LMFDB - Embedded newform 224.2.u.c.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33683 + 0.461403i) q^{2} +(-0.825255 - 0.341832i) q^{3} +(1.57421 - 1.23363i) q^{4} +(-0.175588 - 0.423906i) q^{5} +(1.26095 + 0.0761946i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.53525 + 2.37550i) q^{8} +(-1.55712 - 1.55712i) q^{9} +O(q^{10})$	\(q+(-1.33683 + 0.461403i) q^{2} +(-0.825255 - 0.341832i) q^{3} +(1.57421 - 1.23363i) q^{4} +(-0.175588 - 0.423906i) q^{5} +(1.26095 + 0.0761946i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.53525 + 2.37550i) q^{8} +(-1.55712 - 1.55712i) q^{9} +(0.430322 + 0.485673i) q^{10} +(-2.61442 + 1.08293i) q^{11} +(-1.72082 + 0.479946i) q^{12} +(0.791155 - 1.91002i) q^{13} +(-0.619018 + 1.27154i) q^{14} +0.409853i q^{15} +(0.956298 - 3.88400i) q^{16} -6.96580i q^{17} +(2.80007 + 1.36314i) q^{18} +(0.0847256 - 0.204546i) q^{19} +(-0.799358 - 0.450708i) q^{20} +(-0.825255 + 0.341832i) q^{21} +(2.99537 - 2.65399i) q^{22} +(-5.30048 - 5.30048i) q^{23} +(2.07900 - 1.43560i) q^{24} +(3.38667 - 3.38667i) q^{25} +(-0.176349 + 2.91841i) q^{26} +(1.77825 + 4.29306i) q^{27} +(0.240827 - 1.98545i) q^{28} +(1.39222 + 0.576675i) q^{29} +(-0.189107 - 0.547902i) q^{30} -2.39066 q^{31} +(0.513688 + 5.63348i) q^{32} +2.52775 q^{33} +(3.21404 + 9.31206i) q^{34} +(-0.423906 - 0.175588i) q^{35} +(-4.37216 - 0.530326i) q^{36} +(-2.44954 - 5.91372i) q^{37} +(-0.0188854 + 0.312535i) q^{38} +(-1.30581 + 1.30581i) q^{39} +(1.27656 + 0.233693i) q^{40} +(6.77966 + 6.77966i) q^{41} +(0.945501 - 0.837746i) q^{42} +(-3.54722 + 1.46931i) q^{43} +(-2.77972 + 4.93000i) q^{44} +(-0.386663 + 0.933486i) q^{45} +(9.53148 + 4.64017i) q^{46} -0.928875i q^{47} +(-2.11687 + 2.87840i) q^{48} -1.00000i q^{49} +(-2.96477 + 6.09001i) q^{50} +(-2.38113 + 5.74856i) q^{51} +(-1.11081 - 3.98277i) q^{52} +(-9.57390 + 3.96564i) q^{53} +(-4.35804 - 4.91860i) q^{54} +(0.918122 + 0.918122i) q^{55} +(0.594149 + 2.76532i) q^{56} +(-0.139840 + 0.139840i) q^{57} +(-2.12723 - 0.128541i) q^{58} +(5.17517 + 12.4940i) q^{59} +(0.505608 + 0.645196i) q^{60} +(7.42002 + 3.07347i) q^{61} +(3.19591 - 1.10306i) q^{62} -2.20210 q^{63} +(-3.28602 - 7.29398i) q^{64} -0.948586 q^{65} +(-3.37916 + 1.16631i) q^{66} +(5.00235 + 2.07204i) q^{67} +(-8.59324 - 10.9657i) q^{68} +(2.56238 + 6.18612i) q^{69} +(0.647706 + 0.0391387i) q^{70} +(4.33452 - 4.33452i) q^{71} +(6.08952 - 1.30838i) q^{72} +(0.169663 + 0.169663i) q^{73} +(6.00323 + 6.77540i) q^{74} +(-3.95254 + 1.63719i) q^{75} +(-0.118958 - 0.426519i) q^{76} +(-1.08293 + 2.61442i) q^{77} +(1.14314 - 2.34815i) q^{78} +0.467101i q^{79} +(-1.81437 + 0.276603i) q^{80} +2.45558i q^{81} +(-12.1914 - 5.93508i) q^{82} +(4.32473 - 10.4408i) q^{83} +(-0.877433 + 1.55618i) q^{84} +(-2.95285 + 1.22311i) q^{85} +(4.06408 - 3.60091i) q^{86} +(-0.951808 - 0.951808i) q^{87} +(1.44129 - 7.87314i) q^{88} +(2.43384 - 2.43384i) q^{89} +(0.0861874 - 1.42632i) q^{90} +(-0.791155 - 1.91002i) q^{91} +(-14.8829 - 1.80524i) q^{92} +(1.97291 + 0.817206i) q^{93} +(0.428586 + 1.24174i) q^{94} -0.101585 q^{95} +(1.50178 - 4.82466i) q^{96} +15.1794 q^{97} +(0.461403 + 1.33683i) q^{98} +(5.75724 + 2.38473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−1.33683	+	0.461403i	−0.945280	+	0.326261i
$2$	−1.33683	+	0.461403i	−0.945280	+	0.326261i
$3$	−0.825255	−	0.341832i	−0.476461	−	0.197357i	0.131511	−	0.991315i	$-0.458017\pi$
$3$	−0.825255	−	0.341832i	−0.476461	−	0.197357i	−0.607973	+	0.793958i	$0.708017\pi$
$4$	1.57421	−	1.23363i	0.787107	−	0.616817i
$5$	−0.175588	−	0.423906i	−0.0785252	−	0.189577i	0.879741	−	0.475452i	$-0.157716\pi$
$5$	−0.175588	−	0.423906i	−0.0785252	−	0.189577i	−0.958267	+	0.285876i	$0.907716\pi$
$6$	1.26095	+	0.0761946i	0.514779	+	0.0311063i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−1.53525	+	2.37550i	−0.542793	+	0.839867i
$9$	−1.55712	−	1.55712i	−0.519041	−	0.519041i
$10$	0.430322	+	0.485673i	0.136080	+	0.153583i
$11$	−2.61442	+	1.08293i	−0.788279	+	0.326516i	−0.740251	−	0.672330i	$-0.765293\pi$
$11$	−2.61442	+	1.08293i	−0.788279	+	0.326516i	−0.0480273	+	0.998846i	$0.515293\pi$
$12$	−1.72082	+	0.479946i	−0.496759	+	0.138548i
$13$	0.791155	−	1.91002i	0.219427	−	0.529744i	−0.775383	−	0.631491i	$-0.782443\pi$
$13$	0.791155	−	1.91002i	0.219427	−	0.529744i	0.994810	+	0.101747i	$0.0324433\pi$
$14$	−0.619018	+	1.27154i	−0.165440	+	0.339834i
$15$			0.409853i			0.105823i
$16$	0.956298	−	3.88400i	0.239075	−	0.971001i
$17$		−	6.96580i		−	1.68945i	−0.535198	−	0.844727i	$-0.679763\pi$
$17$		−	6.96580i		−	1.68945i	0.535198	−	0.844727i	$-0.320237\pi$
$18$	2.80007	+	1.36314i	0.659982	+	0.321296i
$19$	0.0847256	−	0.204546i	0.0194374	−	0.0469260i	−0.913863	−	0.406023i	$-0.866915\pi$
$19$	0.0847256	−	0.204546i	0.0194374	−	0.0469260i	0.933300	+	0.359097i	$0.116915\pi$
$20$	−0.799358	−	0.450708i	−0.178742	−	0.100781i
$21$	−0.825255	+	0.341832i	−0.180085	+	0.0745938i
$22$	2.99537	−	2.65399i	0.638614	−	0.565834i
$23$	−5.30048	−	5.30048i	−1.10523	−	1.10523i	−0.993769	−	0.111457i	$-0.964448\pi$
$23$	−5.30048	−	5.30048i	−1.10523	−	1.10523i	−0.111457	−	0.993769i	$-0.535552\pi$
$24$	2.07900	−	1.43560i	0.424373	−	0.293040i
$25$	3.38667	−	3.38667i	0.677334	−	0.677334i
$26$	−0.176349	+	2.91841i	−0.0345849	+	0.572346i
$27$	1.77825	+	4.29306i	0.342224	+	0.826201i
$28$	0.240827	−	1.98545i	0.0455120	−	0.375214i
$29$	1.39222	+	0.576675i	0.258528	+	0.107086i	0.508183	−	0.861249i	$-0.330317\pi$
$29$	1.39222	+	0.576675i	0.258528	+	0.107086i	−0.249655	+	0.968335i	$0.580317\pi$
$30$	−0.189107	−	0.547902i	−0.0345261	−	0.100033i
$31$	−2.39066			−0.429376			−0.214688	−	0.976683i	$-0.568873\pi$
$31$	−2.39066			−0.429376			−0.214688	+	0.976683i	$0.568873\pi$
$32$	0.513688	+	5.63348i	0.0908080	+	0.995868i
$33$	2.52775			0.440024
$34$	3.21404	+	9.31206i	0.551204	+	1.59701i
$35$	−0.423906	−	0.175588i	−0.0716533	−	0.0296798i
$36$	−4.37216	−	0.530326i	−0.728694	−	0.0883876i
$37$	−2.44954	−	5.91372i	−0.402703	−	0.972210i	−0.987007	−	0.160676i	$-0.948633\pi$
$37$	−2.44954	−	5.91372i	−0.402703	−	0.972210i	0.584305	−	0.811534i	$-0.301367\pi$
$38$	−0.0188854	+	0.312535i	−0.00306362	+	0.0506998i
$39$	−1.30581	+	1.30581i	−0.209097	+	0.209097i
$40$	1.27656	+	0.233693i	0.201842	+	0.0369501i
$41$	6.77966	+	6.77966i	1.05881	+	1.05881i	0.998159	+	0.0606459i	$0.0193160\pi$
$41$	6.77966	+	6.77966i	1.05881	+	1.05881i	0.0606459	+	0.998159i	$0.480684\pi$
$42$	0.945501	−	0.837746i	0.145894	−	0.129267i
$43$	−3.54722	+	1.46931i	−0.540946	+	0.224067i	−0.636390	−	0.771368i	$-0.719573\pi$
$43$	−3.54722	+	1.46931i	−0.540946	+	0.224067i	0.0954436	+	0.995435i	$0.469573\pi$
$44$	−2.77972	+	4.93000i	−0.419059	+	0.743226i
$45$	−0.386663	+	0.933486i	−0.0576403	+	0.139156i
$46$	9.53148	+	4.64017i	1.40534	+	0.684155i
$47$		−	0.928875i		−	0.135490i	−0.997703	−	0.0677451i	$-0.978420\pi$
$47$		−	0.928875i		−	0.135490i	0.997703	−	0.0677451i	$-0.0215805\pi$
$48$	−2.11687	+	2.87840i	−0.305543	+	0.415462i
$49$		−	1.00000i		−	0.142857i
$50$	−2.96477	+	6.09001i	−0.419282	+	0.861258i
$51$	−2.38113	+	5.74856i	−0.333425	+	0.804959i
$52$	−1.11081	−	3.98277i	−0.154042	−	0.552311i
$53$	−9.57390	+	3.96564i	−1.31508	+	0.544722i	−0.926361	−	0.376636i	$-0.877081\pi$
$53$	−9.57390	+	3.96564i	−1.31508	+	0.544722i	−0.388715	+	0.921358i	$0.627081\pi$
$54$	−4.35804	−	4.91860i	−0.593054	−	0.669336i
$55$	0.918122	+	0.918122i	0.123800	+	0.123800i
$56$	0.594149	+	2.76532i	0.0793964	+	0.369531i
$57$	−0.139840	+	0.139840i	−0.0185223	+	0.0185223i
$58$	−2.12723	−	0.128541i	−0.279319	−	0.0168783i
$59$	5.17517	+	12.4940i	0.673750	+	1.62658i	0.775185	+	0.631735i	$0.217657\pi$
$59$	5.17517	+	12.4940i	0.673750	+	1.62658i	−0.101435	+	0.994842i	$0.532343\pi$
$60$	0.505608	+	0.645196i	0.0652737	+	0.0832944i
$61$	7.42002	+	3.07347i	0.950036	+	0.393518i	0.803244	−	0.595650i	$-0.203105\pi$
$61$	7.42002	+	3.07347i	0.950036	+	0.393518i	0.146791	+	0.989167i	$0.453105\pi$
$62$	3.19591	−	1.10306i	0.405880	−	0.140089i
$63$	−2.20210			−0.277439
$64$	−3.28602	−	7.29398i	−0.410752	−	0.911747i
$65$	−0.948586			−0.117658
$66$	−3.37916	+	1.16631i	−0.415946	+	0.143563i
$67$	5.00235	+	2.07204i	0.611134	+	0.253140i	0.666713	−	0.745314i	$-0.267701\pi$
$67$	5.00235	+	2.07204i	0.611134	+	0.253140i	−0.0555791	+	0.998454i	$0.517701\pi$
$68$	−8.59324	−	10.9657i	−1.04208	−	1.32978i
$69$	2.56238	+	6.18612i	0.308474	+	0.744722i
$70$	0.647706	+	0.0391387i	0.0774157	+	0.00467796i
$71$	4.33452	−	4.33452i	0.514412	−	0.514412i	−0.401463	−	0.915875i	$-0.631498\pi$
$71$	4.33452	−	4.33452i	0.514412	−	0.514412i	0.915875	+	0.401463i	$0.131498\pi$
$72$	6.08952	−	1.30838i	0.717657	−	0.154194i
$73$	0.169663	+	0.169663i	0.0198576	+	0.0198576i	0.716966	−	0.697108i	$-0.245530\pi$
$73$	0.169663	+	0.169663i	0.0198576	+	0.0198576i	−0.697108	+	0.716966i	$0.745530\pi$
$74$	6.00323	+	6.77540i	0.697861	+	0.787624i
$75$	−3.95254	+	1.63719i	−0.456400	+	0.189047i
$76$	−0.118958	−	0.426519i	−0.0136454	−	0.0489251i
$77$	−1.08293	+	2.61442i	−0.123411	+	0.297941i
$78$	1.14314	−	2.34815i	0.129435	−	0.265875i
