LMFDB - Embedded newform 275.3.x.d.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.690983 - 0.224514i) q^{2} +(-3.23607 - 2.35114i) q^{3} +(-2.80902 + 2.04087i) q^{4} +(-2.76393 - 0.898056i) q^{6} +(0.163119 + 0.224514i) q^{7} +(-3.19098 + 4.39201i) q^{8} +(2.16312 + 6.65740i) q^{9} +(10.3713 + 3.66547i) q^{11} +13.8885 q^{12} +(-10.7533 + 3.49396i) q^{13} +(0.163119 + 0.118513i) q^{14} +(3.07295 - 9.45756i) q^{16} +(19.2705 + 6.26137i) q^{17} +(2.98936 + 4.11450i) q^{18} +(16.9721 - 23.3601i) q^{19} -1.11006i q^{21} +(7.98936 + 0.204270i) q^{22} +27.6180 q^{23} +(20.6525 - 6.71040i) q^{24} +(-6.64590 + 4.82853i) q^{26} +(-2.47214 + 7.60845i) q^{27} +(-0.916408 - 0.297759i) q^{28} +(10.2016 + 14.0413i) q^{29} +(10.6180 + 32.6789i) q^{31} -28.9402i q^{32} +(-24.9443 - 36.2461i) q^{33} +14.7214 q^{34} +(-19.6631 - 14.2861i) q^{36} +(10.7361 - 7.80021i) q^{37} +(6.48278 - 19.9519i) q^{38} +(43.0132 + 13.9758i) q^{39} +(-10.6140 + 14.6089i) q^{41} +(-0.249224 - 0.767031i) q^{42} +34.7931i q^{43} +(-36.6140 + 10.8702i) q^{44} +(19.0836 - 6.20063i) q^{46} +(38.4230 + 27.9159i) q^{47} +(-32.1803 + 23.3804i) q^{48} +(15.1180 - 46.5285i) q^{49} +(-47.6393 - 65.5699i) q^{51} +(23.0755 - 31.7606i) q^{52} +(-12.8475 - 39.5406i) q^{53} +5.81234i q^{54} -1.50658 q^{56} +(-109.846 + 35.6911i) q^{57} +(10.2016 + 7.41192i) q^{58} +(-82.3115 + 59.8028i) q^{59} +(48.4164 + 15.7314i) q^{61} +(14.6738 + 20.1967i) q^{62} +(-1.14183 + 1.57160i) q^{63} +(5.79431 + 17.8330i) q^{64} +(-25.3738 - 19.4451i) q^{66} -40.1803 q^{67} +(-66.9098 + 21.7403i) q^{68} +(-89.3738 - 64.9339i) q^{69} +(8.70820 - 26.8011i) q^{71} +(-36.1418 - 11.7432i) q^{72} +(58.6656 + 80.7463i) q^{73} +(5.66718 - 7.80021i) q^{74} +100.257i q^{76} +(0.868810 + 2.92641i) q^{77} +32.8591 q^{78} +(-125.172 + 40.6709i) q^{79} +(76.8566 - 55.8396i) q^{81} +(-4.05418 + 12.4775i) q^{82} +(119.271 + 38.7533i) q^{83} +(2.26548 + 3.11817i) q^{84} +(7.81153 + 24.0414i) q^{86} -69.4242i q^{87} +(-49.1935 + 33.8545i) q^{88} +88.9493 q^{89} +(-2.53851 - 1.84433i) q^{91} +(-77.5795 + 56.3648i) q^{92} +(42.4721 - 130.716i) q^{93} +(32.8171 + 10.6629i) q^{94} +(-68.0426 + 93.6526i) q^{96} +(-14.9311 - 45.9533i) q^{97} -35.5446i q^{98} +(-1.96807 + 76.9748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 4 q^{3} - 9 q^{4} - 20 q^{6} - 15 q^{7} - 15 q^{8} - 7 q^{9} - q^{11} - 16 q^{12} - 5 q^{13} - 15 q^{14} + 19 q^{16} + 10 q^{17} - 35 q^{18} + 50 q^{19} - 15 q^{22} + 106 q^{23} + 20 q^{24}+ \cdots + 133 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 - 4 * q^3 - 9 * q^4 - 20 * q^6 - 15 * q^7 - 15 * q^8 - 7 * q^9 - q^11 - 16 * q^12 - 5 * q^13 - 15 * q^14 + 19 * q^16 + 10 * q^17 - 35 * q^18 + 50 * q^19 - 15 * q^22 + 106 * q^23 + 20 * q^24 - 40 * q^26 + 8 * q^27 + 50 * q^28 + 90 * q^29 + 38 * q^31 - 64 * q^33 - 120 * q^34 - 63 * q^36 + 34 * q^37 + 55 * q^38 + 20 * q^39 + 85 * q^41 + 160 * q^42 - 19 * q^44 + 130 * q^46 + 24 * q^47 - 84 * q^48 + 56 * q^49 - 280 * q^51 - 100 * q^52 - 114 * q^53 + 70 * q^56 - 180 * q^57 + 90 * q^58 - 128 * q^59 + 140 * q^61 + 90 * q^62 + 105 * q^63 - 149 * q^64 + 140 * q^66 - 116 * q^67 - 290 * q^68 - 116 * q^69 + 8 * q^71 - 35 * q^72 + 20 * q^73 + 130 * q^74 + 160 * q^77 - 280 * q^78 - 210 * q^79 + 95 * q^81 + 270 * q^82 + 410 * q^83 + 340 * q^84 - 170 * q^86 - 78 * q^89 - 75 * q^91 - 241 * q^92 + 152 * q^93 + 375 * q^94 - 460 * q^96 - 176 * q^97 + 133 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.690983	−	0.224514i	0.345492	−	0.112257i	−0.131131	−	0.991365i	$-0.541861\pi$
$2$	0.690983	−	0.224514i	0.345492	−	0.112257i	0.476623	+	0.879108i	$0.341861\pi$
$3$	−3.23607	−	2.35114i	−1.07869	−	0.783714i	−0.101235	−	0.994862i	$-0.532280\pi$
$3$	−3.23607	−	2.35114i	−1.07869	−	0.783714i	−0.977454	+	0.211149i	$0.932280\pi$
$4$	−2.80902	+	2.04087i	−0.702254	+	0.510218i
$5$		0			0
$5$		0			0
$6$	−2.76393	−	0.898056i	−0.460655	−	0.149676i
$7$	0.163119	+	0.224514i	0.0233027	+	0.0320734i	0.820509	−	0.571633i	$-0.193690\pi$
$7$	0.163119	+	0.224514i	0.0233027	+	0.0320734i	−0.797207	+	0.603706i	$0.793690\pi$
$8$	−3.19098	+	4.39201i	−0.398873	+	0.549001i
$9$	2.16312	+	6.65740i	0.240347	+	0.739711i
$10$		0			0
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$12$	13.8885			1.15738
$13$	−10.7533	+	3.49396i	−0.827176	+	0.268766i	−0.691855	−	0.722036i	$-0.743206\pi$
$13$	−10.7533	+	3.49396i	−0.827176	+	0.268766i	−0.135321	+	0.990802i	$0.543206\pi$
$14$	0.163119	+	0.118513i	0.0116514	+	0.00846520i
$15$		0			0
$16$	3.07295	−	9.45756i	0.192059	−	0.591098i
$17$	19.2705	+	6.26137i	1.13356	+	0.368316i	0.814928	−	0.579563i	$-0.196777\pi$
$17$	19.2705	+	6.26137i	1.13356	+	0.368316i	0.318632	+	0.947879i	$0.396777\pi$
$18$	2.98936	+	4.11450i	0.166075	+	0.228583i
$19$	16.9721	−	23.3601i	0.893270	−	1.22948i	−0.0792950	−	0.996851i	$-0.525267\pi$
$19$	16.9721	−	23.3601i	0.893270	−	1.22948i	0.972565	−	0.232630i	$-0.0747331\pi$
$20$		0			0
$21$		−	1.11006i		−	0.0528599i
$22$	7.98936	+	0.204270i	0.363153	+	0.00928498i
$23$	27.6180			1.20078			0.600392	−	0.799706i	$-0.295011\pi$
$23$	27.6180			1.20078			0.600392	+	0.799706i	$0.295011\pi$
$24$	20.6525	−	6.71040i	0.860520	−	0.279600i
$25$		0			0
$26$	−6.64590	+	4.82853i	−0.255611	+	0.185713i
$27$	−2.47214	+	7.60845i	−0.0915606	+	0.281795i
$28$	−0.916408	−	0.297759i	−0.0327289	−	0.0106342i
$29$	10.2016	+	14.0413i	0.351780	+	0.484184i	0.947836	−	0.318759i	$-0.103266\pi$
$29$	10.2016	+	14.0413i	0.351780	+	0.484184i	−0.596055	+	0.802943i	$0.703266\pi$
$30$		0			0
$31$	10.6180	+	32.6789i	0.342517	+	1.05416i	0.962900	+	0.269860i	$0.0869775\pi$
$31$	10.6180	+	32.6789i	0.342517	+	1.05416i	−0.620382	+	0.784300i	$0.713023\pi$
$32$		−	28.9402i		−	0.904382i
$33$	−24.9443	−	36.2461i	−0.755887	−	1.09837i
$34$	14.7214			0.432981
$35$		0			0
$36$	−19.6631	−	14.2861i	−0.546198	−	0.396836i
$37$	10.7361	−	7.80021i	0.290164	−	0.210816i	−0.433175	−	0.901310i	$-0.642607\pi$
$37$	10.7361	−	7.80021i	0.290164	−	0.210816i	0.723339	+	0.690494i	$0.242607\pi$
$38$	6.48278	−	19.9519i	0.170599	−	0.525051i
$39$	43.0132	+	13.9758i	1.10290	+	0.358354i
$40$		0			0
$41$	−10.6140	+	14.6089i	−0.258877	+	0.356314i	−0.918596	−	0.395199i	$-0.870676\pi$
$41$	−10.6140	+	14.6089i	−0.258877	+	0.356314i	0.659718	+	0.751513i	$0.270676\pi$
$42$	−0.249224	−	0.767031i	−0.00593390	−	0.0182627i
$43$			34.7931i			0.809141i	0.914507	+	0.404571i	$0.132579\pi$
$43$			34.7931i			0.809141i	−0.914507	+	0.404571i	$0.867421\pi$
$44$	−36.6140	+	10.8702i	−0.832136	+	0.247049i
$45$		0			0
$46$	19.0836	−	6.20063i	0.414861	−	0.134796i
$47$	38.4230	+	27.9159i	0.817510	+	0.593956i	0.915998	−	0.401182i	$-0.131401\pi$
$47$	38.4230	+	27.9159i	0.817510	+	0.593956i	−0.0984879	+	0.995138i	$0.531401\pi$
$48$	−32.1803	+	23.3804i	−0.670424	+	0.487091i
$49$	15.1180	−	46.5285i	0.308531	−	0.949562i
$50$		0			0
$51$	−47.6393	−	65.5699i	−0.934104	−	1.28568i
$52$	23.0755	−	31.7606i	0.443759	−	0.610782i
$53$	−12.8475	−	39.5406i	−0.242406	−	0.746049i	−0.996052	−	0.0887689i	$-0.971707\pi$
$53$	−12.8475	−	39.5406i	−0.242406	−	0.746049i	0.753646	−	0.657280i	$-0.228293\pi$
$54$			5.81234i			0.107636i
$55$		0			0
$56$	−1.50658			−0.0269032
$57$	−109.846	+	35.6911i	−1.92712	+	0.626160i
$58$	10.2016	+	7.41192i	0.175890	+	0.127792i
$59$	−82.3115	+	59.8028i	−1.39511	+	1.01361i	−0.399828	+	0.916590i	$0.630930\pi$
$59$	−82.3115	+	59.8028i	−1.39511	+	1.01361i	−0.995283	+	0.0970170i	$0.969070\pi$
$60$		0			0
$61$	48.4164	+	15.7314i	0.793712	+	0.257893i	0.677684	−	0.735353i	$-0.262984\pi$
$61$	48.4164	+	15.7314i	0.793712	+	0.257893i	0.116028	+	0.993246i	$0.462984\pi$
$62$	14.6738	+	20.1967i	0.236674	+	0.325753i
$63$	−1.14183	+	1.57160i	−0.0181243	+	0.0249460i
$64$	5.79431	+	17.8330i	0.0905361	+	0.278641i
$65$		0			0
$66$	−25.3738	−	19.4451i	−0.384452	−	0.294623i
$67$	−40.1803			−0.599707			−0.299853	−	0.953985i	$-0.596938\pi$
$67$	−40.1803			−0.599707			−0.299853	+	0.953985i	$0.596938\pi$
$68$	−66.9098	+	21.7403i	−0.983968	+	0.319711i
$69$	−89.3738	−	64.9339i	−1.29527	−	0.941071i
$70$		0			0
$71$	8.70820	−	26.8011i	0.122651	−	0.377480i	−0.870815	−	0.491611i	$-0.836408\pi$
