LMFDB - Embedded newform 400.3.i.b.357.1

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			357.1
Character	$\chi$	$=$	400.357
Dual form			400.3.i.b.93.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 - 1.12822i) q^{4} +(0.714398 + 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(-7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +O(q^{10})$	\(q+(-1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 - 1.12822i) q^{4} +(0.714398 + 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(-7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +(-8.38398 - 8.38398i) q^{11} +(-2.82844 - 9.62081i) q^{12} -12.9652i q^{13} +(-12.1771 + 16.2724i) q^{14} +(13.4542 - 8.65930i) q^{16} +(22.8157 + 22.8157i) q^{17} +(-5.37460 + 0.773673i) q^{18} +(-3.16584 - 3.16584i) q^{19} +(-18.0145 - 18.0145i) q^{21} +(18.9860 + 14.2078i) q^{22} +(3.81600 + 3.81600i) q^{23} +(8.34073 + 18.2393i) q^{24} +(3.69459 + 25.6658i) q^{26} -29.3694i q^{27} +(19.4688 - 35.6829i) q^{28} +(18.3544 + 18.3544i) q^{29} -8.78531 q^{31} +(-24.1664 + 20.9759i) q^{32} +(-21.0186 + 21.0186i) q^{33} +(-51.6674 - 38.6642i) q^{34} +(10.4191 - 3.06312i) q^{36} -32.4039i q^{37} +(7.16923 + 5.36494i) q^{38} -32.5036 q^{39} -0.937574i q^{41} +(40.7949 + 30.5280i) q^{42} -57.8364 q^{43} +(-41.6333 - 22.7153i) q^{44} +(-8.64156 - 6.46672i) q^{46} +(-27.9276 - 27.9276i) q^{47} +(-21.7088 - 33.7296i) q^{48} -54.2688i q^{49} +(57.1987 - 57.1987i) q^{51} +(-14.6276 - 49.7550i) q^{52} -20.6425 q^{53} +(8.36917 + 58.1395i) q^{54} +(-28.3720 + 76.1855i) q^{56} +(-7.93674 + 7.93674i) q^{57} +(-41.5647 - 31.1040i) q^{58} +(40.1490 - 40.1490i) q^{59} +(-25.3893 + 25.3893i) q^{61} +(17.3913 - 2.50348i) q^{62} +(19.5092 - 19.5092i) q^{63} +(41.8623 - 48.4102i) q^{64} +(35.6187 - 47.5978i) q^{66} +29.3419 q^{67} +(113.298 + 61.8162i) q^{68} +(9.56668 - 9.56668i) q^{69} -34.7686i q^{71} +(-19.7526 + 9.03277i) q^{72} +(-76.2777 - 76.2777i) q^{73} +(9.23390 + 64.1466i) q^{74} +(-15.7210 - 8.57745i) q^{76} -120.490 q^{77} +(64.3439 - 9.26230i) q^{78} -17.2292i q^{79} -49.1938 q^{81} +(0.267173 + 1.85602i) q^{82} -73.3919i q^{83} +(-89.4566 - 48.8080i) q^{84} +(114.493 - 16.4812i) q^{86} +(46.0144 - 46.0144i) q^{87} +(88.8901 + 33.1032i) q^{88} -96.9216 q^{89} +(-93.1639 - 93.1639i) q^{91} +(18.9496 + 10.3390i) q^{92} +22.0247i q^{93} +(63.2437 + 47.3270i) q^{94} +(52.5863 + 60.5848i) q^{96} +(53.4378 + 53.4378i) q^{97} +(15.4646 + 107.430i) q^{98} +(-22.7625 - 22.7625i) 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.97960	+	0.284962i	−0.989798	+	0.142481i
$2$	−1.97960	+	0.284962i	−0.989798	+	0.142481i
$3$		−	2.50699i		−	0.835664i	−0.908524	−	0.417832i	$-0.862790\pi$
$3$		−	2.50699i		−	0.835664i	0.908524	−	0.417832i	$-0.137210\pi$
$4$	3.83759	−	1.12822i	0.959398	−	0.282055i
$5$		0			0
$5$		0			0
$6$	0.714398	+	4.96283i	0.119066	+	0.827138i
$7$	7.18571	−	7.18571i	1.02653	−	1.02653i	0.0268912	−	0.999638i	$-0.491439\pi$
$7$	7.18571	−	7.18571i	1.02653	−	1.02653i	0.999638	−	0.0268912i	$-0.00856076\pi$
$8$	−7.27538	+	3.32699i	−0.909422	+	0.415874i
$9$	2.71500			0.301666
$10$		0			0
$11$	−8.38398	−	8.38398i	−0.762180	−	0.762180i	0.214536	−	0.976716i	$-0.431176\pi$
$11$	−8.38398	−	8.38398i	−0.762180	−	0.762180i	−0.976716	+	0.214536i	$0.931176\pi$
$12$	−2.82844	−	9.62081i	−0.235703	−	0.801734i
$13$		−	12.9652i		−	0.997321i	−0.866797	−	0.498660i	$-0.833825\pi$
$13$		−	12.9652i		−	0.997321i	0.866797	−	0.498660i	$-0.166175\pi$
$14$	−12.1771	+	16.2724i	−0.869795	+	1.16232i
$15$		0			0
$16$	13.4542	−	8.65930i	0.840890	−	0.541206i
$17$	22.8157	+	22.8157i	1.34210	+	1.34210i	0.893967	+	0.448132i	$0.147911\pi$
$17$	22.8157	+	22.8157i	1.34210	+	1.34210i	0.448132	+	0.893967i	$0.352089\pi$
$18$	−5.37460	+	0.773673i	−0.298589	+	0.0429818i
$19$	−3.16584	−	3.16584i	−0.166623	−	0.166623i	0.618870	−	0.785493i	$-0.287591\pi$
$19$	−3.16584	−	3.16584i	−0.166623	−	0.166623i	−0.785493	+	0.618870i	$0.787591\pi$
$20$		0			0
$21$	−18.0145	−	18.0145i	−0.857833	−	0.857833i
$22$	18.9860	+	14.2078i	0.863000	+	0.645808i
$23$	3.81600	+	3.81600i	0.165913	+	0.165913i	0.785180	−	0.619267i	$-0.212570\pi$
$23$	3.81600	+	3.81600i	0.165913	+	0.165913i	−0.619267	+	0.785180i	$0.712570\pi$
$24$	8.34073	+	18.2393i	0.347531	+	0.759971i
$25$		0			0
$26$	3.69459	+	25.6658i	0.142100	+	0.987146i
$27$		−	29.3694i		−	1.08776i
$28$	19.4688	−	35.6829i	0.695313	−	1.27439i
$29$	18.3544	+	18.3544i	0.632911	+	0.632911i	0.948797	−	0.315886i	$-0.102302\pi$
$29$	18.3544	+	18.3544i	0.632911	+	0.632911i	−0.315886	+	0.948797i	$0.602302\pi$
$30$		0			0
$31$	−8.78531			−0.283397			−0.141698	−	0.989910i	$-0.545256\pi$
$31$	−8.78531			−0.283397			−0.141698	+	0.989910i	$0.545256\pi$
$32$	−24.1664	+	20.9759i	−0.755199	+	0.655496i
$33$	−21.0186	+	21.0186i	−0.636926	+	0.636926i
$34$	−51.6674	−	38.6642i	−1.51963	−	1.13718i
$35$		0			0
$36$	10.4191	−	3.06312i	0.289418	−	0.0850866i
$37$		−	32.4039i		−	0.875781i	−0.899028	−	0.437891i	$-0.855726\pi$
$37$		−	32.4039i		−	0.875781i	0.899028	−	0.437891i	$-0.144274\pi$
$38$	7.16923	+	5.36494i	0.188664	+	0.141183i
$39$	−32.5036			−0.833425
$40$		0			0
$41$		−	0.937574i		−	0.0228677i	−0.999935	−	0.0114338i	$-0.996360\pi$
$41$		−	0.937574i		−	0.0228677i	0.999935	−	0.0114338i	$-0.00363958\pi$
$42$	40.7949	+	30.5280i	0.971306	+	0.726856i
$43$	−57.8364			−1.34503			−0.672516	−	0.740083i	$-0.734786\pi$
$43$	−57.8364			−1.34503			−0.672516	+	0.740083i	$0.734786\pi$
$44$	−41.6333	−	22.7153i	−0.946211	−	0.516257i
$45$		0			0
$46$	−8.64156	−	6.46672i	−0.187860	−	0.140581i
$47$	−27.9276	−	27.9276i	−0.594205	−	0.594205i	0.344560	−	0.938764i	$-0.388028\pi$
$47$	−27.9276	−	27.9276i	−0.594205	−	0.594205i	−0.938764	+	0.344560i	$0.888028\pi$
$48$	−21.7088	−	33.7296i	−0.452266	−	0.702701i
$49$		−	54.2688i		−	1.10753i
$50$		0			0
$51$	57.1987	−	57.1987i	1.12154	−	1.12154i
$52$	−14.6276	−	49.7550i	−0.281300	−	0.956828i
$53$	−20.6425			−0.389482			−0.194741	−	0.980855i	$-0.562387\pi$
$53$	−20.6425			−0.389482			−0.194741	+	0.980855i	$0.562387\pi$
$54$	8.36917	+	58.1395i	0.154985	+	1.07666i
$55$		0			0
$56$	−28.3720	+	76.1855i	−0.506642	+	1.36046i
$57$	−7.93674	+	7.93674i	−0.139241	+	0.139241i
$58$	−41.5647	−	31.1040i	−0.716632	−	0.536276i
$59$	40.1490	−	40.1490i	0.680492	−	0.680492i	−0.279619	−	0.960111i	$-0.590208\pi$
$59$	40.1490	−	40.1490i	0.680492	−	0.680492i	0.960111	+	0.279619i	$0.0902081\pi$
$60$		0			0
$61$	−25.3893	+	25.3893i	−0.416217	+	0.416217i	−0.883898	−	0.467680i	$-0.845090\pi$
$61$	−25.3893	+	25.3893i	−0.416217	+	0.416217i	0.467680	+	0.883898i	$0.345090\pi$
$62$	17.3913	−	2.50348i	0.280506	−	0.0403788i
$63$	19.5092	−	19.5092i	0.309669	−	0.309669i
$64$	41.8623	−	48.4102i	0.654098	−	0.756410i
$65$		0			0
$66$	35.6187	−	47.5978i	0.539678	−	0.721178i
$67$	29.3419			0.437938			0.218969	−	0.975732i	$-0.429731\pi$
$67$	29.3419			0.437938			0.218969	+	0.975732i	$0.429731\pi$
$68$	113.298	+	61.8162i	1.66615	+	0.909062i
$69$	9.56668	−	9.56668i	0.138648	−	0.138648i
$70$		0			0
$71$		−	34.7686i		−	0.489698i	−0.969561	−	0.244849i	$-0.921262\pi$
$71$		−	34.7686i		−	0.489698i	0.969561	−	0.244849i	$-0.0787385\pi$
$72$	−19.7526	+	9.03277i	−0.274342	+	0.125455i
$73$	−76.2777	−	76.2777i	−1.04490	−	1.04490i	−0.998943	−	0.0459567i	$-0.985366\pi$
$73$	−76.2777	−	76.2777i	−1.04490	−	1.04490i	−0.0459567	−	0.998943i	$-0.514634\pi$
$74$	9.23390	+	64.1466i	0.124782	+	0.866846i
$75$		0			0
$76$	−15.7210	−	8.57745i	−0.206855	−	0.112861i
$77$	−120.490			−1.56480
$78$	64.3439	−	9.26230i	0.824922	−	0.118747i
$79$		−	17.2292i		−	0.218092i	−0.994037	−	0.109046i	$-0.965220\pi$
$79$		−	17.2292i		−	0.218092i	0.994037	−	0.109046i	$-0.0347795\pi$
$80$		0			0
$81$	−49.1938			−0.607331
$82$	0.267173	+	1.85602i	0.00325821	+	0.0226344i
