LMFDB - Embedded newform 804.2.c.b.671.59

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.59
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.60

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.227794 - 1.39575i) q^{2} +(-1.01672 + 1.40224i) q^{3} +(-1.89622 + 0.635885i) q^{4} -3.23506i q^{5} +(2.18877 + 1.09967i) q^{6} -2.61082i q^{7} +(1.31948 + 2.50179i) q^{8} +(-0.932552 - 2.85138i) q^{9} +O(q^{10})$	\(q+(-0.227794 - 1.39575i) q^{2} +(-1.01672 + 1.40224i) q^{3} +(-1.89622 + 0.635885i) q^{4} -3.23506i q^{5} +(2.18877 + 1.09967i) q^{6} -2.61082i q^{7} +(1.31948 + 2.50179i) q^{8} +(-0.932552 - 2.85138i) q^{9} +(-4.51533 + 0.736926i) q^{10} +4.15873 q^{11} +(1.03627 - 3.30547i) q^{12} -2.99057 q^{13} +(-3.64404 + 0.594727i) q^{14} +(4.53633 + 3.28916i) q^{15} +(3.19130 - 2.41155i) q^{16} +1.08168i q^{17} +(-3.76737 + 1.95113i) q^{18} -1.12656i q^{19} +(2.05713 + 6.13439i) q^{20} +(3.66099 + 2.65447i) q^{21} +(-0.947332 - 5.80453i) q^{22} -3.92491 q^{23} +(-4.84966 - 0.693400i) q^{24} -5.46562 q^{25} +(0.681234 + 4.17409i) q^{26} +(4.94646 + 1.59140i) q^{27} +(1.66018 + 4.95068i) q^{28} -6.99278i q^{29} +(3.55749 - 7.08082i) q^{30} +5.46602i q^{31} +(-4.09288 - 3.90491i) q^{32} +(-4.22827 + 5.83153i) q^{33} +(1.50976 - 0.246400i) q^{34} -8.44615 q^{35} +(3.58147 + 4.81384i) q^{36} -9.05940 q^{37} +(-1.57240 + 0.256624i) q^{38} +(3.04058 - 4.19350i) q^{39} +(8.09345 - 4.26860i) q^{40} -11.0925i q^{41} +(2.87102 - 5.71449i) q^{42} +4.33948i q^{43} +(-7.88586 + 2.64447i) q^{44} +(-9.22438 + 3.01686i) q^{45} +(0.894070 + 5.47818i) q^{46} -7.28933 q^{47} +(0.136910 + 6.92685i) q^{48} +0.183642 q^{49} +(1.24503 + 7.62862i) q^{50} +(-1.51678 - 1.09977i) q^{51} +(5.67079 - 1.90166i) q^{52} +7.29838i q^{53} +(1.09442 - 7.26652i) q^{54} -13.4537i q^{55} +(6.53172 - 3.44492i) q^{56} +(1.57971 + 1.14540i) q^{57} +(-9.76015 + 1.59291i) q^{58} -10.7958 q^{59} +(-10.6934 - 3.35239i) q^{60} -4.35052 q^{61} +(7.62919 - 1.24513i) q^{62} +(-7.44442 + 2.43472i) q^{63} +(-4.51794 + 6.60214i) q^{64} +9.67469i q^{65} +(9.10252 + 4.57321i) q^{66} +1.00000i q^{67} +(-0.687826 - 2.05111i) q^{68} +(3.99054 - 5.50367i) q^{69} +(1.92398 + 11.7887i) q^{70} -6.41384 q^{71} +(5.90307 - 6.09539i) q^{72} -7.59766 q^{73} +(2.06367 + 12.6446i) q^{74} +(5.55702 - 7.66411i) q^{75} +(0.716363 + 2.13621i) q^{76} -10.8577i q^{77} +(-6.54569 - 3.28863i) q^{78} -1.40839i q^{79} +(-7.80153 - 10.3241i) q^{80} +(-7.26069 + 5.31811i) q^{81} +(-15.4824 + 2.52681i) q^{82} +8.22823 q^{83} +(-8.62998 - 2.70550i) q^{84} +3.49931 q^{85} +(6.05682 - 0.988506i) q^{86} +(9.80555 + 7.10971i) q^{87} +(5.48736 + 10.4043i) q^{88} +2.52086i q^{89} +(6.31203 + 12.1877i) q^{90} +7.80784i q^{91} +(7.44249 - 2.49579i) q^{92} +(-7.66468 - 5.55743i) q^{93} +(1.66046 + 10.1741i) q^{94} -3.64450 q^{95} +(9.63694 - 1.76898i) q^{96} +6.47906 q^{97} +(-0.0418325 - 0.256318i) q^{98} +(-3.87823 - 11.8581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.227794	−	1.39575i	−0.161074	−	0.986942i
$2$	−0.227794	−	1.39575i	−0.161074	−	0.986942i
$3$	−1.01672	+	1.40224i	−0.587005	+	0.809583i
$3$	−1.01672	+	1.40224i	−0.587005	+	0.809583i
$4$	−1.89622	+	0.635885i	−0.948110	+	0.317942i
$5$		−	3.23506i		−	1.44676i	−0.690448	−	0.723382i	$-0.742587\pi$
$5$		−	3.23506i		−	1.44676i	0.690448	−	0.723382i	$-0.257413\pi$
$6$	2.18877	+	1.09967i	0.893564	+	0.448937i
$7$		−	2.61082i		−	0.986796i	−0.869804	−	0.493398i	$-0.835755\pi$
$7$		−	2.61082i		−	0.986796i	0.869804	−	0.493398i	$-0.164245\pi$
$8$	1.31948	+	2.50179i	0.466507	+	0.884518i
$9$	−0.932552	−	2.85138i	−0.310851	−	0.950459i
$10$	−4.51533	+	0.736926i	−1.42787	+	0.233037i
$11$	4.15873			1.25390			0.626952	−	0.779058i	$-0.284302\pi$
$11$	4.15873			1.25390			0.626952	+	0.779058i	$0.284302\pi$
$12$	1.03627	−	3.30547i	0.299144	−	0.954208i
$13$	−2.99057			−0.829436			−0.414718	−	0.909950i	$-0.636120\pi$
$13$	−2.99057			−0.829436			−0.414718	+	0.909950i	$0.636120\pi$
$14$	−3.64404	+	0.594727i	−0.973910	+	0.158948i
$15$	4.53633	+	3.28916i	1.17128	+	0.849257i
$16$	3.19130	−	2.41155i	0.797825	−	0.602889i
$17$			1.08168i			0.262347i	0.991359	+	0.131173i	$0.0418744\pi$
$17$			1.08168i			0.262347i	−0.991359	+	0.131173i	$0.958126\pi$
$18$	−3.76737	+	1.95113i	−0.887978	+	0.459886i
$19$		−	1.12656i		−	0.258451i	−0.991615	−	0.129225i	$-0.958751\pi$
$19$		−	1.12656i		−	0.258451i	0.991615	−	0.129225i	$-0.0412491\pi$
$20$	2.05713	+	6.13439i	0.459987	+	1.37169i
$21$	3.66099	+	2.65447i	0.798893	+	0.579254i
$22$	−0.947332	−	5.80453i	−0.201972	−	1.23753i
$23$	−3.92491			−0.818400			−0.409200	−	0.912445i	$-0.634192\pi$
$23$	−3.92491			−0.818400			−0.409200	+	0.912445i	$0.634192\pi$
$24$	−4.84966	−	0.693400i	−0.989933	−	0.141540i
$25$	−5.46562			−1.09312
$26$	0.681234	+	4.17409i	0.133601	+	0.818606i
$27$	4.94646	+	1.59140i	0.951946	+	0.306264i
$28$	1.66018	+	4.95068i	0.313744	+	0.935591i
$29$		−	6.99278i		−	1.29853i	−0.760564	−	0.649263i	$-0.775077\pi$
$29$		−	6.99278i		−	1.29853i	0.760564	−	0.649263i	$-0.224923\pi$
$30$	3.55749	−	7.08082i	0.649505	−	1.29277i
$31$			5.46602i			0.981727i	0.871237	+	0.490863i	$0.163319\pi$
$31$			5.46602i			0.981727i	−0.871237	+	0.490863i	$0.836681\pi$
$32$	−4.09288	−	3.90491i	−0.723526	−	0.690298i
$33$	−4.22827	+	5.83153i	−0.736047	+	1.01514i
$34$	1.50976	−	0.246400i	0.258921	−	0.0422573i
$35$	−8.44615			−1.42766
$36$	3.58147	+	4.81384i	0.596912	+	0.802307i
$37$	−9.05940			−1.48936			−0.744678	−	0.667423i	$-0.767397\pi$
$37$	−9.05940			−1.48936			−0.744678	+	0.667423i	$0.767397\pi$
$38$	−1.57240	+	0.256624i	−0.255076	+	0.0416298i
$39$	3.04058	−	4.19350i	0.486883	−	0.671498i
$40$	8.09345	−	4.26860i	1.27969	−	0.674925i
$41$		−	11.0925i		−	1.73236i	−0.499731	−	0.866180i	$-0.666568\pi$
$41$		−	11.0925i		−	1.73236i	0.499731	−	0.866180i	$-0.333432\pi$
$42$	2.87102	−	5.71449i	0.443009	−	0.881765i
$43$			4.33948i			0.661765i	0.943672	+	0.330882i	$0.107346\pi$
$43$			4.33948i			0.661765i	−0.943672	+	0.330882i	$0.892654\pi$
$44$	−7.88586	+	2.64447i	−1.18884	+	0.398669i
$45$	−9.22438	+	3.01686i	−1.37509	+	0.449727i
$46$	0.894070	+	5.47818i	0.131823	+	0.807714i
$47$	−7.28933			−1.06326			−0.531629	−	0.846977i	$-0.678420\pi$
$47$	−7.28933			−1.06326			−0.531629	+	0.846977i	$0.678420\pi$
$48$	0.136910	+	6.92685i	0.0197613	+	0.999805i
$49$	0.183642			0.0262346
$50$	1.24503	+	7.62862i	0.176074	+	1.07885i
$51$	−1.51678	−	1.09977i	−0.212391	−	0.153999i
$52$	5.67079	−	1.90166i	0.786397	−	0.263713i
$53$			7.29838i			1.00251i	0.865300	+	0.501255i	$0.167128\pi$
$53$			7.29838i			1.00251i	−0.865300	+	0.501255i	$0.832872\pi$
$54$	1.09442	−	7.26652i	0.148931	−	0.988848i
$55$		−	13.4537i		−	1.81410i
$56$	6.53172	−	3.44492i	0.872838	−	0.460347i
$57$	1.57971	+	1.14540i	0.209238	+	0.151712i
$58$	−9.76015	+	1.59291i	−1.28157	+	0.209159i
$59$	−10.7958			−1.40549			−0.702744	−	0.711443i	$-0.748042\pi$
$59$	−10.7958			−1.40549			−0.702744	+	0.711443i	$0.748042\pi$
$60$	−10.6934	−	3.35239i	−1.38051	−	0.432791i
$61$	−4.35052			−0.557028			−0.278514	−	0.960432i	$-0.589842\pi$
$61$	−4.35052			−0.557028			−0.278514	+	0.960432i	$0.589842\pi$
$62$	7.62919	−	1.24513i	0.968908	−	0.158131i
$63$	−7.44442	+	2.43472i	−0.937908	+	0.306746i
$64$	−4.51794	+	6.60214i	−0.564742	+	0.825267i
$65$			9.67469i			1.20000i
$66$	9.10252	+	4.57321i	1.12044	+	0.562923i
$67$			1.00000i			0.122169i
$67$			1.00000i			0.122169i
$68$	−0.687826	−	2.05111i	−0.0834111	−	0.248733i
$69$	3.99054	−	5.50367i	0.480405	−	0.662563i
$70$	1.92398	+	11.7887i	0.229959	+	1.40902i
$71$	−6.41384			−0.761182			−0.380591	−	0.924743i	$-0.624279\pi$
$71$	−6.41384			−0.761182			−0.380591	+	0.924743i	$0.624279\pi$
$72$	5.90307	−	6.09539i	0.695683	−	0.718348i
$73$	−7.59766			−0.889239			−0.444619	−	0.895720i	$-0.646661\pi$
$73$	−7.59766			−0.889239			−0.444619	+	0.895720i	$0.646661\pi$
$74$	2.06367	+	12.6446i	0.239897	+	1.46991i
$75$	5.55702	−	7.66411i	0.641669	−	0.884975i
$76$	0.716363	+	2.13621i	0.0821725	+	0.245040i
$77$		−	10.8577i		−	1.23735i
$78$	−6.54569	−	3.28863i	−0.741154	−	0.372364i
