LMFDB - Embedded newform 414.2.m.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	414.25
Dual form			414.2.m.a.265.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.888835 - 0.458227i) q^{2} +(-0.301182 + 1.70566i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.115473 - 0.475985i) q^{5} +(0.513879 + 1.65406i) q^{6} +(1.23894 + 3.57969i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.81858 - 1.02743i) q^{9} +O(q^{10})$	\(q+(0.888835 - 0.458227i) q^{2} +(-0.301182 + 1.70566i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.115473 - 0.475985i) q^{5} +(0.513879 + 1.65406i) q^{6} +(1.23894 + 3.57969i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.81858 - 1.02743i) q^{9} +(-0.320745 - 0.370160i) q^{10} +(0.226813 + 4.76139i) q^{11} +(1.21469 + 1.23472i) q^{12} +(0.731258 - 2.11283i) q^{13} +(2.74152 + 2.61404i) q^{14} +(0.846649 - 0.0535993i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(0.843058 - 1.84604i) q^{17} +(-2.97605 + 0.378329i) q^{18} +(3.03905 + 6.65459i) q^{19} +(-0.454707 - 0.182037i) q^{20} +(-6.47889 + 1.03508i) q^{21} +(2.38340 + 4.12816i) q^{22} +(-4.37181 - 1.97161i) q^{23} +(1.64544 + 0.540858i) q^{24} +(4.23095 - 2.18121i) q^{25} +(-0.318187 - 2.21304i) q^{26} +(2.60136 - 4.49810i) q^{27} +(3.63458 + 1.06721i) q^{28} +(0.962636 + 1.35183i) q^{29} +(0.727971 - 0.435598i) q^{30} +(-2.27672 + 0.911461i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-8.18965 - 1.04718i) q^{33} +(-0.0965644 - 2.02714i) q^{34} +(1.56081 - 1.00307i) q^{35} +(-2.47186 + 1.69998i) q^{36} +(4.11600 - 1.20857i) q^{37} +(5.75052 + 4.52226i) q^{38} +(3.38354 + 1.88363i) q^{39} +(-0.487574 + 0.0465576i) q^{40} +(-0.653905 - 2.69543i) q^{41} +(-5.28437 + 3.88881i) q^{42} +(-2.18286 - 0.873887i) q^{43} +(4.01008 + 2.57712i) q^{44} +(-0.163573 + 1.46024i) q^{45} +(-4.78927 + 0.250841i) q^{46} +(-0.773294 + 1.33938i) q^{47} +(1.71036 - 0.273250i) q^{48} +(-5.77681 + 4.54293i) q^{49} +(2.76113 - 3.87747i) q^{50} +(2.89481 + 1.99397i) q^{51} +(-1.29689 - 1.82123i) q^{52} +(4.02152 - 4.64108i) q^{53} +(0.251031 - 5.19009i) q^{54} +(2.24016 - 0.657771i) q^{55} +(3.71957 - 0.716888i) q^{56} +(-12.2658 + 3.17935i) q^{57} +(1.47507 + 0.760452i) q^{58} +(3.72905 - 10.7744i) q^{59} +(0.447444 - 0.720750i) q^{60} +(-6.23304 - 4.90172i) q^{61} +(-1.60597 + 1.85339i) q^{62} +(0.185831 - 11.3626i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.09012 - 0.104093i) q^{65} +(-7.75910 + 2.82194i) q^{66} +(0.483290 - 10.1455i) q^{67} +(-1.01472 - 1.75754i) q^{68} +(4.67962 - 6.86303i) q^{69} +(0.927671 - 1.60677i) q^{70} +(-12.1527 - 7.81006i) q^{71} +(-1.41810 + 2.64367i) q^{72} +(6.05925 + 13.2679i) q^{73} +(3.10465 - 2.96027i) q^{74} +(2.44612 + 7.87352i) q^{75} +(7.18349 + 1.38450i) q^{76} +(-16.7633 + 6.71101i) q^{77} +(3.87054 + 0.123809i) q^{78} +(3.19230 - 0.615266i) q^{79} +(-0.412039 + 0.264801i) q^{80} +(6.88877 + 5.79180i) q^{81} +(-1.81633 - 2.09616i) q^{82} +(1.81612 - 7.48614i) q^{83} +(-2.91497 + 5.87795i) q^{84} +(-0.976037 - 0.188116i) q^{85} +(-2.34065 + 0.223505i) q^{86} +(-2.59570 + 1.23479i) q^{87} +(4.74521 + 0.453112i) q^{88} +(-2.12756 - 14.7975i) q^{89} +(0.523732 + 1.37287i) q^{90} +8.46926 q^{91} +(-4.14193 + 2.41753i) q^{92} +(-0.868939 - 4.15784i) q^{93} +(-0.0735896 + 1.54484i) q^{94} +(2.81656 - 2.21497i) q^{95} +(1.39502 - 1.02661i) q^{96} +(8.38035 - 7.99065i) q^{97} +(-3.05294 + 6.68500i) q^{98} +(4.25272 - 13.6534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$3$	−0.301182	+	1.70566i	−0.173888	+	0.984765i
$3$	−0.301182	+	1.70566i	−0.173888	+	0.984765i
$4$	0.580057	−	0.814576i	0.290028	−	0.407288i
$5$	−0.115473	−	0.475985i	−0.0516410	−	0.212867i	0.940145	−	0.340774i	$-0.110689\pi$
$5$	−0.115473	−	0.475985i	−0.0516410	−	0.212867i	−0.991786	+	0.127907i	$0.959174\pi$
$6$	0.513879	+	1.65406i	0.209790	+	0.675269i
$7$	1.23894	+	3.57969i	0.468276	+	1.35299i	0.893970	+	0.448127i	$0.147909\pi$
$7$	1.23894	+	3.57969i	0.468276	+	1.35299i	−0.425694	+	0.904867i	$0.639970\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	−2.81858	−	1.02743i	−0.939526	−	0.342477i
$10$	−0.320745	−	0.370160i	−0.101429	−	0.117055i
$11$	0.226813	+	4.76139i	0.0683867	+	1.43561i	0.728808	+	0.684719i	$0.240075\pi$
$11$	0.226813	+	4.76139i	0.0683867	+	1.43561i	−0.660421	+	0.750896i	$0.729622\pi$
$12$	1.21469	+	1.23472i	0.350651	+	0.356432i
$13$	0.731258	−	2.11283i	0.202814	−	0.585994i	−0.797024	−	0.603947i	$-0.793594\pi$
$13$	0.731258	−	2.11283i	0.202814	−	0.585994i	0.999839	+	0.0179533i	$0.00571504\pi$
$14$	2.74152	+	2.61404i	0.732703	+	0.698631i
$15$	0.846649	−	0.0535993i	0.218604	−	0.0138393i
$16$	−0.327068	−	0.945001i	−0.0817670	−	0.236250i
$17$	0.843058	−	1.84604i	0.204471	−	0.447730i	−0.779419	−	0.626503i	$-0.784486\pi$
$17$	0.843058	−	1.84604i	0.204471	−	0.447730i	0.983890	+	0.178773i	$0.0572128\pi$
$18$	−2.97605	+	0.378329i	−0.701461	+	0.0891731i
$19$	3.03905	+	6.65459i	0.697206	+	1.52667i	0.843327	+	0.537401i	$0.180594\pi$
$19$	3.03905	+	6.65459i	0.697206	+	1.52667i	−0.146121	+	0.989267i	$0.546679\pi$
$20$	−0.454707	−	0.182037i	−0.101676	−	0.0407047i
$21$	−6.47889	+	1.03508i	−1.41381	+	0.225873i
$22$	2.38340	+	4.12816i	0.508142	+	0.880127i
$23$	−4.37181	−	1.97161i	−0.911586	−	0.411110i
$23$	−4.37181	−	1.97161i	−0.911586	−	0.411110i
$24$	1.64544	+	0.540858i	0.335874	+	0.110402i
$25$	4.23095	−	2.18121i	0.846190	−	0.436241i
$26$	−0.318187	−	2.21304i	−0.0624016	−	0.434013i
$27$	2.60136	−	4.49810i	0.500632	−	0.865660i
$28$	3.63458	+	1.06721i	0.686872	+	0.201684i
$29$	0.962636	+	1.35183i	0.178757	+	0.251029i	0.894226	−	0.447615i	$-0.147726\pi$
$29$	0.962636	+	1.35183i	0.178757	+	0.251029i	−0.715469	+	0.698644i	$0.753787\pi$
$30$	0.727971	−	0.435598i	0.132909	−	0.0795289i
$31$	−2.27672	+	0.911461i	−0.408911	+	0.163703i	−0.566993	−	0.823723i	$-0.691893\pi$
$31$	−2.27672	+	0.911461i	−0.408911	+	0.163703i	0.158082	+	0.987426i	$0.449469\pi$
$32$	−0.723734	−	0.690079i	−0.127939	−	0.121990i
$33$	−8.18965	−	1.04718i	−1.42563	−	0.182291i
$34$	−0.0965644	−	2.02714i	−0.0165607	−	0.347651i
$35$	1.56081	−	1.00307i	0.263826	−	0.169550i
$36$	−2.47186	+	1.69998i	−0.411976	+	0.283330i
$37$	4.11600	−	1.20857i	0.676665	−	0.198687i	0.0746964	−	0.997206i	$-0.476201\pi$
$37$	4.11600	−	1.20857i	0.676665	−	0.198687i	0.601969	+	0.798519i	$0.294383\pi$
$38$	5.75052	+	4.52226i	0.932858	+	0.733608i
$39$	3.38354	+	1.88363i	0.541799	+	0.301622i
$40$	−0.487574	+	0.0465576i	−0.0770922	+	0.00736141i
$41$	−0.653905	−	2.69543i	−0.102123	−	0.420956i	0.897683	−	0.440641i	$-0.145249\pi$
$41$	−0.653905	−	2.69543i	−0.102123	−	0.420956i	−0.999806	+	0.0196852i	$0.993734\pi$
$42$	−5.28437	+	3.88881i	−0.815395	+	0.600057i
$43$	−2.18286	−	0.873887i	−0.332884	−	0.133267i	0.199199	−	0.979959i	$-0.436166\pi$
$43$	−2.18286	−	0.873887i	−0.332884	−	0.133267i	−0.532082	+	0.846693i	$0.678590\pi$
$44$	4.01008	+	2.57712i	0.604542	+	0.388516i
$45$	−0.163573	+	1.46024i	−0.0243841	+	0.217680i
$46$	−4.78927	+	0.250841i	−0.706139	+	0.0369846i
$47$	−0.773294	+	1.33938i	−0.112797	+	0.195369i	−0.916897	−	0.399124i	$-0.869314\pi$
$47$	−0.773294	+	1.33938i	−0.112797	+	0.195369i	0.804100	+	0.594494i	$0.202647\pi$
$48$	1.71036	−	0.273250i	0.246869	−	0.0394403i
$49$	−5.77681	+	4.54293i	−0.825258	+	0.648990i
$50$	2.76113	−	3.87747i	0.390483	−	0.548357i
$51$	2.89481	+	1.99397i	0.405354	+	0.279211i
$52$	−1.29689	−	1.82123i	−0.179846	−	0.252559i
$53$	4.02152	−	4.64108i	0.552399	−	0.637502i	−0.409042	−	0.912516i	$-0.634137\pi$
$53$	4.02152	−	4.64108i	0.552399	−	0.637502i	0.961440	+	0.275014i	$0.0886824\pi$
$54$	0.251031	−	5.19009i	0.0341610	−	0.706281i
$55$	2.24016	−	0.657771i	0.302063	−	0.0886938i
$56$	3.71957	−	0.716888i	0.497048	−	0.0957982i
$57$	−12.2658	+	3.17935i	−1.62464	+	0.421115i
$58$	1.47507	+	0.760452i	0.193686	+	0.0998523i
$59$	3.72905	−	10.7744i	0.485482	−	1.40271i	−0.390607	−	0.920557i	$-0.627735\pi$
$59$	3.72905	−	10.7744i	0.485482	−	1.40271i	0.876089	−	0.482150i	$-0.160144\pi$
$60$	0.447444	−	0.720750i	0.0577647	−	0.0930485i
$61$	−6.23304	−	4.90172i	−0.798059	−	0.627601i	0.133558	−	0.991041i	$-0.457360\pi$
$61$	−6.23304	−	4.90172i	−0.798059	−	0.627601i	−0.931617	+	0.363440i	$0.881602\pi$
$62$	−1.60597	+	1.85339i	−0.203959	+	0.235381i
$63$	0.185831	−	11.3626i	0.0234125	−	1.43155i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.09012	−	0.104093i	−0.135212	−	0.0129112i
$66$	−7.75910	+	2.82194i	−0.955079	+	0.347357i
$67$	0.483290	−	10.1455i	0.0590432	−	1.23947i	−0.753846	−	0.657051i	$-0.771803\pi$
$67$	0.483290	−	10.1455i	0.0590432	−	1.23947i	0.812889	−	0.582418i	$-0.197893\pi$
$68$	−1.01472	−	1.75754i	−0.123053	−	0.213133i
$69$	4.67962	−	6.86303i	0.563360	−	0.826211i
$70$	0.927671	−	1.60677i	0.110878	−	0.192046i
$71$	−12.1527	−	7.81006i	−1.44226	−	0.926883i	−0.999543	−	0.0302212i	$-0.990379\pi$
$71$	−12.1527	−	7.81006i	−1.44226	−	0.926883i	−0.442715	−	0.896662i	$-0.645985\pi$
$72$	−1.41810	+	2.64367i	−0.167125	+	0.311560i
$73$	6.05925	+	13.2679i	0.709181	+	1.55289i	0.828472	+	0.560031i	$0.189211\pi$
$73$	6.05925	+	13.2679i	0.709181	+	1.55289i	−0.119291	+	0.992859i	$0.538062\pi$
$74$	3.10465	−	2.96027i	0.360908	−	0.344125i
$75$	2.44612	+	7.87352i	0.282453	+	0.909156i
$76$	7.18349	+	1.38450i	0.824003	+	0.158814i
$77$	−16.7633	+	6.71101i	−1.91035	+	0.764790i
$78$	3.87054	+	0.123809i	0.438252	+	0.0140186i
