LMFDB - Embedded newform 275.3.x.b.51.1

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,-5,10] 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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	275.51
Dual form			275.3.x.b.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690983 + 0.951057i) q^{2} +(1.38197 - 4.25325i) q^{3} +(0.809017 + 2.48990i) q^{4} +(3.09017 + 4.25325i) q^{6} +(7.39919 - 2.40414i) q^{7} +(-7.39919 - 2.40414i) q^{8} +(-8.89919 - 6.46564i) q^{9} +(10.8713 + 1.67760i) q^{11} +11.7082 q^{12} +(3.68034 - 5.06555i) q^{13} +(-2.82624 + 8.69827i) q^{14} +(-1.07295 + 0.779543i) q^{16} +(2.98936 + 4.11450i) q^{17} +(12.2984 - 3.99598i) q^{18} +(-15.8541 - 5.15131i) q^{19} -34.7931i q^{21} +(-9.10739 + 9.18005i) q^{22} +31.5066 q^{23} +(-20.4508 + 28.1482i) q^{24} +(2.27458 + 7.00042i) q^{26} +(-7.23607 + 5.25731i) q^{27} +(11.9721 + 16.4782i) q^{28} +(27.2984 - 8.86978i) q^{29} +(-31.4336 - 22.8379i) q^{31} -32.6789i q^{32} +(22.1591 - 43.9201i) q^{33} -5.97871 q^{34} +(8.89919 - 27.3889i) q^{36} +(-21.5689 - 66.3822i) q^{37} +(15.8541 - 11.5187i) q^{38} +(-16.4590 - 22.6538i) q^{39} +(64.5582 + 20.9762i) q^{41} +(33.0902 + 24.0414i) q^{42} +43.0471i q^{43} +(4.61803 + 28.4257i) q^{44} +(-21.7705 + 29.9645i) q^{46} +(-3.71885 + 11.4454i) q^{47} +(1.83282 + 5.64083i) q^{48} +(9.32624 - 6.77591i) q^{49} +(21.6312 - 7.02840i) q^{51} +(15.5902 + 5.06555i) q^{52} +(-30.4508 - 22.1238i) q^{53} -10.5146i q^{54} -60.5279 q^{56} +(-43.8197 + 60.3126i) q^{57} +(-10.4271 + 32.0912i) q^{58} +(17.7533 + 54.6390i) q^{59} +(66.5304 + 91.5712i) q^{61} +(43.4402 - 14.1146i) q^{62} +(-81.3911 - 26.4456i) q^{63} +(26.7877 + 19.4624i) q^{64} +(26.4590 + 51.4226i) q^{66} -93.9443 q^{67} +(-7.82624 + 10.7719i) q^{68} +(43.5410 - 134.005i) q^{69} +(-34.8090 + 25.2902i) q^{71} +(50.3024 + 69.2354i) q^{72} +(-14.9853 + 4.86902i) q^{73} +(78.0370 + 25.3557i) q^{74} -43.6426i q^{76} +(84.4721 - 13.7233i) q^{77} +32.9180 q^{78} +(-45.1099 + 62.0885i) q^{79} +(-18.2320 - 56.1123i) q^{81} +(-64.5582 + 46.9043i) q^{82} +(-15.4123 - 21.2133i) q^{83} +(86.6312 - 28.1482i) q^{84} +(-40.9402 - 29.7448i) q^{86} -128.365i q^{87} +(-76.4058 - 38.5491i) q^{88} -105.215 q^{89} +(15.0532 - 46.3290i) q^{91} +(25.4894 + 78.4482i) q^{92} +(-140.575 + 102.134i) q^{93} +(-8.31559 - 11.4454i) q^{94} +(-138.992 - 45.1612i) q^{96} +(-27.0106 - 19.6244i) q^{97} +13.5518i q^{98} +(-85.8992 - 85.2193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} + 10 q^{3} + q^{4} - 10 q^{6} + 5 q^{7} - 5 q^{8} - 11 q^{9} + q^{11} + 20 q^{12} - 30 q^{13} + 20 q^{14} - 11 q^{16} - 35 q^{17} - 50 q^{19} + 15 q^{22} + 50 q^{23} + 30 q^{24} + 65 q^{26}+ \cdots - 319 q^{99}+O(q^{100}) $ 4 * q - 5 * q^2 + 10 * q^3 + q^4 - 10 * q^6 + 5 * q^7 - 5 * q^8 - 11 * q^9 + q^11 + 20 * q^12 - 30 * q^13 + 20 * q^14 - 11 * q^16 - 35 * q^17 - 50 * q^19 + 15 * q^22 + 50 * q^23 + 30 * q^24 + 65 * q^26 - 20 * q^27 + 30 * q^28 + 60 * q^29 - 43 * q^31 - 50 * q^33 + 70 * q^34 + 11 * q^36 + 30 * q^37 + 50 * q^38 - 200 * q^39 + 95 * q^41 + 110 * q^42 + 14 * q^44 - 20 * q^46 - 35 * q^47 - 100 * q^48 + 6 * q^49 - 70 * q^51 + 40 * q^52 - 10 * q^53 - 260 * q^56 - 220 * q^57 - 35 * q^58 + 33 * q^59 + 85 * q^61 + 15 * q^62 - 55 * q^63 + 11 * q^64 + 240 * q^66 - 340 * q^67 + 40 * q^69 - 137 * q^71 + 275 * q^72 + 110 * q^73 + 55 * q^74 + 320 * q^77 + 400 * q^78 + 70 * q^79 + 59 * q^81 - 95 * q^82 + 115 * q^83 + 190 * q^84 - 5 * q^86 - 205 * q^88 - 318 * q^89 + 295 * q^91 + 55 * q^92 - 370 * q^93 + 45 * q^94 - 310 * q^96 - 155 * q^97 - 319 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−0.690983	+	0.951057i	−0.345492	+	0.475528i	−0.946035	−	0.324064i	$-0.894951\pi$
$2$	−0.690983	+	0.951057i	−0.345492	+	0.475528i	0.600544	+	0.799592i	$0.294951\pi$
$3$	1.38197	−	4.25325i	0.460655	−	1.41775i	−0.403710	−	0.914887i	$-0.632280\pi$
$3$	1.38197	−	4.25325i	0.460655	−	1.41775i	0.864365	−	0.502864i	$-0.167720\pi$
$4$	0.809017	+	2.48990i	0.202254	+	0.622475i
$5$		0			0
$5$		0			0
$6$	3.09017	+	4.25325i	0.515028	+	0.708876i
$7$	7.39919	−	2.40414i	1.05703	−	0.343449i	0.271604	−	0.962409i	$-0.412446\pi$
$7$	7.39919	−	2.40414i	1.05703	−	0.343449i	0.785422	+	0.618960i	$0.212446\pi$
$8$	−7.39919	−	2.40414i	−0.924898	−	0.300518i
$9$	−8.89919	−	6.46564i	−0.988799	−	0.718404i
$10$		0			0
$11$	10.8713	+	1.67760i	0.988302	+	0.152509i
$11$	10.8713	+	1.67760i	0.988302	+	0.152509i
$12$	11.7082			0.975684
$13$	3.68034	−	5.06555i	0.283103	−	0.389658i	−0.643656	−	0.765315i	$-0.722583\pi$
$13$	3.68034	−	5.06555i	0.283103	−	0.389658i	0.926759	+	0.375657i	$0.122583\pi$
$14$	−2.82624	+	8.69827i	−0.201874	+	0.621305i
$15$		0			0
$16$	−1.07295	+	0.779543i	−0.0670593	+	0.0487214i
$17$	2.98936	+	4.11450i	0.175845	+	0.242029i	0.887837	−	0.460158i	$-0.152207\pi$
$17$	2.98936	+	4.11450i	0.175845	+	0.242029i	−0.711993	+	0.702187i	$0.752207\pi$
$18$	12.2984	−	3.99598i	0.683243	−	0.221999i
$19$	−15.8541	−	5.15131i	−0.834426	−	0.271122i	−0.139518	−	0.990220i	$-0.544555\pi$
$19$	−15.8541	−	5.15131i	−0.834426	−	0.271122i	−0.694909	+	0.719098i	$0.744555\pi$
$20$		0			0
$21$		−	34.7931i		−	1.65681i
$22$	−9.10739	+	9.18005i	−0.413972	+	0.417275i
$23$	31.5066			1.36985			0.684926	−	0.728613i	$-0.259835\pi$
$23$	31.5066			1.36985			0.684926	+	0.728613i	$0.259835\pi$
$24$	−20.4508	+	28.1482i	−0.852119	+	1.17284i
$25$		0			0
$26$	2.27458	+	7.00042i	0.0874837	+	0.269247i
$27$	−7.23607	+	5.25731i	−0.268003	+	0.194715i
$28$	11.9721	+	16.4782i	0.427576	+	0.588508i
$29$	27.2984	−	8.86978i	0.941323	−	0.305854i	0.202138	−	0.979357i	$-0.435211\pi$
$29$	27.2984	−	8.86978i	0.941323	−	0.305854i	0.739185	+	0.673503i	$0.235211\pi$
$30$		0			0
$31$	−31.4336	−	22.8379i	−1.01399	−	0.736705i	−0.0489462	−	0.998801i	$-0.515586\pi$
$31$	−31.4336	−	22.8379i	−1.01399	−	0.736705i	−0.965042	+	0.262096i	$0.915586\pi$
$32$		−	32.6789i		−	1.02122i
$33$	22.1591	−	43.9201i	0.671486	−	1.33091i
$34$	−5.97871			−0.175845
$35$		0			0
$36$	8.89919	−	27.3889i	0.247200	−	0.760802i
$37$	−21.5689	−	66.3822i	−0.582943	−	1.79411i	−0.607379	−	0.794412i	$-0.707779\pi$
$37$	−21.5689	−	66.3822i	−0.582943	−	1.79411i	0.0244364	−	0.999701i	$-0.492221\pi$
$38$	15.8541	−	11.5187i	0.417213	−	0.303123i
$39$	−16.4590	−	22.6538i	−0.422025	−	0.580868i
$40$		0			0
$41$	64.5582	+	20.9762i	1.57459	+	0.511616i	0.960656	−	0.277741i	$-0.0895856\pi$
$41$	64.5582	+	20.9762i	1.57459	+	0.511616i	0.613935	+	0.789356i	$0.289586\pi$
$42$	33.0902	+	24.0414i	0.787861	+	0.572415i
$43$			43.0471i			1.00109i	0.865709	+	0.500547i	$0.166868\pi$
$43$			43.0471i			1.00109i	−0.865709	+	0.500547i	$0.833132\pi$
$44$	4.61803	+	28.4257i	0.104955	+	0.646039i
$45$		0			0
$46$	−21.7705	+	29.9645i	−0.473272	+	0.651403i
$47$	−3.71885	+	11.4454i	−0.0791244	+	0.243520i	−0.982792	−	0.184714i	$-0.940864\pi$
$47$	−3.71885	+	11.4454i	−0.0791244	+	0.243520i	0.903668	+	0.428234i	$0.140864\pi$
$48$	1.83282	+	5.64083i	0.0381837	+	0.117517i
$49$	9.32624	−	6.77591i	0.190331	−	0.138284i
$50$		0			0
$51$	21.6312	−	7.02840i	0.424141	−	0.137812i
$52$	15.5902	+	5.06555i	0.299811	+	0.0974145i
$53$	−30.4508	−	22.1238i	−0.574544	−	0.417431i	0.262209	−	0.965011i	$-0.415549\pi$
$53$	−30.4508	−	22.1238i	−0.574544	−	0.417431i	−0.836753	+	0.547580i	$0.815549\pi$
$54$		−	10.5146i		−	0.194715i
$55$		0			0
$56$	−60.5279			−1.08085
$57$	−43.8197	+	60.3126i	−0.768766	+	1.05812i
$58$	−10.4271	+	32.0912i	−0.179777	+	0.553296i
$59$	17.7533	+	54.6390i	0.300903	+	0.926085i	0.981174	+	0.193124i	$0.0618620\pi$
$59$	17.7533	+	54.6390i	0.300903	+	0.926085i	−0.680271	+	0.732961i	$0.738138\pi$
$60$		0			0
$61$	66.5304	+	91.5712i	1.09066	+	1.50117i	0.847213	+	0.531254i	$0.178279\pi$
$61$	66.5304	+	91.5712i	1.09066	+	1.50117i	0.243449	+	0.969914i	$0.421721\pi$
$62$	43.4402	−	14.1146i	0.700648	−	0.227654i
$63$	−81.3911	−	26.4456i	−1.29192	−	0.419771i
$64$	26.7877	+	19.4624i	0.418558	+	0.304100i
$65$		0			0
$66$	26.4590	+	51.4226i	0.400894	+	0.779130i
$67$	−93.9443			−1.40215			−0.701077	−	0.713086i	$-0.747297\pi$
$67$	−93.9443			−1.40215			−0.701077	+	0.713086i	$0.747297\pi$
$68$	−7.82624	+	10.7719i	−0.115092	+	0.158410i
