LMFDB - Embedded newform 354.2.e.c.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			79.2
Character	$\chi$	$=$	354.79
Dual form			354.2.e.c.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.907575 + 0.419889i) q^{2} +(0.947653 - 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(0.401618 - 0.241646i) q^{5} +(0.994138 + 0.108119i) q^{6} +(-0.0924092 - 1.70439i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +O(q^{10})$	\(q+(0.907575 + 0.419889i) q^{2} +(0.947653 - 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(0.401618 - 0.241646i) q^{5} +(0.994138 + 0.108119i) q^{6} +(-0.0924092 - 1.70439i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(0.465963 - 0.0506766i) q^{10} +(-0.0193516 - 0.118039i) q^{11} +(0.856857 + 0.515554i) q^{12} +(4.72869 + 3.59466i) q^{13} +(0.631786 - 1.58566i) q^{14} +(0.303437 - 0.357234i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(0.104267 - 1.92310i) q^{17} +(0.976621 - 0.214970i) q^{18} +(-2.59470 - 2.45783i) q^{19} +(0.444175 + 0.149660i) q^{20} +(-0.631786 - 1.58566i) q^{21} +(0.0320004 - 0.115255i) q^{22} +(-1.36313 - 0.300047i) q^{23} +(0.561187 + 0.827689i) q^{24} +(-2.23914 + 4.22346i) q^{25} +(2.78229 + 5.24795i) q^{26} +(0.561187 - 0.827689i) q^{27} +(1.23920 - 1.17383i) q^{28} +(-7.23008 + 3.34499i) q^{29} +(0.425390 - 0.196807i) q^{30} +(-2.74265 + 2.59798i) q^{31} +(-0.561187 + 0.827689i) q^{32} +(-0.0560287 - 0.105681i) q^{33} +(0.902119 - 1.70158i) q^{34} +(-0.448971 - 0.662183i) q^{35} +(0.976621 + 0.214970i) q^{36} +(2.72619 - 9.81884i) q^{37} +(-1.32287 - 3.32015i) q^{38} +(5.62894 + 1.89661i) q^{39} +(0.340282 + 0.322332i) q^{40} +(-3.58642 + 0.789432i) q^{41} +(0.0924092 - 1.70439i) q^{42} +(-0.304167 + 1.85533i) q^{43} +(0.0774371 - 0.0911660i) q^{44} +(0.173488 - 0.435421i) q^{45} +(-1.11115 - 0.844677i) q^{46} +(-0.307797 - 0.185195i) q^{47} +(0.161782 + 0.986827i) q^{48} +(4.06257 - 0.441831i) q^{49} +(-3.80557 + 2.89292i) q^{50} +(-0.515239 - 1.85572i) q^{51} +(0.321578 + 5.93117i) q^{52} +(-7.66235 - 0.833331i) q^{53} +(0.856857 - 0.515554i) q^{54} +(-0.0362956 - 0.0427305i) q^{55} +(1.61754 - 0.545013i) q^{56} +(-3.24366 - 1.50068i) q^{57} -7.96637 q^{58} +(-7.09097 - 2.95266i) q^{59} +0.468711 q^{60} +(7.17385 + 3.31898i) q^{61} +(-3.58003 + 1.20625i) q^{62} +(-1.10502 - 1.30093i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(2.76776 + 0.301012i) q^{65} +(-0.00647583 - 0.119440i) q^{66} +(-0.655295 - 2.36016i) q^{67} +(1.53321 - 1.16552i) q^{68} +(-1.38758 + 0.150908i) q^{69} +(-0.129432 - 0.789499i) q^{70} +(-1.13312 - 0.681777i) q^{71} +(0.796093 + 0.605174i) q^{72} +(-3.67513 + 9.22387i) q^{73} +(6.59705 - 7.76664i) q^{74} +(-0.773368 + 4.71734i) q^{75} +(0.193492 - 3.56874i) q^{76} +(-0.199396 + 0.0438905i) q^{77} +(4.31232 + 4.08485i) q^{78} +(1.42527 + 0.480228i) q^{79} +(0.173488 + 0.435421i) q^{80} +(0.267528 - 0.963550i) q^{81} +(-3.58642 - 0.789432i) q^{82} +(-5.80425 - 8.56062i) q^{83} +(0.799522 - 1.50806i) q^{84} +(-0.422833 - 0.797547i) q^{85} +(-1.05509 + 1.55614i) q^{86} +(-5.78355 + 5.47847i) q^{87} +(0.108560 - 0.0502250i) q^{88} +(-5.62278 + 2.60137i) q^{89} +(0.340282 - 0.322332i) q^{90} +(5.68972 - 8.39171i) q^{91} +(-0.653785 - 1.23317i) q^{92} +(-1.76955 + 3.33772i) q^{93} +(-0.201588 - 0.297320i) q^{94} +(-1.63600 - 0.360111i) q^{95} +(-0.267528 + 0.963550i) q^{96} +(2.38901 + 5.99597i) q^{97} +(3.87261 + 1.30483i) q^{98} +(-0.0868400 - 0.0822592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{4}{29}\right)$	$1$

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 $

$2$	0.907575	+	0.419889i	0.641753	+	0.296906i
$2$	0.907575	+	0.419889i	0.641753	+	0.296906i
$3$	0.947653	−	0.319302i	0.547128	−	0.184349i
$3$	0.947653	−	0.319302i	0.547128	−	0.184349i
$4$	0.647386	+	0.762162i	0.323693	+	0.381081i
$5$	0.401618	−	0.241646i	0.179609	−	0.108067i	−0.422910	−	0.906172i	$-0.638991\pi$
$5$	0.401618	−	0.241646i	0.179609	−	0.108067i	0.602519	+	0.798104i	$0.294164\pi$
$6$	0.994138	+	0.108119i	0.405855	+	0.0441394i
$7$	−0.0924092	−	1.70439i	−0.0349274	−	0.644198i	−0.962620	−	0.270854i	$-0.912694\pi$
$7$	−0.0924092	−	1.70439i	−0.0349274	−	0.644198i	0.927693	−	0.373344i	$-0.121789\pi$
$8$	0.267528	+	0.963550i	0.0945856	+	0.340666i
$9$	0.796093	−	0.605174i	0.265364	−	0.201725i
$10$	0.465963	−	0.0506766i	0.147351	−	0.0160253i
$11$	−0.0193516	−	0.118039i	−0.00583471	−	0.0355902i	0.983749	−	0.179551i	$-0.0574644\pi$
$11$	−0.0193516	−	0.118039i	−0.00583471	−	0.0355902i	−0.989583	+	0.143961i	$0.954016\pi$
$12$	0.856857	+	0.515554i	0.247353	+	0.148828i
$13$	4.72869	+	3.59466i	1.31150	+	0.996979i	0.998890	+	0.0470990i	$0.0149976\pi$
$13$	4.72869	+	3.59466i	1.31150	+	0.996979i	0.312614	+	0.949880i	$0.398795\pi$
$14$	0.631786	−	1.58566i	0.168852	−	0.423786i
$15$	0.303437	−	0.357234i	0.0783471	−	0.0922373i
$16$	−0.161782	+	0.986827i	−0.0404455	+	0.246707i
$17$	0.104267	−	1.92310i	0.0252886	−	0.466420i	−0.958274	−	0.285852i	$-0.907724\pi$
$17$	0.104267	−	1.92310i	0.0252886	−	0.466420i	0.983562	−	0.180568i	$-0.0577937\pi$
$18$	0.976621	−	0.214970i	0.230192	−	0.0506690i
$19$	−2.59470	−	2.45783i	−0.595265	−	0.563865i	0.329619	−	0.944114i	$-0.393080\pi$
$19$	−2.59470	−	2.45783i	−0.595265	−	0.563865i	−0.924884	+	0.380249i	$0.875838\pi$
$20$	0.444175	+	0.149660i	0.0993206	+	0.0334650i
$21$	−0.631786	−	1.58566i	−0.137867	−	0.346020i
$22$	0.0320004	−	0.115255i	0.00682251	−	0.0245725i
$23$	−1.36313	−	0.300047i	−0.284231	−	0.0625641i	0.0705665	−	0.997507i	$-0.477519\pi$
$23$	−1.36313	−	0.300047i	−0.284231	−	0.0625641i	−0.354798	+	0.934943i	$0.615450\pi$
$24$	0.561187	+	0.827689i	0.114552	+	0.168951i
$25$	−2.23914	+	4.22346i	−0.447828	+	0.844692i
$26$	2.78229	+	5.24795i	0.545652	+	1.02921i
$27$	0.561187	−	0.827689i	0.108001	−	0.159289i
$28$	1.23920	−	1.17383i	0.234186	−	0.221833i
$29$	−7.23008	+	3.34499i	−1.34259	+	0.621150i	−0.953874	−	0.300207i	$-0.902944\pi$
$29$	−7.23008	+	3.34499i	−1.34259	+	0.621150i	−0.388719	+	0.921356i	$0.627082\pi$
$30$	0.425390	−	0.196807i	0.0776653	−	0.0359318i
$31$	−2.74265	+	2.59798i	−0.492595	+	0.466611i	−0.893213	−	0.449634i	$-0.851554\pi$
$31$	−2.74265	+	2.59798i	−0.492595	+	0.466611i	0.400618	+	0.916245i	$0.368796\pi$
$32$	−0.561187	+	0.827689i	−0.0992048	+	0.146316i
$33$	−0.0560287	−	0.105681i	−0.00975334	−	0.0183968i
$34$	0.902119	−	1.70158i	0.154712	−	0.291818i
$35$	−0.448971	−	0.662183i	−0.0758900	−	0.111929i
$36$	0.976621	+	0.214970i	0.162770	+	0.0358284i
$37$	2.72619	−	9.81884i	0.448183	−	1.61421i	−0.302228	−	0.953236i	$-0.597730\pi$
$37$	2.72619	−	9.81884i	0.448183	−	1.61421i	0.750411	−	0.660972i	$-0.229856\pi$
$38$	−1.32287	−	3.32015i	−0.214598	−	0.538599i
$39$	5.62894	+	1.89661i	0.901352	+	0.303701i
$40$	0.340282	+	0.322332i	0.0538033	+	0.0509652i
$41$	−3.58642	+	0.789432i	−0.560105	+	0.123289i	−0.485995	−	0.873962i	$-0.661543\pi$
$41$	−3.58642	+	0.789432i	−0.560105	+	0.123289i	−0.0741103	+	0.997250i	$0.523612\pi$
$42$	0.0924092	−	1.70439i	0.0142591	−	0.262993i
$43$	−0.304167	+	1.85533i	−0.0463850	+	0.282936i	−0.999826	−	0.0186431i	$-0.994065\pi$
$43$	−0.304167	+	1.85533i	−0.0463850	+	0.282936i	0.953441	+	0.301579i	$0.0975137\pi$
$44$	0.0774371	−	0.0911660i	0.0116741	−	0.0137438i
$45$	0.173488	−	0.435421i	0.0258620	−	0.0649088i
$46$	−1.11115	−	0.844677i	−0.163831	−	0.124541i
$47$	−0.307797	−	0.185195i	−0.0448968	−	0.0270135i	0.492928	−	0.870070i	$-0.335926\pi$
$47$	−0.307797	−	0.185195i	−0.0448968	−	0.0270135i	−0.537825	+	0.843056i	$0.680754\pi$
$48$	0.161782	+	0.986827i	0.0233512	+	0.142436i
$49$	4.06257	−	0.441831i	0.580367	−	0.0631187i
$50$	−3.80557	+	2.89292i	−0.538189	+	0.409121i
$51$	−0.515239	−	1.85572i	−0.0721479	−	0.259853i
$52$	0.321578	+	5.93117i	0.0445949	+	0.822505i
$53$	−7.66235	−	0.833331i	−1.05251	−	0.114467i	−0.434524	−	0.900660i	$-0.643084\pi$
$53$	−7.66235	−	0.833331i	−1.05251	−	0.114467i	−0.617981	+	0.786193i	$0.712049\pi$
$54$	0.856857	−	0.515554i	0.116603	−	0.0701580i
$55$	−0.0362956	−	0.0427305i	−0.00489410	−	0.00576178i
$56$	1.61754	−	0.545013i	0.216153	−	0.0728304i
$57$	−3.24366	−	1.50068i	−0.429634	−	0.198770i
$58$	−7.96637			−1.04604
$59$	−7.09097	−	2.95266i	−0.923165	−	0.384403i
$59$	−7.09097	−	2.95266i	−0.923165	−	0.384403i
$60$	0.468711			0.0605103
$61$	7.17385	+	3.31898i	0.918518	+	0.424951i	0.821420	−	0.570323i	$-0.193182\pi$
$61$	7.17385	+	3.31898i	0.918518	+	0.424951i	0.0970973	+	0.995275i	$0.469044\pi$
$62$	−3.58003	+	1.20625i	−0.454664	+	0.153194i
$63$	−1.10502	−	1.30093i	−0.139219	−	0.163901i
$64$	−0.856857	+	0.515554i	−0.107107	+	0.0644442i
$65$	2.76776	+	0.301012i	0.343299	+	0.0373360i
$66$	−0.00647583	−	0.119440i	−0.000797119	−	0.0147020i
$67$	−0.655295	−	2.36016i	−0.0800571	−	0.288340i	0.912675	−	0.408687i	$-0.134013\pi$
$67$	−0.655295	−	2.36016i	−0.0800571	−	0.288340i	−0.992732	+	0.120347i	$0.961599\pi$
$68$	1.53321	−	1.16552i	0.185930	−	0.141340i
$69$	−1.38758	+	0.150908i	−0.167045	+	0.0181672i
$70$	−0.129432	−	0.789499i	−0.0154701	−	0.0943632i
$71$	−1.13312	−	0.681777i	−0.134477	−	0.0809120i	0.446726	−	0.894671i	$-0.352590\pi$
$71$	−1.13312	−	0.681777i	−0.134477	−	0.0809120i	−0.581202	+	0.813759i	$0.697418\pi$
$72$	0.796093	+	0.605174i	0.0938205	+	0.0713205i
$73$	−3.67513	+	9.22387i	−0.430141	+	1.07957i	0.540991	+	0.841028i	$0.318049\pi$
$73$	−3.67513	+	9.22387i	−0.430141	+	1.07957i	−0.971132	+	0.238544i	$0.923330\pi$
$74$	6.59705	−	7.76664i	0.766891	−	0.902854i
$75$	−0.773368	+	4.71734i	−0.0893009	+	0.544711i
