LMFDB - Embedded newform 966.2.y.a.487.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			487.8
Character	$\chi$	$=$	966.487
Dual form			966.2.y.a.121.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 + 0.814576i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(0.170819 - 3.58593i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(2.64569 - 0.0174095i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 + 0.814576i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(0.170819 - 3.58593i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(2.64569 - 0.0174095i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(2.82193 + 2.21919i) q^{10} +(-1.84211 - 2.58689i) q^{11} +(0.995472 - 0.0950560i) q^{12} +(0.629929 - 4.38125i) q^{13} +(-1.52047 + 2.16522i) q^{14} +(3.44458 + 1.01142i) q^{15} +(-0.786053 + 0.618159i) q^{16} +(-6.09578 + 1.17486i) q^{17} +(0.888835 - 0.458227i) q^{18} +(1.35258 + 0.260689i) q^{19} +(-3.44458 + 1.01142i) q^{20} +(-0.606827 + 2.57522i) q^{21} +3.17574 q^{22} +(-2.91341 + 3.80947i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-7.85237 - 0.749810i) q^{25} +(3.20347 + 3.05450i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.881774 - 2.49449i) q^{28} +(-4.44570 - 5.13062i) q^{29} +(-2.82193 + 2.21919i) q^{30} +(-5.80464 + 5.53471i) q^{31} +(-0.0475819 - 0.998867i) q^{32} +(2.94826 - 1.18031i) q^{33} +(2.57888 - 5.64696i) q^{34} +(0.389506 - 9.49025i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-5.12696 - 2.64313i) q^{37} +(-0.996928 + 0.950568i) q^{38} +(4.10924 + 1.64509i) q^{39} +(1.17417 - 3.39255i) q^{40} +(3.89020 + 2.50008i) q^{41} +(-1.74572 - 1.98808i) q^{42} +(-1.33769 + 0.392782i) q^{43} +(-1.84211 + 2.58689i) q^{44} +(-1.79500 + 3.10903i) q^{45} +(-1.41315 - 4.58290i) q^{46} +(1.16528 + 2.01833i) q^{47} +(-0.415415 - 0.909632i) q^{48} +(6.99939 - 0.0921203i) q^{49} +(5.16560 - 5.96142i) q^{50} +(0.295387 - 6.20093i) q^{51} +(-4.34631 + 0.837683i) q^{52} +(-3.50100 - 1.40159i) q^{53} +(0.235759 + 0.971812i) q^{54} +(-9.59106 + 6.16380i) q^{55} +(2.54343 + 0.728674i) q^{56} +(-0.572225 + 1.25300i) q^{57} +(6.75804 - 0.645314i) q^{58} +(-2.74561 - 2.15917i) q^{59} +(-0.170819 - 3.58593i) q^{60} +(-2.66425 - 10.9822i) q^{61} +(-1.14142 - 7.93877i) q^{62} +(-2.35956 - 1.19685i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-15.6033 - 3.00728i) q^{65} +(-0.748710 + 3.08623i) q^{66} +(4.57310 + 0.436678i) q^{67} +(3.10398 + 5.37625i) q^{68} +(-3.01522 - 3.72940i) q^{69} +(7.50460 + 5.82217i) q^{70} +(-2.78733 - 6.10340i) q^{71} +(-0.723734 - 0.690079i) q^{72} +(3.16132 + 9.13405i) q^{73} +(5.12696 - 2.64313i) q^{74} +(2.57994 - 7.45425i) q^{75} +(-0.196036 - 1.36346i) q^{76} +(-4.91870 - 6.81204i) q^{77} +(-3.72364 + 2.39304i) q^{78} +(15.7646 - 6.31120i) q^{79} +(2.08240 + 2.92433i) q^{80} +(0.580057 + 0.814576i) q^{81} +(-4.29304 + 1.71867i) q^{82} +(11.4573 - 7.36316i) q^{83} +(2.63206 - 0.268820i) q^{84} +(3.17171 + 22.0597i) q^{85} +(0.455987 - 1.31749i) q^{86} +(6.03411 - 3.11080i) q^{87} +(-1.03868 - 3.00108i) q^{88} +(-0.130160 - 0.124108i) q^{89} +(-1.49134 - 3.26558i) q^{90} +(1.59032 - 11.6024i) q^{91} +(4.55283 + 1.50722i) q^{92} +(-4.01020 - 6.94587i) q^{93} +(-2.32002 - 0.221535i) q^{94} +(1.16586 - 4.80575i) q^{95} +(0.981929 + 0.189251i) q^{96} +(15.7220 + 10.1039i) q^{97} +(-3.98501 + 5.75497i) q^{98} +(0.451956 + 3.14342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.580057	+	0.814576i	−0.410162	+	0.575992i
$2$	−0.580057	+	0.814576i	−0.410162	+	0.575992i
$3$	−0.235759	+	0.971812i	−0.136115	+	0.561076i
$3$	−0.235759	+	0.971812i	−0.136115	+	0.561076i
$4$	−0.327068	−	0.945001i	−0.163534	−	0.472500i
$5$	0.170819	−	3.58593i	0.0763926	−	1.60368i	−0.557447	−	0.830213i	$-0.688219\pi$
$5$	0.170819	−	3.58593i	0.0763926	−	1.60368i	0.633839	−	0.773465i	$-0.281478\pi$
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	2.64569	−	0.0174095i	0.999978	−	0.00658016i
$7$	2.64569	−	0.0174095i	0.999978	−	0.00658016i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.888835	−	0.458227i	−0.296278	−	0.152742i
$10$	2.82193	+	2.21919i	0.892372	+	0.701769i
$11$	−1.84211	−	2.58689i	−0.555418	−	0.779975i	0.437444	−	0.899246i	$-0.355884\pi$
$11$	−1.84211	−	2.58689i	−0.555418	−	0.779975i	−0.992862	+	0.119270i	$0.961944\pi$
$12$	0.995472	−	0.0950560i	0.287368	−	0.0274403i
$13$	0.629929	−	4.38125i	0.174711	−	1.21514i	−0.694057	−	0.719920i	$-0.744178\pi$
$13$	0.629929	−	4.38125i	0.174711	−	1.21514i	0.868768	−	0.495220i	$-0.164912\pi$
$14$	−1.52047	+	2.16522i	−0.406363	+	0.578679i
$15$	3.44458	+	1.01142i	0.889386	+	0.261147i
$16$	−0.786053	+	0.618159i	−0.196513	+	0.154540i
$17$	−6.09578	+	1.17486i	−1.47844	+	0.284947i	−0.863790	−	0.503851i	$-0.831916\pi$
$17$	−6.09578	+	1.17486i	−1.47844	+	0.284947i	−0.614653	+	0.788798i	$0.710704\pi$
$18$	0.888835	−	0.458227i	0.209501	−	0.108005i
$19$	1.35258	+	0.260689i	0.310304	+	0.0598062i	0.342026	−	0.939690i	$-0.388887\pi$
$19$	1.35258	+	0.260689i	0.310304	+	0.0598062i	−0.0317217	+	0.999497i	$0.510099\pi$
$20$	−3.44458	+	1.01142i	−0.770231	+	0.226160i
$21$	−0.606827	+	2.57522i	−0.132421	+	0.561959i
$22$	3.17574			0.677071
$23$	−2.91341	+	3.80947i	−0.607488	+	0.794328i
$23$	−2.91341	+	3.80947i	−0.607488	+	0.794328i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−7.85237	−	0.749810i	−1.57047	−	0.149962i
$26$	3.20347	+	3.05450i	0.628251	+	0.599036i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−0.881774	−	2.49449i	−0.166640	−	0.471414i
$29$	−4.44570	−	5.13062i	−0.825546	−	0.952731i	0.173941	−	0.984756i	$-0.444350\pi$
$29$	−4.44570	−	5.13062i	−0.825546	−	0.952731i	−0.999487	+	0.0320248i	$0.989804\pi$
$30$	−2.82193	+	2.21919i	−0.515211	+	0.405167i
$31$	−5.80464	+	5.53471i	−1.04254	+	0.994064i	−0.999987	−	0.00503015i	$-0.998399\pi$
$31$	−5.80464	+	5.53471i	−1.04254	+	0.994064i	−0.0425569	+	0.999094i	$0.513550\pi$
$32$	−0.0475819	−	0.998867i	−0.00841137	−	0.176576i
$33$	2.94826	−	1.18031i	0.513226	−	0.205465i
$34$	2.57888	−	5.64696i	0.442274	−	0.968446i
$35$	0.389506	−	9.49025i	0.0658385	−	1.60415i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	−5.12696	−	2.64313i	−0.842867	−	0.434528i	−0.0179883	−	0.999838i	$-0.505726\pi$
$37$	−5.12696	−	2.64313i	−0.842867	−	0.434528i	−0.824878	+	0.565310i	$0.808756\pi$
$38$	−0.996928	+	0.950568i	−0.161723	+	0.154203i
$39$	4.10924	+	1.64509i	0.658005	+	0.263425i
$40$	1.17417	−	3.39255i	0.185653	−	0.536409i
$41$	3.89020	+	2.50008i	0.607547	+	0.390447i	0.807936	−	0.589270i	$-0.200584\pi$
$41$	3.89020	+	2.50008i	0.607547	+	0.390447i	−0.200390	+	0.979716i	$0.564221\pi$
$42$	−1.74572	−	1.98808i	−0.269370	−	0.306768i
$43$	−1.33769	+	0.392782i	−0.203996	+	0.0598987i	−0.382134	−	0.924107i	$-0.624811\pi$
$43$	−1.33769	+	0.392782i	−0.203996	+	0.0598987i	0.178138	+	0.984006i	$0.442993\pi$
$44$	−1.84211	+	2.58689i	−0.277709	+	0.389988i
$45$	−1.79500	+	3.10903i	−0.267583	+	0.463467i
$46$	−1.41315	−	4.58290i	−0.208358	−	0.675712i
$47$	1.16528	+	2.01833i	0.169974	+	0.294404i	0.938411	−	0.345522i	$-0.112298\pi$
$47$	1.16528	+	2.01833i	0.169974	+	0.294404i	−0.768436	+	0.639926i	$0.778965\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	6.99939	−	0.0921203i	0.999913	−	0.0131600i
$50$	5.16560	−	5.96142i	0.730526	−	0.843072i
$51$	0.295387	−	6.20093i	0.0413624	−	0.868304i
$52$	−4.34631	+	0.837683i	−0.602725	+	0.116166i
$53$	−3.50100	−	1.40159i	−0.480899	−	0.192523i	0.118531	−	0.992950i	$-0.462182\pi$
$53$	−3.50100	−	1.40159i	−0.480899	−	0.192523i	−0.599430	+	0.800427i	$0.704606\pi$
$54$	0.235759	+	0.971812i	0.0320827	+	0.132247i
$55$	−9.59106	+	6.16380i	−1.29326	+	0.831127i
$56$	2.54343	+	0.728674i	0.339880	+	0.0973731i
$57$	−0.572225	+	1.25300i	−0.0757930	+	0.165964i
$58$	6.75804	−	0.645314i	0.887374	−	0.0847339i
$59$	−2.74561	−	2.15917i	−0.357449	−	0.281101i	0.423244	−	0.906016i	$-0.360891\pi$
$59$	−2.74561	−	2.15917i	−0.357449	−	0.281101i	−0.780693	+	0.624915i	$0.785134\pi$
$60$	−0.170819	−	3.58593i	−0.0220526	−	0.462942i
$61$	−2.66425	−	10.9822i	−0.341122	−	1.40612i	−0.841472	−	0.540301i	$-0.818310\pi$
$61$	−2.66425	−	10.9822i	−0.341122	−	1.40612i	0.500350	−	0.865823i	$-0.333205\pi$
$62$	−1.14142	−	7.93877i	−0.144961	−	1.00822i
$63$	−2.35956	−	1.19685i	−0.297277	−	0.150789i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−15.6033	−	3.00728i	−1.93535	−	0.373007i
$66$	−0.748710	+	3.08623i	−0.0921599	+	0.379888i
$67$	4.57310	+	0.436678i	0.558694	+	0.0533488i	0.370583	−	0.928799i	$-0.379158\pi$
$67$	4.57310	+	0.436678i	0.558694	+	0.0533488i	0.188110	+	0.982148i	$0.439764\pi$
$68$	3.10398	+	5.37625i	0.376413	+	0.651966i
$69$	−3.01522	−	3.72940i	−0.362990	−	0.448967i
$70$	7.50460	+	5.82217i	0.896971	+	0.695882i
$71$	−2.78733	−	6.10340i	−0.330795	−	0.724341i	0.669026	−	0.743239i	$-0.266711\pi$
$71$	−2.78733	−	6.10340i	−0.330795	−	0.724341i	−0.999821	+	0.0188981i	$0.993984\pi$
$72$	−0.723734	−	0.690079i	−0.0852929	−	0.0813266i
$73$	3.16132	+	9.13405i	0.370005	+	1.06906i	0.964300	+	0.264812i	$0.0853100\pi$
$73$	3.16132	+	9.13405i	0.370005	+	1.06906i	−0.594295	+	0.804247i	$0.702569\pi$
$74$	5.12696	−	2.64313i	0.595997	−	0.307258i
$75$	2.57994	−	7.45425i	0.297906	−	0.860743i
$76$	−0.196036	−	1.36346i	−0.0224868	−	0.156399i
$77$	−4.91870	−	6.81204i	−0.560538	−	0.776304i
$78$	−3.72364	+	2.39304i	−0.421620	+	0.270958i