$79$			0.467101i			0.0525530i	0.999655	+	0.0262765i	$0.00836503\pi$
$79$			0.467101i			0.0525530i	−0.999655	+	0.0262765i	$0.991635\pi$
$80$	−1.81437	+	0.276603i	−0.202853	+	0.0309251i
$81$			2.45558i			0.272842i
$82$	−12.1914	−	5.93508i	−1.34631	−	0.655420i
$83$	4.32473	−	10.4408i	0.474701	−	1.14603i	−0.487362	−	0.873200i	$-0.662041\pi$
$83$	4.32473	−	10.4408i	0.474701	−	1.14603i	0.962063	−	0.272829i	$-0.0879592\pi$
$84$	−0.877433	+	1.55618i	−0.0957358	+	0.169793i
$85$	−2.95285	+	1.22311i	−0.320281	+	0.132665i
$86$	4.06408	−	3.60091i	0.438241	−	0.388296i
$87$	−0.951808	−	0.951808i	−0.102045	−	0.102045i
$88$	1.44129	−	7.87314i	0.153642	−	0.839279i
$89$	2.43384	−	2.43384i	0.257987	−	0.257987i	−0.566248	−	0.824235i	$-0.691606\pi$
$89$	2.43384	−	2.43384i	0.257987	−	0.257987i	0.824235	+	0.566248i	$0.191606\pi$
$90$	0.0861874	−	1.42632i	0.00908495	−	0.150347i
$91$	−0.791155	−	1.91002i	−0.0829356	−	0.200224i
$92$	−14.8829	−	1.80524i	−1.55165	−	0.188209i
$93$	1.97291	+	0.817206i	0.204581	+	0.0847403i
$94$	0.428586	+	1.24174i	0.0442053	+	0.128076i
$95$	−0.101585			−0.0104224
$96$	1.50178	−	4.82466i	0.153275	−	0.492414i
$97$	15.1794			1.54123			0.770615	−	0.637301i	$-0.219949\pi$
$97$	15.1794			1.54123			0.770615	+	0.637301i	$0.219949\pi$
$98$	0.461403	+	1.33683i	0.0466088	+	0.135040i
$99$	5.75724	+	2.38473i	0.578624	+	0.239674i
$100$	1.15343	−	9.50925i	0.115343	−	0.950925i
$101$	−6.10556	−	14.7401i	−0.607526	−	1.46670i	−0.865683	−	0.500593i	$-0.833115\pi$
$101$	−6.10556	−	14.7401i	−0.607526	−	1.46670i	0.258157	−	0.966103i	$-0.416885\pi$
$102$	0.530756	−	8.78349i	0.0525527	−	0.869695i
$103$	1.18807	−	1.18807i	0.117064	−	0.117064i	−0.646148	−	0.763212i	$-0.723621\pi$
$103$	1.18807	−	1.18807i	0.117064	−	0.117064i	0.763212	+	0.646148i	$0.223621\pi$
$104$	3.32263	+	4.81174i	0.325811	+	0.471830i
$105$	0.289810	+	0.289810i	0.0282825	+	0.0282825i
$106$	10.9689	−	9.71880i	1.06539	−	0.943974i
$107$	−8.84093	+	3.66203i	−0.854685	+	0.354022i	−0.766627	−	0.642093i	$-0.778066\pi$
$107$	−8.84093	+	3.66203i	−0.854685	+	0.354022i	−0.0880583	+	0.996115i	$0.528066\pi$
$108$	8.09541	+	4.56450i	0.778981	+	0.439219i
$109$	−2.11109	+	5.09663i	−0.202206	+	0.488169i	−0.992156	−	0.125002i	$-0.960106\pi$
$109$	−2.11109	+	5.09663i	−0.202206	+	0.488169i	0.789950	+	0.613171i	$0.210106\pi$
$110$	−1.65099	−	0.803746i	−0.157416	−	0.0766342i
$111$			5.71766i			0.542697i
$112$	−2.07020	−	3.42261i	−0.195616	−	0.323406i
$113$		−	4.98624i		−	0.469066i	−0.972108	−	0.234533i	$-0.924644\pi$
$113$		−	4.98624i		−	0.469066i	0.972108	−	0.234533i	$-0.0753561\pi$
$114$	0.122420	−	0.251465i	0.0114656	−	0.0235519i
$115$	−1.31621	+	3.17761i	−0.122737	+	0.296313i
$116$	2.90305	−	0.809675i	0.269542	−	0.0751764i
$117$	−4.20606	+	1.74221i	−0.388850	+	0.161067i
$118$	−12.6831	−	14.3144i	−1.16757	−	1.31775i
$119$	−4.92556	−	4.92556i	−0.451525	−	0.451525i
$120$	−0.973606	−	0.629226i	−0.0888776	−	0.0574402i
$121$	−2.11570	+	2.11570i	−0.192336	+	0.192336i
$122$	−11.3374	−	0.685079i	−1.02644	−	0.0620242i
$123$	−3.27745	−	7.91246i	−0.295517	−	0.713442i
$124$	−3.76342	+	2.94920i	−0.337965	+	0.264846i
$125$	−4.14982	−	1.71891i	−0.371171	−	0.153744i
$126$	2.94383	−	1.01606i	0.262258	−	0.0905177i
$127$	5.10133			0.452670			0.226335	−	0.974050i	$-0.427326\pi$
$127$	5.10133			0.452670			0.226335	+	0.974050i	$0.427326\pi$
$128$	7.75831	+	8.23460i	0.685744	+	0.727843i
$129$	3.42962			0.301961
$130$	1.26810	−	0.437681i	0.111219	−	0.0383871i
$131$	16.0417	+	6.64469i	1.40157	+	0.580549i	0.950159	−	0.311767i	$-0.100921\pi$
$131$	16.0417	+	6.64469i	1.40157	+	0.580549i	0.451411	+	0.892316i	$0.350921\pi$
$132$	3.97922	−	3.11831i	0.346346	−	0.271414i
$133$	−0.0847256	−	0.204546i	−0.00734664	−	0.0177364i
$134$	−7.64332	−	0.461860i	−0.660283	−	0.0398986i
$135$	1.50762	−	1.50762i	0.129755	−	0.129755i
$136$	16.5473	+	10.6942i	1.41892	+	0.917023i
$137$	5.82373	+	5.82373i	0.497555	+	0.497555i	0.910676	−	0.413121i	$-0.135561\pi$
$137$	5.82373	+	5.82373i	0.497555	+	0.497555i	−0.413121	+	0.910676i	$0.635561\pi$
$138$	−6.27975	−	7.08749i	−0.534568	−	0.603327i
$139$	3.86636	−	1.60150i	0.327941	−	0.135838i	−0.212638	−	0.977131i	$-0.568205\pi$
$139$	3.86636	−	1.60150i	0.327941	−	0.135838i	0.540578	+	0.841294i	$0.318205\pi$
$140$	−0.883930	+	0.246532i	−0.0747057	+	0.0208358i
$141$	−0.317519	+	0.766559i	−0.0267399	+	0.0645559i
$142$	−3.79454	+	7.79446i	−0.318431	+	0.654097i
$143$			5.85036i			0.489232i
$144$	−7.53695	+	4.55880i	−0.628079	+	0.379900i
$145$		−	0.691427i		−	0.0574199i
$146$	−0.305094	−	0.148527i	−0.0252497	−	0.0122922i
$147$	−0.341832	+	0.825255i	−0.0281938	+	0.0680659i
$148$	−11.1515	−	6.28762i	−0.916645	−	0.516839i
$149$	−5.10381	+	2.11407i	−0.418121	+	0.173191i	−0.581817	−	0.813319i	$-0.697658\pi$
$149$	−5.10381	+	2.11407i	−0.418121	+	0.173191i	0.163697	+	0.986511i	$0.447658\pi$
$150$	4.52845	−	4.01236i	0.369747	−	0.327608i
$151$	−15.9461	−	15.9461i	−1.29768	−	1.29768i	−0.929924	−	0.367753i	$-0.880127\pi$
$151$	−15.9461	−	15.9461i	−1.29768	−	1.29768i	−0.367753	−	0.929924i	$-0.619873\pi$
$152$	0.355824	+	0.515294i	0.0288611	+	0.0417959i
$153$	−10.8466	+	10.8466i	−0.876896	+	0.876896i
$154$	0.241386	−	3.99470i	0.0194514	−	0.321902i
$155$	0.419772	+	1.01342i	0.0337169	+	0.0813997i
$156$	−0.444734	+	3.66652i	−0.0356072	+	0.293556i
$157$	1.57111	+	0.650774i	0.125388	+	0.0519374i	0.444495	−	0.895781i	$-0.353383\pi$
$157$	1.57111	+	0.650774i	0.125388	+	0.0519374i	−0.319107	+	0.947719i	$0.603383\pi$
$158$	−0.215522	−	0.624433i	−0.0171460	−	0.0496772i
$159$	9.25649			0.734088
$160$	2.29787	−	1.20693i	0.181663	−	0.0954159i
$161$	−7.49601			−0.590768
$162$	−1.13301	−	3.28268i	−0.0890178	−	0.257912i
$163$	−8.79789	−	3.64421i	−0.689104	−	0.285436i	0.0105227	−	0.999945i	$-0.496650\pi$
$163$	−8.79789	−	3.64421i	−0.689104	−	0.285436i	−0.699627	+	0.714508i	$0.746650\pi$
$164$	19.0363	+	2.30902i	1.48648	+	0.180304i
$165$	−0.443842	−	1.07153i	−0.0345530	−	0.0834184i
$166$	−0.963986	+	15.9530i	−0.0748198	+	1.23819i
$167$	5.37212	−	5.37212i	0.415707	−	0.415707i	−0.468014	−	0.883721i	$-0.655030\pi$
$167$	5.37212	−	5.37212i	0.415707	−	0.415707i	0.883721	+	0.468014i	$0.155030\pi$
$168$	0.454950	−	2.48519i	0.0351002	−	0.191737i
$169$	6.17015	+	6.17015i	0.474627	+	0.474627i
$170$	3.38310	−	2.99754i	0.259472	−	0.229901i
$171$	−0.450431	+	0.186575i	−0.0344453	+	0.0142677i
$172$	−3.77150	+	6.68898i	−0.287574	+	0.510030i
$173$	2.54841	−	6.15239i	0.193752	−	0.467758i	−0.796911	−	0.604097i	$-0.793534\pi$
$173$	2.54841	−	6.15239i	0.193752	−	0.467758i	0.990662	+	0.136339i	$0.0435338\pi$
$174$	1.71157	+	0.833236i	0.129754	+	0.0631674i
$175$		−	4.78947i		−	0.362050i
$176$	1.70594	+	11.1900i	0.128590	+	0.843481i
$177$		−	12.0798i		−	0.907970i
$178$	−2.13064	+	4.37661i	−0.159698	+	0.328041i
$179$	7.75977	−	18.7337i	0.579992	−	1.40023i	−0.312827	−	0.949810i	$-0.601276\pi$
$179$	7.75977	−	18.7337i	0.579992	−	1.40023i	0.892819	−	0.450415i	$-0.148724\pi$
$180$	0.542890	+	1.94651i	0.0404646	+	0.145084i
$181$	−17.3566	+	7.18933i	−1.29010	+	0.534379i	−0.919017	−	0.394219i	$-0.871015\pi$
$181$	−17.3566	+	7.18933i	−1.29010	+	0.534379i	−0.371088	+	0.928598i	$0.621015\pi$
$182$	1.93893	+	2.18832i	0.143723	+	0.162209i
$183$	−5.07280	−	5.07280i	−0.374992	−	0.374992i
$184$	20.7289	−	4.45374i	1.52815	−	0.328334i
$185$	−2.07675	+	2.07675i	−0.152686	+	0.152686i
$186$	−3.01450	−	0.182156i	−0.221034	−	0.0133563i
$187$	7.54347	+	18.2115i	0.551633	+	1.33176i
$188$	−1.14589	−	1.46225i	−0.0835727	−	0.106645i
$189$	4.29306	+	1.77825i	0.312274	+	0.129348i
$190$	0.135802	−	0.0468716i	0.00985208	−	0.00340043i
$191$	21.9236			1.58634			0.793168	−	0.609003i	$-0.208430\pi$
$191$	21.9236			1.58634			0.793168	+	0.609003i	$0.208430\pi$
$192$	0.218492	+	7.14266i	0.0157683	+	0.515477i
$193$	−7.91907			−0.570027			−0.285014	−	0.958523i	$-0.591998\pi$
$193$	−7.91907			−0.570027			−0.285014	+	0.958523i	$0.591998\pi$
$194$	−20.2922	+	7.00381i	−1.45689	+	0.502844i
$195$	0.782826	+	0.324257i	0.0560593	+	0.0232205i
$196$	−1.23363	−	1.57421i	−0.0881167	−	0.112444i
$197$	2.67859	+	6.46668i	0.190841	+	0.460732i	0.990119	−	0.140230i	$-0.0447843\pi$
$197$	2.67859	+	6.46668i	0.190841	+	0.460732i	−0.799278	+	0.600962i	$0.794784\pi$
$198$	−8.79675	−	0.531557i	−0.625158	−	0.0377761i
$199$	−15.9803	+	15.9803i	−1.13282	+	1.13282i	−0.143108	+	0.989707i	$0.545710\pi$
$199$	−15.9803	+	15.9803i	−1.13282	+	1.13282i	−0.989707	+	0.143108i	$0.954290\pi$
$200$	2.84566	+	13.2444i	0.201218	+	0.936522i
$201$	−3.41993	−	3.41993i	−0.241223	−	0.241223i
$202$	14.9632	+	16.8879i	1.05281	+	1.18823i
$203$	1.39222	−	0.576675i	0.0977145	−	0.0404747i
$204$	3.34320	+	11.9869i	0.234071	+	0.839251i
$205$	1.68352	−	4.06437i	0.117582	−	0.283868i
$206$	−1.04007	+	2.13643i	−0.0724650	+	0.148852i
$207$			16.5070i			1.14732i
$208$	−6.66194	−	4.89940i	−0.461922	−	0.339712i
$209$			0.626521i			0.0433373i
$210$	−0.521144	−	0.253706i	−0.0359624	−	0.0175074i
$211$	2.37390	−	5.73109i	0.163426	−	0.394545i	−0.820860	−	0.571130i	$-0.806505\pi$