$79$	3.19230	−	0.615266i	0.359162	−	0.0692228i	−0.00647829	−	0.999979i	$-0.502062\pi$
$79$	3.19230	−	0.615266i	0.359162	−	0.0692228i	0.365640	+	0.930756i	$0.380850\pi$
$80$	−0.412039	+	0.264801i	−0.0460673	+	0.0296057i
$81$	6.88877	+	5.79180i	0.765419	+	0.643533i
$82$	−1.81633	−	2.09616i	−0.200580	−	0.231482i
$83$	1.81612	−	7.48614i	0.199345	−	0.821711i	−0.781018	−	0.624509i	$-0.785299\pi$
$83$	1.81612	−	7.48614i	0.199345	−	0.821711i	0.980363	−	0.197202i	$-0.0631856\pi$
$84$	−2.91497	+	5.87795i	−0.318050	+	0.641337i
$85$	−0.976037	−	0.188116i	−0.105866	−	0.0204040i
$86$	−2.34065	+	0.223505i	−0.252398	+	0.0241011i
$87$	−2.59570	+	1.23479i	−0.278289	+	0.132383i
$88$	4.74521	+	0.453112i	0.505841	+	0.0483020i
$89$	−2.12756	−	14.7975i	−0.225521	−	1.56853i	−0.716641	−	0.697442i	$-0.754321\pi$
$89$	−2.12756	−	14.7975i	−0.225521	−	1.56853i	0.491120	−	0.871092i	$-0.336588\pi$
$90$	0.523732	+	1.37287i	0.0552062	+	0.144713i
$91$	8.46926			0.887819
$92$	−4.14193	+	2.41753i	−0.431826	+	0.252045i
$93$	−0.868939	−	4.15784i	−0.0901047	−	0.431148i
$94$	−0.0735896	+	1.54484i	−0.00759019	+	0.159338i
$95$	2.81656	−	2.21497i	0.288973	−	0.227251i
$96$	1.39502	−	1.02661i	0.142379	−	0.104778i
$97$	8.38035	−	7.99065i	0.850896	−	0.811328i	−0.132805	−	0.991142i	$-0.542398\pi$
$97$	8.38035	−	7.99065i	0.850896	−	0.811328i	0.983700	+	0.179815i	$0.0575498\pi$
$98$	−3.05294	+	6.68500i	−0.308393	+	0.675287i
$99$	4.25272	−	13.6534i	0.427414	−	1.37222i
$100$	0.677433	−	4.71165i	0.0677433	−	0.471165i
$101$	2.49030	−	10.2652i	0.247794	−	1.02142i	−0.702899	−	0.711290i	$-0.748111\pi$
$101$	2.49030	−	10.2652i	0.247794	−	1.02142i	0.950693	−	0.310132i	$-0.100373\pi$
$102$	3.48670	+	0.445831i	0.345234	+	0.0441439i
$103$	10.9561	+	5.64828i	1.07954	+	0.556542i	0.903826	−	0.427899i	$-0.140746\pi$
$103$	10.9561	+	5.64828i	1.07954	+	0.556542i	0.175714	+	0.984441i	$0.443777\pi$
$104$	−1.98726	−	1.02450i	−0.194866	−	0.100461i
$105$	1.24082	+	2.96433i	0.121091	+	0.289289i
$106$	1.44780	−	5.96793i	0.140623	−	0.579657i
$107$	−1.59912	+	11.1221i	−0.154592	+	1.07521i	0.753803	+	0.657101i	$0.228217\pi$
$107$	−1.59912	+	11.1221i	−0.154592	+	1.07521i	−0.908395	+	0.418113i	$0.862692\pi$
$108$	−2.15511	−	4.72816i	−0.207375	−	0.454967i
$109$	−5.36700	+	11.7521i	−0.514065	+	1.12565i	0.457573	+	0.889172i	$0.348719\pi$
$109$	−5.36700	+	11.7521i	−0.514065	+	1.12565i	−0.971638	+	0.236474i	$0.924008\pi$
$110$	1.68973	−	1.61115i	0.161109	−	0.153617i
$111$	0.821741	+	7.38450i	0.0779962	+	0.700906i
$112$	2.97759	−	2.34160i	0.281356	−	0.221261i
$113$	−0.418285	+	8.78087i	−0.0393489	+	0.826035i	0.889805	+	0.456341i	$0.150840\pi$
$113$	−0.418285	+	8.78087i	−0.0393489	+	0.826035i	−0.929154	+	0.369694i	$0.879463\pi$
$114$	−9.44541	+	8.44643i	−0.884644	+	0.791081i
$115$	−0.433633	+	2.30858i	−0.0404365	+	0.215277i
$116$	1.65956			0.154086
$117$	−4.23190	+	5.20386i	−0.391239	+	0.481097i
$118$	−1.62260	−	11.2854i	−0.149372	−	1.03891i
$119$	7.65274	+	0.730748i	0.701525	+	0.0669875i
$120$	0.0674370	−	0.845659i	0.00615612	−	0.0771978i
$121$	−11.6692	+	1.11428i	−1.06084	+	0.101298i
$122$	−7.78625	−	1.50068i	−0.704934	−	0.135865i
$123$	4.79445	−	0.303525i	0.432301	−	0.0273679i
$124$	−0.578173	+	2.38326i	−0.0519215	+	0.214023i
$125$	−3.13051	−	3.61280i	−0.280001	−	0.323138i
$126$	−5.04145	−	10.1846i	−0.449128	−	0.907316i
$127$	−10.9404	+	7.03096i	−0.970802	+	0.623896i	−0.926967	−	0.375142i	$-0.877594\pi$
$127$	−10.9404	+	7.03096i	−0.970802	+	0.623896i	−0.0438346	+	0.999039i	$0.513957\pi$
$128$	−0.981929	+	0.189251i	−0.0867911	+	0.0167276i
$129$	2.14800	−	3.46003i	0.189121	−	0.304639i
$130$	−1.01663	+	0.406998i	−0.0891645	+	0.0356961i
$131$	−12.2879	−	2.36830i	−1.07360	−	0.206919i	−0.378331	−	0.925670i	$-0.623502\pi$
$131$	−12.2879	−	2.36830i	−1.07360	−	0.206919i	−0.695268	+	0.718751i	$0.744714\pi$
$132$	−5.60347	+	6.06367i	−0.487720	+	0.527774i
$133$	−20.0561	+	19.1235i	−1.73909	+	1.65822i
$134$	−4.21937	−	9.23913i	−0.364498	−	0.798140i
$135$	−2.44142	−	0.718800i	−0.210124	−	0.0618645i
$136$	−1.70727	−	1.09720i	−0.146397	−	0.0940837i
$137$	−3.57213	+	6.18711i	−0.305188	+	0.528601i	−0.977303	−	0.211846i	$-0.932053\pi$
$137$	−3.57213	+	6.18711i	−0.305188	+	0.528601i	0.672115	+	0.740447i	$0.265386\pi$
$138$	1.01459	−	8.24443i	0.0863678	−	0.701812i
$139$	1.43978	+	2.49377i	0.122121	+	0.211519i	0.920604	−	0.390498i	$-0.127697\pi$
$139$	1.43978	+	2.49377i	0.122121	+	0.211519i	−0.798483	+	0.602017i	$0.794364\pi$
$140$	0.0882807	−	1.85324i	0.00746108	−	0.156627i
$141$	−2.05164	−	1.72238i	−0.172779	−	0.145050i
$142$	−14.3805	−	1.37317i	−1.20679	−	0.115234i
$143$	10.2259	+	3.00259i	0.855131	+	0.251089i
$144$	−0.0490575	+	2.99960i	−0.00408812	+	0.249967i
$145$	0.532294	−	0.614300i	0.0442046	−	0.0510149i
$146$	11.4654	+	9.01647i	0.948881	+	0.746208i
$147$	−6.00884	−	11.2215i	−0.495601	−	0.925537i
$148$	1.40304	−	4.05383i	0.115329	−	0.333223i
$149$	17.1404	+	8.83651i	1.40420	+	0.723915i	0.983095	−	0.183098i	$-0.0586124\pi$
$149$	17.1404	+	8.83651i	1.40420	+	0.723915i	0.421104	+	0.907012i	$0.361643\pi$
$150$	5.78205	+	5.87739i	0.472102	+	0.479887i
$151$	−3.99512	+	0.769995i	−0.325118	+	0.0626613i	−0.349199	−	0.937049i	$-0.613546\pi$
$151$	−3.99512	+	0.769995i	−0.325118	+	0.0626613i	0.0240809	+	0.999710i	$0.492334\pi$
$152$	7.01936	−	2.06107i	0.569345	−	0.167175i
$153$	−4.27290	+	4.33702i	−0.345444	+	0.350627i
$154$	−11.8246	+	13.6464i	−0.952857	+	1.09966i
$155$	0.696741	+	0.978436i	0.0559636	+	0.0785899i
$156$	3.49700	−	1.66354i	0.279984	−	0.133190i
$157$	−5.58975	+	7.84970i	−0.446110	+	0.626474i	−0.974997	−	0.222218i	$-0.928670\pi$
$157$	−5.58975	+	7.84970i	−0.446110	+	0.626474i	0.528887	+	0.848692i	$0.322610\pi$
$158$	2.55550	−	2.00967i	0.203305	−	0.159881i
$159$	6.70492	+	8.25718i	0.531735	+	0.654837i
$160$	−0.244896	+	0.424172i	−0.0193607	+	0.0335337i
$161$	1.64133	−	18.0924i	0.129355	−	1.42588i
$162$	8.77693	+	1.99134i	0.689581	+	0.156454i
$163$	13.6005	+	8.74054i	1.06528	+	0.684612i	0.951111	−	0.308850i	$-0.0999441\pi$
$163$	13.6005	+	8.74054i	1.06528	+	0.684612i	0.114166	+	0.993462i	$0.463580\pi$
$164$	−2.57494	−	1.03085i	−0.201069	−	0.0804958i
$165$	0.447238	+	4.01907i	0.0348175	+	0.312884i
$166$	−1.81612	−	7.48614i	−0.140958	−	0.581037i
$167$	−10.5203	+	1.00457i	−0.814085	+	0.0777357i	−0.493789	−	0.869582i	$-0.664388\pi$
$167$	−10.5203	+	1.00457i	−0.814085	+	0.0777357i	−0.320296	+	0.947318i	$0.603782\pi$
$168$	0.102501	+	6.56025i	0.00790815	+	0.506134i
$169$	6.28938	+	4.94602i	0.483798	+	0.380463i
$170$	−0.953736	+	0.280042i	−0.0731482	+	0.0214782i
$171$	−1.72866	−	21.8789i	−0.132194	−	1.67312i
$172$	−1.97803	+	1.27120i	−0.150824	+	0.0969285i
$173$	0.380648	+	7.99078i	0.0289401	+	0.607528i	0.966028	+	0.258436i	$0.0832070\pi$
$173$	0.380648	+	7.99078i	0.0289401	+	0.607528i	−0.937088	+	0.349092i	$0.886490\pi$
$174$	−1.74134	+	2.28694i	−0.132011	+	0.173373i
$175$	13.0499	+	12.4431i	0.986482	+	0.940609i
$176$	4.42534	−	1.77164i	0.333572	−	0.133542i
$177$	17.2544	+	9.60557i	1.29692	+	0.721999i
$178$	−8.67167	−	12.1777i	−0.649969	−	0.912754i
$179$	−0.115270	−	0.0338462i	−0.00861566	−	0.00252979i	0.277422	−	0.960748i	$-0.410520\pi$
$179$	−0.115270	−	0.0338462i	−0.00861566	−	0.00252979i	−0.286038	+	0.958218i	$0.592338\pi$
$180$	1.09460	+	0.980266i	0.0815864	+	0.0730647i
$181$	−3.15253	−	21.9263i	−0.234325	−	1.62977i	−0.679043	−	0.734099i	$-0.737605\pi$
$181$	−3.15253	−	21.9263i	−0.234325	−	1.62977i	0.444717	−	0.895671i	$-0.353304\pi$
$182$	7.52777	−	3.88084i	0.557996	−	0.287667i
$183$	10.2380	−	9.15516i	0.756812	−	0.676769i
$184$	−2.57372	+	4.04672i	−0.189737	+	0.298328i
$185$	−1.05054	−	1.81960i	−0.0772375	−	0.133779i
$186$	−2.67757	−	3.29746i	−0.196329	−	0.241782i
$187$	8.98093	+	3.59542i	0.656751	+	0.262923i
$188$	0.642476	+	1.40683i	0.0468574	+	0.102603i
$189$	19.3247	+	3.73917i	1.40567	+	0.271984i
$190$	1.48850	−	3.25936i	0.107987	−	0.236459i
$191$	3.43600	+	9.92768i	0.248620	+	0.718341i	0.998394	+	0.0566473i	$0.0180410\pi$
$191$	3.43600	+	9.92768i	0.248620	+	0.718341i	−0.749774	+	0.661694i	$0.769838\pi$
$192$	0.769523	−	1.55172i	0.0555356	−	0.111986i
$193$	−2.73452	−	2.60736i	−0.196835	−	0.187682i	0.585251	−	0.810852i	$-0.300996\pi$
$193$	−2.73452	−	2.60736i	−0.196835	−	0.187682i	−0.782086	+	0.623170i	$0.785844\pi$
$194$	3.78723	−	10.9425i	0.271907	−	0.785624i
$195$	0.505872	−	1.82802i	0.0362263	−	0.130907i
$196$	0.349686	+	7.34081i	0.0249775	+	0.524343i
$197$	12.7126	+	14.6711i	0.905733	+	1.04527i	0.998769	+	0.0496094i	$0.0157976\pi$
$197$	12.7126	+	14.6711i	0.905733	+	1.04527i	−0.0930352	+	0.995663i	$0.529657\pi$
$198$	−2.47638	−	14.0843i	−0.175989	−	1.00093i
$199$	2.04818	−	14.2454i	0.145191	−	1.00983i	−0.778761	−	0.627321i	$-0.784152\pi$
$199$	2.04818	−	14.2454i	0.145191	−	1.00983i	0.923952	−	0.382507i	$-0.124939\pi$
$200$	−1.55688	−	4.49830i	−0.110088	−	0.318078i
$201$	17.1592	+	3.87998i	1.21032	+	0.273672i
$202$	−2.49030	−	10.2652i	−0.175217	−	0.722254i
$203$	−3.64649	+	5.12078i	−0.255933	+	0.359408i
$204$	3.30339	−	1.20143i	0.231284	−	0.0841166i
$205$	−1.20748	+	0.622498i	−0.0843339	+	0.0434771i
$206$	12.3264			0.858821
$207$	10.2966	+	10.0489i	0.715663	+	0.698446i
$208$	−2.23580			−0.155025
$209$	−30.9958	+	15.9795i	−2.14403	+	1.10532i
$210$	2.46122	+	2.06623i	0.169840	+	0.142583i
$211$	8.96961	−	12.5961i	0.617493	−	0.867148i	−0.380853	−	0.924636i	$-0.624370\pi$
