LMFDB - Embedded newform 690.2.m.b.271.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	690.271
Dual form			690.2.m.b.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(1.24302 + 2.72183i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(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} +(1.24302 + 2.72183i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(1.52977 - 0.449181i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-0.404992 + 0.886808i) q^{13} +(0.425839 + 2.96177i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.675969 + 0.434419i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-1.37491 - 0.883600i) q^{19} +(-0.654861 + 0.755750i) q^{20} +(-2.87102 - 0.843008i) q^{21} +1.59435 q^{22} +(-4.04911 + 2.56996i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.638429 + 0.736786i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.425839 + 2.96177i) q^{28} +(-1.50468 + 0.966997i) q^{29} +(-0.415415 - 0.909632i) q^{30} +(3.90897 + 4.51120i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-0.662317 + 1.45027i) q^{33} +(-0.770978 + 0.226380i) q^{34} +(-2.87102 + 0.843008i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.999396 + 6.95095i) q^{37} +(-1.07028 - 1.23516i) q^{38} +(-0.404992 - 0.886808i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(0.899209 - 6.25413i) q^{41} +(-2.51722 - 1.61772i) q^{42} +(-1.02231 + 1.17981i) q^{43} +(1.52977 + 0.449181i) q^{44} +1.00000 q^{45} +(-4.60914 + 1.32509i) q^{46} +4.24399 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-1.27923 + 1.47631i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(0.114354 - 0.795348i) q^{51} +(-0.820145 + 0.527075i) q^{52} +(-0.819203 - 1.79380i) q^{53} +(0.654861 + 0.755750i) q^{54} +(0.226900 + 1.57812i) q^{55} +(-1.24302 + 2.72183i) q^{56} +(1.56815 - 0.460451i) q^{57} +(-1.71616 + 0.503910i) q^{58} +(2.74441 - 6.00941i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(-1.52177 - 1.75622i) q^{61} +(2.47968 + 5.42975i) q^{62} +(2.51722 - 1.61772i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.820145 - 0.527075i) q^{65} +(-1.04408 + 1.20493i) q^{66} +(10.7115 + 3.14518i) q^{67} -0.803526 q^{68} +(0.709362 - 4.74308i) q^{69} -2.99223 q^{70} +(4.80594 + 1.41115i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-3.34748 - 2.15129i) q^{73} +(-0.999396 + 6.95095i) q^{74} +(0.841254 - 0.540641i) q^{75} +(-0.678936 - 1.48666i) q^{76} +(3.12412 + 3.60543i) q^{77} +(-0.138744 - 0.964985i) q^{78} +(0.632393 - 1.38475i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.62478 - 5.74746i) q^{82} +(-1.99366 - 13.8662i) q^{83} +(-1.95949 - 2.26138i) q^{84} +(-0.333797 - 0.730913i) q^{85} +(-1.31329 + 0.844002i) q^{86} +(0.254546 - 1.77041i) q^{87} +(1.34125 + 0.861971i) q^{88} +(3.91232 - 4.51506i) q^{89} +(0.959493 + 0.281733i) q^{90} -2.91715 q^{91} +(-4.79575 - 0.0271313i) q^{92} -5.96917 q^{93} +(4.07208 + 1.19567i) q^{94} +(1.07028 - 1.23516i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(0.0304261 - 0.211618i) q^{97} +(-1.64333 + 1.05610i) q^{98} +(-0.662317 - 1.45027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * 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
$7$	1.24302	+	2.72183i	0.469816	+	1.02875i	0.985139	+	0.171758i	$0.0549447\pi$
$7$	1.24302	+	2.72183i	0.469816	+	1.02875i	−0.515323	+	0.856996i	$0.672328\pi$
$8$	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
$11$	1.52977	−	0.449181i	0.461243	−	0.135433i	−0.0428521	−	0.999081i	$-0.513644\pi$
$11$	1.52977	−	0.449181i	0.461243	−	0.135433i	0.504095	+	0.863648i	$0.331826\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	−0.404992	+	0.886808i	−0.112324	+	0.245956i	−0.957443	−	0.288623i	$-0.906803\pi$
$13$	−0.404992	+	0.886808i	−0.112324	+	0.245956i	0.845118	+	0.534579i	$0.179530\pi$
$14$	0.425839	+	2.96177i	0.113810	+	0.791567i
$15$	−0.654861	−	0.755750i	−0.169084	−	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−0.675969	+	0.434419i	−0.163947	+	0.105362i	−0.620041	−	0.784569i	$-0.712884\pi$
$17$	−0.675969	+	0.434419i	−0.163947	+	0.105362i	0.456095	+	0.889931i	$0.349248\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−1.37491	−	0.883600i	−0.315426	−	0.202712i	0.373342	−	0.927694i	$-0.378212\pi$
$19$	−1.37491	−	0.883600i	−0.315426	−	0.202712i	−0.688768	+	0.724982i	$0.741848\pi$
$20$	−0.654861	+	0.755750i	−0.146431	+	0.168991i
$21$	−2.87102	−	0.843008i	−0.626508	−	0.183959i
$22$	1.59435			0.339917
$23$	−4.04911	+	2.56996i	−0.844299	+	0.535873i
$23$	−4.04911	+	2.56996i	−0.844299	+	0.535873i
$24$	−1.00000			−0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	−0.638429	+	0.736786i	−0.125206	+	0.144496i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	−0.425839	+	2.96177i	−0.0804759	+	0.559722i
$29$	−1.50468	+	0.966997i	−0.279411	+	0.179567i	−0.672839	−	0.739789i	$-0.734925\pi$
$29$	−1.50468	+	0.966997i	−0.279411	+	0.179567i	0.393428	+	0.919355i	$0.371289\pi$
$30$	−0.415415	−	0.909632i	−0.0758441	−	0.166075i
$31$	3.90897	+	4.51120i	0.702073	+	0.810235i	0.989031	−	0.147708i	$-0.0471896\pi$
$31$	3.90897	+	4.51120i	0.702073	+	0.810235i	−0.286958	+	0.957943i	$0.592644\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	−0.662317	+	1.45027i	−0.115295	+	0.252460i
$34$	−0.770978	+	0.226380i	−0.132222	+	0.0388238i
$35$	−2.87102	+	0.843008i	−0.485291	+	0.142494i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.999396	+	6.95095i	0.164300	+	1.14273i	0.890413	+	0.455154i	$0.150416\pi$
$37$	0.999396	+	6.95095i	0.164300	+	1.14273i	−0.726113	+	0.687575i	$0.758675\pi$
$38$	−1.07028	−	1.23516i	−0.173622	−	0.200370i
$39$	−0.404992	−	0.886808i	−0.0648505	−	0.142003i
$40$	−0.841254	+	0.540641i	−0.133014	+	0.0854828i
$41$	0.899209	−	6.25413i	0.140433	−	0.976731i	−0.790740	−	0.612153i	$-0.790304\pi$
$41$	0.899209	−	6.25413i	0.140433	−	0.976731i	0.931172	−	0.364579i	$-0.118787\pi$
$42$	−2.51722	−	1.61772i	−0.388416	−	0.249620i
$43$	−1.02231	+	1.17981i	−0.155901	+	0.179919i	−0.828327	−	0.560245i	$-0.810707\pi$
$43$	−1.02231	+	1.17981i	−0.155901	+	0.179919i	0.672426	+	0.740165i	$0.265252\pi$
$44$	1.52977	+	0.449181i	0.230621	+	0.0677165i
$45$	1.00000			0.149071
$46$	−4.60914	+	1.32509i	−0.679580	+	0.195374i
$47$	4.24399			0.619050			0.309525	−	0.950891i	$-0.399830\pi$
$47$	4.24399			0.619050			0.309525	+	0.950891i	$0.399830\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	−1.27923	+	1.47631i	−0.182747	+	0.210901i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	0.114354	−	0.795348i	0.0160127	−	0.111371i
$52$	−0.820145	+	0.527075i	−0.113734	+	0.0730922i
$53$	−0.819203	−	1.79380i	−0.112526	−	0.246398i	0.844987	−	0.534786i	$-0.179608\pi$
$53$	−0.819203	−	1.79380i	−0.112526	−	0.246398i	−0.957514	+	0.288388i	$0.906881\pi$
$54$	0.654861	+	0.755750i	0.0891153	+	0.102844i
$55$	0.226900	+	1.57812i	0.0305952	+	0.212794i
$56$	−1.24302	+	2.72183i	−0.166105	+	0.363719i
$57$	1.56815	−	0.460451i	0.207707	−	0.0609883i
$58$	−1.71616	+	0.503910i	−0.225343	+	0.0661667i
$59$	2.74441	−	6.00941i	0.357291	−	0.782359i	−0.642578	−	0.766220i	$-0.722135\pi$
$59$	2.74441	−	6.00941i	0.357291	−	0.782359i	0.999870	−	0.0161390i	$-0.00513744\pi$
$60$	−0.142315	−	0.989821i	−0.0183728	−	0.127785i
$61$	−1.52177	−	1.75622i	−0.194843	−	0.224861i	0.649918	−	0.760004i	$-0.274803\pi$
$61$	−1.52177	−	1.75622i	−0.194843	−	0.224861i	−0.844761	+	0.535143i	$0.820258\pi$
$62$	2.47968	+	5.42975i	0.314920	+	0.689579i
$63$	2.51722	−	1.61772i	0.317140	−	0.203814i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.820145	−	0.527075i	−0.101726	−	0.0653756i
$66$	−1.04408	+	1.20493i	−0.128517	+	0.148317i
$67$	10.7115	+	3.14518i	1.30862	+	0.384245i	0.860372	−	0.509666i	$-0.170231\pi$
$67$	10.7115	+	3.14518i	1.30862	+	0.384245i	0.448245	+	0.893911i	$0.352049\pi$
$68$	−0.803526			−0.0974419
$69$	0.709362	−	4.74308i	0.0853972	−	0.571000i
$70$	−2.99223			−0.357640
$71$	4.80594	+	1.41115i	0.570360	+	0.167473i	0.554181	−	0.832396i	$-0.313032\pi$
$71$	4.80594	+	1.41115i	0.570360	+	0.167473i	0.0161791	+	0.999869i	$0.494850\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−3.34748	−	2.15129i	−0.391792	−	0.251790i	0.329882	−	0.944022i	$-0.392991\pi$
$73$	−3.34748	−	2.15129i	−0.391792	−	0.251790i	−0.721675	+	0.692232i	$0.756627\pi$
$74$	−0.999396	+	6.95095i	−0.116177	+	0.808032i
$75$	0.841254	−	0.540641i	0.0971396	−	0.0624278i
$76$	−0.678936	−	1.48666i	−0.0778793	−	0.170532i
$77$	3.12412	+	3.60543i	0.356027	+	0.410876i
$78$	−0.138744	−	0.964985i	−0.0157097	−	0.109263i
$79$	0.632393	−	1.38475i	0.0711498	−	0.155796i	−0.870715	−	0.491787i	$-0.836344\pi$
$79$	0.632393	−	1.38475i	0.0711498	−	0.155796i	0.941865	+	0.335991i	$0.109071\pi$
$80$	−0.959493	+	0.281733i	−0.107275	+	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	2.62478	−	5.74746i	0.289858	−	0.634701i
$83$	−1.99366	−	13.8662i	−0.218833	−	1.52202i	−0.742357	−	0.670005i	$-0.766292\pi$
$83$	−1.99366	−	13.8662i	−0.218833	−	1.52202i	0.523524	−	0.852011i	$-0.324617\pi$
$84$	−1.95949	−	2.26138i	−0.213798	−	0.246736i
$85$	−0.333797	−	0.730913i	−0.0362054	−	0.0792787i