$76$	0.193492	−	3.56874i	0.0221950	−	0.409363i
$77$	−0.199396	+	0.0438905i	−0.0227233	+	0.00500178i
$78$	4.31232	+	4.08485i	0.488275	+	0.462518i
$79$	1.42527	+	0.480228i	0.160355	+	0.0540299i	0.398334	−	0.917240i	$-0.369588\pi$
$79$	1.42527	+	0.480228i	0.160355	+	0.0540299i	−0.237979	+	0.971270i	$0.576485\pi$
$80$	0.173488	+	0.435421i	0.0193965	+	0.0486816i
$81$	0.267528	−	0.963550i	0.0297254	−	0.107061i
$82$	−3.58642	−	0.789432i	−0.396054	−	0.0871781i
$83$	−5.80425	−	8.56062i	−0.637099	−	0.939650i	−0.999969	−	0.00781080i	$-0.997514\pi$
$83$	−5.80425	−	8.56062i	−0.637099	−	0.939650i	0.362871	−	0.931839i	$-0.381797\pi$
$84$	0.799522	−	1.50806i	0.0872350	−	0.164543i
$85$	−0.422833	−	0.797547i	−0.0458627	−	0.0865062i
$86$	−1.05509	+	1.55614i	−0.113773	+	0.167803i
$87$	−5.78355	+	5.47847i	−0.620062	+	0.587354i
$88$	0.108560	−	0.0502250i	0.0115725	−	0.00535401i
$89$	−5.62278	+	2.60137i	−0.596013	+	0.275745i	−0.694615	−	0.719382i	$-0.744425\pi$
$89$	−5.62278	+	2.60137i	−0.596013	+	0.275745i	0.0986016	+	0.995127i	$0.468563\pi$
$90$	0.340282	−	0.322332i	0.0358689	−	0.0339768i
$91$	5.68972	−	8.39171i	0.596445	−	0.879690i
$92$	−0.653785	−	1.23317i	−0.0681618	−	0.128567i
$93$	−1.76955	+	3.33772i	−0.183493	+	0.346105i
$94$	−0.201588	−	0.297320i	−0.0207922	−	0.0306662i
$95$	−1.63600	−	0.360111i	−0.167850	−	0.0369466i
$96$	−0.267528	+	0.963550i	−0.0273045	+	0.0983419i
$97$	2.38901	+	5.99597i	0.242568	+	0.608799i	0.998973	−	0.0453041i	$-0.0144257\pi$
$97$	2.38901	+	5.99597i	0.242568	+	0.608799i	−0.756406	+	0.654103i	$0.773046\pi$
$98$	3.87261	+	1.30483i	0.391192	+	0.131808i
$99$	−0.0868400	−	0.0822592i	−0.00872774	−	0.00826736i
$100$	−4.66855	+	1.02763i	−0.466855	+	0.102763i
$101$	0.0503123	−	0.927955i	0.00500626	−	0.0923350i	−0.994962	−	0.100248i	$-0.968036\pi$
$101$	0.0503123	−	0.927955i	0.00500626	−	0.0923350i	0.999969	+	0.00791353i	$0.00251898\pi$
$102$	0.311580	−	1.90055i	0.0308510	−	0.188183i
$103$	11.0423	−	13.0000i	1.08803	−	1.28093i	0.130863	−	0.991400i	$-0.458225\pi$
$103$	11.0423	−	13.0000i	1.08803	−	1.28093i	0.957169	−	0.289530i	$-0.0934989\pi$
$104$	−2.19858	+	5.51801i	−0.215588	+	0.541085i
$105$	−0.636905	−	0.484163i	−0.0621556	−	0.0472494i
$106$	−6.60426	−	3.97365i	−0.641462	−	0.385955i
$107$	1.35257	+	8.25031i	0.130758	+	0.797588i	0.968036	+	0.250811i	$0.0806972\pi$
$107$	1.35257	+	8.25031i	0.130758	+	0.797588i	−0.837278	+	0.546777i	$0.815855\pi$
$108$	0.994138	−	0.108119i	0.0956610	−	0.0104038i
$109$	−4.05276	+	3.08083i	−0.388184	+	0.295090i	−0.781005	−	0.624525i	$-0.785292\pi$
$109$	−4.05276	+	3.08083i	−0.388184	+	0.295090i	0.392820	+	0.919615i	$0.371499\pi$
$110$	−0.0149989	−	0.0540213i	−0.00143009	−	0.00515073i
$111$	−0.551691	−	10.1753i	−0.0523641	−	0.965800i
$112$	1.69689	+	0.184547i	0.160341	+	0.0174381i
$113$	−4.48636	+	2.69935i	−0.422041	+	0.253934i	−0.710696	−	0.703500i	$-0.751620\pi$
$113$	−4.48636	+	2.69935i	−0.422041	+	0.253934i	0.288655	+	0.957433i	$0.406792\pi$
$114$	−2.31375	−	2.72396i	−0.216703	−	0.255122i
$115$	−0.619961	+	0.208889i	−0.0578117	+	0.0194790i
$116$	−7.23008	−	3.34499i	−0.671296	−	0.310575i
$117$	5.93988			0.549142
$118$	−5.19580	−	5.65718i	−0.478312	−	0.520786i
$119$	−3.28734			−0.301350
$120$	0.425390	+	0.196807i	0.0388327	+	0.0179659i
$121$	10.4106	−	3.50775i	0.946421	−	0.318886i
$122$	5.11721	+	6.02444i	0.463290	+	0.545428i
$123$	−3.14662	+	1.89326i	−0.283721	+	0.170709i
$124$	−3.75564	−	0.408450i	−0.337266	−	0.0366799i
$125$	0.248180	+	4.57741i	0.0221979	+	0.409416i
$126$	−0.456642	−	1.64468i	−0.0406809	−	0.146519i
$127$	12.3789	−	9.41017i	1.09845	−	0.835018i	0.111134	−	0.993805i	$-0.464552\pi$
$127$	12.3789	−	9.41017i	1.09845	−	0.835018i	0.987313	+	0.158787i	$0.0507585\pi$
$128$	−0.994138	+	0.108119i	−0.0878702	+	0.00955646i
$129$	0.304167	+	1.85533i	0.0267804	+	0.163353i
$130$	2.38556	+	1.43535i	0.209228	+	0.125888i
$131$	0.0498591	+	0.0379019i	0.00435621	+	0.00331151i	0.607350	−	0.794434i	$-0.292233\pi$
$131$	0.0498591	+	0.0379019i	0.00435621	+	0.00331151i	−0.602994	+	0.797746i	$0.706026\pi$
$132$	0.0442741	−	0.111120i	0.00385356	−	0.00967172i
$133$	−3.94932	+	4.64950i	−0.342449	+	0.403163i
$134$	0.396276	−	2.41718i	0.0342330	−	0.208812i
$135$	0.0253755	−	0.468023i	0.00218397	−	0.0402810i
$136$	1.88090	−	0.414017i	0.161286	−	0.0355016i
$137$	10.4818	+	9.92890i	0.895521	+	0.848283i	0.989087	−	0.147330i	$-0.0470680\pi$
$137$	10.4818	+	9.92890i	0.895521	+	0.848283i	−0.0935661	+	0.995613i	$0.529827\pi$
$138$	−1.32269	−	0.445668i	−0.112595	−	0.0379377i
$139$	−0.348193	−	0.873899i	−0.0295334	−	0.0741231i	0.913470	−	0.406905i	$-0.133392\pi$
$139$	−0.348193	−	0.873899i	−0.0295334	−	0.0741231i	−0.943004	+	0.332782i	$0.892013\pi$
$140$	0.214033	−	0.770877i	0.0180891	−	0.0651510i
$141$	−0.350818	−	0.0772209i	−0.0295442	−	0.00650318i
$142$	−0.742123	−	1.09455i	−0.0622775	−	0.0918525i
$143$	0.332803	−	0.627734i	0.0278304	−	0.0524937i
$144$	0.468408	+	0.883512i	0.0390340	+	0.0736260i
$145$	−2.09543	+	3.09053i	−0.174016	+	0.256654i
$146$	−7.20846	+	6.82821i	−0.596576	+	0.565107i
$147$	3.70883	−	1.71589i	0.305899	−	0.141524i
$148$	9.24845	−	4.27879i	0.760218	−	0.351714i
$149$	13.4967	−	12.7847i	1.10569	−	1.04737i	0.107104	−	0.994248i	$-0.465842\pi$
$149$	13.4967	−	12.7847i	1.10569	−	1.04737i	0.998588	−	0.0531193i	$-0.0169164\pi$
$150$	−2.68265	+	3.95661i	−0.219037	+	0.323056i
$151$	−5.08238	−	9.58639i	−0.413598	−	0.780129i	0.585945	−	0.810351i	$-0.300723\pi$
$151$	−5.08238	−	9.58639i	−0.413598	−	0.780129i	−0.999543	+	0.0302217i	$0.990379\pi$
$152$	1.67409	−	3.15766i	0.135786	−	0.256120i
$153$	−1.08080	−	1.59407i	−0.0873778	−	0.128873i
$154$	−0.199396	−	0.0438905i	−0.0160678	−	0.00353680i
$155$	−0.473709	+	1.70615i	−0.0380492	+	0.137041i
$156$	2.19858	+	5.51801i	0.176027	+	0.441794i
$157$	0.320570	+	0.108013i	0.0255843	+	0.00862036i	0.332065	−	0.943257i	$-0.392255\pi$
$157$	0.320570	+	0.108013i	0.0255843	+	0.00862036i	−0.306480	+	0.951877i	$0.599151\pi$
$158$	1.09189	+	1.03430i	0.0868664	+	0.0822842i
$159$	−7.52734	+	1.65689i	−0.596957	+	0.131400i
$160$	−0.0253755	+	0.468023i	−0.00200611	+	0.0370005i
$161$	−0.385431	+	2.35102i	−0.0303762	+	0.185287i
$162$	0.647386	−	0.762162i	0.0508635	−	0.0598811i
$163$	−8.47782	+	21.2777i	−0.664034	+	1.66660i	0.0786034	+	0.996906i	$0.474954\pi$
$163$	−8.47782	+	21.2777i	−0.664034	+	1.66660i	−0.742637	+	0.669694i	$0.766425\pi$
$164$	−2.92348	−	2.22237i	−0.228285	−	0.173538i
$165$	−0.0480396	−	0.0289044i	−0.00373988	−	0.00225021i
$166$	−1.67328	−	10.2065i	−0.129872	−	0.792182i
$167$	3.33385	−	0.362578i	0.257981	−	0.0280571i	0.0217853	−	0.999763i	$-0.493065\pi$
$167$	3.33385	−	0.362578i	0.257981	−	0.0280571i	0.236195	+	0.971706i	$0.424099\pi$
$168$	1.35884	−	1.03297i	0.104837	−	0.0796951i
$169$	5.96110	+	21.4700i	0.458546	+	1.65153i
$170$	−0.0488713	−	0.901377i	−0.00374825	−	0.0691325i
$171$	−3.55304	−	0.386416i	−0.271707	−	0.0295500i
$172$	−1.61098	+	0.969294i	−0.122836	+	0.0739080i
$173$	10.3645	+	12.2020i	0.787996	+	0.927701i	0.998757	−	0.0498368i	$-0.0158701\pi$
$173$	10.3645	+	12.2020i	0.787996	+	0.927701i	−0.210761	+	0.977538i	$0.567594\pi$
$174$	−7.54936	+	2.54367i	−0.572315	+	0.192836i
$175$	7.40533	+	3.42607i	0.559791	+	0.258987i
$176$	0.119615			0.00901632
$177$	−7.66257	−	0.533939i	−0.575954	−	0.0401333i
$178$	−6.19538			−0.464363
$179$	14.5632	+	6.73767i	1.08851	+	0.503597i	0.880266	−	0.474481i	$-0.157364\pi$
$179$	14.5632	+	6.73767i	1.08851	+	0.503597i	0.208241	+	0.978078i	$0.433226\pi$
$180$	0.444175	−	0.149660i	0.0331069	−	0.0111550i
$181$	5.65530	+	6.65794i	0.420355	+	0.494881i	0.931055	−	0.364879i	$-0.118889\pi$
$181$	5.65530	+	6.65794i	0.420355	+	0.494881i	−0.510700	+	0.859759i	$0.670614\pi$
$182$	8.68744	−	5.22706i	0.643956	−	0.387455i
$183$	7.85808	+	0.854617i	0.580886	+	0.0631751i
$184$	−0.0755648	−	1.39371i	−0.00557071	−	0.102746i
$185$	−1.27779	−	4.60220i	−0.0939453	−	0.338360i
$186$	−3.00747	+	2.28622i	−0.220518	+	0.167634i
$187$	−0.229019	+	0.0249073i	−0.0167475	+	0.00182140i
$188$	−0.0581148	−	0.354484i	−0.00423846	−	0.0258534i
$189$	−1.46256	−	0.879994i	−0.106386	−	0.0640102i
$190$	−1.33359	−	1.01377i	−0.0967486	−	0.0735464i
$191$	10.1808	−	25.5520i	0.736659	−	1.84888i	0.276607	−	0.960983i	$-0.410790\pi$
$191$	10.1808	−	25.5520i	0.736659	−	1.84888i	0.460052	−	0.887892i	$-0.347831\pi$
$192$	−0.647386	+	0.762162i	−0.0467211	+	0.0550043i
$193$	1.10413	−	6.73492i	0.0794774	−	0.484790i	−0.916855	−	0.399221i	$-0.869281\pi$
$193$	1.10413	−	6.73492i	0.0794774	−	0.484790i	0.996332	−	0.0855697i	$-0.0272710\pi$
$194$	−0.349433	+	6.44492i	−0.0250878	+	0.462718i
$195$	2.71899	−	0.598496i	0.194711	−	0.0428592i
$196$	2.96680	+	2.81030i	0.211914	+	0.200736i
$197$	13.9955	+	4.71562i	0.997136	+	0.335974i	0.770108	−	0.637914i	$-0.220203\pi$
$197$	13.9955	+	4.71562i	0.997136	+	0.335974i	0.227028	+	0.973888i	$0.427099\pi$
$198$	−0.0442741	−	0.111120i	−0.00314642	−	0.00789692i
$199$	−0.318062	+	1.14555i	−0.0225468	+	0.0812062i	−0.973968	−	0.226688i	$-0.927210\pi$
$199$	−0.318062	+	1.14555i	−0.0225468	+	0.0812062i	0.951421	+	0.307894i	$0.0996242\pi$
$200$	−4.66855	−	1.02763i	−0.330116	−	0.0726641i
$201$	−1.37460	−	2.02738i	−0.0969565	−	0.143000i
$202$	0.435300	−	0.821064i	0.0306276	−	0.0577698i
$203$	6.36929	+	12.0138i	0.447037	+	0.843201i
$204$	1.08080	−	1.59407i	0.0756714	−	0.111607i
$205$	−1.24961	+	1.18369i	−0.0872766	+	0.0826728i
$206$	15.4803	−	7.16195i	1.07856	−	0.498997i
$207$	−1.26676	+	0.586064i	−0.0880456	+	0.0407342i
