LMFDB - Embedded newform 690.2.m.e.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.2
Root			$0.121066 - 0.842031i$ of defining polynomial
Character	$\chi$	$=$	690.271
Dual form			690.2.m.e.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.22647 + 2.68560i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.22647 + 2.68560i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(-0.332740 + 0.0977012i) q^{11} +(0.959493 - 0.281733i) q^{12} +(-2.39074 + 5.23499i) q^{13} +(0.420170 + 2.92235i) q^{14} +(0.654861 + 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(3.39875 - 2.18424i) q^{17} +(0.142315 - 0.989821i) q^{18} +(0.353661 + 0.227284i) q^{19} +(-0.654861 + 0.755750i) q^{20} +(2.83281 + 0.831787i) q^{21} -0.346787 q^{22} +(4.27109 + 2.18123i) q^{23} +1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-3.76876 + 4.34939i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.420170 + 2.92235i) q^{28} +(3.21798 - 2.06807i) q^{29} +(0.415415 + 0.909632i) q^{30} +(-6.38358 - 7.36705i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-0.144061 + 0.315449i) q^{33} +(3.87645 - 1.13823i) q^{34} +(-2.83281 + 0.831787i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-1.02158 - 7.10522i) q^{37} +(0.275302 + 0.317716i) q^{38} +(2.39074 + 5.23499i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(0.0904755 - 0.629271i) q^{41} +(2.48372 + 1.59619i) q^{42} +(-0.142051 + 0.163936i) q^{43} +(-0.332740 - 0.0977012i) q^{44} +1.00000 q^{45} +(3.48356 + 3.29618i) q^{46} +5.27458 q^{47} +(0.959493 + 0.281733i) q^{48} +(-1.12417 + 1.29737i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(0.574966 - 3.99898i) q^{51} +(-4.84147 + 3.11142i) q^{52} +(1.84214 + 4.03373i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.0493529 - 0.343257i) q^{55} +(-1.22647 + 2.68560i) q^{56} +(0.403369 - 0.118440i) q^{57} +(3.67027 - 1.07769i) q^{58} +(-3.02769 + 6.62972i) q^{59} +(0.142315 + 0.989821i) q^{60} +(-0.141270 - 0.163034i) q^{61} +(-4.04947 - 8.86709i) q^{62} +(2.48372 - 1.59619i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-4.84147 - 3.11142i) q^{65} +(-0.227097 + 0.262084i) q^{66} +(-1.64642 - 0.483433i) q^{67} +4.04010 q^{68} +(4.44543 - 1.79948i) q^{69} -2.95240 q^{70} +(3.18335 + 0.934716i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-3.03256 - 1.94891i) q^{73} +(1.02158 - 7.10522i) q^{74} +(-0.841254 + 0.540641i) q^{75} +(0.174640 + 0.382407i) q^{76} +(-0.670482 - 0.773777i) q^{77} +(0.819031 + 5.69648i) q^{78} +(4.64031 - 10.1609i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.264097 - 0.578291i) q^{82} +(-2.32955 - 16.2024i) q^{83} +(1.93341 + 2.23127i) q^{84} +(1.67832 + 3.67500i) q^{85} +(-0.182483 + 0.117275i) q^{86} +(0.544385 - 3.78628i) q^{87} +(-0.291736 - 0.187487i) q^{88} +(-0.189805 + 0.219047i) q^{89} +(0.959493 + 0.281733i) q^{90} -16.9912 q^{91} +(2.41381 + 4.14409i) q^{92} -9.74800 q^{93} +(5.06092 + 1.48602i) q^{94} +(-0.275302 + 0.317716i) q^{95} +(0.841254 + 0.540641i) q^{96} +(1.46491 - 10.1887i) q^{97} +(-1.44415 + 0.928098i) q^{98} +(0.144061 + 0.315449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	1.22647	+	2.68560i	0.463562	+	1.01506i	0.986661	+	0.162788i	$0.0520487\pi$
$7$	1.22647	+	2.68560i	0.463562	+	1.01506i	−0.523099	+	0.852272i	$0.675224\pi$
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−0.415415	+	0.909632i	−0.131366	+	0.287651i
$11$	−0.332740	+	0.0977012i	−0.100325	+	0.0294580i	−0.331510	−	0.943452i	$-0.607558\pi$
$11$	−0.332740	+	0.0977012i	−0.100325	+	0.0294580i	0.231185	+	0.972910i	$0.425740\pi$
$12$	0.959493	−	0.281733i	0.276982	−	0.0813292i
$13$	−2.39074	+	5.23499i	−0.663072	+	1.45192i	0.216560	+	0.976269i	$0.430516\pi$
$13$	−2.39074	+	5.23499i	−0.663072	+	1.45192i	−0.879632	+	0.475655i	$0.842211\pi$
$14$	0.420170	+	2.92235i	0.112295	+	0.781030i
$15$	0.654861	+	0.755750i	0.169084	+	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	3.39875	−	2.18424i	0.824317	−	0.529756i	−0.0591502	−	0.998249i	$-0.518839\pi$
$17$	3.39875	−	2.18424i	0.824317	−	0.529756i	0.883467	+	0.468493i	$0.155203\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	0.353661	+	0.227284i	0.0811354	+	0.0521426i	0.580580	−	0.814204i	$-0.302826\pi$
$19$	0.353661	+	0.227284i	0.0811354	+	0.0521426i	−0.499444	+	0.866346i	$0.666462\pi$
$20$	−0.654861	+	0.755750i	−0.146431	+	0.168991i
$21$	2.83281	+	0.831787i	0.618169	+	0.181511i
$22$	−0.346787			−0.0739353
$23$	4.27109	+	2.18123i	0.890585	+	0.454817i
$23$	4.27109	+	2.18123i	0.890585	+	0.454817i
$24$	1.00000			0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	−3.76876	+	4.34939i	−0.739116	+	0.852985i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.420170	+	2.92235i	−0.0794047	+	0.552272i
$29$	3.21798	−	2.06807i	0.597563	−	0.384031i	−0.206612	−	0.978423i	$-0.566244\pi$
$29$	3.21798	−	2.06807i	0.597563	−	0.384031i	0.804175	+	0.594392i	$0.202607\pi$
$30$	0.415415	+	0.909632i	0.0758441	+	0.166075i
$31$	−6.38358	−	7.36705i	−1.14653	−	1.32316i	−0.938596	−	0.345017i	$-0.887873\pi$
$31$	−6.38358	−	7.36705i	−1.14653	−	1.32316i	−0.207929	−	0.978144i	$-0.566672\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	−0.144061	+	0.315449i	−0.0250777	+	0.0549126i
$34$	3.87645	−	1.13823i	0.664805	−	0.195204i
$35$	−2.83281	+	0.831787i	−0.478832	+	0.140598i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−1.02158	−	7.10522i	−0.167946	−	1.16809i	−0.883121	−	0.469146i	$-0.844562\pi$
$37$	−1.02158	−	7.10522i	−0.167946	−	1.16809i	0.715175	−	0.698946i	$-0.246347\pi$
$38$	0.275302	+	0.317716i	0.0446599	+	0.0515403i
$39$	2.39074	+	5.23499i	0.382825	+	0.838269i
$40$	−0.841254	+	0.540641i	−0.133014	+	0.0854828i
$41$	0.0904755	−	0.629271i	0.0141299	−	0.0982756i	−0.981536	−	0.191277i	$-0.938737\pi$
$41$	0.0904755	−	0.629271i	0.0141299	−	0.0982756i	0.995666	+	0.0930016i	$0.0296462\pi$
$42$	2.48372	+	1.59619i	0.383246	+	0.246297i
$43$	−0.142051	+	0.163936i	−0.0216626	+	0.0250000i	−0.766478	−	0.642271i	$-0.777992\pi$
$43$	−0.142051	+	0.163936i	−0.0216626	+	0.0250000i	0.744815	+	0.667271i	$0.232538\pi$
$44$	−0.332740	−	0.0977012i	−0.0501624	−	0.0147290i
$45$	1.00000			0.149071
$46$	3.48356	+	3.29618i	0.513623	+	0.485995i
$47$	5.27458			0.769377			0.384688	−	0.923046i	$-0.374309\pi$
$47$	5.27458			0.769377			0.384688	+	0.923046i	$0.374309\pi$
$48$	0.959493	+	0.281733i	0.138491	+	0.0406646i
$49$	−1.12417	+	1.29737i	−0.160596	+	0.185338i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	0.574966	−	3.99898i	0.0805113	−	0.559969i
$52$	−4.84147	+	3.11142i	−0.671391	+	0.431477i
$53$	1.84214	+	4.03373i	0.253038	+	0.554075i	0.992937	−	0.118642i	$-0.0378542\pi$
$53$	1.84214	+	4.03373i	0.253038	+	0.554075i	−0.739899	+	0.672717i	$0.765127\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	−0.0493529	−	0.343257i	−0.00665475	−	0.0462848i
$56$	−1.22647	+	2.68560i	−0.163894	+	0.358878i
$57$	0.403369	−	0.118440i	0.0534275	−	0.0156877i
$58$	3.67027	−	1.07769i	0.481930	−	0.141507i
$59$	−3.02769	+	6.62972i	−0.394172	+	0.863116i	0.603656	+	0.797245i	$0.293710\pi$
$59$	−3.02769	+	6.62972i	−0.394172	+	0.863116i	−0.997828	+	0.0658715i	$0.979017\pi$
$60$	0.142315	+	0.989821i	0.0183728	+	0.127785i
$61$	−0.141270	−	0.163034i	−0.0180877	−	0.0208744i	0.746634	−	0.665235i	$-0.231669\pi$
$61$	−0.141270	−	0.163034i	−0.0180877	−	0.0208744i	−0.764721	+	0.644361i	$0.777123\pi$
$62$	−4.04947	−	8.86709i	−0.514283	−	1.12612i
$63$	2.48372	−	1.59619i	0.312919	−	0.201101i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−4.84147	−	3.11142i	−0.600510	−	0.385924i
$66$	−0.227097	+	0.262084i	−0.0279537	+	0.0322603i
$67$	−1.64642	−	0.483433i	−0.201142	−	0.0590607i	0.179609	−	0.983738i	$-0.442517\pi$
$67$	−1.64642	−	0.483433i	−0.201142	−	0.0590607i	−0.380752	+	0.924677i	$0.624335\pi$
$68$	4.04010			0.489934
$69$	4.44543	−	1.79948i	0.535167	−	0.216632i
$70$	−2.95240			−0.352879
$71$	3.18335	+	0.934716i	0.377794	+	0.110930i	0.465116	−	0.885250i	$-0.346013\pi$
$71$	3.18335	+	0.934716i	0.377794	+	0.110930i	−0.0873217	+	0.996180i	$0.527831\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−3.03256	−	1.94891i	−0.354934	−	0.228103i	0.351007	−	0.936373i	$-0.385839\pi$
$73$	−3.03256	−	1.94891i	−0.354934	−	0.228103i	−0.705941	+	0.708270i	$0.749476\pi$
$74$	1.02158	−	7.10522i	0.118756	−	0.825965i
$75$	−0.841254	+	0.540641i	−0.0971396	+	0.0624278i
$76$	0.174640	+	0.382407i	0.0200325	+	0.0438651i
$77$	−0.670482	−	0.773777i	−0.0764085	−	0.0881801i
$78$	0.819031	+	5.69648i	0.0927370	+	0.645000i
$79$	4.64031	−	10.1609i	0.522076	−	1.14319i	−0.446572	−	0.894748i	$-0.647355\pi$
$79$	4.64031	−	10.1609i	0.522076	−	1.14319i	0.968648	−	0.248439i	$-0.0799175\pi$
$80$	−0.959493	+	0.281733i	−0.107275	+	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	0.264097	−	0.578291i	0.0291646	−	0.0638615i
$83$	−2.32955	−	16.2024i	−0.255701	−	1.77844i	−0.562631	−	0.826708i	$-0.690211\pi$
$83$	−2.32955	−	16.2024i	−0.255701	−	1.77844i	0.306930	−	0.951732i	$-0.400698\pi$
$84$	1.93341	+	2.23127i	0.210952	+	0.243452i
$85$	1.67832	+	3.67500i	0.182039	+	0.398610i
