LMFDB - Embedded newform 966.2.be.b.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.505673 - 0.260692i) q^{5} +(0.755750 - 0.654861i) q^{6} +(2.07574 - 1.64052i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.505673 - 0.260692i) q^{5} +(0.755750 - 0.654861i) q^{6} +(2.07574 - 1.64052i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-0.528163 + 0.211445i) q^{10} +(-0.130321 - 1.36478i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(-1.43972 - 0.207001i) q^{13} +(-2.22228 + 1.43578i) q^{14} +(-0.160282 + 0.545871i) q^{15} +(0.928368 + 0.371662i) q^{16} +(1.89035 - 5.46181i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(0.0356766 + 0.103081i) q^{19} +(0.545871 - 0.160282i) q^{20} +(-0.245128 + 2.63437i) q^{21} +1.37099i q^{22} +(-3.78347 - 2.94710i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.71254 + 3.80923i) q^{25} +(1.41352 + 0.342917i) q^{26} +(0.755750 + 0.654861i) q^{27} +(2.34870 - 1.21803i) q^{28} +(-5.33132 - 6.15267i) q^{29} +(0.211445 - 0.528163i) q^{30} +(-3.01337 + 0.731036i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(1.07767 + 0.847492i) q^{33} +(-2.40097 + 5.25739i) q^{34} +(0.621976 - 1.37069i) q^{35} +(0.142315 - 0.989821i) q^{36} +(6.28775 - 0.299523i) q^{37} +(-0.0257166 - 0.106005i) q^{38} +(1.14333 - 0.899128i) q^{39} +(-0.558635 + 0.107668i) q^{40} +(-4.13284 + 6.43082i) q^{41} +(0.494431 - 2.59914i) q^{42} +(0.493536 + 1.68083i) q^{43} +(0.130321 - 1.36478i) q^{44} +(-0.284458 - 0.492696i) q^{45} +(3.48620 + 3.29339i) q^{46} +(-2.25725 - 1.30323i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(1.61741 - 6.81058i) q^{49} +(3.06235 - 3.53414i) q^{50} +(2.64841 + 5.13719i) q^{51} +(-1.37453 - 0.475729i) q^{52} +(0.00465997 + 0.00592564i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-0.421689 - 0.656161i) q^{55} +(-2.45385 + 0.989260i) q^{56} +(-0.0992226 - 0.0453135i) q^{57} +(4.72233 + 6.63159i) q^{58} +(-2.47952 - 6.19355i) q^{59} +(-0.260692 + 0.505673i) q^{60} +(8.29940 - 7.91346i) q^{61} +(3.06922 - 0.441287i) q^{62} +(-1.73743 - 1.99533i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.781991 + 0.270650i) q^{65} +(-0.992234 - 0.946093i) q^{66} +(0.872871 + 0.621569i) q^{67} +(2.88984 - 5.00536i) q^{68} +(4.74381 - 0.704494i) q^{69} +(-0.749452 + 1.30537i) q^{70} +(-2.01093 - 4.40333i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(2.71127 - 14.0674i) q^{73} +(-6.28775 - 0.299523i) q^{74} +(-0.885002 - 4.59183i) q^{75} +(0.0155237 + 0.107970i) q^{76} +(-2.50947 - 2.61915i) q^{77} +(-1.22362 + 0.786376i) q^{78} +(2.07004 - 2.63227i) q^{79} +(0.566340 - 0.0540789i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(4.72541 - 6.00885i) q^{82} +(5.45937 - 3.50853i) q^{83} +(-0.739257 + 2.54037i) q^{84} +(-0.467954 - 3.25469i) q^{85} +(-0.331528 - 1.72013i) q^{86} +(8.13193 + 0.387372i) q^{87} +(-0.259462 + 1.34622i) q^{88} +(1.59676 - 6.58194i) q^{89} +(0.236336 + 0.517504i) q^{90} +(-3.32808 + 1.93221i) q^{91} +(-3.15735 - 3.60986i) q^{92} +(1.55039 - 2.68535i) q^{93} +(2.12315 + 1.51189i) q^{94} +(0.0449130 + 0.0428245i) q^{95} +(0.945001 - 0.327068i) q^{96} +(2.06907 + 1.32971i) q^{97} +(-2.25747 + 6.62600i) q^{98} +(-1.35704 + 0.195113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	0.505673	−	0.260692i	0.226144	−	0.116585i	−0.341432	−	0.939907i	$-0.610912\pi$
$5$	0.505673	−	0.260692i	0.226144	−	0.116585i	0.567575	+	0.823321i	$0.307882\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	2.07574	−	1.64052i	0.784557	−	0.620057i
$7$	2.07574	−	1.64052i	0.784557	−	0.620057i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	−0.528163	+	0.211445i	−0.167020	+	0.0668647i
$11$	−0.130321	−	1.36478i	−0.0392933	−	0.411498i	−0.993624	−	0.112746i	$-0.964036\pi$
$11$	−0.130321	−	1.36478i	−0.0392933	−	0.411498i	0.954331	−	0.298753i	$-0.0965705\pi$
$12$	−0.814576	+	0.580057i	−0.235148	+	0.167448i
$13$	−1.43972	−	0.207001i	−0.399307	−	0.0574116i	−0.0602636	−	0.998182i	$-0.519194\pi$
$13$	−1.43972	−	0.207001i	−0.399307	−	0.0574116i	−0.339043	+	0.940771i	$0.610103\pi$
$14$	−2.22228	+	1.43578i	−0.593930	+	0.383727i
$15$	−0.160282	+	0.545871i	−0.0413847	+	0.140943i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	1.89035	−	5.46181i	0.458477	−	1.32468i	−0.444801	−	0.895629i	$-0.646726\pi$
$17$	1.89035	−	5.46181i	0.458477	−	1.32468i	0.903279	−	0.429054i	$-0.141153\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	0.0356766	+	0.103081i	0.00818476	+	0.0236483i	0.949019	−	0.315218i	$-0.102078\pi$
$19$	0.0356766	+	0.103081i	0.00818476	+	0.0236483i	−0.940834	+	0.338867i	$0.889956\pi$
$20$	0.545871	−	0.160282i	0.122060	−	0.0358402i
$21$	−0.245128	+	2.63437i	−0.0534914	+	0.574867i
$22$			1.37099i			0.292297i
$23$	−3.78347	−	2.94710i	−0.788907	−	0.614512i
$23$	−3.78347	−	2.94710i	−0.788907	−	0.614512i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−2.71254	+	3.80923i	−0.542508	+	0.761846i
$26$	1.41352	+	0.342917i	0.277215	+	0.0672516i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	2.34870	−	1.21803i	0.443863	−	0.230187i
$29$	−5.33132	−	6.15267i	−0.990002	−	1.14252i	−0.989791	−	0.142523i	$-0.954479\pi$
$29$	−5.33132	−	6.15267i	−0.990002	−	1.14252i	−0.000210253	−	1.00000i	$-0.500067\pi$
$30$	0.211445	−	0.528163i	0.0386044	−	0.0964290i
$31$	−3.01337	+	0.731036i	−0.541218	+	0.131298i	−0.497043	−	0.867726i	$-0.665581\pi$
$31$	−3.01337	+	0.731036i	−0.541218	+	0.131298i	−0.0441745	+	0.999024i	$0.514066\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	1.07767	+	0.847492i	0.187599	+	0.147529i
$34$	−2.40097	+	5.25739i	−0.411763	+	0.901635i
$35$	0.621976	−	1.37069i	0.105133	−	0.231690i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	6.28775	−	0.299523i	1.03370	−	0.0492412i	0.476133	−	0.879373i	$-0.342038\pi$
$37$	6.28775	−	0.299523i	1.03370	−	0.0492412i	0.557567	+	0.830132i	$0.311735\pi$
$38$	−0.0257166	−	0.106005i	−0.00417178	−	0.0171963i
$39$	1.14333	−	0.899128i	0.183080	−	0.143976i
$40$	−0.558635	+	0.107668i	−0.0883280	+	0.0170238i
$41$	−4.13284	+	6.43082i	−0.645440	+	1.00432i	0.352217	+	0.935918i	$0.385428\pi$
$41$	−4.13284	+	6.43082i	−0.645440	+	1.00432i	−0.997658	+	0.0684065i	$0.978209\pi$
$42$	0.494431	−	2.59914i	0.0762924	−	0.401056i
$43$	0.493536	+	1.68083i	0.0752636	+	0.256324i	0.988527	−	0.151046i	$-0.0482641\pi$
$43$	0.493536	+	1.68083i	0.0752636	+	0.256324i	−0.913263	+	0.407370i	$0.866446\pi$
$44$	0.130321	−	1.36478i	0.0196467	−	0.205749i
$45$	−0.284458	−	0.492696i	−0.0424045	−	0.0734468i
$46$	3.48620	+	3.29339i	0.514011	+	0.485584i
$47$	−2.25725	−	1.30323i	−0.329254	−	0.190095i	0.326256	−	0.945282i	$-0.394213\pi$
$47$	−2.25725	−	1.30323i	−0.329254	−	0.190095i	−0.655510	+	0.755186i	$0.727546\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	1.61741	−	6.81058i	0.231059	−	0.972940i
$50$	3.06235	−	3.53414i	0.433081	−	0.499803i
$51$	2.64841	+	5.13719i	0.370851	+	0.719351i
$52$	−1.37453	−	0.475729i	−0.190613	−	0.0659717i
$53$	0.00465997	+	0.00592564i	0.000640097	+	0.000813949i	0.786373	−	0.617752i	$-0.211956\pi$
$53$	0.00465997	+	0.00592564i	0.000640097	+	0.000813949i	−0.785733	+	0.618566i	$0.787714\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	−0.421689	−	0.656161i	−0.0568605	−	0.0884767i
$56$	−2.45385	+	0.989260i	−0.327909	+	0.132195i
$57$	−0.0992226	−	0.0453135i	−0.0131424	−	0.00600191i
$58$	4.72233	+	6.63159i	0.620073	+	0.870770i
$59$	−2.47952	−	6.19355i	−0.322806	−	0.806331i	−0.997659	−	0.0683791i	$-0.978217\pi$
$59$	−2.47952	−	6.19355i	−0.322806	−	0.806331i	0.674853	−	0.737952i	$-0.264207\pi$
$60$	−0.260692	+	0.505673i	−0.0336552	+	0.0652821i
$61$	8.29940	−	7.91346i	1.06263	−	1.01322i	0.0627447	−	0.998030i	$-0.480015\pi$
$61$	8.29940	−	7.91346i	1.06263	−	1.01322i	0.999885	−	0.0151854i	$-0.00483386\pi$
$62$	3.06922	−	0.441287i	0.389791	−	0.0560435i
$63$	−1.73743	−	1.99533i	−0.218895	−	0.251388i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−0.781991	+	0.270650i	−0.0969940	+	0.0335700i
$66$	−0.992234	−	0.946093i	−0.122136	−	0.116456i
$67$	0.872871	+	0.621569i	0.106638	+	0.0759367i	0.632132	−	0.774861i	$-0.282180\pi$
$67$	0.872871	+	0.621569i	0.106638	+	0.0759367i	−0.525494	+	0.850797i	$0.676119\pi$
$68$	2.88984	−	5.00536i	0.350445	−	0.606989i
$69$	4.74381	−	0.704494i	0.571087	−	0.0848111i
$70$	−0.749452	+	1.30537i	−0.0895767	+	0.156021i
$71$	−2.01093	−	4.40333i	−0.238654	−	0.522579i	0.751970	−	0.659198i	$-0.229104\pi$
$71$	−2.01093	−	4.40333i	−0.238654	−	0.522579i	−0.990624	+	0.136618i	$0.956377\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	2.71127	−	14.0674i	0.317331	−	1.64647i	−0.376564	−	0.926391i	$-0.622894\pi$
$73$	2.71127	−	14.0674i	0.317331	−	1.64647i	0.693894	−	0.720077i	$-0.255894\pi$
$74$	−6.28775	−	0.299523i	−0.730937	−	0.0348188i
$75$	−0.885002	−	4.59183i	−0.102191	−	0.530219i
$76$	0.0155237	+	0.107970i	0.00178069	+	0.0123850i
$77$	−2.50947	−	2.61915i	−0.285980	−	0.298480i
$78$	−1.22362	+	0.786376i	−0.138548	+	0.0890395i
$79$	2.07004	−	2.63227i	0.232897	−	0.296153i	−0.655531	−	0.755168i	$-0.727555\pi$
$79$	2.07004	−	2.63227i	0.232897	−	0.296153i	0.888428	+	0.459015i	$0.151798\pi$
$80$	0.566340	−	0.0540789i	0.0633187	−	0.00604621i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	4.72541	−	6.00885i	0.521834	−	0.663566i
$83$	5.45937	−	3.50853i	0.599244	−	0.385111i	−0.205566	−	0.978643i	$-0.565903\pi$
$83$	5.45937	−	3.50853i	0.599244	−	0.385111i	0.804810	+	0.593532i	$0.202267\pi$
