LMFDB - Embedded newform 374.2.g.f.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [374,2,Mod(69,374)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(374, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("374.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 374 = 2 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	374.g (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:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} + 68 x^{12} + 28 x^{11} + 306 x^{10} + 228 x^{9} + 1035 x^{8} + \cdots + 3481 $ x^16 - 4x^15 + 10x^14 - 8x^13 + 68x^12 + 28x^11 + 306x^10 + 228x^9 + 1035x^8 + 264x^7 + 2972x^6 + 4642x^5 + 9487x^4 + 8098x^3 + 7793x^2 + 2124*x + 3481
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			103.3
Root			$1.51735 + 1.10242i$ of defining polynomial
Character	$\chi$	$=$	374.103
Dual form			374.2.g.f.69.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.270560 - 0.832698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0973285 - 0.0707133i) q^{5} +(-0.708335 + 0.514635i) q^{6} +(0.450819 + 1.38748i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.80687 + 1.31277i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.270560 - 0.832698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0973285 - 0.0707133i) q^{5} +(-0.708335 + 0.514635i) q^{6} +(0.450819 + 1.38748i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.80687 + 1.31277i) q^{9} -0.120305 q^{10} +(1.80666 + 2.78137i) q^{11} +0.875550 q^{12} +(-0.107308 - 0.0779639i) q^{13} +(0.450819 - 1.38748i) q^{14} +(-0.0325496 - 0.100177i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.809017 - 0.587785i) q^{17} +(-0.690162 - 2.12410i) q^{18} +(0.832946 - 2.56354i) q^{19} +(0.0973285 + 0.0707133i) q^{20} +1.27732 q^{21} +(0.173231 - 3.31210i) q^{22} +7.64311 q^{23} +(-0.708335 - 0.514635i) q^{24} +(-1.54061 + 4.74152i) q^{25} +(0.0409881 + 0.126148i) q^{26} +(3.70701 - 2.69330i) q^{27} +(-1.18026 + 0.857508i) q^{28} +(-0.812453 - 2.50047i) q^{29} +(-0.0325496 + 0.100177i) q^{30} +(-7.68256 - 5.58170i) q^{31} +1.00000 q^{32} +(2.80485 - 0.751871i) q^{33} -1.00000 q^{34} +(0.141991 + 0.103162i) q^{35} +(-0.690162 + 2.12410i) q^{36} +(2.90334 + 8.93555i) q^{37} +(-2.18068 + 1.58436i) q^{38} +(-0.0939537 + 0.0682613i) q^{39} +(-0.0371762 - 0.114417i) q^{40} +(2.86616 - 8.82113i) q^{41} +(-1.03338 - 0.750792i) q^{42} -1.52139 q^{43} +(-2.08695 + 2.57772i) q^{44} +0.268690 q^{45} +(-6.18341 - 4.49251i) q^{46} +(2.35034 - 7.23359i) q^{47} +(0.270560 + 0.832698i) q^{48} +(3.94126 - 2.86349i) q^{49} +(4.03338 - 2.93042i) q^{50} +(-0.270560 - 0.832698i) q^{51} +(0.0409881 - 0.126148i) q^{52} +(8.48636 + 6.16570i) q^{53} -4.58211 q^{54} +(0.372519 + 0.142952i) q^{55} +1.45888 q^{56} +(-1.90929 - 1.38718i) q^{57} +(-0.812453 + 2.50047i) q^{58} +(0.200475 + 0.616999i) q^{59} +(0.0852160 - 0.0619131i) q^{60} +(-11.2033 + 8.13965i) q^{61} +(2.93448 + 9.03139i) q^{62} +(-1.00686 + 3.09881i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.0159572 q^{65} +(-2.71111 - 1.04037i) q^{66} -5.15478 q^{67} +(0.809017 + 0.587785i) q^{68} +(2.06792 - 6.36440i) q^{69} +(-0.0542356 - 0.166920i) q^{70} +(-8.93737 + 6.49338i) q^{71} +(1.80687 - 1.31277i) q^{72} +(0.431640 + 1.32845i) q^{73} +(2.90334 - 8.93555i) q^{74} +(3.53142 + 2.56573i) q^{75} +2.69547 q^{76} +(-3.04461 + 3.76059i) q^{77} +0.116133 q^{78} +(-3.84597 - 2.79426i) q^{79} +(-0.0371762 + 0.114417i) q^{80} +(0.830750 + 2.55679i) q^{81} +(-7.50370 + 5.45176i) q^{82} +(-10.3532 + 7.52201i) q^{83} +(0.394714 + 1.21481i) q^{84} +(0.0371762 - 0.114417i) q^{85} +(1.23083 + 0.894251i) q^{86} -2.30196 q^{87} +(3.20352 - 0.858742i) q^{88} -3.91389 q^{89} +(-0.217375 - 0.157932i) q^{90} +(0.0597967 - 0.184035i) q^{91} +(2.36185 + 7.26903i) q^{92} +(-6.72646 + 4.88706i) q^{93} +(-6.15326 + 4.47061i) q^{94} +(-0.100207 - 0.308406i) q^{95} +(0.270560 - 0.832698i) q^{96} +(6.07135 + 4.41109i) q^{97} -4.87167 q^{98} +(-0.386897 + 7.39728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} - q^{5} + 2 q^{7} - 4 q^{8} - 13 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 - q^5 + 2 * q^7 - 4 * q^8 - 13 * q^9	\( 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} - q^{5} + 2 q^{7} - 4 q^{8} - 13 q^{9} + 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{13} + 2 q^{14} - 6 q^{15} - 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} - q^{20} + 6 q^{22} - 24 q^{23} - 37 q^{25} + 15 q^{26} - 4 q^{27} - 13 q^{28} - 16 q^{29} - 6 q^{30} + 11 q^{31} + 16 q^{32} + 36 q^{33} - 16 q^{34} + 2 q^{36} + 5 q^{37} - 25 q^{38} - 30 q^{39} - q^{40} + 4 q^{41} + 35 q^{42} + 16 q^{43} + 6 q^{44} + 6 q^{45} - 14 q^{46} - 14 q^{47} + 5 q^{48} + 2 q^{49} + 13 q^{50} - 5 q^{51} + 15 q^{52} + 5 q^{53} - 34 q^{54} + 81 q^{55} + 22 q^{56} - 12 q^{57} - 16 q^{58} + 17 q^{59} + 4 q^{60} - 30 q^{61} - 4 q^{62} + 72 q^{63} - 4 q^{64} + 6 q^{65} + 11 q^{66} + 26 q^{67} + 4 q^{68} - 73 q^{69} - 10 q^{70} - q^{71} - 13 q^{72} - 43 q^{73} + 5 q^{74} + 67 q^{75} + 30 q^{76} + 40 q^{77} + 70 q^{78} - 13 q^{79} - q^{80} - 39 q^{81} - 21 q^{82} - 24 q^{83} - 35 q^{84} + q^{85} + 26 q^{86} - 92 q^{87} - 4 q^{88} + 24 q^{89} - 29 q^{90} - 10 q^{91} + 26 q^{92} + 11 q^{93} - 4 q^{94} - 39 q^{95} + 5 q^{96} + 3 q^{97} + 2 q^{98} + 65 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 - q^5 + 2 * q^7 - 4 * q^8 - 13 * q^9 + 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^13 + 2 * q^14 - 6 * q^15 - 4 * q^16 + 4 * q^17 + 2 * q^18 + 10 * q^19 - q^20 + 6 * q^22 - 24 * q^23 - 37 * q^25 + 15 * q^26 - 4 * q^27 - 13 * q^28 - 16 * q^29 - 6 * q^30 + 11 * q^31 + 16 * q^32 + 36 * q^33 - 16 * q^34 + 2 * q^36 + 5 * q^37 - 25 * q^38 - 30 * q^39 - q^40 + 4 * q^41 + 35 * q^42 + 16 * q^43 + 6 * q^44 + 6 * q^45 - 14 * q^46 - 14 * q^47 + 5 * q^48 + 2 * q^49 + 13 * q^50 - 5 * q^51 + 15 * q^52 + 5 * q^53 - 34 * q^54 + 81 * q^55 + 22 * q^56 - 12 * q^57 - 16 * q^58 + 17 * q^59 + 4 * q^60 - 30 * q^61 - 4 * q^62 + 72 * q^63 - 4 * q^64 + 6 * q^65 + 11 * q^66 + 26 * q^67 + 4 * q^68 - 73 * q^69 - 10 * q^70 - q^71 - 13 * q^72 - 43 * q^73 + 5 * q^74 + 67 * q^75 + 30 * q^76 + 40 * q^77 + 70 * q^78 - 13 * q^79 - q^80 - 39 * q^81 - 21 * q^82 - 24 * q^83 - 35 * q^84 + q^85 + 26 * q^86 - 92 * q^87 - 4 * q^88 + 24 * q^89 - 29 * q^90 - 10 * q^91 + 26 * q^92 + 11 * q^93 - 4 * q^94 - 39 * q^95 + 5 * q^96 + 3 * q^97 + 2 * q^98 + 65 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$.

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.270560	−	0.832698i	0.156208	−	0.480758i	−0.842073	−	0.539363i	$-0.818665\pi$
$3$	0.270560	−	0.832698i	0.156208	−	0.480758i	0.998281	+	0.0586046i	$0.0186651\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.0973285	−	0.0707133i	0.0435266	−	0.0316240i	−0.565809	−	0.824536i	$-0.691436\pi$
$5$	0.0973285	−	0.0707133i	0.0435266	−	0.0316240i	0.609336	+	0.792912i	$0.291436\pi$
$6$	−0.708335	+	0.514635i	−0.289177	+	0.210099i
$7$	0.450819	+	1.38748i	0.170393	+	0.524417i	0.999393	−	0.0348318i	$-0.0110896\pi$
$7$	0.450819	+	1.38748i	0.170393	+	0.524417i	−0.829000	+	0.559249i	$0.811090\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	1.80687	+	1.31277i	0.602289	+	0.437589i
$10$	−0.120305			−0.0380437
$11$	1.80666	+	2.78137i	0.544727	+	0.838613i
$11$	1.80666	+	2.78137i	0.544727	+	0.838613i
$12$	0.875550			0.252750
$13$	−0.107308	−	0.0779639i	−0.0297619	−	0.0216233i	0.572805	−	0.819692i	$-0.305855\pi$
$13$	−0.107308	−	0.0779639i	−0.0297619	−	0.0216233i	−0.602567	+	0.798068i	$0.705855\pi$
$14$	0.450819	−	1.38748i	0.120486	−	0.370819i
$15$	−0.0325496	−	0.100177i	−0.00840428	−	0.0258657i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.809017	−	0.587785i	0.196215	−	0.142559i
$17$	0.809017	−	0.587785i	0.196215	−	0.142559i
$18$	−0.690162	−	2.12410i	−0.162673	−	0.500655i
$19$	0.832946	−	2.56354i	0.191091	−	0.588117i	−0.808909	−	0.587934i	$-0.799942\pi$
$19$	0.832946	−	2.56354i	0.191091	−	0.588117i	1.00000		0.000183454i	$-5.83952e-5\pi$
$20$	0.0973285	+	0.0707133i	0.0217633	+	0.0158120i
$21$	1.27732			0.278735
$22$	0.173231	−	3.31210i	0.0369330	−	0.706142i
$23$	7.64311			1.59370			0.796850	−	0.604177i	$-0.206498\pi$
$23$	7.64311			1.59370			0.796850	+	0.604177i	$0.206498\pi$
$24$	−0.708335	−	0.514635i	−0.144588	−	0.105050i
$25$	−1.54061	+	4.74152i	−0.308123	+	0.948304i
$26$	0.0409881	+	0.126148i	0.00803842	+	0.0247397i
$27$	3.70701	−	2.69330i	0.713414	−	0.518326i
$28$	−1.18026	+	0.857508i	−0.223048	+	0.162054i
$29$	−0.812453	−	2.50047i	−0.150869	−	0.464326i	0.846850	−	0.531832i	$-0.178496\pi$
$29$	−0.812453	−	2.50047i	−0.150869	−	0.464326i	−0.997719	+	0.0675052i	$0.978496\pi$
$30$	−0.0325496	+	0.100177i	−0.00594272	+	0.0182898i
$31$	−7.68256	−	5.58170i	−1.37983	−	1.00250i	−0.996896	−	0.0787271i	$-0.974914\pi$
$31$	−7.68256	−	5.58170i	−1.37983	−	1.00250i	−0.382932	−	0.923777i	$-0.625086\pi$
$32$	1.00000			0.176777
$33$	2.80485	−	0.751871i	0.488261	−	0.130884i
$34$	−1.00000			−0.171499
$35$	0.141991	+	0.103162i	0.0240008	+	0.0174376i
$36$	−0.690162	+	2.12410i	−0.115027	+	0.354017i
$37$	2.90334	+	8.93555i	0.477305	+	1.46899i	0.842823	+	0.538191i	$0.180892\pi$
$37$	2.90334	+	8.93555i	0.477305	+	1.46899i	−0.365518	+	0.930804i	$0.619108\pi$
$38$	−2.18068	+	1.58436i	−0.353753	+	0.257017i
$39$	−0.0939537	+	0.0682613i	−0.0150446	+	0.0109306i
$40$	−0.0371762	−	0.114417i	−0.00587807	−	0.0180908i
$41$	2.86616	−	8.82113i	0.447619	−	1.37763i	−0.431967	−	0.901889i	$-0.642180\pi$
$41$	2.86616	−	8.82113i	0.447619	−	1.37763i	0.879586	−	0.475740i	$-0.157820\pi$
$42$	−1.03338	−	0.750792i	−0.159453	−	0.115850i
$43$	−1.52139			−0.232010			−0.116005	−	0.993249i	$-0.537009\pi$