$211$	8.96961	−	12.5961i	0.617493	−	0.867148i	0.998346	+	0.0574877i	$0.0183090\pi$
$212$	−1.44780	−	5.96793i	−0.0994356	−	0.409879i
$213$	16.9815	−	18.3761i	1.16355	−	1.25911i
$214$	3.67509	+	10.6185i	0.251224	+	0.725863i
$215$	−0.163896	+	1.13992i	−0.0111776	+	0.0777420i
$216$	−4.08211	−	3.21503i	−0.277752	−	0.218755i
$217$	−6.08347	−	7.02070i	−0.412973	−	0.476596i
$218$	0.614740	+	12.9050i	0.0416354	+	0.874035i
$219$	−24.4555	+	6.33898i	−1.65255	+	0.428348i
$220$	0.763617	−	2.20633i	0.0514830	−	0.148750i
$221$	−3.28387	−	3.13117i	−0.220897	−	0.210625i
$222$	4.11417	+	6.18706i	0.276125	+	0.415249i
$223$	0.619578	+	1.79015i	0.0414900	+	0.119877i	0.963843	−	0.266471i	$-0.0858575\pi$
$223$	0.619578	+	1.79015i	0.0414900	+	0.119877i	−0.922353	+	0.386348i	$0.873736\pi$
$224$	1.57360	−	3.44571i	0.105141	−	0.230226i
$225$	−14.1663	+	1.80089i	−0.944420	+	0.120059i
$226$	3.65184	+	7.99642i	0.242917	+	0.531914i
$227$	8.74330	+	3.50029i	0.580313	+	0.232322i	0.643200	−	0.765698i	$-0.277606\pi$
$227$	8.74330	+	3.50029i	0.580313	+	0.232322i	−0.0628868	+	0.998021i	$0.520031\pi$
$228$	−4.52504	+	11.8356i	−0.299678	+	0.783834i
$229$	−8.91504	−	15.4413i	−0.589123	−	1.02039i	−0.994348	−	0.106173i	$-0.966140\pi$
$229$	−8.91504	−	15.4413i	−0.589123	−	1.02039i	0.405225	−	0.914217i	$-0.367193\pi$
$230$	0.672427	+	2.25065i	0.0443385	+	0.148404i
$231$	−6.39792	−	30.6138i	−0.420952	−	2.01424i
$232$	1.47507	−	0.760452i	0.0968432	−	0.0499261i
$233$	1.80430	+	12.5492i	0.118204	+	0.822124i	0.959532	+	0.281600i	$0.0908650\pi$
$233$	1.80430	+	12.5492i	0.118204	+	0.822124i	−0.841328	+	0.540524i	$0.818226\pi$
$234$	−1.37691	+	6.56454i	−0.0900116	+	0.429138i
$235$	0.726822	+	0.213414i	0.0474126	+	0.0139216i
$236$	−6.61350	−	9.28736i	−0.430502	−	0.604556i
$237$	0.0879713	+	5.63030i	0.00571435	+	0.365727i
$238$	7.13687	−	2.85717i	0.462615	−	0.185203i
$239$	2.56574	+	2.44643i	0.165964	+	0.158246i	0.768510	−	0.639838i	$-0.220999\pi$
$239$	2.56574	+	2.44643i	0.165964	+	0.158246i	−0.602546	+	0.798084i	$0.705847\pi$
$240$	−0.327563	−	0.782553i	−0.0211441	−	0.0505136i
$241$	0.957807	+	20.1068i	0.0616978	+	1.29520i	0.791344	+	0.611371i	$0.209382\pi$
$241$	0.957807	+	20.1068i	0.0616978	+	1.29520i	−0.729647	+	0.683824i	$0.760315\pi$
$242$	−9.86144	+	6.33756i	−0.633917	+	0.407394i
$243$	−11.9536	+	10.0055i	−0.766826	+	0.641855i
$244$	−7.60834	+	2.23401i	−0.487074	+	0.143018i
$245$	2.82943	+	2.22509i	0.180766	+	0.142156i
$246$	4.12239	−	2.46673i	0.262834	−	0.157273i
$247$	16.2823	−	1.55478i	1.03602	−	0.0989280i
$248$	0.578173	+	2.38326i	0.0367140	+	0.151337i
$249$	12.2219	+	5.35238i	0.774529	+	0.339193i
$250$	−4.43799	−	1.77670i	−0.280683	−	0.112368i
$251$	2.91637	+	1.87424i	0.184080	+	0.118301i	0.629435	−	0.777053i	$-0.283286\pi$
$251$	2.91637	+	1.87424i	0.184080	+	0.118301i	−0.445355	+	0.895354i	$0.646923\pi$
$252$	−9.14787	−	6.74230i	−0.576262	−	0.424725i
$253$	8.39604	−	21.2631i	0.527854	−	1.33680i
$254$	−6.50243	+	11.2625i	−0.407999	+	0.706674i
$255$	0.614827	−	1.60813i	0.0385020	−	0.100705i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	−6.41460	+	9.00805i	−0.400132	+	0.561907i	−0.964657	−	0.263509i	$-0.915120\pi$
$257$	−6.41460	+	9.00805i	−0.400132	+	0.561907i	0.564525	+	0.825416i	$0.309059\pi$
$258$	0.323738	−	4.05967i	0.0201550	−	0.252744i
$259$	9.42576	+	13.2366i	0.585688	+	0.822484i
$260$	−0.717121	+	0.827602i	−0.0444740	+	0.0513257i
$261$	−1.32435	−	4.79929i	−0.0819751	−	0.297069i
$262$	−12.0071	+	3.52562i	−0.741804	+	0.217813i
$263$	−19.4707	+	3.75266i	−1.20061	+	0.231399i	−0.750072	−	0.661357i	$-0.769981\pi$
$263$	−19.4707	+	3.75266i	−1.20061	+	0.231399i	−0.450541	+	0.892756i	$0.648769\pi$
$264$	−2.20203	+	7.95726i	−0.135526	+	0.489736i
$265$	−2.67346	−	1.37827i	−0.164230	−	0.0846662i
$266$	−9.06372	+	26.1879i	−0.555732	+	1.60568i
$267$	25.8804	+	0.827848i	1.58385	+	0.0506635i
$268$	−7.98394	−	6.27864i	−0.487697	−	0.383529i
$269$	16.3585	−	18.8787i	0.997394	−	1.15105i	0.00887427	−	0.999961i	$-0.497175\pi$
$269$	16.3585	−	18.8787i	0.997394	−	1.15105i	0.988520	−	0.151093i	$-0.0482794\pi$
$270$	−2.49939	+	0.479826i	−0.152108	+	0.0292013i
$271$	−26.3029	−	7.72323i	−1.59779	−	0.469153i	−0.642858	−	0.765985i	$-0.722252\pi$
$271$	−26.3029	−	7.72323i	−1.59779	−	0.469153i	−0.954930	+	0.296832i	$0.904070\pi$
$272$	−2.02025	−	0.192910i	−0.122495	−	0.0116969i
$273$	−2.55079	+	14.4457i	−0.154381	+	0.874294i
$274$	−0.339938	+	7.13617i	−0.0205364	+	0.431112i
$275$	11.3452	+	19.6505i	0.684142	+	1.18497i
$276$	−2.87601	−	7.79285i	−0.173115	−	0.469075i
$277$	11.1039	−	19.2326i	0.667170	−	1.15557i	−0.311522	−	0.950239i	$-0.600839\pi$
$277$	11.1039	−	19.2326i	0.667170	−	1.15557i	0.978692	−	0.205334i	$-0.0658279\pi$
$278$	2.42244	+	1.55681i	0.145288	+	0.0933712i
$279$	7.35358	−	0.229850i	0.440247	−	0.0137607i
$280$	−0.770737	−	1.68768i	−0.0460603	−	0.100858i
$281$	8.15965	−	7.78021i	0.486764	−	0.464128i	−0.406507	−	0.913648i	$-0.633253\pi$
$281$	8.15965	−	7.78021i	0.486764	−	0.464128i	0.893271	+	0.449519i	$0.148405\pi$
$282$	−2.61281	−	0.590797i	−0.155590	−	0.0351814i
$283$	−24.9421	−	4.80719i	−1.48265	−	0.285758i	−0.617222	−	0.786789i	$-0.711742\pi$
$283$	−24.9421	−	4.80719i	−1.48265	−	0.285758i	−0.865429	+	0.501031i	$0.832954\pi$
$284$	−13.4111	+	5.36901i	−0.795804	+	0.318592i
$285$	2.92969	+	5.47121i	0.173540	+	0.324086i
$286$	10.4650	−	2.01696i	0.618808	−	0.119265i
$287$	8.83865	−	5.68026i	0.521729	−	0.335295i
$288$	1.33089	+	2.68863i	0.0784235	+	0.158429i
$289$	8.43552	+	9.73511i	0.496207	+	0.572653i
$290$	0.191633	−	0.789923i	0.0112531	−	0.0463859i
$291$	11.1053	+	16.7007i	0.651007	+	0.979013i
$292$	14.3224	+	2.76042i	0.838156	+	0.161541i
$293$	2.37106	−	0.226409i	0.138519	−	0.0132270i	−0.0255662	−	0.999673i	$-0.508139\pi$
$293$	2.37106	−	0.226409i	0.138519	−	0.0132270i	0.164085	+	0.986446i	$0.447533\pi$
$294$	−10.4829	−	7.22069i	−0.611374	−	0.421119i
$295$	−5.55906	−	0.530825i	−0.323661	−	0.0309059i
$296$	−0.610497	−	4.24610i	−0.0354844	−	0.246799i
$297$	22.0073	+	11.3659i	1.27699	+	0.659515i
$298$	19.2841			1.11710
$299$	−7.36260	+	7.79514i	−0.425790	+	0.450805i
$300$	7.83247	+	2.57454i	0.452208	+	0.148641i
$301$	0.423800	−	8.89667i	0.0244275	−	0.512795i
$302$	−3.19817	+	2.51507i	−0.184034	+	0.144726i
$303$	16.7589	+	7.33930i	0.962773	+	0.421632i
$304$	5.29462	−	5.04841i	0.303667	−	0.289546i
$305$	−1.61340	+	3.53285i	−0.0923829	+	0.202290i
$306$	−1.81057	+	5.81285i	−0.103503	+	0.332299i
$307$	1.75425	−	12.2011i	0.100120	−	0.696351i	−0.876504	−	0.481395i	$-0.840130\pi$
$307$	1.75425	−	12.2011i	0.100120	−	0.696351i	0.976624	−	0.214956i	$-0.0689607\pi$
$308$	−4.25703	+	17.5477i	−0.242567	+	0.999875i
$309$	−12.9339	+	16.9863i	−0.735782	+	0.966319i
$310$	1.06763	+	0.550403i	0.0606375	+	0.0312608i
$311$	−22.3757	−	11.5355i	−1.26881	−	0.654116i	−0.313461	−	0.949601i	$-0.601489\pi$
$311$	−22.3757	−	11.5355i	−1.26881	−	0.654116i	−0.955347	+	0.295485i	$0.904519\pi$
$312$	2.34598	−	3.08103i	0.132815	−	0.174429i
$313$	−4.09701	+	16.8881i	−0.231577	+	0.954573i	0.730743	+	0.682653i	$0.239174\pi$
$313$	−4.09701	+	16.8881i	−0.231577	+	0.954573i	−0.962320	+	0.271920i	$0.912341\pi$
$314$	−1.37142	+	9.53846i	−0.0773939	+	0.538287i
$315$	−5.42986	+	1.22361i	−0.305938	+	0.0689427i
$316$	1.35054	−	2.95726i	0.0759736	−	0.166359i
$317$	0.243516	−	0.232192i	0.0136772	−	0.0130412i	−0.683210	−	0.730222i	$-0.739416\pi$
$317$	0.243516	−	0.232192i	0.0136772	−	0.0130412i	0.696887	+	0.717181i	$0.254568\pi$
$318$	9.74323	+	4.26690i	0.546373	+	0.239276i
$319$	−6.21827	+	4.89010i	−0.348156	+	0.273793i
$320$	−0.0233052	+	0.489237i	−0.00130280	+	0.0273492i
$321$	−18.4889	−	6.07733i	−1.03195	−	0.339204i
$322$	−6.83156	−	16.8333i	−0.380708	−	0.938083i
$323$	14.8467			0.826094
$324$	8.71373	−	2.25185i	0.484096	−	0.125103i
$325$	−1.51460	−	10.5343i	−0.0840151	−	0.584338i
$326$	16.0938	+	1.53677i	0.891353	+	0.0851138i
$327$	−18.4287	−	12.6938i	−1.01911	−	0.701970i
$328$	−2.76106	+	0.263649i	−0.152454	+	0.0145576i
$329$	−5.75264	−	1.10873i	−0.317154	−	0.0611263i
$330$	2.23917	+	3.36736i	0.123262	+	0.185367i
$331$	6.07165	−	25.0277i	0.333728	−	1.37565i	−0.519661	−	0.854372i	$-0.673942\pi$
$331$	6.07165	−	25.0277i	0.333728	−	1.37565i	0.853389	−	0.521274i	$-0.174543\pi$
$332$	−5.04458	−	5.82176i	−0.276857	−	0.319510i
$333$	−12.8430	−	0.822470i	−0.703791	−	0.0450711i
$334$	−8.89049	+	5.71357i	−0.486466	+	0.312633i
$335$	−4.88491	+	0.941490i	−0.266891	+	0.0514391i
$336$	3.09719	+	5.78401i	0.168965	+	0.315544i
$337$	−25.9878	+	10.4039i	−1.41564	+	0.566738i	−0.948311	−	0.317343i	$-0.897209\pi$
$337$	−25.9878	+	10.4039i	−1.41564	+	0.566738i	−0.467333	+	0.884081i	$0.654785\pi$
$338$	7.85662	+	1.51424i	0.427344	+	0.0823637i
$339$	−14.8512	−	3.35810i	−0.806609	−	0.182387i
$340$	−0.719391	+	0.685938i	−0.0390145	+	0.0372002i
$341$	−4.85622	−	10.6336i	−0.262979	−	0.575843i
$342$	−11.5620	−	18.6546i	−0.625200	−	1.00873i
$343$	−1.11257	−	0.715004i	−0.0600730	−	0.0386066i
$344$	−1.17565	+	2.03628i	−0.0633866	+	0.109789i
$345$	−3.80707	−	1.43494i	−0.204966	−	0.0772544i
$346$	3.99992	+	6.92807i	0.215037	+	0.372455i
$347$	−0.715824	+	15.0270i	−0.0384275	+	0.806692i	0.894596	+	0.446876i	$0.147463\pi$
$347$	−0.715824	+	15.0270i	−0.0384275	+	0.806692i	−0.933023	+	0.359816i	$0.882840\pi$
$348$	−0.499829	+	2.83064i	−0.0267936	+	0.151738i
$349$	−35.3679	−	3.37722i	−1.89320	−	0.180779i	−0.917181	−	0.398471i	$-0.869541\pi$
