LMFDB - Embedded newform 605.2.m.f.118.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.6
Character	$\chi$	$=$	605.118
Dual form			605.2.m.f.282.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.175554 + 0.0278050i) q^{2} +(-1.06432 + 2.08884i) q^{3} +(-1.87207 - 0.608271i) q^{4} +(-2.18725 - 0.464678i) q^{5} +(-0.244925 + 0.337111i) q^{6} +(3.97783 - 2.02681i) q^{7} +(-0.628475 - 0.320224i) q^{8} +(-1.46712 - 2.01932i) q^{9} +O(q^{10})$	\(q+(0.175554 + 0.0278050i) q^{2} +(-1.06432 + 2.08884i) q^{3} +(-1.87207 - 0.608271i) q^{4} +(-2.18725 - 0.464678i) q^{5} +(-0.244925 + 0.337111i) q^{6} +(3.97783 - 2.02681i) q^{7} +(-0.628475 - 0.320224i) q^{8} +(-1.46712 - 2.01932i) q^{9} +(-0.371061 - 0.142393i) q^{10} +(3.26305 - 3.26305i) q^{12} +(0.436110 - 2.75349i) q^{13} +(0.754680 - 0.245211i) q^{14} +(3.29857 - 4.07425i) q^{15} +(3.08352 + 2.24031i) q^{16} +(0.487591 + 3.07853i) q^{17} +(-0.201412 - 0.395294i) q^{18} +(0.385927 + 1.18776i) q^{19} +(3.81203 + 2.20035i) q^{20} +10.4662i q^{21} +(1.27860 + 1.27860i) q^{23} +(1.33779 - 0.971964i) q^{24} +(4.56815 + 2.03274i) q^{25} +(0.153122 - 0.471260i) q^{26} +(-1.16696 + 0.184829i) q^{27} +(-8.67962 + 1.37472i) q^{28} +(-2.30912 + 7.10674i) q^{29} +(0.692362 - 0.623535i) q^{30} +(4.15416 - 3.01818i) q^{31} +(1.47655 + 1.47655i) q^{32} +0.554006i q^{34} +(-9.64234 + 2.58473i) q^{35} +(1.51826 + 4.67272i) q^{36} +(1.12366 + 2.20531i) q^{37} +(0.0347254 + 0.219247i) q^{38} +(5.28744 + 3.84155i) q^{39} +(1.22583 + 0.992450i) q^{40} +(10.2749 - 3.33850i) q^{41} +(-0.291014 + 1.83739i) q^{42} +(4.31967 - 4.31967i) q^{43} +(2.27064 + 5.09851i) q^{45} +(0.188911 + 0.260014i) q^{46} +(3.33936 + 1.70149i) q^{47} +(-7.96149 + 4.05658i) q^{48} +(7.60072 - 10.4615i) q^{49} +(0.745437 + 0.483873i) q^{50} +(-6.94950 - 2.25803i) q^{51} +(-2.49130 + 4.88944i) q^{52} +(-0.440586 - 0.0697819i) q^{53} -0.210005 q^{54} -3.14900 q^{56} +(-2.89179 - 0.458015i) q^{57} +(-0.602978 + 1.18341i) q^{58} +(10.7575 + 3.49534i) q^{59} +(-8.65339 + 5.62085i) q^{60} +(0.811610 - 1.11709i) q^{61} +(0.813201 - 0.414347i) q^{62} +(-9.92875 - 5.05895i) q^{63} +(-4.26246 - 5.86677i) q^{64} +(-2.23337 + 5.81993i) q^{65} +(0.721404 - 0.721404i) q^{67} +(0.959778 - 6.05980i) q^{68} +(-4.03161 + 1.30995i) q^{69} +(-1.76462 + 0.185654i) q^{70} +(-2.85431 - 2.07378i) q^{71} +(0.275415 + 1.73890i) q^{72} +(4.23102 + 8.30385i) q^{73} +(0.135945 + 0.418395i) q^{74} +(-9.10802 + 7.37865i) q^{75} -2.45832i q^{76} +(0.821417 + 0.821417i) q^{78} +(4.87103 - 3.53901i) q^{79} +(-5.70342 - 6.33297i) q^{80} +(3.16988 - 9.75589i) q^{81} +(1.89662 - 0.300395i) q^{82} +(-4.82298 + 0.763885i) q^{83} +(6.36630 - 19.5935i) q^{84} +(0.364040 - 6.96009i) q^{85} +(0.878445 - 0.638228i) q^{86} +(-12.3872 - 12.3872i) q^{87} -2.57764i q^{89} +(0.256855 + 0.958199i) q^{90} +(-3.84602 - 11.8368i) q^{91} +(-1.61588 - 3.17135i) q^{92} +(1.88314 + 11.8897i) q^{93} +(0.538928 + 0.391554i) q^{94} +(-0.292194 - 2.77727i) q^{95} +(-4.65581 + 1.51276i) q^{96} +(1.02281 - 6.45779i) q^{97} +(1.62522 - 1.62522i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^5	$ 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.175554	+	0.0278050i	0.124135	+	0.0196611i	0.218193	−	0.975906i	$-0.429984\pi$
$2$	0.175554	+	0.0278050i	0.124135	+	0.0196611i	−0.0940575	+	0.995567i	$0.529984\pi$
$3$	−1.06432	+	2.08884i	−0.614484	+	1.20599i	0.348722	+	0.937226i	$0.386616\pi$
$3$	−1.06432	+	2.08884i	−0.614484	+	1.20599i	−0.963206	+	0.268766i	$0.913384\pi$
$4$	−1.87207	−	0.608271i	−0.936033	−	0.304136i
$5$	−2.18725	−	0.464678i	−0.978169	−	0.207810i
$5$	−2.18725	−	0.464678i	−0.978169	−	0.207810i
$6$	−0.244925	+	0.337111i	−0.0999904	+	0.137625i
$7$	3.97783	−	2.02681i	1.50348	−	0.766061i	0.508029	−	0.861340i	$-0.330374\pi$
$7$	3.97783	−	2.02681i	1.50348	−	0.766061i	0.995451	+	0.0952786i	$0.0303742\pi$
$8$	−0.628475	−	0.320224i	−0.222200	−	0.113216i
$9$	−1.46712	−	2.01932i	−0.489041	−	0.673107i
$10$	−0.371061	−	0.142393i	−0.117340	−	0.0450285i
$11$		0			0
$11$		0			0
$12$	3.26305	−	3.26305i	0.941962	−	0.941962i
$13$	0.436110	−	2.75349i	0.120955	−	0.763681i	−0.850416	−	0.526112i	$-0.823649\pi$
$13$	0.436110	−	2.75349i	0.120955	−	0.763681i	0.971371	−	0.237569i	$-0.0763506\pi$
$14$	0.754680	−	0.245211i	0.201697	−	0.0655353i
$15$	3.29857	−	4.07425i	0.851686	−	1.05197i
$16$	3.08352	+	2.24031i	0.770881	+	0.560078i
$17$	0.487591	+	3.07853i	0.118258	+	0.746653i	0.973545	+	0.228497i	$0.0733812\pi$
$17$	0.487591	+	3.07853i	0.118258	+	0.746653i	−0.855286	+	0.518156i	$0.826619\pi$
$18$	−0.201412	−	0.395294i	−0.0474733	−	0.0931716i
$19$	0.385927	+	1.18776i	0.0885378	+	0.272491i	0.985516	−	0.169584i	$-0.0542424\pi$
$19$	0.385927	+	1.18776i	0.0885378	+	0.272491i	−0.896978	+	0.442075i	$0.854242\pi$
$20$	3.81203	+	2.20035i	0.852396	+	0.492014i
$21$			10.4662i			2.28392i
$22$		0			0
$23$	1.27860	+	1.27860i	0.266606	+	0.266606i	0.827731	−	0.561125i	$-0.189631\pi$
$23$	1.27860	+	1.27860i	0.266606	+	0.266606i	−0.561125	+	0.827731i	$0.689631\pi$
$24$	1.33779	−	0.971964i	0.273076	−	0.198401i
$25$	4.56815	+	2.03274i	0.913630	+	0.406547i
$26$	0.153122	−	0.471260i	0.0300297	−	0.0924218i
$27$	−1.16696	+	0.184829i	−0.224582	+	0.0355704i
$28$	−8.67962	+	1.37472i	−1.64029	+	0.259797i
$29$	−2.30912	+	7.10674i	−0.428793	+	1.31969i	0.470523	+	0.882388i	$0.344065\pi$
$29$	−2.30912	+	7.10674i	−0.428793	+	1.31969i	−0.899316	+	0.437300i	$0.855935\pi$
$30$	0.692362	−	0.623535i	0.126407	−	0.113841i
$31$	4.15416	−	3.01818i	0.746110	−	0.542081i	−0.148509	−	0.988911i	$-0.547447\pi$
$31$	4.15416	−	3.01818i	0.746110	−	0.542081i	0.894619	+	0.446831i	$0.147447\pi$
$32$	1.47655	+	1.47655i	0.261020	+	0.261020i
$33$		0			0
$34$			0.554006i			0.0950112i
$35$	−9.64234	+	2.58473i	−1.62985	+	0.436899i
$36$	1.51826	+	4.67272i	0.253043	+	0.778786i
$37$	1.12366	+	2.20531i	0.184729	+	0.362551i	0.964736	−	0.263220i	$-0.0847845\pi$
$37$	1.12366	+	2.20531i	0.184729	+	0.362551i	−0.780007	+	0.625771i	$0.784785\pi$
$38$	0.0347254	+	0.219247i	0.00563320	+	0.0355666i
$39$	5.28744	+	3.84155i	0.846668	+	0.615140i
$40$	1.22583	+	0.992450i	0.193821	+	0.156920i
$41$	10.2749	−	3.33850i	1.60466	−	0.521387i	0.636409	−	0.771352i	$-0.280419\pi$
$41$	10.2749	−	3.33850i	1.60466	−	0.521387i	0.968255	+	0.249965i	$0.0804193\pi$
$42$	−0.291014	+	1.83739i	−0.0449044	+	0.283515i
$43$	4.31967	−	4.31967i	0.658744	−	0.658744i	−0.296339	−	0.955083i	$-0.595766\pi$
$43$	4.31967	−	4.31967i	0.658744	−	0.658744i	0.955083	+	0.296339i	$0.0957657\pi$
$44$		0			0
$45$	2.27064	+	5.09851i	0.338486	+	0.760041i
$46$	0.188911	+	0.260014i	0.0278535	+	0.0383370i
$47$	3.33936	+	1.70149i	0.487096	+	0.248188i	0.680249	−	0.732981i	$-0.261872\pi$
$47$	3.33936	+	1.70149i	0.487096	+	0.248188i	−0.193154	+	0.981169i	$0.561872\pi$
$48$	−7.96149	+	4.05658i	−1.14914	+	0.585517i
$49$	7.60072	−	10.4615i	1.08582	−	1.49450i
$50$	0.745437	+	0.483873i	0.105421	+	0.0684299i
$51$	−6.94950	−	2.25803i	−0.973125	−	0.316188i
$52$	−2.49130	+	4.88944i	−0.345481	+	0.678044i
$53$	−0.440586	−	0.0697819i	−0.0605191	−	0.00958528i	0.126101	−	0.992017i	$-0.459753\pi$
$53$	−0.440586	−	0.0697819i	−0.0605191	−	0.00958528i	−0.186621	+	0.982432i	$0.559753\pi$
$54$	−0.210005			−0.0285780
$55$		0			0
$56$	−3.14900			−0.420803
$57$	−2.89179	−	0.458015i	−0.383027	−	0.0606656i
$58$	−0.602978	+	1.18341i	−0.0791749	+	0.155390i
$59$	10.7575	+	3.49534i	1.40051	+	0.455054i	0.909357	−	0.416017i	$-0.136574\pi$
$59$	10.7575	+	3.49534i	1.40051	+	0.455054i	0.491157	+	0.871071i	$0.336574\pi$
$60$	−8.65339	+	5.62085i	−1.11715	+	0.725649i
$61$	0.811610	−	1.11709i	0.103916	−	0.143028i	−0.753892	−	0.656998i	$-0.771826\pi$
$61$	0.811610	−	1.11709i	0.103916	−	0.143028i	0.857808	+	0.513970i	$0.171826\pi$
$62$	0.813201	−	0.414347i	0.103277	−	0.0526221i
$63$	−9.92875	−	5.05895i	−1.25090	−	0.637368i
$64$	−4.26246	−	5.86677i	−0.532808	−	0.733347i
$65$	−2.23337	+	5.81993i	−0.277015	+	0.721873i
$66$		0			0
$67$	0.721404	−	0.721404i	0.0881335	−	0.0881335i	−0.661666	−	0.749799i	$-0.730150\pi$