$43$	−1.52139			−0.232010			−0.116005	+	0.993249i	$0.537009\pi$
$44$	−2.08695	+	2.57772i	−0.314619	+	0.388606i
$45$	0.268690			0.0400539
$46$	−6.18341	−	4.49251i	−0.911694	−	0.662384i
$47$	2.35034	−	7.23359i	0.342832	−	1.05513i	−0.619902	−	0.784679i	$-0.712828\pi$
$47$	2.35034	−	7.23359i	0.342832	−	1.05513i	0.962734	−	0.270449i	$-0.0871722\pi$
$48$	0.270560	+	0.832698i	0.0390520	+	0.120190i
$49$	3.94126	−	2.86349i	0.563038	−	0.409071i
$50$	4.03338	−	2.93042i	0.570405	−	0.414424i
$51$	−0.270560	−	0.832698i	−0.0378860	−	0.116601i
$52$	0.0409881	−	0.126148i	0.00568402	−	0.0174936i
$53$	8.48636	+	6.16570i	1.16569	+	0.846924i	0.990487	−	0.137608i	$-0.0439414\pi$
$53$	8.48636	+	6.16570i	1.16569	+	0.846924i	0.175204	+	0.984532i	$0.443941\pi$
$54$	−4.58211			−0.623547
$55$	0.372519	+	0.142952i	0.0502304	+	0.0192756i
$56$	1.45888			0.194951
$57$	−1.90929	−	1.38718i	−0.252892	−	0.183737i
$58$	−0.812453	+	2.50047i	−0.106680	+	0.328328i
$59$	0.200475	+	0.616999i	0.0260996	+	0.0803264i	0.963258	−	0.268578i	$-0.0865537\pi$
$59$	0.200475	+	0.616999i	0.0260996	+	0.0803264i	−0.937158	+	0.348905i	$0.886554\pi$
$60$	0.0852160	−	0.0619131i	0.0110013	−	0.00799294i
$61$	−11.2033	+	8.13965i	−1.43443	+	1.04217i	−0.445261	+	0.895401i	$0.646889\pi$
$61$	−11.2033	+	8.13965i	−1.43443	+	1.04217i	−0.989170	+	0.146774i	$0.953111\pi$
$62$	2.93448	+	9.03139i	0.372679	+	1.14699i
$63$	−1.00686	+	3.09881i	−0.126853	+	0.390413i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.0159572			−0.00197925
$66$	−2.71111	−	1.04037i	−0.333714	−	0.128061i
$67$	−5.15478			−0.629757			−0.314878	−	0.949132i	$-0.601964\pi$
$67$	−5.15478			−0.629757			−0.314878	+	0.949132i	$0.601964\pi$
$68$	0.809017	+	0.587785i	0.0981077	+	0.0712794i
$69$	2.06792	−	6.36440i	0.248948	−	0.766184i
$70$	−0.0542356	−	0.166920i	−0.00648240	−	0.0199508i
$71$	−8.93737	+	6.49338i	−1.06067	+	0.770622i	−0.974212	−	0.225633i	$-0.927555\pi$
$71$	−8.93737	+	6.49338i	−1.06067	+	0.770622i	−0.0864580	+	0.996255i	$0.527555\pi$
$72$	1.80687	−	1.31277i	0.212941	−	0.154711i
$73$	0.431640	+	1.32845i	0.0505196	+	0.155483i	0.973134	−	0.230241i	$-0.0739515\pi$
$73$	0.431640	+	1.32845i	0.0505196	+	0.155483i	−0.922614	+	0.385725i	$0.873952\pi$
$74$	2.90334	−	8.93555i	0.337506	−	1.03874i
$75$	3.53142	+	2.56573i	0.407774	+	0.296265i
$76$	2.69547			0.309191
$77$	−3.04461	+	3.76059i	−0.346965	+	0.428558i
$78$	0.116133			0.0131495
$79$	−3.84597	−	2.79426i	−0.432706	−	0.314379i	0.350024	−	0.936741i	$-0.386173\pi$
$79$	−3.84597	−	2.79426i	−0.432706	−	0.314379i	−0.782730	+	0.622362i	$0.786173\pi$
$80$	−0.0371762	+	0.114417i	−0.00415643	+	0.0127922i
$81$	0.830750	+	2.55679i	0.0923056	+	0.284087i
$82$	−7.50370	+	5.45176i	−0.828645	+	0.602046i
$83$	−10.3532	+	7.52201i	−1.13641	+	0.825648i	−0.986615	−	0.163070i	$-0.947860\pi$
$83$	−10.3532	+	7.52201i	−1.13641	+	0.825648i	−0.149792	+	0.988718i	$0.547860\pi$
$84$	0.394714	+	1.21481i	0.0430669	+	0.132546i
$85$	0.0371762	−	0.114417i	0.00403232	−	0.0124102i
$86$	1.23083	+	0.894251i	0.132724	+	0.0964296i
$87$	−2.30196			−0.246796
$88$	3.20352	−	0.858742i	0.341497	−	0.0915422i
$89$	−3.91389			−0.414871			−0.207436	−	0.978249i	$-0.566512\pi$
$89$	−3.91389			−0.414871			−0.207436	+	0.978249i	$0.566512\pi$
$90$	−0.217375	−	0.157932i	−0.0229133	−	0.0166475i
$91$	0.0597967	−	0.184035i	0.00626839	−	0.0192921i
$92$	2.36185	+	7.26903i	0.246240	+	0.757849i
$93$	−6.72646	+	4.88706i	−0.697502	+	0.506765i
$94$	−6.15326	+	4.47061i	−0.634660	+	0.461108i
$95$	−0.100207	−	0.308406i	−0.0102810	−	0.0316418i
$96$	0.270560	−	0.832698i	0.0276139	−	0.0849869i
$97$	6.07135	+	4.41109i	0.616452	+	0.447879i	0.851680	−	0.524061i	$-0.175584\pi$
$97$	6.07135	+	4.41109i	0.616452	+	0.447879i	−0.235228	+	0.971940i	$0.575584\pi$
$98$	−4.87167			−0.492113
$99$	−0.386897	+	7.39728i	−0.0388846	+	0.743454i
$100$	−4.98553			−0.498553
$101$	0.487754	+	0.354374i	0.0485334	+	0.0352616i	0.611787	−	0.791022i	$-0.290451\pi$
$101$	0.487754	+	0.354374i	0.0485334	+	0.0352616i	−0.563254	+	0.826284i	$0.690451\pi$
$102$	−0.270560	+	0.832698i	−0.0267894	+	0.0824494i
$103$	−5.02220	−	15.4567i	−0.494852	−	1.52300i	−0.817188	−	0.576372i	$-0.804468\pi$
$103$	−5.02220	−	15.4567i	−0.494852	−	1.52300i	0.322336	−	0.946625i	$-0.395532\pi$
$104$	−0.107308	+	0.0779639i	−0.0105224	+	0.00764499i
$105$	0.124320	−	0.0903237i	0.0121324	−	0.00881470i
$106$	−3.24150	−	9.97631i	−0.314842	−	0.968985i
$107$	6.14373	−	18.9085i	0.593937	−	1.82795i	0.0339881	−	0.999422i	$-0.489179\pi$
$107$	6.14373	−	18.9085i	0.593937	−	1.82795i	0.559949	−	0.828527i	$-0.310821\pi$
$108$	3.70701	+	2.69330i	0.356707	+	0.259163i
$109$	−18.5853			−1.78014			−0.890072	−	0.455819i	$-0.849346\pi$
$109$	−18.5853			−1.78014			−0.890072	+	0.455819i	$0.849346\pi$
$110$	−0.217349	−	0.334611i	−0.0207234	−	0.0319039i
$111$	8.22614			0.780790
$112$	−1.18026	−	0.857508i	−0.111524	−	0.0810269i
$113$	−5.66949	+	17.4489i	−0.533341	+	1.64146i	0.213865	+	0.976863i	$0.431395\pi$
$113$	−5.66949	+	17.4489i	−0.533341	+	1.64146i	−0.747206	+	0.664592i	$0.768605\pi$
$114$	0.729286	+	2.24451i	0.0683039	+	0.210218i
$115$	0.743893	−	0.540470i	0.0693684	−	0.0503991i
$116$	2.12703	−	1.54538i	0.197490	−	0.143485i
$117$	−0.0915432	−	0.281741i	−0.00846317	−	0.0260470i
$118$	0.200475	−	0.616999i	0.0184552	−	0.0567993i
$119$	1.18026	+	0.857508i	0.108194	+	0.0786077i
$120$	−0.105333			−0.00961553
$121$	−4.47199	+	10.0499i	−0.406545	+	0.913631i
$122$	13.8480			1.25374
$123$	−6.56987	−	4.77329i	−0.592385	−	0.430393i
$124$	2.93448	−	9.03139i	0.263524	−	0.811043i
$125$	0.371224	+	1.14251i	0.0332033	+	0.102189i
$126$	2.63600	−	1.91517i	0.234834	−	0.170617i
$127$	−7.07174	+	5.13792i	−0.627515	+	0.455916i	−0.855538	−	0.517739i	$-0.826774\pi$
$127$	−7.07174	+	5.13792i	−0.627515	+	0.455916i	0.228023	+	0.973656i	$0.426774\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.411627	+	1.26686i	−0.0362418	+	0.111541i
$130$	0.0129097	+	0.00937943i	0.00113225	+	0.000822630i
$131$	2.90096			0.253458			0.126729	−	0.991937i	$-0.459552\pi$
$131$	2.90096			0.253458			0.126729	+	0.991937i	$0.459552\pi$
$132$	1.58182	+	2.43523i	0.137680	+	0.211959i
$133$	3.93237			0.340979
$134$	4.17031	+	3.02990i	0.360260	+	0.261744i
$135$	0.170346	−	0.524270i	0.0146610	−	0.0451220i
$136$	−0.309017	−	0.951057i	−0.0264980	−	0.0815524i
$137$	15.9104	−	11.5596i	1.35932	−	0.987604i	0.360832	−	0.932631i	$-0.382493\pi$
$137$	15.9104	−	11.5596i	1.35932	−	0.987604i	0.998488	−	0.0549727i	$-0.0175072\pi$
$138$	−5.41389	+	3.93342i	−0.460861	+	0.334835i
$139$	0.571091	+	1.75764i	0.0484393	+	0.149081i	0.972351	−	0.233526i	$-0.0750264\pi$
$139$	0.571091	+	1.75764i	0.0484393	+	0.149081i	−0.923911	+	0.382607i	$0.875026\pi$
$140$	−0.0542356	+	0.166920i	−0.00458375	+	0.0141073i
$141$	−5.38749	−	3.91424i	−0.453708	−	0.329638i
$142$	11.0472			0.927060
$143$	0.0229774	−	0.439317i	0.00192147	−	0.0367375i
$144$	−2.23341			−0.186118
$145$	−0.255892	−	0.185916i	−0.0212507	−	0.0154395i
$146$	0.431640	−	1.32845i	0.0357228	−	0.109943i
$147$	−1.31808	−	4.05663i	−0.108713	−	0.334585i
$148$	−7.60103	+	5.52247i	−0.624801	+	0.453944i
$149$	−2.31022	+	1.67848i	−0.189261	+	0.137506i	−0.678381	−	0.734710i	$-0.737318\pi$
$149$	−2.31022	+	1.67848i	−0.189261	+	0.137506i	0.489120	+	0.872217i	$0.337318\pi$
$150$	−1.34888	−	4.15144i	−0.110136	−	0.338963i
$151$	5.95715	−	18.3342i	0.484786	−	1.49202i	−0.347505	−	0.937678i	$-0.612971\pi$
$151$	5.95715	−	18.3342i	0.484786	−	1.49202i	0.832291	−	0.554339i	$-0.187029\pi$
$152$	−2.18068	−	1.58436i	−0.176877	−	0.128508i
$153$	2.23341			0.180561
$154$	4.67356	−	1.25280i	0.376606	−	0.100954i
$155$	−1.14243			−0.0917624
$156$	−0.0939537	−	0.0682613i	−0.00752231	−	0.00546528i
$157$	1.65705	−	5.09988i	0.132247	−	0.407015i	−0.862905	−	0.505367i	$-0.831357\pi$
$157$	1.65705	−	5.09988i	0.132247	−	0.407015i	0.995152	+	0.0983521i	$0.0313572\pi$
$158$	1.46903	+	4.52121i	0.116870	+	0.359688i
$159$	7.43023	−	5.39838i	0.589256	−	0.428119i
$160$	0.0973285	−	0.0707133i	0.00769450	−	0.00559038i
$161$	3.44566	+	10.6047i	0.271556	+	0.835764i
$162$	0.830750	−	2.55679i	0.0652699	−	0.200880i
$163$	6.59921	+	4.79461i	0.516890	+	0.375543i	0.815431	−	0.578854i	$-0.196500\pi$
$163$	6.59921	+	4.79461i	0.516890	+	0.375543i	−0.298541	+	0.954397i	$0.596500\pi$
$164$	9.27509			0.724263
$165$	0.219824	−	0.271519i	0.0171133	−	0.0211377i
$166$	12.7972			0.993256
$167$	−6.66232	−	4.84046i	−0.515546	−	0.374566i	0.299378	−	0.954135i	$-0.403221\pi$
$167$	−6.66232	−	4.84046i	−0.515546	−	0.374566i	−0.814923	+	0.579569i	$0.803221\pi$
$168$	0.394714	−	1.21481i	0.0304529	−	0.0937243i
$169$	−4.01178	−	12.3470i	−0.308599	−	0.949769i
$170$	−0.0973285	+	0.0707133i	−0.00746476	+	0.00542346i
$171$	4.87036	−	3.53852i	0.372445	−	0.270597i
$172$	−0.470136	−	1.44693i	−0.0358475	−	0.110327i
$173$	1.25556	−	3.86422i	0.0954586	−	0.293791i	−0.891914	−	0.452204i	$-0.850638\pi$
$173$	1.25556	−	3.86422i	0.0954586	−	0.293791i	0.987373	+	0.158413i	$0.0506377\pi$
$174$	1.86232	+	1.35306i	0.141182	+	0.102575i
$175$	−7.27329			−0.549809
$176$	−3.09646	−	1.18825i	−0.233405	−	0.0895675i
$177$	0.568014			0.0426945
$178$	3.16640	+	2.30053i	0.237332	+	0.172432i
$179$	2.20193	−	6.77683i	0.164580	−	0.506524i	−0.834425	−	0.551121i	$-0.814200\pi$
$179$	2.20193	−	6.77683i	0.164580	−	0.506524i	0.999005	+	0.0445969i	$0.0142003\pi$
$180$	0.0830298	+	0.255539i	0.00618867	+	0.0190468i
$181$	−5.93788	+	4.31412i	−0.441359	+	0.320666i	−0.786175	−	0.618004i	$-0.787941\pi$
$181$	−5.93788	+	4.31412i	−0.441359	+	0.320666i	0.344816	+	0.938670i	$0.387941\pi$
$182$	−0.156550	+	0.113740i	−0.0116042	+	0.00843097i