$86$	−0.182483	+	0.117275i	−0.0196777	+	0.0126461i
$87$	0.544385	−	3.78628i	0.0583642	−	0.405932i
$88$	−0.291736	−	0.187487i	−0.0310991	−	0.0199862i
$89$	−0.189805	+	0.219047i	−0.0201193	+	0.0232189i	−0.765720	−	0.643174i	$-0.777617\pi$
$89$	−0.189805	+	0.219047i	−0.0201193	+	0.0232189i	0.745601	+	0.666393i	$0.232163\pi$
$90$	0.959493	+	0.281733i	0.101139	+	0.0296972i
$91$	−16.9912			−1.78117
$92$	2.41381	+	4.14409i	0.251657	+	0.432052i
$93$	−9.74800			−1.01082
$94$	5.06092	+	1.48602i	0.521995	+	0.153271i
$95$	−0.275302	+	0.317716i	−0.0282454	+	0.0325969i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	1.46491	−	10.1887i	0.148739	−	1.03450i	−0.769548	−	0.638589i	$-0.779518\pi$
$97$	1.46491	−	10.1887i	0.148739	−	1.03450i	0.918287	−	0.395915i	$-0.129572\pi$
$98$	−1.44415	+	0.928098i	−0.145881	+	0.0937520i
$99$	0.144061	+	0.315449i	0.0144786	+	0.0317038i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	2.53633	+	17.6406i	0.252374	+	1.75530i	0.583872	+	0.811846i	$0.301537\pi$
$101$	2.53633	+	17.6406i	0.252374	+	1.75530i	−0.331498	+	0.943456i	$0.607554\pi$
$102$	1.67832	−	3.67500i	0.166178	−	0.363879i
$103$	−9.41007	+	2.76305i	−0.927202	+	0.272251i	−0.710265	−	0.703935i	$-0.751425\pi$
$103$	−9.41007	+	2.76305i	−0.927202	+	0.272251i	−0.216937	+	0.976186i	$0.569607\pi$
$104$	−5.52194	+	1.62139i	−0.541471	+	0.158990i
$105$	−1.22647	+	2.68560i	−0.119691	+	0.262087i
$106$	0.631089	+	4.38932i	0.0612968	+	0.426329i
$107$	−4.58998	−	5.29712i	−0.443730	−	0.512092i	0.489189	−	0.872178i	$-0.337293\pi$
$107$	−4.58998	−	5.29712i	−0.443730	−	0.512092i	−0.932919	+	0.360086i	$0.882747\pi$
$108$	−0.415415	−	0.909632i	−0.0399733	−	0.0875294i
$109$	−4.02790	+	2.58857i	−0.385803	+	0.247940i	−0.719137	−	0.694868i	$-0.755463\pi$
$109$	−4.02790	+	2.58857i	−0.385803	+	0.247940i	0.333334	+	0.942809i	$0.391826\pi$
$110$	0.0493529	−	0.343257i	0.00470562	−	0.0327283i
$111$	−6.03876	−	3.88088i	−0.573174	−	0.368356i
$112$	−1.93341	+	2.23127i	−0.182690	+	0.210836i
$113$	−12.0928	−	3.55076i	−1.13759	−	0.334028i	−0.341906	−	0.939734i	$-0.611072\pi$
$113$	−12.0928	−	3.55076i	−1.13759	−	0.334028i	−0.795688	+	0.605707i	$0.792891\pi$
$114$	0.420398			0.0393739
$115$	−2.76687	+	3.91720i	−0.258012	+	0.365281i
$116$	3.82522			0.355162
$117$	5.52194	+	1.62139i	0.510504	+	0.149897i
$118$	−4.77286	+	5.50817i	−0.439377	+	0.507068i
$119$	10.0345	+	6.44875i	0.919857	+	0.591156i
$120$	−0.142315	+	0.989821i	−0.0129915	+	0.0903579i
$121$	−9.15262	+	5.88203i	−0.832056	+	0.534730i
$122$	−0.0896154	−	0.196230i	−0.00811340	−	0.0177659i
$123$	−0.416322	−	0.480461i	−0.0375385	−	0.0433217i
$124$	−1.38729	−	9.64878i	−0.124582	−	0.866486i
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$	2.83281	−	0.831787i	0.252366	−	0.0741015i
$127$	16.8686	−	4.95306i	1.49684	−	0.439513i	0.572126	−	0.820166i	$-0.306119\pi$
$127$	16.8686	−	4.95306i	1.49684	−	0.439513i	0.924718	+	0.380653i	$0.124301\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	0.0308707	+	0.214711i	0.00271802	+	0.0189042i
$130$	−3.76876	−	4.34939i	−0.330543	−	0.381466i
$131$	−5.41130	−	11.8491i	−0.472787	−	1.03526i	−0.984384	−	0.176034i	$-0.943673\pi$
$131$	−5.41130	−	11.8491i	−0.472787	−	1.03526i	0.511597	−	0.859226i	$-0.329054\pi$
$132$	−0.291736	+	0.187487i	−0.0253923	+	0.0163187i
$133$	−0.176639	+	1.22855i	−0.0153165	+	0.106529i
$134$	−1.44353	−	0.927701i	−0.124702	−	0.0801412i
$135$	0.654861	−	0.755750i	0.0563614	−	0.0650446i
$136$	3.87645	+	1.13823i	0.332402	+	0.0976022i
$137$	11.3999			0.973959			0.486979	−	0.873413i	$-0.338099\pi$
$137$	11.3999			0.973959			0.486979	+	0.873413i	$0.338099\pi$
$138$	4.77233	−	0.474163i	0.406248	−	0.0403635i
$139$	−18.5308			−1.57176			−0.785880	−	0.618379i	$-0.787790\pi$
$139$	−18.5308			−1.57176			−0.785880	+	0.618379i	$0.787790\pi$
$140$	−2.83281	−	0.831787i	−0.239416	−	0.0702988i
$141$	3.45412	−	3.98626i	0.290889	−	0.335704i
$142$	2.79106	+	1.79371i	0.234221	+	0.150525i
$143$	0.284029	−	1.97547i	0.0237517	−	0.165197i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	1.58905	+	3.47954i	0.131964	+	0.288960i
$146$	−2.36065	−	2.72434i	−0.195369	−	0.225468i
$147$	0.244307	+	1.69919i	0.0201501	+	0.140147i
$148$	2.98197	−	6.52960i	0.245116	−	0.536730i
$149$	7.06196	−	2.07358i	0.578539	−	0.169874i	0.0206452	−	0.999787i	$-0.493428\pi$
$149$	7.06196	−	2.07358i	0.578539	−	0.169874i	0.557893	+	0.829913i	$0.311610\pi$
$150$	−0.959493	+	0.281733i	−0.0783423	+	0.0230034i
$151$	−2.86104	+	6.26481i	−0.232828	+	0.509823i	−0.989598	−	0.143858i	$-0.954049\pi$
$151$	−2.86104	+	6.26481i	−0.232828	+	0.509823i	0.756770	+	0.653681i	$0.226776\pi$
$152$	0.0598289	+	0.416119i	0.00485276	+	0.0337517i
$153$	−2.64570	−	3.05330i	−0.213892	−	0.246845i
$154$	−0.425324	−	0.931330i	−0.0342736	−	0.0750487i
$155$	8.20054	−	5.27017i	0.658683	−	0.423310i
$156$	−0.819031	+	5.69648i	−0.0655749	+	0.456084i
$157$	3.97870	+	2.55696i	0.317535	+	0.204067i	0.689693	−	0.724102i	$-0.257746\pi$
$157$	3.97870	+	2.55696i	0.317535	+	0.204067i	−0.372158	+	0.928170i	$0.621382\pi$
$158$	7.31499	−	8.44195i	0.581950	−	0.671606i
$159$	4.25483	+	1.24933i	0.337430	+	0.0990785i
$160$	−1.00000			−0.0790569
$161$	−0.619522	+	14.1457i	−0.0488252	+	1.11483i
$162$	−1.00000			−0.0785674
$163$	−11.8711	−	3.48568i	−0.929819	−	0.273020i	−0.218458	−	0.975846i	$-0.570103\pi$
$163$	−11.8711	−	3.48568i	−0.929819	−	0.273020i	−0.711361	+	0.702827i	$0.751921\pi$
$164$	0.416322	−	0.480461i	0.0325093	−	0.0375177i
$165$	−0.291736	−	0.187487i	−0.0227116	−	0.0145959i
$166$	2.32955	−	16.2024i	0.180808	−	1.25755i
$167$	6.69283	−	4.30122i	0.517907	−	0.332838i	−0.255437	−	0.966826i	$-0.582219\pi$
$167$	6.69283	−	4.30122i	0.517907	−	0.332838i	0.773343	+	0.633987i	$0.218583\pi$
$168$	1.22647	+	2.68560i	0.0946243	+	0.207198i
$169$	−13.1763	−	15.2062i	−1.01356	−	1.16971i
$170$	0.574966	+	3.99898i	0.0440979	+	0.306707i
$171$	0.174640	−	0.382407i	0.0133550	−	0.0292434i
$172$	−0.208132	+	0.0611130i	−0.0158699	+	0.00465982i
$173$	0.590686	−	0.173441i	0.0449090	−	0.0131865i	−0.259201	−	0.965823i	$-0.583459\pi$
$173$	0.590686	−	0.173441i	0.0449090	−	0.0131865i	0.304110	+	0.952637i	$0.401641\pi$
$174$	1.58905	−	3.47954i	0.120466	−	0.263783i
$175$	−0.420170	−	2.92235i	−0.0317619	−	0.220909i
$176$	−0.227097	−	0.262084i	−0.0171181	−	0.0197553i
$177$	3.02769	+	6.62972i	0.227575	+	0.498320i
$178$	−0.243829	+	0.156700i	−0.0182758	+	0.0117451i
$179$	−0.483864	+	3.36535i	−0.0361657	+	0.251538i	−0.999882	−	0.0153923i	$-0.995100\pi$
$179$	−0.483864	+	3.36535i	−0.0361657	+	0.251538i	0.963716	+	0.266930i	$0.0860094\pi$
$180$	0.841254	+	0.540641i	0.0627033	+	0.0402970i
$181$	−4.40472	+	5.08332i	−0.327401	+	0.377840i	−0.895456	−	0.445150i	$-0.853150\pi$
$181$	−4.40472	+	5.08332i	−0.327401	+	0.377840i	0.568056	+	0.822990i	$0.307696\pi$
$182$	−16.3030	−	4.78699i	−1.20846	−	0.354835i
$183$	−0.215725			−0.0159468
$184$	1.14851	+	4.65628i	0.0846694	+	0.343265i
$185$	7.17829			0.527758
$186$	−9.35314	−	2.74633i	−0.685805	−	0.201371i
$187$	−0.917495	+	1.05885i	−0.0670939	+	0.0774305i
$188$	4.43726	+	2.85165i	0.323621	+	0.207978i
$189$	0.420170	−	2.92235i	0.0305629	−	0.212570i
$190$	−0.353661	+	0.227284i	−0.0256573	+	0.0164889i
$191$	−7.54901	−	16.5300i	−0.546227	−	1.19607i	−0.958521	−	0.285020i	$-0.908000\pi$
$191$	−7.54901	−	16.5300i	−0.546227	−	1.19607i	0.412294	−	0.911051i	$-0.364728\pi$
$192$	0.654861	+	0.755750i	0.0472605	+	0.0545415i
$193$	2.63740	+	18.3435i	0.189844	+	1.32040i	0.832408	+	0.554164i	$0.186962\pi$
$193$	2.63740	+	18.3435i	0.189844	+	1.32040i	−0.642563	+	0.766233i	$0.722129\pi$
$194$	4.27606	−	9.36325i	0.307003	−	0.672243i
$195$	−5.52194	+	1.62139i	−0.395434	+	0.116110i
$196$	−1.64713	+	0.483640i	−0.117652	+	0.0345457i
$197$	−3.27278	+	7.16639i	−0.233176	+	0.510584i	−0.989661	−	0.143427i	$-0.954188\pi$
$197$	−3.27278	+	7.16639i	−0.233176	+	0.510584i	0.756485	+	0.654011i	$0.226915\pi$
$198$	0.0493529	+	0.343257i	0.00350736	+	0.0243942i
$199$	−12.4117	−	14.3239i	−0.879844	−	1.01539i	−0.999744	−	0.0226081i	$-0.992803\pi$
$199$	−12.4117	−	14.3239i	−0.879844	−	1.01539i	0.119900	−	0.992786i	$-0.461742\pi$
$200$	−0.415415	−	0.909632i	−0.0293743	−	0.0643207i
$201$	−1.44353	+	0.927701i	−0.101819	+	0.0654350i
$202$	−2.53633	+	17.6406i	−0.178456	+	1.24119i
$203$	9.50075	+	6.10576i	0.666822	+	0.428540i
$204$	2.64570	−	3.05330i	0.185236	−	0.213774i
$205$	0.609990	+	0.179109i	0.0426035	+	0.0125095i
$206$	−9.80734			−0.683310
$207$	1.55118	−	4.53804i	0.107815	−	0.315416i
$208$	−5.75506			−0.399042
$209$	−0.139883	−	0.0410734i	−0.00967592	−	0.00284111i
$210$	−1.93341	+	2.23127i	−0.133418	+	0.153973i
$211$	10.5747	+	6.79596i	0.727993	+	0.467853i	0.851409	−	0.524502i	$-0.175748\pi$
$211$	10.5747	+	6.79596i	0.727993	+	0.467853i	−0.123416	+	0.992355i	$0.539385\pi$
$212$	−0.631089	+	4.38932i	−0.0433434	+	0.301460i
$213$	2.79106	−	1.79371i	0.191240	−	0.122903i
$214$	−2.91168	−	6.37569i	−0.199038	−	0.435833i
$215$	−0.142051	−	0.163936i	−0.00968783	−	0.0111803i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	11.9556	−	26.1792i	0.811602	−	1.77716i