$83$		−	73.3919i		−	0.884239i	−0.896956	−	0.442120i	$-0.854227\pi$
$83$		−	73.3919i		−	0.884239i	0.896956	−	0.442120i	$-0.145773\pi$
$84$	−89.4566	−	48.8080i	−1.06496	−	0.581047i
$85$		0			0
$86$	114.493	−	16.4812i	1.33131	−	0.191642i
$87$	46.0144	−	46.0144i	0.528901	−	0.528901i
$88$	88.8901	+	33.1032i	1.01011	+	0.376173i
$89$	−96.9216			−1.08901			−0.544503	−	0.838759i	$-0.683282\pi$
$89$	−96.9216			−1.08901			−0.544503	+	0.838759i	$0.683282\pi$
$90$		0			0
$91$	−93.1639	−	93.1639i	−1.02378	−	1.02378i
$92$	18.9496	+	10.3390i	0.205973	+	0.112380i
$93$			22.0247i			0.236825i
$94$	63.2437	+	47.3270i	0.672805	+	0.503479i
$95$		0			0
$96$	52.5863	+	60.5848i	0.547774	+	0.631092i
$97$	53.4378	+	53.4378i	0.550905	+	0.550905i	0.926702	−	0.375797i	$-0.122631\pi$
$97$	53.4378	+	53.4378i	0.550905	+	0.550905i	−0.375797	+	0.926702i	$0.622631\pi$
$98$	15.4646	+	107.430i	0.157802	+	1.09623i
$99$	−22.7625	−	22.7625i	−0.229924	−	0.229924i
$100$		0			0
$101$	67.9450	+	67.9450i	0.672723	+	0.672723i	0.958343	−	0.285620i	$-0.0921995\pi$
$101$	67.9450	+	67.9450i	0.672723	+	0.672723i	−0.285620	+	0.958343i	$0.592200\pi$
$102$	−96.9308	+	129.530i	−0.950302	+	1.26990i
$103$	132.887	+	132.887i	1.29017	+	1.29017i	0.934681	+	0.355486i	$0.115685\pi$
$103$	132.887	+	132.887i	1.29017	+	1.29017i	0.355486	+	0.934681i	$0.384315\pi$
$104$	43.1350	+	94.3265i	0.414760	+	0.906986i
$105$		0			0
$106$	40.8639	−	5.88235i	0.385508	−	0.0554939i
$107$			44.9125i			0.419743i	0.977729	+	0.209872i	$0.0673046\pi$
$107$			44.9125i			0.419743i	−0.977729	+	0.209872i	$0.932695\pi$
$108$	−33.1352	−	112.708i	−0.306807	−	1.04359i
$109$	31.7568	+	31.7568i	0.291346	+	0.291346i	0.837612	−	0.546266i	$-0.183951\pi$
$109$	31.7568	+	31.7568i	0.291346	+	0.291346i	−0.546266	+	0.837612i	$0.683951\pi$
$110$		0			0
$111$	−81.2363			−0.731859
$112$	34.4550	−	158.901i	0.307634	−	1.41876i
$113$	−5.56976	+	5.56976i	−0.0492899	+	0.0492899i	−0.731322	−	0.682032i	$-0.761096\pi$
$113$	−5.56976	+	5.56976i	−0.0492899	+	0.0492899i	0.682032	+	0.731322i	$0.261096\pi$
$114$	13.4499	−	17.9732i	0.117981	−	0.157660i
$115$		0			0
$116$	91.1447	+	49.7290i	0.785730	+	0.428698i
$117$		−	35.2004i		−	0.300858i
$118$	−68.0379	+	90.9198i	−0.576592	+	0.770507i
$119$	327.894			2.75541
$120$		0			0
$121$			19.5823i			0.161837i
$122$	43.0255	−	57.4954i	0.352668	−	0.471274i
$123$	−2.35049			−0.0191097
$124$	−33.7144	+	9.91176i	−0.271891	+	0.0799336i
$125$		0			0
$126$	−33.0609	+	44.1797i	−0.262388	+	0.350632i
$127$	106.254	+	106.254i	0.836645	+	0.836645i	0.988416	−	0.151771i	$-0.0484977\pi$
$127$	106.254	+	106.254i	0.836645	+	0.836645i	−0.151771	+	0.988416i	$0.548498\pi$
$128$	−69.0753	+	107.762i	−0.539650	+	0.841889i
$129$			144.995i			1.12399i
$130$		0			0
$131$	−59.7795	+	59.7795i	−0.456332	+	0.456332i	−0.897449	−	0.441117i	$-0.854582\pi$
$131$	−59.7795	+	59.7795i	−0.456332	+	0.456332i	0.441117	+	0.897449i	$0.354582\pi$
$132$	−56.9471	+	104.374i	−0.431418	+	0.790714i
$133$	−45.4976			−0.342088
$134$	−58.0850	+	8.36133i	−0.433470	+	0.0623980i
$135$		0			0
$136$	−241.900	−	90.0852i	−1.77868	−	0.662391i
$137$	−126.441	+	126.441i	−0.922925	+	0.922925i	−0.997235	−	0.0743099i	$-0.976325\pi$
$137$	−126.441	+	126.441i	−0.922925	+	0.922925i	0.0743099	+	0.997235i	$0.476325\pi$
$138$	−16.2120	+	21.6643i	−0.117478	+	0.156988i
$139$	−41.3857	+	41.3857i	−0.297739	+	0.297739i	−0.840128	−	0.542389i	$-0.817520\pi$
$139$	−41.3857	+	41.3857i	−0.297739	+	0.297739i	0.542389	+	0.840128i	$0.317520\pi$
$140$		0			0
$141$	−70.0143	+	70.0143i	−0.496555	+	0.496555i
$142$	9.90774	+	68.8277i	0.0697728	+	0.484702i
$143$	−108.700	+	108.700i	−0.760138	+	0.760138i
$144$	36.5282	−	23.5100i	0.253668	−	0.163264i
$145$		0			0
$146$	172.735	+	129.263i	1.18312	+	0.885361i
$147$	−136.051			−0.925519
$148$	−36.5588	−	124.353i	−0.247019	−	0.840223i
$149$	30.0503	−	30.0503i	0.201680	−	0.201680i	−0.599040	−	0.800719i	$-0.704451\pi$
$149$	30.0503	−	30.0503i	0.201680	−	0.201680i	0.800719	+	0.599040i	$0.204451\pi$
$150$		0			0
$151$		−	26.0891i		−	0.172776i	−0.996262	−	0.0863878i	$-0.972468\pi$
$151$		−	26.0891i		−	0.172776i	0.996262	−	0.0863878i	$-0.0275324\pi$
$152$	33.5654	+	12.5000i	0.220825	+	0.0822367i
$153$	61.9445	+	61.9445i	0.404866	+	0.404866i
$154$	238.521	−	34.3350i	1.54884	−	0.222955i
$155$		0			0
$156$	−124.735	+	36.6712i	−0.799586	+	0.235072i
$157$	2.64846			0.0168691			0.00843457	−	0.999964i	$-0.497315\pi$
$157$	2.64846			0.0168691			0.00843457	+	0.999964i	$0.497315\pi$
$158$	4.90969	+	34.1069i	0.0310740	+	0.215866i
$159$			51.7507i			0.325476i
$160$		0			0
$161$	54.8413			0.340629
$162$	97.3838	−	14.0184i	0.601135	−	0.0865333i
$163$			143.714i			0.881682i	0.897585	+	0.440841i	$0.145320\pi$
$163$			143.714i			0.881682i	−0.897585	+	0.440841i	$0.854680\pi$
$164$	−1.05779	−	3.59803i	−0.00644994	−	0.0219392i
$165$		0			0
$166$	20.9139	+	145.286i	0.125987	+	0.875218i
$167$	192.906	−	192.906i	1.15513	−	1.15513i	0.169619	−	0.985510i	$-0.445746\pi$
$167$	192.906	−	192.906i	1.15513	−	1.15513i	0.985510	−	0.169619i	$-0.0542536\pi$
$168$	190.996	+	71.1283i	1.13688	+	0.423382i
$169$	0.904324			0.00535103
$170$		0			0
$171$	−8.59526	−	8.59526i	−0.0502647	−	0.0502647i
$172$	−221.952	+	65.2522i	−1.29042	+	0.379373i
$173$		−	2.04705i		−	0.0118326i	−0.999982	−	0.00591632i	$-0.998117\pi$
$173$		−	2.04705i		−	0.0118326i	0.999982	−	0.00591632i	$-0.00188323\pi$
$174$	−77.9775	+	104.202i	−0.448146	+	0.598863i
$175$		0			0
$176$	−185.400	−	40.2006i	−1.05341	−	0.228413i
$177$	−100.653	−	100.653i	−0.568663	−	0.568663i
$178$	191.865	−	27.6190i	1.07790	−	0.155163i
$179$	−101.208	−	101.208i	−0.565405	−	0.565405i	0.365432	−	0.930838i	$-0.380921\pi$
$179$	−101.208	−	101.208i	−0.565405	−	0.565405i	−0.930838	+	0.365432i	$0.880921\pi$
$180$		0			0
$181$	154.013	+	154.013i	0.850901	+	0.850901i	0.990244	−	0.139343i	$-0.0444991\pi$
$181$	154.013	+	154.013i	0.850901	+	0.850901i	−0.139343	+	0.990244i	$0.544499\pi$
$182$	210.975	+	157.879i	1.15920	+	0.867465i
$183$	63.6506	+	63.6506i	0.347818	+	0.347818i
$184$	−40.4587	−	15.0671i	−0.219884	−	0.0818862i
$185$		0			0
$186$	−6.27621	−	43.6000i	−0.0337431	−	0.234408i
$187$		−	382.573i		−	2.04584i
$188$	−138.683	−	75.6663i	−0.737677	−	0.402480i
$189$	−211.040	−	211.040i	−1.11661	−	1.11661i
$190$		0			0
$191$	45.3049			0.237198			0.118599	−	0.992942i	$-0.462160\pi$
$191$	45.3049			0.237198			0.118599	+	0.992942i	$0.462160\pi$
$192$	−121.364	−	104.948i	−0.632104	−	0.546606i
$193$	176.113	−	176.113i	0.912503	−	0.912503i	−0.0839658	−	0.996469i	$-0.526759\pi$
$193$	176.113	−	176.113i	0.912503	−	0.912503i	0.996469	+	0.0839658i	$0.0267586\pi$
$194$	−121.013	−	90.5575i	−0.623778	−	0.466791i
$195$		0			0
$196$	−61.2271	−	208.261i	−0.312383	−	1.06256i
$197$			308.173i			1.56433i	0.623072	+	0.782164i	$0.285884\pi$
$197$			308.173i			1.56433i	−0.623072	+	0.782164i	$0.714116\pi$
$198$	51.5470	+	38.5741i	0.260338	+	0.194818i
$199$	190.912			0.959358			0.479679	−	0.877444i	$-0.340753\pi$
$199$	190.912			0.959358			0.479679	+	0.877444i	$0.340753\pi$
$200$		0			0
$201$		−	73.5598i		−	0.365969i
$202$	−153.865	−	115.142i	−0.761710	−	0.570009i
$203$	263.779			1.29940
$204$	154.973	−	284.038i	0.759670	−	1.39234i
$205$		0			0
$206$	−300.931	−	225.195i	−1.46083	−	1.09318i
$207$	10.3604	+	10.3604i	0.0500504	+	0.0500504i
$208$	−112.269	−	174.436i	−0.539756	−	0.838637i
$209$			53.0847i			0.253994i
$210$		0			0
$211$	230.999	−	230.999i	1.09478	−	1.09478i	0.0997692	−	0.995011i	$-0.468190\pi$
$211$	230.999	−	230.999i	1.09478	−	1.09478i	0.995011	−	0.0997692i	$-0.0318104\pi$
$212$	−79.2177	+	23.2893i	−0.373668	+	0.109855i
$213$	−87.1645			−0.409223
$214$	−12.7984	−	88.9086i	−0.0598055	−	0.415461i
$215$		0			0
$216$	97.7117	+	213.673i	0.452369	+	0.989229i
