LMFDB - Embedded newform 29.2.d.a.20.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,2,Mod(7,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("29.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	29.d (of order $7$, degree $6$, 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:	$0.231566165862$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			20.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	29.20
Dual form			29.2.d.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.400969 - 0.193096i) q^{2} +(-0.777479 - 0.974928i) q^{3} +(-1.12349 + 1.40881i) q^{4} +(-0.623490 + 0.300257i) q^{5} +(-0.500000 - 0.240787i) q^{6} +(0.222521 + 0.279032i) q^{7} +(-0.376510 + 1.64960i) q^{8} +(0.321552 - 1.40881i) q^{9} +O(q^{10})$	\(q+(0.400969 - 0.193096i) q^{2} +(-0.777479 - 0.974928i) q^{3} +(-1.12349 + 1.40881i) q^{4} +(-0.623490 + 0.300257i) q^{5} +(-0.500000 - 0.240787i) q^{6} +(0.222521 + 0.279032i) q^{7} +(-0.376510 + 1.64960i) q^{8} +(0.321552 - 1.40881i) q^{9} +(-0.192021 + 0.240787i) q^{10} +(-1.09903 - 4.81517i) q^{11} +2.24698 q^{12} +(1.25786 + 5.51107i) q^{13} +(0.143104 + 0.0689153i) q^{14} +(0.777479 + 0.374414i) q^{15} +(-0.634375 - 2.77938i) q^{16} +4.49396 q^{17} +(-0.143104 - 0.626980i) q^{18} +(-1.46950 + 1.84270i) q^{19} +(0.277479 - 1.21572i) q^{20} +(0.0990311 - 0.433884i) q^{21} +(-1.37047 - 1.71851i) q^{22} +(-2.06853 - 0.996152i) q^{23} +(1.90097 - 0.915458i) q^{24} +(-2.81886 + 3.53474i) q^{25} +(1.56853 + 1.96688i) q^{26} +(-4.99396 + 2.40496i) q^{27} -0.643104 q^{28} +(-5.09783 + 1.73553i) q^{29} +0.384043 q^{30} +(6.02930 - 2.90356i) q^{31} +(-2.90097 - 3.63770i) q^{32} +(-3.83997 + 4.81517i) q^{33} +(1.80194 - 0.867767i) q^{34} +(-0.222521 - 0.107160i) q^{35} +(1.62349 + 2.03579i) q^{36} +(1.09903 - 4.81517i) q^{37} +(-0.233406 + 1.02262i) q^{38} +(4.39493 - 5.51107i) q^{39} +(-0.260553 - 1.14156i) q^{40} +3.10992 q^{41} +(-0.0440730 - 0.193096i) q^{42} +(3.06853 + 1.47773i) q^{43} +(8.01842 + 3.86147i) q^{44} +(0.222521 + 0.974928i) q^{45} -1.02177 q^{46} +(1.43416 + 6.28345i) q^{47} +(-2.21648 + 2.77938i) q^{48} +(1.52930 - 6.70031i) q^{49} +(-0.447730 + 1.96163i) q^{50} +(-3.49396 - 4.38129i) q^{51} +(-9.17725 - 4.41953i) q^{52} +(4.22737 - 2.03579i) q^{53} +(-1.53803 + 1.92863i) q^{54} +(2.13102 + 2.67222i) q^{55} +(-0.544073 + 0.262012i) q^{56} +2.93900 q^{57} +(-1.70895 + 1.68027i) q^{58} -12.4940 q^{59} +(-1.40097 + 0.674671i) q^{60} +(-1.02446 - 1.28463i) q^{61} +(1.85690 - 2.32847i) q^{62} +(0.464656 - 0.223767i) q^{63} +(3.27144 + 1.57544i) q^{64} +(-2.43900 - 3.05841i) q^{65} +(-0.609916 + 2.67222i) q^{66} +(0.516926 - 2.26480i) q^{67} +(-5.04892 + 6.33114i) q^{68} +(0.637063 + 2.79116i) q^{69} -0.109916 q^{70} +(1.63222 + 7.15122i) q^{71} +(2.20291 + 1.06086i) q^{72} +(-5.06853 - 2.44088i) q^{73} +(-0.489115 - 2.14295i) q^{74} +5.63773 q^{75} +(-0.945042 - 4.14050i) q^{76} +(1.09903 - 1.37814i) q^{77} +(0.698062 - 3.05841i) q^{78} +(1.03803 - 4.54792i) q^{79} +(1.23005 + 1.54244i) q^{80} +(2.32155 + 1.11800i) q^{81} +(1.24698 - 0.600514i) q^{82} +(2.77748 - 3.48285i) q^{83} +(0.500000 + 0.626980i) q^{84} +(-2.80194 + 1.34934i) q^{85} +1.51573 q^{86} +(5.65548 + 3.62068i) q^{87} +8.35690 q^{88} +(5.11745 - 2.46443i) q^{89} +(0.277479 + 0.347948i) q^{90} +(-1.25786 + 1.57731i) q^{91} +(3.72737 - 1.79500i) q^{92} +(-7.51842 - 3.62068i) q^{93} +(1.78836 + 2.24254i) q^{94} +(0.362937 - 1.59013i) q^{95} +(-1.29105 + 5.65647i) q^{96} +(-0.112605 + 0.141202i) q^{97} +(-0.680604 - 2.98192i) q^{98} -7.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + q^5 - 3 * q^6 + q^7 - 7 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9} + 9 q^{10} - 11 q^{11} + 4 q^{12} - 5 q^{13} + 9 q^{14} + 5 q^{15} + 4 q^{16} + 8 q^{17} - 9 q^{18} + q^{19} + 2 q^{20} + 5 q^{21} + 6 q^{22} - 7 q^{23} + 7 q^{24} - 24 q^{25} + 4 q^{26} - 11 q^{27} - 12 q^{28} + 6 q^{29} - 18 q^{30} + 5 q^{31} - 13 q^{32} + q^{33} + 2 q^{34} - q^{35} + 5 q^{36} + 11 q^{37} + 2 q^{38} + 3 q^{39} + 14 q^{40} + 20 q^{41} - 4 q^{42} + 13 q^{43} + 20 q^{44} + q^{45} + 11 q^{47} + 6 q^{48} - 22 q^{49} + q^{50} - 2 q^{51} - 10 q^{52} + 3 q^{53} + 6 q^{54} - 17 q^{55} - 7 q^{56} - 2 q^{57} - 16 q^{58} - 56 q^{59} - 4 q^{60} + 3 q^{61} + 3 q^{62} + 15 q^{63} + q^{64} + 5 q^{65} - 5 q^{66} + 19 q^{67} - 12 q^{68} - 7 q^{69} - 2 q^{70} + 21 q^{71} - 25 q^{73} - 6 q^{74} + 48 q^{75} - 5 q^{76} + 11 q^{77} + 13 q^{78} - 9 q^{79} - 18 q^{80} + 18 q^{81} - 2 q^{82} + 17 q^{83} + 3 q^{84} - 8 q^{85} - 16 q^{86} - 5 q^{87} + 42 q^{88} + 7 q^{89} + 2 q^{90} + 5 q^{91} - 17 q^{93} + 8 q^{94} + 13 q^{95} - 2 q^{96} + q^{97} + 19 q^{98} - 32 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + q^5 - 3 * q^6 + q^7 - 7 * q^8 + 6 * q^9 + 9 * q^10 - 11 * q^11 + 4 * q^12 - 5 * q^13 + 9 * q^14 + 5 * q^15 + 4 * q^16 + 8 * q^17 - 9 * q^18 + q^19 + 2 * q^20 + 5 * q^21 + 6 * q^22 - 7 * q^23 + 7 * q^24 - 24 * q^25 + 4 * q^26 - 11 * q^27 - 12 * q^28 + 6 * q^29 - 18 * q^30 + 5 * q^31 - 13 * q^32 + q^33 + 2 * q^34 - q^35 + 5 * q^36 + 11 * q^37 + 2 * q^38 + 3 * q^39 + 14 * q^40 + 20 * q^41 - 4 * q^42 + 13 * q^43 + 20 * q^44 + q^45 + 11 * q^47 + 6 * q^48 - 22 * q^49 + q^50 - 2 * q^51 - 10 * q^52 + 3 * q^53 + 6 * q^54 - 17 * q^55 - 7 * q^56 - 2 * q^57 - 16 * q^58 - 56 * q^59 - 4 * q^60 + 3 * q^61 + 3 * q^62 + 15 * q^63 + q^64 + 5 * q^65 - 5 * q^66 + 19 * q^67 - 12 * q^68 - 7 * q^69 - 2 * q^70 + 21 * q^71 - 25 * q^73 - 6 * q^74 + 48 * q^75 - 5 * q^76 + 11 * q^77 + 13 * q^78 - 9 * q^79 - 18 * q^80 + 18 * q^81 - 2 * q^82 + 17 * q^83 + 3 * q^84 - 8 * q^85 - 16 * q^86 - 5 * q^87 + 42 * q^88 + 7 * q^89 + 2 * q^90 + 5 * q^91 - 17 * q^93 + 8 * q^94 + 13 * q^95 - 2 * q^96 + q^97 + 19 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	0.400969	−	0.193096i	0.283528	−	0.136540i	−0.286715	−	0.958016i	$-0.592563\pi$
$2$	0.400969	−	0.193096i	0.283528	−	0.136540i	0.570243	+	0.821476i	$0.306849\pi$
$3$	−0.777479	−	0.974928i	−0.448878	−	0.562875i	0.504981	−	0.863130i	$-0.331499\pi$
$3$	−0.777479	−	0.974928i	−0.448878	−	0.562875i	−0.953859	+	0.300256i	$0.902928\pi$
$4$	−1.12349	+	1.40881i	−0.561745	+	0.704406i
$5$	−0.623490	+	0.300257i	−0.278833	+	0.134279i	−0.568074	−	0.822977i	$-0.692311\pi$
$5$	−0.623490	+	0.300257i	−0.278833	+	0.134279i	0.289241	+	0.957256i	$0.406597\pi$
$6$	−0.500000	−	0.240787i	−0.204124	−	0.0983010i
$7$	0.222521	+	0.279032i	0.0841050	+	0.105464i	0.822104	−	0.569338i	$-0.192800\pi$
$7$	0.222521	+	0.279032i	0.0841050	+	0.105464i	−0.737999	+	0.674802i	$0.764229\pi$
$8$	−0.376510	+	1.64960i	−0.133116	+	0.583221i
$9$	0.321552	−	1.40881i	0.107184	−	0.469604i
$10$	−0.192021	+	0.240787i	−0.0607225	+	0.0761436i
$11$	−1.09903	−	4.81517i	−0.331370	−	1.45183i	−0.816479	−	0.577375i	$-0.804077\pi$
$11$	−1.09903	−	4.81517i	−0.331370	−	1.45183i	0.485109	−	0.874454i	$-0.338780\pi$
$12$	2.24698			0.648647
$13$	1.25786	+	5.51107i	0.348869	+	1.52849i	0.779753	+	0.626087i	$0.215345\pi$
$13$	1.25786	+	5.51107i	0.348869	+	1.52849i	−0.430884	+	0.902407i	$0.641798\pi$
$14$	0.143104	+	0.0689153i	0.0382462	+	0.0184184i
$15$	0.777479	+	0.374414i	0.200744	+	0.0966733i
$16$	−0.634375	−	2.77938i	−0.158594	−	0.694845i
$17$	4.49396			1.08995			0.544973	−	0.838454i	$-0.316540\pi$
$17$	4.49396			1.08995			0.544973	+	0.838454i	$0.316540\pi$
$18$	−0.143104	−	0.626980i	−0.0337300	−	0.147781i
$19$	−1.46950	+	1.84270i	−0.337127	+	0.422743i	−0.921280	−	0.388900i	$-0.872855\pi$
$19$	−1.46950	+	1.84270i	−0.337127	+	0.422743i	0.584153	+	0.811643i	$0.301427\pi$
$20$	0.277479	−	1.21572i	0.0620462	−	0.271842i
$21$	0.0990311	−	0.433884i	0.0216104	−	0.0946812i
$22$	−1.37047	−	1.71851i	−0.292185	−	0.366388i
$23$	−2.06853	−	0.996152i	−0.431319	−	0.207712i	0.205611	−	0.978634i	$-0.434082\pi$
$23$	−2.06853	−	0.996152i	−0.431319	−	0.207712i	−0.636930	+	0.770922i	$0.719796\pi$
$24$	1.90097	−	0.915458i	0.388034	−	0.186867i
$25$	−2.81886	+	3.53474i	−0.563773	+	0.706949i
$26$	1.56853	+	1.96688i	0.307614	+	0.385736i
$27$	−4.99396	+	2.40496i	−0.961088	+	0.462836i
$28$	−0.643104			−0.121535
$29$	−5.09783	+	1.73553i	−0.946644	+	0.322281i
$29$	−5.09783	+	1.73553i	−0.946644	+	0.322281i
$30$	0.384043			0.0701163
$31$	6.02930	−	2.90356i	1.08289	−	0.521495i	0.194654	−	0.980872i	$-0.437642\pi$
$31$	6.02930	−	2.90356i	1.08289	−	0.521495i	0.888241	+	0.459377i	$0.151927\pi$
$32$	−2.90097	−	3.63770i	−0.512824	−	0.643061i
$33$	−3.83997	+	4.81517i	−0.668453	+	0.838214i
$34$	1.80194	−	0.867767i	0.309030	−	0.148821i
$35$	−0.222521	−	0.107160i	−0.0376129	−	0.0181134i
$36$	1.62349	+	2.03579i	0.270582	+	0.339299i
$37$	1.09903	−	4.81517i	0.180680	−	0.791609i	−0.800628	−	0.599162i	$-0.795501\pi$
$37$	1.09903	−	4.81517i	0.180680	−	0.791609i	0.981307	−	0.192447i	$-0.0616424\pi$
$38$	−0.233406	+	1.02262i	−0.0378635	+	0.165891i
$39$	4.39493	−	5.51107i	0.703752	−	0.882477i
$40$	−0.260553	−	1.14156i	−0.0411971	−	0.180496i
$41$	3.10992			0.485687			0.242844	−	0.970065i	$-0.421920\pi$
$41$	3.10992			0.485687			0.242844	+	0.970065i	$0.421920\pi$
$42$	−0.0440730	−	0.193096i	−0.00680061	−	0.0297954i
$43$	3.06853	+	1.47773i	0.467947	+	0.225351i	0.652971	−	0.757383i	$-0.273522\pi$
$43$	3.06853	+	1.47773i	0.467947	+	0.225351i	−0.185025	+	0.982734i	$0.559236\pi$
$44$	8.01842	+	3.86147i	1.20882	+	0.582138i
$45$	0.222521	+	0.974928i	0.0331715	+	0.145334i
$46$	−1.02177			−0.150652
$47$	1.43416	+	6.28345i	0.209193	+	0.916536i	0.965105	+	0.261862i	$0.0843366\pi$
$47$	1.43416	+	6.28345i	0.209193	+	0.916536i	−0.755912	+	0.654673i	$0.772806\pi$
$48$	−2.21648	+	2.77938i	−0.319921	+	0.401169i
$49$	1.52930	−	6.70031i	0.218472	−	0.957188i
$50$	−0.447730	+	1.96163i	−0.0633186	+	0.277417i
$51$	−3.49396	−	4.38129i	−0.489252	−	0.613503i
$52$	−9.17725	−	4.41953i	−1.27266	−	0.612879i
$53$	4.22737	−	2.03579i	0.580673	−	0.279638i	−0.120401	−	0.992725i	$-0.538418\pi$