$71$	8.70820	−	26.8011i	0.122651	−	0.377480i	0.993466	+	0.114131i	$0.0364083\pi$
$72$	−36.1418	−	11.7432i	−0.501970	−	0.163100i
$73$	58.6656	+	80.7463i	0.803639	+	1.10611i	0.992274	+	0.124067i	$0.0395937\pi$
$73$	58.6656	+	80.7463i	0.803639	+	1.10611i	−0.188635	+	0.982047i	$0.560406\pi$
$74$	5.66718	−	7.80021i	0.0765836	−	0.105408i
$75$		0			0
$76$			100.257i			1.31917i
$77$	0.868810	+	2.92641i	0.0112833	+	0.0380054i
$78$	32.8591			0.421271
$79$	−125.172	+	40.6709i	−1.58446	+	0.514822i	−0.963200	−	0.268784i	$-0.913378\pi$
$79$	−125.172	+	40.6709i	−1.58446	+	0.514822i	−0.621258	+	0.783606i	$0.713378\pi$
$80$		0			0
$81$	76.8566	−	55.8396i	0.948847	−	0.689378i
$82$	−4.05418	+	12.4775i	−0.0494412	+	0.152164i
$83$	119.271	+	38.7533i	1.43699	+	0.466908i	0.920959	−	0.389660i	$-0.127407\pi$
$83$	119.271	+	38.7533i	1.43699	+	0.466908i	0.516035	+	0.856567i	$0.327407\pi$
$84$	2.26548	+	3.11817i	0.0269701	+	0.0371211i
$85$		0			0
$86$	7.81153	+	24.0414i	0.0908317	+	0.279551i
$87$		−	69.4242i		−	0.797979i
$88$	−49.1935	+	33.8545i	−0.559017	+	0.384710i
$89$	88.9493			0.999430			0.499715	−	0.866190i	$-0.333438\pi$
$89$	88.9493			0.999430			0.499715	+	0.866190i	$0.333438\pi$
$90$		0			0
$91$	−2.53851	−	1.84433i	−0.0278957	−	0.0202674i
$92$	−77.5795	+	56.3648i	−0.843256	+	0.612661i
$93$	42.4721	−	130.716i	0.456690	−	1.40555i
$94$	32.8171	+	10.6629i	0.349119	+	0.113436i
$95$		0			0
$96$	−68.0426	+	93.6526i	−0.708777	+	0.975548i
$97$	−14.9311	−	45.9533i	−0.153929	−	0.473745i	0.844122	−	0.536152i	$-0.180122\pi$
$97$	−14.9311	−	45.9533i	−0.153929	−	0.473745i	−0.998051	+	0.0624067i	$0.980122\pi$
$98$		−	35.5446i		−	0.362700i
$99$	−1.96807	+	76.9748i	−0.0198795	+	0.777524i
$100$		0			0
$101$	36.5836	−	11.8867i	0.362214	−	0.117690i	−0.122256	−	0.992499i	$-0.539013\pi$
$101$	36.5836	−	11.8867i	0.362214	−	0.117690i	0.484469	+	0.874808i	$0.339013\pi$
$102$	−47.6393	−	34.6120i	−0.467052	−	0.339333i
$103$	102.075	−	74.1622i	0.991024	−	0.720021i	0.0308788	−	0.999523i	$-0.490169\pi$
$103$	102.075	−	74.1622i	0.991024	−	0.720021i	0.960145	+	0.279502i	$0.0901694\pi$
$104$	18.9681	−	58.3777i	0.182385	−	0.561324i
$105$		0			0
$106$	−17.7548	−	24.4374i	−0.167499	−	0.230542i
$107$	−51.5542	+	70.9582i	−0.481815	+	0.663161i	−0.978852	−	0.204568i	$-0.934421\pi$
$107$	−51.5542	+	70.9582i	−0.481815	+	0.663161i	0.497038	+	0.867729i	$0.334421\pi$
$108$	−8.58359	−	26.4176i	−0.0794777	−	0.244607i
$109$		−	144.692i		−	1.32745i	−0.747978	−	0.663723i	$-0.768975\pi$
$109$		−	144.692i		−	1.32745i	0.747978	−	0.663723i	$-0.231025\pi$
$110$		0			0
$111$	−53.0820			−0.478217
$112$	2.62461	−	0.852788i	0.0234340	−	0.00761418i
$113$	−104.867	−	76.1905i	−0.928029	−	0.674252i	0.0174806	−	0.999847i	$-0.494435\pi$
$113$	−104.867	−	76.1905i	−0.928029	−	0.674252i	−0.945509	+	0.325595i	$0.894435\pi$
$114$	−67.8885	+	49.3239i	−0.595514	+	0.432666i
$115$		0			0
$116$	−57.3131	−	18.6221i	−0.494078	−	0.160536i
$117$	−46.5213	−	64.0311i	−0.397618	−	0.547274i
$118$	−43.4493	+	59.8028i	−0.368214	+	0.506804i
$119$	1.73762	+	5.34785i	0.0146019	+	0.0449399i
$120$		0			0
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$	36.9868			0.303171
$123$	68.6950	−	22.3204i	0.558496	−	0.181466i
$124$	−96.5197	−	70.1257i	−0.778385	−	0.565530i
$125$		0			0
$126$	−0.436141	+	1.34230i	−0.00346144	+	0.0106532i
$127$	146.655	+	47.6511i	1.15476	+	0.375205i	0.822936	−	0.568134i	$-0.192335\pi$
$127$	146.655	+	47.6511i	1.15476	+	0.375205i	0.331828	+	0.943340i	$0.392335\pi$
$128$	76.0501	+	104.674i	0.594141	+	0.817766i
$129$	81.8034	−	112.593i	0.634135	−	0.872812i
$130$		0			0
$131$		−	128.496i		−	0.980883i	−0.871474	−	0.490442i	$-0.836836\pi$
$131$		−	128.496i		−	0.980883i	0.871474	−	0.490442i	$-0.163164\pi$
$132$	144.043	+	50.9080i	1.09123	+	0.385667i
$133$	8.01316			0.0602493
$134$	−27.7639	+	9.02105i	−0.207194	+	0.0673213i
$135$		0			0
$136$	−88.9919	+	64.6564i	−0.654352	+	0.475415i
$137$	19.1378	−	58.9000i	0.139692	−	0.429927i	−0.856599	−	0.515984i	$-0.827427\pi$
$137$	19.1378	−	58.9000i	0.139692	−	0.429927i	0.996290	+	0.0860566i	$0.0274266\pi$
$138$	−76.3344	−	24.8025i	−0.553148	−	0.179729i
$139$	134.155	+	184.649i	0.965144	+	1.32841i	0.944462	+	0.328620i	$0.106584\pi$
$139$	134.155	+	184.649i	0.965144	+	1.32841i	0.0206817	+	0.999786i	$0.493416\pi$
$140$		0			0
$141$	−58.7051	−	180.676i	−0.416348	−	1.28139i
$142$		−	20.4742i		−	0.144185i
$143$	−124.333	−	3.17891i	−0.869460	−	0.0222301i
$144$	69.6099			0.483402
$145$		0			0
$146$	58.6656	+	42.6231i	0.401819	+	0.291939i
$147$	−158.318	+	115.025i	−1.07699	+	0.782482i
$148$	−14.2386	+	43.8218i	−0.0962066	+	0.296094i
$149$	−74.8460	−	24.3189i	−0.502322	−	0.163214i	0.0468856	−	0.998900i	$-0.485070\pi$
$149$	−74.8460	−	24.3189i	−0.502322	−	0.163214i	−0.549208	+	0.835686i	$0.685070\pi$
$150$		0			0
$151$	41.7852	−	57.5124i	0.276723	−	0.380877i	−0.647922	−	0.761707i	$-0.724362\pi$
$151$	41.7852	−	57.5124i	0.276723	−	0.380877i	0.924645	+	0.380830i	$0.124362\pi$
$152$	48.4402	+	149.084i	0.318686	+	0.980813i
$153$			141.835i			0.927029i
$154$	1.25735	+	1.82704i	0.00816464	+	0.0118639i
$155$		0			0
$156$	−149.348	+	48.5260i	−0.957356	+	0.311064i
$157$	−173.730	−	126.223i	−1.10656	−	0.803965i	−0.124444	−	0.992227i	$-0.539715\pi$
$157$	−173.730	−	126.223i	−1.10656	−	0.803965i	−0.982119	+	0.188261i	$0.939715\pi$
$158$	−77.3607	+	56.2058i	−0.489625	+	0.355733i
$159$	−51.3901	+	158.162i	−0.323208	+	0.994732i
$160$		0			0
$161$	4.50502	+	6.20063i	0.0279815	+	0.0385133i
$162$	40.5698	−	55.8396i	0.250431	−	0.344689i
$163$	28.1753	+	86.7147i	0.172855	+	0.531992i	0.999529	−	0.0306887i	$-0.00977005\pi$
$163$	28.1753	+	86.7147i	0.172855	+	0.531992i	−0.826674	+	0.562681i	$0.809770\pi$
$164$		−	62.6983i		−	0.382307i
$165$		0			0
$166$	91.1146			0.548883
$167$	−43.1910	+	14.0336i	−0.258629	+	0.0840335i	−0.435461	−	0.900207i	$-0.643415\pi$
$167$	−43.1910	+	14.0336i	−0.258629	+	0.0840335i	0.176833	+	0.984241i	$0.443415\pi$
$168$	4.87539	+	3.54218i	0.0290202	+	0.0210844i
$169$	−33.2984	+	24.1927i	−0.197032	+	0.143152i
$170$		0			0
$171$	192.230	+	62.4595i	1.12415	+	0.365260i
$172$	−71.0081	−	97.7343i	−0.412838	−	0.568223i
$173$	89.0780	−	122.605i	0.514902	−	0.708701i	−0.469835	−	0.882754i	$-0.655686\pi$
$173$	89.0780	−	122.605i	0.514902	−	0.708701i	0.984736	+	0.174053i	$0.0556865\pi$
$174$	−15.5867	−	47.9709i	−0.0895787	−	0.275695i
$175$		0			0
$176$	66.5370	−	86.8237i	0.378051	−	0.493316i
$177$	406.971			2.29927
$178$	61.4625	−	19.9704i	0.345295	−	0.112193i
$179$	137.932	+	100.214i	0.770570	+	0.559852i	0.902134	−	0.431456i	$-0.142000\pi$
$179$	137.932	+	100.214i	0.770570	+	0.559852i	−0.131564	+	0.991308i	$0.542000\pi$
$180$		0			0
$181$	−51.2918	+	157.860i	−0.283380	+	0.872154i	0.703499	+	0.710696i	$0.251620\pi$
$181$	−51.2918	+	157.860i	−0.283380	+	0.872154i	−0.986880	+	0.161458i	$0.948380\pi$
$182$	−2.16814	−	0.704473i	−0.0119129	−	0.00387073i
$183$	−119.692	−	164.742i	−0.654054	−	0.900229i
$184$	−88.1287	+	121.299i	−0.478960	+	0.659232i
$185$		0			0
$186$		−	99.8580i		−	0.536871i
$187$	176.910	+	135.574i	0.946042	+	0.724995i
$188$	−164.904			−0.877147
$189$	−2.11146	+	0.686054i	−0.0111717	+	0.00362991i
$190$		0			0
$191$	−9.05573	+	6.57937i	−0.0474122	+	0.0344470i	−0.611239	−	0.791446i	$-0.709329\pi$
$191$	−9.05573	+	6.57937i	−0.0474122	+	0.0344470i	0.563827	+	0.825893i	$0.309329\pi$
$192$	23.1772	−	71.3322i	0.120715	−	0.371522i
$193$	−119.472	−	38.8189i	−0.619027	−	0.201134i	−0.0173185	−	0.999850i	$-0.505513\pi$
$193$	−119.472	−	38.8189i	−0.619027	−	0.201134i	−0.601708	+	0.798716i	$0.705513\pi$
$194$	−20.6343	−	28.4007i	−0.106362	−	0.146395i
$195$		0			0
$196$	52.4919	+	161.553i	0.267816	+	0.824252i
$197$		−	361.517i		−	1.83511i	−0.397607	−	0.917556i	$-0.630159\pi$
$197$		−	361.517i		−	1.83511i	0.397607	−	0.917556i	$-0.369841\pi$
$198$	15.9220	+	53.6302i	0.0804143	+	0.270859i
$199$	267.692			1.34519			0.672593	−	0.740013i	$-0.265181\pi$
$199$	267.692			1.34519			0.672593	+	0.740013i	$0.265181\pi$
$200$		0			0
$201$	130.026	+	94.4696i	0.646897	+	0.469998i
$202$	22.6099	−	16.4271i	0.111930	−	0.0813221i
$203$	−1.48840	+	4.58082i	−0.00733201	+	0.0225656i
$204$	267.639	+	86.9613i	1.31196	+	0.426281i