$86$	−1.31329	+	0.844002i	−0.141616	+	0.0910111i
$87$	0.254546	−	1.77041i	0.0272902	−	0.189808i
$88$	1.34125	+	0.861971i	0.142978	+	0.0918864i
$89$	3.91232	−	4.51506i	0.414705	−	0.478595i	−0.509511	−	0.860464i	$-0.670174\pi$
$89$	3.91232	−	4.51506i	0.414705	−	0.478595i	0.924217	+	0.381869i	$0.124719\pi$
$90$	0.959493	+	0.281733i	0.101139	+	0.0296972i
$91$	−2.91715			−0.305800
$92$	−4.79575	−	0.0271313i	−0.499992	−	0.00282863i
$93$	−5.96917			−0.618974
$94$	4.07208	+	1.19567i	0.420003	+	0.123324i
$95$	1.07028	−	1.23516i	0.109808	−	0.126725i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	0.0304261	−	0.211618i	0.00308930	−	0.0214865i	−0.988218	−	0.153050i	$-0.951091\pi$
$97$	0.0304261	−	0.211618i	0.00308930	−	0.0214865i	0.991308	+	0.131563i	$0.0419996\pi$
$98$	−1.64333	+	1.05610i	−0.166002	+	0.106683i
$99$	−0.662317	−	1.45027i	−0.0665654	−	0.145758i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−1.36495	−	9.49344i	−0.135818	−	0.944632i	−0.937773	−	0.347248i	$-0.887116\pi$
$101$	−1.36495	−	9.49344i	−0.135818	−	0.944632i	0.801956	−	0.597384i	$-0.203793\pi$
$102$	0.333797	−	0.730913i	0.0330508	−	0.0723712i
$103$	17.1438	−	5.03387i	1.68923	−	0.496002i	0.710939	−	0.703253i	$-0.248270\pi$
$103$	17.1438	−	5.03387i	1.68923	−	0.496002i	0.978288	+	0.207252i	$0.0664518\pi$
$104$	−0.935418	+	0.274663i	−0.0917252	+	0.0269330i
$105$	1.24302	−	2.72183i	0.121306	−	0.265623i
$106$	−0.280646	−	1.95194i	−0.0272588	−	0.189589i
$107$	4.62525	+	5.33783i	0.447140	+	0.516027i	0.933913	−	0.357502i	$-0.116371\pi$
$107$	4.62525	+	5.33783i	0.447140	+	0.516027i	−0.486772	+	0.873529i	$0.661826\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	−9.32818	+	5.99485i	−0.893477	+	0.574203i	−0.904849	−	0.425732i	$-0.860016\pi$
$109$	−9.32818	+	5.99485i	−0.893477	+	0.574203i	0.0113719	+	0.999935i	$0.496380\pi$
$110$	−0.226900	+	1.57812i	−0.0216340	+	0.150468i
$111$	−5.90764	−	3.79661i	−0.560729	−	0.360358i
$112$	−1.95949	+	2.26138i	−0.185155	+	0.213680i
$113$	−6.20687	−	1.82250i	−0.583893	−	0.171447i	−0.0235724	−	0.999722i	$-0.507504\pi$
$113$	−6.20687	−	1.82250i	−0.583893	−	0.171447i	−0.560321	+	0.828276i	$0.689322\pi$
$114$	1.63436			0.153071
$115$	−1.96755	−	4.37364i	−0.183475	−	0.407844i
$116$	−1.78861			−0.166069
$117$	0.935418	+	0.274663i	0.0864794	+	0.0253926i
$118$	4.32629	−	4.99280i	0.398267	−	0.459625i
$119$	−2.02265	−	1.29988i	−0.185416	−	0.119160i
$120$	0.142315	−	0.989821i	0.0129915	−	0.0903579i
$121$	−7.11536	+	4.57276i	−0.646851	+	0.415706i
$122$	−0.965346	−	2.11381i	−0.0873983	−	0.191376i
$123$	4.13770	+	4.77516i	0.373084	+	0.430562i
$124$	0.849501	+	5.90841i	0.0762875	+	0.530591i
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$	2.87102	−	0.843008i	0.255771	−	0.0751011i
$127$	12.4270	−	3.64889i	1.10271	−	0.323786i	0.320784	−	0.947152i	$-0.396053\pi$
$127$	12.4270	−	3.64889i	1.10271	−	0.323786i	0.781930	+	0.623366i	$0.214235\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	−0.222170	−	1.54522i	−0.0195609	−	0.136049i
$130$	−0.638429	−	0.736786i	−0.0559939	−	0.0646204i
$131$	−6.67755	−	14.6218i	−0.583420	−	1.27751i	−0.939338	−	0.342994i	$-0.888559\pi$
$131$	−6.67755	−	14.6218i	−0.583420	−	1.27751i	0.355918	−	0.934517i	$-0.384168\pi$
$132$	−1.34125	+	0.861971i	−0.116741	+	0.0750250i
$133$	0.695972	−	4.84059i	0.0603484	−	0.419732i
$134$	9.39150	+	6.03555i	0.811302	+	0.521392i
$135$	−0.654861	+	0.755750i	−0.0563614	+	0.0650446i
$136$	−0.770978	−	0.226380i	−0.0661108	−	0.0194119i
$137$	12.5301			1.07052			0.535259	−	0.844688i	$-0.320214\pi$
$137$	12.5301			1.07052			0.535259	+	0.844688i	$0.320214\pi$
$138$	2.01691	−	4.35110i	0.171691	−	0.370390i
$139$	6.13485			0.520351			0.260176	−	0.965561i	$-0.416220\pi$
$139$	6.13485			0.520351			0.260176	+	0.965561i	$0.416220\pi$
$140$	−2.87102	−	0.843008i	−0.242646	−	0.0712472i
$141$	−2.77923	+	3.20740i	−0.234053	+	0.270112i
$142$	4.21370	+	2.70798i	0.353606	+	0.227248i
$143$	−0.221207	+	1.53853i	−0.0184982	+	0.128658i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−0.743017	−	1.62698i	−0.0617042	−	0.135113i
$146$	−2.60579	−	3.00724i	−0.215657	−	0.248881i
$147$	−0.278002	−	1.93355i	−0.0229292	−	0.159476i
$148$	−2.91722	+	6.38783i	−0.239794	+	0.525076i
$149$	12.3772	−	3.63429i	1.01398	−	0.297732i	0.267801	−	0.963474i	$-0.413703\pi$
$149$	12.3772	−	3.63429i	1.01398	−	0.297732i	0.746182	+	0.665742i	$0.231885\pi$
$150$	0.959493	−	0.281733i	0.0783423	−	0.0230034i
$151$	2.40145	−	5.25844i	0.195427	−	0.427926i	−0.786396	−	0.617722i	$-0.788056\pi$
$151$	2.40145	−	5.25844i	0.195427	−	0.427926i	0.981823	+	0.189797i	$0.0607829\pi$
$152$	−0.232593	−	1.61772i	−0.0188658	−	0.131214i
$153$	0.526198	+	0.607265i	0.0425406	+	0.0490944i
$154$	1.98181	+	4.33955i	0.159698	+	0.349691i
$155$	−5.02158	+	3.22718i	−0.403343	+	0.259213i
$156$	0.138744	−	0.964985i	0.0111084	−	0.0772606i
$157$	5.68077	+	3.65081i	0.453375	+	0.291366i	0.747330	−	0.664453i	$-0.231335\pi$
$157$	5.68077	+	3.65081i	0.453375	+	0.291366i	−0.293955	+	0.955819i	$0.594972\pi$
$158$	0.996905	−	1.15049i	0.0793095	−	0.0915281i
$159$	1.89213	+	0.555580i	0.150056	+	0.0440603i
$160$	−1.00000			−0.0790569
$161$	−12.0281	−	7.82649i	−0.947946	−	0.616814i
$162$	−1.00000			−0.0785674
$163$	16.1904	+	4.75393i	1.26813	+	0.372357i	0.845515	−	0.533952i	$-0.179294\pi$
$163$	16.1904	+	4.75393i	1.26813	+	0.372357i	0.422616	+	0.906309i	$0.361112\pi$
$164$	4.13770	−	4.77516i	0.323100	−	0.372878i
$165$	−1.34125	−	0.861971i	−0.104416	−	0.0671044i
$166$	1.99366	−	13.8662i	0.154738	−	1.07623i
$167$	4.35503	−	2.79881i	0.337002	−	0.216578i	−0.361184	−	0.932495i	$-0.617627\pi$
$167$	4.35503	−	2.79881i	0.337002	−	0.216578i	0.698186	+	0.715916i	$0.253991\pi$
$168$	−1.24302	−	2.72183i	−0.0959008	−	0.209993i
$169$	7.89078	+	9.10645i	0.606983	+	0.700496i
$170$	−0.114354	−	0.795348i	−0.00877053	−	0.0610004i
$171$	−0.678936	+	1.48666i	−0.0519195	+	0.113688i
$172$	−1.49788	+	0.439817i	−0.114212	+	0.0335357i
$173$	−22.7443	+	6.67834i	−1.72922	+	0.507745i	−0.986766	−	0.162152i	$-0.948157\pi$
$173$	−22.7443	+	6.67834i	−1.72922	+	0.507745i	−0.742455	+	0.669896i	$0.766338\pi$
$174$	0.743017	−	1.62698i	0.0563279	−	0.123341i
$175$	−0.425839	−	2.96177i	−0.0321904	−	0.223889i
$176$	1.04408	+	1.20493i	0.0787003	+	0.0908250i
$177$	2.74441	+	6.00941i	0.206282	+	0.451695i
$178$	5.02588	−	3.22994i	0.376706	−	0.242094i
$179$	2.83821	−	19.7402i	0.212138	−	1.47545i	−0.553861	−	0.832609i	$-0.686846\pi$
$179$	2.83821	−	19.7402i	0.212138	−	1.47545i	0.765998	−	0.642842i	$-0.222245\pi$
$180$	0.841254	+	0.540641i	0.0627033	+	0.0402970i
$181$	−13.2089	+	15.2438i	−0.981807	+	1.13307i	0.00929406	+	0.999957i	$0.497042\pi$
$181$	−13.2089	+	15.2438i	−0.981807	+	1.13307i	−0.991101	+	0.133109i	$0.957504\pi$
$182$	−2.79898	−	0.821856i	−0.207474	−	0.0609200i
$183$	2.32381			0.171781
$184$	−4.59385	−	1.37715i	−0.338663	−	0.101525i
$185$	−7.02243			−0.516299
$186$	−5.72738	−	1.68171i	−0.419952	−	0.123309i
$187$	−0.838944	+	0.968193i	−0.0613497	+	0.0708013i
$188$	3.57028	+	2.29448i	0.260389	+	0.167342i
$189$	−0.425839	+	2.96177i	−0.0309752	+	0.215437i
$190$	1.37491	−	0.883600i	0.0997463	−	0.0641031i
$191$	0.412044	+	0.902250i	0.0298144	+	0.0652845i	0.923953	−	0.382505i	$-0.124939\pi$
$191$	0.412044	+	0.902250i	0.0298144	+	0.0652845i	−0.894139	+	0.447790i	$0.852211\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	−0.594966	−	4.13808i	−0.0428266	−	0.297865i	−0.999966	−	0.00823798i	$-0.997378\pi$
$193$	−0.594966	−	4.13808i	−0.0428266	−	0.297865i	0.957140	−	0.289627i	$-0.0935314\pi$
$194$	0.0888133	−	0.194474i	0.00637642	−	0.0139624i
$195$	0.935418	−	0.274663i	0.0669866	−	0.0196691i
$196$	−1.87430	+	0.550345i	−0.133879	+	0.0393104i
$197$	2.07307	−	4.53939i	0.147700	−	0.323418i	−0.821293	−	0.570507i	$-0.806747\pi$
$197$	2.07307	−	4.53939i	0.147700	−	0.323418i	0.968993	+	0.247089i	$0.0794740\pi$
$198$	−0.226900	−	1.57812i	−0.0161251	−	0.112152i
$199$	0.481050	+	0.555161i	0.0341007	+	0.0393544i	0.772544	−	0.634962i	$-0.218984\pi$
$199$	0.481050	+	0.555161i	0.0341007	+	0.0393544i	−0.738443	+	0.674316i	$0.764439\pi$
$200$	−0.415415	−	0.909632i	−0.0293743	−	0.0643207i
$201$	−9.39150	+	6.03555i	−0.662425	+	0.425715i
$202$	1.36495	−	9.49344i	0.0960375	−	0.667956i
$203$	−4.50234	−	2.89348i	−0.316002	−	0.203082i
$204$	0.526198	−	0.607265i	0.0368412	−	0.0425170i
$205$	6.06250	+	1.78011i	0.423424	+	0.124328i
$206$	17.8675			1.24489
$207$	3.12005	+	3.64216i	0.216858	+	0.253147i
$208$	−0.974908			−0.0675977
$209$	−2.50019	−	0.734121i	−0.172942	−	0.0507802i
$210$	1.95949	−	2.26138i	0.135218	−	0.156050i
$211$	−8.04246	−	5.16857i	−0.553665	−	0.355819i	0.233697	−	0.972309i	$-0.424918\pi$
$211$	−8.04246	−	5.16857i	−0.553665	−	0.355819i	−0.787363	+	0.616490i	$0.788554\pi$
$212$	0.280646	−	1.95194i	0.0192749	−	0.134060i
$213$	−4.21370	+	2.70798i	−0.288718	+	0.185548i
$214$	2.93406	+	6.42469i	0.200568	+	0.439183i
$215$	−1.02231	−	1.17981i	−0.0697211	−	0.0804624i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	−7.41978	+	16.2470i	−0.503687	+	1.10292i
$218$	−10.6393	+	3.12397i	−0.720582	+	0.211582i