$53$	4.22737	−	2.03579i	0.580673	−	0.279638i	0.701075	+	0.713088i	$0.252704\pi$
$54$	−1.53803	+	1.92863i	−0.209300	+	0.262453i
$55$	2.13102	+	2.67222i	0.287347	+	0.360322i
$56$	−0.544073	+	0.262012i	−0.0727048	+	0.0350128i
$57$	2.93900			0.389280
$58$	−1.70895	+	1.68027i	−0.224396	+	0.220630i
$59$	−12.4940			−1.62657			−0.813287	−	0.581862i	$-0.802324\pi$
$59$	−12.4940			−1.62657			−0.813287	+	0.581862i	$0.802324\pi$
$60$	−1.40097	+	0.674671i	−0.180864	+	0.0870997i
$61$	−1.02446	−	1.28463i	−0.131168	−	0.164480i	0.711910	−	0.702271i	$-0.247830\pi$
$61$	−1.02446	−	1.28463i	−0.131168	−	0.164480i	−0.843078	+	0.537791i	$0.819259\pi$
$62$	1.85690	−	2.32847i	0.235826	−	0.295716i
$63$	0.464656	−	0.223767i	0.0585412	−	0.0281919i
$64$	3.27144	+	1.57544i	0.408930	+	0.196930i
$65$	−2.43900	−	3.05841i	−0.302521	−	0.379349i
$66$	−0.609916	+	2.67222i	−0.0750755	+	0.328927i
$67$	0.516926	−	2.26480i	0.0631526	−	0.276689i	−0.933486	−	0.358614i	$-0.883249\pi$
$67$	0.516926	−	2.26480i	0.0631526	−	0.276689i	0.996639	+	0.0819245i	$0.0261066\pi$
$68$	−5.04892	+	6.33114i	−0.612271	+	0.767764i
$69$	0.637063	+	2.79116i	0.0766934	+	0.336016i
$70$	−0.109916			−0.0131375
$71$	1.63222	+	7.15122i	0.193709	+	0.848694i	0.974587	+	0.224010i	$0.0719148\pi$
$71$	1.63222	+	7.15122i	0.193709	+	0.848694i	−0.780878	+	0.624683i	$0.785228\pi$
$72$	2.20291	+	1.06086i	0.259615	+	0.125024i
$73$	−5.06853	−	2.44088i	−0.593227	−	0.285683i	0.113083	−	0.993586i	$-0.463927\pi$
$73$	−5.06853	−	2.44088i	−0.593227	−	0.285683i	−0.706310	+	0.707903i	$0.749642\pi$
$74$	−0.489115	−	2.14295i	−0.0568584	−	0.249113i
$75$	5.63773			0.650989
$76$	−0.945042	−	4.14050i	−0.108404	−	0.474948i
$77$	1.09903	−	1.37814i	0.125246	−	0.157054i
$78$	0.698062	−	3.05841i	0.0790400	−	0.346297i
$79$	1.03803	−	4.54792i	0.116788	−	0.511681i	−0.882367	−	0.470563i	$-0.844051\pi$
$79$	1.03803	−	4.54792i	0.116788	−	0.511681i	0.999154	−	0.0411178i	$-0.0130919\pi$
$80$	1.23005	+	1.54244i	0.137524	+	0.172450i
$81$	2.32155	+	1.11800i	0.257950	+	0.124222i
$82$	1.24698	−	0.600514i	0.137706	−	0.0663156i
$83$	2.77748	−	3.48285i	0.304868	−	0.382292i	−0.605671	−	0.795715i	$-0.707095\pi$
$83$	2.77748	−	3.48285i	0.304868	−	0.382292i	0.910539	+	0.413423i	$0.135667\pi$
$84$	0.500000	+	0.626980i	0.0545545	+	0.0684091i
$85$	−2.80194	+	1.34934i	−0.303913	+	0.146357i
$86$	1.51573			0.163445
$87$	5.65548	+	3.62068i	0.606331	+	0.388178i
$88$	8.35690			0.890848
$89$	5.11745	−	2.46443i	0.542449	−	0.261229i	−0.142533	−	0.989790i	$-0.545525\pi$
$89$	5.11745	−	2.46443i	0.542449	−	0.261229i	0.684981	+	0.728561i	$0.259810\pi$
$90$	0.277479	+	0.347948i	0.0292489	+	0.0366769i
$91$	−1.25786	+	1.57731i	−0.131860	+	0.165347i
$92$	3.72737	−	1.79500i	0.388605	−	0.187142i
$93$	−7.51842	−	3.62068i	−0.779624	−	0.375447i
$94$	1.78836	+	2.24254i	0.184456	+	0.231300i
$95$	0.362937	−	1.59013i	0.0372365	−	0.163144i
$96$	−1.29105	+	5.65647i	−0.131768	+	0.577311i
$97$	−0.112605	+	0.141202i	−0.0114333	+	0.0143369i	−0.787515	−	0.616295i	$-0.788633\pi$
$97$	−0.112605	+	0.141202i	−0.0114333	+	0.0143369i	0.776082	+	0.630632i	$0.217204\pi$
$98$	−0.680604	−	2.98192i	−0.0687514	−	0.301219i
$99$	−7.13706			−0.717302
$100$	−1.81282	−	7.94250i	−0.181282	−	0.794250i
$101$	−2.90970	−	1.40124i	−0.289526	−	0.139428i	0.283484	−	0.958977i	$-0.408510\pi$
$101$	−2.90970	−	1.40124i	−0.289526	−	0.139428i	−0.573009	+	0.819549i	$0.694224\pi$
$102$	−2.24698	−	1.08209i	−0.222484	−	0.107143i
$103$	3.03803	+	13.3105i	0.299346	+	1.31152i	0.871104	+	0.491099i	$0.163405\pi$
$103$	3.03803	+	13.3105i	0.299346	+	1.31152i	−0.571758	+	0.820423i	$0.693738\pi$
$104$	−9.56465			−0.937891
$105$	0.0685317	+	0.300257i	0.00668801	+	0.0293021i
$106$	1.30194	−	1.63258i	0.126455	−	0.158570i
$107$	−3.61476	+	15.8373i	−0.349452	+	1.53105i	0.428976	+	0.903316i	$0.358874\pi$
$107$	−3.61476	+	15.8373i	−0.349452	+	1.53105i	−0.778428	+	0.627734i	$0.783983\pi$
$108$	2.22252	−	9.73750i	0.213862	−	0.936991i
$109$	3.40850	+	4.27413i	0.326475	+	0.409387i	0.917798	−	0.397048i	$-0.129965\pi$
$109$	3.40850	+	4.27413i	0.326475	+	0.409387i	−0.591323	+	0.806435i	$0.701394\pi$
$110$	1.37047	+	0.659983i	0.130669	+	0.0629269i
$111$	−5.54892	+	2.67222i	−0.526680	+	0.253636i
$112$	0.634375	−	0.795481i	0.0599428	−	0.0751659i
$113$	−6.65548	−	8.34571i	−0.626095	−	0.785098i	0.363093	−	0.931753i	$-0.381721\pi$
$113$	−6.65548	−	8.34571i	−0.626095	−	0.785098i	−0.989188	+	0.146655i	$0.953149\pi$
$114$	1.17845	−	0.567511i	0.110372	−	0.0531522i
$115$	1.58881			0.148157
$116$	3.28232	−	9.13174i	0.304756	−	0.847861i
$117$	8.16852			0.755180
$118$	−5.00969	+	2.41254i	−0.461179	+	0.222092i
$119$	1.00000	+	1.25396i	0.0916698	+	0.114950i
$120$	−0.910362	+	1.14156i	−0.0831043	+	0.104210i
$121$	−12.0673	+	5.81132i	−1.09703	+	0.528302i
$122$	−0.658834	−	0.317278i	−0.0596480	−	0.0287250i
$123$	−2.41789	−	3.03194i	−0.218014	−	0.273381i
$124$	−2.68329	+	11.7563i	−0.240967	+	1.05574i
$125$	1.46615	−	6.42361i	0.131136	−	0.574546i
$126$	0.143104	−	0.179447i	0.0127487	−	0.0159864i
$127$	0.230718	+	1.01084i	0.0204729	+	0.0896976i	0.984132	−	0.177437i	$-0.0567805\pi$
$127$	0.230718	+	1.01084i	0.0204729	+	0.0896976i	−0.963659	+	0.267134i	$0.913923\pi$
$128$	10.9215			0.965337
$129$	−0.945042	−	4.14050i	−0.0832063	−	0.364551i
$130$	−1.56853	−	0.755365i	−0.137569	−	0.0662499i
$131$	−7.22737	−	3.48052i	−0.631458	−	0.304094i	0.0906414	−	0.995884i	$-0.471108\pi$
$131$	−7.22737	−	3.48052i	−0.631458	−	0.304094i	−0.722099	+	0.691790i	$0.756823\pi$
$132$	−2.46950	−	10.8196i	−0.214942	−	0.941724i
$133$	−0.841166			−0.0729384
$134$	−0.230054	−	1.00793i	−0.0198736	−	0.0870720i
$135$	2.39158	−	2.99894i	0.205834	−	0.258108i
$136$	−1.69202	+	7.41323i	−0.145090	+	0.635679i
$137$	−3.83459	+	16.8005i	−0.327611	+	1.43536i	0.496058	+	0.868289i	$0.334780\pi$
$137$	−3.83459	+	16.8005i	−0.327611	+	1.43536i	−0.823670	+	0.567070i	$0.808077\pi$
$138$	0.794405	+	0.996152i	0.0676242	+	0.0847981i
$139$	15.0172	+	7.23191i	1.27374	+	0.613403i	0.943775	−	0.330589i	$-0.107247\pi$
$139$	15.0172	+	7.23191i	1.27374	+	0.613403i	0.329969	+	0.943992i	$0.392962\pi$
$140$	0.400969	−	0.193096i	0.0338881	−	0.0163196i
$141$	5.01089	−	6.28345i	0.421993	−	0.529162i
$142$	2.03534	+	2.55224i	0.170802	+	0.214179i
$143$	25.1543	−	12.1137i	2.10351	−	1.01300i
$144$	−4.11960			−0.343300
$145$	2.65734	−	2.61275i	0.220680	−	0.216977i
$146$	−2.50365			−0.207203
$147$	−7.72132	+	3.71839i	−0.636844	+	0.306688i
$148$	5.54892	+	6.95812i	0.456118	+	0.571954i
$149$	11.6012	−	14.5474i	0.950406	−	1.19177i	−0.0309396	−	0.999521i	$-0.509850\pi$
$149$	11.6012	−	14.5474i	0.950406	−	1.19177i	0.981346	−	0.192251i	$-0.0615786\pi$
$150$	2.26055	−	1.08863i	0.184573	−	0.0888859i
$151$	6.78232	+	3.26619i	0.551938	+	0.265799i	0.688998	−	0.724764i	$-0.258051\pi$
$151$	6.78232	+	3.26619i	0.551938	+	0.265799i	−0.137060	+	0.990563i	$0.543765\pi$
$152$	−2.48643	−	3.11788i	−0.201676	−	0.252893i
$153$	1.44504	−	6.33114i	0.116825	−	0.511843i
$154$	0.174563	−	0.764811i	0.0140667	−	0.0616302i
$155$	−2.88740	+	3.62068i	−0.231921	+	0.290820i
$156$	2.82640	+	12.3833i	0.226293	+	0.991454i
$157$	−18.2392			−1.45565			−0.727824	−	0.685764i	$-0.759468\pi$
$157$	−18.2392			−1.45565			−0.727824	+	0.685764i	$0.759468\pi$
$158$	−0.461968	−	2.02401i	−0.0367522	−	0.161022i
$159$	−5.27144	−	2.53859i	−0.418052	−	0.201323i
$160$	2.90097	+	1.39703i	0.229342	+	0.110445i
$161$	−0.182333	−	0.798852i	−0.0143698	−	0.0629584i
$162$	1.14675			0.0900973
$163$	−2.81282	−	12.3238i	−0.220317	−	0.965273i	−0.957240	−	0.289296i	$-0.906579\pi$
$163$	−2.81282	−	12.3238i	−0.220317	−	0.965273i	0.736922	−	0.675977i	$-0.236278\pi$
$164$	−3.49396	+	4.38129i	−0.272832	+	0.342121i
$165$	0.948394	−	4.15519i	0.0738324	−	0.323481i
$166$	0.441157	−	1.93284i	0.0342404	−	0.150017i
$167$	−0.496648	−	0.622776i	−0.0384317	−	0.0481919i	0.762244	−	0.647290i	$-0.224098\pi$
$167$	−0.496648	−	0.622776i	−0.0384317	−	0.0481919i	−0.800676	+	0.599098i	$0.795526\pi$
$168$	0.678448	+	0.326723i	0.0523434	+	0.0252073i
$169$	−17.0770	+	8.22386i	−1.31362	+	0.632605i
$170$	−0.862937	+	1.08209i	−0.0661842	+	0.0829924i
$171$	2.12349	+	2.66277i	0.162387	+	0.203627i
$172$	−5.52930	+	2.66277i	−0.421605	+	0.203034i
$173$	−9.15346			−0.695924			−0.347962	−	0.937509i	$-0.613126\pi$
$173$	−9.15346			−0.695924			−0.347962	+	0.937509i	$0.613126\pi$
$174$	2.96681	+	0.359726i	0.224913	+	0.0272708i
$175$	−1.61356			−0.121974
$176$	−12.6860	+	6.10925i	−0.956242	+	0.460502i
$177$	9.71379	+	12.1807i	0.730133	+	0.915558i
$178$	1.57606	−	1.97632i	0.118131	−	0.148132i
$179$	−3.06853	+	1.47773i	−0.229353	+	0.110450i	−0.545031	−	0.838416i	$-0.683482\pi$
$179$	−3.06853	+	1.47773i	−0.229353	+	0.110450i	0.315678	+	0.948866i	$0.397768\pi$
$180$	−1.62349	−	0.781831i	−0.121008	−	0.0582743i
$181$	7.90246	+	9.90937i	0.587385	+	0.736558i	0.983353	−	0.181707i	$-0.0581621\pi$
$181$	7.90246	+	9.90937i	0.587385	+	0.736558i	−0.395967	+	0.918265i	$0.629591\pi$
$182$	−0.199791	+	0.875342i	−0.0148095	+	0.0648847i
$183$	−0.455927	+	1.99755i	−0.0337031	+	0.147663i
$184$	2.42208	−	3.03719i	0.178558	−	0.223904i
$185$	0.760553	+	3.33220i	0.0559170	+	0.244988i
$186$	−3.71379			−0.272308
$187$	−4.93900	−	21.6392i	−0.361176	−	1.58241i
$188$	−10.4635	−	5.03894i	−0.763126	−	0.367502i
$189$	−1.78232	−	0.858322i	−0.129645	−	0.0624337i
$190$	−0.161522	−	0.707674i	−0.0117180	−	0.0513401i
$191$	−10.6703			−0.772072			−0.386036	−	0.922484i	$-0.626156\pi$
$191$	−10.6703			−0.772072			−0.386036	+	0.922484i	$0.626156\pi$
$192$	−1.00753	−	4.41429i	−0.0727124	−	0.318574i
$193$	14.1712	−	17.7701i	1.02007	−	1.27912i	0.0603421	−	0.998178i	$-0.480781\pi$
$193$	14.1712	−	17.7701i	1.02007	−	1.27912i	0.959724	−	0.280945i	$-0.0906477\pi$
$194$	−0.0178854	+	0.0783611i	−0.00128410	+	0.00562600i
$195$	−1.08546	+	4.75570i	−0.0777312	+	0.340563i
$196$	7.72132	+	9.68223i	0.551523	+	0.691588i
$197$	17.6211	+	8.48587i	1.25545	+	0.604593i	0.938968	−	0.344005i	$-0.111784\pi$
