LMFDB - Embedded newform 880.2.cz.a.763.58

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(147,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 15, 5, 4]))

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

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

chi := DirichletCharacter("880.147");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cz (of order $20$, degree $8$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$1120$
Relative dimension:	$140$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			763.58
Character	$\chi$	$=$	880.763
Dual form			880.2.cz.a.707.58

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.420899 + 1.35013i) q^{2} +(-0.618224 - 0.200873i) q^{3} +(-1.64569 - 1.13653i) q^{4} +(0.266898 + 2.22008i) q^{5} +(0.531414 - 0.750134i) q^{6} +(2.32748 + 1.18591i) q^{7} +(2.22713 - 1.74352i) q^{8} +(-2.08520 - 1.51499i) q^{9} +O(q^{10})$	\(q+(-0.420899 + 1.35013i) q^{2} +(-0.618224 - 0.200873i) q^{3} +(-1.64569 - 1.13653i) q^{4} +(0.266898 + 2.22008i) q^{5} +(0.531414 - 0.750134i) q^{6} +(2.32748 + 1.18591i) q^{7} +(2.22713 - 1.74352i) q^{8} +(-2.08520 - 1.51499i) q^{9} +(-3.10973 - 0.574083i) q^{10} +(-2.39581 - 2.29349i) q^{11} +(0.789106 + 1.03321i) q^{12} +(-2.56289 - 1.86205i) q^{13} +(-2.58076 + 2.64324i) q^{14} +(0.280952 - 1.42612i) q^{15} +(1.41658 + 3.74076i) q^{16} +(-0.895798 + 5.65584i) q^{17} +(2.92308 - 2.17763i) q^{18} +(-2.14774 - 4.21517i) q^{19} +(2.08397 - 3.95690i) q^{20} +(-1.20069 - 1.20069i) q^{21} +(4.10490 - 2.26932i) q^{22} +(-1.65259 - 1.65259i) q^{23} +(-1.72710 + 0.630518i) q^{24} +(-4.85753 + 1.18507i) q^{25} +(3.59272 - 2.67649i) q^{26} +(2.13105 + 2.93314i) q^{27} +(-2.48248 - 4.59689i) q^{28} +(0.435264 - 0.854255i) q^{29} +(1.80719 + 0.979574i) q^{30} +(-2.42909 + 3.34336i) q^{31} +(-5.64674 + 0.338088i) q^{32} +(1.02045 + 1.89914i) q^{33} +(-7.25907 - 3.58998i) q^{34} +(-2.01162 + 5.48371i) q^{35} +(1.70976 + 4.86310i) q^{36} +(-2.28283 - 7.02584i) q^{37} +(6.59499 - 1.12556i) q^{38} +(1.21040 + 1.66598i) q^{39} +(4.46519 + 4.47908i) q^{40} +(-6.45452 - 2.09720i) q^{41} +(2.12645 - 1.11571i) q^{42} -2.73314 q^{43} +(1.33613 + 6.49729i) q^{44} +(2.80686 - 5.03366i) q^{45} +(2.92678 - 1.53563i) q^{46} +(2.78013 - 1.41655i) q^{47} +(-0.124348 - 2.59718i) q^{48} +(-0.103724 - 0.142763i) q^{49} +(0.444530 - 7.05708i) q^{50} +(1.68991 - 3.31664i) q^{51} +(2.10144 + 5.97716i) q^{52} +(4.08050 - 5.61633i) q^{53} +(-4.85707 + 1.64264i) q^{54} +(4.45230 - 5.93102i) q^{55} +(7.25127 - 1.41684i) q^{56} +(0.481068 + 3.03734i) q^{57} +(0.970150 + 0.947217i) q^{58} +(0.540048 - 1.05990i) q^{59} +(-2.08319 + 2.02764i) q^{60} +(1.53629 - 9.69978i) q^{61} +(-3.49156 - 4.68680i) q^{62} +(-3.05662 - 5.99896i) q^{63} +(1.92024 - 7.76612i) q^{64} +(3.44987 - 6.18680i) q^{65} +(-2.99359 + 0.578386i) q^{66} +14.3088 q^{67} +(7.90226 - 8.28966i) q^{68} +(0.689710 + 1.35363i) q^{69} +(-6.55702 - 5.02402i) q^{70} +(-6.10934 + 4.43870i) q^{71} +(-7.28543 + 0.261521i) q^{72} +(-13.3265 - 6.79020i) q^{73} +(10.4466 - 0.124951i) q^{74} +(3.24109 + 0.243108i) q^{75} +(-1.25618 + 9.37783i) q^{76} +(-2.85632 - 8.17926i) q^{77} +(-2.75874 + 0.932992i) q^{78} +(4.19372 + 3.04692i) q^{79} +(-7.92671 + 4.14333i) q^{80} +(1.66115 + 5.11249i) q^{81} +(5.54818 - 7.83171i) q^{82} +(-4.97411 - 6.84628i) q^{83} +(0.611336 + 3.34058i) q^{84} +(-12.7955 - 0.479211i) q^{85} +(1.15038 - 3.69009i) q^{86} +(-0.440688 + 0.440688i) q^{87} +(-9.33454 - 0.930753i) q^{88} -2.99274 q^{89} +(5.61468 + 5.90828i) q^{90} +(-3.75685 - 7.37322i) q^{91} +(0.841424 + 4.59787i) q^{92} +(2.17332 - 1.57901i) q^{93} +(0.742367 + 4.34976i) q^{94} +(8.78479 - 5.89317i) q^{95} +(3.55887 + 0.925265i) q^{96} +(-17.4692 + 2.76685i) q^{97} +(0.236406 - 0.0799513i) q^{98} +(1.52114 + 8.41200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9}+O(q^{10}) $ 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9	$ 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9} - 8 q^{10} - 16 q^{11} - 44 q^{12} - 12 q^{13} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 10 q^{18} - 6 q^{20} - 32 q^{21} - 10 q^{22} - 32 q^{23} - 24 q^{24} + 20 q^{26} - 22 q^{28} + 36 q^{30} - 36 q^{32} - 16 q^{33} - 32 q^{34} + 14 q^{35} + 20 q^{36} - 12 q^{37} - 26 q^{38} - 88 q^{40} - 6 q^{42} + 32 q^{43} + 80 q^{44} - 8 q^{45} - 12 q^{46} - 18 q^{48} + 16 q^{50} - 12 q^{51} + 34 q^{52} - 168 q^{54} - 16 q^{55} - 80 q^{56} - 24 q^{57} + 38 q^{58} + 16 q^{59} - 32 q^{60} - 12 q^{61} + 96 q^{62} + 36 q^{63} - 32 q^{65} - 24 q^{66} - 32 q^{67} - 38 q^{68} + 36 q^{69} - 42 q^{70} - 56 q^{71} - 76 q^{72} + 100 q^{74} + 30 q^{75} - 32 q^{76} - 108 q^{78} + 102 q^{80} - 240 q^{81} - 18 q^{82} + 24 q^{84} + 14 q^{85} - 4 q^{86} - 32 q^{87} - 98 q^{88} - 44 q^{90} - 28 q^{91} - 48 q^{92} - 36 q^{93} - 48 q^{94} - 120 q^{95} + 20 q^{96} - 12 q^{97} - 284 q^{98} + 20 q^{99}+O(q^{100}) $ 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9 - 8 * q^10 - 16 * q^11 - 44 * q^12 - 12 * q^13 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 10 * q^18 - 6 * q^20 - 32 * q^21 - 10 * q^22 - 32 * q^23 - 24 * q^24 + 20 * q^26 - 22 * q^28 + 36 * q^30 - 36 * q^32 - 16 * q^33 - 32 * q^34 + 14 * q^35 + 20 * q^36 - 12 * q^37 - 26 * q^38 - 88 * q^40 - 6 * q^42 + 32 * q^43 + 80 * q^44 - 8 * q^45 - 12 * q^46 - 18 * q^48 + 16 * q^50 - 12 * q^51 + 34 * q^52 - 168 * q^54 - 16 * q^55 - 80 * q^56 - 24 * q^57 + 38 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 96 * q^62 + 36 * q^63 - 32 * q^65 - 24 * q^66 - 32 * q^67 - 38 * q^68 + 36 * q^69 - 42 * q^70 - 56 * q^71 - 76 * q^72 + 100 * q^74 + 30 * q^75 - 32 * q^76 - 108 * q^78 + 102 * q^80 - 240 * q^81 - 18 * q^82 + 24 * q^84 + 14 * q^85 - 4 * q^86 - 32 * q^87 - 98 * q^88 - 44 * q^90 - 28 * q^91 - 48 * q^92 - 36 * q^93 - 48 * q^94 - 120 * q^95 + 20 * q^96 - 12 * q^97 - 284 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.420899	+	1.35013i	−0.297620	+	0.954684i
$2$	−0.420899	+	1.35013i	−0.297620	+	0.954684i
$3$	−0.618224	−	0.200873i	−0.356932	−	0.115974i	0.125062	−	0.992149i	$-0.460087\pi$
$3$	−0.618224	−	0.200873i	−0.356932	−	0.115974i	−0.481994	+	0.876175i	$0.660087\pi$
$4$	−1.64569	−	1.13653i	−0.822844	−	0.568267i
$5$	0.266898	+	2.22008i	0.119360	+	0.992851i
$5$	0.266898	+	2.22008i	0.119360	+	0.992851i
$6$	0.531414	−	0.750134i	0.216949	−	0.306241i
$7$	2.32748	+	1.18591i	0.879704	+	0.448232i	0.834668	−	0.550754i	$-0.185660\pi$
$7$	2.32748	+	1.18591i	0.879704	+	0.448232i	0.0450362	+	0.998985i	$0.485660\pi$
$8$	2.22713	−	1.74352i	0.787410	−	0.616429i
$9$	−2.08520	−	1.51499i	−0.695067	−	0.504995i
$10$	−3.10973	−	0.574083i	−0.983383	−	0.181541i
$11$	−2.39581	−	2.29349i	−0.722364	−	0.691513i
$11$	−2.39581	−	2.29349i	−0.722364	−	0.691513i
$12$	0.789106	+	1.03321i	0.227795	+	0.298261i
$13$	−2.56289	−	1.86205i	−0.710817	−	0.516439i	0.172620	−	0.984988i	$-0.444777\pi$
$13$	−2.56289	−	1.86205i	−0.710817	−	0.516439i	−0.883437	+	0.468550i	$0.844777\pi$
$14$	−2.58076	+	2.64324i	−0.689737	+	0.706437i
$15$	0.280952	−	1.42612i	0.0725416	−	0.368223i
$16$	1.41658	+	3.74076i	0.354146	+	0.935190i
$17$	−0.895798	+	5.65584i	−0.217263	+	1.37174i	0.602078	+	0.798437i	$0.294340\pi$
$17$	−0.895798	+	5.65584i	−0.217263	+	1.37174i	−0.819341	+	0.573307i	$0.805660\pi$
$18$	2.92308	−	2.17763i	0.688977	−	0.513272i
$19$	−2.14774	−	4.21517i	−0.492724	−	0.967026i	−0.994766	−	0.102182i	$-0.967417\pi$
$19$	−2.14774	−	4.21517i	−0.492724	−	0.967026i	0.502041	−	0.864844i	$-0.332583\pi$
$20$	2.08397	−	3.95690i	0.465989	−	0.884790i
$21$	−1.20069	−	1.20069i	−0.262011	−	0.262011i
$22$	4.10490	−	2.26932i	0.875167	−	0.483821i
$23$	−1.65259	−	1.65259i	−0.344589	−	0.344589i	0.513501	−	0.858089i	$-0.328348\pi$
$23$	−1.65259	−	1.65259i	−0.344589	−	0.344589i	−0.858089	+	0.513501i	$0.828348\pi$
$24$	−1.72710	+	0.630518i	−0.352542	+	0.128704i
$25$	−4.85753	+	1.18507i	−0.971506	+	0.237014i
$26$	3.59272	−	2.67649i	0.704590	−	0.524903i
$27$	2.13105	+	2.93314i	0.410121	+	0.564483i
$28$	−2.48248	−	4.59689i	−0.469144	−	0.868731i
$29$	0.435264	−	0.854255i	0.0808266	−	0.158631i	−0.847056	−	0.531504i	$-0.821627\pi$
$29$	0.435264	−	0.854255i	0.0808266	−	0.158631i	0.927883	+	0.372873i	$0.121627\pi$
$30$	1.80719	+	0.979574i	0.329947	+	0.178845i
$31$	−2.42909	+	3.34336i	−0.436278	+	0.600485i	−0.969380	−	0.245566i	$-0.921026\pi$
$31$	−2.42909	+	3.34336i	−0.436278	+	0.600485i	0.533102	+	0.846051i	$0.321026\pi$
$32$	−5.64674	+	0.338088i	−0.998212	+	0.0597660i
$33$	1.02045	+	1.89914i	0.177637	+	0.330599i
$34$	−7.25907	−	3.58998i	−1.24492	−	0.615676i
$35$	−2.01162	+	5.48371i	−0.340025	+	0.926916i
$36$	1.70976	+	4.86310i	0.284960	+	0.810516i
$37$	−2.28283	−	7.02584i	−0.375296	−	1.15504i	−0.943279	−	0.332001i	$-0.892276\pi$
$37$	−2.28283	−	7.02584i	−0.375296	−	1.15504i	0.567983	−	0.823040i	$-0.307724\pi$
$38$	6.59499	−	1.12556i	1.06985	−	0.182590i
$39$	1.21040	+	1.66598i	0.193820	+	0.266770i
$40$	4.46519	+	4.47908i	0.706008	+	0.708204i
$41$	−6.45452	−	2.09720i	−1.00803	−	0.327528i	−0.241958	−	0.970287i	$-0.577790\pi$
$41$	−6.45452	−	2.09720i	−1.00803	−	0.327528i	−0.766068	+	0.642759i	$0.777790\pi$
$42$	2.12645	−	1.11571i	0.328118	−	0.172158i
$43$	−2.73314			−0.416801			−0.208400	−	0.978044i	$-0.566826\pi$
$43$	−2.73314			−0.416801			−0.208400	+	0.978044i	$0.566826\pi$
$44$	1.33613	+	6.49729i	0.201429	+	0.979503i
$45$	2.80686	−	5.03366i	0.418422	−	0.750374i
$46$	2.92678	−	1.53563i	0.431530	−	0.226417i
$47$	2.78013	−	1.41655i	0.405524	−	0.206625i	−0.239317	−	0.970941i	$-0.576924\pi$
$47$	2.78013	−	1.41655i	0.405524	−	0.206625i	0.644841	+	0.764317i	$0.276924\pi$
$48$	−0.124348	−	2.59718i	−0.0179480	−	0.374871i
$49$	−0.103724	−	0.142763i	−0.0148177	−	0.0203948i
$50$	0.444530	−	7.05708i	0.0628660	−	0.998022i
$51$	1.68991	−	3.31664i	0.236635	−	0.464422i
$52$	2.10144	+	5.97716i	0.291417	+	0.828882i