$84$	−0.739257	+	2.54037i	−0.0806595	+	0.277178i
$85$	−0.467954	−	3.25469i	−0.0507567	−	0.353021i
$86$	−0.331528	−	1.72013i	−0.0357496	−	0.185487i
$87$	8.13193	+	0.387372i	0.871835	+	0.0415306i
$88$	−0.259462	+	1.34622i	−0.0276588	+	0.143507i
$89$	1.59676	−	6.58194i	0.169256	−	0.697684i	−0.822415	−	0.568888i	$-0.807374\pi$
$89$	1.59676	−	6.58194i	0.169256	−	0.697684i	0.991671	−	0.128796i	$-0.0411112\pi$
$90$	0.236336	+	0.517504i	0.0249120	+	0.0545497i
$91$	−3.32808	+	1.93221i	−0.348877	+	0.202550i
$92$	−3.15735	−	3.60986i	−0.329177	−	0.376354i
$93$	1.55039	−	2.68535i	0.160768	−	0.278458i
$94$	2.12315	+	1.51189i	0.218987	+	0.155940i
$95$	0.0449130	+	0.0428245i	0.00460798	+	0.00439370i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	2.06907	+	1.32971i	0.210082	+	0.135011i	0.641451	−	0.767164i	$-0.278333\pi$
$97$	2.06907	+	1.32971i	0.210082	+	0.135011i	−0.431369	+	0.902176i	$0.641969\pi$
$98$	−2.25747	+	6.62600i	−0.228039	+	0.669327i
$99$	−1.35704	+	0.195113i	−0.136387	+	0.0196096i
$100$	−3.38442	+	3.22704i	−0.338442	+	0.322704i
$101$	3.34776	−	6.49375i	0.333115	−	0.646152i	−0.661483	−	0.749960i	$-0.730072\pi$
$101$	3.34776	−	6.49375i	0.333115	−	0.646152i	0.994597	+	0.103808i	$0.0331028\pi$
$102$	−2.14809	−	5.36568i	−0.212693	−	0.531281i
$103$	2.99117	+	4.20051i	0.294729	+	0.413889i	0.935215	−	0.354081i	$-0.115206\pi$
$103$	2.99117	+	4.20051i	0.294729	+	0.413889i	−0.640486	+	0.767970i	$0.721267\pi$
$104$	1.32308	+	0.604232i	0.129739	+	0.0592498i
$105$	0.562806	+	1.39603i	0.0549242	+	0.136239i
$106$	−0.00407561	−	0.00634177i	−0.000395858	−	0.000615967i
$107$	3.06523	+	3.21472i	0.296327	+	0.310778i	0.855019	−	0.518596i	$-0.173545\pi$
$107$	3.06523	+	3.21472i	0.296327	+	0.310778i	−0.558692	+	0.829375i	$0.688697\pi$
$108$	0.618159	+	0.786053i	0.0594824	+	0.0756380i
$109$	−9.94386	−	3.44160i	−0.952449	−	0.329646i	−0.193724	−	0.981056i	$-0.562057\pi$
$109$	−9.94386	−	3.44160i	−0.952449	−	0.329646i	−0.758726	+	0.651410i	$0.774178\pi$
$110$	0.357407	+	0.693274i	0.0340775	+	0.0661011i
$111$	−4.12227	+	4.75736i	−0.391269	+	0.451548i
$112$	2.53677	−	0.751528i	0.239702	−	0.0710127i
$113$	−5.17486	+	2.36328i	−0.486810	+	0.222319i	−0.643671	−	0.765302i	$-0.722590\pi$
$113$	−5.17486	+	2.36328i	−0.486810	+	0.222319i	0.156862	+	0.987621i	$0.449862\pi$
$114$	0.0944660	+	0.0545400i	0.00884755	+	0.00510814i
$115$	−2.68148	−	0.503945i	−0.250049	−	0.0469932i
$116$	−4.07058	−	7.05045i	−0.377944	−	0.654618i
$117$	−0.138261	+	1.44794i	−0.0127823	+	0.133862i
$118$	1.87956	+	6.40120i	0.173028	+	0.589278i
$119$	−5.03631	−	14.4385i	−0.461678	−	1.32357i
$120$	0.307579	−	0.478603i	0.0280780	−	0.0436902i
$121$	8.95556	−	1.72604i	0.814142	−	0.156913i
$122$	−9.01404	+	7.08872i	−0.816093	+	0.641783i
$123$	−1.80222	−	7.42885i	−0.162501	−	0.669836i
$124$	−3.09727	+	0.147541i	−0.278143	+	0.0132496i
$125$	−0.783446	+	5.44899i	−0.0700736	+	0.487372i
$126$	1.53989	+	2.15145i	0.137184	+	0.191666i
$127$	−8.49232	+	18.5956i	−0.753571	+	1.65009i	0.00626834	+	0.999980i	$0.498005\pi$
$127$	−8.49232	+	18.5956i	−0.753571	+	1.65009i	−0.759840	+	0.650111i	$0.774723\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	−1.55705	−	0.802717i	−0.137091	−	0.0706753i
$130$	0.804177	−	0.195091i	0.0705310	−	0.0171106i
$131$	−2.05079	+	5.12263i	−0.179178	+	0.447566i	−0.990582	−	0.136920i	$-0.956280\pi$
$131$	−2.05079	+	5.12263i	−0.179178	+	0.447566i	0.811404	+	0.584486i	$0.198704\pi$
$132$	0.897809	+	1.03613i	0.0781443	+	0.0901833i
$133$	0.243161	+	0.155441i	0.0210847	+	0.0134784i
$134$	−0.809835	−	0.701726i	−0.0699591	−	0.0606199i
$135$	0.552879	+	0.134127i	0.0475843	+	0.0115438i
$136$	−3.35255	+	4.70800i	−0.287479	+	0.403707i
$137$	−5.45167	+	3.14752i	−0.465768	+	0.268911i	−0.714466	−	0.699670i	$-0.753330\pi$
$137$	−5.45167	+	3.14752i	−0.465768	+	0.268911i	0.248699	+	0.968581i	$0.419997\pi$
$138$	−4.78929	+	0.250377i	−0.407692	+	0.0213135i
$139$		−	12.5404i		−	1.06367i	−0.846850	−	0.531833i	$-0.821504\pi$
$139$		−	12.5404i		−	1.06367i	0.846850	−	0.531833i	$-0.178496\pi$
$140$	0.870142	−	1.22821i	0.0735404	−	0.103803i
$141$	2.50087	−	0.734323i	0.210612	−	0.0618411i
$142$	1.58327	+	4.57454i	0.132865	+	0.383887i
$143$	−0.0948852	+	1.99189i	−0.00793470	+	0.166570i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−4.29986	−	1.72140i	−0.357084	−	0.142955i
$146$	−4.03619	+	13.7460i	−0.334038	+	1.13763i
$147$	3.81291	+	5.87041i	0.314483	+	0.484183i
$148$	6.23081	+	0.895855i	0.512170	+	0.0736389i
$149$	18.5455	−	13.2062i	1.51931	−	1.08190i	0.550272	−	0.834985i	$-0.314524\pi$
$149$	18.5455	−	13.2062i	1.51931	−	1.08190i	0.969038	−	0.246911i	$-0.0794154\pi$
$150$	0.444514	+	4.65516i	0.0362944	+	0.380092i
$151$	−6.30421	+	2.52382i	−0.513029	+	0.205386i	−0.613708	−	0.789533i	$-0.710323\pi$
$151$	−6.30421	+	2.52382i	−0.513029	+	0.205386i	0.100679	+	0.994919i	$0.467899\pi$
$152$	−0.00519023	−	0.108956i	−0.000420984	−	0.00883753i
$153$	−5.54557	−	1.62833i	−0.448333	−	0.131642i
$154$	2.24914	+	2.84583i	0.181241	+	0.229323i
$155$	−1.33320	+	1.15523i	−0.107086	+	0.0927902i
$156$	1.29283	−	0.666502i	0.103510	−	0.0533629i
$157$	10.3365	+	1.99219i	0.824939	+	0.158994i	0.584214	−	0.811599i	$-0.301403\pi$
$157$	10.3365	+	1.99219i	0.824939	+	0.158994i	0.240725	+	0.970593i	$0.422615\pi$
$158$	−2.31088	+	2.42358i	−0.183843	+	0.192809i
$159$	−0.00750434		0.000716577i	−0.000595133		5.68283e-5i
$160$	−0.568916			−0.0449768
$161$	−12.6883	+	0.0894278i	−0.999975	+	0.00704790i
$162$	1.00000			0.0785674
$163$	21.4323	+	2.04654i	1.67871	+	0.160297i	0.890460	−	0.455061i	$-0.150382\pi$
$163$	21.4323	+	2.04654i	1.67871	+	0.160297i	0.788248	+	0.615358i	$0.210989\pi$
$164$	−5.27519	+	5.53246i	−0.411923	+	0.432012i
$165$	0.765885	+	0.147612i	0.0596240	+	0.0114916i
$166$	−5.76816	+	2.97369i	−0.447696	+	0.230803i
$167$	−1.98099	+	1.71654i	−0.153294	+	0.132830i	−0.728131	−	0.685438i	$-0.759611\pi$
$167$	−1.98099	+	1.71654i	−0.153294	+	0.132830i	0.574837	+	0.818268i	$0.305065\pi$
$168$	0.977387	−	2.45860i	0.0754070	−	0.189685i
$169$	−10.4435	−	3.06648i	−0.803343	−	0.235883i
$170$	0.156457	+	3.28443i	0.0119997	+	0.251905i
$171$	0.101266	−	0.0405409i	0.00774403	−	0.00310024i
$172$	0.166518	+	1.74386i	0.0126969	+	0.132968i
$173$	16.7388	−	11.9197i	1.27263	−	0.906237i	0.274169	−	0.961681i	$-0.411597\pi$
$173$	16.7388	−	11.9197i	1.27263	−	0.906237i	0.998462	+	0.0554449i	$0.0176577\pi$
$174$	−8.05829	−	1.15861i	−0.610897	−	0.0878338i
$175$	0.618571	+	12.3569i	0.0467596	+	0.934097i
$176$	0.386253	−	1.31546i	0.0291149	−	0.0991564i
$177$	6.19355	+	2.47952i	0.465536	+	0.186372i
$178$	−2.21518	+	6.40036i	−0.166035	+	0.479727i
$179$	−0.518069	+	10.8756i	−0.0387223	+	0.812881i	0.893076	+	0.449905i	$0.148542\pi$
$179$	−0.518069	+	10.8756i	−0.0387223	+	0.812881i	−0.931799	+	0.362976i	$0.881761\pi$
$180$	−0.186074	−	0.537626i	−0.0138692	−	0.0400723i
$181$	−3.04696	+	0.894667i	−0.226478	+	0.0665001i	−0.393003	−	0.919537i	$-0.628564\pi$
$181$	−3.04696	+	0.894667i	−0.226478	+	0.0665001i	0.166524	+	0.986037i	$0.446746\pi$
$182$	3.49667	−	1.60710i	0.259191	−	0.119126i
$183$			11.4675i			0.847700i
$184$	2.79992	+	3.89364i	0.206413	+	0.287043i
$185$	3.10146	−	1.79063i	0.228024	−	0.131650i
$186$	−1.79863	+	2.52582i	−0.131882	+	0.185202i
$187$	−7.70055	−	1.86813i	−0.563120	−	0.136611i
$188$	−1.96983	−	1.70686i	−0.143664	−	0.124486i
$189$	2.64305	+	0.119502i	0.192254	+	0.00869250i
$190$	−0.0406389	−	0.0468998i	−0.00294826	−	0.00340247i
$191$	−4.16432	+	10.4020i	−0.301320	+	0.752660i	0.698011	+	0.716087i	$0.254068\pi$
$191$	−4.16432	+	10.4020i	−0.301320	+	0.752660i	−0.999331	+	0.0365732i	$0.988356\pi$
$192$	−0.971812	+	0.235759i	−0.0701345	+	0.0170144i
$193$	8.22315	+	4.23933i	0.591915	+	0.305154i	0.728036	−	0.685539i	$-0.240433\pi$
$193$	8.22315	+	4.23933i	0.591915	+	0.305154i	−0.136121	+	0.990692i	$0.543464\pi$
$194$	−1.93330	−	1.52036i	−0.138803	−	0.109156i
$195$	0.343757	−	0.752723i	0.0246170	−	0.0539036i
$196$	2.87709	−	6.38141i	0.205507	−	0.455815i
$197$	0.401728	−	2.79408i	0.0286219	−	0.199070i	−0.970493	−	0.241128i	$-0.922483\pi$
$197$	0.401728	−	2.79408i	0.0286219	−	0.199070i	0.999115	+	0.0420585i	$0.0133916\pi$
$198$	1.36944	−	0.0652345i	0.0973219	−	0.00463601i
$199$	2.60401	+	10.7339i	0.184594	+	0.760906i	0.986541	+	0.163511i	$0.0522821\pi$
$199$	2.60401	+	10.7339i	0.184594	+	0.760906i	−0.801948	+	0.597394i	$0.796203\pi$
$200$	3.67585	−	2.89072i	0.259922	−	0.204405i
$201$	−1.05220	+	0.202795i	−0.0742165	+	0.0143041i
$202$	−3.94987	+	6.14612i	−0.277912	+	0.432440i
$203$	−21.1600	−	4.02524i	−1.48514	−	0.282517i
$204$	1.62833	+	5.54557i	0.114006	+	0.388268i
$205$	−0.413397	+	4.32929i	−0.0288729	+	0.302371i
$206$	−2.57834	−	4.46582i	−0.179642	−	0.311149i
$207$	−2.76373	+	3.91941i	−0.192093	+	0.272418i
$208$	−1.25966	−	0.727263i	−0.0873414	−	0.0504266i
$209$	0.136034	−	0.0621244i	0.00940964	−	0.00429724i
$210$	−0.427556	−	1.44321i	−0.0295042	−	0.0995909i
$211$	−6.74135	+	7.77993i	−0.464093	+	0.535592i	−0.938759	−	0.344574i	$-0.888023\pi$
$211$	−6.74135	+	7.77993i	−0.464093	+	0.535592i	0.474666	+	0.880166i	$0.342569\pi$
$212$	0.00345433	+	0.00670046i	0.000237244	+	0.000460190i
$213$	4.57454	+	1.58327i	0.313443	+	0.108484i
$214$	−2.74577	−	3.49153i	−0.187697	−	0.238676i
$215$	0.687748	+	0.721289i	0.0469040	+	0.0491915i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	−5.05571	+	6.46093i	−0.343204	+	0.438596i
