LMFDB - Embedded newform 462.2.u.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	462.13
Dual form			462.2.u.a.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-3.76443 + 1.22314i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.44620 - 2.21552i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-3.76443 + 1.22314i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.44620 - 2.21552i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.95815 q^{10} +(3.31549 - 0.0867606i) q^{11} +1.00000i q^{12} +(0.469755 - 1.44576i) q^{13} +(0.690781 + 2.55398i) q^{14} +(-3.20221 - 2.32654i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.91759 - 5.90174i) q^{17} +(0.587785 - 0.809017i) q^{18} +(5.30211 - 3.85221i) q^{19} +(-3.76443 - 1.22314i) q^{20} +(0.942339 - 2.47225i) q^{21} +(-3.18003 - 0.942028i) q^{22} -1.15101 q^{23} +(0.309017 - 0.951057i) q^{24} +(8.62977 - 6.26990i) q^{25} +(-0.893526 + 1.22983i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.132252 - 2.64244i) q^{28} +(-0.0126757 + 0.0174466i) q^{29} +(2.32654 + 3.20221i) q^{30} +(5.54661 + 1.80220i) q^{31} -1.00000i q^{32} +(2.01899 + 2.63129i) q^{33} +6.20546i q^{34} +(8.15398 + 6.57126i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-5.14257 - 3.73630i) q^{37} +(-6.23301 + 2.02523i) q^{38} +(1.44576 - 0.469755i) q^{39} +(3.20221 + 2.32654i) q^{40} +(-6.06909 + 4.40945i) q^{41} +(-1.66018 + 2.06005i) q^{42} -8.11341i q^{43} +(2.73328 + 1.87861i) q^{44} -3.95815i q^{45} +(1.09467 + 0.355681i) q^{46} +(0.361302 + 0.497290i) q^{47} +(-0.587785 + 0.809017i) q^{48} +(-2.81704 + 6.40814i) q^{49} +(-10.1449 + 3.29628i) q^{50} +(3.64748 - 5.02032i) q^{51} +(1.22983 - 0.893526i) q^{52} +(2.09190 - 6.43819i) q^{53} +1.00000 q^{54} +(-12.3748 + 4.38190i) q^{55} +(-0.942339 + 2.47225i) q^{56} +(6.23301 + 2.02523i) q^{57} +(0.0174466 - 0.0126757i) q^{58} +(3.63275 - 5.00005i) q^{59} +(-1.22314 - 3.76443i) q^{60} +(-3.52032 - 10.8344i) q^{61} +(-4.71822 - 3.42799i) q^{62} +(2.55398 - 0.690781i) q^{63} +(-0.309017 + 0.951057i) q^{64} +6.01702i q^{65} +(-1.10706 - 3.12641i) q^{66} -14.4455 q^{67} +(1.91759 - 5.90174i) q^{68} +(-0.676545 - 0.931185i) q^{69} +(-5.72427 - 8.76936i) q^{70} +(-2.09182 - 6.43795i) q^{71} +(0.951057 - 0.309017i) q^{72} +(12.2934 + 8.93169i) q^{73} +(3.73630 + 5.14257i) q^{74} +(10.1449 + 3.29628i) q^{75} +6.55377 q^{76} +(-4.98707 - 7.22005i) q^{77} -1.52016 q^{78} +(-11.7961 - 3.83279i) q^{79} +(-2.32654 - 3.20221i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(7.13464 - 2.31819i) q^{82} +(1.65276 + 5.08668i) q^{83} +(2.21552 - 1.44620i) q^{84} +(14.4373 + 19.8712i) q^{85} +(-2.50718 + 7.71631i) q^{86} -0.0215652 q^{87} +(-2.01899 - 2.63129i) q^{88} -0.0879436i q^{89} +(-1.22314 + 3.76443i) q^{90} +(-3.88246 + 1.05010i) q^{91} +(-0.931185 - 0.676545i) q^{92} +(1.80220 + 5.54661i) q^{93} +(-0.189948 - 0.584599i) q^{94} +(-15.2476 + 20.9866i) q^{95} +(0.809017 - 0.587785i) q^{96} +(0.719804 + 0.233879i) q^{97} +(4.65939 - 5.22399i) q^{98} +(-0.942028 + 3.18003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−3.76443	+	1.22314i	−1.68350	+	0.547003i	−0.985586	−	0.169175i	$-0.945890\pi$
$5$	−3.76443	+	1.22314i	−1.68350	+	0.547003i	−0.697917	+	0.716178i	$0.745890\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−1.44620	−	2.21552i	−0.546611	−	0.837387i
$7$	−1.44620	−	2.21552i	−0.546611	−	0.837387i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	3.95815			1.25168
$11$	3.31549	−	0.0867606i	0.999658	−	0.0261593i
$11$	3.31549	−	0.0867606i	0.999658	−	0.0261593i
$12$			1.00000i			0.288675i
$13$	0.469755	−	1.44576i	0.130286	−	0.400981i	−0.864541	−	0.502563i	$-0.832391\pi$
$13$	0.469755	−	1.44576i	0.130286	−	0.400981i	0.994827	+	0.101582i	$0.0323905\pi$
$14$	0.690781	+	2.55398i	0.184619	+	0.682580i
$15$	−3.20221	−	2.32654i	−0.826808	−	0.600711i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.91759	−	5.90174i	−0.465085	−	1.43138i	−0.858876	−	0.512183i	$-0.828837\pi$
$17$	−1.91759	−	5.90174i	−0.465085	−	1.43138i	0.393792	−	0.919200i	$-0.371163\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	5.30211	−	3.85221i	1.21639	−	0.883757i	0.220593	−	0.975366i	$-0.429201\pi$
$19$	5.30211	−	3.85221i	1.21639	−	0.883757i	0.995795	+	0.0916086i	$0.0292009\pi$
$20$	−3.76443	−	1.22314i	−0.841752	−	0.273502i
$21$	0.942339	−	2.47225i	0.205635	−	0.539488i
$22$	−3.18003	−	0.942028i	−0.677984	−	0.200841i
$23$	−1.15101			−0.240002			−0.120001	−	0.992774i	$-0.538290\pi$
$23$	−1.15101			−0.240002			−0.120001	+	0.992774i	$0.538290\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	8.62977	−	6.26990i	1.72595	−	1.25398i
$26$	−0.893526	+	1.22983i	−0.175235	+	0.241190i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	0.132252	−	2.64244i	0.0249932	−	0.499375i
$29$	−0.0126757	+	0.0174466i	−0.00235382	+	0.00323976i	−0.810192	−	0.586164i	$-0.800637\pi$
$29$	−0.0126757	+	0.0174466i	−0.00235382	+	0.00323976i	0.807838	+	0.589404i	$0.200637\pi$
$30$	2.32654	+	3.20221i	0.424767	+	0.584642i
$31$	5.54661	+	1.80220i	0.996200	+	0.323685i	0.761346	−	0.648346i	$-0.224539\pi$
$31$	5.54661	+	1.80220i	0.996200	+	0.323685i	0.234854	+	0.972031i	$0.424539\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.01899	+	2.63129i	0.351460	+	0.458049i
$34$			6.20546i			1.06423i
$35$	8.15398	+	6.57126i	1.37827	+	1.11075i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−5.14257	−	3.73630i	−0.845434	−	0.614244i	0.0784495	−	0.996918i	$-0.475003\pi$
$37$	−5.14257	−	3.73630i	−0.845434	−	0.614244i	−0.923883	+	0.382675i	$0.875003\pi$
$38$	−6.23301	+	2.02523i	−1.01113	+	0.328535i
$39$	1.44576	−	0.469755i	0.231506	−	0.0752209i
$40$	3.20221	+	2.32654i	0.506314	+	0.367859i
$41$	−6.06909	+	4.40945i	−0.947833	+	0.688641i	−0.950293	−	0.311356i	$-0.899217\pi$
$41$	−6.06909	+	4.40945i	−0.947833	+	0.688641i	0.00246070	+	0.999997i	$0.499217\pi$
$42$	−1.66018	+	2.06005i	−0.256172	+	0.317872i
$43$		−	8.11341i		−	1.23728i	−0.785673	−	0.618642i	$-0.787683\pi$
$43$		−	8.11341i		−	1.23728i	0.785673	−	0.618642i	$-0.212317\pi$
$44$	2.73328	+	1.87861i	0.412058	+	0.283210i
$45$		−	3.95815i		−	0.590047i
$46$	1.09467	+	0.355681i	0.161401	+	0.0524423i
$47$	0.361302	+	0.497290i	0.0527013	+	0.0725371i	0.834554	−	0.550926i	$-0.185725\pi$
$47$	0.361302	+	0.497290i	0.0527013	+	0.0725371i	−0.781853	+	0.623463i	$0.785725\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	−2.81704	+	6.40814i	−0.402434	+	0.915449i
$50$	−10.1449	+	3.29628i	−1.43471	+	0.466164i
$51$	3.64748	−	5.02032i	0.510749	−	0.702986i
$52$	1.22983	−	0.893526i	0.170547	−	0.123910i
$53$	2.09190	−	6.43819i	0.287344	−	0.884354i	−0.698342	−	0.715764i	$-0.746079\pi$
$53$	2.09190	−	6.43819i	0.287344	−	0.884354i	0.985686	−	0.168590i	$-0.0539214\pi$
$54$	1.00000			0.136083
$55$	−12.3748	+	4.38190i	−1.66862	+	0.590856i
$56$	−0.942339	+	2.47225i	−0.125925	+	0.330368i
$57$	6.23301	+	2.02523i	0.825582	+	0.268248i
$58$	0.0174466	−	0.0126757i	0.00229086	−	0.00166440i
$59$	3.63275	−	5.00005i	0.472944	−	0.650951i	−0.504186	−	0.863595i	$-0.668207\pi$
$59$	3.63275	−	5.00005i	0.472944	−	0.650951i	0.977130	+	0.212644i	$0.0682074\pi$
$60$	−1.22314	−	3.76443i	−0.157906	−	0.485986i
$61$	−3.52032	−	10.8344i	−0.450731	−	1.38721i	−0.876075	−	0.482175i	$-0.839847\pi$
$61$	−3.52032	−	10.8344i	−0.450731	−	1.38721i	0.425344	−	0.905032i	$-0.360153\pi$
$62$	−4.71822	−	3.42799i	−0.599215	−	0.435355i
$63$	2.55398	−	0.690781i	0.321771	−	0.0870302i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$			6.01702i			0.746319i
$66$	−1.10706	−	3.12641i	−0.136269	−	0.384834i
$67$	−14.4455			−1.76480			−0.882402	−	0.470496i	$-0.844075\pi$
$67$	−14.4455			−1.76480			−0.882402	+	0.470496i	$0.844075\pi$
$68$	1.91759	−	5.90174i	0.232542	−	0.715692i
$69$	−0.676545	−	0.931185i	−0.0814465	−	0.112101i
$70$	−5.72427	−	8.76936i	−0.684181	−	1.04814i
$71$	−2.09182	−	6.43795i	−0.248253	−	0.764044i	−0.995084	−	0.0990309i	$-0.968426\pi$
$71$	−2.09182	−	6.43795i	−0.248253	−	0.764044i	0.746831	−	0.665014i	$-0.231574\pi$
$72$	0.951057	−	0.309017i	0.112083	−	0.0364180i
$73$	12.2934	+	8.93169i	1.43884	+	1.04537i	0.988284	+	0.152624i	$0.0487723\pi$
$73$	12.2934	+	8.93169i	1.43884	+	1.04537i	0.450551	+	0.892751i	$0.351228\pi$
$74$	3.73630	+	5.14257i	0.434336	+	0.597812i
$75$	10.1449	+	3.29628i	1.17143	+	0.380622i
$76$	6.55377			0.751769
$77$	−4.98707	−	7.22005i	−0.568329	−	0.822801i
$78$	−1.52016			−0.172124
$79$	−11.7961	−	3.83279i	−1.32717	−	0.431223i	−0.442217	−	0.896908i	$-0.645808\pi$
$79$	−11.7961	−	3.83279i	−1.32717	−	0.431223i	−0.884950	+	0.465685i	$0.845808\pi$
$80$	−2.32654	−	3.20221i	−0.260116	−	0.358018i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	7.13464	−	2.31819i	0.787889	−	0.256001i
$83$	1.65276	+	5.08668i	0.181414	+	0.558335i	0.999868	−	0.0162366i	$-0.00516851\pi$
$83$	1.65276	+	5.08668i	0.181414	+	0.558335i	−0.818454	+	0.574572i	$0.805169\pi$
