LMFDB - Embedded newform 67.2.e.c.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (of order $11$, degree $10$, 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:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			59.1
Root			$1.58638 + 0.465803i$ of defining polynomial
Character	$\chi$	$=$	67.59
Dual form			67.2.e.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118239 + 0.822373i) q^{2} +(-0.927853 - 1.07080i) q^{3} +(1.25667 + 0.368991i) q^{4} +(1.58839 + 1.02080i) q^{5} +(0.990306 - 0.636431i) q^{6} +(-0.0441131 + 0.306813i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.141244 - 0.982373i) q^{9} +O(q^{10})$	\(q+(-0.118239 + 0.822373i) q^{2} +(-0.927853 - 1.07080i) q^{3} +(1.25667 + 0.368991i) q^{4} +(1.58839 + 1.02080i) q^{5} +(0.990306 - 0.636431i) q^{6} +(-0.0441131 + 0.306813i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.141244 - 0.982373i) q^{9} +(-1.02729 + 1.18555i) q^{10} +(-5.16179 - 3.31728i) q^{11} +(-0.770889 - 1.68801i) q^{12} +(0.568799 + 1.24550i) q^{13} +(-0.247099 - 0.0725549i) q^{14} +(-0.380725 - 2.64800i) q^{15} +(0.281663 + 0.181014i) q^{16} +(-3.89389 + 1.14335i) q^{17} +(0.791177 + 0.232311i) q^{18} +(-0.632271 - 4.39754i) q^{19} +(1.61942 + 1.86891i) q^{20} +(0.369466 - 0.237442i) q^{21} +(3.33837 - 3.85268i) q^{22} +(3.85782 + 4.45216i) q^{23} +(3.73831 - 1.09767i) q^{24} +(-0.596112 - 1.30530i) q^{25} +(-1.09152 + 0.320498i) q^{26} +(-4.75882 + 3.05831i) q^{27} +(-0.168647 + 0.369285i) q^{28} +0.562147 q^{29} +2.22266 q^{30} +(-0.926398 + 2.02853i) q^{31} +(-3.78366 + 4.36657i) q^{32} +(1.23724 + 8.60519i) q^{33} +(-0.479849 - 3.33742i) q^{34} +(-0.383263 + 0.442310i) q^{35} +(0.539984 - 1.18240i) q^{36} +6.62989 q^{37} +3.69118 q^{38} +(0.805914 - 1.76471i) q^{39} +(-4.36779 + 2.80701i) q^{40} +(3.65820 - 1.07414i) q^{41} +(0.151580 + 0.331914i) q^{42} +(6.00167 - 1.76225i) q^{43} +(-5.26261 - 6.07337i) q^{44} +(1.22716 - 1.41621i) q^{45} +(-4.11748 + 2.64615i) q^{46} +(-3.38107 - 3.90197i) q^{47} +(-0.0675124 - 0.469559i) q^{48} +(6.62426 + 1.94506i) q^{49} +(1.14393 - 0.335888i) q^{50} +(4.83726 + 3.10872i) q^{51} +(0.255215 + 1.77506i) q^{52} +(0.820876 + 0.241031i) q^{53} +(-1.95239 - 4.27514i) q^{54} +(-4.81267 - 10.5383i) q^{55} +(-0.717047 - 0.460818i) q^{56} +(-4.12223 + 4.75731i) q^{57} +(-0.0664679 + 0.462294i) q^{58} +(-0.875798 + 1.91773i) q^{59} +(0.498644 - 3.46815i) q^{60} +(-10.9586 + 7.04270i) q^{61} +(-1.55867 - 1.00170i) q^{62} +(0.295175 + 0.0866711i) q^{63} +(-2.70506 - 3.12181i) q^{64} +(-0.367924 + 2.55896i) q^{65} -7.22297 q^{66} +(-1.38406 - 8.06749i) q^{67} -5.31521 q^{68} +(1.18788 - 8.26190i) q^{69} +(-0.318427 - 0.367484i) q^{70} +(13.2501 + 3.89057i) q^{71} +(2.29589 + 1.47548i) q^{72} +(-11.2289 + 7.21638i) q^{73} +(-0.783915 + 5.45225i) q^{74} +(-0.844614 + 1.84945i) q^{75} +(0.828099 - 5.75955i) q^{76} +(1.24549 - 1.43737i) q^{77} +(1.35596 + 0.871420i) q^{78} +(5.27568 + 11.5521i) q^{79} +(0.262613 + 0.575042i) q^{80} +(4.83351 + 1.41925i) q^{81} +(0.450804 + 3.13541i) q^{82} +(-7.74631 - 4.97825i) q^{83} +(0.551910 - 0.162056i) q^{84} +(-7.35216 - 2.15879i) q^{85} +(0.739593 + 5.14398i) q^{86} +(-0.521590 - 0.601947i) q^{87} +(14.1940 - 9.12191i) q^{88} +(8.97242 - 10.3547i) q^{89} +(1.01956 + 1.17663i) q^{90} +(-0.407226 + 0.119572i) q^{91} +(3.20519 + 7.01839i) q^{92} +(3.03171 - 0.890190i) q^{93} +(3.60865 - 2.31914i) q^{94} +(3.48471 - 7.63044i) q^{95} +8.18641 q^{96} +4.95063 q^{97} +(-2.38281 + 5.21763i) q^{98} +(-3.98788 + 4.60226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.118239	+	0.822373i	−0.0836079	+	0.581506i	0.904351	+	0.426789i	$0.140355\pi$
$2$	−0.118239	+	0.822373i	−0.0836079	+	0.581506i	−0.987959	+	0.154716i	$0.950554\pi$
$3$	−0.927853	−	1.07080i	−0.535696	−	0.618227i	0.421794	−	0.906692i	$-0.361401\pi$
$3$	−0.927853	−	1.07080i	−0.535696	−	0.618227i	−0.957490	+	0.288465i	$0.906855\pi$
$4$	1.25667	+	0.368991i	0.628334	+	0.184496i
$5$	1.58839	+	1.02080i	0.710351	+	0.456515i	0.845268	−	0.534342i	$-0.179441\pi$
$5$	1.58839	+	1.02080i	0.710351	+	0.456515i	−0.134917	+	0.990857i	$0.543077\pi$
$6$	0.990306	−	0.636431i	0.404291	−	0.259822i
$7$	−0.0441131	+	0.306813i	−0.0166732	+	0.115965i	−0.996458	−	0.0840882i	$-0.973202\pi$
$7$	−0.0441131	+	0.306813i	−0.0166732	+	0.115965i	0.979785	+	0.200053i	$0.0641113\pi$
$8$	−1.14231	+	2.50132i	−0.403869	+	0.884350i
$9$	0.141244	−	0.982373i	0.0470813	−	0.327458i
$10$	−1.02729	+	1.18555i	−0.324857	+	0.374905i
$11$	−5.16179	−	3.31728i	−1.55634	−	1.00020i	−0.983580	−	0.180472i	$-0.942237\pi$
$11$	−5.16179	−	3.31728i	−1.55634	−	1.00020i	−0.572757	−	0.819725i	$-0.694126\pi$
$12$	−0.770889	−	1.68801i	−0.222536	−	0.487287i
$13$	0.568799	+	1.24550i	0.157756	+	0.345438i	0.971962	−	0.235139i	$-0.0755544\pi$
$13$	0.568799	+	1.24550i	0.157756	+	0.345438i	−0.814206	+	0.580577i	$0.802827\pi$
$14$	−0.247099	−	0.0725549i	−0.0660400	−	0.0193911i
$15$	−0.380725	−	2.64800i	−0.0983028	−	0.683711i
$16$	0.281663	+	0.181014i	0.0704157	+	0.0452534i
$17$	−3.89389	+	1.14335i	−0.944407	+	0.277303i	−0.717456	−	0.696603i	$-0.754694\pi$
$17$	−3.89389	+	1.14335i	−0.944407	+	0.277303i	−0.226951	+	0.973906i	$0.572876\pi$
$18$	0.791177	+	0.232311i	0.186482	+	0.0547561i
$19$	−0.632271	−	4.39754i	−0.145053	−	1.00886i	−0.924169	−	0.381985i	$-0.875241\pi$
$19$	−0.632271	−	4.39754i	−0.145053	−	1.00886i	0.779116	−	0.626880i	$-0.215668\pi$
$20$	1.61942	+	1.86891i	0.362113	+	0.417901i
$21$	0.369466	−	0.237442i	0.0806241	−	0.0518140i
$22$	3.33837	−	3.85268i	0.711743	−	0.821395i
$23$	3.85782	+	4.45216i	0.804411	+	0.928339i	0.998615	−	0.0526219i	$-0.0167578\pi$
$23$	3.85782	+	4.45216i	0.804411	+	0.928339i	−0.194204	+	0.980961i	$0.562212\pi$
$24$	3.73831	−	1.09767i	0.763080	−	0.224061i
$25$	−0.596112	−	1.30530i	−0.119222	−	0.261061i
$26$	−1.09152	+	0.320498i	−0.214064	+	0.0628549i
$27$	−4.75882	+	3.05831i	−0.915836	+	0.588572i
$28$	−0.168647	+	0.369285i	−0.0318713	+	0.0697884i
$29$	0.562147			0.104388			0.0521940	−	0.998637i	$-0.483379\pi$
$29$	0.562147			0.104388			0.0521940	+	0.998637i	$0.483379\pi$
$30$	2.22266			0.405801
$31$	−0.926398	+	2.02853i	−0.166386	+	0.364334i	−0.974397	−	0.224832i	$-0.927817\pi$
$31$	−0.926398	+	2.02853i	−0.166386	+	0.364334i	0.808012	+	0.589167i	$0.200544\pi$
$32$	−3.78366	+	4.36657i	−0.668862	+	0.771908i
$33$	1.23724	+	8.60519i	0.215376	+	1.49797i
$34$	−0.479849	−	3.33742i	−0.0822934	−	0.572363i
$35$	−0.383263	+	0.442310i	−0.0647833	+	0.0747640i
$36$	0.539984	−	1.18240i	0.0899973	−	0.197067i
$37$	6.62989			1.08995			0.544974	−	0.838453i	$-0.316540\pi$
$37$	6.62989			1.08995			0.544974	+	0.838453i	$0.316540\pi$
$38$	3.69118			0.598788
$39$	0.805914	−	1.76471i	0.129050	−	0.282579i
$40$	−4.36779	+	2.80701i	−0.690608	+	0.443827i
$41$	3.65820	−	1.07414i	0.571314	−	0.167753i	0.0166998	−	0.999861i	$-0.494684\pi$
$41$	3.65820	−	1.07414i	0.571314	−	0.167753i	0.554614	+	0.832108i	$0.312866\pi$
$42$	0.151580	+	0.331914i	0.0233893	+	0.0512155i
$43$	6.00167	−	1.76225i	0.915247	−	0.268741i	0.209999	−	0.977702i	$-0.432654\pi$
$43$	6.00167	−	1.76225i	0.915247	−	0.268741i	0.705248	+	0.708961i	$0.250836\pi$
$44$	−5.26261	−	6.07337i	−0.793368	−	0.915596i
$45$	1.22716	−	1.41621i	0.182934	−	0.211117i
$46$	−4.11748	+	2.64615i	−0.607090	+	0.390153i
$47$	−3.38107	−	3.90197i	−0.493180	−	0.569160i	0.453532	−	0.891240i	$-0.350164\pi$
$47$	−3.38107	−	3.90197i	−0.493180	−	0.569160i	−0.946713	+	0.322079i	$0.895618\pi$
$48$	−0.0675124	−	0.469559i	−0.00974457	−	0.0677750i
$49$	6.62426	+	1.94506i	0.946323	+	0.277866i
$50$	1.14393	−	0.335888i	0.161776	−	0.0475018i
$51$	4.83726	+	3.10872i	0.677351	+	0.435307i
$52$	0.255215	+	1.77506i	0.0353919	+	0.246156i
$53$	0.820876	+	0.241031i	0.112756	+	0.0331081i	0.337624	−	0.941281i	$-0.390377\pi$
$53$	0.820876	+	0.241031i	0.112756	+	0.0331081i	−0.224868	+	0.974389i	$0.572195\pi$
$54$	−1.95239	−	4.27514i	−0.265687	−	0.581773i
$55$	−4.81267	−	10.5383i	−0.648941	−	1.42098i
$56$	−0.717047	−	0.460818i	−0.0958195	−	0.0615795i
$57$	−4.12223	+	4.75731i	−0.546003	+	0.630121i
$58$	−0.0664679	+	0.462294i	−0.00872766	+	0.0607022i
$59$	−0.875798	+	1.91773i	−0.114019	+	0.249667i	−0.958035	−	0.286651i	$-0.907458\pi$
$59$	−0.875798	+	1.91773i	−0.114019	+	0.249667i	0.844016	+	0.536318i	$0.180185\pi$
$60$	0.498644	−	3.46815i	0.0643747	−	0.447736i
$61$	−10.9586	+	7.04270i	−1.40311	+	0.901725i	−0.999910	−	0.0133866i	$-0.995739\pi$
$61$	−10.9586	+	7.04270i	−1.40311	+	0.901725i	−0.403201	+	0.915111i	$0.632102\pi$
$62$	−1.55867	−	1.00170i	−0.197951	−	0.127216i
$63$	0.295175	+	0.0866711i	0.0371885	+	0.0109195i
$64$	−2.70506	−	3.12181i	−0.338133	−	0.390226i
$65$	−0.367924	+	2.55896i	−0.0456353	+	0.317400i
$66$	−7.22297			−0.889086
$67$	−1.38406	−	8.06749i	−0.169090	−	0.985601i
$67$	−1.38406	−	8.06749i	−0.169090	−	0.985601i
$68$	−5.31521			−0.644564
$69$	1.18788	−	8.26190i	0.143004	−	0.994616i
$70$	−0.318427	−	0.367484i	−0.0380593	−	0.0439227i
$71$	13.2501	+	3.89057i	1.57250	+	0.461726i	0.947727	−	0.319084i	$-0.103375\pi$
$71$	13.2501	+	3.89057i	1.57250	+	0.461726i	0.624769	+	0.780810i	$0.285193\pi$
$72$	2.29589	+	1.47548i	0.270573	+	0.173887i
$73$	−11.2289	+	7.21638i	−1.31424	+	0.844613i	−0.994686	−	0.102953i	$-0.967171\pi$