$205$		0			0
$206$	53.8820	−	74.1622i	0.261563	−	0.360011i
$207$	59.7411	+	183.864i	0.288604	+	0.888233i
$208$			112.437i			0.540561i
$209$	261.649	−	180.065i	1.25191	−	0.861554i
$210$		0			0
$211$	−214.971	+	69.8482i	−1.01882	+	0.331034i	−0.770360	−	0.637609i	$-0.779924\pi$
$211$	−214.971	+	69.8482i	−1.01882	+	0.331034i	−0.248458	+	0.968643i	$0.579924\pi$
$212$	116.786	+	84.8501i	0.550878	+	0.400236i
$213$	−91.1935	+	66.2560i	−0.428138	+	0.311061i
$214$	−19.6919	+	60.6056i	−0.0920184	+	0.283204i
$215$		0			0
$216$	−25.5279	−	35.1361i	−0.118185	−	0.162667i
$217$	−5.60488	+	7.71445i	−0.0258289	+	0.0355505i
$218$	−32.4853	−	99.9794i	−0.149015	−	0.458621i
$219$		−	399.232i		−	1.82298i
$220$		0			0
$221$	−229.098			−1.03664
$222$	−36.6788	+	11.9177i	−0.165220	+	0.0536832i
$223$	226.619	+	164.648i	1.01623	+	0.738333i	0.965506	−	0.260379i	$-0.0838477\pi$
$223$	226.619	+	164.648i	1.01623	+	0.738333i	0.0507223	+	0.998713i	$0.483848\pi$
$224$	6.49749	−	4.72070i	0.0290066	−	0.0210746i
$225$		0			0
$226$	−89.5673	−	29.1022i	−0.396316	−	0.128771i
$227$	−51.2392	−	70.5247i	−0.225723	−	0.310681i	0.681102	−	0.732189i	$-0.261501\pi$
$227$	−51.2392	−	70.5247i	−0.225723	−	0.310681i	−0.906825	+	0.421507i	$0.861501\pi$
$228$	235.718	−	324.438i	1.03385	−	1.42298i
$229$	33.1722	+	102.094i	0.144857	+	0.445823i	0.996993	−	0.0774974i	$-0.0246929\pi$
$229$	33.1722	+	102.094i	0.144857	+	0.445823i	−0.852136	+	0.523321i	$0.824693\pi$
$230$		0			0
$231$	4.06888	−	11.5128i	0.0176142	−	0.0498388i
$232$	−94.2229			−0.406133
$233$	125.326	−	40.7210i	0.537881	−	0.174768i	−0.0274639	−	0.999623i	$-0.508743\pi$
$233$	125.326	−	40.7210i	0.537881	−	0.174768i	0.565345	+	0.824855i	$0.308743\pi$
$234$	−46.5213	−	33.7997i	−0.198809	−	0.144443i
$235$		0			0
$236$	109.165	−	335.974i	0.462562	−	1.42362i
$237$	500.689	+	162.684i	2.11261	+	0.686429i
$238$	2.40133	+	3.30515i	0.0100896	+	0.0138872i
$239$	−54.0983	+	74.4599i	−0.226353	+	0.311548i	−0.907055	−	0.421013i	$-0.861675\pi$
$239$	−54.0983	+	74.4599i	−0.226353	+	0.311548i	0.680702	+	0.732560i	$0.261675\pi$
$240$		0			0
$241$			26.5140i			0.110017i	0.998486	+	0.0550083i	$0.0175185\pi$
$241$			26.5140i			0.110017i	−0.998486	+	0.0550083i	$0.982481\pi$
$242$	82.1115	+	31.4033i	0.339304	+	0.129766i
$243$	−308.000			−1.26749
$244$	−168.108	+	54.6217i	−0.688969	+	0.223859i
$245$		0			0
$246$	42.4559	−	30.8460i	0.172585	−	0.125390i
$247$	−100.887	+	310.498i	−0.408449	+	1.25708i
$248$	−177.408	−	57.6434i	−0.715356	−	0.232433i
$249$	−294.853	−	405.830i	−1.18415	−	1.62984i
$250$		0			0
$251$	−41.7279	−	128.425i	−0.166247	−	0.511655i	0.832879	−	0.553455i	$-0.186691\pi$
$251$	−41.7279	−	128.425i	−0.166247	−	0.511655i	−0.999126	+	0.0417998i	$0.986691\pi$
$252$		−	6.74498i		−	0.0267658i
$253$	286.436	+	101.233i	1.13216	+	0.400131i
$254$	112.034			0.441080
$255$		0			0
$256$	15.3713	+	11.1679i	0.0600442	+	0.0436247i
$257$	−197.636	+	143.591i	−0.769013	+	0.558720i	−0.901661	−	0.432443i	$-0.857652\pi$
$257$	−197.636	+	143.591i	−0.769013	+	0.558720i	0.132649	+	0.991163i	$0.457652\pi$
$258$	31.2461	−	96.1657i	0.121109	−	0.372735i
$259$	3.50251	+	1.13804i	0.0135232	+	0.00439396i
$260$		0			0
$261$	−71.4114	+	98.2893i	−0.273607	+	0.376587i
$262$	−28.8491	−	88.7883i	−0.110111	−	0.338887i
$263$			1.93304i			0.00734998i	0.999993	+	0.00367499i	$0.00116979\pi$
$263$			1.93304i			0.00734998i	−0.999993	+	0.00367499i	$0.998830\pi$
$264$	238.790	+	6.10532i	0.904508	+	0.0231262i
$265$		0			0
$266$	5.53695	−	1.79907i	0.0208156	−	0.00676340i
$267$	−287.846	−	209.132i	−1.07807	−	0.783267i
$268$	112.867	−	82.0029i	0.421146	−	0.305981i
$269$	−56.6149	+	174.243i	−0.210464	+	0.647743i	0.788980	+	0.614419i	$0.210609\pi$
$269$	−56.6149	+	174.243i	−0.210464	+	0.647743i	−0.999445	+	0.0333242i	$0.989391\pi$
$270$		0			0
$271$	298.339	+	410.629i	1.10088	+	1.51524i	0.834208	+	0.551449i	$0.185925\pi$
$271$	298.339	+	410.629i	1.10088	+	1.51524i	0.266675	+	0.963786i	$0.414075\pi$
$272$	118.435	−	163.011i	0.435421	−	0.599306i
$273$	3.87849	+	11.9368i	0.0142069	+	0.0437245i
$274$		−	44.9956i		−	0.164217i
$275$		0			0
$276$	383.574			1.38976
$277$	−33.6985	+	10.9493i	−0.121655	+	0.0395282i	−0.369212	−	0.929345i	$-0.620372\pi$
$277$	−33.6985	+	10.9493i	−0.121655	+	0.0395282i	0.247557	+	0.968873i	$0.420372\pi$
$278$	134.155	+	97.4693i	0.482572	+	0.350609i
$279$	−194.589	+	141.377i	−0.697450	+	0.506727i
$280$		0			0
$281$	−325.066	−	105.620i	−1.15682	−	0.375873i	−0.333110	−	0.942888i	$-0.608098\pi$
$281$	−325.066	−	105.620i	−1.15682	−	0.375873i	−0.823707	+	0.567015i	$0.808098\pi$
$282$	−81.1285	−	111.664i	−0.287690	−	0.395971i
$283$	−243.002	+	334.463i	−0.858664	+	1.18185i	0.123222	+	0.992379i	$0.460677\pi$
$283$	−243.002	+	334.463i	−0.858664	+	1.18185i	−0.981886	+	0.189471i	$0.939323\pi$
$284$	30.2361	+	93.0570i	0.106465	+	0.327666i
$285$		0			0
$286$	−86.6256	+	25.7179i	−0.302887	+	0.0899227i
$287$	−5.01124			−0.0174608
$288$	192.667	−	62.6012i	0.668981	−	0.217365i
$289$	98.3419	+	71.4496i	0.340283	+	0.247230i
$290$		0			0
$291$	−59.7245	+	183.813i	−0.205239	+	0.631660i
$292$	−329.586	−	107.089i	−1.12872	−	0.366743i
$293$	−113.360	−	156.026i	−0.386893	−	0.532513i	0.570501	−	0.821297i	$-0.306749\pi$
$293$	−113.360	−	156.026i	−0.386893	−	0.532513i	−0.957394	+	0.288784i	$0.906749\pi$
$294$	−83.5704	+	115.025i	−0.284253	+	0.391241i
$295$		0			0
$296$			72.0433i			0.243389i
$297$	−53.5279	+	69.8482i	−0.180228	+	0.235179i
$298$	−57.1772			−0.191870
$299$	−296.985	+	96.4962i	−0.993260	+	0.322730i
$300$		0			0
$301$	−7.81153	+	5.67541i	−0.0259519	+	0.0188552i
$302$	15.9605	−	49.1215i	0.0528494	−	0.162654i
$303$	−146.334	−	47.5469i	−0.482952	−	0.156921i
$304$	−168.776	−	232.300i	−0.555183	−	0.764143i
$305$		0			0
$306$	31.8441	+	98.0059i	0.104066	+	0.320281i
$307$		−	335.115i		−	1.09158i	−0.837922	−	0.545790i	$-0.816230\pi$
$307$		−	335.115i		−	1.09158i	0.837922	−	0.545790i	$-0.183770\pi$
$308$	−8.41294	−	6.44722i	−0.0273147	−	0.0209325i
$309$	−504.689			−1.63330
$310$		0			0
$311$	−175.687	−	127.644i	−0.564910	−	0.410431i	0.268343	−	0.963323i	$-0.413524\pi$
$311$	−175.687	−	127.644i	−0.564910	−	0.410431i	−0.833253	+	0.552893i	$0.813524\pi$
$312$	−198.636	+	144.318i	−0.636655	+	0.462557i
$313$	−183.753	+	565.533i	−0.587069	+	1.80681i	0.00372731	+	0.999993i	$0.498814\pi$
$313$	−183.753	+	565.533i	−0.587069	+	1.80681i	−0.590797	+	0.806821i	$0.701186\pi$
$314$	−148.384	−	48.2127i	−0.472559	−	0.153544i
$315$		0			0
$316$	268.607	−	369.706i	0.850022	−	1.16995i
$317$	22.1860	+	68.2814i	0.0699872	+	0.215399i	0.979932	−	0.199330i	$-0.0638765\pi$
$317$	22.1860	+	68.2814i	0.0699872	+	0.215399i	−0.909945	+	0.414729i	$0.863877\pi$
$318$			120.825i			0.379954i
$319$	54.3363	+	183.021i	0.170333	+	0.573733i
$320$		0			0
$321$	333.666	−	108.415i	1.03946	−	0.337740i
$322$	4.50502	+	3.27309i	0.0139908	+	0.0101649i
$323$	473.328	−	343.893i	1.46541	−	1.06468i
$324$	−101.930	+	313.709i	−0.314599	+	0.968237i
$325$		0			0
$326$	38.9373	+	53.5926i	0.119440	+	0.164395i
$327$	−340.190	+	468.232i	−1.04034	+	1.43190i
$328$	−30.2933	−	93.2333i	−0.0923578	−	0.284248i
$329$			13.1801i			0.0400611i
$330$		0			0
$331$	−292.681			−0.884232			−0.442116	−	0.896958i	$-0.645772\pi$
$331$	−292.681			−0.884232			−0.442116	+	0.896958i	$0.645772\pi$
$332$	−414.123	+	134.557i	−1.24736	+	0.405292i
$333$	75.1525	+	54.6015i	0.225683	+	0.163968i
$334$	−26.6935	+	19.3940i	−0.0799206	+	0.0580657i
$335$		0			0
$336$	−10.4984	−	3.41115i	−0.0312454	−	0.0101522i
$337$	−230.410	−	317.132i	−0.683710	−	0.941046i	0.316261	−	0.948672i	$-0.397572\pi$
$337$	−230.410	−	317.132i	−0.683710	−	0.941046i	−0.999971	+	0.00762639i	$0.997572\pi$
$338$	−17.5770	+	24.1927i	−0.0520030	+	0.0715760i
$339$	160.223	+	493.115i	0.472634	+	1.45462i
$340$		0			0
$341$	−9.66061	+	377.844i	−0.0283302	+	1.10805i
$342$	146.851			0.429389
$343$	25.8450	−	8.39755i	0.0753499	−	0.0244827i
$344$	−152.812	−	111.024i	−0.444220	−	0.322744i
$345$		0			0
$346$	34.0248	−	104.717i	0.0983375	−	0.302652i
$347$	−60.4984	−	19.6571i	−0.174347	−	0.0566488i	0.220543	−	0.975377i	$-0.429217\pi$