$183$	3.74671	+	11.5312i	0.276965	+	0.852410i
$184$	2.36185	−	7.26903i	0.174118	−	0.535880i
$185$	0.914440	+	0.664379i	0.0672309	+	0.0488461i
$186$	8.31437			0.609639
$187$	3.09646	+	1.18825i	0.226436	+	0.0868932i
$188$	7.60585			0.554714
$189$	5.40808	+	3.92920i	0.393380	+	0.285807i
$190$	−0.100207	+	0.308406i	−0.00726980	+	0.0223741i
$191$	−2.48728	−	7.65508i	−0.179974	−	0.553902i	0.819852	−	0.572575i	$-0.194056\pi$
$191$	−2.48728	−	7.65508i	−0.179974	−	0.553902i	−0.999826	+	0.0186737i	$0.994056\pi$
$192$	−0.708335	+	0.514635i	−0.0511197	+	0.0371406i
$193$	9.58871	−	6.96661i	0.690210	−	0.501467i	−0.186519	−	0.982451i	$-0.559721\pi$
$193$	9.58871	−	6.96661i	0.690210	−	0.501467i	0.876729	+	0.480984i	$0.159721\pi$
$194$	−2.31905	−	7.13730i	−0.166498	−	0.512428i
$195$	−0.00431739	+	0.0132876i	−0.000309175	+	0.000951541i
$196$	3.94126	+	2.86349i	0.281519	+	0.204535i
$197$	−8.46442			−0.603065			−0.301533	−	0.953456i	$-0.597498\pi$
$197$	−8.46442			−0.603065			−0.301533	+	0.953456i	$0.597498\pi$
$198$	4.66102	−	5.75711i	0.331244	−	0.409140i
$199$	−3.17230			−0.224879			−0.112439	−	0.993659i	$-0.535866\pi$
$199$	−3.17230			−0.224879			−0.112439	+	0.993659i	$0.535866\pi$
$200$	4.03338	+	2.93042i	0.285203	+	0.207212i
$201$	−1.39468	+	4.29237i	−0.0983729	+	0.302761i
$202$	−0.186306	−	0.573390i	−0.0131084	−	0.0403436i
$203$	3.10308	−	2.25452i	0.217794	−	0.158236i
$204$	0.708335	−	0.514635i	0.0495934	−	0.0360317i
$205$	−0.344812	−	1.06122i	−0.0240827	−	0.0741191i
$206$	−5.02220	+	15.4567i	−0.349913	+	1.07692i
$207$	13.8101	+	10.0336i	0.959868	+	0.697385i
$208$	0.132640			0.00919694
$209$	8.63500	−	2.31471i	0.597295	−	0.160112i
$210$	−0.153668			−0.0106041
$211$	9.43788	+	6.85702i	0.649730	+	0.472057i	0.863179	−	0.504897i	$-0.168470\pi$
$211$	9.43788	+	6.85702i	0.649730	+	0.472057i	−0.213449	+	0.976954i	$0.568470\pi$
$212$	−3.24150	+	9.97631i	−0.222627	+	0.685176i
$213$	2.98893	+	9.19897i	0.204798	+	0.630303i
$214$	−16.0845	+	11.6861i	−1.09951	+	0.798843i
$215$	−0.148075	+	0.107583i	−0.0100986	+	0.00733707i
$216$	−1.41595	−	4.35785i	−0.0963433	−	0.296514i
$217$	4.28105	−	13.1757i	0.290617	−	0.894426i
$218$	15.0358	+	10.9241i	1.01835	+	0.739876i
$219$	1.22298			0.0826415
$220$	−0.0208405	+	0.398461i	−0.00140507	+	0.0268642i
$221$	−0.132640			−0.00892234
$222$	−6.65508	−	4.83520i	−0.446660	−	0.324517i
$223$	1.31611	−	4.05058i	0.0881334	−	0.271247i	−0.897270	−	0.441482i	$-0.854453\pi$
$223$	1.31611	−	4.05058i	0.0881334	−	0.271247i	0.985403	+	0.170236i	$0.0544528\pi$
$224$	0.450819	+	1.38748i	0.0301216	+	0.0927047i
$225$	−9.00819	+	6.54483i	−0.600546	+	0.436322i
$226$	14.8429	−	10.7840i	0.987337	−	0.717342i
$227$	−6.09936	−	18.7719i	−0.404829	−	1.24593i	−0.921038	−	0.389472i	$-0.872658\pi$
$227$	−6.09936	−	18.7719i	−0.404829	−	1.24593i	0.516210	−	0.856462i	$-0.327342\pi$
$228$	0.729286	−	2.24451i	0.0482981	−	0.148646i
$229$	−0.463983	−	0.337103i	−0.0306609	−	0.0222764i	0.572349	−	0.820010i	$-0.306032\pi$
$229$	−0.463983	−	0.337103i	−0.0306609	−	0.0222764i	−0.603010	+	0.797734i	$0.706032\pi$
$230$	−0.919503			−0.0606302
$231$	2.30768	+	3.55270i	0.151834	+	0.233751i
$232$	−2.62915			−0.172612
$233$	8.54497	+	6.20828i	0.559800	+	0.406718i	0.831386	−	0.555696i	$-0.187548\pi$
$233$	8.54497	+	6.20828i	0.559800	+	0.406718i	−0.271586	+	0.962414i	$0.587548\pi$
$234$	−0.0915432	+	0.281741i	−0.00598437	+	0.0184180i
$235$	−0.282757	−	0.870235i	−0.0184450	−	0.0567679i
$236$	−0.524851	+	0.381326i	−0.0341649	+	0.0248222i
$237$	−3.36734	+	2.44652i	−0.218732	+	0.158918i
$238$	−0.450819	−	1.38748i	−0.0292222	−	0.0899368i
$239$	6.04349	−	18.6000i	0.390921	−	1.20313i	−0.541172	−	0.840912i	$-0.682019\pi$
$239$	6.04349	−	18.6000i	0.390921	−	1.20313i	0.932093	−	0.362219i	$-0.117981\pi$
$240$	0.0852160	+	0.0619131i	0.00550067	+	0.00399647i
$241$	−20.0960			−1.29450			−0.647248	−	0.762280i	$-0.724080\pi$
$241$	−20.0960			−1.29450			−0.647248	+	0.762280i	$0.724080\pi$
$242$	9.52513	−	5.50200i	0.612298	−	0.353682i
$243$	16.1001			1.03282
$244$	−11.2033	−	8.13965i	−0.717215	−	0.521087i
$245$	0.181110	−	0.557400i	0.0115707	−	0.0356110i
$246$	2.50947	+	7.72334i	0.159998	+	0.492422i
$247$	−0.289246	+	0.210149i	−0.0184043	+	0.0133715i
$248$	−7.68256	+	5.58170i	−0.487843	+	0.354439i
$249$	3.46241	+	10.6562i	0.219421	+	0.675309i
$250$	0.371224	−	1.14251i	0.0234783	−	0.0722587i
$251$	2.30607	+	1.67546i	0.145558	+	0.105754i	0.658181	−	0.752860i	$-0.271326\pi$
$251$	2.30607	+	1.67546i	0.145558	+	0.105754i	−0.512623	+	0.858614i	$0.671326\pi$
$252$	−3.25828			−0.205252
$253$	13.8085	+	21.2583i	0.868131	+	1.33650i
$254$	8.74115			0.548468
$255$	−0.0852160	−	0.0619131i	−0.00533643	−	0.00387715i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.26958	−	19.2958i	−0.391086	−	1.20364i	−0.931968	−	0.362540i	$-0.881910\pi$
$257$	−6.26958	−	19.2958i	−0.391086	−	1.20364i	0.540883	−	0.841098i	$-0.318090\pi$
$258$	1.07765	−	0.782962i	0.0670918	−	0.0487451i
$259$	−11.0890	+	8.05663i	−0.689037	+	0.500614i
$260$	−0.00493106	−	0.0151762i	−0.000305811	−	0.000941190i
$261$	1.81454	−	5.58459i	0.112317	−	0.345677i
$262$	−2.34693	−	1.70514i	−0.144994	−	0.105344i
$263$	−20.8656			−1.28663			−0.643315	−	0.765602i	$-0.722441\pi$
$263$	−20.8656			−1.28663			−0.643315	+	0.765602i	$0.722441\pi$
$264$	0.151673	−	2.89991i	0.00933481	−	0.178477i
$265$	1.26196			0.0775217
$266$	−3.18135	−	2.31139i	−0.195061	−	0.141720i
$267$	−1.05894	+	3.25909i	−0.0648062	+	0.199453i
$268$	−1.59292	−	4.90249i	−0.0973028	−	0.299467i
$269$	−12.9467	+	9.40634i	−0.789376	+	0.573515i	−0.907778	−	0.419451i	$-0.862223\pi$
$269$	−12.9467	+	9.40634i	−0.789376	+	0.573515i	0.118402	+	0.992966i	$0.462223\pi$
$270$	−0.445971	+	0.324017i	−0.0271409	+	0.0197190i
$271$	−7.02095	−	21.6083i	−0.426492	−	1.31261i	−0.901558	−	0.432658i	$-0.857576\pi$
$271$	−7.02095	−	21.6083i	−0.426492	−	1.31261i	0.475066	−	0.879950i	$-0.342424\pi$
$272$	−0.309017	+	0.951057i	−0.0187369	+	0.0576663i
$273$	−0.137067	−	0.0995851i	−0.00829568	−	0.00602716i
$274$	−19.6664			−1.18809
$275$	−15.9713	+	4.28128i	−0.963103	+	0.258171i
$276$	6.69193			0.402807
$277$	−10.1559	−	7.37866i	−0.610206	−	0.443341i	0.239281	−	0.970950i	$-0.423088\pi$
$277$	−10.1559	−	7.37866i	−0.610206	−	0.443341i	−0.849487	+	0.527610i	$0.823088\pi$
$278$	0.571091	−	1.75764i	0.0342518	−	0.105416i
$279$	−6.55389	−	20.1708i	−0.392371	−	1.20759i
$280$	0.141991	−	0.103162i	0.00848557	−	0.00616513i
$281$	6.47153	−	4.70184i	0.386059	−	0.280488i	−0.377780	−	0.925895i	$-0.623312\pi$
$281$	6.47153	−	4.70184i	0.386059	−	0.280488i	0.763839	+	0.645407i	$0.223312\pi$
$282$	2.05784	+	6.33337i	0.122542	+	0.377147i
$283$	−8.21736	+	25.2904i	−0.488471	+	1.50336i	0.338419	+	0.940996i	$0.390108\pi$
$283$	−8.21736	+	25.2904i	−0.488471	+	1.50336i	−0.826890	+	0.562364i	$0.809892\pi$
$284$	−8.93737	−	6.49338i	−0.530335	−	0.385311i
$285$	−0.283921			−0.0168180
$286$	−0.276813	+	0.341909i	−0.0163683	+	0.0202175i
$287$	13.5312			0.798724
$288$	1.80687	+	1.31277i	0.106471	+	0.0773555i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	0.0977419	+	0.300819i	0.00573960	+	0.0176647i
$291$	5.31577	−	3.86213i	0.311616	−	0.226402i
$292$	−1.13005	+	0.821027i	−0.0661310	+	0.0480470i
$293$	9.31494	+	28.6684i	0.544185	+	1.67483i	0.722921	+	0.690931i	$0.242799\pi$
$293$	9.31494	+	28.6684i	0.544185	+	1.67483i	−0.178736	+	0.983897i	$0.557201\pi$
$294$	−1.31808	+	4.05663i	−0.0768719	+	0.236587i
$295$	0.0631420	+	0.0458753i	0.00367627	+	0.00267097i
$296$	9.39539			0.546096
$297$	14.1883	+	5.44469i	0.823291	+	0.315933i
$298$	2.85559			0.165420
$299$	−0.820168	−	0.595887i	−0.0474316	−	0.0344610i
$300$	−1.34888	+	4.15144i	−0.0778778	+	0.239683i
$301$	−0.685872	−	2.11090i	−0.0395330	−	0.121670i
$302$	−15.5960	+	11.3312i	−0.897450	+	0.652035i
$303$	0.427053	−	0.310272i	0.0245336	−	0.0178247i
$304$	0.832946	+	2.56354i	0.0477727	+	0.147029i
$305$	−0.514816	+	1.58444i	−0.0294783	+	0.0907248i
$306$	−1.80687	−	1.31277i	−0.103292	−	0.0750459i
$307$	15.1612			0.865297			0.432649	−	0.901563i	$-0.357579\pi$
$307$	15.1612			0.865297			0.432649	+	0.901563i	$0.357579\pi$
$308$	−4.51737	−	1.73351i	−0.257401	−	0.0987759i
$309$	−14.2296			−0.809493
$310$	0.924248	+	0.671505i	0.0524937	+	0.0381389i
$311$	−0.614474	+	1.89116i	−0.0348436	+	0.107238i	−0.966966	−	0.254907i	$-0.917955\pi$
$311$	−0.614474	+	1.89116i	−0.0348436	+	0.107238i	0.932122	+	0.362144i	$0.117955\pi$
$312$	0.0358871	+	0.110449i	0.00203171	+	0.00625295i
$313$	−16.3021	+	11.8442i	−0.921448	+	0.669471i	−0.943884	−	0.330277i	$-0.892858\pi$
$313$	−16.3021	+	11.8442i	−0.921448	+	0.669471i	0.0224359	+	0.999748i	$0.492858\pi$
$314$	−4.33822	+	3.15190i	−0.244820	+	0.177872i
$315$	0.121130	+	0.372801i	0.00682493	+	0.0210050i
$316$	1.46903	−	4.52121i	0.0826394	−	0.254338i
$317$	−13.1420	−	9.54826i	−0.738131	−	0.536283i	0.153994	−	0.988072i	$-0.450786\pi$
$317$	−13.1420	−	9.54826i	−0.738131	−	0.536283i	−0.892125	+	0.451788i	$0.850786\pi$
$318$	−9.18427			−0.515028
$319$	5.48691	−	6.77722i	0.307208	−	0.379452i
$320$	−0.120305			−0.00672524
$321$	−14.0828	−	10.2317i	−0.786024	−	0.571080i
$322$	3.44566	−	10.6047i	0.192019	−	0.590974i
$323$	−0.832946	−	2.56354i	−0.0463463	−	0.142639i
$324$	−2.17493	+	1.58018i	−0.120830	+	0.0877878i
$325$	0.534988	−	0.388691i	0.0296758	−	0.0215607i
$326$	−2.52067	−	7.75784i	−0.139607	−	0.429667i
$327$	−5.02842	+	15.4759i	−0.278072	+	0.855819i
$328$	−7.50370	−	5.45176i	−0.414323	−	0.301023i
$329$	11.0960			0.611744
$330$	−0.337436	+	0.0904537i	−0.0185752	+	0.00497931i
$331$	−16.0144			−0.880232			−0.440116	−	0.897941i	$-0.645063\pi$
$331$	−16.0144			−0.880232			−0.440116	+	0.897941i	$0.645063\pi$