$73$	−11.2289	+	7.21638i	−1.31424	+	0.844613i	−0.319558	+	0.947567i	$0.603534\pi$
$74$	−0.783915	+	5.45225i	−0.0911283	+	0.633811i
$75$	−0.844614	+	1.84945i	−0.0975276	+	0.213556i
$76$	0.828099	−	5.75955i	0.0949894	−	0.660666i
$77$	1.24549	−	1.43737i	0.141937	−	0.163803i
$78$	1.35596	+	0.871420i	0.153532	+	0.0986689i
$79$	5.27568	+	11.5521i	0.593561	+	1.29972i	0.933266	+	0.359185i	$0.116945\pi$
$79$	5.27568	+	11.5521i	0.593561	+	1.29972i	−0.339706	+	0.940532i	$0.610327\pi$
$80$	0.262613	+	0.575042i	0.0293610	+	0.0642916i
$81$	4.83351	+	1.41925i	0.537057	+	0.157694i
$82$	0.450804	+	3.13541i	0.0497829	+	0.346248i
$83$	−7.74631	−	4.97825i	−0.850268	−	0.546434i	0.0413904	−	0.999143i	$-0.486821\pi$
$83$	−7.74631	−	4.97825i	−0.850268	−	0.546434i	−0.891658	+	0.452709i	$0.850458\pi$
$84$	0.551910	−	0.162056i	0.0602184	−	0.0176817i
$85$	−7.35216	−	2.15879i	−0.797453	−	0.234153i
$86$	0.739593	+	5.14398i	0.0797524	+	0.554690i
$87$	−0.521590	−	0.601947i	−0.0559203	−	0.0645355i
$88$	14.1940	−	9.12191i	1.51308	−	0.972399i
$89$	8.97242	−	10.3547i	0.951074	−	1.09760i	−0.0440558	−	0.999029i	$-0.514028\pi$
$89$	8.97242	−	10.3547i	0.951074	−	1.09760i	0.995130	−	0.0985693i	$-0.0314266\pi$
$90$	1.01956	+	1.17663i	0.107471	+	0.124028i
$91$	−0.407226	+	0.119572i	−0.0426889	+	0.0125346i
$92$	3.20519	+	7.01839i	0.334164	+	0.731718i
$93$	3.03171	−	0.890190i	0.314374	−	0.0923084i
$94$	3.60865	−	2.31914i	0.372204	−	0.239201i
$95$	3.48471	−	7.63044i	0.357523	−	0.782867i
$96$	8.18641			0.835522
$97$	4.95063			0.502660			0.251330	−	0.967901i	$-0.419132\pi$
$97$	4.95063			0.502660			0.251330	+	0.967901i	$0.419132\pi$
$98$	−2.38281	+	5.21763i	−0.240701	+	0.527061i
$99$	−3.98788	+	4.60226i	−0.400797	+	0.462544i
$100$	−0.267470	−	1.86029i	−0.0267470	−	0.186029i
$101$	0.573243	+	3.98699i	0.0570398	+	0.396721i	0.998262	+	0.0589324i	$0.0187696\pi$
$101$	0.573243	+	3.98699i	0.0570398	+	0.396721i	−0.941222	+	0.337788i	$0.890321\pi$
$102$	−3.12848	+	3.61046i	−0.309766	+	0.357489i
$103$	−4.78743	+	10.4830i	−0.471720	+	1.03292i	0.512938	+	0.858426i	$0.328557\pi$
$103$	−4.78743	+	10.4830i	−0.471720	+	1.03292i	−0.984658	+	0.174497i	$0.944170\pi$
$104$	−3.76513			−0.369201
$105$	0.829237			0.0809253
$106$	−0.295277	+	0.646567i	−0.0286799	+	0.0628001i
$107$	10.0688	−	6.47085i	0.973392	−	0.625561i	0.0457185	−	0.998954i	$-0.485442\pi$
$107$	10.0688	−	6.47085i	0.973392	−	0.625561i	0.927673	+	0.373394i	$0.121806\pi$
$108$	−7.10875	+	2.08732i	−0.684040	+	0.200852i
$109$	−2.81276	−	6.15909i	−0.269414	−	0.589934i	0.725773	−	0.687935i	$-0.241482\pi$
$109$	−2.81276	−	6.15909i	−0.269414	−	0.589934i	−0.995186	+	0.0980009i	$0.968755\pi$
$110$	9.23545	−	2.71177i	0.880566	−	0.258557i
$111$	−6.15157	−	7.09929i	−0.583881	−	0.673835i
$112$	−0.0679624	+	0.0784328i	−0.00642185	+	0.00741121i
$113$	−7.33968	+	4.71693i	−0.690459	+	0.443731i	−0.838249	−	0.545288i	$-0.816420\pi$
$113$	−7.33968	+	4.71693i	−0.690459	+	0.443731i	0.147790	+	0.989019i	$0.452784\pi$
$114$	−3.42487	−	3.95251i	−0.320769	−	0.370187i
$115$	1.58297	+	11.0098i	0.147613	+	1.02667i
$116$	0.706432	+	0.207427i	0.0655906	+	0.0192591i
$117$	1.30388	−	0.382854i	0.120544	−	0.0353949i
$118$	−1.47354	−	0.946985i	−0.135650	−	0.0871770i
$119$	−0.179023	−	1.24513i	−0.0164110	−	0.114141i
$120$	7.05841	+	2.07254i	0.644342	+	0.189196i
$121$	11.0701	+	24.2402i	1.00638	+	2.20366i
$122$	−4.49598	−	9.84483i	−0.407047	−	0.891309i
$123$	−4.54446	−	2.92055i	−0.409760	−	0.263337i
$124$	−1.91268	+	2.20736i	−0.171764	+	0.198226i
$125$	1.72913	−	12.0264i	0.154658	−	1.07567i
$126$	−0.106177	+	0.232496i	−0.00945902	+	0.0207124i
$127$	1.04395	−	7.26082i	0.0926354	−	0.644294i	−0.889614	−	0.456713i	$-0.849026\pi$
$127$	1.04395	−	7.26082i	0.0926354	−	0.644294i	0.982249	−	0.187580i	$-0.0600644\pi$
$128$	−6.83406	+	4.39198i	−0.604051	+	0.388200i
$129$	−7.45569	−	4.79148i	−0.656437	−	0.421866i
$130$	−2.06092	−	0.605141i	−0.180755	−	0.0530744i
$131$	7.18723	+	8.29450i	0.627951	+	0.724694i	0.977196	−	0.212337i	$-0.0681075\pi$
$131$	7.18723	+	8.29450i	0.627951	+	0.724694i	−0.349245	+	0.937031i	$0.613562\pi$
$132$	−1.62044	+	11.2704i	−0.141041	+	0.980963i
$133$	1.37712			0.119411
$134$	6.79814	−	0.184319i	0.587270	−	0.0159227i
$135$	−10.6808			−0.919257
$136$	1.58817	−	11.0459i	0.136184	−	0.947181i
$137$	−3.38812	−	3.91010i	−0.289467	−	0.334062i	0.592327	−	0.805698i	$-0.298209\pi$
$137$	−3.38812	−	3.91010i	−0.289467	−	0.334062i	−0.881794	+	0.471635i	$0.843664\pi$
$138$	6.65391	+	1.95377i	0.566419	+	0.166316i
$139$	−7.01665	−	4.50933i	−0.595145	−	0.382476i	0.208116	−	0.978104i	$-0.433267\pi$
$139$	−7.01665	−	4.50933i	−0.595145	−	0.382476i	−0.803261	+	0.595628i	$0.796903\pi$
$140$	−0.644843	+	0.414416i	−0.0544992	+	0.0350245i
$141$	−1.04109	+	7.24091i	−0.0876752	+	0.609794i
$142$	−4.76619	+	10.4365i	−0.399969	+	0.875811i
$143$	1.19564	−	8.31584i	0.0999843	−	0.695406i
$144$	0.217606	−	0.251131i	0.0181339	−	0.0209276i
$145$	0.892910	+	0.573838i	0.0741521	+	0.0476547i
$146$	−4.60686	−	10.0876i	−0.381266	−	0.834857i
$147$	−4.06358	−	8.89799i	−0.335158	−	0.733894i
$148$	8.33158	+	2.44637i	0.684852	+	0.201091i
$149$	−3.25675	−	22.6512i	−0.266804	−	1.85566i	−0.478189	−	0.878257i	$-0.658707\pi$
$149$	−3.25675	−	22.6512i	−0.266804	−	1.85566i	0.211386	−	0.977403i	$-0.432202\pi$
$150$	−1.42107	−	0.913265i	−0.116030	−	0.0745678i
$151$	−10.3549	+	3.04049i	−0.842673	+	0.247431i	−0.674453	−	0.738318i	$-0.735620\pi$
$151$	−10.3549	+	3.04049i	−0.842673	+	0.247431i	−0.168221	+	0.985749i	$0.553802\pi$
$152$	11.7219	+	3.44186i	0.950772	+	0.279172i
$153$	0.573207	+	3.98675i	0.0463411	+	0.322309i
$154$	1.03479	+	1.19421i	0.0833856	+	0.0962322i
$155$	−3.54220	+	2.27643i	−0.284516	+	0.182848i
$156$	1.66393	−	1.92028i	0.133221	−	0.153745i
$157$	−6.10900	−	7.05016i	−0.487551	−	0.562664i	0.457658	−	0.889128i	$-0.348688\pi$
$157$	−6.10900	−	7.05016i	−0.487551	−	0.562664i	−0.945210	+	0.326464i	$0.894143\pi$
$158$	−10.1240	+	2.97266i	−0.805419	+	0.236492i
$159$	−0.503556	−	1.10263i	−0.0399346	−	0.0874446i
$160$	−10.4673	+	3.07348i	−0.827515	+	0.242980i
$161$	−1.53616	+	0.987231i	−0.121067	+	0.0778047i
$162$	−1.73866	+	3.80714i	−0.136602	+	0.299117i
$163$	−11.2536			−0.881449			−0.440725	−	0.897642i	$-0.645278\pi$
$163$	−11.2536			−0.881449			−0.440725	+	0.897642i	$0.645278\pi$
$164$	4.99349			0.389926
$165$	−6.81894	+	14.9314i	−0.530854	+	1.16241i
$166$	5.00990	−	5.78173i	0.388844	−	0.448750i
$167$	1.75405	+	12.1997i	0.135733	+	0.944043i	0.937891	+	0.346931i	$0.112776\pi$
$167$	1.75405	+	12.1997i	0.135733	+	0.944043i	−0.802158	+	0.597112i	$0.796315\pi$
$168$	0.171871	+	1.19539i	0.0132601	+	0.0922261i
$169$	7.28546	−	8.40787i	0.560420	−	0.646759i
$170$	2.64464	−	5.79096i	0.202835	−	0.444147i
$171$	−4.40933			−0.337190
$172$	8.19237			0.624662
$173$	4.21745	−	9.23494i	0.320647	−	0.702119i	−0.678835	−	0.734291i	$-0.737515\pi$
$173$	4.21745	−	9.23494i	0.320647	−	0.702119i	0.999482	+	0.0321714i	$0.0102423\pi$
$174$	0.556697	−	0.357768i	0.0422031	−	0.0271223i
$175$	0.426781	−	0.125314i	0.0322616	−	0.00947286i
$176$	−0.853411	−	1.86871i	−0.0643282	−	0.140859i
$177$	2.86612	−	0.841568i	0.215431	−	0.0632561i
$178$	7.45455	+	8.60301i	0.558742	+	0.644823i
$179$	2.82192	−	3.25667i	0.210920	−	0.243415i	−0.640425	−	0.768021i	$-0.721242\pi$
$179$	2.82192	−	3.25667i	0.210920	−	0.243415i	0.851345	+	0.524606i	$0.175787\pi$
$180$	2.06470	−	1.32690i	0.153894	−	0.0989014i
$181$	−8.74755	−	10.0952i	−0.650200	−	0.750371i	0.330944	−	0.943650i	$-0.392633\pi$
$181$	−8.74755	−	10.0952i	−0.650200	−	0.750371i	−0.981144	+	0.193280i	$0.938087\pi$
$182$	−0.0501829	−	0.349030i	−0.00371981	−	0.0258718i
$183$	17.7093	+	5.19993i	1.30911	+	0.384390i
$184$	−15.5431	+	4.56387i	−1.14585	+	0.336453i
$185$	10.5309	+	6.76778i	0.774246	+	0.497577i
$186$	0.373601	+	2.59845i	0.0273938	+	0.190528i
$187$	23.8922	+	7.01539i	1.74717	+	0.513016i
$188$	−2.80910	−	6.15107i	−0.204874	−	0.448613i
$189$	−0.728404	−	1.59498i	−0.0529836	−	0.116018i
$190$	5.86304	+	3.76795i	0.425350	+	0.273356i
$191$	4.47954	−	5.16966i	0.324128	−	0.374064i	−0.570177	−	0.821522i	$-0.693125\pi$
$191$	4.47954	−	5.16966i	0.324128	−	0.374064i	0.894305	+	0.447458i	$0.147671\pi$
$192$	−0.832931	+	5.79317i	−0.0601116	+	0.418086i
$193$	8.39439	−	18.3811i	0.604241	−	1.32310i	−0.322203	−	0.946671i	$-0.604423\pi$
$193$	8.39439	−	18.3811i	0.604241	−	1.32310i	0.926444	−	0.376433i	$-0.122849\pi$
$194$	−0.585359	+	4.07126i	−0.0420264	+	0.292300i
$195$	3.08152	−	1.98037i	0.220672	−	0.141817i
$196$	7.60679	+	4.88859i	0.543342	+	0.349185i
$197$	−6.15016	−	1.80585i	−0.438181	−	0.128661i	0.0551993	−	0.998475i	$-0.482421\pi$
$197$	−6.15016	−	1.80585i	−0.438181	−	0.128661i	−0.493380	+	0.869814i	$0.664239\pi$
$198$	−3.31325	−	3.82369i	−0.235462	−	0.271738i
$199$	−3.65782	+	25.4407i	−0.259296	+	1.80344i	0.278575	+	0.960415i	$0.410138\pi$
$199$	−3.65782	+	25.4407i	−0.259296	+	1.80344i	−0.537871	+	0.843027i	$0.680771\pi$
$200$	3.94593			0.279019
$201$	−7.35446	+	8.96750i	−0.518744	+	0.632519i
$202$	−3.34658			−0.235464
$203$	−0.0247980	+	0.172474i	−0.00174048	+	0.0121053i
$204$	4.93174	+	5.69153i	0.345291	+	0.398487i
$205$	6.90713	+	2.02812i	0.482415	+	0.141650i