$217$	−63.1286	+	63.1286i	−0.290915	+	0.290915i
$218$	−71.9150	−	53.8160i	−0.329885	−	0.246863i
$219$	−191.228	+	191.228i	−0.873185	+	0.873185i
$220$		0			0
$221$	295.809	−	295.809i	1.33850	−	1.33850i
$222$	160.815	−	23.1493i	0.724392	−	0.104276i
$223$	60.6724	−	60.6724i	0.272073	−	0.272073i	−0.557861	−	0.829934i	$-0.688378\pi$
$223$	60.6724	−	60.6724i	0.272073	−	0.272073i	0.829934	+	0.557861i	$0.188378\pi$
$224$	−22.9260	+	324.379i	−0.102348	+	1.44812i
$225$		0			0
$226$	9.43869	−	12.6130i	0.0417641	−	0.0558099i
$227$	202.529			0.892199			0.446099	−	0.894983i	$-0.352813\pi$
$227$	202.529			0.892199			0.446099	+	0.894983i	$0.352813\pi$
$228$	−21.5036	+	39.4124i	−0.0943139	+	0.172861i
$229$	137.361	−	137.361i	0.599829	−	0.599829i	−0.340438	−	0.940267i	$-0.610575\pi$
$229$	137.361	−	137.361i	0.599829	−	0.599829i	0.940267	+	0.340438i	$0.110575\pi$
$230$		0			0
$231$			302.067i			1.30765i
$232$	−194.600	−	72.4704i	−0.838795	−	0.312372i
$233$	−197.272	−	197.272i	−0.846660	−	0.846660i	0.143055	−	0.989715i	$-0.454308\pi$
$233$	−197.272	−	197.272i	−0.846660	−	0.846660i	−0.989715	+	0.143055i	$0.954308\pi$
$234$	10.0308	+	69.6826i	0.0428667	+	0.297789i
$235$		0			0
$236$	108.779	−	199.373i	0.460927	−	0.844799i
$237$	−43.1935			−0.182251
$238$	−649.097	+	93.4374i	−2.72730	+	0.392594i
$239$			411.923i			1.72353i	0.507310	+	0.861763i	$0.330640\pi$
$239$			411.923i			1.72353i	−0.507310	+	0.861763i	$0.669360\pi$
$240$		0			0
$241$	−293.936			−1.21965			−0.609826	−	0.792535i	$-0.708761\pi$
$241$	−293.936			−1.21965			−0.609826	+	0.792535i	$0.708761\pi$
$242$	−5.58023	−	38.7651i	−0.0230588	−	0.160186i
$243$		−	140.996i		−	0.580231i
$244$	−68.7890	+	126.078i	−0.281922	+	0.516714i
$245$		0			0
$246$	4.65302	−	0.669801i	0.0189147	−	0.00272277i
$247$	−41.0457	+	41.0457i	−0.166177	+	0.166177i
$248$	63.9164	−	29.2286i	0.257728	−	0.117857i
$249$	−183.993			−0.738926
$250$		0			0
$251$	198.365	+	198.365i	0.790298	+	0.790298i	0.981542	−	0.191244i	$-0.0612523\pi$
$251$	198.365	+	198.365i	0.790298	+	0.790298i	−0.191244	+	0.981542i	$0.561252\pi$
$252$	52.8576	−	96.8789i	0.209752	−	0.384440i
$253$		−	63.9866i		−	0.252911i
$254$	−240.618	−	180.061i	−0.947315	−	0.708902i
$255$		0			0
$256$	106.033	−	233.009i	0.414191	−	0.910190i
$257$	239.646	+	239.646i	0.932473	+	0.932473i	0.997860	−	0.0653871i	$-0.0208282\pi$
$257$	239.646	+	239.646i	0.932473	+	0.932473i	−0.0653871	+	0.997860i	$0.520828\pi$
$258$	−41.3182	−	287.032i	−0.160148	−	1.11253i
$259$	−232.845	−	232.845i	−0.899015	−	0.899015i
$260$		0			0
$261$	49.8322	+	49.8322i	0.190928	+	0.190928i
$262$	101.304	−	135.374i	0.386658	−	0.516695i
$263$	−142.437	−	142.437i	−0.541585	−	0.541585i	0.382408	−	0.923993i	$-0.375095\pi$
$263$	−142.437	−	142.437i	−0.541585	−	0.541585i	−0.923993	+	0.382408i	$0.875095\pi$
$264$	82.9895	−	222.847i	0.314354	−	0.844116i
$265$		0			0
$266$	90.0669	−	12.9651i	0.338597	−	0.0487411i
$267$			242.981i			0.910043i
$268$	112.602	−	33.1041i	0.420157	−	0.123523i
$269$	−269.805	−	269.805i	−1.00299	−	1.00299i	−0.999996	−	0.00299625i	$-0.999046\pi$
$269$	−269.805	−	269.805i	−1.00299	−	1.00299i	−0.00299625	−	0.999996i	$-0.500954\pi$
$270$		0			0
$271$	71.4599			0.263690			0.131845	−	0.991270i	$-0.457910\pi$
$271$	71.4599			0.263690			0.131845	+	0.991270i	$0.457910\pi$
$272$	504.536	+	109.400i	1.85491	+	0.402205i
$273$	−233.561	+	233.561i	−0.855535	+	0.855535i
$274$	214.271	−	286.332i	0.782010	−	1.04501i
$275$		0			0
$276$	25.9197	−	47.5064i	0.0939120	−	0.172124i
$277$		−	256.078i		−	0.924470i	−0.886758	−	0.462235i	$-0.847048\pi$
$277$		−	256.078i		−	0.924470i	0.886758	−	0.462235i	$-0.152952\pi$
$278$	70.1335	−	93.7202i	0.252279	−	0.337123i
$279$	−23.8521			−0.0854914
$280$		0			0
$281$			315.882i			1.12413i	0.827092	+	0.562067i	$0.189994\pi$
$281$			315.882i			1.12413i	−0.827092	+	0.562067i	$0.810006\pi$
$282$	118.648	−	158.551i	0.420739	−	0.562239i
$283$	8.65428			0.0305805			0.0152903	−	0.999883i	$-0.495133\pi$
$283$	8.65428			0.0305805			0.0152903	+	0.999883i	$0.495133\pi$
$284$	−39.2266	−	133.428i	−0.138122	−	0.469816i
$285$		0			0
$286$	184.206	−	246.157i	0.644078	−	0.860688i
$287$	−6.73713	−	6.73713i	−0.0234743	−	0.0234743i
$288$	−65.6116	+	56.9494i	−0.227818	+	0.197741i
$289$			752.111i			2.60246i
$290$		0			0
$291$	133.968	−	133.968i	0.460372	−	0.460372i
$292$	−378.781	−	206.665i	−1.29719	−	0.707756i
$293$	533.382			1.82042			0.910208	−	0.414151i	$-0.135921\pi$
$293$	533.382			1.82042			0.910208	+	0.414151i	$0.135921\pi$
$294$	269.326	−	38.7695i	0.916076	−	0.131869i
$295$		0			0
$296$	107.807	+	235.751i	0.364215	+	0.796455i
$297$	−246.232	+	246.232i	−0.829066	+	0.829066i
$298$	−50.9241	+	68.0505i	−0.170886	+	0.228357i
$299$	49.4751	−	49.4751i	0.165469	−	0.165469i
$300$		0			0
$301$	−415.595	+	415.595i	−1.38072	+	1.38072i
$302$	7.43442	+	51.6459i	0.0246173	+	0.171013i
$303$	170.338	−	170.338i	0.562170	−	0.562170i
$304$	−70.0080	−	15.1800i	−0.230289	−	0.0499342i
$305$		0			0
$306$	−140.277	−	104.973i	−0.458422	−	0.343050i
$307$	−322.054			−1.04903			−0.524517	−	0.851400i	$-0.675754\pi$
$307$	−322.054			−1.04903			−0.524517	+	0.851400i	$0.675754\pi$
$308$	−462.390	+	135.939i	−1.50127	+	0.441360i
$309$	333.147	−	333.147i	1.07815	−	1.07815i
$310$		0			0
$311$		−	10.0499i		−	0.0323149i	−0.999869	−	0.0161575i	$-0.994857\pi$
$311$		−	10.0499i		−	0.0323149i	0.999869	−	0.0161575i	$-0.00514331\pi$
$312$	236.476	−	108.139i	0.757935	−	0.346599i
$313$	13.4351	+	13.4351i	0.0429237	+	0.0429237i	0.728243	−	0.685319i	$-0.240337\pi$
$313$	13.4351	+	13.4351i	0.0429237	+	0.0429237i	−0.685319	+	0.728243i	$0.740337\pi$
$314$	−5.24287	+	0.754711i	−0.0166970	+	0.00240354i
$315$		0			0
$316$	−19.4384	−	66.1188i	−0.0615139	−	0.209237i
$317$	182.394			0.575377			0.287688	−	0.957724i	$-0.407113\pi$
$317$	182.394			0.575377			0.287688	+	0.957724i	$0.407113\pi$
$318$	−14.7470	−	102.445i	−0.0463742	−	0.322155i
$319$		−	307.766i		−	0.964785i
$320$		0			0
$321$	112.595			0.350764
$322$	−108.564	+	15.6277i	−0.337154	+	0.0485333i
$323$		−	144.462i		−	0.447250i
$324$	−188.786	+	55.5015i	−0.582672	+	0.171301i
$325$		0			0
$326$	−40.9532	−	284.496i	−0.125623	−	0.872687i
$327$	79.6139	−	79.6139i	0.243468	−	0.243468i
$328$	3.11930	+	6.82121i	0.00951006	+	0.0207964i
$329$	−401.359			−1.21994
$330$		0			0
$331$	−213.565	−	213.565i	−0.645211	−	0.645211i	0.306621	−	0.951832i	$-0.400802\pi$
$331$	−213.565	−	213.565i	−0.645211	−	0.645211i	−0.951832	+	0.306621i	$0.900802\pi$
$332$	−82.8022	−	281.648i	−0.249404	−	0.848337i
$333$		−	87.9766i		−	0.264194i
$334$	−326.906	+	436.848i	−0.978759	+	1.30793i
$335$		0			0
$336$	−398.364	−	86.3783i	−1.18561	−	0.257078i
$337$	99.5263	+	99.5263i	0.295330	+	0.295330i	0.839182	−	0.543851i	$-0.183034\pi$
$337$	99.5263	+	99.5263i	0.295330	+	0.295330i	−0.543851	+	0.839182i	$0.683034\pi$
$338$	−1.79020	+	0.257699i	−0.00529644	+	0.000762422i
$339$	13.9633	+	13.9633i	0.0411898	+	0.0411898i
$340$		0			0
$341$	73.6559	+	73.6559i	0.216000	+	0.216000i
$342$	19.4645	+	14.5658i	0.0569136	+	0.0425901i
$343$	−37.8598	−	37.8598i	−0.110378	−	0.110378i
$344$	420.782	−	192.421i	1.22320	−	0.559364i
$345$		0			0
$346$	0.583332	+	4.05232i	0.00168593	+	0.0117119i
$347$			481.819i			1.38853i	0.719721	+	0.694264i	$0.244270\pi$
$347$			481.819i			1.38853i	−0.719721	+	0.694264i	$0.755730\pi$
$348$	124.670	−	228.499i	0.358247	−	0.656606i
$349$	398.473	+	398.473i	1.14176	+	1.14176i	0.988129	+	0.153628i	$0.0490957\pi$
$349$	398.473	+	398.473i	1.14176	+	1.14176i	0.153628	+	0.988129i	$0.450904\pi$
$350$		0			0
$351$	−380.779			−1.08484
$352$	378.472	+	26.7491i	1.07520	+	0.0759917i
$353$	−356.849	+	356.849i	−1.01090	+	1.01090i	−0.0109648	+	0.999940i	$0.503490\pi$