$218$	−4.59403	+	1.34893i	−0.311147	+	0.0913609i
$219$	−3.45879	+	1.01559i	−0.233724	+	0.0686274i
$220$	0.144061	−	0.315449i	0.00971256	−	0.0212675i
$221$	3.30896	+	23.0144i	0.222585	+	1.54811i
$222$	−4.70078	−	5.42499i	−0.315496	−	0.364101i
$223$	8.74038	+	19.1388i	0.585299	+	1.28163i	0.938242	+	0.345981i	$0.112454\pi$
$223$	8.74038	+	19.1388i	0.585299	+	1.28163i	−0.352943	+	0.935645i	$0.614819\pi$
$224$	−2.48372	+	1.59619i	−0.165950	+	0.106650i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	−10.6026	−	6.81386i	−0.705273	−	0.453251i
$227$	14.5093	−	16.7446i	0.963017	−	1.11138i	−0.0307079	−	0.999528i	$-0.509776\pi$
$227$	14.5093	−	16.7446i	0.963017	−	1.11138i	0.993725	−	0.111852i	$-0.0356784\pi$
$228$	0.403369	+	0.118440i	0.0267138	+	0.00784386i
$229$	19.9430			1.31787			0.658936	−	0.752199i	$-0.271007\pi$
$229$	19.9430			1.31787			0.658936	+	0.752199i	$0.271007\pi$
$230$	−3.75839	+	2.97901i	−0.247821	+	0.196430i
$231$	−1.02385			−0.0673646
$232$	3.67027	+	1.07769i	0.240965	+	0.0707537i
$233$	9.97082	−	11.5069i	0.653210	−	0.753845i	−0.328442	−	0.944524i	$-0.606524\pi$
$233$	9.97082	−	11.5069i	0.653210	−	0.753845i	0.981652	+	0.190679i	$0.0610691\pi$
$234$	4.84147	+	3.11142i	0.316497	+	0.203400i
$235$	−0.750651	+	5.22089i	−0.0489671	+	0.340574i
$236$	−6.13136	+	3.94038i	−0.399117	+	0.256497i
$237$	−4.64031	−	10.1609i	−0.301421	−	0.660019i
$238$	7.81117	+	9.01457i	0.506323	+	0.584328i
$239$	−2.92470	−	20.3417i	−0.189183	−	1.31580i	−0.834129	−	0.551569i	$-0.814029\pi$
$239$	−2.92470	−	20.3417i	−0.189183	−	1.31580i	0.644946	−	0.764228i	$-0.276880\pi$
$240$	−0.415415	+	0.909632i	−0.0268149	+	0.0587165i
$241$	−21.3434	+	6.26697i	−1.37485	+	0.403691i	−0.883972	−	0.467539i	$-0.845141\pi$
$241$	−21.3434	+	6.26697i	−1.37485	+	0.403691i	−0.490874	+	0.871231i	$0.663322\pi$
$242$	−10.4390	+	3.06518i	−0.671046	+	0.197037i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	−0.0307009	−	0.213529i	−0.00196542	−	0.0136698i
$245$	−1.12417	−	1.29737i	−0.0718209	−	0.0828857i
$246$	−0.264097	−	0.578291i	−0.0168382	−	0.0368705i
$247$	−2.03534	+	1.30804i	−0.129506	+	0.0832283i
$248$	1.38729	−	9.64878i	0.0880927	−	0.612698i
$249$	−13.7705	−	8.84974i	−0.872667	−	0.560829i
$250$	0.654861	−	0.755750i	0.0414170	−	0.0477978i
$251$	13.7477	+	4.03668i	0.867746	+	0.254793i	0.685156	−	0.728396i	$-0.259734\pi$
$251$	13.7477	+	4.03668i	0.867746	+	0.254793i	0.182590	+	0.983189i	$0.441552\pi$
$252$	2.95240			0.185984
$253$	−1.63427	−	0.308490i	−0.102746	−	0.0193946i
$254$	17.5807			1.10311
$255$	3.87645	+	1.13823i	0.242752	+	0.0712786i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	16.3367	+	10.4990i	1.01906	+	0.654909i	0.939722	−	0.341939i	$-0.111084\pi$
$257$	16.3367	+	10.4990i	1.01906	+	0.654909i	0.0793362	+	0.996848i	$0.474720\pi$
$258$	−0.0308707	+	0.214711i	−0.00192193	+	0.0133673i
$259$	17.8288	−	11.4579i	1.10783	−	0.711959i
$260$	−2.39074	−	5.23499i	−0.148267	−	0.324660i
$261$	−2.50498	−	2.89090i	−0.155055	−	0.178943i
$262$	−1.85383	−	12.8937i	−0.114530	−	0.796572i
$263$	9.42067	−	20.6284i	0.580904	−	1.27200i	−0.359881	−	0.932998i	$-0.617183\pi$
$263$	9.42067	−	20.6284i	0.580904	−	1.27200i	0.940785	−	0.339004i	$-0.110090\pi$
$264$	−0.332740	+	0.0977012i	−0.0204787	+	0.00601309i
$265$	−4.25483	+	1.24933i	−0.261372	+	0.0767458i
$266$	−0.515606	+	1.12902i	−0.0316138	+	0.0692246i
$267$	0.0412486	+	0.286890i	0.00252437	+	0.0175574i
$268$	−1.12369	−	1.29681i	−0.0686406	−	0.0792154i
$269$	12.4780	+	27.3231i	0.760798	+	1.66592i	0.745928	+	0.666027i	$0.232006\pi$
$269$	12.4780	+	27.3231i	0.760798	+	1.66592i	0.0148703	+	0.999889i	$0.495266\pi$
$270$	0.841254	−	0.540641i	0.0511971	−	0.0329024i
$271$	0.822521	−	5.72076i	0.0499646	−	0.347511i	−0.949469	−	0.313861i	$-0.898378\pi$
$271$	0.822521	−	5.72076i	0.0499646	−	0.347511i	0.999434	−	0.0336507i	$-0.0107134\pi$
$272$	3.39875	+	2.18424i	0.206079	+	0.132439i
$273$	−11.1269	+	12.8411i	−0.673430	+	0.777180i
$274$	10.9381	+	3.21172i	0.660796	+	0.194027i
$275$	0.346787			0.0209120
$276$	4.71261	+	0.889565i	0.283666	+	0.0535455i
$277$	4.35921			0.261919			0.130960	−	0.991388i	$-0.458194\pi$
$277$	4.35921			0.261919			0.130960	+	0.991388i	$0.458194\pi$
$278$	−17.7801	−	5.22072i	−1.06638	−	0.313118i
$279$	−6.38358	+	7.36705i	−0.382175	+	0.441054i
$280$	−2.48372	−	1.59619i	−0.148430	−	0.0953905i
$281$	−2.82007	+	19.6140i	−0.168231	+	1.17007i	0.714307	+	0.699832i	$0.246742\pi$
$281$	−2.82007	+	19.6140i	−0.168231	+	1.17007i	−0.882538	+	0.470240i	$0.844167\pi$
$282$	4.43726	−	2.85165i	0.264235	−	0.169814i
$283$	−2.99166	−	6.55083i	−0.177836	−	0.389406i	0.799632	−	0.600490i	$-0.205028\pi$
$283$	−2.99166	−	6.55083i	−0.177836	−	0.389406i	−0.977468	+	0.211084i	$0.932301\pi$
$284$	2.17266	+	2.50738i	0.128924	+	0.148786i
$285$	0.0598289	+	0.416119i	0.00354396	+	0.0246488i
$286$	0.829078	−	1.81543i	0.0490244	−	0.107348i
$287$	1.80093	−	0.528802i	0.106306	−	0.0312142i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−0.281488	+	0.616373i	−0.0165581	+	0.0362572i
$290$	0.544385	+	3.78628i	0.0319674	+	0.222338i
$291$	−6.74078	−	7.77927i	−0.395151	−	0.456029i
$292$	−1.49749	−	3.27905i	−0.0876342	−	0.191892i
$293$	9.03805	−	5.80840i	0.528009	−	0.339330i	−0.249324	−	0.968420i	$-0.580209\pi$
$293$	9.03805	−	5.80840i	0.528009	−	0.339330i	0.777333	+	0.629090i	$0.216572\pi$
$294$	−0.244307	+	1.69919i	−0.0142482	+	0.0990987i
$295$	−6.13136	−	3.94038i	−0.356981	−	0.229418i
$296$	4.70078	−	5.42499i	0.273227	−	0.315321i
$297$	0.332740	+	0.0977012i	0.0193075	+	0.00566920i
$298$	7.36010			0.426359
$299$	−21.6298	+	17.1444i	−1.25088	+	0.991486i
$300$	−1.00000			−0.0577350
$301$	−0.614488	−	0.180430i	−0.0354185	−	0.0103998i
$302$	−4.51015	+	5.20499i	−0.259530	+	0.299514i
$303$	14.9928	+	9.63528i	0.861313	+	0.553532i
$304$	−0.0598289	+	0.416119i	−0.00343142	+	0.0238661i
$305$	0.181479	−	0.116630i	0.0103915	−	0.00667820i
$306$	−1.67832	−	3.67500i	−0.0959430	−	0.210086i
$307$	6.63438	+	7.65648i	0.378644	+	0.436979i	0.912800	−	0.408408i	$-0.133916\pi$
$307$	6.63438	+	7.65648i	0.378644	+	0.436979i	−0.534156	+	0.845386i	$0.679370\pi$
$308$	−0.145710	−	1.01343i	−0.00830258	−	0.0577457i
$309$	−4.07412	+	8.92107i	−0.231768	+	0.507502i
$310$	9.35314	−	2.74633i	0.531223	−	0.155981i
$311$	−18.6805	+	5.48508i	−1.05927	+	0.311030i	−0.764558	−	0.644555i	$-0.777043\pi$
$311$	−18.6805	+	5.48508i	−1.05927	+	0.311030i	−0.294714	+	0.955586i	$0.595224\pi$
$312$	−2.39074	+	5.23499i	−0.135349	+	0.296373i
$313$	4.69396	+	32.6472i	0.265319	+	1.84533i	0.491037	+	0.871139i	$0.336618\pi$
$313$	4.69396	+	32.6472i	0.265319	+	1.84533i	−0.225719	+	0.974193i	$0.572473\pi$
$314$	3.09716	+	3.57431i	0.174783	+	0.201710i
$315$	1.22647	+	2.68560i	0.0691038	+	0.151316i
$316$	9.39706	−	6.03912i	0.528626	−	0.339727i
$317$	−1.89175	+	13.1574i	−0.106252	+	0.738996i	0.865143	+	0.501525i	$0.167227\pi$
$317$	−1.89175	+	13.1574i	−0.106252	+	0.738996i	−0.971395	+	0.237471i	$0.923682\pi$
$318$	3.73051	+	2.39745i	0.209196	+	0.134442i
$319$	−0.868696	+	1.00253i	−0.0486376	+	0.0561308i
$320$	−0.959493	−	0.281733i	−0.0536373	−	0.0157493i
$321$	−7.00909			−0.391209
$322$	−4.57972	+	13.3981i	−0.255218	+	0.746648i
$323$	1.69845			0.0945042
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	3.76876	−	4.34939i	0.209053	−	0.241261i
$326$	−10.4082	−	6.68897i	−0.576459	−	0.370468i
$327$	−0.681399	+	4.73924i	−0.0376815	+	0.262080i
$328$	0.534820	−	0.343708i	0.0295305	−	0.0189781i
$329$	6.46912	+	14.1654i	0.356654	+	0.780964i
$330$	−0.227097	−	0.262084i	−0.0125013	−	0.0144273i
$331$	3.98739	+	27.7329i	0.219167	+	1.52434i	0.741125	+	0.671367i	$0.234292\pi$
$331$	3.98739	+	27.7329i	0.219167	+	1.52434i	−0.521959	+	0.852971i	$0.674799\pi$
$332$	6.79992	−	14.8897i	0.373194	−	0.817181i
$333$	−6.88752	+	2.02236i	−0.377434	+	0.110824i
$334$	7.63351	−	2.24140i	0.417687	−	0.122644i
$335$	0.712823	−	1.56086i	0.0389457	−	0.0852791i
$336$	0.420170	+	2.92235i	0.0229222	+	0.159427i
$337$	4.87231	+	5.62295i	0.265412	+	0.306302i	0.872775	−	0.488123i	$-0.162318\pi$
$337$	4.87231	+	5.62295i	0.265412	+	0.306302i	−0.607363	+	0.794424i	$0.707773\pi$
$338$	−8.35846	−	18.3025i	−0.454640	−	0.995523i
$339$	−10.6026	+	6.81386i	−0.575853	+	0.370078i
$340$	−0.574966	+	3.99898i	−0.0311819	+	0.216875i
$341$	2.84384	+	1.82763i	0.154003	+	0.0989715i
$342$	0.275302	−	0.317716i	0.0148866	−	0.0171801i
$343$	14.9667	+	4.39461i	0.808124	+	0.237287i
$344$	−0.216919			−0.0116955
$345$	1.14851	+	4.65628i	0.0618338	+	0.250686i
$346$	0.615623			0.0330961
$347$	19.9581	+	5.86022i	1.07141	+	0.314593i	0.769436	−	0.638724i	$-0.220538\pi$
$347$	19.9581	+	5.86022i	1.07141	+	0.314593i	0.301970	+	0.953317i	$0.402356\pi$
$348$	2.50498	−	2.89090i	0.134281	−	0.154969i
$349$	−24.8810	−	15.9901i	−1.33185	−	0.855928i	−0.335563	−	0.942018i	$-0.608926\pi$
$349$	−24.8810	−	15.9901i	−1.33185	−	0.855928i	−0.996287	+	0.0860896i	$0.972563\pi$
$350$	0.420170	−	2.92235i	0.0224590	−	0.156206i
$351$	4.84147	−	3.11142i	0.258418	−	0.166075i
$352$	−0.144061	−	0.315449i	−0.00767845	−	0.0168135i
$353$	−21.0906	−	24.3398i	−1.12254	−	1.29548i	−0.950617	−	0.310367i	$-0.899548\pi$
