LMFDB - Embedded newform 966.2.bf.a.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(11,966)]

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([33, 44, 27]))

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

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

chi := DirichletCharacter("966.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bf (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:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	966.11
Dual form			966.2.bf.a.527.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458227 + 0.888835i) q^{2} +(-0.777131 + 1.54792i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-2.85699 - 2.72413i) q^{5} +(-1.01975 - 1.40004i) q^{6} +(2.56739 + 0.639162i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-1.79214 - 2.40588i) q^{9} +O(q^{10})$	\(q+(-0.458227 + 0.888835i) q^{2} +(-0.777131 + 1.54792i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-2.85699 - 2.72413i) q^{5} +(-1.01975 - 1.40004i) q^{6} +(2.56739 + 0.639162i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-1.79214 - 2.40588i) q^{9} +(3.73045 - 1.29112i) q^{10} +(0.427250 - 0.220263i) q^{11} +(1.71168 - 0.264852i) q^{12} +(-1.61891 + 1.86832i) q^{13} +(-1.74455 + 1.98910i) q^{14} +(6.43700 - 2.30539i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(4.00689 + 0.382612i) q^{17} +(2.95963 - 0.490477i) q^{18} +(-0.137504 - 1.44001i) q^{19} +(-0.561797 + 3.90738i) q^{20} +(-2.98457 + 3.47741i) q^{21} +0.480685i q^{22} +(-4.42930 + 1.83884i) q^{23} +(-0.548928 + 1.64277i) q^{24} +(0.503572 + 10.5713i) q^{25} +(-0.918804 - 2.29506i) q^{26} +(5.11684 - 0.904408i) q^{27} +(-0.968584 - 2.46208i) q^{28} +(-2.16531 + 0.988865i) q^{29} +(-0.900490 + 6.77782i) q^{30} +(8.07392 + 3.23231i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(0.00892075 + 0.832523i) q^{33} +(-2.17614 + 3.38615i) q^{34} +(-5.59382 - 8.81997i) q^{35} +(-0.920230 + 2.85538i) q^{36} +(-9.30729 + 2.25792i) q^{37} +(1.34294 + 0.537630i) q^{38} +(-1.63392 - 3.95788i) q^{39} +(-3.21559 - 2.28981i) q^{40} +(2.64929 + 9.02265i) q^{41} +(-1.72323 - 4.24623i) q^{42} +(-7.71280 - 1.10893i) q^{43} +(-0.427250 - 0.220263i) q^{44} +(-1.43382 + 11.7556i) q^{45} +(0.395192 - 4.77952i) q^{46} +(-3.68976 + 2.13028i) q^{47} +(-1.20861 - 1.24067i) q^{48} +(6.18294 + 3.28195i) q^{49} +(-9.62687 - 4.39644i) q^{50} +(-3.70613 + 5.90503i) q^{51} +(2.46095 + 0.234992i) q^{52} +(-0.806189 + 0.155380i) q^{53} +(-1.54080 + 4.96245i) q^{54} +(-1.82067 - 0.534597i) q^{55} +(2.63222 + 0.267279i) q^{56} +(2.33588 + 0.906227i) q^{57} +(0.113265 - 2.37773i) q^{58} +(-1.06138 + 0.367348i) q^{59} +(-5.61174 - 3.90617i) q^{60} +(4.53014 + 5.76054i) q^{61} +(-6.57268 + 5.69526i) q^{62} +(-3.06336 - 7.32228i) q^{63} +(0.959493 - 0.281733i) q^{64} +(9.71476 - 0.927647i) q^{65} +(-0.744063 - 0.373555i) q^{66} +(-13.5212 + 0.644096i) q^{67} +(-2.01256 - 3.48586i) q^{68} +(0.595753 - 8.28523i) q^{69} +(10.4027 - 0.930444i) q^{70} +(1.57967 + 2.45801i) q^{71} +(-2.11629 - 2.12634i) q^{72} +(0.621825 + 0.873231i) q^{73} +(2.25792 - 9.30729i) q^{74} +(-16.7549 - 7.43577i) q^{75} +(-1.09323 + 0.947292i) q^{76} +(1.23770 - 0.292417i) q^{77} +(4.26661 + 0.361324i) q^{78} +(-0.121598 + 0.630911i) q^{79} +(3.50873 - 1.80888i) q^{80} +(-2.57650 + 8.62332i) q^{81} +(-9.23363 - 1.77964i) q^{82} +(8.30712 + 2.43919i) q^{83} +(4.56383 + 0.414065i) q^{84} +(-10.4054 - 12.0084i) q^{85} +(4.51987 - 6.34727i) q^{86} +(0.152043 - 4.12022i) q^{87} +(0.391554 - 0.278825i) q^{88} +(-1.72648 + 0.691177i) q^{89} +(-9.79176 - 6.66114i) q^{90} +(-5.35053 + 3.76196i) q^{91} +(4.06712 + 2.54136i) q^{92} +(-11.2779 + 9.98589i) q^{93} +(-0.202726 - 4.25574i) q^{94} +(-3.52992 + 4.48865i) q^{95} +(1.65657 - 0.505754i) q^{96} +(-2.98223 - 10.1566i) q^{97} +(-5.75030 + 3.99174i) q^{98} +(-1.29561 - 0.633170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$3$	−0.777131	+	1.54792i	−0.448677	+	0.893694i
$3$	−0.777131	+	1.54792i	−0.448677	+	0.893694i
$4$	−0.580057	−	0.814576i	−0.290028	−	0.407288i
$5$	−2.85699	−	2.72413i	−1.27768	−	1.21827i	−0.963132	−	0.269028i	$-0.913298\pi$
$5$	−2.85699	−	2.72413i	−1.27768	−	1.21827i	−0.314551	−	0.949241i	$-0.601854\pi$
$6$	−1.01975	−	1.40004i	−0.416310	−	0.571564i
$7$	2.56739	+	0.639162i	0.970381	+	0.241581i
$7$	2.56739	+	0.639162i	0.970381	+	0.241581i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−1.79214	−	2.40588i	−0.597379	−	0.801959i
$10$	3.73045	−	1.29112i	1.17967	−	0.408288i
$11$	0.427250	−	0.220263i	0.128821	−	0.0664116i	−0.392611	−	0.919704i	$-0.628428\pi$
$11$	0.427250	−	0.220263i	0.128821	−	0.0664116i	0.521432	+	0.853293i	$0.325398\pi$
$12$	1.71168	−	0.264852i	0.494120	−	0.0764562i
$13$	−1.61891	+	1.86832i	−0.449005	+	0.518179i	−0.934453	−	0.356086i	$-0.884111\pi$
$13$	−1.61891	+	1.86832i	−0.449005	+	0.518179i	0.485448	+	0.874265i	$0.338656\pi$
$14$	−1.74455	+	1.98910i	−0.466252	+	0.531610i
$15$	6.43700	−	2.30539i	1.66203	−	0.595249i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	4.00689	+	0.382612i	0.971814	+	0.0927970i	0.568870	−	0.822427i	$-0.307381\pi$
$17$	4.00689	+	0.382612i	0.971814	+	0.0927970i	0.402944	+	0.915224i	$0.367987\pi$
$18$	2.95963	−	0.490477i	0.697592	−	0.115606i
$19$	−0.137504	−	1.44001i	−0.0315455	−	0.330360i	−0.997445	−	0.0714416i	$-0.977240\pi$
$19$	−0.137504	−	1.44001i	−0.0315455	−	0.330360i	0.965899	−	0.258918i	$-0.0833660\pi$
$20$	−0.561797	+	3.90738i	−0.125622	+	0.873717i
$21$	−2.98457	+	3.47741i	−0.651286	+	0.758832i
$22$			0.480685i			0.102482i
$23$	−4.42930	+	1.83884i	−0.923572	+	0.383425i
$23$	−4.42930	+	1.83884i	−0.923572	+	0.383425i
$24$	−0.548928	+	1.64277i	−0.112049	+	0.335328i
$25$	0.503572	+	10.5713i	0.100714	+	2.11425i
$26$	−0.918804	−	2.29506i	−0.180192	−	0.450098i
$27$	5.11684	−	0.904408i	0.984736	−	0.174053i
$28$	−0.968584	−	2.46208i	−0.183045	−	0.465290i
$29$	−2.16531	+	0.988865i	−0.402088	+	0.183628i	−0.606186	−	0.795323i	$-0.707301\pi$
$29$	−2.16531	+	0.988865i	−0.402088	+	0.183628i	0.204098	+	0.978951i	$0.434574\pi$
$30$	−0.900490	+	6.77782i	−0.164406	+	1.23746i
$31$	8.07392	+	3.23231i	1.45012	+	0.580540i	0.957172	−	0.289519i	$-0.0934955\pi$
$31$	8.07392	+	3.23231i	1.45012	+	0.580540i	0.492947	+	0.870059i	$0.335920\pi$
$32$	−0.690079	−	0.723734i	−0.121990	−	0.127939i
$33$	0.00892075	+	0.832523i	0.00155290	+	0.144924i
$34$	−2.17614	+	3.38615i	−0.373206	+	0.580719i
$35$	−5.59382	−	8.81997i	−0.945529	−	1.49085i
$36$	−0.920230	+	2.85538i	−0.153372	+	0.475896i
$37$	−9.30729	+	2.25792i	−1.53011	+	0.371200i	−0.910433	−	0.413657i	$-0.864251\pi$
$37$	−9.30729	+	2.25792i	−1.53011	+	0.371200i	−0.619676	+	0.784858i	$0.712736\pi$
$38$	1.34294	+	0.537630i	0.217853	+	0.0872152i
$39$	−1.63392	−	3.95788i	−0.261636	−	0.633768i
$40$	−3.21559	−	2.28981i	−0.508429	−	0.362051i
$41$	2.64929	+	9.02265i	0.413750	+	1.40910i	0.858208	+	0.513302i	$0.171578\pi$
$41$	2.64929	+	9.02265i	0.413750	+	1.40910i	−0.444458	+	0.895800i	$0.646604\pi$
$42$	−1.72323	−	4.24623i	−0.265901	−	0.655208i
$43$	−7.71280	−	1.10893i	−1.17619	−	0.169111i	−0.473623	−	0.880728i	$-0.657054\pi$
$43$	−7.71280	−	1.10893i	−1.17619	−	0.169111i	−0.702568	+	0.711617i	$0.747963\pi$
$44$	−0.427250	−	0.220263i	−0.0644103	−	0.0332058i
$45$	−1.43382	+	11.7556i	−0.213741	+	1.75242i
$46$	0.395192	−	4.77952i	0.0582679	−	0.704702i
$47$	−3.68976	+	2.13028i	−0.538207	+	0.310734i	−0.744352	−	0.667788i	$-0.767241\pi$
$47$	−3.68976	+	2.13028i	−0.538207	+	0.310734i	0.206145	+	0.978521i	$0.433908\pi$
$48$	−1.20861	−	1.24067i	−0.174448	−	0.179075i
$49$	6.18294	+	3.28195i	0.883278	+	0.468850i
$50$	−9.62687	−	4.39644i	−1.36144	−	0.621751i
$51$	−3.70613	+	5.90503i	−0.518963	+	0.826869i
$52$	2.46095	+	0.234992i	0.341273	+	0.0325876i
$53$	−0.806189	+	0.155380i	−0.110739	+	0.0213431i	−0.244319	−	0.969695i	$-0.578565\pi$
$53$	−0.806189	+	0.155380i	−0.110739	+	0.0213431i	0.133581	+	0.991038i	$0.457352\pi$
$54$	−1.54080	+	4.96245i	−0.209677	+	0.675304i
$55$	−1.82067	−	0.534597i	−0.245499	−	0.0720850i
$56$	2.63222	+	0.267279i	0.351745	+	0.0357167i
$57$	2.33588	+	0.906227i	0.309394	+	0.120033i
$58$	0.113265	−	2.37773i	0.0148725	−	0.312211i
$59$	−1.06138	+	0.367348i	−0.138180	+	0.0478246i	−0.395283	−	0.918559i	$-0.629353\pi$
$59$	−1.06138	+	0.367348i	−0.138180	+	0.0478246i	0.257103	+	0.966384i	$0.417232\pi$
$60$	−5.61174	−	3.90617i	−0.724473	−	0.504284i
$61$	4.53014	+	5.76054i	0.580025	+	0.737562i	0.984188	−	0.177125i	$-0.0566796\pi$
$61$	4.53014	+	5.76054i	0.580025	+	0.737562i	−0.404163	+	0.914687i	$0.632437\pi$
$62$	−6.57268	+	5.69526i	−0.834731	+	0.723298i
$63$	−3.06336	−	7.32228i	−0.385947	−	0.922521i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	9.71476	−	0.927647i	1.20497	−	0.115060i
$66$	−0.744063	−	0.373555i	−0.0915879	−	0.0459814i
$67$	−13.5212	+	0.644096i	−1.65188	+	0.0786888i	−0.852700	−	0.522401i	$-0.825036\pi$
$67$	−13.5212	+	0.644096i	−1.65188	+	0.0786888i	−0.799181	+	0.601090i	$0.794733\pi$
$68$	−2.01256	−	3.48586i	−0.244059	−	0.422722i
$69$	0.595753	−	8.28523i	0.0717203	−	0.997425i
$70$	10.4027	−	0.930444i	1.24337	−	0.111209i
$71$	1.57967	+	2.45801i	0.187472	+	0.291712i	0.922249	−	0.386597i	$-0.126350\pi$
$71$	1.57967	+	2.45801i	0.187472	+	0.291712i	−0.734777	+	0.678309i	$0.762713\pi$
$72$	−2.11629	−	2.12634i	−0.249407	−	0.250592i
$73$	0.621825	+	0.873231i	0.0727791	+	0.102204i	0.849361	−	0.527812i	$-0.176988\pi$
$73$	0.621825	+	0.873231i	0.0727791	+	0.102204i	−0.776582	+	0.630016i	$0.783048\pi$