$69$	43.5410	−	134.005i	0.631029	−	1.94211i
$70$		0			0
$71$	−34.8090	+	25.2902i	−0.490268	+	0.356200i	−0.805287	−	0.592885i	$-0.797989\pi$
$71$	−34.8090	+	25.2902i	−0.490268	+	0.356200i	0.315019	+	0.949085i	$0.397989\pi$
$72$	50.3024	+	69.2354i	0.698645	+	0.961602i
$73$	−14.9853	+	4.86902i	−0.205278	+	0.0666989i	−0.409851	−	0.912152i	$-0.634419\pi$
$73$	−14.9853	+	4.86902i	−0.205278	+	0.0666989i	0.204573	+	0.978851i	$0.434419\pi$
$74$	78.0370	+	25.3557i	1.05455	+	0.342645i
$75$		0			0
$76$		−	43.6426i		−	0.574245i
$77$	84.4721	−	13.7233i	1.09704	−	0.178225i
$78$	32.9180			0.422025
$79$	−45.1099	+	62.0885i	−0.571011	+	0.785930i	−0.992674	−	0.120823i	$-0.961447\pi$
$79$	−45.1099	+	62.0885i	−0.571011	+	0.785930i	0.421663	+	0.906753i	$0.361447\pi$
$80$		0			0
$81$	−18.2320	−	56.1123i	−0.225086	−	0.692745i
$82$	−64.5582	+	46.9043i	−0.787296	+	0.572004i
$83$	−15.4123	−	21.2133i	−0.185691	−	0.255582i	0.706015	−	0.708197i	$-0.250491\pi$
$83$	−15.4123	−	21.2133i	−0.185691	−	0.255582i	−0.891706	+	0.452615i	$0.850491\pi$
$84$	86.6312	−	28.1482i	1.03132	−	0.335097i
$85$		0			0
$86$	−40.9402	−	29.7448i	−0.476049	−	0.345870i
$87$		−	128.365i		−	1.47546i
$88$	−76.4058	−	38.5491i	−0.868247	−	0.438058i
$89$	−105.215			−1.18219			−0.591094	−	0.806602i	$-0.701304\pi$
$89$	−105.215			−1.18219			−0.591094	+	0.806602i	$0.701304\pi$
$90$		0			0
$91$	15.0532	−	46.3290i	0.165420	−	0.509110i
$92$	25.4894	+	78.4482i	0.277058	+	0.852698i
$93$	−140.575	+	102.134i	−1.51156	+	1.09822i
$94$	−8.31559	−	11.4454i	−0.0884638	−	0.121760i
$95$		0			0
$96$	−138.992	−	45.1612i	−1.44783	−	0.470429i
$97$	−27.0106	−	19.6244i	−0.278460	−	0.202313i	0.439785	−	0.898103i	$-0.355055\pi$
$97$	−27.0106	−	19.6244i	−0.278460	−	0.202313i	−0.718246	+	0.695790i	$0.755055\pi$
$98$			13.5518i			0.138284i
$99$	−85.8992	−	85.2193i	−0.867669	−	0.860801i
$100$		0			0
$101$	−57.8738	+	79.6565i	−0.573008	+	0.788678i	−0.992907	−	0.118893i	$-0.962066\pi$
$101$	−57.8738	+	79.6565i	−0.573008	+	0.788678i	0.419899	+	0.907571i	$0.362066\pi$
$102$	−8.26238	+	25.4290i	−0.0810037	+	0.249304i
$103$	48.7041	+	149.896i	0.472856	+	1.45530i	0.848828	+	0.528669i	$0.177309\pi$
$103$	48.7041	+	149.896i	0.472856	+	1.45530i	−0.375972	+	0.926631i	$0.622691\pi$
$104$	−39.4098	+	28.6329i	−0.378941	+	0.275317i
$105$		0			0
$106$	42.0820	−	13.6733i	0.397000	−	0.128993i
$107$	−29.9139	−	9.71961i	−0.279569	−	0.0908375i	0.165876	−	0.986147i	$-0.446955\pi$
$107$	−29.9139	−	9.71961i	−0.279569	−	0.0908375i	−0.445446	+	0.895309i	$0.646955\pi$
$108$	−18.9443	−	13.7638i	−0.175410	−	0.127443i
$109$		−	22.2298i		−	0.203943i	−0.994787	−	0.101972i	$-0.967485\pi$
$109$		−	22.2298i		−	0.203943i	0.994787	−	0.101972i	$-0.0325151\pi$
$110$		0			0
$111$	−312.148			−2.81214
$112$	−6.06482	+	8.34751i	−0.0541502	+	0.0745313i
$113$	−58.0426	+	178.637i	−0.513651	+	1.58086i	0.272072	+	0.962277i	$0.412291\pi$
$113$	−58.0426	+	178.637i	−0.513651	+	1.58086i	−0.785723	+	0.618579i	$0.787709\pi$
$114$	−27.0820	−	83.3499i	−0.237562	−	0.731140i
$115$		0			0
$116$	44.1697	+	60.7944i	0.380773	+	0.524089i
$117$	−65.5041	+	21.2836i	−0.559864	+	0.181911i
$118$	−64.2320	−	20.8702i	−0.544339	−	0.176866i
$119$	32.0106	+	23.2571i	0.268997	+	0.195438i
$120$		0			0
$121$	115.371	+	36.4754i	0.953482	+	0.301450i
$122$	−133.061			−1.09066
$123$	178.435	−	245.594i	1.45069	−	1.99670i
$124$	31.4336	−	96.7428i	0.253497	−	0.780184i
$125$		0			0
$126$	81.3911	−	59.1341i	0.645961	−	0.469318i
$127$	−79.1788	−	108.980i	−0.623455	−	0.858112i	0.374144	−	0.927371i	$-0.377937\pi$
$127$	−79.1788	−	108.980i	−0.623455	−	0.858112i	−0.997599	+	0.0692585i	$0.977937\pi$
$128$	87.2984	−	28.3650i	0.682019	−	0.221601i
$129$	183.090	+	59.4896i	1.41930	+	0.461160i
$130$		0			0
$131$			47.8554i			0.365308i	0.983177	+	0.182654i	$0.0584688\pi$
$131$			47.8554i			0.365308i	−0.983177	+	0.182654i	$0.941531\pi$
$132$	127.284	+	19.6417i	0.964270	+	0.148801i
$133$	−129.692			−0.975127
$134$	64.9139	−	89.3463i	0.484432	−	0.666764i
$135$		0			0
$136$	−12.2270	−	37.6308i	−0.0899042	−	0.276697i
$137$	123.651	−	89.8377i	0.902561	−	0.655749i	−0.0365612	−	0.999331i	$-0.511640\pi$
$137$	123.651	−	89.8377i	0.902561	−	0.655749i	0.939123	+	0.343582i	$0.111640\pi$
$138$	97.3607	+	134.005i	0.705512	+	0.971054i
$139$	−116.732	+	37.9285i	−0.839799	+	0.272867i	−0.697167	−	0.716909i	$-0.745556\pi$
$139$	−116.732	+	37.9285i	−0.839799	+	0.272867i	−0.142632	+	0.989776i	$0.545556\pi$
$140$		0			0
$141$	43.5410	+	31.6344i	0.308802	+	0.224357i
$142$		−	50.5805i		−	0.356200i
$143$	48.5081	−	48.8951i	0.339218	−	0.341924i
$144$	14.5886			0.101310
$145$		0			0
$146$	5.72387	−	17.6163i	0.0392046	−	0.120659i
$147$	−15.9311	−	49.0309i	−0.108375	−	0.333544i
$148$	147.835	−	107.409i	0.998887	−	0.725734i
$149$	66.6018	+	91.6695i	0.446992	+	0.615231i	0.971748	−	0.236021i	$-0.0758435\pi$
$149$	66.6018	+	91.6695i	0.446992	+	0.615231i	−0.524756	+	0.851253i	$0.675843\pi$
$150$		0			0
$151$	132.245	+	42.9691i	0.875796	+	0.284563i	0.712211	−	0.701966i	$-0.247694\pi$
$151$	132.245	+	42.9691i	0.875796	+	0.284563i	0.163585	+	0.986529i	$0.447694\pi$
$152$	104.923	+	76.2310i	0.690283	+	0.501520i
$153$		−	55.9438i		−	0.365646i
$154$	−45.3171	+	89.8204i	−0.294267	+	0.583249i
$155$		0			0
$156$	43.0902	−	59.3085i	0.276219	−	0.380183i
$157$	−34.6115	+	106.523i	−0.220455	+	0.678491i	0.778266	+	0.627935i	$0.216099\pi$
$157$	−34.6115	+	106.523i	−0.220455	+	0.678491i	−0.998721	+	0.0505565i	$0.983901\pi$
$158$	−27.8795	−	85.8041i	−0.176452	−	0.543064i
$159$	−136.180	+	98.9408i	−0.856480	+	0.622269i
$160$		0			0
$161$	233.123	−	75.7463i	1.44797	−	0.470474i
$162$	65.9640	+	21.4330i	0.407185	+	0.132302i
$163$	−171.290	−	124.450i	−1.05086	−	0.763495i	−0.0784845	−	0.996915i	$-0.525008\pi$
$163$	−171.290	−	124.450i	−1.05086	−	0.763495i	−0.972376	+	0.233421i	$0.925008\pi$
$164$			177.714i			1.08362i
$165$		0			0
$166$	30.8247			0.185691
$167$	−47.5623	+	65.4639i	−0.284804	+	0.391999i	−0.927318	−	0.374275i	$-0.877892\pi$
$167$	−47.5623	+	65.4639i	−0.284804	+	0.391999i	0.642514	+	0.766274i	$0.277892\pi$
$168$	−83.6475	+	257.440i	−0.497901	+	1.53238i
$169$	40.1089	+	123.443i	0.237331	+	0.730430i
$170$		0			0
$171$	107.782	+	148.349i	0.630305	+	0.867540i
$172$	−107.183	+	34.8258i	−0.623156	+	0.202476i
$173$	−101.343	−	32.9285i	−0.585800	−	0.190338i	0.00109704	−	0.999999i	$-0.499651\pi$
$173$	−101.343	−	32.9285i	−0.585800	−	0.190338i	−0.586897	+	0.809661i	$0.699651\pi$
$174$	122.082	+	88.6978i	0.701621	+	0.509757i
$175$		0			0
$176$	−12.9721	+	6.67469i	−0.0737053	+	0.0379244i
$177$	256.928			1.45157
$178$	72.7016	−	100.065i	0.408436	−	0.562164i
$179$	48.1337	−	148.140i	0.268903	−	0.827599i	−0.721865	−	0.692034i	$-0.756715\pi$
$179$	48.1337	−	148.140i	0.268903	−	0.827599i	0.990768	−	0.135566i	$-0.0432851\pi$
$180$		0			0
$181$	11.4787	−	8.33977i	0.0634183	−	0.0460761i	−0.555624	−	0.831433i	$-0.687521\pi$
$181$	11.4787	−	8.33977i	0.0634183	−	0.0460761i	0.619043	+	0.785357i	$0.287521\pi$
$182$	33.6600	+	46.3290i	0.184945	+	0.254555i
$183$	481.418	−	156.422i	2.63070	−	0.854767i
$184$	−233.123	−	75.7463i	−1.26697	−	0.411665i
$185$		0			0
$186$		−	204.268i		−	1.09822i
$187$	25.5958	+	49.7450i	0.136876	+	0.266016i
$188$	−31.5066			−0.167588
$189$	−40.9017	+	56.2964i	−0.216411	+	0.297864i
$190$		0			0
$191$	4.77960	+	14.7101i	0.0250241	+	0.0770162i	0.962789	−	0.270255i	$-0.0871082\pi$
$191$	4.77960	+	14.7101i	0.0250241	+	0.0770162i	−0.937765	+	0.347272i	$0.887108\pi$
$192$	119.798	−	87.0386i	0.623950	−	0.453326i
$193$	56.1215	+	77.2446i	0.290785	+	0.400231i	0.929269	−	0.369404i	$-0.120438\pi$
$193$	56.1215	+	77.2446i	0.290785	+	0.400231i	−0.638484	+	0.769635i	$0.720438\pi$
$194$	37.3278	−	12.1285i	0.192411	−	0.0625182i
$195$		0			0
$196$	24.4164	+	17.7396i	0.124574	+	0.0905080i
$197$			226.588i			1.15020i	0.818085	+	0.575098i	$0.195036\pi$
$197$			226.588i			1.15020i	−0.818085	+	0.575098i	$0.804964\pi$
$198$	140.403	−	22.8099i	0.709107	−	0.115201i
$199$	−27.2887			−0.137129			−0.0685645	−	0.997647i	$-0.521842\pi$
$199$	−27.2887			−0.137129			−0.0685645	+	0.997647i	$0.521842\pi$
$200$		0			0
