3251	+	91.3251i	0.234769	+	0.234769i	0.814680	−	0.579911i	$-0.196913\pi$
$389$	91.3251	+	91.3251i	0.234769	+	0.234769i	−0.579911	+	0.814680i	$0.696913\pi$
$390$		0			0
$391$		−	27.6463i		−	0.0707067i
$392$	−41.5179	+	60.3499i	−0.105913	+	0.153954i
$393$	30.4244	−	30.4244i	0.0774158	−	0.0774158i
$394$	128.663	−	43.0284i	0.326557	−	0.109209i
$395$		0			0
$396$	−3.07747	+	21.8492i	−0.00777140	+	0.0551747i
$397$	181.720			0.457732			0.228866	−	0.973458i	$-0.426498\pi$
$397$	181.720			0.457732			0.228866	+	0.973458i	$0.426498\pi$
$398$	−176.831	−	528.758i	−0.444298	−	1.32854i
$399$		−	428.011i		−	1.07271i
$400$		0			0
$401$	−559.201			−1.39452			−0.697258	−	0.716821i	$-0.745597\pi$
$401$	−559.201			−1.39452			−0.697258	+	0.716821i	$0.745597\pi$
$402$	573.755	−	191.879i	1.42725	−	0.477310i
$403$			501.324i			1.24398i
$404$	−51.2933	+	364.167i	−0.126964	+	0.901405i
$405$		0			0
$406$	−120.001	−	358.826i	−0.295569	−	0.883808i
$407$	194.668	+	194.668i	0.478301	+	0.478301i
$408$	38.0399	+	205.768i	0.0932351	+	0.504334i
$409$	−724.291			−1.77088			−0.885441	−	0.464752i	$-0.846144\pi$
$409$	−724.291			−1.77088			−0.885441	+	0.464752i	$0.846144\pi$
$410$		0			0
$411$	339.453	−	339.453i	0.825919	−	0.825919i
$412$	25.9607	−	184.313i	0.0630114	−	0.447363i
$413$		−	590.362i		−	1.42945i
$414$	6.86647	+	3.42480i	0.0165857	+	0.00827246i
$415$		0			0
$416$	29.0764	+	677.776i	0.0698952	+	1.62927i
$417$	453.471	−	453.471i	1.08746	−	1.08746i
$418$	−161.775	+	54.1017i	−0.387021	+	0.129430i
$419$	76.4657	−	76.4657i	0.182496	−	0.182496i	−0.609947	−	0.792442i	$-0.708809\pi$
$419$	76.4657	−	76.4657i	0.182496	−	0.182496i	0.792442	+	0.609947i	$0.208809\pi$
$420$		0			0
$421$	470.702	−	470.702i	1.11806	−	1.11806i	0.126030	−	0.992026i	$-0.459776\pi$
$421$	470.702	−	470.702i	1.11806	−	1.11806i	0.992026	−	0.126030i	$-0.0402236\pi$
$422$	−33.5159	+	67.1969i	−0.0794215	+	0.159234i
$423$	61.8165	−	61.8165i	0.146138	−	0.146138i
$424$	653.939	+	449.879i	1.54231	+	1.06103i
$425$		0			0
$426$	128.713	+	384.876i	0.302143	+	0.903465i
$427$		−	130.555i		−	0.305749i
$428$	48.0145	+	63.7577i	0.112183	+	0.148967i
$429$	−175.209	+	175.209i	−0.408413	+	0.408413i
$430$		0			0
$431$	185.108			0.429485			0.214742	−	0.976671i	$-0.431109\pi$
$431$	185.108			0.429485			0.214742	+	0.976671i	$0.431109\pi$
$432$	−439.635	−	126.353i	−1.01767	−	0.292483i
$433$	354.954	+	354.954i	0.819756	+	0.819756i	0.986072	−	0.166317i	$-0.0531874\pi$
$433$	354.954	+	354.954i	0.819756	+	0.819756i	−0.166317	+	0.986072i	$0.553187\pi$
$434$	−160.980	+	322.753i	−0.370922	+	0.743671i
$435$		0			0
$436$	24.7869	−	175.980i	0.0568507	−	0.403623i
$437$			59.3208i			0.135745i
$438$	59.5760	−	119.445i	0.136018	−	0.272707i
$439$	−155.719			−0.354714			−0.177357	−	0.984147i	$-0.556755\pi$
$439$	−155.719			−0.354714			−0.177357	+	0.984147i	$0.556755\pi$
$440$		0			0
$441$			11.9847i			0.0271763i
$442$	178.491	−	357.861i	0.403826	−	0.809641i
$443$	728.951			1.64549			0.822744	−	0.568412i	$-0.192442\pi$
$443$	728.951			1.64549			0.822744	+	0.568412i	$0.192442\pi$
$444$	−578.858	+	435.925i	−1.30373	+	0.981813i
$445$		0			0
$446$	−113.833	+	228.227i	−0.255232	+	0.511721i
$447$	507.390	−	507.390i	1.13510	−	1.13510i
$448$	−198.921	+	445.690i	−0.444020	+	0.994843i
$449$			46.9465i			0.104558i	0.998633	+	0.0522790i	$0.0166485\pi$
$449$			46.9465i			0.104558i	−0.998633	+	0.0522790i	$0.983351\pi$
$450$		0			0
$451$	−3.52391	−	3.52391i	−0.00781355	−	0.00781355i
$452$	−269.887	−	38.0138i	−0.597096	−	0.0841014i
$453$	277.616			0.612839
$454$	−219.511	−	656.381i	−0.483505	−	1.44577i
$455$		0			0
$456$	−81.6223	−	441.518i	−0.178996	−	0.968241i
$457$	−227.434	−	227.434i	−0.497667	−	0.497667i	0.413044	−	0.910711i	$-0.364466\pi$
$457$	−227.434	−	227.434i	−0.497667	−	0.497667i	−0.910711	+	0.413044i	$0.864466\pi$
$458$	92.7579	−	185.973i	0.202528	−	0.406054i
$459$	190.670	+	190.670i	0.415403	+	0.415403i
$460$		0			0
$461$	265.869	+	265.869i	0.576722	+	0.576722i	0.933999	−	0.357277i	$-0.116295\pi$
$461$	265.869	+	265.869i	0.576722	+	0.576722i	−0.357277	+	0.933999i	$0.616295\pi$
$462$	−169.061	+	56.5385i	−0.365933	+	0.122378i
$463$	−1.16661	−	1.16661i	−0.00251968	−	0.00251968i	0.705846	−	0.708366i	$-0.250567\pi$
$463$	−1.16661	−	1.16661i	−0.00251968	−	0.00251968i	−0.708366	+	0.705846i	$0.750567\pi$
$464$	−192.217	−	347.266i	−0.414260	−	0.748417i
$465$		0			0
$466$	219.693	+	109.576i	0.471444	+	0.235143i
$467$	−632.343			−1.35405			−0.677027	−	0.735958i	$-0.736732\pi$
$467$	−632.343			−1.35405			−0.677027	+	0.735958i	$0.736732\pi$
$468$	66.7702	+	88.6631i	0.142671	+	0.189451i
$469$	−588.175	−	588.175i	−1.25411	−	1.25411i
$470$		0			0
$471$			77.3400i			0.164204i
$472$	−112.583	−	608.993i	−0.238523	−	1.29024i
$473$	−28.5322	+	28.5322i	−0.0603217	+	0.0603217i
