LMFDB - Embedded newform 224.2.u.c.85.1

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			85.1
Character	$\chi$	$=$	224.85
Dual form			224.2.u.c.29.1

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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	−0.607973	−	0.793958i	$-0.708017\pi$
$3$	−0.825255	+	0.341832i	−0.476461	+	0.197357i	0.131511	+	0.991315i	$0.458017\pi$
$4$	1.57421	+	1.23363i	0.787107	+	0.616817i
$5$	−0.175588	+	0.423906i	−0.0785252	+	0.189577i	−0.958267	−	0.285876i	$-0.907716\pi$
$5$	−0.175588	+	0.423906i	−0.0785252	+	0.189577i	0.879741	+	0.475452i	$0.157716\pi$
$6$	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	−0.0480273	−	0.998846i	$-0.515293\pi$
$11$	−2.61442	−	1.08293i	−0.788279	−	0.326516i	−0.740251	+	0.672330i	$0.765293\pi$
$12$	−1.72082	−	0.479946i	−0.496759	−	0.138548i
$13$	0.791155	+	1.91002i	0.219427	+	0.529744i	0.994810	−	0.101747i	$-0.0324433\pi$
$13$	0.791155	+	1.91002i	0.219427	+	0.529744i	−0.775383	+	0.631491i	$0.782443\pi$
$14$	−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	$0.320237\pi$
$17$			6.96580i			1.68945i	−0.535198	+	0.844727i	$0.679763\pi$
$18$	2.80007	−	1.36314i	0.659982	−	0.321296i
$19$	0.0847256	+	0.204546i	0.0194374	+	0.0469260i	0.933300	−	0.359097i	$-0.116915\pi$
$19$	0.0847256	+	0.204546i	0.0194374	+	0.0469260i	−0.913863	+	0.406023i	$0.866915\pi$
$20$	−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	−0.111457	+	0.993769i	$0.535552\pi$
$23$	−5.30048	+	5.30048i	−1.10523	+	1.10523i	−0.993769	+	0.111457i	$0.964448\pi$
$24$	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	−0.249655	−	0.968335i	$-0.580317\pi$
$29$	1.39222	−	0.576675i	0.258528	−	0.107086i	0.508183	+	0.861249i	$0.330317\pi$
$30$	−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	0.584305	+	0.811534i	$0.301367\pi$
$37$	−2.44954	+	5.91372i	−0.402703	+	0.972210i	−0.987007	+	0.160676i	$0.948633\pi$
$38$	−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	0.0606459	−	0.998159i	$-0.480684\pi$
$41$	6.77966	−	6.77966i	1.05881	−	1.05881i	0.998159	−	0.0606459i	$-0.0193160\pi$
$42$	0.945501	+	0.837746i	0.145894	+	0.129267i
$43$	−3.54722	−	1.46931i	−0.540946	−	0.224067i	0.0954436	−	0.995435i	$-0.469573\pi$
$43$	−3.54722	−	1.46931i	−0.540946	−	0.224067i	−0.636390	+	0.771368i	$0.719573\pi$
$44$	−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	$0.0215805\pi$
$47$			0.928875i			0.135490i	−0.997703	+	0.0677451i	$0.978420\pi$
$48$	−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	−0.388715	−	0.921358i	$-0.627081\pi$
$53$	−9.57390	−	3.96564i	−1.31508	−	0.544722i	−0.926361	+	0.376636i	$0.877081\pi$
$54$	−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	−0.101435	−	0.994842i	$-0.532343\pi$
$59$	5.17517	−	12.4940i	0.673750	−	1.62658i	0.775185	−	0.631735i	$-0.217657\pi$
$60$	0.505608	−	0.645196i	0.0652737	−	0.0832944i
$61$	7.42002	−	3.07347i	0.950036	−	0.393518i	0.146791	−	0.989167i	$-0.453105\pi$
$61$	7.42002	−	3.07347i	0.950036	−	0.393518i	0.803244	+	0.595650i	$0.203105\pi$
$62$	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	−0.0555791	−	0.998454i	$-0.517701\pi$
$67$	5.00235	−	2.07204i	0.611134	−	0.253140i	0.666713	+	0.745314i	$0.267701\pi$
$68$	−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	0.915875	−	0.401463i	$-0.131498\pi$
$71$	4.33452	+	4.33452i	0.514412	+	0.514412i	−0.401463	+	0.915875i	$0.631498\pi$
$72$	6.08952	+	1.30838i	0.717657	+	0.154194i
$73$	0.169663	−	0.169663i	0.0198576	−	0.0198576i	−0.697108	−	0.716966i	$-0.745530\pi$