$206$	−8.05489	−	5.17656i	−0.561211	−	0.360668i
$207$	4.91858	−	3.16098i	0.341865	−	0.219703i
$208$	−0.0652423	+	0.453770i	−0.00452374	+	0.0314633i
$209$	−11.3242	+	24.7966i	−0.783313	+	1.71522i
$210$	−0.0980486	+	0.681943i	−0.00676599	+	0.0470585i
$211$	−9.68780	+	11.1803i	−0.666935	+	0.769684i	−0.983894	−	0.178755i	$-0.942793\pi$
$211$	−9.68780	+	11.1803i	−0.666935	+	0.769684i	0.316958	+	0.948439i	$0.397338\pi$
$212$	0.942630	+	0.605792i	0.0647401	+	0.0416059i
$213$	−8.12810	−	17.7981i	−0.556929	−	1.21950i
$214$	4.13092	+	9.04546i	0.282384	+	0.618335i
$215$	11.3319	+	3.32735i	0.772830	+	0.226923i
$216$	−2.21374	−	15.3969i	−0.150626	−	1.04763i
$217$	−0.581513	−	0.373716i	−0.0394757	−	0.0253695i
$218$	5.39765	−	1.58489i	0.365575	−	0.107343i
$219$	18.1461	+	5.32817i	1.22620	+	0.360044i
$220$	−2.15940	−	15.0190i	−0.145587	−	1.01258i
$221$	−3.63887	−	4.19949i	−0.244777	−	0.282488i
$222$	6.56563	−	4.21947i	0.440656	−	0.283192i
$223$	−6.84234	+	7.89648i	−0.458197	+	0.528787i	−0.937091	−	0.349085i	$-0.886492\pi$
$223$	−6.84234	+	7.89648i	−0.458197	+	0.528787i	0.478894	+	0.877873i	$0.341038\pi$
$224$	−1.17281	−	1.35350i	−0.0783619	−	0.0904345i
$225$	−1.36649	+	0.401238i	−0.0910995	+	0.0267492i
$226$	−3.01124	−	6.59369i	−0.200304	−	0.438606i
$227$	13.8795	−	4.07539i	0.921215	−	0.270493i	0.213461	−	0.976952i	$-0.431526\pi$
$227$	13.8795	−	4.07539i	0.921215	−	0.270493i	0.707755	+	0.706458i	$0.249708\pi$
$228$	−6.93568	+	4.45729i	−0.459327	+	0.295191i
$229$	2.01936	−	4.42178i	0.133443	−	0.292200i	−0.831101	−	0.556122i	$-0.812289\pi$
$229$	2.01936	−	4.42178i	0.133443	−	0.292200i	0.964544	+	0.263922i	$0.0850161\pi$
$230$	−9.24136			−0.609357
$231$	−2.69477			−0.177303
$232$	−0.642148	+	1.40611i	−0.0421591	+	0.0923156i
$233$	−14.1022	+	16.2748i	−0.923864	+	1.06620i	0.0737582	+	0.997276i	$0.476501\pi$
$233$	−14.1022	+	16.2748i	−0.923864	+	1.06620i	−0.997622	+	0.0689198i	$0.978045\pi$
$234$	0.160679	+	1.11755i	0.0105039	+	0.0730562i
$235$	−1.38735	−	9.64925i	−0.0905009	−	0.629448i
$236$	−1.80821	+	2.08679i	−0.117705	+	0.135838i
$237$	7.47497	−	16.3679i	0.485551	−	1.06321i
$238$	1.04513			0.0677459
$239$	−14.0649			−0.909784			−0.454892	−	0.890547i	$-0.650322\pi$
$239$	−14.0649			−0.909784			−0.454892	+	0.890547i	$0.650322\pi$
$240$	0.372089	−	0.814760i	0.0240182	−	0.0525925i
$241$	17.8679	−	11.4830i	1.15098	−	0.739687i	0.181142	−	0.983457i	$-0.442020\pi$
$241$	17.8679	−	11.4830i	1.15098	−	0.739687i	0.969833	+	0.243770i	$0.0783841\pi$
$242$	−21.2434	+	6.23764i	−1.36558	+	0.400970i
$243$	4.08473	+	8.94431i	0.262036	+	0.573778i
$244$	−16.3701	+	4.80669i	−1.04799	+	0.307717i
$245$	8.53642	+	9.85155i	0.545372	+	0.629393i
$246$	2.93912	−	3.39192i	0.187391	−	0.216261i
$247$	5.11748	−	3.28880i	0.325617	−	0.209262i
$248$	−4.01576	−	4.63444i	−0.255001	−	0.294287i
$249$	1.85673	+	12.9138i	0.117665	+	0.818381i
$250$	9.68573	+	2.84399i	0.612579	+	0.179869i
$251$	2.46240	−	0.723026i	0.155425	−	0.0456370i	−0.203094	−	0.979159i	$-0.565100\pi$
$251$	2.46240	−	0.723026i	0.155425	−	0.0456370i	0.358520	+	0.933522i	$0.383282\pi$
$252$	0.338956	+	0.217834i	0.0213522	+	0.0137222i
$253$	−5.14418	−	35.7785i	−0.323412	−	2.24938i
$254$	5.84767	+	1.71703i	0.366915	+	0.107736i
$255$	4.51009	+	9.87573i	0.282433	+	0.618442i
$256$	−6.23574	−	13.6544i	−0.389734	−	0.853398i
$257$	−7.87476	−	5.06080i	−0.491214	−	0.315684i	0.271479	−	0.962444i	$-0.412487\pi$
$257$	−7.87476	−	5.06080i	−0.491214	−	0.315684i	−0.762693	+	0.646760i	$0.776123\pi$
$258$	4.82194	−	5.56482i	0.300201	−	0.346451i
$259$	−0.292465	+	2.03414i	−0.0181729	+	0.126395i
$260$	−1.40659	+	3.08001i	−0.0872332	+	0.191014i
$261$	0.0793998	−	0.552238i	0.00491473	−	0.0341827i
$262$	−7.67099	+	4.92985i	−0.473916	+	0.304567i
$263$	8.81379	+	5.66428i	0.543481	+	0.349274i	0.783399	−	0.621519i	$-0.213484\pi$
$263$	8.81379	+	5.66428i	0.543481	+	0.349274i	−0.239918	+	0.970793i	$0.577120\pi$
$264$	−22.9377	−	6.73510i	−1.41172	−	0.414517i
$265$	1.05783	+	1.22080i	0.0649819	+	0.0749931i
$266$	−0.162829	+	1.13250i	−0.00998371	+	0.0694382i
$267$	−19.4129			−1.18805
$268$	1.23753	−	10.6489i	0.0755940	−	0.650483i
$269$	−9.30643			−0.567423			−0.283711	−	0.958910i	$-0.591566\pi$
$269$	−9.30643			−0.567423			−0.283711	+	0.958910i	$0.591566\pi$
$270$	1.26289	−	8.78360i	0.0768571	−	0.534553i
$271$	−14.3739	−	16.5883i	−0.873150	−	1.00767i	−0.999876	−	0.0157311i	$-0.994992\pi$
$271$	−14.3739	−	16.5883i	−0.873150	−	1.00767i	0.126726	−	0.991938i	$-0.459553\pi$
$272$	−1.30373	−	0.382808i	−0.0790500	−	0.0232112i
$273$	0.505884	+	0.325112i	0.0306175	+	0.0196767i
$274$	3.61617	−	2.32397i	0.218461	−	0.140396i
$275$	−1.25305	+	8.71516i	−0.0755619	+	0.525544i
$276$	4.54134	−	9.94415i	0.273357	−	0.598568i
$277$	−0.814576	+	5.66550i	−0.0489431	+	0.340407i	0.950607	+	0.310398i	$0.100462\pi$
$277$	−0.814576	+	5.66550i	−0.0489431	+	0.340407i	−0.999550	+	0.0300083i	$0.990447\pi$
$278$	4.53800	−	5.23713i	0.272171	−	0.314102i
$279$	1.86192	+	1.19659i	0.111470	+	0.0716377i
$280$	−0.668551	−	1.46392i	−0.0399535	−	0.0874860i
$281$	3.43601	+	7.52382i	0.204975	+	0.448833i	0.984002	−	0.178157i	$-0.0570136\pi$
$281$	3.43601	+	7.52382i	0.204975	+	0.448833i	−0.779027	+	0.626991i	$0.784286\pi$
$282$	−5.83163	−	1.71232i	−0.347269	−	0.101967i
$283$	−0.828850	−	5.76478i	−0.0492700	−	0.342680i	−0.999514	−	0.0311738i	$-0.990075\pi$
$283$	−0.828850	−	5.76478i	−0.0492700	−	0.342680i	0.950244	−	0.311507i	$-0.100834\pi$
$284$	15.2154	+	9.77832i	0.902866	+	0.580237i
$285$	−11.4040	+	3.34851i	−0.675513	+	0.198349i
$286$	6.69736	+	1.96652i	0.396023	+	0.116283i
$287$	0.168187	+	1.16977i	0.00992777	+	0.0690492i
$288$	3.75519	+	4.33372i	0.221277	+	0.255367i
$289$	−0.446181	+	0.286743i	−0.0262459	+	0.0168672i
$290$	−0.577486	+	0.666455i	−0.0339112	+	0.0391356i
$291$	−4.59346	−	5.30113i	−0.269273	−	0.310758i
$292$	−16.7738	+	4.92523i	−0.981612	+	0.288227i
$293$	11.5290	+	25.2449i	0.673529	+	1.47482i	0.869357	+	0.494185i	$0.164534\pi$
$293$	11.5290	+	25.2449i	0.673529	+	1.47482i	−0.195827	+	0.980638i	$0.562739\pi$
$294$	7.79794	−	2.28968i	0.454785	−	0.133537i
$295$	−3.34873	+	2.15210i	−0.194970	+	0.125300i
$296$	−7.57343	+	16.5835i	−0.440197	+	0.963896i
$297$	34.7093			2.01404
$298$	19.0128			1.10138
$299$	−3.35082	+	7.33727i	−0.193783	+	0.424326i
$300$	−1.74383	+	2.01249i	−0.100680	+	0.116191i
$301$	0.275930	+	1.91913i	0.0159043	+	0.110617i
$302$	−1.27605	−	8.87513i	−0.0734285	−	0.510707i
$303$	3.73739	−	4.31317i	0.214707	−	0.247785i
$304$	0.617928	−	1.35307i	0.0354406	−	0.0776041i
$305$	−24.5958			−1.40835
$306$	−3.34637			−0.191299
$307$	−6.70527	+	14.6825i	−0.382690	+	0.837974i	0.616046	+	0.787710i	$0.288734\pi$
$307$	−6.70527	+	14.6825i	−0.382690	+	0.837974i	−0.998736	+	0.0502639i	$0.983994\pi$
$308$	2.09554	−	1.34672i	0.119405	−	0.0767367i
$309$	15.6673	−	4.60032i	0.891279	−	0.261703i
$310$	−1.45325	−	3.18218i	−0.0825391	−	0.180735i
$311$	20.7622	−	6.09632i	1.17731	−	0.345691i	0.366176	−	0.930545i	$-0.380667\pi$
$311$	20.7622	−	6.09632i	1.17731	−	0.345691i	0.811138	+	0.584855i	$0.198848\pi$
$312$	3.49349	+	4.03170i	0.197780	+	0.228250i
$313$	−4.48788	+	5.17929i	−0.253670	+	0.292751i	−0.868274	−	0.496085i	$-0.834770\pi$
$313$	−4.48788	+	5.17929i	−0.253670	+	0.292751i	0.614604	+	0.788836i	$0.289316\pi$
$314$	6.52019	−	4.19027i	0.367956	−	0.236471i
$315$	0.380380	+	0.438981i	0.0214320	+	0.0247338i
$316$	2.36715	+	16.4639i	0.133163	+	0.926166i
$317$	−11.5994	−	3.40589i	−0.651486	−	0.191294i	−0.0607434	−	0.998153i	$-0.519347\pi$
$317$	−11.5994	−	3.40589i	−0.651486	−	0.191294i	−0.590743	+	0.806860i	$0.701165\pi$
$318$	0.966318	−	0.283737i	0.0541884	−	0.0159112i
$319$	−2.90168	−	1.86480i	−0.162463	−	0.104409i
$320$	−1.10997	−	7.71999i	−0.0620490	−	0.431560i
$321$	−16.2714	−	4.77771i	−0.908181	−	0.266666i
$322$	−0.630238	−	1.38003i	−0.0351218	−	0.0769060i
$323$	7.48992	+	16.4006i	0.416750	+	0.912555i
$324$	5.55043	+	3.56704i	0.308357	+	0.198169i
$325$	1.28668	−	1.48491i	0.0713722	−	0.0823679i
$326$	1.33062	−	9.25465i	0.0736961	−	0.512568i
$327$	−3.98532	+	8.72664i	−0.220389	+	0.482584i
$328$	−1.49203	+	10.3773i	−0.0823838	+	0.572992i
$329$	1.34633	−	0.865231i	0.0742253	−	0.0477017i
$330$	−11.4729	−	7.37319i	−0.631563	−	0.405881i
$331$	15.0215	+	4.41072i	0.825658	+	0.242435i	0.667151	−	0.744923i	$-0.267514\pi$
$331$	15.0215	+	4.41072i	0.825658	+	0.242435i	0.158508	+	0.987358i	$0.449332\pi$
$332$	−7.89761	−	9.11433i	−0.433438	−	0.500214i
$333$	0.936433	−	6.51303i	0.0513162	−	0.356912i
$334$	−10.2401			−0.560315
$335$	6.03685	−	14.2272i	0.329828	−	0.777314i
$336$	0.147045			0.00802197
$337$	−0.307747	+	2.14042i	−0.0167640	+	0.116596i	−0.996485	−	0.0837696i	$-0.973304\pi$
$337$	−0.307747	+	2.14042i	−0.0167640	+	0.116596i	0.979721	+	0.200366i	$0.0642131\pi$
$338$	6.05298	+	6.98551i	0.329239	+	0.379962i
$339$	11.8610	+	3.48271i	0.644203	+	0.189155i
$340$	−8.44265	−	5.42576i	−0.457867	−	0.294253i
$341$	11.5111	−	7.39771i	0.623359	−	0.400608i
$342$	0.521357	−	3.62612i	0.0281917	−	0.196078i
$343$	−1.79035	+	3.92031i	−0.0966696	+	0.211677i
$344$	−2.44785	+	17.0252i	−0.131979	+	0.917935i
$345$	10.3206	−	11.9106i	0.555640	−	0.641243i
$346$	7.09590	+	4.56026i	0.381478	+	0.245161i
$347$	0.525301	+	1.15025i	0.0281996	+	0.0617486i	0.923208	−	0.384301i	$-0.125558\pi$