$84$	2.21552	−	1.44620i	0.241733	−	0.157793i
$85$	14.4373	+	19.8712i	1.56594	+	2.15534i
$86$	−2.50718	+	7.71631i	−0.270356	+	0.832071i
$87$	−0.0215652			−0.00231204
$88$	−2.01899	−	2.63129i	−0.215225	−	0.280497i
$89$		−	0.0879436i		−	0.00932200i	−0.999989	−	0.00466100i	$-0.998516\pi$
$89$		−	0.0879436i		−	0.00932200i	0.999989	−	0.00466100i	$-0.00148365\pi$
$90$	−1.22314	+	3.76443i	−0.128930	+	0.396806i
$91$	−3.88246	+	1.05010i	−0.406992	+	0.110080i
$92$	−0.931185	−	0.676545i	−0.0970827	−	0.0705347i
$93$	1.80220	+	5.54661i	0.186880	+	0.575156i
$94$	−0.189948	−	0.584599i	−0.0195916	−	0.0602968i
$95$	−15.2476	+	20.9866i	−1.56437	+	2.15318i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	0.719804	+	0.233879i	0.0730851	+	0.0237468i	0.345331	−	0.938481i	$-0.387767\pi$
$97$	0.719804	+	0.233879i	0.0730851	+	0.0237468i	−0.272246	+	0.962228i	$0.587767\pi$
$98$	4.65939	−	5.22399i	0.470669	−	0.527703i
$99$	−0.942028	+	3.18003i	−0.0946774	+	0.319605i
$100$	10.6670			1.06670
$101$	1.57924	−	4.86039i	0.157140	−	0.483627i	−0.841232	−	0.540675i	$-0.818169\pi$
$101$	1.57924	−	4.86039i	0.157140	−	0.483627i	0.998371	+	0.0570482i	$0.0181689\pi$
$102$	−5.02032	+	3.64748i	−0.497086	+	0.361154i
$103$	−5.25834	+	7.23749i	−0.518120	+	0.713131i	−0.985262	−	0.171051i	$-0.945284\pi$
$103$	−5.25834	+	7.23749i	−0.518120	+	0.713131i	0.467142	+	0.884182i	$0.345284\pi$
$104$	−1.44576	+	0.469755i	−0.141768	+	0.0460632i
$105$	−0.523473	+	10.4592i	−0.0510857	+	1.02071i
$106$	−3.97902	+	5.47666i	−0.386477	+	0.531940i
$107$	−2.51268	−	3.45840i	−0.242910	−	0.334336i	0.670103	−	0.742268i	$-0.266250\pi$
$107$	−2.51268	−	3.45840i	−0.242910	−	0.334336i	−0.913012	+	0.407932i	$0.866250\pi$
$108$	−0.951057	−	0.309017i	−0.0915155	−	0.0297352i
$109$			10.8114i			1.03555i	0.855517	+	0.517775i	$0.173239\pi$
$109$			10.8114i			1.03555i	−0.855517	+	0.517775i	$0.826761\pi$
$110$	13.1232	−	0.343412i	1.25125	−	0.0327431i
$111$		−	6.35657i		−	0.603339i
$112$	1.66018	−	2.06005i	0.156873	−	0.194656i
$113$	9.51695	−	6.91447i	0.895280	−	0.650459i	−0.0419695	−	0.999119i	$-0.513363\pi$
$113$	9.51695	−	6.91447i	0.895280	−	0.650459i	0.937249	+	0.348660i	$0.113363\pi$
$114$	−5.30211	−	3.85221i	−0.496588	−	0.360792i
$115$	4.33289	−	1.40784i	0.404044	−	0.131282i
$116$	−0.0205098	+	0.00666403i	−0.00190428	+	0.000618739i
$117$	1.22983	+	0.893526i	0.113698	+	0.0826065i
$118$	−5.00005	+	3.63275i	−0.460292	+	0.334422i
$119$	−10.3022	+	12.7835i	−0.944401	+	1.17186i
$120$			3.95815i			0.361328i
$121$	10.9849	−	0.575308i	0.998631	−	0.0523007i
$122$			11.3920i			1.03138i
$123$	−7.13464	−	2.31819i	−0.643309	−	0.209024i
$124$	3.42799	+	4.71822i	0.307843	+	0.423709i
$125$	−13.1845	+	18.1469i	−1.17926	+	1.62311i
$126$	−2.64244	−	0.132252i	−0.235408	−	0.0117819i
$127$	4.84181	−	1.57320i	0.429641	−	0.139599i	−0.0862104	−	0.996277i	$-0.527476\pi$
$127$	4.84181	−	1.57320i	0.429641	−	0.139599i	0.515851	+	0.856678i	$0.327476\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	6.56389	−	4.76894i	0.577918	−	0.419882i
$130$	1.85936	−	5.72253i	0.163077	−	0.501899i
$131$	13.3994			1.17071			0.585355	−	0.810777i	$-0.300955\pi$
$131$	13.3994			1.17071			0.585355	+	0.810777i	$0.300955\pi$
$132$	0.0867606	+	3.31549i	0.00755155	+	0.288576i
$133$	−16.2025	−	6.17587i	−1.40494	−	0.535516i
$134$	13.7385	+	4.46392i	1.18683	+	0.385624i
$135$	3.20221	−	2.32654i	0.275603	−	0.200237i
$136$	−3.64748	+	5.02032i	−0.312769	+	0.430489i
$137$	−3.94069	−	12.1282i	−0.336676	−	1.03618i	−0.965890	−	0.258951i	$-0.916623\pi$
$137$	−3.94069	−	12.1282i	−0.336676	−	1.03618i	0.629214	−	0.777232i	$-0.283377\pi$
$138$	0.355681	+	1.09467i	0.0302776	+	0.0931848i
$139$	−7.34614	−	5.33728i	−0.623091	−	0.452702i	0.230909	−	0.972975i	$-0.425830\pi$
$139$	−7.34614	−	5.33728i	−0.623091	−	0.452702i	−0.854000	+	0.520273i	$0.825830\pi$
$140$	2.73422	+	10.1091i	0.231084	+	0.854371i
$141$	−0.189948	+	0.584599i	−0.0159965	+	0.0492321i
$142$			6.76926i			0.568064i
$143$	1.43203	−	4.83415i	0.119753	−	0.404252i
$144$	−1.00000			−0.0833333
$145$	0.0263772	−	0.0811808i	0.00219051	−	0.00674170i
$146$	−8.93169	−	12.2934i	−0.739192	−	1.01741i
$147$	−6.84011	+	1.48758i	−0.564163	+	0.122694i
$148$	−1.96429	−	6.04546i	−0.161463	−	0.496933i
$149$	−8.46374	+	2.75004i	−0.693377	+	0.225292i	−0.634442	−	0.772970i	$-0.718770\pi$
$149$	−8.46374	+	2.75004i	−0.693377	+	0.225292i	−0.0589343	+	0.998262i	$0.518770\pi$
$150$	−8.62977	−	6.26990i	−0.704618	−	0.511935i
$151$	10.3153	+	14.1978i	0.839446	+	1.15540i	0.986091	+	0.166209i	$0.0531527\pi$
$151$	10.3153	+	14.1978i	0.839446	+	1.15540i	−0.146645	+	0.989189i	$0.546847\pi$
$152$	−6.23301	−	2.02523i	−0.505564	−	0.164268i
$153$	6.20546			0.501682
$154$	2.51186	+	8.40777i	0.202412	+	0.677517i
$155$	−23.0841			−1.85416
$156$	1.44576	+	0.469755i	0.115753	+	0.0376105i
$157$	6.63574	+	9.13331i	0.529590	+	0.728918i	0.987068	−	0.160303i	$-0.0512472\pi$
$157$	6.63574	+	9.13331i	0.529590	+	0.728918i	−0.457478	+	0.889221i	$0.651247\pi$
$158$	10.0344	+	7.29040i	0.798292	+	0.579993i
$159$	6.43819	−	2.09190i	0.510582	−	0.165898i
$160$	1.22314	+	3.76443i	0.0966975	+	0.297604i
$161$	1.66458	+	2.55008i	0.131187	+	0.200974i
$162$	0.587785	+	0.809017i	0.0461808	+	0.0635624i
$163$	−6.20079	+	19.0841i	−0.485683	+	1.49478i	0.345306	+	0.938490i	$0.387775\pi$
$163$	−6.20079	+	19.0841i	−0.485683	+	1.49478i	−0.830989	+	0.556288i	$0.812225\pi$
$164$	−7.50181			−0.585793
$165$	−10.8188	−	7.43581i	−0.842239	−	0.578877i
$166$		−	5.34845i		−	0.415120i
$167$	−2.13500	+	6.57085i	−0.165211	+	0.508468i	−0.999052	−	0.0435374i	$-0.986137\pi$
$167$	−2.13500	+	6.57085i	−0.165211	+	0.508468i	0.833841	+	0.552005i	$0.186137\pi$
$168$	−2.55398	+	0.690781i	−0.197044	+	0.0532949i
$169$	8.64768	+	6.28291i	0.665206	+	0.483301i
$170$	−7.59013	−	23.3600i	−0.582136	−	1.79163i
$171$	2.02523	+	6.23301i	0.154873	+	0.476650i
$172$	4.76894	−	6.56389i	0.363629	−	0.500492i
$173$	10.4469	−	7.59008i	0.794259	−	0.577063i	−0.114965	−	0.993370i	$-0.536676\pi$
$173$	10.4469	−	7.59008i	0.794259	−	0.577063i	0.909224	+	0.416306i	$0.136676\pi$
$174$	0.0205098	+	0.00666403i	0.00155484	+	0.000505198i
$175$	−26.3714	−	10.0519i	−1.99349	−	0.759853i
$176$	1.10706	+	3.12641i	0.0834476	+	0.235662i
$177$	6.18040			0.464548
$178$	−0.0271761	+	0.0836394i	−0.00203693	+	0.00626903i
$179$	16.0039	−	11.6275i	1.19619	−	0.869083i	0.202286	−	0.979326i	$-0.435163\pi$
$179$	16.0039	−	11.6275i	1.19619	−	0.869083i	0.993905	+	0.110243i	$0.0351629\pi$
$180$	2.32654	−	3.20221i	0.173410	−	0.238679i
$181$	−1.47664	+	0.479789i	−0.109758	+	0.0356624i	−0.363381	−	0.931641i	$-0.618378\pi$
$181$	−1.47664	+	0.479789i	−0.109758	+	0.0356624i	0.253623	+	0.967303i	$0.418378\pi$
$182$	4.01693	+	0.201044i	0.297755	+	0.0149023i
$183$	6.69605	−	9.21632i	0.494986	−	0.681290i
$184$	0.676545	+	0.931185i	0.0498756	+	0.0686478i
$185$	23.9288	+	7.77495i	1.75928	+	0.571626i
$186$		−	5.83205i		−	0.427626i
$187$	−6.86980	−	19.4008i	−0.502369	−	1.41873i
$188$			0.614684i			0.0448304i
$189$	2.06005	+	1.66018i	0.149846	+	0.120761i
$190$	20.9866	−	15.2476i	1.52253	−	1.10618i
$191$	−5.64913	−	4.10433i	−0.408757	−	0.296979i	0.364341	−	0.931265i	$-0.381294\pi$
$191$	−5.64913	−	4.10433i	−0.408757	−	0.296979i	−0.773098	+	0.634286i	$0.781294\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$	9.91526	−	3.22166i	0.713716	−	0.231900i	0.0704193	−	0.997517i	$-0.477566\pi$
$193$	9.91526	−	3.22166i	0.713716	−	0.231900i	0.643296	+	0.765617i	$0.277566\pi$
$194$	−0.612302	−	0.444864i	−0.0439607	−	0.0319393i
$195$	−4.86787	+	3.53672i	−0.348595	+	0.253269i
$196$	−6.04564	+	3.52848i	−0.431832	+	0.252035i
$197$		−	6.95233i		−	0.495333i	−0.968845	−	0.247666i	$-0.920336\pi$
$197$		−	6.95233i		−	0.495333i	0.968845	−	0.247666i	$-0.0796637\pi$
$198$	1.87861	−	2.73328i	0.133507	−	0.194246i
$199$		−	2.01227i		−	0.142646i	−0.997453	−	0.0713229i	$-0.977278\pi$
$199$		−	2.01227i		−	0.142646i	0.997453	−	0.0713229i	$-0.0227221\pi$
$200$	−10.1449	−	3.29628i	−0.717353	−	0.233082i
$201$	−8.49088	−	11.6867i	−0.598900	−	0.824316i
$202$	−3.00389	+	4.13449i	−0.211353	+	0.290902i
$203$	0.0569849	+	0.00285204i	0.00399956	+	0.000200174i
$204$	5.90174	−	1.91759i	0.413205	−	0.134258i
$205$	17.4533	−	24.0224i	1.21899	−	1.67780i
$206$	7.23749	−	5.25834i	0.504260	−	0.366366i
$207$	0.355681	−	1.09467i	0.0247215	−	0.0760850i
$208$	1.52016			0.105404
$209$	17.2449	−	13.2320i	1.19285	−	0.915275i
$210$	3.72992	−	9.78553i	0.257389	−	0.675266i
$211$	−16.0537	−	5.21618i	−1.10519	−	0.359097i	−0.301089	−	0.953596i	$-0.597350\pi$
$211$	−16.0537	−	5.21618i	−1.10519	−	0.359097i	−0.804096	+	0.594499i	$0.797350\pi$
$212$	5.47666	−	3.97902i	0.376138	−	0.273280i
$213$	3.97887	−	5.47645i	0.272628	−	0.375240i
$214$	1.32099	+	4.06560i	0.0903012	+	0.277918i
$215$	9.92381	+	30.5424i	0.676798	+	2.08297i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−4.02867	−	14.8949i	−0.273484	−	1.01113i
