LMFDB - Embedded newform 275.3.x.a.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(51,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.x (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-5,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			226.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	275.226
Dual form			275.3.x.a.101.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.92705 + 0.951057i) q^{2} +(3.73607 + 2.71441i) q^{3} +(4.42705 - 3.21644i) q^{4} +(-13.5172 - 4.39201i) q^{6} +(-6.38197 - 8.78402i) q^{7} +(-2.66312 + 3.66547i) q^{8} +(3.80902 + 11.7229i) q^{9} +(10.3713 - 3.66547i) q^{11} +25.2705 q^{12} +(10.8541 - 3.52671i) q^{13} +(27.0344 + 19.6417i) q^{14} +(-2.45492 + 7.55545i) q^{16} +(21.4443 + 6.96767i) q^{17} +(-22.2984 - 30.6911i) q^{18} +(4.96149 - 6.82891i) q^{19} -50.1410i q^{21} +(-26.8713 + 20.5927i) q^{22} -0.472136 q^{23} +(-19.8992 + 6.46564i) q^{24} +(-28.4164 + 20.6457i) q^{26} +(-4.74671 + 14.6089i) q^{27} +(-56.5066 - 18.3601i) q^{28} +(-9.67376 - 13.3148i) q^{29} +(9.96556 + 30.6708i) q^{31} -42.5730i q^{32} +(48.6976 + 14.4576i) q^{33} -69.3951 q^{34} +(54.5689 + 39.6466i) q^{36} +(7.18034 - 5.21682i) q^{37} +(-8.02786 + 24.7072i) q^{38} +(50.1246 + 16.2865i) q^{39} +(15.5902 - 21.4580i) q^{41} +(47.6869 + 146.765i) q^{42} +50.0350i q^{43} +(34.1246 - 49.5860i) q^{44} +(1.38197 - 0.449028i) q^{46} +(28.3607 + 20.6052i) q^{47} +(-29.6803 + 21.5640i) q^{48} +(-21.2877 + 65.5169i) q^{49} +(61.2041 + 84.2403i) q^{51} +(36.7082 - 50.5245i) q^{52} +(-10.3951 - 31.9929i) q^{53} -47.2753i q^{54} +49.1935 q^{56} +(37.0729 - 12.0457i) q^{57} +(40.9787 + 29.7728i) q^{58} +(89.4681 - 65.0024i) q^{59} +(-71.4296 - 23.2089i) q^{61} +(-58.3394 - 80.2973i) q^{62} +(78.6656 - 108.274i) q^{63} +(30.6697 + 94.3916i) q^{64} +(-156.290 + 3.99598i) q^{66} -44.4508 q^{67} +(117.346 - 38.1280i) q^{68} +(-1.76393 - 1.28157i) q^{69} +(-16.2148 + 49.9040i) q^{71} +(-53.1140 - 17.2578i) q^{72} +(46.3197 + 63.7535i) q^{73} +(-16.0557 + 22.0988i) q^{74} -46.1903i q^{76} +(-98.3870 - 67.7090i) q^{77} -162.207 q^{78} +(-121.151 + 39.3643i) q^{79} +(32.3607 - 23.5114i) q^{81} +(-25.2254 + 77.6359i) q^{82} +(-35.6287 - 11.5765i) q^{83} +(-161.276 - 221.977i) q^{84} +(-47.5861 - 146.455i) q^{86} -76.0035i q^{87} +(-14.1844 + 47.7773i) q^{88} +108.326 q^{89} +(-100.249 - 72.8353i) q^{91} +(-2.09017 + 1.51860i) q^{92} +(-46.0213 + 141.639i) q^{93} +(-102.610 - 33.3400i) q^{94} +(115.561 - 159.056i) q^{96} +(-19.1008 - 58.7863i) q^{97} -212.017i q^{98} +(82.4746 + 107.621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} + 6 q^{3} + 11 q^{4} - 25 q^{6} - 30 q^{7} + 5 q^{8} + 13 q^{9} - q^{11} + 34 q^{12} + 30 q^{13} + 50 q^{14} - 21 q^{16} + 50 q^{17} - 40 q^{18} - 45 q^{19} - 65 q^{22} + 16 q^{23} - 55 q^{24}+ \cdots + 113 q^{99}+O(q^{100}) $ 4 * q - 5 * q^2 + 6 * q^3 + 11 * q^4 - 25 * q^6 - 30 * q^7 + 5 * q^8 + 13 * q^9 - q^11 + 34 * q^12 + 30 * q^13 + 50 * q^14 - 21 * q^16 + 50 * q^17 - 40 * q^18 - 45 * q^19 - 65 * q^22 + 16 * q^23 - 55 * q^24 - 60 * q^26 - 57 * q^27 - 150 * q^28 - 70 * q^29 + 98 * q^31 + 121 * q^33 - 130 * q^34 + 102 * q^36 - 16 * q^37 - 50 * q^38 + 120 * q^39 + 40 * q^41 + 70 * q^42 + 56 * q^44 + 10 * q^46 + 24 * q^47 - 74 * q^48 + 11 * q^49 + 95 * q^51 + 120 * q^52 + 106 * q^53 + 155 * q^57 + 70 * q^58 + 217 * q^59 - 80 * q^61 - 50 * q^62 + 100 * q^63 + 31 * q^64 - 330 * q^66 - 66 * q^67 + 210 * q^68 - 16 * q^69 + 38 * q^71 - 85 * q^72 + 230 * q^73 - 100 * q^74 - 300 * q^78 - 100 * q^79 + 40 * q^81 - 45 * q^82 - 185 * q^83 - 180 * q^84 - 45 * q^86 - 135 * q^88 + 402 * q^89 - 240 * q^91 + 14 * q^92 - 278 * q^93 - 160 * q^94 + 100 * q^96 - 101 * q^97 + 113 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−2.92705	+	0.951057i	−1.46353	+	0.475528i	−0.929145	−	0.369716i	$-0.879455\pi$
$2$	−2.92705	+	0.951057i	−1.46353	+	0.475528i	−0.534381	+	0.845244i	$0.679455\pi$
$3$	3.73607	+	2.71441i	1.24536	+	0.904804i	0.997943	−	0.0641060i	$-0.0204196\pi$
$3$	3.73607	+	2.71441i	1.24536	+	0.904804i	0.247413	+	0.968910i	$0.420420\pi$
$4$	4.42705	−	3.21644i	1.10676	−	0.804110i
$5$		0			0
$5$		0			0
$6$	−13.5172	−	4.39201i	−2.25287	−	0.732002i
$7$	−6.38197	−	8.78402i	−0.911709	−	1.25486i	−0.966580	−	0.256367i	$-0.917474\pi$
$7$	−6.38197	−	8.78402i	−0.911709	−	1.25486i	0.0548701	−	0.998494i	$-0.482526\pi$
$8$	−2.66312	+	3.66547i	−0.332890	+	0.458184i
$9$	3.80902	+	11.7229i	0.423224	+	1.30255i
$10$		0			0
$11$	10.3713	−	3.66547i	0.942848	−	0.333224i
$11$	10.3713	−	3.66547i	0.942848	−	0.333224i
$12$	25.2705			2.10588
$13$	10.8541	−	3.52671i	0.834931	−	0.271286i	0.139810	−	0.990178i	$-0.455351\pi$
$13$	10.8541	−	3.52671i	0.834931	−	0.271286i	0.695121	+	0.718893i	$0.255351\pi$
$14$	27.0344	+	19.6417i	1.93103	+	1.40298i
$15$		0			0
$16$	−2.45492	+	7.55545i	−0.153432	+	0.472216i
$17$	21.4443	+	6.96767i	1.26143	+	0.409863i	0.862003	−	0.506903i	$-0.169210\pi$
$17$	21.4443	+	6.96767i	1.26143	+	0.409863i	0.399425	+	0.916766i	$0.369210\pi$
$18$	−22.2984	−	30.6911i	−1.23880	−	1.70506i
$19$	4.96149	−	6.82891i	0.261131	−	0.359416i	−0.658239	−	0.752809i	$-0.728699\pi$
$19$	4.96149	−	6.82891i	0.261131	−	0.359416i	0.919371	+	0.393392i	$0.128699\pi$
$20$		0			0
$21$		−	50.1410i		−	2.38767i
$22$	−26.8713	+	20.5927i	−1.22142	+	0.936033i
$23$	−0.472136			−0.0205277			−0.0102638	−	0.999947i	$-0.503267\pi$
$23$	−0.472136			−0.0205277			−0.0102638	+	0.999947i	$0.503267\pi$
$24$	−19.8992	+	6.46564i	−0.829133	+	0.269402i
$25$		0			0
$26$	−28.4164	+	20.6457i	−1.09294	+	0.794066i
$27$	−4.74671	+	14.6089i	−0.175804	+	0.541069i
$28$	−56.5066	−	18.3601i	−2.01809	−	0.655718i
$29$	−9.67376	−	13.3148i	−0.333578	−	0.459131i	0.608974	−	0.793190i	$-0.291581\pi$
$29$	−9.67376	−	13.3148i	−0.333578	−	0.459131i	−0.942552	+	0.334059i	$0.891581\pi$
$30$		0			0
$31$	9.96556	+	30.6708i	0.321470	+	0.989382i	0.973009	+	0.230767i	$0.0741235\pi$
$31$	9.96556	+	30.6708i	0.321470	+	0.989382i	−0.651539	+	0.758615i	$0.725876\pi$
$32$		−	42.5730i		−	1.33041i
$33$	48.6976	+	14.4576i	1.47568	+	0.438109i
$34$	−69.3951			−2.04103
$35$		0			0
$36$	54.5689	+	39.6466i	1.51580	+	1.10129i
$37$	7.18034	−	5.21682i	0.194063	−	0.140995i	−0.486511	−	0.873675i	$-0.661731\pi$
$37$	7.18034	−	5.21682i	0.194063	−	0.140995i	0.680574	+	0.732679i	$0.261731\pi$
$38$	−8.02786	+	24.7072i	−0.211260	+	0.650190i
$39$	50.1246	+	16.2865i	1.28525	+	0.417602i
$40$		0			0
$41$	15.5902	−	21.4580i	0.380248	−	0.523367i	−0.575402	−	0.817871i	$-0.695154\pi$
$41$	15.5902	−	21.4580i	0.380248	−	0.523367i	0.955650	+	0.294504i	$0.0951545\pi$
$42$	47.6869	+	146.765i	1.13540	+	3.49441i
$43$			50.0350i			1.16360i	0.813330	+	0.581802i	$0.197652\pi$
$43$			50.0350i			1.16360i	−0.813330	+	0.581802i	$0.802348\pi$
$44$	34.1246	−	49.5860i	0.775559	−	1.12695i
$45$		0			0
$46$	1.38197	−	0.449028i	0.0300427	−	0.00976148i
$47$	28.3607	+	20.6052i	0.603419	+	0.438409i	0.847091	−	0.531448i	$-0.178352\pi$
$47$	28.3607	+	20.6052i	0.603419	+	0.438409i	−0.243672	+	0.969858i	$0.578352\pi$
$48$	−29.6803	+	21.5640i	−0.618340	+	0.449251i
$49$	−21.2877	+	65.5169i	−0.434443	+	1.33708i
$50$		0			0
$51$	61.2041	+	84.2403i	1.20008	+	1.65177i
$52$	36.7082	−	50.5245i	0.705927	−	0.971625i
$53$	−10.3951	−	31.9929i	−0.196134	−	0.603640i	−0.999961	−	0.00877654i	$-0.997206\pi$
$53$	−10.3951	−	31.9929i	−0.196134	−	0.603640i	0.803827	−	0.594863i	$-0.202794\pi$
$54$		−	47.2753i		−	0.875469i
$55$		0			0
$56$	49.1935			0.878455
$57$	37.0729	−	12.0457i	0.650403	−	0.211329i
$58$	40.9787	+	29.7728i	0.706530	+	0.513324i
$59$	89.4681	−	65.0024i	1.51641	−	1.10173i	0.553176	−	0.833065i	$-0.313416\pi$
$59$	89.4681	−	65.0024i	1.51641	−	1.10173i	0.963232	−	0.268670i	$-0.0865842\pi$
$60$		0			0
$61$	−71.4296	−	23.2089i	−1.17098	−	0.380473i	−0.341969	−	0.939711i	$-0.611094\pi$
$61$	−71.4296	−	23.2089i	−1.17098	−	0.380473i	−0.829007	+	0.559238i	$0.811094\pi$
$62$	−58.3394	−	80.2973i	−0.940958	−	1.29512i
$63$	78.6656	−	108.274i	1.24866	−	1.71863i
$64$	30.6697	+	94.3916i	0.479214	+	1.47487i
$65$		0			0
$66$	−156.290	+	3.99598i	−2.36803	+	0.0605452i
$67$	−44.4508			−0.663446			−0.331723	−	0.943377i	$-0.607630\pi$