$201$	−129.828	+	399.569i	−0.645909	+	1.98790i
$202$	−35.7680	−	110.083i	−0.177069	−	0.544963i
$203$	180.662	−	131.258i	0.889958	−	0.646593i
$204$	35.0000	+	48.1734i	0.171569	+	0.236144i
$205$		0			0
$206$	−176.213	−	57.2551i	−0.855404	−	0.277938i
$207$	−280.383	−	203.710i	−1.35451	−	0.984107i
$208$			8.30406i			0.0399234i
$209$	−163.713	−	82.5984i	−0.783317	−	0.395208i
$210$		0			0
$211$	198.612	−	273.367i	0.941291	−	1.29558i	−0.0139978	−	0.999902i	$-0.504456\pi$
$211$	198.612	−	273.367i	0.941291	−	1.29558i	0.955289	−	0.295674i	$-0.0955442\pi$
$212$	30.4508	−	93.7181i	0.143636	−	0.442066i
$213$	59.4609	+	183.002i	0.279159	+	0.859164i
$214$	29.9139	−	21.7337i	0.139785	−	0.101559i
$215$		0			0
$216$	66.1803	−	21.5033i	0.306390	−	0.0995523i
$217$	−287.489	−	93.4108i	−1.32483	−	0.430464i
$218$	21.1418	+	15.3604i	0.0969809	+	0.0704607i
$219$			70.4651i			0.321758i
$220$		0			0
$221$	31.8441			0.144091
$222$	215.689	−	296.870i	0.971571	−	1.33725i
$223$	16.2188	−	49.9165i	0.0727303	−	0.223841i	−0.908083	−	0.418790i	$-0.862454\pi$
$223$	16.2188	−	49.9165i	0.0727303	−	0.223841i	0.980813	+	0.194949i	$0.0624543\pi$
$224$	−78.5648	−	241.798i	−0.350736	−	1.07945i
$225$		0			0
$226$	−129.787	−	178.637i	−0.574279	−	0.790428i
$227$	312.192	−	101.437i	1.37529	−	0.446860i	0.474175	−	0.880431i	$-0.342746\pi$
$227$	312.192	−	101.437i	1.37529	−	0.446860i	0.901120	+	0.433570i	$0.142746\pi$
$228$	−185.623	−	60.3126i	−0.814136	−	0.264529i
$229$	−292.289	−	212.360i	−1.27637	−	0.927337i	−0.276933	−	0.960889i	$-0.589318\pi$
$229$	−292.289	−	212.360i	−1.27637	−	0.927337i	−0.999437	+	0.0335523i	$0.989318\pi$
$230$		0			0
$231$	58.3688	−	378.247i	0.252679	−	1.63743i
$232$	−223.310			−0.962543
$233$	57.1443	−	78.6524i	0.245255	−	0.337564i	−0.668588	−	0.743633i	$-0.733101\pi$
$233$	57.1443	−	78.6524i	0.245255	−	0.337564i	0.913842	+	0.406069i	$0.133101\pi$
$234$	25.0203	−	77.0046i	0.106924	−	0.329080i
$235$		0			0
$236$	−121.683	+	88.4078i	−0.515605	+	0.374609i
$237$	201.738	+	277.668i	0.851214	+	1.17159i
$238$	−44.2376	+	14.3737i	−0.185872	+	0.0603936i
$239$	310.267	+	100.812i	1.29819	+	0.421807i	0.874951	−	0.484211i	$-0.160893\pi$
$239$	310.267	+	100.812i	1.29819	+	0.421807i	0.423239	+	0.906018i	$0.360893\pi$
$240$		0			0
$241$		−	141.891i		−	0.588761i	−0.955688	−	0.294381i	$-0.904887\pi$
$241$		−	141.891i		−	0.588761i	0.955688	−	0.294381i	$-0.0951133\pi$
$242$	−114.410	+	84.5207i	−0.472768	+	0.349259i
$243$	−344.354			−1.41710
$244$	−174.179	+	239.737i	−0.713847	+	0.982527i
$245$		0			0
$246$	110.279	+	339.403i	0.448287	+	1.37969i
$247$	−84.4427	+	61.3512i	−0.341873	+	0.248386i
$248$	177.678	+	244.553i	0.716443	+	0.986099i
$249$	−111.525	+	36.2366i	−0.447891	+	0.145528i
$250$		0			0
$251$	−340.216	−	247.181i	−1.35544	−	0.984786i	−0.998720	−	0.0505747i	$-0.983895\pi$
$251$	−340.216	−	247.181i	−1.35544	−	0.984786i	−0.356721	−	0.934211i	$-0.616105\pi$
$252$		−	224.050i		−	0.889089i
$253$	342.518	+	52.8554i	1.35383	+	0.208915i
$254$	158.358			0.623455
$255$		0			0
$256$	−74.2730	+	228.589i	−0.290129	+	0.892925i
$257$	−11.5304	−	35.4869i	−0.0448653	−	0.138081i	0.926115	−	0.377242i	$-0.123128\pi$
$257$	−11.5304	−	35.4869i	−0.0448653	−	0.138081i	−0.970980	+	0.239161i	$0.923128\pi$
$258$	−183.090	+	133.023i	−0.709652	+	0.515592i
$259$	−319.184	−	439.320i	−1.23237	−	1.69621i
$260$		0			0
$261$	−300.282	−	97.5676i	−1.15051	−	0.373822i
$262$	−45.5132	−	33.0672i	−0.173714	−	0.126211i
$263$		−	156.447i		−	0.594857i	−0.954744	−	0.297428i	$-0.903871\pi$
$263$		−	156.447i		−	0.594857i	0.954744	−	0.297428i	$-0.0961289\pi$
$264$	−269.549	+	271.700i	−1.02102	+	1.02917i
$265$		0			0
$266$	89.6149	−	123.344i	0.336898	−	0.463701i
$267$	−145.403	+	447.505i	−0.544581	+	1.67605i
$268$	−76.0025	−	233.912i	−0.283591	−	0.872805i
$269$	233.003	−	169.286i	0.866180	−	0.629317i	−0.0633789	−	0.997990i	$-0.520188\pi$
$269$	233.003	−	169.286i	0.866180	−	0.629317i	0.929559	+	0.368673i	$0.120188\pi$
$270$		0			0
$271$	−140.158	+	45.5399i	−0.517186	+	0.168044i	−0.555968	−	0.831204i	$-0.687652\pi$
$271$	−140.158	+	45.5399i	−0.517186	+	0.168044i	0.0387817	+	0.999248i	$0.487652\pi$
$272$	−6.41486	−	2.08431i	−0.0235840	−	0.00766291i
$273$	−176.246	−	128.050i	−0.645590	−	0.469049i
$274$			179.675i			0.655749i
$275$		0			0
$276$	368.885			1.33654
$277$	134.375	−	184.951i	0.485108	−	0.667693i	−0.494369	−	0.869252i	$-0.664601\pi$
$277$	134.375	−	184.951i	0.485108	−	0.667693i	0.979476	+	0.201559i	$0.0646008\pi$
$278$	44.5877	−	137.227i	0.160387	−	0.493621i
$279$	132.072	+	406.477i	0.473378	+	1.45691i
$280$		0			0
$281$	0.163119	+	0.224514i	0.000580495	+	0.000798982i	0.809307	−	0.587386i	$-0.199843\pi$
$281$	0.163119	+	0.224514i	0.000580495	+	0.000798982i	−0.808727	+	0.588185i	$0.799843\pi$
$282$	−60.1722	+	19.5511i	−0.213377	+	0.0693303i
$283$	−212.931	−	69.1853i	−0.752405	−	0.244471i	−0.0923891	−	0.995723i	$-0.529450\pi$
$283$	−212.931	−	69.1853i	−0.752405	−	0.244471i	−0.660016	+	0.751252i	$0.729450\pi$
$284$	−91.1312	−	66.2107i	−0.320884	−	0.233136i
$285$		0			0
$286$	12.9837	+	79.9197i	0.0453977	+	0.279439i
$287$	528.108			1.84010
$288$	−211.290	+	290.816i	−0.733647	+	1.00978i
$289$	81.3131	−	250.256i	0.281360	−	0.865937i
$290$		0			0
$291$	−120.795	+	87.7629i	−0.415104	+	0.301591i
$292$	−24.2467	−	33.3727i	−0.0830367	−	0.114290i
$293$	−313.867	+	101.982i	−1.07122	+	0.348060i	−0.790962	−	0.611865i	$-0.790420\pi$
$293$	−313.867	+	101.982i	−1.07122	+	0.348060i	−0.280257	+	0.959925i	$0.590420\pi$
$294$	57.6393	+	18.7282i	0.196052	+	0.0637012i
$295$		0			0
$296$			543.029i			1.83456i
$297$	−87.4853	+	45.0147i	−0.294563	+	0.151565i
$298$	−133.204			−0.446992
$299$	115.955	−	159.598i	0.387809	−	0.533773i
$300$		0			0
$301$	103.491	+	318.513i	0.343825	+	1.05818i
$302$	−132.245	+	96.0817i	−0.437898	+	0.318151i
$303$	258.820	+	356.235i	0.854190	+	1.17569i
$304$	21.0263	−	6.83186i	0.0691655	−	0.0224732i
$305$		0			0
$306$	53.2057	+	38.6562i	0.173875	+	0.126327i
$307$			300.291i			0.978146i	0.872243	+	0.489073i	$0.162665\pi$
$307$			300.291i			0.978146i	−0.872243	+	0.489073i	$0.837335\pi$
$308$	102.509	+	199.225i	0.332822	+	0.646833i
$309$	704.853			2.28108
$310$		0			0
$311$	−18.2877	+	56.2838i	−0.0588030	+	0.180977i	−0.976143	−	0.217127i	$-0.930332\pi$
$311$	−18.2877	+	56.2838i	−0.0588030	+	0.180977i	0.917340	+	0.398104i	$0.130332\pi$
$312$	67.3200	+	207.190i	0.215769	+	0.664070i
$313$	−119.294	+	86.6724i	−0.381132	+	0.276909i	−0.761812	−	0.647798i	$-0.775690\pi$
$313$	−119.294	+	86.6724i	−0.381132	+	0.276909i	0.380680	+	0.924707i	$0.375690\pi$
$314$	−77.3936	−	106.523i	−0.246476	−	0.339246i
$315$		0			0
$316$	−191.089	−	62.0885i	−0.604711	−	0.196482i
$317$	−61.5304	−	44.7044i	−0.194102	−	0.141023i	0.486490	−	0.873686i	$-0.338277\pi$
$317$	−61.5304	−	44.7044i	−0.194102	−	0.141023i	−0.680592	+	0.732663i	$0.738277\pi$
$318$		−	197.882i		−	0.622269i
$319$	311.649	−	50.6305i	0.976957	−	0.158716i
$320$		0			0
$321$	−82.6800	+	113.799i	−0.257570	+	0.354515i
$322$	−89.0451	+	274.053i	−0.276538	+	0.851095i
$323$	−26.1985	−	80.6308i	−0.0811100	−	0.249631i
$324$	124.964	−	90.7917i	0.385691	−	0.280221i
$325$		0			0
$326$	236.717	−	76.9141i	0.726127	−	0.235933i
$327$	−94.5492	−	30.7209i	−0.289141	−	0.0939476i
$328$	−427.249	−	310.414i	−1.30259	−	0.946385i
$329$			93.6275i			0.284582i
$330$		0			0
$331$	581.731			1.75750			0.878748	−	0.477285i	$-0.158379\pi$
$331$	581.731			1.75750			0.878748	+	0.477285i	$0.158379\pi$
$332$	40.3500	−	55.5371i	0.121536	−	0.167280i
$333$	−237.258	+	730.204i	−0.712486	+	2.19281i
$334$	−29.3951	−	90.4689i	−0.0880093	−	0.270865i
$335$		0			0
$336$	27.1227	+	37.3312i	0.0807223	+	0.111105i
$337$	−401.264	+	130.379i	−1.19070	+	0.386880i	−0.836330	−	0.548227i	$-0.815303\pi$
$337$	−401.264	+	130.379i	−1.19070	+	0.386880i	−0.354365	+	0.935107i	$0.615303\pi$
$338$	−145.116	−	47.1509i	−0.429336	−	0.139500i
$339$	679.574	+	493.740i	2.00464	+	1.45646i
$340$		0			0
$341$	−303.412	−	301.011i	−0.889772	−	0.882730i
$342$	−215.564			−0.630305
$343$	−171.358	+	235.854i	−0.499586	+	0.687622i
$344$	103.491	−	318.513i	0.300847	−	0.925911i