$67$	0.721404	−	0.721404i	0.0881335	−	0.0881335i	0.749799	+	0.661666i	$0.230150\pi$
$68$	0.959778	−	6.05980i	0.116390	−	0.734859i
$69$	−4.03161	+	1.30995i	−0.485349	+	0.157699i
$70$	−1.76462	+	0.185654i	−0.210913	+	0.0221899i
$71$	−2.85431	−	2.07378i	−0.338744	−	0.246112i	0.405388	−	0.914145i	$-0.367137\pi$
$71$	−2.85431	−	2.07378i	−0.338744	−	0.246112i	−0.744132	+	0.668033i	$0.767137\pi$
$72$	0.275415	+	1.73890i	0.0324580	+	0.204932i
$73$	4.23102	+	8.30385i	0.495204	+	0.971892i	0.994428	+	0.105419i	$0.0336184\pi$
$73$	4.23102	+	8.30385i	0.495204	+	0.971892i	−0.499224	+	0.866473i	$0.666382\pi$
$74$	0.135945	+	0.418395i	0.0158032	+	0.0486374i
$75$	−9.10802	+	7.37865i	−1.05170	+	0.852013i
$76$		−	2.45832i		−	0.281989i
$77$		0			0
$78$	0.821417	+	0.821417i	0.0930072	+	0.0930072i
$79$	4.87103	−	3.53901i	0.548034	−	0.398170i	−0.279026	−	0.960284i	$-0.590012\pi$
$79$	4.87103	−	3.53901i	0.548034	−	0.398170i	0.827060	+	0.562114i	$0.190012\pi$
$80$	−5.70342	−	6.33297i	−0.637662	−	0.708048i
$81$	3.16988	−	9.75589i	0.352209	−	1.08399i
$82$	1.89662	−	0.300395i	0.209447	−	0.0331731i
$83$	−4.82298	+	0.763885i	−0.529391	+	0.0838472i	−0.415407	−	0.909635i	$-0.636361\pi$
$83$	−4.82298	+	0.763885i	−0.529391	+	0.0838472i	−0.113983	+	0.993483i	$0.536361\pi$
$84$	6.36630	−	19.5935i	0.694621	−	2.13782i
$85$	0.364040	−	6.96009i	0.0394857	−	0.754928i
$86$	0.878445	−	0.638228i	0.0947252	−	0.0688219i
$87$	−12.3872	−	12.3872i	−1.32805	−	1.32805i
$88$		0			0
$89$		−	2.57764i		−	0.273229i	−0.990624	−	0.136615i	$-0.956378\pi$
$89$		−	2.57764i		−	0.273229i	0.990624	−	0.136615i	$-0.0436222\pi$
$90$	0.256855	+	0.958199i	0.0270749	+	0.101003i
$91$	−3.84602	−	11.8368i	−0.403173	−	1.24084i
$92$	−1.61588	−	3.17135i	−0.168468	−	0.330636i
$93$	1.88314	+	11.8897i	0.195273	+	1.23290i
$94$	0.538928	+	0.391554i	0.0555862	+	0.0403857i
$95$	−0.292194	−	2.77727i	−0.0299784	−	0.284942i
$96$	−4.65581	+	1.51276i	−0.475181	+	0.154396i
$97$	1.02281	−	6.45779i	0.103851	−	0.655689i	−0.879764	−	0.475410i	$-0.842300\pi$
$97$	1.02281	−	6.45779i	0.103851	−	0.655689i	0.983615	−	0.180279i	$-0.0577002\pi$
$98$	1.62522	−	1.62522i	0.164172	−	0.164172i
$99$		0			0
$100$	−7.31542	−	6.58409i	−0.731542	−	0.658409i
$101$	7.15995	+	9.85482i	0.712441	+	0.980591i	0.999741	+	0.0227507i	$0.00724240\pi$
$101$	7.15995	+	9.85482i	0.712441	+	0.980591i	−0.287300	+	0.957841i	$0.592758\pi$
$102$	−1.15723	−	0.589638i	−0.114583	−	0.0583828i
$103$	−11.4446	+	5.83130i	−1.12767	+	0.574575i	−0.915363	−	0.402629i	$-0.868096\pi$
$103$	−11.4446	+	5.83130i	−1.12767	+	0.574575i	−0.212303	+	0.977204i	$0.568096\pi$
$104$	−1.15582	+	1.59085i	−0.113337	+	0.155995i
$105$	4.86342	−	22.8923i	0.474621	−	2.23406i
$106$	−0.0754063	−	0.0245010i	−0.00732411	−	0.00237975i
$107$	−4.54181	+	8.91381i	−0.439074	+	0.861730i	0.560366	+	0.828245i	$0.310661\pi$
$107$	−4.54181	+	8.91381i	−0.439074	+	0.861730i	−0.999439	+	0.0334850i	$0.989339\pi$
$108$	2.29706	+	0.363819i	0.221035	+	0.0350085i
$109$	8.79661			0.842562			0.421281	−	0.906930i	$-0.361581\pi$
$109$	8.79661			0.842562			0.421281	+	0.906930i	$0.361581\pi$
$110$		0			0
$111$	−5.80247			−0.550746
$112$	16.8064	+	2.66188i	1.58806	+	0.251524i
$113$	4.46369	−	8.76048i	0.419908	−	0.824117i	−0.580046	−	0.814584i	$-0.696965\pi$
$113$	4.46369	−	8.76048i	0.419908	−	0.824117i	0.999955	−	0.00953315i	$-0.00303454\pi$
$114$	−0.494931	−	0.160813i	−0.0463545	−	0.0150615i
$115$	−2.20248	−	3.39075i	−0.205382	−	0.316189i
$116$	8.64565	−	11.8997i	0.802729	−	1.10486i
$117$	−6.20001	+	3.15906i	−0.573191	+	0.292055i
$118$	1.79134	+	0.912735i	0.164907	+	0.0840241i
$119$	8.17914	+	11.2576i	0.749781	+	1.03198i
$120$	−3.37774	+	1.50429i	−0.308344	+	0.137322i
$121$		0			0
$122$	0.173542	−	0.173542i	0.0157118	−	0.0157118i
$123$	−3.96211	+	25.0158i	−0.357251	+	2.25559i
$124$	−9.61274	+	3.12337i	−0.863250	+	0.280487i
$125$	−9.04713	−	6.56883i	−0.809200	−	0.587534i
$126$	−1.60237	−	1.16419i	−0.142750	−	0.103714i
$127$	1.20964	+	7.63739i	0.107338	+	0.677709i	0.981412	+	0.191914i	$0.0614696\pi$
$127$	1.20964	+	7.63739i	0.107338	+	0.677709i	−0.874073	+	0.485794i	$0.838530\pi$
$128$	−2.48118	−	4.86959i	−0.219307	−	0.430415i
$129$	4.42560	+	13.6206i	0.389653	+	1.19923i
$130$	−0.553900	+	0.959613i	−0.0485803	+	0.0841636i
$131$		−	19.6002i		−	1.71248i	−0.516578	−	0.856240i	$-0.672794\pi$
$131$		−	19.6002i		−	1.71248i	0.516578	−	0.856240i	$-0.327206\pi$
$132$		0			0
$133$	3.94252	+	3.94252i	0.341860	+	0.341860i
$134$	0.146704	−	0.106587i	0.0126733	−	0.00920769i
$135$	2.63833	+	0.137995i	0.227072	+	0.0118767i
$136$	0.679380	−	2.09092i	0.0582564	−	0.179295i
$137$	8.09573	−	1.28224i	0.691665	−	0.109549i	0.199301	−	0.979938i	$-0.436133\pi$
$137$	8.09573	−	1.28224i	0.691665	−	0.109549i	0.492364	+	0.870389i	$0.336133\pi$
$138$	−0.744189	+	0.117868i	−0.0633496	+	0.0100336i
$139$	−3.83671	+	11.8082i	−0.325426	+	1.00156i	0.645822	+	0.763488i	$0.276515\pi$
$139$	−3.83671	+	11.8082i	−0.325426	+	1.00156i	−0.971248	+	0.238070i	$0.923485\pi$
$140$	19.6233	+	1.02638i	1.65847	+	0.0867446i
$141$	−7.10827	+	5.16446i	−0.598624	+	0.434926i
$142$	−0.443424	−	0.443424i	−0.0372113	−	0.0372113i
$143$		0			0
$144$		−	9.51344i		−	0.792787i
$145$	8.35297	−	14.4712i	0.693677	−	1.20177i
$146$	0.511884	+	1.57542i	0.0423638	+	0.130383i
$147$	13.7628	+	27.0110i	1.13514	+	2.22783i
$148$	−0.762142	−	4.81198i	−0.0626477	−	0.395542i
$149$	1.20989	+	0.879034i	0.0991177	+	0.0720133i	0.636240	−	0.771491i	$-0.280489\pi$
$149$	1.20989	+	0.879034i	0.0991177	+	0.0720133i	−0.537122	+	0.843504i	$0.680489\pi$
$150$	−1.80411	+	1.04210i	−0.147305	+	0.0850874i
$151$	−5.64126	+	1.83296i	−0.459079	+	0.149164i	−0.529421	−	0.848359i	$-0.677591\pi$
$151$	−5.64126	+	1.83296i	−0.459079	+	0.149164i	0.0703422	+	0.997523i	$0.477591\pi$
$152$	0.137804	−	0.870063i	0.0111774	−	0.0705714i
$153$	5.50119	−	5.50119i	0.444745	−	0.444745i
$154$		0			0
$155$	−10.4887	+	4.67117i	−0.842472	+	0.375197i
$156$	−7.56173	−	10.4078i	−0.605423	−	0.833294i
$157$	−10.4180	−	5.30824i	−0.831448	−	0.423644i	−0.0141784	−	0.999899i	$-0.504513\pi$
$157$	−10.4180	−	5.30824i	−0.831448	−	0.423644i	−0.817270	+	0.576256i	$0.804513\pi$
$158$	0.953532	−	0.485849i	0.0758589	−	0.0386521i
$159$	0.614686	−	0.846042i	0.0487477	−	0.0670955i
$160$	−2.54348	−	3.91572i	−0.201079	−	0.309565i
$161$	7.67751	+	2.49457i	0.605073	+	0.196600i
$162$	0.827748	−	1.62455i	0.0650340	−	0.127636i
$163$	6.77261	+	1.07268i	0.530472	+	0.0840184i	0.415924	−	0.909399i	$-0.363458\pi$
$163$	6.77261	+	1.07268i	0.530472	+	0.0840184i	0.114547	+	0.993418i	$0.463458\pi$
$164$	−21.2659			−1.66059
$165$		0			0
$166$	−0.867933			−0.0673647
$167$	−12.3370	−	1.95399i	−0.954669	−	0.151205i	−0.340382	−	0.940287i	$-0.610556\pi$
$167$	−12.3370	−	1.95399i	−0.954669	−	0.151205i	−0.614287	+	0.789083i	$0.710556\pi$
$168$	3.35154	−	6.57776i	0.258577	−	0.507485i
$169$	4.97222	+	1.61557i	0.382478	+	0.124275i
$170$	0.257434	−	1.21175i	0.0197443	−	0.0929370i
$171$	1.83227	−	2.52191i	0.140117	−	0.192855i
$172$	−10.7143	+	5.45919i	−0.816954	+	0.416259i
$173$	−21.0477	−	10.7243i	−1.60023	−	0.815357i	−0.999878	−	0.0156192i	$-0.995028\pi$
$173$	−21.0477	−	10.7243i	−1.60023	−	0.815357i	−0.600350	−	0.799738i	$-0.704972\pi$
$174$	−1.83020	−	2.51905i	−0.138747	−	0.190969i
$175$	22.2913	−	1.17287i	1.68506	−	0.0886606i
$176$		0			0
$177$	−18.7506	+	18.7506i	−1.40938	+	1.40938i
$178$	0.0716713	−	0.452515i	0.00537199	−	0.0339174i
$179$	18.3705	−	5.96895i	1.37308	−	0.446140i	0.472690	−	0.881229i	$-0.343283\pi$
$179$	18.3705	−	5.96895i	1.37308	−	0.446140i	0.900388	+	0.435088i	$0.143283\pi$
$180$	−1.14950	−	10.9259i	−0.0856790	−	0.814369i
$181$	−10.8933	−	7.91444i	−0.809692	−	0.588275i	0.104050	−	0.994572i	$-0.466820\pi$
$181$	−10.8933	−	7.91444i	−0.809692	−	0.588275i	−0.913741	+	0.406297i	$0.866820\pi$
$182$	−0.346061	−	2.18494i	−0.0256518	−	0.161959i
$183$	1.46960	+	2.88426i	0.108636	+	0.213210i
$184$	−0.394129	−	1.21300i	−0.0290555	−	0.0894238i
$185$	−1.43297	−	5.34571i	−0.105354	−	0.393024i
$186$			2.13964i			0.156886i
