LMFDB - Embedded newform 275.3.x.c.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.c.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	−0.600544	−	0.799592i	$-0.705049\pi$
$2$	0.690983	−	0.951057i	0.345492	−	0.475528i	0.946035	+	0.324064i	$0.105049\pi$
$3$	−1.38197	+	4.25325i	−0.460655	+	1.41775i	0.403710	+	0.914887i	$0.367720\pi$
$3$	−1.38197	+	4.25325i	−0.460655	+	1.41775i	−0.864365	+	0.502864i	$0.832280\pi$
$4$	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	−0.785422	−	0.618960i	$-0.787554\pi$
$7$	−7.39919	+	2.40414i	−1.05703	+	0.343449i	−0.271604	+	0.962409i	$0.587554\pi$
$8$	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	−0.926759	−	0.375657i	$-0.877417\pi$
$13$	−3.68034	+	5.06555i	−0.283103	+	0.389658i	0.643656	+	0.765315i	$0.277417\pi$
$14$	−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	0.711993	−	0.702187i	$-0.247793\pi$
$17$	−2.98936	−	4.11450i	−0.175845	−	0.242029i	−0.887837	+	0.460158i	$0.847793\pi$
$18$	−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	$-0.740165\pi$
$23$	−31.5066			−1.36985			−0.684926	+	0.728613i	$0.740165\pi$
$24$	−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	$0.292221\pi$
$37$	21.5689	+	66.3822i	0.582943	+	1.79411i	−0.0244364	+	0.999701i	$0.507779\pi$
$38$	−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	$-0.833132\pi$
$43$		−	43.0471i		−	1.00109i	0.865709	−	0.500547i	$-0.166868\pi$
$44$	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	−0.903668	−	0.428234i	$-0.859136\pi$
$47$	3.71885	−	11.4454i	0.0791244	−	0.243520i	0.982792	+	0.184714i	$0.0591359\pi$
$48$	−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	0.836753	−	0.547580i	$-0.184451\pi$
$53$	30.4508	+	22.1238i	0.574544	+	0.417431i	−0.262209	+	0.965011i	$0.584451\pi$
$54$		−	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	$-0.252703\pi$
$67$	93.9443			1.40215			0.701077	+	0.713086i	$0.252703\pi$
$68$	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	−0.204573	−	0.978851i	$-0.565581\pi$
$73$	14.9853	−	4.86902i	0.205278	−	0.0666989i	0.409851	+	0.912152i	$0.365581\pi$
$74$	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	0.891706	−	0.452615i	$-0.149509\pi$
$83$	15.4123	+	21.2133i	0.185691	+	0.255582i	−0.706015	+	0.708197i	$0.749509\pi$
$84$	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	0.718246	−	0.695790i	$-0.244945\pi$
$97$	27.0106	+	19.6244i	0.278460	+	0.202313i	−0.439785	+	0.898103i	$0.644945\pi$
$98$		−	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	$-0.822691\pi$
$103$	−48.7041	−	149.896i	−0.472856	−	1.45530i	0.375972	−	0.926631i	$-0.377309\pi$
$104$	−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	0.445446	−	0.895309i	$-0.353045\pi$
$107$	29.9139	+	9.71961i	0.279569	+	0.0908375i	−0.165876	+	0.986147i	$0.553045\pi$
$108$	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	$-0.587709\pi$
$113$	58.0426	−	178.637i	0.513651	−	1.58086i	0.785723	−	0.618579i	$-0.212291\pi$
$114$	−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	0.997599	−	0.0692585i	$-0.0220633\pi$
$127$	79.1788	+	108.980i	0.623455	+	0.858112i	−0.374144	+	0.927371i	$0.622063\pi$
$128$	−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	−0.939123	−	0.343582i	$-0.888360\pi$
$137$	−123.651	+	89.8377i	−0.902561	+	0.655749i	0.0365612	+	0.999331i	$0.488360\pi$
$138$	−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	$-0.783901\pi$
$157$	34.6115	−	106.523i	0.220455	−	0.678491i	0.998721	−	0.0505565i	$-0.0160995\pi$
$158$	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	0.972376	−	0.233421i	$-0.0749919\pi$
$163$	171.290	+	124.450i	1.05086	+	0.763495i	0.0784845	+	0.996915i	$0.474992\pi$
$164$			177.714i			1.08362i
$165$		0			0
$166$	30.8247			0.185691
$167$	47.5623	−	65.4639i	0.284804	−	0.391999i	−0.642514	−	0.766274i	$-0.722108\pi$
$167$	47.5623	−	65.4639i	0.284804	−	0.391999i	0.927318	+	0.374275i	$0.122108\pi$
$168$	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	0.586897	−	0.809661i	$-0.300349\pi$
