LMFDB - Embedded newform 400.3.t.b.157.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(157,400)]

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, 1]))

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

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

chi := DirichletCharacter("400.157");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.t (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			157.19
Character	$\chi$	$=$	400.157
Dual form			400.3.t.b.293.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89674 - 0.634321i) q^{2} -2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 + 5.39242i) q^{7} +(4.53426 - 6.59094i) q^{8} -1.30888 q^{9} +O(q^{10})$	\(q+(1.89674 - 0.634321i) q^{2} -2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 + 5.39242i) q^{7} +(4.53426 - 6.59094i) q^{8} -1.30888 q^{9} +(2.98007 - 2.98007i) q^{11} +(-8.86141 + 6.67333i) q^{12} -21.2000 q^{13} +(-6.80752 + 13.6486i) q^{14} +(4.41955 - 15.3775i) q^{16} +(-6.66924 - 6.66924i) q^{17} +(-2.48261 + 0.830250i) q^{18} +(-14.3102 + 14.3102i) q^{19} +(14.9547 - 14.9547i) q^{21} +(3.76211 - 7.54275i) q^{22} +(2.07267 + 2.07267i) q^{23} +(-12.5748 + 18.2786i) q^{24} +(-40.2109 + 13.4476i) q^{26} +28.5895 q^{27} +(-4.25454 + 30.2060i) q^{28} +(-17.5413 + 17.5413i) q^{29} -23.6474 q^{31} +(-1.37153 - 31.9706i) q^{32} +(-8.26459 + 8.26459i) q^{33} +(-16.8803 - 8.41940i) q^{34} +(-4.18223 + 3.14954i) q^{36} -65.3234 q^{37} +(-18.0655 + 36.2201i) q^{38} +58.7936 q^{39} -1.18249i q^{41} +(18.8792 - 37.8514i) q^{42} +9.57434i q^{43} +(2.35123 - 16.6930i) q^{44} +(5.24607 + 2.61659i) q^{46} +(47.2286 + 47.2286i) q^{47} +(-12.2567 + 42.6462i) q^{48} -9.15649i q^{49} +(18.4957 + 18.4957i) q^{51} +(-67.7397 + 51.0133i) q^{52} -99.2178i q^{53} +(54.2269 - 18.1349i) q^{54} +(11.0905 + 59.9918i) q^{56} +(39.6863 - 39.6863i) q^{57} +(-22.1445 + 44.3981i) q^{58} +(54.7400 + 54.7400i) q^{59} +(-12.1054 - 12.1054i) q^{61} +(-44.8531 + 15.0000i) q^{62} +(7.05803 - 7.05803i) q^{63} +(-22.8811 - 59.7700i) q^{64} +(-10.4334 + 20.9182i) q^{66} -109.074i q^{67} +(-37.3582 - 5.26193i) q^{68} +(-5.74812 - 5.74812i) q^{69} -73.1674i q^{71} +(-5.93479 + 8.62675i) q^{72} +(17.0166 + 17.0166i) q^{73} +(-123.902 + 41.4360i) q^{74} +(-11.2905 + 80.1595i) q^{76} +32.1396i q^{77} +(111.516 - 37.2940i) q^{78} +2.15129i q^{79} -67.5069 q^{81} +(-0.750081 - 2.24289i) q^{82} -76.4850 q^{83} +(11.7991 - 83.7699i) q^{84} +(6.07320 + 18.1601i) q^{86} +(48.6470 - 48.6470i) q^{87} +(-6.12907 - 33.1539i) q^{88} +38.7296 q^{89} +(114.319 - 114.319i) q^{91} +(11.6102 + 1.63531i) q^{92} +65.5810 q^{93} +(119.539 + 59.6224i) q^{94} +(3.80365 + 88.6636i) q^{96} +(-8.53929 - 8.53929i) q^{97} +(-5.80816 - 17.3675i) q^{98} +(-3.90055 + 3.90055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{8} + 108 q^{9}+O(q^{10}) $ 44 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^8 + 108 * q^9	$ 44 q + 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{8} + 108 q^{9} - 4 q^{11} + 44 q^{12} + 4 q^{13} + 24 q^{16} + 4 q^{17} + 42 q^{18} - 32 q^{19} - 4 q^{21} - 16 q^{22} - 36 q^{24} - 52 q^{26} + 40 q^{27} + 104 q^{28} - 8 q^{31} + 12 q^{32} + 4 q^{33} + 88 q^{34} - 116 q^{36} + 4 q^{37} + 68 q^{38} - 72 q^{39} - 244 q^{42} + 168 q^{44} + 108 q^{46} + 4 q^{47} + 4 q^{48} - 100 q^{51} - 264 q^{52} - 228 q^{54} - 172 q^{56} + 36 q^{57} - 332 q^{58} - 64 q^{59} - 36 q^{61} - 84 q^{62} + 200 q^{63} + 176 q^{64} + 276 q^{66} - 440 q^{68} + 60 q^{69} + 288 q^{72} + 48 q^{73} - 284 q^{74} + 252 q^{76} + 132 q^{78} + 100 q^{81} + 388 q^{82} - 156 q^{83} - 288 q^{84} + 20 q^{86} + 36 q^{87} - 160 q^{88} + 188 q^{91} + 352 q^{92} + 40 q^{93} + 340 q^{94} - 24 q^{96} + 4 q^{97} + 818 q^{98} + 92 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^8 + 108 * q^9 - 4 * q^11 + 44 * q^12 + 4 * q^13 + 24 * q^16 + 4 * q^17 + 42 * q^18 - 32 * q^19 - 4 * q^21 - 16 * q^22 - 36 * q^24 - 52 * q^26 + 40 * q^27 + 104 * q^28 - 8 * q^31 + 12 * q^32 + 4 * q^33 + 88 * q^34 - 116 * q^36 + 4 * q^37 + 68 * q^38 - 72 * q^39 - 244 * q^42 + 168 * q^44 + 108 * q^46 + 4 * q^47 + 4 * q^48 - 100 * q^51 - 264 * q^52 - 228 * q^54 - 172 * q^56 + 36 * q^57 - 332 * q^58 - 64 * q^59 - 36 * q^61 - 84 * q^62 + 200 * q^63 + 176 * q^64 + 276 * q^66 - 440 * q^68 + 60 * q^69 + 288 * q^72 + 48 * q^73 - 284 * q^74 + 252 * q^76 + 132 * q^78 + 100 * q^81 + 388 * q^82 - 156 * q^83 - 288 * q^84 + 20 * q^86 + 36 * q^87 - 160 * q^88 + 188 * q^91 + 352 * q^92 + 40 * q^93 + 340 * q^94 - 24 * q^96 + 4 * q^97 + 818 * q^98 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.89674	−	0.634321i	0.948372	−	0.317161i
$2$	1.89674	−	0.634321i	0.948372	−	0.317161i
$3$	−2.77329			−0.924429			−0.462215	−	0.886768i	$-0.652945\pi$
$3$	−2.77329			−0.924429			−0.462215	+	0.886768i	$0.652945\pi$
$4$	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	$-0.933363\pi$
$7$	−5.39242	+	5.39242i	−0.770346	+	0.770346i	0.207821	+	0.978167i	$0.433363\pi$
$8$	4.53426	−	6.59094i	0.566782	−	0.823868i
$9$	−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	$0.188643\pi$
$12$	−8.86141	+	6.67333i	−0.738451	+	0.556111i
$13$	−21.2000			−1.63077			−0.815383	−	0.578921i	$-0.803474\pi$
$13$	−21.2000			−1.63077			−0.815383	+	0.578921i	$0.803474\pi$
$14$	−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	0.483201	−	0.875509i	$-0.339474\pi$
$17$	−6.66924	−	6.66924i	−0.392308	−	0.392308i	−0.875509	+	0.483201i	$0.839474\pi$
$18$	−2.48261	+	0.830250i	−0.137923	+	0.0461250i
$19$	−14.3102	+	14.3102i	−0.753169	+	0.753169i	−0.975069	−	0.221901i	$-0.928774\pi$
$19$	−14.3102	+	14.3102i	−0.753169	+	0.753169i	0.221901	+	0.975069i	$0.428774\pi$
$20$		0			0
$21$	14.9547	−	14.9547i	0.712131	−	0.712131i
$22$	3.76211	−	7.54275i	0.171005	−	0.342852i
$23$	2.07267	+	2.07267i	0.0901163	+	0.0901163i	0.750728	−	0.660612i	$-0.229703\pi$
$23$	2.07267	+	2.07267i	0.0901163	+	0.0901163i	−0.660612	+	0.750728i	$0.729703\pi$
$24$	−12.5748	+	18.2786i	−0.523950	+	0.761607i
$25$		0			0
$26$	−40.2109	+	13.4476i	−1.54657	+	0.517215i
$27$	28.5895			1.05887
$28$	−4.25454	+	30.2060i	−0.151948	+	1.07879i
$29$	−17.5413	+	17.5413i	−0.604872	+	0.604872i	−0.941601	−	0.336730i	$-0.890679\pi$
$29$	−17.5413	+	17.5413i	−0.604872	+	0.604872i	0.336730	+	0.941601i	$0.390679\pi$
$30$		0			0
$31$	−23.6474			−0.762819			−0.381410	−	0.924406i	$-0.624561\pi$
$31$	−23.6474			−0.762819			−0.381410	+	0.924406i	$0.624561\pi$
$32$	−1.37153	−	31.9706i	−0.0428603	−	0.999081i
$33$	−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
$37$	−65.3234			−1.76550			−0.882749	−	0.469845i	$-0.844310\pi$