$211$	2.37390	−	5.73109i	0.163426	−	0.394545i	0.984285	+	0.176585i	$0.0565052\pi$
$212$	−10.1792	+	18.0534i	−0.699112	+	1.23992i
$213$	−5.05876	+	2.09541i	−0.346620	+	0.143575i
$214$	10.1291	−	8.97474i	0.692412	−	0.613501i
$215$	1.24570	+	1.24570i	0.0849559	+	0.0849559i
$216$	−12.9282	−	2.36670i	−0.879655	−	0.161033i
$217$	−1.69046	+	1.69046i	−0.114756	+	0.114756i
$218$	0.470564	−	7.78738i	0.0318706	−	0.527428i
$219$	−0.0820191	−	0.198012i	−0.00554234	−	0.0133804i
$220$	2.57795	+	0.312694i	0.173805	+	0.0210819i
$221$	−13.3048	−	5.51103i	−0.894977	−	0.370712i
$222$	−2.63815	−	7.64353i	−0.177061	−	0.513000i
$223$	−10.2125			−0.683880			−0.341940	−	0.939722i	$-0.611084\pi$
$223$	−10.2125			−0.683880			−0.341940	+	0.939722i	$0.611084\pi$
$224$	4.34671	+	3.62024i	0.290426	+	0.241888i
$225$	−10.5469			−0.703128
$226$	2.30067	+	6.66574i	0.153038	+	0.443398i
$227$	10.9190	+	4.52281i	0.724722	+	0.300190i	0.714381	−	0.699757i	$-0.246708\pi$
$227$	10.9190	+	4.52281i	0.724722	+	0.300190i	0.0103408	+	0.999947i	$0.496708\pi$
$228$	−0.0476269	+	0.392651i	−0.00315417	+	0.0260039i
$229$	9.21240	+	22.2407i	0.608772	+	1.46971i	0.864336	+	0.502914i	$0.167739\pi$
$229$	9.21240	+	22.2407i	0.608772	+	1.46971i	−0.255564	+	0.966792i	$0.582261\pi$
$230$	0.293384	−	4.85521i	0.0193452	−	0.320143i
$231$	1.78739	−	1.78739i	0.117601	−	0.117601i
$232$	−3.50729	+	2.42187i	−0.230265	+	0.159004i
$233$	0.630649	+	0.630649i	0.0413152	+	0.0413152i	0.727463	−	0.686147i	$-0.240699\pi$
$233$	0.630649	+	0.630649i	0.0413152	+	0.0413152i	−0.686147	+	0.727463i	$0.740699\pi$
$234$	4.81891	−	4.26972i	0.315022	−	0.279120i
$235$	−0.393756	+	0.163099i	−0.0256858	+	0.0106394i
$236$	23.5598	+	13.2839i	1.53361	+	0.864709i
$237$	0.159670	−	0.385478i	0.0103717	−	0.0250395i
$238$	8.85729	+	4.31195i	0.574133	+	0.279502i
$239$		−	22.2467i		−	1.43902i	−0.694483	−	0.719509i	$-0.744367\pi$
$239$		−	22.2467i		−	1.43902i	0.694483	−	0.719509i	$-0.255633\pi$
$240$	1.59187	+	0.391941i	0.102755	+	0.0252997i
$241$		−	18.8940i		−	1.21707i	−0.793528	−	0.608534i	$-0.791758\pi$
$241$		−	18.8940i		−	1.21707i	0.793528	−	0.608534i	$-0.208242\pi$
$242$	1.85213	−	3.80451i	0.119060	−	0.244563i
$243$	6.17413	−	14.9057i	0.396071	−	0.956199i
$244$	15.4722	−	4.31528i	0.990508	−	0.276257i
$245$	−0.423906	+	0.175588i	−0.0270824	+	0.0112179i
$246$	8.03221	+	9.06536i	0.512115	+	0.577986i
$247$	−0.323655	−	0.323655i	−0.0205936	−	0.0205936i
$248$	3.67027	−	5.67903i	0.233062	−	0.360619i
$249$	−7.13801	+	7.13801i	−0.452353	+	0.452353i
$250$	6.34070	+	0.383147i	0.401021	+	0.0242323i
$251$	−10.6325	−	25.6692i	−0.671119	−	1.62022i	−0.779713	−	0.626137i	$-0.784635\pi$
$251$	−10.6325	−	25.6692i	−0.671119	−	1.62022i	0.108594	−	0.994086i	$-0.465365\pi$
$252$	−3.46658	+	2.71659i	−0.218374	+	0.171129i
$253$	19.5978	+	8.11765i	1.23210	+	0.510353i
$254$	−6.81959	+	2.35377i	−0.427899	+	0.147689i
$255$	2.85495			0.178784
$256$	−14.1710	−	7.42853i	−0.885687	−	0.464283i
$257$	20.3363			1.26855			0.634273	−	0.773109i	$-0.281300\pi$
$257$	20.3363			1.26855			0.634273	+	0.773109i	$0.281300\pi$
$258$	−4.58481	+	1.58244i	−0.285438	+	0.0985183i
$259$	−5.91372	−	2.44954i	−0.367461	−	0.152207i
$260$	−1.49328	+	1.17021i	−0.0926091	+	0.0725732i
$261$	−1.26990	−	3.06581i	−0.0786048	−	0.189769i
$262$	−24.5109	−	1.48111i	−1.51429	−	0.0915031i
$263$	13.5981	−	13.5981i	0.838495	−	0.838495i	−0.150166	−	0.988661i	$-0.547981\pi$
$263$	13.5981	−	13.5981i	0.838495	−	0.838495i	0.988661	+	0.150166i	$0.0479807\pi$
$264$	−3.88072	+	6.00467i	−0.238842	+	0.369562i
$265$	3.36212	+	3.36212i	0.206533	+	0.206533i
$266$	0.207641	+	0.234349i	0.0127313	+	0.0143689i
$267$	−2.84051	+	1.17658i	−0.173836	+	0.0720053i
$268$	10.4309	−	2.90923i	0.637169	−	0.177709i
$269$	2.65856	−	6.41832i	0.162095	−	0.391332i	−0.821875	−	0.569669i	$-0.807072\pi$
$269$	2.65856	−	6.41832i	0.162095	−	0.391332i	0.983970	+	0.178337i	$0.0570716\pi$
$270$	−1.31981	+	2.71105i	−0.0803208	+	0.164989i
$271$		−	0.953295i		−	0.0579086i	−0.999581	−	0.0289543i	$-0.990782\pi$
$271$		−	0.953295i		−	0.0579086i	0.999581	−	0.0289543i	$-0.00921772\pi$
$272$	−27.0552	−	6.66138i	−1.64046	−	0.403905i
$273$			1.84669i			0.111767i
$274$	−10.4724	−	5.09824i	−0.632662	−	0.307996i
$275$	−5.18666	+	12.5217i	−0.312768	+	0.755088i
$276$	11.6651	+	6.57725i	0.702159	+	0.395904i
$277$	19.9308	−	8.25559i	1.19752	−	0.496030i	0.307325	−	0.951605i	$-0.400566\pi$
$277$	19.9308	−	8.25559i	1.19752	−	0.496030i	0.890198	+	0.455574i	$0.150566\pi$
$278$	−4.42972	+	3.92488i	−0.265677	+	0.235399i
$279$	3.72256	+	3.72256i	0.222864	+	0.222864i
$280$	1.06791	−	0.737420i	0.0638199	−	0.0440692i
$281$	−17.4709	+	17.4709i	−1.04223	+	1.04223i	−0.0431601	+	0.999068i	$0.513743\pi$
$281$	−17.4709	+	17.4709i	−1.04223	+	1.04223i	−0.999068	+	0.0431601i	$0.986257\pi$
$282$	0.0707752	−	1.17126i	0.00421460	−	0.0697476i
$283$	−5.86867	−	14.1682i	−0.348856	−	0.842213i	−0.996756	−	0.0804875i	$-0.974352\pi$
$283$	−5.86867	−	14.1682i	−0.348856	−	0.842213i	0.647899	−	0.761726i	$-0.275648\pi$
$284$	1.47625	−	12.1707i	0.0875994	−	0.722196i
$285$	0.0838335	+	0.0347250i	0.00496587	+	0.00205693i
$286$	−2.69938	−	7.82092i	−0.159618	−	0.462461i
$287$	9.58789			0.565955
$288$	7.97215	−	9.57190i	0.469763	−	0.564030i
$289$	−31.5223			−1.85425
$290$	0.319027	+	0.924318i	0.0187339	+	0.0542778i
$291$	−12.5268	−	5.18879i	−0.734337	−	0.304172i
$292$	0.476388	+	0.0577840i	0.0278785	+	0.00338155i
$293$	−13.0272	−	31.4505i	−0.761059	−	1.83736i	−0.478416	−	0.878133i	$-0.658789\pi$
$293$	−13.0272	−	31.4505i	−0.761059	−	1.83736i	−0.282643	−	0.959225i	$-0.591211\pi$
$294$	0.0761946	−	1.26095i	0.00444376	−	0.0735399i
$295$	4.38758	−	4.38758i	0.255455	−	0.255455i
$296$	17.8087	+	3.26014i	1.03511	+	0.189492i
$297$	−9.29818	−	9.29818i	−0.539535	−	0.539535i
$298$	5.84748	−	5.18106i	0.338735	−	0.300131i
$299$	−14.3175	+	5.93051i	−0.828003	+	0.342970i
$300$	−4.20244	+	7.45328i	−0.242628	+	0.430315i
$301$	−1.46931	+	3.54722i	−0.0846895	+	0.204458i
$302$	28.6748	+	13.9596i	1.65005	+	0.803285i
$303$			14.2514i			0.818724i
$304$	−0.713433	−	0.524681i	−0.0409182	−	0.0300925i
$305$		−	3.68506i		−	0.211006i
$306$	9.49537	−	19.5047i	0.542814	−	1.11501i
$307$	4.75711	−	11.4847i	0.271502	−	0.655465i	−0.728046	−	0.685529i	$-0.759571\pi$
$307$	4.75711	−	11.4847i	0.271502	−	0.655465i	0.999548	+	0.0300639i	$0.00957107\pi$
$308$	1.52048	+	5.45160i	0.0866372	+	0.310634i
$309$	−1.38659	+	0.574343i	−0.0788801	+	0.0326732i
$310$	−1.02876	−	1.16108i	−0.0584294	−	0.0659450i
$311$	5.71908	+	5.71908i	0.324299	+	0.324299i	0.850414	−	0.526115i	$-0.176352\pi$
$311$	5.71908	+	5.71908i	0.324299	+	0.324299i	−0.526115	+	0.850414i	$0.676352\pi$
$312$	−1.09721	−	5.10670i	−0.0621173	−	0.289110i
$313$	−8.59321	+	8.59321i	−0.485717	+	0.485717i	−0.906952	−	0.421235i	$-0.861597\pi$
$313$	−8.59321	+	8.59321i	−0.485717	+	0.485717i	0.421235	+	0.906952i	$0.361597\pi$
$314$	−2.40057	−	0.145058i	−0.135472	−	0.00818610i
$315$	0.386663	+	0.933486i	0.0217860	+	0.0525960i
$316$	0.576231	+	0.735317i	0.0324155	+	0.0413648i
$317$	12.5549	+	5.20040i	0.705152	+	0.292084i	0.706297	−	0.707916i	$-0.250364\pi$
$317$	12.5549	+	5.20040i	0.705152	+	0.292084i	−0.00114478	+	0.999999i	$0.500364\pi$
$318$	−12.3743	+	4.27098i	−0.693918	+	0.239505i
$319$	−4.26434			−0.238757
$320$	−2.51498	+	2.67370i	−0.140592	+	0.149464i
$321$	8.54782			0.477093
$322$	10.0209	−	3.45868i	0.558441	−	0.192745i
$323$	−1.42482	−	0.590181i	−0.0792792	−	0.0328385i
$324$	3.02928	+	3.86560i	0.168293	+	0.214756i
$325$	−3.78922	−	9.14798i	−0.210188	−	0.507438i
$326$	13.4427	+	0.812297i	0.744523	+	0.0449890i
$327$	3.48438	−	3.48438i	0.192687	−	0.192687i
$328$	−26.5136	+	5.69663i	−1.46397	+	0.314544i
$329$	−0.656814	−	0.656814i	−0.0362113	−	0.0362113i
$330$	1.08775	+	1.22766i	0.0598785	+	0.0675804i
$331$	−1.09528	+	0.453681i	−0.0602021	+	0.0249365i	−0.412581	−	0.910921i	$-0.635373\pi$
$331$	−1.09528	+	0.453681i	−0.0602021	+	0.0249365i	0.352379	+	0.935857i	$0.385373\pi$
$332$	−6.07209	−	21.7712i	−0.333249	−	1.19485i
$333$	−5.39415	+	13.0226i	−0.295598	+	0.713636i
$334$	−4.70289	+	9.66032i	−0.257330	+	0.528589i
$335$		−	2.48435i		−	0.135735i
$336$	0.538487	+	3.53219i	0.0293769	+	0.192697i
$337$			17.7644i			0.967687i	0.875155	+	0.483843i	$0.160760\pi$
$337$			17.7644i			0.967687i	−0.875155	+	0.483843i	$0.839240\pi$
$338$	−11.0953	−	5.40149i	−0.603507	−	0.293803i
$339$	−1.70446	+	4.11492i	−0.0925733	+	0.223492i
$340$	−3.13954	+	5.56816i	−0.170266	+	0.301976i
$341$	6.25021	−	2.58892i	0.338468	−	0.140198i
$342$	0.516062	−	0.457248i	0.0279054	−	0.0247251i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	1.95553	−	10.6822i	0.105435	−	0.575945i
$345$	2.17242	−	2.17242i	0.116959	−	0.116959i
$346$	−0.568042	+	9.40053i	−0.0305381	+	0.505376i
$347$	−2.82825	−	6.82800i	−0.151828	−	0.366546i	0.829605	−	0.558351i	$-0.188566\pi$
$347$	−2.82825	−	6.82800i	−0.151828	−	0.366546i	−0.981433	+	0.191805i	$0.938566\pi$
$348$	−2.67253	−	0.324167i	−0.143263	−	0.0173772i