$353$	−356.849	+	356.849i	−1.01090	+	1.01090i	−0.999940	+	0.0109648i	$0.996510\pi$
$354$	227.935	+	170.570i	0.643884	+	0.481837i
$355$		0			0
$356$	−371.946	+	109.349i	−1.04479	+	0.307160i
$357$		−	822.027i		−	2.30260i
$358$	229.190	+	171.510i	0.640197	+	0.479077i
$359$	−417.857			−1.16395			−0.581974	−	0.813207i	$-0.697719\pi$
$359$	−417.857			−1.16395			−0.581974	+	0.813207i	$0.697719\pi$
$360$		0			0
$361$		−	340.955i		−	0.944473i
$362$	−348.772	−	260.996i	−0.963457	−	0.720982i
$363$	49.0927			0.135242
$364$	−462.635	−	252.416i	−1.27097	−	0.693450i
$365$		0			0
$366$	−144.141	−	107.864i	−0.393827	−	0.294712i
$367$	109.049	+	109.049i	0.297136	+	0.297136i	0.839891	−	0.542755i	$-0.182619\pi$
$367$	109.049	+	109.049i	0.297136	+	0.297136i	−0.542755	+	0.839891i	$0.682619\pi$
$368$	84.3853	+	18.2975i	0.229308	+	0.0497214i
$369$		−	2.54551i		−	0.00689841i
$370$		0			0
$371$	−148.331	+	148.331i	−0.399815	+	0.399815i
$372$	24.8487	+	84.5218i	0.0667976	+	0.227209i
$373$	308.832			0.827968			0.413984	−	0.910284i	$-0.364137\pi$
$373$	308.832			0.827968			0.413984	+	0.910284i	$0.364137\pi$
$374$	109.019	+	757.339i	0.291494	+	2.02497i
$375$		0			0
$376$	296.099	+	110.269i	0.787497	+	0.293269i
$377$	237.968	−	237.968i	0.631216	−	0.631216i
$378$	477.912	+	357.635i	1.26432	+	0.946124i
$379$	−28.3677	+	28.3677i	−0.0748489	+	0.0748489i	−0.743540	−	0.668691i	$-0.766855\pi$
$379$	−28.3677	+	28.3677i	−0.0748489	+	0.0748489i	0.668691	+	0.743540i	$0.266855\pi$
$380$		0			0
$381$	266.377	−	266.377i	0.699153	−	0.699153i
$382$	−89.6853	+	12.9102i	−0.234778	+	0.0337963i
$383$	−422.953	+	422.953i	−1.10432	+	1.10432i	−0.110433	+	0.993884i	$0.535224\pi$
$383$	−422.953	+	422.953i	−1.10432	+	1.10432i	−0.993884	+	0.110433i	$0.964776\pi$
$384$	270.158	+	173.171i	0.703536	+	0.450966i
$385$		0			0
$386$	−298.447	+	398.818i	−0.773179	+	1.03321i
$387$	−157.026			−0.405751
$388$	265.362	+	144.783i	0.683923	+	0.373152i
$389$	−178.975	+	178.975i	−0.460089	+	0.460089i	−0.898685	−	0.438595i	$-0.855476\pi$
$389$	−178.975	+	178.975i	−0.460089	+	0.460089i	0.438595	+	0.898685i	$0.355476\pi$
$390$		0			0
$391$			174.129i			0.445344i
$392$	180.552	+	394.826i	0.460591	+	1.00721i
$393$	149.867	+	149.867i	0.381340	+	0.381340i
$394$	−87.8177	−	610.057i	−0.222888	−	1.54837i
$395$		0			0
$396$	−113.034	−	61.6721i	−0.285440	−	0.155738i
$397$	−20.4646			−0.0515480			−0.0257740	−	0.999668i	$-0.508205\pi$
$397$	−20.4646			−0.0515480			−0.0257740	+	0.999668i	$0.508205\pi$
$398$	−377.929	+	54.4028i	−0.949570	+	0.136690i
$399$			114.062i			0.285870i
$400$		0			0
$401$	97.7306			0.243717			0.121859	−	0.992547i	$-0.461115\pi$
$401$	97.7306			0.243717			0.121859	+	0.992547i	$0.461115\pi$
$402$	20.9618	+	145.619i	0.0521437	+	0.362235i
$403$			113.903i			0.282638i
$404$	337.402	+	184.088i	0.835154	+	0.455664i
$405$		0			0
$406$	−522.176	+	75.1671i	−1.28615	+	0.185141i
$407$	−271.674	+	271.674i	−0.667503	+	0.667503i
$408$	−225.843	+	606.442i	−0.553536	+	1.48638i
$409$	346.930			0.848239			0.424120	−	0.905606i	$-0.360584\pi$
$409$	346.930			0.848239			0.424120	+	0.905606i	$0.360584\pi$
$410$		0			0
$411$	316.986	+	316.986i	0.771255	+	0.771255i
$412$	659.893	+	360.041i	1.60168	+	0.873886i
$413$		−	576.998i		−	1.39709i
$414$	−23.4618	−	17.5571i	−0.0566710	−	0.0424085i
$415$		0			0
$416$	271.956	+	313.321i	0.653740	+	0.753176i
$417$	103.753	+	103.753i	0.248809	+	0.248809i
$418$	−15.1272	−	105.086i	−0.0361894	−	0.251403i
$419$	−94.6547	−	94.6547i	−0.225906	−	0.225906i	0.585074	−	0.810980i	$-0.301065\pi$
$419$	−94.6547	−	94.6547i	−0.225906	−	0.225906i	−0.810980	+	0.585074i	$0.801065\pi$
$420$		0			0
$421$	303.154	+	303.154i	0.720080	+	0.720080i	0.968621	−	0.248541i	$-0.0799512\pi$
$421$	303.154	+	303.154i	0.720080	+	0.720080i	−0.248541	+	0.968621i	$0.579951\pi$
$422$	−391.458	+	523.109i	−0.927625	+	1.23960i
$423$	−75.8234	−	75.8234i	−0.179252	−	0.179252i
$424$	150.182	−	68.6775i	0.354204	−	0.161975i
$425$		0			0
$426$	172.550	−	24.8386i	0.405048	−	0.0583066i
$427$			364.880i			0.854519i
$428$	50.6712	+	172.356i	0.118391	+	0.402701i
$429$	272.509	+	272.509i	0.635220	+	0.635220i
$430$		0			0
$431$	505.491			1.17283			0.586416	−	0.810010i	$-0.300538\pi$
$431$	505.491			1.17283			0.586416	+	0.810010i	$0.300538\pi$
$432$	−254.318	−	395.143i	−0.588700	−	0.914682i
$433$	−8.23935	+	8.23935i	−0.0190285	+	0.0190285i	−0.716557	−	0.697529i	$-0.754283\pi$
$433$	−8.23935	+	8.23935i	−0.0190285	+	0.0190285i	0.697529	+	0.716557i	$0.254283\pi$
$434$	106.980	−	142.958i	0.246497	−	0.329397i
$435$		0			0
$436$	157.698	+	86.0409i	0.361693	+	0.197341i
$437$		−	24.1617i		−	0.0552900i
$438$	324.060	−	433.046i	0.739864	−	0.988689i
$439$	195.298			0.444870			0.222435	−	0.974948i	$-0.428600\pi$
$439$	195.298			0.444870			0.222435	+	0.974948i	$0.428600\pi$
$440$		0			0
$441$		−	147.340i		−	0.334103i
$442$	−501.288	+	669.877i	−1.13414	+	1.51556i
$443$	−401.681			−0.906729			−0.453365	−	0.891325i	$-0.649776\pi$
$443$	−401.681			−0.906729			−0.453365	+	0.891325i	$0.649776\pi$
$444$	−311.752	+	91.6525i	−0.702144	+	0.206425i
$445$		0			0
$446$	−102.817	+	137.396i	−0.230532	+	0.308063i
$447$	−75.3357	−	75.3357i	−0.168536	−	0.168536i
$448$	−47.0517	−	648.672i	−0.105026	−	1.44793i
$449$		−	189.448i		−	0.421934i	−0.977493	−	0.210967i	$-0.932339\pi$
$449$		−	189.448i		−	0.421934i	0.977493	−	0.210967i	$-0.0676613\pi$
$450$		0			0
$451$	−7.86061	+	7.86061i	−0.0174293	+	0.0174293i
$452$	−15.0905	+	27.6584i	−0.0333862	+	0.0611911i
$453$	−65.4052			−0.144382
$454$	−400.926	+	57.7132i	−0.883096	+	0.127122i
$455$		0			0
$456$	31.3373	−	84.1482i	0.0687222	−	0.184536i
$457$	488.804	−	488.804i	1.06959	−	1.06959i	0.0722037	−	0.997390i	$-0.476997\pi$
$457$	488.804	−	488.804i	1.06959	−	1.06959i	0.997390	−	0.0722037i	$-0.0230032\pi$
$458$	−232.776	+	311.062i	−0.508245	+	0.679174i
$459$	670.083	−	670.083i	1.45988	−	1.45988i
$460$		0			0
$461$	392.290	−	392.290i	0.850954	−	0.850954i	−0.139297	−	0.990251i	$-0.544484\pi$
$461$	392.290	−	392.290i	0.850954	−	0.850954i	0.990251	+	0.139297i	$0.0444842\pi$
$462$	−86.0776	−	597.969i	−0.186315	−	1.29431i
$463$	70.7053	−	70.7053i	0.152711	−	0.152711i	−0.626616	−	0.779328i	$-0.715561\pi$
$463$	70.7053	−	70.7053i	0.152711	−	0.152711i	0.779328	+	0.626616i	$0.215561\pi$
$464$	405.881	+	88.0083i	0.874744	+	0.189673i
$465$		0			0
$466$	446.733	+	334.303i	0.958655	+	0.717389i
$467$	−918.293			−1.96637			−0.983183	−	0.182623i	$-0.941541\pi$
$467$	−918.293			−1.96637			−0.983183	+	0.182623i	$0.941541\pi$
$468$	−39.7138	−	135.085i	−0.0848586	−	0.288643i
$469$	210.842	−	210.842i	0.449557	−	0.449557i
$470$		0			0
$471$		−	6.63965i		−	0.0140969i
$472$	−158.524	+	425.675i	−0.335856	+	0.901854i
$473$	484.899	+	484.899i	1.02516	+	1.02516i
$474$	85.5057	−	12.3085i	0.180392	−	0.0259674i
$475$		0			0
$476$	1258.32	−	369.936i	2.64353	−	0.777177i
$477$	−56.0445			−0.117494
$478$	−117.383	−	815.441i	−0.245570	−	1.70594i
$479$		−	49.5880i		−	0.103524i	−0.998659	−	0.0517620i	$-0.983516\pi$
$479$		−	49.5880i		−	0.103524i	0.998659	−	0.0517620i	$-0.0164837\pi$
$480$		0			0
$481$	−420.122			−0.873435
$482$	581.875	−	83.7608i	1.20721	−	0.173778i
$483$		−	137.487i		−	0.284652i
$484$	22.0932	+	75.1490i	0.0456471	+	0.155267i
$485$		0			0
$486$	40.1786	+	279.115i	0.0826720	+	0.574311i
$487$	644.145	−	644.145i	1.32268	−	1.32268i	0.411081	−	0.911599i	$-0.365151\pi$
$487$	644.145	−	644.145i	1.32268	−	1.32268i	0.911599	−	0.411081i	$-0.134849\pi$
$488$	100.247	−	269.186i	0.205424	−	0.551611i
$489$	360.290			0.736790
$490$		0			0
$491$	−541.213	−	541.213i	−1.10227	−	1.10227i	−0.994137	−	0.108130i	$-0.965514\pi$
$491$	−541.213	−	541.213i	−1.10227	−	1.10227i	−0.108130	−	0.994137i	$-0.534486\pi$
$492$	−9.02022	+	2.65187i	−0.0183338	+	0.00538998i
