LMFDB - Embedded newform 880.2.ch.a.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(3,880)]

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, 15, 16]))

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

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

chi := DirichletCharacter("880.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.ch (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			3.14
Character	$\chi$	$=$	880.3
Dual form			880.2.ch.a.587.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35013 + 0.420899i) q^{2} +(-0.200873 - 0.618224i) q^{3} +(1.64569 - 1.13653i) q^{4} +(0.939878 + 2.02895i) q^{5} +(0.531414 + 0.750134i) q^{6} +(-1.18591 - 2.32748i) q^{7} +(-1.74352 + 2.22713i) q^{8} +(2.08520 - 1.51499i) q^{9} +O(q^{10})$	\(q+(-1.35013 + 0.420899i) q^{2} +(-0.200873 - 0.618224i) q^{3} +(1.64569 - 1.13653i) q^{4} +(0.939878 + 2.02895i) q^{5} +(0.531414 + 0.750134i) q^{6} +(-1.18591 - 2.32748i) q^{7} +(-1.74352 + 2.22713i) q^{8} +(2.08520 - 1.51499i) q^{9} +(-2.12294 - 2.34374i) q^{10} +(-2.39581 + 2.29349i) q^{11} +(-1.03321 - 0.789106i) q^{12} +(-1.86205 - 2.56289i) q^{13} +(2.58076 + 2.64324i) q^{14} +(1.06555 - 0.988617i) q^{15} +(1.41658 - 3.74076i) q^{16} +(-5.65584 + 0.895798i) q^{17} +(-2.17763 + 2.92308i) q^{18} +(2.14774 - 4.21517i) q^{19} +(3.85271 + 2.27081i) q^{20} +(-1.20069 + 1.20069i) q^{21} +(2.26932 - 4.10490i) q^{22} +(-1.65259 - 1.65259i) q^{23} +(1.72710 + 0.630518i) q^{24} +(-3.23326 + 3.81393i) q^{25} +(3.59272 + 2.67649i) q^{26} +(-2.93314 - 2.13105i) q^{27} +(-4.59689 - 2.48248i) q^{28} +(-0.435264 - 0.854255i) q^{29} +(-1.02252 + 1.78325i) q^{30} +(-2.42909 - 3.34336i) q^{31} +(-0.338088 + 5.64674i) q^{32} +(1.89914 + 1.02045i) q^{33} +(7.25907 - 3.58998i) q^{34} +(3.60772 - 4.59369i) q^{35} +(1.70976 - 4.86310i) q^{36} +(7.02584 + 2.28283i) q^{37} +(-1.12556 + 6.59499i) q^{38} +(-1.21040 + 1.66598i) q^{39} +(-6.15744 - 1.44429i) q^{40} +(-6.45452 + 2.09720i) q^{41} +(1.11571 - 2.12645i) q^{42} -2.73314i q^{43} +(-1.33613 + 6.49729i) q^{44} +(5.03366 + 2.80686i) q^{45} +(2.92678 + 1.53563i) q^{46} +(1.41655 - 2.78013i) q^{47} +(-2.59718 - 0.124348i) q^{48} +(0.103724 - 0.142763i) q^{49} +(2.76003 - 6.51016i) q^{50} +(1.68991 + 3.31664i) q^{51} +(-5.97716 - 2.10144i) q^{52} +(-5.61633 + 4.08050i) q^{53} +(4.85707 + 1.64264i) q^{54} +(-6.90514 - 2.70537i) q^{55} +(7.25127 + 1.41684i) q^{56} +(-3.03734 - 0.481068i) q^{57} +(0.947217 + 0.970150i) q^{58} +(-0.540048 - 1.05990i) q^{59} +(0.629965 - 2.83799i) q^{60} +(1.53629 + 9.69978i) q^{61} +(4.68680 + 3.49156i) q^{62} +(-5.99896 - 3.05662i) q^{63} +(-1.92024 - 7.76612i) q^{64} +(3.44987 - 6.18680i) q^{65} +(-2.99359 - 0.578386i) q^{66} -14.3088i q^{67} +(-8.28966 + 7.90226i) q^{68} +(-0.689710 + 1.35363i) q^{69} +(-2.93740 + 7.72056i) q^{70} +(-6.10934 - 4.43870i) q^{71} +(-0.261521 + 7.28543i) q^{72} +(-6.79020 - 13.3265i) q^{73} +(-10.4466 - 0.124951i) q^{74} +(3.00734 + 1.23276i) q^{75} +(-1.25618 - 9.37783i) q^{76} +(8.17926 + 2.85632i) q^{77} +(0.932992 - 2.75874i) q^{78} +(-4.19372 + 3.04692i) q^{79} +(8.92122 - 0.641686i) q^{80} +(1.66115 - 5.11249i) q^{81} +(7.83171 - 5.54818i) q^{82} +(-6.84628 - 4.97411i) q^{83} +(-0.611336 + 3.34058i) q^{84} +(-7.13333 - 10.6335i) q^{85} +(1.15038 + 3.69009i) q^{86} +(-0.440688 + 0.440688i) q^{87} +(-0.930753 - 9.33454i) q^{88} +2.99274 q^{89} +(-7.97749 - 1.67096i) q^{90} +(-3.75685 + 7.37322i) q^{91} +(-4.59787 - 0.841424i) q^{92} +(-1.57901 + 2.17332i) q^{93} +(-0.742367 + 4.34976i) q^{94} +(10.5710 + 0.395898i) q^{95} +(3.55887 - 0.925265i) q^{96} +(-2.76685 + 17.4692i) q^{97} +(-0.0799513 + 0.236406i) q^{98} +(-1.52114 + 8.41200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1120 q - 6 q^{2} - 12 q^{3} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} - 264 q^{9}+O(q^{10}) $ 1120 * q - 6 * q^2 - 12 * q^3 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 - 264 * q^9	$ 1120 q - 6 q^{2} - 12 q^{3} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} - 264 q^{9} - 24 q^{10} - 16 q^{11} - 20 q^{12} + 24 q^{15} - 12 q^{16} - 12 q^{17} + 14 q^{18} - 6 q^{20} - 32 q^{21} - 22 q^{22} - 32 q^{23} + 24 q^{24} + 20 q^{26} + 12 q^{27} - 22 q^{28} - 36 q^{32} - 16 q^{33} + 32 q^{34} - 26 q^{35} + 20 q^{36} - 42 q^{38} + 36 q^{40} + 42 q^{42} - 80 q^{44} + 16 q^{45} - 12 q^{46} + 6 q^{48} - 68 q^{50} - 12 q^{51} + 2 q^{52} - 12 q^{53} + 168 q^{54} - 16 q^{55} - 80 q^{56} + 24 q^{57} - 50 q^{58} - 16 q^{59} + 52 q^{60} - 12 q^{61} - 124 q^{62} - 36 q^{63} - 32 q^{65} - 24 q^{66} + 50 q^{68} - 36 q^{69} + 30 q^{70} - 56 q^{71} - 52 q^{72} - 100 q^{74} - 42 q^{75} - 32 q^{76} + 12 q^{77} - 132 q^{78} + 46 q^{80} - 240 q^{81} + 30 q^{82} + 108 q^{83} - 24 q^{84} - 26 q^{85} - 4 q^{86} - 32 q^{87} - 130 q^{88} - 4 q^{90} - 28 q^{91} - 68 q^{92} + 48 q^{94} + 120 q^{95} + 20 q^{96} - 12 q^{97} - 172 q^{98} - 20 q^{99}+O(q^{100}) $ 1120 * q - 6 * q^2 - 12 * q^3 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 - 264 * q^9 - 24 * q^10 - 16 * q^11 - 20 * q^12 + 24 * q^15 - 12 * q^16 - 12 * q^17 + 14 * q^18 - 6 * q^20 - 32 * q^21 - 22 * q^22 - 32 * q^23 + 24 * q^24 + 20 * q^26 + 12 * q^27 - 22 * q^28 - 36 * q^32 - 16 * q^33 + 32 * q^34 - 26 * q^35 + 20 * q^36 - 42 * q^38 + 36 * q^40 + 42 * q^42 - 80 * q^44 + 16 * q^45 - 12 * q^46 + 6 * q^48 - 68 * q^50 - 12 * q^51 + 2 * q^52 - 12 * q^53 + 168 * q^54 - 16 * q^55 - 80 * q^56 + 24 * q^57 - 50 * q^58 - 16 * q^59 + 52 * q^60 - 12 * q^61 - 124 * q^62 - 36 * q^63 - 32 * q^65 - 24 * q^66 + 50 * q^68 - 36 * q^69 + 30 * q^70 - 56 * q^71 - 52 * q^72 - 100 * q^74 - 42 * q^75 - 32 * q^76 + 12 * q^77 - 132 * q^78 + 46 * q^80 - 240 * q^81 + 30 * q^82 + 108 * q^83 - 24 * q^84 - 26 * q^85 - 4 * q^86 - 32 * q^87 - 130 * q^88 - 4 * q^90 - 28 * q^91 - 68 * q^92 + 48 * q^94 + 120 * q^95 + 20 * q^96 - 12 * q^97 - 172 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.35013	+	0.420899i	−0.954684	+	0.297620i
$2$	−1.35013	+	0.420899i	−0.954684	+	0.297620i
$3$	−0.200873	−	0.618224i	−0.115974	−	0.356932i	0.876175	−	0.481994i	$-0.160087\pi$
$3$	−0.200873	−	0.618224i	−0.115974	−	0.356932i	−0.992149	+	0.125062i	$0.960087\pi$
$4$	1.64569	−	1.13653i	0.822844	−	0.568267i
$5$	0.939878	+	2.02895i	0.420326	+	0.907373i
$5$	0.939878	+	2.02895i	0.420326	+	0.907373i
$6$	0.531414	+	0.750134i	0.216949	+	0.306241i
$7$	−1.18591	−	2.32748i	−0.448232	−	0.879704i	−0.998985	−	0.0450362i	$-0.985660\pi$
$7$	−1.18591	−	2.32748i	−0.448232	−	0.879704i	0.550754	−	0.834668i	$-0.314340\pi$
$8$	−1.74352	+	2.22713i	−0.616429	+	0.787410i
$9$	2.08520	−	1.51499i	0.695067	−	0.504995i
$10$	−2.12294	−	2.34374i	−0.671332	−	0.741157i
$11$	−2.39581	+	2.29349i	−0.722364	+	0.691513i
$11$	−2.39581	+	2.29349i	−0.722364	+	0.691513i
$12$	−1.03321	−	0.789106i	−0.298261	−	0.227795i
$13$	−1.86205	−	2.56289i	−0.516439	−	0.710817i	0.468550	−	0.883437i	$-0.344777\pi$
$13$	−1.86205	−	2.56289i	−0.516439	−	0.710817i	−0.984988	+	0.172620i	$0.944777\pi$
$14$	2.58076	+	2.64324i	0.689737	+	0.706437i
$15$	1.06555	−	0.988617i	0.275123	−	0.255260i
$16$	1.41658	−	3.74076i	0.354146	−	0.935190i
$17$	−5.65584	+	0.895798i	−1.37174	+	0.217263i	−0.798437	−	0.602078i	$-0.794340\pi$
$17$	−5.65584	+	0.895798i	−1.37174	+	0.217263i	−0.573307	+	0.819341i	$0.694340\pi$
$18$	−2.17763	+	2.92308i	−0.513272	+	0.688977i
$19$	2.14774	−	4.21517i	0.492724	−	0.967026i	−0.502041	−	0.864844i	$-0.667417\pi$
$19$	2.14774	−	4.21517i	0.492724	−	0.967026i	0.994766	−	0.102182i	$-0.0325825\pi$
$20$	3.85271	+	2.27081i	0.861493	+	0.507769i
$21$	−1.20069	+	1.20069i	−0.262011	+	0.262011i
$22$	2.26932	−	4.10490i	0.483821	−	0.875167i
$23$	−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
$25$	−3.23326	+	3.81393i	−0.646651	+	0.762786i
$26$	3.59272	+	2.67649i	0.704590	+	0.524903i
$27$	−2.93314	−	2.13105i	−0.564483	−	0.410121i
$28$	−4.59689	−	2.48248i	−0.868731	−	0.469144i
$29$	−0.435264	−	0.854255i	−0.0808266	−	0.158631i	0.847056	−	0.531504i	$-0.178373\pi$
$29$	−0.435264	−	0.854255i	−0.0808266	−	0.158631i	−0.927883	+	0.372873i	$0.878373\pi$
$30$	−1.02252	+	1.78325i	−0.186686	+	0.325575i
$31$	−2.42909	−	3.34336i	−0.436278	−	0.600485i	0.533102	−	0.846051i	$-0.321026\pi$
$31$	−2.42909	−	3.34336i	−0.436278	−	0.600485i	−0.969380	+	0.245566i	$0.921026\pi$
$32$	−0.338088	+	5.64674i	−0.0597660	+	0.998212i
$33$	1.89914	+	1.02045i	0.330599	+	0.177637i
$34$	7.25907	−	3.58998i	1.24492	−	0.615676i
$35$	3.60772	−	4.59369i	0.609816	−	0.776476i
$36$	1.70976	−	4.86310i	0.284960	−	0.810516i
$37$	7.02584	+	2.28283i	1.15504	+	0.375296i	0.823040	−	0.567983i	$-0.192276\pi$
$37$	7.02584	+	2.28283i	1.15504	+	0.375296i	0.332001	+	0.943279i	$0.392276\pi$
$38$	−1.12556	+	6.59499i	−0.182590	+	1.06985i
$39$	−1.21040	+	1.66598i	−0.193820	+	0.266770i
$40$	−6.15744	−	1.44429i	−0.973576	−	0.228362i
$41$	−6.45452	+	2.09720i	−1.00803	+	0.327528i	−0.766068	−	0.642759i	$-0.777790\pi$
$41$	−6.45452	+	2.09720i	−1.00803	+	0.327528i	−0.241958	+	0.970287i	$0.577790\pi$
$42$	1.11571	−	2.12645i	0.172158	−	0.328118i
$43$		−	2.73314i		−	0.416801i	−0.978044	−	0.208400i	$-0.933174\pi$
$43$		−	2.73314i		−	0.416801i	0.978044	−	0.208400i	$-0.0668257\pi$
$44$	−1.33613	+	6.49729i	−0.201429	+	0.979503i
$45$	5.03366	+	2.80686i	0.750374	+	0.418422i
$46$	2.92678	+	1.53563i	0.431530	+	0.226417i
$47$	1.41655	−	2.78013i	0.206625	−	0.405524i	−0.764317	−	0.644841i	$-0.776924\pi$
$47$	1.41655	−	2.78013i	0.206625	−	0.405524i	0.970941	+	0.239317i	$0.0769236\pi$
$48$	−2.59718	−	0.124348i	−0.374871	−	0.0179480i
$49$	0.103724	−	0.142763i	0.0148177	−	0.0203948i
$50$	2.76003	−	6.51016i	0.390328	−	0.920676i
$51$	1.68991	+	3.31664i	0.236635	+	0.464422i
