LMFDB - Embedded newform 561.2.m.d.256.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			256.3
Character	$\chi$	$=$	561.256
Dual form			561.2.m.d.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0552438 - 0.0401370i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.616593 + 1.89768i) q^{4} +(0.989888 + 0.719196i) q^{5} +(0.0552438 + 0.0401370i) q^{6} +(-1.39118 + 4.28160i) q^{7} +(0.0843066 + 0.259469i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.0552438 - 0.0401370i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.616593 + 1.89768i) q^{4} +(0.989888 + 0.719196i) q^{5} +(0.0552438 + 0.0401370i) q^{6} +(-1.39118 + 4.28160i) q^{7} +(0.0843066 + 0.259469i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.0835515 q^{10} +(0.994067 - 3.16415i) q^{11} -1.99534 q^{12} +(0.245510 - 0.178374i) q^{13} +(0.0949965 + 0.292369i) q^{14} +(-0.378104 + 1.16368i) q^{15} +(-3.21345 - 2.33471i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.0211013 + 0.0649430i) q^{18} +(1.18776 + 3.65556i) q^{19} +(-1.97516 + 1.43504i) q^{20} -4.50194 q^{21} +(-0.0720833 - 0.214698i) q^{22} -0.932914 q^{23} +(-0.220718 + 0.160361i) q^{24} +(-1.08245 - 3.33144i) q^{25} +(0.00640355 - 0.0197081i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-7.26730 - 5.28001i) q^{28} +(1.56528 - 4.81744i) q^{29} +(0.0258188 + 0.0794622i) q^{30} +(-0.697466 + 0.506739i) q^{31} -0.816875 q^{32} +(3.31647 - 0.0323619i) q^{33} -0.0682851 q^{34} +(-4.45641 + 3.23777i) q^{35} +(-0.616593 - 1.89768i) q^{36} +(-1.73178 + 5.32987i) q^{37} +(0.212340 + 0.154274i) q^{38} +(0.245510 + 0.178374i) q^{39} +(-0.103155 + 0.317478i) q^{40} +(2.73851 + 8.42826i) q^{41} +(-0.248704 + 0.180694i) q^{42} +9.36261 q^{43} +(5.39160 + 3.83741i) q^{44} -1.22357 q^{45} +(-0.0515377 + 0.0374444i) q^{46} +(3.05028 + 9.38781i) q^{47} +(1.22743 - 3.77764i) q^{48} +(-10.7336 - 7.79840i) q^{49} +(-0.193512 - 0.140595i) q^{50} +(0.309017 - 0.951057i) q^{51} +(0.187116 + 0.575884i) q^{52} +(1.99239 - 1.44756i) q^{53} -0.0682851 q^{54} +(3.25966 - 2.41722i) q^{55} -1.22823 q^{56} +(-3.10961 + 2.25926i) q^{57} +(-0.106885 - 0.328960i) q^{58} +(-1.45643 + 4.48242i) q^{59} +(-1.97516 - 1.43504i) q^{60} +(0.275297 + 0.200015i) q^{61} +(-0.0181917 + 0.0559883i) q^{62} +(-1.39118 - 4.28160i) q^{63} +(6.38178 - 4.63663i) q^{64} +0.371313 q^{65} +(0.181915 - 0.134901i) q^{66} -10.4800 q^{67} +(1.61426 - 1.17283i) q^{68} +(-0.288286 - 0.887254i) q^{69} +(-0.116235 + 0.357734i) q^{70} +(2.20954 + 1.60533i) q^{71} +(-0.220718 - 0.160361i) q^{72} +(-2.84163 + 8.74563i) q^{73} +(0.118255 + 0.363950i) q^{74} +(2.83389 - 2.05894i) q^{75} -7.66945 q^{76} +(12.1647 + 8.65808i) q^{77} +0.0207223 q^{78} +(9.44065 - 6.85903i) q^{79} +(-1.50184 - 4.62220i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.489570 + 0.355694i) q^{82} +(2.55834 + 1.85874i) q^{83} +(2.77586 - 8.54323i) q^{84} +(-0.378104 - 1.16368i) q^{85} +(0.517226 - 0.375787i) q^{86} +5.06536 q^{87} +(0.904805 - 0.00882905i) q^{88} -5.45209 q^{89} +(-0.0675946 + 0.0491103i) q^{90} +(0.422176 + 1.29933i) q^{91} +(0.575229 - 1.77037i) q^{92} +(-0.697466 - 0.506739i) q^{93} +(0.545307 + 0.396189i) q^{94} +(-1.45331 + 4.47283i) q^{95} +(-0.252428 - 0.776895i) q^{96} +(-10.5882 + 7.69277i) q^{97} -0.905968 q^{98} +(1.05562 + 3.14415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.0552438	−	0.0401370i	0.0390633	−	0.0283811i	−0.568082	−	0.822972i	$-0.692314\pi$
$2$	0.0552438	−	0.0401370i	0.0390633	−	0.0283811i	0.607146	+	0.794591i	$0.292314\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.616593	+	1.89768i	−0.308297	+	0.948839i
$5$	0.989888	+	0.719196i	0.442691	+	0.321634i	0.786703	−	0.617331i	$-0.211786\pi$
$5$	0.989888	+	0.719196i	0.442691	+	0.321634i	−0.344012	+	0.938965i	$0.611786\pi$
$6$	0.0552438	+	0.0401370i	0.0225532	+	0.0163859i
$7$	−1.39118	+	4.28160i	−0.525815	+	1.61829i	0.236884	+	0.971538i	$0.423874\pi$
$7$	−1.39118	+	4.28160i	−0.525815	+	1.61829i	−0.762699	+	0.646754i	$0.776126\pi$
$8$	0.0843066	+	0.259469i	0.0298069	+	0.0917362i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.0835515			0.0264213
$11$	0.994067	−	3.16415i	0.299722	−	0.954026i
$11$	0.994067	−	3.16415i	0.299722	−	0.954026i
$12$	−1.99534			−0.576004
$13$	0.245510	−	0.178374i	0.0680923	−	0.0494720i	−0.553218	−	0.833036i	$-0.686600\pi$
$13$	0.245510	−	0.178374i	0.0680923	−	0.0494720i	0.621311	+	0.783564i	$0.286600\pi$
$14$	0.0949965	+	0.292369i	0.0253889	+	0.0781390i
$15$	−0.378104	+	1.16368i	−0.0976259	+	0.300462i
$16$	−3.21345	−	2.33471i	−0.803363	−	0.583677i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−0.0211013	+	0.0649430i	−0.00497361	+	0.0153072i
$19$	1.18776	+	3.65556i	0.272492	+	0.838644i	0.989872	+	0.141962i	$0.0453411\pi$
$19$	1.18776	+	3.65556i	0.272492	+	0.838644i	−0.717380	+	0.696682i	$0.754659\pi$
$20$	−1.97516	+	1.43504i	−0.441659	+	0.320884i
$21$	−4.50194			−0.982403
$22$	−0.0720833	−	0.214698i	−0.0153682	−	0.0457739i
$23$	−0.932914			−0.194526			−0.0972630	−	0.995259i	$-0.531009\pi$
$23$	−0.932914			−0.194526			−0.0972630	+	0.995259i	$0.531009\pi$
$24$	−0.220718	+	0.160361i	−0.0450538	+	0.0327335i
$25$	−1.08245	−	3.33144i	−0.216490	−	0.666287i
$26$	0.00640355	−	0.0197081i	0.00125584	−	0.00386507i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−7.26730	−	5.28001i	−1.37339	−	0.997827i
$29$	1.56528	−	4.81744i	0.290666	−	0.894577i	−0.693977	−	0.719997i	$-0.744143\pi$
$29$	1.56528	−	4.81744i	0.290666	−	0.894577i	0.984643	−	0.174580i	$-0.0558567\pi$
$30$	0.0258188	+	0.0794622i	0.00471385	+	0.0145077i
$31$	−0.697466	+	0.506739i	−0.125269	+	0.0910129i	−0.648655	−	0.761082i	$-0.724668\pi$
$31$	−0.697466	+	0.506739i	−0.125269	+	0.0910129i	0.523387	+	0.852095i	$0.324668\pi$
$32$	−0.816875			−0.144405
$33$	3.31647	−	0.0323619i	0.577323	−	0.00563349i
$34$	−0.0682851			−0.0117108
$35$	−4.45641	+	3.23777i	−0.753271	+	0.547284i
$36$	−0.616593	−	1.89768i	−0.102766	−	0.316280i
$37$	−1.73178	+	5.32987i	−0.284703	+	0.876225i	0.701785	+	0.712389i	$0.252387\pi$
$37$	−1.73178	+	5.32987i	−0.284703	+	0.876225i	−0.986488	+	0.163836i	$0.947613\pi$
$38$	0.212340	+	0.154274i	0.0344461	+	0.0250265i
$39$	0.245510	+	0.178374i	0.0393131	+	0.0285627i
$40$	−0.103155	+	0.317478i	−0.0163102	+	0.0501977i
$41$	2.73851	+	8.42826i	0.427683	+	1.31627i	0.900402	+	0.435060i	$0.143273\pi$
$41$	2.73851	+	8.42826i	0.427683	+	1.31627i	−0.472719	+	0.881213i	$0.656727\pi$
$42$	−0.248704	+	0.180694i	−0.0383759	+	0.0278817i
$43$	9.36261			1.42778			0.713892	−	0.700256i	$-0.246931\pi$
$43$	9.36261			1.42778			0.713892	+	0.700256i	$0.246931\pi$
$44$	5.39160	+	3.83741i	0.812814	+	0.578511i
$45$	−1.22357			−0.182399
$46$	−0.0515377	+	0.0374444i	−0.00759883	+	0.00552087i
$47$	3.05028	+	9.38781i	0.444930	+	1.36935i	0.882561	+	0.470198i	$0.155818\pi$
$47$	3.05028	+	9.38781i	0.444930	+	1.36935i	−0.437631	+	0.899155i	$0.644182\pi$
$48$	1.22743	−	3.77764i	0.177164	−	0.545255i
$49$	−10.7336	−	7.79840i	−1.53337	−	1.11406i
$50$	−0.193512	−	0.140595i	−0.0273668	−	0.0198831i
$51$	0.309017	−	0.951057i	0.0432710	−	0.133175i
$52$	0.187116	+	0.575884i	0.0259483	+	0.0798607i
$53$	1.99239	−	1.44756i	0.273676	−	0.198837i	−0.442478	−	0.896779i	$-0.645901\pi$
$53$	1.99239	−	1.44756i	0.273676	−	0.198837i	0.716154	+	0.697942i	$0.245901\pi$
$54$	−0.0682851			−0.00929242
$55$	3.25966	−	2.41722i	0.439532	−	0.325938i
$56$	−1.22823			−0.164129
$57$	−3.10961	+	2.25926i	−0.411878	+	0.299247i
$58$	−0.106885	−	0.328960i	−0.0140347	−	0.0431945i
$59$	−1.45643	+	4.48242i	−0.189611	+	0.583562i	−0.999997	−	0.00233370i	$-0.999257\pi$
$59$	−1.45643	+	4.48242i	−0.189611	+	0.583562i	0.810387	+	0.585896i	$0.199257\pi$
$60$	−1.97516	−	1.43504i	−0.254992	−	0.185263i
$61$	0.275297	+	0.200015i	0.0352481	+	0.0256092i	0.605270	−	0.796020i	$-0.293065\pi$
$61$	0.275297	+	0.200015i	0.0352481	+	0.0256092i	−0.570022	+	0.821630i	$0.693065\pi$
$62$	−0.0181917	+	0.0559883i	−0.00231035	+	0.00711053i
$63$	−1.39118	−	4.28160i	−0.175272	−	0.539430i
$64$	6.38178	−	4.63663i	0.797722	−	0.579579i
$65$	0.371313			0.0460558
$66$	0.181915	−	0.134901i	0.0223922	−	0.0166051i
$67$	−10.4800			−1.28034			−0.640171	−	0.768233i	$-0.721136\pi$
$67$	−10.4800			−1.28034			−0.640171	+	0.768233i	$0.721136\pi$
$68$	1.61426	−	1.17283i	0.195758	−	0.142226i
$69$	−0.288286	−	0.887254i	−0.0347056	−	0.106813i
$70$	−0.116235	+	0.357734i	−0.0138927	+	0.0427574i
$71$	2.20954	+	1.60533i	0.262224	+	0.190517i	0.711127	−	0.703064i	$-0.248185\pi$
$71$	2.20954	+	1.60533i	0.262224	+	0.190517i	−0.448903	+	0.893581i	$0.648185\pi$
$72$	−0.220718	−	0.160361i	−0.0260118	−	0.0188987i
$73$	−2.84163	+	8.74563i	−0.332587	+	1.02360i	0.635311	+	0.772256i	$0.280872\pi$
$73$	−2.84163	+	8.74563i	−0.332587	+	1.02360i	−0.967898	+	0.251342i	$0.919128\pi$
$74$	0.118255	+	0.363950i	0.0137468	+	0.0423084i
$75$	2.83389	−	2.05894i	0.327229	−	0.237746i
$76$	−7.66945			−0.879747
$77$	12.1647	+	8.65808i	1.38629	+	0.986679i
$78$	0.0207223			0.00234634
