LMFDB - Embedded newform 672.2.bs.a.155.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.15
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.838438 + 1.13887i) q^{2} +(-0.303955 - 1.70517i) q^{3} +(-0.594043 - 1.90974i) q^{4} +(-1.38677 + 3.34796i) q^{5} +(2.19681 + 1.08352i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.67301 + 0.924664i) q^{8} +(-2.81522 + 1.03659i) q^{9} +O(q^{10})$	\(q+(-0.838438 + 1.13887i) q^{2} +(-0.303955 - 1.70517i) q^{3} +(-0.594043 - 1.90974i) q^{4} +(-1.38677 + 3.34796i) q^{5} +(2.19681 + 1.08352i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.67301 + 0.924664i) q^{8} +(-2.81522 + 1.03659i) q^{9} +(-2.65017 - 4.38641i) q^{10} +(-0.378180 + 0.913007i) q^{11} +(-3.07588 + 1.59342i) q^{12} +(4.13390 - 1.71232i) q^{13} +(-0.212436 - 1.39817i) q^{14} +(6.13037 + 1.34705i) q^{15} +(-3.29423 + 2.26894i) q^{16} -3.26447 q^{17} +(1.17985 - 4.07529i) q^{18} +(-2.64793 - 6.39267i) q^{19} +(7.21754 + 0.659543i) q^{20} +(1.42067 + 0.990810i) q^{21} +(-0.722715 - 1.19620i) q^{22} +(4.18817 - 4.18817i) q^{23} +(0.764235 - 4.83900i) q^{24} +(-5.75018 - 5.75018i) q^{25} +(-1.51592 + 6.14364i) q^{26} +(2.62327 + 4.48536i) q^{27} +(1.77044 + 0.930340i) q^{28} +(-8.17496 + 3.38618i) q^{29} +(-6.67405 + 5.85226i) q^{30} +3.54789i q^{31} +(0.177986 - 5.65405i) q^{32} +(1.67178 + 0.367349i) q^{33} +(2.73705 - 3.71780i) q^{34} +(-1.38677 - 3.34796i) q^{35} +(3.65199 + 4.76057i) q^{36} +(-3.50173 - 1.45046i) q^{37} +(9.50054 + 2.34421i) q^{38} +(-4.17632 - 6.52855i) q^{39} +(-6.80260 + 7.66684i) q^{40} +(-5.55858 - 5.55858i) q^{41} +(-2.31954 + 0.787221i) q^{42} +(-6.28829 - 2.60469i) q^{43} +(1.96826 + 0.179861i) q^{44} +(0.433598 - 10.8628i) q^{45} +(1.25825 + 8.28130i) q^{46} -8.07759i q^{47} +(4.87022 + 4.92757i) q^{48} -1.00000i q^{49} +(11.3699 - 1.72753i) q^{50} +(0.992252 + 5.56648i) q^{51} +(-5.72580 - 6.87750i) q^{52} +(-8.16987 - 3.38407i) q^{53} +(-7.30768 - 0.773139i) q^{54} +(-2.53226 - 2.53226i) q^{55} +(-2.54394 + 1.23627i) q^{56} +(-10.0957 + 6.45826i) q^{57} +(2.99779 - 12.1493i) q^{58} +(2.98401 + 1.23602i) q^{59} +(-1.06918 - 12.5076i) q^{60} +(0.512237 + 1.23665i) q^{61} +(-4.04058 - 2.97468i) q^{62} +(1.25768 - 2.72364i) q^{63} +(6.28999 + 4.94328i) q^{64} +16.2147i q^{65} +(-1.82005 + 1.59594i) q^{66} +(-2.07847 + 0.860932i) q^{67} +(1.93923 + 6.23429i) q^{68} +(-8.41457 - 5.86853i) q^{69} +(4.97561 + 1.22771i) q^{70} +(-5.42590 - 5.42590i) q^{71} +(-8.48362 + 0.167689i) q^{72} +(-4.26813 + 4.26813i) q^{73} +(4.58787 - 2.77189i) q^{74} +(-8.05724 + 11.5528i) q^{75} +(-10.6354 + 8.85438i) q^{76} +(-0.378180 - 0.913007i) q^{77} +(10.9367 + 0.717505i) q^{78} +14.7584 q^{79} +(-3.02797 - 14.1754i) q^{80} +(6.85095 - 5.83647i) q^{81} +(10.9910 - 1.66996i) q^{82} +(-3.68658 + 1.52703i) q^{83} +(1.04825 - 3.30169i) q^{84} +(4.52707 - 10.9293i) q^{85} +(8.23875 - 4.97766i) q^{86} +(8.25884 + 12.9105i) q^{87} +(-1.85511 + 2.09079i) q^{88} +(7.82842 - 7.82842i) q^{89} +(12.0077 + 9.60157i) q^{90} +(-1.71232 + 4.13390i) q^{91} +(-10.4863 - 5.51037i) q^{92} +(6.04976 - 1.07840i) q^{93} +(9.19932 + 6.77256i) q^{94} +25.0745 q^{95} +(-9.69523 + 1.41508i) q^{96} +0.711404 q^{97} +(1.13887 + 0.838438i) q^{98} +(0.118245 - 2.96234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

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 $

$2$	−0.838438	+	1.13887i	−0.592865	+	0.805302i
$2$	−0.838438	+	1.13887i	−0.592865	+	0.805302i
$3$	−0.303955	−	1.70517i	−0.175489	−	0.984481i
$3$	−0.303955	−	1.70517i	−0.175489	−	0.984481i
$4$	−0.594043	−	1.90974i	−0.297021	−	0.954871i
$5$	−1.38677	+	3.34796i	−0.620183	+	1.49725i	0.231306	+	0.972881i	$0.425700\pi$
$5$	−1.38677	+	3.34796i	−0.620183	+	1.49725i	−0.851489	+	0.524373i	$0.824300\pi$
$6$	2.19681	+	1.08352i	0.896846	+	0.442344i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.67301	+	0.924664i	0.945053	+	0.326918i
$9$	−2.81522	+	1.03659i	−0.938407	+	0.345531i
$10$	−2.65017	−	4.38641i	−0.838056	−	1.38710i
$11$	−0.378180	+	0.913007i	−0.114026	+	0.275282i	−0.970582	−	0.240772i	$-0.922600\pi$
$11$	−0.378180	+	0.913007i	−0.114026	+	0.275282i	0.856556	+	0.516054i	$0.172600\pi$
$12$	−3.07588	+	1.59342i	−0.887929	+	0.459981i
$13$	4.13390	−	1.71232i	1.14654	−	0.474912i	0.273167	−	0.961967i	$-0.411929\pi$
$13$	4.13390	−	1.71232i	1.14654	−	0.474912i	0.873371	+	0.487055i	$0.161929\pi$
$14$	−0.212436	−	1.39817i	−0.0567760	−	0.373676i
$15$	6.13037	+	1.34705i	1.58285	+	0.347807i
$16$	−3.29423	+	2.26894i	−0.823557	+	0.567234i
$17$	−3.26447			−0.791749			−0.395875	−	0.918305i	$-0.629559\pi$
$17$	−3.26447			−0.791749			−0.395875	+	0.918305i	$0.629559\pi$
$18$	1.17985	−	4.07529i	0.278093	−	0.960554i
$19$	−2.64793	−	6.39267i	−0.607477	−	1.46658i	−0.865735	−	0.500503i	$-0.833148\pi$
$19$	−2.64793	−	6.39267i	−0.607477	−	1.46658i	0.258258	−	0.966076i	$-0.416852\pi$
$20$	7.21754	+	0.659543i	1.61389	+	0.147478i
$21$	1.42067	+	0.990810i	0.310015	+	0.216212i
$22$	−0.722715	−	1.19620i	−0.154083	−	0.255030i
$23$	4.18817	−	4.18817i	0.873294	−	0.873294i	−0.119536	−	0.992830i	$-0.538141\pi$
$23$	4.18817	−	4.18817i	0.873294	−	0.873294i	0.992830	+	0.119536i	$0.0381407\pi$
$24$	0.764235	−	4.83900i	0.155999	−	0.987757i
$25$	−5.75018	−	5.75018i	−1.15004	−	1.15004i
$26$	−1.51592	+	6.14364i	−0.297296	+	1.20487i
$27$	2.62327	+	4.48536i	0.504848	+	0.863208i
$28$	1.77044	+	0.930340i	0.334582	+	0.175818i
$29$	−8.17496	+	3.38618i	−1.51805	+	0.628798i	−0.977200	−	0.212320i	$-0.931898\pi$
$29$	−8.17496	+	3.38618i	−1.51805	+	0.628798i	−0.540852	+	0.841118i	$0.681898\pi$
$30$	−6.67405	+	5.85226i	−1.21851	+	1.06847i
$31$			3.54789i			0.637219i	0.947886	+	0.318610i	$0.103216\pi$
$31$			3.54789i			0.637219i	−0.947886	+	0.318610i	$0.896784\pi$
$32$	0.177986	−	5.65405i	0.0314638	−	0.999505i
$33$	1.67178	+	0.367349i	0.291020	+	0.0639472i
$34$	2.73705	−	3.71780i	0.469401	−	0.637597i
$35$	−1.38677	−	3.34796i	−0.234407	−	0.565909i
$36$	3.65199	+	4.76057i	0.608664	+	0.793428i
$37$	−3.50173	−	1.45046i	−0.575681	−	0.238455i	0.0757960	−	0.997123i	$-0.475850\pi$
$37$	−3.50173	−	1.45046i	−0.575681	−	0.238455i	−0.651477	+	0.758669i	$0.725850\pi$
$38$	9.50054	+	2.34421i	1.54119	+	0.380282i
$39$	−4.17632	−	6.52855i	−0.668746	−	1.04540i
$40$	−6.80260	+	7.66684i	−1.07558	+	1.21223i
$41$	−5.55858	−	5.55858i	−0.868104	−	0.868104i	0.124158	−	0.992262i	$-0.460377\pi$
$41$	−5.55858	−	5.55858i	−0.868104	−	0.868104i	−0.992262	+	0.124158i	$0.960377\pi$
$42$	−2.31954	+	0.787221i	−0.357913	+	0.121471i
$43$	−6.28829	−	2.60469i	−0.958955	−	0.397212i	−0.152366	−	0.988324i	$-0.548689\pi$
$43$	−6.28829	−	2.60469i	−0.958955	−	0.397212i	−0.806590	+	0.591112i	$0.798689\pi$
$44$	1.96826	+	0.179861i	0.296727	+	0.0271151i
$45$	0.433598	−	10.8628i	0.0646370	−	1.61933i
$46$	1.25825	+	8.28130i	0.185519	+	1.22101i
$47$		−	8.07759i		−	1.17824i	−0.808046	−	0.589119i	$-0.799475\pi$
$47$		−	8.07759i		−	1.17824i	0.808046	−	0.589119i	$-0.200525\pi$
$48$	4.87022	+	4.92757i	0.702956	+	0.711233i
$49$		−	1.00000i		−	0.142857i
$50$	11.3699	−	1.72753i	1.60794	−	0.244309i
$51$	0.992252	+	5.56648i	0.138943	+	0.779463i
$52$	−5.72580	−	6.87750i	−0.794026	−	0.953737i
$53$	−8.16987	−	3.38407i	−1.12222	−	0.464838i	−0.257089	−	0.966388i	$-0.582763\pi$
$53$	−8.16987	−	3.38407i	−1.12222	−	0.464838i	−0.865129	+	0.501550i	$0.832763\pi$
$54$	−7.30768	−	0.773139i	−0.994450	−	0.105211i
$55$	−2.53226	−	2.53226i	−0.341450	−	0.341450i
$56$	−2.54394	+	1.23627i	−0.339948	+	0.165203i
$57$	−10.0957	+	6.45826i	−1.33721	+	0.855418i
$58$	2.99779	−	12.1493i	0.393629	−	1.59528i
$59$	2.98401	+	1.23602i	0.388486	+	0.160916i	0.568373	−	0.822771i	$-0.307573\pi$
$59$	2.98401	+	1.23602i	0.388486	+	0.160916i	−0.179887	+	0.983687i	$0.557573\pi$
$60$	−1.06918	−	12.5076i	−0.138030	−	1.61473i
$61$	0.512237	+	1.23665i	0.0655852	+	0.158337i	0.953274	−	0.302108i	$-0.0976902\pi$
$61$	0.512237	+	1.23665i	0.0655852	+	0.158337i	−0.887689	+	0.460444i	$0.847690\pi$
$62$	−4.04058	−	2.97468i	−0.513154	−	0.377785i
$63$	1.25768	−	2.72364i	0.158453	−	0.343147i
$64$	6.28999	+	4.94328i	0.786249	+	0.617910i
$65$			16.2147i			2.01119i
$66$	−1.82005	+	1.59594i	−0.224033	+	0.196447i
$67$	−2.07847	+	0.860932i	−0.253926	+	0.105180i	−0.506016	−	0.862524i	$-0.668882\pi$
$67$	−2.07847	+	0.860932i	−0.253926	+	0.105180i	0.252090	+	0.967704i	$0.418882\pi$
$68$	1.93923	+	6.23429i	0.235166	+	0.756018i
$69$	−8.41457	−	5.86853i	−1.01299	−	0.706488i
$70$	4.97561	+	1.22771i	0.594699	+	0.146739i
$71$	−5.42590	−	5.42590i	−0.643936	−	0.643936i	0.307585	−	0.951521i	$-0.400479\pi$
$71$	−5.42590	−	5.42590i	−0.643936	−	0.643936i	−0.951521	+	0.307585i	$0.900479\pi$
$72$	−8.48362	+	0.167689i	−0.999805	+	0.0197623i
$73$	−4.26813	+	4.26813i	−0.499547	+	0.499547i	−0.911297	−	0.411750i	$-0.864918\pi$
$73$	−4.26813	+	4.26813i	−0.499547	+	0.499547i	0.411750	+	0.911297i	$0.364918\pi$
$74$	4.58787	−	2.77189i	0.533329	−	0.322225i
$75$	−8.05724	+	11.5528i	−0.930370	+	1.33401i
$76$	−10.6354	+	8.85438i	−1.21996	+	1.01567i
$77$	−0.378180	−	0.913007i	−0.0430976	−	0.104047i