$73$	0.169663	−	0.169663i	0.0198576	−	0.0198576i	0.716966	+	0.697108i	$0.245530\pi$
$74$	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	$-0.991635\pi$
$79$		−	0.467101i		−	0.0525530i	0.999655	−	0.0262765i	$-0.00836503\pi$
$80$	−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	0.962063	+	0.272829i	$0.0879592\pi$
$83$	4.32473	+	10.4408i	0.474701	+	1.14603i	−0.487362	+	0.873200i	$0.662041\pi$
$84$	−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	0.824235	−	0.566248i	$-0.191606\pi$
$89$	2.43384	+	2.43384i	0.257987	+	0.257987i	−0.566248	+	0.824235i	$0.691606\pi$
$90$	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	0.258157	+	0.966103i	$0.416885\pi$
$101$	−6.10556	+	14.7401i	−0.607526	+	1.46670i	−0.865683	+	0.500593i	$0.833115\pi$
$102$	0.530756	+	8.78349i	0.0525527	+	0.869695i
$103$	1.18807	+	1.18807i	0.117064	+	0.117064i	0.763212	−	0.646148i	$-0.223621\pi$
$103$	1.18807	+	1.18807i	0.117064	+	0.117064i	−0.646148	+	0.763212i	$0.723621\pi$
$104$	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	−0.0880583	−	0.996115i	$-0.528066\pi$
$107$	−8.84093	−	3.66203i	−0.854685	−	0.354022i	−0.766627	+	0.642093i	$0.778066\pi$
$108$	8.09541	−	4.56450i	0.778981	−	0.439219i
$109$	−2.11109	−	5.09663i	−0.202206	−	0.488169i	0.789950	−	0.613171i	$-0.210106\pi$
$109$	−2.11109	−	5.09663i	−0.202206	−	0.488169i	−0.992156	+	0.125002i	$0.960106\pi$
$110$	−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	$0.0753561\pi$
$113$			4.98624i			0.469066i	−0.972108	+	0.234533i	$0.924644\pi$
$114$	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	0.451411	−	0.892316i	$-0.350921\pi$
$131$	16.0417	−	6.64469i	1.40157	−	0.580549i	0.950159	+	0.311767i	$0.100921\pi$
$132$	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	−0.413121	−	0.910676i	$-0.635561\pi$
$137$	5.82373	−	5.82373i	0.497555	−	0.497555i	0.910676	+	0.413121i	$0.135561\pi$
$138$	−6.27975	+	7.08749i	−0.534568	+	0.603327i
$139$	3.86636	+	1.60150i	0.327941	+	0.135838i	0.540578	−	0.841294i	$-0.318205\pi$
$139$	3.86636	+	1.60150i	0.327941	+	0.135838i	−0.212638	+	0.977131i	$0.568205\pi$
$140$	−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	0.163697	−	0.986511i	$-0.447658\pi$
$149$	−5.10381	−	2.11407i	−0.418121	−	0.173191i	−0.581817	+	0.813319i	$0.697658\pi$
$150$	4.52845	+	4.01236i	0.369747	+	0.327608i
$151$	−15.9461	+	15.9461i	−1.29768	+	1.29768i	−0.367753	+	0.929924i	$0.619873\pi$
$151$	−15.9461	+	15.9461i	−1.29768	+	1.29768i	−0.929924	+	0.367753i	$0.880127\pi$
$152$	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	−0.319107	−	0.947719i	$-0.603383\pi$
$157$	1.57111	−	0.650774i	0.125388	−	0.0519374i	0.444495	+	0.895781i	$0.353383\pi$
$158$	−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	−0.699627	−	0.714508i	$-0.746650\pi$
$163$	−8.79789	+	3.64421i	−0.689104	+	0.285436i	0.0105227	+	0.999945i	$0.496650\pi$
$164$	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	0.883721	−	0.468014i	$-0.155030\pi$
$167$	5.37212	+	5.37212i	0.415707	+	0.415707i	−0.468014	+	0.883721i	$0.655030\pi$
$168$	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	0.990662	−	0.136339i	$-0.0435338\pi$
$173$	2.54841	+	6.15239i	0.193752	+	0.467758i	−0.796911	+	0.604097i	$0.793534\pi$
$174$	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	0.892819	+	0.450415i	$0.148724\pi$
$179$	7.75977	+	18.7337i	0.579992	+	1.40023i	−0.312827	+	0.949810i	$0.601276\pi$
$180$	0.542890	−	1.94651i	0.0404646	−	0.145084i