$197$	17.6211	+	8.48587i	1.25545	+	0.604593i	0.316483	+	0.948598i	$0.397498\pi$
$198$	−2.86174	+	1.37814i	−0.203375	+	0.0979402i
$199$	−0.545565	+	0.684117i	−0.0386741	+	0.0484958i	−0.800792	−	0.598942i	$-0.795588\pi$
$199$	−0.545565	+	0.684117i	−0.0386741	+	0.0484958i	0.762118	+	0.647438i	$0.224159\pi$
$200$	−4.76958	−	5.98086i	−0.337260	−	0.422911i
$201$	−2.60992	+	1.25687i	−0.184089	+	0.0886527i
$202$	−1.43727			−0.101126
$203$	−1.61865	−	1.03627i	−0.113607	−	0.0727318i
$204$	10.0978			0.706990
$205$	−1.93900	+	0.933774i	−0.135426	+	0.0652176i
$206$	3.78836	+	4.75046i	0.263948	+	0.330980i
$207$	−2.06853	+	2.59386i	−0.143773	+	0.180286i
$208$	14.5194	−	6.99216i	1.00674	−	0.484819i
$209$	10.4879	+	5.05072i	0.725464	+	0.349365i
$210$	0.0854576	+	0.107160i	0.00589713	+	0.00739477i
$211$	4.06518	−	17.8107i	0.279858	−	1.22614i	−0.618114	−	0.786088i	$-0.712103\pi$
$211$	4.06518	−	17.8107i	0.279858	−	1.22614i	0.897972	−	0.440052i	$-0.145040\pi$
$212$	−1.88135	+	8.24275i	−0.129212	+	0.566115i
$213$	5.70291	−	7.15122i	0.390757	−	0.489993i
$214$	1.60872	+	7.04826i	0.109970	+	0.481809i
$215$	−2.35690			−0.160739
$216$	−2.08695	−	9.14352i	−0.141999	−	0.622138i
$217$	2.15183	+	1.03627i	0.146076	+	0.0703465i
$218$	2.19202	+	1.05562i	0.148462	+	0.0714957i
$219$	1.56100	+	6.83918i	0.105483	+	0.462149i
$220$	−6.15883			−0.415228
$221$	5.65279	+	24.7665i	0.380248	+	1.66598i
$222$	−1.70895	+	2.14295i	−0.114697	+	0.143826i
$223$	0.404617	−	1.77274i	0.0270951	−	0.118712i	−0.959572	−	0.281464i	$-0.909180\pi$
$223$	0.404617	−	1.77274i	0.0270951	−	0.118712i	0.986667	+	0.162752i	$0.0520372\pi$
$224$	0.369510	−	1.61893i	0.0246889	−	0.108169i
$225$	4.07338	+	5.10785i	0.271558	+	0.340523i
$226$	−4.28017	−	2.06122i	−0.284713	−	0.137110i
$227$	12.4840	−	6.01199i	0.828594	−	0.399030i	0.0290066	−	0.999579i	$-0.490766\pi$
$227$	12.4840	−	6.01199i	0.828594	−	0.399030i	0.799588	+	0.600549i	$0.205051\pi$
$228$	−3.30194	+	4.14050i	−0.218676	+	0.274211i
$229$	−7.96346	−	9.98586i	−0.526240	−	0.659884i	0.445681	−	0.895192i	$-0.352962\pi$
$229$	−7.96346	−	9.98586i	−0.526240	−	0.659884i	−0.971921	+	0.235308i	$0.924390\pi$
$230$	0.637063	−	0.306794i	0.0420067	−	0.0202294i
$231$	−2.19806			−0.144622
$232$	−0.943550	−	9.06283i	−0.0619471	−	0.595004i
$233$	−8.86592			−0.580826			−0.290413	−	0.956901i	$-0.593793\pi$
$233$	−8.86592			−0.580826			−0.290413	+	0.956901i	$0.593793\pi$
$234$	3.27532	−	1.57731i	0.214115	−	0.103112i
$235$	−2.78083	−	3.48705i	−0.181401	−	0.227470i
$236$	14.0368	−	17.6016i	0.913720	−	1.14577i
$237$	−5.24094	+	2.52390i	−0.340436	+	0.163945i
$238$	0.643104	+	0.309703i	0.0416862	+	0.0200750i
$239$	−15.9393	−	19.9872i	−1.03103	−	1.29287i	−0.955268	−	0.295741i	$-0.904433\pi$
$239$	−15.9393	−	19.9872i	−1.03103	−	1.29287i	−0.0757593	−	0.997126i	$-0.524138\pi$
$240$	0.547425	−	2.39843i	0.0353362	−	0.154818i
$241$	−2.16541	+	9.48727i	−0.139486	+	0.611129i	0.856062	+	0.516873i	$0.172904\pi$
$241$	−2.16541	+	9.48727i	−0.139486	+	0.611129i	−0.995548	+	0.0942554i	$0.969953\pi$
$242$	−3.71648	+	4.66032i	−0.238904	+	0.299577i
$243$	2.98523	+	13.0791i	0.191503	+	0.839028i
$244$	2.96077			0.189544
$245$	1.05831	+	4.63676i	0.0676130	+	0.296232i
$246$	−1.55496	−	0.748828i	−0.0991405	−	0.0477436i
$247$	−12.0036	−	5.78065i	−0.763774	−	0.367814i
$248$	2.51961	+	11.0392i	0.159996	+	0.700987i
$249$	−5.55496			−0.352031
$250$	−0.652497	−	2.85878i	−0.0412676	−	0.180805i
$251$	−6.08546	+	7.63092i	−0.384111	+	0.481660i	−0.935871	−	0.352343i	$-0.885385\pi$
$251$	−6.08546	+	7.63092i	−0.384111	+	0.481660i	0.551760	+	0.834003i	$0.313956\pi$
$252$	−0.206791	+	0.906013i	−0.0130266	+	0.0570734i
$253$	−2.52326	+	11.0551i	−0.158636	+	0.695030i
$254$	0.287700	+	0.360765i	0.0180519	+	0.0226364i
$255$	3.49396	+	1.68260i	0.218800	+	0.105369i
$256$	−2.16368	+	1.04197i	−0.135230	+	0.0651233i
$257$	10.1984	−	12.7883i	0.636156	−	0.797714i	−0.354360	−	0.935109i	$-0.615301\pi$
$257$	10.1984	−	12.7883i	0.636156	−	0.797714i	0.990516	+	0.137394i	$0.0438728\pi$
$258$	−1.17845	−	1.47773i	−0.0733670	−	0.0919993i
$259$	1.58815	−	0.764811i	0.0986826	−	0.0475230i
$260$	7.04892			0.437155
$261$	0.805823	+	7.73995i	0.0498792	+	0.479091i
$262$	−3.57002			−0.220557
$263$	−21.3741	+	10.2932i	−1.31798	+	0.634708i	−0.954867	−	0.297035i	$-0.904002\pi$
$263$	−21.3741	+	10.2932i	−1.31798	+	0.634708i	−0.363118	+	0.931743i	$0.618288\pi$
$264$	−6.49731	−	8.14737i	−0.399882	−	0.501436i
$265$	−2.02446	+	2.53859i	−0.124362	+	0.155944i
$266$	−0.337282	+	0.162426i	−0.0206801	+	0.00995899i
$267$	−6.38135	−	3.07310i	−0.390533	−	0.188071i
$268$	2.60992	+	3.27273i	0.159426	+	0.199914i
$269$	−5.64191	+	24.7188i	−0.343993	+	1.50713i	0.446568	+	0.894750i	$0.352646\pi$
$269$	−5.64191	+	24.7188i	−0.343993	+	1.50713i	−0.790561	+	0.612383i	$0.790211\pi$
$270$	0.379863	−	1.66429i	0.0231177	−	0.101285i
$271$	−0.750332	+	0.940887i	−0.0455794	+	0.0571548i	−0.804099	−	0.594496i	$-0.797352\pi$
$271$	−0.750332	+	0.940887i	−0.0455794	+	0.0571548i	0.758519	+	0.651651i	$0.225923\pi$
$272$	−2.85086	−	12.4904i	−0.172858	−	0.757342i
$273$	2.51573			0.152259
$274$	1.70655	+	7.47690i	0.103097	+	0.451696i
$275$	20.1184	+	9.68851i	1.21319	+	0.584239i
$276$	−4.64795	−	2.23833i	−0.279774	−	0.134732i
$277$	−2.37316	−	10.3975i	−0.142589	−	0.624724i	−0.994828	−	0.101572i	$-0.967613\pi$
$277$	−2.37316	−	10.3975i	−0.142589	−	0.624724i	0.852239	−	0.523153i	$-0.175244\pi$
$278$	7.41789			0.444896
$279$	−2.15183	−	9.42780i	−0.128827	−	0.564427i
$280$	0.260553	−	0.326723i	0.0155710	−	0.0195255i
$281$	3.62253	−	15.8713i	0.216102	−	0.946805i	−0.744225	−	0.667929i	$-0.767181\pi$
$281$	3.62253	−	15.8713i	0.216102	−	0.946805i	0.960327	−	0.278876i	$-0.0899618\pi$
$282$	0.795897	−	3.48705i	0.0473950	−	0.207651i
$283$	−3.27144	−	4.10225i	−0.194467	−	0.243854i	0.675032	−	0.737788i	$-0.264130\pi$
$283$	−3.27144	−	4.10225i	−0.194467	−	0.243854i	−0.869499	+	0.493935i	$0.835558\pi$
$284$	−11.9085	−	5.73483i	−0.706640	−	0.340300i
$285$	−1.83244	+	0.882455i	−0.108544	+	0.0522721i
$286$	7.74698	−	9.71441i	0.458089	−	0.574425i
$287$	0.692021	+	0.867767i	0.0408487	+	0.0512227i
$288$	−6.05765	+	2.91721i	−0.356950	+	0.171898i
$289$	3.19567			0.187981
$290$	0.560999	−	1.56075i	0.0329430	−	0.0916506i
$291$	0.225209			0.0132020
$292$	9.13318	−	4.39831i	0.534479	−	0.257391i
$293$	4.21714	+	5.28813i	0.246368	+	0.308936i	0.889604	−	0.456732i	$-0.150980\pi$
$293$	4.21714	+	5.28813i	0.246368	+	0.308936i	−0.643236	+	0.765668i	$0.722409\pi$
$294$	−2.37800	+	2.98192i	−0.138688	+	0.173909i
$295$	7.78986	−	3.75140i	0.453543	−	0.218415i
$296$	7.52930	+	3.62592i	0.437632	+	0.210752i
$297$	17.0688	+	21.4036i	0.990434	+	1.24196i
$298$	1.84266	−	8.07321i	0.106742	−	0.467669i
$299$	2.88793	−	12.6528i	0.167013	−	0.731733i
$300$	−6.33393	+	7.94250i	−0.365690	+	0.458560i
$301$	0.270479	+	1.18505i	0.0155901	+	0.0683049i
$302$	3.35019			0.192782
$303$	0.896125	+	3.92618i	0.0514810	+	0.225553i
$304$	6.05376	+	2.91534i	0.347207	+	0.167206i
$305$	1.02446	+	0.493353i	0.0586603	+	0.0282493i
$306$	−0.643104	−	2.81762i	−0.0367638	−	0.161073i
$307$	4.51812			0.257863			0.128931	−	0.991654i	$-0.458845\pi$
$307$	4.51812			0.257863			0.128931	+	0.991654i	$0.458845\pi$
$308$	0.706791	+	3.09666i	0.0402732	+	0.176448i
$309$	10.6148	−	13.3105i	0.603853	−	0.757207i
$310$	−0.458615	+	2.00933i	−0.0260476	+	0.114122i
$311$	2.80745	−	12.3002i	0.159196	−	0.697482i	−0.830822	−	0.556538i	$-0.812129\pi$
$311$	2.80745	−	12.3002i	0.159196	−	0.697482i	0.990018	−	0.140944i	$-0.0450136\pi$
$312$	7.43631	+	9.32484i	0.420998	+	0.527915i
$313$	−17.3349	−	8.34804i	−0.979826	−	0.471859i	−0.125781	−	0.992058i	$-0.540144\pi$
$313$	−17.3349	−	8.34804i	−0.979826	−	0.471859i	−0.854045	+	0.520199i	$0.825858\pi$
$314$	−7.31336	+	3.52193i	−0.412717	+	0.198754i
$315$	−0.222521	+	0.279032i	−0.0125376	+	0.0157217i
$316$	5.24094	+	6.57193i	0.294826	+	0.369700i
$317$	−2.58426	+	1.24451i	−0.145147	+	0.0698989i	−0.505047	−	0.863092i	$-0.668525\pi$
$317$	−2.58426	+	1.24451i	−0.145147	+	0.0698989i	0.359901	+	0.932991i	$0.382811\pi$
$318$	−2.60388			−0.146018
$319$	13.9596	+	22.6395i	0.781586	+	1.26757i
$320$	−2.51275			−0.140467
$321$	18.2506	−	8.78904i	1.01865	−	0.490556i
$322$	−0.227365	−	0.285107i	−0.0126706	−	0.0158884i
$323$	−6.60388	+	8.28100i	−0.367449	+	0.460767i
$324$	−4.18329	+	2.01457i	−0.232405	+	0.111920i
$325$	−23.0260	−	11.0887i	−1.27725	−	0.615091i
$326$	−3.50753	−	4.39831i	−0.194264	−	0.243600i
$327$	1.51693	−	6.64609i	0.0838862	−	0.367529i
$328$	−1.17092	+	5.13011i	−0.0646530	+	0.283263i
$329$	−1.43416	+	1.79838i	−0.0790676	+	0.0991477i
$330$	−0.422075	−	1.84923i	−0.0232345	−	0.101797i
$331$	3.13408			0.172265			0.0861323	−	0.996284i	$-0.472549\pi$
$331$	3.13408			0.172265			0.0861323	+	0.996284i	$0.472549\pi$
$332$	1.78621	+	7.82589i	0.0980309	+	0.429501i
$333$	−6.43027	−	3.09666i	−0.352377	−	0.169696i
$334$	−0.319396	−	0.153813i	−0.0174766	−	0.00841628i
$335$	0.357724	+	1.56729i	0.0195445	+	0.0856302i
$336$	−1.26875			−0.0692160
$337$	−1.10872	−	4.85762i	−0.0603958	−	0.264611i	0.935711	−	0.352768i	$-0.114760\pi$
$337$	−1.10872	−	4.85762i	−0.0603958	−	0.264611i	−0.996107	+	0.0881567i	$0.971902\pi$
$338$	−5.25936	+	6.59502i	−0.286071	+	0.358722i
$339$	−2.96197	+	12.9772i	−0.160872	+	0.704826i
$340$	1.24698	−	5.46337i	0.0676270	−	0.296293i
$341$	−20.6075	−	25.8410i	−1.11596	−	1.39937i
$342$	1.36563	+	0.657650i	0.0738445	+	0.0355617i
$343$	4.46077	−	2.14819i	0.240859	−	0.115992i
$344$	−3.59299	+	4.50547i	−0.193721	+	0.242919i
$345$	−1.23527	−	1.54898i	−0.0665045	−	0.0833940i
$346$	−3.67025	+	1.76750i	−0.197314	+	0.0950214i
$347$	20.1172			1.07995			0.539974	−	0.841682i	$-0.318434\pi$
$347$	20.1172			1.07995			0.539974	+	0.841682i	$0.318434\pi$
$348$	−11.4547	+	3.89971i	−0.614038	+	0.209046i