$53$	4.08050	−	5.61633i	0.560500	−	0.771463i	−0.430890	−	0.902405i	$-0.641800\pi$
$53$	4.08050	−	5.61633i	0.560500	−	0.771463i	0.991390	+	0.130942i	$0.0418002\pi$
$54$	−4.85707	+	1.64264i	−0.660964	+	0.223535i
$55$	4.45230	−	5.93102i	0.600348	−	0.799739i
$56$	7.25127	−	1.41684i	0.968991	−	0.189333i
$57$	0.481068	+	3.03734i	0.0637190	+	0.402306i
$58$	0.970150	+	0.947217i	0.127387	+	0.124376i
$59$	0.540048	−	1.05990i	0.0703083	−	0.137988i	−0.853177	−	0.521621i	$-0.825327\pi$
$59$	0.540048	−	1.05990i	0.0703083	−	0.137988i	0.923485	+	0.383634i	$0.125327\pi$
$60$	−2.08319	+	2.02764i	−0.268939	+	0.261767i
$61$	1.53629	−	9.69978i	0.196702	−	1.24193i	−0.669719	−	0.742615i	$-0.733585\pi$
$61$	1.53629	−	9.69978i	0.196702	−	1.24193i	0.866421	−	0.499314i	$-0.166415\pi$
$62$	−3.49156	−	4.68680i	−0.443429	−	0.595224i
$63$	−3.05662	−	5.99896i	−0.385098	−	0.755797i
$64$	1.92024	−	7.76612i	0.240030	−	0.970765i
$65$	3.44987	−	6.18680i	0.427903	−	0.767378i
$66$	−2.99359	+	0.578386i	−0.368486	+	0.0711944i
$67$	14.3088			1.74810			0.874051	−	0.485835i	$-0.161484\pi$
$67$	14.3088			1.74810			0.874051	+	0.485835i	$0.161484\pi$
$68$	7.90226	−	8.28966i	0.958290	−	1.00527i
$69$	0.689710	+	1.35363i	0.0830313	+	0.162958i
$70$	−6.55702	−	5.02402i	−0.783714	−	0.600486i
$71$	−6.10934	+	4.43870i	−0.725046	+	0.526777i	−0.887992	−	0.459858i	$-0.847900\pi$
$71$	−6.10934	+	4.43870i	−0.725046	+	0.526777i	0.162947	+	0.986635i	$0.447900\pi$
$72$	−7.28543	+	0.261521i	−0.858597	+	0.0308205i
$73$	−13.3265	−	6.79020i	−1.55975	−	0.794733i	−0.560313	−	0.828281i	$-0.689319\pi$
$73$	−13.3265	−	6.79020i	−1.55975	−	0.794733i	−0.999437	+	0.0335482i	$0.989319\pi$
$74$	10.4466	−	0.124951i	1.21440	−	0.0145253i
$75$	3.24109	+	0.243108i	0.374249	+	0.0280717i
$76$	−1.25618	+	9.37783i	−0.144093	+	1.07571i
$77$	−2.85632	−	8.17926i	−0.325508	−	0.932113i
$78$	−2.75874	+	0.932992i	−0.312366	+	0.105641i
$79$	4.19372	+	3.04692i	0.471830	+	0.342805i	0.798154	−	0.602453i	$-0.205810\pi$
$79$	4.19372	+	3.04692i	0.471830	+	0.342805i	−0.326324	+	0.945258i	$0.605810\pi$
$80$	−7.92671	+	4.14333i	−0.886233	+	0.463239i
$81$	1.66115	+	5.11249i	0.184572	+	0.568054i
$82$	5.54818	−	7.83171i	0.612694	−	0.864868i
$83$	−4.97411	−	6.84628i	−0.545980	−	0.751477i	0.443480	−	0.896284i	$-0.353744\pi$
$83$	−4.97411	−	6.84628i	−0.545980	−	0.751477i	−0.989460	+	0.144808i	$0.953744\pi$
$84$	0.611336	+	3.34058i	0.0667022	+	0.364487i
$85$	−12.7955	−	0.479211i	−1.38787	−	0.0519777i
$86$	1.15038	−	3.69009i	0.124048	−	0.397913i
$87$	−0.440688	+	0.440688i	−0.0472467	+	0.0472467i
$88$	−9.33454	−	0.930753i	−0.995066	−	0.0992186i
$89$	−2.99274			−0.317229			−0.158615	−	0.987341i	$-0.550703\pi$
$89$	−2.99274			−0.317229			−0.158615	+	0.987341i	$0.550703\pi$
$90$	5.61468	+	5.90828i	0.591840	+	0.622787i
$91$	−3.75685	−	7.37322i	−0.393824	−	0.772924i
$92$	0.841424	+	4.59787i	0.0877246	+	0.479361i
$93$	2.17332	−	1.57901i	0.225362	−	0.163735i
$94$	0.742367	+	4.34976i	0.0765693	+	0.448643i
$95$	8.78479	−	5.89317i	0.901301	−	0.604627i
$96$	3.55887	+	0.925265i	0.363225	+	0.0944345i
$97$	−17.4692	+	2.76685i	−1.77373	+	0.280931i	−0.955721	−	0.294275i	$-0.904922\pi$
$97$	−17.4692	+	2.76685i	−1.77373	+	0.280931i	−0.818009	+	0.575206i	$0.804922\pi$
$98$	0.236406	−	0.0799513i	0.0238806	−	0.00807630i
$99$	1.52114	+	8.41200i	0.152880	+	0.845438i
$100$	9.34086	+	3.57049i	0.934086	+	0.357049i
$101$	2.08060	+	13.1364i	0.207028	+	1.30712i	0.844045	+	0.536272i	$0.180168\pi$
$101$	2.08060	+	13.1364i	0.207028	+	1.30712i	−0.637018	+	0.770849i	$0.719832\pi$
$102$	3.76660	+	3.67756i	0.372949	+	0.364133i
$103$	4.10552	−	8.05755i	0.404529	−	0.793934i	−0.595426	−	0.803410i	$-0.703017\pi$
$103$	4.10552	−	8.05755i	0.404529	−	0.793934i	0.999955	+	0.00947678i	$0.00301660\pi$
$104$	−8.95442	+	0.321431i	−0.878053	+	0.0315189i
$105$	2.34516	−	2.98608i	0.228864	−	0.291412i
$106$	5.86529	+	7.87311i	0.569687	+	0.764704i
$107$	15.6930	+	5.09896i	1.51710	+	0.492935i	0.944950	−	0.327216i	$-0.106110\pi$
$107$	15.6930	+	5.09896i	1.51710	+	0.492935i	0.572148	+	0.820150i	$0.306110\pi$
$108$	−0.173435	−	7.24905i	−0.0166888	−	0.697540i
$109$	−3.85263	−	3.85263i	−0.369015	−	0.369015i	0.498103	−	0.867118i	$-0.334030\pi$
$109$	−3.85263	−	3.85263i	−0.369015	−	0.369015i	−0.867118	+	0.498103i	$0.834030\pi$
$110$	6.13367	+	8.50753i	0.584823	+	0.811161i
$111$			4.80211i			0.455796i
$112$	−1.13914	+	10.3865i	−0.107638	+	0.981430i
$113$	−3.91467	+	1.99462i	−0.368261	+	0.187638i	−0.628321	−	0.777954i	$-0.716258\pi$
$113$	−3.91467	+	1.99462i	−0.368261	+	0.187638i	0.260060	+	0.965592i	$0.416258\pi$
$114$	−4.30328	−	0.628910i	−0.403039	−	0.0589028i
$115$	3.22781	−	4.10996i	0.300995	−	0.383255i
$116$	−1.68720	+	0.911145i	−0.156652	+	0.0845977i
$117$	2.52316	+	7.76548i	0.233266	+	0.717919i
$118$	1.20370	+	1.17525i	0.110810	+	0.108190i
$119$	−8.79227	+	12.1015i	−0.805986	+	1.10934i
$120$	−1.86076	−	3.66601i	−0.169863	−	0.334659i
$121$	0.479811	+	10.9895i	0.0436192	+	0.999048i
$122$	12.4493	+	6.15681i	1.12711	+	0.557412i
$123$	3.56907	+	2.59308i	0.321812	+	0.233810i
$124$	7.79737	−	2.74138i	0.700224	−	0.246184i
$125$	−3.92742	−	10.4678i	−0.351279	−	0.936271i
$126$	9.38588	−	1.60188i	0.836161	−	0.142706i
$127$	−7.01253	−	1.11068i	−0.622261	−	0.0985565i	−0.162660	−	0.986682i	$-0.552008\pi$
$127$	−7.01253	−	1.11068i	−0.622261	−	0.0985565i	−0.459601	+	0.888126i	$0.652008\pi$
$128$	9.67703	+	5.86132i	0.855337	+	0.518073i
$129$	1.68970	+	0.549016i	0.148769	+	0.0483381i
$130$	6.90092	+	7.26177i	0.605251	+	0.636900i
$131$	10.6115	+	10.6115i	0.927134	+	0.927134i	0.997520	−	0.0703858i	$-0.0224230\pi$
$131$	10.6115	+	10.6115i	0.927134	+	0.927134i	−0.0703858	+	0.997520i	$0.522423\pi$
$132$	0.479103	−	4.28517i	0.0417006	−	0.372977i
$133$		−	12.3577i		−	1.07155i
$134$	−6.02256	+	19.3187i	−0.520270	+	1.66888i
$135$	−5.94304	+	5.51396i	−0.511495	+	0.474566i
$136$	7.86604	+	14.1582i	0.674508	+	1.21405i
$137$	7.83332	+	1.24068i	0.669245	+	0.105998i	0.481806	−	0.876278i	$-0.339981\pi$
$137$	7.83332	+	1.24068i	0.669245	+	0.105998i	0.187440	+	0.982276i	$0.439981\pi$
$138$	−2.11787	+	0.361454i	−0.180285	+	0.0307690i
$139$	−4.96747	+	9.74921i	−0.421335	+	0.826917i	0.578601	+	0.815611i	$0.303599\pi$
$139$	−4.96747	+	9.74921i	−0.421335	+	0.826917i	−0.999936	+	0.0113060i	$0.996401\pi$
$140$	9.54291	−	6.73821i	0.806523	−	0.569483i
$141$	−2.00329	+	0.317290i	−0.168708	+	0.0267207i
$142$	−3.42139	−	10.1166i	−0.287117	−	0.848969i
$143$	1.86961	+	10.3391i	0.156344	+	0.864596i
$144$	2.71334	−	9.94634i	0.226112	−	0.828862i
$145$	2.01269	+	0.738324i	0.167145	+	0.0613145i
$146$	14.7767	−	15.1345i	1.22293	−	1.25254i
$147$	0.0354472	+	0.109095i	0.00292363	+	0.00899802i
$148$	−4.22827	+	14.1569i	−0.347562	+	1.16369i
$149$	−1.67460	+	10.5730i	−0.137189	+	0.866174i	0.819079	+	0.573681i	$0.194485\pi$
$149$	−1.67460	+	10.5730i	−0.137189	+	0.866174i	−0.956267	+	0.292494i	$0.905515\pi$
$150$	−1.69240	+	4.27356i	−0.138184	+	0.348935i
$151$	−1.54389	+	4.75160i	−0.125640	+	0.386680i	−0.994017	−	0.109224i	$-0.965163\pi$
$151$	−1.54389	+	4.75160i	−0.125640	+	0.386680i	0.868377	+	0.495904i	$0.165163\pi$
$152$	−12.1325	−	5.64311i	−0.984079	−	0.457717i
$153$	10.4364	−	10.4364i	0.843737	−	0.843737i
$154$	12.2453	−	0.413764i	0.986752	−	0.0333420i
$155$	−8.07085	−	4.50045i	−0.648266	−	0.361485i
$156$	−0.0985084	−	4.11735i	−0.00788699	−	0.329651i
$157$	−21.0061	−	6.82529i	−1.67647	−	0.544717i	−0.692246	−	0.721662i	$-0.743379\pi$
$157$	−21.0061	−	6.82529i	−1.67647	−	0.544717i	−0.984221	+	0.176945i	$0.943379\pi$
$158$	−5.87886	+	4.37961i	−0.467697	+	0.348423i
$159$	−3.65084	+	2.65249i	−0.289530	+	0.210356i
$160$	−2.25769	−	12.4460i	−0.178486	−	0.983942i
$161$	−1.88654	−	5.80618i	−0.148680	−	0.457591i
$162$	−7.60169	+	0.0909230i	−0.597245	+	0.00714359i
$163$	−5.62774	+	7.74592i	−0.440798	+	0.606707i	−0.970389	−	0.241546i	$-0.922345\pi$
$163$	−5.62774	+	7.74592i	−0.440798	+	0.606707i	0.529591	+	0.848253i	$0.322345\pi$
$164$	8.23859	+	10.7871i	0.643326	+	0.842332i
$165$	−3.94390	+	2.77235i	−0.307032	+	0.215828i
$166$	11.3369	−	3.83410i	0.879918	−	0.297584i
$167$	−13.7533	+	2.17831i	−1.06426	+	0.168563i	−0.663920	−	0.747803i	$-0.731109\pi$
$167$	−13.7533	+	2.17831i	−1.06426	+	0.168563i	−0.400342	+	0.916366i	$0.631109\pi$
$168$	−4.76751	−	0.580662i	−0.367822	−	0.0447990i
$169$	−0.916047	−	2.81930i	−0.0704652	−	0.216869i
$170$	6.03261	−	17.0739i	0.462680	−	1.30951i
$171$	−1.90746	+	12.0433i	−0.145867	+	0.920971i
$172$	4.49791	+	3.10631i	0.342962	+	0.236854i
$173$	−3.78439	+	11.6472i	−0.287722	+	0.885518i	0.697847	+	0.716247i	$0.254141\pi$
$173$	−3.78439	+	11.6472i	−0.287722	+	0.885518i	−0.985569	+	0.169271i	$0.945859\pi$
$174$	−0.409500	−	0.780470i	−0.0310441	−	0.0591673i
$175$	−12.7112	−	3.00236i	−0.960875	−	0.226957i
$176$	5.18553	−	12.2111i	0.390874	−	0.920444i
$177$	−0.546777	+	0.546777i	−0.0410983	+	0.0410983i
$178$	1.25964	−	4.04058i	0.0944139	−	0.302854i
$179$	0.0797421	+	0.156503i	0.00596020	+	0.0116976i	0.893967	−	0.448132i	$-0.147911\pi$
$179$	0.0797421	+	0.156503i	0.00596020	+	0.0116976i	−0.888007	+	0.459829i	$0.847911\pi$
$180$	−10.3401	+	5.09375i	−0.770709	+	0.379666i
$181$	−18.9720	−	3.00487i	−1.41018	−	0.223350i	−0.595543	−	0.803323i	$-0.703063\pi$
$181$	−18.9720	−	3.00487i	−1.41018	−	0.223350i	−0.814636	+	0.579973i	$0.803063\pi$
$182$	11.5360	−	1.96884i	0.855109	−	0.145940i
$183$	−2.89820	+	5.68804i	−0.214241	+	0.420472i
$184$	−6.56186	−	0.799206i	−0.483747	−	0.0589182i
$185$	14.9887	−	6.94326i	1.10199	−	0.510479i
$186$	1.21711	+	3.59885i	0.0892431	+	0.263881i
$187$	15.1178	−	11.4958i	1.10552	−	0.840658i
$188$	−6.18519	−	0.828516i	−0.451101	−	0.0604257i
$189$	1.48154	+	9.35405i	0.107766	+	0.680407i
$190$	4.25902	+	14.3410i	0.308982	+	1.04041i
$191$	5.19916	−	1.68931i	0.376198	−	0.122234i	−0.114814	−	0.993387i	$-0.536627\pi$
$191$	5.19916	−	1.68931i	0.376198	−	0.122234i	0.491012	+	0.871153i	$0.336627\pi$