$347$	0.525301	+	1.15025i	0.0281996	+	0.0617486i	−0.895008	+	0.446050i	$0.852830\pi$
$348$	−0.433352	−	0.948909i	−0.0232301	−	0.0508669i
$349$	10.7314	+	3.15103i	0.574440	+	0.168671i	0.556034	−	0.831160i	$-0.312322\pi$
$349$	10.7314	+	3.15103i	0.574440	+	0.168671i	0.0184066	+	0.999831i	$0.494141\pi$
$350$	0.0525927	+	0.365790i	0.00281120	+	0.0195523i
$351$	−6.51592	−	4.18753i	−0.347794	−	0.223514i
$352$	34.0156	−	9.98787i	1.81304	−	0.532355i
$353$	−10.4306	−	3.06269i	−0.555163	−	0.163011i	−0.00789642	−	0.999969i	$-0.502514\pi$
$353$	−10.4306	−	3.06269i	−0.555163	−	0.163011i	−0.547267	+	0.836958i	$0.684332\pi$
$354$	0.353195	+	2.45653i	0.0187721	+	0.130563i
$355$	17.0748	+	19.7054i	0.906238	+	1.04585i
$356$	15.0962	−	9.70171i	0.800095	−	0.514190i
$357$	−1.16718	+	1.34700i	−0.0617738	+	0.0712908i
$358$	2.34454	+	2.70574i	0.123913	+	0.143003i
$359$	−16.0836	+	4.72257i	−0.848860	+	0.249248i	−0.677100	−	0.735891i	$-0.736763\pi$
$359$	−16.0836	+	4.72257i	−0.848860	+	0.249248i	−0.171760	+	0.985139i	$0.554945\pi$
$360$	2.14061	+	4.68727i	0.112820	+	0.247041i
$361$	−0.708221	+	0.207952i	−0.0372748	+	0.0109449i
$362$	9.33633	−	6.00010i	0.490707	−	0.315358i
$363$	15.6850	−	34.3453i	0.823247	−	1.80266i
$364$	−0.555869			−0.0291355
$365$	−25.2024			−1.31915
$366$	−6.37023	+	13.9489i	−0.332977	+	0.729118i
$367$	14.8331	−	17.1183i	0.774283	−	0.893570i	−0.222400	−	0.974956i	$-0.571389\pi$
$367$	14.8331	−	17.1183i	0.774283	−	0.893570i	0.996683	+	0.0813852i	$0.0259344\pi$
$368$	0.280702	+	1.95233i	0.0146326	+	0.101772i
$369$	−0.538512	−	3.74543i	−0.0280338	−	0.194979i
$370$	−6.81081	+	7.86009i	−0.354077	+	0.408627i
$371$	−0.110163	+	0.241223i	−0.00571937	+	0.0125237i
$372$	4.13833			0.214562
$373$	−21.7707			−1.12724			−0.563621	−	0.826034i	$-0.690592\pi$
$373$	−21.7707			−1.12724			−0.563621	+	0.826034i	$0.690592\pi$
$374$	−8.59428	+	18.8188i	−0.444400	+	0.973099i
$375$	−14.4822	+	9.30717i	−0.747859	+	0.480620i
$376$	13.6223	−	3.99987i	0.702518	−	0.206278i
$377$	0.319748	+	0.700151i	0.0164679	+	0.0360596i
$378$	1.39780	−	0.410430i	0.0718949	−	0.0211103i
$379$	−4.46483	−	5.15269i	−0.229343	−	0.264676i	0.629401	−	0.777081i	$-0.283300\pi$
$379$	−4.46483	−	5.15269i	−0.229343	−	0.264676i	−0.858744	+	0.512405i	$0.828755\pi$
$380$	7.19469	−	8.30311i	0.369080	−	0.425941i
$381$	−8.74352	+	5.61912i	−0.447944	+	0.287876i
$382$	3.72174	+	4.29511i	0.190421	+	0.219757i
$383$	−2.09826	−	14.5937i	−0.107216	−	0.745703i	−0.970520	−	0.241020i	$-0.922518\pi$
$383$	−2.09826	−	14.5937i	−0.107216	−	0.745703i	0.863304	−	0.504684i	$-0.168391\pi$
$384$	11.0439	+	3.24279i	0.563584	+	0.165483i
$385$	3.44559	−	1.01172i	0.175603	−	0.0515618i
$386$	14.1236	+	9.07670i	0.718873	+	0.461992i
$387$	−0.883488	−	6.14479i	−0.0449102	−	0.312357i
$388$	6.22130	+	1.82674i	0.315839	+	0.0927386i
$389$	1.57914	+	3.45782i	0.0800653	+	0.175319i	0.945431	−	0.325822i	$-0.105641\pi$
$389$	1.57914	+	3.45782i	0.0800653	+	0.175319i	−0.865366	+	0.501141i	$0.832914\pi$
$390$	1.26425	+	2.76832i	0.0640177	+	0.140179i
$391$	−20.1123	−	12.9254i	−1.01712	−	0.653665i
$392$	−12.4322	+	14.3475i	−0.627921	+	0.724660i
$393$	2.21306	−	15.3922i	0.111634	−	0.776432i
$394$	2.21227	−	4.84420i	0.111453	−	0.244047i
$395$	−3.41254	+	23.7347i	−0.171704	+	1.19422i
$396$	−6.70963	+	4.31202i	−0.337172	+	0.216687i
$397$	−16.4785	−	10.5901i	−0.827030	−	0.531500i	0.0573030	−	0.998357i	$-0.481750\pi$
$397$	−16.4785	−	10.5901i	−0.827030	−	0.531500i	−0.884333	+	0.466857i	$0.845386\pi$
$398$	−20.4892	−	6.01618i	−1.02703	−	0.301564i
$399$	−1.27776	−	1.47461i	−0.0639681	−	0.0738231i
$400$	0.0683752	−	0.475560i	0.00341876	−	0.0237780i
$401$	−27.8007			−1.38830			−0.694149	−	0.719831i	$-0.744219\pi$
$401$	−27.8007			−1.38830			−0.694149	+	0.719831i	$0.744219\pi$
$402$	−6.50505	−	7.10843i	−0.324442	−	0.354536i
$403$	−3.05346			−0.152103
$404$	−0.750789	+	5.22185i	−0.0373531	+	0.259797i
$405$	6.22875	+	7.18836i	0.309509	+	0.357192i
$406$	−0.138906	−	0.0407865i	−0.00689379	−	0.00202420i
$407$	−34.2221	−	21.9932i	−1.69633	−	1.09016i
$408$	−13.3016	+	8.54840i	−0.658526	+	0.423209i
$409$	0.478600	−	3.32873i	0.0236652	−	0.164595i	−0.974562	−	0.224120i	$-0.928049\pi$
$409$	0.478600	−	3.32873i	0.0236652	−	0.164595i	0.998227	+	0.0595244i	$0.0189584\pi$
$410$	−2.48457	+	5.44044i	−0.122704	+	0.268684i
$411$	−1.04326	+	7.25600i	−0.0514600	+	0.357912i
$412$	−9.88436	+	11.4072i	−0.486967	+	0.561990i
$413$	−0.549751	−	0.353304i	−0.0270515	−	0.0173849i
$414$	2.01793	+	4.41866i	0.0991760	+	0.217165i
$415$	−7.22239	−	15.8148i	−0.354533	−	0.776320i
$416$	−7.59069	−	2.22883i	−0.372164	−	0.109277i
$417$	1.68184	+	11.6974i	0.0823599	+	0.572826i
$418$	−19.0531	−	12.2447i	−0.931916	−	0.598906i
$419$	7.32715	−	2.15145i	0.357955	−	0.105105i	−0.0978104	−	0.995205i	$-0.531184\pi$
$419$	7.32715	−	2.15145i	0.357955	−	0.105105i	0.455765	+	0.890100i	$0.349366\pi$
$420$	1.04208	+	0.305981i	0.0508481	+	0.0149304i
$421$	4.74715	+	33.0172i	0.231362	+	1.60916i	0.692221	+	0.721686i	$0.256632\pi$
$421$	4.74715	+	33.0172i	0.231362	+	1.60916i	−0.460859	+	0.887473i	$0.652459\pi$
$422$	−8.04891	−	9.28894i	−0.391815	−	0.452178i
$423$	−4.31075	+	2.77035i	−0.209596	+	0.134699i
$424$	−1.54059	+	1.77794i	−0.0748179	+	0.0863444i
$425$	3.81361	+	4.40114i	0.184987	+	0.213487i
$426$	15.5977	−	4.57990i	0.755712	−	0.221897i
$427$	−1.67737	−	3.67294i	−0.0811738	−	0.177746i
$428$	15.0409	−	4.41640i	0.727028	−	0.213475i
$429$	−10.0140	+	6.43560i	−0.483480	+	0.310713i
$430$	−4.07621	+	8.92564i	−0.196572	+	0.430433i
$431$	16.0350			0.772377			0.386188	−	0.922420i	$-0.373791\pi$
$431$	16.0350			0.772377			0.386188	+	0.922420i	$0.373791\pi$
$432$	−1.89398			−0.0911241
$433$	16.8202	−	36.8312i	0.808329	−	1.76999i	0.193899	−	0.981022i	$-0.437887\pi$
$433$	16.8202	−	36.8312i	0.808329	−	1.76999i	0.614430	−	0.788971i	$-0.289386\pi$
$434$	0.376092	−	0.434033i	0.0180530	−	0.0208343i
$435$	−0.214023	−	1.48857i	−0.0102616	−	0.0713713i
$436$	−1.26206	−	8.77782i	−0.0604417	−	0.420381i
$437$	17.1394	−	19.7799i	0.819887	−	0.946200i
$438$	−6.52733	+	14.2929i	−0.311888	+	0.682939i
$439$	10.2247			0.487998			0.243999	−	0.969775i	$-0.421541\pi$
$439$	10.2247			0.487998			0.243999	+	0.969775i	$0.421541\pi$
$440$	31.8572			1.51873
$441$	2.84641	−	6.23277i	0.135543	−	0.296799i
$442$	3.88380	−	2.49597i	0.184734	−	0.118721i
$443$	24.0773	−	7.06972i	1.14394	−	0.335893i	0.345771	−	0.938319i	$-0.387618\pi$
$443$	24.0773	−	7.06972i	1.14394	−	0.335893i	0.798174	+	0.602427i	$0.205799\pi$
$444$	−5.11091	−	11.1913i	−0.242553	−	0.531117i
$445$	24.8218	−	7.28834i	1.17667	−	0.345500i
$446$	−5.68482	−	6.56063i	−0.269184	−	0.310655i
$447$	−21.2331	+	24.5043i	−1.00429	+	1.15902i
$448$	1.07714	−	0.692237i	0.0508902	−	0.0327051i
$449$	3.51657	+	4.05834i	0.165957	+	0.191525i	0.832637	−	0.553820i	$-0.186830\pi$
$449$	3.51657	+	4.05834i	0.165957	+	0.191525i	−0.666679	+	0.745345i	$0.732285\pi$
$450$	−0.168394	−	1.17121i	−0.00793819	−	0.0552113i
$451$	−22.4461	−	6.59076i	−1.05694	−	0.310347i
$452$	−10.9641	+	3.21934i	−0.515706	+	0.151425i
$453$	12.8636	+	8.26695i	0.604386	+	0.388415i
$454$	1.71039	+	11.8960i	0.0802725	+	0.558307i
$455$	−0.768894	−	0.225768i	−0.0360463	−	0.0105842i
$456$	−7.19067	−	15.7454i	−0.336734	−	0.737344i
$457$	3.62644	+	7.94079i	0.169638	+	0.371455i	0.975288	−	0.220936i	$-0.0709113\pi$
$457$	3.62644	+	7.94079i	0.169638	+	0.371455i	−0.805651	+	0.592391i	$0.798184\pi$
$458$	3.39759	+	2.18350i	0.158759	+	0.102028i
$459$	15.0336	−	17.3497i	0.701709	−	0.809816i
$460$	−2.07326	+	14.4198i	−0.0966660	+	0.672327i
$461$	−4.91610	+	10.7647i	−0.228965	+	0.501364i	−0.988890	−	0.148646i	$-0.952508\pi$
$461$	−4.91610	+	10.7647i	−0.228965	+	0.501364i	0.759925	+	0.650011i	$0.225236\pi$
$462$	0.318628	−	2.21610i	0.0148239	−	0.103102i
$463$	15.9394	−	10.2436i	0.740767	−	0.476062i	−0.115038	−	0.993361i	$-0.536699\pi$
$463$	15.9394	−	10.2436i	0.740767	−	0.476062i	0.855805	+	0.517299i	$0.173062\pi$
$464$	0.158336	+	0.101756i	0.00735056	+	0.00472392i
$465$	5.72425	+	1.68079i	0.265456	+	0.0779448i
$466$	−11.7165	−	13.5216i	−0.542757	−	0.626375i
$467$	−0.156344	+	1.08739i	−0.00723473	+	0.0503186i	−0.993119	−	0.117110i	$-0.962637\pi$
$467$	−0.156344	+	1.08739i	−0.00723473	+	0.0503186i	0.985884	+	0.167428i	$0.0535462\pi$
$468$	1.77982			0.0822720
$469$	2.53627	−	0.0687662i	0.117114	−	0.00317533i
$470$	8.09933			0.373594
$471$	−1.88106	+	13.0830i	−0.0866745	+	0.602834i
$472$	−3.79642	−	4.38130i	−0.174744	−	0.201666i
$473$	−36.8252	−	10.8129i	−1.69323	−	0.497176i
$474$	12.5767	+	8.08254i	0.577666	+	0.371243i
$475$	−5.36322	+	3.44673i	−0.246081	+	0.158147i
$476$	0.234471	−	1.63078i	0.0107469	−	0.0747466i
$477$	0.352726	−	0.772362i	0.0161502	−	0.0353640i
$478$	1.66303	−	11.5666i	0.0760651	−	0.529044i
$479$	−1.65359	+	1.90835i	−0.0755547	+	0.0871947i	−0.792268	−	0.610173i	$-0.791100\pi$
$479$	−1.65359	+	1.90835i	−0.0755547	+	0.0871947i	0.716714	+	0.697368i	$0.245645\pi$
$480$	13.0032	+	8.35667i	0.593514	+	0.381428i
$481$	3.77107	+	8.25750i	0.171946	+	0.376510i
$482$	7.33064	+	16.0519i	0.333902	+	0.731143i
$483$	2.48246	+	0.728916i	0.112956	+	0.0331668i
$484$	4.96707	+	34.5467i	0.225776	+	1.57030i