$67$	−44.4508			−0.663446			−0.331723	+	0.943377i	$0.607630\pi$
$68$	117.346	−	38.1280i	1.72568	−	0.560706i
$69$	−1.76393	−	1.28157i	−0.0255642	−	0.0185735i
$70$		0			0
$71$	−16.2148	+	49.9040i	−0.228377	+	0.702873i	0.769554	+	0.638582i	$0.220479\pi$
$71$	−16.2148	+	49.9040i	−0.228377	+	0.702873i	−0.997931	+	0.0642910i	$0.979521\pi$
$72$	−53.1140	−	17.2578i	−0.737694	−	0.239691i
$73$	46.3197	+	63.7535i	0.634516	+	0.873336i	0.998308	−	0.0581439i	$-0.0185182\pi$
$73$	46.3197	+	63.7535i	0.634516	+	0.873336i	−0.363792	+	0.931480i	$0.618518\pi$
$74$	−16.0557	+	22.0988i	−0.216969	+	0.298633i
$75$		0			0
$76$		−	46.1903i		−	0.607767i
$77$	−98.3870	−	67.7090i	−1.27775	−	0.879338i
$78$	−162.207			−2.07957
$79$	−121.151	+	39.3643i	−1.53356	+	0.498283i	−0.949590	−	0.313495i	$-0.898500\pi$
$79$	−121.151	+	39.3643i	−1.53356	+	0.498283i	−0.583966	+	0.811778i	$0.698500\pi$
$80$		0			0
$81$	32.3607	−	23.5114i	0.399515	−	0.290264i
$82$	−25.2254	+	77.6359i	−0.307627	+	0.946779i
$83$	−35.6287	−	11.5765i	−0.429261	−	0.139475i	0.0864145	−	0.996259i	$-0.472459\pi$
$83$	−35.6287	−	11.5765i	−0.429261	−	0.139475i	−0.515676	+	0.856784i	$0.672459\pi$
$84$	−161.276	−	221.977i	−1.91995	−	2.64258i
$85$		0			0
$86$	−47.5861	−	146.455i	−0.553327	−	1.70296i
$87$		−	76.0035i		−	0.873604i
$88$	−14.1844	+	47.7773i	−0.161186	+	0.542924i
$89$	108.326			1.21715			0.608574	−	0.793497i	$-0.291742\pi$
$89$	108.326			1.21715			0.608574	+	0.793497i	$0.291742\pi$
$90$		0			0
$91$	−100.249	−	72.8353i	−1.10164	−	0.800388i
$92$	−2.09017	+	1.51860i	−0.0227192	+	0.0165065i
$93$	−46.0213	+	141.639i	−0.494853	+	1.52300i
$94$	−102.610	−	33.3400i	−1.09159	−	0.354681i
$95$		0			0
$96$	115.561	−	159.056i	1.20376	−	1.65683i
$97$	−19.1008	−	58.7863i	−0.196916	−	0.606044i	−0.999949	−	0.0101097i	$-0.996782\pi$
$97$	−19.1008	−	58.7863i	−0.196916	−	0.606044i	0.803033	−	0.595934i	$-0.203218\pi$
$98$		−	212.017i		−	2.16344i
$99$	82.4746	+	107.621i	0.833077	+	1.08708i
$100$		0			0
$101$	54.8460	−	17.8205i	0.543029	−	0.176441i	−0.0246418	−	0.999696i	$-0.507845\pi$
$101$	54.8460	−	17.8205i	0.543029	−	0.176441i	0.567671	+	0.823255i	$0.307845\pi$
$102$	−259.265	−	188.367i	−2.54181	−	1.84673i
$103$	88.9230	−	64.6063i	0.863330	−	0.627246i	−0.0654589	−	0.997855i	$-0.520851\pi$
$103$	88.9230	−	64.6063i	0.863330	−	0.627246i	0.928789	+	0.370609i	$0.120851\pi$
$104$	−15.9787	+	49.1774i	−0.153641	+	0.472860i
$105$		0			0
$106$	60.8541	+	83.7585i	0.574095	+	0.790174i
$107$	−32.9803	+	45.3934i	−0.308227	+	0.424238i	−0.934827	−	0.355103i	$-0.884446\pi$
$107$	−32.9803	+	45.3934i	−0.308227	+	0.424238i	0.626600	+	0.779341i	$0.284446\pi$
$108$	25.9746	+	79.9417i	0.240506	+	0.740201i
$109$		−	64.2478i		−	0.589430i	−0.955585	−	0.294715i	$-0.904775\pi$
$109$		−	64.2478i		−	0.589430i	0.955585	−	0.294715i	$-0.0952247\pi$
$110$		0			0
$111$	40.9868			0.369251
$112$	82.0344	−	26.6546i	0.732450	−	0.237988i
$113$	7.25329	+	5.26982i	0.0641884	+	0.0466356i	0.619417	−	0.785062i	$-0.287369\pi$
$113$	7.25329	+	5.26982i	0.0641884	+	0.0466356i	−0.555228	+	0.831698i	$0.687369\pi$
$114$	−97.0582	+	70.5169i	−0.851388	+	0.618570i
$115$		0			0
$116$	−85.6525	−	27.8302i	−0.738383	−	0.239915i
$117$	82.6869	+	113.809i	0.706726	+	0.972725i
$118$	−200.057	+	275.354i	−1.69540	+	2.33351i
$119$	−75.6525	−	232.834i	−0.635735	−	1.95659i
$120$		0			0
$121$	94.1287	−	76.0315i	0.777923	−	0.628360i
$122$	231.151			1.89468
$123$	116.492	−	37.8505i	0.947088	−	0.307728i
$124$	142.769	+	103.728i	1.15136	+	0.836514i
$125$		0			0
$126$	−127.284	+	391.739i	−1.01019	+	3.10904i
$127$	−143.387	−	46.5893i	−1.12903	−	0.366845i	−0.315824	−	0.948818i	$-0.602281\pi$
$127$	−143.387	−	46.5893i	−1.12903	−	0.366845i	−0.813208	+	0.581973i	$0.802281\pi$
$128$	−79.4483	−	109.351i	−0.620690	−	0.854307i
$129$	−135.816	+	186.934i	−1.05283	+	1.44910i
$130$		0			0
$131$			97.0983i			0.741208i	0.928791	+	0.370604i	$0.120849\pi$
$131$			97.0983i			0.741208i	−0.928791	+	0.370604i	$0.879151\pi$
$132$	262.089	−	92.6283i	1.98552	−	0.701729i
$133$	−91.6494			−0.689093
$134$	130.110	−	42.2753i	0.970969	−	0.315487i
$135$		0			0
$136$	−82.6484	+	60.0476i	−0.607709	+	0.441526i
$137$	−64.7239	+	199.200i	−0.472437	+	1.45401i	0.376946	+	0.926235i	$0.376974\pi$
$137$	−64.7239	+	199.200i	−0.472437	+	1.45401i	−0.849383	+	0.527777i	$0.823026\pi$
$138$	6.38197	+	2.07363i	0.0462461	+	0.0150263i
$139$	−4.72136	−	6.49839i	−0.0339666	−	0.0467510i	0.791696	−	0.610915i	$-0.209198\pi$
$139$	−4.72136	−	6.49839i	−0.0339666	−	0.0467510i	−0.825663	+	0.564164i	$0.809198\pi$
$140$		0			0
$141$	50.0263	+	153.965i	0.354797	+	1.09195i
$142$		−	161.493i		−	1.13727i
$143$	99.6443	−	76.3620i	0.696814	−	0.534000i
$144$	−97.9230			−0.680021
$145$		0			0
$146$	−196.213	−	142.557i	−1.34393	−	0.976420i
$147$	−257.372	+	186.992i	−1.75083	+	1.27205i
$148$	15.0081	−	46.1903i	0.101406	−	0.312096i
$149$	−44.3951	−	14.4248i	−0.297954	−	0.0968111i	0.156225	−	0.987721i	$-0.450067\pi$
$149$	−44.3951	−	14.4248i	−0.297954	−	0.0968111i	−0.454179	+	0.890910i	$0.650067\pi$
$150$		0			0
$151$	44.1459	−	60.7616i	0.292357	−	0.402395i	−0.637421	−	0.770516i	$-0.719999\pi$
$151$	44.1459	−	60.7616i	0.292357	−	0.402395i	0.929778	+	0.368121i	$0.119999\pi$
$152$	11.8181	+	36.3724i	0.0777507	+	0.239292i
$153$			277.930i			1.81654i
$154$	352.379	+	104.616i	2.28817	+	0.679326i
$155$		0			0
$156$	274.289	−	89.1218i	1.75826	−	0.571294i
$157$	−29.9311	−	21.7462i	−0.190644	−	0.138511i	0.488369	−	0.872637i	$-0.337592\pi$
$157$	−29.9311	−	21.7462i	−0.190644	−	0.138511i	−0.679013	+	0.734126i	$0.737592\pi$
$158$	317.177	−	230.443i	2.00745	−	1.45850i
$159$	48.0050	−	147.744i	0.301918	−	0.929209i
$160$		0			0
$161$	3.01316	+	4.14725i	0.0187153	+	0.0257593i
$162$	−72.3607	+	99.5959i	−0.446671	+	0.614790i
$163$	−14.5263	−	44.7074i	−0.0891185	−	0.274278i	0.896558	−	0.442927i	$-0.146060\pi$
$163$	−14.5263	−	44.7074i	−0.0891185	−	0.274278i	−0.985676	+	0.168648i	$0.946060\pi$
$164$		−	145.141i		−	0.885004i
$165$		0			0
$166$	115.297			0.694559
$167$	−45.2786	+	14.7119i	−0.271130	+	0.0880953i	−0.441426	−	0.897297i	$-0.645527\pi$
$167$	−45.2786	+	14.7119i	−0.271130	+	0.0880953i	0.170297	+	0.985393i	$0.445527\pi$
$168$	183.790	+	133.531i	1.09399	+	0.794830i
$169$	−31.3500	+	22.7771i	−0.185503	+	0.134776i
$170$		0			0
$171$	98.9534	+	32.1519i	0.578675	+	0.188023i
$172$	160.935	+	221.507i	0.935666	+	1.28783i
$173$	112.207	−	154.439i	0.648593	−	0.892712i	−0.350444	−	0.936584i	$-0.613969\pi$
$173$	112.207	−	154.439i	0.648593	−	0.892712i	0.999037	+	0.0438716i	$0.0139692\pi$
$174$	72.2837	+	222.466i	0.415423	+	1.27854i
$175$		0			0
$176$	2.23356	+	87.3584i	0.0126907	+	0.496355i
$177$	510.702			2.88532
$178$	−317.076	+	103.024i	−1.78133	+	0.578789i
$179$	−208.919	−	151.788i	−1.16714	−	0.847980i	−0.176480	−	0.984304i	$-0.556471\pi$
$179$	−208.919	−	151.788i	−1.16714	−	0.847980i	−0.990664	+	0.136324i	$0.956471\pi$
$180$		0			0
$181$	−50.8115	+	156.382i	−0.280727	+	0.863988i	0.706920	+	0.707293i	$0.250084\pi$
$181$	−50.8115	+	156.382i	−0.280727	+	0.863988i	−0.987647	+	0.156695i	$0.949916\pi$
$182$	362.705	+	117.850i	1.99289	+	0.647528i
$183$	−203.867	−	280.599i	−1.11403	−	1.53333i
$184$	1.25735	−	1.73060i	0.00683345	−	0.00940543i
$185$		0			0
$186$		−	458.353i		−	2.46426i
$187$	247.945	−	6.33939i	1.32591	−	0.0339005i
$188$	191.830			1.02037
$189$	158.618	−	51.5381i	0.839249	−	0.272688i
$190$		0			0
$191$	30.7426	−	22.3358i	0.160956	−	0.116942i	−0.504392	−	0.863475i	$-0.668283\pi$
$191$	30.7426	−	22.3358i	0.160956	−	0.116942i	0.665348	+	0.746533i	$0.268283\pi$
$192$	−141.634	+	435.904i	−0.737676	+	2.27033i
$193$	−4.47214	−	1.45309i	−0.0231717	−	0.00752894i	0.297408	−	0.954750i	$-0.403878\pi$
$193$	−4.47214	−	1.45309i	−0.0231717	−	0.00752894i	−0.320580	+	0.947221i	$0.603878\pi$
$194$	111.818	+	153.904i	0.576382	+	0.793322i
$195$		0			0
$196$	116.489	+	358.517i	0.594333	+	1.82917i
$197$		−	107.254i		−	0.544439i	−0.962235	−	0.272219i	$-0.912242\pi$
$197$		−	107.254i		−	0.544439i	0.962235	−	0.272219i	$-0.0877576\pi$
$198$	−343.761	−	236.573i	−1.73617	−	1.19481i