$208$	−4.31232	+	4.08485i	−0.299006	+	0.283233i
$209$	−0.239909	+	0.353839i	−0.0165948	+	0.0244756i
$210$	−0.374745	−	0.706844i	−0.0258598	−	0.0487768i
$211$	3.90193	−	7.35982i	0.268620	−	0.506671i	−0.712103	−	0.702075i	$-0.752257\pi$
$211$	3.90193	−	7.35982i	0.268620	−	0.506671i	0.980723	+	0.195404i	$0.0626019\pi$
$212$	−4.32537	−	6.37944i	−0.297068	−	0.438142i
$213$	−1.29150	−	0.284280i	−0.0884920	−	0.0194786i
$214$	−2.23666	+	8.05571i	−0.152895	+	0.550677i
$215$	0.326175	+	0.818637i	0.0222449	+	0.0558306i
$216$	0.947653	+	0.319302i	0.0644796	+	0.0217257i
$217$	4.68141	+	4.43447i	0.317795	+	0.301031i
$218$	−4.97179	+	1.09437i	−0.336732	+	0.0741204i
$219$	−0.537549	+	9.91450i	−0.0363242	+	0.669960i
$220$	0.00907028	−	0.0553263i	0.000611518	−	0.00373010i
$221$	7.40594	−	8.71894i	0.498177	−	0.586500i
$222$	3.77181	−	9.46653i	0.253147	−	0.635352i
$223$	−10.5996	−	8.05763i	−0.709804	−	0.539579i	0.186808	−	0.982396i	$-0.440186\pi$
$223$	−10.5996	−	8.05763i	−0.709804	−	0.539579i	−0.896612	+	0.442818i	$0.853979\pi$
$224$	1.46256	+	0.879994i	0.0977215	+	0.0587971i
$225$	0.773368	+	4.71734i	0.0515579	+	0.314489i
$226$	−5.20514	+	0.566093i	−0.346240	+	0.0376559i
$227$	7.75020	−	5.89155i	0.514399	−	0.391036i	−0.315521	−	0.948919i	$-0.602179\pi$
$227$	7.75020	−	5.89155i	0.514399	−	0.391036i	0.829920	+	0.557883i	$0.188386\pi$
$228$	−0.956143	−	3.44371i	−0.0633221	−	0.228066i
$229$	0.831666	+	15.3392i	0.0549581	+	1.01364i	0.887829	+	0.460174i	$0.152213\pi$
$229$	0.831666	+	15.3392i	0.0549581	+	1.01364i	−0.832871	+	0.553468i	$0.813304\pi$
$230$	−0.650372	−	0.0707322i	−0.0428842	−	0.00466394i
$231$	−0.174944	+	0.105261i	−0.0115105	+	0.00692563i
$232$	−5.15732	−	6.07167i	−0.338595	−	0.398624i
$233$	−25.2740	+	8.51581i	−1.65576	+	0.557889i	−0.983260	−	0.182211i	$-0.941675\pi$
$233$	−25.2740	+	8.51581i	−1.65576	+	0.557889i	−0.672497	+	0.740100i	$0.734778\pi$
$234$	5.39089	+	2.49409i	0.352413	+	0.163044i
$235$	−0.168369			−0.0109832
$236$	−2.34019	−	7.31598i	−0.152333	−	0.476229i
$237$	1.50399			0.0976950
$238$	−2.98351	−	1.38032i	−0.193392	−	0.0894728i
$239$	19.3024	−	6.50374i	1.24857	−	0.420692i	0.384060	−	0.923308i	$-0.374526\pi$
$239$	19.3024	−	6.50374i	1.24857	−	0.420692i	0.864510	+	0.502616i	$0.167629\pi$
$240$	0.303437	+	0.357234i	0.0195868	+	0.0230593i
$241$	−1.78692	+	1.07515i	−0.115105	+	0.0692566i	−0.571942	−	0.820294i	$-0.693810\pi$
$241$	−1.78692	+	1.07515i	−0.115105	+	0.0692566i	0.456837	+	0.889550i	$0.348982\pi$
$242$	10.9213	+	1.18776i	0.702047	+	0.0763523i
$243$	−0.0541389	−	0.998533i	−0.00347301	−	0.0640559i
$244$	2.11465	+	7.61630i	0.135377	+	0.487583i
$245$	1.52483	−	1.15915i	0.0974181	−	0.0740553i
$246$	−3.65075	+	0.397043i	−0.232764	+	0.0253146i
$247$	−3.43448	−	20.9494i	−0.218530	−	1.33298i
$248$	−3.23702	−	1.94765i	−0.205551	−	0.123676i
$249$	−8.23383	−	6.25920i	−0.521798	−	0.396660i
$250$	−1.69676	+	4.25856i	−0.107313	+	0.269335i
$251$	−8.73070	+	10.2786i	−0.551077	+	0.648778i	−0.965222	−	0.261433i	$-0.915805\pi$
$251$	−8.73070	+	10.2786i	−0.551077	+	0.648778i	0.414145	+	0.910211i	$0.364081\pi$
$252$	0.276144	−	1.68441i	0.0173955	−	0.106108i
$253$	−0.00903868	+	0.166709i	−0.000568257	+	0.0104809i
$254$	15.1860	−	3.34269i	0.952854	−	0.209739i
$255$	−0.655357	−	0.620787i	−0.0410400	−	0.0388752i
$256$	−0.947653	−	0.319302i	−0.0592283	−	0.0199563i
$257$	4.24560	+	10.6556i	0.264833	+	0.664681i	0.999912	−	0.0133013i	$-0.00423404\pi$
$257$	4.24560	+	10.6556i	0.264833	+	0.664681i	−0.735079	+	0.677982i	$0.762855\pi$
$258$	−0.502981	+	1.81157i	−0.0313142	+	0.112784i
$259$	−16.9870	−	3.73913i	−1.05552	−	0.232338i
$260$	1.56239	+	2.30436i	0.0968955	+	0.142910i
$261$	−3.73152	+	7.03839i	−0.230975	+	0.435665i
$262$	0.0293363	+	0.0553342i	0.00181240	+	0.00341856i
$263$	7.11482	−	10.4936i	0.438718	−	0.647061i	−0.542479	−	0.840069i	$-0.682514\pi$
$263$	7.11482	−	10.4936i	0.438718	−	0.647061i	0.981197	+	0.193008i	$0.0618245\pi$
$264$	0.0868400	−	0.0822592i	0.00534463	−	0.00506270i
$265$	−3.27871	+	1.51689i	−0.201410	+	0.0931820i
$266$	−5.53658	+	2.56149i	−0.339469	+	0.157055i
$267$	−4.49782	+	4.26056i	−0.275262	+	0.260742i
$268$	1.37460	−	2.02738i	0.0839668	−	0.123842i
$269$	−6.79528	−	12.8173i	−0.414315	−	0.781482i	0.585253	−	0.810851i	$-0.300995\pi$
$269$	−6.79528	−	12.8173i	−0.414315	−	0.781482i	−0.999569	+	0.0293689i	$0.990650\pi$
$270$	0.219548	−	0.414112i	0.0133613	−	0.0252020i
$271$	6.22065	+	9.17477i	0.377878	+	0.557328i	0.968307	−	0.249761i	$-0.0803521\pi$
$271$	6.22065	+	9.17477i	0.377878	+	0.557328i	−0.590430	+	0.807089i	$0.701042\pi$
$272$	1.88090	+	0.414017i	0.114046	+	0.0251034i
$273$	2.71240	−	9.76917i	0.164162	−	0.591257i
$274$	5.34400	+	13.4124i	0.322843	+	0.810274i
$275$	0.541865	+	0.182576i	0.0326757	+	0.0110097i
$276$	−1.01331	−	0.959862i	−0.0609943	−	0.0577769i
$277$	−6.21256	+	1.36749i	−0.373277	+	0.0821644i	−0.397647	−	0.917539i	$-0.630173\pi$
$277$	−6.21256	+	1.36749i	−0.373277	+	0.0821644i	0.0243701	+	0.999703i	$0.492242\pi$
$278$	0.0509291	−	0.939332i	0.00305452	−	0.0563374i
$279$	−0.611177	+	3.72802i	−0.0365902	+	0.223191i
$280$	0.517934	−	0.609759i	0.0309525	−	0.0364401i
$281$	10.7925	−	27.0872i	0.643827	−	1.61588i	−0.136592	−	0.990627i	$-0.543615\pi$
$281$	10.7925	−	27.0872i	0.643827	−	1.61588i	0.780419	−	0.625257i	$-0.215006\pi$
$282$	−0.285970	−	0.217389i	−0.0170293	−	0.0129453i
$283$	−7.59884	−	4.57207i	−0.451704	−	0.271781i	0.271470	−	0.962447i	$-0.412490\pi$
$283$	−7.59884	−	4.57207i	−0.451704	−	0.271781i	−0.723174	+	0.690666i	$0.757318\pi$
$284$	−0.213943	−	1.30499i	−0.0126952	−	0.0774372i
$285$	−1.66535	+	0.181117i	−0.0986466	+	0.0107285i
$286$	0.565623	−	0.429975i	0.0334460	−	0.0254250i
$287$	1.67692	+	6.03971i	0.0989853	+	0.356513i
$288$	0.0541389	+	0.998533i	0.00319017	+	0.0588391i
$289$	13.2129	+	1.43699i	0.777230	+	0.0845288i
$290$	−3.19944	+	1.92504i	−0.187878	+	0.113042i
$291$	4.17848	+	4.91929i	0.244947	+	0.288374i
$292$	−9.40931	+	3.17037i	−0.550638	+	0.185532i
$293$	9.79595	+	4.53209i	0.572285	+	0.264767i	0.684617	−	0.728903i	$-0.259970\pi$
$293$	9.79595	+	4.53209i	0.572285	+	0.264767i	−0.112331	+	0.993671i	$0.535832\pi$
$294$	4.08652			0.238331
$295$	−3.56136	+	0.527660i	−0.207350	+	0.0307216i
$296$	10.1903			0.592298
$297$	−0.108560	−	0.0502250i	−0.00629927	−	0.00291435i
$298$	17.6174	−	5.93601i	1.02055	−	0.343864i
$299$	−5.36724	−	6.31880i	−0.310395	−	0.365426i
$300$	−4.09604	+	2.46451i	−0.236485	+	0.142288i
$301$	3.19032	+	0.346968i	0.183887	+	0.0199989i
$302$	−0.587424	−	10.8344i	−0.0338025	−	0.623450i
$303$	−0.248619	−	0.895444i	−0.0142828	−	0.0514419i
$304$	2.84523	−	2.16288i	0.163185	−	0.124050i
$305$	3.68317	−	0.400568i	0.210897	−	0.0229365i
$306$	−0.311580	−	1.90055i	−0.0178118	−	0.108647i
$307$	−29.8407	−	17.9546i	−1.70310	−	1.02472i	−0.908844	−	0.417137i	$-0.863034\pi$
$307$	−29.8407	−	17.9546i	−1.70310	−	1.02472i	−0.794255	−	0.607584i	$-0.792139\pi$
$308$	−0.162538	−	0.123558i	−0.00926147	−	0.00704039i
$309$	6.31336	−	15.8453i	0.359155	−	0.901410i
$310$	−1.14632	+	1.34955i	−0.0651065	+	0.0766494i
$311$	0.237469	−	1.44850i	0.0134656	−	0.0821366i	−0.979239	−	0.202710i	$-0.935025\pi$
$311$	0.237469	−	1.44850i	0.0134656	−	0.0821366i	0.992704	+	0.120574i	$0.0384733\pi$
$312$	−0.321578	+	5.93117i	−0.0182058	+	0.335786i
$313$	−23.6714	+	5.21048i	−1.33799	+	0.294514i	−0.825608	−	0.564244i	$-0.809168\pi$
$313$	−23.6714	+	5.21048i	−1.33799	+	0.294514i	−0.512381	+	0.858758i	$0.671237\pi$
$314$	0.245589	+	0.232634i	0.0138594	+	0.0131283i
$315$	−0.758159	−	0.255453i	−0.0427174	−	0.0143932i
$316$	0.556686	+	1.39718i	0.0313160	+	0.0785973i
$317$	2.00882	−	7.23511i	0.112827	−	0.406364i	−0.885471	−	0.464695i	$-0.846164\pi$
$317$	2.00882	−	7.23511i	0.112827	−	0.406364i	0.998297	+	0.0583306i	$0.0185777\pi$
$318$	−7.52734	−	1.65689i	−0.422112	−	0.0929139i
$319$	0.534754	+	0.788703i	0.0299405	+	0.0441589i
$320$	−0.219548	+	0.414112i	−0.0122731	+	0.0231495i
$321$	3.91611	+	7.38656i	0.218576	+	0.412277i
$322$	−1.33698	+	1.97189i	−0.0745068	+	0.109889i
$323$	−4.99719	+	4.73359i	−0.278051	+	0.263384i
$324$	0.907575	−	0.419889i	0.0504209	−	0.0233272i
$325$	−25.7701	+	11.9225i	−1.42947	+	0.661343i
$326$	−16.6285	+	15.7514i	−0.920970	+	0.872389i
$327$	−2.85690	+	4.21361i	−0.157987	+	0.233013i
$328$	−1.72013	−	3.24450i	−0.0949781	−	0.179148i
$329$	−0.287202	+	0.541720i	−0.0158339	+	0.0298660i
$330$	−0.0314629	−	0.0464043i	−0.00173197	−	0.00255447i
$331$	−14.8741	−	3.27404i	−0.817556	−	0.179958i	−0.213545	−	0.976933i	$-0.568501\pi$
$331$	−14.8741	−	3.27404i	−0.817556	−	0.179958i	−0.604011	+	0.796976i	$0.706432\pi$
$332$	2.76699	−	9.96580i	0.151858	−	0.546945i
$333$	−3.77181	−	9.46653i	−0.206694	−	0.518763i
$334$	3.17796	+	1.07078i	0.173890	+	0.0585904i
$335$	−0.833501	−	0.789534i	−0.0455390	−	0.0431369i
$336$	1.66699	−	0.366931i	0.0909415	−	0.0200177i
$337$	0.728472	−	13.4359i	0.0396824	−	0.731899i	−0.909217	−	0.416322i	$-0.863319\pi$
$337$	0.728472	−	13.4359i	0.0396824	−	0.731899i	0.948900	−	0.315577i	$-0.102198\pi$
$338$	−3.60485	+	21.9886i	−0.196078	+	1.19602i
$339$	−3.38960	+	3.99055i	−0.184098	+	0.216737i
$340$	0.334124	−	0.838588i	0.0181204	−	0.0454788i
$341$	0.359738	+	0.273466i	0.0194809	+	0.0148090i
$342$	−3.06240	−	1.84258i	−0.165595	−	0.0996354i
$343$	−3.06148	−	18.6742i	−0.165304	−	1.00831i
$344$	−1.86908	+	0.203275i	−0.100774	+	0.0109598i
$345$	−0.520809	+	0.395909i	−0.0280394	+	0.0213150i
$346$	4.28305	+	15.4262i	0.230258	+	0.829316i