$78$	10.9367	+	0.717505i	1.23834	+	0.0812414i
$79$	14.7584			1.66045			0.830224	−	0.557429i	$-0.188212\pi$
$79$	14.7584			1.66045			0.830224	+	0.557429i	$0.188212\pi$
$80$	−3.02797	−	14.1754i	−0.338537	−	1.58486i
$81$	6.85095	−	5.83647i	0.761217	−	0.648497i
$82$	10.9910	−	1.66996i	1.21375	−	0.184417i
$83$	−3.68658	+	1.52703i	−0.404654	+	0.167613i	−0.575721	−	0.817646i	$-0.695279\pi$
$83$	−3.68658	+	1.52703i	−0.404654	+	0.167613i	0.171067	+	0.985259i	$0.445279\pi$
$84$	1.04825	−	3.30169i	0.114374	−	0.360244i
$85$	4.52707	−	10.9293i	0.491029	−	1.18545i
$86$	8.23875	−	4.97766i	0.888407	−	0.536755i
$87$	8.25884	+	12.9105i	0.885441	+	1.38415i
$88$	−1.85511	+	2.09079i	−0.197755	+	0.222879i
$89$	7.82842	−	7.82842i	0.829811	−	0.829811i	−0.157680	−	0.987490i	$-0.550401\pi$
$89$	7.82842	−	7.82842i	0.829811	−	0.829811i	0.987490	+	0.157680i	$0.0504014\pi$
$90$	12.0077	+	9.60157i	1.26572	+	1.01209i
$91$	−1.71232	+	4.13390i	−0.179500	+	0.433351i
$92$	−10.4863	−	5.51037i	−1.09327	−	0.574496i
$93$	6.04976	−	1.07840i	0.627330	−	0.111825i
$94$	9.19932	+	6.77256i	0.948837	+	0.698537i
$95$	25.0745			2.57259
$96$	−9.69523	+	1.41508i	−0.989516	+	0.144426i
$97$	0.711404			0.0722321			0.0361160	−	0.999348i	$-0.488501\pi$
$97$	0.711404			0.0722321			0.0361160	+	0.999348i	$0.488501\pi$
$98$	1.13887	+	0.838438i	0.115043	+	0.0846951i
$99$	0.118245	−	2.96234i	0.0118840	−	0.297726i
$100$	−7.56550	+	14.3972i	−0.756550	+	1.43972i
$101$	7.04511	−	17.0084i	0.701015	−	1.69240i	−0.0203025	−	0.999794i	$-0.506463\pi$
$101$	7.04511	−	17.0084i	0.701015	−	1.69240i	0.721317	−	0.692605i	$-0.243537\pi$
$102$	−7.17143	−	3.53710i	−0.710077	−	0.350225i
$103$	0.952773	−	0.952773i	0.0938795	−	0.0938795i	−0.658607	−	0.752487i	$-0.728854\pi$
$103$	0.952773	−	0.952773i	0.0938795	−	0.0938795i	0.752487	+	0.658607i	$0.228854\pi$
$104$	12.6333	−	0.754578i	1.23880	−	0.0739924i
$105$	−5.28733	+	3.38231i	−0.515991	+	0.330080i
$106$	10.7039	−	6.46707i	1.03966	−	0.628137i
$107$	−5.51676	+	13.3186i	−0.533325	+	1.28756i	0.395984	+	0.918258i	$0.370404\pi$
$107$	−5.51676	+	13.3186i	−0.533325	+	1.28756i	−0.929309	+	0.369303i	$0.879596\pi$
$108$	7.00755	−	7.67426i	0.674301	−	0.738456i
$109$	−7.83171	+	3.24400i	−0.750142	+	0.310719i	−0.724800	−	0.688960i	$-0.758068\pi$
$109$	−7.83171	+	3.24400i	−0.750142	+	0.310719i	−0.0253425	+	0.999679i	$0.508068\pi$
$110$	5.00706	−	0.760769i	0.477405	−	0.0725364i
$111$	−1.40892	+	6.41193i	−0.133729	+	0.608593i
$112$	0.724990	−	3.93375i	0.0685051	−	0.371704i
$113$	5.19609			0.488807			0.244403	−	0.969674i	$-0.421408\pi$
$113$	5.19609			0.488807			0.244403	+	0.969674i	$0.421408\pi$
$114$	1.10955	−	16.9126i	0.103919	−	1.58401i
$115$	8.21380	+	19.8299i	0.765940	+	1.84914i
$116$	11.3230	+	13.6005i	1.05131	+	1.26278i
$117$	−9.86288	+	9.10573i	−0.911823	+	0.841825i
$118$	−3.90958	+	2.36207i	−0.359906	+	0.217447i
$119$	2.30833	−	2.30833i	0.211604	−	0.211604i
$120$	15.1410	+	9.26922i	1.38218	+	0.846160i
$121$	7.08761	+	7.08761i	0.644328	+	0.644328i
$122$	−1.83786	−	0.453483i	−0.166392	−	0.0410565i
$123$	−7.78877	+	11.1679i	−0.702290	+	1.00697i
$124$	6.77555	−	2.10760i	0.608462	−	0.189268i
$125$	10.4857	−	4.34333i	0.937872	−	0.388479i
$126$	2.04738	+	3.71594i	0.182395	+	0.331042i
$127$			7.52117i			0.667395i	0.942680	+	0.333698i	$0.108296\pi$
$127$			7.52117i			0.667395i	−0.942680	+	0.333698i	$0.891704\pi$
$128$	−10.9035	+	3.01884i	−0.963744	+	0.266830i
$129$	−2.53009	+	11.5143i	−0.222762	+	1.01378i
$130$	−18.4665	−	13.5951i	−1.61961	−	1.19237i
$131$	−4.09884	−	9.89548i	−0.358118	−	0.864572i	−0.995565	−	0.0940782i	$-0.970010\pi$
$131$	−4.09884	−	9.89548i	−0.358118	−	0.864572i	0.637447	−	0.770494i	$-0.279990\pi$
$132$	−0.291570	−	3.41090i	−0.0253779	−	0.296880i
$133$	6.39267	+	2.64793i	0.554315	+	0.229605i
$134$	0.762183	−	3.08895i	0.0658426	−	0.266844i
$135$	−18.6547	+	2.56244i	−1.60554	+	0.220540i
$136$	−8.72596	−	3.01853i	−0.748245	−	0.258837i
$137$	−1.32146	−	1.32146i	−0.112900	−	0.112900i	0.648400	−	0.761300i	$-0.275439\pi$
$137$	−1.32146	−	1.32146i	−0.112900	−	0.112900i	−0.761300	+	0.648400i	$0.775439\pi$
$138$	13.7386	−	4.66268i	1.16951	−	0.396914i
$139$	2.81500	+	1.16601i	0.238766	+	0.0988999i	0.498858	−	0.866684i	$-0.333753\pi$
$139$	2.81500	+	1.16601i	0.238766	+	0.0988999i	−0.260092	+	0.965584i	$0.583753\pi$
$140$	−5.56994	+	4.63721i	−0.470746	+	0.391915i
$141$	−13.7737	+	2.45523i	−1.15995	+	0.206767i
$142$	10.7287	−	1.63010i	0.900330	−	0.136795i
$143$			4.42185i			0.369774i
$144$	6.92202	−	9.80233i	0.576835	−	0.816861i
$145$		−	32.0653i		−	2.66288i
$146$	−1.28228	−	8.43940i	−0.106122	−	0.698450i
$147$	−1.70517	+	0.303955i	−0.140640	+	0.0250698i
$148$	−0.689835	+	7.54904i	−0.0567041	+	0.620527i
$149$	−0.128534	−	0.0532404i	−0.0105299	−	0.00436162i	0.377412	−	0.926045i	$-0.376814\pi$
$149$	−0.128534	−	0.0532404i	−0.0105299	−	0.00436162i	−0.387942	+	0.921684i	$0.626814\pi$
$150$	−6.40166	−	18.8625i	−0.522693	−	1.54011i
$151$	−12.9375	−	12.9375i	−1.05284	−	1.05284i	−0.998524	−	0.0543163i	$-0.982702\pi$
$151$	−12.9375	−	12.9375i	−1.05284	−	1.05284i	−0.0543163	−	0.998524i	$-0.517298\pi$
$152$	−1.16688	−	19.5361i	−0.0946464	−	1.58459i
$153$	9.19020	−	3.38392i	0.742984	−	0.273574i
$154$	1.35688	+	0.334803i	0.109340	+	0.0269792i
$155$	−11.8782	−	4.92010i	−0.954079	−	0.395192i
$156$	−9.98692	+	11.8539i	−0.799594	+	0.949074i
$157$	0.666674	+	1.60949i	0.0532064	+	0.128452i	0.948248	−	0.317532i	$-0.102854\pi$
$157$	0.666674	+	1.60949i	0.0532064	+	0.128452i	−0.895041	+	0.445983i	$0.852854\pi$
$158$	−12.3740	+	16.8079i	−0.984423	+	1.33716i
$159$	−3.28715	+	14.9596i	−0.260688	+	1.18638i
$160$	18.6827	+	8.43677i	1.47700	+	0.666985i
$161$			5.92297i			0.466795i
$162$	0.902876	+	12.6959i	0.0709366	+	0.997481i
$163$	−13.5676	+	5.61989i	−1.06270	+	0.440183i	−0.844408	−	0.535701i	$-0.820048\pi$
$163$	−13.5676	+	5.61989i	−1.06270	+	0.440183i	−0.218289	+	0.975884i	$0.570048\pi$
$164$	−7.31342	+	13.9175i	−0.571082	+	1.08677i
$165$	−3.54825	+	5.08764i	−0.276231	+	0.396072i
$166$	1.35188	−	5.47884i	0.104926	−	0.425241i
$167$	9.56742	+	9.56742i	0.740349	+	0.740349i	0.972645	−	0.232296i	$-0.0746237\pi$
$167$	9.56742	+	9.56742i	0.740349	+	0.740349i	−0.232296	+	0.972645i	$0.574624\pi$
$168$	2.88130	+	3.96209i	0.222297	+	0.305682i
$169$	4.96473	−	4.96473i	0.381902	−	0.381902i
$170$	8.65138	+	14.3193i	0.663530	+	1.09824i
$171$	14.0811	+	15.2520i	1.07681	+	1.16635i
$172$	−1.23878	+	13.5563i	−0.0944563	+	1.03366i
$173$	0.236859	+	0.571829i	0.0180081	+	0.0434753i	0.932628	−	0.360840i	$-0.117510\pi$
$173$	0.236859	+	0.571829i	0.0180081	+	0.0434753i	−0.914620	+	0.404315i	$0.867510\pi$
$174$	−21.6279	−	1.41889i	−1.63960	−	0.107566i
$175$	8.13198			0.614720
$176$	−0.825745	−	3.86572i	−0.0622428	−	0.291390i
$177$	1.20062	−	5.46395i	0.0902440	−	0.410696i
$178$	2.35189	+	15.4792i	0.176282	+	1.16021i
$179$	−15.9234	+	6.59567i	−1.19017	+	0.492984i	−0.887810	−	0.460210i	$-0.847774\pi$
$179$	−15.9234	+	6.59567i	−1.19017	+	0.492984i	−0.302358	+	0.953194i	$0.597774\pi$
$180$	−21.0027	+	5.62489i	−1.56545	+	0.419254i
$181$	−6.36532	+	15.3672i	−0.473130	+	1.14224i	0.489642	+	0.871924i	$0.337128\pi$
$181$	−6.36532	+	15.3672i	−0.473130	+	1.14224i	−0.962772	+	0.270314i	$0.912872\pi$
$182$	−3.27230	−	5.41613i	−0.242559	−	0.401470i
$183$	1.95300	−	1.24934i	0.144370	−	0.0923537i
$184$	15.0677	−	7.32238i	1.11080	−	0.539813i
$185$	9.71219	−	9.71219i	0.714055	−	0.714055i
$186$	−3.84419	+	7.79405i	−0.281870	+	0.571487i
$187$	1.23456	−	2.98048i	0.0902797	−	0.217954i
$188$	−15.4261	+	4.79843i	−1.12507	+	0.349962i
$189$	−5.02656	−	1.31670i	−0.365628	−	0.0957756i
$190$	−21.0234	+	28.5565i	−1.52520	+	2.07171i
$191$	−1.56310			−0.113102			−0.0565512	−	0.998400i	$-0.518010\pi$
$191$	−1.56310			−0.113102			−0.0565512	+	0.998400i	$0.518010\pi$
$192$	6.51726	−	12.2281i	0.470343	−	0.882484i
$193$	−22.4079			−1.61296			−0.806478	−	0.591264i	$-0.798629\pi$
$193$	−22.4079			−1.61296			−0.806478	+	0.591264i	$0.798629\pi$
$194$	−0.596468	+	0.810195i	−0.0428239	+	0.0581686i
$195$	27.6489	−	4.92856i	1.97998	−	0.352941i
$196$	−1.90974	+	0.594043i	−0.136410	+	0.0424316i
$197$	−9.98215	+	24.0990i	−0.711199	+	1.71699i	−0.0142153	+	0.999899i	$0.504525\pi$
$197$	−9.98215	+	24.0990i	−0.711199	+	1.71699i	−0.696984	+	0.717087i	$0.745475\pi$
$198$	3.27457	+	2.61840i	0.232714	+	0.186082i
$199$	14.1550	−	14.1550i	1.00342	−	1.00342i	0.00342391	−	0.999994i	$-0.498910\pi$
$199$	14.1550	−	14.1550i	1.00342	−	1.00342i	0.999994	−	0.00342391i	$-0.00108987\pi$
$200$	−10.0533	−	20.6873i	−0.710876	−	1.46281i
$201$	2.09980	+	3.28247i	0.148108	+	0.231528i
$202$	13.4634	+	22.2839i	0.947284	+	1.56789i
$203$	3.38618	−	8.17496i	0.237663	−	0.573770i
$204$	10.0411	−	5.20167i	0.703017	−	0.364190i
$205$	26.3184	−	10.9014i	1.83816	−	0.761389i
$206$	0.286242	+	1.88393i	0.0199434	+	0.131259i
$207$	−7.44920	+	16.1321i	−0.517755	+	1.12126i
$208$	−9.73287	+	15.0203i	−0.674853	+	1.04147i
$209$	6.83795			0.472991
$210$	0.581092	−	8.85744i	0.0400992	−	0.611221i
