LMFDB - Embedded newform 205.2.y.a.112.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [205,2,Mod(7,205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("205.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(205, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([10, 39])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 205 = 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	205.y (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.63693324144$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$19$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			112.3
Character	$\chi$	$=$	205.112
Dual form			205.2.y.a.108.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.04338 - 1.48460i) q^{2} +(0.187032 + 0.451535i) q^{3} +(1.35331 + 4.16507i) q^{4} +(-0.132700 - 2.23213i) q^{5} +(0.288172 - 1.20032i) q^{6} +(-1.41072 + 2.30209i) q^{7} +(1.85714 - 5.71568i) q^{8} +(1.95242 - 1.95242i) q^{9} +(-3.04266 + 4.75808i) q^{10} +(0.977668 - 1.14470i) q^{11} +(-1.62756 + 1.39007i) q^{12} +(1.30912 - 5.45288i) q^{13} +(6.30031 - 2.60967i) q^{14} +(0.983065 - 0.477398i) q^{15} +(-5.19427 + 3.77386i) q^{16} +(-4.18800 - 3.57689i) q^{17} +(-6.88808 + 1.09096i) q^{18} +(-0.582947 + 0.951283i) q^{19} +(9.11739 - 3.57348i) q^{20} +(-1.30332 - 0.206426i) q^{21} +(-3.69717 + 0.887611i) q^{22} +(0.0295421 + 0.186521i) q^{23} +(2.92817 - 0.230452i) q^{24} +(-4.96478 + 0.592408i) q^{25} +(-10.7704 + 9.19877i) q^{26} +(2.60136 + 1.07752i) q^{27} +(-11.4975 - 2.76031i) q^{28} +(0.457515 - 5.81328i) q^{29} +(-2.71752 - 0.483953i) q^{30} +(-2.25433 - 0.732477i) q^{31} +4.19687 q^{32} +(0.699729 + 0.227356i) q^{33} +(3.24741 + 13.5264i) q^{34} +(5.32575 + 2.84342i) q^{35} +(10.7742 + 5.48973i) q^{36} +(-0.643890 + 1.26371i) q^{37} +(2.60345 - 1.07839i) q^{38} +(2.70702 - 0.428749i) q^{39} +(-13.0046 - 3.38689i) q^{40} +(6.39331 - 0.354419i) q^{41} +(2.35672 + 2.35672i) q^{42} +(6.24668 - 8.59782i) q^{43} +(6.09086 + 2.52292i) q^{44} +(-4.61713 - 4.09896i) q^{45} +(0.216544 - 0.424991i) q^{46} +(3.44394 - 2.11045i) q^{47} +(-2.67552 - 1.63956i) q^{48} +(-0.131539 - 0.258159i) q^{49} +(11.0244 + 6.16020i) q^{50} +(0.831801 - 2.56002i) q^{51} +(24.4833 - 1.92688i) q^{52} +(8.34874 + 9.77512i) q^{53} +(-3.71587 - 6.06374i) q^{54} +(-2.68486 - 2.03038i) q^{55} +(10.5381 + 12.3385i) q^{56} +(-0.538568 - 0.0853007i) q^{57} +(-9.56526 + 11.1995i) q^{58} +(-7.92949 + 10.9140i) q^{59} +(3.31879 + 3.44847i) q^{60} +(0.951982 - 6.01058i) q^{61} +(3.51901 + 4.84351i) q^{62} +(1.74032 + 7.24895i) q^{63} +(1.81275 + 1.31704i) q^{64} +(-12.3452 - 2.19853i) q^{65} +(-1.09228 - 1.50339i) q^{66} +(8.43726 + 0.664027i) q^{67} +(9.23032 - 22.2840i) q^{68} +(-0.0786956 + 0.0482247i) q^{69} +(-6.66118 - 13.7168i) q^{70} +(-9.32066 - 7.96059i) q^{71} +(-7.53348 - 14.7853i) q^{72} +11.1962i q^{73} +(3.19181 - 1.62631i) q^{74} +(-1.19607 - 2.13097i) q^{75} +(-4.75108 - 1.14063i) q^{76} +(1.25599 + 3.86553i) q^{77} +(-6.16797 - 3.14274i) q^{78} +(-0.310189 + 0.748863i) q^{79} +(9.11301 + 11.0935i) q^{80} -6.90727i q^{81} +(-13.5901 - 8.76729i) q^{82} +(-7.86724 + 7.86724i) q^{83} +(-0.904026 - 5.70780i) q^{84} +(-7.42832 + 9.82279i) q^{85} +(-25.5286 + 8.29475i) q^{86} +(2.71047 - 0.880685i) q^{87} +(-4.72709 - 7.71391i) q^{88} +(0.326486 - 0.0783823i) q^{89} +(3.34922 + 15.2303i) q^{90} +(10.7062 + 10.7062i) q^{91} +(-0.736895 + 0.375467i) q^{92} +(-0.0908932 - 1.15491i) q^{93} +(-10.1704 - 0.800430i) q^{94} +(2.20074 + 1.17498i) q^{95} +(0.784950 + 1.89504i) q^{96} +(-0.877983 + 11.1558i) q^{97} +(-0.114480 + 0.722798i) q^{98} +(-0.326120 - 4.14375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) $ 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/205\mathbb{Z}\right)^\times$.

$n$	$6$	$42$
$\chi(n)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.04338	−	1.48460i	−1.44488	−	1.04977i	−0.986993	−	0.160762i	$-0.948605\pi$
$2$	−2.04338	−	1.48460i	−1.44488	−	1.04977i	−0.457892	−	0.889008i	$-0.651395\pi$
$3$	0.187032	+	0.451535i	0.107983	+	0.260694i	0.968630	−	0.248509i	$-0.0799404\pi$
$3$	0.187032	+	0.451535i	0.107983	+	0.260694i	−0.860647	+	0.509203i	$0.829940\pi$
$4$	1.35331	+	4.16507i	0.676657	+	2.08254i
$5$	−0.132700	−	2.23213i	−0.0593454	−	0.998238i
$5$	−0.132700	−	2.23213i	−0.0593454	−	0.998238i
$6$	0.288172	−	1.20032i	0.117646	−	0.490030i
$7$	−1.41072	+	2.30209i	−0.533202	+	0.870107i	−0.999898	−	0.0143110i	$-0.995445\pi$
$7$	−1.41072	+	2.30209i	−0.533202	+	0.870107i	0.466695	+	0.884418i	$0.345445\pi$
$8$	1.85714	−	5.71568i	0.656597	−	2.02080i
$9$	1.95242	−	1.95242i	0.650806	−	0.650806i
$10$	−3.04266	+	4.75808i	−0.962173	+	1.50464i
$11$	0.977668	−	1.14470i	0.294778	−	0.345141i	−0.593176	−	0.805073i	$-0.702126\pi$
$11$	0.977668	−	1.14470i	0.294778	−	0.345141i	0.887954	+	0.459932i	$0.152126\pi$
$12$	−1.62756	+	1.39007i	−0.469837	+	0.401279i
$13$	1.30912	−	5.45288i	0.363085	−	1.51236i	−0.429765	−	0.902941i	$-0.641404\pi$
$13$	1.30912	−	5.45288i	0.363085	−	1.51236i	0.792850	−	0.609417i	$-0.208596\pi$
$14$	6.30031	−	2.60967i	1.68383	−	0.697465i
$15$	0.983065	−	0.477398i	0.253826	−	0.123264i
$16$	−5.19427	+	3.77386i	−1.29857	+	0.943465i
$17$	−4.18800	−	3.57689i	−1.01574	−	0.867523i	−0.0245123	−	0.999700i	$-0.507803\pi$
$17$	−4.18800	−	3.57689i	−1.01574	−	0.867523i	−0.991226	+	0.132177i	$0.957803\pi$
$18$	−6.88808	+	1.09096i	−1.62354	+	0.257143i
$19$	−0.582947	+	0.951283i	−0.133737	+	0.218239i	−0.912497	−	0.409082i	$-0.865849\pi$
$19$	−0.582947	+	0.951283i	−0.133737	+	0.218239i	0.778760	+	0.627322i	$0.215849\pi$
$20$	9.11739	−	3.57348i	2.03871	−	0.799054i
$21$	−1.30332	−	0.206426i	−0.284408	−	0.0450459i
$22$	−3.69717	+	0.887611i	−0.788239	+	0.189239i
$23$	0.0295421	+	0.186521i	0.00615995	+	0.0388924i	0.990577	−	0.136958i	$-0.0437325\pi$
$23$	0.0295421	+	0.186521i	0.00615995	+	0.0388924i	−0.984417	+	0.175850i	$0.943733\pi$
$24$	2.92817	−	0.230452i	0.597711	−	0.0470409i
$25$	−4.96478	+	0.592408i	−0.992956	+	0.118482i
$26$	−10.7704	+	9.19877i	−2.11224	+	1.80403i
$27$	2.60136	+	1.07752i	0.500631	+	0.207368i
$28$	−11.4975	−	2.76031i	−2.17283	−	0.521649i
$29$	0.457515	−	5.81328i	0.0849584	−	1.07950i	−0.795682	−	0.605714i	$-0.792888\pi$
$29$	0.457515	−	5.81328i	0.0849584	−	1.07950i	0.880641	−	0.473785i	$-0.157112\pi$
$30$	−2.71752	−	0.483953i	−0.496148	−	0.0883574i
$31$	−2.25433	−	0.732477i	−0.404890	−	0.131557i	0.0994898	−	0.995039i	$-0.468279\pi$
$31$	−2.25433	−	0.732477i	−0.404890	−	0.131557i	−0.504380	+	0.863482i	$0.668279\pi$
$32$	4.19687			0.741909
$33$	0.699729	+	0.227356i	0.121807	+	0.0395775i
$34$	3.24741	+	13.5264i	0.556926	+	2.31976i
$35$	5.32575	+	2.84342i	0.900217	+	0.480626i
$36$	10.7742	+	5.48973i	1.79570	+	0.914955i
$37$	−0.643890	+	1.26371i	−0.105855	+	0.207752i	−0.937858	−	0.347019i	$-0.887194\pi$
$37$	−0.643890	+	1.26371i	−0.105855	+	0.207752i	0.832003	+	0.554771i	$0.187194\pi$
$38$	2.60345	−	1.07839i	0.422336	−	0.174937i
$39$	2.70702	−	0.428749i	0.433470	−	0.0686548i
$40$	−13.0046	−	3.38689i	−2.05620	−	0.535515i
$41$	6.39331	−	0.354419i	0.998467	−	0.0553510i
$41$	6.39331	−	0.354419i	0.998467	−	0.0553510i
$42$	2.35672	+	2.35672i	0.363650	+	0.363650i
$43$	6.24668	−	8.59782i	0.952610	−	1.31116i	0.00225154	−	0.999997i	$-0.499283\pi$
$43$	6.24668	−	8.59782i	0.952610	−	1.31116i	0.950358	−	0.311158i	$-0.100717\pi$
$44$	6.09086	+	2.52292i	0.918232	+	0.380344i
$45$	−4.61713	−	4.09896i	−0.688281	−	0.611036i
$46$	0.216544	−	0.424991i	0.0319276	−	0.0626615i
$47$	3.44394	−	2.11045i	0.502350	−	0.307840i	−0.248138	−	0.968725i	$-0.579819\pi$
$47$	3.44394	−	2.11045i	0.502350	−	0.307840i	0.750488	+	0.660884i	$0.229819\pi$
$48$	−2.67552	−	1.63956i	−0.386179	−	0.236651i
$49$	−0.131539	−	0.258159i	−0.0187912	−	0.0368799i
$50$	11.0244	+	6.16020i	1.55909	+	0.871184i
$51$	0.831801	−	2.56002i	0.116475	−	0.358475i
$52$	24.4833	−	1.92688i	3.39523	−	0.267210i
$53$	8.34874	+	9.77512i	1.14679	+	1.34272i	0.930459	+	0.366395i	$0.119408\pi$
$53$	8.34874	+	9.77512i	1.14679	+	1.34272i	0.216329	+	0.976321i	$0.430592\pi$
$54$	−3.71587	−	6.06374i	−0.505665	−	0.825171i
$55$	−2.68486	−	2.03038i	−0.362026	−	0.273776i
$56$	10.5381	+	12.3385i	1.40821	+	1.64880i
$57$	−0.538568	−	0.0853007i	−0.0713350	−	0.0112984i
$58$	−9.56526	+	11.1995i	−1.25598	+	1.47056i
$59$	−7.92949	+	10.9140i	−1.03233	+	1.42088i	−0.129149	+	0.991625i	$0.541225\pi$
$59$	−7.92949	+	10.9140i	−1.03233	+	1.42088i	−0.903182	+	0.429257i	$0.858775\pi$
$60$	3.31879	+	3.44847i	0.428455	+	0.445195i
$61$	0.951982	−	6.01058i	0.121889	−	0.769575i	−0.848708	−	0.528862i	$-0.822619\pi$
$61$	0.951982	−	6.01058i	0.121889	−	0.769575i	0.970596	−	0.240713i	$-0.0773813\pi$
$62$	3.51901	+	4.84351i	0.446915	+	0.615126i
$63$	1.74032	+	7.24895i	0.219260	+	0.913282i
$64$	1.81275	+	1.31704i	0.226594	+	0.164630i
$65$	−12.3452	−	2.19853i	−1.53124	−	0.272694i
$66$	−1.09228	−	1.50339i	−0.134450	−	0.185054i
$67$	8.43726	+	0.664027i	1.03078	+	0.0811238i	0.582549	−	0.812796i	$-0.302056\pi$
$67$	8.43726	+	0.664027i	1.03078	+	0.0811238i	0.448227	+	0.893920i	$0.352056\pi$
$68$	9.23032	−	22.2840i	1.11934	−	2.70233i
$69$	−0.0786956	+	0.0482247i	−0.00947384	+	0.00580557i
$70$	−6.66118	−	13.7168i	−0.796163	−	1.63947i
$71$	−9.32066	−	7.96059i	−1.10616	−	0.944748i	−0.107383	−	0.994218i	$-0.534247\pi$
$71$	−9.32066	−	7.96059i	−1.10616	−	0.944748i	−0.998776	+	0.0494693i	$0.984247\pi$