$52$	−5.97716	−	2.10144i	−0.828882	−	0.291417i
$53$	−5.61633	+	4.08050i	−0.771463	+	0.560500i	−0.902405	−	0.430890i	$-0.858200\pi$
$53$	−5.61633	+	4.08050i	−0.771463	+	0.560500i	0.130942	+	0.991390i	$0.458200\pi$
$54$	4.85707	+	1.64264i	0.660964	+	0.223535i
$55$	−6.90514	−	2.70537i	−0.931089	−	0.364792i
$56$	7.25127	+	1.41684i	0.968991	+	0.189333i
$57$	−3.03734	−	0.481068i	−0.402306	−	0.0637190i
$58$	0.947217	+	0.970150i	0.124376	+	0.127387i
$59$	−0.540048	−	1.05990i	−0.0703083	−	0.137988i	0.853177	−	0.521621i	$-0.174673\pi$
$59$	−0.540048	−	1.05990i	−0.0703083	−	0.137988i	−0.923485	+	0.383634i	$0.874673\pi$
$60$	0.629965	−	2.83799i	0.0813281	−	0.366383i
$61$	1.53629	+	9.69978i	0.196702	+	1.24193i	0.866421	+	0.499314i	$0.166415\pi$
$61$	1.53629	+	9.69978i	0.196702	+	1.24193i	−0.669719	+	0.742615i	$0.733585\pi$
$62$	4.68680	+	3.49156i	0.595224	+	0.443429i
$63$	−5.99896	−	3.05662i	−0.755797	−	0.385098i
$64$	−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
$67$		−	14.3088i		−	1.74810i	−0.485835	−	0.874051i	$-0.661484\pi$
$67$		−	14.3088i		−	1.74810i	0.485835	−	0.874051i	$-0.338516\pi$
$68$	−8.28966	+	7.90226i	−1.00527	+	0.958290i
$69$	−0.689710	+	1.35363i	−0.0830313	+	0.162958i
$70$	−2.93740	+	7.72056i	−0.351087	+	0.922783i
$71$	−6.10934	−	4.43870i	−0.725046	−	0.526777i	0.162947	−	0.986635i	$-0.447900\pi$
$71$	−6.10934	−	4.43870i	−0.725046	−	0.526777i	−0.887992	+	0.459858i	$0.847900\pi$
$72$	−0.261521	+	7.28543i	−0.0308205	+	0.858597i
$73$	−6.79020	−	13.3265i	−0.794733	−	1.55975i	−0.828281	−	0.560313i	$-0.810681\pi$
$73$	−6.79020	−	13.3265i	−0.794733	−	1.55975i	0.0335482	−	0.999437i	$-0.489319\pi$
$74$	−10.4466	−	0.124951i	−1.21440	−	0.0145253i
$75$	3.00734	+	1.23276i	0.347257	+	0.142347i
$76$	−1.25618	−	9.37783i	−0.144093	−	1.07571i
$77$	8.17926	+	2.85632i	0.932113	+	0.325508i
$78$	0.932992	−	2.75874i	0.105641	−	0.312366i
$79$	−4.19372	+	3.04692i	−0.471830	+	0.342805i	−0.798154	−	0.602453i	$-0.794190\pi$
$79$	−4.19372	+	3.04692i	−0.471830	+	0.342805i	0.326324	+	0.945258i	$0.394190\pi$
$80$	8.92122	−	0.641686i	0.997423	−	0.0717427i
$81$	1.66115	−	5.11249i	0.184572	−	0.568054i
$82$	7.83171	−	5.54818i	0.864868	−	0.612694i
$83$	−6.84628	−	4.97411i	−0.751477	−	0.545980i	0.144808	−	0.989460i	$-0.453744\pi$
$83$	−6.84628	−	4.97411i	−0.751477	−	0.545980i	−0.896284	+	0.443480i	$0.853744\pi$
$84$	−0.611336	+	3.34058i	−0.0667022	+	0.364487i
$85$	−7.13333	−	10.6335i	−0.773719	−	1.15336i
$86$	1.15038	+	3.69009i	0.124048	+	0.397913i
$87$	−0.440688	+	0.440688i	−0.0472467	+	0.0472467i
$88$	−0.930753	−	9.33454i	−0.0992186	−	0.995066i
$89$	2.99274			0.317229			0.158615	−	0.987341i	$-0.449297\pi$
$89$	2.99274			0.317229			0.158615	+	0.987341i	$0.449297\pi$
$90$	−7.97749	−	1.67096i	−0.840901	−	0.176134i
$91$	−3.75685	+	7.37322i	−0.393824	+	0.772924i
$92$	−4.59787	−	0.841424i	−0.479361	−	0.0877246i
$93$	−1.57901	+	2.17332i	−0.163735	+	0.225362i
$94$	−0.742367	+	4.34976i	−0.0765693	+	0.448643i
$95$	10.5710	+	0.395898i	1.08456	+	0.0406182i
$96$	3.55887	−	0.925265i	0.363225	−	0.0944345i
$97$	−2.76685	+	17.4692i	−0.280931	+	1.77373i	0.294275	+	0.955721i	$0.404922\pi$
$97$	−2.76685	+	17.4692i	−0.280931	+	1.77373i	−0.575206	+	0.818009i	$0.695078\pi$
$98$	−0.0799513	+	0.236406i	−0.00807630	+	0.0238806i
$99$	−1.52114	+	8.41200i	−0.152880	+	0.845438i
$100$	−0.986279	+	9.95124i	−0.0986279	+	0.995124i
$101$	2.08060	−	13.1364i	0.207028	−	1.30712i	−0.637018	−	0.770849i	$-0.719832\pi$
$101$	2.08060	−	13.1364i	0.207028	−	1.30712i	0.844045	−	0.536272i	$-0.180168\pi$
$102$	−3.67756	−	3.76660i	−0.364133	−	0.372949i
$103$	−8.05755	+	4.10552i	−0.793934	+	0.404529i	−0.803410	−	0.595426i	$-0.796983\pi$
$103$	−8.05755	+	4.10552i	−0.793934	+	0.404529i	0.00947678	+	0.999955i	$0.496983\pi$
$104$	8.95442	+	0.321431i	0.878053	+	0.0315189i
$105$	−3.56463	−	1.30763i	−0.347872	−	0.127612i
$106$	5.86529	−	7.87311i	0.569687	−	0.764704i
$107$	−5.09896	−	15.6930i	−0.492935	−	1.51710i	−0.820150	−	0.572148i	$-0.806110\pi$
$107$	−5.09896	−	15.6930i	−0.492935	−	1.51710i	0.327216	−	0.944950i	$-0.393890\pi$
$108$	−7.24905	−	0.173435i	−0.697540	−	0.0166888i
$109$	3.85263	−	3.85263i	0.369015	−	0.369015i	−0.498103	−	0.867118i	$-0.665970\pi$
$109$	3.85263	−	3.85263i	0.369015	−	0.369015i	0.867118	+	0.498103i	$0.165970\pi$
$110$	10.4615	+	0.746234i	0.997466	+	0.0711506i
$111$		−	4.80211i		−	0.455796i
$112$	−10.3865	+	1.13914i	−0.981430	+	0.107638i
$113$	1.99462	−	3.91467i	0.187638	−	0.368261i	−0.777954	−	0.628321i	$-0.783742\pi$
$113$	1.99462	−	3.91467i	0.187638	−	0.368261i	0.965592	+	0.260060i	$0.0837424\pi$
$114$	4.30328	−	0.628910i	0.403039	−	0.0589028i
$115$	1.79978	−	4.90625i	0.167831	−	0.457510i
$116$	−1.68720	−	0.911145i	−0.156652	−	0.0845977i
$117$	−7.76548	−	2.52316i	−0.717919	−	0.233266i
$118$	1.17525	+	1.20370i	0.108190	+	0.110810i
$119$	8.79227	+	12.1015i	0.805986	+	1.10934i
$120$	0.343972	+	4.09680i	0.0314002	+	0.373985i
$121$	0.479811	−	10.9895i	0.0436192	−	0.999048i
$122$	−6.15681	−	12.4493i	−0.557412	−	1.12711i
$123$	2.59308	+	3.56907i	0.233810	+	0.321812i
$124$	−7.79737	−	2.74138i	−0.700224	−	0.246184i
$125$	−10.7771	−	2.97548i	−0.963936	−	0.266135i
$126$	9.38588	+	1.60188i	0.836161	+	0.142706i
$127$	1.11068	+	7.01253i	0.0985565	+	0.622261i	0.986682	+	0.162660i	$0.0520075\pi$
$127$	1.11068	+	7.01253i	0.0985565	+	0.622261i	−0.888126	+	0.459601i	$0.847992\pi$
$128$	5.86132	+	9.67703i	0.518073	+	0.855337i
$129$	−1.68970	+	0.549016i	−0.148769	+	0.0483381i
$130$	−2.05375	+	9.80501i	−0.180125	+	0.859956i
$131$	10.6115	−	10.6115i	0.927134	−	0.927134i	−0.0703858	−	0.997520i	$-0.522423\pi$
$131$	10.6115	−	10.6115i	0.927134	−	0.927134i	0.997520	+	0.0703858i	$0.0224230\pi$
$132$	4.28517	−	0.479103i	0.372977	−	0.0417006i
$133$	−12.3577			−1.07155
$134$	6.02256	+	19.3187i	0.520270	+	1.66888i
$135$	1.56700	−	7.95412i	0.134866	−	0.684582i
$136$	7.86604	−	14.1582i	0.674508	−	1.21405i
$137$	−1.24068	−	7.83332i	−0.105998	−	0.669245i	−0.982276	−	0.187440i	$-0.939981\pi$
$137$	−1.24068	−	7.83332i	−0.105998	−	0.669245i	0.876278	−	0.481806i	$-0.160019\pi$
$138$	0.361454	−	2.11787i	0.0307690	−	0.180285i
$139$	4.96747	+	9.74921i	0.421335	+	0.826917i	0.999936	+	0.0113060i	$0.00359889\pi$
$139$	4.96747	+	9.74921i	0.421335	+	0.826917i	−0.578601	+	0.815611i	$0.696401\pi$
$140$	0.716299	−	11.6601i	0.0605383	−	0.985457i
$141$	−2.00329	−	0.317290i	−0.168708	−	0.0267207i
$142$	10.1166	+	3.42139i	0.848969	+	0.287117i
$143$	10.3391	+	1.86961i	0.864596	+	0.156344i
$144$	−2.71334	−	9.94634i	−0.226112	−	0.828862i
$145$	1.32414	−	1.68602i	0.109964	−	0.140017i
$146$	14.7767	+	15.1345i	1.22293	+	1.25254i
$147$	−0.109095	−	0.0354472i	−0.00899802	−	0.00292363i
$148$	14.1569	−	4.22827i	1.16369	−	0.347562i
$149$	1.67460	+	10.5730i	0.137189	+	0.866174i	0.956267	+	0.292494i	$0.0944850\pi$
$149$	1.67460	+	10.5730i	0.137189	+	0.866174i	−0.819079	+	0.573681i	$0.805515\pi$
$150$	−4.57916	−	0.398602i	−0.373887	−	0.0325457i
$151$	−1.54389	−	4.75160i	−0.125640	−	0.386680i	0.868377	−	0.495904i	$-0.165163\pi$
$151$	−1.54389	−	4.75160i	−0.125640	−	0.386680i	−0.994017	+	0.109224i	$0.965163\pi$
$152$	5.64311	+	12.1325i	0.457717	+	0.984079i
$153$	−10.4364	+	10.4364i	−0.843737	+	0.843737i
$154$	−12.2453	−	0.413764i	−0.986752	−	0.0333420i
$155$	4.50045	−	8.07085i	0.361485	−	0.648266i
$156$	−0.0985084	+	4.11735i	−0.00788699	+	0.329651i
$157$	6.82529	+	21.0061i	0.544717	+	1.67647i	0.721662	+	0.692246i	$0.243379\pi$
$157$	6.82529	+	21.0061i	0.544717	+	1.67647i	−0.176945	+	0.984221i	$0.556621\pi$
$158$	4.37961	−	5.87886i	0.348423	−	0.467697i
$159$	3.65084	+	2.65249i	0.289530	+	0.210356i
$160$	−11.7747	+	4.62129i	−0.930872	+	0.365345i
$161$	−1.88654	+	5.80618i	−0.148680	+	0.457591i
$162$	−0.0909230	+	7.60169i	−0.00714359	+	0.597245i
$163$	7.74592	−	5.62774i	0.606707	−	0.440798i	−0.241546	−	0.970389i	$-0.577655\pi$
$163$	7.74592	−	5.62774i	0.606707	−	0.440798i	0.848253	+	0.529591i	$0.177655\pi$
$164$	−8.23859	+	10.7871i	−0.643326	+	0.842332i
$165$	−0.285469	+	4.81236i	−0.0222237	+	0.374642i
$166$	11.3369	+	3.83410i	0.879918	+	0.297584i
$167$	−2.17831	+	13.7533i	−0.168563	+	1.06426i	0.747803	+	0.663920i	$0.231109\pi$
$167$	−2.17831	+	13.7533i	−0.168563	+	1.06426i	−0.916366	+	0.400342i	$0.868891\pi$
$168$	−0.580662	−	4.76751i	−0.0447990	−	0.367822i
$169$	0.916047	−	2.81930i	0.0704652	−	0.216869i
$170$	14.1065	+	11.3541i	1.08192	+	0.870822i
$171$	−1.90746	−	12.0433i	−0.145867	−	0.920971i
$172$	−3.10631	−	4.49791i	−0.236854	−	0.342962i
$173$	11.6472	−	3.78439i	0.885518	−	0.287722i	0.169271	−	0.985569i	$-0.445859\pi$
$173$	11.6472	−	3.78439i	0.885518	−	0.287722i	0.716247	+	0.697847i	$0.245859\pi$
$174$	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
$178$	−4.04058	+	1.25964i	−0.302854	+	0.0944139i
$179$	−0.0797421	+	0.156503i	−0.00596020	+	0.0116976i	−0.893967	−	0.448132i	$-0.852089\pi$
$179$	−0.0797421	+	0.156503i	−0.00596020	+	0.0116976i	0.888007	+	0.459829i	$0.152089\pi$
$180$	11.4739	−	1.10171i	0.855216	−	0.0821166i
$181$	−18.9720	+	3.00487i	−1.41018	+	0.223350i	−0.814636	−	0.579973i	$-0.803063\pi$
$181$	−18.9720	+	3.00487i	−1.41018	+	0.223350i	−0.595543	+	0.803323i	$0.703063\pi$
$182$	1.96884	−	11.5360i	0.145940	−	0.855109i
$183$	5.68804	−	2.89820i	0.420472	−	0.214241i
$184$	6.56186	−	0.799206i	0.483747	−	0.0589182i
$185$	1.97168	+	16.4007i	0.144961	+	1.20580i
$186$	1.21711	−	3.59885i	0.0892431	−	0.263881i
$187$	11.4958	−	15.1178i	0.840658	−	1.10552i
$188$	−0.828516	−	6.18519i	−0.0604257	−	0.451101i
$189$	−1.48154	+	9.35405i	−0.107766	+	0.680407i
$190$	−14.4388	+	3.91479i	−1.04750	+	0.284009i
$191$	5.19916	+	1.68931i	0.376198	+	0.122234i	0.491012	−	0.871153i	$-0.336627\pi$