$347$	−60.4984	−	19.6571i	−0.174347	−	0.0566488i	−0.394890	+	0.918729i	$0.629217\pi$
$348$	141.686	+	195.014i	0.407143	+	0.560384i
$349$	144.289	−	198.596i	0.413435	−	0.569044i	−0.550617	−	0.834758i	$-0.685608\pi$
$349$	144.289	−	198.596i	0.413435	−	0.569044i	0.964052	+	0.265714i	$0.0856076\pi$
$350$		0			0
$351$		−	90.4534i		−	0.257702i
$352$	106.080	−	300.149i	0.301362	−	0.852695i
$353$	−216.535			−0.613413			−0.306707	−	0.951804i	$-0.599227\pi$
$353$	−216.535			−0.613413			−0.306707	+	0.951804i	$0.599227\pi$
$354$	281.210	−	91.3706i	0.794378	−	0.258109i
$355$		0			0
$356$	−249.860	+	181.534i	−0.701854	+	0.509927i
$357$	6.95048	−	21.3914i	0.0194691	−	0.0599199i
$358$	117.808	+	38.2782i	0.329073	+	0.106922i
$359$	−401.418	−	552.505i	−1.11816	−	1.53901i	−0.808818	−	0.588059i	$-0.799892\pi$
$359$	−401.418	−	552.505i	−1.11816	−	1.53901i	−0.309339	−	0.950952i	$-0.600108\pi$
$360$		0			0
$361$	−146.088	−	449.612i	−0.404675	−	1.24546i
$362$			120.594i			0.333133i
$363$	−125.846	−	467.353i	−0.346683	−	1.28747i
$364$	10.8948			0.0299306
$365$		0			0
$366$	−119.692	−	86.9613i	−0.327027	−	0.237599i
$367$	59.6180	−	43.3150i	0.162447	−	0.118025i	−0.503592	−	0.863942i	$-0.667988\pi$
$367$	59.6180	−	43.3150i	0.162447	−	0.118025i	0.666039	+	0.745917i	$0.267988\pi$
$368$	84.8688	−	261.199i	0.230622	−	0.709781i
$369$	−120.216	−	39.0607i	−0.325790	−	0.105855i
$370$		0			0
$371$	6.78175	−	9.33427i	0.0182796	−	0.0251598i
$372$	147.469	+	453.863i	0.396422	+	1.22006i
$373$			58.3795i			0.156514i	0.996933	+	0.0782568i	$0.0249354\pi$
$373$			58.3795i			0.156514i	−0.996933	+	0.0782568i	$0.975065\pi$
$374$	152.680	+	53.9607i	0.408235	+	0.144280i
$375$		0			0
$376$	−245.214	+	79.6749i	−0.652165	+	0.211901i
$377$	−158.761	−	115.346i	−0.421116	−	0.305959i
$378$	−1.30495	+	0.948103i	−0.00345225	+	0.00250821i
$379$	−57.9346	+	178.304i	−0.152862	+	0.470460i	−0.997938	−	0.0641858i	$-0.979555\pi$
$379$	−57.9346	+	178.304i	−0.152862	+	0.470460i	0.845076	+	0.534646i	$0.179555\pi$
$380$		0			0
$381$	−362.551	−	499.009i	−0.951578	−	1.30973i
$382$	−4.78019	+	6.57937i	−0.0125136	+	0.0172235i
$383$	1.89202	+	5.82303i	0.00493999	+	0.0152037i	0.953496	−	0.301405i	$-0.0974557\pi$
$383$	1.89202	+	5.82303i	0.00493999	+	0.0152037i	−0.948556	+	0.316609i	$0.897456\pi$
$384$		−	517.537i		−	1.34775i
$385$		0			0
$386$	−91.2686			−0.236447
$387$	−231.631	+	75.2615i	−0.598530	+	0.194474i
$388$	135.726	+	98.6110i	0.349810	+	0.254152i
$389$	182.923	−	132.901i	0.470239	−	0.341649i	−0.327295	−	0.944922i	$-0.606137\pi$
$389$	182.923	−	132.901i	0.470239	−	0.341649i	0.797534	+	0.603273i	$0.206137\pi$
$390$		0			0
$391$	532.214	+	172.927i	1.36116	+	0.442268i
$392$	156.112	+	214.870i	0.398246	+	0.548139i
$393$	−302.111	+	415.821i	−0.768731	+	1.05807i
$394$	−81.1656	−	249.802i	−0.206004	−	0.634016i
$395$		0			0
$396$	−151.567	−	220.240i	−0.382746	−	0.556162i
$397$	215.123			0.541873			0.270936	−	0.962597i	$-0.412667\pi$
$397$	215.123			0.541873			0.270936	+	0.962597i	$0.412667\pi$
$398$	184.971	−	60.1006i	0.464750	−	0.151006i
$399$	−25.9311	−	18.8401i	−0.0649903	−	0.0472182i
$400$		0			0
$401$	−167.199	+	514.586i	−0.416955	+	1.28326i	0.493535	+	0.869726i	$0.335705\pi$
$401$	−167.199	+	514.586i	−0.416955	+	1.28326i	−0.910490	+	0.413531i	$0.864295\pi$
$402$	111.056	+	36.0842i	0.276258	+	0.0897617i
$403$	−228.358	−	314.307i	−0.566644	−	0.779919i
$404$	−78.5047	+	108.052i	−0.194318	+	0.267456i
$405$		0			0
$406$			3.49943i			0.00861929i
$407$	139.939	−	41.5458i	0.343830	−	0.102078i
$408$	440.000			1.07843
$409$	348.785	−	113.327i	0.852774	−	0.277083i	0.150167	−	0.988661i	$-0.452019\pi$
$409$	348.785	−	113.327i	0.852774	−	0.277083i	0.702608	+	0.711578i	$0.252019\pi$
$410$		0			0
$411$	−200.413	+	145.609i	−0.487624	+	0.354279i
$412$	−135.376	+	416.646i	−0.328583	+	1.01128i
$413$	−26.8531	−	8.72511i	−0.0650197	−	0.0211262i
$414$	82.5602	+	113.634i	0.199421	+	0.274479i
$415$		0			0
$416$	101.116	+	311.203i	0.243067	+	0.748083i
$417$		−	912.952i		−	2.18933i
$418$	140.368	−	183.166i	0.335809	−	0.438195i
$419$	164.543			0.392704			0.196352	−	0.980533i	$-0.437090\pi$
$419$	164.543			0.392704			0.196352	+	0.980533i	$0.437090\pi$
$420$		0			0
$421$	−97.2887	−	70.6844i	−0.231090	−	0.167896i	0.466215	−	0.884672i	$-0.345617\pi$
$421$	−97.2887	−	70.6844i	−0.231090	−	0.167896i	−0.697304	+	0.716775i	$0.745617\pi$
$422$	−132.859	+	96.5278i	−0.314832	+	0.228739i
$423$	−102.734	+	316.183i	−0.242870	+	0.747476i
$424$	214.659	+	69.7470i	0.506271	+	0.164498i
$425$		0			0
$426$	−48.1378	+	66.2560i	−0.112999	+	0.155530i
$427$	4.36570	+	13.4363i	0.0102241	+	0.0314666i
$428$		−	304.538i		−	0.711538i
$429$	394.875	+	302.611i	0.920455	+	0.705387i
$430$		0			0
$431$	514.135	−	167.052i	1.19289	−	0.387593i	0.355748	−	0.934582i	$-0.384226\pi$
$431$	514.135	−	167.052i	1.19289	−	0.387593i	0.837140	+	0.546989i	$0.184226\pi$
$432$	64.3607	+	46.7608i	0.148983	+	0.108243i
$433$	172.618	−	125.414i	0.398656	−	0.289641i	−0.370337	−	0.928897i	$-0.620758\pi$
$433$	172.618	−	125.414i	0.398656	−	0.289641i	0.768993	+	0.639257i	$0.220758\pi$
$434$	−2.14087	+	6.58893i	−0.00493289	+	0.0151819i
$435$		0			0
$436$	295.297	+	406.441i	0.677286	+	0.932205i
$437$	468.737	−	645.161i	1.07262	−	1.47634i
$438$	−89.6331	−	275.862i	−0.204642	−	0.629823i
$439$		−	29.8597i		−	0.0680175i	−0.999422	−	0.0340087i	$-0.989173\pi$
$439$		−	29.8597i		−	0.0680175i	0.999422	−	0.0340087i	$-0.0108274\pi$
$440$		0			0
$441$	342.461			0.776555
$442$	−158.303	+	51.4358i	−0.358152	+	0.116371i
$443$	−46.3262	−	33.6580i	−0.104574	−	0.0759774i	0.534269	−	0.845314i	$-0.320587\pi$
$443$	−46.3262	−	33.6580i	−0.104574	−	0.0759774i	−0.638843	+	0.769337i	$0.720587\pi$
$444$	149.108	−	108.334i	0.335830	−	0.243994i
$445$		0			0
$446$	193.556	+	62.8901i	0.433981	+	0.141009i
$447$	185.029	+	254.671i	0.413936	+	0.569734i
$448$	−3.05861	+	4.20981i	−0.00682725	+	0.00939690i
$449$	183.771	+	565.590i	0.409291	+	1.25967i	0.917259	+	0.398291i	$0.130397\pi$
$449$	183.771	+	565.590i	0.409291	+	1.25967i	−0.507968	+	0.861376i	$0.669603\pi$
$450$		0			0
$451$	−163.629	+	112.608i	−0.362814	+	0.249686i
$452$	450.069			0.995728
$453$	−270.440	+	87.8712i	−0.596997	+	0.193976i
$454$	−51.2392	−	37.2274i	−0.112862	−	0.0819988i
$455$		0			0
$456$	193.761	−	596.335i	0.424914	−	1.30775i
$457$	451.899	+	146.831i	0.988837	+	0.321293i	0.758396	−	0.651794i	$-0.225983\pi$
$457$	451.899	+	146.831i	0.988837	+	0.321293i	0.230441	+	0.973086i	$0.425983\pi$
$458$	45.8429	+	63.0973i	0.100094	+	0.137767i
$459$	−95.2786	+	131.140i	−0.207579	+	0.285708i
$460$		0			0
$461$		−	290.362i		−	0.629853i	−0.949116	−	0.314927i	$-0.898020\pi$
$461$		−	290.362i		−	0.629853i	0.949116	−	0.314927i	$-0.101980\pi$
$462$	0.226751	−	8.86865i	0.000490803	−	0.0191962i
$463$	−86.1358			−0.186039			−0.0930193	−	0.995664i	$-0.529652\pi$
$463$	−86.1358			−0.186039			−0.0930193	+	0.995664i	$0.529652\pi$
$464$	164.146	−	53.3342i	0.353763	−	0.114944i
$465$		0			0
$466$	77.4559	−	56.2750i	0.166214	−	0.120762i
$467$	−69.8177	+	214.877i	−0.149503	+	0.460122i	−0.997563	−	0.0697786i	$-0.977771\pi$
$467$	−69.8177	+	214.877i	−0.149503	+	0.460122i	0.848060	+	0.529900i	$0.177771\pi$
$468$	261.358	+	84.9204i	0.558458	+	0.181454i
$469$	−6.55418	−	9.02105i	−0.0139748	−	0.0192346i
$470$		0			0
$471$	265.437	+	816.930i	0.563559	+	1.73446i
$472$		−	552.343i		−	1.17022i
$473$	−127.533	+	360.850i	−0.269626	+	0.762897i
$474$	382.492			0.806946
$475$		0			0
$476$	−15.7953	−	11.4759i	−0.0331833	−	0.0241091i
$477$	235.447	−	171.062i	0.493599	−	0.358621i
$478$	−20.6637	+	63.5964i	−0.0432295	+	0.133047i
$479$	79.9888	+	25.9899i	0.166991	+	0.0542587i	0.391319	−	0.920255i	$-0.372019\pi$
$479$	79.9888	+	25.9899i	0.166991	+	0.0542587i	−0.224328	+	0.974514i	$0.572019\pi$
$480$		0			0
$481$	−88.1945	+	121.389i	−0.183356	+	0.252369i
$482$	5.95277	+	18.3207i	0.0123501	+	0.0380098i
$483$		−	30.6576i		−	0.0634733i
$484$	−419.580	−	21.4694i	−0.866900	−	0.0443583i
$485$		0			0
$486$	−212.823	+	69.1503i	−0.437907	+	0.142285i
$487$	535.336	+	388.945i	1.09925	+	0.798654i	0.980938	−	0.194322i	$-0.0622506\pi$
$487$	535.336	+	388.945i	1.09925	+	0.798654i	0.118315	+	0.992976i	$0.462251\pi$