$219$	3.81797	−	1.12106i	0.257994	−	0.0757540i
$220$	−0.662317	+	1.45027i	−0.0446534	+	0.0977774i
$221$	−0.111484	−	0.775391i	−0.00749925	−	0.0521584i
$222$	−4.59871	−	5.30720i	−0.308645	−	0.356196i
$223$	0.766671	+	1.67878i	0.0513401	+	0.112419i	0.933564	−	0.358412i	$-0.116682\pi$
$223$	0.766671	+	1.67878i	0.0513401	+	0.112419i	−0.882224	+	0.470831i	$0.843954\pi$
$224$	−2.51722	+	1.61772i	−0.168189	+	0.108089i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	−5.44199	−	3.49736i	−0.361996	−	0.232641i
$227$	0.462908	−	0.534225i	0.0307243	−	0.0354577i	−0.740179	−	0.672409i	$-0.765259\pi$
$227$	0.462908	−	0.534225i	0.0307243	−	0.0354577i	0.770904	+	0.636952i	$0.219805\pi$
$228$	1.56815	+	0.460451i	0.103853	+	0.0304941i
$229$	0.634910			0.0419560			0.0209780	−	0.999780i	$-0.493322\pi$
$229$	0.634910			0.0419560			0.0209780	+	0.999780i	$0.493322\pi$
$230$	−0.655652	−	4.75080i	−0.0432324	−	0.313259i
$231$	−4.77066			−0.313887
$232$	−1.71616	−	0.503910i	−0.112672	−	0.0330833i
$233$	−5.18417	+	5.98285i	−0.339626	+	0.391949i	−0.899711	−	0.436486i	$-0.856223\pi$
$233$	−5.18417	+	5.98285i	−0.339626	+	0.391949i	0.560085	+	0.828435i	$0.310768\pi$
$234$	0.820145	+	0.527075i	0.0536146	+	0.0344560i
$235$	−0.603983	+	4.20080i	−0.0393995	+	0.274030i
$236$	5.55768	−	3.57170i	0.361774	−	0.232498i
$237$	0.632393	+	1.38475i	0.0410784	+	0.0899490i
$238$	−1.57450	−	1.81707i	−0.102060	−	0.117783i
$239$	0.918852	+	6.39076i	0.0594356	+	0.413384i	0.997718	+	0.0675144i	$0.0215069\pi$
$239$	0.918852	+	6.39076i	0.0594356	+	0.413384i	−0.938283	+	0.345869i	$0.887584\pi$
$240$	0.415415	−	0.909632i	0.0268149	−	0.0587165i
$241$	13.5447	−	3.97707i	0.872488	−	0.256186i	0.185315	−	0.982679i	$-0.440670\pi$
$241$	13.5447	−	3.97707i	0.872488	−	0.256186i	0.687173	+	0.726494i	$0.258851\pi$
$242$	−8.11543	+	2.38291i	−0.521680	+	0.153179i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−0.330713	−	2.30016i	−0.0211717	−	0.147252i
$245$	−1.27923	−	1.47631i	−0.0817267	−	0.0943177i
$246$	2.62478	+	5.74746i	0.167350	+	0.366445i
$247$	1.34041	−	0.861429i	0.0852882	−	0.0548114i
$248$	−0.849501	+	5.90841i	−0.0539434	+	0.375185i
$249$	11.7850	+	7.57374i	0.746842	+	0.479966i
$250$	0.654861	−	0.755750i	0.0414170	−	0.0477978i
$251$	−2.28317	−	0.670400i	−0.144113	−	0.0423153i	0.208881	−	0.977941i	$-0.433018\pi$
$251$	−2.28317	−	0.670400i	−0.144113	−	0.0423153i	−0.352993	+	0.935626i	$0.614836\pi$
$252$	2.99223			0.188493
$253$	−5.03983	+	5.75022i	−0.316852	+	0.361513i
$254$	12.9516			0.812655
$255$	0.770978	+	0.226380i	0.0482805	+	0.0141764i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	6.10744	+	3.92501i	0.380972	+	0.244836i	0.717085	−	0.696986i	$-0.245476\pi$
$257$	6.10744	+	3.92501i	0.380972	+	0.244836i	−0.336113	+	0.941822i	$0.609112\pi$
$258$	0.222170	−	1.54522i	0.0138317	−	0.0962014i
$259$	−17.6770	+	11.3603i	−1.09840	+	0.705897i
$260$	−0.404992	−	0.886808i	−0.0251165	−	0.0549975i
$261$	1.17129	+	1.35174i	0.0725012	+	0.0836708i
$262$	−2.28763	−	15.9108i	−0.141330	−	0.982972i
$263$	−12.1342	+	26.5701i	−0.748225	+	1.63838i	0.0213044	+	0.999773i	$0.493218\pi$
$263$	−12.1342	+	26.5701i	−0.748225	+	1.63838i	−0.769529	+	0.638611i	$0.779509\pi$
$264$	−1.52977	+	0.449181i	−0.0941508	+	0.0276452i
$265$	1.89213	−	0.555580i	0.116233	−	0.0341290i
$266$	2.03153	−	4.44843i	0.124561	−	0.272751i
$267$	0.850228	+	5.91347i	0.0520331	+	0.361898i
$268$	7.31067	+	8.43696i	0.446570	+	0.515369i
$269$	−11.3388	−	24.8285i	−0.691338	−	1.51382i	−0.850168	−	0.526512i	$-0.823499\pi$
$269$	−11.3388	−	24.8285i	−0.691338	−	1.51382i	0.158830	−	0.987306i	$-0.449228\pi$
$270$	−0.841254	+	0.540641i	−0.0511971	+	0.0329024i
$271$	−0.153611	+	1.06838i	−0.00933118	+	0.0648998i	−0.993955	−	0.109788i	$-0.964983\pi$
$271$	−0.153611	+	1.06838i	−0.00933118	+	0.0648998i	0.984624	+	0.174688i	$0.0558917\pi$
$272$	−0.675969	−	0.434419i	−0.0409867	−	0.0263405i
$273$	1.91033	−	2.20463i	0.115618	−	0.133430i
$274$	12.0225	+	3.53014i	0.726308	+	0.213263i
$275$	−1.59435			−0.0961430
$276$	3.16106	−	3.60662i	0.190273	−	0.217093i
$277$	−18.3184			−1.10065			−0.550323	−	0.834952i	$-0.685496\pi$
$277$	−18.3184			−1.10065			−0.550323	+	0.834952i	$0.685496\pi$
$278$	5.88635	+	1.72839i	0.353040	+	0.103662i
$279$	3.90897	−	4.51120i	0.234024	−	0.270078i
$280$	−2.51722	−	1.61772i	−0.150433	−	0.0966773i
$281$	−0.787000	+	5.47371i	−0.0469485	+	0.326534i	0.952789	+	0.303633i	$0.0981995\pi$
$281$	−0.787000	+	5.47371i	−0.0469485	+	0.326534i	−0.999738	+	0.0229015i	$0.992710\pi$
$282$	−3.57028	+	2.29448i	−0.212607	+	0.136634i
$283$	2.15676	+	4.72265i	0.128206	+	0.280733i	0.962840	−	0.270073i	$-0.0870478\pi$
$283$	2.15676	+	4.72265i	0.128206	+	0.280733i	−0.834634	+	0.550806i	$0.814321\pi$
$284$	3.28009	+	3.78542i	0.194637	+	0.224623i
$285$	0.232593	+	1.61772i	0.0137776	+	0.0958255i
$286$	−0.645699	+	1.41388i	−0.0381810	+	0.0836046i
$287$	18.1404	−	5.32650i	1.07079	−	0.314413i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−6.79384	+	14.8764i	−0.399638	+	0.875084i
$290$	−0.254546	−	1.77041i	−0.0149475	−	0.103962i
$291$	0.140005	+	0.161575i	0.00820726	+	0.00947168i
$292$	−1.65300	−	3.61956i	−0.0967345	−	0.211819i
$293$	−11.0859	+	7.12446i	−0.647644	+	0.416215i	−0.822804	−	0.568325i	$-0.807592\pi$
$293$	−11.0859	+	7.12446i	−0.647644	+	0.416215i	0.175161	+	0.984540i	$0.443955\pi$
$294$	0.278002	−	1.93355i	0.0162134	−	0.112767i
$295$	5.55768	+	3.57170i	0.323580	+	0.207953i
$296$	−4.59871	+	5.30720i	−0.267295	+	0.308475i
$297$	1.52977	+	0.449181i	0.0887662	+	0.0260641i
$298$	12.8998			0.747264
$299$	−0.639200	−	4.63160i	−0.0369659	−	0.267852i
$300$	1.00000			0.0577350
$301$	−4.48199	−	1.31603i	−0.258338	−	0.0758548i
$302$	3.78565	−	4.36887i	0.217839	−	0.251400i
$303$	8.06851	+	5.18532i	0.463524	+	0.297889i
$304$	0.232593	−	1.61772i	0.0133401	−	0.0927827i
$305$	1.95491	−	1.25635i	0.111938	−	0.0719382i
$306$	0.333797	+	0.730913i	0.0190819	+	0.0417835i
$307$	−4.81572	−	5.55763i	−0.274848	−	0.317191i	0.601498	−	0.798875i	$-0.294571\pi$
$307$	−4.81572	−	5.55763i	−0.274848	−	0.317191i	−0.876345	+	0.481684i	$0.840025\pi$
$308$	0.678936	+	4.72210i	0.0386860	+	0.269067i
$309$	−7.42245	+	16.2529i	−0.422248	+	0.924595i
$310$	−5.72738	+	1.68171i	−0.325293	+	0.0955147i
$311$	−22.9076	+	6.72628i	−1.29897	+	0.381412i	−0.856861	−	0.515548i	$-0.827588\pi$
$311$	−22.9076	+	6.72628i	−1.29897	+	0.381412i	−0.442111	+	0.896961i	$0.645770\pi$
$312$	0.404992	−	0.886808i	0.0229281	−	0.0502056i
$313$	−3.13670	−	21.8163i	−0.177297	−	1.23313i	−0.862984	−	0.505231i	$-0.831407\pi$
$313$	−3.13670	−	21.8163i	−0.177297	−	1.23313i	0.685687	−	0.727897i	$-0.259502\pi$
$314$	4.42211	+	5.10338i	0.249554	+	0.288001i
$315$	1.24302	+	2.72183i	0.0700361	+	0.153358i
$316$	1.28065	−	0.823027i	0.0720424	−	0.0462989i
$317$	1.04694	−	7.28165i	0.0588022	−	0.408978i	−0.939067	−	0.343734i	$-0.888308\pi$
$317$	1.04694	−	7.28165i	0.0588022	−	0.408978i	0.997869	−	0.0652443i	$-0.0207827\pi$
$318$	1.65896	+	1.06615i	0.0930299	+	0.0597867i
$319$	−1.86745	+	2.15515i	−0.104557	+	0.120665i
$320$	−0.959493	−	0.281733i	−0.0536373	−	0.0157493i
$321$	−7.06296			−0.394216
$322$	−9.33589	−	10.8982i	−0.520269	−	0.607331i
$323$	1.31325			0.0730711
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	0.638429	−	0.736786i	0.0354137	−	0.0408696i
$326$	14.1953	+	9.12273i	0.786202	+	0.505261i
$327$	1.57805	−	10.9756i	0.0872662	−	0.606950i
$328$	5.31541	−	3.41601i	0.293495	−	0.188618i
$329$	5.27536	+	11.5514i	0.290840	+	0.636850i
$330$	−1.04408	−	1.20493i	−0.0574746	−	0.0663292i
$331$	−0.708989	−	4.93113i	−0.0389696	−	0.271039i	0.961016	−	0.276494i	$-0.0891727\pi$
$331$	−0.708989	−	4.93113i	−0.0389696	−	0.271039i	−0.999985	+	0.00545498i	$0.998264\pi$
$332$	5.81947	−	12.7429i	0.319385	−	0.699356i
$333$	6.73797	−	1.97845i	0.369239	−	0.108418i
$334$	4.96714	−	1.45848i	0.271790	−	0.0798046i
$335$	−4.63757	+	10.1549i	−0.253377	+	0.554819i
$336$	−0.425839	−	2.96177i	−0.0232314	−	0.161578i
$337$	15.1970	+	17.5383i	0.827833	+	0.955370i	0.999557	−	0.0297754i	$-0.00947920\pi$
$337$	15.1970	+	17.5383i	0.827833	+	0.955370i	−0.171724	+	0.985145i	$0.554934\pi$
$338$	5.00557	+	10.9607i	0.272267	+	0.596181i
$339$	5.44199	−	3.49736i	0.295568	−	0.189950i
$340$	0.114354	−	0.795348i	0.00620170	−	0.0431338i
$341$	8.00617	+	5.14525i	0.433558	+	0.278631i
$342$	−1.07028	+	1.23516i	−0.0578739	+	0.0667900i
$343$	14.4888	+	4.25430i	0.782322	+	0.229711i
$344$	−1.56111			−0.0841696
$345$	4.59385	+	1.37715i	0.247325	+	0.0741434i
$346$	−23.7045			−1.27436
$347$	−8.41884	−	2.47199i	−0.451947	−	0.132704i	0.0478343	−	0.998855i	$-0.484768\pi$
$347$	−8.41884	−	2.47199i	−0.451947	−	0.132704i	−0.499781	+	0.866152i	$0.666586\pi$
$348$	1.17129	−	1.35174i	0.0627879	−	0.0724611i
$349$	−15.8606	−	10.1930i	−0.848998	−	0.545618i	0.0422642	−	0.999106i	$-0.486543\pi$
$349$	−15.8606	−	10.1930i	−0.848998	−	0.545618i	−0.891262	+	0.453489i	$0.850179\pi$
$350$	0.425839	−	2.96177i	0.0227620	−	0.158313i
$351$	−0.820145	+	0.527075i	−0.0437761	+	0.0281332i
$352$	0.662317	+	1.45027i	0.0353016	+	0.0772998i