$187$		0			0
$188$	−5.21654	−	5.21654i	−0.380455	−	0.380455i
$189$	−4.26738	+	3.10043i	−0.310406	+	0.225523i
$190$	0.0259263	−	0.495685i	0.00188089	−	0.0359608i
$191$	−4.12622	+	12.6992i	−0.298562	+	0.918881i	0.683439	+	0.730008i	$0.260484\pi$
$191$	−4.12622	+	12.6992i	−0.298562	+	0.918881i	−0.982001	+	0.188873i	$0.939516\pi$
$192$	16.7914	−	2.65949i	1.21181	−	0.191932i
$193$	−3.18937	+	0.505146i	−0.229576	+	0.0363612i	−0.270162	−	0.962815i	$-0.587077\pi$
$193$	−3.18937	+	0.505146i	−0.229576	+	0.0363612i	0.0405866	+	0.999176i	$0.487077\pi$
$194$	0.359118	−	1.10525i	0.0257832	−	0.0793525i
$195$	−9.77988	−	10.8594i	−0.700352	−	0.777657i
$196$	−20.5925	+	14.9613i	−1.47089	+	1.06866i
$197$	3.61891	+	3.61891i	0.257837	+	0.257837i	0.824174	−	0.566337i	$-0.191640\pi$
$197$	3.61891	+	3.61891i	0.257837	+	0.257837i	−0.566337	+	0.824174i	$0.691640\pi$
$198$		0			0
$199$			7.26740i			0.515173i	0.966255	+	0.257586i	$0.0829272\pi$
$199$			7.26740i			0.515173i	−0.966255	+	0.257586i	$0.917073\pi$
$200$	−2.22004	−	2.74036i	−0.156980	−	0.193772i
$201$	0.739095	+	2.27470i	0.0521317	+	0.160445i
$202$	0.982944	+	1.92914i	0.0691597	+	0.135734i
$203$	5.21870	+	32.9496i	0.366281	+	2.31261i
$204$	11.6364	+	8.45437i	0.814714	+	0.591924i
$205$	−24.0250	+	2.52765i	−1.67798	+	0.176539i
$206$	−2.17128	+	0.705492i	−0.151280	+	0.0491539i
$207$	0.706039	−	4.45776i	0.0490731	−	0.309835i
$208$	7.51343	−	7.51343i	0.520962	−	0.520962i
$209$		0			0
$210$	1.49031	−	3.88360i	0.102841	−	0.267994i
$211$	−8.45172	−	11.6328i	−0.581840	−	0.800835i	0.412055	−	0.911159i	$-0.364811\pi$
$211$	−8.45172	−	11.6328i	−0.581840	−	0.800835i	−0.993896	+	0.110324i	$0.964811\pi$
$212$	0.782359	+	0.398632i	0.0537327	+	0.0273782i
$213$	7.36967	−	3.75504i	0.504962	−	0.257291i
$214$	−1.04518	+	1.43857i	−0.0714472	+	0.0983386i
$215$	−11.4555	+	7.44096i	−0.781257	+	0.507469i
$216$	0.792595	+	0.257530i	0.0539293	+	0.0175227i
$217$	10.4073	−	20.4255i	0.706494	−	1.38657i
$218$	1.54428	+	0.244590i	0.104592	+	0.0165657i
$219$	−21.8485			−1.47639
$220$		0			0
$221$	8.68934			0.584508
$222$	−1.01865	−	0.161338i	−0.0683671	−	0.0108283i
$223$	−4.93173	+	9.67906i	−0.330253	+	0.648158i	−0.995106	−	0.0988167i	$-0.968494\pi$
$223$	−4.93173	+	9.67906i	−0.330253	+	0.648158i	0.664853	+	0.746974i	$0.268494\pi$
$224$	8.86618	+	2.88080i	0.592397	+	0.192481i
$225$	−2.59729	−	12.2068i	−0.173153	−	0.813789i
$226$	1.02720	−	1.41383i	0.0683286	−	0.0940463i
$227$	13.8230	−	7.04318i	0.917467	−	0.467473i	0.0695357	−	0.997579i	$-0.477848\pi$
$227$	13.8230	−	7.04318i	0.917467	−	0.467473i	0.847931	+	0.530107i	$0.177848\pi$
$228$	5.13503	+	2.61643i	0.340076	+	0.173277i
$229$	−12.1528	−	16.7269i	−0.803081	−	1.10535i	−0.992354	−	0.123422i	$-0.960613\pi$
$229$	−12.1528	−	16.7269i	−0.803081	−	1.10535i	0.189273	−	0.981924i	$-0.439387\pi$
$230$	−0.292374	−	0.656500i	−0.0192786	−	0.0432883i
$231$		0			0
$232$	3.72697	−	3.72697i	0.244688	−	0.244688i
$233$	−2.89260	+	18.2632i	−0.189501	+	1.19646i	0.691156	+	0.722705i	$0.257102\pi$
$233$	−2.89260	+	18.2632i	−0.189501	+	1.19646i	−0.880657	+	0.473755i	$0.842898\pi$
$234$	−1.17628	+	0.382195i	−0.0768955	+	0.0249849i
$235$	−6.51338	−	5.27331i	−0.424886	−	0.343993i
$236$	−18.0127	−	13.0870i	−1.17253	−	0.851892i
$237$	2.20811	+	13.9414i	0.143432	+	0.905593i
$238$	1.12286	+	2.20374i	0.0727844	+	0.142847i
$239$	5.13209	+	15.7950i	0.331967	+	1.02169i	0.968197	+	0.250190i	$0.0804932\pi$
$239$	5.13209	+	15.7950i	0.331967	+	1.02169i	−0.636229	+	0.771500i	$0.719507\pi$
$240$	19.2988	−	5.17324i	1.24573	−	0.333931i
$241$			13.5493i			0.872789i	0.899755	+	0.436395i	$0.143745\pi$
$241$			13.5493i			0.872789i	−0.899755	+	0.436395i	$0.856255\pi$
$242$		0			0
$243$	14.4984	+	14.4984i	0.930070	+	0.930070i
$244$	−2.19888	+	1.59758i	−0.140769	+	0.102275i
$245$	−21.4859	+	19.3500i	−1.37268	+	1.23623i
$246$	−1.39113	+	4.28145i	−0.0886951	+	0.272975i
$247$	3.43880	−	0.544652i	0.218806	−	0.0346554i
$248$	−3.57728	+	0.566586i	−0.227158	+	0.0359782i
$249$	3.53754	−	10.8874i	0.224183	−	0.689963i
$250$	−1.40561	−	1.40474i	−0.0888988	−	0.0888436i
$251$	5.33201	−	3.87393i	0.336554	−	0.244521i	−0.406653	−	0.913583i	$-0.633304\pi$
$251$	5.33201	−	3.87393i	0.336554	−	0.244521i	0.743206	+	0.669062i	$0.233304\pi$
$252$	15.5101	+	15.5101i	0.977043	+	0.977043i
$253$		0			0
$254$			1.37441i			0.0862381i
$255$	14.1511	+	8.16817i	0.886174	+	0.511510i
$256$	4.18164	+	12.8697i	0.261352	+	0.804359i
$257$	−7.18893	−	14.1091i	−0.448433	−	0.880099i	−0.998974	−	0.0452910i	$-0.985578\pi$
$257$	−7.18893	−	14.1091i	−0.448433	−	0.880099i	0.550541	−	0.834808i	$-0.314422\pi$
$258$	0.398211	+	2.51421i	0.0247916	+	0.156528i
$259$	8.93948	+	6.49491i	0.555472	+	0.403574i
$260$	7.72111	−	9.53680i	0.478843	−	0.591447i
$261$	17.7386	−	5.76361i	1.09799	−	0.356758i
$262$	0.544985	−	3.44090i	0.0336693	−	0.212580i
$263$	−21.0043	+	21.0043i	−1.29518	+	1.29518i	−0.363637	+	0.931541i	$0.618465\pi$
$263$	−21.0043	+	21.0043i	−1.29518	+	1.29518i	−0.931541	+	0.363637i	$0.881535\pi$
$264$		0			0
$265$	0.931246	+	0.357361i	0.0572060	+	0.0219525i
$266$	0.582504	+	0.801748i	0.0357156	+	0.0491583i
$267$	5.38427	+	2.74342i	0.329512	+	0.167895i
$268$	−1.78933	+	0.911707i	−0.109300	+	0.0556914i
$269$	−2.52630	+	3.47716i	−0.154031	+	0.212006i	−0.879058	−	0.476715i	$-0.841827\pi$
$269$	−2.52630	+	3.47716i	−0.154031	+	0.212006i	0.725027	+	0.688721i	$0.241827\pi$
$270$	0.459333	+	0.0975845i	0.0279541	+	0.00593881i
$271$	19.8046	+	6.43490i	1.20304	+	0.390892i	0.840879	−	0.541222i	$-0.182038\pi$
$271$	19.8046	+	6.43490i	1.20304	+	0.390892i	0.362163	+	0.932115i	$0.382038\pi$
$272$	−5.39336	+	10.5851i	−0.327021	+	0.641814i
$273$	28.8186	+	4.56442i	1.74418	+	0.276251i
$274$	1.45689			0.0880140
$275$		0			0
$276$	8.34425			0.502265
$277$	9.60074	+	1.52061i	0.576853	+	0.0913645i	0.438042	−	0.898954i	$-0.355672\pi$
$277$	9.60074	+	1.52061i	0.576853	+	0.0913645i	0.138811	+	0.990319i	$0.455672\pi$
$278$	−1.00188	+	1.96630i	−0.0600887	+	0.117931i
$279$	−12.1893	−	3.96056i	−0.729757	−	0.237112i
$280$	6.88766	+	1.46327i	0.411617	+	0.0874473i
$281$	−0.501682	+	0.690506i	−0.0299278	+	0.0411921i	−0.823719	−	0.566999i	$-0.808104\pi$
$281$	−0.501682	+	0.690506i	−0.0299278	+	0.0411921i	0.793791	+	0.608191i	$0.208104\pi$
$282$	−1.39148	+	0.708997i	−0.0828617	+	0.0422201i
$283$	8.65761	+	4.41127i	0.514642	+	0.262223i	0.691967	−	0.721929i	$-0.256744\pi$
$283$	8.65761	+	4.41127i	0.514642	+	0.262223i	−0.177325	+	0.984152i	$0.556744\pi$
$284$	4.08204	+	5.61844i	0.242224	+	0.333393i
$285$	6.11225	+	2.34555i	0.362059	+	0.138938i
$286$		0			0
$287$	34.1052	−	34.1052i	2.01316	−	2.01316i
$288$	0.815352	−	5.14793i	0.0480451	−	0.303345i
$289$	6.92836	−	2.25116i	0.407551	−	0.132421i
$290$	1.86877	−	2.30823i	0.109738	−	0.135544i
$291$	12.4007	+	9.00963i	0.726941	+	0.528154i
$292$	−2.86976	−	18.1190i	−0.167940	−	1.06033i
$293$	−12.1164	−	23.7799i	−0.707850	−	1.38923i	−0.911957	−	0.410286i	$-0.865429\pi$
$293$	−12.1164	−	23.7799i	−0.707850	−	1.38923i	0.204107	−	0.978949i	$-0.434571\pi$
$294$	1.66507	+	5.12457i	0.0971090	+	0.298871i
$295$	−21.9053	−	12.6440i	−1.27537	−	0.736161i
$296$		−	1.74581i		−	0.101473i
$297$		0			0
$298$	0.187959	+	0.187959i	0.0108882	+	0.0108882i
$299$	4.07821	−	2.96299i	0.235849	−	0.171354i
$300$	21.5390	−	8.27318i	1.24356	−	0.477653i
$301$	8.42780	−	25.9381i	0.485770	−	1.49505i
$302$	−1.04131	+	0.164928i	−0.0599207	+	0.00949051i
$303$	−28.2056	+	4.46733i	−1.62037	+	0.256641i
$304$	−1.47094	+	4.52709i	−0.0843642	+	0.259646i
$305$	−2.29428	+	2.06621i	−0.131370	+	0.118311i
$306$	1.11872	−	0.812795i	0.0639528	−	0.0464644i
$307$	4.08294	+	4.08294i	0.233026	+	0.233026i	0.813954	−	0.580929i	$-0.197311\pi$
$307$	4.08294	+	4.08294i	0.233026	+	0.233026i	−0.580929	+	0.813954i	$0.697311\pi$
$308$		0			0
$309$		−	30.1122i		−	1.71302i
$310$	−1.97121	+	0.528404i	−0.111957	+	0.0300113i
$311$	−0.236944	−	0.729239i	−0.0134359	−	0.0413514i	0.944114	−	0.329620i	$-0.106921\pi$
$311$	−0.236944	−	0.729239i	−0.0134359	−	0.0413514i	−0.957550	+	0.288268i	$0.906921\pi$