$72$	−7.53348	−	14.7853i	−0.887830	−	1.74246i
$73$			11.1962i			1.31042i	0.755446	+	0.655211i	$0.227420\pi$
$73$			11.1962i			1.31042i	−0.755446	+	0.655211i	$0.772580\pi$
$74$	3.19181	−	1.62631i	0.371040	−	0.189054i
$75$	−1.19607	−	2.13097i	−0.138110	−	0.246064i
$76$	−4.75108	−	1.14063i	−0.544986	−	0.130840i
$77$	1.25599	+	3.86553i	0.143133	+	0.440518i
$78$	−6.16797	−	3.14274i	−0.698385	−	0.355845i
$79$	−0.310189	+	0.748863i	−0.0348990	+	0.0842537i	−0.940368	−	0.340159i	$-0.889519\pi$
$79$	−0.310189	+	0.748863i	−0.0348990	+	0.0842537i	0.905469	+	0.424412i	$0.139519\pi$
$80$	9.11301	+	11.0935i	1.01887	+	1.24029i
$81$		−	6.90727i		−	0.767475i
$82$	−13.5901	−	8.76729i	−1.50078	−	0.968185i
$83$	−7.86724	+	7.86724i	−0.863541	+	0.863541i	−0.991748	−	0.128206i	$-0.959078\pi$
$83$	−7.86724	+	7.86724i	−0.863541	+	0.863541i	0.128206	+	0.991748i	$0.459078\pi$
$84$	−0.904026	−	5.70780i	−0.0986374	−	0.622772i
$85$	−7.42832	+	9.82279i	−0.805714	+	1.06543i
$86$	−25.5286	+	8.29475i	−2.75282	+	0.894446i
$87$	2.71047	−	0.880685i	0.290593	−	0.0944194i
$88$	−4.72709	−	7.71391i	−0.503909	−	0.822305i
$89$	0.326486	−	0.0783823i	0.0346074	−	0.00830851i	−0.216105	−	0.976370i	$-0.569335\pi$
$89$	0.326486	−	0.0783823i	0.0346074	−	0.00830851i	0.250712	+	0.968062i	$0.419335\pi$
$90$	3.34922	+	15.2303i	0.353039	+	1.60541i
$91$	10.7062	+	10.7062i	1.12232	+	1.12232i
$92$	−0.736895	+	0.375467i	−0.0768266	+	0.0391451i
$93$	−0.0908932	−	1.15491i	−0.00942519	−	0.119758i
$94$	−10.1704	−	0.800430i	−1.04900	−	0.0825580i
$95$	2.20074	+	1.17498i	0.225791	+	0.120550i
$96$	0.784950	+	1.89504i	0.0801136	+	0.193411i
$97$	−0.877983	+	11.1558i	−0.0891457	+	1.13270i	0.775848	+	0.630920i	$0.217322\pi$
$97$	−0.877983	+	11.1558i	−0.0891457	+	1.13270i	−0.864994	+	0.501783i	$0.832678\pi$
$98$	−0.114480	+	0.722798i	−0.0115642	+	0.0730136i
$99$	−0.326120	−	4.14375i	−0.0327763	−	0.416463i
$100$	−9.18634	−	19.8770i	−0.918634	−	1.98770i
$101$	6.26504	+	3.83922i	0.623395	+	0.382017i	0.798031	−	0.602616i	$-0.205875\pi$
$101$	6.26504	+	3.83922i	0.623395	+	0.382017i	−0.174636	+	0.984633i	$0.555875\pi$
$102$	−5.50029	+	3.99619i	−0.544609	+	0.395682i
$103$	−2.12264	+	1.54219i	−0.209150	+	0.151956i	−0.687429	−	0.726252i	$-0.741261\pi$
$103$	−2.12264	+	1.54219i	−0.209150	+	0.151956i	0.478279	+	0.878208i	$0.341261\pi$
$104$	−28.7357	−	17.6093i	−2.81777	−	1.72673i
$105$	−0.287818	+	2.93658i	−0.0280881	+	0.286580i
$106$	−2.54748	−	32.3688i	−0.247433	−	3.14393i
$107$	1.96400	−	12.4002i	0.189867	−	1.19877i	−0.690091	−	0.723723i	$-0.742429\pi$
$107$	1.96400	−	12.4002i	0.189867	−	1.19877i	0.879958	−	0.475052i	$-0.157571\pi$
$108$	−0.967485	+	12.2931i	−0.0930963	+	1.18290i
$109$	−0.00402588	−	0.00971932i	−0.000385609	−	0.000930942i	0.923687	−	0.383149i	$-0.125160\pi$
$109$	−0.00402588	−	0.00971932i	−0.000385609	−	0.000930942i	−0.924072	+	0.382218i	$0.875160\pi$
$110$	2.47188	+	8.13476i	0.235684	+	0.775619i
$111$	−0.691036	−	0.0543857i	−0.0655902	−	0.00516206i
$112$	−1.36009	−	17.2815i	−0.128516	−	1.63295i
$113$	1.93544	−	0.986154i	0.182071	−	0.0927696i	−0.360579	−	0.932729i	$-0.617421\pi$
$113$	1.93544	−	0.986154i	0.182071	−	0.0927696i	0.542650	+	0.839959i	$0.317421\pi$
$114$	0.973858	+	0.973858i	0.0912102	+	0.0912102i
$115$	0.412419	−	0.0906931i	0.0384583	−	0.00845717i
$116$	24.8319	−	5.96161i	2.30558	−	0.553522i
$117$	−8.09035	−	13.2023i	−0.747953	−	1.22055i
$118$	32.4058	−	10.5293i	2.98320	−	0.969300i
$119$	14.1424	−	4.59514i	1.29643	−	0.421236i
$120$	−0.902969	−	6.50547i	−0.0824294	−	0.593866i
$121$	1.36627	+	8.62629i	0.124206	+	0.784208i
$122$	−10.8686	+	10.8686i	−0.983993	+	0.983993i
$123$	1.35579	+	2.82052i	0.122247	+	0.254317i
$124$		−	10.3807i		−	0.932218i
$125$	1.98116	+	11.0034i	0.177200	+	0.984175i
$126$	7.20566	−	17.3960i	0.641931	−	1.54976i
$127$	6.32122	+	3.22082i	0.560917	+	0.285802i	0.711372	−	0.702815i	$-0.248074\pi$
$127$	6.32122	+	3.22082i	0.560917	+	0.285802i	−0.150455	+	0.988617i	$0.548074\pi$
$128$	−4.34266	−	13.3653i	−0.383841	−	1.18134i
$129$	5.05055	+	1.21253i	0.444676	+	0.106757i
$130$	21.9621	+	22.8202i	1.92620	+	2.00146i
$131$	−5.31741	+	2.70936i	−0.464584	+	0.236718i	−0.670583	−	0.741835i	$-0.733956\pi$
$131$	−5.31741	+	2.70936i	−0.464584	+	0.236718i	0.205998	+	0.978552i	$0.433956\pi$
$132$			3.22211i			0.280448i
$133$	−1.36756	−	2.68399i	−0.118583	−	0.232731i
$134$	−16.2547	−	13.8828i	−1.40419	−	1.19929i
$135$	2.05995	−	5.94954i	0.177293	−	0.512055i
$136$	−28.2220	+	17.2945i	−2.42002	+	1.48299i
$137$	2.52570	−	6.09758i	0.215785	−	0.520952i	−0.778508	−	0.627635i	$-0.784023\pi$
$137$	2.52570	−	6.09758i	0.215785	−	0.520952i	0.994293	+	0.106683i	$0.0340231\pi$
$138$	0.232399	+	0.0182902i	0.0197831	+	0.00155697i
$139$	10.2482	+	14.1054i	0.869239	+	1.19640i	0.979287	+	0.202479i	$0.0648996\pi$
$139$	10.2482	+	14.1054i	0.869239	+	1.19640i	−0.110048	+	0.993926i	$0.535100\pi$
$140$	−4.63564	+	26.0302i	−0.391783	+	2.19995i
$141$	1.59707	+	1.16034i	0.134497	+	0.0977181i
$142$	7.22731	+	30.1039i	0.606503	+	2.52626i
$143$	−4.96204	−	6.82967i	−0.414947	−	0.571125i
$144$	−2.77324	+	17.5095i	−0.231103	+	1.45913i
$145$	−13.0367	−	0.249807i	−1.08264	−	0.0207454i
$146$	16.6219	−	22.8781i	1.37564	−	1.89341i
$147$	0.0919660	−	0.107678i	0.00758523	−	0.00888116i
$148$	−6.13481	−	0.971659i	−0.504279	−	0.0798699i
$149$	−3.99049	−	4.67226i	−0.326913	−	0.382766i	0.572471	−	0.819925i	$-0.305985\pi$
$149$	−3.99049	−	4.67226i	−0.326913	−	0.382766i	−0.899384	+	0.437159i	$0.855985\pi$
$150$	−0.719630	+	6.13006i	−0.0587576	+	0.500517i
$151$	−8.48840	−	13.8518i	−0.690777	−	1.12724i	−0.985173	−	0.171562i	$-0.945119\pi$
$151$	−8.48840	−	13.8518i	−0.690777	−	1.12724i	0.294397	−	0.955683i	$-0.404881\pi$
$152$	4.35462	+	5.09860i	0.353206	+	0.413551i
$153$	−15.1603	+	1.19314i	−1.22564	+	0.0964597i
$154$	3.17231	−	9.76337i	0.255632	−	0.786755i
$155$	−1.33583	+	5.12916i	−0.107297	+	0.411984i
$156$	5.44922	+	10.6947i	0.436287	+	0.856261i
$157$	−0.323736	−	0.198386i	−0.0258370	−	0.0158329i	0.509520	−	0.860459i	$-0.329823\pi$
$157$	−0.323736	−	0.198386i	−0.0258370	−	0.0158329i	−0.535357	+	0.844626i	$0.679823\pi$
$158$	1.74559	−	1.06970i	0.138872	−	0.0851009i
$159$	−2.85233	+	5.59801i	−0.226204	+	0.443951i
$160$	−0.556927	−	9.36795i	−0.0440289	−	0.740602i
$161$	−0.471064	−	0.195121i	−0.0371250	−	0.0153777i
$162$	−10.2545	+	14.1142i	−0.805672	+	1.10891i
$163$	17.6926	+	17.6926i	1.38579	+	1.38579i	0.833945	+	0.551847i	$0.186077\pi$
$163$	17.6926	+	17.6926i	1.38579	+	1.38579i	0.551847	+	0.833945i	$0.313923\pi$
$164$	10.1283	+	26.1490i	0.790891	+	2.04189i
$165$	0.414632	−	1.59205i	0.0322791	−	0.123941i
$166$	27.7554	−	4.39603i	2.15424	−	0.341198i
$167$	−15.2296	+	6.30830i	−1.17850	+	0.488151i	−0.883994	−	0.467498i	$-0.845155\pi$
$167$	−15.2296	+	6.30830i	−1.17850	+	0.488151i	−0.294507	+	0.955649i	$0.595155\pi$
$168$	−3.60031	+	7.06602i	−0.277770	+	0.545155i
$169$	−16.4371	−	8.37510i	−1.26439	−	0.644238i
$170$	29.7618	−	9.04358i	2.28262	−	0.693611i
$171$	0.719146	+	2.99546i	0.0549945	+	0.229068i
$172$	44.2643	+	14.3823i	3.37512	+	1.09664i
$173$	−10.9628			−0.833483			−0.416741	−	0.909025i	$-0.636828\pi$
$173$	−10.9628			−0.833483			−0.416741	+	0.909025i	$0.636828\pi$
$174$	−6.84597	−	2.22439i	−0.518992	−	0.168631i
$175$	5.64014	−	12.2651i	0.426355	−	0.927153i
$176$	−0.758328	+	9.63548i	−0.0571612	+	0.726301i
$177$	−6.41113	−	1.53917i	−0.481890	−	0.115691i
$178$	−0.783499	−	0.324536i	−0.0587258	−	0.0243250i
$179$	−3.05721	+	2.61111i	−0.228507	+	0.195163i	−0.756329	−	0.654192i	$-0.773009\pi$
$179$	−3.05721	+	2.61111i	−0.228507	+	0.195163i	0.527822	+	0.849355i	$0.323009\pi$
$180$	10.8240	−	24.7779i	0.806776	−	1.84683i
$181$	−3.95900	+	0.311580i	−0.294270	+	0.0231595i	−0.224735	−	0.974420i	$-0.572152\pi$
$181$	−3.95900	+	0.311580i	−0.294270	+	0.0231595i	−0.0695351	+	0.997580i	$0.522152\pi$
$182$	−5.98238	−	37.7712i	−0.443443	−	2.79979i
$183$	2.89204	−	0.694317i	0.213786	−	0.0513254i
$184$	1.12096	+	0.177542i	0.0826382	+	0.0130886i
$185$	2.90620	+	1.26955i	0.213668	+	0.0933392i
$186$	−1.52885	+	2.49485i	−0.112100	+	0.182931i
$187$	−8.18894	+	1.29700i	−0.598835	+	0.0948461i
$188$	13.4509	+	11.4882i	0.981008	+	0.837860i
$189$	−6.15032	+	4.46847i	−0.447370	+	0.325033i
$190$	−2.75257	−	5.66814i	−0.199693	−	0.411210i
$191$	12.1842	−	5.04685i	0.881616	−	0.365177i	0.104492	−	0.994526i	$-0.466678\pi$
$191$	12.1842	−	5.04685i	0.881616	−	0.365177i	0.777123	+	0.629349i	$0.216678\pi$
$192$	−0.255648	+	1.06485i	−0.0184498	+	0.0768489i
$193$	−3.29664	+	2.81559i	−0.237297	+	0.202671i	−0.760142	−	0.649757i	$-0.774871\pi$
$193$	−3.29664	+	2.81559i	−0.237297	+	0.202671i	0.522845	+	0.852428i	$0.324871\pi$
$194$	18.3560	−	21.4921i	1.31788	−	1.54304i
$195$	−1.31624	−	5.98551i	−0.0942583	−	0.428631i
$196$	0.897239	−	0.897239i	0.0640885	−	0.0640885i
$197$	2.50251	−	7.70193i	0.178296	−	0.548740i	−0.821472	−	0.570248i	$-0.806847\pi$
$197$	2.50251	−	7.70193i	0.178296	−	0.548740i	0.999769	+	0.0215086i	$0.00684693\pi$
$198$	−5.48543	+	8.95140i	−0.389832	+	0.636148i
$199$	4.08106	−	16.9988i	0.289298	−	1.20501i	−0.618560	−	0.785738i	$-0.712284\pi$
$199$	4.08106	−	16.9988i	0.289298	−	1.20501i	0.907858	−	0.419277i	$-0.137716\pi$
$200$	−5.83426	+	29.4773i	−0.412545	+	2.08436i
$201$	1.27821	+	3.93392i	0.0901577	+	0.277477i
$202$	−7.10212	−	17.1460i	−0.499704	−	1.20639i