$353$	−21.0906	−	24.3398i	−1.12254	−	1.29548i	−0.171921	−	0.985111i	$-0.554997\pi$
$354$	1.03724	+	7.21417i	0.0551288	+	0.383429i
$355$	−1.37824	+	3.01793i	−0.0731494	+	0.160175i
$356$	−0.278100	+	0.0816575i	−0.0147393	+	0.00432784i
$357$	11.4448	−	3.36050i	0.605724	−	0.177857i
$358$	−1.41239	+	3.09271i	−0.0746473	+	0.163455i
$359$	−0.967592	−	6.72975i	−0.0510676	−	0.355183i	−0.999293	−	0.0375859i	$-0.988033\pi$
$359$	−0.967592	−	6.72975i	−0.0510676	−	0.355183i	0.948226	−	0.317597i	$-0.102876\pi$
$360$	0.654861	+	0.755750i	0.0345142	+	0.0398315i
$361$	−7.81947	−	17.1222i	−0.411551	−	0.901171i
$362$	−5.65844	+	3.63646i	−0.297401	+	0.191128i
$363$	−1.54835	+	10.7690i	−0.0812672	+	0.565226i
$364$	−14.2939	−	9.18616i	−0.749206	−	0.481486i
$365$	2.36065	−	2.72434i	0.123562	−	0.142598i
$366$	−0.206987	−	0.0607767i	−0.0108194	−	0.00317685i
$367$	−0.567641			−0.0296306			−0.0148153	−	0.999890i	$-0.504716\pi$
$367$	−0.567641			−0.0296306			−0.0148153	+	0.999890i	$0.504716\pi$
$368$	−0.209837	+	4.79124i	−0.0109385	+	0.249761i
$369$	−0.635742			−0.0330954
$370$	6.88752	+	2.02236i	0.358065	+	0.105137i
$371$	−8.57363	+	9.89450i	−0.445121	+	0.513697i
$372$	−8.20054	−	5.27017i	−0.425178	−	0.273245i
$373$	−1.93369	+	13.4491i	−0.100122	+	0.696367i	0.876499	+	0.481403i	$0.159873\pi$
$373$	−1.93369	+	13.4491i	−0.100122	+	0.696367i	−0.976622	+	0.214964i	$0.931037\pi$
$374$	−1.17864	+	0.757467i	−0.0609461	+	0.0391677i
$375$	−0.415415	−	0.909632i	−0.0214519	−	0.0469732i
$376$	3.45412	+	3.98626i	0.178132	+	0.205576i
$377$	3.13297	+	21.7903i	0.161356	+	1.12226i
$378$	1.22647	−	2.68560i	0.0630829	−	0.138132i
$379$	11.0344	−	3.24000i	0.566801	−	0.166428i	0.0142373	−	0.999899i	$-0.495468\pi$
$379$	11.0344	−	3.24000i	0.566801	−	0.166428i	0.552563	+	0.833471i	$0.313650\pi$
$380$	−0.403369	+	0.118440i	−0.0206924	+	0.00607583i
$381$	7.30329	−	15.9920i	0.374159	−	0.819294i
$382$	−2.58618	−	17.9873i	−0.132320	−	0.920308i
$383$	−12.0395	−	13.8944i	−0.615191	−	0.709969i	0.359595	−	0.933108i	$-0.382915\pi$
$383$	−12.0395	−	13.8944i	−0.615191	−	0.709969i	−0.974786	+	0.223140i	$0.928369\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	0.861321	−	0.553537i	0.0438970	−	0.0282109i
$386$	−2.63740	+	18.3435i	−0.134240	+	0.933661i
$387$	0.182483	+	0.117275i	0.00927616	+	0.00596142i
$388$	6.74078	−	7.77927i	0.342211	−	0.394933i
$389$	−8.36837	−	2.45717i	−0.424293	−	0.124584i	0.0626132	−	0.998038i	$-0.480057\pi$
$389$	−8.36837	−	2.45717i	−0.424293	−	0.124584i	−0.486906	+	0.873454i	$0.661875\pi$
$390$	−5.75506			−0.291419
$391$	19.2807	−	1.91567i	0.975067	−	0.0968794i
$392$	−1.71666			−0.0867045
$393$	−12.4986	−	3.66992i	−0.630470	−	0.185123i
$394$	−5.15921	+	5.95405i	−0.259917	+	0.299961i
$395$	9.39706	+	6.03912i	0.472817	+	0.303861i
$396$	−0.0493529	+	0.343257i	−0.00248008	+	0.0172493i
$397$	−12.1959	+	7.83784i	−0.612095	+	0.393370i	−0.809642	−	0.586924i	$-0.800339\pi$
$397$	−12.1959	+	7.83784i	−0.612095	+	0.393370i	0.197547	+	0.980293i	$0.436703\pi$
$398$	−7.87346	−	17.2405i	−0.394661	−	0.864186i
$399$	0.812802	+	0.938023i	0.0406910	+	0.0469599i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	2.31828	−	5.07632i	0.115769	−	0.253499i	−0.842873	−	0.538112i	$-0.819138\pi$
$401$	2.31828	−	5.07632i	0.115769	−	0.253499i	0.958643	+	0.284613i	$0.0918650\pi$
$402$	−1.64642	+	0.483433i	−0.0821160	+	0.0241114i
$403$	53.8279	−	15.8053i	2.68136	−	0.787318i
$404$	−7.40351	+	16.2114i	−0.368338	+	0.806549i
$405$	−0.142315	−	0.989821i	−0.00707168	−	0.0491846i
$406$	7.39571	+	8.53511i	0.367043	+	0.423590i
$407$	1.03411	+	2.26438i	0.0512588	+	0.112241i
$408$	3.39875	−	2.18424i	0.168263	−	0.108136i
$409$	−5.16417	+	35.9176i	−0.255352	+	1.77601i	0.309582	+	0.950873i	$0.399811\pi$
$409$	−5.16417	+	35.9176i	−0.255352	+	1.77601i	−0.564934	+	0.825136i	$0.691098\pi$
$410$	0.534820	+	0.343708i	0.0264129	+	0.0169745i
$411$	7.46534	−	8.61547i	0.368238	−	0.424970i
$412$	−9.41007	−	2.76305i	−0.463601	−	0.136126i
$413$	−21.5181			−1.05884
$414$	2.76687	−	3.91720i	0.135984	−	0.192520i
$415$	16.3690			0.803521
$416$	−5.52194	−	1.62139i	−0.270735	−	0.0794951i
$417$	−12.1351	+	14.0046i	−0.594257	+	0.685809i
$418$	−0.122645	−	0.0788192i	−0.00599877	−	0.00385517i
$419$	−3.48059	+	24.2081i	−0.170038	+	1.18264i	0.708761	+	0.705449i	$0.249255\pi$
$419$	−3.48059	+	24.2081i	−0.170038	+	1.18264i	−0.878799	+	0.477192i	$0.841655\pi$
$420$	−2.48372	+	1.59619i	−0.121193	+	0.0778860i
$421$	10.5510	+	23.1034i	0.514222	+	1.12599i	0.971581	+	0.236708i	$0.0760684\pi$
$421$	10.5510	+	23.1034i	0.514222	+	1.12599i	−0.457358	+	0.889282i	$0.651204\pi$
$422$	8.23172	+	9.49991i	0.400714	+	0.462449i
$423$	−0.750651	−	5.22089i	−0.0364979	−	0.253849i
$424$	−1.84214	+	4.03373i	−0.0894623	+	0.195895i
$425$	−3.87645	+	1.13823i	−0.188035	+	0.0552121i
$426$	3.18335	−	0.934716i	0.154234	−	0.0452871i
$427$	0.264580	−	0.579350i	0.0128039	−	0.0280367i
$428$	−0.997498	−	6.93775i	−0.0482159	−	0.335349i
$429$	−1.30696	−	1.50831i	−0.0631006	−	0.0728219i
$430$	−0.0901112	−	0.197316i	−0.00434555	−	0.00951542i
$431$	−20.1669	+	12.9605i	−0.971405	+	0.624284i	−0.927132	−	0.374735i	$-0.877734\pi$
$431$	−20.1669	+	12.9605i	−0.971405	+	0.624284i	−0.0442731	+	0.999019i	$0.514097\pi$
$432$	0.142315	−	0.989821i	0.00684713	−	0.0476228i
$433$	−18.2945	−	11.7572i	−0.879178	−	0.565014i	0.0213689	−	0.999772i	$-0.493198\pi$
$433$	−18.2945	−	11.7572i	−0.879178	−	0.565014i	−0.900547	+	0.434758i	$0.856834\pi$
$434$	18.8469	−	21.7505i	0.904680	−	1.04406i
$435$	3.67027	+	1.07769i	0.175976	+	0.0516712i
$436$	−4.78797			−0.229302
$437$	1.01476	+	1.74217i	0.0485426	+	0.0833392i
$438$	−3.60481			−0.172245
$439$	28.3812	+	8.33348i	1.35456	+	0.397735i	0.876843	−	0.480778i	$-0.159646\pi$
$439$	28.3812	+	8.33348i	1.35456	+	0.397735i	0.477719	+	0.878513i	$0.341464\pi$
$440$	0.227097	−	0.262084i	0.0108264	−	0.0124944i
$441$	1.44415	+	0.928098i	0.0687690	+	0.0441951i
$442$	−3.30896	+	23.0144i	−0.157391	+	1.09468i
$443$	26.6149	−	17.1043i	1.26451	−	0.812651i	0.275615	−	0.961268i	$-0.411118\pi$
$443$	26.6149	−	17.1043i	1.26451	−	0.812651i	0.988895	+	0.148617i	$0.0474821\pi$
$444$	−2.98197	−	6.52960i	−0.141518	−	0.309881i
$445$	−0.189805	−	0.219047i	−0.00899763	−	0.0103838i
$446$	2.99432	+	20.8260i	0.141785	+	0.986137i
$447$	3.05750	−	6.69498i	0.144615	−	0.316662i
$448$	−2.83281	+	0.831787i	−0.133838	+	0.0392982i
$449$	11.0865	−	3.25529i	0.523205	−	0.153627i	−0.00945661	−	0.999955i	$-0.503010\pi$
$449$	11.0865	−	3.25529i	0.523205	−	0.153627i	0.532661	+	0.846329i	$0.321192\pi$
$450$	−0.415415	+	0.909632i	−0.0195829	+	0.0428805i
$451$	0.0313757	+	0.218223i	0.00147742	+	0.0102757i
$452$	−8.25341	−	9.52495i	−0.388208	−	0.448016i
$453$	2.86104	+	6.26481i	0.134423	+	0.294346i
$454$	18.6391	−	11.9786i	0.874776	−	0.562184i
$455$	2.41811	−	16.8183i	0.113363	−	0.788454i
$456$	0.353661	+	0.227284i	0.0165617	+	0.0106436i
$457$	16.6005	−	19.1580i	0.776539	−	0.896173i	−0.220316	−	0.975429i	$-0.570709\pi$
$457$	16.6005	−	19.1580i	0.776539	−	0.896173i	0.996854	+	0.0792552i	$0.0252542\pi$
$458$	19.1352	+	5.61860i	0.894129	+	0.262540i
$459$	−4.04010			−0.188576
$460$	−4.44543	+	1.79948i	−0.207269	+	0.0839011i
$461$	−11.6638			−0.543237			−0.271619	−	0.962405i	$-0.587559\pi$
$461$	−11.6638			−0.543237			−0.271619	+	0.962405i	$0.587559\pi$
$462$	−0.982381	−	0.288453i	−0.0457045	−	0.0134200i
$463$	3.09152	−	3.56780i	0.143675	−	0.165810i	−0.679351	−	0.733813i	$-0.737739\pi$
$463$	3.09152	−	3.56780i	0.143675	−	0.165810i	0.823026	+	0.568004i	$0.192284\pi$
$464$	3.21798	+	2.06807i	0.149391	+	0.0960076i
$465$	1.38729	−	9.64878i	0.0643338	−	0.447451i
$466$	12.8088	−	8.23172i	0.593357	−	0.381327i
$467$	4.83077	+	10.5779i	0.223541	+	0.489488i	0.987859	−	0.155352i	$-0.0496513\pi$
$467$	4.83077	+	10.5779i	0.223541	+	0.489488i	−0.764318	+	0.644840i	$0.776924\pi$
$468$	3.76876	+	4.34939i	0.174211	+	0.201050i
$469$	−0.720982	−	5.01454i	−0.0332919	−	0.231550i
$470$	−2.19114	+	4.79793i	−0.101070	+	0.221312i
$471$	4.53792	−	1.33245i	0.209096	−	0.0613962i
$472$	−6.99313	+	2.05337i	−0.321885	+	0.0945139i
$473$	0.0312494	−	0.0684267i	0.00143685	−	0.00314626i
$474$	−1.58970	−	11.0566i	−0.0730173	−	0.507847i
$475$	−0.275302	−	0.317716i	−0.0126317	−	0.0145778i
$476$	4.95506	+	10.8501i	0.227115	+	0.497312i
$477$	3.73051	−	2.39745i	0.170808	−	0.109772i
$478$	2.92470	−	20.3417i	0.133773	−	0.930409i
$479$	−21.0079	−	13.5010i	−0.959876	−	0.616875i	−0.0359125	−	0.999355i	$-0.511434\pi$
$479$	−21.0079	−	13.5010i	−0.959876	−	0.616875i	−0.923964	+	0.382480i	$0.875070\pi$
$480$	−0.654861	+	0.755750i	−0.0298902	+	0.0344951i
$481$	39.6381	+	11.6388i	1.80734	+	0.530683i
$482$	−22.2444			−1.01321
$483$	10.2849	+	9.73163i	0.467978	+	0.442805i
$484$	−10.8797			−0.494534
$485$	9.87650	+	2.90000i	0.448469	+	0.131682i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	12.8251	+	8.24216i	0.581159	+	0.373488i	0.797944	−	0.602731i	$-0.205921\pi$
$487$	12.8251	+	8.24216i	0.581159	+	0.373488i	−0.216786	+	0.976219i	$0.569557\pi$
$488$	0.0307009	−	0.213529i	0.00138976	−	0.00966601i