$79$	9.44065	−	6.85903i	1.06216	−	0.771701i	0.0876698	−	0.996150i	$-0.472058\pi$
$79$	9.44065	−	6.85903i	1.06216	−	0.771701i	0.974486	+	0.224448i	$0.0720580\pi$
$80$	−1.50184	−	4.62220i	−0.167911	−	0.516778i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.489570	+	0.355694i	0.0540640	+	0.0392798i
$83$	2.55834	+	1.85874i	0.280814	+	0.204024i	0.719273	−	0.694728i	$-0.244475\pi$
$83$	2.55834	+	1.85874i	0.280814	+	0.204024i	−0.438458	+	0.898752i	$0.644475\pi$
$84$	2.77586	−	8.54323i	0.302872	−	0.932143i
$85$	−0.378104	−	1.16368i	−0.0410111	−	0.126219i
$86$	0.517226	−	0.375787i	0.0557739	−	0.0405221i
$87$	5.06536			0.543063
$88$	0.904805	−	0.00882905i	0.0964525	−	0.000941180i
$89$	−5.45209			−0.577920			−0.288960	−	0.957341i	$-0.593309\pi$
$89$	−5.45209			−0.577920			−0.288960	+	0.957341i	$0.593309\pi$
$90$	−0.0675946	+	0.0491103i	−0.00712510	+	0.00517668i
$91$	0.422176	+	1.29933i	0.0442561	+	0.136206i
$92$	0.575229	−	1.77037i	0.0599717	−	0.184574i
$93$	−0.697466	−	0.506739i	−0.0723238	−	0.0525463i
$94$	0.545307	+	0.396189i	0.0562442	+	0.0408638i
$95$	−1.45331	+	4.47283i	−0.149107	+	0.458903i
$96$	−0.252428	−	0.776895i	−0.0257634	−	0.0792915i
$97$	−10.5882	+	7.69277i	−1.07507	+	0.781083i	−0.976816	−	0.214079i	$-0.931325\pi$
$97$	−10.5882	+	7.69277i	−1.07507	+	0.781083i	−0.0982515	+	0.995162i	$0.531325\pi$
$98$	−0.905968			−0.0915166
$99$	1.05562	+	3.14415i	0.106094	+	0.315999i
$100$	6.98943			0.698943
$101$	14.5488	−	10.5703i	1.44766	−	1.05179i	0.461292	−	0.887248i	$-0.347386\pi$
$101$	14.5488	−	10.5703i	1.44766	−	1.05179i	0.986370	−	0.164540i	$-0.0526140\pi$
$102$	−0.0211013	−	0.0649430i	−0.00208934	−	0.00643031i
$103$	2.52359	−	7.76681i	0.248657	−	0.765287i	−0.746357	−	0.665546i	$-0.768199\pi$
$103$	2.52359	−	7.76681i	0.248657	−	0.765287i	0.995013	−	0.0997407i	$-0.0318013\pi$
$104$	0.0669806	+	0.0486643i	0.00656799	+	0.00477192i
$105$	−4.45641	−	3.23777i	−0.434901	−	0.315974i
$106$	0.0519667	−	0.159937i	0.00504745	−	0.0155345i
$107$	5.30301	+	16.3210i	0.512662	+	1.57781i	0.787497	+	0.616319i	$0.211377\pi$
$107$	5.30301	+	16.3210i	0.512662	+	1.57781i	−0.274835	+	0.961491i	$0.588623\pi$
$108$	1.61426	−	1.17283i	0.155332	−	0.112856i
$109$	12.0798			1.15703			0.578516	−	0.815671i	$-0.303632\pi$
$109$	12.0798			1.15703			0.578516	+	0.815671i	$0.303632\pi$
$110$	0.0830558	−	0.264369i	0.00791906	−	0.0252066i
$111$	−5.60415			−0.531923
$112$	14.4668	−	10.5107i	1.36698	−	0.993169i
$113$	−3.27671	−	10.0847i	−0.308247	−	0.948686i	−0.978446	−	0.206504i	$-0.933791\pi$
$113$	−3.27671	−	10.0847i	−0.308247	−	0.948686i	0.670199	−	0.742181i	$-0.266209\pi$
$114$	−0.0811066	+	0.249621i	−0.00759633	+	0.0233791i
$115$	−0.923481	−	0.670948i	−0.0861150	−	0.0625662i
$116$	8.17681	+	5.94080i	0.759198	+	0.551590i
$117$	−0.0937766	+	0.288615i	−0.00866965	+	0.0266824i
$118$	0.0994523	+	0.306083i	0.00915533	+	0.0281772i
$119$	3.64214	−	2.64617i	0.333875	−	0.242574i
$120$	−0.333816			−0.0304731
$121$	−9.02366	−	6.29075i	−0.820333	−	0.571886i
$122$	0.0232364			0.00210373
$123$	−7.16951	+	5.20895i	−0.646453	+	0.469675i
$124$	−0.531574	−	1.63602i	−0.0477368	−	0.146919i
$125$	3.21497	−	9.89466i	0.287556	−	0.885005i
$126$	−0.248704	−	0.180694i	−0.0221563	−	0.0160975i
$127$	8.21586	+	5.96917i	0.729039	+	0.529678i	0.889259	−	0.457403i	$-0.151220\pi$
$127$	8.21586	+	5.96917i	0.729039	+	0.529678i	−0.160220	+	0.987081i	$0.551220\pi$
$128$	0.671310	−	2.06608i	0.0593360	−	0.182617i
$129$	2.89321	+	8.90437i	0.254733	+	0.783986i
$130$	0.0205128	−	0.0149034i	0.00179909	−	0.00130711i
$131$	17.4368			1.52346			0.761729	−	0.647896i	$-0.224351\pi$
$131$	17.4368			1.52346			0.761729	+	0.647896i	$0.224351\pi$
$132$	−1.98350	+	6.31354i	−0.172641	+	0.549523i
$133$	−17.3040			−1.50045
$134$	−0.578958	+	0.420637i	−0.0500143	+	0.0363375i
$135$	−0.378104	−	1.16368i	−0.0325420	−	0.100154i
$136$	0.0843066	−	0.259469i	0.00722923	−	0.0222493i
$137$	9.27310	+	6.73730i	0.792254	+	0.575606i	0.908632	−	0.417599i	$-0.137128\pi$
$137$	9.27310	+	6.73730i	0.792254	+	0.575606i	−0.116378	+	0.993205i	$0.537128\pi$
$138$	−0.0515377	−	0.0374444i	−0.00438718	−	0.00318748i
$139$	−1.95995	+	6.03211i	−0.166241	+	0.511637i	−0.999126	−	0.0418098i	$-0.986688\pi$
$139$	−1.95995	+	6.03211i	−0.166241	+	0.511637i	0.832885	+	0.553446i	$0.186688\pi$
$140$	−3.39646	−	10.4532i	−0.287053	−	0.883459i
$141$	−7.98575	+	5.80198i	−0.672521	+	0.488615i
$142$	0.186496			0.0156504
$143$	−0.320347	−	0.954146i	−0.0267888	−	0.0797897i
$144$	3.97204			0.331004
$145$	5.01414	−	3.64298i	0.416401	−	0.302533i
$146$	0.194041	+	0.597196i	0.0160589	+	0.0494243i
$147$	4.09986	−	12.6181i	0.338151	−	1.04072i
$148$	−9.04657	−	6.57272i	−0.743623	−	0.540274i
$149$	−15.7433	−	11.4382i	−1.28974	−	0.937052i	−0.289941	−	0.957044i	$-0.593636\pi$
$149$	−15.7433	−	11.4382i	−1.28974	−	0.937052i	−0.999800	+	0.0199925i	$0.993636\pi$
$150$	0.0739152	−	0.227487i	0.00603515	−	0.0185743i
$151$	−3.71916	−	11.4464i	−0.302661	−	0.931495i	−0.980540	−	0.196321i	$-0.937101\pi$
$151$	−3.71916	−	11.4464i	−0.302661	−	0.931495i	0.677879	−	0.735174i	$-0.262899\pi$
$152$	−0.848370	+	0.616377i	−0.0688119	+	0.0499948i
$153$	1.00000			0.0808452
$154$	1.01953	−	0.00994856i	0.0821563	−	0.000801677i
$155$	−1.05486			−0.0847282
$156$	−0.489876	+	0.355916i	−0.0392215	+	0.0284961i
$157$	−2.89084	−	8.89710i	−0.230714	−	0.710065i	−0.997661	−	0.0683548i	$-0.978225\pi$
$157$	−2.89084	−	8.89710i	−0.230714	−	0.710065i	0.766947	−	0.641711i	$-0.221775\pi$
$158$	0.246237	−	0.757838i	0.0195895	−	0.0602904i
$159$	1.99239	+	1.44756i	0.158007	+	0.114799i
$160$	−0.808615	−	0.587493i	−0.0639266	−	0.0464454i
$161$	1.29785	−	3.99436i	0.102285	−	0.314800i
$162$	−0.0211013	−	0.0649430i	−0.00165787	−	0.00510240i
$163$	13.6991	−	9.95295i	1.07299	−	0.779575i	0.0965451	−	0.995329i	$-0.469221\pi$
$163$	13.6991	−	9.95295i	1.07299	−	0.779575i	0.976448	+	0.215754i	$0.0692208\pi$
$164$	−17.6827			−1.38078
$165$	3.30620	+	2.35315i	0.257388	+	0.183193i
$166$	0.215937			0.0167600
$167$	4.08026	−	2.96448i	0.315740	−	0.229398i	−0.418616	−	0.908163i	$-0.637485\pi$
$167$	4.08026	−	2.96448i	0.315740	−	0.229398i	0.734355	+	0.678765i	$0.237485\pi$
$168$	−0.379543	−	1.16811i	−0.0292824	−	0.0901219i
$169$	−3.98876	+	12.2761i	−0.306828	+	0.944319i
$170$	−0.0675946	−	0.0491103i	−0.00518427	−	0.00376659i
$171$	−3.10961	−	2.25926i	−0.237798	−	0.172770i
$172$	−5.77292	+	17.7672i	−0.440181	+	1.35474i
$173$	−3.18565	−	9.80441i	−0.242200	−	0.745416i	−0.996084	−	0.0884083i	$-0.971822\pi$
$173$	−3.18565	−	9.80441i	−0.242200	−	0.745416i	0.753884	−	0.657008i	$-0.228178\pi$
$174$	0.279830	−	0.203308i	0.0212138	−	0.0154128i
$175$	15.7697			1.19208
$176$	−10.5818	+	7.84698i	−0.797629	+	0.591488i
$177$	−4.71310			−0.354258
$178$	−0.301194	+	0.218830i	−0.0225755	+	0.0164020i
$179$	−4.81321	−	14.8135i	−0.359756	−	1.10722i	−0.953200	−	0.302340i	$-0.902232\pi$
$179$	−4.81321	−	14.8135i	−0.359756	−	1.10722i	0.593444	−	0.804875i	$-0.297768\pi$
$180$	0.754444	−	2.32194i	0.0562329	−	0.173067i
$181$	13.4745	+	9.78978i	1.00155	+	0.727669i	0.962420	−	0.271565i	$-0.0875412\pi$
$181$	13.4745	+	9.78978i	1.00155	+	0.727669i	0.0391303	+	0.999234i	$0.487541\pi$
$182$	0.0754736	+	0.0548348i	0.00559448	+	0.00406463i
$183$	−0.105154	+	0.323630i	−0.00777320	+	0.0239235i
$184$	−0.0786509	−	0.242062i	−0.00579822	−	0.0178451i
$185$	−5.54748	+	4.03048i	−0.407859	+	0.296327i
$186$	−0.0588696			−0.00431653
$187$	−2.66406	+	1.97555i	−0.194815	+	0.144467i
$188$	−19.6958			−1.43647
$189$	3.64214	−	2.64617i	0.264927	−	0.192481i
$190$	0.0992396	+	0.305428i	0.00719959	+	0.0221581i
$191$	−4.78802	+	14.7360i	−0.346449	+	1.06626i	0.614355	+	0.789030i	$0.289416\pi$
$191$	−4.78802	+	14.7360i	−0.346449	+	1.06626i	−0.960804	+	0.277230i	$0.910584\pi$
$192$	6.38178	+	4.63663i	0.460565	+	0.334620i
$193$	−9.00610	−	6.54332i	−0.648274	−	0.470998i	0.214409	−	0.976744i	$-0.431217\pi$
$193$	−9.00610	−	6.54332i	−0.648274	−	0.470998i	−0.862683	+	0.505746i	$0.831217\pi$
$194$	−0.276167	+	0.849956i	−0.0198277	+	0.0610233i
$195$	0.114742	+	0.353140i	0.00821685	+	0.0252889i
$196$	21.4171	−	15.5604i	1.52979	−	1.11146i
$197$	16.6917			1.18924			0.594619	−	0.804008i	$-0.297303\pi$
$197$	16.6917			1.18924			0.594619	+	0.804008i	$0.297303\pi$
$198$	0.184513	+	0.131325i	0.0131128	+	0.00933287i
$199$	−10.1920			−0.722494			−0.361247	−	0.932470i	$-0.617649\pi$
$199$	−10.1920			−0.722494			−0.361247	+	0.932470i	$0.617649\pi$
$200$	0.773147	−	0.561724i	0.0546698	−	0.0397199i
$201$	−3.23851	−	9.96712i	−0.228427	−	0.703026i
$202$	0.379471	−	1.16789i	0.0266995	−	0.0821726i
$203$	18.4488	+	13.4038i	1.29485	+	0.940763i
$204$	1.61426	+	1.17283i	0.113021	+	0.0821145i
$205$	−3.35075	+	10.3126i	−0.234027	+	0.720260i
$206$	−0.172324	−	0.530358i	−0.0120064	−	0.0369518i
$207$	0.754744	−	0.548353i	0.0524583	−	0.0381132i
$208$	−1.20539			−0.0835785
$209$	12.7475	−	0.124389i	0.881761	−	0.00860418i
$210$	−0.376144			−0.0259564