$37$	−65.3234			−1.76550			−0.882749	+	0.469845i	$0.844310\pi$
$38$	−18.0655	+	36.2201i	−0.475409	+	0.953159i
$39$	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	$-0.00459040\pi$
$42$	18.8792	−	37.8514i	0.449505	−	0.901224i
$43$			9.57434i			0.222659i	0.993784	+	0.111330i	$0.0355109\pi$
$43$			9.57434i			0.222659i	−0.993784	+	0.111330i	$0.964489\pi$
$44$	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	0.999988	+	0.00487524i	$0.00155184\pi$
$47$	47.2286	+	47.2286i	1.00486	+	1.00486i	0.00487524	+	0.999988i	$0.498448\pi$
$48$	−12.2567	+	42.6462i	−0.255347	+	0.888463i
$49$		−	9.15649i		−	0.186867i
$50$		0			0
$51$	18.4957	+	18.4957i	0.362661	+	0.362661i
$52$	−67.7397	+	51.0133i	−1.30269	+	0.981024i
$53$		−	99.2178i		−	1.87203i	−0.351955	−	0.936017i	$-0.614483\pi$
$53$		−	99.2178i		−	1.87203i	0.351955	−	0.936017i	$-0.385517\pi$
$54$	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
$58$	−22.1445	+	44.3981i	−0.381802	+	0.765485i
$59$	54.7400	+	54.7400i	0.927796	+	0.927796i	0.997563	−	0.0697673i	$-0.0222257\pi$
$59$	54.7400	+	54.7400i	0.927796	+	0.927796i	−0.0697673	+	0.997563i	$0.522226\pi$
$60$		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	$0.794815\pi$
$62$	−44.8531	+	15.0000i	−0.723436	+	0.241936i
$63$	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
$67$		−	109.074i		−	1.62798i	−0.580882	−	0.813988i	$-0.697292\pi$
$67$		−	109.074i		−	1.62798i	0.580882	−	0.813988i	$-0.302708\pi$
$68$	−37.3582	−	5.26193i	−0.549385	−	0.0773813i
$69$	−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	$-0.172306\pi$
$72$	−5.93479	+	8.62675i	−0.0824277	+	0.119816i
$73$	17.0166	+	17.0166i	0.233103	+	0.233103i	0.813987	−	0.580883i	$-0.197293\pi$
$73$	17.0166	+	17.0166i	0.233103	+	0.233103i	−0.580883	+	0.813987i	$0.697293\pi$
$74$	−123.902	+	41.4360i	−1.67435	+	0.559946i
$75$		0			0
$76$	−11.2905	+	80.1595i	−0.148560	+	1.05473i
$77$			32.1396i			0.417397i
$78$	111.516	−	37.2940i	1.42970	−	0.478129i
$79$			2.15129i			0.0272315i	0.999907	+	0.0136157i	$0.00433416\pi$
$79$			2.15129i			0.0272315i	−0.999907	+	0.0136157i	$0.995666\pi$
$80$		0			0
$81$	−67.5069			−0.833419
$82$	−0.750081	−	2.24289i	−0.00914732	−	0.0273523i
$83$	−76.4850			−0.921506			−0.460753	−	0.887528i	$-0.652421\pi$
$83$	−76.4850			−0.921506			−0.460753	+	0.887528i	$0.652421\pi$
$84$	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
$88$	−6.12907	−	33.1539i	−0.0696485	−	0.376748i
$89$	38.7296			0.435164			0.217582	−	0.976042i	$-0.430183\pi$
$89$	38.7296			0.435164			0.217582	+	0.976042i	$0.430183\pi$
$90$		0			0
$91$	114.319	−	114.319i	1.25626	−	1.25626i
$92$	11.6102	+	1.63531i	0.126198	+	0.0177751i
$93$	65.5810			0.705172
$94$	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	0.661718	−	0.749752i	$-0.269827\pi$
$97$	−8.53929	−	8.53929i	−0.0880339	−	0.0880339i	−0.749752	+	0.661718i	$0.769827\pi$
$98$	−5.80816	−	17.3675i	−0.0592669	−	0.177220i
$99$	−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	$0.0995852\pi$
$102$	46.8138	+	23.3494i	0.458959	+	0.228916i
$103$	32.9039	+	32.9039i	0.319456	+	0.319456i	0.848558	−	0.529102i	$-0.177471\pi$
$103$	32.9039	+	32.9039i	0.319456	+	0.319456i	−0.529102	+	0.848558i	$0.677471\pi$
$104$	−96.1261	+	139.728i	−0.924289	+	1.34354i
$105$		0			0
$106$	−62.9359	−	188.191i	−0.593735	−	1.77538i
$107$	19.9537			0.186484			0.0932418	−	0.995643i	$-0.470277\pi$
$107$	19.9537			0.186484			0.0932418	+	0.995643i	$0.470277\pi$
$108$	91.3512	−	68.7946i	0.845845	−	0.636987i
$109$	31.4162	−	31.4162i	0.288222	−	0.288222i	−0.548155	−	0.836377i	$-0.684670\pi$
$109$	31.4162	−	31.4162i	0.288222	−	0.288222i	0.836377	+	0.548155i	$0.184670\pi$
$110$		0			0
$111$	181.161			1.63208
$112$	59.0900	+	106.754i	0.527589	+	0.953162i
$113$	48.1807	−	48.1807i	0.426378	−	0.426378i	−0.461014	−	0.887393i	$-0.652514\pi$
$113$	48.1807	−	48.1807i	0.426378	−	0.426378i	0.887393	+	0.461014i	$0.152514\pi$
$114$	50.1009	−	100.449i	0.439481	−	0.881128i
$115$		0			0
$116$	−13.8398	+	98.2586i	−0.119309	+	0.847057i
$117$	27.7482			0.237164
$118$	138.550	+	69.1050i	1.17416	+	0.585635i
$119$	71.9267			0.604426
$120$		0			0
$121$			103.238i			0.853210i
$122$	−30.6395	−	15.2821i	−0.251144	−	0.125263i
$123$			3.27939i			0.0266617i
$124$	−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	0.928050	+	0.372456i	$0.121484\pi$
$127$	165.164	+	165.164i	1.30051	+	1.30051i	0.372456	+	0.928050i	$0.378516\pi$
$128$	−81.3129	−	98.8545i	−0.635257	−	0.772301i
$129$		−	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	$0.731140\pi$
$132$	−6.52063	+	46.2946i	−0.0493987	+	0.350717i
$133$		−	154.333i		−	1.16040i
$134$	−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	$-0.967665\pi$
$137$	−122.401	+	122.401i	−0.893436	+	0.893436i	0.101408	+	0.994845i	$0.467665\pi$
$138$	−14.5489	−	7.25656i	−0.105427	−	0.0525837i
$139$	−163.514	−	163.514i	−1.17636	−	1.17636i	−0.980665	−	0.195693i	$-0.937305\pi$
$139$	−163.514	−	163.514i	−1.17636	−	1.17636i	−0.195693	−	0.980665i	$-0.562695\pi$
$140$		0			0
$141$	−130.978	−	130.978i	−0.928925	−	0.928925i
$142$	−46.4116	−	138.780i	−0.326842	−	0.977322i
$143$	−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
$147$			25.3936i			0.172745i
$148$	−208.726	+	157.187i	−1.41031	+	1.06207i
$149$	−182.956	−	182.956i	−1.22789	−	1.22789i	−0.964759	−	0.263134i	$-0.915244\pi$
$149$	−182.956	−	182.956i	−1.22789	−	1.22789i	−0.263134	−	0.964759i	$-0.584756\pi$
$150$		0			0
$151$			100.104i			0.662938i	0.943466	+	0.331469i	$0.107544\pi$
$151$			100.104i			0.662938i	−0.943466	+	0.331469i	$0.892456\pi$
$152$	29.4316	+	159.204i	0.193629	+	1.04739i
$153$	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
$157$		−	27.8875i		−	0.177627i	−0.996048	−	0.0888136i	$-0.971692\pi$
$157$		−	27.8875i		−	0.177627i	0.996048	−	0.0888136i	$-0.0283076\pi$
$158$	1.36461	+	4.08044i	0.00863675	+	0.0258256i
$159$			275.159i			1.73056i
$160$		0			0
$161$	−22.3535			−0.138841
$162$	−128.043	+	42.8211i	−0.790391	+	0.264328i
$163$	122.177			0.749552			0.374776	−	0.927115i	$-0.377720\pi$
$163$	122.177			0.749552			0.374776	+	0.927115i	$0.377720\pi$
$164$	−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	$-0.892476\pi$
$167$	−102.217	+	102.217i	−0.612078	+	0.612078i	0.331409	+	0.943487i	$0.392476\pi$
$168$	−30.7572	−	166.374i	−0.183079	−	0.990324i
$169$	280.439			1.65940
$170$		0			0
$171$	18.7303	−	18.7303i	0.109534	−	0.109534i
$172$	23.0386	+	30.5926i	0.133945	+	0.177864i
$173$	−144.968			−0.837968			−0.418984	−	0.907994i	$-0.637614\pi$
$173$	−144.968			−0.837968			−0.418984	+	0.907994i	$0.637614\pi$
$174$	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