$173$	101.343	+	32.9285i	0.585800	+	0.190338i	−0.00109704	+	0.999999i	$0.500349\pi$
$174$	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	0.638484	−	0.769635i	$-0.279562\pi$
$193$	−56.1215	−	77.2446i	−0.290785	−	0.400231i	−0.929269	+	0.369404i	$0.879562\pi$
$194$	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	$-0.804964\pi$
$197$		−	226.588i		−	1.15020i	0.818085	−	0.575098i	$-0.195036\pi$
$198$	−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	−0.980813	−	0.194949i	$-0.937546\pi$
$223$	−16.2188	+	49.9165i	−0.0727303	+	0.223841i	0.908083	+	0.418790i	$0.137546\pi$
$224$	−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	−0.901120	−	0.433570i	$-0.857254\pi$
$227$	−312.192	+	101.437i	−1.37529	+	0.446860i	−0.474175	+	0.880431i	$0.657254\pi$
$228$	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	−0.913842	−	0.406069i	$-0.866899\pi$
$233$	−57.1443	+	78.6524i	−0.245255	+	0.337564i	0.668588	+	0.743633i	$0.266899\pi$
$234$	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	0.970980	−	0.239161i	$-0.0768724\pi$
$257$	11.5304	+	35.4869i	0.0448653	+	0.138081i	−0.926115	+	0.377242i	$0.876872\pi$
$258$	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	$0.0961289\pi$
$263$			156.447i			0.594857i	−0.954744	+	0.297428i	$0.903871\pi$
$264$	−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	−0.979476	−	0.201559i	$-0.935399\pi$
$277$	−134.375	+	184.951i	−0.485108	+	0.667693i	0.494369	+	0.869252i	$0.335399\pi$
$278$	−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	0.660016	−	0.751252i	$-0.270550\pi$
$283$	212.931	+	69.1853i	0.752405	+	0.244471i	0.0923891	+	0.995723i	$0.470550\pi$
$284$	−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	0.280257	−	0.959925i	$-0.409580\pi$
$293$	313.867	−	101.982i	1.07122	−	0.348060i	0.790962	+	0.611865i	$0.209580\pi$
$294$	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	$-0.837335\pi$
$307$		−	300.291i		−	0.978146i	0.872243	−	0.489073i	$-0.162665\pi$
$308$	−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	−0.380680	−	0.924707i	$-0.624310\pi$
$313$	119.294	−	86.6724i	0.381132	−	0.276909i	0.761812	+	0.647798i	$0.224310\pi$
$314$	−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	0.680592	−	0.732663i	$-0.261723\pi$
$317$	61.5304	+	44.7044i	0.194102	+	0.141023i	−0.486490	+	0.873686i	$0.661723\pi$
$318$			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	0.354365	−	0.935107i	$-0.384697\pi$
$337$	401.264	−	130.379i	1.19070	−	0.386880i	0.836330	+	0.548227i	$0.184697\pi$
$338$	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	0.659135	−	0.752025i	$-0.270923\pi$
$347$	−90.1393	−	124.066i	−0.259767	−	0.357539i	−0.918902	+	0.394486i	$0.870923\pi$
$348$	−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	$-0.444283\pi$
$353$	122.947			0.348293			0.174146	+	0.984720i	$0.444283\pi$
$354$	−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	0.944831	−	0.327557i	$-0.106225\pi$
$367$	−4.43577	−	13.6519i	−0.0120866	−	0.0371987i	−0.956918	+	0.290359i	$0.906225\pi$
$368$	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	$0.0744674\pi$
$373$			172.936i			0.463636i	−0.972759	+	0.231818i	$0.925533\pi$
$374$	−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	0.367452	−	0.930043i	$-0.380230\pi$
$383$	−154.549	−	112.287i	−0.403523	−	0.293176i	−0.770974	+	0.636866i	$0.780230\pi$
$384$		−	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	$-0.529520\pi$
$397$	−73.5298			−0.185214			−0.0926068	+	0.995703i	$0.529520\pi$
$398$	−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	$-0.904621\pi$
$433$	−154.137	−	474.384i	−0.355974	−	1.09558i	0.599468	−	0.800398i	$-0.295379\pi$
$434$	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	−0.859272	−	0.511520i	$-0.829083\pi$
$443$	60.4950	−	186.184i	0.136558	−	0.420281i	0.995829	+	0.0912390i	$0.0290827\pi$
$444$	−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	0.570406	−	0.821363i	$-0.306786\pi$
$457$	−176.869	−	243.440i	−0.387022	−	0.532690i	−0.957428	+	0.288673i	$0.906786\pi$