$79$	15.7646	−	6.31120i	1.77366	−	0.710066i	0.776899	−	0.629626i	$-0.216792\pi$
$79$	15.7646	−	6.31120i	1.77366	−	0.710066i	0.996759	−	0.0804397i	$-0.0256324\pi$
$80$	2.08240	+	2.92433i	0.232820	+	0.326950i
$81$	0.580057	+	0.814576i	0.0644508	+	0.0905084i
$82$	−4.29304	+	1.71867i	−0.474087	+	0.189796i
$83$	11.4573	−	7.36316i	1.25760	−	0.808211i	0.269647	−	0.962959i	$-0.413093\pi$
$83$	11.4573	−	7.36316i	1.25760	−	0.808211i	0.987954	+	0.154748i	$0.0494565\pi$
$84$	2.63206	−	0.268820i	0.287181	−	0.0293307i
$85$	3.17171	+	22.0597i	0.344020	+	2.39271i
$86$	0.455987	−	1.31749i	0.0491704	−	0.142068i
$87$	6.03411	−	3.11080i	0.646924	−	0.333513i
$88$	−1.03868	−	3.00108i	−0.110724	−	0.319916i
$89$	−0.130160	−	0.124108i	−0.0137970	−	0.0131554i	0.683149	−	0.730279i	$-0.260610\pi$
$89$	−0.130160	−	0.124108i	−0.0137970	−	0.0131554i	−0.696946	+	0.717123i	$0.745458\pi$
$90$	−1.49134	−	3.26558i	−0.157201	−	0.344222i
$91$	1.59032	−	11.6024i	0.166711	−	1.21626i
$92$	4.55283	+	1.50722i	0.474666	+	0.157139i
$93$	−4.01020	−	6.94587i	−0.415839	−	0.720254i
$94$	−2.32002	−	0.221535i	−0.239291	−	0.0228496i
$95$	1.16586	−	4.80575i	0.119615	−	0.493059i
$96$	0.981929	+	0.189251i	0.100218	+	0.0193154i
$97$	15.7220	+	10.1039i	1.59633	+	1.02590i	0.968975	+	0.247159i	$0.0794968\pi$
$97$	15.7220	+	10.1039i	1.59633	+	1.02590i	0.627350	+	0.778737i	$0.284140\pi$
$98$	−3.98501	+	5.75497i	−0.402547	+	0.581340i
$99$	0.451956	+	3.14342i	0.0454232	+	0.315926i
$100$	1.85969	+	7.66573i	0.185969	+	0.766573i
$101$	−0.204516	−	4.29332i	−0.0203501	−	0.427201i	−0.985937	−	0.167119i	$-0.946553\pi$
$101$	−0.204516	−	4.29332i	−0.0203501	−	0.427201i	0.965587	−	0.260082i	$-0.0837496\pi$
$102$	4.87979	+	3.83751i	0.483171	+	0.379970i
$103$	3.88518	−	0.370990i	0.382818	−	0.0365547i	0.0981267	−	0.995174i	$-0.468715\pi$
$103$	3.88518	−	0.370990i	0.382818	−	0.0365547i	0.284691	+	0.958619i	$0.408109\pi$
$104$	1.83875	−	4.02631i	0.180305	−	0.394812i
$105$	9.13091	+	2.61594i	0.891085	+	0.255289i
$106$	3.17248	−	2.03883i	0.308138	−	0.198029i
$107$	0.833321	+	3.43500i	0.0805602	+	0.332074i	0.997803	−	0.0662557i	$-0.0211053\pi$
$107$	0.833321	+	3.43500i	0.0805602	+	0.332074i	−0.917243	+	0.398329i	$0.869590\pi$
$108$	−0.928368	−	0.371662i	−0.0893322	−	0.0357632i
$109$	−8.33713	+	1.60685i	−0.798552	+	0.153908i	−0.572175	−	0.820132i	$-0.693900\pi$
$109$	−8.33713	+	1.60685i	−0.798552	+	0.153908i	−0.226377	+	0.974040i	$0.572688\pi$
$110$	0.542478	−	11.3880i	0.0517232	−	1.08580i
$111$	3.77735	−	4.35930i	0.358530	−	0.413766i
$112$	−2.06889	+	1.64914i	−0.195492	+	0.155829i
$113$	−2.20651	−	4.83158i	−0.207571	−	0.454517i	0.777001	−	0.629500i	$-0.216740\pi$
$113$	−2.20651	−	4.83158i	−0.207571	−	0.454517i	−0.984571	+	0.174983i	$0.944013\pi$
$114$	−0.688739	−	1.19293i	−0.0645063	−	0.111728i
$115$	13.1628	+	11.0980i	1.22744	+	1.03490i
$116$	−3.39439	+	5.87925i	−0.315161	+	0.545875i
$117$	−2.56751	+	3.60556i	−0.237366	+	0.333334i
$118$	3.35142	−	0.984067i	0.308524	−	0.0905907i
$119$	−16.1071	+	3.21446i	−1.47654	+	0.294669i
$120$	3.02010	+	1.94090i	0.275696	+	0.177179i
$121$	0.299151	−	0.864340i	0.0271956	−	0.0785764i
$122$	10.4912	+	4.20006i	0.949832	+	0.380255i
$123$	−3.34675	+	3.19112i	−0.301767	+	0.287734i
$124$	7.12882	+	3.67516i	0.640187	+	0.330039i
$125$	−1.47555	+	10.2627i	−0.131977	+	0.917923i
$126$	2.34361	−	1.22780i	0.208785	−	0.109381i
$127$	4.90360	−	10.7374i	0.435124	−	0.952789i	−0.557343	−	0.830282i	$-0.688179\pi$
$127$	4.90360	−	10.7374i	0.435124	−	0.952789i	0.992468	−	0.122507i	$-0.0390935\pi$
$128$	−0.928368	+	0.371662i	−0.0820569	+	0.0328506i
$129$	−0.0663371	−	1.39259i	−0.00584066	−	0.122610i
$130$	11.5004	−	10.9656i	1.00866	−	0.961751i
$131$	5.16752	−	4.06378i	0.451488	−	0.355054i	−0.366375	−	0.930467i	$-0.619401\pi$
$131$	5.16752	−	4.06378i	0.451488	−	0.355054i	0.817863	+	0.575413i	$0.195159\pi$
$132$	−2.07967	−	2.40007i	−0.181012	−	0.208899i
$133$	3.58306	+	0.666157i	0.310691	+	0.0577631i
$134$	−3.00837	+	3.47184i	−0.259883	+	0.299921i
$135$	−2.59820	−	2.47738i	−0.223618	−	0.213219i
$136$	−6.17985	−	0.590104i	−0.529918	−	0.0506010i
$137$	6.39824	−	11.0821i	0.546639	−	0.946806i	−0.451863	−	0.892087i	$-0.649240\pi$
$137$	6.39824	−	11.0821i	0.546639	−	0.946806i	0.998502	−	0.0547187i	$-0.0174262\pi$
$138$	4.78688	−	0.292859i	0.407486	−	0.0249298i
$139$	−7.44637			−0.631593			−0.315796	−	0.948827i	$-0.602272\pi$
$139$	−7.44637			−0.631593			−0.315796	+	0.948827i	$0.602272\pi$
$140$	−9.09569	+	2.73587i	−0.768726	+	0.231224i
$141$	−2.23616	+	0.656597i	−0.188319	+	0.0552954i
$142$	6.58850	+	1.26983i	0.552894	+	0.106562i
$143$	−12.4942	+	6.44120i	−1.04482	+	0.538640i
$144$	0.981929	−	0.189251i	0.0818274	−	0.0157709i
$145$	−19.1574	+	15.0656i	−1.59094	+	1.25113i
$146$	−9.27412	−	2.72313i	−0.767532	−	0.225368i
$147$	−1.56065	+	6.82381i	−0.128720	+	0.562818i
$148$	−0.820897	+	5.70946i	−0.0674773	+	0.469315i
$149$	6.71258	−	0.640974i	0.549916	−	0.0525106i	0.183600	−	0.983001i	$-0.441225\pi$
$149$	6.71258	−	0.640974i	0.549916	−	0.0525106i	0.366316	+	0.930490i	$0.380619\pi$
$150$	4.57554	+	6.42545i	0.373591	+	0.524635i
$151$	−10.0031	−	7.86654i	−0.814043	−	0.640170i	0.121813	−	0.992553i	$-0.461129\pi$
$151$	−10.0031	−	7.86654i	−0.814043	−	0.640170i	−0.935856	+	0.352383i	$0.885371\pi$
$152$	1.22435	+	0.631197i	0.0993080	+	0.0511968i
$153$	5.95650	+	1.74899i	0.481554	+	0.141397i
$154$	8.40205	−	0.0552881i	0.677056	−	0.00445524i
$155$	18.8556	+	21.7605i	1.51452	+	1.74784i
$156$	0.210612	−	4.42129i	0.0168625	−	0.353986i
$157$	−1.17606	−	3.39801i	−0.0938599	−	0.271190i	0.888292	−	0.459279i	$-0.151892\pi$
$157$	−1.17606	−	3.39801i	−0.0938599	−	0.271190i	−0.982152	+	0.188088i	$0.939771\pi$
$158$	−4.00342	+	16.5023i	−0.318495	+	1.31286i
$159$	2.18747	−	3.07187i	0.173478	−	0.243615i
$160$	−3.59000			−0.283814
$161$	−7.64168	+	10.1294i	−0.602249	+	0.798309i
$162$	−1.00000			−0.0785674
$163$	−0.652768	+	0.916684i	−0.0511287	+	0.0718003i	−0.839349	−	0.543593i	$-0.817063\pi$
$163$	−0.652768	+	0.916684i	−0.0511287	+	0.0718003i	0.788220	+	0.615393i	$0.211003\pi$
$164$	1.09022	−	4.49394i	0.0851316	−	0.350917i
$165$	−3.72888	−	10.7739i	−0.290293	−	0.838745i
$166$	−0.648033	+	13.6039i	−0.0502971	+	1.05587i
$167$	−9.02815	−	10.4190i	−0.698620	−	0.806250i	0.289946	−	0.957043i	$-0.406363\pi$
$167$	−9.02815	−	10.4190i	−0.698620	−	0.806250i	−0.988565	+	0.150793i	$0.951817\pi$
$168$	−1.30777	+	2.29994i	−0.100897	+	0.177444i
$169$	−6.32513	−	1.85722i	−0.486548	−	0.142863i
$170$	−19.8091	−	10.2123i	−1.51929	−	0.783248i
$171$	−1.08277	−	0.851500i	−0.0828015	−	0.0651159i
$172$	0.808696	+	1.13565i	0.0616625	+	0.0865929i
$173$	−10.7616	+	1.02761i	−0.818188	+	0.0781275i	−0.495752	−	0.868464i	$-0.665108\pi$
$173$	−10.7616	+	1.02761i	−0.818188	+	0.0781275i	−0.322436	+	0.946591i	$0.604502\pi$
$174$	−0.966144	+	6.71968i	−0.0732432	+	0.509417i
$175$	−20.7880	−	1.84706i	−1.57143	−	0.139625i
$176$	3.04710	+	0.894711i	0.229684	+	0.0674414i
$177$	2.74561	−	2.15917i	0.206373	−	0.162294i
$178$	0.176595	−	0.0340360i	0.0132364	−	0.00255110i
$179$	−8.92310	+	4.60018i	−0.666944	+	0.343834i	−0.758226	−	0.651992i	$-0.773934\pi$
$179$	−8.92310	+	4.60018i	−0.666944	+	0.343834i	0.0912823	+	0.995825i	$0.470903\pi$
$180$	3.52512	+	0.679412i	0.262747	+	0.0506404i
$181$	−22.7288	+	6.67378i	−1.68942	+	0.496058i	−0.978331	−	0.207045i	$-0.933615\pi$
$181$	−22.7288	+	6.67378i	−1.68942	+	0.496058i	−0.711088	+	0.703103i	$0.751797\pi$
$182$	8.52857	+	8.02550i	0.632180	+	0.594889i
$183$	11.3007			0.835374
$184$	−3.86865	+	2.83435i	−0.285201	+	0.208951i
$185$	−10.3539	+	17.9334i	−0.761232	+	1.31849i
$186$	7.98409	+	0.762388i	0.585422	+	0.0559010i
$187$	14.2683	+	13.6048i	1.04340	+	0.994885i
$188$	1.52620	−	1.76133i	0.111309	−	0.128458i
$189$	1.71940	−	2.01088i	0.125068	−	0.146270i
$190$	3.23838	+	3.73729i	0.234937	+	0.271131i
$191$	−0.879700	+	0.691803i	−0.0636528	+	0.0500571i	−0.649479	−	0.760380i	$-0.725013\pi$
$191$	−0.879700	+	0.691803i	−0.0636528	+	0.0500571i	0.585826	+	0.810437i	$0.300770\pi$
$192$	−0.723734	+	0.690079i	−0.0522310	+	0.0498022i
$193$	−0.249999	−	5.24813i	−0.0179953	−	0.377769i	−0.989844	−	0.142161i	$-0.954595\pi$
$193$	−0.249999	−	5.24813i	−0.0179953	−	0.377769i	0.971848	−	0.235608i	$-0.0757081\pi$
$194$	−17.3500	+	6.94591i	−1.24566	+	0.498687i
$195$	6.60112	−	14.4544i	0.472716	−	1.03510i
$196$	−2.37633	−	6.58430i	−0.169738	−	0.470307i
$197$	1.18835	−	8.26517i	0.0846665	−	0.588869i	−0.902683	−	0.430307i	$-0.858405\pi$
$197$	1.18835	−	8.26517i	0.0846665	−	0.588869i	0.987349	−	0.158562i	$-0.0506856\pi$
$198$	−2.82271	−	1.45521i	−0.200602	−	0.103417i
$199$	−5.60303	+	5.34248i	−0.397189	+	0.378719i	−0.862185	−	0.506594i	$-0.830904\pi$
$199$	−5.60303	+	5.34248i	−0.397189	+	0.378719i	0.464996	+	0.885313i	$0.346056\pi$
$200$	−7.32305	−	2.93171i	−0.517818	−	0.207303i
$201$	−1.50252	+	4.34124i	−0.105980	+	0.306208i
$202$	3.61587	+	2.32378i	0.254411	+	0.163500i
$203$	−11.8513	−	13.4966i	−0.831798	−	0.947278i
$204$	−5.95650	+	1.74899i	−0.417038	+	0.122453i
$205$	9.62963	−	13.5229i	0.672563	−	0.944482i
$206$	−1.95143	+	3.37997i	−0.135962	+	0.235494i
$207$	4.33514	−	2.05099i	0.301313	−	0.142553i
$208$	2.21315	+	3.83329i	0.153454	+	0.265791i
$209$	−1.81724	−	3.97920i	−0.125701	−	0.275247i
$210$	−7.42733	+	5.92043i	−0.512534	+	0.408548i