$353$	−6.68945	−	7.72003i	−0.356043	−	0.410896i	0.549267	−	0.835647i	$-0.314907\pi$
$353$	−6.68945	−	7.72003i	−0.356043	−	0.410896i	−0.905310	+	0.424751i	$0.860362\pi$
$354$	0.940192	+	6.53918i	0.0499706	+	0.347553i
$355$	−2.08074	+	4.55619i	−0.110434	+	0.241818i
$356$	5.73228	−	1.68315i	0.303810	−	0.0892067i
$357$	2.30694	−	0.677379i	0.122096	−	0.0358507i
$358$	8.28470	−	18.1410i	0.437860	−	0.958780i
$359$	1.25988	+	8.76264i	0.0664938	+	0.462474i	0.995679	+	0.0928604i	$0.0296010\pi$
$359$	1.25988	+	8.76264i	0.0664938	+	0.462474i	−0.929185	+	0.369614i	$0.879490\pi$
$360$	0.654861	+	0.755750i	0.0345142	+	0.0398315i
$361$	−6.78326	−	14.8533i	−0.357014	−	0.781751i
$362$	−16.9685	+	10.9050i	−0.891845	+	0.573154i
$363$	1.20371	−	8.37195i	0.0631781	−	0.439414i
$364$	−2.45406	−	1.57713i	−0.128628	−	0.0826640i
$365$	2.60579	−	3.00724i	0.136393	−	0.157406i
$366$	2.22968	+	0.654693i	0.116547	+	0.0342214i
$367$	10.3255			0.538986			0.269493	−	0.963002i	$-0.413144\pi$
$367$	10.3255			0.538986			0.269493	+	0.963002i	$0.413144\pi$
$368$	−4.01978	−	2.61561i	−0.209545	−	0.136348i
$369$	−6.31845			−0.328925
$370$	−6.73797	−	1.97845i	−0.350290	−	0.102855i
$371$	3.86414	−	4.45946i	0.200616	−	0.231523i
$372$	−5.02158	−	3.22718i	−0.260357	−	0.167321i
$373$	5.09538	−	35.4392i	0.263829	−	1.83497i	−0.239525	−	0.970890i	$-0.576992\pi$
$373$	5.09538	−	35.4392i	0.263829	−	1.83497i	0.503354	−	0.864081i	$-0.332099\pi$
$374$	−1.07773	+	0.692617i	−0.0557282	+	0.0358144i
$375$	0.415415	+	0.909632i	0.0214519	+	0.0469732i
$376$	2.77923	+	3.20740i	0.143328	+	0.165409i
$377$	−0.248159	−	1.72598i	−0.0127808	−	0.0888927i
$378$	−1.24302	+	2.72183i	−0.0639339	+	0.139996i
$379$	−16.1303	+	4.73627i	−0.828556	+	0.243286i	−0.668397	−	0.743805i	$-0.733019\pi$
$379$	−16.1303	+	4.73627i	−0.828556	+	0.243286i	−0.160160	+	0.987091i	$0.551201\pi$
$380$	1.56815	−	0.460451i	0.0804446	−	0.0236207i
$381$	−5.38029	+	11.7812i	−0.275640	+	0.603568i
$382$	0.141160	+	0.981789i	0.00722237	+	0.0502327i
$383$	16.2021	+	18.6982i	0.827887	+	0.955432i	0.999558	−	0.0297220i	$-0.00946219\pi$
$383$	16.2021	+	18.6982i	0.827887	+	0.955432i	−0.171671	+	0.985154i	$0.554917\pi$
$384$	−0.415415	−	0.909632i	−0.0211991	−	0.0464195i
$385$	−4.01334	+	2.57922i	−0.204539	+	0.131449i
$386$	0.594966	−	4.13808i	0.0302830	−	0.210623i
$387$	1.31329	+	0.844002i	0.0667584	+	0.0429030i
$388$	0.140005	−	0.161575i	0.00710769	−	0.00820272i
$389$	−22.6578	−	6.65294i	−1.14880	−	0.337318i	−0.348728	−	0.937224i	$-0.613386\pi$
$389$	−22.6578	−	6.65294i	−1.14880	−	0.337318i	−0.800070	+	0.599906i	$0.795204\pi$
$390$	0.974908			0.0493664
$391$	1.62064	−	3.49622i	0.0819592	−	0.176812i
$392$	−1.95343			−0.0986632
$393$	15.4233	+	4.52868i	0.778001	+	0.228442i
$394$	3.26799	−	3.77146i	0.164639	−	0.190003i
$395$	1.28065	+	0.823027i	0.0644367	+	0.0414110i
$396$	0.226900	−	1.57812i	0.0114021	−	0.0793037i
$397$	−22.0616	+	14.1781i	−1.10724	+	0.711580i	−0.960690	−	0.277623i	$-0.910453\pi$
$397$	−22.0616	+	14.1781i	−1.10724	+	0.711580i	−0.146550	+	0.989203i	$0.546817\pi$
$398$	0.305157	+	0.668201i	0.0152961	+	0.0334939i
$399$	3.20251	+	3.69589i	0.160326	+	0.185026i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	−4.59087	+	10.0526i	−0.229257	+	0.502003i	−0.988945	−	0.148285i	$-0.952625\pi$
$401$	−4.59087	+	10.0526i	−0.229257	+	0.502003i	0.759687	+	0.650288i	$0.225352\pi$
$402$	−10.7115	+	3.14518i	−0.534241	+	0.156867i
$403$	−5.58367	+	1.63951i	−0.278142	+	0.0816699i
$404$	3.98427	−	8.72433i	0.198225	−	0.434052i
$405$	−0.142315	−	0.989821i	−0.00707168	−	0.0491846i
$406$	−3.50477	−	4.04473i	−0.173939	−	0.200736i
$407$	4.65108	+	10.1844i	0.230545	+	0.504824i
$408$	0.675969	−	0.434419i	0.0334655	−	0.0215069i
$409$	1.95444	−	13.5934i	0.0966409	−	0.672152i	−0.882700	−	0.469937i	$-0.844277\pi$
$409$	1.95444	−	13.5934i	0.0966409	−	0.672152i	0.979341	−	0.202216i	$-0.0648142\pi$
$410$	5.31541	+	3.41601i	0.262510	+	0.168705i
$411$	−8.20547	+	9.46962i	−0.404746	+	0.467102i
$412$	17.1438	+	5.03387i	0.844614	+	0.248001i
$413$	19.7679			0.972716
$414$	1.96755	+	4.37364i	0.0966998	+	0.214953i
$415$	14.0088			0.687666
$416$	−0.935418	−	0.274663i	−0.0458626	−	0.0134665i
$417$	−4.01747	+	4.63641i	−0.196737	+	0.227046i
$418$	−2.19209	−	1.40877i	−0.107218	−	0.0689051i
$419$	−1.70342	+	11.8476i	−0.0832177	+	0.578792i	0.904962	+	0.425492i	$0.139899\pi$
$419$	−1.70342	+	11.8476i	−0.0832177	+	0.578792i	−0.988180	+	0.153300i	$0.951010\pi$
$420$	2.51722	−	1.61772i	0.122828	−	0.0789367i
$421$	7.84603	+	17.1804i	0.382392	+	0.837322i	0.998756	+	0.0498609i	$0.0158778\pi$
$421$	7.84603	+	17.1804i	0.382392	+	0.837322i	−0.616364	+	0.787461i	$0.711395\pi$
$422$	−6.26052	−	7.22503i	−0.304758	−	0.351709i
$423$	−0.603983	−	4.20080i	−0.0293667	−	0.204250i
$424$	0.819203	−	1.79380i	0.0397840	−	0.0871148i
$425$	0.770978	−	0.226380i	0.0373979	−	0.0109810i
$426$	−4.80594	+	1.41115i	−0.232848	+	0.0683705i
$427$	2.88853	−	6.32501i	0.139786	−	0.306089i
$428$	1.00516	+	6.99107i	0.0485864	+	0.337926i
$429$	−1.01788	−	1.17470i	−0.0491437	−	0.0567149i
$430$	−0.648510	−	1.42004i	−0.0312739	−	0.0684804i
$431$	21.3786	−	13.7392i	1.02977	−	0.661793i	0.0873340	−	0.996179i	$-0.472165\pi$
$431$	21.3786	−	13.7392i	1.02977	−	0.661793i	0.942436	+	0.334386i	$0.108529\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	8.88803	+	5.71199i	0.427131	+	0.274501i	0.736495	−	0.676443i	$-0.236480\pi$
$433$	8.88803	+	5.71199i	0.427131	+	0.274501i	−0.309363	+	0.950944i	$0.600116\pi$
$434$	−11.6965	+	13.4985i	−0.561452	+	0.647950i
$435$	1.71616	+	0.503910i	0.0822836	+	0.0241607i
$436$	−11.0884			−0.531039
$437$	7.83797	+	0.0443422i	0.374941	+	0.00212118i
$438$	3.97915			0.190131
$439$	−29.0861	−	8.54044i	−1.38820	−	0.407613i	−0.499586	−	0.866264i	$-0.666515\pi$
$439$	−29.0861	−	8.54044i	−1.38820	−	0.407613i	−0.888616	+	0.458651i	$0.848333\pi$
$440$	−1.04408	+	1.20493i	−0.0497745	+	0.0574428i
$441$	1.64333	+	1.05610i	0.0782539	+	0.0502907i
$442$	0.111484	−	0.775391i	0.00530277	−	0.0368816i
$443$	−26.0760	+	16.7580i	−1.23891	+	0.796198i	−0.985254	−	0.171097i	$-0.945269\pi$
$443$	−26.0760	+	16.7580i	−1.23891	+	0.796198i	−0.253654	+	0.967295i	$0.581632\pi$
$444$	−2.91722	−	6.38783i	−0.138445	−	0.303153i
$445$	3.91232	+	4.51506i	0.185462	+	0.214034i
$446$	0.262650	+	1.82677i	0.0124368	+	0.0865001i
$447$	−5.35876	+	11.7340i	−0.253461	+	0.555002i
$448$	−2.87102	+	0.843008i	−0.135643	+	0.0398284i
$449$	−6.11055	+	1.79422i	−0.288375	+	0.0846745i	−0.422721	−	0.906260i	$-0.638925\pi$
$449$	−6.11055	+	1.79422i	−0.288375	+	0.0846745i	0.134346	+	0.990935i	$0.457107\pi$
$450$	−0.415415	+	0.909632i	−0.0195829	+	0.0428805i
$451$	−1.43365	−	9.97128i	−0.0675081	−	0.469529i
$452$	−4.23623	−	4.88887i	−0.199256	−	0.229953i
$453$	2.40145	+	5.25844i	0.112830	+	0.247063i
$454$	0.594666	−	0.382169i	0.0279091	−	0.0179361i
$455$	0.415153	−	2.88746i	0.0194627	−	0.135366i
$456$	1.37491	+	0.883600i	0.0643860	+	0.0413783i
$457$	−23.8425	+	27.5157i	−1.11531	+	1.28713i	−0.161446	+	0.986882i	$0.551616\pi$
$457$	−23.8425	+	27.5157i	−1.11531	+	1.28713i	−0.953860	+	0.300250i	$0.902930\pi$
$458$	0.609191	+	0.178875i	0.0284656	+	0.00835827i
$459$	−0.803526			−0.0375054
$460$	0.709362	−	4.74308i	0.0330742	−	0.221147i
$461$	6.45146			0.300474			0.150237	−	0.988650i	$-0.451996\pi$
$461$	6.45146			0.300474			0.150237	+	0.988650i	$0.451996\pi$
$462$	−4.57742	−	1.34405i	−0.212961	−	0.0625309i
$463$	11.3031	−	13.0445i	0.525300	−	0.606229i	−0.429650	−	0.902996i	$-0.641363\pi$
$463$	11.3031	−	13.0445i	0.525300	−	0.606229i	0.954950	+	0.296767i	$0.0959084\pi$
$464$	−1.50468	−	0.966997i	−0.0698529	−	0.0448917i
$465$	0.849501	−	5.90841i	0.0393947	−	0.273996i
$466$	−6.65974	+	4.27995i	−0.308506	+	0.198265i
$467$	12.0366	+	26.3565i	0.556989	+	1.21964i	0.953441	+	0.301580i	$0.0975141\pi$
$467$	12.0366	+	26.3565i	0.556989	+	1.21964i	−0.396452	+	0.918055i	$0.629759\pi$
$468$	0.638429	+	0.736786i	0.0295114	+	0.0340580i
$469$	4.75393	+	33.0643i	0.219516	+	1.52677i
$470$	−1.76302	+	3.86047i	−0.0813220	+	0.178070i
$471$	−6.47921	+	1.90247i	−0.298546	+	0.0876611i
$472$	6.33882	−	1.86124i	0.291768	−	0.0856707i
$473$	−1.03395	+	2.26404i	−0.0475412	+	0.104101i
$474$	0.216648	+	1.50682i	0.00995098	+	0.0692106i
$475$	1.07028	+	1.23516i	0.0491076	+	0.0566732i
$476$	−0.998797	−	2.18706i	−0.0457798	−	0.100244i
$477$	−1.65896	+	1.06615i	−0.0759586	+	0.0488156i
$478$	−0.918852	+	6.39076i	−0.0420273	+	0.292306i
$479$	27.0720	+	17.3981i	1.23695	+	0.794940i	0.984959	−	0.172789i	$-0.0552778\pi$
$479$	27.0720	+	17.3981i	1.23695	+	0.794940i	0.251992	+	0.967729i	$0.418914\pi$
$480$	0.654861	−	0.755750i	0.0298902	−	0.0344951i
$481$	−6.56890	−	1.92880i	−0.299516	−	0.0879459i
$482$	14.1165			0.642987
$483$	13.7916	−	3.96497i	0.627539	−	0.180412i
$484$	−8.45804			−0.384457
$485$	0.205134	+	0.0602328i	0.00931465	+	0.00273503i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	−22.2751	−	14.3153i	−1.00938	−	0.648689i	−0.0721471	−	0.997394i	$-0.522985\pi$
$487$	−22.2751	−	14.3153i	−1.00938	−	0.648689i	−0.937232	+	0.348705i	$0.886621\pi$