$79$		−	1.40839i		−	0.158456i	−0.996857	−	0.0792282i	$-0.974754\pi$
$79$		−	1.40839i		−	0.158456i	0.996857	−	0.0792282i	$-0.0252456\pi$
$80$	−7.80153	−	10.3241i	−0.872237	−	1.15426i
$81$	−7.26069	+	5.31811i	−0.806744	+	0.590901i
$82$	−15.4824	+	2.52681i	−1.70974	+	0.279039i
$83$	8.22823			0.903165			0.451583	−	0.892229i	$-0.350860\pi$
$83$	8.22823			0.903165			0.451583	+	0.892229i	$0.350860\pi$
$84$	−8.62998	−	2.70550i	−0.941608	−	0.295194i
$85$	3.49931			0.379553
$86$	6.05682	−	0.988506i	0.653124	−	0.106593i
$87$	9.80555	+	7.10971i	1.05126	+	0.762241i
$88$	5.48736	+	10.4043i	0.584955	+	1.10910i
$89$			2.52086i			0.267211i	0.991035	+	0.133606i	$0.0426555\pi$
$89$			2.52086i			0.267211i	−0.991035	+	0.133606i	$0.957344\pi$
$90$	6.31203	+	12.1877i	0.665346	+	1.28469i
$91$			7.80784i			0.818484i
$92$	7.44249	−	2.49579i	0.775934	−	0.260204i
$93$	−7.66468	−	5.55743i	−0.794790	−	0.576278i
$94$	1.66046	+	10.1741i	0.171264	+	1.04937i
$95$	−3.64450			−0.373917
$96$	9.63694	−	1.76898i	0.983567	−	0.180546i
$97$	6.47906			0.657849			0.328925	−	0.944356i	$-0.393314\pi$
$97$	6.47906			0.657849			0.328925	+	0.944356i	$0.393314\pi$
$98$	−0.0418325	−	0.256318i	−0.00422572	−	0.0258920i
$99$	−3.87823	−	11.8581i	−0.389777	−	1.19178i
$100$	10.3640	−	3.47550i	1.03640	−	0.347550i
$101$		−	15.2307i		−	1.51551i	−0.652538	−	0.757756i	$-0.726296\pi$
$101$		−	15.2307i		−	1.51551i	0.652538	−	0.757756i	$-0.273704\pi$
$102$	−1.18949	+	2.36756i	−0.117777	+	0.234423i
$103$		−	12.5990i		−	1.24141i	−0.784043	−	0.620706i	$-0.786846\pi$
$103$		−	12.5990i		−	1.24141i	0.784043	−	0.620706i	$-0.213154\pi$
$104$	−3.94601	−	7.48180i	−0.386938	−	0.733651i
$105$	8.58739	−	11.8435i	0.838043	−	1.15581i
$106$	10.1867	−	1.66252i	0.989419	−	0.161479i
$107$	17.1498			1.65793			0.828965	−	0.559300i	$-0.188930\pi$
$107$	17.1498			1.65793			0.828965	+	0.559300i	$0.188930\pi$
$108$	−10.3915	+	0.127739i	−0.999924	+	0.0122917i
$109$	16.0729			1.53950			0.769751	−	0.638344i	$-0.220380\pi$
$109$	16.0729			1.53950			0.769751	+	0.638344i	$0.220380\pi$
$110$	−18.7780	+	3.06468i	−1.79041	+	0.292205i
$111$	9.21090	−	12.7035i	0.874260	−	1.20576i
$112$	−6.29612	−	8.33190i	−0.594928	−	0.787290i
$113$			3.02772i			0.284824i	0.989807	+	0.142412i	$0.0454857\pi$
$113$			3.02772i			0.284824i	−0.989807	+	0.142412i	$0.954514\pi$
$114$	1.23884	−	2.46579i	0.116028	−	0.230942i
$115$			12.6973i			1.18403i
$116$	4.44660	+	13.2598i	0.412856	+	1.23115i
$117$	2.78887	+	8.52725i	0.257831	+	0.788345i
$118$	2.45920	+	15.0681i	0.226388	+	1.38714i
$119$	2.82407			0.258882
$120$	−2.24319	+	15.6889i	−0.204774	+	1.43220i
$121$	6.29501			0.572274
$122$	0.991022	+	6.07223i	0.0897229	+	0.549754i
$123$	15.5544	+	11.2780i	1.40249	+	1.01690i
$124$	−3.47576	−	10.3648i	−0.312133	−	0.930785i
$125$			1.50630i			0.134728i
$126$	5.09405	+	9.83591i	0.453814	+	0.876253i
$127$			19.8009i			1.75705i	0.477699	+	0.878523i	$0.341471\pi$
$127$			19.8009i			1.75705i	−0.477699	+	0.878523i	$0.658529\pi$
$128$	10.2441	+	4.80198i	0.905457	+	0.424439i
$129$	−6.08499	−	4.41205i	−0.535754	−	0.388459i
$130$	13.5034	−	2.20383i	1.18433	−	0.193289i
$131$	7.15906			0.625490			0.312745	−	0.949837i	$-0.398751\pi$
$131$	7.15906			0.625490			0.312745	+	0.949837i	$0.398751\pi$
$132$	4.30955	−	13.7466i	0.375098	−	1.19648i
$133$	−2.94124			−0.255038
$134$	1.39575	−	0.227794i	0.120574	−	0.0196784i
$135$	5.14826	−	16.0021i	0.443092	−	1.37724i
$136$	−2.70615	+	1.42726i	−0.232050	+	0.122387i
$137$			2.53021i			0.216171i	0.994142	+	0.108085i	$0.0344720\pi$
$137$			2.53021i			0.216171i	−0.994142	+	0.108085i	$0.965528\pi$
$138$	−8.59075	−	4.31609i	−0.731293	−	0.367410i
$139$			3.11696i			0.264377i	0.991225	+	0.132189i	$0.0422005\pi$
$139$			3.11696i			0.264377i	−0.991225	+	0.132189i	$0.957800\pi$
$140$	16.0158	−	5.37078i	1.35358	−	0.453913i
$141$	7.41123	−	10.2214i	0.624138	−	0.860796i
$142$	1.46103	+	8.95209i	0.122607	+	0.751243i
$143$	−12.4370			−1.04003
$144$	−9.85230	−	6.85070i	−0.821025	−	0.570892i
$145$	−22.6221			−1.87866
$146$	1.73070	+	10.6044i	0.143234	+	0.877627i
$147$	−0.186713	+	0.257510i	−0.0153998	+	0.0212391i
$148$	17.1786	−	5.76074i	1.41207	−	0.473530i
$149$		−	4.28321i		−	0.350894i	−0.984489	−	0.175447i	$-0.943863\pi$
$149$		−	4.28321i		−	0.350894i	0.984489	−	0.175447i	$-0.0561371\pi$
$150$	−11.9630	−	6.01035i	−0.976775	−	0.490743i
$151$		−	10.6716i		−	0.868441i	−0.900807	−	0.434221i	$-0.857024\pi$
$151$		−	10.6716i		−	0.868441i	0.900807	−	0.434221i	$-0.142976\pi$
$152$	2.81842	−	1.48648i	0.228604	−	0.120569i
$153$	3.08429	−	1.00873i	0.249350	−	0.0815506i
$154$	−15.1546	+	2.47331i	−1.22119	+	0.199305i
$155$	17.6829			1.42033
$156$	−3.09903	+	9.88526i	−0.248121	+	0.791455i
$157$	21.2525			1.69614			0.848068	−	0.529887i	$-0.177766\pi$
$157$	21.2525			1.69614			0.848068	+	0.529887i	$0.177766\pi$
$158$	−1.96576	+	0.320823i	−0.156387	+	0.0255233i
$159$	−10.2341	−	7.42042i	−0.811615	−	0.588478i
$160$	−12.6326	+	13.2407i	−0.998697	+	1.04677i
$161$			10.2472i			0.807594i
$162$	9.07668	+	8.92266i	0.713131	+	0.701030i
$163$		−	4.37045i		−	0.342320i	−0.985243	−	0.171160i	$-0.945248\pi$
$163$		−	4.37045i		−	0.342320i	0.985243	−	0.171160i	$-0.0547515\pi$
$164$	7.05356	+	21.0339i	0.550791	+	1.64247i
$165$	18.8654	+	13.6787i	1.46867	+	1.06489i
$166$	−1.87434	−	11.4845i	−0.145477	−	0.891372i
$167$	−20.8508			−1.61349			−0.806743	−	0.590902i	$-0.798772\pi$
$167$	−20.8508			−1.61349			−0.806743	+	0.590902i	$0.798772\pi$
$168$	−1.81034	+	12.6616i	−0.139671	+	0.976861i
$169$	−4.05646			−0.312036
$170$	−0.797121	−	4.88415i	−0.0611364	−	0.374597i
$171$	−3.21225	+	1.05058i	−0.245647	+	0.0803396i
$172$	−2.75941	−	8.22861i	−0.210403	−	0.627426i
$173$		−	7.75563i		−	0.589650i	−0.955551	−	0.294825i	$-0.904739\pi$
$173$		−	7.75563i		−	0.589650i	0.955551	−	0.294825i	$-0.0952614\pi$
$174$	7.68972	−	15.3056i	0.582956	−	1.16032i
$175$			14.2697i			1.07869i
$176$	13.2718	−	10.0290i	1.00040	−	0.755964i
$177$	10.9763	−	15.1382i	0.825028	−	1.13786i
$178$	3.51849	−	0.574237i	0.263722	−	0.0430409i
$179$	14.0070			1.04693			0.523465	−	0.852047i	$-0.324639\pi$
$179$	14.0070			1.04693			0.523465	+	0.852047i	$0.324639\pi$
$180$	15.5731	−	11.5863i	1.16075	−	0.863590i
$181$	4.51200			0.335374			0.167687	−	0.985840i	$-0.446370\pi$
$181$	4.51200			0.335374			0.167687	+	0.985840i	$0.446370\pi$
$182$	10.8978	−	1.77858i	0.807796	−	0.131837i
$183$	4.42328	−	6.10048i	0.326978	−	0.450960i
$184$	−5.17885	−	9.81932i	−0.381790	−	0.723890i
$185$			29.3077i			2.15475i
$186$	−6.01080	+	11.9639i	−0.440733	+	0.877235i
$187$			4.49842i			0.328957i
$188$	13.8222	−	4.63518i	1.00809	−	0.338055i
$189$	4.15484	−	12.9143i	0.302220	−	0.939377i
$190$	0.830193	+	5.08679i	0.0602285	+	0.369035i
$191$	−24.0356			−1.73915			−0.869577	−	0.493798i	$-0.835608\pi$
$191$	−24.0356			−1.73915			−0.869577	+	0.493798i	$0.835608\pi$
$192$	−4.66429	−	13.0478i	−0.336616	−	0.941642i
$193$	1.67928			0.120877			0.0604386	−	0.998172i	$-0.480750\pi$
$193$	1.67928			0.120877			0.0604386	+	0.998172i	$0.480750\pi$
$194$	−1.47589	−	9.04313i	−0.105963	−	0.649259i
$195$	−13.5662	−	9.83647i	−0.971498	−	0.704404i
$196$	−0.348226	+	0.116775i	−0.0248733	+	0.00834109i
$197$		−	23.3035i		−	1.66030i	−0.557537	−	0.830152i	$-0.688253\pi$
$197$		−	23.3035i		−	1.66030i	0.557537	−	0.830152i	$-0.311747\pi$
$198$	−15.6675	+	8.11422i	−1.11344	+	0.576653i
$199$		−	7.20815i		−	0.510973i	−0.966813	−	0.255486i	$-0.917764\pi$
$199$		−	7.20815i		−	0.510973i	0.966813	−	0.255486i	$-0.0822356\pi$
$200$	−7.21178	−	13.6738i	−0.509950	−	0.966887i
$201$	−1.40224	−	1.01672i	−0.0989064	−	0.0717141i
$202$	−21.2582	+	3.46946i	−1.49572	+	0.244110i
$203$	−18.2568			−1.28138
$204$	3.57547	+	1.12091i	0.250333	+	0.0784795i
$205$	−35.8850			−2.50632
$206$	−17.5850	+	2.86996i	−1.22520	+	0.199960i
$207$	3.66018	+	11.1914i	0.254400	+	0.777856i
$208$	−9.54383	+	7.21193i	−0.661745	+	0.500058i
$209$		−	4.68506i		−	0.324073i
$210$	−18.4867	−	9.28794i	−1.27570	−	0.640929i
$211$			8.65489i			0.595827i	0.954593	+	0.297914i	$0.0962907\pi$