$211$	16.0982	−	18.5784i	1.10825	−	1.27899i	0.151377	−	0.988476i	$-0.451629\pi$
$211$	16.0982	−	18.5784i	1.10825	−	1.27899i	0.956872	−	0.290511i	$-0.0938252\pi$
$212$	−0.179438	+	3.76686i	−0.0123238	+	0.258709i
$213$	6.58850	−	1.26983i	0.451436	−	0.0870072i
$214$	−3.28144	−	1.31369i	−0.224314	−	0.0898020i
$215$	1.17999	+	4.86397i	0.0804744	+	0.331720i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−15.2609	+	14.7442i	−1.03598	+	1.00090i
$218$	3.52711	−	7.72329i	0.238886	−	0.523087i
$219$	−9.62188	+	0.918778i	−0.650187	+	0.0620853i
$220$	8.96173	+	7.04758i	0.604200	+	0.475148i
$221$	1.30747	+	27.4472i	0.0879500	+	1.84630i
$222$	1.35990	+	5.60558i	0.0912704	+	0.376222i
$223$	3.21695	+	22.3744i	0.215423	+	1.49830i	0.754643	+	0.656136i	$0.227810\pi$
$223$	3.21695	+	22.3744i	0.215423	+	1.49830i	−0.539219	+	0.842165i	$0.681281\pi$
$224$	−0.143277	−	2.64187i	−0.00957309	−	0.176517i
$225$	6.63588	+	4.26462i	0.442392	+	0.284308i
$226$	5.21559	+	1.00522i	0.346936	+	0.0668664i
$227$	3.90375	−	16.0915i	0.259101	−	1.06803i	−0.682390	−	0.730988i	$-0.739059\pi$
$227$	3.90375	−	16.0915i	0.259101	−	1.06803i	0.941491	−	0.337039i	$-0.109426\pi$
$228$	1.37124	+	0.130938i	0.0908126	+	0.00867155i
$229$	−7.44756	−	12.8995i	−0.492148	−	0.852426i	0.507811	−	0.861469i	$-0.330455\pi$
$229$	−7.44756	−	12.8995i	−0.492148	−	0.852426i	−0.999959	+	0.00904272i	$0.997122\pi$
$230$	−16.6754	+	4.28463i	−1.09954	+	0.282520i
$231$	7.77964	−	3.17405i	0.511863	−	0.208837i
$232$	−2.82016	−	6.17529i	−0.185153	−	0.405428i
$233$	5.47696	+	5.22227i	0.358808	+	0.342122i	0.847945	−	0.530084i	$-0.177840\pi$
$233$	5.47696	+	5.22227i	0.358808	+	0.342122i	−0.489137	+	0.872207i	$0.662688\pi$
$234$	−1.44770	−	4.18286i	−0.0946392	−	0.273442i
$235$	7.43665	−	3.83386i	0.485114	−	0.250094i
$236$	−1.14242	+	3.30080i	−0.0743652	+	0.214864i
$237$	2.41665	+	16.8082i	0.156978	+	1.09181i
$238$	6.72462	−	14.9850i	0.435892	−	0.971335i
$239$	−7.78427	+	5.00265i	−0.503522	+	0.323594i	−0.767624	−	0.640901i	$-0.778561\pi$
$239$	−7.78427	+	5.00265i	−0.503522	+	0.323594i	0.264101	+	0.964495i	$0.414925\pi$
$240$	−3.33284	+	1.33427i	−0.215134	+	0.0861266i
$241$	14.4610	+	20.3076i	0.931513	+	1.30813i	0.951282	+	0.308322i	$0.0997675\pi$
$241$	14.4610	+	20.3076i	0.931513	+	1.30813i	−0.0197691	+	0.999805i	$0.506293\pi$
$242$	0.530546	+	0.745048i	0.0341048	+	0.0478935i
$243$	−0.928368	+	0.371662i	−0.0595548	+	0.0238422i
$244$	−9.50678	+	6.10964i	−0.608609	+	0.391129i
$245$	0.865292	−	25.1151i	0.0552815	−	1.60454i
$246$	−0.658105	−	4.57722i	−0.0419592	−	0.291833i
$247$	1.99418	−	5.76180i	0.126886	−	0.366614i
$248$	−7.12882	+	3.67516i	−0.452681	+	0.233373i
$249$	4.45444	+	12.8703i	0.282289	+	0.815620i
$250$	−7.50384	−	7.15490i	−0.474585	−	0.452515i
$251$	9.18001	+	20.1014i	0.579437	+	1.26879i	0.941618	+	0.336682i	$0.109305\pi$
$251$	9.18001	+	20.1014i	0.579437	+	1.26879i	−0.362181	+	0.932108i	$0.617968\pi$
$252$	−0.359289	+	2.62124i	−0.0226331	+	0.165123i
$253$	15.2215	+	0.519199i	0.956967	+	0.0326417i
$254$	5.90205	+	10.2227i	0.370328	+	0.641426i
$255$	−22.1857	−	2.11847i	−1.38932	−	0.132664i
$256$	0.235759	−	0.971812i	0.0147349	−	0.0607382i
$257$	17.9759	+	3.46458i	1.12131	+	0.216115i	0.716024	−	0.698076i	$-0.245960\pi$
$257$	17.9759	+	3.46458i	1.12131	+	0.216115i	0.405285	+	0.914190i	$0.367172\pi$
$258$	1.17285	+	0.753743i	0.0730183	+	0.0469260i
$259$	−13.6104	−	6.90366i	−0.845708	−	0.428972i
$260$	2.26144	+	15.7287i	0.140249	+	0.975451i
$261$	1.60051	+	6.59741i	0.0990694	+	0.408370i
$262$	0.312804	+	6.56656i	0.0193251	+	0.405683i
$263$	−9.92310	−	7.80361i	−0.611885	−	0.481191i	0.263473	−	0.964667i	$-0.415132\pi$
$263$	−9.92310	−	7.80361i	−0.611885	−	0.481191i	−0.875358	+	0.483475i	$0.839374\pi$
$264$	3.16136	−	0.301874i	0.194569	−	0.0185790i
$265$	−5.62404	+	12.3149i	−0.345482	+	0.756500i
$266$	−2.62102	+	2.53227i	−0.160705	+	0.155263i
$267$	0.151296	−	0.0972318i	0.00925914	−	0.00595049i
$268$	−1.08305	−	4.46441i	−0.0661581	−	0.272707i
$269$	15.6468	+	6.26404i	0.954004	+	0.381926i	0.795853	−	0.605489i	$-0.207023\pi$
$269$	15.6468	+	6.26404i	0.954004	+	0.381926i	0.158151	+	0.987415i	$0.449447\pi$
$270$	3.52512	−	0.679412i	0.214532	−	0.0413477i
$271$	1.45671	−	30.5801i	0.0884889	−	1.85761i	−0.323256	−	0.946312i	$-0.604778\pi$
$271$	1.45671	−	30.5801i	0.0884889	−	1.85761i	0.411745	−	0.911299i	$-0.364919\pi$
$272$	4.06535	−	4.69167i	0.246498	−	0.284474i
$273$	10.9004	+	4.28087i	0.659724	+	0.259090i
$274$	5.31585	+	11.6401i	0.321142	+	0.703204i
$275$	12.5253	+	21.6944i	0.755303	+	1.30822i
$276$	−2.53811	+	4.06915i	−0.152776	+	0.244934i
$277$	5.87565	−	10.1769i	0.353033	−	0.611472i	−0.633746	−	0.773541i	$-0.718484\pi$
$277$	5.87565	−	10.1769i	0.353033	−	0.611472i	0.986779	+	0.162069i	$0.0518169\pi$
$278$	4.31932	−	6.06563i	0.259055	−	0.363792i
$279$	7.69552	−	2.25961i	0.460719	−	0.135279i
$280$	3.04744	−	8.99609i	0.182119	−	0.537619i
$281$	15.9751	+	10.2666i	0.952997	+	0.612454i	0.922052	−	0.387067i	$-0.126512\pi$
$281$	15.9751	+	10.2666i	0.952997	+	0.612454i	0.0309454	+	0.999521i	$0.490148\pi$
$282$	0.762254	−	2.20239i	0.0453916	−	0.131150i
$283$	11.9840	+	4.79766i	0.712373	+	0.285191i	0.699406	−	0.714725i	$-0.253448\pi$
$283$	11.9840	+	4.79766i	0.712373	+	0.285191i	0.0129671	+	0.999916i	$0.495872\pi$
$284$	−4.85608	+	4.63026i	−0.288155	+	0.274755i
$285$	4.39542	+	2.26600i	0.260362	+	0.134226i
$286$	2.00049	−	13.9137i	0.118292	−	0.822736i
$287$	10.3358	+	6.54672i	0.610103	+	0.386440i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	19.9959	−	8.00516i	1.17623	−	0.470892i
$290$	−1.15965	−	24.3441i	−0.0680971	−	1.42953i
$291$	−13.5257	+	12.8967i	−0.792890	+	0.756019i
$292$	7.59771	−	5.97491i	0.444623	−	0.349655i
$293$	18.5801	+	21.4426i	1.08546	+	1.25269i	0.965637	+	0.259895i	$0.0836881\pi$
$293$	18.5801	+	21.4426i	1.08546	+	1.25269i	0.119826	+	0.992795i	$0.461766\pi$
$294$	−4.65325	−	5.22946i	−0.271383	−	0.304988i
$295$	−8.21166	+	9.47676i	−0.478101	+	0.551758i
$296$	−4.17462	−	3.98050i	−0.242645	−	0.231362i
$297$	−3.16136	−	0.301874i	−0.183441	−	0.0175165i
$298$	−3.37156	+	5.83971i	−0.195309	+	0.338285i
$299$	14.8550	+	15.1641i	0.859086	+	0.876961i
$300$	−7.88809			−0.455419
$301$	−3.53229	+	1.06247i	−0.203598	+	0.0612397i
$302$	12.2103	−	3.58526i	0.702622	−	0.206309i
$303$	4.22051	+	0.813438i	0.242462	+	0.0467308i
$304$	−1.22435	+	0.631197i	−0.0702213	+	0.0362016i
$305$	−39.8365	+	7.67785i	−2.28103	+	0.439632i
$306$	−4.87979	+	3.83751i	−0.278959	+	0.219376i
$307$	−26.0032	−	7.63522i	−1.48408	−	0.435765i	−0.563433	−	0.826162i	$-0.690520\pi$
$307$	−26.0032	−	7.63522i	−1.48408	−	0.435765i	−0.920647	+	0.390396i	$0.872338\pi$
$308$	−4.82863	+	6.87618i	−0.275137	+	0.391807i
$309$	−0.555434	+	3.86313i	−0.0315975	+	0.219766i
$310$	−28.6629	+	2.73697i	−1.62794	+	0.155450i
$311$	−18.4251	−	25.8744i	−1.04479	−	1.46720i	−0.876462	−	0.481472i	$-0.840102\pi$
$311$	−18.4251	−	25.8744i	−1.04479	−	1.46720i	−0.168329	−	0.985731i	$-0.553837\pi$
$312$	3.47931	+	2.73616i	0.196977	+	0.154904i
$313$	9.18602	+	4.73572i	0.519224	+	0.267679i	0.697857	−	0.716237i	$-0.254137\pi$
$313$	9.18602	+	4.73572i	0.519224	+	0.267679i	−0.178633	+	0.983916i	$0.557167\pi$
$314$	3.45012	+	1.01305i	0.194701	+	0.0571695i
$315$	−4.69489	+	8.25679i	−0.264527	+	0.465217i
$316$	−11.1202	−	12.8334i	−0.625560	−	0.721934i
$317$	1.22764	−	25.7712i	0.0689509	−	1.44746i	−0.653967	−	0.756523i	$-0.726897\pi$
$317$	1.22764	−	25.7712i	0.0689509	−	1.44746i	0.722918	−	0.690934i	$-0.242800\pi$
$318$	1.23342	+	3.56372i	0.0691666	+	0.199844i
$319$	−5.08283	+	20.9517i	−0.284584	+	1.17307i
$320$	2.08240	−	2.92433i	0.116410	−	0.163475i
$321$	−3.53463			−0.197284
$322$	−3.81856	−	12.1004i	−0.212800	−	0.674326i
$323$	−8.55133			−0.475809
$324$	0.580057	−	0.814576i	0.0322254	−	0.0452542i
$325$	−8.23154	+	33.9309i	−0.456604	+	1.88215i
$326$	−0.368067	−	1.06346i	−0.0203853	−	0.0588995i
$327$	0.403997	−	8.48094i	0.0223411	−	0.468997i
$328$	3.02826	+	3.49480i	0.167208	+	0.192968i
$329$	3.11812	+	5.31960i	0.171908	+	0.293279i
$330$	10.9391	+	3.21201i	0.602178	+	0.176815i
$331$	3.25312	+	1.67710i	0.178808	+	0.0921817i	0.545306	−	0.838237i	$-0.316413\pi$
$331$	3.25312	+	1.67710i	0.178808	+	0.0921817i	−0.366499	+	0.930419i	$0.619444\pi$
$332$	−10.7055	−	8.41890i	−0.587541	−	0.462047i
$333$	3.34587	+	4.69862i	0.183353	+	0.257483i
$334$	13.7239	−	1.31048i	0.750941	−	0.0717062i
$335$	2.34707	−	16.3242i	0.128234	−	0.891889i
$336$	−1.11490	−	2.39938i	−0.0608226	−	0.130897i
$337$	−10.7634	−	3.16041i	−0.586318	−	0.172159i	−0.0248988	−	0.999690i	$-0.507926\pi$
$337$	−10.7634	−	3.16041i	−0.586318	−	0.172159i	−0.561419	+	0.827531i	$0.689745\pi$
$338$	5.18178	−	4.07500i	0.281852	−	0.221651i
$339$	5.21559	−	1.00522i	0.283272	−	0.0545962i
$340$	19.8091	−	10.2123i	1.07430	−	0.553840i
$341$	25.0105	+	4.82037i	1.35439	+	0.261038i
$342$	1.32168	−	0.388080i	0.0714683	−	0.0209850i
$343$	18.5167	−	0.365578i	0.999805	−	0.0197394i
$344$	−1.39417			−0.0751684
$345$	−13.8884	+	10.1753i	−0.747729	+	0.547821i
$346$	5.40527	−	9.36220i	0.290589	−	0.503315i
$347$	29.5294	+	2.81972i	1.58522	+	0.151370i	0.850121	−	0.526587i	$-0.176529\pi$
$347$	29.5294	+	2.81972i	1.58522	+	0.151370i	0.735101	+	0.677958i	$0.237135\pi$
$348$	−4.91327	−	4.68479i	−0.263379	−	0.251131i
$349$	−2.08142	+	2.40208i	−0.111416	+	0.128580i	−0.808718	−	0.588197i	$-0.799838\pi$