$203$	12.7372	+	9.25415i	0.893980	+	0.649514i
$204$	11.7884			0.825351
$205$	−1.63950	−	14.2236i	−0.114508	−	0.993422i
$206$	6.62687			0.461716
$207$	0.421846	+	0.306489i	0.0293203	+	0.0213024i
$208$	13.7785	+	33.2642i	0.955366	+	2.30646i
$209$	0.519007	+	1.59734i	0.0359005	+	0.110490i
$210$	4.94776	−	5.57323i	0.341428	−	0.384590i
$211$	0.984313	−	4.09996i	0.0677629	−	0.282253i	−0.928193	−	0.372100i	$-0.878638\pi$
$211$	0.984313	−	4.09996i	0.0677629	−	0.282253i	0.995956	+	0.0898472i	$0.0286379\pi$
$212$	−29.4156	+	48.0019i	−2.02027	+	3.29679i
$213$	1.85123	−	5.69749i	0.126844	−	0.390386i
$214$	−22.4226	+	22.4226i	−1.53277	+	1.53277i
$215$	−20.0204	−	12.8025i	−1.36538	−	0.873120i
$216$	10.9898	−	12.8674i	0.747762	−	0.875517i
$217$	4.86646	−	4.15635i	0.330357	−	0.282152i
$218$	−0.00620292	+	0.0258370i	−0.000420115	+	0.00174990i
$219$	−5.05550	+	2.09406i	−0.341619	+	0.141503i
$220$	4.82321	−	13.9304i	0.325181	−	0.939186i
$221$	−24.9869	+	18.1541i	−1.68080	+	1.22118i
$222$	1.33130	+	1.13704i	0.0893513	+	0.0763132i
$223$	12.4941	−	1.97887i	0.836667	−	0.132515i	0.276623	−	0.960978i	$-0.410785\pi$
$223$	12.4941	−	1.97887i	0.836667	−	0.132515i	0.560043	+	0.828463i	$0.310785\pi$
$224$	−5.92062	+	9.66157i	−0.395588	+	0.645541i
$225$	−8.53670	+	10.8500i	−0.569113	+	0.723330i
$226$	−5.41887	−	0.858265i	−0.360458	−	0.0570909i
$227$	17.8126	−	4.27644i	1.18227	−	0.283837i	0.405780	−	0.913971i	$-0.367000\pi$
$227$	17.8126	−	4.27644i	1.18227	−	0.283837i	0.776487	+	0.630133i	$0.217000\pi$
$228$	−0.373568	−	2.35861i	−0.0247401	−	0.156203i
$229$	14.5015	−	1.14129i	0.958287	−	0.0754188i	0.410340	−	0.911932i	$-0.365410\pi$
$229$	14.5015	−	1.14129i	0.958287	−	0.0754188i	0.547946	+	0.836514i	$0.315410\pi$
$230$	−0.977369	−	0.426957i	−0.0644458	−	0.0281527i
$231$	−1.51051	+	1.29010i	−0.0993845	+	0.0848824i
$232$	−32.3772	−	13.4111i	−2.12567	−	0.880479i
$233$	11.7475	+	2.82033i	0.769605	+	0.184766i	0.599190	−	0.800607i	$-0.295489\pi$
$233$	11.7475	+	2.82033i	0.769605	+	0.184766i	0.170414	+	0.985372i	$0.445489\pi$
$234$	−3.06843	+	38.9881i	−0.200590	+	2.54873i
$235$	−5.16780	−	7.40725i	−0.337110	−	0.483196i
$236$	−56.1887	−	18.2568i	−3.65758	−	1.18842i
$237$	−0.396153			−0.0257329
$238$	−35.7202	−	11.6062i	−2.31540	−	0.752318i
$239$	2.06069	+	8.58340i	0.133295	+	0.555214i	0.998548	+	0.0538777i	$0.0171581\pi$
$239$	2.06069	+	8.58340i	0.133295	+	0.555214i	−0.865252	+	0.501336i	$0.832842\pi$
$240$	−3.30467	+	6.18968i	−0.213316	+	0.399542i
$241$	0.340339	+	0.173411i	0.0219232	+	0.0111704i	0.464918	−	0.885354i	$-0.346084\pi$
$241$	0.340339	+	0.173411i	0.0219232	+	0.0111704i	−0.442995	+	0.896524i	$0.646084\pi$
$242$	10.0148	−	19.6551i	0.643775	−	1.26348i
$243$	10.9229	−	4.52443i	0.700707	−	0.290242i
$244$	26.3228	−	4.16913i	1.68515	−	0.266901i
$245$	−0.558789	+	0.327869i	−0.0356997	+	0.0209468i
$246$	1.41696	−	7.77617i	0.0903418	−	0.495791i
$247$	4.42409	+	4.42409i	0.281498	+	0.281498i
$248$	−8.37321	+	11.5247i	−0.531699	+	0.731821i
$249$	−5.02376	−	2.08091i	−0.318368	−	0.131872i
$250$	12.2874	−	25.4253i	0.777124	−	1.60804i
$251$	−9.99500	+	19.6163i	−0.630879	+	1.23817i	0.325362	+	0.945589i	$0.394514\pi$
$251$	−9.99500	+	19.6163i	−0.630879	+	1.23817i	−0.956241	+	0.292580i	$0.905486\pi$
$252$	−27.8372	+	17.0587i	−1.75358	+	1.07460i
$253$	0.242394	+	0.148539i	0.0152392	+	0.00933857i
$254$	−8.13499	−	15.9658i	−0.510435	−	1.00178i
$255$	−5.82467	−	1.51697i	−0.364755	−	0.0949963i
$256$	−9.58367	+	29.4955i	−0.598979	+	1.84347i
$257$	25.6823	−	2.02124i	1.60202	−	0.126082i	0.754301	−	0.656529i	$-0.227976\pi$
$257$	25.6823	−	2.02124i	1.60202	−	0.126082i	0.847718	+	0.530447i	$0.177976\pi$
$258$	−8.52004	−	9.97569i	−0.530435	−	0.621059i
$259$	−2.00081	−	3.26503i	−0.124324	−	0.202879i
$260$	−7.54998	−	54.3942i	−0.468230	−	3.37338i
$261$	−10.4567	−	12.2432i	−0.647253	−	0.757835i
$262$	14.8878	+	2.35799i	0.919770	+	0.145677i
$263$	3.73054	−	4.36790i	0.230035	−	0.269336i	−0.633369	−	0.773850i	$-0.718328\pi$
$263$	3.73054	−	4.36790i	0.230035	−	0.269336i	0.863404	+	0.504514i	$0.168328\pi$
$264$	2.59898	−	3.57719i	0.159956	−	0.220161i
$265$	20.7114	−	19.9326i	1.27229	−	1.22445i
$266$	−1.19021	+	7.51468i	−0.0729764	+	0.460755i
$267$	0.0964556	+	0.132760i	0.00590299	+	0.00812477i
$268$	8.65255	+	36.0405i	0.528539	+	2.20152i
$269$	−8.29189	−	6.02441i	−0.505565	−	0.367315i	0.305573	−	0.952168i	$-0.401152\pi$
$269$	−8.29189	−	6.02441i	−0.505565	−	0.367315i	−0.811139	+	0.584854i	$0.801152\pi$
$270$	−13.0419	+	9.09894i	−0.793707	+	0.553744i
$271$	9.77793	+	13.4582i	0.593967	+	0.817525i	0.995139	−	0.0984772i	$-0.0313971\pi$
$271$	9.77793	+	13.4582i	0.593967	+	0.817525i	−0.401172	+	0.916003i	$0.631397\pi$
$272$	35.2523	+	2.77441i	2.13748	+	0.168223i
$273$	−2.83183	+	6.83663i	−0.171390	+	0.413772i
$274$	−14.2134	+	8.71000i	−0.858665	+	0.526190i
$275$	−4.17578	+	6.26238i	−0.251809	+	0.377635i
$276$	−0.307359	−	0.262510i	−0.0185009	−	0.0158012i
$277$	−5.82815	−	11.4384i	−0.350180	−	0.687266i	0.646986	−	0.762502i	$-0.276029\pi$
$277$	−5.82815	−	11.4384i	−0.350180	−	0.687266i	−0.997166	+	0.0752356i	$0.976029\pi$
$278$		−	44.0371i		−	2.64117i
$279$	−5.83150	+	2.97130i	−0.349123	+	0.177887i
$280$	26.1427	−	25.1597i	1.56233	−	1.50358i
$281$	0.864909	+	0.207646i	0.0515962	+	0.0123871i	0.259161	−	0.965834i	$-0.416554\pi$
$281$	0.864909	+	0.207646i	0.0515962	+	0.0123871i	−0.207565	+	0.978221i	$0.566554\pi$
$282$	−1.54077	−	4.74201i	−0.0917517	−	0.282383i
$283$	1.76130	+	0.897426i	0.104698	+	0.0533464i	0.505555	−	0.862794i	$-0.331288\pi$
$283$	1.76130	+	0.897426i	0.104698	+	0.0533464i	−0.400857	+	0.916141i	$0.631288\pi$
$284$	20.5427	−	49.5944i	1.21898	−	2.94289i
$285$	−0.118934	+	1.21347i	−0.00704504	+	0.0718798i
$286$			21.3222i			1.26081i
$287$	−8.20327	+	15.2179i	−0.484224	+	0.898287i
$288$	8.19405	−	8.19405i	0.482839	−	0.482839i
$289$	2.08581	+	13.1693i	0.122695	+	0.774664i
$290$	26.2680	+	19.8647i	1.54251	+	1.16650i
$291$	−5.20146	+	1.69006i	−0.304915	+	0.0990729i
$292$	−46.6332	+	15.1520i	−2.72900	+	0.886707i
$293$	−13.6815	−	22.3262i	−0.799282	−	1.30431i	−0.948904	−	0.315566i	$-0.897806\pi$
$293$	−13.6815	−	22.3262i	−0.799282	−	1.30431i	0.149622	−	0.988743i	$-0.452194\pi$
$294$	−0.347780	+	0.0834946i	−0.0202830	+	0.00486951i
$295$	25.4137	+	16.2513i	1.47964	+	0.946189i
$296$	6.02714	+	6.02714i	0.350321	+	0.350321i
$297$	3.77670	−	1.92432i	0.219146	−	0.111661i
$298$	1.21763	+	15.4714i	0.0705354	+	0.896237i
$299$	1.05575	+	0.0830895i	0.0610558	+	0.00480519i
$300$	7.25701	−	7.86558i	0.418984	−	0.454120i
$301$	10.9806	+	26.5095i	0.632912	+	1.52798i
$302$	−3.21940	+	40.9063i	−0.185256	+	2.35390i
$303$	−0.561781	+	3.54694i	−0.0322735	+	0.203767i
$304$	−0.562023	−	7.14118i	−0.0322342	−	0.409575i
$305$	−13.5427	−	1.32734i	−0.775453	−	0.0760032i
$306$	32.7495	+	20.0689i	1.87216	+	1.14726i
$307$	−3.27958	+	2.38275i	−0.187175	+	0.135991i	−0.677427	−	0.735590i	$-0.736905\pi$
$307$	−3.27958	+	2.38275i	−0.187175	+	0.135991i	0.490251	+	0.871581i	$0.336905\pi$
$308$	−14.4005	+	10.4626i	−0.820544	+	0.596160i
$309$	−1.09335	−	0.670007i	−0.0621987	−	0.0381154i
$310$	10.3444	−	8.49762i	0.587520	−	0.482633i
$311$	−0.0855078	−	1.08648i	−0.00484870	−	0.0616086i	0.994017	−	0.109226i	$-0.0348372\pi$
$311$	−0.0855078	−	1.08648i	−0.00484870	−	0.0616086i	−0.998866	+	0.0476173i	$0.984837\pi$
$312$	2.57671	−	16.2687i	0.145877	−	0.921033i
$313$	2.48660	−	31.5953i	0.140551	−	1.78587i	−0.373020	−	0.927823i	$-0.621678\pi$
$313$	2.48660	−	31.5953i	0.140551	−	1.78587i	0.513571	−	0.858047i	$-0.328322\pi$
$314$	0.366991	+	0.885995i	0.0207105	+	0.0499996i
$315$	15.9496	−	4.84655i	0.898660	−	0.273072i
$316$	−3.53885	−	0.278514i	−0.199076	−	0.0156676i
$317$	1.32007	+	16.7731i	0.0741427	+	0.942073i	0.915689	+	0.401888i	$0.131646\pi$
$317$	1.32007	+	16.7731i	0.0741427	+	0.942073i	−0.841546	+	0.540185i	$0.818354\pi$
$318$	14.1392	−	7.20427i	0.792886	−	0.403996i
$319$	−6.20718	−	6.20718i	−0.347535	−	0.347535i
$320$	2.69925	−	4.22106i	0.150893	−	0.235965i
$321$	5.96647	−	1.43242i	0.333016	−	0.0799500i
$322$	0.672884	+	1.09805i	0.0374983	+	0.0611917i
$323$	5.84401	−	1.89883i	0.325170	−	0.105654i
$324$	28.7693	−	9.34771i	1.59829	−	0.519317i
$325$	−3.26917	+	27.8479i	−0.181341	+	1.54472i
$326$	−9.88621	−	62.4191i	−0.547547	−	3.45707i
$327$	0.00363565	−	0.00363565i	0.000201052	−	0.000201052i
$328$	9.84750	−	37.2003i	0.543737	−	2.05404i
$329$			10.9055i			0.601239i
$330$	−3.21081	+	2.63760i	−0.176749	+	0.145195i
$331$	10.5230	−	25.4049i	0.578398	−	1.39638i	−0.315852	−	0.948809i	$-0.602290\pi$
$331$	10.5230	−	25.4049i	0.578398	−	1.39638i	0.894250	−	0.447568i	$-0.147710\pi$
$332$	−43.4145	−	22.1208i	−2.38268	−	1.21404i
$333$	1.21014	+	3.72442i	0.0663152	+	0.204097i
$334$	40.4851	+	9.71960i	2.21524	+	0.531833i
$335$	0.362564	−	18.9212i	0.0198090	−	1.03377i
$336$	7.54884	−	3.84632i	0.411823	−	0.209834i
$337$		−	25.6662i		−	1.39813i	−0.715060	−	0.699064i	$-0.753600\pi$
$337$		−	25.6662i		−	1.39813i	0.715060	−	0.699064i	$-0.246400\pi$
$338$	21.1534	+	41.5159i	1.15059	+	2.25817i
$339$	0.807272	+	0.689475i	0.0438450	+	0.0374472i
$340$	−50.9655	−	17.6462i	−2.76399	−	0.956998i
$341$	−3.04246	+	1.86442i	−0.164758	+	0.100964i
$342$	2.97757	−	7.18849i	0.161009	−	0.388709i
$343$	−18.0615	−	1.42147i	−0.975231	−	0.0767523i
$344$	−37.5414	−	51.6713i	−2.02410	−	2.78593i