$218$	3.34092	−	10.2823i	0.226276	−	0.696405i
$219$			15.1955i			1.02682i
$220$	−12.5870	−	3.72869i	−0.848618	−	0.251388i
$221$	−9.43328			−0.634551
$222$	−1.96429	+	6.04546i	−0.131834	+	0.405744i
$223$	−7.81834	−	10.7610i	−0.523555	−	0.720611i	0.462576	−	0.886579i	$-0.346925\pi$
$223$	−7.81834	−	10.7610i	−0.523555	−	0.720611i	−0.986131	+	0.165968i	$0.946925\pi$
$224$	−2.21552	+	1.44620i	−0.148030	+	0.0966280i
$225$	3.29628	+	10.1449i	0.219752	+	0.676327i
$226$	−11.1879	+	3.63515i	−0.744205	+	0.241807i
$227$	−5.31062	−	3.85839i	−0.352478	−	0.256090i	0.397430	−	0.917633i	$-0.369902\pi$
$227$	−5.31062	−	3.85839i	−0.352478	−	0.256090i	−0.749908	+	0.661542i	$0.769902\pi$
$228$	3.85221	+	5.30211i	0.255119	+	0.351141i
$229$	−1.11534	−	0.362397i	−0.0737041	−	0.0239479i	0.271933	−	0.962316i	$-0.412337\pi$
$229$	−1.11534	−	0.362397i	−0.0737041	−	0.0239479i	−0.345637	+	0.938368i	$0.612337\pi$
$230$	−4.55587			−0.300405
$231$	2.90982	−	8.27846i	0.191452	−	0.544683i
$232$	0.0215652			0.00141583
$233$	11.2686	+	3.66139i	0.738231	+	0.239866i	0.653909	−	0.756573i	$-0.273128\pi$
$233$	11.2686	+	3.66139i	0.738231	+	0.239866i	0.0843214	+	0.996439i	$0.473128\pi$
$234$	−0.893526	−	1.22983i	−0.0584117	−	0.0803967i
$235$	−1.96835	−	1.43009i	−0.128401	−	0.0932887i
$236$	5.87791	−	1.90985i	0.382620	−	0.124321i
$237$	−3.83279	−	11.7961i	−0.248967	−	0.766240i
$238$	13.7483	−	8.97431i	0.891170	−	0.581718i
$239$	0.333702	+	0.459301i	0.0215854	+	0.0297097i	0.819673	−	0.572831i	$-0.194155\pi$
$239$	0.333702	+	0.459301i	0.0215854	+	0.0297097i	−0.798088	+	0.602541i	$0.794155\pi$
$240$	1.22314	−	3.76443i	0.0789531	−	0.242993i
$241$	−15.6217			−1.00628			−0.503142	−	0.864204i	$-0.667823\pi$
$241$	−15.6217			−1.00628			−0.503142	+	0.864204i	$0.667823\pi$
$242$	−10.6251	−	2.84738i	−0.683006	−	0.183037i
$243$		−	1.00000i		−	0.0641500i
$244$	3.52032	−	10.8344i	0.225365	−	0.693603i
$245$	2.76649	−	27.5686i	0.176745	−	1.76129i
$246$	6.06909	+	4.40945i	0.386951	+	0.281136i
$247$	−3.07866	−	9.47515i	−0.195891	−	0.602890i
$248$	−1.80220	−	5.54661i	−0.114440	−	0.352210i
$249$	−3.14374	+	4.32699i	−0.199226	+	0.274212i
$250$	18.1469	−	13.1845i	1.14771	−	0.833860i
$251$	−14.8900	−	4.83806i	−0.939850	−	0.305376i	−0.201265	−	0.979537i	$-0.564505\pi$
$251$	−14.8900	−	4.83806i	−0.939850	−	0.305376i	−0.738584	+	0.674161i	$0.764505\pi$
$252$	2.47225	+	0.942339i	0.155737	+	0.0593618i
$253$	−3.81615	+	0.0998622i	−0.239920	+	0.00627828i
$254$	−5.09098			−0.319436
$255$	−7.59013	+	23.3600i	−0.475312	+	1.46286i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	14.2679	−	19.6380i	0.890005	−	1.22499i	−0.0835425	−	0.996504i	$-0.526623\pi$
$257$	14.2679	−	19.6380i	0.890005	−	1.22499i	0.973548	−	0.228483i	$-0.0733766\pi$
$258$	−7.71631	+	2.50718i	−0.480397	+	0.156090i
$259$	−0.840667	+	16.7969i	−0.0522365	+	1.04371i
$260$	−3.53672	+	4.86787i	−0.219338	+	0.301893i
$261$	−0.0126757	−	0.0174466i	−0.000784608	−	0.00107992i
$262$	−12.7436	−	4.14064i	−0.787301	−	0.255810i
$263$			16.3003i			1.00512i	0.864543	+	0.502559i	$0.167608\pi$
$263$			16.3003i			1.00512i	−0.864543	+	0.502559i	$0.832392\pi$
$264$	0.942028	−	3.18003i	0.0579778	−	0.195717i
$265$			26.7948i			1.64599i
$266$	13.5011	+	10.8805i	0.827804	+	0.667124i
$267$	0.0711479	−	0.0516920i	0.00435418	−	0.00316350i
$268$	−11.6867	−	8.49088i	−0.713878	−	0.518663i
$269$	−9.82140	+	3.19117i	−0.598822	+	0.194569i	−0.592715	−	0.805412i	$-0.701944\pi$
$269$	−9.82140	+	3.19117i	−0.598822	+	0.194569i	−0.00610675	+	0.999981i	$0.501944\pi$
$270$	−3.76443	+	1.22314i	−0.229096	+	0.0744377i
$271$	−0.357395	−	0.259662i	−0.0217102	−	0.0157734i	0.576877	−	0.816831i	$-0.304271\pi$
$271$	−0.357395	−	0.259662i	−0.0217102	−	0.0157734i	−0.598587	+	0.801057i	$0.704271\pi$
$272$	5.02032	−	3.64748i	0.304402	−	0.221161i
$273$	−3.13160	−	2.52374i	−0.189533	−	0.152744i
$274$			12.7524i			0.770398i
$275$	28.0679	−	21.5365i	1.69256	−	1.29870i
$276$		−	1.15101i		−	0.0692825i
$277$	−10.9960	−	3.57282i	−0.660686	−	0.214670i	−0.0405660	−	0.999177i	$-0.512916\pi$
$277$	−10.9960	−	3.57282i	−0.660686	−	0.214670i	−0.620120	+	0.784507i	$0.712916\pi$
$278$	5.33728	+	7.34614i	0.320109	+	0.440592i
$279$	−3.42799	+	4.71822i	−0.205228	+	0.282473i
$280$	0.523473	−	10.4592i	0.0312835	−	0.625057i
$281$	8.78410	−	2.85413i	0.524015	−	0.170263i	−0.0350515	−	0.999386i	$-0.511160\pi$
$281$	8.78410	−	2.85413i	0.524015	−	0.170263i	0.559067	+	0.829123i	$0.311160\pi$
$282$	0.361302	−	0.497290i	0.0215152	−	0.0296132i
$283$	−5.50445	+	3.99922i	−0.327206	+	0.237729i	−0.739244	−	0.673438i	$-0.764817\pi$
$283$	−5.50445	+	3.99922i	−0.327206	+	0.237729i	0.412038	+	0.911167i	$0.364817\pi$
$284$	2.09182	−	6.43795i	0.124127	−	0.382022i
$285$	−25.9408			−1.53660
$286$	−2.85578	+	4.15502i	−0.168866	+	0.245692i
$287$	18.5463	+	7.06925i	1.09475	+	0.417284i
$288$	0.951057	+	0.309017i	0.0560415	+	0.0182090i
$289$	−17.4001	+	12.6419i	−1.02354	+	0.743643i
$290$	−0.0501725	+	0.0690565i	−0.00294623	+	0.00405514i
$291$	0.233879	+	0.719804i	0.0137102	+	0.0421957i
$292$	4.69567	+	14.4518i	0.274793	+	0.845726i
$293$	2.05946	+	1.49629i	0.120315	+	0.0874140i	0.646316	−	0.763070i	$-0.276309\pi$
$293$	2.05946	+	1.49629i	0.120315	+	0.0874140i	−0.526001	+	0.850484i	$0.676309\pi$
$294$	6.96502	+	0.698936i	0.406208	+	0.0407628i
$295$	−7.55948	+	23.2657i	−0.440130	+	1.35458i
$296$			6.35657i			0.369468i
$297$	−3.12641	+	1.10706i	−0.181413	+	0.0642380i
$298$	8.89930			0.515523
$299$	−0.540691	+	1.66408i	−0.0312690	+	0.0962360i
$300$	6.26990	+	8.62977i	0.361993	+	0.498240i
$301$	−17.9754	+	11.7336i	−1.03609	+	0.676312i
$302$	−5.42307	−	16.6905i	−0.312062	−	0.960429i
$303$	4.86039	−	1.57924i	0.279222	−	0.0907248i
$304$	5.30211	+	3.85221i	0.304097	+	0.220939i
$305$	26.5040	+	36.4796i	1.51761	+	2.08882i
$306$	−5.90174	−	1.91759i	−0.337380	−	0.109621i
$307$	−2.17574			−0.124176			−0.0620880	−	0.998071i	$-0.519776\pi$
$307$	−2.17574			−0.124176			−0.0620880	+	0.998071i	$0.519776\pi$
$308$	0.209219	−	8.77247i	0.0119214	−	0.499858i
$309$	−8.94602			−0.508922
$310$	21.9543	+	7.13339i	1.24692	+	0.405149i
$311$	−0.106489	−	0.146570i	−0.00603846	−	0.00831122i	0.805987	−	0.591933i	$-0.201635\pi$
$311$	−0.106489	−	0.146570i	−0.00603846	−	0.00831122i	−0.812026	+	0.583622i	$0.801635\pi$
$312$	−1.22983	−	0.893526i	−0.0696256	−	0.0505860i
$313$	2.49567	−	0.810893i	0.141064	−	0.0458344i	−0.237634	−	0.971355i	$-0.576372\pi$
$313$	2.49567	−	0.810893i	0.141064	−	0.0458344i	0.378698	+	0.925520i	$0.376372\pi$
$314$	−3.48862	−	10.7369i	−0.196874	−	0.605916i
$315$	−8.76936	+	5.72427i	−0.494097	+	0.322526i
$316$	−7.29040	−	10.0344i	−0.410117	−	0.564478i
$317$	0.198843	−	0.611975i	0.0111681	−	0.0343719i	−0.945317	−	0.326153i	$-0.894248\pi$
$317$	0.198843	−	0.611975i	0.0111681	−	0.0343719i	0.956485	+	0.291781i	$0.0942477\pi$
$318$	−6.76952			−0.379616
$319$	−0.0405126	+	0.0589439i	−0.00226827	+	0.00330023i
$320$		−	3.95815i		−	0.221268i
$321$	1.32099	−	4.06560i	0.0737306	−	0.226919i
$322$	−0.795094	−	2.93965i	−0.0443089	−	0.163820i
$323$	−32.9020	−	23.9047i	−1.83072	−	1.33009i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−5.01087	−	15.4219i	−0.277953	−	0.855451i
$326$	11.7946	−	16.2339i	0.653242	−	0.899111i
$327$	−8.74665	+	6.35481i	−0.483691	+	0.351422i
$328$	7.13464	+	2.31819i	0.393945	+	0.128000i
$329$	0.579240	−	1.51965i	0.0319346	−	0.0837809i
$330$	7.99146	+	10.4151i	0.439915	+	0.573330i
$331$	−2.98085			−0.163842			−0.0819211	−	0.996639i	$-0.526106\pi$
$331$	−2.98085			−0.163842			−0.0819211	+	0.996639i	$0.526106\pi$
$332$	−1.65276	+	5.08668i	−0.0907071	+	0.279168i
$333$	5.14257	−	3.73630i	0.281811	−	0.204748i
$334$	4.06101	−	5.58950i	0.222209	−	0.305844i
$335$	54.3792	−	17.6689i	2.97105	−	0.965354i
$336$	2.64244	+	0.132252i	0.144157	+	0.00721492i
$337$	1.55813	−	2.14458i	0.0848768	−	0.116823i	−0.764467	−	0.644663i	$-0.776998\pi$
$337$	1.55813	−	2.14458i	0.0848768	−	0.116823i	0.849344	+	0.527840i	$0.176998\pi$
$338$	−6.28291	−	8.64768i	−0.341745	−	0.470372i
$339$	11.1879	+	3.63515i	0.607641	+	0.197434i
$340$			24.5622i			1.33207i
$341$	18.5461	+	5.49395i	1.00433	+	0.297514i
$342$		−	6.55377i		−	0.354387i
$343$	18.2713	−	3.02624i	0.986560	−	0.163401i
$344$	−6.56389	+	4.76894i	−0.353901	+	0.257124i
$345$	3.68577	+	2.67787i	0.198435	+	0.144172i
$346$	−12.2810	+	3.99034i	−0.660231	+	0.214522i
$347$	7.89531	−	2.56534i	0.423843	−	0.137715i	−0.0893264	−	0.996002i	$-0.528471\pi$
$347$	7.89531	−	2.56534i	0.423843	−	0.137715i	0.513169	+	0.858288i	$0.328471\pi$
$348$	−0.0174466	−	0.0126757i	−0.000935238	−	0.000679490i
$349$	27.7303	−	20.1472i	1.48437	−	1.07846i	0.508252	−	0.861208i	$-0.330292\pi$
$349$	27.7303	−	20.1472i	1.48437	−	1.07846i	0.976116	−	0.217249i	$-0.0697083\pi$
$350$	21.9745	+	17.7091i	1.17459	+	0.946594i