$349$	−0.734679	−	0.304314i	−0.0393265	−	0.0162896i	0.362934	−	0.931815i	$-0.381775\pi$
$349$	−0.734679	−	0.304314i	−0.0393265	−	0.0162896i	−0.402260	+	0.915525i	$0.631775\pi$
$350$	2.20988	+	6.40270i	0.118123	+	0.342239i
$351$	9.60670			0.512768
$352$	−7.44367	−	14.1720i	−0.396749	−	0.755371i
$353$	−5.07705			−0.270224			−0.135112	−	0.990830i	$-0.543139\pi$
$353$	−5.07705			−0.270224			−0.135112	+	0.990830i	$0.543139\pi$
$354$	5.57364	+	16.1485i	0.296236	+	0.858286i
$355$	−2.59852	−	1.07634i	−0.137915	−	0.0571263i
$356$	0.828919	−	6.83385i	0.0439326	−	0.362194i
$357$	2.38113	+	5.74856i	0.126023	+	0.304246i
$358$	−1.72966	+	28.6242i	−0.0914153	+	1.51283i
$359$	5.51522	−	5.51522i	0.291082	−	0.291082i	−0.546426	−	0.837508i	$-0.684012\pi$
$359$	5.51522	−	5.51522i	0.291082	−	0.291082i	0.837508	+	0.546426i	$0.184012\pi$
$360$	−1.62387	−	2.35165i	−0.0855857	−	0.123943i
$361$	13.4004	+	13.4004i	0.705283	+	0.705283i
$362$	19.8856	−	17.6193i	1.04516	−	0.926049i
$363$	2.46920	−	1.02278i	0.129600	−	0.0536819i
$364$	−3.60171	−	2.03078i	−0.188781	−	0.106442i
$365$	0.0421305	−	0.101712i	0.00220521	−	0.00532385i
$366$	9.12206	+	4.44085i	0.476818	+	0.232127i
$367$			31.4495i			1.64165i	0.571180	+	0.820825i	$0.306486\pi$
$367$			31.4495i			1.64165i	−0.571180	+	0.820825i	$0.693514\pi$
$368$	−25.6559	+	15.5183i	−1.33741	+	0.808945i
$369$		−	21.1135i		−	1.09913i
$370$	1.81804	−	3.73448i	0.0945154	−	0.194147i
$371$	−3.96564	+	9.57390i	−0.205886	+	0.497052i
$372$	4.11391	−	1.14739i	0.213296	−	0.0594894i
$373$	33.9265	−	14.0528i	1.75665	−	0.727627i	0.759638	−	0.650346i	$-0.225376\pi$
$373$	33.9265	−	14.0528i	1.75665	−	0.727627i	0.997009	−	0.0772813i	$-0.0246240\pi$
$374$	−18.4872	−	20.8651i	−0.955949	−	1.07891i
$375$	2.83708	+	2.83708i	0.146506	+	0.146506i
$376$	2.20654	+	1.42605i	0.113794	+	0.0735431i
$377$	2.20292	−	2.20292i	0.113456	−	0.113456i
$378$	−6.55957	−	0.396372i	−0.337388	−	0.0203872i
$379$	1.04966	+	2.53411i	0.0539175	+	0.130168i	0.948543	−	0.316649i	$-0.102558\pi$
$379$	1.04966	+	2.53411i	0.0539175	+	0.130168i	−0.894625	+	0.446817i	$0.852558\pi$
$380$	−0.159916	+	0.125319i	−0.00820354	+	0.00642871i
$381$	−4.20990	−	1.74380i	−0.215680	−	0.0893374i
$382$	−29.3081	+	10.1156i	−1.49953	+	0.517560i
$383$	−18.1753			−0.928712			−0.464356	−	0.885649i	$-0.653714\pi$
$383$	−18.1753			−0.928712			−0.464356	+	0.885649i	$0.653714\pi$
$384$	−3.58773	−	9.44769i	−0.183086	−	0.482125i
$385$	1.29842			0.0661736
$386$	10.5864	−	3.65389i	0.538835	−	0.185978i
$387$	7.81135	+	3.23557i	0.397073	+	0.164473i
$388$	23.8956	−	18.7258i	1.21311	−	0.950657i
$389$	1.38053	+	3.33289i	0.0699955	+	0.168984i	0.955006	−	0.296588i	$-0.0958487\pi$
$389$	1.38053	+	3.33289i	0.0699955	+	0.168984i	−0.885010	+	0.465572i	$0.845849\pi$
$390$	−1.19612	−	0.0722771i	−0.0605677	−	0.00365990i
$391$	−36.9221	+	36.9221i	−1.86723	+	1.86723i
$392$	2.37550	+	1.53525i	0.119981	+	0.0775418i
$393$	−10.9671	−	10.9671i	−0.553219	−	0.553219i
$394$	−6.56456	−	7.40893i	−0.330718	−	0.373256i
$395$	0.198007	−	0.0820172i	0.00996282	−	0.00412673i
$396$	12.0050	−	3.34825i	0.603274	−	0.168256i
$397$	9.27254	−	22.3859i	0.465376	−	1.12352i	−0.500784	−	0.865572i	$-0.666955\pi$
$397$	9.27254	−	22.3859i	0.465376	−	1.12352i	0.966160	−	0.257944i	$-0.0830450\pi$
$398$	13.9896	−	28.7363i	0.701233	−	1.44042i
$399$			0.197764i			0.00990059i
$400$	−9.91517	−	16.3925i	−0.495759	−	0.819625i
$401$			9.89930i			0.494348i	0.968971	+	0.247174i	$0.0795018\pi$
$401$			9.89930i			0.494348i	−0.968971	+	0.247174i	$0.920498\pi$
$402$	6.14982	+	2.99388i	0.306725	+	0.149321i
$403$	−1.89139	+	4.56621i	−0.0942167	+	0.227459i
$404$	−27.7953	−	15.6721i	−1.38287	−	0.779715i
$405$	1.04094	−	0.431169i	0.0517245	−	0.0214250i
$406$	−1.59507	+	1.41329i	−0.0791622	+	0.0701403i
$407$	12.8083	+	12.8083i	0.634884	+	0.634884i
$408$	−10.0001	−	14.4819i	−0.495078	−	0.716959i
$409$	22.5950	−	22.5950i	1.11725	−	1.11725i	0.125106	−	0.992143i	$-0.460073\pi$
$409$	22.5950	−	22.5950i	1.11725	−	1.11725i	0.992143	−	0.125106i	$-0.0399271\pi$
$410$	−0.375257	+	6.21014i	−0.0185326	+	0.306697i
$411$	−2.81533	−	6.79681i	−0.138870	−	0.335262i
$412$	0.404635	−	3.33593i	0.0199349	−	0.164350i
$413$	12.4940	+	5.17517i	0.614788	+	0.254654i
$414$	−7.61639	−	22.0670i	−0.374325	−	1.08453i
$415$	−5.18530			−0.254536
$416$	11.1665	+	3.47581i	0.547481	+	0.170415i
$417$	−3.73818			−0.183060
$418$	−0.289079	−	0.837550i	−0.0141393	−	0.0409659i
$419$	−1.73910	−	0.720360i	−0.0849607	−	0.0351919i	0.339798	−	0.940498i	$-0.389641\pi$
$419$	−1.73910	−	0.720360i	−0.0849607	−	0.0351919i	−0.424759	+	0.905306i	$0.639641\pi$
$420$	0.813741	+	0.0987035i	0.0397065	+	0.00481624i
$421$	10.8523	+	26.1998i	0.528910	+	1.27690i	0.932238	+	0.361846i	$0.117853\pi$
$421$	10.8523	+	26.1998i	0.528910	+	1.27690i	−0.403328	+	0.915055i	$0.632147\pi$
$422$	−0.529143	+	8.75680i	−0.0257583	+	0.426275i
$423$	−1.44637	+	1.44637i	−0.0703250	+	0.0703250i
$424$	5.27794	−	28.8311i	0.256319	−	1.40016i
$425$	−23.5908	−	23.5908i	−1.14432	−	1.14432i
$426$	5.79586	−	5.13533i	0.280810	−	0.248807i
$427$	7.42002	−	3.07347i	0.359080	−	0.148736i
$428$	−9.39991	+	16.6713i	−0.454362	+	0.805837i
$429$	1.99984	−	4.82804i	0.0965532	−	0.233100i
$430$	−2.24005	−	1.09051i	−0.108025	−	0.0525892i
$431$			17.1918i			0.828100i	0.910254	+	0.414050i	$0.135886\pi$
$431$			17.1918i			0.828100i	−0.910254	+	0.414050i	$0.864114\pi$
$432$	18.3748	−	2.80127i	0.884059	−	0.134776i
$433$			21.8067i			1.04796i	0.851730	+	0.523982i	$0.175554\pi$
$433$			21.8067i			1.04796i	−0.851730	+	0.523982i	$0.824446\pi$
$434$	1.47986	−	3.03983i	0.0710358	−	0.145916i
$435$	−0.236352	+	0.570604i	−0.0113322	+	0.0273583i
$436$	2.96406	+	10.6275i	0.141953	+	0.508965i
$437$	−1.53328	+	0.635104i	−0.0733465	+	0.0303811i
$438$	0.201009	+	0.226864i	0.00960457	+	0.0108400i
$439$	18.9425	+	18.9425i	0.904078	+	0.904078i	0.995786	−	0.0917084i	$-0.0292328\pi$
$439$	18.9425	+	18.9425i	0.904078	+	0.904078i	−0.0917084	+	0.995786i	$0.529233\pi$
$440$	−3.59055	+	0.771455i	−0.171173	+	0.0367777i
$441$	−1.55712	+	1.55712i	−0.0741487	+	0.0741487i
$442$	20.3290	+	1.22841i	0.966953	+	0.0584296i
$443$	10.7340	+	25.9141i	0.509986	+	1.23122i	0.943891	+	0.330257i	$0.107136\pi$
$443$	10.7340	+	25.9141i	0.509986	+	1.23122i	−0.433905	+	0.900959i	$0.642864\pi$
$444$	7.05350	+	9.00082i	0.334744	+	0.427160i
$445$	−1.45907	−	0.604368i	−0.0691667	−	0.0286498i
$446$	13.6524	−	4.71209i	0.646458	−	0.223124i
$447$	4.93461			0.233399
$448$	−7.48119	−	2.83405i	−0.353453	−	0.133896i
$449$	24.6114			1.16149			0.580743	−	0.814087i	$-0.302762\pi$
$449$	24.6114			1.16149			0.580743	+	0.814087i	$0.302762\pi$
$450$	14.0994	−	4.86638i	0.664652	−	0.229404i
$451$	−25.0668	−	10.3830i	−1.18035	−	0.488917i
$452$	−6.15119	−	7.84940i	−0.289328	−	0.369205i
$453$	7.70872	+	18.6105i	0.362187	+	0.874398i
$454$	−16.6837	−	1.00814i	−0.783005	−	0.0473143i
$455$	−0.670752	+	0.670752i	−0.0314453	+	0.0314453i
$456$	−0.117501	−	0.546881i	−0.00550250	−	0.0256101i
$457$	−3.43461	−	3.43461i	−0.160664	−	0.160664i	0.622197	−	0.782861i	$-0.286240\pi$
$457$	−3.43461	−	3.43461i	−0.160664	−	0.160664i	−0.782861	+	0.622197i	$0.786240\pi$
$458$	−22.5773	−	25.4813i	−1.05497	−	1.19066i
$459$	29.9046	−	12.3869i	1.39583	−	0.578171i
$460$	1.84801	+	6.62595i	0.0861639	+	0.308937i
$461$	3.31004	−	7.99114i	0.154164	−	0.372185i	−0.827862	−	0.560932i	$-0.810443\pi$
$461$	3.31004	−	7.99114i	0.154164	−	0.372185i	0.982026	+	0.188748i	$0.0604428\pi$
$462$	−1.56472	+	3.21413i	−0.0727974	+	0.149535i
$463$		−	21.6208i		−	1.00480i	−0.864634	−	0.502401i	$-0.832450\pi$
$463$		−	21.6208i		−	1.00480i	0.864634	−	0.502401i	$-0.167550\pi$
$464$	3.57118	−	4.85590i	0.165788	−	0.225430i
$465$		−	0.979820i		−	0.0454381i
$466$	−1.13405	−	0.552086i	−0.0525340	−	0.0255749i
$467$	−5.16334	+	12.4654i	−0.238931	+	0.576831i	−0.997173	−	0.0751430i	$-0.976059\pi$
$467$	−5.16334	+	12.4654i	−0.238931	+	0.576831i	0.758242	+	0.651974i	$0.226059\pi$
$468$	−4.47199	+	7.93134i	−0.206718	+	0.366626i
$469$	5.00235	−	2.07204i	0.230987	−	0.0956780i
$470$	0.451129	−	0.399716i	0.0208090	−	0.0184375i
$471$	−1.07411	−	1.07411i	−0.0494923	−	0.0494923i
$472$	−37.6246	−	6.88773i	−1.73181	−	0.317033i
$473$	7.68279	−	7.68279i	0.353255	−	0.353255i
$474$	−0.0355906	+	0.588989i	−0.00163473	+	0.0270532i
$475$	−0.405791	−	0.979665i	−0.0186190	−	0.0449501i
$476$	−13.8302	−	1.67755i	−0.633907	−	0.0768904i
$477$	21.0827	+	8.73275i	0.965312	+	0.399845i
$478$	10.2647	+	29.7400i	0.469496	+	1.36027i
$479$	2.96383			0.135421			0.0677104	−	0.997705i	$-0.478431\pi$
$479$	2.96383			0.135421			0.0677104	+	0.997705i	$0.478431\pi$
$480$	−2.30890	+	0.210536i	−0.105386	+	0.00960962i
$481$	−13.2333			−0.603386
$482$	8.71774	+	25.2580i	0.397082	+	1.15047i
$483$	6.18612	+	2.56238i	0.281478	+	0.116592i
$484$	−0.720565	+	5.94056i	−0.0327530	+	0.270025i
$485$	−2.66531	−	6.43463i	−0.121026	−	0.292181i
$486$	−1.37622	+	22.7751i	−0.0624266	+	1.03310i
$487$	−22.8755	+	22.8755i	−1.03659	+	1.03659i	−0.0372822	+	0.999305i	$0.511870\pi$