$191$	5.19916	+	1.68931i	0.376198	+	0.122234i	−0.114814	+	0.993387i	$0.536627\pi$
$192$	−4.41548	+	2.74715i	−0.318660	+	0.198258i
$193$	0.580803	+	3.66705i	0.0418071	+	0.263960i	0.999734	−	0.0230517i	$-0.00733823\pi$
$193$	0.580803	+	3.66705i	0.0418071	+	0.263960i	−0.957927	+	0.287011i	$0.907338\pi$
$194$	−3.61716	−	24.7502i	−0.259697	−	1.77696i
$195$	−4.51781	−	0.890029i	−0.323527	−	0.0637363i
$196$	0.00844153	−	0.352830i	0.000602967	−	0.0252021i
$197$		−	7.92706i		−	0.564780i	−0.959300	−	0.282390i	$-0.908873\pi$
$197$		−	7.92706i		−	0.564780i	0.959300	−	0.282390i	$-0.0911271\pi$
$198$	−1.48687	−	11.9975i	−0.105667	−	0.852627i
$199$			19.2478i			1.36444i	0.731148	+	0.682219i	$0.238985\pi$
$199$			19.2478i			1.36444i	−0.731148	+	0.682219i	$0.761015\pi$
$200$	−2.85686	−	13.8506i	−0.202011	−	0.979383i
$201$	−8.84606	+	2.87426i	−0.623953	+	0.202735i
$202$	2.72002	+	18.6115i	0.191380	+	1.30950i
$203$	−1.47207	+	2.02614i	−0.103319	+	0.142207i
$204$	6.55054	+	3.53751i	0.458629	+	0.247675i
$205$	−10.3216	−	11.1248i	−0.720890	−	0.776987i
$206$	9.15071	−	8.93439i	0.637560	−	0.622489i
$207$	−5.94963	−	0.942328i	−0.413528	−	0.0654963i
$208$	−12.2249	+	3.33493i	−0.847644	+	0.231236i
$209$	4.52188	+	15.0246i	0.312785	+	1.03927i
$210$	5.36308	+	0.265121i	0.370088	+	0.0182951i
$211$	−2.91142	+	18.3820i	−0.200430	+	1.26547i	0.658189	+	0.752853i	$0.271323\pi$
$211$	−2.91142	+	18.3820i	−0.200430	+	1.26547i	−0.858619	+	0.512614i	$0.828677\pi$
$212$	−4.60511	+	13.0984i	−0.316280	+	0.899601i
$213$	−1.51691	+	4.66856i	−0.103937	+	0.319884i
$214$	13.4894	+	19.0414i	0.922116	+	1.30164i
$215$	5.54541	−	2.56882i	0.378194	−	0.175192i
$216$	9.86014	−	2.81695i	0.670897	−	0.191669i
$217$	−4.90091	+	9.61858i	−0.332696	+	0.652952i
$218$	−3.57997	+	6.82311i	−0.242466	+	0.462119i
$219$	−6.87480	+	6.87480i	−0.464556	+	0.464556i
$220$	−14.4385	+	3.39572i	−0.973441	+	0.228940i
$221$	12.8273	+	12.8273i	0.862856	+	0.862856i
$222$	2.02120	+	6.48345i	0.135654	+	0.435141i
$223$	15.3145	+	7.80315i	1.02554	+	0.522538i	0.884045	−	0.467402i	$-0.154810\pi$
$223$	15.3145	+	7.80315i	1.02554	+	0.522538i	0.141493	+	0.989939i	$0.454810\pi$
$224$	13.5436	−	5.90963i	0.904920	−	0.394854i
$225$	−0.963939	+	12.8511i	−0.0642626	+	0.856743i
$226$	−1.04532	+	6.12483i	−0.0695335	+	0.407418i
$227$	20.6103	+	6.69670i	1.36795	+	0.444475i	0.898691	−	0.438583i	$-0.144519\pi$
$227$	20.6103	+	6.69670i	1.36795	+	0.444475i	0.469264	+	0.883058i	$0.344519\pi$
$228$	−5.54527	+	2.66035i	−0.367244	+	0.176186i
$229$	2.45743	+	0.389219i	0.162392	+	0.0257203i	0.237101	−	0.971485i	$-0.423803\pi$
$229$	2.45743	+	0.389219i	0.162392	+	0.0257203i	−0.0747090	+	0.997205i	$0.523803\pi$
$230$	−0.364905	+	7.38159i	−0.0240611	+	0.486727i
$231$	0.122855	−	5.63038i	0.00808324	−	0.370452i
$232$	2.66143	+	0.520022i	0.174732	+	0.0341411i
$233$	−4.23231	+	26.7218i	−0.277268	+	1.75060i	0.318944	+	0.947774i	$0.396672\pi$
$233$	−4.23231	+	26.7218i	−0.277268	+	1.75060i	−0.596212	+	0.802827i	$0.703328\pi$
$234$	11.5464	+	0.138105i	0.754810	+	0.00902822i
$235$	6.97212	+	0.261116i	0.454811	+	0.0170333i
$236$	−2.09337	−	1.13049i	−0.136267	−	0.0735886i
$237$	2.72608	+	1.98062i	0.177078	+	0.128655i
$238$	−16.9642	−	12.6379i	−1.09963	−	0.819196i
$239$	−3.27449	−	10.0778i	−0.211809	−	0.651882i	−0.999365	−	0.0356380i	$-0.988654\pi$
$239$	−3.27449	−	10.0778i	−0.211809	−	0.651882i	0.787556	−	0.616244i	$-0.211346\pi$
$240$	−2.18874	−	5.38642i	−0.141283	−	0.347692i
$241$	4.15786			0.267832			0.133916	−	0.990993i	$-0.457245\pi$
$241$	4.15786			0.267832			0.133916	+	0.990993i	$0.457245\pi$
$242$	3.97767	+	15.0392i	0.255694	+	0.966758i
$243$	−14.3710			−0.921902
$244$	13.5524	+	14.2168i	0.867602	+	0.910135i
$245$	0.387147	+	0.0762697i	0.0247339	+	0.00487269i
$246$	−5.00320	−	3.72727i	−0.318993	−	0.237642i
$247$	−14.8022	+	2.34444i	−0.941841	+	0.149173i
$248$	11.6813	+	0.419316i	0.741763	+	0.0266266i
$249$	−1.69988	+	5.23170i	−0.107726	+	0.331546i
$250$	15.8029	−	0.518798i	0.999462	−	0.0328117i
$251$	−24.8388	−	3.93408i	−1.56781	−	0.248317i	−0.688741	−	0.725007i	$-0.741836\pi$
$251$	−24.8388	−	3.93408i	−1.56781	−	0.248317i	−0.879071	+	0.476690i	$0.841836\pi$
$252$	−13.3464	+	1.78777i	−0.840742	+	0.112619i
$253$	7.74948	+	0.169093i	0.487206	+	0.0106308i
$254$	−4.45112	−	9.00033i	−0.279288	−	0.564731i
$255$	−5.14097	+	6.54598i	−0.321940	+	0.409925i
$256$	−11.9866	−	10.5982i	−0.749161	−	0.662388i
$257$	0.467375	+	0.917276i	0.0291541	+	0.0572181i	0.905124	−	0.425147i	$-0.139778\pi$
$257$	0.467375	+	0.917276i	0.0291541	+	0.0572181i	−0.875970	+	0.482365i	$0.839778\pi$
$258$	2.05023	−	1.45243i	0.127641	−	0.0904245i
$259$	−3.01876	−	19.0597i	−0.187577	−	1.18431i
$260$	−1.35409	−	14.1024i	−0.0839774	−	0.874596i
$261$	−2.20180	−	1.12187i	−0.136288	−	0.0694421i
$262$	−9.86055	+	18.7933i	−0.609187	+	1.16105i
$263$	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
$267$	−0.601161	−	1.85018i	−0.0367904	−	0.113229i
$268$	−16.2625	−	23.5479i	−0.993388	−	1.43842i
$269$	23.6690	−	3.74880i	1.44312	−	0.228569i	0.614741	−	0.788729i	$-0.289261\pi$
$269$	23.6690	−	3.74880i	1.44312	−	0.228569i	0.828384	+	0.560161i	$0.189261\pi$
$270$	1.23223	+	11.3986i	0.0749912	+	0.693698i
$271$	−25.7243	−	8.35834i	−1.56264	−	0.507733i	−0.605129	−	0.796127i	$-0.706879\pi$
$271$	−25.7243	−	8.35834i	−1.56264	−	0.507733i	−0.957512	+	0.288395i	$0.906879\pi$
$272$	−4.66101	+	22.4261i	−0.282615	+	1.35978i
$273$	5.31296	+	0.841490i	0.321555	+	0.0509293i
$274$	4.97210	+	10.0538i	0.300376	+	0.607371i
$275$	−1.00093	−	16.5529i	−0.0603586	−	0.998177i
$276$	0.403400	+	3.01153i	0.0242818	+	0.181273i
$277$	1.72269	+	2.37108i	0.103506	+	0.142464i	0.857628	−	0.514270i	$-0.171937\pi$
$277$	1.72269	+	2.37108i	0.103506	+	0.142464i	−0.754122	+	0.656735i	$0.771937\pi$
$278$	−10.8101	−	11.0719i	−0.648349	−	0.664047i
$279$	−10.1303	−	3.29153i	−0.606484	−	0.197059i
$280$	3.94062	+	16.0441i	0.235497	+	0.958818i
$281$	13.1280	−	18.0691i	0.783151	−	1.07791i	−0.211777	−	0.977318i	$-0.567925\pi$
$281$	13.1280	−	18.0691i	0.783151	−	1.07791i	0.994927	−	0.100596i	$-0.0320751\pi$
$282$	2.83825	−	0.414800i	0.169015	−	0.0247010i
$283$	7.33429	−	2.38306i	0.435978	−	0.141658i	−0.0828010	−	0.996566i	$-0.526387\pi$
$283$	7.33429	−	2.38306i	0.435978	−	0.141658i	0.518779	+	0.854908i	$0.326387\pi$
$284$	−15.0988	−	0.361242i	−0.895949	−	0.0214358i
$285$	−1.87867	−	6.61475i	−0.111283	−	0.391824i
$286$	−14.7460	+	1.82749i	−0.871948	+	0.108062i
$287$	12.5357	+	12.5357i	0.739956	+	0.739956i
$288$	7.84976	+	12.2868i	0.462551	+	0.724006i
$289$	15.0182	−	4.87970i	0.883421	−	0.287041i
$290$	−1.07812	+	2.83368i	−0.0633091	+	0.166399i
$291$	11.3557	−	1.79856i	0.665681	−	0.105434i
$292$	−26.3206	−	14.2140i	−1.54030	−	0.831812i
$293$	2.28029	−	7.01802i	0.133216	−	0.409997i	−0.862092	−	0.506751i	$-0.830846\pi$
$293$	2.28029	−	7.01802i	0.133216	−	0.409997i	0.995308	+	0.0967545i	$0.0308462\pi$
$294$	0.162212	+	0.00194020i	0.00946040	+	0.000113155i
$295$	1.64291	−	2.09191i	0.0956539	−	0.121796i
$296$	−17.3339	+	11.6673i	−1.00751	+	0.678148i
$297$	11.9148	−	1.62153i	0.691366	−	0.0940909i
$298$	−6.71109	−	13.5701i	−0.388763	−	0.786093i
$299$	−1.15820	+	7.31260i	−0.0669805	+	0.422898i
$300$	6.35022	−	1.38920i	0.366630	−	0.0802053i
$301$	−6.36133	+	3.24126i	−0.366661	+	0.186823i
$302$	4.08439	+	5.76545i	0.235030	+	0.331764i
$303$	−8.53918	+	1.35247i	−0.490563	+	0.0776976i
$304$	−12.7255	−	14.0053i	−0.729857	−	0.803259i
$305$	−18.2364	+	12.2337i	−1.04421	+	0.700498i
$306$	9.69785	−	18.4832i	0.554389	−	1.05662i
$307$		−	24.5310i		−	1.40006i	−0.714114	−	0.700030i	$-0.753170\pi$
$307$		−	24.5310i		−	1.40006i	0.714114	−	0.700030i	$-0.246830\pi$
$308$	16.7068	−	4.59538i	0.951960	−	0.261846i
$309$	4.15668	+	4.15668i	0.236465	+	0.236465i
$310$	−2.67917	+	12.7909i	−0.152167	+	0.726475i
$311$	4.39622	+	13.5302i	0.249286	+	0.767225i	0.994902	+	0.100848i	$0.0321557\pi$
$311$	4.39622	+	13.5302i	0.249286	+	0.767225i	−0.745615	+	0.666377i	$0.767844\pi$
$312$	−1.59999	−	5.60040i	−0.0905814	−	0.317060i
$313$	13.0780	−	2.07136i	0.739214	−	0.117080i	0.224539	−	0.974465i	$-0.427912\pi$
$313$	13.0780	−	2.07136i	0.739214	−	0.117080i	0.514675	+	0.857385i	$0.327912\pi$
$314$	−18.0564	−	25.4881i	−1.01898	−	1.43838i
$315$	0.563435	−	15.0444i	0.0317459	−	0.847657i
$316$	−3.43864	+	9.78058i	−0.193438	+	0.550201i
$317$	8.70694	−	6.32596i	0.489030	−	0.355301i	−0.315781	−	0.948832i	$-0.602266\pi$
$317$	8.70694	−	6.32596i	0.489030	−	0.355301i	0.804811	+	0.593531i	$0.202266\pi$
$318$	−6.04553	−	2.04457i	−0.339016	−	0.114654i
$319$	3.00203	+	1.04836i	0.168082	+	0.0586967i
$320$	13.9523	−	11.1953i	0.779955	−	0.625835i
$321$	−8.67754	+	6.30460i	−0.484333	+	0.351888i
$322$	0.103260	−	8.63313i	0.00575446	−	0.481106i
$323$	−8.37132	+	25.7643i	−0.465793	+	1.43356i
$324$	−3.07678	−	10.3015i	−0.170932	−	0.572306i
$325$	15.7951	+	1.18476i	0.876157	+	0.0657188i
$326$	−8.08927	+	10.8584i	−0.448023	+	0.601392i
$327$	−3.15568	−	1.60790i	−0.174509	−	0.0889170i
$328$	6.58287	−	18.0316i	0.363478	−	0.995628i
$329$	−8.15059			−0.449357
$330$	−1.64010	−	6.61746i	−0.0902844	−	0.364279i
$331$	−0.367838	−	0.367838i	−0.0202182	−	0.0202182i	0.696925	−	0.717144i	$-0.254551\pi$
$331$	−0.367838	−	0.367838i	−0.0202182	−	0.0202182i	−0.717144	+	0.696925i	$0.754551\pi$
$332$	−16.9201	−	0.404817i	−0.928610	−	0.0222172i
$333$	18.1087	−	5.88389i	0.992353	−	0.322435i
$334$	−2.84775	−	19.4856i	−0.155822	−	1.06620i
$335$	29.0319	−	13.4486i	1.58618	−	0.734773i
$336$	2.79061	+	6.19235i	0.152240	+	0.337820i
$337$	−3.76709	−	7.39332i	−0.205206	−	0.402740i	0.765350	−	0.643614i	$-0.222566\pi$
$337$	−3.76709	−	7.39332i	−0.205206	−	0.402740i	−0.970556	+	0.240874i	$0.922566\pi$