$211$	3.87219	+	9.34829i	0.266573	+	0.643563i	0.999317	−	0.0369403i	$-0.0117611\pi$
$211$	3.87219	+	9.34829i	0.266573	+	0.643563i	−0.732745	+	0.680503i	$0.761761\pi$
$212$	−1.60945	+	17.6126i	−0.110537	+	1.20964i
$213$	−7.60286	+	10.9013i	−0.520940	+	0.746947i
$214$	−10.5427	−	17.4497i	−0.720685	−	1.19284i
$215$	17.4408	−	17.4408i	1.18945	−	1.18945i
$216$	2.86458	+	14.4151i	0.194910	+	0.980821i
$217$	−2.50873	−	2.50873i	−0.170304	−	0.170304i
$218$	2.87192	−	11.6392i	0.194511	−	0.788305i
$219$	8.57522	+	5.98057i	0.579459	+	0.404130i
$220$	−3.33170	+	6.34024i	−0.224623	+	0.427459i
$221$	−13.4950	+	5.58981i	−0.907771	+	0.376011i
$222$	−6.12105	−	6.98058i	−0.410818	−	0.468506i
$223$			4.01245i			0.268693i	0.990934	+	0.134347i	$0.0428936\pi$
$223$			4.01245i			0.268693i	−0.990934	+	0.134347i	$0.957106\pi$
$224$	3.87216	+	4.12387i	0.258720	+	0.275538i
$225$	22.1486	+	10.2274i	1.47657	+	0.681829i
$226$	−4.35660	+	5.91766i	−0.289797	+	0.393637i
$227$	−3.03414	−	7.32506i	−0.201383	−	0.486181i	0.790634	−	0.612290i	$-0.209751\pi$
$227$	−3.03414	−	7.32506i	−0.201383	−	0.486181i	−0.992016	+	0.126108i	$0.959751\pi$
$228$	18.3309	+	15.4438i	1.21399	+	1.02279i
$229$	−18.9882	−	7.86518i	−1.25478	−	0.519746i	−0.346475	−	0.938059i	$-0.612621\pi$
$229$	−18.9882	−	7.86518i	−1.25478	−	0.519746i	−0.908303	+	0.418313i	$0.862621\pi$
$230$	−29.4704	−	7.27168i	−1.94322	−	0.479480i
$231$	−1.44188	+	0.922376i	−0.0948691	+	0.0606879i
$232$	−24.9829	+	1.49221i	−1.64020	+	0.0979683i
$233$	14.4363	+	14.4363i	0.945756	+	0.945756i	0.998603	−	0.0528463i	$-0.0168293\pi$
$233$	14.4363	+	14.4363i	0.945756	+	0.945756i	−0.0528463	+	0.998603i	$0.516829\pi$
$234$	−2.10081	−	18.8671i	−0.137334	−	1.23338i
$235$	27.0435	+	11.2018i	1.76412	+	0.730723i
$236$	0.587846	−	6.43295i	0.0382655	−	0.418749i
$237$	−4.48589	−	25.1656i	−0.291390	−	1.63468i
$238$	0.693491	+	4.56427i	0.0449523	+	0.295858i
$239$		−	14.8442i		−	0.960192i	−0.877216	−	0.480096i	$-0.840602\pi$
$239$		−	14.8442i		−	0.960192i	0.877216	−	0.480096i	$-0.159398\pi$
$240$	−23.2512	+	9.47191i	−1.50086	+	0.611409i
$241$		−	17.1188i		−	1.10272i	−0.834267	−	0.551361i	$-0.814109\pi$
$241$		−	17.1188i		−	1.10272i	0.834267	−	0.551361i	$-0.185891\pi$
$242$	−14.0144	+	2.12933i	−0.900879	+	0.136879i
$243$	−12.0346	−	9.90803i	−0.772018	−	0.635600i
$244$	2.05739	−	1.71286i	0.131711	−	0.109655i
$245$	3.34796	+	1.38677i	0.213893	+	0.0885975i
$246$	−6.18835	−	18.2340i	−0.394555	−	1.16256i
$247$	−21.8926	−	21.8926i	−1.39299	−	1.39299i
$248$	−3.28060	+	9.48354i	−0.208318	+	0.602206i
$249$	3.72440	+	5.82210i	0.236024	+	0.368960i
$250$	−3.84515	+	15.5835i	−0.243189	+	0.985586i
$251$	17.9903	+	7.45183i	1.13554	+	0.470355i	0.869660	−	0.493651i	$-0.164338\pi$
$251$	17.9903	+	7.45183i	1.13554	+	0.470355i	0.265878	+	0.964007i	$0.414338\pi$
$252$	−5.94857	−	0.783886i	−0.374725	−	0.0493802i
$253$	2.23995	+	5.40771i	0.140824	+	0.339980i
$254$	−8.56562	−	6.30603i	−0.537455	−	0.395676i
$255$	−20.0124	−	4.39741i	−1.25322	−	0.275376i
$256$	5.70386	−	14.9488i	0.356491	−	0.934299i
$257$		−	2.47735i		−	0.154533i	−0.997010	−	0.0772663i	$-0.975381\pi$
$257$		−	2.47735i		−	0.154533i	0.997010	−	0.0772663i	$-0.0246192\pi$
$258$	−10.9920	−	12.5355i	−0.684330	−	0.780426i
$259$	3.50173	−	1.45046i	0.217587	−	0.0901275i
$260$	30.9660	−	9.63224i	1.92043	−	0.597366i
$261$	19.5042	−	18.0069i	1.20728	−	1.11460i
$262$	14.7063	+	3.62871i	0.908557	+	0.224182i
$263$	−2.18068	−	2.18068i	−0.134466	−	0.134466i	0.636670	−	0.771136i	$-0.280311\pi$
$263$	−2.18068	−	2.18068i	−0.134466	−	0.134466i	−0.771136	+	0.636670i	$0.780311\pi$
$264$	4.12903	+	2.52777i	0.254124	+	0.155573i
$265$	22.6595	−	22.6595i	1.39196	−	1.39196i
$266$	−8.37550	+	5.06028i	−0.513535	+	0.310266i
$267$	−15.7283	−	10.9693i	−0.962555	−	0.671311i
$268$	2.87886	+	3.45792i	0.175854	+	0.211226i
$269$	9.64403	+	23.2828i	0.588007	+	1.41957i	0.885405	+	0.464821i	$0.153881\pi$
$269$	9.64403	+	23.2828i	0.588007	+	1.41957i	−0.297398	+	0.954754i	$0.596119\pi$
$270$	12.7225	−	23.3937i	0.774268	−	1.42369i
$271$	22.8488			1.38796			0.693982	−	0.719992i	$-0.255855\pi$
$271$	22.8488			1.38796			0.693982	+	0.719992i	$0.255855\pi$
$272$	10.7539	−	7.40687i	0.652051	−	0.449107i
$273$	7.56948	+	1.66328i	0.458126	+	0.100666i
$274$	2.61294	−	0.397007i	0.157853	−	0.0239841i
$275$	7.42455	−	3.07535i	0.447717	−	0.185451i
$276$	−6.20877	+	19.5558i	−0.373724	+	1.17712i
$277$	2.72624	−	6.58174i	0.163804	−	0.395458i	−0.820570	−	0.571545i	$-0.806344\pi$
$277$	2.72624	−	6.58174i	0.163804	−	0.395458i	0.984375	+	0.176087i	$0.0563441\pi$
$278$	−3.68814	+	2.22829i	−0.221200	+	0.133644i
$279$	−3.67771	−	9.98809i	−0.220179	−	0.597971i
$280$	−0.611117	−	10.2314i	−0.0365212	−	0.611445i
$281$	−15.1287	+	15.1287i	−0.902503	+	0.902503i	−0.995652	−	0.0931495i	$-0.970307\pi$
$281$	−15.1287	+	15.1287i	−0.902503	+	0.902503i	0.0931495	+	0.995652i	$0.470307\pi$
$282$	8.75220	−	17.7450i	0.521186	−	1.05670i
$283$	−2.62909	+	6.34718i	−0.156283	+	0.377301i	−0.982555	−	0.185970i	$-0.940457\pi$
$283$	−2.62909	+	6.34718i	−0.156283	+	0.377301i	0.826272	+	0.563271i	$0.190457\pi$
$284$	−7.13885	+	13.5853i	−0.423613	+	0.806138i
$285$	−7.62152	−	42.7563i	−0.451460	−	2.53266i
$286$	−5.03590	−	3.70745i	−0.297779	−	0.219226i
$287$	7.86102			0.464021
$288$	5.35988	+	16.1019i	0.315834	+	0.948815i
$289$	−6.34326			−0.373133
$290$	36.5182	+	26.8848i	2.14442	+	1.57873i
$291$	−0.216235	−	1.21307i	−0.0126759	−	0.0711111i
$292$	10.6865	+	5.61557i	0.625379	+	0.328627i
$293$	0.523579	−	1.26403i	0.0305878	−	0.0738455i	−0.907848	−	0.419300i	$-0.862275\pi$
$293$	0.523579	−	1.26403i	0.0305878	−	0.0738455i	0.938435	+	0.345455i	$0.112275\pi$
$294$	1.08352	−	2.19681i	0.0631919	−	0.128121i
$295$	−8.27629	+	8.27629i	−0.481864	+	0.481864i
$296$	−8.01898	−	7.11503i	−0.466094	−	0.413553i
$297$	−5.08724	+	0.698791i	−0.295191	+	0.0405480i
$298$	0.168401	−	0.101744i	0.00975523	−	0.00589388i
$299$	10.1420	−	24.4850i	0.586527	−	1.41600i
$300$	26.8493	+	8.52437i	1.55014	+	0.492155i
$301$	6.28829	−	2.60469i	0.362451	−	0.150132i
$302$	25.5814	−	3.88682i	1.47205	−	0.223661i
$303$	−31.1436	−	6.84333i	−1.78916	−	0.393139i
$304$	23.2274	+	15.0509i	1.33219	+	0.863230i
$305$	−4.85061			−0.277745
$306$	−3.85157	+	13.3036i	−0.220180	+	0.760518i
$307$	−6.96234	−	16.8086i	−0.397362	−	0.959317i	−0.988289	−	0.152592i	$-0.951238\pi$
$307$	−6.96234	−	16.8086i	−0.397362	−	0.959317i	0.590927	−	0.806725i	$-0.298762\pi$
$308$	−1.51895	+	1.26459i	−0.0865504	+	0.0720568i
$309$	−1.91424	−	1.33504i	−0.108897	−	0.0759479i
$310$	15.5625	−	9.40248i	0.883889	−	0.534025i
$311$	1.76390	−	1.76390i	0.100021	−	0.100021i	−0.655325	−	0.755347i	$-0.727468\pi$
$311$	1.76390	−	1.76390i	0.100021	−	0.100021i	0.755347	+	0.655325i	$0.227468\pi$
$312$	−5.12664	−	21.3126i	−0.290239	−	1.20659i
$313$	4.77817	+	4.77817i	0.270078	+	0.270078i	0.829132	−	0.559053i	$-0.188835\pi$
$313$	4.77817	+	4.77817i	0.270078	+	0.270078i	−0.559053	+	0.829132i	$0.688835\pi$
$314$	−2.39197	−	0.590207i	−0.134987	−	0.0333073i
$315$	7.37454	+	7.98774i	0.415508	+	0.450058i
$316$	−8.76711	−	28.1847i	−0.493189	−	1.58551i
$317$	−2.08604	+	0.864065i	−0.117164	+	0.0485308i	−0.440495	−	0.897755i	$-0.645197\pi$
$317$	−2.08604	+	0.864065i	−0.117164	+	0.0485308i	0.323332	+	0.946286i	$0.395197\pi$
$318$	−14.2810	−	16.2864i	−0.800838	−	0.913294i
$319$		−	8.74439i		−	0.489592i
$320$	−25.2727	+	14.2035i	−1.41279	+	0.793997i
$321$	24.3874	+	5.35875i	1.36117	+	0.299096i
$322$	−6.74548	−	4.96604i	−0.375911	−	0.276747i
$323$	8.64408	+	20.8687i	0.480970	+	1.16116i
$324$	−15.2159	−	9.61644i	−0.845329	−	0.534246i
$325$	−33.6168	−	13.9245i	−1.86472	−	0.772394i
$326$	4.97529	−	20.1636i	0.275556	−	1.11676i
$327$	7.91207	+	12.3684i	0.437539	+	0.683973i
$328$	−9.71833	−	19.9980i	−0.536605	−	1.10420i
$329$	5.71172	+	5.71172i	0.314897	+	0.314897i
$330$	−2.81916	−	8.30666i	−0.155190	−	0.457267i
$331$	−10.8342	−	4.48765i	−0.595499	−	0.246664i	0.0645154	−	0.997917i	$-0.479450\pi$
$331$	−10.8342	−	4.48765i	−0.595499	−	0.246664i	−0.660014	+	0.751253i	$0.729450\pi$
$332$	5.10622	+	6.13329i	0.280240	+	0.336608i
$333$	11.3617	+	0.453513i	0.622617	+	0.0248524i
$334$	−18.9177	+	2.87434i	−1.03513	+	0.157277i
$335$		−	8.15256i		−	0.445422i
$336$	−6.92808	−	0.0405484i	−0.377958	−	0.00221210i
$337$			11.5608i			0.629755i	0.949132	+	0.314878i	$0.101963\pi$
$337$			11.5608i			0.629755i	−0.949132	+	0.314878i	$0.898037\pi$
$338$	1.49155	+	9.81679i	0.0811298	+	0.533963i
$339$	−1.57938	−	8.86022i	−0.0857800	−	0.481221i
$340$	−23.5614	−	2.15305i	−1.27780	−	0.116766i
$341$	−3.23925	−	1.34174i	−0.175415	−	0.0726593i
$342$	−29.1761	+	3.24870i	−1.57766	+	0.175669i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−14.4002	−	12.7769i	−0.776407	−	0.688886i
$345$	31.3167	−	20.0333i	1.68603	−	1.07856i
$346$	−0.849829	−	0.209692i	−0.0456871	−	0.0112731i
$347$	−5.79074	−	2.39860i	−0.310863	−	0.128764i	0.221797	−	0.975093i	$-0.428808\pi$
$347$	−5.79074	−	2.39860i	−0.310863	−	0.128764i	−0.532660	+	0.846329i	$0.678808\pi$
$348$	19.7496	−	23.4416i	1.05869	−	1.25660i