$74$	2.25792	−	9.30729i	0.262478	−	1.08195i
$75$	−16.7549	−	7.43577i	−1.93468	−	0.858608i
$76$	−1.09323	+	0.947292i	−0.125403	+	0.108662i
$77$	1.23770	−	0.292417i	0.141049	−	0.0333240i
$78$	4.26661	+	0.361324i	0.483098	+	0.0409119i
$79$	−0.121598	+	0.630911i	−0.0136809	+	0.0709831i	−0.988128	−	0.153636i	$-0.950902\pi$
$79$	−0.121598	+	0.630911i	−0.0136809	+	0.0709831i	0.974447	+	0.224619i	$0.0721138\pi$
$80$	3.50873	−	1.80888i	0.392288	−	0.202239i
$81$	−2.57650	+	8.62332i	−0.286278	+	0.958147i
$82$	−9.23363	−	1.77964i	−1.01968	−	0.196528i
$83$	8.30712	+	2.43919i	0.911825	+	0.267736i	0.703809	−	0.710389i	$-0.251481\pi$
$83$	8.30712	+	2.43919i	0.911825	+	0.267736i	0.208016	+	0.978125i	$0.433299\pi$
$84$	4.56383	+	0.414065i	0.497955	+	0.0451782i
$85$	−10.4054	−	12.0084i	−1.12862	−	1.30250i
$86$	4.51987	−	6.34727i	0.487390	−	0.684443i
$87$	0.152043	−	4.12022i	0.0163007	−	0.441734i
$88$	0.391554	−	0.278825i	0.0417398	−	0.0297228i
$89$	−1.72648	+	0.691177i	−0.183006	+	0.0732646i	−0.461356	−	0.887215i	$-0.652637\pi$
$89$	−1.72648	+	0.691177i	−0.183006	+	0.0732646i	0.278350	+	0.960480i	$0.410213\pi$
$90$	−9.79176	−	6.66114i	−1.03214	−	0.702146i
$91$	−5.35053	+	3.76196i	−0.560888	+	0.394360i
$92$	4.06712	+	2.54136i	0.424027	+	0.264956i
$93$	−11.2779	+	9.98589i	−1.16946	+	1.03549i
$94$	−0.202726	−	4.25574i	−0.0209096	−	0.438946i
$95$	−3.52992	+	4.48865i	−0.362162	+	0.460526i
$96$	1.65657	−	0.505754i	0.169073	−	0.0516183i
$97$	−2.98223	−	10.1566i	−0.302800	−	1.03124i	−0.960574	−	0.278026i	$-0.910320\pi$
$97$	−2.98223	−	10.1566i	−0.302800	−	1.03124i	0.657774	−	0.753216i	$-0.271498\pi$
$98$	−5.75030	+	3.99174i	−0.580868	+	0.403227i
$99$	−1.29561	−	0.633170i	−0.130214	−	0.0636360i
$100$	8.31900	−	6.54214i	0.831900	−	0.654214i
$101$	11.5327	+	12.0952i	1.14755	+	1.20351i	0.975868	+	0.218361i	$0.0700709\pi$
$101$	11.5327	+	12.0952i	1.14755	+	1.20351i	0.171680	+	0.985153i	$0.445081\pi$
$102$	−3.55035	−	5.99998i	−0.351537	−	0.594087i
$103$	−11.6641	−	0.555632i	−1.14930	−	0.0547480i	−0.535732	−	0.844388i	$-0.679964\pi$
$103$	−11.6641	−	0.555632i	−1.14930	−	0.0547480i	−0.613570	+	0.789640i	$0.710267\pi$
$104$	−1.33654	+	2.07970i	−0.131059	+	0.203931i
$105$	17.9998	−	1.80454i	1.75660	−	0.176105i
$106$	0.231310	−	0.787768i	0.0224668	−	0.0765148i
$107$	9.58621	−	7.53868i	0.926733	−	0.728791i	−0.0359692	−	0.999353i	$-0.511452\pi$
$107$	9.58621	−	7.53868i	0.926733	−	0.728791i	0.962703	+	0.270562i	$0.0872094\pi$
$108$	−3.70477	−	3.64345i	−0.356491	−	0.350591i
$109$	0.438787	−	4.59519i	0.0420282	−	0.440139i	−0.949828	−	0.312774i	$-0.898742\pi$
$109$	0.438787	−	4.59519i	0.0420282	−	0.440139i	0.991856	−	0.127365i	$-0.0406521\pi$
$110$	1.30945	−	1.37331i	0.124851	−	0.130940i
$111$	3.73789	−	16.1617i	0.354784	−	1.53400i
$112$	−1.44372	+	2.21713i	−0.136419	+	0.209499i
$113$	−8.04591	+	5.17079i	−0.756895	+	0.486427i	−0.861293	−	0.508109i	$-0.830345\pi$
$113$	−8.04591	+	5.17079i	−0.756895	+	0.486427i	0.104398	+	0.994536i	$0.466709\pi$
$114$	−1.87585	+	1.66095i	−0.175689	+	0.155563i
$115$	17.6637	+	6.81243i	1.64715	+	0.635263i
$116$	2.06151	+	1.19021i	0.191406	+	0.110509i
$117$	7.39626	+	0.546614i	0.683785	+	0.0505345i
$118$	0.159842	−	1.11172i	0.0147146	−	0.102342i
$119$	10.0427	+	3.54337i	0.920612	+	0.324820i
$120$	6.04339	−	3.19801i	0.551683	−	0.291937i
$121$	−6.24660	+	8.77212i	−0.567873	+	0.797466i
$122$	−7.19601	+	1.38692i	−0.651496	+	0.125566i
$123$	−16.0252	−	2.91088i	−1.44495	−	0.262465i
$124$	−2.05037	−	8.45175i	−0.184129	−	0.758989i
$125$	14.4333	−	16.6569i	1.29095	−	1.48984i
$126$	7.91202	+	0.632443i	0.704859	+	0.0563425i
$127$	11.8814	+	7.63572i	1.05430	+	0.677561i	0.948484	−	0.316825i	$-0.102617\pi$
$127$	11.8814	+	7.63572i	1.05430	+	0.677561i	0.105821	+	0.994385i	$0.466253\pi$
$128$	−0.189251	+	0.981929i	−0.0167276	+	0.0867911i
$129$	7.71040	−	11.0770i	0.678863	−	0.975279i
$130$	−3.62704	+	9.05990i	−0.318112	+	0.794605i
$131$	11.0237	+	3.81535i	0.963149	+	0.333349i	0.762987	−	0.646414i	$-0.223732\pi$
$131$	11.0237	+	3.81535i	0.963149	+	0.333349i	0.200162	+	0.979763i	$0.435853\pi$
$132$	0.672978	−	0.490177i	0.0585753	−	0.0426644i
$133$	0.567372	−	3.78494i	0.0491974	−	0.328196i
$134$	5.62329	−	12.3133i	0.485778	−	1.06371i
$135$	−17.0825	−	11.3551i	−1.47022	−	0.977288i
$136$	4.02056	−	0.191523i	0.344760	−	0.0164230i
$137$	1.42730	−	2.47216i	0.121943	−	0.211211i	−0.798591	−	0.601874i	$-0.794421\pi$
$137$	1.42730	−	2.47216i	0.121943	−	0.211211i	0.920534	+	0.390663i	$0.127754\pi$
$138$	7.09122	+	4.32604i	0.603645	+	0.368257i
$139$	2.88466			0.244674			0.122337	−	0.992489i	$-0.460961\pi$
$139$	2.88466			0.244674			0.122337	+	0.992489i	$0.460961\pi$
$140$	−3.93980	+	9.67268i	−0.332974	+	0.817491i
$141$	−0.430091	−	7.36698i	−0.0362202	−	0.620411i
$142$	−2.90861	+	0.277739i	−0.244085	+	0.0233073i
$143$	−0.280158	+	1.15483i	−0.0234280	+	0.0965714i
$144$	2.85971	−	0.906684i	0.238309	−	0.0755570i
$145$	8.88007	+	3.07342i	0.737449	+	0.255234i
$146$	−1.06110	+	0.152563i	−0.0878169	+	0.0126262i
$147$	−9.88517	+	7.02022i	−0.815315	+	0.579018i
$148$	7.23801	+	6.27177i	0.594961	+	0.515536i
$149$	−0.841900	+	17.6736i	−0.0689711	+	1.44788i	0.653734	+	0.756725i	$0.273202\pi$
$149$	−0.841900	+	17.6736i	−0.0689711	+	1.44788i	−0.722705	+	0.691157i	$0.757101\pi$
$150$	14.2867	−	11.4850i	1.16650	−	0.937750i
$151$	7.48151	+	21.6164i	0.608837	+	1.75912i	0.649965	+	0.759964i	$0.274783\pi$
$151$	7.48151	+	21.6164i	0.608837	+	1.75912i	−0.0411289	+	0.999154i	$0.513095\pi$
$152$	−0.341038	−	1.40578i	−0.0276619	−	0.114024i
$153$	−6.26038	−	10.3258i	−0.506122	−	0.834791i
$154$	−0.307236	+	1.23410i	−0.0247577	+	0.0994469i
$155$	−14.2618	−	31.2291i	−1.14554	−	2.50838i
$156$	−2.27623	+	3.62674i	−0.182244	+	0.290372i
$157$	−15.4906	+	11.0308i	−1.23628	+	0.880353i	−0.995912	−	0.0903282i	$-0.971208\pi$
$157$	−15.4906	+	11.0308i	−1.23628	+	0.880353i	−0.240371	+	0.970681i	$0.577269\pi$
$158$	−0.505057	−	0.397181i	−0.0401802	−	0.0315980i
$159$	0.385997	−	1.36867i	0.0306116	−	0.108543i
$160$			3.94756i			0.312082i
$161$	−12.5470	+	1.88998i	−0.988845	+	0.148951i
$162$	−6.48409	−	6.24152i	−0.509438	−	0.490380i
$163$	13.0840	+	6.74525i	1.02481	+	0.528329i	0.886825	−	0.462105i	$-0.152906\pi$
$163$	13.0840	+	6.74525i	1.02481	+	0.528329i	0.137989	+	0.990434i	$0.455936\pi$
$164$	5.81290	−	7.39170i	0.453911	−	0.577195i
$165$	2.24241	−	2.40281i	0.174572	−	0.187058i
$166$	−5.97458	+	6.26596i	−0.463717	+	0.486333i
$167$	−20.1360	+	9.19579i	−1.55817	+	0.711591i	−0.993511	−	0.113734i	$-0.963719\pi$
$167$	−20.1360	+	9.19579i	−1.55817	+	0.711591i	−0.564657	+	0.825326i	$0.690991\pi$
$168$	−2.45930	+	3.86676i	−0.189739	+	0.298327i
$169$	0.980336	+	6.81838i	0.0754104	+	0.524491i
$170$	15.4415	−	3.74607i	1.18431	−	0.287311i
$171$	−3.21805	+	2.91150i	−0.246091	+	0.222648i
$172$	3.57055	+	6.92590i	0.272252	+	0.528095i
$173$	−6.72581	−	0.320390i	−0.511354	−	0.0243588i	−0.209680	−	0.977770i	$-0.567242\pi$
$173$	−6.72581	−	0.320390i	−0.511354	−	0.0243588i	−0.301674	+	0.953411i	$0.597545\pi$
$174$	3.59252	+	2.02313i	0.272349	+	0.153373i
$175$	−5.46389	+	27.4624i	−0.413032	+	2.07596i
$176$	0.0684086	+	0.475792i	0.00515649	+	0.0358642i
$177$	0.256206	−	1.92842i	0.0192576	−	0.144949i
$178$	0.176775	−	1.85127i	0.0132498	−	0.138758i
$179$	−16.1817	−	3.92565i	−1.20948	−	0.293417i	−0.420189	−	0.907437i	$-0.638036\pi$
$179$	−16.1817	−	3.92565i	−1.20948	−	0.293417i	−0.789290	+	0.614020i	$0.789551\pi$
$180$	10.4075	−	5.65095i	0.775729	−	0.421197i
$181$	11.3687	+	1.63458i	0.845032	+	0.121497i	0.551214	−	0.834364i	$-0.314165\pi$
$181$	11.3687	+	1.63458i	0.845032	+	0.121497i	0.293818	+	0.955861i	$0.405074\pi$
$182$	−0.892008	−	6.47957i	−0.0661200	−	0.480298i
$183$	−12.4374	+	2.53562i	−0.919399	+	0.187438i
$184$	−4.12252	+	2.45048i	−0.303916	+	0.180652i
$185$	32.7417	+	18.9034i	2.40722	+	1.38981i
$186$	−3.70799	−	14.6000i	−0.271883	−	1.07052i
$187$	1.79622	−	0.719098i	0.131353	−	0.0525856i
$188$	3.87555	+	1.76990i	0.282653	+	0.129084i
$189$	13.7150	+	0.948526i	0.997617	+	0.0689951i
$190$	−2.37217	−	5.19433i	−0.172096	−	0.376837i
$191$	2.56406	−	7.40836i	0.185529	−	0.536050i	−0.813430	−	0.581662i	$-0.802403\pi$
$191$	2.56406	−	7.40836i	0.185529	−	0.536050i	0.998959	+	0.0456120i	$0.0145238\pi$
$192$	−0.309551	+	1.70416i	−0.0223399	+	0.122988i
$193$	0.706282	−	0.673438i	0.0508393	−	0.0484751i	−0.664234	−	0.747525i	$-0.731242\pi$
$193$	0.706282	−	0.673438i	0.0508393	−	0.0484751i	0.715073	+	0.699050i	$0.246393\pi$
$194$	10.3940	+	2.00329i	0.746249	+	0.143828i
$195$	−6.11371	+	15.7586i	−0.437812	+	1.12850i
$196$	−0.913059	−	6.94020i	−0.0652185	−	0.495728i
$197$	6.11610	+	5.29963i	0.435754	+	0.377583i	0.844934	−	0.534871i	$-0.179640\pi$
$197$	6.11610	+	5.29963i	0.435754	+	0.377583i	−0.409180	+	0.912454i	$0.634185\pi$
$198$	1.15647	−	0.861452i	0.0821867	−	0.0612208i
$199$	−8.85094	+	22.1086i	−0.627427	+	1.56724i	0.184092	+	0.982909i	$0.441066\pi$
$199$	−8.85094	+	22.1086i	−0.627427	+	1.56724i	−0.811518	+	0.584327i	$0.801359\pi$
$200$	2.00289	+	10.3920i	0.141626	+	0.734826i
$201$	9.51075	−	21.4304i	0.670837	−	1.51158i
$202$	−16.0352	+	4.70836i	−1.12823	+	0.331279i
$203$	−6.19124	+	1.15481i	−0.434540	+	0.0810520i
$204$	6.95986	−	0.406324i	0.487288	−	0.0284483i
$205$	17.0099	−	32.9946i	1.18802	−	2.30444i
$206$	5.83869	−	10.1129i	0.406801	−	0.704599i
$207$	12.3619	+	7.36089i	0.859214	+	0.511617i
$208$	−1.23607	−	2.14094i	−0.0857062	−	0.148448i
$209$	−0.375928	−	0.584955i	−0.0260035	−	0.0404622i