$345$	0.118087	+	0.169259i	0.00635757	+	0.00911260i
$346$	22.4010	+	16.2753i	1.20429	+	0.874965i
$347$	3.07881	+	12.8242i	0.165279	+	0.688438i	0.992044	+	0.125890i	$0.0401787\pi$
$347$	3.07881	+	12.8242i	0.165279	+	0.688438i	−0.826765	+	0.562548i	$0.809821\pi$
$348$	7.33624	+	10.0975i	0.393264	+	0.541281i
$349$	3.55315	−	22.4337i	0.190196	−	1.20085i	−0.689134	−	0.724634i	$-0.742009\pi$
$349$	3.55315	−	22.4337i	0.190196	−	1.20085i	0.879329	−	0.476214i	$-0.157991\pi$
$350$	−29.7337	+	16.6888i	−1.58933	+	0.892055i
$351$	9.28106	−	12.7743i	0.495386	−	0.681841i
$352$	4.10315	−	4.80417i	0.218699	−	0.256063i
$353$	2.33760	+	0.370239i	0.124418	+	0.0197058i	0.218333	−	0.975874i	$-0.429938\pi$
$353$	2.33760	+	0.370239i	0.124418	+	0.0197058i	−0.0939150	+	0.995580i	$0.529938\pi$
$354$	10.8153	+	12.6631i	0.574826	+	0.673034i
$355$	−16.5322	+	21.8613i	−0.877438	+	1.16028i
$356$	0.768306	+	1.25376i	0.0407201	+	0.0664492i
$357$	4.71995	+	5.52635i	0.249806	+	0.292486i
$358$	10.1235	−	0.796735i	0.535043	−	0.0421088i
$359$	−11.2254	+	34.5481i	−0.592452	+	1.82338i	−0.0254289	+	0.999677i	$0.508095\pi$
$359$	−11.2254	+	34.5481i	−0.592452	+	1.82338i	−0.567023	+	0.823702i	$0.691905\pi$
$360$	−32.0030	+	18.7777i	−1.68670	+	0.989672i
$361$	8.06071	+	15.8200i	0.424248	+	0.832633i
$362$	8.55229	+	5.24085i	0.449498	+	0.275453i
$363$	−3.63954	+	2.23031i	−0.191026	+	0.117061i
$364$	−30.1033	+	59.0810i	−1.57784	+	3.09669i
$365$	24.9914	−	1.48575i	1.30811	−	0.0777675i
$366$	−6.94030	−	2.87477i	−0.362775	−	0.150266i
$367$	4.40427	−	6.06196i	0.229901	−	0.316432i	−0.678445	−	0.734651i	$-0.737346\pi$
$367$	4.40427	−	6.06196i	0.229901	−	0.316432i	0.908346	+	0.418220i	$0.137346\pi$
$368$	−0.857354	−	0.857354i	−0.0446927	−	0.0446927i
$369$	11.7904	−	13.1744i	0.613785	−	0.685831i
$370$	−4.05368	−	6.90870i	−0.210741	−	0.359166i
$371$	−34.2809	+	5.42956i	−1.77978	+	0.281889i
$372$	4.68727	−	1.94153i	0.243024	−	0.100664i
$373$	−10.5949	+	20.7937i	−0.548584	+	1.07666i	0.435705	+	0.900090i	$0.356499\pi$
$373$	−10.5949	+	20.7937i	−0.548584	+	1.07666i	−0.984289	+	0.176567i	$0.943501\pi$
$374$	18.6586	+	9.50704i	0.964814	+	0.491597i
$375$	−4.59789	+	2.95255i	−0.237434	+	0.152469i
$376$	−5.66678	−	23.6038i	−0.292242	−	1.21727i
$377$	−31.1002	−	10.1051i	−1.60174	−	0.520437i
$378$	19.2013			0.987609
$379$	−16.2591	−	5.28290i	−0.835174	−	0.271365i	−0.139951	−	0.990158i	$-0.544695\pi$
$379$	−16.2591	−	5.28290i	−0.835174	−	0.271365i	−0.695223	+	0.718794i	$0.744695\pi$
$380$	−1.91557	+	10.7564i	−0.0982665	+	0.551790i
$381$	−0.272044	+	3.45665i	−0.0139372	+	0.177089i
$382$	−32.3894	−	7.77600i	−1.65719	−	0.397855i
$383$	−22.0051	−	9.11480i	−1.12441	−	0.465745i	−0.258531	−	0.966003i	$-0.583238\pi$
$383$	−22.0051	−	9.11480i	−1.12441	−	0.465745i	−0.865876	+	0.500258i	$0.833238\pi$
$384$	5.22271	−	4.46061i	0.266520	−	0.227630i
$385$	8.46169	−	3.31648i	0.431248	−	0.169024i
$386$	10.9163	−	0.859131i	0.555625	−	0.0437286i
$387$	−4.59040	−	28.9827i	−0.233343	−	1.47327i
$388$	−47.6531	+	11.4405i	−2.41922	+	0.580803i
$389$	25.3850	+	4.02058i	1.28707	+	0.203852i	0.762205	−	0.647335i	$-0.224117\pi$
$389$	25.3850	+	4.02058i	1.28707	+	0.203852i	0.524863	+	0.851187i	$0.324117\pi$
$390$	−6.19650	+	14.1847i	−0.313772	+	0.718272i
$391$	0.543443	−	0.886819i	0.0274831	−	0.0448484i
$392$	−1.71984	+	0.272396i	−0.0868650	+	0.0137581i
$393$	−2.21790	−	1.89426i	−0.111878	−	0.0955529i
$394$	−16.5478	+	12.0227i	−0.833668	+	0.605696i
$395$	1.71272	+	0.593007i	0.0861763	+	0.0298374i
$396$	16.8177	−	6.96612i	0.845121	−	0.350061i
$397$	−1.32389	+	5.51440i	−0.0664442	+	0.276760i	−0.995695	−	0.0926893i	$-0.970454\pi$
$397$	−1.32389	+	5.51440i	−0.0664442	+	0.276760i	0.929251	+	0.369449i	$0.120454\pi$
$398$	−33.5756	+	28.6763i	−1.68299	+	1.43741i
$399$	0.956138	−	1.11949i	0.0478668	−	0.0560448i
$400$	23.5528	−	21.8135i	1.17764	−	1.09068i
$401$	7.97276	−	7.97276i	0.398141	−	0.398141i	−0.479436	−	0.877577i	$-0.659159\pi$
$401$	7.97276	−	7.97276i	0.398141	−	0.398141i	0.877577	+	0.479436i	$0.159159\pi$
$402$	3.22843	−	9.93609i	0.161020	−	0.495567i
$403$	−6.94531	+	11.3337i	−0.345971	+	0.564573i
$404$	−7.51207	+	31.2900i	−0.373740	+	1.55674i
$405$	−15.4179	+	0.916598i	−0.766122	+	0.0455461i
$406$	−12.2883	−	37.8194i	−0.609857	−	1.87695i
$407$	0.817056	+	1.97255i	0.0405000	+	0.0977756i
$408$	−13.0875	−	9.50861i	−0.647927	−	0.470747i
$409$	4.68923			0.231868			0.115934	−	0.993257i	$-0.463014\pi$
$409$	4.68923			0.231868			0.115934	+	0.993257i	$0.463014\pi$
$410$	−17.7663	+	31.4983i	−0.877415	+	1.55559i
$411$	3.22566			0.159110
$412$	−9.29592	−	6.75388i	−0.457977	−	0.332740i
$413$	−13.9387	−	33.6510i	−0.685878	−	1.65586i
$414$	−0.406976	−	1.25254i	−0.0200018	−	0.0615592i
$415$	18.6047	+	16.5167i	0.913267	+	0.810772i
$416$	5.49422	−	22.8851i	0.269376	−	1.12203i
$417$	−4.45235	+	7.26557i	−0.218033	+	0.355797i
$418$	1.31088	−	4.03448i	0.0641174	−	0.197333i
$419$	−21.0706	+	21.0706i	−1.02937	+	1.02937i	−0.0298113	+	0.999556i	$0.509491\pi$
$419$	−21.0706	+	21.0706i	−1.02937	+	1.02937i	−0.999556	+	0.0298113i	$0.990509\pi$
$420$	−12.6206	+	2.77533i	−0.615821	+	0.135422i
$421$	−0.599134	+	0.701495i	−0.0292000	+	0.0341888i	−0.774814	−	0.632190i	$-0.782156\pi$
$421$	−0.599134	+	0.701495i	−0.0292000	+	0.0341888i	0.745614	+	0.666378i	$0.232156\pi$
$422$	−8.09812	+	6.91644i	−0.394210	+	0.336687i
$423$	2.60353	−	10.8445i	0.126588	−	0.527277i
$424$	71.3762	−	29.5650i	3.46633	−	1.43580i
$425$	22.9115	+	15.2775i	1.11137	+	0.741066i
$426$	−12.2412	+	8.89378i	−0.593090	+	0.430905i
$427$	12.4939	+	10.6708i	0.604622	+	0.516396i
$428$	54.3058	−	8.60119i	2.62497	−	0.415754i
$429$	2.15577	−	3.51790i	0.104082	−	0.169846i
$430$	21.9026	+	55.8824i	1.05624	+	2.69489i
$431$	29.7670	+	4.71463i	1.43383	+	0.227096i	0.824517	−	0.565837i	$-0.191447\pi$
$431$	29.7670	+	4.71463i	1.43383	+	0.227096i	0.609309	+	0.792933i	$0.291447\pi$
$432$	−17.5785	+	4.22023i	−0.845748	+	0.203046i
$433$	3.03931	+	19.1895i	0.146060	+	0.922187i	0.946483	+	0.322752i	$0.104608\pi$
$433$	3.03931	+	19.1895i	0.146060	+	0.922187i	−0.800423	+	0.599435i	$0.795392\pi$
$434$	−16.1145	+	1.26824i	−0.773522	+	0.0608775i
$435$	−2.32548	−	5.93325i	−0.111498	−	0.284477i
$436$	0.0350334	−	0.0299214i	0.00167780	−	0.00143297i
$437$	−0.194656	−	0.0806291i	−0.00931166	−	0.00385701i
$438$	13.4391	+	3.22645i	0.642146	+	0.154166i
$439$	2.83497	−	36.0216i	0.135306	−	1.71922i	−0.437239	−	0.899346i	$-0.644043\pi$
$439$	2.83497	−	36.0216i	0.135306	−	1.71922i	0.572544	−	0.819874i	$-0.305957\pi$
$440$	−16.5911	+	11.5751i	−0.790951	+	0.551821i
$441$	−0.760853	−	0.247216i	−0.0362311	−	0.0117722i
$442$	78.0092			3.71052
$443$	31.8279	+	10.3415i	1.51219	+	0.491340i	0.943545	−	0.331243i	$-0.107468\pi$
$443$	31.8279	+	10.3415i	1.51219	+	0.491340i	0.568644	+	0.822583i	$0.307468\pi$
$444$	−0.708668	−	2.95182i	−0.0336319	−	0.140087i
$445$	−0.218284	−	0.718356i	−0.0103477	−	0.0340534i
$446$	−28.4680	−	14.5052i	−1.34800	−	0.686839i
$447$	1.36334	−	2.67571i	0.0644838	−	0.126557i
$448$	−5.58923	+	2.31514i	−0.264066	+	0.109380i
$449$	−6.50975	+	1.03104i	−0.307214	+	0.0486579i	−0.308138	−	0.951342i	$-0.599706\pi$
$449$	−6.50975	+	1.03104i	−0.307214	+	0.0486579i	0.000923944		1.00000i	$0.499706\pi$
$450$	33.5515	−	9.49696i	1.58163	−	0.447691i
$451$	5.84483	−	7.66494i	0.275222	−	0.360928i
$452$	6.72666	+	6.72666i	0.316396	+	0.316396i
$453$	4.66698	−	6.42355i	0.219274	−	0.301805i
$454$	−42.7467	−	17.7063i	−2.00620	−	0.830997i
$455$	22.4769	−	25.3183i	1.05373	−	1.18694i
$456$	−1.48774	+	2.91986i	−0.0696700	+	0.136735i
$457$	1.66054	−	1.01758i	0.0776767	−	0.0476004i	−0.483118	−	0.875555i	$-0.660496\pi$
$457$	1.66054	−	1.01758i	0.0776767	−	0.0476004i	0.560795	+	0.827955i	$0.310496\pi$
$458$	−31.3264	−	19.1968i	−1.46379	−	0.897009i
$459$	−7.04031	−	13.8174i	−0.328614	−	0.644941i
$460$	0.935876	+	1.59502i	0.0436354	+	0.0743681i
$461$	−8.46828	+	26.0627i	−0.394407	+	1.21386i	0.535015	+	0.844842i	$0.320306\pi$
$461$	−8.46828	+	26.0627i	−0.394407	+	1.21386i	−0.929422	+	0.369018i	$0.879694\pi$
$462$	5.00183	−	0.393653i	0.232706	−	0.0183144i
$463$	−5.50921	−	6.45046i	−0.256035	−	0.299778i	0.617469	−	0.786595i	$-0.288158\pi$
$463$	−5.50921	−	6.45046i	−0.256035	−	0.299778i	−0.873504	+	0.486817i	$0.838158\pi$
$464$	19.5620	+	31.9223i	0.908145	+	1.48196i
$465$	−2.56584	+	0.356142i	−0.118988	+	0.0165157i
$466$	−19.8175	−	23.2033i	−0.918028	−	1.07487i
$467$	4.83670	+	0.766058i	0.223816	+	0.0354489i	0.267335	−	0.963604i	$-0.413857\pi$
$467$	4.83670	+	0.766058i	0.223816	+	0.0354489i	−0.0435193	+	0.999053i	$0.513857\pi$
$468$	44.0396	−	51.5637i	2.03573	−	2.38353i
$469$	−13.4313	+	18.4866i	−0.620198	+	0.853630i
$470$	−0.437042	+	22.8079i	−0.0201592	+	1.05205i
$471$	0.0290291	−	0.183283i	0.00133759	−	0.00844523i
$472$	47.6548	+	65.5912i	2.19349	+	3.01908i
$473$	−3.73476	−	15.5564i	−0.171725	−	0.715284i
$474$	0.809490	+	0.588129i	0.0371811	+	0.0270137i
$475$	2.33066	−	5.06826i	0.106938	−	0.232548i
$476$	38.2782	+	52.6855i	1.75448	+	2.41483i
$477$	35.3853	+	2.78489i	1.62018	+	0.127511i
$478$	8.53215	−	20.5984i	0.390251	−	0.942150i
$479$	14.5302	−	8.90411i	0.663902	−	0.406839i	−0.149324	−	0.988788i	$-0.547710\pi$
$479$	14.5302	−	8.90411i	0.663902	−	0.406839i	0.813225	+	0.581949i	$0.197710\pi$
$480$	4.12580	−	2.00358i	0.188316	−	0.0914505i