$485$	7.86354	+	5.05359i	0.357065	+	0.229472i
$486$	−7.83854	+	2.30160i	−0.355563	+	0.104403i
$487$	13.7840	+	4.04736i	0.624615	+	0.183403i	0.578698	−	0.815542i	$-0.303561\pi$
$487$	13.7840	+	4.04736i	0.624615	+	0.183403i	0.0459166	+	0.998945i	$0.485379\pi$
$488$	−5.09781	−	35.4561i	−0.230767	−	1.60502i
$489$	10.4417	+	12.0503i	0.472189	+	0.544935i
$490$	−9.11100	+	5.85528i	−0.411593	+	0.264515i
$491$	12.9127	−	14.9020i	0.582741	−	0.672519i	−0.385451	−	0.922728i	$-0.625954\pi$
$491$	12.9127	−	14.9020i	0.582741	−	0.672519i	0.968192	+	0.250209i	$0.0804995\pi$
$492$	−4.63322	−	5.34703i	−0.208882	−	0.241063i
$493$	−2.18894	+	0.642730i	−0.0985848	+	0.0289471i
$494$	2.09954	+	4.59735i	0.0944626	+	0.206844i
$495$	−11.0323	+	3.23937i	−0.495865	+	0.145599i
$496$	−0.628123	+	0.403670i	−0.0282036	+	0.0181253i
$497$	−1.77818	+	3.89368i	−0.0797624	+	0.174655i
$498$	−10.8395			−0.485731
$499$	−2.72400			−0.121943			−0.0609715	−	0.998140i	$-0.519420\pi$
$499$	−2.72400			−0.121943			−0.0609715	+	0.998140i	$0.519420\pi$
$500$	6.61058	−	14.4751i	0.295634	−	0.647348i
$501$	11.4360	−	13.1978i	0.510921	−	0.589634i
$502$	0.303445	+	2.11050i	0.0135434	+	0.0941964i
$503$	0.380990	+	2.64984i	0.0169875	+	0.118151i	0.996551	−	0.0829858i	$-0.0264456\pi$
$503$	0.380990	+	2.64984i	0.0169875	+	0.118151i	−0.979563	+	0.201137i	$0.935537\pi$
$504$	−0.553974	+	0.639321i	−0.0246760	+	0.0284776i
$505$	−3.15938	+	6.91808i	−0.140591	+	0.307850i
$506$	30.0316			1.33507
$507$	−15.7630			−0.700059
$508$	3.99108	−	8.73924i	0.177075	−	0.387741i
$509$	8.30734	−	5.33881i	0.368216	−	0.236638i	−0.343427	−	0.939180i	$-0.611588\pi$
$509$	8.30734	−	5.33881i	0.368216	−	0.236638i	0.711643	+	0.702541i	$0.247951\pi$
$510$	−8.65481	+	2.54128i	−0.383241	+	0.112530i
$511$	−1.71874	−	3.76352i	−0.0760326	−	0.166488i
$512$	−3.62289	+	1.06378i	−0.160111	+	0.0470127i
$513$	16.4579	+	18.9934i	0.726634	+	0.838581i
$514$	5.09298	−	5.87761i	0.224642	−	0.259250i
$515$	−18.3054	+	11.7641i	−0.806631	+	0.518390i
$516$	−7.60132	−	8.77239i	−0.334629	−	0.386183i
$517$	4.50847	+	31.3571i	0.198282	+	1.37908i
$518$	−1.63824	−	0.481031i	−0.0719802	−	0.0211353i
$519$	−13.8019	+	4.05262i	−0.605838	+	0.177890i
$520$	−5.98051	−	3.84344i	−0.262263	−	0.168546i
$521$	5.55166	+	38.6127i	0.243223	+	1.69165i	0.635737	+	0.771906i	$0.280696\pi$
$521$	5.55166	+	38.6127i	0.243223	+	1.69165i	−0.392514	+	0.919746i	$0.628395\pi$
$522$	0.444758	+	0.130593i	0.0194665	+	0.00571588i
$523$	−3.09332	−	6.77343i	−0.135262	−	0.296181i	0.829865	−	0.557964i	$-0.188417\pi$
$523$	−3.09332	−	6.77343i	−0.135262	−	0.296181i	−0.965127	+	0.261782i	$0.915690\pi$
$524$	5.97137	+	13.0755i	0.260860	+	0.571204i
$525$	−0.530176	−	0.340724i	−0.0231388	−	0.0148704i
$526$	−5.70029	+	6.57848i	−0.248544	+	0.286836i
$527$	1.28797	−	8.95806i	0.0561051	−	0.390219i
$528$	−1.20917	+	2.64772i	−0.0526225	+	0.115227i
$529$	−1.66572	+	11.5853i	−0.0724226	+	0.503710i
$530$	−1.12903	+	0.725584i	−0.0490420	+	0.0315173i
$531$	1.76023	+	1.13123i	0.0763873	+	0.0490912i
$532$	1.73058	+	0.508143i	0.0750300	+	0.0220308i
$533$	3.41862	+	3.94529i	0.148077	+	0.170890i
$534$	2.29537	−	15.9647i	0.0993305	−	0.690859i
$535$	22.5987			0.977027
$536$	21.7604	+	5.75363i	0.939907	+	0.248519i
$537$	−6.10558			−0.263475
$538$	1.10039	−	7.65336i	0.0474410	−	0.329960i
$539$	−27.7407	−	32.0145i	−1.19488	−	1.37896i
$540$	−13.4222	−	3.94112i	−0.577601	−	0.169599i
$541$	38.8645	+	24.9767i	1.67092	+	1.07383i	0.898811	+	0.438336i	$0.144432\pi$
$541$	38.8645	+	24.9767i	1.67092	+	1.07383i	0.772104	+	0.635496i	$0.219205\pi$
$542$	15.3414	−	9.85929i	0.658968	−	0.423493i
$543$	−2.69351	+	18.7337i	−0.115589	+	0.803942i
$544$	9.74063	−	21.3290i	0.417626	−	0.914473i
$545$	1.81942	−	12.6543i	0.0779352	−	0.542051i
$546$	−0.327179	+	0.377585i	−0.0140020	+	0.0161591i
$547$	−1.94518	−	1.25009i	−0.0831700	−	0.0534501i	0.498395	−	0.866950i	$-0.333923\pi$
$547$	−1.94518	−	1.25009i	−0.0831700	−	0.0534501i	−0.581565	+	0.813500i	$0.697559\pi$
$548$	−2.81495	−	6.16389i	−0.120249	−	0.263308i
$549$	5.37072	+	11.7602i	0.229217	+	0.501914i
$550$	−7.01896	−	2.06095i	−0.299289	−	0.0878793i
$551$	−0.355429	−	2.47206i	−0.0151418	−	0.105313i
$552$	19.3087	+	12.4090i	0.821834	+	0.528161i
$553$	−3.77708	+	1.10905i	−0.160618	+	0.0471616i
$554$	−4.56284	−	1.33977i	−0.193856	−	0.0569214i
$555$	−2.52417	−	17.5560i	−0.107145	−	0.745210i
$556$	−7.15371	−	8.25582i	−0.303385	−	0.350125i
$557$	8.51537	−	5.47250i	0.360808	−	0.231877i	−0.347659	−	0.937621i	$-0.613023\pi$
$557$	8.51537	−	5.47250i	0.360808	−	0.231877i	0.708467	+	0.705744i	$0.249387\pi$
$558$	−1.20419	+	1.38971i	−0.0509776	+	0.0588313i
$559$	5.60862	+	6.47269i	0.237219	+	0.273766i
$560$	−0.188015	+	0.0552062i	−0.00794509	+	0.00233289i
$561$	−14.6564	−	32.0931i	−0.618794	−	1.35497i
$562$	−6.59366	+	1.93607i	−0.278137	+	0.0816683i
$563$	2.01990	−	1.29811i	0.0851288	−	0.0547090i	−0.497384	−	0.867531i	$-0.665706\pi$
$563$	2.01990	−	1.29811i	0.0851288	−	0.0547090i	0.582513	+	0.812822i	$0.302070\pi$
$564$	−3.98013	+	8.71527i	−0.167594	+	0.366979i
$565$	−16.4733			−0.693038
$566$	4.83880			0.203390
$567$	−0.648665	+	1.42038i	−0.0272414	+	0.0596503i
$568$	−24.8673	+	28.6984i	−1.04341	+	1.20416i
$569$	−1.16665	−	8.11423i	−0.0489085	−	0.340166i	−0.999553	−	0.0298850i	$-0.990486\pi$
$569$	−1.16665	−	8.11423i	−0.0489085	−	0.340166i	0.950645	−	0.310281i	$-0.100423\pi$
$570$	−1.40532	−	9.77425i	−0.0588626	−	0.409398i
$571$	−10.0505	+	11.5989i	−0.420599	+	0.485397i	−0.926019	−	0.377476i	$-0.876792\pi$
$571$	−10.0505	+	11.5989i	−0.420599	+	0.485397i	0.505420	+	0.862873i	$0.331337\pi$
$572$	4.57099	−	10.0091i	0.191123	−	0.418501i
$573$	−9.69203			−0.404890
$574$	−0.981871			−0.0409825
$575$	3.51172	−	7.68960i	0.146449	−	0.320679i
$576$	−3.44886	+	2.21645i	−0.143702	+	0.0923519i
$577$	−8.03072	+	2.35803i	−0.334323	+	0.0981662i	−0.444586	−	0.895736i	$-0.646649\pi$
$577$	−8.03072	+	2.35803i	−0.334323	+	0.0981662i	0.110262	+	0.993903i	$0.464831\pi$
$578$	−0.183054	−	0.400832i	−0.00761403	−	0.0166724i
$579$	−27.4713	+	8.06630i	−1.14167	+	0.335224i
$580$	0.910350	+	1.05060i	0.0378002	+	0.0436238i
$581$	1.86911	−	2.15706i	0.0775436	−	0.0894901i
$582$	4.90264	−	3.15073i	0.203221	−	0.130602i
$583$	−3.43762	−	3.96722i	−0.142372	−	0.164306i
$584$	−5.22353	−	36.3305i	−0.216151	−	1.50337i
$585$	2.46189	+	0.722877i	0.101787	+	0.0298873i
$586$	−22.1239	+	6.49617i	−0.913931	+	0.268354i
$587$	−27.5740	−	17.7207i	−1.13810	−	0.731413i	−0.170866	−	0.985294i	$-0.554656\pi$
$587$	−27.5740	−	17.7207i	−1.13810	−	0.731413i	−0.967235	+	0.253881i	$0.918293\pi$
$588$	−1.82329	−	12.6812i	−0.0751911	−	0.522966i
$589$	9.50627	+	2.79129i	0.391699	+	0.115013i
$590$	−1.37388	−	3.00837i	−0.0565615	−	0.123853i
$591$	3.77274	+	8.26115i	0.155190	+	0.339818i
$592$	1.86739	+	1.20010i	0.0767495	+	0.0493239i
$593$	5.19871	−	5.99963i	0.213485	−	0.246375i	−0.638900	−	0.769290i	$-0.720610\pi$
$593$	5.19871	−	5.99963i	0.213485	−	0.246375i	0.852385	+	0.522915i	$0.175155\pi$
$594$	−4.10401	+	28.5440i	−0.168389	+	1.17117i
$595$	0.986671	−	2.16051i	0.0404496	−	0.0885722i
$596$	4.26544	−	29.6668i	0.174719	−	1.21520i
$597$	30.6358	−	19.6884i	1.25384	−	0.805794i
$598$	−5.63778	−	3.62318i	−0.230546	−	0.148163i
$599$	13.0944	+	3.84487i	0.535023	+	0.157097i	0.538073	−	0.842898i	$-0.319153\pi$
$599$	13.0944	+	3.84487i	0.535023	+	0.157097i	−0.00304967	+	0.999995i	$0.500971\pi$
$600$	−3.66124	−	4.22530i	−0.149470	−	0.172497i
$601$	1.26447	−	8.79457i	0.0515787	−	0.358738i	−0.947644	−	0.319328i	$-0.896543\pi$
$601$	1.26447	−	8.79457i	0.0515787	−	0.358738i	0.999223	−	0.0394104i	$-0.0125480\pi$
$602$	−1.61087			−0.0656541
$603$	−8.12078	+	0.220180i	−0.330704	+	0.00896642i
$604$	−14.1346			−0.575130
$605$	−7.16064	+	49.8034i	−0.291122	+	2.02479i
$606$	3.10513	+	3.58351i	0.126137	+	0.145570i
$607$	4.22651	+	1.24102i	0.171549	+	0.0503713i	0.366379	−	0.930466i	$-0.380597\pi$
$607$	4.22651	+	1.24102i	0.171549	+	0.0503713i	−0.194830	+	0.980837i	$0.562416\pi$
$608$	21.5945	+	13.8779i	0.875772	+	0.562824i
$609$	0.207694	−	0.133477i	0.00841619	−	0.00540876i
$610$	2.90820	−	20.2269i	0.117749	−	0.818965i
$611$	2.93673	−	6.43054i	0.118807	−	0.260152i
$612$	−0.750742	+	5.22153i	−0.0303469	+	0.211068i
$613$	−16.0236	+	18.4922i	−0.647185	+	0.746892i	−0.980628	−	0.195879i	$-0.937244\pi$
$613$	−16.0236	+	18.4922i	−0.647185	+	0.746892i	0.333443	+	0.942770i	$0.391790\pi$
$614$	−11.2817	−	7.25028i	−0.455291	−	0.292598i
$615$	−4.23710	−	9.27795i	−0.170856	−	0.374123i
$616$	2.17258	+	4.75729i	0.0875359	+	0.191677i
$617$	−2.98117	−	0.875350i	−0.120017	−	0.0352403i	0.221172	−	0.975235i	$-0.429012\pi$
$617$	−2.98117	−	0.875350i	−0.120017	−	0.0352403i	−0.341190	+	0.939994i	$0.610830\pi$
$618$	1.93069	+	13.4283i	0.0776639	+	0.540164i
$619$	−27.2423	−	17.5076i	−1.09496	−	0.703689i	−0.136996	−	0.990572i	$-0.543745\pi$
$619$	−27.2423	−	17.5076i	−1.09496	−	0.703689i	−0.957966	+	0.286882i	$0.907381\pi$
$620$	−5.29136	+	1.55368i	−0.212506	+	0.0623974i
$621$	−31.9748	−	9.38863i	−1.28310	−	0.376753i
$622$	2.55855	+	17.7951i	0.102588	+	0.713518i
$623$	2.78117	+	3.20964i	0.111425	+	0.128591i
$624$	0.546432	−	0.351171i	0.0218748	−	0.0140581i
$625$	10.3245	−	11.9151i	0.412980	−	0.476604i