$332$	−10.3532	−	7.52201i	−0.568203	−	0.412824i
$333$	−6.48434	+	19.9568i	−0.355340	+	1.09362i
$334$	2.54478	+	7.83203i	0.139244	+	0.428549i
$335$	−0.501707	+	0.364512i	−0.0274112	+	0.0199154i
$336$	−1.03338	+	0.750792i	−0.0563753	+	0.0409590i
$337$	0.380325	+	1.17052i	0.0207176	+	0.0637623i	0.960881	−	0.276962i	$-0.0893277\pi$
$337$	0.380325	+	1.17052i	0.0207176	+	0.0637623i	−0.940163	+	0.340724i	$0.889328\pi$
$338$	−4.01178	+	12.3470i	−0.218212	+	0.671588i
$339$	12.9957	+	9.44195i	0.705831	+	0.512816i
$340$	0.120305			0.00652444
$341$	1.64503	−	31.4522i	0.0890835	−	1.70323i
$342$	−6.02009			−0.325529
$343$	14.0116	+	10.1801i	0.756558	+	0.549671i
$344$	−0.470136	+	1.44693i	−0.0253480	+	0.0780132i
$345$	−0.248781	−	0.765668i	−0.0133939	−	0.0412222i
$346$	−3.28710	+	2.38822i	−0.176716	+	0.128392i
$347$	−17.1074	+	12.4293i	−0.918376	+	0.667239i	−0.943119	−	0.332455i	$-0.892123\pi$
$347$	−17.1074	+	12.4293i	−0.918376	+	0.667239i	0.0247433	+	0.999694i	$0.492123\pi$
$348$	−0.711344	−	2.18929i	−0.0381320	−	0.117358i
$349$	2.93236	−	9.02489i	0.156966	−	0.483091i	−0.841389	−	0.540430i	$-0.818262\pi$
$349$	2.93236	−	9.02489i	0.156966	−	0.483091i	0.998355	+	0.0573388i	$0.0182615\pi$
$350$	5.88421	+	4.27513i	0.314524	+	0.228515i
$351$	−0.607772			−0.0324405
$352$	1.80666	+	2.78137i	0.0962950	+	0.148247i
$353$	1.34305			0.0714833			0.0357417	−	0.999361i	$-0.488621\pi$
$353$	1.34305			0.0714833			0.0357417	+	0.999361i	$0.488621\pi$
$354$	−0.459533	−	0.333870i	−0.0244239	−	0.0177450i
$355$	−0.410693	+	1.26398i	−0.0217973	+	0.0670852i
$356$	−1.20946	−	3.72233i	−0.0641012	−	0.197283i
$357$	1.03338	−	0.750792i	0.0546921	−	0.0397361i
$358$	−5.76471	+	4.18831i	−0.304675	+	0.221359i
$359$	7.94302	+	24.4461i	0.419216	+	1.29022i	0.908425	+	0.418048i	$0.137286\pi$
$359$	7.94302	+	24.4461i	0.419216	+	1.29022i	−0.489208	+	0.872167i	$0.662714\pi$
$360$	0.0830298	−	0.255539i	0.00437605	−	0.0134681i
$361$	9.49337	+	6.89734i	0.499651	+	0.363018i
$362$	7.33962			0.385762
$363$	7.15862	+	6.44293i	0.375730	+	0.338166i
$364$	0.193506			0.0101425
$365$	0.135950	+	0.0987735i	0.00711595	+	0.00517004i
$366$	3.74671	−	11.5312i	0.195844	−	0.602745i
$367$	7.72899	+	23.7874i	0.403450	+	1.24169i	0.922182	+	0.386755i	$0.126404\pi$
$367$	7.72899	+	23.7874i	0.403450	+	1.24169i	−0.518732	+	0.854937i	$0.673596\pi$
$368$	−6.18341	+	4.49251i	−0.322333	+	0.234188i
$369$	16.7589	−	12.1760i	0.872431	−	0.633858i
$370$	−0.349285	−	1.07499i	−0.0181585	−	0.0558860i
$371$	−4.72896	+	14.5542i	−0.245515	+	0.755619i
$372$	−6.72646	−	4.88706i	−0.348751	−	0.253382i
$373$	5.43001			0.281155			0.140578	−	0.990070i	$-0.455104\pi$
$373$	5.43001			0.281155			0.140578	+	0.990070i	$0.455104\pi$
$374$	−1.80666	−	2.78137i	−0.0934199	−	0.143821i
$375$	1.05180			0.0543149
$376$	−6.15326	−	4.47061i	−0.317330	−	0.230554i
$377$	−0.107764	+	0.331663i	−0.00555012	+	0.0170815i
$378$	−2.06570	−	6.35758i	−0.106248	−	0.326999i
$379$	2.98920	−	2.17178i	0.153545	−	0.111557i	−0.508360	−	0.861144i	$-0.669748\pi$
$379$	2.98920	−	2.17178i	0.153545	−	0.111557i	0.661905	+	0.749588i	$0.269748\pi$
$380$	0.262346	−	0.190606i	0.0134581	−	0.00977786i
$381$	2.36500	+	7.27873i	0.121163	+	0.372901i
$382$	−2.48728	+	7.65508i	−0.127261	+	0.391668i
$383$	1.94548	+	1.41348i	0.0994096	+	0.0722253i	0.636380	−	0.771376i	$-0.280431\pi$
$383$	1.94548	+	1.41348i	0.0994096	+	0.0722253i	−0.536970	+	0.843601i	$0.680431\pi$
$384$	0.875550			0.0446802
$385$	−0.0304039	+	0.581307i	−0.00154952	+	0.0296261i
$386$	−11.8523			−0.603266
$387$	−2.74895	−	1.99723i	−0.139737	−	0.101525i
$388$	−2.31905	+	7.13730i	−0.117732	+	0.362342i
$389$	−8.61419	−	26.5118i	−0.436757	−	1.34420i	−0.891276	−	0.453462i	$-0.850189\pi$
$389$	−8.61419	−	26.5118i	−0.436757	−	1.34420i	0.454519	−	0.890737i	$-0.349811\pi$
$390$	0.0113031	−	0.00821216i	0.000572353	−	0.000415839i
$391$	6.18341	−	4.49251i	0.312708	−	0.227196i
$392$	−1.50543	−	4.63323i	−0.0760356	−	0.234014i
$393$	0.784884	−	2.41562i	0.0395921	−	0.121852i
$394$	6.84786	+	4.97526i	0.344990	+	0.250650i
$395$	−0.571914			−0.0287761
$396$	−7.15479	+	1.91792i	−0.359542	+	0.0963793i
$397$	−20.1130			−1.00944			−0.504722	−	0.863282i	$-0.668405\pi$
$397$	−20.1130			−1.00944			−0.504722	+	0.863282i	$0.668405\pi$
$398$	2.56645	+	1.86463i	0.128644	+	0.0934656i
$399$	1.06394	−	3.27447i	0.0532636	−	0.163929i
$400$	−1.54061	−	4.74152i	−0.0770306	−	0.237076i
$401$	5.49673	−	3.99361i	0.274494	−	0.199431i	−0.442018	−	0.897006i	$-0.645737\pi$
$401$	5.49673	−	3.99361i	0.274494	−	0.199431i	0.716512	+	0.697575i	$0.245737\pi$
$402$	3.65131	−	2.65283i	0.182111	−	0.132311i
$403$	0.389229	+	1.19792i	0.0193889	+	0.0596729i
$404$	−0.186306	+	0.573390i	−0.00926905	+	0.0285272i
$405$	0.261655	+	0.190103i	0.0130017	+	0.00944630i
$406$	−3.83562			−0.190359
$407$	−19.6077	+	24.2187i	−0.971918	+	1.20048i
$408$	−0.875550			−0.0433462
$409$	13.6500	+	9.91730i	0.674949	+	0.490379i	0.871678	−	0.490079i	$-0.163032\pi$
$409$	13.6500	+	9.91730i	0.674949	+	0.490379i	−0.196729	+	0.980458i	$0.563032\pi$
$410$	−0.344812	+	1.06122i	−0.0170291	+	0.0524101i
$411$	−5.32093	−	16.3761i	−0.262462	−	0.807776i
$412$	13.1483	−	9.55279i	0.647769	−	0.470632i
$413$	−0.765694	+	0.556309i	−0.0376773	+	0.0273742i
$414$	−5.27499	−	16.2347i	−0.259252	−	0.797894i
$415$	−0.475751	+	1.46421i	−0.0233537	+	0.0718753i
$416$	−0.107308	−	0.0779639i	−0.00526121	−	0.00382250i
$417$	1.61810			0.0792385
$418$	−8.34641	−	3.20288i	−0.408236	−	0.156658i
$419$	−19.9568			−0.974953			−0.487476	−	0.873136i	$-0.662082\pi$
$419$	−19.9568			−0.974953			−0.487476	+	0.873136i	$0.662082\pi$
$420$	0.124320	+	0.0903237i	0.00606619	+	0.00440735i
$421$	−1.28919	+	3.96773i	−0.0628314	+	0.193375i	−0.977545	−	0.210728i	$-0.932416\pi$
$421$	−1.28919	+	3.96773i	−0.0628314	+	0.193375i	0.914713	+	0.404104i	$0.132416\pi$
$422$	−3.60495	−	11.0949i	−0.175486	−	0.540091i
$423$	13.7428	−	9.98470i	0.668196	−	0.485473i
$424$	8.48636	−	6.16570i	0.412134	−	0.299433i
$425$	1.54061	+	4.74152i	0.0747307	+	0.229997i
$426$	2.98893	−	9.19897i	0.144814	−	0.445692i
$427$	−16.3442	−	11.8748i	−0.790952	−	0.574660i
$428$	19.8815			0.961010
$429$	−0.359602	−	0.137995i	−0.0173617	−	0.00666245i
$430$	0.183031			0.00882652
$431$	−2.51732	−	1.82894i	−0.121255	−	0.0880968i	0.525505	−	0.850791i	$-0.323876\pi$
$431$	−2.51732	−	1.82894i	−0.121255	−	0.0880968i	−0.646760	+	0.762694i	$0.723876\pi$
$432$	−1.41595	+	4.35785i	−0.0681250	+	0.209667i
$433$	8.58966	+	26.4362i	0.412793	+	1.27044i	0.914210	+	0.405240i	$0.132812\pi$
$433$	8.58966	+	26.4362i	0.412793	+	1.27044i	−0.501418	+	0.865205i	$0.667188\pi$
$434$	−11.2079	+	8.14304i	−0.537998	+	0.390878i
$435$	−0.224046	+	0.162779i	−0.0107422	+	0.00780466i
$436$	−5.74316	−	17.6756i	−0.275047	−	0.846509i
$437$	6.36630	−	19.5935i	0.304541	−	0.937282i
$438$	−0.989413	−	0.718851i	−0.0472760	−	0.0343480i
$439$	17.0281			0.812705			0.406353	−	0.913716i	$-0.366800\pi$
$439$	17.0281			0.812705			0.406353	+	0.913716i	$0.366800\pi$
$440$	0.251070	−	0.310112i	0.0119693	−	0.0147840i
$441$	10.8804			0.518116
$442$	0.107308	+	0.0779639i	0.00510413	+	0.00370837i
$443$	7.07449	−	21.7730i	0.336119	−	1.03447i	−0.630049	−	0.776555i	$-0.716965\pi$
$443$	7.07449	−	21.7730i	0.336119	−	1.03447i	0.966168	−	0.257913i	$-0.0830347\pi$
$444$	2.54202	+	7.82352i	0.120639	+	0.371288i
$445$	−0.380933	+	0.276764i	−0.0180580	+	0.0131199i
$446$	−3.44563	+	2.50339i	−0.163155	+	0.118539i
$447$	0.772609	+	2.37785i	0.0365431	+	0.112468i
$448$	0.450819	−	1.38748i	0.0212992	−	0.0655522i
$449$	8.17402	+	5.93877i	0.385756	+	0.280268i	0.763714	−	0.645555i	$-0.223374\pi$
$449$	8.17402	+	5.93877i	0.385756	+	0.280268i	−0.377958	+	0.925823i	$0.623374\pi$
$450$	11.1347			0.524896
$451$	29.7130	−	7.96490i	1.39913	−	0.375053i
$452$	−18.3469			−0.862964
$453$	−13.6551	−	9.92101i	−0.641572	−	0.466130i
$454$	−6.09936	+	18.7719i	−0.286257	+	0.881008i
$455$	−0.00719382	−	0.0221403i	−0.000337252	−	0.00103795i
$456$	−1.90929	+	1.38718i	−0.0894109	+	0.0649608i
$457$	33.7417	−	24.5148i	1.57837	−	1.14675i	0.659834	−	0.751412i	$-0.270627\pi$
$457$	33.7417	−	24.5148i	1.57837	−	1.14675i	0.918535	−	0.395340i	$-0.129373\pi$
$458$	0.177226	+	0.545445i	0.00828121	+	0.0254870i
$459$	1.41595	−	4.35785i	0.0660909	−	0.203407i
$460$	0.743893	+	0.540470i	0.0346842	+	0.0251995i
$461$	−12.0145			−0.559569			−0.279785	−	0.960063i	$-0.590263\pi$
$461$	−12.0145			−0.559569			−0.279785	+	0.960063i	$0.590263\pi$
$462$	0.221272	−	4.23062i	0.0102945	−	0.196826i
$463$	−19.0604			−0.885813			−0.442907	−	0.896568i	$-0.646053\pi$
$463$	−19.0604			−0.885813			−0.442907	+	0.896568i	$0.646053\pi$
$464$	2.12703	+	1.54538i	0.0987449	+	0.0717424i
$465$	−0.309097	+	0.951301i	−0.0143340	+	0.0441155i
$466$	−3.26389	−	10.0452i	−0.151197	−	0.465336i
$467$	3.98263	−	2.89355i	0.184294	−	0.133897i	−0.491813	−	0.870701i	$-0.663666\pi$
$467$	3.98263	−	2.89355i	0.184294	−	0.133897i	0.676107	+	0.736803i	$0.263666\pi$
$468$	0.239663	−	0.174126i	0.0110784	−	0.00804896i
$469$	−2.32387	−	7.15214i	−0.107306	−	0.330255i
$470$	−0.282757	+	0.870235i	−0.0130426	+	0.0401410i
$471$	−3.79833	−	2.75965i	−0.175018	−	0.127158i
$472$	0.648751			0.0298612
$473$	−2.74863	−	4.23155i	−0.126382	−	0.194567i
$474$	4.16226			0.191179
$475$	10.8718	+	7.89885i	0.498834	+	0.362424i
$476$	−0.450819	+	1.38748i	−0.0206632	+	0.0635949i
$477$	7.23961	+	22.2812i	0.331479	+	1.02019i
$478$	−15.8221	+	11.4954i	−0.723685	+	0.525788i
$479$	−25.7430	+	18.7034i	−1.17623	+	0.854580i	−0.991741	−	0.128255i	$-0.959062\pi$
$479$	−25.7430	+	18.7034i	−1.17623	+	0.854580i	−0.184487	+	0.982835i	$0.559062\pi$