$181$	−17.3566	−	7.18933i	−1.29010	−	0.534379i	−0.371088	−	0.928598i	$-0.621015\pi$
$181$	−17.3566	−	7.18933i	−1.29010	−	0.534379i	−0.919017	+	0.394219i	$0.871015\pi$
$182$	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	−0.799278	−	0.600962i	$-0.794784\pi$
$197$	2.67859	−	6.46668i	0.190841	−	0.460732i	0.990119	+	0.140230i	$0.0447843\pi$
$198$	−8.79675	+	0.531557i	−0.625158	+	0.0377761i
$199$	−15.9803	−	15.9803i	−1.13282	−	1.13282i	−0.989707	−	0.143108i	$-0.954290\pi$
$199$	−15.9803	−	15.9803i	−1.13282	−	1.13282i	−0.143108	−	0.989707i	$-0.545710\pi$
$200$	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	0.984285	−	0.176585i	$-0.0565052\pi$
$211$	2.37390	+	5.73109i	0.163426	+	0.394545i	−0.820860	+	0.571130i	$0.806505\pi$
$212$	−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	0.0103408	−	0.999947i	$-0.496708\pi$
$227$	10.9190	−	4.52281i	0.724722	−	0.300190i	0.714381	+	0.699757i	$0.246708\pi$
$228$	−0.0476269	−	0.392651i	−0.00315417	−	0.0260039i
$229$	9.21240	−	22.2407i	0.608772	−	1.46971i	−0.255564	−	0.966792i	$-0.582261\pi$
$229$	9.21240	−	22.2407i	0.608772	−	1.46971i	0.864336	−	0.502914i	$-0.167739\pi$
$230$	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	−0.686147	−	0.727463i	$-0.740699\pi$
$233$	0.630649	−	0.630649i	0.0413152	−	0.0413152i	0.727463	+	0.686147i	$0.240699\pi$
$234$	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	$0.255633\pi$
$239$			22.2467i			1.43902i	−0.694483	+	0.719509i	$0.744367\pi$
$240$	1.59187	−	0.391941i	0.102755	−	0.0252997i
$241$			18.8940i			1.21707i	0.793528	+	0.608534i	$0.208242\pi$
$241$			18.8940i			1.21707i	−0.793528	+	0.608534i	$0.791758\pi$
$242$	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	0.108594	+	0.994086i	$0.465365\pi$
$251$	−10.6325	+	25.6692i	−0.671119	+	1.62022i	−0.779713	+	0.626137i	$0.784635\pi$
$252$	−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	0.988661	−	0.150166i	$-0.0479807\pi$
$263$	13.5981	+	13.5981i	0.838495	+	0.838495i	−0.150166	+	0.988661i	$0.547981\pi$
$264$	−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	0.983970	−	0.178337i	$-0.0570716\pi$
$269$	2.65856	+	6.41832i	0.162095	+	0.391332i	−0.821875	+	0.569669i	$0.807072\pi$
$270$	−1.31981	−	2.71105i	−0.0803208	−	0.164989i
$271$			0.953295i			0.0579086i	0.999581	+	0.0289543i	$0.00921772\pi$
$271$			0.953295i			0.0579086i	−0.999581	+	0.0289543i	$0.990782\pi$
$272$	−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	0.890198	−	0.455574i	$-0.150566\pi$
$277$	19.9308	+	8.25559i	1.19752	+	0.496030i	0.307325	+	0.951605i	$0.400566\pi$
$278$	−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	−0.999068	−	0.0431601i	$-0.986257\pi$
$281$	−17.4709	−	17.4709i	−1.04223	−	1.04223i	−0.0431601	−	0.999068i	$-0.513743\pi$
$282$	0.0707752	+	1.17126i	0.00421460	+	0.0697476i
$283$	−5.86867	+	14.1682i	−0.348856	+	0.842213i	0.647899	+	0.761726i	$0.275648\pi$
$283$	−5.86867	+	14.1682i	−0.348856	+	0.842213i	−0.996756	+	0.0804875i	$0.974352\pi$
$284$	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	−0.282643	+	0.959225i	$0.591211\pi$
$293$	−13.0272	+	31.4505i	−0.761059	+	1.83736i	−0.478416	+	0.878133i	$0.658789\pi$
$294$	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	0.999548	−	0.0300639i	$-0.00957107\pi$
$307$	4.75711	+	11.4847i	0.271502	+	0.655465i	−0.728046	+	0.685529i	$0.759571\pi$
$308$	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	−0.526115	−	0.850414i	$-0.676352\pi$