$199$	18.5936			0.0934354			0.0467177	−	0.998908i	$-0.485124\pi$
$199$	18.5936			0.0934354			0.0467177	+	0.998908i	$0.485124\pi$
$200$		0			0
$201$	−166.071	−	120.658i	−0.826226	−	0.600288i
$202$	−143.589	+	104.323i	−0.710835	+	0.516452i
$203$	−55.2198	+	169.949i	−0.272019	+	0.837188i
$204$	541.908	+	176.076i	2.65641	+	0.863120i
$205$		0			0
$206$	−198.838	+	273.677i	−0.965232	+	1.32853i
$207$	−1.79837	−	5.53483i	−0.00868780	−	0.0267383i
$208$			90.6654i			0.435891i
$209$	26.4261	−	89.0110i	0.126441	−	0.425890i
$210$		0			0
$211$	−92.8829	+	30.1795i	−0.440203	+	0.143031i	−0.520729	−	0.853722i	$-0.674340\pi$
$211$	−92.8829	+	30.1795i	−0.440203	+	0.143031i	0.0805260	+	0.996753i	$0.474340\pi$
$212$	−148.923	−	108.199i	−0.702467	−	0.510372i
$213$	−196.039	+	142.431i	−0.920373	+	0.668690i
$214$	53.3632	−	164.235i	0.249361	−	0.767453i
$215$		0			0
$216$	−40.9073	−	56.3041i	−0.189386	−	0.260667i
$217$	205.813	−	283.278i	0.948449	−	1.30543i
$218$	61.1033	+	188.057i	0.280290	+	0.862645i
$219$			363.918i			1.66173i
$220$		0			0
$221$	257.331			1.16439
$222$	−119.971	+	38.9808i	−0.540408	+	0.175589i
$223$	−306.920	−	222.990i	−1.37632	−	0.999957i	−0.997213	−	0.0746047i	$-0.976230\pi$
$223$	−306.920	−	222.990i	−1.37632	−	0.999957i	−0.379109	−	0.925352i	$-0.623770\pi$
$224$	−373.962	+	271.700i	−1.66948	+	1.21294i
$225$		0			0
$226$	−26.2426	−	8.52675i	−0.116118	−	0.0377290i
$227$	−122.513	−	168.624i	−0.539703	−	0.742837i	0.448867	−	0.893598i	$-0.351828\pi$
$227$	−122.513	−	168.624i	−0.539703	−	0.742837i	−0.988570	+	0.150761i	$0.951828\pi$
$228$	125.379	−	172.570i	0.549910	−	0.756886i
$229$	−19.2179	−	59.1466i	−0.0839209	−	0.258282i	0.900287	−	0.435296i	$-0.143356\pi$
$229$	−19.2179	−	59.1466i	−0.0839209	−	0.258282i	−0.984208	+	0.177014i	$0.943356\pi$
$230$		0			0
$231$	−183.790	−	520.028i	−0.795629	−	2.25121i
$232$	74.5673			0.321411
$233$	−263.488	+	85.6124i	−1.13085	+	0.367435i	−0.813899	−	0.581007i	$-0.802659\pi$
$233$	−263.488	+	85.6124i	−1.13085	+	0.367435i	−0.316950	+	0.948442i	$0.602659\pi$
$234$	−350.267	−	254.484i	−1.49687	−	1.08754i
$235$		0			0
$236$	187.003	−	575.538i	0.792388	−	2.43872i
$237$	−559.479	−	181.786i	−2.36067	−	0.767029i
$238$	442.877	+	609.568i	1.86083	+	2.56121i
$239$	−87.2179	+	120.045i	−0.364928	+	0.502281i	−0.951514	−	0.307607i	$-0.900472\pi$
$239$	−87.2179	+	120.045i	−0.364928	+	0.502281i	0.586585	+	0.809888i	$0.300472\pi$
$240$		0			0
$241$			413.928i			1.71754i	0.512358	+	0.858772i	$0.328772\pi$
$241$			413.928i			1.71754i	−0.512358	+	0.858772i	$0.671228\pi$
$242$	−203.209	+	312.070i	−0.839707	+	1.28954i
$243$	322.967			1.32908
$244$	−390.872	+	127.002i	−1.60194	+	0.520500i
$245$		0			0
$246$	−304.980	+	221.581i	−1.23975	+	0.900735i
$247$	29.7690	−	91.6194i	0.120522	−	0.370929i
$248$	−138.962	−	45.1516i	−0.560332	−	0.182063i
$249$	−101.688	−	139.961i	−0.408385	−	0.562094i
$250$		0			0
$251$	115.281	+	354.797i	0.459285	+	1.41353i	0.866030	+	0.499992i	$0.166664\pi$
$251$	115.281	+	354.797i	0.459285	+	1.41353i	−0.406745	+	0.913542i	$0.633336\pi$
$252$		−	732.358i		−	2.90618i
$253$	−4.89667	+	1.73060i	−0.0193544	+	0.00684031i
$254$	464.010			1.82681
$255$		0			0
$256$	15.3713	+	11.1679i	0.0600442	+	0.0436247i
$257$	165.102	−	119.953i	0.642419	−	0.466745i	−0.218261	−	0.975890i	$-0.570038\pi$
$257$	165.102	−	119.953i	0.642419	−	0.466745i	0.860681	+	0.509145i	$0.170038\pi$
$258$	219.754	−	676.334i	0.851761	−	2.62145i
$259$	−91.6494	−	29.7787i	−0.353859	−	0.114976i
$260$		0			0
$261$	119.241	−	164.121i	0.456862	−	0.628817i
$262$	−92.3460	−	284.212i	−0.352466	−	1.08478i
$263$			64.2788i			0.244406i	0.992505	+	0.122203i	$0.0389959\pi$
$263$			64.2788i			0.244406i	−0.992505	+	0.122203i	$0.961004\pi$
$264$	−182.681	+	139.997i	−0.691975	+	0.530292i
$265$		0			0
$266$	268.262	−	87.1637i	1.00851	−	0.327683i
$267$	404.714	+	294.042i	1.51578	+	1.10128i
$268$	−196.786	+	142.974i	−0.734277	+	0.533483i
$269$	−69.0050	+	212.376i	−0.256524	+	0.789500i	0.737001	+	0.675891i	$0.236241\pi$
$269$	−69.0050	+	212.376i	−0.256524	+	0.789500i	−0.993526	+	0.113609i	$0.963759\pi$
$270$		0			0
$271$	−165.220	−	227.406i	−0.609667	−	0.839135i	0.386883	−	0.922129i	$-0.373552\pi$
$271$	−165.220	−	227.406i	−0.609667	−	0.839135i	−0.996550	+	0.0829940i	$0.973552\pi$
$272$	−105.288	+	144.916i	−0.387087	+	0.532780i
$273$	−176.833	−	544.235i	−0.647739	−	1.99354i
$274$		−	644.623i		−	2.35264i
$275$		0			0
$276$	−11.9311			−0.0432287
$277$	−114.538	+	37.2156i	−0.413494	+	0.134352i	−0.508374	−	0.861136i	$-0.669753\pi$
$277$	−114.538	+	37.2156i	−0.413494	+	0.134352i	0.0948799	+	0.995489i	$0.469753\pi$
$278$	20.0000	+	14.5309i	0.0719424	+	0.0522692i
$279$	−321.594	+	233.651i	−1.15267	+	0.837460i
$280$		0			0
$281$	−385.665	−	125.310i	−1.37247	−	0.445944i	−0.472286	−	0.881446i	$-0.656571\pi$
$281$	−385.665	−	125.310i	−1.37247	−	0.445944i	−0.900188	+	0.435502i	$0.856571\pi$
$282$	−292.859	−	403.086i	−1.03851	−	1.42938i
$283$	−324.259	+	446.305i	−1.14579	+	1.57705i	−0.391959	+	0.919983i	$0.628202\pi$
$283$	−324.259	+	446.305i	−1.14579	+	1.57705i	−0.753834	+	0.657065i	$0.771798\pi$
$284$	88.7295	+	273.081i	0.312428	+	0.961554i
$285$		0			0
$286$	−219.039	+	318.283i	−0.765872	+	1.11288i
$287$	−287.984			−1.00343
$288$	499.081	−	162.161i	1.73292	−	0.563060i
$289$	177.503	+	128.963i	0.614196	+	0.446239i
$290$		0			0
$291$	88.2082	−	271.477i	0.303121	−	0.932910i
$292$	410.119	+	133.256i	1.40452	+	0.456355i
$293$	189.259	+	260.493i	0.645936	+	0.889055i	0.998915	−	0.0465766i	$-0.0148312\pi$
$293$	189.259	+	260.493i	0.645936	+	0.889055i	−0.352979	+	0.935631i	$0.614831\pi$
$294$	575.502	−	792.110i	1.95749	−	2.69425i
$295$		0			0
$296$			40.2123i			0.135852i
$297$	4.31870	+	168.912i	0.0145411	+	0.568728i
$298$	143.666			0.482099
$299$	−5.12461	+	1.66509i	−0.0171392	+	0.00556885i
$300$		0			0
$301$	439.508	−	319.322i	1.46016	−	1.06087i
$302$	−71.4296	+	219.838i	−0.236522	+	0.727939i
$303$	253.281	+	82.2958i	0.835909	+	0.271603i
$304$	39.4154	+	54.2507i	0.129656	+	0.178456i
$305$		0			0
$306$	−264.327	−	813.515i	−0.863814	−	2.65855i
$307$			100.126i			0.326143i	0.986614	+	0.163072i	$0.0521401\pi$
$307$			100.126i			0.326143i	−0.986614	+	0.163072i	$0.947860\pi$
$308$	−653.346	+	16.7046i	−2.12125	+	0.0542356i
$309$	507.591			1.64269
$310$		0			0
$311$	159.456	+	115.851i	0.512720	+	0.372513i	0.813854	−	0.581069i	$-0.197365\pi$
$311$	159.456	+	115.851i	0.512720	+	0.372513i	−0.301135	+	0.953582i	$0.597365\pi$
$312$	−193.185	+	140.357i	−0.619184	+	0.449863i
$313$	75.0886	−	231.099i	0.239900	−	0.738335i	−0.756534	−	0.653955i	$-0.773109\pi$
$313$	75.0886	−	231.099i	0.239900	−	0.738335i	0.996434	−	0.0843809i	$-0.0268913\pi$
$314$	108.292	+	35.1861i	0.344878	+	0.112058i
$315$		0			0
$316$	−409.728	+	563.943i	−1.29661	+	1.78463i
$317$	174.790	+	537.949i	0.551389	+	1.69700i	0.705294	+	0.708915i	$0.250815\pi$
$317$	174.790	+	537.949i	0.551389	+	1.69700i	−0.153906	+	0.988086i	$0.549185\pi$
$318$			478.111i			1.50349i
$319$	−149.135	−	102.633i	−0.467507	−	0.321734i
$320$		0			0
$321$	−246.433	+	80.0709i	−0.767704	+	0.249442i
$322$	−12.7639	−	9.27354i	−0.0396395	−	0.0287998i
$323$	153.977	−	111.871i	0.476709	−	0.346350i
$324$	67.6393	−	208.172i	0.208763	−	0.642507i
$325$		0			0
$326$	85.0385	+	117.045i	0.260854	+	0.359035i
$327$	174.395	−	240.034i	0.533318	−	0.734050i
$328$	37.1353	+	114.291i	0.113217	+	0.348447i
$329$		−	380.623i		−	1.15691i
$330$		0			0
$331$	−144.353			−0.436110			−0.218055	−	0.975936i	$-0.569971\pi$
$331$	−144.353			−0.436110			−0.218055	+	0.975936i	$0.569971\pi$
$332$	−194.965	+	63.3480i	−0.587244	+	0.190807i
$333$	88.5066	+	64.3038i	0.265786	+	0.193104i
$334$	118.541	−	86.1251i	0.354913	−	0.257860i
$335$		0			0
$336$	378.838	+	123.092i	1.12749	+	0.366345i
$337$	113.715	+	156.516i	0.337434	+	0.464439i	0.943690	−	0.330831i	$-0.107329\pi$
$337$	113.715	+	156.516i	0.337434	+	0.464439i	−0.606256	+	0.795270i	$0.707329\pi$
$338$	70.1008	−	96.4855i	0.207399	−	0.285460i
$339$	12.7943	+	39.3768i	0.0377413	+	0.116156i
$340$		0			0
$341$	215.779	+	281.569i	0.632783	+	0.825715i
$342$	−320.220			−0.936315
$343$	205.374	−	66.7300i	0.598758	−	0.194548i