$211$			8.65489i			0.595827i	−0.954593	+	0.297914i	$0.903709\pi$
$212$	−4.64093	−	13.8393i	−0.318740	−	0.950489i
$213$	6.52109	−	8.99374i	0.446818	−	0.616241i
$214$	−3.90661	−	23.9367i	−0.267050	−	1.63628i
$215$	14.0385			0.957417
$216$	2.54541	+	14.4748i	0.173193	+	0.984888i
$217$	14.2708			0.968764
$218$	−3.66130	−	22.4337i	−0.247974	−	1.51940i
$219$	7.72471	−	10.6537i	0.521988	−	0.719913i
$220$	8.55502	+	25.5112i	0.576780	+	1.71997i
$221$		−	3.23485i		−	0.217600i
$222$	−19.8290	−	9.96232i	−1.33083	−	0.668627i
$223$			14.5494i			0.974299i	0.873319	+	0.487150i	$0.161963\pi$
$223$			14.5494i			0.974299i	−0.873319	+	0.487150i	$0.838037\pi$
$224$	−10.1950	+	10.6858i	−0.681183	+	0.713972i
$225$	5.09697	+	15.5845i	0.339798	+	1.03897i
$226$	4.22593	−	0.689695i	0.281104	−	0.0458778i
$227$	5.67277			0.376515			0.188257	−	0.982120i	$-0.439716\pi$
$227$	5.67277			0.376515			0.188257	+	0.982120i	$0.439716\pi$
$228$	−3.72382	−	1.16742i	−0.246616	−	0.0773141i
$229$	−18.3662			−1.21367			−0.606837	−	0.794827i	$-0.707562\pi$
$229$	−18.3662			−1.21367			−0.606837	+	0.794827i	$0.707562\pi$
$230$	17.7223	−	2.89237i	1.16857	−	0.190717i
$231$	15.2251	+	11.0392i	1.00173	+	0.726328i
$232$	17.4945	−	9.22684i	1.14857	−	0.605771i
$233$		−	18.7939i		−	1.23123i	−0.788048	−	0.615613i	$-0.788908\pi$
$233$		−	18.7939i		−	1.23123i	0.788048	−	0.615613i	$-0.211092\pi$
$234$	11.2666	−	5.83501i	0.736521	−	0.381446i
$235$			23.5814i			1.53828i
$236$	20.4711	−	6.86486i	1.33256	−	0.446864i
$237$	1.97490	+	1.43194i	0.128284	+	0.0930147i
$238$	−0.643306	−	3.94169i	−0.0416993	−	0.255502i
$239$	−9.37631			−0.606503			−0.303251	−	0.952911i	$-0.598072\pi$
$239$	−9.37631			−0.606503			−0.303251	+	0.952911i	$0.598072\pi$
$240$	22.4088	−	0.442913i	1.44648	−	0.0285899i
$241$	11.7970			0.759913			0.379957	−	0.925004i	$-0.375939\pi$
$241$	11.7970			0.759913			0.379957	+	0.925004i	$0.375939\pi$
$242$	−1.43396	−	8.78624i	−0.0921787	−	0.564801i
$243$	−0.0751581	−	15.5883i	−0.00482140	−	0.999988i
$244$	8.24955	−	2.76643i	0.528123	−	0.177103i
$245$		−	0.594094i		−	0.0379553i
$246$	12.1981	−	24.2790i	0.777720	−	1.54797i
$247$			3.36907i			0.214369i
$248$	−13.6749	+	7.21232i	−0.868355	+	0.457983i
$249$	−8.36582	+	11.5379i	−0.530162	+	0.731188i
$250$	2.10242	−	0.343126i	0.132968	−	0.0217012i
$251$	−1.22232			−0.0771524			−0.0385762	−	0.999256i	$-0.512282\pi$
$251$	−1.22232			−0.0771524			−0.0385762	+	0.999256i	$0.512282\pi$
$252$	12.5681	−	9.35056i	0.791713	−	0.589030i
$253$	−16.3226			−1.02620
$254$	27.6371	−	4.51052i	1.73410	−	0.283015i
$255$	−3.55783	+	4.90687i	−0.222800	+	0.307280i
$256$	4.36881	−	15.3920i	0.273051	−	0.962000i
$257$		−	8.99599i		−	0.561154i	−0.959831	−	0.280577i	$-0.909474\pi$
$257$		−	8.99599i		−	0.561154i	0.959831	−	0.280577i	$-0.0905259\pi$
$258$	−4.77198	+	9.49815i	−0.297091	+	0.591329i
$259$			23.6524i			1.46969i
$260$	−6.15199	−	18.3453i	−0.381530	−	1.13773i
$261$	−19.9390	+	6.52113i	−1.23420	+	0.403648i
$262$	−1.63079	−	9.99224i	−0.100750	−	0.617322i
$263$	7.86586			0.485030			0.242515	−	0.970148i	$-0.422028\pi$
$263$	7.86586			0.485030			0.242515	+	0.970148i	$0.422028\pi$
$264$	−20.1684	−	2.88366i	−1.24128	−	0.177477i
$265$	23.6107			1.45039
$266$	0.669997	+	4.10523i	0.0410801	+	0.251708i
$267$	−3.53486	−	2.56302i	−0.216330	−	0.156854i
$268$	−0.635885	−	1.89622i	−0.0388428	−	0.115830i
$269$		−	24.1824i		−	1.47443i	−0.675660	−	0.737214i	$-0.736141\pi$
$269$		−	24.1824i		−	1.47443i	0.675660	−	0.737214i	$-0.263859\pi$
$270$	−23.5076	−	3.54050i	−1.43063	−	0.215468i
$271$		−	26.9981i		−	1.64002i	−0.572350	−	0.820009i	$-0.693968\pi$
$271$		−	26.9981i		−	1.64002i	0.572350	−	0.820009i	$-0.306032\pi$
$272$	2.60854	+	3.45198i	0.158166	+	0.209307i
$273$	−10.9485	−	7.93840i	−0.662631	−	0.480454i
$274$	3.53154	−	0.576366i	0.213348	−	0.0348196i
$275$	−22.7300			−1.37067
$276$	−4.06725	+	12.9737i	−0.244820	+	0.780924i
$277$	1.34161			0.0806097			0.0403049	−	0.999187i	$-0.487167\pi$
$277$	1.34161			0.0806097			0.0403049	+	0.999187i	$0.487167\pi$
$278$	4.35049	−	0.710024i	0.260925	−	0.0425844i
$279$	15.5857	−	5.09735i	0.933091	−	0.305170i
$280$	−11.1445	−	21.1305i	−0.666013	−	1.26279i
$281$			19.2066i			1.14577i	0.819636	+	0.572884i	$0.194176\pi$
$281$			19.2066i			1.14577i	−0.819636	+	0.572884i	$0.805824\pi$
$282$	−15.9547	−	8.01583i	−0.950089	−	0.477336i
$283$		−	25.8817i		−	1.53851i	−0.638944	−	0.769253i	$-0.720628\pi$
$283$		−	25.8817i		−	1.53851i	0.638944	−	0.769253i	$-0.279372\pi$
$284$	12.1620	−	4.07846i	0.721685	−	0.242012i
$285$	3.70544	−	5.11046i	0.219491	−	0.302717i
$286$	2.83307	+	17.3589i	0.167523	+	1.02645i
$287$	−28.9605			−1.70949
$288$	−7.31756	+	15.3119i	−0.431191	+	0.902261i
$289$	15.8300			0.931174
$290$	5.15316	+	31.5747i	0.302604	+	1.85413i
$291$	−6.58741	+	9.08520i	−0.386161	+	0.532584i
$292$	14.4068	−	4.83124i	0.843096	−	0.282727i
$293$			31.5384i			1.84249i	0.388981	+	0.921246i	$0.372827\pi$
$293$			31.5384i			1.84249i	−0.388981	+	0.921246i	$0.627173\pi$
$294$	0.401951	+	0.201945i	0.0234423	+	0.0117777i
$295$			34.9249i			2.03341i
$296$	−11.9537	−	22.6648i	−0.694795	−	1.31736i
$297$	20.5710	+	6.61818i	1.19365	+	0.384026i
$298$	−5.97827	+	0.975687i	−0.346312	+	0.0565200i
$299$	11.7377			0.678811
$300$	−5.66384	+	18.0665i	−0.327002	+	1.04307i
$301$	11.3296			0.653027
$302$	−14.8948	+	2.43092i	−0.857102	+	0.139884i
$303$	21.3571	+	15.4854i	1.22693	+	0.889613i
$304$	−2.71676	−	3.59520i	−0.155817	−	0.206199i
$305$			14.0742i			0.805887i
$306$	−2.11051	−	4.07510i	−0.120650	−	0.232958i
$307$		−	25.2342i		−	1.44019i	−0.693874	−	0.720097i	$-0.744097\pi$
$307$		−	25.2342i		−	1.44019i	0.693874	−	0.720097i	$-0.255903\pi$
$308$	6.90423	+	20.5885i	0.393405	+	1.17314i
$309$	17.6668	+	12.8096i	1.00503	+	0.728715i
$310$	−4.02806	−	24.6809i	−0.228778	−	1.40178i
$311$	−15.4442			−0.875763			−0.437881	−	0.899033i	$-0.644271\pi$
$311$	−15.4442			−0.875763			−0.437881	+	0.899033i	$0.644271\pi$
$312$	14.5033	+	2.07367i	0.821086	+	0.117398i
$313$	9.59148			0.542143			0.271071	−	0.962559i	$-0.412622\pi$
$313$	9.59148			0.542143			0.271071	+	0.962559i	$0.412622\pi$
$314$	−4.84119	−	29.6632i	−0.273204	−	1.67399i
$315$	7.87647	+	24.0831i	0.443789	+	1.35693i
$316$	0.895574	+	2.67062i	0.0503800	+	0.150234i
$317$		−	2.95546i		−	0.165995i	−0.996550	−	0.0829976i	$-0.973551\pi$
$317$		−	2.95546i		−	0.165995i	0.996550	−	0.0829976i	$-0.0264494\pi$
$318$	−8.02578	+	15.9745i	−0.450063	+	0.895806i
$319$		−	29.0810i		−	1.62823i
$320$	21.3583	+	14.6158i	1.19397	+	0.817049i
$321$	−17.4365	+	24.0481i	−0.973213	+	1.34223i
$322$	14.3025	−	2.33425i	0.797049	−	0.130083i
$323$	1.21858			0.0678037
$324$	10.3862	−	14.7013i	0.577009	−	0.816738i
$325$	16.3453			0.906676
$326$	−6.10005	+	0.995561i	−0.337850	+	0.0551390i
$327$	−16.3416	+	22.5380i	−0.903695	+	1.24636i
$328$	27.7512	−	14.6364i	1.53230	−	0.808159i
$329$			19.0311i			1.04922i
$330$	14.7946	−	29.4472i	0.814417	−	1.62101i
$331$		−	3.38615i		−	0.186119i	−0.995661	−	0.0930597i	$-0.970335\pi$
$331$		−	3.38615i		−	0.186119i	0.995661	−	0.0930597i	$-0.0296648\pi$
$332$	−15.6025	+	5.23220i	−0.856300	+	0.287154i
$333$	8.44836	+	25.8318i	0.462967	+	1.41557i
$334$	4.74969	+	29.1025i	0.259891	+	1.59242i
$335$	3.23506			0.176750
$336$	18.0847	−	0.357447i	0.986603	−	0.0195003i
$337$	−30.7038			−1.67254			−0.836272	−	0.548314i	$-0.815270\pi$
$337$	−30.7038			−1.67254			−0.836272	+	0.548314i	$0.815270\pi$
$338$	0.924036	+	5.66180i	0.0502610	+	0.307961i
$339$	−4.24558	−	3.07835i	−0.230588	−	0.167193i
$340$	−6.63546	+	2.22516i	−0.359858	+	0.120676i
$341$			22.7317i			1.23099i
$342$	2.19807	+	4.24418i	0.118858	+	0.229499i
$343$		−	18.7552i		−	1.01268i
$344$	−10.8565	+	5.72586i	−0.585343	+	0.308718i
$345$	−17.8047	−	12.9097i	−0.958572	−	0.695032i
$346$	−10.8249	+	1.76668i	−0.581950	+	0.0949775i
$347$	−9.71409			−0.521480			−0.260740	−	0.965409i	$-0.583966\pi$
$347$	−9.71409			−0.521480			−0.260740	+	0.965409i	$0.583966\pi$
$348$	−23.1144	−	7.24638i	−1.23906	−	0.388447i
$349$	5.18227			0.277400			0.138700	−	0.990334i	$-0.455708\pi$