$493$			837.538i			1.69886i
$494$	69.5574	−	92.9503i	0.140804	−	0.188159i
$495$		0			0
$496$	−118.200	+	76.0746i	−0.238306	+	0.153376i
$497$	−249.837	−	249.837i	−0.502690	−	0.502690i
$498$	364.231	−	52.4310i	0.731388	−	0.105283i
$499$	142.483	+	142.483i	0.285537	+	0.285537i	0.835313	−	0.549775i	$-0.185287\pi$
$499$	142.483	+	142.483i	0.285537	+	0.285537i	−0.549775	+	0.835313i	$0.685287\pi$
$500$		0			0
$501$	−483.615	−	483.615i	−0.965299	−	0.965299i
$502$	−449.209	−	336.156i	−0.894838	−	0.669633i
$503$	307.222	+	307.222i	0.610780	+	0.610780i	0.943149	−	0.332370i	$-0.107848\pi$
$503$	307.222	+	307.222i	0.610780	+	0.610780i	−0.332370	+	0.943149i	$0.607848\pi$
$504$	−77.0298	+	206.844i	−0.152837	+	0.410404i
$505$		0			0
$506$	18.2338	+	126.668i	0.0360351	+	0.250331i
$507$		−	2.26713i		−	0.00447166i
$508$	527.637	+	287.881i	1.03866	+	0.566695i
$509$	−268.080	−	268.080i	−0.526681	−	0.526681i	0.392900	−	0.919581i	$-0.371472\pi$
$509$	−268.080	−	268.080i	−0.526681	−	0.526681i	−0.919581	+	0.392900i	$0.871472\pi$
$510$		0			0
$511$	−1096.22			−2.14524
$512$	−143.504	+	491.478i	−0.280280	+	0.959918i
$513$	−92.9789	+	92.9789i	−0.181245	+	0.181245i
$514$	−542.691	−	406.111i	−1.05582	−	0.790099i
$515$		0			0
$516$	163.587	+	556.433i	0.317028	+	1.07836i
$517$			468.289i			0.905782i
$518$	527.291	+	394.587i	1.01794	+	0.761750i
$519$	−5.13193			−0.00988811
$520$		0			0
$521$		−	364.737i		−	0.700071i	−0.936736	−	0.350036i	$-0.886169\pi$
$521$		−	364.737i		−	0.700071i	0.936736	−	0.350036i	$-0.113831\pi$
$522$	−112.848	−	84.4473i	−0.216184	−	0.161776i
$523$	−434.085			−0.829991			−0.414996	−	0.909823i	$-0.636217\pi$
$523$	−434.085			−0.829991			−0.414996	+	0.909823i	$0.636217\pi$
$524$	−161.965	+	296.854i	−0.309093	+	0.566515i
$525$		0			0
$526$	322.557	+	241.378i	0.613225	+	0.458894i
$527$	−200.443	−	200.443i	−0.380347	−	0.380347i
$528$	−100.783	+	464.795i	−0.190876	+	0.880293i
$529$		−	499.876i		−	0.944946i
$530$		0			0
$531$	109.005	−	109.005i	0.205282	−	0.205282i
$532$	−174.601	+	51.3314i	−0.328198	+	0.0964875i
$533$	−12.1558			−0.0228064
$534$	−69.2406	−	481.005i	−0.129664	−	0.900758i
$535$		0			0
$536$	−213.473	+	97.6201i	−0.398271	+	0.182127i
$537$	−253.726	+	253.726i	−0.472489	+	0.472489i
$538$	610.988	+	457.220i	1.13567	+	0.849851i
$539$	−454.988	+	454.988i	−0.844134	+	0.844134i
$540$		0			0
$541$	−299.573	+	299.573i	−0.553739	+	0.553739i	−0.927518	−	0.373779i	$-0.878062\pi$
$541$	−299.573	+	299.573i	−0.553739	+	0.553739i	0.373779	+	0.927518i	$0.378062\pi$
$542$	−141.462	+	20.3634i	−0.261000	+	0.0375709i
$543$	386.109	−	386.109i	0.711067	−	0.711067i
$544$	−1029.95	−	72.7934i	−1.89329	−	0.133811i
$545$		0			0
$546$	395.800	−	528.913i	0.724909	−	0.968704i
$547$	9.98799			0.0182596			0.00912979	−	0.999958i	$-0.497094\pi$
$547$	9.98799			0.0182596			0.00912979	+	0.999958i	$0.497094\pi$
$548$	−342.575	+	627.881i	−0.625137	+	1.14577i
$549$	−68.9318	+	68.9318i	−0.125559	+	0.125559i
$550$		0			0
$551$		−	116.214i		−	0.210916i
$552$	−37.7730	+	101.429i	−0.0684293	+	0.183749i
$553$	−123.804	−	123.804i	−0.223877	−	0.223877i
$554$	72.9727	+	506.931i	0.131720	+	0.915038i
$555$		0			0
$556$	−112.129	+	205.513i	−0.201671	+	0.369629i
$557$	360.011			0.646339			0.323170	−	0.946341i	$-0.395252\pi$
$557$	360.011			0.646339			0.323170	+	0.946341i	$0.395252\pi$
$558$	47.2175	−	6.79695i	0.0846191	−	0.0121809i
$559$			749.859i			1.34143i
$560$		0			0
$561$	−959.106			−1.70964
$562$	−90.0144	−	625.318i	−0.160168	−	1.11267i
$563$		−	524.373i		−	0.931392i	−0.884945	−	0.465696i	$-0.845804\pi$
$563$		−	524.373i		−	0.931392i	0.884945	−	0.465696i	$-0.154196\pi$
$564$	−189.695	+	347.678i	−0.336338	+	0.616450i
$565$		0			0
$566$	−17.1320	+	2.46615i	−0.0302685	+	0.00435715i
$567$	−353.492	+	353.492i	−0.623443	+	0.623443i
$568$	115.675	+	252.955i	0.203653	+	0.445343i
$569$	606.955			1.06670			0.533352	−	0.845893i	$-0.320932\pi$
$569$	606.955			1.06670			0.533352	+	0.845893i	$0.320932\pi$
$570$		0			0
$571$	763.721	+	763.721i	1.33752	+	1.33752i	0.898460	+	0.439056i	$0.144687\pi$
$571$	763.721	+	763.721i	1.33752	+	1.33752i	0.439056	+	0.898460i	$0.355313\pi$
$572$	−294.508	+	539.783i	−0.514874	+	0.943676i
$573$		−	113.579i		−	0.198218i
$574$	15.2566	+	11.4170i	0.0265795	+	0.0198902i
$575$		0			0
$576$	113.656	−	131.434i	0.197319	−	0.228183i
$577$	95.1565	+	95.1565i	0.164916	+	0.164916i	0.784740	−	0.619824i	$-0.212796\pi$
$577$	95.1565	+	95.1565i	0.164916	+	0.164916i	−0.619824	+	0.784740i	$0.712796\pi$
$578$	−214.324	−	1488.88i	−0.370802	−	2.57591i
$579$	−441.514	−	441.514i	−0.762545	−	0.762545i
$580$		0			0
$581$	−527.372	−	527.372i	−0.907698	−	0.907698i
$582$	−227.027	+	303.378i	−0.390080	+	0.521269i
$583$	173.067	+	173.067i	0.296855	+	0.296855i
$584$	808.724	+	301.174i	1.38480	+	0.515709i
$585$		0			0
$586$	−1055.88	+	151.994i	−1.80184	+	0.259375i
$587$		−	445.447i		−	0.758853i	−0.925222	−	0.379427i	$-0.876121\pi$
$587$		−	445.447i		−	0.758853i	0.925222	−	0.379427i	$-0.123879\pi$
$588$	−522.109	+	153.496i	−0.887941	+	0.261047i
$589$	27.8129	+	27.8129i	0.0472205	+	0.0472205i
$590$		0			0
$591$	772.586			1.30725
$592$	−280.595	−	435.970i	−0.473979	−	0.736436i
$593$	359.016	−	359.016i	0.605424	−	0.605424i	−0.336323	−	0.941747i	$-0.609183\pi$
$593$	359.016	−	359.016i	0.605424	−	0.605424i	0.941747	+	0.336323i	$0.109183\pi$
$594$	417.274	−	557.608i	0.702481	−	0.938733i
$595$		0			0
$596$	81.4173	−	149.224i	0.136606	−	0.250376i
$597$		−	478.615i		−	0.801700i
$598$	−83.8422	+	112.039i	−0.140204	+	0.187357i
$599$	−66.3175			−0.110714			−0.0553568	−	0.998467i	$-0.517630\pi$
$599$	−66.3175			−0.110714			−0.0553568	+	0.998467i	$0.517630\pi$
$600$		0			0
$601$		−	512.825i		−	0.853287i	−0.904420	−	0.426643i	$-0.859696\pi$
$601$		−	512.825i		−	0.853287i	0.904420	−	0.426643i	$-0.140304\pi$
$602$	704.281	−	941.139i	1.16990	−	1.56335i
$603$	79.6631			0.132111
$604$	−29.4343	−	100.119i	−0.0487322	−	0.165761i
$605$		0			0
$606$	−288.659	+	385.739i	−0.476336	+	0.636533i
$607$	700.017	+	700.017i	1.15324	+	1.15324i	0.985899	+	0.167341i	$0.0535182\pi$
$607$	700.017	+	700.017i	1.15324	+	1.15324i	0.167341	+	0.985899i	$0.446482\pi$
$608$	142.913	+	10.1006i	0.235055	+	0.0166128i
$609$		−	661.292i		−	1.08586i
$610$		0			0
$611$	−362.086	+	362.086i	−0.592613	+	0.592613i
$612$	307.605	+	167.831i	0.502623	+	0.274233i
$613$	−402.030			−0.655840			−0.327920	−	0.944705i	$-0.606348\pi$
$613$	−402.030			−0.655840			−0.327920	+	0.944705i	$0.606348\pi$
$614$	637.536	−	91.7732i	1.03833	−	0.149468i
$615$		0			0
$616$	876.608	−	400.868i	1.42307	−	0.650760i
$617$	451.281	−	451.281i	0.731412	−	0.731412i	−0.239488	−	0.970899i	$-0.576979\pi$
$617$	451.281	−	451.281i	0.731412	−	0.731412i	0.970899	+	0.239488i	$0.0769794\pi$
$618$	−564.562	+	754.431i	−0.913531	+	1.22076i
$619$	−141.521	+	141.521i	−0.228629	+	0.228629i	−0.812120	−	0.583491i	$-0.801686\pi$
$619$	−141.521	+	141.521i	−0.228629	+	0.228629i	0.583491	+	0.812120i	$0.301686\pi$
$620$		0			0
$621$	112.074	−	112.074i	0.180473	−	0.180473i
$622$	2.86386	+	19.8948i	0.00460427	+	0.0319853i
$623$	−696.450	+	696.450i	−1.11790	+	1.11790i
$624$	−437.311	+	281.458i	−0.700818	+	0.451055i
$625$		0			0
$626$	−30.4246	−	22.7676i	−0.0486016	−	0.0363700i
$627$	133.083			0.212254
$628$	10.1637	−	2.98804i	0.0161842	−	0.00475803i
$629$	739.318	−	739.318i	1.17539	−	1.17539i
$630$		0			0
$631$			430.554i			0.682335i	0.940002	+	0.341168i	$0.110822\pi$
$631$			430.554i			0.682335i	−0.940002	+	0.341168i	$0.889178\pi$
$632$	57.3215	+	125.349i	0.0906986	+	0.198337i
$633$	−579.111	−	579.111i	−0.914868	−	0.914868i
$634$	−361.067	+	51.9756i	−0.569506	+	0.0819804i
$635$		0			0
$636$	58.3862	+	198.598i	0.0918021	+	0.312261i
$637$	−703.604			−1.10456
$638$	87.7019	+	609.253i	0.137464	+	0.954942i