$349$	−35.3679	−	3.37722i	−1.89320	−	0.180779i	−0.976017	+	0.217693i	$0.930147\pi$
$350$	17.3010	+	5.08003i	0.924777	+	0.271539i
$351$	−7.60146	−	8.78550i	−0.405736	−	0.468936i
$352$	3.12159	−	3.60250i	0.166381	−	0.192014i
$353$	7.42940	+	5.84254i	0.395427	+	0.310967i	0.795999	−	0.605298i	$-0.206946\pi$
$353$	7.42940	+	5.84254i	0.395427	+	0.310967i	−0.400572	+	0.916265i	$0.631189\pi$
$354$	19.7378	+	0.631363i	1.04905	+	0.0335566i
$355$	−2.31417	+	6.68635i	−0.122823	+	0.354874i
$356$	−13.2878	−	6.85035i	−0.704253	−	0.363068i
$357$	−3.55128	+	12.8329i	−0.187954	+	0.679190i
$358$	−0.117965	+	0.0227359i	−0.00623465	+	0.00120163i
$359$	−26.7193	+	7.84548i	−1.41019	+	0.414069i	−0.896170	−	0.443710i	$-0.853662\pi$
$359$	−26.7193	+	7.84548i	−1.41019	+	0.414069i	−0.514019	+	0.857779i	$0.671844\pi$
$360$	1.42210	+	0.369722i	0.0749512	+	0.0194861i
$361$	−22.6054	+	26.0880i	−1.18976	+	1.37305i
$362$	−12.8493	−	18.0443i	−0.675344	−	0.948388i
$363$	1.61399	−	20.2394i	0.0847123	−	1.06229i
$364$	4.91265	−	6.89885i	0.257493	−	0.361598i
$365$	5.61564	−	4.41619i	0.293936	−	0.231154i
$366$	4.90473	−	12.8287i	0.256374	−	0.670569i
$367$	17.1668	−	29.7337i	0.896098	−	1.55209i	0.0636579	−	0.997972i	$-0.479723\pi$
$367$	17.1668	−	29.7337i	0.896098	−	1.55209i	0.832440	−	0.554115i	$-0.186943\pi$
$368$	−0.433295	+	4.77622i	−0.0225871	+	0.248978i
$369$	−0.926291	+	8.26913i	−0.0482208	+	0.430474i
$370$	−1.76755	−	1.13593i	−0.0918904	−	0.0590544i
$371$	21.5961	+	8.64576i	1.12121	+	0.448865i
$372$	−3.89091	−	1.70397i	−0.201734	−	0.0883465i
$373$	−2.74531	−	11.3163i	−0.142147	−	0.585936i	−0.997673	−	0.0681775i	$-0.978282\pi$
$373$	−2.74531	−	11.3163i	−0.142147	−	0.585936i	0.855527	−	0.517759i	$-0.173234\pi$
$374$	9.63009	−	0.919562i	0.497960	−	0.0475494i
$375$	7.10507	−	4.25148i	0.366904	−	0.219546i
$376$	1.21570	+	0.956038i	0.0626950	+	0.0493039i
$377$	3.56013	−	1.04535i	0.183356	−	0.0538382i
$378$	18.8899	−	5.53160i	0.971591	−	0.284515i
$379$	12.6841	−	8.15160i	0.651541	−	0.418720i	−0.172688	−	0.984977i	$-0.555245\pi$
$379$	12.6841	−	8.15160i	0.651541	−	0.418720i	0.824229	+	0.566257i	$0.191609\pi$
$380$	−0.170494	−	3.57911i	−0.00874615	−	0.183604i
$381$	−8.69740	−	20.7782i	−0.445581	−	1.06450i
$382$	7.60316	+	7.24960i	0.389012	+	0.370922i
$383$	11.6156	−	4.65020i	0.593531	−	0.237614i	−0.0553963	−	0.998464i	$-0.517642\pi$
$383$	11.6156	−	4.65020i	0.593531	−	0.237614i	0.648927	+	0.760851i	$0.275218\pi$
$384$	−0.0270593	−	1.73184i	−0.00138086	−	0.0883776i
$385$	5.13004	+	7.20414i	0.261451	+	0.367157i
$386$	−3.62530	−	1.06448i	−0.184523	−	0.0541808i
$387$	5.25472	+	4.70586i	0.267112	+	0.239213i
$388$	−1.64791	−	11.4615i	−0.0836599	−	0.581868i
$389$	1.28678	−	0.663382i	0.0652424	−	0.0336348i	−0.425297	−	0.905054i	$-0.639830\pi$
$389$	1.28678	−	0.663382i	0.0652424	−	0.0336348i	0.490539	+	0.871419i	$0.336800\pi$
$390$	−0.388010	−	1.85661i	−0.0196477	−	0.0940133i
$391$	−7.32536	+	6.40835i	−0.370459	+	0.324084i
$392$	3.67456	+	6.36453i	0.185594	+	0.321457i
$393$	7.74042	−	20.2457i	0.390453	−	1.02126i
$394$	18.0221	+	7.21495i	0.907939	+	0.363484i
$395$	−0.661481	−	1.44844i	−0.0332827	−	0.0728790i
$396$	−8.65491	−	11.3839i	−0.434926	−	0.572063i
$397$	−2.40072	+	5.25685i	−0.120489	+	0.263834i	−0.960260	−	0.279107i	$-0.909962\pi$
$397$	−2.40072	+	5.25685i	−0.120489	+	0.263834i	0.839771	+	0.542940i	$0.182689\pi$
$398$	−4.70712	−	13.6003i	−0.235946	−	0.681723i
$399$	−26.5777	−	39.9687i	−1.33055	−	2.00094i
$400$	−3.44505	−	3.28485i	−0.172252	−	0.164242i
$401$	−5.39881	+	15.5988i	−0.269604	+	0.778968i	0.726203	+	0.687481i	$0.241283\pi$
$401$	−5.39881	+	15.5988i	−0.269604	+	0.778968i	−0.995806	+	0.0914877i	$0.970838\pi$
$402$	17.0297	−	4.41416i	0.849362	−	0.220158i
$403$	0.260894	+	5.47684i	0.0129961	+	0.272821i
$404$	−6.91724	−	7.98292i	−0.344145	−	0.397165i
$405$	1.96134	−	3.94774i	0.0974599	−	0.196165i
$406$	−0.894653	+	6.22245i	−0.0444009	+	0.308815i
$407$	6.68802	+	19.3238i	0.331513	+	0.957843i
$408$	2.38565	−	2.58157i	0.118107	−	0.127807i
$409$	−4.05405	−	16.7110i	−0.200460	−	0.826307i	−0.979845	−	0.199762i	$-0.935983\pi$
$409$	−4.05405	−	16.7110i	−0.200460	−	0.826307i	0.779385	−	0.626546i	$-0.215532\pi$
$410$	−0.788003	+	1.10660i	−0.0389167	+	0.0546509i
$411$	−9.47727	−	7.95631i	−0.467479	−	0.392456i
$412$	10.9561	−	5.64828i	0.539770	−	0.278271i
$413$	43.1890			2.12519
$414$	13.7566	+	4.21363i	0.676102	+	0.207089i
$415$	−3.77300			−0.185209
$416$	−1.98726	+	1.02450i	−0.0974332	+	0.0502303i
$417$	−4.68718	+	1.70470i	−0.229532	+	0.0834796i
$418$	−20.2280	+	28.4062i	−0.989383	+	1.38939i
$419$	0.739756	+	3.04932i	0.0361395	+	0.148969i	0.987023	−	0.160581i	$-0.0513368\pi$
$419$	0.739756	+	3.04932i	0.0361395	+	0.148969i	−0.950883	+	0.309550i	$0.899822\pi$
$420$	3.13442	+	0.708741i	0.152944	+	0.0345830i
$421$	−3.72950	−	10.7757i	−0.181765	−	0.525175i	0.816903	−	0.576775i	$-0.195689\pi$
$421$	−3.72950	−	10.7757i	−0.181765	−	0.525175i	−0.998668	+	0.0516002i	$0.983568\pi$
$422$	2.20066	−	15.3059i	0.107126	−	0.745081i
$423$	3.55572	−	2.98065i	0.172885	−	0.144924i
$424$	−4.02152	−	4.64108i	−0.195302	−	0.225391i
$425$	−0.459657	−	9.64938i	−0.0222966	−	0.468064i
$426$	6.67333	−	24.1147i	0.323324	−	1.16836i
$427$	9.82424	−	28.3853i	0.475428	−	1.37366i
$428$	8.13221	+	7.75405i	0.393085	+	0.374806i
$429$	−8.20126	+	16.5376i	−0.395961	+	0.798442i
$430$	0.376666	+	1.08830i	0.0181644	+	0.0524827i
$431$	−3.47922	+	7.61843i	−0.167588	+	0.366967i	−0.974729	−	0.223393i	$-0.928287\pi$
$431$	−3.47922	+	7.61843i	−0.167588	+	0.366967i	0.807140	+	0.590360i	$0.201014\pi$
$432$	−5.10153	−	0.987102i	−0.245448	−	0.0474920i
$433$	−5.64731	−	12.3659i	−0.271393	−	0.594267i	0.724037	−	0.689761i	$-0.242284\pi$
$433$	−5.64731	−	12.3659i	−0.271393	−	0.594267i	−0.995430	+	0.0954938i	$0.969557\pi$
$434$	−8.62427	−	3.45264i	−0.413978	−	0.165732i
$435$	0.887472	+	1.09293i	0.0425510	+	0.0524021i
$436$	6.45980	+	11.1887i	0.309369	+	0.535842i
$437$	−0.165882	−	35.0844i	−0.00793523	−	1.67832i
$438$	−18.8322	+	16.8405i	−0.899839	+	0.804669i
$439$	0.138093	−	0.0711921i	0.00659083	−	0.00339781i	−0.454928	−	0.890528i	$-0.650335\pi$
$439$	0.138093	−	0.0711921i	0.00659083	−	0.00339781i	0.461519	+	0.887130i	$0.347305\pi$
$440$	−0.332267	−	2.31097i	−0.0158402	−	0.110171i
$441$	20.9499	−	6.86933i	0.997616	−	0.327111i
$442$	−4.35361	−	1.27833i	−0.207080	−	0.0608042i
$443$	−20.9842	−	29.4682i	−0.996989	−	1.40008i	−0.915005	−	0.403441i	$-0.867814\pi$
$443$	−20.9842	−	29.4682i	−0.996989	−	1.40008i	−0.0819835	−	0.996634i	$-0.526125\pi$
$444$	6.49189	+	3.61406i	0.308092	+	0.171516i
$445$	−6.79773	+	2.72140i	−0.322243	+	0.129007i
$446$	1.37100	+	1.30724i	0.0649186	+	0.0618998i
$447$	−20.2345	+	26.5744i	−0.957059	+	1.25693i
$448$	−0.180241	−	3.78373i	−0.00851561	−	0.178765i
$449$	−21.1802	+	13.6117i	−0.999555	+	0.642375i	−0.934670	−	0.355518i	$-0.884305\pi$
$449$	−21.1802	+	13.6117i	−0.999555	+	0.642375i	−0.0648857	+	0.997893i	$0.520668\pi$
$450$	−11.7663	+	8.09207i	−0.554669	+	0.381464i
$451$	12.6857	−	3.72486i	0.597346	−	0.175397i
$452$	6.91006	+	5.43413i	0.325022	+	0.255600i
$453$	−0.110095	−	7.04623i	−0.00517270	−	0.331061i
$454$	9.37528	−	0.895231i	0.440004	−	0.0420152i
$455$	−0.977968	−	4.03124i	−0.0458478	−	0.188987i
$456$	1.40138	+	12.5934i	0.0656258	+	0.589741i
$457$	−7.28818	−	2.91775i	−0.340927	−	0.136486i	0.194880	−	0.980827i	$-0.437568\pi$
$457$	−7.28818	−	2.91775i	−0.340927	−	0.136486i	−0.535807	+	0.844341i	$0.679992\pi$
$458$	−14.9996	−	9.63967i	−0.700886	−	0.450432i
$459$	−6.11057	−	8.59437i	−0.285217	−	0.401151i
$460$	1.62899	+	1.69234i	0.0759519	+	0.0789056i
$461$	12.6176	−	21.8543i	0.587658	−	1.01785i	−0.406880	−	0.913482i	$-0.633383\pi$
$461$	12.6176	−	21.8543i	0.587658	−	1.01785i	0.994538	−	0.104373i	$-0.0332834\pi$
$462$	−19.7147	−	24.2789i	−0.917213	−	1.12956i
$463$	−10.5451	+	8.29278i	−0.490073	+	0.385398i	−0.832393	−	0.554185i	$-0.813030\pi$
$463$	−10.5451	+	8.29278i	−0.490073	+	0.385398i	0.342320	+	0.939584i	$0.388787\pi$
$464$	0.962636	−	1.35183i	0.0446893	−	0.0627573i
$465$	−1.87873	+	0.893718i	−0.0871240	+	0.0414452i
$466$	7.35409	+	10.3274i	0.340672	+	0.478407i
$467$	−22.8147	+	26.3296i	−1.05574	+	1.21839i	−0.0806122	+	0.996746i	$0.525688\pi$
$467$	−22.8147	+	26.3296i	−1.05574	+	1.21839i	−0.975128	+	0.221643i	$0.928858\pi$
$468$	1.78420	+	6.46574i	0.0824746	+	0.298879i
$469$	36.9165	−	10.8397i	1.70464	−	0.500529i
$470$	0.743817	−	0.143359i	0.0343097	−	0.00661265i
$471$	−11.7054	−	11.8984i	−0.539357	−	0.548250i
$472$	−10.1340	−	5.22445i	−0.466456	−	0.240475i
$473$	3.66582	−	10.5917i	0.168555	−	0.487006i
$474$	2.65815	+	4.96410i	0.122093	+	0.228009i
$475$	27.3731	+	21.5264i	1.25596	+	0.987701i
$476$	5.03427	−	5.80986i	0.230746	−	0.266295i
$477$	−16.1034	+	8.94942i	−0.737323	+	0.409766i
$478$	3.40154	+	0.998782i	0.155583	+	0.0456832i
$479$	19.7001	+	1.88113i	0.900121	+	0.0859511i	0.534847	−	0.844949i	$-0.320369\pi$
$479$	19.7001	+	1.88113i	0.900121	+	0.0859511i	0.365274	+	0.930900i	$0.380975\pi$
$480$	−0.649736	−	0.545463i	−0.0296563	−	0.0248969i
$481$	0.456360	−	9.58017i	0.0208082	−	0.436818i
$482$	10.0648	+	17.4328i	0.458440	+	0.794041i
$483$	30.3653	+	8.24869i	1.38167	+	0.375328i
$484$	−5.86116	+	10.1518i	−0.266416	+	0.461446i
$485$	−4.77113	−	3.06622i	−0.216646	−	0.139230i
$486$	−6.04001	+	14.3707i	−0.273980	+	0.651870i