$489$	−10.4082	+	6.68897i	−0.470677	+	0.302486i
$490$	−0.713127	−	1.56153i	−0.0322158	−	0.0705428i
$491$	−19.6154	−	22.6374i	−0.885230	−	1.02161i	−0.999603	−	0.0281721i	$-0.991031\pi$
$491$	−19.6154	−	22.6374i	−0.885230	−	1.02161i	0.114373	−	0.993438i	$-0.463514\pi$
$492$	−0.0904755	−	0.629271i	−0.00407895	−	0.0283697i
$493$	6.41993	−	14.0577i	0.289139	−	0.633126i
$494$	−2.32141	+	0.681628i	−0.104445	+	0.0306679i
$495$	−0.332740	+	0.0977012i	−0.0149555	+	0.00439134i
$496$	4.04947	−	8.86709i	0.181826	−	0.398144i
$497$	1.39402	+	9.69560i	0.0625302	+	0.434907i
$498$	−10.7194	−	12.3708i	−0.480348	−	0.554351i
$499$	−0.526653	−	1.15321i	−0.0235762	−	0.0516247i	0.897478	−	0.441060i	$-0.145397\pi$
$499$	−0.526653	−	1.15321i	−0.0235762	−	0.0516247i	−0.921054	+	0.389435i	$0.872670\pi$
$500$	0.841254	−	0.540641i	0.0376220	−	0.0241782i
$501$	1.13223	−	7.87480i	0.0505841	−	0.351820i
$502$	12.0535	+	7.74634i	0.537976	+	0.345736i
$503$	8.11695	−	9.36746i	0.361917	−	0.417675i	−0.545364	−	0.838199i	$-0.683609\pi$
$503$	8.11695	−	9.36746i	0.361917	−	0.417675i	0.907281	+	0.420525i	$0.138154\pi$
$504$	2.83281	+	0.831787i	0.126183	+	0.0370507i
$505$	−17.8220			−0.793067
$506$	−1.48116	−	0.756421i	−0.0658456	−	0.0336270i
$507$	−20.1207			−0.893594
$508$	16.8686	+	4.95306i	0.748422	+	0.219757i
$509$	−11.3842	+	13.1381i	−0.504598	+	0.582337i	−0.949707	−	0.313139i	$-0.898619\pi$
$509$	−11.3842	+	13.1381i	−0.504598	+	0.582337i	0.445110	+	0.895476i	$0.353165\pi$
$510$	3.39875	+	2.18424i	0.150499	+	0.0967199i
$511$	1.51463	−	10.5345i	0.0670035	−	0.466020i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	−0.174640	−	0.382407i	−0.00771053	−	0.0168837i
$514$	12.7171	+	14.6763i	0.560927	+	0.647344i
$515$	−1.39573	−	9.70751i	−0.0615032	−	0.427764i
$516$	−0.0901112	+	0.197316i	−0.00396693	+	0.00868635i
$517$	−1.75506	+	0.515333i	−0.0771876	+	0.0226643i
$518$	20.3347	−	5.97081i	0.893455	−	0.262342i
$519$	0.255739	−	0.559990i	0.0112257	−	0.0245809i
$520$	−0.819031	−	5.69648i	−0.0359169	−	0.249807i
$521$	7.77442	+	8.97216i	0.340604	+	0.393078i	0.900048	−	0.435790i	$-0.143531\pi$
$521$	7.77442	+	8.97216i	0.340604	+	0.393078i	−0.559445	+	0.828868i	$0.688986\pi$
$522$	−1.58905	−	3.47954i	−0.0695509	−	0.152295i
$523$	−26.2445	+	16.8663i	−1.14759	+	0.737513i	−0.969158	−	0.246438i	$-0.920740\pi$
$523$	−26.2445	+	16.8663i	−1.14759	+	0.737513i	−0.178435	+	0.983952i	$0.557103\pi$
$524$	1.85383	−	12.8937i	0.0809848	−	0.563262i
$525$	−2.48372	−	1.59619i	−0.108398	−	0.0696633i
$526$	14.8508	−	17.1387i	0.647524	−	0.747283i
$527$	−37.7876	−	11.0954i	−1.64605	−	0.483325i
$528$	−0.346787			−0.0150920
$529$	13.4845	+	18.6325i	0.586283	+	0.810107i
$530$	−4.43446			−0.192621
$531$	6.99313	+	2.05337i	0.303476	+	0.0891086i
$532$	−0.812802	+	0.938023i	−0.0352394	+	0.0406685i
$533$	3.07792	+	1.97806i	0.133320	+	0.0856793i
$534$	−0.0412486	+	0.286890i	−0.00178500	+	0.0124150i
$535$	5.89642	−	3.78940i	0.254925	−	0.163830i
$536$	−0.712823	−	1.56086i	−0.0307892	−	0.0674190i
$537$	2.22650	+	2.56952i	0.0960805	+	0.110883i
$538$	4.27478	+	29.7317i	0.184299	+	1.28183i
$539$	0.247303	−	0.541519i	0.0106521	−	0.0233249i
$540$	0.959493	−	0.281733i	0.0412900	−	0.0121238i
$541$	23.6122	−	6.93317i	1.01517	−	0.298080i	0.268502	−	0.963279i	$-0.413471\pi$
$541$	23.6122	−	6.93317i	1.01517	−	0.298080i	0.746666	+	0.665199i	$0.231653\pi$
$542$	2.40093	−	5.25730i	0.103129	−	0.225820i
$543$	0.957238	+	6.65774i	0.0410790	+	0.285711i
$544$	2.64570	+	3.05330i	0.113434	+	0.130909i
$545$	−1.98900	−	4.35529i	−0.0851992	−	0.186560i
$546$	−14.2939	+	9.18616i	−0.611724	+	0.393131i
$547$	5.33379	−	37.0973i	0.228056	−	1.58617i	−0.478226	−	0.878237i	$-0.658720\pi$
$547$	5.33379	−	37.0973i	0.228056	−	1.58617i	0.706282	−	0.707930i	$-0.250371\pi$
$548$	9.59020	+	6.16325i	0.409673	+	0.263281i
$549$	−0.141270	+	0.163034i	−0.00602925	+	0.00695812i
$550$	0.332740	+	0.0977012i	0.0141881	+	0.00416599i
$551$	1.60811			0.0685079
$552$	4.27109	+	2.18123i	0.181790	+	0.0928392i
$553$	32.9792			1.40242
$554$	4.18263	+	1.22813i	0.177703	+	0.0521783i
$555$	4.70078	−	5.42499i	0.199537	−	0.230278i
$556$	−15.5891	−	10.0185i	−0.661124	−	0.424879i
$557$	−5.34586	+	37.1813i	−0.226512	+	1.57542i	0.486125	+	0.873889i	$0.338410\pi$
$557$	−5.34586	+	37.1813i	−0.226512	+	1.57542i	−0.712637	+	0.701533i	$0.752499\pi$
$558$	−8.20054	+	5.27017i	−0.347157	+	0.223104i
$559$	−0.518596	−	1.13557i	−0.0219343	−	0.0480293i
$560$	−1.93341	−	2.23127i	−0.0817015	−	0.0942886i
$561$	0.199391	+	1.38679i	0.00841828	+	0.0585505i
$562$	−8.23173	+	18.0250i	−0.347235	+	0.760338i
$563$	−30.2456	+	8.88091i	−1.27470	+	0.374286i	−0.847947	−	0.530082i	$-0.822161\pi$
$563$	−30.2456	+	8.88091i	−1.27470	+	0.374286i	−0.426754	+	0.904368i	$0.640343\pi$
$564$	5.06092	−	1.48602i	0.213103	−	0.0625728i
$565$	5.23560	−	11.4644i	0.220264	−	0.482310i
$566$	−1.02490	−	7.12832i	−0.0430797	−	0.299626i
$567$	−1.93341	−	2.23127i	−0.0811956	−	0.0937047i
$568$	1.37824	+	3.01793i	0.0578297	+	0.126629i
$569$	−1.13699	+	0.730700i	−0.0476652	+	0.0306326i	−0.564256	−	0.825600i	$-0.690837\pi$
$569$	−1.13699	+	0.730700i	−0.0476652	+	0.0306326i	0.516591	+	0.856232i	$0.327201\pi$
$570$	−0.0598289	+	0.416119i	−0.00250595	+	0.0174293i
$571$	−13.9278	−	8.95086i	−0.582861	−	0.374582i	0.215733	−	0.976452i	$-0.430786\pi$
$571$	−13.9278	−	8.95086i	−0.582861	−	0.374582i	−0.798594	+	0.601871i	$0.794422\pi$
$572$	1.30696	−	1.50831i	0.0546467	−	0.0630656i
$573$	−17.4361	−	5.11971i	−0.728404	−	0.213879i
$574$	1.87696			0.0783429
$575$	−3.48356	−	3.29618i	−0.145275	−	0.137460i
$576$	1.00000			0.0416667
$577$	−36.6055	−	10.7484i	−1.52391	−	0.447460i	−0.590728	−	0.806870i	$-0.701160\pi$
$577$	−36.6055	−	10.7484i	−1.52391	−	0.447460i	−0.933179	+	0.359411i	$0.882978\pi$
$578$	−0.443738	+	0.512101i	−0.0184571	+	0.0213006i
$579$	15.5903	+	10.0192i	0.647909	+	0.416386i
$580$	−0.544385	+	3.78628i	−0.0226044	+	0.157217i
$581$	40.6559	−	26.1280i	1.68669	−	1.08397i
$582$	−4.27606	−	9.36325i	−0.177248	−	0.388119i
$583$	−1.00705	−	1.16220i	−0.0417079	−	0.0481335i
$584$	−0.513018	−	3.56812i	−0.0212288	−	0.147650i
$585$	−2.39074	+	5.23499i	−0.0988449	+	0.216440i
$586$	10.3084	−	3.02681i	0.425834	−	0.125036i
$587$	−22.8381	+	6.70588i	−0.942631	+	0.276781i	−0.716716	−	0.697365i	$-0.754355\pi$
$587$	−22.8381	+	6.70588i	−0.942631	+	0.276781i	−0.225915	+	0.974147i	$0.572537\pi$
$588$	−0.713127	+	1.56153i	−0.0294089	+	0.0643964i
$589$	−0.583212	−	4.05633i	−0.0240308	−	0.167138i
$590$	−4.77286	−	5.50817i	−0.196495	−	0.226768i
$591$	3.27278	+	7.16639i	0.134624	+	0.294786i
$592$	6.03876	−	3.88088i	0.248191	−	0.159503i
$593$	−0.0159378	+	0.110850i	−0.000654485	+	0.00455204i	−0.990146	−	0.140038i	$-0.955277\pi$
$593$	−0.0159378	+	0.110850i	−0.000654485	+	0.00455204i	0.989492	+	0.144590i	$0.0461865\pi$
$594$	0.291736	+	0.187487i	0.0119701	+	0.00769269i
$595$	−7.81117	+	9.01457i	−0.320227	+	0.369561i
$596$	7.06196	+	2.07358i	0.289269	+	0.0849371i
$597$	−18.9532			−0.775704
$598$	−25.5837	+	10.3561i	−1.04620	+	0.423493i
$599$	−25.9804			−1.06153			−0.530766	−	0.847519i	$-0.678096\pi$
$599$	−25.9804			−1.06153			−0.530766	+	0.847519i	$0.678096\pi$
$600$	−0.959493	−	0.281733i	−0.0391711	−	0.0115017i
$601$	1.89211	−	2.18361i	0.0771807	−	0.0890713i	−0.715846	−	0.698258i	$-0.753959\pi$
$601$	1.89211	−	2.18361i	0.0771807	−	0.0890713i	0.793027	+	0.609187i	$0.208504\pi$
$602$	−0.538764	−	0.346243i	−0.0219584	−	0.0141118i
$603$	−0.244202	+	1.69846i	−0.00994468	+	0.0691668i
$604$	−5.79387	+	3.72350i	−0.235749	+	0.151507i
$605$	−4.51961	−	9.89656i	−0.183748	−	0.402352i
$606$	11.6709	+	13.4689i	0.474098	+	0.547138i
$607$	−0.261313	−	1.81747i	−0.0106063	−	0.0737688i	0.983831	−	0.179100i	$-0.0573187\pi$
$607$	−0.261313	−	1.81747i	−0.0106063	−	0.0737688i	−0.994437	+	0.105332i	$0.966410\pi$
$608$	−0.174640	+	0.382407i	−0.00708257	+	0.0155087i
$609$	10.8361	−	3.18176i	0.439101	−	0.128932i
$610$	0.206987	−	0.0607767i	0.00838064	−	0.00246078i
$611$	−12.6102	+	27.6124i	−0.510152	+	1.11708i
$612$	−0.574966	−	3.99898i	−0.0232416	−	0.161649i
$613$	−21.1326	−	24.3883i	−0.853538	−	0.985035i	0.146454	−	0.989218i	$-0.453214\pi$
$613$	−21.1326	−	24.3883i	−0.853538	−	0.985035i	−0.999991	+	0.00418250i	$0.998669\pi$
$614$	4.20856	+	9.21546i	0.169844	+	0.371906i
$615$	0.534820	−	0.343708i	0.0215660	−	0.0138596i
$616$	0.145710	−	1.01343i	0.00587081	−	0.0408324i
$617$	−30.7061	−	19.7336i	−1.23618	−	0.794445i	−0.251339	−	0.967899i	$-0.580871\pi$
$617$	−30.7061	−	19.7336i	−1.23618	−	0.794445i	−0.984842	+	0.173454i	$0.944507\pi$
$618$	−6.42244	+	7.41189i	−0.258348	+	0.298150i
$619$	−30.1359	−	8.84871i	−1.21127	−	0.355660i	−0.387115	−	0.922031i	$-0.626528\pi$
$619$	−30.1359	−	8.84871i	−1.21127	−	0.355660i	−0.824150	+	0.566372i	$0.808347\pi$
$620$	9.74800			0.391489
$621$	−2.41381	−	4.14409i	−0.0968630	−	0.166297i
$622$	−19.4691			−0.780639
$623$	−0.821062	−	0.241086i	−0.0328952	−	0.00965889i
$624$	−3.76876	+	4.34939i	−0.150871	+	0.174115i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−4.69396	+	32.6472i	−0.187609	+	1.30485i