$218$	9.57169	+	4.37125i	0.648277	+	0.296058i
$219$	8.31008	+	11.6699i	0.561543	+	0.788577i
$220$	−0.289889	−	0.724108i	−0.0195443	−	0.0488194i
$221$	−3.85218	+	7.47218i	−0.259125	+	0.502633i
$222$	4.55582	−	4.34397i	0.305767	−	0.291548i
$223$	−21.1401	+	3.03949i	−1.41565	+	0.203539i	−0.807305	−	0.590135i	$-0.799075\pi$
$223$	−21.1401	+	3.03949i	−1.41565	+	0.203539i	−0.608343	+	0.793674i	$0.708166\pi$
$224$	−2.59672	+	0.506989i	−0.173501	+	0.0338746i
$225$	3.93398	+	2.52822i	0.262266	+	0.168548i
$226$	5.37607	−	1.86068i	0.357611	−	0.123770i
$227$	18.1719	+	17.3269i	1.20611	+	1.15002i	0.984592	+	0.174868i	$0.0559499\pi$
$227$	18.1719	+	17.3269i	1.20611	+	1.15002i	0.221519	+	0.975156i	$0.428899\pi$
$228$	−0.0888539	−	0.0632726i	−0.00588449	−	0.00419033i
$229$	1.25397	−	2.17194i	0.0828648	−	0.143526i	−0.821615	−	0.570043i	$-0.806926\pi$
$229$	1.25397	−	2.17194i	0.0828648	−	0.143526i	0.904479	+	0.426517i	$0.140260\pi$
$230$	2.62144	+	0.756555i	0.172852	+	0.0498857i
$231$	3.62730	−	0.00876697i	0.238659	−	0.000576825i
$232$	3.38196	+	7.40545i	0.222036	+	0.486192i
$233$	−3.62880	+	14.9581i	−0.237730	+	0.979938i	0.720389	+	0.693570i	$0.243963\pi$
$233$	−3.62880	+	14.9581i	−0.237730	+	0.979938i	−0.958120	+	0.286368i	$0.907552\pi$
$234$	0.275271	−	1.42824i	0.0179950	−	0.0933670i
$235$	−1.48117	−	0.0705570i	−0.0966211	−	0.00460263i
$236$	−1.26258	−	6.55087i	−0.0821868	−	0.426426i
$237$	0.476571	+	3.31463i	0.0309566	+	0.215308i
$238$	3.64104	+	14.8518i	0.236014	+	0.962700i
$239$	−24.7381	+	15.8982i	−1.60017	+	1.02837i	−0.633036	+	0.774123i	$0.718191\pi$
$239$	−24.7381	+	15.8982i	−1.60017	+	1.02837i	−0.967139	+	0.254247i	$0.918172\pi$
$240$	−0.351681	+	0.447198i	−0.0227009	+	0.0288665i
$241$	7.17362	−	0.684997i	0.462093	−	0.0441246i	0.138586	−	0.990350i	$-0.455744\pi$
$241$	7.17362	−	0.684997i	0.462093	−	0.0441246i	0.323507	+	0.946226i	$0.395138\pi$
$242$	−9.07908	+	0.866947i	−0.583625	+	0.0557295i
$243$	0.618159	−	0.786053i	0.0396549	−	0.0504253i
$244$	9.64705	−	6.19978i	0.617589	−	0.396901i
$245$	−0.957586	−	3.86557i	−0.0611779	−	0.246962i
$246$	1.08790	+	7.56652i	0.0693620	+	0.482424i
$247$	−0.0300265	−	0.155792i	−0.00191054	−	0.00991283i
$248$	3.09727	+	0.147541i	0.196677	+	0.00936886i
$249$	−1.22816	+	6.37230i	−0.0778314	+	0.403828i
$250$	1.29786	−	5.34984i	0.0820838	−	0.338354i
$251$	−5.90009	−	12.9194i	−0.372410	−	0.815464i	−0.999338	−	0.0363869i	$-0.988415\pi$
$251$	−5.90009	−	12.9194i	−0.372410	−	0.815464i	0.626928	−	0.779077i	$-0.284312\pi$
$252$	−1.32841	−	2.28808i	−0.0836819	−	0.144136i
$253$	−3.52909	+	5.54769i	−0.221872	+	0.348780i
$254$	10.2215	−	17.7041i	0.641353	−	1.11086i
$255$	2.67845	+	1.90732i	0.167731	+	0.119441i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	15.0742	−	5.21724i	0.940305	−	0.325443i	0.186436	−	0.982467i	$-0.440306\pi$
$257$	15.0742	−	5.21724i	0.940305	−	0.325443i	0.753869	+	0.657024i	$0.228185\pi$
$258$	1.47370	+	0.947089i	0.0917485	+	0.0589632i
$259$	12.5604	−	10.9369i	0.780464	−	0.679586i
$260$	−0.819080	+	0.117766i	−0.0507972	+	0.00730353i
$261$	−5.89203	+	5.61804i	−0.364708	+	0.347748i
$262$	2.52844	−	4.90449i	0.156208	−	0.303000i
$263$	3.36139	+	8.39636i	0.207272	+	0.517741i	0.995181	−	0.0980501i	$-0.0312606\pi$
$263$	3.36139	+	8.39636i	0.207272	+	0.517741i	−0.787909	+	0.615792i	$0.788836\pi$
$264$	−0.795254	−	1.11678i	−0.0489445	−	0.0687329i
$265$	0.00390119	+	0.00178161i	0.000239648	+	0.000109444i
$266$	−0.227284	−	0.177851i	−0.0139357	−	0.0109047i
$267$	3.66168	+	5.69769i	0.224091	+	0.348693i
$268$	0.739465	+	0.775528i	0.0451700	+	0.0473729i
$269$	0.166611	+	0.211863i	0.0101584	+	0.0129175i	0.791106	−	0.611679i	$-0.209506\pi$
$269$	0.166611	+	0.211863i	0.0101584	+	0.0129175i	−0.780947	+	0.624597i	$0.785263\pi$
$270$	−0.537626	−	0.186074i	−0.0327189	−	0.0113241i
$271$	−10.2542	−	19.8904i	−0.622900	−	1.20826i	−0.963414	−	0.268018i	$-0.913631\pi$
$271$	−10.2542	−	19.8904i	−0.622900	−	1.20826i	0.340514	−	0.940239i	$-0.389399\pi$
$272$	3.78489	−	4.36800i	0.229493	−	0.264849i
$273$	0.898233	−	3.74202i	0.0543635	−	0.226477i
$274$	5.72617	−	2.61506i	0.345931	−	0.157981i
$275$	5.55228	+	3.20561i	0.334815	+	0.193306i
$276$	4.79140	+	0.206008i	0.288409	+	0.0124002i
$277$	6.55488	+	11.3534i	0.393844	+	0.682158i	0.992953	−	0.118509i	$-0.0378116\pi$
$277$	6.55488	+	11.3534i	0.393844	+	0.682158i	−0.599109	+	0.800668i	$0.704478\pi$
$278$	−1.19204	+	12.4836i	−0.0714940	+	0.748719i
$279$	0.873590	+	2.97517i	0.0523005	+	0.178119i
$280$	−0.982951	+	1.13994i	−0.0587426	+	0.0681245i
$281$	17.6413	−	27.4504i	1.05239	−	1.63755i	0.333032	−	0.942915i	$-0.391928\pi$
$281$	17.6413	−	27.4504i	1.05239	−	1.63755i	0.719359	−	0.694638i	$-0.244435\pi$
$282$	−2.55935	+	0.493275i	−0.152407	+	0.0293741i
$283$	−10.5243	+	8.27640i	−0.625605	+	0.491981i	−0.879908	−	0.475143i	$-0.842396\pi$
$283$	−10.5243	+	8.27640i	−0.625605	+	0.491981i	0.254304	+	0.967124i	$0.418154\pi$
$284$	−1.14126	−	4.70433i	−0.0677212	−	0.279151i
$285$	−0.0619871	+	0.00295281i	−0.00367180	+	0.000174909i
$286$	0.283796	−	1.97385i	0.0167812	−	0.116716i
$287$	1.97116	+	20.1287i	0.116354	+	1.18816i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	−12.8950	−	10.1408i	−0.758532	−	0.596516i
$290$	4.11676	+	2.12234i	0.241744	+	0.124628i
$291$	−2.39017	+	0.579850i	−0.140114	+	0.0339914i
$292$	5.32456	−	13.3001i	0.311596	−	0.778329i
$293$	5.99682	+	6.92070i	0.350338	+	0.404312i	0.903379	−	0.428842i	$-0.141078\pi$
$293$	5.99682	+	6.92070i	0.350338	+	0.404312i	−0.553041	+	0.833154i	$0.686533\pi$
$294$	−3.23762	−	6.20627i	−0.188822	−	0.361957i
$295$	−2.86844	−	2.48552i	−0.167007	−	0.144712i
$296$	−6.11744	−	1.48408i	−0.355569	−	0.0862601i
$297$	0.795254	−	1.11678i	0.0461453	−	0.0648020i
$298$	−19.7169	+	11.3836i	−1.14217	+	0.659432i
$299$	4.83708	+	5.02618i	0.279736	+	0.290671i
$300$		−	4.67633i		−	0.269988i
$301$	3.78188	+	2.67932i	0.217984	+	0.154433i
$302$	6.51557	−	1.91314i	0.374929	−	0.110089i
$303$	2.38953	+	6.90409i	0.137275	+	0.396630i
$304$	−0.00519023	+	0.108956i	−0.000297680	+	0.00624908i
$305$	2.13380	−	6.16521i	0.122181	−	0.353019i
$306$	5.36568	+	2.14809i	0.306735	+	0.122798i
$307$	0.677997	−	2.30904i	0.0386953	−	0.131784i	−0.937880	−	0.346960i	$-0.887214\pi$
$307$	0.677997	−	2.30904i	0.0386953	−	0.131784i	0.976575	+	0.215175i	$0.0690323\pi$
$308$	−1.96844	−	3.04674i	−0.112162	−	0.173604i
$309$	−5.10420	−	0.733873i	−0.290368	−	0.0417486i
$310$	1.43698	−	1.02327i	0.0816149	−	0.0581177i
$311$	2.29884	+	24.0745i	0.130355	+	1.36514i	0.789789	+	0.613379i	$0.210190\pi$
$311$	2.29884	+	24.0745i	0.130355	+	1.36514i	−0.659434	+	0.751763i	$0.729204\pi$
$312$	−1.35033	+	0.540593i	−0.0764477	+	0.0306050i
$313$	0.344199	+	7.22562i	0.0194553	+	0.408416i	0.987498	+	0.157631i	$0.0503857\pi$
$313$	0.344199	+	7.22562i	0.0194553	+	0.408416i	−0.968043	+	0.250785i	$0.919311\pi$
$314$	−10.1003	−	2.96571i	−0.569992	−	0.167365i
$315$	−1.39874	−	0.556051i	−0.0788099	−	0.0313299i
$316$	2.53079	−	2.19294i	0.142368	−	0.123363i
$317$	−20.1514	+	10.3887i	−1.13181	+	0.583490i	−0.919257	−	0.393659i	$-0.871209\pi$
$317$	−20.1514	+	10.3887i	−1.13181	+	0.583490i	−0.212556	+	0.977149i	$0.568179\pi$
$318$	0.00740224	+	0.00142667i	0.000415097	+	8.00034e-5i
$319$	−7.70229	+	8.07793i	−0.431246	+	0.452277i
$320$	0.566340	+	0.0540789i	0.0316594	+	0.00302310i
$321$	−4.44185			−0.247920
$322$	12.6393	+	1.11707i	0.704361	+	0.0622521i
$323$	0.630448			0.0350791
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	4.69381	−	4.92273i	0.260366	−	0.273064i
$326$	−21.1407	−	4.07454i	−1.17088	−	0.225668i
$327$	9.35286	−	4.82173i	0.517214	−	0.266642i
$328$	5.77720	−	5.00597i	0.318992	−	0.276408i
$329$	−6.82344	+	0.997902i	−0.376189	+	0.0550161i
$330$	−0.748385	−	0.219746i	−0.0411973	−	0.0120966i
$331$	0.560904	+	11.7748i	0.0308301	+	0.647203i	0.960411	+	0.278586i	$0.0898656\pi$
$331$	0.560904	+	11.7748i	0.0308301	+	0.647203i	−0.929581	+	0.368617i	$0.879831\pi$
$332$	6.02471	−	2.41193i	0.330649	−	0.132372i
$333$	−0.598367	−	6.26638i	−0.0327903	−	0.343396i
$334$	2.13519	−	1.52046i	0.116832	−	0.0831958i
$335$	0.603426	+	0.0867595i	0.0329687	+	0.00474018i
$336$	−1.20667	+	2.35456i	−0.0658290	+	0.128452i
$337$	−5.16499	+	17.5903i	−0.281355	+	0.958207i	0.690639	+	0.723200i	$0.257330\pi$
$337$	−5.16499	+	17.5903i	−0.281355	+	0.958207i	−0.971994	+	0.235007i	$0.924489\pi$
$338$	10.1047	+	4.04531i	0.549622	+	0.220036i
$339$	1.86068	−	5.37607i	0.101058	−	0.291988i
$340$	0.156457	−	3.28443i	0.00848506	−	0.178123i
$341$	1.39041	+	4.01734i	0.0752951	+	0.217551i
$342$	−0.104661	+	0.0307314i	−0.00565944	+	0.00166176i
$343$	−7.81554	−	16.7904i	−0.422000	−	0.906596i
$344$		−	1.75179i		−	0.0944502i
$345$	2.21516	−	1.59292i	0.119260	−	0.0857598i
$346$	−17.7961	+	10.2746i	−0.956724	+	0.552365i
$347$	−9.06206	+	12.7259i	−0.486477	+	0.683162i	−0.982736	−	0.185013i	$-0.940767\pi$
$347$	−9.06206	+	12.7259i	−0.486477	+	0.683162i	0.496259	+	0.868175i	$0.334707\pi$
$348$	7.91167	+	1.91935i	0.424110	+	0.102888i
$349$	−3.39407	−	2.94098i	−0.181680	−	0.157427i	0.559273	−	0.828984i	$-0.311080\pi$
$349$	−3.39407	−	2.94098i	−0.181680	−	0.157427i	−0.740953	+	0.671557i	$0.765626\pi$
$350$	0.558832	−	12.3598i	0.0298708	−	0.660659i
$351$	−0.952512	−	1.09926i	−0.0508413	−	0.0586740i
$352$	−0.509547	+	1.27279i	−0.0271589	+	0.0678397i