$311$	5.71908	−	5.71908i	0.324299	−	0.324299i	0.850414	+	0.526115i	$0.176352\pi$
$312$	−1.09721	+	5.10670i	−0.0621173	+	0.289110i
$313$	−8.59321	−	8.59321i	−0.485717	−	0.485717i	0.421235	−	0.906952i	$-0.361597\pi$
$313$	−8.59321	−	8.59321i	−0.485717	−	0.485717i	−0.906952	+	0.421235i	$0.861597\pi$
$314$	−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	−0.00114478	−	0.999999i	$-0.500364\pi$
$317$	12.5549	−	5.20040i	0.705152	−	0.292084i	0.706297	+	0.707916i	$0.250364\pi$
$318$	−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	0.352379	−	0.935857i	$-0.385373\pi$
$331$	−1.09528	−	0.453681i	−0.0602021	−	0.0249365i	−0.412581	+	0.910921i	$0.635373\pi$
$332$	−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	$-0.839240\pi$
$337$		−	17.7644i		−	0.967687i	0.875155	−	0.483843i	$-0.160760\pi$
$338$	−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	−0.981433	−	0.191805i	$-0.938566\pi$
$347$	−2.82825	+	6.82800i	−0.151828	+	0.366546i	0.829605	+	0.558351i	$0.188566\pi$
$348$	−2.67253	+	0.324167i	−0.143263	+	0.0173772i
$349$	−0.734679	+	0.304314i	−0.0393265	+	0.0162896i	−0.402260	−	0.915525i	$-0.631775\pi$
$349$	−0.734679	+	0.304314i	−0.0393265	+	0.0162896i	0.362934	+	0.931815i	$0.381775\pi$
$350$	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	0.837508	−	0.546426i	$-0.184012\pi$
$359$	5.51522	+	5.51522i	0.291082	+	0.291082i	−0.546426	+	0.837508i	$0.684012\pi$
$360$	−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	$-0.693514\pi$
$367$		−	31.4495i		−	1.64165i	0.571180	−	0.820825i	$-0.306486\pi$
$368$	−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	0.997009	+	0.0772813i	$0.0246240\pi$
$373$	33.9265	+	14.0528i	1.75665	+	0.727627i	0.759638	+	0.650346i	$0.225376\pi$
$374$	−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	−0.894625	−	0.446817i	$-0.852558\pi$
$379$	1.04966	−	2.53411i	0.0539175	−	0.130168i	0.948543	+	0.316649i	$0.102558\pi$
$380$	−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	−0.885010	−	0.465572i	$-0.845849\pi$
$389$	1.38053	−	3.33289i	0.0699955	−	0.168984i	0.955006	+	0.296588i	$0.0958487\pi$
$390$	−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	0.966160	+	0.257944i	$0.0830450\pi$
$397$	9.27254	+	22.3859i	0.465376	+	1.12352i	−0.500784	+	0.865572i	$0.666955\pi$
$398$	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	$-0.920498\pi$
$401$		−	9.89930i		−	0.494348i	0.968971	−	0.247174i	$-0.0795018\pi$
$402$	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	0.992143	+	0.125106i	$0.0399271\pi$
$409$	22.5950	+	22.5950i	1.11725	+	1.11725i	0.125106	+	0.992143i	$0.460073\pi$
$410$	−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	−0.424759	−	0.905306i	$-0.639641\pi$
$419$	−1.73910	+	0.720360i	−0.0849607	+	0.0351919i	0.339798	+	0.940498i	$0.389641\pi$
$420$	0.813741	−	0.0987035i	0.0397065	−	0.00481624i
$421$	10.8523	−	26.1998i	0.528910	−	1.27690i	−0.403328	−	0.915055i	$-0.632147\pi$
$421$	10.8523	−	26.1998i	0.528910	−	1.27690i	0.932238	−	0.361846i	$-0.117853\pi$
$422$	−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	$-0.864114\pi$
$431$		−	17.1918i		−	0.828100i	0.910254	−	0.414050i	$-0.135886\pi$
$432$	18.3748	+	2.80127i	0.884059	+	0.134776i
$433$		−	21.8067i		−	1.04796i	−0.851730	−	0.523982i	$-0.824446\pi$
$433$		−	21.8067i		−	1.04796i	0.851730	−	0.523982i	$-0.175554\pi$
$434$	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	−0.0917084	−	0.995786i	$-0.529233\pi$
$439$	18.9425	−	18.9425i	0.904078	−	0.904078i	0.995786	+	0.0917084i	$0.0292328\pi$