$211$	9.19397	−	6.67981i	0.632939	−	0.459857i	−0.224478	−	0.974479i	$-0.572068\pi$
$211$	9.19397	−	6.67981i	0.632939	−	0.459857i	0.857417	+	0.514622i	$0.172068\pi$
$212$	1.51850	+	4.67347i	0.104291	+	0.320975i
$213$	−0.843970	+	2.59747i	−0.0578278	+	0.177976i
$214$	0.948034	+	0.688787i	0.0648063	+	0.0470845i
$215$	9.26793	+	6.73355i	0.632068	+	0.459224i
$216$	0.0843066	−	0.259469i	0.00573634	−	0.0176546i
$217$	−1.19935	−	3.69123i	−0.0814174	−	0.250577i
$218$	0.667333	−	0.484846i	0.0451975	−	0.0328379i
$219$	−9.19569			−0.621387
$220$	2.57723	+	7.67622i	0.173757	+	0.517531i
$221$	−0.303468			−0.0204134
$222$	−0.309595	+	0.224934i	−0.0207786	+	0.0150966i
$223$	6.43861	+	19.8160i	0.431161	+	1.32698i	0.896969	+	0.442093i	$0.145764\pi$
$223$	6.43861	+	19.8160i	0.431161	+	1.32698i	−0.465808	+	0.884886i	$0.654236\pi$
$224$	1.13642	−	3.49753i	0.0759300	−	0.233689i
$225$	2.83389	+	2.05894i	0.188926	+	0.137263i
$226$	−0.585786	−	0.425598i	−0.0389659	−	0.0283104i
$227$	0.823071	−	2.53315i	0.0546291	−	0.168131i	−0.920019	−	0.391873i	$-0.871827\pi$
$227$	0.823071	−	2.53315i	0.0546291	−	0.168131i	0.974648	+	0.223742i	$0.0718272\pi$
$228$	−2.36999	−	7.29408i	−0.156957	−	0.483063i
$229$	−7.25075	+	5.26798i	−0.479143	+	0.348118i	−0.800994	−	0.598673i	$-0.795695\pi$
$229$	−7.25075	+	5.26798i	−0.479143	+	0.348118i	0.321851	+	0.946790i	$0.395695\pi$
$230$	−0.0779464			−0.00513963
$231$	−4.47523	+	14.2448i	−0.294448	+	0.937239i
$232$	1.38194			0.0907289
$233$	−13.7407	+	9.98319i	−0.900182	+	0.654020i	−0.938513	−	0.345245i	$-0.887796\pi$
$233$	−13.7407	+	9.98319i	−0.900182	+	0.654020i	0.0383308	+	0.999265i	$0.487796\pi$
$234$	0.00640355	+	0.0197081i	0.000418613	+	0.00128836i
$235$	−3.73223	+	11.4866i	−0.243464	+	0.749305i
$236$	−7.60818	−	5.52766i	−0.495250	−	0.359820i
$237$	9.44065	+	6.85903i	0.613236	+	0.445542i
$238$	0.0949965	−	0.292369i	0.00615771	−	0.0189515i
$239$	1.71912	+	5.29089i	0.111200	+	0.342239i	0.991136	−	0.132854i	$-0.0424142\pi$
$239$	1.71912	+	5.29089i	0.111200	+	0.342239i	−0.879935	+	0.475094i	$0.842414\pi$
$240$	3.93188	−	2.85668i	0.253802	−	0.184398i
$241$	−19.7746			−1.27380			−0.636898	−	0.770948i	$-0.719783\pi$
$241$	−19.7746			−1.27380			−0.636898	+	0.770948i	$0.719783\pi$
$242$	−0.750993	+	0.0146577i	−0.0482757	+	0.000942234i
$243$	1.00000			0.0641500
$244$	−0.549309	+	0.399097i	−0.0351659	+	0.0255495i
$245$	−5.01646	−	15.4391i	−0.320490	−	0.986367i
$246$	−0.186999	+	0.575525i	−0.0119226	+	0.0366941i
$247$	0.943665	+	0.685613i	0.0600440	+	0.0436245i
$248$	−0.190284	−	0.138249i	−0.0120830	−	0.00877885i
$249$	−0.977200	+	3.00751i	−0.0619275	+	0.190593i
$250$	−0.219534	−	0.675658i	−0.0138846	−	0.0427323i
$251$	−0.439568	+	0.319365i	−0.0277453	+	0.0201581i	−0.601571	−	0.798819i	$-0.705458\pi$
$251$	−0.439568	+	0.319365i	−0.0277453	+	0.0201581i	0.573826	+	0.818977i	$0.305458\pi$
$252$	8.98288			0.565868
$253$	−0.927379	+	2.95188i	−0.0583038	+	0.185583i
$254$	0.693460			0.0435115
$255$	0.989888	−	0.719196i	0.0619892	−	0.0450378i
$256$	4.82940	+	14.8634i	0.301838	+	0.928961i
$257$	6.30689	−	19.4106i	0.393413	−	1.21080i	−0.536778	−	0.843724i	$-0.680359\pi$
$257$	6.30689	−	19.4106i	0.393413	−	1.21080i	0.930191	−	0.367077i	$-0.119641\pi$
$258$	0.517226	+	0.375787i	0.0322011	+	0.0233955i
$259$	−20.4111	−	14.8296i	−1.26829	−	0.921464i
$260$	−0.228949	+	0.704633i	−0.0141988	+	0.0436995i
$261$	1.56528	+	4.81744i	0.0968885	+	0.298192i
$262$	0.963274	−	0.699859i	0.0595112	−	0.0432375i
$263$	−6.22797			−0.384033			−0.192017	−	0.981392i	$-0.561503\pi$
$263$	−6.22797			−0.384033			−0.192017	+	0.981392i	$0.561503\pi$
$264$	0.287997	+	0.857792i	0.0177250	+	0.0527935i
$265$	3.01332			0.185107
$266$	−0.955941	+	0.694532i	−0.0586125	+	0.0425845i
$267$	−1.68479	−	5.18524i	−0.103107	−	0.317332i
$268$	6.46193	−	19.8878i	0.394725	−	1.21484i
$269$	−2.81945	−	2.04845i	−0.171905	−	0.124896i	0.498506	−	0.866886i	$-0.333882\pi$
$269$	−2.81945	−	2.04845i	−0.171905	−	0.124896i	−0.670411	+	0.741990i	$0.733882\pi$
$270$	−0.0675946	−	0.0491103i	−0.00411368	−	0.00298876i
$271$	−4.64279	+	14.2890i	−0.282029	+	0.867997i	0.705244	+	0.708964i	$0.250837\pi$
$271$	−4.64279	+	14.2890i	−0.282029	+	0.867997i	−0.987273	+	0.159032i	$0.949163\pi$
$272$	1.22743	+	3.77764i	0.0744238	+	0.229053i
$273$	−1.10527	+	0.803027i	−0.0668941	+	0.0486014i
$274$	0.782696			0.0472844
$275$	−11.6172	+	0.113360i	−0.700543	+	0.00683587i
$276$	1.86148			0.112048
$277$	9.81359	−	7.12999i	0.589642	−	0.428400i	−0.252546	−	0.967585i	$-0.581268\pi$
$277$	9.81359	−	7.12999i	0.589642	−	0.428400i	0.842187	+	0.539185i	$0.181268\pi$
$278$	0.133835	+	0.411903i	0.00802692	+	0.0247043i
$279$	0.266408	−	0.819920i	0.0159494	−	0.0490873i
$280$	−1.21581	−	0.883336i	−0.0726584	−	0.0527894i
$281$	10.7183	+	7.78730i	0.639400	+	0.464551i	0.859644	−	0.510893i	$-0.170685\pi$
$281$	10.7183	+	7.78730i	0.639400	+	0.464551i	−0.220244	+	0.975445i	$0.570685\pi$
$282$	−0.208289	+	0.641047i	−0.0124034	+	0.0381738i
$283$	5.32142	+	16.3776i	0.316325	+	0.973550i	0.975205	+	0.221302i	$0.0710305\pi$
$283$	5.32142	+	16.3776i	0.316325	+	0.973550i	−0.658880	+	0.752248i	$0.728969\pi$
$284$	−4.40878	+	3.20317i	−0.261613	+	0.190073i
$285$	−4.70302			−0.278583
$286$	−0.0559937	−	0.0398529i	−0.00331098	−	0.00235655i
$287$	−39.8962			−2.35500
$288$	0.660866	−	0.480147i	0.0389419	−	0.0282930i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	0.130782	−	0.402505i	0.00767976	−	0.0236359i
$291$	−10.5882	−	7.69277i	−0.620691	−	0.450958i
$292$	−14.8443	−	10.7850i	−0.868694	−	0.631143i
$293$	−4.26262	+	13.1190i	−0.249025	+	0.766419i	0.745924	+	0.666032i	$0.232008\pi$
$293$	−4.26262	+	13.1190i	−0.249025	+	0.766419i	−0.994948	+	0.100388i	$0.967992\pi$
$294$	−0.279960	−	0.861627i	−0.0163276	−	0.0502511i
$295$	−4.66544	+	3.38964i	−0.271632	+	0.197353i
$296$	−1.52894			−0.0888676
$297$	−2.66406	+	1.97555i	−0.154584	+	0.114633i
$298$	−1.32881			−0.0769761
$299$	−0.229040	+	0.166407i	−0.0132457	+	0.00962359i
$300$	2.15985	+	6.64734i	0.124699	+	0.383784i
$301$	−13.0250	+	40.0869i	−0.750750	+	2.31057i
$302$	−0.664884	−	0.483067i	−0.0382598	−	0.0277974i
$303$	14.5488	+	10.5703i	0.835808	+	0.607250i
$304$	4.71786	−	14.5201i	0.270588	−	0.832783i
$305$	0.128663	+	0.395984i	0.00736722	+	0.0226740i
$306$	0.0552438	−	0.0401370i	0.00315808	−	0.00229448i
$307$	7.93592			0.452927			0.226463	−	0.974020i	$-0.427284\pi$
$307$	7.93592			0.452927			0.226463	+	0.974020i	$0.427284\pi$
$308$	−23.9309	+	17.7461i	−1.36359	+	1.01118i
$309$	8.16651			0.464577
$310$	−0.0582743	+	0.0423388i	−0.00330976	+	0.00240468i
$311$	−9.70300	−	29.8628i	−0.550207	−	1.69336i	−0.708278	−	0.705934i	$-0.750528\pi$
$311$	−9.70300	−	29.8628i	−0.550207	−	1.69336i	0.158071	−	0.987428i	$-0.449472\pi$
$312$	−0.0255843	+	0.0787405i	−0.00144843	+	0.00445780i
$313$	7.17849	+	5.21548i	0.405752	+	0.294796i	0.771880	−	0.635768i	$-0.219317\pi$
$313$	7.17849	+	5.21548i	0.405752	+	0.294796i	−0.366128	+	0.930565i	$0.619317\pi$
$314$	−0.516804	−	0.375480i	−0.0291649	−	0.0211895i
$315$	1.70220	−	5.23883i	0.0959080	−	0.295174i
$316$	7.19520	+	22.1445i	0.404762	+	1.24573i
$317$	10.6562	−	7.74216i	0.598510	−	0.434843i	−0.246839	−	0.969056i	$-0.579392\pi$
$317$	10.6562	−	7.74216i	0.598510	−	0.434843i	0.845350	+	0.534213i	$0.179392\pi$
$318$	0.168168			0.00943039
$319$	−13.6871	−	9.74164i	−0.766331	−	0.545427i
$320$	9.65189			0.539557
$321$	−13.8835	+	10.0869i	−0.774900	+	0.562998i
$322$	−0.0886236	−	0.272755i	−0.00493880	−	0.0152001i
$323$	1.18776	−	3.65556i	0.0660890	−	0.203401i
$324$	1.61426	+	1.17283i	0.0896812	+	0.0651572i
$325$	−0.859993	−	0.624822i	−0.0477038	−	0.0346589i
$326$	0.357307	−	1.09968i	0.0197894	−	0.0609055i
$327$	3.73286	+	11.4885i	0.206427	+	0.635318i
$328$	−1.95600	+	1.42112i	−0.108002	+	0.0784680i
$329$	−44.4383			−2.44996
$330$	0.277096	−	0.00270389i	0.0152536	−	0.000148844i
$331$	−31.2764			−1.71911			−0.859554	−	0.511046i	$-0.829258\pi$
$331$	−31.2764			−1.71911			−0.859554	+	0.511046i	$0.829258\pi$
$332$	−5.10475	+	3.70882i	−0.280160	+	0.203548i
$333$	−1.73178	−	5.32987i	−0.0949009	−	0.292075i
$334$	0.106424	−	0.327538i	0.00582324	−	0.0179221i
$335$	−10.3741	−	7.53720i	−0.566796	−	0.411801i
$336$	14.4668	+	10.5107i	0.789226	+	0.573406i
$337$	−0.914423	+	2.81431i	−0.0498118	+	0.153305i	−0.972868	−	0.231359i	$-0.925683\pi$
$337$	−0.914423	+	2.81431i	−0.0498118	+	0.153305i	0.923057	+	0.384664i	$0.125683\pi$
$338$	0.272373	+	0.838278i	0.0148151	+	0.0455963i
$339$	8.57853	−	6.23267i	0.465922	−	0.338512i
$340$	2.44143			0.132405
$341$	0.910068	+	2.71062i	0.0492830	+	0.146788i
$342$	−0.262467			−0.0141926
$343$	22.8269	−	16.5847i	1.23254	−	0.895491i
$344$	0.789330	+	2.42931i	0.0425578	+	0.130980i
$345$	0.352738	−	1.08562i	0.0189908	−	0.0584476i
$346$	−0.569507	−	0.413771i	−0.0306169	−	0.0222445i
$347$	−1.66055	−	1.20646i	−0.0891431	−	0.0647663i	0.542321	−	0.840171i	$-0.317546\pi$
$347$	−1.66055	−	1.20646i	−0.0891431	−	0.0647663i	−0.631464	+	0.775405i	$0.717546\pi$