$487$	−22.8755	+	22.8755i	−1.03659	+	1.03659i	−0.999305	+	0.0372822i	$0.988130\pi$
$488$	−18.6926	+	12.9077i	−0.846175	+	0.584305i
$489$	6.01480	+	6.01480i	0.271999	+	0.271999i
$490$	0.485673	−	0.430322i	0.0219405	−	0.0194400i
$491$	−24.7708	+	10.2604i	−1.11789	+	0.463045i	−0.863648	−	0.504095i	$-0.831826\pi$
$491$	−24.7708	+	10.2604i	−1.11789	+	0.463045i	−0.254242	+	0.967141i	$0.581826\pi$
$492$	−14.9205	−	8.41273i	−0.672667	−	0.379275i
$493$	4.01700	−	9.69790i	0.180917	−	0.436771i
$494$	0.582006	+	0.283335i	0.0261857	+	0.0127478i
$495$		−	2.85926i		−	0.128514i
$496$	−2.28619	+	9.28535i	−0.102653	+	0.416925i
$497$		−	6.12993i		−	0.274965i
$498$	6.24878	−	12.8358i	0.280015	−	0.575186i
$499$	−5.00028	+	12.0717i	−0.223843	+	0.540405i	−0.995406	−	0.0957485i	$-0.969476\pi$
$499$	−5.00028	+	12.0717i	−0.223843	+	0.540405i	0.771562	+	0.636154i	$0.219476\pi$
$500$	−8.65321	+	2.41342i	−0.386983	+	0.107931i
$501$	−6.26974	+	2.59701i	−0.280111	+	0.116026i
$502$	26.0577	+	29.4094i	1.16301	+	1.31260i
$503$	5.62313	+	5.62313i	0.250723	+	0.250723i	0.821267	−	0.570544i	$-0.193268\pi$
$503$	5.62313	+	5.62313i	0.250723	+	0.250723i	−0.570544	+	0.821267i	$0.693268\pi$
$504$	3.38078	−	5.23110i	0.150592	−	0.233012i
$505$	−5.17637	+	5.17637i	−0.230345	+	0.230345i
$506$	−29.9443	−	1.80943i	−1.33119	−	0.0804390i
$507$	−2.98279	−	7.20110i	−0.132471	−	0.319812i
$508$	8.03058	−	6.29317i	0.356299	−	0.279214i
$509$	−15.7699	−	6.53209i	−0.698987	−	0.289530i	0.00475194	−	0.999989i	$-0.498487\pi$
$509$	−15.7699	−	6.53209i	−0.698987	−	0.289530i	−0.703739	+	0.710459i	$0.748487\pi$
$510$	−3.81657	+	1.31728i	−0.169001	+	0.0583303i
$511$	0.239940			0.0106143
$512$	22.3717	+	3.39212i	0.988699	+	0.149912i
$513$	1.02879			0.0454222
$514$	−27.1862	+	9.38326i	−1.19913	+	0.413878i
$515$	−0.712244	−	0.295021i	−0.0313852	−	0.0130002i
$516$	5.39896	−	4.23089i	0.237676	−	0.186255i
$517$	1.00591	+	2.42847i	0.0442397	+	0.106804i
$518$	9.03585	+	0.546005i	0.397013	+	0.0239901i
$519$	−4.20617	+	4.20617i	−0.184630	+	0.184630i
$520$	1.45632	−	2.25337i	0.0638637	−	0.0988167i
$521$	27.4517	+	27.4517i	1.20268	+	1.20268i	0.973349	+	0.229330i	$0.0736536\pi$
$521$	27.4517	+	27.4517i	1.20268	+	1.20268i	0.229330	+	0.973349i	$0.426346\pi$
$522$	3.11221	+	3.51252i	0.136218	+	0.153739i
$523$	−34.9352	+	14.4706i	−1.52761	+	0.632757i	−0.979099	−	0.203385i	$-0.934806\pi$
$523$	−34.9352	+	14.4706i	−1.52761	+	0.632757i	−0.548512	+	0.836143i	$0.684806\pi$
$524$	33.4502	−	9.32941i	1.46128	−	0.407557i
$525$	−1.63719	+	3.95254i	−0.0714530	+	0.172503i
$526$	−11.9041	+	24.4525i	−0.519044	+	1.06618i
$527$			16.6529i			0.725411i
$528$	2.41728	−	9.81778i	0.105199	−	0.427264i
$529$			33.1902i			1.44305i
$530$	−6.04587	−	2.94328i	−0.262616	−	0.127848i
$531$	11.3963	−	27.5130i	0.494556	−	1.19396i
$532$	−0.385710	−	0.217478i	−0.0167227	−	0.00942888i
$533$	18.3130	−	7.58551i	0.793226	−	0.328565i
$534$	3.25439	−	2.88350i	0.140831	−	0.124781i
$535$	3.10472	+	3.10472i	0.134229	+	0.134229i
$536$	−12.6020	+	8.70199i	−0.544323	+	0.375869i
$537$	−12.8076	+	12.8076i	−0.552688	+	0.552688i
$538$	−0.592594	+	9.80686i	−0.0255486	+	0.422804i
$539$	1.08293	+	2.61442i	0.0466451	+	0.112611i
$540$	0.513466	−	4.23316i	0.0220961	−	0.182166i
$541$	−0.0811782	−	0.0336251i	−0.00349012	−	0.00144566i	0.380938	−	0.924601i	$-0.375601\pi$
$541$	−0.0811782	−	0.0336251i	−0.00349012	−	0.00144566i	−0.384428	+	0.923155i	$0.625601\pi$
$542$	0.439854	+	1.27439i	0.0188933	+	0.0547398i
$543$	16.7812			0.720149
$544$	39.2417	−	3.57824i	1.68247	−	0.153416i
$545$	2.53118			0.108424
$546$	−0.852071	−	2.46871i	−0.0364653	−	0.105651i
$547$	−12.6813	−	5.25276i	−0.542212	−	0.224592i	0.0947302	−	0.995503i	$-0.469801\pi$
$547$	−12.6813	−	5.25276i	−0.542212	−	0.224592i	−0.636943	+	0.770911i	$0.719801\pi$
$548$	16.3522	+	1.98345i	0.698529	+	0.0847288i
$549$	−6.76810	−	16.3397i	−0.288856	−	0.697359i
$550$	1.15611	−	19.1325i	0.0492968	−	0.815813i
$551$	0.235913	−	0.235913i	0.0100502	−	0.0100502i
$552$	−18.6290	−	3.41031i	−0.792904	−	0.145152i
$553$	0.330290	+	0.330290i	0.0140454	+	0.0140454i
$554$	−22.8348	+	20.2324i	−0.970158	+	0.859593i
$555$	2.42375	−	1.00395i	0.102883	−	0.0426154i
$556$	4.11082	−	7.29078i	0.174338	−	0.309198i
$557$	−1.97657	+	4.77187i	−0.0837500	+	0.202190i	−0.960207	−	0.279290i	$-0.909901\pi$
$557$	−1.97657	+	4.77187i	−0.0837500	+	0.202190i	0.876457	+	0.481481i	$0.159901\pi$
$558$	−6.69402	−	3.25882i	−0.283380	−	0.137957i
$559$			7.93771i			0.335729i
$560$	−1.08736	+	1.47854i	−0.0459495	+	0.0624797i
$561$		−	17.6078i		−	0.743401i
$562$	15.2945	−	31.4168i	0.645158	−	1.32524i
$563$	−11.6999	+	28.2460i	−0.493091	+	1.19043i	0.460048	+	0.887894i	$0.347832\pi$
$563$	−11.6999	+	28.2460i	−0.493091	+	1.19043i	−0.953139	+	0.302533i	$0.902168\pi$
$564$	0.445809	+	1.59843i	0.0187720	+	0.0673060i
$565$	−2.11370	+	0.875523i	−0.0889240	+	0.0368335i
$566$	14.3827	+	16.2326i	0.604548	+	0.682309i
$567$	1.73636	+	1.73636i	0.0729201	+	0.0729201i
$568$	3.64209	+	16.9512i	0.152819	+	0.711257i
$569$	15.2976	−	15.2976i	0.641308	−	0.641308i	−0.309569	−	0.950877i	$-0.600185\pi$
$569$	15.2976	−	15.2976i	0.641308	−	0.641308i	0.950877	+	0.309569i	$0.100185\pi$
$570$	−0.128093	−	0.00774023i	−0.00536523	−	0.000324202i
$571$	−4.17965	−	10.0906i	−0.174913	−	0.422277i	0.811973	−	0.583695i	$-0.198393\pi$
$571$	−4.17965	−	10.0906i	−0.174913	−	0.422277i	−0.986886	+	0.161417i	$0.948393\pi$
$572$	7.21720	+	9.20972i	0.301766	+	0.385078i
$573$	−18.0926	−	7.49419i	−0.755828	−	0.313074i
$574$	−12.8174	+	4.42388i	−0.534986	+	0.184649i
$575$	−35.9019			−1.49721
$576$	−6.24088	+	16.4744i	−0.260037	+	0.686431i
$577$	−12.0481			−0.501567			−0.250784	−	0.968043i	$-0.580688\pi$
$577$	−12.0481			−0.501567			−0.250784	+	0.968043i	$0.580688\pi$
$578$	42.1399	−	14.5445i	1.75279	−	0.604971i
$579$	6.53525	+	2.70699i	0.271596	+	0.112499i
$580$	−0.852967	−	1.08845i	−0.0354175	−	0.0451956i
$581$	−4.32473	−	10.4408i	−0.179420	−	0.433158i
$582$	19.1404	+	1.15659i	0.793393	+	0.0479420i
$583$	20.7357	−	20.7357i	0.858786	−	0.858786i
$584$	−0.663510	+	0.142560i	−0.0274563	+	0.00589917i
$585$	1.47706	+	1.47706i	0.0610691	+	0.0610691i
$586$	31.9265	+	36.0331i	1.31887	+	1.48851i
$587$	38.0844	−	15.7751i	1.57191	−	0.651107i	0.584805	−	0.811174i	$-0.301171\pi$
$587$	38.0844	−	15.7751i	1.57191	−	0.651107i	0.987106	+	0.160067i	$0.0511709\pi$
$588$	0.479946	+	1.72082i	0.0197926	+	0.0709656i
$589$	−0.202550	+	0.489000i	−0.00834594	+	0.0201489i
$590$	−3.84099	+	7.88988i	−0.158131	+	0.324821i
$591$		−	6.25229i		−	0.257185i
$592$	−25.3114	+	3.85876i	−1.04029	+	0.158594i
$593$			37.8260i			1.55333i	0.629916	+	0.776663i	$0.283089\pi$
$593$			37.8260i			1.55333i	−0.629916	+	0.776663i	$0.716911\pi$
$594$	16.7203	+	8.13984i	0.686041	+	0.333982i
$595$	−1.22311	+	2.95285i	−0.0501426	+	0.121055i
$596$	−5.42651	+	9.62423i	−0.222278	+	0.394224i
$597$	18.6504	−	7.72526i	0.763311	−	0.316174i
$598$	16.4037	−	14.5342i	0.670796	−	0.594348i
$599$	−26.1072	−	26.1072i	−1.06671	−	1.06671i	−0.997610	−	0.0690998i	$-0.977987\pi$
$599$	−26.1072	−	26.1072i	−1.06671	−	1.06671i	−0.0690998	−	0.997610i	$-0.522013\pi$
$600$	2.17897	−	11.9028i	0.0889561	−	0.485928i
$601$	14.4627	−	14.4627i	0.589944	−	0.589944i	−0.347672	−	0.937616i	$-0.613028\pi$
$601$	14.4627	−	14.4627i	0.589944	−	0.589944i	0.937616	+	0.347672i	$0.113028\pi$
$602$	0.327510	−	5.41997i	0.0133483	−	0.220901i
$603$	−4.56285	−	11.0157i	−0.185814	−	0.448594i
$604$	−44.7742	−	5.43094i	−1.82184	−	0.220982i
$605$	1.26835	+	0.525367i	0.0515657	+	0.0213592i
$606$	−6.57566	−	19.0517i	−0.267118	−	0.773923i
$607$	−24.8541			−1.00880			−0.504399	−	0.863471i	$-0.668286\pi$
$607$	−24.8541			−1.00880			−0.504399	+	0.863471i	$0.668286\pi$
$608$	1.19583	+	0.372227i	0.0484972	+	0.0150958i
$609$	−1.34606			−0.0545451
$610$	1.70030	+	4.92628i	0.0688430	+	0.199459i
$611$	−1.77417	−	0.734884i	−0.0717751	−	0.0297302i
$612$	−3.69414	+	30.4556i	−0.149327	+	1.23109i
$613$	−9.97940	−	24.0924i	−0.403064	−	0.973083i	−0.986918	−	0.161224i	$-0.948456\pi$
$613$	−9.97940	−	24.0924i	−0.403064	−	0.973083i	0.583853	−	0.811859i	$-0.301544\pi$
$614$	−1.06036	+	17.5480i	−0.0427928	+	0.708178i
$615$	−2.77866	+	2.77866i	−0.112046	+	0.112046i
$616$	−4.54800	−	6.58630i	−0.183244	−	0.265369i
$617$	−23.5196	−	23.5196i	−0.946865	−	0.946865i	0.0517933	−	0.998658i	$-0.483506\pi$
$617$	−23.5196	−	23.5196i	−0.946865	−	0.946865i	−0.998658	+	0.0517933i	$0.983506\pi$
$618$	1.58862	−	1.40757i	0.0639038	−	0.0566209i
$619$	38.4562	−	15.9291i	1.54569	−	0.640244i	0.563156	−	0.826351i	$-0.309587\pi$
$619$	38.4562	−	15.9291i	1.54569	−	0.640244i	0.982529	+	0.186107i	$0.0595871\pi$
$620$	1.91100	+	1.07749i	0.0767475	+	0.0432731i
$621$	13.3297	−	32.1809i	0.534904	−	1.29137i
$622$	−10.2842	−	5.00662i	−0.412360	−	0.200747i
$623$		−	3.44197i		−	0.137900i
$624$	3.82303	+	6.32052i	0.153044	+	0.253023i
$625$		−	21.8864i		−	0.875456i
$626$	7.52270	−	15.4526i	0.300668	−	0.617609i
$627$	0.214165	−	0.517040i	0.00855292	−	0.0206486i