$353$	6.55956	−	1.59133i	0.349130	−	0.0846980i	−0.0573592	−	0.998354i	$-0.518268\pi$
$353$	6.55956	−	1.59133i	0.349130	−	0.0846980i	0.406489	+	0.913656i	$0.366753\pi$
$354$	−5.92981	−	3.05703i	−0.315166	−	0.162479i
$355$	−2.16479	−	1.70241i	−0.114895	−	0.0903545i
$356$	2.81355	−	6.16081i	0.149118	−	0.326522i
$357$	13.9251	+	6.31873i	0.736992	+	0.334423i
$358$	1.54951	−	10.7771i	0.0818944	−	0.569588i
$359$	29.9393	−	1.42619i	1.58014	−	0.0752712i	0.760955	−	0.648805i	$-0.224731\pi$
$359$	29.9393	−	1.42619i	1.58014	−	0.0752712i	0.819182	+	0.573533i	$0.194428\pi$
$360$	0.134127	+	0.552879i	0.00706912	+	0.0291393i
$361$	14.9257	−	11.7377i	0.785561	−	0.617772i
$362$	3.11820	−	0.600984i	0.163889	−	0.0315870i
$363$	−4.93085	+	7.67255i	−0.258802	+	0.402704i
$364$	−3.63361	+	1.26745i	−0.190453	+	0.0664322i
$365$	−2.29625	−	7.82032i	−0.120191	−	0.409334i
$366$	1.09005	−	11.4155i	0.0569780	−	0.596700i
$367$	−15.9348	−	27.6000i	−0.831792	−	1.44071i	−0.896616	−	0.442809i	$-0.853982\pi$
$367$	−15.9348	−	27.6000i	−0.831792	−	1.44071i	0.0648236	−	0.997897i	$-0.479352\pi$
$368$	−2.41712	−	4.14216i	−0.126001	−	0.215925i
$369$	6.62018	+	3.82216i	0.344633	+	0.198974i
$370$	−3.25763	+	1.48771i	−0.169356	+	0.0773423i
$371$	0.0193940	+	0.00465533i	0.00100689	+	0.000241693i
$372$	2.03058	−	2.34341i	0.105281	−	0.121500i
$373$	−5.95956	−	11.5599i	−0.308575	−	0.598551i	0.682649	−	0.730746i	$-0.260828\pi$
$373$	−5.95956	−	11.5599i	−0.308575	−	0.598551i	−0.991224	+	0.132195i	$0.957797\pi$
$374$	7.48810	+	2.59166i	0.387201	+	0.134011i
$375$	−3.40298	−	4.32724i	−0.175729	−	0.223458i
$376$	1.79866	+	1.88638i	0.0927587	+	0.0972826i
$377$	6.40201	+	9.96172i	0.329720	+	0.513055i
$378$	−2.61972	−	0.370199i	−0.134744	−	0.0190410i
$379$	−0.501739	−	0.229137i	−0.0257726	−	0.0117700i	0.402487	−	0.915426i	$-0.368146\pi$
$379$	−0.501739	−	0.229137i	−0.0257726	−	0.0117700i	−0.428260	+	0.903656i	$0.640873\pi$
$380$	0.0359968	+	0.0505504i	0.00184660	+	0.00259318i
$381$	−7.59788	−	18.9786i	−0.389251	−	0.972303i
$382$	5.13423	−	9.95902i	0.262690	−	0.509548i
$383$	−2.79862	+	2.66848i	−0.143003	+	0.136353i	−0.758204	−	0.652017i	$-0.773923\pi$
$383$	−2.79862	+	2.66848i	−0.143003	+	0.136353i	0.615202	+	0.788370i	$0.289075\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	−1.95176	−	0.670233i	−0.0994709	−	0.0341582i
$386$	−7.78294	−	5.00179i	−0.396141	−	0.254585i
$387$	1.65544	−	0.572954i	0.0841509	−	0.0291249i
$388$	1.78003	+	1.69725i	0.0903671	+	0.0861649i
$389$	−13.3940	−	9.53783i	−0.679104	−	0.483587i	0.187707	−	0.982225i	$-0.439894\pi$
$389$	−13.3940	−	9.53783i	−0.679104	−	0.483587i	−0.866811	+	0.498638i	$0.833834\pi$
$390$	−0.413751	+	0.716639i	−0.0209511	+	0.0362884i
$391$	−23.2486	+	15.0935i	−1.17573	+	0.763313i
$392$	−3.47066	+	6.07903i	−0.175295	+	0.307037i
$393$	−2.29221	−	5.01924i	−0.115627	−	0.253187i
$394$	−0.665503	+	2.74324i	−0.0335275	+	0.138202i
$395$	0.360549	−	1.87071i	0.0181412	−	0.0941255i
$396$	−1.36944	−	0.0652345i	−0.0688170	−	0.00327816i
$397$	−4.76166	−	24.7058i	−0.238981	−	1.23995i	−0.880946	−	0.473217i	$-0.843093\pi$
$397$	−4.76166	−	24.7058i	−0.238981	−	1.23995i	0.641965	−	0.766734i	$-0.278119\pi$
$398$	−1.57190	−	10.9328i	−0.0787923	−	0.548013i
$399$	−0.280298	+	0.0687173i	−0.0140325	+	0.00344017i
$400$	−3.93398	+	2.52822i	−0.196699	+	0.126411i
$401$	−10.6842	+	13.5861i	−0.533544	+	0.678456i	−0.975858	−	0.218404i	$-0.929915\pi$
$401$	−10.6842	+	13.5861i	−0.533544	+	0.678456i	0.442315	+	0.896860i	$0.354157\pi$
$402$	1.06671	−	0.101859i	0.0532028	−	0.00508025i
$403$	4.48974	−	0.428718i	0.223650	−	0.0213560i
$404$	4.51621	−	5.74283i	0.224690	−	0.285717i
$405$	−0.478603	+	0.307579i	−0.0237820	+	0.0152837i
$406$	20.6816	+	6.01840i	1.02641	+	0.298688i
$407$	−1.22821	−	8.54240i	−0.0608802	−	0.423431i
$408$	−1.09381	−	5.67524i	−0.0541518	−	0.280966i
$409$	−16.3636	−	0.779496i	−0.809130	−	0.0385436i	−0.361060	−	0.932542i	$-0.617585\pi$
$409$	−16.3636	−	0.779496i	−0.809130	−	0.0385436i	−0.448069	+	0.893999i	$0.647888\pi$
$410$	0.823050	−	4.27039i	0.0406475	−	0.210899i
$411$	1.48411	−	6.11760i	0.0732059	−	0.301759i
$412$	2.14216	+	4.69069i	0.105537	+	0.231094i
$413$	−15.3075	−	8.78851i	−0.753231	−	0.432454i
$414$	3.12378	−	3.63895i	0.153526	−	0.178845i
$415$	1.84601	−	3.19738i	0.0906171	−	0.156953i
$416$	1.18482	+	0.843708i	0.0580907	+	0.0413662i
$417$	9.07593	+	8.65389i	0.444450	+	0.423783i
$418$	−0.141323	+	0.0489123i	−0.00691233	+	0.00239238i
$419$	23.2716	+	14.9558i	1.13689	+	0.730637i	0.966988	−	0.254824i	$-0.0820174\pi$
$419$	23.2716	+	14.9558i	1.13689	+	0.730637i	0.169905	+	0.985460i	$0.445654\pi$
$420$	0.288434	+	1.47732i	0.0140742	+	0.0720857i
$421$	7.70849	−	1.10831i	0.375689	−	0.0540159i	0.0481159	−	0.998842i	$-0.484678\pi$
$421$	7.70849	−	1.10831i	0.375689	−	0.0540159i	0.327573	+	0.944826i	$0.393769\pi$
$422$	7.45035	−	7.10389i	0.362677	−	0.345812i
$423$	−1.19435	+	2.31671i	−0.0580711	+	0.112642i
$424$	−0.00280177	−	0.00699848i	−0.000136066	−	0.000339876i
$425$	15.6776	+	22.0162i	0.760477	+	1.06794i
$426$	−4.40333	−	2.01093i	−0.213342	−	0.0974301i
$427$	4.24525	−	30.0416i	0.205442	−	1.45382i
$428$	2.40145	+	3.73672i	0.116078	+	0.180621i
$429$	−1.37612	−	1.44323i	−0.0664396	−	0.0696798i
$430$	−0.616071	−	0.783397i	−0.0297096	−	0.0377788i
$431$	3.09022	+	1.06954i	0.148851	+	0.0515177i	0.400477	−	0.916307i	$-0.368844\pi$
$431$	3.09022	+	1.06954i	0.148851	+	0.0515177i	−0.251627	+	0.967824i	$0.580966\pi$
$432$	0.458227	+	0.888835i	0.0220464	+	0.0427641i
$433$	20.6992	−	23.8882i	0.994741	−	1.14799i	0.00575555	−	0.999983i	$-0.498168\pi$
$433$	20.6992	−	23.8882i	0.994741	−	1.14799i	0.988986	−	0.148009i	$-0.0472866\pi$
$434$	5.64696	−	5.95110i	0.271063	−	0.285662i
$435$	4.21308	−	1.92405i	0.202002	−	0.0922512i
$436$	−9.11284	−	5.26130i	−0.436426	−	0.251971i
$437$	0.168808	−	0.495145i	0.00807516	−	0.0236860i
$438$	−7.16316	−	12.4070i	−0.342269	−	0.592827i
$439$	3.22014	−	33.7228i	0.153689	−	1.60950i	−0.509108	−	0.860703i	$-0.670025\pi$
$439$	3.22014	−	33.7228i	0.153689	−	1.60950i	0.662797	−	0.748799i	$-0.269369\pi$
$440$	0.219746	+	0.748385i	0.0104760	+	0.0356779i
$441$	−6.87982	−	1.29152i	−0.327611	−	0.0615008i
$442$	4.54501	−	7.07217i	0.216184	−	0.336389i
$443$	23.9506	−	4.61611i	1.13793	−	0.219318i	0.414721	−	0.909948i	$-0.363879\pi$
$443$	23.9506	−	4.61611i	1.13793	−	0.219318i	0.723208	+	0.690631i	$0.242667\pi$
$444$	−4.94811	+	3.89124i	−0.234827	+	0.184670i
$445$	−0.908423	−	3.74457i	−0.0430634	−	0.177510i
$446$	21.3333	−	1.01623i	1.01016	−	0.0481200i
$447$	−3.24010	+	22.5354i	−0.153251	+	1.06589i
$448$	2.63316	−	0.257860i	0.124405	−	0.0121827i
$449$	−12.7469	+	27.9118i	−0.601563	+	1.31724i	0.326634	+	0.945151i	$0.394086\pi$
$449$	−12.7469	+	27.9118i	−0.601563	+	1.31724i	−0.928197	+	0.372089i	$0.878642\pi$
$450$	−3.67585	−	2.89072i	−0.173281	−	0.136270i
$451$	9.31528	+	4.80236i	0.438639	+	0.226134i
$452$	−5.52860	+	1.34122i	−0.260043	+	0.0630858i
$453$	2.52382	−	6.30421i	0.118580	−	0.296198i
$454$	−16.4426	−	18.9758i	−0.771689	−	0.890576i
$455$	−1.17921	+	1.84467i	−0.0552820	+	0.0864794i
$456$	0.0824371	+	0.0714322i	0.00386047	+	0.00334512i
$457$	7.32596	+	1.77726i	0.342694	+	0.0831366i	0.403412	−	0.915018i	$-0.367824\pi$
$457$	7.32596	+	1.77726i	0.342694	+	0.0831366i	−0.0607184	+	0.998155i	$0.519339\pi$
$458$	−1.45475	+	2.04291i	−0.0679760	+	0.0954589i
$459$	5.00536	−	2.88984i	0.233630	−	0.134886i
$460$	−2.53765	−	1.00231i	−0.118319	−	0.0467331i
$461$		−	24.6630i		−	1.14867i	−0.818620	−	0.574335i	$-0.805261\pi$
$461$		−	24.6630i		−	1.14867i	0.818620	−	0.574335i	$-0.194739\pi$
$462$	−3.61170	−	0.336069i	−0.168032	−	0.0156353i
$463$	−16.9514	+	4.97739i	−0.787800	+	0.231319i	−0.650797	−	0.759252i	$-0.725565\pi$
$463$	−16.9514	+	4.97739i	−0.787800	+	0.231319i	−0.137003	+	0.990571i	$0.543747\pi$
$464$	−2.66271	−	7.69340i	−0.123613	−	0.357157i
$465$	0.0839384	−	1.76208i	0.00389255	−	0.0817147i
$466$	5.03422	−	14.5454i	0.233206	−	0.673804i
$467$	−27.1897	−	10.8851i	−1.25819	−	0.503704i	−0.355776	−	0.934571i	$-0.615783\pi$
$467$	−27.1897	−	10.8851i	−1.25819	−	0.503704i	−0.902415	+	0.430868i	$0.858208\pi$
$468$	−0.409787	+	1.39561i	−0.0189424	+	0.0645120i
$469$	2.83155	−	0.141743i	0.130749	−	0.00654510i
$470$	1.46776	+	0.211032i	0.0677027	+	0.00973418i
$471$	−8.57479	+	6.10608i	−0.395105	+	0.281353i
$472$	0.634160	+	6.64123i	0.0291896	+	0.305687i
$473$	2.22965	−	0.892619i	0.102520	−	0.0410426i
$474$	−0.159338	−	3.34492i	−0.00731864	−	0.153637i
$475$	−0.489432	−	0.143710i	−0.0224567	−	0.00659388i
$476$	−2.21280	−	15.1307i	−0.101424	−	0.693513i
$477$	0.00569720	−	0.00493665i	0.000260857	−	0.000226034i
$478$	26.1373	−	13.4747i	1.19549	−	0.616319i
$479$	29.5023	+	5.68610i	1.34799	+	0.259804i	0.811625	−	0.584179i	$-0.198584\pi$
$479$	29.5023	+	5.68610i	1.34799	+	0.259804i	0.536369	+	0.843984i	$0.319796\pi$
$480$	0.392597	−	0.411744i	0.0179195	−	0.0187935i
$481$	−9.11461	−	0.870340i	−0.415590	−	0.0396841i
$482$	−7.20625			−0.328236
$483$	8.69118	−	9.24464i	0.395462	−	0.420646i
$484$	9.12038			0.414563
$485$	1.39292	+	0.133007i	0.0632490	+	0.00603955i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	11.3355	+	2.18474i	0.513661	+	0.0990001i	0.439494	−	0.898246i	$-0.355158\pi$
$487$	11.3355	+	2.18474i	0.513661	+	0.0990001i	0.0741676	+	0.997246i	$0.476370\pi$
$488$	−10.1927	+	5.25470i	−0.461402	+	0.237869i