$344$	−183.402	−	133.249i	−0.533144	−	0.387352i
$345$		0			0
$346$	−181.554	+	558.766i	−0.524723	+	1.61493i
$347$	249.410	+	81.0382i	0.718760	+	0.233539i	0.645486	−	0.763772i	$-0.276655\pi$
$347$	249.410	+	81.0382i	0.718760	+	0.233539i	0.0732747	+	0.997312i	$0.476655\pi$
$348$	−244.461	−	336.472i	−0.702474	−	0.966872i
$349$	70.2310	−	96.6647i	0.201235	−	0.276976i	−0.696458	−	0.717597i	$-0.745242\pi$
$349$	70.2310	−	96.6647i	0.201235	−	0.276976i	0.897693	+	0.440621i	$0.145242\pi$
$350$		0			0
$351$			175.306i			0.499449i
$352$	−156.050	−	441.539i	−0.443324	−	1.25437i
$353$	−150.674			−0.426838			−0.213419	−	0.976961i	$-0.568460\pi$
$353$	−150.674			−0.426838			−0.213419	+	0.976961i	$0.568460\pi$
$354$	−1494.85	+	485.706i	−4.22274	+	1.37205i
$355$		0			0
$356$	479.566	−	348.425i	1.34709	−	0.978722i
$357$	349.366	−	1075.24i	0.978615	−	3.01187i
$358$	755.876	+	245.599i	2.11138	+	0.686031i
$359$	160.143	+	220.418i	0.446080	+	0.613977i	0.971550	−	0.236836i	$-0.0761103\pi$
$359$	160.143	+	220.418i	0.446080	+	0.613977i	−0.525470	+	0.850812i	$0.676110\pi$
$360$		0			0
$361$	89.5375	+	275.568i	0.248026	+	0.763347i
$362$		−	506.062i		−	1.39796i
$363$	558.052	−	28.5549i	1.53733	−	0.0786636i
$364$	−678.079			−1.86285
$365$		0			0
$366$	863.596	+	627.439i	2.35955	+	1.71431i
$367$	−523.912	+	380.644i	−1.42755	+	1.03718i	−0.437087	+	0.899419i	$0.643990\pi$
$367$	−523.912	+	380.644i	−1.42755	+	1.03718i	−0.990466	+	0.137758i	$0.956010\pi$
$368$	1.15905	−	3.56720i	0.00314960	−	0.00969348i
$369$	310.935	+	101.029i	0.842641	+	0.273791i
$370$		0			0
$371$	−214.685	+	295.489i	−0.578666	+	0.796465i
$372$	251.835	+	775.068i	0.676975	+	2.08352i
$373$		−	402.936i		−	1.08026i	−0.841583	−	0.540129i	$-0.818376\pi$
$373$		−	402.936i		−	1.08026i	0.841583	−	0.540129i	$-0.181624\pi$
$374$	−719.719	+	254.366i	−1.92438	+	0.680122i
$375$		0			0
$376$	−151.056	+	49.0810i	−0.401744	+	0.130535i
$377$	−151.957	−	110.404i	−0.403070	−	0.292848i
$378$	−415.267	+	301.709i	−1.09859	+	0.798173i
$379$	41.9023	−	128.962i	0.110560	−	0.340269i	−0.880435	−	0.474167i	$-0.842749\pi$
$379$	41.9023	−	128.962i	0.110560	−	0.340269i	0.990995	+	0.133898i	$0.0427494\pi$
$380$		0			0
$381$	−409.241	−	563.272i	−1.07412	−	1.47840i
$382$	−68.7426	+	94.6161i	−0.179955	+	0.247686i
$383$	170.833	+	525.769i	0.446039	+	1.37277i	0.881341	+	0.472481i	$0.156642\pi$
$383$	170.833	+	525.769i	0.446039	+	1.37277i	−0.435302	+	0.900285i	$0.643358\pi$
$384$		−	624.199i		−	1.62552i
$385$		0			0
$386$	14.4721			0.0374926
$387$	−586.558	+	190.584i	−1.51565	+	0.492465i
$388$	−273.643	−	198.813i	−0.705265	−	0.512405i
$389$	107.164	−	77.8593i	0.275486	−	0.200152i	−0.441460	−	0.897281i	$-0.645539\pi$
$389$	107.164	−	77.8593i	0.275486	−	0.200152i	0.716946	+	0.697129i	$0.245539\pi$
$390$		0			0
$391$	−10.1246	−	3.28969i	−0.0258941	−	0.00841352i
$392$	−183.458	−	252.509i	−0.468006	−	0.644155i
$393$	−263.565	+	362.766i	−0.670648	+	0.923068i
$394$	102.005	+	313.939i	0.258896	+	0.796800i
$395$		0			0
$396$	711.275	+	211.167i	1.79615	+	0.533251i
$397$	110.721			0.278895			0.139448	−	0.990229i	$-0.455467\pi$
$397$	110.721			0.278895			0.139448	+	0.990229i	$0.455467\pi$
$398$	−54.4245	+	17.6836i	−0.136745	+	0.0444312i
$399$	−342.408	−	248.774i	−0.858166	−	0.623494i
$400$		0			0
$401$	9.64494	−	29.6841i	0.0240522	−	0.0740251i	−0.938310	−	0.345795i	$-0.887609\pi$
$401$	9.64494	−	29.6841i	0.0240522	−	0.0740251i	0.962362	+	0.271770i	$0.0876091\pi$
$402$	600.852	+	195.229i	1.49466	+	0.485643i
$403$	216.334	+	297.759i	0.536810	+	0.738855i
$404$	185.487	−	255.301i	0.459127	−	0.631934i
$405$		0			0
$406$		−	549.967i		−	1.35460i
$407$	55.3475	−	80.4247i	0.135989	−	0.197604i
$408$	−471.774			−1.15631
$409$	436.217	−	141.735i	1.06654	−	0.346541i	0.277404	−	0.960753i	$-0.410526\pi$
$409$	436.217	−	141.735i	1.06654	−	0.346541i	0.789141	+	0.614212i	$0.210526\pi$
$410$		0			0
$411$	−782.523	+	568.536i	−1.90395	+	1.38330i
$412$	185.864	−	572.031i	0.451127	−	1.38842i
$413$	−1141.96	−	371.047i	−2.76505	−	0.898418i
$414$	10.5279	+	14.4904i	0.0254296	+	0.0350009i
$415$		0			0
$416$	−150.143	−	462.092i	−0.360920	−	1.11080i
$417$		−	37.0942i		−	0.0889548i
$418$	7.30399	+	285.672i	0.0174737	+	0.683427i
$419$	−47.0476			−0.112285			−0.0561427	−	0.998423i	$-0.517880\pi$
$419$	−47.0476			−0.112285			−0.0561427	+	0.998423i	$0.517880\pi$
$420$		0			0
$421$	122.931	+	89.3147i	0.291998	+	0.212149i	0.724134	−	0.689660i	$-0.242240\pi$
$421$	122.931	+	89.3147i	0.291998	+	0.212149i	−0.432136	+	0.901809i	$0.642240\pi$
$422$	243.171	−	176.674i	0.576234	−	0.418658i
$423$	−133.528	+	410.957i	−0.315669	+	0.971528i
$424$	144.952	+	47.0979i	0.341869	+	0.111080i
$425$		0			0
$426$	438.358	−	603.347i	1.02901	−	1.41631i
$427$	251.994	+	775.557i	0.590149	+	1.81629i
$428$			307.038i			0.717379i
$429$	579.556	−	14.8179i	1.35095	−	0.0345406i
$430$		0			0
$431$	−492.254	+	159.943i	−1.14212	+	0.371098i	−0.818170	−	0.574976i	$-0.805011\pi$
$431$	−492.254	+	159.943i	−1.14212	+	0.371098i	−0.323951	+	0.946074i	$0.605011\pi$
$432$	−98.7239	−	71.7271i	−0.228527	−	0.166035i
$433$	336.791	−	244.693i	0.777809	−	0.565111i	−0.126512	−	0.991965i	$-0.540378\pi$
$433$	336.791	−	244.693i	0.777809	−	0.565111i	0.904321	+	0.426854i	$0.140378\pi$
$434$	−333.013	+	1024.91i	−0.767311	+	2.36154i
$435$		0			0
$436$	−206.649	−	284.428i	−0.473966	−	0.652359i
$437$	−2.34250	+	3.22417i	−0.00536041	+	0.00737797i
$438$	−346.107	−	1065.21i	−0.790198	−	2.43198i
$439$			685.921i			1.56246i	0.624242	+	0.781231i	$0.285408\pi$
$439$			685.921i			1.56246i	−0.624242	+	0.781231i	$0.714592\pi$
$440$		0			0
$441$	−849.137			−1.92548
$442$	−753.222	+	244.737i	−1.70412	+	0.553703i
$443$	−468.163	−	340.140i	−1.05680	−	0.767810i	−0.0833065	−	0.996524i	$-0.526548\pi$
$443$	−468.163	−	340.140i	−1.05680	−	0.767810i	−0.973494	+	0.228714i	$0.926548\pi$
$444$	181.451	−	131.832i	0.408673	−	0.296918i
$445$		0			0
$446$	1110.45	+	360.806i	2.48979	+	0.808982i
$447$	−126.708	−	174.399i	−0.283464	−	0.390154i
$448$	633.405	−	871.807i	1.41385	−	1.94600i
$449$	−262.733	−	808.609i	−0.585151	−	1.80091i	−0.598662	−	0.801002i	$-0.704301\pi$
$449$	−262.733	−	808.609i	−0.585151	−	1.80091i	0.0135103	−	0.999909i	$-0.495699\pi$
$450$		0			0
$451$	83.0370	−	279.693i	0.184117	−	0.620163i
$452$	49.0608			0.108541
$453$	329.864	−	107.179i	0.728177	−	0.236599i
$454$	518.972	+	377.055i	1.14311	+	0.830517i
$455$		0			0
$456$	−54.5764	+	167.969i	−0.119685	+	0.368353i
$457$	387.747	+	125.987i	0.848462	+	0.275682i	0.700802	−	0.713356i	$-0.252826\pi$
$457$	387.747	+	125.987i	0.848462	+	0.275682i	0.147660	+	0.989038i	$0.452826\pi$
$458$	112.503	+	154.848i	0.245641	+	0.338096i
$459$	−203.580	+	280.203i	−0.443528	+	0.610464i
$460$		0			0
$461$		−	721.774i		−	1.56567i	−0.622229	−	0.782835i	$-0.713773\pi$
$461$		−	721.774i		−	1.56567i	0.622229	−	0.782835i	$-0.286227\pi$
$462$	1032.54	+	1347.35i	2.23493	+	2.91635i
$463$	−775.669			−1.67531			−0.837656	−	0.546198i	$-0.816075\pi$
$463$	−775.669			−1.67531			−0.837656	+	0.546198i	$0.816075\pi$
$464$	124.348	−	40.4030i	0.267990	−	0.0870753i
$465$		0			0
$466$	689.820	−	501.184i	1.48030	−	1.07550i
$467$	−144.385	+	444.372i	−0.309176	+	0.951545i	0.668910	+	0.743343i	$0.266761\pi$
$467$	−144.385	+	444.372i	−0.309176	+	0.951545i	−0.978086	+	0.208202i	$0.933239\pi$
$468$	732.118	+	237.880i	1.56436	+	0.508290i
$469$	283.684	+	390.457i	0.604870	+	0.832531i
$470$		0			0
$471$	−52.7965	−	162.491i	−0.112094	−	0.344991i
$472$			501.051i			1.06155i
$473$	183.402	+	518.929i	0.387741	+	1.09710i
$474$	1810.51			3.81965
$475$		0			0
$476$	−1083.82	−	787.438i	−2.27692	−	1.65428i
$477$	335.456	−	243.723i	0.703262	−	0.510950i
$478$	141.122	−	434.327i	0.295233	−	0.908635i
$479$	−8.26238	−	2.68461i	−0.0172492	−	0.00560461i	0.300380	−	0.953820i	$-0.402887\pi$
$479$	−8.26238	−	2.68461i	−0.0172492	−	0.00560461i	−0.317629	+	0.948215i	$0.602887\pi$
$480$		0			0
$481$	59.5379	−	81.9469i	0.123779	−	0.170368i
$482$	−393.669	−	1211.59i	−0.816741	−	2.51367i
$483$			23.6734i			0.0490132i
$484$	172.162	−	639.355i	0.355706	−	1.32098i
$485$		0			0
$486$	−945.342	+	307.160i	−1.94515	+	0.632017i