$349$	−2.08142	+	2.40208i	−0.111416	+	0.128580i	0.697302	+	0.716777i	$0.254384\pi$
$350$	13.5628	−	15.8620i	0.724963	−	0.847861i
$351$	−2.89861	−	3.34518i	−0.154716	−	0.178552i
$352$	−2.49630	+	1.96312i	−0.133053	+	0.104634i
$353$	4.26689	−	4.06847i	0.227104	−	0.216543i	−0.567981	−	0.823042i	$-0.692275\pi$
$353$	4.26689	−	4.06847i	0.227104	−	0.216543i	0.795084	+	0.606499i	$0.207427\pi$
$354$	0.166199	+	3.48896i	0.00883340	+	0.185436i
$355$	−22.3625	+	8.95260i	−1.18688	+	0.475155i
$356$	−0.0747105	+	0.163593i	−0.00395965	+	0.00867042i
$357$	0.673548	−	16.4109i	0.0356479	−	0.868557i
$358$	1.42871	−	9.93691i	0.0755098	−	0.525182i
$359$	29.7827	+	15.3540i	1.57187	+	0.810356i	0.999950	−	0.00995360i	$-0.00316838\pi$
$359$	29.7827	+	15.3540i	1.57187	+	0.810356i	0.571920	+	0.820309i	$0.306199\pi$
$360$	−2.59820	+	2.47738i	−0.136937	+	0.130570i
$361$	−15.8775	−	6.35638i	−0.835656	−	0.334546i
$362$	7.74770	−	22.3855i	0.407210	−	1.17656i
$363$	0.769448	+	0.494494i	0.0403856	+	0.0259542i
$364$	−11.4844	+	2.29192i	−0.601948	+	0.120129i
$365$	33.2941	−	9.77603i	1.74269	−	0.511701i
$366$	−6.55507	+	9.20530i	−0.342639	+	0.481169i
$367$	7.46608	−	12.9316i	0.389726	−	0.675025i	−0.602686	−	0.797978i	$-0.705903\pi$
$367$	7.46608	−	12.9316i	0.389726	−	0.675025i	0.992413	+	0.122953i	$0.0392363\pi$
$368$	−0.0647586	−	4.79539i	−0.00337578	−	0.249977i
$369$	−2.31214	−	4.00475i	−0.120365	−	0.208479i
$370$	−8.60230	−	18.8364i	−0.447213	−	0.979259i
$371$	−9.28697	−	3.64722i	−0.482156	−	0.189354i
$372$	−5.25225	+	6.06142i	−0.272316	+	0.314270i
$373$	1.03584	−	21.7450i	0.0536338	−	1.12591i	−0.798299	−	0.602261i	$-0.794267\pi$
$373$	1.03584	−	21.7450i	0.0536338	−	1.12591i	0.851933	−	0.523650i	$-0.175430\pi$
$374$	−19.3586	+	3.73107i	−1.00101	+	0.192929i
$375$	−9.62553	−	3.85348i	−0.497060	−	0.198993i
$376$	0.549452	+	2.26487i	0.0283358	+	0.116802i
$377$	−25.2790	+	16.2458i	−1.30193	+	0.836702i
$378$	0.640665	+	2.56701i	0.0329522	+	0.132033i
$379$	13.9703	−	30.5907i	0.717607	−	1.57134i	−0.0996211	−	0.995025i	$-0.531763\pi$
$379$	13.9703	−	30.5907i	0.717607	−	1.57134i	0.817228	−	0.576314i	$-0.195510\pi$
$380$	−4.92275	+	0.470066i	−0.252532	+	0.0241139i
$381$	9.27865	+	7.29681i	0.475360	+	0.373827i
$382$	−0.0532506	−	1.11787i	−0.00272454	−	0.0571951i
$383$	4.66590	+	19.2331i	0.238416	+	0.982765i	0.957636	+	0.287982i	$0.0929844\pi$
$383$	4.66590	+	19.2331i	0.238416	+	0.982765i	−0.719220	+	0.694783i	$0.755500\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−25.2677	+	16.4745i	−1.28776	+	0.839619i
$386$	4.42001	+	2.84057i	0.224973	+	0.144581i
$387$	1.36897	+	0.263848i	0.0695888	+	0.0134121i
$388$	4.40604	−	18.1619i	0.223683	−	0.922033i
$389$	21.4115	+	2.04455i	1.08561	+	0.103663i	0.622485	−	0.782632i	$-0.286123\pi$
$389$	21.4115	+	2.04455i	1.08561	+	0.103663i	0.463121	+	0.886295i	$0.346729\pi$
$390$	7.94521	+	13.7615i	0.402321	+	0.696841i
$391$	13.2839	−	26.6445i	0.671796	−	1.34747i
$392$	6.74182	+	1.88357i	0.340513	+	0.0951346i
$393$	2.73094	+	5.97993i	0.137758	+	0.301647i
$394$	6.04329	+	5.76227i	0.304457	+	0.290299i
$395$	−19.9386	−	57.6089i	−1.00322	−	2.89862i
$396$	2.82271	−	1.45521i	0.141847	−	0.0731271i
$397$	−9.76954	+	28.2272i	−0.490319	+	1.41668i	0.380363	+	0.924837i	$0.375799\pi$
$397$	−9.76954	+	28.2272i	−0.490319	+	1.41668i	−0.870682	+	0.491847i	$0.836322\pi$
$398$	−1.10178	−	7.66304i	−0.0552272	−	0.384113i
$399$	−1.49212	+	3.32501i	−0.0746993	+	0.166459i
$400$	6.63588	−	4.26462i	0.331794	−	0.213231i
$401$	−25.5440	+	10.2263i	−1.27561	+	0.510676i	−0.907869	−	0.419254i	$-0.862292\pi$
$401$	−25.5440	+	10.2263i	−1.27561	+	0.510676i	−0.367737	+	0.929930i	$0.619867\pi$
$402$	−2.66473	−	3.74208i	−0.132904	−	0.186638i
$403$	20.5925	+	28.9181i	1.02578	+	1.44051i
$404$	−3.99030	+	1.59748i	−0.198525	+	0.0794774i
$405$	3.02010	−	1.94090i	0.150070	−	0.0964441i
$406$	17.8685	−	1.82496i	0.886797	−	0.0905711i
$407$	2.60696	+	18.1318i	0.129222	+	0.898760i
$408$	2.03043	−	5.86653i	0.100521	−	0.290436i
$409$	−19.4143	+	10.0088i	−0.959975	+	0.494902i	−0.865655	−	0.500640i	$-0.833098\pi$
$409$	−19.4143	+	10.0088i	−0.959975	+	0.494902i	−0.0943198	+	0.995542i	$0.530068\pi$
$410$	5.42971	+	15.6881i	0.268154	+	0.774782i
$411$	9.26125	+	8.83058i	0.456824	+	0.435581i
$412$	−1.62130	−	3.55016i	−0.0798759	−	0.174904i
$413$	−7.30165	−	5.66472i	−0.359290	−	0.278742i
$414$	−0.843946	+	4.72099i	−0.0414777	+	0.232024i
$415$	−24.4467	−	42.3428i	−1.20004	−	2.07853i
$416$	−4.40626	−	0.420747i	−0.216035	−	0.0206288i
$417$	1.75555	−	7.23647i	0.0859695	−	0.354371i
$418$	4.29546	+	0.827883i	0.210098	+	0.0404931i
$419$	−3.75940	−	2.41602i	−0.183659	−	0.118030i	0.445581	−	0.895242i	$-0.352997\pi$
$419$	−3.75940	−	2.41602i	−0.183659	−	0.118030i	−0.629240	+	0.777211i	$0.716634\pi$
$420$	−0.514364	−	9.48431i	−0.0250984	−	0.462787i
$421$	4.25124	+	29.5680i	0.207193	+	1.44106i	0.782261	+	0.622951i	$0.214067\pi$
$421$	4.25124	+	29.5680i	0.207193	+	1.44106i	−0.575068	+	0.818106i	$0.695024\pi$
$422$	5.79559	+	23.8897i	0.282125	+	1.16293i
$423$	−0.110893	−	2.32793i	−0.00539180	−	0.113188i
$424$	−2.96431	−	2.33116i	−0.143960	−	0.113211i
$425$	48.7472	−	4.65479i	2.36459	−	0.225791i
$426$	−2.78733	+	6.10340i	−0.135047	+	0.295711i
$427$	−7.23998	−	29.0091i	−0.350367	−	1.40385i
$428$	2.97352	−	1.91097i	0.143731	−	0.0923700i
$429$	−3.31402	−	13.6606i	−0.160002	−	0.659538i
$430$	−4.64653	−	1.86019i	−0.224076	−	0.0897064i
$431$	−27.0768	+	5.21862i	−1.30424	+	0.251372i	−0.793610	−	0.608427i	$-0.791801\pi$
$431$	−27.0768	+	5.21862i	−1.30424	+	0.251372i	−0.510632	+	0.859799i	$0.670589\pi$
$432$	−0.0475819	+	0.998867i	−0.00228929	+	0.0480580i
$433$	20.9257	−	24.1496i	1.00563	−	1.16055i	0.0186269	−	0.999827i	$-0.494071\pi$
$433$	20.9257	−	24.1496i	1.00563	−	1.16055i	0.986999	−	0.160727i	$-0.0513840\pi$
$434$	−3.15807	−	20.9837i	−0.151592	−	1.00725i
$435$	−10.1244	−	22.1693i	−0.485426	−	1.06294i
$436$	4.24528	+	7.35304i	0.203312	+	0.352147i
$437$	−4.93372	+	4.39313i	−0.236012	+	0.210152i
$438$	4.83283	−	8.37070i	0.230921	−	0.399967i
$439$	−15.5750	+	21.8721i	−0.743355	+	1.04390i	0.253706	+	0.967282i	$0.418351\pi$
$439$	−15.5750	+	21.8721i	−0.743355	+	1.04390i	−0.997061	+	0.0766149i	$0.975589\pi$
$440$	−10.9391	+	3.21201i	−0.521501	+	0.153127i
$441$	−6.26352	−	3.12543i	−0.298263	−	0.148830i
$442$	−23.1162	−	14.8559i	−1.09953	−	0.706623i
$443$	−2.45062	+	7.08060i	−0.116432	+	0.336410i	−0.988127	−	0.153640i	$-0.950900\pi$
$443$	−2.45062	+	7.08060i	−0.116432	+	0.336410i	0.871694	+	0.490050i	$0.163021\pi$
$444$	−5.35499	−	2.14381i	−0.254136	−	0.101741i
$445$	−0.467275	+	0.445546i	−0.0221510	+	0.0211209i
$446$	−20.0917	−	10.3580i	−0.951368	−	0.490464i
$447$	−0.959645	+	6.67448i	−0.0453896	+	0.315692i
$448$	2.23511	+	1.41572i	0.105599	+	0.0668867i
$449$	−2.45407	+	5.37366i	−0.115815	+	0.253599i	−0.958658	−	0.284560i	$-0.908153\pi$
$449$	−2.45407	+	5.37366i	−0.115815	+	0.253599i	0.842844	+	0.538159i	$0.180880\pi$
$450$	−7.32305	+	2.93171i	−0.345212	+	0.138202i
$451$	−0.698767	−	14.6689i	−0.0329036	−	0.690733i
$452$	−3.84417	+	3.66541i	−0.180814	+	0.172406i
$453$	10.0031	−	7.86654i	0.469988	−	0.369602i
$454$	10.8433	+	12.5139i	0.508902	+	0.587305i
$455$	−41.3338	−	7.68470i	−1.93776	−	0.360264i
$456$	−0.902056	+	1.04103i	−0.0422426	+	0.0487506i
$457$	−23.7487	−	22.6443i	−1.11092	−	1.05926i	−0.997841	−	0.0656694i	$-0.979082\pi$
$457$	−23.7487	−	22.6443i	−1.11092	−	1.05926i	−0.113074	−	0.993587i	$-0.536070\pi$
$458$	14.8277	+	1.41587i	0.692851	+	0.0661593i
$459$	−3.10398	+	5.37625i	−0.144881	+	0.250942i
$460$	6.18251	−	16.0687i	0.288261	−	0.749206i
$461$	−5.99193			−0.279072			−0.139536	−	0.990217i	$-0.544561\pi$
$461$	−5.99193			−0.279072			−0.139536	+	0.990217i	$0.544561\pi$
$462$	−1.92713	+	8.17824i	−0.0896581	+	0.380486i
$463$	26.2311	−	7.70216i	1.21906	−	0.357950i	0.391952	−	0.919986i	$-0.371800\pi$
$463$	26.2311	−	7.70216i	1.21906	−	0.357950i	0.827113	+	0.562036i	$0.189982\pi$
$464$	6.66609	+	1.28478i	0.309466	+	0.0596446i
$465$	−25.5925	+	13.1938i	−1.18682	+	0.611849i
$466$	−7.43089	+	1.43219i	−0.344229	+	0.0663447i
$467$	−2.79497	+	2.19799i	−0.129336	+	0.101711i	−0.680731	−	0.732533i	$-0.738338\pi$
$467$	−2.79497	+	2.19799i	−0.129336	+	0.101711i	0.551396	+	0.834244i	$0.314095\pi$
$468$	4.24701	+	1.24703i	0.196318	+	0.0576441i
$469$	12.1066	+	1.07570i	0.559033	+	0.0496713i
$470$	−1.19071	+	8.28158i	−0.0549234	+	0.382001i
$471$	3.57949	−	0.341800i	0.164934	−	0.0157493i
$472$	−2.02609	−	2.84524i	−0.0932582	−	0.130963i
$473$	3.48026	+	2.73691i	0.160023	+	0.125843i
$474$	−15.0933	−	7.78115i	−0.693259	−	0.357400i
$475$	−10.4255	−	3.06121i	−0.478356	−	0.140458i
$476$	8.30578	+	14.1699i	0.380695	+	0.649475i
$477$	2.46957	+	2.85003i	0.113074	+	0.130494i
$478$	0.440284	−	9.24270i	0.0201381	−	0.422751i
$479$	6.65873	+	19.2392i	0.304245	+	0.879059i	0.988687	+	0.149992i	$0.0479247\pi$
$479$	6.65873	+	19.2392i	0.304245	+	0.879059i	−0.684442	+	0.729067i	$0.739954\pi$
$480$	0.846374	−	3.48880i	0.0386315	−	0.159241i
$481$	−14.8098	+	20.7975i	−0.675270	+	0.948284i
$482$	−24.9303			−1.13554
$483$	−8.04228	−	9.81437i	−0.365936	−	0.446569i
$484$	−0.914645			−0.0415748
$485$	38.9175	−	54.6520i	1.76715	−	2.48162i
$486$	0.235759	−	0.971812i	0.0106942	−	0.0440823i
$487$	−8.50200	−	24.5649i	−0.385262	−	1.11314i	−0.956343	−	0.292248i	$-0.905597\pi$