$178$	73.4602	−	24.5670i	0.412698	−	0.138017i
$179$	71.1438	−	71.1438i	0.397451	−	0.397451i	−0.479882	−	0.877333i	$-0.659320\pi$
$179$	71.1438	−	71.1438i	0.397451	−	0.397451i	0.877333	+	0.479882i	$0.159320\pi$
$180$		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	$0.978216\pi$
$182$	144.319	−	289.349i	0.792963	−	1.58983i
$183$	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
$187$	−39.7496			−0.212565
$188$	264.554	+	37.2626i	1.40720	+	0.198205i
$189$	−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	$0.684832\pi$
$192$	63.4558	+	165.759i	0.330499	+	0.863331i
$193$	90.2693	−	90.2693i	0.467717	−	0.467717i	−0.433457	−	0.901174i	$-0.642707\pi$
$193$	90.2693	−	90.2693i	0.467717	−	0.467717i	0.901174	+	0.433457i	$0.142707\pi$
$194$	−21.6135	−	10.7802i	−0.111410	−	0.0555680i
$195$		0			0
$196$	−22.0332	−	29.2575i	−0.112414	−	0.149273i
$197$	−67.8338			−0.344334			−0.172167	−	0.985068i	$-0.555077\pi$
$197$	−67.8338			−0.344334			−0.172167	+	0.985068i	$0.555077\pi$
$198$	−4.92414	+	9.87254i	−0.0248694	+	0.0498613i
$199$	−278.771			−1.40086			−0.700430	−	0.713721i	$-0.747009\pi$
$199$	−278.771			−1.40086			−0.700430	+	0.713721i	$0.747009\pi$
$200$		0			0
$201$			302.495i			1.50495i
$202$	82.0723	−	164.549i	0.406299	−	0.814599i
$203$		−	189.180i		−	0.931922i
$204$	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
$208$	−93.6942	+	326.003i	−0.450453	+	1.56732i
$209$			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	$0.778358\pi$
$212$	−238.747	−	317.028i	−1.12616	−	1.49542i
$213$			202.914i			0.952648i
$214$	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
$218$	39.6605	−	79.5164i	0.181929	−	0.364754i
$219$	−47.1918	−	47.1918i	−0.215488	−	0.215488i
$220$		0			0
$221$	141.388	+	141.388i	0.639763	+	0.639763i
$222$	343.615	−	114.914i	1.54782	−	0.517631i
$223$	−90.1705	+	90.1705i	−0.404352	+	0.404352i	−0.879764	−	0.475412i	$-0.842299\pi$
$223$	−90.1705	+	90.1705i	−0.404352	+	0.404352i	0.475412	+	0.879764i	$0.342299\pi$
$224$	179.795	+	165.003i	0.802656	+	0.736621i
$225$		0			0
$226$	60.8244	−	121.949i	0.269135	−	0.539595i
$227$			346.057i			1.52448i	0.647294	+	0.762240i	$0.275900\pi$
$227$			346.057i			1.52448i	−0.647294	+	0.762240i	$0.724100\pi$
$228$	31.3119	−	222.305i	0.137333	−	0.975023i
$229$	−73.4761	−	73.4761i	−0.320856	−	0.320856i	0.528239	−	0.849096i	$-0.322852\pi$
$229$	−73.4761	−	73.4761i	−0.320856	−	0.320856i	−0.849096	+	0.528239i	$0.822852\pi$
$230$		0			0
$231$		−	89.1323i		−	0.385854i
$232$	36.0770	+	195.150i	0.155504	+	0.841165i
$233$	86.7985	+	86.7985i	0.372526	+	0.372526i	0.868396	−	0.495871i	$-0.165151\pi$
$233$	86.7985	+	86.7985i	0.372526	+	0.372526i	−0.495871	+	0.868396i	$0.665151\pi$
$234$	52.6312	−	17.6013i	0.224920	−	0.0752191i
$235$		0			0
$236$	306.629	+	43.1890i	1.29928	+	0.183004i
$237$		−	5.96613i		−	0.0251736i
$238$	136.427	−	45.6246i	0.573221	−	0.191700i
$239$			204.791i			0.856868i	0.903573	+	0.428434i	$0.140935\pi$
$239$			204.791i			0.856868i	−0.903573	+	0.428434i	$0.859065\pi$
$240$		0			0
$241$	98.8804			0.410292			0.205146	−	0.978731i	$-0.434233\pi$
$241$	98.8804			0.410292			0.205146	+	0.978731i	$0.434233\pi$
$242$	65.4863	+	195.817i	0.270604	+	0.809160i
$243$	−70.0893			−0.288433
$244$	−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
$248$	−107.223	+	155.859i	−0.432352	+	0.628462i
$249$	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	$0.284445\pi$
$252$	5.56868	−	39.5360i	0.0220979	−	0.156889i
$253$	12.3534			0.0488277
$254$	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	0.304672	−	0.952457i	$-0.401453\pi$
$257$	−166.481	−	166.481i	−0.647785	−	0.647785i	−0.952457	+	0.304672i	$0.901453\pi$
$258$	−16.8427	−	50.3631i	−0.0652819	−	0.195206i
$259$	352.252	−	352.252i	1.36005	−	1.36005i
$260$		0			0
$261$	22.9594	−	22.9594i	0.0879671	−	0.0879671i
$262$	27.7671	+	13.8494i	0.105981	+	0.0528604i
$263$	78.7097	+	78.7097i	0.299276	+	0.299276i	0.840730	−	0.541454i	$-0.182126\pi$
$263$	78.7097	+	78.7097i	0.299276	+	0.299276i	−0.541454	+	0.840730i	$0.682126\pi$
$264$	16.9977	+	91.9452i	0.0643851	+	0.348277i
$265$		0			0
$266$	−97.8969	−	292.731i	−0.368034	−	1.10049i
$267$	−107.408			−0.402279
$268$	−262.464	−	348.522i	−0.979345	−	1.30046i
$269$	−98.2650	+	98.2650i	−0.365297	+	0.365297i	−0.865759	−	0.500461i	$-0.833164\pi$
$269$	−98.2650	+	98.2650i	−0.365297	+	0.365297i	0.500461	+	0.865759i	$0.333164\pi$
$270$		0			0
$271$	−115.967			−0.427922			−0.213961	−	0.976842i	$-0.568637\pi$
$271$	−115.967			−0.427922			−0.213961	+	0.976842i	$0.568637\pi$
$272$	−132.031	+	73.0812i	−0.485409	+	0.268681i
$273$	−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
$277$	−340.610			−1.22964			−0.614819	−	0.788668i	$-0.710771\pi$
$277$	−340.610			−1.22964			−0.614819	+	0.788668i	$0.710771\pi$
$278$	−413.864	−	206.423i	−1.48872	−	0.742530i
$279$	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	$-0.0589814\pi$
$282$	−331.515	−	165.350i	−1.17558	−	0.586348i
$283$			561.986i			1.98582i	0.118887	+	0.992908i	$0.462068\pi$
$283$			561.986i			1.98582i	−0.118887	+	0.992908i	$0.537932\pi$
$284$	−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
$288$	1.79517	+	41.8456i	0.00623322	+	0.145297i
$289$		−	200.043i		−	0.692189i
$290$		0			0
$291$	23.6819	+	23.6819i	0.0813811	+	0.0813811i
$292$	95.3193	+	13.4258i	0.326436	+	0.0459787i
$293$			1.90920i			0.00651604i	0.999995	+	0.00325802i	$0.00103706\pi$
$293$			1.90920i			0.00651604i	−0.999995	+	0.00325802i	$0.998963\pi$
$294$	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
$298$	−463.074	−	230.968i	−1.55394	−	0.775060i
$299$	−43.9406	−	43.9406i	−0.146959	−	0.146959i
$300$		0			0
$301$	−51.6289	−	51.6289i	−0.171525	−	0.171525i
$302$	63.4978	+	189.871i	0.210258	+	0.628712i
$303$	−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
$307$		−	465.516i		−	1.51634i	−0.652058	−	0.758169i	$-0.726094\pi$
$307$		−	465.516i		−	1.51634i	0.652058	−	0.758169i	$-0.273906\pi$
$308$	77.3372	+	102.695i	0.251095	+	0.333425i
$309$	−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	$0.889086\pi$
$312$	266.585	−	387.505i	0.854440	−	1.24200i
$313$	46.0307	+	46.0307i	0.147063	+	0.147063i	0.776805	−	0.629742i	$-0.216839\pi$
$313$	46.0307	+	46.0307i	0.147063	+	0.147063i	−0.629742	+	0.776805i	$0.716839\pi$
$314$	−17.6896	−	52.8954i	−0.0563364	−	0.168457i
$315$		0			0
$316$	5.17661	+	6.87395i	0.0163817	+	0.0217530i
$317$			430.649i			1.35851i	0.733901	+	0.679257i	$0.237698\pi$
$317$			430.649i			1.35851i	−0.733901	+	0.679257i	$0.762302\pi$
$318$	174.539	+	521.907i	0.548866	+	1.64122i
$319$			104.548i			0.327738i
$320$		0			0