$210$	−6.64403	+	16.8257i	−0.458482	+	1.16109i
$211$	3.20656	−	7.02138i	0.220748	−	0.483372i	−0.766563	−	0.642169i	$-0.778035\pi$
$211$	3.20656	−	7.02138i	0.220748	−	0.483372i	0.987311	+	0.158798i	$0.0507618\pi$
$212$	0.594204	+	0.566573i	0.0408101	+	0.0389124i
$213$	−5.03242	+	0.535009i	−0.344815	+	0.0366582i
$214$	2.30799	+	11.9750i	0.157771	+	0.818593i
$215$	19.0145	+	24.1789i	1.29678	+	1.64899i
$216$	4.93605	−	1.62340i	0.335855	−	0.110459i
$217$	18.6629	+	13.4591i	1.26692	+	0.913666i
$218$	3.88330	+	2.49565i	0.263010	+	0.169027i
$219$	−1.83493	+	0.283923i	−0.123993	+	0.0191857i
$220$	0.620622	+	1.79317i	0.0418424	+	0.120896i
$221$	−7.20165	+	6.86676i	−0.484435	+	0.461908i
$222$	12.6523	+	10.7281i	0.849165	+	0.720021i
$223$	9.70521	+	11.2004i	0.649909	+	0.750035i	0.981094	−	0.193531i	$-0.0619939\pi$
$223$	9.70521	+	11.2004i	0.649909	+	0.750035i	−0.331185	+	0.943566i	$0.607448\pi$
$224$	−1.30912	−	2.29918i	−0.0874690	−	0.153620i
$225$	24.5307	−	20.1567i	1.63538	−	1.34378i
$226$	−0.909134	−	9.52088i	−0.0604747	−	0.633320i
$227$	5.12155	+	4.02763i	0.339929	+	0.267323i	0.773500	−	0.633796i	$-0.218504\pi$
$227$	5.12155	+	4.02763i	0.339929	+	0.267323i	−0.433571	+	0.901119i	$0.642747\pi$
$228$	−0.616751	−	2.42841i	−0.0408453	−	0.160826i
$229$	7.18445	−	4.14795i	0.474762	−	0.274104i	−0.243469	−	0.969909i	$-0.578285\pi$
$229$	7.18445	−	4.14795i	0.474762	−	0.274104i	0.718231	+	0.695805i	$0.244952\pi$
$230$	−14.1491	+	12.5785i	−0.932964	+	0.829400i
$231$	−0.509214	+	2.14311i	−0.0335038	+	0.141006i
$232$	−2.00254	+	1.28696i	−0.131473	+	0.0844928i
$233$	−1.50777	−	3.76622i	−0.0987771	−	0.246733i	0.870746	−	0.491733i	$-0.163636\pi$
$233$	−1.50777	−	3.76622i	−0.0987771	−	0.246733i	−0.969523	+	0.245000i	$0.921212\pi$
$234$	−3.87501	+	6.32359i	−0.253318	+	0.413386i
$235$	16.3448	+	3.96520i	1.06621	+	0.258661i
$236$	0.914895	+	0.651494i	0.0595546	+	0.0424086i
$237$	−0.882105	−	0.678525i	−0.0572989	−	0.0440750i
$238$	−7.75130	+	7.30264i	−0.502442	+	0.473360i
$239$	5.15173	−	17.5452i	0.333238	−	1.13490i	−0.607090	−	0.794633i	$-0.707663\pi$
$239$	5.15173	−	17.5452i	0.333238	−	1.13490i	0.940328	−	0.340270i	$-0.110519\pi$
$240$	0.0732605	+	6.83699i	0.00472895	+	0.441326i
$241$	−10.8305	−	21.0082i	−0.697651	−	1.35325i	−0.925197	−	0.379487i	$-0.876100\pi$
$241$	−10.8305	−	21.0082i	−0.697651	−	1.35325i	0.227546	−	0.973767i	$-0.426930\pi$
$242$	−4.93461	−	9.57182i	−0.317209	−	0.615300i
$243$	−11.3460	−	10.6897i	−0.727844	−	0.685743i
$244$	2.06466	−	7.03159i	0.132176	−	0.450151i
$245$	−8.72412	−	26.2196i	−0.557363	−	1.67511i
$246$	9.93048	−	12.9099i	0.633144	−	0.823108i
$247$	2.91300	+	2.07434i	0.185350	+	0.131987i
$248$	8.45175	+	2.05037i	0.536686	+	0.130199i
$249$	−10.2314	+	10.9632i	−0.648389	+	0.694766i
$250$	8.19154	+	20.4615i	0.518078	+	1.29410i
$251$	−6.20727	+	3.98917i	−0.391799	+	0.251794i	−0.721678	−	0.692229i	$-0.756629\pi$
$251$	−6.20727	+	3.98917i	−0.391799	+	0.251794i	0.329878	+	0.944023i	$0.392992\pi$
$252$	−4.18763	+	6.74268i	−0.263796	+	0.424749i
$253$	−1.48739	+	1.76125i	−0.0935112	+	0.110729i
$254$	−12.2313	+	7.06173i	−0.767459	+	0.443092i
$255$	26.6744	−	6.77458i	1.67042	−	0.424241i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	−1.81925	−	19.0521i	−0.113482	−	1.18844i	−0.855408	−	0.517955i	$-0.826693\pi$
$257$	−1.81925	−	19.0521i	−0.113482	−	1.18844i	0.741926	−	0.670482i	$-0.233913\pi$
$258$	6.31256	+	11.9291i	0.393003	+	0.742671i
$259$	−25.3386	−	0.151905i	−1.57446	−	0.00943892i
$260$	−6.39075	−	7.37532i	−0.396338	−	0.457398i
$261$	6.25962	+	3.43730i	0.387461	+	0.212763i
$262$	−8.44259	+	8.04999i	−0.521585	+	0.497330i
$263$	−4.95711	−	14.3226i	−0.305668	−	0.883171i	−0.988315	−	0.152423i	$-0.951292\pi$
$263$	−4.95711	−	14.3226i	−0.305668	−	0.883171i	0.682647	−	0.730748i	$-0.260829\pi$
$264$	0.127310	+	0.822779i	0.00783541	+	0.0506386i
$265$	2.72655	+	1.75224i	0.167490	+	0.107640i
$266$	3.10420	+	2.23866i	0.190331	+	0.137261i
$267$	0.271809	−	3.20959i	0.0166344	−	0.196424i
$268$	8.36775	+	10.6405i	0.511142	+	0.649969i
$269$	−2.86689	−	14.8748i	−0.174797	−	0.906935i	−0.958347	−	0.285606i	$-0.907805\pi$
$269$	−2.86689	−	14.8748i	−0.174797	−	0.906935i	0.783550	−	0.621329i	$-0.213407\pi$
$270$	17.9204	−	9.98031i	1.09060	−	0.607382i
$271$	−12.9624	−	12.3596i	−0.787407	−	0.750791i	0.185337	−	0.982675i	$-0.440662\pi$
$271$	−12.9624	−	12.3596i	−0.787407	−	0.750791i	−0.972743	+	0.231884i	$0.925511\pi$
$272$	−1.67210	+	3.66138i	−0.101386	+	0.222004i
$273$	−1.66516	−	11.2057i	−0.100780	−	0.678203i
$274$	1.54331	+	2.40144i	0.0932350	+	0.145077i
$275$	2.54361	+	4.40565i	0.153385	+	0.265671i
$276$	−7.09452	+	4.32062i	−0.427040	+	0.260071i
$277$	10.1579	−	17.5940i	0.610329	−	1.05712i	−0.380856	−	0.924635i	$-0.624371\pi$
$277$	10.1579	−	17.5940i	0.610329	−	1.05712i	0.991185	−	0.132487i	$-0.0422962\pi$
$278$	−1.32183	+	2.56399i	−0.0792780	+	0.153778i
$279$	−6.69302	−	25.2176i	−0.400701	−	1.50974i
$280$	−6.79210	−	7.93411i	−0.405906	−	0.474154i
$281$	20.8644	−	6.12633i	1.24466	−	0.365466i	0.407898	−	0.913028i	$-0.366262\pi$
$281$	20.8644	−	6.12633i	1.24466	−	0.365466i	0.836765	+	0.547562i	$0.184444\pi$
$282$	6.74511	+	2.99346i	0.401665	+	0.178258i
$283$	−5.55582	−	28.8264i	−0.330259	−	1.71355i	−0.644840	−	0.764318i	$-0.723076\pi$
$283$	−5.55582	−	28.8264i	−0.330259	−	1.71355i	0.314580	−	0.949231i	$-0.398136\pi$
$284$	1.08594	−	2.71254i	0.0644386	−	0.160960i
$285$	−4.20489	−	8.95231i	−0.249076	−	0.530289i
$286$	−0.898074	−	0.778186i	−0.0531042	−	0.0460151i
$287$	1.03481	+	24.8580i	0.0610830	+	1.46732i
$288$	−0.504501	+	2.95728i	−0.0297280	+	0.174259i
$289$	−0.783985	−	0.151101i	−0.0461168	−	0.00888828i
$290$	−6.80085	+	6.48459i	−0.399359	+	0.380789i
$291$	18.0392	+	3.27670i	1.05747	+	0.192084i
$292$	0.350619	−	1.01305i	0.0205184	−	0.0592841i
$293$	0.605831	+	1.32659i	0.0353930	+	0.0775000i	0.926503	−	0.376288i	$-0.122800\pi$
$293$	0.605831	+	1.32659i	0.0353930	+	0.0775000i	−0.891110	+	0.453788i	$0.850072\pi$
$294$	−1.71017	−	12.0031i	−0.0997393	−	0.700037i
$295$	4.03306	+	1.84184i	0.234814	+	0.107236i
$296$	−8.89122	+	3.55951i	−0.516792	+	0.206892i
$297$	1.98696	−	1.51346i	0.115295	−	0.0878196i
$298$	−15.3232	−	8.84684i	−0.887648	−	0.512484i
$299$	3.73508	−	11.2523i	0.216005	−	0.650736i
$300$	3.66178	+	17.9613i	0.211413	+	1.03699i
$301$	−19.0929	−	7.77679i	−1.10050	−	0.448247i
$302$	−22.6416	−	3.25538i	−1.30288	−	0.187326i
$303$	−27.6848	+	8.45224i	−1.59045	+	0.485568i
$304$	1.40578	+	0.341038i	0.0806270	+	0.0195599i
$305$	2.74992	−	28.7985i	0.157460	−	1.64900i
$306$	12.0466	−	0.832897i	0.688658	−	0.0476135i
$307$	2.40482	+	16.7259i	0.137250	+	0.954598i	0.935766	+	0.352623i	$0.114710\pi$
$307$	2.40482	+	16.7259i	0.137250	+	0.954598i	−0.798515	+	0.601975i	$0.794381\pi$
$308$	−0.956131	−	0.838581i	−0.0544806	−	0.0477826i
$309$	9.92464	−	17.6234i	0.564593	−	1.00256i
$310$	34.2927	+	1.63356i	1.94769	+	0.0927800i
$311$	−2.67656	−	5.19179i	−0.151774	−	0.294400i	0.800675	−	0.599099i	$-0.204474\pi$
$311$	−2.67656	−	5.19179i	−0.151774	−	0.294400i	−0.952449	+	0.304699i	$0.901444\pi$
$312$	−2.18055	−	3.68507i	−0.123449	−	0.208626i
$313$	18.4029	−	4.46449i	1.04019	−	0.252348i	0.320942	−	0.947099i	$-0.396001\pi$
$313$	18.4029	−	4.46449i	1.04019	−	0.252348i	0.719250	+	0.694751i	$0.244486\pi$
$314$	−2.70636	−	18.8232i	−0.152729	−	1.06225i
$315$	−11.1949	+	29.2646i	−0.630760	+	1.64888i
$316$	0.584459	−	0.266914i	0.0328784	−	0.0150151i
$317$	−12.2338	+	12.8304i	−0.687116	+	0.720626i	−0.971225	−	0.238166i	$-0.923454\pi$
$317$	−12.2338	+	12.8304i	−0.687116	+	0.720626i	0.284109	+	0.958792i	$0.408302\pi$
$318$	1.03965	+	0.970249i	0.0583005	+	0.0544089i
$319$	−0.707319	+	0.899430i	−0.0396023	+	0.0503584i
$320$	−3.50873	−	1.80888i	−0.196144	−	0.101119i
$321$	4.21956	+	20.6973i	0.235513	+	1.15521i
$322$	4.06950	−	12.0183i	0.226784	−	0.669753i
$323$		−	5.82256i		−	0.323976i
$324$	8.51887	−	2.90326i	0.473270	−	0.161292i
$325$	−20.5658	−	16.1731i	−1.14078	−	0.897123i
$326$	−11.9908	+	8.53863i	−0.664111	+	0.472911i
$327$	6.77201	+	4.25027i	0.374493	+	0.235041i
$328$	3.90638	+	8.55378i	0.215694	+	0.472304i
$329$	−10.8346	+	3.11091i	−0.597333	+	0.171510i
$330$	1.10817	+	3.09417i	0.0610026	+	0.170328i
$331$	−4.57125	−	18.8429i	−0.251258	−	1.03570i	−0.947972	−	0.318352i	$-0.896871\pi$
$331$	−4.57125	−	18.8429i	−0.251258	−	1.03570i	0.696714	−	0.717349i	$-0.254645\pi$
$332$	−2.83170	−	8.18165i	−0.155410	−	0.449026i
$333$	22.1122	+	18.3457i	1.21174	+	1.00534i
$334$	1.05329	−	22.1113i	0.0576336	−	1.20988i
$335$	40.3846	+	34.9934i	2.20644	+	1.91190i
$336$	−2.30999	−	3.95777i	−0.126021	−	0.215914i
$337$	6.92942	−	0.996301i	0.377470	−	0.0542720i	0.0490311	−	0.998797i	$-0.484387\pi$
$337$	6.92942	−	0.996301i	0.377470	−	0.0542720i	0.328439	+	0.944525i	$0.393478\pi$
$338$	−6.50964	−	2.25301i	−0.354078	−	0.122547i
$339$	−1.75127	−	16.4728i	−0.0951158	−	0.894681i
$340$	−3.74607	+	15.4415i	−0.203159	+	0.837434i
$341$	4.16154	−	0.397379i	0.225360	−	0.0215193i
$342$	−1.11325	−	4.19445i	−0.0601977	−	0.226810i
$343$	13.7763	+	12.3779i	0.743850	+	0.668346i
$344$	−7.79211			−0.420122
$345$	−24.2721	+	22.0479i	−1.30677	+	1.18702i
$346$	3.36672	−	5.83132i	0.180996	−	0.313494i
$347$	24.8878	−	1.18555i	1.33605	−	0.0636439i	0.632649	−	0.774438i	$-0.281967\pi$
$347$	24.8878	−	1.18555i	1.33605	−	0.0636439i	0.703400	+	0.710794i	$0.251664\pi$
$348$	−3.44442	+	2.26611i	−0.184640	+	0.121476i
$349$	7.70494	−	16.8715i	0.412436	−	0.903108i	−0.583421	−	0.812170i	$-0.698286\pi$