$488$	0.330713	−	2.30016i	0.0149707	−	0.104123i
$489$	−14.1953	+	9.12273i	−0.641931	+	0.412544i
$490$	−0.811485	−	1.77690i	−0.0366591	−	0.0802723i
$491$	19.1837	+	22.1391i	0.865746	+	0.999125i	0.999967	+	0.00817303i	$0.00260159\pi$
$491$	19.1837	+	22.1391i	0.865746	+	0.999125i	−0.134220	+	0.990952i	$0.542853\pi$
$492$	0.899209	+	6.25413i	0.0405395	+	0.281958i
$493$	0.597033	−	1.30732i	0.0268890	−	0.0588788i
$494$	1.52881	−	0.448898i	0.0687842	−	0.0201969i
$495$	1.52977	−	0.449181i	0.0687580	−	0.0201892i
$496$	−2.47968	+	5.42975i	−0.111341	+	0.243803i
$497$	2.13295	+	14.8350i	0.0956760	+	0.665441i
$498$	9.17382	+	10.5872i	0.411089	+	0.474422i
$499$	−14.3457	−	31.4127i	−0.642202	−	1.40623i	−0.898217	−	0.439553i	$-0.855137\pi$
$499$	−14.3457	−	31.4127i	−0.642202	−	1.40623i	0.256015	−	0.966673i	$-0.417590\pi$
$500$	0.841254	−	0.540641i	0.0376220	−	0.0241782i
$501$	−0.736740	+	5.12414i	−0.0329151	+	0.228930i
$502$	−2.00181	−	1.28649i	−0.0893453	−	0.0574188i
$503$	0.0815619	−	0.0941275i	0.00363667	−	0.00419694i	−0.753928	−	0.656957i	$-0.771843\pi$
$503$	0.0815619	−	0.0941275i	0.00363667	−	0.00419694i	0.757565	+	0.652760i	$0.226389\pi$
$504$	2.87102	+	0.843008i	0.127885	+	0.0375506i
$505$	9.59106			0.426797
$506$	−6.45571	+	4.09741i	−0.286991	+	0.182152i
$507$	−12.0496			−0.535139
$508$	12.4270	+	3.64889i	0.551357	+	0.161893i
$509$	0.478832	−	0.552602i	0.0212239	−	0.0244936i	−0.745038	−	0.667022i	$-0.767569\pi$
$509$	0.478832	−	0.552602i	0.0212239	−	0.0244936i	0.766262	+	0.642528i	$0.222114\pi$
$510$	0.675969	+	0.434419i	0.0299324	+	0.0192364i
$511$	1.69448	−	11.7853i	0.0749592	−	0.521353i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	−0.678936	−	1.48666i	−0.0299758	−	0.0656378i
$514$	4.75424	+	5.48669i	0.209701	+	0.242007i
$515$	2.54282	+	17.6857i	0.112050	+	0.779324i
$516$	0.648510	−	1.42004i	0.0285491	−	0.0625137i
$517$	6.49233	−	1.90632i	0.285532	−	0.0838399i
$518$	−20.1616	+	5.91997i	−0.885848	+	0.260108i
$519$	9.84722	−	21.5624i	0.432245	−	0.946485i
$520$	−0.138744	−	0.964985i	−0.00608432	−	0.0423174i
$521$	6.49754	+	7.49856i	0.284662	+	0.328518i	0.880014	−	0.474947i	$-0.157533\pi$
$521$	6.49754	+	7.49856i	0.284662	+	0.328518i	−0.595352	+	0.803465i	$0.702987\pi$
$522$	0.743017	+	1.62698i	0.0325210	+	0.0712110i
$523$	−10.1093	+	6.49685i	−0.442049	+	0.284088i	−0.742672	−	0.669655i	$-0.766442\pi$
$523$	−10.1093	+	6.49685i	−0.442049	+	0.284088i	0.300623	+	0.953743i	$0.402805\pi$
$524$	2.28763	−	15.9108i	0.0999354	−	0.695066i
$525$	2.51722	+	1.61772i	0.109861	+	0.0706031i
$526$	−19.1283	+	22.0753i	−0.834035	+	0.962527i
$527$	−4.60210	−	1.35130i	−0.200470	−	0.0588634i
$528$	−1.59435			−0.0693852
$529$	9.79065	−	20.8121i	0.425680	−	0.904874i
$530$	1.97201			0.0856587
$531$	−6.33882	−	1.86124i	−0.275081	−	0.0807711i
$532$	3.20251	−	3.69589i	0.138846	−	0.160237i
$533$	5.18204	+	3.33030i	0.224459	+	0.144251i
$534$	−0.850228	+	5.91347i	−0.0367930	+	0.255901i
$535$	−5.94174	+	3.81852i	−0.256884	+	0.165089i
$536$	4.63757	+	10.1549i	0.200312	+	0.438623i
$537$	13.0600	+	15.0721i	0.563581	+	0.650407i
$538$	−3.88449	−	27.0172i	−0.167472	−	1.16480i
$539$	−1.29379	+	2.83301i	−0.0557276	+	0.122026i
$540$	−0.959493	+	0.281733i	−0.0412900	+	0.0121238i
$541$	11.4828	−	3.37165i	0.493684	−	0.144959i	−0.0254078	−	0.999677i	$-0.508088\pi$
$541$	11.4828	−	3.37165i	0.493684	−	0.144959i	0.519092	+	0.854718i	$0.326270\pi$
$542$	−0.448387	+	0.981831i	−0.0192599	+	0.0421732i
$543$	−2.87056	−	19.9652i	−0.123188	−	0.856788i
$544$	−0.526198	−	0.607265i	−0.0225605	−	0.0260363i
$545$	−4.60630	−	10.0864i	−0.197312	−	0.432053i
$546$	2.45406	−	1.57713i	0.105024	−	0.0674949i
$547$	3.05397	−	21.2408i	0.130578	−	0.908192i	−0.814224	−	0.580551i	$-0.802837\pi$
$547$	3.05397	−	21.2408i	0.130578	−	0.908192i	0.944802	−	0.327641i	$-0.106254\pi$
$548$	10.5410	+	6.77428i	0.450289	+	0.289383i
$549$	−1.52177	+	1.75622i	−0.0649476	+	0.0749536i
$550$	−1.52977	−	0.449181i	−0.0652296	−	0.0191531i
$551$	2.92323			0.124534
$552$	4.04911	−	2.56996i	0.172342	−	0.109385i
$553$	4.55512			0.193703
$554$	−17.5764	−	5.16089i	−0.746749	−	0.219265i
$555$	4.59871	−	5.30720i	0.195205	−	0.225278i
$556$	5.16097	+	3.31675i	0.218874	+	0.140662i
$557$	4.21110	−	29.2888i	0.178430	−	1.24101i	−0.681967	−	0.731383i	$-0.738875\pi$
$557$	4.21110	−	29.2888i	0.178430	−	1.24101i	0.860397	−	0.509625i	$-0.170216\pi$
$558$	5.02158	−	3.22718i	0.212581	−	0.136617i
$559$	−0.632238	−	1.38441i	−0.0267408	−	0.0585542i
$560$	−1.95949	−	2.26138i	−0.0828037	−	0.0955606i
$561$	−0.182320	−	1.26806i	−0.00769755	−	0.0535377i
$562$	−2.29724	+	5.03026i	−0.0969033	+	0.212189i
$563$	−18.7711	+	5.51170i	−0.791108	+	0.232290i	−0.652232	−	0.758019i	$-0.726167\pi$
$563$	−18.7711	+	5.51170i	−0.791108	+	0.232290i	−0.138876	+	0.990310i	$0.544349\pi$
$564$	−4.07208	+	1.19567i	−0.171466	+	0.0503469i
$565$	2.68728	−	5.88433i	0.113055	−	0.247555i
$566$	0.738874	+	5.13898i	0.0310572	+	0.216008i
$567$	−1.95949	−	2.26138i	−0.0822910	−	0.0949688i
$568$	2.08074	+	4.55619i	0.0873061	+	0.191174i
$569$	−7.50745	+	4.82475i	−0.314729	+	0.202264i	−0.688462	−	0.725272i	$-0.741714\pi$
$569$	−7.50745	+	4.82475i	−0.314729	+	0.202264i	0.373733	+	0.927536i	$0.378078\pi$
$570$	−0.232593	+	1.61772i	−0.00974225	+	0.0677589i
$571$	−12.2307	−	7.86019i	−0.511838	−	0.328939i	0.259098	−	0.965851i	$-0.416575\pi$
$571$	−12.2307	−	7.86019i	−0.511838	−	0.328939i	−0.770936	+	0.636913i	$0.780211\pi$
$572$	−1.01788	+	1.17470i	−0.0425597	+	0.0491165i
$573$	−0.951706	−	0.279446i	−0.0397581	−	0.0116740i
$574$	18.9062			0.789131
$575$	4.60914	−	1.32509i	0.192214	−	0.0552600i
$576$	1.00000			0.0416667
$577$	−38.1822	−	11.2113i	−1.58955	−	0.466733i	−0.636934	−	0.770918i	$-0.719798\pi$
$577$	−38.1822	−	11.2113i	−1.58955	−	0.466733i	−0.952613	+	0.304185i	$0.901616\pi$
$578$	−10.7098	+	12.3598i	−0.445470	+	0.514099i
$579$	3.51697	+	2.26022i	0.146160	+	0.0939315i
$580$	0.254546	−	1.77041i	0.0105695	−	0.0735122i
$581$	35.2633	−	22.6623i	1.46297	−	0.940193i
$582$	0.0888133	+	0.194474i	0.00368143	+	0.00806120i
$583$	−2.05893	−	2.37614i	−0.0852723	−	0.0984095i
$584$	−0.566293	−	3.93865i	−0.0234334	−	0.162983i
$585$	−0.404992	+	0.886808i	−0.0167443	+	0.0366650i
$586$	−12.6440	+	3.71262i	−0.522319	+	0.153367i
$587$	−31.2889	+	9.18725i	−1.29143	+	0.379198i	−0.854103	−	0.520104i	$-0.825893\pi$
$587$	−31.2889	+	9.18725i	−1.29143	+	0.379198i	−0.437328	+	0.899302i	$0.644075\pi$
$588$	0.811485	−	1.77690i	0.0334651	−	0.0732783i
$589$	−1.38839	−	9.65645i	−0.0572075	−	0.397887i
$590$	4.32629	+	4.99280i	0.178110	+	0.205550i
$591$	2.07307	+	4.53939i	0.0852747	+	0.186726i
$592$	−5.90764	+	3.79661i	−0.242803	+	0.156040i
$593$	2.70197	−	18.7926i	0.110957	−	0.771721i	−0.856036	−	0.516916i	$-0.827080\pi$
$593$	2.70197	−	18.7926i	0.110957	−	0.771721i	0.966993	−	0.254804i	$-0.0820111\pi$
$594$	1.34125	+	0.861971i	0.0550323	+	0.0353671i
$595$	1.57450	−	1.81707i	0.0645484	−	0.0744928i
$596$	12.3772	+	3.63429i	0.506992	+	0.148866i
$597$	−0.734584			−0.0300645
$598$	0.691563	−	4.62407i	0.0282801	−	0.189092i
$599$	44.7599			1.82884			0.914419	−	0.404768i	$-0.132648\pi$
$599$	44.7599			1.82884			0.914419	+	0.404768i	$0.132648\pi$
$600$	0.959493	+	0.281733i	0.0391711	+	0.0115017i
$601$	10.7600	−	12.4177i	0.438910	−	0.506529i	−0.492594	−	0.870259i	$-0.663951\pi$
$601$	10.7600	−	12.4177i	0.438910	−	0.506529i	0.931505	+	0.363730i	$0.118497\pi$
$602$	−3.92967	−	2.52545i	−0.160161	−	0.102930i
$603$	1.58876	−	11.0501i	0.0646993	−	0.449994i
$604$	4.86315	−	3.12536i	0.197879	−	0.127169i
$605$	−3.51360	−	7.69371i	−0.142848	−	0.312794i
$606$	6.28081	+	7.24844i	0.255140	+	0.294448i
$607$	−3.64058	−	25.3208i	−0.147767	−	1.02774i	−0.919864	−	0.392236i	$-0.871702\pi$
$607$	−3.64058	−	25.3208i	−0.147767	−	1.02774i	0.772098	−	0.635504i	$-0.219208\pi$
$608$	0.678936	−	1.48666i	0.0275345	−	0.0602921i
$609$	5.13515	−	1.50782i	0.208087	−	0.0610998i
$610$	2.22968	−	0.654693i	0.0902771	−	0.0265077i
$611$	−1.71878	+	3.76361i	−0.0695345	+	0.152259i
$612$	0.114354	+	0.795348i	0.00462247	+	0.0321500i
$613$	−13.6896	−	15.7986i	−0.552917	−	0.638101i	0.408643	−	0.912694i	$-0.366002\pi$
$613$	−13.6896	−	15.7986i	−0.552917	−	0.638101i	−0.961560	+	0.274594i	$0.911457\pi$
$614$	−3.05488	−	6.68926i	−0.123285	−	0.269956i
$615$	−5.31541	+	3.41601i	−0.214338	+	0.137747i
$616$	−0.678936	+	4.72210i	−0.0273551	+	0.190259i
$617$	22.5638	+	14.5009i	0.908385	+	0.583784i	0.909266	−	0.416216i	$-0.136644\pi$
$617$	22.5638	+	14.5009i	0.908385	+	0.583784i	−0.000880605		1.00000i	$0.500280\pi$
$618$	−11.7008	+	13.5034i	−0.470673	+	0.543186i
$619$	−47.2663	−	13.8786i	−1.89979	−	0.557829i	−0.989644	−	0.143544i	$-0.954150\pi$
$619$	−47.2663	−	13.8786i	−1.89979	−	0.557829i	−0.910147	−	0.414285i	$-0.864032\pi$
$620$	−5.96917			−0.239728
$621$	−4.79575	−	0.0271313i	−0.192447	−	0.00108874i
$622$	−23.8747			−0.957288
$623$	17.1523	+	5.03637i	0.687192	+	0.201778i
$624$	0.638429	−	0.736786i	0.0255576	−	0.0294951i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	3.13670	−	21.8163i	0.125368	−	0.871953i
$627$	2.19209	−	1.40877i	0.0875435	−	0.0562608i