$349$	20.4892			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$349$	20.4892			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$350$	−0.646989	+	0.311573i	−0.0345830	+	0.0166543i
$351$	−19.5356	−	24.4969i	−1.04274	−	1.30755i
$352$	−14.3279	+	17.9666i	−0.763679	+	0.957623i
$353$	−16.2153	+	7.80887i	−0.863052	+	0.415624i	−0.812406	−	0.583092i	$-0.801843\pi$
$353$	−16.2153	+	7.80887i	−0.863052	+	0.415624i	−0.0506467	+	0.998717i	$0.516128\pi$
$354$	6.24698	+	3.00839i	0.332023	+	0.159894i
$355$	−3.16487	−	3.96863i	−0.167974	−	0.210633i
$356$	−2.27748	+	9.97829i	−0.120706	+	0.528848i
$357$	0.445042	−	1.94986i	0.0235541	−	0.103197i
$358$	−0.945042	+	1.18505i	−0.0499470	+	0.0626316i
$359$	−5.25786	−	23.0362i	−0.277499	−	1.21580i	−0.900943	−	0.433937i	$-0.857124\pi$
$359$	−5.25786	−	23.0362i	−0.277499	−	1.21580i	0.623444	−	0.781868i	$-0.285733\pi$
$360$	−1.69202			−0.0891774
$361$	2.99180	+	13.1079i	0.157463	+	0.689892i
$362$	5.08211	+	2.44741i	0.267110	+	0.128633i
$363$	15.0477	+	7.24660i	0.789801	+	0.380348i
$364$	−0.808938	−	3.54419i	−0.0423999	−	0.185766i
$365$	3.89307			0.203772
$366$	0.202907	+	0.888992i	0.0106061	+	0.0464684i
$367$	−18.4822	+	23.1759i	−0.964762	+	1.20977i	0.0129705	+	0.999916i	$0.495871\pi$
$367$	−18.4822	+	23.1759i	−0.964762	+	1.20977i	−0.977732	+	0.209857i	$0.932700\pi$
$368$	−1.45646	+	6.38117i	−0.0759232	+	0.332641i
$369$	1.00000	−	4.38129i	0.0520579	−	0.228081i
$370$	0.948394	+	1.18925i	0.0493047	+	0.0618261i
$371$	1.50873	+	0.726566i	0.0783293	+	0.0377214i
$372$	13.5477	−	6.52424i	0.702417	−	0.338266i
$373$	−15.7044	+	19.6927i	−0.813143	+	1.01965i	0.186167	+	0.982518i	$0.440393\pi$
$373$	−15.7044	+	19.6927i	−0.813143	+	1.01965i	−0.999310	+	0.0371310i	$0.988178\pi$
$374$	−6.15883	−	7.72293i	−0.318466	−	0.399343i
$375$	−7.40246	+	3.56484i	−0.382261	+	0.184087i
$376$	−10.9051			−0.562390
$377$	−15.9770	−	25.9114i	−0.822859	−	1.33451i
$378$	−0.880395			−0.0452826
$379$	24.2424	−	11.6745i	1.24525	−	0.599681i	0.309016	−	0.951057i	$-0.400000\pi$
$379$	24.2424	−	11.6745i	1.24525	−	0.599681i	0.936234	+	0.351376i	$0.114286\pi$
$380$	1.83244	+	2.29780i	0.0940020	+	0.117875i
$381$	0.806118	−	1.01084i	0.0412987	−	0.0517869i
$382$	−4.27844	+	2.06039i	−0.218904	+	0.105419i
$383$	17.7213	+	8.53414i	0.905517	+	0.436074i	0.827879	−	0.560907i	$-0.189548\pi$
$383$	17.7213	+	8.53414i	0.905517	+	0.436074i	0.0776388	+	0.996982i	$0.475262\pi$
$384$	−8.49127	−	10.6477i	−0.433318	−	0.543364i
$385$	−0.271438	+	1.18925i	−0.0138338	+	0.0606097i
$386$	2.25086	−	9.86168i	0.114566	−	0.501946i
$387$	3.06853	−	3.84782i	0.155982	−	0.195596i
$388$	−0.0724165	−	0.317278i	−0.00367639	−	0.0161073i
$389$	24.8552			1.26021			0.630103	−	0.776511i	$-0.283012\pi$
$389$	24.8552			1.26021			0.630103	+	0.776511i	$0.283012\pi$
$390$	0.483074	+	2.11649i	0.0244614	+	0.107172i
$391$	−9.29590	−	4.47667i	−0.470114	−	0.226395i
$392$	10.4770	+	5.04547i	0.529170	+	0.254835i
$393$	2.22587	+	9.75219i	0.112280	+	0.491933i
$394$	8.70410			0.438506
$395$	0.718341	+	3.14726i	0.0361436	+	0.158356i
$396$	8.01842	−	10.0548i	0.402941	−	0.505272i
$397$	0.888887	−	3.89447i	0.0446120	−	0.195458i	−0.947711	−	0.319129i	$-0.896610\pi$
$397$	0.888887	−	3.89447i	0.0446120	−	0.195458i	0.992323	+	0.123671i	$0.0394668\pi$
$398$	−0.0866540	+	0.379656i	−0.00434357	+	0.0190304i
$399$	0.653989	+	0.820077i	0.0327404	+	0.0410552i
$400$	11.6126	+	5.59234i	0.580630	+	0.279617i
$401$	22.4405	−	10.8068i	1.12062	−	0.539664i	0.220539	−	0.975378i	$-0.429218\pi$
$401$	22.4405	−	10.8068i	1.12062	−	0.539664i	0.900085	+	0.435714i	$0.143504\pi$
$402$	−0.803798	+	1.00793i	−0.0400898	+	0.0502710i
$403$	23.5858	+	29.5756i	1.17489	+	1.47327i
$404$	5.24309	−	2.52494i	0.260854	−	0.125621i
$405$	−1.78315			−0.0886055
$406$	−0.849126	−	0.102957i	−0.0421414	−	0.00510965i
$407$	−24.3937			−1.20915
$408$	8.54288	−	4.11403i	0.422935	−	0.203675i
$409$	0.176587	+	0.221434i	0.00873169	+	0.0109492i	0.786178	−	0.618000i	$-0.212057\pi$
$409$	0.176587	+	0.221434i	0.00873169	+	0.0109492i	−0.777446	+	0.628949i	$0.783485\pi$
$410$	−0.597171	+	0.748828i	−0.0294922	+	0.0369820i
$411$	19.3605	−	9.32355i	0.954985	−	0.459897i
$412$	−22.1652	−	10.6742i	−1.09200	−	0.525879i
$413$	−2.78017	−	3.48622i	−0.136803	−	0.171546i
$414$	−0.328552	+	1.43948i	−0.0161475	+	0.0707467i
$415$	−0.685981	+	3.00548i	−0.0336735	+	0.147533i
$416$	16.3986	−	20.5632i	0.804006	−	1.00819i
$417$	−4.62498	−	20.2634i	−0.226486	−	0.992301i
$418$	5.18060			0.253392
$419$	5.89426	+	25.8245i	0.287954	+	1.26161i	0.887328	+	0.461139i	$0.152559\pi$
$419$	5.89426	+	25.8245i	0.287954	+	1.26161i	−0.599374	+	0.800469i	$0.704584\pi$
$420$	−0.500000	−	0.240787i	−0.0243975	−	0.0117492i
$421$	15.8409	+	7.62859i	0.772040	+	0.371795i	0.778062	−	0.628187i	$-0.216203\pi$
$421$	15.8409	+	7.62859i	0.772040	+	0.371795i	−0.00602261	+	0.999982i	$0.501917\pi$
$422$	−1.80917	−	7.92651i	−0.0880693	−	0.385857i
$423$	9.31336			0.452831
$424$	1.76659	+	7.73995i	0.0857934	+	0.375885i
$425$	−12.6679	+	15.8850i	−0.614481	+	0.770535i
$426$	0.905813	−	3.96863i	0.0438868	−	0.192281i
$427$	0.130490	−	0.571714i	0.00631486	−	0.0276672i
$428$	−18.2506	−	22.8856i	−0.882177	−	1.10622i
$429$	−31.3669	−	15.1055i	−1.51441	−	0.729300i
$430$	−0.945042	+	0.455108i	−0.0455740	+	0.0219473i
$431$	−17.3300	+	21.7312i	−0.834759	+	1.04675i	0.163428	+	0.986555i	$0.447745\pi$
$431$	−17.3300	+	21.7312i	−0.834759	+	1.04675i	−0.998186	+	0.0601992i	$0.980826\pi$
$432$	9.85235	+	12.3545i	0.474021	+	0.594404i
$433$	−5.29374	+	2.54933i	−0.254401	+	0.122513i	−0.556738	−	0.830688i	$-0.687947\pi$
$433$	−5.29374	+	2.54933i	−0.254401	+	0.122513i	0.302337	+	0.953201i	$0.402233\pi$
$434$	1.06292			0.0510217
$435$	−4.61327	−	0.559360i	−0.221189	−	0.0268192i
$436$	−9.85086			−0.471770
$437$	4.87531	−	2.34783i	0.233218	−	0.112312i
$438$	1.94653	+	2.44088i	0.0930090	+	0.116630i
$439$	−9.81431	+	12.3068i	−0.468412	+	0.587370i	−0.958781	−	0.284145i	$-0.908290\pi$
$439$	−9.81431	+	12.3068i	−0.468412	+	0.587370i	0.490370	+	0.871515i	$0.336862\pi$
$440$	−5.21044	+	2.50922i	−0.248398	+	0.119622i
$441$	−8.94773	−	4.30900i	−0.426082	−	0.205190i
$442$	7.04892	+	8.83906i	0.335283	+	0.420431i
$443$	−1.49947	+	6.56960i	−0.0712419	+	0.312131i	−0.997976	−	0.0635859i	$-0.979746\pi$
$443$	−1.49947	+	6.56960i	−0.0712419	+	0.312131i	0.926735	+	0.375717i	$0.122603\pi$
$444$	2.46950	−	10.8196i	0.117197	−	0.513475i
$445$	−2.45071	+	3.07310i	−0.116175	+	0.145679i
$446$	−0.180071	−	0.788944i	−0.00852663	−	0.0373576i
$447$	−23.2024			−1.09743
$448$	0.288364	+	1.26341i	0.0136239	+	0.0596903i
$449$	−11.1000	−	5.34547i	−0.523841	−	0.252269i	0.153224	−	0.988191i	$-0.451034\pi$
$449$	−11.1000	−	5.34547i	−0.523841	−	0.252269i	−0.677065	+	0.735923i	$0.736749\pi$
$450$	2.61960	+	1.26154i	0.123489	+	0.0594693i
$451$	−3.41789	−	14.9748i	−0.160942	−	0.705135i
$452$	19.2349			0.904733
$453$	−2.08881	−	9.15167i	−0.0981409	−	0.429983i
$454$	3.84481	−	4.82124i	0.180446	−	0.226272i
$455$	0.310667	−	1.36112i	0.0145643	−	0.0638103i
$456$	−1.10656	+	4.84817i	−0.0518196	+	0.227037i
$457$	8.51842	+	10.6818i	0.398475	+	0.499672i	0.940076	−	0.340964i	$-0.110753\pi$
$457$	8.51842	+	10.6818i	0.398475	+	0.499672i	−0.541602	+	0.840635i	$0.682182\pi$
$458$	−5.12133	−	2.46630i	−0.239304	−	0.115243i
$459$	−22.4426	+	10.8078i	−1.04753	+	0.504465i
$460$	−1.78501	+	2.23833i	−0.0832266	+	0.104363i
$461$	7.23759	+	9.07565i	0.337088	+	0.422695i	0.921268	−	0.388929i	$-0.127155\pi$
$461$	7.23759	+	9.07565i	0.337088	+	0.422695i	−0.584180	+	0.811624i	$0.698584\pi$
$462$	−0.881355	+	0.424438i	−0.0410043	+	0.0197466i
$463$	−7.24267			−0.336595			−0.168298	−	0.985736i	$-0.553827\pi$
$463$	−7.24267			−0.336595			−0.168298	+	0.985736i	$0.553827\pi$
$464$	8.05765	+	13.0678i	0.374067	+	0.606659i
$465$	5.77479			0.267800
$466$	−3.55496	+	1.71198i	−0.164680	+	0.0793058i
$467$	−1.28650	−	1.61322i	−0.0595323	−	0.0746511i	0.751174	−	0.660104i	$-0.229488\pi$
$467$	−1.28650	−	1.61322i	−0.0595323	−	0.0746511i	−0.810706	+	0.585453i	$0.800917\pi$
$468$	−9.17725	+	11.5079i	−0.424219	+	0.531953i
$469$	0.746980	−	0.359726i	0.0344923	−	0.0166106i
$470$	−1.78836	−	0.861231i	−0.0824911	−	0.0397256i
$471$	14.1806	+	17.7819i	0.653408	+	0.819347i
$472$	4.70410	−	20.6100i	0.216524	−	0.948653i
$473$	3.74309	−	16.3996i	0.172108	−	0.754053i
$474$	−1.61410	+	2.02401i	−0.0741379	+	0.0929660i
$475$	−2.37113	−	10.3886i	−0.108795	−	0.476662i
$476$	−2.89008			−0.132467
$477$	−1.50873	−	6.61017i	−0.0690800	−	0.302659i
$478$	−10.2506	−	4.93644i	−0.468853	−	0.225788i
$479$	3.50388	+	1.68738i	0.160097	+	0.0770985i	0.512216	−	0.858857i	$-0.328825\pi$
$479$	3.50388	+	1.68738i	0.160097	+	0.0770985i	−0.352120	+	0.935955i	$0.614539\pi$
$480$	−0.893436	−	3.91440i	−0.0407796	−	0.178667i
$481$	27.9191			1.27300
$482$	0.963697	+	4.22223i	0.0438952	+	0.192317i
$483$	−0.637063	+	0.798852i	−0.0289874	+	0.0363490i
$484$	5.37047	−	23.5296i	0.244112	−	1.06953i
$485$	0.0278111	−	0.121848i	0.00126284	−	0.00553284i
$486$	3.72252	+	4.66789i	0.168857	+	0.211740i
$487$	−8.87047	−	4.27179i	−0.401959	−	0.193573i	0.221971	−	0.975053i	$-0.428751\pi$
$487$	−8.87047	−	4.27179i	−0.401959	−	0.193573i	−0.623931	+	0.781480i	$0.714465\pi$
$488$	2.50484	−	1.20627i	0.113389	−	0.0546053i
$489$	−9.82789	+	12.3238i	−0.444432	+	0.557301i
$490$	1.31969	+	1.65484i	0.0596176	+	0.0747581i
$491$	−7.01961	+	3.38047i	−0.316791	+	0.152558i	−0.585521	−	0.810657i	$-0.699110\pi$
$491$	−7.01961	+	3.38047i	−0.316791	+	0.152558i	0.268731	+	0.963215i	$0.413396\pi$
$492$	6.98792			0.315040
$493$	−22.9095	+	7.79942i	−1.03179	+	0.351268i
$494$	−5.92931			−0.266772
$495$	4.44989	−	2.14295i	0.200008	−	0.0963185i
$496$	−11.8949	−	14.9158i	−0.534098	−	0.669738i
$497$	−1.63222	+	2.04674i	−0.0732150	+	0.0918087i
$498$	−2.22737	+	1.07264i	−0.0998106	+	0.0480663i
$499$	18.5286	+	8.92292i	0.829456	+	0.399445i	0.799911	−	0.600119i	$-0.204880\pi$
$499$	18.5286	+	8.92292i	0.829456	+	0.399445i	0.0295448	+	0.999563i	$0.490594\pi$