$345$		0			0
$346$	101.343	−	73.6303i	0.292900	−	0.212804i
$347$	90.1393	+	124.066i	0.259767	+	0.357539i	0.918902	−	0.394486i	$-0.129077\pi$
$347$	90.1393	+	124.066i	0.259767	+	0.357539i	−0.659135	+	0.752025i	$0.729077\pi$
$348$	319.615	−	103.849i	0.918434	−	0.298417i
$349$	221.620	+	72.0087i	0.635014	+	0.206329i	0.608795	−	0.793328i	$-0.291653\pi$
$349$	221.620	+	72.0087i	0.635014	+	0.206329i	0.0262192	+	0.999656i	$0.491653\pi$
$350$		0			0
$351$			56.0034i			0.159554i
$352$	54.8222	−	355.263i	0.155745	−	1.00927i
$353$	−122.947			−0.348293			−0.174146	−	0.984720i	$-0.555717\pi$
$353$	−122.947			−0.348293			−0.174146	+	0.984720i	$0.555717\pi$
$354$	−177.533	+	244.353i	−0.501505	+	0.690263i
$355$		0			0
$356$	−85.1205	−	261.974i	−0.239103	−	0.735882i
$357$	143.156	−	104.009i	0.400997	−	0.291341i
$358$	107.630	+	148.140i	0.300643	+	0.413800i
$359$	−653.554	+	212.352i	−1.82048	+	0.591511i	−0.820686	+	0.571379i	$0.806409\pi$
$359$	−653.554	+	212.352i	−1.82048	+	0.591511i	−0.999797	+	0.0201317i	$0.993591\pi$
$360$		0			0
$361$	−67.2386	−	48.8517i	−0.186256	−	0.135323i
$362$			16.6795i			0.0460761i
$363$	314.579	−	440.296i	0.866608	−	1.21294i
$364$	127.533			0.350365
$365$		0			0
$366$	−183.885	+	565.941i	−0.502419	+	1.54629i
$367$	4.43577	+	13.6519i	0.0120866	+	0.0371987i	0.956918	−	0.290359i	$-0.0937746\pi$
$367$	4.43577	+	13.6519i	0.0120866	+	0.0371987i	−0.944831	+	0.327557i	$0.893775\pi$
$368$	−33.8050	+	24.5607i	−0.0918613	+	0.0667411i
$369$	−438.891	−	604.082i	−1.18941	−	1.63708i
$370$		0			0
$371$	−278.500	−	90.4903i	−0.750675	−	0.243909i
$372$	−368.031	−	267.390i	−0.989332	−	0.718791i
$373$		−	172.936i		−	0.463636i	−0.972759	−	0.231818i	$-0.925533\pi$
$373$		−	172.936i		−	0.463636i	0.972759	−	0.231818i	$-0.0744674\pi$
$374$	−64.9965	−	10.0299i	−0.173788	−	0.0268179i
$375$		0			0
$376$	55.0329	−	75.7463i	0.146364	−	0.201453i
$377$	55.5370	−	170.925i	0.147313	−	0.453382i
$378$	−25.2786	−	77.7997i	−0.0668747	−	0.205819i
$379$	−69.8895	+	50.7777i	−0.184405	+	0.133978i	−0.676158	−	0.736757i	$-0.736356\pi$
$379$	−69.8895	+	50.7777i	−0.184405	+	0.133978i	0.491753	+	0.870735i	$0.336356\pi$
$380$		0			0
$381$	−572.943	+	186.160i	−1.50379	+	0.488610i
$382$	−17.2928	−	5.61876i	−0.0452690	−	0.0147088i
$383$	154.549	+	112.287i	0.403523	+	0.293176i	0.770974	−	0.636866i	$-0.219770\pi$
$383$	154.549	+	112.287i	0.403523	+	0.293176i	−0.367452	+	0.930043i	$0.619770\pi$
$384$		−	410.502i		−	1.06901i
$385$		0			0
$386$	−112.243			−0.290785
$387$	278.327	−	383.084i	0.719191	−	0.989881i
$388$	27.0106	−	83.1302i	0.0696151	−	0.214253i
$389$	154.529	+	475.593i	0.397248	+	1.22260i	0.927197	+	0.374574i	$0.122211\pi$
$389$	154.529	+	475.593i	0.397248	+	1.22260i	−0.529949	+	0.848029i	$0.677789\pi$
$390$		0			0
$391$	94.1844	+	129.634i	0.240881	+	0.331544i
$392$	−85.2968	+	27.7146i	−0.217594	+	0.0707006i
$393$	203.541	+	66.1345i	0.517916	+	0.168281i
$394$	−215.498	−	156.569i	−0.546950	−	0.397383i
$395$		0			0
$396$	142.693	−	282.824i	0.360337	−	0.714202i
$397$	73.5298			0.185214			0.0926068	−	0.995703i	$-0.470480\pi$
$397$	73.5298			0.185214			0.0926068	+	0.995703i	$0.470480\pi$
$398$	18.8560	−	25.9531i	0.0473769	−	0.0652088i
$399$	−179.230	+	551.613i	−0.449198	+	1.38249i
$400$		0			0
$401$	−40.0664	+	29.1099i	−0.0999161	+	0.0725933i	−0.636622	−	0.771176i	$-0.719669\pi$
$401$	−40.0664	+	29.1099i	−0.0999161	+	0.0725933i	0.536705	+	0.843770i	$0.319669\pi$
$402$	−290.304	−	399.569i	−0.722149	−	0.993952i
$403$	−231.373	+	75.1776i	−0.574126	+	0.186545i
$404$	−245.158	−	79.6565i	−0.606825	−	0.197170i
$405$		0			0
$406$			262.517i			0.646593i
$407$	−123.120	−	757.846i	−0.302505	−	1.86203i
$408$	−176.950			−0.433702
$409$	416.798	−	573.673i	1.01907	−	1.40262i	0.106208	−	0.994344i	$-0.466129\pi$
$409$	416.798	−	573.673i	1.01907	−	1.40262i	0.912857	−	0.408279i	$-0.133871\pi$
$410$		0			0
$411$	−211.221	−	650.071i	−0.513920	−	1.58168i
$412$	−333.823	+	242.537i	−0.810250	+	0.588681i
$413$	262.720	+	361.603i	0.636125	+	0.875552i
$414$	387.480	−	125.900i	0.935941	−	0.304106i
$415$		0			0
$416$	−165.537	−	120.270i	−0.397925	−	0.289110i
$417$			548.907i			1.31632i
$418$	191.679	−	98.6265i	0.458562	−	0.235948i
$419$	−512.689			−1.22360			−0.611801	−	0.791012i	$-0.709554\pi$
$419$	−512.689			−1.22360			−0.611801	+	0.791012i	$0.709554\pi$
$420$		0			0
$421$	−47.9662	+	147.625i	−0.113934	+	0.350652i	−0.991723	−	0.128395i	$-0.959018\pi$
$421$	−47.9662	+	147.625i	−0.113934	+	0.350652i	0.877789	+	0.479047i	$0.159018\pi$
$422$	122.749	+	377.783i	0.290875	+	0.895221i
$423$	107.097	−	77.8103i	0.253184	−	0.183949i
$424$	172.123	+	236.907i	0.405950	+	0.558742i
$425$		0			0
$426$	−215.132	−	69.9005i	−0.505004	−	0.164086i
$427$	712.421	+	517.604i	1.66843	+	1.21219i
$428$		−	82.3459i		−	0.192397i
$429$	−140.927	−	273.889i	−0.328501	−	0.638435i
$430$		0			0
$431$	413.259	−	568.802i	0.958837	−	1.31973i	0.0113492	−	0.999936i	$-0.496387\pi$
$431$	413.259	−	568.802i	0.958837	−	1.31973i	0.947488	−	0.319791i	$-0.103613\pi$
$432$	3.66563	−	11.2817i	0.00848526	−	0.0261149i
$433$	154.137	+	474.384i	0.355974	+	1.09558i	0.955442	+	0.295177i	$0.0953787\pi$
$433$	154.137	+	474.384i	0.355974	+	1.09558i	−0.599468	+	0.800398i	$0.704621\pi$
$434$	287.489	−	208.873i	0.662417	−	0.481274i
$435$		0			0
$436$	55.3500	−	17.9843i	0.126950	−	0.0412484i
$437$	−499.508	−	162.300i	−1.14304	−	0.371396i
$438$	−67.0163	−	48.6902i	−0.153005	−	0.111165i
$439$			564.968i			1.28694i	0.765470	+	0.643472i	$0.222507\pi$
$439$			564.968i			1.28694i	−0.765470	+	0.643472i	$0.777493\pi$
$440$		0			0
$441$	−126.807			−0.287543
$442$	−22.0037	+	30.2855i	−0.0497821	+	0.0685192i
$443$	−60.4950	+	186.184i	−0.136558	+	0.420281i	−0.995829	−	0.0912390i	$-0.970917\pi$
$443$	−60.4950	+	186.184i	−0.136558	+	0.420281i	0.859272	+	0.511520i	$0.170917\pi$
$444$	−252.533	−	777.216i	−0.568768	−	1.75049i
$445$		0			0
$446$	36.2664	+	49.9165i	0.0813149	+	0.111920i
$447$	481.935	−	156.590i	1.07815	−	0.350314i
$448$	244.998	+	79.6046i	0.546870	+	0.177689i
$449$	140.159	+	101.832i	0.312158	+	0.226796i	0.732822	−	0.680420i	$-0.238203\pi$
$449$	140.159	+	101.832i	0.312158	+	0.226796i	−0.420664	+	0.907217i	$0.638203\pi$
$450$		0			0
$451$	666.644	+	336.342i	1.47815	+	0.745770i
$452$	−491.745			−1.08793
$453$	365.517	−	503.090i	0.806880	−	1.11058i
$454$	−119.247	+	367.004i	−0.262658	+	0.808378i
$455$		0			0
$456$	469.230	−	340.915i	1.02901	−	0.747622i
$457$	176.869	+	243.440i	0.387022	+	0.532690i	0.957428	−	0.288673i	$-0.0932140\pi$
$457$	176.869	+	243.440i	0.387022	+	0.532690i	−0.570406	+	0.821363i	$0.693214\pi$
$458$	403.933	−	131.246i	0.881950	−	0.286563i
$459$	−43.2624	−	14.0568i	−0.0942535	−	0.0306248i
$460$		0			0
$461$		−	389.513i		−	0.844930i	−0.906379	−	0.422465i	$-0.861165\pi$
$461$		−	389.513i		−	0.844930i	0.906379	−	0.422465i	$-0.138835\pi$
$462$	319.402	+	316.874i	0.691346	+	0.685875i
$463$	36.6718			0.0792048			0.0396024	−	0.999216i	$-0.487391\pi$
$463$	36.6718			0.0792048			0.0396024	+	0.999216i	$0.487391\pi$
$464$	−22.3754	+	30.7971i	−0.0482228	+	0.0663730i
$465$		0			0
$466$	35.3171	+	108.695i	0.0757879	+	0.233251i
$467$	87.4468	−	63.5338i	0.187252	−	0.136047i	−0.490210	−	0.871604i	$-0.663080\pi$
$467$	87.4468	−	63.5338i	0.187252	−	0.136047i	0.677462	+	0.735558i	$0.263080\pi$
$468$	−105.988	−	145.880i	−0.226470	−	0.311709i
$469$	−695.111	+	225.855i	−1.48211	+	0.481568i
$470$		0			0
$471$	405.238	+	294.423i	0.860378	+	0.625101i
$472$		−	446.966i		−	0.946961i
$473$	−72.2157	+	467.979i	−0.152676	+	0.989384i
$474$	−403.475			−0.851214
$475$		0			0
$476$	−32.0106	+	98.5186i	−0.0672493	+	0.206972i
$477$	127.943	+	393.768i	0.268224	+	0.825510i
$478$	−310.267	+	225.422i	−0.649095	+	0.471595i
$479$	241.542	+	332.454i	0.504262	+	0.694057i	0.982939	−	0.183934i	$-0.0588833\pi$
$479$	241.542	+	332.454i	0.504262	+	0.694057i	−0.478676	+	0.877991i	$0.658883\pi$
$480$		0			0
$481$	−415.643	−	135.051i	−0.864123	−	0.280771i
$482$	134.947	+	98.0446i	0.279973	+	0.203412i
$483$		−	1096.21i		−	2.26959i
$484$	2.51722	+	316.772i	0.00520087	+	0.654488i
$485$		0			0
$486$	237.943	−	327.501i	0.489595	−	0.673869i