$628$	3.27607	−	0.913713i	0.130730	−	0.0364611i
$629$	−41.1938	+	17.0630i	−1.64250	+	0.680347i
$630$	−0.947615	−	1.06950i	−0.0377539	−	0.0426100i
$631$	11.4573	+	11.4573i	0.456108	+	0.456108i	0.897376	−	0.441267i	$-0.145471\pi$
$631$	11.4573	+	11.4573i	0.456108	+	0.456108i	−0.441267	+	0.897376i	$0.645471\pi$
$632$	−1.10960	−	0.717116i	−0.0441375	−	0.0285254i
$633$	−3.91814	+	3.91814i	−0.155732	+	0.155732i
$634$	−19.1832	−	1.15917i	−0.761861	−	0.0460367i
$635$	−0.895731	−	2.16249i	−0.0355460	−	0.0858156i
$636$	14.5717	−	11.4191i	0.577806	−	0.452798i
$637$	−1.91002	−	0.791155i	−0.0756777	−	0.0313467i
$638$	5.70069	−	1.96758i	0.225693	−	0.0778974i
$639$	−13.4988			−0.534002
$640$	2.12844	−	4.73469i	0.0841339	−	0.187155i
$641$	−6.35924			−0.251175			−0.125587	−	0.992083i	$-0.540082\pi$
$641$	−6.35924			−0.251175			−0.125587	+	0.992083i	$0.540082\pi$
$642$	−11.4270	+	3.94399i	−0.450986	+	0.155657i
$643$	−25.2199	−	10.4464i	−0.994574	−	0.411966i	−0.174770	−	0.984609i	$-0.555918\pi$
$643$	−25.2199	−	10.4464i	−0.994574	−	0.411966i	−0.819805	+	0.572643i	$0.805918\pi$
$644$	−11.8003	+	9.24733i	−0.464998	+	0.364396i
$645$	−0.602199	−	1.45384i	−0.0237116	−	0.0572448i
$646$	2.17705	+	0.131552i	0.0856550	+	0.00517584i
$647$	11.9189	−	11.9189i	0.468580	−	0.468580i	−0.432874	−	0.901454i	$-0.642500\pi$
$647$	11.9189	−	11.9189i	0.468580	−	0.468580i	0.901454	+	0.432874i	$0.142500\pi$
$648$	−5.83323	−	3.76992i	−0.229151	−	0.148097i
$649$	−27.0602	−	27.0602i	−1.06221	−	1.06221i
$650$	9.28643	+	10.4809i	0.364244	+	0.411095i
$651$	1.97291	−	0.817206i	0.0773244	−	0.0320288i
$652$	−18.3454	+	5.11661i	−0.718461	+	0.200382i
$653$	−16.0678	+	38.7910i	−0.628780	+	1.51801i	0.212359	+	0.977192i	$0.431885\pi$
$653$	−16.0678	+	38.7910i	−0.628780	+	1.51801i	−0.841139	+	0.540819i	$0.818115\pi$
$654$	−3.05031	+	6.26572i	−0.119277	+	0.245009i
$655$		−	7.96691i		−	0.311293i
$656$	32.8156	−	19.8489i	1.28123	−	0.774968i
$657$		−	0.528373i		−	0.0206138i
$658$	1.18110	+	0.574990i	0.0460442	+	0.0224155i
$659$	7.12738	−	17.2070i	0.277643	−	0.670291i	−0.722126	−	0.691762i	$-0.756835\pi$
$659$	7.12738	−	17.2070i	0.277643	−	0.670291i	0.999769	+	0.0214709i	$0.00683492\pi$
$660$	−2.02057	−	1.13928i	−0.0786508	−	0.0443463i
$661$	33.8178	−	14.0078i	1.31536	−	0.544840i	0.388916	−	0.921273i	$-0.372850\pi$
$661$	33.8178	−	14.0078i	1.31536	−	0.544840i	0.926444	+	0.376434i	$0.122850\pi$
$662$	1.25487	−	1.11186i	0.0487720	−	0.0432137i
$663$	9.09601	+	9.09601i	0.353260	+	0.353260i
$664$	18.1627	+	26.3027i	0.704848	+	1.02074i
$665$	−0.0718314	+	0.0718314i	−0.00278550	+	0.00278550i
$666$	1.20236	−	19.8979i	0.0465905	−	0.771028i
$667$	−4.32276	−	10.4361i	−0.167378	−	0.404086i
$668$	1.82964	−	15.0841i	0.0707909	−	0.583622i
$669$	8.42793	+	3.49096i	0.325843	+	0.134968i
$670$	1.14629	+	3.32115i	0.0442850	+	0.128307i
$671$	−22.7274			−0.877382
$672$	−2.34963	−	4.47347i	−0.0906389	−	0.172568i
$673$	−15.8505			−0.610991			−0.305495	−	0.952194i	$-0.598822\pi$
$673$	−15.8505			−0.610991			−0.305495	+	0.952194i	$0.598822\pi$
$674$	−8.19654	−	23.7479i	−0.315719	−	0.914734i
$675$	20.5615	+	8.51686i	0.791413	+	0.327814i
$676$	17.3248	+	2.10143i	0.666340	+	0.0808243i
$677$	−7.98658	−	19.2813i	−0.306949	−	0.741041i	−0.999801	−	0.0199610i	$-0.993646\pi$
$677$	−7.98658	−	19.2813i	−0.306949	−	0.741041i	0.692851	−	0.721080i	$-0.256354\pi$
$678$	0.379925	−	6.28738i	0.0145909	−	0.241465i
$679$	10.7334	−	10.7334i	0.411911	−	0.411911i
$680$	1.62786	−	8.89227i	0.0624254	−	0.341003i
$681$	−7.46495	−	7.46495i	−0.286058	−	0.286058i
$682$	−7.16092	+	6.34481i	−0.274206	+	0.242955i
$683$	11.4860	−	4.75764i	0.439498	−	0.182046i	−0.151952	−	0.988388i	$-0.548556\pi$
$683$	11.4860	−	4.75764i	0.439498	−	0.182046i	0.591450	+	0.806342i	$0.298556\pi$
$684$	−0.478910	+	0.849374i	−0.0183116	+	0.0324766i
$685$	1.44614	−	3.49130i	0.0552542	−	0.133396i
$686$	1.27154	+	0.619018i	0.0485477	+	0.0236342i
$687$		−	21.5033i		−	0.820404i
$688$	2.31460	+	15.1825i	0.0882431	+	0.578828i
$689$			21.4238i			0.816180i
$690$	−1.90178	+	3.90650i	−0.0723997	+	0.148718i
$691$	11.9990	−	28.9682i	0.456464	−	1.10200i	−0.513355	−	0.858176i	$-0.671598\pi$
$691$	11.9990	−	28.9682i	0.456464	−	1.10200i	0.969819	−	0.243825i	$-0.0784023\pi$
$692$	−3.57806	−	12.8290i	−0.136018	−	0.487685i
$693$	5.75724	−	2.38473i	0.218699	−	0.0905882i
$694$	6.93134	+	7.82289i	0.263110	+	0.296953i
$695$	−1.35777	−	1.35777i	−0.0515033	−	0.0515033i
$696$	3.72229	−	0.799760i	0.141093	−	0.0303148i
$697$	47.2257	−	47.2257i	1.78880	−	1.78880i
$698$	1.12255	+	0.0678318i	0.0424892	+	0.00256747i
$699$	−0.304871	−	0.736023i	−0.0115313	−	0.0278389i
$700$	−5.90845	−	7.53965i	−0.223319	−	0.284972i
$701$	−41.9077	−	17.3587i	−1.58283	−	0.655630i	−0.593971	−	0.804486i	$-0.702441\pi$
$701$	−41.9077	−	17.3587i	−1.58283	−	0.655630i	−0.988859	+	0.148856i	$0.952441\pi$
$702$	−12.8425	+	4.43256i	−0.484709	+	0.167296i
$703$	−1.41716			−0.0534494
$704$	16.4899	+	15.5110i	0.621487	+	0.584593i
$705$	0.380702			0.0143381
$706$	6.78714	−	2.34257i	0.255437	−	0.0881637i
$707$	−14.7401	−	6.10556i	−0.554359	−	0.229623i
$708$	−14.9020	−	19.0161i	−0.560051	−	0.714670i
$709$	15.0903	+	36.4312i	0.566728	+	1.36820i	0.904298	+	0.426902i	$0.140395\pi$
$709$	15.0903	+	36.4312i	0.566728	+	1.36820i	−0.337569	+	0.941301i	$0.609605\pi$
$710$	3.97040	+	0.239917i	0.149006	+	0.00900394i
$711$	0.727334	−	0.727334i	0.0272771	−	0.0272771i
$712$	2.04504	+	9.51815i	0.0766412	+	0.356708i
$713$	12.6717	+	12.6717i	0.474558	+	0.474558i
$714$	−5.83557	−	6.58617i	−0.218391	−	0.246481i
$715$	2.48001	−	1.02725i	0.0927470	−	0.0384171i
$716$	−10.8950	−	39.0636i	−0.407166	−	1.45988i
$717$	−7.60463	+	18.3592i	−0.284000	+	0.685637i
$718$	−4.82816	+	9.91764i	−0.180185	+	0.370123i
$719$		−	52.3678i		−	1.95299i	−0.215538	−	0.976495i	$-0.569151\pi$
$719$		−	52.3678i		−	1.95299i	0.215538	−	0.976495i	$-0.430849\pi$
$720$	3.25590	+	2.39449i	0.121340	+	0.0892374i
$721$		−	1.68019i		−	0.0625736i
$722$	−24.0970	−	11.7310i	−0.896796	−	0.436583i
$723$	−6.45856	+	15.5924i	−0.240197	+	0.579886i
$724$	−18.4540	+	32.7292i	−0.685837	+	1.21637i
$725$	6.66798	−	2.76197i	0.247643	−	0.102577i
$726$	−2.82899	+	2.50658i	−0.104994	+	0.0930278i
$727$	27.5847	+	27.5847i	1.02306	+	1.02306i	0.999728	+	0.0233314i	$0.00742728\pi$
$727$	27.5847	+	27.5847i	1.02306	+	1.02306i	0.0233314	+	0.999728i	$0.492573\pi$
$728$	5.75187	+	1.05296i	0.213179	+	0.0390254i
$729$	−4.98140	+	4.98140i	−0.184496	+	0.184496i
$730$	−0.00939093	+	0.155411i	−0.000347574	+	0.00575201i
$731$	10.2349	+	24.7092i	0.378551	+	0.913904i
$732$	−14.2436	−	1.72770i	−0.526460	−	0.0638575i
$733$	−25.6783	−	10.6363i	−0.948449	−	0.392861i	−0.145801	−	0.989314i	$-0.546576\pi$
$733$	−25.6783	−	10.6363i	−0.948449	−	0.392861i	−0.802648	+	0.596453i	$0.796576\pi$
$734$	−14.5109	−	42.0425i	−0.535607	−	1.55182i
$735$	0.409853			0.0151176
$736$	27.1374	−	32.5830i	1.00030	−	1.20102i
$737$	−15.3221			−0.564398
$738$	9.74186	+	28.2251i	0.358603	+	1.03898i
$739$	8.42293	+	3.48889i	0.309842	+	0.128341i	0.532186	−	0.846627i	$-0.321371\pi$
$739$	8.42293	+	3.48889i	0.309842	+	0.128341i	−0.222344	+	0.974968i	$0.571371\pi$
$740$	−0.707302	+	5.83121i	−0.0260009	+	0.214360i
$741$	0.156462	+	0.377733i	0.00574778	+	0.0138764i
$742$	0.883944	−	14.6284i	0.0324506	−	0.537026i
$743$	24.3741	−	24.3741i	0.894199	−	0.894199i	−0.100716	−	0.994915i	$-0.532113\pi$
$743$	24.3741	−	24.3741i	0.894199	−	0.894199i	0.994915	+	0.100716i	$0.0321135\pi$
$744$	−4.97018	+	3.43203i	−0.182216	+	0.125824i
$745$	1.79233	+	1.79233i	0.0656661	+	0.0656661i
$746$	−38.8698	+	34.4400i	−1.42313	+	1.26094i
$747$	−22.9918	+	9.52351i	−0.841225	+	0.348447i
$748$	34.3414	+	19.3630i	1.25565	+	0.707981i
$749$	−3.66203	+	8.84093i	−0.133808	+	0.323040i
$750$	−5.10173	−	2.48365i	−0.186289	−	0.0906900i
$751$		−	51.6433i		−	1.88449i	−0.334922	−	0.942246i	$-0.608710\pi$
$751$		−	51.6433i		−	1.88449i	0.334922	−	0.942246i	$-0.391290\pi$
$752$	−3.60775	−	0.888281i	−0.131561	−	0.0323923i
$753$			24.8182i			0.904424i
$754$	−1.92849	+	3.96136i	−0.0702314	+	0.144264i
$755$	−3.95972	+	9.55960i	−0.144109	+	0.347910i
$756$	8.95190	−	2.49673i	0.325578	−	0.0908051i
$757$	−27.9391	+	11.5727i	−1.01546	+	0.420619i	−0.827445	−	0.561547i	$-0.810206\pi$
$757$	−27.9391	+	11.5727i	−1.01546	+	0.420619i	−0.188018	+	0.982165i	$0.560206\pi$
$758$	−2.57246	−	2.90335i	−0.0934360	−	0.105454i
$759$	−13.3983	−	13.3983i	−0.486327	−	0.486327i
$760$	0.155958	−	0.241315i	0.00565720	−	0.00875342i
$761$	−9.95169	+	9.95169i	−0.360748	+	0.360748i	−0.864088	−	0.503340i	$-0.832104\pi$
$761$	−9.95169	+	9.95169i	−0.360748	+	0.360748i	0.503340	+	0.864088i	$0.332104\pi$
$762$	6.43250	+	0.388694i	0.233025	+	0.0140809i
$763$	2.11109	+	5.09663i	0.0764267	+	0.184510i
$764$	34.5124	−	27.0457i	1.24862	−	0.978479i
$765$	6.50247	+	2.69341i	0.235097	+	0.0973805i
$766$	24.2972	−	8.38613i	0.877893	−	0.303003i
$767$	27.9581			1.00951
$768$	9.15537	+	10.9745i	0.330366	+	0.396009i
$769$	40.9565			1.47693			0.738465	−	0.674292i	$-0.235551\pi$