$487$	−9.70343	−	21.2475i	−0.439704	−	0.962818i	−0.991652	−	0.128940i	$-0.958843\pi$
$487$	−9.70343	−	21.2475i	−0.439704	−	0.962818i	0.551948	−	0.833878i	$-0.313885\pi$
$488$	−5.73888	+	5.47201i	−0.259787	+	0.247706i
$489$	−19.0047	+	20.5655i	−0.859421	+	0.930002i
$490$	3.53449	+	0.681218i	0.159672	+	0.0307743i
$491$	−16.5979	+	6.64480i	−0.749053	+	0.299876i	−0.714602	−	0.699531i	$-0.753392\pi$
$491$	−16.5979	+	6.64480i	−0.749053	+	0.299876i	−0.0344505	+	0.999406i	$0.510968\pi$
$492$	2.53381	−	4.08150i	0.114233	−	0.184008i
$493$	3.30710	−	0.637390i	0.148944	−	0.0287066i
$494$	13.7599	−	8.84294i	0.619087	−	0.397863i
$495$	−6.98989	−	0.447635i	−0.314172	−	0.0201197i
$496$	1.60597	+	1.85339i	0.0721104	+	0.0832198i
$497$	12.9011	−	53.1790i	0.578693	−	2.38540i
$498$	13.3158	−	0.842993i	0.596696	−	0.0377754i
$499$	37.3924	+	7.20680i	1.67392	+	0.322621i	0.935927	−	0.352193i	$-0.114564\pi$
$499$	37.3924	+	7.20680i	1.67392	+	0.322621i	0.737988	+	0.674814i	$0.235776\pi$
$500$	−4.75877	+	0.454407i	−0.212819	+	0.0203217i
$501$	1.45508	−	18.2466i	0.0650080	−	0.815200i
$502$	3.45100	+	0.329531i	0.154026	+	0.0147077i
$503$	−0.332646	−	2.31361i	−0.0148320	−	0.103159i	0.981061	−	0.193701i	$-0.0620491\pi$
$503$	−0.332646	−	2.31361i	−0.0148320	−	0.103159i	−0.995893	+	0.0905422i	$0.971140\pi$
$504$	−11.2205	−	1.80100i	−0.499799	−	0.0802229i
$505$	−5.17363			−0.230223
$506$	−2.28062	−	22.7467i	−0.101386	−	1.01121i
$507$	−10.3305	+	9.23791i	−0.458793	+	0.410270i
$508$	−0.618796	+	12.9901i	−0.0274546	+	0.576344i
$509$	10.1591	−	7.98924i	0.450296	−	0.354117i	−0.367111	−	0.930177i	$-0.619653\pi$
$509$	10.1591	−	7.98924i	0.450296	−	0.354117i	0.817407	+	0.576060i	$0.195411\pi$
$510$	−0.190409	−	1.71110i	−0.00843146	−	0.0757686i
$511$	−39.9879	+	38.1283i	−1.76896	+	1.68670i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	37.8387	+	3.64103i	1.67062	+	0.160755i
$514$	−1.57380	+	10.9460i	−0.0694173	+	0.482808i
$515$	1.42336	−	5.86718i	0.0627209	−	0.258539i
$516$	−1.57250	−	3.75672i	−0.0692254	−	0.165381i
$517$	−6.55273	−	3.37817i	−0.288189	−	0.148572i
$518$	14.4433	+	7.44605i	0.634603	+	0.327161i
$519$	−13.7442	−	1.75743i	−0.603305	−	0.0771424i
$520$	−0.258174	+	1.06421i	−0.0113217	+	0.0466685i
$521$	−2.38601	+	16.5951i	−0.104533	+	0.727044i	0.868384	+	0.495892i	$0.165159\pi$
$521$	−2.38601	+	16.5951i	−0.104533	+	0.727044i	−0.972918	+	0.231152i	$0.925750\pi$
$522$	−3.37629	−	3.65893i	−0.147776	−	0.160147i
$523$	8.84904	−	19.3767i	0.386942	−	0.847284i	−0.611488	−	0.791254i	$-0.709429\pi$
$523$	8.84904	−	19.3767i	0.386942	−	0.847284i	0.998429	−	0.0560297i	$-0.0178442\pi$
$524$	−9.05684	+	8.63568i	−0.395650	+	0.377252i
$525$	−25.1541	+	18.5112i	−1.09782	+	0.807893i
$526$	−15.5866	+	12.2575i	−0.679610	+	0.534451i
$527$	−0.236814	+	4.97133i	−0.0103158	+	0.216554i
$528$	1.68898	+	8.08172i	0.0735036	+	0.351712i
$529$	15.2255	+	17.2390i	0.661978	+	0.749523i
$530$	−3.00783			−0.130652
$531$	−21.5806	+	26.5371i	−0.936518	+	1.15161i
$532$	3.94383	+	27.4300i	0.170987	+	1.18924i
$533$	−6.17316	−	0.589466i	−0.267389	−	0.0255326i
$534$	23.3828	−	11.1233i	1.01187	−	0.481351i
$535$	5.47860	−	0.523143i	0.236861	−	0.0226175i
$536$	−9.97345	−	1.92223i	−0.430787	−	0.0830275i
$537$	0.0924475	−	0.186417i	0.00398940	−	0.00804451i
$538$	5.88928	−	24.2759i	0.253905	−	1.04661i
$539$	−22.9409	−	26.4753i	−0.988136	−	1.14037i
$540$	−2.00168	+	1.57177i	−0.0861385	+	0.0676384i
$541$	11.7301	−	7.53849i	0.504317	−	0.324105i	−0.263624	−	0.964626i	$-0.584918\pi$
$541$	11.7301	−	7.53849i	0.504317	−	0.324105i	0.767941	+	0.640521i	$0.221281\pi$
$542$	−26.9179	+	5.18801i	−1.15622	+	0.222844i
$543$	38.3484	+	1.22667i	1.64569	+	0.0526413i
$544$	−1.88406	+	0.754265i	−0.0807785	+	0.0323388i
$545$	6.21356	+	1.19757i	0.266160	+	0.0512981i
$546$	4.35217	+	14.0087i	0.186256	+	0.599517i
$547$	−28.2575	+	26.9434i	−1.20820	+	1.15202i	−0.224071	+	0.974573i	$0.571935\pi$
$547$	−28.2575	+	26.9434i	−1.20820	+	1.15202i	−0.984131	+	0.177445i	$0.943217\pi$
$548$	2.96783	+	6.49865i	0.126780	+	0.277609i
$549$	12.5321	+	20.2199i	0.534858	+	0.862964i
$550$	19.0884	+	12.2674i	0.813932	+	0.523083i
$551$	−6.07040	+	10.5142i	−0.258608	+	0.447922i
$552$	−6.12719	−	5.60870i	−0.260791	−	0.238722i
$553$	6.15754	+	10.6652i	0.261845	+	0.453529i
$554$	1.05669	−	22.1827i	0.0448945	−	0.942452i
$555$	3.42002	−	1.24384i	0.145172	−	0.0527983i
$556$	2.86652	+	0.273720i	0.121568	+	0.0116083i
$557$	−13.2782	−	3.89884i	−0.562616	−	0.165199i	−0.0119559	−	0.999929i	$-0.503806\pi$
$557$	−13.2782	−	3.89884i	−0.562616	−	0.165199i	−0.550660	+	0.834730i	$0.685624\pi$
$558$	6.43080	−	3.57390i	0.272237	−	0.151295i
$559$	−3.44261	+	3.97299i	−0.145607	+	0.168039i
$560$	−1.45840	−	1.14690i	−0.0616285	−	0.0484652i
$561$	−8.83748	+	14.2356i	−0.373119	+	0.601026i
$562$	3.68749	−	10.6543i	0.155547	−	0.449424i
$563$	10.8456	+	5.59130i	0.457088	+	0.235645i	0.671364	−	0.741128i	$-0.265709\pi$
$563$	10.8456	+	5.59130i	0.457088	+	0.235645i	−0.214276	+	0.976773i	$0.568739\pi$
$564$	−2.59308	+	0.672137i	−0.109188	+	0.0283021i
$565$	4.22786	−	0.814854i	0.177868	−	0.0342812i
$566$	−24.3722	+	7.15632i	−1.02444	+	0.300802i
$567$	−12.1980	+	31.8353i	−0.512269	+	1.33696i
$568$	−9.46007	+	10.9175i	−0.396936	+	0.458088i
$569$	15.9360	+	22.3790i	0.668072	+	0.938176i	0.999987	−	0.00513312i	$-0.00163393\pi$
$569$	15.9360	+	22.3790i	0.668072	+	0.938176i	−0.331914	+	0.943309i	$0.607695\pi$
$570$	5.11106	+	3.52054i	0.214079	+	0.147459i
$571$	−23.3219	+	32.7510i	−0.975990	+	1.37059i	−0.0476452	+	0.998864i	$0.515172\pi$
$571$	−23.3219	+	32.7510i	−0.975990	+	1.37059i	−0.928344	+	0.371721i	$0.878768\pi$
$572$	8.37743	−	6.58808i	0.350278	−	0.275461i
$573$	−17.9681	+	2.87062i	−0.750630	+	0.119922i
$574$	5.25326	−	9.09892i	0.219267	−	0.379781i
$575$	−22.7974	+	1.19403i	−0.950718	+	0.0497946i
$576$	2.41494	+	1.77990i	0.100623	+	0.0741625i
$577$	−9.42218	−	6.05526i	−0.392250	−	0.252084i	0.329618	−	0.944114i	$-0.393080\pi$
$577$	−9.42218	−	6.05526i	−0.392250	−	0.252084i	−0.721868	+	0.692030i	$0.756716\pi$
$578$	11.9587	+	4.78753i	0.497415	+	0.199135i
$579$	5.27087	−	3.87888i	0.219050	−	0.161201i
$580$	−0.191633	−	0.789923i	−0.00795714	−	0.0327998i
$581$	29.0481	−	2.77376i	1.20512	−	0.115075i
$582$	17.5235	+	9.75542i	0.726374	+	0.404375i
$583$	23.0102	+	18.0954i	0.952984	+	0.749435i
$584$	13.9952	−	4.10935i	0.579124	−	0.170046i
$585$	2.96563	+	1.41342i	0.122614	+	0.0584375i
$586$	2.00374	−	1.28773i	0.0827737	−	0.0531954i
$587$	0.734102	+	15.4107i	0.0302996	+	0.636068i	0.962034	+	0.272928i	$0.0879921\pi$
$587$	0.734102	+	15.4107i	0.0302996	+	0.636068i	−0.931735	+	0.363139i	$0.881705\pi$
$588$	−12.6263	−	1.61448i	−0.520698	−	0.0665799i
$589$	−12.9845	−	12.3807i	−0.535016	−	0.510136i
$590$	−5.18432	+	2.07549i	−0.213435	+	0.0854466i
$591$	−28.8528	+	17.2647i	−1.18684	+	0.710175i
$592$	−2.48831	−	3.49434i	−0.102269	−	0.143616i
$593$	−19.0298	−	5.58767i	−0.781462	−	0.229458i	−0.133417	−	0.991060i	$-0.542595\pi$
$593$	−19.0298	−	5.58767i	−0.781462	−	0.229458i	−0.648045	+	0.761602i	$0.724413\pi$
$594$	24.7690	+	0.0180784i	1.01628	+	0.000741764i
$595$	−0.535857	−	3.72697i	−0.0219680	−	0.152791i
$596$	17.1404	−	8.83651i	0.702099	−	0.361957i
$597$	23.6809	+	7.78396i	0.969197	+	0.318576i
$598$	−2.97220	+	10.3023i	−0.121542	+	0.421294i
$599$	−11.0515	−	19.1417i	−0.451551	−	0.782109i	0.546932	−	0.837177i	$-0.315796\pi$
$599$	−11.0515	−	19.1417i	−0.451551	−	0.782109i	−0.998483	+	0.0550681i	$0.982462\pi$
$600$	8.14150	−	1.30070i	0.332375	−	0.0531009i
$601$	−8.19642	−	3.28135i	−0.334339	−	0.133849i	0.198418	−	0.980118i	$-0.436420\pi$
$601$	−8.19642	−	3.28135i	−0.334339	−	0.133849i	−0.532757	+	0.846268i	$0.678844\pi$
$602$	−3.70000	−	8.10187i	−0.150801	−	0.330208i
$603$	−11.7860	+	28.0993i	−0.479963	+	1.14429i
$604$	−1.69017	+	3.70097i	−0.0687722	+	0.150590i
$605$	1.87786	+	5.42571i	0.0763458	+	0.220587i
$606$	18.2590	−	1.15593i	0.741719	−	0.0469565i
$607$	−6.84169	−	6.52354i	−0.277696	−	0.264782i	0.538413	−	0.842681i	$-0.319024\pi$
$607$	−6.84169	−	6.52354i	−0.277696	−	0.264782i	−0.816108	+	0.577899i	$0.803873\pi$
$608$	2.39273	−	6.91334i	0.0970380	−	0.280373i
$609$	−7.63607	−	7.76198i	−0.309429	−	0.314531i
$610$	0.184800	+	3.87942i	0.00748232	+	0.157073i
$611$	2.26442	+	2.61328i	0.0916085	+	0.105722i
$612$	1.05431	+	5.99632i	0.0426178	+	0.242387i
$613$	−3.93843	+	27.3924i	−0.159072	+	1.10637i	0.741278	+	0.671198i	$0.234220\pi$
$613$	−3.93843	+	27.3924i	−0.159072	+	1.10637i	−0.900349	+	0.435168i	$0.856689\pi$
$614$	−4.03161	−	11.6486i	−0.162703	−	0.470098i
$615$	−0.698101	−	2.24704i	−0.0281501	−	0.0906092i
$616$	4.25703	+	17.5477i	0.171521	+	0.707018i
$617$	21.4419	−	30.1109i	0.863219	−	1.21222i	−0.112600	−	0.993640i	$-0.535918\pi$
$617$	21.4419	−	30.1109i	0.863219	−	1.21222i	0.975819	−	0.218581i	$-0.0701427\pi$
$618$	−3.71250	+	21.0247i	−0.149338	+	0.845737i
$619$	29.8133	−	15.3698i	1.19830	−	0.617766i	0.260678	−	0.965426i	$-0.416054\pi$
$619$	29.8133	−	15.3698i	1.19830	−	0.617766i	0.937621	+	0.347660i	$0.113024\pi$
$620$	1.20116			0.0482397
$621$	−20.2412	+	14.5360i	−0.812250	+	0.583309i
$622$	−25.1742			−1.00939
$623$	50.3346	−	25.9493i	2.01661	−	1.03964i
$624$	0.673383	−	3.81352i	0.0269569	−	0.152663i
$625$	12.4475	−	17.4801i	0.497900	−	0.699203i
$626$	4.09701	+	16.8881i	0.163750	+	0.674985i
$627$	−17.9202	−	57.6812i	−0.715663	−	2.30356i