$474$	3.78444	+	11.3162i	0.00798406	+	0.0238739i
$475$		0			0
$476$	229.826	−	173.077i	0.482827	−	0.363606i
$477$	129.864			0.272252
$478$	−388.437	+	129.904i	−0.812630	+	0.271765i
$479$			552.415i			1.15327i	0.817003	+	0.576633i	$0.195634\pi$
$479$			552.415i			1.15327i	−0.817003	+	0.576633i	$0.804366\pi$
$480$		0			0
$481$	1384.85			2.87912
$482$	−62.7219	−	187.551i	−0.130128	−	0.389110i
$483$			61.9926i			0.128349i
$484$	−248.421	−	329.875i	−0.513267	−	0.681560i
$485$		0			0
$486$	−132.941	+	44.4591i	−0.273542	+	0.0914796i
$487$	285.326	+	285.326i	0.585886	+	0.585886i	0.936515	−	0.350629i	$-0.114032\pi$
$487$	285.326	+	285.326i	0.585886	+	0.585886i	−0.350629	+	0.936515i	$0.614032\pi$
$488$	−24.8970	−	134.675i	−0.0510185	−	0.275973i
$489$	338.832			0.692908
$490$		0			0
$491$	−617.833	+	617.833i	−1.25831	+	1.25831i	−0.306418	+	0.951897i	$0.599130\pi$
$491$	−617.833	+	617.833i	−1.25831	+	1.25831i	−0.951897	+	0.306418i	$0.900870\pi$
$492$	10.4786	−	7.89117i	0.0212979	−	0.0160390i
$493$			233.974i			0.474592i
$494$	−382.989	+	767.864i	−0.775281	+	1.55438i
$495$		0			0
$496$	−104.511	+	363.638i	−0.210707	+	0.733141i
$497$	394.550	−	394.550i	0.793862	−	0.793862i
$498$	134.549	+	402.327i	0.270179	+	0.807886i
$499$	−430.585	+	430.585i	−0.862895	+	0.862895i	−0.991673	−	0.128778i	$-0.958894\pi$
$499$	−430.585	+	430.585i	−0.862895	+	0.862895i	0.128778	+	0.991673i	$0.458894\pi$
$500$		0			0
$501$	283.477	−	283.477i	0.565823	−	0.565823i
$502$	97.0337	+	48.3976i	0.193294	+	0.0964096i
$503$	−102.108	+	102.108i	−0.202998	+	0.202998i	−0.801283	−	0.598285i	$-0.795849\pi$
$503$	−102.108	+	102.108i	−0.202998	+	0.202998i	0.598285	+	0.801283i	$0.295849\pi$
$504$	14.5162	+	78.5220i	0.0288019	+	0.155798i
$505$		0			0
$506$	23.4313	−	7.83604i	0.0463069	−	0.0154862i
$507$			777.737i			1.53400i
$508$	−130.312	+	925.178i	−0.256520	+	1.82122i
$509$	350.381	−	350.381i	0.688372	−	0.688372i	−0.273500	−	0.961872i	$-0.588181\pi$
$509$	350.381	−	350.381i	0.688372	−	0.688372i	0.961872	+	0.273500i	$0.0881813\pi$
$510$		0			0
$511$	−183.521			−0.359141
$512$	−120.205	+	497.689i	−0.234775	+	0.972050i
$513$	−409.121	−	409.121i	−0.797507	−	0.797507i
$514$	421.374	+	210.169i	0.819793	+	0.408889i
$515$		0			0
$516$	−63.8927	−	84.8421i	−0.123823	−	0.164423i
$517$		−	281.489i		−	0.544466i
$518$	891.572	+	444.691i	1.72118	+	0.858476i
$519$	−402.039			−0.774642
$520$		0			0
$521$			89.0292i			0.170881i	0.996343	+	0.0854407i	$0.0272298\pi$
$521$			89.0292i			0.170881i	−0.996343	+	0.0854407i	$0.972770\pi$
$522$	−58.1118	−	28.9845i	−0.111325	−	0.0555258i
$523$	399.222			0.763331			0.381666	−	0.924300i	$-0.375351\pi$
$523$	399.222			0.763331			0.381666	+	0.924300i	$0.375351\pi$
$524$	−61.4521	−	8.65557i	−0.117275	−	0.0165183i
$525$		0			0
$526$	199.219	+	99.3649i	0.378744	+	0.188907i
$527$	157.710	−	157.710i	0.299260	−	0.299260i
$528$	−163.614	+	90.5630i	−0.309876	+	0.171521i
$529$			520.408i			0.983758i
$530$		0			0
$531$	−71.6480	−	71.6480i	−0.134930	−	0.134930i
$532$	−493.137	+	371.371i	−0.926950	+	0.698065i
$533$	−25.0688			−0.0470334
$534$	203.726	−	68.1314i	0.381510	−	0.127587i
$535$		0			0
$536$	−718.903	−	494.571i	−1.34124	−	0.922707i
$537$	197.302	+	197.302i	0.367415	+	0.367415i
$538$	−248.715	−	124.052i	−0.462296	−	0.230580i
$539$	27.2870	+	27.2870i	0.0506252	+	0.0506252i
$540$		0			0
$541$	151.552	+	151.552i	0.280133	+	0.280133i	0.833162	−	0.553029i	$-0.186528\pi$
$541$	151.552	+	151.552i	0.280133	+	0.280133i	−0.553029	+	0.833162i	$0.686528\pi$
$542$	73.5603	+	219.960i	0.135720	+	0.405830i
$543$	535.116	+	535.116i	0.985480	+	0.985480i
$544$	204.072	−	222.367i	0.375133	−	0.408762i
$545$		0			0
$546$	−400.239	+	802.449i	−0.733038	+	1.46969i
$547$	327.523			0.598762			0.299381	−	0.954134i	$-0.403220\pi$
$547$	327.523			0.598762			0.299381	+	0.954134i	$0.403220\pi$
$548$	−685.636	−	96.5723i	−1.25116	−	0.176227i
$549$	−15.8445	−	15.8445i	−0.0288607	−	0.0288607i
$550$		0			0
$551$		−	502.039i		−	0.911141i
$552$	11.8221	+	63.9490i	0.0214168	+	0.115850i
$553$	11.6006	−	11.6006i	0.0209777	−	0.0209777i
$554$	646.049	−	216.056i	1.16615	−	0.389993i
$555$		0			0
$556$	−915.933	−	129.010i	−1.64736	−	0.232032i
$557$	−609.704			−1.09462			−0.547311	−	0.836930i	$-0.684348\pi$
$557$	−609.704			−1.09462			−0.547311	+	0.836930i	$0.684348\pi$
$558$	19.6332	+	58.7072i	0.0351850	+	0.105210i
$559$			202.976i			0.363105i
$560$		0			0
$561$	110.237			0.196501
$562$	−196.391	+	65.6784i	−0.349451	+	0.116865i
$563$		−	104.576i		−	0.185748i	−0.995678	−	0.0928738i	$-0.970395\pi$
$563$		−	104.576i		−	0.185748i	0.995678	−	0.0928738i	$-0.0296053\pi$
$564$	733.684	+	103.340i	1.30086	+	0.183227i
$565$		0			0
$566$	356.479	+	1065.94i	0.629822	+	1.88329i
$567$	−364.026	−	364.026i	−0.642021	−	0.642021i