$321$	−55.3375			−0.172391
$322$	−42.3988	+	14.1793i	−0.131673	+	0.0440350i
$323$	190.876			0.590948
$324$	−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
$328$	−7.79375	−	5.36173i	−0.0237614	−	0.0163467i
$329$	−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	$0.247481\pi$
$332$	−244.390	+	184.045i	−0.736116	+	0.554352i
$333$	85.5005			0.256758
$334$	−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	0.958022	−	0.286695i	$-0.0925567\pi$
$337$	226.237	+	226.237i	0.671327	+	0.671327i	−0.286695	+	0.958022i	$0.592557\pi$
$338$	531.920	−	177.888i	1.57373	−	0.526297i
$339$	−133.619	+	133.619i	−0.394156	+	0.394156i
$340$		0			0
$341$	−70.4709	+	70.4709i	−0.206659	+	0.206659i
$342$	23.6456	−	47.4077i	0.0691391	−	0.138619i
$343$	−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
$347$	−231.886			−0.668259			−0.334130	−	0.942527i	$-0.608442\pi$
$347$	−231.886			−0.668259			−0.334130	+	0.942527i	$0.608442\pi$
$348$	38.3817	−	272.499i	0.110292	−	0.783044i
$349$	−205.898	+	205.898i	−0.589965	+	0.589965i	−0.937622	−	0.347657i	$-0.886978\pi$
$349$	−205.898	+	205.898i	−0.589965	+	0.589965i	0.347657	+	0.937622i	$0.386978\pi$
$350$		0			0
$351$	−606.096			−1.72677
$352$	−99.3618	−	91.1873i	−0.282278	−	0.259055i
$353$	299.539	−	299.539i	0.848551	−	0.848551i	−0.141401	−	0.989952i	$-0.545161\pi$
$353$	299.539	−	299.539i	0.848551	−	0.848551i	0.989952	+	0.141401i	$0.0451607\pi$
$354$	−384.240	−	191.648i	−1.08542	−	0.541378i
$355$		0			0
$356$	123.752	−	93.1947i	0.347617	−	0.261783i
$357$	−199.473			−0.558749
$358$	89.8135	−	180.070i	0.250876	−	0.502987i
$359$	108.844			0.303187			0.151593	−	0.988443i	$-0.451560\pi$
$359$	108.844			0.303187			0.151593	+	0.988443i	$0.451560\pi$
$360$		0			0
$361$		−	48.5638i		−	0.134526i
$362$	−243.589	+	488.378i	−0.672898	+	1.34911i
$363$		−	286.310i		−	0.788732i
$364$	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	0.232610	−	0.972570i	$-0.425274\pi$
$367$	−271.565	−	271.565i	−0.739960	−	0.739960i	−0.972570	+	0.232610i	$0.925274\pi$
$368$	41.0328	−	22.7123i	0.111502	−	0.0617181i
$369$			1.54774i			0.00419442i
$370$		0			0
$371$	535.025	+	535.025i	1.44211	+	1.44211i
$372$	209.549	−	157.807i	0.563305	−	0.424212i
$373$			205.735i			0.551569i	0.961220	+	0.275784i	$0.0889376\pi$
$373$			205.735i			0.551569i	−0.961220	+	0.275784i	$0.911062\pi$
$374$	−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
$378$	−194.623	+	390.206i	−0.514877	+	1.03229i
$379$	−146.474	−	146.474i	−0.386475	−	0.386475i	0.486953	−	0.873428i	$-0.338108\pi$
$379$	−146.474	−	146.474i	−0.386475	−	0.386475i	−0.873428	+	0.486953i	$0.838108\pi$
$380$		0			0
$381$	−458.048	−	458.048i	−1.20223	−	1.20223i
$382$	−397.478	+	132.927i	−1.04052	+	0.347977i
$383$	−77.8502	+	77.8502i	−0.203264	+	0.203264i	−0.801397	−	0.598133i	$-0.795910\pi$
$383$	−77.8502	+	77.8502i	−0.203264	+	0.203264i	0.598133	+	0.801397i	$0.295910\pi$
$384$	225.504	+	274.152i	0.587250	+	0.713937i
$385$		0			0
$386$	113.958	−	228.477i	0.295228	−	0.591910i
$387$		−	12.5317i		−	0.0323815i
$388$	−47.8334	−	6.73737i	−0.123282	−	0.0173643i
$389$	−91.3251	−	91.3251i	−0.234769	−	0.234769i	0.579911	−	0.814680i	$-0.303087\pi$
$389$	−91.3251	−	91.3251i	−0.234769	−	0.234769i	−0.814680	+	0.579911i	$0.803087\pi$
$390$		0			0
$391$		−	27.6463i		−	0.0707067i
$392$	−60.3499	−	41.5179i	−0.153954	−	0.105913i
$393$	−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
$397$			181.720i			0.457732i	0.973458	+	0.228866i	$0.0735017\pi$
$397$			181.720i			0.457732i	−0.973458	+	0.228866i	$0.926498\pi$
$398$	−528.758	+	176.831i	−1.32854	+	0.444298i
$399$			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	$0.745597\pi$
$402$	191.879	+	573.755i	0.477310	+	1.42725i
$403$	501.324			1.24398
$404$	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
$408$	205.768	−	38.0399i	0.504334	−	0.0932351i
$409$	724.291			1.77088			0.885441	−	0.464752i	$-0.153856\pi$
$409$	724.291			1.77088			0.885441	+	0.464752i	$0.153856\pi$
$410$		0			0
$411$	339.453	−	339.453i	0.825919	−	0.825919i
$412$	184.313	+	25.9607i	0.447363	+	0.0630114i
$413$	−590.362			−1.42945
$414$	−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
$418$	54.1017	+	161.775i	0.129430	+	0.387021i
$419$	−76.4657	+	76.4657i	−0.182496	+	0.182496i	−0.792442	−	0.609947i	$-0.791191\pi$
$419$	−76.4657	+	76.4657i	−0.182496	+	0.182496i	0.609947	+	0.792442i	$0.291191\pi$
$420$		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	$-0.0402236\pi$
$422$	−67.1969	−	33.5159i	−0.159234	−	0.0794215i
$423$	−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
$427$	130.555			0.305749
$428$	63.7577	−	48.0145i	0.148967	−	0.112183i
$429$	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	$0.431109\pi$
$432$	126.353	−	439.635i	0.292483	−	1.01767i
$433$	354.954	−	354.954i	0.819756	−	0.819756i	−0.166317	−	0.986072i	$-0.553187\pi$
$433$	354.954	−	354.954i	0.819756	−	0.819756i	0.986072	+	0.166317i	$0.0531874\pi$
$434$	160.980	−	322.753i	0.370922	−	0.743671i
$435$		0			0
$436$	24.7869	−	175.980i	0.0568507	−	0.403623i
$437$	−59.3208			−0.135745
$438$	−119.445	−	59.5760i	−0.272707	−	0.136018i
$439$	155.719			0.354714			0.177357	−	0.984147i	$-0.443245\pi$
$439$	155.719			0.354714			0.177357	+	0.984147i	$0.443245\pi$
$440$		0			0
$441$			11.9847i			0.0271763i
$442$	357.861	+	178.491i	0.809641	+	0.403826i
$443$		−	728.951i		−	1.64549i	−0.568412	−	0.822744i	$-0.692442\pi$
$443$		−	728.951i		−	1.64549i	0.568412	−	0.822744i	$-0.307558\pi$
$444$	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
$448$	445.690	+	198.921i	0.994843	+	0.444020i
$449$		−	46.9465i		−	0.104558i	−0.998633	−	0.0522790i	$-0.983351\pi$
$449$		−	46.9465i		−	0.104558i	0.998633	−	0.0522790i	$-0.0166485\pi$
$450$		0			0
$451$	−3.52391	−	3.52391i	−0.00781355	−	0.00781355i
$452$	38.0138	−	269.887i	0.0841014	−	0.597096i
$453$		−	277.616i		−	0.612839i
$454$	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	$-0.635534\pi$
$457$	227.434	−	227.434i	0.497667	−	0.497667i	0.910711	+	0.413044i	$0.135534\pi$
$458$	−185.973	−	92.7579i	−0.406054	−	0.202528i
$459$	−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	$0.616295\pi$
$462$	−56.5385	−	169.061i	−0.122378	−	0.365933i
$463$	−1.16661	+	1.16661i	−0.00251968	+	0.00251968i	−0.708366	−	0.705846i	$-0.750567\pi$
$463$	−1.16661	+	1.16661i	−0.00251968	+	0.00251968i	0.705846	+	0.708366i	$0.250567\pi$
$464$	192.217	+	347.266i	0.414260	+	0.748417i
$465$		0			0
$466$	219.693	+	109.576i	0.471444	+	0.235143i
$467$		−	632.343i		−	1.35405i	−0.735958	−	0.677027i	$-0.763268\pi$
$467$		−	632.343i		−	1.35405i	0.735958	−	0.677027i	$-0.236732\pi$