$338$	−0.0501399	+	4.19198i	−0.00272725	+	0.228014i
$339$	−2.82081	−	0.446772i	−0.153205	−	0.0242653i
$340$	−23.8245	−	9.39211i	−1.29207	−	0.509359i
$341$	13.4876	+	2.43895i	0.730395	+	0.132077i
$342$	7.64431	+	15.4571i	0.413357	+	0.835824i
$343$	−18.5155	−	2.93257i	−0.999743	−	0.158344i
$344$	6.08708	+	4.76530i	0.328193	+	0.256928i
$345$	−3.39469	−	0.127136i	−0.182764	−	0.00684477i
$346$	−14.1323	+	10.0117i	−0.759758	+	0.538232i
$347$	−4.00167	−	2.90738i	−0.214821	−	0.156076i	0.475171	−	0.879893i	$-0.342386\pi$
$347$	−4.00167	−	2.90738i	−0.214821	−	0.156076i	−0.689992	+	0.723817i	$0.742386\pi$
$348$	−0.224379	+	1.22609i	−0.0120280	+	0.0657254i
$349$	4.03006	+	2.05342i	0.215724	+	0.109917i	0.558514	−	0.829495i	$-0.311372\pi$
$349$	4.03006	+	2.05342i	0.215724	+	0.109917i	−0.342790	+	0.939412i	$0.611372\pi$
$350$	−18.4254	+	1.29655i	−0.984880	+	0.0693033i
$351$			11.4854i			0.613047i
$352$	−12.1408	−	14.3039i	−0.647104	−	0.762402i
$353$	−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
$355$	3.26385	−	16.5674i	0.173227	−	0.879305i
$356$	4.92511	−	3.40135i	0.261031	−	0.180271i
$357$	5.71532	−	7.86646i	0.302487	−	0.416337i
$358$	0.0417902	−	0.244862i	0.00220868	−	0.0129414i
$359$	5.50543	+	1.78882i	0.290565	+	0.0944104i	0.450673	−	0.892689i	$-0.351184\pi$
$359$	5.50543	+	1.78882i	0.290565	+	0.0944104i	−0.160107	+	0.987100i	$0.551184\pi$
$360$	−15.0276	+	6.31681i	−0.792022	+	0.332925i
$361$	−1.98696	−	2.73481i	−0.104577	−	0.143937i
$362$	24.3499	−	12.0423i	1.27980	−	0.632927i
$363$	−6.89038	+	1.91087i	−0.361651	+	0.100295i
$364$	2.19732	+	16.4038i	0.115171	+	0.859793i
$365$	20.6568	−	26.3023i	1.08123	−	1.37672i
$366$	−6.45973	+	6.30702i	−0.337655	+	0.329673i
$367$	13.6056	−	6.93240i	0.710206	−	0.361868i	−0.0612744	−	0.998121i	$-0.519516\pi$
$367$	13.6056	−	6.93240i	0.710206	−	0.361868i	0.771481	+	0.636253i	$0.219516\pi$
$368$	−8.52297	+	3.84091i	−0.444290	+	0.200221i
$369$	−10.2817	+	14.1516i	−0.535245	+	0.736702i
$370$	−9.56504	−	21.3131i	−0.497263	−	1.10801i
$371$	16.1577	+	8.23278i	0.838868	+	0.427425i
$372$	−0.128507	+	5.37119i	−0.00666278	+	0.278483i
$373$	24.1126			1.24850			0.624251	−	0.781224i	$-0.285404\pi$
$373$	24.1126			1.24850			0.624251	+	0.781224i	$0.285404\pi$
$374$	−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
$377$	−1.37888	+	2.70620i	−0.0710157	+	0.139376i
$378$	−1.93684	−	13.2527i	−0.0996205	−	0.681648i
$379$	30.2563	−	4.79213i	1.55416	−	0.246155i	0.680523	−	0.732727i	$-0.261753\pi$
$379$	30.2563	−	4.79213i	1.55416	−	0.246155i	0.873641	+	0.486571i	$0.161753\pi$
$380$	17.8465	−	11.3627i	0.915505	−	0.582896i
$381$	4.11221	−	2.09528i	0.210675	−	0.107344i
$382$	−7.73056	−	0.0924645i	−0.395530	−	0.00473090i
$383$	−0.176143	+	1.11212i	−0.00900048	+	0.0568268i	−0.991780	−	0.127956i	$-0.959158\pi$
$383$	−0.176143	+	1.11212i	−0.00900048	+	0.0568268i	0.982779	+	0.184783i	$0.0591583\pi$
$384$	4.80519	−	5.56747i	0.245214	−	0.284114i
$385$	1.89218	+	19.2799i	0.0964342	+	0.982594i
$386$	−2.32761	−	4.70652i	−0.118472	−	0.239556i
$387$	−4.14068	−	5.69915i	−0.210482	−	0.289704i
$388$	15.3010	+	31.8935i	0.776789	+	1.61915i
$389$	12.7529	−	6.49792i	0.646597	−	0.329458i	−0.0997519	−	0.995012i	$-0.531805\pi$
$389$	12.7529	−	6.49792i	0.646597	−	0.329458i	0.746349	+	0.665555i	$0.231805\pi$
$390$	6.47424	−	0.699888i	0.327836	−	0.0354402i
$391$	10.8272	+	7.86640i	0.547553	+	0.397821i
$392$	0.137108	+	0.479918i	0.00692502	+	0.0242395i
$393$	−8.69188	−	4.42873i	−0.438447	−	0.223400i
$394$	3.33649	+	10.7025i	0.168090	+	0.539186i
$395$	−10.1236	−	5.64511i	−0.509375	−	0.284036i
$396$	7.05720	+	15.5724i	0.354638	+	0.782541i
$397$	16.3434			0.820253			0.410127	−	0.912029i	$-0.365485\pi$
$397$	16.3434			0.820253			0.410127	+	0.912029i	$0.365485\pi$
$398$	−8.10135	−	25.9869i	−0.406084	−	1.30261i
$399$	2.48234	+	7.63985i	0.124272	+	0.382471i
$400$	9.68681	+	17.4976i	0.484341	+	0.874879i
$401$	−26.0729	−	18.9431i	−1.30202	−	0.945972i	−0.302045	−	0.953294i	$-0.597669\pi$
$401$	−26.0729	−	18.9431i	−1.30202	−	0.945972i	−0.999973	+	0.00732209i	$0.997669\pi$
$402$	10.7335	−	7.60391i	0.535340	−	0.379249i
$403$	−4.04557	+	12.4510i	−0.201524	+	0.620228i
$404$	−11.5059	−	23.9831i	−0.572442	−	1.19320i
$405$	11.9342	−	1.43473i	0.593018	−	0.0712925i
$406$	1.13469	−	3.35514i	0.0563137	−	0.166513i
$407$	−22.0682	+	10.6445i	−1.09388	+	0.527626i
$408$	−10.3330	−	2.01898i	−0.511560	−	0.0999545i
$409$	−30.2329	+	21.9655i	−1.49492	+	1.08613i	−0.522574	+	0.852594i	$0.675028\pi$
$409$	−30.2329	+	21.9655i	−1.49492	+	1.08613i	−0.972349	+	0.233531i	$0.924972\pi$
$410$	18.6178	+	10.6755i	0.919469	+	0.527226i
$411$	−4.59353	+	2.34052i	−0.226582	+	0.115449i
$412$	−8.59415	+	15.9141i	−0.423403	+	0.784031i
$413$	−1.82645	+	2.51390i	−0.0898740	+	0.123701i
$414$	8.42938	−	1.23193i	0.414281	−	0.0605458i
$415$	3.65754	−	18.5658i	0.179542	−	0.911359i
$416$	15.1015	−	9.64802i	0.740412	−	0.473033i
$417$	5.02936	−	5.02936i	0.246289	−	0.246289i
$418$	−12.4289	−	18.3818i	−0.607919	−	0.899084i
$419$	−17.8489	−	17.8489i	−0.871976	−	0.871976i	0.120711	−	0.992688i	$-0.461482\pi$
$419$	−17.8489	−	17.8489i	−0.871976	−	0.871976i	−0.992688	+	0.120711i	$0.961482\pi$
$420$	−7.35243	+	1.89937i	−0.358762	+	0.0926796i
$421$	22.9465	+	11.6918i	1.11834	+	0.569824i	0.912629	−	0.408788i	$-0.134048\pi$
$421$	22.9465	+	11.6918i	1.11834	+	0.569824i	0.205714	+	0.978612i	$0.434048\pi$
$422$	−3.80616	−	26.0434i	−0.185281	−	1.26777i
$423$	−1.25808	−	7.94318i	−0.0611698	−	0.386211i
$424$	0.704387	−	19.6228i	0.0342081	−	0.952966i
$425$	14.8703	−	24.4673i	0.721315	−	1.18684i
$426$	0.0830280	−	6.94161i	0.00402272	−	0.336322i
$427$	20.7541	−	15.0787i	1.00436	−	0.729712i
$428$	−26.2269	−	20.0306i	−1.26772	−	0.968217i
$429$	−0.921006	−	6.76741i	−0.0444666	−	0.326734i
$430$	−6.40579	+	5.80229i	−0.308915	+	0.279811i
$431$	15.8029	+	21.7508i	0.761199	+	1.04770i	0.997113	+	0.0759268i	$0.0241915\pi$
$431$	15.8029	+	21.7508i	0.761199	+	1.04770i	−0.235914	+	0.971774i	$0.575808\pi$
$432$	−12.1268	+	7.95337i	−0.583451	+	0.382656i
$433$	6.84272	−	3.48654i	0.328840	−	0.167552i	−0.281774	−	0.959481i	$-0.590923\pi$
$433$	6.84272	−	3.48654i	0.328840	−	0.167552i	0.610614	+	0.791928i	$0.290923\pi$
$434$	2.56841	−	15.0491i	0.123288	−	0.722380i
$435$	−1.30833	−	0.479940i	−0.0627294	−	0.0230113i
$436$	1.96159	−	10.7189i	0.0939430	−	0.513341i
$437$	−10.5153	+	3.41662i	−0.503013	+	0.163439i
$438$	6.38827	−	12.1755i	0.305243	−	0.581766i
$439$		−	5.32777i		−	0.254281i	−0.991885	−	0.127140i	$-0.959420\pi$
$439$		−	5.32777i		−	0.254281i	0.991885	−	0.127140i	$-0.0405798\pi$
$440$	18.0645	−	10.6618i	0.861191	−	0.508281i
$441$		−	0.454830i		−	0.0216586i
$442$	−22.7174	−	11.9195i	−1.08056	−	0.566952i
$443$	16.9539	−	5.50867i	0.805506	−	0.261725i	0.122813	−	0.992430i	$-0.460809\pi$
$443$	16.9539	−	5.50867i	0.805506	−	0.261725i	0.682693	+	0.730705i	$0.260809\pi$
$444$	−5.45775	−	7.90277i	−0.259014	−	0.375049i
$445$	2.81281	+	6.07211i	0.133340	+	0.287845i
$446$	−23.9609	−	4.08938i	−1.13458	−	0.193638i
$447$	6.20011	−	3.15911i	0.293255	−	0.149421i
$448$	−15.7982	+	13.6792i	−0.746397	+	0.646283i
$449$	−2.43432	−	3.35055i	−0.114882	−	0.158122i	0.747703	−	0.664033i	$-0.231157\pi$
$449$	−2.43432	−	3.35055i	−0.114882	−	0.158122i	−0.862586	+	0.505911i	$0.831157\pi$
$450$	−4.10759	−	17.7564i	−0.193633	−	0.837045i
$451$	10.6539	−	19.8279i	0.501672	−	0.933657i
$452$	−1.16662	−	8.70928i	−0.0548733	−	0.409650i
$453$	−2.62743	+	1.90894i	−0.123447	+	0.0896898i
$454$	−30.6452	−	0.366544i	−1.43825	−	0.0172028i
$455$	−18.4909	−	0.692509i	−0.866865	−	0.0324653i
$456$	6.36708	−	5.92581i	0.298166	−	0.277502i
$457$	−1.13957	−	7.19494i	−0.0533067	−	0.336565i	−0.999900	−	0.0141355i	$-0.995500\pi$
$457$	−1.13957	−	7.19494i	−0.0533067	−	0.336565i	0.946593	−	0.322430i	$-0.104500\pi$
$458$	−3.48167	+	0.508835i	−0.162688	+	0.0237763i
$459$	18.4984	+	9.42540i	0.863430	+	0.439940i
$460$	−2.61423	−	10.1197i	−0.121889	−	0.471832i
$461$	−7.92561	−	7.92561i	−0.369132	−	0.369132i	0.498028	−	0.867161i	$-0.334058\pi$
$461$	−7.92561	−	7.92561i	−0.369132	−	0.369132i	−0.867161	+	0.498028i	$0.834058\pi$
$462$	2.20395	+	7.65343i	0.102537	+	0.356070i
$463$	11.0663	−	11.0663i	0.514296	−	0.514296i	−0.401544	−	0.915840i	$-0.631526\pi$
$463$	11.0663	−	11.0663i	0.514296	−	0.514296i	0.915840	+	0.401544i	$0.131526\pi$
$464$	−3.81215	+	0.418097i	−0.176975	+	0.0194097i
$465$	−5.89362	−	1.16107i	−0.273310	−	0.0538433i
$466$	−5.53299	−	37.8592i	−0.256311	−	1.75379i
$467$	−18.4022	+	25.3284i	−0.851551	+	1.17206i	0.131968	+	0.991254i	$0.457870\pi$
$467$	−18.4022	+	25.3284i	−0.851551	+	1.17206i	−0.983519	+	0.180805i	$0.942130\pi$
$468$	−15.6472	+	4.67339i	−0.723293	+	0.216028i
$469$	−33.3035	+	16.9690i	−1.53781	+	0.783554i
$470$	−9.52316	+	2.58202i	−0.439271	+	0.119100i
$471$	11.6154	−	8.43911i	0.535211	−	0.388854i
$472$	3.30213	+	0.645210i	0.151993	+	0.0296982i
$473$	6.26844	+	6.54810i	0.288223	+	0.301082i
$474$	−4.51420	−	1.52668i	−0.207344	−	0.0701227i
$475$	9.13217	+	21.8200i	0.419013	+	1.00117i
$476$	28.2231	+	9.92263i	1.29360	+	0.454803i
$477$	−5.52927	+	17.0173i	−0.253168	+	0.779170i
$478$	8.66273	+	12.2281i	0.396224	+	0.559303i
$479$	−8.63011	−	6.27014i	−0.394320	−	0.286490i	0.372904	−	0.927870i	$-0.378362\pi$
$479$	−8.63011	−	6.27014i	−0.394320	−	0.286490i	−0.767223	+	0.641380i	$0.778362\pi$
$480$	5.22222	+	6.35112i	0.238360	+	0.289887i
$481$	−7.23180	−	22.2572i	−0.329742	−	1.01484i
$482$	−5.61365	+	1.75004i	−0.255695	+	0.0797121i
$483$	3.96848			0.180572
$484$	−11.7003	−	18.6307i	−0.531834	−	0.846849i
$485$	−38.0446	+	10.8051i	−1.72752	+	0.490636i
$486$	19.4027	−	6.04875i	0.880125	−	0.274377i