$568$	331.760	−	482.242i	0.584084	−	0.849018i
$569$	−153.954			−0.270569			−0.135284	−	0.990807i	$-0.543195\pi$
$569$	−153.954			−0.270569			−0.135284	+	0.990807i	$0.543195\pi$
$570$		0			0
$571$	475.501	−	475.501i	0.832751	−	0.832751i	−0.155141	−	0.987892i	$-0.549583\pi$
$571$	475.501	−	475.501i	0.832751	−	0.832751i	0.987892	+	0.155141i	$0.0495832\pi$
$572$	353.892	+	49.8460i	0.618692	+	0.0871433i
$573$			581.164i			1.01425i
$574$	−16.1394	−	8.04985i	−0.0281173	−	0.0140241i
$575$		0			0
$576$	29.9485	+	78.2318i	0.0519940	+	0.135819i
$577$	−430.563	+	430.563i	−0.746210	+	0.746210i	−0.973765	−	0.227555i	$-0.926927\pi$
$577$	−430.563	+	430.563i	−0.746210	+	0.746210i	0.227555	+	0.973765i	$0.426927\pi$
$578$	379.429	−	126.891i	0.656452	−	0.219535i
$579$	250.343	−	250.343i	0.432371	−	0.432371i
$580$		0			0
$581$	412.440	−	412.440i	0.709879	−	0.709879i
$582$	29.8966	−	59.9404i	0.0513687	−	0.102990i
$583$	295.676	−	295.676i	0.507163	−	0.507163i
$584$	−189.313	+	34.9977i	−0.324165	+	0.0599276i
$585$		0			0
$586$	1.21105	+	3.62126i	0.00206663	+	0.00617963i
$587$		−	24.8014i		−	0.0422512i	−0.999777	−	0.0211256i	$-0.993275\pi$
$587$		−	24.8014i		−	0.0422512i	0.999777	−	0.0211256i	$-0.00672498\pi$
$588$	−81.1394	+	61.1043i	−0.137992	+	0.103919i
$589$	−338.399	+	338.399i	−0.574531	+	0.574531i
$590$		0			0
$591$	188.123			0.318312
$592$	1004.51	+	288.700i	1.69681	+	0.487669i
$593$	−714.962	−	714.962i	−1.20567	−	1.20567i	−0.972416	−	0.233255i	$-0.925062\pi$
$593$	−714.962	−	714.962i	−1.20567	−	1.20567i	−0.233255	−	0.972416i	$-0.574938\pi$
$594$	−107.557	+	215.643i	−0.181072	+	0.363036i
$595$		0			0
$596$	−1024.84	−	144.350i	−1.71953	−	0.242197i
$597$		−	773.113i		−	1.29500i
$598$	55.4716	−	111.217i	0.0927619	−	0.185981i
$599$	898.559			1.50010			0.750049	−	0.661382i	$-0.230030\pi$
$599$	898.559			1.50010			0.750049	+	0.661382i	$0.230030\pi$
$600$		0			0
$601$			498.405i			0.829293i	0.909983	+	0.414646i	$0.136095\pi$
$601$			498.405i			0.829293i	−0.909983	+	0.414646i	$0.863905\pi$
$602$	−65.1775	+	130.676i	−0.108268	+	0.217070i
$603$	−142.765			−0.236758
$604$	−240.878	−	319.858i	−0.398805	−	0.529567i
$605$		0			0
$606$	−227.610	+	456.342i	−0.375594	+	0.753039i
$607$	−476.327	+	476.327i	−0.784723	+	0.784723i	−0.980624	−	0.195900i	$-0.937237\pi$
$607$	−476.327	+	476.327i	−0.784723	+	0.784723i	0.195900	+	0.980624i	$0.437237\pi$
$608$	−437.879	+	477.133i	−0.720195	+	0.784758i
$609$		−	524.651i		−	0.861495i
$610$		0			0
$611$	−1001.24	−	1001.24i	−1.63870	−	1.63870i
$612$	6.88722	−	48.8973i	0.0112536	−	0.0798976i
$613$	−294.722			−0.480787			−0.240393	−	0.970676i	$-0.577276\pi$
$613$	−294.722			−0.480787			−0.240393	+	0.970676i	$0.577276\pi$
$614$	295.286	+	882.964i	0.480923	+	1.43805i
$615$		0			0
$616$	211.830	+	145.729i	0.343880	+	0.236573i
$617$	−248.885	−	248.885i	−0.403379	−	0.403379i	0.476043	−	0.879422i	$-0.342071\pi$
$617$	−248.885	−	248.885i	−0.403379	−	0.403379i	−0.879422	+	0.476043i	$0.842071\pi$
$618$	115.199	−	230.965i	0.186406	−	0.373730i
$619$	−320.358	−	320.358i	−0.517541	−	0.517541i	0.399286	−	0.916826i	$-0.369258\pi$
$619$	−320.358	−	320.358i	−0.517541	−	0.517541i	−0.916826	+	0.399286i	$0.869258\pi$
$620$		0			0
$621$	59.2567	+	59.2567i	0.0954214	+	0.0954214i
$622$	402.822	−	134.714i	0.647623	−	0.216582i
$623$	−208.847	−	208.847i	−0.335227	−	0.335227i
$624$	−259.841	+	904.099i	−0.416412	+	1.44888i
$625$		0			0
$626$	116.507	+	58.1103i	0.186113	+	0.0928279i
$627$	−236.536			−0.377250
$628$	89.1081	−	67.1053i	0.141892	−	0.106856i
$629$	−435.658	−	435.658i	−0.692619	−	0.692619i
$630$		0			0
$631$		−	110.857i		−	0.175685i	−0.996134	−	0.0878423i	$-0.972003\pi$
$631$		−	110.857i		−	0.175685i	0.996134	−	0.0878423i	$-0.0279972\pi$
$632$	9.75448	−	14.1790i	0.0154343	−	0.0224351i
$633$	−73.6276	+	73.6276i	−0.116315	+	0.116315i
$634$	−273.170	−	816.830i	−0.430867	−	1.28838i
$635$		0			0
$636$	662.113	+	879.210i	1.04106	+	1.38241i
$637$	194.117			0.304737
$638$	−198.302	+	66.3173i	−0.310818	+	0.103946i
$639$		−	95.7673i		−	0.149871i
$640$		0			0
$641$	−370.450			−0.577926			−0.288963	−	0.957340i	$-0.593310\pi$
$641$	−370.450			−0.577926			−0.288963	+	0.957340i	$0.593310\pi$
$642$	35.1017	+	104.961i	0.0546756	+	0.163491i
$643$		−	686.295i		−	1.06733i	−0.845695	−	0.533667i	$-0.820814\pi$
$643$		−	686.295i		−	1.06733i	0.845695	−	0.533667i	$-0.179186\pi$
$644$	71.4255	−	53.7889i	0.110909	−	0.0835232i
$645$		0			0
$646$	362.043	−	121.077i	0.560439	−	0.187426i
$647$	499.985	+	499.985i	0.772774	+	0.772774i	0.978591	−	0.205817i	$-0.0659851\pi$
$647$	499.985	+	499.985i	0.772774	+	0.772774i	−0.205817	+	0.978591i	$0.565985\pi$
$648$	−444.934	−	306.094i	−0.686627	−	0.472367i
$649$	−326.258			−0.502708
$650$		0			0
$651$	−353.641	+	353.641i	−0.543227	+	0.543227i