$769$	40.9565			1.47693			0.738465	+	0.674292i	$0.235551\pi$
$770$	−1.73576	+	0.599096i	−0.0625526	+	0.0215899i
$771$	−16.7827	−	6.95161i	−0.604413	−	0.250356i
$772$	−12.4663	+	9.76923i	−0.448672	+	0.351602i
$773$	16.5319	+	39.9115i	0.594610	+	1.43552i	0.879007	+	0.476809i	$0.158207\pi$
$773$	16.5319	+	39.9115i	0.594610	+	1.43552i	−0.284397	+	0.958707i	$0.591793\pi$
$774$	−11.9353	−	0.721211i	−0.429007	−	0.0259234i
$775$	−8.09639	+	8.09639i	−0.290831	+	0.290831i
$776$	−23.3041	+	36.0586i	−0.836569	+	1.29443i
$777$	4.04300	+	4.04300i	0.145042	+	0.145042i
$778$	−3.38333	−	3.81852i	−0.121298	−	0.136900i
$779$	1.96116	−	0.812339i	0.0702659	−	0.0291051i
$780$	1.63235	−	0.455270i	0.0584475	−	0.0163013i
$781$	−6.63829	+	16.0262i	−0.237537	+	0.573464i
$782$	32.3224	−	66.3944i	1.15585	−	2.37426i
$783$			7.00235i			0.250243i
$784$	−3.88400	−	0.956298i	−0.138714	−	0.0341535i
$785$		−	0.780270i		−	0.0278490i
$786$	19.7214	+	9.60089i	0.703440	+	0.342452i
$787$	2.66376	−	6.43089i	0.0949528	−	0.229236i	−0.869266	−	0.494345i	$-0.835408\pi$
$787$	2.66376	−	6.43089i	0.0949528	−	0.229236i	0.964219	+	0.265109i	$0.0854079\pi$
$788$	12.1942	+	6.87554i	0.434400	+	0.244931i
$789$	−15.8702	+	6.57364i	−0.564993	+	0.234028i
$790$	−0.226858	+	0.201004i	−0.00807125	+	0.00715140i
$791$	−3.52580	−	3.52580i	−0.125363	−	0.125363i
$792$	−14.5037	+	10.0152i	−0.515367	+	0.355874i
$793$	11.7408	−	11.7408i	0.416927	−	0.416927i
$794$	−2.06686	+	34.2045i	−0.0733500	+	1.21387i
$795$	−1.62533	−	3.92389i	−0.0576444	−	0.139166i
$796$	−5.44259	+	44.8703i	−0.192907	+	1.59039i
$797$	−28.6814	−	11.8802i	−1.01595	−	0.420819i	−0.188326	−	0.982107i	$-0.560306\pi$
$797$	−28.6814	−	11.8802i	−1.01595	−	0.420819i	−0.827621	+	0.561288i	$0.810306\pi$
$798$	−0.0912491	−	0.264377i	−0.00323018	−	0.00935883i
$799$	−6.47035			−0.228905
$800$	20.8184	+	17.3390i	0.736043	+	0.613028i
$801$	−7.57958			−0.267811
$802$	−4.56757	−	13.2337i	−0.161287	−	0.467297i
$803$	−0.627305	−	0.259838i	−0.0221371	−	0.00916949i
$804$	−9.60263	−	1.16476i	−0.338659	−	0.0410779i
$805$	1.31621	+	3.17761i	0.0463902	+	0.111996i
$806$	0.421592	−	6.97693i	0.0148499	−	0.245752i
$807$	−4.38798	+	4.38798i	−0.154464	+	0.154464i
$808$	44.3887	+	8.12599i	1.56159	+	0.285871i
$809$	23.4079	+	23.4079i	0.822977	+	0.822977i	0.986534	−	0.163557i	$-0.0522968\pi$
$809$	23.4079	+	23.4079i	0.822977	+	0.822977i	−0.163557	+	0.986534i	$0.552297\pi$
$810$	−1.19261	+	1.05669i	−0.0419040	+	0.0371283i
$811$	−2.08381	+	0.863141i	−0.0731723	+	0.0303090i	−0.418969	−	0.908000i	$-0.637609\pi$
$811$	−2.08381	+	0.863141i	−0.0731723	+	0.0303090i	0.345797	+	0.938309i	$0.387609\pi$
$812$	1.48024	−	2.62529i	0.0519463	−	0.0921298i
$813$	−0.325867	+	0.786712i	−0.0114286	+	0.0275912i
$814$	−23.0323	−	11.2127i	−0.807280	−	0.393004i
$815$			4.36936i			0.153052i
$816$	20.0504	+	14.7457i	0.701903	+	0.516201i
$817$			0.850057i			0.0297397i
$818$	−19.7802	+	40.6310i	−0.691597	+	1.42063i
$819$	−1.74221	+	4.20606i	−0.0608776	+	0.146972i
$820$	−2.36372	−	8.47503i	−0.0825448	−	0.295961i
$821$	−16.3532	+	6.77370i	−0.570729	+	0.236404i	−0.649336	−	0.760502i	$-0.724953\pi$
$821$	−16.3532	+	6.77370i	−0.570729	+	0.236404i	0.0786064	+	0.996906i	$0.474953\pi$
$822$	6.89968	+	7.78715i	0.240654	+	0.271608i
$823$	25.7691	+	25.7691i	0.898255	+	0.898255i	0.995282	−	0.0970271i	$-0.0309334\pi$
$823$	25.7691	+	25.7691i	0.898255	+	0.898255i	−0.0970271	+	0.995282i	$0.530933\pi$
$824$	0.998283	+	4.64626i	0.0347768	+	0.161860i
$825$	8.56064	−	8.56064i	0.298043	−	0.298043i
$826$	−19.0901	−	1.15355i	−0.664230	−	0.0401371i
$827$	13.7738	+	33.2529i	0.478962	+	1.15632i	0.960096	+	0.279670i	$0.0902249\pi$
$827$	13.7738	+	33.2529i	0.478962	+	1.15632i	−0.481134	+	0.876647i	$0.659775\pi$
$828$	20.3636	+	25.9855i	0.707683	+	0.903060i
$829$	−13.6960	−	5.67306i	−0.475681	−	0.197033i	0.131945	−	0.991257i	$-0.457878\pi$
$829$	−13.6960	−	5.67306i	−0.475681	−	0.197033i	−0.607625	+	0.794224i	$0.707878\pi$
$830$	6.93185	−	2.39252i	0.240608	−	0.0830454i
$831$	−19.2700			−0.668468
$832$	−16.5314	+	0.505690i	−0.573122	+	0.0175316i
$833$	−6.96580			−0.241351
$834$	4.99730	−	1.72481i	0.173042	−	0.0597253i
$835$	−3.22056	−	1.33400i	−0.111452	−	0.0461649i
$836$	0.772897	+	0.986278i	0.0267312	+	0.0341111i
$837$	−4.25119	−	10.2633i	−0.146943	−	0.354751i
$838$	2.65726	+	0.160569i	0.0917934	+	0.00554676i
$839$	2.46322	−	2.46322i	0.0850399	−	0.0850399i	−0.663307	−	0.748347i	$-0.730848\pi$
$839$	2.46322	−	2.46322i	0.0850399	−	0.0850399i	0.748347	+	0.663307i	$0.230848\pi$
$840$	−1.13337	+	0.243513i	−0.0391051	+	0.00840201i
$841$	−18.9004	−	18.9004i	−0.651737	−	0.651737i
$842$	−26.5964	−	30.0173i	−0.916571	−	1.03447i
$843$	20.3901	−	8.44586i	0.702272	−	0.290891i
$844$	−3.33305	−	11.9505i	−0.114728	−	0.411353i
$845$	1.53216	−	3.69897i	0.0527080	−	0.127248i
$846$	1.26619	−	2.60091i	0.0435325	−	0.0894211i
$847$			2.99205i			0.102808i
$848$	6.24706	+	40.9774i	0.214525	+	1.40717i
$849$			13.6985i			0.470131i
$850$	42.4218	+	20.6520i	1.45505	+	0.708357i
$851$	−18.3618	+	44.3293i	−0.629435	+	1.51959i
$852$	−5.37861	+	9.53927i	−0.184268	+	0.326810i
$853$	33.9962	−	14.0817i	1.16401	−	0.482147i	0.284800	−	0.958587i	$-0.408073\pi$
$853$	33.9962	−	14.0817i	1.16401	−	0.482147i	0.879207	+	0.476440i	$0.158073\pi$
$854$	−8.50117	+	7.53232i	−0.290904	+	0.257751i
$855$	0.158180	+	0.158180i	0.00540965	+	0.00540965i
$856$	4.87386	−	26.6238i	0.166585	−	0.909982i
$857$	−1.30014	+	1.30014i	−0.0444118	+	0.0444118i	−0.728964	−	0.684552i	$-0.759998\pi$
$857$	−1.30014	+	1.30014i	−0.0444118	+	0.0444118i	0.684552	+	0.728964i	$0.259998\pi$
$858$	−0.445766	+	7.37699i	−0.0152182	+	0.251846i
$859$	7.44491	+	17.9736i	0.254017	+	0.613251i	0.998521	−	0.0543667i	$-0.0173140\pi$
$859$	7.44491	+	17.9736i	0.254017	+	0.613251i	−0.744504	+	0.667618i	$0.767314\pi$
$860$	3.49773	+	0.424260i	0.119272	+	0.0144672i
$861$	−7.91246	−	3.27745i	−0.269656	−	0.111695i
$862$	−7.93236	−	22.9825i	−0.270177	−	0.782786i
$863$	31.5009			1.07230			0.536151	−	0.844122i	$-0.319878\pi$
$863$	31.5009			1.07230			0.536151	+	0.844122i	$0.319878\pi$
$864$	−23.2714	+	12.2230i	−0.791710	+	0.415835i
$865$	−3.05551			−0.103890
$866$	−10.0617	−	29.1518i	−0.341910	−	0.990618i
$867$	26.0139	+	10.7753i	0.883480	+	0.365949i
$868$	−0.575736	+	4.74654i	−0.0195418	+	0.161108i
$869$	−0.505838	−	1.22120i	−0.0171594	−	0.0414264i
$870$	0.0526830	−	0.871852i	0.00178612	−	0.0295585i
$871$	7.91527	−	7.91527i	0.268199	−	0.268199i
$872$	−8.86600	−	12.8395i	−0.300241	−	0.434800i
$873$	−23.6361	−	23.6361i	−0.799962	−	0.799962i
$874$	1.75669	−	1.55648i	0.0594208	−	0.0526488i
$875$	−4.14982	+	1.71891i	−0.140290	+	0.0581098i
$876$	−0.373390	−	0.210531i	−0.0126157	−	0.00711319i
$877$	−9.17785	+	22.1573i	−0.309914	+	0.748199i	0.689793	+	0.724006i	$0.257701\pi$
$877$	−9.17785	+	22.1573i	−0.309914	+	0.748199i	−0.999707	+	0.0241924i	$0.992299\pi$
$878$	−34.0630	−	16.5827i	−1.14957	−	0.559640i
$879$			30.4078i			1.02563i
$880$	4.44399	−	2.68799i	0.149807	−	0.0906122i
$881$			2.06908i			0.0697090i	0.999392	+	0.0348545i	$0.0110968\pi$
$881$			2.06908i			0.0697090i	−0.999392	+	0.0348545i	$0.988903\pi$
$882$	1.36314	−	2.80007i	0.0458994	−	0.0942831i
$883$	−11.0536	+	26.6857i	−0.371982	+	0.898044i	0.621432	+	0.783468i	$0.286551\pi$
$883$	−11.0536	+	26.6857i	−0.371982	+	0.898044i	−0.993414	+	0.114576i	$0.963449\pi$
$884$	−27.7432	+	7.73770i	−0.933104	+	0.260247i
$885$	−5.12069	+	2.12106i	−0.172130	+	0.0712986i
$886$	−26.3063	−	29.6900i	−0.883778	−	0.997455i
$887$	5.41162	+	5.41162i	0.181704	+	0.181704i	0.792098	−	0.610394i	$-0.208989\pi$
$887$	5.41162	+	5.41162i	0.181704	+	0.181704i	−0.610394	+	0.792098i	$0.708989\pi$
$888$	−13.5823	−	8.77804i	−0.455793	−	0.294572i
$889$	3.60718	−	3.60718i	0.120981	−	0.120981i
$890$	2.22939	+	0.134714i	0.0747292	+	0.00451563i
$891$	−2.65922	−	6.41992i	−0.0890872	−	0.215075i
$892$	−16.0767	+	12.5985i	−0.538287	+	0.421829i
$893$	−0.189997	−	0.0786994i	−0.00635801	−	0.00263358i
$894$	−6.59672	+	2.27684i	−0.220627	+	0.0761491i
$895$	−9.30387			−0.310994
$896$	11.3087	+	0.336793i	0.377797	+	0.0112515i
$897$	13.8428			0.462199
$898$	−32.9012	+	11.3558i	−1.09793	+	0.378948i
$899$	−3.32832	−	1.37864i	−0.111006	−	0.0459801i
$900$	−16.6031	+	13.0110i	−0.553437	+	0.433701i
$901$	27.6238	+	66.6898i	0.920283	+	2.22176i
$902$	38.3008	+	2.31438i	1.27528	+	0.0770605i
$903$	2.42511	−	2.42511i	0.0807025	−	0.0807025i
$904$	11.8448	+	7.65512i	0.393953	+	0.254605i
$905$	6.09521	+	6.09521i	0.202612	+	0.202612i
$906$	−18.8922	−	21.3222i	−0.627651	−	0.708383i
$907$	31.1677	−	12.9101i	1.03491	−	0.428673i	0.200426	−	0.979709i	$-0.435767\pi$
$907$	31.1677	−	12.9101i	1.03491	−	0.428673i	0.834481	+	0.551036i	$0.185767\pi$
$908$	22.7684	−	6.35021i	0.755596	−	0.210739i
$909$	−13.4451	+	32.4593i	−0.445945	+	1.07661i
$910$	0.587192	−	1.20617i	0.0194652	−	0.0399840i
$911$		−	3.23730i		−	0.107256i	−0.998561	−	0.0536282i	$-0.982921\pi$
$911$		−	3.23730i		−	0.107256i	0.998561	−	0.0536282i	$-0.0170786\pi$
$912$	0.409412	+	0.676870i	0.0135570	+	0.0224134i