$349$	5.18227			0.277400			0.138700	+	0.990334i	$0.455708\pi$
$350$	19.9169	−	3.25055i	1.06460	−	0.173749i
$351$	−14.7928	−	4.75919i	−0.789579	−	0.254027i
$352$	−17.0212	−	16.2395i	−0.907231	−	0.865567i
$353$			22.1370i			1.17823i	0.808048	+	0.589117i	$0.200524\pi$
$353$			22.1370i			1.17823i	−0.808048	+	0.589117i	$0.799476\pi$
$354$	−23.6295	−	11.8717i	−1.25589	−	0.630975i
$355$			20.7492i			1.10125i
$356$	−1.60298	−	4.78011i	−0.0849577	−	0.253346i
$357$	−2.87130	+	3.96003i	−0.151965	+	0.209587i
$358$	−3.19070	−	19.5502i	−0.168634	−	1.03326i
$359$	4.25093			0.224356			0.112178	−	0.993688i	$-0.464217\pi$
$359$	4.25093			0.224356			0.112178	+	0.993688i	$0.464217\pi$
$360$	−19.7190	−	19.0968i	−1.03928	−	1.00649i
$361$	17.7309			0.933203
$362$	−1.02780	−	6.29761i	−0.0540202	−	0.330995i
$363$	−6.40028	+	8.82711i	−0.335927	+	0.463303i
$364$	−4.96488	−	14.8054i	−0.260231	−	0.776013i
$365$			24.5789i			1.28652i
$366$	−9.52232	−	4.78412i	−0.497740	−	0.250070i
$367$			31.1196i			1.62443i	0.583360	+	0.812214i	$0.301738\pi$
$367$			31.1196i			1.62443i	−0.583360	+	0.812214i	$0.698262\pi$
$368$	−12.5256	+	9.46514i	−0.652941	+	0.493404i
$369$	−31.6290	+	10.3444i	−1.64654	+	0.538505i
$370$	40.9062	−	6.67611i	2.12661	−	0.347075i
$371$	19.0547			0.989272
$372$	18.0678	+	5.66426i	0.936772	+	0.293678i
$373$	27.5690			1.42747			0.713736	−	0.700415i	$-0.247002\pi$
$373$	27.5690			1.42747			0.713736	+	0.700415i	$0.247002\pi$
$374$	6.27866	−	1.02471i	0.324662	−	0.0529866i
$375$	−2.11220	−	1.53149i	−0.109073	−	0.0790858i
$376$	−9.61814	−	18.2364i	−0.496018	−	0.940471i
$377$			20.9124i			1.07704i
$378$	−18.9715	−	2.85732i	−0.975790	−	0.146965i
$379$		−	4.09032i		−	0.210106i	−0.994467	−	0.105053i	$-0.966499\pi$
$379$		−	4.09032i		−	0.210106i	0.994467	−	0.105053i	$-0.0335012\pi$
$380$	6.91076	−	2.31748i	0.354515	−	0.118884i
$381$	−27.7656	−	20.1320i	−1.42248	−	1.03139i
$382$	5.47515	+	33.5476i	0.280133	+	1.71644i
$383$	18.0031			0.919915			0.459957	−	0.887941i	$-0.347865\pi$
$383$	18.0031			0.919915			0.459957	+	0.887941i	$0.347865\pi$
$384$	−17.1489	+	9.48237i	−0.875126	+	0.483895i
$385$	−35.1252			−1.79015
$386$	−0.382529	−	2.34385i	−0.0194702	−	0.119299i
$387$	12.3735	−	4.04679i	0.628980	−	0.205710i
$388$	−12.2857	+	4.11994i	−0.623713	+	0.209158i
$389$		−	1.49646i		−	0.0758733i	−0.999280	−	0.0379367i	$-0.987921\pi$
$389$		−	1.49646i		−	0.0758733i	0.999280	−	0.0379367i	$-0.0120785\pi$
$390$	−10.6389	+	21.1757i	−0.538723	+	1.07227i
$391$		−	4.24551i		−	0.214705i
$392$	0.242312	+	0.459435i	0.0122386	+	0.0232050i
$393$	−7.27877	+	10.0387i	−0.367166	+	0.506386i
$394$	−32.5258	+	5.30839i	−1.63862	+	0.267433i
$395$	−4.55623			−0.229249
$396$	14.8944	+	20.0195i	0.748470	+	1.00602i
$397$	23.9101			1.20001			0.600007	−	0.799995i	$-0.295165\pi$
$397$	23.9101			1.20001			0.600007	+	0.799995i	$0.295165\pi$
$398$	−10.0608	+	1.64197i	−0.504300	+	0.0823046i
$399$	2.99043	−	4.12433i	0.149709	−	0.206475i
$400$	−17.4424	+	13.1806i	−0.872122	+	0.659032i
$401$		−	38.7009i		−	1.93263i	−0.257362	−	0.966315i	$-0.582853\pi$
$401$		−	38.7009i		−	1.93263i	0.257362	−	0.966315i	$-0.417147\pi$
$402$	−1.09967	+	2.18877i	−0.0548463	+	0.109166i
$403$		−	16.3466i		−	0.814280i
$404$	9.68497	+	28.8808i	0.481845	+	1.43687i
$405$	17.2044	+	23.4888i	0.854894	+	1.16717i
$406$	4.15879	+	25.4819i	0.206397	+	1.26465i
$407$	−37.6756			−1.86751
$408$	0.750039	−	5.24579i	0.0371325	−	0.259705i
$409$	−1.56362			−0.0773161			−0.0386581	−	0.999252i	$-0.512308\pi$
$409$	−1.56362			−0.0773161			−0.0386581	+	0.999252i	$0.512308\pi$
$410$	8.17437	+	50.0864i	0.403703	+	2.47359i
$411$	−3.54796	−	2.57252i	−0.175008	−	0.126893i
$412$	8.01148	+	23.8904i	0.394697	+	1.17700i
$413$			28.1857i			1.38693i
$414$	14.7866	−	7.65802i	0.726721	−	0.376371i
$415$		−	26.6188i		−	1.30667i
$416$	12.2401	+	11.6779i	0.600118	+	0.572558i
$417$	−4.37073	−	3.16908i	−0.214035	−	0.155191i
$418$	−6.53916	+	1.06723i	−0.319841	+	0.0521998i
$419$	−14.5659			−0.711591			−0.355796	−	0.934564i	$-0.615790\pi$
$419$	−14.5659			−0.711591			−0.355796	+	0.934564i	$0.615790\pi$
$420$	−8.75246	+	27.9185i	−0.427076	+	1.36228i
$421$	17.2049			0.838513			0.419257	−	0.907868i	$-0.362291\pi$
$421$	17.2049			0.838513			0.419257	+	0.907868i	$0.362291\pi$
$422$	12.0800	−	1.97153i	0.588047	−	0.0959725i
$423$	6.79768	+	20.7846i	0.330515	+	1.01058i
$424$	−18.2590	+	9.63007i	−0.886737	+	0.467678i
$425$		−	5.91207i		−	0.286777i
$426$	−14.0384	−	7.05308i	−0.680165	−	0.341723i
$427$			11.3584i			0.549672i
$428$	−32.5197	+	10.9053i	−1.57190	+	0.527126i
$429$	12.6450	−	17.4396i	0.610504	−	0.841993i
$430$	−3.19788	−	19.5942i	−0.154215	−	0.944915i
$431$	32.3120			1.55641			0.778206	−	0.628009i	$-0.216130\pi$
$431$	32.3120			1.55641			0.778206	+	0.628009i	$0.216130\pi$
$432$	19.6234	−	6.85003i	0.944130	−	0.329572i
$433$	−25.3542			−1.21844			−0.609222	−	0.792999i	$-0.708518\pi$
$433$	−25.3542			−1.21844			−0.609222	+	0.792999i	$0.708518\pi$
$434$	−3.25079	−	19.9184i	−0.156043	−	0.956114i
$435$	23.0003	−	31.7215i	1.10278	−	1.52093i
$436$	−30.4777	+	10.2205i	−1.45962	+	0.489473i
$437$			4.42165i			0.211516i
$438$	−16.6296	−	8.35489i	−0.794591	−	0.399212i
$439$			16.7788i			0.800809i	0.916338	+	0.400405i	$0.131130\pi$
$439$			16.7788i			0.800809i	−0.916338	+	0.400405i	$0.868870\pi$
$440$	33.6585	−	17.7519i	1.60460	−	0.846291i
$441$	−0.171256	−	0.523633i	−0.00815504	−	0.0249349i
$442$	−4.51504	+	0.736879i	−0.214758	+	0.0350498i
$443$	24.4788			1.16302			0.581512	−	0.813538i	$-0.302461\pi$
$443$	24.4788			1.16302			0.581512	+	0.813538i	$0.302461\pi$
$444$	−9.38796	+	29.9456i	−0.445533	+	1.42116i
$445$	8.15515			0.386591
$446$	20.3073	−	3.31426i	0.961577	−	0.156935i
$447$	6.00608	+	4.35483i	0.284078	+	0.205976i
$448$	17.2370	+	11.7955i	0.814370	+	0.557285i
$449$		−	1.92796i		−	0.0909859i	−0.998965	−	0.0454930i	$-0.985514\pi$
$449$		−	1.92796i		−	0.0909859i	0.998965	−	0.0454930i	$-0.0144859\pi$
$450$	20.5910	−	10.6641i	0.970670	−	0.502712i
$451$		−	46.1308i		−	2.17221i
$452$	−1.92528	−	5.74122i	−0.0905575	−	0.270044i
$453$	14.9641	+	10.8500i	0.703076	+	0.509779i
$454$	−1.29222	−	7.91775i	−0.0606469	−	0.371598i
$455$	25.2588			1.18415
$456$	−0.781158	+	5.46344i	−0.0365811	+	0.255849i
$457$	−5.30529			−0.248171			−0.124085	−	0.992272i	$-0.539600\pi$
$457$	−5.30529			−0.248171			−0.124085	+	0.992272i	$0.539600\pi$
$458$	4.18371	+	25.6346i	0.195492	+	1.19783i
$459$	−1.72139	+	5.35050i	−0.0803474	+	0.249740i
$460$	−8.07403	−	24.0769i	−0.376454	−	1.12259i
$461$		−	30.2693i		−	1.40978i	−0.709316	−	0.704890i	$-0.750996\pi$
$461$		−	30.2693i		−	1.40978i	0.709316	−	0.704890i	$-0.249004\pi$
$462$	11.9398	−	23.7650i	0.555490	−	1.10565i
$463$		−	26.3826i		−	1.22610i	−0.790043	−	0.613051i	$-0.789942\pi$
$463$		−	26.3826i		−	1.22610i	0.790043	−	0.613051i	$-0.210058\pi$
$464$	−16.8635	−	22.3161i	−0.782866	−	1.03600i
$465$	−17.9786	+	24.7957i	−0.833738	+	1.14987i
$466$	−26.2315	+	4.28112i	−1.21515	+	0.198319i
$467$	−37.9451			−1.75589			−0.877944	−	0.478763i	$-0.841085\pi$
$467$	−37.9451			−1.75589			−0.877944	+	0.478763i	$0.841085\pi$
$468$	−10.7107	−	14.3962i	−0.495100	−	0.665462i
$469$	2.61082			0.120556
$470$	32.9137	−	5.37170i	1.51820	−	0.247778i
$471$	−21.6079	+	29.8011i	−0.995640	+	1.37316i
$472$	−14.2448	−	27.0087i	−0.655670	−	1.24318i
$473$			18.0467i			0.829789i
$474$	1.54876	−	3.08265i	0.0711369	−	0.141591i
$475$			6.15735i			0.282519i
$476$	−5.35507	+	1.79579i	−0.245449	+	0.0823097i
$477$	20.8104	−	6.80611i	0.952844	−	0.311631i
$478$	2.13586	+	13.0870i	0.0976921	+	0.598583i
$479$	6.83815			0.312443			0.156221	−	0.987722i	$-0.450069\pi$
$479$	6.83815			0.312443			0.156221	+	0.987722i	$0.450069\pi$
$480$	−5.72277	−	31.1761i	−0.261208	−	1.42299i
$481$	27.0928			1.23533
$482$	−2.68729	−	16.4657i	−0.122403	−	0.749990i
$483$	−14.3691	−	10.4186i	−0.653815	−	0.474062i
$484$	−11.9367	+	4.00290i	−0.542578	+	0.181950i
$485$		−	20.9602i		−	0.951752i
$486$	−21.7402	+	3.65581i	−0.986154	+	0.165831i
$487$		−	12.7986i		−	0.579959i	−0.957033	−	0.289980i	$-0.906351\pi$