$652$	−293.993	−	390.389i	−0.450910	−	0.598756i
$653$		−	599.129i		−	0.917502i	−0.888565	−	0.458751i	$-0.848297\pi$
$653$		−	599.129i		−	0.917502i	0.888565	−	0.458751i	$-0.151703\pi$
$654$	109.990	−	220.522i	0.168180	−	0.337189i
$655$		0			0
$656$	−18.1838	−	5.22608i	−0.0277192	−	0.00796659i
$657$	−22.2726	+	22.2726i	−0.0339005	+	0.0339005i
$658$	−323.093	−	966.112i	−0.491023	−	1.46826i
$659$	−55.5691	+	55.5691i	−0.0843233	+	0.0843233i	−0.748010	−	0.663687i	$-0.768991\pi$
$659$	−55.5691	+	55.5691i	−0.0843233	+	0.0843233i	0.663687	+	0.748010i	$0.268991\pi$
$660$		0			0
$661$	24.3517	−	24.3517i	0.0368407	−	0.0368407i	−0.688446	−	0.725287i	$-0.741707\pi$
$661$	24.3517	−	24.3517i	0.0368407	−	0.0368407i	0.725287	+	0.688446i	$0.241707\pi$
$662$	−9.37681	−	4.67689i	−0.0141644	−	0.00706478i
$663$	392.109	−	392.109i	0.591416	−	0.591416i
$664$	346.802	−	504.108i	0.522293	−	0.759199i
$665$		0			0
$666$	162.173	−	54.2348i	0.243502	−	0.0814336i
$667$			72.7147i			0.109018i
$668$	−572.575	−	80.6477i	−0.857149	−	0.120730i
$669$	−250.069	+	250.069i	−0.373795	+	0.373795i
$670$		0			0
$671$	−72.1498			−0.107526
$672$	−457.601	+	498.623i	−0.680954	+	0.741998i
$673$	348.271	+	348.271i	0.517490	+	0.517490i	0.916811	−	0.399321i	$-0.130754\pi$
$673$	348.271	+	348.271i	0.517490	+	0.517490i	−0.399321	+	0.916811i	$0.630754\pi$
$674$	−572.621	−	285.607i	−0.849586	−	0.423749i
$675$		0			0
$676$	896.079	−	674.817i	1.32556	−	0.998250i
$677$		−	780.155i		−	1.15237i	−0.817319	−	0.576185i	$-0.804541\pi$
$677$		−	780.155i		−	1.15237i	0.817319	−	0.576185i	$-0.195459\pi$
$678$	−338.198	−	168.684i	−0.498818	−	0.248796i
$679$	−92.0950			−0.135633
$680$		0			0
$681$		−	959.715i		−	1.40927i
$682$	178.366	+	88.9640i	0.261534	+	0.130446i
$683$	−170.375			−0.249451			−0.124725	−	0.992191i	$-0.539805\pi$
$683$	−170.375			−0.249451			−0.124725	+	0.992191i	$0.539805\pi$
$684$	−14.7779	+	104.919i	−0.0216052	+	0.153390i
$685$		0			0
$686$	−543.807	−	271.235i	−0.792722	−	0.395387i
$687$	203.770	−	203.770i	0.296609	−	0.296609i
$688$	−42.3142	+	147.229i	−0.0615032	+	0.213996i
$689$		−	2103.41i		−	3.05285i
$690$		0			0
$691$	−51.2626	−	51.2626i	−0.0741861	−	0.0741861i	0.669040	−	0.743226i	$-0.266705\pi$
$691$	−51.2626	−	51.2626i	−0.0741861	−	0.0741861i	−0.743226	+	0.669040i	$0.766705\pi$
$692$	348.836	+	463.214i	0.504098	+	0.669384i
$693$	42.0668			0.0607025
$694$	439.828	−	147.090i	0.633758	−	0.211946i
$695$		0			0
$696$	−100.052	−	541.208i	−0.143752	−	0.777597i
$697$	7.88633	+	7.88633i	0.0113147	+	0.0113147i
$698$	−521.141	−	259.930i	−0.746620	−	0.372393i
$699$	240.717	+	240.717i	0.344374	+	0.344374i
$700$		0			0
$701$	68.3903	+	68.3903i	0.0975610	+	0.0975610i	0.754203	−	0.656642i	$-0.228024\pi$
$701$	68.3903	+	68.3903i	0.0975610	+	0.0975610i	−0.656642	+	0.754203i	$0.728024\pi$
$702$	384.460	+	1149.61i	0.547663	+	1.63762i
$703$	934.792	+	934.792i	1.32972	+	1.32972i
$704$	246.306	+	109.932i	0.349866	+	0.156153i
$705$		0			0
$706$	378.144	−	758.152i	0.535615	−	1.07387i
$707$	701.142			0.991714
$708$	119.775	−	850.371i	0.169174	−	1.20109i
$709$	815.622	+	815.622i	1.15038	+	1.15038i	0.986476	+	0.163908i	$0.0524101\pi$
$709$	815.622	+	815.622i	1.15038	+	1.15038i	0.163908	+	0.986476i	$0.447590\pi$
$710$		0			0
$711$		−	2.81577i		−	0.00396030i
$712$	−255.265	−	175.610i	−0.358518	−	0.246643i
$713$	49.0133	−	49.0133i	0.0687424	−	0.0687424i
$714$	378.350	−	126.530i	0.529902	−	0.177213i
$715$		0			0
$716$	56.1313	−	398.516i	0.0783957	−	0.556587i
$717$	−567.946			−0.792114
$718$	69.0420	+	206.449i	0.0961588	+	0.287534i
$719$		−	125.050i		−	0.173922i	−0.996212	−	0.0869612i	$-0.972284\pi$
$719$		−	125.050i		−	0.173922i	0.996212	−	0.0869612i	$-0.0277156\pi$
$720$		0			0
$721$	−354.864			−0.492183
$722$	−92.1131	+	30.8051i	−0.127581	+	0.0426663i
$723$		−	274.224i		−	0.379286i
$724$	152.237	−	1080.84i	0.210273	−	1.49288i
$725$		0			0
$726$	−181.612	−	543.056i	−0.250155	−	0.748011i
$727$	−307.763	−	307.763i	−0.423333	−	0.423333i	0.463016	−	0.886350i	$-0.346767\pi$
$727$	−307.763	−	307.763i	−0.423333	−	0.423333i	−0.886350	+	0.463016i	$0.846767\pi$
$728$	1271.82	−	235.119i	1.74701	−	0.322966i
$729$	−801.940			−1.10005
$730$		0			0
$731$	63.8535	−	63.8535i	0.0873510	−	0.0873510i
$732$	26.4876	−	188.054i	0.0361852	−	0.256905i
$733$			94.8581i			0.129411i	0.997904	+	0.0647054i	$0.0206108\pi$
$733$			94.8581i			0.129411i	−0.997904	+	0.0647054i	$0.979389\pi$
$734$	687.350	+	342.830i	0.936444	+	0.467071i
$735$		0			0
$736$	63.4219	−	69.1073i	0.0861710	−	0.0938959i
$737$	−325.049	+	325.049i	−0.441044	+	0.441044i
$738$	−2.93567	+	0.981765i	−0.00397787	+	0.00133030i
$739$	761.284	−	761.284i	1.03015	−	1.03015i	0.0306228	−	0.999531i	$-0.490251\pi$
$739$	761.284	−	761.284i	1.03015	−	1.03015i	0.999531	−	0.0306228i	$-0.00974907\pi$