$481$	6.04791	+	5.16540i	0.275761	+	0.235522i
$482$	−0.437994	−	0.859611i	−0.0199501	−	0.0391542i
$483$		−	0.249196i		−	0.0113388i
$484$	−34.0802	+	17.3647i	−1.54910	+	0.789305i
$485$	25.0177	+	0.479386i	1.13600	+	0.0217678i
$486$	−29.0366	−	6.97108i	−1.31713	−	0.316215i
$487$	−9.15794	−	28.1852i	−0.414986	−	1.27719i	−0.912264	−	0.409603i	$-0.865667\pi$
$487$	−9.15794	−	28.1852i	−0.414986	−	1.27719i	0.497278	−	0.867591i	$-0.334333\pi$
$488$	−32.5866	−	16.6037i	−1.47512	−	0.751613i
$489$	−4.67975	+	11.2979i	−0.211626	+	0.510910i
$490$	1.62857	+	0.159618i	0.0735712	+	0.00721082i
$491$			28.5652i			1.28913i	0.764549	+	0.644565i	$0.222962\pi$
$491$			28.5652i			1.28913i	−0.764549	+	0.644565i	$0.777038\pi$
$492$	−9.91285	+	9.46400i	−0.446906	+	0.426670i
$493$	−22.7095	+	22.7095i	−1.02279	+	1.02279i
$494$	−2.47208	−	15.6081i	−0.111224	−	0.702240i
$495$	−9.20611	+	1.27782i	−0.413784	+	0.0574337i
$496$	14.4739	−	4.70285i	0.649897	−	0.211164i
$497$	31.4748	−	10.2268i	1.41184	−	0.458734i
$498$	7.17611	+	11.7103i	0.321569	+	0.524753i
$499$	−21.9254	+	5.26382i	−0.981515	+	0.235641i	−0.692289	−	0.721620i	$-0.743398\pi$
$499$	−21.9254	+	5.26382i	−0.981515	+	0.235641i	−0.289226	+	0.957261i	$0.593398\pi$
$500$	−43.1489	+	23.1428i	−1.92968	+	1.03498i
$501$	−5.69684	−	5.69684i	−0.254516	−	0.254516i
$502$	49.5459	−	25.2449i	2.21134	−	1.12673i
$503$	−0.0196411	−	0.249564i	−0.000875752	−	0.0111275i	0.996464	−	0.0840216i	$-0.0267765\pi$
$503$	−0.0196411	−	0.249564i	−0.000875752	−	0.0111275i	−0.997340	+	0.0728941i	$0.976776\pi$
$504$	44.6647	+	3.51519i	1.98952	+	0.156579i
$505$	7.73826	−	14.4938i	0.344348	−	0.644967i
$506$	−0.274780	−	0.663378i	−0.0122155	−	0.0294908i
$507$	0.707396	−	8.98832i	0.0314166	−	0.399185i
$508$	−4.86036	+	30.6871i	−0.215644	+	1.36152i
$509$	1.94044	+	24.6556i	0.0860085	+	1.09284i	0.876832	+	0.480797i	$0.159653\pi$
$509$	1.94044	+	24.6556i	0.0860085	+	1.09284i	−0.790823	+	0.612044i	$0.790347\pi$
$510$	9.64990	+	11.7470i	0.427305	+	0.520168i
$511$	−25.7747	−	15.7948i	−1.14021	−	0.698720i
$512$	40.6336	−	29.5220i	1.79577	−	1.30470i
$513$	−2.54148	+	1.84649i	−0.112209	+	0.0815245i
$514$	−55.4794	−	33.9978i	−2.44709	−	1.49958i
$515$	3.72403	+	4.53335i	0.164100	+	0.199763i
$516$	1.78471	+	22.6768i	0.0785673	+	0.998292i
$517$	0.951194	−	6.00560i	0.0418335	−	0.264126i
$518$	−0.758848	+	9.64208i	−0.0333419	+	0.423649i
$519$	−2.05039	−	4.95007i	−0.0900020	−	0.217284i
$520$	−35.4929	+	66.4785i	−1.55647	+	2.91528i
$521$	−0.817416	−	0.0643320i	−0.0358116	−	0.00281844i	0.0605406	−	0.998166i	$-0.480718\pi$
$521$	−0.817416	−	0.0643320i	−0.0358116	−	0.00281844i	−0.0963523	+	0.995347i	$0.530718\pi$
$522$	3.19068	+	40.5415i	0.139652	+	1.77445i
$523$	−13.6722	+	6.96632i	−0.597842	+	0.304616i	−0.726600	−	0.687060i	$-0.758901\pi$
$523$	−13.6722	+	6.96632i	−0.597842	+	0.304616i	0.128758	+	0.991676i	$0.458901\pi$
$524$	−18.4808	−	18.4808i	−0.807338	−	0.807338i
$525$	6.59300	+	0.252761i	0.287742	+	0.0110314i
$526$	−14.1075	+	3.38691i	−0.615115	+	0.147676i
$527$	6.82115	+	11.1311i	0.297134	+	0.484879i
$528$	−4.49259	+	1.45973i	−0.195515	+	0.0635266i
$529$	21.8404	−	7.09637i	0.949582	−	0.308538i
$530$	−71.9132	+	9.98164i	−3.12371	+	0.433575i
$531$	5.82702	+	36.7904i	0.252871	+	1.59657i
$532$	9.32828	−	9.32828i	0.404432	−	0.404432i
$533$	6.43701	−	35.3259i	0.278818	−	1.53014i
$534$		−	0.414476i		−	0.0179361i
$535$	−27.9395	−	2.73839i	−1.20793	−	0.118391i
$536$	19.4645	−	46.9915i	0.840739	−	2.02972i
$537$	−1.75080	−	0.892079i	−0.0755527	−	0.0384960i
$538$	7.99961	+	24.6203i	0.344887	+	1.06145i
$539$	−0.424116	−	0.101821i	−0.0182680	−	0.00438576i
$540$	27.5681	+	0.528255i	1.18634	+	0.0227325i
$541$	24.5324	−	12.4999i	1.05473	−	0.537411i	0.161435	−	0.986883i	$-0.448388\pi$
$541$	24.5324	−	12.4999i	1.05473	−	0.537411i	0.893294	+	0.449472i	$0.148388\pi$
$542$		−	42.0164i		−	1.80476i
$543$	−0.881148	−	1.72935i	−0.0378137	−	0.0742136i
$544$	−17.5765	−	15.0117i	−0.753586	−	0.643623i
$545$	−0.0211605	+	0.0102760i	−0.000906417	+	0.000440176i
$546$	15.9361	−	9.76568i	0.682004	−	0.417933i
$547$	−7.85226	+	18.9570i	−0.335738	+	0.810544i	0.662377	+	0.749171i	$0.269548\pi$
$547$	−7.85226	+	18.9570i	−0.335738	+	0.810544i	−0.998115	+	0.0613728i	$0.980452\pi$
$548$	28.8150	+	2.26779i	1.23091	+	0.0968751i
$549$	−9.87649	−	13.5938i	−0.421518	−	0.580170i
$550$	17.8298	−	6.59703i	0.760265	−	0.281298i
$551$	5.26337	+	3.82406i	0.224227	+	0.162910i
$552$	0.129489	+	0.539359i	0.00551140	+	0.0229566i
$553$	−1.28636	−	1.77052i	−0.0547015	−	0.0752901i
$554$	−5.07232	+	32.0254i	−0.215502	+	1.36063i
$555$	−0.0296951	+	1.54970i	−0.00126048	+	0.0657809i
$556$	−44.8811	+	61.7735i	−1.90338	+	2.61978i
$557$	−11.2900	+	13.2189i	−0.478373	+	0.560103i	−0.946144	−	0.323747i	$-0.895057\pi$
$557$	−11.2900	+	13.2189i	−0.478373	+	0.560103i	0.467771	+	0.883850i	$0.345057\pi$
$558$	16.3271	+	2.58596i	0.691183	+	0.109473i
$559$	−38.7052	−	45.3180i	−1.63706	−	1.91675i
$560$	−38.3941	+	5.32915i	−1.62245	+	0.225198i
$561$	−2.11724	−	3.45502i	−0.0893898	−	0.145871i
$562$	−1.45906	−	1.70834i	−0.0615469	−	0.0720621i
$563$	29.5520	−	2.32580i	1.24547	−	0.0980206i	0.561467	−	0.827499i	$-0.310237\pi$
$563$	29.5520	−	2.32580i	1.24547	−	0.0980206i	0.684004	+	0.729479i	$0.260237\pi$
$564$	−2.67156	+	8.22221i	−0.112493	+	0.346217i
$565$	−2.45806	−	4.18928i	−0.103411	−	0.176244i
$566$	−2.26667	−	4.44860i	−0.0952754	−	0.186989i
$567$	15.9011	+	9.74423i	0.667785	+	0.409219i
$568$	−62.8099	+	38.4900i	−2.63545	+	1.61500i
$569$	2.33565	−	4.58398i	0.0979156	−	0.192170i	−0.836853	−	0.547428i	$-0.815607\pi$
$569$	2.33565	−	4.58398i	0.0979156	−	0.192170i	0.934768	+	0.355258i	$0.115607\pi$
$570$	2.04454	−	2.30301i	0.0856365	−	0.0964623i
$571$	5.49735	+	2.27708i	0.230057	+	0.0952927i	0.494734	−	0.869044i	$-0.335265\pi$
$571$	5.49735	+	2.27708i	0.230057	+	0.0952927i	−0.264677	+	0.964337i	$0.585265\pi$
$572$	21.7309	−	29.9100i	0.908613	−	1.25060i
$573$	4.55766	+	4.55766i	0.190399	+	0.190399i
$574$	39.3549	−	18.9174i	1.64264	−	0.789597i
$575$	−0.257167	−	0.908536i	−0.0107246	−	0.0378886i
$576$	6.11066	−	0.967834i	0.254611	−	0.0403264i
$577$	−6.38659	+	2.64541i	−0.265877	+	0.110130i	−0.511640	−	0.859200i	$-0.670962\pi$
$577$	−6.38659	+	2.64541i	−0.265877	+	0.110130i	0.245762	+	0.969330i	$0.420962\pi$
$578$	15.2890	−	30.0064i	0.635939	−	1.24810i
$579$	−1.88792	−	0.961942i	−0.0784591	−	0.0399769i
$580$	−16.6023	−	54.6369i	−0.689372	−	2.26867i
$581$	−7.01259	−	29.2095i	−0.290931	−	1.21182i
$582$	13.1376	+	4.26866i	0.544571	+	0.176942i
$583$	19.3519			0.801474
$584$	63.9941	+	20.7930i	2.64810	+	0.860419i
$585$	−28.3955	+	19.8106i	−1.17401	+	0.819069i
$586$	−5.18898	+	65.9323i	−0.214355	+	2.72364i
$587$	−45.2627	−	10.8666i	−1.86819	−	0.448513i	−0.869245	−	0.494382i	$-0.835394\pi$
$587$	−45.2627	−	10.8666i	−1.86819	−	0.448513i	−0.998947	+	0.0458685i	$0.985394\pi$
$588$	0.572947	+	0.237323i	0.0236279	+	0.00978702i
$589$	2.01095	−	1.71751i	0.0828598	−	0.0707689i
$590$	−27.8030	−	70.9367i	−1.14463	−	2.92042i
$591$	3.94574	−	0.310537i	0.162306	−	0.0127738i
$592$	−1.42451	−	8.99398i	−0.0585469	−	0.369650i
$593$	−32.7091	+	7.85275i	−1.34320	+	0.322474i	−0.840418	−	0.541939i	$-0.817690\pi$
$593$	−32.7091	+	7.85275i	−1.34320	+	0.322474i	−0.502783	+	0.864413i	$0.667690\pi$
$594$	−10.5741	−	1.67477i	−0.433859	−	0.0687165i
$595$	−12.1336	−	30.9579i	−0.497431	−	1.26915i
$596$	14.0599	−	22.9437i	0.575917	−	0.939811i
$597$	8.43886	−	1.33658i	0.345379	−	0.0547027i
$598$	−2.03394	−	1.73715i	−0.0831742	−	0.0710375i
$599$	−9.34648	+	6.79062i	−0.381887	+	0.277457i	−0.762123	−	0.647432i	$-0.775843\pi$
$599$	−9.34648	+	6.79062i	−0.381887	+	0.277457i	0.380236	+	0.924890i	$0.375843\pi$
$600$	−14.4012	+	2.87882i	−0.587927	+	0.117527i
$601$	−12.3643	+	5.12147i	−0.504351	+	0.208909i	−0.620327	−	0.784343i	$-0.713000\pi$
$601$	−12.3643	+	5.12147i	−0.504351	+	0.208909i	0.115977	+	0.993252i	$0.463000\pi$
$602$	16.9185	−	70.4707i	0.689547	−	2.87217i
$603$	17.7695	−	15.1766i	0.723631	−	0.618039i
$604$	46.2064	−	54.1007i	1.88011	−	2.20133i
$605$	19.0737	−	4.19440i	0.775455	−	0.170527i
$606$	6.41372	−	6.41372i	0.260539	−	0.260539i
$607$	−3.36623	+	10.3602i	−0.136631	+	0.420507i	−0.995840	−	0.0911177i	$-0.970956\pi$
$607$	−3.36623	+	10.3602i	−0.136631	+	0.420507i	0.859209	+	0.511624i	$0.170956\pi$
$608$	−2.44656	+	3.99242i	−0.0992209	+	0.161914i
$609$	−1.79630	+	7.48214i	−0.0727899	+	0.303192i
$610$	25.7023	+	22.8177i	1.04065	+	0.923863i
$611$	−6.99949	−	21.5422i	−0.283169	−	0.871505i
$612$	−25.4862	−	61.5291i	−1.03022	−	2.48716i
$613$	−6.50581	−	4.72675i	−0.262767	−	0.190911i	0.448599	−	0.893733i	$-0.351923\pi$
$613$	−6.50581	−	4.72675i	−0.262767	−	0.190911i	−0.711366	+	0.702822i	$0.751923\pi$
$614$	10.2388			0.413206
$615$	6.11584	−	3.40057i	0.246614	−	0.137124i
$616$	24.4267			0.984179
$617$	8.13053	+	5.90717i	0.327323	+	0.237814i	0.739294	−	0.673383i	$-0.235160\pi$
$617$	8.13053	+	5.90717i	0.327323	+	0.237814i	−0.411971	+	0.911197i	$0.635160\pi$
$618$	1.23944	+	2.99227i	0.0498575	+	0.120367i
$619$	2.93368	+	9.02893i	0.117915	+	0.362904i	0.992544	−	0.121889i	$-0.0388952\pi$
$619$	2.93368	+	9.02893i	0.117915	+	0.362904i	−0.874629	+	0.484792i	$0.838895\pi$
$620$	−23.1711	+	1.37753i	−0.930575	+	0.0553229i
$621$	−0.124130	+	0.517040i	−0.00498118	+	0.0207481i
$622$	−1.43826	+	2.34703i	−0.0576691	+	0.0941074i