$192$	−2.74715	+	4.41548i	−0.198258	+	0.318660i
$193$	3.66705	+	0.580803i	0.263960	+	0.0418071i	0.287011	−	0.957927i	$-0.407338\pi$
$193$	3.66705	+	0.580803i	0.263960	+	0.0418071i	−0.0230517	+	0.999734i	$0.507338\pi$
$194$	3.61716	−	24.7502i	0.259697	−	1.77696i
$195$	−3.37555	+	3.13184i	−0.241728	+	0.224276i
$196$	0.00844153	+	0.352830i	0.000602967	+	0.0252021i
$197$	7.92706			0.564780			0.282390	−	0.959300i	$-0.408873\pi$
$197$	7.92706			0.564780			0.282390	+	0.959300i	$0.408873\pi$
$198$	−11.9975	−	1.48687i	−0.852627	−	0.105667i
$199$			19.2478i			1.36444i	0.731148	+	0.682219i	$0.238985\pi$
$199$			19.2478i			1.36444i	−0.731148	+	0.682219i	$0.761015\pi$
$200$	−8.75217	+	11.1085i	−0.618872	+	0.785492i
$201$	−8.84606	−	2.87426i	−0.623953	−	0.202735i
$202$	−18.6115	−	2.72002i	−1.30950	−	0.191380i
$203$	2.02614	−	1.47207i	0.142207	−	0.103319i
$204$	−6.55054	+	3.53751i	−0.458629	+	0.247675i
$205$	2.93326	−	14.8893i	0.204868	−	1.03991i
$206$	9.15071	+	8.93439i	0.637560	+	0.622489i
$207$	0.942328	+	5.94963i	0.0654963	+	0.413528i
$208$	3.33493	−	12.2249i	0.231236	−	0.847644i
$209$	−4.52188	+	15.0246i	−0.312785	+	1.03927i
$210$	3.04452	+	4.42310i	0.210092	+	0.305223i
$211$	−2.91142	−	18.3820i	−0.200430	−	1.26547i	−0.858619	−	0.512614i	$-0.828677\pi$
$211$	−2.91142	−	18.3820i	−0.200430	−	1.26547i	0.658189	−	0.752853i	$-0.271323\pi$
$212$	−13.0984	+	4.60511i	−0.899601	+	0.316280i
$213$	4.66856	−	1.51691i	0.319884	−	0.103937i
$214$	−13.4894	+	19.0414i	−0.922116	+	1.30164i
$215$	−0.729471	−	6.06781i	−0.0497495	−	0.413821i
$216$	9.86014	+	2.81695i	0.670897	+	0.191669i
$217$	−9.61858	+	4.90091i	−0.652952	+	0.332696i
$218$	6.82311	−	3.57997i	0.462119	−	0.242466i
$219$	6.87480	+	6.87480i	0.464556	+	0.464556i
$220$	−14.0679	+	4.70043i	−0.948458	+	0.316903i
$221$	12.8273	−	12.8273i	0.862856	−	0.862856i
$222$	−6.48345	−	2.02120i	−0.435141	−	0.135654i
$223$	7.80315	+	15.3145i	0.522538	+	1.02554i	0.989939	+	0.141493i	$0.0451901\pi$
$223$	7.80315	+	15.3145i	0.522538	+	1.02554i	−0.467402	+	0.884045i	$0.654810\pi$
$224$	−13.5436	−	5.90963i	−0.904920	−	0.394854i
$225$	11.9243	+	4.88798i	0.794953	+	0.325865i
$226$	−1.04532	−	6.12483i	−0.0695335	−	0.407418i
$227$	−6.69670	−	20.6103i	−0.444475	−	1.36795i	−0.883058	−	0.469264i	$-0.844519\pi$
$227$	−6.69670	−	20.6103i	−0.444475	−	1.36795i	0.438583	−	0.898691i	$-0.355481\pi$
$228$	2.66035	−	5.54527i	0.176186	−	0.367244i
$229$	−2.45743	+	0.389219i	−0.162392	+	0.0257203i	−0.237101	−	0.971485i	$-0.576197\pi$
$229$	−2.45743	+	0.389219i	−0.162392	+	0.0257203i	0.0747090	+	0.997205i	$0.476197\pi$
$230$	4.19038	+	6.08783i	0.276306	+	0.401420i
$231$	0.122855	+	5.63038i	0.00808324	+	0.370452i
$232$	−0.520022	−	2.66143i	−0.0341411	−	0.174732i
$233$	26.7218	−	4.23231i	1.75060	−	0.277268i	0.802827	−	0.596212i	$-0.203328\pi$
$233$	26.7218	−	4.23231i	1.75060	−	0.277268i	0.947774	+	0.318944i	$0.103328\pi$
$234$	−11.5464	+	0.138105i	−0.754810	+	0.00902822i
$235$	3.88686	+	5.79405i	0.253551	+	0.377962i
$236$	−2.09337	+	1.13049i	−0.136267	+	0.0735886i
$237$	−1.98062	−	2.72608i	−0.128655	−	0.177078i
$238$	−12.6379	−	16.9642i	−0.819196	−	1.09963i
$239$	3.27449	−	10.0778i	0.211809	−	0.651882i	−0.787556	−	0.616244i	$-0.788654\pi$
$239$	3.27449	−	10.0778i	0.211809	−	0.651882i	0.999365	−	0.0356380i	$-0.0113463\pi$
$240$	5.73277	−	0.969245i	0.370049	−	0.0625645i
$241$	4.15786			0.267832			0.133916	−	0.990993i	$-0.457245\pi$
$241$	4.15786			0.267832			0.133916	+	0.990993i	$0.457245\pi$
$242$	−15.0392	−	3.97767i	−0.966758	−	0.255694i
$243$		−	14.3710i		−	0.921902i
$244$	−13.5524	+	14.2168i	−0.867602	+	0.910135i
$245$	0.289263	−	0.268379i	0.0184803	−	0.0171461i
$246$	−5.00320	+	3.72727i	−0.318993	+	0.237642i
$247$	−2.34444	+	14.8022i	−0.149173	+	0.941841i
$248$	0.419316	+	11.6813i	0.0266266	+	0.741763i
$249$	1.69988	+	5.23170i	0.107726	+	0.331546i
$250$	15.7859	−	0.896629i	0.998391	−	0.0567078i
$251$	−24.8388	+	3.93408i	−1.56781	+	0.248317i	−0.879071	−	0.476690i	$-0.841836\pi$
$251$	−24.8388	+	3.93408i	−1.56781	+	0.248317i	−0.688741	+	0.725007i	$0.741836\pi$
$252$	−1.78777	+	13.3464i	−0.112619	+	0.840742i
$253$	0.169093	+	7.74948i	0.0106308	+	0.487206i
$254$	4.45112	−	9.00033i	0.279288	−	0.564731i
$255$	7.81424	+	2.86654i	0.489347	+	0.179510i
$256$	−11.9866	+	10.5982i	−0.749161	+	0.662388i
$257$	−0.917276	−	0.467375i	−0.0572181	−	0.0291541i	0.425147	−	0.905124i	$-0.360222\pi$
$257$	−0.917276	−	0.467375i	−0.0572181	−	0.0291541i	−0.482365	+	0.875970i	$0.660222\pi$
$258$	−1.45243	+	2.05023i	−0.0904245	+	0.127641i
$259$	3.01876	−	19.0597i	0.187577	−	1.18431i
$260$	−12.7089	+	6.26065i	−0.788173	+	0.388269i
$261$	−2.20180	+	1.12187i	−0.136288	+	0.0694421i
$262$	−18.7933	+	9.86055i	−1.16105	+	0.609187i
$263$	15.2743	+	15.2743i	0.941856	+	0.941856i	0.998400	−	0.0565443i	$-0.0180082\pi$
$263$	15.2743	+	15.2743i	0.941856	+	0.941856i	−0.0565443	+	0.998400i	$0.518008\pi$
$264$	5.58388	+	2.45047i	0.343664	+	0.150816i
$265$	13.5578	+	7.56007i	0.832849	+	0.464411i
$266$	16.6845	+	5.20135i	1.02299	+	0.318915i
$267$	1.85018	+	0.601161i	0.113229	+	0.0367904i
$268$	−23.5479	−	16.2625i	−1.43842	−	0.993388i
$269$	−23.6690	−	3.74880i	−1.44312	−	0.228569i	−0.614741	−	0.788729i	$-0.710739\pi$
$269$	−23.6690	−	3.74880i	−1.44312	−	0.228569i	−0.828384	+	0.560161i	$0.810739\pi$
$270$	−4.94313	−	10.3447i	−0.300829	−	0.629557i
$271$	−25.7243	+	8.35834i	−1.56264	+	0.507733i	−0.957512	−	0.288395i	$-0.906879\pi$
$271$	−25.7243	+	8.35834i	−1.56264	+	0.507733i	−0.605129	+	0.796127i	$0.706879\pi$
$272$	−22.4261	+	4.66101i	−1.35978	+	0.282615i
$273$	0.841490	+	5.31296i	0.0509293	+	0.321555i
$274$	−4.97210	+	10.0538i	−0.300376	+	0.607371i
$275$	14.3557	+	8.30149i	0.865679	+	0.500599i
$276$	0.403400	−	3.01153i	0.0242818	−	0.181273i
$277$	−2.37108	−	1.72269i	−0.142464	−	0.103506i	0.514270	−	0.857628i	$-0.328063\pi$
$277$	−2.37108	−	1.72269i	−0.142464	−	0.103506i	−0.656735	+	0.754122i	$0.728063\pi$
$278$	−11.0719	−	10.8101i	−0.664047	−	0.648349i
$279$	10.1303	−	3.29153i	0.606484	−	0.197059i
$280$	5.08084	+	15.7203i	0.303639	+	0.939465i
$281$	13.1280	+	18.0691i	0.783151	+	1.07791i	0.994927	+	0.100596i	$0.0320751\pi$
$281$	13.1280	+	18.0691i	0.783151	+	1.07791i	−0.211777	+	0.977318i	$0.567925\pi$
$282$	0.414800	−	2.83825i	0.0247010	−	0.169015i
$283$	−2.38306	+	7.33429i	−0.141658	+	0.435978i	−0.996566	−	0.0828010i	$-0.973613\pi$
$283$	−2.38306	+	7.33429i	−0.141658	+	0.435978i	0.854908	+	0.518779i	$0.173613\pi$
$284$	15.0988	−	0.361242i	0.895949	−	0.0214358i
$285$	−6.61475	+	1.87867i	−0.391824	+	0.111283i
$286$	−14.7460	−	1.82749i	−0.871948	−	0.108062i
$287$	−12.5357	−	12.5357i	−0.739956	−	0.739956i
$288$	12.2868	+	7.84976i	0.724006	+	0.462551i
$289$	−15.0182	−	4.87970i	−0.883421	−	0.287041i
$290$	−1.84397	+	2.40662i	−0.108282	+	0.141322i
$291$	11.3557	+	1.79856i	0.665681	+	0.105434i
$292$	14.2140	+	26.3206i	0.831812	+	1.54030i
$293$	−7.01802	+	2.28029i	−0.409997	+	0.133216i	−0.506751	−	0.862092i	$-0.669154\pi$
$293$	−7.01802	+	2.28029i	−0.409997	+	0.133216i	0.0967545	+	0.995308i	$0.469154\pi$
$294$	−0.162212	+	0.00194020i	−0.00946040	+	0.000113155i
$295$	2.49721	+	0.916065i	0.145393	+	0.0533353i
$296$	−17.3339	−	11.6673i	−1.00751	−	0.678148i
$297$	1.62153	−	11.9148i	0.0940909	−	0.691366i
$298$	−13.5701	−	6.71109i	−0.786093	−	0.388763i
$299$	1.15820	+	7.31260i	0.0669805	+	0.422898i
$300$	−5.05753	−	4.08369i	−0.291997	−	0.235772i
$301$	−6.36133	−	3.24126i	−0.366661	−	0.186823i
$302$	−5.76545	−	4.08439i	−0.331764	−	0.235030i
$303$	1.35247	−	8.53918i	0.0776976	−	0.490563i
$304$	12.7255	−	14.0053i	0.729857	−	0.803259i
$305$	21.9443	+	0.821846i	1.25653	+	0.0470588i
$306$	9.69785	+	18.4832i	0.554389	+	1.05662i
$307$	24.5310			1.40006			0.700030	−	0.714114i	$-0.253170\pi$
$307$	24.5310			1.40006			0.700030	+	0.714114i	$0.253170\pi$
$308$	−4.59538	+	16.7068i	−0.261846	+	0.951960i
$309$	−4.15668	+	4.15668i	−0.236465	+	0.236465i
$310$	9.47319	−	9.00245i	0.538041	−	0.511305i
$311$	4.39622	−	13.5302i	0.249286	−	0.767225i	−0.745615	−	0.666377i	$-0.767844\pi$
$311$	4.39622	−	13.5302i	0.249286	−	0.767225i	0.994902	−	0.100848i	$-0.0321557\pi$
$312$	5.60040	+	1.59999i	0.317060	+	0.0905814i
$313$	−2.07136	+	13.0780i	−0.117080	+	0.739214i	0.857385	+	0.514675i	$0.172088\pi$
$313$	−2.07136	+	13.0780i	−0.117080	+	0.739214i	−0.974465	+	0.224539i	$0.927912\pi$
$314$	18.0564	−	25.4881i	1.01898	−	1.43838i
$315$	12.5024	−	8.38706i	0.704429	−	0.472557i
$316$	−3.43864	−	9.78058i	−0.193438	−	0.550201i
$317$	6.32596	−	8.70694i	0.355301	−	0.489030i	−0.593531	−	0.804811i	$-0.702266\pi$
$317$	6.32596	−	8.70694i	0.355301	−	0.489030i	0.948832	+	0.315781i	$0.102266\pi$
$318$	−2.04457	−	6.04553i	−0.114654	−	0.339016i
$319$	−3.00203	+	1.04836i	−0.168082	+	0.0586967i
$320$	17.7539	+	2.19034i	0.992475	+	0.122444i
$321$	−8.67754	−	6.30460i	−0.484333	−	0.351888i
$322$	8.63313	−	0.103260i	0.481106	−	0.00575446i
$323$	25.7643	−	8.37132i	1.43356	−	0.465793i
$324$	3.07678	−	10.3015i	0.170932	−	0.572306i
$325$	14.6560	+	6.00774i	0.812967	+	0.333250i
$326$	−8.08927	−	10.8584i	−0.448023	−	0.601392i
$327$	1.60790	+	3.15568i	0.0889170	+	0.174509i
$328$	−18.0316	+	6.58287i	−0.995628	+	0.363478i
$329$	8.15059			0.449357
$330$	−2.08305	−	6.49165i	−0.114668	−	0.357354i
$331$	−0.367838	+	0.367838i	−0.0202182	+	0.0202182i	−0.717144	−	0.696925i	$-0.754551\pi$
$331$	−0.367838	+	0.367838i	−0.0202182	+	0.0202182i	0.696925	+	0.717144i	$0.254551\pi$
$332$	0.404817	+	16.9201i	0.0222172	+	0.928610i
$333$	−5.88389	+	18.1087i	−0.322435	+	0.992353i
$334$	2.84775	−	19.4856i	0.155822	−	1.06620i
$335$	3.81900	+	31.7668i	0.208654	+	1.73560i
$336$	2.79061	−	6.19235i	0.152240	−	0.337820i
$337$	7.39332	+	3.76709i	0.402740	+	0.205206i	0.643614	−	0.765350i	$-0.277434\pi$
$337$	7.39332	+	3.76709i	0.402740	+	0.205206i	−0.240874	+	0.970556i	$0.577434\pi$