$740$		0			0
$741$	−841.348	+	841.348i	−1.13542	+	1.13542i
$742$	675.427	−	1354.18i	0.910279	−	1.82504i
$743$	−700.467	+	700.467i	−0.942754	+	0.942754i	−0.998448	−	0.0556935i	$-0.982263\pi$
$743$	−700.467	+	700.467i	−0.942754	+	0.942754i	0.0556935	+	0.998448i	$0.482263\pi$
$744$	−297.361	+	432.241i	−0.399679	+	0.580969i
$745$		0			0
$746$	130.502	+	390.227i	0.174936	+	0.523092i
$747$		−	100.110i		−	0.134016i
$748$	−95.6490	−	127.011i	−0.127873	−	0.169800i
$749$	107.599	−	107.599i	0.143657	−	0.143657i
$750$		0			0
$751$	268.325			0.357291			0.178645	−	0.983914i	$-0.442829\pi$
$751$	268.325			0.357291			0.178645	+	0.983914i	$0.442829\pi$
$752$	−517.529	−	934.986i	−0.688203	−	1.24333i
$753$	106.320	+	106.320i	0.141195	+	0.141195i
$754$	−469.463	+	941.239i	−0.622630	+	1.24833i
$755$		0			0
$756$	−121.635	+	863.574i	−0.160893	+	1.14229i
$757$		−	777.969i		−	1.02770i	−0.857880	−	0.513850i	$-0.828219\pi$
$757$		−	777.969i		−	1.02770i	0.857880	−	0.513850i	$-0.171781\pi$
$758$	184.912	−	370.736i	0.243948	−	0.489097i
$759$	34.2596			0.0451378
$760$		0			0
$761$		−	1058.98i		−	1.39156i	−0.718254	−	0.695781i	$-0.755058\pi$
$761$		−	1058.98i		−	1.39156i	0.718254	−	0.695781i	$-0.244942\pi$
$762$	−578.250	+	1159.35i	−0.758858	+	1.52146i
$763$	−338.819			−0.444062
$764$	669.595	−	504.257i	0.876433	−	0.660022i
$765$		0			0
$766$	−98.2799	+	197.044i	−0.128303	+	0.257238i
$767$	−1160.49	+	1160.49i	−1.51302	+	1.51302i
$768$	−376.954	+	601.624i	−0.490825	+	0.783364i
$769$			262.583i			0.341461i	0.985318	+	0.170730i	$0.0546127\pi$
$769$			262.583i			0.341461i	−0.985318	+	0.170730i	$0.945387\pi$
$770$		0			0
$771$	461.699	+	461.699i	0.598832	+	0.598832i
$772$	−505.649	−	71.2211i	−0.654986	−	0.0922553i
$773$	405.962			0.525177			0.262588	−	0.964908i	$-0.415424\pi$
$773$	405.962			0.525177			0.262588	+	0.964908i	$0.415424\pi$
$774$	7.94909	+	23.7693i	0.0102701	+	0.0307097i
$775$		0			0
$776$	−95.0013	+	17.5627i	−0.122424	+	0.0226323i
$777$	976.895	+	976.895i	1.25727	+	1.25727i
$778$	115.291	−	231.150i	0.148189	−	0.297108i
$779$	−16.9217	−	16.9217i	−0.0217224	−	0.0217224i
$780$		0			0
$781$	−218.044	−	218.044i	−0.279185	−	0.279185i
$782$	−52.4380	+	17.5366i	−0.0670562	+	0.0224254i
$783$	−501.496	−	501.496i	−0.640480	−	0.640480i
$784$	140.804	+	40.4675i	0.179597	+	0.0516168i
$785$		0			0
$786$	−77.0061	−	38.4085i	−0.0979722	−	0.0488657i
$787$	−107.060			−0.136036			−0.0680181	−	0.997684i	$-0.521668\pi$
$787$	−107.060			−0.136036			−0.0680181	+	0.997684i	$0.521668\pi$
$788$	−163.228	−	216.747i	−0.207142	−	0.275060i
$789$	218.285	+	218.285i	0.276660	+	0.276660i
$790$		0			0
$791$			519.622i			0.656918i
$792$	43.3944	−	8.02221i	0.0547909	−	0.0101291i
$793$	−256.634	+	256.634i	−0.323624	+	0.323624i
$794$	−115.269	−	344.675i	−0.145174	−	0.434100i
$795$		0			0
$796$	−890.751	+	670.804i	−1.11903	+	0.842719i
$797$	615.958			0.772846			0.386423	−	0.922322i	$-0.373711\pi$
$797$	615.958			0.772846			0.386423	+	0.922322i	$0.373711\pi$
$798$	−811.827	+	271.496i	−1.01733	+	0.340221i
$799$			629.957i			0.788432i
$800$		0			0
$801$	−50.6924			−0.0632864
$802$	354.713	+	1060.66i	0.442285	+	1.32252i
$803$			101.421i			0.126303i
$804$	−727.889	−	966.553i	−0.905335	−	1.20218i
$805$		0			0
$806$	950.883	−	318.000i	1.17976	−	0.394542i
$807$	−272.517	−	272.517i	−0.337692	−	0.337692i
$808$	723.269	−	133.709i	0.895135	−	0.165481i
$809$	304.293			0.376135			0.188067	−	0.982156i	$-0.439778\pi$
$809$	304.293			0.376135			0.188067	+	0.982156i	$0.439778\pi$
$810$		0			0
$811$	−20.2059	+	20.2059i	−0.0249148	+	0.0249148i	−0.719454	−	0.694540i	$-0.755608\pi$
$811$	−20.2059	+	20.2059i	−0.0249148	+	0.0249148i	0.694540	+	0.719454i	$0.255608\pi$
$812$	−604.482	+	455.222i	−0.744436	+	0.560618i
$813$			321.610i			0.395584i
$814$	245.754	−	492.718i	0.301909	−	0.605305i
$815$		0			0
$816$	366.161	−	202.675i	0.448726	−	0.248377i
$817$	−137.011	+	137.011i	−0.167700	+	0.167700i
$818$	459.433	+	1373.79i	0.561654	+	1.67945i
$819$	149.630	−	149.630i	0.182699	−	0.182699i
$820$		0			0
$821$	−381.316	+	381.316i	−0.464453	+	0.464453i	−0.900112	−	0.435659i	$-0.856515\pi$
$821$	−381.316	+	381.316i	−0.464453	+	0.464453i	0.435659	+	0.900112i	$0.356515\pi$
$822$	−859.176	−	428.533i	−1.04523	−	0.521329i
$823$	−420.324	+	420.324i	−0.510721	+	0.510721i	−0.914747	−	0.404026i	$-0.867610\pi$
$823$	−420.324	+	420.324i	−0.510721	+	0.510721i	0.404026	+	0.914747i	$0.367610\pi$
$824$	−366.063	+	67.6731i	−0.444251	+	0.0821276i
$825$		0			0
$826$	−1119.77	+	374.479i	−1.35565	+	0.453365i
$827$		−	844.006i		−	1.02056i	−0.860007	−	0.510281i	$-0.829541\pi$
$827$		−	844.006i		−	1.02056i	0.860007	−	0.510281i	$-0.170459\pi$
$828$	2.14042	−	15.1964i	0.00258505	−	0.0183531i
$829$	−222.833	+	222.833i	−0.268798	+	0.268798i	−0.828616	−	0.559818i	$-0.810871\pi$