$628$	3.15181	+	9.10655i	0.125771	+	0.363391i
$629$	1.23896	−	8.61718i	0.0494007	−	0.343589i
$630$	−4.26556	+	3.57570i	−0.169944	+	0.142459i
$631$	−6.47491	−	7.47244i	−0.257762	−	0.297473i	0.612088	−	0.790790i	$-0.290330\pi$
$631$	−6.47491	−	7.47244i	−0.257762	−	0.297473i	−0.869850	+	0.493317i	$0.835784\pi$
$632$	−0.154691	−	3.24737i	−0.00615329	−	0.129173i
$633$	18.7831	+	19.0928i	0.746563	+	0.758872i
$634$	0.110049	−	0.317966i	0.00437060	−	0.0126280i
$635$	4.60995	+	4.39557i	0.182940	+	0.174433i
$636$	10.6153	−	0.672031i	0.420925	−	0.0266478i
$637$	5.37411	+	15.5275i	0.212930	+	0.615221i
$638$	−3.28625	+	7.19588i	−0.130104	+	0.284887i
$639$	26.2290	+	34.4993i	1.03760	+	1.36477i
$640$	0.203467	+	0.445530i	0.00804273	+	0.0176111i
$641$	8.32889	+	3.33439i	0.328972	+	0.131700i	0.530268	−	0.847830i	$-0.322091\pi$
$641$	8.32889	+	3.33439i	0.328972	+	0.131700i	−0.201297	+	0.979530i	$0.564515\pi$
$642$	−19.2184	+	3.07037i	−0.758490	+	0.121178i
$643$	7.66733	+	13.2802i	0.302370	+	0.523720i	0.976672	−	0.214735i	$-0.0688888\pi$
$643$	7.66733	+	13.2802i	0.302370	+	0.523720i	−0.674302	+	0.738455i	$0.735556\pi$
$644$	−13.7856	−	11.8316i	−0.543228	−	0.466232i
$645$	−1.89496	−	0.622876i	−0.0746140	−	0.0245257i
$646$	13.1963	−	6.80316i	0.519201	−	0.267667i
$647$	4.00494	+	27.8550i	0.157451	+	1.09509i	0.903310	+	0.428989i	$0.141130\pi$
$647$	4.00494	+	27.8550i	0.157451	+	1.09509i	−0.745859	+	0.666104i	$0.767961\pi$
$648$	6.71322	−	5.99439i	0.263720	−	0.235482i
$649$	52.1469	+	15.3117i	2.04695	+	0.601038i
$650$	−6.17333	−	8.66923i	−0.242138	−	0.340035i
$651$	13.8072	−	8.26184i	0.541146	−	0.323807i
$652$	15.0089	−	6.00866i	0.587795	−	0.235317i
$653$	7.11892	+	6.78788i	0.278585	+	0.265630i	0.816470	−	0.577388i	$-0.195928\pi$
$653$	7.11892	+	6.78788i	0.278585	+	0.265630i	−0.537885	+	0.843018i	$0.680777\pi$
$654$	−22.1967	−	2.83821i	−0.867960	−	0.110983i
$655$	0.291643	+	6.12233i	0.0113954	+	0.239219i
$656$	−2.33331	+	1.49953i	−0.0911006	+	0.0585468i
$657$	−3.44660	−	43.6221i	−0.134464	−	1.70186i
$658$	−5.62120	+	1.65053i	−0.219137	+	0.0643445i
$659$	9.89532	+	7.78177i	0.385467	+	0.303135i	0.792023	−	0.610491i	$-0.209028\pi$
$659$	9.89532	+	7.78177i	0.385467	+	0.303135i	−0.406556	+	0.913626i	$0.633270\pi$
$660$	3.53326	+	1.96698i	0.137532	+	0.0765646i
$661$	−9.41481	+	0.899006i	−0.366194	+	0.0349673i	−0.276531	−	0.961005i	$-0.589185\pi$
$661$	−9.41481	+	0.899006i	−0.366194	+	0.0349673i	−0.0896626	+	0.995972i	$0.528579\pi$
$662$	−6.07165	−	25.0277i	−0.235981	−	0.972729i
$663$	6.32976	−	4.65813i	0.245828	−	0.180907i
$664$	−7.15148	−	2.86302i	−0.277531	−	0.111107i
$665$	11.4184	+	7.33818i	0.442788	+	0.284562i
$666$	−11.7922	+	5.15395i	−0.456937	+	0.199712i
$667$	−1.54317	−	7.80791i	−0.0597519	−	0.302323i
$668$	−5.28407	+	9.15229i	−0.204447	+	0.354113i
$669$	−3.24000	+	0.517629i	−0.125266	+	0.0200127i
$670$	−3.91047	+	3.07523i	−0.151075	+	0.118806i
$671$	21.9253	−	30.7897i	0.846416	−	1.18862i
$672$	5.40328	+	3.72182i	0.208436	+	0.143572i
$673$	−28.3599	−	39.8259i	−1.09319	−	1.53518i	−0.819256	−	0.573429i	$-0.805613\pi$
$673$	−28.3599	−	39.8259i	−1.09319	−	1.53518i	−0.273938	−	0.961747i	$-0.588326\pi$
$674$	−18.3315	+	21.1557i	−0.706103	+	0.814886i
$675$	1.19493	−	24.7053i	0.0459930	−	0.950909i
$676$	7.67710	−	2.25420i	0.295273	−	0.0867001i
$677$	6.56478	−	1.26526i	0.252305	−	0.0486278i	−0.0615304	−	0.998105i	$-0.519598\pi$
$677$	6.56478	−	1.26526i	0.252305	−	0.0486278i	0.313835	+	0.949477i	$0.398386\pi$
$678$	−14.7391	+	3.82043i	−0.566051	+	0.146723i
$679$	38.9868	+	20.0991i	1.49618	+	0.771332i
$680$	−0.325105	+	0.939331i	−0.0124672	+	0.0360217i
$681$	−8.60364	+	13.8589i	−0.329692	+	0.531074i
$682$	−9.18899	−	7.22630i	−0.351865	−	0.276709i
$683$	−29.4340	+	33.9687i	−1.12626	+	1.29978i	−0.177382	+	0.984142i	$0.556763\pi$
$683$	−29.4340	+	33.9687i	−1.12626	+	1.29978i	−0.948881	+	0.315634i	$0.897783\pi$
$684$	−18.8247	−	11.2829i	−0.719782	−	0.431412i
$685$	3.35746	+	0.985839i	0.128282	+	0.0376670i
$686$	−1.31652	−	0.125713i	−0.0502651	−	0.00479974i
$687$	29.0227	−	10.5554i	1.10729	−	0.402714i
$688$	−0.111879	+	2.34863i	−0.00426535	+	0.0895407i
$689$	−6.86506	−	11.8906i	−0.261538	−	0.452997i
$690$	−4.04138	+	0.469076i	−0.153853	+	0.0178574i
$691$	−11.0380	+	19.1183i	−0.419904	+	0.727295i	−0.995929	−	0.0901370i	$-0.971270\pi$
$691$	−11.0380	+	19.1183i	−0.419904	+	0.727295i	0.576026	+	0.817432i	$0.304603\pi$
$692$	6.72990	+	4.32504i	0.255832	+	0.164413i
$693$	54.1437	−	1.69236i	2.05675	−	0.0642875i
$694$	6.24952	+	13.6845i	0.237229	+	0.519458i
$695$	1.02074	−	0.973277i	0.0387190	−	0.0369185i
$696$	0.852810	+	2.74501i	0.0323257	+	0.104049i
$697$	−5.52715	−	1.06527i	−0.209356	−	0.0403500i
$698$	−32.9837	+	13.2047i	−1.24845	+	0.499805i
$699$	−21.9481	−	0.702064i	−0.830154	−	0.0265545i
$700$	17.7055	−	3.41246i	0.669207	−	0.128979i
$701$	−6.32357	+	4.06391i	−0.238838	+	0.153492i	−0.654585	−	0.755989i	$-0.727157\pi$
$701$	−6.32357	+	4.06391i	−0.238838	+	0.153492i	0.415747	+	0.909480i	$0.363520\pi$
$702$	−10.7822	−	4.32568i	−0.406948	−	0.163262i
$703$	20.5512	+	23.7174i	0.775104	+	0.894517i
$704$	1.12381	−	4.63242i	0.0423553	−	0.174591i
$705$	−0.582919	+	1.17544i	−0.0219540	+	0.0442695i
$706$	9.28072	+	1.78871i	0.349284	+	0.0673191i
$707$	39.8314	−	3.80344i	1.49801	−	0.143043i
$708$	17.8330	−	8.48322i	0.670205	−	0.318819i
$709$	15.6815	+	1.49740i	0.588930	+	0.0562360i	0.385267	−	0.922805i	$-0.374109\pi$
$709$	15.6815	+	1.49740i	0.588930	+	0.0562360i	0.203663	+	0.979041i	$0.434715\pi$
$710$	1.00695	+	7.00347i	0.0377901	+	0.262836i
$711$	−9.62990	−	1.54570i	−0.361149	−	0.0579682i
$712$	−14.9497			−0.560263
$713$	11.7504	+	0.504072i	0.440058	+	0.0188776i
$714$	2.72388	+	13.0336i	0.101938	+	0.487772i
$715$	0.248377	−	5.21408i	0.00928878	−	0.194996i
$716$	−0.0944333	+	0.0742632i	−0.00352914	+	0.00277535i
$717$	−4.94554	+	3.63947i	−0.184695	+	0.135918i
$718$	−20.1540	+	19.2168i	−0.752141	+	0.717165i
$719$	13.9866	−	30.6263i	0.521611	−	1.14217i	−0.447215	−	0.894426i	$-0.647584\pi$
$719$	13.9866	−	30.6263i	0.521611	−	1.14217i	0.968826	−	0.247742i	$-0.0796884\pi$
$720$	1.43343	−	0.323021i	0.0534207	−	0.0120383i
$721$	−6.64507	+	46.2174i	−0.247475	+	1.72123i
$722$	−8.13825	+	33.5463i	−0.302874	+	1.24846i
$723$	−34.5840	−	4.42213i	−1.28619	−	0.164461i
$724$	−19.6893	−	10.1505i	−0.731747	−	0.377242i
$725$	7.02149	+	3.61983i	0.260772	+	0.134437i
$726$	−7.83966	−	18.7291i	−0.290957	−	0.695101i
$727$	2.60790	−	10.7499i	0.0967218	−	0.398693i	−0.902785	−	0.430092i	$-0.858481\pi$
$727$	2.60790	−	10.7499i	0.0967218	−	0.398693i	0.999507	+	0.0313991i	$0.00999629\pi$
$728$	1.20530	−	8.38305i	0.0446714	−	0.310697i
$729$	−13.4659	−	23.4024i	−0.498735	−	0.866754i
$730$	2.96777	−	6.49850i	0.109842	−	0.240520i
$731$	−3.45351	+	3.29292i	−0.127733	+	0.121793i
$732$	−1.51897	−	13.6501i	−0.0561428	−	0.504523i
$733$	28.9613	−	22.7754i	1.06971	−	0.841230i	0.0818619	−	0.996644i	$-0.473913\pi$
$733$	28.9613	−	22.7754i	1.06971	−	0.841230i	0.987850	+	0.155413i	$0.0496709\pi$
$734$	1.63366	−	34.2946i	0.0602993	−	1.26584i
$735$	−4.64743	+	4.15590i	−0.171423	+	0.153293i
$736$	1.80346	+	4.44382i	0.0664765	+	0.163801i
$737$	48.4163			1.78344
$738$	2.96581	+	7.77435i	0.109173	+	0.286178i
$739$	2.17705	+	15.1417i	0.0800842	+	0.556998i	0.989876	+	0.141934i	$0.0453319\pi$
$739$	2.17705	+	15.1417i	0.0800842	+	0.556998i	−0.909792	+	0.415065i	$0.863759\pi$
$740$	−2.09157	−	0.199721i	−0.0768878	−	0.00734190i
$741$	−2.25203	+	28.2405i	−0.0827305	+	1.03744i
$742$	23.1571	−	2.21123i	0.850122	−	0.0811768i
$743$	−37.3778	−	7.20399i	−1.37126	−	0.264289i	−0.550153	−	0.835064i	$-0.685431\pi$
$743$	−37.3778	−	7.20399i	−1.37126	−	0.264289i	−0.821106	+	0.570775i	$0.806643\pi$
$744$	−4.23918	+	0.268372i	−0.155416	+	0.00983900i
$745$	2.22679	−	9.17896i	0.0815834	−	0.336291i
$746$	−7.62556	−	8.80037i	−0.279192	−	0.322204i
$747$	−12.8104	+	19.2343i	−0.468707	+	0.703748i
$748$	8.13820	−	5.23010i	0.297562	−	0.191231i
$749$	−41.7948	+	8.05529i	−1.52715	+	0.294334i
$750$	4.36710	−	7.03460i	0.159464	−	0.256867i
$751$	−33.0055	+	13.2134i	−1.20439	+	0.482164i	−0.885059	−	0.465480i	$-0.845882\pi$
$751$	−33.0055	+	13.2134i	−1.20439	+	0.482164i	−0.319329	+	0.947644i	$0.603458\pi$
$752$	1.51864	+	0.292694i	0.0553791	+	0.0106734i
$753$	−4.07518	+	4.40987i	−0.148508	+	0.160704i
$754$	2.68536	−	2.56049i	0.0977952	−	0.0932475i
$755$	0.827833	+	1.81270i	0.0301279	+	0.0659710i
$756$	14.2553	−	13.5725i	0.518459	−	0.493628i
$757$	10.7245	+	6.89222i	0.389789	+	0.250502i	0.720827	−	0.693115i	$-0.243762\pi$
$757$	10.7245	+	6.89222i	0.389789	+	0.250502i	−0.331038	+	0.943618i	$0.607399\pi$
$758$	7.53884	−	13.0576i	0.273823	−	0.474275i
$759$	33.7390	+	20.7249i	1.22465	+	0.752266i
$760$	−1.79158	−	3.10311i	−0.0649875	−	0.112562i
$761$	−0.931718	+	19.5592i	−0.0337748	+	0.709020i	0.916953	+	0.398994i	$0.130641\pi$
$761$	−0.931718	+	19.5592i	−0.0337748	+	0.709020i	−0.950728	+	0.310025i	$0.899662\pi$
$762$	−17.2517	−	14.4830i	−0.624962	−	0.524665i
$763$	−48.7182	−	4.65202i	−1.76372	−	0.168415i
$764$	10.0799	+	2.95973i	0.364679	+	0.107079i
$765$	2.55776	+	1.53303i	0.0924760	+	0.0554268i
$766$	8.19354	−	9.45585i	0.296045	−	0.341654i
$767$	−20.0376	−	15.7577i	−0.723515	−	0.568978i
$768$	−0.817626	−	1.52692i	−0.0295035	−	0.0550980i
$769$	3.82346	−	11.0472i	0.137878	−	0.398371i	−0.854832	−	0.518906i	$-0.826340\pi$