$623$	−0.280137	+	0.862174i	−0.0112235	+	0.0345423i
$624$	−12.4429	+	12.4429i	−0.498116	+	0.498116i
$625$	24.2981	−	5.88235i	0.971924	−	0.235294i
$626$	−51.9874	+	60.8694i	−2.07783	+	2.43283i
$627$	−0.624184	+	0.533104i	−0.0249275	+	0.0212901i
$628$	0.388175	−	1.61686i	0.0154899	−	0.0645199i
$629$	7.21674	−	2.98927i	0.287750	−	0.119190i
$630$	−39.7863	−	13.7755i	−1.58512	−	0.548829i
$631$	11.0056	−	7.99602i	0.438125	−	0.318317i	−0.346764	−	0.937952i	$-0.612720\pi$
$631$	11.0056	−	7.99602i	0.438125	−	0.318317i	0.784890	+	0.619636i	$0.212720\pi$
$632$	3.70420	+	3.16368i	0.147345	+	0.125845i
$633$	2.03537	−	0.322371i	0.0808988	−	0.0128131i
$634$	22.2040	−	36.2336i	0.881832	−	1.43902i
$635$	6.35045	−	14.5372i	0.252010	−	0.576890i
$636$	−27.1762	−	4.30429i	−1.07761	−	0.170676i
$637$	−1.57991	+	0.379303i	−0.0625984	+	0.0150285i
$638$	3.46842	+	21.8988i	0.137316	+	0.866980i
$639$	−33.7402	+	2.65541i	−1.33474	+	0.105046i
$640$	−29.2569	+	11.4670i	−1.15648	+	0.453272i
$641$	14.5983	−	12.4681i	0.576597	−	0.492461i	−0.312662	−	0.949865i	$-0.601221\pi$
$641$	14.5983	−	12.4681i	0.576597	−	0.492461i	0.889259	+	0.457404i	$0.151221\pi$
$642$	−14.3183	−	5.93084i	−0.565098	−	0.234071i
$643$	13.4036	+	3.21792i	0.528586	+	0.126902i	0.488950	−	0.872312i	$-0.337380\pi$
$643$	13.4036	+	3.21792i	0.528586	+	0.126902i	0.0396364	+	0.999214i	$0.487380\pi$
$644$	0.175196	−	2.22608i	0.00690369	−	0.0877197i
$645$	2.03631	−	11.4344i	0.0801796	−	0.450228i
$646$	−14.7605	−	4.79598i	−0.580745	−	0.188695i
$647$	−29.7860			−1.17101			−0.585505	−	0.810669i	$-0.699104\pi$
$647$	−29.7860			−1.17101			−0.585505	+	0.810669i	$0.699104\pi$
$648$	−39.4797	−	12.8277i	−1.55091	−	0.503921i
$649$	4.74088	+	19.7472i	0.186096	+	0.775145i
$650$	48.0231	−	52.0503i	1.88362	−	2.04158i
$651$	2.78692	+	1.42001i	0.109228	+	0.0556545i
$652$	−49.7474	+	97.6347i	−1.94826	+	3.82367i
$653$	−5.90466	+	2.44579i	−0.231067	+	0.0957112i	−0.495213	−	0.868772i	$-0.664910\pi$
$653$	−5.90466	+	2.44579i	−0.231067	+	0.0957112i	0.264146	+	0.964483i	$0.414910\pi$
$654$	−0.0128265	+	0.00203151i	−0.000501555	+	7.94385e-5i
$655$	6.75325	+	11.5096i	0.263871	+	0.449718i
$656$	−31.8710	+	25.9684i	−1.24436	+	1.01390i
$657$	21.8597	+	21.8597i	0.852830	+	0.852830i
$658$	16.1903	−	22.2840i	0.631163	−	0.868722i
$659$	19.7735	+	8.19043i	0.770264	+	0.319054i	0.732980	−	0.680251i	$-0.238129\pi$
$659$	19.7735	+	8.19043i	0.770264	+	0.319054i	0.0372849	+	0.999305i	$0.488129\pi$
$660$	7.19215	−	0.427575i	0.279954	−	0.0166433i
$661$	−1.24699	+	2.44736i	−0.0485025	+	0.0951914i	−0.913986	−	0.405747i	$-0.867012\pi$
$661$	−1.24699	+	2.44736i	−0.0485025	+	0.0951914i	0.865483	+	0.500938i	$0.167012\pi$
$662$	−59.2185	+	36.2892i	−2.30159	+	1.41042i
$663$	−12.8706	−	7.88709i	−0.499851	−	0.306309i
$664$	30.3561	+	59.5771i	1.17804	+	2.31204i
$665$	−5.80953	+	3.40874i	−0.225284	+	0.132185i
$666$	3.05651	−	9.40697i	0.118437	−	0.364513i
$667$	1.09782	−	0.0864000i	0.0425076	−	0.00334542i
$668$	−46.8850	−	54.8952i	−1.81403	−	2.12396i
$669$	3.23033	+	5.27141i	0.124892	+	0.203805i
$670$	−28.8312	+	38.1248i	−1.11385	+	1.47289i
$671$	−5.94960	−	6.96609i	−0.229682	−	0.268923i
$672$	−5.46988	−	0.866344i	−0.211005	−	0.0334200i
$673$	−19.7170	+	23.0856i	−0.760034	+	0.889885i	−0.996656	−	0.0817167i	$-0.973960\pi$
$673$	−19.7170	+	23.0856i	−0.760034	+	0.889885i	0.236622	+	0.971602i	$0.423960\pi$
$674$	−38.1040	+	52.4457i	−1.46771	+	2.02013i
$675$	−13.5535	−	3.80857i	−0.521674	−	0.146592i
$676$	12.6384	−	79.7957i	0.486092	−	3.06907i
$677$	−7.90741	−	10.8836i	−0.303906	−	0.418291i	0.629562	−	0.776950i	$-0.283234\pi$
$677$	−7.90741	−	10.8836i	−0.303906	−	0.418291i	−0.933469	+	0.358659i	$0.883234\pi$
$678$	−0.625965	−	2.60733i	−0.0240401	−	0.100134i
$679$	−24.4431	−	17.7590i	−0.938040	−	0.681526i
$680$	42.3485	+	60.7001i	1.62399	+	2.32774i
$681$	5.26250	+	7.24321i	0.201659	+	0.277560i
$682$	8.98480	+	0.707119i	0.344046	+	0.0270770i
$683$	−6.01907	+	14.5313i	−0.230313	+	0.556025i	−0.996214	−	0.0869334i	$-0.972293\pi$
$683$	−6.01907	+	14.5313i	−0.230313	+	0.556025i	0.765901	+	0.642959i	$0.222293\pi$
$684$	−11.5031	+	7.04909i	−0.439831	+	0.269529i
$685$	−13.9457	−	4.82854i	−0.532839	−	0.184489i
$686$	34.7962	+	29.7187i	1.32852	+	1.13467i
$687$	3.22758	+	6.33448i	0.123140	+	0.241676i
$688$			68.2335i			2.60138i
$689$	64.2321	−	32.7279i	2.44705	−	1.24683i
$690$	0.00998661	−	0.521171i	0.000380184	−	0.0198406i
$691$	−4.26481	−	1.02389i	−0.162241	−	0.0389506i	0.151511	−	0.988456i	$-0.451586\pi$
$691$	−4.26481	−	1.02389i	−0.162241	−	0.0389506i	−0.313752	+	0.949505i	$0.601586\pi$
$692$	−14.8361	−	45.6607i	−0.563982	−	1.73576i
$693$	9.99935	+	5.09492i	0.379844	+	0.193540i
$694$	12.7476	−	30.7754i	0.483892	−	1.16822i
$695$	30.1251	−	24.7470i	1.14271	−	0.938708i
$696$		−	17.1277i		−	0.649225i
$697$	−28.0429	−	21.3838i	−1.06220	−	0.809970i
$698$	−40.5655	+	40.5655i	−1.53543	+	1.53543i
$699$	0.923683	+	5.83190i	0.0349369	+	0.220583i
$700$	58.7179	+	6.89311i	2.21933	+	0.260535i
$701$	−4.19230	+	1.36216i	−0.158341	+	0.0514481i	−0.387115	−	0.922031i	$-0.626528\pi$
$701$	−4.19230	+	1.36216i	−0.158341	+	0.0514481i	0.228774	+	0.973480i	$0.426528\pi$
$702$	−37.9294	+	12.3240i	−1.43155	+	0.465140i
$703$	−0.826788	−	1.34920i	−0.0311829	−	0.0508859i
$704$	3.27989	−	0.787432i	0.123616	−	0.0296775i
$705$	2.37809	−	3.71884i	0.0895640	−	0.140059i
$706$	−4.22693	−	4.22693i	−0.159083	−	0.159083i
$707$	−17.6764	+	9.00660i	−0.664791	+	0.338728i
$708$	−2.26549	−	28.7858i	−0.0851424	−	1.08184i
$709$	7.14901	+	0.562640i	0.268487	+	0.0211304i	0.211988	−	0.977272i	$-0.432006\pi$
$709$	7.14901	+	0.562640i	0.268487	+	0.0211304i	0.0564989	+	0.998403i	$0.482006\pi$
$710$	66.2367	−	20.1271i	2.48582	−	0.755356i
$711$	0.856474	+	2.06771i	0.0321203	+	0.0775452i
$712$	0.158321	−	2.01165i	0.00593332	−	0.0753899i
$713$	0.0700249	−	0.442120i	0.00262245	−	0.0165575i
$714$	−1.44021	−	18.2996i	−0.0538986	−	0.684847i
$715$	−14.5862	+	11.9822i	−0.545494	+	0.448109i
$716$	−15.0128	−	9.19987i	−0.561056	−	0.343815i
$717$	−3.49029	+	2.53585i	−0.130347	+	0.0947029i
$718$	74.2277	−	53.9296i	2.77015	−	2.01263i
$719$	11.3146	+	6.93361i	0.421964	+	0.258580i	0.717232	−	0.696835i	$-0.245409\pi$
$719$	11.3146	+	6.93361i	0.421964	+	0.258580i	−0.295268	+	0.955415i	$0.595409\pi$
$720$	39.4515	+	3.86670i	1.47027	+	0.144103i
$721$	−0.555799	−	7.06209i	−0.0206990	−	0.263006i
$722$	7.01535	−	44.2932i	0.261084	−	1.64842i
$723$	−0.0146471	+	0.186108i	−0.000544730	+	0.00692145i
$724$	−6.65552	−	16.0679i	−0.247351	−	0.597157i
$725$	1.17237	+	29.1327i	0.0435408	+	1.08196i
$726$	10.7481	+	0.845891i	0.398898	+	0.0313940i
$727$	0.717319	+	9.11440i	0.0266039	+	0.338034i	0.995787	+	0.0916938i	$0.0292281\pi$
$727$	0.717319	+	9.11440i	0.0266039	+	0.338034i	−0.969183	+	0.246340i	$0.920772\pi$
$728$	81.0761	−	41.3104i	3.00488	−	1.53106i
$729$	−10.5667	−	10.5667i	−0.391358	−	0.391358i
$730$	−53.2726	−	34.0663i	−1.97171	−	1.26085i
$731$	−56.9145	+	13.6640i	−2.10506	+	0.505380i
$732$	6.80572	+	11.1059i	0.251547	+	0.410487i
$733$	−3.55639	+	1.15554i	−0.131358	+	0.0426809i	−0.373958	−	0.927445i	$-0.622000\pi$
$733$	−3.55639	+	1.15554i	−0.131358	+	0.0426809i	0.242600	+	0.970126i	$0.422000\pi$
$734$	−17.9992	+	5.84828i	−0.664361	+	0.215864i
$735$	−0.252556	−	0.190991i	−0.00931565	−	0.00704480i
$736$	0.123984	+	0.782806i	0.00457012	+	0.0288546i
$737$	9.00896	−	9.00896i	0.331849	−	0.331849i
$738$	−43.6510	+	9.41614i	−1.60681	+	0.346613i
$739$		−	6.27043i		−	0.230662i	−0.993327	−	0.115331i	$-0.963207\pi$
$739$		−	6.27043i		−	0.230662i	0.993327	−	0.115331i	$-0.0367928\pi$
$740$	−1.35477	+	13.8226i	−0.0498025	+	0.508130i
$741$	−1.17019	+	2.82508i	−0.0429878	+	0.103782i
$742$	78.1095	+	39.7988i	2.86749	+	1.46106i
$743$	−10.7744	−	33.1602i	−0.395275	−	1.21653i	−0.928747	−	0.370713i	$-0.879113\pi$
$743$	−10.7744	−	33.1602i	−0.395275	−	1.21653i	0.533473	−	0.845817i	$-0.320887\pi$
$744$	−6.76988	−	1.62530i	−0.248196	−	0.0595866i
$745$	−9.89953	+	9.52728i	−0.362691	+	0.349053i
$746$	52.5197	−	26.7601i	1.92288	−	0.979758i
$747$			30.7203i			1.12400i
$748$	−16.4843	−	32.3523i	−0.602727	−	1.18292i
$749$	25.7757	+	22.0146i	0.941825	+	0.804394i
$750$	13.7786	+	0.792845i	0.503122	+	0.0289506i
$751$	1.39203	−	0.853038i	0.0507960	−	0.0311278i	−0.496869	−	0.867826i	$-0.665517\pi$
$751$	1.39203	−	0.853038i	0.0507960	−	0.0311278i	0.547665	+	0.836698i	$0.315517\pi$
$752$	−9.92421	+	23.9592i	−0.361899	+	0.873701i
$753$	−10.7268	−	0.844220i	−0.390908	−	0.0307651i
$754$	48.5474	+	66.8198i	1.76799	+	2.43343i
$755$	−29.7926	+	20.7853i	−1.08426	+	0.756456i
$756$	−26.9348	−	19.5693i	−0.979611	−	0.711729i
$757$	−6.39456	−	26.6352i	−0.232414	−	0.968074i	−0.959540	−	0.281571i	$-0.909145\pi$
$757$	−6.39456	−	26.6352i	−0.232414	−	0.968074i	0.727126	−	0.686504i	$-0.240855\pi$
$758$	25.3805	+	34.9332i	0.921860	+	1.26883i
$759$	−0.0217352	+	0.137231i	−0.000788939	+	0.00498116i
$760$	10.8029	−	10.3966i	0.391861	−	0.377126i
$761$	2.44087	−	3.35957i	0.0884816	−	0.121784i	−0.762481	−	0.647010i	$-0.776019\pi$
$761$	2.44087	−	3.35957i	0.0884816	−	0.121784i	0.850963	+	0.525226i	$0.176019\pi$
$762$	5.68763	−	6.65935i	0.206041	−	0.241243i
$763$	0.0280541	+	0.00444334i	0.00101563	+	0.000160860i
$764$	37.5095	+	43.9180i	1.35705	+	1.58890i
$765$	4.67502	+	33.6814i	0.169026	+	1.21775i