$829$	−222.833	+	222.833i	−0.268798	+	0.268798i	0.559818	+	0.828616i	$0.310871\pi$
$830$		0			0
$831$	944.609			1.13671
$832$	1267.12	−	485.078i	1.52298	−	0.583026i
$833$	−61.0668	−	61.0668i	−0.0733095	−	0.0733095i
$834$	−1147.76	−	572.471i	−1.37622	−	0.686417i
$835$		0			0
$836$	205.234	+	272.527i	0.245496	+	0.325990i
$837$			676.067i			0.807726i
$838$	−193.540	−	96.5320i	−0.230954	−	0.115193i
$839$	−554.445			−0.660841			−0.330420	−	0.943834i	$-0.607191\pi$
$839$	−554.445			−0.660841			−0.330420	+	0.943834i	$0.607191\pi$
$840$		0			0
$841$			225.607i			0.268260i
$842$	−1191.38	−	594.225i	−1.41494	−	0.705730i
$843$	−287.150			−0.340628
$844$	148.715	+	20.9466i	0.176203	+	0.0248183i
$845$		0			0
$846$	−156.462	−	78.0386i	−0.184943	−	0.0922442i
$847$	−556.705	+	556.705i	−0.657267	+	0.657267i
$848$	438.498	−	1525.72i	0.517096	−	1.79920i
$849$			1558.55i			1.83575i
$850$		0			0
$851$	−135.394	−	135.394i	−0.159100	−	0.159100i
$852$	648.366	−	488.270i	0.760993	−	0.573087i
$853$	−431.993			−0.506440			−0.253220	−	0.967409i	$-0.581490\pi$
$853$	−431.993			−0.506440			−0.253220	+	0.967409i	$0.581490\pi$
$854$	−247.629	+	82.8137i	−0.289964	+	0.0969715i
$855$		0			0
$856$	90.4754	−	131.514i	0.105696	−	0.153638i
$857$	457.844	+	457.844i	0.534241	+	0.534241i	0.921831	−	0.387591i	$-0.126693\pi$
$857$	457.844	+	457.844i	0.534241	+	0.534241i	−0.387591	+	0.921831i	$0.626693\pi$
$858$	443.465	+	221.188i	0.516859	+	0.257795i
$859$	−822.277	−	822.277i	−0.957249	−	0.957249i	0.0418737	−	0.999123i	$-0.486667\pi$
$859$	−822.277	−	822.277i	−0.957249	−	0.957249i	−0.999123	+	0.0418737i	$0.986667\pi$
$860$		0			0
$861$	−17.6839	−	17.6839i	−0.0205388	−	0.0205388i
$862$	−117.418	−	351.102i	−0.136216	−	0.407311i
$863$	−132.089	−	132.089i	−0.153058	−	0.153058i	0.626424	−	0.779482i	$-0.284518\pi$
$863$	−132.089	−	132.089i	−0.153058	−	0.153058i	−0.779482	+	0.626424i	$0.784518\pi$
$864$	39.2113	+	914.023i	0.0453835	+	1.05790i
$865$		0			0
$866$	448.102	−	898.412i	0.517439	−	1.03743i
$867$	554.775			0.639879
$868$	714.293	+	100.609i	0.822919	+	0.115909i
$869$	−6.41098	−	6.41098i	−0.00737742	−	0.00737742i
$870$		0			0
$871$			2312.37i			2.65485i
$872$	−349.511	+	64.6133i	−0.400816	+	0.0740978i
$873$	−11.1769	+	11.1769i	−0.0128029	+	0.0128029i
$874$	112.516	−	37.6284i	0.128737	−	0.0430531i
$875$		0			0
$876$	−264.348	−	37.2336i	−0.301767	−	0.0425041i
$877$	−363.488			−0.414468			−0.207234	−	0.978291i	$-0.566446\pi$
$877$	−363.488			−0.414468			−0.207234	+	0.978291i	$0.566446\pi$
$878$	98.7761	+	295.360i	0.112501	+	0.336401i
$879$			5.29476i			0.00602362i
$880$		0			0
$881$	−242.827			−0.275627			−0.137813	−	0.990458i	$-0.544007\pi$
$881$	−242.827			−0.275627			−0.137813	+	0.990458i	$0.544007\pi$
$882$	22.7320	−	7.60218i	0.0257732	−	0.00861925i
$883$		−	1629.94i		−	1.84592i	−0.384899	−	0.922959i	$-0.625764\pi$
$883$		−	1629.94i		−	1.84592i	0.384899	−	0.922959i	$-0.374236\pi$
$884$	−791.992	−	111.553i	−0.895918	−	0.126191i
$885$		0			0
$886$	−462.389	−	1382.63i	−0.521884	−	1.56053i
$887$	196.533	+	196.533i	0.221570	+	0.221570i	0.809160	−	0.587589i	$-0.199923\pi$
$887$	196.533	+	196.533i	0.221570	+	0.221570i	−0.587589	+	0.809160i	$0.699923\pi$
$888$	1194.02	+	821.429i	1.34462	+	0.925032i
$889$	1781.27			2.00368
$890$		0			0
$891$	−201.175	+	201.175i	−0.225786	+	0.225786i
$892$	505.096	+	71.1431i	0.566251	+	0.0797569i
$893$		−	1351.70i		−	1.51366i
$894$	−1284.24	−	640.540i	−1.43651	−	0.716488i
$895$		0			0
$896$	971.539	+	94.5917i	1.08431	+	0.105571i
$897$	121.860	−	121.860i	0.135853	−	0.135853i
$898$	89.0455	−	29.7792i	0.0991598	−	0.0331617i
$899$	−414.806	+	414.806i	−0.461408	+	0.461408i
$900$		0			0
$901$	−661.707	+	661.707i	−0.734414	+	0.734414i
$902$	−4.44867	+	8.91925i	−0.00493200	+	0.00988830i
$903$	−143.182	+	143.182i	−0.158562	+	0.158562i
$904$	99.0927	+	536.020i	0.109616	+	0.592943i
$905$		0			0
$906$	−176.098	−	526.567i	−0.194368	−	0.581199i
$907$		−	188.488i		−	0.207814i	−0.994587	−	0.103907i	$-0.966866\pi$
$907$		−	188.488i		−	0.207814i	0.994587	−	0.103907i	$-0.0331345\pi$
$908$	−1105.75	+	832.713i	−1.21778	+	0.917085i
$909$	85.0925	−	85.0925i	0.0936112	−	0.0936112i
$910$		0			0
$911$	1051.06			1.15374			0.576870	−	0.816836i	$-0.304274\pi$
$911$	1051.06			1.15374			0.576870	+	0.816836i	$0.304274\pi$
$912$	−785.672	+	434.881i	−0.861482	+	0.476843i
$913$	−227.930	−	227.930i	−0.249650	−	0.249650i
$914$	−287.118	+	575.650i	−0.314133	+	0.629814i
$915$		0			0
$916$	−411.581	−	57.9715i	−0.449324	−	0.0632877i
$917$			118.315i			0.129024i
$918$	240.706	−	482.598i	0.262207	−	0.525706i
$919$	−158.471			−0.172439			−0.0862195	−	0.996276i	$-0.527479\pi$
$919$	−158.471			−0.172439			−0.0862195	+	0.996276i	$0.527479\pi$
$920$		0			0
$921$			1291.01i			1.40175i