$487$	98.1616	−	302.110i	0.201564	−	0.620350i	−0.798273	−	0.602295i	$-0.794253\pi$
$487$	98.1616	−	302.110i	0.201564	−	0.620350i	0.999837	−	0.0180541i	$-0.00574710\pi$
$488$	−272.121	−	837.501i	−0.557624	−	1.71619i
$489$	−766.033	+	556.556i	−1.56653	+	1.13815i
$490$		0			0
$491$	248.678	−	80.8004i	0.506473	−	0.164563i	−0.0446247	−	0.999004i	$-0.514209\pi$
$491$	248.678	−	80.8004i	0.506473	−	0.164563i	0.551098	+	0.834441i	$0.314209\pi$
$492$	755.861	+	245.594i	1.53630	+	0.499175i
$493$	118.099	+	85.8041i	0.239552	+	0.174045i
$494$		−	122.702i		−	0.248386i
$495$		0			0
$496$	51.5298			0.103891
$497$	−196.757	+	270.813i	−0.395890	+	0.544895i
$498$	42.5987	−	131.105i	0.0855395	−	0.263263i
$499$	−186.253	−	573.229i	−0.373253	−	1.14875i	−0.944650	−	0.328081i	$-0.893598\pi$
$499$	−186.253	−	573.229i	−0.373253	−	1.14875i	0.571397	−	0.820674i	$-0.306402\pi$
$500$		0			0
$501$	212.705	+	292.763i	0.424561	+	0.584358i
$502$	470.167	−	152.766i	0.936587	−	0.304316i
$503$	−458.794	−	149.071i	−0.912115	−	0.296364i	−0.184887	−	0.982760i	$-0.559192\pi$
$503$	−458.794	−	149.071i	−0.912115	−	0.296364i	−0.727228	+	0.686396i	$0.759192\pi$
$504$	538.649	+	391.351i	1.06875	+	0.776491i
$505$		0			0
$506$	−286.943	+	289.232i	−0.567080	+	0.571605i
$507$	580.462			1.14490
$508$	207.293	−	285.314i	0.408057	−	0.561642i
$509$	−88.1190	+	271.202i	−0.173122	+	0.532814i	−0.999543	−	0.0302387i	$-0.990373\pi$
$509$	−88.1190	+	271.202i	−0.173122	+	0.532814i	0.826421	+	0.563053i	$0.190373\pi$
$510$		0			0
$511$	−99.1732	+	72.0535i	−0.194077	+	0.141005i
$512$	49.7339	+	68.4529i	0.0971366	+	0.133697i
$513$	141.803	−	46.0747i	0.276420	−	0.0898143i
$514$	41.7173	+	13.5548i	0.0811621	+	0.0263711i
$515$		0			0
$516$			504.004i			0.976752i
$517$	−59.6296	+	118.188i	−0.115338	+	0.228604i
$518$	638.369			1.23237
$519$	−280.106	+	385.533i	−0.539704	+	0.742839i
$520$		0			0
$521$	159.996	+	492.417i	0.307094	+	0.945138i	0.978888	+	0.204400i	$0.0655242\pi$
$521$	159.996	+	492.417i	0.307094	+	0.945138i	−0.671794	+	0.740738i	$0.734476\pi$
$522$	300.282	−	218.168i	0.575253	−	0.417946i
$523$	−314.428	−	432.773i	−0.601201	−	0.827482i	0.394617	−	0.918846i	$-0.370877\pi$
$523$	−314.428	−	432.773i	−0.601201	−	0.827482i	−0.995818	+	0.0913639i	$0.970877\pi$
$524$	−119.155	+	38.7158i	−0.227395	+	0.0738851i
$525$		0			0
$526$	148.790	+	108.102i	0.282871	+	0.205518i
$527$		−	197.604i		−	0.374960i
$528$	10.4621	+	64.3980i	0.0198146	+	0.121966i
$529$	463.664			0.876492
$530$		0			0
$531$	195.286	−	601.029i	0.367771	−	1.13188i
$532$	−104.923	−	322.920i	−0.197224	−	0.606992i
$533$	343.853	−	249.824i	0.645127	−	0.468712i
$534$	−325.132	−	447.505i	−0.608861	−	0.838025i
$535$		0			0
$536$	695.111	+	225.855i	1.29685	+	0.421372i
$537$	−563.559	−	409.450i	−1.04946	−	0.762476i
$538$			338.572i			0.629317i
$539$	112.756	−	58.0174i	0.209194	−	0.107639i
$540$		0			0
$541$	−176.151	+	242.451i	−0.325602	+	0.448153i	−0.940167	−	0.340713i	$-0.889332\pi$
$541$	−176.151	+	242.451i	−0.325602	+	0.448153i	0.614565	+	0.788866i	$0.289332\pi$
$542$	53.5354	−	164.765i	0.0987738	−	0.303995i
$543$	−19.6080	−	60.3472i	−0.0361105	−	0.111137i
$544$	134.457	−	97.6890i	0.247164	−	0.179575i
$545$		0			0
$546$	243.566	−	79.1394i	0.446092	−	0.144944i
$547$	−431.699	−	140.268i	−0.789212	−	0.256431i	−0.113444	−	0.993544i	$-0.536188\pi$
$547$	−431.699	−	140.268i	−0.789212	−	0.256431i	−0.675769	+	0.737114i	$0.736188\pi$
$548$	323.722	+	235.198i	0.590734	+	0.429193i
$549$		−	1245.07i		−	2.26789i
$550$		0			0
$551$	−478.482			−0.868389
$552$	−644.336	+	886.853i	−1.16728	+	1.60662i
$553$	−184.507	+	567.855i	−0.333648	+	1.02686i
$554$	83.0482	+	255.596i	0.149906	+	0.461365i
$555$		0			0
$556$	−188.876	−	259.966i	−0.339706	−	0.467565i
$557$	338.185	−	109.883i	0.607155	−	0.197277i	0.0107261	−	0.999942i	$-0.496586\pi$
$557$	338.185	−	109.883i	0.607155	−	0.197277i	0.596429	+	0.802666i	$0.296586\pi$
$558$	−477.842	−	155.260i	−0.856348	−	0.278244i
$559$	218.057	+	158.428i	0.390085	+	0.283413i
$560$		0			0
$561$	246.950	−	40.1195i	0.440197	−	0.0715143i
$562$	−0.326238			−0.000580495
$563$	288.909	−	397.649i	0.513160	−	0.706305i	−0.471288	−	0.881979i	$-0.656211\pi$
$563$	288.909	−	397.649i	0.513160	−	0.706305i	0.984448	+	0.175675i	$0.0562107\pi$
$564$	−43.5410	+	134.005i	−0.0772004	+	0.237598i
$565$		0			0
$566$	212.931	−	154.703i	0.376202	−	0.273327i
$567$	−269.804	−	371.353i	−0.475845	−	0.654944i
$568$	318.360	−	103.441i	0.560492	−	0.182115i
$569$	275.249	+	89.4339i	0.483742	+	0.157177i	0.540728	−	0.841198i	$-0.318149\pi$
$569$	275.249	+	89.4339i	0.483742	+	0.157177i	−0.0569857	+	0.998375i	$0.518149\pi$
$570$		0			0
$571$		−	566.789i		−	0.992626i	−0.868144	−	0.496313i	$-0.834687\pi$
$571$		−	566.789i		−	0.992626i	0.868144	−	0.496313i	$-0.165313\pi$
$572$	160.988	+	81.2233i	0.281447	+	0.141999i
$573$	69.1710			0.120717
$574$	−364.914	+	502.261i	−0.635738	+	0.875019i
$575$		0			0
$576$	−112.552	−	346.400i	−0.195403	−	0.601388i
$577$	−182.749	+	132.775i	−0.316723	+	0.230113i	−0.734776	−	0.678310i	$-0.762713\pi$
$577$	−182.749	+	132.775i	−0.316723	+	0.230113i	0.418053	+	0.908423i	$0.362713\pi$
$578$	181.822	+	250.256i	0.314570	+	0.432969i
$579$	406.099	−	131.950i	0.701380	−	0.227892i
$580$		0			0
$581$	−165.039	−	119.907i	−0.284059	−	0.206381i
$582$		−	175.526i		−	0.301591i
$583$	−293.926	−	291.600i	−0.504161	−	0.500171i
$584$	122.585			0.209905
$585$		0			0
$586$	119.887	−	368.973i	0.204585	−	0.629647i
$587$	−142.055	−	437.200i	−0.242001	−	0.744803i	−0.996115	−	0.0880598i	$-0.971933\pi$
$587$	−142.055	−	437.200i	−0.242001	−	0.744803i	0.754114	−	0.656744i	$-0.228067\pi$
$588$	109.193	−	79.3337i	0.185703	−	0.134921i
$589$	380.707	+	523.998i	0.646362	+	0.889641i
$590$		0			0
$591$	963.738	+	313.138i	1.63069	+	0.529844i
$592$	74.8901	+	54.4108i	0.126504	+	0.0919102i
$593$			810.678i			1.36708i	0.729914	+	0.683539i	$0.239560\pi$
$593$			810.678i			1.36708i	−0.729914	+	0.683539i	$0.760440\pi$
$594$	17.6393	−	114.308i	0.0296958	−	0.192437i
$595$		0			0
$596$	−174.366	+	239.994i	−0.292560	+	0.402674i
$597$	−37.7120	+	116.066i	−0.0631693	+	0.194415i
$598$	71.6641	+	220.559i	0.119840	+	0.368828i
$599$	−193.976	+	140.932i	−0.323832	+	0.235278i	−0.737809	−	0.675009i	$-0.764140\pi$
$599$	−193.976	+	140.932i	−0.323832	+	0.235278i	0.413977	+	0.910288i	$0.364140\pi$
$600$		0			0
$601$	−754.088	+	245.018i	−1.25472	+	0.407684i	−0.859611	−	0.510949i	$-0.829294\pi$
$601$	−754.088	+	245.018i	−1.25472	+	0.407684i	−0.395112	+	0.918633i	$0.629294\pi$
$602$	−374.435	−	121.661i	−0.621985	−	0.202095i
$603$	836.028	+	607.410i	1.38645	+	1.00731i
$604$			364.040i			0.602715i
$605$		0			0
$606$	−517.639			−0.854190
$607$	−134.536	+	185.173i	−0.221640	+	0.305062i	−0.905328	−	0.424713i	$-0.860375\pi$
$607$	−134.536	+	185.173i	−0.221640	+	0.305062i	0.683688	+	0.729775i	$0.260375\pi$
$608$	−168.339	+	518.095i	−0.276874	+	0.852131i
$609$	−308.607	−	949.794i	−0.506744	−	1.55960i
$610$		0			0
$611$	44.2908	+	60.9611i	0.0724891	+	0.0997727i
$612$	139.294	−	45.2595i	0.227605	−	0.0739534i
$613$	1084.01	+	352.217i	1.76837	+	0.574579i	0.998012	−	0.0630314i	$-0.0200768\pi$
$613$	1084.01	+	352.217i	1.76837	+	0.574579i	0.770359	+	0.637610i	$0.220077\pi$
$614$	−285.594	−	207.496i	−0.465136	−	0.337941i
$615$		0			0
$616$	−658.018	−	101.541i	−1.06821	−	0.164840i
$617$	−640.748			−1.03849			−0.519244	−	0.854626i	$-0.673787\pi$
$617$	−640.748			−1.03849			−0.519244	+	0.854626i	$0.673787\pi$
$618$	−487.041	+	670.355i	−0.788093	+	1.08472i
$619$	272.338	−	838.172i	0.439965	−	1.35407i	−0.447947	−	0.894060i	$-0.647845\pi$
$619$	272.338	−	838.172i	0.439965	−	1.35407i	0.887912	−	0.460013i	$-0.152155\pi$
$620$		0			0
$621$	−227.984	+	165.640i	−0.367124	+	0.266731i
$622$	−40.8926	−	56.2838i	−0.0657437	−	0.0904885i
$623$	−778.504	+	252.951i	−1.24960	+	0.406021i
$624$	35.3193	+	11.4759i	0.0566014	+	0.0183909i
$625$		0			0
$626$		−	173.345i		−	0.276909i
$627$	−577.558	+	582.166i	−0.921145	+	0.928494i
$628$	−293.233			−0.466931
$629$	208.652	−	287.185i	0.331721	−	0.456574i
$630$		0			0
$631$	27.5482	+	84.7846i	0.0436580	+	0.134365i	0.970510	−	0.241062i	$-0.0774958\pi$