$348$	−3.12327	+	9.61242i	−0.167425	+	0.515280i
$349$	−4.71053	−	14.4975i	−0.252149	−	0.776035i	−0.994378	−	0.105888i	$-0.966231\pi$
$349$	−4.71053	−	14.4975i	−0.252149	−	0.776035i	0.742229	−	0.670146i	$-0.233769\pi$
$350$	0.871181	−	0.632950i	0.0465666	−	0.0338326i
$351$	−0.303468			−0.0161979
$352$	−0.812029	+	2.58471i	−0.0432813	+	0.137766i
$353$	−6.51264			−0.346633			−0.173316	−	0.984866i	$-0.555448\pi$
$353$	−6.51264			−0.346633			−0.173316	+	0.984866i	$0.555448\pi$
$354$	−0.260370	+	0.189170i	−0.0138385	+	0.0100542i
$355$	1.03265	+	3.17818i	0.0548076	+	0.168681i
$356$	3.36172	−	10.3463i	0.178171	−	0.548353i
$357$	3.64214	+	2.64617i	0.192763	+	0.140050i
$358$	−0.860470	−	0.625168i	−0.0454773	−	0.0330412i
$359$	5.87839	−	18.0918i	0.310250	−	0.954850i	−0.667416	−	0.744685i	$-0.732600\pi$
$359$	5.87839	−	18.0918i	0.310250	−	0.954850i	0.977666	−	0.210165i	$-0.0674002\pi$
$360$	−0.103155	−	0.317478i	−0.00543674	−	0.0167326i
$361$	3.41896	−	2.48402i	0.179945	−	0.130738i
$362$	1.13731			0.0597759
$363$	3.19439	−	10.5260i	0.167662	−	0.552470i
$364$	−2.72601			−0.142882
$365$	−9.10271	+	6.61350i	−0.476457	+	0.346167i
$366$	0.00718044	+	0.0220991i	0.000375328	+	0.00115514i
$367$	6.61756	−	20.3668i	0.345434	−	1.06314i	−0.615917	−	0.787811i	$-0.711214\pi$
$367$	6.61756	−	20.3668i	0.345434	−	1.06314i	0.961351	−	0.275326i	$-0.0887857\pi$
$368$	2.99788	+	2.17808i	0.156275	+	0.113540i
$369$	−7.16951	−	5.20895i	−0.373230	−	0.271167i
$370$	−0.144693	+	0.445318i	−0.00752222	+	0.0231510i
$371$	3.42609	+	10.5444i	0.177874	+	0.547439i
$372$	1.39168	−	1.01111i	0.0721552	−	0.0524238i
$373$	−0.300687			−0.0155690			−0.00778448	−	0.999970i	$-0.502478\pi$
$373$	−0.300687			−0.0155690			−0.00778448	+	0.999970i	$0.502478\pi$
$374$	−0.0678799	+	0.216064i	−0.00350999	+	0.0111724i
$375$	10.4039			0.537253
$376$	−2.17869	+	1.58291i	−0.112357	+	0.0816323i
$377$	−0.475012	−	1.46194i	−0.0244644	−	0.0752936i
$378$	0.0949965	−	0.292369i	0.00488609	−	0.0150379i
$379$	22.2549	+	16.1691i	1.14316	+	0.830551i	0.987556	−	0.157269i	$-0.0502691\pi$
$379$	22.2549	+	16.1691i	1.14316	+	0.830551i	0.155599	+	0.987820i	$0.450269\pi$
$380$	−7.59190	−	5.51584i	−0.389456	−	0.282956i
$381$	−3.13818	+	9.65832i	−0.160774	+	0.494811i
$382$	0.326950	+	1.00625i	0.0167282	+	0.0514842i
$383$	26.5324	−	19.2769i	1.35574	−	0.985004i	0.357038	−	0.934090i	$-0.383787\pi$
$383$	26.5324	−	19.2769i	1.35574	−	0.985004i	0.998703	−	0.0509137i	$-0.0162133\pi$
$384$	2.17240			0.110860
$385$	5.81482	+	17.3193i	0.296351	+	0.882674i
$386$	−0.760160			−0.0386911
$387$	−7.57451	+	5.50320i	−0.385034	+	0.279744i
$388$	−8.06980	−	24.8363i	−0.409682	−	1.26087i
$389$	−4.04452	+	12.4478i	−0.205065	+	0.631126i	0.794645	+	0.607074i	$0.207657\pi$
$389$	−4.04452	+	12.4478i	−0.205065	+	0.631126i	−0.999711	+	0.0240524i	$0.992343\pi$
$390$	0.0205128	+	0.0149034i	0.00103870	+	0.000754663i
$391$	0.754744	+	0.548353i	0.0381690	+	0.0277314i
$392$	1.11853	−	3.44249i	0.0564944	−	0.173872i
$393$	5.38826	+	16.5834i	0.271802	+	0.836520i
$394$	0.922116	−	0.669956i	0.0464555	−	0.0337519i
$395$	14.2782			0.718413
$396$	−6.61747	+	0.0645730i	−0.332540	+	0.00324492i
$397$	24.8906			1.24922			0.624612	−	0.780935i	$-0.285257\pi$
$397$	24.8906			1.24922			0.624612	+	0.780935i	$0.285257\pi$
$398$	−0.563047	+	0.409077i	−0.0282230	+	0.0205052i
$399$	−5.34724	−	16.4571i	−0.267697	−	0.823887i
$400$	−4.29954	+	13.2326i	−0.214977	+	0.661631i
$401$	−5.59989	−	4.06856i	−0.279645	−	0.203174i	0.439118	−	0.898430i	$-0.355291\pi$
$401$	−5.59989	−	4.06856i	−0.279645	−	0.203174i	−0.718763	+	0.695256i	$0.755291\pi$
$402$	−0.578958	−	0.420637i	−0.0288758	−	0.0209795i
$403$	−0.0808463	+	0.248819i	−0.00402724	+	0.0123946i
$404$	11.0884	+	34.1266i	0.551669	+	1.69786i
$405$	0.989888	−	0.719196i	0.0491879	−	0.0357371i
$406$	1.55717			0.0772810
$407$	15.1430	+	10.7778i	0.750610	+	0.534238i
$408$	0.272822			0.0135067
$409$	−25.7888	+	18.7366i	−1.27517	+	0.926467i	−0.999396	−	0.0347545i	$-0.988935\pi$
$409$	−25.7888	+	18.7366i	−1.27517	+	0.926467i	−0.275777	+	0.961222i	$0.588935\pi$
$410$	0.228806	+	0.704194i	0.0112999	+	0.0347777i
$411$	−3.54201	+	10.9012i	−0.174714	+	0.537715i
$412$	13.1829	+	9.57793i	0.649474	+	0.471871i
$413$	−17.1658	−	12.4717i	−0.844673	−	0.613691i
$414$	0.0196857	−	0.0605862i	0.000967498	−	0.00297765i
$415$	1.19567	+	3.67990i	0.0586932	+	0.180639i
$416$	−0.200551	+	0.145709i	−0.00983284	+	0.00714398i
$417$	−6.34253			−0.310595
$418$	0.699226	−	0.518516i	0.0342003	−	0.0253615i
$419$	22.0040			1.07497			0.537483	−	0.843274i	$-0.319375\pi$
$419$	22.0040			1.07497			0.537483	+	0.843274i	$0.319375\pi$
$420$	8.89205	−	6.46045i	0.433887	−	0.315238i
$421$	−3.42614	−	10.5446i	−0.166980	−	0.513912i	0.832197	−	0.554480i	$-0.187083\pi$
$421$	−3.42614	−	10.5446i	−0.166980	−	0.513912i	−0.999177	+	0.0405688i	$0.987083\pi$
$422$	0.239802	−	0.738036i	0.0116734	−	0.0359270i
$423$	−7.98575	−	5.80198i	−0.388280	−	0.282102i
$424$	0.543568	+	0.394925i	0.0263980	+	0.0191793i
$425$	−1.08245	+	3.33144i	−0.0525065	+	0.161598i
$426$	0.0576305	+	0.177369i	0.00279221	+	0.00859354i
$427$	−1.23937	+	0.900453i	−0.0599772	+	0.0435760i
$428$	−34.2418			−1.65514
$429$	0.808454	−	0.599516i	0.0390326	−	0.0289449i
$430$	0.782260			0.0377239
$431$	26.6674	−	19.3750i	1.28452	−	0.933260i	0.284843	−	0.958574i	$-0.408059\pi$
$431$	26.6674	−	19.3750i	1.28452	−	0.933260i	0.999680	+	0.0253139i	$0.00805853\pi$
$432$	1.22743	+	3.77764i	0.0590547	+	0.181752i
$433$	7.50463	−	23.0969i	0.360649	−	1.10996i	−0.592011	−	0.805930i	$-0.701666\pi$
$433$	7.50463	−	23.0969i	0.360649	−	1.10996i	0.952661	−	0.304035i	$-0.0983341\pi$
$434$	−0.214412	−	0.155779i	−0.0102921	−	0.00747764i
$435$	5.01414	+	3.64298i	0.240409	+	0.174668i
$436$	−7.44830	+	22.9235i	−0.356709	+	1.09784i
$437$	−1.10808	−	3.41033i	−0.0530068	−	0.163138i
$438$	−0.508005	+	0.369087i	−0.0242734	+	0.0176357i
$439$	20.4906			0.977965			0.488982	−	0.872294i	$-0.337368\pi$
$439$	20.4906			0.977965			0.488982	+	0.872294i	$0.337368\pi$
$440$	0.902005	+	0.641992i	0.0430014	+	0.0306058i
$441$	13.2674			0.631783
$442$	−0.0167647	+	0.0121803i	−0.000797415	+	0.000579356i
$443$	−8.07568	−	24.8544i	−0.383687	−	1.18087i	−0.937428	−	0.348178i	$-0.886800\pi$
$443$	−8.07568	−	24.8544i	−0.383687	−	1.18087i	0.553741	−	0.832689i	$-0.313200\pi$
$444$	3.45548	−	10.6349i	0.163990	−	0.504709i
$445$	−5.39696	−	3.92112i	−0.255840	−	0.185879i
$446$	1.15105	+	0.836286i	0.0545037	+	0.0395993i
$447$	6.01341	−	18.5074i	0.284424	−	0.875368i
$448$	10.9740	+	33.7746i	0.518474	+	1.59570i
$449$	18.9489	−	13.7672i	0.894254	−	0.649714i	−0.0427294	−	0.999087i	$-0.513605\pi$
$449$	18.9489	−	13.7672i	0.894254	−	0.649714i	0.936984	+	0.349373i	$0.113605\pi$
$450$	0.239194			0.0112757
$451$	29.3905	−	0.286791i	1.38395	−	0.0135045i
$452$	21.1579			0.995182
$453$	9.73689	−	7.07426i	0.457479	−	0.332378i
$454$	−0.0562035	−	0.172977i	−0.00263776	−	0.00811819i
$455$	−0.516562	+	1.58981i	−0.0242168	+	0.0745316i
$456$	−0.848370	−	0.616377i	−0.0397286	−	0.0288645i
$457$	−15.8651	−	11.5266i	−0.742137	−	0.539194i	0.151243	−	0.988497i	$-0.451672\pi$
$457$	−15.8651	−	11.5266i	−0.742137	−	0.539194i	−0.893380	+	0.449303i	$0.851672\pi$
$458$	−0.189118	+	0.582046i	−0.00883692	+	0.0271972i
$459$	0.309017	+	0.951057i	0.0144237	+	0.0443915i
$460$	1.84266	−	1.33877i	0.0859142	−	0.0624203i
$461$	−39.6691			−1.84758			−0.923788	−	0.382905i	$-0.874924\pi$
$461$	−39.6691			−1.84758			−0.923788	+	0.382905i	$0.874924\pi$
$462$	0.324514	+	0.966559i	0.0150978	+	0.0449684i
$463$	−17.0875			−0.794125			−0.397062	−	0.917792i	$-0.629970\pi$
$463$	−17.0875			−0.794125			−0.397062	+	0.917792i	$0.629970\pi$
$464$	−16.2773	+	11.8261i	−0.755654	+	0.549015i
$465$	−0.325969	−	1.00323i	−0.0151164	−	0.0465236i
$466$	−0.358392	+	1.10302i	−0.0166022	+	0.0510964i
$467$	−15.0382	−	10.9259i	−0.695885	−	0.505590i	0.182704	−	0.983168i	$-0.441515\pi$
$467$	−15.0382	−	10.9259i	−0.695885	−	0.505590i	−0.878589	+	0.477578i	$0.841515\pi$
$468$	−0.489876	−	0.355916i	−0.0226445	−	0.0164522i
$469$	14.5796	−	44.8713i	0.673223	−	2.07197i
$470$	0.254856	+	0.784366i	0.0117556	+	0.0361801i
$471$	7.56832	−	5.49871i	0.348730	−	0.253367i
$472$	−1.28584			−0.0591855
$473$	9.30706	−	29.6247i	0.427939	−	1.36214i
$474$	0.796838			0.0366000
$475$	10.8926	−	7.91393i	0.499786	−	0.363116i
$476$	2.77586	+	8.54323i	0.127231	+	0.391578i
$477$	−0.761026	+	2.34220i	−0.0348450	+	0.107242i
$478$	0.307331	+	0.223289i	0.0140570	+	0.0102130i
$479$	−7.28258	−	5.29110i	−0.332750	−	0.241757i	0.408847	−	0.912603i	$-0.365931\pi$
$479$	−7.28258	−	5.29110i	−0.332750	−	0.241757i	−0.741596	+	0.670846i	$0.765931\pi$
$480$	0.308863	−	0.950584i	0.0140976	−	0.0433880i
$481$	0.525539	+	1.61744i	0.0239625	+	0.0737490i
$482$	−1.09243	+	0.793694i	−0.0497586	+	0.0361518i
$483$	4.19992			0.191103
$484$	17.5017	−	13.2452i	0.795534	−	0.602054i
$485$	−16.0137			−0.727146
$486$	0.0552438	−	0.0401370i	0.00250591	−	0.00182065i