$487$	−645.822	−	469.217i	−1.32612	−	0.963484i	−0.999834	−	0.0182139i	$-0.994202\pi$
$487$	−645.822	−	469.217i	−1.32612	−	0.963484i	−0.326288	−	0.945270i	$-0.605798\pi$
$488$	275.297	−	200.015i	0.564133	−	0.409866i
$489$	67.0830	−	206.460i	0.137184	−	0.422209i
$490$		0			0
$491$	−87.5364	−	120.483i	−0.178282	−	0.245384i	0.710519	−	0.703678i	$-0.248460\pi$
$491$	−87.5364	−	120.483i	−0.178282	−	0.245384i	−0.888800	+	0.458295i	$0.848460\pi$
$492$	393.972	−	542.255i	0.800755	−	1.10214i
$493$	−114.674	−	352.930i	−0.232604	−	0.715881i
$494$			296.487i			0.600176i
$495$		0			0
$496$	−256.197			−0.516525
$497$	541.840	−	176.054i	1.09022	−	0.354234i
$498$	430.757	+	312.963i	0.864973	+	0.628440i
$499$	−493.030	+	358.207i	−0.988036	+	0.717850i	−0.959490	−	0.281743i	$-0.909088\pi$
$499$	−493.030	+	358.207i	−0.988036	+	0.717850i	−0.0285456	+	0.999592i	$0.509088\pi$
$500$		0			0
$501$	−209.098	−	67.9402i	−0.417362	−	0.135609i
$502$	−674.864	−	928.871i	−1.34435	−	1.85034i
$503$	88.0720	−	121.221i	0.175093	−	0.240995i	−0.712446	−	0.701727i	$-0.752413\pi$
$503$	88.0720	−	121.221i	0.175093	−	0.240995i	0.887540	+	0.460731i	$0.152413\pi$
$504$	187.379	+	576.693i	0.371783	+	1.14423i
$505$		0			0
$506$	12.6869	−	9.72257i	0.0250730	−	0.0192146i
$507$	−178.952			−0.352963
$508$	−784.633	+	254.943i	−1.54455	+	0.501856i
$509$	−256.395	−	186.282i	−0.503723	−	0.365976i	0.306714	−	0.951802i	$-0.400770\pi$
$509$	−256.395	−	186.282i	−0.503723	−	0.365976i	−0.810437	+	0.585825i	$0.800770\pi$
$510$		0			0
$511$	264.402	−	813.746i	0.517421	−	1.59246i
$512$	458.586	+	149.004i	0.895677	+	0.291023i
$513$	76.2119	+	104.897i	0.148561	+	0.204477i
$514$	−369.179	+	508.131i	−0.718247	+	0.988582i
$515$		0			0
$516$			1264.41i			2.45041i
$517$	369.666	+	109.748i	0.715021	+	0.212279i
$518$	296.584			0.572555
$519$	838.423	−	272.420i	1.61546	−	0.524895i
$520$		0			0
$521$	−298.555	+	216.913i	−0.573042	+	0.416340i	−0.836209	−	0.548411i	$-0.815233\pi$
$521$	−298.555	+	216.913i	−0.573042	+	0.416340i	0.263167	+	0.964750i	$0.415233\pi$
$522$	−192.936	+	593.796i	−0.369609	+	1.13754i
$523$	−466.990	−	151.734i	−0.892907	−	0.290123i	−0.173601	−	0.984816i	$-0.555540\pi$
$523$	−466.990	−	151.734i	−0.892907	−	0.290123i	−0.719306	+	0.694693i	$0.755540\pi$
$524$	312.311	+	429.859i	0.596013	+	0.820342i
$525$		0			0
$526$	−61.1327	−	188.147i	−0.116222	−	0.357694i
$527$			727.150i			1.37979i
$528$	−228.782	+	332.440i	−0.433299	+	0.629621i
$529$	−528.777			−0.999579
$530$		0			0
$531$	1102.80	+	801.235i	2.07685	+	1.50892i
$532$	−405.736	+	294.785i	−0.762662	+	0.554107i
$533$	93.5410	−	287.890i	0.175499	−	0.540131i
$534$	−1464.27	−	475.770i	−2.74208	−	0.890955i
$535$		0			0
$536$	118.378	−	162.933i	0.220854	−	0.303980i
$537$	−368.519	−	1134.18i	−0.686255	−	2.11207i
$538$		−	687.262i		−	1.27744i
$539$	19.3682	+	757.526i	0.0359336	+	1.40543i
$540$		0			0
$541$	−418.618	+	136.017i	−0.773786	+	0.251418i	−0.669185	−	0.743096i	$-0.733357\pi$
$541$	−418.618	+	136.017i	−0.773786	+	0.251418i	−0.104601	+	0.994514i	$0.533357\pi$
$542$	699.882	+	508.494i	1.29130	+	0.938181i
$543$	−614.320	+	446.330i	−1.13134	+	0.821970i
$544$	296.635	−	912.948i	0.545284	−	1.67821i
$545$		0			0
$546$	1035.20	+	1424.83i	1.89597	+	2.60957i
$547$	−350.478	+	482.392i	−0.640728	+	0.881886i	−0.998654	−	0.0518636i	$-0.983484\pi$
$547$	−350.478	+	482.392i	−0.640728	+	0.881886i	0.357926	+	0.933750i	$0.383484\pi$
$548$	354.178	+	1090.05i	0.646310	+	1.98914i
$549$		−	925.768i		−	1.68628i
$550$		0			0
$551$	−138.922			−0.252127
$552$	9.39512	−	3.05266i	0.0170201	−	0.00553018i
$553$	1118.96	+	812.971i	2.02343	+	1.47011i
$554$	299.864	−	217.864i	0.541271	−	0.393256i
$555$		0			0
$556$	−41.8034	−	13.5827i	−0.0751860	−	0.0244294i
$557$	352.889	+	485.709i	0.633552	+	0.872010i	0.998251	−	0.0591158i	$-0.0188281\pi$
$557$	352.889	+	485.709i	0.633552	+	0.872010i	−0.364699	+	0.931125i	$0.618828\pi$
$558$	719.105	−	989.763i	1.28872	−	1.77377i
$559$	176.459	+	543.085i	0.315669	+	0.971529i
$560$		0			0
$561$	943.548	+	649.341i	1.68190	+	1.15747i
$562$	1248.04			2.22071
$563$	632.047	−	205.365i	1.12264	−	0.364768i	0.311866	−	0.950126i	$-0.399046\pi$
$563$	632.047	−	205.365i	1.12264	−	0.364768i	0.810775	+	0.585358i	$0.199046\pi$
$564$	716.689	+	520.705i	1.27072	+	0.923236i
$565$		0			0
$566$	524.663	−	1614.75i	0.926966	−	2.85291i
$567$	−413.050	−	134.208i	−0.728482	−	0.236698i
$568$	−139.740	−	192.335i	−0.246020	−	0.338618i
$569$	−255.449	+	351.595i	−0.448943	+	0.617917i	−0.972170	−	0.234276i	$-0.924728\pi$
$569$	−255.449	+	351.595i	−0.448943	+	0.617917i	0.523227	+	0.852193i	$0.324728\pi$
$570$		0			0
$571$			807.082i			1.41345i	0.707487	+	0.706727i	$0.249829\pi$
$571$			807.082i			1.41345i	−0.707487	+	0.706727i	$0.750171\pi$
$572$	195.517	−	658.559i	0.341812	−	1.15133i
$573$	175.485			0.306257
$574$	842.943	−	273.889i	1.46854	−	0.477158i
$575$		0			0
$576$	−989.727	+	719.079i	−1.71828	+	1.24840i
$577$	224.288	−	690.288i	0.388715	−	1.19634i	−0.545035	−	0.838413i	$-0.683484\pi$
$577$	224.288	−	690.288i	0.388715	−	1.19634i	0.933750	−	0.357927i	$-0.116516\pi$
$578$	−642.210	−	208.667i	−1.11109	−	0.361015i
$579$	−12.7639	−	17.5680i	−0.0220448	−	0.0303420i
$580$		0			0
$581$	125.693	+	386.844i	0.216339	+	0.665824i
$582$			878.518i			1.50948i
$583$	−225.080	−	293.706i	−0.386072	−	0.503783i
$584$	−357.041			−0.611372
$585$		0			0
$586$	−801.715	−	582.480i	−1.36811	−	0.993993i
$587$	−153.232	+	111.330i	−0.261043	+	0.189659i	−0.710607	−	0.703590i	$-0.751579\pi$
$587$	−153.232	+	111.330i	−0.261043	+	0.189659i	0.449564	+	0.893248i	$0.351579\pi$
$588$	−537.952	+	1655.65i	−0.914884	+	2.81572i
$589$	258.892	+	84.1192i	0.439546	+	0.142817i
$590$		0			0
$591$	291.133	−	400.710i	0.492610	−	0.678020i
$592$	21.7883	+	67.0576i	0.0368046	+	0.113273i
$593$			216.058i			0.364348i	0.983266	+	0.182174i	$0.0583134\pi$
$593$			216.058i			0.364348i	−0.983266	+	0.182174i	$0.941687\pi$
$594$	−173.286	−	490.308i	−0.291728	−	0.825434i
$595$		0			0
$596$	−242.936	+	78.9347i	−0.407611	+	0.132441i
$597$	69.4671	+	50.4708i	0.116360	+	0.0845407i
$598$	13.4164	−	9.74759i	0.0224355	−	0.0163003i
$599$	−309.617	+	952.903i	−0.516890	+	1.59082i	0.262928	+	0.964815i	$0.415312\pi$
$599$	−309.617	+	952.903i	−0.516890	+	1.59082i	−0.779817	+	0.626007i	$0.784688\pi$
$600$		0			0
$601$	230.744	+	317.592i	0.383934	+	0.528440i	0.956621	−	0.291334i	$-0.0940992\pi$
$601$	230.744	+	317.592i	0.383934	+	0.528440i	−0.572688	+	0.819774i	$0.694099\pi$
$602$	−982.771	+	1352.67i	−1.63251	+	2.24696i
$603$	−169.314	−	521.095i	−0.280786	−	0.864171i
$604$		−	410.987i		−	0.680443i
$605$		0			0
$606$	−819.633			−1.35253
$607$	501.620	−	162.986i	0.826392	−	0.268511i	0.134867	−	0.990864i	$-0.456939\pi$
$607$	501.620	−	162.986i	0.826392	−	0.268511i	0.691525	+	0.722353i	$0.256939\pi$
$608$	−290.727	−	211.226i	−0.478170	−	0.347411i
$609$	−667.617	+	485.052i	−1.09625	+	0.796473i
$610$		0			0
$611$	380.498	+	123.631i	0.622747	+	0.202343i
$612$	893.946	+	1230.41i	1.46070	+	2.01047i
$613$	−157.852	+	217.265i	−0.257508	+	0.354429i	−0.918123	−	0.396296i	$-0.870295\pi$
$613$	−157.852	+	217.265i	−0.257508	+	0.354429i	0.660615	+	0.750725i	$0.270295\pi$
$614$	−95.2254	−	293.074i	−0.155090	−	0.477319i
$615$		0			0
$616$	510.202	−	180.317i	0.828249	−	0.292723i
$617$	−623.989			−1.01133			−0.505664	−	0.862731i	$-0.668752\pi$
$617$	−623.989			−1.01133			−0.505664	+	0.862731i	$0.668752\pi$
$618$	−1485.74	+	482.747i	−2.40412	+	0.781144i
$619$	−727.247	−	528.376i	−1.17487	−	0.853596i	−0.183290	−	0.983059i	$-0.558675\pi$
$619$	−727.247	−	528.376i	−1.17487	−	0.853596i	−0.991584	+	0.129463i	$0.958675\pi$
$620$		0			0
$621$	2.24109	−	6.89737i	0.00360885	−	0.0111069i
$622$	−576.917	−	187.452i	−0.927519	−	0.301369i
$623$	−691.334	−	951.540i	−1.10969	−	1.52735i
$624$	−246.103	+	338.732i	−0.394396	+	0.542840i
$625$		0			0
$626$			747.852i			1.19465i
$627$	340.342	−	260.820i	0.542811	−	0.415981i
$628$	−202.452			−0.322376
$629$	190.326	−	61.8407i	0.302585	−	0.0983160i
$630$		0			0
$631$	861.325	−	625.789i	1.36502	−	0.991742i	0.366908	−	0.930257i	$-0.380416\pi$