$631$	27.5482	+	84.7846i	0.0436580	+	0.134365i	−0.926852	+	0.375428i	$0.877496\pi$
$632$	483.046	−	350.953i	0.764313	−	0.555306i
$633$	−888.222	−	1222.53i	−1.40319	−	1.93133i
$634$	85.0329	−	27.6289i	0.134121	−	0.0435786i
$635$		0			0
$636$	−356.525	−	259.030i	−0.560574	−	0.407281i
$637$		−	72.1802i		−	0.113313i
$638$	−167.192	+	331.381i	−0.262056	+	0.519406i
$639$	473.289			0.740672
$640$		0			0
$641$	159.465	−	490.782i	0.248775	−	0.765650i	−0.746218	−	0.665702i	$-0.768132\pi$
$641$	159.465	−	490.782i	0.248775	−	0.765650i	0.994993	−	0.0999481i	$-0.0318677\pi$
$642$	−51.0990	−	157.267i	−0.0795935	−	0.244964i
$643$	835.995	−	607.386i	1.30015	−	0.944612i	0.300190	−	0.953879i	$-0.402950\pi$
$643$	835.995	−	607.386i	1.30015	−	0.944612i	0.999957	+	0.00926699i	$0.00294982\pi$
$644$	377.201	+	519.173i	0.585716	+	0.806169i
$645$		0			0
$646$	94.7871	+	30.7982i	0.146729	+	0.0476752i
$647$	5.09172	+	3.69935i	0.00786974	+	0.00571770i	0.591713	−	0.806149i	$-0.298452\pi$
$647$	5.09172	+	3.69935i	0.00786974	+	0.00571770i	−0.583843	+	0.811866i	$0.698452\pi$
$648$			459.018i			0.708361i
$649$	101.339	+	623.781i	0.156147	+	0.961142i
$650$		0			0
$651$	−794.599	+	1093.67i	−1.22058	+	1.67999i
$652$	171.290	−	527.177i	0.262715	−	0.808554i
$653$	−3.92609	−	12.0833i	−0.00601239	−	0.0185042i	0.948005	−	0.318254i	$-0.103097\pi$
$653$	−3.92609	−	12.0833i	−0.00601239	−	0.0185042i	−0.954018	+	0.299750i	$0.903097\pi$
$654$	94.5492	−	68.6940i	0.144571	−	0.105037i
$655$		0			0
$656$	−85.6196	+	27.8195i	−0.130518	+	0.0424078i
$657$	164.838	+	53.5592i	0.250895	+	0.0815208i
$658$	−89.0451	−	64.6950i	−0.135327	−	0.0983207i
$659$		−	14.9239i		−	0.0226463i	−0.999936	−	0.0113232i	$-0.996396\pi$
$659$		−	14.9239i		−	0.0226463i	0.999936	−	0.0113232i	$-0.00360435\pi$
$660$		0			0
$661$	−1024.09			−1.54931			−0.774654	−	0.632386i	$-0.782076\pi$
$661$	−1024.09			−1.54931			−0.774654	+	0.632386i	$0.782076\pi$
$662$	−401.967	+	553.259i	−0.607200	+	0.835739i
$663$	44.0074	−	135.441i	0.0663762	−	0.204285i
$664$	63.0391	+	194.014i	0.0949384	+	0.292190i
$665$		0			0
$666$	−530.524	−	730.204i	−0.796583	−	1.09640i
$667$	860.078	−	279.456i	1.28947	−	0.418975i
$668$	−201.477	−	65.4639i	−0.301613	−	0.0979998i
$669$	−189.894	−	137.966i	−0.283847	−	0.206227i
$670$		0			0
$671$	569.653	+	1107.11i	0.848962	+	1.64994i
$672$	−1137.00			−1.69197
$673$	−54.2376	+	74.6517i	−0.0805908	+	0.110924i	−0.847409	−	0.530941i	$-0.821839\pi$
$673$	−54.2376	+	74.6517i	−0.0805908	+	0.110924i	0.766818	+	0.641864i	$0.221839\pi$
$674$	153.269	−	471.714i	0.227403	−	0.699873i
$675$		0			0
$676$	−274.911	+	199.734i	−0.406673	+	0.295465i
$677$	276.561	+	380.654i	0.408510	+	0.562265i	0.962854	−	0.270022i	$-0.0870309\pi$
$677$	276.561	+	380.654i	0.408510	+	0.562265i	−0.554344	+	0.832287i	$0.687031\pi$
$678$	−939.149	+	305.148i	−1.38517	+	0.450071i
$679$	−247.037	−	80.2671i	−0.363824	−	0.118214i
$680$		0			0
$681$		−	1468.01i		−	2.15567i
$682$	495.931	−	80.5689i	0.727172	−	0.118136i
$683$	72.7933			0.106579			0.0532894	−	0.998579i	$-0.483029\pi$
$683$	72.7933			0.106579			0.0532894	+	0.998579i	$0.483029\pi$
$684$	−282.177	+	388.384i	−0.412540	+	0.567812i
$685$		0			0
$686$	−105.905	−	325.943i	−0.154381	−	0.475135i
$687$	−1307.15	+	949.704i	−1.90270	+	1.38239i
$688$	−33.5571	−	46.1873i	−0.0487748	−	0.0671327i
$689$	−224.139	+	72.8272i	−0.325311	+	0.105700i
$690$		0			0
$691$	−186.180	−	135.268i	−0.269435	−	0.195756i	0.444861	−	0.895600i	$-0.353253\pi$
$691$	−186.180	−	135.268i	−0.269435	−	0.195756i	−0.714296	+	0.699843i	$0.753253\pi$
$692$		−	278.975i		−	0.403142i
$693$	−840.463	−	424.040i	−1.21279	−	0.611890i
$694$	−180.279			−0.259767
$695$		0			0
$696$	−308.607	+	949.794i	−0.443401	+	1.36465i
$697$	106.681	+	328.330i	0.153057	+	0.471062i
$698$	−221.620	+	161.016i	−0.317507	+	0.230682i
$699$	−255.557	−	351.744i	−0.365604	−	0.503211i
$700$		0			0
$701$	938.374	+	304.896i	1.33862	+	0.434944i	0.888850	−	0.458199i	$-0.151505\pi$
$701$	938.374	+	304.896i	1.33862	+	0.434944i	0.449772	+	0.893144i	$0.351505\pi$
$702$	−53.2624	−	38.6974i	−0.0758723	−	0.0551245i
$703$			1163.54i			1.65510i
$704$	258.568	+	256.521i	0.367284	+	0.364377i
$705$		0			0
$706$	84.9545	−	116.930i	0.120332	−	0.165623i
$707$	−236.714	+	728.530i	−0.334814	+	1.03045i
$708$	207.859	+	639.725i	0.293586	+	0.903566i
$709$	682.272	−	495.700i	0.962302	−	0.699153i	0.00861746	−	0.999963i	$-0.497257\pi$
$709$	682.272	−	495.700i	0.962302	−	0.699153i	0.953684	+	0.300810i	$0.0972569\pi$
$710$		0			0
$711$	802.883	−	260.872i	1.12923	−	0.366909i
$712$	778.504	+	252.951i	1.09340	+	0.355269i
$713$	−990.366	−	719.543i	−1.38901	−	1.00918i
$714$			208.018i			0.291341i
$715$		0			0
$716$	407.795			0.569546
$717$	857.558	−	1180.33i	1.19604	−	1.64620i
$718$	249.635	−	768.298i	0.347681	−	1.07005i
$719$	98.8044	+	304.089i	0.137419	+	0.422933i	0.995958	−	0.0898151i	$-0.0286276\pi$
$719$	98.8044	+	304.089i	0.137419	+	0.422933i	−0.858539	+	0.512748i	$0.828628\pi$
$720$		0			0
$721$	720.742	+	992.016i	0.999642	+	1.37589i
$722$	92.9214	−	30.1920i	0.128700	−	0.0418172i
$723$	−603.500	−	196.089i	−0.834717	−	0.271216i
$724$	30.0517	+	21.8338i	0.0415078	+	0.0301572i
$725$		0			0
$726$	201.378	+	603.419i	0.277380	+	0.831155i
$727$	475.109			0.653520			0.326760	−	0.945107i	$-0.394043\pi$
$727$	475.109			0.653520			0.326760	+	0.945107i	$0.394043\pi$
$728$	−222.763	+	306.607i	−0.305993	+	0.421164i
$729$	−311.798	+	959.616i	−0.427707	+	1.31635i
$730$		0			0
$731$	−177.117	+	128.683i	−0.242294	+	0.176037i
$732$	778.951	+	1072.13i	1.06414	+	1.46466i
$733$	−89.3531	+	29.0326i	−0.121901	+	0.0396079i	−0.369332	−	0.929297i	$-0.620413\pi$
$733$	−89.3531	+	29.0326i	−0.121901	+	0.0396079i	0.247431	+	0.968905i	$0.420413\pi$
$734$	−16.0488	−	5.21457i	−0.0218648	−	0.00710431i
$735$		0			0
$736$		−	1029.60i		−	1.39892i
$737$	−1021.30	−	157.601i	−1.38575	−	0.213841i
$738$	877.782			1.18941
$739$	403.140	−	554.874i	0.545521	−	0.750845i	−0.443875	−	0.896089i	$-0.646397\pi$
$739$	403.140	−	554.874i	0.545521	−	0.750845i	0.989396	+	0.145244i	$0.0463966\pi$
$740$		0			0
$741$	144.245	+	443.942i	0.194663	+	0.599112i
$742$	278.500	−	202.342i	0.375337	−	0.272699i
$743$	−577.765	−	795.226i	−0.777611	−	1.07029i	−0.995541	−	0.0943258i	$-0.969930\pi$
$743$	−577.765	−	795.226i	−0.777611	−	1.07029i	0.217930	−	0.975964i	$-0.430070\pi$
$744$	1285.69	−	417.746i	1.72808	−	0.561486i
$745$		0			0
$746$	164.472	+	119.496i	0.220472	+	0.160182i
$747$			288.431i			0.386120i
$748$	−103.152	+	103.975i	−0.137904	+	0.139005i
$749$	−244.706			−0.326710
$750$		0			0
$751$	254.520	−	783.330i	0.338907	−	1.04305i	−0.625858	−	0.779937i	$-0.715251\pi$
$751$	254.520	−	783.330i	0.338907	−	1.04305i	0.964765	−	0.263113i	$-0.0847491\pi$
$752$	−4.93208	−	15.1794i	−0.00655861	−	0.0201853i
$753$	−1521.49	+	1105.43i	−2.02057	+	1.46803i
$754$	124.184	+	170.925i	0.164701	+	0.226691i
$755$		0			0
$756$	−173.262	−	56.2964i	−0.229183	−	0.0744661i
$757$	464.114	+	337.199i	0.613097	+	0.445441i	0.850503	−	0.525969i	$-0.176297\pi$
$757$	464.114	+	337.199i	0.613097	+	0.445441i	−0.237407	+	0.971410i	$0.576297\pi$
$758$		−	101.555i		−	0.133978i
$759$	698.156	−	1383.77i	0.919837	−	1.82315i
$760$		0			0
$761$	−885.011	+	1218.11i	−1.16296	+	1.60067i	−0.463290	+	0.886207i	$0.653331\pi$
$761$	−885.011	+	1218.11i	−1.16296	+	1.60067i	−0.699668	+	0.714468i	$0.746669\pi$
$762$	218.845	−	673.535i	0.287198	−	0.883904i
$763$	−53.4437	−	164.483i	−0.0700441	−	0.215574i
$764$	−32.7599	+	23.8014i	−0.0428794	+	0.0311537i
$765$		0			0
$766$	−213.582	+	69.3969i	−0.278827	+	0.0905965i
$767$	342.115	+	111.160i	0.446043	+	0.144928i
$768$	869.604	+	631.804i	1.13230	+	0.822662i
$769$		−	741.194i		−	0.963841i	−0.876215	−	0.481921i	$-0.839939\pi$
$769$		−	741.194i		−	0.963841i	0.876215	−	0.481921i	$-0.160061\pi$
$770$		0			0
$771$	−166.869			−0.216432
$772$	−146.928	+	202.229i	−0.190321	+	0.261955i
$773$	349.452	−	1075.50i	0.452072	−	1.39134i	−0.422466	−	0.906379i	$-0.638835\pi$
$773$	349.452	−	1075.50i	0.452072	−	1.39134i	0.874538	−	0.484956i	$-0.161165\pi$
$774$	172.015	+	529.409i	0.222242	+	0.683991i