$639$		−	94.3966i		−	0.147726i
$640$		0			0
$641$	244.316			0.381147			0.190574	−	0.981673i	$-0.438965\pi$
$641$	244.316			0.381147			0.190574	+	0.981673i	$0.438965\pi$
$642$	−222.893	+	32.0854i	−0.347185	+	0.0499773i
$643$		−	521.720i		−	0.811384i	−0.914010	−	0.405692i	$-0.867031\pi$
$643$		−	521.720i		−	0.811384i	0.914010	−	0.405692i	$-0.132969\pi$
$644$	210.459	−	61.8731i	0.326799	−	0.0960763i
$645$		0			0
$646$	41.1662	+	285.976i	0.0637248	+	0.442687i
$647$	−7.36567	+	7.36567i	−0.0113843	+	0.0113843i	−0.712776	−	0.701392i	$-0.752562\pi$
$647$	−7.36567	+	7.36567i	−0.0113843	+	0.0113843i	0.701392	+	0.712776i	$0.252562\pi$
$648$	357.904	−	163.667i	0.552320	−	0.252573i
$649$	−673.218			−1.03732
$650$		0			0
$651$	158.263	+	158.263i	0.243107	+	0.243107i
$652$	162.141	+	551.517i	0.248683	+	0.845885i
$653$			171.839i			0.263154i	0.991306	+	0.131577i	$0.0420040\pi$
$653$			171.839i			0.263154i	−0.991306	+	0.131577i	$0.957996\pi$
$654$	−134.916	+	180.290i	−0.206294	+	0.275673i
$655$		0			0
$656$	−8.11874	−	12.6143i	−0.0123761	−	0.0192292i
$657$	−207.094	−	207.094i	−0.315211	−	0.315211i
$658$	794.529	−	114.372i	1.20749	−	0.173818i
$659$	66.3827	+	66.3827i	0.100732	+	0.100732i	0.755677	−	0.654945i	$-0.227308\pi$
$659$	66.3827	+	66.3827i	0.100732	+	0.100732i	−0.654945	+	0.755677i	$0.727308\pi$
$660$		0			0
$661$	−38.9121	−	38.9121i	−0.0588685	−	0.0588685i	0.677060	−	0.735928i	$-0.263254\pi$
$661$	−38.9121	−	38.9121i	−0.0588685	−	0.0588685i	−0.735928	+	0.677060i	$0.763254\pi$
$662$	483.630	+	361.914i	0.730559	+	0.546698i
$663$	−741.591	−	741.591i	−1.11854	−	1.11854i
$664$	244.174	+	533.954i	0.367732	+	0.804147i
$665$		0			0
$666$	25.0700	+	174.158i	0.0376427	+	0.261498i
$667$			140.081i			0.210017i
$668$	522.655	−	957.937i	0.782418	−	1.43404i
$669$	−152.105	−	152.105i	−0.227362	−	0.227362i
$670$		0			0
$671$	425.726			0.634465
$672$	813.215	+	57.4752i	1.21014	+	0.0855286i
$673$	−58.7394	+	58.7394i	−0.0872799	+	0.0872799i	−0.749399	−	0.662119i	$-0.769657\pi$
$673$	−58.7394	+	58.7394i	−0.0872799	+	0.0872799i	0.662119	+	0.749399i	$0.269657\pi$
$674$	−225.383	−	168.661i	−0.334396	−	0.250238i
$675$		0			0
$676$	3.47043	−	1.02028i	0.00513377	−	0.00150929i
$677$			408.523i			0.603431i	0.953398	+	0.301716i	$0.0975593\pi$
$677$			408.523i			0.603431i	−0.953398	+	0.301716i	$0.902441\pi$
$678$	−31.6208	−	23.6627i	−0.0466383	−	0.0349008i
$679$	767.977			1.13104
$680$		0			0
$681$		−	507.738i		−	0.745578i
$682$	−166.798	−	124.820i	−0.244572	−	0.183020i
$683$	−611.720			−0.895636			−0.447818	−	0.894125i	$-0.647799\pi$
$683$	−611.720			−0.895636			−0.447818	+	0.894125i	$0.647799\pi$
$684$	−42.6824	−	23.2877i	−0.0624012	−	0.0340464i
$685$		0			0
$686$	85.7357	+	64.1585i	0.124979	+	0.0935254i
$687$	−344.363	−	344.363i	−0.501256	−	0.501256i
$688$	−778.144	+	500.823i	−1.13102	+	0.727940i
$689$			267.634i			0.388438i
$690$		0			0
$691$	−528.007	+	528.007i	−0.764120	+	0.764120i	−0.977064	−	0.212944i	$-0.931695\pi$
$691$	−528.007	+	528.007i	−0.764120	+	0.764120i	0.212944	+	0.977064i	$0.431695\pi$
$692$	−2.30952	−	7.85573i	−0.00333746	−	0.0113522i
$693$	−327.129			−0.472048
$694$	−137.300	−	953.806i	−0.197839	−	1.37436i
$695$		0			0
$696$	−181.683	+	487.861i	−0.261038	+	0.700950i
$697$	21.3914	−	21.3914i	0.0306907	−	0.0306907i
$698$	−902.365	−	675.265i	−1.29279	−	0.967429i
$699$	−494.559	+	494.559i	−0.707523	+	0.707523i
$700$		0			0
$701$	163.932	−	163.932i	0.233855	−	0.233855i	−0.580445	−	0.814300i	$-0.697121\pi$
$701$	163.932	−	163.932i	0.233855	−	0.233855i	0.814300	+	0.580445i	$0.197121\pi$
$702$	753.789	−	108.508i	1.07377	−	0.154569i
$703$	−102.586	+	102.586i	−0.145926	+	0.145926i
$704$	−756.843	+	54.8979i	−1.07506	+	0.0779800i
$705$		0			0
$706$	604.729	−	808.106i	0.856556	−	1.14463i
$707$	976.466			1.38114
$708$	−499.825	−	272.707i	−0.705968	−	0.385180i
$709$	−820.614	+	820.614i	−1.15742	+	1.15742i	−0.172397	+	0.985027i	$0.555151\pi$
$709$	−820.614	+	820.614i	−1.15742	+	1.15742i	−0.985027	+	0.172397i	$0.944849\pi$
$710$		0			0
$711$		−	46.7773i		−	0.0657909i
$712$	705.141	−	322.457i	0.990367	−	0.452889i
$713$	−33.5248	−	33.5248i	−0.0470193	−	0.0470193i
$714$	234.247	+	1627.28i	0.328077	+	2.27910i
$715$		0			0
$716$	−502.578	−	274.209i	−0.701924	−	0.382973i
$717$	1032.69			1.44029
$718$	827.188	−	119.074i	1.15207	−	0.165841i
$719$		−	578.830i		−	0.805048i	−0.915409	−	0.402524i	$-0.868133\pi$
$719$		−	578.830i		−	0.805048i	0.915409	−	0.402524i	$-0.131867\pi$
$720$		0			0
$721$	1909.78			2.64879
$722$	97.1594	+	674.953i	0.134570	+	0.934837i
$723$			736.896i			1.01922i
$724$	764.800	+	417.279i	1.05635	+	0.576352i
$725$		0			0
$726$	−97.1837	+	13.9896i	−0.133862	+	0.0192694i
$727$	−771.845	+	771.845i	−1.06168	+	1.06168i	−0.0637163	+	0.997968i	$0.520295\pi$
$727$	−771.845	+	771.845i	−1.06168	+	1.06168i	−0.997968	+	0.0637163i	$0.979705\pi$
$728$	987.758	+	367.847i	1.35681	+	0.505285i
$729$	−796.220			−1.09221
$730$		0			0
$731$	−1319.58	−	1319.58i	−1.80517	−	1.80517i
$732$	316.077	+	172.453i	0.431799	+	0.235592i
$733$			455.036i			0.620785i	0.950608	+	0.310393i	$0.100461\pi$
$733$			455.036i			0.620785i	−0.950608	+	0.310393i	$0.899539\pi$
$734$	−246.948	−	184.798i	−0.336441	−	0.251769i
$735$		0			0
$736$	−172.263	−	12.1749i	−0.234053	−	0.0165420i
$737$	−246.002	−	246.002i	−0.333788	−	0.333788i
$738$	0.725375	+	5.03908i	0.000982893	+	0.00682803i
$739$	723.106	+	723.106i	0.978493	+	0.978493i	0.999774	−	0.0212803i	$-0.00677425\pi$
$739$	723.106	+	723.106i	0.978493	+	0.978493i	−0.0212803	+	0.999774i	$0.506774\pi$
$740$		0			0
$741$	102.901	+	102.901i	0.138868	+	0.138868i
$742$	251.367	−	335.905i	0.338770	−	0.452702i
$743$	−134.068	−	134.068i	−0.180442	−	0.180442i	0.611107	−	0.791548i	$-0.290725\pi$
$743$	−134.068	−	134.068i	−0.180442	−	0.180442i	−0.791548	+	0.611107i	$0.790725\pi$
$744$	−73.2759	−	160.238i	−0.0984891	−	0.215374i
$745$		0			0
$746$	−611.362	+	88.0056i	−0.819521	+	0.117970i
$747$		−	199.259i		−	0.266745i
$748$	−431.626	−	1468.16i	−0.577041	−	1.96278i
$749$	322.728	+	322.728i	0.430879	+	0.430879i
$750$		0			0
$751$	−216.822			−0.288711			−0.144356	−	0.989526i	$-0.546111\pi$
$751$	−216.822			−0.288711			−0.144356	+	0.989526i	$0.546111\pi$
$752$	−617.578	−	133.911i	−0.821248	−	0.178073i
$753$	497.299	−	497.299i	0.660423	−	0.660423i
$754$	−403.269	+	538.893i	−0.534839	+	0.714712i
$755$		0			0
$756$	−1047.98	−	571.785i	−1.38622	−	0.756330i
$757$		−	747.764i		−	0.987800i	−0.869519	−	0.493900i	$-0.835571\pi$
$757$		−	747.764i		−	0.987800i	0.869519	−	0.493900i	$-0.164429\pi$
$758$	48.0729	−	64.2403i	0.0634207	−	0.0847498i
$759$	−160.414			−0.211349
$760$		0			0
$761$			1410.33i			1.85326i	0.375978	+	0.926629i	$0.377307\pi$
$761$			1410.33i			1.85326i	−0.375978	+	0.926629i	$0.622693\pi$
$762$	−451.412	+	603.227i	−0.592404	+	0.791636i
$763$	456.390			0.598152
$764$	173.862	−	51.1139i	0.227568	−	0.0669030i
$765$		0			0
$766$	716.750	−	957.802i	0.935705	−	1.25039i
$767$	−520.539	−	520.539i	−0.678669	−	0.678669i
$768$	−584.150	−	265.824i	−0.760613	−	0.346124i
$769$			925.036i			1.20291i	0.798907	+	0.601454i	$0.205412\pi$
$769$			925.036i			1.20291i	−0.798907	+	0.601454i	$0.794588\pi$
$770$		0			0
$771$	600.789	−	600.789i	0.779234	−	0.779234i
$772$	477.156	−	874.545i	0.618077	−	1.13283i
$773$	−146.591			−0.189639			−0.0948196	−	0.995494i	$-0.530227\pi$
$773$	−146.591			−0.189639			−0.0948196	+	0.995494i	$0.530227\pi$
$774$	310.847	−	44.7464i	0.401611	−	0.0578119i
$775$		0			0
$776$	−566.567	−	210.993i	−0.730113	−	0.271899i
$777$	−583.740	+	583.740i	−0.751274	+	0.751274i
$778$	303.296	−	405.298i	0.389841	−	0.520949i
$779$	−2.96821	+	2.96821i	−0.00381029	+	0.00381029i
$780$		0			0
$781$	−291.499	+	291.499i	−0.373238	+	0.373238i