$338$	4.19198	−	0.0501399i	0.228014	−	0.00272725i
$339$	2.82081	−	0.446772i	0.153205	−	0.0242653i
$340$	20.5128	+	15.3312i	1.11246	+	0.831450i
$341$	13.4876	−	2.43895i	0.730395	−	0.132077i
$342$	−15.4571	−	7.64431i	−0.835824	−	0.413357i
$343$	−2.93257	−	18.5155i	−0.158344	−	0.999743i
$344$	−6.08708	+	4.76530i	−0.328193	+	0.256928i
$345$	−2.82109	+	1.89249i	−0.151882	+	0.101888i
$346$	−14.1323	−	10.0117i	−0.759758	−	0.538232i
$347$	2.90738	+	4.00167i	0.156076	+	0.214821i	0.879893	−	0.475171i	$-0.157614\pi$
$347$	2.90738	+	4.00167i	0.156076	+	0.214821i	−0.723817	+	0.689992i	$0.757614\pi$
$348$	1.22609	−	0.224379i	0.0657254	−	0.0120280i
$349$	−4.03006	+	2.05342i	−0.215724	+	0.109917i	−0.558514	−	0.829495i	$-0.688628\pi$
$349$	−4.03006	+	2.05342i	−0.215724	+	0.109917i	0.342790	+	0.939412i	$0.388628\pi$
$350$	9.40369	−	15.8980i	0.502648	−	0.849785i
$351$		−	11.4854i		−	0.613047i
$352$	14.3039	+	12.1408i	0.762402	+	0.647104i
$353$	−18.5581	−	18.5581i	−0.987749	−	0.987749i	0.0121771	−	0.999926i	$-0.496124\pi$
$353$	−18.5581	−	18.5581i	−0.987749	−	0.987749i	−0.999926	+	0.0121771i	$0.996124\pi$
$354$	−0.508081	−	0.968356i	−0.0270042	−	0.0514676i
$355$	−11.4848	−	12.3786i	−0.609552	−	0.656986i
$356$	4.92511	+	3.40135i	0.261031	+	0.180271i
$357$	7.86646	−	5.71532i	0.416337	−	0.302487i
$358$	−0.244862	+	0.0417902i	−0.0129414	+	0.00220868i
$359$	−5.50543	+	1.78882i	−0.290565	+	0.0944104i	−0.450673	−	0.892689i	$-0.648816\pi$
$359$	−5.50543	+	1.78882i	−0.290565	+	0.0944104i	0.160107	+	0.987100i	$0.448816\pi$
$360$	−2.52507	−	16.1045i	−0.133083	−	0.848780i
$361$	−1.98696	+	2.73481i	−0.104577	+	0.143937i
$362$	12.0423	−	24.3499i	0.632927	−	1.27980i
$363$	1.91087	−	6.89038i	0.100295	−	0.361651i
$364$	−2.19732	+	16.4038i	−0.115171	+	0.859793i
$365$	11.5180	−	31.3982i	0.602878	−	1.64346i
$366$	−6.45973	−	6.30702i	−0.337655	−	0.329673i
$367$	6.93240	−	13.6056i	0.361868	−	0.710206i	−0.636253	−	0.771481i	$-0.719516\pi$
$367$	6.93240	−	13.6056i	0.361868	−	0.710206i	0.998121	+	0.0612744i	$0.0195165\pi$
$368$	3.84091	−	8.52297i	0.200221	−	0.444290i
$369$	10.2817	+	14.1516i	0.535245	+	0.736702i
$370$	3.06559	+	23.1590i	0.159372	+	1.20398i
$371$	16.1577	−	8.23278i	0.838868	−	0.427425i
$372$	−5.37119	+	0.128507i	−0.278483	+	0.00666278i
$373$			24.1126i			1.24850i	0.781224	+	0.624251i	$0.214596\pi$
$373$			24.1126i			1.24850i	−0.781224	+	0.624251i	$0.785404\pi$
$374$	9.15778	+	25.2495i	0.473537	+	1.30562i
$375$	0.325322	+	7.26038i	0.0167995	+	0.374924i
$376$	3.72194	−	8.00207i	0.191944	−	0.412675i
$377$	−2.70620	+	1.37888i	−0.139376	+	0.0710157i
$378$	−13.2527	−	1.93684i	−0.681648	−	0.0996205i
$379$	−30.2563	−	4.79213i	−1.55416	−	0.246155i	−0.680523	−	0.732727i	$-0.738247\pi$
$379$	−30.2563	−	4.79213i	−1.55416	−	0.246155i	−0.873641	+	0.486571i	$0.838247\pi$
$380$	−21.1548	−	0.285888i	−1.08522	−	0.0146657i
$381$	4.11221	+	2.09528i	0.210675	+	0.107344i
$382$	0.0924645	+	7.73056i	0.00473090	+	0.395530i
$383$	1.11212	−	0.176143i	0.0568268	−	0.00900048i	−0.127956	−	0.991780i	$-0.540842\pi$
$383$	1.11212	−	0.176143i	0.0568268	−	0.00900048i	0.184783	+	0.982779i	$0.440842\pi$
$384$	−4.80519	−	5.56747i	−0.245214	−	0.284114i
$385$	17.3963	−	8.52430i	0.886597	−	0.434439i
$386$	−2.32761	+	4.70652i	−0.118472	+	0.239556i
$387$	5.69915	+	4.14068i	0.289704	+	0.210482i
$388$	31.8935	+	15.3010i	1.61915	+	0.776789i
$389$	−12.7529	−	6.49792i	−0.646597	−	0.329458i	0.0997519	−	0.995012i	$-0.468195\pi$
$389$	−12.7529	−	6.49792i	−0.646597	−	0.329458i	−0.746349	+	0.665555i	$0.768195\pi$
$390$	−2.80762	−	5.87562i	−0.142169	−	0.297523i
$391$	10.8272	−	7.86640i	0.547553	−	0.397821i
$392$	−0.479918	−	0.137108i	−0.0242395	−	0.00692502i
$393$	−4.42873	−	8.69188i	−0.223400	−	0.438447i
$394$	−3.33649	+	10.7025i	−0.168090	+	0.539186i
$395$	−5.64511	+	10.1236i	−0.284036	+	0.509375i
$396$	7.05720	−	15.5724i	0.354638	−	0.782541i
$397$		−	16.3434i		−	0.820253i	−0.912029	−	0.410127i	$-0.865485\pi$
$397$		−	16.3434i		−	0.820253i	0.912029	−	0.410127i	$-0.134515\pi$
$398$	−25.9869	−	8.10135i	−1.30261	−	0.406084i
$399$	−2.48234	+	7.63985i	−0.124272	+	0.382471i
$400$	−11.3142	−	16.4921i	−0.565708	−	0.824605i
$401$	−26.0729	+	18.9431i	−1.30202	+	0.945972i	−0.999973	−	0.00732209i	$-0.997669\pi$
$401$	−26.0729	+	18.9431i	−1.30202	+	0.945972i	−0.302045	+	0.953294i	$0.597669\pi$
$402$	7.60391	−	10.7335i	0.379249	−	0.535340i
$403$	12.4510	−	4.04557i	0.620228	−	0.201524i
$404$	11.5059	−	23.9831i	0.572442	−	1.19320i
$405$	−10.9068	+	5.05240i	−0.541963	+	0.251056i
$406$	1.13469	+	3.35514i	0.0563137	+	0.166513i
$407$	−10.6445	+	22.0682i	−0.527626	+	1.09388i
$408$	−2.01898	−	10.3330i	−0.0999545	−	0.511560i
$409$	30.2329	+	21.9655i	1.49492	+	1.08613i	0.972349	+	0.233531i	$0.0750281\pi$
$409$	30.2329	+	21.9655i	1.49492	+	1.08613i	0.522574	+	0.852594i	$0.324972\pi$
$410$	18.8678	+	10.2272i	0.931816	+	0.505083i
$411$	−4.59353	−	2.34052i	−0.226582	−	0.115449i
$412$	−15.9141	+	8.59415i	−0.784031	+	0.423403i
$413$	2.51390	−	1.82645i	0.123701	−	0.0898740i
$414$	−8.42938	−	1.23193i	−0.414281	−	0.0605458i
$415$	13.8717	−	12.8702i	0.680936	−	0.631773i
$416$	15.1015	+	9.64802i	0.740412	+	0.473033i
$417$	5.02936	−	5.02936i	0.246289	−	0.246289i
$418$	−18.3818	−	12.4289i	−0.899084	−	0.607919i
$419$	17.8489	−	17.8489i	0.871976	−	0.871976i	−0.120711	−	0.992688i	$-0.538518\pi$
$419$	17.8489	−	17.8489i	0.871976	−	0.871976i	0.992688	+	0.120711i	$0.0385175\pi$
$420$	−7.25319	+	2.24881i	−0.353919	+	0.109731i
$421$	22.9465	−	11.6918i	1.11834	−	0.569824i	0.205714	−	0.978612i	$-0.434048\pi$
$421$	22.9465	−	11.6918i	1.11834	−	0.569824i	0.912629	+	0.408788i	$0.134048\pi$
$422$	26.0434	+	3.80616i	1.26777	+	0.185281i
$423$	−7.94318	−	1.25808i	−0.386211	−	0.0611698i
$424$	−0.704387	−	19.6228i	−0.0342081	−	0.952966i
$425$	−2.35122	−	28.5350i	−0.114051	−	1.38415i
$426$	0.0830280	+	6.94161i	0.00402272	+	0.336322i
$427$	15.0787	−	20.7541i	0.729712	−	1.00436i
$428$	−20.0306	−	26.2269i	−0.968217	−	1.26772i
$429$	0.921006	−	6.76741i	0.0444666	−	0.326734i
$430$	8.49935	+	1.56905i	0.409875	+	0.0756664i
$431$	15.8029	−	21.7508i	0.761199	−	1.04770i	−0.235914	−	0.971774i	$-0.575808\pi$
$431$	15.8029	−	21.7508i	0.761199	−	1.04770i	0.997113	−	0.0759268i	$-0.0241915\pi$
$432$	−7.95337	+	12.1268i	−0.382656	+	0.583451i
$433$	−3.48654	+	6.84272i	−0.167552	+	0.328840i	−0.959481	−	0.281774i	$-0.909077\pi$
$433$	−3.48654	+	6.84272i	−0.167552	+	0.328840i	0.791928	+	0.610614i	$0.209077\pi$
$434$	−2.56841	−	15.0491i	−0.123288	−	0.722380i
$435$	−1.09598	−	0.860745i	−0.0525483	−	0.0412695i
$436$	1.96159	+	10.7189i	0.0939430	+	0.513341i
$437$	−3.41662	+	10.5153i	−0.163439	+	0.503013i
$438$	−12.1755	+	6.38827i	−0.581766	+	0.305243i
$439$		−	5.32777i		−	0.254281i	−0.991885	−	0.127140i	$-0.959420\pi$
$439$		−	5.32777i		−	0.254281i	0.991885	−	0.127140i	$-0.0405798\pi$
$440$	−0.425024	−	20.9719i	−0.0202622	−	0.999795i
$441$			0.454830i			0.0216586i
$442$	11.9195	+	22.7174i	0.566952	+	1.08056i
$443$	−5.50867	+	16.9539i	−0.261725	+	0.805506i	0.730705	+	0.682693i	$0.239191\pi$
$443$	−5.50867	+	16.9539i	−0.261725	+	0.805506i	−0.992430	+	0.122813i	$0.960809\pi$
$444$	5.45775	−	7.90277i	0.259014	−	0.375049i
$445$	−0.798756	−	6.64412i	−0.0378647	−	0.314962i
$446$	−23.9609	+	4.08938i	−1.13458	+	0.193638i
$447$	3.15911	−	6.20011i	0.149421	−	0.293255i
$448$	13.6792	−	15.7982i	0.646283	−	0.746397i
$449$	2.43432	−	3.35055i	0.114882	−	0.158122i	−0.747703	−	0.664033i	$-0.768843\pi$
$449$	2.43432	−	3.35055i	0.114882	−	0.158122i	0.862586	+	0.505911i	$0.168843\pi$
$450$	−11.6183	+	14.0420i	−0.547693	+	0.661945i
$451$	10.6539	+	19.8279i	0.501672	+	0.933657i
$452$	8.70928	+	1.16662i	0.409650	+	0.0548733i
$453$	1.90894	−	2.62743i	0.0896898	−	0.123447i
$454$	30.6452	−	0.366544i	1.43825	−	0.0172028i
$455$	15.3665	−	10.3084i	0.720391	−	0.483266i
$456$	6.36708	+	5.92581i	0.298166	+	0.277502i
$457$	7.19494	+	1.13957i	0.336565	+	0.0533067i	0.322430	−	0.946593i	$-0.395500\pi$
$457$	7.19494	+	1.13957i	0.336565	+	0.0533067i	0.0141355	+	0.999900i	$0.495500\pi$
$458$	0.508835	−	3.48167i	0.0237763	−	0.162688i
$459$	−18.4984	+	9.42540i	−0.863430	+	0.439940i
$460$	−9.98307	+	3.09519i	−0.465463	+	0.144314i
$461$	−7.92561	+	7.92561i	−0.369132	+	0.369132i	−0.867161	−	0.498028i	$-0.834058\pi$
$461$	−7.92561	+	7.92561i	−0.369132	+	0.369132i	0.498028	+	0.867161i	$0.334058\pi$
$462$	−7.65343	−	2.20395i	−0.356070	−	0.102537i
$463$	−11.0663	+	11.0663i	−0.514296	+	0.514296i	−0.915840	−	0.401544i	$-0.868474\pi$
$463$	−11.0663	+	11.0663i	−0.514296	+	0.514296i	0.401544	+	0.915840i	$0.368474\pi$
$464$	3.81215	+	0.418097i	0.176975	+	0.0194097i
$465$	4.08558	+	4.40350i	0.189464	+	0.204208i
$466$	−5.53299	+	37.8592i	−0.256311	+	1.75379i
$467$	−25.3284	+	18.4022i	−1.17206	+	0.851551i	−0.991254	−	0.131968i	$-0.957870\pi$
$467$	−25.3284	+	18.4022i	−1.17206	+	0.851551i	−0.180805	+	0.983519i	$0.557870\pi$
$468$	4.67339	−	15.6472i	0.216028	−	0.723293i
$469$	33.3035	+	16.9690i	1.53781	+	0.783554i
$470$	−9.45868	+	2.80906i	−0.436296	+	0.129572i
$471$	11.6154	+	8.43911i	0.535211	+	0.388854i
$472$	−0.645210	−	3.30213i	−0.0296982	−	0.151993i
$473$	6.54810	+	6.26844i	0.301082	+	0.288223i
$474$	4.51420	−	1.52668i	0.207344	−	0.0701227i
$475$	15.4280	+	17.9301i	0.707884	+	0.822689i
$476$	28.2231	−	9.92263i	1.29360	−	0.454803i
$477$	−17.0173	+	5.52927i	−0.779170	+	0.253168i
$478$	12.2281	+	8.66273i	0.559303	+	0.396224i
$479$	8.63011	−	6.27014i	0.394320	−	0.286490i	−0.372904	−	0.927870i	$-0.621638\pi$
$479$	8.63011	−	6.27014i	0.394320	−	0.286490i	0.767223	+	0.641380i	$0.221638\pi$
$480$	−1.10431	+	8.14793i	−0.0504047	+	0.371900i
$481$	−7.23180	+	22.2572i	−0.329742	+	1.01484i
$482$	−1.75004	+	5.61365i	−0.0797121	+	0.255695i
$483$			3.96848i			0.180572i
$484$	11.7003	−	18.6307i	0.531834	−	0.846849i
$485$	−10.8051	−	38.0446i	−0.490636	−	1.72752i
$486$	19.4027	+	6.04875i	0.880125	+	0.274377i