$480$	−0.0325496	−	0.100177i	−0.00148568	−	0.00457245i
$481$	0.385099	−	1.18521i	0.0175590	−	0.0540410i
$482$	16.2580	+	11.8121i	0.740531	+	0.538027i
$483$	9.76273			0.444219
$484$	−10.9400	−	1.14752i	−0.497272	−	0.0521599i
$485$	0.902839			0.0409958
$486$	−13.0253	−	9.46343i	−0.590839	−	0.429270i
$487$	5.09049	−	15.6669i	0.230672	−	0.709936i	−0.766994	−	0.641654i	$-0.778248\pi$
$487$	5.09049	−	15.6669i	0.230672	−	0.709936i	0.997666	−	0.0682814i	$-0.0217516\pi$
$488$	4.27927	+	13.1702i	0.193713	+	0.596188i
$489$	5.77794	−	4.19792i	0.261288	−	0.189837i
$490$	−0.474152	+	0.344492i	−0.0214200	+	0.0155626i
$491$	10.8968	+	33.5370i	0.491767	+	1.51350i	0.821935	+	0.569582i	$0.192895\pi$
$491$	10.8968	+	33.5370i	0.491767	+	1.51350i	−0.330167	+	0.943922i	$0.607105\pi$
$492$	2.50947	−	7.72334i	0.113135	−	0.348195i
$493$	−2.12703	−	1.54538i	−0.0957966	−	0.0696003i
$494$	0.357527			0.0160859
$495$	0.485430	+	0.747325i	0.0218185	+	0.0335898i
$496$	9.49616			0.426390
$497$	−13.0385	−	9.47306i	−0.584859	−	0.424925i
$498$	3.46241	−	10.6562i	0.155154	−	0.477516i
$499$	−9.87250	−	30.3844i	−0.441954	−	1.36019i	−0.885790	−	0.464086i	$-0.846383\pi$
$499$	−9.87250	−	30.3844i	−0.441954	−	1.36019i	0.443836	−	0.896108i	$-0.353617\pi$
$500$	−0.971877	+	0.706110i	−0.0434637	+	0.0315782i
$501$	−5.83320	+	4.23806i	−0.260608	+	0.189343i
$502$	−0.880841	−	2.71095i	−0.0393139	−	0.120996i
$503$	−5.03560	+	15.4980i	−0.224526	+	0.691020i	0.773813	+	0.633414i	$0.218347\pi$
$503$	−5.03560	+	15.4980i	−0.224526	+	0.691020i	−0.998339	+	0.0576066i	$0.981653\pi$
$504$	2.63600	+	1.91517i	0.117417	+	0.0853084i
$505$	0.0725314			0.00322761
$506$	1.32403	−	25.3147i	0.0588602	−	1.12538i
$507$	−11.3667			−0.504815
$508$	−7.07174	−	5.13792i	−0.313758	−	0.227958i
$509$	0.551942	−	1.69870i	0.0244644	−	0.0752937i	−0.938079	−	0.346422i	$-0.887397\pi$
$509$	0.551942	−	1.69870i	0.0244644	−	0.0752937i	0.962543	+	0.271128i	$0.0873966\pi$
$510$	0.0325496	+	0.100177i	0.00144132	+	0.00443593i
$511$	−1.64860	+	1.19778i	−0.0729299	+	0.0529867i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−3.81665	−	11.7464i	−0.168509	−	0.518618i
$514$	−6.26958	+	19.2958i	−0.276539	+	0.851100i
$515$	−1.58180	−	1.14924i	−0.0697024	−	0.0506418i
$516$	−1.33205			−0.0586404
$517$	24.3655	−	6.53146i	1.07159	−	0.287253i
$518$	13.7068			0.602240
$519$	−2.87802	−	2.09101i	−0.126331	−	0.0917850i
$520$	−0.00493106	+	0.0151762i	−0.000216241	+	0.000665522i
$521$	−3.51837	−	10.8284i	−0.154142	−	0.474401i	0.843931	−	0.536452i	$-0.180236\pi$
$521$	−3.51837	−	10.8284i	−0.154142	−	0.474401i	−0.998073	+	0.0620509i	$0.980236\pi$
$522$	−4.75053	+	3.45147i	−0.207925	+	0.151067i
$523$	14.9594	−	10.8686i	0.654129	−	0.475253i	−0.210546	−	0.977584i	$-0.567524\pi$
$523$	14.9594	−	10.8686i	0.654129	−	0.475253i	0.864675	+	0.502331i	$0.167524\pi$
$524$	0.896446	+	2.75898i	0.0391614	+	0.120527i
$525$	−1.96786	+	6.05645i	−0.0858844	+	0.264325i
$526$	16.8806	+	12.2645i	0.736031	+	0.534758i
$527$	−9.49616			−0.413659
$528$	−1.82723	+	2.25692i	−0.0795199	+	0.0982200i
$529$	35.4172			1.53988
$530$	−1.02095	−	0.741763i	−0.0443472	−	0.0322201i
$531$	−0.447743	+	1.37801i	−0.0194304	+	0.0598007i
$532$	1.21517	+	3.73990i	0.0526842	+	0.162145i
$533$	−0.995292	+	0.723122i	−0.0431109	+	0.0313219i
$534$	2.77234	−	2.01423i	0.119971	−	0.0871641i
$535$	−0.739120	−	2.27478i	−0.0319549	−	0.0983472i
$536$	−1.59292	+	4.90249i	−0.0688035	+	0.211755i
$537$	−5.04730	−	3.66708i	−0.217807	−	0.158246i
$538$	16.0030			0.689940
$539$	15.0849	+	5.78875i	0.649754	+	0.249339i
$540$	0.551250			0.0237220
$541$	19.8982	+	14.4569i	0.855491	+	0.621551i	0.926655	−	0.375914i	$-0.122671\pi$
$541$	19.8982	+	14.4569i	0.855491	+	0.621551i	−0.0711635	+	0.997465i	$0.522671\pi$
$542$	−7.02095	+	21.6083i	−0.301576	+	0.928154i
$543$	1.98581	+	6.11168i	0.0852191	+	0.262277i
$544$	0.809017	−	0.587785i	0.0346863	−	0.0252011i
$545$	−1.80888	+	1.31423i	−0.0774837	+	0.0562952i
$546$	0.0523550	+	0.161132i	0.00224059	+	0.00689582i
$547$	−2.26796	+	6.98005i	−0.0969708	+	0.298445i	−0.987762	−	0.155967i	$-0.950151\pi$
$547$	−2.26796	+	6.98005i	−0.0969708	+	0.298445i	0.890792	+	0.454412i	$0.150151\pi$
$548$	15.9104	+	11.5596i	0.679660	+	0.493802i
$549$	−30.9283			−1.31999
$550$	15.4375	+	5.92404i	0.658257	+	0.252602i
$551$	−7.08680			−0.301908
$552$	−5.41389	−	3.93342i	−0.230430	−	0.167417i
$553$	2.14314	−	6.59591i	0.0911356	−	0.280486i
$554$	3.87919	+	11.9389i	0.164811	+	0.507236i
$555$	0.800638	−	0.581697i	0.0339852	−	0.0246917i
$556$	−1.49514	+	1.08628i	−0.0634079	+	0.0460685i
$557$	−3.92884	−	12.0917i	−0.166470	−	0.512342i	0.832672	−	0.553767i	$-0.186810\pi$
$557$	−3.92884	−	12.0917i	−0.166470	−	0.512342i	−0.999142	+	0.0414249i	$0.986810\pi$
$558$	−6.55389	+	20.1708i	−0.277448	+	0.853898i
$559$	0.163258	+	0.118614i	0.00690506	+	0.00501682i
$560$	−0.175510			−0.00741666
$561$	1.82723	−	2.25692i	0.0771457	−	0.0952874i
$562$	−7.99925			−0.337428
$563$	11.3548	+	8.24975i	0.478548	+	0.347686i	0.800763	−	0.598981i	$-0.204427\pi$
$563$	11.3548	+	8.24975i	0.478548	+	0.347686i	−0.322215	+	0.946666i	$0.604427\pi$
$564$	2.05784	−	6.33337i	0.0866506	−	0.266683i
$565$	0.682067	+	2.09919i	0.0286948	+	0.0883134i
$566$	21.5133	−	15.6303i	0.904272	−	0.656992i
$567$	−3.17297	+	2.30529i	−0.133252	+	0.0968133i
$568$	3.41377	+	10.5065i	0.143239	+	0.440843i
$569$	9.36764	−	28.8306i	0.392712	−	1.20864i	−0.538017	−	0.842934i	$-0.680826\pi$
$569$	9.36764	−	28.8306i	0.392712	−	1.20864i	0.930729	−	0.365709i	$-0.119174\pi$
$570$	0.229697	+	0.166885i	0.00962095	+	0.00699003i
$571$	16.7495			0.700944			0.350472	−	0.936573i	$-0.386021\pi$
$571$	16.7495			0.700944			0.350472	+	0.936573i	$0.386021\pi$
$572$	0.424916	−	0.113904i	0.0177666	−	0.00476255i
$573$	−7.04732			−0.294406
$574$	−10.9470	−	7.95346i	−0.456919	−	0.331971i
$575$	−11.7751	+	36.2400i	−0.491055	+	1.51131i
$576$	−0.690162	−	2.12410i	−0.0287568	−	0.0885042i
$577$	29.4291	−	21.3815i	1.22515	−	0.890125i	0.228634	−	0.973512i	$-0.426574\pi$
$577$	29.4291	−	21.3815i	1.22515	−	0.890125i	0.996517	+	0.0833878i	$0.0265740\pi$
$578$	−0.809017	+	0.587785i	−0.0336507	+	0.0244486i
$579$	−3.20676	−	9.86938i	−0.133268	−	0.410157i
$580$	0.0977419	−	0.300819i	0.00405851	−	0.0124908i
$581$	−15.1040	−	10.9737i	−0.626620	−	0.455266i
$582$	−6.57066			−0.272362
$583$	−1.81715	+	34.7430i	−0.0752586	+	1.43891i
$584$	1.39682			0.0578006
$585$	−0.0288326	−	0.0209481i	−0.00119208	−	0.000866098i
$586$	9.31494	−	28.6684i	0.384797	−	1.18428i
$587$	−9.46374	−	29.1264i	−0.390610	−	1.20218i	−0.932328	−	0.361615i	$-0.882226\pi$
$587$	−9.46374	−	29.1264i	−0.390610	−	1.20218i	0.541717	−	0.840561i	$-0.317774\pi$
$588$	3.45077	−	2.50713i	0.142307	−	0.103392i
$589$	−20.7081	+	15.0453i	−0.853262	+	0.619931i
$590$	−0.0241181	−	0.0742279i	−0.000992926	−	0.00305591i
$591$	−2.29013	+	7.04831i	−0.0942035	+	0.289929i
$592$	−7.60103	−	5.52247i	−0.312400	−	0.226972i
$593$	31.8601			1.30834			0.654168	−	0.756349i	$-0.273019\pi$
$593$	31.8601			1.30834			0.654168	+	0.756349i	$0.273019\pi$
$594$	−8.27830	−	12.7445i	−0.339663	−	0.522915i
$595$	0.175510			0.00719521
$596$	−2.31022	−	1.67848i	−0.0946304	−	0.0687530i
$597$	−0.858298	+	2.64157i	−0.0351278	+	0.108112i
$598$	0.313276	+	0.964166i	0.0128108	+	0.0394277i
$599$	29.1943	−	21.2109i	1.19284	−	0.866652i	0.199283	−	0.979942i	$-0.436139\pi$
$599$	29.1943	−	21.2109i	1.19284	−	0.866652i	0.993562	+	0.113290i	$0.0361388\pi$
$600$	3.53142	−	2.56573i	0.144170	−	0.104745i
$601$	5.27115	+	16.2229i	0.215015	+	0.661748i	0.999153	+	0.0411607i	$0.0131056\pi$
$601$	5.27115	+	16.2229i	0.215015	+	0.661748i	−0.784138	+	0.620587i	$0.786894\pi$
$602$	−0.685872	+	2.11090i	−0.0279540	+	0.0860337i
$603$	−9.31401	−	6.76702i	−0.379296	−	0.275575i
$604$	19.2777			0.784400
$605$	0.275412	+	1.29438i	0.0111971	+	0.0526238i
$606$	−0.527867			−0.0214431
$607$	15.1590	+	11.0137i	0.615286	+	0.447032i	0.851272	−	0.524725i	$-0.175832\pi$
$607$	15.1590	+	11.0137i	0.615286	+	0.447032i	−0.235985	+	0.971757i	$0.575832\pi$
$608$	0.832946	−	2.56354i	0.0337804	−	0.103965i
$609$	−1.03777	−	3.19391i	−0.0420524	−	0.129424i
$610$	1.34781	−	0.979238i	0.0545710	−	0.0396482i
$611$	−0.816170	+	0.592982i	−0.0330187	+	0.0239895i
$612$	0.690162	+	2.12410i	0.0278982	+	0.0858617i
$613$	−7.03316	+	21.6458i	−0.284067	+	0.874267i	0.702610	+	0.711575i	$0.252018\pi$
$613$	−7.03316	+	21.6458i	−0.284067	+	0.874267i	−0.986677	+	0.162692i	$0.947982\pi$
$614$	−12.2657	−	8.91155i	−0.495003	−	0.359641i
$615$	−0.976971			−0.0393953
$616$	2.63569	+	4.05768i	0.106195	+	0.163489i
$617$	−2.57624			−0.103715			−0.0518577	−	0.998654i	$-0.516514\pi$
$617$	−2.57624			−0.103715			−0.0518577	+	0.998654i	$0.516514\pi$
$618$	11.5120	+	8.36394i	0.463080	+	0.336447i
$619$	−8.53857	+	26.2790i	−0.343194	+	1.05624i	0.619349	+	0.785116i	$0.287397\pi$
$619$	−8.53857	+	26.2790i	−0.343194	+	1.05624i	−0.962543	+	0.271128i	$0.912603\pi$
$620$	−0.353031	−	1.08652i	−0.0141781	−	0.0436356i
$621$	28.3331	−	20.5852i	1.13697	−	0.826056i
$622$	1.60871	−	1.16880i	0.0645035	−	0.0468645i
$623$	−1.76445	−	5.43043i	−0.0706914	−	0.217566i
$624$	0.0358871	−	0.110449i	0.00143663	−	0.00442150i
$625$	−20.0500	−	14.5671i	−0.801998	−	0.582686i
$626$	20.1505			0.805375
$627$	0.408829	−	7.81661i	0.0163271	−	0.312165i
$628$	5.36233			0.213980
$629$	7.60103	+	5.52247i	0.303073	+	0.220195i
$630$	0.121130	−	0.372801i	0.00482595	−	0.0148528i
$631$	10.2733	+	31.6181i	0.408975	+	1.25870i	0.917530	+	0.397666i	$0.130180\pi$
$631$	10.2733	+	31.6181i	0.408975	+	1.25870i	−0.508555	+	0.861029i	$0.669820\pi$
$632$	−3.84597	+	2.79426i	−0.152985	+	0.111150i
$633$	8.26334	−	6.00367i	0.328438	−	0.238624i