$626$	−3.72866	−	4.30311i	−0.149027	−	0.171987i
$627$	37.0594	−	10.8816i	1.48001	−	0.434570i
$628$	−5.07554	−	11.1139i	−0.202536	−	0.443492i
$629$	−25.8161	+	7.58028i	−1.02935	+	0.302246i
$630$	−0.405982	+	0.260909i	−0.0161747	+	0.0103949i
$631$	2.55252	−	5.58924i	0.101614	−	0.222504i	−0.851996	−	0.523548i	$-0.824608\pi$
$631$	2.55252	−	5.58924i	0.101614	−	0.222504i	0.953610	+	0.301044i	$0.0973352\pi$
$632$	−34.9221			−1.38913
$633$	20.9607			0.833114
$634$	4.17242	−	9.13632i	0.165708	−	0.362849i
$635$	9.07003	−	10.4674i	0.359933	−	0.415385i
$636$	−0.225941	−	1.57145i	−0.00895915	−	0.0623122i
$637$	1.34531	+	9.35683i	0.0533031	+	0.370731i
$638$	1.87665	−	2.16577i	0.0742974	−	0.0857438i
$639$	5.69349	−	12.4670i	0.225231	−	0.493187i
$640$	−15.3385			−0.606307
$641$	39.9235			1.57688			0.788442	−	0.615110i	$-0.210888\pi$
$641$	39.9235			1.57688			0.788442	+	0.615110i	$0.210888\pi$
$642$	5.85298	−	12.8162i	0.230999	−	0.505817i
$643$	−20.9033	+	13.4337i	−0.824346	+	0.529775i	−0.883477	−	0.468475i	$-0.844804\pi$
$643$	−20.9033	+	13.4337i	−0.824346	+	0.529775i	0.0591305	+	0.998250i	$0.481167\pi$
$644$	−2.29473	+	0.673792i	−0.0904249	+	0.0265511i
$645$	−6.95143	−	15.2215i	−0.273712	−	0.599346i
$646$	−14.3730	+	4.22031i	−0.565500	+	0.166046i
$647$	12.5255	+	14.4552i	0.492427	+	0.568291i	0.946513	−	0.322667i	$-0.104579\pi$
$647$	12.5255	+	14.4552i	0.492427	+	0.568291i	−0.454086	+	0.890958i	$0.650034\pi$
$648$	−9.07138	+	10.4689i	−0.356357	+	0.411258i
$649$	10.8823	−	6.99365i	0.427169	−	0.274525i
$650$	1.06901	+	1.23371i	0.0419301	+	0.0483900i
$651$	0.139384	+	0.969438i	0.00546290	+	0.0379953i
$652$	−14.1420	−	4.15248i	−0.553845	−	0.162624i
$653$	23.5099	−	6.90314i	0.920014	−	0.270141i	0.212764	−	0.977104i	$-0.431753\pi$
$653$	23.5099	−	6.90314i	0.920014	−	0.270141i	0.707250	+	0.706963i	$0.249935\pi$
$654$	−6.70533	−	4.30926i	−0.262199	−	0.168505i
$655$	2.94913	+	20.5116i	0.115232	+	0.801456i
$656$	1.22481	+	0.359637i	0.0478209	+	0.0140415i
$657$	5.50316	+	12.0503i	0.214699	+	0.470125i
$658$	0.552354	+	1.20949i	0.0215330	+	0.0471507i
$659$	16.2758	+	10.4598i	0.634015	+	0.407457i	0.817794	−	0.575511i	$-0.195197\pi$
$659$	16.2758	+	10.4598i	0.634015	+	0.407457i	−0.183779	+	0.982968i	$0.558833\pi$
$660$	−14.0787	+	16.2477i	−0.548013	+	0.632440i
$661$	−4.48810	+	31.2154i	−0.174567	+	1.21414i	0.694518	+	0.719476i	$0.255618\pi$
$661$	−4.48810	+	31.2154i	−0.174567	+	1.21414i	−0.869085	+	0.494663i	$0.835291\pi$
$662$	−5.40340	+	11.8318i	−0.210009	+	0.459856i
$663$	−1.12047	+	7.79301i	−0.0435153	+	0.302656i
$664$	21.3009	−	13.6893i	0.826636	−	0.531247i
$665$	2.18740	+	1.40576i	0.0848237	+	0.0545129i
$666$	5.24542	+	1.54019i	0.203256	+	0.0596813i
$667$	2.16866	+	2.50277i	0.0839708	+	0.0969075i
$668$	−2.29732	+	15.9782i	−0.0888861	+	0.618216i
$669$	14.8042			0.572365
$670$	10.9863	+	6.64676i	0.424437	+	0.256787i
$671$	79.9288			3.08562
$672$	−0.361128	+	2.51170i	−0.0139308	+	0.0968909i
$673$	13.5625	+	15.6519i	0.522794	+	0.603337i	0.954328	−	0.298760i	$-0.0965729\pi$
$673$	13.5625	+	15.6519i	0.522794	+	0.603337i	−0.431534	+	0.902097i	$0.642027\pi$
$674$	−1.72384	−	0.506165i	−0.0663998	−	0.0194968i
$675$	6.82881	+	4.38861i	0.262841	+	0.168918i
$676$	12.2578	−	7.87764i	0.471456	−	0.302986i
$677$	1.20525	−	8.38273i	0.0463217	−	0.322174i	−0.953465	−	0.301505i	$-0.902511\pi$
$677$	1.20525	−	8.38273i	0.0463217	−	0.322174i	0.999786	−	0.0206697i	$-0.00657983\pi$
$678$	−4.26653	+	9.34241i	−0.163855	+	0.358793i
$679$	−0.218388	+	1.51892i	−0.00838094	+	0.0582908i
$680$	13.7983	−	15.9241i	0.529140	−	0.610661i
$681$	−17.2421	−	11.0808i	−0.660718	−	0.424618i
$682$	4.72262	+	10.3411i	0.180838	+	0.395981i
$683$	−6.39385	−	14.0006i	−0.244654	−	0.535717i	0.746973	−	0.664854i	$-0.231506\pi$
$683$	−6.39385	−	14.0006i	−0.244654	−	0.535717i	−0.991627	+	0.129137i	$0.958779\pi$
$684$	−5.54107	−	1.62700i	−0.211868	−	0.0622101i
$685$	−1.39024	−	9.66936i	−0.0531185	−	0.369447i
$686$	−3.01227	−	1.93587i	−0.115009	−	0.0739118i
$687$	−6.60852	+	1.94044i	−0.252131	+	0.0740322i
$688$	2.00944	+	0.590025i	0.0766092	+	0.0224945i
$689$	0.166710	+	1.15949i	0.00635115	+	0.0441732i
$690$	8.57463	+	9.89565i	0.326431	+	0.376721i
$691$	−43.1090	+	27.7045i	−1.63995	+	1.05393i	−0.699139	+	0.714986i	$0.746433\pi$
$691$	−43.1090	+	27.7045i	−1.63995	+	1.05393i	−0.940807	+	0.338943i	$0.889931\pi$
$692$	8.70755	−	10.0490i	0.331011	−	0.382008i
$693$	−1.23612	−	1.42655i	−0.0469562	−	0.0541903i
$694$	−1.00805	+	0.295989i	−0.0382649	+	0.0112356i
$695$	−6.54209	−	14.3252i	−0.248156	−	0.543385i
$696$	2.10148	−	0.617051i	0.0796564	−	0.0233892i
$697$	−13.0165	+	8.36519i	−0.493035	+	0.316854i
$698$	−3.86020	+	8.45267i	−0.146111	+	0.319938i
$699$	30.5118			1.15406
$700$	0.582562			0.0220188
$701$	0.671224	−	1.46978i	0.0253518	−	0.0555127i	−0.896533	−	0.442978i	$-0.853922\pi$
$701$	0.671224	−	1.46978i	0.0253518	−	0.0555127i	0.921884	+	0.387465i	$0.126649\pi$
$702$	4.21415	−	4.86339i	0.159053	−	0.183557i
$703$	−4.19189	−	29.1552i	−0.158100	−	1.09961i
$704$	3.60705	+	25.0876i	0.135946	+	0.945523i
$705$	−9.04516	+	10.4387i	−0.340660	+	0.393143i
$706$	3.75198	−	8.21569i	0.141208	−	0.309202i
$707$	−1.24855			−0.0469566
$708$	3.91229			0.147033
$709$	5.23108	−	11.4545i	0.196457	−	0.430182i	−0.785607	−	0.618725i	$-0.787649\pi$
$709$	5.23108	−	11.4545i	0.196457	−	0.430182i	0.982065	+	0.188544i	$0.0603767\pi$
$710$	−18.2241	+	11.7119i	−0.683939	+	0.439541i
$711$	12.0937	−	3.55102i	0.453548	−	0.133174i
$712$	15.6512	+	34.2712i	0.586552	+	1.28437i
$713$	−12.6052	+	3.70122i	−0.472069	+	0.138612i
$714$	−0.969730	−	1.11913i	−0.0362912	−	0.0418823i
$715$	10.3879	−	11.9883i	0.388487	−	0.448338i
$716$	4.74791	−	3.05129i	0.177438	−	0.114032i
$717$	13.0502	+	15.0607i	0.487368	+	0.562452i
$718$	−1.98200	−	13.7851i	−0.0739676	−	0.514456i
$719$	−34.2557	−	10.0584i	−1.27752	−	0.375114i	−0.428534	−	0.903526i	$-0.640970\pi$
$719$	−34.2557	−	10.0584i	−1.27752	−	0.375114i	−0.848989	+	0.528411i	$0.822788\pi$
$720$	0.601998	−	0.176763i	0.0224352	−	0.00658755i
$721$	−3.00514	−	1.93129i	−0.111917	−	0.0719249i
$722$	−0.0872749	−	0.607010i	−0.00324803	−	0.0225906i
$723$	−28.8749	−	8.47843i	−1.07387	−	0.315316i
$724$	−7.26772	−	15.9141i	−0.270103	−	0.591443i
$725$	−0.335102	−	0.733772i	−0.0124454	−	0.0272516i
$726$	26.3901	+	16.9599i	0.979427	+	0.629439i
$727$	20.4468	−	23.5968i	0.758329	−	0.875159i	−0.237019	−	0.971505i	$-0.576170\pi$
$727$	20.4468	−	23.5968i	0.758329	−	0.875159i	0.995348	+	0.0963465i	$0.0307157\pi$
$728$	0.166092	−	1.15519i	0.00615576	−	0.0428143i
$729$	12.0656	−	26.4199i	0.446873	−	0.978516i
$730$	2.97992	−	20.7258i	0.110292	−	0.767095i
$731$	−21.3550	+	13.7240i	−0.789843	+	0.507601i
$732$	20.3360	+	13.0692i	0.751642	+	0.483051i
$733$	46.4201	+	13.6302i	1.71457	+	0.503442i	0.983813	−	0.179199i	$-0.0573505\pi$
$733$	46.4201	+	13.6302i	1.71457	+	0.503442i	0.730754	+	0.682641i	$0.239169\pi$
$734$	12.3238	+	14.2224i	0.454880	+	0.524960i
$735$	2.62850	−	18.2816i	0.0969535	−	0.674327i
$736$	−34.0373			−1.25463
$737$	−19.6179	+	46.2340i	−0.722634	+	1.70305i
$738$	3.14382			0.115725
$739$	0.679882	−	4.72868i	0.0250099	−	0.173947i	−0.973488	−	0.228738i	$-0.926540\pi$
$739$	0.679882	−	4.72868i	0.0250099	−	0.173947i	0.998498	+	0.0547907i	$0.0174491\pi$
$740$	10.7366	+	12.3907i	0.394684	+	0.455490i
$741$	−8.26992	−	2.42827i	−0.303803	−	0.0892047i
$742$	−0.185350	−	0.119117i	−0.00680440	−	0.00437292i
$743$	−18.3095	+	11.7668i	−0.671712	+	0.431683i	−0.831542	−	0.555462i	$-0.812542\pi$
$743$	−18.3095	+	11.7668i	−0.671712	+	0.431683i	0.159830	+	0.987144i	$0.448905\pi$
$744$	−1.23652	+	8.60016i	−0.0453329	+	0.315297i
$745$	17.9493	−	39.3035i	0.657612	−	1.43997i
$746$	2.57415	−	17.9036i	0.0942463	−	0.655498i
$747$	−5.98462	+	6.90662i	−0.218966	+	0.252700i
$748$	27.4360	+	17.6320i	1.00316	+	0.644692i
$749$	1.54118	+	3.37470i	0.0563133	+	0.123309i
$750$	−5.94159	−	13.0103i	−0.216956	−	0.475068i
$751$	−24.9780	−	7.33419i	−0.911458	−	0.267628i	−0.207804	−	0.978171i	$-0.566632\pi$
$751$	−24.9780	−	7.33419i	−0.911458	−	0.267628i	−0.703655	+	0.710542i	$0.748450\pi$
$752$	−0.246013	−	1.71106i	−0.00897118	−	0.0623959i
$753$	−3.05897	−	1.96588i	−0.111475	−	0.0716406i
$754$	−0.613592	+	0.180167i	−0.0223457	+	0.00656129i
$755$	−19.5514	−	5.74082i	−0.711550	−	0.208930i
$756$	−0.326828	−	2.27314i	−0.0118866	−	0.0826732i
$757$	−19.3533	−	22.3349i	−0.703409	−	0.811777i	0.285800	−	0.958289i	$-0.407741\pi$
$757$	−19.3533	−	22.3349i	−0.703409	−	0.811777i	−0.989209	+	0.146512i	$0.953195\pi$
$758$	4.76535	−	3.06251i	0.173085	−	0.111235i
$759$	−33.5386	+	38.7056i	−1.21737	+	1.40493i
$760$	15.1055	+	17.4327i	0.547936	+	0.632352i
$761$	−9.19955	+	2.70123i	−0.333483	+	0.0979196i	−0.444188	−	0.895934i	$-0.646508\pi$
$761$	−9.19955	+	2.70123i	−0.333483	+	0.0979196i	0.110704	+	0.993853i	$0.464689\pi$
$762$	−3.58718	−	7.85484i	−0.129950	−	0.284551i
$763$	2.01377	−	0.591296i	0.0729034	−	0.0214064i
$764$	7.53686	−	4.84364i	0.272674	−	0.175237i
$765$	−3.15918	+	6.91765i	−0.114221	+	0.250108i
$766$	12.2496			0.442595
$767$	−2.88668			−0.104232
$768$	−8.83525	+	19.3465i	−0.318814	+	0.698106i
$769$	18.0631	−	20.8459i	0.651371	−	0.751723i	−0.329971	−	0.943991i	$-0.607039\pi$