$628$	2.80519	+	6.14251i	0.111939	+	0.245113i
$629$	−3.69519	−	4.26447i	−0.147337	−	0.170036i
$630$	0.425839	+	2.96177i	0.0169658	+	0.118000i
$631$	4.41587	−	9.66940i	0.175793	−	0.384933i	−0.801141	−	0.598476i	$-0.795773\pi$
$631$	4.41587	−	9.66940i	0.175793	−	0.384933i	0.976934	+	0.213543i	$0.0685005\pi$
$632$	1.46065	−	0.428886i	0.0581016	−	0.0170602i
$633$	9.17283	−	2.69339i	0.364587	−	0.107053i
$634$	3.05601	−	6.69173i	0.121370	−	0.265763i
$635$	1.84320	+	12.8198i	0.0731453	+	0.508737i
$636$	1.29139	+	1.49035i	0.0512070	+	0.0590961i
$637$	−0.791123	−	1.73232i	−0.0313454	−	0.0686369i
$638$	−2.39898	+	1.54173i	−0.0949767	+	0.0610378i
$639$	0.712831	−	4.95785i	0.0281992	−	0.196129i
$640$	−0.841254	−	0.540641i	−0.0332535	−	0.0213707i
$641$	−3.79664	+	4.38156i	−0.149958	+	0.173061i	−0.825759	−	0.564024i	$-0.809253\pi$
$641$	−3.79664	+	4.38156i	−0.149958	+	0.173061i	0.675800	+	0.737085i	$0.263798\pi$
$642$	−6.77686	−	1.98987i	−0.267461	−	0.0785337i
$643$	6.66779			0.262952			0.131476	−	0.991319i	$-0.458028\pi$
$643$	6.66779			0.262952			0.131476	+	0.991319i	$0.458028\pi$
$644$	−5.88736	−	13.0869i	−0.231994	−	0.515698i
$645$	1.56111			0.0614688
$646$	1.26005	+	0.369985i	0.0495761	+	0.0145569i
$647$	32.4120	−	37.4054i	1.27425	−	1.47056i	0.462417	−	0.886662i	$-0.346982\pi$
$647$	32.4120	−	37.4054i	1.27425	−	1.47056i	0.811829	−	0.583896i	$-0.198472\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	1.49900	−	10.4257i	0.0588407	−	0.409246i
$650$	0.820145	−	0.527075i	0.0321687	−	0.0206736i
$651$	−7.41978	−	16.2470i	−0.290804	−	0.636772i
$652$	11.0501	+	12.7525i	0.432754	+	0.499425i
$653$	−5.13536	−	35.7172i	−0.200962	−	1.39772i	−0.801438	−	0.598079i	$-0.795931\pi$
$653$	−5.13536	−	35.7172i	−0.200962	−	1.39772i	0.600475	−	0.799643i	$-0.294978\pi$
$654$	4.60630	−	10.0864i	0.180120	−	0.394409i
$655$	15.4233	−	4.52868i	0.602637	−	0.176950i
$656$	6.06250	−	1.78011i	0.236701	−	0.0695017i
$657$	−1.65300	+	3.61956i	−0.0644897	+	0.141213i
$658$	1.80726	+	12.5697i	0.0704542	+	0.490020i
$659$	−14.8580	−	17.1470i	−0.578784	−	0.667953i	0.388559	−	0.921424i	$-0.372973\pi$
$659$	−14.8580	−	17.1470i	−0.578784	−	0.667953i	−0.967343	+	0.253471i	$0.918428\pi$
$660$	−0.662317	−	1.45027i	−0.0257807	−	0.0564518i
$661$	24.0004	−	15.4241i	0.933506	−	0.599928i	0.0169598	−	0.999856i	$-0.494601\pi$
$661$	24.0004	−	15.4241i	0.933506	−	0.599928i	0.916547	+	0.399928i	$0.130965\pi$
$662$	0.708989	−	4.93113i	0.0275557	−	0.191654i
$663$	0.659008	+	0.423519i	0.0255938	+	0.0164481i
$664$	9.17382	−	10.5872i	0.356013	−	0.410861i
$665$	4.69227	+	1.37778i	0.181959	+	0.0534279i
$666$	7.02243			0.272114
$667$	3.60747	−	7.78244i	0.139682	−	0.301337i
$668$	5.17683			0.200298
$669$	−1.77080	−	0.519953i	−0.0684630	−	0.0201025i
$670$	−7.31067	+	8.43696i	−0.282436	+	0.325948i
$671$	−3.11682	−	2.00306i	−0.120323	−	0.0773272i
$672$	0.425839	−	2.96177i	0.0164271	−	0.114253i
$673$	−27.7781	+	17.8519i	−1.07077	+	0.688141i	−0.952407	−	0.304829i	$-0.901401\pi$
$673$	−27.7781	+	17.8519i	−1.07077	+	0.688141i	−0.118362	+	0.992971i	$0.537764\pi$
$674$	9.64030	+	21.1093i	0.371331	+	0.813101i
$675$	−0.654861	−	0.755750i	−0.0252056	−	0.0290888i
$676$	1.71483	+	11.9269i	0.0659550	+	0.458727i
$677$	−7.73997	+	16.9482i	−0.297471	+	0.651371i	−0.998064	−	0.0621897i	$-0.980192\pi$
$677$	−7.73997	+	16.9482i	−0.297471	+	0.651371i	0.700593	+	0.713561i	$0.252919\pi$
$678$	6.20687	−	1.82250i	0.238373	−	0.0699928i
$679$	0.613808	−	0.180230i	0.0235558	−	0.00691660i
$680$	0.333797	−	0.730913i	0.0128005	−	0.0280292i
$681$	0.100600	+	0.699686i	0.00385499	+	0.0268120i
$682$	6.23228	+	7.19243i	0.238646	+	0.275412i
$683$	−6.58520	−	14.4196i	−0.251976	−	0.551750i	0.740801	−	0.671724i	$-0.234446\pi$
$683$	−6.58520	−	14.4196i	−0.251976	−	0.551750i	−0.992777	+	0.119974i	$0.961719\pi$
$684$	−1.37491	+	0.883600i	−0.0525709	+	0.0337853i
$685$	−1.78322	+	12.4026i	−0.0681333	+	0.473878i
$686$	12.7033	+	8.16394i	0.485016	+	0.311701i
$687$	−0.415777	+	0.479833i	−0.0158629	+	0.0183068i
$688$	−1.49788	−	0.439817i	−0.0571060	−	0.0167678i
$689$	1.92253			0.0732426
$690$	4.01978	+	2.61561i	0.153030	+	0.0995744i
$691$	42.3686			1.61178			0.805888	−	0.592068i	$-0.201688\pi$
$691$	42.3686			1.61178			0.805888	+	0.592068i	$0.201688\pi$
$692$	−22.7443	−	6.67834i	−0.864610	−	0.253872i
$693$	3.12412	−	3.60543i	0.118676	−	0.136959i
$694$	−7.38137	−	4.74372i	−0.280193	−	0.180069i
$695$	−0.873081	+	6.07241i	−0.0331178	+	0.230340i
$696$	1.50468	−	0.966997i	0.0570346	−	0.0366539i
$697$	2.10908	+	4.61824i	0.0798870	+	0.174928i
$698$	−12.3464	−	14.2485i	−0.467319	−	0.539315i
$699$	−1.12663	−	7.83586i	−0.0426130	−	0.296380i
$700$	1.24302	−	2.72183i	0.0469816	−	0.102875i
$701$	46.4592	−	13.6416i	1.75474	−	0.515238i	0.763326	−	0.646013i	$-0.223565\pi$
$701$	46.4592	−	13.6416i	1.75474	−	0.515238i	0.991412	+	0.130776i	$0.0417468\pi$
$702$	−0.935418	+	0.274663i	−0.0353051	+	0.0103665i
$703$	4.76778	−	10.4400i	0.179820	−	0.393751i
$704$	0.226900	+	1.57812i	0.00855161	+	0.0594777i
$705$	−2.77923	−	3.20740i	−0.104672	−	0.120798i
$706$	−4.24349	−	9.29195i	−0.159706	−	0.349707i
$707$	24.1428	−	15.5157i	0.907985	−	0.583526i
$708$	−0.940192	+	6.53918i	−0.0353346	+	0.245757i
$709$	25.7210	+	16.5299i	0.965974	+	0.620794i	0.925645	−	0.378393i	$-0.123523\pi$
$709$	25.7210	+	16.5299i	0.965974	+	0.620794i	0.0403286	+	0.999186i	$0.487160\pi$
$710$	−3.28009	+	3.78542i	−0.123099	+	0.142064i
$711$	−1.46065	−	0.428886i	−0.0547787	−	0.0160845i
$712$	5.97428			0.223896
$713$	−27.4215	−	8.22046i	−1.02694	−	0.307859i
$714$	2.40433			0.0899799
$715$	−1.49138	−	0.437910i	−0.0557746	−	0.0163769i
$716$	13.0600	−	15.0721i	0.488076	−	0.563269i
$717$	−5.43153	−	3.49063i	−0.202844	−	0.130360i
$718$	−1.25988	+	8.76264i	−0.0470182	+	0.327019i
$719$	−5.34597	+	3.43565i	−0.199371	+	0.128128i	−0.636517	−	0.771262i	$-0.719626\pi$
$719$	−5.34597	+	3.43565i	−0.199371	+	0.128128i	0.437146	+	0.899390i	$0.355989\pi$
$720$	0.415415	+	0.909632i	0.0154816	+	0.0339000i
$721$	35.0113	+	40.4052i	1.30389	+	1.50477i
$722$	−2.32384	−	16.1627i	−0.0864844	−	0.601512i
$723$	−5.86419	+	12.8408i	−0.218092	+	0.477554i
$724$	−19.3535	+	5.68269i	−0.719265	+	0.211195i
$725$	1.71616	−	0.503910i	0.0637366	−	0.0187148i
$726$	3.51360	−	7.69371i	0.130402	−	0.285540i
$727$	−3.49170	−	24.2853i	−0.129500	−	0.900692i	−0.946189	−	0.323614i	$-0.895102\pi$
$727$	−3.49170	−	24.2853i	−0.129500	−	0.900692i	0.816689	−	0.577078i	$-0.195807\pi$
$728$	−1.91033	−	2.20463i	−0.0708014	−	0.0817092i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	3.34748	−	2.15129i	0.123896	−	0.0796229i
$731$	0.178519	−	1.24163i	0.00660277	−	0.0459233i
$732$	1.95491	+	1.25635i	0.0722557	+	0.0464359i
$733$	2.74147	−	3.16383i	0.101259	−	0.116859i	−0.702858	−	0.711330i	$-0.748093\pi$
$733$	2.74147	−	3.16383i	0.101259	−	0.116859i	0.804117	+	0.594471i	$0.202639\pi$
$734$	9.90723	+	2.90902i	0.365682	+	0.107374i
$735$	1.95343			0.0720534
$736$	−3.12005	−	3.64216i	−0.115006	−	0.134252i
$737$	17.7989			0.655629
$738$	−6.06250	−	1.78011i	−0.223164	−	0.0655268i
$739$	22.7481	−	26.2527i	0.836802	−	0.965722i	−0.162979	−	0.986630i	$-0.552110\pi$
$739$	22.7481	−	26.2527i	0.836802	−	0.965722i	0.999781	+	0.0209080i	$0.00665571\pi$
$740$	−5.90764	−	3.79661i	−0.217169	−	0.139566i
$741$	−0.226757	+	1.57713i	−0.00833013	+	0.0579373i
$742$	4.96399	−	3.19016i	0.182234	−	0.117115i
$743$	6.40427	+	14.0234i	0.234950	+	0.514468i	0.989978	−	0.141225i	$-0.0451040\pi$
$743$	6.40427	+	14.0234i	0.234950	+	0.514468i	−0.755028	+	0.655693i	$0.772377\pi$
$744$	−3.90897	−	4.51120i	−0.143310	−	0.165389i
$745$	1.83583	+	12.7685i	0.0672596	+	0.467801i
$746$	14.8734	−	32.5681i	0.544552	−	1.19240i
$747$	−13.4414	+	3.94674i	−0.491794	+	0.144404i
$748$	−1.22921	+	0.360928i	−0.0449443	+	0.0131969i
$749$	−8.77937	+	19.2241i	−0.320791	+	0.702435i
$750$	0.142315	+	0.989821i	0.00519660	+	0.0361432i
$751$	12.8195	+	14.7945i	0.467791	+	0.539859i	0.939796	−	0.341737i	$-0.111015\pi$
$751$	12.8195	+	14.7945i	0.467791	+	0.539859i	−0.472005	+	0.881596i	$0.656470\pi$
$752$	1.76302	+	3.86047i	0.0642907	+	0.140777i
$753$	2.00181	−	1.28649i	0.0729502	−	0.0468822i
$754$	0.248159	−	1.72598i	0.00903742	−	0.0628567i
$755$	4.86315	+	3.12536i	0.176988	+	0.113743i
$756$	−1.95949	+	2.26138i	−0.0712661	+	0.0822454i
$757$	−31.9428	−	9.37925i	−1.16098	−	0.340895i	−0.356167	−	0.934422i	$-0.615917\pi$
$757$	−31.9428	−	9.37925i	−1.16098	−	0.340895i	−0.804813	+	0.593528i	$0.797735\pi$
$758$	−16.8112			−0.610612
$759$	−1.04534	−	7.57445i	−0.0379434	−	0.274935i
$760$	1.63436			0.0592843
$761$	12.2802	+	3.60578i	0.445156	+	0.130709i	0.496625	−	0.867965i	$-0.334572\pi$
$761$	12.2802	+	3.60578i	0.445156	+	0.130709i	−0.0514696	+	0.998675i	$0.516391\pi$
$762$	−8.48149	+	9.78816i	−0.307252	+	0.354588i
$763$	−27.9120	−	17.9380i	−1.01048	−	0.649398i
$764$	−0.141160	+	0.981789i	−0.00510699	+	0.0355199i
$765$	−0.675969	+	0.434419i	−0.0244397	+	0.0157065i
$766$	10.2779	+	22.5054i	0.371355	+	0.813154i