$489$	−16.2711	+	14.0990i	−0.735806	+	0.637580i
$490$	0.585804	+	3.93909i	0.0264639	+	0.177950i
$491$	−7.74416	−	2.27389i	−0.349489	−	0.102619i	0.102276	−	0.994756i	$-0.467387\pi$
$491$	−7.74416	−	2.27389i	−0.349489	−	0.102619i	−0.451765	+	0.892137i	$0.649206\pi$
$492$	−0.363732	−	7.63567i	−0.0163983	−	0.344243i
$493$	−43.6828	+	17.4880i	−1.96737	+	0.787618i
$494$	0.0150816	+	0.157941i	0.000678551	+	0.00710611i
$495$	−0.635353	+	0.452433i	−0.0285570	+	0.0203353i
$496$	−3.06922	−	0.441287i	−0.137812	−	0.0198144i
$497$	−11.3979	−	5.84121i	−0.511267	−	0.262014i
$498$	1.82832	−	6.22670i	0.0819291	−	0.279025i
$499$	−19.8833	−	7.96008i	−0.890100	−	0.356342i	−0.118878	−	0.992909i	$-0.537930\pi$
$499$	−19.8833	−	7.96008i	−0.890100	−	0.356342i	−0.771222	+	0.636567i	$0.780354\pi$
$500$	−1.80052	+	5.20225i	−0.0805215	+	0.232652i
$501$	0.124723	−	2.61825i	0.00557221	−	0.116975i
$502$	4.64530	+	13.4217i	0.207330	+	0.599041i
$503$	13.8978	−	4.08076i	0.619673	−	0.181952i	0.0431969	−	0.999067i	$-0.486246\pi$
$503$	13.8978	−	4.08076i	0.619673	−	0.181952i	0.576476	+	0.817114i	$0.304428\pi$
$504$	1.10490	+	2.40400i	0.0492161	+	0.107083i
$505$		−	4.15645i		−	0.184960i
$506$	4.04045	−	5.18711i	0.179620	−	0.230595i
$507$	9.42613	−	5.44218i	0.418629	−	0.241696i
$508$	−11.8581	+	16.6524i	−0.526118	+	0.738829i
$509$	−21.6209	−	5.24516i	−0.958328	−	0.232488i	−0.274055	−	0.961714i	$-0.588365\pi$
$509$	−21.6209	−	5.24516i	−0.958328	−	0.232488i	−0.684273	+	0.729226i	$0.739880\pi$
$510$	−2.48502	−	2.15329i	−0.110039	−	0.0953491i
$511$	−17.4499	−	33.6482i	−0.771940	−	1.48851i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−0.0405409	+	0.101266i	−0.00178993	+	0.00447102i
$514$	−15.5019	+	3.76072i	−0.683760	+	0.165878i
$515$	2.60760	+	1.34431i	0.114904	+	0.0592373i
$516$	−1.37700	−	1.08288i	−0.0606190	−	0.0476713i
$517$	−1.48446	+	3.25051i	−0.0652863	+	0.142957i
$518$	−13.5431	+	9.69343i	−0.595051	+	0.425905i
$519$	−2.92445	+	20.3400i	−0.128369	+	0.892827i
$520$	0.826566	−	0.0393742i	0.0362473	−	0.00172667i
$521$	−5.38348	−	22.1910i	−0.235855	−	0.972207i	−0.959427	−	0.281958i	$-0.909016\pi$
$521$	−5.38348	−	22.1910i	−0.235855	−	0.972207i	0.723572	−	0.690249i	$-0.242499\pi$
$522$	6.39938	−	5.03253i	0.280093	−	0.220268i
$523$	31.8912	−	6.14652i	1.39450	−	0.268769i	0.563997	−	0.825777i	$-0.309263\pi$
$523$	31.8912	−	6.14652i	1.39450	−	0.268769i	0.830507	+	0.557008i	$0.188051\pi$
$524$	−2.98319	+	4.64194i	−0.130321	+	0.202784i
$525$	−9.37000	−	8.07959i	−0.408941	−	0.352622i
$526$	−2.54805	−	8.67786i	−0.111100	−	0.378373i
$527$	−1.70355	+	17.8404i	−0.0742078	+	0.777139i
$528$	0.685496	+	1.18731i	0.0298324	+	0.0516712i
$529$	5.62924	+	22.3005i	0.244750	+	0.969586i
$530$	−0.00371417	−	0.00214438i	−0.000161333	−	9.31459e-5i
$531$	−6.06855	+	2.77141i	−0.263353	+	0.120269i
$532$	0.209349	+	0.198650i	0.00907644	+	0.00861258i
$533$	7.28131	−	8.40308i	0.315389	−	0.363978i
$534$	−3.10350	−	6.01996i	−0.134302	−	0.260509i
$535$	2.38805	+	0.826514i	0.103245	+	0.0357333i
$536$	−0.662398	−	0.842307i	−0.0286112	−	0.0363821i
$537$	−7.51353	−	7.87997i	−0.324233	−	0.340046i
$538$	−0.145718	−	0.226741i	−0.00628233	−	0.00977550i
$539$	−9.50576	−	1.31985i	−0.409442	−	0.0568502i
$540$	0.517504	+	0.236336i	0.0222698	+	0.0101703i
$541$	6.78874	+	9.53345i	0.291871	+	0.409875i	0.934310	−	0.356462i	$-0.116017\pi$
$541$	6.78874	+	9.53345i	0.291871	+	0.409875i	−0.642439	+	0.766336i	$0.722078\pi$
$542$	8.31709	+	20.7751i	0.357250	+	0.892366i
$543$	1.45514	−	2.82258i	0.0624460	−	0.121128i
$544$	−4.18296	+	3.98844i	−0.179343	+	0.171003i
$545$	−5.92554	+	0.851964i	−0.253822	+	0.0364941i
$546$	−1.24987	+	3.63969i	−0.0534894	+	0.155764i
$547$	29.6004	+	19.0231i	1.26562	+	0.813367i	0.989044	−	0.147624i	$-0.0471625\pi$
$547$	29.6004	+	19.0231i	1.26562	+	0.813367i	0.276580	+	0.960991i	$0.410799\pi$
$548$	−5.94882	+	2.05891i	−0.254121	+	0.0879522i
$549$	−8.29940	−	7.91346i	−0.354210	−	0.337738i
$550$	−5.22243	−	3.71887i	−0.222685	−	0.158573i
$551$	0.444018	−	0.769062i	0.0189158	−	0.0327632i
$552$	−4.75013	−	0.660527i	−0.202179	−	0.0281139i
$553$	−0.0214137	−	8.85983i	−0.000910604	−	0.376758i
$554$	−5.44599	−	11.9251i	−0.231378	−	0.506647i
$555$	−0.844314	+	3.48031i	−0.0358391	+	0.147731i
$556$	2.37329	−	12.3138i	0.100650	−	0.522222i
$557$	32.8027	+	1.56259i	1.38990	+	0.0662089i	0.729126	−	0.684380i	$-0.239927\pi$
$557$	32.8027	+	1.56259i	1.38990	+	0.0662089i	0.660770	+	0.750589i	$0.270230\pi$
$558$	−0.586826	−	3.04474i	−0.0248423	−	0.128894i
$559$	−0.362622	−	2.52209i	−0.0153373	−	0.106673i
$560$	1.08686	−	1.04134i	0.0459281	−	0.0440048i
$561$	6.66602	−	4.28399i	0.281440	−	0.180870i
$562$	−20.1707	+	25.6492i	−0.850852	+	1.08195i
$563$	−22.2546	+	2.12506i	−0.937919	+	0.0895604i	−0.552807	−	0.833309i	$-0.686443\pi$
$563$	−22.2546	+	2.12506i	−0.937919	+	0.0895604i	−0.385112	+	0.922870i	$0.625837\pi$
$564$	2.59465	−	0.247759i	0.109255	−	0.0104325i
$565$	−2.00070	+	2.54409i	−0.0841699	+	0.107031i
$566$	11.2634	−	7.23853i	0.473435	−	0.304258i
$567$	−1.91040	+	1.83040i	−0.0802293	+	0.0768696i
$568$	0.688915	+	4.79151i	0.0289062	+	0.201047i
$569$	−1.38347	−	7.17810i	−0.0579979	−	0.300922i	0.941334	−	0.337477i	$-0.109574\pi$
$569$	−1.38347	−	7.17810i	−0.0579979	−	0.300922i	−0.999332	+	0.0365555i	$0.988361\pi$
$570$	0.0619871	+	0.00295281i	0.00259635	+	0.000123679i
$571$	−6.10370	+	31.6690i	−0.255432	+	1.32531i	0.596905	+	0.802312i	$0.296397\pi$
$571$	−6.10370	+	31.6690i	−0.255432	+	1.32531i	−0.852336	+	0.522994i	$0.824815\pi$
$572$	−0.470137	+	1.93793i	−0.0196574	+	0.0810290i
$573$	−4.65455	−	10.1920i	−0.194447	−	0.425778i
$574$	−0.0488825	−	20.2249i	−0.00204032	−	0.844172i
$575$	21.4890	−	6.41798i	0.896152	−	0.267648i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	26.6750	+	18.9952i	1.11049	+	0.790779i	0.979668	−	0.200627i	$-0.0642979\pi$
$577$	26.6750	+	18.9952i	1.11049	+	0.790779i	0.130825	+	0.991405i	$0.458237\pi$
$578$	11.8727	+	11.3206i	0.493840	+	0.470875i
$579$	−8.74277	+	3.02590i	−0.363337	+	0.125752i
$580$	−3.89638	−	2.50405i	−0.161788	−	0.103975i
$581$	5.57646	−	16.2390i	0.231350	−	0.673707i
$582$	2.43447	−	0.350024i	0.100912	−	0.0145090i
$583$	0.00747993	−	0.00713210i	0.000309787	−	0.000295381i
$584$	−6.56470	+	12.7337i	−0.271649	+	0.526926i
$585$	0.307552	+	0.768227i	0.0127157	+	0.0317623i
$586$	−5.31181	−	7.45940i	−0.219429	−	0.308145i
$587$	39.5105	+	18.0438i	1.63077	+	0.744748i	0.999525	−	0.0308338i	$-0.00981625\pi$
$587$	39.5105	+	18.0438i	1.63077	+	0.744748i	0.631247	+	0.775582i	$0.282544\pi$
$588$	2.63302	+	6.48592i	0.108584	+	0.267475i
$589$	−0.182862	−	0.284540i	−0.00753472	−	0.0117242i
$590$	2.61919	+	2.74692i	0.107830	+	0.113089i
$591$	1.74495	+	2.21888i	0.0717775	+	0.0912725i
$592$	5.94867	+	2.05886i	0.244489	+	0.0846184i
$593$	6.67641	+	12.9504i	0.274167	+	0.531811i	0.985213	−	0.171336i	$-0.0548083\pi$
$593$	6.67641	+	12.9504i	0.274167	+	0.531811i	−0.711045	+	0.703146i	$0.751778\pi$
$594$	−0.897809	+	1.03613i	−0.0368376	+	0.0425128i
$595$	−6.31072	−	5.98821i	−0.258714	−	0.245493i
$596$	20.7097	−	9.45780i	0.848302	−	0.387407i
$597$	−9.56546	−	5.52262i	−0.391488	−	0.226026i
$598$	−4.33741	−	5.46321i	−0.177370	−	0.223407i
$599$	−2.69369	−	4.66561i	−0.110061	−	0.190632i	0.805734	−	0.592278i	$-0.201771\pi$
$599$	−2.69369	−	4.66561i	−0.110061	−	0.190632i	−0.915795	+	0.401647i	$0.868438\pi$
$600$	−0.444514	+	4.65516i	−0.0181472	+	0.190046i
$601$	−4.44226	−	15.1289i	−0.181204	−	0.617123i	−0.999126	−	0.0417945i	$-0.986693\pi$
$601$	−4.44226	−	15.1289i	−0.181204	−	0.617123i	0.817923	−	0.575328i	$-0.195126\pi$
$602$	−3.51007	−	3.02667i	−0.143060	−	0.123358i
$603$	0.579332	−	0.901458i	0.0235922	−	0.0367102i
$604$	−6.66792	+	1.28514i	−0.271314	+	0.0522915i
$605$	4.07862	−	3.20746i	0.165819	−	0.130402i
$606$	−1.72243	−	7.09997i	−0.0699691	−	0.288416i
$607$	40.3260	−	1.92097i	1.63678	−	0.0779696i	0.791111	−	0.611672i	$-0.209503\pi$
$607$	40.3260	−	1.92097i	1.63678	−	0.0779696i	0.845672	+	0.533702i	$0.179200\pi$
$608$	0.0155237	−	0.107970i	0.000629569	−	0.00437875i
$609$	17.5153	−	12.5365i	0.709755	−	0.508004i
$610$	−2.71018	+	5.93447i	−0.109732	+	0.240280i
$611$	2.98005	+	2.34354i	0.120560	+	0.0948093i
$612$	−5.13719	−	2.64841i	−0.207659	−	0.107055i
$613$	−4.02374	+	0.976148i	−0.162517	+	0.0394263i	−0.316192	−	0.948695i	$-0.602404\pi$
$613$	−4.02374	+	0.976148i	−0.162517	+	0.0394263i	0.153675	+	0.988121i	$0.450889\pi$
$614$	−0.894415	+	2.23414i	−0.0360957	+	0.0901626i
$615$	−2.84798	−	3.28674i	−0.114841	−	0.132534i
$616$	1.66992	+	3.22005i	0.0672828	+	0.129740i
$617$	14.0236	+	12.1515i	0.564570	+	0.489202i	0.889749	−	0.456450i	$-0.150879\pi$
$617$	14.0236	+	12.1515i	0.564570	+	0.489202i	−0.325180	+	0.945652i	$0.605425\pi$
$618$	5.01133	+	1.21573i	0.201585	+	0.0489040i
$619$	0.0960756	−	0.134919i	0.00386160	−	0.00542286i	−0.812641	−	0.582765i	$-0.801971\pi$
$619$	0.0960756	−	0.134919i	0.00386160	−	0.00542286i	0.816502	+	0.577342i	$0.195910\pi$
$620$	−1.52774	+	0.882041i	−0.0613555	+	0.0354236i
$621$	−0.929415	−	4.70491i	−0.0372962	−	0.188802i
$622$		−	24.1840i		−	0.969692i
$623$	−7.48332	−	16.2819i	−0.299813	−	0.652322i
$624$	1.39561	−	0.409787i	0.0558690	−	0.0164046i
$625$	−6.62305	−	19.1361i	−0.264922	−	0.765442i
$626$	0.344199	−	7.22562i	0.0137569	−	0.288794i
$627$	−0.0489123	+	0.141323i	−0.00195337	+	0.00564389i
$628$	9.77264	+	3.91238i	0.389971	+	0.156121i