$487$	9.99478	+	30.7608i	0.452907	+	1.39390i	0.873575	+	0.486689i	$0.161796\pi$
$487$	9.99478	+	30.7608i	0.452907	+	1.39390i	−0.420669	+	0.907214i	$0.638204\pi$
$488$	−0.0286883	+	0.0882935i	−0.00129866	+	0.00399686i
$489$	13.6991	+	9.95295i	0.619493	+	0.450088i
$490$	−0.896807	−	0.651568i	−0.0405136	−	0.0294349i
$491$	−2.70617	+	8.32873i	−0.122128	+	0.375870i	−0.993367	−	0.114988i	$-0.963317\pi$
$491$	−2.70617	+	8.32873i	−0.122128	+	0.375870i	0.871239	+	0.490859i	$0.163317\pi$
$492$	−5.46425	−	16.8172i	−0.246347	−	0.758179i
$493$	−4.09796	+	2.97734i	−0.184563	+	0.134093i
$494$	0.0796501			0.00358363
$495$	−1.21631	+	3.87155i	−0.0546690	+	0.174013i
$496$	3.42436			0.153758
$497$	−9.94722	+	7.22708i	−0.446194	+	0.324179i
$498$	0.0667282	+	0.205368i	0.00299016	+	0.00920277i
$499$	13.2524	−	40.7867i	0.593260	−	1.82587i	0.0300545	−	0.999548i	$-0.490432\pi$
$499$	13.2524	−	40.7867i	0.593260	−	1.82587i	0.563205	−	0.826317i	$-0.309568\pi$
$500$	16.7945	+	12.2020i	0.751075	+	0.545688i
$501$	4.08026	+	2.96448i	0.182292	+	0.132443i
$502$	−0.0114651	+	0.0352859i	−0.000511712	+	0.00157489i
$503$	4.16201	+	12.8093i	0.185575	+	0.571140i	0.999958	−	0.00918734i	$-0.00292446\pi$
$503$	4.16201	+	12.8093i	0.185575	+	0.571140i	−0.814383	+	0.580328i	$0.802924\pi$
$504$	0.993657	−	0.721934i	0.0442610	−	0.0321575i
$505$	22.0039			0.979159
$506$	0.0672475	+	0.200295i	0.00298952	+	0.00890421i
$507$	−12.9079			−0.573260
$508$	−16.3934	+	11.9105i	−0.727340	+	0.528443i
$509$	−8.11743	−	24.9829i	−0.359799	−	1.10735i	−0.953174	−	0.302421i	$-0.902205\pi$
$509$	−8.11743	−	24.9829i	−0.359799	−	1.10735i	0.593375	−	0.804926i	$-0.297795\pi$
$510$	0.0258188	−	0.0794622i	0.00114328	−	0.00351865i
$511$	−33.4920	−	24.3334i	−1.48160	−	1.07645i
$512$	4.37839	+	3.18109i	0.193499	+	0.140585i
$513$	1.18776	−	3.65556i	0.0524411	−	0.161397i
$514$	−0.430667	−	1.32546i	−0.0189959	−	0.0584633i
$515$	8.08393	−	5.87332i	0.356221	−	0.258809i
$516$	−18.6816			−0.822410
$517$	32.7366	−	0.319442i	1.43975	−	0.0140491i
$518$	−1.72280			−0.0756956
$519$	8.34013	−	6.05946i	0.366091	−	0.265981i
$520$	0.0313042	+	0.0963443i	0.00137278	+	0.00422498i
$521$	6.25797	−	19.2600i	0.274166	−	0.843798i	−0.715272	−	0.698846i	$-0.753697\pi$
$521$	6.25797	−	19.2600i	0.274166	−	0.843798i	0.989439	−	0.144952i	$-0.0463027\pi$
$522$	0.279830	+	0.203308i	0.0122478	+	0.00889856i
$523$	−19.9991	−	14.5302i	−0.874498	−	0.635360i	0.0572921	−	0.998357i	$-0.481753\pi$
$523$	−19.9991	−	14.5302i	−0.874498	−	0.635360i	−0.931790	+	0.362997i	$0.881753\pi$
$524$	−10.7514	+	33.0894i	−0.469677	+	1.44552i
$525$	4.87312	+	14.9979i	0.212680	+	0.654563i
$526$	−0.344057	+	0.249972i	−0.0150016	+	0.0108993i
$527$	0.862115			0.0375543
$528$	−10.7329	−	7.63899i	−0.467088	−	0.332444i
$529$	−22.1297			−0.962160
$530$	0.166467	−	0.120946i	0.00723088	−	0.00525354i
$531$	−1.45643	−	4.48242i	−0.0632036	−	0.194521i
$532$	10.6696	−	32.8375i	0.462584	−	1.42369i
$533$	2.17571	+	1.58075i	0.0942406	+	0.0684698i
$534$	−0.301194	−	0.218830i	−0.0130339	−	0.00946971i
$535$	−6.48860	+	19.9699i	−0.280527	+	0.863372i
$536$	−0.883538	−	2.71925i	−0.0381630	−	0.117454i
$537$	12.6011	−	9.15527i	0.543779	−	0.395079i
$538$	−0.237976			−0.0102599
$539$	−35.3452	+	26.2105i	−1.52243	+	1.12897i
$540$	2.44143			0.105063
$541$	7.68732	−	5.58517i	0.330504	−	0.240125i	−0.410141	−	0.912022i	$-0.634520\pi$
$541$	7.68732	−	5.58517i	0.330504	−	0.240125i	0.740644	+	0.671897i	$0.234520\pi$
$542$	0.317033	+	0.975728i	0.0136177	+	0.0419111i
$543$	−5.14679	+	15.8402i	−0.220870	+	0.679768i
$544$	0.660866	+	0.480147i	0.0283344	+	0.0205861i
$545$	11.9576	+	8.68772i	0.512208	+	0.372141i
$546$	−0.0288284	+	0.0887246i	−0.00123374	+	0.00379706i
$547$	4.99464	+	15.3719i	0.213555	+	0.657256i	0.999253	+	0.0386451i	$0.0123042\pi$
$547$	4.99464	+	15.3719i	0.213555	+	0.657256i	−0.785698	+	0.618611i	$0.787696\pi$
$548$	−18.5030	+	13.4432i	−0.790407	+	0.574264i
$549$	−0.340285			−0.0145230
$550$	−0.637228	+	0.472541i	−0.0271715	+	0.0201492i
$551$	19.4697			0.829435
$552$	0.205911	−	0.149603i	0.00876414	−	0.00636752i
$553$	16.2340	+	49.9632i	0.690341	+	2.12465i
$554$	0.255964	−	0.787776i	0.0108749	−	0.0334694i
$555$	−5.54748	−	4.03048i	−0.235478	−	0.171084i
$556$	−10.2385	−	7.43871i	−0.434209	−	0.315472i
$557$	−1.21105	+	3.72723i	−0.0513138	+	0.157928i	−0.973430	−	0.228986i	$-0.926459\pi$
$557$	−1.21105	+	3.72723i	−0.0513138	+	0.157928i	0.922116	+	0.386914i	$0.126459\pi$
$558$	−0.0181917	−	0.0559883i	−0.000770117	−	0.00237018i
$559$	2.29862	−	1.67004i	0.0972212	−	0.0706353i
$560$	21.8797			0.924587
$561$	−2.70210	−	1.92319i	−0.114083	−	0.0811971i
$562$	0.904678			0.0381616
$563$	16.5384	−	12.0158i	0.697009	−	0.506407i	−0.181948	−	0.983308i	$-0.558240\pi$
$563$	16.5384	−	12.0158i	0.697009	−	0.506407i	0.878957	+	0.476902i	$0.158240\pi$
$564$	−6.08634	−	18.7318i	−0.256281	−	0.788753i
$565$	4.00928	−	12.3393i	0.168672	−	0.519118i
$566$	0.951324	+	0.691178i	0.0399871	+	0.0290524i
$567$	3.64214	+	2.64617i	0.152956	+	0.111129i
$568$	−0.230253	+	0.708647i	−0.00966122	+	0.0297342i
$569$	−9.24277	−	28.4463i	−0.387477	−	1.19253i	−0.934667	−	0.355524i	$-0.884302\pi$
$569$	−9.24277	−	28.4463i	−0.387477	−	1.19253i	0.547190	−	0.837008i	$-0.315698\pi$
$570$	−0.259813	+	0.188765i	−0.0108823	+	0.00790649i
$571$	9.68322			0.405230			0.202615	−	0.979258i	$-0.435056\pi$
$571$	9.68322			0.405230			0.202615	+	0.979258i	$0.435056\pi$
$572$	2.00819	−	0.0195958i	0.0839665	−	0.000819342i
$573$	−15.4943			−0.647286
$574$	−2.20402	+	1.60131i	−0.0919938	+	0.0668374i
$575$	1.00983	+	3.10795i	0.0421129	+	0.129610i
$576$	−2.43762	+	7.50223i	−0.101568	+	0.312593i
$577$	−6.29933	−	4.57673i	−0.262245	−	0.190532i	0.448891	−	0.893586i	$-0.351819\pi$
$577$	−6.29933	−	4.57673i	−0.262245	−	0.190532i	−0.711136	+	0.703054i	$0.751819\pi$
$578$	0.0552438	+	0.0401370i	0.00229784	+	0.00166948i
$579$	3.44003	−	10.5873i	0.142963	−	0.439994i
$580$	3.82153	+	11.7615i	0.158680	+	0.488368i
$581$	−11.5175	+	8.36795i	−0.477826	+	0.347161i
$582$	−0.893696			−0.0370449
$583$	−2.59972	−	7.74319i	−0.107669	−	0.320690i
$584$	−2.50879			−0.103814
$585$	−0.300399	+	0.218253i	−0.0124200	+	0.00902363i
$586$	0.291073	+	0.895831i	0.0120241	+	0.0370065i
$587$	−12.8788	+	39.6369i	−0.531565	+	1.63599i	0.219390	+	0.975637i	$0.429593\pi$
$587$	−12.8788	+	39.6369i	−0.531565	+	1.63599i	−0.750956	+	0.660353i	$0.770407\pi$
$588$	21.4171	+	15.5604i	0.883227	+	0.641702i
$589$	−2.68084	−	1.94775i	−0.110462	−	0.0802554i
$590$	−0.121687	+	0.374513i	−0.00500976	+	0.0154185i
$591$	5.15803	+	15.8748i	0.212173	+	0.653002i
$592$	18.0087	−	13.0841i	0.740152	−	0.537752i
$593$	18.3334			0.752861			0.376431	−	0.926445i	$-0.377151\pi$
$593$	18.3334			0.752861			0.376431	+	0.926445i	$0.377151\pi$
$594$	−0.0678799	+	0.216064i	−0.00278515	+	0.00886522i
$595$	5.50843			0.225824
$596$	31.4132	−	22.8230i	1.28673	−	0.934867i
$597$	−3.14951	−	9.69320i	−0.128901	−	0.396716i
$598$	−0.00597396	+	0.0183860i	−0.000244293	+	0.000751858i
$599$	−3.03786	−	2.20713i	−0.124124	−	0.0901810i	0.523991	−	0.851724i	$-0.324442\pi$
$599$	−3.03786	−	2.20713i	−0.124124	−	0.0901810i	−0.648115	+	0.761542i	$0.724442\pi$
$600$	0.773147	+	0.561724i	0.0315636	+	0.0229323i
$601$	−3.46322	+	10.6587i	−0.141268	+	0.434777i	−0.996512	−	0.0834478i	$-0.973407\pi$
$601$	−3.46322	+	10.6587i	−0.141268	+	0.434777i	0.855245	+	0.518224i	$0.173407\pi$
$602$	0.889415	+	2.73734i	0.0362499	+	0.111566i
$603$	8.47854	−	6.16002i	0.345273	−	0.250855i
$604$	24.0148			0.977148
$605$	−4.40814	−	12.7169i	−0.179216	−	0.517016i
$606$	1.22799			0.0498839
$607$	−2.50232	+	1.81804i	−0.101566	+	0.0737921i	−0.637409	−	0.770526i	$-0.719994\pi$
$607$	−2.50232	+	1.81804i	−0.101566	+	0.0737921i	0.535843	+	0.844318i	$0.319994\pi$
$608$	−0.970256	−	2.98614i	−0.0393491	−	0.121104i
$609$	−7.04680	+	21.6878i	−0.285551	+	0.878835i
$610$	0.0230014	+	0.0167115i	0.000931301	+	0.000676630i
$611$	2.42341	+	1.76071i	0.0980409	+	0.0712309i
$612$	−0.616593	+	1.89768i	−0.0249243	+	0.0767091i
$613$	−5.66409	−	17.4323i	−0.228771	−	0.704084i	−0.997887	−	0.0649747i	$-0.979303\pi$
$613$	−5.66409	−	17.4323i	−0.228771	−	0.704084i	0.769116	−	0.639109i	$-0.220697\pi$
$614$	0.438410	−	0.318524i	0.0176928	−	0.0128546i
$615$	−10.8433			−0.437243
$616$	−1.22094	+	3.88629i	−0.0491931	+	0.156583i
$617$	35.3139			1.42168			0.710842	−	0.703351i	$-0.248314\pi$
$617$	35.3139			1.42168			0.710842	+	0.703351i	$0.248314\pi$
$618$	0.451149	−	0.327779i	0.0181479	−	0.0131852i
$619$	2.57005	+	7.90981i	0.103299	+	0.317922i	0.989328	−	0.145709i	$-0.0465463\pi$
$619$	2.57005	+	7.90981i	0.103299	+	0.317922i	−0.886028	+	0.463631i	$0.846546\pi$
$620$	0.650418	−	2.00178i	0.0261214	−	0.0803934i
$621$	0.754744	+	0.548353i	0.0302868	+	0.0220047i
$622$	−1.73463	−	1.26028i	−0.0695524	−	0.0505328i
$623$	7.58481	−	23.3436i	0.303879	−	0.935243i
$624$	−0.372485	−	1.14639i	−0.0149113	−	0.0458924i
$625$	−3.87079	+	2.81230i	−0.154832	+	0.112492i