$351$			1.52016i			0.0811400i
$352$	−0.0867606	−	3.31549i	−0.00462436	−	0.176716i
$353$			12.9526i			0.689395i	0.938714	+	0.344698i	$0.112019\pi$
$353$			12.9526i			0.689395i	−0.938714	+	0.344698i	$0.887981\pi$
$354$	−5.87791	−	1.90985i	−0.312408	−	0.101507i
$355$	15.7490	+	21.6766i	0.835870	+	1.15048i
$356$	0.0516920	−	0.0711479i	0.00273967	−	0.00377083i
$357$	−16.3976	−	0.820683i	−0.867852	−	0.0434351i
$358$	−18.8138	+	6.11296i	−0.994338	+	0.323080i
$359$	−5.28727	+	7.27730i	−0.279051	+	0.384081i	−0.925419	−	0.378945i	$-0.876287\pi$
$359$	−5.28727	+	7.27730i	−0.279051	+	0.384081i	0.646368	+	0.763026i	$0.276287\pi$
$360$	−3.20221	+	2.32654i	−0.168771	+	0.122620i
$361$	7.40154	−	22.7796i	0.389555	−	1.19893i
$362$	1.55263			0.0816044
$363$	6.92222	+	8.54885i	0.363322	+	0.448698i
$364$	−3.75820	−	1.43250i	−0.196983	−	0.0750836i
$365$	−57.2023	−	18.5862i	−2.99411	−	0.972844i
$366$	−9.21632	+	6.69605i	−0.481745	+	0.350008i
$367$	16.7610	−	23.0696i	0.874918	−	1.20422i	−0.102885	−	0.994693i	$-0.532807\pi$
$367$	16.7610	−	23.0696i	0.874918	−	1.20422i	0.977803	−	0.209528i	$-0.0671928\pi$
$368$	−0.355681	−	1.09467i	−0.0185411	−	0.0570638i
$369$	−2.31819	−	7.13464i	−0.120680	−	0.371415i
$370$	−20.3551	−	14.7888i	−1.05821	−	0.768835i
$371$	−17.2892	+	4.67626i	−0.897612	+	0.242779i
$372$	−1.80220	+	5.54661i	−0.0934398	+	0.287578i
$373$		−	2.53707i		−	0.131365i	−0.997841	−	0.0656823i	$-0.979078\pi$
$373$		−	2.53707i		−	0.131365i	0.997841	−	0.0656823i	$-0.0209224\pi$
$374$	0.538390	+	20.5741i	0.0278395	+	1.06386i
$375$	−22.4308			−1.15832
$376$	0.189948	−	0.584599i	0.00979580	−	0.0301484i
$377$	0.0192691	+	0.0265217i	0.000992410	+	0.00136593i
$378$	−1.44620	−	2.21552i	−0.0743843	−	0.113954i
$379$	6.16778	+	18.9825i	0.316817	+	0.975064i	0.975000	+	0.222205i	$0.0713256\pi$
$379$	6.16778	+	18.9825i	0.316817	+	0.975064i	−0.658182	+	0.752859i	$0.728674\pi$
$380$	−24.6712	+	8.01616i	−1.26561	+	0.411220i
$381$	4.11869	+	2.99240i	0.211007	+	0.153305i
$382$	4.10433	+	5.64913i	0.209996	+	0.289035i
$383$	−23.6465	−	7.68322i	−1.20828	−	0.392594i	−0.365479	−	0.930819i	$-0.619095\pi$
$383$	−23.6465	−	7.68322i	−1.20828	−	0.392594i	−0.842801	+	0.538225i	$0.819095\pi$
$384$	1.00000			0.0510310
$385$	27.6046	+	21.0795i	1.40686	+	1.07431i
$386$	−10.4255			−0.530645
$387$	7.71631	+	2.50718i	0.392242	+	0.127447i
$388$	0.444864	+	0.612302i	0.0225845	+	0.0310849i
$389$	24.7152	+	17.9566i	1.25311	+	0.910437i	0.998398	−	0.0565797i	$-0.0180195\pi$
$389$	24.7152	+	17.9566i	1.25311	+	0.910437i	0.254711	+	0.967017i	$0.418020\pi$
$390$	5.72253	−	1.85936i	0.289771	−	0.0941524i
$391$	2.20716	+	6.79295i	0.111621	+	0.343534i
$392$	6.84011	−	1.48758i	0.345478	−	0.0751342i
$393$	7.87597	+	10.8403i	0.397290	+	0.546823i
$394$	−2.14839	+	6.61206i	−0.108234	+	0.333111i
$395$	49.0937			2.47017
$396$	−2.63129	+	2.01899i	−0.132227	+	0.101458i
$397$			25.8080i			1.29527i	0.761952	+	0.647633i	$0.224241\pi$
$397$			25.8080i			1.29527i	−0.761952	+	0.647633i	$0.775759\pi$
$398$	−0.621825	+	1.91378i	−0.0311693	+	0.0959291i
$399$	−4.52722	−	16.7382i	−0.226645	−	0.837958i
$400$	8.62977	+	6.26990i	0.431489	+	0.313495i
$401$	9.84796	+	30.3089i	0.491784	+	1.51355i	0.821910	+	0.569618i	$0.192909\pi$
$401$	9.84796	+	30.3089i	0.491784	+	1.51355i	−0.330126	+	0.943937i	$0.607091\pi$
$402$	4.46392	+	13.7385i	0.222640	+	0.685216i
$403$	5.21109	−	7.17245i	0.259583	−	0.357285i
$404$	4.13449	−	3.00389i	0.205699	−	0.149449i
$405$	3.76443	+	1.22314i	0.187056	+	0.0607782i
$406$	−0.0533146	−	0.0203218i	−0.00264596	−	0.00100855i
$407$	−17.3743	−	11.9415i	−0.861213	−	0.591917i
$408$	−6.20546			−0.307216
$409$	9.19451	−	28.2978i	0.454639	−	1.39924i	−0.416919	−	0.908943i	$-0.636890\pi$
$409$	9.19451	−	28.2978i	0.454639	−	1.39924i	0.871558	−	0.490292i	$-0.163110\pi$
$410$	−24.0224	+	17.4533i	−1.18638	+	0.861957i
$411$	7.49565	−	10.3169i	0.369733	−	0.508894i
$412$	−8.50817	+	2.76447i	−0.419168	+	0.136196i
$413$	−16.3314	−	0.817369i	−0.803614	−	0.0402201i
$414$	−0.676545	+	0.931185i	−0.0332504	+	0.0457652i
$415$	−12.4434	−	17.1269i	−0.610823	−	0.840725i
$416$	−1.44576	−	0.469755i	−0.0708840	−	0.0230316i
$417$		−	9.08033i		−	0.444665i
$418$	−20.4898	+	7.25540i	−1.00219	+	0.354873i
$419$			34.5006i			1.68546i	0.538334	+	0.842732i	$0.319054\pi$
$419$			34.5006i			1.68546i	−0.538334	+	0.842732i	$0.680946\pi$
$420$	−6.57126	+	8.15398i	−0.320645	+	0.397874i
$421$	21.1283	−	15.3506i	1.02973	−	0.748144i	0.0614767	−	0.998109i	$-0.480419\pi$
$421$	21.1283	−	15.3506i	1.02973	−	0.748144i	0.968255	+	0.249965i	$0.0804190\pi$
$422$	13.6561	+	9.92176i	0.664770	+	0.482984i
$423$	−0.584599	+	0.189948i	−0.0284242	+	0.00923557i
$424$	−6.43819	+	2.09190i	−0.312666	+	0.101591i
$425$	−53.5517	−	38.9076i	−2.59764	−	1.88730i
$426$	−5.47645	+	3.97887i	−0.265335	+	0.192777i
$427$	−18.9128	+	23.4680i	−0.915254	+	1.13570i
$428$		−	4.27482i		−	0.206631i
$429$	4.75263	−	1.68290i	0.229459	−	0.0812512i
$430$		−	32.1141i		−	1.54868i
$431$	−0.425489	−	0.138250i	−0.0204951	−	0.00665926i	0.298752	−	0.954331i	$-0.403430\pi$
$431$	−0.425489	−	0.138250i	−0.0204951	−	0.00665926i	−0.319247	+	0.947672i	$0.603430\pi$
$432$	−0.587785	−	0.809017i	−0.0282798	−	0.0389238i
$433$	−1.09403	+	1.50581i	−0.0525758	+	0.0723644i	−0.834495	−	0.551015i	$-0.814241\pi$
$433$	−1.09403	+	1.50581i	−0.0525758	+	0.0723644i	0.781920	+	0.623379i	$0.214241\pi$
$434$	−0.771298	+	15.4109i	−0.0370235	+	0.739745i
$435$	0.0811808	−	0.0263772i	0.00389232	−	0.00126469i
$436$	−6.35481	+	8.74665i	−0.304340	+	0.418888i
$437$	−6.10277	+	4.43392i	−0.291935	+	0.212103i
$438$	4.69567	−	14.4518i	0.224368	−	0.690532i
$439$	11.3434			0.541390			0.270695	−	0.962665i	$-0.412746\pi$
$439$	11.3434			0.541390			0.270695	+	0.962665i	$0.412746\pi$
$440$	10.8188	+	7.43581i	0.515764	+	0.354488i
$441$	−5.22399	−	4.65939i	−0.248762	−	0.221876i
$442$	8.97158	+	2.91504i	0.426735	+	0.138655i
$443$	−12.6315	+	9.17733i	−0.600141	+	0.436028i	−0.845929	−	0.533295i	$-0.820953\pi$
$443$	−12.6315	+	9.17733i	−0.600141	+	0.436028i	0.245788	+	0.969324i	$0.420953\pi$
$444$	3.73630	−	5.14257i	0.177317	−	0.244056i
$445$	0.107567	+	0.331057i	0.00509917	+	0.0156936i
$446$	4.11034	+	12.6503i	0.194630	+	0.599011i
$447$	−7.19969	−	5.23088i	−0.340534	−	0.247412i
$448$	2.55398	−	0.690781i	0.120664	−	0.0326363i
$449$	−11.5924	+	35.6778i	−0.547080	+	1.68374i	0.168912	+	0.985631i	$0.445975\pi$
$449$	−11.5924	+	35.6778i	−0.547080	+	1.68374i	−0.715992	+	0.698108i	$0.754025\pi$
$450$		−	10.6670i		−	0.502846i
$451$	−19.7394	+	15.1461i	−0.929494	+	0.713200i
$452$	11.7636			0.553313
$453$	−5.42307	+	16.6905i	−0.254798	+	0.784187i
$454$	3.85839	+	5.31062i	0.181083	+	0.249240i
$455$	13.3308	−	8.70179i	0.624958	−	0.407946i
$456$	−2.02523	−	6.23301i	−0.0948399	−	0.291887i
$457$	−22.0627	+	7.16861i	−1.03205	+	0.335334i	−0.775601	−	0.631224i	$-0.782553\pi$
$457$	−22.0627	+	7.16861i	−1.03205	+	0.335334i	−0.256450	+	0.966557i	$0.582553\pi$
$458$	0.948769	+	0.689321i	0.0443331	+	0.0322099i
$459$	3.64748	+	5.02032i	0.170250	+	0.234329i
$460$	4.33289	+	1.40784i	0.202022	+	0.0656409i
$461$	26.7136			1.24417			0.622087	−	0.782948i	$-0.286285\pi$
$461$	26.7136			1.24417			0.622087	+	0.782948i	$0.286285\pi$
$462$	−5.32559	+	6.97410i	−0.247769	+	0.324465i
$463$	20.4183			0.948920			0.474460	−	0.880277i	$-0.342643\pi$
$463$	20.4183			0.948920			0.474460	+	0.880277i	$0.342643\pi$
$464$	−0.0205098	−	0.00666403i	−0.000952142	−	0.000309370i
$465$	−13.5685	−	18.6755i	−0.629225	−	0.866054i
$466$	−9.58565	−	6.96438i	−0.444046	−	0.322619i
$467$	−27.5643	+	8.95617i	−1.27552	+	0.414442i	−0.867001	−	0.498307i	$-0.833955\pi$
$467$	−27.5643	+	8.95617i	−1.27552	+	0.414442i	−0.408521	+	0.912749i	$0.633955\pi$
$468$	0.469755	+	1.44576i	0.0217144	+	0.0668301i
$469$	20.8911	+	32.0044i	0.964661	+	1.47782i
$470$	1.43009	+	1.96835i	0.0659651	+	0.0907931i
$471$	−3.48862	+	10.7369i	−0.160747	+	0.494728i
$472$	−6.18040			−0.284476
$473$	−0.703925	−	26.8999i	−0.0323665	−	1.23686i
$474$			12.4032i			0.569697i
$475$	21.6031	−	66.4874i	0.991216	−	3.05065i
$476$	−15.8486	+	4.28662i	−0.726421	+	0.196477i
$477$	5.47666	+	3.97902i	0.250759	+	0.182187i
$478$	−0.175438	−	0.539941i	−0.00802433	−	0.0246963i
$479$	−0.706835	−	2.17542i	−0.0322961	−	0.0993973i	0.933609	−	0.358293i	$-0.116641\pi$
$479$	−0.706835	−	2.17542i	−0.0322961	−	0.0993973i	−0.965905	+	0.258896i	$0.916641\pi$
$480$	−2.32654	+	3.20221i	−0.106192	+	0.146160i
$481$	−7.81752	+	5.67976i	−0.356448	+	0.258975i
$482$	14.8572	+	4.82738i	0.676725	+	0.219881i
$483$	−1.08464	+	2.84557i	−0.0493528	+	0.129478i
$484$	9.22516	+	5.99135i	0.419326	+	0.272334i
$485$	−2.99572			−0.136029
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	15.2603	−	11.0873i	0.691510	−	0.502412i	−0.185646	−	0.982617i	$-0.559438\pi$
$487$	15.2603	−	11.0873i	0.691510	−	0.502412i	0.877156	+	0.480205i	$0.159438\pi$