$775$		0			0
$776$	152.677	+	210.142i	0.196749	+	0.270801i
$777$	−2309.64	+	750.448i	−2.97251	+	0.965827i
$778$	−559.093	−	181.660i	−0.718628	−	0.233496i
$779$	−915.458	−	665.119i	−1.17517	−	0.853811i
$780$		0			0
$781$	−420.847	+	216.543i	−0.538857	+	0.277263i
$782$	−188.369			−0.240881
$783$	−150.902	+	207.698i	−0.192722	+	0.265260i
$784$	−4.72447	+	14.5404i	−0.00602610	+	0.0185464i
$785$		0			0
$786$	−203.541	+	147.881i	−0.258958	+	0.188144i
$787$	−557.821	−	767.774i	−0.708794	−	0.975571i	−0.999822	−	0.0188564i	$-0.993997\pi$
$787$	−557.821	−	767.774i	−0.708794	−	0.975571i	0.291029	−	0.956714i	$-0.406003\pi$
$788$	−564.182	+	183.314i	−0.715967	+	0.232632i
$789$	−665.410	−	216.205i	−0.843359	−	0.274024i
$790$		0			0
$791$			1461.31i			1.84742i
$792$	430.705	+	837.067i	0.543819	+	1.05690i
$793$	708.713			0.893712
$794$	−50.8078	+	69.9310i	−0.0639897	+	0.0880743i
$795$		0			0
$796$	−22.0770	−	67.9461i	−0.0277349	−	0.0853594i
$797$	786.819	−	571.658i	0.987226	−	0.717262i	0.0279144	−	0.999610i	$-0.491113\pi$
$797$	786.819	−	571.658i	0.987226	−	0.717262i	0.959312	+	0.282348i	$0.0911134\pi$
$798$	−400.770	−	551.613i	−0.502218	−	0.691244i
$799$	−58.2092	+	18.9133i	−0.0728525	+	0.0236712i
$800$		0			0
$801$	936.326	+	680.281i	1.16895	+	0.849289i
$802$		−	58.2198i		−	0.0725933i
$803$	−171.078	+	27.7933i	−0.213049	+	0.0346119i
$804$	−1099.92			−1.36806
$805$		0			0
$806$	88.3766	−	271.995i	0.109648	−	0.337463i
$807$	−398.016	−	1224.97i	−0.493204	−	1.51793i
$808$	619.725	−	450.256i	0.766986	−	0.557248i
$809$	−41.5053	−	57.1271i	−0.0513044	−	0.0706144i	0.782594	−	0.622532i	$-0.213896\pi$
$809$	−41.5053	−	57.1271i	−0.0513044	−	0.0706144i	−0.833898	+	0.551918i	$0.813896\pi$
$810$		0			0
$811$	−302.664	−	98.3416i	−0.373199	−	0.121260i	0.116411	−	0.993201i	$-0.462861\pi$
$811$	−302.664	−	98.3416i	−0.373199	−	0.121260i	−0.489610	+	0.871941i	$0.662861\pi$
$812$	472.978	+	343.639i	0.582485	+	0.423200i
$813$			659.060i			0.810652i
$814$	805.828	+	406.565i	0.989961	+	0.499466i
$815$		0			0
$816$	−17.7302	+	24.4036i	−0.0217282	+	0.0299063i
$817$	221.749	−	682.473i	0.271418	−	0.835340i
$818$	257.595	+	792.796i	0.314909	+	0.969189i
$819$	−433.508	+	314.962i	−0.529314	+	0.384569i
$820$		0			0
$821$	262.403	−	85.2598i	0.319613	−	0.103849i	−0.144817	−	0.989459i	$-0.546259\pi$
$821$	262.403	−	85.2598i	0.319613	−	0.103849i	0.464430	+	0.885610i	$0.346259\pi$
$822$	764.205	+	248.305i	0.929689	+	0.302074i
$823$	140.225	+	101.880i	0.170383	+	0.123791i	0.669709	−	0.742624i	$-0.266419\pi$
$823$	140.225	+	101.880i	0.170383	+	0.123791i	−0.499326	+	0.866414i	$0.666419\pi$
$824$		−	1226.20i		−	1.48811i
$825$		0			0
$826$	−525.440			−0.636125
$827$	−197.323	+	271.592i	−0.238602	+	0.328407i	−0.911479	−	0.411347i	$-0.865058\pi$
$827$	−197.323	+	271.592i	−0.238602	+	0.328407i	0.672877	+	0.739754i	$0.265058\pi$
$828$	280.383	−	862.930i	0.338627	−	1.04219i
$829$	301.853	+	929.007i	0.364116	+	1.12064i	0.950532	+	0.310625i	$0.100538\pi$
$829$	301.853	+	929.007i	0.364116	+	1.12064i	−0.586416	+	0.810010i	$0.699462\pi$
$830$		0			0
$831$	−600.942	−	827.126i	−0.723156	−	0.995338i
$832$	197.176	−	64.0663i	0.236990	−	0.0770028i
$833$	55.7589	+	18.1172i	0.0669375	+	0.0217493i
$834$	−522.041	−	379.285i	−0.625949	−	0.454778i
$835$		0			0
$836$	73.2148	−	474.453i	0.0875775	−	0.567527i
$837$	347.522			0.415199
$838$	354.259	−	487.596i	0.422744	−	0.581857i
$839$	−228.765	+	704.065i	−0.272663	+	0.839171i	0.717165	+	0.696904i	$0.245439\pi$
$839$	−228.765	+	704.065i	−0.272663	+	0.839171i	−0.989828	+	0.142268i	$0.954561\pi$
$840$		0			0
$841$	−13.8551	+	10.0663i	−0.0164745	+	0.0119694i
$842$	−107.256	−	147.625i	−0.127382	−	0.175326i
$843$	1.18034	−	0.383516i	0.00140017	−	0.000454941i
$844$	841.336	+	273.367i	0.996843	+	0.323894i
$845$		0			0
$846$			155.621i			0.183949i
$847$	941.346	−	7.48038i	1.11139	−	0.00883162i
$848$	49.9187			0.0588664
$849$	−588.525	+	810.036i	−0.693198	+	0.954106i
$850$		0			0
$851$	−679.562	−	2091.48i	−0.798545	−	2.45767i
$852$	−407.551	+	296.103i	−0.478346	+	0.347539i
$853$	255.804	+	352.084i	0.299888	+	0.412760i	0.932194	−	0.361958i	$-0.117892\pi$
$853$	255.804	+	352.084i	0.299888	+	0.412760i	−0.632306	+	0.774718i	$0.717892\pi$
$854$	−984.541	+	319.897i	−1.15286	+	0.374587i
$855$		0			0
$856$	197.971	+	143.834i	0.231275	+	0.168031i
$857$		−	1045.99i		−	1.22053i	−0.792198	−	0.610264i	$-0.791063\pi$
$857$		−	1045.99i		−	1.22053i	0.792198	−	0.610264i	$-0.208937\pi$
$858$	357.862	+	55.2231i	0.417088	+	0.0643626i
$859$	−415.346			−0.483523			−0.241762	−	0.970336i	$-0.577725\pi$
$859$	−415.346			−0.483523			−0.241762	+	0.970336i	$0.577725\pi$
$860$		0			0
$861$	729.828	−	2246.18i	0.847651	−	2.60880i
$862$	255.408	+	786.065i	0.296297	+	0.911909i
$863$	620.069	−	450.507i	0.718504	−	0.522024i	−0.167402	−	0.985889i	$-0.553538\pi$
$863$	620.069	−	450.507i	0.718504	−	0.522024i	0.885906	+	0.463865i	$0.153538\pi$
$864$	171.803	+	236.467i	0.198847	+	0.273689i
$865$		0			0
$866$	−557.672	−	181.199i	−0.643963	−	0.209236i
$867$	−952.030	−	691.690i	−1.09807	−	0.797797i
$868$		−	791.389i		−	0.911738i
$869$	−594.564	+	599.307i	−0.684193	+	0.689652i
$870$		0			0
$871$	−345.747	+	475.880i	−0.396954	+	0.546360i
$872$	−53.4437	+	164.483i	−0.0612886	+	0.188627i
$873$	113.489	+	349.282i	0.129998	+	0.400094i
$874$	499.508	−	362.914i	0.571520	−	0.415234i
$875$		0			0
$876$	−175.451	+	57.0074i	−0.200286	+	0.0650770i
$877$	634.180	+	206.058i	0.723124	+	0.234957i	0.647377	−	0.762170i	$-0.275866\pi$
$877$	634.180	+	206.058i	0.723124	+	0.234957i	0.0757471	+	0.997127i	$0.475866\pi$
$878$	−537.317	−	390.383i	−0.611978	−	0.444628i
$879$			1475.89i			1.67906i
$880$		0			0
$881$	1206.85			1.36987			0.684934	−	0.728606i	$-0.259831\pi$
$881$	1206.85			1.36987			0.684934	+	0.728606i	$0.259831\pi$
$882$	87.6211	−	120.600i	0.0993437	−	0.136735i
$883$	−160.368	+	493.563i	−0.181617	+	0.558961i	−0.999874	−	0.0158926i	$-0.994941\pi$
$883$	−160.368	+	493.563i	−0.181617	+	0.558961i	0.818256	+	0.574854i	$0.194941\pi$
$884$	25.7624	+	79.2885i	0.0291430	+	0.0896928i
$885$		0			0
$886$	−135.271	−	186.184i	−0.152676	−	0.210140i
$887$	−1498.64	+	486.939i	−1.68956	+	0.548973i	−0.986728	−	0.162380i	$-0.948083\pi$
$887$	−1498.64	+	486.939i	−1.68956	+	0.548973i	−0.702836	+	0.711352i	$0.748083\pi$
$888$	2309.64	+	750.448i	2.60095	+	0.845099i
$889$	−847.863	−	616.008i	−0.953726	−	0.692923i
$890$		0			0
$891$	−104.072	−	640.601i	−0.116804	−	0.718969i
$892$	137.408			0.154045
$893$	117.918	−	162.300i	0.132047	−	0.181747i
$894$	−184.083	+	566.549i	−0.205909	+	0.633723i
$895$		0			0
$896$	577.744	−	419.755i	0.644803	−	0.468477i
$897$	−518.566	−	713.745i	−0.578112	−	0.795702i
$898$	−193.695	+	62.9353i	−0.215696	+	0.0700839i
$899$	−1060.65	−	344.627i	−1.17982	−	0.383345i
$900$		0			0
$901$		−	191.426i		−	0.212459i
$902$	−780.520	+	401.609i	−0.865322	+	0.445243i
$903$	1497.74			1.65863
$904$	858.936	−	1182.22i	0.950150	−	1.30777i
$905$		0			0
$906$	225.902	+	695.254i	0.249340	+	0.767388i
$907$	−671.009	+	487.517i	−0.739812	+	0.537505i	−0.892652	−	0.450746i	$-0.851158\pi$
$907$	−671.009	+	487.517i	−0.739812	+	0.537505i	0.152840	+	0.988251i	$0.451158\pi$
$908$	505.137	+	695.262i	0.556318	+	0.765707i
$909$	1030.06	−	334.687i	1.13318	−	0.368192i
$910$		0			0
$911$	−655.918	−	476.553i	−0.719998	−	0.523109i	0.166385	−	0.986061i	$-0.446790\pi$
$911$	−655.918	−	476.553i	−0.719998	−	0.523109i	−0.886384	+	0.462952i	$0.846790\pi$
$912$		−	98.8716i		−	0.108412i
$913$	−131.965	−	256.472i	−0.144540	−	0.280911i
$914$	−353.738			−0.387022
$915$		0			0
$916$	292.289	−	899.572i	0.319092	−	0.982066i
$917$	115.051	+	354.091i	0.125465	+	0.386140i
$918$	43.2624	−	31.4320i	0.0471268	−	0.0342396i
$919$	580.114	+	798.459i	0.631245	+	0.868834i	0.998111	−	0.0614396i	$-0.0195692\pi$
$919$	580.114	+	798.459i	0.631245	+	0.868834i	−0.366866	+	0.930274i	$0.619569\pi$
$920$		0			0
$921$	1277.21	+	414.992i	1.38677	+	0.450588i
$922$	370.449	+	269.147i	0.401788	+	0.291916i
$923$			269.404i			0.291878i
$924$	989.017	−	160.676i	1.07036	−	0.173891i
$925$		0			0