$626$	0.605901			0.0242167
$627$	4.05748	+	12.0851i	0.162040	+	0.482633i
$628$	18.6663			0.744866
$629$	4.53386	−	3.29404i	0.180777	−	0.131342i
$630$	−0.116235	−	0.357734i	−0.00463090	−	0.0142525i
$631$	4.21878	−	12.9841i	0.167947	−	0.516887i	−0.831295	−	0.555832i	$-0.812400\pi$
$631$	4.21878	−	12.9841i	0.167947	−	0.516887i	0.999241	+	0.0389450i	$0.0123997\pi$
$632$	2.57562	+	1.87129i	0.102453	+	0.0744361i
$633$	9.19397	+	6.67981i	0.365427	+	0.265499i
$634$	0.277941	−	0.855413i	0.0110384	−	0.0339728i
$635$	3.83978	+	11.8176i	0.152377	+	0.468968i
$636$	−3.97549	+	2.88836i	−0.157639	+	0.114531i
$637$	−4.02624			−0.159525
$638$	−1.14713	+	0.0111936i	−0.0454152	+	0.000443160i
$639$	−2.73114			−0.108042
$640$	2.15044	−	1.56238i	0.0850035	−	0.0617587i
$641$	−14.0952	−	43.3806i	−0.556728	−	1.71343i	−0.691336	−	0.722534i	$-0.742977\pi$
$641$	−14.0952	−	43.3806i	−0.556728	−	1.71343i	0.134608	−	0.990899i	$-0.457023\pi$
$642$	−0.362117	+	1.11448i	−0.0142916	+	0.0439850i
$643$	−3.93160	−	2.85647i	−0.155047	−	0.112648i	0.507557	−	0.861618i	$-0.330549\pi$
$643$	−3.93160	−	2.85647i	−0.155047	−	0.112648i	−0.662604	+	0.748970i	$0.730549\pi$
$644$	6.77977	+	4.92579i	0.267160	+	0.194103i
$645$	−3.54004	+	10.8951i	−0.139389	+	0.428994i
$646$	−0.0811066	−	0.249621i	−0.00319110	−	0.00982119i
$647$	32.0603	−	23.2932i	1.26042	−	0.915748i	0.261641	−	0.965165i	$-0.415736\pi$
$647$	32.0603	−	23.2932i	1.26042	−	0.915748i	0.998778	+	0.0494168i	$0.0157362\pi$
$648$	0.272822			0.0107175
$649$	12.7353	+	9.06418i	0.499903	+	0.355800i
$650$	−0.0725878			−0.00284713
$651$	3.13995	−	2.28131i	0.123064	−	0.0894114i
$652$	10.4407	+	32.1333i	0.408891	+	1.25844i
$653$	−10.4326	+	32.1081i	−0.408258	+	1.25649i	0.509887	+	0.860242i	$0.329687\pi$
$653$	−10.4326	+	32.1081i	−0.408258	+	1.25649i	−0.918144	+	0.396246i	$0.870313\pi$
$654$	0.667333	+	0.484846i	0.0260948	+	0.0189590i
$655$	17.2604	+	12.5405i	0.674422	+	0.489996i
$656$	10.8775	−	33.4774i	0.424694	−	1.30707i
$657$	−2.84163	−	8.74563i	−0.110862	−	0.341199i
$658$	−2.45494	+	1.78362i	−0.0957035	+	0.0695327i
$659$	9.48851			0.369620			0.184810	−	0.982774i	$-0.440833\pi$
$659$	9.48851			0.369620			0.184810	+	0.982774i	$0.440833\pi$
$660$	−6.50411	+	4.82318i	−0.253172	+	0.187742i
$661$	−44.4936			−1.73060			−0.865299	−	0.501256i	$-0.832872\pi$
$661$	−44.4936			−1.73060			−0.865299	+	0.501256i	$0.832872\pi$
$662$	−1.72783	+	1.25534i	−0.0671540	+	0.0487902i
$663$	−0.0937766	−	0.288615i	−0.00364198	−	0.0112089i
$664$	−0.266602	+	0.820515i	−0.0103461	+	0.0318422i
$665$	−17.1291	−	12.4450i	−0.664237	−	0.482596i
$666$	−0.309595	−	0.224934i	−0.0119966	−	0.00871601i
$667$	−1.46027	+	4.49426i	−0.0565420	+	0.174018i
$668$	3.10977	+	9.57089i	0.120321	+	0.370309i
$669$	−16.8565	+	12.2470i	−0.651710	+	0.473495i
$670$	−0.875624			−0.0338283
$671$	0.906539	−	0.672251i	0.0349965	−	0.0259520i
$672$	3.67752			0.141863
$673$	3.32339	−	2.41459i	0.128107	−	0.0930755i	−0.521886	−	0.853015i	$-0.674771\pi$
$673$	3.32339	−	2.41459i	0.128107	−	0.0930755i	0.649994	+	0.759940i	$0.274771\pi$
$674$	0.0624415	+	0.192175i	0.00240516	+	0.00740231i
$675$	−1.08245	+	3.33144i	−0.0416635	+	0.128227i
$676$	−20.8367	−	15.1388i	−0.801413	−	0.582261i
$677$	26.0986	+	18.9618i	1.00305	+	0.728760i	0.962741	−	0.270427i	$-0.0871648\pi$
$677$	26.0986	+	18.9618i	1.00305	+	0.728760i	0.0403120	+	0.999187i	$0.487165\pi$
$678$	0.223750	−	0.688633i	0.00859308	−	0.0264468i
$679$	−18.2073	−	56.0364i	−0.698733	−	2.15048i
$680$	0.270063	−	0.196212i	0.0103564	−	0.00752440i
$681$	2.66351			0.102066
$682$	0.159072	+	0.113217i	0.00609117	+	0.00433532i
$683$	15.5608			0.595418			0.297709	−	0.954657i	$-0.403777\pi$
$683$	15.5608			0.595418			0.297709	+	0.954657i	$0.403777\pi$
$684$	6.20472	−	4.50799i	0.237243	−	0.172367i
$685$	4.33389	+	13.3383i	0.165589	+	0.509632i
$686$	0.595385	−	1.83241i	0.0227319	−	0.0699616i
$687$	−7.25075	−	5.26798i	−0.276633	−	0.200986i
$688$	−30.0863	−	21.8590i	−1.14703	−	0.833365i
$689$	0.230947	−	0.710781i	0.00879837	−	0.0270786i
$690$	−0.0240868	−	0.0741314i	−0.000916967	−	0.00282214i
$691$	−32.5206	+	23.6276i	−1.23714	+	0.898836i	−0.997404	−	0.0720019i	$-0.977061\pi$
$691$	−32.5206	+	23.6276i	−1.23714	+	0.898836i	−0.239737	+	0.970838i	$0.577061\pi$
$692$	20.5699			0.781949
$693$	−14.9305	+	0.145691i	−0.567164	+	0.00553436i
$694$	−0.140159			−0.00532036
$695$	−6.27840	+	4.56152i	−0.238153	+	0.173028i
$696$	0.427043	+	1.31430i	0.0161870	+	0.0498186i
$697$	2.73851	−	8.42826i	0.103728	−	0.319243i
$698$	−0.842115	−	0.611832i	−0.0318745	−	0.0231582i
$699$	−13.7407	−	9.98319i	−0.519720	−	0.377599i
$700$	−9.72352	+	29.9259i	−0.367514	+	1.13109i
$701$	−8.93465	−	27.4980i	−0.337457	−	1.03859i	−0.965499	−	0.260407i	$-0.916143\pi$
$701$	−8.93465	−	27.4980i	−0.337457	−	1.03859i	0.628042	−	0.778180i	$-0.283857\pi$
$702$	−0.0167647	+	0.0121803i	−0.000632743	+	0.000459715i
$703$	−21.5406			−0.812420
$704$	−8.32708	−	24.8020i	−0.313839	−	0.934761i
$705$	−12.0778			−0.454875
$706$	−0.359783	+	0.261398i	−0.0135406	+	0.00983783i
$707$	25.0180	+	76.9974i	0.940898	+	2.89579i
$708$	2.90606	−	8.94395i	0.109217	−	0.336134i
$709$	−4.42159	−	3.21247i	−0.166056	−	0.120647i	0.501654	−	0.865069i	$-0.332725\pi$
$709$	−4.42159	−	3.21247i	−0.166056	−	0.120647i	−0.667710	+	0.744422i	$0.732725\pi$
$710$	0.184610	+	0.134127i	0.00692831	+	0.00503371i
$711$	−3.60601	+	11.0981i	−0.135236	+	0.416213i
$712$	−0.459647	−	1.41465i	−0.0172260	−	0.0530162i
$713$	0.650676	−	0.472744i	0.0243680	−	0.0177044i
$714$	0.307415			0.0115047
$715$	0.369110	−	1.17489i	0.0138039	−	0.0439384i
$716$	31.0791			1.16148
$717$	−4.50070	+	3.26995i	−0.168082	+	0.122119i
$718$	−0.401407	−	1.23540i	−0.0149804	−	0.0461048i
$719$	9.15834	−	28.1865i	0.341548	−	1.05118i	−0.621858	−	0.783130i	$-0.713622\pi$
$719$	9.15834	−	28.1865i	0.341548	−	1.05118i	0.963406	−	0.268047i	$-0.0863783\pi$
$720$	3.93188	+	2.85668i	0.146532	+	0.106462i
$721$	29.7436	+	21.6100i	1.10771	+	0.804798i
$722$	0.0891752	−	0.274453i	0.00331876	−	0.0102141i
$723$	−6.11070	−	18.8068i	−0.227259	−	0.699432i
$724$	−26.8861	+	19.5339i	−0.999215	+	0.725972i
$725$	−17.7433			−0.658971
$726$	−0.246010	−	0.709707i	−0.00913028	−	0.0263397i
$727$	9.96682			0.369649			0.184824	−	0.982772i	$-0.440828\pi$
$727$	9.96682			0.369649			0.184824	+	0.982772i	$0.440828\pi$
$728$	−0.301543	+	0.219084i	−0.0111759	+	0.00811977i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.237422	+	0.730710i	−0.00878739	+	0.0270448i
$731$	−7.57451	−	5.50320i	−0.280153	−	0.203543i
$732$	−0.549309	−	0.399097i	−0.0203031	−	0.0147510i
$733$	11.0789	−	34.0973i	0.409208	−	1.25941i	−0.508123	−	0.861285i	$-0.669660\pi$
$733$	11.0789	−	34.0973i	0.409208	−	1.25941i	0.917330	−	0.398127i	$-0.130340\pi$
$734$	−0.451881	−	1.39075i	−0.0166792	−	0.0513334i
$735$	13.1333	−	9.54188i	0.484428	−	0.351958i
$736$	0.762075			0.0280905
$737$	−10.4179	+	33.1604i	−0.383747	+	1.22148i
$738$	−0.605142			−0.0222756
$739$	−14.6273	+	10.6274i	−0.538074	+	0.390934i	−0.823369	−	0.567506i	$-0.807908\pi$
$739$	−14.6273	+	10.6274i	−0.538074	+	0.390934i	0.285295	+	0.958440i	$0.407908\pi$
$740$	−4.22802	−	13.0125i	−0.155425	−	0.478349i
$741$	−0.360448	+	1.10935i	−0.0132414	+	0.0407528i
$742$	0.612492	+	0.445001i	0.0224853	+	0.0163365i
$743$	−5.29827	−	3.84942i	−0.194375	−	0.141222i	0.486341	−	0.873769i	$-0.338331\pi$
$743$	−5.29827	−	3.84942i	−0.194375	−	0.141222i	−0.680716	+	0.732547i	$0.738331\pi$
$744$	0.0726820	−	0.223692i	0.00266465	−	0.00820096i
$745$	−7.35781	−	22.6450i	−0.269569	−	0.829649i
$746$	−0.0166111	+	0.0120687i	−0.000608175	+	0.000441865i
$747$	−3.16228			−0.115702
$748$	−2.10632	−	6.27363i	−0.0770148	−	0.229387i
$749$	−77.2573			−2.82292
$750$	0.574749	−	0.417579i	0.0209869	−	0.0152478i
$751$	−6.58041	−	20.2524i	−0.240123	−	0.739022i	−0.996400	−	0.0847711i	$-0.972984\pi$
$751$	−6.58041	−	20.2524i	−0.240123	−	0.739022i	0.756278	−	0.654251i	$-0.227016\pi$
$752$	12.1159	−	37.2888i	0.441820	−	1.35978i
$753$	−0.439568	−	0.319365i	−0.0160188	−	0.0116383i
$754$	−0.0849192	−	0.0616974i	−0.00309258	−	0.00224689i
$755$	4.55065	−	14.0055i	0.165615	−	0.509711i
$756$	2.77586	+	8.54323i	0.100957	+	0.310714i
$757$	−39.2069	+	28.4854i	−1.42500	+	1.03532i	−0.434076	+	0.900876i	$0.642925\pi$
$757$	−39.2069	+	28.4854i	−1.42500	+	1.03532i	−0.990921	+	0.134445i	$0.957075\pi$
$758$	1.87842			0.0682273
$759$	−3.09398	+	0.0301909i	−0.112304	+	0.00109586i
$760$	−1.28309			−0.0465424
$761$	26.2531	−	19.0740i	0.951675	−	0.691432i	0.000472258	−	1.00000i	$-0.499850\pi$
$761$	26.2531	−	19.0740i	0.951675	−	0.691432i	0.951202	+	0.308568i	$0.0998497\pi$
$762$	0.214291	+	0.659519i	0.00776294	+	0.0238919i
$763$	−16.8051	+	51.7207i	−0.608385	+	1.87242i
$764$	−25.0119	−	18.1722i	−0.904900	−	0.657448i
$765$	0.989888	+	0.719196i	0.0357895	+	0.0260026i
$766$	0.692033	−	2.12986i	0.0250042	−	0.0769549i
$767$	0.441979	+	1.36027i	0.0159589	+	0.0491165i
$768$	−12.6435	+	9.18607i	−0.456234	+	0.331474i