$349$	6.11567	+	14.7645i	0.327365	+	0.790328i	0.998786	+	0.0492526i	$0.0156839\pi$
$349$	6.11567	+	14.7645i	0.327365	+	0.790328i	−0.671422	+	0.741075i	$0.734316\pi$
$350$	−6.81816	+	9.26125i	−0.364446	+	0.495035i
$351$	18.5247	+	14.0502i	0.988776	+	0.749943i
$352$	5.09488	+	2.30075i	0.271558	+	0.122631i
$353$			1.67879i			0.0893530i	0.999002	+	0.0446765i	$0.0142257\pi$
$353$			1.67879i			0.0893530i	−0.999002	+	0.0446765i	$0.985774\pi$
$354$	5.21608	+	5.94853i	0.277231	+	0.316161i
$355$	25.6902	−	10.6412i	1.36349	−	0.564778i
$356$	−19.6007	−	10.2998i	−1.03883	−	0.545890i
$357$	−4.63772	−	3.23447i	−0.245454	−	0.171186i
$358$	5.83915	−	23.6647i	0.308609	−	1.25072i
$359$	15.6864	+	15.6864i	0.827898	+	0.827898i	0.987226	−	0.159328i	$-0.0509327\pi$
$359$	15.6864	+	15.6864i	0.827898	+	0.827898i	−0.159328	+	0.987226i	$0.550933\pi$
$360$	11.2034	−	28.6354i	0.590472	−	1.50922i
$361$	−20.4197	+	20.4197i	−1.07472	+	1.07472i
$362$	−12.1643	−	20.1337i	−0.639343	−	1.05821i
$363$	9.93128	−	14.2399i	0.521257	−	0.747402i
$364$	8.91188	+	0.814372i	0.467109	+	0.0426847i
$365$	−8.37061	−	20.2084i	−0.438138	−	1.05776i
$366$	−0.214640	+	3.27170i	−0.0112194	+	0.171015i
$367$	−9.05621			−0.472730			−0.236365	−	0.971664i	$-0.575956\pi$
$367$	−9.05621			−0.472730			−0.236365	+	0.971664i	$0.575956\pi$
$368$	−4.29409	+	23.2995i	−0.223845	+	1.21457i
$369$	21.4106	+	9.88666i	1.11459	+	0.514679i
$370$	2.91784	+	19.2040i	0.151691	+	0.998368i
$371$	8.16987	−	3.38407i	0.424158	−	0.175692i
$372$	−5.65328	−	10.9129i	−0.293109	−	0.565805i
$373$	4.22344	−	10.1963i	0.218681	−	0.527943i	−0.776025	−	0.630702i	$-0.782767\pi$
$373$	4.22344	−	10.1963i	0.218681	−	0.527943i	0.994706	+	0.102759i	$0.0327670\pi$
$374$	2.35928	+	3.90495i	0.121995	+	0.201920i
$375$	−10.5933	−	16.5598i	−0.547037	−	0.855144i
$376$	7.46906	−	21.5915i	0.385187	−	1.11350i
$377$	−27.9963	+	27.9963i	−1.44188	+	1.44188i
$378$	5.71400	−	4.62062i	0.293897	−	0.237659i
$379$	9.44144	−	22.7937i	0.484974	−	1.17083i	−0.472245	−	0.881467i	$-0.656556\pi$
$379$	9.44144	−	22.7937i	0.484974	−	1.17083i	0.957219	−	0.289364i	$-0.0934438\pi$
$380$	−14.8953	−	47.8858i	−0.764113	−	2.45649i
$381$	12.8249	−	2.28610i	0.657038	−	0.117120i
$382$	1.31057	−	1.78017i	0.0670544	−	0.0910815i
$383$	17.3845			0.888305			0.444152	−	0.895951i	$-0.353505\pi$
$383$	17.3845			0.888305			0.444152	+	0.895951i	$0.353505\pi$
$384$	8.46182	+	17.6748i	0.431816	+	0.901962i
$385$	3.58116			0.182513
$386$	18.7876	−	25.5197i	0.956266	−	1.29892i
$387$	20.4029	+	0.814403i	1.03714	+	0.0413984i
$388$	−0.422604	−	1.35860i	−0.0214545	−	0.0689723i
$389$	−6.73235	+	16.2533i	−0.341344	+	0.824076i	0.656237	+	0.754555i	$0.272147\pi$
$389$	−6.73235	+	16.2533i	−0.341344	+	0.824076i	−0.997580	+	0.0695215i	$0.977853\pi$
$390$	−17.5689	+	35.6208i	−0.889637	+	1.80373i
$391$	−13.6721	+	13.6721i	−0.691430	+	0.691430i
$392$	0.924664	−	2.67301i	0.0467026	−	0.135008i
$393$	−15.6276	+	9.99702i	−0.788310	+	0.504283i
$394$	−19.0762	−	31.5739i	−0.961046	−	1.59067i
$395$	−20.4665	+	49.4105i	−1.02978	+	2.48611i
$396$	−5.72754	+	1.53394i	−0.287820	+	0.0770833i
$397$	−27.7342	+	11.4879i	−1.39194	+	0.576560i	−0.947646	−	0.319322i	$-0.896545\pi$
$397$	−27.7342	+	11.4879i	−1.39194	+	0.576560i	−0.444292	+	0.895882i	$0.646545\pi$
$398$	4.25258	+	27.9887i	0.213162	+	1.40295i
$399$	2.57209	−	11.7055i	0.128766	−	0.586006i
$400$	31.9892	+	5.89560i	1.59946	+	0.294780i
$401$	−15.1147			−0.754793			−0.377396	−	0.926052i	$-0.623181\pi$
$401$	−15.1147			−0.754793			−0.377396	+	0.926052i	$0.623181\pi$
$402$	−5.49885	−	0.360752i	−0.274258	−	0.0179927i
$403$	6.07511	+	14.6666i	0.302623	+	0.730596i
$404$	−36.6667	−	3.35063i	−1.82424	−	0.166700i
$405$	10.0396	+	31.0306i	0.498871	+	1.54192i
$406$	6.47110	+	10.7106i	0.321155	+	0.531559i
$407$	2.64857	−	2.64857i	0.131285	−	0.131285i
$408$	−2.49482	+	15.7968i	−0.123512	+	0.782056i
$409$	−16.2376	−	16.2376i	−0.802896	−	0.802896i	0.180651	−	0.983547i	$-0.442180\pi$
$409$	−16.2376	−	16.2376i	−0.802896	−	0.802896i	−0.983547	+	0.180651i	$0.942180\pi$
$410$	−9.65104	+	39.1133i	−0.476631	+	1.93167i
$411$	−1.85165	+	2.65499i	−0.0913354	+	0.130961i
$412$	−2.38554	−	1.25356i	−0.117527	−	0.0617586i
$413$	−2.98401	+	1.23602i	−0.146834	+	0.0608205i
$414$	−12.1266	−	22.0094i	−0.595989	−	1.08170i
$415$		−	14.4602i		−	0.709821i
$416$	−8.94576	−	23.6781i	−0.438602	−	1.16091i
$417$	1.13262	−	5.15448i	0.0554645	−	0.252416i
$418$	−5.73320	+	7.78753i	−0.280420	+	0.380900i
$419$	−0.582085	−	1.40528i	−0.0284367	−	0.0686523i	0.909023	−	0.416745i	$-0.136829\pi$
$419$	−0.582085	−	1.40528i	−0.0284367	−	0.0686523i	−0.937460	+	0.348093i	$0.886829\pi$
$420$	9.60025	+	8.08820i	0.468444	+	0.394664i
$421$	23.5356	+	9.74876i	1.14705	+	0.475125i	0.873545	−	0.486744i	$-0.161815\pi$
$421$	23.5356	+	9.74876i	1.14705	+	0.475125i	0.273510	+	0.961869i	$0.411815\pi$
$422$	−13.8931	−	3.42805i	−0.676304	−	0.166875i
$423$	8.37317	+	22.7402i	0.407117	+	1.10567i
$424$	−18.7090	−	16.6000i	−0.908591	−	0.806170i
$425$	18.7713	+	18.7713i	0.910540	+	0.910540i
$426$	−6.04065	−	17.7987i	−0.292670	−	0.862352i
$427$	−1.23665	−	0.512237i	−0.0598456	−	0.0247889i
$428$	28.7123	+	2.62375i	1.38786	+	0.126824i
$429$	7.54001	−	1.34404i	0.364035	−	0.0648911i
$430$	5.23975	+	34.4859i	0.252683	+	1.66306i
$431$		−	9.17873i		−	0.442124i	−0.975260	−	0.221062i	$-0.929048\pi$
$431$		−	9.17873i		−	0.442124i	0.975260	−	0.221062i	$-0.0709523\pi$
$432$	−18.8186	−	8.82376i	−0.905412	−	0.424533i
$433$		−	8.98199i		−	0.431647i	−0.976432	−	0.215824i	$-0.930756\pi$
$433$		−	8.98199i		−	0.431647i	0.976432	−	0.215824i	$-0.0692436\pi$
$434$	4.96054	−	0.753699i	0.238113	−	0.0361787i
$435$	−54.6769	+	9.74642i	−2.62155	+	0.467305i
$436$	10.8476	+	13.0295i	0.519505	+	0.623999i
$437$	−37.8636	−	15.6836i	−1.81126	−	0.750249i
$438$	−14.0009	+	4.75170i	−0.668988	+	0.227045i
$439$	3.95814	+	3.95814i	0.188912	+	0.188912i	0.795225	−	0.606314i	$-0.207352\pi$
$439$	3.95814	+	3.95814i	0.188912	+	0.188912i	−0.606314	+	0.795225i	$0.707352\pi$
$440$	−4.42728	−	9.11027i	−0.211062	−	0.434315i
$441$	1.03659	+	2.81522i	0.0493615	+	0.134058i
$442$	4.94866	−	20.0557i	0.235384	−	0.953953i
$443$	−14.1315	−	5.85347i	−0.671409	−	0.278107i	0.0208216	−	0.999783i	$-0.493372\pi$
$443$	−14.1315	−	5.85347i	−0.671409	−	0.278107i	−0.692230	+	0.721677i	$0.743372\pi$
$444$	13.0821	−	1.11828i	0.620848	−	0.0530714i
$445$	15.3530	+	37.0655i	0.727803	+	1.75707i
$446$	−4.56965	−	3.36419i	−0.216379	−	0.159299i
$447$	−0.0517155	+	0.235355i	−0.00244606	+	0.0111319i
$448$	−7.94312	+	0.952271i	−0.375277	+	0.0449906i
$449$		−	9.01943i		−	0.425653i	−0.977090	−	0.212827i	$-0.931733\pi$
$449$		−	9.01943i		−	0.425653i	0.977090	−	0.212827i	$-0.0682670\pi$
$450$	−30.2179	+	16.6493i	−1.42449	+	0.784854i
$451$	7.17717	−	2.97288i	0.337960	−	0.139987i
$452$	−3.08670	−	9.92318i	−0.145186	−	0.466747i
$453$	−18.1283	+	25.9931i	−0.851740	+	1.22126i
$454$	10.8862	+	2.68613i	0.510916	+	0.126066i
$455$	−11.4656	−	11.4656i	−0.537513	−	0.537513i
$456$	−32.9578	+	7.92784i	−1.54339	+	0.371255i
$457$	−25.5762	+	25.5762i	−1.19640	+	1.19640i	−0.221169	+	0.975236i	$0.570987\pi$
$457$	−25.5762	+	25.5762i	−1.19640	+	1.19640i	−0.975236	+	0.221169i	$0.929013\pi$
$458$	24.8779	−	15.0306i	1.16247	−	0.702335i
$459$	−8.56358	−	14.6423i	−0.399713	−	0.683444i
$460$	32.9906	−	27.4660i	1.53819	−	1.28061i
$461$	−9.68036	−	23.3705i	−0.450860	−	1.08847i	−0.971996	−	0.234998i	$-0.924492\pi$
$461$	−9.68036	−	23.3705i	−0.450860	−	1.08847i	0.521136	−	0.853473i	$-0.325508\pi$
$462$	0.158467	−	2.41547i	0.00737255	−	0.112378i
$463$	19.6379			0.912650			0.456325	−	0.889813i	$-0.349166\pi$
$463$	19.6379			0.912650			0.456325	+	0.889813i	$0.349166\pi$
$464$	19.2471	−	29.7033i	0.893526	−	1.37894i
$465$	−4.77919	+	21.7498i	−0.221629	+	1.00862i
$466$	−28.5451	+	4.33711i	−1.32233	+	0.200913i
$467$	−19.9742	+	8.27358i	−0.924295	+	0.382856i	−0.793511	−	0.608555i	$-0.791749\pi$
$467$	−19.9742	+	8.27358i	−0.924295	+	0.382856i	−0.130784	+	0.991411i	$0.541749\pi$
$468$	23.2486	+	13.4264i	1.07466	+	0.620634i
$469$	0.860932	−	2.07847i	0.0397541	−	0.0959750i
$470$	−35.4316	+	21.4070i	−1.63434	+	0.987429i
$471$	2.54182	−	1.62601i	0.117121	−	0.0749225i
$472$	6.83341	+	6.06311i	0.314533	+	0.279077i
$473$	4.75621	−	4.75621i	0.218691	−	0.218691i
$474$	32.4214	+	15.9910i	1.48917	+	0.734489i
$475$	−21.5329	+	51.9850i	−0.987998	+	2.38524i
$476$	−5.77955	−	3.03706i	−0.264905	−	0.139204i
$477$	26.5079	+	1.05809i	1.21371	+	0.0484466i
$478$	16.9056	+	12.4460i	0.773244	+	0.569265i
$479$	−37.5509			−1.71575			−0.857873	−	0.513862i	$-0.828214\pi$
$479$	−37.5509			−1.71575			−0.857873	+	0.513862i	$0.828214\pi$
$480$	8.70742	−	34.4217i	0.397438	−	1.57113i
$481$	−16.9595			−0.773285
$482$	19.4961	+	14.3531i	0.888023	+	0.653765i
$483$	10.0997	−	1.80032i	0.459551	−	0.0819173i
$484$	9.32516	−	17.7459i	0.423871	−	0.806630i
$485$	−0.986554	+	2.38175i	−0.0447971	+	0.108150i
$486$	21.3742	−	5.39853i	0.969553	−	0.244882i
$487$	26.4243	−	26.4243i	1.19740	−	1.19740i	0.222458	−	0.974942i	$-0.428592\pi$