$922$	335.639	−	672.931i	0.364033	−	0.729860i
$923$	−1551.15			−1.68055
$924$	214.478	+	284.802i	0.232119	+	0.308227i
$925$		0			0
$926$	−1.47276	+	2.95277i	−0.00159045	+	0.00318874i
$927$	−43.0673	+	43.0673i	−0.0464588	+	0.0464588i
$928$	−536.747	+	584.864i	−0.578391	+	0.630241i
$929$			1081.59i			1.16425i	0.813100	+	0.582124i	$0.197778\pi$
$929$			1081.59i			1.16425i	−0.813100	+	0.582124i	$0.802222\pi$
$930$		0			0
$931$	131.031	+	131.031i	0.140743	+	0.140743i
$932$	68.4827	−	486.207i	0.0734793	−	0.521682i
$933$	588.978			0.631273
$934$	401.109	+	1199.39i	0.429453	+	1.28415i
$935$		0			0
$936$	125.817	−	182.887i	0.134420	−	0.195392i
$937$	484.345	+	484.345i	0.516910	+	0.516910i	0.916635	−	0.399725i	$-0.130894\pi$
$937$	484.345	+	484.345i	0.516910	+	0.516910i	−0.399725	+	0.916635i	$0.630894\pi$
$938$	−742.526	+	1488.71i	−0.791605	+	1.58711i
$939$	127.656	+	127.656i	0.135949	+	0.135949i
$940$		0			0
$941$	555.577	+	555.577i	0.590411	+	0.590411i	0.937742	−	0.347331i	$-0.112912\pi$
$941$	555.577	+	555.577i	0.590411	+	0.590411i	−0.347331	+	0.937742i	$0.612912\pi$
$942$	146.694	−	49.0584i	0.155726	−	0.0520790i
$943$	2.45092	+	2.45092i	0.00259907	+	0.00259907i
$944$	−1083.69	+	599.838i	−1.14798	+	0.635422i
$945$		0			0
$946$	72.2168	+	36.0197i	0.0763391	+	0.0380758i
$947$	476.289			0.502945			0.251473	−	0.967864i	$-0.419085\pi$
$947$	476.289			0.502945			0.251473	+	0.967864i	$0.419085\pi$
$948$	19.0634	−	14.3562i	0.0201091	−	0.0151437i
$949$	360.750	+	360.750i	0.380137	+	0.380137i
$950$		0			0
$951$		−	1194.31i		−	1.25585i
$952$	−474.065	−	326.134i	−0.497967	−	0.342578i
$953$	−80.9782	+	80.9782i	−0.0849719	+	0.0849719i	−0.748315	−	0.663343i	$-0.769137\pi$
$953$	−80.9782	+	80.9782i	−0.0849719	+	0.0849719i	0.663343	+	0.748315i	$0.269137\pi$
$954$	−82.3755	−	246.319i	−0.0863475	−	0.258196i
$955$		0			0
$956$	492.788	+	654.365i	0.515468	+	0.684482i
$957$	−289.943			−0.302971
$958$	1047.79	−	350.408i	1.09373	−	0.365771i
$959$			1320.07i			1.37651i
$960$		0			0
$961$	−401.801			−0.418107
$962$	−878.443	−	2626.71i	−0.913142	−	2.73047i
$963$		−	26.1170i		−	0.0271205i
$964$	−315.950	+	237.935i	−0.327749	+	0.246820i
$965$		0			0
$966$	117.584	−	39.3232i	0.121723	−	0.0407073i
$967$	226.347	+	226.347i	0.234072	+	0.234072i	0.814390	−	0.580318i	$-0.197072\pi$
$967$	226.347	+	226.347i	0.234072	+	0.234072i	−0.580318	+	0.814390i	$0.697072\pi$
$968$	−468.109	+	680.438i	−0.483584	+	0.702932i
$969$	529.355			0.546290
$970$		0			0
$971$	−375.576	+	375.576i	−0.386793	+	0.386793i	−0.873542	−	0.486749i	$-0.838183\pi$
$971$	−375.576	+	375.576i	−0.386793	+	0.386793i	0.486749	+	0.873542i	$0.338183\pi$
$972$	168.655	+	223.954i	0.173513	+	0.230406i
$973$			1763.47i			1.81241i
$974$	360.203	−	722.180i	0.369818	−	0.741458i
$975$		0			0
$976$	−239.651	+	132.650i	−0.245544	+	0.135912i
$977$	−201.023	+	201.023i	−0.205756	+	0.205756i	−0.802461	−	0.596705i	$-0.796476\pi$
$977$	−201.023	+	201.023i	−0.205756	+	0.205756i	0.596705	+	0.802461i	$0.296476\pi$
$978$	−214.928	−	642.677i	−0.219763	−	0.657134i
$979$	−115.417	+	115.417i	−0.117893	+	0.117893i
$980$		0			0
$981$	−41.1200	+	41.1200i	−0.0419164	+	0.0419164i
$982$	1563.77	+	779.966i	1.59244	+	0.794263i
$983$	−536.933	+	536.933i	−0.546218	+	0.546218i	−0.925345	−	0.379126i	$-0.876225\pi$
$983$	−536.933	+	536.933i	−0.546218	+	0.546218i	0.379126	+	0.925345i	$0.376225\pi$
$984$	−21.6143	−	14.8696i	−0.0219658	−	0.0151114i
$985$		0			0
$986$	443.789	−	148.415i	0.450090	−	0.150522i
$987$		−	1412.58i		−	1.43119i
$988$	1699.38	+	239.359i	1.72002	+	0.242266i
$989$	19.8445	−	19.8445i	0.0200652	−	0.0200652i
$990$		0			0
$991$	−1164.95			−1.17553			−0.587764	−	0.809032i	$-0.699992\pi$
$991$	−1164.95			−1.17553			−0.587764	+	0.809032i	$0.699992\pi$
$992$	756.021	−	32.4331i	0.762118	−	0.0326947i
$993$	−10.2742	−	10.2742i	−0.0103466	−	0.0103466i
$994$	−998.631	−	498.088i	−1.00466	−	0.501095i
$995$		0			0
$996$	677.765	−	510.410i	0.680487	−	0.512459i
$997$			1493.41i			1.49790i	0.662627	+	0.748950i	$0.269442\pi$
$997$			1493.41i			1.49790i	−0.662627	+	0.748950i	$0.730558\pi$
$998$	1089.84	+	543.580i	1.09202	+	0.544669i
$999$	1867.56			1.86943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.i.b.93.9		44
5.2	odd	4		400.3.t.b.157.19		44
5.3	odd	4		80.3.t.a.77.4	yes	44
5.4	even	2		80.3.i.a.13.14	✓	44
16.5	even	4		400.3.t.b.293.19		44
20.3	even	4		320.3.t.a.17.7		44
20.19	odd	2		320.3.i.a.273.7		44
40.3	even	4		640.3.t.a.417.16		44
40.13	odd	4		640.3.t.b.417.7		44
40.19	odd	2		640.3.i.a.33.16		44
40.29	even	2		640.3.i.b.33.7		44
80.3	even	4		640.3.i.a.97.7		44
80.13	odd	4		640.3.i.b.97.16		44
80.19	odd	4		640.3.t.a.353.16		44
80.29	even	4		640.3.t.b.353.7		44
80.37	odd	4	inner	400.3.i.b.357.9		44
80.43	even	4		320.3.i.a.177.16		44