$440$	−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	−0.433905	−	0.900959i	$-0.642864\pi$
$443$	10.7340	−	25.9141i	0.509986	−	1.23122i	0.943891	−	0.330257i	$-0.107136\pi$
$444$	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	−0.782861	−	0.622197i	$-0.786240\pi$
$457$	−3.43461	+	3.43461i	−0.160664	+	0.160664i	0.622197	+	0.782861i	$0.286240\pi$
$458$	−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	0.982026	−	0.188748i	$-0.0604428\pi$
$461$	3.31004	+	7.99114i	0.154164	+	0.372185i	−0.827862	+	0.560932i	$0.810443\pi$
$462$	−1.56472	−	3.21413i	−0.0727974	−	0.149535i
$463$			21.6208i			1.00480i	0.864634	+	0.502401i	$0.167550\pi$
$463$			21.6208i			1.00480i	−0.864634	+	0.502401i	$0.832450\pi$
$464$	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	0.758242	−	0.651974i	$-0.226059\pi$
$467$	−5.16334	−	12.4654i	−0.238931	−	0.576831i	−0.997173	+	0.0751430i	$0.976059\pi$
$468$	−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	−0.999305	−	0.0372822i	$-0.988130\pi$
$487$	−22.8755	−	22.8755i	−1.03659	−	1.03659i	−0.0372822	−	0.999305i	$-0.511870\pi$
$488$	−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	−0.254242	−	0.967141i	$-0.581826\pi$
$491$	−24.7708	−	10.2604i	−1.11789	−	0.463045i	−0.863648	+	0.504095i	$0.831826\pi$
$492$	−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	0.771562	−	0.636154i	$-0.219476\pi$
$499$	−5.00028	−	12.0717i	−0.223843	−	0.540405i	−0.995406	+	0.0957485i	$0.969476\pi$
$500$	−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	−0.570544	−	0.821267i	$-0.693268\pi$
$503$	5.62313	−	5.62313i	0.250723	−	0.250723i	0.821267	+	0.570544i	$0.193268\pi$
$504$	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	−0.703739	−	0.710459i	$-0.748487\pi$
$509$	−15.7699	+	6.53209i	−0.698987	+	0.289530i	0.00475194	+	0.999989i	$0.498487\pi$
$510$	−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	0.229330	−	0.973349i	$-0.426346\pi$
$521$	27.4517	−	27.4517i	1.20268	−	1.20268i	0.973349	−	0.229330i	$-0.0736536\pi$
$522$	3.11221	−	3.51252i	0.136218	−	0.153739i
$523$	−34.9352	−	14.4706i	−1.52761	−	0.632757i	−0.548512	−	0.836143i	$-0.684806\pi$
$523$	−34.9352	−	14.4706i	−1.52761	−	0.632757i	−0.979099	+	0.203385i	$0.934806\pi$
$524$	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	−0.384428	−	0.923155i	$-0.625601\pi$
$541$	−0.0811782	+	0.0336251i	−0.00349012	+	0.00144566i	0.380938	+	0.924601i	$0.375601\pi$
$542$	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	−0.636943	−	0.770911i	$-0.719801\pi$
$547$	−12.6813	+	5.25276i	−0.542212	+	0.224592i	0.0947302	+	0.995503i	$0.469801\pi$
$548$	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	0.876457	−	0.481481i	$-0.159901\pi$
$557$	−1.97657	−	4.77187i	−0.0837500	−	0.202190i	−0.960207	+	0.279290i	$0.909901\pi$
$558$	−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	−0.953139	−	0.302533i	$-0.902168\pi$
$563$	−11.6999	−	28.2460i	−0.493091	−	1.19043i	0.460048	−	0.887894i	$-0.347832\pi$
$564$	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	0.950877	−	0.309569i	$-0.100185\pi$
$569$	15.2976	+	15.2976i	0.641308	+	0.641308i	−0.309569	+	0.950877i	$0.600185\pi$
$570$	−0.128093	+	0.00774023i	−0.00536523	+	0.000324202i
$571$	−4.17965	+	10.0906i	−0.174913	+	0.422277i	−0.986886	−	0.161417i	$-0.948393\pi$
$571$	−4.17965	+	10.0906i	−0.174913	+	0.422277i	0.811973	+	0.583695i	$0.198393\pi$
$572$	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	0.987106	−	0.160067i	$-0.0511709\pi$