$347$	0.817838	+	15.0841i	0.0439039	+	0.809759i	0.934718	+	0.355391i	$0.115652\pi$
$347$	0.817838	+	15.0841i	0.0439039	+	0.809759i	−0.890814	+	0.454368i	$0.849865\pi$
$348$	−7.91967	−	0.861316i	−0.424539	−	0.0461714i
$349$	−20.9200	+	12.5872i	−1.11982	+	0.673776i	−0.950171	−	0.311728i	$-0.899092\pi$
$349$	−20.9200	+	12.5872i	−1.11982	+	0.673776i	−0.169653	+	0.985504i	$0.554265\pi$
$350$	5.28233	+	6.21884i	0.282352	+	0.332411i
$351$	5.62894	−	1.89661i	0.300451	−	0.101234i
$352$	0.108560	+	0.0502250i	0.00578625	+	0.00267700i
$353$	5.50915			0.293223			0.146611	−	0.989194i	$-0.453163\pi$
$353$	5.50915			0.293223			0.146611	+	0.989194i	$0.453163\pi$
$354$	−6.73016	−	3.70202i	−0.357704	−	0.196760i
$355$	−0.619831			−0.0328972
$356$	−5.62278	−	2.60137i	−0.298007	−	0.137872i
$357$	−3.11526	+	1.04965i	−0.164877	+	0.0555535i
$358$	10.3882	+	12.2299i	0.549031	+	0.646369i
$359$	−24.8049	+	14.9246i	−1.30915	+	0.787691i	−0.987265	−	0.159087i	$-0.949145\pi$
$359$	−24.8049	+	14.9246i	−1.30915	+	0.787691i	−0.321888	+	0.946778i	$0.604318\pi$
$360$	0.465963	+	0.0506766i	0.0245584	+	0.00267089i
$361$	−0.337103	−	6.21749i	−0.0177422	−	0.327236i
$362$	2.33702	+	8.41718i	0.122831	+	0.442397i
$363$	8.74563	−	6.64826i	0.459027	−	0.348943i
$364$	10.0793	−	1.09619i	0.528298	−	0.0574559i
$365$	0.752911	+	4.59255i	0.0394091	+	0.240385i
$366$	6.77295	+	4.07515i	0.354028	+	0.213012i
$367$	−3.78412	−	2.87662i	−0.197530	−	0.150158i	0.501734	−	0.865022i	$-0.332696\pi$
$367$	−3.78412	−	2.87662i	−0.197530	−	0.150158i	−0.699264	+	0.714864i	$0.746489\pi$
$368$	0.516623	−	1.29663i	0.0269308	−	0.0675913i
$369$	−2.37738	+	2.79887i	−0.123762	+	0.145703i
$370$	0.772718	−	4.71337i	0.0401717	−	0.245037i
$371$	−0.712247	+	13.1366i	−0.0369780	+	0.682020i
$372$	−3.68946	+	0.812112i	−0.191290	+	0.0421060i
$373$	13.1539	+	12.4601i	0.681085	+	0.645158i	0.947892	−	0.318592i	$-0.103210\pi$
$373$	13.1539	+	12.4601i	0.681085	+	0.645158i	−0.266807	+	0.963750i	$0.585969\pi$
$374$	−0.218310	−	0.0735573i	−0.0112886	−	0.00380356i
$375$	1.69676	+	4.25856i	0.0876205	+	0.219911i
$376$	0.0961006	−	0.346123i	0.00495601	−	0.0178499i
$377$	−46.2130	−	10.1722i	−2.38009	−	0.523897i
$378$	−0.957885	−	1.41278i	−0.0492683	−	0.0726653i
$379$	3.90012	−	7.35641i	0.200336	−	0.377873i	−0.762906	−	0.646510i	$-0.776228\pi$
$379$	3.90012	−	7.35641i	0.200336	−	0.377873i	0.963242	+	0.268636i	$0.0865729\pi$
$380$	−0.784662	−	1.48003i	−0.0402523	−	0.0759239i
$381$	8.72619	−	12.8702i	0.447056	−	0.659359i
$382$	19.9689	−	18.9155i	1.02170	−	0.967802i
$383$	1.73699	−	0.803616i	0.0887560	−	0.0410629i	−0.375009	−	0.927021i	$-0.622360\pi$
$383$	1.73699	−	0.803616i	0.0887560	−	0.0410629i	0.463765	+	0.885958i	$0.346498\pi$
$384$	−0.907575	+	0.419889i	−0.0463145	+	0.0214274i
$385$	−0.0694753	+	0.0658105i	−0.00354079	+	0.00335401i
$386$	3.83001	−	5.64884i	0.194942	−	0.287518i
$387$	0.880656	+	1.66109i	0.0447662	+	0.0844381i
$388$	−3.02329	+	5.70253i	−0.153484	+	0.289502i
$389$	−13.2187	−	19.4961i	−0.670214	−	0.988492i	−0.999027	−	0.0440967i	$-0.985959\pi$
$389$	−13.2187	−	19.4961i	−0.670214	−	0.988492i	0.328813	−	0.944395i	$-0.393351\pi$
$390$	2.71899	+	0.598496i	0.137682	+	0.0303060i
$391$	−0.719149	+	2.59014i	−0.0363689	+	0.130989i
$392$	1.51258	+	3.79628i	0.0763967	+	0.191741i
$393$	0.0593513	+	0.0199978i	0.00299388	+	0.00100875i
$394$	10.7219	+	10.1563i	0.540162	+	0.511668i
$395$	0.688458	−	0.151541i	0.0346401	−	0.00762485i
$396$	0.00647583	−	0.119440i	0.000325422	−	0.00600206i
$397$	−1.06650	+	6.50534i	−0.0535259	+	0.326493i	0.946467	+	0.322800i	$0.104624\pi$
$397$	−1.06650	+	6.50534i	−0.0535259	+	0.326493i	−0.999993	+	0.00369371i	$0.998824\pi$
$398$	−0.769671	+	0.906127i	−0.0385801	+	0.0454200i
$399$	−2.25799	+	5.66714i	−0.113041	+	0.283712i
$400$	−3.80557	−	2.89292i	−0.190279	−	0.144646i
$401$	−22.4430	−	13.5035i	−1.12075	−	0.674332i	−0.170356	−	0.985383i	$-0.554492\pi$
$401$	−22.4430	−	13.5035i	−1.12075	−	0.674332i	−0.950393	+	0.311050i	$0.899319\pi$
$402$	−0.396276	−	2.41718i	−0.0197644	−	0.120558i
$403$	−22.3080	+	2.42614i	−1.11124	+	0.120855i
$404$	0.739824	−	0.562399i	0.0368076	−	0.0279804i
$405$	−0.125393	−	0.451626i	−0.00623085	−	0.0224415i
$406$	0.736166	+	13.5778i	0.0365353	+	0.673854i
$407$	−1.21176	−	0.131787i	−0.0600650	−	0.00653246i
$408$	1.65024	−	0.992917i	0.0816991	−	0.0491567i
$409$	−10.1687	−	11.9715i	−0.502809	−	0.591952i	0.450941	−	0.892554i	$-0.351088\pi$
$409$	−10.1687	−	11.9715i	−0.502809	−	0.591952i	−0.953750	+	0.300602i	$0.902813\pi$
$410$	−1.63114	+	0.549594i	−0.0805561	+	0.0271425i
$411$	13.1034	+	6.06229i	0.646345	+	0.299031i
$412$	17.0568			0.840327
$413$	−4.37720	+	12.3586i	−0.215388	+	0.608128i
$414$	−1.39576			−0.0685978
$415$	−4.39973	−	2.03553i	−0.215974	−	0.0999203i
$416$	−5.62894	+	1.89661i	−0.275982	+	0.0929890i
$417$	−0.609004	−	0.716974i	−0.0298230	−	0.0351104i
$418$	−0.366308	+	0.220400i	−0.0179167	+	0.0107801i
$419$	−7.77919	−	0.846038i	−0.380039	−	0.0413317i	−0.0838937	−	0.996475i	$-0.526736\pi$
$419$	−7.77919	−	0.846038i	−0.380039	−	0.0413317i	−0.296145	+	0.955143i	$0.595701\pi$
$420$	−0.0433132	−	0.798865i	−0.00211347	−	0.0389806i
$421$	0.660247	+	2.37799i	0.0321785	+	0.115896i	0.977895	−	0.209096i	$-0.0670521\pi$
$421$	0.660247	+	2.37799i	0.0321785	+	0.115896i	−0.945717	+	0.324992i	$0.894638\pi$
$422$	6.63160	−	5.04121i	0.322821	−	0.245402i
$423$	−0.357111	+	0.0388381i	−0.0173633	+	0.00188838i
$424$	−1.24694	−	7.60600i	−0.0605568	−	0.369380i
$425$	7.88867	+	4.74645i	0.382656	+	0.230237i
$426$	−1.05277	−	0.800292i	−0.0510067	−	0.0387743i
$427$	4.99389	−	12.5337i	0.241671	−	0.606550i
$428$	−5.41244	+	6.37202i	−0.261620	+	0.308003i
$429$	0.114946	−	0.701139i	0.00554964	−	0.0338513i
$430$	−0.0477085	+	0.879932i	−0.00230071	+	0.0424341i
$431$	20.6188	−	4.53854i	0.993171	−	0.218614i	0.311480	−	0.950253i	$-0.399175\pi$
$431$	20.6188	−	4.53854i	0.993171	−	0.218614i	0.681692	+	0.731639i	$0.261244\pi$
$432$	0.725995	+	0.687699i	0.0349295	+	0.0330870i
$433$	−3.58998	−	1.20961i	−0.172524	−	0.0581300i	0.231714	−	0.972784i	$-0.425567\pi$
$433$	−3.58998	−	1.20961i	−0.172524	−	0.0581300i	−0.404238	+	0.914654i	$0.632463\pi$
$434$	2.38675	+	5.99029i	0.114568	+	0.287543i
$435$	−0.998931	+	3.59782i	−0.0478951	+	0.172502i
$436$	−4.97179	−	1.09437i	−0.238106	−	0.0524110i
$437$	2.79944	+	4.12886i	0.133915	+	0.197510i
$438$	−4.65086	+	8.77245i	−0.222227	+	0.419164i
$439$	13.0289	+	24.5752i	0.621837	+	1.17291i	0.971725	+	0.236117i	$0.0758749\pi$
$439$	13.0289	+	24.5752i	0.621837	+	1.17291i	−0.349888	+	0.936792i	$0.613780\pi$
$440$	0.0314629	−	0.0464043i	0.00149993	−	0.00221224i
$441$	2.96680	−	2.81030i	0.141276	−	0.133824i
$442$	10.3824	−	4.80343i	0.493842	−	0.228476i
$443$	−19.7146	+	9.12093i	−0.936668	+	0.433349i	−0.827999	−	0.560729i	$-0.810521\pi$
$443$	−19.7146	+	9.12093i	−0.936668	+	0.433349i	−0.108669	+	0.994078i	$0.534659\pi$
$444$	7.39810	−	7.00785i	0.351098	−	0.332578i
$445$	−1.62960	+	2.40348i	−0.0772504	+	0.113936i
$446$	−6.23665	−	11.7636i	−0.295314	−	0.557022i
$447$	8.70799	−	16.4250i	0.411874	−	0.776877i
$448$	0.957885	+	1.41278i	0.0452558	+	0.0667474i
$449$	14.9320	+	3.28677i	0.704682	+	0.155112i	0.552834	−	0.833291i	$-0.313546\pi$
$449$	14.9320	+	3.28677i	0.704682	+	0.155112i	0.151848	+	0.988404i	$0.451477\pi$
$450$	−1.27887	+	4.60607i	−0.0602864	+	0.217132i
$451$	0.162587	+	0.408062i	0.00765591	+	0.0192149i
$452$	−4.96175	−	1.67181i	−0.233381	−	0.0786352i
$453$	−7.87728	−	7.46176i	−0.370107	−	0.350584i
$454$	9.50769	−	2.09280i	0.446218	−	0.0982200i
$455$	0.257275	−	4.74516i	0.0120612	−	0.222457i
$456$	0.578207	−	3.52690i	0.0270770	−	0.165162i
$457$	19.1252	−	22.5159i	0.894640	−	1.05325i	−0.103639	−	0.994615i	$-0.533049\pi$
$457$	19.1252	−	22.5159i	0.894640	−	1.05325i	0.998279	−	0.0586366i	$-0.0186753\pi$
$458$	−5.68596	+	14.2707i	−0.265687	+	0.666825i
$459$	−1.53321	−	1.16552i	−0.0715643	−	0.0544018i
$460$	−0.560562	−	0.337279i	−0.0261363	−	0.0157257i
$461$	−6.26612	−	38.2216i	−0.291842	−	1.78016i	−0.572050	−	0.820219i	$-0.693852\pi$
$461$	−6.26612	−	38.2216i	−0.291842	−	1.78016i	0.280207	−	0.959939i	$-0.409597\pi$
$462$	−0.202973	+	0.0220746i	−0.00944316	+	0.00102701i
$463$	15.9372	−	12.1151i	0.740663	−	0.563037i	−0.165377	−	0.986230i	$-0.552884\pi$
$463$	15.9372	−	12.1151i	0.740663	−	0.563037i	0.906039	+	0.423193i	$0.139091\pi$
$464$	−2.13123	−	7.67600i	−0.0989399	−	0.356349i
$465$	0.0958631	+	1.76809i	0.00444555	+	0.0819933i
$466$	−26.5138	−	2.88355i	−1.22823	−	0.133578i
$467$	3.38993	−	2.03965i	0.156867	−	0.0943839i	−0.434956	−	0.900452i	$-0.643236\pi$
$467$	3.38993	−	2.03965i	0.156867	−	0.0943839i	0.591823	+	0.806068i	$0.298408\pi$
$468$	3.84539	+	4.52715i	0.177753	+	0.209268i
$469$	−3.96207	+	1.33498i	−0.182952	+	0.0616436i
$470$	−0.152807	−	0.0706962i	−0.00704847	−	0.00326097i
$471$	0.338278			0.0155870
$472$	0.947998	−	7.62242i	0.0436352	−	0.350850i
$473$	0.224888			0.0103404
$474$	1.36499	+	0.631511i	0.0626960	+	0.0290063i
$475$	16.1904	−	5.45519i	0.742868	−	0.250301i
$476$	−2.12818	−	2.50549i	−0.0975450	−	0.114839i
$477$	−6.60426	+	3.97365i	−0.302388	+	0.181941i
$478$	20.2492	+	2.20224i	0.926179	+	0.100728i
$479$	2.03860	+	37.5997i	0.0931460	+	1.71798i	0.555698	+	0.831384i	$0.312451\pi$
$479$	2.03860	+	37.5997i	0.0931460	+	1.71798i	−0.462552	+	0.886592i	$0.653066\pi$
$480$	0.125393	+	0.451626i	0.00572340	+	0.0206138i
$481$	48.1867	−	36.6306i	2.19713	−	1.67021i
$482$	−2.07321	+	0.225475i	−0.0944320	+	0.0102701i