$487$		−	12.7986i		−	0.579959i	0.957033	−	0.289980i	$-0.0936485\pi$
$488$	−5.74044	−	10.8841i	−0.259857	−	0.492701i
$489$	6.12842	+	4.44354i	0.277137	+	0.200944i
$490$	−0.829205	+	0.135331i	−0.0374596	+	0.00611362i
$491$	37.3728			1.68661			0.843305	−	0.537435i	$-0.180607\pi$
$491$	37.3728			1.68661			0.843305	+	0.537435i	$0.180607\pi$
$492$	−36.6660	−	11.4948i	−1.65303	−	0.518226i
$493$	7.56397			0.340664
$494$	4.70236	−	0.767452i	0.211569	−	0.0345293i
$495$	−38.3617	+	12.5463i	−1.72423	+	0.563914i
$496$	13.1816	+	17.4437i	0.591872	+	0.783247i
$497$			16.7453i			0.751131i
$498$	18.0097	+	9.04830i	0.807036	+	0.405464i
$499$		−	17.3343i		−	0.775991i	−0.921661	−	0.387996i	$-0.873168\pi$
$499$		−	17.3343i		−	0.775991i	0.921661	−	0.387996i	$-0.126832\pi$
$500$	−0.957834	−	2.85628i	−0.0428356	−	0.127737i
$501$	21.1995	−	29.2379i	0.947124	−	1.30625i
$502$	0.278438	+	1.70605i	0.0124273	+	0.0761450i
$503$	−10.4435			−0.465652			−0.232826	−	0.972518i	$-0.574797\pi$
$503$	−10.4435			−0.465652			−0.232826	+	0.972518i	$0.574797\pi$
$504$	−15.9139	−	15.4118i	−0.708863	−	0.686497i
$505$	−49.2723			−2.19259
$506$	3.71819	+	22.7823i	0.165294	+	1.01280i
$507$	4.12430	−	5.68813i	0.183166	−	0.252619i
$508$	−12.5911	−	37.5469i	−0.558639	−	1.66587i
$509$			18.7018i			0.828941i	0.910063	+	0.414471i	$0.136033\pi$
$509$			18.7018i			0.828941i	−0.910063	+	0.414471i	$0.863967\pi$
$510$	7.65920	+	3.84807i	0.339155	+	0.170395i
$511$			19.8361i			0.877497i
$512$	−22.4785	−	2.59155i	−0.993420	−	0.114532i
$513$	1.79281	−	5.57249i	0.0791543	−	0.246031i
$514$	−12.5561	+	2.04923i	−0.553827	+	0.0903876i
$515$	−40.7584			−1.79603
$516$	14.3440	+	4.49686i	0.631461	+	0.197963i
$517$	−30.3143			−1.33322
$518$	33.0128	−	5.38787i	1.45050	−	0.236730i
$519$	10.8753	+	7.88533i	0.477371	+	0.346127i
$520$	−24.2041	+	12.7656i	−1.06142	+	0.559807i
$521$		−	34.2957i		−	1.50252i	−0.660006	−	0.751261i	$-0.729446\pi$
$521$		−	34.2957i		−	1.50252i	0.660006	−	0.751261i	$-0.270554\pi$
$522$	13.6438	+	26.3444i	0.597174	+	1.15306i
$523$		−	32.6298i		−	1.42680i	−0.700756	−	0.713401i	$-0.747154\pi$
$523$		−	32.6298i		−	1.42680i	0.700756	−	0.713401i	$-0.252846\pi$
$524$	−13.5752	+	4.55234i	−0.593033	+	0.198870i
$525$	−20.0096	−	14.5083i	−0.873289	−	0.633196i
$526$	−1.79179	−	10.9788i	−0.0781259	−	0.478696i
$527$	−5.91251			−0.257553
$528$	0.569372	+	28.8069i	0.0247787	+	1.25366i
$529$	−7.59508			−0.330221
$530$	−5.37837	−	32.9546i	−0.233621	−	1.43145i
$531$	10.0676	+	30.7828i	0.436897	+	1.33586i
$532$	5.57725	−	1.87029i	0.241804	−	0.0810875i
$533$			33.1730i			1.43688i
$534$	−2.77211	+	5.51760i	−0.119961	+	0.238770i
$535$		−	55.4805i		−	2.39863i
$536$	−2.50179	+	1.31948i	−0.108061	+	0.0569929i
$537$	−14.2412	+	19.6411i	−0.614553	+	0.847577i
$538$	−33.7525	+	5.50860i	−1.45517	+	0.237493i
$539$	0.763718			0.0328957
$540$	0.413243	+	33.6172i	0.0177831	+	1.44665i
$541$	35.6014			1.53062			0.765312	−	0.643660i	$-0.222585\pi$
$541$	35.6014			1.53062			0.765312	+	0.643660i	$0.222585\pi$
$542$	−37.6825	+	6.15000i	−1.61860	+	0.264165i
$543$	−4.58745	+	6.32690i	−0.196866	+	0.271513i
$544$	4.22388	−	4.42720i	0.181097	−	0.189814i
$545$		−	51.9967i		−	2.22729i
$546$	−8.58601	+	17.0896i	−0.367447	+	0.731367i
$547$			38.3114i			1.63808i	0.573737	+	0.819039i	$0.305493\pi$
$547$			38.3114i			1.63808i	−0.573737	+	0.819039i	$0.694507\pi$
$548$	−1.60892	−	4.79784i	−0.0687298	−	0.204954i
$549$	4.05709	+	12.4050i	0.173152	+	0.529432i
$550$	5.17775	+	31.7253i	0.220780	+	1.35277i
$551$	−7.87779			−0.335605
$552$	19.0345	+	2.72153i	0.810161	+	0.115836i
$553$	−3.67705			−0.156364
$554$	−0.305611	−	1.87255i	−0.0129842	−	0.0795572i
$555$	−41.0964	−	29.7978i	−1.74445	−	1.26485i
$556$	−1.98203	−	5.91045i	−0.0840567	−	0.250659i
$557$		−	17.0527i		−	0.722545i	−0.932460	−	0.361272i	$-0.882342\pi$
$557$		−	17.0527i		−	0.722545i	0.932460	−	0.361272i	$-0.117658\pi$
$558$	−10.6649	−	20.5925i	−0.451483	−	0.871752i
$559$		−	12.9775i		−	0.548892i
$560$	−26.9542	+	20.3683i	−1.13902	+	0.860720i
$561$	−6.30787	−	4.57365i	−0.266318	−	0.193100i
$562$	26.8075	−	4.37514i	1.13081	−	0.184554i
$563$	−36.2075			−1.52597			−0.762983	−	0.646419i	$-0.776266\pi$
$563$	−36.2075			−1.52597			−0.762983	+	0.646419i	$0.776266\pi$
$564$	−7.55369	+	24.0947i	−0.318068	+	1.01457i
$565$	9.79485			0.412072
$566$	−36.1243	+	5.89568i	−1.51842	+	0.247814i
$567$	13.8846	+	18.9563i	0.583099	+	0.796091i
$568$	−8.46294	−	16.0461i	−0.355097	−	0.673279i
$569$			10.3612i			0.434365i	0.976131	+	0.217183i	$0.0696867\pi$
$569$			10.3612i			0.434365i	−0.976131	+	0.217183i	$0.930313\pi$
$570$	−7.97698	−	4.00773i	−0.334119	−	0.167865i
$571$			11.5307i			0.482546i	0.970457	+	0.241273i	$0.0775649\pi$
$571$			11.5307i			0.482546i	−0.970457	+	0.241273i	$0.922435\pi$
$572$	23.5833	−	7.90849i	0.986066	−	0.330670i
$573$	24.4375	−	33.7036i	1.02089	−	1.40799i
$574$	6.59702	+	40.4216i	0.275354	+	1.68716i
$575$	21.4521			0.894613
$576$	23.0384	+	6.72551i	0.959933	+	0.280230i
$577$	32.2814			1.34389			0.671947	−	0.740600i	$-0.265458\pi$
$577$	32.2814			1.34389			0.671947	+	0.740600i	$0.265458\pi$
$578$	−3.60596	−	22.0946i	−0.149988	−	0.919015i
$579$	−1.70736	+	2.35475i	−0.0709555	+	0.0978602i
$580$	42.8964	−	14.3850i	1.78118	−	0.597305i
$581$		−	21.4824i		−	0.891240i
$582$	14.1812	+	7.12480i	0.587830	+	0.295333i
$583$			30.3520i			1.25705i
$584$	−10.0250	−	19.0078i	−0.414836	−	0.786547i
$585$	27.5862	−	9.02215i	1.14055	−	0.373020i
$586$	44.0196	−	7.18424i	1.81843	−	0.296778i
$587$	26.2487			1.08340			0.541699	−	0.840572i	$-0.317781\pi$
$587$	26.2487			1.08340			0.541699	+	0.840572i	$0.317781\pi$
$588$	0.190302	−	0.607024i	0.00784793	−	0.0250333i
$589$	6.15781			0.253728
$590$	48.7464	−	7.95568i	2.00686	−	0.327530i
$591$	32.6771	+	23.6932i	1.34415	+	0.974607i
$592$	−28.9113	+	21.8472i	−1.18825	+	0.897916i
$593$		−	0.287414i		−	0.0118027i	−0.999983	−	0.00590135i	$-0.998122\pi$
$593$		−	0.287414i		−	0.0118027i	0.999983	−	0.00590135i	$-0.00187847\pi$
$594$	4.55138	−	30.2195i	0.186745	−	1.23992i
$595$		−	9.13605i		−	0.374542i
$596$	2.72363	+	8.12190i	0.111564	+	0.332686i
$597$	10.1076	+	7.32869i	0.413675	+	0.299943i
$598$	−2.67378	−	16.3829i	−0.109339	−	0.669947i
$599$	−0.121916			−0.00498135			−0.00249067	−	0.999997i	$-0.500793\pi$
$599$	−0.121916			−0.00498135			−0.00249067	+	0.999997i	$0.500793\pi$
$600$	26.5064	+	3.78986i	1.08212	+	0.154720i
$601$	−6.74019			−0.274938			−0.137469	−	0.990506i	$-0.543897\pi$
$601$	−6.74019			−0.274938			−0.137469	+	0.990506i	$0.543897\pi$
$602$	−2.58081	−	15.8132i	−0.105186	−	0.644500i
$603$	2.85138	−	0.932552i	0.116117	−	0.0379764i
$604$	6.78590	+	20.2357i	0.276114	+	0.823378i
$605$		−	20.3647i		−	0.827944i
$606$	16.7487	−	33.3366i	0.680369	−	1.35421i
$607$		−	32.8710i		−	1.33419i	−0.744971	−	0.667097i	$-0.767537\pi$
$607$		−	32.8710i		−	1.33419i	0.744971	−	0.667097i	$-0.232463\pi$
$608$	−4.39912	+	4.61088i	−0.178408	+	0.186996i
$609$	18.5621	−	25.6005i	0.752176	−	1.03738i
$610$	19.6440	−	3.20602i	0.795364	−	0.129808i
$611$	21.7993			0.881905
$612$	−5.20705	+	3.87401i	−0.210483	+	0.156598i
$613$	12.7397			0.514553			0.257277	−	0.966338i	$-0.417175\pi$
$613$	12.7397			0.514553			0.257277	+	0.966338i	$0.417175\pi$
$614$	−35.2206	+	5.74820i	−1.42139	+	0.231978i
$615$	36.4851	−	50.3193i	1.47122	−	2.02907i
$616$	27.1636	−	14.3265i	1.09445	−	0.577231i
$617$			31.1640i			1.25461i	0.778772	+	0.627307i	$0.215843\pi$
$617$			31.1640i			1.25461i	−0.778772	+	0.627307i	$0.784157\pi$
$618$	13.8546	−	27.5763i	0.557315	−	1.10928i
$619$		−	26.4870i		−	1.06460i	−0.846556	−	0.532300i	$-0.821328\pi$
$619$		−	26.4870i		−	1.06460i	0.846556	−	0.532300i	$-0.178672\pi$
$620$	−33.5307	+	11.2443i	−1.34663	+	0.451582i
$621$	−19.4144	−	6.24609i	−0.779073	−	0.250647i
$622$	3.51810	+	21.5563i	0.141063	+	0.864327i
$623$	6.58151			0.263683
$624$	−0.409440	−	20.7153i	−0.0163907	−	0.829274i
$625$	−22.4551			−0.898204
$626$	−2.18488	−	13.3873i	−0.0873253	−	0.535063i
$627$	6.56958	+	4.76341i	0.262364	+	0.190232i