$627$	−0.122645	+	0.0788192i	−0.00489797	+	0.00314774i
$628$	1.96470	+	4.30210i	0.0784002	+	0.171672i
$629$	−18.9916	−	21.9175i	−0.757245	−	0.873907i
$630$	0.420170	+	2.92235i	0.0167400	+	0.116429i
$631$	15.0632	−	32.9837i	0.599655	−	1.31306i	−0.329774	−	0.944060i	$-0.606973\pi$
$631$	15.0632	−	32.9837i	0.599655	−	1.31306i	0.929429	−	0.369001i	$-0.120300\pi$
$632$	10.7178	−	3.14704i	0.426332	−	0.125182i
$633$	12.0610	−	3.54143i	0.479382	−	0.140759i
$634$	−5.52201	+	12.0915i	−0.219307	+	0.480215i
$635$	2.50200	+	17.4018i	0.0992887	+	0.690568i
$636$	2.90395	+	3.35134i	0.115149	+	0.132889i
$637$	−4.10409	−	8.98671i	−0.162610	−	0.356066i
$638$	−1.11595	+	0.717179i	−0.0441810	+	0.0283934i
$639$	0.472164	−	3.28397i	0.0186785	−	0.129912i
$640$	−0.841254	−	0.540641i	−0.0332535	−	0.0213707i
$641$	14.8484	−	17.1359i	0.586476	−	0.676829i	−0.382508	−	0.923952i	$-0.624940\pi$
$641$	14.8484	−	17.1359i	0.586476	−	0.676829i	0.968984	+	0.247123i	$0.0794852\pi$
$642$	−6.72517	−	1.97469i	−0.265421	−	0.0779348i
$643$	−25.0817			−0.989125			−0.494562	−	0.869142i	$-0.664672\pi$
$643$	−25.0817			−0.989125			−0.494562	+	0.869142i	$0.664672\pi$
$644$	−8.16889	+	11.5651i	−0.321899	+	0.455730i
$645$	−0.216919			−0.00854116
$646$	1.62965	+	0.478508i	0.0641177	+	0.0188267i
$647$	−23.6910	+	27.3409i	−0.931391	+	1.07488i	0.0656369	+	0.997844i	$0.479092\pi$
$647$	−23.6910	+	27.3409i	−0.931391	+	1.07488i	−0.997028	+	0.0770391i	$0.975453\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	0.359702	−	2.50178i	0.0141195	−	0.0982035i
$650$	4.84147	−	3.11142i	0.189898	−	0.122040i
$651$	−11.9556	−	26.1792i	−0.468579	−	1.02604i
$652$	−8.10214	−	9.35036i	−0.317304	−	0.366189i
$653$	1.19079	+	8.28216i	0.0465994	+	0.324106i	0.999765	+	0.0216584i	$0.00689461\pi$
$653$	1.19079	+	8.28216i	0.0465994	+	0.324106i	−0.953166	+	0.302448i	$0.902196\pi$
$654$	−1.98900	+	4.35529i	−0.0777759	+	0.170305i
$655$	12.4986	−	3.66992i	0.488360	−	0.143395i
$656$	0.609990	−	0.179109i	0.0238161	−	0.00699304i
$657$	−1.49749	+	3.27905i	−0.0584228	+	0.127928i
$658$	2.21622	+	15.4142i	0.0863974	+	0.600907i
$659$	−21.2658	−	24.5420i	−0.828397	−	0.956021i	0.171176	−	0.985240i	$-0.445243\pi$
$659$	−21.2658	−	24.5420i	−0.828397	−	0.956021i	−0.999573	+	0.0292193i	$0.990698\pi$
$660$	−0.144061	−	0.315449i	−0.00560755	−	0.0122788i
$661$	22.9952	−	14.7781i	0.894408	−	0.574801i	−0.0107188	−	0.999943i	$-0.503412\pi$
$661$	22.9952	−	14.7781i	0.894408	−	0.574801i	0.905127	+	0.425141i	$0.139776\pi$
$662$	−3.98739	+	27.7329i	−0.154974	+	1.07787i
$663$	19.5600	+	12.5704i	0.759647	+	0.488196i
$664$	10.7194	−	12.3708i	0.415993	−	0.480082i
$665$	−1.19091	−	0.349681i	−0.0461813	−	0.0135601i
$666$	−7.17829			−0.278153
$667$	18.2552	−	1.81378i	0.706844	−	0.0702297i
$668$	7.95578			0.307818
$669$	20.1878	+	5.92768i	0.780507	+	0.229177i
$670$	1.12369	−	1.29681i	0.0434121	−	0.0501002i
$671$	0.0629347	+	0.0404457i	0.00242957	+	0.00156139i
$672$	−0.420170	+	2.92235i	−0.0162084	+	0.112732i
$673$	9.79822	−	6.29693i	0.377694	−	0.242729i	−0.337996	−	0.941148i	$-0.609749\pi$
$673$	9.79822	−	6.29693i	0.377694	−	0.242729i	0.715689	+	0.698419i	$0.246113\pi$
$674$	3.09078	+	6.76787i	0.119052	+	0.260689i
$675$	0.654861	+	0.755750i	0.0252056	+	0.0290888i
$676$	−2.86348	−	19.9159i	−0.110134	−	0.765998i
$677$	6.39623	−	14.0058i	0.245827	−	0.538286i	−0.745990	−	0.665958i	$-0.768023\pi$
$677$	6.39623	−	14.0058i	0.245827	−	0.538286i	0.991816	+	0.127672i	$0.0407504\pi$
$678$	−12.0928	+	3.55076i	−0.464421	+	0.136366i
$679$	29.1594	−	8.56196i	1.11903	−	0.328578i
$680$	−1.67832	+	3.67500i	−0.0643605	+	0.140930i
$681$	−3.15317	−	21.9308i	−0.120830	−	0.840391i
$682$	2.21374	+	2.55480i	0.0847686	+	0.0978282i
$683$	−1.96507	−	4.30290i	−0.0751913	−	0.164646i	0.868304	−	0.496033i	$-0.165211\pi$
$683$	−1.96507	−	4.30290i	−0.0751913	−	0.164646i	−0.943495	+	0.331387i	$0.892483\pi$
$684$	0.353661	−	0.227284i	0.0135226	−	0.00869043i
$685$	−1.62237	+	11.2839i	−0.0619877	+	0.431134i
$686$	13.1223	+	8.43320i	0.501012	+	0.321981i
$687$	13.0599	−	15.0719i	0.498267	−	0.575030i
$688$	−0.208132	−	0.0611130i	−0.00793495	−	0.00232991i
$689$	−25.5206			−0.972257
$690$	−0.209837	+	4.79124i	−0.00798835	+	0.182399i
$691$	−23.9406			−0.910744			−0.455372	−	0.890301i	$-0.650494\pi$
$691$	−23.9406			−0.910744			−0.455372	+	0.890301i	$0.650494\pi$
$692$	0.590686	+	0.173441i	0.0224545	+	0.00659324i
$693$	−0.670482	+	0.773777i	−0.0254695	+	0.0293934i
$694$	17.4986	+	11.2457i	0.664239	+	0.426880i
$695$	2.63720	−	18.3422i	0.100035	−	0.695758i
$696$	3.21798	−	2.06807i	0.121977	−	0.0783899i
$697$	−1.06698	−	2.33635i	−0.0404146	−	0.0884956i
$698$	−19.3682	−	22.3521i	−0.733099	−	0.846041i
$699$	−2.16687	−	15.0709i	−0.0819584	−	0.570033i
$700$	1.22647	−	2.68560i	0.0463562	−	0.101506i
$701$	43.9725	−	12.9115i	1.66082	−	0.487660i	0.689269	−	0.724505i	$-0.257932\pi$
$701$	43.9725	−	12.9115i	1.66082	−	0.487660i	0.971547	+	0.236845i	$0.0761135\pi$
$702$	5.52194	−	1.62139i	0.208412	−	0.0611954i
$703$	1.25361	−	2.74503i	0.0472809	−	0.103531i
$704$	−0.0493529	−	0.343257i	−0.00186006	−	0.0129370i
$705$	3.45412	+	3.98626i	0.130090	+	0.150131i
$706$	−13.3789	−	29.2958i	−0.503523	−	1.10256i
$707$	−44.2647	+	28.4472i	−1.66475	+	1.06987i
$708$	−1.03724	+	7.21417i	−0.0389819	+	0.271125i
$709$	−29.8328	−	19.1724i	−1.12040	−	0.720035i	−0.156862	−	0.987621i	$-0.550138\pi$
$709$	−29.8328	−	19.1724i	−1.12040	−	0.720035i	−0.963534	+	0.267586i	$0.913774\pi$
$710$	−2.17266	+	2.50738i	−0.0815385	+	0.0941004i
$711$	−10.7178	−	3.14704i	−0.401950	−	0.118023i
$712$	−0.289841			−0.0108622
$713$	−11.1957	−	45.3894i	−0.419282	−	1.69985i
$714$	11.9280			0.446394
$715$	1.91494	+	0.562277i	0.0716146	+	0.0210280i
$716$	−2.22650	+	2.56952i	−0.0832082	+	0.0960273i
$717$	−17.2885	−	11.1107i	−0.645652	−	0.414935i
$718$	0.967592	−	6.72975i	0.0361102	−	0.251152i
$719$	14.9429	−	9.60324i	0.557277	−	0.358140i	−0.231485	−	0.972838i	$-0.574358\pi$
$719$	14.9429	−	9.60324i	0.557277	−	0.358140i	0.788763	+	0.614698i	$0.210722\pi$
$720$	0.415415	+	0.909632i	0.0154816	+	0.0339000i
$721$	−18.9616	−	21.8829i	−0.706167	−	0.814960i
$722$	−2.67883	−	18.6317i	−0.0996957	−	0.693399i
$723$	−9.24066	+	20.2342i	−0.343664	+	0.752519i
$724$	−6.45374	+	1.89499i	−0.239851	+	0.0704267i
$725$	−3.67027	+	1.07769i	−0.136310	+	0.0400243i
$726$	−4.51961	+	9.89656i	−0.167738	+	0.367296i
$727$	−2.43279	−	16.9204i	−0.0902272	−	0.627544i	−0.983886	−	0.178797i	$-0.942779\pi$
$727$	−2.43279	−	16.9204i	−0.0902272	−	0.627544i	0.893659	−	0.448747i	$-0.148130\pi$
$728$	−11.1269	−	12.8411i	−0.412390	−	0.475924i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	3.03256	−	1.94891i	0.112240	−	0.0721323i
$731$	−0.124721	+	0.867452i	−0.00461296	+	0.0320839i
$732$	−0.181479	−	0.116630i	−0.00670767	−	0.00431076i
$733$	−12.3810	+	14.2884i	−0.457302	+	0.527755i	−0.936836	−	0.349768i	$-0.886260\pi$
$733$	−12.3810	+	14.2884i	−0.457302	+	0.527755i	0.479534	+	0.877523i	$0.340806\pi$
$734$	−0.544648	−	0.159923i	−0.0201033	−	0.00590287i
$735$	−1.71666			−0.0633200
$736$	−1.55118	+	4.53804i	−0.0571774	+	0.167274i
$737$	0.595062			0.0219194
$738$	−0.609990	−	0.179109i	−0.0224540	−	0.00659310i
$739$	−7.48772	+	8.64129i	−0.275440	+	0.317875i	−0.876568	−	0.481278i	$-0.840173\pi$
$739$	−7.48772	+	8.64129i	−0.275440	+	0.317875i	0.601128	+	0.799153i	$0.294718\pi$
$740$	6.03876	+	3.88088i	0.221989	+	0.142664i
$741$	−0.344319	+	2.39479i	−0.0126489	+	0.0879748i
$742$	−11.0139	+	7.07823i	−0.404334	+	0.259850i
$743$	8.33223	+	18.2450i	0.305680	+	0.669345i	0.998668	−	0.0516039i	$-0.0164333\pi$
$743$	8.33223	+	18.2450i	0.305680	+	0.669345i	−0.692988	+	0.720949i	$0.743706\pi$
$744$	−6.38358	−	7.36705i	−0.234034	−	0.270089i
$745$	1.04745	+	7.28518i	0.0383757	+	0.266909i
$746$	−5.64440	+	12.3595i	−0.206656	+	0.452514i
$747$	−15.7059	+	4.61167i	−0.574649	+	0.168732i
$748$	−1.34430	+	0.394722i	−0.0491525	+	0.0144325i
$749$	8.59645	−	18.8236i	0.314107	−	0.687799i
$750$	−0.142315	−	0.989821i	−0.00519660	−	0.0361432i
$751$	−1.57083	−	1.81284i	−0.0573205	−	0.0661514i	0.726365	−	0.687309i	$-0.241208\pi$
$751$	−1.57083	−	1.81284i	−0.0573205	−	0.0661514i	−0.783686	+	0.621158i	$0.786663\pi$
$752$	2.19114	+	4.79793i	0.0799027	+	0.174962i
$753$	12.0535	−	7.74634i	0.439255	−	0.282292i
$754$	−3.13297	+	21.7903i	−0.114096	+	0.793555i
$755$	−5.79387	−	3.72350i	−0.210861	−	0.135512i
$756$	1.93341	−	2.23127i	0.0703175	−	0.0811507i
$757$	42.3356	+	12.4308i	1.53871	+	0.451807i	0.937704	−	0.347436i	$-0.112948\pi$
$757$	42.3356	+	12.4308i	1.53871	+	0.451807i	0.601009	+	0.799243i	$0.294766\pi$
$758$	11.5003			0.417709
$759$	−1.30336	+	1.03308i	−0.0473090	+	0.0374985i
$760$	−0.420398			−0.0152494
$761$	14.9885	+	4.40103i	0.543334	+	0.159537i	0.541871	−	0.840462i	$-0.317716\pi$
$761$	14.9885	+	4.40103i	0.543334	+	0.159537i	0.00146288	+	0.999999i	$0.499534\pi$
$762$	11.5129	−	13.2866i	0.417069	−	0.481323i
$763$	−11.8920	−	7.64250i	−0.430518	−	0.276677i
$764$	2.58618	−	17.9873i	0.0935646	−	0.650756i
$765$	3.39875	−	2.18424i	0.122882	−	0.0789714i