$349$	7.70494	−	16.8715i	0.412436	−	0.903108i	0.995857	−	0.0909383i	$-0.0289866\pi$
$350$	−21.9058	−	17.4405i	−1.17092	−	0.932234i
$351$	−6.59398	+	11.0241i	−0.351961	+	0.588421i
$352$	−0.454248	−	0.157217i	−0.0242115	−	0.00837967i
$353$	4.67678	−	11.6820i	0.248920	−	0.621772i	−0.750307	−	0.661090i	$-0.770094\pi$
$353$	4.67678	−	11.6820i	0.248920	−	0.621772i	0.999227	+	0.0393176i	$0.0125184\pi$
$354$	1.59664	+	1.11138i	0.0848607	+	0.0590690i
$355$	2.18285	−	11.3257i	0.115854	−	0.601106i
$356$	1.56447	+	1.00542i	0.0829168	+	0.0532874i
$357$	−13.2893	+	12.7917i	−0.703347	+	0.677007i
$358$	10.9042	−	12.5841i	0.576302	−	0.665088i
$359$	−2.43155	−	10.0230i	−0.128332	−	0.528992i	−0.999291	−	0.0376372i	$-0.988017\pi$
$359$	−2.43155	−	10.0230i	−0.128332	−	0.528992i	0.870959	−	0.491355i	$-0.163498\pi$
$360$	0.253767	+	11.8400i	0.0133747	+	0.624021i
$361$	16.6019	−	3.19976i	0.873786	−	0.168408i
$362$	−6.66233	+	9.35593i	−0.350164	+	0.491737i
$363$	−8.72415	−	16.4863i	−0.457899	−	0.865309i
$364$	6.16801	+	2.17626i	0.323292	+	0.114067i
$365$	0.602250	−	4.18874i	0.0315232	−	0.219249i
$366$	3.44540	−	12.2167i	0.180094	−	0.638576i
$367$	−29.7207	−	17.1592i	−1.55141	−	0.895705i	−0.998028	−	0.0627752i	$-0.980005\pi$
$367$	−29.7207	−	17.1592i	−1.55141	−	0.895705i	−0.553379	−	0.832930i	$-0.686662\pi$
$368$	−0.289027	−	4.78711i	−0.0150666	−	0.249546i
$369$	16.9595	−	22.5437i	0.882877	−	1.17358i
$370$	−31.8051	+	20.4399i	−1.65347	+	1.06262i
$371$	−2.16911	−	0.116365i	−0.112615	−	0.00604135i
$372$	14.6761	+	3.39429i	0.760918	+	0.175986i
$373$	−0.714030	+	0.748853i	−0.0369711	+	0.0387741i	−0.741960	−	0.670444i	$-0.766104\pi$
$373$	−0.714030	+	0.748853i	−0.0369711	+	0.0387741i	0.704989	+	0.709218i	$0.250952\pi$
$374$	−0.183916	+	1.92605i	−0.00951006	+	0.0995938i
$375$	14.5671	+	35.2863i	0.752241	+	1.82217i
$376$	−3.34903	+	2.63371i	−0.172713	+	0.135823i
$377$	1.65793	−	5.64639i	0.0853877	−	0.290804i
$378$	−7.12764	+	11.7557i	−0.366606	+	0.604648i
$379$	−3.09942	+	4.82279i	−0.159206	+	0.247730i	−0.911688	−	0.410883i	$-0.865220\pi$
$379$	−3.09942	+	4.82279i	−0.159206	+	0.247730i	0.752481	+	0.658613i	$0.228857\pi$
$380$	5.70390	+	0.271710i	0.292604	+	0.0139384i
$381$	−21.0529	+	12.4576i	−1.07857	+	0.638221i
$382$	5.40989	+	5.67373i	0.276794	+	0.290293i
$383$	−1.05017	+	0.825863i	−0.0536612	+	0.0421996i	−0.644629	−	0.764495i	$-0.722988\pi$
$383$	−1.05017	+	0.825863i	−0.0536612	+	0.0421996i	0.590968	+	0.806695i	$0.298746\pi$
$384$	−1.37288	−	1.05603i	−0.0700594	−	0.0538905i
$385$	−4.33267	−	2.53622i	−0.220813	−	0.129258i
$386$	0.274939	+	0.936355i	0.0139940	+	0.0476592i
$387$	11.1544	+	20.5434i	0.567011	+	1.04428i
$388$	−6.54342	+	8.32063i	−0.332192	+	0.422416i
$389$	1.18351	+	24.8448i	0.0600061	+	1.25968i	0.805268	+	0.592911i	$0.202022\pi$
$389$	1.18351	+	24.8448i	0.0600061	+	1.25968i	−0.745262	+	0.666772i	$0.767675\pi$
$390$	−11.2053	−	12.6551i	−0.567405	−	0.640816i
$391$	−18.4513	+	5.67335i	−0.933121	+	0.286913i
$392$	6.58708	+	2.36862i	0.332698	+	0.119633i
$393$	−14.4728	+	14.0989i	−0.730054	+	0.711194i
$394$	−7.51306	+	3.00778i	−0.378502	+	0.151530i
$395$	2.06609	−	1.47126i	0.103956	−	0.0740269i
$396$	0.235765	+	1.42265i	0.0118476	+	0.0714909i
$397$	−9.51556	+	13.3627i	−0.477572	+	0.670657i	−0.981140	−	0.193299i	$-0.938081\pi$
$397$	−9.51556	+	13.3627i	−0.477572	+	0.670657i	0.503567	+	0.863956i	$0.332021\pi$
$398$	−15.5952	−	17.9978i	−0.781715	−	0.902147i
$399$	5.41787	+	3.81964i	0.271233	+	0.191221i
$400$	−10.1546	−	2.98165i	−0.507728	−	0.149082i
$401$	−17.0771	−	3.29135i	−0.852791	−	0.164362i	−0.255919	−	0.966698i	$-0.582378\pi$
$401$	−17.0771	−	3.29135i	−0.852791	−	0.164362i	−0.596872	+	0.802336i	$0.703590\pi$
$402$	14.6900	+	18.2735i	0.732671	+	0.911397i
$403$	−19.1100	+	9.85187i	−0.951935	+	0.490756i
$404$	3.16280	−	16.4102i	0.157355	−	0.816436i
$405$	30.8521	−	17.6180i	1.53305	−	0.875445i
$406$	1.81055	−	6.03216i	0.0898562	−	0.299371i
$407$	−3.47920	+	3.01474i	−0.172458	+	0.149435i
$408$	−2.82804	+	6.37236i	−0.140009	+	0.315479i
$409$	−0.789214	+	3.25318i	−0.0390241	+	0.160860i	−0.987990	−	0.154520i	$-0.950617\pi$
$409$	−0.789214	+	3.25318i	−0.0390241	+	0.160860i	0.948966	+	0.315380i	$0.102132\pi$
$410$	21.5324	+	30.2380i	1.06341	+	1.49335i
$411$	2.71751	+	4.13054i	0.134045	+	0.203745i
$412$	6.31326	+	9.82363i	0.311032	+	0.483976i
$413$	−2.95977	+	0.264729i	−0.145641	+	0.0130264i
$414$	−12.2072	+	7.61477i	−0.599950	+	0.374245i
$415$	−17.0887	−	29.5984i	−0.838849	−	1.45293i
$416$	2.46935	−	0.117629i	0.121070	−	0.00576726i
$417$	−2.24176	+	4.46524i	−0.109779	+	0.218664i
$418$	0.692189	−	0.0660960i	0.0338561	−	0.00323286i
$419$	−3.82939	+	1.12441i	−0.187078	+	0.0549310i	−0.373929	−	0.927457i	$-0.621990\pi$
$419$	−3.82939	+	1.12441i	−0.187078	+	0.0549310i	0.186852	+	0.982388i	$0.440172\pi$
$420$	−11.9108	−	13.6154i	−0.581189	−	0.664366i
$421$	−9.13918	+	7.91914i	−0.445416	+	0.385955i	−0.848489	−	0.529212i	$-0.822487\pi$
$421$	−9.13918	+	7.91914i	−0.445416	+	0.385955i	0.403073	+	0.915168i	$0.367942\pi$
$422$	4.77152	+	6.06748i	0.232274	+	0.295360i
$423$	11.7378	+	5.05935i	0.570709	+	0.245994i
$424$	−0.775870	+	0.268531i	−0.0376796	+	0.0130410i
$425$	−2.02694	+	42.5506i	−0.0983208	+	2.06401i
$426$	1.83045	−	4.71815i	0.0886857	−	0.228595i
$427$	7.94870	+	17.6850i	0.384665	+	0.855839i
$428$	−11.7014	−	3.43583i	−0.565607	−	0.166077i
$429$	−1.56986	−	1.33111i	−0.0757937	−	0.0642667i
$430$	−30.2040	+	5.82134i	−1.45657	+	0.280730i
$431$	−28.8213	−	2.75210i	−1.38827	−	0.132564i	−0.626002	−	0.779821i	$-0.715310\pi$
$431$	−28.8213	−	2.75210i	−1.38827	−	0.132564i	−0.762272	+	0.647257i	$0.775916\pi$
$432$	−0.818888	+	5.13122i	−0.0393988	+	0.246876i
$433$	23.8421	+	10.8883i	1.14578	+	0.523259i	0.895564	−	0.444932i	$-0.146772\pi$
$433$	23.8421	+	10.8883i	1.14578	+	0.523259i	0.250213	+	0.968191i	$0.419499\pi$
$434$	−20.5148	+	10.4209i	−0.984742	+	0.500220i
$435$	−11.6584	+	11.3572i	−0.558977	+	0.544537i
$436$	−3.99765	+	2.30805i	−0.191453	+	0.110535i
$437$	3.25699	+	6.12536i	0.155803	+	0.293016i
$438$	0.588455	−	1.76106i	0.0281175	−	0.0841465i
$439$	25.0551	+	12.9168i	1.19582	+	0.616486i	0.936962	−	0.349431i	$-0.113625\pi$
$439$	25.0551	+	12.9168i	1.19582	+	0.616486i	0.258853	+	0.965917i	$0.416655\pi$
$440$	−1.87822	−	0.270047i	−0.0895406	−	0.0128740i
$441$	−3.18470	−	20.7571i	−0.151652	−	0.988434i
$442$	−2.80343	−	9.54761i	−0.133346	−	0.454133i
$443$	−32.1840	−	22.9181i	−1.52911	−	1.08887i	−0.964691	−	0.263386i	$-0.915161\pi$
$443$	−32.1840	−	22.9181i	−1.52911	−	1.08887i	−0.564419	−	0.825488i	$-0.690900\pi$
$444$	−15.3331	+	6.32990i	−0.727677	+	0.300404i
$445$	6.81537	+	2.72846i	0.323080	+	0.129342i
$446$	−14.4025	+	3.49401i	−0.681979	+	0.165446i
$447$	−26.7032	−	15.0379i	−1.26302	−	0.711270i
$448$	2.64346	−	0.110045i	0.124892	−	0.00519912i
$449$	−9.48819	+	14.7639i	−0.447776	+	0.696752i	−0.989617	−	0.143728i	$-0.954091\pi$
$449$	−9.48819	+	14.7639i	−0.447776	+	0.696752i	0.541842	+	0.840481i	$0.317727\pi$
$450$	6.67535	+	31.0401i	0.314679	+	1.46324i
$451$	3.11926	+	3.27139i	0.146880	+	0.154044i
$452$	8.87909	+	3.55465i	0.417637	+	0.167197i
$453$	−39.2746	−	5.21796i	−1.84528	−	0.245161i
$454$	−5.92673	+	2.70665i	−0.278155	+	0.127029i
$455$	25.5345	+	3.82768i	1.19707	+	0.179444i
$456$	2.44107	+	0.564573i	0.114314	+	0.0264385i
$457$	−7.91749	−	19.7769i	−0.370365	−	0.925126i	−0.990106	−	0.140320i	$-0.955187\pi$
$457$	−7.91749	−	19.7769i	−0.370365	−	0.925126i	0.619741	−	0.784806i	$-0.287237\pi$
$458$	0.394734	+	8.28649i	0.0184447	+	0.387202i
$459$	20.8487	−	1.66610i	0.973132	−	0.0777670i
$460$	−4.69670	−	18.3400i	−0.218985	−	0.855107i
$461$		−	2.33130i		−	0.108579i	−0.998525	−	0.0542896i	$-0.982711\pi$
$461$		−	2.33130i		−	0.108579i	0.998525	−	0.0542896i	$-0.0172894\pi$
$462$	−1.67154	−	1.43464i	−0.0777669	−	0.0667453i
$463$	−2.49735	+	17.3694i	−0.116062	+	0.807226i	0.845763	+	0.533559i	$0.179146\pi$
$463$	−2.49735	+	17.3694i	−0.116062	+	0.807226i	−0.961825	+	0.273667i	$0.911763\pi$
$464$	−0.226274	−	2.36965i	−0.0105045	−	0.110008i
$465$	59.4235	+	2.19283i	2.75570	+	0.101690i
$466$	4.03845	+	0.385625i	0.187078	+	0.0178637i
$467$	−4.87708	+	14.0914i	−0.225684	+	0.652072i	0.774134	+	0.633022i	$0.218186\pi$
$467$	−4.87708	+	14.0914i	−0.225684	+	0.652072i	−0.999819	+	0.0190505i	$0.993936\pi$
$468$	−3.84500	−	6.34189i	−0.177735	−	0.293154i
$469$	−35.1259	−	6.98862i	−1.62196	−	0.322704i
$470$	−11.0140	+	12.7108i	−0.508039	+	0.586308i
$471$	−5.03662	−	32.5506i	−0.232075	−	1.49985i
$472$	−0.998300	+	0.514659i	−0.0459505	+	0.0236891i
$473$	−3.53955	+	1.22505i	−0.162749	+	0.0563278i
$474$	1.00730	−	0.473128i	0.0462669	−	0.0217315i
$475$	15.1534	−	2.17874i	0.695288	−	0.0999673i
$476$	−2.93899	−	10.2359i	−0.134708	−	0.469161i
$477$	1.81863	+	1.66113i	0.0832691	+	0.0760579i
$478$	13.2341	+	12.6187i	0.605314	+	0.577166i
$479$	−7.86310	−	11.0422i	−0.359274	−	0.504530i	0.594893	−	0.803805i	$-0.297195\pi$
$479$	−7.86310	−	11.0422i	−0.359274	−	0.504530i	−0.954167	+	0.299275i	$0.903255\pi$
$480$	−6.11053	−	3.06777i	−0.278906	−	0.140024i
$481$	10.8491	−	21.0444i	0.494678	−	0.959542i
$482$	23.6356			1.07657
$483$	6.82514	−	20.8906i	0.310554	−	0.950556i
$484$	10.7689			0.489497
$485$	−19.1476	+	37.1411i	−0.869447	+	1.68649i
$486$	14.7004	−	5.18641i	0.666823	−	0.235260i
$487$	−17.3532	−	24.3691i	−0.786347	−	1.10427i	−0.992073	−	0.125660i	$-0.959895\pi$
$487$	−17.3532	−	24.3691i	−0.786347	−	1.10427i	0.205727	−	0.978610i	$-0.434044\pi$