$628$	−40.2995	+	13.5142i	−1.60812	+	0.539274i
$629$		−	9.79940i		−	0.390728i
$630$	31.8198	−	16.4795i	1.26773	−	0.656561i
$631$			40.8252i			1.62523i	0.582804	+	0.812613i	$0.301956\pi$
$631$			40.8252i			1.62523i	−0.582804	+	0.812613i	$0.698044\pi$
$632$	3.52350	−	1.85835i	0.140157	−	0.0739210i
$633$	−12.1362	−	8.79962i	−0.482372	−	0.349753i
$634$	−4.12507	+	0.673235i	−0.163828	+	0.0267376i
$635$	64.0571			2.54203
$636$	24.1246	+	7.56306i	0.956602	+	0.299895i
$637$	−0.549196			−0.0217599
$638$	−40.5898	+	6.62448i	−1.60696	+	0.262266i
$639$	5.98124	+	18.2883i	0.236614	+	0.723473i
$640$	15.5347	−	33.1402i	0.614062	−	1.30998i
$641$			20.5534i			0.811811i	0.913915	+	0.405905i	$0.133044\pi$
$641$			20.5534i			0.811811i	−0.913915	+	0.405905i	$0.866956\pi$
$642$	37.5370	+	18.8590i	1.48147	+	0.744306i
$643$		−	12.9876i		−	0.512179i	−0.966653	−	0.256090i	$-0.917566\pi$
$643$		−	12.9876i		−	0.512179i	0.966653	−	0.256090i	$-0.0824342\pi$
$644$	−6.51605	−	19.4310i	−0.256768	−	0.765688i
$645$	−14.2732	+	19.6853i	−0.562008	+	0.775109i
$646$	−0.277585	−	1.70083i	−0.0109214	−	0.0669184i
$647$	−30.1132			−1.18387			−0.591936	−	0.805985i	$-0.701636\pi$
$647$	−30.1132			−1.18387			−0.591936	+	0.805985i	$0.701636\pi$
$648$	−22.8852	−	11.1476i	−0.899014	−	0.437919i
$649$	−44.8966			−1.76235
$650$	−3.72336	−	22.8140i	−0.146042	−	0.894837i
$651$	−14.5094	+	20.0111i	−0.568669	+	0.784295i
$652$	2.77910	+	8.28734i	0.108838	+	0.324557i
$653$			1.17412i			0.0459467i	0.999736	+	0.0229734i	$0.00731329\pi$
$653$			1.17412i			0.0459467i	−0.999736	+	0.0229734i	$0.992687\pi$
$654$	35.1799	+	17.6748i	1.37564	+	0.691139i
$655$		−	23.1600i		−	0.904936i
$656$	−26.7502	−	35.3996i	−1.04442	−	1.38212i
$657$	7.08521	+	21.6638i	0.276420	+	0.845185i
$658$	26.5626	−	4.33516i	1.03552	−	0.169002i
$659$	−1.23315			−0.0480368			−0.0240184	−	0.999712i	$-0.507646\pi$
$659$	−1.23315			−0.0480368			−0.0240184	+	0.999712i	$0.507646\pi$
$660$	−44.4710	−	13.9417i	−1.73103	−	0.542678i
$661$	−1.03589			−0.0402914			−0.0201457	−	0.999797i	$-0.506413\pi$
$661$	−1.03589			−0.0402914			−0.0201457	+	0.999797i	$0.506413\pi$
$662$	−4.72621	+	0.771343i	−0.183689	+	0.0299791i
$663$	4.53604	+	3.28895i	0.176165	+	0.127732i
$664$	10.8570	+	20.5853i	0.421333	+	0.798866i
$665$			9.51510i			0.368980i
$666$	34.1301	−	17.6761i	1.32252	−	0.684935i
$667$			27.4460i			1.06271i
$668$	39.5378	−	13.2587i	1.52976	−	0.512996i
$669$	−20.4017	−	14.7927i	−0.788776	−	0.571918i
$670$	−0.736926	−	4.51533i	−0.0284699	−	0.174442i
$671$	−18.0926			−0.698459
$672$	−4.61849	−	25.1603i	−0.178162	−	0.970579i
$673$	−6.37442			−0.245716			−0.122858	−	0.992424i	$-0.539206\pi$
$673$	−6.37442			−0.245716			−0.122858	+	0.992424i	$0.539206\pi$
$674$	6.99414	+	42.8548i	0.269404	+	1.65071i
$675$	−27.0355	−	8.69797i	−1.04060	−	0.334785i
$676$	7.69195	−	2.57944i	0.295844	−	0.0992093i
$677$			5.59222i			0.214926i	0.994209	+	0.107463i	$0.0342728\pi$
$677$			5.59222i			0.214926i	−0.994209	+	0.107463i	$0.965727\pi$
$678$	−3.32948	+	6.62699i	−0.127868	+	0.254508i
$679$		−	16.9156i		−	0.649162i
$680$	4.61727	+	8.75455i	0.177064	+	0.335722i
$681$	−5.76763	+	7.95458i	−0.221016	+	0.304820i
$682$	31.7277	−	5.17814i	1.21492	−	0.198281i
$683$	−16.9753			−0.649541			−0.324771	−	0.945793i	$-0.605287\pi$
$683$	−16.9753			−0.649541			−0.324771	+	0.945793i	$0.605287\pi$
$684$	5.42309	−	4.03475i	0.207357	−	0.154272i
$685$	8.18539			0.312748
$686$	−26.1775	+	4.27231i	−0.999460	+	0.163117i
$687$	18.6733	−	25.7538i	0.712432	−	0.982570i
$688$	10.4649	+	13.8486i	0.398970	+	0.527973i
$689$		−	21.8263i		−	0.831517i
$690$	−13.9628	+	27.7916i	−0.531555	+	1.05801i
$691$		−	11.3603i		−	0.432165i	−0.976375	−	0.216082i	$-0.930672\pi$
$691$		−	11.3603i		−	0.432165i	0.976375	−	0.216082i	$-0.0693280\pi$
$692$	4.93169	+	14.7064i	0.187475	+	0.559053i
$693$	−30.9593	+	10.1253i	−1.17605	+	0.384630i
$694$	2.21281	+	13.5584i	0.0839970	+	0.514670i
$695$	10.0836			0.382491
$696$	−4.84879	+	33.9126i	−0.183793	+	1.28545i
$697$	11.9986			0.454479
$698$	−1.18049	−	7.23314i	−0.0446821	−	0.273778i
$699$	26.3535	+	19.1081i	0.996781	+	0.722736i
$700$	−9.07390	−	27.0585i	−0.342961	−	1.02272i
$701$		−	8.74801i		−	0.330408i	−0.986259	−	0.165204i	$-0.947172\pi$
$701$		−	8.74801i		−	0.330408i	0.986259	−	0.165204i	$-0.0528282\pi$
$702$	−3.27293	+	21.7311i	−0.123529	+	0.820186i
$703$			10.2060i			0.384926i
$704$	−18.7889	+	27.4565i	−0.708132	+	1.03481i
$705$	−33.0668	−	23.9758i	−1.24537	−	0.902980i
$706$	30.8976	−	5.04267i	1.16285	−	0.189783i
$707$	−39.7646			−1.49550
$708$	−11.1873	+	35.6851i	−0.420444	+	1.34113i
$709$	13.6988			0.514469			0.257235	−	0.966349i	$-0.417189\pi$
$709$	13.6988			0.514469			0.257235	+	0.966349i	$0.417189\pi$
$710$	28.9606	−	4.72652i	1.08687	−	0.177383i
$711$	−4.01585	+	1.31340i	−0.150606	+	0.0492563i
$712$	−6.30668	+	3.32623i	−0.236353	+	0.124656i
$713$		−	21.4537i		−	0.803446i
$714$	6.18126	+	3.10554i	0.231328	+	0.116222i
$715$			40.2344i			1.50468i
$716$	−26.5603	+	8.90682i	−0.992605	+	0.332863i
$717$	9.53310	−	13.1478i	0.356020	−	0.491015i
$718$	−0.968336	−	5.93323i	−0.0361380	−	0.221426i
$719$	−0.956487			−0.0356709			−0.0178355	−	0.999841i	$-0.505678\pi$
$719$	−0.956487			−0.0356709			−0.0178355	+	0.999841i	$0.505678\pi$
$720$	−22.1624	+	31.8728i	−0.825945	+	1.18783i
$721$	−32.8935			−1.22502
$722$	−4.03898	−	24.7478i	−0.150315	−	0.921018i
$723$	−11.9943	+	16.5423i	−0.446073	+	0.615213i
$724$	−8.55574	+	2.86911i	−0.317972	+	0.106630i
$725$			38.2198i			1.41945i
$726$	13.7784	+	6.92241i	0.511363	+	0.256915i
$727$			1.99104i			0.0738435i	0.999318	+	0.0369218i	$0.0117552\pi$
$727$			1.99104i			0.0738435i	−0.999318	+	0.0369218i	$0.988245\pi$
$728$	−19.5336	+	10.3023i	−0.723963	+	0.381828i
$729$	21.9349	+	15.7436i	0.812404	+	0.583095i
$730$	34.3059	−	5.59892i	1.26972	−	0.207225i
$731$	−4.69394			−0.173612
$732$	−4.50830	+	14.3805i	−0.166632	+	0.531520i
$733$	−31.0630			−1.14734			−0.573668	−	0.819088i	$-0.694480\pi$
$733$	−31.0630			−1.14734			−0.573668	+	0.819088i	$0.694480\pi$
$734$	43.4350	−	7.08884i	1.60322	−	0.261654i
$735$	0.833062	+	0.604028i	0.0307279	+	0.0222799i
$736$	16.0642	+	15.3264i	0.592134	+	0.564940i
$737$			4.15873i			0.153189i
$738$	21.6430	+	41.7896i	0.796689	+	1.53830i
$739$			31.1144i			1.14456i	0.820058	+	0.572280i	$0.193941\pi$
$739$			31.1144i			1.14456i	−0.820058	+	0.572280i	$0.806059\pi$
$740$	−18.6363	−	55.5739i	−0.685085	−	2.04294i
$741$	−4.72424	−	3.42540i	−0.173549	−	0.125835i
$742$	−4.34054	−	26.5956i	−0.159346	−	0.976354i
$743$	15.7374			0.577348			0.288674	−	0.957427i	$-0.406786\pi$
$743$	15.7374			0.577348			0.288674	+	0.957427i	$0.406786\pi$
$744$	3.79014	−	26.5084i	0.138953	−	0.971843i
$745$	−13.8564			−0.507660
$746$	−6.28005	−	38.4794i	−0.229929	−	1.40883i
$747$	−7.67325	−	23.4618i	−0.280749	−	0.858421i
$748$	−2.86048	−	8.53000i	−0.104589	−	0.311888i
$749$		−	44.7749i		−	1.63604i
$750$	−1.65643	+	3.29695i	−0.0604842	+	0.120388i
$751$			46.1090i			1.68254i	0.540615	+	0.841270i	$0.318191\pi$
$751$			46.1090i			1.68254i	−0.540615	+	0.841270i	$0.681809\pi$
$752$	−23.2625	+	17.5786i	−0.848295	+	0.641026i
$753$	1.24276	−	1.71399i	0.0452888	−	0.0624613i
$754$	29.1884	−	4.76372i	1.06298	−	0.173484i
$755$	−34.5232			−1.25643
$756$	0.333503	+	27.1303i	0.0121294	+	0.986721i
$757$	5.22299			0.189833			0.0949164	−	0.995485i	$-0.469742\pi$
$757$	5.22299			0.189833			0.0949164	+	0.995485i	$0.469742\pi$
$758$	−5.70906	+	0.931749i	−0.207362	+	0.0338427i
$759$	16.5956	−	22.8882i	0.602381	−	0.830791i
$760$	−4.80884	−	9.11777i	−0.174435	−	0.330736i
$761$		−	19.0003i		−	0.688760i	−0.938830	−	0.344380i	$-0.888089\pi$
$761$		−	19.0003i		−	0.688760i	0.938830	−	0.344380i	$-0.111911\pi$
$762$	−21.7744	+	43.3397i	−0.788803	+	1.57003i
$763$		−	41.9633i		−	1.51917i
$764$	45.5768	−	15.2839i	1.64891	−	0.552951i
$765$	−3.26329	−	9.97785i	−0.117984	−	0.360750i
$766$	−4.10099	−	25.1278i	−0.148175	−	0.907903i
$767$	32.2855			1.16576
$768$	17.1414	+	21.7755i	0.618537	+	0.785756i
$769$	−26.1731			−0.943825			−0.471912	−	0.881645i	$-0.656436\pi$