$587$	38.0844	+	15.7751i	1.57191	+	0.651107i	0.584805	+	0.811174i	$0.301171\pi$
$588$	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	$-0.716911\pi$
$593$		−	37.8260i		−	1.55333i	0.629916	−	0.776663i	$-0.283089\pi$
$594$	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	−0.0690998	+	0.997610i	$0.522013\pi$
$599$	−26.1072	+	26.1072i	−1.06671	+	1.06671i	−0.997610	+	0.0690998i	$0.977987\pi$
$600$	2.17897	+	11.9028i	0.0889561	+	0.485928i
$601$	14.4627	+	14.4627i	0.589944	+	0.589944i	0.937616	−	0.347672i	$-0.113028\pi$
$601$	14.4627	+	14.4627i	0.589944	+	0.589944i	−0.347672	+	0.937616i	$0.613028\pi$
$602$	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	0.583853	+	0.811859i	$0.301544\pi$
$613$	−9.97940	+	24.0924i	−0.403064	+	0.973083i	−0.986918	+	0.161224i	$0.948456\pi$
$614$	−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	−0.998658	−	0.0517933i	$-0.983506\pi$
$617$	−23.5196	+	23.5196i	−0.946865	+	0.946865i	0.0517933	+	0.998658i	$0.483506\pi$
$618$	1.58862	+	1.40757i	0.0639038	+	0.0566209i
$619$	38.4562	+	15.9291i	1.54569	+	0.640244i	0.982529	−	0.186107i	$-0.0595871\pi$
$619$	38.4562	+	15.9291i	1.54569	+	0.640244i	0.563156	+	0.826351i	$0.309587\pi$
$620$	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	−0.441267	−	0.897376i	$-0.645471\pi$
$631$	11.4573	−	11.4573i	0.456108	−	0.456108i	0.897376	+	0.441267i	$0.145471\pi$
$632$	−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	−0.819805	−	0.572643i	$-0.805918\pi$
$643$	−25.2199	+	10.4464i	−0.994574	+	0.411966i	−0.174770	+	0.984609i	$0.555918\pi$
$644$	−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	0.901454	−	0.432874i	$-0.142500\pi$
$647$	11.9189	+	11.9189i	0.468580	+	0.468580i	−0.432874	+	0.901454i	$0.642500\pi$
$648$	−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	−0.841139	−	0.540819i	$-0.818115\pi$
$653$	−16.0678	−	38.7910i	−0.628780	−	1.51801i	0.212359	−	0.977192i	$-0.431885\pi$
$654$	−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	0.999769	−	0.0214709i	$-0.00683492\pi$
$659$	7.12738	+	17.2070i	0.277643	+	0.670291i	−0.722126	+	0.691762i	$0.756835\pi$
$660$	−2.02057	+	1.13928i	−0.0786508	+	0.0443463i
$661$	33.8178	+	14.0078i	1.31536	+	0.544840i	0.926444	−	0.376434i	$-0.122850\pi$
$661$	33.8178	+	14.0078i	1.31536	+	0.544840i	0.388916	+	0.921273i	$0.372850\pi$
$662$	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	0.692851	+	0.721080i	$0.256354\pi$
$677$	−7.98658	+	19.2813i	−0.306949	+	0.741041i	−0.999801	+	0.0199610i	$0.993646\pi$
$678$	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	0.591450	−	0.806342i	$-0.298556\pi$
$683$	11.4860	+	4.75764i	0.439498	+	0.182046i	−0.151952	+	0.988388i	$0.548556\pi$
$684$	−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	0.969819	+	0.243825i	$0.0784023\pi$
$691$	11.9990	+	28.9682i	0.456464	+	1.10200i	−0.513355	+	0.858176i	$0.671598\pi$
$692$	−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	−0.988859	−	0.148856i	$-0.952441\pi$
$701$	−41.9077	+	17.3587i	−1.58283	+	0.655630i	−0.593971	+	0.804486i	$0.702441\pi$
$702$	−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	−0.337569	−	0.941301i	$-0.609605\pi$
$709$	15.0903	−	36.4312i	0.566728	−	1.36820i	0.904298	−	0.426902i	$-0.140395\pi$
$710$	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	$0.430849\pi$
$719$			52.3678i			1.95299i	−0.215538	+	0.976495i	$0.569151\pi$
$720$	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	0.0233314	−	0.999728i	$-0.492573\pi$