$926$	−25.3396	+	34.8770i	−0.0273646	+	0.0376641i
$927$	535.746	−	1648.86i	0.577935	−	1.77870i
$928$	−289.855	−	892.082i	−0.312344	−	0.961295i
$929$	1172.73	−	852.035i	1.26235	−	0.917153i	0.263482	−	0.964664i	$-0.415129\pi$
$929$	1172.73	−	852.035i	1.26235	−	0.917153i	0.998871	+	0.0475119i	$0.0151292\pi$
$930$		0			0
$931$	−182.764	+	59.3836i	−0.196309	+	0.0637847i
$932$	242.067	+	78.6524i	0.259729	+	0.0843910i
$933$	214.116	+	155.565i	0.229492	+	0.166736i
$934$			127.068i			0.136047i
$935$		0			0
$936$	535.846			0.572485
$937$	296.805	−	408.517i	0.316761	−	0.435984i	−0.620714	−	0.784037i	$-0.713157\pi$
$937$	296.805	−	408.517i	0.316761	−	0.435984i	0.937475	+	0.348053i	$0.113157\pi$
$938$	265.509	−	817.152i	0.283058	−	0.871164i
$939$	203.779	+	627.167i	0.217017	+	0.667910i
$940$		0			0
$941$	79.5072	+	109.432i	0.0844922	+	0.116294i	0.849171	−	0.528118i	$-0.177102\pi$
$941$	79.5072	+	109.432i	0.0844922	+	0.116294i	−0.764679	+	0.644412i	$0.777102\pi$
$942$	−560.025	+	181.963i	−0.594507	+	0.193167i
$943$	2034.01	+	660.890i	2.15696	+	0.700837i
$944$	−61.6418	−	44.7854i	−0.0652986	−	0.0474422i
$945$		0			0
$946$	−395.174	−	392.047i	−0.417732	−	0.414426i
$947$	177.422			0.187352			0.0936759	−	0.995603i	$-0.470138\pi$
$947$	177.422			0.187352			0.0936759	+	0.995603i	$0.470138\pi$
$948$	−528.156	+	726.944i	−0.557127	+	0.766819i
$949$	−30.4867	+	93.8284i	−0.0321251	+	0.0988708i
$950$		0			0
$951$	−275.172	+	199.924i	−0.289350	+	0.210225i
$952$	−180.939	−	249.042i	−0.190062	−	0.261598i
$953$	716.160	−	232.694i	0.751480	−	0.244171i	0.0918618	−	0.995772i	$-0.470718\pi$
$953$	716.160	−	232.694i	0.751480	−	0.244171i	0.659618	+	0.751601i	$0.270718\pi$
$954$	−462.902	−	150.406i	−0.485223	−	0.157658i
$955$		0			0
$956$			854.093i			0.893403i
$957$	215.344	−	1395.49i	0.225020	−	1.45820i
$958$	−483.083			−0.504262
$959$	698.934	−	962.000i	0.728815	−	1.00313i
$960$		0			0
$961$	169.539	+	521.789i	0.176420	+	0.542964i
$962$	415.643	−	301.983i	0.432062	−	0.313911i
$963$	203.366	+	279.909i	0.211179	+	0.290664i
$964$	353.295	−	114.793i	0.366489	−	0.119079i
$965$		0			0
$966$	1042.56	+	757.463i	1.07925	+	0.784123i
$967$			1243.20i			1.28563i	0.766024	+	0.642813i	$0.222233\pi$
$967$			1243.20i			1.28563i	−0.766024	+	0.642813i	$0.777767\pi$
$968$	−765.962	−	547.258i	−0.791283	−	0.565349i
$969$	−379.149			−0.391278
$970$		0			0
$971$	−289.889	+	892.185i	−0.298546	+	0.918831i	0.683461	+	0.729987i	$0.260474\pi$
$971$	−289.889	+	892.185i	−0.298546	+	0.918831i	−0.982007	+	0.188844i	$0.939526\pi$
$972$	−278.589	−	857.408i	−0.286614	−	0.882107i
$973$	−772.536	+	561.281i	−0.793974	+	0.576856i
$974$	219.496	+	302.110i	0.225355	+	0.310175i
$975$		0			0
$976$	−142.767	−	46.3879i	−0.146278	−	0.0475286i
$977$	1071.31	+	778.352i	1.09653	+	0.796676i	0.980490	−	0.196569i	$-0.0629799\pi$
$977$	1071.31	+	778.352i	1.09653	+	0.796676i	0.116040	+	0.993245i	$0.462980\pi$
$978$		−	1113.11i		−	1.13815i
$979$	−1143.82	−	176.508i	−1.16836	−	0.180294i
$980$		0			0
$981$	−143.730	+	197.827i	−0.146514	+	0.201659i
$982$	−94.9866	+	292.339i	−0.0967277	+	0.297697i
$983$	−114.160	−	351.348i	−0.116134	−	0.357424i	0.876048	−	0.482224i	$-0.160171\pi$
$983$	−114.160	−	351.348i	−0.116134	−	0.357424i	−0.992182	+	0.124800i	$0.960171\pi$
$984$	−1910.71	+	1388.21i	−1.94178	+	1.41079i
$985$		0			0
$986$	−163.209	+	53.0299i	−0.165527	+	0.0537828i
$987$	398.222	+	129.390i	0.403467	+	0.131094i
$988$	−221.074	−	160.620i	−0.223759	−	0.162570i
$989$			1356.27i			1.37135i
$990$		0			0
$991$	393.721			0.397297			0.198648	−	0.980071i	$-0.436345\pi$
$991$	393.721			0.397297			0.198648	+	0.980071i	$0.436345\pi$
$992$	−746.318	+	1027.22i	−0.752336	+	1.03550i
$993$	803.933	−	2474.25i	0.809600	−	2.49169i
$994$	−121.603	−	374.254i	−0.122337	−	0.376513i
$995$		0			0
$996$	−180.451	−	248.369i	−0.181176	−	0.249367i
$997$	840.247	−	273.013i	0.842775	−	0.273834i	0.144358	−	0.989525i	$-0.453888\pi$
$997$	840.247	−	273.013i	0.842775	−	0.273834i	0.698417	+	0.715691i	$0.253888\pi$
$998$	673.871	+	218.954i	0.675221	+	0.219393i
$999$	505.066	+	366.952i	0.505571	+	0.367319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.b.51.1	✓	4
5.2	odd	4		275.3.q.b.249.1		8
5.3	odd	4		275.3.q.b.249.2		8
5.4	even	2		275.3.x.c.51.1	yes	4
11.8	odd	10	inner	275.3.x.b.151.1	yes	4
55.8	even	20		275.3.q.b.74.1		8
55.19	odd	10		275.3.x.c.151.1	yes	4
55.52	even	20		275.3.q.b.74.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.q.b.74.1		8	55.8	even	20
275.3.q.b.74.2		8	55.52	even	20
275.3.q.b.249.1		8	5.2	odd	4
275.3.q.b.249.2		8	5.3	odd	4
275.3.x.b.51.1	✓	4	1.1	even	1	trivial
275.3.x.b.151.1	yes	4	11.8	odd	10	inner
275.3.x.c.51.1	yes	4	5.4	even	2
275.3.x.c.151.1	yes	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+(-0.690983 + 0.951057i) q^{2} +(1.38197 - 4.25325i) q^{3} +(0.809017 + 2.48990i) q^{4} +(3.09017 + 4.25325i) q^{6} +(7.39919 - 2.40414i) q^{7} +(-7.39919 - 2.40414i) q^{8} +(-8.89919 - 6.46564i) q^{9} +(10.8713 + 1.67760i) q^{11} +11.7082 q^{12} +(3.68034 - 5.06555i) q^{13} +(-2.82624 + 8.69827i) q^{14} +(-1.07295 + 0.779543i) q^{16} +(2.98936 + 4.11450i) q^{17} +(12.2984 - 3.99598i) q^{18} +(-15.8541 - 5.15131i) q^{19} -34.7931i q^{21} +(-9.10739 + 9.18005i) q^{22} +31.5066 q^{23} +(-20.4508 + 28.1482i) q^{24} +(2.27458 + 7.00042i) q^{26} +(-7.23607 + 5.25731i) q^{27} +(11.9721 + 16.4782i) q^{28} +(27.2984 - 8.86978i) q^{29} +(-31.4336 - 22.8379i) q^{31} -32.6789i q^{32} +(22.1591 - 43.9201i) q^{33} -5.97871 q^{34} +(8.89919 - 27.3889i) q^{36} +(-21.5689 - 66.3822i) q^{37} +(15.8541 - 11.5187i) q^{38} +(-16.4590 - 22.6538i) q^{39} +(64.5582 + 20.9762i) q^{41} +(33.0902 + 24.0414i) q^{42} +43.0471i q^{43} +(4.61803 + 28.4257i) q^{44} +(-21.7705 + 29.9645i) q^{46} +(-3.71885 + 11.4454i) q^{47} +(1.83282 + 5.64083i) q^{48} +(9.32624 - 6.77591i) q^{49} +(21.6312 - 7.02840i) q^{51} +(15.5902 + 5.06555i) q^{52} +(-30.4508 - 22.1238i) q^{53} -10.5146i q^{54} -60.5279 q^{56} +(-43.8197 + 60.3126i) q^{57} +(-10.4271 + 32.0912i) q^{58} +(17.7533 + 54.6390i) q^{59} +(66.5304 + 91.5712i) q^{61} +(43.4402 - 14.1146i) q^{62} +(-81.3911 - 26.4456i) q^{63} +(26.7877 + 19.4624i) q^{64} +(26.4590 + 51.4226i) q^{66} -93.9443 q^{67} +(-7.82624 + 10.7719i) q^{68} +(43.5410 - 134.005i) q^{69} +(-34.8090 + 25.2902i) q^{71} +(50.3024 + 69.2354i) q^{72} +(-14.9853 + 4.86902i) q^{73} +(78.0370 + 25.3557i) q^{74} -43.6426i q^{76} +(84.4721 - 13.7233i) q^{77} +32.9180 q^{78} +(-45.1099 + 62.0885i) q^{79} +(-18.2320 - 56.1123i) q^{81} +(-64.5582 + 46.9043i) q^{82} +(-15.4123 - 21.2133i) q^{83} +(86.6312 - 28.1482i) q^{84} +(-40.9402 - 29.7448i) q^{86} -128.365i q^{87} +(-76.4058 - 38.5491i) q^{88} -105.215 q^{89} +(15.0532 - 46.3290i) q^{91} +(25.4894 + 78.4482i) q^{92} +(-140.575 + 102.134i) q^{93} +(-8.31559 - 11.4454i) q^{94} +(-138.992 - 45.1612i) q^{96} +(-27.0106 - 19.6244i) q^{97} +13.5518i q^{98} +(-85.8992 - 85.2193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} + 10 q^{3} + q^{4} - 10 q^{6} + 5 q^{7} - 5 q^{8} - 11 q^{9} + q^{11} + 20 q^{12} - 30 q^{13} + 20 q^{14} - 11 q^{16} - 35 q^{17} - 50 q^{19} + 15 q^{22} + 50 q^{23} + 30 q^{24} + 65 q^{26}+ \cdots - 319 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 10 * q^3 + q^4 - 10 * q^6 + 5 * q^7 - 5 * q^8 - 11 * q^9 + q^11 + 20 * q^12 - 30 * q^13 + 20 * q^14 - 11 * q^16 - 35 * q^17 - 50 * q^19 + 15 * q^22 + 50 * q^23 + 30 * q^24 + 65 * q^26 - 20 * q^27 + 30 * q^28 + 60 * q^29 - 43 * q^31 - 50 * q^33 + 70 * q^34 + 11 * q^36 + 30 * q^37 + 50 * q^38 - 200 * q^39 + 95 * q^41 + 110 * q^42 + 14 * q^44 - 20 * q^46 - 35 * q^47 - 100 * q^48 + 6 * q^49 - 70 * q^51 + 40 * q^52 - 10 * q^53 - 260 * q^56 - 220 * q^57 - 35 * q^58 + 33 * q^59 + 85 * q^61 + 15 * q^62 - 55 * q^63 + 11 * q^64 + 240 * q^66 - 340 * q^67 + 40 * q^69 - 137 * q^71 + 275 * q^72 + 110 * q^73 + 55 * q^74 + 320 * q^77 + 400 * q^78 + 70 * q^79 + 59 * q^81 - 95 * q^82 + 115 * q^83 + 190 * q^84 - 5 * q^86 - 205 * q^88 - 318 * q^89 + 295 * q^91 + 55 * q^92 - 370 * q^93 + 45 * q^94 - 310 * q^96 - 155 * q^97 - 319 * q^99

Introduction

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