$767$	4.21773	+	4.86752i	0.152293	+	0.175756i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	20.9349	−	45.8410i	0.754931	−	1.65307i	−0.00236655	−	0.999997i	$-0.500753\pi$
$769$	20.9349	−	45.8410i	0.754931	−	1.65307i	0.757297	−	0.653070i	$-0.226519\pi$
$770$	−4.57742	+	1.34405i	−0.164959	+	0.0484362i
$771$	−6.96585	+	2.04536i	−0.250869	+	0.0736618i
$772$	1.73670	−	3.80283i	0.0625051	−	0.136867i
$773$	−5.15554	−	35.8576i	−0.185432	−	1.28971i	−0.843656	−	0.536884i	$-0.819601\pi$
$773$	−5.15554	−	35.8576i	−0.185432	−	1.28971i	0.658224	−	0.752822i	$-0.271308\pi$
$774$	1.02231	+	1.17981i	0.0367462	+	0.0424074i
$775$	−2.47968	−	5.42975i	−0.0890728	−	0.195042i
$776$	0.179855	−	0.115586i	0.00645642	−	0.00414929i
$777$	2.99042	−	20.7988i	0.107281	−	0.746154i
$778$	−19.8657	−	12.7669i	−0.712219	−	0.457716i
$779$	−6.76248	+	7.80432i	−0.242291	+	0.279619i
$780$	0.935418	+	0.274663i	0.0334933	+	0.00983453i
$781$	7.98584			0.285756
$782$	2.53999	−	2.89802i	0.0908299	−	0.103633i
$783$	−1.78861			−0.0639198
$784$	−1.87430	−	0.550345i	−0.0669394	−	0.0196552i
$785$	−4.42211	+	5.10338i	−0.157832	+	0.182148i
$786$	13.5226	+	8.69048i	0.482337	+	0.309979i
$787$	−0.813375	+	5.65715i	−0.0289937	+	0.201656i	−0.999170	−	0.0407467i	$-0.987026\pi$
$787$	−0.813375	+	5.65715i	−0.0289937	+	0.201656i	0.970176	+	0.242402i	$0.0779354\pi$
$788$	4.19816	−	2.69799i	0.149553	−	0.0961120i
$789$	−12.1342	−	26.5701i	−0.431988	−	0.945922i
$790$	0.996905	+	1.15049i	0.0354683	+	0.0409326i
$791$	−2.75471	−	19.1594i	−0.0979462	−	0.681231i
$792$	0.662317	−	1.45027i	0.0235344	−	0.0515332i
$793$	2.17373	−	0.638266i	0.0771915	−	0.0226655i
$794$	−25.1624	+	7.38835i	−0.892980	+	0.262203i
$795$	−0.819203	+	1.79380i	−0.0290541	+	0.0636197i
$796$	0.104542	+	0.727107i	0.00370540	+	0.0257716i
$797$	−22.9351	−	26.4685i	−0.812403	−	0.937563i	0.186589	−	0.982438i	$-0.440257\pi$
$797$	−22.9351	−	26.4685i	−0.812403	−	0.937563i	−0.998993	+	0.0448747i	$0.985711\pi$
$798$	2.03153	+	4.44843i	0.0719155	+	0.157473i
$799$	−2.86881	+	1.84367i	−0.101491	+	0.0652244i
$800$	0.142315	−	0.989821i	0.00503159	−	0.0349955i
$801$	−5.02588	−	3.22994i	−0.177581	−	0.114124i
$802$	−7.23706	+	8.35201i	−0.255549	+	0.294920i
$803$	−6.08718	−	1.78736i	−0.214812	−	0.0630745i
$804$	−11.1637			−0.393713
$805$	9.45860	−	10.7918i	0.333372	−	0.380362i
$806$	−5.81939			−0.204979
$807$	26.1894	+	7.68991i	0.921911	+	0.270698i
$808$	6.28081	−	7.24844i	0.220958	−	0.254999i
$809$	−11.5316	−	7.41089i	−0.405428	−	0.260553i	0.321996	−	0.946741i	$-0.395646\pi$
$809$	−11.5316	−	7.41089i	−0.405428	−	0.260553i	−0.727424	+	0.686188i	$0.759283\pi$
$810$	0.142315	−	0.989821i	0.00500043	−	0.0347788i
$811$	6.42281	−	4.12769i	0.225535	−	0.144943i	−0.422994	−	0.906133i	$-0.639021\pi$
$811$	6.42281	−	4.12769i	0.225535	−	0.144943i	0.648529	+	0.761190i	$0.275384\pi$
$812$	−2.22328	−	4.86829i	−0.0780217	−	0.170844i
$813$	−0.706838	−	0.815734i	−0.0247899	−	0.0286091i
$814$	1.59339	+	11.0823i	0.0558482	+	0.388433i
$815$	−7.00968	+	15.3491i	−0.245538	+	0.537654i
$816$	0.770978	−	0.226380i	0.0269896	−	0.00792487i
$817$	2.44807	−	0.718817i	0.0856470	−	0.0251482i
$818$	5.70499	−	12.4922i	0.199470	−	0.436779i
$819$	0.415153	+	2.88746i	0.0145066	+	0.100896i
$820$	4.13770	+	4.77516i	0.144495	+	0.166756i
$821$	13.3546	+	29.2424i	0.466077	+	1.02057i	0.986060	+	0.166390i	$0.0532111\pi$
$821$	13.3546	+	29.2424i	0.466077	+	1.02057i	−0.519983	+	0.854177i	$0.674062\pi$
$822$	−10.5410	+	6.77428i	−0.367659	+	0.236280i
$823$	−4.23608	+	29.4626i	−0.147661	+	1.02700i	0.772375	+	0.635167i	$0.219069\pi$
$823$	−4.23608	+	29.4626i	−0.147661	+	1.02700i	−0.920035	+	0.391835i	$0.871840\pi$
$824$	15.0311	+	9.65992i	0.523634	+	0.336519i
$825$	1.04408	−	1.20493i	0.0363501	−	0.0419503i
$826$	18.9672	+	5.56927i	0.659953	+	0.193780i
$827$	−18.0791			−0.628673			−0.314337	−	0.949312i	$-0.601782\pi$
$827$	−18.0791			−0.628673			−0.314337	+	0.949312i	$0.601782\pi$
$828$	0.655652	+	4.75080i	0.0227855	+	0.165102i
$829$	−6.45333			−0.224133			−0.112067	−	0.993701i	$-0.535747\pi$
$829$	−6.45333			−0.224133			−0.112067	+	0.993701i	$0.535747\pi$
$830$	13.4414	+	3.94674i	0.466556	+	0.136993i
$831$	11.9960	−	13.8441i	0.416137	−	0.480248i
$832$	−0.820145	−	0.527075i	−0.0284334	−	0.0182730i
$833$	0.223382	−	1.55366i	0.00773973	−	0.0538310i
$834$	−5.16097	+	3.31675i	−0.178710	+	0.114850i
$835$	2.15053	+	4.70901i	0.0744223	+	0.162962i
$836$	−1.70640	−	1.96929i	−0.0590169	−	0.0681092i
$837$	0.849501	+	5.90841i	0.0293631	+	0.204225i
$838$	−4.97227	+	10.8878i	−0.171764	+	0.376111i
$839$	−22.0997	+	6.48905i	−0.762965	+	0.224027i	−0.639990	−	0.768383i	$-0.721062\pi$
$839$	−22.0997	+	6.48905i	−0.762965	+	0.224027i	−0.122975	+	0.992410i	$0.539244\pi$
$840$	2.87102	−	0.843008i	0.0990597	−	0.0290865i
$841$	−10.7181	+	23.4693i	−0.369588	+	0.809286i
$842$	2.68793	+	18.6950i	0.0926322	+	0.644271i
$843$	−3.62138	−	4.17929i	−0.124727	−	0.143942i
$844$	−3.97140	−	8.69616i	−0.136701	−	0.299334i
$845$	−10.1367	+	6.51448i	−0.348714	+	0.224105i
$846$	0.603983	−	4.20080i	0.0207654	−	0.144426i
$847$	−21.2908	−	13.6828i	−0.731560	−	0.470145i
$848$	1.29139	−	1.49035i	0.0443466	−	0.0511787i
$849$	−4.98152	−	1.46271i	−0.170965	−	0.0502000i
$850$	0.803526			0.0275607
$851$	−21.9103	−	25.5768i	−0.751076	−	0.876761i
$852$	−5.00883			−0.171600
$853$	33.6935	+	9.89329i	1.15364	+	0.338740i	0.801959	−	0.597379i	$-0.203791\pi$
$853$	33.6935	+	9.89329i	1.15364	+	0.338740i	0.351683	+	0.936119i	$0.385609\pi$
$854$	4.55349	−	5.25501i	0.155817	−	0.179823i
$855$	−1.37491	−	0.883600i	−0.0470209	−	0.0302185i
$856$	−1.00516	+	6.99107i	−0.0343558	+	0.238950i
$857$	−9.14115	+	5.87466i	−0.312256	+	0.200674i	−0.687376	−	0.726302i	$-0.741238\pi$
$857$	−9.14115	+	5.87466i	−0.312256	+	0.200674i	0.375121	+	0.926976i	$0.377601\pi$
$858$	−0.645699	−	1.41388i	−0.0220438	−	0.0482692i
$859$	16.0892	+	18.5679i	0.548955	+	0.633528i	0.960639	−	0.277799i	$-0.0896048\pi$
$859$	16.0892	+	18.5679i	0.548955	+	0.633528i	−0.411684	+	0.911327i	$0.635059\pi$
$860$	−0.222170	−	1.54522i	−0.00757592	−	0.0526917i
$861$	−7.85393	+	17.1977i	−0.267661	+	0.586097i
$862$	24.3834	−	7.15961i	0.830501	−	0.243857i
$863$	−51.2557	+	15.0500i	−1.74476	+	0.512309i	−0.989677	−	0.143315i	$-0.954224\pi$
$863$	−51.2557	+	15.0500i	−1.74476	+	0.512309i	−0.755087	+	0.655624i	$0.772406\pi$
$864$	−0.415415	+	0.909632i	−0.0141327	+	0.0309463i
$865$	−3.37351	−	23.4633i	−0.114703	−	0.797775i
$866$	6.91875	+	7.98466i	0.235109	+	0.271330i
$867$	−6.79384	−	14.8764i	−0.230731	−	0.505230i
$868$	−15.0257	+	9.65645i	−0.510007	+	0.327761i
$869$	0.345413	−	2.40240i	0.0117173	−	0.0814959i
$870$	1.50468	+	0.966997i	0.0510133	+	0.0327843i
$871$	−7.12723	+	8.22526i	−0.241497	+	0.278702i
$872$	−10.6393	−	3.12397i	−0.360291	−	0.105791i
$873$	−0.213794			−0.00723583
$874$	7.50799	+	2.25076i	0.253961	+	0.0761330i
$875$	2.99223			0.101156
$876$	3.81797	+	1.12106i	0.128997	+	0.0378770i
$877$	−6.91551	+	7.98093i	−0.233520	+	0.269497i	−0.860400	−	0.509619i	$-0.829786\pi$
$877$	−6.91551	+	7.98093i	−0.233520	+	0.269497i	0.626880	+	0.779116i	$0.284332\pi$
$878$	−25.5018	−	16.3890i	−0.860643	−	0.553102i
$879$	1.87540	−	13.0437i	0.0632556	−	0.439952i
$880$	−1.34125	+	0.861971i	−0.0452136	+	0.0290570i
$881$	−1.70826	−	3.74057i	−0.0575529	−	0.126023i	0.878670	−	0.477429i	$-0.158431\pi$
$881$	−1.70826	−	3.74057i	−0.0575529	−	0.126023i	−0.936223	+	0.351406i	$0.885704\pi$
$882$	1.27923	+	1.47631i	0.0430738	+	0.0497098i
$883$	5.69348	+	39.5990i	0.191601	+	1.33261i	0.827772	+	0.561065i	$0.189608\pi$
$883$	5.69348	+	39.5990i	0.191601	+	1.33261i	−0.636171	+	0.771548i	$0.719483\pi$
$884$	0.325421	−	0.712573i	0.0109451	−	0.0239664i
$885$	−6.33882	+	1.86124i	−0.213077	+	0.0625650i
$886$	−29.7410	+	8.73275i	−0.999169	+	0.293382i
$887$	−13.3943	+	29.3295i	−0.449738	+	0.984789i	0.539969	+	0.841685i	$0.318436\pi$
$887$	−13.3943	+	29.3295i	−0.449738	+	0.984789i	−0.989708	+	0.143104i	$0.954292\pi$
$888$	−0.999396	−	6.95095i	−0.0335375	−	0.233259i
$889$	25.3786	+	29.2884i	0.851169	+	0.982302i
$890$	2.48181	+	5.43439i	0.0831903	+	0.182161i
$891$	−1.34125	+	0.861971i	−0.0449337	+	0.0288771i
$892$	−0.262650	+	1.82677i	−0.00879417	+	0.0611648i
$893$	−5.83510	−	3.74999i	−0.195264	−	0.125489i
$894$	−8.44756	+	9.74900i	−0.282529	+	0.326055i
$895$	19.1354	+	5.61865i	0.639624	+	0.187811i
$896$	−2.99223			−0.0999633
$897$	3.91891	+	2.54997i	0.130849	+	0.0851412i
$898$	−6.36852			−0.212520
$899$	−10.2441	−	3.00793i	−0.341658	−	0.100320i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	1.33302	+	0.856679i	0.0444093	+	0.0285401i
$902$	1.43365	−	9.97128i	0.0477355	−	0.332007i
$903$	3.92967	−	2.52545i	0.130771	−	0.0840416i
$904$	−2.68728	−	5.88433i	−0.0893777	−	0.195710i
$905$	−13.2089	−	15.2438i	−0.439078	−	0.506723i
$906$	0.822700	+	5.72200i	0.0273324	+	0.190101i
$907$	−16.0389	+	35.1202i	−0.532562	+	1.16615i	0.431899	+	0.901922i	$0.357844\pi$
$907$	−16.0389	+	35.1202i	−0.532562	+	1.16615i	−0.964461	+	0.264226i	$0.914883\pi$
$908$	0.678247	−	0.199151i	0.0225084	−	0.00660907i
$909$	−9.20255	+	2.70211i	−0.305229	+	0.0896235i
$910$	1.21183	−	2.65353i	0.0401717	−	0.0879637i