$727$	27.5847	−	27.5847i	1.02306	−	1.02306i	0.999728	−	0.0233314i	$-0.00742728\pi$
$728$	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	−0.802648	−	0.596453i	$-0.796576\pi$
$733$	−25.6783	+	10.6363i	−0.948449	+	0.392861i	−0.145801	+	0.989314i	$0.546576\pi$
$734$	−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	−0.222344	−	0.974968i	$-0.571371\pi$
$739$	8.42293	−	3.48889i	0.309842	−	0.128341i	0.532186	+	0.846627i	$0.321371\pi$
$740$	−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	0.994915	−	0.100716i	$-0.0321135\pi$
$743$	24.3741	+	24.3741i	0.894199	+	0.894199i	−0.100716	+	0.994915i	$0.532113\pi$
$744$	−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	$0.391290\pi$
$751$			51.6433i			1.88449i	−0.334922	+	0.942246i	$0.608710\pi$
$752$	−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	−0.188018	−	0.982165i	$-0.560206\pi$
$757$	−27.9391	−	11.5727i	−1.01546	−	0.420619i	−0.827445	+	0.561547i	$0.810206\pi$
$758$	−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	0.503340	−	0.864088i	$-0.332104\pi$
$761$	−9.95169	−	9.95169i	−0.360748	−	0.360748i	−0.864088	+	0.503340i	$0.832104\pi$
$762$	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	−0.284397	−	0.958707i	$-0.591793\pi$
$773$	16.5319	−	39.9115i	0.594610	−	1.43552i	0.879007	−	0.476809i	$-0.158207\pi$
$774$	−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	0.964219	−	0.265109i	$-0.0854079\pi$
$787$	2.66376	+	6.43089i	0.0949528	+	0.229236i	−0.869266	+	0.494345i	$0.835408\pi$
$788$	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	−0.827621	−	0.561288i	$-0.810306\pi$
$797$	−28.6814	+	11.8802i	−1.01595	+	0.420819i	−0.188326	+	0.982107i	$0.560306\pi$
$798$	−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	−0.163557	−	0.986534i	$-0.552297\pi$
$809$	23.4079	−	23.4079i	0.822977	−	0.822977i	0.986534	+	0.163557i	$0.0522968\pi$
$810$	−1.19261	−	1.05669i	−0.0419040	−	0.0371283i
$811$	−2.08381	−	0.863141i	−0.0731723	−	0.0303090i	0.345797	−	0.938309i	$-0.387609\pi$
$811$	−2.08381	−	0.863141i	−0.0731723	−	0.0303090i	−0.418969	+	0.908000i	$0.637609\pi$
$812$	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	0.0786064	−	0.996906i	$-0.474953\pi$
$821$	−16.3532	−	6.77370i	−0.570729	−	0.236404i	−0.649336	+	0.760502i	$0.724953\pi$
$822$	6.89968	−	7.78715i	0.240654	−	0.271608i
$823$	25.7691	−	25.7691i	0.898255	−	0.898255i	−0.0970271	−	0.995282i	$-0.530933\pi$
$823$	25.7691	−	25.7691i	0.898255	−	0.898255i	0.995282	+	0.0970271i	$0.0309334\pi$
$824$	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	−0.481134	−	0.876647i	$-0.659775\pi$
$827$	13.7738	−	33.2529i	0.478962	−	1.15632i	0.960096	−	0.279670i	$-0.0902249\pi$
$828$	20.3636	−	25.9855i	0.707683	−	0.903060i
$829$	−13.6960	+	5.67306i	−0.475681	+	0.197033i	−0.607625	−	0.794224i	$-0.707878\pi$
$829$	−13.6960	+	5.67306i	−0.475681	+	0.197033i	0.131945	+	0.991257i	$0.457878\pi$
$830$	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	0.748347	−	0.663307i	$-0.230848\pi$
$839$	2.46322	+	2.46322i	0.0850399	+	0.0850399i	−0.663307	+	0.748347i	$0.730848\pi$
$840$	−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	0.879207	−	0.476440i	$-0.158073\pi$
$853$	33.9962	+	14.0817i	1.16401	+	0.482147i	0.284800	+	0.958587i	$0.408073\pi$
$854$	−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	0.684552	−	0.728964i	$-0.259998\pi$
$857$	−1.30014	−	1.30014i	−0.0444118	−	0.0444118i	−0.728964	+	0.684552i	$0.759998\pi$
$858$	−0.445766	−	7.37699i	−0.0152182	−	0.251846i