$488$	5.30384	+	5.05720i	0.240094	+	0.228929i
$489$	−20.6091	+	15.0110i	−0.931974	+	0.678822i
$490$	27.3026	+	4.26023i	1.23340	+	0.192458i
$491$	−11.9498	+	1.71813i	−0.539288	+	0.0775380i	−0.406577	−	0.913617i	$-0.633278\pi$
$491$	−11.9498	+	1.71813i	−0.539288	+	0.0775380i	−0.132712	+	0.991155i	$0.542368\pi$
$492$	6.92441	+	14.7422i	0.312176	+	0.664631i
$493$	−9.05453	+	3.13380i	−0.407795	+	0.141139i
$494$	−3.17856	+	1.63866i	−0.143010	+	0.0737269i
$495$	1.97671	+	5.33838i	0.0888466	+	0.239942i
$496$	−5.69526	+	6.57268i	−0.255725	+	0.295122i
$497$	2.48455	+	7.32032i	0.111447	+	0.328361i
$498$	−5.05620	−	14.1177i	−0.226574	−	0.632628i
$499$	−3.12946	+	9.04199i	−0.140094	+	0.404775i	−0.993121	−	0.117092i	$-0.962643\pi$
$499$	−3.12946	+	9.04199i	−0.140094	+	0.404775i	0.853027	+	0.521867i	$0.174764\pi$
$500$	−21.9405	−	2.09506i	−0.981207	−	0.0936939i
$501$	1.41390	−	38.3153i	0.0631683	−	1.71180i
$502$	−0.701380	−	7.34518i	−0.0313041	−	0.327832i
$503$	−1.49888	+	10.4249i	−0.0668317	+	0.464825i	0.928733	+	0.370749i	$0.120899\pi$
$503$	−1.49888	+	10.4249i	−0.0668317	+	0.464825i	−0.995565	+	0.0940763i	$0.970010\pi$
$504$	−4.07425	−	6.81179i	−0.181481	−	0.303421i
$505$		−	65.9723i		−	2.93573i
$506$	−0.883904	−	2.12909i	−0.0392943	−	0.0946498i
$507$	−11.3162	−	3.78129i	−0.502569	−	0.167933i
$508$	−0.672021	−	14.1075i	−0.0298161	−	0.625918i
$509$	9.66720	+	24.1475i	0.428491	+	1.07032i	0.972844	+	0.231463i	$0.0743512\pi$
$509$	9.66720	+	24.1475i	0.428491	+	1.07032i	−0.544352	+	0.838857i	$0.683225\pi$
$510$	−6.20144	+	26.8135i	−0.274605	+	1.18732i
$511$	1.03833	+	2.63937i	0.0459330	+	0.116759i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−2.00594	−	7.24392i	−0.0885643	−	0.319827i
$514$	17.7678	+	7.11316i	0.783704	+	0.313748i
$515$	31.8107	+	33.3621i	1.40175	+	1.47011i
$516$	−13.4956	+	0.144609i	−0.594109	+	0.00636607i
$517$	−1.10723	+	1.72288i	−0.0486958	+	0.0757721i
$518$	11.7458	−	22.4522i	0.516082	−	0.986494i
$519$	5.72277	−	10.1620i	0.251202	−	0.446064i
$520$	9.48386	−	2.30076i	0.415895	−	0.100895i
$521$	22.5021	+	9.00848i	0.985835	+	0.394669i	0.807865	−	0.589367i	$-0.200623\pi$
$521$	22.5021	+	9.00848i	0.985835	+	0.394669i	0.177970	+	0.984036i	$0.443047\pi$
$522$	−5.92352	+	3.98871i	−0.259265	+	0.174581i
$523$	1.39933	+	0.996458i	0.0611884	+	0.0435720i	0.610242	−	0.792215i	$-0.291072\pi$
$523$	1.39933	+	0.996458i	0.0611884	+	0.0435720i	−0.549053	+	0.835787i	$0.685012\pi$
$524$	−3.28650	−	11.1928i	−0.143571	−	0.488960i
$525$	−38.2635	−	29.7996i	−1.66996	−	1.30056i
$526$	15.0019	+	2.15695i	0.654116	+	0.0940476i
$527$	31.1146	+	16.0407i	1.35537	+	0.698744i
$528$	−0.789652	−	0.263861i	−0.0343652	−	0.0114831i
$529$	16.2373	−	16.2896i	0.705970	−	0.708241i
$530$	−2.80683	+	1.62053i	−0.121921	+	0.0703911i
$531$	2.78594	+	1.89522i	0.120899	+	0.0822455i
$532$	−3.41223	+	1.73331i	−0.147939	+	0.0751486i
$533$	−21.1462	−	9.65714i	−0.915943	−	0.418297i
$534$	2.72825	+	1.71231i	0.118063	+	0.0740990i
$535$	−47.9240	−	4.57619i	−2.07193	−	0.197846i
$536$	−13.2919	+	2.56181i	−0.574124	+	0.110653i
$537$	18.6519	−	21.9973i	0.804890	−	0.949256i
$538$	14.5350	+	4.26785i	0.626647	+	0.184000i
$539$	3.36455	+	0.0403425i	0.144921	+	0.00173767i
$540$	0.659244	+	20.5015i	0.0283693	+	0.882246i
$541$	0.0795830	−	1.67065i	0.00342154	−	0.0718270i	−0.996511	−	0.0834646i	$-0.973401\pi$
$541$	0.0795830	−	1.67065i	0.00342154	−	0.0718270i	0.999932	+	0.0116377i	$0.00370447\pi$
$542$	16.9253	−	5.85791i	0.727005	−	0.251619i
$543$	−11.3652	+	16.3277i	−0.487727	+	0.700687i
$544$	−2.48816	−	3.16396i	−0.106679	−	0.135654i
$545$	−13.7715	+	11.9331i	−0.589906	+	0.511157i
$546$	10.7231	+	3.65471i	0.458906	+	0.156407i
$547$	−8.73776	+	2.56564i	−0.373599	+	0.109699i	−0.463142	−	0.886284i	$-0.653278\pi$
$547$	−8.73776	+	2.56564i	−0.373599	+	0.109699i	0.0895421	+	0.995983i	$0.471460\pi$
$548$	−2.84168	+	0.271347i	−0.121390	+	0.0115914i
$549$	5.74054	−	21.2226i	0.245000	−	0.905761i
$550$	−5.08145	+	0.242059i	−0.216674	+	0.0103214i
$551$	1.72171	+	2.98209i	0.0733473	+	0.127041i
$552$	−0.589422	−	8.28569i	−0.0250875	−	0.352662i
$553$	−0.715444	+	1.54207i	−0.0304238	+	0.0655756i
$554$	10.9836	+	17.0907i	0.466646	+	0.726116i
$555$	−54.7056	+	35.9912i	−2.32212	+	1.52774i
$556$	−1.67327	−	2.34978i	−0.0709624	−	0.0996528i
$557$	−0.352733	+	1.45398i	−0.0149458	+	0.0616073i	−0.978796	−	0.204837i	$-0.934334\pi$
$557$	−0.352733	+	1.45398i	−0.0149458	+	0.0616073i	0.963850	+	0.266444i	$0.0858488\pi$
$558$	25.4812	+	5.60638i	1.07871	+	0.237337i
$559$	14.5582	−	12.6147i	0.615745	−	0.533546i
$560$	10.1644	−	2.40144i	0.429526	−	0.101479i
$561$	−0.282789	+	3.33924i	−0.0119393	+	0.140983i
$562$	−4.11530	+	21.3522i	−0.173594	+	0.900689i
$563$	5.71229	−	2.94489i	0.240744	−	0.124112i	−0.333633	−	0.942703i	$-0.608275\pi$
$563$	5.71229	−	2.94489i	0.240744	−	0.124112i	0.574377	+	0.818591i	$0.305244\pi$
$564$	−5.75148	+	4.62361i	−0.242181	+	0.194689i
$565$	37.0730	+	7.14523i	1.55967	+	0.300602i
$566$	28.1677	+	8.27079i	1.18398	+	0.347647i
$567$	−12.1266	+	20.4926i	−0.509268	+	0.860608i
$568$	1.91340	+	2.20818i	0.0802844	+	0.0926532i
$569$	2.23491	−	3.13850i	0.0936925	−	0.131573i	−0.765069	−	0.643948i	$-0.777295\pi$
$569$	2.23491	−	3.13850i	0.0936925	−	0.131573i	0.858761	+	0.512376i	$0.171235\pi$
$570$	9.88392	+	0.364734i	0.413992	+	0.0152770i
$571$	32.0112	−	22.7951i	1.33963	−	0.953945i	0.339718	−	0.940527i	$-0.389668\pi$
$571$	32.0112	−	22.7951i	1.33963	−	0.953945i	0.999910	−	0.0134175i	$-0.00427106\pi$
$572$	1.10320	−	0.441655i	0.0461271	−	0.0184665i
$573$	9.47497	+	9.72623i	0.395823	+	0.406319i
$574$	−22.5688	−	10.4708i	−0.942004	−	0.437043i
$575$	−21.6694	−	45.8973i	−0.903675	−	1.91405i
$576$	−2.39736	−	1.80352i	−0.0998898	−	0.0751467i
$577$	0.461219	+	9.68218i	0.0192008	+	0.403074i	0.987925	+	0.154934i	$0.0495164\pi$
$577$	0.461219	+	9.68218i	0.0192008	+	0.403074i	−0.968724	+	0.248141i	$0.920181\pi$
$578$	0.493546	−	0.627595i	0.0205288	−	0.0261045i
$579$	0.493558	+	1.61662i	0.0205116	+	0.0671844i
$580$	−2.64741	−	9.01625i	−0.109928	−	0.374379i
$581$	19.7685	+	11.5719i	0.820138	+	0.480085i
$582$	−11.1785	+	14.5324i	−0.463362	+	0.602386i
$583$	−0.310219	+	0.243959i	−0.0128480	+	0.0101038i
$584$	0.739770	+	0.775848i	0.0306119	+	0.0321048i
$585$	−19.6420	−	21.7101i	−0.812096	−	0.897600i
$586$	−1.45672	−	0.0693923i	−0.0601767	−	0.00286657i
$587$	−18.8153	+	29.2771i	−0.776589	+	1.20840i	0.197070	+	0.980389i	$0.436857\pi$
$587$	−18.8153	+	29.2771i	−0.776589	+	1.20840i	−0.973659	+	0.228007i	$0.926779\pi$
$588$	11.4525	+	3.98009i	0.472292	+	0.164136i
$589$	3.54435	−	12.0709i	0.146042	−	0.497375i
$590$	−3.48514	+	2.74075i	−0.143481	+	0.112835i
$591$	−12.9564	+	5.34875i	−0.532956	+	0.220018i
$592$	0.910376	−	9.53389i	0.0374162	−	0.391840i
$593$	23.7531	−	24.9115i	0.975422	−	1.02299i	−0.0243072	−	0.999705i	$-0.507738\pi$
$593$	23.7531	−	24.9115i	0.975422	−	1.02299i	0.999729	−	0.0232882i	$-0.00741353\pi$
$594$	0.434735	+	2.45959i	0.0178374	+	0.100918i
$595$	−19.0392	−	37.4810i	−0.780532	−	1.53657i
$596$	14.8849	−	9.56593i	0.609708	−	0.391836i
$597$	−27.3441	−	30.8818i	−1.11912	−	1.26391i
$598$	8.28991	+	8.47596i	0.339000	+	0.346608i
$599$	−31.9985	−	18.4743i	−1.30742	−	0.754840i	−0.325756	−	0.945454i	$-0.605619\pi$
$599$	−31.9985	−	18.4743i	−1.30742	−	0.754840i	−0.981665	+	0.190613i	$0.938952\pi$
$600$	−17.6425	−	4.97562i	−0.720254	−	0.203129i
$601$	4.73171	−	32.9098i	0.193011	−	1.34242i	−0.630973	−	0.775805i	$-0.717344\pi$
$601$	4.73171	−	32.9098i	0.193011	−	1.34242i	0.823984	−	0.566613i	$-0.191747\pi$
$602$	15.6612	−	13.4070i	0.638302	−	0.546427i
$603$	25.7815	+	31.3761i	1.04990	+	1.27773i
$604$	13.2685	−	18.6330i	0.539888	−	0.758166i
$605$	41.7429	−	8.04528i	1.69709	−	0.327087i
$606$	5.17327	−	28.4803i	0.210150	−	1.15693i
$607$	2.20423	+	9.08594i	0.0894667	+	0.368787i	0.998891	−	0.0470827i	$-0.0149924\pi$
$607$	2.20423	+	9.08594i	0.0894667	+	0.368787i	−0.909424	+	0.415870i	$0.863477\pi$
$608$	−0.947292	+	1.09323i	−0.0384178	+	0.0443365i
$609$	3.02384	−	10.4810i	0.122532	−	0.424712i
$610$	24.3370	+	15.6405i	0.985378	+	0.633264i
$611$	1.99333	−	10.3424i	0.0806417	−	0.418409i
$612$	−4.77976	+	11.0891i	−0.193210	+	0.448250i
$613$	−6.92166	+	17.2895i	−0.279563	+	0.698315i	0.720426	+	0.693532i	$0.243947\pi$
$613$	−6.92166	+	17.2895i	−0.279563	+	0.698315i	−0.999989	+	0.00478238i	$0.998478\pi$
$614$	−15.9685	−	5.52676i	−0.644437	−	0.223042i
$615$	37.8542	+	51.9712i	1.52643	+	2.09568i
$616$	1.18349	−	0.465584i	0.0476840	−	0.0187589i
$617$	−11.2776	+	24.6944i	−0.454018	+	0.994160i	0.534793	+	0.844983i	$0.320390\pi$
$617$	−11.2776	+	24.6944i	−0.454018	+	0.994160i	−0.988811	+	0.149177i	$0.952338\pi$
$618$	11.1166	+	16.8969i	0.447174	+	0.679693i
$619$	−15.4443	+	0.735702i	−0.620758	+	0.0295704i	−0.355606	−	0.934636i	$-0.615725\pi$
$619$	−15.4443	+	0.735702i	−0.620758	+	0.0295704i	−0.265153	+	0.964206i	$0.585422\pi$
$620$	−17.1658	+	29.7320i	−0.689394	+	1.19407i
$621$	−21.0009	+	13.4150i	−0.842738	+	0.538324i
$622$	5.84112			0.234208
$623$	−4.87430	+	0.671019i	−0.195285	+	0.0268838i
$624$	4.27460	−	0.249556i	0.171121	−	0.00999022i
$625$	−33.9347	+	3.24037i	−1.35739	+	0.129615i
$626$	−4.46449	+	18.4029i	−0.178437	+	0.735527i
$627$	1.19761	−	0.127321i	0.0478280	−	0.00508471i
$628$	17.9708	+	6.21977i	0.717114	+	0.248196i
$629$	−38.1572	+	5.48618i	−1.52143	+	0.218748i
$630$	−20.8817	−	23.3602i	−0.831945	−	0.930695i