$769$	18.0631	−	20.8459i	0.651371	−	0.751723i	0.981342	+	0.192268i	$0.0615844\pi$
$770$	0.424604	+	2.95318i	0.0153017	+	0.106425i
$771$	1.88752	+	13.1280i	0.0679773	+	0.472792i
$772$	17.3314	−	20.0016i	0.623772	−	0.719872i
$773$	−15.3074	+	33.5185i	−0.550568	+	1.20558i	0.405947	+	0.913896i	$0.366942\pi$
$773$	−15.3074	+	33.5185i	−0.550568	+	1.20558i	−0.956516	+	0.291680i	$0.905786\pi$
$774$	5.15778			0.185392
$775$	3.20008			0.114950
$776$	−5.65518	+	12.3831i	−0.203009	+	0.444528i
$777$	2.44952	−	1.57421i	0.0878761	−	0.0564745i
$778$	−3.03034	+	0.889788i	−0.108643	+	0.0319004i
$779$	−7.03656	−	15.4079i	−0.252111	−	0.552046i
$780$	4.60319	−	1.35162i	0.164821	−	0.0483957i
$781$	−55.4880	−	64.0365i	−1.98552	−	2.29141i
$782$	13.0076	−	15.0115i	0.465149	−	0.536811i
$783$	−2.67516	+	1.71922i	−0.0956023	+	0.0614399i
$784$	1.51373	+	1.74693i	0.0540616	+	0.0623905i
$785$	−2.50670	−	17.4345i	−0.0894679	−	0.622263i
$786$	12.3964	+	3.63992i	0.442166	+	0.129832i
$787$	44.9005	−	13.1840i	1.60053	−	0.469958i	0.644837	−	0.764320i	$-0.276925\pi$
$787$	44.9005	−	13.1840i	1.60053	−	0.469958i	0.955694	+	0.294362i	$0.0951070\pi$
$788$	−7.06237	−	4.53871i	−0.251586	−	0.161685i
$789$	−2.11260	−	14.6934i	−0.0752104	−	0.523100i
$790$	−19.1153	−	5.61276i	−0.680093	−	0.199693i
$791$	−1.12344	−	2.45999i	−0.0399449	−	0.0874672i
$792$	−6.95631	−	15.2322i	−0.247182	−	0.541252i
$793$	−15.0049	−	9.64307i	−0.532840	−	0.342435i
$794$	10.6574	−	12.2993i	0.378216	−	0.436485i
$795$	0.325722	−	2.26545i	0.0115522	−	0.0803471i
$796$	−13.9841	+	30.6208i	−0.495652	+	1.08533i
$797$	−6.31433	+	43.9172i	−0.223665	+	1.55563i	0.500339	+	0.865830i	$0.333209\pi$
$797$	−6.31433	+	43.9172i	−0.223665	+	1.55563i	−0.724004	+	0.689796i	$0.757700\pi$
$798$	1.36377	−	0.876439i	0.0482768	−	0.0310256i
$799$	17.6268	+	11.3281i	0.623593	+	0.400759i
$800$	7.95518	+	2.33585i	0.281258	+	0.0825849i
$801$	−8.90490	−	10.2768i	−0.314639	−	0.363113i
$802$	3.28713	−	22.8625i	0.116073	−	0.807304i
$803$	81.9000			2.89019
$804$	−12.5510	+	8.55544i	−0.442641	+	0.301727i
$805$	−3.44779			−0.121519
$806$	0.361039	−	2.51108i	0.0127171	−	0.0884491i
$807$	8.63500	+	9.96532i	0.303966	+	0.350796i
$808$	−10.6276	−	3.12054i	−0.373877	−	0.109780i
$809$	−46.6294	−	29.9669i	−1.63940	−	1.05358i	−0.941294	−	0.337589i	$-0.890389\pi$
$809$	−46.6294	−	29.9669i	−1.63940	−	1.05358i	−0.698109	−	0.715992i	$-0.745975\pi$
$810$	−6.64800	+	4.27241i	−0.233587	+	0.150117i
$811$	−0.553275	+	3.84811i	−0.0194281	+	0.135126i	−0.997227	−	0.0744202i	$-0.976289\pi$
$811$	−0.553275	+	3.84811i	−0.0194281	+	0.135126i	0.977799	+	0.209546i	$0.0671985\pi$
$812$	−0.0948043	+	0.207593i	−0.00332698	+	0.00728507i
$813$	−4.42594	+	30.7831i	−0.155224	+	1.07961i
$814$	22.1330	−	25.5429i	0.775762	−	0.895278i
$815$	−17.8751	−	11.4876i	−0.626138	−	0.402395i
$816$	0.799755	+	1.75122i	0.0279970	+	0.0613050i
$817$	−11.5442	−	25.2784i	−0.403882	−	0.884379i
$818$	2.68087	+	0.787175i	0.0937345	+	0.0275229i
$819$	0.0599465	+	0.416937i	0.00209470	+	0.0145690i
$820$	7.93162	+	5.09734i	0.276984	+	0.178007i
$821$	−41.9213	+	12.3092i	−1.46306	+	0.429594i	−0.913837	−	0.406080i	$-0.866895\pi$
$821$	−41.9213	+	12.3092i	−1.46306	+	0.429594i	−0.549225	+	0.835674i	$0.685077\pi$
$822$	−5.84379	−	1.71589i	−0.203826	−	0.0598486i
$823$	3.96555	+	27.5810i	0.138230	+	0.961413i	0.934371	+	0.356301i	$0.115962\pi$
$823$	3.96555	+	27.5810i	0.138230	+	0.961413i	−0.796141	+	0.605111i	$0.793129\pi$
$824$	−20.7526	−	23.9498i	−0.722952	−	0.834331i
$825$	10.4948	−	6.74463i	0.365384	−	0.234818i
$826$	0.355550	−	0.410326i	0.0123712	−	0.0142771i
$827$	−9.41944	−	10.8706i	−0.327546	−	0.378008i	0.567961	−	0.823055i	$-0.307732\pi$
$827$	−9.41944	−	10.8706i	−0.327546	−	0.378008i	−0.895507	+	0.445047i	$0.853187\pi$
$828$	7.34739	−	2.15739i	0.255340	−	0.0749744i
$829$	18.3675	+	40.2192i	0.637929	+	1.39687i	0.901733	+	0.432293i	$0.142296\pi$
$829$	18.3675	+	40.2192i	0.637929	+	1.39687i	−0.263804	+	0.964576i	$0.584977\pi$
$830$	13.8597	−	4.06957i	0.481076	−	0.141257i
$831$	6.82242	−	4.38450i	0.236667	−	0.152097i
$832$	2.34956	−	5.14483i	0.0814564	−	0.178365i
$833$	−28.0180			−0.970767
$834$	−9.81852			−0.339987
$835$	−9.66732	+	21.1685i	−0.334551	+	0.732566i
$836$	−23.3805	+	26.9825i	−0.808632	+	0.933211i
$837$	−1.79530	−	12.4866i	−0.0620548	−	0.431601i
$838$	0.902934	+	6.28004i	0.0311913	+	0.216940i
$839$	−24.7815	+	28.5994i	−0.855553	+	0.987361i	−0.999998	−	0.00215180i	$-0.999315\pi$
$839$	−24.7815	+	28.5994i	−0.855553	+	0.987361i	0.144444	+	0.989513i	$0.453861\pi$
$840$	−0.947250	+	2.07419i	−0.0326832	+	0.0715663i
$841$	−28.6840			−0.989103
$842$	−27.7138			−0.955079
$843$	4.86839	−	10.6603i	0.167676	−	0.367160i
$844$	−16.2998	+	10.4752i	−0.561062	+	0.360572i
$845$	20.1549	−	5.91802i	0.693350	−	0.203586i
$846$	−1.76856	−	3.87261i	−0.0608043	−	0.133143i
$847$	−7.92556	+	2.32715i	−0.272326	+	0.0799620i
$848$	0.187580	+	0.216479i	0.00644153	+	0.00743393i
$849$	−5.40387	+	6.23640i	−0.185460	+	0.214033i
$850$	−4.07030	+	2.61582i	−0.139610	+	0.0897220i
$851$	25.5769	+	29.5173i	0.876766	+	1.01184i
$852$	−3.64700	−	25.3655i	−0.124944	−	0.869007i
$853$	−2.41280	−	0.708463i	−0.0826128	−	0.0242573i	0.240165	−	0.970732i	$-0.422798\pi$
$853$	−2.41280	−	0.708463i	−0.0826128	−	0.0242573i	−0.322778	+	0.946475i	$0.604617\pi$
$854$	3.21886	−	0.945141i	0.110147	−	0.0323421i
$855$	−7.00375	−	4.50104i	−0.239523	−	0.153932i
$856$	4.68389	+	32.5771i	0.160092	+	1.11346i
$857$	−41.4358	−	12.1666i	−1.41542	−	0.415604i	−0.517469	−	0.855702i	$-0.673126\pi$
$857$	−41.4358	−	12.1666i	−1.41542	−	0.415604i	−0.897950	+	0.440097i	$0.854944\pi$
$858$	−4.10841	−	8.99617i	−0.140259	−	0.307124i
$859$	1.83445	+	4.01689i	0.0625907	+	0.137055i	0.938342	−	0.345707i	$-0.112361\pi$
$859$	1.83445	+	4.01689i	0.0625907	+	0.137055i	−0.875752	+	0.482762i	$0.839634\pi$
$860$	13.0127	+	8.36276i	0.443729	+	0.285168i
$861$	1.09653	−	1.26547i	0.0373698	−	0.0431270i
$862$	−1.89596	+	13.1867i	−0.0645768	+	0.449142i
$863$	−9.77552	+	21.4054i	−0.332763	+	0.728648i	−0.999867	−	0.0163159i	$-0.994806\pi$
$863$	−9.77552	+	21.4054i	−0.332763	+	0.728648i	0.667104	+	0.744964i	$0.267534\pi$
$864$	4.65142	−	32.3514i	0.158245	−	1.10062i
$865$	16.1260	−	10.3635i	0.548300	−	0.352371i
$866$	28.3002	+	18.1874i	0.961678	+	0.618033i
$867$	0.721035	+	0.211715i	0.0244876	+	0.00719022i
$868$	−0.592872	−	0.684210i	−0.0201234	−	0.0232236i
$869$	11.0897	−	77.1306i	0.376192	−	2.61648i
$870$	1.24946			0.0423608
$871$	9.26077	−	6.31262i	0.313789	−	0.213895i
$872$	18.6189			0.630516
$873$	0.699246	−	4.86337i	0.0236659	−	0.164600i
$874$	14.2399	+	16.4337i	0.481672	+	0.555879i
$875$	3.61358	+	1.06104i	0.122161	+	0.0358698i
$876$	20.8376	+	13.3915i	0.704036	+	0.452456i
$877$	−14.8055	+	9.51489i	−0.499945	+	0.321295i	−0.766194	−	0.642609i	$-0.777852\pi$
$877$	−14.8055	+	9.51489i	−0.499945	+	0.321295i	0.266249	+	0.963904i	$0.414216\pi$
$878$	−1.20896	+	8.40852i	−0.0408005	+	0.283774i
$879$	16.3351	−	35.7688i	0.550968	−	1.20645i
$880$	0.552023	−	3.83940i	0.0186087	−	0.129426i
$881$	4.17892	−	4.82274i	0.140792	−	0.162482i	−0.680975	−	0.732307i	$-0.738444\pi$
$881$	4.17892	−	4.82274i	0.140792	−	0.162482i	0.821766	+	0.569825i	$0.192989\pi$
$882$	4.78911	+	3.07777i	0.161258	+	0.103634i
$883$	22.6129	+	49.5152i	0.760983	+	1.66632i	0.745559	+	0.666439i	$0.232182\pi$
$883$	22.6129	+	49.5152i	0.760983	+	1.66632i	0.0154238	+	0.999881i	$0.495090\pi$
$884$	−3.02329	−	6.62007i	−0.101684	−	0.222657i
$885$	5.41159	+	1.58899i	0.181909	+	0.0534132i
$886$	2.96707	+	20.6364i	0.0996806	+	0.693294i
$887$	4.79879	+	3.08400i	0.161128	+	0.103551i	0.618720	−	0.785612i	$-0.287652\pi$
$887$	4.79879	+	3.08400i	0.161128	+	0.103551i	−0.457592	+	0.889162i	$0.651288\pi$
$888$	24.7846	−	7.27742i	0.831718	−	0.244214i
$889$	2.18166	+	0.640594i	0.0731707	+	0.0214848i
$890$	3.05882	+	21.2746i	0.102532	+	0.713125i
$891$	−20.2415	−	23.3599i	−0.678116	−	0.782588i
$892$	−11.5123	+	7.39849i	−0.385460	+	0.247720i
$893$	−15.0213	+	17.3355i	−0.502669	+	0.580111i
$894$	−17.6411	−	20.3589i	−0.590007	−	0.680905i
$895$	7.80673	−	2.29226i	0.260950	−	0.0766219i
$896$	−1.04605	−	2.29052i	−0.0349460	−	0.0765210i
$897$	10.9658	−	3.21986i	0.366138	−	0.107508i
$898$	−3.75327	+	2.41208i	−0.125248	+	0.0804921i
$899$	−0.520771	+	1.14033i	−0.0173687	+	0.0380322i
$900$	−1.86528			−0.0621760
$901$	−3.47198			−0.115668
$902$	8.07407	−	17.6798i	0.268837	−	0.588671i
$903$	1.79898	−	2.07614i	0.0598664	−	0.0690896i
$904$	−3.41432	−	23.7471i	−0.113559	−	0.789817i
$905$	−3.58937	−	24.9646i	−0.119315	−	0.829852i
$906$	−8.31950	+	9.60122i	−0.276397	+	0.318979i
$907$	7.17877	−	15.7193i	0.238367	−	0.521951i	−0.752207	−	0.658926i	$-0.771011\pi$
$907$	7.17877	−	15.7193i	0.238367	−	0.521951i	0.990574	+	0.136975i	$0.0437381\pi$
$908$	18.9457			0.628736
$909$	3.99768			0.132595
$910$	0.276579	−	0.605623i	0.00916850	−	0.0200762i
$911$	23.9669	−	15.4026i	0.794058	−	0.510310i	−0.0796137	−	0.996826i	$-0.525369\pi$
$911$	23.9669	−	15.4026i	0.794058	−	0.510310i	0.873672	+	0.486516i	$0.161732\pi$
$912$	−2.02222	+	0.593777i	−0.0669623	+	0.0196619i
$913$	23.4706	+	51.3933i	0.776762	+	1.70087i
$914$	−6.95909	+	2.04337i	−0.230186	+	0.0675887i
$915$	22.8213	+	26.3372i	0.754449	+	0.870681i