$629$	10.2501	−	34.9087i	0.408699	−	1.39190i
$630$	1.33955	+	0.686492i	0.0533689	+	0.0273505i
$631$	−23.8240	−	3.42537i	−0.948416	−	0.136362i	−0.349289	−	0.937015i	$-0.613577\pi$
$631$	−23.8240	−	3.42537i	−0.948416	−	0.136362i	−0.599128	+	0.800653i	$0.704486\pi$
$632$	−2.72778	+	1.94244i	−0.108505	+	0.0772663i
$633$	−0.978537	−	10.2477i	−0.0388934	−	0.407310i
$634$	21.0476	−	8.42620i	0.835908	−	0.334647i
$635$	0.553394	+	11.6172i	0.0219608	+	0.461013i
$636$	−0.00723311	−	0.00212383i	−0.000286812	−	8.42155e-5i
$637$	−3.73841	+	9.47053i	−0.148121	+	0.375236i
$638$	8.43527	−	7.30921i	0.333956	−	0.289374i
$639$	−4.30266	+	2.21818i	−0.170211	+	0.0877497i
$640$	−0.558635	−	0.107668i	−0.0220820	−	0.00425595i
$641$	−19.5939	+	20.5495i	−0.773913	+	0.811656i	−0.986201	−	0.165551i	$-0.947060\pi$
$641$	−19.5939	+	20.5495i	−0.773913	+	0.811656i	0.212289	+	0.977207i	$0.431908\pi$
$642$	4.42174	+	0.422225i	0.174512	+	0.0166639i
$643$	−35.4865			−1.39945			−0.699726	−	0.714411i	$-0.746695\pi$
$643$	−35.4865			−1.39945			−0.699726	+	0.714411i	$0.746695\pi$
$644$	−12.4759	−	2.31346i	−0.491619	−	0.0911630i
$645$	−0.996621			−0.0392419
$646$	−0.627594	−	0.0599279i	−0.0246923	−	0.00235783i
$647$	−4.10983	+	4.31027i	−0.161574	+	0.169454i	−0.799545	−	0.600607i	$-0.794926\pi$
$647$	−4.10983	+	4.31027i	−0.161574	+	0.169454i	0.637970	+	0.770061i	$0.279774\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	−8.12973	+	4.19117i	−0.319120	+	0.164518i
$650$	−5.14049	+	4.45426i	−0.201627	+	0.174711i
$651$	−1.18716	−	8.11754i	−0.0465284	−	0.318151i
$652$	20.6577	+	6.06565i	0.809018	+	0.237549i
$653$	1.50294	+	31.5507i	0.0588147	+	1.23467i	0.814666	+	0.579930i	$0.196920\pi$
$653$	1.50294	+	31.5507i	0.0588147	+	1.23467i	−0.755852	+	0.654743i	$0.772777\pi$
$654$	−9.76884	+	3.91085i	−0.381992	+	0.152927i
$655$	0.298401	+	3.12500i	0.0116595	+	0.122104i
$656$	−6.22688	+	4.43414i	−0.243119	+	0.173124i
$657$	−14.1805	−	2.03885i	−0.553234	−	0.0795430i
$658$	6.88740	−	0.344774i	0.268499	−	0.0134407i
$659$	2.70318	−	9.20618i	0.105301	−	0.358622i	−0.889939	−	0.456080i	$-0.849253\pi$
$659$	2.70318	−	9.20618i	0.105301	−	0.358622i	0.995240	+	0.0974582i	$0.0310712\pi$
$660$	0.724108	+	0.289889i	0.0281859	+	0.0112839i
$661$	−6.28076	+	18.1471i	−0.244293	+	0.705839i	0.754480	+	0.656323i	$0.227889\pi$
$661$	−6.28076	+	18.1471i	−0.244293	+	0.705839i	−0.998773	+	0.0495160i	$0.984232\pi$
$662$	0.560904	−	11.7748i	0.0218001	−	0.457641i
$663$	−2.74956	−	7.94434i	−0.106784	−	0.308533i
$664$	−6.22670	+	1.82832i	−0.241643	+	0.0709527i
$665$	0.163482	+	0.0152120i	0.00633956	+	0.000589896i
$666$			6.29488i			0.243922i
$667$	2.03836	+	38.9904i	0.0789254	+	1.50971i
$668$	−2.27005	+	1.31061i	−0.0878307	+	0.0507091i
$669$	12.3886	−	17.3973i	0.478970	−	0.672619i
$670$	−0.592446	−	0.143726i	−0.0228882	−	0.00555262i
$671$	−11.8818	−	10.2956i	−0.458690	−	0.397457i
$672$	1.42502	−	2.22920i	0.0549712	−	0.0859932i
$673$	−14.9981	−	17.3087i	−0.578135	−	0.667203i	0.389068	−	0.921209i	$-0.372797\pi$
$673$	−14.9981	−	17.3087i	−0.578135	−	0.667203i	−0.967203	+	0.254006i	$0.918252\pi$
$674$	6.81367	−	17.0197i	0.262453	−	0.655576i
$675$	−4.54452	+	1.10249i	−0.174919	+	0.0424348i
$676$	−9.67440	−	4.98750i	−0.372092	−	0.191827i
$677$	−8.98124	−	7.06293i	−0.345177	−	0.271450i	0.430486	−	0.902597i	$-0.358342\pi$
$677$	−8.98124	−	7.06293i	−0.345177	−	0.271450i	−0.775663	+	0.631147i	$0.782585\pi$
$678$	−2.36328	+	5.17486i	−0.0907612	+	0.198739i
$679$	6.47625	−	0.634206i	0.248536	−	0.0243386i
$680$	−0.467954	+	3.25469i	−0.0179452	+	0.124812i
$681$	−25.0801	+	1.19471i	−0.961071	+	0.0457814i
$682$	−1.00225	−	4.13131i	−0.0383780	−	0.158196i
$683$	11.7123	−	9.21062i	0.448157	−	0.352435i	−0.368431	−	0.929655i	$-0.620105\pi$
$683$	11.7123	−	9.21062i	0.448157	−	0.352435i	0.816588	+	0.577220i	$0.195863\pi$
$684$	0.107109	−	0.0206435i	0.00409541	−	0.000789325i
$685$	−1.93623	+	3.01283i	−0.0739794	+	0.115114i
$686$	6.18412	+	17.4573i	0.236111	+	0.666522i
$687$	0.706569	+	2.40635i	0.0269573	+	0.0918081i
$688$	−0.166518	+	1.74386i	−0.00634845	+	0.0664840i
$689$	−0.00548245	−	0.00949588i	−0.000208865	−	0.000361764i
$690$	−2.35654	+	1.37514i	−0.0897121	+	0.0523507i
$691$	12.7540	+	7.36352i	0.485185	+	0.280121i	0.722575	−	0.691293i	$-0.242959\pi$
$691$	12.7540	+	7.36352i	0.485185	+	0.280121i	−0.237390	+	0.971414i	$0.576292\pi$
$692$	18.6922	−	8.53643i	0.710570	−	0.324506i
$693$	−2.49678	+	2.63125i	−0.0948447	+	0.0999528i
$694$	10.2307	−	11.8069i	0.388352	−	0.448182i
$695$	−3.26919	−	6.34135i	−0.124008	−	0.240541i
$696$	−7.69340	−	2.66271i	−0.291617	−	0.100930i
$697$	27.3114	+	34.7293i	1.03449	+	1.31546i
$698$	3.09914	+	3.25029i	0.117304	+	0.123025i
$699$	−8.32153	−	12.9486i	−0.314749	−	0.489759i
$700$	−1.73117	+	12.2507i	−0.0654322	+	0.463033i
$701$	−8.10644	−	3.70209i	−0.306176	−	0.139826i	0.256402	−	0.966570i	$-0.417463\pi$
$701$	−8.10644	−	3.70209i	−0.306176	−	0.139826i	−0.562578	+	0.826744i	$0.690190\pi$
$702$	0.843708	+	1.18482i	0.0318437	+	0.0447182i
$703$	0.255200	+	0.637460i	0.00962507	+	0.0240423i
$704$	0.628225	−	1.21859i	0.0236771	−	0.0459272i
$705$	1.07319	−	1.02329i	0.0404187	−	0.0385392i
$706$	−6.68112	+	0.960600i	−0.251447	+	0.0361527i
$707$	−3.70402	−	18.9714i	−0.139304	−	0.713493i
$708$	5.61237	+	3.60685i	0.210926	+	0.135554i
$709$	36.5145	−	12.6378i	1.37133	−	0.474622i	0.460595	−	0.887610i	$-0.347636\pi$
$709$	36.5145	−	12.6378i	1.37133	−	0.474622i	0.910736	+	0.412988i	$0.135515\pi$
$710$	1.99316	+	1.90048i	0.0748021	+	0.0713236i
$711$	−2.72778	−	1.94244i	−0.102300	−	0.0728473i
$712$	−3.38643	+	5.86547i	−0.126912	+	0.219818i
$713$	13.5554	+	6.11485i	0.507655	+	0.229003i
$714$	−13.2614	−	7.61378i	−0.496294	−	0.284939i
$715$	0.471289	+	1.03198i	0.0176252	+	0.0385938i
$716$	−2.56693	+	10.5810i	−0.0959306	+	0.395431i
$717$	5.56517	−	28.8748i	0.207835	−	1.07835i
$718$	−29.9393	−	1.42619i	−1.11733	−	0.0532248i
$719$	6.72749	+	34.9055i	0.250893	+	1.30176i	0.860661	+	0.509178i	$0.170050\pi$
$719$	6.72749	+	34.9055i	0.250893	+	1.30176i	−0.609768	+	0.792580i	$0.708738\pi$
$720$	−0.0809652	−	0.563125i	−0.00301739	−	0.0209864i
$721$	13.0999	+	3.81211i	0.487866	+	0.141971i
$722$	−15.9738	+	10.2657i	−0.594484	+	0.382051i
$723$	−4.45461	+	5.66449i	−0.165669	+	0.210665i
$724$	−3.16121	+	0.301859i	−0.117485	+	0.0112185i
$725$	37.8984	−	3.61886i	1.40751	−	0.134401i
$726$	5.63784	−	7.16910i	0.209240	−	0.266070i
$727$	22.5915	−	14.5187i	0.837873	−	0.538469i	−0.0498974	−	0.998754i	$-0.515889\pi$
$727$	22.5915	−	14.5187i	0.837873	−	0.538469i	0.887771	+	0.460286i	$0.152253\pi$
$728$	3.73763	−	0.916310i	0.138526	−	0.0339607i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	1.54249	+	8.00319i	0.0570900	+	0.296211i
$731$	10.1133	+	0.481757i	0.374055	+	0.0178184i
$732$	−2.17023	+	11.2602i	−0.0802141	+	0.416190i
$733$	−6.38434	+	26.3166i	−0.235811	+	0.972026i	0.723646	+	0.690171i	$0.242465\pi$
$733$	−6.38434	+	26.3166i	−0.235811	+	0.972026i	−0.959457	+	0.281855i	$0.909050\pi$
$734$	13.2391	+	28.9897i	0.488666	+	1.07003i
$735$	3.45846	+	1.97451i	0.127567	+	0.0728310i
$736$	2.01244	+	4.35317i	0.0741796	+	0.160460i
$737$	0.734554	−	1.27229i	0.0270577	−	0.0468652i
$738$	−6.22688	−	4.43414i	−0.229215	−	0.163223i
$739$	−10.0124	−	9.54684i	−0.368314	−	0.351186i	0.483208	−	0.875505i	$-0.339471\pi$
$739$	−10.0124	−	9.54684i	−0.368314	−	0.351186i	−0.851522	+	0.524319i	$0.824320\pi$
$740$	3.38429	−	1.17132i	0.124409	−	0.0430584i
$741$	0.133473	+	0.0857779i	0.00490325	+	0.00315113i
$742$	−0.0188637	−	0.00647777i	−0.000692507	−	0.000237806i
$743$	0.351744	−	0.0505732i	0.0129042	−	0.00185535i	−0.135860	−	0.990728i	$-0.543380\pi$
$743$	0.351744	−	0.0505732i	0.0129042	−	0.00185535i	0.148764	+	0.988873i	$0.452471\pi$
$744$	−2.24414	+	2.13978i	−0.0822741	+	0.0784482i
$745$	5.93522	−	11.5127i	0.217449	−	0.421793i
$746$	4.83374	+	12.0741i	0.176976	+	0.442064i
$747$	−3.76432	−	5.28625i	−0.137729	−	0.193414i
$748$	−7.20784	−	3.29171i	−0.263545	−	0.120357i
$749$	11.6364	+	1.64437i	0.425185	+	0.0600839i
$750$	2.97624	+	4.63112i	0.108677	+	0.169105i
$751$	−33.3588	−	34.9857i	−1.21728	−	1.27665i	−0.949718	−	0.313106i	$-0.898630\pi$
$751$	−33.3588	−	34.9857i	−1.21728	−	1.27665i	−0.267562	−	0.963541i	$-0.586218\pi$
$752$	−1.61120	−	2.04881i	−0.0587545	−	0.0747124i
$753$	13.4217	+	4.64530i	0.489115	+	0.169284i
$754$	−5.42610	−	10.5252i	−0.197607	−	0.383304i
$755$	−2.52993	+	2.91969i	−0.0920734	+	0.106258i
$756$	2.57267	+	0.617543i	0.0935672	+	0.0224598i
$757$	27.7725	−	12.6833i	1.00941	−	0.460982i	0.159098	−	0.987263i	$-0.449141\pi$
$757$	27.7725	−	12.6833i	1.00941	−	0.460982i	0.850311	+	0.526281i	$0.176414\pi$
$758$	0.477686	+	0.275792i	0.0173503	+	0.0100172i
$759$	−1.57970	−	6.38246i	−0.0573395	−	0.231669i
$760$	−0.0310287	−	0.0537432i	−0.00112553	−	0.00194947i
$761$	−2.68142	+	28.0811i	−0.0972015	+	1.01794i	0.806919	+	0.590662i	$0.201133\pi$
$761$	−2.68142	+	28.0811i	−0.0972015	+	1.01794i	−0.904120	+	0.427278i	$0.859473\pi$
$762$	5.75945	+	19.6149i	0.208643	+	0.710572i
$763$	−26.2869	+	9.16919i	−0.951650	+	0.331947i
$764$	−6.05765	+	9.42589i	−0.219158	+	0.341017i
$765$	−3.22874	+	0.622288i	−0.116735	+	0.0224989i
$766$	3.03960	−	2.39037i	0.109825	−	0.0863675i
$767$	2.28775	+	9.43024i	0.0826059	+	0.340506i
$768$	−0.998867	+	0.0475819i	−0.0360435	+	0.00171696i
$769$	−5.84002	+	40.6182i	−0.210597	+	1.46473i	0.560575	+	0.828104i	$0.310580\pi$