$468$	88.6631	−	66.7702i	0.189451	−	0.142671i
$469$	588.175	+	588.175i	1.25411	+	1.25411i
$470$		0			0
$471$			77.3400i			0.164204i
$472$	608.993	−	112.583i	1.29024	−	0.238523i
$473$	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
$477$			129.864i			0.272252i
$478$	129.904	+	388.437i	0.271765	+	0.812630i
$479$		−	552.415i		−	1.15327i	−0.817003	−	0.576633i	$-0.804366\pi$
$479$		−	552.415i		−	1.15327i	0.817003	−	0.576633i	$-0.195634\pi$
$480$		0			0
$481$	1384.85			2.87912
$482$	187.551	−	62.7219i	0.389110	−	0.130128i
$483$	61.9926			0.128349
$484$	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	$-0.885968\pi$
$487$	−285.326	+	285.326i	−0.585886	+	0.585886i	0.350629	+	0.936515i	$0.385968\pi$
$488$	−134.675	+	24.8970i	−0.275973	+	0.0510185i
$489$	−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	$0.900870\pi$
$492$	7.89117	+	10.4786i	0.0160390	+	0.0212979i
$493$	233.974			0.474592
$494$	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
$498$	402.327	−	134.549i	0.807886	−	0.270179i
$499$	430.585	−	430.585i	0.862895	−	0.862895i	−0.128778	−	0.991673i	$-0.541106\pi$
$499$	430.585	−	430.585i	0.862895	−	0.862895i	0.991673	+	0.128778i	$0.0411056\pi$
$500$		0			0
$501$	283.477	−	283.477i	0.565823	−	0.565823i
$502$	−48.3976	+	97.0337i	−0.0964096	+	0.193294i
$503$	102.108	+	102.108i	0.202998	+	0.202998i	0.801283	−	0.598285i	$-0.204151\pi$
$503$	102.108	+	102.108i	0.202998	+	0.202998i	−0.598285	+	0.801283i	$0.704151\pi$
$504$	−14.5162	−	78.5220i	−0.0288019	−	0.155798i
$505$		0			0
$506$	23.4313	−	7.83604i	0.0463069	−	0.0154862i
$507$	−777.737			−1.53400
$508$	925.178	+	130.312i	1.82122	+	0.256520i
$509$	−350.381	+	350.381i	−0.688372	+	0.688372i	−0.961872	−	0.273500i	$-0.911819\pi$
$509$	−350.381	+	350.381i	−0.688372	+	0.688372i	0.273500	+	0.961872i	$0.411819\pi$
$510$		0			0
$511$	−183.521			−0.359141
$512$	−497.689	−	120.205i	−0.972050	−	0.234775i
$513$	−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
$517$	281.489			0.544466
$518$	444.691	−	891.572i	0.858476	−	1.72118i
$519$	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	$0.972770\pi$
$522$	28.9845	−	58.1118i	0.0555258	−	0.111325i
$523$		−	399.222i		−	0.763331i	−0.924300	−	0.381666i	$-0.875351\pi$
$523$		−	399.222i		−	0.763331i	0.924300	−	0.381666i	$-0.124649\pi$
$524$	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
$528$	90.5630	+	163.614i	0.171521	+	0.309876i
$529$		−	520.408i		−	0.983758i
$530$		0			0
$531$	−71.6480	−	71.6480i	−0.134930	−	0.134930i
$532$	−371.371	−	493.137i	−0.698065	−	0.926950i
$533$			25.0688i			0.0470334i
$534$	−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
$538$	−124.052	+	248.715i	−0.230580	+	0.462296i
$539$	−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	$0.686528\pi$
$542$	−219.960	+	73.5603i	−0.405830	+	0.135720i
$543$	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
$547$			327.523i			0.598762i	0.954134	+	0.299381i	$0.0967802\pi$
$547$			327.523i			0.598762i	−0.954134	+	0.299381i	$0.903220\pi$
$548$	−96.5723	+	685.636i	−0.176227	+	1.25116i
$549$	15.8445	+	15.8445i	0.0288607	+	0.0288607i
$550$		0			0
$551$		−	502.039i		−	0.911141i
$552$	−63.9490	+	11.8221i	−0.115850	+	0.0214168i
$553$	−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
$557$		−	609.704i		−	1.09462i	−0.836930	−	0.547311i	$-0.815652\pi$
$557$		−	609.704i		−	1.09462i	0.836930	−	0.547311i	$-0.184348\pi$
$558$	58.7072	−	19.6332i	0.105210	−	0.0351850i
$559$		−	202.976i		−	0.363105i
$560$		0			0
$561$	110.237			0.196501
$562$	−65.6784	−	196.391i	−0.116865	−	0.349451i
$563$	−104.576			−0.185748			−0.0928738	−	0.995678i	$-0.529605\pi$
$563$	−104.576			−0.185748			−0.0928738	+	0.995678i	$0.529605\pi$
$564$	−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
$568$	−482.242	−	331.760i	−0.849018	−	0.584084i
$569$	153.954			0.270569			0.135284	−	0.990807i	$-0.456805\pi$
$569$	153.954			0.270569			0.135284	+	0.990807i	$0.456805\pi$
$570$		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	$0.0495832\pi$
$572$	−49.8460	+	353.892i	−0.0871433	+	0.618692i
$573$	581.164			1.01425
$574$	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	0.227555	−	0.973765i	$-0.426927\pi$
$577$	−430.563	−	430.563i	−0.746210	−	0.746210i	−0.973765	+	0.227555i	$0.926927\pi$
$578$	−126.891	−	379.429i	−0.219535	−	0.656452i
$579$	−250.343	+	250.343i	−0.432371	+	0.432371i
$580$		0			0
$581$	412.440	−	412.440i	0.709879	−	0.709879i
$582$	59.9404	+	29.8966i	0.102990	+	0.0513687i
$583$	−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
$587$	24.8014			0.0422512			0.0211256	−	0.999777i	$-0.493275\pi$
$587$	24.8014			0.0422512			0.0211256	+	0.999777i	$0.493275\pi$
$588$	61.1043	+	81.1394i	0.103919	+	0.137992i
$589$	338.399	−	338.399i	0.574531	−	0.574531i
$590$		0			0
$591$	188.123			0.318312
$592$	−288.700	+	1004.51i	−0.487669	+	1.69681i
$593$	−714.962	+	714.962i	−1.20567	+	1.20567i	−0.233255	+	0.972416i	$0.574938\pi$
$593$	−714.962	+	714.962i	−1.20567	+	1.20567i	−0.972416	+	0.233255i	$0.925062\pi$
$594$	107.557	−	215.643i	0.181072	−	0.363036i
$595$		0			0
$596$	−1024.84	−	144.350i	−1.71953	−	0.242197i
$597$	773.113			1.29500
$598$	−111.217	−	55.4716i	−0.185981	−	0.0927619i
$599$	−898.559			−1.50010			−0.750049	−	0.661382i	$-0.769970\pi$
$599$	−898.559			−1.50010			−0.750049	+	0.661382i	$0.769970\pi$
$600$		0			0
$601$			498.405i			0.829293i	0.909983	+	0.414646i	$0.136095\pi$
$601$			498.405i			0.829293i	−0.909983	+	0.414646i	$0.863905\pi$
$602$	−130.676	−	65.1775i	−0.217070	−	0.108268i
$603$			142.765i			0.236758i
$604$	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	0.195900	−	0.980624i	$-0.437237\pi$
$607$	−476.327	−	476.327i	−0.784723	−	0.784723i	−0.980624	+	0.195900i	$0.937237\pi$
$608$	477.133	+	437.879i	0.784758	+	0.720195i
$609$			524.651i			0.861495i
$610$		0			0
$611$	−1001.24	−	1001.24i	−1.63870	−	1.63870i
$612$	48.8973	+	6.88722i	0.0798976	+	0.0112536i
$613$			294.722i			0.480787i	0.970676	+	0.240393i	$0.0772764\pi$
$613$			294.722i			0.480787i	−0.970676	+	0.240393i	$0.922724\pi$
$614$	−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	$-0.657929\pi$
$617$	248.885	−	248.885i	0.403379	−	0.403379i	0.879422	+	0.476043i	$0.157929\pi$
$618$	−230.965	−	115.199i	−0.373730	−	0.186406i
$619$	320.358	+	320.358i	0.517541	+	0.517541i	0.916826	−	0.399286i	$-0.130742\pi$
$619$	320.358	+	320.358i	0.517541	+	0.517541i	−0.399286	+	0.916826i	$0.630742\pi$
$620$		0			0
$621$	59.2567	+	59.2567i	0.0954214	+	0.0954214i
$622$	134.714	+	402.822i	0.216582	+	0.647623i
$623$	−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
$627$		−	236.536i		−	0.377250i