$769$	3.82346	−	11.0472i	0.137878	−	0.398371i	0.992709	+	0.120535i	$0.0384609\pi$
$770$	7.86089	+	4.05257i	0.283287	+	0.146044i
$771$	−13.4327	−	13.6542i	−0.483768	−	0.491745i
$772$	−3.71007	+	0.715058i	−0.133528	+	0.0257355i
$773$	−6.59625	+	1.93683i	−0.237251	+	0.0696630i	−0.398196	−	0.917300i	$-0.630364\pi$
$773$	−6.59625	+	1.93683i	−0.237251	+	0.0696630i	0.160946	+	0.986963i	$0.448546\pi$
$774$	6.82693	+	1.77489i	0.245389	+	0.0637971i
$775$	−7.64460	+	8.82234i	−0.274602	+	0.316908i
$776$	−6.71667	−	9.43224i	−0.241114	−	0.338598i
$777$	−25.4161	+	12.0905i	−0.911798	+	0.433746i
$778$	0.839758	−	1.17927i	0.0301068	−	0.0422790i
$779$	15.9497	−	12.5430i	0.571459	−	0.449400i
$780$	−1.19563	−	1.47243i	−0.0428103	−	0.0527214i
$781$	34.4304	−	59.6352i	1.23202	−	2.13391i
$782$	−3.57456	+	9.05265i	−0.127826	+	0.323722i
$783$	8.58485	−	0.813431i	0.306798	−	0.0290697i
$784$	6.18248	+	3.97324i	0.220803	+	0.141901i
$785$	4.38180	+	1.75421i	0.156393	+	0.0626104i
$786$	−2.39717	−	21.5420i	−0.0855043	−	0.768378i
$787$	6.20750	+	25.5877i	0.221274	+	0.912102i	0.968795	+	0.247864i	$0.0797287\pi$
$787$	6.20750	+	25.5877i	0.221274	+	0.912102i	−0.747521	+	0.664238i	$0.768756\pi$
$788$	19.3247	−	1.84529i	0.688415	−	0.0657357i
$789$	−0.536559	−	34.3406i	−0.0191020	−	1.22256i
$790$	−1.25166	−	0.984318i	−0.0445322	−	0.0350205i
$791$	−31.9510	+	9.38166i	−1.13605	+	0.333573i
$792$	−12.9092	−	6.15251i	−0.458708	−	0.218620i
$793$	−14.9145	+	9.58494i	−0.529628	+	0.340371i
$794$	0.274981	+	5.77255i	0.00975869	+	0.204860i
$795$	3.15606	−	4.14492i	0.111934	−	0.147005i
$796$	−10.4159	−	9.93152i	−0.369181	−	0.352013i
$797$	34.0240	−	13.6211i	1.20519	−	0.482485i	0.319867	−	0.947462i	$-0.396362\pi$
$797$	34.0240	−	13.6211i	1.20519	−	0.482485i	0.885323	+	0.464977i	$0.153937\pi$
$798$	−41.9379	−	23.3470i	−1.48459	−	0.826474i
$799$	1.82062	+	2.55671i	0.0644091	+	0.0904499i
$800$	−4.56729	−	1.34108i	−0.161478	−	0.0474142i
$801$	−9.20675	+	43.8939i	−0.325304	+	1.55092i
$802$	2.34915	+	16.3387i	0.0829512	+	0.576939i
$803$	−61.7994	+	31.8598i	−2.18085	+	1.12431i
$804$	13.1139	−	11.7269i	0.462491	−	0.413576i
$805$	−8.80126	+	1.30793i	−0.310204	+	0.0460985i
$806$	2.74152	+	4.74846i	0.0965661	+	0.167257i
$807$	27.2738	+	33.5880i	0.960083	+	1.18235i
$808$	−9.80627	−	3.92584i	−0.344983	−	0.138111i
$809$	13.5375	+	29.6429i	0.475953	+	1.04219i	0.983557	+	0.180600i	$0.0578040\pi$
$809$	13.5375	+	29.6429i	0.475953	+	1.04219i	−0.507604	+	0.861590i	$0.669469\pi$
$810$	−0.0656498	−	4.40763i	−0.00230670	−	0.154869i
$811$	12.8643	−	28.1688i	0.451725	−	0.989141i	−0.537571	−	0.843219i	$-0.680658\pi$
$811$	12.8643	−	28.1688i	0.451725	−	0.989141i	0.989296	−	0.145922i	$-0.0466148\pi$
$812$	2.05609	+	5.94069i	0.0721547	+	0.208477i
$813$	21.0952	−	42.5378i	0.739841	−	1.49187i
$814$	14.7992	+	14.1110i	0.518712	+	0.494591i
$815$	2.58987	−	7.48295i	0.0907193	−	0.262116i
$816$	0.937502	−	3.38776i	0.0328191	−	0.118595i
$817$	−0.818473	−	17.1819i	−0.0286347	−	0.601117i
$818$	−11.2608	−	12.9957i	−0.393725	−	0.454383i
$819$	−23.8713	−	8.70158i	−0.834129	−	0.304058i
$820$	−0.193334	+	1.34467i	−0.00675151	+	0.0469578i
$821$	−18.0544	−	52.1648i	−0.630103	−	1.82056i	−0.568851	−	0.822441i	$-0.692612\pi$
$821$	−18.0544	−	52.1648i	−0.630103	−	1.82056i	−0.0612520	−	0.998122i	$-0.519509\pi$
$822$	−12.0695	−	2.72911i	−0.420973	−	0.0951886i
$823$	9.57667	+	39.4756i	0.333822	+	1.37603i	0.853243	+	0.521513i	$0.174632\pi$
$823$	9.57667	+	39.4756i	0.333822	+	1.37603i	−0.519422	+	0.854518i	$0.673853\pi$
$824$	7.15001	−	10.0408i	0.249083	−	0.349787i
$825$	−36.9341	+	13.4327i	−1.28588	+	0.467668i
$826$	38.3879	−	19.7904i	1.33569	−	0.688595i
$827$	26.0506			0.905869			0.452935	−	0.891544i	$-0.350377\pi$
$827$	26.0506			0.905869			0.452935	+	0.891544i	$0.350377\pi$
$828$	14.1582	−	2.55844i	0.492031	−	0.0889118i
$829$	−17.7871			−0.617772			−0.308886	−	0.951099i	$-0.599956\pi$
$829$	−17.7871			−0.617772			−0.308886	+	0.951099i	$0.599956\pi$
$830$	−3.35358	+	1.72889i	−0.116404	+	0.0600107i
$831$	29.4600	+	24.7321i	1.02196	+	0.857946i
$832$	−1.29689	+	1.82123i	−0.0449616	+	0.0631397i
$833$	3.51624	+	14.4942i	0.121831	+	0.502193i
$834$	−3.38499	+	3.66299i	−0.117213	+	0.126839i
$835$	1.69297	+	4.89150i	0.0585875	+	0.169277i
$836$	−4.96286	+	34.5174i	−0.171644	+	1.19381i
$837$	−1.82272	+	12.6120i	−0.0630025	+	0.435933i
$838$	2.05480	+	2.37137i	0.0709819	+	0.0819175i
$839$	−2.33966	−	49.1154i	−0.0807739	−	1.69565i	−0.568521	−	0.822669i	$-0.692484\pi$
$839$	−2.33966	−	49.1154i	−0.0807739	−	1.69565i	0.487747	−	0.872985i	$-0.337819\pi$
$840$	3.11075	−	0.806319i	0.107331	−	0.0278207i
$841$	8.58419	−	24.8024i	0.296006	−	0.855254i
$842$	−8.25262	−	7.86886i	−0.284404	−	0.271179i
$843$	10.8129	+	16.2609i	0.372415	+	0.560054i
$844$	−5.05756	−	14.6129i	−0.174088	−	0.502995i
$845$	1.62798	−	3.56478i	0.0560042	−	0.122632i
$846$	1.79463	−	4.27863i	0.0617007	−	0.147102i
$847$	−18.4463	−	40.3917i	−0.633821	−	1.38787i
$848$	−5.70114	−	2.28239i	−0.195778	−	0.0783777i
$849$	15.7116	−	41.0949i	0.539219	−	1.41037i
$850$	−4.83016	−	8.36608i	−0.165673	−	0.286954i
$851$	−20.3772	−	2.83153i	−0.698521	−	0.0970635i
$852$	−5.11853	−	24.4919i	−0.175358	−	0.839080i
$853$	−13.4666	+	6.94253i	−0.461089	+	0.237708i	−0.673088	−	0.739562i	$-0.735033\pi$
$853$	−13.4666	+	6.94253i	−0.461089	+	0.237708i	0.212000	+	0.977270i	$0.432002\pi$
$854$	−4.27475	−	29.7316i	−0.146279	−	1.01739i
$855$	−10.2144	+	3.34923i	−0.349326	+	0.114541i
$856$	10.7813	+	3.16568i	0.368497	+	0.108201i
$857$	3.39578	+	4.76871i	0.115998	+	0.162896i	0.868493	−	0.495702i	$-0.165089\pi$
$857$	3.39578	+	4.76871i	0.115998	+	0.162896i	−0.752495	+	0.658598i	$0.771150\pi$
$858$	0.288387	+	18.4572i	0.00984537	+	0.630119i
$859$	4.73171	−	1.89429i	0.161444	−	0.0646324i	−0.289533	−	0.957168i	$-0.593500\pi$
$859$	4.73171	−	1.89429i	0.161444	−	0.0646324i	0.450977	+	0.892536i	$0.351076\pi$
$860$	0.833483	+	0.794725i	0.0284215	+	0.0270999i
$861$	7.02656	+	16.7866i	0.239465	+	0.572084i
$862$	0.398512	+	8.36580i	0.0135734	+	0.284940i
$863$	46.4677	−	29.8630i	1.58178	−	1.01655i	0.606634	−	0.794982i	$-0.292520\pi$
$863$	46.4677	−	29.8630i	1.58178	−	1.01655i	0.975145	−	0.221566i	$-0.0711168\pi$
$864$	−4.98674	+	1.46029i	−0.169652	+	0.0496799i
$865$	3.75954	−	1.10390i	0.127828	−	0.0375337i
$866$	−10.6859	−	8.40349i	−0.363122	−	0.285562i
$867$	−19.1455	+	11.4561i	−0.650214	+	0.389070i
$868$	−9.24765	+	0.883044i	−0.313886	+	0.0299725i
$869$	3.65358	+	15.0603i	0.123939	+	0.510884i
$870$	1.28963	+	0.564773i	0.0437225	+	0.0191476i
$871$	−21.0823	−	8.44008i	−0.714347	−	0.285981i
$872$	10.8687	+	6.98487i	0.368059	+	0.236537i
$873$	−31.8305	+	13.9120i	−1.07730	+	0.470851i
$874$	−16.2241	−	31.1083i	−0.548787	−	1.05225i
$875$	9.05417	−	15.6823i	0.306087	−	0.530158i
$876$	−9.02201	+	23.5978i	−0.304825	+	0.797297i
$877$	2.49744	−	1.96401i	0.0843327	−	0.0663199i	−0.575103	−	0.818081i	$-0.695038\pi$
$877$	2.49744	−	1.96401i	0.0843327	−	0.0663199i	0.659435	+	0.751761i	$0.270795\pi$
$878$	0.0901201	−	0.126556i	0.00304141	−	0.00427106i
$879$	−0.327945	+	4.11243i	−0.0110613	+	0.138709i
$880$	−1.35428	−	1.90182i	−0.0456527	−	0.0641103i
$881$	−15.1828	+	17.5219i	−0.511523	+	0.590329i	−0.951488	−	0.307686i	$-0.900445\pi$
$881$	−15.1828	+	17.5219i	−0.511523	+	0.590329i	0.439965	+	0.898015i	$0.354991\pi$
$882$	15.4733	−	15.7055i	0.521014	−	0.528832i
$883$	25.0272	−	7.34865i	0.842233	−	0.247302i	0.167969	−	0.985792i	$-0.446279\pi$
$883$	25.0272	−	7.34865i	0.842233	−	0.247302i	0.674264	+	0.738490i	$0.264461\pi$
$884$	−4.45541	+	0.858709i	−0.149852	+	0.0288815i
$885$	2.57970	−	9.32201i	0.0867157	−	0.313356i
$886$	−32.1546	−	16.5768i	−1.08025	−	0.556910i
$887$	−4.12949	+	11.9314i	−0.138655	+	0.400616i	−0.992855	−	0.119328i	$-0.961926\pi$
$887$	−4.12949	+	11.9314i	−0.138655	+	0.400616i	0.854200	+	0.519944i	$0.174047\pi$
$888$	7.42629	+	0.237548i	0.249210	+	0.00797159i
$889$	−38.7231	−	30.4522i	−1.29873	−	1.02133i
$890$	−4.79504	+	5.53377i	−0.160730	+	0.185493i
$891$	−26.0146	+	34.1138i	−0.871520	+	1.14285i
$892$	1.81761	+	0.533697i	0.0608579	+	0.0178695i
$893$	−11.2631	−	1.07550i	−0.376906	−	0.0359902i
$894$	−5.80805	+	32.8923i	−0.194250	+	1.10008i
$895$	−0.00279980	+	0.0587750i	−9.35869e−5	+	0.00196463i
$896$	−1.89401	−	3.28053i	−0.0632745	−	0.109595i
$897$	−11.0784	−	14.9059i	−0.369897	−	0.497693i
$898$	−12.5885	+	21.8039i	−0.420083	+	0.727605i
$899$	−3.42380	−	2.20034i	−0.114190	−	0.0733855i
$900$	−6.75030	+	12.5841i	−0.225010	+	0.419472i
$901$	−5.17725	−	11.3366i	−0.172479	−	0.377677i
$902$	9.56867	−	9.12371i	0.318602	−	0.303786i
$903$	15.0471	+	3.40238i	0.500735	+	0.113224i
$904$	8.63197	+	1.66368i	0.287095	+	0.0553330i
$905$	−10.0726	+	4.03245i	−0.334823	+	0.134043i
$906$	−3.32663	−	6.21249i	−0.110520	−	0.206396i
$907$	31.3605	−	6.04424i	1.04131	−	0.200696i	0.360197	−	0.932876i	$-0.382709\pi$
$907$	31.3605	−	6.04424i	1.04131	−	0.200696i	0.681111	+	0.732180i	$0.261497\pi$
$908$	7.92286	−	5.09171i	0.262929	−	0.168974i
$909$	−17.5659	+	26.3745i	−0.582623	+	0.874789i
$910$	−2.71647	−	3.13498i	−0.0900502	−	0.103923i
$911$	−4.84091	+	19.9545i	−0.160387	+	0.661123i	0.833670	+	0.552262i	$0.186235\pi$
$911$	−4.84091	+	19.9545i	−0.160387	+	0.661123i	−0.994057	+	0.108860i	$0.965280\pi$
$912$	7.01624	+	10.5513i	0.232331	+	0.349389i
$913$	36.0564	+	6.94930i	1.19329	+	0.229988i