$483$	0.385431	+	2.35102i	0.0175377	+	0.106975i
$484$	9.41317	+	5.66372i	0.427871	+	0.257442i
$485$	2.40837	+	1.83080i	0.109359	+	0.0831322i
$486$	0.370138	−	0.928977i	0.0167898	−	0.0421392i
$487$	−1.85293	+	2.18144i	−0.0839645	+	0.0988506i	−0.802540	−	0.596598i	$-0.796519\pi$
$487$	−1.85293	+	2.18144i	−0.0839645	+	0.0988506i	0.718576	+	0.695449i	$0.244794\pi$
$488$	−1.27879	+	7.80028i	−0.0578882	+	0.353102i
$489$	−1.24002	+	22.8709i	−0.0560758	+	1.03426i
$490$	1.87062	−	0.411754i	0.0845058	−	0.0186011i
$491$	14.5104	+	13.7450i	0.654845	+	0.620302i	0.941211	−	0.337818i	$-0.109689\pi$
$491$	14.5104	+	13.7450i	0.654845	+	0.620302i	−0.286366	+	0.958120i	$0.592447\pi$
$492$	−3.48005	−	1.17256i	−0.156893	−	0.0528633i
$493$	5.67889	+	14.2529i	0.255764	+	0.641920i
$494$	5.67937	−	20.4552i	0.255527	−	0.920325i
$495$	−0.0547541	−	0.0120523i	−0.00246101	−	0.000541710i
$496$	−2.12004	−	3.12683i	−0.0951927	−	0.140399i
$497$	−1.05730	+	1.99428i	−0.0474264	+	0.0894557i
$498$	−4.84465	−	9.13799i	−0.217094	−	0.409483i
$499$	5.29552	−	7.81030i	0.237060	−	0.349637i	−0.690486	−	0.723345i	$-0.742603\pi$
$499$	5.29552	−	7.81030i	0.237060	−	0.349637i	0.927546	+	0.373708i	$0.121914\pi$
$500$	−3.32806	+	3.15251i	−0.148835	+	0.140984i
$501$	3.04356	−	1.40810i	0.135976	−	0.0629093i
$502$	−12.2396	+	5.66266i	−0.546281	+	0.252737i
$503$	−16.0550	+	15.2081i	−0.715856	+	0.678095i	−0.956240	−	0.292583i	$-0.905485\pi$
$503$	−16.0550	+	15.2081i	−0.715856	+	0.678095i	0.240384	+	0.970678i	$0.422727\pi$
$504$	0.957885	−	1.41278i	0.0426676	−	0.0629300i
$505$	−0.204030	−	0.384841i	−0.00907921	−	0.0171252i
$506$	−0.0782025	+	0.147505i	−0.00347652	+	0.00655742i
$507$	12.5044	+	18.4427i	0.555342	+	0.819068i
$508$	15.1860	+	3.34269i	0.673769	+	0.148308i
$509$	10.7130	−	38.5846i	0.474844	−	1.71023i	−0.206655	−	0.978414i	$-0.566258\pi$
$509$	10.7130	−	38.5846i	0.474844	−	1.71023i	0.681499	−	0.731819i	$-0.261329\pi$
$510$	−0.334124	−	0.838588i	−0.0147953	−	0.0371333i
$511$	16.0607	+	5.41147i	0.710482	+	0.239389i
$512$	−0.725995	−	0.687699i	−0.0320848	−	0.0303923i
$513$	−3.49043	+	0.768301i	−0.154106	+	0.0339213i
$514$	−0.620990	+	11.4535i	−0.0273907	+	0.505191i
$515$	1.29340	−	7.88937i	0.0569939	−	0.347647i
$516$	−1.21715	+	1.43294i	−0.0535821	+	0.0630818i
$517$	−0.0159040	+	0.0399160i	−0.000699456	+	0.00175550i
$518$	−13.8470	−	10.5262i	−0.608402	−	0.462495i
$519$	13.7180	+	8.25387i	0.602155	+	0.362305i
$520$	0.450415	+	2.74741i	0.0197520	+	0.120482i
$521$	6.96174	−	0.757135i	0.304999	−	0.0331707i	0.0456603	−	0.998957i	$-0.485461\pi$
$521$	6.96174	−	0.757135i	0.304999	−	0.0331707i	0.259339	+	0.965786i	$0.416495\pi$
$522$	−6.34197	+	4.82104i	−0.277581	+	0.211011i
$523$	9.39769	+	33.8474i	0.410932	+	1.48004i	0.822553	+	0.568689i	$0.192549\pi$
$523$	9.39769	+	33.8474i	0.410932	+	1.48004i	−0.411620	+	0.911355i	$0.635037\pi$
$524$	0.00339071	+	0.0625379i	0.000148124	+	0.00273198i
$525$	8.11164	+	0.882194i	0.354021	+	0.0385021i
$526$	10.8634	−	6.53627i	0.473665	−	0.284995i
$527$	4.71020	+	5.54528i	0.205180	+	0.241556i
$528$	0.113354	−	0.0381933i	0.00493308	−	0.00166215i
$529$	−19.1062	−	8.83945i	−0.830702	−	0.384324i
$530$	−3.61261			−0.156922
$531$	−7.43194	+	1.94068i	−0.322519	+	0.0842184i
$532$	−6.10041			−0.264486
$533$	−19.7968	−	9.15900i	−0.857497	−	0.396720i
$534$	−5.87107	+	1.97819i	−0.254066	+	0.0856049i
$535$	2.53687	+	2.98663i	0.109678	+	0.129123i
$536$	2.09882	−	1.26282i	0.0906553	−	0.0545455i
$537$	15.9522	+	1.73491i	0.688390	+	0.0748669i
$538$	−0.785402	−	14.4859i	−0.0338611	−	0.624531i
$539$	−0.130770	−	0.470992i	−0.00563268	−	0.0202871i
$540$	0.373137	−	0.283652i	0.0160573	−	0.0122064i
$541$	41.0707	−	4.46671i	1.76577	−	0.192039i	0.833185	−	0.552994i	$-0.186515\pi$
$541$	41.0707	−	4.46671i	1.76577	−	0.192039i	0.932583	+	0.360955i	$0.117549\pi$
$542$	1.79332	+	10.9388i	0.0770298	+	0.469861i
$543$	7.48516	+	4.50367i	0.321219	+	0.193271i
$544$	1.53321	+	1.16552i	0.0657360	+	0.0499712i
$545$	−0.883194	+	2.21665i	−0.0378319	+	0.0949508i
$546$	6.56367	−	7.72735i	0.280899	−	0.330700i
$547$	−5.10915	+	31.1645i	−0.218452	+	1.33250i	0.618744	+	0.785593i	$0.287642\pi$
$547$	−5.10915	+	31.1645i	−0.218452	+	1.33250i	−0.837196	+	0.546904i	$0.815806\pi$
$548$	−0.781649	+	14.4167i	−0.0333904	+	0.615850i
$549$	7.71961	−	1.69922i	0.329465	−	0.0725207i
$550$	0.415122	+	0.393224i	0.0177009	+	0.0167671i
$551$	26.9813	+	9.09106i	1.14944	+	0.387292i
$552$	−0.516623	−	1.29663i	−0.0219889	−	0.0551881i
$553$	0.686787	−	2.47358i	0.0292051	−	0.105187i
$554$	−6.21256	−	1.36749i	−0.263946	−	0.0580990i
$555$	−2.68039	−	3.95329i	−0.113776	−	0.167808i
$556$	0.440637	−	0.831130i	0.0186872	−	0.0352478i
$557$	4.91433	+	9.26940i	0.208227	+	0.392757i	0.965524	−	0.260313i	$-0.0838256\pi$
$557$	4.91433	+	9.26940i	0.208227	+	0.392757i	−0.757298	+	0.653070i	$0.773481\pi$
$558$	−2.12004	+	3.12683i	−0.0897486	+	0.132369i
$559$	−8.10761	+	7.67993i	−0.342915	+	0.324827i
$560$	0.726095	−	0.335927i	0.0306831	−	0.0141955i
$561$	−0.209078	+	0.0967296i	−0.00882726	+	0.00408393i
$562$	21.1686	−	20.0520i	0.892944	−	0.845842i
$563$	−19.7536	+	29.1344i	−0.832517	+	1.22787i	0.138857	+	0.990312i	$0.455657\pi$
$563$	−19.7536	+	29.1344i	−0.832517	+	1.22787i	−0.971373	+	0.237558i	$0.923653\pi$
$564$	−0.168260	−	0.317372i	−0.00708503	−	0.0133638i
$565$	−1.14952	+	2.16822i	−0.0483605	+	0.0912176i
$566$	−4.97676	−	7.34017i	−0.209189	−	0.308530i
$567$	−1.66699	−	0.366931i	−0.0700068	−	0.0154097i
$568$	0.353784	−	1.27421i	0.0148444	−	0.0534648i
$569$	12.9255	+	32.4405i	0.541865	+	1.35998i	0.903872	+	0.427803i	$0.140712\pi$
$569$	12.9255	+	32.4405i	0.541865	+	1.35998i	−0.362007	+	0.932175i	$0.617909\pi$
$570$	−1.58748	−	0.534883i	−0.0664921	−	0.0224038i
$571$	1.33962	+	1.26896i	0.0560615	+	0.0531043i	0.715217	−	0.698902i	$-0.246328\pi$
$571$	1.33962	+	1.26896i	0.0560615	+	0.0531043i	−0.659156	+	0.752006i	$0.729086\pi$
$572$	0.693887	−	0.152736i	0.0290129	−	0.00638622i
$573$	1.48912	−	27.4652i	0.0622088	−	1.14737i
$574$	−1.01408	+	6.18561i	−0.0423268	+	0.258182i
$575$	4.31946	−	5.08526i	0.180134	−	0.212070i
$576$	−0.370138	+	0.928977i	−0.0154224	+	0.0387074i
$577$	−13.3954	−	10.1829i	−0.557658	−	0.423921i	0.288012	−	0.957627i	$-0.407006\pi$
$577$	−13.3954	−	10.1829i	−0.557658	−	0.423921i	−0.845670	+	0.533706i	$0.820799\pi$
$578$	11.3883	+	6.85213i	0.473692	+	0.285011i
$579$	−1.10413	−	6.73492i	−0.0458863	−	0.279894i
$580$	−3.71204	+	0.403708i	−0.154134	+	0.0167631i
$581$	−14.0543	+	10.6838i	−0.583069	+	0.443237i
$582$	1.72673	+	6.21912i	0.0715753	+	0.257791i
$583$	0.0499127	+	0.920585i	0.00206717	+	0.0381267i
$584$	−9.87086	−	1.07352i	−0.408459	−	0.0444226i
$585$	2.38556	−	1.43535i	0.0986309	−	0.0593442i
$586$	6.98759	+	8.22642i	0.288655	+	0.339830i
$587$	−22.5574	+	7.60046i	−0.931042	+	0.313705i	−0.743641	−	0.668579i	$-0.766903\pi$
$587$	−22.5574	+	7.60046i	−0.931042	+	0.313705i	−0.187401	+	0.982284i	$0.560006\pi$
$588$	3.70883	+	1.71589i	0.152949	+	0.0707620i
$589$	13.5017			0.556330
$590$	−3.45376	−	1.01648i	−0.142189	−	0.0418480i
$591$	14.7686			0.607497
$592$	9.24845	+	4.27879i	0.380109	+	0.175857i
$593$	18.1086	−	6.10150i	0.743631	−	0.250558i	0.0781173	−	0.996944i	$-0.475109\pi$
$593$	18.1086	−	6.10150i	0.743631	−	0.250558i	0.665514	+	0.746386i	$0.268213\pi$
$594$	−0.0774371	−	0.0911660i	−0.00317728	−	0.00374059i
$595$	−1.32026	+	0.794372i	−0.0541252	+	0.0325661i
$596$	18.4816	+	2.01000i	0.757037	+	0.0823327i
$597$	0.0643652	+	1.18715i	0.00263429	+	0.0485867i
$598$	−2.21798	−	7.98844i	−0.0906999	−	0.326671i
$599$	38.5712	−	29.3211i	1.57598	−	1.19803i	0.701858	−	0.712317i	$-0.252354\pi$
$599$	38.5712	−	29.3211i	1.57598	−	1.19803i	0.874120	−	0.485710i	$-0.161439\pi$
$600$	−4.75229	+	0.516842i	−0.194011	+	0.0211000i
$601$	−2.51473	−	15.3392i	−0.102578	−	0.625698i	−0.987212	−	0.159412i	$-0.949040\pi$
$601$	−2.51473	−	15.3392i	−0.102578	−	0.625698i	0.884634	−	0.466286i	$-0.154408\pi$
$602$	2.74977	+	1.65448i	0.112072	+	0.0674315i
$603$	−1.94998	−	1.48234i	−0.0794095	−	0.0603655i
$604$	4.01612	−	10.0797i	0.163413	−	0.410137i
$605$	3.33346	−	3.92446i	0.135525	−	0.159552i
$606$	0.150347	−	0.917076i	0.00610743	−	0.0372536i
$607$	1.02599	−	18.9233i	0.0416436	−	0.768072i	−0.900908	−	0.434011i	$-0.857098\pi$
$607$	1.02599	−	18.9233i	0.0416436	−	0.768072i	0.942551	−	0.334061i	$-0.108419\pi$
$608$	3.49043	−	0.768301i	0.141556	−	0.0311587i
$609$	9.87189	+	9.35115i	0.400029	+	0.378928i
$610$	3.51095	+	1.18298i	0.142154	+	0.0478973i
$611$	−0.789765	−	1.98216i	−0.0319505	−	0.0801896i
$612$	0.515239	−	1.85572i	0.0208273	−	0.0750132i
$613$	20.9125	+	4.60320i	0.844649	+	0.185921i	0.616156	−	0.787624i	$-0.288689\pi$
$613$	20.9125	+	4.60320i	0.844649	+	0.185921i	0.228493	+	0.973546i	$0.426620\pi$
$614$	−19.5438	−	28.8249i	−0.788722	−	1.16328i
$615$	−0.806242	+	1.52073i	−0.0325108	+	0.0613219i
$616$	−0.0956349	−	0.180386i	−0.00385324	−	0.00726798i
$617$	2.78168	−	4.10267i	0.111986	−	0.165167i	−0.767566	−	0.640970i	$-0.778532\pi$
$617$	2.78168	−	4.10267i	0.111986	−	0.165167i	0.879552	+	0.475803i	$0.157842\pi$
$618$	12.3831	−	11.7299i	0.498123	−	0.471847i
$619$	−0.294347	+	0.136179i	−0.0118308	+	0.00547351i	−0.425796	−	0.904819i	$-0.640006\pi$
$619$	−0.294347	+	0.136179i	−0.0118308	+	0.00547351i	0.413965	+	0.910293i	$0.364144\pi$
$620$	−1.60703	+	0.743493i	−0.0645400	+	0.0298594i
$621$	−1.01331	+	0.959862i	−0.0406629	+	0.0385179i
$622$	0.823728	−	1.21491i	0.0330285	−	0.0487134i
$623$	4.95335	+	9.34300i	0.198452	+	0.374319i