$628$	−67.1053	−	89.1081i	−0.106856	−	0.141892i
$629$	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	$-0.0279972\pi$
$632$	14.1790	+	9.75448i	0.0224351	+	0.0154343i
$633$	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
$637$			194.117i			0.304737i
$638$	66.3173	+	198.302i	0.103946	+	0.310818i
$639$			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	$0.593310\pi$
$642$	−104.961	+	35.1017i	−0.163491	+	0.0546756i
$643$	−686.295			−1.06733			−0.533667	−	0.845695i	$-0.679186\pi$
$643$	−686.295			−1.06733			−0.533667	+	0.845695i	$0.679186\pi$
$644$	−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	$-0.934015\pi$
$647$	−499.985	+	499.985i	−0.772774	+	0.772774i	0.205817	+	0.978591i	$0.434015\pi$
$648$	−306.094	+	444.934i	−0.472367	+	0.686627i
$649$	326.258			0.502708
$650$		0			0
$651$	−353.641	+	353.641i	−0.543227	+	0.543227i
$652$	390.389	−	293.993i	0.598756	−	0.450910i
$653$	−599.129			−0.917502			−0.458751	−	0.888565i	$-0.651703\pi$
$653$	−599.129			−0.917502			−0.458751	+	0.888565i	$0.651703\pi$
$654$	−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
$658$	−966.112	+	323.093i	−1.46826	+	0.491023i
$659$	55.5691	−	55.5691i	0.0843233	−	0.0843233i	−0.663687	−	0.748010i	$-0.731009\pi$
$659$	55.5691	−	55.5691i	0.0843233	−	0.0843233i	0.748010	+	0.663687i	$0.231009\pi$
$660$		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	$0.241707\pi$
$662$	4.67689	−	9.37681i	0.00706478	−	0.0141644i
$663$	−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
$667$	−72.7147			−0.109018
$668$	−80.6477	+	572.575i	−0.120730	+	0.857149i
$669$	250.069	−	250.069i	0.373795	−	0.373795i
$670$		0			0
$671$	−72.1498			−0.107526
$672$	−498.623	−	457.601i	−0.741998	−	0.680954i
$673$	348.271	−	348.271i	0.517490	−	0.517490i	−0.399321	−	0.916811i	$-0.630754\pi$
$673$	348.271	−	348.271i	0.517490	−	0.517490i	0.916811	+	0.399321i	$0.130754\pi$
$674$	572.621	+	285.607i	0.849586	+	0.423749i
$675$		0			0
$676$	896.079	−	674.817i	1.32556	−	0.998250i
$677$	780.155			1.15237			0.576185	−	0.817319i	$-0.304541\pi$
$677$	780.155			1.15237			0.576185	+	0.817319i	$0.304541\pi$
$678$	−168.684	+	338.198i	−0.248796	+	0.498818i
$679$	92.0950			0.135633
$680$		0			0
$681$		−	959.715i		−	1.40927i
$682$	−88.9640	+	178.366i	−0.130446	+	0.261534i
$683$			170.375i			0.249451i	0.992191	+	0.124725i	$0.0398050\pi$
$683$			170.375i			0.249451i	−0.992191	+	0.124725i	$0.960195\pi$
$684$	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
$688$	147.229	+	42.3142i	0.213996	+	0.0615032i
$689$			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	$0.766705\pi$
$692$	−463.214	+	348.836i	−0.669384	+	0.504098i
$693$		−	42.0668i		−	0.0607025i
$694$	−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
$698$	−259.930	+	521.141i	−0.372393	+	0.746620i
$699$	−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	$0.728024\pi$
$702$	−1149.61	+	384.460i	−1.63762	+	0.547663i
$703$	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
$707$			701.142i			0.991714i
$708$	−850.371	−	119.775i	−1.20109	−	0.169174i
$709$	−815.622	−	815.622i	−1.15038	−	1.15038i	−0.986476	−	0.163908i	$-0.947590\pi$
$709$	−815.622	−	815.622i	−1.15038	−	1.15038i	−0.163908	−	0.986476i	$-0.552410\pi$
$710$		0			0
$711$		−	2.81577i		−	0.00396030i
$712$	175.610	−	255.265i	0.246643	−	0.358518i
$713$	−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
$717$		−	567.946i		−	0.792114i
$718$	206.449	−	69.0420i	0.287534	−	0.0961588i
$719$			125.050i			0.173922i	0.996212	+	0.0869612i	$0.0277156\pi$
$719$			125.050i			0.173922i	−0.996212	+	0.0869612i	$0.972284\pi$
$720$		0			0
$721$	−354.864			−0.492183
$722$	−30.8051	−	92.1131i	−0.0426663	−	0.127581i
$723$	−274.224			−0.379286
$724$	−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	$-0.653233\pi$
$727$	307.763	−	307.763i	0.423333	−	0.423333i	0.886350	+	0.463016i	$0.153233\pi$
$728$	−235.119	−	1271.82i	−0.322966	−	1.74701i
$729$	801.940			1.10005
$730$		0			0
$731$	63.8535	−	63.8535i	0.0873510	−	0.0873510i
$732$	188.054	+	26.4876i	0.256905	+	0.0361852i
$733$	94.8581			0.129411			0.0647054	−	0.997904i	$-0.479389\pi$
$733$	94.8581			0.129411			0.0647054	+	0.997904i	$0.479389\pi$
$734$	−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
$738$	0.981765	+	2.93567i	0.00133030	+	0.00397787i
$739$	−761.284	+	761.284i	−1.03015	+	1.03015i	−0.0306228	+	0.999531i	$0.509749\pi$
$739$	−761.284	+	761.284i	−1.03015	+	1.03015i	−0.999531	+	0.0306228i	$0.990251\pi$
$740$		0			0
$741$	−841.348	+	841.348i	−1.13542	+	1.13542i
$742$	1354.18	+	675.427i	1.82504	+	0.910279i
$743$	700.467	+	700.467i	0.942754	+	0.942754i	0.998448	−	0.0556935i	$-0.0177370\pi$
$743$	700.467	+	700.467i	0.942754	+	0.942754i	−0.0556935	+	0.998448i	$0.517737\pi$
$744$	297.361	−	432.241i	0.399679	−	0.580969i
$745$		0			0
$746$	130.502	+	390.227i	0.174936	+	0.523092i
$747$	100.110			0.134016
$748$	−127.011	+	95.6490i	−0.169800	+	0.127873i
$749$	−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	$0.442829\pi$
$752$	934.986	−	517.529i	1.24333	−	0.688203i
$753$	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
$757$	777.969			1.02770			0.513850	−	0.857880i	$-0.328219\pi$
$757$	777.969			1.02770			0.513850	+	0.857880i	$0.328219\pi$
$758$	−370.736	−	184.912i	−0.489097	−	0.243948i
$759$	−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	$-0.244942\pi$
$762$	−1159.35	−	578.250i	−1.52146	−	0.758858i
$763$			338.819i			0.444062i
$764$	−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
$768$	601.624	+	376.954i	0.783364	+	0.490825i
$769$		−	262.583i		−	0.341461i	−0.985318	−	0.170730i	$-0.945387\pi$
$769$		−	262.583i		−	0.341461i	0.985318	−	0.170730i	$-0.0546127\pi$
$770$		0			0
$771$	461.699	+	461.699i	0.598832	+	0.598832i
$772$	71.2211	−	505.649i	0.0922553	−	0.654986i
$773$		−	405.962i		−	0.525177i	−0.964908	−	0.262588i	$-0.915424\pi$
$773$		−	405.962i		−	0.525177i	0.964908	−	0.262588i	$-0.0845761\pi$
$774$	−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
$778$	−231.150	−	115.291i	−0.297108	−	0.148189i
$779$	16.9217	+	16.9217i	0.0217224	+	0.0217224i
$780$		0			0
$781$	−218.044	−	218.044i	−0.279185	−	0.279185i
$782$	−17.5366	−	52.4380i	−0.0224254	−	0.0670562i
$783$	−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
$787$		−	107.060i		−	0.136036i	−0.997684	−	0.0680181i	$-0.978332\pi$
$787$		−	107.060i		−	0.136036i	0.997684	−	0.0680181i	$-0.0216676\pi$
$788$	−216.747	+	163.228i	−0.275060	+	0.207142i
$789$	−218.285	−	218.285i	−0.276660	−	0.276660i
$790$		0			0
$791$			519.622i			0.656918i
$792$	8.02221	+	43.3944i	0.0101291	+	0.0547909i