$500$	7.40246	+	9.28239i	0.331048	+	0.415121i
$501$	−0.221029	+	0.968391i	−0.00987485	+	0.0432645i
$502$	−0.966575	+	4.23484i	−0.0431404	+	0.189010i
$503$	5.13437	−	6.43830i	0.228930	−	0.287070i	−0.654078	−	0.756427i	$-0.726943\pi$
$503$	5.13437	−	6.43830i	0.228930	−	0.287070i	0.883008	+	0.469358i	$0.155514\pi$
$504$	0.194177	+	0.850747i	0.00864935	+	0.0378953i
$505$	2.23490			0.0994517
$506$	1.12296	+	4.92000i	0.0499215	+	0.218721i
$507$	21.2947	+	10.2550i	0.945731	+	0.455440i
$508$	−1.68329	−	0.810631i	−0.0746840	−	0.0359659i
$509$	−1.76151	−	7.71769i	−0.0780777	−	0.342081i	0.920768	−	0.390110i	$-0.127563\pi$
$509$	−1.76151	−	7.71769i	−0.0780777	−	0.342081i	−0.998846	+	0.0480294i	$0.984706\pi$
$510$	1.72587			0.0764230
$511$	−0.446771	−	1.95743i	−0.0197640	−	0.0865916i
$512$	−14.2853	+	17.9132i	−0.631327	+	0.791659i
$513$	2.90701	−	12.7364i	0.128348	−	0.562328i
$514$	1.61984	−	7.09699i	0.0714482	−	0.313035i
$515$	−5.89075	−	7.38676i	−0.259577	−	0.325500i
$516$	6.89493	+	3.32042i	0.303532	+	0.146173i
$517$	28.6797	−	13.8114i	1.26133	−	0.607425i
$518$	0.489115	−	0.613331i	0.0214905	−	0.0269482i
$519$	7.11662	+	8.92396i	0.312385	+	0.391718i
$520$	5.96346	−	2.87185i	0.261515	−	0.125939i
$521$	−3.52542			−0.154451			−0.0772257	−	0.997014i	$-0.524606\pi$
$521$	−3.52542			−0.154451			−0.0772257	+	0.997014i	$0.524606\pi$
$522$	1.81767	+	2.94788i	0.0795571	+	0.129025i
$523$	10.0301			0.438587			0.219294	−	0.975659i	$-0.429625\pi$
$523$	10.0301			0.438587			0.219294	+	0.975659i	$0.429625\pi$
$524$	13.0233	−	6.27167i	0.568924	−	0.273979i
$525$	1.25451	+	1.57311i	0.0547514	+	0.0686561i
$526$	−6.58277	+	8.25453i	−0.287022	+	0.359915i
$527$	27.0954	−	13.0485i	1.18030	−	0.568401i
$528$	15.8192	+	7.61811i	0.688441	+	0.331535i
$529$	−11.0538	−	13.8610i	−0.480598	−	0.602651i
$530$	−0.321552	+	1.40881i	−0.0139673	+	0.0611949i
$531$	−4.01746	+	17.6016i	−0.174343	+	0.763846i
$532$	0.945042	−	1.18505i	0.0409728	−	0.0513782i
$533$	3.91185	+	17.1390i	0.169441	+	0.742370i
$534$	−3.15213			−0.136406
$535$	−2.50149	−	10.9598i	−0.108149	−	0.473831i
$536$	3.54138	+	1.70544i	0.152965	+	0.0736638i
$537$	3.82640	+	1.84270i	0.165121	+	0.0795182i
$538$	2.51089	+	11.0009i	0.108252	+	0.474283i
$539$	−33.9439			−1.46207
$540$	1.53803	+	6.73856i	0.0661864	+	0.289981i
$541$	5.12767	−	6.42990i	0.220456	−	0.276443i	−0.659288	−	0.751890i	$-0.729142\pi$
$541$	5.12767	−	6.42990i	0.220456	−	0.276443i	0.879744	+	0.475447i	$0.157714\pi$
$542$	−0.119178	+	0.522153i	−0.00511913	+	0.0224284i
$543$	3.51693	−	15.4087i	0.150926	−	0.661249i
$544$	−13.0368	−	16.3477i	−0.558950	−	0.700901i
$545$	−3.40850	−	1.64145i	−0.146004	−	0.0703119i
$546$	1.00873	−	0.485778i	0.0431696	−	0.0207894i
$547$	16.1253	−	20.2205i	0.689467	−	0.864564i	−0.306721	−	0.951800i	$-0.599232\pi$
$547$	16.1253	−	20.2205i	0.689467	−	0.864564i	0.996188	+	0.0872352i	$0.0278032\pi$
$548$	−19.3605	−	24.2774i	−0.827041	−	1.03708i
$549$	−2.13922	+	1.03019i	−0.0912997	+	0.0439676i
$550$	9.93767			0.423744
$551$	4.29321	−	11.9441i	0.182897	−	0.508837i
$552$	−4.84415			−0.206181
$553$	1.50000	−	0.722362i	0.0637865	−	0.0307180i
$554$	−2.95928	−	3.71082i	−0.125728	−	0.157658i
$555$	2.65734	−	3.33220i	0.112798	−	0.141444i
$556$	−27.0601	+	13.0315i	−1.14760	+	0.552657i
$557$	−20.7310	−	9.98353i	−0.878401	−	0.423016i	−0.0603609	−	0.998177i	$-0.519225\pi$
$557$	−20.7310	−	9.98353i	−0.878401	−	0.423016i	−0.818040	+	0.575161i	$0.804939\pi$
$558$	−2.68329	−	3.36474i	−0.113593	−	0.142441i
$559$	−4.28405	+	18.7697i	−0.181196	+	0.793872i
$560$	−0.156678	+	0.686450i	−0.00662084	+	0.0290078i
$561$	−17.2567	+	21.6392i	−0.728577	+	0.913607i
$562$	−1.61218	−	7.06341i	−0.0680056	−	0.297952i
$563$	43.1159			1.81712			0.908559	−	0.417757i	$-0.137184\pi$
$563$	43.1159			1.81712			0.908559	+	0.417757i	$0.137184\pi$
$564$	3.22252	+	14.1188i	0.135693	+	0.594508i
$565$	6.65548	+	3.20511i	0.279998	+	0.134840i
$566$	−2.10388	−	1.01317i	−0.0884325	−	0.0425868i
$567$	0.204636	+	0.896567i	0.00859388	+	0.0376523i
$568$	−12.4112			−0.520762
$569$	5.40999	+	23.7027i	0.226799	+	0.993670i	0.952231	+	0.305377i	$0.0987825\pi$
$569$	5.40999	+	23.7027i	0.226799	+	0.993670i	−0.725433	+	0.688293i	$0.758360\pi$
$570$	−0.564351	+	0.707674i	−0.0236381	+	0.0296412i
$571$	−4.11410	+	18.0250i	−0.172170	+	0.754324i	0.812933	+	0.582357i	$0.197869\pi$
$571$	−4.11410	+	18.0250i	−0.172170	+	0.754324i	−0.985103	+	0.171967i	$0.944988\pi$
$572$	−11.1947	+	49.0472i	−0.468074	+	2.05077i
$573$	8.29590	+	10.4027i	0.346566	+	0.434580i
$574$	0.445042	+	0.214321i	0.0185757	+	0.00894558i
$575$	9.35205	−	4.50371i	0.390008	−	0.187818i
$576$	3.27144	−	4.10225i	0.136310	−	0.170927i
$577$	−23.6042	−	29.5987i	−0.982654	−	1.23221i	−0.972654	−	0.232260i	$-0.925388\pi$
$577$	−23.6042	−	29.5987i	−0.982654	−	1.23221i	−0.0100007	−	0.999950i	$-0.503183\pi$
$578$	1.28136	−	0.617072i	0.0532977	−	0.0256668i
$579$	−28.3424			−1.17787
$580$	0.695374	+	6.67909i	0.0288738	+	0.277334i
$581$	1.58987			0.0659591
$582$	0.0903019	−	0.0434871i	0.00374314	−	0.00180260i
$583$	−14.4487	−	18.1181i	−0.598404	−	0.750374i
$584$	5.93482	−	7.44203i	0.245585	−	0.307953i
$585$	−5.09299	+	2.45265i	−0.210569	+	0.101405i
$586$	2.71206	+	1.30606i	0.112034	+	0.0539529i
$587$	−9.00030	−	11.2860i	−0.371482	−	0.465824i	0.560592	−	0.828092i	$-0.310574\pi$
$587$	−9.00030	−	11.2860i	−0.371482	−	0.465824i	−0.932074	+	0.362269i	$0.882002\pi$
$588$	3.43631	−	15.0555i	0.141711	−	0.620877i
$589$	−3.50969	+	15.3770i	−0.144614	+	0.633596i
$590$	2.39911	−	3.00839i	0.0987697	−	0.123853i
$591$	−5.42692	−	23.7769i	−0.223234	−	0.978050i
$592$	−14.0804			−0.578700
$593$	2.89320	+	12.6759i	0.118809	+	0.520538i	0.998950	+	0.0458241i	$0.0145914\pi$
$593$	2.89320	+	12.6759i	0.118809	+	0.520538i	−0.880140	+	0.474714i	$0.842551\pi$
$594$	10.9770	+	5.28626i	0.450393	+	0.216898i
$595$	−1.00000	−	0.481575i	−0.0409960	−	0.0197426i
$596$	7.46077	+	32.6878i	0.305605	+	1.33894i
$597$	1.09113			0.0446570
$598$	−1.28525	−	5.63104i	−0.0525577	−	0.230270i
$599$	7.54019	−	9.45510i	0.308084	−	0.386325i	−0.603552	−	0.797323i	$-0.706249\pi$
$599$	7.54019	−	9.45510i	0.308084	−	0.386325i	0.911636	+	0.410999i	$0.134820\pi$
$600$	−2.12266	+	9.29999i	−0.0866573	+	0.379670i
$601$	4.97272	−	21.7869i	0.202842	−	0.888707i	−0.766355	−	0.642418i	$-0.777932\pi$
$601$	4.97272	−	21.7869i	0.202842	−	0.888707i	0.969196	−	0.246289i	$-0.0792113\pi$
$602$	0.337282	+	0.422938i	0.0137466	+	0.0172377i
$603$	−3.02446	−	1.45650i	−0.123165	−	0.0593134i
$604$	−12.2213	+	5.88548i	−0.497279	+	0.239477i
$605$	5.77897	−	7.24660i	0.234949	−	0.294616i
$606$	1.11745	+	1.40124i	0.0453933	+	0.0569214i
$607$	−37.3620	+	17.9926i	−1.51648	+	0.730297i	−0.992593	−	0.121491i	$-0.961232\pi$
$607$	−37.3620	+	17.9926i	−1.51648	+	0.730297i	−0.523886	+	0.851789i	$0.675518\pi$
$608$	10.9661			0.444736
$609$	0.248176	+	2.38374i	0.0100566	+	0.0965940i
$610$	0.506041			0.0204890
$611$	−32.8245	+	15.8075i	−1.32794	+	0.639502i
$612$	7.29590	+	9.14877i	0.294919	+	0.369817i
$613$	16.0764	−	20.1591i	0.649318	−	0.814219i	−0.342816	−	0.939403i	$-0.611381\pi$
$613$	16.0764	−	20.1591i	0.649318	−	0.814219i	0.992134	+	0.125184i	$0.0399520\pi$
$614$	1.81163	−	0.872433i	0.0731113	−	0.0352085i
$615$	2.41789	+	1.16440i	0.0974989	+	0.0469530i
$616$	1.85958	+	2.33184i	0.0749248	+	0.0939527i
$617$	−1.97272	+	8.64306i	−0.0794188	+	0.347956i	−0.998988	−	0.0449710i	$-0.985680\pi$
$617$	−1.97272	+	8.64306i	−0.0794188	+	0.347956i	0.919570	+	0.392927i	$0.128538\pi$
$618$	1.68598	−	7.38676i	0.0678201	−	0.297139i
$619$	18.3626	−	23.0259i	0.738054	−	0.925490i	−0.261153	−	0.965297i	$-0.584103\pi$
$619$	18.3626	−	23.0259i	0.738054	−	0.925490i	0.999207	+	0.0398069i	$0.0126743\pi$
$620$	−1.85690	−	8.13559i	−0.0745747	−	0.326733i
$621$	12.7259			0.510672
$622$	−1.24943	−	5.47412i	−0.0500976	−	0.219492i
$623$	1.82640	+	0.879546i	0.0731730	+	0.0352383i
$624$	−18.1054	−	8.71909i	−0.724795	−	0.349043i
$625$	−4.01560	−	17.5935i	−0.160624	−	0.703739i
$626$	−8.56273			−0.342235
$627$	−3.23005	−	14.1518i	−0.128996	−	0.565168i
$628$	20.4916	−	25.6956i	0.817703	−	1.02537i
$629$	4.93900	−	21.6392i	0.196931	−	0.862811i
$630$	−0.0353438	+	0.154851i	−0.00140813	+	0.00616942i
$631$	14.8210	+	18.5850i	0.590015	+	0.739856i	0.983785	−	0.179353i	$-0.0574005\pi$
$631$	14.8210	+	18.5850i	0.590015	+	0.739856i	−0.393769	+	0.919209i	$0.628829\pi$
$632$	7.11141	+	3.42467i	0.282877	+	0.136226i
$633$	−20.5248	+	9.88420i	−0.815786	+	0.392862i
$634$	−0.795897	+	0.998023i	−0.0316091	+	0.0396366i
$635$	−0.447362	−	0.560974i	−0.0177530	−	0.0222616i
$636$	9.49880	−	4.57438i	0.376652	−	0.181386i
$637$	38.8495			1.53927
$638$	9.96897	+	6.38220i	0.394675	+	0.252674i
$639$	10.5996			0.419312
$640$	−6.80947	+	3.27927i	−0.269168	+	0.129624i
$641$	17.7479	+	22.2552i	0.701001	+	0.879028i	0.997098	−	0.0761300i	$-0.0242564\pi$
$641$	17.7479	+	22.2552i	0.701001	+	0.879028i	−0.296096	+	0.955158i	$0.595685\pi$
$642$	5.62080	−	7.04826i	0.221835	−	0.278173i
$643$	17.4308	−	8.39423i	0.687404	−	0.331036i	−0.0573702	−	0.998353i	$-0.518272\pi$
$643$	17.4308	−	8.39423i	0.687404	−	0.331036i	0.744774	+	0.667317i	$0.232557\pi$
$644$	1.33028	+	0.640630i	0.0524204	+	0.0252443i
$645$	1.83244	+	2.29780i	0.0721521	+	0.0904759i
$646$	−1.04892	+	4.59561i	−0.0412691	+	0.180812i
$647$	−5.05443	+	22.1449i	−0.198710	+	0.870605i	0.772996	+	0.634411i	$0.218757\pi$
$647$	−5.05443	+	22.1449i	−0.198710	+	0.870605i	−0.971706	+	0.236194i	$0.924100\pi$
$648$	−2.71834	+	3.40869i	−0.106787	+	0.133906i
$649$	13.7313	+	60.1605i	0.538999	+	2.36151i
$650$	−11.3739			−0.446120
$651$	−0.662718	−	2.90356i	−0.0259740	−	0.113799i
$652$	20.5221	+	9.88291i	0.803706	+	0.387044i
$653$	−20.6603	−	9.94949i	−0.808501	−	0.389354i	−0.0164928	−	0.999864i	$-0.505250\pi$
$653$	−20.6603	−	9.94949i	−0.808501	−	0.389354i	−0.792008	+	0.610510i	$0.790964\pi$