$769$	−39.6970			−1.43151			−0.715755	−	0.698351i	$-0.753917\pi$
$769$	−39.6970			−1.43151			−0.715755	+	0.698351i	$0.753917\pi$
$770$	1.01638	+	0.723395i	0.0366277	+	0.0260694i
$771$	20.4095			0.735031
$772$	17.9702	−	13.0561i	0.646762	−	0.469900i
$773$	3.05403	+	9.39933i	0.109846	+	0.338070i	0.990837	−	0.135062i	$-0.0431233\pi$
$773$	3.05403	+	9.39933i	0.109846	+	0.338070i	−0.880991	+	0.473132i	$0.843123\pi$
$774$	−0.197563	+	0.608036i	−0.00710125	+	0.0218554i
$775$	2.44314	+	1.77504i	0.0877601	+	0.0637615i
$776$	−2.88869	−	2.09876i	−0.103698	−	0.0753410i
$777$	7.79636	−	23.9947i	0.279693	−	0.860806i
$778$	0.276181	+	0.849996i	0.00990155	+	0.0304739i
$779$	−27.5573	+	20.0216i	−0.987344	+	0.717348i
$780$	−0.740895			−0.0265283
$781$	7.27592	−	5.39551i	0.260353	−	0.193067i
$782$	0.0637041			0.00227806
$783$	−4.09796	+	2.97734i	−0.146449	+	0.106402i
$784$	16.2848	+	50.1196i	0.581602	+	1.78999i
$785$	3.53714	−	10.8862i	0.126246	−	0.388545i
$786$	0.963274	+	0.699859i	0.0343588	+	0.0249632i
$787$	−7.24932	−	5.26694i	−0.258410	−	0.187746i	0.451036	−	0.892506i	$-0.351055\pi$
$787$	−7.24932	−	5.26694i	−0.258410	−	0.187746i	−0.709446	+	0.704760i	$0.751055\pi$
$788$	−10.2920	+	31.6756i	−0.366638	+	1.12840i
$789$	−1.92455	−	5.92315i	−0.0685158	−	0.210870i
$790$	0.788780	−	0.573082i	0.0280635	−	0.0203894i
$791$	47.7370			1.69733
$792$	−0.726813	+	0.538974i	−0.0258262	+	0.0191516i
$793$	0.103265			0.00366707
$794$	1.37505	−	0.999033i	0.0487988	−	0.0354544i
$795$	0.931167	+	2.86584i	0.0330251	+	0.101641i
$796$	6.28434	−	19.3412i	0.222742	−	0.685531i
$797$	23.3429	+	16.9596i	0.826850	+	0.600741i	0.918666	−	0.395035i	$-0.129267\pi$
$797$	23.3429	+	16.9596i	0.826850	+	0.600741i	−0.0918167	+	0.995776i	$0.529267\pi$
$798$	−0.955941	−	0.694532i	−0.0338400	−	0.0245862i
$799$	3.05028	−	9.38781i	0.107911	−	0.332117i
$800$	0.884226	+	2.72137i	0.0312621	+	0.0962149i
$801$	4.41083	−	3.20466i	0.155849	−	0.113231i
$802$	−0.472658			−0.0166902
$803$	24.8477	+	17.6851i	0.876856	+	0.624092i
$804$	20.9112			0.737482
$805$	4.15745	−	3.02057i	0.146531	−	0.106461i
$806$	0.00552059	+	0.0169906i	0.000194455	+	0.000598470i
$807$	1.07694	−	3.31447i	0.0379099	−	0.116675i
$808$	3.96924	+	2.88382i	0.139637	+	0.101452i
$809$	7.13278	+	5.18227i	0.250775	+	0.182199i	0.706070	−	0.708142i	$-0.250466\pi$
$809$	7.13278	+	5.18227i	0.250775	+	0.182199i	−0.455295	+	0.890341i	$0.650466\pi$
$810$	0.0258188	−	0.0794622i	0.000907181	−	0.00279202i
$811$	4.82256	+	14.8423i	0.169343	+	0.521185i	0.999330	−	0.0365982i	$-0.0116522\pi$
$811$	4.82256	+	14.8423i	0.169343	+	0.521185i	−0.829987	+	0.557783i	$0.811652\pi$
$812$	−36.8115	+	26.7451i	−1.29183	+	0.938570i
$813$	−15.0244			−0.526928
$814$	1.26915	−	0.0123843i	0.0444835	−	0.000434069i
$815$	20.7186			0.725742
$816$	−3.21345	+	2.33471i	−0.112493	+	0.0817312i
$817$	11.1206	+	34.2256i	0.389060	+	1.19740i
$818$	−0.672638	+	2.07017i	−0.0235182	+	0.0723817i
$819$	−1.10527	−	0.803027i	−0.0386213	−	0.0280600i
$820$	−17.5039	−	12.7173i	−0.611261	−	0.444107i
$821$	−9.65762	+	29.7231i	−0.337053	+	1.03734i	0.628648	+	0.777690i	$0.283608\pi$
$821$	−9.65762	+	29.7231i	−0.337053	+	1.03734i	−0.965702	+	0.259654i	$0.916392\pi$
$822$	0.241866	+	0.744388i	0.00843606	+	0.0259635i
$823$	−31.1977	+	22.6665i	−1.08748	+	0.790103i	−0.978973	−	0.203992i	$-0.934608\pi$
$823$	−31.1977	+	22.6665i	−1.08748	+	0.790103i	−0.108511	+	0.994095i	$0.534608\pi$
$824$	2.22800			0.0776162
$825$	−3.69772	−	11.0136i	−0.128738	−	0.383443i
$826$	−1.44888			−0.0504129
$827$	−34.7926	+	25.2783i	−1.20986	+	0.879012i	−0.995218	−	0.0976818i	$-0.968857\pi$
$827$	−34.7926	+	25.2783i	−1.20986	+	0.879012i	−0.214638	+	0.976694i	$0.568857\pi$
$828$	0.575229	+	1.77037i	0.0199906	+	0.0615247i
$829$	0.963127	−	2.96420i	0.0334508	−	0.102951i	−0.932937	−	0.360039i	$-0.882763\pi$
$829$	0.963127	−	2.96420i	0.0334508	−	0.102951i	0.966388	+	0.257089i	$0.0827632\pi$
$830$	0.213753	+	0.155301i	0.00741949	+	0.00539057i
$831$	9.81359	+	7.12999i	0.340430	+	0.247337i
$832$	0.739739	−	2.27668i	0.0256458	−	0.0789298i
$833$	4.09986	+	12.6181i	0.142052	+	0.437191i
$834$	−0.350386	+	0.254570i	−0.0121329	+	0.00881504i
$835$	6.17104			0.213558
$836$	−7.62395	+	24.2673i	−0.263680	+	0.839302i
$837$	0.862115			0.0297991
$838$	1.21559	−	0.883175i	0.0419917	−	0.0305088i
$839$	2.79926	+	8.61523i	0.0966411	+	0.297431i	0.987678	−	0.156500i	$-0.0500212\pi$
$839$	2.79926	+	8.61523i	0.0966411	+	0.297431i	−0.891037	+	0.453931i	$0.850021\pi$
$840$	0.464397	−	1.42927i	0.0160232	−	0.0493144i
$841$	2.70385	+	1.96446i	0.0932362	+	0.0677401i
$842$	−0.612501	−	0.445008i	−0.0211082	−	0.0153360i
$843$	−4.09403	+	12.6001i	−0.141006	+	0.433971i
$844$	7.00719	+	21.5659i	0.241197	+	0.742330i
$845$	−12.7774	+	9.28331i	−0.439555	+	0.319356i
$846$	−0.674037			−0.0231739
$847$	39.4879	−	29.8842i	1.35682	−	1.02683i
$848$	−9.78208			−0.335918
$849$	−13.9317	+	10.1219i	−0.478133	+	0.347384i
$850$	0.0739152	+	0.227487i	0.00253527	+	0.00780276i
$851$	1.61560	−	4.97231i	0.0553821	−	0.170449i
$852$	−4.40878	−	3.20317i	−0.151042	−	0.109739i
$853$	−19.7408	−	14.3425i	−0.675913	−	0.491079i	0.196087	−	0.980587i	$-0.437177\pi$
$853$	−19.7408	−	14.3425i	−0.675913	−	0.491079i	−0.871999	+	0.489507i	$0.837177\pi$
$854$	−0.0323259	+	0.0994889i	−0.00110617	+	0.00340444i
$855$	−1.45331	−	4.47283i	−0.0497022	−	0.152968i
$856$	−3.78772	+	2.75194i	−0.129461	+	0.0940592i
$857$	20.6633			0.705846			0.352923	−	0.935652i	$-0.385188\pi$
$857$	20.6633			0.705846			0.352923	+	0.935652i	$0.385188\pi$
$858$	0.0205994	−	0.0655684i	0.000703250	−	0.00223847i
$859$	−10.1686			−0.346949			−0.173474	−	0.984838i	$-0.555499\pi$
$859$	−10.1686			−0.346949			−0.173474	+	0.984838i	$0.555499\pi$
$860$	−18.4927	+	13.4357i	−0.630594	+	0.458153i
$861$	−12.3286	−	37.9435i	−0.420157	−	1.29311i
$862$	0.695554	−	2.14070i	0.0236907	−	0.0729124i
$863$	26.2385	+	19.0634i	0.893169	+	0.648925i	0.936702	−	0.350127i	$-0.113862\pi$
$863$	26.2385	+	19.0634i	0.893169	+	0.648925i	−0.0435335	+	0.999052i	$0.513862\pi$
$864$	0.660866	+	0.480147i	0.0224831	+	0.0163349i
$865$	3.89786	−	11.9964i	0.132531	−	0.407889i
$866$	−0.512454	−	1.57717i	−0.0174139	−	0.0535945i
$867$	−0.809017	+	0.587785i	−0.0274757	+	0.0199622i
$868$	7.74428			0.262858
$869$	−12.3184	−	36.6899i	−0.417872	−	1.24462i
$870$	0.423218			0.0143484
$871$	−2.57296	+	1.86937i	−0.0871814	+	0.0633410i
$872$	1.01840	+	3.13433i	0.0344875	+	0.106142i
$873$	4.04433	−	12.4472i	0.136880	−	0.421273i
$874$	−0.198095	−	0.143924i	−0.00670066	−	0.00486832i
$875$	37.8923	+	27.5304i	1.28099	+	0.930697i
$876$	5.67000	−	17.4505i	0.191572	−	0.589597i
$877$	−16.3137	−	50.2084i	−0.550874	−	1.69542i	−0.706597	−	0.707616i	$-0.749771\pi$
$877$	−16.3137	−	50.2084i	−0.550874	−	1.69542i	0.155723	−	0.987801i	$-0.450229\pi$
$878$	1.13198	−	0.822432i	0.0382025	−	0.0277557i
$879$	−13.7941			−0.465264
$880$	−16.1183	+	0.157281i	−0.543346	+	0.00530195i
$881$	−5.65290			−0.190451			−0.0952255	−	0.995456i	$-0.530357\pi$
$881$	−5.65290			−0.190451			−0.0952255	+	0.995456i	$0.530357\pi$
$882$	0.732944	−	0.532515i	0.0246795	−	0.0179307i
$883$	−6.00664	−	18.4866i	−0.202140	−	0.622122i	−0.999819	−	0.0190398i	$-0.993939\pi$
$883$	−6.00664	−	18.4866i	−0.202140	−	0.622122i	0.797679	−	0.603082i	$-0.206061\pi$
$884$	0.187116	−	0.575884i	0.00629339	−	0.0193691i
$885$	−4.66544	−	3.38964i	−0.156827	−	0.113942i
$886$	−1.44371	−	1.04892i	−0.0485024	−	0.0352391i
$887$	−11.8277	+	36.4020i	−0.397136	+	1.22226i	0.530149	+	0.847904i	$0.322136\pi$
$887$	−11.8277	+	36.4020i	−0.397136	+	1.22226i	−0.927285	+	0.374355i	$0.877864\pi$
$888$	−0.472467	−	1.45410i	−0.0158550	−	0.0487966i
$889$	−36.9873	+	26.8728i	−1.24051	+	0.901286i
$890$	−0.455530			−0.0152694
$891$	−2.70210	−	1.92319i	−0.0905238	−	0.0644293i
$892$	−41.5744			−1.39201
$893$	−30.6947	+	22.3010i	−1.02716	+	0.746275i
$894$	−0.410626	−	1.26378i	−0.0137334	−	0.0422670i
$895$	5.88929	−	18.1254i	0.196857	−	0.605864i
$896$	7.91221	+	5.74856i	0.264328	+	0.192046i
$897$	−0.229040	−	0.166407i	−0.00764743	−	0.00555618i
$898$	0.494237	−	1.52110i	0.0164929	−	0.0507599i
$899$	1.34945	+	4.15319i	0.0450068	+	0.138517i
$900$	−5.65456	+	4.10828i	−0.188485	+	0.136943i
$901$	−2.46273			−0.0820455
$902$	1.61213	−	1.19549i	0.0536782	−	0.0398055i
$903$	−42.1499			−1.40266
$904$	2.34041	−	1.70041i	0.0778409	−	0.0565548i
$905$	6.29746	+	19.3816i	0.209335	+	0.644265i
$906$	0.253963	−	0.781618i	0.00843736	−	0.0259675i
$907$	−9.44271	−	6.86053i	−0.313540	−	0.227800i	0.419874	−	0.907582i	$-0.362074\pi$
$907$	−9.44271	−	6.86053i	−0.313540	−	0.227800i	−0.733414	+	0.679782i	$0.762074\pi$
$908$	4.29961	+	3.12385i	0.142688	+	0.103669i
$909$	−5.55716	+	17.1032i	−0.184319	+	0.567276i
$910$	0.0352735	+	0.108561i	0.00116930	+	0.00359875i
$911$	20.2032	−	14.6785i	0.669363	−	0.486321i	−0.200449	−	0.979704i	$-0.564240\pi$
$911$	20.2032	−	14.6785i	0.669363	−	0.486321i	0.869812	+	0.493383i	$0.164240\pi$