$488$	−6.69605	+	9.21632i	−0.303116	+	0.417203i
$489$	−19.0841	+	6.20079i	−0.863011	+	0.280409i
$490$	−11.1503	+	25.3644i	−0.503718	+	1.14585i
$491$	23.3722	−	32.1691i	1.05477	−	1.45177i	0.170179	−	0.985413i	$-0.445565\pi$
$491$	23.3722	−	32.1691i	1.05477	−	1.45177i	0.884595	−	0.466359i	$-0.154435\pi$
$492$	−4.40945	−	6.06909i	−0.198793	−	0.273616i
$493$	0.127273	+	0.0413533i	0.00573207	+	0.00186246i
$494$			9.96277i			0.448246i
$495$	−0.343412	−	13.1232i	−0.0154352	−	0.589845i
$496$			5.83205i			0.261867i
$497$	−11.2382	+	13.9450i	−0.504103	+	0.625519i
$498$	4.32699	−	3.14374i	0.193897	−	0.140874i
$499$	19.2652	+	13.9970i	0.862428	+	0.626591i	0.928544	−	0.371221i	$-0.121061\pi$
$499$	19.2652	+	13.9970i	0.862428	+	0.626591i	−0.0661163	+	0.997812i	$0.521061\pi$
$500$	−21.3330	+	6.93150i	−0.954039	+	0.309986i
$501$	−6.57085	+	2.13500i	−0.293564	+	0.0953848i
$502$	12.6662	+	9.20254i	0.565320	+	0.410729i
$503$	−29.4399	+	21.3893i	−1.31266	+	0.953703i	−0.312667	+	0.949863i	$0.601222\pi$
$503$	−29.4399	+	21.3893i	−1.31266	+	0.953703i	−0.999993	+	0.00383982i	$0.998778\pi$
$504$	−2.06005	−	1.66018i	−0.0917618	−	0.0739504i
$505$			20.2282i			0.900143i
$506$	3.66024	+	1.08428i	0.162717	+	0.0482022i
$507$			10.6891i			0.474720i
$508$	4.84181	+	1.57320i	0.214820	+	0.0697994i
$509$	−3.18287	−	4.38085i	−0.141078	−	0.194178i	0.732631	−	0.680626i	$-0.238292\pi$
$509$	−3.18287	−	4.38085i	−0.141078	−	0.194178i	−0.873709	+	0.486448i	$0.838292\pi$
$510$	14.4373	−	19.8712i	0.639294	−	0.879912i
$511$	2.00963	−	40.1532i	0.0889008	−	1.77627i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−3.85221	+	5.30211i	−0.170079	+	0.234094i
$514$	−19.6380	+	14.2679i	−0.866197	+	0.629329i
$515$	10.9422	−	33.6767i	0.482171	−	1.48397i
$516$	8.11341			0.357173
$517$	1.24104	+	1.61741i	0.0545808	+	0.0711337i
$518$	5.99004	−	15.7150i	0.263187	−	0.690477i
$519$	12.2810	+	3.99034i	0.539076	+	0.175157i
$520$	4.86787	−	3.53672i	0.213470	−	0.155095i
$521$	−3.11967	+	4.29386i	−0.136675	+	0.188117i	−0.871868	−	0.489741i	$-0.837091\pi$
$521$	−3.11967	+	4.29386i	−0.136675	+	0.188117i	0.735193	+	0.677858i	$0.237091\pi$
$522$	0.00666403	+	0.0205098i	0.000291676	+	0.000897688i
$523$	−6.81913	−	20.9871i	−0.298180	−	0.917702i	−0.982135	−	0.188178i	$-0.939742\pi$
$523$	−6.81913	−	20.9871i	−0.298180	−	0.917702i	0.683955	−	0.729524i	$-0.260258\pi$
$524$	10.8403	+	7.87597i	0.473562	+	0.344063i
$525$	−7.36855	−	27.2433i	−0.321590	−	1.18899i
$526$	5.03706	−	15.5025i	0.219626	−	0.675940i
$527$		−	36.1905i		−	1.57648i
$528$	−1.87861	+	2.73328i	−0.0817558	+	0.118951i
$529$	−21.6752			−0.942399
$530$	8.28005	−	25.4834i	0.359662	−	1.10693i
$531$	3.63275	+	5.00005i	0.157648	+	0.216984i
$532$	−9.47803	−	14.5200i	−0.410925	−	0.629522i
$533$	3.52401	+	10.8458i	0.152642	+	0.469783i
$534$	−0.0836394	+	0.0271761i	−0.00361943	+	0.00117602i
$535$	13.6889	+	9.94556i	0.591822	+	0.429984i
$536$	8.49088	+	11.6867i	0.366750	+	0.504788i
$537$	18.8138	+	6.11296i	0.811874	+	0.263794i
$538$	10.3268			0.445221
$539$	−8.78388	+	21.4905i	−0.378349	+	0.925663i
$540$	3.95815			0.170332
$541$	−24.8098	−	8.06118i	−1.06666	−	0.346577i	−0.277471	−	0.960734i	$-0.589496\pi$
$541$	−24.8098	−	8.06118i	−1.06666	−	0.346577i	−0.789184	+	0.614157i	$0.789496\pi$
$542$	0.259662	+	0.357395i	0.0111535	+	0.0153514i
$543$	−1.25610	−	0.912613i	−0.0539046	−	0.0391640i
$544$	−5.90174	+	1.91759i	−0.253035	+	0.0822161i
$545$	−13.2239	−	40.6989i	−0.566449	−	1.74335i
$546$	2.19845	+	3.36794i	0.0940848	+	0.144134i
$547$	15.5145	+	21.3538i	0.663350	+	0.913023i	0.999587	−	0.0287543i	$-0.00915404\pi$
$547$	15.5145	+	21.3538i	0.663350	+	0.913023i	−0.336236	+	0.941778i	$0.609154\pi$
$548$	3.94069	−	12.1282i	0.168338	−	0.518092i
$549$	11.3920			0.486198
$550$	−33.3493	+	11.8090i	−1.42202	+	0.503536i
$551$			0.141334i			0.00602101i
$552$	−0.355681	+	1.09467i	−0.0151388	+	0.0465924i
$553$	8.56788	+	31.6775i	0.364343	+	1.34706i
$554$	9.35376	+	6.79591i	0.397403	+	0.288730i
$555$	7.77495	+	23.9288i	0.330028	+	1.01572i
$556$	−2.80597	−	8.63590i	−0.119000	−	0.366244i
$557$	−2.85167	+	3.92499i	−0.120829	+	0.166307i	−0.865147	−	0.501519i	$-0.832775\pi$
$557$	−2.85167	+	3.92499i	−0.120829	+	0.166307i	0.744318	+	0.667826i	$0.232775\pi$
$558$	4.71822	−	3.42799i	0.199738	−	0.145118i
$559$	−11.7300	−	3.81131i	−0.496127	−	0.161201i
$560$	−3.72992	+	9.78553i	−0.157618	+	0.413514i
$561$	11.6576	−	16.9613i	0.492185	−	0.716106i
$562$	−9.23615			−0.389603
$563$	1.55008	−	4.77067i	0.0653282	−	0.201060i	−0.913064	−	0.407816i	$-0.866291\pi$
$563$	1.55008	−	4.77067i	0.0653282	−	0.201060i	0.978393	+	0.206756i	$0.0662906\pi$
$564$	−0.497290	+	0.361302i	−0.0209397	+	0.0152136i
$565$	−27.3685	+	37.6696i	−1.15140	+	1.58477i
$566$	6.47087	−	2.10251i	0.271991	−	0.0883752i
$567$	−0.132252	+	2.64244i	−0.00555405	+	0.110972i
$568$	−3.97887	+	5.47645i	−0.166950	+	0.229787i
$569$	−5.65550	−	7.78413i	−0.237091	−	0.326328i	0.673847	−	0.738871i	$-0.264641\pi$
$569$	−5.65550	−	7.78413i	−0.237091	−	0.326328i	−0.910938	+	0.412543i	$0.864641\pi$
$570$	24.6712	+	8.01616i	1.03336	+	0.335760i
$571$		−	24.0899i		−	1.00813i	−0.863665	−	0.504065i	$-0.831837\pi$
$571$		−	24.0899i		−	1.00813i	0.863665	−	0.504065i	$-0.168163\pi$
$572$	3.99998	−	3.06918i	0.167247	−	0.128329i
$573$		−	6.98271i		−	0.291707i
$574$	−15.4541	−	12.4544i	−0.645040	−	0.519836i
$575$	−9.93293	+	7.21670i	−0.414232	+	0.300957i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−4.18731	+	1.36054i	−0.174320	+	0.0566400i	−0.394877	−	0.918734i	$-0.629213\pi$
$577$	−4.18731	+	1.36054i	−0.174320	+	0.0566400i	0.220557	+	0.975374i	$0.429213\pi$
$578$	20.4551	−	6.64626i	0.850819	−	0.276448i
$579$	8.43442	+	6.12797i	0.350523	+	0.254670i
$580$	0.0690565	−	0.0501725i	0.00286742	−	0.00208330i
$581$	8.87941	−	11.0181i	0.368380	−	0.457106i
$582$		−	0.756847i		−	0.0313723i
$583$	6.37708	−	21.5273i	0.264112	−	0.891568i
$584$		−	15.1955i		−	0.628794i
$585$	−5.72253	−	1.85936i	−0.236597	−	0.0768751i
$586$	−1.49629	−	2.05946i	−0.0618110	−	0.0850756i
$587$	19.2408	−	26.4827i	0.794152	−	1.09306i	−0.199427	−	0.979913i	$-0.563908\pi$
$587$	19.2408	−	26.4827i	0.794152	−	1.09306i	0.993579	−	0.113144i	$-0.0360920\pi$
$588$	−6.40814	−	2.81704i	−0.264267	−	0.116173i
$589$	36.3512	−	11.8112i	1.49782	−	0.486673i
$590$	14.3790	−	19.7910i	0.591974	−	0.814782i
$591$	5.62455	−	4.08648i	0.231363	−	0.168095i
$592$	1.96429	−	6.04546i	0.0807317	−	0.248467i
$593$	−32.2197			−1.32310			−0.661552	−	0.749899i	$-0.730102\pi$
$593$	−32.2197			−1.32310			−0.661552	+	0.749899i	$0.730102\pi$
$594$	3.31549	−	0.0867606i	0.136036	−	0.00355983i
$595$	23.1459	−	60.7237i	0.948889	−	2.48943i
$596$	−8.46374	−	2.75004i	−0.346688	−	0.112646i
$597$	1.62796	−	1.18278i	0.0666279	−	0.0484080i
$598$	1.02846	−	1.41555i	0.0420567	−	0.0578861i
$599$	12.1196	+	37.3002i	0.495192	+	1.52404i	0.816657	+	0.577123i	$0.195825\pi$
$599$	12.1196	+	37.3002i	0.495192	+	1.52404i	−0.321465	+	0.946922i	$0.604175\pi$
$600$	−3.29628	−	10.1449i	−0.134570	−	0.414164i
$601$	8.30406	+	6.03325i	0.338729	+	0.246101i	0.744126	−	0.668040i	$-0.232866\pi$
$601$	8.30406	+	6.03325i	0.338729	+	0.246101i	−0.405396	+	0.914141i	$0.632866\pi$
$602$	20.7215	−	5.60459i	0.844545	−	0.228426i
$603$	4.46392	−	13.7385i	0.181785	−	0.559476i
$604$			17.5494i			0.714075i
$605$	−40.6484	+	15.6018i	−1.65259	+	0.634303i
$606$	−5.11052			−0.207601
$607$	−10.1271	+	31.1682i	−0.411048	+	1.26508i	0.504690	+	0.863301i	$0.331607\pi$
$607$	−10.1271	+	31.1682i	−0.411048	+	1.26508i	−0.915738	+	0.401776i	$0.868393\pi$
$608$	−3.85221	−	5.30211i	−0.156228	−	0.215029i
$609$	0.0311876	+	0.0477782i	0.00126378	+	0.00193607i
$610$	−13.9340	−	42.8843i	−0.564170	−	1.73634i
$611$	0.888683	−	0.288750i	0.0359523	−	0.0116816i
$612$	5.02032	+	3.64748i	0.202935	+	0.147441i
$613$	−27.2552	−	37.5136i	−1.10083	−	1.51516i	−0.834283	−	0.551336i	$-0.814118\pi$
$613$	−27.2552	−	37.5136i	−1.10083	−	1.51516i	−0.266544	−	0.963823i	$-0.585882\pi$
$614$	2.06925	+	0.672340i	0.0835082	+	0.0271335i
$615$	29.6933			1.19735
$616$	−2.90982	+	8.27846i	−0.117240	+	0.333549i
$617$	36.9072			1.48583			0.742914	−	0.669387i	$-0.233443\pi$
$617$	36.9072			1.48583			0.742914	+	0.669387i	$0.233443\pi$
$618$	8.50817	+	2.76447i	0.342249	+	0.111203i
$619$	2.96273	+	4.07785i	0.119082	+	0.163903i	0.864397	−	0.502810i	$-0.167701\pi$
$619$	2.96273	+	4.07785i	0.119082	+	0.163903i	−0.745314	+	0.666713i	$0.767701\pi$
$620$	−18.6755	−	13.5685i	−0.750025	−	0.544925i
$621$	1.09467	−	0.355681i	0.0439277	−	0.0142730i
$622$	0.0559847	+	0.172303i	0.00224478	+	0.00690873i
$623$	−0.194841	+	0.127184i	−0.00780613	+	0.00509551i
$624$	0.893526	+	1.22983i	0.0357697	+	0.0492327i
$625$	10.9545	−	33.7146i	0.438181	−	1.34858i
$626$	−2.62410			−0.104880
$627$	20.8412	+	6.17384i	0.832316	+	0.246559i
$628$			11.2894i			0.450496i
$629$	−12.1893	+	37.5148i	−0.486020	+	1.49581i