$488$	−223.589	+	162.447i	−0.458173	+	0.332882i
$489$	112.701	−	346.859i	0.230473	−	0.709323i
$490$		0			0
$491$	−438.057	−	602.934i	−0.892174	−	1.22797i	−0.972898	−	0.231235i	$-0.925723\pi$
$491$	−438.057	−	602.934i	−0.892174	−	1.22797i	0.0807242	−	0.996736i	$-0.474277\pi$
$492$	−147.413	+	202.896i	−0.299619	+	0.412390i
$493$	108.673	+	334.460i	0.220431	+	0.678417i
$494$			237.200i			0.480161i
$495$		0			0
$496$	341.692			0.688895
$497$	7.43769	−	2.41665i	0.0149652	−	0.00486248i
$498$	−294.853	−	214.223i	−0.592074	−	0.430167i
$499$	−224.927	+	163.419i	−0.450756	+	0.327493i	−0.789894	−	0.613243i	$-0.789864\pi$
$499$	−224.927	+	163.419i	−0.450756	+	0.327493i	0.339138	+	0.940736i	$0.389864\pi$
$500$		0			0
$501$	172.764	+	56.1344i	0.344838	+	0.112045i
$502$	−57.6666	−	79.3713i	−0.114874	−	0.158110i
$503$	−158.365	+	217.971i	−0.314842	+	0.433342i	−0.936884	−	0.349642i	$-0.886303\pi$
$503$	−158.365	+	217.971i	−0.314842	+	0.433342i	0.622042	+	0.782984i	$0.286303\pi$
$504$	−3.25891	−	10.0299i	−0.00646609	−	0.0199006i
$505$		0			0
$506$	220.650	+	5.64152i	0.436068	+	0.0111493i
$507$	164.636			0.324726
$508$	−509.206	+	165.451i	−1.00237	+	0.325691i
$509$	−424.177	−	308.183i	−0.833354	−	0.605467i	0.0871522	−	0.996195i	$-0.472223\pi$
$509$	−424.177	−	308.183i	−0.833354	−	0.605467i	−0.920506	+	0.390728i	$0.872223\pi$
$510$		0			0
$511$	−8.55920	+	26.3425i	−0.0167499	+	0.0515509i
$512$	−479.078	−	155.662i	−0.935699	−	0.304027i
$513$	135.777	+	186.881i	0.264673	+	0.364291i
$514$	−104.325	+	143.591i	−0.202967	+	0.279360i
$515$		0			0
$516$			483.225i			0.936483i
$517$	296.172	+	430.363i	0.572867	+	0.832424i
$518$	2.67568			0.00516541
$519$	−576.525	+	187.324i	−1.11084	+	0.360933i
$520$		0			0
$521$	308.640	−	224.240i	0.592400	−	0.430404i	−0.250773	−	0.968046i	$-0.580685\pi$
$521$	308.640	−	224.240i	0.592400	−	0.430404i	0.843173	+	0.537642i	$0.180685\pi$
$522$	−27.2767	+	83.9491i	−0.0522543	+	0.160822i
$523$	−607.503	−	197.390i	−1.16157	−	0.377418i	−0.336083	−	0.941832i	$-0.609102\pi$
$523$	−607.503	−	197.390i	−1.16157	−	0.377418i	−0.825492	+	0.564414i	$0.809102\pi$
$524$	262.243	+	360.947i	0.500464	+	0.688829i
$525$		0			0
$526$	0.433995	+	1.33570i	0.000825086	+	0.00253935i
$527$			696.223i			1.32111i
$528$	−419.453	+	124.529i	−0.794418	+	0.235851i
$529$	233.756			0.441882
$530$		0			0
$531$	−576.181	−	418.620i	−1.08509	−	0.788361i
$532$	−22.5091	+	16.3538i	−0.0423103	+	0.0307402i
$533$	63.0923	−	194.178i	0.118372	−	0.364312i
$534$	−245.850	−	79.8814i	−0.460393	−	0.149591i
$535$		0			0
$536$	128.215	−	176.473i	0.239207	−	0.329240i
$537$	−210.741	−	648.596i	−0.392442	−	1.20781i
$538$			133.110i			0.247416i
$539$	327.343	−	427.148i	0.607315	−	0.792482i
$540$		0			0
$541$	117.236	−	38.0923i	0.216703	−	0.0704109i	−0.198654	−	0.980070i	$-0.563657\pi$
$541$	117.236	−	38.0923i	0.216703	−	0.0704109i	0.415356	+	0.909659i	$0.363657\pi$
$542$	298.339	+	216.756i	0.550442	+	0.399919i
$543$	537.135	−	390.251i	0.989198	−	0.718695i
$544$	181.205	−	557.693i	0.333098	−	1.02517i
$545$		0			0
$546$	5.35995	+	7.37733i	0.00981675	+	0.0135116i
$547$	199.538	−	274.640i	0.364786	−	0.502085i	−0.586688	−	0.809813i	$-0.699569\pi$
$547$	199.538	−	274.640i	0.364786	−	0.502085i	0.951474	+	0.307728i	$0.0995687\pi$
$548$	66.4489	+	204.509i	0.121257	+	0.373191i
$549$			356.356i			0.649100i
$550$		0			0
$551$	501.151			0.909530
$552$	570.381	−	185.328i	1.03330	−	0.335739i
$553$	−29.5492	−	21.4687i	−0.0534343	−	0.0388223i
$554$	−20.8268	+	15.1316i	−0.0375936	+	0.0273133i
$555$		0			0
$556$	−753.687	−	244.888i	−1.35555	−	0.440446i
$557$	310.414	+	427.248i	0.557296	+	0.767052i	0.990980	−	0.134013i	$-0.0427865\pi$
$557$	310.414	+	427.248i	0.557296	+	0.767052i	−0.433684	+	0.901065i	$0.642787\pi$
$558$	−102.716	+	141.377i	−0.184079	+	0.253364i
$559$	−121.565	−	374.140i	−0.217469	−	0.669302i
$560$		0			0
$561$	−253.738	−	854.667i	−0.452297	−	1.52347i
$562$	−248.328			−0.441865
$563$	244.087	−	79.3087i	0.433547	−	0.140868i	−0.0841094	−	0.996457i	$-0.526805\pi$
$563$	244.087	−	79.3087i	0.433547	−	0.140868i	0.517657	+	0.855589i	$0.326805\pi$
$564$	533.639	+	387.712i	0.946169	+	0.687432i
$565$		0			0
$566$	−92.8185	+	285.666i	−0.163990	+	0.504710i
$567$	25.0735	+	8.14689i	0.0442214	+	0.0143684i
$568$	89.9230	+	123.768i	0.158315	+	0.217902i
$569$	146.337	−	201.415i	0.257182	−	0.353981i	−0.660828	−	0.750537i	$-0.729795\pi$
$569$	146.337	−	201.415i	0.257182	−	0.353981i	0.918010	+	0.396556i	$0.129795\pi$
$570$		0			0
$571$		−	393.435i		−	0.689028i	−0.938781	−	0.344514i	$-0.888044\pi$
$571$		−	393.435i		−	0.689028i	0.938781	−	0.344514i	$-0.111956\pi$
$572$	355.741	−	244.818i	0.621924	−	0.428003i
$573$	44.7740			0.0781396
$574$	−3.46268	+	1.12509i	−0.00603254	+	0.00196009i
$575$		0			0
$576$	−106.188	+	77.1500i	−0.184354	+	0.133941i
$577$	−76.8228	+	236.436i	−0.133142	+	0.409768i	−0.995296	−	0.0968772i	$-0.969115\pi$
$577$	−76.8228	+	236.436i	−0.133142	+	0.409768i	0.862155	+	0.506645i	$0.169115\pi$
$578$	83.9940	+	27.2913i	0.145318	+	0.0472168i
$579$	295.351	+	406.516i	0.510106	+	0.702101i
$580$		0			0
$581$	10.7546	+	33.0993i	0.0185105	+	0.0569695i
$582$			140.421i			0.241273i
$583$	11.6891	−	457.181i	0.0200499	−	0.784186i
$584$	−541.840			−0.927808
$585$		0			0
$586$	−113.360	−	82.3607i	−0.193447	−	0.140547i
$587$	−308.959	+	224.472i	−0.526336	+	0.382406i	−0.818986	−	0.573814i	$-0.805463\pi$
$587$	−308.959	+	224.472i	−0.526336	+	0.382406i	0.292649	+	0.956220i	$0.405463\pi$
$588$	209.967	−	646.213i	0.357088	−	1.09900i
$589$	943.596	+	306.593i	1.60203	+	0.520531i
$590$		0			0
$591$	−849.978	+	1169.89i	−1.43820	+	1.97952i
$592$	−40.7796	−	125.507i	−0.0688845	−	0.212005i
$593$			467.858i			0.788968i	0.918903	+	0.394484i	$0.129077\pi$
$593$			467.858i			0.788968i	−0.918903	+	0.394484i	$0.870923\pi$
$594$	−21.3050	+	60.2817i	−0.0358669	+	0.101484i
$595$		0			0
$596$	259.875	−	84.4386i	0.436033	−	0.141676i
$597$	−866.269	−	629.382i	−1.45104	−	1.05424i
$598$	−183.547	+	133.354i	−0.306934	+	0.223001i
$599$	180.089	−	554.257i	0.300649	−	0.925304i	−0.680616	−	0.732641i	$-0.738288\pi$
$599$	180.089	−	554.257i	0.300649	−	0.925304i	0.981265	−	0.192663i	$-0.0617124\pi$
$600$		0			0
$601$	439.974	+	605.572i	0.732070	+	1.00761i	0.999036	+	0.0439019i	$0.0139789\pi$
$601$	439.974	+	605.572i	0.732070	+	1.00761i	−0.266966	+	0.963706i	$0.586021\pi$
$602$	−4.12343	+	5.67541i	−0.00684954	+	0.00942759i
$603$	−86.9149	−	267.496i	−0.144137	−	0.443609i
$604$			246.832i			0.408662i
$605$		0			0
$606$	−111.790			−0.184471
$607$	715.161	−	232.370i	1.17819	−	0.382817i	0.346496	−	0.938052i	$-0.387372\pi$
$607$	715.161	−	232.370i	1.17819	−	0.382817i	0.831694	+	0.555235i	$0.187372\pi$
$608$	−676.048	−	491.178i	−1.11192	−	0.807858i
$609$	15.5867	−	11.3244i	0.0255939	−	0.0185951i
$610$		0			0
$611$	−510.710	−	165.940i	−0.835860	−	0.271587i
$612$	−289.468	−	398.418i	−0.472987	−	0.651010i
$613$	589.502	−	811.379i	0.961666	−	1.32362i	0.0155207	−	0.999880i	$-0.495059\pi$
$613$	589.502	−	811.379i	0.961666	−	1.32362i	0.946146	−	0.323741i	$-0.104941\pi$
$614$	−75.2380	−	231.559i	−0.122537	−	0.377131i
$615$		0			0
$616$	−15.6252	−	5.52231i	−0.0253656	−	0.00896480i
$617$	−436.456			−0.707384			−0.353692	−	0.935362i	$-0.615074\pi$
$617$	−436.456			−0.707384			−0.353692	+	0.935362i	$0.615074\pi$
$618$	−348.731	+	113.310i	−0.564290	+	0.183349i
$619$	−102.839	−	74.7172i	−0.166138	−	0.120706i	0.501610	−	0.865094i	$-0.332741\pi$
$619$	−102.839	−	74.7172i	−0.166138	−	0.120706i	−0.667748	+	0.744388i	$0.732741\pi$
$620$		0			0
$621$	−68.2755	+	210.130i	−0.109945	+	0.338374i
$622$	−150.055	−	48.7557i	−0.241245	−	0.0783853i
$623$	14.5093	+	19.9704i	0.0232894	+	0.0320552i
$624$	264.354	−	363.853i	0.423645	−	0.583097i
$625$		0			0
$626$			432.028i			0.690141i
$627$	−1270.07	−	32.4729i	−2.02563	−	0.0517908i
$628$	745.616			1.18729
$629$	255.729	−	83.0915i	0.406565	−	0.132101i
$630$		0			0
$631$	182.154	−	132.343i	0.288675	−	0.209735i	−0.434017	−	0.900905i	$-0.642904\pi$
$631$	182.154	−	132.343i	0.288675	−	0.209735i	0.722692	+	0.691170i	$0.242904\pi$
$632$	220.795	−	679.538i	0.349360	−	1.07522i