$631$	861.325	−	625.789i	1.36502	−	0.991742i	0.998108	−	0.0614849i	$-0.0195836\pi$
$632$	178.351	−	548.907i	0.282200	−	0.868523i
$633$	−428.937	−	139.370i	−0.677625	−	0.220174i
$634$	−1023.24	−	1408.37i	−1.61394	−	2.22140i
$635$		0			0
$636$	−262.690	−	808.477i	−0.413035	−	1.27119i
$637$			786.203i			1.23423i
$638$	534.135	+	158.577i	0.837202	+	0.248553i
$639$	−646.784			−1.01218
$640$		0			0
$641$	717.550	+	521.330i	1.11942	+	0.813308i	0.984121	−	0.177497i	$-0.0568000\pi$
$641$	717.550	+	521.330i	1.11942	+	0.813308i	0.135301	+	0.990805i	$0.456800\pi$
$642$	645.170	−	468.743i	1.00494	−	0.730130i
$643$	323.852	−	996.713i	0.503657	−	1.55010i	−0.299359	−	0.954141i	$-0.596773\pi$
$643$	323.852	−	996.713i	0.503657	−	1.55010i	0.803016	−	0.595957i	$-0.203227\pi$
$644$	26.6788	+	8.66846i	0.0414267	+	0.0134603i
$645$		0			0
$646$	−344.303	+	473.893i	−0.532977	+	0.733580i
$647$	−388.461	−	1195.56i	−0.600403	−	1.84785i	−0.525745	−	0.850642i	$-0.676214\pi$
$647$	−388.461	−	1195.56i	−0.600403	−	1.84785i	−0.0746578	−	0.997209i	$-0.523786\pi$
$648$			181.231i			0.279677i
$649$	689.638	−	1002.10i	1.06262	−	1.54407i
$650$		0			0
$651$	1537.87	−	499.683i	2.36231	−	0.767562i
$652$	−208.107	−	151.199i	−0.319183	−	0.231900i
$653$	−139.031	+	101.012i	−0.212912	+	0.154689i	−0.689130	−	0.724638i	$-0.742007\pi$
$653$	−139.031	+	101.012i	−0.212912	+	0.154689i	0.476218	+	0.879327i	$0.342007\pi$
$654$	−282.177	+	868.452i	−0.431464	+	1.32791i
$655$		0			0
$656$	123.853	+	170.468i	0.188800	+	0.259860i
$657$	−570.947	+	785.841i	−0.869022	+	1.19611i
$658$	361.994	+	1114.10i	0.550143	+	1.69316i
$659$		−	719.550i		−	1.09188i	−0.837824	−	0.545941i	$-0.816172\pi$
$659$		−	719.550i		−	1.09188i	0.837824	−	0.545941i	$-0.183828\pi$
$660$		0			0
$661$	655.240			0.991286			0.495643	−	0.868526i	$-0.334932\pi$
$661$	655.240			0.991286			0.495643	+	0.868526i	$0.334932\pi$
$662$	422.527	−	137.287i	0.638259	−	0.207383i
$663$	961.407	+	698.503i	1.45009	+	1.05355i
$664$	137.317	−	99.7663i	0.206802	−	0.150250i
$665$		0			0
$666$	−320.220	−	104.046i	−0.480811	−	0.156225i
$667$	4.56733	+	6.28639i	0.00684757	+	0.00942488i
$668$	−153.131	+	210.766i	−0.229238	+	0.315519i
$669$	−541.386	−	1666.21i	−0.809246	−	2.49060i
$670$		0			0
$671$	−825.890	+	21.1161i	−1.23084	+	0.0314696i
$672$	−2134.65			−3.17657
$673$	650.235	−	211.274i	0.966173	−	0.313929i	0.216903	−	0.976193i	$-0.430404\pi$
$673$	650.235	−	211.274i	0.966173	−	0.313929i	0.749270	+	0.662264i	$0.230404\pi$
$674$	−481.706	−	349.980i	−0.714697	−	0.519258i
$675$		0			0
$676$	−65.5269	+	201.671i	−0.0969333	+	0.298330i
$677$	719.490	+	233.777i	1.06276	+	0.345313i	0.787665	−	0.616104i	$-0.211290\pi$
$677$	719.490	+	233.777i	1.06276	+	0.345313i	0.275098	+	0.961416i	$0.411290\pi$
$678$	−74.8992	−	103.090i	−0.110471	−	0.152050i
$679$	−394.479	+	542.954i	−0.580971	+	0.799638i
$680$		0			0
$681$		−	962.541i		−	1.41342i
$682$	−899.384	−	618.948i	−1.31874	−	0.907548i
$683$	781.639			1.14442			0.572210	−	0.820107i	$-0.306086\pi$
$683$	781.639			1.14442			0.572210	+	0.820107i	$0.306086\pi$
$684$	541.486	−	175.940i	0.791647	−	0.257222i
$685$		0			0
$686$	−537.676	+	390.644i	−0.783784	+	0.569452i
$687$	88.7489	−	273.141i	0.129183	−	0.397585i
$688$	−378.037	−	122.832i	−0.549472	−	0.178534i
$689$	−225.659	−	310.594i	−0.327517	−	0.450789i
$690$		0			0
$691$	−290.643	−	894.507i	−0.420612	−	1.29451i	−0.907134	−	0.420842i	$-0.861735\pi$
$691$	−290.643	−	894.507i	−0.420612	−	1.29451i	0.486522	−	0.873668i	$-0.338265\pi$
$692$		−	1044.62i		−	1.50956i
$693$	418.992	−	1411.29i	0.604606	−	2.03649i
$694$	−807.107			−1.16298
$695$		0			0
$696$	278.589	+	202.406i	0.400271	+	0.290814i
$697$	483.832	−	351.525i	0.694164	−	0.504340i
$698$	−113.636	+	349.736i	−0.162803	+	0.501055i
$699$	−1216.80	−	395.361i	−1.74077	−	0.565609i
$700$		0			0
$701$	−3.94427	+	5.42882i	−0.00562664	+	0.00774440i	−0.811821	−	0.583906i	$-0.801524\pi$
$701$	−3.94427	+	5.42882i	−0.00562664	+	0.00774440i	0.806194	+	0.591651i	$0.201524\pi$
$702$	−166.726	−	513.131i	−0.237502	−	0.730956i
$703$		−	74.9171i		−	0.106568i
$704$	664.075	+	866.547i	0.943288	+	1.23089i
$705$		0			0
$706$	441.030	−	143.299i	0.624688	−	0.202973i
$707$	−506.561	−	368.038i	−0.716494	−	0.520563i
$708$	2260.90	−	1642.64i	3.19337	−	2.32012i
$709$	−307.854	+	947.478i	−0.434209	+	1.33636i	0.459686	+	0.888081i	$0.347962\pi$
$709$	−307.854	+	947.478i	−0.434209	+	1.33636i	−0.893895	+	0.448276i	$0.852038\pi$
$710$		0			0
$711$	−922.932	−	1270.31i	−1.29808	−	1.78665i
$712$	−288.486	+	397.066i	−0.405176	+	0.557678i
$713$	−4.70510	−	14.4808i	−0.00659902	−	0.0203097i
$714$			3479.54i			4.87331i
$715$		0			0
$716$	−1413.11			−1.97362
$717$	−651.704	+	211.751i	−0.908932	+	0.295330i
$718$	−678.376	−	492.869i	−0.944813	−	0.686447i
$719$	478.315	−	347.516i	0.665250	−	0.483333i	−0.203182	−	0.979141i	$-0.565128\pi$
$719$	478.315	−	347.516i	0.665250	−	0.483333i	0.868432	+	0.495808i	$0.165128\pi$
$720$		0			0
$721$	−1135.01	−	368.786i	−1.57421	−	0.511493i
$722$	−524.162	−	721.447i	−0.725986	−	0.999234i
$723$	−1123.57	+	1546.46i	−1.55404	+	2.13895i
$724$	278.048	+	855.743i	0.384044	+	1.18196i
$725$		0			0
$726$	−1606.29	+	614.321i	−2.21252	+	0.846172i
$727$	1276.13			1.75534			0.877670	−	0.479266i	$-0.159097\pi$
$727$	1276.13			1.75534			0.877670	+	0.479266i	$0.159097\pi$
$728$	533.951	−	173.491i	0.733449	−	0.238312i
$729$	915.382	+	665.064i	1.25567	+	0.912297i
$730$		0			0
$731$	−348.627	+	1072.96i	−0.476918	+	1.46780i
$732$	−1805.06	−	586.500i	−2.46593	−	0.801230i
$733$	−19.8208	−	27.2811i	−0.0270407	−	0.0372184i	0.795283	−	0.606239i	$-0.207322\pi$
$733$	−19.8208	−	27.2811i	−0.0270407	−	0.0372184i	−0.822323	+	0.569021i	$0.807322\pi$
$734$	1171.50	−	1612.43i	1.59605	−	2.19678i
$735$		0			0
$736$			20.1003i			0.0273101i
$737$	−461.014	+	162.933i	−0.625528	+	0.221076i
$738$	−1006.21			−1.36342
$739$	1127.54	−	366.361i	1.52577	−	0.495752i	0.578361	−	0.815781i	$-0.303692\pi$
$739$	1127.54	−	366.361i	1.52577	−	0.495752i	0.947408	+	0.320028i	$0.103692\pi$
$740$		0			0
$741$	359.912	−	261.491i	0.485711	−	0.352890i
$742$	347.368	−	1069.09i	0.468150	−	1.44082i
$743$	1302.85	+	423.321i	1.75350	+	0.569746i	0.996494	−	0.0836663i	$-0.0266630\pi$
$743$	1302.85	+	423.321i	1.75350	+	0.569746i	0.757003	+	0.653412i	$0.226663\pi$
$744$	−396.613	−	545.891i	−0.533082	−	0.733724i
$745$		0			0
$746$	383.215	+	1179.41i	0.513693	+	1.58098i
$747$		−	461.768i		−	0.618163i
$748$	1077.28	−	825.566i	1.44021	−	1.10370i
$749$	609.216			0.813372
$750$		0			0
$751$	316.835	+	230.194i	0.421884	+	0.306517i	0.778395	−	0.627774i	$-0.216034\pi$
$751$	316.835	+	230.194i	0.421884	+	0.306517i	−0.356512	+	0.934291i	$0.616034\pi$
$752$	−225.305	+	163.694i	−0.299608	+	0.217678i
$753$	−532.370	+	1638.46i	−0.706998	+	2.17592i
$754$	549.787	+	178.637i	0.729161	+	0.236919i
$755$		0			0
$756$	536.441	−	738.347i	0.709578	−	0.976650i
$757$	73.9880	+	227.712i	0.0977385	+	0.300808i	0.987958	−	0.154724i	$-0.0494489\pi$
$757$	73.9880	+	227.712i	0.0977385	+	0.300808i	−0.890219	+	0.455532i	$0.849449\pi$
$758$			417.330i			0.550567i
$759$	−22.9919	−	6.82596i	−0.0302923	−	0.00899335i
$760$		0			0
$761$	31.0228	−	10.0799i	0.0407659	−	0.0132456i	−0.288563	−	0.957461i	$-0.593177\pi$
$761$	31.0228	−	10.0799i	0.0407659	−	0.0132456i	0.329329	+	0.944215i	$0.393177\pi$
$762$	1733.57	+	1259.51i	2.27503	+	1.65291i
$763$	−564.354	+	410.028i	−0.739652	+	0.537389i
$764$	64.2574	−	197.764i	0.0841065	−	0.258853i
$765$		0			0
$766$	−1000.07	−	1376.48i	−1.30558	−	1.79697i
$767$	741.851	−	1021.07i	0.967211	−	1.33125i
$768$	27.1140	+	83.4482i	0.0353046	+	0.108657i
$769$			80.9870i			0.105315i	0.998613	+	0.0526573i	$0.0167691\pi$
$769$			80.9870i			0.105315i	−0.998613	+	0.0526573i	$0.983231\pi$
$770$		0			0
$771$	942.435			1.22235
$772$	−24.4721	+	7.95148i	−0.0316997	+	0.0102998i
$773$	232.654	+	169.033i	0.300976	+	0.218672i	0.728015	−	0.685561i	$-0.240443\pi$
$773$	232.654	+	169.033i	0.300976	+	0.218672i	−0.427039	+	0.904233i	$0.640443\pi$
$774$	1535.63	−	1115.70i	1.98402	−	1.44147i
$775$		0			0
$776$	266.347	+	86.5414i	0.343231	+	0.111522i