$630$	10.1091	−	2.73422i	0.402754	−	0.108934i
$631$	11.1850	+	8.12640i	0.445269	+	0.323507i	0.787725	−	0.616027i	$-0.211259\pi$
$631$	11.1850	+	8.12640i	0.445269	+	0.323507i	−0.342456	+	0.939534i	$0.611259\pi$
$632$	3.83279	+	11.7961i	0.152460	+	0.469225i
$633$	−5.21618	−	16.0537i	−0.207324	−	0.638079i
$634$	−0.378221	+	0.520577i	−0.0150211	+	0.0206748i
$635$	−16.3024	+	11.8444i	−0.646941	+	0.470030i
$636$	6.43819	+	2.09190i	0.255291	+	0.0829491i
$637$	7.94130	+	7.08300i	0.314646	+	0.280639i
$638$	0.0567444	−	0.0435399i	0.00224653	−	0.00172376i
$639$	6.76926			0.267788
$640$	−1.22314	+	3.76443i	−0.0483487	+	0.148802i
$641$	−4.28005	+	3.10964i	−0.169052	+	0.122823i	−0.669094	−	0.743178i	$-0.733318\pi$
$641$	−4.28005	+	3.10964i	−0.169052	+	0.122823i	0.500042	+	0.866001i	$0.333318\pi$
$642$	−2.51268	+	3.45840i	−0.0991674	+	0.136492i
$643$	−15.4829	+	5.03070i	−0.610586	+	0.198391i	−0.597956	−	0.801529i	$-0.704020\pi$
$643$	−15.4829	+	5.03070i	−0.610586	+	0.198391i	−0.0126300	+	0.999920i	$0.504020\pi$
$644$	−0.152223	+	3.04147i	−0.00599842	+	0.119851i
$645$	−18.8762	+	25.9809i	−0.743250	+	1.02300i
$646$	23.9047	+	32.9020i	0.940519	+	1.29451i
$647$	35.9245	+	11.6726i	1.41234	+	0.458897i	0.913160	−	0.407602i	$-0.133635\pi$
$647$	35.9245	+	11.6726i	1.41234	+	0.458897i	0.499179	+	0.866499i	$0.333635\pi$
$648$			1.00000i			0.0392837i
$649$	11.6105	−	16.8928i	0.455754	−	0.663100i
$650$			16.2155i			0.636024i
$651$	9.68227	−	12.0143i	0.379478	−	0.470877i
$652$	−16.2339	+	11.7946i	−0.635767	+	0.461912i
$653$	7.53003	+	5.47089i	0.294673	+	0.214092i	0.725292	−	0.688441i	$-0.241705\pi$
$653$	7.53003	+	5.47089i	0.294673	+	0.214092i	−0.430619	+	0.902534i	$0.641705\pi$
$654$	10.2823	−	3.34092i	0.402070	−	0.130640i
$655$	−50.4411	+	16.3893i	−1.97090	+	0.640383i
$656$	−6.06909	−	4.40945i	−0.236958	−	0.172160i
$657$	−12.2934	+	8.93169i	−0.479612	+	0.348458i
$658$	−1.02049	+	1.26628i	−0.0397827	+	0.0493646i
$659$		−	1.25185i		−	0.0487653i	−0.999703	−	0.0243827i	$-0.992238\pi$
$659$		−	1.25185i		−	0.0487653i	0.999703	−	0.0243827i	$-0.00776201\pi$
$660$	−4.38190	−	12.3748i	−0.170565	−	0.481689i
$661$			30.6457i			1.19198i	0.802993	+	0.595989i	$0.203240\pi$
$661$			30.6457i			1.19198i	−0.802993	+	0.595989i	$0.796760\pi$
$662$	2.83495	+	0.921132i	0.110184	+	0.0358008i
$663$	−5.54474	−	7.63168i	−0.215340	−	0.296390i
$664$	3.14374	−	4.32699i	0.122001	−	0.167920i
$665$	68.5472	+	3.43072i	2.65815	+	0.133038i
$666$	−6.04546	+	1.96429i	−0.234257	+	0.0761146i
$667$	0.0145899	−	0.0200812i	0.000564922	−	0.000777548i
$668$	−5.58950	+	4.06101i	−0.216264	+	0.157125i
$669$	4.11034	−	12.6503i	0.158915	−	0.489090i
$670$	−57.1777			−2.20897
$671$	−12.6116	−	35.6160i	−0.486865	−	1.37494i
$672$	−2.47225	−	0.942339i	−0.0953689	−	0.0363515i
$673$	7.24228	+	2.35316i	0.279169	+	0.0907076i	0.445255	−	0.895404i	$-0.353113\pi$
$673$	7.24228	+	2.35316i	0.279169	+	0.0907076i	−0.166086	+	0.986111i	$0.553113\pi$
$674$	−2.14458	+	1.55813i	−0.0826063	+	0.0600170i
$675$	−6.26990	+	8.62977i	−0.241328	+	0.332160i
$676$	3.30312	+	10.1660i	0.127043	+	0.390998i
$677$	−1.53505	−	4.72439i	−0.0589966	−	0.181573i	0.917215	−	0.398392i	$-0.130432\pi$
$677$	−1.53505	−	4.72439i	−0.0589966	−	0.181573i	−0.976212	+	0.216819i	$0.930432\pi$
$678$	−9.51695	−	6.91447i	−0.365496	−	0.265549i
$679$	−0.522816	−	1.93297i	−0.0200638	−	0.0741807i
$680$	7.59013	−	23.3600i	0.291068	−	0.895816i
$681$		−	6.56429i		−	0.251544i
$682$	−15.9406	−	10.9561i	−0.610399	−	0.419531i
$683$	−16.7599			−0.641298			−0.320649	−	0.947198i	$-0.603901\pi$
$683$	−16.7599			−0.641298			−0.320649	+	0.947198i	$0.603901\pi$
$684$	−2.02523	+	6.23301i	−0.0774365	+	0.238325i
$685$	29.6689	+	40.8358i	1.13359	+	1.56025i
$686$	−18.3122	−	2.76803i	−0.699164	−	0.105684i
$687$	−0.362397	−	1.11534i	−0.0138263	−	0.0425531i
$688$	7.71631	−	2.50718i	0.294182	−	0.0955854i
$689$	−8.32538	−	6.04874i	−0.317172	−	0.230439i
$690$	−2.67787	−	3.68577i	−0.101945	−	0.140315i
$691$	−29.4277	−	9.56164i	−1.11948	−	0.363742i	−0.309912	−	0.950765i	$-0.600300\pi$
$691$	−29.4277	−	9.56164i	−1.11948	−	0.363742i	−0.809570	+	0.587023i	$0.800300\pi$
$692$	12.9130			0.490879
$693$	8.40777	−	2.51186i	0.319385	−	0.0954178i
$694$	−8.30162			−0.315125
$695$	34.1822	+	11.1065i	1.29661	+	0.421293i
$696$	0.0126757	+	0.0174466i	0.000480472	+	0.000661313i
$697$	37.6615	+	27.3627i	1.42653	+	1.03644i
$698$	−32.5989	+	10.5920i	−1.23389	+	0.400914i
$699$	3.66139	+	11.2686i	0.138487	+	0.426218i
$700$	−15.4265	−	23.6329i	−0.583069	−	0.893239i
$701$	−9.00286	−	12.3914i	−0.340033	−	0.468015i	0.604418	−	0.796667i	$-0.293406\pi$
$701$	−9.00286	−	12.3914i	−0.340033	−	0.468015i	−0.944451	+	0.328652i	$0.893406\pi$
$702$	0.469755	−	1.44576i	0.0177297	−	0.0545665i
$703$	−41.6595			−1.57122
$704$	−0.942028	+	3.18003i	−0.0355040	+	0.119852i
$705$		−	2.43301i		−	0.0916326i
$706$	4.00256	−	12.3186i	0.150638	−	0.463617i
$707$	−13.0522	+	3.53025i	−0.490877	+	0.132769i
$708$	5.00005	+	3.63275i	0.187913	+	0.136527i
$709$	0.781519	+	2.40527i	0.0293505	+	0.0903317i	0.964659	−	0.263502i	$-0.0848777\pi$
$709$	0.781519	+	2.40527i	0.0293505	+	0.0903317i	−0.935308	+	0.353834i	$0.884878\pi$
$710$	−8.27974	−	25.4824i	−0.310733	−	0.956338i
$711$	7.29040	−	10.0344i	0.273412	−	0.376319i
$712$	−0.0711479	+	0.0516920i	−0.00266638	+	0.00193724i
$713$	−6.38418	−	2.07435i	−0.239090	−	0.0776849i
$714$	15.3414	+	5.84765i	0.574138	+	0.218843i
$715$	0.522041	+	19.9494i	0.0195232	+	0.746064i
$716$	19.7820			0.739287
$717$	−0.175438	+	0.539941i	−0.00655184	+	0.0201645i
$718$	7.27730	−	5.28727i	0.271587	−	0.197319i
$719$	−12.0558	+	16.5933i	−0.449604	+	0.618827i	−0.972312	−	0.233685i	$-0.924922\pi$
$719$	−12.0558	+	16.5933i	−0.449604	+	0.618827i	0.522708	+	0.852512i	$0.324922\pi$
$720$	3.76443	−	1.22314i	0.140292	−	0.0455836i
$721$	23.6394	+	1.18313i	0.880376	+	0.0440620i
$722$	−14.0786	+	19.3775i	−0.523950	+	0.721156i
$723$	−9.18222	−	12.6382i	−0.341491	−	0.470021i
$724$	−1.47664	−	0.479789i	−0.0548788	−	0.0178312i
$725$			0.230036i			0.00854332i
$726$	−3.94169	−	10.2695i	−0.146290	−	0.381138i
$727$			40.7485i			1.51128i	0.654989	+	0.755638i	$0.272673\pi$
$727$			40.7485i			1.51128i	−0.654989	+	0.755638i	$0.727327\pi$
$728$	3.13160	+	2.52374i	0.116065	+	0.0935361i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	48.6592	+	35.3530i	1.80096	+	1.30847i
$731$	−47.8833	+	15.5582i	−1.77103	+	0.575442i
$732$	10.8344	−	3.52032i	0.400452	−	0.130115i
$733$	12.0661	+	8.76651i	0.445670	+	0.323799i	0.787884	−	0.615824i	$-0.211177\pi$
$733$	12.0661	+	8.76651i	0.445670	+	0.323799i	−0.342214	+	0.939622i	$0.611177\pi$
$734$	−23.0696	+	16.7610i	−0.851513	+	0.618660i
$735$	23.9296	−	13.9663i	0.882656	−	0.515154i
$736$			1.15101i			0.0424267i
$737$	−47.8941	+	1.25330i	−1.76420	+	0.0461661i
$738$			7.50181i			0.276145i
$739$	−15.5212	−	5.04313i	−0.570955	−	0.185514i	0.00928964	−	0.999957i	$-0.497043\pi$
$739$	−15.5212	−	5.04313i	−0.570955	−	0.185514i	−0.580244	+	0.814442i	$0.697043\pi$
$740$	14.7888	+	20.3551i	0.543649	+	0.748268i
$741$	5.85597	−	8.06005i	0.215124	−	0.296093i
$742$	17.8881	+	0.895281i	0.656692	+	0.0328668i
$743$	7.67644	−	2.49423i	0.281621	−	0.0915043i	−0.164801	−	0.986327i	$-0.552698\pi$
$743$	7.67644	−	2.49423i	0.281621	−	0.0915043i	0.446422	+	0.894823i	$0.352698\pi$
$744$	3.42799	−	4.71822i	0.125676	−	0.172979i
$745$	28.4975	−	20.7046i	1.04407	−	0.758559i
$746$	−0.783998	+	2.41290i	−0.0287042	+	0.0883425i
$747$	−5.34845			−0.195690
$748$	5.84572	−	19.7335i	0.213741	−	0.721530i
$749$	−4.02833	+	10.5684i	−0.147192	+	0.386161i
$750$	21.3330	+	6.93150i	0.778969	+	0.253102i
$751$	−5.86785	+	4.26324i	−0.214121	+	0.155568i	−0.689676	−	0.724118i	$-0.742247\pi$
$751$	−5.86785	+	4.26324i	−0.214121	+	0.155568i	0.475555	+	0.879686i	$0.342247\pi$
$752$	−0.361302	+	0.497290i	−0.0131753	+	0.0181343i
$753$	−4.83806	−	14.8900i	−0.176309	−	0.542622i
$754$	−0.0101304	−	0.0311781i	−0.000368926	−	0.00113544i
$755$	−56.1970	−	40.8295i	−2.04522	−	1.48594i
$756$	0.690781	+	2.55398i	0.0251235	+	0.0928874i
$757$	15.4389	−	47.5160i	0.561136	−	1.72700i	−0.118028	−	0.993010i	$-0.537657\pi$
$757$	15.4389	−	47.5160i	0.561136	−	1.72700i	0.679163	−	0.733987i	$-0.262343\pi$
$758$		−	19.9594i		−	0.724956i
$759$	−2.32387	−	3.02864i	−0.0843511	−	0.109933i
$760$	25.9408			0.940973
$761$	−4.48521	+	13.8041i	−0.162589	+	0.500397i	−0.998851	−	0.0479336i	$-0.984736\pi$
$761$	−4.48521	+	13.8041i	−0.162589	+	0.500397i	0.836262	+	0.548330i	$0.184736\pi$
$762$	−2.99240	−	4.11869i	−0.108403	−	0.149204i
$763$	23.9530	−	15.6355i	0.867155	−	0.566042i
$764$	−2.15778	−	6.64095i	−0.0780656	−	0.240261i
$765$	−23.3600	+	7.59013i	−0.844583	+	0.274422i
$766$	20.1149	+	14.6143i	0.726782	+	0.528038i
$767$	−5.52235	−	7.60087i	−0.199401	−	0.274451i
$768$	−0.951057	−	0.309017i	−0.0343183	−	0.0111507i