$633$	859.882	+	279.393i	1.35842	+	0.441379i
$634$	30.6602	+	42.2002i	0.0483600	+	0.0665618i
$635$		0			0
$636$	−178.433	−	549.162i	−0.280556	−	0.863462i
$637$			553.156i			0.868377i
$638$	78.6362	+	114.265i	0.123254	+	0.179099i
$639$	197.262			0.308705
$640$		0			0
$641$	852.241	+	619.190i	1.32955	+	0.965975i	0.999760	+	0.0219202i	$0.00697799\pi$
$641$	852.241	+	619.190i	1.32955	+	0.965975i	0.329790	+	0.944054i	$0.393022\pi$
$642$	206.217	−	149.825i	0.321210	−	0.233373i
$643$	259.872	−	799.805i	0.404156	−	1.24386i	−0.517442	−	0.855718i	$-0.673116\pi$
$643$	259.872	−	799.805i	0.404156	−	1.24386i	0.921598	−	0.388146i	$-0.126884\pi$
$644$	−25.3094	−	8.22352i	−0.0393003	−	0.0127694i
$645$		0			0
$646$	249.853	−	343.893i	0.386769	−	0.532342i
$647$	−19.8766	−	61.1738i	−0.0307211	−	0.0945499i	0.934520	−	0.355910i	$-0.115829\pi$
$647$	−19.8766	−	61.1738i	−0.0307211	−	0.0945499i	−0.965241	+	0.261360i	$0.915829\pi$
$648$			515.738i			0.795892i
$649$	−1072.88	+	318.524i	−1.65314	+	0.490792i
$650$		0			0
$651$	36.2755	−	11.7866i	0.0557228	−	0.0181054i
$652$	−256.118	−	186.081i	−0.392820	−	0.285400i
$653$	−865.002	+	628.461i	−1.32466	+	0.962421i	−0.324797	+	0.945784i	$0.605296\pi$
$653$	−865.002	+	628.461i	−1.32466	+	0.962421i	−0.999862	+	0.0166374i	$0.994704\pi$
$654$	−129.941	+	399.918i	−0.198687	+	0.611495i
$655$		0			0
$656$	105.548	+	145.275i	0.160897	+	0.221455i
$657$	−410.659	+	565.224i	−0.625052	+	0.860311i
$658$	2.95912	+	9.10724i	0.00449714	+	0.0138408i
$659$		−	283.355i		−	0.429978i	−0.976617	−	0.214989i	$-0.931028\pi$
$659$		−	283.355i		−	0.429978i	0.976617	−	0.214989i	$-0.0689715\pi$
$660$		0			0
$661$	−845.155			−1.27860			−0.639300	−	0.768957i	$-0.720776\pi$
$661$	−845.155			−1.27860			−0.639300	+	0.768957i	$0.720776\pi$
$662$	−202.237	+	65.7109i	−0.305495	+	0.0992612i
$663$	741.378	+	538.642i	1.11822	+	0.812432i
$664$	−550.795	+	400.176i	−0.829511	+	0.602675i
$665$		0			0
$666$	64.1879	+	20.8559i	0.0963782	+	0.0313152i
$667$	281.749	+	387.794i	0.422412	+	0.581400i
$668$	92.6834	−	127.568i	0.138748	−	0.190970i
$669$	−346.243	−	1065.63i	−0.517553	−	1.59286i
$670$		0			0
$671$	444.479	+	340.625i	0.662413	+	0.507637i
$672$	−32.1253			−0.0478056
$673$	422.060	−	137.135i	0.627132	−	0.203767i	0.0218275	−	0.999762i	$-0.493052\pi$
$673$	422.060	−	137.135i	0.627132	−	0.203767i	0.605304	+	0.795994i	$0.293052\pi$
$674$	−230.410	−	167.403i	−0.341855	−	0.248372i
$675$		0			0
$676$	44.1616	−	135.915i	0.0653278	−	0.201058i
$677$	−914.604	−	297.173i	−1.35097	−	0.438955i	−0.457949	−	0.888979i	$-0.651416\pi$
$677$	−914.604	−	297.173i	−1.35097	−	0.438955i	−0.893017	+	0.450023i	$0.851416\pi$
$678$	221.423	+	304.762i	0.326582	+	0.449502i
$679$	7.88160	−	10.8481i	0.0116077	−	0.0159766i
$680$		0			0
$681$			348.693i			0.512031i
$682$	78.1559	+	263.253i	0.114598	+	0.386001i
$683$	488.033			0.714542			0.357271	−	0.934001i	$-0.383707\pi$
$683$	488.033			0.714542			0.357271	+	0.934001i	$0.383707\pi$
$684$	−667.450	+	216.868i	−0.975804	+	0.317058i
$685$		0			0
$686$	15.9731	−	11.6051i	0.0232844	−	0.0169171i
$687$	132.689	−	408.374i	0.193142	−	0.594431i
$688$	329.058	+	106.917i	0.478281	+	0.155403i
$689$	276.306	+	380.303i	0.401025	+	0.551964i
$690$		0			0
$691$	−153.473	−	472.340i	−0.222102	−	0.683560i	−0.998573	−	0.0534066i	$-0.982992\pi$
$691$	−153.473	−	472.340i	−0.222102	−	0.683560i	0.776471	−	0.630153i	$-0.217008\pi$
$692$			526.197i			0.760400i
$693$	−17.6030	+	12.1142i	−0.0254011	+	0.0174808i
$694$	−46.2167			−0.0665947
$695$		0			0
$696$	304.912	+	221.531i	0.438092	+	0.318292i
$697$	−296.008	+	215.062i	−0.424689	+	0.308555i
$698$	55.1134	−	169.622i	0.0789590	−	0.243011i
$699$	−501.305	−	162.884i	−0.717174	−	0.233024i
$700$		0			0
$701$	294.515	−	405.366i	0.420136	−	0.578268i	−0.545518	−	0.838099i	$-0.683667\pi$
$701$	294.515	−	405.366i	0.420136	−	0.578268i	0.965654	+	0.259831i	$0.0836670\pi$
$702$	−20.3081	−	62.5018i	−0.0289289	−	0.0890339i
$703$		−	383.182i		−	0.545067i
$704$	−5.27184	+	206.191i	−0.00748840	+	0.292885i
$705$		0			0
$706$	−149.622	+	48.6151i	−0.211929	+	0.0688599i
$707$	8.63621	+	6.27458i	0.0122153	+	0.00887493i
$708$	−1143.19	+	830.574i	−1.61467	+	1.17313i
$709$	−0.643159	+	1.97944i	−0.000907135	+	0.00279188i	−0.951509	−	0.307621i	$-0.900467\pi$
$709$	−0.643159	+	1.97944i	−0.000907135	+	0.00279188i	0.950602	+	0.310413i	$0.100467\pi$
$710$		0			0
$711$	−541.525	−	745.345i	−0.761638	−	1.04831i
$712$	−283.836	+	390.666i	−0.398646	+	0.548689i
$713$	293.249	+	902.528i	0.411289	+	1.26582i
$714$		−	16.3416i		−	0.0228873i
$715$		0			0
$716$	−591.976			−0.826783
$717$	350.132	−	113.765i	0.488329	−	0.158668i
$718$	−401.418	−	291.647i	−0.559078	−	0.406194i
$719$	−568.638	+	413.140i	−0.790874	+	0.574603i	−0.908223	−	0.418487i	$-0.862560\pi$
$719$	−568.638	+	413.140i	−0.790874	+	0.574603i	0.117349	+	0.993091i	$0.462560\pi$
$720$		0			0
$721$	33.3009	+	10.8201i	0.0461871	+	0.0150071i
$722$	−201.888	−	277.875i	−0.279624	−	0.384869i
$723$	62.3382	−	85.8012i	0.0862216	−	0.118674i
$724$	−178.092	−	548.111i	−0.245984	−	0.757060i
$725$		0			0
$726$	−191.885	−	294.679i	−0.264304	−	0.405894i
$727$	−1163.47			−1.60037			−0.800184	−	0.599754i	$-0.795265\pi$
$727$	−1163.47			−1.60037			−0.800184	+	0.599754i	$0.795265\pi$
$728$	16.2007	−	5.26392i	0.0222537	−	0.00723065i
$729$	304.999	+	221.595i	0.418381	+	0.303971i
$730$		0			0
$731$	−217.852	+	670.480i	−0.298019	+	0.917209i
$732$	672.433	+	218.487i	0.918625	+	0.298479i
$733$	−768.849	−	1058.23i	−1.04891	−	1.44370i	−0.889752	−	0.456443i	$-0.849123\pi$
$733$	−768.849	−	1058.23i	−1.04891	−	1.44370i	−0.159155	−	0.987254i	$-0.550877\pi$
$734$	31.4702	−	43.3150i	0.0428750	−	0.0590123i
$735$		0			0
$736$		−	799.272i		−	1.08597i
$737$	−416.723	−	147.280i	−0.565432	−	0.199837i
$738$	−91.8371			−0.124441
$739$	−1085.92	+	352.838i	−1.46945	+	0.477453i	−0.930942	−	0.365167i	$-0.881012\pi$
$739$	−1085.92	+	352.838i	−1.46945	+	0.477453i	−0.538508	+	0.842621i	$0.681012\pi$
$740$		0			0
$741$	1056.50	−	767.594i	1.42578	−	1.03589i
$742$	2.59040	−	7.97242i	0.00349110	−	0.0107445i
$743$	542.947	+	176.414i	0.730749	+	0.237435i	0.650677	−	0.759354i	$-0.274485\pi$
$743$	542.947	+	176.414i	0.730749	+	0.237435i	0.0800717	+	0.996789i	$0.474485\pi$
$744$	438.577	+	603.650i	0.589486	+	0.811357i
$745$		0			0
$746$	13.1070	+	40.3393i	0.0175697	+	0.0540741i
$747$			877.859i			1.17518i
$748$	−773.632	−	19.7800i	−1.03427	−	0.0264438i
$749$	−24.3406			−0.0324974
$750$		0			0
$751$	496.597	+	360.799i	0.661247	+	0.480424i	0.867084	−	0.498162i	$-0.165992\pi$
$751$	496.597	+	360.799i	0.661247	+	0.480424i	−0.205837	+	0.978586i	$0.565992\pi$
$752$	382.089	−	277.604i	0.508097	−	0.369154i
$753$	−166.912	+	513.702i	−0.221662	+	0.682207i
$754$	−135.598	−	44.0584i	−0.179838	−	0.0584329i
$755$		0			0
$756$	4.53097	−	6.23634i	0.00599335	−	0.00824913i
$757$	251.984	+	775.528i	0.332872	+	1.02448i	0.967761	+	0.251872i	$0.0810461\pi$
$757$	251.984	+	775.528i	0.332872	+	1.02448i	−0.634888	+	0.772604i	$0.718954\pi$
$758$			136.212i			0.179700i
$759$	−688.912	−	1001.05i	−0.907657	−	1.31890i
$760$		0			0
$761$	−488.577	+	158.748i	−0.642020	+	0.208605i	−0.611892	−	0.790941i	$-0.709591\pi$
$761$	−488.577	+	158.748i	−0.642020	+	0.208605i	−0.0301278	+	0.999546i	$0.509591\pi$
$762$	−362.551	−	263.409i	−0.475789	−	0.345681i
$763$	32.4853	−	23.6019i	0.0425757	−	0.0309331i
$764$	12.0100	−	36.9631i	0.0157200	−	0.0483811i
$765$		0			0
$766$	2.61470	+	3.59883i	0.00341345	+	0.00469821i
$767$	676.171	−	930.670i	0.881579	−	1.21339i
$768$	−23.4853	−	72.2803i	−0.0305798	−	0.0941150i
$769$			501.416i			0.652036i	0.945364	+	0.326018i	$0.105707\pi$
$769$			501.416i			0.652036i	−0.945364	+	0.326018i	$0.894293\pi$
$770$		0			0
$771$	977.167			1.26740
$772$	414.823	−	134.784i	0.537336	−	0.174591i
$773$	−363.619	−	264.185i	−0.470400	−	0.341765i	0.327197	−	0.944956i	$-0.393896\pi$
$773$	−363.619	−	264.185i	−0.470400	−	0.341765i	−0.797597	+	0.603191i	$0.793896\pi$
$774$	−143.156	+	104.009i	−0.184956	+	0.134378i
$775$		0			0
$776$	249.472	+	81.0584i	0.321485	+	0.104457i
$777$	−8.65869	−	11.9177i	−0.0111437	−	0.0153380i
$778$	96.5585	−	132.901i	0.124111	−	0.170824i