$487$	2.00683	+	3.93863i	0.0909383	+	0.178476i	0.931996	−	0.362470i	$-0.118066\pi$
$487$	2.00683	+	3.93863i	0.0909383	+	0.178476i	−0.841057	+	0.540946i	$0.818066\pi$
$488$	−13.4903	−	24.2813i	−0.610676	−	1.09916i
$489$	5.03515	−	3.65825i	0.227697	−	0.165432i
$490$	0.240595	+	0.503502i	0.0108690	+	0.0227459i
$491$	−26.0179	−	13.2568i	−1.17417	−	0.598271i	−0.245581	−	0.969376i	$-0.578979\pi$
$491$	−26.0179	−	13.2568i	−1.17417	−	0.598271i	−0.928591	+	0.371105i	$0.878979\pi$
$492$	−2.92645	−	8.32377i	−0.131935	−	0.375264i
$493$	4.44162	+	3.22703i	0.200041	+	0.145338i
$494$	−18.9981	−	9.39551i	−0.854764	−	0.422724i
$495$	−18.2694	+	5.62220i	−0.821146	+	0.252699i
$496$	−15.9477	−	4.35051i	−0.716074	−	0.195344i
$497$	−19.4833	+	3.08584i	−0.873943	+	0.138419i
$498$	−7.77894	+	0.0930432i	−0.348583	+	0.00416936i
$499$	14.5111	+	7.39379i	0.649607	+	0.330991i	0.747555	−	0.664200i	$-0.231228\pi$
$499$	14.5111	+	7.39379i	0.649607	+	0.330991i	−0.0979477	+	0.995192i	$0.531228\pi$
$500$	−5.43372	+	21.6904i	−0.243003	+	0.970025i
$501$	8.94019	+	1.41599i	0.399418	+	0.0632616i
$502$	5.14311	−	35.1914i	0.229548	−	1.57067i
$503$	16.5217	−	8.41823i	0.736667	−	0.375350i	−0.0450495	−	0.998985i	$-0.514345\pi$
$503$	16.5217	−	8.41823i	0.736667	−	0.375350i	0.781716	+	0.623634i	$0.214345\pi$
$504$	−17.2668	−	8.03118i	−0.769126	−	0.357737i
$505$	−28.6086	+	8.12519i	−1.27307	+	0.361566i
$506$	−10.5340	−	3.03345i	−0.468292	−	0.134853i
$507$			1.92697i			0.0855798i
$508$	10.2781	+	9.79780i	0.456018	+	0.434707i
$509$	27.9198	−	14.2259i	1.23752	−	0.630550i	0.292099	−	0.956388i	$-0.405646\pi$
$509$	27.9198	−	14.2259i	1.23752	−	0.630550i	0.945426	+	0.325838i	$0.105646\pi$
$510$	−7.15920	+	9.34370i	−0.317015	+	0.413746i
$511$	−22.9646	−	31.6081i	−1.01589	−	1.39826i
$512$	−9.26379	−	20.6442i	−0.409405	−	0.912353i
$513$	7.78675	−	15.2824i	0.343793	−	0.674732i
$514$	1.01710	−	1.04172i	0.0448622	−	0.0459484i
$515$	18.9842	+	6.96406i	0.836543	+	0.306873i
$516$	−2.15674	−	2.82391i	−0.0949452	−	0.124315i
$517$	−9.90950	−	2.98242i	−0.435820	−	0.131167i
$518$	24.4625	+	12.0979i	1.07482	+	0.531552i
$519$	4.67921	−	6.44038i	0.205394	−	0.282701i
$520$	−3.10352	−	19.7938i	−0.136098	−	0.868013i
$521$	−22.0445	+	7.16269i	−0.965787	+	0.313803i	−0.749114	−	0.662441i	$-0.769521\pi$
$521$	−22.0445	+	7.16269i	−0.965787	+	0.313803i	−0.216673	+	0.976244i	$0.569521\pi$
$522$	−0.587937	−	3.44490i	−0.0257333	−	0.150779i
$523$	29.8395	−	21.6796i	1.30479	−	0.947985i	0.304799	−	0.952417i	$-0.401411\pi$
$523$	29.8395	−	21.6796i	1.30479	−	0.947985i	0.999990	+	0.00443188i	$0.00141072\pi$
$524$	−5.40292	−	29.5236i	−0.236028	−	1.28975i
$525$	7.25527	+	4.40947i	0.316646	+	0.192445i
$526$	−27.0512	+	14.1934i	−1.17949	+	0.618860i
$527$	−16.7335	−	16.7335i	−0.728925	−	0.728925i
$528$	−5.65870	+	6.50755i	−0.246263	+	0.283205i
$529$		−	17.5379i		−	0.762517i
$530$	−15.9135	+	15.1227i	−0.691239	+	0.656890i
$531$	−2.73185	+	1.39195i	−0.118552	+	0.0604053i
$532$	−14.0450	+	20.3370i	−0.608927	+	0.881720i
$533$	12.6371	+	17.3935i	0.547374	+	0.753396i
$534$	−1.59038	+	2.24495i	−0.0688226	+	0.0971487i
$535$	−7.13168	+	36.2006i	−0.308329	+	1.56509i
$536$	31.8677	−	24.9478i	1.37647	−	1.07758i
$537$	−0.0178613	−	0.112772i	−0.000770772	−	0.00486646i
$538$	15.0236	−	30.3783i	0.647714	−	1.30970i
$539$	−0.0789242	+	0.579923i	−0.00339951	+	0.0249791i
$540$	16.0472	−	2.31980i	0.690561	−	0.0998282i
$541$	−27.5847	+	4.36899i	−1.18596	+	0.187837i	−0.718083	−	0.695957i	$-0.754980\pi$
$541$	−27.5847	+	4.36899i	−1.18596	+	0.187837i	−0.467875	+	0.883794i	$0.654980\pi$
$542$	−0.457494	−	38.2491i	−0.0196511	−	1.64294i
$543$	11.1254	+	5.66865i	0.477435	+	0.243265i
$544$	3.14617	−	32.2400i	0.134891	−	1.38228i
$545$	7.52489	−	9.58141i	0.322331	−	0.410423i
$546$	−7.52735	−	1.10010i	−0.322141	−	0.0470798i
$547$	1.70398	−	5.24432i	0.0728571	−	0.224231i	−0.907996	−	0.418978i	$-0.862389\pi$
$547$	1.70398	−	5.24432i	0.0728571	−	0.224231i	0.980854	+	0.194747i	$0.0623885\pi$
$548$	−11.4811	−	10.9446i	−0.490450	−	0.467530i
$549$	−17.8985	+	17.8985i	−0.763890	+	0.763890i
$550$	−17.2504	+	15.8879i	−0.735557	+	0.677462i
$551$	−4.53566			−0.193226
$552$	3.89616	+	1.81219i	0.165832	+	0.0771320i
$553$	6.14743	+	12.0650i	0.261415	+	0.513056i
$554$	3.32384	−	2.47618i	0.141216	−	0.105203i
$555$	−10.6611	+	1.28167i	−0.452537	+	0.0544040i
$556$	19.2552	−	10.3985i	0.816603	−	0.440993i
$557$	−15.5717	+	5.05956i	−0.659795	+	0.214380i	−0.619728	−	0.784817i	$-0.712757\pi$
$557$	−15.5717	+	5.05956i	−0.659795	+	0.214380i	−0.0400669	+	0.999197i	$0.512757\pi$
$558$	0.180162	+	15.0626i	0.00762687	+	0.637650i
$559$	7.00474	+	5.08924i	0.296269	+	0.215252i
$560$	−23.3629	+	0.243156i	−0.987261	+	0.0102752i
$561$	−11.6554	+	4.07024i	−0.492091	+	0.171846i
$562$	−29.9212	+	10.1192i	−1.26215	+	0.426853i
$563$	−2.71950	+	3.74308i	−0.114613	+	0.157752i	−0.862469	−	0.506109i	$-0.831083\pi$
$563$	−2.71950	+	3.74308i	−0.114613	+	0.157752i	0.747856	+	0.663861i	$0.231083\pi$
$564$	3.65741	+	1.75465i	0.154005	+	0.0738840i
$565$	−5.47304	−	8.15852i	−0.230253	−	0.343232i
$566$	−8.89921	−	6.30442i	−0.374062	−	0.264995i
$567$	−2.19666	+	13.8692i	−0.0922511	+	0.582451i
$568$	−5.86734	+	20.5374i	−0.246188	+	0.861729i
$569$	8.45995	−	26.0370i	0.354660	−	1.09153i	−0.601547	−	0.798837i	$-0.705449\pi$
$569$	8.45995	−	26.0370i	0.354660	−	1.09153i	0.956207	−	0.292692i	$-0.0945512\pi$
$570$	0.247695	−	9.72149i	0.0103748	−	0.407188i
$571$	13.9687	−	13.9687i	0.584572	−	0.584572i	−0.351584	−	0.936156i	$-0.614357\pi$
$571$	13.9687	−	13.9687i	0.584572	−	0.584572i	0.936156	+	0.351584i	$0.114357\pi$
$572$	8.67390	−	19.1398i	0.362674	−	0.800273i
$573$	−3.55359			−0.148453
$574$	22.2010	−	11.6485i	0.926651	−	0.486199i
$575$	9.98594	+	6.06906i	0.416442	+	0.253097i
$576$	−15.7697	+	13.2848i	−0.657069	+	0.553532i
$577$	−1.05812	+	6.68071i	−0.0440501	+	0.278122i	−0.999875	−	0.0158154i	$-0.994966\pi$
$577$	−1.05812	+	6.68071i	−0.0440501	+	0.278122i	0.955825	+	0.293937i	$0.0949656\pi$
$578$	12.9093	−	18.2226i	0.536958	−	0.757959i
$579$	−2.15039	−	1.09568i	−0.0893671	−	0.0455348i
$580$	−2.47313	−	3.50254i	−0.102691	−	0.145435i
$581$	−3.45807	−	21.8334i	−0.143465	−	0.905802i
$582$	−7.20788	+	14.5746i	−0.298776	+	0.604136i
$583$	−22.6571	+	4.09707i	−0.938362	+	0.169683i
$584$	−41.5188	+	8.11243i	−1.71806	+	0.335695i
$585$	−16.5666	+	7.67421i	−0.684944	+	0.317289i
$586$	−0.124812	−	10.4350i	−0.00515593	−	0.431065i
$587$	7.74222	−	2.51560i	0.319556	−	0.103830i	−0.144847	−	0.989454i	$-0.546269\pi$
$587$	7.74222	−	2.51560i	0.319556	−	0.103830i	0.464403	+	0.885624i	$0.346269\pi$
$588$	0.0656553	−	0.219824i	0.00270758	−	0.00906537i
$589$	19.3099	+	3.05838i	0.795649	+	0.126018i
$590$	−2.28788	+	2.98598i	−0.0941904	+	0.122931i
$591$	−4.90070	−	1.59233i	−0.201588	−	0.0654999i
$592$	23.0482	−	18.4922i	0.947274	−	0.760026i
$593$	16.4374	+	16.4374i	0.675005	+	0.675005i	0.958865	−	0.283861i	$-0.0916154\pi$
$593$	16.4374	+	16.4374i	0.675005	+	0.675005i	−0.283861	+	0.958865i	$0.591615\pi$
$594$	15.4040	+	7.20420i	0.632033	+	0.295592i
$595$	−29.2130	−	16.2897i	−1.19762	−	0.667812i
$596$	14.7724	−	15.4966i	0.605103	−	0.634767i
$597$	3.86636	−	11.8994i	0.158240	−	0.487011i
$598$	−10.3604	−	1.51414i	−0.423669	−	0.0619178i
$599$	8.56255	+	11.7853i	0.349856	+	0.481536i	0.947288	−	0.320384i	$-0.103812\pi$
$599$	8.56255	+	11.7853i	0.349856	+	0.481536i	−0.597431	+	0.801920i	$0.703812\pi$
$600$	7.64221	−	5.10949i	0.311992	−	0.208594i
$601$	30.5746	−	9.93428i	1.24716	−	0.405228i	0.390259	−	0.920705i	$-0.372385\pi$
$601$	30.5746	−	9.93428i	1.24716	−	0.405228i	0.856903	+	0.515477i	$0.172385\pi$
$602$	7.05359	−	7.22437i	0.287483	−	0.294443i
$603$	−29.8368	−	21.6777i	−1.21505	−	0.882783i
$604$	7.94112	−	6.06498i	0.323119	−	0.246780i
$605$	−24.2696	+	3.99830i	−0.986700	+	0.162554i
$606$	10.9597	+	5.42014i	0.445209	+	0.220178i
$607$	0.498667	+	3.14846i	0.0202403	+	0.127792i	0.995740	−	0.0922107i	$-0.0293933\pi$
$607$	0.498667	+	3.14846i	0.0202403	+	0.127792i	−0.975499	+	0.220003i	$0.929393\pi$
$608$	13.5528	+	23.0758i	0.549639	+	0.935849i
$609$	−1.54831	+	0.503076i	−0.0627406	+	0.0203856i
$610$	−10.3459	+	29.2817i	−0.418895	+	1.18558i
$611$	−9.76284	−	1.54628i	−0.394962	−	0.0625559i
$612$	−29.0365	+	5.31377i	−1.17373	+	0.214797i
$613$	−23.2861	−	7.56610i	−0.940515	−	0.305592i	−0.201660	−	0.979456i	$-0.564633\pi$
$613$	−23.2861	−	7.56610i	−0.940515	−	0.305592i	−0.738856	+	0.673864i	$0.764633\pi$
$614$	−10.3251	+	33.1200i	−0.416686	+	1.33661i
$615$	−4.80427	+	8.61571i	−0.193727	+	0.347419i
$616$	−20.6222	−	13.2362i	−0.830890	−	0.533303i
$617$	7.14027	+	7.14027i	0.287456	+	0.287456i	0.836074	−	0.548617i	$-0.184846\pi$
$617$	7.14027	+	7.14027i	0.287456	+	0.287456i	−0.548617	+	0.836074i	$0.684846\pi$
$618$	−3.86251	−	7.36159i	−0.155373	−	0.296127i
$619$	3.57562	−	1.82187i	0.143716	−	0.0732270i	−0.380654	−	0.924718i	$-0.624301\pi$
$619$	3.57562	−	1.82187i	0.143716	−	0.0732270i	0.524370	+	0.851491i	$0.324301\pi$
$620$	8.16720	+	16.5791i	0.328003	+	0.665834i
$621$	1.32552	−	8.36903i	0.0531914	−	0.335837i
$622$	16.4171	+	11.6303i	0.658265	+	0.466332i
$623$	−6.96553	−	3.54911i	−0.279068	−	0.142192i
$624$	−4.51739	+	6.88783i	−0.180840	+	0.275734i
$625$	22.1912	−	11.5130i	0.887648	−	0.460522i
$626$	−16.7852	−	8.30112i	−0.670871	−	0.331780i
$627$	5.81357	−	8.38022i	0.232171	−	0.334674i
$628$	26.8123	+	35.1064i	1.06993	+	1.40090i
$629$	41.7820	−	6.61762i	1.66596	−	0.263862i
$630$	6.06137	+	20.4099i	0.241491	+	0.813150i
$631$	−13.9158	−	42.8284i	−0.553979	−	1.70497i	−0.698624	−	0.715489i	$-0.746204\pi$
$631$	−13.9158	−	42.8284i	−0.553979	−	1.70497i	0.144644	−	0.989484i	$-0.453796\pi$
$632$	14.6523	−	0.525967i	0.582839	−	0.0209218i
$633$	−1.89254	+	11.9490i	−0.0752216	+	0.474930i
$634$	9.09289	+	12.2056i	0.361125	+	0.484746i
$635$	0.594160	−	15.8648i	0.0235785	−	0.629576i