$487$	26.4243	−	26.4243i	1.19740	−	1.19740i	0.974942	−	0.222458i	$-0.0714081\pi$
$488$	0.225730	+	3.77922i	0.0102183	+	0.171077i
$489$	13.7068	+	21.4269i	0.619844	+	0.968958i
$490$	−4.38641	+	2.65017i	−0.198158	+	0.119722i
$491$	1.72521	−	4.16503i	0.0778577	−	0.187965i	−0.880158	−	0.474681i	$-0.842563\pi$
$491$	1.72521	−	4.16503i	0.0778577	−	0.187965i	0.958016	+	0.286716i	$0.0925635\pi$
$492$	25.9547	+	8.24034i	1.17013	+	0.371503i
$493$	26.6869	−	11.0541i	1.20192	−	0.497850i
$494$	43.2883	−	6.57719i	1.94763	−	0.295922i
$495$	9.75381	+	4.50396i	0.438401	+	0.202438i
$496$	−8.04993	−	11.6875i	−0.361452	−	0.524786i
$497$	7.67338			0.344198
$498$	−9.75328	−	0.639864i	−0.437055	−	0.0286730i
$499$	−16.1323	−	38.9469i	−0.722183	−	1.74350i	−0.667037	−	0.745025i	$-0.732438\pi$
$499$	−16.1323	−	38.9469i	−0.722183	−	1.74350i	−0.0551455	−	0.998478i	$-0.517562\pi$
$500$	−14.5236	−	17.4449i	−0.649516	−	0.780160i
$501$	13.4060	−	19.2222i	0.598937	−	0.858783i
$502$	−23.5704	+	14.2407i	−1.05200	+	0.635593i
$503$	−2.13440	+	2.13440i	−0.0951684	+	0.0951684i	−0.753088	−	0.657920i	$-0.771437\pi$
$503$	−2.13440	+	2.13440i	−0.0951684	+	0.0951684i	0.657920	+	0.753088i	$0.271437\pi$
$504$	5.88025	−	6.11740i	0.261927	−	0.272491i
$505$	47.1735	+	47.1735i	2.09919	+	2.09919i
$506$	−8.03673	−	1.98303i	−0.357276	−	0.0881563i
$507$	−9.97477	−	6.95666i	−0.442995	−	0.308956i
$508$	14.3635	−	4.46789i	0.637276	−	0.198231i
$509$	21.6049	−	8.94906i	0.957622	−	0.396660i	0.151532	−	0.988452i	$-0.451579\pi$
$509$	21.6049	−	8.94906i	0.957622	−	0.396660i	0.806091	+	0.591792i	$0.201579\pi$
$510$	21.7872	−	19.1045i	0.964754	−	0.845962i
$511$		−	6.03605i		−	0.267019i
$512$	12.2424	+	19.0296i	0.541041	+	0.840996i
$513$	21.7272	−	28.6466i	0.959279	−	1.26478i
$514$	2.82137	+	2.07710i	0.124445	+	0.0916170i
$515$	1.86857	+	4.51113i	0.0823390	+	0.198784i
$516$	23.4924	−	2.00818i	1.03419	−	0.0884050i
$517$	7.37490	+	3.05478i	0.324348	+	0.134349i
$518$	−1.28410	+	5.20413i	−0.0564200	+	0.228657i
$519$	0.903071	−	0.577696i	0.0396404	−	0.0253580i
$520$	−14.9932	+	43.3422i	−0.657495	+	1.90068i
$521$	20.7497	+	20.7497i	0.909062	+	0.909062i	0.996197	−	0.0871345i	$-0.0277710\pi$
$521$	20.7497	+	20.7497i	0.909062	+	0.909062i	−0.0871345	+	0.996197i	$0.527771\pi$
$522$	4.15444	+	37.3105i	0.181835	+	1.63304i
$523$	−31.2842	−	12.9583i	−1.36796	−	0.566628i	−0.426726	−	0.904381i	$-0.640333\pi$
$523$	−31.2842	−	12.9583i	−1.36796	−	0.566628i	−0.941235	+	0.337753i	$0.890333\pi$
$524$	−16.4629	+	13.7061i	−0.719186	+	0.598752i
$525$	−2.47176	−	13.8664i	−0.107876	−	0.605180i
$526$	4.31187	−	0.655142i	0.188006	−	0.0285655i
$527$		−	11.5820i		−	0.504518i
$528$	−6.34073	+	2.58304i	−0.275945	+	0.112412i
$529$		−	12.0815i		−	0.525284i
$530$	6.80759	+	44.8047i	0.295703	+	1.94619i
$531$	−9.68191	−	0.386463i	−0.420159	−	0.0167711i
$532$	1.25935	−	13.7813i	0.0545995	−	0.597497i
$533$	−32.4967	−	13.4606i	−1.40759	−	0.583042i
$534$	25.6798	−	8.71536i	1.11127	−	0.377151i
$535$	−36.9398	−	36.9398i	−1.59705	−	1.59705i
$536$	−6.35186	+	0.379392i	−0.274358	+	0.0163872i
$537$	16.0868	+	25.1473i	0.694195	+	1.08519i
$538$	−34.6019	−	8.53787i	−1.49179	−	0.368094i
$539$	0.913007	+	0.378180i	0.0393260	+	0.0162894i
$540$	15.9753	+	34.1034i	0.687466	+	1.46758i
$541$	−8.53807	−	20.6127i	−0.367080	−	0.886210i	−0.994226	−	0.107308i	$-0.965777\pi$
$541$	−8.53807	−	20.6127i	−0.367080	−	0.886210i	0.627145	−	0.778902i	$-0.284223\pi$
$542$	−19.1573	+	26.0217i	−0.822876	+	1.11773i
$543$	28.1386	+	6.18301i	1.20754	+	0.265338i
$544$	−0.581030	+	18.4575i	−0.0249115	+	0.791357i
$545$		−	30.7190i		−	1.31586i
$546$	−8.24080	+	7.22609i	−0.352673	+	0.309248i
$547$	−6.05859	+	2.50955i	−0.259046	+	0.107301i	−0.508427	−	0.861105i	$-0.669773\pi$
$547$	−6.05859	+	2.50955i	−0.259046	+	0.107301i	0.249381	+	0.968406i	$0.419773\pi$
$548$	−1.73865	+	3.30866i	−0.0742713	+	0.141339i
$549$	−2.72396	−	2.95046i	−0.116256	−	0.125923i
$550$	−2.72261	+	11.0341i	−0.116092	+	0.470495i
$551$	43.2935	+	43.2935i	1.84436	+	1.84436i
$552$	−17.0658	−	23.4673i	−0.726369	−	0.998835i
$553$	−10.4358	+	10.4358i	−0.443774	+	0.443774i
$554$	5.20995	+	8.62321i	0.221349	+	0.366365i
$555$	−19.5130	−	13.6089i	−0.828282	−	0.577665i
$556$	0.554551	−	6.06859i	0.0235182	−	0.257366i
$557$	4.79202	+	11.5690i	0.203044	+	0.490192i	0.992298	−	0.123875i	$-0.0395322\pi$
$557$	4.79202	+	11.5690i	0.203044	+	0.490192i	−0.789254	+	0.614068i	$0.789532\pi$
$558$	14.4587	+	4.18597i	0.612083	+	0.177206i
$559$	−30.4552			−1.28812
$560$	12.1646	+	7.88245i	0.514050	+	0.333094i
$561$	−5.45748	−	1.19920i	−0.230415	−	0.0506301i
$562$	−4.54512	−	29.9141i	−0.191724	−	1.26185i
$563$	29.5106	−	12.2237i	1.24373	−	0.515168i	0.338848	−	0.940841i	$-0.389963\pi$
$563$	29.5106	−	12.2237i	1.24373	−	0.515168i	0.904877	+	0.425673i	$0.139963\pi$
$564$	12.8710	+	24.8457i	0.541967	+	1.04619i
$565$	−7.20578	+	17.3963i	−0.303149	+	0.731868i
$566$	−5.02428	−	8.31591i	−0.211186	−	0.349544i
$567$	−0.717345	+	8.97137i	−0.0301256	+	0.376762i
$568$	−9.48637	−	19.5206i	−0.398039	−	0.819068i
$569$	12.7889	−	12.7889i	0.536140	−	0.536140i	−0.386253	−	0.922393i	$-0.626231\pi$
$569$	12.7889	−	12.7889i	0.536140	−	0.536140i	0.922393	+	0.386253i	$0.126231\pi$
$570$	55.0840	+	27.1686i	2.30721	+	1.13797i
$571$	−1.27051	+	3.06727i	−0.0531690	+	0.128361i	−0.948232	−	0.317578i	$-0.897130\pi$
$571$	−1.27051	+	3.06727i	−0.0531690	+	0.128361i	0.895063	+	0.445940i	$0.147130\pi$
$572$	8.44459	−	2.62677i	0.353086	−	0.109831i
$573$	0.475114	+	2.66536i	0.0198482	+	0.111347i
$574$	−6.59098	+	8.95266i	−0.275102	+	0.373677i
$575$	−48.1654			−2.00864
$576$	−22.8319	−	7.39627i	−0.951329	−	0.308178i
$577$	−10.9212			−0.454654			−0.227327	−	0.973818i	$-0.572999\pi$
$577$	−10.9212			−0.454654			−0.227327	+	0.973818i	$0.572999\pi$
$578$	5.31843	−	7.22414i	0.221218	−	0.300485i
$579$	6.81100	+	38.2093i	0.283056	+	1.58793i
$580$	−61.2364	+	19.0482i	−2.54271	+	0.790932i
$581$	1.52703	−	3.68658i	0.0633519	−	0.152945i
$582$	1.56282	+	0.770817i	0.0647810	+	0.0319514i
$583$	6.17936	−	6.17936i	0.255923	−	0.255923i
$584$	−15.3554	+	7.46218i	−0.635409	+	0.308787i
$585$	−16.8081	−	45.6481i	−0.694928	−	1.88732i
$586$	1.00058	+	1.65610i	0.0413334	+	0.0684128i
$587$	7.31821	−	17.6677i	0.302055	−	0.729225i	−0.697861	−	0.716234i	$-0.745865\pi$
$587$	7.31821	−	17.6677i	0.302055	−	0.729225i	0.999916	−	0.0129917i	$-0.00413550\pi$
$588$	1.59342	+	3.07588i	0.0657116	+	0.126847i
$589$	22.6805	−	9.39456i	0.934532	−	0.387096i
$590$	−2.48645	−	16.3648i	−0.102365	−	0.673727i
$591$	44.1271	+	9.69625i	1.81515	+	0.398850i
$592$	14.8265	−	3.16704i	0.609366	−	0.130165i
$593$	−47.7117			−1.95929			−0.979643	−	0.200747i	$-0.935663\pi$
$593$	−47.7117			−1.95929			−0.979643	+	0.200747i	$0.935663\pi$
$594$	3.46950	−	6.37959i	0.142355	−	0.261758i
$595$	4.52707	+	10.9293i	0.185592	+	0.448058i
$596$	−0.0253209	+	0.277093i	−0.00103719	+	0.0113502i
$597$	−28.4391	−	19.8342i	−1.16393	−	0.811758i
$598$	19.3817	+	32.0795i	0.792577	+	1.31183i
$599$	−28.3161	+	28.3161i	−1.15696	+	1.15696i	−0.171839	+	0.985125i	$0.554971\pi$
$599$	−28.3161	+	28.3161i	−1.15696	+	1.15696i	−0.985125	+	0.171839i	$0.945029\pi$
$600$	−32.2196	+	23.4306i	−1.31536	+	0.956551i
$601$	8.26293	+	8.26293i	0.337052	+	0.337052i	0.855257	−	0.518205i	$-0.173399\pi$
$601$	8.26293	+	8.26293i	0.337052	+	0.337052i	−0.518205	+	0.855257i	$0.673399\pi$
$602$	−2.30594	+	9.34541i	−0.0939830	+	0.380891i
$603$	4.95893	−	4.57824i	0.201943	−	0.186440i
$604$	−17.0219	+	32.3927i	−0.692610	+	1.31804i
$605$	−33.5579	+	13.9002i	−1.36432	+	0.565122i
$606$	33.9057	−	29.7308i	1.37732	−	1.20773i
$607$			35.3706i			1.43565i	0.696224	+	0.717824i	$0.254862\pi$
$607$			35.3706i			1.43565i	−0.696224	+	0.717824i	$0.745138\pi$
$608$	−36.6158	+	13.8337i	−1.48497	+	0.561032i
$609$	−14.9690	−	3.28920i	−0.606573	−	0.133285i
$610$	4.06693	−	5.52420i	0.164665	−	0.223668i
$611$	−13.8314	−	33.3920i	−0.559559	−	1.35090i
$612$	−11.9218	−	15.5407i	−0.481910	−	0.628196i
$613$	−12.8226	−	5.31128i	−0.517899	−	0.214521i	0.108395	−	0.994108i	$-0.465429\pi$
$613$	−12.8226	−	5.31128i	−0.517899	−	0.214521i	−0.626294	+	0.779587i	$0.715429\pi$
$614$	24.9803	+	6.16377i	1.00812	+	0.248749i
$615$	−26.5884	−	41.5638i	−1.07215	−	1.67601i
$616$	−0.166655	−	2.79017i	−0.00671472	−	0.112419i
$617$	25.5629	+	25.5629i	1.02913	+	1.02913i	0.999563	+	0.0295625i	$0.00941139\pi$
$617$	25.5629	+	25.5629i	1.02913	+	1.02913i	0.0295625	+	0.999563i	$0.490589\pi$
$618$	3.12541	−	1.06072i	0.125722	−	0.0426684i
$619$	−0.472404	−	0.195676i	−0.0189875	−	0.00786489i	0.373169	−	0.927763i	$-0.378271\pi$
$619$	−0.472404	−	0.195676i	−0.0189875	−	0.00786489i	−0.392157	+	0.919898i	$0.628271\pi$
$620$	−2.33998	+	25.6070i	−0.0939759	+	1.02840i
$621$	29.7721	+	7.79875i	1.19472	+	0.312953i
$622$	0.529928	+	3.48776i	0.0212482	+	0.139847i
$623$			11.0711i			0.443552i
$624$	28.5706	+	12.0307i	1.14374	+	0.481614i
$625$			0.469150i			0.0187660i
$626$	−9.44792	+	1.43551i	−0.377615	+	0.0573744i
$627$	−2.07843	−	11.6599i	−0.0830046	−	0.465651i