$312$	−2.09287	−	4.10748i	−0.118485	−	0.232540i
$313$	−4.19579	−	26.4912i	−0.237160	−	1.49737i	−0.762784	−	0.646653i	$-0.776168\pi$
$313$	−4.19579	−	26.4912i	−0.237160	−	1.49737i	0.525624	−	0.850717i	$-0.323832\pi$
$314$	−1.68133	−	1.22156i	−0.0948829	−	0.0689365i
$315$	19.3659	+	15.6789i	1.09115	+	0.883405i
$316$	−11.2716	+	3.66236i	−0.634076	+	0.206024i
$317$	−2.97124	+	18.7597i	−0.166881	+	1.05365i	0.752014	+	0.659147i	$0.229083\pi$
$317$	−2.97124	+	18.7597i	−0.166881	+	1.05365i	−0.918895	+	0.394501i	$0.870917\pi$
$318$	0.131435	−	0.131435i	0.00737050	−	0.00737050i
$319$		0			0
$320$	6.59692	+	14.8128i	0.368779	+	0.828060i
$321$	−13.7856	−	18.9742i	−0.769436	−	1.05904i
$322$	1.27846	+	0.651406i	0.0712456	+	0.0363014i
$323$	−3.46839	+	1.76723i	−0.192986	+	0.0983314i
$324$	−11.8685	+	16.3355i	−0.659358	+	0.907529i
$325$	7.58933	−	11.6919i	0.420981	−	0.648547i
$326$	1.15913	+	0.376625i	0.0641984	+	0.0208593i
$327$	−9.36238	+	18.3747i	−0.517741	+	1.01612i
$328$	−7.52656	−	1.19209i	−0.415585	−	0.0658222i
$329$	16.7320			0.922465
$330$		0			0
$331$	−0.0204452			−0.00112377			−0.000561885	−	1.00000i	$-0.500179\pi$
$331$	−0.0204452			−0.00112377			−0.000561885		1.00000i	$0.500179\pi$
$332$	9.49359	+	1.50364i	0.521028	+	0.0825228i
$333$	2.80468	−	5.50450i	0.153696	−	0.301645i
$334$	−2.11149	−	0.686064i	−0.115535	−	0.0375397i
$335$	−1.91311	+	1.24267i	−0.104525	+	0.0678944i
$336$	−23.4476	+	32.2728i	−1.27917	+	1.76063i
$337$	14.0850	−	7.17665i	0.767257	−	0.390937i	−0.0261269	−	0.999659i	$-0.508317\pi$
$337$	14.0850	−	7.17665i	0.767257	−	0.390937i	0.793384	+	0.608722i	$0.208317\pi$
$338$	0.827972	+	0.421873i	0.0450358	+	0.0229469i
$339$	13.5485	+	18.6479i	0.735851	+	1.01281i
$340$	−4.91513	+	12.8083i	−0.266561	+	0.694629i
$341$		0			0
$342$	0.391784	−	0.391784i	0.0211853	−	0.0211853i
$343$	4.14223	−	26.1530i	0.223659	−	1.41213i
$344$	−4.09807	+	1.33154i	−0.220953	+	0.0717921i
$345$	9.42686	−	0.991791i	0.507525	−	0.0533962i
$346$	−3.39682	−	2.46793i	−0.182614	−	0.132677i
$347$	3.42466	+	21.6225i	0.183845	+	1.16075i	0.891104	+	0.453799i	$0.149932\pi$
$347$	3.42466	+	21.6225i	0.183845	+	1.16075i	−0.707259	+	0.706955i	$0.750068\pi$
$348$	15.6549	+	30.7244i	0.839190	+	1.64700i
$349$	−8.64803	−	26.6159i	−0.462919	−	1.42472i	−0.861581	−	0.507620i	$-0.830526\pi$
$349$	−8.64803	−	26.6159i	−0.462919	−	1.42472i	0.398663	−	0.917098i	$-0.369474\pi$
$350$	3.94594	+	0.413908i	0.210919	+	0.0221243i
$351$			3.29383i			0.175812i
$352$		0			0
$353$	−9.36952	−	9.36952i	−0.498689	−	0.498689i	0.412340	−	0.911030i	$-0.364711\pi$
$353$	−9.36952	−	9.36952i	−0.498689	−	0.498689i	−0.911030	+	0.412340i	$0.864711\pi$
$354$	−3.81311	+	2.77039i	−0.202665	+	0.147245i
$355$	5.27945	+	5.86221i	0.280204	+	0.311134i
$356$	−1.56790	+	4.82551i	−0.0830987	+	0.255751i
$357$	−32.2206	+	5.10324i	−1.70529	+	0.270092i
$358$	3.39099	−	0.537080i	0.179219	−	0.0283856i
$359$	−0.524759	+	1.61504i	−0.0276957	+	0.0852386i	−0.963949	−	0.266087i	$-0.914269\pi$
$359$	−0.524759	+	1.61504i	−0.0276957	+	0.0852386i	0.936253	+	0.351326i	$0.114269\pi$
$360$	0.205627	−	3.93140i	0.0108375	−	0.207203i
$361$	14.1095	−	10.2511i	0.742604	−	0.539534i
$362$	−1.69230	−	1.69230i	−0.0889453	−	0.0889453i
$363$		0			0
$364$			24.4988i			1.28408i
$365$	−5.39570	−	20.1287i	−0.282424	−	1.05358i
$366$	0.177798	+	0.547205i	0.00929364	+	0.0286029i
$367$	−9.72692	−	19.0902i	−0.507741	−	0.996498i	−0.992545	−	0.121875i	$-0.961109\pi$
$367$	−9.72692	−	19.0902i	−0.507741	−	0.996498i	0.484804	−	0.874623i	$-0.338891\pi$
$368$	1.07813	+	6.80703i	0.0562013	+	0.354841i
$369$	−21.8160	−	15.8503i	−1.13570	−	0.825131i
$370$	−0.102927	−	0.978305i	−0.00535089	−	0.0508597i
$371$	−1.89401	+	0.615401i	−0.0983321	+	0.0319500i
$372$	3.70679	−	23.4037i	0.192188	−	1.21343i
$373$	−6.29327	+	6.29327i	−0.325853	+	0.325853i	−0.851007	−	0.525154i	$-0.824008\pi$
$373$	−6.29327	+	6.29327i	−0.325853	+	0.325853i	0.525154	+	0.851007i	$0.324008\pi$
$374$		0			0
$375$	23.3502	−	11.9067i	1.20580	−	0.614858i
$376$	−1.55385	−	2.13869i	−0.0801335	−	0.110294i
$377$	18.5613	+	9.45746i	0.955956	+	0.487084i
$378$	−0.835364	+	0.425639i	−0.0429665	+	0.0218925i
$379$	19.0090	−	26.1637i	0.976427	−	1.34394i	0.0376952	−	0.999289i	$-0.487998\pi$
$379$	19.0090	−	26.1637i	0.976427	−	1.34394i	0.938732	−	0.344648i	$-0.112002\pi$
$380$	−1.14233	+	5.37697i	−0.0586001	+	0.275833i
$381$	−17.2407	−	5.60185i	−0.883269	−	0.286991i
$382$	−1.07748	+	2.11466i	−0.0551284	+	0.108196i
$383$	−22.7533	−	3.60377i	−1.16264	−	0.184144i	−0.454851	−	0.890568i	$-0.650307\pi$
$383$	−22.7533	−	3.60377i	−1.16264	−	0.184144i	−0.707789	+	0.706424i	$0.750307\pi$
$384$	12.8125			0.653838
$385$		0			0
$386$	−0.573952			−0.0292134
$387$	−15.0603	−	2.38532i	−0.765559	−	0.121253i
$388$	−5.84286	+	11.4673i	−0.296626	+	0.582162i
$389$	13.6518	+	4.43572i	0.692171	+	0.224900i	0.633916	−	0.773402i	$-0.281446\pi$
$389$	13.6518	+	4.43572i	0.692171	+	0.224900i	0.0582550	+	0.998302i	$0.481446\pi$
$390$	−1.41495	−	2.17834i	−0.0716489	−	0.110305i
$391$	−3.31276	+	4.55963i	−0.167534	+	0.230590i
$392$	−8.12688	+	4.14085i	−0.410470	+	0.209145i
$393$	40.9417	+	20.8609i	2.06524	+	1.05229i
$394$	0.534691	+	0.735939i	0.0269374	+	0.0370761i
$395$	−12.2987	+	5.47725i	−0.618814	+	0.275590i
$396$		0			0
$397$	−8.05942	+	8.05942i	−0.404491	+	0.404491i	−0.879812	−	0.475321i	$-0.842332\pi$
$397$	−8.05942	+	8.05942i	−0.404491	+	0.404491i	0.475321	+	0.879812i	$0.342332\pi$
$398$	−0.202070	+	1.27582i	−0.0101289	+	0.0639512i
$399$	−12.4314	+	4.03920i	−0.622348	+	0.202213i
$400$	9.53203	+	16.5021i	0.476601	+	0.825103i
$401$	18.0602	+	13.1215i	0.901884	+	0.655257i	0.938949	−	0.344056i	$-0.111801\pi$
$401$	18.0602	+	13.1215i	0.901884	+	0.655257i	−0.0370655	+	0.999313i	$0.511801\pi$
$402$	0.0665030	+	0.419883i	0.00331687	+	0.0209419i
$403$	−6.49885	−	12.7547i	−0.323731	−	0.635357i
$404$	−7.40949	−	22.8041i	−0.368636	−	1.13455i
$405$	−11.4667	+	19.8656i	−0.569784	+	0.987130i
$406$			5.92954i			0.294278i
$407$		0			0
$408$	3.64452	+	3.64452i	0.180430	+	0.180430i
$409$	−2.28030	+	1.65673i	−0.112753	+	0.0819202i	−0.642733	−	0.766090i	$-0.722200\pi$
$409$	−2.28030	+	1.65673i	−0.112753	+	0.0819202i	0.529980	+	0.848010i	$0.322200\pi$
$410$	−4.28798	−	0.224278i	−0.211768	−	0.0110763i
$411$	−5.93803	+	18.2754i	−0.292901	+	0.901458i
$412$	24.9720	−	3.95518i	1.23028	−	0.194858i
$413$	49.8761	−	7.89960i	2.45424	−	0.388714i
$414$	0.247896	−	0.762946i	0.0121834	−	0.0374967i
$415$	10.9040	+	0.570323i	0.535258	+	0.0279961i
$416$	4.70962	−	3.42174i	0.230908	−	0.167765i
$417$	−20.5819	−	20.5819i	−1.00790	−	1.00790i
$418$		0			0
$419$			24.7639i			1.20980i	0.796303	+	0.604898i	$0.206786\pi$
$419$			24.7639i			1.20980i	−0.796303	+	0.604898i	$0.793214\pi$
$420$	−23.0294	+	39.8976i	−1.12372	+	1.94680i
$421$	8.84136	+	27.2109i	0.430902	+	1.32618i	0.897229	+	0.441566i	$0.145577\pi$
$421$	8.84136	+	27.2109i	0.430902	+	1.32618i	−0.466327	+	0.884612i	$0.654423\pi$
$422$	−1.16028	−	2.27719i	−0.0564817	−	0.110852i
$423$	−1.46340	−	9.23954i	−0.0711529	−	0.449242i
$424$	0.254551	+	0.184942i	0.0123621	+	0.00898159i
$425$	−4.03045	+	15.0543i	−0.195506	+	0.730242i
$426$	1.39819	−	0.454298i	0.0677423	−	0.0220108i
$427$	0.964333	−	6.08856i	0.0466673	−	0.294646i
$428$	13.9246	−	13.9246i	0.673070	−	0.673070i
$429$		0			0
$430$	−2.21795	+	0.987771i	−0.106959	+	0.0476346i
$431$	19.9182	+	27.4151i	0.959428	+	1.32054i	0.947210	+	0.320614i	$0.103889\pi$
$431$	19.9182	+	27.4151i	0.959428	+	1.32054i	0.0122178	+	0.999925i	$0.496111\pi$
$432$	−4.01244	−	2.04444i	−0.193048	−	0.0983631i
$433$	−2.37765	+	1.21148i	−0.114263	+	0.0582198i	−0.510188	−	0.860063i	$-0.670424\pi$
$433$	−2.37765	+	1.21148i	−0.114263	+	0.0582198i	0.395925	+	0.918283i	$0.370424\pi$
$434$	2.39498	−	3.29640i	0.114963	−	0.158232i
$435$	21.3379	+	32.8500i	1.02307	+	1.57504i
$436$	−16.4678	−	5.35072i	−0.788666	−	0.256253i
$437$	−1.02522	+	2.01211i	−0.0490431	+	0.0962524i
$438$	−3.83560	−	0.607500i	−0.183272	−	0.0290275i