$487$	−8.50200	−	24.5649i	−0.385262	−	1.11314i	0.571080	−	0.820894i	$-0.306524\pi$
$488$	0.537710	−	11.2879i	0.0243410	−	0.510981i
$489$	−0.736949	−	0.850484i	−0.0333260	−	0.0384602i
$490$	19.9562	+	15.2730i	0.901530	+	0.689965i
$491$	12.7795	+	3.75240i	0.576731	+	0.169343i	0.557073	−	0.830463i	$-0.311924\pi$
$491$	12.7795	+	3.75240i	0.576731	+	0.169343i	0.0196575	+	0.999807i	$0.493742\pi$
$492$	4.11023	+	2.11897i	0.185303	+	0.0955306i
$493$	33.1278	+	26.0520i	1.49200	+	1.17332i
$494$	3.53668	+	4.96658i	0.159123	+	0.223457i
$495$	11.3493	−	1.08373i	0.510113	−	0.0487099i
$496$	1.14142	−	7.93877i	0.0512514	−	0.356461i
$497$	−7.48068	−	16.0992i	−0.335555	−	0.722149i
$498$	−13.0676	−	3.83700i	−0.585575	−	0.171940i
$499$	−7.90405	+	6.21581i	−0.353834	+	0.278258i	−0.779216	−	0.626756i	$-0.784382\pi$
$499$	−7.90405	+	6.21581i	−0.353834	+	0.278258i	0.425382	+	0.905014i	$0.360140\pi$
$500$	10.1809	−	1.96220i	0.455302	−	0.0877523i
$501$	12.2538	−	6.31728i	0.547460	−	0.282235i
$502$	−21.6991	−	4.18215i	−0.968476	−	0.186659i
$503$	−9.06835	+	2.66271i	−0.404338	+	0.118724i	−0.477577	−	0.878590i	$-0.658485\pi$
$503$	−9.06835	+	2.66271i	−0.404338	+	0.118724i	0.0732387	+	0.997314i	$0.476667\pi$
$504$	−1.92679	−	1.81314i	−0.0858262	−	0.0807636i
$505$	−15.4305			−0.686648
$506$	−9.25225	+	12.0979i	−0.411313	+	0.537817i
$507$	3.29608	−	5.70897i	0.146384	−	0.253544i
$508$	−11.7507	−	1.12205i	−0.521351	−	0.0497830i
$509$	5.29254	+	5.04643i	0.234588	+	0.223679i	0.798250	−	0.602326i	$-0.205759\pi$
$509$	5.29254	+	5.04643i	0.234588	+	0.223679i	−0.563662	+	0.826006i	$0.690608\pi$
$510$	14.5946	−	16.8431i	0.646260	−	0.745824i
$511$	8.52292	+	24.1109i	0.377032	+	1.06660i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	1.08277	−	0.851500i	0.0478055	−	0.0375947i
$514$	−13.2492	+	12.6331i	−0.584399	+	0.557223i
$515$	−0.666681	−	13.9954i	−0.0293775	−	0.616709i
$516$	−1.29430	+	0.518159i	−0.0569784	+	0.0228107i
$517$	3.07461	−	6.73245i	0.135221	−	0.296093i
$518$	13.5183	−	7.08217i	0.593962	−	0.311173i
$519$	1.53850	−	10.7005i	0.0675326	−	0.469700i
$520$	−14.1240	−	7.28141i	−0.619377	−	0.319311i
$521$	26.5107	−	25.2779i	1.16145	−	1.10744i	0.168901	−	0.985633i	$-0.445978\pi$
$521$	26.5107	−	25.2779i	1.16145	−	1.10744i	0.992553	−	0.121811i	$-0.0388703\pi$
$522$	−6.30248	−	2.52313i	−0.275852	−	0.110435i
$523$	−12.6928	+	36.6734i	−0.555016	+	1.60361i	0.222624	+	0.974904i	$0.428538\pi$
$523$	−12.6928	+	36.6734i	−0.555016	+	1.60361i	−0.777640	+	0.628710i	$0.783583\pi$
$524$	−5.53041	−	3.55418i	−0.241597	−	0.155265i
$525$	6.69596	−	19.7666i	0.292236	−	0.862684i
$526$	12.1126	−	3.55658i	0.528134	−	0.155074i
$527$	28.8813	−	40.5580i	1.25809	−	1.76674i
$528$	−1.58787	+	2.75028i	−0.0691033	+	0.119690i
$529$	−6.02406	−	22.1971i	−0.261916	−	0.965091i
$530$	−6.76918	−	11.7246i	−0.294034	−	0.509283i
$531$	1.45101	+	3.17726i	0.0629684	+	0.137882i
$532$	−0.542387	−	3.60388i	−0.0235155	−	0.156248i
$533$	13.4040	−	15.4691i	0.580592	−	0.670039i
$534$	−0.00855739	+	0.179642i	−0.000370315	+	0.00777386i
$535$	12.4600	−	2.40147i	0.538693	−	0.103825i
$536$	4.26483	+	1.70738i	0.184213	+	0.0737477i
$537$	−2.36681	−	9.75611i	−0.102135	−	0.421007i
$538$	−14.1786	+	9.11203i	−0.611282	+	0.392847i
$539$	−13.1320	−	17.9369i	−0.565634	−	0.772598i
$540$	−1.49134	+	3.26558i	−0.0641770	+	0.140528i
$541$	14.3881	−	1.37389i	0.618591	−	0.0590683i	0.218944	−	0.975737i	$-0.429739\pi$
$541$	14.3881	−	1.37389i	0.618591	−	0.0590683i	0.399647	+	0.916669i	$0.369133\pi$
$542$	24.0649	+	18.9248i	1.03367	+	0.812891i
$543$	−1.12714	−	23.6615i	−0.0483701	−	1.01541i
$544$	1.46358	+	6.03297i	0.0627506	+	0.258661i
$545$	4.33791	+	30.1708i	0.185816	+	1.29238i
$546$	−9.80996	+	6.39608i	−0.419827	+	0.273727i
$547$	0.0362179	+	0.0232758i	0.00154857	+	0.000995203i	0.541415	−	0.840756i	$-0.317889\pi$
$547$	0.0362179	+	0.0232758i	0.00154857	+	0.000995203i	−0.539866	+	0.841751i	$0.681525\pi$
$548$	−12.5652	−	2.42175i	−0.536760	−	0.103452i
$549$	−2.66425	+	10.9822i	−0.113707	+	0.468708i
$550$	−24.9371	−	2.38121i	−1.06332	−	0.101535i
$551$	−4.67569	−	8.09854i	−0.199191	−	0.345009i
$552$	−1.84239	−	4.42782i	−0.0784172	−	0.188461i
$553$	41.5985	−	16.9720i	1.76895	−	0.721721i
$554$	4.88166	+	10.6894i	0.207402	+	0.454147i
$555$	−14.9869	−	14.2900i	−0.636158	−	0.606576i
$556$	2.43547	+	7.03682i	0.103287	+	0.298428i
$557$	−14.1175	+	7.27809i	−0.598178	+	0.308382i	−0.730594	−	0.682812i	$-0.760757\pi$
$557$	−14.1175	+	7.27809i	−0.598178	+	0.308382i	0.132416	+	0.991194i	$0.457727\pi$
$558$	−2.62322	+	7.57929i	−0.111050	+	0.320857i
$559$	0.878225	+	6.10819i	0.0371450	+	0.258349i
$560$	5.56031	+	7.70062i	0.234966	+	0.325411i
$561$	−16.5852	+	10.6587i	−0.700229	+	0.450010i
$562$	−17.6294	+	7.05775i	−0.743652	+	0.297713i
$563$	24.4800	+	34.3774i	1.03171	+	1.44883i	0.888353	+	0.459162i	$0.151850\pi$
$563$	24.4800	+	34.3774i	1.03171	+	1.44883i	0.143357	+	0.989671i	$0.454210\pi$
$564$	1.35186	+	1.89843i	0.0569237	+	0.0799381i
$565$	−17.7026	+	7.08706i	−0.744755	+	0.298155i
$566$	−10.8594	+	6.97894i	−0.456456	+	0.293347i
$567$	1.54883	+	2.14502i	0.0650449	+	0.0900824i
$568$	−0.954897	−	6.64146i	−0.0400666	−	0.278669i
$569$	0.858629	−	2.48085i	0.0359956	−	0.104002i	−0.925571	−	0.378574i	$-0.876415\pi$
$569$	0.858629	−	2.48085i	0.0359956	−	0.104002i	0.961567	+	0.274571i	$0.0885359\pi$
$570$	−4.39542	+	2.26600i	−0.184104	+	0.0949121i
$571$	12.1557	+	35.1215i	0.508699	+	1.46979i	0.848450	+	0.529275i	$0.177536\pi$
$571$	12.1557	+	35.1215i	0.508699	+	1.46979i	−0.339751	+	0.940516i	$0.610343\pi$
$572$	10.1734	+	9.70031i	0.425371	+	0.405590i
$573$	−0.464906	−	1.01800i	−0.0194217	−	0.0425276i
$574$	−11.3281	+	4.62182i	−0.472828	+	0.192911i
$575$	25.7336	−	27.7288i	1.07316	−	1.15637i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−12.8817	−	1.23006i	−0.536273	−	0.0512079i	−0.176594	−	0.984284i	$-0.556508\pi$
$577$	−12.8817	−	1.23006i	−0.536273	−	0.0512079i	−0.359680	+	0.933076i	$0.617114\pi$
$578$	−5.07796	+	20.9317i	−0.211215	+	0.870642i
$579$	5.15913	+	0.994341i	0.214406	+	0.0413234i
$580$	20.5028	+	13.1763i	0.851331	+	0.547118i
$581$	30.1843	−	19.6801i	1.25226	−	0.816469i
$582$	−2.65969	−	18.4985i	−0.110248	−	0.766789i
$583$	2.82349	+	11.6386i	0.116937	+	0.482020i
$584$	0.459910	+	9.65470i	0.0190312	+	0.399514i
$585$	12.4907	+	9.82281i	0.516427	+	0.406123i
$586$	−28.2442	+	2.69699i	−1.16676	+	0.111412i
$587$	6.96869	−	15.2593i	0.287628	−	0.629818i	−0.709569	−	0.704636i	$-0.751110\pi$
$587$	6.96869	−	15.2593i	0.287628	−	0.629818i	0.997197	+	0.0748177i	$0.0238375\pi$
$588$	6.95894	−	0.757038i	0.286982	−	0.0312197i
$589$	−9.29411	+	5.97296i	−0.382957	+	0.246112i
$590$	−2.95631	−	12.1861i	−0.121709	−	0.501693i
$591$	7.75202	+	3.10344i	0.318875	+	0.127658i
$592$	5.66394	−	1.09163i	0.232786	−	0.0448659i
$593$	−1.72254	+	36.1606i	−0.0707364	+	1.48494i	0.632819	+	0.774300i	$0.281898\pi$
$593$	−1.72254	+	36.1606i	−0.0707364	+	1.48494i	−0.703556	+	0.710640i	$0.748405\pi$
$594$	2.07967	−	2.40007i	0.0853299	−	0.0984760i
$595$	8.77542	+	58.3081i	0.359757	+	2.39040i
$596$	−2.80119	−	6.13375i	−0.114741	−	0.251248i
$597$	−3.87092	−	6.70463i	−0.158426	−	0.274402i
$598$	−20.9690	+	3.30448i	−0.857487	+	0.135130i
$599$	0.730804	−	1.26579i	0.0298598	−	0.0517188i	−0.850709	−	0.525636i	$-0.823827\pi$
$599$	0.730804	−	1.26579i	0.0298598	−	0.0517188i	0.880569	+	0.473918i	$0.157161\pi$
$600$	4.57554	−	6.42545i	0.186796	−	0.262318i
$601$	−1.91914	+	0.563510i	−0.0782834	+	0.0229861i	−0.320640	−	0.947201i	$-0.603898\pi$
$601$	−1.91914	+	0.563510i	−0.0782834	+	0.0229861i	0.242356	+	0.970187i	$0.422080\pi$
$602$	1.18347	−	3.49361i	0.0482345	−	0.142389i
$603$	−3.86464	−	2.48365i	−0.157380	−	0.101142i
$604$	−4.16219	+	12.0259i	−0.169357	+	0.489325i
$605$	−3.04837	−	1.22038i	−0.123934	−	0.0496156i
$606$	−3.11075	+	2.96609i	−0.126365	+	0.120489i
$607$	12.7582	+	6.57729i	0.517838	+	0.266964i	0.697273	−	0.716806i	$-0.254397\pi$
$607$	12.7582	+	6.57729i	0.517838	+	0.266964i	−0.179435	+	0.983770i	$0.557427\pi$
$608$	0.196036	−	1.36346i	0.00795029	−	0.0552955i
$609$	15.9102	−	8.33527i	0.644715	−	0.337762i
$610$	16.8532	−	36.9034i	0.682367	−	1.49418i
$611$	9.57686	−	3.83400i	0.387438	−	0.155107i
$612$	−0.295387	−	6.20093i	−0.0119403	−	0.250658i
$613$	4.50657	−	4.29701i	0.182019	−	0.173554i	−0.593592	−	0.804766i	$-0.702291\pi$
$613$	4.50657	−	4.29701i	0.182019	−	0.173554i	0.775611	+	0.631212i	$0.217442\pi$
$614$	21.3028	−	16.7527i	0.859711	−	0.676084i
$615$	10.8715	+	12.5463i	0.438380	+	0.505917i
$616$	−2.80029	−	7.92186i	−0.112827	−	0.319181i
$617$	31.1986	−	36.0051i	1.25601	−	1.44951i	0.413793	−	0.910371i	$-0.364204\pi$
$617$	31.1986	−	36.0051i	1.25601	−	1.44951i	0.842216	−	0.539140i	$-0.181251\pi$
$618$	−2.82463	−	2.69328i	−0.113623	−	0.108339i
$619$	−17.7145	−	1.69153i	−0.712006	−	0.0679883i	−0.267233	−	0.963632i	$-0.586109\pi$
$619$	−17.7145	−	1.69153i	−0.712006	−	0.0679883i	−0.444773	+	0.895644i	$0.646715\pi$
$620$	14.3966	−	24.9357i	0.578182	−	1.00144i
$621$	0.971123	+	4.69648i	0.0389698	+	0.188463i
$622$	31.7643			1.27363
$623$	−0.346525	−	0.326085i	−0.0138832	−	0.0130643i
$624$	−4.24701	+	1.24703i	−0.170016	+	0.0499213i
$625$	−2.17842	−	0.419856i	−0.0871369	−	0.0167943i
$626$	−9.18602	+	4.73572i	−0.367147	+	0.189278i
$627$	4.29546	−	0.827883i	0.171544	−	0.0330625i