$769$	−5.84002	+	40.6182i	−0.210597	+	1.46473i	−0.771171	+	0.636628i	$0.780329\pi$
$770$	1.87921	+	0.852725i	0.0677221	+	0.0307301i
$771$	−6.62652	+	14.5100i	−0.238648	+	0.522567i
$772$	7.27225	+	5.71896i	0.261734	+	0.205830i
$773$	24.0512	+	12.3992i	0.865060	+	0.445970i	0.832842	−	0.553511i	$-0.186712\pi$
$773$	24.0512	+	12.3992i	0.865060	+	0.445970i	0.0322187	+	0.999481i	$0.489743\pi$
$774$	−1.70241	+	0.413000i	−0.0611919	+	0.0148450i
$775$	5.38921	−	13.4616i	0.193586	−	0.483555i
$776$	−1.61063	−	1.85877i	−0.0578183	−	0.0667259i
$777$	−0.752252	+	16.6377i	−0.0269869	+	0.596874i
$778$	12.4267	+	10.7678i	0.445520	+	0.386045i
$779$	−0.810338	−	0.196586i	−0.0290334	−	0.00704342i
$780$	0.479999	−	0.674064i	0.0171867	−	0.0241354i
$781$	−5.74753	+	3.31834i	−0.205663	+	0.118740i
$782$	24.5780	−	12.8153i	0.878908	−	0.458273i
$783$		−	8.14115i		−	0.290941i
$784$	4.03279	−	5.72159i	0.144028	−	0.204343i
$785$	5.74621	−	1.68724i	0.205091	−	0.0602202i
$786$	1.80472	+	5.21440i	0.0643723	+	0.185992i
$787$	1.52591	−	32.0328i	0.0543928	−	1.14184i	−0.792428	−	0.609966i	$-0.791183\pi$
$787$	1.52591	−	32.0328i	0.0543928	−	1.14184i	0.846820	−	0.531879i	$-0.178514\pi$
$788$	0.923251	−	2.66756i	0.0328895	−	0.0950278i
$789$	−8.39636	−	3.36139i	−0.298918	−	0.119669i
$790$	−0.536739	+	1.82796i	−0.0190963	+	0.0650361i
$791$	−6.86468	+	13.3950i	−0.244080	+	0.476271i
$792$	1.35704	+	0.195113i	0.0482203	+	0.00693303i
$793$	−13.5869	+	9.67519i	−0.482485	+	0.343576i
$794$	2.39166	+	25.0466i	0.0848768	+	0.888870i
$795$	−0.00398155	+	0.00159397i	−0.000141211	+	5.65323e-5i
$796$	0.525554	+	11.0327i	0.0186278	+	0.391045i
$797$	11.4547	+	3.36342i	0.405748	+	0.119138i	0.478237	−	0.878231i	$-0.341276\pi$
$797$	11.4547	+	3.36342i	0.405748	+	0.119138i	−0.0724890	+	0.997369i	$0.523094\pi$
$798$	0.285561	−	0.0417621i	0.0101087	−	0.00147836i
$799$	−11.3850	+	9.86514i	−0.402772	+	0.349004i
$800$	4.15649	−	2.14282i	0.146954	−	0.0757601i
$801$	−6.65046	−	1.28177i	−0.234983	−	0.0452892i
$802$	11.9273	−	12.5090i	0.421166	−	0.441706i
$803$	−19.5523	−	1.86702i	−0.689987	−	0.0658858i
$804$	−1.07157			−0.0377912
$805$	−6.39280	+	3.35296i	−0.225316	+	0.118176i
$806$	−4.51016			−0.158864
$807$	−0.268307	−	0.0256202i	−0.00944486	−	0.000901874i
$808$	−5.04165	+	5.28753i	−0.177365	+	0.186015i
$809$	−52.1163	−	10.0446i	−1.83231	−	0.353149i	−0.848057	−	0.529905i	$-0.822228\pi$
$809$	−52.1163	−	10.0446i	−1.83231	−	0.353149i	−0.984255	+	0.176755i	$0.943440\pi$
$810$	0.505673	−	0.260692i	0.0177675	−	0.00915980i
$811$	6.41235	−	5.55633i	0.225168	−	0.195109i	−0.534970	−	0.844871i	$-0.679677\pi$
$811$	6.41235	−	5.55633i	0.225168	−	0.195109i	0.760138	+	0.649762i	$0.225131\pi$
$812$	−20.0158	−	7.95706i	−0.702418	−	0.279238i
$813$	21.4716	+	6.30463i	0.753042	+	0.221113i
$814$	0.410643	+	8.62047i	0.0143930	+	0.302147i
$815$	11.3713	−	4.55236i	0.398318	−	0.159462i
$816$	0.549394	+	5.75352i	0.0192326	+	0.201413i
$817$	−0.155653	+	0.110840i	−0.00544562	+	0.00387781i
$818$	16.2154	+	2.33143i	0.566960	+	0.0815165i
$819$	2.08837	+	3.23237i	0.0729737	+	0.112948i
$820$	−1.22525	+	4.17282i	−0.0427876	+	0.145721i
$821$	21.2246	+	8.49704i	0.740743	+	0.296549i	0.711176	−	0.703014i	$-0.248163\pi$
$821$	21.2246	+	8.49704i	0.740743	+	0.296549i	0.0295672	+	0.999563i	$0.490587\pi$
$822$	−2.05891	+	5.94882i	−0.0718126	+	0.207489i
$823$	0.103172	−	2.16585i	0.00359636	−	0.0754968i	−0.996356	−	0.0852963i	$-0.972816\pi$
$823$	0.103172	−	2.16585i	0.00359636	−	0.0754968i	0.999952	+	0.00979951i	$0.00311933\pi$
$824$	−1.68659	−	4.87307i	−0.0587550	−	0.169762i
$825$	−6.15152	+	1.80625i	−0.214169	+	0.0628855i
$826$	14.4028	+	10.2038i	0.501136	+	0.355035i
$827$			13.4665i			0.468275i	0.972204	+	0.234137i	$0.0752266\pi$
$827$			13.4665i			0.468275i	−0.972204	+	0.234137i	$0.924773\pi$
$828$	−3.45554	+	3.32554i	−0.120088	+	0.115571i
$829$	19.2919	−	11.1382i	0.670036	−	0.386846i	−0.126054	−	0.992023i	$-0.540231\pi$
$829$	19.2919	−	11.1382i	0.670036	−	0.386846i	0.796090	+	0.605178i	$0.206898\pi$
$830$	−2.14158	+	3.00743i	−0.0743354	+	0.104389i
$831$	−12.7402	−	3.09074i	−0.441953	−	0.107217i
$832$	−1.09926	−	0.952512i	−0.0381099	−	0.0330224i
$833$	−34.1406	−	21.7084i	−1.18290	−	0.752150i
$834$	−8.21223	−	9.47742i	−0.284366	−	0.328176i
$835$	−0.554244	+	1.38443i	−0.0191804	+	0.0479103i
$836$	0.145332	−	0.0352572i	0.00502642	−	0.00121940i
$837$	−2.75608	−	1.42086i	−0.0952641	−	0.0491121i
$838$	−21.7446	−	17.1001i	−0.751155	−	0.590715i
$839$	2.49513	−	5.46358i	0.0861416	−	0.188624i	−0.861659	−	0.507488i	$-0.830574\pi$
$839$	2.49513	−	5.46358i	0.0861416	−	0.188624i	0.947800	+	0.318864i	$0.103301\pi$
$840$	−0.146700	−	1.49804i	−0.00506165	−	0.0516874i
$841$	−5.30527	+	36.8990i	−0.182940	+	1.27238i
$842$	−7.77894	+	0.370557i	−0.268080	+	0.0127702i
$843$	7.69290	+	31.7106i	0.264957	+	1.09217i
$844$	−8.09188	+	6.36353i	−0.278534	+	0.219042i
$845$	−6.08038	+	1.17190i	−0.209172	+	0.0403145i
$846$	1.40915	−	2.19269i	0.0484477	−	0.0753862i
$847$	15.7578	−	18.2746i	0.541446	−	0.627922i
$848$	0.00212383	+	0.00723311i	7.29327e−5	+	0.000248386i
$849$	1.27269	−	13.3282i	0.0436785	−	0.457421i
$850$	−13.5139	−	23.4067i	−0.463522	−	0.802844i
$851$	−24.6722	−	17.3974i	−0.845753	−	0.596375i
$852$	4.19224	+	2.42039i	0.143624	+	0.0829213i
$853$	23.1692	−	10.5810i	0.793298	−	0.362287i	0.0228083	−	0.999740i	$-0.492739\pi$
$853$	23.1692	−	10.5810i	0.793298	−	0.362287i	0.770489	+	0.637453i	$0.220012\pi$
$854$	−7.08166	+	29.5020i	−0.242329	+	1.00954i
$855$	0.0406389	−	0.0468998i	0.00138982	−	0.00160394i
$856$	−2.03537	−	3.94807i	−0.0695676	−	0.134942i
$857$	16.1507	+	5.58982i	0.551698	+	0.190945i	0.588672	−	0.808372i	$-0.299651\pi$
$857$	16.1507	+	5.58982i	0.551698	+	0.190945i	−0.0369744	+	0.999316i	$0.511772\pi$
$858$	1.23270	+	1.56750i	0.0420836	+	0.0535137i
$859$	−18.4694	−	19.3701i	−0.630167	−	0.660900i	0.328806	−	0.944397i	$-0.393354\pi$
$859$	−18.4694	−	19.3701i	−0.630167	−	0.660900i	−0.958973	+	0.283498i	$0.908505\pi$
$860$	0.538814	+	0.838411i	0.0183734	+	0.0285896i
$861$	−15.9281	−	12.4638i	−0.542828	−	0.424765i
$862$	−2.97456	−	1.35844i	−0.101314	−	0.0462685i
$863$	32.0504	+	45.0085i	1.09101	+	1.53211i	0.822446	+	0.568844i	$0.192609\pi$
$863$	32.0504	+	45.0085i	1.09101	+	1.53211i	0.268562	+	0.963262i	$0.413451\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	5.35701	−	10.3911i	0.182144	−	0.353310i
$866$	−22.8762	+	21.8124i	−0.777366	+	0.741217i
$867$	16.2378	−	2.33465i	0.551465	−	0.0792888i
$868$	−6.18708	+	5.38737i	−0.210003	+	0.182859i
$869$	−3.86225	−	2.48211i	−0.131018	−	0.0842000i
$870$	−4.37690	+	1.51486i	−0.148391	+	0.0513585i
$871$	−1.12803	−	1.07557i	−0.0382217	−	0.0364443i
$872$	8.57146	+	6.10371i	0.290266	+	0.206698i
$873$	1.22975	−	2.12999i	0.0416208	−	0.0720893i
$874$	−0.215110	+	0.476856i	−0.00727619	+	0.0161299i
$875$	7.31293	+	12.5960i	0.247222	+	0.425821i
$876$	5.95137	+	13.0317i	0.201078	+	0.440300i
$877$	−1.18474	+	4.88357i	−0.0400059	+	0.164906i	−0.988310	−	0.152456i	$-0.951282\pi$
$877$	−1.18474	+	4.88357i	−0.0400059	+	0.164906i	0.948304	+	0.317362i	$0.102797\pi$
$878$	−6.41111	+	33.2640i	−0.216365	+	1.12261i
$879$	−9.14703	−	0.435727i	−0.308522	−	0.0146967i
$880$	−0.147612	−	0.765885i	−0.00497601	−	0.0258180i
$881$	0.639355	+	4.44681i	0.0215404	+	0.149817i	0.997753	−	0.0669982i	$-0.0213422\pi$
$881$	0.639355	+	4.44681i	0.0215404	+	0.149817i	−0.976213	+	0.216815i	$0.930433\pi$
$882$	6.72591	+	1.93964i	0.226473	+	0.0653110i
$883$	24.8587	−	15.9757i	0.836561	−	0.537625i	−0.0507957	−	0.998709i	$-0.516176\pi$
$883$	24.8587	−	15.9757i	0.836561	−	0.537625i	0.887356	+	0.461084i	$0.152539\pi$
$884$	−5.19668	+	6.60812i	−0.174783	+	0.222255i
$885$	3.77830	−	0.360784i	0.127006	−	0.0121276i
$886$	−24.2810	+	2.31855i	−0.815735	+	0.0778933i
$887$	−33.1380	+	42.1384i	−1.11267	+	1.41487i	−0.213672	+	0.976905i	$0.568542\pi$
$887$	−33.1380	+	42.1384i	−1.11267	+	1.41487i	−0.898993	+	0.437963i	$0.855700\pi$
$888$	5.29559	−	3.40327i	0.177708	−	0.114206i
$889$	12.8785	+	52.5314i	0.431931	+	1.76185i
$890$	0.548366	+	3.81397i	0.0183813	+	0.127844i
$891$	0.259462	+	1.34622i	0.00869231	+	0.0451000i
$892$	−21.3333	−	1.01623i	−0.714293	−	0.0340260i
$893$	0.0538064	−	0.279174i	0.00180056	−	0.00934220i
$894$	5.36755	−	22.1253i	0.179518	−	0.739982i
$895$	2.57321	+	5.63455i	0.0860131	+	0.188342i
$896$	−2.64574	+	0.00639462i	−0.0883881	+	0.000213629i
$897$	−6.97558	+	0.0323043i	−0.232908	+	0.00107861i
$898$	15.3424	−	26.5738i	0.511981	−	0.886778i
$899$	20.5631	+	14.6429i	0.685817	+	0.488368i
$900$	3.38442	+	3.22704i	0.112814	+	0.107568i
$901$	0.0411737	−	0.0142504i	0.00137170	−	0.000474748i
$902$	−8.81660	−	5.66609i	−0.293561	−	0.188660i
$903$	−4.54891	+	0.888139i	−0.151378	+	0.0295554i
$904$	5.63105	−	0.809623i	0.187286	−	0.0269277i
$905$	−1.30753	+	1.24673i	−0.0434638	+	0.0414426i
$906$	−3.11165	+	6.03576i	−0.103378	+	0.200525i
$907$	20.0790	+	50.1548i	0.666711	+	1.66536i	0.743853	+	0.668343i	$0.232996\pi$
$907$	20.0790	+	50.1548i	0.666711	+	1.66536i	−0.0771424	+	0.997020i	$0.524580\pi$
$908$	14.5644	+	20.4528i	0.483336	+	0.678750i
$909$	−6.64569	−	3.03498i	−0.220424	−	0.100664i
$910$	1.34921	−	1.72422i	0.0447260	−	0.0571575i
$911$	−4.07914	−	6.34727i	−0.135148	−	0.210294i	0.767083	−	0.641548i	$-0.221708\pi$
$911$	−4.07914	−	6.34727i	−0.135148	−	0.210294i	−0.902231	+	0.431254i	$0.858071\pi$