$634$	5.01982	+	15.4494i	0.199362	+	0.613574i
$635$	−0.324963	+	1.00013i	−0.0128957	+	0.0396890i
$636$	7.43023	+	5.39838i	0.294628	+	0.214060i
$637$	−0.646179			−0.0256025
$638$	−8.42256	+	2.25776i	−0.333452	+	0.0893857i
$639$	−24.6729			−0.976046
$640$	0.0973285	+	0.0707133i	0.00384725	+	0.00279519i
$641$	5.61222	−	17.2727i	0.221670	−	0.682229i	−0.776943	−	0.629571i	$-0.783231\pi$
$641$	5.61222	−	17.2727i	0.221670	−	0.682229i	0.998613	−	0.0526579i	$-0.0167693\pi$
$642$	5.37914	+	16.5553i	0.212298	+	0.653386i
$643$	−24.4701	+	17.7786i	−0.965007	+	0.701118i	−0.954308	−	0.298824i	$-0.903405\pi$
$643$	−24.4701	+	17.7786i	−0.965007	+	0.701118i	−0.0106985	+	0.999943i	$0.503405\pi$
$644$	−9.02085	+	6.55403i	−0.355471	+	0.258265i
$645$	0.0495207	+	0.152409i	0.00194988	+	0.00600110i
$646$	−0.832946	+	2.56354i	−0.0327718	+	0.100861i
$647$	13.4659	+	9.78353i	0.529398	+	0.384630i	0.820133	−	0.572173i	$-0.193900\pi$
$647$	13.4659	+	9.78353i	0.529398	+	0.384630i	−0.290734	+	0.956804i	$0.593900\pi$
$648$	2.68836			0.105609
$649$	−1.35391	+	1.67230i	−0.0531456	+	0.0656435i
$650$	−0.661281			−0.0259376
$651$	−9.81311	−	7.12964i	−0.384606	−	0.279433i
$652$	−2.52067	+	7.75784i	−0.0987172	+	0.303820i
$653$	−4.74718	−	14.6103i	−0.185771	−	0.571745i	0.814189	−	0.580599i	$-0.197182\pi$
$653$	−4.74718	−	14.6103i	−0.185771	−	0.571745i	−0.999961	+	0.00885387i	$0.997182\pi$
$654$	13.1646	−	9.56463i	0.514776	−	0.374007i
$655$	0.282346	−	0.205137i	0.0110322	−	0.00801535i
$656$	2.86616	+	8.82113i	0.111905	+	0.344407i
$657$	−0.964029	+	2.96698i	−0.0376104	+	0.115753i
$658$	−8.97687	−	6.52208i	−0.349955	−	0.254257i
$659$	9.66950			0.376670			0.188335	−	0.982105i	$-0.439691\pi$
$659$	9.66950			0.376670			0.188335	+	0.982105i	$0.439691\pi$
$660$	0.326159	+	0.125161i	0.0126957	+	0.00487190i
$661$	−50.0393			−1.94630			−0.973152	−	0.230164i	$-0.926074\pi$
$661$	−50.0393			−1.94630			−0.973152	+	0.230164i	$0.926074\pi$
$662$	12.9559	+	9.41304i	0.503547	+	0.365848i
$663$	−0.0358871	+	0.110449i	−0.00139374	+	0.00428949i
$664$	3.95455	+	12.1709i	0.153466	+	0.472321i
$665$	0.382731	−	0.278071i	0.0148417	−	0.0107831i
$666$	16.9762	−	12.3340i	0.657816	−	0.477931i
$667$	−6.20967	−	19.1114i	−0.240440	−	0.739997i
$668$	2.54478	−	7.83203i	0.0984605	−	0.303030i
$669$	−3.01682	−	2.19185i	−0.116637	−	0.0847417i
$670$	0.620144			0.0239583
$671$	−42.8798	−	16.4548i	−1.65536	−	0.635232i
$672$	1.27732			0.0492738
$673$	1.34053	+	0.973952i	0.0516736	+	0.0375431i	0.613322	−	0.789833i	$-0.289833\pi$
$673$	1.34053	+	0.973952i	0.0516736	+	0.0375431i	−0.561649	+	0.827376i	$0.689833\pi$
$674$	0.380325	−	1.17052i	0.0146496	−	0.0450868i
$675$	7.05926	+	21.7262i	0.271711	+	0.836241i
$676$	10.5030	−	7.63087i	0.403961	−	0.293495i
$677$	31.5488	−	22.9215i	1.21252	−	0.880946i	0.217061	−	0.976158i	$-0.430353\pi$
$677$	31.5488	−	22.9215i	1.21252	−	0.880946i	0.995457	+	0.0952119i	$0.0303529\pi$
$678$	−4.96393	−	15.2774i	−0.190638	−	0.586725i
$679$	−3.38322	+	10.4125i	−0.129836	+	0.399594i
$680$	−0.0973285	−	0.0707133i	−0.00373238	−	0.00271173i
$681$	−17.2815			−0.662230
$682$	−19.8180	+	24.4785i	−0.758871	+	0.937328i
$683$	−3.38675			−0.129590			−0.0647952	−	0.997899i	$-0.520639\pi$
$683$	−3.38675			−0.129590			−0.0647952	+	0.997899i	$0.520639\pi$
$684$	4.87036	+	3.53852i	0.186223	+	0.135299i
$685$	0.731121	−	2.25016i	0.0279347	−	0.0859741i
$686$	−5.35197	−	16.4717i	−0.204339	−	0.628891i
$687$	−0.406240	+	0.295151i	−0.0154990	+	0.0112607i
$688$	1.23083	−	0.894251i	0.0469250	−	0.0340930i
$689$	−0.429953	−	1.32326i	−0.0163799	−	0.0504122i
$690$	−0.248781	+	0.765668i	−0.00947091	+	0.0291485i
$691$	8.61274	+	6.25752i	0.327644	+	0.238047i	0.739430	−	0.673233i	$-0.235095\pi$
$691$	8.61274	+	6.25752i	0.327644	+	0.238047i	−0.411786	+	0.911280i	$0.635095\pi$
$692$	4.06308			0.154455
$693$	−10.4380	+	2.79802i	−0.396506	+	0.106288i
$694$	21.1460			0.802690
$695$	0.179872	+	0.130685i	0.00682293	+	0.00495715i
$696$	−0.711344	+	2.18929i	−0.0269634	+	0.0829848i
$697$	−2.86616	−	8.82113i	−0.108564	−	0.334124i
$698$	−7.67703	+	5.57769i	−0.290580	+	0.211119i
$699$	7.48155	−	5.43566i	0.282978	−	0.205596i
$700$	−2.24757	−	6.91731i	−0.0849501	−	0.261450i
$701$	−11.3306	+	34.8720i	−0.427950	+	1.31710i	0.472190	+	0.881497i	$0.343464\pi$
$701$	−11.3306	+	34.8720i	−0.427950	+	1.31710i	−0.900141	+	0.435599i	$0.856536\pi$
$702$	0.491698	+	0.357240i	0.0185580	+	0.0134831i
$703$	25.3250			0.955150
$704$	0.173231	−	3.31210i	0.00652890	−	0.124829i
$705$	−0.801145			−0.0301729
$706$	−1.08655	−	0.789425i	−0.0408929	−	0.0297104i
$707$	−0.271798	+	0.836507i	−0.0102220	+	0.0314601i
$708$	0.175526	+	0.540213i	0.00659667	+	0.0203025i
$709$	0.0268237	−	0.0194886i	0.00100739	−	0.000731909i	−0.587281	−	0.809383i	$-0.699802\pi$
$709$	0.0268237	−	0.0194886i	0.00100739	−	0.000731909i	0.588289	+	0.808651i	$0.299802\pi$
$710$	1.07521	−	0.781184i	0.0403518	−	0.0293173i
$711$	−3.28095	−	10.0977i	−0.123045	−	0.378694i
$712$	−1.20946	+	3.72233i	−0.0453264	+	0.139500i
$713$	−58.7187	−	42.6616i	−2.19903	−	1.59769i
$714$	−1.27732			−0.0478026
$715$	−0.0288292	−	0.0443829i	−0.00107815	−	0.00165983i
$716$	7.12558			0.266295
$717$	−13.8530	−	10.0648i	−0.517350	−	0.375877i
$718$	7.94302	−	24.4461i	0.296431	−	0.912320i
$719$	4.15274	+	12.7808i	0.154871	+	0.476644i	0.998148	−	0.0608354i	$-0.0193765\pi$
$719$	4.15274	+	12.7808i	0.154871	+	0.476644i	−0.843277	+	0.537480i	$0.819376\pi$
$720$	−0.217375	+	0.157932i	−0.00810108	+	0.00588578i
$721$	19.1818	−	13.9364i	0.714366	−	0.519018i
$722$	−3.62614	−	11.1601i	−0.134951	−	0.415337i
$723$	−5.43716	+	16.7339i	−0.202210	+	0.622339i
$724$	−5.93788	−	4.31412i	−0.220679	−	0.160333i
$725$	13.1077			0.486808
$726$	−2.00438	−	9.42017i	−0.0743897	−	0.349615i
$727$	33.5724			1.24513			0.622565	−	0.782568i	$-0.286091\pi$
$727$	33.5724			1.24513			0.622565	+	0.782568i	$0.286091\pi$
$728$	−0.156550	−	0.113740i	−0.00580212	−	0.00421549i
$729$	1.86380	−	5.73619i	0.0690297	−	0.212452i
$730$	−0.0519283	−	0.159819i	−0.00192195	−	0.00591516i
$731$	−1.23083	+	0.894251i	−0.0455239	+	0.0330751i
$732$	−9.80902	+	7.12667i	−0.362552	+	0.263409i
$733$	−3.70710	−	11.4093i	−0.136925	−	0.421411i	0.858960	−	0.512043i	$-0.171111\pi$
$733$	−3.70710	−	11.4093i	−0.136925	−	0.421411i	−0.995884	+	0.0906320i	$0.971111\pi$
$734$	7.72899	−	23.7874i	0.285282	−	0.878009i
$735$	−0.415144	−	0.301620i	−0.0153128	−	0.0111254i
$736$	7.64311			0.281729
$737$	−9.31291	−	14.3373i	−0.343046	−	0.528123i
$738$	−20.7151			−0.762533
$739$	23.8190	+	17.3055i	0.876194	+	0.636592i	0.932242	−	0.361836i	$-0.117850\pi$
$739$	23.8190	+	17.3055i	0.876194	+	0.636592i	−0.0560475	+	0.998428i	$0.517850\pi$
$740$	−0.349285	+	1.07499i	−0.0128400	+	0.0395174i
$741$	0.0967326	+	0.297712i	0.00355356	+	0.0109367i
$742$	12.3806	−	8.99502i	0.454505	−	0.330218i
$743$	0.551182	−	0.400457i	0.0202209	−	0.0146913i	−0.577629	−	0.816299i	$-0.696022\pi$
$743$	0.551182	−	0.400457i	0.0202209	−	0.0146913i	0.597850	+	0.801608i	$0.296022\pi$
$744$	2.56928	+	7.90743i	0.0941944	+	0.289901i
$745$	−0.106160	+	0.326727i	−0.00388940	+	0.0119704i
$746$	−4.39297	−	3.19168i	−0.160838	−	0.116856i
$747$	−28.5814			−1.04574
$748$	−0.173231	+	3.31210i	−0.00633397	+	0.121102i
$749$	29.0048			1.05981
$750$	−0.850927	−	0.618235i	−0.0310715	−	0.0225747i
$751$	4.56152	−	14.0389i	0.166452	−	0.512287i	−0.832688	−	0.553742i	$-0.813199\pi$
$751$	4.56152	−	14.0389i	0.166452	−	0.512287i	0.999140	+	0.0414551i	$0.0131994\pi$
$752$	2.35034	+	7.23359i	0.0857080	+	0.263782i
$753$	2.01908	−	1.46695i	0.0735794	−	0.0534586i
$754$	0.282130	−	0.204979i	0.0102746	−	0.00746490i
$755$	−0.716673	−	2.20569i	−0.0260824	−	0.0802734i
$756$	−2.06570	+	6.35758i	−0.0751289	+	0.231223i
$757$	−12.9518	−	9.41007i	−0.470743	−	0.342015i	0.326988	−	0.945029i	$-0.393966\pi$
$757$	−12.9518	−	9.41007i	−0.470743	−	0.342015i	−0.797731	+	0.603014i	$0.793966\pi$
$758$	−3.69485			−0.134203
$759$	21.4378	−	5.74664i	0.778141	−	0.208590i
$760$	−0.324278			−0.0117628
$761$	−24.1567	−	17.5509i	−0.875681	−	0.636219i	0.0564246	−	0.998407i	$-0.482030\pi$
$761$	−24.1567	−	17.5509i	−0.875681	−	0.636219i	−0.932105	+	0.362188i	$0.882030\pi$
$762$	2.36500	−	7.27873i	0.0856750	−	0.263681i
$763$	−8.37858	−	25.7866i	−0.303325	−	0.933538i
$764$	6.51180	−	4.73110i	0.235589	−	0.171165i
$765$	0.217375	−	0.157932i	0.00785920	−	0.00571004i
$766$	−0.743109	−	2.28705i	−0.0268496	−	0.0826346i
$767$	0.0265910	−	0.0818388i	0.000960147	−	0.00295503i
$768$	−0.708335	−	0.514635i	−0.0255598	−	0.0185703i
$769$	−20.6198			−0.743570			−0.371785	−	0.928319i	$-0.621254\pi$
$769$	−20.6198			−0.743570			−0.371785	+	0.928319i	$0.621254\pi$
$770$	0.366281	−	0.452416i	0.0131998	−	0.0163039i
$771$	−17.7638			−0.639749
$772$	9.58871	+	6.96661i	0.345105	+	0.250734i
$773$	−13.4134	+	41.2822i	−0.482446	+	1.48482i	0.353200	+	0.935548i	$0.385094\pi$
$773$	−13.4134	+	41.2822i	−0.482446	+	1.48482i	−0.835646	+	0.549269i	$0.814906\pi$
$774$	1.05001	+	3.23159i	0.0377417	+	0.116157i
$775$	38.3016	−	27.8277i	1.37583	−	0.999602i
$776$	6.07135	−	4.41109i	0.217949	−	0.158349i
$777$	3.70850	+	11.4136i	0.133042	+	0.409460i
$778$	−8.61419	+	26.5118i	−0.308834	+	0.950492i
$779$	−20.2260	−	14.6950i	−0.724671	−	0.526505i
$780$	−0.0139714			−0.000500255
$781$	−34.2072	−	13.1268i	−1.22403	−	0.469714i
$782$	−7.64311			−0.273317
$783$	−9.74630	−	7.08110i	−0.348304	−	0.253058i
$784$	−1.50543	+	4.63323i	−0.0537653	+	0.165473i
$785$	−0.199351	−	0.613540i	−0.00711515	−	0.0218982i
$786$	−2.05485	+	1.49294i	−0.0732942	+	0.0532513i
$787$	−26.8283	+	19.4919i	−0.956327	+	0.694812i	−0.952295	−	0.305180i	$-0.901284\pi$