$779$	161.124	+	495.888i	0.206834	+	0.636569i
$780$		0			0
$781$	188.554	−	246.043i	0.241427	−	0.315036i
$782$	406.575			0.519917
$783$	−132.053	+	42.9065i	−0.168650	+	0.0547976i
$784$	−393.590	−	285.960i	−0.502028	−	0.364744i
$785$		0			0
$786$	−115.396	+	355.153i	−0.146815	+	0.451849i
$787$	−547.379	−	177.854i	−0.695526	−	0.225990i	−0.0601458	−	0.998190i	$-0.519157\pi$
$787$	−547.379	−	177.854i	−0.695526	−	0.225990i	−0.635380	+	0.772200i	$0.719157\pi$
$788$	737.809	+	1015.51i	0.936306	+	1.28872i
$789$	4.54486	−	6.25546i	0.00576028	−	0.00792834i
$790$		0			0
$791$		−	35.9723i		−	0.0454770i
$792$	−331.794	−	254.269i	−0.418932	−	0.321047i
$793$	−575.601			−0.725852
$794$	148.647	−	48.2982i	0.187212	−	0.0608290i
$795$		0			0
$796$	−751.951	+	546.325i	−0.944662	+	0.686337i
$797$	−7.71885	+	23.7562i	−0.00968488	+	0.0298070i	−0.955782	−	0.294076i	$-0.904988\pi$
$797$	−7.71885	+	23.7562i	−0.00968488	+	0.0298070i	0.946097	+	0.323883i	$0.104988\pi$
$798$	−22.1478	−	7.19626i	−0.0277542	−	0.00901787i
$799$	565.639	+	778.535i	0.707933	+	0.974386i
$800$		0			0
$801$	192.408	+	592.171i	0.240210	+	0.739289i
$802$			393.109i			0.490160i
$803$	312.467	+	1052.48i	0.389125	+	1.31069i
$804$	−558.046			−0.694088
$805$		0			0
$806$	−228.358	−	165.911i	−0.283322	−	0.205846i
$807$	592.879	−	430.752i	0.734671	−	0.533769i
$808$	−64.5310	+	198.606i	−0.0798651	+	0.245799i
$809$	−711.977	−	231.335i	−0.880070	−	0.285952i	−0.166084	−	0.986112i	$-0.553112\pi$
$809$	−711.977	−	231.335i	−0.880070	−	0.285952i	−0.713987	+	0.700159i	$0.753112\pi$
$810$		0			0
$811$	138.201	−	190.218i	0.170409	−	0.234547i	−0.715268	−	0.698851i	$-0.753695\pi$
$811$	138.201	−	190.218i	0.170409	−	0.234547i	0.885676	+	0.464303i	$0.153695\pi$
$812$	−5.16792	−	15.9052i	−0.00636443	−	0.0195877i
$813$		−	2030.26i		−	2.49725i
$814$	87.3676	−	60.1256i	0.107331	−	0.0738644i
$815$		0			0
$816$	−766.525	+	249.059i	−0.939369	+	0.305219i
$817$	812.771	+	590.513i	0.994824	+	0.722782i
$818$	215.561	−	156.614i	0.263522	−	0.191460i
$819$	6.78736	−	20.8894i	0.00828738	−	0.0255059i
$820$		0			0
$821$	−90.2423	−	124.208i	−0.109918	−	0.151288i	0.750514	−	0.660854i	$-0.229806\pi$
$821$	−90.2423	−	124.208i	−0.109918	−	0.151288i	−0.860432	+	0.509566i	$0.829806\pi$
$822$	−105.791	+	145.609i	−0.128699	+	0.177140i
$823$	−399.465	−	1229.43i	−0.485377	−	1.49384i	−0.831434	−	0.555624i	$-0.812480\pi$
$823$	−399.465	−	1229.43i	−0.485377	−	1.49384i	0.346057	−	0.938214i	$-0.387520\pi$
$824$			684.967i			0.831270i
$825$		0			0
$826$	−20.5140			−0.0248353
$827$	−594.248	+	193.083i	−0.718559	+	0.233474i	−0.645398	−	0.763846i	$-0.723309\pi$
$827$	−594.248	+	193.083i	−0.718559	+	0.233474i	−0.0731605	+	0.997320i	$0.523309\pi$
$828$	−543.057	−	394.554i	−0.655866	−	0.476514i
$829$	1192.01	−	866.043i	1.43788	−	1.04468i	0.449405	−	0.893328i	$-0.351636\pi$
$829$	1192.01	−	866.043i	1.43788	−	1.04468i	0.988479	−	0.151355i	$-0.0483638\pi$
$830$		0			0
$831$	134.794	+	43.7973i	0.162207	+	0.0527043i
$832$	−124.616	−	171.519i	−0.149779	−	0.206152i
$833$	582.664	−	801.969i	0.699477	−	0.962748i
$834$	−204.971	−	630.835i	−0.245768	−	0.756396i
$835$		0			0
$836$	−367.489	+	1039.80i	−0.439580	+	1.24378i
$837$	−274.885			−0.328417
$838$	113.696	−	36.9422i	0.135676	−	0.0440838i
$839$	1083.63	+	787.303i	1.29157	+	0.938383i	0.999836	−	0.0181155i	$-0.00576666\pi$
$839$	1083.63	+	787.303i	1.29157	+	0.938383i	0.291737	+	0.956498i	$0.405767\pi$
$840$		0			0
$841$	166.797	−	513.350i	0.198332	−	0.610404i
$842$	−83.0945	−	26.9990i	−0.0986870	−	0.0320654i
$843$	803.607	+	1106.07i	0.953270	+	1.31206i
$844$	461.305	−	634.932i	0.546570	−	0.752289i
$845$		0			0
$846$			241.542i			0.285511i
$847$	−1.71597	+	33.5354i	−0.00202594	+	0.0395931i
$848$	−413.438			−0.487544
$849$	1572.74	−	511.015i	1.85246	−	0.601902i
$850$		0			0
$851$	296.509	−	215.426i	0.348424	−	0.253145i
$852$	120.944	−	372.228i	0.141953	−	0.436888i
$853$	−1106.68	−	359.583i	−1.29740	−	0.421551i	−0.422724	−	0.906259i	$-0.638926\pi$
$853$	−1106.68	−	359.583i	−1.29740	−	0.421551i	−0.874676	+	0.484708i	$0.838926\pi$
$854$	6.03326	+	8.30406i	0.00706470	+	0.00972373i
$855$		0			0
$856$	−147.141	−	452.853i	−0.171894	−	0.529034i
$857$		−	1069.27i		−	1.24769i	−0.781549	−	0.623844i	$-0.785570\pi$
$857$		−	1069.27i		−	1.24769i	0.781549	−	0.623844i	$-0.214430\pi$
$858$	340.793	+	120.444i	0.397194	+	0.140378i
$859$	998.288			1.16215			0.581076	−	0.813849i	$-0.302632\pi$
$859$	998.288			1.16215			0.581076	+	0.813849i	$0.302632\pi$
$860$		0			0
$861$	16.2167	+	11.7821i	0.0188347	+	0.0136842i
$862$	317.753	−	230.861i	0.368623	−	0.267820i
$863$	−217.399	+	669.085i	−0.251911	+	0.775301i	0.742512	+	0.669833i	$0.233634\pi$
$863$	−217.399	+	669.085i	−0.251911	+	0.775301i	−0.994423	+	0.105468i	$0.966366\pi$
$864$	220.190	+	71.5442i	0.254850	+	0.0828058i
$865$		0			0
$866$	91.1189	−	125.414i	0.105218	−	0.144820i
$867$	−150.253	−	462.431i	−0.173302	−	0.533370i
$868$		−	33.1089i		−	0.0381438i
$869$	−1447.28	−	37.0036i	−1.66545	−	0.0425818i
$870$		0			0
$871$	432.071	−	140.388i	0.496063	−	0.161181i
$872$	635.487	+	461.708i	0.728770	+	0.529482i
$873$	273.631	−	198.805i	0.313438	−	0.227726i
$874$	179.042	−	551.033i	0.204853	−	0.630473i
$875$		0			0
$876$	814.780	+	1121.45i	0.930114	+	1.28019i
$877$	198.377	−	273.042i	0.226199	−	0.311336i	−0.680800	−	0.732470i	$-0.738368\pi$
$877$	198.377	−	273.042i	0.226199	−	0.311336i	0.906999	+	0.421133i	$0.138368\pi$
$878$	−6.70391	−	20.6325i	−0.00763544	−	0.0234995i
$879$			771.436i			0.877629i
$880$		0			0
$881$	−1011.82			−1.14849			−0.574246	−	0.818682i	$-0.694705\pi$
$881$	−1011.82			−1.14849			−0.574246	+	0.818682i	$0.694705\pi$
$882$	236.635	−	76.8873i	0.268293	−	0.0871738i
$883$	260.572	+	189.317i	0.295099	+	0.214402i	0.725476	−	0.688247i	$-0.241620\pi$
$883$	260.572	+	189.317i	0.295099	+	0.214402i	−0.430377	+	0.902649i	$0.641620\pi$
$884$	643.541	−	467.560i	0.727988	−	0.528914i
$885$		0			0
$886$	−39.5673	−	12.8562i	−0.0446584	−	0.0145104i
$887$	437.553	+	602.240i	0.493296	+	0.678963i	0.980992	−	0.194050i	$-0.0621625\pi$
$887$	437.553	+	602.240i	0.493296	+	0.678963i	−0.487696	+	0.873014i	$0.662163\pi$
$888$	169.384	−	233.137i	0.190748	−	0.262542i
$889$	13.2239	+	40.6989i	0.0148750	+	0.0457805i
$890$		0			0
$891$	1001.78	−	297.415i	1.12434	−	0.333799i
$892$	−972.603			−1.09036
$893$	1304.24	−	423.773i	1.46052	−	0.474550i
$894$	185.029	+	134.432i	0.206968	+	0.150371i
$895$		0			0
$896$	−11.0956	+	34.1486i	−0.0123834	+	0.0381123i
$897$	1187.94	+	385.985i	1.32435	+	0.430306i
$898$	253.966	+	349.554i	0.282813	+	0.389258i
$899$	−350.535	+	482.470i	−0.389916	+	0.536674i
$900$		0			0
$901$		−	842.411i		−	0.934973i
$902$	−87.7829	+	114.547i	−0.0973203	+	0.126993i
$903$	38.6223			0.0427711
$904$	669.259	−	217.456i	0.740331	−	0.240548i
$905$		0			0
$906$	−167.141	+	121.435i	−0.184482	+	0.134034i
$907$	173.823	−	534.971i	0.191646	−	0.589825i	−0.808354	−	0.588697i	$-0.799641\pi$
$907$	173.823	−	534.971i	0.191646	−	0.589825i	0.999999	−	0.00112787i	$-0.000359011\pi$
$908$	287.863	+	93.5325i	0.317030	+	0.103009i
$909$	158.269	+	217.839i	0.174114	+	0.239647i
$910$		0			0
$911$	−21.9218	−	67.4684i	−0.0240634	−	0.0740597i	0.938304	−	0.345813i	$-0.112397\pi$
$911$	−21.9218	−	67.4684i	−0.0240634	−	0.0740597i	−0.962367	+	0.271753i	$0.912397\pi$
$912$			1148.55i			1.25938i
$913$	1094.94	+	839.106i	1.19928	+	0.919064i
$914$	345.220			0.377702
$915$		0			0
$916$	−301.541	−	219.082i	−0.329193	−	0.239173i
$917$	28.8491	−	20.9601i	0.0314603	−	0.0228572i
$918$	−36.3932	+	112.007i	−0.0396440	+	0.122012i
$919$	64.4021	+	20.9255i	0.0700784	+	0.0227699i	0.343846	−	0.939026i	$-0.388270\pi$
$919$	64.4021	+	20.9255i	0.0700784	+	0.0227699i	−0.273768	+	0.961796i	$0.588270\pi$
$920$		0			0
$921$	−787.902	+	1084.45i	−0.855486	+	1.17748i
$922$	−65.1904	−	200.635i	−0.0707054	−	0.217609i
$923$			318.626i			0.345207i
$924$	12.0665	+	40.6436i	0.0130590	+	0.0439866i
$925$		0			0
$926$	−59.5184	+	19.3387i	−0.0642747	+	0.0208841i
$927$	714.528	+	519.135i	0.770796	+	0.560016i
$928$	406.359	−	295.237i	0.437887	−	0.318144i
$929$	385.947	−	1187.82i	0.415443	−	1.27860i	−0.496411	−	0.868088i	$-0.665349\pi$