$654$	−0.675096	−	2.95779i	−0.0263983	−	0.115659i
$655$	5.55124			0.216905
$656$	−1.97285	−	8.64363i	−0.0770270	−	0.337477i
$657$	−5.06853	+	6.35574i	−0.197742	+	0.247961i
$658$	−0.227792	+	0.998023i	−0.00888027	+	0.0389070i
$659$	4.26755	−	18.6974i	0.166240	−	0.728346i	−0.821237	−	0.570587i	$-0.806716\pi$
$659$	4.26755	−	18.6974i	0.166240	−	0.728346i	0.987478	−	0.157759i	$-0.0504271\pi$
$660$	4.78836	+	6.00442i	0.186387	+	0.233722i
$661$	3.05107	+	1.46932i	0.118673	+	0.0571499i	0.492278	−	0.870438i	$-0.336164\pi$
$661$	3.05107	+	1.46932i	0.118673	+	0.0571499i	−0.373605	+	0.927588i	$0.621879\pi$
$662$	1.25667	−	0.605180i	0.0488418	−	0.0235210i
$663$	19.7506	−	24.7665i	0.767051	−	0.961851i
$664$	4.69955	+	5.89305i	0.182378	+	0.228695i
$665$	0.524459	−	0.252566i	0.0203376	−	0.00979409i
$666$	−3.17629			−0.123079
$667$	12.2739	+	1.48821i	0.475247	+	0.0576238i
$668$	1.43535			0.0555355
$669$	−2.04288	+	0.983797i	−0.0789822	+	0.0380358i
$670$	0.446074	+	0.559360i	0.0172334	+	0.0216099i
$671$	−5.05980	+	6.34479i	−0.195332	+	0.244938i
$672$	−1.86563	+	0.898438i	−0.0719680	+	0.0346580i
$673$	−4.29805	−	2.06983i	−0.165678	−	0.0797862i	0.349207	−	0.937046i	$-0.386451\pi$
$673$	−4.29805	−	2.06983i	−0.165678	−	0.0797862i	−0.514885	+	0.857259i	$0.672165\pi$
$674$	−1.38255	−	1.73366i	−0.0532539	−	0.0667782i
$675$	5.57636	−	24.4316i	0.214634	−	0.940374i
$676$	7.59999	−	33.2977i	0.292307	−	1.28068i
$677$	−26.8662	+	33.6892i	−1.03255	+	1.29478i	−0.0779309	+	0.996959i	$0.524831\pi$
$677$	−26.8662	+	33.6892i	−1.03255	+	1.29478i	−0.954622	+	0.297821i	$0.903740\pi$
$678$	1.31820	+	5.77541i	0.0506252	+	0.221803i
$679$	−0.0644568			−0.00247362
$680$	−1.17092	−	5.13011i	−0.0449025	−	0.196731i
$681$	−15.5673	−	7.49683i	−0.596542	−	0.287279i
$682$	−13.2528	−	6.38220i	−0.507475	−	0.244387i
$683$	−5.21432	−	22.8454i	−0.199521	−	0.874157i	−0.971223	−	0.238173i	$-0.923452\pi$
$683$	−5.21432	−	22.8454i	−0.199521	−	0.874157i	0.771702	−	0.635984i	$-0.219406\pi$
$684$	−6.13706			−0.234656
$685$	−2.65362	−	11.6263i	−0.101390	−	0.444217i
$686$	1.37382	−	1.72272i	0.0524528	−	0.0657737i
$687$	−3.54407	+	15.5276i	−0.135215	+	0.592415i
$688$	2.16056	−	9.46604i	0.0823707	−	0.360890i
$689$	16.5368	+	20.7365i	0.630003	+	0.789999i
$690$	−0.794405	−	0.382565i	−0.0302425	−	0.0145640i
$691$	−38.8657	+	18.7167i	−1.47852	+	0.712018i	−0.987278	−	0.159005i	$-0.949171\pi$
$691$	−38.8657	+	18.7167i	−1.47852	+	0.712018i	−0.491243	+	0.871023i	$0.663457\pi$
$692$	10.2838	−	12.8955i	0.390932	−	0.490213i
$693$	−1.58815	−	1.99147i	−0.0603287	−	0.0756498i
$694$	8.06638	−	3.88456i	0.306195	−	0.147456i
$695$	−11.5345			−0.437529
$696$	−8.10202	+	7.96605i	−0.307106	+	0.301952i
$697$	13.9758			0.529373
$698$	8.21552	−	3.95639i	0.310962	−	0.149751i
$699$	6.89307	+	8.64363i	0.260720	+	0.326932i
$700$	1.81282	−	2.27321i	0.0685183	−	0.0859192i
$701$	−3.81186	+	1.83570i	−0.143972	+	0.0693333i	−0.504483	−	0.863422i	$-0.668317\pi$
$701$	−3.81186	+	1.83570i	−0.143972	+	0.0693333i	0.360511	+	0.932755i	$0.382602\pi$
$702$	−12.5635	−	6.05024i	−0.474177	−	0.228352i
$703$	7.25786	+	9.10107i	0.273736	+	0.343254i
$704$	3.99061	−	17.4840i	0.150402	−	0.658953i
$705$	−1.23759	+	5.42222i	−0.0466102	+	0.204213i
$706$	−4.99396	+	6.26223i	−0.187950	+	0.235682i
$707$	−0.256478	−	1.12370i	−0.00964586	−	0.0422613i
$708$	−28.0737			−1.05507
$709$	−3.18287	−	13.9450i	−0.119535	−	0.523717i	−0.998871	−	0.0475144i	$-0.984870\pi$
$709$	−3.18287	−	13.9450i	−0.119535	−	0.523717i	0.879336	−	0.476203i	$-0.157987\pi$
$710$	−2.03534	−	0.980170i	−0.0763851	−	0.0367851i
$711$	−6.07338	−	2.92478i	−0.227769	−	0.109688i
$712$	2.13856	+	9.36962i	0.0801457	+	0.351141i
$713$	−15.3642			−0.575393
$714$	−0.198062	−	0.867767i	−0.00741229	−	0.0324754i
$715$	−12.0462	+	15.1055i	−0.450503	+	0.564913i
$716$	1.36563	−	5.98319i	0.0510358	−	0.223602i
$717$	−7.09365	+	31.0793i	−0.264917	+	1.16068i
$718$	−6.55645	−	8.22153i	−0.244685	−	0.306825i
$719$	21.1194	+	10.1706i	0.787620	+	0.379298i	0.784051	−	0.620696i	$-0.213150\pi$
$719$	21.1194	+	10.1706i	0.787620	+	0.379298i	0.00356825	+	0.999994i	$0.498864\pi$
$720$	2.56853	−	1.23694i	0.0957235	−	0.0460980i
$721$	−3.03803	+	3.80957i	−0.113142	+	0.141876i
$722$	3.73072	+	4.67817i	0.138843	+	0.174104i
$723$	10.9330	−	5.26504i	0.406601	−	0.195809i
$724$	−22.8388			−0.848796
$725$	8.23543	−	22.9118i	0.305856	−	0.850922i
$726$	7.43296			0.275863
$727$	−46.8482	+	22.5609i	−1.73750	+	0.836738i	−0.753763	+	0.657146i	$0.771763\pi$
$727$	−46.8482	+	22.5609i	−1.73750	+	0.836738i	−0.983741	+	0.179592i	$0.942522\pi$
$728$	−2.12833	−	2.66885i	−0.0788813	−	0.0989140i
$729$	15.2500	−	19.1228i	0.564813	−	0.708254i
$730$	1.56100	−	0.751737i	0.0577752	−	0.0278231i
$731$	13.7899	+	6.64084i	0.510036	+	0.245621i
$732$	−2.30194	−	2.88654i	−0.0850821	−	0.106690i
$733$	−7.60806	+	33.3331i	−0.281010	+	1.23119i	0.615491	+	0.788144i	$0.288958\pi$
$733$	−7.60806	+	33.3331i	−0.281010	+	1.23119i	−0.896501	+	0.443041i	$0.853899\pi$
$734$	−2.93559	+	12.8617i	−0.108355	+	0.474733i
$735$	3.69769	−	4.63676i	0.136391	−	0.171030i
$736$	2.37704	+	10.4145i	0.0876190	+	0.383884i
$737$	−11.4735			−0.422632
$738$	−0.445042	−	1.94986i	−0.0163822	−	0.0717752i
$739$	−35.8342	−	17.2569i	−1.31818	−	0.634804i	−0.363269	−	0.931684i	$-0.618339\pi$
$739$	−35.8342	−	17.2569i	−1.31818	−	0.634804i	−0.954915	+	0.296881i	$0.904054\pi$
$740$	−5.54892	−	2.67222i	−0.203982	−	0.0982327i
$741$	3.69687	+	16.1970i	0.135808	+	0.595013i
$742$	0.745251			0.0273590
$743$	−1.59730	−	6.99824i	−0.0585993	−	0.256740i	0.937140	−	0.348954i	$-0.113463\pi$
$743$	−1.59730	−	6.99824i	−0.0585993	−	0.256740i	−0.995739	+	0.0922133i	$0.970606\pi$
$744$	8.80343	−	11.0392i	0.322749	−	0.404715i
$745$	−2.86526	+	12.5535i	−0.104975	+	0.459925i
$746$	−2.49439	+	10.9286i	−0.0913260	+	0.400125i
$747$	−4.01357	−	5.03286i	−0.146849	−	0.184143i
$748$	36.0344	+	17.3533i	1.31755	+	0.634499i
$749$	−5.22348	+	2.51550i	−0.190862	+	0.0919142i
$750$	−2.27980	+	2.85878i	−0.0832465	+	0.104388i
$751$	−16.9393	−	21.2412i	−0.618124	−	0.775103i	0.369955	−	0.929050i	$-0.379373\pi$
$751$	−16.9393	−	21.2412i	−0.618124	−	0.775103i	−0.988079	+	0.153947i	$0.950802\pi$
$752$	16.5543	−	7.97213i	0.603673	−	0.290714i
$753$	12.1709			0.443533
$754$	−11.4097	−	7.30457i	−0.415517	−	0.266017i
$755$	−5.20941			−0.189590
$756$	3.21164	−	1.54664i	0.116806	−	0.0562508i
$757$	14.7721	+	18.5236i	0.536901	+	0.673253i	0.974101	−	0.226111i	$-0.0726013\pi$
$757$	14.7721	+	18.5236i	0.536901	+	0.673253i	−0.437200	+	0.899364i	$0.644030\pi$
$758$	7.46615	−	9.36225i	0.271183	−	0.340052i
$759$	12.7397	−	6.13514i	0.462423	−	0.222691i
$760$	2.48643	+	1.19740i	0.0901922	+	0.0434343i
$761$	−8.88740	−	11.1444i	−0.322168	−	0.403986i	0.594204	−	0.804315i	$-0.297467\pi$
$761$	−8.88740	−	11.1444i	−0.322168	−	0.403986i	−0.916372	+	0.400329i	$0.868896\pi$
$762$	0.128039	−	0.560974i	0.00463835	−	0.0203219i
$763$	−0.434157	+	1.90216i	−0.0157175	+	0.0688630i
$764$	11.9879	−	15.0324i	0.433708	−	0.543852i
$765$	1.00000	+	4.38129i	0.0361551	+	0.158406i
$766$	8.75361			0.316281
$767$	−15.7157	−	68.8550i	−0.567461	−	2.48621i
$768$	2.69806	+	1.29932i	0.0973579	+	0.0468851i
$769$	40.2793	+	19.3975i	1.45251	+	0.699491i	0.983029	−	0.183453i	$-0.0587275\pi$
$769$	40.2793	+	19.3975i	1.45251	+	0.699491i	0.469479	+	0.882944i	$0.344442\pi$
$770$	0.120801	+	0.529265i	0.00435338	+	0.0190734i
$771$	−20.3967			−0.734570
$772$	9.11356	+	39.9291i	0.328004	+	1.43708i
$773$	14.3083	−	17.9420i	0.514633	−	0.645329i	−0.454827	−	0.890580i	$-0.650299\pi$
$773$	14.3083	−	17.9420i	0.514633	−	0.645329i	0.969460	+	0.245251i	$0.0788703\pi$
$774$	0.487386	−	2.13538i	0.0175187	−	0.0767546i
$775$	−6.73245	+	29.4968i	−0.241837	+	1.05956i
$776$	−0.190530	−	0.238916i	−0.00683961	−	0.00857660i
$777$	−1.98039	−	0.953703i	−0.0710459	−	0.0342139i
$778$	9.96615	−	4.79944i	0.357304	−	0.172068i
$779$	−4.57002	+	5.73063i	−0.163738	+	0.205321i
$780$	−5.48039	−	6.87219i	−0.196229	−	0.246064i
$781$	32.6405	−	15.7188i	1.16797	−	0.562464i
$782$	−4.59179			−0.164202
$783$	21.2845	−	20.9273i	0.760645	−	0.747881i
$784$	−19.5929			−0.699745
$785$	11.3720	−	5.47645i	0.405883	−	0.195463i
$786$	2.77562	+	3.48052i	0.0990030	+	0.124146i
$787$	8.93631	−	11.2058i	0.318545	−	0.399443i	−0.596619	−	0.802525i	$-0.703490\pi$
$787$	8.93631	−	11.2058i	0.318545	−	0.399443i	0.915164	+	0.403082i	$0.132061\pi$
$788$	−31.7521	+	15.2910i	−1.13112	+	0.544720i
$789$	26.6531	+	12.8355i	0.948875	+	0.456954i
$790$	0.895756	+	1.12324i	0.0318696	+	0.0399632i
$791$	0.847740	−	3.71419i	0.0301422	−	0.132061i
$792$	2.68718	−	11.7733i	0.0954847	−	0.418346i
$793$	5.79105	−	7.26175i	0.205646	−	0.257872i
$794$	−0.395592	−	1.73320i	−0.0140390	−	0.0615090i
$795$	4.04892			0.143600
$796$	−0.350855	−	1.53720i	−0.0124357	−	0.0544845i
$797$	−9.18382	−	4.42270i	−0.325308	−	0.156660i	0.264101	−	0.964495i	$-0.414925\pi$
$797$	−9.18382	−	4.42270i	−0.325308	−	0.156660i	−0.589409	+	0.807835i	$0.700639\pi$
$798$	0.420583	+	0.202542i	0.0148885	+	0.00716992i
$799$	6.44504	+	28.2376i	0.228009	+	0.998974i
$800$	21.0358			0.743727
$801$	−1.82640	−	8.00197i	−0.0645325	−	0.282736i
$802$	6.91119	−	8.66636i	0.244043	−	0.306020i
$803$	−6.18276	+	27.0884i	−0.218185	+	0.955930i
$804$	1.16152	−	5.08896i	0.0409637	−	0.179474i
$805$	0.353543	+	0.443330i	0.0124608	+	0.0156253i
$806$	15.1681	+	7.30457i	0.534273	+	0.257292i
$807$	28.4855	−	13.7179i	1.00274	−	0.482893i
$808$	3.40701	−	4.27225i	0.119858	−	0.150297i
$809$	5.59448	+	7.01526i	0.196692	+	0.246643i	0.870390	−	0.492363i	$-0.163867\pi$
$809$	5.59448	+	7.01526i	0.196692	+	0.246643i	−0.673698	+	0.739006i	$0.735295\pi$
$810$	−0.714988	+	0.344320i	−0.0251221	+	0.0120982i
$811$	−28.5628			−1.00298			−0.501489	−	0.865164i	$-0.667214\pi$
$811$	−28.5628			−1.00298			−0.501489	+	0.865164i	$0.667214\pi$
$812$	3.27844	−	1.11613i	0.115051	−	0.0391685i