$439$	25.1409			1.19991			0.599956	−	0.800033i	$-0.295185\pi$
$439$	25.1409			1.19991			0.599956	+	0.800033i	$0.295185\pi$
$440$		0			0
$441$	−32.2763			−1.53697
$442$	1.52545	+	0.241607i	0.0725582	+	0.0114921i
$443$	−5.68271	+	11.1530i	−0.269994	+	0.529893i	−0.985700	−	0.168509i	$-0.946105\pi$
$443$	−5.68271	+	11.1530i	−0.269994	+	0.529893i	0.715706	+	0.698401i	$0.246105\pi$
$444$	10.8626	+	3.52948i	0.515517	+	0.167502i
$445$	−1.19777	+	5.63794i	−0.0567798	+	0.267264i
$446$	−1.13491	+	1.56207i	−0.0537396	+	0.0739662i
$447$	−3.12386	+	1.59169i	−0.147754	+	0.0752842i
$448$	−28.8462	−	14.6979i	−1.36285	−	0.694409i
$449$	−7.17069	−	9.86961i	−0.338406	−	0.465776i	0.605569	−	0.795793i	$-0.292946\pi$
$449$	−7.17069	−	9.86961i	−0.338406	−	0.465776i	−0.943975	+	0.330017i	$0.892946\pi$
$450$	−0.116553	−	2.21518i	−0.00549436	−	0.104425i
$451$		0			0
$452$	−13.6851	+	13.6851i	−0.643692	+	0.643692i
$453$	2.17534	−	13.7345i	0.102206	−	0.645304i
$454$	2.62252	−	0.852110i	0.123081	−	0.0399915i
$455$	2.91190	+	27.6773i	0.136512	+	1.29753i
$456$	1.67075	+	1.21387i	0.0782402	+	0.0568448i
$457$	−4.72598	−	29.8386i	−0.221072	−	1.39579i	−0.809441	−	0.587201i	$-0.800230\pi$
$457$	−4.72598	−	29.8386i	−0.221072	−	1.39579i	0.588370	−	0.808592i	$-0.299770\pi$
$458$	−1.66838	−	3.27439i	−0.0779585	−	0.153002i
$459$	−1.13800	−	3.50241i	−0.0531174	−	0.163479i
$460$	2.06069	+	7.68741i	0.0960801	+	0.358427i
$461$			16.7546i			0.780340i	0.920743	+	0.390170i	$0.127584\pi$
$461$			16.7546i			0.780340i	−0.920743	+	0.390170i	$0.872416\pi$
$462$		0			0
$463$	−15.7524	−	15.7524i	−0.732077	−	0.732077i	0.238954	−	0.971031i	$-0.423195\pi$
$463$	−15.7524	−	15.7524i	−0.732077	−	0.732077i	−0.971031	+	0.238954i	$0.923195\pi$
$464$	−23.0415	+	16.7406i	−1.06968	+	0.777165i
$465$	1.40597	−	26.8808i	0.0652003	−	1.24657i
$466$	−1.01562	+	3.12574i	−0.0470475	+	0.144797i
$467$	−31.9281	+	5.05691i	−1.47745	+	0.234006i	−0.842564	−	0.538596i	$-0.818955\pi$
$467$	−31.9281	+	5.05691i	−1.47745	+	0.234006i	−0.634891	+	0.772602i	$0.718955\pi$
$468$	13.5284	−	2.14269i	0.625351	−	0.0990458i
$469$	1.40748	−	4.33177i	0.0649913	−	0.200023i
$470$	−0.996826	−	1.10686i	−0.0459801	−	0.0510555i
$471$	22.1761	−	16.1119i	1.02182	−	0.742397i
$472$	−5.64156	−	5.64156i	−0.259674	−	0.259674i
$473$		0			0
$474$			2.50887i			0.115236i
$475$	−0.651434	+	6.21036i	−0.0298899	+	0.284951i
$476$	−8.46421	−	26.0502i	−0.387956	−	1.19401i
$477$	0.505481	+	0.992063i	0.0231444	+	0.0454234i
$478$	0.461780	+	2.91557i	0.0211213	+	0.133355i
$479$	−15.4314	−	11.2116i	−0.705079	−	0.512270i	0.176503	−	0.984300i	$-0.443521\pi$
$479$	−15.4314	−	11.2116i	−0.705079	−	0.512270i	−0.881583	+	0.472030i	$0.843521\pi$
$480$	10.8864	−	1.14534i	0.496893	−	0.0522776i
$481$	6.56234	−	2.13223i	0.299217	−	0.0972214i
$482$	−0.376740	+	2.37864i	−0.0171600	+	0.108344i
$483$	−13.3821	+	13.3821i	−0.608905	+	0.608905i
$484$		0			0
$485$	−5.23794	+	13.6495i	−0.237843	+	0.619794i
$486$	2.14212	+	2.94837i	0.0971685	+	0.133741i
$487$	−24.5758	−	12.5220i	−1.11363	−	0.567425i	−0.202396	−	0.979304i	$-0.564873\pi$
$487$	−24.5758	−	12.5220i	−1.11363	−	0.567425i	−0.911239	+	0.411879i	$0.864873\pi$
$488$	−0.867795	+	0.442163i	−0.0392832	+	0.0200158i
$489$	−9.44885	+	13.0052i	−0.427292	+	0.588116i
$490$	−4.30997	+	2.79956i	−0.194704	+	0.126471i
$491$	−35.5076	−	11.5371i	−1.60243	−	0.520662i	−0.634726	−	0.772737i	$-0.718887\pi$
$491$	−35.5076	−	11.5371i	−1.60243	−	0.520662i	−0.967708	+	0.252075i	$0.918887\pi$
$492$	22.6337	−	44.4211i	1.02041	−	2.00266i
$493$	−23.0042	−	3.64351i	−1.03606	−	0.164095i
$494$	0.618839			0.0278429
$495$		0			0
$496$	19.5711			0.878769
$497$	−15.5571	−	2.46400i	−0.697832	−	0.110526i
$498$	0.923756	−	1.81297i	0.0413945	−	0.0812413i
$499$	−13.4267	−	4.36259i	−0.601061	−	0.195297i	−0.00734745	−	0.999973i	$-0.502339\pi$
$499$	−13.4267	−	4.36259i	−0.601061	−	0.195297i	−0.593714	+	0.804676i	$0.702339\pi$
$500$	12.9412	+	17.8004i	0.578748	+	0.796058i
$501$	17.2121	−	23.6904i	0.768980	−	1.05841i
$502$	1.04377	−	0.531828i	0.0465858	−	0.0237366i
$503$	−11.1484	−	5.68041i	−0.497084	−	0.253277i	0.187428	−	0.982278i	$-0.439985\pi$
$503$	−11.1484	−	5.68041i	−0.497084	−	0.253277i	−0.684512	+	0.729001i	$0.739985\pi$
$504$	4.61998	+	6.35885i	0.205790	+	0.283246i
$505$	−11.0813	−	24.8821i	−0.493111	−	1.10724i
$506$		0			0
$507$	−8.66669	+	8.66669i	−0.384901	+	0.384901i
$508$	2.38107	−	15.0335i	0.105643	−	0.667003i
$509$	−2.02279	+	0.657243i	−0.0896585	+	0.0291318i	−0.353503	−	0.935433i	$-0.615009\pi$
$509$	−2.02279	+	0.657243i	−0.0896585	+	0.0291318i	0.263844	+	0.964565i	$0.415009\pi$
$510$	2.25716	+	1.82743i	0.0999488	+	0.0809198i
$511$	33.6606	+	24.4559i	1.48906	+	1.08186i
$512$	2.08617	+	13.1716i	0.0921966	+	0.582107i
$513$	−0.669897	−	1.31475i	−0.0295767	−	0.0580475i
$514$	−0.869742	−	2.67679i	−0.0383627	−	0.118068i
$515$	27.7418	−	7.43648i	1.22245	−	0.327691i
$516$		−	28.1907i		−	1.24102i
$517$		0			0
$518$	1.38877	+	1.38877i	0.0610191	+	0.0610191i
$519$	44.8029	−	32.5512i	1.96663	−	1.42884i
$520$	3.26730	−	2.94250i	0.143281	−	0.129037i
$521$	7.68427	−	23.6498i	0.336654	−	1.03612i	−0.629247	−	0.777205i	$-0.716637\pi$
$521$	7.68427	−	23.6498i	0.336654	−	1.03612i	0.965901	−	0.258910i	$-0.0833633\pi$
$522$	3.27433	−	0.518603i	0.143314	−	0.0226987i
$523$	−19.0167	+	3.01195i	−0.831541	+	0.131703i	−0.557670	−	0.830063i	$-0.688304\pi$
$523$	−19.0167	+	3.01195i	−0.831541	+	0.131703i	−0.273872	+	0.961766i	$0.588304\pi$
$524$	−11.9223	+	36.6929i	−0.520826	+	1.60294i
$525$	−21.2751	+	47.8113i	−0.928520	+	2.08665i
$526$	−4.27141	+	3.10336i	−0.186242	+	0.135313i
$527$	11.3171	+	11.3171i	0.492980	+	0.492980i
$528$		0			0
$529$		−	19.7304i		−	0.857843i
$530$	0.153548	+	0.0886295i	0.00666968	+	0.00384982i
$531$	−8.72444	−	26.8511i	−0.378608	−	1.16524i
$532$	−4.98254	−	9.77879i	−0.216021	−	0.423964i
$533$	−4.71157	−	29.7477i	−0.204081	−	1.28851i
$534$	0.868950	+	0.631329i	0.0376031	+	0.0273203i
$535$	14.0761	−	17.3863i	0.608565	−	0.751674i
$536$	−0.684396	+	0.222374i	−0.0295614	+	0.00960508i
$537$	−7.08389	+	44.7259i	−0.305693	+	1.93007i
$538$	−0.540186	+	0.540186i	−0.0232891	+	0.0232891i
$539$		0			0
$540$	−4.85520	−	1.86316i	−0.208934	−	0.0801776i
$541$	19.6436	+	27.0372i	0.844546	+	1.16242i	0.985038	+	0.172337i	$0.0551317\pi$
$541$	19.6436	+	27.0372i	0.844546	+	1.16242i	−0.140492	+	0.990082i	$0.544868\pi$
$542$	3.29785	+	1.68034i	0.141655	+	0.0721768i
$543$	28.1259	−	14.3309i	1.20700	−	0.614996i
$544$	−3.82566	+	5.26557i	−0.164024	+	0.225760i
$545$	−19.2404	−	4.08759i	−0.824168	−	0.175093i
$546$	4.93231	+	1.60261i	0.211084	+	0.0685852i
$547$	−13.1554	+	25.8190i	−0.562486	+	1.10394i	0.418200	+	0.908355i	$0.362661\pi$
$547$	−13.1554	+	25.8190i	−0.562486	+	1.10394i	−0.980686	+	0.195586i	$0.937339\pi$
$548$	−15.9357	−	2.52397i	−0.680739	−	0.107818i
$549$	−3.44649			−0.147093
$550$		0			0
$551$	−9.33227			−0.397568
$552$	2.95325	+	0.467748i	0.125699	+	0.0199087i
$553$	12.2033	−	23.9502i	0.518935	−	1.01847i
$554$	1.64317	+	0.533898i	0.0698116	+	0.0226832i
$555$	12.6915	+	2.69628i	0.538723	+	0.114451i
$556$	14.3652	−	19.7720i	0.609219	−	0.838518i
$557$	17.1929	−	8.76023i	0.728487	−	0.371183i	−0.0500790	−	0.998745i	$-0.515947\pi$
$557$	17.1929	−	8.76023i	0.728487	−	0.371183i	0.778566	+	0.627562i	$0.215947\pi$
$558$	−2.02977	−	1.03422i	−0.0859268	−	0.0437819i
$559$	−10.0103	−	13.7780i	−0.423392	−	0.582749i
$560$	−35.5230	−	13.6318i	−1.50112	−	0.576047i
$561$		0			0
$562$	−0.107272	+	0.107272i	−0.00452499	+	0.00452499i
$563$	0.167182	−	1.05554i	0.00704587	−	0.0444859i	−0.983915	−	0.178638i	$-0.942831\pi$
$563$	0.167182	−	1.05554i	0.00704587	−	0.0444859i	0.990961	+	0.134152i	$0.0428310\pi$
$564$	16.4486	−	5.34446i	0.692609	−	0.225042i
$565$	−13.8340	+	17.0872i	−0.582002	+	0.718864i
$566$	1.39722	+	1.01514i	0.0587297	+	0.0426696i
$567$	−7.16405	−	45.2320i	−0.300862	−	1.89957i
$568$	1.12979	+	2.21734i	0.0474049	+	0.0930373i
$569$	2.43796	+	7.50327i	0.102205	+	0.314553i	0.989064	−	0.147486i	$-0.0471180\pi$