$487$	−3.93863	−	2.00683i	−0.178476	−	0.0909383i	0.362470	−	0.931996i	$-0.381934\pi$
$487$	−3.93863	−	2.00683i	−0.178476	−	0.0909383i	−0.540946	+	0.841057i	$0.681934\pi$
$488$	−24.2813	−	13.4903i	−1.09916	−	0.610676i
$489$	−5.03515	−	3.65825i	−0.227697	−	0.165432i
$490$	−0.554800	+	0.0599759i	−0.0250633	+	0.00270943i
$491$	−26.0179	+	13.2568i	−1.17417	+	0.598271i	−0.928591	−	0.371105i	$-0.878979\pi$
$491$	−26.0179	+	13.2568i	−1.17417	+	0.598271i	−0.245581	+	0.969376i	$0.578979\pi$
$492$	8.32377	+	2.92645i	0.375264	+	0.131935i
$493$	3.22703	+	4.44162i	0.145338	+	0.200041i
$494$	18.9981	−	9.39551i	0.854764	−	0.422724i
$495$	−18.4972	+	4.81995i	−0.831387	+	0.216641i
$496$	−15.9477	+	4.35051i	−0.716074	+	0.195344i
$497$	−3.08584	+	19.4833i	−0.138419	+	0.873943i
$498$	0.0930432	−	7.77894i	0.00416936	−	0.348583i
$499$	−14.5111	+	7.39379i	−0.649607	+	0.330991i	−0.747555	−	0.664200i	$-0.768772\pi$
$499$	−14.5111	+	7.39379i	−0.649607	+	0.330991i	0.0979477	+	0.995192i	$0.468772\pi$
$500$	−21.1175	+	7.35185i	−0.944405	+	0.328785i
$501$	8.94019	−	1.41599i	0.399418	−	0.0632616i
$502$	35.1914	−	5.14311i	1.57067	−	0.229548i
$503$	−8.41823	+	16.5217i	−0.375350	+	0.736667i	−0.998985	−	0.0450495i	$-0.985655\pi$
$503$	−8.41823	+	16.5217i	−0.375350	+	0.736667i	0.623634	+	0.781716i	$0.285655\pi$
$504$	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
$507$	−1.92697			−0.0855798
$508$	9.79780	+	10.2781i	0.434707	+	0.456018i
$509$	−27.9198	−	14.2259i	−1.23752	−	0.630550i	−0.292099	−	0.956388i	$-0.594354\pi$
$509$	−27.9198	−	14.2259i	−1.23752	−	0.630550i	−0.945426	+	0.325838i	$0.894354\pi$
$510$	4.18578	−	11.0017i	0.185349	−	0.487165i
$511$	−22.9646	+	31.6081i	−1.01589	+	1.39826i
$512$	20.6442	+	9.26379i	0.912353	+	0.409405i
$513$	−15.2824	+	7.78675i	−0.674732	+	0.343793i
$514$	−1.01710	−	1.04172i	−0.0448622	−	0.0459484i
$515$	−15.9030	−	12.4896i	−0.700770	−	0.550360i
$516$	−2.15674	+	2.82391i	−0.0949452	+	0.124315i
$517$	2.98242	+	9.90950i	0.131167	+	0.435820i
$518$	12.0979	+	24.4625i	0.531552	+	1.07482i
$519$	−4.67921	−	6.44038i	−0.205394	−	0.282701i
$520$	7.76389	+	18.4701i	0.340469	+	0.809970i
$521$	−22.0445	−	7.16269i	−0.965787	−	0.313803i	−0.216673	−	0.976244i	$-0.569521\pi$
$521$	−22.0445	−	7.16269i	−0.965787	−	0.313803i	−0.749114	+	0.662441i	$0.769521\pi$
$522$	3.44490	+	0.587937i	0.150779	+	0.0257333i
$523$	−21.6796	+	29.8395i	−0.947985	+	1.30479i	0.00443188	+	0.999990i	$0.498589\pi$
$523$	−21.6796	+	29.8395i	−0.947985	+	1.30479i	−0.952417	+	0.304799i	$0.901411\pi$
$524$	5.40292	−	29.5236i	0.236028	−	1.28975i
$525$	−0.697203	−	8.46146i	−0.0304284	−	0.369288i
$526$	−27.0512	−	14.1934i	−1.17949	−	0.618860i
$527$	16.7335	+	16.7335i	0.728925	+	0.728925i
$528$	6.50755	−	5.65870i	0.283205	−	0.246263i
$529$		−	17.5379i		−	0.762517i
$530$	21.4868	+	4.50060i	0.933326	+	0.195493i
$531$	−2.73185	−	1.39195i	−0.118552	−	0.0604053i
$532$	−20.3370	+	14.0450i	−0.881720	+	0.608927i
$533$	17.3935	+	12.6371i	0.753396	+	0.547374i
$534$	1.59038	+	2.24495i	0.0688226	+	0.0971487i
$535$	27.0478	−	25.0950i	1.16938	−	1.08495i
$536$	31.8677	+	24.9478i	1.37647	+	1.07758i
$537$	0.112772	+	0.0178613i	0.00486646	+	0.000770772i
$538$	−30.3783	+	15.0236i	−1.30970	+	0.647714i
$539$	0.0789242	+	0.579923i	0.00339951	+	0.0249791i
$540$	−6.46133	−	14.8709i	−0.278052	−	0.639944i
$541$	−27.5847	−	4.36899i	−1.18596	−	0.187837i	−0.467875	−	0.883794i	$-0.654980\pi$
$541$	−27.5847	−	4.36899i	−1.18596	−	0.187837i	−0.718083	+	0.695957i	$0.754980\pi$
$542$	38.2491	+	0.457494i	1.64294	+	0.0196511i
$543$	5.66865	+	11.1254i	0.243265	+	0.477435i
$544$	−3.14617	−	32.2400i	−0.134891	−	1.38228i
$545$	11.4378	+	4.19578i	0.489941	+	0.179727i
$546$	−7.52735	+	1.10010i	−0.322141	+	0.0470798i
$547$	5.24432	−	1.70398i	0.224231	−	0.0728571i	−0.194747	−	0.980854i	$-0.562389\pi$
$547$	5.24432	−	1.70398i	0.224231	−	0.0728571i	0.418978	+	0.907996i	$0.362389\pi$
$548$	−10.9446	−	11.4811i	−0.467530	−	0.490450i
$549$	17.8985	+	17.8985i	0.763890	+	0.763890i
$550$	8.31848	+	21.9272i	0.354701	+	0.934980i
$551$	−4.53566			−0.193226
$552$	−1.81219	−	3.89616i	−0.0771320	−	0.165832i
$553$	12.0650	+	6.14743i	0.513056	+	0.261415i
$554$	−3.32384	−	2.47618i	−0.141216	−	0.105203i
$555$	9.74322	−	4.51339i	0.413577	−	0.191583i
$556$	19.2552	+	10.3985i	0.816603	+	0.440993i
$557$	−5.05956	+	15.5717i	−0.214380	+	0.659795i	0.784817	+	0.619728i	$0.212757\pi$
$557$	−5.05956	+	15.5717i	−0.214380	+	0.659795i	−0.999197	+	0.0400669i	$0.987243\pi$
$558$	15.0626	+	0.180162i	0.637650	+	0.00762687i
$559$	−7.00474	+	5.08924i	−0.296269	+	0.215252i
$560$	−12.0733	−	20.0030i	−0.510189	−	0.845280i
$561$	−11.6554	−	4.07024i	−0.492091	−	0.171846i
$562$	−10.1192	+	29.9212i	−0.426853	+	1.26215i
$563$	3.74308	−	2.71950i	0.157752	−	0.114613i	−0.506109	−	0.862469i	$-0.668917\pi$
$563$	3.74308	−	2.71950i	0.157752	−	0.114613i	0.663861	+	0.747856i	$0.268917\pi$
$564$	−3.65741	+	1.75465i	−0.154005	+	0.0738840i
$565$	9.81736	+	0.367674i	0.413019	+	0.0154682i
$566$	−8.89921	+	6.30442i	−0.374062	+	0.264995i
$567$	−13.8692	+	2.19666i	−0.582451	+	0.0922511i
$568$	20.5374	−	5.86734i	0.861729	−	0.246188i
$569$	−8.45995	−	26.0370i	−0.354660	−	1.09153i	−0.956207	−	0.292692i	$-0.905449\pi$
$569$	−8.45995	−	26.0370i	−0.354660	−	1.09153i	0.601547	−	0.798837i	$-0.294551\pi$
$570$	5.32058	+	8.14003i	0.222855	+	0.340948i
$571$	13.9687	+	13.9687i	0.584572	+	0.584572i	0.936156	−	0.351584i	$-0.114357\pi$
$571$	13.9687	+	13.9687i	0.584572	+	0.584572i	−0.351584	+	0.936156i	$0.614357\pi$
$572$	19.1398	−	8.67390i	0.800273	−	0.362674i
$573$		−	3.55359i		−	0.148453i
$574$	−22.2010	−	11.6485i	−0.926651	−	0.486199i
$575$	11.6461	−	0.959610i	0.485676	−	0.0400185i
$576$	−15.7697	−	13.2848i	−0.657069	−	0.553532i
$577$	−6.68071	+	1.05812i	−0.278122	+	0.0440501i	−0.293937	−	0.955825i	$-0.594966\pi$
$577$	−6.68071	+	1.05812i	−0.278122	+	0.0440501i	0.0158154	+	0.999875i	$0.494966\pi$
$578$	−18.2226	+	12.9093i	−0.757959	+	0.536958i
$579$	2.15039	−	1.09568i	0.0893671	−	0.0455348i
$580$	0.262903	−	4.27960i	0.0109165	−	0.177701i
$581$	−3.45807	+	21.8334i	−0.143465	+	0.905802i
$582$	−14.5746	+	7.20788i	−0.604136	+	0.298776i
$583$	4.09707	−	22.6571i	0.169683	−	0.938362i
$584$	41.5188	+	8.11243i	1.71806	+	0.335695i
$585$	−2.17925	−	18.1272i	−0.0901010	−	0.749468i
$586$	−0.124812	+	10.4350i	−0.00515593	+	0.431065i
$587$	2.51560	−	7.74222i	0.103830	−	0.319556i	−0.885624	−	0.464403i	$-0.846269\pi$
$587$	2.51560	−	7.74222i	0.103830	−	0.319556i	0.989454	+	0.144847i	$0.0462691\pi$
$588$	−0.219824	+	0.0656553i	−0.00906537	+	0.00270758i
$589$	−19.3099	+	3.05838i	−0.795649	+	0.126018i
$590$	−1.33766	+	3.51584i	−0.0550704	+	0.144745i
$591$	−4.90070	+	1.59233i	−0.201588	+	0.0654999i
$592$	18.4922	−	23.0482i	0.760026	−	0.947274i
$593$	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
$595$	−16.2897	+	29.2130i	−0.667812	+	1.19762i
$596$	14.7724	+	15.4966i	0.605103	+	0.634767i
$597$	11.8994	−	3.86636i	0.487011	−	0.158240i
$598$	−1.51414	−	10.3604i	−0.0619178	−	0.423669i
$599$	−8.56255	+	11.7853i	−0.349856	+	0.481536i	−0.947288	−	0.320384i	$-0.896188\pi$
$599$	−8.56255	+	11.7853i	−0.349856	+	0.481536i	0.597431	+	0.801920i	$0.296188\pi$
$600$	−7.98889	+	4.54839i	−0.326145	+	0.185687i
$601$	30.5746	+	9.93428i	1.24716	+	0.405228i	0.856903	−	0.515477i	$-0.172385\pi$
$601$	30.5746	+	9.93428i	1.24716	+	0.405228i	0.390259	+	0.920705i	$0.372385\pi$
$602$	7.22437	−	7.05359i	0.294443	−	0.287483i
$603$	−21.6777	−	29.8368i	−0.882783	−	1.21505i
$604$	−7.94112	−	6.06498i	−0.323119	−	0.246780i
$605$	22.7481	−	9.35531i	0.924844	−	0.380347i
$606$	10.9597	−	5.42014i	0.445209	−	0.220178i
$607$	−3.14846	−	0.498667i	−0.127792	−	0.0202403i	0.0922107	−	0.995740i	$-0.470607\pi$
$607$	−3.14846	−	0.498667i	−0.127792	−	0.0202403i	−0.220003	+	0.975499i	$0.570607\pi$
$608$	23.0758	+	13.5528i	0.935849	+	0.549639i
$609$	1.54831	+	0.503076i	0.0627406	+	0.0203856i
$610$	19.4723	−	24.1927i	0.788412	−	0.979533i
$611$	−9.76284	+	1.54628i	−0.394962	+	0.0625559i
$612$	−5.31377	+	29.0365i	−0.214797	+	1.17373i
$613$	−7.56610	−	23.2861i	−0.305592	−	0.940515i	−0.979456	−	0.201660i	$-0.935367\pi$
$613$	−7.56610	−	23.2861i	−0.305592	−	0.940515i	0.673864	−	0.738856i	$-0.264633\pi$
$614$	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	0.548617	−	0.836074i	$-0.315154\pi$
$617$	−7.14027	−	7.14027i	−0.287456	−	0.287456i	−0.836074	+	0.548617i	$0.815154\pi$
$618$	−7.36159	−	3.86251i	−0.296127	−	0.155373i
$619$	−3.57562	−	1.82187i	−0.143716	−	0.0732270i	0.380654	−	0.924718i	$-0.375699\pi$
$619$	−3.57562	−	1.82187i	−0.143716	−	0.0732270i	−0.524370	+	0.851491i	$0.675699\pi$
$620$	−1.76645	−	18.3970i	−0.0709425	−	0.738842i
$621$	1.32552	+	8.36903i	0.0531914	+	0.335837i
$622$	−11.6303	−	16.4171i	−0.466332	−	0.658265i
$623$	−3.54911	−	6.96553i	−0.142192	−	0.279068i
$624$	4.51739	+	6.88783i	0.180840	+	0.275734i
$625$	−4.09209	−	24.6628i	−0.163684	−	0.986513i
$626$	−16.7852	+	8.30112i	−0.670871	+	0.331780i
$627$	8.38022	−	5.81357i	0.334674	−	0.232171i
$628$	35.1064	+	26.8123i	1.40090	+	1.06993i
$629$	−41.7820	−	6.61762i	−1.66596	−	0.263862i
$630$	5.57146	+	20.5490i	0.221972	+	0.818693i
$631$	−13.9158	+	42.8284i	−0.553979	+	1.70497i	0.144644	+	0.989484i	$0.453796\pi$
$631$	−13.9158	+	42.8284i	−0.553979	+	1.70497i	−0.698624	+	0.715489i	$0.746204\pi$
$632$	0.525967	−	14.6523i	0.0209218	−	0.582839i
$633$	11.9490	−	1.89254i	0.474930	−	0.0752216i
$634$	−9.09289	+	12.2056i	−0.361125	+	0.484746i
$635$	−13.1842	+	8.84443i	−0.523197	+	0.350980i
$636$	9.02279	+	0.215872i	0.357777	+	0.00855989i
$637$	−0.559025			−0.0221494
$638$	−4.49438	−	0.151864i	−0.177934	−	0.00601234i
$639$	−19.4638			−0.769975