$628$	−2.82647	+	2.22276i	−0.112788	+	0.0886977i
$629$	34.3581	+	10.0885i	1.36995	+	0.402253i
$630$	−4.00248	−	8.61375i	−0.159463	−	0.343180i
$631$	2.60746	−	18.1353i	0.103801	−	0.721955i	−0.869751	−	0.493491i	$-0.835721\pi$
$631$	2.60746	−	18.1353i	0.103801	−	0.721955i	0.973552	−	0.228464i	$-0.0733702\pi$
$632$	16.9041	−	1.61415i	0.672409	−	0.0642073i
$633$	14.2594	+	20.0245i	0.566759	+	0.795901i
$634$	20.2805	+	15.9488i	0.805443	+	0.633407i
$635$	−37.6659	−	19.4181i	−1.49473	−	0.770585i
$636$	−3.61838	−	1.06245i	−0.143478	−	0.0421289i
$637$	4.00552	−	30.7241i	0.158704	−	1.21733i
$638$	−14.1184	−	16.2935i	−0.558954	−	0.645067i
$639$	−0.319263	+	6.70215i	−0.0126298	+	0.265133i
$640$	1.17417	+	3.39255i	0.0464133	+	0.134102i
$641$	6.95442	−	28.6665i	0.274683	−	1.13226i	−0.652542	−	0.757753i	$-0.726297\pi$
$641$	6.95442	−	28.6665i	0.274683	−	1.13226i	0.927225	−	0.374506i	$-0.122188\pi$
$642$	2.05029	−	2.87923i	0.0809184	−	0.113634i
$643$	−13.6370			−0.537791			−0.268896	−	0.963169i	$-0.586659\pi$
$643$	−13.6370			−0.537791			−0.268896	+	0.963169i	$0.586659\pi$
$644$	12.0716	+	3.90839i	0.475689	+	0.154012i
$645$	−5.00506			−0.197074
$646$	4.96026	−	6.96571i	0.195159	−	0.274062i
$647$	4.47539	−	18.4478i	0.175946	−	0.725259i	−0.813647	−	0.581360i	$-0.802521\pi$
$647$	4.47539	−	18.4478i	0.175946	−	0.725259i	0.989592	−	0.143899i	$-0.0459640\pi$
$648$	0.327068	+	0.945001i	0.0128484	+	0.0371231i
$649$	−0.527807	+	11.0800i	−0.0207182	+	0.434929i
$650$	−22.8645	−	26.3870i	−0.896820	−	1.03499i
$651$	−10.7307	−	18.3068i	−0.420569	−	0.717502i
$652$	1.07977	+	0.317048i	0.0422869	+	0.0124166i
$653$	−34.7517	−	17.9158i	−1.35994	−	0.701098i	−0.384866	−	0.922973i	$-0.625752\pi$
$653$	−34.7517	−	17.9158i	−1.35994	−	0.701098i	−0.975075	+	0.221874i	$0.928782\pi$
$654$	6.67403	+	5.24852i	0.260975	+	0.205233i
$655$	−13.6897	−	19.2245i	−0.534902	−	0.751165i
$656$	−4.60335	+	0.439566i	−0.179731	+	0.0171622i
$657$	1.37557	−	9.56727i	0.0536659	−	0.373255i
$658$	−6.14191	−	0.545723i	−0.239437	−	0.0212745i
$659$	−37.6850	−	11.0653i	−1.46800	−	0.431043i	−0.552551	−	0.833479i	$-0.686345\pi$
$659$	−37.6850	−	11.0653i	−1.46800	−	0.431043i	−0.915448	+	0.402436i	$0.868164\pi$
$660$	−8.96173	+	7.04758i	−0.348835	+	0.274327i
$661$	−14.2689	+	2.75011i	−0.554998	+	0.106967i	−0.459035	−	0.888418i	$-0.651805\pi$
$661$	−14.2689	+	2.75011i	−0.554998	+	0.106967i	−0.0959622	+	0.995385i	$0.530593\pi$
$662$	−3.25312	+	1.67710i	−0.126436	+	0.0651823i
$663$	−26.9818	−	5.20031i	−1.04788	−	0.201963i
$664$	13.0676	−	3.83700i	0.507123	−	0.148905i
$665$	3.00085	−	12.7348i	0.116368	−	0.493836i
$666$	−5.76817			−0.223512
$667$	32.4971	−	1.98816i	1.25829	−	0.0769817i
$668$	−6.89319	+	11.9393i	−0.266705	+	0.461947i
$669$	−22.5021	−	2.14869i	−0.869983	−	0.0830733i
$670$	11.9359	+	11.3809i	0.461124	+	0.439681i
$671$	−23.5018	+	27.1225i	−0.907277	+	1.04705i
$672$	2.60118	+	0.483606i	0.100343	+	0.0186555i
$673$	−8.73634	−	10.0823i	−0.336761	−	0.388643i	0.561960	−	0.827165i	$-0.310048\pi$
$673$	−8.73634	−	10.0823i	−0.336761	−	0.388643i	−0.898721	+	0.438522i	$0.855502\pi$
$674$	8.81776	−	6.93437i	0.339648	−	0.267102i
$675$	−5.70888	+	5.44340i	−0.219735	+	0.209517i
$676$	0.313667	+	6.58469i	0.0120641	+	0.253257i
$677$	−38.2998	+	15.3329i	−1.47198	+	0.589293i	−0.962522	−	0.271202i	$-0.912579\pi$
$677$	−38.2998	+	15.3329i	−1.47198	+	0.589293i	−0.509459	+	0.860495i	$0.670155\pi$
$678$	−2.20651	+	4.83158i	−0.0847404	+	0.185556i
$679$	41.7715	+	26.4581i	1.60304	+	1.01537i
$680$	−3.17171	+	22.0597i	−0.121630	+	0.845952i
$681$	14.7175	+	7.58741i	0.563977	+	0.290750i
$682$	−18.4341	+	17.5768i	−0.705877	+	0.673052i
$683$	16.7103	+	6.68979i	0.639401	+	0.255978i	0.668630	−	0.743595i	$-0.266881\pi$
$683$	16.7103	+	6.68979i	0.639401	+	0.255978i	−0.0292291	+	0.999573i	$0.509305\pi$
$684$	−0.450529	+	1.30172i	−0.0172264	+	0.0497724i
$685$	−38.6466	−	24.8367i	−1.47661	−	0.948961i
$686$	−10.4429	+	15.2953i	−0.398713	+	0.583976i
$687$	14.2918	−	4.19644i	0.545264	−	0.160104i
$688$	0.808696	−	1.13565i	0.0308312	−	0.0432964i
$689$	−8.34609	+	14.4558i	−0.317961	+	0.550724i
$690$	−0.232483	−	17.2155i	−0.00885049	−	0.655381i
$691$	−13.8383	−	23.9686i	−0.526432	−	0.911807i	−0.999526	−	0.0307950i	$-0.990196\pi$
$691$	−13.8383	−	23.9686i	−0.526432	−	0.911807i	0.473094	−	0.881012i	$-0.343137\pi$
$692$	4.49086	+	9.83361i	0.170717	+	0.373818i
$693$	1.25046	+	8.30866i	0.0475011	+	0.315620i
$694$	−19.4256	+	22.4184i	−0.737386	+	0.850989i
$695$	−1.27198	+	26.7022i	−0.0482490	+	1.01287i
$696$	6.66609	−	1.28478i	0.252678	−	0.0486996i
$697$	−26.6510	−	10.6695i	−1.00948	−	0.404135i
$698$	−0.749338	−	3.08882i	−0.0283629	−	0.116913i
$699$	−6.36631	+	4.09138i	−0.240796	+	0.154750i
$700$	5.05362	+	20.2488i	0.191009	+	0.765333i
$701$	−18.7460	+	41.0480i	−0.708026	+	1.55036i	0.121935	+	0.992538i	$0.461090\pi$
$701$	−18.7460	+	41.0480i	−0.708026	+	1.55036i	−0.829960	+	0.557822i	$0.811637\pi$
$702$	4.40626	−	0.420747i	0.166304	−	0.0158801i
$703$	−6.24561	−	4.91160i	−0.235558	−	0.185245i
$704$	−0.151108	−	3.17215i	−0.00569510	−	0.119555i
$705$	1.97253	+	8.13089i	0.0742899	+	0.306227i
$706$	0.839040	+	5.83565i	0.0315777	+	0.219628i
$707$	−0.615831	−	11.3553i	−0.0231607	−	0.427058i
$708$	−2.93842	−	1.88841i	−0.110433	−	0.0709708i
$709$	−14.3952	−	2.77444i	−0.540621	−	0.104196i	−0.0883716	−	0.996088i	$-0.528166\pi$
$709$	−14.3952	−	2.77444i	−0.540621	−	0.104196i	−0.452250	+	0.891891i	$0.649378\pi$
$710$	5.67896	−	23.4090i	0.213128	−	0.878524i
$711$	−16.9041	−	1.61415i	−0.633954	−	0.0605352i
$712$	−0.0899227	−	0.155751i	−0.00337000	−	0.00583701i
$713$	−4.17299	−	38.2375i	−0.156280	−	1.43200i
$714$	12.9772	+	10.0679i	0.485661	+	0.376782i
$715$	20.9635	+	45.9036i	0.783989	+	1.71670i
$716$	7.26563	+	6.92777i	0.271529	+	0.258903i
$717$	−3.02642	−	8.74426i	−0.113024	−	0.326560i
$718$	−29.7827	+	15.3540i	−1.11148	+	0.573008i
$719$	−1.67672	+	4.84455i	−0.0625309	+	0.180671i	−0.971939	−	0.235235i	$-0.924414\pi$
$719$	−1.67672	+	4.84455i	−0.0625309	+	0.180671i	0.909408	+	0.415906i	$0.136535\pi$
$720$	−0.510910	−	3.55346i	−0.0190405	−	0.132430i
$721$	10.2725	−	1.04916i	0.382569	−	0.0390729i
$722$	14.3876	−	9.24634i	0.535450	−	0.344113i
$723$	−23.1445	+	9.26564i	−0.860751	+	0.344593i
$724$	13.7406	+	19.2960i	0.510665	+	0.717129i
$725$	31.0623	+	43.6209i	1.15363	+	1.62004i
$726$	−0.849127	+	0.339939i	−0.0315141	+	0.0126163i
$727$	37.7758	−	24.2770i	1.40103	−	0.900384i	0.401147	−	0.916014i	$-0.368612\pi$
$727$	37.7758	−	24.2770i	1.40103	−	0.900384i	0.999878	+	0.0156293i	$0.00497518\pi$
$728$	4.79468	−	10.6844i	0.177703	−	0.395990i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−11.3491	+	32.7912i	−0.420051	+	1.21366i
$731$	7.69281	−	3.96592i	0.284529	−	0.146685i
$732$	−3.69611	−	10.6792i	−0.136612	−	0.394715i
$733$	−5.29986	−	5.05341i	−0.195755	−	0.186652i	0.585862	−	0.810411i	$-0.300756\pi$
$733$	−5.29986	−	5.05341i	−0.195755	−	0.186652i	−0.781617	+	0.623759i	$0.785605\pi$
$734$	6.20304	+	13.5828i	0.228958	+	0.501349i
$735$	24.2031	+	6.76201i	0.892746	+	0.249420i
$736$	3.94378	+	2.72885i	0.145370	+	0.100587i
$737$	−7.29454	−	12.6345i	−0.268698	−	0.465398i
$738$	4.60335	+	0.439566i	0.169452	+	0.0161807i
$739$	2.09168	−	8.62203i	0.0769437	−	0.317166i	−0.920313	−	0.391182i	$-0.872066\pi$
$739$	2.09168	−	8.62203i	0.0769437	−	0.317166i	0.997257	+	0.0740156i	$0.0235815\pi$
$740$	20.3335	+	3.91896i	0.747475	+	0.144064i
$741$	5.12924	+	3.29636i	0.188427	+	0.121095i
$742$	8.35791	−	5.44935i	0.306829	−	0.200052i
$743$	−1.84362	−	12.8227i	−0.0676359	−	0.470418i	−0.995287	−	0.0969706i	$-0.969085\pi$
$743$	−1.84362	−	12.8227i	−0.0676359	−	0.470418i	0.927651	−	0.373447i	$-0.121824\pi$
$744$	−1.89088	−	7.79432i	−0.0693231	−	0.285754i
$745$	−1.15185	−	24.1803i	−0.0422006	−	0.885899i
$746$	17.1121	+	13.4571i	0.626517	+	0.492699i
$747$	−13.5576	+	1.29460i	−0.496048	+	0.0473669i
$748$	8.18987	−	17.9333i	0.299451	−	0.655707i
$749$	2.26451	+	9.07344i	0.0827435	+	0.331536i
$750$	8.72231	−	5.60549i	0.318494	−	0.204683i
$751$	6.24530	+	25.7435i	0.227894	+	0.939392i	0.964713	+	0.263302i	$0.0848117\pi$
$751$	6.24530	+	25.7435i	0.227894	+	0.939392i	−0.736819	+	0.676090i	$0.763673\pi$
$752$	−2.16363	−	0.866185i	−0.0788993	−	0.0315865i
$753$	−21.6991	+	4.18215i	−0.790758	+	0.152406i
$754$	1.42980	−	30.0151i	0.0520702	−	1.09309i
$755$	−29.9176	+	34.5268i	−1.08881	+	1.25656i
$756$	−2.46265	−	0.967143i	−0.0895656	−	0.0351746i
$757$	−13.7580	−	30.1258i	−0.500044	−	1.09494i	−0.976455	−	0.215720i	$-0.930790\pi$
$757$	−13.7580	−	30.1258i	−0.500044	−	1.09494i	0.476412	−	0.879222i	$-0.341937\pi$
$758$	16.8149	+	29.1242i	0.610744	+	1.05784i
$759$	−4.09316	+	14.6700i	−0.148572	+	0.532488i
$760$	2.47257	−	4.28262i	0.0896896	−	0.155347i
$761$	−16.9041	+	23.7385i	−0.612774	+	0.860521i	−0.998059	−	0.0622769i	$-0.980164\pi$
$761$	−16.9041	+	23.7385i	−0.612774	+	0.860521i	0.385285	+	0.922798i	$0.374103\pi$
$762$	−11.3260	+	3.32560i	−0.410296	+	0.120474i
$763$	−22.0295	+	4.39638i	−0.797522	+	0.159160i
$764$	0.941476	+	0.605050i	0.0340614	+	0.0218899i
$765$	7.28922	−	21.0608i	0.263542	−	0.761456i
$766$	−18.3733	−	7.35556i	−0.663854	−	0.265767i
$767$	−11.1894	+	10.6691i	−0.404027	+	0.385239i
$768$	0.888835	+	0.458227i	0.0320731	+	0.0165348i
$769$	3.75138	−	26.0914i	0.135278	−	0.940879i	−0.803242	−	0.595653i	$-0.796893\pi$