$782$	−49.6204	−	344.706i	−0.0634532	−	0.440800i
$783$	539.058	−	539.058i	0.688453	−	0.688453i
$784$	−469.930	−	730.145i	−0.599400	−	0.931307i
$785$		0			0
$786$	−339.382	−	253.969i	−0.431783	−	0.323116i
$787$	389.164			0.494491			0.247245	−	0.968953i	$-0.420475\pi$
$787$	389.164			0.494491			0.247245	+	0.968953i	$0.420475\pi$
$788$	347.687	+	1182.64i	0.441227	+	1.50081i
$789$	−357.088	+	357.088i	−0.452583	+	0.452583i
$790$		0			0
$791$			80.0453i			0.101195i
$792$	241.336	+	89.8752i	0.304718	+	0.113479i
$793$	329.176	+	329.176i	0.415102	+	0.415102i
$794$	40.5115	−	5.83163i	0.0510221	−	0.00734463i
$795$		0			0
$796$	732.643	−	215.391i	0.920406	−	0.270592i
$797$	−225.230			−0.282597			−0.141298	−	0.989967i	$-0.545128\pi$
$797$	−225.230			−0.282597			−0.141298	+	0.989967i	$0.545128\pi$
$798$	−32.5034	−	225.797i	−0.0407311	−	0.282953i
$799$		−	1274.38i		−	1.59496i
$800$		0			0
$801$	−263.142			−0.328517
$802$	−193.467	+	27.8496i	−0.241231	+	0.0347251i
$803$			1279.02i			1.59280i
$804$	−82.9917	−	282.293i	−0.103223	−	0.351110i
$805$		0			0
$806$	−32.4581	−	225.482i	−0.0402706	−	0.279754i
$807$	−676.398	+	676.398i	−0.838164	+	0.838164i
$808$	−720.378	−	268.273i	−0.891557	−	0.332021i
$809$	389.024			0.480870			0.240435	−	0.970665i	$-0.422710\pi$
$809$	389.024			0.480870			0.240435	+	0.970665i	$0.422710\pi$
$810$		0			0
$811$	235.660	+	235.660i	0.290580	+	0.290580i	0.837309	−	0.546730i	$-0.184127\pi$
$811$	235.660	+	235.660i	0.290580	+	0.290580i	−0.546730	+	0.837309i	$0.684127\pi$
$812$	1012.28	−	297.601i	1.24665	−	0.366504i
$813$		−	179.149i		−	0.220356i
$814$	460.387	−	615.221i	0.565586	−	0.755800i
$815$		0			0
$816$	274.264	−	1264.87i	0.336108	−	1.55008i
$817$	183.101	+	183.101i	0.224114	+	0.224114i
$818$	−686.781	+	98.8620i	−0.839585	+	0.120858i
$819$	−252.940	−	252.940i	−0.308840	−	0.308840i
$820$		0			0
$821$	423.452	+	423.452i	0.515775	+	0.515775i	0.916290	−	0.400515i	$-0.131169\pi$
$821$	423.452	+	423.452i	0.515775	+	0.515775i	−0.400515	+	0.916290i	$0.631169\pi$
$822$	−717.833	−	537.174i	−0.873276	−	0.653497i
$823$	−543.405	−	543.405i	−0.660274	−	0.660274i	0.295171	−	0.955445i	$-0.404623\pi$
$823$	−543.405	−	543.405i	−0.660274	−	0.660274i	−0.955445	+	0.295171i	$0.904623\pi$
$824$	−1408.92	−	524.691i	−1.70985	−	0.636761i
$825$		0			0
$826$	164.423	+	1142.22i	0.199059	+	1.38284i
$827$		−	912.383i		−	1.10324i	−0.834094	−	0.551622i	$-0.814009\pi$
$827$		−	912.383i		−	1.10324i	0.834094	−	0.551622i	$-0.185991\pi$
$828$	51.4480	+	28.0703i	0.0621353	+	0.0339013i
$829$	−401.447	−	401.447i	−0.484254	−	0.484254i	0.422233	−	0.906487i	$-0.361246\pi$
$829$	−401.447	−	401.447i	−0.484254	−	0.484254i	−0.906487	+	0.422233i	$0.861246\pi$
$830$		0			0
$831$	−641.985			−0.772546
$832$	−627.647	−	542.752i	−0.754383	−	0.652346i
$833$	1238.18	−	1238.18i	1.48641	−	1.48641i
$834$	−234.956	−	175.824i	−0.281721	−	0.210820i
$835$		0			0
$836$	59.8913	+	203.718i	0.0716403	+	0.243681i
$837$			258.019i			0.308267i
$838$	214.351	+	160.405i	0.255789	+	0.191414i
$839$	−355.908			−0.424205			−0.212102	−	0.977247i	$-0.568031\pi$
$839$	−355.908			−0.424205			−0.212102	+	0.977247i	$0.568031\pi$
$840$		0			0
$841$		−	167.230i		−	0.198847i
$842$	−686.509	−	513.734i	−0.815331	−	0.610135i
$843$	791.912			0.939398
$844$	625.861	−	1147.10i	0.741541	−	1.35912i
$845$		0			0
$846$	171.706	+	128.493i	0.202963	+	0.151883i
$847$	140.713	+	140.713i	0.166131	+	0.166131i
$848$	−277.730	+	178.750i	−0.327511	+	0.210790i
$849$		−	21.6962i		−	0.0255550i
$850$		0			0
$851$	123.653	−	123.653i	0.145304	−	0.145304i
$852$	−334.502	+	98.3408i	−0.392608	+	0.115423i
$853$	−184.144			−0.215878			−0.107939	−	0.994158i	$-0.534425\pi$
$853$	−184.144			−0.215878			−0.107939	+	0.994158i	$0.534425\pi$
$854$	−103.977	−	722.314i	−0.121753	−	0.845801i
$855$		0			0
$856$	−149.423	−	326.756i	−0.174560	−	0.381724i
$857$	503.631	−	503.631i	0.587667	−	0.587667i	−0.349332	−	0.936999i	$-0.613591\pi$
$857$	503.631	−	503.631i	0.587667	−	0.587667i	0.936999	+	0.349332i	$0.113591\pi$
$858$	−617.113	−	461.803i	−0.719246	−	0.538232i
$859$	−136.193	+	136.193i	−0.158548	+	0.158548i	−0.781923	−	0.623375i	$-0.785761\pi$
$859$	−136.193	+	136.193i	−0.158548	+	0.158548i	0.623375	+	0.781923i	$0.285761\pi$
$860$		0			0
$861$	−16.8899	+	16.8899i	−0.0196166	+	0.0196166i
$862$	−1000.67	+	144.046i	−1.16087	+	0.167107i
$863$	778.037	−	778.037i	0.901550	−	0.901550i	−0.0940206	−	0.995570i	$-0.529972\pi$
$863$	778.037	−	778.037i	0.901550	−	0.901550i	0.995570	+	0.0940206i	$0.0299720\pi$
$864$	616.048	+	709.751i	0.713019	+	0.821471i
$865$		0			0
$866$	13.9627	−	18.6585i	0.0161232	−	0.0215456i
$867$	1885.54			2.17478
$868$	−171.039	+	313.485i	−0.197050	+	0.361158i
$869$	−144.450	+	144.450i	−0.166225	+	0.166225i
$870$		0			0
$871$		−	380.422i		−	0.436765i
$872$	−336.697	−	125.388i	−0.386120	−	0.143794i
$873$	145.084	+	145.084i	0.166190	+	0.166190i
$874$	6.88519	+	47.8304i	0.00787779	+	0.0547259i
$875$		0			0
$876$	−518.106	+	949.600i	−0.591446	+	1.08402i
$877$	450.954			0.514201			0.257101	−	0.966385i	$-0.417233\pi$
$877$	450.954			0.514201			0.257101	+	0.966385i	$0.417233\pi$
$878$	−386.610	+	55.6525i	−0.440331	+	0.0633856i
$879$		−	1337.18i		−	1.52126i
$880$		0			0
$881$	929.171			1.05468			0.527339	−	0.849655i	$-0.323190\pi$
$881$	929.171			1.05468			0.527339	+	0.849655i	$0.323190\pi$
$882$	41.9863	+	291.673i	0.0476035	+	0.330695i
$883$		−	244.738i		−	0.277166i	−0.990351	−	0.138583i	$-0.955745\pi$
$883$		−	244.738i		−	0.277166i	0.990351	−	0.138583i	$-0.0442548\pi$
$884$	801.458	−	1468.93i	0.906626	−	1.66169i
$885$		0			0
$886$	795.166	−	114.464i	0.897478	−	0.129192i
$887$	−987.070	+	987.070i	−1.11282	+	1.11282i	−0.120050	+	0.992768i	$0.538306\pi$
$887$	−987.070	+	987.070i	−1.11282	+	1.11282i	−0.992768	+	0.120050i	$0.961694\pi$
$888$	591.025	−	270.272i	0.665569	−	0.304361i
$889$	1527.02			1.71768
$890$		0			0
$891$	412.440	+	412.440i	0.462896	+	0.462896i
$892$	164.384	−	301.288i	0.184287	−	0.337766i
$893$			176.829i			0.198017i
$894$	170.602	+	127.666i	0.190830	+	0.142804i
$895$		0			0
$896$	277.990	+	1270.70i	0.310257	+	1.41819i
$897$	−124.034	−	124.034i	−0.138276	−	0.138276i
$898$	53.9857	+	375.031i	0.0601177	+	0.417629i
$899$	−161.249	−	161.249i	−0.179365	−	0.179365i
$900$		0			0
$901$	−470.974	−	470.974i	−0.522723	−	0.522723i
$902$	13.3208	−	17.8008i	0.0147681	−	0.0197348i
$903$	1041.89	+	1041.89i	1.15381	+	1.15381i
$904$	21.9916	−	59.0526i	0.0243270	−	0.0653237i
$905$		0			0
$906$	129.476	−	18.6380i	0.142909	−	0.0205718i
$907$		−	160.752i		−	0.177235i	−0.996066	−	0.0886177i	$-0.971755\pi$
$907$		−	160.752i		−	0.177235i	0.996066	−	0.0886177i	$-0.0282449\pi$
$908$	777.224	−	228.497i	0.855974	−	0.251649i
$909$	184.471	+	184.471i	0.202938	+	0.202938i
$910$		0			0
$911$	36.8062			0.0404020			0.0202010	−	0.999796i	$-0.493569\pi$
$911$	36.8062			0.0404020			0.0202010	+	0.999796i	$0.493569\pi$
$912$	−38.0561	+	175.509i	−0.0417282	+	0.192444i
$913$	−615.316	+	615.316i	−0.673950	+	0.673950i
$914$	−828.344	+	1106.93i	−0.906284	+	1.21108i
$915$		0			0
$916$	372.162	−	682.109i	0.406290	−	0.744660i
$917$			859.116i			0.936877i
$918$	−1135.54	+	1517.44i	−1.23698	+	1.65299i
$919$	−502.632			−0.546934			−0.273467	−	0.961881i	$-0.588170\pi$
$919$	−502.632			−0.546934			−0.273467	+	0.961881i	$0.588170\pi$
$920$		0			0
$921$			807.386i			0.876640i
$922$	−664.787	+	888.363i	−0.721027	+	0.963517i
$923$	−450.781			−0.488386
$924$	340.798	+	1159.21i	0.368829	+	1.25455i
$925$		0			0
$926$	−119.820	+	160.116i	−0.129395	+	0.172912i
$927$	360.789	+	360.789i	0.389200	+	0.389200i
$928$	−828.560	−	58.5597i	−0.892845	−	0.0631032i
$929$		−	1098.03i		−	1.18195i	−0.806690	−	0.590975i	$-0.798743\pi$