$624$	−2.78229	+	5.24795i	−0.111381	+	0.210086i
$625$	−12.2075	−	18.0046i	−0.488298	−	0.720186i
$626$	−23.6714	−	5.21048i	−0.946101	−	0.208253i
$627$	−0.114369	+	0.411920i	−0.00456746	+	0.0164505i
$628$	0.125210	+	0.314253i	0.00499641	+	0.0125400i
$629$	−18.5984	−	6.26651i	−0.741565	−	0.249862i
$630$	−0.580824	−	0.550186i	−0.0231406	−	0.0219199i
$631$	16.8102	−	3.70019i	0.669202	−	0.147302i	0.132641	−	0.991164i	$-0.457654\pi$
$631$	16.8102	−	3.70019i	0.669202	−	0.147302i	0.536561	+	0.843862i	$0.319723\pi$
$632$	−0.0814246	+	1.50179i	−0.00323890	+	0.0597380i
$633$	1.34767	−	8.22044i	0.0535652	−	0.326733i
$634$	4.86110	−	5.72293i	0.193059	−	0.227287i
$635$	2.69765	−	6.77060i	0.107053	−	0.268683i
$636$	−6.13592	−	4.66440i	−0.243305	−	0.184956i
$637$	20.7989	+	12.5143i	0.824081	+	0.495833i
$638$	0.154162	+	0.940345i	0.00610332	+	0.0372286i
$639$	−1.31466	+	0.142978i	−0.0520073	+	0.00565613i
$640$	−0.373137	+	0.283652i	−0.0147496	+	0.0112123i
$641$	7.35881	+	26.5040i	0.290655	+	1.04685i	0.954313	+	0.298809i	$0.0965895\pi$
$641$	7.35881	+	26.5040i	0.290655	+	1.04685i	−0.663657	+	0.748037i	$0.730997\pi$
$642$	0.452626	+	8.34819i	0.0178637	+	0.329477i
$643$	−46.3075	−	5.03624i	−1.82619	−	0.198610i	−0.870337	−	0.492457i	$-0.836099\pi$
$643$	−46.3075	−	5.03624i	−1.82619	−	0.198610i	−0.955853	+	0.293847i	$0.905064\pi$
$644$	−2.04138	+	1.22826i	−0.0804417	+	0.0484002i
$645$	0.570492	+	0.671636i	0.0224631	+	0.0264456i
$646$	−6.52291	+	2.19782i	−0.256640	+	0.0864722i
$647$	−40.6414	−	18.8027i	−1.59778	−	0.739210i	−0.599642	−	0.800268i	$-0.704691\pi$
$647$	−40.6414	−	18.8027i	−1.59778	−	0.739210i	−0.998134	+	0.0610578i	$0.980553\pi$
$648$	1.00000			0.0392837
$649$	−0.211308	+	0.894151i	−0.00829457	+	0.0350985i
$650$	−28.3945			−1.11372
$651$	5.85229	+	2.70756i	0.229369	+	0.106117i
$652$	−21.7055	+	7.31343i	−0.850053	+	0.286416i
$653$	32.1737	+	37.8779i	1.25906	+	1.48228i	0.807309	+	0.590129i	$0.200923\pi$
$653$	32.1737	+	37.8779i	1.25906	+	1.48228i	0.451747	+	0.892146i	$0.350801\pi$
$654$	−4.36210	+	2.62459i	−0.170572	+	0.102630i
$655$	0.0291832	+	0.00317386i	0.00114028	+	0.000124013i
$656$	−0.198813	−	3.66689i	−0.00776235	−	0.143168i
$657$	2.65631	+	9.56715i	0.103632	+	0.373250i
$658$	−0.488119	+	0.371059i	−0.0190289	+	0.0144654i
$659$	−1.16110	+	0.126277i	−0.0452301	+	0.00491907i	−0.130706	−	0.991421i	$-0.541724\pi$
$659$	−1.16110	+	0.126277i	−0.0452301	+	0.00491907i	0.0854760	+	0.996340i	$0.472759\pi$
$660$	−0.00907028	−	0.0553263i	−0.000353060	−	0.00215357i
$661$	−12.8142	−	7.71002i	−0.498413	−	0.299885i	0.244061	−	0.969760i	$-0.421520\pi$
$661$	−12.8142	−	7.71002i	−0.498413	−	0.299885i	−0.742474	+	0.669875i	$0.766348\pi$
$662$	−12.1247	−	9.21693i	−0.471238	−	0.358226i
$663$	4.23429	−	10.6273i	0.164446	−	0.412729i
$664$	6.69579	−	7.88289i	0.259847	−	0.305915i
$665$	−0.462588	+	2.82166i	−0.0179384	+	0.109419i
$666$	0.551691	−	10.1753i	0.0213776	−	0.394286i
$667$	10.8592	−	2.39028i	0.420469	−	0.0925522i
$668$	2.43463	+	2.30620i	0.0941986	+	0.0892297i
$669$	−12.6176	−	4.25136i	−0.487824	−	0.164367i
$670$	−0.424948	−	1.06654i	−0.0164172	−	0.0412040i
$671$	0.252944	−	0.911023i	0.00976481	−	0.0351697i
$672$	1.66699	+	0.366931i	0.0643053	+	0.0141547i
$673$	11.6996	+	17.2557i	0.450987	+	0.665156i	0.983426	−	0.181312i	$-0.0580345\pi$
$673$	11.6996	+	17.2557i	0.450987	+	0.665156i	−0.532438	+	0.846469i	$0.678724\pi$
$674$	6.30272	−	11.8882i	0.242772	−	0.457916i
$675$	2.23914	+	4.22346i	0.0861844	+	0.162561i
$676$	−12.5044	+	18.4427i	−0.480940	+	0.709334i
$677$	−15.5815	+	14.7596i	−0.598845	+	0.567256i	−0.925909	−	0.377746i	$-0.876699\pi$
$677$	−15.5815	+	14.7596i	−0.598845	+	0.567256i	0.327064	+	0.945002i	$0.393941\pi$
$678$	−4.75191	+	2.19847i	−0.182496	+	0.0844316i
$679$	9.99870	−	4.62589i	0.383715	−	0.177525i
$680$	0.655357	−	0.620787i	0.0251318	−	0.0238061i
$681$	5.46332	−	8.05780i	0.209355	−	0.308775i
$682$	0.211664	+	0.399241i	0.00810504	+	0.0152877i
$683$	−22.6530	+	42.7281i	−0.866793	+	1.63495i	−0.0982368	+	0.995163i	$0.531320\pi$
$683$	−22.6530	+	42.7281i	−0.866793	+	1.63495i	−0.768556	+	0.639782i	$0.779025\pi$
$684$	−2.00567	−	2.95815i	−0.0766889	−	0.113108i
$685$	6.60896	+	1.45474i	0.252515	+	0.0555828i
$686$	5.06257	−	18.2337i	0.193290	−	0.696167i
$687$	5.68596	+	14.2707i	0.216933	+	0.544460i
$688$	−1.78168	−	0.600319i	−0.0679261	−	0.0228870i
$689$	−33.2374	−	31.4841i	−1.26624	−	1.19945i
$690$	−0.638912	+	0.140635i	−0.0243230	+	0.00535389i
$691$	−0.693666	+	12.7939i	−0.0263883	+	0.486704i	0.955232	+	0.295858i	$0.0956056\pi$
$691$	−0.693666	+	12.7939i	−0.0263883	+	0.486704i	−0.981620	+	0.190845i	$0.938877\pi$
$692$	−2.59008	+	15.7988i	−0.0984602	+	0.600581i
$693$	−0.132177	+	0.155610i	−0.00502098	+	0.00591115i
$694$	−5.59142	+	14.0334i	−0.212247	+	0.532700i
$695$	−0.351015	−	0.266834i	−0.0133147	−	0.0101216i
$696$	−6.82604	−	4.10709i	−0.258741	−	0.155679i
$697$	1.14421	+	6.97936i	0.0433400	+	0.264362i
$698$	−24.2717	+	2.63971i	−0.918699	+	0.0999145i
$699$	−21.2319	+	16.1401i	−0.803064	+	0.610473i
$700$	2.18289	+	7.86206i	0.0825055	+	0.297158i
$701$	−1.86268	−	34.3552i	−0.0703526	−	1.29758i	−0.794217	−	0.607635i	$-0.792119\pi$
$701$	−1.86268	−	34.3552i	−0.0703526	−	1.29758i	0.723864	−	0.689943i	$-0.242364\pi$
$702$	5.90506	+	0.642214i	0.222872	+	0.0242388i
$703$	−31.2067	+	18.7764i	−1.17698	+	0.708166i
$704$	0.0774371	+	0.0911660i	0.00291852	+	0.00343595i
$705$	−0.159555	+	0.0537604i	−0.00600919	+	0.00202473i
$706$	4.99997	+	2.31323i	0.188176	+	0.0870597i
$707$	−1.58624			−0.0596569
$708$	−4.55369	−	6.18578i	−0.171138	−	0.232476i
$709$	−47.7284			−1.79248			−0.896240	−	0.443570i	$-0.853712\pi$
$709$	−47.7284			−1.79248			−0.896240	+	0.443570i	$0.853712\pi$
$710$	−0.562543	−	0.260260i	−0.0211119	−	0.00976739i
$711$	1.42527	−	0.480228i	0.0534516	−	0.0180100i
$712$	−4.01080	−	4.72188i	−0.150311	−	0.176960i
$713$	4.51810	−	2.71845i	0.169204	−	0.101807i
$714$	−3.26807	−	0.355424i	−0.122305	−	0.0133014i
$715$	−0.0180292	−	0.332530i	−0.000674256	−	0.0124359i
$716$	4.29284	+	15.4614i	0.160431	+	0.577820i
$717$	16.2153	−	12.3266i	0.605573	−	0.460345i
$718$	−28.7790	+	3.12991i	−1.07402	+	0.116807i
$719$	−1.94693	−	11.8757i	−0.0726081	−	0.442890i	−0.997963	−	0.0637889i	$-0.979682\pi$
$719$	−1.94693	−	11.8757i	−0.0726081	−	0.442890i	0.925355	−	0.379101i	$-0.123767\pi$
$720$	0.401618	+	0.241646i	0.0149674	+	0.00900560i
$721$	−23.1775	−	17.6191i	−0.863175	−	0.656169i
$722$	2.30471	−	5.78439i	0.0857724	−	0.215273i
$723$	−1.35008	+	1.58944i	−0.0502100	+	0.0591118i
$724$	−1.41326	+	8.62051i	−0.0525235	+	0.320379i
$725$	2.06170	−	38.0259i	0.0765697	−	1.41225i
$726$	10.7289	−	2.36160i	0.398185	−	0.0876472i
$727$	−1.98990	−	1.88493i	−0.0738013	−	0.0699083i	0.649910	−	0.760011i	$-0.274807\pi$
$727$	−1.98990	−	1.88493i	−0.0738013	−	0.0699083i	−0.723711	+	0.690103i	$0.757565\pi$
$728$	9.60799	+	3.23731i	0.356096	+	0.119983i
$729$	−0.370138	−	0.928977i	−0.0137088	−	0.0344065i
$730$	−1.24504	+	4.48423i	−0.0460810	+	0.165969i
$731$	3.53628	+	0.778393i	0.130794	+	0.0287899i
$732$	4.43585	+	6.54240i	0.163954	+	0.241814i
$733$	−6.62017	+	12.4870i	−0.244522	+	0.461217i	−0.975146	−	0.221563i	$-0.928884\pi$
$733$	−6.62017	+	12.4870i	−0.244522	+	0.461217i	0.730624	+	0.682780i	$0.239229\pi$
$734$	−2.22652	−	4.19966i	−0.0821823	−	0.155012i
$735$	1.07490	−	1.58535i	0.0396481	−	0.0584766i
$736$	1.01331	−	0.959862i	0.0373512	−	0.0353810i
$737$	−0.265911	+	0.123023i	−0.00979494	+	0.00453162i
$738$	−3.33287	+	1.54195i	−0.122685	+	0.0567600i
$739$	−31.1898	+	29.5446i	−1.14734	+	1.08682i	−0.152196	+	0.988350i	$0.548635\pi$
$739$	−31.1898	+	29.5446i	−1.14734	+	1.08682i	−0.995141	+	0.0984648i	$0.968607\pi$
$740$	2.68039	−	3.95329i	0.0985332	−	0.145326i
$741$	−9.94386	−	18.7561i	−0.365297	−	0.689023i
$742$	−6.16235	+	11.6234i	−0.226227	+	0.426709i
$743$	11.8204	+	17.4339i	0.433650	+	0.639586i	0.980239	−	0.197815i	$-0.0633845\pi$
$743$	11.8204	+	17.4339i	0.433650	+	0.639586i	−0.546589	+	0.837401i	$0.684074\pi$
$744$	−3.68946	−	0.812112i	−0.135262	−	0.0297735i
$745$	2.33114	−	8.39600i	0.0854063	−	0.307606i
$746$	6.70634	+	16.8316i	0.245537	+	0.616250i
$747$	−9.80139	−	3.30247i	−0.358614	−	0.120831i
$748$	−0.167247	−	0.158425i	−0.00611516	−	0.00579259i
$749$	13.9367	−	3.06771i	0.509238	−	0.112092i
$750$	−0.248180	+	4.57741i	−0.00906226	+	0.167144i
$751$	6.61518	−	40.3508i	0.241391	−	1.47242i	−0.536434	−	0.843942i	$-0.680229\pi$
$751$	6.61518	−	40.3508i	0.241391	−	1.47242i	0.777825	−	0.628480i	$-0.216323\pi$
$752$	0.232552	−	0.273781i	0.00848029	−	0.00998377i
$753$	−4.99171	+	12.5283i	−0.181908	+	0.456555i
$754$	−37.6705	−	28.6364i	−1.37188	−	1.04288i
$755$	−4.35769	−	2.62193i	−0.158592	−	0.0954219i
$756$	−0.276144	−	1.68441i	−0.0100433	−	0.0612612i
$757$	−48.4226	+	5.26627i	−1.75995	+	0.191406i	−0.930280	−	0.366851i	$-0.880436\pi$
$757$	−48.4226	+	5.26627i	−1.75995	+	0.191406i	−0.829668	+	0.558257i	$0.811470\pi$
$758$	6.62853	−	5.03888i	0.240759	−	0.183020i
$759$	0.0446648	+	0.160868i	0.00162123	+	0.00583914i
$760$	−0.0906917	−	1.67271i	−0.00328973	−	0.0606755i
$761$	15.0649	+	1.63840i	0.546100	+	0.0593920i	0.377011	−	0.926209i	$-0.376952\pi$
$761$	15.0649	+	1.63840i	0.546100	+	0.0593920i	0.169089	+	0.985601i	$0.445917\pi$
$762$	13.3237	−	8.01662i	0.482668	−	0.290411i
$763$	5.62544	+	6.62278i	0.203655	+	0.239761i
$764$	26.0657	−	8.78255i	0.943023	−	0.317741i
$765$	−0.819269	−	0.379034i	−0.0296207	−	0.0137040i