$766$	31.4328	+	51.2937i	1.13571	+	1.85332i
$767$	49.1321	+	57.5263i	1.77406	+	2.07716i
$768$	−15.1107	+	1.18924i	−0.545261	+	0.0429130i
$769$	−3.13719	+	9.65528i	−0.113130	+	0.348178i	−0.991552	−	0.129707i	$-0.958596\pi$
$769$	−3.13719	+	9.65528i	−0.113130	+	0.348178i	0.878422	+	0.477885i	$0.158596\pi$
$770$	−22.2141	−	5.78540i	−0.800539	−	0.208491i
$771$	5.71608	+	11.2184i	0.205860	+	0.404022i
$772$	−16.1885	−	9.92036i	−0.582639	−	0.357041i
$773$	26.3870	−	16.1699i	0.949073	−	0.581592i	0.0404369	−	0.999182i	$-0.487125\pi$
$773$	26.3870	−	16.1699i	0.949073	−	0.581592i	0.908636	+	0.417590i	$0.137125\pi$
$774$	−33.6477	+	66.0374i	−1.20944	+	2.37366i
$775$	11.6262	+	2.30110i	0.417625	+	0.0826581i
$776$	62.1326	+	25.7362i	2.23043	+	0.923875i
$777$	1.10006	−	1.51410i	0.0394644	−	0.0543181i
$778$	−45.9020	−	45.9020i	−1.64567	−	1.64567i
$779$	−3.38981	+	6.28845i	−0.121452	+	0.225307i
$780$	23.1488	−	13.5825i	0.828860	−	0.486333i
$781$	−18.2250	+	2.88656i	−0.652142	+	0.103289i
$782$	−2.42703	+	1.00531i	−0.0867904	+	0.0359498i
$783$	7.45406	−	14.6294i	0.266386	−	0.522813i
$784$	1.65750	+	0.844540i	0.0591965	+	0.0301621i
$785$	−0.399862	+	0.748946i	−0.0142717	+	0.0267310i
$786$	1.71977	+	7.16338i	0.0613423	+	0.255509i
$787$	−20.7804	−	6.75197i	−0.740743	−	0.240682i	−0.0857495	−	0.996317i	$-0.527328\pi$
$787$	−20.7804	−	6.75197i	−0.740743	−	0.240682i	−0.654993	+	0.755635i	$0.727328\pi$
$788$	35.4658			1.26342
$789$	2.66999	+	0.867533i	0.0950542	+	0.0308850i
$790$	−2.61935	−	3.75444i	−0.0931923	−	0.133577i
$791$	−0.460148	+	5.84673i	−0.0163610	+	0.207886i
$792$	−24.2900	−	5.83152i	−0.863108	−	0.207214i
$793$	−31.5287	−	13.0596i	−1.11962	−	0.463761i
$794$	10.8919	−	9.30255i	0.386539	−	0.330135i
$795$	12.8740	+	5.62390i	0.456593	+	0.199459i
$796$	76.3243	−	6.00686i	2.70524	−	0.212907i
$797$	−2.31607	−	14.6231i	−0.0820393	−	0.517976i	−0.994148	−	0.108027i	$-0.965547\pi$
$797$	−2.31607	−	14.6231i	−0.0820393	−	0.517976i	0.912109	−	0.409949i	$-0.134453\pi$
$798$	−3.61575	+	0.868065i	−0.127996	+	0.0307292i
$799$	−21.9720	−	3.48003i	−0.777315	−	0.123115i
$800$	−20.8366	+	2.48626i	−0.736684	+	0.0879027i
$801$	0.484401	−	0.790471i	0.0171155	−	0.0279299i
$802$	−28.1277	+	4.45499i	−0.993223	+	0.157311i
$803$	12.8164	+	10.9462i	0.452280	+	0.386284i
$804$	−14.6552	+	10.6477i	−0.516850	+	0.375514i
$805$	−0.373024	+	1.07737i	−0.0131474	+	0.0379722i
$806$	31.0179	−	12.8480i	1.09256	−	0.452553i
$807$	1.16938	−	4.87083i	0.0411643	−	0.171462i
$808$	33.5788	−	28.6790i	1.18130	−	1.00892i
$809$	−10.7746	+	12.6154i	−0.378814	+	0.443534i	−0.916756	−	0.399448i	$-0.869202\pi$
$809$	−10.7746	+	12.6154i	−0.378814	+	0.443534i	0.537942	+	0.842982i	$0.319202\pi$
$810$	32.8654	+	21.0165i	1.15477	+	0.738443i
$811$	−13.7055	+	13.7055i	−0.481264	+	0.481264i	−0.905535	−	0.424271i	$-0.860530\pi$
$811$	−13.7055	+	13.7055i	−0.481264	+	0.481264i	0.424271	+	0.905535i	$0.360530\pi$
$812$	−21.3067	+	65.5754i	−0.747720	+	2.30124i
$813$	−4.24805	+	6.93219i	−0.148986	+	0.243122i
$814$	1.25889	−	5.24366i	0.0441241	−	0.183790i
$815$	37.1443	−	41.8400i	1.30111	−	1.46559i
$816$	5.34055	+	16.4365i	0.186957	+	0.575394i
$817$	4.53748	+	10.9544i	0.158746	+	0.383247i
$818$	−9.58186	−	6.96163i	−0.335022	−	0.243408i
$819$	41.8060			1.46082
$820$	57.0238	−	26.0777i	1.99136	−	0.910674i
$821$	30.9535			1.08029			0.540143	−	0.841573i	$-0.318370\pi$
$821$	30.9535			1.08029			0.540143	+	0.841573i	$0.318370\pi$
$822$	−6.59124	−	4.78881i	−0.229896	−	0.167029i
$823$	−7.60826	−	18.3680i	−0.265207	−	0.640267i	0.734038	−	0.679108i	$-0.237633\pi$
$823$	−7.60826	−	18.3680i	−0.265207	−	0.640267i	−0.999245	+	0.0388411i	$0.987633\pi$
$824$	4.87261	+	14.9964i	0.169746	+	0.522423i
$825$	−3.60869	−	0.714246i	−0.125638	−	0.0248669i
$826$	−21.4762	+	89.4550i	−0.747254	+	3.11254i
$827$	−1.20123	+	1.96022i	−0.0417708	+	0.0681637i	−0.872844	−	0.487999i	$-0.837727\pi$
$827$	−1.20123	+	1.96022i	−0.0417708	+	0.0681637i	0.831073	+	0.556163i	$0.187727\pi$
$828$	−0.705659	+	2.17179i	−0.0245233	+	0.0754751i
$829$	2.27132	−	2.27132i	0.0788863	−	0.0788863i	−0.666563	−	0.745449i	$-0.732235\pi$
$829$	2.27132	−	2.27132i	0.0788863	−	0.0788863i	0.745449	+	0.666563i	$0.232235\pi$
$830$	−13.4956	−	61.3703i	−0.468441	−	2.13019i
$831$	4.07478	−	4.77096i	0.141353	−	0.165503i
$832$	9.55479	−	8.16056i	0.331253	−	0.282916i
$833$	−0.372523	+	1.55167i	−0.0129071	+	0.0537621i
$834$	19.8843	−	8.23634i	0.688537	−	0.285201i
$835$	16.1019	+	33.1573i	0.557229	+	1.14745i
$836$	−5.95066	+	4.32341i	−0.205808	+	0.149528i
$837$	−5.07507	−	4.33452i	−0.175420	−	0.149823i
$838$	74.3366	−	11.7738i	2.56791	−	0.406718i
$839$	−0.0587201	+	0.0958225i	−0.00202724	+	0.00330816i	−0.853652	−	0.520844i	$-0.825618\pi$
$839$	−0.0587201	+	0.0958225i	−0.00202724	+	0.00330816i	0.851625	+	0.524152i	$0.175618\pi$
$840$	16.2500	+	7.09870i	0.560678	+	0.244928i
$841$	−4.94193	−	0.782725i	−0.170411	−	0.0269905i
$842$	2.26569	−	0.543945i	0.0780810	−	0.0187456i
$843$	0.0680061	+	0.429373i	0.00234225	+	0.0147884i
$844$	18.4087	−	1.44880i	0.633654	−	0.0498697i
$845$	−16.5131	+	37.8010i	−0.568067	+	1.30039i
$846$	−21.4197	+	18.2941i	−0.736424	+	0.628966i
$847$	−21.7859	−	9.02402i	−0.748573	−	0.310069i
$848$	−80.2555	−	19.2677i	−2.75599	−	0.661654i
$849$	−0.0758004	+	0.963135i	−0.00260146	+	0.0330547i
$850$	−24.1358	−	65.2319i	−0.827852	−	2.23744i
$851$	−0.254730	−	0.0827667i	−0.00873202	−	0.00283721i
$852$	26.2358			0.898822
$853$	48.2294	+	15.6707i	1.65134	+	0.536554i	0.979030	−	0.203714i	$-0.0653012\pi$
$853$	48.2294	+	15.6707i	1.65134	+	0.536554i	0.672312	+	0.740268i	$0.265301\pi$
$854$	−9.68786	−	40.3529i	−0.331512	−	1.38085i
$855$	6.59081	−	2.00272i	0.225401	−	0.0684917i
$856$	−67.2282	−	34.2545i	−2.29781	−	1.17079i
$857$	−19.2659	+	37.8115i	−0.658112	+	1.29162i	0.284804	+	0.958586i	$0.408071\pi$
$857$	−19.2659	+	37.8115i	−0.658112	+	1.29162i	−0.942916	+	0.333031i	$0.891929\pi$
$858$	−9.62773	+	3.98794i	−0.328685	+	0.136146i
$859$	25.6148	−	4.05699i	0.873966	−	0.138423i	0.296692	−	0.954973i	$-0.404116\pi$
$859$	25.6148	−	4.05699i	0.873966	−	0.138423i	0.577274	+	0.816551i	$0.304116\pi$
$860$	26.2293	−	100.712i	0.894412	−	3.43425i
$861$	−8.40571	−	0.857823i	−0.286466	−	0.0292345i
$862$	−53.8258	−	53.8258i	−1.83332	−	1.83332i
$863$	−29.2241	+	40.2235i	−0.994800	+	1.36922i	−0.0663383	+	0.997797i	$0.521132\pi$
$863$	−29.2241	+	40.2235i	−0.994800	+	1.36922i	−0.928462	+	0.371428i	$0.878868\pi$
$864$	10.9176	+	4.52220i	0.371423	+	0.153848i
$865$	1.45476	+	24.4703i	0.0494634	+	0.832014i
$866$	22.2782	−	43.7235i	0.757045	−	1.48578i
$867$	−5.55628	+	3.40489i	−0.188701	+	0.115636i
$868$	23.8974	+	14.6443i	0.811130	+	0.497061i
$869$	0.553963	+	1.08721i	0.0187919	+	0.0368812i
$870$	−4.05666	+	15.5763i	−0.137534	+	0.528085i
$871$	14.6663	−	45.1381i	0.496947	−	1.52945i
$872$	−0.0630291	+	0.00496050i	−0.00213444	+	0.000167984i
$873$	20.0666	+	23.4950i	0.679153	+	0.795186i
$874$	0.278053	+	0.453742i	0.00940529	+	0.0153480i
$875$	−28.1257	−	10.9619i	−0.950821	−	0.370581i
$876$	−15.5636	−	18.2226i	−0.525845	−	0.615685i
$877$	25.1784	+	3.98786i	0.850214	+	0.134661i	0.566310	−	0.824192i	$-0.308370\pi$
$877$	25.1784	+	3.98786i	0.850214	+	0.134661i	0.283903	+	0.958853i	$0.408370\pi$
$878$	−59.2706	+	69.3970i	−2.00029	+	2.34203i
$879$	7.52217	−	10.3534i	0.253717	−	0.349211i
$880$	21.6082	+	0.414054i	0.728413	+	0.0139578i
$881$	0.334496	−	2.11193i	0.0112695	−	0.0711526i	−0.981413	−	0.191909i	$-0.938532\pi$
$881$	0.334496	−	2.11193i	0.0112695	−	0.0711526i	0.992682	+	0.120757i	$0.0385321\pi$
$882$	1.18769	+	1.63472i	0.0399916	+	0.0550438i
$883$	9.91387	+	41.2942i	0.333628	+	1.38966i	0.847044	+	0.531522i	$0.178380\pi$
$883$	9.91387	+	41.2942i	0.333628	+	1.38966i	−0.513416	+	0.858140i	$0.671620\pi$
$884$	−109.428	−	79.5043i	−3.68047	−	2.67402i
$885$	−2.58488	+	14.5147i	−0.0868896	+	0.487906i
$886$	−49.6834	−	68.3833i	−1.66915	−	2.29738i
$887$	−28.3648	−	2.23236i	−0.952397	−	0.0749553i	−0.407269	−	0.913308i	$-0.633519\pi$
$887$	−28.3648	−	2.23236i	−0.952397	−	0.0749553i	−0.545128	+	0.838353i	$0.683519\pi$
$888$	−1.59420	+	3.84874i	−0.0534978	+	0.129155i
$889$	−16.3321	+	10.0083i	−0.547760	+	0.335668i
$890$	−0.620435	+	1.79194i	−0.0207970	+	0.0600658i
$891$	−7.90677	−	6.75302i	−0.264887	−	0.226235i
$892$	25.1506	+	49.3608i	0.842104	+	1.65272i
$893$			4.50644i			0.150802i
$894$	−6.75817	+	3.44346i	−0.226027	+	0.115166i
$895$	6.23402	+	6.47759i	0.208380	+	0.216522i
$896$	36.8945	+	8.85758i	1.23256	+	0.295911i
$897$	0.159942	+	0.492250i	0.00534030	+	0.0164357i
$898$	14.8326	+	7.55756i	0.494969	+	0.252199i
$899$	−5.28949	+	12.7700i	−0.176414	+	0.425902i
$900$	−56.7437	−	20.8726i	−1.89146	−	0.695753i
$901$		−	70.8007i		−	2.35871i
$902$	−23.3225	+	6.98512i	−0.776556	+	0.232579i
$903$	−9.91626	+	9.91626i	−0.329992	+	0.329992i
$904$	−2.04217	−	12.8938i	−0.0679216	−	0.428840i
$905$	1.22085	+	8.79564i	0.0405823	+	0.292377i
$906$	−19.0728	+	6.19712i	−0.633651	+	0.205886i
$907$	−47.1302	+	15.3135i	−1.56493	+	0.508478i	−0.958120	−	0.286366i	$-0.907553\pi$
$907$	−47.1302	+	15.3135i	−1.56493	+	0.508478i	−0.606814	+	0.794844i	$0.707553\pi$
$908$	41.9178	+	68.4037i	1.39109	+	2.27005i
$909$	19.7277	−	4.73621i	0.654328	−	0.157090i
$910$	−83.5163	+	18.3657i	−2.76854	+	0.608816i
$911$	−32.1694	−	32.1694i	−1.06582	−	1.06582i	−0.997676	−	0.0681439i	$-0.978292\pi$