$793$	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
$797$			615.958i			0.772846i	0.922322	+	0.386423i	$0.126289\pi$
$797$			615.958i			0.772846i	−0.922322	+	0.386423i	$0.873711\pi$
$798$	271.496	+	811.827i	0.340221	+	1.01733i
$799$		−	629.957i		−	0.788432i
$800$		0			0
$801$	−50.6924			−0.0632864
$802$	−1060.66	+	354.713i	−1.32252	+	0.442285i
$803$	101.421			0.126303
$804$	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
$808$	−133.709	−	723.269i	−0.165481	−	0.895135i
$809$	−304.293			−0.376135			−0.188067	−	0.982156i	$-0.560222\pi$
$809$	−304.293			−0.376135			−0.188067	+	0.982156i	$0.560222\pi$
$810$		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	$0.255608\pi$
$812$	−455.222	−	604.482i	−0.560618	−	0.744436i
$813$	321.610			0.395584
$814$	−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
$818$	1373.79	−	459.433i	1.67945	−	0.561654i
$819$	−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	$0.356515\pi$
$822$	428.533	−	859.176i	0.521329	−	1.04523i
$823$	420.324	+	420.324i	0.510721	+	0.510721i	0.914747	−	0.404026i	$-0.132390\pi$
$823$	420.324	+	420.324i	0.510721	+	0.510721i	−0.404026	+	0.914747i	$0.632390\pi$
$824$	366.063	−	67.6731i	0.444251	−	0.0821276i
$825$		0			0
$826$	−1119.77	+	374.479i	−1.35565	+	0.453365i
$827$	844.006			1.02056			0.510281	−	0.860007i	$-0.329541\pi$
$827$	844.006			1.02056			0.510281	+	0.860007i	$0.329541\pi$
$828$	−15.1964	−	2.14042i	−0.0183531	−	0.00258505i
$829$	222.833	−	222.833i	0.268798	−	0.268798i	−0.559818	−	0.828616i	$-0.689129\pi$
$829$	222.833	−	222.833i	0.268798	−	0.268798i	0.828616	+	0.559818i	$0.189129\pi$
$830$		0			0
$831$	944.609			1.13671
$832$	485.078	+	1267.12i	0.583026	+	1.52298i
$833$	−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
$837$	−676.067			−0.807726
$838$	−96.5320	+	193.540i	−0.115193	+	0.230954i
$839$	554.445			0.660841			0.330420	−	0.943834i	$-0.392809\pi$
$839$	554.445			0.660841			0.330420	+	0.943834i	$0.392809\pi$
$840$		0			0
$841$			225.607i			0.268260i
$842$	594.225	−	1191.38i	0.705730	−	1.41494i
$843$			287.150i			0.340628i
$844$	−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
$848$	−1525.72	−	438.498i	−1.79920	−	0.517096i
$849$		−	1558.55i		−	1.83575i
$850$		0			0
$851$	−135.394	−	135.394i	−0.159100	−	0.159100i
$852$	488.270	+	648.366i	0.573087	+	0.760993i
$853$			431.993i			0.506440i	0.967409	+	0.253220i	$0.0814896\pi$
$853$			431.993i			0.506440i	−0.967409	+	0.253220i	$0.918510\pi$
$854$	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	$-0.873307\pi$
$857$	−457.844	+	457.844i	−0.534241	+	0.534241i	0.387591	+	0.921831i	$0.373307\pi$
$858$	221.188	−	443.465i	0.257795	−	0.516859i
$859$	822.277	+	822.277i	0.957249	+	0.957249i	0.999123	−	0.0418737i	$-0.0133327\pi$
$859$	822.277	+	822.277i	0.957249	+	0.957249i	−0.0418737	+	0.999123i	$0.513333\pi$
$860$		0			0
$861$	−17.6839	−	17.6839i	−0.0205388	−	0.0205388i
$862$	351.102	−	117.418i	0.407311	−	0.136216i
$863$	−132.089	+	132.089i	−0.153058	+	0.153058i	−0.779482	−	0.626424i	$-0.784518\pi$
$863$	−132.089	+	132.089i	−0.153058	+	0.153058i	0.626424	+	0.779482i	$0.284518\pi$
$864$	−39.2113	−	914.023i	−0.0453835	−	1.05790i
$865$		0			0
$866$	448.102	−	898.412i	0.517439	−	1.03743i
$867$			554.775i			0.639879i
$868$	100.609	−	714.293i	0.115909	−	0.822919i
$869$	6.41098	+	6.41098i	0.00737742	+	0.00737742i
$870$		0			0
$871$			2312.37i			2.65485i
$872$	−64.6133	−	349.511i	−0.0740978	−	0.400816i
$873$	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
$877$		−	363.488i		−	0.414468i	−0.978291	−	0.207234i	$-0.933554\pi$
$877$		−	363.488i		−	0.414468i	0.978291	−	0.207234i	$-0.0664461\pi$
$878$	295.360	−	98.7761i	0.336401	−	0.112501i
$879$		−	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	$0.544007\pi$
$882$	7.60218	+	22.7320i	0.00861925	+	0.0257732i
$883$	−1629.94			−1.84592			−0.922959	−	0.384899i	$-0.874236\pi$
$883$	−1629.94			−1.84592			−0.922959	+	0.384899i	$0.874236\pi$
$884$	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	$-0.800077\pi$
$887$	−196.533	+	196.533i	−0.221570	+	0.221570i	0.587589	+	0.809160i	$0.300077\pi$
$888$	821.429	−	1194.02i	0.925032	−	1.34462i
$889$	−1781.27			−2.00368
$890$		0			0
$891$	−201.175	+	201.175i	−0.225786	+	0.225786i
$892$	−71.1431	+	505.096i	−0.0797569	+	0.566251i
$893$	−1351.70			−1.51366
$894$	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
$898$	−29.7792	−	89.0455i	−0.0331617	−	0.0991598i
$899$	414.806	−	414.806i	0.461408	−	0.461408i
$900$		0			0
$901$	−661.707	+	661.707i	−0.734414	+	0.734414i
$902$	−8.91925	−	4.44867i	−0.00988830	−	0.00493200i
$903$	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
$907$	188.488			0.207814			0.103907	−	0.994587i	$-0.466866\pi$
$907$	188.488			0.207814			0.103907	+	0.994587i	$0.466866\pi$
$908$	832.713	+	1105.75i	0.917085	+	1.21778i
$909$	−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	$0.304274\pi$
$912$	−434.881	−	785.672i	−0.476843	−	0.861482i
$913$	−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
$917$	−118.315			−0.129024
$918$	−482.598	−	240.706i	−0.525706	−	0.262207i
$919$	158.471			0.172439			0.0862195	−	0.996276i	$-0.472521\pi$
$919$	158.471			0.172439			0.0862195	+	0.996276i	$0.472521\pi$
$920$		0			0
$921$			1291.01i			1.40175i
$922$	672.931	+	335.639i	0.729860	+	0.364033i
$923$			1551.15i			1.68055i
$924$	−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
$928$	584.864	+	536.747i	0.630241	+	0.578391i
$929$		−	1081.59i		−	1.16425i	−0.813100	−	0.582124i	$-0.802222\pi$
$929$		−	1081.59i		−	1.16425i	0.813100	−	0.582124i	$-0.197778\pi$
$930$		0			0
$931$	131.031	+	131.031i	0.140743	+	0.140743i
$932$	486.207	+	68.4827i	0.521682	+	0.0734793i
$933$		−	588.978i		−	0.631273i
$934$	−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	$-0.869106\pi$
$937$	−484.345	+	484.345i	−0.516910	+	0.516910i	0.399725	+	0.916635i	$0.369106\pi$
$938$	1488.71	+	742.526i	1.58711	+	0.791605i
$939$	−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	$0.612912\pi$
$942$	49.0584	+	146.694i	0.0520790	+	0.155726i
$943$	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
$947$			476.289i			0.502945i	0.967864	+	0.251473i	$0.0809149\pi$
$947$			476.289i			0.502945i	−0.967864	+	0.251473i	$0.919085\pi$
$948$	−14.3562	−	19.0634i	−0.0151437	−	0.0201091i
$949$	−360.750	−	360.750i	−0.380137	−	0.380137i
$950$		0			0
$951$		−	1194.31i		−	1.25585i
$952$	326.134	−	474.065i	0.342578	−	0.497967i
$953$	80.9782	+	80.9782i	0.0849719	+	0.0849719i	0.748315	−	0.663343i	$-0.230863\pi$
$953$	80.9782	+	80.9782i	0.0849719	+	0.0849719i	−0.663343	+	0.748315i	$0.730863\pi$
$954$	82.3755	+	246.319i	0.0863475	+	0.258196i