$859$	7.44491	−	17.9736i	0.254017	−	0.613251i	−0.744504	−	0.667618i	$-0.767314\pi$
$859$	7.44491	−	17.9736i	0.254017	−	0.613251i	0.998521	+	0.0543667i	$0.0173140\pi$
$860$	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	−0.999707	−	0.0241924i	$-0.992299\pi$
$877$	−9.17785	−	22.1573i	−0.309914	−	0.748199i	0.689793	−	0.724006i	$-0.257701\pi$
$878$	−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	$-0.988903\pi$
$881$		−	2.06908i		−	0.0697090i	0.999392	−	0.0348545i	$-0.0110968\pi$
$882$	1.36314	+	2.80007i	0.0458994	+	0.0942831i
$883$	−11.0536	−	26.6857i	−0.371982	−	0.898044i	−0.993414	−	0.114576i	$-0.963449\pi$
$883$	−11.0536	−	26.6857i	−0.371982	−	0.898044i	0.621432	−	0.783468i	$-0.286551\pi$
$884$	−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	−0.610394	−	0.792098i	$-0.708989\pi$
$887$	5.41162	−	5.41162i	0.181704	−	0.181704i	0.792098	+	0.610394i	$0.208989\pi$
$888$	−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	0.834481	−	0.551036i	$-0.185767\pi$
$907$	31.1677	+	12.9101i	1.03491	+	0.428673i	0.200426	+	0.979709i	$0.435767\pi$
$908$	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	$0.0170786\pi$
$911$			3.23730i			0.107256i	−0.998561	+	0.0536282i	$0.982921\pi$
$912$	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	−0.0584021	+	0.998293i	$0.518601\pi$
$919$	−32.0337	+	32.0337i	−1.05670	+	1.05670i	−0.998293	+	0.0584021i	$0.981399\pi$
$920$	−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	−0.725129	−	0.688613i	$-0.758220\pi$
$937$	−1.11776	+	1.11776i	−0.0365156	+	0.0365156i	0.688613	+	0.725129i	$0.258220\pi$
$938$	−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	−0.944553	−	0.328359i	$-0.893504\pi$
$941$	−15.6090	−	37.6834i	−0.508838	−	1.22844i	0.435715	−	0.900085i	$-0.356496\pi$
$942$	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	−0.830676	−	0.556756i	$-0.812046\pi$
$947$	−19.6022	−	47.3239i	−0.636985	−	1.53782i	0.193691	−	0.981063i	$-0.437954\pi$
$948$	−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	0.791270	−	0.611467i	$-0.209420\pi$
$953$	5.55062	+	5.55062i	0.179802	+	0.179802i	−0.611467	+	0.791270i	$0.709420\pi$
$954$	−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	0.395370	−	0.918522i	$-0.370616\pi$
$967$	−16.2683	−	16.2683i	−0.523152	−	0.523152i	−0.918522	+	0.395370i	$0.870616\pi$
$968$	−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	−0.00149157	−	0.999999i	$-0.500475\pi$
$971$	−22.1134	−	9.15966i	−0.709652	−	0.293948i	−0.708161	+	0.706051i	$0.750475\pi$
$972$	−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	$0.0234642\pi$
$977$			4.60405i			0.147296i	−0.997284	+	0.0736482i	$0.976536\pi$
$978$	−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	−0.315384	−	0.948964i	$-0.602133\pi$
$983$	19.8645	−	19.8645i	0.633580	−	0.633580i	0.948964	+	0.315384i	$0.102133\pi$
$984$	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	0.351280	+	0.936270i	$0.385746\pi$
$997$	−17.6555	+	42.6242i	−0.559156	+	1.34992i	−0.910436	+	0.413651i	$0.864254\pi$
$998$	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.85.1	yes	52
4.3	odd	2		896.2.u.c.561.9		52
32.3	odd	8		896.2.u.c.337.9		52
32.29	even	8	inner	224.2.u.c.29.1	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.1	✓	52	32.29	even	8	inner
224.2.u.c.85.1	yes	52	1.1	even	1	trivial
896.2.u.c.337.9		52	32.3	odd	8
896.2.u.c.561.9		52	4.3	odd	2

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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