$766$	−7.63735	−	16.7235i	−0.275949	−	0.604244i
$767$	−27.4681	−	31.6999i	−0.991816	−	1.14462i
$768$	0.142315	+	0.989821i	0.00513534	+	0.0357171i
$769$	0.0990297	−	0.216845i	0.00357110	−	0.00781962i	−0.907838	−	0.419321i	$-0.862268\pi$
$769$	0.0990297	−	0.216845i	0.00357110	−	0.00781962i	0.911409	+	0.411501i	$0.134995\pi$
$770$	0.982381	−	0.288453i	0.0354025	−	0.0103951i
$771$	18.6329	−	5.47111i	0.671048	−	0.197037i
$772$	−7.69854	+	16.8575i	−0.277077	+	0.606713i
$773$	6.14193	+	42.7180i	0.220910	+	1.53646i	0.734609	+	0.678491i	$0.237366\pi$
$773$	6.14193	+	42.7180i	0.220910	+	1.53646i	−0.513699	+	0.857970i	$0.671725\pi$
$774$	0.142051	+	0.163936i	0.00510593	+	0.00589256i
$775$	4.04947	+	8.86709i	0.145461	+	0.318515i
$776$	8.65940	−	5.56506i	0.310854	−	0.199774i
$777$	3.01610	−	20.9775i	0.108202	−	0.752562i
$778$	−7.33713	−	4.71528i	−0.263049	−	0.169051i
$779$	0.175021	−	0.201985i	0.00627078	−	0.00723686i
$780$	−5.52194	−	1.62139i	−0.197717	−	0.0580550i
$781$	−1.15055			−0.0411699
$782$	19.0394	+	3.59393i	0.680848	+	0.128519i
$783$	−3.82522			−0.136702
$784$	−1.64713	−	0.483640i	−0.0588259	−	0.0172728i
$785$	−3.09716	+	3.57431i	−0.110542	+	0.127573i
$786$	−10.9584	−	7.04252i	−0.390872	−	0.251198i
$787$	−7.41924	+	51.6019i	−0.264467	+	1.83941i	0.233674	+	0.972315i	$0.424925\pi$
$787$	−7.41924	+	51.6019i	−0.264467	+	1.83941i	−0.498142	+	0.867096i	$0.665984\pi$
$788$	−6.62768	+	4.25935i	−0.236101	+	0.151733i
$789$	−9.42067	−	20.6284i	−0.335385	−	0.734390i
$790$	7.31499	+	8.44195i	0.260256	+	0.300351i
$791$	−5.29554	−	36.8313i	−0.188288	−	1.30957i
$792$	−0.144061	+	0.315449i	−0.00511897	+	0.0112090i
$793$	1.19122	−	0.349774i	0.0423015	−	0.0124208i
$794$	−13.9101	+	4.08436i	−0.493650	+	0.144949i
$795$	−1.84214	+	4.03373i	−0.0653340	+	0.143062i
$796$	−2.69733	−	18.7603i	−0.0956042	−	0.664942i
$797$	14.7512	+	17.0238i	0.522513	+	0.603013i	0.954258	−	0.298983i	$-0.0966474\pi$
$797$	14.7512	+	17.0238i	0.522513	+	0.603013i	−0.431745	+	0.901996i	$0.642102\pi$
$798$	0.515606	+	1.12902i	0.0182522	+	0.0399668i
$799$	17.9270	−	11.5210i	0.634211	−	0.407582i
$800$	0.142315	−	0.989821i	0.00503159	−	0.0349955i
$801$	0.243829	+	0.156700i	0.00861529	+	0.00553671i
$802$	3.65453	−	4.21756i	0.129046	−	0.148927i
$803$	1.19946	+	0.352195i	0.0423282	+	0.0124287i
$804$	−1.71593			−0.0605161
$805$	−13.9135	−	2.62635i	−0.490386	−	0.0925667i
$806$	56.1004			1.97605
$807$	28.8208	+	8.46254i	1.01454	+	0.297895i
$808$	−11.6709	+	13.4689i	−0.410581	+	0.473836i
$809$	13.7830	+	8.85777i	0.484583	+	0.311423i	0.760024	−	0.649896i	$-0.225187\pi$
$809$	13.7830	+	8.85777i	0.484583	+	0.311423i	−0.275441	+	0.961318i	$0.588824\pi$
$810$	0.142315	−	0.989821i	0.00500043	−	0.0347788i
$811$	−43.5856	+	28.0107i	−1.53050	+	0.983590i	−0.540682	+	0.841227i	$0.681834\pi$
$811$	−43.5856	+	28.0107i	−1.53050	+	0.983590i	−0.989814	+	0.142363i	$0.954530\pi$
$812$	4.69152	+	10.2730i	0.164640	+	0.360511i
$813$	−3.78482	−	4.36792i	−0.132740	−	0.153190i
$814$	0.354270	+	2.46400i	0.0124171	+	0.0863631i
$815$	5.13964	−	11.2542i	0.180034	−	0.394219i
$816$	3.87645	−	1.13823i	0.135703	−	0.0398459i
$817$	−0.0874982	+	0.0256918i	−0.00306117	+	0.000898842i
$818$	−15.0741	+	33.0077i	−0.527054	+	1.15409i
$819$	2.41811	+	16.8183i	0.0844955	+	0.587679i
$820$	0.416322	+	0.480461i	0.0145386	+	0.0167784i
$821$	−10.2203	−	22.3793i	−0.356691	−	0.781044i	−0.999882	−	0.0153388i	$-0.995117\pi$
$821$	−10.2203	−	22.3793i	−0.356691	−	0.781044i	0.643191	−	0.765705i	$-0.277610\pi$
$822$	9.59020	−	6.16325i	0.334497	−	0.214968i
$823$	−4.23751	+	29.4725i	−0.147710	+	1.02735i	0.772245	+	0.635325i	$0.219134\pi$
$823$	−4.23751	+	29.4725i	−0.147710	+	1.02735i	−0.919955	+	0.392023i	$0.871775\pi$
$824$	−8.25046	−	5.30225i	−0.287418	−	0.184713i
$825$	0.227097	−	0.262084i	0.00790651	−	0.00912460i
$826$	−20.6465	−	6.06236i	−0.718384	−	0.210937i
$827$	4.21601			0.146605			0.0733025	−	0.997310i	$-0.476646\pi$
$827$	4.21601			0.146605			0.0733025	+	0.997310i	$0.476646\pi$
$828$	3.75839	−	2.97901i	0.130613	−	0.103528i
$829$	−49.4871			−1.71876			−0.859379	−	0.511339i	$-0.829150\pi$
$829$	−49.4871			−1.71876			−0.859379	+	0.511339i	$0.829150\pi$
$830$	15.7059	+	4.61167i	0.545160	+	0.160074i
$831$	2.85467	−	3.29447i	0.0990275	−	0.114284i
$832$	−4.84147	−	3.11142i	−0.167848	−	0.107869i
$833$	−0.987022	+	6.86489i	−0.0341983	+	0.237854i
$834$	−15.5891	+	10.0185i	−0.539806	+	0.346912i
$835$	3.30495	+	7.23683i	0.114373	+	0.250441i
$836$	−0.0954712	−	0.110180i	−0.00330194	−	0.00381064i
$837$	1.38729	+	9.64878i	0.0479516	+	0.333511i
$838$	−10.1598	+	22.2469i	−0.350965	+	0.768505i
$839$	4.68379	−	1.37528i	0.161702	−	0.0474801i	−0.199879	−	0.979821i	$-0.564055\pi$
$839$	4.68379	−	1.37528i	0.161702	−	0.0474801i	0.361582	+	0.932340i	$0.382237\pi$
$840$	−2.83281	+	0.831787i	−0.0977411	+	0.0286994i
$841$	−5.96857	+	13.0693i	−0.205813	+	0.450667i
$842$	3.61460	+	25.1401i	0.124567	+	0.866385i
$843$	12.9765	+	14.9757i	0.446935	+	0.515790i
$844$	5.22185	+	11.4342i	0.179743	+	0.393583i
$845$	16.9266	−	10.8781i	0.582294	−	0.374218i
$846$	0.750651	−	5.22089i	0.0258079	−	0.179498i
$847$	−27.0222	−	17.3661i	−0.928493	−	0.596706i
$848$	−2.90395	+	3.35134i	−0.0997222	+	0.115086i
$849$	−6.90991	−	2.02893i	−0.237147	−	0.0696328i
$850$	−4.04010			−0.138574
$851$	11.1349	−	32.5754i	0.381698	−	1.11667i
$852$	3.31774			0.113664
$853$	−45.4393	−	13.3422i	−1.55581	−	0.456828i	−0.612980	−	0.790098i	$-0.710030\pi$
$853$	−45.4393	−	13.3422i	−1.55581	−	0.456828i	−0.942831	+	0.333271i	$0.891848\pi$
$854$	0.417085	−	0.481342i	0.0142724	−	0.0164712i
$855$	0.353661	+	0.227284i	0.0120950	+	0.00777296i
$856$	0.997498	−	6.93775i	0.0340938	−	0.237127i
$857$	18.2738	−	11.7438i	0.624220	−	0.401162i	−0.189945	−	0.981795i	$-0.560831\pi$
$857$	18.2738	−	11.7438i	0.624220	−	0.401162i	0.814166	+	0.580633i	$0.197195\pi$
$858$	−0.829078	−	1.81543i	−0.0283042	−	0.0619776i
$859$	10.0179	+	11.5612i	0.341806	+	0.394465i	0.900462	−	0.434934i	$-0.143228\pi$
$859$	10.0179	+	11.5612i	0.341806	+	0.394465i	−0.558657	+	0.829399i	$0.688683\pi$
$860$	−0.0308707	−	0.214711i	−0.00105268	−	0.00732157i
$861$	0.779719	−	1.70735i	0.0265727	−	0.0581862i
$862$	−23.0014	+	6.75381i	−0.783430	+	0.230036i
$863$	−7.09174	+	2.08232i	−0.241406	+	0.0708831i	−0.400197	−	0.916429i	$-0.631058\pi$
$863$	−7.09174	+	2.08232i	−0.241406	+	0.0708831i	0.158792	+	0.987312i	$0.449240\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	0.0876123	+	0.609357i	0.00297891	+	0.0207188i
$866$	−14.2411	−	16.4351i	−0.483932	−	0.558487i
$867$	0.281488	+	0.616373i	0.00955983	+	0.0209331i
$868$	24.2113	−	15.5596i	0.821784	−	0.528129i
$869$	−0.551287	+	3.83429i	−0.0187011	+	0.130069i
$870$	3.21798	+	2.06807i	0.109100	+	0.0701141i
$871$	6.46693	−	7.46324i	0.219124	−	0.252882i
$872$	−4.59403	−	1.34893i	−0.155573	−	0.0456804i
$873$	−10.2935			−0.348381
$874$	0.482832	+	1.95749i	0.0163320	+	0.0662131i
$875$	2.95240			0.0998093
$876$	−3.45879	−	1.01559i	−0.116862	−	0.0343137i
$877$	−14.1989	+	16.3864i	−0.479462	+	0.553329i	−0.943019	−	0.332738i	$-0.892027\pi$
$877$	−14.1989	+	16.3864i	−0.479462	+	0.553329i	0.463557	+	0.886067i	$0.346573\pi$
$878$	24.8838	+	15.9918i	0.839786	+	0.539698i
$879$	1.52897	−	10.6342i	0.0515708	−	0.358683i
$880$	0.291736	−	0.187487i	0.00983441	−	0.00632019i
$881$	6.55607	+	14.3558i	0.220880	+	0.483659i	0.987337	−	0.158636i	$-0.0507097\pi$
$881$	6.55607	+	14.3558i	0.220880	+	0.483659i	−0.766458	+	0.642295i	$0.777982\pi$
$882$	1.12417	+	1.29737i	0.0378529	+	0.0436846i
$883$	2.65271	+	18.4500i	0.0892709	+	0.620893i	0.984513	+	0.175312i	$0.0560935\pi$
$883$	2.65271	+	18.4500i	0.0892709	+	0.620893i	−0.895242	+	0.445580i	$0.852997\pi$
$884$	−9.65882	+	21.1499i	−0.324861	+	0.711347i
$885$	−6.99313	+	2.05337i	−0.235071	+	0.0690232i
$886$	30.3556	−	8.91321i	1.01982	−	0.299445i
$887$	10.1265	−	22.1740i	0.340015	−	0.744529i	−0.659962	−	0.751299i	$-0.729428\pi$
$887$	10.1265	−	22.1740i	0.340015	−	0.744529i	0.999977	+	0.00677014i	$0.00215502\pi$
$888$	−1.02158	−	7.10522i	−0.0342819	−	0.238436i
$889$	33.9907	+	39.2274i	1.14001	+	1.31564i
$890$	−0.120404	−	0.263648i	−0.00403596	−	0.00883751i
$891$	0.291736	−	0.187487i	0.00977352	−	0.00628106i
$892$	−2.99432	+	20.8260i	−0.100257	+	0.697304i
$893$	1.86542	+	1.19883i	0.0624237	+	0.0401173i
$894$	4.81984	−	5.56239i	0.161200	−	0.186034i
$895$	−3.26224	−	0.957879i	−0.109044	−	0.0320184i
$896$	−2.95240			−0.0986327
$897$	−1.20762	+	27.5739i	−0.0403214	+	0.920665i
$898$	11.5545			0.385580
$899$	−35.7778	−	10.5053i	−1.19326	−	0.350371i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	15.0716	+	9.68593i	0.502108	+	0.322685i
$902$	−0.0313757	+	0.218223i	−0.00104470	+	0.00726603i
$903$	−0.538764	+	0.346243i	−0.0179289	+	0.0115222i
$904$	−5.23560	−	11.4644i	−0.174134	−	0.381299i
$905$	−4.40472	−	5.08332i	−0.146418	−	0.168975i
$906$	0.980149	+	6.81709i	0.0325633	+	0.226483i
$907$	7.14268	−	15.6403i	0.237169	−	0.519327i	−0.753198	−	0.657793i	$-0.771490\pi$
$907$	7.14268	−	15.6403i	0.237169	−	0.519327i	0.990367	+	0.138466i	$0.0442173\pi$