$458$	−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	$-0.512609\pi$
$463$	−36.6718			−0.0792048			−0.0396024	+	0.999216i	$0.512609\pi$
$464$	−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	−0.677462	−	0.735558i	$-0.736920\pi$
$467$	−87.4468	+	63.5338i	−0.187252	+	0.136047i	0.490210	+	0.871604i	$0.336920\pi$
$468$	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	$0.205747\pi$
$487$	−98.1616	+	302.110i	−0.201564	+	0.620350i	−0.999837	+	0.0180541i	$0.994253\pi$
$488$	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	0.727228	−	0.686396i	$-0.240808\pi$
$503$	458.794	+	149.071i	0.912115	+	0.296364i	0.184887	+	0.982760i	$0.440808\pi$
$504$	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	0.995818	−	0.0913639i	$-0.0291226\pi$
$523$	314.428	+	432.773i	0.601201	+	0.827482i	−0.394617	+	0.918846i	$0.629123\pi$
$524$	−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	0.675769	−	0.737114i	$-0.263812\pi$
$547$	431.699	+	140.268i	0.789212	+	0.256431i	0.113444	+	0.993544i	$0.463812\pi$
$548$	−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	−0.596429	−	0.802666i	$-0.703414\pi$
$557$	−338.185	+	109.883i	−0.607155	+	0.197277i	−0.0107261	+	0.999942i	$0.503414\pi$
$558$	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	−0.984448	−	0.175675i	$-0.943789\pi$
$563$	−288.909	+	397.649i	−0.513160	+	0.706305i	0.471288	+	0.881979i	$0.343789\pi$
$564$	−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	−0.418053	−	0.908423i	$-0.637287\pi$
$577$	182.749	−	132.775i	0.316723	−	0.230113i	0.734776	+	0.678310i	$0.237287\pi$
$578$	−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	$0.0280667\pi$
$587$	142.055	+	437.200i	0.242001	+	0.744803i	−0.754114	+	0.656744i	$0.771933\pi$
$588$	−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	$-0.760440\pi$
$593$		−	810.678i		−	1.36708i	0.729914	−	0.683539i	$-0.239560\pi$
$594$	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	−0.683688	−	0.729775i	$-0.739625\pi$
$607$	134.536	−	185.173i	0.221640	−	0.305062i	0.905328	+	0.424713i	$0.139625\pi$
$608$	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	−0.770359	−	0.637610i	$-0.779923\pi$
$613$	−1084.01	−	352.217i	−1.76837	−	0.574579i	−0.998012	+	0.0630314i	$0.979923\pi$
$614$	−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	$-0.326213\pi$
$617$	640.748			1.03849			0.519244	+	0.854626i	$0.326213\pi$
$618$	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	−0.999957	−	0.00926699i	$-0.997050\pi$
$643$	−835.995	+	607.386i	−1.30015	+	0.944612i	−0.300190	+	0.953879i	$0.597050\pi$
$644$	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	0.583843	−	0.811866i	$-0.301548\pi$
$647$	−5.09172	−	3.69935i	−0.00786974	−	0.00571770i	−0.591713	+	0.806149i	$0.701548\pi$
$648$		−	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	0.954018	−	0.299750i	$-0.0969034\pi$
$653$	3.92609	+	12.0833i	0.00601239	+	0.0185042i	−0.948005	+	0.318254i	$0.896903\pi$
$654$	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	−0.766818	−	0.641864i	$-0.778161\pi$
$673$	54.2376	−	74.6517i	0.0805908	−	0.110924i	0.847409	+	0.530941i	$0.178161\pi$
$674$	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	0.554344	−	0.832287i	$-0.312969\pi$
$677$	−276.561	−	380.654i	−0.408510	−	0.562265i	−0.962854	+	0.270022i	$0.912969\pi$
$678$	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	$-0.516971\pi$
$683$	−72.7933			−0.106579			−0.0532894	+	0.998579i	$0.516971\pi$
$684$	−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	$-0.605957\pi$
$727$	−475.109			−0.653520			−0.326760	+	0.945107i	$0.605957\pi$
$728$	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	−0.247431	−	0.968905i	$-0.579587\pi$
$733$	89.3531	−	29.0326i	0.121901	−	0.0396079i	0.369332	+	0.929297i	$0.379587\pi$
$734$	−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	$0.0300696\pi$
$743$	577.765	+	795.226i	0.777611	+	1.07029i	−0.217930	+	0.975964i	$0.569930\pi$