$569$	2.43796	+	7.50327i	0.102205	+	0.314553i	−0.886860	+	0.462039i	$0.847118\pi$
$570$	1.00781	+	0.581722i	0.0422126	+	0.0243657i
$571$		−	12.2418i		−	0.512302i	−0.966637	−	0.256151i	$-0.917546\pi$
$571$		−	12.2418i		−	0.512302i	0.966637	−	0.256151i	$-0.0824544\pi$
$572$		0			0
$573$	−22.1350	−	22.1350i	−0.924701	−	0.924701i
$574$	6.93560	−	5.03901i	0.289486	−	0.210324i
$575$	3.24177	+	8.43987i	0.135191	+	0.351967i
$576$	−5.59335	+	17.2146i	−0.233056	+	0.717274i
$577$	−45.9272	+	7.27415i	−1.91197	+	0.302827i	−0.995302	−	0.0968174i	$-0.969134\pi$
$577$	−45.9272	+	7.27415i	−1.91197	+	0.302827i	−0.916670	+	0.399644i	$0.869134\pi$
$578$	1.27890	−	0.202557i	0.0531951	−	0.00842527i
$579$	2.33933	−	7.19971i	0.0972192	−	0.299210i
$580$	−24.4398	+	22.0102i	−1.01481	+	0.913926i
$581$	−17.6368	+	12.8139i	−0.731696	+	0.531608i
$582$	1.92648	+	1.92648i	0.0798551	+	0.0798551i
$583$		0			0
$584$		−	6.57364i		−	0.272019i
$585$	15.0289	−	4.02866i	0.621370	−	0.166565i
$586$	−1.46589	−	4.51155i	−0.0605554	−	0.186370i
$587$	2.47831	+	4.86395i	0.102291	+	0.200757i	0.936480	−	0.350722i	$-0.114064\pi$
$587$	2.47831	+	4.86395i	0.102291	+	0.200757i	−0.834189	+	0.551479i	$0.814064\pi$
$588$	−9.33485	−	58.9379i	−0.384963	−	2.43056i
$589$	5.18808	+	3.76936i	0.213771	+	0.155314i
$590$	−3.49399	−	2.82878i	−0.143845	−	0.116459i
$591$	−11.4110	+	3.70766i	−0.469386	+	0.152513i
$592$	−1.47574	+	9.31747i	−0.0606527	+	0.382946i
$593$	28.4741	−	28.4741i	1.16929	−	1.16929i	0.186913	−	0.982376i	$-0.440152\pi$
$593$	28.4741	−	28.4741i	1.16929	−	1.16929i	0.982376	−	0.186913i	$-0.0598483\pi$
$594$		0			0
$595$	−12.6587	−	28.4239i	−0.518955	−	1.16527i
$596$	−1.73030	−	2.38155i	−0.0708757	−	0.0975521i
$597$	−15.1804	−	7.73482i	−0.621294	−	0.316565i
$598$	0.798333	−	0.406771i	0.0326462	−	0.0166341i
$599$	4.08303	−	5.61980i	0.166828	−	0.229619i	−0.717415	−	0.696646i	$-0.754675\pi$
$599$	4.08303	−	5.61980i	0.166828	−	0.229619i	0.884243	+	0.467027i	$0.154675\pi$
$600$	8.08699	−	1.72069i	0.330150	−	0.0702470i
$601$	23.1053	+	7.50735i	0.942483	+	0.306231i	0.739657	−	0.672984i	$-0.234988\pi$
$601$	23.1053	+	7.50735i	0.942483	+	0.306231i	0.202826	+	0.979215i	$0.434988\pi$
$602$	2.20074	−	4.31920i	0.0896956	−	0.176038i
$603$	−2.51514	−	0.398358i	−0.102424	−	0.0162224i
$604$	11.6757			0.475079
$605$		0			0
$606$	−5.07582			−0.206191
$607$	3.97442	+	0.629487i	0.161317	+	0.0255501i	0.236570	−	0.971614i	$-0.423977\pi$
$607$	3.97442	+	0.629487i	0.161317	+	0.0255501i	−0.0752535	+	0.997164i	$0.523977\pi$
$608$	−1.18395	+	2.32364i	−0.0480156	+	0.0942360i
$609$	−74.3807	−	24.1678i	−3.01406	−	0.979327i
$610$	−0.460222	+	0.298939i	−0.0186338	+	0.0121037i
$611$	6.14136	−	8.45286i	0.248453	−	0.341966i
$612$	−13.6448	+	6.95237i	−0.551558	+	0.281033i
$613$	41.0680	+	20.9252i	1.65872	+	0.845161i	0.995292	+	0.0969234i	$0.0309002\pi$
$613$	41.0680	+	20.9252i	1.65872	+	0.845161i	0.663431	+	0.748238i	$0.269100\pi$
$614$	0.603250	+	0.830303i	0.0243452	+	0.0335083i
$615$	20.2904	−	52.8747i	0.818188	−	2.13211i
$616$		0			0
$617$	6.94955	−	6.94955i	0.279778	−	0.279778i	−0.553242	−	0.833021i	$-0.686610\pi$
$617$	6.94955	−	6.94955i	0.279778	−	0.279778i	0.833021	+	0.553242i	$0.186610\pi$
$618$	0.837271	−	5.28632i	0.0336800	−	0.212647i
$619$	−19.8128	+	6.43756i	−0.796343	+	0.258747i	−0.678803	−	0.734321i	$-0.737501\pi$
$619$	−19.8128	+	6.43756i	−0.796343	+	0.258747i	−0.117540	+	0.993068i	$0.537501\pi$
$620$	22.4769	−	2.36477i	0.902692	−	0.0949714i
$621$	−1.72840	−	1.25575i	−0.0693582	−	0.0503917i
$622$	−0.0213200	−	0.134609i	−0.000854854	−	0.00539734i
$623$	−5.22437	−	10.2534i	−0.209310	−	0.410794i
$624$	7.69768	+	23.6910i	0.308154	+	0.948399i
$625$	16.7360	+	18.5717i	0.669439	+	0.742867i
$626$		−	4.76730i		−	0.190540i
$627$		0			0
$628$	16.2744	+	16.2744i	0.649418	+	0.649418i
$629$	−6.24122	+	4.53451i	−0.248854	+	0.180803i
$630$	2.96381	+	3.29096i	0.118081	+	0.131115i
$631$	−9.36619	+	28.8262i	−0.372862	+	1.14755i	0.572047	+	0.820221i	$0.306149\pi$
$631$	−9.36619	+	28.8262i	−0.372862	+	1.14755i	−0.944910	+	0.327332i	$0.893851\pi$
$632$	−4.19460	+	0.664359i	−0.166852	+	0.0264268i
$633$	33.2943	−	5.27331i	1.32333	−	0.209595i
$634$	−1.04323	+	3.21072i	−0.0414318	+	0.127514i
$635$	0.903131	−	17.2670i	0.0358396	−	0.685220i
$636$	−1.66536	+	1.20995i	−0.0660357	+	0.0479777i
$637$	−25.4909	−	25.4909i	−1.00998	−	1.00998i
$638$		0			0
$639$			8.80625i			0.348370i
$640$	3.16418	+	11.8040i	0.125075	+	0.466593i
$641$	−10.4502	−	32.1625i	−0.412759	−	1.27034i	−0.914240	−	0.405174i	$-0.867211\pi$
$641$	−10.4502	−	32.1625i	−0.412759	−	1.27034i	0.501480	−	0.865169i	$-0.332789\pi$
$642$	−1.89254	−	3.71431i	−0.0746925	−	0.146592i
$643$	1.97627	+	12.4777i	0.0779364	+	0.492071i	0.995522	+	0.0945322i	$0.0301355\pi$
$643$	1.97627	+	12.4777i	0.0779364	+	0.492071i	−0.917585	+	0.397539i	$0.869864\pi$
$644$	−12.8554	−	9.34002i	−0.506575	−	0.368048i
$645$	−3.35072	−	31.8482i	−0.131934	−	1.25402i
$646$	−0.658027	+	0.213806i	−0.0258897	+	0.00841209i
$647$	−1.44674	+	9.13437i	−0.0568773	+	0.359109i	0.942792	+	0.333382i	$0.108190\pi$
$647$	−1.44674	+	9.13437i	−0.0568773	+	0.359109i	−0.999669	+	0.0257267i	$0.991810\pi$
$648$	−5.11626	+	5.11626i	−0.200986	+	0.200986i
$649$		0			0
$650$	1.65743	−	1.84153i	0.0650098	−	0.0722308i
$651$	31.5889	+	43.4784i	1.23807	+	1.70405i
$652$	−12.0263	−	6.12770i	−0.470986	−	0.239979i
$653$	−3.72144	+	1.89617i	−0.145631	+	0.0742027i	−0.525287	−	0.850925i	$-0.676042\pi$
$653$	−3.72144	+	1.89617i	−0.145631	+	0.0742027i	0.379656	+	0.925128i	$0.376042\pi$
$654$	−2.15451	+	2.96543i	−0.0842481	+	0.115958i
$655$	−9.10780	+	42.8707i	−0.355871	+	1.67510i
$656$	39.1620	+	12.7245i	1.52902	+	0.496809i
$657$	10.5607	−	20.7266i	0.412013	−	0.808620i
$658$	2.93737	+	0.465234i	0.114511	+	0.0181367i
$659$	−16.5191			−0.643494			−0.321747	−	0.946826i	$-0.604270\pi$
$659$	−16.5191			−0.643494			−0.321747	+	0.946826i	$0.604270\pi$
$660$		0			0
$661$	35.6112			1.38512			0.692558	−	0.721362i	$-0.256484\pi$
$661$	35.6112			1.38512			0.692558	+	0.721362i	$0.256484\pi$
$662$	−0.00358924		0.000568479i	−0.000139500		2.20946e-5i
$663$	−9.24821	+	18.1506i	−0.359171	+	0.704912i
$664$	3.27574	+	1.06435i	0.127123	+	0.0413048i
$665$	−6.79129	−	10.4553i	−0.263355	−	0.405439i
$666$	0.645426	−	0.888352i	0.0250097	−	0.0344230i
$667$	−12.0391	+	6.13422i	−0.466155	+	0.237518i
$668$	21.9072	+	11.1623i	0.847615	+	0.431881i
$669$	−14.9691	−	20.6032i	−0.578738	−	0.796564i
$670$	−0.370407	+	0.164962i	−0.0143101	+	0.00637304i
$671$		0			0
$672$	−15.4539	+	15.4539i	−0.596149	+	0.596149i
$673$	−1.00274	+	6.33102i	−0.0386526	+	0.244043i	−0.999448	−	0.0332145i	$-0.989426\pi$
$673$	−1.00274	+	6.33102i	−0.0386526	+	0.244043i	0.960796	+	0.277258i	$0.0894255\pi$
$674$	2.67222	−	0.868257i	0.102930	−	0.0334440i
$675$	−5.70658	−	1.52781i	−0.219646	−	0.0588053i
$676$	−8.32562	−	6.04892i	−0.320216	−	0.232651i
$677$	−4.32390	−	27.3000i	−0.166181	−	1.04922i	−0.919936	−	0.392069i	$-0.871760\pi$
$677$	−4.32390	−	27.3000i	−0.166181	−	1.04922i	0.753755	−	0.657155i	$-0.228240\pi$
$678$	1.85998	+	3.65042i	0.0714322	+	0.140194i
$679$	−9.02012	−	27.7611i	−0.346160	−	1.06537i
$680$	−2.45758	+	4.25767i	−0.0942439	+	0.163274i
$681$			36.3703i			1.39371i
$682$		0			0
$683$	−5.39890	−	5.39890i	−0.206583	−	0.206583i	0.596230	−	0.802814i	$-0.296665\pi$
$683$	−5.39890	−	5.39890i	−0.206583	−	0.206583i	−0.802814	+	0.596230i	$0.796665\pi$
$684$	−4.96414	+	3.60666i	−0.189809	+	0.137904i
$685$	−18.3032	−	0.957330i	−0.699330	−	0.0365777i
$686$	1.45437	−	4.47609i	0.0555281	−	0.170898i
$687$	47.8743	−	7.58255i	1.82652	−	0.289292i
$688$	22.9972	−	3.64240i	0.876761	−	0.138865i
$689$	−0.384287	+	1.18272i	−0.0146402	+	0.0450579i
$690$	1.68250	+	0.0880013i	0.0640517	+	0.00335015i
$691$	20.5343	−	14.9191i	0.781162	−	0.567548i	−0.124165	−	0.992262i	$-0.539625\pi$
$691$	20.5343	−	14.9191i	0.781162	−	0.567548i	0.905328	+	0.424714i	$0.139625\pi$
$692$	32.8794	+	32.8794i	1.24989	+	1.24989i
$693$		0			0
$694$			3.89113i			0.147705i
$695$	13.8789	−	24.0447i	0.526456	−	0.912066i