$769$	42.2987			1.52533			0.762665	−	0.646794i	$-0.223890\pi$
$769$	42.2987			1.52533			0.762665	+	0.646794i	$0.223890\pi$
$770$	−19.7396	−	28.5781i	−0.711365	−	1.02988i
$771$	24.2740			0.874205
$772$	9.91526	+	3.22166i	0.356858	+	0.115950i
$773$	6.45134	+	8.87951i	0.232039	+	0.319374i	0.909120	−	0.416534i	$-0.136755\pi$
$773$	6.45134	+	8.87951i	0.232039	+	0.319374i	−0.677081	+	0.735908i	$0.736755\pi$
$774$	−6.56389	−	4.76894i	−0.235934	−	0.171416i
$775$	59.1656	−	19.2241i	2.12529	−	0.690548i
$776$	−0.233879	−	0.719804i	−0.00839575	−	0.0258395i
$777$	−14.0831	+	9.19284i	−0.505228	+	0.329791i
$778$	−17.9566	−	24.7152i	−0.643776	−	0.886082i
$779$	−15.1929	+	46.7588i	−0.544341	+	1.67531i
$780$	−6.01702			−0.215444
$781$	−7.49396	−	21.1635i	−0.268155	−	0.757289i
$782$		−	7.14253i		−	0.255416i
$783$	0.00666403	−	0.0205098i	0.000238153	−	0.000732959i
$784$	−6.96502	−	0.698936i	−0.248751	−	0.0249620i
$785$	−36.1511	−	26.2653i	−1.29029	−	0.937448i
$786$	−4.14064	−	12.7436i	−0.147692	−	0.454548i
$787$	0.267163	+	0.822243i	0.00952333	+	0.0293098i	0.955705	−	0.294325i	$-0.0950949\pi$
$787$	0.267163	+	0.822243i	0.00952333	+	0.0293098i	−0.946182	+	0.323635i	$0.895095\pi$
$788$	4.08648	−	5.62455i	0.145575	−	0.200366i
$789$	−13.1872	+	9.58105i	−0.469476	+	0.341094i
$790$	−46.6909	−	15.1708i	−1.66119	−	0.539752i
$791$	−29.0825	−	11.0853i	−1.03406	−	0.394148i
$792$	3.12641	−	1.10706i	0.111092	−	0.0393376i
$793$	−17.3176			−0.614967
$794$	7.97511	−	24.5449i	0.283026	−	0.871065i
$795$	−21.6774	+	15.7496i	−0.768820	+	0.558580i
$796$	1.18278	−	1.62796i	0.0419226	−	0.0577014i
$797$	43.9573	−	14.2826i	1.55705	−	0.505916i	0.601031	−	0.799225i	$-0.294757\pi$
$797$	43.9573	−	14.2826i	1.55705	−	0.505916i	0.956017	+	0.293310i	$0.0947567\pi$
$798$	−0.866747	+	17.3180i	−0.0306825	+	0.613049i
$799$	2.24205	−	3.08591i	0.0793179	−	0.109172i
$800$	−6.26990	−	8.62977i	−0.221674	−	0.305108i
$801$	0.0836394	+	0.0271761i	0.00295525	+	0.000960219i
$802$		−	31.8687i		−	1.12532i
$803$	41.5336	+	28.5463i	1.46569	+	1.00738i
$804$		−	14.4455i		−	0.509455i
$805$	−9.38529	−	7.56357i	−0.330788	−	0.266581i
$806$	−7.17245	+	5.21109i	−0.252639	+	0.183553i
$807$	−8.35458	−	6.06996i	−0.294095	−	0.213673i
$808$	−4.86039	+	1.57924i	−0.170988	+	0.0555573i
$809$	17.8605	−	5.80322i	0.627941	−	0.204030i	0.0222781	−	0.999752i	$-0.492908\pi$
$809$	17.8605	−	5.80322i	0.627941	−	0.204030i	0.605663	+	0.795721i	$0.292908\pi$
$810$	−3.20221	−	2.32654i	−0.112514	−	0.0817464i
$811$	23.0648	−	16.7576i	0.809915	−	0.588438i	−0.103891	−	0.994589i	$-0.533129\pi$
$811$	23.0648	−	16.7576i	0.809915	−	0.588438i	0.913806	+	0.406151i	$0.133129\pi$
$812$	0.0444254	+	0.0358023i	0.00155903	+	0.00125641i
$813$		−	0.441764i		−	0.0154933i
$814$	12.8338	+	16.7260i	0.449825	+	0.586245i
$815$		−	79.4250i		−	2.78214i
$816$	5.90174	+	1.91759i	0.206602	+	0.0671292i
$817$	−31.2546	−	43.0182i	−1.09346	−	1.50502i
$818$	−17.4890	+	24.0715i	−0.611488	+	0.841641i
$819$	0.201044	−	4.01693i	0.00702503	−	0.140363i
$820$	28.2400	−	9.17574i	0.986184	−	0.320431i
$821$	−3.41592	+	4.70161i	−0.119216	+	0.164087i	−0.864454	−	0.502711i	$-0.832336\pi$
$821$	−3.41592	+	4.70161i	−0.119216	+	0.164087i	0.745238	+	0.666799i	$0.232336\pi$
$822$	−10.3169	+	7.49565i	−0.359842	+	0.261441i
$823$	−6.92128	+	21.3015i	−0.241261	+	0.742524i	0.754968	+	0.655761i	$0.227652\pi$
$823$	−6.92128	+	21.3015i	−0.241261	+	0.742524i	−0.996229	+	0.0867629i	$0.972348\pi$
$824$	8.94602			0.311650
$825$	33.9213	+	10.0486i	1.18099	+	0.349847i
$826$	15.2795	+	5.82404i	0.531641	+	0.202644i
$827$	20.4277	+	6.63737i	0.710342	+	0.230804i	0.641831	−	0.766846i	$-0.278175\pi$
$827$	20.4277	+	6.63737i	0.710342	+	0.230804i	0.0685112	+	0.997650i	$0.478175\pi$
$828$	0.931185	−	0.676545i	0.0323609	−	0.0235116i
$829$	18.4532	−	25.3986i	0.640906	−	0.882131i	−0.357758	−	0.933814i	$-0.616459\pi$
$829$	18.4532	−	25.3986i	0.640906	−	0.882131i	0.998664	+	0.0516831i	$0.0164586\pi$
$830$	6.54189	+	20.1339i	0.227072	+	0.698856i
$831$	−3.57282	−	10.9960i	−0.123940	−	0.381447i
$832$	1.22983	+	0.893526i	0.0426368	+	0.0309775i
$833$	43.2212	+	4.33722i	1.49752	+	0.150276i
$834$	−2.80597	+	8.63590i	−0.0971630	+	0.299037i
$835$		−	27.3469i		−	0.946379i
$836$	21.7290	−	0.568609i	0.751512	−	0.0196658i
$837$	−5.83205			−0.201585
$838$	10.6613	−	32.8120i	0.368287	−	1.13347i
$839$	3.57724	+	4.92365i	0.123500	+	0.169983i	0.866290	−	0.499541i	$-0.166498\pi$
$839$	3.57724	+	4.92365i	0.123500	+	0.169983i	−0.742790	+	0.669524i	$0.766498\pi$
$840$	8.76936	−	5.72427i	0.302572	−	0.197506i
$841$	8.96135	+	27.5802i	0.309012	+	0.951041i
$842$	−24.8378	+	8.07030i	−0.855968	+	0.278121i
$843$	7.47220	+	5.42887i	0.257356	+	0.186980i
$844$	−9.92176	−	13.6561i	−0.341521	−	0.470063i
$845$	−40.2384	−	13.0743i	−1.38424	−	0.449768i
$846$	0.614684			0.0211333
$847$	−17.1610	−	23.5053i	−0.589658	−	0.807653i
$848$	6.76952			0.232466
$849$	−6.47087	−	2.10251i	−0.222080	−	0.0721581i
$850$	38.9076	+	53.5517i	1.33452	+	1.83681i
$851$	5.91914	+	4.30051i	0.202905	+	0.147419i
$852$	6.43795	−	2.09182i	0.220561	−	0.0716645i
$853$	5.20735	+	16.0266i	0.178296	+	0.548739i	0.999769	−	0.0215089i	$-0.00684703\pi$
$853$	5.20735	+	16.0266i	0.178296	+	0.548739i	−0.821472	+	0.570248i	$0.806847\pi$
$854$	25.2392	−	16.4750i	0.863666	−	0.563765i
$855$	−15.2476	−	20.9866i	−0.521458	−	0.717726i
$856$	−1.32099	+	4.06560i	−0.0451506	+	0.138959i
$857$	−19.6343			−0.670696			−0.335348	−	0.942094i	$-0.608854\pi$
$857$	−19.6343			−0.670696			−0.335348	+	0.942094i	$0.608854\pi$
$858$	−5.04007	+	0.131890i	−0.172065	+	0.00450265i
$859$		−	11.6939i		−	0.398991i	−0.979899	−	0.199495i	$-0.936070\pi$
$859$		−	11.6939i		−	0.398991i	0.979899	−	0.199495i	$-0.0639303\pi$
$860$	−9.92381	+	30.5424i	−0.338399	+	1.04149i
$861$	5.18211	+	19.1595i	0.176606	+	0.652953i
$862$	0.361943	+	0.262967i	0.0123278	+	0.00895668i
$863$	2.96295	+	9.11903i	0.100860	+	0.310415i	0.988737	−	0.149667i	$-0.0478200\pi$
$863$	2.96295	+	9.11903i	0.100860	+	0.310415i	−0.887876	+	0.460082i	$0.847820\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−30.0427	+	41.3502i	−1.02148	+	1.40595i
$866$	1.50581	−	1.09403i	0.0511693	−	0.0371767i
$867$	−20.4551	−	6.64626i	−0.694691	−	0.225719i
$868$	5.49576	−	14.4182i	0.186538	−	0.489387i
$869$	−39.4425	−	11.6841i	−1.33799	−	0.396357i
$870$	−0.0853585			−0.00289393
$871$	−6.78586	+	20.8847i	−0.229930	+	0.707652i
$872$	8.74665	−	6.35481i	0.296199	−	0.215201i
$873$	−0.444864	+	0.612302i	−0.0150563	+	0.0207233i
$874$	7.17424	−	2.33105i	0.242672	−	0.0788490i
$875$	59.2721	+	2.96651i	2.00376	+	0.100286i
$876$	−8.93169	+	12.2934i	−0.301774	+	0.415356i
$877$	−3.05749	−	4.20827i	−0.103244	−	0.142103i	0.754269	−	0.656566i	$-0.227991\pi$
$877$	−3.05749	−	4.20827i	−0.103244	−	0.142103i	−0.857513	+	0.514462i	$0.827991\pi$
$878$	−10.7882	−	3.50530i	−0.364084	−	0.118298i
$879$			2.54563i			0.0858621i
$880$	−7.99146	−	10.4151i	−0.269392	−	0.351091i
$881$			27.9500i			0.941660i	0.882224	+	0.470830i	$0.156046\pi$
$881$			27.9500i			0.941660i	−0.882224	+	0.470830i	$0.843954\pi$
$882$	3.52848	+	6.04564i	0.118810	+	0.203567i
$883$	−8.80881	+	6.39997i	−0.296440	+	0.215376i	−0.726056	−	0.687635i	$-0.758649\pi$
$883$	−8.80881	+	6.39997i	−0.296440	+	0.215376i	0.429616	+	0.903012i	$0.358649\pi$
$884$	−7.63168	−	5.54474i	−0.256681	−	0.186490i
$885$	−23.2657	+	7.55948i	−0.782068	+	0.254109i
$886$	14.8492	−	4.82481i	0.498870	−	0.162093i
$887$	18.1292	+	13.1716i	0.608717	+	0.442259i	0.848962	−	0.528453i	$-0.177228\pi$
$887$	18.1292	+	13.1716i	0.608717	+	0.442259i	−0.240245	+	0.970712i	$0.577228\pi$
$888$	−5.14257	+	3.73630i	−0.172573	+	0.125382i
$889$	−10.4876	−	8.45196i	−0.351744	−	0.283469i
$890$		−	0.348094i		−	0.0116682i
$891$	−2.73328	−	1.87861i	−0.0915685	−	0.0629356i
$892$		−	13.3014i		−	0.445362i
$893$	3.83133	+	1.24487i	0.128210	+	0.0416581i
$894$	5.23088	+	7.19969i	0.174947	+	0.240794i
$895$	−46.0236	+	63.3461i	−1.53840	+	2.11743i
$896$	−2.64244	−	0.132252i	−0.0882779	−	0.00441822i
$897$	−1.66408	+	0.540691i	−0.0555619	+	0.0180532i
$898$	22.0501	−	30.3493i	0.735821	−	1.01277i
$899$	−0.101750	+	0.0739254i	−0.00339354	+	0.00246555i
$900$	−3.29628	+	10.1449i	−0.109876	+	0.338163i
$901$	−42.0080			−1.39949
$902$	23.4537	−	8.30493i	0.780923	−	0.276524i
$903$	−20.0583	−	7.64558i	−0.667500	−	0.254429i
$904$	−11.1879	−	3.63515i	−0.372102	−	0.120903i
$905$	4.97185	−	3.61226i	0.165270	−	0.120076i
$906$	10.3153	−	14.1978i	0.342702	−	0.471689i
$907$	−4.11050	−	12.6508i	−0.136487	−	0.420063i	0.859332	−	0.511419i	$-0.170880\pi$
$907$	−4.11050	−	12.6508i	−0.136487	−	0.420063i	−0.995818	+	0.0913557i	$0.970880\pi$
$908$	−2.02848	−	6.24301i	−0.0673173	−	0.207181i
$909$	4.13449	+	3.00389i	0.137133	+	0.0996326i
$910$	−15.3674	+	4.15644i	−0.509423	+	0.137785i
$911$	0.324703	−	0.999334i	0.0107579	−	0.0331094i	−0.945533	−	0.325525i	$-0.894459\pi$