$769$	−26.1731			−0.943825			−0.471912	+	0.881645i	$0.656436\pi$
$770$	8.00130	+	49.0259i	0.288347	+	1.76677i
$771$	12.6145	+	9.14642i	0.454301	+	0.329400i
$772$	−3.18429	+	1.06783i	−0.114605	+	0.0384320i
$773$			14.3331i			0.515525i	0.966208	+	0.257763i	$0.0829852\pi$
$773$			14.3331i			0.515525i	−0.966208	+	0.257763i	$0.917015\pi$
$774$	−8.46690	−	16.3484i	−0.304337	−	0.587633i
$775$		−	29.8752i		−	1.07315i
$776$	8.54900	+	16.2093i	0.306891	+	0.581879i
$777$	−33.1664	−	24.0480i	−1.18984	−	0.862716i
$778$	−2.08867	+	0.340883i	−0.0748826	+	0.0122213i
$779$	−12.4964			−0.447730
$780$	31.9794	+	10.0256i	1.14505	+	0.358973i
$781$	−26.6734			−0.954449
$782$	−5.92566	+	0.967100i	−0.211901	+	0.0345834i
$783$	11.1283	−	34.5895i	0.397692	−	1.23613i
$784$	0.586058	−	0.442863i	0.0209306	−	0.0158165i
$785$		−	68.7532i		−	2.45391i
$786$	15.6696	+	7.87257i	0.558915	+	0.280805i
$787$			44.2462i			1.57721i	0.614902	+	0.788603i	$0.289195\pi$
$787$			44.2462i			1.57721i	−0.614902	+	0.788603i	$0.710805\pi$
$788$	14.8183	+	44.1885i	0.527881	+	1.57415i
$789$	−7.99740	+	11.0298i	−0.284715	+	0.392672i
$790$	1.03788	+	6.35935i	0.0369261	+	0.226255i
$791$	7.90481			0.281063
$792$	24.5493	−	25.3491i	0.872320	−	0.900740i
$793$	13.0106			0.462019
$794$	−5.44657	−	33.3724i	−0.193291	−	1.18434i
$795$	−24.0055	+	33.1078i	−0.851388	+	1.17421i
$796$	4.58355	+	13.6682i	0.162460	+	0.484458i
$797$			32.1926i			1.14032i	0.821534	+	0.570160i	$0.193119\pi$
$797$			32.1926i			1.14032i	−0.821534	+	0.570160i	$0.806881\pi$
$798$	−6.43772	−	3.23439i	−0.227893	−	0.114496i
$799$		−	7.88475i		−	0.278942i
$800$	22.3701	+	21.3428i	0.790903	+	0.754581i
$801$	7.18793	−	2.35084i	0.253973	−	0.0830627i
$802$	−54.0167	+	8.81582i	−1.90739	+	0.311297i
$803$	−31.5966			−1.11502
$804$	3.30547	+	1.03627i	0.116575	+	0.0365463i
$805$	33.1504			1.16840
$806$	−22.8157	+	3.72364i	−0.803647	+	0.131160i
$807$	33.9095	+	24.5868i	1.19367	+	0.865496i
$808$	38.1041	−	20.0966i	1.34050	−	0.706997i
$809$		−	14.8604i		−	0.522462i	−0.965276	−	0.261231i	$-0.915871\pi$
$809$		−	14.8604i		−	0.522462i	0.965276	−	0.261231i	$-0.0841285\pi$
$810$	28.8654	−	29.3636i	1.01423	−	1.03173i
$811$		−	33.8874i		−	1.18995i	−0.803745	−	0.594974i	$-0.797162\pi$
$811$		−	33.8874i		−	1.18995i	0.803745	−	0.594974i	$-0.202838\pi$
$812$	34.6190	−	11.6092i	1.21489	−	0.407405i
$813$	37.8578	+	27.4496i	1.32773	+	0.962699i
$814$	8.58226	+	52.5856i	0.300808	+	1.84312i
$815$	−14.1387			−0.495256
$816$	−7.49266	+	0.148093i	−0.262295	+	0.00518430i
$817$	4.88869			0.171034
$818$	0.356183	+	2.18242i	0.0124536	+	0.0763065i
$819$	22.2631	−	7.28121i	0.777935	−	0.254426i
$820$	68.0458	−	22.8187i	2.37626	−	0.796864i
$821$			3.97262i			0.138646i	0.997594	+	0.0693228i	$0.0220838\pi$
$821$			3.97262i			0.138646i	−0.997594	+	0.0693228i	$0.977916\pi$
$822$	−2.78239	+	5.53806i	−0.0970469	+	0.193162i
$823$		−	15.7228i		−	0.548063i	−0.961721	−	0.274032i	$-0.911643\pi$
$823$		−	15.7228i		−	0.548063i	0.961721	−	0.274032i	$-0.0883573\pi$
$824$	31.5200	−	16.6241i	1.09805	−	0.579127i
$825$	23.1101	−	31.8729i	0.804591	−	1.10967i
$826$	39.3401	−	6.42053i	1.36882	−	0.223399i
$827$	5.88716			0.204717			0.102358	−	0.994748i	$-0.467361\pi$
$827$	5.88716			0.204717			0.102358	+	0.994748i	$0.467361\pi$
$828$	−14.0569	−	18.8939i	−0.488513	−	0.656608i
$829$	43.2482			1.50207			0.751035	−	0.660262i	$-0.229555\pi$
$829$	43.2482			1.50207			0.751035	+	0.660262i	$0.229555\pi$
$830$	−37.1531	+	6.06360i	−1.28960	+	0.210471i
$831$	−1.36405	+	1.88126i	−0.0473183	+	0.0652603i
$832$	13.5112	−	19.7442i	0.468418	−	0.684506i
$833$			0.198643i			0.00688256i
$834$	−3.42762	+	6.82233i	−0.118689	+	0.236238i
$835$			67.4537i			2.33433i
$836$	2.97916	+	8.88391i	0.103036	+	0.307256i
$837$	−8.69861	+	27.0375i	−0.300668	+	0.934552i
$838$	3.31802	+	20.3303i	0.114619	+	0.702300i
$839$	14.2934			0.493462			0.246731	−	0.969084i	$-0.420644\pi$
$839$	14.2934			0.493462			0.246731	+	0.969084i	$0.420644\pi$
$840$	40.9609	+	5.85656i	1.41329	+	0.202071i
$841$	−19.8989			−0.686169
$842$	−3.91916	−	24.0136i	−0.135063	−	0.827564i
$843$	−26.9322	−	19.5278i	−0.927595	−	0.672572i
$844$	−5.50351	−	16.4116i	−0.189439	−	0.564910i
$845$			13.1229i			0.451442i
$846$	27.4616	−	14.2225i	0.944150	−	0.488978i
$847$		−	16.4351i		−	0.564717i
$848$	17.6004	+	23.2913i	0.604401	+	0.799827i
$849$	36.2923	+	26.3145i	1.24555	+	0.903111i
$850$	−8.25175	+	1.34673i	−0.283033	+	0.0461925i
$851$	35.5574			1.21889
$852$	−6.64644	+	21.2008i	−0.227703	+	0.726326i
$853$	−31.8512			−1.09057			−0.545283	−	0.838252i	$-0.683578\pi$
$853$	−31.8512			−1.09057			−0.545283	+	0.838252i	$0.683578\pi$
$854$	15.8535	−	2.58738i	0.542495	−	0.0885382i
$855$	3.39868	+	10.3918i	0.116232	+	0.355393i
$856$	22.6288	+	42.9052i	0.773436	+	1.46647i
$857$		−	36.0927i		−	1.23290i	−0.787393	−	0.616451i	$-0.788570\pi$
$857$		−	36.0927i		−	1.23290i	0.787393	−	0.616451i	$-0.211430\pi$
$858$	−27.2218	−	13.6765i	−0.929335	−	0.466909i
$859$			21.7188i			0.741037i	0.928825	+	0.370519i	$0.120820\pi$
$859$			21.7188i			0.741037i	−0.928825	+	0.370519i	$0.879180\pi$
$860$	−26.6201	+	8.92686i	−0.907737	+	0.304403i
$861$	29.4448	−	40.6096i	1.00348	−	1.38397i
$862$	−7.36046	−	45.0993i	−0.250698	−	1.53609i
$863$	−30.9714			−1.05428			−0.527139	−	0.849779i	$-0.676735\pi$
$863$	−30.9714			−1.05428			−0.527139	+	0.849779i	$0.676735\pi$
$864$	−14.0310	−	25.8289i	−0.477344	−	0.878717i
$865$	−25.0899			−0.853084
$866$	5.77552	+	35.3880i	0.196260	+	1.20253i
$867$	−16.0947	+	22.1974i	−0.546604	+	0.753863i
$868$	−27.0605	+	9.07457i	−0.918495	+	0.308011i
$869$		−	5.85711i		−	0.198689i
$870$	−49.5146	−	24.8767i	−1.67870	−	0.843399i
$871$		−	2.99057i		−	0.101332i
$872$	21.2078	+	40.2110i	0.718188	+	1.36172i
$873$	−6.04206	−	18.4742i	−0.204493	−	0.625258i
$874$	6.17151	−	1.00722i	0.208754	−	0.0340699i
$875$	3.93268			0.132949
$876$	−7.87320	+	25.1139i	−0.266011	+	0.848519i
$877$	45.6116			1.54020			0.770098	−	0.637926i	$-0.220207\pi$
$877$	45.6116			1.54020			0.770098	+	0.637926i	$0.220207\pi$
$878$	23.4190	−	3.82211i	0.790352	−	0.128990i
$879$	−44.2244	−	32.0658i	−1.49165	−	1.08155i
$880$	−32.4444	−	42.9349i	−1.09370	−	1.44734i
$881$		−	26.5644i		−	0.894977i	−0.894290	−	0.447489i	$-0.852319\pi$
$881$		−	26.5644i		−	0.894977i	0.894290	−	0.447489i	$-0.147681\pi$
$882$	−0.691848	+	0.358310i	−0.0232957	+	0.0120649i
$883$			34.2796i			1.15360i	0.816886	+	0.576800i	$0.195699\pi$
$883$			34.2796i			1.15360i	−0.816886	+	0.576800i	$0.804301\pi$
$884$	2.05699	+	6.13399i	0.0691842	+	0.206309i
$885$	−48.9731	−	35.5089i	−1.64621	−	1.19362i
$886$	−5.57612	−	34.1663i	−0.187334	−	1.14784i
$887$	39.7420			1.33441			0.667203	−	0.744876i	$-0.267491\pi$
$887$	39.7420			1.33441			0.667203	+	0.744876i	$0.267491\pi$
$888$	43.9350	+	6.28179i	1.47436	+	0.210803i
$889$	51.6965			1.73385
$890$	−1.85769	−	11.3825i	−0.0622700	−	0.381543i
$891$	−30.1952	+	22.1166i	−1.01158	+	0.740933i
$892$	−9.25173	−	27.5888i	−0.309771	−	0.923743i
$893$			8.21188i			0.274800i
$894$	4.71010	−	9.37498i	0.157529	−	0.313546i
$895$		−	45.3134i		−	1.51466i
$896$	12.5371	−	26.7454i	0.418834	−	0.893501i
$897$	−11.9340	+	16.4591i	−0.398465	+	0.549554i
$898$	−2.69094	+	0.439176i	−0.0897978	+	0.0146555i
$899$	38.2227			1.27480
$900$	−19.5749	−	26.3106i	−0.652498	−	0.877021i
$901$	−7.89453			−0.263005
$902$	−64.3869	+	10.5083i	−2.14385	+	0.349888i
$903$	−11.5190	+	15.8868i	−0.383330	+	0.528679i
$904$	−7.57472	+	3.99501i	−0.251931	+	0.132872i
$905$		−	14.5966i		−	0.485207i
$906$	11.7352	−	23.3577i	0.389875	−	0.776008i
$907$		−	17.6213i		−	0.585105i	−0.956249	−	0.292553i	$-0.905495\pi$
$907$		−	17.6213i		−	0.585105i	0.956249	−	0.292553i	$-0.0945047\pi$
$908$	−10.7568	+	3.60723i	−0.356977	+	0.119710i
$909$	−43.4285	+	14.2034i	−1.44043	+	0.471098i
$910$	−5.75380	−	35.2549i	−0.190737	−	1.16869i
$911$	41.3022			1.36840			0.684202	−	0.729293i	$-0.260151\pi$
$911$	41.3022			1.36840			0.684202	+	0.729293i	$0.260151\pi$
$912$	7.80352	−	0.154238i	0.258400	−	0.00510732i
$913$	34.2190			1.13248