$636$	9.02279	−	0.215872i	0.357777	−	0.00855989i
$637$			0.559025i			0.0221494i
$638$	−0.151864	−	4.49438i	−0.00601234	−	0.177934i
$639$	19.4638			0.769975
$640$	−10.4298	+	23.0482i	−0.412276	+	0.911059i
$641$	−7.64209	+	23.5199i	−0.301844	+	0.928981i	0.678992	+	0.734146i	$0.262417\pi$
$641$	−7.64209	+	23.5199i	−0.301844	+	0.928981i	−0.980836	+	0.194835i	$0.937583\pi$
$642$	12.1644	−	9.06218i	0.480090	−	0.357656i
$643$	−9.68439	−	13.3294i	−0.381915	−	0.525661i	0.574176	−	0.818732i	$-0.305323\pi$
$643$	−9.68439	−	13.3294i	−0.381915	−	0.525661i	−0.956091	+	0.293071i	$0.905323\pi$
$644$	−3.49426	+	11.6993i	−0.137693	+	0.461017i
$645$	−0.767883	+	3.89780i	−0.0302354	+	0.153476i
$646$	0.458205	+	38.3085i	0.0180278	+	1.50723i
$647$	22.0570	−	3.49348i	0.867150	−	0.137343i	0.293019	−	0.956107i	$-0.405340\pi$
$647$	22.0570	−	3.49348i	0.867150	−	0.137343i	0.574131	+	0.818764i	$0.305340\pi$
$648$	12.6133	+	8.48994i	0.495499	+	0.333516i
$649$	−3.72473	+	1.30073i	−0.146208	+	0.0510583i
$650$	−14.2799	+	17.2588i	−0.560104	+	0.676945i
$651$	6.93090	−	1.09775i	0.271643	−	0.0430241i
$652$	18.0650	−	6.35126i	0.707480	−	0.248734i
$653$	9.47209	+	29.1521i	0.370671	+	1.14081i	0.946353	+	0.323135i	$0.104737\pi$
$653$	9.47209	+	29.1521i	0.370671	+	1.14081i	−0.575681	+	0.817674i	$0.695263\pi$
$654$	−4.93733	+	0.842648i	−0.193065	+	0.0329501i
$655$	−20.7263	+	26.3907i	−0.809843	+	1.03117i
$656$	−1.29824	−	27.1157i	−0.0506878	−	1.05869i
$657$	17.5014	+	34.3484i	0.682794	+	1.34006i
$658$	−3.43057	+	11.0043i	−0.133738	+	0.428994i
$659$	−25.4490	+	25.4490i	−0.991351	+	0.991351i	−0.999963	−	0.00861234i	$-0.997259\pi$
$659$	−25.4490	+	25.4490i	−0.991351	+	0.991351i	0.00861234	+	0.999963i	$0.497259\pi$
$660$	9.64131	−	0.0800561i	0.375288	−	0.00311618i
$661$	−13.3978	−	13.3978i	−0.521116	−	0.521116i	0.396793	−	0.917908i	$-0.370123\pi$
$661$	−13.3978	−	13.3978i	−0.521116	−	0.521116i	−0.917908	+	0.396793i	$0.870123\pi$
$662$	−0.341805	−	0.651450i	−0.0132846	−	0.0253193i
$663$	−10.5068	+	5.35348i	−0.408050	+	0.207912i
$664$	−23.0147	−	6.57509i	−0.893142	−	0.255163i
$665$	27.4352	−	3.29826i	1.06389	−	0.127901i
$666$	−21.9726	−	15.5659i	−0.851421	−	0.603168i
$667$	−2.13104	+	0.692418i	−0.0825144	+	0.0268105i
$668$	25.1094	+	12.0463i	0.971511	+	0.466084i
$669$	−1.74781	−	11.0353i	−0.0675744	−	0.426648i
$670$	−44.4966	−	8.21445i	−1.71905	−	0.317352i
$671$	−25.9270	+	19.7153i	−1.00090	+	0.761102i
$672$	7.18590	+	6.37403i	0.277202	+	0.245883i
$673$	3.20690	+	20.2476i	0.123617	+	0.780488i	0.969133	+	0.246538i	$0.0792929\pi$
$673$	3.20690	+	20.2476i	0.123617	+	0.780488i	−0.845516	+	0.533950i	$0.820707\pi$
$674$	−8.19789	+	8.39637i	−0.315771	+	0.323416i
$675$	−13.8276	−	11.7224i	−0.532226	−	0.451194i
$676$	−1.69670	+	5.68081i	−0.0652578	+	0.218493i
$677$	30.6371	−	22.2591i	1.17748	−	0.855488i	0.185593	−	0.982627i	$-0.440579\pi$
$677$	30.6371	−	22.2591i	1.17748	−	0.855488i	0.991885	+	0.127139i	$0.0405793\pi$
$678$	−0.584075	+	3.99650i	−0.0224313	+	0.153485i
$679$	−43.9404	−	14.2771i	−1.68628	−	0.547905i
$680$	−29.3329	+	21.2421i	−1.12486	+	0.814595i
$681$			14.0870i			0.539814i
$682$	−2.38401	+	19.2365i	−0.0912886	+	0.736605i
$683$	43.4754			1.66354			0.831770	−	0.555120i	$-0.187328\pi$
$683$	43.4754			1.66354			0.831770	+	0.555120i	$0.187328\pi$
$684$	16.8267	−	17.6516i	0.643383	−	0.674924i
$685$	−0.663704	+	17.7217i	−0.0253588	+	0.677113i
$686$	26.2326	+	3.83381i	1.00156	+	0.146375i
$687$	1.59743	+	0.253008i	0.0609457	+	0.00965286i
$688$	−3.87173	−	10.2240i	−0.147608	−	0.389788i
$689$	−20.9157	+	6.79594i	−0.796827	+	0.258905i
$690$	−1.36771	−	4.60538i	−0.0520680	−	0.175324i
$691$	3.14559	+	19.8604i	0.119664	+	0.755527i	0.972423	+	0.233223i	$0.0749273\pi$
$691$	3.14559	+	19.8604i	0.119664	+	0.755527i	−0.852760	+	0.522304i	$0.825073\pi$
$692$	19.4653	−	14.8665i	0.739961	−	0.565141i
$693$	−6.43546	+	21.3827i	−0.244463	+	0.812261i
$694$	−6.62647	+	2.24104i	−0.251538	+	0.0850687i
$695$	−22.9698	−	8.42614i	−0.871296	−	0.319622i
$696$	−0.213120	+	1.74982i	−0.00807831	+	0.0663268i
$697$	17.6434	−	34.6271i	0.668291	−	1.31159i
$698$	−1.07613	−	6.30537i	−0.0407321	−	0.238662i
$699$	−17.3702	−	2.75117i	−0.657001	−	0.104059i
$700$	17.5064	+	19.3876i	0.661678	+	0.732784i
$701$	11.1825	+	21.9468i	0.422356	+	0.828920i	0.999921	+	0.0125757i	$0.00400306\pi$
$701$	11.1825	+	21.9468i	0.422356	+	0.828920i	−0.577565	+	0.816345i	$0.695997\pi$
$702$	15.5068	+	4.83420i	0.585266	+	0.182455i
$703$	−24.7122	+	24.7122i	−0.932037	+	0.932037i
$704$	−22.4121	+	14.2021i	−0.844686	+	0.535262i
$705$	−1.23908	−	4.36279i	−0.0466666	−	0.164312i
$706$	32.8669	−	17.2447i	1.23696	−	0.649014i
$707$	−10.7360	+	33.0421i	−0.403770	+	1.24268i
$708$	1.52126	−	0.278394i	0.0571723	−	0.0104627i
$709$	2.48297	−	15.6769i	0.0932499	−	0.588757i	−0.896174	−	0.443703i	$-0.853665\pi$
$709$	2.48297	−	15.6769i	0.0932499	−	0.588757i	0.989424	−	0.145054i	$-0.0463355\pi$
$710$	21.5466	−	10.2959i	0.808629	−	0.386398i
$711$	−4.12871	−	12.7069i	−0.154839	−	0.476544i
$712$	−6.66522	+	5.21791i	−0.249790	+	0.195549i
$713$	9.53949	−	1.51091i	0.357257	−	0.0565839i
$714$	4.40543	+	13.0263i	0.164869	+	0.487497i
$715$	−22.4546	+	6.91016i	−0.839754	+	0.258425i
$716$	0.0466398	−	0.348184i	0.00174301	−	0.0130123i
$717$	−4.04874	+	5.57261i	−0.151203	+	0.208113i
$718$	−0.0979113	−	8.18594i	−0.00365402	−	0.305497i
$719$	−10.9426	−	33.6777i	−0.408088	−	1.25597i	−0.918289	−	0.395911i	$-0.870429\pi$
$719$	−10.9426	−	33.6777i	−0.408088	−	1.25597i	0.510200	−	0.860056i	$-0.329571\pi$
$720$	22.8059	+	3.36918i	0.849925	+	0.125562i
$721$	19.1110	−	13.8850i	0.711732	−	0.517104i
$722$	−2.85604	−	3.83372i	−0.106291	−	0.142676i
$723$	−2.57049	−	0.835204i	−0.0955976	−	0.0310616i
$724$	27.8069	+	26.5074i	1.03344	+	0.985140i
$725$	−1.10196	+	4.66539i	−0.0409257	+	0.173268i
$726$	8.49860	+	5.48007i	0.315413	+	0.203384i
$727$	−1.67696	+	1.67696i	−0.0621951	+	0.0621951i	−0.737520	−	0.675325i	$-0.764003\pi$
$727$	−1.67696	+	1.67696i	−0.0621951	+	0.0621951i	0.675325	+	0.737520i	$0.264003\pi$
$728$	−21.2224	−	9.87100i	−0.786554	−	0.365844i
$729$	2.09669	−	6.45295i	0.0776552	−	0.238998i
$730$	37.5437	+	28.7662i	1.38956	+	1.06469i
$731$	2.44834	−	15.4582i	0.0905553	−	0.571744i
$732$	11.2342	−	6.06684i	0.415227	−	0.224237i
$733$	10.4792	+	32.2518i	0.387060	+	1.19125i	0.934975	+	0.354713i	$0.115421\pi$
$733$	10.4792	+	32.2518i	0.387060	+	1.19125i	−0.547916	+	0.836534i	$0.684579\pi$
$734$	15.4515	+	15.0862i	0.570323	+	0.556842i
$735$	−0.232739	+	0.107813i	−0.00858472	+	0.00397674i
$736$	9.89046	+	8.77302i	0.364567	+	0.323378i
$737$	−34.2812	−	32.8171i	−1.26277	−	1.20883i
$738$	−23.4340	+	7.92526i	−0.862618	+	0.291733i
$739$	−10.7141	+	1.69695i	−0.394125	+	0.0624233i	−0.350352	−	0.936618i	$-0.613938\pi$
$739$	−10.7141	+	1.69695i	−0.394125	+	0.0624233i	−0.0437736	+	0.999041i	$0.513938\pi$
$740$	−32.5579	−	5.60866i	−1.19685	−	0.206179i
$741$	4.42275	−	8.68014i	0.162474	−	0.318873i
$742$	4.31454	+	25.2802i	0.158392	+	0.928065i
$743$	25.1165	+	3.97807i	0.921437	+	0.145941i	0.599091	−	0.800681i	$-0.295529\pi$
$743$	25.1165	+	3.97807i	0.921437	+	0.145941i	0.322346	+	0.946622i	$0.395529\pi$
$744$	2.08723	−	7.30588i	0.0765214	−	0.267847i
$745$	−23.9199	−	0.895834i	−0.876357	−	0.0328208i
$746$	−32.5550	−	10.1489i	−1.19193	−	0.371579i
$747$			21.8116i			0.798044i
$748$	−37.9446	+	1.73669i	−1.38739	+	0.0634996i
$749$	30.4782	+	30.4782i	1.11365	+	1.11365i
$750$	−9.93936	−	2.61666i	−0.362934	−	0.0955468i
$751$	−51.5118	−	16.7372i	−1.87969	−	0.610749i	−0.987153	−	0.159777i	$-0.948923\pi$
$751$	−51.5118	−	16.7372i	−1.87969	−	0.610749i	−0.892538	−	0.450972i	$-0.851077\pi$
$752$	9.23726	+	8.39315i	0.336848	+	0.306067i
$753$	16.1462	+	2.55731i	0.588401	+	0.0931935i
$754$	−0.722624	−	4.23408i	−0.0263164	−	0.154196i
$755$	−10.9610	−	2.15937i	−0.398912	−	0.0785874i
$756$	8.19305	−	17.0777i	0.297978	−	0.621109i
$757$	−7.02376	−	5.10306i	−0.255283	−	0.185474i	0.452782	−	0.891621i	$-0.350432\pi$
$757$	−7.02376	−	5.10306i	−0.255283	−	0.185474i	−0.708065	+	0.706147i	$0.750432\pi$
$758$	19.2048	−	38.8329i	0.697551	−	1.41048i
$759$	1.45213	−	4.82488i	0.0527088	−	0.175132i
$760$	9.29002	−	28.4414i	0.336984	−	1.03168i
$761$	5.80985	−	7.99658i	0.210607	−	0.289876i	−0.690625	−	0.723213i	$-0.742664\pi$
$761$	5.80985	−	7.99658i	0.210607	−	0.289876i	0.901232	+	0.433338i	$0.142664\pi$
$762$	−4.55971	+	4.67011i	−0.165181	+	0.169180i
$763$	−4.39804	−	13.5358i	−0.159220	−	0.490028i
$764$	−10.4762	−	3.12894i	−0.379014	−	0.113201i
$765$	25.9552	+	20.3843i	0.938413	+	0.736996i
$766$	−0.230275	+	1.57565i	−0.00832018	+	0.0569304i
$767$	−3.35767	+	1.71082i	−0.121239	+	0.0617741i
$768$	9.53929	−	4.14428i	0.344219	−	0.149544i
$769$			7.22602i			0.260577i	0.991476	+	0.130289i	$0.0415904\pi$
$769$			7.22602i			0.260577i	−0.991476	+	0.130289i	$0.958410\pi$
$770$	4.18683	+	27.0751i	0.150883	+	0.975718i
$771$	0.473199	+	0.473199i	0.0170418	+	0.0170418i
$772$	−5.37471	−	5.12354i	−0.193440	−	0.184400i
$773$	−38.0364	−	12.3588i	−1.36807	−	0.444514i	−0.469343	−	0.883016i	$-0.655509\pi$
$773$	−38.0364	−	12.3588i	−1.36807	−	0.444514i	−0.898730	+	0.438502i	$0.855509\pi$
$774$	−7.98921	+	5.95178i	−0.287166	+	0.213932i
$775$	7.83727	−	19.1191i	0.281523	−	0.686779i
$776$	−34.0822	+	36.6201i	−1.22348	+	1.31459i
$777$	−5.69486	+	11.1768i	−0.204302	+	0.400965i
$778$	14.1407	−	14.4831i	0.506969	−	0.519243i
$779$	5.02255	+	31.7111i	0.179951	+	1.13617i
$780$	9.11455	−	1.31761i	0.326353	−	0.0471780i
$781$	24.8169	+	3.37744i	0.888020	+	0.120854i
$782$	6.06350	+	17.9290i	0.216830	+	0.641140i
$783$	3.43322	−	0.543769i	0.122693	−	0.0194327i
$784$	0.387111	−	0.590242i	0.0138254	−	0.0210801i
$785$	9.54621	−	48.4569i	0.340719	−	1.72950i
$786$	13.5992	−	2.32096i	0.485067	−	0.0827858i
$787$	23.2250	−	16.8740i	0.827882	−	0.601491i	−0.0910774	−	0.995844i	$-0.529031\pi$