$913$			31.9801i			1.05839i
$914$	6.17622	+	3.00674i	0.204291	+	0.0994541i
$915$	−1.25967	+	3.04111i	−0.0416434	+	0.100536i
$916$	41.9391	+	23.6469i	1.38571	+	0.781315i
$917$	16.0417	−	6.64469i	0.529744	−	0.219427i
$918$	−34.2619	+	30.3572i	−1.13081	+	1.00194i
$919$	−32.0337	−	32.0337i	−1.05670	−	1.05670i	−0.998293	−	0.0584021i	$-0.981399\pi$
$919$	−32.0337	−	32.0337i	−1.05670	−	1.05670i	−0.0584021	−	0.998293i	$-0.518601\pi$
$920$	−5.52770	−	8.00507i	−0.182243	−	0.263919i
$921$	−7.85166	+	7.85166i	−0.258721	+	0.258721i
$922$	−0.737810	+	12.2100i	−0.0242985	+	0.402116i
$923$	−4.84973	−	11.7083i	−0.159631	−	0.385383i
$924$	0.608749	−	5.01871i	0.0200264	−	0.165103i
$925$	−28.3236	−	11.7320i	−0.931274	−	0.385746i
$926$	9.97590	+	28.9032i	0.327829	+	0.949820i
$927$	−3.69996			−0.121522
$928$	−2.53352	+	8.13926i	−0.0831670	+	0.267184i
$929$	32.9600			1.08138			0.540691	−	0.841221i	$-0.318163\pi$
$929$	32.9600			1.08138			0.540691	+	0.841221i	$0.318163\pi$
$930$	0.452092	+	1.30985i	0.0148247	+	0.0429517i
$931$	−0.204546	−	0.0847256i	−0.00670371	−	0.00277677i
$932$	1.77077	+	0.214787i	0.0580034	+	0.00703558i
$933$	−2.76474	−	6.67466i	−0.0905134	−	0.218519i
$934$	1.15091	−	19.0465i	0.0376590	−	0.623220i
$935$	6.39545	−	6.39545i	0.209154	−	0.209154i
$936$	2.31873	−	12.6662i	0.0757902	−	0.414008i
$937$	−1.11776	−	1.11776i	−0.0365156	−	0.0365156i	0.688613	−	0.725129i	$-0.258220\pi$
$937$	−1.11776	−	1.11776i	−0.0365156	−	0.0365156i	−0.725129	+	0.688613i	$0.758220\pi$
$938$	−5.73123	+	5.07806i	−0.187131	+	0.165805i
$939$	10.0290	−	4.15416i	0.327285	−	0.135566i
$940$	−0.418652	+	0.742503i	−0.0136549	+	0.0242178i
$941$	−15.6090	+	37.6834i	−0.508838	+	1.22844i	0.435715	+	0.900085i	$0.356496\pi$
$941$	−15.6090	+	37.6834i	−0.508838	+	1.22844i	−0.944553	+	0.328359i	$0.893504\pi$
$942$	1.93150	+	0.940301i	0.0629315	+	0.0306367i
$943$		−	71.8709i		−	2.34044i
$944$	53.4757	−	8.15244i	1.74048	−	0.265339i
$945$		−	2.13210i		−	0.0693571i
$946$	−6.72569	+	13.8154i	−0.218671	+	0.449178i
$947$	−19.6022	+	47.3239i	−0.636985	+	1.53782i	0.193691	+	0.981063i	$0.437954\pi$
$947$	−19.6022	+	47.3239i	−0.636985	+	1.53782i	−0.830676	+	0.556756i	$0.812046\pi$
$948$	−0.224183	−	0.803798i	−0.00728113	−	0.0261062i
$949$	0.458290	−	0.189830i	0.0148767	−	0.00616213i
$950$	0.994493	+	1.12241i	0.0322656	+	0.0364158i
$951$	−8.58332	−	8.58332i	−0.278333	−	0.278333i
$952$	19.2626	−	4.13872i	0.624306	−	0.134137i
$953$	5.55062	−	5.55062i	0.179802	−	0.179802i	−0.611467	−	0.791270i	$-0.709420\pi$
$953$	5.55062	−	5.55062i	0.179802	−	0.179802i	0.791270	+	0.611467i	$0.209420\pi$
$954$	−32.2133	−	1.94654i	−1.04294	−	0.0630215i
$955$	−3.84952	−	9.29356i	−0.124567	−	0.300732i
$956$	−27.4443	−	35.0210i	−0.887611	−	1.13266i
$957$	3.51917	+	1.45769i	0.113759	+	0.0471204i
$958$	−3.96213	+	1.36752i	−0.128010	+	0.0441826i
$959$	8.23600			0.265954
$960$	2.98945	−	1.34678i	0.0964842	−	0.0434673i
$961$	−25.2847			−0.815636
$962$	17.6906	−	6.10588i	0.570368	−	0.196862i
$963$	19.4686	+	8.06418i	0.627368	+	0.259865i
$964$	−23.3082	−	29.7432i	−0.750708	−	0.957962i
$965$	1.39049	+	3.35694i	0.0447615	+	0.108064i
$966$	−9.45207	−	0.571156i	−0.304115	−	0.0183766i
$967$	−16.2683	+	16.2683i	−0.523152	+	0.523152i	−0.918522	−	0.395370i	$-0.870616\pi$
$967$	−16.2683	+	16.2683i	−0.523152	+	0.523152i	0.395370	+	0.918522i	$0.370616\pi$
$968$	−1.77772	−	8.27397i	−0.0571381	−	0.265935i
$969$	0.974100	+	0.974100i	0.0312926	+	0.0312926i
$970$	6.53202	+	7.37220i	0.209730	+	0.236707i
$971$	−22.1134	+	9.15966i	−0.709652	+	0.293948i	−0.708161	−	0.706051i	$-0.750475\pi$
$971$	−22.1134	+	9.15966i	−0.709652	+	0.293948i	−0.00149157	+	0.999999i	$0.500475\pi$
$972$	−8.66873	−	31.0813i	−0.278050	−	0.996934i
$973$	1.60150	−	3.86636i	0.0513417	−	0.123950i
$974$	20.0257	−	41.1354i	0.641666	−	1.31806i
$975$			8.84469i			0.283257i
$976$	19.0331	−	25.8802i	0.609235	−	0.828406i
$977$		−	4.60405i		−	0.147296i	−0.997284	−	0.0736482i	$-0.976536\pi$
$977$		−	4.60405i		−	0.147296i	0.997284	−	0.0736482i	$-0.0234642\pi$
$978$	−10.8160	−	5.26550i	−0.345858	−	0.168372i
$979$	−3.72741	+	8.99877i	−0.119129	+	0.287602i
$980$	−0.450708	+	0.799358i	−0.0143974	+	0.0255345i
$981$	11.2233	−	4.64885i	0.358333	−	0.148426i
$982$	28.3801	−	25.1457i	0.905645	−	0.802432i
$983$	19.8645	+	19.8645i	0.633580	+	0.633580i	0.948964	−	0.315384i	$-0.102133\pi$
$983$	19.8645	+	19.8645i	0.633580	+	0.633580i	−0.315384	+	0.948964i	$0.602133\pi$
$984$	23.8278	+	4.36201i	0.759601	+	0.139056i
$985$	2.27094	−	2.27094i	0.0723582	−	0.0723582i
$986$	−0.895393	+	14.8179i	−0.0285151	+	0.471897i
$987$	0.317519	+	0.766559i	0.0101067	+	0.0243998i
$988$	−0.908773	−	0.110230i	−0.0289119	−	0.00350690i
$989$	26.5900	+	11.0139i	0.845513	+	0.350223i
$990$	1.31927	+	3.82233i	0.0419292	+	0.121482i
$991$	−1.04980			−0.0333479			−0.0166740	−	0.999861i	$-0.505308\pi$
$991$	−1.04980			−0.0333479			−0.0166740	+	0.999861i	$0.505308\pi$
$992$	−1.22806	−	13.4678i	−0.0389908	−	0.427602i
$993$	1.05897			0.0336054
$994$	2.82837	+	8.19466i	0.0897105	+	0.259919i
$995$	9.58011	+	3.96821i	0.303710	+	0.125801i
$996$	−2.43107	+	20.0424i	−0.0770313	+	0.635069i
$997$	−17.6555	−	42.6242i	−0.559156	−	1.34992i	−0.910436	−	0.413651i	$-0.864254\pi$
$997$	−17.6555	−	42.6242i	−0.559156	−	1.34992i	0.351280	−	0.936270i	$-0.385746\pi$
$998$	1.11457	−	18.4450i	0.0352810	−	0.583865i
$999$	21.0321	−	21.0321i	0.665426	−	0.665426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.29.1	✓	52
4.3	odd	2		896.2.u.c.337.9		52
32.11	odd	8		896.2.u.c.561.9		52
32.21	even	8	inner	224.2.u.c.85.1	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.1	✓	52	1.1	even	1	trivial
224.2.u.c.85.1	yes	52	32.21	even	8	inner
896.2.u.c.337.9		52	4.3	odd	2
896.2.u.c.561.9		52	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33683 + 0.461403i) q^{2} +(-0.825255 - 0.341832i) q^{3} +(1.57421 - 1.23363i) q^{4} +(-0.175588 - 0.423906i) q^{5} +(1.26095 + 0.0761946i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.53525 + 2.37550i) q^{8} +(-1.55712 - 1.55712i) q^{9} +O(q^{10})\)	\(q+(-1.33683 + 0.461403i) q^{2} +(-0.825255 - 0.341832i) q^{3} +(1.57421 - 1.23363i) q^{4} +(-0.175588 - 0.423906i) q^{5} +(1.26095 + 0.0761946i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.53525 + 2.37550i) q^{8} +(-1.55712 - 1.55712i) q^{9} +(0.430322 + 0.485673i) q^{10} +(-2.61442 + 1.08293i) q^{11} +(-1.72082 + 0.479946i) q^{12} +(0.791155 - 1.91002i) q^{13} +(-0.619018 + 1.27154i) q^{14} +0.409853i q^{15} +(0.956298 - 3.88400i) q^{16} -6.96580i q^{17} +(2.80007 + 1.36314i) q^{18} +(0.0847256 - 0.204546i) q^{19} +(-0.799358 - 0.450708i) q^{20} +(-0.825255 + 0.341832i) q^{21} +(2.99537 - 2.65399i) q^{22} +(-5.30048 - 5.30048i) q^{23} +(2.07900 - 1.43560i) q^{24} +(3.38667 - 3.38667i) q^{25} +(-0.176349 + 2.91841i) q^{26} +(1.77825 + 4.29306i) q^{27} +(0.240827 - 1.98545i) q^{28} +(1.39222 + 0.576675i) q^{29} +(-0.189107 - 0.547902i) q^{30} -2.39066 q^{31} +(0.513688 + 5.63348i) q^{32} +2.52775 q^{33} +(3.21404 + 9.31206i) q^{34} +(-0.423906 - 0.175588i) q^{35} +(-4.37216 - 0.530326i) q^{36} +(-2.44954 - 5.91372i) q^{37} +(-0.0188854 + 0.312535i) q^{38} +(-1.30581 + 1.30581i) q^{39} +(1.27656 + 0.233693i) q^{40} +(6.77966 + 6.77966i) q^{41} +(0.945501 - 0.837746i) q^{42} +(-3.54722 + 1.46931i) q^{43} +(-2.77972 + 4.93000i) q^{44} +(-0.386663 + 0.933486i) q^{45} +(9.53148 + 4.64017i) q^{46} -0.928875i q^{47} +(-2.11687 + 2.87840i) q^{48} -1.00000i q^{49} +(-2.96477 + 6.09001i) q^{50} +(-2.38113 + 5.74856i) q^{51} +(-1.11081 - 3.98277i) q^{52} +(-9.57390 + 3.96564i) q^{53} +(-4.35804 - 4.91860i) q^{54} +(0.918122 + 0.918122i) q^{55} +(0.594149 + 2.76532i) q^{56} +(-0.139840 + 0.139840i) q^{57} +(-2.12723 - 0.128541i) q^{58} +(5.17517 + 12.4940i) q^{59} +(0.505608 + 0.645196i) q^{60} +(7.42002 + 3.07347i) q^{61} +(3.19591 - 1.10306i) q^{62} -2.20210 q^{63} +(-3.28602 - 7.29398i) q^{64} -0.948586 q^{65} +(-3.37916 + 1.16631i) q^{66} +(5.00235 + 2.07204i) q^{67} +(-8.59324 - 10.9657i) q^{68} +(2.56238 + 6.18612i) q^{69} +(0.647706 + 0.0391387i) q^{70} +(4.33452 - 4.33452i) q^{71} +(6.08952 - 1.30838i) q^{72} +(0.169663 + 0.169663i) q^{73} +(6.00323 + 6.77540i) q^{74} +(-3.95254 + 1.63719i) q^{75} +(-0.118958 - 0.426519i) q^{76} +(-1.08293 + 2.61442i) q^{77} +(1.14314 - 2.34815i) q^{78} +0.467101i q^{79} +(-1.81437 + 0.276603i) q^{80} +2.45558i q^{81} +(-12.1914 - 5.93508i) q^{82} +(4.32473 - 10.4408i) q^{83} +(-0.877433 + 1.55618i) q^{84} +(-2.95285 + 1.22311i) q^{85} +(4.06408 - 3.60091i) q^{86} +(-0.951808 - 0.951808i) q^{87} +(1.44129 - 7.87314i) q^{88} +(2.43384 - 2.43384i) q^{89} +(0.0861874 - 1.42632i) q^{90} +(-0.791155 - 1.91002i) q^{91} +(-14.8829 - 1.80524i) q^{92} +(1.97291 + 0.817206i) q^{93} +(0.428586 + 1.24174i) q^{94} -0.101585 q^{95} +(1.50178 - 4.82466i) q^{96} +15.1794 q^{97} +(0.461403 + 1.33683i) q^{98} +(5.75724 + 2.38473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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