$908$	21.2588	−	6.24216i	0.705500	−	0.207153i
$909$	17.1000	−	5.02103i	0.567173	−	0.166537i
$910$	7.05842	−	15.4558i	0.233984	−	0.512354i
$911$	−0.0274808	−	0.191133i	−0.000910481	−	0.00633253i	0.989361	−	0.145480i	$-0.0464728\pi$
$911$	−0.0274808	−	0.191133i	−0.000910481	−	0.00633253i	−0.990272	+	0.139148i	$0.955564\pi$
$912$	0.275302	+	0.317716i	0.00911616	+	0.0105206i
$913$	2.35812	+	5.16357i	0.0780425	+	0.170889i
$914$	21.3255	−	13.7051i	0.705385	−	0.453323i
$915$	0.0307009	−	0.213529i	0.00101494	−	0.00705906i
$916$	16.7771	+	10.7820i	0.554332	+	0.356248i
$917$	25.1851	−	29.0651i	0.831684	−	0.959815i
$918$	−3.87645	−	1.13823i	−0.127942	−	0.0375671i
$919$	−20.4801			−0.675575			−0.337787	−	0.941222i	$-0.609678\pi$
$919$	−20.4801			−0.675575			−0.337787	+	0.941222i	$0.609678\pi$
$920$	−4.77233	+	0.474163i	−0.157339	+	0.0156327i
$921$	10.1310			0.333827
$922$	−11.1913	−	3.28607i	−0.368567	−	0.108221i
$923$	−12.5038	+	14.4301i	−0.411567	+	0.474974i
$924$	−0.861321	−	0.553537i	−0.0283354	−	0.0182100i
$925$	−1.02158	+	7.10522i	−0.0335892	+	0.233618i
$926$	3.97146	−	2.55230i	0.130510	−	0.0838738i
$927$	4.07412	+	8.92107i	0.133812	+	0.293006i
$928$	2.50498	+	2.89090i	0.0822301	+	0.0948986i
$929$	−5.04088	−	35.0601i	−0.165386	−	1.15028i	−0.888272	−	0.459318i	$-0.848094\pi$
$929$	−5.04088	−	35.0601i	−0.165386	−	1.15028i	0.722886	−	0.690967i	$-0.242815\pi$
$930$	4.04947	−	8.86709i	0.132787	−	0.290763i
$931$	−0.692448	+	0.203321i	−0.0226941	+	0.00666358i
$932$	14.6091	−	4.28962i	0.478537	−	0.140511i
$933$	−8.08775	+	17.7097i	−0.264781	+	0.579790i
$934$	1.65495	+	11.5104i	0.0541516	+	0.376633i
$935$	−0.917495	−	1.05885i	−0.0300053	−	0.0346280i
$936$	2.39074	+	5.23499i	0.0781438	+	0.171111i
$937$	40.0779	−	25.7565i	1.30929	−	0.841428i	0.315097	−	0.949059i	$-0.397963\pi$
$937$	40.0779	−	25.7565i	1.30929	−	0.841428i	0.994191	+	0.107631i	$0.0343265\pi$
$938$	0.720982	−	5.01454i	0.0235409	−	0.163731i
$939$	27.7470	+	17.8319i	0.905490	+	0.581923i
$940$	−3.45412	+	3.98626i	−0.112661	+	0.130018i
$941$	47.5162	+	13.9520i	1.54898	+	0.454822i	0.940796	−	0.338972i	$-0.110079\pi$
$941$	47.5162	+	13.9520i	1.54898	+	0.454822i	0.608186	+	0.793794i	$0.291897\pi$
$942$	4.72949			0.154095
$943$	1.75901	−	2.49033i	0.0572813	−	0.0810962i
$944$	−7.28836			−0.237216
$945$	2.83281	+	0.831787i	0.0921512	+	0.0270580i
$946$	0.0492616	−	0.0568509i	0.00160163	−	0.00184838i
$947$	4.52598	+	2.90867i	0.147074	+	0.0945190i	0.612109	−	0.790774i	$-0.290322\pi$
$947$	4.52598	+	2.90867i	0.147074	+	0.0945190i	−0.465034	+	0.885293i	$0.653958\pi$
$948$	1.58970	−	11.0566i	0.0516310	−	0.359102i
$949$	17.4526	−	11.2161i	0.566535	−	0.364090i
$950$	−0.174640	−	0.382407i	−0.00566606	−	0.0124069i
$951$	8.70490	+	10.0460i	0.282276	+	0.325763i
$952$	1.69753	+	11.8066i	0.0550172	+	0.382653i
$953$	1.02160	−	2.23698i	0.0330927	−	0.0724630i	−0.892364	−	0.451317i	$-0.850954\pi$
$953$	1.02160	−	2.23698i	0.0330927	−	0.0724630i	0.925457	+	0.378854i	$0.123682\pi$
$954$	4.25483	−	1.24933i	0.137755	−	0.0404486i
$955$	17.4361	−	5.11971i	0.564220	−	0.165670i
$956$	8.53715	−	18.6938i	0.276111	−	0.604599i
$957$	0.188786	+	1.31303i	0.00610257	+	0.0424443i
$958$	−16.3533	−	18.8727i	−0.528351	−	0.609749i
$959$	13.9816	+	30.6155i	0.451491	+	0.988627i
$960$	−0.841254	+	0.540641i	−0.0271513	+	0.0174491i
$961$	−9.11150	+	63.3719i	−0.293919	+	2.04425i
$962$	34.7534	+	22.3347i	1.12050	+	0.720099i
$963$	−4.58998	+	5.29712i	−0.147910	+	0.170697i
$964$	−21.3434	−	6.26697i	−0.687423	−	0.201846i
$965$	−18.5322			−0.596572
$966$	7.12654	+	12.2350i	0.229293	+	0.393655i
$967$	−15.7924			−0.507848			−0.253924	−	0.967224i	$-0.581721\pi$
$967$	−15.7924			−0.507848			−0.253924	+	0.967224i	$0.581721\pi$
$968$	−10.4390	−	3.06518i	−0.335523	−	0.0985185i
$969$	1.11225	−	1.28360i	0.0357305	−	0.0412352i
$970$	8.65940	+	5.56506i	0.278037	+	0.178683i
$971$	0.298918	−	2.07902i	0.00959274	−	0.0667190i	−0.984463	−	0.175593i	$-0.943816\pi$
$971$	0.298918	−	2.07902i	0.00959274	−	0.0667190i	0.994056	+	0.108875i	$0.0347247\pi$
$972$	−0.841254	+	0.540641i	−0.0269832	+	0.0173411i
$973$	−22.7275	−	49.7662i	−0.728609	−	1.59543i
$974$	9.98346	+	11.5215i	0.319891	+	0.369174i
$975$	−0.819031	−	5.69648i	−0.0262300	−	0.182434i
$976$	0.0896154	−	0.196230i	0.00286852	−	0.00628118i
$977$	−42.5005	+	12.4793i	−1.35971	+	0.399247i	−0.878661	−	0.477446i	$-0.841563\pi$
$977$	−42.5005	+	12.4793i	−1.35971	+	0.399247i	−0.481050	+	0.876693i	$0.659745\pi$
$978$	−11.8711	+	3.48568i	−0.379597	+	0.111460i
$979$	0.0417546	−	0.0914298i	0.00133448	−	0.00292211i
$980$	−0.244307	−	1.69919i	−0.00780408	−	0.0542786i
$981$	3.13545	+	3.61851i	0.100107	+	0.115530i
$982$	−12.4431	−	27.2467i	−0.397077	−	0.869477i
$983$	41.4232	−	26.6211i	1.32120	−	0.849081i	0.325847	−	0.945422i	$-0.394351\pi$
$983$	41.4232	−	26.6211i	1.32120	−	0.849081i	0.995348	+	0.0963417i	$0.0307142\pi$
$984$	0.0904755	−	0.629271i	0.00288425	−	0.0200604i
$985$	−6.62768	−	4.25935i	−0.211175	−	0.135714i
$986$	10.1204	−	11.6795i	0.322299	−	0.371952i
$987$	14.9419	+	4.38733i	0.475605	+	0.139650i
$988$	−2.41942			−0.0769719
$989$	−0.964297	+	0.390340i	−0.0306629	+	0.0124121i
$990$	−0.346787			−0.0110216
$991$	26.3034	+	7.72338i	0.835555	+	0.245341i	0.671402	−	0.741094i	$-0.265693\pi$
$991$	26.3034	+	7.72338i	0.835555	+	0.245341i	0.164154	+	0.986435i	$0.447511\pi$
$992$	6.38358	−	7.36705i	0.202679	−	0.233904i
$993$	23.5703	+	15.1477i	0.747981	+	0.480698i
$994$	−1.39402	+	9.69560i	−0.0442155	+	0.307526i
$995$	15.9445	−	10.2469i	0.505474	−	0.324848i
$996$	−6.79992	−	14.8897i	−0.215464	−	0.471800i
$997$	−35.3607	−	40.8084i	−1.11988	−	1.29242i	−0.951826	−	0.306639i	$-0.900796\pi$
$997$	−35.3607	−	40.8084i	−1.11988	−	1.29242i	−0.168059	−	0.985777i	$-0.553750\pi$
$998$	−0.180423	−	1.25487i	−0.00571120	−	0.0397222i
$999$	−2.98197	+	6.52960i	−0.0943453	+	0.206587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.271.2	✓	20
23.9	even	11	inner	690.2.m.e.331.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.271.2	✓	20	1.1	even	1	trivial
690.2.m.e.331.2	yes	20	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.22647 + 2.68560i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(1.22647 + 2.68560i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(-0.332740 + 0.0977012i) q^{11} +(0.959493 - 0.281733i) q^{12} +(-2.39074 + 5.23499i) q^{13} +(0.420170 + 2.92235i) q^{14} +(0.654861 + 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(3.39875 - 2.18424i) q^{17} +(0.142315 - 0.989821i) q^{18} +(0.353661 + 0.227284i) q^{19} +(-0.654861 + 0.755750i) q^{20} +(2.83281 + 0.831787i) q^{21} -0.346787 q^{22} +(4.27109 + 2.18123i) q^{23} +1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-3.76876 + 4.34939i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.420170 + 2.92235i) q^{28} +(3.21798 - 2.06807i) q^{29} +(0.415415 + 0.909632i) q^{30} +(-6.38358 - 7.36705i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-0.144061 + 0.315449i) q^{33} +(3.87645 - 1.13823i) q^{34} +(-2.83281 + 0.831787i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-1.02158 - 7.10522i) q^{37} +(0.275302 + 0.317716i) q^{38} +(2.39074 + 5.23499i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(0.0904755 - 0.629271i) q^{41} +(2.48372 + 1.59619i) q^{42} +(-0.142051 + 0.163936i) q^{43} +(-0.332740 - 0.0977012i) q^{44} +1.00000 q^{45} +(3.48356 + 3.29618i) q^{46} +5.27458 q^{47} +(0.959493 + 0.281733i) q^{48} +(-1.12417 + 1.29737i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(0.574966 - 3.99898i) q^{51} +(-4.84147 + 3.11142i) q^{52} +(1.84214 + 4.03373i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.0493529 - 0.343257i) q^{55} +(-1.22647 + 2.68560i) q^{56} +(0.403369 - 0.118440i) q^{57} +(3.67027 - 1.07769i) q^{58} +(-3.02769 + 6.62972i) q^{59} +(0.142315 + 0.989821i) q^{60} +(-0.141270 - 0.163034i) q^{61} +(-4.04947 - 8.86709i) q^{62} +(2.48372 - 1.59619i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-4.84147 - 3.11142i) q^{65} +(-0.227097 + 0.262084i) q^{66} +(-1.64642 - 0.483433i) q^{67} +4.04010 q^{68} +(4.44543 - 1.79948i) q^{69} -2.95240 q^{70} +(3.18335 + 0.934716i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-3.03256 - 1.94891i) q^{73} +(1.02158 - 7.10522i) q^{74} +(-0.841254 + 0.540641i) q^{75} +(0.174640 + 0.382407i) q^{76} +(-0.670482 - 0.773777i) q^{77} +(0.819031 + 5.69648i) q^{78} +(4.64031 - 10.1609i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.264097 - 0.578291i) q^{82} +(-2.32955 - 16.2024i) q^{83} +(1.93341 + 2.23127i) q^{84} +(1.67832 + 3.67500i) q^{85} +(-0.182483 + 0.117275i) q^{86} +(0.544385 - 3.78628i) q^{87} +(-0.291736 - 0.187487i) q^{88} +(-0.189805 + 0.219047i) q^{89} +(0.959493 + 0.281733i) q^{90} -16.9912 q^{91} +(2.41381 + 4.14409i) q^{92} -9.74800 q^{93} +(5.06092 + 1.48602i) q^{94} +(-0.275302 + 0.317716i) q^{95} +(0.841254 + 0.540641i) q^{96} +(1.46491 - 10.1887i) q^{97} +(-1.44415 + 0.928098i) q^{98} +(0.144061 + 0.315449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

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