$911$	−32.1694	−	32.1694i	−1.06582	−	1.06582i	−0.0681439	−	0.997676i	$-0.521708\pi$
$912$	3.11938	−	1.58940i	0.103293	−	0.0526304i
$913$	1.31410	+	16.6972i	0.0434903	+	0.552596i
$914$	−4.90380	−	0.385938i	−0.162203	−	0.0127657i
$915$	−1.93358	−	6.36326i	−0.0639221	−	0.210363i
$916$	24.3787	+	58.8553i	0.805494	+	1.94463i
$917$	1.26421	−	16.0633i	0.0417478	−	0.530457i
$918$	−6.12729	+	38.6862i	−0.202231	+	1.27683i
$919$	2.70276	+	34.3418i	0.0891559	+	1.13283i	0.864954	+	0.501851i	$0.167348\pi$
$919$	2.70276	+	34.3418i	0.0891559	+	1.13283i	−0.775798	+	0.630981i	$0.782652\pi$
$920$	0.247546	−	2.52568i	0.00816134	−	0.0832693i
$921$	−1.68928	−	1.03519i	−0.0556637	−	0.0341108i
$922$	55.9965	−	40.6838i	1.84415	−	1.33985i
$923$	−55.6101	+	40.4031i	−1.83043	+	1.32988i
$924$	−7.41757	−	4.54549i	−0.244020	−	0.149536i
$925$	2.44814	−	6.65547i	0.0804945	−	0.218830i
$926$	1.68104	+	21.3597i	0.0552425	+	0.701923i
$927$	−1.13328	+	7.15527i	−0.0372219	+	0.235010i
$928$	1.92013	−	24.3976i	0.0630314	−	0.800890i
$929$	6.73286	+	16.2546i	0.220898	+	0.533295i	0.995012	−	0.0997508i	$-0.0318046\pi$
$929$	6.73286	+	16.2546i	0.220898	+	0.533295i	−0.774115	+	0.633046i	$0.781805\pi$
$930$	5.77170	+	3.08151i	0.189262	+	0.101047i
$931$	0.322262	+	0.0253626i	0.0105617	+	0.000831226i
$932$	4.15120	+	52.7460i	0.135977	+	1.72775i
$933$	0.474591	−	0.241816i	0.0155374	−	0.00791671i
$934$	−8.74590	−	8.74590i	−0.286175	−	0.286175i
$935$	3.98175	+	18.1066i	0.130217	+	0.592151i
$936$	−90.4847	+	21.7235i	−2.95759	+	0.710054i
$937$	−11.7876	−	19.2357i	−0.385086	−	0.628402i	0.600094	−	0.799930i	$-0.295130\pi$
$937$	−11.7876	−	19.2357i	−0.385086	−	0.628402i	−0.985179	+	0.171527i	$0.945130\pi$
$938$	54.8903	−	17.8349i	1.79223	−	0.582331i
$939$	14.7315	−	4.78654i	0.480743	−	0.156203i
$940$	23.8581	−	31.5486i	0.778165	−	1.02900i
$941$	2.96377	+	18.7125i	0.0966163	+	0.610011i	0.987723	+	0.156217i	$0.0499299\pi$
$941$	2.96377	+	18.7125i	0.0966163	+	0.610011i	−0.891107	+	0.453794i	$0.850070\pi$
$942$	−0.331419	+	0.331419i	−0.0107982	+	0.0107982i
$943$	0.254978	+	1.18202i	0.00830323	+	0.0384918i
$944$		−	86.6151i		−	2.81908i
$945$	10.7903	+	13.1353i	0.351010	+	0.427292i
$946$	−15.4635	+	37.3322i	−0.502762	+	1.21377i
$947$	−15.6300	−	7.96388i	−0.507907	−	0.258791i	0.181207	−	0.983445i	$-0.442000\pi$
$947$	−15.6300	−	7.96388i	−0.507907	−	0.258791i	−0.689113	+	0.724654i	$0.742000\pi$
$948$	−0.536120	−	1.65001i	−0.0174124	−	0.0535898i
$949$	61.0518	+	14.6572i	1.98183	+	0.475794i
$950$	−12.2867	+	6.89626i	−0.398634	+	0.223744i
$951$	−7.32676	+	3.73317i	−0.237586	+	0.121056i
$952$		−	89.3672i		−	2.89641i
$953$	−10.3144	−	20.2432i	−0.334117	−	0.655742i	0.661430	−	0.750007i	$-0.269950\pi$
$953$	−10.3144	−	20.2432i	−0.334117	−	0.655742i	−0.995547	+	0.0942648i	$0.969950\pi$
$954$	−68.1711	−	58.2236i	−2.20712	−	1.88506i
$955$	−12.8821	−	26.5269i	−0.416853	−	0.858390i
$956$	−32.9618	+	20.1990i	−1.06606	+	0.653282i
$957$	1.64182	−	3.96370i	0.0530724	−	0.128128i
$958$	−42.9097	−	3.37707i	−1.38635	−	0.109108i
$959$	10.4741	+	14.4164i	0.338227	+	0.465529i
$960$	2.41081	+	0.429333i	0.0778084	+	0.0138566i
$961$	−20.5340	−	14.9188i	−0.662388	−	0.481253i
$962$	−4.68960	−	19.5336i	−0.151199	−	0.629788i
$963$	−20.3759	−	28.0450i	−0.656603	−	0.903736i
$964$	−0.261685	+	1.65222i	−0.00842832	+	0.0532143i
$965$	6.72223	+	6.98488i	0.216396	+	0.224851i
$966$	−0.369956	+	0.509200i	−0.0119031	+	0.0163833i
$967$	6.02375	−	7.05290i	0.193711	−	0.226806i	−0.655047	−	0.755588i	$-0.727351\pi$
$967$	6.02375	−	7.05290i	0.193711	−	0.226806i	0.848758	+	0.528782i	$0.177351\pi$
$968$	51.8425	+	8.21104i	1.66628	+	0.263913i
$969$	1.95041	+	2.28363i	0.0626561	+	0.0733609i
$970$	−50.4089	−	38.1209i	−1.61853	−	1.22399i
$971$	15.2236	+	24.8427i	0.488549	+	0.797240i	0.997997	−	0.0632617i	$-0.0201503\pi$
$971$	15.2236	+	24.8427i	0.488549	+	0.797240i	−0.509448	+	0.860502i	$0.670150\pi$
$972$	33.6268	+	39.3719i	1.07858	+	1.26285i
$973$	−46.9292	+	3.69341i	−1.50448	+	0.118405i
$974$	−23.1307	+	71.1889i	−0.741154	+	2.28104i
$975$	−13.1857	+	3.73230i	−0.422282	+	0.119529i
$976$	17.7382	+	34.8132i	0.567786	+	1.11434i
$977$	0.882129	+	0.540570i	0.0282218	+	0.0172944i	0.536538	−	0.843876i	$-0.319732\pi$
$977$	0.882129	+	0.540570i	0.0282218	+	0.0172944i	−0.508316	+	0.861171i	$0.669732\pi$
$978$	26.3354	−	16.1383i	0.842113	−	0.516047i
$979$	0.229470	−	0.450361i	0.00733390	−	0.0143936i
$980$	−2.12181	−	1.88369i	−0.0677789	−	0.0601722i
$981$	−0.0268364	−	0.0111160i	−0.000856819	−	0.000354906i
$982$	42.4079	−	58.3695i	1.35329	−	1.86264i
$983$	−12.7300	−	12.7300i	−0.406025	−	0.406025i	0.474325	−	0.880350i	$-0.342692\pi$
$983$	−12.7300	−	12.7300i	−0.406025	−	0.406025i	−0.880350	+	0.474325i	$0.842692\pi$
$984$	18.6390	−	2.51115i	0.594191	−	0.0800526i
$985$	−17.5238	−	4.56387i	−0.558354	−	0.145417i
$986$	80.1186	−	12.6895i	2.55150	−	0.404117i
$987$	−4.92422	+	2.03968i	−0.156739	+	0.0649236i
$988$	−12.4395	+	24.4138i	−0.395752	+	0.776708i
$989$	1.78822	+	0.911141i	0.0568619	+	0.0289726i
$990$	20.7086	+	11.0563i	0.658162	+	0.351393i
$991$	−9.86144	−	41.0759i	−0.313259	−	1.30482i	−0.877647	−	0.479308i	$-0.840888\pi$
$991$	−9.86144	−	41.0759i	−0.313259	−	1.30482i	0.564388	−	0.825510i	$-0.309112\pi$
$992$	−9.46115	−	3.07411i	−0.300392	−	0.0976032i
$993$	13.4393			0.426484
$994$	−79.4976	−	25.8303i	−2.52151	−	0.819288i
$995$	−38.4851	−	6.85369i	−1.22006	−	0.217276i
$996$	1.86841	−	23.7405i	0.0592030	−	0.752245i
$997$	38.0116	+	9.12579i	1.20384	+	0.289017i	0.785262	−	0.619164i	$-0.212528\pi$
$997$	38.0116	+	9.12579i	1.20384	+	0.289017i	0.418579	+	0.908181i	$0.362528\pi$
$998$	52.6165	+	21.7944i	1.66554	+	0.689891i
$999$	−3.03665	+	2.59354i	−0.0960754	+	0.0820561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	205.2.y.a.112.3	yes	304
5.3	odd	4		205.2.bb.a.153.3	yes	304
41.26	odd	40		205.2.bb.a.67.3	yes	304
205.108	even	40	inner	205.2.y.a.108.3	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
205.2.y.a.108.3	✓	304	205.108	even	40	inner
205.2.y.a.112.3	yes	304	1.1	even	1	trivial
205.2.bb.a.67.3	yes	304	41.26	odd	40
205.2.bb.a.153.3	yes	304	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.y (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04338 - 1.48460i) q^{2} +(0.187032 + 0.451535i) q^{3} +(1.35331 + 4.16507i) q^{4} +(-0.132700 - 2.23213i) q^{5} +(0.288172 - 1.20032i) q^{6} +(-1.41072 + 2.30209i) q^{7} +(1.85714 - 5.71568i) q^{8} +(1.95242 - 1.95242i) q^{9} +(-3.04266 + 4.75808i) q^{10} +(0.977668 - 1.14470i) q^{11} +(-1.62756 + 1.39007i) q^{12} +(1.30912 - 5.45288i) q^{13} +(6.30031 - 2.60967i) q^{14} +(0.983065 - 0.477398i) q^{15} +(-5.19427 + 3.77386i) q^{16} +(-4.18800 - 3.57689i) q^{17} +(-6.88808 + 1.09096i) q^{18} +(-0.582947 + 0.951283i) q^{19} +(9.11739 - 3.57348i) q^{20} +(-1.30332 - 0.206426i) q^{21} +(-3.69717 + 0.887611i) q^{22} +(0.0295421 + 0.186521i) q^{23} +(2.92817 - 0.230452i) q^{24} +(-4.96478 + 0.592408i) q^{25} +(-10.7704 + 9.19877i) q^{26} +(2.60136 + 1.07752i) q^{27} +(-11.4975 - 2.76031i) q^{28} +(0.457515 - 5.81328i) q^{29} +(-2.71752 - 0.483953i) q^{30} +(-2.25433 - 0.732477i) q^{31} +4.19687 q^{32} +(0.699729 + 0.227356i) q^{33} +(3.24741 + 13.5264i) q^{34} +(5.32575 + 2.84342i) q^{35} +(10.7742 + 5.48973i) q^{36} +(-0.643890 + 1.26371i) q^{37} +(2.60345 - 1.07839i) q^{38} +(2.70702 - 0.428749i) q^{39} +(-13.0046 - 3.38689i) q^{40} +(6.39331 - 0.354419i) q^{41} +(2.35672 + 2.35672i) q^{42} +(6.24668 - 8.59782i) q^{43} +(6.09086 + 2.52292i) q^{44} +(-4.61713 - 4.09896i) q^{45} +(0.216544 - 0.424991i) q^{46} +(3.44394 - 2.11045i) q^{47} +(-2.67552 - 1.63956i) q^{48} +(-0.131539 - 0.258159i) q^{49} +(11.0244 + 6.16020i) q^{50} +(0.831801 - 2.56002i) q^{51} +(24.4833 - 1.92688i) q^{52} +(8.34874 + 9.77512i) q^{53} +(-3.71587 - 6.06374i) q^{54} +(-2.68486 - 2.03038i) q^{55} +(10.5381 + 12.3385i) q^{56} +(-0.538568 - 0.0853007i) q^{57} +(-9.56526 + 11.1995i) q^{58} +(-7.92949 + 10.9140i) q^{59} +(3.31879 + 3.44847i) q^{60} +(0.951982 - 6.01058i) q^{61} +(3.51901 + 4.84351i) q^{62} +(1.74032 + 7.24895i) q^{63} +(1.81275 + 1.31704i) q^{64} +(-12.3452 - 2.19853i) q^{65} +(-1.09228 - 1.50339i) q^{66} +(8.43726 + 0.664027i) q^{67} +(9.23032 - 22.2840i) q^{68} +(-0.0786956 + 0.0482247i) q^{69} +(-6.66118 - 13.7168i) q^{70} +(-9.32066 - 7.96059i) q^{71} +(-7.53348 - 14.7853i) q^{72} +11.1962i q^{73} +(3.19181 - 1.62631i) q^{74} +(-1.19607 - 2.13097i) q^{75} +(-4.75108 - 1.14063i) q^{76} +(1.25599 + 3.86553i) q^{77} +(-6.16797 - 3.14274i) q^{78} +(-0.310189 + 0.748863i) q^{79} +(9.11301 + 11.0935i) q^{80} -6.90727i q^{81} +(-13.5901 - 8.76729i) q^{82} +(-7.86724 + 7.86724i) q^{83} +(-0.904026 - 5.70780i) q^{84} +(-7.42832 + 9.82279i) q^{85} +(-25.5286 + 8.29475i) q^{86} +(2.71047 - 0.880685i) q^{87} +(-4.72709 - 7.71391i) q^{88} +(0.326486 - 0.0783823i) q^{89} +(3.34922 + 15.2303i) q^{90} +(10.7062 + 10.7062i) q^{91} +(-0.736895 + 0.375467i) q^{92} +(-0.0908932 - 1.15491i) q^{93} +(-10.1704 - 0.800430i) q^{94} +(2.20074 + 1.17498i) q^{95} +(0.784950 + 1.89504i) q^{96} +(-0.877983 + 11.1558i) q^{97} +(-0.114480 + 0.722798i) q^{98} +(-0.326120 - 4.14375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) \) 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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