$769$	3.75138	−	26.0914i	0.135278	−	0.940879i	0.938520	−	0.345226i	$-0.112198\pi$
$770$	1.23697	−	30.1386i	0.0445773	−	1.08612i
$771$	−7.60491	+	16.6524i	−0.273884	+	0.599722i
$772$	−4.87772	+	1.95274i	−0.175553	+	0.0702808i
$773$	1.28090	+	26.8894i	0.0460708	+	0.967146i	0.897045	+	0.441939i	$0.145709\pi$
$773$	1.28090	+	26.8894i	0.0460708	+	0.967146i	−0.850974	+	0.525207i	$0.823988\pi$
$774$	−1.00901	+	0.962085i	−0.0362680	+	0.0345814i
$775$	49.7302	−	39.1082i	1.78636	−	1.40481i
$776$	12.2385	+	14.1240i	0.439338	+	0.507023i
$777$	9.91782	−	11.5991i	0.355800	−	0.416116i
$778$	−14.0853	+	16.2553i	−0.504983	+	0.582782i
$779$	4.61008	+	4.39570i	0.165173	+	0.157492i
$780$	−15.8185	−	1.51048i	−0.566392	−	0.0540839i
$781$	−10.6542	+	18.4537i	−0.381238	+	0.660324i
$782$	13.9986	+	26.2761i	0.500588	+	0.939631i
$783$	−6.78878			−0.242611
$784$	−5.44495	+	4.39915i	−0.194463	+	0.157112i
$785$	−12.3859	+	3.63683i	−0.442072	+	0.129804i
$786$	−6.45521	−	1.24414i	−0.230250	−	0.0443770i
$787$	34.6592	−	17.8681i	1.23547	−	0.636927i	0.288260	−	0.957552i	$-0.406923\pi$
$787$	34.6592	−	17.8681i	1.23547	−	0.636927i	0.947206	+	0.320625i	$0.103893\pi$
$788$	−8.19926	+	1.58028i	−0.292087	+	0.0562951i
$789$	9.92310	−	7.80361i	0.353272	−	0.277816i
$790$	58.4924	+	17.1749i	2.08107	+	0.611056i
$791$	−5.92186	−	12.7445i	−0.210557	−	0.453141i
$792$	−0.451956	+	3.14342i	−0.0160595	+	0.111697i
$793$	−49.7939	+	4.75475i	−1.76823	+	0.168846i
$794$	−17.3263	−	24.3314i	−0.614889	−	0.863490i
$795$	−10.6419	−	8.36886i	−0.377428	−	0.296813i
$796$	6.88122	+	3.54752i	0.243898	+	0.125738i
$797$	8.63464	+	2.53536i	0.305855	+	0.0898071i	0.431058	−	0.902324i	$-0.358140\pi$
$797$	8.63464	+	2.53536i	0.305855	+	0.0898071i	−0.125204	+	0.992131i	$0.539958\pi$
$798$	−1.84296	−	3.14414i	−0.0652401	−	0.111301i
$799$	−9.47458	−	10.9342i	−0.335187	−	0.386826i
$800$	−0.375330	+	7.87915i	−0.0132699	+	0.278570i
$801$	0.0588217	+	0.169954i	0.00207836	+	0.00600503i
$802$	6.48689	−	26.7393i	0.229060	−	0.944199i
$803$	17.8052	−	25.0039i	0.628332	−	0.882369i
$804$	4.59391			0.162015
$805$	35.0180	+	29.1328i	1.23422	+	1.02680i
$806$	−35.5007			−1.25046
$807$	−9.77635	+	13.7290i	−0.344144	+	0.483282i
$808$	1.01334	−	4.17703i	0.0356491	−	0.146947i
$809$	17.7680	+	51.3372i	0.624688	+	1.80492i	0.592690	+	0.805431i	$0.298066\pi$
$809$	17.7680	+	51.3372i	0.624688	+	1.80492i	0.0319984	+	0.999488i	$0.489813\pi$
$810$	−0.170819	+	3.58593i	−0.00600197	+	0.125997i
$811$	30.3425	+	35.0171i	1.06547	+	1.22962i	0.972244	+	0.233971i	$0.0751720\pi$
$811$	30.3425	+	35.0171i	1.06547	+	1.22962i	0.0932245	+	0.995645i	$0.470283\pi$
$812$	−8.87816	+	15.6138i	−0.311562	+	0.547937i
$813$	29.3747	+	8.62519i	1.03022	+	0.302499i
$814$	−16.2819	−	8.39391i	−0.570681	−	0.294206i
$815$	3.17566	+	2.49737i	0.111239	+	0.0874790i
$816$	3.60097	+	5.05686i	0.126059	+	0.177025i
$817$	−1.91174	+	0.182549i	−0.0668832	+	0.00638657i
$818$	3.10850	−	21.6201i	0.108686	−	0.755928i
$819$	−6.73007	+	9.58391i	−0.235168	+	0.334889i
$820$	−15.9287	−	4.67709i	−0.556255	−	0.163331i
$821$	−41.0296	+	32.2660i	−1.43194	+	1.12609i	−0.460824	+	0.887492i	$0.652446\pi$
$821$	−41.0296	+	32.2660i	−1.43194	+	1.12609i	−0.971118	+	0.238600i	$0.923312\pi$
$822$	−12.5652	+	2.42175i	−0.438263	+	0.0844682i
$823$	29.0330	−	14.9675i	1.01203	−	0.521736i	0.129291	−	0.991607i	$-0.458730\pi$
$823$	29.0330	−	14.9675i	1.01203	−	0.521736i	0.882735	+	0.469871i	$0.155700\pi$
$824$	3.83232	+	0.738619i	0.133505	+	0.0257310i
$825$	−24.0358	+	7.05756i	−0.836820	+	0.245713i
$826$	8.84971	−	2.66189i	0.307921	−	0.0926189i
$827$	22.5173			0.783002			0.391501	−	0.920178i	$-0.371956\pi$
$827$	22.5173			0.783002			0.391501	+	0.920178i	$0.371956\pi$
$828$	−3.35607	−	3.42590i	−0.116631	−	0.119058i
$829$	−16.9868	+	29.4220i	−0.589976	+	1.02187i	0.404259	+	0.914645i	$0.367529\pi$
$829$	−16.9868	+	29.4220i	−0.589976	+	1.02187i	−0.994235	+	0.107224i	$0.965804\pi$
$830$	48.6719	+	4.64760i	1.68943	+	0.161321i
$831$	8.50481	+	8.10932i	0.295029	+	0.281309i
$832$	2.89861	−	3.34518i	0.100491	−	0.115973i
$833$	−42.5585	+	8.78489i	−1.47457	+	0.304378i
$834$	4.87633	+	5.62759i	0.168854	+	0.194867i
$835$	−38.9042	+	30.5946i	−1.34633	+	1.05877i
$836$	−3.16599	+	3.01876i	−0.109498	+	0.104406i
$837$	0.381626	+	8.01132i	0.0131909	+	0.276912i
$838$	4.14870	−	1.66089i	0.143315	−	0.0573745i
$839$	−12.7247	+	27.8631i	−0.439304	+	0.961941i	0.552422	+	0.833565i	$0.313704\pi$
$839$	−12.7247	+	27.8631i	−0.439304	+	0.961941i	−0.991726	+	0.128376i	$0.959023\pi$
$840$	8.02405	+	5.08245i	0.276856	+	0.175361i
$841$	−2.43180	+	16.9136i	−0.0838553	+	0.583226i
$842$	−26.5514	−	13.6882i	−0.915020	−	0.471726i
$843$	−13.7435	+	13.1044i	−0.473351	+	0.451339i
$844$	−22.8218	−	9.13646i	−0.785558	−	0.314490i
$845$	−7.74033	+	22.3642i	−0.266276	+	0.769353i
$846$	1.96060	+	1.26000i	0.0674068	+	0.0433197i
$847$	0.776415	−	2.29199i	0.0266779	−	0.0787536i
$848$	3.61838	−	1.06245i	0.124256	−	0.0364847i
$849$	−7.48774	+	10.5151i	−0.256979	+	0.360876i
$850$	−24.4845	+	42.4084i	−0.839811	+	1.45459i
$851$	25.0059	−	11.8304i	0.857190	−	0.405542i
$852$	−3.35488	−	5.81082i	−0.114936	−	0.199075i
$853$	−12.0739	−	26.4381i	−0.413401	−	0.905222i	−0.995734	−	0.0922717i	$-0.970587\pi$
$853$	−12.0739	−	26.4381i	−0.413401	−	0.905222i	0.582333	−	0.812951i	$-0.302140\pi$
$854$	27.8297	+	10.9294i	0.952313	+	0.373997i
$855$	−3.23838	+	3.73729i	−0.110750	+	0.127813i
$856$	−0.168185	+	3.53063i	−0.00574843	+	0.120674i
$857$	43.5505	−	8.39367i	1.48766	−	0.286722i	0.620282	−	0.784379i	$-0.287018\pi$
$857$	43.5505	−	8.39367i	1.48766	−	0.286722i	0.867374	+	0.497656i	$0.165806\pi$
$858$	13.0499	+	5.22439i	0.445516	+	0.178358i
$859$	5.50800	+	22.7043i	0.187930	+	0.774660i	0.985253	+	0.171106i	$0.0547341\pi$
$859$	5.50800	+	22.7043i	0.187930	+	0.774660i	−0.797322	+	0.603554i	$0.793751\pi$
$860$	4.21052	−	2.70594i	0.143578	−	0.0922717i
$861$	−8.79893	+	8.50100i	−0.299867	+	0.289713i
$862$	11.4551	−	25.0832i	0.390162	−	0.854336i
$863$	34.3013	−	3.27538i	1.16763	−	0.111495i	0.506823	−	0.862050i	$-0.330820\pi$
$863$	34.3013	−	3.27538i	1.16763	−	0.111495i	0.660808	+	0.750555i	$0.270214\pi$
$864$	−0.786053	−	0.618159i	−0.0267421	−	0.0210302i
$865$	1.84664	+	38.7658i	0.0627878	+	1.31808i
$866$	7.53355	+	31.0537i	0.256000	+	1.05525i
$867$	3.06529	+	21.3196i	0.104103	+	0.724050i
$868$	18.9247	+	9.59925i	0.642345	+	0.325820i
$869$	−45.3666	−	29.1553i	−1.53895	−	0.989026i
$870$	23.9313	+	4.61237i	0.811346	+	0.156374i
$871$	4.79393	−	19.7608i	0.162436	−	0.669570i
$872$	−8.45212	−	0.807079i	−0.286225	−	0.0273312i
$873$	−9.34438	−	16.1849i	−0.316259	−	0.547777i
$874$	−0.716697	−	6.56716i	−0.0242426	−	0.222137i
$875$	−3.72519	+	27.1776i	−0.125935	+	0.918772i
$876$	4.01526	+	8.79218i	0.135663	+	0.297060i
$877$	−35.3205	−	33.6780i	−1.19269	−	1.13723i	−0.987354	−	0.158533i	$-0.949323\pi$
$877$	−35.3205	−	33.6780i	−1.19269	−	1.13723i	−0.205334	−	0.978692i	$-0.565828\pi$
$878$	−8.78205	−	25.3741i	−0.296380	−	0.856334i
$879$	−25.2186	+	13.0011i	−0.850602	+	0.438516i
$880$	3.72888	−	10.7739i	0.125700	−	0.363187i
$881$	0.0542731	+	0.377478i	0.00182851	+	0.0127176i	0.990715	−	0.135953i	$-0.0434097\pi$
$881$	0.0542731	+	0.377478i	0.00182851	+	0.0127176i	−0.988887	+	0.148671i	$0.952501\pi$
$882$	6.17910	−	3.28919i	0.208061	−	0.110753i
$883$	−44.6030	+	28.6646i	−1.50101	+	0.964640i	−0.506251	+	0.862386i	$0.668969\pi$
$883$	−44.6030	+	28.6646i	−1.50101	+	0.964640i	−0.994758	+	0.102254i	$0.967394\pi$
$884$	25.5100	−	10.2127i	0.857994	−	0.343489i
$885$	−7.27365	−	10.2144i	−0.244501	−	0.343354i
$886$	−4.34619	−	6.10337i	−0.146013	−	0.205047i
$887$	−18.9699	+	7.59441i	−0.636948	+	0.254995i	−0.667583	−	0.744535i	$-0.732671\pi$
$887$	−18.9699	+	7.59441i	−0.636948	+	0.254995i	0.0306355	+	0.999531i	$0.490247\pi$
$888$	4.85250	−	3.11851i	0.162839	−	0.104650i
$889$	12.7865	−	28.4932i	0.428845	−	0.955632i
$890$	−0.0918849	−	0.639073i	−0.00307999	−	0.0214218i
$891$	1.03868	−	3.00108i	0.0347972	−	0.100540i
$892$	20.0917	−	10.3580i	0.672719	−	0.346811i
$893$	1.04999	+	3.03374i	0.0351365	+	0.101520i
$894$	−4.88022	−	4.65328i	−0.163219	−	0.155629i
$895$	14.9717	+	32.7834i	0.500449	+	1.09583i
$896$	−2.44971	+	0.999468i	−0.0818390	+	0.0333899i
$897$	−18.2388	+	10.8612i	−0.608976	+	0.362644i
$898$	−2.95376	−	5.11605i	−0.0985681	−	0.170725i
$899$	54.2022	+	5.17568i	1.80774	+	0.172619i
$900$	1.85969	−	7.66573i	0.0619896	−	0.255524i
$901$	22.9880	+	4.43057i	0.765841	+	0.147604i
$902$	12.3543	+	7.93961i	0.411352	+	0.264360i
$903$	−0.199752	−	3.68321i	−0.00664733	−	0.122569i
$904$	−0.755916	−	5.25751i	−0.0251414	−	0.174862i
$905$	20.0492	+	82.6440i	0.666458	+	2.74718i
$906$	0.605516	+	12.7113i	0.0201169	+	0.422306i
$907$	34.1753	+	26.8757i	1.13477	+	0.892393i	0.995204	−	0.0978193i	$-0.0311867\pi$
$907$	34.1753	+	26.8757i	1.13477	+	0.892393i	0.139566	+	0.990213i	$0.455429\pi$
$908$	−16.4832	+	1.57396i	−0.547015	+	0.0522336i
$909$	−1.78553	+	3.90977i	−0.0592224	+	0.129679i
$910$	30.2357	−	29.2120i	1.00230	−	0.968367i
$911$	−26.9136	+	17.2963i	−0.891687	+	0.573053i	−0.904314	−	0.426868i	$-0.859617\pi$
$911$	−26.9136	+	17.2963i	−0.891687	+	0.573053i	0.0126269	+	0.999920i	$0.495981\pi$
$912$	−0.324753	−	1.33865i	−0.0107536	−	0.0443271i
$913$	−40.1533	−	16.0749i	−1.32888	−	0.532003i