$777$	−261.577	−	360.029i	−0.336649	−	0.463358i
$778$	−239.626	+	329.817i	−0.308003	+	0.423929i
$779$	−69.1844	−	212.928i	−0.0888118	−	0.273335i
$780$		0			0
$781$	14.7527	+	577.005i	0.0188895	+	0.738803i
$782$	32.7639			0.0418976
$783$	240.433	−	78.1213i	0.307066	−	0.0997718i
$784$	−442.750	−	321.677i	−0.564732	−	0.410302i
$785$		0			0
$786$	426.457	−	1312.50i	0.542566	−	1.66985i
$787$	75.9709	+	24.6845i	0.0965323	+	0.0313653i	0.356885	−	0.934148i	$-0.383839\pi$
$787$	75.9709	+	24.6845i	0.0965323	+	0.0313653i	−0.260353	+	0.965514i	$0.583839\pi$
$788$	−344.978	−	474.821i	−0.437789	−	0.602565i
$789$	−174.479	+	240.150i	−0.221140	+	0.304372i
$790$		0			0
$791$		−	97.3449i		−	0.123066i
$792$	−614.120	+	15.7016i	−0.775404	+	0.0198253i
$793$	−857.155			−1.08090
$794$	−324.087	+	105.302i	−0.408170	+	0.132623i
$795$		0			0
$796$	82.3150	−	59.8053i	0.103411	−	0.0751323i
$797$	−267.409	+	823.002i	−0.335520	+	1.03262i	0.630945	+	0.775827i	$0.282667\pi$
$797$	−267.409	+	823.002i	−0.335520	+	1.03262i	−0.966465	+	0.256797i	$0.917333\pi$
$798$	1238.84	+	402.525i	1.55244	+	0.504417i
$799$	464.604	+	639.472i	0.581481	+	0.800341i
$800$		0			0
$801$	412.616	+	1269.90i	0.515127	+	1.58540i
$802$			96.0597i			0.119775i
$803$	714.083	+	491.425i	0.889269	+	0.611987i
$804$	−1123.30			−1.39713
$805$		0			0
$806$	−916.407	−	665.809i	−1.13698	−	0.826065i
$807$	−834.282	+	606.142i	−1.03381	+	0.751105i
$808$	−80.7407	+	248.494i	−0.0999266	+	0.307543i
$809$	−164.498	−	53.4487i	−0.203335	−	0.0660676i	0.205579	−	0.978641i	$-0.434092\pi$
$809$	−164.498	−	53.4487i	−0.203335	−	0.0660676i	−0.408914	+	0.912573i	$0.634092\pi$
$810$		0			0
$811$	−508.782	+	700.279i	−0.627352	+	0.863476i	−0.997862	−	0.0653524i	$-0.979183\pi$
$811$	−508.782	+	700.279i	−0.627352	+	0.863476i	0.370510	+	0.928828i	$0.379183\pi$
$812$	302.170	+	929.985i	0.372131	+	1.14530i
$813$		−	1298.08i		−	1.59665i
$814$	−85.5166	+	288.046i	−0.105057	+	0.353865i
$815$		0			0
$816$	−786.724	+	255.622i	−0.964123	+	0.313263i
$817$	341.684	+	248.248i	0.418218	+	0.303853i
$818$	−1142.03	+	829.733i	−1.39612	+	1.01434i
$819$	471.994	−	1452.65i	0.576305	−	1.77368i
$820$		0			0
$821$	−66.2686	−	91.2109i	−0.0807169	−	0.111097i	0.766749	−	0.641947i	$-0.221873\pi$
$821$	−66.2686	−	91.2109i	−0.0807169	−	0.111097i	−0.847466	+	0.530849i	$0.821873\pi$
$822$	1749.77	−	2408.36i	2.12868	−	2.92987i
$823$	123.479	+	380.030i	0.150035	+	0.461761i	0.997624	−	0.0688924i	$-0.0219465\pi$
$823$	123.479	+	380.030i	0.150035	+	0.461761i	−0.847589	+	0.530654i	$0.821947\pi$
$824$			497.999i			0.604367i
$825$		0			0
$826$	3695.47			4.47394
$827$	−698.603	+	226.990i	−0.844744	+	0.274474i	−0.699243	−	0.714884i	$-0.746479\pi$
$827$	−698.603	+	226.990i	−0.844744	+	0.274474i	−0.145501	+	0.989358i	$0.546479\pi$
$828$	−25.7639	−	18.7186i	−0.0311159	−	0.0226070i
$829$	251.233	−	182.531i	0.303055	−	0.220183i	−0.425856	−	0.904791i	$-0.640027\pi$
$829$	251.233	−	182.531i	0.303055	−	0.220183i	0.728911	+	0.684609i	$0.240027\pi$
$830$		0			0
$831$	−528.940	−	171.863i	−0.636510	−	0.206815i
$832$	665.784	+	916.373i	0.800221	+	1.10141i
$833$	−913.000	+	1256.64i	−1.09604	+	1.50857i
$834$	35.2786	+	108.576i	0.0423005	+	0.130188i
$835$		0			0
$836$	−169.309	−	479.054i	−0.202523	−	0.573031i
$837$	−495.370			−0.591840
$838$	137.711	−	44.7449i	0.164333	−	0.0533949i
$839$	534.323	+	388.208i	0.636857	+	0.462704i	0.858769	−	0.512363i	$-0.171230\pi$
$839$	534.323	+	388.208i	0.636857	+	0.462704i	−0.221912	+	0.975067i	$0.571230\pi$
$840$		0			0
$841$	176.181	−	542.230i	0.209490	−	0.644745i
$842$	−444.769	−	144.514i	−0.528229	−	0.171632i
$843$	−1100.73	−	1515.02i	−1.30573	−	1.79718i
$844$	−314.127	+	432.359i	−0.372188	+	0.512273i
$845$		0			0
$846$		−	1329.88i		−	1.57197i
$847$	−1268.59	−	341.598i	−1.49774	−	0.403303i
$848$	267.240			0.315141
$849$	−2422.91	+	787.251i	−2.85384	+	0.927269i
$850$		0			0
$851$	−3.39010	+	2.46305i	−0.00398366	+	0.00289430i
$852$	−409.756	+	1261.10i	−0.480934	+	1.48016i
$853$	464.919	+	151.061i	0.545040	+	0.177094i	0.568579	−	0.822629i	$-0.307493\pi$
$853$	464.919	+	151.061i	0.545040	+	0.177094i	−0.0235392	+	0.999723i	$0.507493\pi$
$854$	−1475.20	−	2030.43i	−1.72740	−	2.37756i
$855$		0			0
$856$	−78.5579	−	241.776i	−0.0917732	−	0.282449i
$857$		−	433.345i		−	0.505653i	−0.967512	−	0.252827i	$-0.918640\pi$
$857$		−	433.345i		−	0.505653i	0.967512	−	0.252827i	$-0.0813602\pi$
$858$	−1682.30	+	594.563i	−1.96072	+	0.692964i
$859$	−199.533			−0.232285			−0.116143	−	0.993233i	$-0.537053\pi$
$859$	−199.533			−0.232285			−0.116143	+	0.993233i	$0.537053\pi$
$860$		0			0
$861$	−1075.93	−	781.707i	−1.24962	−	0.907905i
$862$	1288.74	−	936.323i	1.49506	−	1.08622i
$863$	295.364	−	909.036i	0.342252	−	1.05334i	−0.620786	−	0.783980i	$-0.713186\pi$
$863$	295.364	−	909.036i	0.342252	−	1.05334i	0.963038	−	0.269364i	$-0.0868136\pi$
$864$	621.944	+	202.082i	0.719843	+	0.233891i
$865$		0			0
$866$	−753.088	+	1036.54i	−0.869617	+	1.19692i
$867$	313.102	+	963.630i	0.361133	+	1.11145i
$868$		−	1916.07i		−	2.20746i
$869$	−1112.21	+	852.335i	−1.27987	+	0.980823i
$870$		0			0
$871$	−482.474	+	156.765i	−0.553931	+	0.179983i
$872$	235.498	+	171.100i	0.270067	+	0.196215i
$873$	616.393	−	447.836i	0.706063	−	0.512985i
$874$	3.79024	−	11.6652i	0.00433666	−	0.0133469i
$875$		0			0
$876$	1170.52	+	1611.08i	1.33621	+	1.83914i
$877$	−184.805	+	254.363i	−0.210724	+	0.290037i	−0.901276	−	0.433246i	$-0.857368\pi$
$877$	−184.805	+	254.363i	−0.210724	+	0.290037i	0.690551	+	0.723284i	$0.257368\pi$
$878$	−652.349	−	2007.73i	−0.742995	−	2.28670i
$879$			1486.95i			1.69164i
$880$		0			0
$881$	330.178			0.374777			0.187388	−	0.982286i	$-0.439998\pi$
$881$	330.178			0.374777			0.187388	+	0.982286i	$0.439998\pi$
$882$	2485.47	−	807.577i	2.81799	−	0.915620i
$883$	−817.950	−	594.275i	−0.926330	−	0.673018i	0.0187613	−	0.999824i	$-0.494028\pi$
$883$	−817.950	−	594.275i	−0.926330	−	0.673018i	−0.945092	+	0.326806i	$0.894028\pi$
$884$	1139.22	−	827.691i	1.28871	−	0.936302i
$885$		0			0
$886$	1693.83	+	550.358i	1.91177	+	0.621172i
$887$	135.458	+	186.442i	0.152715	+	0.210194i	0.878519	−	0.477708i	$-0.158532\pi$
$887$	135.458	+	186.442i	0.152715	+	0.210194i	−0.725804	+	0.687901i	$0.758532\pi$
$888$	−109.153	+	150.236i	−0.122920	+	0.169185i
$889$	505.850	+	1556.85i	0.569010	+	1.75123i
$890$		0			0
$891$	249.443	−	362.461i	0.279958	−	0.406803i
$892$	−2075.99			−2.32734
$893$	281.423	−	91.4398i	0.315143	−	0.102396i
$894$	536.745	+	389.968i	0.600385	+	0.436206i
$895$		0			0
$896$	−453.507	+	1395.75i	−0.506147	+	1.55776i
$897$	−23.6656	−	7.68943i	−0.0263831	−	0.00857239i
$898$	1538.07	+	2116.97i	1.71277	+	2.35742i
$899$	311.971	−	429.392i	0.347020	−	0.477633i
$900$		0			0
$901$		−	758.494i		−	0.841836i
$902$	22.9508	+	897.650i	0.0254444	+	0.995177i
$903$	2508.80			2.77830
$904$	−38.6327	+	12.5525i	−0.0427353	+	0.0138856i
$905$		0			0
$906$	−863.596	+	627.439i	−0.953196	+	0.692537i
$907$	−356.661	+	1097.69i	−0.393232	+	1.21024i	0.537099	+	0.843519i	$0.319520\pi$
$907$	−356.661	+	1097.69i	−0.393232	+	1.21024i	−0.930330	+	0.366723i	$0.880480\pi$
$908$	−1084.74	−	352.453i	−1.19465	−	0.388164i
$909$	417.818	+	575.078i	0.459646	+	0.632649i
$910$		0			0
$911$	187.421	+	576.824i	0.205732	+	0.633177i	0.999683	+	0.0251948i	$0.00802062\pi$
$911$	187.421	+	576.824i	0.205732	+	0.633177i	−0.793951	+	0.607982i	$0.791979\pi$
$912$			309.674i			0.339555i
$913$	−411.950	+	10.5326i	−0.451204	+	0.0115363i
$914$	−1254.78			−1.37284
$915$		0			0
$916$	−275.320	−	200.032i	−0.300568	−	0.218375i
$917$	852.914	−	619.678i	0.930113	−	0.675767i
$918$	329.399	−	1013.78i	0.358822	−	1.10434i
$919$	−1094.16	−	355.514i	−1.19060	−	0.386849i	−0.354304	−	0.935130i	$-0.615282\pi$
$919$	−1094.16	−	355.514i	−1.19060	−	0.386849i	−0.836294	+	0.548281i	$0.815282\pi$
$920$		0			0
$921$	−271.783	+	374.077i	−0.295096	+	0.406164i
$922$	686.448	+	2112.67i	0.744520	+	2.29140i
$923$			598.848i			0.648806i
$924$	−2486.29	−	1711.04i	−2.69079	−	1.85178i
$925$		0			0
$926$	2270.42	−	737.706i	2.45186	−	0.796658i
$927$	1096.09	+	796.353i	1.18240	+	0.859065i
$928$	−566.851	+	411.841i	−0.610831	+	0.443795i