$916$	4.16927	−	4.81159i	0.137756	−	0.158979i
$917$	−2.86192	+	1.83924i	−0.0945088	+	0.0607371i
$918$	12.4904	+	14.4147i	0.412244	+	0.475755i
$919$	−2.92474	−	20.3420i	−0.0964783	−	0.671021i	−0.979464	−	0.201621i	$-0.935379\pi$
$919$	−2.92474	−	20.3420i	−0.0964783	−	0.671021i	0.882985	−	0.469401i	$-0.155530\pi$
$920$	−29.3474	−	8.61716i	−0.967554	−	0.284100i
$921$	21.9435	−	6.44320i	0.723064	−	0.212311i
$922$	−8.27137	−	5.31568i	−0.272403	−	0.175063i
$923$	2.69093	+	18.7159i	0.0885732	+	0.616040i
$924$	−3.38643	−	0.994345i	−0.111405	−	0.0327115i
$925$	−3.95216	−	8.65402i	−0.129946	−	0.284542i
$926$	6.53943	+	14.3193i	0.214899	+	0.470563i
$927$	9.62204	+	6.18371i	0.316029	+	0.203100i
$928$	−2.12697	+	2.45465i	−0.0698212	+	0.0805780i
$929$	4.15339	−	28.8874i	0.136268	−	0.947766i	−0.800878	−	0.598828i	$-0.795633\pi$
$929$	4.15339	−	28.8874i	0.136268	−	0.947766i	0.937146	−	0.348938i	$-0.113458\pi$
$930$	−2.05907	+	4.50874i	−0.0675196	+	0.147847i
$931$	4.36515	−	30.3603i	0.143062	−	0.995017i
$932$	−23.7270	+	15.2484i	−0.777204	+	0.499479i
$933$	−25.7922	−	16.5756i	−0.844398	−	0.542662i
$934$	−0.875759	−	0.257146i	−0.0286557	−	0.00841407i
$935$	30.7890	+	35.5324i	1.00691	+	1.16203i
$936$	−0.531802	+	3.69876i	−0.0173825	+	0.120898i
$937$	43.1732			1.41041			0.705204	−	0.709005i	$-0.250855\pi$
$937$	43.1732			1.41041			0.705204	+	0.709005i	$0.250855\pi$
$938$	−0.243335	+	2.09389i	−0.00794518	+	0.0683679i
$939$	9.71007			0.316876
$940$	1.81705	−	12.6378i	0.0592655	−	0.412201i
$941$	32.2031	+	37.1644i	1.04979	+	1.21152i	0.976792	+	0.214191i	$0.0687116\pi$
$941$	32.2031	+	37.1644i	1.04979	+	1.21152i	0.0729991	+	0.997332i	$0.476743\pi$
$942$	−10.5367	−	3.09386i	−0.343305	−	0.100803i
$943$	18.8949	+	12.1430i	0.615303	+	0.395431i
$944$	−0.593815	+	0.381622i	−0.0193270	+	0.0124207i
$945$	0.471163	−	3.27701i	0.0153269	−	0.106601i
$946$	13.2464	−	29.0056i	0.430678	−	0.943053i
$947$	−4.07475	+	28.3405i	−0.132412	+	0.920944i	0.809986	+	0.586449i	$0.199475\pi$
$947$	−4.07475	+	28.3405i	−0.132412	+	0.920944i	−0.942398	+	0.334494i	$0.891434\pi$
$948$	15.4332	−	17.8108i	0.501246	−	0.578468i
$949$	−15.3750	−	9.88088i	−0.499092	−	0.320747i
$950$	−2.20036	−	4.81811i	−0.0713890	−	0.156320i
$951$	7.11551	+	15.5808i	0.230736	+	0.505242i
$952$	3.31898	+	0.974540i	0.107569	+	0.0315850i
$953$	1.12276	+	7.80893i	0.0363696	+	0.252956i	0.999892	−	0.0146701i	$-0.00466982\pi$
$953$	1.12276	+	7.80893i	0.0363696	+	0.252956i	−0.963523	+	0.267626i	$0.913761\pi$
$954$	0.593464	+	0.381396i	0.0192141	+	0.0123482i
$955$	12.3925	−	3.63875i	0.401010	−	0.117747i
$956$	−17.6749	−	5.18983i	−0.571648	−	0.167851i
$957$	0.695510	+	4.83738i	0.0224826	+	0.156370i
$958$	−1.37386	−	1.58551i	−0.0443873	−	0.0512256i
$959$	1.34913	−	0.867034i	0.0435657	−	0.0279980i
$960$	−7.23667	+	8.35157i	−0.233563	+	0.269546i
$961$	17.0440	+	19.6698i	0.549805	+	0.634509i
$962$	−7.23664	+	2.12487i	−0.233319	+	0.0685085i
$963$	−4.93463	−	10.8053i	−0.159016	−	0.348197i
$964$	26.6912	−	7.83725i	0.859666	−	0.252421i
$965$	32.0970	−	20.6275i	1.03324	−	0.664023i
$966$	−0.892966	+	1.95532i	−0.0287307	+	0.0629115i
$967$	7.84337			0.252226			0.126113	−	0.992016i	$-0.459750\pi$
$967$	7.84337			0.252226			0.126113	+	0.992016i	$0.459750\pi$
$968$	−73.2781			−2.35525
$969$	10.6122	−	23.2376i	0.340914	−	0.746499i
$970$	−5.08572	+	5.86923i	−0.163293	+	0.188450i
$971$	−3.34779	−	23.2844i	−0.107436	−	0.747232i	−0.970319	−	0.241829i	$-0.922253\pi$
$971$	−3.34779	−	23.2844i	−0.107436	−	0.747232i	0.862883	−	0.505403i	$-0.168656\pi$
$972$	1.83278	+	12.7473i	0.0587864	+	0.408869i
$973$	1.69305	−	1.95388i	0.0542767	−	0.0626386i
$974$	−4.95826	+	10.8571i	−0.158873	+	0.347883i
$975$	−2.78389			−0.0891559
$976$	−4.36147			−0.139607
$977$	−15.9430	+	34.9102i	−0.510060	+	1.11688i	0.463007	+	0.886355i	$0.346770\pi$
$977$	−15.9430	+	34.9102i	−0.510060	+	1.11688i	−0.973067	+	0.230521i	$0.925957\pi$
$978$	−11.1445	+	7.16214i	−0.356362	+	0.229020i
$979$	−80.6632	+	23.6849i	−2.57801	+	0.756971i
$980$	7.09231	+	15.5300i	0.226556	+	0.496088i
$981$	−6.44781	+	1.89325i	−0.205863	+	0.0604468i
$982$	10.7282	+	12.3810i	0.342352	+	0.395095i
$983$	22.8415	−	26.3605i	0.728532	−	0.840771i	−0.263774	−	0.964585i	$-0.584967\pi$
$983$	22.8415	−	26.3605i	0.728532	−	0.840771i	0.992305	+	0.123814i	$0.0395126\pi$
$984$	12.4964	−	8.03097i	0.398372	−	0.256018i
$985$	−7.92546	−	9.14647i	−0.252526	−	0.291431i
$986$	−0.269745	−	1.87612i	−0.00859044	−	0.0597478i
$987$	−2.17568	−	0.638838i	−0.0692527	−	0.0203344i
$988$	7.64452	−	2.24463i	0.243204	−	0.0714113i
$989$	30.9992	+	19.9220i	0.985717	+	0.633482i
$990$	−1.35952	−	9.45569i	−0.0432085	−	0.300521i
$991$	−30.5234	−	8.96247i	−0.969607	−	0.284702i	−0.241679	−	0.970356i	$-0.577698\pi$
$991$	−30.5234	−	8.96247i	−0.969607	−	0.284702i	−0.727928	+	0.685654i	$0.759516\pi$
$992$	−5.35255	−	11.7204i	−0.169944	−	0.372124i
$993$	−9.21479	−	20.1776i	−0.292422	−	0.640316i
$994$	−2.99180	−	1.92272i	−0.0948943	−	0.0609848i
$995$	−31.7799	+	36.6759i	−1.00749	+	1.16270i
$996$	−2.43180	+	16.9135i	−0.0770545	+	0.535926i
$997$	13.1382	−	28.7686i	0.416091	−	0.911112i	−0.579291	−	0.815120i	$-0.696671\pi$
$997$	13.1382	−	28.7686i	0.416091	−	0.911112i	0.995382	−	0.0959911i	$-0.0306020\pi$
$998$	0.322084	−	2.24014i	0.0101954	−	0.0709105i
$999$	−31.5505	+	20.2763i	−0.998214	+	0.641513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.59.1	yes	20
3.2	odd	2		603.2.u.c.595.1		20
67.5	odd	22		4489.2.a.m.1.3		10
67.25	even	11	inner	67.2.e.c.25.1	✓	20
67.62	even	11		4489.2.a.l.1.8		10
201.92	odd	22		603.2.u.c.226.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.25.1	✓	20	67.25	even	11	inner
67.2.e.c.59.1	yes	20	1.1	even	1	trivial
603.2.u.c.226.1		20	201.92	odd	22
603.2.u.c.595.1		20	3.2	odd	2
4489.2.a.l.1.8		10	67.62	even	11
4489.2.a.m.1.3		10	67.5	odd	22

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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118239 + 0.822373i) q^{2} +(-0.927853 - 1.07080i) q^{3} +(1.25667 + 0.368991i) q^{4} +(1.58839 + 1.02080i) q^{5} +(0.990306 - 0.636431i) q^{6} +(-0.0441131 + 0.306813i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.141244 - 0.982373i) q^{9} +O(q^{10})\)	\(q+(-0.118239 + 0.822373i) q^{2} +(-0.927853 - 1.07080i) q^{3} +(1.25667 + 0.368991i) q^{4} +(1.58839 + 1.02080i) q^{5} +(0.990306 - 0.636431i) q^{6} +(-0.0441131 + 0.306813i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.141244 - 0.982373i) q^{9} +(-1.02729 + 1.18555i) q^{10} +(-5.16179 - 3.31728i) q^{11} +(-0.770889 - 1.68801i) q^{12} +(0.568799 + 1.24550i) q^{13} +(-0.247099 - 0.0725549i) q^{14} +(-0.380725 - 2.64800i) q^{15} +(0.281663 + 0.181014i) q^{16} +(-3.89389 + 1.14335i) q^{17} +(0.791177 + 0.232311i) q^{18} +(-0.632271 - 4.39754i) q^{19} +(1.61942 + 1.86891i) q^{20} +(0.369466 - 0.237442i) q^{21} +(3.33837 - 3.85268i) q^{22} +(3.85782 + 4.45216i) q^{23} +(3.73831 - 1.09767i) q^{24} +(-0.596112 - 1.30530i) q^{25} +(-1.09152 + 0.320498i) q^{26} +(-4.75882 + 3.05831i) q^{27} +(-0.168647 + 0.369285i) q^{28} +0.562147 q^{29} +2.22266 q^{30} +(-0.926398 + 2.02853i) q^{31} +(-3.78366 + 4.36657i) q^{32} +(1.23724 + 8.60519i) q^{33} +(-0.479849 - 3.33742i) q^{34} +(-0.383263 + 0.442310i) q^{35} +(0.539984 - 1.18240i) q^{36} +6.62989 q^{37} +3.69118 q^{38} +(0.805914 - 1.76471i) q^{39} +(-4.36779 + 2.80701i) q^{40} +(3.65820 - 1.07414i) q^{41} +(0.151580 + 0.331914i) q^{42} +(6.00167 - 1.76225i) q^{43} +(-5.26261 - 6.07337i) q^{44} +(1.22716 - 1.41621i) q^{45} +(-4.11748 + 2.64615i) q^{46} +(-3.38107 - 3.90197i) q^{47} +(-0.0675124 - 0.469559i) q^{48} +(6.62426 + 1.94506i) q^{49} +(1.14393 - 0.335888i) q^{50} +(4.83726 + 3.10872i) q^{51} +(0.255215 + 1.77506i) q^{52} +(0.820876 + 0.241031i) q^{53} +(-1.95239 - 4.27514i) q^{54} +(-4.81267 - 10.5383i) q^{55} +(-0.717047 - 0.460818i) q^{56} +(-4.12223 + 4.75731i) q^{57} +(-0.0664679 + 0.462294i) q^{58} +(-0.875798 + 1.91773i) q^{59} +(0.498644 - 3.46815i) q^{60} +(-10.9586 + 7.04270i) q^{61} +(-1.55867 - 1.00170i) q^{62} +(0.295175 + 0.0866711i) q^{63} +(-2.70506 - 3.12181i) q^{64} +(-0.367924 + 2.55896i) q^{65} -7.22297 q^{66} +(-1.38406 - 8.06749i) q^{67} -5.31521 q^{68} +(1.18788 - 8.26190i) q^{69} +(-0.318427 - 0.367484i) q^{70} +(13.2501 + 3.89057i) q^{71} +(2.29589 + 1.47548i) q^{72} +(-11.2289 + 7.21638i) q^{73} +(-0.783915 + 5.45225i) q^{74} +(-0.844614 + 1.84945i) q^{75} +(0.828099 - 5.75955i) q^{76} +(1.24549 - 1.43737i) q^{77} +(1.35596 + 0.871420i) q^{78} +(5.27568 + 11.5521i) q^{79} +(0.262613 + 0.575042i) q^{80} +(4.83351 + 1.41925i) q^{81} +(0.450804 + 3.13541i) q^{82} +(-7.74631 - 4.97825i) q^{83} +(0.551910 - 0.162056i) q^{84} +(-7.35216 - 2.15879i) q^{85} +(0.739593 + 5.14398i) q^{86} +(-0.521590 - 0.601947i) q^{87} +(14.1940 - 9.12191i) q^{88} +(8.97242 - 10.3547i) q^{89} +(1.01956 + 1.17663i) q^{90} +(-0.407226 + 0.119572i) q^{91} +(3.20519 + 7.01839i) q^{92} +(3.03171 - 0.890190i) q^{93} +(3.60865 - 2.31914i) q^{94} +(3.48471 - 7.63044i) q^{95} +8.18641 q^{96} +4.95063 q^{97} +(-2.38281 + 5.21763i) q^{98} +(-3.98788 + 4.60226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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