$914$	1.20851	+	7.40484i	0.0399740	+	0.244930i
$915$	−19.7354	−	14.3096i	−0.652433	−	0.473060i
$916$	34.8264	−	11.6788i	1.15070	−	0.385878i
$917$		−	18.6910i		−	0.617231i
$918$	7.86007	+	1.18381i	0.259421	+	0.0390716i
$919$			14.7692i			0.487190i	0.969877	+	0.243595i	$0.0783267\pi$
$919$			14.7692i			0.487190i	−0.969877	+	0.243595i	$0.921673\pi$
$920$	−31.7661	+	16.7539i	−1.04730	+	0.552359i
$921$	35.3844	+	25.6562i	1.16596	+	0.845400i
$922$	−42.2482	+	6.89515i	−1.39137	+	0.227080i
$923$	19.1811			0.631352
$924$	−35.8897	−	11.2514i	−1.18069	−	0.370145i
$925$	49.5152			1.62805
$926$	−36.8234	+	6.00979i	−1.21009	+	0.197494i
$927$	−35.9244	+	11.7492i	−1.17991	+	0.385894i
$928$	−27.3062	+	28.6206i	−0.896369	+	0.939517i
$929$			16.4570i			0.539937i	0.962869	+	0.269969i	$0.0870134\pi$
$929$			16.4570i			0.539937i	−0.962869	+	0.269969i	$0.912987\pi$
$930$	38.7039	+	19.4453i	1.26915	+	0.637637i
$931$		−	0.206884i		−	0.00678036i
$932$	11.9507	+	35.6373i	0.391459	+	1.16734i
$933$	15.7025	−	21.6565i	0.514077	−	0.709003i
$934$	8.64365	+	52.9617i	0.282829	+	1.73296i
$935$	14.5527			0.475923
$936$	−17.6536	+	18.2287i	−0.577025	+	0.595824i
$937$	7.76741			0.253750			0.126875	−	0.991919i	$-0.459505\pi$
$937$	7.76741			0.253750			0.126875	+	0.991919i	$0.459505\pi$
$938$	−0.594727	−	3.64404i	−0.0194185	−	0.118982i
$939$	−9.75187	+	13.4496i	−0.318240	+	0.438910i
$940$	−14.9951	−	44.7156i	−0.489085	−	1.45846i
$941$			9.72840i			0.317137i	0.987348	+	0.158568i	$0.0506878\pi$
$941$			9.72840i			0.317137i	−0.987348	+	0.158568i	$0.949312\pi$
$942$	46.5170	+	23.3707i	1.51561	+	0.761458i
$943$			43.5372i			1.41777i
$944$	−34.4525	+	26.0346i	−1.12133	+	0.847353i
$945$	−41.7785	−	13.4412i	−1.35906	−	0.437241i
$946$	25.1887	−	4.11093i	0.818954	−	0.133658i
$947$	18.7775			0.610188			0.305094	−	0.952322i	$-0.401312\pi$
$947$	18.7775			0.610188			0.305094	+	0.952322i	$0.401312\pi$
$948$	−4.65540	−	1.45947i	−0.151200	−	0.0474013i
$949$	22.7214			0.737567
$950$	8.59411	−	1.40261i	0.278830	−	0.0455066i
$951$	4.14426	+	3.00488i	0.134387	+	0.0974400i
$952$	3.72631	+	7.06525i	0.120770	+	0.228986i
$953$			32.0596i			1.03851i	0.854619	+	0.519256i	$0.173791\pi$
$953$			32.0596i			1.03851i	−0.854619	+	0.519256i	$0.826209\pi$
$954$	−14.2401	−	27.4957i	−0.461040	−	0.890206i
$955$			77.7566i			2.51614i
$956$	17.7795	−	5.96225i	0.575031	−	0.192833i
$957$	40.7786	+	29.5673i	1.31818	+	0.955777i
$958$	−1.55769	−	9.54432i	−0.0503266	−	0.308363i
$959$	6.60592			0.213316
$960$	−42.2103	+	15.0893i	−1.36233	+	0.487004i
$961$	1.12258			0.0362122
$962$	−6.17157	−	37.8147i	−0.198979	−	1.21920i
$963$	−15.9930	−	48.9004i	−0.515369	−	1.57579i
$964$	−22.3698	+	7.50155i	−0.720481	+	0.241609i
$965$		−	5.43257i		−	0.174881i
$966$	−11.2685	+	22.4289i	−0.362559	+	0.721636i
$967$			53.2987i			1.71397i	0.515342	+	0.856985i	$0.327665\pi$
$967$			53.2987i			1.71397i	−0.515342	+	0.856985i	$0.672335\pi$
$968$	8.30615	+	15.7488i	0.266970	+	0.506186i
$969$	−1.23896	+	1.70874i	−0.0398011	+	0.0548928i
$970$	−29.2551	+	4.77459i	−0.939324	+	0.153303i
$971$	26.8570			0.861881			0.430941	−	0.902380i	$-0.358182\pi$
$971$	26.8570			0.861881			0.430941	+	0.902380i	$0.358182\pi$
$972$	10.0549	+	29.5110i	0.322510	+	0.946566i
$973$	8.13781			0.260886
$974$	−17.8636	+	2.91544i	−0.572386	+	0.0934166i
$975$	−16.6187	+	22.9201i	−0.532223	+	0.734030i
$976$	−13.8838	+	10.4915i	−0.444411	+	0.335826i
$977$		−	34.4994i		−	1.10373i	−0.833933	−	0.551866i	$-0.813916\pi$
$977$		−	34.4994i		−	1.10373i	0.833933	−	0.551866i	$-0.186084\pi$
$978$	4.80604	−	9.56594i	0.153680	−	0.305885i
$979$			10.4836i			0.335057i
$980$	0.377775	+	1.12653i	0.0120676	+	0.0359858i
$981$	−14.9888	−	45.8298i	−0.478555	−	1.46323i
$982$	−8.51329	−	52.1630i	−0.271670	−	1.66459i
$983$	42.1510			1.34441			0.672203	−	0.740367i	$-0.265348\pi$
$983$	42.1510			1.34441			0.672203	+	0.740367i	$0.265348\pi$
$984$	−7.69156	+	53.7950i	−0.245198	+	1.71492i
$985$	−75.3882			−2.40207
$986$	−1.72302	−	10.5574i	−0.0548722	−	0.336216i
$987$	−26.6862	−	19.3493i	−0.849430	−	0.615897i
$988$	−2.14234	−	6.38849i	−0.0681568	−	0.203245i
$989$		−	17.0321i		−	0.541589i
$990$	26.2500	+	50.6852i	0.834280	+	1.61088i
$991$		−	16.5488i		−	0.525689i	−0.964838	−	0.262844i	$-0.915339\pi$
$991$		−	16.5488i		−	0.525689i	0.964838	−	0.262844i	$-0.0846606\pi$
$992$	21.3443	−	22.3718i	0.677684	−	0.710305i
$993$	4.74819	+	3.44277i	0.150679	+	0.109253i
$994$	23.3723	−	3.81448i	0.741323	−	0.120988i
$995$	−23.3188			−0.739256
$996$	8.52664	−	27.1982i	0.270177	−	0.861807i
$997$	−46.5445			−1.47408			−0.737039	−	0.675850i	$-0.763777\pi$
$997$	−46.5445			−1.47408			−0.737039	+	0.675850i	$0.763777\pi$
$998$	−24.1943	+	3.94865i	−0.765858	+	0.124992i
$999$	−44.8120	−	14.4171i	−1.41779	−	0.456137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.59	✓	128
3.2	odd	2	inner	804.2.c.b.671.70	yes	128
4.3	odd	2	inner	804.2.c.b.671.69	yes	128
12.11	even	2	inner	804.2.c.b.671.60	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.59	✓	128	1.1	even	1	trivial
804.2.c.b.671.60	yes	128	12.11	even	2	inner
804.2.c.b.671.69	yes	128	4.3	odd	2	inner
804.2.c.b.671.70	yes	128	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.227794 - 1.39575i) q^{2} +(-1.01672 + 1.40224i) q^{3} +(-1.89622 + 0.635885i) q^{4} -3.23506i q^{5} +(2.18877 + 1.09967i) q^{6} -2.61082i q^{7} +(1.31948 + 2.50179i) q^{8} +(-0.932552 - 2.85138i) q^{9} +O(q^{10})\)	\(q+(-0.227794 - 1.39575i) q^{2} +(-1.01672 + 1.40224i) q^{3} +(-1.89622 + 0.635885i) q^{4} -3.23506i q^{5} +(2.18877 + 1.09967i) q^{6} -2.61082i q^{7} +(1.31948 + 2.50179i) q^{8} +(-0.932552 - 2.85138i) q^{9} +(-4.51533 + 0.736926i) q^{10} +4.15873 q^{11} +(1.03627 - 3.30547i) q^{12} -2.99057 q^{13} +(-3.64404 + 0.594727i) q^{14} +(4.53633 + 3.28916i) q^{15} +(3.19130 - 2.41155i) q^{16} +1.08168i q^{17} +(-3.76737 + 1.95113i) q^{18} -1.12656i q^{19} +(2.05713 + 6.13439i) q^{20} +(3.66099 + 2.65447i) q^{21} +(-0.947332 - 5.80453i) q^{22} -3.92491 q^{23} +(-4.84966 - 0.693400i) q^{24} -5.46562 q^{25} +(0.681234 + 4.17409i) q^{26} +(4.94646 + 1.59140i) q^{27} +(1.66018 + 4.95068i) q^{28} -6.99278i q^{29} +(3.55749 - 7.08082i) q^{30} +5.46602i q^{31} +(-4.09288 - 3.90491i) q^{32} +(-4.22827 + 5.83153i) q^{33} +(1.50976 - 0.246400i) q^{34} -8.44615 q^{35} +(3.58147 + 4.81384i) q^{36} -9.05940 q^{37} +(-1.57240 + 0.256624i) q^{38} +(3.04058 - 4.19350i) q^{39} +(8.09345 - 4.26860i) q^{40} -11.0925i q^{41} +(2.87102 - 5.71449i) q^{42} +4.33948i q^{43} +(-7.88586 + 2.64447i) q^{44} +(-9.22438 + 3.01686i) q^{45} +(0.894070 + 5.47818i) q^{46} -7.28933 q^{47} +(0.136910 + 6.92685i) q^{48} +0.183642 q^{49} +(1.24503 + 7.62862i) q^{50} +(-1.51678 - 1.09977i) q^{51} +(5.67079 - 1.90166i) q^{52} +7.29838i q^{53} +(1.09442 - 7.26652i) q^{54} -13.4537i q^{55} +(6.53172 - 3.44492i) q^{56} +(1.57971 + 1.14540i) q^{57} +(-9.76015 + 1.59291i) q^{58} -10.7958 q^{59} +(-10.6934 - 3.35239i) q^{60} -4.35052 q^{61} +(7.62919 - 1.24513i) q^{62} +(-7.44442 + 2.43472i) q^{63} +(-4.51794 + 6.60214i) q^{64} +9.67469i q^{65} +(9.10252 + 4.57321i) q^{66} +1.00000i q^{67} +(-0.687826 - 2.05111i) q^{68} +(3.99054 - 5.50367i) q^{69} +(1.92398 + 11.7887i) q^{70} -6.41384 q^{71} +(5.90307 - 6.09539i) q^{72} -7.59766 q^{73} +(2.06367 + 12.6446i) q^{74} +(5.55702 - 7.66411i) q^{75} +(0.716363 + 2.13621i) q^{76} -10.8577i q^{77} +(-6.54569 - 3.28863i) q^{78} -1.40839i q^{79} +(-7.80153 - 10.3241i) q^{80} +(-7.26069 + 5.31811i) q^{81} +(-15.4824 + 2.52681i) q^{82} +8.22823 q^{83} +(-8.62998 - 2.70550i) q^{84} +3.49931 q^{85} +(6.05682 - 0.988506i) q^{86} +(9.80555 + 7.10971i) q^{87} +(5.48736 + 10.4043i) q^{88} +2.52086i q^{89} +(6.31203 + 12.1877i) q^{90} +7.80784i q^{91} +(7.44249 - 2.49579i) q^{92} +(-7.66468 - 5.55743i) q^{93} +(1.66046 + 10.1741i) q^{94} -3.64450 q^{95} +(9.63694 - 1.76898i) q^{96} +6.47906 q^{97} +(-0.0418325 - 0.256318i) q^{98} +(-3.87823 - 11.8581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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