$787$	23.2250	−	16.8740i	0.827882	−	0.601491i	0.918959	+	0.394352i	$0.129031\pi$
$788$	−13.0455	−	9.00937i	−0.464726	−	0.320945i
$789$	−6.37476	−	12.5112i	−0.226947	−	0.445409i
$790$	−11.2922	−	11.8826i	−0.401757	−	0.422765i
$791$	−11.4767			−0.408066
$792$	18.0543	+	16.0825i	0.641532	+	0.571467i
$793$	−21.9988	+	21.9988i	−0.781200	+	0.781200i
$794$	22.0657	+	6.87892i	0.783083	+	0.244124i
$795$	−6.86315	−	7.39722i	−0.243411	−	0.262352i
$796$	21.8757	−	31.6758i	0.775364	−	1.12272i
$797$	−11.2908	−	15.5405i	−0.399941	−	0.550472i	0.560788	−	0.827959i	$-0.310498\pi$
$797$	−11.2908	−	15.5405i	−0.399941	−	0.550472i	−0.960729	+	0.277488i	$0.910498\pi$
$798$	−9.26996	−	6.56707i	−0.328153	−	0.232472i
$799$	5.52134	+	16.9929i	0.195331	+	0.601167i
$800$	27.0286	−	8.33407i	0.955604	−	0.294654i
$801$	6.24045	+	4.53396i	0.220496	+	0.160199i
$802$	−14.6015	−	43.1748i	−0.515597	−	1.52456i
$803$	16.3545	+	46.8322i	0.577139	+	1.65267i
$804$	11.2912	+	14.7840i	0.398209	+	0.521391i
$805$	12.3867	−	5.73794i	0.436573	−	0.202236i
$806$	0.221434	+	18.5132i	0.00779970	+	0.652099i
$807$	13.8797	+	7.07207i	0.488589	+	0.248949i
$808$	27.5374	+	25.6289i	0.968763	+	0.901623i
$809$	−13.8740	+	10.0801i	−0.487785	+	0.354396i	−0.804332	−	0.594181i	$-0.797476\pi$
$809$	−13.8740	+	10.0801i	−0.487785	+	0.354396i	0.316547	+	0.948577i	$0.397476\pi$
$810$	−2.23073	−	16.8521i	−0.0783799	−	0.592122i
$811$	2.72790	+	5.35381i	0.0957896	+	0.187998i	0.933929	−	0.357458i	$-0.116357\pi$
$811$	2.72790	+	5.35381i	0.0957896	+	0.187998i	−0.838140	+	0.545456i	$0.816357\pi$
$812$	−5.00745	+	0.119804i	−0.175727	+	0.00420431i
$813$	17.5824			0.616640
$814$	−25.3147	−	23.6599i	−0.887280	−	0.829278i
$815$	−18.6986	−	10.4267i	−0.654984	−	0.365230i
$816$	14.8007	+	1.62326i	0.518126	+	0.0568255i
$817$	5.87007	+	11.5207i	0.205368	+	0.403057i
$818$	−42.3813	+	31.5731i	−1.48183	+	1.10393i
$819$	−3.33656	+	21.0662i	−0.116589	+	0.736113i
$820$	−21.7494	+	21.1694i	−0.759522	+	0.739268i
$821$	−13.0680	+	25.6475i	−0.456078	+	0.895103i	0.542409	+	0.840114i	$0.317512\pi$
$821$	−13.0680	+	25.6475i	−0.456078	+	0.895103i	−0.998487	+	0.0549886i	$0.982488\pi$
$822$	5.09341	−	5.21673i	0.177653	−	0.181954i
$823$	−0.383567	−	2.42175i	−0.0133703	−	0.0844169i	0.980101	−	0.198500i	$-0.0636070\pi$
$823$	−0.383567	−	2.42175i	−0.0133703	−	0.0844169i	−0.993471	+	0.114083i	$0.963607\pi$
$824$	−4.90498	−	25.1033i	−0.170873	−	0.874515i
$825$	−7.20748	−	8.01585i	−0.250932	−	0.279076i
$826$	1.40785	+	4.16284i	0.0489854	+	0.144844i
$827$	4.18832	−	5.76472i	0.145642	−	0.200459i	−0.729963	−	0.683486i	$-0.760463\pi$
$827$	4.18832	−	5.76472i	0.145642	−	0.200459i	0.875605	+	0.483027i	$0.160463\pi$
$828$	5.21117	−	10.8622i	0.181101	−	0.377488i
$829$	8.80196	−	17.2748i	0.305705	−	0.599979i	−0.686134	−	0.727475i	$-0.740694\pi$
$829$	8.80196	−	17.2748i	0.305705	−	0.599979i	0.991839	+	0.127495i	$0.0406938\pi$
$830$	11.5378	+	24.1456i	0.400484	+	0.838107i
$831$	1.11982	+	1.54130i	0.0388460	+	0.0534670i
$832$	−19.3823	+	16.3281i	−0.671959	+	0.566076i
$833$	0.900364	−	0.458758i	0.0311957	−	0.0158950i
$834$	4.67343	+	8.90713i	0.161828	+	0.308429i
$835$	−8.50675	−	29.9521i	−0.294388	−	1.03653i
$836$	24.5175	−	19.5865i	0.847956	−	0.677412i
$837$	−14.9831			−0.517890
$838$	16.5857	+	31.6109i	0.572944	+	1.09198i
$839$	3.12992	+	1.01697i	0.108057	+	0.0351098i	0.362546	−	0.931966i	$-0.381907\pi$
$839$	3.12992	+	1.01697i	0.108057	+	0.0351098i	−0.254489	+	0.967076i	$0.581907\pi$
$840$	0.0166771	−	10.7392i	0.000575415	−	0.370539i
$841$	16.5055	+	22.7178i	0.569154	+	0.783374i
$842$	6.12730	+	35.9017i	0.211161	+	1.23726i
$843$	−4.48644	−	13.8078i	−0.154521	−	0.475567i
$844$	−16.1004	+	33.5599i	−0.554200	+	1.15518i
$845$	6.01459	−	2.78617i	0.206908	−	0.0958470i
$846$	5.04184	−	10.1948i	0.173342	−	0.350504i
$847$	−11.9158	+	26.1469i	−0.409433	+	0.898418i
$848$	26.7897	+	7.30819i	0.919963	+	0.250964i
$849$	2.94653	−	4.05555i	0.101125	−	0.139186i
$850$	39.5155	+	8.83591i	1.35537	+	0.303069i
$851$	−7.83824	+	15.3834i	−0.268691	+	0.527337i
$852$	−9.40701	−	2.80962i	−0.322279	−	0.0962559i
$853$	−24.5411	−	33.7780i	−0.840272	−	1.15654i	−0.985923	−	0.167200i	$-0.946528\pi$
$853$	−24.5411	−	33.7780i	−0.840272	−	1.15654i	0.145651	−	0.989336i	$-0.453472\pi$
$854$	21.6741	+	29.0936i	0.741672	+	0.995563i
$855$	−27.2461	−	1.02041i	−0.931798	−	0.0348971i
$856$	43.8405	−	16.0050i	1.49844	−	0.547041i
$857$	5.32372	+	5.32372i	0.181855	+	0.181855i	0.792164	−	0.610309i	$-0.208955\pi$
$857$	5.32372	+	5.32372i	0.181855	+	0.181855i	−0.610309	+	0.792164i	$0.708955\pi$
$858$	8.74922	+	4.09187i	0.298694	+	0.139694i
$859$	0.455854	+	0.455854i	0.0155535	+	0.0155535i	0.714841	−	0.699287i	$-0.246499\pi$
$859$	0.455854	+	0.455854i	0.0155535	+	0.0155535i	−0.699287	+	0.714841i	$0.746499\pi$
$860$	−5.69578	+	10.8148i	−0.194225	+	0.368781i
$861$	5.23177	+	10.2679i	0.178298	+	0.349930i
$862$	22.7150	+	30.4908i	0.773675	+	1.03852i
$863$	6.54698	−	41.3360i	0.222862	−	1.40709i	−0.581786	−	0.813342i	$-0.697646\pi$
$863$	6.54698	−	41.3360i	0.222862	−	1.40709i	0.804648	−	0.593753i	$-0.202354\pi$
$864$	−13.0252	−	15.8422i	−0.443125	−	0.538963i
$865$	−26.8677	−	5.29306i	−0.913530	−	0.179969i
$866$	−7.77107	−	7.58737i	−0.264072	−	0.257829i
$867$	8.30439	+	6.03349i	0.282032	+	0.204908i
$868$	21.3992	+	2.86646i	0.726338	+	0.0972941i
$869$	−3.05929	−	16.9181i	−0.103779	−	0.573907i
$870$	1.62341	−	1.11743i	0.0550388	−	0.0378844i
$871$	−36.6719	−	26.6437i	−1.24258	−	0.902787i
$872$	−15.2975	−	1.86316i	−0.518038	−	0.0630947i
$873$	40.6185	+	20.6962i	1.37473	+	0.700459i
$874$	−12.7589	−	9.03873i	−0.431576	−	0.305739i
$875$	3.27290	−	29.0212i	0.110644	−	0.981096i
$876$	−3.50034	−	19.1272i	−0.118266	−	0.646249i
$877$	−48.5637	−	15.7793i	−1.63988	−	0.532829i	−0.663369	−	0.748293i	$-0.730874\pi$
$877$	−48.5637	−	15.7793i	−1.63988	−	0.532829i	−0.976512	+	0.215463i	$0.930874\pi$
$878$	7.19317	+	2.24245i	0.242758	+	0.0756790i
$879$	4.79676			0.161791
$880$	28.4936	+	8.25319i	0.960519	+	0.278215i
$881$	−19.0860			−0.643024			−0.321512	−	0.946906i	$-0.604191\pi$
$881$	−19.0860			−0.643024			−0.321512	+	0.946906i	$0.604191\pi$
$882$	−0.614079	−	0.191437i	−0.0206771	−	0.00644603i
$883$	−44.6392	−	14.5041i	−1.50223	−	0.488103i	−0.561561	−	0.827435i	$-0.689799\pi$
$883$	−44.6392	−	14.5041i	−1.50223	−	0.488103i	−0.940667	+	0.339332i	$0.889799\pi$
$884$	−35.6883	+	6.53108i	−1.20033	+	0.219664i
$885$	−1.35982	−	1.06796i	−0.0457100	−	0.0358990i
$886$	−20.5714	−	14.5733i	−0.691109	−	0.489599i
$887$	41.3135	+	21.0503i	1.38717	+	0.706800i	0.978570	−	0.205913i	$-0.0660163\pi$
$887$	41.3135	+	21.0503i	1.38717	+	0.706800i	0.408602	+	0.912712i	$0.366016\pi$
$888$	8.37259	+	10.6949i	0.280966	+	0.358898i
$889$	−15.0043	−	10.9013i	−0.503230	−	0.365618i
$890$	9.30661	+	1.71808i	0.311958	+	0.0575901i
$891$	7.74564	−	16.0584i	0.259489	−	0.537976i
$892$	4.56393	−	34.0715i	0.152812	−	1.14080i
$893$	−11.9420	−	8.67635i	−0.399623	−	0.290343i
$894$	7.04127	+	6.87482i	0.235495	+	0.229928i
$895$	−0.326166	+	0.218804i	−0.0109025	+	0.00731382i
$896$	15.5721	+	25.1182i	0.520226	+	0.839140i
$897$	0.752877	−	4.75348i	0.0251378	−	0.158714i
$898$	3.49907	+	4.69688i	0.116765	+	0.156737i
$899$	1.79878	+	3.53031i	0.0599927	+	0.117742i
$900$	−14.0683	−	21.5965i	−0.468944	−	0.719882i
$901$	28.1098	+	28.1098i	0.936473	+	0.936473i
$902$	−31.2543	+	6.03859i	−1.04066	+	0.201063i
$903$	3.28165	+	3.28165i	0.109206	+	0.109206i
$904$	−5.24081	+	11.2676i	−0.174307	+	0.374755i
$905$	1.60747	−	42.9214i	0.0534340	−	1.42676i
$906$	2.74390	+	3.68319i	0.0911598	+	0.122366i
$907$	−16.1399	−	22.2147i	−0.535918	−	0.737628i	0.452100	−	0.891967i	$-0.350675\pi$
$907$	−16.1399	−	22.2147i	−0.535918	−	0.737628i	−0.988018	+	0.154339i	$0.950675\pi$
$908$	−12.4036	+	41.5292i	−0.411629	+	1.37819i
$909$	15.5630	−	30.5441i	0.516192	−	1.01308i
$910$	7.44994	+	25.0855i	0.246963	+	0.831576i
$911$	10.2464	−	14.1029i	0.339477	−	0.467251i	−0.604811	−	0.796369i	$-0.706751\pi$
$911$	10.2464	−	14.1029i	0.339477	−	0.467251i	0.944289	+	0.329118i	$0.106751\pi$
$912$	−10.6805	+	6.10221i	−0.353667	+	0.202064i
$913$	−3.78484	+	27.8105i	−0.125260	+	0.920392i
$914$	−4.56690	+	9.23445i	−0.151060	+	0.305448i
$915$	−13.4014	−	4.91611i	−0.443038	−	0.162522i
$916$	4.48653	+	2.15242i	0.148239	+	0.0711180i
$917$	12.1138	+	37.2824i	0.400033	+	1.23117i
$918$	−4.93955	−	28.9423i	−0.163029	−	0.955239i
$919$	−17.2008	−	23.6748i	−0.567401	−	0.780961i	0.424843	−	0.905267i	$-0.360329\pi$
$919$	−17.2008	−	23.6748i	−0.567401	−	0.780961i	−0.992244	+	0.124306i	$0.960329\pi$
$920$	0.0229539	−	14.7812i	0.000756767	−	0.487321i
$921$	−15.1657	−	4.92763i	−0.499726	−	0.162371i
$922$	−7.36470	−	14.0365i	−0.242544	−	0.462266i
$923$	23.9226			0.787423
$924$	6.19693	−	9.40547i	0.203864	−	0.309417i
$925$	19.4151	+	31.4229i	0.638363	+	1.03318i
$926$	−10.2832	−	19.5988i	−0.337925	−	0.644055i
$927$	−20.7679	+	10.5818i	−0.682108	+	0.347551i
$928$	−2.16901	+	4.97091i	−0.0712013	+	0.163178i
$929$	−23.8085	−	32.7696i	−0.781132	−	1.07514i	−0.995156	−	0.0983078i	$-0.968657\pi$
$929$	−23.8085	−	32.7696i	−0.781132	−	1.07514i	0.214024	−	0.976828i	$-0.431343\pi$
$930$	−7.66491	+	3.66262i	−0.251342	+	0.120102i
$931$	−0.379001	+	0.743831i	−0.0124213	+	0.0243781i
$932$	−48.7859	−	23.4051i	−1.59803	−	0.766660i
$933$	−5.43569	+	7.48159i	−0.177957	+	0.244936i
$934$	−14.1846	−	41.9420i	−0.464134	−	1.37239i
$935$	29.5566	+	30.4945i	0.966604	+	0.997277i
$936$	19.1587	+	12.8956i	0.626222	+	0.421505i
$937$	5.21015	+	32.8956i	0.170208	+	1.07465i	0.913844	+	0.406066i	$0.133100\pi$
$937$	5.21015	+	32.8956i	0.170208	+	1.07465i	−0.743636	+	0.668585i	$0.766900\pi$
$938$	−36.9277	+	37.8217i	−1.20573	+	1.23492i
$939$	3.90759	−	7.66908i	0.127519	−	0.250271i
$940$	0.188558	−	13.9528i	0.00615010	−	0.455089i
$941$	−0.820989	+	5.18352i	−0.0267635	+	0.168978i	−0.997450	−	0.0713721i	$-0.977262\pi$