$914$	32.2211	−	6.21010i	1.06578	−	0.205412i
$915$	1.93038	−	40.5236i	0.0638164	−	1.33967i
$916$	−9.75422	+	11.2570i	−0.322289	+	0.371941i
$917$	13.6009	−	10.8415i	0.449142	−	0.358017i
$918$	−2.57888	−	5.64696i	−0.0851158	−	0.186377i
$919$	−9.96978	−	17.2682i	−0.328873	−	0.569624i	0.653416	−	0.756999i	$-0.273335\pi$
$919$	−9.96978	−	17.2682i	−0.328873	−	0.569624i	−0.982288	+	0.187375i	$0.940002\pi$
$920$	9.50296	+	14.3569i	0.313303	+	0.473332i
$921$	13.5505	−	23.4701i	0.446504	−	0.773367i
$922$	3.47566	−	4.88088i	0.114465	−	0.160743i
$923$	−28.4964	+	8.36729i	−0.937969	+	0.275413i
$924$	−5.54396	−	6.31364i	−0.182383	−	0.207703i
$925$	38.2769	+	24.5991i	1.25854	+	0.808813i
$926$	−8.94156	+	25.8349i	−0.293838	+	0.848989i
$927$	−3.62328	−	1.45054i	−0.119004	−	0.0476421i
$928$	−4.91327	+	4.68479i	−0.161286	+	0.153786i
$929$	−29.0448	−	14.9737i	−0.952930	−	0.491270i	−0.0896382	−	0.995974i	$-0.528571\pi$
$929$	−29.0448	−	14.9737i	−0.952930	−	0.491270i	−0.863292	+	0.504705i	$0.831601\pi$
$930$	4.09771	−	28.5002i	0.134369	−	0.934557i
$931$	9.49129	+	1.70007i	0.311064	+	0.0557174i
$932$	3.14371	−	6.88377i	0.102976	−	0.225485i
$933$	29.4889	−	11.8056i	0.965424	−	0.386497i
$934$	−0.169187	−	3.55167i	−0.00553596	−	0.116214i
$935$	51.2233	−	48.8414i	1.67518	−	1.59728i
$936$	−3.47931	+	2.73616i	−0.113725	+	0.0894341i
$937$	−28.2344	−	32.5842i	−0.922378	−	1.06448i	−0.997731	−	0.0673235i	$-0.978554\pi$
$937$	−28.2344	−	32.5842i	−0.922378	−	1.06448i	0.0753537	−	0.997157i	$-0.475991\pi$
$938$	−7.89878	+	9.23781i	−0.257904	+	0.301625i
$939$	−6.76792	+	7.81059i	−0.220863	+	0.254889i
$940$	−6.05529	−	5.77371i	−0.197502	−	0.188318i
$941$	7.28415	+	0.695552i	0.237457	+	0.0226744i	0.213106	−	0.977029i	$-0.431642\pi$
$941$	7.28415	+	0.695552i	0.237457	+	0.0226744i	0.0243507	+	0.999703i	$0.492248\pi$
$942$	−1.79789	+	3.11403i	−0.0585783	+	0.101461i
$943$	−20.8577	+	7.53582i	−0.679221	+	0.245400i
$944$	3.49291			0.113685
$945$	−6.91718	−	6.50916i	−0.225016	−	0.211743i
$946$	−4.24817	+	1.24738i	−0.138120	+	0.0405557i
$947$	−12.0522	−	2.32287i	−0.391643	−	0.0754830i	−0.0103719	−	0.999946i	$-0.503302\pi$
$947$	−12.0522	−	2.32287i	−0.391643	−	0.0754830i	−0.381271	+	0.924463i	$0.624514\pi$
$948$	15.0933	−	7.78115i	0.490208	−	0.252720i
$949$	42.0099	−	8.09675i	1.36370	−	0.262832i
$950$	8.54099	−	6.71671i	0.277106	−	0.217919i
$951$	24.7554	+	7.26883i	0.802748	+	0.235708i
$952$	−16.3603	−	1.45365i	−0.530239	−	0.0471130i
$953$	−5.53812	+	38.5184i	−0.179397	+	1.24773i	0.678765	+	0.734356i	$0.262516\pi$
$953$	−5.53812	+	38.5184i	−0.179397	+	1.24773i	−0.858162	+	0.513379i	$0.828394\pi$
$954$	−3.75406	+	0.358469i	−0.121542	+	0.0116059i
$955$	2.33049	+	3.27272i	0.0754129	+	0.105903i
$956$	7.27349	+	5.71993i	0.235241	+	0.184996i
$957$	−19.1628	−	9.87910i	−0.619445	−	0.319346i
$958$	−19.5342	−	5.73576i	−0.631121	−	0.185314i
$959$	16.7349	−	29.4312i	0.540397	−	0.950382i
$960$	2.35095	+	2.71314i	0.0758765	+	0.0875662i
$961$	1.58576	−	33.2892i	0.0511535	−	1.07384i
$962$	−8.35060	−	24.1275i	−0.269234	−	0.777901i
$963$	0.833321	−	3.43500i	0.0268534	−	0.110691i
$964$	14.4610	−	20.3076i	0.465756	−	0.654063i
$965$	−18.8621			−0.607194
$966$	12.6595	−	0.858153i	0.407314	−	0.0276106i
$967$	4.90995			0.157893			0.0789466	−	0.996879i	$-0.474844\pi$
$967$	4.90995			0.157893			0.0789466	+	0.996879i	$0.474844\pi$
$968$	0.530546	−	0.745048i	0.0170524	−	0.0239467i
$969$	2.01605	−	8.31028i	0.0647649	−	0.266965i
$970$	21.9438	+	63.4026i	0.704574	+	2.03573i
$971$	2.34875	−	49.3064i	0.0753750	−	1.58232i	−0.572070	−	0.820205i	$-0.693859\pi$
$971$	2.34875	−	49.3064i	0.0753750	−	1.58232i	0.647445	−	0.762112i	$-0.275837\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	−19.7008	+	0.129637i	−0.631579	+	0.00415598i
$974$	24.9416	+	7.32352i	0.799181	+	0.234661i
$975$	−31.0337	−	15.9990i	−0.993875	−	0.512378i
$976$	8.88297	+	6.98565i	0.284337	+	0.223605i
$977$	−8.39598	−	11.7905i	−0.268611	−	0.377212i	0.658135	−	0.752900i	$-0.271346\pi$
$977$	−8.39598	−	11.7905i	−0.268611	−	0.377212i	−0.926746	+	0.375688i	$0.877406\pi$
$978$	1.12026	−	0.106971i	0.0358218	−	0.00342057i
$979$	−0.0812822	+	0.565330i	−0.00259779	+	0.0180680i
$980$	−24.0168	+	7.39664i	−0.767188	+	0.236277i
$981$	8.14663	+	2.39207i	0.260102	+	0.0763728i
$982$	−10.4695	+	8.23327i	−0.334094	+	0.262734i
$983$	1.57971	−	0.304465i	0.0503850	−	0.00971091i	−0.163996	−	0.986461i	$-0.552439\pi$
$983$	1.57971	−	0.304465i	0.0503850	−	0.00971091i	0.214381	+	0.976750i	$0.431226\pi$
$984$	−4.11023	+	2.11897i	−0.131029	+	0.0675503i
$985$	−29.4353	−	5.67319i	−0.937887	−	0.180763i
$986$	−40.4373	+	11.8735i	−1.28779	+	0.378128i
$987$	−5.90478	+	1.77609i	−0.187951	+	0.0565334i
$988$	−6.09713			−0.193976
$989$	2.40096	−	6.24023i	0.0763461	−	0.198428i
$990$	−5.70046	+	9.87348i	−0.181172	+	0.313800i
$991$	−9.39265	−	0.896890i	−0.298367	−	0.0284906i	−0.0552012	−	0.998475i	$-0.517580\pi$
$991$	−9.39265	−	0.896890i	−0.298367	−	0.0284906i	−0.243166	+	0.969985i	$0.578186\pi$
$992$	5.80464	+	5.53471i	0.184298	+	0.175727i
$993$	−2.39678	+	2.76603i	−0.0760594	+	0.0877772i
$994$	17.4533	+	3.24488i	0.553584	+	0.102921i
$995$	18.2007	+	21.0047i	0.577000	+	0.665894i
$996$	10.7055	−	8.41890i	0.339217	−	0.266763i
$997$	25.3570	−	24.1778i	0.803064	−	0.765720i	−0.172600	−	0.984992i	$-0.555217\pi$
$997$	25.3570	−	24.1778i	0.803064	−	0.765720i	0.975664	+	0.219272i	$0.0703683\pi$
$998$	−0.478453	−	10.0440i	−0.0151452	−	0.317936i
$999$	−5.35499	+	2.14381i	−0.169424	+	0.0678273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.487.8	yes	160
7.2	even	3	inner	966.2.y.a.625.1	yes	160
23.6	even	11	inner	966.2.y.a.949.1	yes	160
161.121	even	33	inner	966.2.y.a.121.8	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.121.8	✓	160	161.121	even	33	inner
966.2.y.a.487.8	yes	160	1.1	even	1	trivial
966.2.y.a.625.1	yes	160	7.2	even	3	inner
966.2.y.a.949.1	yes	160	23.6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.580057 + 0.814576i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(0.170819 - 3.58593i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(2.64569 - 0.0174095i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 + 0.814576i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(0.170819 - 3.58593i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(2.64569 - 0.0174095i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(2.82193 + 2.21919i) q^{10} +(-1.84211 - 2.58689i) q^{11} +(0.995472 - 0.0950560i) q^{12} +(0.629929 - 4.38125i) q^{13} +(-1.52047 + 2.16522i) q^{14} +(3.44458 + 1.01142i) q^{15} +(-0.786053 + 0.618159i) q^{16} +(-6.09578 + 1.17486i) q^{17} +(0.888835 - 0.458227i) q^{18} +(1.35258 + 0.260689i) q^{19} +(-3.44458 + 1.01142i) q^{20} +(-0.606827 + 2.57522i) q^{21} +3.17574 q^{22} +(-2.91341 + 3.80947i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-7.85237 - 0.749810i) q^{25} +(3.20347 + 3.05450i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.881774 - 2.49449i) q^{28} +(-4.44570 - 5.13062i) q^{29} +(-2.82193 + 2.21919i) q^{30} +(-5.80464 + 5.53471i) q^{31} +(-0.0475819 - 0.998867i) q^{32} +(2.94826 - 1.18031i) q^{33} +(2.57888 - 5.64696i) q^{34} +(0.389506 - 9.49025i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-5.12696 - 2.64313i) q^{37} +(-0.996928 + 0.950568i) q^{38} +(4.10924 + 1.64509i) q^{39} +(1.17417 - 3.39255i) q^{40} +(3.89020 + 2.50008i) q^{41} +(-1.74572 - 1.98808i) q^{42} +(-1.33769 + 0.392782i) q^{43} +(-1.84211 + 2.58689i) q^{44} +(-1.79500 + 3.10903i) q^{45} +(-1.41315 - 4.58290i) q^{46} +(1.16528 + 2.01833i) q^{47} +(-0.415415 - 0.909632i) q^{48} +(6.99939 - 0.0921203i) q^{49} +(5.16560 - 5.96142i) q^{50} +(0.295387 - 6.20093i) q^{51} +(-4.34631 + 0.837683i) q^{52} +(-3.50100 - 1.40159i) q^{53} +(0.235759 + 0.971812i) q^{54} +(-9.59106 + 6.16380i) q^{55} +(2.54343 + 0.728674i) q^{56} +(-0.572225 + 1.25300i) q^{57} +(6.75804 - 0.645314i) q^{58} +(-2.74561 - 2.15917i) q^{59} +(-0.170819 - 3.58593i) q^{60} +(-2.66425 - 10.9822i) q^{61} +(-1.14142 - 7.93877i) q^{62} +(-2.35956 - 1.19685i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-15.6033 - 3.00728i) q^{65} +(-0.748710 + 3.08623i) q^{66} +(4.57310 + 0.436678i) q^{67} +(3.10398 + 5.37625i) q^{68} +(-3.01522 - 3.72940i) q^{69} +(7.50460 + 5.82217i) q^{70} +(-2.78733 - 6.10340i) q^{71} +(-0.723734 - 0.690079i) q^{72} +(3.16132 + 9.13405i) q^{73} +(5.12696 - 2.64313i) q^{74} +(2.57994 - 7.45425i) q^{75} +(-0.196036 - 1.36346i) q^{76} +(-4.91870 - 6.81204i) q^{77} +(-3.72364 + 2.39304i) q^{78} +(15.7646 - 6.31120i) q^{79} +(2.08240 + 2.92433i) q^{80} +(0.580057 + 0.814576i) q^{81} +(-4.29304 + 1.71867i) q^{82} +(11.4573 - 7.36316i) q^{83} +(2.63206 - 0.268820i) q^{84} +(3.17171 + 22.0597i) q^{85} +(0.455987 - 1.31749i) q^{86} +(6.03411 - 3.11080i) q^{87} +(-1.03868 - 3.00108i) q^{88} +(-0.130160 - 0.124108i) q^{89} +(-1.49134 - 3.26558i) q^{90} +(1.59032 - 11.6024i) q^{91} +(4.55283 + 1.50722i) q^{92} +(-4.01020 - 6.94587i) q^{93} +(-2.32002 - 0.221535i) q^{94} +(1.16586 - 4.80575i) q^{95} +(0.981929 + 0.189251i) q^{96} +(15.7220 + 10.1039i) q^{97} +(-3.98501 + 5.75497i) q^{98} +(0.451956 + 3.14342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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Database

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