$914$	−7.81498	+	0.746240i	−0.258497	+	0.0246834i
$915$	−5.53993	−	3.81595i	−0.183144	−	0.126151i
$916$	−17.7493	−	1.69486i	−0.586455	−	0.0559997i
$917$	−6.74622	−	46.9210i	−0.222780	−	1.54947i
$918$	−9.36946	−	4.83895i	−0.309238	−	0.159709i
$919$	−17.1406			−0.565415			−0.282708	−	0.959206i	$-0.591233\pi$
$919$	−17.1406			−0.565415			−0.282708	+	0.959206i	$0.591233\pi$
$920$	2.22337	+	0.757765i	0.0733025	+	0.0249828i
$921$	20.2826	+	6.66690i	0.668333	+	0.219682i
$922$	1.20074	−	25.2065i	0.0395441	−	0.830133i
$923$	−25.3881	+	19.9654i	−0.835659	+	0.657169i
$924$	−28.6484	−	12.5461i	−0.942463	−	0.412738i
$925$	14.7784	−	14.0912i	0.485912	−	0.463316i
$926$	−5.57291	+	12.2030i	−0.183137	+	0.401014i
$927$	−25.0775	−	27.1768i	−0.823654	−	0.892604i
$928$	0.236179	−	1.64266i	0.00775297	−	0.0539231i
$929$	0.793835	−	3.27223i	0.0260449	−	0.107358i	−0.957305	−	0.289078i	$-0.906651\pi$
$929$	0.793835	−	3.27223i	0.0260449	−	0.107358i	0.983350	+	0.181720i	$0.0581664\pi$
$930$	−1.26036	+	1.65525i	−0.0413287	+	0.0542779i
$931$	−47.7873	−	24.6361i	−1.56617	−	0.807415i
$932$	11.2689	+	5.80950i	0.369124	+	0.190296i
$933$	26.4148	−	34.6911i	0.864782	−	1.13574i
$934$	−8.21362	+	33.8570i	−0.268758	+	1.10784i
$935$	0.674315	−	4.68996i	0.0220525	−	0.153378i
$936$	4.54863	+	4.92941i	0.148677	+	0.161123i
$937$	−13.2628	+	29.0416i	−0.433278	+	0.948747i	0.559505	+	0.828827i	$0.310991\pi$
$937$	−13.2628	+	29.0416i	−0.433278	+	0.948747i	−0.992784	+	0.119920i	$0.961736\pi$
$938$	27.8456	−	26.5508i	0.909193	−	0.866913i
$939$	−27.5715	−	12.0745i	−0.899762	−	0.394038i
$940$	0.595440	−	0.468259i	0.0194211	−	0.0152729i
$941$	−2.17181	+	45.5920i	−0.0707991	+	1.48626i	0.632056	+	0.774923i	$0.282211\pi$
$941$	−2.17181	+	45.5920i	−0.0707991	+	1.48626i	−0.702855	+	0.711333i	$0.748092\pi$
$942$	−15.8564	−	5.21201i	−0.516628	−	0.169816i
$943$	−2.45560	+	13.0732i	−0.0799653	+	0.425721i
$944$	−11.4015			−0.371086
$945$	−0.451692	−	9.63005i	−0.0146935	−	0.313266i
$946$	−1.59508	−	11.0940i	−0.0518606	−	0.360698i
$947$	−14.5340	−	1.38783i	−0.472292	−	0.0450985i	−0.143803	−	0.989606i	$-0.545933\pi$
$947$	−14.5340	−	1.38783i	−0.472292	−	0.0450985i	−0.328489	+	0.944508i	$0.606539\pi$
$948$	4.63734	+	3.19424i	0.150614	+	0.103744i
$949$	32.4637	−	3.09991i	1.05382	−	0.100627i
$950$	34.1942	+	6.59038i	1.10940	+	0.213820i
$951$	0.322698	+	0.485288i	0.0104642	+	0.0157365i
$952$	1.81241	−	7.47085i	0.0587405	−	0.242132i
$953$	13.7726	+	15.8944i	0.446139	+	0.514872i	0.933621	−	0.358261i	$-0.116630\pi$
$953$	13.7726	+	15.8944i	0.446139	+	0.514872i	−0.487483	+	0.873133i	$0.662085\pi$
$954$	−10.2124	+	15.3336i	−0.330638	+	0.496442i
$955$	4.32866	−	2.78186i	0.140072	−	0.0900189i
$956$	3.48108	−	0.670922i	0.112586	−	0.0216992i
$957$	−6.46804	−	12.0791i	−0.209082	−	0.390462i
$958$	18.3721	−	7.35509i	0.593577	−	0.237632i
$959$	−26.5736	−	5.12164i	−0.858106	−	0.165386i
$960$	−0.827454	−	0.187100i	−0.0267060	−	0.00603864i
$961$	−18.0831	+	17.2422i	−0.583325	+	0.556199i
$962$	−3.98426	−	8.72431i	−0.128458	−	0.281283i
$963$	15.9344	−	29.7055i	0.513480	−	0.957246i
$964$	16.9341	+	10.8829i	0.545412	+	0.350515i
$965$	−0.925302	+	1.60267i	−0.0297865	+	0.0515918i
$966$	30.7695	−	6.58244i	0.989992	−	0.211787i
$967$	1.61187	+	2.79184i	0.0518343	+	0.0897796i	0.890778	−	0.454438i	$-0.150160\pi$
$967$	1.61187	+	2.79184i	0.0518343	+	0.0897796i	−0.838944	+	0.544218i	$0.816827\pi$
$968$	−0.557770	+	11.7090i	−0.0179274	+	0.376343i
$969$	−4.47157	+	25.3235i	−0.143648	+	0.813508i
$970$	−5.64577	−	0.539106i	−0.181275	−	0.0173097i
$971$	−11.5129	−	3.38049i	−0.369466	−	0.108485i	0.0917286	−	0.995784i	$-0.470761\pi$
$971$	−11.5129	−	3.38049i	−0.369466	−	0.108485i	−0.461194	+	0.887299i	$0.652579\pi$
$972$	1.21648	+	15.5409i	0.0390186	+	0.498475i
$973$	−7.14313	+	8.24361i	−0.228998	+	0.264278i
$974$	−18.3609	−	14.4392i	−0.588323	−	0.462662i
$975$	18.4242	+	0.589342i	0.590045	+	0.0188740i
$976$	−2.59350	+	7.49342i	−0.0830159	+	0.239859i
$977$	28.6283	+	14.7589i	0.915901	+	0.472180i	0.850676	−	0.525691i	$-0.176193\pi$
$977$	28.6283	+	14.7589i	0.915901	+	0.472180i	0.0652255	+	0.997871i	$0.479223\pi$
$978$	−7.46838	+	26.9877i	−0.238812	+	0.862973i
$979$	69.9743	−	13.4864i	2.23639	−	0.431028i
$980$	3.45373	−	1.01411i	0.110326	−	0.0323945i
$981$	27.2018	−	27.6100i	0.868486	−	0.881518i
$982$	−11.7080	+	13.5117i	−0.373617	+	0.431177i
$983$	24.2402	+	34.0406i	0.773141	+	1.08573i	0.993888	+	0.110394i	$0.0352113\pi$
$983$	24.2402	+	34.0406i	0.773141	+	1.08573i	−0.220747	+	0.975331i	$0.570849\pi$
$984$	0.381885	−	4.78884i	0.0121741	−	0.152663i
$985$	5.51527	−	7.74511i	0.175731	−	0.246780i
$986$	2.64739	−	2.08193i	0.0843102	−	0.0663023i
$987$	3.62372	−	9.47815i	0.115344	−	0.301693i
$988$	8.17820	−	14.1651i	0.260183	−	0.450651i
$989$	7.82011	+	8.12423i	0.248665	+	0.258336i
$990$	−6.41798	+	2.80508i	−0.203977	+	0.0891512i
$991$	11.1587	+	7.17127i	0.354468	+	0.227803i	0.705740	−	0.708470i	$-0.250614\pi$
$991$	11.1587	+	7.17127i	0.354468	+	0.227803i	−0.351272	+	0.936273i	$0.614251\pi$
$992$	2.27672	+	0.911461i	0.0722860	+	0.0289389i
$993$	40.8602	+	17.8941i	1.29666	+	0.567852i
$994$	−12.9011	−	53.1790i	−0.409198	−	1.68674i
$995$	−7.01709	+	0.670051i	−0.222457	+	0.0212421i
$996$	11.4493	−	6.85095i	0.362785	−	0.217081i
$997$	21.1892	+	16.6634i	0.671070	+	0.527735i	0.894547	−	0.446974i	$-0.147498\pi$
$997$	21.1892	+	16.6634i	0.671070	+	0.527735i	−0.223477	+	0.974709i	$0.571741\pi$
$998$	36.5381	−	10.7285i	1.15659	−	0.339606i
$999$	5.27093	−	21.6581i	0.166765	−	0.685231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.25.5	✓	240
9.4	even	3	inner	414.2.m.a.301.9	yes	240
23.12	even	11	inner	414.2.m.a.403.9	yes	240
207.58	even	33	inner	414.2.m.a.265.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.25.5	✓	240	1.1	even	1	trivial
414.2.m.a.265.5	yes	240	207.58	even	33	inner
414.2.m.a.301.9	yes	240	9.4	even	3	inner
414.2.m.a.403.9	yes	240	23.12	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.888835 - 0.458227i) q^{2} +(-0.301182 + 1.70566i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.115473 - 0.475985i) q^{5} +(0.513879 + 1.65406i) q^{6} +(1.23894 + 3.57969i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.81858 - 1.02743i) q^{9} +O(q^{10})\)	\(q+(0.888835 - 0.458227i) q^{2} +(-0.301182 + 1.70566i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.115473 - 0.475985i) q^{5} +(0.513879 + 1.65406i) q^{6} +(1.23894 + 3.57969i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.81858 - 1.02743i) q^{9} +(-0.320745 - 0.370160i) q^{10} +(0.226813 + 4.76139i) q^{11} +(1.21469 + 1.23472i) q^{12} +(0.731258 - 2.11283i) q^{13} +(2.74152 + 2.61404i) q^{14} +(0.846649 - 0.0535993i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(0.843058 - 1.84604i) q^{17} +(-2.97605 + 0.378329i) q^{18} +(3.03905 + 6.65459i) q^{19} +(-0.454707 - 0.182037i) q^{20} +(-6.47889 + 1.03508i) q^{21} +(2.38340 + 4.12816i) q^{22} +(-4.37181 - 1.97161i) q^{23} +(1.64544 + 0.540858i) q^{24} +(4.23095 - 2.18121i) q^{25} +(-0.318187 - 2.21304i) q^{26} +(2.60136 - 4.49810i) q^{27} +(3.63458 + 1.06721i) q^{28} +(0.962636 + 1.35183i) q^{29} +(0.727971 - 0.435598i) q^{30} +(-2.27672 + 0.911461i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-8.18965 - 1.04718i) q^{33} +(-0.0965644 - 2.02714i) q^{34} +(1.56081 - 1.00307i) q^{35} +(-2.47186 + 1.69998i) q^{36} +(4.11600 - 1.20857i) q^{37} +(5.75052 + 4.52226i) q^{38} +(3.38354 + 1.88363i) q^{39} +(-0.487574 + 0.0465576i) q^{40} +(-0.653905 - 2.69543i) q^{41} +(-5.28437 + 3.88881i) q^{42} +(-2.18286 - 0.873887i) q^{43} +(4.01008 + 2.57712i) q^{44} +(-0.163573 + 1.46024i) q^{45} +(-4.78927 + 0.250841i) q^{46} +(-0.773294 + 1.33938i) q^{47} +(1.71036 - 0.273250i) q^{48} +(-5.77681 + 4.54293i) q^{49} +(2.76113 - 3.87747i) q^{50} +(2.89481 + 1.99397i) q^{51} +(-1.29689 - 1.82123i) q^{52} +(4.02152 - 4.64108i) q^{53} +(0.251031 - 5.19009i) q^{54} +(2.24016 - 0.657771i) q^{55} +(3.71957 - 0.716888i) q^{56} +(-12.2658 + 3.17935i) q^{57} +(1.47507 + 0.760452i) q^{58} +(3.72905 - 10.7744i) q^{59} +(0.447444 - 0.720750i) q^{60} +(-6.23304 - 4.90172i) q^{61} +(-1.60597 + 1.85339i) q^{62} +(0.185831 - 11.3626i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.09012 - 0.104093i) q^{65} +(-7.75910 + 2.82194i) q^{66} +(0.483290 - 10.1455i) q^{67} +(-1.01472 - 1.75754i) q^{68} +(4.67962 - 6.86303i) q^{69} +(0.927671 - 1.60677i) q^{70} +(-12.1527 - 7.81006i) q^{71} +(-1.41810 + 2.64367i) q^{72} +(6.05925 + 13.2679i) q^{73} +(3.10465 - 2.96027i) q^{74} +(2.44612 + 7.87352i) q^{75} +(7.18349 + 1.38450i) q^{76} +(-16.7633 + 6.71101i) q^{77} +(3.87054 + 0.123809i) q^{78} +(3.19230 - 0.615266i) q^{79} +(-0.412039 + 0.264801i) q^{80} +(6.88877 + 5.79180i) q^{81} +(-1.81633 - 2.09616i) q^{82} +(1.81612 - 7.48614i) q^{83} +(-2.91497 + 5.87795i) q^{84} +(-0.976037 - 0.188116i) q^{85} +(-2.34065 + 0.223505i) q^{86} +(-2.59570 + 1.23479i) q^{87} +(4.74521 + 0.453112i) q^{88} +(-2.12756 - 14.7975i) q^{89} +(0.523732 + 1.37287i) q^{90} +8.46926 q^{91} +(-4.14193 + 2.41753i) q^{92} +(-0.868939 - 4.15784i) q^{93} +(-0.0735896 + 1.54484i) q^{94} +(2.81656 - 2.21497i) q^{95} +(1.39502 - 1.02661i) q^{96} +(8.38035 - 7.99065i) q^{97} +(-3.05294 + 6.68500i) q^{98} +(4.25272 - 13.6534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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