$929$	385.947	−	1187.82i	0.415443	−	1.27860i	0.911854	−	0.410515i	$-0.134651\pi$
$930$		0			0
$931$	−830.328	−	1142.85i	−0.891866	−	1.22755i
$932$	−268.937	+	370.160i	−0.288559	+	0.397168i
$933$	268.426	+	826.129i	0.287702	+	0.885455i
$934$			164.151i			0.175751i
$935$		0			0
$936$	429.674			0.459053
$937$	515.209	−	167.401i	0.549849	−	0.178657i	−0.0208996	−	0.999782i	$-0.506653\pi$
$937$	515.209	−	167.401i	0.549849	−	0.178657i	0.570749	+	0.821125i	$0.306653\pi$
$938$	−6.55418	−	4.76189i	−0.00698739	−	0.00507664i
$939$	1924.28	−	1398.07i	2.04929	−	1.48890i
$940$		0			0
$941$	−561.217	−	182.350i	−0.596405	−	0.193784i	−0.00476834	−	0.999989i	$-0.501518\pi$
$941$	−561.217	−	182.350i	−0.596405	−	0.193784i	−0.591636	+	0.806205i	$0.701518\pi$
$942$	366.824	+	504.890i	0.389410	+	0.535977i
$943$	−293.137	+	403.468i	−0.310856	+	0.427856i
$944$	312.650	+	962.238i	0.331197	+	1.01932i
$945$		0			0
$946$	−7.10716	+	277.974i	−0.00751286	+	0.293842i
$947$	527.364			0.556878			0.278439	−	0.960454i	$-0.410183\pi$
$947$	527.364			0.556878			0.278439	+	0.960454i	$0.410183\pi$
$948$	−1738.46	+	564.860i	−1.83382	+	0.595844i
$949$	−912.973	−	663.313i	−0.962036	−	0.698960i
$950$		0			0
$951$	88.7438	−	273.125i	0.0933163	−	0.287198i
$952$	−29.0325	−	9.43324i	−0.0304963	−	0.00990886i
$953$	−1038.40	−	1429.23i	−1.08961	−	1.49972i	−0.848483	−	0.529223i	$-0.822483\pi$
$953$	−1038.40	−	1429.23i	−1.08961	−	1.49972i	−0.241125	−	0.970494i	$-0.577517\pi$
$954$	124.284	−	171.062i	0.130277	−	0.179310i
$955$		0			0
$956$		−	319.567i		−	0.334275i
$957$	254.472	−	720.021i	0.265906	−	0.752373i
$958$	61.1060			0.0637849
$959$	16.3456	−	5.31101i	0.0170444	−	0.00553807i
$960$		0			0
$961$	−177.706	+	129.111i	−0.184917	+	0.134350i
$962$	−33.6873	+	103.679i	−0.0350180	+	0.107774i
$963$	−583.915	−	189.725i	−0.606350	−	0.197015i
$964$	−54.1117	−	74.4783i	−0.0561325	−	0.0772597i
$965$		0			0
$966$	−6.88307	−	21.1839i	−0.00712533	−	0.0219295i
$967$			1457.23i			1.50696i	0.657470	+	0.753481i	$0.271627\pi$
$967$			1457.23i			1.50696i	−0.657470	+	0.753481i	$0.728373\pi$
$968$	−634.294	+	170.799i	−0.655263	+	0.176445i
$969$	−2340.26			−2.41513
$970$		0			0
$971$	−151.983	−	110.422i	−0.156522	−	0.113720i	0.506768	−	0.862083i	$-0.330840\pi$
$971$	−151.983	−	110.422i	−0.156522	−	0.113720i	−0.663290	+	0.748363i	$0.730840\pi$
$972$	865.177	−	628.588i	0.890100	−	0.646696i
$973$	−19.5729	+	60.2393i	−0.0201161	+	0.0619109i
$974$	457.232	+	148.564i	0.469437	+	0.152529i
$975$		0			0
$976$	297.562	−	409.559i	0.304879	−	0.419631i
$977$	−389.172	−	1197.75i	−0.398334	−	1.22595i	−0.926335	−	0.376702i	$-0.877058\pi$
$977$	−389.172	−	1197.75i	−0.398334	−	1.22595i	0.528001	−	0.849244i	$-0.322942\pi$
$978$		−	264.977i		−	0.270937i
$979$	922.522	+	326.041i	0.942310	+	0.333035i
$980$		0			0
$981$	963.269	−	312.985i	0.981926	−	0.319047i
$982$	−438.057	−	318.267i	−0.446087	−	0.324101i
$983$	−842.819	+	612.344i	−0.857395	+	0.622934i	−0.927175	−	0.374628i	$-0.877770\pi$
$983$	−842.819	+	612.344i	−0.857395	+	0.622934i	0.0697799	+	0.997562i	$0.477770\pi$
$984$	−121.173	+	372.933i	−0.123144	+	0.378997i
$985$		0			0
$986$	150.182	+	206.708i	0.152314	+	0.209643i
$987$	30.9883	−	42.6518i	0.0313965	−	0.0432135i
$988$	−350.293	−	1078.09i	−0.354548	−	1.09119i
$989$			960.916i			0.971604i
$990$		0			0
$991$	−664.312			−0.670345			−0.335173	−	0.942157i	$-0.608795\pi$
$991$	−664.312			−0.670345			−0.335173	+	0.942157i	$0.608795\pi$
$992$	945.736	−	307.288i	0.953363	−	0.309767i
$993$	947.135	+	688.134i	0.953811	+	0.692985i
$994$	4.59675	−	3.33973i	0.00462449	−	0.00335989i
$995$		0			0
$996$	1656.49	+	538.227i	1.66315	+	0.540389i
$997$	116.026	+	159.697i	0.116375	+	0.160177i	0.863231	−	0.504809i	$-0.168437\pi$
$997$	116.026	+	159.697i	0.116375	+	0.160177i	−0.746855	+	0.664987i	$0.768437\pi$
$998$	−118.731	+	163.419i	−0.118969	+	0.163747i
$999$	32.8065	+	100.968i	0.0328393	+	0.101069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.d.226.1		4
5.2	odd	4		275.3.q.c.149.2		8
5.3	odd	4		275.3.q.c.149.1		8
5.4	even	2		55.3.i.a.6.1	✓	4
11.2	odd	10	inner	275.3.x.d.101.1		4
55.2	even	20		275.3.q.c.24.1		8
55.13	even	20		275.3.q.c.24.2		8
55.14	even	10		605.3.c.a.241.3		4
55.19	odd	10		605.3.c.a.241.2		4
55.24	odd	10		55.3.i.a.46.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.6.1	✓	4	5.4	even	2
55.3.i.a.46.1	yes	4	55.24	odd	10
275.3.q.c.24.1		8	55.2	even	20
275.3.q.c.24.2		8	55.13	even	20
275.3.q.c.149.1		8	5.3	odd	4
275.3.q.c.149.2		8	5.2	odd	4
275.3.x.d.101.1		4	11.2	odd	10	inner
275.3.x.d.226.1		4	1.1	even	1	trivial
605.3.c.a.241.2		4	55.19	odd	10
605.3.c.a.241.3		4	55.14	even	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 - 0.224514i) q^{2} +(-3.23607 - 2.35114i) q^{3} +(-2.80902 + 2.04087i) q^{4} +(-2.76393 - 0.898056i) q^{6} +(0.163119 + 0.224514i) q^{7} +(-3.19098 + 4.39201i) q^{8} +(2.16312 + 6.65740i) q^{9} +(10.3713 + 3.66547i) q^{11} +13.8885 q^{12} +(-10.7533 + 3.49396i) q^{13} +(0.163119 + 0.118513i) q^{14} +(3.07295 - 9.45756i) q^{16} +(19.2705 + 6.26137i) q^{17} +(2.98936 + 4.11450i) q^{18} +(16.9721 - 23.3601i) q^{19} -1.11006i q^{21} +(7.98936 + 0.204270i) q^{22} +27.6180 q^{23} +(20.6525 - 6.71040i) q^{24} +(-6.64590 + 4.82853i) q^{26} +(-2.47214 + 7.60845i) q^{27} +(-0.916408 - 0.297759i) q^{28} +(10.2016 + 14.0413i) q^{29} +(10.6180 + 32.6789i) q^{31} -28.9402i q^{32} +(-24.9443 - 36.2461i) q^{33} +14.7214 q^{34} +(-19.6631 - 14.2861i) q^{36} +(10.7361 - 7.80021i) q^{37} +(6.48278 - 19.9519i) q^{38} +(43.0132 + 13.9758i) q^{39} +(-10.6140 + 14.6089i) q^{41} +(-0.249224 - 0.767031i) q^{42} +34.7931i q^{43} +(-36.6140 + 10.8702i) q^{44} +(19.0836 - 6.20063i) q^{46} +(38.4230 + 27.9159i) q^{47} +(-32.1803 + 23.3804i) q^{48} +(15.1180 - 46.5285i) q^{49} +(-47.6393 - 65.5699i) q^{51} +(23.0755 - 31.7606i) q^{52} +(-12.8475 - 39.5406i) q^{53} +5.81234i q^{54} -1.50658 q^{56} +(-109.846 + 35.6911i) q^{57} +(10.2016 + 7.41192i) q^{58} +(-82.3115 + 59.8028i) q^{59} +(48.4164 + 15.7314i) q^{61} +(14.6738 + 20.1967i) q^{62} +(-1.14183 + 1.57160i) q^{63} +(5.79431 + 17.8330i) q^{64} +(-25.3738 - 19.4451i) q^{66} -40.1803 q^{67} +(-66.9098 + 21.7403i) q^{68} +(-89.3738 - 64.9339i) q^{69} +(8.70820 - 26.8011i) q^{71} +(-36.1418 - 11.7432i) q^{72} +(58.6656 + 80.7463i) q^{73} +(5.66718 - 7.80021i) q^{74} +100.257i q^{76} +(0.868810 + 2.92641i) q^{77} +32.8591 q^{78} +(-125.172 + 40.6709i) q^{79} +(76.8566 - 55.8396i) q^{81} +(-4.05418 + 12.4775i) q^{82} +(119.271 + 38.7533i) q^{83} +(2.26548 + 3.11817i) q^{84} +(7.81153 + 24.0414i) q^{86} -69.4242i q^{87} +(-49.1935 + 33.8545i) q^{88} +88.9493 q^{89} +(-2.53851 - 1.84433i) q^{91} +(-77.5795 + 56.3648i) q^{92} +(42.4721 - 130.716i) q^{93} +(32.8171 + 10.6629i) q^{94} +(-68.0426 + 93.6526i) q^{96} +(-14.9311 - 45.9533i) q^{97} -35.5446i q^{98} +(-1.96807 + 76.9748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 4 q^{3} - 9 q^{4} - 20 q^{6} - 15 q^{7} - 15 q^{8} - 7 q^{9} - q^{11} - 16 q^{12} - 5 q^{13} - 15 q^{14} + 19 q^{16} + 10 q^{17} - 35 q^{18} + 50 q^{19} - 15 q^{22} + 106 q^{23} + 20 q^{24}+ \cdots + 133 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - 4 * q^3 - 9 * q^4 - 20 * q^6 - 15 * q^7 - 15 * q^8 - 7 * q^9 - q^11 - 16 * q^12 - 5 * q^13 - 15 * q^14 + 19 * q^16 + 10 * q^17 - 35 * q^18 + 50 * q^19 - 15 * q^22 + 106 * q^23 + 20 * q^24 - 40 * q^26 + 8 * q^27 + 50 * q^28 + 90 * q^29 + 38 * q^31 - 64 * q^33 - 120 * q^34 - 63 * q^36 + 34 * q^37 + 55 * q^38 + 20 * q^39 + 85 * q^41 + 160 * q^42 - 19 * q^44 + 130 * q^46 + 24 * q^47 - 84 * q^48 + 56 * q^49 - 280 * q^51 - 100 * q^52 - 114 * q^53 + 70 * q^56 - 180 * q^57 + 90 * q^58 - 128 * q^59 + 140 * q^61 + 90 * q^62 + 105 * q^63 - 149 * q^64 + 140 * q^66 - 116 * q^67 - 290 * q^68 - 116 * q^69 + 8 * q^71 - 35 * q^72 + 20 * q^73 + 130 * q^74 + 160 * q^77 - 280 * q^78 - 210 * q^79 + 95 * q^81 + 270 * q^82 + 410 * q^83 + 340 * q^84 - 170 * q^86 - 78 * q^89 - 75 * q^91 - 241 * q^92 + 152 * q^93 + 375 * q^94 - 460 * q^96 - 176 * q^97 + 133 * q^99

Introduction

L-functions

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