$628$	2.67768	−	2.22928i	0.106851	−	0.0889581i
$629$	11.4313	+	4.73499i	0.455795	+	0.188796i
$630$	−15.2801	+	1.70140i	−0.608773	+	0.0677855i
$631$	−8.71541	−	8.71541i	−0.346955	−	0.346955i	0.512019	−	0.858974i	$-0.328898\pi$
$631$	−8.71541	−	8.71541i	−0.346955	−	0.346955i	−0.858974	+	0.512019i	$0.828898\pi$
$632$	39.4494	+	13.6466i	1.56921	+	0.542831i
$633$	14.7635	−	9.44421i	0.586796	−	0.375374i
$634$	0.764958	−	3.10019i	0.0303803	−	0.123124i
$635$	−25.1806	−	10.4301i	−0.999260	−	0.413907i
$636$	30.5217	−	2.60906i	1.21027	−	0.103456i
$637$	−1.71232	−	4.13390i	−0.0678445	−	0.163791i
$638$	9.95870	+	7.33163i	0.394269	+	0.290262i
$639$	20.8996	+	9.65067i	0.826774	+	0.381775i
$640$	5.01371	−	40.6910i	0.198184	−	1.60845i
$641$			16.9518i			0.669555i	0.942297	+	0.334777i	$0.108661\pi$
$641$			16.9518i			0.669555i	−0.942297	+	0.334777i	$0.891339\pi$
$642$	−26.5503	+	23.2811i	−1.04785	+	0.918830i
$643$	10.3117	−	4.27126i	0.406656	−	0.168442i	−0.169973	−	0.985449i	$-0.554368\pi$
$643$	10.3117	−	4.27126i	0.406656	−	0.168442i	0.576628	+	0.817006i	$0.304368\pi$
$644$	11.3113	−	3.51849i	0.445729	−	0.138648i
$645$	−35.0409	−	24.4384i	−1.37973	−	0.962260i
$646$	−31.0142	−	7.65261i	−1.22024	−	0.301088i
$647$	−1.75000	−	1.75000i	−0.0687996	−	0.0687996i	0.671870	−	0.740669i	$-0.265491\pi$
$647$	−1.75000	−	1.75000i	−0.0687996	−	0.0687996i	−0.740669	+	0.671870i	$0.765491\pi$
$648$	23.7095	−	9.26614i	0.931396	−	0.364008i
$649$	−2.25699	+	2.25699i	−0.0885946	+	0.0885946i
$650$	44.0438	−	26.6102i	1.72754	−	1.04374i
$651$	−3.51528	+	5.04037i	−0.137775	+	0.197548i
$652$	18.7923	+	22.5722i	0.735962	+	0.883994i
$653$	−1.64313	−	3.96687i	−0.0643007	−	0.155236i	0.888463	−	0.458948i	$-0.151774\pi$
$653$	−1.64313	−	3.96687i	−0.0643007	−	0.155236i	−0.952764	+	0.303713i	$0.901774\pi$
$654$	−20.7197	−	1.35932i	−0.810206	−	0.0531536i
$655$	38.8138			1.51658
$656$	30.9233	+	5.69916i	1.20735	+	0.222515i
$657$	7.59142	−	16.4400i	0.296170	−	0.641387i
$658$	−11.2938	+	1.71597i	−0.440279	+	0.0668956i
$659$	19.7539	−	8.18233i	0.769502	−	0.318738i	0.0368314	−	0.999321i	$-0.488274\pi$
$659$	19.7539	−	8.18233i	0.769502	−	0.318738i	0.732671	+	0.680583i	$0.238274\pi$
$660$	11.8239	+	3.75397i	0.460244	+	0.146123i
$661$	5.48126	−	13.2329i	0.213196	−	0.514702i	−0.780715	−	0.624888i	$-0.785145\pi$
$661$	5.48126	−	13.2329i	0.213196	−	0.514702i	0.993911	+	0.110186i	$0.0351447\pi$
$662$	14.1946	−	8.57606i	0.551689	−	0.333318i
$663$	13.6335	+	21.3122i	0.529479	+	0.827698i
$664$	−11.2663	+	0.672925i	−0.437215	+	0.0261146i
$665$	−17.7303	+	17.7303i	−0.687553	+	0.687553i
$666$	−10.0426	+	12.5592i	−0.389142	+	0.486660i
$667$	−20.0562	+	48.4200i	−0.776580	+	1.87483i
$668$	12.5879	−	23.9548i	0.487039	−	0.926838i
$669$	6.84192	−	1.21961i	0.264524	−	0.0471527i
$670$	9.28470	+	6.83542i	0.358699	+	0.264075i
$671$	−1.32279			−0.0510656
$672$	5.85495	−	7.85618i	0.225860	−	0.303059i
$673$	−38.0370			−1.46622			−0.733110	−	0.680110i	$-0.761932\pi$
$673$	−38.0370			−1.46622			−0.733110	+	0.680110i	$0.761932\pi$
$674$	−13.1662	−	9.69299i	−0.507143	−	0.373360i
$675$	10.7073	−	40.8759i	0.412126	−	1.57331i
$676$	−12.4306	−	6.53209i	−0.478100	−	0.251234i
$677$	14.4691	−	34.9314i	0.556091	−	1.34252i	−0.356748	−	0.934201i	$-0.616114\pi$
$677$	14.4691	−	34.9314i	0.556091	−	1.34252i	0.912838	−	0.408321i	$-0.133886\pi$
$678$	11.4148	+	5.63004i	0.438384	+	0.216221i
$679$	−0.503038	+	0.503038i	−0.0193048	+	0.0193048i
$680$	22.2068	−	25.0282i	0.851594	−	0.959786i
$681$	−11.5682	+	7.40022i	−0.443296	+	0.283577i
$682$	4.24397	−	2.56411i	0.162510	−	0.0981848i
$683$	10.0282	−	24.2103i	0.383719	−	0.926381i	−0.607520	−	0.794304i	$-0.707836\pi$
$683$	10.0282	−	24.2103i	0.383719	−	0.926381i	0.991240	−	0.132076i	$-0.0421644\pi$
$684$	20.7625	−	35.9516i	0.793875	−	1.37464i
$685$	6.25677	−	2.59164i	0.239059	−	0.0990214i
$686$	−1.39817	+	0.212436i	−0.0533823	+	0.00811085i
$687$	−7.63992	+	34.7689i	−0.291481	+	1.32652i
$688$	26.6249	−	5.68727i	1.01507	−	0.216825i
$689$	−39.5680			−1.50742
$690$	−3.44179	+	52.4623i	−0.131027	+	1.99721i
$691$	1.18418	+	2.85887i	0.0450484	+	0.108757i	0.944802	−	0.327642i	$-0.106254\pi$
$691$	1.18418	+	2.85887i	0.0450484	+	0.108757i	−0.899754	+	0.436398i	$0.856254\pi$
$692$	0.951340	−	0.792030i	0.0361645	−	0.0301085i
$693$	2.01108	+	2.17830i	0.0763945	+	0.0827468i
$694$	7.58687	−	4.58381i	0.287994	−	0.173999i
$695$	−7.80753	+	7.80753i	−0.296157	+	0.296157i
$696$	10.1381	+	42.1465i	0.384285	+	1.59756i
$697$	18.1458	+	18.1458i	0.687321	+	0.687321i
$698$	−21.9425	−	5.41421i	−0.830535	−	0.204931i
$699$	20.2284	−	29.0045i	0.765110	−	1.09705i
$700$	−4.83074	−	15.5300i	−0.182585	−	0.586978i
$701$	−11.2618	+	4.66481i	−0.425354	+	0.176187i	−0.585083	−	0.810974i	$-0.698938\pi$
$701$	−11.2618	+	4.66481i	−0.425354	+	0.176187i	0.159729	+	0.987161i	$0.448938\pi$
$702$	−31.5331	+	9.31700i	−1.19014	+	0.351648i
$703$			26.2261i			0.989137i
$704$	−6.89200	+	3.87336i	−0.259752	+	0.145983i
$705$	10.8809	−	49.5186i	0.409800	−	1.86498i
$706$	−1.91192	−	1.40756i	−0.0719561	−	0.0529743i
$707$	7.04511	+	17.0084i	0.264959	+	0.639667i
$708$	−11.1480	+	0.952950i	−0.418966	+	0.0358141i
$709$	39.5539	+	16.3838i	1.48548	+	0.615306i	0.970328	−	0.241793i	$-0.0777356\pi$
$709$	39.5539	+	16.3838i	1.48548	+	0.615306i	0.515152	+	0.857099i	$0.327736\pi$
$710$	−9.42068	+	38.1798i	−0.353552	+	1.43286i
$711$	−41.5482	+	15.2984i	−1.55818	+	0.573736i
$712$	28.1641	−	13.6868i	1.05549	−	0.512935i
$713$	14.8591	+	14.8591i	0.556479	+	0.556479i
$714$	7.57207	−	2.56986i	0.283378	−	0.0961744i
$715$	−14.8042	−	6.13209i	−0.553645	−	0.229327i
$716$	22.0552	+	26.4914i	0.824241	+	0.990030i
$717$	−25.3119	+	4.51198i	−0.945291	+	0.168503i
$718$	−31.0169	+	4.71268i	−1.15754	+	0.175875i
$719$		−	45.1990i		−	1.68564i	−0.538196	−	0.842820i	$-0.680894\pi$
$719$		−	45.1990i		−	1.68564i	0.538196	−	0.842820i	$-0.319106\pi$
$720$	23.2186	+	36.7682i	0.865305	+	1.37027i
$721$			1.34743i			0.0501807i
$722$	−6.13469	−	40.3760i	−0.228309	−	1.50264i
$723$	−29.1906	+	5.20336i	−1.08561	+	0.193515i
$724$	33.1287	+	3.02732i	1.23122	+	0.112509i
$725$	66.4786	+	27.5363i	2.46895	+	1.02267i
$726$	7.89062	+	23.2497i	0.292849	+	0.862878i
$727$	−11.0717	−	11.0717i	−0.410628	−	0.410628i	0.471329	−	0.881957i	$-0.343774\pi$
$727$	−11.0717	−	11.0717i	−0.410628	−	0.410628i	−0.881957	+	0.471329i	$0.843774\pi$
$728$	−8.39952	+	9.46665i	−0.311307	+	0.350858i
$729$	−13.2369	+	23.5326i	−0.490256	+	0.871578i
$730$	30.0330	+	7.41051i	1.11157	+	0.274275i
$731$	20.5279	+	8.50294i	0.759252	+	0.314493i
$732$	−3.54608	−	2.98757i	−0.131067	−	0.110424i
$733$	11.7736	+	28.4239i	0.434867	+	1.04986i	0.977697	+	0.210020i	$0.0673528\pi$
$733$	11.7736	+	28.4239i	0.434867	+	1.04986i	−0.542830	+	0.839843i	$0.682647\pi$
$734$	7.59307	−	10.3138i	0.280265	−	0.380690i
$735$	1.34705	−	6.13037i	0.0496868	−	0.226122i
$736$	−22.9347	−	24.4256i	−0.845384	−	0.900338i
$737$		−	2.22325i		−	0.0818944i
$738$	−29.2111	+	16.0945i	−1.07527	+	0.592448i
$739$	0.181978	−	0.0753778i	0.00669417	−	0.00277282i	−0.379334	−	0.925260i	$-0.623847\pi$
$739$	0.181978	−	0.0753778i	0.00669417	−	0.00277282i	0.386028	+	0.922487i	$0.373847\pi$
$740$	−24.3172	−	12.7783i	−0.893920	−	0.469741i
$741$	−30.6762	+	43.9850i	−1.12692	+	1.61583i
$742$	−2.99592	+	12.1417i	−0.109984	+	0.445737i
$743$	−26.2149	−	26.2149i	−0.961731	−	0.961731i	0.0375636	−	0.999294i	$-0.488040\pi$
$743$	−26.2149	−	26.2149i	−0.961731	−	0.961731i	−0.999294	+	0.0375636i	$0.988040\pi$
$744$	17.1682	+	2.71142i	0.629418	+	0.0994054i
$745$	0.356494	−	0.356494i	0.0130609	−	0.0130609i
$746$	8.07113	+	13.3589i	0.295505	+	0.489104i
$747$	8.79562	−	8.12040i	0.321815	−	0.297110i
$748$	−6.42533	−	0.587150i	−0.234933	−	0.0214683i
$749$	−5.51676	−	13.3186i	−0.201578	−	0.486652i
$750$	27.7413	+	1.81997i	1.01297	+	0.0664558i
$751$	12.6023			0.459865			0.229933	−	0.973207i	$-0.426149\pi$
$751$	12.6023			0.459865			0.229933	+	0.973207i	$0.426149\pi$
$752$	18.3275	+	26.6094i	0.668337	+	0.970346i
$753$	7.23840	−	32.9416i	0.263782	−	1.20046i
$754$	−8.41093	−	55.3572i	−0.306308	−	2.01599i
$755$	61.2557	−	25.3729i	2.22932	−	0.923415i
$756$	0.471440	+	10.3816i	0.0171461	+	0.377575i
$757$	−10.1135	+	24.4162i	−0.367583	+	0.887423i	0.626563	+	0.779371i	$0.284461\pi$
$757$	−10.1135	+	24.4162i	−0.367583	+	0.887423i	−0.994145	+	0.108052i	$0.965539\pi$
$758$	18.0429	+	29.8636i	0.655348	+	1.08470i
$759$	8.54023	−	5.46320i	0.309991	−	0.198302i
$760$	67.0244	+	23.1855i	2.43123	+	0.841026i
$761$	20.1333	−	20.1333i	0.729830	−	0.729830i	−0.240756	−	0.970586i	$-0.577395\pi$
$761$	20.1333	−	20.1333i	0.729830	−	0.729830i	0.970586	+	0.240756i	$0.0773952\pi$
$762$	−8.14930	+	16.5226i	−0.295218	+	0.598551i
$763$	3.24400	−	7.83171i	0.117441	−	0.283527i
$764$	0.928551	+	2.98513i	0.0335938	+	0.107998i
$765$	−1.41547	+	35.4611i	−0.0511763	+	1.28210i
$766$	−14.5758	+	19.7986i	−0.526645	+	0.715353i
$767$	14.4521			0.521835
$768$	−27.2240	−	5.18230i	−0.982360	−	0.187000i
$769$	40.3656			1.45562			0.727810	−	0.685778i	$-0.240538\pi$