$787$	−26.8283	+	19.4919i	−0.956327	+	0.694812i	−0.00403230	+	0.999992i	$0.501284\pi$
$788$	−2.61565	−	8.05014i	−0.0931787	−	0.286775i
$789$	−5.64540	+	17.3748i	−0.200982	+	0.618558i
$790$	0.462688	+	0.336163i	0.0164617	+	0.0119601i
$791$	−26.7659			−0.951685
$792$	6.91567	+	2.65385i	0.245738	+	0.0943003i
$793$	1.83680			0.0652267
$794$	16.2718	+	11.8221i	0.577464	+	0.419552i
$795$	0.341436	−	1.05083i	0.0121095	−	0.0372692i
$796$	−0.980296	−	3.01704i	−0.0347457	−	0.106936i
$797$	−11.3576	+	8.25178i	−0.402307	+	0.292293i	−0.770480	−	0.637464i	$-0.779983\pi$
$797$	−11.3576	+	8.25178i	−0.402307	+	0.292293i	0.368173	+	0.929757i	$0.379983\pi$
$798$	−2.78543	+	2.02374i	−0.0986032	+	0.0716394i
$799$	−2.35034	−	7.23359i	−0.0831489	−	0.255906i
$800$	−1.54061	+	4.74152i	−0.0544689	+	0.167638i
$801$	−7.07188	−	5.13802i	−0.249873	−	0.181543i
$802$	−6.79434			−0.239916
$803$	−2.91508	+	3.60060i	−0.102871	+	0.127062i
$804$	−4.51327			−0.159171
$805$	1.08525	+	0.788481i	0.0382501	+	0.0277903i
$806$	0.389229	−	1.19792i	0.0137100	−	0.0421951i
$807$	4.32978	+	13.3257i	0.152415	+	0.469086i
$808$	0.487754	−	0.354374i	0.0171591	−	0.0124668i
$809$	−7.63221	+	5.54513i	−0.268334	+	0.194956i	−0.713813	−	0.700336i	$-0.753033\pi$
$809$	−7.63221	+	5.54513i	−0.268334	+	0.194956i	0.445479	+	0.895292i	$0.353033\pi$
$810$	−0.0999432	−	0.307593i	−0.00351164	−	0.0108077i
$811$	−6.44652	+	19.8404i	−0.226368	+	0.696689i	0.771782	+	0.635887i	$0.219366\pi$
$811$	−6.44652	+	19.8404i	−0.226368	+	0.696689i	−0.998150	+	0.0608017i	$0.980634\pi$
$812$	3.10308	+	2.25452i	0.108897	+	0.0791182i
$813$	−19.8927			−0.697669
$814$	30.0984	−	8.06821i	1.05495	−	0.282791i
$815$	0.981334			0.0343746
$816$	0.708335	+	0.514635i	0.0247967	+	0.0180158i
$817$	−1.26724	+	3.90015i	−0.0443350	+	0.136449i
$818$	−5.21384	−	16.0465i	−0.182297	−	0.561054i
$819$	0.349640	−	0.254028i	0.0122174	−	0.00887647i
$820$	0.902731	−	0.655872i	0.0315247	−	0.0229041i
$821$	9.81626	+	30.2113i	0.342590	+	1.05438i	0.962862	+	0.269996i	$0.0870223\pi$
$821$	9.81626	+	30.2113i	0.342590	+	1.05438i	−0.620272	+	0.784387i	$0.712978\pi$
$822$	−5.32093	+	16.3761i	−0.185589	+	0.571184i
$823$	4.45237	+	3.23484i	0.155200	+	0.112759i	0.662675	−	0.748907i	$-0.269421\pi$
$823$	4.45237	+	3.23484i	0.155200	+	0.112759i	−0.507475	+	0.861666i	$0.669421\pi$
$824$	−16.2522			−0.566171
$825$	−0.756168	+	14.4576i	−0.0263264	+	0.503348i
$826$	0.946450			0.0329312
$827$	−5.26769	−	3.82720i	−0.183175	−	0.133085i	0.492419	−	0.870358i	$-0.336113\pi$
$827$	−5.26769	−	3.82720i	−0.183175	−	0.133085i	−0.675594	+	0.737274i	$0.736113\pi$
$828$	−5.27499	+	16.2347i	−0.183319	+	0.564196i
$829$	2.02955	+	6.24632i	0.0704893	+	0.216944i	0.980095	−	0.198529i	$-0.0636163\pi$
$829$	2.02955	+	6.24632i	0.0704893	+	0.216944i	−0.909606	+	0.415472i	$0.863616\pi$
$830$	1.24553	−	0.904933i	0.0432331	−	0.0314107i
$831$	−8.89196	+	6.46039i	−0.308459	+	0.224108i
$832$	0.0409881	+	0.126148i	0.00142101	+	0.00437340i
$833$	1.50543	−	4.63323i	0.0521600	−	0.160532i
$834$	−1.30907	−	0.951093i	−0.0453293	−	0.0329337i
$835$	−0.990719			−0.0342852
$836$	4.86978	+	7.49709i	0.168425	+	0.259292i
$837$	−43.5125			−1.50401
$838$	16.1454	+	11.7303i	0.557733	+	0.405217i
$839$	−10.1446	+	31.2220i	−0.350232	+	1.07790i	0.608491	+	0.793560i	$0.291775\pi$
$839$	−10.1446	+	31.2220i	−0.350232	+	1.07790i	−0.958723	+	0.284342i	$0.908225\pi$
$840$	−0.0474860	−	0.146147i	−0.00163842	−	0.00504255i
$841$	17.8692	−	12.9827i	0.616179	−	0.447681i
$842$	3.37515	−	2.45219i	0.116315	−	0.0845081i
$843$	−2.16427	−	6.66095i	−0.0745416	−	0.229415i
$844$	−3.60495	+	11.0949i	−0.124087	+	0.381902i
$845$	−1.26356	−	0.918029i	−0.0434677	−	0.0315812i
$846$	−16.9870			−0.584025
$847$	−15.9601	−	1.67409i	−0.548396	−	0.0575225i
$848$	−10.4897			−0.360218
$849$	18.8360	+	13.6851i	0.646449	+	0.469673i
$850$	1.54061	−	4.74152i	0.0528426	−	0.162633i
$851$	22.1905	+	68.2954i	0.760681	+	2.34114i
$852$	−7.82511	+	5.68528i	−0.268084	+	0.194774i
$853$	13.9292	−	10.1201i	0.476926	−	0.346507i	−0.323208	−	0.946328i	$-0.604762\pi$
$853$	13.9292	−	10.1201i	0.476926	−	0.346507i	0.800134	+	0.599821i	$0.204762\pi$
$854$	6.24294	+	19.2138i	0.213629	+	0.657482i
$855$	0.223804	−	0.688798i	0.00765394	−	0.0235564i
$856$	−16.0845	−	11.6861i	−0.549757	−	0.399422i
$857$	3.96083			0.135300			0.0676498	−	0.997709i	$-0.478450\pi$
$857$	3.96083			0.135300			0.0676498	+	0.997709i	$0.478450\pi$
$858$	0.209812	+	0.323009i	0.00716288	+	0.0110273i
$859$	−11.6086			−0.396079			−0.198040	−	0.980194i	$-0.563457\pi$
$859$	−11.6086			−0.396079			−0.198040	+	0.980194i	$0.563457\pi$
$860$	−0.148075	−	0.107583i	−0.00504931	−	0.00366854i
$861$	3.66101	−	11.2674i	0.124767	−	0.383993i
$862$	0.961530	+	2.95928i	0.0327498	+	0.100794i
$863$	−16.0178	+	11.6376i	−0.545253	+	0.396150i	−0.826032	−	0.563623i	$-0.809407\pi$
$863$	−16.0178	+	11.6376i	−0.545253	+	0.396150i	0.280779	+	0.959772i	$0.409407\pi$
$864$	3.70701	−	2.69330i	0.126115	−	0.0916279i
$865$	−0.151050	−	0.464884i	−0.00513585	−	0.0158065i
$866$	8.58966	−	26.4362i	0.291888	−	0.898340i
$867$	−0.708335	−	0.514635i	−0.0240563	−	0.0174779i
$868$	13.8538			0.470227
$869$	0.823521	−	15.7453i	0.0279361	−	0.534124i
$870$	0.276936			0.00938902
$871$	0.553150	+	0.401887i	0.0187428	+	0.0136174i
$872$	−5.74316	+	17.6756i	−0.194488	+	0.598572i
$873$	5.17939	+	15.9405i	0.175296	+	0.539505i
$874$	−16.6672	+	12.1094i	−0.563776	+	0.409607i
$875$	−1.41785	+	1.03013i	−0.0479321	+	0.0348247i
$876$	0.377922	+	1.16312i	0.0127688	+	0.0392983i
$877$	9.98466	−	30.7296i	0.337158	−	1.03767i	−0.628491	−	0.777817i	$-0.716327\pi$
$877$	9.98466	−	30.7296i	0.337158	−	1.03767i	0.965649	−	0.259849i	$-0.0836729\pi$
$878$	−13.7760	−	10.0088i	−0.464917	−	0.337782i
$879$	26.3924			0.890193
$880$	−0.385399	+	0.103311i	−0.0129918	+	0.00348260i
$881$	58.1195			1.95810			0.979048	−	0.203631i	$-0.0652743\pi$
$881$	58.1195			1.95810			0.979048	+	0.203631i	$0.0652743\pi$
$882$	−8.80246	−	6.39536i	−0.296394	−	0.215343i
$883$	−6.48904	+	19.9712i	−0.218374	+	0.672085i	0.780523	+	0.625127i	$0.214953\pi$
$883$	−6.48904	+	19.9712i	−0.218374	+	0.672085i	−0.998897	+	0.0469582i	$0.985047\pi$
$884$	−0.0409881	−	0.126148i	−0.00137858	−	0.00424283i
$885$	0.0552840	−	0.0401662i	0.00185835	−	0.00135017i
$886$	−18.5213	+	13.4565i	−0.622234	+	0.452079i
$887$	−1.68504	−	5.18601i	−0.0565780	−	0.174129i	0.918774	−	0.394784i	$-0.129181\pi$
$887$	−1.68504	−	5.18601i	−0.0565780	−	0.174129i	−0.975352	+	0.220655i	$0.929181\pi$
$888$	2.54202	−	7.82352i	0.0853045	−	0.262540i
$889$	−10.3168	−	7.49560i	−0.346015	−	0.251395i
$890$	0.470859			0.0157832
$891$	−5.61048	+	6.92985i	−0.187958	+	0.232159i
$892$	4.25903			0.142603
$893$	−16.5859	−	12.0504i	−0.555027	−	0.403251i
$894$	0.772609	−	2.37785i	0.0258399	−	0.0795271i
$895$	−0.264902	−	0.815284i	−0.00885469	−	0.0272519i
$896$	−1.18026	+	0.857508i	−0.0394297	+	0.0286473i
$897$	−0.718099	+	0.521729i	−0.0239766	+	0.0174200i
$898$	−3.12220	−	9.60914i	−0.104189	−	0.320661i
$899$	−7.71519	+	23.7449i	−0.257316	+	0.791937i
$900$	−9.00819	−	6.54483i	−0.300273	−	0.218161i
$901$	10.4897			0.349463
$902$	−28.7199	−	11.0211i	−0.956269	−	0.366962i
$903$	−1.94331			−0.0646692
$904$	14.8429	+	10.7840i	0.493668	+	0.358671i
$905$	−0.272859	+	0.839774i	−0.00907015	+	0.0279150i
$906$	5.21578	+	16.0525i	0.173283	+	0.533309i
$907$	−36.3901	+	26.4389i	−1.20831	+	0.877890i	−0.995076	−	0.0991107i	$-0.968400\pi$
$907$	−36.3901	+	26.4389i	−1.20831	+	0.877890i	−0.213236	+	0.977001i	$0.568400\pi$
$908$	15.9683	−	11.6017i	0.529927	−	0.385015i
$909$	0.416097	+	1.28062i	0.0138011	+	0.0424753i
$910$	−0.00719382	+	0.0221403i	−0.000238473	+	0.000733944i
$911$	−5.97174	−	4.33872i	−0.197853	−	0.143748i	0.484448	−	0.874820i	$-0.339020\pi$
$911$	−5.97174	−	4.33872i	−0.197853	−	0.143748i	−0.682301	+	0.731072i	$0.739020\pi$
$912$	2.36002			0.0781480
$913$	−39.6260	−	15.2062i	−1.31143	−	0.503253i
$914$	−41.7070			−1.37954
$915$	1.18007	+	0.857372i	0.0390119	+	0.0283438i
$916$	0.177226	−	0.545445i	0.00585570	−	0.0180220i
$917$	1.30781	+	4.02502i	0.0431876	+	0.132918i
$918$	−3.70701	+	2.69330i	−0.122350	+	0.0888921i
$919$	−17.4934	+	12.7097i	−0.577053	+	0.419254i	−0.837661	−	0.546191i	$-0.816077\pi$
$919$	−17.4934	+	12.7097i	−0.577053	+	0.419254i	0.260607	+	0.965445i	$0.416077\pi$
$920$	−0.284142	−	0.874499i	−0.00936788	−	0.0288314i
$921$	4.10202	−	12.6247i	0.135166	−	0.415999i
$922$	9.71990	+	7.06192i	0.320108	+	0.232572i
$923$	1.46530			0.0482310
$924$	−2.66571	+	3.29258i	−0.0876954	+	0.108318i
$925$	−46.8410			−1.54012
$926$	15.4202	+	11.2034i	0.506739	+	0.368168i
$927$	11.2166	−	34.5212i	0.368403	−	1.13383i
$928$	−0.812453	−	2.50047i	−0.0266701	−	0.0820821i
$929$	0.815623	−	0.592584i	0.0267597	−	0.0194421i	−0.574325	−	0.818627i	$-0.694735\pi$
$929$	0.815623	−	0.592584i	0.0267597	−	0.0194421i	0.601085	+	0.799185i	$0.294735\pi$
$930$	0.809225	−	0.587937i	0.0265355	−	0.0192792i
$931$	−4.05783	−	12.4887i	−0.132990	−	0.409302i
$932$	−3.26389	+	10.0452i	−0.106912	+	0.329042i
$933$	1.40851	+	1.02334i	0.0461125	+	0.0335027i
$934$	−4.92280			−0.161079
$935$	0.385399	−	0.103311i	0.0126039	−	0.00337862i
$936$	−0.296240			−0.00968291
$937$	49.0182	+	35.6138i	1.60135	+	1.16345i	0.884858	+	0.465862i	$0.154256\pi$
$937$	49.0182	+	35.6138i	1.60135	+	1.16345i	0.716497	+	0.697590i	$0.245744\pi$
$938$	−2.32387	+	7.15214i	−0.0758771	+	0.233526i
$939$	5.45191	+	16.7793i	0.177916	+	0.547570i
$940$	0.740266	−	0.537835i	0.0241448	−	0.0175422i
$941$	17.3359	−	12.5953i	0.565134	−	0.410594i	−0.268200	−	0.963363i	$-0.586429\pi$
$941$	17.3359	−	12.5953i	0.565134	−	0.410594i	0.833334	+	0.552769i	$0.186429\pi$