$766$	1.91388			0.0691512
$767$	−22.9172	−	39.4518i	−0.827493	−	1.42452i
$768$	−1.00000			−0.0360844
$769$	24.1434	+	11.1699i	0.870635	+	0.402799i	0.803754	−	0.594962i	$-0.202833\pi$
$769$	24.1434	+	11.1699i	0.870635	+	0.402799i	0.0668812	+	0.997761i	$0.478695\pi$
$770$	−0.0906872	+	0.0305561i	−0.00326814	+	0.00110116i
$771$	7.42572	+	8.74223i	0.267431	+	0.314844i
$772$	5.84791	−	3.51857i	0.210471	−	0.126636i
$773$	−38.7872	−	4.21836i	−1.39508	−	0.151724i	−0.620502	−	0.784205i	$-0.713071\pi$
$773$	−38.7872	−	4.21836i	−1.39508	−	0.151724i	−0.774576	+	0.632481i	$0.782037\pi$
$774$	0.101787	+	1.87734i	0.00365865	+	0.0674798i
$775$	−4.83129	−	17.4007i	−0.173545	−	0.625053i
$776$	−5.13829	+	3.90603i	−0.184454	+	0.140218i
$777$	−17.2917	+	1.88059i	−0.620338	+	0.0674658i
$778$	−3.81075	−	23.2446i	−0.136622	−	0.833358i
$779$	11.2460	+	6.76648i	0.402929	+	0.242434i
$780$	2.21639	+	1.68486i	0.0793595	+	0.0603275i
$781$	−0.0585487	+	0.146946i	−0.00209504	+	0.00525815i
$782$	−1.74025	+	2.04879i	−0.0622313	+	0.0732644i
$783$	−1.28882	+	7.86143i	−0.0460585	+	0.280945i
$784$	−0.221240	+	4.08053i	−0.00790142	+	0.145733i
$785$	0.154848	−	0.0340846i	0.00552675	−	0.00121653i
$786$	0.0454689	+	0.0430705i	0.00162182	+	0.00153627i
$787$	46.0135	+	15.5038i	1.64020	+	0.552649i	0.980097	−	0.198521i	$-0.0636139\pi$
$787$	46.0135	+	15.5038i	1.64020	+	0.552649i	0.660108	+	0.751171i	$0.270510\pi$
$788$	5.46640	+	13.7196i	0.194733	+	0.488742i
$789$	3.39177	−	12.2160i	0.120750	−	0.434902i
$790$	0.688458	+	0.151541i	0.0244942	+	0.00539159i
$791$	5.01532	+	7.39705i	0.178324	+	0.263009i
$792$	0.0560287	−	0.105681i	0.00199089	−	0.00375522i
$793$	21.9924	+	41.4820i	0.780972	+	1.47307i
$794$	−3.69944	+	5.45627i	−0.131288	+	0.193636i
$795$	−2.62274	+	2.48439i	−0.0930188	+	0.0881121i
$796$	−1.07901	+	0.499202i	−0.0382444	+	0.0176937i
$797$	−13.7619	+	6.36695i	−0.487473	+	0.225529i	−0.648200	−	0.761470i	$-0.724478\pi$
$797$	−13.7619	+	6.36695i	−0.487473	+	0.225529i	0.160727	+	0.986999i	$0.448616\pi$
$798$	−4.42887	+	4.19525i	−0.156780	+	0.148510i
$799$	−0.388242	+	0.572615i	−0.0137350	+	0.0202577i
$800$	−2.23914	−	4.22346i	−0.0791655	−	0.149322i
$801$	−2.90197	+	5.47369i	−0.102536	+	0.193403i
$802$	−14.6987	−	21.6790i	−0.519030	−	0.765512i
$803$	1.15990	+	0.255313i	0.0409319	+	0.00900980i
$804$	0.655295	−	2.36016i	0.0231105	−	0.0832364i
$805$	0.413318	+	1.03735i	0.0145676	+	0.0365618i
$806$	−21.2649	−	7.16499i	−0.749025	−	0.252376i
$807$	−10.5321	−	9.97657i	−0.370749	−	0.351192i
$808$	0.907591	−	0.199776i	0.0319289	−	0.00702809i
$809$	1.55262	−	28.6364i	0.0545872	−	1.00680i	−0.835062	−	0.550156i	$-0.814568\pi$
$809$	1.55262	−	28.6364i	0.0545872	−	1.00680i	0.889649	−	0.456645i	$-0.150949\pi$
$810$	0.0758290	−	0.462536i	0.00266436	−	0.0162519i
$811$	14.1416	−	16.6488i	0.496579	−	0.584618i	−0.455590	−	0.890190i	$-0.650572\pi$
$811$	14.1416	−	16.6488i	0.496579	−	0.584618i	0.952169	+	0.305572i	$0.0988476\pi$
$812$	−5.03304	+	12.6320i	−0.176625	+	0.443295i
$813$	8.82454	+	6.70824i	0.309490	+	0.235268i
$814$	−1.04443	−	0.628414i	−0.0366073	−	0.0220259i
$815$	1.73682	+	10.5941i	0.0608382	+	0.371097i
$816$	1.91463	−	0.208229i	0.0670256	−	0.00728947i
$817$	5.34931	−	4.06644i	0.187149	−	0.142267i
$818$	−4.20214	−	15.1347i	−0.146924	−	0.529174i
$819$	−0.548899	−	10.1239i	−0.0191801	−	0.353756i
$820$	−1.71115	−	0.186099i	−0.0597559	−	0.00649884i
$821$	−33.3218	+	20.0491i	−1.16294	+	0.699717i	−0.960144	−	0.279505i	$-0.909830\pi$
$821$	−33.3218	+	20.0491i	−1.16294	+	0.699717i	−0.202794	+	0.979221i	$0.565002\pi$
$822$	9.34686	+	11.0040i	0.326009	+	0.383808i
$823$	−37.1027	+	12.5014i	−1.29332	+	0.435770i	−0.880068	−	0.474847i	$-0.842503\pi$
$823$	−37.1027	+	12.5014i	−1.29332	+	0.435770i	−0.413251	+	0.910617i	$0.635607\pi$
$824$	15.4803	+	7.16195i	0.539282	+	0.249498i
$825$	0.571797			0.0199074
$826$	−9.16189	+	9.37843i	−0.318783	+	0.326317i
$827$	20.1010			0.698979			0.349490	−	0.936940i	$-0.386355\pi$
$827$	20.1010			0.698979			0.349490	+	0.936940i	$0.386355\pi$
$828$	−1.26676	−	0.586064i	−0.0440228	−	0.0203671i
$829$	−26.9797	+	9.09052i	−0.937044	+	0.315727i	−0.746070	−	0.665868i	$-0.768061\pi$
$829$	−26.9797	+	9.09052i	−0.937044	+	0.315727i	−0.190975	+	0.981595i	$0.561165\pi$
$830$	−3.13839	−	3.69480i	−0.108935	−	0.128248i
$831$	−5.45071	+	3.27959i	−0.189083	+	0.113768i
$832$	−5.90506	−	0.642214i	−0.204721	−	0.0222648i
$833$	−0.426091	−	7.85879i	−0.0147632	−	0.272291i
$834$	−0.251667	−	0.906422i	−0.00871451	−	0.0313868i
$835$	1.25132	−	0.951227i	0.0433036	−	0.0329186i
$836$	−0.424996	+	0.0462211i	−0.0146988	+	0.00159859i
$837$	0.611177	+	3.72802i	0.0211254	+	0.128859i
$838$	−6.70496	−	4.03424i	−0.231619	−	0.139361i
$839$	20.5959	+	15.6566i	0.711048	+	0.540524i	0.896998	−	0.442035i	$-0.145743\pi$
$839$	20.5959	+	15.6566i	0.711048	+	0.540524i	−0.185950	+	0.982559i	$0.559536\pi$
$840$	0.296125	−	0.743217i	0.0102173	−	0.0256434i
$841$	22.3109	−	26.2665i	0.769343	−	0.905740i
$842$	−0.399270	+	2.43544i	−0.0137598	+	0.0839308i
$843$	1.57859	−	29.1153i	0.0543694	−	1.00278i
$844$	8.13543	−	1.79074i	0.280033	−	0.0616399i
$845$	7.58221	+	7.18225i	0.260836	+	0.247077i
$846$	−0.340413	−	0.114698i	−0.0117036	−	0.00394341i
$847$	−6.94060	−	17.4196i	−0.238482	−	0.598544i
$848$	2.06198	−	7.42660i	0.0708088	−	0.255030i
$849$	−8.66093	−	1.90641i	−0.297242	−	0.0654280i
$850$	5.16658	+	7.62013i	0.177212	+	0.261368i
$851$	−6.66225	+	12.5663i	−0.228379	+	0.430768i
$852$	−0.619431	−	1.16837i	−0.0212213	−	0.0400277i
$853$	19.6742	−	29.0172i	0.673630	−	0.993530i	−0.325222	−	0.945638i	$-0.605439\pi$
$853$	19.6742	−	29.0172i	0.673630	−	0.993530i	0.998852	−	0.0478925i	$-0.0152505\pi$
$854$	9.79511	−	9.27842i	0.335182	−	0.317501i
$855$	−1.52034	+	0.703384i	−0.0519945	+	0.0240552i
$856$	−7.58774	+	3.51046i	−0.259344	+	0.119985i
$857$	−11.4207	+	10.8182i	−0.390123	+	0.369544i	−0.857474	−	0.514528i	$-0.827967\pi$
$857$	−11.4207	+	10.8182i	−0.390123	+	0.369544i	0.467351	+	0.884072i	$0.345209\pi$
$858$	0.398722	−	0.588072i	0.0136122	−	0.0200764i
$859$	10.3252	+	19.4753i	0.352290	+	0.664489i	0.994807	−	0.101782i	$-0.0324545\pi$
$859$	10.3252	+	19.4753i	0.352290	+	0.664489i	−0.642517	+	0.766272i	$0.722110\pi$
$860$	−0.412773	+	0.778572i	−0.0140754	+	0.0265491i
$861$	3.51762	+	5.18811i	0.119880	+	0.176810i
$862$	20.6188	+	4.53854i	0.702278	+	0.154583i
$863$	8.37245	−	30.1548i	0.285002	−	1.02648i	−0.672982	−	0.739659i	$-0.734987\pi$
$863$	8.37245	−	30.1548i	0.285002	−	1.02648i	0.957983	−	0.286824i	$-0.0925994\pi$
$864$	0.370138	+	0.928977i	0.0125924	+	0.0316044i
$865$	7.11112	+	2.39602i	0.241785	+	0.0814670i
$866$	−2.75028	−	2.60520i	−0.0934583	−	0.0885284i
$867$	12.9801	−	2.85713i	0.440827	−	0.0970333i
$868$	−0.349102	+	6.43881i	−0.0118493	+	0.218547i
$869$	0.0291046	−	0.177530i	0.000987307	−	0.00602231i
$870$	−2.41729	+	2.84586i	−0.0819539	+	0.0964836i
$871$	5.38528	−	13.5160i	0.182473	−	0.457974i
$872$	−4.05276	−	3.08083i	−0.137244	−	0.104330i
$873$	5.53049	+	3.32758i	0.187179	+	0.112622i
$874$	0.807036	+	4.92270i	0.0272984	+	0.166513i
$875$	7.77876	−	0.845991i	0.262970	−	0.0285997i
$876$	−7.90446	+	6.00881i	−0.267067	+	0.203019i
$877$	4.20152	+	15.1325i	0.141875	+	0.510989i	0.999997	−	0.00245760i	$-0.000782278\pi$
$877$	4.20152	+	15.1325i	0.141875	+	0.510989i	−0.858122	+	0.513446i	$0.828368\pi$
$878$	1.50589	+	27.7745i	0.0508214	+	0.937345i
$879$	10.7303	+	1.16699i	0.361923	+	0.0393615i
$880$	0.0480396	−	0.0289044i	0.00161941	−	0.000974369i
$881$	26.6509	+	31.3759i	0.897891	+	1.05708i	0.998069	+	0.0621098i	$0.0197829\pi$
$881$	26.6509	+	31.3759i	0.897891	+	1.05708i	−0.100178	+	0.994970i	$0.531941\pi$
$882$	3.87261	−	1.30483i	0.130397	−	0.0439360i
$883$	7.76991	+	3.59474i	0.261478	+	0.120973i	0.546249	−	0.837623i	$-0.316055\pi$
$883$	7.76991	+	3.59474i	0.261478	+	0.120973i	−0.284771	+	0.958596i	$0.591917\pi$
$884$	11.4397			0.384760
$885$	−3.20645	+	1.63719i	−0.107784	+	0.0550334i
$886$	−21.7222			−0.729773
$887$	27.8287	+	12.8749i	0.934397	+	0.432298i	0.827180	−	0.561937i	$-0.189944\pi$
$887$	27.8287	+	12.8749i	0.934397	+	0.432298i	0.107217	+	0.994236i	$0.465806\pi$
$888$	9.65685	−	3.25377i	0.324063	−	0.109189i
$889$	−17.1825	−	20.2288i	−0.576283	−	0.678453i
$890$	−2.48818	+	1.49709i	−0.0834039	+	0.0501825i
$891$	−0.118914	−	0.0129327i	−0.00398376	−	0.000433260i
$892$	−0.720836	−	13.2950i	−0.0241354	−	0.445151i
$893$	0.343462	+	1.23704i	0.0114935	+	0.0413959i
$894$	14.7998	−	11.2506i	0.494981	−	0.376275i
$895$	7.47698	−	0.813171i	0.249928	−	0.0271813i
$896$	0.276144	+	1.68441i	0.00922533	+	0.0562720i
$897$	−7.10389	−	4.27427i	−0.237192	−	0.142714i
$898$	12.1718	+	9.25276i	0.406178	+	0.308768i
$899$	11.1394	−	27.9578i	0.371520	−	0.932444i
$900$	−3.09471	+	3.64337i	−0.103157	+	0.121446i
$901$	−2.40151	+	14.6486i	−0.0800060	+	0.488015i
$902$	−0.0237810	+	0.438616i	−0.000791822	+	0.0146043i
$903$	3.13410	−	0.689868i	0.104296	−	0.0229574i
$904$	−3.80119	−	3.60068i	−0.126426	−	0.119757i
$905$	3.88013	+	1.30737i	0.128980	+	0.0434584i
$906$	−4.01612	−	10.0797i	−0.133427	−	0.334875i
$907$	−14.9925	+	53.9980i	−0.497817	+	1.79297i	0.104276	+	0.994548i	$0.466748\pi$
$907$	−14.9925	+	53.9980i	−0.497817	+	1.79297i	−0.602093	+	0.798426i	$0.705666\pi$
$908$	9.50769	+	2.09280i	0.315524	+	0.0694520i
$909$	−0.521521	−	0.769186i	−0.0172978	−	0.0255123i
$910$	2.22594	−	4.19856i	0.0737891	−	0.139181i
$911$	22.8863	+	43.1681i	0.758257	+	1.43022i	0.897981	+	0.440034i	$0.145034\pi$