$911$	4.72731	+	32.8792i	0.156623	+	1.08934i	0.904800	+	0.425837i	$0.140020\pi$
$911$	4.72731	+	32.8792i	0.156623	+	1.08934i	−0.748177	+	0.663499i	$0.769071\pi$
$912$	1.07028	+	1.23516i	0.0354404	+	0.0409004i
$913$	−9.27828	−	20.3166i	−0.307066	−	0.672381i
$914$	−30.6288	+	19.6839i	−1.01311	+	0.651087i
$915$	−0.330713	+	2.30016i	−0.0109330	+	0.0760409i
$916$	0.534120	+	0.343258i	0.0176478	+	0.0113416i
$917$	31.4977	−	36.3503i	1.04014	−	1.20039i
$918$	−0.770978	−	0.226380i	−0.0254461	−	0.00747164i
$919$	39.5537			1.30475			0.652377	−	0.757894i	$-0.273772\pi$
$919$	39.5537			1.30475			0.652377	+	0.757894i	$0.273772\pi$
$920$	2.01691	−	4.35110i	0.0664955	−	0.143452i
$921$	7.35380			0.242316
$922$	6.19013	+	1.81759i	0.203861	+	0.0598590i
$923$	−3.19778	+	3.69044i	−0.105256	+	0.121472i
$924$	−4.01334	−	2.57922i	−0.132029	−	0.0848499i
$925$	0.999396	−	6.95095i	0.0328599	−	0.228546i
$926$	14.5203	−	9.33164i	0.477167	−	0.306657i
$927$	−7.42245	−	16.2529i	−0.243785	−	0.533815i
$928$	−1.17129	−	1.35174i	−0.0384496	−	0.0443732i
$929$	1.59483	+	11.0923i	0.0523246	+	0.363925i	0.999115	+	0.0420732i	$0.0133963\pi$
$929$	1.59483	+	11.0923i	0.0523246	+	0.363925i	−0.946790	+	0.321852i	$0.895695\pi$
$930$	2.47968	−	5.42975i	0.0813120	−	0.178048i
$931$	3.06328	−	0.899460i	0.100395	−	0.0294786i
$932$	−7.59577	+	2.23032i	−0.248808	+	0.0730565i
$933$	9.91791	−	21.7172i	0.324698	−	0.710989i
$934$	4.12357	+	28.6800i	0.134927	+	0.938439i
$935$	−0.838944	−	0.968193i	−0.0274364	−	0.0316633i
$936$	0.404992	+	0.886808i	0.0132376	+	0.0289862i
$937$	3.89353	−	2.50222i	0.127196	−	0.0817440i	−0.475496	−	0.879718i	$-0.657731\pi$
$937$	3.89353	−	2.50222i	0.127196	−	0.0817440i	0.602692	+	0.797974i	$0.294095\pi$
$938$	−4.75393	+	33.0643i	−0.155221	+	1.07959i
$939$	18.5417	+	11.9160i	0.605087	+	0.388866i
$940$	−2.77923	+	3.20740i	−0.0906483	+	0.104614i
$941$	17.8144	+	5.23079i	0.580734	+	0.170519i	0.558889	−	0.829243i	$-0.311228\pi$
$941$	17.8144	+	5.23079i	0.580734	+	0.170519i	0.0218448	+	0.999761i	$0.493046\pi$
$942$	−6.75275			−0.220016
$943$	12.4319	+	27.6346i	0.404837	+	0.899907i
$944$	6.60642			0.215021
$945$	−2.87102	−	0.843008i	−0.0933944	−	0.0274231i
$946$	−1.62992	+	1.88103i	−0.0529934	+	0.0611577i
$947$	−51.1922	−	32.8992i	−1.66352	−	1.06908i	−0.912746	−	0.408527i	$-0.866043\pi$
$947$	−51.1922	−	32.8992i	−1.66352	−	1.06908i	−0.750778	−	0.660555i	$-0.770321\pi$
$948$	−0.216648	+	1.50682i	−0.00703641	+	0.0489393i
$949$	3.26348	−	2.09731i	0.105937	−	0.0680817i
$950$	0.678936	+	1.48666i	0.0220276	+	0.0482337i
$951$	4.81750	+	5.55969i	0.156218	+	0.180285i
$952$	−0.342172	−	2.37986i	−0.0110899	−	0.0771318i
$953$	−14.3892	+	31.5079i	−0.466111	+	1.02064i	0.519941	+	0.854202i	$0.325954\pi$
$953$	−14.3892	+	31.5079i	−0.466111	+	1.02064i	−0.986052	+	0.166438i	$0.946773\pi$
$954$	−1.89213	+	0.555580i	−0.0612600	+	0.0179876i
$955$	−0.951706	+	0.279446i	−0.0307965	+	0.00904267i
$956$	−2.68212	+	5.87302i	−0.0867458	+	0.189947i
$957$	−0.405836	−	2.82265i	−0.0131188	−	0.0912434i
$958$	21.0738	+	24.3204i	0.680863	+	0.785758i
$959$	15.5751	+	34.1048i	0.502947	+	1.10130i
$960$	0.841254	−	0.540641i	0.0271513	−	0.0174491i
$961$	−0.659058	+	4.58385i	−0.0212599	+	0.147866i
$962$	−5.75941	−	3.70135i	−0.185691	−	0.119336i
$963$	4.62525	−	5.33783i	0.149047	−	0.172009i
$964$	13.5447	+	3.97707i	0.436244	+	0.128093i
$965$	4.18063			0.134579
$966$	14.3500	+	0.0811830i	0.461703	+	0.00261202i
$967$	40.3627			1.29798			0.648988	−	0.760798i	$-0.275192\pi$
$967$	40.3627			1.29798			0.648988	+	0.760798i	$0.275192\pi$
$968$	−8.11543	−	2.38291i	−0.260840	−	0.0765895i
$969$	−0.859995	+	0.992487i	−0.0276270	+	0.0318833i
$970$	0.179855	+	0.115586i	0.00577480	+	0.00371124i
$971$	−1.51896	+	10.5646i	−0.0487457	+	0.339034i	0.950825	+	0.309729i	$0.100238\pi$
$971$	−1.51896	+	10.5646i	−0.0487457	+	0.339034i	−0.999571	+	0.0293048i	$0.990671\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	7.62572	+	16.6980i	0.244469	+	0.535313i
$974$	−17.3397	−	20.0111i	−0.555599	−	0.641196i
$975$	0.138744	+	0.964985i	0.00444336	+	0.0309043i
$976$	0.965346	−	2.11381i	0.0309000	−	0.0676615i
$977$	1.99916	−	0.587005i	0.0639587	−	0.0187800i	−0.249597	−	0.968350i	$-0.580298\pi$
$977$	1.99916	−	0.587005i	0.0639587	−	0.0187800i	0.313555	+	0.949570i	$0.398480\pi$
$978$	−16.1904	+	4.75393i	−0.517712	+	0.152014i
$979$	3.95687	−	8.66433i	0.126462	−	0.276913i
$980$	−0.278002	−	1.93355i	−0.00888046	−	0.0617649i
$981$	7.26137	+	8.38007i	0.231838	+	0.267555i
$982$	12.1693	+	26.6470i	0.388337	+	0.850340i
$983$	−40.1650	+	25.8125i	−1.28106	+	0.823289i	−0.991019	−	0.133724i	$-0.957307\pi$
$983$	−40.1650	+	25.8125i	−1.28106	+	0.823289i	−0.290045	+	0.957013i	$0.593670\pi$
$984$	−0.899209	+	6.25413i	−0.0286657	+	0.199374i
$985$	4.19816	+	2.69799i	0.133764	+	0.0859651i
$986$	0.941164	−	1.08616i	0.0299728	−	0.0345904i
$987$	−12.1846	−	3.57772i	−0.387840	−	0.113880i
$988$	1.59335			0.0506911
$989$	1.10740	−	7.40449i	0.0352131	−	0.235449i
$990$	1.59435			0.0506718
$991$	14.5653	+	4.27675i	0.462681	+	0.135856i	0.504762	−	0.863259i	$-0.331580\pi$
$991$	14.5653	+	4.27675i	0.462681	+	0.135856i	−0.0420803	+	0.999114i	$0.513399\pi$
$992$	−3.90897	+	4.51120i	−0.124110	+	0.143231i
$993$	4.19099	+	2.69338i	0.132997	+	0.0854720i
$994$	−2.13295	+	14.8350i	−0.0676532	+	0.470538i
$995$	−0.617971	+	0.397146i	−0.0195910	+	0.0125904i
$996$	5.81947	+	12.7429i	0.184397	+	0.403773i
$997$	5.86834	+	6.77243i	0.185852	+	0.214485i	0.841028	−	0.540992i	$-0.181951\pi$
$997$	5.86834	+	6.77243i	0.185852	+	0.214485i	−0.655176	+	0.755476i	$0.727405\pi$
$998$	−4.91462	−	34.1819i	−0.155570	−	1.08201i
$999$	−2.91722	+	6.38783i	−0.0922968	+	0.202102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.b.271.1	✓	10
23.9	even	11	inner	690.2.m.b.331.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.b.271.1	✓	10	1.1	even	1	trivial
690.2.m.b.331.1	yes	10	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)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(1.24302 + 2.72183i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(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} +(1.24302 + 2.72183i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(1.52977 - 0.449181i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-0.404992 + 0.886808i) q^{13} +(0.425839 + 2.96177i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.675969 + 0.434419i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-1.37491 - 0.883600i) q^{19} +(-0.654861 + 0.755750i) q^{20} +(-2.87102 - 0.843008i) q^{21} +1.59435 q^{22} +(-4.04911 + 2.56996i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.638429 + 0.736786i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.425839 + 2.96177i) q^{28} +(-1.50468 + 0.966997i) q^{29} +(-0.415415 - 0.909632i) q^{30} +(3.90897 + 4.51120i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-0.662317 + 1.45027i) q^{33} +(-0.770978 + 0.226380i) q^{34} +(-2.87102 + 0.843008i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.999396 + 6.95095i) q^{37} +(-1.07028 - 1.23516i) q^{38} +(-0.404992 - 0.886808i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(0.899209 - 6.25413i) q^{41} +(-2.51722 - 1.61772i) q^{42} +(-1.02231 + 1.17981i) q^{43} +(1.52977 + 0.449181i) q^{44} +1.00000 q^{45} +(-4.60914 + 1.32509i) q^{46} +4.24399 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-1.27923 + 1.47631i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(0.114354 - 0.795348i) q^{51} +(-0.820145 + 0.527075i) q^{52} +(-0.819203 - 1.79380i) q^{53} +(0.654861 + 0.755750i) q^{54} +(0.226900 + 1.57812i) q^{55} +(-1.24302 + 2.72183i) q^{56} +(1.56815 - 0.460451i) q^{57} +(-1.71616 + 0.503910i) q^{58} +(2.74441 - 6.00941i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(-1.52177 - 1.75622i) q^{61} +(2.47968 + 5.42975i) q^{62} +(2.51722 - 1.61772i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.820145 - 0.527075i) q^{65} +(-1.04408 + 1.20493i) q^{66} +(10.7115 + 3.14518i) q^{67} -0.803526 q^{68} +(0.709362 - 4.74308i) q^{69} -2.99223 q^{70} +(4.80594 + 1.41115i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-3.34748 - 2.15129i) q^{73} +(-0.999396 + 6.95095i) q^{74} +(0.841254 - 0.540641i) q^{75} +(-0.678936 - 1.48666i) q^{76} +(3.12412 + 3.60543i) q^{77} +(-0.138744 - 0.964985i) q^{78} +(0.632393 - 1.38475i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.62478 - 5.74746i) q^{82} +(-1.99366 - 13.8662i) q^{83} +(-1.95949 - 2.26138i) q^{84} +(-0.333797 - 0.730913i) q^{85} +(-1.31329 + 0.844002i) q^{86} +(0.254546 - 1.77041i) q^{87} +(1.34125 + 0.861971i) q^{88} +(3.91232 - 4.51506i) q^{89} +(0.959493 + 0.281733i) q^{90} -2.91715 q^{91} +(-4.79575 - 0.0271313i) q^{92} -5.96917 q^{93} +(4.07208 + 1.19567i) q^{94} +(1.07028 - 1.23516i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(0.0304261 - 0.211618i) q^{97} +(-1.64333 + 1.05610i) q^{98} +(-0.662317 - 1.45027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * q^99

Introduction

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