$640$	−14.1253	+	20.9875i	−0.558350	+	0.829606i
$641$	−7.64209	−	23.5199i	−0.301844	−	0.928981i	−0.980836	−	0.194835i	$-0.937583\pi$
$641$	−7.64209	−	23.5199i	−0.301844	−	0.928981i	0.678992	−	0.734146i	$-0.262417\pi$
$642$	9.06218	−	12.1644i	0.357656	−	0.480090i
$643$	−13.3294	−	9.68439i	−0.525661	−	0.381915i	0.293071	−	0.956091i	$-0.405323\pi$
$643$	−13.3294	−	9.68439i	−0.525661	−	0.381915i	−0.818732	+	0.574176i	$0.805323\pi$
$644$	3.49426	+	11.6993i	0.137693	+	0.461017i
$645$	−2.70203	−	2.91230i	−0.106392	−	0.114672i
$646$	0.458205	−	38.3085i	0.0180278	−	1.50723i
$647$	3.49348	−	22.0570i	0.137343	−	0.867150i	−0.818764	−	0.574131i	$-0.805340\pi$
$647$	3.49348	−	22.0570i	0.137343	−	0.867150i	0.956107	−	0.293019i	$-0.0946599\pi$
$648$	8.48994	+	12.6133i	0.333516	+	0.495499i
$649$	3.72473	+	1.30073i	0.146208	+	0.0510583i
$650$	−21.8241	+	5.04857i	−0.856013	+	0.198021i
$651$	6.93090	+	1.09775i	0.271643	+	0.0430241i
$652$	6.35126	−	18.0650i	0.248734	−	0.707480i
$653$	29.1521	+	9.47209i	1.14081	+	0.370671i	0.817674	−	0.575681i	$-0.195263\pi$
$653$	29.1521	+	9.47209i	1.14081	+	0.370671i	0.323135	+	0.946353i	$0.395263\pi$
$654$	4.93733	+	0.842648i	0.193065	+	0.0329501i
$655$	31.5038	+	11.5567i	1.23096	+	0.451558i
$656$	−1.29824	+	27.1157i	−0.0506878	+	1.05869i
$657$	−34.3484	−	17.5014i	−1.34006	−	0.682794i
$658$	11.0043	−	3.43057i	0.428994	−	0.133738i
$659$	25.4490	+	25.4490i	0.991351	+	0.991351i	0.999963	−	0.00861234i	$-0.00274143\pi$
$659$	25.4490	+	25.4490i	0.991351	+	0.991351i	−0.00861234	+	0.999963i	$0.502741\pi$
$660$	4.99962	+	8.24409i	0.194610	+	0.320901i
$661$	−13.3978	+	13.3978i	−0.521116	+	0.521116i	−0.917908	−	0.396793i	$-0.870123\pi$
$661$	−13.3978	+	13.3978i	−0.521116	+	0.521116i	0.396793	+	0.917908i	$0.370123\pi$
$662$	0.651450	+	0.341805i	0.0253193	+	0.0132846i
$663$	5.35348	−	10.5068i	0.207912	−	0.408050i
$664$	23.0147	−	6.57509i	0.893142	−	0.255163i
$665$	−11.6148	−	25.0732i	−0.450401	−	0.972297i
$666$	−21.9726	+	15.5659i	−0.851421	+	0.603168i
$667$	−0.692418	+	2.13104i	−0.0268105	+	0.0825144i
$668$	12.0463	+	25.1094i	0.466084	+	0.971511i
$669$	1.74781	−	11.0353i	0.0675744	−	0.426648i
$670$	−33.5362	+	30.3767i	−1.29562	+	1.17356i
$671$	−25.9270	−	19.7153i	−1.00090	−	0.761102i
$672$	−6.37403	−	7.18590i	−0.245883	−	0.277202i
$673$	20.2476	+	3.20690i	0.780488	+	0.123617i	0.533950	−	0.845516i	$-0.320707\pi$
$673$	20.2476	+	3.20690i	0.780488	+	0.123617i	0.246538	+	0.969133i	$0.420707\pi$
$674$	8.19789	+	8.39637i	0.315771	+	0.323416i
$675$	17.6113	−	4.29655i	0.677858	−	0.165374i
$676$	−1.69670	−	5.68081i	−0.0652578	−	0.218493i
$677$	22.2591	−	30.6371i	0.855488	−	1.17748i	−0.127139	−	0.991885i	$-0.540579\pi$
$677$	22.2591	−	30.6371i	0.855488	−	1.17748i	0.982627	−	0.185593i	$-0.0594207\pi$
$678$	3.99650	−	0.584075i	0.153485	−	0.0224313i
$679$	43.9404	−	14.2771i	1.68628	−	0.547905i
$680$	36.1193	+	2.65284i	1.38511	+	0.101732i
$681$		−	14.0870i		−	0.539814i
$682$	−19.2365	+	2.38401i	−0.736605	+	0.0912886i
$683$			43.4754i			1.66354i	0.555120	+	0.831770i	$0.312672\pi$
$683$			43.4754i			1.66354i	−0.555120	+	0.831770i	$0.687328\pi$
$684$	−16.8267	−	17.6516i	−0.643383	−	0.674924i
$685$	14.7273	−	9.87963i	0.562701	−	0.377481i
$686$	26.2326	−	3.83381i	1.00156	−	0.146375i
$687$	−0.253008	−	1.59743i	−0.00965286	−	0.0609457i
$688$	−10.2240	−	3.87173i	−0.389788	−	0.147608i
$689$	20.9157	+	6.79594i	0.796827	+	0.258905i
$690$	4.63678	−	1.25717i	0.176519	−	0.0478597i
$691$	3.14559	−	19.8604i	0.119664	−	0.755527i	−0.852760	−	0.522304i	$-0.825073\pi$
$691$	3.14559	−	19.8604i	0.119664	−	0.755527i	0.972423	−	0.233223i	$-0.0749273\pi$
$692$	14.8665	−	19.4653i	0.565141	−	0.739961i
$693$	21.3827	−	6.43546i	0.812261	−	0.244463i
$694$	6.62647	+	2.24104i	0.251538	+	0.0850687i
$695$	−15.1118	+	19.2418i	−0.573224	+	0.729883i
$696$	−0.213120	−	1.74982i	−0.00807831	−	0.0663268i
$697$	34.6271	−	17.6434i	1.31159	−	0.668291i
$698$	−6.30537	−	1.07613i	−0.238662	−	0.0407321i
$699$	17.3702	−	2.75117i	0.657001	−	0.104059i
$700$	24.3309	−	9.50573i	0.919623	−	0.359283i
$701$	11.1825	−	21.9468i	0.422356	−	0.828920i	−0.577565	−	0.816345i	$-0.695997\pi$
$701$	11.1825	−	21.9468i	0.422356	−	0.828920i	0.999921	−	0.0125757i	$-0.00400306\pi$
$702$	−4.83420	−	15.5068i	−0.182455	−	0.585266i
$703$	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
$707$	−33.0421	+	10.7360i	−1.24268	+	0.403770i
$708$	−0.278394	+	1.52126i	−0.0104627	+	0.0571723i
$709$	−2.48297	−	15.6769i	−0.0932499	−	0.588757i	−0.989424	−	0.145054i	$-0.953665\pi$
$709$	−2.48297	−	15.6769i	−0.0932499	−	0.588757i	0.896174	−	0.443703i	$-0.146335\pi$
$710$	2.56658	+	23.7418i	0.0963218	+	0.891014i
$711$	−4.12871	+	12.7069i	−0.154839	+	0.476544i
$712$	−5.21791	+	6.66522i	−0.195549	+	0.249790i
$713$	−1.51091	+	9.53949i	−0.0565839	+	0.357257i
$714$	−4.40543	+	13.0263i	−0.164869	+	0.487497i
$715$	5.92413	+	22.7346i	0.221550	+	0.850227i
$716$	0.0466398	+	0.348184i	0.00174301	+	0.0130123i
$717$	−5.57261	+	4.04874i	−0.208113	+	0.151203i
$718$	−8.18594	−	0.0979113i	−0.305497	−	0.00365402i
$719$	10.9426	−	33.6777i	0.408088	−	1.25597i	−0.510200	−	0.860056i	$-0.670429\pi$
$719$	10.9426	−	33.6777i	0.408088	−	1.25597i	0.918289	−	0.395911i	$-0.129571\pi$
$720$	17.6304	−	14.8536i	0.657046	−	0.553560i
$721$	19.1110	+	13.8850i	0.711732	+	0.517104i
$722$	3.83372	+	2.85604i	0.142676	+	0.106291i
$723$	−0.835204	−	2.57049i	−0.0310616	−	0.0955976i
$724$	−27.8069	+	26.5074i	−1.03344	+	0.985140i
$725$	4.66539	+	1.10196i	0.173268	+	0.0409257i
$726$	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	$0.264003\pi$
$728$	−9.87100	−	21.2224i	−0.365844	−	0.786554i
$729$	−2.09669	−	6.45295i	−0.0776552	−	0.238998i
$730$	−16.8188	+	44.2058i	−0.622491	+	1.63613i
$731$	2.44834	+	15.4582i	0.0905553	+	0.571744i
$732$	6.06684	−	11.2342i	0.224237	−	0.415227i
$733$	32.2518	+	10.4792i	1.19125	+	0.387060i	0.836534	−	0.547916i	$-0.184579\pi$
$733$	32.2518	+	10.4792i	1.19125	+	0.387060i	0.354713	+	0.934975i	$0.384579\pi$
$734$	−15.4515	+	15.0862i	−0.570323	+	0.556842i
$735$	−0.0306157	−	0.254664i	−0.00112928	−	0.00939344i
$736$	9.89046	−	8.77302i	0.364567	−	0.323378i
$737$	32.8171	+	34.2812i	1.20883	+	1.26277i
$738$	7.92526	−	23.4340i	0.291733	−	0.862618i
$739$	10.7141	+	1.69695i	0.394125	+	0.0624233i	0.350352	−	0.936618i	$-0.386062\pi$
$739$	10.7141	+	1.69695i	0.394125	+	0.0624233i	0.0437736	+	0.999041i	$0.486062\pi$
$740$	21.8847	+	24.7495i	0.804496	+	0.909809i
$741$	4.42275	+	8.68014i	0.162474	+	0.318873i
$742$	−25.2802	−	4.31454i	−0.928065	−	0.158392i
$743$	3.97807	+	25.1165i	0.145941	+	0.921437i	0.946622	+	0.322346i	$0.104471\pi$
$743$	3.97807	+	25.1165i	0.145941	+	0.921437i	−0.800681	+	0.599091i	$0.795529\pi$
$744$	−2.08723	−	7.30588i	−0.0765214	−	0.267847i
$745$	−19.8782	+	13.3350i	−0.728279	+	0.488557i
$746$	−32.5550	+	10.1489i	−1.19193	+	0.371579i
$747$	−21.8116			−0.798044
$748$	1.73669	−	37.9446i	0.0634996	−	1.38739i
$749$	−30.4782	+	30.4782i	−1.11365	+	1.11365i
$750$	−3.49511	−	9.66551i	−0.127623	−	0.352934i
$751$	−51.5118	+	16.7372i	−1.87969	+	0.610749i	−0.892538	+	0.450972i	$0.851077\pi$
$751$	−51.5118	+	16.7372i	−1.87969	+	0.610749i	−0.987153	+	0.159777i	$0.948923\pi$
$752$	−8.39315	−	9.23726i	−0.306067	−	0.336848i
$753$	2.55731	+	16.1462i	0.0931935	+	0.588401i
$754$	0.722624	−	4.23408i	0.0263164	−	0.154196i
$755$	8.18969	−	7.59840i	0.298053	−	0.276534i
$756$	8.19305	+	17.0777i	0.297978	+	0.621109i
$757$	5.10306	+	7.02376i	0.185474	+	0.255283i	0.891621	−	0.452782i	$-0.149568\pi$
$757$	5.10306	+	7.02376i	0.185474	+	0.255283i	−0.706147	+	0.708065i	$0.749568\pi$
$758$	−38.8329	+	19.2048i	−1.41048	+	0.697551i
$759$	−1.45213	−	4.82488i	−0.0527088	−	0.175132i
$760$	−19.3125	+	22.8527i	−0.700536	+	0.828954i
$761$	5.80985	+	7.99658i	0.210607	+	0.289876i	0.901232	−	0.433338i	$-0.142664\pi$
$761$	5.80985	+	7.99658i	0.210607	+	0.289876i	−0.690625	+	0.723213i	$0.742664\pi$
$762$	−4.67011	+	4.55971i	−0.169180	+	0.165181i
$763$	−13.5358	−	4.39804i	−0.490028	−	0.159220i
$764$	10.4762	−	3.12894i	0.379014	−	0.113201i
$765$	−30.9840	−	11.3660i	−1.12023	−	0.410939i
$766$	−0.230275	−	1.57565i	−0.00832018	−	0.0569304i
$767$	−1.71082	+	3.35767i	−0.0617741	+	0.121239i
$768$	−4.14428	+	9.53929i	−0.149544	+	0.344219i
$769$			7.22602i			0.260577i	0.991476	+	0.130289i	$0.0415904\pi$
$769$			7.22602i			0.260577i	−0.991476	+	0.130289i	$0.958410\pi$
$770$	−10.6696	−	25.2339i	−0.384504	−	0.909366i
$771$	0.473199	−	0.473199i	0.0170418	−	0.0170418i
$772$	5.12354	+	5.37471i	0.184400	+	0.193440i
$773$	−12.3588	−	38.0364i	−0.444514	−	1.36807i	−0.883016	−	0.469343i	$-0.844491\pi$
$773$	−12.3588	−	38.0364i	−0.444514	−	1.36807i	0.438502	−	0.898730i	$-0.355509\pi$
$774$	7.98921	+	5.95178i	0.287166	+	0.213932i
$775$	20.6052	+	1.54556i	0.740161	+	0.0555180i
$776$	−34.0822	−	36.6201i	−1.22348	−	1.31459i
$777$	−11.1768	+	5.69486i	−0.400965	+	0.204302i
$778$	−14.4831	+	14.1407i	−0.519243	+	0.506969i
$779$	−5.02255	+	31.7111i	−0.179951	+	1.13617i
$780$	−8.44646	+	3.66994i	−0.302432	+	0.131405i
$781$	24.8169	−	3.37744i	0.888020	−	0.120854i
$782$	−17.9290	−	6.06350i	−0.641140	−	0.216830i
$783$	−0.543769	+	3.43322i	−0.0194327	+	0.122693i
$784$	−0.387111	−	0.590242i	−0.0138254	−	0.0210801i
$785$	−36.2053	+	33.5913i	−1.29222	+	1.19892i
$786$	13.5992	+	2.32096i	0.485067	+	0.0827858i
$787$	16.8740	−	23.2250i	0.601491	−	0.827882i	−0.394352	−	0.918959i	$-0.629031\pi$
$787$	16.8740	−	23.2250i	0.601491	−	0.827882i	0.995844	+	0.0910774i	$0.0290311\pi$
$788$	−9.00937	−	13.0455i	−0.320945	−	0.464726i
$789$	6.37476	−	12.5112i	0.226947	−	0.445409i
$790$	16.0442	+	3.36060i	0.570827	+	0.119565i
$791$	−11.4767			−0.408066
$792$	−16.0825	−	18.0543i	−0.571467	−	0.641532i