$912$	15.2673			0.505551
$913$	8.42450	−	6.24726i	0.278810	−	0.206754i
$914$	−1.33909			−0.0442932
$915$	−0.336844	+	0.244732i	−0.0111357	+	0.00809058i
$916$	−5.52617	−	17.0078i	−0.182590	−	0.561953i
$917$	−24.2576	+	74.6572i	−0.801057	+	2.46540i
$918$	0.0552438	+	0.0401370i	0.00182332	+	0.00132472i
$919$	14.4857	+	10.5245i	0.477839	+	0.347170i	0.800488	−	0.599348i	$-0.204574\pi$
$919$	14.4857	+	10.5245i	0.477839	+	0.347170i	−0.322650	+	0.946518i	$0.604574\pi$
$920$	0.0962347	−	0.296180i	0.00317277	−	0.00976477i
$921$	2.45233	+	7.54751i	0.0808071	+	0.248699i
$922$	−2.19147	+	1.59220i	−0.0721724	+	0.0524363i
$923$	0.828813			0.0272807
$924$	−24.2726	−	17.2758i	−0.798511	−	0.568331i
$925$	19.6307			0.645453
$926$	−0.943980	+	0.685842i	−0.0310211	+	0.0225382i
$927$	2.52359	+	7.76681i	0.0828856	+	0.255096i
$928$	−1.27864	+	3.93525i	−0.0419734	+	0.129181i
$929$	41.8142	+	30.3798i	1.37188	+	0.996728i	0.997588	+	0.0694171i	$0.0221139\pi$
$929$	41.8142	+	30.3798i	1.37188	+	0.996728i	0.374291	+	0.927311i	$0.377886\pi$
$930$	−0.0582743	−	0.0423388i	−0.00191089	−	0.00138834i
$931$	15.7586	−	48.5000i	0.516467	−	1.58952i
$932$	−10.4725	−	32.2310i	−0.343037	−	1.05576i
$933$	25.4028	−	18.4562i	0.831650	−	0.604229i
$934$	−1.26930			−0.0415328
$935$	−4.05792	+	0.0395971i	−0.132708	+	0.00129496i
$936$	−0.0827926			−0.00270616
$937$	33.7240	−	24.5019i	1.10172	−	0.800443i	0.120376	−	0.992728i	$-0.461590\pi$
$937$	33.7240	−	24.5019i	1.10172	−	0.800443i	0.981339	+	0.192285i	$0.0615899\pi$
$938$	−0.995568	−	3.06404i	−0.0325065	−	0.100045i
$939$	−2.74194	+	8.43883i	−0.0894799	+	0.275391i
$940$	−19.4967	−	14.1652i	−0.635911	−	0.462016i
$941$	−5.18724	−	3.76875i	−0.169099	−	0.122858i	0.500017	−	0.866016i	$-0.333327\pi$
$941$	−5.18724	−	3.76875i	−0.169099	−	0.122858i	−0.669116	+	0.743158i	$0.733327\pi$
$942$	0.197401	−	0.607539i	0.00643168	−	0.0197947i
$943$	−2.55479	−	7.86284i	−0.0831955	−	0.256049i
$944$	15.1453	−	11.0037i	0.492938	−	0.358141i
$945$	5.50843			0.179189
$946$	−0.674888	−	2.01014i	−0.0219425	−	0.0653552i
$947$	−28.6404			−0.930689			−0.465345	−	0.885130i	$-0.654070\pi$
$947$	−28.6404			−0.930689			−0.465345	+	0.885130i	$0.654070\pi$
$948$	−18.8373	+	13.6861i	−0.611806	+	0.444503i
$949$	0.862341	+	2.65401i	0.0279928	+	0.0861529i
$950$	0.284107	−	0.874391i	0.00921764	−	0.0283690i
$951$	10.6562	+	7.74216i	0.345550	+	0.251057i
$952$	0.993657	+	0.721934i	0.0322046	+	0.0233980i
$953$	0.913796	−	2.81237i	0.0296008	−	0.0911018i	−0.935165	−	0.354213i	$-0.884749\pi$
$953$	0.913796	−	2.81237i	0.0296008	−	0.0911018i	0.964765	+	0.263111i	$0.0847487\pi$
$954$	0.0519667	+	0.159937i	0.00168248	+	0.00517816i
$955$	−15.3377	+	11.1435i	−0.496315	+	0.360594i
$956$	−11.1004			−0.359013
$957$	5.03530	−	16.0275i	0.162768	−	0.518097i
$958$	−0.614686			−0.0198596
$959$	−41.7469	+	30.3309i	−1.34808	+	0.979436i
$960$	2.98260	+	9.17949i	0.0962629	+	0.296267i
$961$	−9.34985	+	28.7759i	−0.301608	+	0.928254i
$962$	0.0939520	+	0.0682601i	0.00302913	+	0.00220079i
$963$	−13.8835	−	10.0869i	−0.447388	−	0.325047i
$964$	12.1929	−	37.5259i	0.392707	−	1.20863i
$965$	−4.20911	−	12.9543i	−0.135496	−	0.417014i
$966$	0.232020	−	0.168572i	0.00746511	−	0.00542372i
$967$	24.0387			0.773032			0.386516	−	0.922283i	$-0.373678\pi$
$967$	24.0387			0.773032			0.386516	+	0.922283i	$0.373678\pi$
$968$	0.871500	−	2.87171i	0.0280111	−	0.0923004i
$969$	3.84369			0.123477
$970$	−0.884659	+	0.642743i	−0.0284047	+	0.0206372i
$971$	7.22281	+	22.2295i	0.231791	+	0.713379i	0.997531	+	0.0702289i	$0.0223730\pi$
$971$	7.22281	+	22.2295i	0.231791	+	0.713379i	−0.765740	+	0.643150i	$0.777627\pi$
$972$	−0.616593	+	1.89768i	−0.0197772	+	0.0608681i
$973$	−23.1004	−	16.7834i	−0.740565	−	0.538052i
$974$	1.78679	+	1.29818i	0.0572526	+	0.0415964i
$975$	0.328488	−	1.01098i	0.0105200	−	0.0323774i
$976$	−0.417676	−	1.28547i	−0.0133695	−	0.0411470i
$977$	−26.4444	+	19.2130i	−0.846032	+	0.614678i	−0.924049	−	0.382274i	$-0.875141\pi$
$977$	−26.4444	+	19.2130i	−0.846032	+	0.614678i	0.0780171	+	0.996952i	$0.475141\pi$
$978$	1.15627			0.0369734
$979$	−5.41974	+	17.2512i	−0.173216	+	0.551351i
$980$	32.3915			1.03471
$981$	−9.77274	+	7.10031i	−0.312020	+	0.226696i
$982$	0.184791	+	0.568728i	0.00589692	+	0.0181488i
$983$	−11.0240	+	33.9285i	−0.351612	+	1.08215i	0.606336	+	0.795208i	$0.292639\pi$
$983$	−11.0240	+	33.9285i	−0.351612	+	1.08215i	−0.957948	+	0.286942i	$0.907361\pi$
$984$	−1.95600	−	1.42112i	−0.0623550	−	0.0453035i
$985$	16.5230	+	12.0046i	0.526465	+	0.382499i
$986$	−0.106885	+	0.328960i	−0.00340393	+	0.0104762i
$987$	−13.7322	−	42.2633i	−0.437100	−	1.34526i
$988$	−1.88293	+	1.36803i	−0.0599040	+	0.0435228i
$989$	−8.73451			−0.277741
$990$	0.0881989	+	0.262698i	0.00280314	+	0.00834910i
$991$	10.1506			0.322444			0.161222	−	0.986918i	$-0.448456\pi$
$991$	10.1506			0.322444			0.161222	+	0.986918i	$0.448456\pi$
$992$	0.569743	−	0.413942i	0.0180894	−	0.0131427i
$993$	−9.66494	−	29.7456i	−0.306708	−	0.943949i
$994$	−0.259449	+	0.798502i	−0.00822923	+	0.0253270i
$995$	−10.0890	−	7.33007i	−0.319842	−	0.232379i
$996$	−5.10475	−	3.70882i	−0.161750	−	0.117518i
$997$	−10.1738	+	31.3117i	−0.322207	+	0.991651i	0.650479	+	0.759524i	$0.274568\pi$
$997$	−10.1738	+	31.3117i	−0.322207	+	0.991651i	−0.972686	+	0.232126i	$0.925432\pi$
$998$	−0.904943	−	2.78513i	−0.0286455	−	0.0881616i
$999$	4.53386	−	3.29404i	0.143445	−	0.104219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.256.3	yes	24
11.2	odd	10		6171.2.a.bl.1.6		12
11.4	even	5	inner	561.2.m.d.103.3	✓	24
11.9	even	5		6171.2.a.bk.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.103.3	✓	24	11.4	even	5	inner
561.2.m.d.256.3	yes	24	1.1	even	1	trivial
6171.2.a.bk.1.7		12	11.9	even	5
6171.2.a.bl.1.6		12	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0552438 - 0.0401370i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.616593 + 1.89768i) q^{4} +(0.989888 + 0.719196i) q^{5} +(0.0552438 + 0.0401370i) q^{6} +(-1.39118 + 4.28160i) q^{7} +(0.0843066 + 0.259469i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.0552438 - 0.0401370i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.616593 + 1.89768i) q^{4} +(0.989888 + 0.719196i) q^{5} +(0.0552438 + 0.0401370i) q^{6} +(-1.39118 + 4.28160i) q^{7} +(0.0843066 + 0.259469i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.0835515 q^{10} +(0.994067 - 3.16415i) q^{11} -1.99534 q^{12} +(0.245510 - 0.178374i) q^{13} +(0.0949965 + 0.292369i) q^{14} +(-0.378104 + 1.16368i) q^{15} +(-3.21345 - 2.33471i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.0211013 + 0.0649430i) q^{18} +(1.18776 + 3.65556i) q^{19} +(-1.97516 + 1.43504i) q^{20} -4.50194 q^{21} +(-0.0720833 - 0.214698i) q^{22} -0.932914 q^{23} +(-0.220718 + 0.160361i) q^{24} +(-1.08245 - 3.33144i) q^{25} +(0.00640355 - 0.0197081i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-7.26730 - 5.28001i) q^{28} +(1.56528 - 4.81744i) q^{29} +(0.0258188 + 0.0794622i) q^{30} +(-0.697466 + 0.506739i) q^{31} -0.816875 q^{32} +(3.31647 - 0.0323619i) q^{33} -0.0682851 q^{34} +(-4.45641 + 3.23777i) q^{35} +(-0.616593 - 1.89768i) q^{36} +(-1.73178 + 5.32987i) q^{37} +(0.212340 + 0.154274i) q^{38} +(0.245510 + 0.178374i) q^{39} +(-0.103155 + 0.317478i) q^{40} +(2.73851 + 8.42826i) q^{41} +(-0.248704 + 0.180694i) q^{42} +9.36261 q^{43} +(5.39160 + 3.83741i) q^{44} -1.22357 q^{45} +(-0.0515377 + 0.0374444i) q^{46} +(3.05028 + 9.38781i) q^{47} +(1.22743 - 3.77764i) q^{48} +(-10.7336 - 7.79840i) q^{49} +(-0.193512 - 0.140595i) q^{50} +(0.309017 - 0.951057i) q^{51} +(0.187116 + 0.575884i) q^{52} +(1.99239 - 1.44756i) q^{53} -0.0682851 q^{54} +(3.25966 - 2.41722i) q^{55} -1.22823 q^{56} +(-3.10961 + 2.25926i) q^{57} +(-0.106885 - 0.328960i) q^{58} +(-1.45643 + 4.48242i) q^{59} +(-1.97516 - 1.43504i) q^{60} +(0.275297 + 0.200015i) q^{61} +(-0.0181917 + 0.0559883i) q^{62} +(-1.39118 - 4.28160i) q^{63} +(6.38178 - 4.63663i) q^{64} +0.371313 q^{65} +(0.181915 - 0.134901i) q^{66} -10.4800 q^{67} +(1.61426 - 1.17283i) q^{68} +(-0.288286 - 0.887254i) q^{69} +(-0.116235 + 0.357734i) q^{70} +(2.20954 + 1.60533i) q^{71} +(-0.220718 - 0.160361i) q^{72} +(-2.84163 + 8.74563i) q^{73} +(0.118255 + 0.363950i) q^{74} +(2.83389 - 2.05894i) q^{75} -7.66945 q^{76} +(12.1647 + 8.65808i) q^{77} +0.0207223 q^{78} +(9.44065 - 6.85903i) q^{79} +(-1.50184 - 4.62220i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.489570 + 0.355694i) q^{82} +(2.55834 + 1.85874i) q^{83} +(2.77586 - 8.54323i) q^{84} +(-0.378104 - 1.16368i) q^{85} +(0.517226 - 0.375787i) q^{86} +5.06536 q^{87} +(0.904805 - 0.00882905i) q^{88} -5.45209 q^{89} +(-0.0675946 + 0.0491103i) q^{90} +(0.422176 + 1.29933i) q^{91} +(0.575229 - 1.77037i) q^{92} +(-0.697466 - 0.506739i) q^{93} +(0.545307 + 0.396189i) q^{94} +(-1.45331 + 4.47283i) q^{95} +(-0.252428 - 0.776895i) q^{96} +(-10.5882 + 7.69277i) q^{97} -0.905968 q^{98} +(1.05562 + 3.14415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more