$744$	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	0.237407	−	0.971410i	$-0.423703\pi$
$757$	−464.114	−	337.199i	−0.613097	−	0.445441i	−0.850503	+	0.525969i	$0.823703\pi$
$758$			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	$0.361165\pi$
$773$	−349.452	+	1075.50i	−0.452072	+	1.39134i	−0.874538	+	0.484956i	$0.838835\pi$
$774$	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	$0.00600254\pi$
$787$	557.821	+	767.774i	0.708794	+	0.975571i	−0.291029	+	0.956714i	$0.593997\pi$
$788$	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	−0.959312	−	0.282348i	$-0.908887\pi$
$797$	−786.819	+	571.658i	−0.987226	+	0.717262i	−0.0279144	+	0.999610i	$0.508887\pi$
$798$	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	0.499326	−	0.866414i	$-0.333581\pi$
$823$	−140.225	−	101.880i	−0.170383	−	0.123791i	−0.669709	+	0.742624i	$0.733581\pi$
$824$		−	1226.20i		−	1.48811i
$825$		0			0
$826$	−525.440			−0.636125
$827$	197.323	−	271.592i	0.238602	−	0.328407i	−0.672877	−	0.739754i	$-0.734942\pi$
$827$	197.323	−	271.592i	0.238602	−	0.328407i	0.911479	+	0.411347i	$0.134942\pi$
$828$	−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	0.632306	−	0.774718i	$-0.282108\pi$
$853$	−255.804	−	352.084i	−0.299888	−	0.412760i	−0.932194	+	0.361958i	$0.882108\pi$
$854$	−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	$0.208937\pi$
$857$			1045.99i			1.22053i	−0.792198	+	0.610264i	$0.791063\pi$
$858$	−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	−0.885906	−	0.463865i	$-0.846462\pi$
$863$	−620.069	+	450.507i	−0.718504	+	0.522024i	0.167402	+	0.985889i	$0.446462\pi$
$864$	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	−0.0757471	−	0.997127i	$-0.524134\pi$
$877$	−634.180	−	206.058i	−0.723124	−	0.234957i	−0.647377	+	0.762170i	$0.724134\pi$
$878$	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	−0.818256	−	0.574854i	$-0.805059\pi$
$883$	160.368	−	493.563i	0.181617	−	0.558961i	0.999874	+	0.0158926i	$0.00505898\pi$
$884$	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	0.702836	−	0.711352i	$-0.251917\pi$
$887$	1498.64	−	486.939i	1.68956	−	0.548973i	0.986728	+	0.162380i	$0.0519170\pi$
$888$	−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	−0.152840	−	0.988251i	$-0.548842\pi$
$907$	671.009	−	487.517i	0.739812	−	0.537505i	0.892652	+	0.450746i	$0.148842\pi$
$908$	−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	−0.937475	−	0.348053i	$-0.886843\pi$
$937$	−296.805	+	408.517i	−0.316761	+	0.435984i	0.620714	+	0.784037i	$0.286843\pi$
$938$	−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	$-0.529862\pi$
$947$	−177.422			−0.187352			−0.0936759	+	0.995603i	$0.529862\pi$
$948$	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	−0.659618	−	0.751601i	$-0.729282\pi$
$953$	−716.160	+	232.694i	−0.751480	+	0.244171i	−0.0918618	+	0.995772i	$0.529282\pi$
$954$	−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	$-0.777767\pi$
$967$		−	1243.20i		−	1.28563i	0.766024	−	0.642813i	$-0.222233\pi$
$968$	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	−0.116040	−	0.993245i	$-0.537020\pi$
$977$	−1071.31	−	778.352i	−1.09653	−	0.796676i	−0.980490	+	0.196569i	$0.937020\pi$
$978$			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	0.992182	−	0.124800i	$-0.0398290\pi$
$983$	114.160	+	351.348i	0.116134	+	0.357424i	−0.876048	+	0.482224i	$0.839829\pi$
$984$	−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	−0.698417	−	0.715691i	$-0.746112\pi$
$997$	−840.247	+	273.013i	−0.842775	+	0.273834i	−0.144358	+	0.989525i	$0.546112\pi$
$998$	−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.c.51.1	yes	4
5.2	odd	4		275.3.q.b.249.2		8
5.3	odd	4		275.3.q.b.249.1		8
5.4	even	2		275.3.x.b.51.1	✓	4
11.8	odd	10	inner	275.3.x.c.151.1	yes	4
55.8	even	20		275.3.q.b.74.2		8
55.19	odd	10		275.3.x.b.151.1	yes	4
55.52	even	20		275.3.q.b.74.1		8

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

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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