$942$	1.45083	+	4.46520i	0.0472707	+	0.145484i
$943$	21.9064	−	67.4209i	0.713370	−	2.19553i
$944$	−0.524851	−	0.381326i	−0.0170824	−	0.0124111i
$945$	0.804208			0.0261609
$946$	−0.263553	+	5.03900i	−0.00856884	+	0.163832i
$947$	23.8595			0.775330			0.387665	−	0.921800i	$-0.373282\pi$
$947$	23.8595			0.775330			0.387665	+	0.921800i	$0.373282\pi$
$948$	−3.36734	−	2.44652i	−0.109366	−	0.0794592i
$949$	0.0572528	−	0.176206i	0.00185850	−	0.00571988i
$950$	−4.15267	−	12.7806i	−0.134730	−	0.414658i
$951$	−11.5065	+	8.35998i	−0.373125	+	0.271091i
$952$	1.18026	−	0.857508i	0.0382524	−	0.0277920i
$953$	4.38759	+	13.5036i	0.142128	+	0.437425i	0.996630	−	0.0820225i	$-0.0261379\pi$
$953$	4.38759	+	13.5036i	0.142128	+	0.437425i	−0.854503	+	0.519447i	$0.826138\pi$
$954$	7.23961	−	22.2812i	0.234391	−	0.721381i
$955$	−0.783400	−	0.569173i	−0.0253502	−	0.0184180i
$956$	19.5572			0.632524
$957$	−4.15884	−	6.40258i	−0.134436	−	0.206966i
$958$	31.8201			1.02806
$959$	23.2114	+	16.8641i	0.749536	+	0.544569i
$960$	−0.0325496	+	0.100177i	−0.00105053	+	0.00323321i
$961$	18.2867	+	56.2808i	0.589895	+	1.81551i
$962$	−1.00820	+	0.732502i	−0.0325057	+	0.0236168i
$963$	35.9233	−	26.0998i	1.15761	−	0.841054i
$964$	−6.21000	−	19.1124i	−0.200011	−	0.615569i
$965$	0.440623	−	1.35610i	0.0141842	−	0.0436544i
$966$	−7.89821	−	5.73839i	−0.254121	−	0.184630i
$967$	17.7926			0.572170			0.286085	−	0.958204i	$-0.407646\pi$
$967$	17.7926			0.572170			0.286085	+	0.958204i	$0.407646\pi$
$968$	8.17614	+	7.35872i	0.262791	+	0.236518i
$969$	−2.36002			−0.0758147
$970$	−0.730412	−	0.530675i	−0.0234521	−	0.0170390i
$971$	18.1375	−	55.8216i	0.582061	−	1.79140i	−0.0287038	−	0.999588i	$-0.509138\pi$
$971$	18.1375	−	55.8216i	0.582061	−	1.79140i	0.610765	−	0.791812i	$-0.290862\pi$
$972$	4.97522	+	15.3121i	0.159580	+	0.491137i
$973$	−2.18123	+	1.58475i	−0.0699269	+	0.0508048i
$974$	−13.3271	+	9.68268i	−0.427027	+	0.310253i
$975$	−0.178916	−	0.550647i	−0.00572990	−	0.0176348i
$976$	4.27927	−	13.1702i	0.136976	−	0.421569i
$977$	−23.8540	−	17.3309i	−0.763157	−	0.554466i	0.136720	−	0.990610i	$-0.456344\pi$
$977$	−23.8540	−	17.3309i	−0.763157	−	0.554466i	−0.899877	+	0.436144i	$0.856344\pi$
$978$	−7.14193			−0.228374
$979$	−7.07105	−	10.8860i	−0.225992	−	0.347917i
$980$	0.586085			0.0187218
$981$	−33.5811	−	24.3981i	−1.07216	−	0.778971i
$982$	10.8968	−	33.5370i	0.347732	−	1.07021i
$983$	−18.2887	−	56.2869i	−0.583320	−	1.79527i	−0.605914	−	0.795530i	$-0.707193\pi$
$983$	−18.2887	−	56.2869i	−0.583320	−	1.79527i	0.0225942	−	0.999745i	$-0.492807\pi$
$984$	−6.56987	+	4.77329i	−0.209440	+	0.152167i
$985$	−0.823830	+	0.598547i	−0.0262494	+	0.0190713i
$986$	0.812453	+	2.50047i	0.0258738	+	0.0796313i
$987$	3.00214	−	9.23963i	0.0955591	−	0.294101i
$988$	−0.289246	−	0.210149i	−0.00920213	−	0.00668574i
$989$	−11.6282			−0.369754
$990$	0.0465455	−	0.889927i	0.00147931	−	0.0282837i
$991$	−17.2675			−0.548519			−0.274260	−	0.961656i	$-0.588433\pi$
$991$	−17.2675			−0.548519			−0.274260	+	0.961656i	$0.588433\pi$
$992$	−7.68256	−	5.58170i	−0.243921	−	0.177219i
$993$	−4.33286	+	13.3352i	−0.137499	+	0.423179i
$994$	4.98028	+	15.3277i	0.157965	+	0.486166i
$995$	−0.308756	+	0.224324i	−0.00978822	+	0.00711155i
$996$	−9.06471	+	6.58589i	−0.287226	+	0.208682i
$997$	13.6603	+	42.0421i	0.432626	+	1.33149i	0.895500	+	0.445062i	$0.146818\pi$
$997$	13.6603	+	42.0421i	0.432626	+	1.33149i	−0.462874	+	0.886424i	$0.653182\pi$
$998$	−9.87250	+	30.3844i	−0.312509	+	0.961803i
$999$	34.8288	+	25.3046i	1.10193	+	0.800602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.f.103.3	yes	16
11.3	even	5	inner	374.2.g.f.69.3	✓	16
11.5	even	5		4114.2.a.bi.1.6		8
11.6	odd	10		4114.2.a.bg.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.f.69.3	✓	16	11.3	even	5	inner
374.2.g.f.103.3	yes	16	1.1	even	1	trivial
4114.2.a.bg.1.6		8	11.6	odd	10
4114.2.a.bi.1.6		8	11.5	even	5

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:	\( N \)	\(=\)	\( 374 = 2 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	374.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.270560 - 0.832698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0973285 - 0.0707133i) q^{5} +(-0.708335 + 0.514635i) q^{6} +(0.450819 + 1.38748i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.80687 + 1.31277i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.270560 - 0.832698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0973285 - 0.0707133i) q^{5} +(-0.708335 + 0.514635i) q^{6} +(0.450819 + 1.38748i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.80687 + 1.31277i) q^{9} -0.120305 q^{10} +(1.80666 + 2.78137i) q^{11} +0.875550 q^{12} +(-0.107308 - 0.0779639i) q^{13} +(0.450819 - 1.38748i) q^{14} +(-0.0325496 - 0.100177i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.809017 - 0.587785i) q^{17} +(-0.690162 - 2.12410i) q^{18} +(0.832946 - 2.56354i) q^{19} +(0.0973285 + 0.0707133i) q^{20} +1.27732 q^{21} +(0.173231 - 3.31210i) q^{22} +7.64311 q^{23} +(-0.708335 - 0.514635i) q^{24} +(-1.54061 + 4.74152i) q^{25} +(0.0409881 + 0.126148i) q^{26} +(3.70701 - 2.69330i) q^{27} +(-1.18026 + 0.857508i) q^{28} +(-0.812453 - 2.50047i) q^{29} +(-0.0325496 + 0.100177i) q^{30} +(-7.68256 - 5.58170i) q^{31} +1.00000 q^{32} +(2.80485 - 0.751871i) q^{33} -1.00000 q^{34} +(0.141991 + 0.103162i) q^{35} +(-0.690162 + 2.12410i) q^{36} +(2.90334 + 8.93555i) q^{37} +(-2.18068 + 1.58436i) q^{38} +(-0.0939537 + 0.0682613i) q^{39} +(-0.0371762 - 0.114417i) q^{40} +(2.86616 - 8.82113i) q^{41} +(-1.03338 - 0.750792i) q^{42} -1.52139 q^{43} +(-2.08695 + 2.57772i) q^{44} +0.268690 q^{45} +(-6.18341 - 4.49251i) q^{46} +(2.35034 - 7.23359i) q^{47} +(0.270560 + 0.832698i) q^{48} +(3.94126 - 2.86349i) q^{49} +(4.03338 - 2.93042i) q^{50} +(-0.270560 - 0.832698i) q^{51} +(0.0409881 - 0.126148i) q^{52} +(8.48636 + 6.16570i) q^{53} -4.58211 q^{54} +(0.372519 + 0.142952i) q^{55} +1.45888 q^{56} +(-1.90929 - 1.38718i) q^{57} +(-0.812453 + 2.50047i) q^{58} +(0.200475 + 0.616999i) q^{59} +(0.0852160 - 0.0619131i) q^{60} +(-11.2033 + 8.13965i) q^{61} +(2.93448 + 9.03139i) q^{62} +(-1.00686 + 3.09881i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.0159572 q^{65} +(-2.71111 - 1.04037i) q^{66} -5.15478 q^{67} +(0.809017 + 0.587785i) q^{68} +(2.06792 - 6.36440i) q^{69} +(-0.0542356 - 0.166920i) q^{70} +(-8.93737 + 6.49338i) q^{71} +(1.80687 - 1.31277i) q^{72} +(0.431640 + 1.32845i) q^{73} +(2.90334 - 8.93555i) q^{74} +(3.53142 + 2.56573i) q^{75} +2.69547 q^{76} +(-3.04461 + 3.76059i) q^{77} +0.116133 q^{78} +(-3.84597 - 2.79426i) q^{79} +(-0.0371762 + 0.114417i) q^{80} +(0.830750 + 2.55679i) q^{81} +(-7.50370 + 5.45176i) q^{82} +(-10.3532 + 7.52201i) q^{83} +(0.394714 + 1.21481i) q^{84} +(0.0371762 - 0.114417i) q^{85} +(1.23083 + 0.894251i) q^{86} -2.30196 q^{87} +(3.20352 - 0.858742i) q^{88} -3.91389 q^{89} +(-0.217375 - 0.157932i) q^{90} +(0.0597967 - 0.184035i) q^{91} +(2.36185 + 7.26903i) q^{92} +(-6.72646 + 4.88706i) q^{93} +(-6.15326 + 4.47061i) q^{94} +(-0.100207 - 0.308406i) q^{95} +(0.270560 - 0.832698i) q^{96} +(6.07135 + 4.41109i) q^{97} -4.87167 q^{98} +(-0.386897 + 7.39728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} - q^{5} + 2 q^{7} - 4 q^{8} - 13 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 - q^5 + 2 * q^7 - 4 * q^8 - 13 * q^9	\( 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} - q^{5} + 2 q^{7} - 4 q^{8} - 13 q^{9} + 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{13} + 2 q^{14} - 6 q^{15} - 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} - q^{20} + 6 q^{22} - 24 q^{23} - 37 q^{25} + 15 q^{26} - 4 q^{27} - 13 q^{28} - 16 q^{29} - 6 q^{30} + 11 q^{31} + 16 q^{32} + 36 q^{33} - 16 q^{34} + 2 q^{36} + 5 q^{37} - 25 q^{38} - 30 q^{39} - q^{40} + 4 q^{41} + 35 q^{42} + 16 q^{43} + 6 q^{44} + 6 q^{45} - 14 q^{46} - 14 q^{47} + 5 q^{48} + 2 q^{49} + 13 q^{50} - 5 q^{51} + 15 q^{52} + 5 q^{53} - 34 q^{54} + 81 q^{55} + 22 q^{56} - 12 q^{57} - 16 q^{58} + 17 q^{59} + 4 q^{60} - 30 q^{61} - 4 q^{62} + 72 q^{63} - 4 q^{64} + 6 q^{65} + 11 q^{66} + 26 q^{67} + 4 q^{68} - 73 q^{69} - 10 q^{70} - q^{71} - 13 q^{72} - 43 q^{73} + 5 q^{74} + 67 q^{75} + 30 q^{76} + 40 q^{77} + 70 q^{78} - 13 q^{79} - q^{80} - 39 q^{81} - 21 q^{82} - 24 q^{83} - 35 q^{84} + q^{85} + 26 q^{86} - 92 q^{87} - 4 q^{88} + 24 q^{89} - 29 q^{90} - 10 q^{91} + 26 q^{92} + 11 q^{93} - 4 q^{94} - 39 q^{95} + 5 q^{96} + 3 q^{97} + 2 q^{98} + 65 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 - q^5 + 2 * q^7 - 4 * q^8 - 13 * q^9 + 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^13 + 2 * q^14 - 6 * q^15 - 4 * q^16 + 4 * q^17 + 2 * q^18 + 10 * q^19 - q^20 + 6 * q^22 - 24 * q^23 - 37 * q^25 + 15 * q^26 - 4 * q^27 - 13 * q^28 - 16 * q^29 - 6 * q^30 + 11 * q^31 + 16 * q^32 + 36 * q^33 - 16 * q^34 + 2 * q^36 + 5 * q^37 - 25 * q^38 - 30 * q^39 - q^40 + 4 * q^41 + 35 * q^42 + 16 * q^43 + 6 * q^44 + 6 * q^45 - 14 * q^46 - 14 * q^47 + 5 * q^48 + 2 * q^49 + 13 * q^50 - 5 * q^51 + 15 * q^52 + 5 * q^53 - 34 * q^54 + 81 * q^55 + 22 * q^56 - 12 * q^57 - 16 * q^58 + 17 * q^59 + 4 * q^60 - 30 * q^61 - 4 * q^62 + 72 * q^63 - 4 * q^64 + 6 * q^65 + 11 * q^66 + 26 * q^67 + 4 * q^68 - 73 * q^69 - 10 * q^70 - q^71 - 13 * q^72 - 43 * q^73 + 5 * q^74 + 67 * q^75 + 30 * q^76 + 40 * q^77 + 70 * q^78 - 13 * q^79 - q^80 - 39 * q^81 - 21 * q^82 - 24 * q^83 - 35 * q^84 + q^85 + 26 * q^86 - 92 * q^87 - 4 * q^88 + 24 * q^89 - 29 * q^90 - 10 * q^91 + 26 * q^92 + 11 * q^93 - 4 * q^94 - 39 * q^95 + 5 * q^96 + 3 * q^97 + 2 * q^98 + 65 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more