$912$	−0.0752738	−	0.0789449i	−0.00249256	−	0.00261413i
$913$	−5.49986	−	6.99364i	−0.182019	−	0.231456i
$914$	−7.12385	−	2.46559i	−0.235636	−	0.0815544i
$915$	2.98948	+	5.79879i	0.0988293	+	0.191702i
$916$	1.64235	−	1.89538i	0.0542649	−	0.0626250i
$917$	4.14684	+	13.9976i	0.136941	+	0.462242i
$918$	−5.25739	+	2.40097i	−0.173520	+	0.0792438i
$919$	−8.58655	−	4.95745i	−0.283244	−	0.163531i	0.351647	−	0.936133i	$-0.385622\pi$
$919$	−8.58655	−	4.95745i	−0.283244	−	0.163531i	−0.634891	+	0.772602i	$0.718955\pi$
$920$	2.43089	+	1.23899i	0.0801439	+	0.0408484i
$921$	1.20326	+	2.08411i	0.0396489	+	0.0686738i
$922$	−2.34437	+	24.5513i	−0.0772076	+	0.808555i
$923$	1.98369	+	6.75583i	0.0652940	+	0.222371i
$924$	3.56340	+	0.677862i	0.117227	+	0.0223000i
$925$	−15.9148	+	24.7640i	−0.523277	+	0.814234i
$926$	17.3478	−	3.34351i	0.570084	−	0.109875i
$927$	4.05343	−	3.18765i	0.133132	−	0.104696i
$928$	1.91935	+	7.91167i	0.0630057	+	0.259713i
$929$	−33.2965	+	1.58611i	−1.09242	+	0.0520385i	−0.586049	−	0.810276i	$-0.699317\pi$
$929$	−33.2965	+	1.58611i	−1.09242	+	0.0520385i	−0.506374	+	0.862314i	$0.669014\pi$
$930$	−0.251055	+	1.74613i	−0.00823242	+	0.0572578i
$931$	0.759743	−	0.0762543i	0.0248996	−	0.00249914i
$932$	−6.39406	+	14.0010i	−0.209444	+	0.458619i
$933$	−19.0099	−	14.9496i	−0.622358	−	0.489427i
$934$	26.0319	+	13.4204i	0.851791	+	0.439129i
$935$	−4.38097	+	1.06281i	−0.143273	+	0.0347576i
$936$	0.540593	−	1.35033i	0.0176698	−	0.0441371i
$937$	1.66567	+	1.92228i	0.0544150	+	0.0627983i	0.782305	−	0.622896i	$-0.214044\pi$
$937$	1.66567	+	1.92228i	0.0544150	+	0.0627983i	−0.727890	+	0.685694i	$0.759499\pi$
$938$	−2.83220	−	0.128054i	−0.0924747	−	0.00418112i
$939$	−5.46695	−	4.73714i	−0.178407	−	0.154591i
$940$	−1.44105	−	0.349596i	−0.0470020	−	0.0114026i
$941$	12.9143	−	18.1356i	0.420995	−	0.591205i	−0.548550	−	0.836118i	$-0.684820\pi$
$941$	12.9143	−	18.1356i	0.420995	−	0.591205i	0.969545	+	0.244913i	$0.0787593\pi$
$942$	9.11638	−	5.26335i	0.297028	−	0.171489i
$943$	34.5887	−	12.1509i	1.12636	−	0.395688i
$944$		−	6.67144i		−	0.217137i
$945$	1.36767	−	0.628594i	0.0444904	−	0.0204482i
$946$	−2.30441	+	0.676635i	−0.0749227	+	0.0219993i
$947$	3.39099	+	9.79762i	0.110192	+	0.318380i	0.986592	−	0.163204i	$-0.0521829\pi$
$947$	3.39099	+	9.79762i	0.110192	+	0.318380i	−0.876400	+	0.481584i	$0.840062\pi$
$948$	−0.159338	+	3.34492i	−0.00517506	+	0.108638i
$949$	−6.81544	+	19.6919i	−0.221239	+	0.639227i
$950$	0.473555	+	0.189583i	0.0153642	+	0.00615088i
$951$	6.38734	−	21.7533i	0.207124	−	0.705399i
$952$	0.764519	+	15.2725i	0.0247782	+	0.494984i
$953$	−31.7301	−	4.56210i	−1.02784	−	0.147781i	−0.392290	−	0.919842i	$-0.628317\pi$
$953$	−31.7301	−	4.56210i	−1.02784	−	0.147781i	−0.635549	+	0.772061i	$0.719226\pi$
$954$	−0.00614066	+	0.00437274i	−0.000198811	+	0.000141573i
$955$	0.605931	+	6.34560i	0.0196075	+	0.205339i
$956$	−27.2998	+	10.9292i	−0.882939	+	0.353475i
$957$	−0.531084	−	11.1488i	−0.0171675	−	0.360390i
$958$	−28.8282	−	8.46472i	−0.931396	−	0.273483i
$959$	−6.15270	+	15.4770i	−0.198681	+	0.499778i
$960$	−0.429958	+	0.372561i	−0.0138768	+	0.0120243i
$961$	−19.0079	+	9.79925i	−0.613158	+	0.316105i
$962$	8.99061	+	1.73280i	0.289869	+	0.0558676i
$963$	3.06523	−	3.21472i	0.0987756	−	0.103593i
$964$	7.17362	+	0.684997i	0.231047	+	0.0220623i
$965$	5.26339			0.169434
$966$	−9.53059	+	8.37663i	−0.306642	+	0.269514i
$967$	15.4543			0.496977			0.248489	−	0.968635i	$-0.420066\pi$
$967$	15.4543			0.496977			0.248489	+	0.968635i	$0.420066\pi$
$968$	−9.07908	−	0.866947i	−0.291813	−	0.0278647i
$969$	−0.435059	+	0.456277i	−0.0139761	+	0.0146577i
$970$	−1.37396	−	0.264810i	−0.0441153	−	0.00850254i
$971$	−1.78712	+	0.921325i	−0.0573514	+	0.0295667i	−0.486664	−	0.873589i	$-0.661786\pi$
$971$	−1.78712	+	0.921325i	−0.0573514	+	0.0295667i	0.429312	+	0.903156i	$0.358756\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	−20.5728	−	26.0307i	−0.659533	−	0.834506i
$974$	−11.0765	−	3.25236i	−0.354914	−	0.104212i
$975$	0.323645	+	6.79414i	0.0103649	+	0.217587i
$976$	10.6460	−	4.26203i	0.340771	−	0.136424i
$977$	−0.707410	−	7.40833i	−0.0226320	−	0.237014i	−0.999709	−	0.0241267i	$-0.992319\pi$
$977$	−0.707410	−	7.40833i	−0.0226320	−	0.237014i	0.977077	−	0.212887i	$-0.0682866\pi$
$978$	17.5377	−	12.4885i	0.560792	−	0.399339i
$979$	−9.19103	−	1.32147i	−0.293746	−	0.0422344i
$980$	−0.208717	−	3.97694i	−0.00666723	−	0.127039i
$981$	−2.96456	+	10.0964i	−0.0946511	+	0.322352i
$982$	7.49294	+	2.99972i	0.239109	+	0.0957250i
$983$	7.53459	−	21.7698i	0.240316	−	0.694348i	−0.758760	−	0.651371i	$-0.774194\pi$
$983$	7.53459	−	21.7698i	0.240316	−	0.694348i	0.999076	−	0.0429777i	$-0.0136844\pi$
$984$	−0.363732	+	7.63567i	−0.0115953	+	0.243416i
$985$	−0.525252	−	1.51762i	−0.0167359	−	0.0483553i
$986$	45.1473	−	13.2565i	1.43778	−	0.422172i
$987$	3.98650	−	5.62699i	0.126892	−	0.179109i
$988$		−	0.158660i		−	0.00504763i
$989$	3.08629	−	7.81386i	0.0981383	−	0.248466i
$990$	0.675482	−	0.389990i	0.0214682	−	0.0123947i
$991$	30.5799	−	42.9435i	0.971404	−	1.36415i	0.0403810	−	0.999184i	$-0.487143\pi$
$991$	30.5799	−	42.9435i	0.971404	−	1.36415i	0.931023	−	0.364961i	$-0.118918\pi$
$992$	3.01337	+	0.731036i	0.0956747	+	0.0232104i
$993$	−8.90891	−	7.71961i	−0.282716	−	0.244974i
$994$	10.7911	+	6.89820i	0.342272	+	0.218798i
$995$	4.11502	+	4.74899i	0.130455	+	0.150553i
$996$	−2.41193	+	6.02471i	−0.0764249	+	0.190900i
$997$	−29.8789	+	7.24854i	−0.946274	+	0.229563i	−0.679067	−	0.734076i	$-0.737616\pi$
$997$	−29.8789	+	7.24854i	−0.946274	+	0.229563i	−0.267206	+	0.963639i	$0.586100\pi$
$998$	19.0366	+	9.81407i	0.602594	+	0.310659i
$999$	4.94811	+	3.89124i	0.156551	+	0.123113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.6	✓	320
7.3	odd	6	inner	966.2.be.b.157.6	yes	320
23.17	odd	22	inner	966.2.be.b.523.6	yes	320
161.17	even	66	inner	966.2.be.b.661.6	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.6	✓	320	1.1	even	1	trivial
966.2.be.b.157.6	yes	320	7.3	odd	6	inner
966.2.be.b.523.6	yes	320	23.17	odd	22	inner
966.2.be.b.661.6	yes	320	161.17	even	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.505673 - 0.260692i) q^{5} +(0.755750 - 0.654861i) q^{6} +(2.07574 - 1.64052i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.505673 - 0.260692i) q^{5} +(0.755750 - 0.654861i) q^{6} +(2.07574 - 1.64052i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-0.528163 + 0.211445i) q^{10} +(-0.130321 - 1.36478i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(-1.43972 - 0.207001i) q^{13} +(-2.22228 + 1.43578i) q^{14} +(-0.160282 + 0.545871i) q^{15} +(0.928368 + 0.371662i) q^{16} +(1.89035 - 5.46181i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(0.0356766 + 0.103081i) q^{19} +(0.545871 - 0.160282i) q^{20} +(-0.245128 + 2.63437i) q^{21} +1.37099i q^{22} +(-3.78347 - 2.94710i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.71254 + 3.80923i) q^{25} +(1.41352 + 0.342917i) q^{26} +(0.755750 + 0.654861i) q^{27} +(2.34870 - 1.21803i) q^{28} +(-5.33132 - 6.15267i) q^{29} +(0.211445 - 0.528163i) q^{30} +(-3.01337 + 0.731036i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(1.07767 + 0.847492i) q^{33} +(-2.40097 + 5.25739i) q^{34} +(0.621976 - 1.37069i) q^{35} +(0.142315 - 0.989821i) q^{36} +(6.28775 - 0.299523i) q^{37} +(-0.0257166 - 0.106005i) q^{38} +(1.14333 - 0.899128i) q^{39} +(-0.558635 + 0.107668i) q^{40} +(-4.13284 + 6.43082i) q^{41} +(0.494431 - 2.59914i) q^{42} +(0.493536 + 1.68083i) q^{43} +(0.130321 - 1.36478i) q^{44} +(-0.284458 - 0.492696i) q^{45} +(3.48620 + 3.29339i) q^{46} +(-2.25725 - 1.30323i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(1.61741 - 6.81058i) q^{49} +(3.06235 - 3.53414i) q^{50} +(2.64841 + 5.13719i) q^{51} +(-1.37453 - 0.475729i) q^{52} +(0.00465997 + 0.00592564i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-0.421689 - 0.656161i) q^{55} +(-2.45385 + 0.989260i) q^{56} +(-0.0992226 - 0.0453135i) q^{57} +(4.72233 + 6.63159i) q^{58} +(-2.47952 - 6.19355i) q^{59} +(-0.260692 + 0.505673i) q^{60} +(8.29940 - 7.91346i) q^{61} +(3.06922 - 0.441287i) q^{62} +(-1.73743 - 1.99533i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.781991 + 0.270650i) q^{65} +(-0.992234 - 0.946093i) q^{66} +(0.872871 + 0.621569i) q^{67} +(2.88984 - 5.00536i) q^{68} +(4.74381 - 0.704494i) q^{69} +(-0.749452 + 1.30537i) q^{70} +(-2.01093 - 4.40333i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(2.71127 - 14.0674i) q^{73} +(-6.28775 - 0.299523i) q^{74} +(-0.885002 - 4.59183i) q^{75} +(0.0155237 + 0.107970i) q^{76} +(-2.50947 - 2.61915i) q^{77} +(-1.22362 + 0.786376i) q^{78} +(2.07004 - 2.63227i) q^{79} +(0.566340 - 0.0540789i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(4.72541 - 6.00885i) q^{82} +(5.45937 - 3.50853i) q^{83} +(-0.739257 + 2.54037i) q^{84} +(-0.467954 - 3.25469i) q^{85} +(-0.331528 - 1.72013i) q^{86} +(8.13193 + 0.387372i) q^{87} +(-0.259462 + 1.34622i) q^{88} +(1.59676 - 6.58194i) q^{89} +(0.236336 + 0.517504i) q^{90} +(-3.32808 + 1.93221i) q^{91} +(-3.15735 - 3.60986i) q^{92} +(1.55039 - 2.68535i) q^{93} +(2.12315 + 1.51189i) q^{94} +(0.0449130 + 0.0428245i) q^{95} +(0.945001 - 0.327068i) q^{96} +(2.06907 + 1.32971i) q^{97} +(-2.25747 + 6.62600i) q^{98} +(-1.35704 + 0.195113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

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