$793$	21.9988	−	21.9988i	0.781200	−	0.781200i
$794$	−22.0657	+	6.87892i	−0.783083	+	0.244124i
$795$	−1.95042	+	9.90038i	−0.0691742	+	0.351130i
$796$	21.8757	+	31.6758i	0.775364	+	1.12272i
$797$	15.5405	+	11.2908i	0.550472	+	0.399941i	0.827959	−	0.560788i	$-0.189502\pi$
$797$	15.5405	+	11.2908i	0.550472	+	0.399941i	−0.277488	+	0.960729i	$0.589502\pi$
$798$	−6.56707	−	9.26996i	−0.232472	−	0.328153i
$799$	−5.52134	+	16.9929i	−0.195331	+	0.601167i
$800$	−20.4431	−	19.5468i	−0.722774	−	0.691084i
$801$	6.24045	−	4.53396i	0.220496	−	0.160199i
$802$	43.1748	+	14.6015i	1.52456	+	0.515597i
$803$	46.8322	+	16.3545i	1.65267	+	0.577139i
$804$	−11.2912	+	14.7840i	−0.398209	+	0.521391i
$805$	−13.5536	+	1.62941i	−0.477700	+	0.0574291i
$806$	0.221434	−	18.5132i	0.00779970	−	0.652099i
$807$	−7.07207	−	13.8797i	−0.248949	−	0.488589i
$808$	25.6289	+	27.5374i	0.901623	+	0.968763i
$809$	13.8740	+	10.0801i	0.487785	+	0.354396i	0.804332	−	0.594181i	$-0.202524\pi$
$809$	13.8740	+	10.0801i	0.487785	+	0.354396i	−0.316547	+	0.948577i	$0.602524\pi$
$810$	−15.5089	+	6.96018i	−0.544926	+	0.244556i
$811$	2.72790	−	5.35381i	0.0957896	−	0.187998i	−0.838140	−	0.545456i	$-0.816357\pi$
$811$	2.72790	−	5.35381i	0.0957896	−	0.187998i	0.933929	+	0.357458i	$0.116357\pi$
$812$	−0.119804	+	5.00745i	−0.00420431	+	0.175727i
$813$			17.5824i			0.616640i
$814$	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
$817$	−11.5207	−	5.87007i	−0.403057	−	0.205368i
$818$	31.5731	−	42.3813i	1.10393	−	1.48183i
$819$	3.33656	+	21.0662i	0.116589	+	0.736113i
$820$	−29.6298	−	6.57709i	−1.03472	−	0.229682i
$821$	−13.0680	−	25.6475i	−0.456078	−	0.895103i	−0.998487	−	0.0549886i	$-0.982488\pi$
$821$	−13.0680	−	25.6475i	−0.456078	−	0.895103i	0.542409	−	0.840114i	$-0.317512\pi$
$822$	5.21673	−	5.09341i	0.181954	−	0.177653i
$823$	−2.42175	−	0.383567i	−0.0844169	−	0.0133703i	0.114083	−	0.993471i	$-0.463607\pi$
$823$	−2.42175	−	0.383567i	−0.0844169	−	0.0133703i	−0.198500	+	0.980101i	$0.563607\pi$
$824$	4.90498	−	25.1033i	0.170873	−	0.874515i
$825$	−10.0323	+	3.94383i	−0.349281	+	0.137307i
$826$	1.40785	−	4.16284i	0.0489854	−	0.144844i
$827$	5.76472	−	4.18832i	0.200459	−	0.145642i	−0.483027	−	0.875605i	$-0.660463\pi$
$827$	5.76472	−	4.18832i	0.200459	−	0.145642i	0.683486	+	0.729963i	$0.260463\pi$
$828$	−10.8622	+	5.21117i	−0.377488	+	0.181101i
$829$	−8.80196	−	17.2748i	−0.305705	−	0.599979i	0.686134	−	0.727475i	$-0.259306\pi$
$829$	−8.80196	−	17.2748i	−0.305705	−	0.599979i	−0.991839	+	0.127495i	$0.959306\pi$
$830$	2.87617	+	26.6057i	0.0998332	+	0.923496i
$831$	1.11982	−	1.54130i	0.0388460	−	0.0534670i
$832$	−16.3281	+	19.3823i	−0.566076	+	0.671959i
$833$	−0.458758	+	0.900364i	−0.0158950	+	0.0311957i
$834$	−4.67343	+	8.90713i	−0.161828	+	0.308429i
$835$	−29.9521	+	8.50675i	−1.03653	+	0.294388i
$836$	24.5175	+	19.5865i	0.847956	+	0.677412i
$837$			14.9831i			0.517890i
$838$	31.6109	+	16.5857i	1.09198	+	0.572944i
$839$	−3.12992	+	1.01697i	−0.108057	+	0.0351098i	−0.362546	−	0.931966i	$-0.618093\pi$
$839$	−3.12992	+	1.01697i	−0.108057	+	0.0351098i	0.254489	+	0.967076i	$0.418093\pi$
$840$	9.12728	−	5.65901i	0.314921	−	0.195255i
$841$	16.5055	−	22.7178i	0.569154	−	0.783374i
$842$	−35.9017	−	6.12730i	−1.23726	−	0.211161i
$843$	−13.8078	−	4.48644i	−0.475567	−	0.154521i
$844$	16.1004	+	33.5599i	0.554200	+	1.15518i
$845$	6.58119	−	0.791190i	0.226400	−	0.0272178i
$846$	5.04184	+	10.1948i	0.173342	+	0.350504i
$847$	−26.1469	+	11.9158i	−0.898418	+	0.409433i
$848$	7.30819	+	26.7897i	0.250964	+	0.919963i
$849$	−2.94653	−	4.05555i	−0.101125	−	0.139186i
$850$	−9.77853	+	39.2929i	−0.335401	+	1.34774i
$851$	−7.83824	−	15.3834i	−0.268691	−	0.527337i
$852$	2.80962	+	9.40701i	0.0962559	+	0.322279i
$853$	−33.7780	−	24.5411i	−1.15654	−	0.840272i	−0.167200	−	0.985923i	$-0.553472\pi$
$853$	−33.7780	−	24.5411i	−1.15654	−	0.840272i	−0.989336	+	0.145651i	$0.953472\pi$
$854$	−21.6741	+	29.0936i	−0.741672	+	0.995563i
$855$	22.6424	−	15.1893i	0.774352	−	0.519465i
$856$	43.8405	+	16.0050i	1.49844	+	0.547041i
$857$	−5.32372	−	5.32372i	−0.181855	−	0.181855i	0.610309	−	0.792164i	$-0.291045\pi$
$857$	−5.32372	−	5.32372i	−0.181855	−	0.181855i	−0.792164	+	0.610309i	$0.791045\pi$
$858$	4.09187	+	8.74922i	0.139694	+	0.298694i
$859$	−0.455854	+	0.455854i	−0.0155535	+	0.0155535i	−0.714841	−	0.699287i	$-0.753501\pi$
$859$	−0.455854	+	0.455854i	−0.0155535	+	0.0155535i	0.699287	+	0.714841i	$0.253501\pi$
$860$	6.20646	−	10.5300i	0.211639	−	0.359071i
$861$	5.23177	−	10.2679i	0.178298	−	0.349930i
$862$	−30.4908	−	22.7150i	−1.03852	−	0.773675i
$863$	−41.3360	+	6.54698i	−1.40709	+	0.222862i	−0.813342	−	0.581786i	$-0.802354\pi$
$863$	−41.3360	+	6.54698i	−1.40709	+	0.222862i	−0.593753	+	0.804648i	$0.702354\pi$
$864$	13.0252	−	15.8422i	0.443125	−	0.538963i
$865$	18.6253	+	20.0746i	0.633278	+	0.682558i
$866$	−7.77107	+	7.58737i	−0.264072	+	0.257829i
$867$	−6.03349	−	8.30439i	−0.204908	−	0.282032i
$868$	2.86646	+	21.3992i	0.0972941	+	0.726338i
$869$	3.05929	−	16.9181i	0.103779	−	0.573907i
$870$	1.96841	+	0.0973074i	0.0667354	+	0.00329903i
$871$	−36.6719	+	26.6437i	−1.24258	+	0.902787i
$872$	1.86316	+	15.2975i	0.0630947	+	0.518038i
$873$	20.6962	+	40.6185i	0.700459	+	1.37473i
$874$	12.7589	−	9.03873i	0.431576	−	0.305739i
$875$	5.85533	+	28.6122i	0.197946	+	0.967268i
$876$	−3.50034	+	19.1272i	−0.118266	+	0.646249i
$877$	15.7793	+	48.5637i	0.532829	+	1.63988i	0.748293	+	0.663369i	$0.230874\pi$
$877$	15.7793	+	48.5637i	0.532829	+	1.63988i	−0.215463	+	0.976512i	$0.569126\pi$
$878$	2.24245	+	7.19317i	0.0756790	+	0.242758i
$879$	−4.79676			−0.161791
$880$	−19.9019	+	21.9981i	−0.670891	+	0.741556i
$881$	−19.0860			−0.643024			−0.321512	−	0.946906i	$-0.604191\pi$
$881$	−19.0860			−0.643024			−0.321512	+	0.946906i	$0.604191\pi$
$882$	0.191437	+	0.614079i	0.00644603	+	0.0206771i
$883$	−14.5041	−	44.6392i	−0.488103	−	1.50223i	−0.827435	−	0.561561i	$-0.810201\pi$
$883$	−14.5041	−	44.6392i	−0.488103	−	1.50223i	0.339332	−	0.940667i	$-0.389799\pi$
$884$	35.6883	+	6.53108i	1.20033	+	0.219664i
$885$	−1.62329	−	0.595478i	−0.0545662	−	0.0200168i
$886$	−20.5714	+	14.5733i	−0.691109	+	0.489599i
$887$	−21.0503	−	41.3135i	−0.706800	−	1.38717i	−0.912712	−	0.408602i	$-0.866016\pi$
$887$	−21.0503	−	41.3135i	−0.706800	−	1.38717i	0.205913	−	0.978570i	$-0.433984\pi$
$888$	10.6949	+	8.37259i	0.358898	+	0.280966i
$889$	15.0043	−	10.9013i	0.503230	−	0.365618i
$890$	−6.35339	−	7.01421i	−0.212966	−	0.235117i
$891$	7.74564	+	16.0584i	0.259489	+	0.537976i
$892$	34.0715	−	4.56393i	1.14080	−	0.152812i
$893$	−8.67635	−	11.9420i	−0.290343	−	0.399623i
$894$	−7.04127	+	6.87482i	−0.235495	+	0.229928i
$895$	−0.392484	−	0.0146991i	−0.0131193	−	0.000491335i
$896$	15.5721	−	25.1182i	0.520226	−	0.839140i
$897$	4.75348	−	0.752877i	0.158714	−	0.0251378i
$898$	4.69688	+	3.49907i	0.156737	+	0.116765i
$899$	−1.79878	+	3.53031i	−0.0599927	+	0.117742i
$900$	13.0194	+	22.2445i	0.433980	+	0.741484i
$901$	28.1098	−	28.1098i	0.936473	−	0.936473i
$902$	−6.03859	+	31.2543i	−0.201063	+	1.04066i
$903$	3.28165	+	3.28165i	0.109206	+	0.109206i
$904$	5.24081	+	11.2676i	0.174307	+	0.374755i
$905$	−23.9281	−	35.6690i	−0.795397	−	1.18568i
$906$	2.74390	−	3.68319i	0.0911598	−	0.122366i
$907$	22.2147	+	16.1399i	0.737628	+	0.535918i	0.891967	−	0.452100i	$-0.149325\pi$
$907$	22.2147	+	16.1399i	0.737628	+	0.535918i	−0.154339	+	0.988018i	$0.549325\pi$
$908$	41.5292	−	12.4036i	1.37819	−	0.411629i
$909$	−15.5630	−	30.5441i	−0.516192	−	1.01308i
$910$	25.2565	−	6.84780i	0.837245	−	0.227002i
$911$	10.2464	+	14.1029i	0.339477	+	0.467251i	0.944289	−	0.329118i	$-0.106751\pi$
$911$	10.2464	+	14.1029i	0.339477	+	0.467251i	−0.604811	+	0.796369i	$0.706751\pi$
$912$	−6.10221	+	10.6805i	−0.202064	+	0.353667i
$913$	27.8105	−	3.78484i	0.920392	−	0.125260i
$914$	4.56690	+	9.23445i	0.151060	+	0.305448i
$915$	11.2264	+	8.81677i	0.371132	+	0.291474i
$916$	4.48653	−	2.15242i	0.148239	−	0.0711180i
$917$	−37.2824	−	12.1138i	−1.23117	−	0.400033i
$918$	−28.9423	−	4.93955i	−0.955239	−	0.163029i
$919$	17.2008	−	23.6748i	0.567401	−	0.780961i	−0.424843	−	0.905267i	$-0.639671\pi$
$919$	17.2008	−	23.6748i	0.567401	−	0.780961i	0.992244	+	0.124306i	$0.0396706\pi$
$920$	7.78890	+	12.5625i	0.256792	+	0.414174i
$921$	−15.1657	+	4.92763i	−0.499726	+	0.162371i
$922$	14.0365	+	7.36470i	0.462266	+	0.242544i
$923$			23.9226i			0.787423i
$924$	−6.19693	−	9.40547i	−0.203864	−	0.309417i
$925$	−31.4229	+	19.4151i	−1.03318	+	0.638363i
$926$	−10.2832	+	19.5988i	−0.337925	+	0.644055i
$927$	−10.5818	+	20.7679i	−0.347551	+	0.682108i
$928$	4.97091	−	2.16901i	0.163178	−	0.0712013i
$929$	23.8085	−	32.7696i	0.781132	−	1.07514i	−0.214024	−	0.976828i	$-0.568657\pi$
$929$	23.8085	−	32.7696i	0.781132	−	1.07514i	0.995156	−	0.0983078i	$-0.0313430\pi$
$930$	8.44583	−	0.913024i	0.276950	−	0.0299392i
$931$	−0.379001	−	0.743831i	−0.0124213	−	0.0243781i
$932$	23.4051	+	48.7859i	0.766660	+	1.59803i
$933$	7.48159	−	5.43569i	0.244936	−	0.177957i
$934$	14.1846	−	41.9420i	0.464134	−	1.37239i
$935$	41.4779	+	9.11555i	1.35647	+	0.298110i
$936$	19.1587	−	12.8956i	0.626222	−	0.421505i
$937$	−32.8956	−	5.21015i	−1.07465	−	0.170208i	−0.406066	−	0.913844i	$-0.633100\pi$
$937$	−32.8956	−	5.21015i	−1.07465	−	0.170208i	−0.668585	+	0.743636i	$0.733100\pi$
$938$	37.8217	−	36.9277i	1.23492	−	1.20573i
$939$	−3.90759	−	7.66908i	−0.127519	−	0.250271i
$940$	11.7707	−	7.49434i	0.383918	−	0.244438i
$941$	−0.820989	−	5.18352i	−0.0267635	−	0.168978i	0.970686	−	0.240350i	$-0.0772622\pi$
$941$	−0.820989	−	5.18352i	−0.0267635	−	0.168978i	−0.997450	+	0.0713721i	$0.977262\pi$
$942$	−12.1303	+	16.2828i	−0.395227	+	0.530522i