$929$		−	1098.03i		−	1.18195i	0.806690	−	0.590975i	$-0.201257\pi$
$930$		0			0
$931$	−171.806	+	171.806i	−0.184540	+	0.184540i
$932$	−979.615	−	534.483i	−1.05109	−	0.573479i
$933$	−25.1951			−0.0270044
$934$	1817.85	−	261.679i	1.94630	−	0.280170i
$935$		0			0
$936$	117.111	+	256.096i	0.125119	+	0.273607i
$937$	−68.4855	+	68.4855i	−0.0730902	+	0.0730902i	−0.742707	−	0.669617i	$-0.766458\pi$
$937$	−68.4855	+	68.4855i	−0.0730902	+	0.0730902i	0.669617	+	0.742707i	$0.266458\pi$
$938$	−357.300	+	477.464i	−0.380917	+	0.509024i
$939$	33.6817	−	33.6817i	0.0358698	−	0.0358698i
$940$		0			0
$941$	−517.439	+	517.439i	−0.549882	+	0.549882i	−0.926407	−	0.376525i	$-0.877119\pi$
$941$	−517.439	+	517.439i	−0.549882	+	0.549882i	0.376525	+	0.926407i	$0.377119\pi$
$942$	1.89205	+	13.1438i	0.00200855	+	0.0139531i
$943$	3.57779	−	3.57779i	0.00379405	−	0.00379405i
$944$	192.512	−	887.837i	0.203932	−	0.940506i
$945$		0			0
$946$	−1098.08	−	821.726i	−1.16076	−	0.868632i
$947$	−1065.70			−1.12534			−0.562672	−	0.826680i	$-0.690227\pi$
$947$	−1065.70			−1.12534			−0.562672	+	0.826680i	$0.690227\pi$
$948$	−165.759	+	48.7318i	−0.174851	+	0.0514049i
$949$	−988.954	+	988.954i	−1.04210	+	1.04210i
$950$		0			0
$951$		−	457.261i		−	0.480821i
$952$	−2385.55	+	1090.90i	−2.50583	+	1.14590i
$953$	−620.695	−	620.695i	−0.651306	−	0.651306i	0.302001	−	0.953307i	$-0.402345\pi$
$953$	−620.695	−	620.695i	−0.651306	−	0.651306i	−0.953307	+	0.302001i	$0.902345\pi$
$954$	110.945	−	15.9706i	0.116295	−	0.0167406i
$955$		0			0
$956$	464.740	+	1580.79i	0.486130	+	1.65355i
$957$	−771.567			−0.806236
$958$	14.1307	+	98.1641i	0.0147502	+	0.102468i
$959$			1817.13i			1.89482i
$960$		0			0
$961$	−883.818			−0.919686
$962$	831.672	−	119.719i	0.864524	−	0.124448i
$963$			121.937i			0.126622i
$964$	−1128.01	+	331.625i	−1.17013	+	0.344009i
$965$		0			0
$966$	39.1786	+	272.168i	0.0405575	+	0.281747i
$967$	1139.87	−	1139.87i	1.17877	−	1.17877i	0.198709	−	0.980059i	$-0.436325\pi$
$967$	1139.87	−	1139.87i	1.17877	−	1.17877i	0.980059	−	0.198709i	$-0.0636748\pi$
$968$	−65.1502	−	142.469i	−0.0673039	−	0.147179i
$969$	−362.164			−0.373751
$970$		0			0
$971$	470.641	+	470.641i	0.484697	+	0.484697i	0.906628	−	0.421931i	$-0.138648\pi$
$971$	470.641	+	470.641i	0.484697	+	0.484697i	−0.421931	+	0.906628i	$0.638648\pi$
$972$	−159.075	−	541.086i	−0.163657	−	0.556672i
$973$			594.771i			0.611275i
$974$	−1091.59	+	1458.70i	−1.12073	+	1.49764i
$975$		0			0
$976$	−121.740	+	561.446i	−0.124733	+	0.575252i
$977$	2.84469	+	2.84469i	0.00291165	+	0.00291165i	0.708561	−	0.705649i	$-0.249345\pi$
$977$	2.84469	+	2.84469i	0.00291165	+	0.00291165i	−0.705649	+	0.708561i	$0.749345\pi$
$978$	−713.229	+	102.669i	−0.729273	+	0.104979i
$979$	812.589	+	812.589i	0.830019	+	0.830019i
$980$		0			0
$981$	86.2195	+	86.2195i	0.0878894	+	0.0878894i
$982$	1225.61	+	917.157i	1.24807	+	0.933968i
$983$	177.652	+	177.652i	0.180724	+	0.180724i	0.791671	−	0.610947i	$-0.209211\pi$
$983$	177.652	+	177.652i	0.180724	+	0.180724i	−0.610947	+	0.791671i	$0.709211\pi$
$984$	17.1007	−	7.82006i	0.0173788	−	0.00794721i
$985$		0			0
$986$	−238.667	−	1657.99i	−0.242056	−	1.68153i
$987$			1006.20i			1.01946i
$988$	−111.208	+	203.825i	−0.112559	+	0.206301i
$989$	−220.704	−	220.704i	−0.223158	−	0.223158i
$990$		0			0
$991$	1697.53			1.71295			0.856474	−	0.516190i	$-0.172650\pi$
$991$	1697.53			1.71295			0.856474	+	0.516190i	$0.172650\pi$
$992$	212.309	−	184.279i	0.214021	−	0.185766i
$993$	−535.405	+	535.405i	−0.539179	+	0.539179i
$994$	565.770	+	423.382i	0.569185	+	0.425937i
$995$		0			0
$996$	−706.089	+	207.584i	−0.708925	+	0.208418i
$997$			1315.01i			1.31897i	0.751720	+	0.659483i	$0.229225\pi$
$997$			1315.01i			1.31897i	−0.751720	+	0.659483i	$0.770775\pi$
$998$	−322.661	−	241.457i	−0.323308	−	0.241941i
$999$	−951.683			−0.952636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.i.b.357.1		44
5.2	odd	4		80.3.t.a.53.11	yes	44
5.3	odd	4		400.3.t.b.293.12		44
5.4	even	2		80.3.i.a.37.22	yes	44
16.13	even	4		400.3.t.b.157.12		44
20.7	even	4		320.3.t.a.113.17		44
20.19	odd	2		320.3.i.a.177.6		44
40.19	odd	2		640.3.i.a.97.17		44
40.27	even	4		640.3.t.a.353.6		44
40.29	even	2		640.3.i.b.97.6		44
40.37	odd	4		640.3.t.b.353.17		44
80.13	odd	4	inner	400.3.i.b.93.1		44
80.19	odd	4		320.3.t.a.17.17		44
80.27	even	4		640.3.i.a.33.6		44
80.29	even	4		80.3.t.a.77.11	yes	44
80.37	odd	4		640.3.i.b.33.17		44
80.59	odd	4		640.3.t.a.417.6		44
80.67	even	4		320.3.i.a.273.17		44
80.69	even	4		640.3.t.b.417.17		44
80.77	odd	4		80.3.i.a.13.22	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.22	✓	44	80.77	odd	4
80.3.i.a.37.22	yes	44	5.4	even	2
80.3.t.a.53.11	yes	44	5.2	odd	4
80.3.t.a.77.11	yes	44	80.29	even	4
320.3.i.a.177.6		44	20.19	odd	2
320.3.i.a.273.17		44	80.67	even	4
320.3.t.a.17.17		44	80.19	odd	4
320.3.t.a.113.17		44	20.7	even	4
400.3.i.b.93.1		44	80.13	odd	4	inner
400.3.i.b.357.1		44	1.1	even	1	trivial
400.3.t.b.157.12		44	16.13	even	4
400.3.t.b.293.12		44	5.3	odd	4
640.3.i.a.33.6		44	80.27	even	4
640.3.i.a.97.17		44	40.19	odd	2
640.3.i.b.33.17		44	80.37	odd	4
640.3.i.b.97.6		44	40.29	even	2
640.3.t.a.353.6		44	40.27	even	4
640.3.t.a.417.6		44	80.59	odd	4
640.3.t.b.353.17		44	40.37	odd	4
640.3.t.b.417.17		44	80.69	even	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)

\(f(q)\)	\(=\)	\(q+(-1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 - 1.12822i) q^{4} +(0.714398 + 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(-7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +O(q^{10})\)	\(q+(-1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 - 1.12822i) q^{4} +(0.714398 + 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(-7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +(-8.38398 - 8.38398i) q^{11} +(-2.82844 - 9.62081i) q^{12} -12.9652i q^{13} +(-12.1771 + 16.2724i) q^{14} +(13.4542 - 8.65930i) q^{16} +(22.8157 + 22.8157i) q^{17} +(-5.37460 + 0.773673i) q^{18} +(-3.16584 - 3.16584i) q^{19} +(-18.0145 - 18.0145i) q^{21} +(18.9860 + 14.2078i) q^{22} +(3.81600 + 3.81600i) q^{23} +(8.34073 + 18.2393i) q^{24} +(3.69459 + 25.6658i) q^{26} -29.3694i q^{27} +(19.4688 - 35.6829i) q^{28} +(18.3544 + 18.3544i) q^{29} -8.78531 q^{31} +(-24.1664 + 20.9759i) q^{32} +(-21.0186 + 21.0186i) q^{33} +(-51.6674 - 38.6642i) q^{34} +(10.4191 - 3.06312i) q^{36} -32.4039i q^{37} +(7.16923 + 5.36494i) q^{38} -32.5036 q^{39} -0.937574i q^{41} +(40.7949 + 30.5280i) q^{42} -57.8364 q^{43} +(-41.6333 - 22.7153i) q^{44} +(-8.64156 - 6.46672i) q^{46} +(-27.9276 - 27.9276i) q^{47} +(-21.7088 - 33.7296i) q^{48} -54.2688i q^{49} +(57.1987 - 57.1987i) q^{51} +(-14.6276 - 49.7550i) q^{52} -20.6425 q^{53} +(8.36917 + 58.1395i) q^{54} +(-28.3720 + 76.1855i) q^{56} +(-7.93674 + 7.93674i) q^{57} +(-41.5647 - 31.1040i) q^{58} +(40.1490 - 40.1490i) q^{59} +(-25.3893 + 25.3893i) q^{61} +(17.3913 - 2.50348i) q^{62} +(19.5092 - 19.5092i) q^{63} +(41.8623 - 48.4102i) q^{64} +(35.6187 - 47.5978i) q^{66} +29.3419 q^{67} +(113.298 + 61.8162i) q^{68} +(9.56668 - 9.56668i) q^{69} -34.7686i q^{71} +(-19.7526 + 9.03277i) q^{72} +(-76.2777 - 76.2777i) q^{73} +(9.23390 + 64.1466i) q^{74} +(-15.7210 - 8.57745i) q^{76} -120.490 q^{77} +(64.3439 - 9.26230i) q^{78} -17.2292i q^{79} -49.1938 q^{81} +(0.267173 + 1.85602i) q^{82} -73.3919i q^{83} +(-89.4566 - 48.8080i) q^{84} +(114.493 - 16.4812i) q^{86} +(46.0144 - 46.0144i) q^{87} +(88.8901 + 33.1032i) q^{88} -96.9216 q^{89} +(-93.1639 - 93.1639i) q^{91} +(18.9496 + 10.3390i) q^{92} +22.0247i q^{93} +(63.2437 + 47.3270i) q^{94} +(52.5863 + 60.5848i) q^{96} +(53.4378 + 53.4378i) q^{97} +(15.4646 + 107.430i) q^{98} +(-22.7625 - 22.7625i) 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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