$696$	3.81837	+	11.7517i	0.144735	+	0.445448i
$697$	15.2876	+	30.0036i	0.579060	+	1.13647i
$698$	−0.778141	−	4.91299i	−0.0294531	−	0.185959i
$699$	−35.0702	−	25.4800i	−1.32648	−	0.963741i
$700$	−42.4442	−	11.3635i	−1.60424	−	0.429499i
$701$	−29.5187	+	9.59120i	−1.11491	+	0.362255i	−0.807821	−	0.589428i	$-0.799353\pi$
$701$	−29.5187	+	9.59120i	−1.11491	+	0.362255i	−0.307084	+	0.951682i	$0.599353\pi$
$702$	−0.0915851	+	0.578246i	−0.00345666	+	0.0218245i
$703$	−2.18573	+	2.18573i	−0.0824364	+	0.0824364i
$704$		0			0
$705$	17.9474	−	7.99293i	0.675938	−	0.301031i
$706$	−1.38434	−	1.90538i	−0.0521002	−	0.0717098i
$707$	48.4549	+	24.6890i	1.82233	+	0.928526i
$708$	46.5079	−	23.6970i	1.74788	−	0.890587i
$709$	−29.2576	+	40.2696i	−1.09879	+	1.51236i	−0.261817	+	0.965117i	$0.584322\pi$
$709$	−29.2576	+	40.2696i	−1.09879	+	1.51236i	−0.836975	+	0.547241i	$0.815678\pi$
$710$	0.763831	+	1.17593i	0.0286661	+	0.0441319i
$711$	−14.2928	−	4.64402i	−0.536022	−	0.174164i
$712$	−0.825422	+	1.61998i	−0.0309340	+	0.0607114i
$713$	9.17053	+	1.45247i	0.343439	+	0.0543954i
$714$	−5.79835			−0.216998
$715$		0			0
$716$	−38.0216			−1.42093
$717$	−38.4553	−	6.09072i	−1.43614	−	0.227462i
$718$	−0.137030	+	0.268936i	−0.00511391	+	0.0100366i
$719$	−34.6985	−	11.2742i	−1.29403	−	0.420457i	−0.420532	−	0.907278i	$-0.638157\pi$
$719$	−34.6985	−	11.2742i	−1.29403	−	0.420457i	−0.873502	+	0.486820i	$0.838157\pi$
$720$	−4.42069	+	20.8083i	−0.164749	+	0.775479i
$721$	−33.7057	+	46.3919i	−1.25526	+	1.72772i
$722$	2.76201	−	1.40731i	0.102791	−	0.0523748i
$723$	−28.3024	−	14.4208i	−1.05258	−	0.536315i
$724$	15.5788	+	21.4424i	0.578983	+	0.796902i
$725$	−24.9945	+	27.7708i	−0.928273	+	1.03138i
$726$		0			0
$727$	−17.4528	+	17.4528i	−0.647287	+	0.647287i	−0.952336	−	0.305050i	$-0.901327\pi$
$727$	−17.4528	+	17.4528i	−0.647287	+	0.647287i	0.305050	+	0.952336i	$0.401327\pi$
$728$	−1.37331	+	8.67075i	−0.0508983	+	0.321359i
$729$	−16.4479	+	5.34425i	−0.609182	+	0.197935i
$730$	−0.387558	−	3.68370i	−0.0143442	−	0.136340i
$731$	15.4045	+	11.1920i	0.569755	+	0.413951i
$732$	−0.996783	−	6.29344i	−0.0368421	−	0.232612i
$733$	4.23102	+	8.30385i	0.156276	+	0.306710i	0.955848	−	0.293861i	$-0.0949402\pi$
$733$	4.23102	+	8.30385i	0.156276	+	0.306710i	−0.799572	+	0.600570i	$0.794940\pi$
$734$	−1.17680	−	3.62181i	−0.0434364	−	0.133684i
$735$	−17.5513	−	65.4752i	−0.647389	−	2.41509i
$736$			3.77583i			0.139179i
$737$		0			0
$738$	−3.38917	−	3.38917i	−0.124757	−	0.124757i
$739$	−29.3354	+	21.3134i	−1.07912	+	0.784026i	−0.977529	−	0.210800i	$-0.932393\pi$
$739$	−29.3354	+	21.3134i	−1.07912	+	0.784026i	−0.101590	+	0.994826i	$0.532393\pi$
$740$	−0.569022	+	10.8792i	−0.0209177	+	0.399926i
$741$	−2.52228	+	7.76278i	−0.0926583	+	0.285173i
$742$	−0.349613	+	0.0553732i	−0.0128347	+	0.00203281i
$743$	41.4295	−	6.56179i	1.51990	−	0.240729i	0.660030	−	0.751239i	$-0.270543\pi$
$743$	41.4295	−	6.56179i	1.51990	−	0.240729i	0.859872	+	0.510510i	$0.170543\pi$
$744$	2.62385	−	8.07539i	0.0961952	−	0.296058i
$745$	−2.23786	−	2.48488i	−0.0819888	−	0.0910388i
$746$	−1.27979	+	0.929825i	−0.0468566	+	0.0340433i
$747$	8.61843	+	8.61843i	0.315332	+	0.315332i
$748$		0			0
$749$			44.6630i			1.63195i
$750$	4.43029	−	1.44101i	0.161771	−	0.0526183i
$751$	−5.63645	−	17.3472i	−0.205677	−	0.633008i	−0.999685	−	0.0251010i	$-0.992009\pi$
$751$	−5.63645	−	17.3472i	−0.205677	−	0.633008i	0.794008	−	0.607907i	$-0.207991\pi$
$752$	6.48513	+	12.7278i	0.236488	+	0.464134i
$753$	2.41707	+	15.2608i	0.0880831	+	0.556135i
$754$	2.99555	+	2.17639i	0.109091	+	0.0792596i
$755$	13.1906	−	1.38777i	0.480055	−	0.0505061i
$756$	9.87472	−	3.20849i	0.359140	−	0.116692i
$757$	−3.08890	+	19.5025i	−0.112268	+	0.708832i	0.865776	+	0.500432i	$0.166826\pi$
$757$	−3.08890	+	19.5025i	−0.112268	+	0.708832i	−0.978044	+	0.208400i	$0.933174\pi$
$758$	4.06459	−	4.06459i	0.147633	−	0.147633i
$759$		0			0
$760$	−0.705712	+	1.83901i	−0.0255989	+	0.0667080i
$761$	−25.9630	−	35.7350i	−0.941158	−	1.29539i	−0.955345	−	0.295494i	$-0.904516\pi$
$761$	−25.9630	−	35.7350i	−0.941158	−	1.29539i	0.0141864	−	0.999899i	$-0.495484\pi$
$762$	−2.87092	−	1.46281i	−0.104002	−	0.0529919i
$763$	34.9914	−	17.8290i	1.26678	−	0.645454i
$764$	15.4491	−	21.2639i	0.558929	−	0.769300i
$765$	−14.5888	+	9.47620i	−0.527458	+	0.342613i
$766$	−3.89423	−	1.26531i	−0.140704	−	0.0457176i
$767$	14.3159	−	28.0965i	0.516916	−	1.01450i
$768$	−31.3334	−	4.96273i	−1.13065	−	0.179077i
$769$	−19.2821			−0.695332			−0.347666	−	0.937618i	$-0.613026\pi$
$769$	−19.2821			−0.695332			−0.347666	+	0.937618i	$0.613026\pi$
$770$		0			0
$771$	37.1229			1.33695
$772$	6.27798	+	0.994334i	0.225949	+	0.0357869i
$773$	13.0396	−	25.5917i	0.469003	−	0.920471i	−0.528437	−	0.848972i	$-0.677222\pi$
$773$	13.0396	−	25.5917i	0.469003	−	0.920471i	0.997441	−	0.0714986i	$-0.0227781\pi$
$774$	−2.57758	−	0.837505i	−0.0926490	−	0.0301035i
$775$	25.1120	−	5.34316i	0.902050	−	0.191932i
$776$	−2.71075	+	3.73103i	−0.0973104	+	0.133936i
$777$	−23.0813	+	11.7605i	−0.828035	+	0.421905i
$778$	2.27329	+	1.15830i	0.0815012	+	0.0415270i
$779$	7.93070	+	10.9157i	0.284147	+	0.391094i
$780$	11.7031	+	26.2783i	0.419039	+	0.940915i
$781$		0			0
$782$	−0.708350	+	0.708350i	−0.0253305	+	0.0253305i
$783$	1.38113	−	8.72011i	0.0493575	−	0.311631i
$784$	46.8740	−	15.2303i	1.67407	−	0.543938i
$785$	20.3202	+	16.4515i	0.725259	+	0.587179i
$786$	6.60745	+	4.80059i	0.235680	+	0.171232i
$787$	6.70201	+	42.3148i	0.238901	+	1.50836i	0.757213	+	0.653168i	$0.226561\pi$
$787$	6.70201	+	42.3148i	0.238901	+	1.50836i	−0.518312	+	0.855192i	$0.673439\pi$
$788$	−4.57357	−	8.97613i	−0.162927	−	0.319761i
$789$	−21.5193	−	66.2297i	−0.766108	−	2.35784i
$790$	−2.31138	+	0.619589i	−0.0822352	+	0.0220440i
$791$		−	43.8948i		−	1.56072i
$792$		0			0
$793$	−2.72193	−	2.72193i	−0.0966587	−	0.0966587i
$794$	−1.63896	+	1.19077i	−0.0581644	+	0.0422589i
$795$	−1.73761	+	1.56488i	−0.0616267	+	0.0555005i
$796$	4.42055	−	13.6051i	0.156682	−	0.482219i
$797$	7.96988	−	1.26231i	0.282308	−	0.0447132i	−0.0136748	−	0.999906i	$-0.504353\pi$
$797$	7.96988	−	1.26231i	0.282308	−	0.0447132i	0.295983	+	0.955193i	$0.404353\pi$
$798$	−2.29469	+	0.363443i	−0.0812312	+	0.0128658i
$799$	−3.60984	+	11.1099i	−0.127707	+	0.393042i
$800$	3.74367	+	9.74657i	0.132359	+	0.344593i
$801$	−5.20508	+	3.78171i	−0.183912	+	0.133620i
$802$	2.80570	+	2.80570i	0.0990727	+	0.0990727i
$803$		0			0
$804$		−	4.70796i		−	0.166037i
$805$	−15.6335	−	9.02383i	−0.551008	−	0.318048i
$806$	−0.786254	−	2.41984i	−0.0276946	−	0.0852353i
$807$	−4.57444	−	8.97784i	−0.161028	−	0.316035i
$808$	−1.34410	−	8.48630i	−0.0472852	−	0.298547i
$809$	20.8720	+	15.1644i	0.733822	+	0.533153i	0.890770	−	0.454454i	$-0.150166\pi$
$809$	20.8720	+	15.1644i	0.733822	+	0.533153i	−0.156948	+	0.987607i	$0.550166\pi$
$810$	−2.56539	+	3.16866i	−0.0901385	+	0.111335i
$811$	5.06847	−	1.64685i	0.177978	−	0.0578286i	−0.218672	−	0.975798i	$-0.570173\pi$
$811$	5.06847	−	1.64685i	0.177978	−	0.0578286i	0.396650	+	0.917970i	$0.370173\pi$
$812$	10.2725	−	64.8582i	0.360495	−	2.27608i
$813$	−34.5198	+	34.5198i	−1.21066	+	1.21066i
$814$		0			0
$815$	−14.3150	−	5.49329i	−0.501431	−	0.192422i
$816$	−16.3703	−	22.5317i	−0.573074	−	0.788769i
$817$	6.79783	+	3.46367i	0.237826	+	0.121178i
$818$	−0.446381	+	0.227443i	−0.0156073	+	0.00795234i
$819$	−18.2598	+	25.1325i	−0.638049	+	0.878199i
$820$	46.5140	+	9.88181i	1.62434	+	0.345088i
$821$	1.02612	+	0.333406i	0.0358118	+	0.0116360i	0.326868	−	0.945070i	$-0.394007\pi$
$821$	1.02612	+	0.333406i	0.0358118	+	0.0116360i	−0.291056	+	0.956706i	$0.594007\pi$
$822$	−1.55059	+	3.04321i	−0.0540832	+	0.106144i
$823$	39.5254	+	6.26021i	1.37777	+	0.218217i	0.800988	−	0.598681i	$-0.204308\pi$
$823$	39.5254	+	6.26021i	1.37777	+	0.218217i	0.576782	+	0.816898i	$0.304308\pi$
$824$	9.05995			0.315618
$825$		0			0
$826$	8.97561			0.312301
$827$	2.85794	+	0.452654i	0.0993805	+	0.0157403i	0.205927	−	0.978567i	$-0.433979\pi$
$827$	2.85794	+	0.452654i	0.0993805	+	0.0157403i	−0.106546	+	0.994308i	$0.533979\pi$