$911$	22.8863	+	43.1681i	0.758257	+	1.43022i	−0.139724	+	0.990190i	$0.544622\pi$
$912$	2.00567	−	2.95815i	0.0664145	−	0.0979541i
$913$	−0.898168	+	0.850790i	−0.0297250	+	0.0281570i
$914$	26.8118	−	12.4044i	0.886855	−	0.410303i
$915$	3.36246	−	1.55564i	0.111160	−	0.0514279i
$916$	−11.1525	+	10.5642i	−0.368490	+	0.349052i
$917$	0.0599922	−	0.0884818i	0.00198112	−	0.00292193i
$918$	−0.902119	−	1.70158i	−0.0297744	−	0.0561604i
$919$	7.48236	−	14.1132i	0.246820	−	0.465553i	−0.728886	−	0.684635i	$-0.759962\pi$
$919$	7.48236	−	14.1132i	0.246820	−	0.465553i	0.975706	+	0.219082i	$0.0703064\pi$
$920$	−0.367132	−	0.541480i	−0.0121040	−	0.0178521i
$921$	−34.0116	−	7.48651i	−1.12072	−	0.246689i
$922$	10.3619	−	37.3201i	0.341250	−	1.22907i
$923$	−2.90743	−	7.29710i	−0.0956992	−	0.240187i
$924$	−0.193482	−	0.0651917i	−0.00636510	−	0.00214465i
$925$	35.3652	+	33.4997i	1.16280	+	1.10146i
$926$	19.5512	−	4.30354i	0.642492	−	0.141423i
$927$	0.923435	−	17.0318i	0.0303296	−	0.559396i
$928$	1.28882	−	7.86143i	0.0423074	−	0.258064i
$929$	7.17221	−	8.44377i	0.235312	−	0.277031i	−0.631813	−	0.775121i	$-0.717689\pi$
$929$	7.17221	−	8.44377i	0.235312	−	0.277031i	0.867126	+	0.498089i	$0.165965\pi$
$930$	−0.655399	+	1.64493i	−0.0214914	+	0.0539393i
$931$	−11.6271	−	8.83867i	−0.381062	−	0.289676i
$932$	−22.8525	−	13.7499i	−0.748558	−	0.450392i
$933$	−0.237469	−	1.44850i	−0.00777438	−	0.0474216i
$934$	3.93305	−	0.427745i	0.128693	−	0.0139962i
$935$	−0.0859594	+	0.0653447i	−0.00281117	+	0.00213700i
$936$	1.58909	+	5.72337i	0.0519409	+	0.187074i
$937$	−2.29502	−	42.3292i	−0.0749751	−	1.38283i	−0.757912	−	0.652357i	$-0.773780\pi$
$937$	−2.29502	−	42.3292i	−0.0749751	−	1.38283i	0.682937	−	0.730477i	$-0.260702\pi$
$938$	−4.15642	−	0.452038i	−0.135712	−	0.0147596i
$939$	−20.7686	+	12.4961i	−0.677758	+	0.407793i
$940$	−0.109000	−	0.128324i	−0.00355517	−	0.00418547i
$941$	12.8498	−	4.32959i	0.418891	−	0.141141i	−0.101960	−	0.994789i	$-0.532511\pi$
$941$	12.8498	−	4.32959i	0.418891	−	0.141141i	0.520851	+	0.853648i	$0.325615\pi$
$942$	0.307013	+	0.142039i	0.0100030	+	0.00462789i
$943$	5.12561			0.166913
$944$	4.06095	−	6.51987i	0.132173	−	0.212204i
$945$	−0.800038			−0.0260253
$946$	0.204103	+	0.0944282i	0.00663597	+	0.00307013i
$947$	31.3597	−	10.5663i	1.01905	−	0.343359i	0.240307	−	0.970697i	$-0.422752\pi$
$947$	31.3597	−	10.5663i	1.01905	−	0.343359i	0.778747	+	0.627338i	$0.215855\pi$
$948$	0.973666	+	1.14629i	0.0316232	+	0.0372297i
$949$	−50.5352	+	30.4060i	−1.64044	+	0.987022i
$950$	16.9846	+	1.84719i	0.551054	+	0.0599307i
$951$	−0.406519	−	7.49780i	−0.0131823	−	0.243133i
$952$	−0.879457	−	3.16752i	−0.0285034	−	0.102660i
$953$	4.73154	−	3.59683i	0.153270	−	0.116513i	−0.525729	−	0.850652i	$-0.676207\pi$
$953$	4.73154	−	3.59683i	0.153270	−	0.116513i	0.678999	+	0.734140i	$0.262414\pi$
$954$	−7.66235	+	0.833331i	−0.248078	+	0.0269801i
$955$	−2.08571	−	12.7223i	−0.0674921	−	0.411684i
$956$	17.4530	+	10.5011i	0.564471	+	0.339631i
$957$	0.758595	+	0.576669i	0.0245219	+	0.0186411i
$958$	−13.9375	+	34.9806i	−0.450302	+	1.13017i
$959$	15.9541	−	18.7826i	0.515184	−	0.606521i
$960$	−0.0758290	+	0.462536i	−0.00244737	+	0.0149283i
$961$	−0.905655	+	16.7038i	−0.0292147	+	0.538833i
$962$	59.1139	−	13.0119i	1.90591	−	0.419522i
$963$	6.06965	+	5.74948i	0.195592	+	0.185274i
$964$	−1.97627	−	0.665881i	−0.0636512	−	0.0214466i
$965$	−1.18402	−	2.97168i	−0.0381151	−	0.0956617i
$966$	−0.637361	+	2.29557i	−0.0205068	+	0.0738587i
$967$	−13.0052	−	2.86266i	−0.418218	−	0.0920568i	0.000875816	−	1.00000i	$-0.499721\pi$
$967$	−13.0052	−	2.86266i	−0.418218	−	0.0920568i	−0.419094	+	0.907943i	$0.637652\pi$
$968$	6.16503	+	9.09274i	0.198152	+	0.292252i
$969$	−3.22416	+	6.08141i	−0.103575	+	0.195363i
$970$	1.41705	+	2.67284i	0.0454987	+	0.0858196i
$971$	−3.76324	+	5.55037i	−0.120768	+	0.178120i	−0.883268	−	0.468869i	$-0.844662\pi$
$971$	−3.76324	+	5.55037i	−0.120768	+	0.178120i	0.762500	+	0.646989i	$0.223972\pi$
$972$	0.725995	−	0.687699i	0.0232863	−	0.0220580i
$973$	−1.45729	+	0.674213i	−0.0467185	+	0.0216143i
$974$	−2.59764	+	1.20180i	−0.0832338	+	0.0385081i
$975$	−20.6142	+	19.5269i	−0.660184	+	0.625360i
$976$	−4.43585	+	6.54240i	−0.141988	+	0.209417i
$977$	−6.08741	−	11.4821i	−0.194754	−	0.367344i	0.766833	−	0.641847i	$-0.221832\pi$
$977$	−6.08741	−	11.4821i	−0.194754	−	0.367344i	−0.961586	+	0.274503i	$0.911487\pi$
$978$	−10.7286	+	20.2364i	−0.343064	+	0.647088i
$979$	0.415874	+	0.613368i	0.0132914	+	0.0196033i
$980$	1.87062	+	0.411754i	0.0597546	+	0.0131530i
$981$	−1.36194	+	4.90525i	−0.0434833	+	0.156613i
$982$	7.39791	+	18.5674i	0.236077	+	0.592508i
$983$	−56.1033	−	18.9034i	−1.78942	−	0.602925i	−0.789477	−	0.613781i	$-0.789648\pi$
$983$	−56.1033	−	18.9034i	−1.78942	−	0.602925i	−0.999941	+	0.0108555i	$0.996545\pi$
$984$	−2.66606	−	2.52543i	−0.0849909	−	0.0805076i
$985$	6.76034	−	1.48806i	0.215402	−	0.0474137i
$986$	−0.830633	+	15.3201i	−0.0264527	+	0.487892i
$987$	−0.0991956	+	0.605066i	−0.00315743	+	0.0192595i
$988$	13.7434	−	16.1800i	0.437235	−	0.514753i
$989$	0.971304	−	2.43779i	0.0308857	−	0.0775172i
$990$	−0.0446328	−	0.0339290i	−0.00141852	−	0.00107833i
$991$	10.8497	+	6.52807i	0.344653	+	0.207371i	0.677347	−	0.735664i	$-0.263130\pi$
$991$	10.8497	+	6.52807i	0.344653	+	0.207371i	−0.332693	+	0.943035i	$0.607957\pi$
$992$	−0.611177	−	3.72802i	−0.0194049	−	0.118365i
$993$	−15.1409	+	1.64667i	−0.480483	+	0.0522556i
$994$	−1.79696	+	1.36601i	−0.0569960	+	0.0433272i
$995$	0.149079	+	0.536934i	0.00472612	+	0.0170220i
$996$	−0.559948	−	10.3276i	−0.0177426	−	0.327244i
$997$	−39.9624	−	4.34617i	−1.26562	−	0.137645i	−0.549425	−	0.835543i	$-0.685153\pi$
$997$	−39.9624	−	4.34617i	−1.26562	−	0.137645i	−0.716197	+	0.697899i	$0.754119\pi$
$998$	8.08554	−	4.86491i	0.255943	−	0.153996i
$999$	−6.59705	−	7.76664i	−0.208721	−	0.245726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.79.2	✓	84
59.3	even	29	inner	354.2.e.c.121.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.79.2	✓	84	1.1	even	1	trivial
354.2.e.c.121.2	yes	84	59.3	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.907575 + 0.419889i) q^{2} +(0.947653 - 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(0.401618 - 0.241646i) q^{5} +(0.994138 + 0.108119i) q^{6} +(-0.0924092 - 1.70439i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +O(q^{10})\)	\(q+(0.907575 + 0.419889i) q^{2} +(0.947653 - 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(0.401618 - 0.241646i) q^{5} +(0.994138 + 0.108119i) q^{6} +(-0.0924092 - 1.70439i) q^{7} +(0.267528 + 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(0.465963 - 0.0506766i) q^{10} +(-0.0193516 - 0.118039i) q^{11} +(0.856857 + 0.515554i) q^{12} +(4.72869 + 3.59466i) q^{13} +(0.631786 - 1.58566i) q^{14} +(0.303437 - 0.357234i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(0.104267 - 1.92310i) q^{17} +(0.976621 - 0.214970i) q^{18} +(-2.59470 - 2.45783i) q^{19} +(0.444175 + 0.149660i) q^{20} +(-0.631786 - 1.58566i) q^{21} +(0.0320004 - 0.115255i) q^{22} +(-1.36313 - 0.300047i) q^{23} +(0.561187 + 0.827689i) q^{24} +(-2.23914 + 4.22346i) q^{25} +(2.78229 + 5.24795i) q^{26} +(0.561187 - 0.827689i) q^{27} +(1.23920 - 1.17383i) q^{28} +(-7.23008 + 3.34499i) q^{29} +(0.425390 - 0.196807i) q^{30} +(-2.74265 + 2.59798i) q^{31} +(-0.561187 + 0.827689i) q^{32} +(-0.0560287 - 0.105681i) q^{33} +(0.902119 - 1.70158i) q^{34} +(-0.448971 - 0.662183i) q^{35} +(0.976621 + 0.214970i) q^{36} +(2.72619 - 9.81884i) q^{37} +(-1.32287 - 3.32015i) q^{38} +(5.62894 + 1.89661i) q^{39} +(0.340282 + 0.322332i) q^{40} +(-3.58642 + 0.789432i) q^{41} +(0.0924092 - 1.70439i) q^{42} +(-0.304167 + 1.85533i) q^{43} +(0.0774371 - 0.0911660i) q^{44} +(0.173488 - 0.435421i) q^{45} +(-1.11115 - 0.844677i) q^{46} +(-0.307797 - 0.185195i) q^{47} +(0.161782 + 0.986827i) q^{48} +(4.06257 - 0.441831i) q^{49} +(-3.80557 + 2.89292i) q^{50} +(-0.515239 - 1.85572i) q^{51} +(0.321578 + 5.93117i) q^{52} +(-7.66235 - 0.833331i) q^{53} +(0.856857 - 0.515554i) q^{54} +(-0.0362956 - 0.0427305i) q^{55} +(1.61754 - 0.545013i) q^{56} +(-3.24366 - 1.50068i) q^{57} -7.96637 q^{58} +(-7.09097 - 2.95266i) q^{59} +0.468711 q^{60} +(7.17385 + 3.31898i) q^{61} +(-3.58003 + 1.20625i) q^{62} +(-1.10502 - 1.30093i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(2.76776 + 0.301012i) q^{65} +(-0.00647583 - 0.119440i) q^{66} +(-0.655295 - 2.36016i) q^{67} +(1.53321 - 1.16552i) q^{68} +(-1.38758 + 0.150908i) q^{69} +(-0.129432 - 0.789499i) q^{70} +(-1.13312 - 0.681777i) q^{71} +(0.796093 + 0.605174i) q^{72} +(-3.67513 + 9.22387i) q^{73} +(6.59705 - 7.76664i) q^{74} +(-0.773368 + 4.71734i) q^{75} +(0.193492 - 3.56874i) q^{76} +(-0.199396 + 0.0438905i) q^{77} +(4.31232 + 4.08485i) q^{78} +(1.42527 + 0.480228i) q^{79} +(0.173488 + 0.435421i) q^{80} +(0.267528 - 0.963550i) q^{81} +(-3.58642 - 0.789432i) q^{82} +(-5.80425 - 8.56062i) q^{83} +(0.799522 - 1.50806i) q^{84} +(-0.422833 - 0.797547i) q^{85} +(-1.05509 + 1.55614i) q^{86} +(-5.78355 + 5.47847i) q^{87} +(0.108560 - 0.0502250i) q^{88} +(-5.62278 + 2.60137i) q^{89} +(0.340282 - 0.322332i) q^{90} +(5.68972 - 8.39171i) q^{91} +(-0.653785 - 1.23317i) q^{92} +(-1.76955 + 3.33772i) q^{93} +(-0.201588 - 0.297320i) q^{94} +(-1.63600 - 0.360111i) q^{95} +(-0.267528 + 0.963550i) q^{96} +(2.38901 + 5.99597i) q^{97} +(3.87261 + 1.30483i) q^{98} +(-0.0868400 - 0.0822592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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