$769$	40.3656			1.45562			0.727810	+	0.685778i	$0.240538\pi$
$770$	−3.00258	+	4.07847i	−0.108206	+	0.146978i
$771$	−4.22430	+	0.753002i	−0.152134	+	0.0271187i
$772$	13.3112	+	42.7933i	0.479082	+	1.54016i
$773$	13.0211	−	31.4357i	0.468337	−	1.13066i	−0.496552	−	0.868007i	$-0.665401\pi$
$773$	13.0211	−	31.4357i	0.468337	−	1.13066i	0.964889	−	0.262658i	$-0.0845990\pi$
$774$	−18.0341	+	22.5534i	−0.648222	+	0.810667i
$775$	20.4010	−	20.4010i	0.732824	−	0.732824i
$776$	1.90159	+	0.657809i	0.0682631	+	0.0236140i
$777$	−3.53766	−	5.53018i	−0.126913	−	0.198394i
$778$	−12.8657	−	21.2947i	−0.461259	−	0.763451i
$779$	−20.8154	+	50.2529i	−0.745790	+	1.80050i
$780$	−25.8369	−	49.8745i	−0.925109	−	1.78579i
$781$	7.00586	−	2.90192i	0.250689	−	0.103839i
$782$	−4.10752	−	27.0340i	−0.146885	−	0.966734i
$783$	−36.6334	−	27.7848i	−1.30917	−	0.992947i
$784$	2.26894	+	3.29423i	0.0810334	+	0.117651i
$785$	−6.31305			−0.225322
$786$	1.71752	−	26.1797i	0.0612619	−	0.933799i
$787$	−5.73151	−	13.8371i	−0.204306	−	0.493239i	0.788202	−	0.615417i	$-0.211012\pi$
$787$	−5.73151	−	13.8371i	−0.204306	−	0.493239i	−0.992508	+	0.122178i	$0.961012\pi$
$788$	51.9528	+	4.74747i	1.85074	+	0.169122i
$789$	−3.05560	+	4.38126i	−0.108782	+	0.155977i
$790$	−39.1122	−	64.7363i	−1.39155	−	2.30322i
$791$	−3.67419	+	3.67419i	−0.130639	+	0.130639i
$792$	3.05524	−	7.80903i	0.108563	−	0.277482i
$793$	4.23507	+	4.23507i	0.150392	+	0.150392i
$794$	10.1702	−	41.2175i	0.360928	−	1.46275i
$795$	−45.5258	−	31.7508i	−1.61463	−	1.12609i
$796$	−35.4410	−	18.6237i	−1.25617	−	0.660098i
$797$	25.6987	−	10.6448i	0.910296	−	0.377057i	0.122126	−	0.992515i	$-0.461029\pi$
$797$	25.6987	−	10.6448i	0.910296	−	0.377057i	0.788170	+	0.615457i	$0.211029\pi$
$798$	11.1744	+	12.7436i	0.395571	+	0.451118i
$799$			26.3690i			0.932869i
$800$	−33.5352	+	31.4883i	−1.18565	+	1.11328i
$801$	−13.9239	+	30.1536i	−0.491975	+	1.06543i
$802$	12.6728	−	17.2137i	0.447490	−	0.607836i
$803$	−2.28271	−	5.51096i	−0.0805552	−	0.194477i
$804$	5.02130	−	5.96000i	0.177088	−	0.210193i
$805$	−19.8299	−	8.21380i	−0.698911	−	0.289498i
$806$	−21.7969	−	5.37830i	−0.767765	−	0.189442i
$807$	36.7697	−	23.5217i	1.29436	−	0.828001i
$808$	34.5587	−	38.9493i	1.21577	−	1.37023i
$809$	−18.4526	−	18.4526i	−0.648757	−	0.648757i	0.303935	−	0.952693i	$-0.401699\pi$
$809$	−18.4526	−	18.4526i	−0.648757	−	0.648757i	−0.952693	+	0.303935i	$0.901699\pi$
$810$	−43.7573	−	14.5835i	−1.53748	−	0.512410i
$811$	−24.2158	−	10.0305i	−0.850333	−	0.352220i	−0.0854138	−	0.996346i	$-0.527221\pi$
$811$	−24.2158	−	10.0305i	−0.850333	−	0.352220i	−0.764919	+	0.644126i	$0.777221\pi$
$812$	−17.6236	−	1.61045i	−0.618467	−	0.0565158i
$813$	−6.94501	−	38.9611i	−0.243572	−	1.36642i
$814$	0.795710	+	5.23703i	0.0278896	+	0.183558i
$815$		−	53.2173i		−	1.86412i
$816$	−15.8987	−	16.0859i	−0.556565	−	0.563118i
$817$			47.0960i			1.64768i
$818$	32.1067	−	4.87826i	1.12258	−	0.170564i
$819$	0.535386	−	13.4128i	0.0187079	−	0.468682i
$820$	−36.4532	−	43.7854i	−1.27300	−	1.52905i
$821$	35.4541	+	14.6856i	1.23736	+	0.512530i	0.902888	−	0.429877i	$-0.141443\pi$
$821$	35.4541	+	14.6856i	1.23736	+	0.512530i	0.334469	+	0.942407i	$0.391443\pi$
$822$	−1.47118	−	4.33483i	−0.0513133	−	0.151195i
$823$	0.0338137	+	0.0338137i	0.00117867	+	0.00117867i	0.707696	−	0.706517i	$-0.249735\pi$
$823$	0.0338137	+	0.0338137i	0.00117867	+	0.00117867i	−0.706517	+	0.707696i	$0.749735\pi$
$824$	3.42777	−	1.66578i	0.119412	−	0.0580302i
$825$	−7.50074	−	11.7254i	−0.261142	−	0.408225i
$826$	1.09425	−	4.43473i	0.0380738	−	0.154304i
$827$	21.8273	+	9.04116i	0.759009	+	0.314392i	0.728412	−	0.685140i	$-0.240259\pi$
$827$	21.8273	+	9.04116i	0.759009	+	0.314392i	0.0305977	+	0.999532i	$0.490259\pi$
$828$	35.2332	+	4.64293i	1.22444	+	0.161353i
$829$	17.5433	+	42.3533i	0.609304	+	1.47099i	0.863759	+	0.503905i	$0.168104\pi$
$829$	17.5433	+	42.3533i	0.609304	+	1.47099i	−0.254455	+	0.967085i	$0.581896\pi$
$830$	16.4682	+	12.1239i	0.571620	+	0.420828i
$831$	−12.0517	−	2.64816i	−0.418067	−	0.0918637i
$832$	34.4667	+	9.66456i	1.19492	+	0.335058i
$833$			3.26447i			0.113107i
$834$	4.92065	+	5.61162i	0.170388	+	0.194314i
$835$	−45.2992	+	18.7635i	−1.56764	+	0.649339i
$836$	−4.06203	−	13.0587i	−0.140488	−	0.451645i
$837$	−15.9135	+	9.30706i	−0.550053	+	0.321699i
$838$	2.08847	+	0.515320i	0.0721450	+	0.0178014i
$839$	−7.35162	−	7.35162i	−0.253806	−	0.253806i	0.568723	−	0.822529i	$-0.307438\pi$
$839$	−7.35162	−	7.35162i	−0.253806	−	0.253806i	−0.822529	+	0.568723i	$0.807438\pi$
$840$	−17.2606	+	4.15196i	−0.595548	+	0.143256i
$841$	34.8577	−	34.8577i	1.20199	−	1.20199i
$842$	−30.8357	+	18.6302i	−1.06267	+	0.642039i
$843$	30.3955	+	21.1986i	1.04688	+	0.730118i
$844$	15.5526	−	12.9482i	0.535342	−	0.445694i
$845$	9.73677	+	23.5066i	0.334955	+	0.808653i
$846$	−32.9185	−	9.53033i	−1.13176	−	0.327660i
$847$	−10.0234			−0.344408
$848$	34.5916	−	7.38901i	1.18788	−	0.253740i
$849$	11.6222	+	2.55379i	0.398872	+	0.0876458i
$850$	−37.1165	+	5.63945i	−1.27309	+	0.193432i
$851$	−20.7406	+	8.59105i	−0.710980	+	0.294497i
$852$	25.3351	+	8.04365i	0.867968	+	0.275571i
$853$	−12.9501	+	31.2644i	−0.443404	+	1.07047i	0.531342	+	0.847157i	$0.321688\pi$
$853$	−12.9501	+	31.2644i	−0.443404	+	1.07047i	−0.974746	+	0.223315i	$0.928312\pi$
$854$	1.62022	−	0.978901i	0.0554429	−	0.0334973i
$855$	−70.5902	+	25.9920i	−2.41414	+	0.888908i
$856$	−27.0616	+	30.4997i	−0.924947	+	1.04246i
$857$	−0.0339928	+	0.0339928i	−0.00116117	+	0.00116117i	−0.707687	−	0.706526i	$-0.750261\pi$
$857$	−0.0339928	+	0.0339928i	−0.00116117	+	0.00116117i	0.706526	+	0.707687i	$0.250261\pi$
$858$	−4.79114	+	9.71398i	−0.163567	+	0.331630i
$859$	−9.52933	+	23.0058i	−0.325137	+	0.784949i	0.673803	+	0.738911i	$0.264660\pi$
$859$	−9.52933	+	23.0058i	−0.325137	+	0.784949i	−0.998940	+	0.0460382i	$0.985340\pi$
$860$	−43.6681	−	22.9469i	−1.48907	−	0.782482i
$861$	−2.38940	−	13.4044i	−0.0814305	−	0.456820i
$862$	10.4534	+	7.69580i	0.356043	+	0.262120i
$863$	−7.78546			−0.265020			−0.132510	−	0.991182i	$-0.542304\pi$
$863$	−7.78546			−0.265020			−0.132510	+	0.991182i	$0.542304\pi$
$864$	25.8274	−	14.0338i	0.878665	−	0.477439i
$865$	−2.24293			−0.0762619
$866$	10.2293	+	7.53085i	0.347606	+	0.255909i
$867$	1.92807	+	10.8163i	0.0654806	+	0.367342i
$868$	−3.30074	+	6.28133i	−0.112034	+	0.213202i
$869$	−5.58133	+	13.4745i	−0.189334	+	0.457092i
$870$	34.7433	−	70.4415i	1.17791	−	2.38819i
$871$	−7.11802	+	7.11802i	−0.241185	+	0.241185i
$872$	−23.9339	+	1.42955i	−0.810503	+	0.0484108i
$873$	−2.00276	+	0.737435i	−0.0677831	+	0.0249584i
$874$	49.6078	−	29.9719i	1.67801	−	1.01381i
$875$	−4.34333	+	10.4857i	−0.146831	+	0.354482i
$876$	6.32731	−	19.9292i	0.213780	−	0.673344i
$877$	43.6551	−	18.0825i	1.47413	−	0.610603i	0.506331	−	0.862339i	$-0.331002\pi$
$877$	43.6551	−	18.0825i	1.47413	−	0.610603i	0.967796	+	0.251736i	$0.0810015\pi$
$878$	−7.82645	+	1.18914i	−0.264130	+	0.0401316i
$879$	−2.31453	−	0.508583i	−0.0780673	−	0.0171541i
$880$	14.0874	+	2.59631i	0.474886	+	0.0875215i
$881$	−6.59425			−0.222166			−0.111083	−	0.993811i	$-0.535432\pi$
$881$	−6.59425			−0.222166			−0.111083	+	0.993811i	$0.535432\pi$
$882$	−4.07529	−	1.17985i	−0.137222	−	0.0397275i
$883$	3.08349	+	7.44420i	0.103768	+	0.250517i	0.967233	−	0.253891i	$-0.0817106\pi$
$883$	3.08349	+	7.44420i	0.103768	+	0.250517i	−0.863465	+	0.504409i	$0.831711\pi$
$884$	18.6917	+	22.4514i	0.628669	+	0.755121i
$885$	16.6281	+	11.5969i	0.558948	+	0.389825i
$886$	18.5147	−	11.1862i	0.622015	−	0.375807i
$887$	11.0165	−	11.0165i	0.369898	−	0.369898i	−0.497542	−	0.867440i	$-0.665764\pi$
$887$	11.0165	−	11.0165i	0.369898	−	0.369898i	0.867440	+	0.497542i	$0.165764\pi$
$888$	−9.69494	+	15.8364i	−0.325341	+	0.531434i
$889$	−5.31827	−	5.31827i	−0.178369	−	0.178369i
$890$	−55.0852	−	13.5920i	−1.84646	−	0.455606i
$891$	2.73785	+	8.46221i	0.0917215	+	0.283495i
$892$	7.66274	−	2.38357i	0.256568	−	0.0798077i
$893$	−51.6374	+	21.3889i	−1.72798	+	0.715753i
$894$	−0.224678	−	0.256228i	−0.00751435	−	0.00856954i
$895$		−	62.4575i		−	2.08772i
$896$	5.57531	−	9.84459i	0.186258	−	0.328885i
$897$	−44.8338	−	9.85152i	−1.49696	−	0.328933i
$898$	10.2719	+	7.56224i	0.342779	+	0.252355i
$899$	−12.0138	−	29.0038i	−0.400682	−	0.967332i
$900$	6.37454	−	48.3737i	0.212485	−	1.61246i
$901$	26.6703	+	11.0472i	0.888515	+	0.368035i
$902$	−2.63189	+	10.6664i	−0.0876324	+	0.355153i
$903$	−6.35281	−	9.93090i	−0.211408	−	0.330480i
$904$	13.8892	+	4.80463i	0.461948	+	0.159800i
$905$	−42.6217	−	42.6217i	−1.41679	−	1.41679i
$906$	−14.4033	−	42.4393i	−0.478518	−	1.40995i
$907$	11.4597	+	4.74676i	0.380513	+	0.157614i	0.564738	−	0.825270i	$-0.308977\pi$
$907$	11.4597	+	4.74676i	0.380513	+	0.157614i	−0.184224	+	0.982884i	$0.558977\pi$
$908$	−12.1866	+	10.1458i	−0.404425	+	0.336701i
$909$	−2.20278	+	55.1853i	−0.0730615	+	1.83038i
$910$	22.6709	−	3.44460i	0.751533	−	0.114187i
$911$		−	20.2458i		−	0.670774i	−0.942080	−	0.335387i	$-0.891133\pi$
$911$		−	20.2458i		−	0.670774i	0.942080	−	0.335387i	$-0.108867\pi$
$912$	18.6043	−	44.1816i	0.616050	−	1.46300i