80.53	odd	4		80.3.i.a.37.14	yes	44
80.59	odd	4		320.3.t.a.113.7		44
80.69	even	4		80.3.t.a.53.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.14	✓	44	5.4	even	2
80.3.i.a.37.14	yes	44	80.53	odd	4
80.3.t.a.53.4	yes	44	80.69	even	4
80.3.t.a.77.4	yes	44	5.3	odd	4
320.3.i.a.177.16		44	80.43	even	4
320.3.i.a.273.7		44	20.19	odd	2
320.3.t.a.17.7		44	20.3	even	4
320.3.t.a.113.7		44	80.59	odd	4
400.3.i.b.93.9		44	1.1	even	1	trivial
400.3.i.b.357.9		44	80.37	odd	4	inner
400.3.t.b.157.19		44	5.2	odd	4
400.3.t.b.293.19		44	16.5	even	4
640.3.i.a.33.16		44	40.19	odd	2
640.3.i.a.97.7		44	80.3	even	4
640.3.i.b.33.7		44	40.29	even	2
640.3.i.b.97.16		44	80.13	odd	4
640.3.t.a.353.16		44	80.19	odd	4
640.3.t.a.417.16		44	40.3	even	4
640.3.t.b.353.7		44	80.29	even	4
640.3.t.b.417.7		44	40.13	odd	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.634321 - 1.89674i) q^{2} -2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(5.39242 + 5.39242i) q^{7} +(6.59094 + 4.53426i) q^{8} +1.30888 q^{9} +O(q^{10})\)	\(q+(-0.634321 - 1.89674i) q^{2} -2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(5.39242 + 5.39242i) q^{7} +(6.59094 + 4.53426i) q^{8} +1.30888 q^{9} +(2.98007 - 2.98007i) q^{11} +(6.67333 + 8.86141i) q^{12} -21.2000i q^{13} +(6.80752 - 13.6486i) q^{14} +(4.41955 - 15.3775i) q^{16} +(-6.66924 + 6.66924i) q^{17} +(-0.830250 - 2.48261i) q^{18} +(14.3102 - 14.3102i) q^{19} +(14.9547 - 14.9547i) q^{21} +(-7.54275 - 3.76211i) q^{22} +(-2.07267 + 2.07267i) q^{23} +(12.5748 - 18.2786i) q^{24} +(-40.2109 + 13.4476i) q^{26} -28.5895i q^{27} +(-30.2060 - 4.25454i) q^{28} +(17.5413 - 17.5413i) q^{29} -23.6474 q^{31} +(-31.9706 + 1.37153i) q^{32} +(-8.26459 - 8.26459i) q^{33} +(16.8803 + 8.41940i) q^{34} +(-4.18223 + 3.14954i) q^{36} +65.3234i q^{37} +(-36.2201 - 18.0655i) q^{38} -58.7936 q^{39} -1.18249i q^{41} +(-37.8514 - 18.8792i) q^{42} -9.57434 q^{43} +(-2.35123 + 16.6930i) q^{44} +(5.24607 + 2.61659i) q^{46} +(47.2286 - 47.2286i) q^{47} +(-42.6462 - 12.2567i) q^{48} +9.15649i q^{49} +(18.4957 + 18.4957i) q^{51} +(51.0133 + 67.7397i) q^{52} +99.2178 q^{53} +(-54.2269 + 18.1349i) q^{54} +(11.0905 + 59.9918i) q^{56} +(-39.6863 - 39.6863i) q^{57} +(-44.3981 - 22.1445i) q^{58} +(-54.7400 - 54.7400i) q^{59} +(-12.1054 - 12.1054i) q^{61} +(15.0000 + 44.8531i) q^{62} +(7.05803 + 7.05803i) q^{63} +(22.8811 + 59.7700i) q^{64} +(-10.4334 + 20.9182i) q^{66} -109.074 q^{67} +(5.26193 - 37.3582i) q^{68} +(5.74812 + 5.74812i) q^{69} -73.1674i q^{71} +(8.62675 + 5.93479i) q^{72} +(-17.0166 + 17.0166i) q^{73} +(123.902 - 41.4360i) q^{74} +(-11.2905 + 80.1595i) q^{76} +32.1396 q^{77} +(37.2940 + 111.516i) q^{78} -2.15129i q^{79} -67.5069 q^{81} +(-2.24289 + 0.750081i) q^{82} -76.4850i q^{83} +(-11.7991 + 83.7699i) q^{84} +(6.07320 + 18.1601i) q^{86} +(-48.6470 - 48.6470i) q^{87} +(33.1539 - 6.12907i) q^{88} -38.7296 q^{89} +(114.319 - 114.319i) q^{91} +(1.63531 - 11.6102i) q^{92} +65.5810i q^{93} +(-119.539 - 59.6224i) q^{94} +(3.80365 + 88.6636i) q^{96} +(-8.53929 + 8.53929i) q^{97} +(17.3675 - 5.80816i) q^{98} +(3.90055 - 3.90055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9	\( 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9} - 4 q^{11} + 8 q^{12} + 24 q^{16} + 4 q^{17} - 22 q^{18} + 32 q^{19} - 4 q^{21} - 92 q^{22} + 36 q^{24} - 52 q^{26} - 36 q^{28} - 8 q^{31} + 132 q^{32} + 4 q^{33} - 88 q^{34} - 116 q^{36} + 216 q^{38} + 72 q^{39} - 16 q^{42} - 124 q^{43} - 168 q^{44} + 108 q^{46} + 4 q^{47} - 340 q^{48} - 100 q^{51} - 48 q^{52} + 4 q^{53} + 228 q^{54} - 172 q^{56} - 36 q^{57} - 16 q^{58} + 64 q^{59} - 36 q^{61} + 356 q^{62} + 200 q^{63} - 176 q^{64} + 276 q^{66} + 292 q^{67} + 72 q^{68} - 60 q^{69} - 448 q^{72} - 48 q^{73} + 284 q^{74} + 252 q^{76} - 192 q^{77} - 620 q^{78} + 100 q^{81} + 240 q^{82} + 288 q^{84} + 20 q^{86} - 36 q^{87} + 624 q^{88} + 188 q^{91} + 412 q^{92} - 340 q^{94} - 24 q^{96} + 4 q^{97} + 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9 - 4 * q^11 + 8 * q^12 + 24 * q^16 + 4 * q^17 - 22 * q^18 + 32 * q^19 - 4 * q^21 - 92 * q^22 + 36 * q^24 - 52 * q^26 - 36 * q^28 - 8 * q^31 + 132 * q^32 + 4 * q^33 - 88 * q^34 - 116 * q^36 + 216 * q^38 + 72 * q^39 - 16 * q^42 - 124 * q^43 - 168 * q^44 + 108 * q^46 + 4 * q^47 - 340 * q^48 - 100 * q^51 - 48 * q^52 + 4 * q^53 + 228 * q^54 - 172 * q^56 - 36 * q^57 - 16 * q^58 + 64 * q^59 - 36 * q^61 + 356 * q^62 + 200 * q^63 - 176 * q^64 + 276 * q^66 + 292 * q^67 + 72 * q^68 - 60 * q^69 - 448 * q^72 - 48 * q^73 + 284 * q^74 + 252 * q^76 - 192 * q^77 - 620 * q^78 + 100 * q^81 + 240 * q^82 + 288 * q^84 + 20 * q^86 - 36 * q^87 + 624 * q^88 + 188 * q^91 + 412 * q^92 - 340 * q^94 - 24 * q^96 + 4 * q^97 + 78 * q^98 - 92 * q^99

Introduction

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