$631$	33.2296	+	28.7936i	1.32285	+	1.14626i	0.978232	+	0.207514i	$0.0665372\pi$
$631$	33.2296	+	28.7936i	1.32285	+	1.14626i	0.344619	+	0.938743i	$0.388008\pi$
$632$	−0.0305725	+	0.641795i	−0.00121611	+	0.0255292i
$633$	8.37664	+	10.4200i	0.332942	+	0.414159i
$634$	−5.79828	−	16.7530i	−0.230279	−	0.665347i
$635$	−13.1443	−	54.1817i	−0.521617	−	2.15013i
$636$	−1.33879	+	0.479482i	−0.0530863	+	0.0190127i
$637$	−16.1414	+	6.23854i	−0.639545	+	0.247180i
$638$	−0.475332	−	1.04083i	−0.0188186	−	0.0412070i
$639$	3.08269	−	8.20557i	0.121949	−	0.324607i
$640$	3.21559	−	2.28981i	0.127107	−	0.0905127i
$641$	30.0897	+	23.6628i	1.18847	+	0.934624i	0.998884	−	0.0472395i	$-0.0150424\pi$
$641$	30.0897	+	23.6628i	1.18847	+	0.934624i	0.189588	+	0.981864i	$0.439285\pi$
$642$	−20.3300	−	5.73353i	−0.802360	−	0.226285i
$643$		−	37.2776i		−	1.47009i	−0.678021	−	0.735043i	$-0.737162\pi$
$643$		−	37.2776i		−	1.47009i	0.678021	−	0.735043i	$-0.262838\pi$
$644$	8.81752	+	9.12421i	0.347459	+	0.359544i
$645$	−52.2038	+	10.6428i	−2.05552	+	0.419061i
$646$	5.17530	+	2.66805i	0.203619	+	0.104973i
$647$	21.8422	−	27.7746i	0.858704	−	1.09193i	−0.136158	−	0.990687i	$-0.543475\pi$
$647$	21.8422	−	27.7746i	0.858704	−	1.09193i	0.994862	−	0.101244i	$-0.0322821\pi$
$648$	−1.32305	+	8.90222i	−0.0519742	+	0.349712i
$649$	−0.372562	+	0.390732i	−0.0146244	+	0.0153376i
$650$	23.7990	−	10.8686i	0.933474	−	0.426303i
$651$	−35.3372	+	18.4292i	−1.38498	+	0.722299i
$652$	−2.09492	−	14.5705i	−0.0820435	−	0.570625i
$653$	−32.9342	+	7.98976i	−1.28882	+	0.312663i	−0.820881	−	0.571099i	$-0.806517\pi$
$653$	−32.9342	+	7.98976i	−1.28882	+	0.312663i	−0.467935	+	0.883763i	$0.655002\pi$
$654$	−6.88091	+	4.07161i	−0.269065	+	0.159213i
$655$	−21.1011	−	40.9305i	−0.824490	−	1.59929i
$656$	−9.39291	−	0.447440i	−0.366732	−	0.0174696i
$657$	0.986493	−	3.06098i	0.0384867	−	0.119420i
$658$	2.19963	−	11.0557i	0.0857507	−	0.430996i
$659$	−1.68353	−	11.7092i	−0.0655811	−	0.456126i	−0.995980	−	0.0895775i	$-0.971448\pi$
$659$	−1.68353	−	11.7092i	−0.0655811	−	0.456126i	0.930399	−	0.366549i	$-0.119461\pi$
$660$	−3.25800	−	0.432852i	−0.126817	−	0.0168487i
$661$	−4.22641	+	44.2610i	−0.164388	+	1.72155i	0.417834	+	0.908523i	$0.362789\pi$
$661$	−4.22641	+	44.2610i	−0.164388	+	1.72155i	−0.582222	+	0.813030i	$0.697817\pi$
$662$	18.8429	+	4.57125i	0.732351	+	0.177667i
$663$	−5.03259	−	16.4840i	−0.195450	−	0.640184i
$664$	8.56970	+	1.23214i	0.332569	+	0.0478162i
$665$	−11.9316	+	9.26792i	−0.462689	+	0.359394i
$666$	−26.4387	+	11.2476i	−1.02448	+	0.435837i
$667$	7.77244	−	8.36165i	0.300950	−	0.323764i
$668$	19.1707	+	11.0682i	0.741736	+	0.428241i
$669$	−24.8796	+	6.31875i	−0.961901	+	0.244297i
$670$	−49.6087	+	19.8603i	−1.91655	+	0.767271i
$671$	3.20433	+	1.46337i	0.123702	+	0.0564928i
$672$	4.57631	−	0.239650i	0.176535	−	0.00924471i
$673$	9.10571	+	19.9387i	0.350999	+	0.768581i	0.999970	+	0.00776768i	$0.00247255\pi$
$673$	9.10571	+	19.9387i	0.350999	+	0.768581i	−0.648971	+	0.760814i	$0.724800\pi$
$674$	−2.28970	+	6.61565i	−0.0881959	+	0.254825i
$675$	12.1374	+	53.6361i	0.467170	+	2.06445i
$676$	4.98544	−	4.75361i	0.191748	−	0.182831i
$677$	23.0168	+	4.43612i	0.884607	+	0.170494i	0.611268	−	0.791424i	$-0.290660\pi$
$677$	23.0168	+	4.43612i	0.884607	+	0.170494i	0.273339	+	0.961918i	$0.411872\pi$
$678$	15.4441	+	5.99170i	0.593128	+	0.230110i
$679$	−1.16486	−	27.9819i	−0.0447032	−	1.07385i
$680$	−12.0084	−	10.4054i	−0.460502	−	0.399027i
$681$	−10.2146	+	4.79777i	−0.391424	+	0.183851i
$682$	−1.55372	+	3.88101i	−0.0594951	+	0.148612i
$683$	−3.41276	−	17.7071i	−0.130586	−	0.677542i	−0.986932	−	0.161140i	$-0.948483\pi$
$683$	−3.41276	−	17.7071i	−0.130586	−	0.677542i	0.856346	−	0.516403i	$-0.172729\pi$
$684$	4.23829	+	0.932510i	0.162055	+	0.0356554i
$685$	−10.8123	+	3.17477i	−0.413115	+	0.121302i
$686$	−17.3146	+	6.57296i	−0.661075	+	0.250957i
$687$	0.837445	+	14.3445i	0.0319505	+	0.547276i
$688$	3.57055	−	6.92590i	0.136126	−	0.264048i
$689$	1.01485	−	1.75777i	0.0386626	−	0.0669656i
$690$	−8.47481	−	31.6768i	−0.322631	−	1.20592i
$691$	0.780261	+	1.35145i	0.0296825	+	0.0514116i	0.880485	−	0.474074i	$-0.157217\pi$
$691$	0.780261	+	1.35145i	0.0296825	+	0.0514116i	−0.850803	+	0.525485i	$0.823884\pi$
$692$	3.64037	+	5.66452i	0.138386	+	0.215333i
$693$	−2.92164	−	2.45370i	−0.110984	−	0.0932084i
$694$	−10.3505	+	22.6644i	−0.392900	+	0.860331i
$695$	−8.24144	−	7.85820i	−0.312616	−	0.298078i
$696$	−0.435872	−	4.09992i	−0.0165217	−	0.155407i
$697$	7.16325	+	37.1665i	0.271327	+	1.40778i
$698$	11.4653	+	14.5794i	0.433970	+	0.551837i
$699$	7.00155	+	0.592937i	0.264823	+	0.0224269i
$700$	25.5396	−	11.4790i	0.965305	−	0.433865i
$701$	−15.3488	−	9.86410i	−0.579718	−	0.372562i	0.217676	−	0.976021i	$-0.430152\pi$
$701$	−15.3488	−	9.86410i	−0.579718	−	0.372562i	−0.797394	+	0.603459i	$0.793789\pi$
$702$	−6.77704	−	10.9125i	−0.255783	−	0.411865i
$703$	4.53121	+	13.0921i	0.170898	+	0.493777i
$704$	0.347888	−	0.331710i	0.0131115	−	0.0125018i
$705$	−18.8398	+	22.2190i	−0.709549	+	0.836815i
$706$	8.24039	+	9.50991i	0.310131	+	0.357910i
$707$	21.8782	+	38.4242i	0.822813	+	1.44509i
$708$	−1.71946	+	0.909892i	−0.0646211	+	0.0341958i
$709$	4.02173	+	42.1175i	0.151039	+	1.58175i	0.680067	+	0.733150i	$0.261951\pi$
$709$	4.02173	+	42.1175i	0.151039	+	1.58175i	−0.529028	+	0.848604i	$0.677443\pi$
$710$	9.06645	+	7.12994i	0.340258	+	0.267582i
$711$	1.73582	−	0.838128i	0.0650982	−	0.0314323i
$712$	−1.61054	+	0.929845i	−0.0603575	+	0.0348474i
$713$	−41.7055	+	0.529813i	−1.56188	+	0.0198416i
$714$	−5.28015	−	17.6735i	−0.197605	−	0.661415i
$715$	3.94630	−	2.53613i	0.147583	−	0.0948461i
$716$	6.18859	+	15.4583i	0.231278	+	0.577706i
$717$	23.1550	+	21.6094i	0.864741	+	0.807017i
$718$	10.0230	+	2.43155i	0.374054	+	0.0907445i
$719$	33.7440	+	24.0290i	1.25844	+	0.896132i	0.997599	−	0.0692502i	$-0.0220607\pi$
$719$	33.7440	+	24.0290i	1.25844	+	0.896132i	0.260841	+	0.965382i	$0.416000\pi$
$720$	−10.6401	−	5.19983i	−0.396532	−	0.193786i
$721$	−29.5912	−	8.88180i	−1.10204	−	0.330776i
$722$	−4.76339	+	16.2226i	−0.177275	+	0.603743i
$723$	40.9357	−	0.438639i	1.52242	−	0.0163132i
$724$	−5.26303	−	10.2089i	−0.195599	−	0.379409i
$725$	−11.5440	−	22.3921i	−0.428732	−	0.831623i
$726$	18.6513	−	0.199855i	0.692214	−	0.00741730i
$727$	−1.97736	+	6.73428i	−0.0733363	+	0.249761i	−0.988000	−	0.154456i	$-0.950638\pi$
$727$	−1.97736	+	6.73428i	−0.0733363	+	0.249761i	0.914663	+	0.404216i	$0.132456\pi$
$728$	−4.76069	+	4.48513i	−0.176443	+	0.166230i
$729$	25.3641	−	9.25542i	0.939411	−	0.342793i
$730$	3.44714	+	2.45469i	0.127584	+	0.0908523i
$731$	−30.4801	−	7.39439i	−1.12735	−	0.273491i
$732$	9.27985	+	8.66040i	0.342993	+	0.320098i
$733$	−3.60231	−	8.99814i	−0.133054	−	0.332354i	0.846847	−	0.531837i	$-0.178498\pi$
$733$	−3.60231	−	8.99814i	−0.133054	−	0.332354i	−0.979901	+	0.199483i	$0.936074\pi$
$734$	28.8705	−	18.5540i	1.06563	−	0.684839i
$735$	47.3658	+	6.87182i	1.74711	+	0.253471i
$736$	4.38740	+	1.93669i	0.161722	+	0.0713872i
$737$	−5.63507	+	3.25341i	−0.207571	+	0.119841i
$738$	12.2663	+	25.4043i	0.451530	+	0.935146i
$739$	2.48723	+	1.95598i	0.0914944	+	0.0719520i	0.662858	−	0.748745i	$-0.269343\pi$
$739$	2.48723	+	1.95598i	0.0914944	+	0.0719520i	−0.571364	+	0.820697i	$0.693586\pi$
$740$	−3.59377	−	37.6356i	−0.132110	−	1.38351i
$741$	−5.47470	+	2.89707i	−0.201118	+	0.106427i
$742$	1.09737	−	1.87466i	0.0402858	−	0.0688210i
$743$	−16.4735	−	19.0115i	−0.604355	−	0.697463i	0.368303	−	0.929706i	$-0.379939\pi$
$743$	−16.4735	−	19.0115i	−0.604355	−	0.697463i	−0.972658	+	0.232243i	$0.925394\pi$
$744$	−9.74193	+	11.4893i	−0.357156	+	0.421216i
$745$	50.5506	−	48.1999i	1.85203	−	1.76591i
$746$	−0.338420	−	0.977800i	−0.0123904	−	0.0357998i
$747$	−9.01909	−	24.3573i	−0.329991	−	0.891186i
$748$	−1.62767	−	1.04604i	−0.0595135	−	0.0382470i
$749$	29.4299	−	13.2276i	1.07535	−	0.483324i
$750$	−38.0387	−	3.22136i	−1.38898	−	0.117628i
$751$	−19.3824	−	24.6467i	−0.707274	−	0.899372i	0.291082	−	0.956698i	$-0.405985\pi$
$751$	−19.3824	−	24.6467i	−0.707274	−	0.899372i	−0.998355	+	0.0573264i	$0.981742\pi$
$752$	−0.806318	−	4.18357i	−0.0294034	−	0.152559i
$753$	−1.35107	−	12.7085i	−0.0492358	−	0.463123i
$754$	4.25900	+	4.06095i	0.155104	+	0.147891i
$755$	37.5113	−	82.1384i	1.36518	−	2.98932i
$756$	−7.18281	−	11.7221i	−0.261236	−	0.426328i
$757$	−7.57221	−	11.7826i	−0.275217	−	0.428246i	0.675939	−	0.736958i	$-0.263738\pi$
$757$	−7.57221	−	11.7826i	−0.275217	−	0.428246i	−0.951155	+	0.308712i	$0.900102\pi$
$758$	−2.86643	−	4.96480i	−0.104113	−	0.180330i
$759$	−1.57039	−	3.67109i	−0.0570016	−	0.133252i
$760$	−2.85518	+	4.94532i	−0.103568	+	0.179386i
$761$	1.45127	−	2.81507i	0.0526085	−	0.102046i	−0.861065	−	0.508494i	$-0.830202\pi$
$761$	1.45127	−	2.81507i	0.0526085	−	0.102046i	0.913674	+	0.406448i	$0.133233\pi$
$762$	−1.42572	−	24.4210i	−0.0516484	−	0.884678i
$763$	4.06361	−	11.5172i	0.147112	−	0.416949i
$764$	−7.52197	+	2.20865i	−0.272135	+	0.0799062i
$765$	−10.2430	+	46.5547i	−0.370336	+	1.68319i
$766$	−0.252841	−	1.31186i	−0.00913550	−	0.0473995i
$767$	1.03196	−	2.57771i	0.0372619	−	0.0930757i
$768$	1.56773	−	0.736360i	0.0565705	−	0.0265711i
$769$	0.0500264	+	0.0433482i	0.00180400	+	0.00156317i	0.655762	−	0.754967i	$-0.272347\pi$
$769$	0.0500264	+	0.0433482i	0.00180400	+	0.00156317i	−0.653958	+	0.756531i	$0.726893\pi$
$770$	4.23963	−	2.68887i	0.152786	−	0.0969000i
$771$	30.9050	+	11.9899i	1.11302	+	0.431806i
$772$	−0.958250	−	0.184688i	−0.0344882	−	0.00664705i