$913$		−	3.94336i		−	0.130506i
$914$	−7.68386	−	50.5720i	−0.254160	−	1.67277i
$915$	1.47437	+	8.27112i	0.0487411	+	0.273435i
$916$	−3.74065	+	40.9349i	−0.123595	+	1.35253i
$917$	9.89548	+	4.09884i	0.326778	+	0.135356i
$918$	23.8557	+	2.52388i	0.787355	+	0.0833006i
$919$	21.5980	+	21.5980i	0.712453	+	0.712453i	0.967048	−	0.254595i	$-0.0819420\pi$
$919$	21.5980	+	21.5980i	0.712453	+	0.712453i	−0.254595	+	0.967048i	$0.581942\pi$
$920$	3.61962	+	60.6005i	0.119335	+	1.99794i
$921$	−26.5453	+	16.9811i	−0.874697	+	0.559545i
$922$	34.7323	+	8.57003i	1.14385	+	0.282239i
$923$	−31.7210	−	13.1393i	−1.04411	−	0.432485i
$924$	2.61804	+	2.20570i	0.0861272	+	0.0725621i
$925$	11.7951	+	28.4760i	0.387822	+	0.936285i
$926$	−16.4651	+	22.3650i	−0.541078	+	0.734958i
$927$	−1.69463	+	3.66991i	−0.0556590	+	0.120536i
$928$	17.6906	+	46.8244i	0.580723	+	1.53708i
$929$		−	42.1602i		−	1.38323i	−0.722266	−	0.691615i	$-0.756899\pi$
$929$		−	42.1602i		−	1.38323i	0.722266	−	0.691615i	$-0.243101\pi$
$930$	−20.7631	−	23.6788i	−0.680850	−	0.776457i
$931$	−6.39267	+	2.64793i	−0.209511	+	0.0867824i
$932$	18.9939	−	36.1455i	0.622165	−	1.18398i
$933$	−3.54389	−	2.47160i	−0.116022	−	0.0809166i
$934$	7.32460	−	29.6849i	0.239668	−	0.971318i
$935$	8.26649	+	8.26649i	0.270343	+	0.270343i
$936$	−34.7833	+	15.2199i	−1.13693	+	0.497477i
$937$	−31.0132	+	31.0132i	−1.01316	+	1.01316i	−0.0132456	+	0.999912i	$0.504216\pi$
$937$	−31.0132	+	31.0132i	−1.01316	+	1.01316i	−0.999912	+	0.0132456i	$0.995784\pi$
$938$	1.64527	+	2.72316i	0.0537199	+	0.0889143i
$939$	6.69526	−	9.59996i	0.218491	−	0.313283i
$940$	5.32752	−	58.3004i	0.173764	−	1.90155i
$941$	20.5184	+	49.5358i	0.668881	+	1.61482i	0.783485	+	0.621411i	$0.213440\pi$
$941$	20.5184	+	49.5358i	0.668881	+	1.61482i	−0.114604	+	0.993411i	$0.536560\pi$
$942$	−0.279353	+	4.25811i	−0.00910182	+	0.138737i
$943$	−46.5605			−1.51622
$944$	−12.6345	+	2.69881i	−0.411217	+	0.0878388i
$945$	11.3789	−	15.0028i	0.370157	−	0.488040i
$946$	1.42891	+	9.40449i	0.0464579	+	0.305766i
$947$	35.7872	−	14.8235i	1.16293	−	0.481700i	0.284078	−	0.958801i	$-0.408312\pi$
$947$	35.7872	−	14.8235i	1.16293	−	0.481700i	0.878848	+	0.477101i	$0.158312\pi$
$948$	−45.3950	+	23.5163i	−1.47436	+	0.763775i
$949$	−10.3356	+	24.9524i	−0.335509	+	0.809990i
$950$	−41.1501	−	68.1094i	−1.33509	−	2.20976i
$951$	2.10744	+	3.29442i	0.0683385	+	0.106829i
$952$	8.30461	−	4.03576i	0.269154	−	0.130800i
$953$	12.2847	−	12.2847i	0.397939	−	0.397939i	−0.479566	−	0.877506i	$-0.659206\pi$
$953$	12.2847	−	12.2847i	0.397939	−	0.397939i	0.877506	+	0.479566i	$0.159206\pi$
$954$	−23.4303	+	29.3019i	−0.758583	+	0.948683i
$955$	2.16767	−	5.23321i	0.0701441	−	0.169343i
$956$	−28.3486	+	8.81809i	−0.916859	+	0.285197i
$957$	−14.9107	+	2.65790i	−0.481994	+	0.0859178i
$958$	31.4841	−	42.7656i	1.01721	−	1.38169i
$959$	1.86883			0.0603477
$960$	31.9011	+	38.7770i	1.02960	+	1.25152i
$961$	18.4125			0.593952
$962$	14.2195	−	19.3146i	0.458454	−	0.622728i
$963$	1.72491	−	43.2135i	0.0555845	−	1.39254i
$964$	−32.6926	+	10.1693i	−1.05296	+	0.327532i
$965$	31.0746	−	75.0208i	1.00033	−	2.41500i
$966$	−6.41763	+	13.0117i	−0.206484	+	0.418643i
$967$	4.53023	−	4.53023i	0.145682	−	0.145682i	−0.630504	−	0.776186i	$-0.717152\pi$
$967$	4.53023	−	4.53023i	0.145682	−	0.145682i	0.776186	+	0.630504i	$0.217152\pi$
$968$	12.3916	+	25.4989i	0.398282	+	0.819567i
$969$	32.9572	−	21.0828i	1.05874	−	0.677277i
$970$	−1.88534	−	3.12051i	−0.0605345	−	0.100193i
$971$	2.84384	−	6.86563i	0.0912631	−	0.220329i	−0.871656	−	0.490117i	$-0.836954\pi$
$971$	2.84384	−	6.86563i	0.0912631	−	0.220329i	0.962920	+	0.269789i	$0.0869539\pi$
$972$	−11.7727	+	28.8687i	−0.377610	+	0.925965i
$973$	−2.81500	+	1.16601i	−0.0902449	+	0.0373807i
$974$	7.93867	+	52.2490i	0.254371	+	1.67417i
$975$	−13.5257	+	61.5548i	−0.433170	+	1.97133i
$976$	−4.49330	−	2.91157i	−0.143827	−	0.0931970i
$977$	−3.95302			−0.126468			−0.0632341	−	0.997999i	$-0.520141\pi$
$977$	−3.95302			−0.126468			−0.0632341	+	0.997999i	$0.520141\pi$
$978$	−35.8947	−	2.35487i	−1.14779	−	0.0753006i
$979$	4.18685	+	10.1080i	0.133812	+	0.323052i
$980$	0.659543	−	7.21754i	0.0210683	−	0.230556i
$981$	18.6853	−	17.2509i	0.596576	−	0.550778i
$982$	3.29694	+	5.45691i	0.105210	+	0.174137i
$983$	−42.3045	+	42.3045i	−1.34930	+	1.34930i	−0.462885	+	0.886418i	$0.653186\pi$
$983$	−42.3045	+	42.3045i	−1.34930	+	1.34930i	−0.886418	+	0.462885i	$0.846814\pi$
$984$	−31.1460	+	22.6499i	−0.992899	+	0.722053i
$985$	−66.8397	−	66.8397i	−2.12969	−	2.12969i
$986$	−9.78617	+	39.6610i	−0.311655	+	1.26306i
$987$	8.00336	−	11.4756i	0.254750	−	0.365272i
$988$	−28.8040	+	54.8143i	−0.916379	+	1.74387i
$989$	−37.2453	+	15.4275i	−1.18433	+	0.490567i
$990$	−13.3074	+	7.33201i	−0.422937	+	0.233027i
$991$		−	1.95693i		−	0.0621639i	−0.999517	−	0.0310819i	$-0.990105\pi$
$991$		−	1.95693i		−	0.0621639i	0.999517	−	0.0310819i	$-0.00989528\pi$
$992$	20.0599	+	0.631475i	0.636904	+	0.0200493i
$993$	−4.35912	+	19.8381i	−0.138333	+	0.629544i
$994$	−6.43366	+	8.73897i	−0.204063	+	0.277183i
$995$	27.7606	+	67.0199i	0.880069	+	2.12467i
$996$	8.90625	−	10.5712i	0.282205	−	0.334962i
$997$	−16.0593	−	6.65197i	−0.508602	−	0.210670i	0.113600	−	0.993527i	$-0.463762\pi$
$997$	−16.0593	−	6.65197i	−0.508602	−	0.210670i	−0.622202	+	0.782857i	$0.713762\pi$
$998$	57.8814	+	14.2820i	1.83220	+	0.452088i
$999$	−2.68013	−	19.5115i	−0.0847955	−	0.617316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.15	✓	192
3.2	odd	2	inner	672.2.bs.a.155.34	yes	192
32.19	odd	8	inner	672.2.bs.a.659.34	yes	192
96.83	even	8	inner	672.2.bs.a.659.15	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.15	✓	192	1.1	even	1	trivial
672.2.bs.a.155.34	yes	192	3.2	odd	2	inner
672.2.bs.a.659.15	yes	192	96.83	even	8	inner
672.2.bs.a.659.34	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.838438 + 1.13887i) q^{2} +(-0.303955 - 1.70517i) q^{3} +(-0.594043 - 1.90974i) q^{4} +(-1.38677 + 3.34796i) q^{5} +(2.19681 + 1.08352i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.67301 + 0.924664i) q^{8} +(-2.81522 + 1.03659i) q^{9} +O(q^{10})\)	\(q+(-0.838438 + 1.13887i) q^{2} +(-0.303955 - 1.70517i) q^{3} +(-0.594043 - 1.90974i) q^{4} +(-1.38677 + 3.34796i) q^{5} +(2.19681 + 1.08352i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.67301 + 0.924664i) q^{8} +(-2.81522 + 1.03659i) q^{9} +(-2.65017 - 4.38641i) q^{10} +(-0.378180 + 0.913007i) q^{11} +(-3.07588 + 1.59342i) q^{12} +(4.13390 - 1.71232i) q^{13} +(-0.212436 - 1.39817i) q^{14} +(6.13037 + 1.34705i) q^{15} +(-3.29423 + 2.26894i) q^{16} -3.26447 q^{17} +(1.17985 - 4.07529i) q^{18} +(-2.64793 - 6.39267i) q^{19} +(7.21754 + 0.659543i) q^{20} +(1.42067 + 0.990810i) q^{21} +(-0.722715 - 1.19620i) q^{22} +(4.18817 - 4.18817i) q^{23} +(0.764235 - 4.83900i) q^{24} +(-5.75018 - 5.75018i) q^{25} +(-1.51592 + 6.14364i) q^{26} +(2.62327 + 4.48536i) q^{27} +(1.77044 + 0.930340i) q^{28} +(-8.17496 + 3.38618i) q^{29} +(-6.67405 + 5.85226i) q^{30} +3.54789i q^{31} +(0.177986 - 5.65405i) q^{32} +(1.67178 + 0.367349i) q^{33} +(2.73705 - 3.71780i) q^{34} +(-1.38677 - 3.34796i) q^{35} +(3.65199 + 4.76057i) q^{36} +(-3.50173 - 1.45046i) q^{37} +(9.50054 + 2.34421i) q^{38} +(-4.17632 - 6.52855i) q^{39} +(-6.80260 + 7.66684i) q^{40} +(-5.55858 - 5.55858i) q^{41} +(-2.31954 + 0.787221i) q^{42} +(-6.28829 - 2.60469i) q^{43} +(1.96826 + 0.179861i) q^{44} +(0.433598 - 10.8628i) q^{45} +(1.25825 + 8.28130i) q^{46} -8.07759i q^{47} +(4.87022 + 4.92757i) q^{48} -1.00000i q^{49} +(11.3699 - 1.72753i) q^{50} +(0.992252 + 5.56648i) q^{51} +(-5.72580 - 6.87750i) q^{52} +(-8.16987 - 3.38407i) q^{53} +(-7.30768 - 0.773139i) q^{54} +(-2.53226 - 2.53226i) q^{55} +(-2.54394 + 1.23627i) q^{56} +(-10.0957 + 6.45826i) q^{57} +(2.99779 - 12.1493i) q^{58} +(2.98401 + 1.23602i) q^{59} +(-1.06918 - 12.5076i) q^{60} +(0.512237 + 1.23665i) q^{61} +(-4.04058 - 2.97468i) q^{62} +(1.25768 - 2.72364i) q^{63} +(6.28999 + 4.94328i) q^{64} +16.2147i q^{65} +(-1.82005 + 1.59594i) q^{66} +(-2.07847 + 0.860932i) q^{67} +(1.93923 + 6.23429i) q^{68} +(-8.41457 - 5.86853i) q^{69} +(4.97561 + 1.22771i) q^{70} +(-5.42590 - 5.42590i) q^{71} +(-8.48362 + 0.167689i) q^{72} +(-4.26813 + 4.26813i) q^{73} +(4.58787 - 2.77189i) q^{74} +(-8.05724 + 11.5528i) q^{75} +(-10.6354 + 8.85438i) q^{76} +(-0.378180 - 0.913007i) q^{77} +(10.9367 + 0.717505i) q^{78} +14.7584 q^{79} +(-3.02797 - 14.1754i) q^{80} +(6.85095 - 5.83647i) q^{81} +(10.9910 - 1.66996i) q^{82} +(-3.68658 + 1.52703i) q^{83} +(1.04825 - 3.30169i) q^{84} +(4.52707 - 10.9293i) q^{85} +(8.23875 - 4.97766i) q^{86} +(8.25884 + 12.9105i) q^{87} +(-1.85511 + 2.09079i) q^{88} +(7.82842 - 7.82842i) q^{89} +(12.0077 + 9.60157i) q^{90} +(-1.71232 + 4.13390i) q^{91} +(-10.4863 - 5.51037i) q^{92} +(6.04976 - 1.07840i) q^{93} +(9.19932 + 6.77256i) q^{94} +25.0745 q^{95} +(-9.69523 + 1.41508i) q^{96} +0.711404 q^{97} +(1.13887 + 0.838438i) q^{98} +(0.118245 - 2.96234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

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