$955$		0			0
$956$	492.788	+	654.365i	0.515468	+	0.684482i
$957$		−	289.943i		−	0.302971i
$958$	−350.408	−	1047.79i	−0.365771	−	1.09373i
$959$		−	1320.07i		−	1.37651i
$960$		0			0
$961$	−401.801			−0.418107
$962$	2626.71	−	878.443i	2.73047	−	0.913142i
$963$	−26.1170			−0.0271205
$964$	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	$-0.802928\pi$
$967$	−226.347	+	226.347i	−0.234072	+	0.234072i	0.580318	+	0.814390i	$0.302928\pi$
$968$	680.438	+	468.109i	0.702932	+	0.483584i
$969$	−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	$0.338183\pi$
$972$	−223.954	+	168.655i	−0.230406	+	0.173513i
$973$	1763.47			1.81241
$974$	−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	0.596705	−	0.802461i	$-0.296476\pi$
$977$	−201.023	−	201.023i	−0.205756	−	0.205756i	−0.802461	+	0.596705i	$0.796476\pi$
$978$	−642.677	+	214.928i	−0.657134	+	0.219763i
$979$	115.417	−	115.417i	0.117893	−	0.117893i
$980$		0			0
$981$	−41.1200	+	41.1200i	−0.0419164	+	0.0419164i
$982$	−779.966	+	1563.77i	−0.794263	+	1.59244i
$983$	536.933	+	536.933i	0.546218	+	0.546218i	0.925345	−	0.379126i	$-0.123775\pi$
$983$	536.933	+	536.933i	0.546218	+	0.546218i	−0.379126	+	0.925345i	$0.623775\pi$
$984$	21.6143	+	14.8696i	0.0219658	+	0.0151114i
$985$		0			0
$986$	443.789	−	148.415i	0.450090	−	0.150522i
$987$	1412.58			1.43119
$988$	239.359	−	1699.38i	0.242266	−	1.72002i
$989$	−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	$0.699992\pi$
$992$	32.4331	+	756.021i	0.0326947	+	0.762118i
$993$	−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
$997$	−1493.41			−1.49790			−0.748950	−	0.662627i	$-0.769442\pi$
$997$	−1493.41			−1.49790			−0.748950	+	0.662627i	$0.769442\pi$
$998$	543.580	−	1089.84i	0.544669	−	1.09202i
$999$	−1867.56			−1.86943

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.14	✓	44	5.2	odd	4
80.3.i.a.37.14	yes	44	80.69	even	4
80.3.t.a.53.4	yes	44	80.37	odd	4
80.3.t.a.77.4	yes	44	5.4	even	2
320.3.i.a.177.16		44	80.59	odd	4
320.3.i.a.273.7		44	20.7	even	4
320.3.t.a.17.7		44	20.19	odd	2
320.3.t.a.113.7		44	80.27	even	4
400.3.i.b.93.9		44	5.3	odd	4
400.3.i.b.357.9		44	16.5	even	4
400.3.t.b.157.19		44	1.1	even	1	trivial
400.3.t.b.293.19		44	80.53	odd	4	inner
640.3.i.a.33.16		44	40.27	even	4
640.3.i.a.97.7		44	80.19	odd	4
640.3.i.b.33.7		44	40.37	odd	4
640.3.i.b.97.16		44	80.29	even	4
640.3.t.a.353.16		44	80.67	even	4
640.3.t.a.417.16		44	40.19	odd	2
640.3.t.b.353.7		44	80.77	odd	4
640.3.t.b.417.7		44	40.29	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.89674 - 0.634321i) q^{2} -2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 + 5.39242i) q^{7} +(4.53426 - 6.59094i) q^{8} -1.30888 q^{9} +O(q^{10})\)	\(q+(1.89674 - 0.634321i) q^{2} -2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 + 5.39242i) q^{7} +(4.53426 - 6.59094i) q^{8} -1.30888 q^{9} +(2.98007 - 2.98007i) q^{11} +(-8.86141 + 6.67333i) q^{12} -21.2000 q^{13} +(-6.80752 + 13.6486i) q^{14} +(4.41955 - 15.3775i) q^{16} +(-6.66924 - 6.66924i) q^{17} +(-2.48261 + 0.830250i) q^{18} +(-14.3102 + 14.3102i) q^{19} +(14.9547 - 14.9547i) q^{21} +(3.76211 - 7.54275i) q^{22} +(2.07267 + 2.07267i) q^{23} +(-12.5748 + 18.2786i) q^{24} +(-40.2109 + 13.4476i) q^{26} +28.5895 q^{27} +(-4.25454 + 30.2060i) q^{28} +(-17.5413 + 17.5413i) q^{29} -23.6474 q^{31} +(-1.37153 - 31.9706i) q^{32} +(-8.26459 + 8.26459i) q^{33} +(-16.8803 - 8.41940i) q^{34} +(-4.18223 + 3.14954i) q^{36} -65.3234 q^{37} +(-18.0655 + 36.2201i) q^{38} +58.7936 q^{39} -1.18249i q^{41} +(18.8792 - 37.8514i) q^{42} +9.57434i q^{43} +(2.35123 - 16.6930i) q^{44} +(5.24607 + 2.61659i) q^{46} +(47.2286 + 47.2286i) q^{47} +(-12.2567 + 42.6462i) q^{48} -9.15649i q^{49} +(18.4957 + 18.4957i) q^{51} +(-67.7397 + 51.0133i) q^{52} -99.2178i q^{53} +(54.2269 - 18.1349i) q^{54} +(11.0905 + 59.9918i) q^{56} +(39.6863 - 39.6863i) q^{57} +(-22.1445 + 44.3981i) q^{58} +(54.7400 + 54.7400i) q^{59} +(-12.1054 - 12.1054i) q^{61} +(-44.8531 + 15.0000i) q^{62} +(7.05803 - 7.05803i) q^{63} +(-22.8811 - 59.7700i) q^{64} +(-10.4334 + 20.9182i) q^{66} -109.074i q^{67} +(-37.3582 - 5.26193i) q^{68} +(-5.74812 - 5.74812i) q^{69} -73.1674i q^{71} +(-5.93479 + 8.62675i) q^{72} +(17.0166 + 17.0166i) q^{73} +(-123.902 + 41.4360i) q^{74} +(-11.2905 + 80.1595i) q^{76} +32.1396i q^{77} +(111.516 - 37.2940i) q^{78} +2.15129i q^{79} -67.5069 q^{81} +(-0.750081 - 2.24289i) q^{82} -76.4850 q^{83} +(11.7991 - 83.7699i) q^{84} +(6.07320 + 18.1601i) q^{86} +(48.6470 - 48.6470i) q^{87} +(-6.12907 - 33.1539i) q^{88} +38.7296 q^{89} +(114.319 - 114.319i) q^{91} +(11.6102 + 1.63531i) q^{92} +65.5810 q^{93} +(119.539 + 59.6224i) q^{94} +(3.80365 + 88.6636i) q^{96} +(-8.53929 - 8.53929i) q^{97} +(-5.80816 - 17.3675i) q^{98} +(-3.90055 + 3.90055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{8} + 108 q^{9}+O(q^{10}) \) 44 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^8 + 108 * q^9	\( 44 q + 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{8} + 108 q^{9} - 4 q^{11} + 44 q^{12} + 4 q^{13} + 24 q^{16} + 4 q^{17} + 42 q^{18} - 32 q^{19} - 4 q^{21} - 16 q^{22} - 36 q^{24} - 52 q^{26} + 40 q^{27} + 104 q^{28} - 8 q^{31} + 12 q^{32} + 4 q^{33} + 88 q^{34} - 116 q^{36} + 4 q^{37} + 68 q^{38} - 72 q^{39} - 244 q^{42} + 168 q^{44} + 108 q^{46} + 4 q^{47} + 4 q^{48} - 100 q^{51} - 264 q^{52} - 228 q^{54} - 172 q^{56} + 36 q^{57} - 332 q^{58} - 64 q^{59} - 36 q^{61} - 84 q^{62} + 200 q^{63} + 176 q^{64} + 276 q^{66} - 440 q^{68} + 60 q^{69} + 288 q^{72} + 48 q^{73} - 284 q^{74} + 252 q^{76} + 132 q^{78} + 100 q^{81} + 388 q^{82} - 156 q^{83} - 288 q^{84} + 20 q^{86} + 36 q^{87} - 160 q^{88} + 188 q^{91} + 352 q^{92} + 40 q^{93} + 340 q^{94} - 24 q^{96} + 4 q^{97} + 818 q^{98} + 92 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^8 + 108 * q^9 - 4 * q^11 + 44 * q^12 + 4 * q^13 + 24 * q^16 + 4 * q^17 + 42 * q^18 - 32 * q^19 - 4 * q^21 - 16 * q^22 - 36 * q^24 - 52 * q^26 + 40 * q^27 + 104 * q^28 - 8 * q^31 + 12 * q^32 + 4 * q^33 + 88 * q^34 - 116 * q^36 + 4 * q^37 + 68 * q^38 - 72 * q^39 - 244 * q^42 + 168 * q^44 + 108 * q^46 + 4 * q^47 + 4 * q^48 - 100 * q^51 - 264 * q^52 - 228 * q^54 - 172 * q^56 + 36 * q^57 - 332 * q^58 - 64 * q^59 - 36 * q^61 - 84 * q^62 + 200 * q^63 + 176 * q^64 + 276 * q^66 - 440 * q^68 + 60 * q^69 + 288 * q^72 + 48 * q^73 - 284 * q^74 + 252 * q^76 + 132 * q^78 + 100 * q^81 + 388 * q^82 - 156 * q^83 - 288 * q^84 + 20 * q^86 + 36 * q^87 - 160 * q^88 + 188 * q^91 + 352 * q^92 + 40 * q^93 + 340 * q^94 - 24 * q^96 + 4 * q^97 + 818 * q^98 + 92 * q^99

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