$929$	444.730	−	1368.74i	0.478719	−	1.47335i	−0.362157	−	0.932117i	$-0.617960\pi$
$929$	444.730	−	1368.74i	0.478719	−	1.47335i	0.840876	−	0.541228i	$-0.182040\pi$
$930$		0			0
$931$	341.790	+	470.434i	0.367121	+	0.505299i
$932$	−891.107	+	1226.50i	−0.956123	+	1.31599i
$933$	281.269	+	865.658i	0.301468	+	0.927822i
$934$		−	1438.02i		−	1.53963i
$935$		0			0
$936$	−637.368			−0.680948
$937$	−467.559	+	151.919i	−0.498996	+	0.162133i	−0.547692	−	0.836680i	$-0.684493\pi$
$937$	−467.559	+	151.919i	−0.498996	+	0.162133i	0.0486963	+	0.998814i	$0.484493\pi$
$938$	−1201.70	−	873.089i	−1.28113	−	0.930799i
$939$	907.834	−	659.580i	0.966810	−	0.702428i
$940$		0			0
$941$	1702.39	+	553.141i	1.80913	+	0.587822i	1.00000		0.000194881i	$6.20325e-5\pi$
$941$	1702.39	+	553.141i	1.80913	+	0.587822i	0.809132	+	0.587628i	$0.199938\pi$
$942$	309.076	+	425.406i	0.328106	+	0.451599i
$943$	−7.36068	+	10.1311i	−0.00780560	+	0.0107435i
$944$	271.486	+	835.547i	0.287591	+	0.885113i
$945$		0			0
$946$	−1030.36	−	1344.51i	−1.08917	−	1.42125i
$947$	1111.85			1.17407			0.587037	−	0.809560i	$-0.300294\pi$
$947$	1111.85			1.17407			0.587037	+	0.809560i	$0.300294\pi$
$948$	−3061.55	+	994.756i	−3.22948	+	1.04932i
$949$	727.599	+	528.631i	0.766700	+	0.557040i
$950$		0			0
$951$	−807.187	+	2484.27i	−0.848777	+	2.61227i
$952$	1054.92	+	342.764i	1.10811	+	0.360046i
$953$	−175.776	−	241.935i	−0.184445	−	0.253867i	0.706775	−	0.707439i	$-0.250150\pi$
$953$	−175.776	−	241.935i	−0.184445	−	0.253867i	−0.891220	+	0.453572i	$0.850150\pi$
$954$	−750.102	+	1032.43i	−0.786271	+	1.08221i
$955$		0			0
$956$			811.977i			0.849348i
$957$	−278.589	−	788.257i	−0.291106	−	0.823675i
$958$	26.7376			0.0279098
$959$	2162.84	−	702.749i	2.25531	−	0.732794i
$960$		0			0
$961$	−63.9224	+	46.4423i	−0.0665165	+	0.0483271i
$962$	−96.3344	+	296.487i	−0.100140	+	0.308198i
$963$	−657.767	−	213.722i	−0.683040	−	0.221933i
$964$	1331.38	+	1832.48i	1.38109	+	1.90091i
$965$		0			0
$966$	−22.5147	−	69.2931i	−0.0233072	−	0.0717320i
$967$		−	246.770i		−	0.255191i	−0.991826	−	0.127596i	$-0.959274\pi$
$967$		−	246.770i		−	0.255191i	0.991826	−	0.127596i	$-0.0407259\pi$
$968$	28.0153	+	547.507i	0.0289414	+	0.565606i
$969$	878.933			0.907052
$970$		0			0
$971$	−161.120	−	117.060i	−0.165932	−	0.120556i	0.501720	−	0.865030i	$-0.332701\pi$
$971$	−161.120	−	117.060i	−0.165932	−	0.120556i	−0.667652	+	0.744473i	$0.732701\pi$
$972$	1429.79	−	1038.81i	1.47098	−	1.06873i
$973$	−26.9505	+	82.9451i	−0.0276983	+	0.0852467i
$974$	2336.60	+	759.209i	2.39898	+	0.779475i
$975$		0			0
$976$	350.707	−	482.707i	0.359331	−	0.494577i
$977$	72.9462	+	224.505i	0.0746635	+	0.229790i	0.981423	−	0.191858i	$-0.0614515\pi$
$977$	72.9462	+	224.505i	0.0746635	+	0.229790i	−0.906759	+	0.421649i	$0.861451\pi$
$978$			668.119i			0.683149i
$979$	1123.49	−	397.066i	1.14759	−	0.405584i
$980$		0			0
$981$	753.174	−	244.721i	0.767762	−	0.249461i
$982$	370.810	+	269.409i	0.377607	+	0.274347i
$983$	301.034	−	218.714i	0.306241	−	0.222497i	−0.424041	−	0.905643i	$-0.639389\pi$
$983$	301.034	−	218.714i	0.306241	−	0.222497i	0.730282	+	0.683146i	$0.239389\pi$
$984$	−171.492	+	527.798i	−0.174280	+	0.536380i
$985$		0			0
$986$	671.312	+	923.982i	0.680844	+	0.937101i
$987$	1033.17	−	1422.03i	1.04678	−	1.44076i
$988$	−162.900	−	501.354i	−0.164878	−	0.507443i
$989$		−	23.6233i		−	0.0238861i
$990$		0			0
$991$	−759.033			−0.765927			−0.382963	−	0.923764i	$-0.625096\pi$
$991$	−759.033			−0.765927			−0.382963	+	0.923764i	$0.625096\pi$
$992$	1305.75	−	424.264i	1.31628	−	0.427685i
$993$	−539.311	−	391.832i	−0.543113	−	0.394594i
$994$	−1418.55	+	1030.64i	−1.42712	+	1.03686i
$995$		0			0
$996$	−900.355	−	292.543i	−0.903971	−	0.293718i
$997$	415.743	+	572.222i	0.416994	+	0.573944i	0.964907	−	0.262592i	$-0.0845774\pi$
$997$	415.743	+	572.222i	0.416994	+	0.573944i	−0.547913	+	0.836536i	$0.684577\pi$
$998$	1102.45	−	1517.39i	1.10466	−	1.52043i
$999$	42.1289	+	129.659i	0.0421711	+	0.129789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.a.226.1		4
5.2	odd	4		275.3.q.a.149.1		8
5.3	odd	4		275.3.q.a.149.2		8
5.4	even	2		55.3.i.b.6.1	✓	4
11.2	odd	10	inner	275.3.x.a.101.1		4
55.2	even	20		275.3.q.a.24.2		8
55.13	even	20		275.3.q.a.24.1		8
55.14	even	10		605.3.c.b.241.1		4
55.19	odd	10		605.3.c.b.241.4		4
55.24	odd	10		55.3.i.b.46.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.b.6.1	✓	4	5.4	even	2
55.3.i.b.46.1	yes	4	55.24	odd	10
275.3.q.a.24.1		8	55.13	even	20
275.3.q.a.24.2		8	55.2	even	20
275.3.q.a.149.1		8	5.2	odd	4
275.3.q.a.149.2		8	5.3	odd	4
275.3.x.a.101.1		4	11.2	odd	10	inner
275.3.x.a.226.1		4	1.1	even	1	trivial
605.3.c.b.241.1		4	55.14	even	10
605.3.c.b.241.4		4	55.19	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.92705 + 0.951057i) q^{2} +(3.73607 + 2.71441i) q^{3} +(4.42705 - 3.21644i) q^{4} +(-13.5172 - 4.39201i) q^{6} +(-6.38197 - 8.78402i) q^{7} +(-2.66312 + 3.66547i) q^{8} +(3.80902 + 11.7229i) q^{9} +(10.3713 - 3.66547i) q^{11} +25.2705 q^{12} +(10.8541 - 3.52671i) q^{13} +(27.0344 + 19.6417i) q^{14} +(-2.45492 + 7.55545i) q^{16} +(21.4443 + 6.96767i) q^{17} +(-22.2984 - 30.6911i) q^{18} +(4.96149 - 6.82891i) q^{19} -50.1410i q^{21} +(-26.8713 + 20.5927i) q^{22} -0.472136 q^{23} +(-19.8992 + 6.46564i) q^{24} +(-28.4164 + 20.6457i) q^{26} +(-4.74671 + 14.6089i) q^{27} +(-56.5066 - 18.3601i) q^{28} +(-9.67376 - 13.3148i) q^{29} +(9.96556 + 30.6708i) q^{31} -42.5730i q^{32} +(48.6976 + 14.4576i) q^{33} -69.3951 q^{34} +(54.5689 + 39.6466i) q^{36} +(7.18034 - 5.21682i) q^{37} +(-8.02786 + 24.7072i) q^{38} +(50.1246 + 16.2865i) q^{39} +(15.5902 - 21.4580i) q^{41} +(47.6869 + 146.765i) q^{42} +50.0350i q^{43} +(34.1246 - 49.5860i) q^{44} +(1.38197 - 0.449028i) q^{46} +(28.3607 + 20.6052i) q^{47} +(-29.6803 + 21.5640i) q^{48} +(-21.2877 + 65.5169i) q^{49} +(61.2041 + 84.2403i) q^{51} +(36.7082 - 50.5245i) q^{52} +(-10.3951 - 31.9929i) q^{53} -47.2753i q^{54} +49.1935 q^{56} +(37.0729 - 12.0457i) q^{57} +(40.9787 + 29.7728i) q^{58} +(89.4681 - 65.0024i) q^{59} +(-71.4296 - 23.2089i) q^{61} +(-58.3394 - 80.2973i) q^{62} +(78.6656 - 108.274i) q^{63} +(30.6697 + 94.3916i) q^{64} +(-156.290 + 3.99598i) q^{66} -44.4508 q^{67} +(117.346 - 38.1280i) q^{68} +(-1.76393 - 1.28157i) q^{69} +(-16.2148 + 49.9040i) q^{71} +(-53.1140 - 17.2578i) q^{72} +(46.3197 + 63.7535i) q^{73} +(-16.0557 + 22.0988i) q^{74} -46.1903i q^{76} +(-98.3870 - 67.7090i) q^{77} -162.207 q^{78} +(-121.151 + 39.3643i) q^{79} +(32.3607 - 23.5114i) q^{81} +(-25.2254 + 77.6359i) q^{82} +(-35.6287 - 11.5765i) q^{83} +(-161.276 - 221.977i) q^{84} +(-47.5861 - 146.455i) q^{86} -76.0035i q^{87} +(-14.1844 + 47.7773i) q^{88} +108.326 q^{89} +(-100.249 - 72.8353i) q^{91} +(-2.09017 + 1.51860i) q^{92} +(-46.0213 + 141.639i) q^{93} +(-102.610 - 33.3400i) q^{94} +(115.561 - 159.056i) q^{96} +(-19.1008 - 58.7863i) q^{97} -212.017i q^{98} +(82.4746 + 107.621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} + 6 q^{3} + 11 q^{4} - 25 q^{6} - 30 q^{7} + 5 q^{8} + 13 q^{9} - q^{11} + 34 q^{12} + 30 q^{13} + 50 q^{14} - 21 q^{16} + 50 q^{17} - 40 q^{18} - 45 q^{19} - 65 q^{22} + 16 q^{23} - 55 q^{24}+ \cdots + 113 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 6 * q^3 + 11 * q^4 - 25 * q^6 - 30 * q^7 + 5 * q^8 + 13 * q^9 - q^11 + 34 * q^12 + 30 * q^13 + 50 * q^14 - 21 * q^16 + 50 * q^17 - 40 * q^18 - 45 * q^19 - 65 * q^22 + 16 * q^23 - 55 * q^24 - 60 * q^26 - 57 * q^27 - 150 * q^28 - 70 * q^29 + 98 * q^31 + 121 * q^33 - 130 * q^34 + 102 * q^36 - 16 * q^37 - 50 * q^38 + 120 * q^39 + 40 * q^41 + 70 * q^42 + 56 * q^44 + 10 * q^46 + 24 * q^47 - 74 * q^48 + 11 * q^49 + 95 * q^51 + 120 * q^52 + 106 * q^53 + 155 * q^57 + 70 * q^58 + 217 * q^59 - 80 * q^61 - 50 * q^62 + 100 * q^63 + 31 * q^64 - 330 * q^66 - 66 * q^67 + 210 * q^68 - 16 * q^69 + 38 * q^71 - 85 * q^72 + 230 * q^73 - 100 * q^74 - 300 * q^78 - 100 * q^79 + 40 * q^81 - 45 * q^82 - 185 * q^83 - 180 * q^84 - 45 * q^86 - 135 * q^88 + 402 * q^89 - 240 * q^91 + 14 * q^92 - 278 * q^93 - 160 * q^94 + 100 * q^96 - 101 * q^97 + 113 * q^99

Introduction

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