$813$	1.50066			0.0526306
$814$	−9.78113	+	4.71034i	−0.342828	+	0.165097i
$815$	5.45407	+	6.83918i	0.191048	+	0.239566i
$816$	−9.96077	+	12.4904i	−0.348697	+	0.437252i
$817$	−7.23221	+	3.48285i	−0.253023	+	0.121849i
$818$	0.113564	+	0.0546896i	0.00397068	+	0.00191218i
$819$	1.81767	+	2.27928i	0.0635144	+	0.0796446i
$820$	0.862937	−	3.78077i	0.0301351	−	0.132030i
$821$	−2.52230	+	11.0509i	−0.0880290	+	0.385680i	−0.999680	−	0.0252844i	$-0.991951\pi$
$821$	−2.52230	+	11.0509i	−0.0880290	+	0.385680i	0.911651	+	0.410965i	$0.134808\pi$
$822$	5.96263	−	7.47690i	0.207971	−	0.260787i
$823$	−1.26218	−	5.52996i	−0.0439967	−	0.192762i	0.948154	−	0.317812i	$-0.102948\pi$
$823$	−1.26218	−	5.52996i	−0.0439967	−	0.192762i	−0.992150	+	0.125050i	$0.960091\pi$
$824$	−23.1008			−0.804755
$825$	−6.19604	−	27.1466i	−0.215718	−	0.945124i
$826$	−1.78794	−	0.861025i	−0.0622103	−	0.0299589i
$827$	2.61572	+	1.25966i	0.0909575	+	0.0438028i	0.478809	−	0.877919i	$-0.341069\pi$
$827$	2.61572	+	1.25966i	0.0909575	+	0.0438028i	−0.387852	+	0.921722i	$0.626783\pi$
$828$	−1.33028	−	5.82834i	−0.0462305	−	0.202549i
$829$	−45.2137			−1.57034			−0.785169	−	0.619282i	$-0.787424\pi$
$829$	−45.2137			−1.57034			−0.785169	+	0.619282i	$0.787424\pi$
$830$	0.305290	+	1.33756i	0.0105968	+	0.0464275i
$831$	−8.29172	+	10.3975i	−0.287636	+	0.360685i
$832$	−4.56734	+	20.0108i	−0.158344	+	0.693750i
$833$	6.87263	−	30.1109i	0.238122	−	1.04328i
$834$	−5.76726	−	7.23191i	−0.199704	−	0.250421i
$835$	0.496648	+	0.239173i	0.0171872	+	0.00827692i
$836$	−18.8986	+	9.10107i	−0.653621	+	0.314767i
$837$	−23.1271	+	29.0005i	−0.799391	+	1.00240i
$838$	7.35003	+	9.21664i	0.253902	+	0.318384i
$839$	41.1073	−	19.7962i	1.41918	−	0.683442i	0.442229	−	0.896902i	$-0.354188\pi$
$839$	41.1073	−	19.7962i	1.41918	−	0.683442i	0.976952	+	0.213460i	$0.0684734\pi$
$840$	−0.521106			−0.0179799
$841$	22.9758	−	17.6949i	0.792270	−	0.610170i
$842$	7.82477			0.269659
$843$	−18.2899	+	8.80793i	−0.629936	+	0.303361i
$844$	20.5248	+	25.7372i	0.706491	+	0.885912i
$845$	8.17808	−	10.2550i	0.281334	−	0.352782i
$846$	3.73437	−	1.79838i	0.128390	−	0.0618294i
$847$	−4.30678	−	2.07404i	−0.147983	−	0.0712648i
$848$	−8.33997	−	10.4580i	−0.286396	−	0.359129i
$849$	−1.45593	+	6.37883i	−0.0499673	+	0.218921i
$850$	−2.01208	+	8.81551i	−0.0690138	+	0.302369i
$851$	−7.07002	+	8.86553i	−0.242357	+	0.303906i
$852$	3.66756	+	16.0686i	0.125649	+	0.550503i
$853$	−36.9288			−1.26442			−0.632210	−	0.774797i	$-0.717852\pi$
$853$	−36.9288			−1.26442			−0.632210	+	0.774797i	$0.717852\pi$
$854$	−0.0580735	−	0.254437i	−0.00198724	−	0.00870665i
$855$	−2.12349	−	1.02262i	−0.0726218	−	0.0349728i
$856$	−24.7642	−	11.9258i	−0.846423	−	0.407616i
$857$	−7.91066	−	34.6589i	−0.270223	−	1.18392i	−0.909750	−	0.415156i	$-0.863727\pi$
$857$	−7.91066	−	34.6589i	−0.270223	−	1.18392i	0.639527	−	0.768768i	$-0.279130\pi$
$858$	−15.4940			−0.528955
$859$	−9.43070	−	41.3186i	−0.321771	−	1.40977i	−0.834399	−	0.551161i	$-0.814185\pi$
$859$	−9.43070	−	41.3186i	−0.321771	−	1.40977i	0.512628	−	0.858611i	$-0.328672\pi$
$860$	2.64795	−	3.32042i	0.0902943	−	0.113225i
$861$	0.307979	−	1.34934i	0.0104959	−	0.0459855i
$862$	−2.75259	+	12.0599i	−0.0937537	+	0.410762i
$863$	31.0371	+	38.9193i	1.05652	+	1.32483i	0.943550	+	0.331231i	$0.107464\pi$
$863$	31.0371	+	38.9193i	1.05652	+	1.32483i	0.112966	+	0.993599i	$0.463965\pi$
$864$	23.2359	+	11.1898i	0.790500	+	0.380685i
$865$	5.70709	−	2.74839i	0.194047	−	0.0934480i
$866$	−1.63036	+	2.04440i	−0.0554018	+	0.0694717i
$867$	−2.48457	−	3.11555i	−0.0843803	−	0.105810i
$868$	−3.87747	+	1.86729i	−0.131610	+	0.0633800i
$869$	−23.0398			−0.781572
$870$	−1.95779	+	0.666520i	−0.0663752	+	0.0225971i
$871$	13.1317			0.444950
$872$	−8.33393	+	4.01341i	−0.282222	+	0.135911i
$873$	0.162718	+	0.204042i	0.00550719	+	0.00690579i
$874$	1.50149	−	1.88281i	0.0507887	−	0.0636870i
$875$	2.11865	−	1.02029i	0.0716233	−	0.0344920i
$876$	−11.3889	−	5.48460i	−0.384795	−	0.185307i
$877$	13.6501	+	17.1167i	0.460931	+	0.577990i	0.956925	−	0.290337i	$-0.0937674\pi$
$877$	13.6501	+	17.1167i	0.460931	+	0.577990i	−0.495993	+	0.868326i	$0.665196\pi$
$878$	−1.55884	+	6.82974i	−0.0526084	+	0.230492i
$879$	1.87681	−	8.22282i	0.0633031	−	0.277349i
$880$	6.07524	−	7.61811i	0.204796	−	0.256806i
$881$	7.46130	+	32.6901i	0.251378	+	1.10136i	0.930199	+	0.367055i	$0.119634\pi$
$881$	7.46130	+	32.6901i	0.251378	+	1.10136i	−0.678822	+	0.734303i	$0.737509\pi$
$882$	−4.41981			−0.148823
$883$	3.58868	+	15.7230i	0.120769	+	0.529122i	0.998730	+	0.0503898i	$0.0160464\pi$
$883$	3.58868	+	15.7230i	0.120769	+	0.529122i	−0.877961	+	0.478732i	$0.841096\pi$
$884$	−41.2422	−	19.8612i	−1.38713	−	0.668004i
$885$	−9.71379	−	4.67792i	−0.326526	−	0.157246i
$886$	0.667326	+	2.92375i	0.0224192	+	0.0982252i
$887$	52.7391			1.77081			0.885403	−	0.464823i	$-0.153882\pi$
$887$	52.7391			1.77081			0.885403	+	0.464823i	$0.153882\pi$
$888$	−2.31886	−	10.1596i	−0.0778160	−	0.340934i
$889$	−0.230718	+	0.289311i	−0.00773802	+	0.00970317i
$890$	−0.389256	+	1.70544i	−0.0130479	+	0.0571665i
$891$	2.83190	−	12.4074i	0.0948724	−	0.415663i
$892$	2.04288	+	2.56169i	0.0684006	+	0.0857716i
$893$	−13.6860	−	6.59082i	−0.457984	−	0.220553i
$894$	−9.30343	+	4.48030i	−0.311153	+	0.149844i
$895$	1.46950	−	1.84270i	0.0491200	−	0.0615945i
$896$	2.43027	+	3.04746i	0.0811897	+	0.101809i
$897$	−14.5809	+	7.02180i	−0.486842	+	0.234451i
$898$	−5.48294			−0.182968
$899$	−25.6972	+	25.2659i	−0.857048	+	0.842666i
$900$	−11.7724			−0.392413
$901$	18.9976	−	9.14877i	0.632902	−	0.304790i
$902$	−4.26205	−	5.34444i	−0.141911	−	0.177950i
$903$	0.945042	−	1.18505i	0.0314490	−	0.0394358i
$904$	16.2729	−	7.83663i	0.541230	−	0.260642i
$905$	−7.90246	−	3.80562i	−0.262687	−	0.126503i
$906$	−2.60470	−	3.26619i	−0.0865355	−	0.108512i
$907$	6.64084	−	29.0954i	0.220506	−	0.966098i	−0.736593	−	0.676336i	$-0.763567\pi$
$907$	6.64084	−	29.0954i	0.220506	−	0.966098i	0.957099	−	0.289762i	$-0.0935761\pi$
$908$	−5.55592	+	24.3421i	−0.184380	+	0.807820i
$909$	−2.90970	+	3.64865i	−0.0965086	+	0.121018i
$910$	−0.138260	−	0.605756i	−0.00458327	−	0.0200806i
$911$	−9.34050			−0.309465			−0.154732	−	0.987956i	$-0.549452\pi$
$911$	−9.34050			−0.309465			−0.154732	+	0.987956i	$0.549452\pi$
$912$	−1.86443	−	8.16860i	−0.0617374	−	0.270489i
$913$	−19.8230	−	9.54627i	−0.656047	−	0.315936i
$914$	5.47823	+	2.63818i	0.181204	+	0.0872631i
$915$	−0.315511	−	1.38235i	−0.0104305	−	0.0456989i
$916$	23.0151			0.760439
$917$	−0.637063	−	2.79116i	−0.0210377	−	0.0921721i
$918$	−6.91185	+	8.66719i	−0.228125	+	0.286060i
$919$	4.09903	−	17.9590i	0.135215	−	0.592414i	−0.861234	−	0.508209i	$-0.830308\pi$
$919$	4.09903	−	17.9590i	0.135215	−	0.592414i	0.996448	−	0.0842049i	$-0.0268350\pi$
$920$	−0.598203	+	2.62090i	−0.0197222	+	0.0864085i
$921$	−3.51275	−	4.40484i	−0.115749	−	0.145145i
$922$	4.65452	+	2.24150i	0.153289	+	0.0738199i
$923$	−37.3577	+	17.9905i	−1.22964	+	0.592166i
$924$	2.46950	−	3.09666i	0.0812406	−	0.101872i
$925$	13.9224	+	17.4581i	0.457765	+	0.574019i
$926$	−2.90408	+	1.39853i	−0.0954341	+	0.0459587i
$927$	19.7289			0.647981
$928$	21.1020	+	13.5097i	0.692708	+	0.443476i
$929$	−4.84654			−0.159010			−0.0795050	−	0.996834i	$-0.525334\pi$
$929$	−4.84654			−0.159010			−0.0795050	+	0.996834i	$0.525334\pi$
$930$	2.31551	−	1.11509i	0.0759286	−	0.0365653i
$931$	10.0993	+	12.6642i	0.330992	+	0.415051i
$932$	9.96077	−	12.4904i	0.326276	−	0.409137i
$933$	−14.1746	+	6.82611i	−0.464054	+	0.223477i
$934$	−0.827356	−	0.398434i	−0.0270719	−	0.0130371i
$935$	9.57673	+	12.0088i	0.313193	+	0.392731i
$936$	−3.07553	+	13.4748i	−0.100527	+	0.440437i
$937$	9.94989	−	43.5933i	0.325049	−	1.42413i	−0.503394	−	0.864057i	$-0.667916\pi$
$937$	9.94989	−	43.5933i	0.325049	−	1.42413i	0.828443	−	0.560074i	$-0.189227\pi$
$938$	0.230054	−	0.288478i	0.00751152	−	0.00941915i
$939$	5.33877	+	23.3907i	0.174224	+	0.763326i
$940$	8.03684			0.262133
$941$	−3.02297	−	13.2445i	−0.0985459	−	0.431758i	0.901453	−	0.432876i	$-0.142501\pi$
$941$	−3.02297	−	13.2445i	−0.0985459	−	0.431758i	−0.999999	+	0.00111821i	$0.999644\pi$
$942$	9.11960	+	4.39177i	0.297133	+	0.143092i
$943$	−6.43296	−	3.09795i	−0.209486	−	0.100883i
$944$	7.92585	+	34.7254i	0.257965	+	1.13022i
$945$	1.36898			0.0445328
$946$	−1.66583	−	7.29850i	−0.0541609	−	0.237295i
$947$	9.35958	−	11.7365i	0.304146	−	0.381387i	−0.606147	−	0.795353i	$-0.707285\pi$
$947$	9.35958	−	11.7365i	0.304146	−	0.381387i	0.910292	+	0.413966i	$0.135857\pi$
$948$	2.33244	−	10.2191i	0.0757540	−	0.331900i
$949$	7.07630	−	31.0033i	0.229706	−	1.00641i
$950$	−2.95675	−	3.70765i	−0.0959298	−	0.120292i
$951$	3.22252	+	1.55188i	0.104497	+	0.0503233i
$952$	−2.44504	+	1.17747i	−0.0792443	+	0.0381620i
$953$	32.3247	−	40.5339i	1.04710	−	1.31302i	0.0989849	−	0.995089i	$-0.468440\pi$
$953$	32.3247	−	40.5339i	1.04710	−	1.31302i	0.948114	−	0.317931i	$-0.102988\pi$
$954$	−1.88135	−	2.35914i	−0.0609111	−	0.0763801i
$955$	6.65279	−	3.20382i	0.215279	−	0.103673i
$956$	46.0659			1.48988
$957$	11.2186	−	31.2113i	0.362647	−	1.00892i
$958$	1.73078			0.0559188
$959$	−5.54115	+	2.66848i	−0.178933	+	0.0861696i
$960$	1.95361	+	2.44975i	0.0630524	+	0.0790652i
$961$	8.59365	−	10.7761i	0.277215	−	0.347616i
$962$	11.1947	−	5.39109i	0.360932	−	0.173816i
$963$	21.1494	+	10.1850i	0.681531	+	0.328208i
$964$	−10.9330	−	13.7095i	−0.352127	−	0.441553i
$965$	−3.50000	+	15.3345i	−0.112669	+	0.493635i
$966$	−0.101187	+	0.443330i	−0.00325564	+	0.0142639i
$967$	−25.9527	+	32.5437i	−0.834583	+	1.04653i	0.163615	+	0.986524i	$0.447685\pi$
$967$	−25.9527	+	32.5437i	−0.834583	+	1.04653i	−0.998198	+	0.0600094i	$0.980887\pi$
$968$	−5.04288	−	22.0943i	−0.162084	−	0.710137i
$969$	13.2078			0.424294
$970$	−0.0123771	−	0.0542276i	−0.000397404	−	0.00174114i
$971$	50.2497	+	24.1990i	1.61259	+	0.776583i	0.999906	−	0.0137446i	$-0.00437519\pi$