$941$	−0.820989	+	5.18352i	−0.0267635	+	0.168978i	0.970686	+	0.240350i	$0.0772622\pi$
$942$	−16.2828	+	12.1303i	−0.530522	+	0.395227i
$943$	7.20085	+	14.1325i	0.234492	+	0.460216i
$944$	4.72987	+	0.518748i	0.153944	+	0.0168838i
$945$	−20.3714	+	5.78571i	−0.662680	+	0.188209i
$946$	−11.2193	+	6.20239i	−0.364770	+	0.201657i
$947$	52.7600			1.71447			0.857235	−	0.514925i	$-0.172180\pi$
$947$	52.7600			1.71447			0.857235	+	0.514925i	$0.172180\pi$
$948$	0.161192	+	6.73732i	0.00523527	+	0.218818i
$949$	21.5107	+	42.2171i	0.698266	+	1.37043i
$950$	−30.7015	+	13.2830i	−0.996089	+	0.430957i
$951$	−5.65985	+	4.11212i	−0.183533	+	0.133345i
$952$	1.51774	+	42.2812i	0.0491904	+	1.37034i
$953$	−2.85562	−	1.45501i	−0.0925025	−	0.0471324i	0.407127	−	0.913371i	$-0.366531\pi$
$953$	−2.85562	−	1.45501i	−0.0925025	−	0.0471324i	−0.499630	+	0.866239i	$0.666531\pi$
$954$	−0.302645	−	25.3028i	−0.00979849	−	0.819209i
$955$	5.13806	+	11.0917i	0.166264	+	0.358919i
$956$	−16.8426	+	12.8634i	−0.544729	+	0.416033i
$957$	2.06652	−	0.0450913i	0.0668010	−	0.00145760i
$958$	4.83309	+	14.2908i	0.156150	+	0.461716i
$959$	16.7605	+	12.1772i	0.541226	+	0.393224i
$960$	−10.5359	−	4.92041i	−0.340046	−	0.158806i
$961$	4.30197	+	13.2401i	0.138773	+	0.427100i
$962$	−27.0062	−	19.1319i	−0.870714	−	0.616836i
$963$	−24.9981	−	34.4070i	−0.805554	−	1.10875i
$964$	−6.84255	−	4.72555i	−0.220384	−	0.152200i
$965$	−0.310703	+	8.29616i	−0.0100019	+	0.267063i
$966$	−5.35795	−	1.67033i	−0.172389	−	0.0537419i
$967$	40.7331	−	40.7331i	1.30989	−	1.30989i	0.388393	−	0.921494i	$-0.373030\pi$
$967$	40.7331	−	40.7331i	1.30989	−	1.30989i	0.921494	−	0.388393i	$-0.126970\pi$
$968$	20.2291	+	23.6386i	0.650189	+	0.759773i
$969$	−17.6097			−0.565704
$970$	55.9129	+	1.42461i	1.79526	+	0.0457415i
$971$	17.2465	+	33.8481i	0.553466	+	1.08624i	0.983072	+	0.183222i	$0.0586526\pi$
$971$	17.2465	+	33.8481i	0.553466	+	1.08624i	−0.429606	+	0.903017i	$0.641347\pi$
$972$	−16.3332	+	23.6502i	−0.523886	+	0.758582i
$973$	−23.1233	+	16.8001i	−0.741300	+	0.538586i
$974$	−6.16233	+	1.05172i	−0.197454	+	0.0336992i
$975$	−7.85388	−	6.65812i	−0.251525	−	0.213231i
$976$	38.4608	−	7.99364i	1.23110	−	0.255870i
$977$	14.4762	−	2.29280i	0.463134	−	0.0733533i	0.0794930	−	0.996835i	$-0.474670\pi$
$977$	14.4762	−	2.29280i	0.463134	−	0.0733533i	0.383641	+	0.923482i	$0.374670\pi$
$978$	2.81982	+	8.33785i	0.0901679	+	0.266615i
$979$	7.17003	+	6.86381i	0.229155	+	0.219368i
$980$	−0.781058	+	0.112910i	−0.0249500	+	0.00360679i
$981$	2.19682	+	13.8702i	0.0701391	+	0.442841i
$982$	28.8493	−	29.5477i	0.920617	−	0.942906i
$983$	5.05295	−	9.91698i	0.161164	−	0.316303i	−0.796276	−	0.604933i	$-0.793200\pi$
$983$	5.05295	−	9.91698i	0.161164	−	0.316303i	0.957441	+	0.288630i	$0.0931999\pi$
$984$	12.4699	−	0.447624i	0.397525	−	0.0142697i
$985$	2.11572	+	17.5987i	0.0674123	+	0.560742i
$986$	−6.22637	+	4.63851i	−0.198288	+	0.147720i
$987$	−5.03889	−	1.63724i	−0.160390	−	0.0521138i
$988$	20.6814	−	21.6953i	0.657963	−	0.690218i
$989$	4.51676	+	4.51676i	0.143625	+	0.143625i
$990$	0.0988598	−	27.0323i	0.00314197	−	0.859144i
$991$			16.3295i			0.518722i	0.965780	+	0.259361i	$0.0835120\pi$
$991$			16.3295i			0.518722i	−0.965780	+	0.259361i	$0.916488\pi$
$992$	12.5861	−	19.7003i	0.399609	−	0.625486i
$993$	0.301295	−	0.153517i	0.00956130	−	0.00487173i
$994$	4.03419	−	27.6037i	0.127957	−	0.875536i
$995$	−42.7316	+	5.13719i	−1.35468	+	0.162860i
$996$	3.14852	−	10.5417i	0.0997648	−	0.334027i
$997$	−15.4301	−	47.4890i	−0.488677	−	1.50399i	−0.826584	−	0.562814i	$-0.809719\pi$
$997$	−15.4301	−	47.4890i	−0.488677	−	1.50399i	0.337907	−	0.941180i	$-0.390281\pi$
$998$	−16.0903	+	16.4798i	−0.509328	+	0.521660i
$999$	15.7429	−	21.6683i	0.498085	−	0.685555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cz.a.763.58	yes	1120
5.2	odd	4		880.2.ch.a.587.14	yes	1120
11.3	even	5	inner	880.2.cz.a.443.113	yes	1120
16.3	odd	4		880.2.ch.a.323.45	yes	1120
55.47	odd	20		880.2.ch.a.267.45	yes	1120
80.67	even	4	inner	880.2.cz.a.147.113	yes	1120
176.3	odd	20		880.2.ch.a.3.14	✓	1120
880.707	even	20	inner	880.2.cz.a.707.58	yes	1120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.ch.a.3.14	✓	1120	176.3	odd	20
880.2.ch.a.267.45	yes	1120	55.47	odd	20
880.2.ch.a.323.45	yes	1120	16.3	odd	4
880.2.ch.a.587.14	yes	1120	5.2	odd	4
880.2.cz.a.147.113	yes	1120	80.67	even	4	inner
880.2.cz.a.443.113	yes	1120	11.3	even	5	inner
880.2.cz.a.707.58	yes	1120	880.707	even	20	inner
880.2.cz.a.763.58	yes	1120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cz (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.420899 + 1.35013i) q^{2} +(-0.618224 - 0.200873i) q^{3} +(-1.64569 - 1.13653i) q^{4} +(0.266898 + 2.22008i) q^{5} +(0.531414 - 0.750134i) q^{6} +(2.32748 + 1.18591i) q^{7} +(2.22713 - 1.74352i) q^{8} +(-2.08520 - 1.51499i) q^{9} +O(q^{10})\)	\(q+(-0.420899 + 1.35013i) q^{2} +(-0.618224 - 0.200873i) q^{3} +(-1.64569 - 1.13653i) q^{4} +(0.266898 + 2.22008i) q^{5} +(0.531414 - 0.750134i) q^{6} +(2.32748 + 1.18591i) q^{7} +(2.22713 - 1.74352i) q^{8} +(-2.08520 - 1.51499i) q^{9} +(-3.10973 - 0.574083i) q^{10} +(-2.39581 - 2.29349i) q^{11} +(0.789106 + 1.03321i) q^{12} +(-2.56289 - 1.86205i) q^{13} +(-2.58076 + 2.64324i) q^{14} +(0.280952 - 1.42612i) q^{15} +(1.41658 + 3.74076i) q^{16} +(-0.895798 + 5.65584i) q^{17} +(2.92308 - 2.17763i) q^{18} +(-2.14774 - 4.21517i) q^{19} +(2.08397 - 3.95690i) q^{20} +(-1.20069 - 1.20069i) q^{21} +(4.10490 - 2.26932i) q^{22} +(-1.65259 - 1.65259i) q^{23} +(-1.72710 + 0.630518i) q^{24} +(-4.85753 + 1.18507i) q^{25} +(3.59272 - 2.67649i) q^{26} +(2.13105 + 2.93314i) q^{27} +(-2.48248 - 4.59689i) q^{28} +(0.435264 - 0.854255i) q^{29} +(1.80719 + 0.979574i) q^{30} +(-2.42909 + 3.34336i) q^{31} +(-5.64674 + 0.338088i) q^{32} +(1.02045 + 1.89914i) q^{33} +(-7.25907 - 3.58998i) q^{34} +(-2.01162 + 5.48371i) q^{35} +(1.70976 + 4.86310i) q^{36} +(-2.28283 - 7.02584i) q^{37} +(6.59499 - 1.12556i) q^{38} +(1.21040 + 1.66598i) q^{39} +(4.46519 + 4.47908i) q^{40} +(-6.45452 - 2.09720i) q^{41} +(2.12645 - 1.11571i) q^{42} -2.73314 q^{43} +(1.33613 + 6.49729i) q^{44} +(2.80686 - 5.03366i) q^{45} +(2.92678 - 1.53563i) q^{46} +(2.78013 - 1.41655i) q^{47} +(-0.124348 - 2.59718i) q^{48} +(-0.103724 - 0.142763i) q^{49} +(0.444530 - 7.05708i) q^{50} +(1.68991 - 3.31664i) q^{51} +(2.10144 + 5.97716i) q^{52} +(4.08050 - 5.61633i) q^{53} +(-4.85707 + 1.64264i) q^{54} +(4.45230 - 5.93102i) q^{55} +(7.25127 - 1.41684i) q^{56} +(0.481068 + 3.03734i) q^{57} +(0.970150 + 0.947217i) q^{58} +(0.540048 - 1.05990i) q^{59} +(-2.08319 + 2.02764i) q^{60} +(1.53629 - 9.69978i) q^{61} +(-3.49156 - 4.68680i) q^{62} +(-3.05662 - 5.99896i) q^{63} +(1.92024 - 7.76612i) q^{64} +(3.44987 - 6.18680i) q^{65} +(-2.99359 + 0.578386i) q^{66} +14.3088 q^{67} +(7.90226 - 8.28966i) q^{68} +(0.689710 + 1.35363i) q^{69} +(-6.55702 - 5.02402i) q^{70} +(-6.10934 + 4.43870i) q^{71} +(-7.28543 + 0.261521i) q^{72} +(-13.3265 - 6.79020i) q^{73} +(10.4466 - 0.124951i) q^{74} +(3.24109 + 0.243108i) q^{75} +(-1.25618 + 9.37783i) q^{76} +(-2.85632 - 8.17926i) q^{77} +(-2.75874 + 0.932992i) q^{78} +(4.19372 + 3.04692i) q^{79} +(-7.92671 + 4.14333i) q^{80} +(1.66115 + 5.11249i) q^{81} +(5.54818 - 7.83171i) q^{82} +(-4.97411 - 6.84628i) q^{83} +(0.611336 + 3.34058i) q^{84} +(-12.7955 - 0.479211i) q^{85} +(1.15038 - 3.69009i) q^{86} +(-0.440688 + 0.440688i) q^{87} +(-9.33454 - 0.930753i) q^{88} -2.99274 q^{89} +(5.61468 + 5.90828i) q^{90} +(-3.75685 - 7.37322i) q^{91} +(0.841424 + 4.59787i) q^{92} +(2.17332 - 1.57901i) q^{93} +(0.742367 + 4.34976i) q^{94} +(8.78479 - 5.89317i) q^{95} +(3.55887 + 0.925265i) q^{96} +(-17.4692 + 2.76685i) q^{97} +(0.236406 - 0.0799513i) q^{98} +(1.52114 + 8.41200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9}+O(q^{10}) \) 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9	\( 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9} - 8 q^{10} - 16 q^{11} - 44 q^{12} - 12 q^{13} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 10 q^{18} - 6 q^{20} - 32 q^{21} - 10 q^{22} - 32 q^{23} - 24 q^{24} + 20 q^{26} - 22 q^{28} + 36 q^{30} - 36 q^{32} - 16 q^{33} - 32 q^{34} + 14 q^{35} + 20 q^{36} - 12 q^{37} - 26 q^{38} - 88 q^{40} - 6 q^{42} + 32 q^{43} + 80 q^{44} - 8 q^{45} - 12 q^{46} - 18 q^{48} + 16 q^{50} - 12 q^{51} + 34 q^{52} - 168 q^{54} - 16 q^{55} - 80 q^{56} - 24 q^{57} + 38 q^{58} + 16 q^{59} - 32 q^{60} - 12 q^{61} + 96 q^{62} + 36 q^{63} - 32 q^{65} - 24 q^{66} - 32 q^{67} - 38 q^{68} + 36 q^{69} - 42 q^{70} - 56 q^{71} - 76 q^{72} + 100 q^{74} + 30 q^{75} - 32 q^{76} - 108 q^{78} + 102 q^{80} - 240 q^{81} - 18 q^{82} + 24 q^{84} + 14 q^{85} - 4 q^{86} - 32 q^{87} - 98 q^{88} - 44 q^{90} - 28 q^{91} - 48 q^{92} - 36 q^{93} - 48 q^{94} - 120 q^{95} + 20 q^{96} - 12 q^{97} - 284 q^{98} + 20 q^{99}+O(q^{100}) \) 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9 - 8 * q^10 - 16 * q^11 - 44 * q^12 - 12 * q^13 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 10 * q^18 - 6 * q^20 - 32 * q^21 - 10 * q^22 - 32 * q^23 - 24 * q^24 + 20 * q^26 - 22 * q^28 + 36 * q^30 - 36 * q^32 - 16 * q^33 - 32 * q^34 + 14 * q^35 + 20 * q^36 - 12 * q^37 - 26 * q^38 - 88 * q^40 - 6 * q^42 + 32 * q^43 + 80 * q^44 - 8 * q^45 - 12 * q^46 - 18 * q^48 + 16 * q^50 - 12 * q^51 + 34 * q^52 - 168 * q^54 - 16 * q^55 - 80 * q^56 - 24 * q^57 + 38 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 96 * q^62 + 36 * q^63 - 32 * q^65 - 24 * q^66 - 32 * q^67 - 38 * q^68 + 36 * q^69 - 42 * q^70 - 56 * q^71 - 76 * q^72 + 100 * q^74 + 30 * q^75 - 32 * q^76 - 108 * q^78 + 102 * q^80 - 240 * q^81 - 18 * q^82 + 24 * q^84 + 14 * q^85 - 4 * q^86 - 32 * q^87 - 98 * q^88 - 44 * q^90 - 28 * q^91 - 48 * q^92 - 36 * q^93 - 48 * q^94 - 120 * q^95 + 20 * q^96 - 12 * q^97 - 284 * q^98 + 20 * q^99

Introduction

L-functions

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