$943$	14.1325	+	7.20085i	0.460216	+	0.234492i
$944$	−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
$947$		−	52.7600i		−	1.71447i	−0.514925	−	0.857235i	$-0.672180\pi$
$947$		−	52.7600i		−	1.71447i	0.514925	−	0.857235i	$-0.327820\pi$
$948$	6.73732	+	0.161192i	0.218818	+	0.00523527i
$949$	−21.5107	+	42.2171i	−0.698266	+	1.37043i
$950$	−21.5136	−	25.6161i	−0.697994	−	0.831096i
$951$	−5.65985	−	4.11212i	−0.183533	−	0.133345i
$952$	−42.2812	−	1.51774i	−1.37034	−	0.0491904i
$953$	−1.45501	−	2.85562i	−0.0471324	−	0.0925025i	0.866239	−	0.499630i	$-0.166531\pi$
$953$	−1.45501	−	2.85562i	−0.0471324	−	0.0925025i	−0.913371	+	0.407127i	$0.866531\pi$
$954$	0.302645	−	25.3028i	0.00979849	−	0.819209i
$955$	1.45906	+	12.1366i	0.0472140	+	0.392730i
$956$	−16.8426	−	12.8634i	−0.544729	−	0.416033i
$957$	0.0450913	−	2.06652i	0.00145760	−	0.0668010i
$958$	14.2908	+	4.83309i	0.461716	+	0.156150i
$959$	−16.7605	+	12.1772i	−0.541226	+	0.393224i
$960$	−9.72383	−	6.37679i	−0.313835	−	0.205810i
$961$	4.30197	−	13.2401i	0.138773	−	0.427100i
$962$	19.1319	+	27.0062i	0.616836	+	0.870714i
$963$	−34.4070	−	24.9981i	−1.10875	−	0.805554i
$964$	6.84255	−	4.72555i	0.220384	−	0.152200i
$965$	−6.89436	+	4.62500i	−0.221937	+	0.148884i
$966$	−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	$-0.126970\pi$
$968$	23.6386	+	20.2291i	0.759773	+	0.650189i
$969$	17.6097			0.565704
$970$	46.8172	−	30.6012i	1.50321	−	0.982546i
$971$	17.2465	−	33.8481i	0.553466	−	1.08624i	−0.429606	−	0.903017i	$-0.641347\pi$
$971$	17.2465	−	33.8481i	0.553466	−	1.08624i	0.983072	−	0.183222i	$-0.0586526\pi$
$972$	−23.6502	+	16.3332i	−0.758582	+	0.523886i
$973$	16.8001	−	23.1233i	0.538586	−	0.741300i
$974$	6.16233	+	1.05172i	0.197454	+	0.0336992i
$975$	−2.44037	−	10.0029i	−0.0781545	−	0.320350i
$976$	38.4608	+	7.99364i	1.23110	+	0.255870i
$977$	2.29280	−	14.4762i	0.0733533	−	0.463134i	−0.923482	−	0.383641i	$-0.874670\pi$
$977$	2.29280	−	14.4762i	0.0733533	−	0.463134i	0.996835	−	0.0794930i	$-0.0253301\pi$
$978$	8.33785	+	2.81982i	0.266615	+	0.0901679i
$979$	−7.17003	+	6.86381i	−0.229155	+	0.219368i
$980$	0.723807	−	0.314490i	0.0231212	−	0.0100460i
$981$	2.19682	−	13.8702i	0.0701391	−	0.442841i
$982$	29.5477	−	28.8493i	0.942906	−	0.920617i
$983$	−9.91698	+	5.05295i	−0.316303	+	0.161164i	−0.604933	−	0.796276i	$-0.706800\pi$
$983$	−9.91698	+	5.05295i	−0.316303	+	0.161164i	0.288630	+	0.957441i	$0.406800\pi$
$984$	−12.4699	−	0.447624i	−0.397525	−	0.0142697i
$985$	16.0836	−	7.45047i	0.512466	−	0.237392i
$986$	−6.22637	−	4.63851i	−0.198288	−	0.147720i
$987$	1.63724	+	5.03889i	0.0521138	+	0.160390i
$988$	−21.6953	+	20.6814i	−0.690218	+	0.657963i
$989$	−4.51676	+	4.51676i	−0.143625	+	0.143625i
$990$	22.9449	−	14.2930i	0.729236	−	0.454261i
$991$		−	16.3295i		−	0.518722i	−0.965780	−	0.259361i	$-0.916488\pi$
$991$		−	16.3295i		−	0.518722i	0.965780	−	0.259361i	$-0.0835120\pi$
$992$	19.7003	−	12.5861i	0.625486	−	0.399609i
$993$	−0.153517	+	0.301295i	−0.00487173	+	0.00956130i
$994$	−4.03419	−	27.6037i	−0.127957	−	0.875536i
$995$	−39.0527	+	18.0906i	−1.23805	+	0.573509i
$996$	3.14852	+	10.5417i	0.0997648	+	0.334027i
$997$	47.4890	+	15.4301i	1.50399	+	0.488677i	0.941180	−	0.337907i	$-0.109719\pi$
$997$	47.4890	+	15.4301i	1.50399	+	0.488677i	0.562814	+	0.826584i	$0.309719\pi$
$998$	16.4798	−	16.0903i	0.521660	−	0.509328i
$999$	−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.ch.a.3.14	✓	1120
5.2	odd	4		880.2.cz.a.707.58	yes	1120
11.4	even	5	inner	880.2.ch.a.323.45	yes	1120
16.11	odd	4		880.2.cz.a.443.113	yes	1120
55.37	odd	20		880.2.cz.a.147.113	yes	1120
80.27	even	4	inner	880.2.ch.a.267.45	yes	1120
176.59	odd	20		880.2.cz.a.763.58	yes	1120
880.587	even	20	inner	880.2.ch.a.587.14	yes	1120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.ch.a.3.14	✓	1120	1.1	even	1	trivial
880.2.ch.a.267.45	yes	1120	80.27	even	4	inner
880.2.ch.a.323.45	yes	1120	11.4	even	5	inner
880.2.ch.a.587.14	yes	1120	880.587	even	20	inner
880.2.cz.a.147.113	yes	1120	55.37	odd	20
880.2.cz.a.443.113	yes	1120	16.11	odd	4
880.2.cz.a.707.58	yes	1120	5.2	odd	4
880.2.cz.a.763.58	yes	1120	176.59	odd	20

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.ch (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35013 + 0.420899i) q^{2} +(-0.200873 - 0.618224i) q^{3} +(1.64569 - 1.13653i) q^{4} +(0.939878 + 2.02895i) q^{5} +(0.531414 + 0.750134i) q^{6} +(-1.18591 - 2.32748i) q^{7} +(-1.74352 + 2.22713i) q^{8} +(2.08520 - 1.51499i) q^{9} +O(q^{10})\)	\(q+(-1.35013 + 0.420899i) q^{2} +(-0.200873 - 0.618224i) q^{3} +(1.64569 - 1.13653i) q^{4} +(0.939878 + 2.02895i) q^{5} +(0.531414 + 0.750134i) q^{6} +(-1.18591 - 2.32748i) q^{7} +(-1.74352 + 2.22713i) q^{8} +(2.08520 - 1.51499i) q^{9} +(-2.12294 - 2.34374i) q^{10} +(-2.39581 + 2.29349i) q^{11} +(-1.03321 - 0.789106i) q^{12} +(-1.86205 - 2.56289i) q^{13} +(2.58076 + 2.64324i) q^{14} +(1.06555 - 0.988617i) q^{15} +(1.41658 - 3.74076i) q^{16} +(-5.65584 + 0.895798i) q^{17} +(-2.17763 + 2.92308i) q^{18} +(2.14774 - 4.21517i) q^{19} +(3.85271 + 2.27081i) q^{20} +(-1.20069 + 1.20069i) q^{21} +(2.26932 - 4.10490i) q^{22} +(-1.65259 - 1.65259i) q^{23} +(1.72710 + 0.630518i) q^{24} +(-3.23326 + 3.81393i) q^{25} +(3.59272 + 2.67649i) q^{26} +(-2.93314 - 2.13105i) q^{27} +(-4.59689 - 2.48248i) q^{28} +(-0.435264 - 0.854255i) q^{29} +(-1.02252 + 1.78325i) q^{30} +(-2.42909 - 3.34336i) q^{31} +(-0.338088 + 5.64674i) q^{32} +(1.89914 + 1.02045i) q^{33} +(7.25907 - 3.58998i) q^{34} +(3.60772 - 4.59369i) q^{35} +(1.70976 - 4.86310i) q^{36} +(7.02584 + 2.28283i) q^{37} +(-1.12556 + 6.59499i) q^{38} +(-1.21040 + 1.66598i) q^{39} +(-6.15744 - 1.44429i) q^{40} +(-6.45452 + 2.09720i) q^{41} +(1.11571 - 2.12645i) q^{42} -2.73314i q^{43} +(-1.33613 + 6.49729i) q^{44} +(5.03366 + 2.80686i) q^{45} +(2.92678 + 1.53563i) q^{46} +(1.41655 - 2.78013i) q^{47} +(-2.59718 - 0.124348i) q^{48} +(0.103724 - 0.142763i) q^{49} +(2.76003 - 6.51016i) q^{50} +(1.68991 + 3.31664i) q^{51} +(-5.97716 - 2.10144i) q^{52} +(-5.61633 + 4.08050i) q^{53} +(4.85707 + 1.64264i) q^{54} +(-6.90514 - 2.70537i) q^{55} +(7.25127 + 1.41684i) q^{56} +(-3.03734 - 0.481068i) q^{57} +(0.947217 + 0.970150i) q^{58} +(-0.540048 - 1.05990i) q^{59} +(0.629965 - 2.83799i) q^{60} +(1.53629 + 9.69978i) q^{61} +(4.68680 + 3.49156i) q^{62} +(-5.99896 - 3.05662i) q^{63} +(-1.92024 - 7.76612i) q^{64} +(3.44987 - 6.18680i) q^{65} +(-2.99359 - 0.578386i) q^{66} -14.3088i q^{67} +(-8.28966 + 7.90226i) q^{68} +(-0.689710 + 1.35363i) q^{69} +(-2.93740 + 7.72056i) q^{70} +(-6.10934 - 4.43870i) q^{71} +(-0.261521 + 7.28543i) q^{72} +(-6.79020 - 13.3265i) q^{73} +(-10.4466 - 0.124951i) q^{74} +(3.00734 + 1.23276i) q^{75} +(-1.25618 - 9.37783i) q^{76} +(8.17926 + 2.85632i) q^{77} +(0.932992 - 2.75874i) q^{78} +(-4.19372 + 3.04692i) q^{79} +(8.92122 - 0.641686i) q^{80} +(1.66115 - 5.11249i) q^{81} +(7.83171 - 5.54818i) q^{82} +(-6.84628 - 4.97411i) q^{83} +(-0.611336 + 3.34058i) q^{84} +(-7.13333 - 10.6335i) q^{85} +(1.15038 + 3.69009i) q^{86} +(-0.440688 + 0.440688i) q^{87} +(-0.930753 - 9.33454i) q^{88} +2.99274 q^{89} +(-7.97749 - 1.67096i) q^{90} +(-3.75685 + 7.37322i) q^{91} +(-4.59787 - 0.841424i) q^{92} +(-1.57901 + 2.17332i) q^{93} +(-0.742367 + 4.34976i) q^{94} +(10.5710 + 0.395898i) q^{95} +(3.55887 - 0.925265i) q^{96} +(-2.76685 + 17.4692i) q^{97} +(-0.0799513 + 0.236406i) q^{98} +(-1.52114 + 8.41200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1120 q - 6 q^{2} - 12 q^{3} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} - 264 q^{9}+O(q^{10}) \) 1120 * q - 6 * q^2 - 12 * q^3 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 - 264 * q^9	\( 1120 q - 6 q^{2} - 12 q^{3} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} - 264 q^{9} - 24 q^{10} - 16 q^{11} - 20 q^{12} + 24 q^{15} - 12 q^{16} - 12 q^{17} + 14 q^{18} - 6 q^{20} - 32 q^{21} - 22 q^{22} - 32 q^{23} + 24 q^{24} + 20 q^{26} + 12 q^{27} - 22 q^{28} - 36 q^{32} - 16 q^{33} + 32 q^{34} - 26 q^{35} + 20 q^{36} - 42 q^{38} + 36 q^{40} + 42 q^{42} - 80 q^{44} + 16 q^{45} - 12 q^{46} + 6 q^{48} - 68 q^{50} - 12 q^{51} + 2 q^{52} - 12 q^{53} + 168 q^{54} - 16 q^{55} - 80 q^{56} + 24 q^{57} - 50 q^{58} - 16 q^{59} + 52 q^{60} - 12 q^{61} - 124 q^{62} - 36 q^{63} - 32 q^{65} - 24 q^{66} + 50 q^{68} - 36 q^{69} + 30 q^{70} - 56 q^{71} - 52 q^{72} - 100 q^{74} - 42 q^{75} - 32 q^{76} + 12 q^{77} - 132 q^{78} + 46 q^{80} - 240 q^{81} + 30 q^{82} + 108 q^{83} - 24 q^{84} - 26 q^{85} - 4 q^{86} - 32 q^{87} - 130 q^{88} - 4 q^{90} - 28 q^{91} - 68 q^{92} + 48 q^{94} + 120 q^{95} + 20 q^{96} - 12 q^{97} - 172 q^{98} - 20 q^{99}+O(q^{100}) \) 1120 * q - 6 * q^2 - 12 * q^3 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 - 264 * q^9 - 24 * q^10 - 16 * q^11 - 20 * q^12 + 24 * q^15 - 12 * q^16 - 12 * q^17 + 14 * q^18 - 6 * q^20 - 32 * q^21 - 22 * q^22 - 32 * q^23 + 24 * q^24 + 20 * q^26 + 12 * q^27 - 22 * q^28 - 36 * q^32 - 16 * q^33 + 32 * q^34 - 26 * q^35 + 20 * q^36 - 42 * q^38 + 36 * q^40 + 42 * q^42 - 80 * q^44 + 16 * q^45 - 12 * q^46 + 6 * q^48 - 68 * q^50 - 12 * q^51 + 2 * q^52 - 12 * q^53 + 168 * q^54 - 16 * q^55 - 80 * q^56 + 24 * q^57 - 50 * q^58 - 16 * q^59 + 52 * q^60 - 12 * q^61 - 124 * q^62 - 36 * q^63 - 32 * q^65 - 24 * q^66 + 50 * q^68 - 36 * q^69 + 30 * q^70 - 56 * q^71 - 52 * q^72 - 100 * q^74 - 42 * q^75 - 32 * q^76 + 12 * q^77 - 132 * q^78 + 46 * q^80 - 240 * q^81 + 30 * q^82 + 108 * q^83 - 24 * q^84 - 26 * q^85 - 4 * q^86 - 32 * q^87 - 130 * q^88 - 4 * q^90 - 28 * q^91 - 68 * q^92 + 48 * q^94 + 120 * q^95 + 20 * q^96 - 12 * q^97 - 172 * q^98 - 20 * q^99

Introduction

L-functions

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