$971$	50.2497	+	24.1990i	1.61259	+	0.776583i	0.612685	+	0.790327i	$0.290089\pi$
$972$	−21.7799	−	10.4887i	−0.698592	−	0.336424i
$973$	1.32371	+	5.79954i	0.0424361	+	0.185925i
$974$	−4.38165			−0.140397
$975$	7.09150	+	31.0699i	0.227110	+	0.995033i
$976$	−2.92058	+	3.66230i	−0.0934856	+	0.117227i
$977$	−10.8943	+	47.7309i	−0.348538	+	1.52705i	0.431962	+	0.901892i	$0.357821\pi$
$977$	−10.8943	+	47.7309i	−0.348538	+	1.52705i	−0.780501	+	0.625155i	$0.785036\pi$
$978$	−1.56100	+	6.83918i	−0.0499152	+	0.218693i
$979$	−17.4909	−	21.9329i	−0.559012	−	0.700978i
$980$	−7.72132	−	3.71839i	−0.246649	−	0.118780i
$981$	7.11745	−	3.42758i	0.227243	−	0.109434i
$982$	−2.16189	+	2.71092i	−0.0689887	+	0.0865091i
$983$	3.22550	+	4.04466i	0.102878	+	0.129004i	0.830605	−	0.556862i	$-0.187995\pi$
$983$	3.22550	+	4.04466i	0.102878	+	0.129004i	−0.727727	+	0.685867i	$0.759423\pi$
$984$	5.91185	−	2.84700i	0.188463	−	0.0907590i
$985$	−13.5345			−0.431246
$986$	−7.67994	+	7.55106i	−0.244579	+	0.240475i
$987$	2.86831			0.0912994
$988$	21.6298	−	10.4164i	0.688136	−	0.331389i
$989$	−4.87531	−	6.11345i	−0.155026	−	0.194396i
$990$	1.37047	−	1.71851i	0.0435564	−	0.0546180i
$991$	15.1838	−	7.31214i	0.482330	−	0.232278i	−0.176886	−	0.984231i	$-0.556602\pi$
$991$	15.1838	−	7.31214i	0.482330	−	0.232278i	0.659216	+	0.751953i	$0.270888\pi$
$992$	−28.0531	−	13.5097i	−0.890687	−	0.428932i
$993$	−2.43668	−	3.05550i	−0.0773257	−	0.0969634i
$994$	−0.259251	+	1.13585i	−0.00822295	+	0.0360271i
$995$	0.134743	−	0.590349i	0.00427165	−	0.0187153i
$996$	6.24094	−	7.82589i	0.197752	−	0.247973i
$997$	−8.50245	−	37.2517i	−0.269275	−	1.17977i	−0.910858	−	0.412719i	$-0.864579\pi$
$997$	−8.50245	−	37.2517i	−0.269275	−	1.17977i	0.641583	−	0.767054i	$-0.278278\pi$
$998$	9.15239			0.289714
$999$	6.09179	+	26.6899i	0.192736	+	0.844431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.2.d.a.20.1	yes	6
3.2	odd	2		261.2.k.a.136.1		6
4.3	odd	2		464.2.u.f.49.1		6
5.2	odd	4		725.2.r.b.49.2		12
5.3	odd	4		725.2.r.b.49.1		12
5.4	even	2		725.2.l.b.426.1		6
29.2	odd	28		841.2.e.b.196.2		12
29.3	odd	28		841.2.e.c.267.2		12
29.4	even	14		841.2.a.f.1.2		3
29.5	even	14		841.2.d.a.645.1		6
29.6	even	14		841.2.d.c.778.1		6
29.7	even	7		841.2.d.b.574.1		6
29.8	odd	28		841.2.e.b.236.2		12
29.9	even	14		841.2.d.a.605.1		6
29.10	odd	28		841.2.b.c.840.3		6
29.11	odd	28		841.2.e.d.651.2		12
29.12	odd	4		841.2.e.d.270.2		12
29.13	even	14		841.2.d.d.190.1		6
29.14	odd	28		841.2.e.c.63.1		12
29.15	odd	28		841.2.e.c.63.2		12
29.16	even	7	inner	29.2.d.a.16.1	✓	6
29.17	odd	4		841.2.e.d.270.1		12
29.18	odd	28		841.2.e.d.651.1		12
29.19	odd	28		841.2.b.c.840.4		6
29.20	even	7		841.2.d.e.605.1		6
29.21	odd	28		841.2.e.b.236.1		12
29.22	even	14		841.2.d.c.574.1		6
29.23	even	7		841.2.d.b.778.1		6
29.24	even	7		841.2.d.e.645.1		6
29.25	even	7		841.2.a.e.1.2		3
29.26	odd	28		841.2.e.c.267.1		12
29.27	odd	28		841.2.e.b.196.1		12
29.28	even	2		841.2.d.d.571.1		6
87.62	odd	14		7569.2.a.p.1.2		3
87.74	odd	14		261.2.k.a.190.1		6
87.83	odd	14		7569.2.a.r.1.2		3
116.103	odd	14		464.2.u.f.161.1		6
145.74	even	14		725.2.l.b.451.1		6
145.103	odd	28		725.2.r.b.74.2		12
145.132	odd	28		725.2.r.b.74.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	29.16	even	7	inner
29.2.d.a.20.1	yes	6	1.1	even	1	trivial
261.2.k.a.136.1		6	3.2	odd	2
261.2.k.a.190.1		6	87.74	odd	14
464.2.u.f.49.1		6	4.3	odd	2
464.2.u.f.161.1		6	116.103	odd	14
725.2.l.b.426.1		6	5.4	even	2
725.2.l.b.451.1		6	145.74	even	14
725.2.r.b.49.1		12	5.3	odd	4
725.2.r.b.49.2		12	5.2	odd	4
725.2.r.b.74.1		12	145.132	odd	28
725.2.r.b.74.2		12	145.103	odd	28
841.2.a.e.1.2		3	29.25	even	7
841.2.a.f.1.2		3	29.4	even	14
841.2.b.c.840.3		6	29.10	odd	28
841.2.b.c.840.4		6	29.19	odd	28
841.2.d.a.605.1		6	29.9	even	14
841.2.d.a.645.1		6	29.5	even	14
841.2.d.b.574.1		6	29.7	even	7
841.2.d.b.778.1		6	29.23	even	7
841.2.d.c.574.1		6	29.22	even	14
841.2.d.c.778.1		6	29.6	even	14
841.2.d.d.190.1		6	29.13	even	14
841.2.d.d.571.1		6	29.28	even	2
841.2.d.e.605.1		6	29.20	even	7
841.2.d.e.645.1		6	29.24	even	7
841.2.e.b.196.1		12	29.27	odd	28
841.2.e.b.196.2		12	29.2	odd	28
841.2.e.b.236.1		12	29.21	odd	28
841.2.e.b.236.2		12	29.8	odd	28
841.2.e.c.63.1		12	29.14	odd	28
841.2.e.c.63.2		12	29.15	odd	28
841.2.e.c.267.1		12	29.26	odd	28
841.2.e.c.267.2		12	29.3	odd	28
841.2.e.d.270.1		12	29.17	odd	4
841.2.e.d.270.2		12	29.12	odd	4
841.2.e.d.651.1		12	29.18	odd	28
841.2.e.d.651.2		12	29.11	odd	28
7569.2.a.p.1.2		3	87.62	odd	14
7569.2.a.r.1.2		3	87.83	odd	14

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.400969 - 0.193096i) q^{2} +(-0.777479 - 0.974928i) q^{3} +(-1.12349 + 1.40881i) q^{4} +(-0.623490 + 0.300257i) q^{5} +(-0.500000 - 0.240787i) q^{6} +(0.222521 + 0.279032i) q^{7} +(-0.376510 + 1.64960i) q^{8} +(0.321552 - 1.40881i) q^{9} +O(q^{10})\)	\(q+(0.400969 - 0.193096i) q^{2} +(-0.777479 - 0.974928i) q^{3} +(-1.12349 + 1.40881i) q^{4} +(-0.623490 + 0.300257i) q^{5} +(-0.500000 - 0.240787i) q^{6} +(0.222521 + 0.279032i) q^{7} +(-0.376510 + 1.64960i) q^{8} +(0.321552 - 1.40881i) q^{9} +(-0.192021 + 0.240787i) q^{10} +(-1.09903 - 4.81517i) q^{11} +2.24698 q^{12} +(1.25786 + 5.51107i) q^{13} +(0.143104 + 0.0689153i) q^{14} +(0.777479 + 0.374414i) q^{15} +(-0.634375 - 2.77938i) q^{16} +4.49396 q^{17} +(-0.143104 - 0.626980i) q^{18} +(-1.46950 + 1.84270i) q^{19} +(0.277479 - 1.21572i) q^{20} +(0.0990311 - 0.433884i) q^{21} +(-1.37047 - 1.71851i) q^{22} +(-2.06853 - 0.996152i) q^{23} +(1.90097 - 0.915458i) q^{24} +(-2.81886 + 3.53474i) q^{25} +(1.56853 + 1.96688i) q^{26} +(-4.99396 + 2.40496i) q^{27} -0.643104 q^{28} +(-5.09783 + 1.73553i) q^{29} +0.384043 q^{30} +(6.02930 - 2.90356i) q^{31} +(-2.90097 - 3.63770i) q^{32} +(-3.83997 + 4.81517i) q^{33} +(1.80194 - 0.867767i) q^{34} +(-0.222521 - 0.107160i) q^{35} +(1.62349 + 2.03579i) q^{36} +(1.09903 - 4.81517i) q^{37} +(-0.233406 + 1.02262i) q^{38} +(4.39493 - 5.51107i) q^{39} +(-0.260553 - 1.14156i) q^{40} +3.10992 q^{41} +(-0.0440730 - 0.193096i) q^{42} +(3.06853 + 1.47773i) q^{43} +(8.01842 + 3.86147i) q^{44} +(0.222521 + 0.974928i) q^{45} -1.02177 q^{46} +(1.43416 + 6.28345i) q^{47} +(-2.21648 + 2.77938i) q^{48} +(1.52930 - 6.70031i) q^{49} +(-0.447730 + 1.96163i) q^{50} +(-3.49396 - 4.38129i) q^{51} +(-9.17725 - 4.41953i) q^{52} +(4.22737 - 2.03579i) q^{53} +(-1.53803 + 1.92863i) q^{54} +(2.13102 + 2.67222i) q^{55} +(-0.544073 + 0.262012i) q^{56} +2.93900 q^{57} +(-1.70895 + 1.68027i) q^{58} -12.4940 q^{59} +(-1.40097 + 0.674671i) q^{60} +(-1.02446 - 1.28463i) q^{61} +(1.85690 - 2.32847i) q^{62} +(0.464656 - 0.223767i) q^{63} +(3.27144 + 1.57544i) q^{64} +(-2.43900 - 3.05841i) q^{65} +(-0.609916 + 2.67222i) q^{66} +(0.516926 - 2.26480i) q^{67} +(-5.04892 + 6.33114i) q^{68} +(0.637063 + 2.79116i) q^{69} -0.109916 q^{70} +(1.63222 + 7.15122i) q^{71} +(2.20291 + 1.06086i) q^{72} +(-5.06853 - 2.44088i) q^{73} +(-0.489115 - 2.14295i) q^{74} +5.63773 q^{75} +(-0.945042 - 4.14050i) q^{76} +(1.09903 - 1.37814i) q^{77} +(0.698062 - 3.05841i) q^{78} +(1.03803 - 4.54792i) q^{79} +(1.23005 + 1.54244i) q^{80} +(2.32155 + 1.11800i) q^{81} +(1.24698 - 0.600514i) q^{82} +(2.77748 - 3.48285i) q^{83} +(0.500000 + 0.626980i) q^{84} +(-2.80194 + 1.34934i) q^{85} +1.51573 q^{86} +(5.65548 + 3.62068i) q^{87} +8.35690 q^{88} +(5.11745 - 2.46443i) q^{89} +(0.277479 + 0.347948i) q^{90} +(-1.25786 + 1.57731i) q^{91} +(3.72737 - 1.79500i) q^{92} +(-7.51842 - 3.62068i) q^{93} +(1.78836 + 2.24254i) q^{94} +(0.362937 - 1.59013i) q^{95} +(-1.29105 + 5.65647i) q^{96} +(-0.112605 + 0.141202i) q^{97} +(-0.680604 - 2.98192i) q^{98} -7.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + q^5 - 3 * q^6 + q^7 - 7 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9} + 9 q^{10} - 11 q^{11} + 4 q^{12} - 5 q^{13} + 9 q^{14} + 5 q^{15} + 4 q^{16} + 8 q^{17} - 9 q^{18} + q^{19} + 2 q^{20} + 5 q^{21} + 6 q^{22} - 7 q^{23} + 7 q^{24} - 24 q^{25} + 4 q^{26} - 11 q^{27} - 12 q^{28} + 6 q^{29} - 18 q^{30} + 5 q^{31} - 13 q^{32} + q^{33} + 2 q^{34} - q^{35} + 5 q^{36} + 11 q^{37} + 2 q^{38} + 3 q^{39} + 14 q^{40} + 20 q^{41} - 4 q^{42} + 13 q^{43} + 20 q^{44} + q^{45} + 11 q^{47} + 6 q^{48} - 22 q^{49} + q^{50} - 2 q^{51} - 10 q^{52} + 3 q^{53} + 6 q^{54} - 17 q^{55} - 7 q^{56} - 2 q^{57} - 16 q^{58} - 56 q^{59} - 4 q^{60} + 3 q^{61} + 3 q^{62} + 15 q^{63} + q^{64} + 5 q^{65} - 5 q^{66} + 19 q^{67} - 12 q^{68} - 7 q^{69} - 2 q^{70} + 21 q^{71} - 25 q^{73} - 6 q^{74} + 48 q^{75} - 5 q^{76} + 11 q^{77} + 13 q^{78} - 9 q^{79} - 18 q^{80} + 18 q^{81} - 2 q^{82} + 17 q^{83} + 3 q^{84} - 8 q^{85} - 16 q^{86} - 5 q^{87} + 42 q^{88} + 7 q^{89} + 2 q^{90} + 5 q^{91} - 17 q^{93} + 8 q^{94} + 13 q^{95} - 2 q^{96} + q^{97} + 19 q^{98} - 32 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + q^5 - 3 * q^6 + q^7 - 7 * q^8 + 6 * q^9 + 9 * q^10 - 11 * q^11 + 4 * q^12 - 5 * q^13 + 9 * q^14 + 5 * q^15 + 4 * q^16 + 8 * q^17 - 9 * q^18 + q^19 + 2 * q^20 + 5 * q^21 + 6 * q^22 - 7 * q^23 + 7 * q^24 - 24 * q^25 + 4 * q^26 - 11 * q^27 - 12 * q^28 + 6 * q^29 - 18 * q^30 + 5 * q^31 - 13 * q^32 + q^33 + 2 * q^34 - q^35 + 5 * q^36 + 11 * q^37 + 2 * q^38 + 3 * q^39 + 14 * q^40 + 20 * q^41 - 4 * q^42 + 13 * q^43 + 20 * q^44 + q^45 + 11 * q^47 + 6 * q^48 - 22 * q^49 + q^50 - 2 * q^51 - 10 * q^52 + 3 * q^53 + 6 * q^54 - 17 * q^55 - 7 * q^56 - 2 * q^57 - 16 * q^58 - 56 * q^59 - 4 * q^60 + 3 * q^61 + 3 * q^62 + 15 * q^63 + q^64 + 5 * q^65 - 5 * q^66 + 19 * q^67 - 12 * q^68 - 7 * q^69 - 2 * q^70 + 21 * q^71 - 25 * q^73 - 6 * q^74 + 48 * q^75 - 5 * q^76 + 11 * q^77 + 13 * q^78 - 9 * q^79 - 18 * q^80 + 18 * q^81 - 2 * q^82 + 17 * q^83 + 3 * q^84 - 8 * q^85 - 16 * q^86 - 5 * q^87 + 42 * q^88 + 7 * q^89 + 2 * q^90 + 5 * q^91 - 17 * q^93 + 8 * q^94 + 13 * q^95 - 2 * q^96 + q^97 + 19 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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