$773$	−15.7570	+	15.0242i	−0.566739	+	0.540384i	−0.918354	−	0.395760i	$-0.870481\pi$
$773$	−15.7570	+	15.0242i	−0.566739	+	0.540384i	0.351615	+	0.936145i	$0.385633\pi$
$774$	−23.3710	+	0.500912i	−0.840052	+	0.0180049i
$775$	−30.1038	+	86.9793i	−1.08136	+	3.12439i
$776$	−4.39731	−	9.62876i	−0.157854	−	0.345652i
$777$	19.9265	−	39.1041i	0.714860	−	1.40285i
$778$	−22.6253	−	10.3326i	−0.811156	−	0.370443i
$779$	12.6284	−	5.05564i	0.452459	−	0.181137i
$780$	16.3829	−	4.16081i	0.586601	−	0.148981i
$781$	1.21632	+	0.702242i	0.0435233	+	0.0251282i
$782$	3.41219	−	18.9998i	0.122020	−	0.679432i
$783$	−10.1852	+	7.01819i	−0.363990	+	0.250810i
$784$	−5.12369	+	4.76946i	−0.182989	+	0.170338i
$785$	74.3057	+	10.6835i	2.65208	+	0.381312i
$786$	−5.89978	−	19.3244i	−0.210438	−	0.689278i
$787$	−0.182080	−	0.0441722i	−0.00649046	−	0.00157457i	0.232512	−	0.972593i	$-0.425305\pi$
$787$	−0.182080	−	0.0441722i	−0.00649046	−	0.00157457i	−0.239003	+	0.971019i	$0.576821\pi$
$788$	0.769266	−	8.05612i	0.0274040	−	0.286987i
$789$	26.0227	+	3.45733i	0.926431	+	0.123084i
$790$	0.360967	+	2.51058i	0.0128426	+	0.0893225i
$791$	−23.9619	+	8.13278i	−0.851988	+	0.289168i
$792$	−1.37254	−	0.442340i	−0.0487710	−	0.0157179i
$793$	−18.0965	−	0.862040i	−0.642624	−	0.0306119i
$794$	−7.51699	−	14.5809i	−0.266768	−	0.517458i
$795$	−4.83122	+	2.85876i	−0.171346	+	0.101390i
$796$	23.1432	−	5.61447i	0.820288	−	0.199000i
$797$	0.224120	+	1.55879i	0.00793875	+	0.0552152i	0.993406	−	0.114652i	$-0.0365752\pi$
$797$	0.224120	+	1.55879i	0.00793875	+	0.0552152i	−0.985467	+	0.169867i	$0.945666\pi$
$798$	−5.87764	+	3.06534i	−0.208066	+	0.108512i
$799$	−15.5995	+	7.12407i	−0.551872	+	0.252032i
$800$	7.30328	−	7.65946i	0.258210	−	0.270803i
$801$	4.75697	+	2.91501i	0.168079	+	0.102997i
$802$	10.7507	−	13.6706i	0.379619	−	0.482725i
$803$	0.458015	+	0.236123i	0.0161630	+	0.00833260i
$804$	−22.9734	+	4.68361i	−0.810211	+	0.165178i
$805$	40.9952	+	28.7801i	1.44489	+	1.01437i
$806$		−	21.5000i		−	0.757305i
$807$	25.2531	+	7.12196i	0.888950	+	0.250705i
$808$	13.1366	+	10.3308i	0.462146	+	0.363435i
$809$	−28.6209	+	20.3808i	−1.00626	+	0.716552i	−0.959313	−	0.282346i	$-0.908887\pi$
$809$	−28.6209	+	20.3808i	−1.00626	+	0.716552i	−0.0469435	+	0.998898i	$0.514948\pi$
$810$	1.52225	+	35.4954i	0.0534866	+	1.24718i
$811$	−3.72789	−	8.16294i	−0.130904	−	0.286640i	0.832818	−	0.553546i	$-0.186726\pi$
$811$	−3.72789	−	8.16294i	−0.130904	−	0.286640i	−0.963722	+	0.266907i	$0.913999\pi$
$812$	4.53195	+	4.37338i	0.159040	+	0.153475i
$813$	29.2051	−	10.4597i	1.02427	−	0.366839i
$814$	−1.08535	−	4.47387i	−0.0380415	−	0.156809i
$815$	−19.0057	−	54.9135i	−0.665742	−	1.92354i
$816$	−4.36810	−	5.43364i	−0.152914	−	0.190216i
$817$	−0.536330	+	11.2590i	−0.0187638	+	0.393901i
$818$	−2.52991	−	2.19218i	−0.0884561	−	0.0766476i
$819$	18.6397	+	6.13078i	0.651324	+	0.214227i
$820$	−36.7433	+	5.28289i	−1.28313	+	0.184487i
$821$	−23.3854	−	8.09376i	−0.816156	−	0.282474i	−0.113077	−	0.993586i	$-0.536071\pi$
$821$	−23.3854	−	8.09376i	−0.816156	−	0.282474i	−0.703079	+	0.711112i	$0.748192\pi$
$822$	−4.91661	+	0.522697i	−0.171486	+	0.0182312i
$823$	−0.384895	+	1.58656i	−0.0134166	+	0.0553040i	−0.978126	−	0.208011i	$-0.933301\pi$
$823$	−0.384895	+	1.58656i	−0.0134166	+	0.0553040i	0.964710	+	0.263315i	$0.0848160\pi$
$824$	−11.6245	+	1.11000i	−0.404959	+	0.0386689i
$825$	−8.79633	+	0.513538i	−0.306249	+	0.0178791i
$826$	1.12095	−	2.75206i	0.0390027	−	0.0957563i
$827$	−0.864006			−0.0300444			−0.0150222	−	0.999887i	$-0.504782\pi$
$827$	−0.864006			−0.0300444			−0.0150222	+	0.999887i	$0.504782\pi$
$828$	−1.17462	−	14.3395i	−0.0408209	−	0.498331i
$829$	10.0805	−	17.4599i	0.350110	−	0.606408i	−0.636159	−	0.771558i	$-0.719478\pi$
$829$	10.0805	−	17.4599i	0.350110	−	0.606408i	0.986268	+	0.165151i	$0.0528110\pi$
$830$	34.1386	−	1.62622i	1.18497	−	0.0564470i
$831$	19.3402	+	29.3965i	0.670903	+	1.01975i
$832$	−1.02697	+	2.24874i	−0.0356036	+	0.0779611i
$833$	23.5187	+	15.5161i	0.814874	+	0.537601i
$834$	−2.94163	−	4.03865i	−0.101860	−	0.139847i
$835$	82.5787	+	28.5808i	2.85775	+	0.989078i
$836$	−0.258431	+	0.645529i	−0.00893801	+	0.0223261i
$837$	44.2363	+	9.23709i	1.52903	+	0.319281i
$838$	0.755311	−	3.91893i	0.0260918	−	0.135377i
$839$	−33.5425	−	21.5564i	−1.15801	−	0.744211i	−0.186795	−	0.982399i	$-0.559810\pi$
$839$	−33.5425	−	21.5564i	−1.15801	−	0.744211i	−0.971219	+	0.238188i	$0.923446\pi$
$840$	17.5598	−	4.34781i	0.605869	−	0.150014i
$841$	−15.2802	+	17.6343i	−0.526905	+	0.608080i
$842$	−2.85100	−	11.7520i	−0.0982520	−	0.405000i
$843$	−6.73124	+	37.0574i	−0.231836	+	1.27632i
$844$	−7.57943	+	1.46082i	−0.260895	+	0.0502833i
$845$	15.7734	−	22.1506i	0.542620	−	0.762003i
$846$	−9.87548	+	8.11460i	−0.339526	+	0.278986i
$847$	−21.6442	+	18.5288i	−0.743705	+	0.636658i
$848$	0.116844	−	0.812669i	0.00401244	−	0.0279072i
$849$	48.9386	+	13.8018i	1.67957	+	0.473678i
$850$	−36.8917	−	21.2994i	−1.26538	−	0.730565i
$851$	37.0728	−	27.1157i	1.27084	−	0.929513i
$852$	3.35489	+	3.78895i	0.114937	+	0.129807i
$853$	11.6355	−	7.47766i	0.398391	−	0.256030i	−0.326071	−	0.945345i	$-0.605725\pi$
$853$	11.6355	−	7.47766i	0.398391	−	0.256030i	0.724462	+	0.689315i	$0.242088\pi$
$854$	−19.3614	−	1.03867i	−0.662533	−	0.0355424i
$855$	17.1252	+	0.448271i	0.585671	+	0.0153305i
$856$	8.41577	−	8.82620i	0.287645	−	0.301673i
$857$	−3.70815	+	38.8335i	−0.126668	+	1.32653i	0.678990	+	0.734148i	$0.262418\pi$
$857$	−3.70815	+	38.8335i	−0.126668	+	1.32653i	−0.805658	+	0.592381i	$0.798188\pi$
$858$	1.90249	−	0.785398i	0.0649501	−	0.0268131i
$859$	17.2855	−	13.5935i	0.589773	−	0.463803i	−0.278125	−	0.960545i	$-0.589713\pi$
$859$	17.2855	−	13.5935i	0.589773	−	0.463803i	0.867898	+	0.496742i	$0.165471\pi$
$860$	8.66605	−	29.5139i	0.295510	−	1.00641i
$861$	−39.2824	−	17.7161i	−1.33874	−	0.603762i
$862$	15.6529	−	24.3563i	0.533138	−	0.829580i
$863$	8.23510	+	0.392286i	0.280326	+	0.0133536i	0.187274	−	0.982308i	$-0.440035\pi$
$863$	8.23510	+	0.392286i	0.280326	+	0.0133536i	0.0930519	+	0.995661i	$0.470338\pi$
$864$	−4.18557	−	3.07912i	−0.142396	−	0.104754i
$865$	18.3427	+	19.2373i	0.623672	+	0.654089i
$866$	−20.6030	+	16.2024i	−0.700118	+	0.550579i
$867$	0.843151	−	1.09612i	0.0286349	−	0.0372263i
$868$	0.137942	−	23.0094i	0.00468204	−	0.780990i
$869$	0.0870133	+	0.296340i	0.00295173	+	0.0100527i
$870$	−4.75251	−	15.5666i	−0.161125	−	0.527756i
$871$	20.6863	−	26.3048i	0.700928	−	0.891303i
$872$	−0.219642	−	4.61086i	−0.00743803	−	0.156144i
$873$	−19.0909	+	25.3768i	−0.646128	+	0.858875i
$874$	−6.93688	+	0.0881238i	−0.234643	+	0.00298083i
$875$	47.7023	−	33.5395i	1.61263	−	1.13384i
$876$	1.29564	+	1.33000i	0.0437757	+	0.0449366i
$877$	−41.7823	+	16.7271i	−1.41089	+	0.564835i	−0.947050	−	0.321085i	$-0.895952\pi$
$877$	−41.7823	+	16.7271i	−1.41089	+	0.564835i	−0.463839	+	0.885920i	$0.653528\pi$
$878$	−22.9618	+	16.3511i	−0.774925	+	0.551821i
$879$	−2.52426	−	0.0931497i	−0.0851413	−	0.00314186i
$880$	1.10068	−	1.54569i	0.0371038	−	0.0521050i
$881$	20.2183	+	23.3331i	0.681171	+	0.786114i	0.986081	−	0.166268i	$-0.0531716\pi$
$881$	20.2183	+	23.3331i	0.681171	+	0.786114i	−0.304909	+	0.952381i	$0.598626\pi$
$882$	19.9090	+	6.68079i	0.670370	+	0.224954i
$883$	−4.14596	−	1.21736i	−0.139523	−	0.0409676i	0.211226	−	0.977437i	$-0.432255\pi$
$883$	−4.14596	−	1.21736i	−0.139523	−	0.0409676i	−0.350748	+	0.936470i	$0.614073\pi$
$884$	9.77086	+	1.88318i	0.328630	+	0.0633381i
$885$	−5.98524	+	4.81152i	−0.201192	+	0.161737i
$886$	35.1180	−	18.1046i	1.17981	−	0.608236i
$887$	−7.87845	+	40.8773i	−0.264533	+	1.37253i	0.570035	+	0.821620i	$0.306930\pi$
$887$	−7.87845	+	40.8773i	−0.264533	+	1.37253i	−0.834568	+	0.550905i	$0.814283\pi$
$888$	1.39979	−	16.5291i	0.0469740	−	0.554681i
$889$	25.6237	+	27.1980i	0.859392	+	0.912191i
$890$	−5.54814	+	4.80749i	−0.185974	+	0.161147i
$891$	0.798586	+	4.25182i	0.0267536	+	0.142441i
$892$	3.49401	−	14.4025i	0.116988	−	0.482232i
$893$	3.57498	+	5.02035i	0.119632	+	0.168000i
$894$	25.6024	−	16.8440i	0.856271	−	0.563346i
$895$	35.5370	+	55.2967i	1.18787	+	1.84836i
$896$	−1.11349	+	2.40003i	−0.0371992	+	0.0801793i
$897$	14.5150	+	14.5261i	0.484642	+	0.485013i
$898$	−8.77495	−	15.1987i	−0.292824	−	0.507186i
$899$	−20.6789	+	0.985057i	−0.689679	+	0.0328535i
$900$	−30.6484	−	8.29011i	−1.02161	−	0.276337i
$901$	−3.28976	+	0.314134i	−0.109598	+	0.0104653i
$902$	−4.33705	+	1.27347i	−0.144408	+	0.0424020i
$903$	26.8756	−	23.5108i	0.894364	−	0.782392i
$904$	−7.22813	+	6.26321i	−0.240404	+	0.208311i
$905$	−28.0275	−	35.6399i	−0.931667	−	1.18471i
$906$	22.6346	−	32.5177i	0.751984	−	1.08033i
$907$	−0.361812	+	0.125224i	−0.0120138	+	0.00415801i	−0.333068	−	0.942903i	$-0.608084\pi$
$907$	−0.361812	+	0.125224i	−0.0120138	+	0.00415801i	0.321054	+	0.947061i	$0.395963\pi$
$908$	0.310021	−	6.50815i	0.0102884	−	0.215980i
$909$	8.43129	−	49.4225i	0.279648	−	1.63924i
$910$	−15.1027	+	20.9420i	−0.500651	+	0.694220i
$911$	3.88535	+	1.14084i	0.128727	+	0.0377978i	0.345462	−	0.938433i	$-0.387722\pi$
$911$	3.88535	+	1.14084i	0.128727	+	0.0377978i	−0.216734	+	0.976231i	$0.569541\pi$
$912$	−1.62038	+	1.91101i	−0.0536560	+	0.0632798i
$913$	4.08648	−	0.787604i	0.135243	−	0.0260659i
$914$	21.2065	+	2.02497i	0.701447	+	0.0669801i
$915$	42.4408	+	26.6369i	1.40305	+	0.880588i
$916$	−7.54621	−	3.44624i	−0.249334	−	0.113867i
$917$	25.8636	+	16.8414i	0.854090	+	0.556153i
$918$	−8.07252	+	19.2945i	−0.266433	+	0.636813i
$919$	10.4759	−	6.04829i	0.345569	−	0.199515i	−0.317163	−	0.948371i	$-0.602730\pi$