$911$	0.324703	−	0.999334i	0.0107579	−	0.0331094i	0.956291	+	0.292415i	$0.0944590\pi$
$912$			6.55377i			0.217017i
$913$	5.92104	+	16.7214i	0.195958	+	0.553399i
$914$	23.1981			0.767326
$915$	−13.9340	+	42.8843i	−0.460643	+	1.41771i
$916$	−0.689321	−	0.948769i	−0.0227758	−	0.0313482i
$917$	−19.3781	−	29.6866i	−0.639923	−	0.980338i
$918$	−1.91759	−	5.90174i	−0.0632900	−	0.194787i
$919$	51.0212	−	16.5778i	1.68303	−	0.546851i	0.697538	−	0.716548i	$-0.254279\pi$
$919$	51.0212	−	16.5778i	1.68303	−	0.546851i	0.985496	+	0.169697i	$0.0542790\pi$
$920$	−3.68577	−	2.67787i	−0.121516	−	0.0882868i
$921$	−1.27887	−	1.76021i	−0.0421401	−	0.0580009i
$922$	−25.4061	−	8.25495i	−0.836706	−	0.271862i
$923$	−10.2904			−0.338711
$924$	7.22005	−	4.98707i	0.237522	−	0.164062i
$925$	−67.8054			−2.22943
$926$	−19.4190	−	6.30961i	−0.638147	−	0.207347i
$927$	−5.25834	−	7.23749i	−0.172707	−	0.237710i
$928$	0.0174466	+	0.0126757i	0.000572714	+	0.000416101i
$929$	−48.3620	+	15.7138i	−1.58670	+	0.515552i	−0.963773	−	0.266724i	$-0.914059\pi$
$929$	−48.3620	+	15.7138i	−1.58670	+	0.515552i	−0.622932	+	0.782276i	$0.714059\pi$
$930$	7.13339	+	21.9543i	0.233913	+	0.719911i
$931$	9.74927	+	44.8285i	0.319519	+	1.46919i
$932$	6.96438	+	9.58565i	0.228126	+	0.313988i
$933$	0.0559847	−	0.172303i	0.00183286	−	0.00564096i
$934$	28.9828			0.948345
$935$	49.5907	+	64.6302i	1.62179	+	2.11363i
$936$		−	1.52016i		−	0.0496879i
$937$	5.72837	−	17.6301i	0.187138	−	0.575951i	−0.812841	−	0.582486i	$-0.802080\pi$
$937$	5.72837	−	17.6301i	0.187138	−	0.575951i	0.999979	+	0.00653484i	$0.00208012\pi$
$938$	−9.97871	−	36.8937i	−0.325816	−	1.20462i
$939$	2.12294	+	1.54241i	0.0692797	+	0.0503346i
$940$	−0.751842	−	2.31393i	−0.0245224	−	0.0754722i
$941$	11.7967	+	36.3065i	0.384562	+	1.18356i	0.936798	+	0.349872i	$0.113775\pi$
$941$	11.7967	+	36.3065i	0.384562	+	1.18356i	−0.552236	+	0.833688i	$0.686225\pi$
$942$	6.63574	−	9.13331i	0.216204	−	0.297579i
$943$	6.98557	−	5.07531i	0.227481	−	0.165275i
$944$	5.87791	+	1.90985i	0.191310	+	0.0621603i
$945$	−9.78553	−	3.72992i	−0.318323	−	0.121334i
$946$	−7.64306	+	25.8009i	−0.248497	+	0.838859i
$947$	5.16697			0.167904			0.0839520	−	0.996470i	$-0.473246\pi$
$947$	5.16697			0.167904			0.0839520	+	0.996470i	$0.473246\pi$
$948$	3.83279	−	11.7961i	0.124483	−	0.383120i
$949$	18.6879	−	13.5776i	0.606636	−	0.440747i
$950$	−41.0915	+	56.5575i	−1.33318	+	1.83497i
$951$	0.611975	−	0.198843i	0.0198446	−	0.00644792i
$952$	16.3976	+	0.820683i	0.531449	+	0.0265985i
$953$	−4.89129	+	6.73229i	−0.158445	+	0.218080i	−0.880857	−	0.473382i	$-0.843033\pi$
$953$	−4.89129	+	6.73229i	−0.158445	+	0.218080i	0.722413	+	0.691462i	$0.243033\pi$
$954$	−3.97902	−	5.47666i	−0.128826	−	0.177313i
$955$	26.2859	+	8.54081i	0.850592	+	0.276374i
$956$			0.567728i			0.0183616i
$957$	−0.0714993	+	0.00187101i	−0.00231125	+	6.04813e-5i
$958$			2.28737i			0.0739015i
$959$	−21.1713	+	26.2704i	−0.683655	+	0.848317i
$960$	3.20221	−	2.32654i	0.103351	−	0.0750889i
$961$	2.43738	+	1.77086i	0.0786251	+	0.0571245i
$962$	9.19005	−	2.98603i	0.296299	−	0.0962734i
$963$	4.06560	−	1.32099i	0.131012	−	0.0425684i
$964$	−12.6382	−	9.18222i	−0.407051	−	0.295740i
$965$	−33.3847	+	24.2554i	−1.07469	+	0.780810i
$966$	1.91088	−	2.37113i	0.0614817	−	0.0762898i
$967$			52.8888i			1.70079i	0.526145	+	0.850395i	$0.323637\pi$
$967$			52.8888i			1.70079i	−0.526145	+	0.850395i	$0.676363\pi$
$968$	−6.92222	−	8.54885i	−0.222489	−	0.274770i
$969$		−	40.6692i		−	1.30648i
$970$	2.84910	+	0.925727i	0.0914790	+	0.0297233i
$971$	8.99798	+	12.3847i	0.288759	+	0.397442i	0.928611	−	0.371056i	$-0.121004\pi$
$971$	8.99798	+	12.3847i	0.288759	+	0.397442i	−0.639852	+	0.768498i	$0.721004\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	−1.20089	+	23.9942i	−0.0384987	+	0.769220i
$974$	−17.9396	+	5.82892i	−0.574821	+	0.186771i
$975$	9.53123	−	13.1186i	0.305244	−	0.420132i
$976$	9.21632	−	6.69605i	0.295007	−	0.214335i
$977$	−14.5235	+	44.6987i	−0.464648	+	1.43004i	0.394777	+	0.918777i	$0.370822\pi$
$977$	−14.5235	+	44.6987i	−0.464648	+	1.43004i	−0.859425	+	0.511262i	$0.829178\pi$
$978$	20.0662			0.641645
$979$	−0.00763005	−	0.291576i	−0.000243857	−	0.00931881i
$980$	18.4426	−	20.6774i	0.589126	−	0.660515i
$981$	−10.2823	−	3.34092i	−0.328289	−	0.106667i
$982$	−32.1691	+	23.3722i	−1.02656	+	0.745838i
$983$	13.8549	−	19.0697i	0.441903	−	0.608228i	−0.528730	−	0.848790i	$-0.677332\pi$
$983$	13.8549	−	19.0697i	0.441903	−	0.608228i	0.970634	+	0.240562i	$0.0773317\pi$
$984$	2.31819	+	7.13464i	0.0739011	+	0.227444i
$985$	8.50365	+	26.1715i	0.270949	+	0.833895i
$986$	−0.108264	−	0.0786587i	−0.00344784	−	0.00250500i
$987$	1.56989	−	0.424612i	0.0499702	−	0.0135155i
$988$	3.07866	−	9.47515i	0.0979453	−	0.301445i
$989$			9.33860i			0.296950i
$990$	−3.72869	+	12.5870i	−0.118506	+	0.400043i
$991$	47.3182			1.50311			0.751556	−	0.659669i	$-0.229304\pi$
$991$	47.3182			1.50311			0.751556	+	0.659669i	$0.229304\pi$
$992$	1.80220	−	5.54661i	0.0572200	−	0.176105i
$993$	−1.75210	−	2.41156i	−0.0556011	−	0.0765284i
$994$	14.9974	−	9.78968i	0.475689	−	0.310510i
$995$	2.46128	+	7.57503i	0.0780278	+	0.240145i
$996$	−5.08668	+	1.65276i	−0.161178	+	0.0523698i
$997$	27.2915	+	19.8284i	0.864330	+	0.627972i	0.929059	−	0.369930i	$-0.120618\pi$
$997$	27.2915	+	19.8284i	0.864330	+	0.627972i	−0.0647296	+	0.997903i	$0.520618\pi$
$998$	−13.9970	−	19.2652i	−0.443067	−	0.609829i
$999$	6.04546	+	1.96429i	0.191270	+	0.0621473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.13.1	✓	32
7.6	odd	2		462.2.u.b.13.4	yes	32
11.6	odd	10		462.2.u.b.391.4	yes	32
77.6	even	10	inner	462.2.u.a.391.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.13.1	✓	32	1.1	even	1	trivial
462.2.u.a.391.1	yes	32	77.6	even	10	inner
462.2.u.b.13.4	yes	32	7.6	odd	2
462.2.u.b.391.4	yes	32	11.6	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-3.76443 + 1.22314i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.44620 - 2.21552i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-3.76443 + 1.22314i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.44620 - 2.21552i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.95815 q^{10} +(3.31549 - 0.0867606i) q^{11} +1.00000i q^{12} +(0.469755 - 1.44576i) q^{13} +(0.690781 + 2.55398i) q^{14} +(-3.20221 - 2.32654i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.91759 - 5.90174i) q^{17} +(0.587785 - 0.809017i) q^{18} +(5.30211 - 3.85221i) q^{19} +(-3.76443 - 1.22314i) q^{20} +(0.942339 - 2.47225i) q^{21} +(-3.18003 - 0.942028i) q^{22} -1.15101 q^{23} +(0.309017 - 0.951057i) q^{24} +(8.62977 - 6.26990i) q^{25} +(-0.893526 + 1.22983i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.132252 - 2.64244i) q^{28} +(-0.0126757 + 0.0174466i) q^{29} +(2.32654 + 3.20221i) q^{30} +(5.54661 + 1.80220i) q^{31} -1.00000i q^{32} +(2.01899 + 2.63129i) q^{33} +6.20546i q^{34} +(8.15398 + 6.57126i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-5.14257 - 3.73630i) q^{37} +(-6.23301 + 2.02523i) q^{38} +(1.44576 - 0.469755i) q^{39} +(3.20221 + 2.32654i) q^{40} +(-6.06909 + 4.40945i) q^{41} +(-1.66018 + 2.06005i) q^{42} -8.11341i q^{43} +(2.73328 + 1.87861i) q^{44} -3.95815i q^{45} +(1.09467 + 0.355681i) q^{46} +(0.361302 + 0.497290i) q^{47} +(-0.587785 + 0.809017i) q^{48} +(-2.81704 + 6.40814i) q^{49} +(-10.1449 + 3.29628i) q^{50} +(3.64748 - 5.02032i) q^{51} +(1.22983 - 0.893526i) q^{52} +(2.09190 - 6.43819i) q^{53} +1.00000 q^{54} +(-12.3748 + 4.38190i) q^{55} +(-0.942339 + 2.47225i) q^{56} +(6.23301 + 2.02523i) q^{57} +(0.0174466 - 0.0126757i) q^{58} +(3.63275 - 5.00005i) q^{59} +(-1.22314 - 3.76443i) q^{60} +(-3.52032 - 10.8344i) q^{61} +(-4.71822 - 3.42799i) q^{62} +(2.55398 - 0.690781i) q^{63} +(-0.309017 + 0.951057i) q^{64} +6.01702i q^{65} +(-1.10706 - 3.12641i) q^{66} -14.4455 q^{67} +(1.91759 - 5.90174i) q^{68} +(-0.676545 - 0.931185i) q^{69} +(-5.72427 - 8.76936i) q^{70} +(-2.09182 - 6.43795i) q^{71} +(0.951057 - 0.309017i) q^{72} +(12.2934 + 8.93169i) q^{73} +(3.73630 + 5.14257i) q^{74} +(10.1449 + 3.29628i) q^{75} +6.55377 q^{76} +(-4.98707 - 7.22005i) q^{77} -1.52016 q^{78} +(-11.7961 - 3.83279i) q^{79} +(-2.32654 - 3.20221i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(7.13464 - 2.31819i) q^{82} +(1.65276 + 5.08668i) q^{83} +(2.21552 - 1.44620i) q^{84} +(14.4373 + 19.8712i) q^{85} +(-2.50718 + 7.71631i) q^{86} -0.0215652 q^{87} +(-2.01899 - 2.63129i) q^{88} -0.0879436i q^{89} +(-1.22314 + 3.76443i) q^{90} +(-3.88246 + 1.05010i) q^{91} +(-0.931185 - 0.676545i) q^{92} +(1.80220 + 5.54661i) q^{93} +(-0.189948 - 0.584599i) q^{94} +(-15.2476 + 20.9866i) q^{95} +(0.809017 - 0.587785i) q^{96} +(0.719804 + 0.233879i) q^{97} +(4.65939 - 5.22399i) q^{98} +(-0.942028 + 3.18003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

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