$919$	10.4759	−	6.04829i	0.345569	−	0.199515i	0.662732	+	0.748857i	$0.269397\pi$
$920$	18.4534	+	4.22929i	0.608391	+	0.139435i
$921$	−27.7593	−	9.27573i	−0.914699	−	0.305646i
$922$	2.07214	+	1.06826i	0.0682423	+	0.0351813i
$923$	−7.14969	−	1.02797i	−0.235335	−	0.0338361i
$924$	2.04110	−	0.828332i	0.0671472	−	0.0272501i
$925$	−28.5560	−	97.2528i	−0.938916	−	3.19765i
$926$	−14.2942	−	10.1789i	−0.469737	−	0.334498i
$927$	19.5670	+	29.0583i	0.642663	+	0.954399i
$928$	2.20991	+	0.884715i	0.0725439	+	0.0290422i
$929$	−25.4817	+	6.18180i	−0.836028	+	0.202818i	−0.630849	−	0.775906i	$-0.717293\pi$
$929$	−25.4817	+	6.18180i	−0.836028	+	0.202818i	−0.205180	+	0.978724i	$0.565778\pi$
$930$	−29.1785	+	51.8129i	−0.956801	+	1.69901i
$931$	3.87585	−	9.35475i	0.127026	−	0.306590i
$932$	−2.19328	+	3.41281i	−0.0718433	+	0.111790i
$933$	10.1165	−	0.108402i	0.331200	−	0.00354892i
$934$	−10.2901	−	10.7920i	−0.336703	−	0.353124i
$935$	−7.09069	−	2.83868i	−0.231890	−	0.0928349i
$936$	7.39877	−	0.511548i	0.241836	−	0.0167205i
$937$	−12.4929	+	5.70531i	−0.408125	+	0.186384i	−0.608889	−	0.793255i	$-0.708385\pi$
$937$	−12.4929	+	5.70531i	−0.408125	+	0.186384i	0.200764	+	0.979640i	$0.435657\pi$
$938$	22.3073	−	28.0188i	0.728361	−	0.914845i
$939$	−7.39075	+	31.9557i	−0.241188	+	1.04284i
$940$	−6.25094	−	15.6141i	−0.203883	−	0.509276i
$941$	−2.45317	−	51.4984i	−0.0799711	−	1.67880i	−0.581413	−	0.813609i	$-0.697500\pi$
$941$	−2.45317	−	51.4984i	−0.0799711	−	1.67880i	0.501441	−	0.865192i	$-0.332803\pi$
$942$	31.2400	+	10.4388i	1.01786	+	0.340115i
$943$	−28.3257	−	35.0924i	−0.922413	−	1.14276i
$944$		−	1.12316i		−	0.0365556i
$945$	−36.5996	−	40.0713i	−1.19058	−	1.30352i
$946$	0.533047	−	3.70743i	0.0173309	−	0.120539i
$947$	3.64438	+	38.1657i	0.118427	+	1.24022i	0.837948	+	0.545749i	$0.183755\pi$
$947$	3.64438	+	38.1657i	0.118427	+	1.24022i	−0.719522	+	0.694470i	$0.755639\pi$
$948$	−0.0410393	+	1.11212i	−0.00133289	+	0.0361201i
$949$	−2.63816	−	0.251913i	−0.0856382	−	0.00817746i
$950$	−5.00717	+	14.4673i	−0.162454	+	0.469380i
$951$	−10.3532	−	28.9078i	−0.335727	−	0.937400i
$952$	10.4447	+	2.07808i	0.338516	+	0.0673509i
$953$	−26.6463	+	30.7514i	−0.863158	+	0.996137i	0.136827	+	0.990595i	$0.456310\pi$
$953$	−26.6463	+	30.7514i	−0.863158	+	0.996137i	−0.999985	+	0.00554202i	$0.998236\pi$
$954$	−2.30981	+	0.855285i	−0.0747830	+	0.0276909i
$955$	−27.5068	+	14.1808i	−0.890100	+	0.458878i
$956$	−17.2802	+	5.98073i	−0.558881	+	0.193431i
$957$	−0.842569	−	1.79385i	−0.0272364	−	0.0579870i
$958$	13.4178	−	1.92918i	0.433508	−	0.0623291i
$959$	5.24454	−	5.43471i	0.169355	−	0.175496i
$960$	5.52675	−	4.02552i	0.178375	−	0.129923i
$961$	32.3046	+	30.8024i	1.04208	+	0.993625i
$962$	13.7336	+	19.2862i	0.442790	+	0.621812i
$963$	−35.3169	−	9.55291i	−1.13807	−	0.307838i
$964$	−10.8305	+	21.0082i	−0.348826	+	0.676627i
$965$	−3.85237			−0.124012
$966$	15.4409	+	15.6391i	0.496801	+	0.503178i
$967$	6.66119			0.214209			0.107105	−	0.994248i	$-0.465842\pi$
$967$	6.66119			0.214209			0.107105	+	0.994248i	$0.465842\pi$
$968$	−4.93461	+	9.57182i	−0.158605	+	0.307650i
$969$	9.01288	+	4.52489i	0.289535	+	0.145360i
$970$	−24.2384	−	34.0381i	−0.778249	−	1.09290i
$971$	−3.40594	−	3.24756i	−0.109302	−	0.104219i	0.633458	−	0.773777i	$-0.281635\pi$
$971$	−3.40594	−	3.24756i	−0.109302	−	0.104219i	−0.742760	+	0.669558i	$0.766483\pi$
$972$	−2.12624	+	15.4428i	−0.0681992	+	0.495327i
$973$	7.40604	+	1.84377i	0.237427	+	0.0591085i
$974$	29.6118	−	4.25753i	0.948823	−	0.136420i
$975$	41.0170	−	19.2656i	1.31360	−	0.616994i
$976$	−6.92538	+	2.39690i	−0.221676	+	0.0767229i
$977$	41.8479	−	21.5741i	1.33883	−	0.690217i	0.367968	−	0.929838i	$-0.380054\pi$
$977$	41.8479	−	21.5741i	1.33883	−	0.690217i	0.970866	+	0.239621i	$0.0770233\pi$
$978$	−3.89871	−	25.1965i	−0.124667	−	0.805696i
$979$	−0.585396	+	0.675583i	−0.0187093	+	0.0215917i
$980$	−16.2974	+	22.3153i	−0.520601	+	0.712837i
$981$	−11.8418	+	7.17953i	−0.378081	+	0.229225i
$982$	3.94860	−	11.4087i	0.126005	−	0.364067i
$983$	−31.2205	−	2.98120i	−0.995779	−	0.0950854i	−0.415577	−	0.909558i	$-0.636420\pi$
$983$	−31.2205	−	2.98120i	−0.995779	−	0.0950854i	−0.580202	+	0.814473i	$0.697026\pi$
$984$	−16.2764	−	0.600626i	−0.518872	−	0.0191473i
$985$	−3.03673	−	31.8020i	−0.0967581	−	1.01330i
$986$	1.36359	−	9.48398i	0.0434256	−	0.302031i
$987$	3.60448	−	19.1888i	0.114732	−	0.610785i
$988$		−	3.57610i		−	0.113771i
$989$	36.2014	−	9.27083i	1.15114	−	0.294795i
$990$	−5.65072	−	0.689215i	−0.179592	−	0.0219047i
$991$	2.49449	+	52.3657i	0.0792399	+	1.66345i	0.592764	+	0.805376i	$0.298037\pi$
$991$	2.49449	+	52.3657i	0.0792399	+	1.66345i	−0.513524	+	0.858075i	$0.671660\pi$
$992$	−3.23231	−	8.07392i	−0.102626	−	0.256347i
$993$	32.7199	+	7.56748i	1.03833	+	0.240147i
$994$	−7.64504	−	1.14601i	−0.242486	−	0.0363493i
$995$	85.5137	−	39.0528i	2.71097	−	1.23806i
$996$	14.8652	+	1.97496i	0.471021	+	0.0625790i
$997$	−15.3232	−	6.13448i	−0.485290	−	0.194281i	0.116098	−	0.993238i	$-0.462961\pi$
$997$	−15.3232	−	6.13448i	−0.485290	−	0.194281i	−0.601388	+	0.798957i	$0.705385\pi$
$998$	−6.60284	−	6.92485i	−0.209009	−	0.219202i
$999$	−45.5818	+	19.9710i	−1.44214	+	0.631855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bf.a.11.11	✓	1280
3.2	odd	2	inner	966.2.bf.a.11.57	yes	1280
7.2	even	3	inner	966.2.bf.a.149.43	yes	1280
21.2	odd	6	inner	966.2.bf.a.149.19	yes	1280
23.21	odd	22	inner	966.2.bf.a.389.19	yes	1280
69.44	even	22	inner	966.2.bf.a.389.43	yes	1280
161.44	odd	66	inner	966.2.bf.a.527.57	yes	1280
483.44	even	66	inner	966.2.bf.a.527.11	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.11	✓	1280	1.1	even	1	trivial
966.2.bf.a.11.57	yes	1280	3.2	odd	2	inner
966.2.bf.a.149.19	yes	1280	21.2	odd	6	inner
966.2.bf.a.149.43	yes	1280	7.2	even	3	inner
966.2.bf.a.389.19	yes	1280	23.21	odd	22	inner
966.2.bf.a.389.43	yes	1280	69.44	even	22	inner
966.2.bf.a.527.11	yes	1280	483.44	even	66	inner
966.2.bf.a.527.57	yes	1280	161.44	odd	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.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-0.777131 + 1.54792i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-2.85699 - 2.72413i) q^{5} +(-1.01975 - 1.40004i) q^{6} +(2.56739 + 0.639162i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-1.79214 - 2.40588i) q^{9} +O(q^{10})\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-0.777131 + 1.54792i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-2.85699 - 2.72413i) q^{5} +(-1.01975 - 1.40004i) q^{6} +(2.56739 + 0.639162i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-1.79214 - 2.40588i) q^{9} +(3.73045 - 1.29112i) q^{10} +(0.427250 - 0.220263i) q^{11} +(1.71168 - 0.264852i) q^{12} +(-1.61891 + 1.86832i) q^{13} +(-1.74455 + 1.98910i) q^{14} +(6.43700 - 2.30539i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(4.00689 + 0.382612i) q^{17} +(2.95963 - 0.490477i) q^{18} +(-0.137504 - 1.44001i) q^{19} +(-0.561797 + 3.90738i) q^{20} +(-2.98457 + 3.47741i) q^{21} +0.480685i q^{22} +(-4.42930 + 1.83884i) q^{23} +(-0.548928 + 1.64277i) q^{24} +(0.503572 + 10.5713i) q^{25} +(-0.918804 - 2.29506i) q^{26} +(5.11684 - 0.904408i) q^{27} +(-0.968584 - 2.46208i) q^{28} +(-2.16531 + 0.988865i) q^{29} +(-0.900490 + 6.77782i) q^{30} +(8.07392 + 3.23231i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(0.00892075 + 0.832523i) q^{33} +(-2.17614 + 3.38615i) q^{34} +(-5.59382 - 8.81997i) q^{35} +(-0.920230 + 2.85538i) q^{36} +(-9.30729 + 2.25792i) q^{37} +(1.34294 + 0.537630i) q^{38} +(-1.63392 - 3.95788i) q^{39} +(-3.21559 - 2.28981i) q^{40} +(2.64929 + 9.02265i) q^{41} +(-1.72323 - 4.24623i) q^{42} +(-7.71280 - 1.10893i) q^{43} +(-0.427250 - 0.220263i) q^{44} +(-1.43382 + 11.7556i) q^{45} +(0.395192 - 4.77952i) q^{46} +(-3.68976 + 2.13028i) q^{47} +(-1.20861 - 1.24067i) q^{48} +(6.18294 + 3.28195i) q^{49} +(-9.62687 - 4.39644i) q^{50} +(-3.70613 + 5.90503i) q^{51} +(2.46095 + 0.234992i) q^{52} +(-0.806189 + 0.155380i) q^{53} +(-1.54080 + 4.96245i) q^{54} +(-1.82067 - 0.534597i) q^{55} +(2.63222 + 0.267279i) q^{56} +(2.33588 + 0.906227i) q^{57} +(0.113265 - 2.37773i) q^{58} +(-1.06138 + 0.367348i) q^{59} +(-5.61174 - 3.90617i) q^{60} +(4.53014 + 5.76054i) q^{61} +(-6.57268 + 5.69526i) q^{62} +(-3.06336 - 7.32228i) q^{63} +(0.959493 - 0.281733i) q^{64} +(9.71476 - 0.927647i) q^{65} +(-0.744063 - 0.373555i) q^{66} +(-13.5212 + 0.644096i) q^{67} +(-2.01256 - 3.48586i) q^{68} +(0.595753 - 8.28523i) q^{69} +(10.4027 - 0.930444i) q^{70} +(1.57967 + 2.45801i) q^{71} +(-2.11629 - 2.12634i) q^{72} +(0.621825 + 0.873231i) q^{73} +(2.25792 - 9.30729i) q^{74} +(-16.7549 - 7.43577i) q^{75} +(-1.09323 + 0.947292i) q^{76} +(1.23770 - 0.292417i) q^{77} +(4.26661 + 0.361324i) q^{78} +(-0.121598 + 0.630911i) q^{79} +(3.50873 - 1.80888i) q^{80} +(-2.57650 + 8.62332i) q^{81} +(-9.23363 - 1.77964i) q^{82} +(8.30712 + 2.43919i) q^{83} +(4.56383 + 0.414065i) q^{84} +(-10.4054 - 12.0084i) q^{85} +(4.51987 - 6.34727i) q^{86} +(0.152043 - 4.12022i) q^{87} +(0.391554 - 0.278825i) q^{88} +(-1.72648 + 0.691177i) q^{89} +(-9.79176 - 6.66114i) q^{90} +(-5.35053 + 3.76196i) q^{91} +(4.06712 + 2.54136i) q^{92} +(-11.2779 + 9.98589i) q^{93} +(-0.202726 - 4.25574i) q^{94} +(-3.52992 + 4.48865i) q^{95} +(1.65657 - 0.505754i) q^{96} +(-2.98223 - 10.1566i) q^{97} +(-5.75030 + 3.99174i) q^{98} +(-1.29561 - 0.633170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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