$828$	−4.03328	+	7.91575i	−0.140166	+	0.275091i
$829$	38.5306	+	12.5193i	1.33822	+	0.434815i	0.888714	−	0.458462i	$-0.151600\pi$
$829$	38.5306	+	12.5193i	1.33822	+	0.434815i	0.449507	+	0.893277i	$0.351600\pi$
$830$	1.89839	+	0.403310i	0.0658941	+	0.0139991i
$831$	−13.3945	+	18.4360i	−0.464651	+	0.639538i
$832$	−18.0130	+	9.17809i	−0.624489	+	0.318193i
$833$	35.9120	+	18.2981i	1.24428	+	0.633991i
$834$	−3.04096	−	4.18552i	−0.105300	−	0.144933i
$835$	26.0762	+	10.0066i	0.902406	+	0.346294i
$836$		0			0
$837$	−4.28992	+	4.28992i	−0.148281	+	0.148281i
$838$	−0.688562	+	4.34741i	−0.0237860	+	0.150179i
$839$	−40.0048	+	12.9983i	−1.38112	+	0.448752i	−0.903037	−	0.429564i	$-0.858667\pi$
$839$	−40.0048	+	12.9983i	−1.38112	+	0.448752i	−0.478081	+	0.878316i	$0.658667\pi$
$840$	−10.3872	+	12.8298i	−0.358392	+	0.442672i
$841$	−21.7122	−	15.7748i	−0.748697	−	0.543960i
$842$	0.795537	+	5.02282i	0.0274160	+	0.173098i
$843$	−0.908407	−	1.78285i	−0.0312872	−	0.0614046i
$844$	8.74629	+	26.9183i	0.301060	+	0.926566i
$845$	−10.1248	−	5.84415i	−0.348303	−	0.201045i
$846$		−	1.66273i		−	0.0571658i
$847$		0			0
$848$	−1.20222	−	1.20222i	−0.0412845	−	0.0412845i
$849$	−18.4289	+	13.3894i	−0.632478	+	0.459522i
$850$	−1.12615	+	2.53078i	−0.0386266	+	0.0868051i
$851$	−1.38299	+	4.25641i	−0.0474083	+	0.145908i
$852$	−16.0806	+	2.54692i	−0.550912	+	0.0872559i
$853$	−26.9403	+	4.26692i	−0.922418	+	0.146097i	−0.599541	−	0.800344i	$-0.704650\pi$
$853$	−26.9403	+	4.26692i	−0.922418	+	0.146097i	−0.322877	+	0.946441i	$0.604650\pi$
$854$	0.338585	−	1.04206i	0.0115861	−	0.0356585i
$855$	−5.17952	+	4.66463i	−0.177136	+	0.159527i
$856$	5.70883	−	4.14771i	0.195124	−	0.141766i
$857$	23.4018	+	23.4018i	0.799391	+	0.799391i	0.982999	−	0.183608i	$-0.0587778\pi$
$857$	23.4018	+	23.4018i	0.799391	+	0.799391i	−0.183608	+	0.982999i	$0.558778\pi$
$858$		0			0
$859$		−	31.9233i		−	1.08921i	−0.838693	−	0.544605i	$-0.816679\pi$
$859$		−	31.9233i		−	1.08921i	0.838693	−	0.544605i	$-0.183321\pi$
$860$	25.9715	−	6.96194i	0.885622	−	0.237400i
$861$	34.9415	+	107.539i	1.19080	+	3.66492i
$862$	2.73445	+	5.36666i	0.0931357	+	0.182789i
$863$	−4.52707	−	28.5828i	−0.154103	−	0.972969i	−0.936622	−	0.350342i	$-0.886065\pi$
$863$	−4.52707	−	28.5828i	−0.154103	−	0.972969i	0.782519	−	0.622627i	$-0.213935\pi$
$864$	−1.99600	−	1.45018i	−0.0679052	−	0.0493360i
$865$	41.0533	+	33.2373i	1.39585	+	1.13010i
$866$	−0.451092	+	0.146569i	−0.0153287	+	0.00498061i
$867$	−2.67166	+	16.8682i	−0.0907343	+	0.572874i
$868$	−31.9074	+	31.9074i	−1.08301	+	1.08301i
$869$		0			0
$870$	2.83256	+	6.36025i	0.0960326	+	0.215633i
$871$	−1.67177	−	2.30099i	−0.0566457	−	0.0779661i
$872$	−5.52845	−	2.81689i	−0.187217	−	0.0953918i
$873$	−14.5410	+	7.40899i	−0.492137	+	0.250756i
$874$	−0.235929	+	0.324728i	−0.00798042	+	0.0109841i
$875$	−49.3017	−	7.79292i	−1.66670	−	0.263449i
$876$	40.9019	+	13.2898i	1.38195	+	0.449022i
$877$	−0.899725	+	1.76581i	−0.0303816	+	0.0596272i	−0.905698	−	0.423923i	$-0.860653\pi$
$877$	−0.899725	+	1.76581i	−0.0303816	+	0.0596272i	0.875317	+	0.483550i	$0.160653\pi$
$878$	4.41360	+	0.699045i	0.148952	+	0.0235916i
$879$	62.5680			2.11037
$880$		0			0
$881$	25.3007			0.852401			0.426201	−	0.904629i	$-0.359852\pi$
$881$	25.3007			0.852401			0.426201	+	0.904629i	$0.359852\pi$
$882$	−5.66624	−	0.897444i	−0.190792	−	0.0302185i
$883$	−1.85864	+	3.64779i	−0.0625482	+	0.122758i	−0.920164	−	0.391533i	$-0.871945\pi$
$883$	−1.85864	+	3.64779i	−0.0625482	+	0.122758i	0.857616	+	0.514291i	$0.171945\pi$
$884$	−16.2670	−	5.28548i	−0.547119	−	0.177770i
$885$	49.7254	−	32.2994i	1.67150	−	1.08573i
$886$	−1.30773	+	1.79994i	−0.0439341	+	0.0604701i
$887$	−17.8564	+	9.09830i	−0.599560	+	0.305491i	−0.727303	−	0.686316i	$-0.759227\pi$
$887$	−17.8564	+	9.09830i	−0.599560	+	0.305491i	0.127744	+	0.991807i	$0.459227\pi$
$888$	3.64671	+	1.85809i	0.122376	+	0.0623534i
$889$	20.2913	+	27.9285i	0.680548	+	0.936693i
$890$	−0.367037	+	0.956460i	−0.0123031	+	0.0320606i
$891$		0			0
$892$	15.1200	−	15.1200i	0.506256	−	0.506256i
$893$	−0.732214	+	4.62302i	−0.0245026	+	0.154703i
$894$	−0.592664	+	0.192568i	−0.0198216	+	0.00644044i
$895$	−42.9546	+	4.51921i	−1.43582	+	0.151061i
$896$	−19.7394	−	14.3415i	−0.659448	−	0.479117i
$897$	1.84871	+	11.6723i	0.0617266	+	0.389726i
$898$	−0.984420	−	1.93203i	−0.0328505	−	0.0644727i
$899$	11.8569	+	36.4919i	0.395451	+	1.21707i
$900$	−2.56277	+	24.4319i	−0.0854258	+	0.814396i
$901$		−	1.39038i		−	0.0463203i
$902$		0			0
$903$	45.2107	+	45.2107i	1.50452	+	1.50452i
$904$	−5.61064	+	4.07637i	−0.186607	+	0.135578i
$905$	20.1487	+	22.3727i	0.669766	+	0.743695i
$906$	0.763778	−	2.35067i	0.0253748	−	0.0780957i
$907$	−12.3115	+	1.94994i	−0.408795	+	0.0647468i	−0.357446	−	0.933934i	$-0.616352\pi$
$907$	−12.3115	+	1.94994i	−0.408795	+	0.0647468i	−0.0513496	+	0.998681i	$0.516352\pi$
$908$	−30.1618	+	4.77716i	−1.00095	+	0.158536i
$909$	9.39553	−	28.9165i	0.311630	−	0.959099i
$910$	−0.258372	+	4.93983i	−0.00856496	+	0.163754i
$911$	−25.1173	+	18.2488i	−0.832173	+	0.604609i	−0.920173	−	0.391512i	$-0.871952\pi$
$911$	−25.1173	+	18.2488i	−0.832173	+	0.604609i	0.0880004	+	0.996120i	$0.471952\pi$
$912$	−7.89082	−	7.89082i	−0.261291	−	0.261291i
$913$		0			0
$914$		−	5.36970i		−	0.177614i
$915$	−1.87414	−	6.99149i	−0.0619572	−	0.231131i
$916$	12.5764	+	38.7061i	0.415536	+	1.27889i
$917$	−39.7259	−	77.9665i	−1.31186	−	2.57468i
$918$	−0.102396	−	0.646505i	−0.00337958	−	0.0213379i
$919$	−17.8265	−	12.9517i	−0.588041	−	0.427237i	0.253573	−	0.967316i	$-0.418394\pi$
$919$	−17.8265	−	12.9517i	−0.588041	−	0.427237i	−0.841614	+	0.540079i	$0.818394\pi$
$920$	0.298403	+	2.83629i	0.00983806	+	0.0935096i
$921$	−12.8741	+	4.18306i	−0.424217	+	0.137837i
$922$	−0.465862	+	2.94134i	−0.0153424	+	0.0968679i
$923$	−6.95491	+	6.95491i	−0.228924	+	0.228924i
$924$		0			0
$925$	0.650239	+	12.3583i	0.0213797	+	0.406338i
$926$	−2.32740	−	3.20340i	−0.0764832	−	0.105270i
$927$	28.5659	+	14.5550i	0.938226	+	0.478050i
$928$	−13.9030	+	7.08395i	−0.456389	+	0.232542i
$929$	−11.6958	+	16.0979i	−0.383727	+	0.528154i	−0.956567	−	0.291513i	$-0.905841\pi$
$929$	−11.6958	+	16.0979i	−0.383727	+	0.528154i	0.572840	+	0.819667i	$0.305841\pi$
$930$	0.994245	−	4.67994i	0.0326026	−	0.153461i
$931$	15.3591	+	4.99047i	0.503374	+	0.163556i
$932$	16.5241	−	32.4304i	0.541265	−	1.06229i
$933$	1.77545	+	0.281203i	0.0581256	+	0.00920618i
$934$	−5.74571			−0.188005
$935$		0			0
$936$	4.90816			0.160428
$937$	−11.5153	−	1.82384i	−0.376188	−	0.0595824i	−0.0345227	−	0.999404i	$-0.510991\pi$
$937$	−11.5153	−	1.82384i	−0.376188	−	0.0595824i	−0.341666	+	0.939822i	$0.610991\pi$
$938$	0.367534	−	0.721325i	0.0120004	−	0.0235521i
$939$	59.8015	+	19.4307i	1.95155	+	0.634096i
$940$	8.98587	+	13.8339i	0.293087	+	0.451212i
$941$	−0.0748640	+	0.103042i	−0.00244050	+	0.00335906i	−0.810236	−	0.586104i	$-0.800661\pi$
$941$	−0.0748640	+	0.103042i	−0.00244050	+	0.00335906i	0.807795	+	0.589464i	$0.200661\pi$
$942$	4.34110	−	2.21190i	0.141441	−	0.0720677i
$943$	17.4060	+	8.86880i	0.566817	+	0.288808i
$944$	25.3405	+	34.8782i	0.824763	+	1.13519i
$945$	10.7745	−	4.79847i	0.350496	−	0.156094i
$946$		0			0
$947$	41.6247	−	41.6247i	1.35262	−	1.35262i	0.469903	−	0.882718i	$-0.344289\pi$
$947$	41.6247	−	41.6247i	1.35262	−	1.35262i	0.882718	−	0.469903i	$-0.155711\pi$
$948$	4.34645	−	27.4424i	0.141166	−	0.891288i
$949$	24.7097	−	8.02868i	0.802112	−	0.260622i
$950$	−0.287041	+	1.07214i	−0.00931285	+	0.0347849i
$951$	−36.0236	−	26.1727i	−1.16815	−	0.848707i
$952$	−1.53543	−	9.69430i	−0.0497634	−	0.314194i
$953$	19.1607	+	37.6049i	0.620674	+	1.21814i	0.960664	+	0.277713i	$0.0895765\pi$
$953$	19.1607	+	37.6049i	0.620674	+	1.21814i	−0.339990	+	0.940429i	$0.610424\pi$
$954$	0.0611550	+	0.188216i	0.00197996	+	0.00609371i
$955$	14.9261	−	25.8590i	0.482998	−	0.836777i
$956$		−	32.6909i		−	1.05730i
$957$		0			0
$958$	−2.39731	−	2.39731i	−0.0774536	−	0.0774536i
$959$	29.6046	−	21.5090i	0.955983	−	0.694562i
$960$	−37.9628	−	1.98560i	−1.22524	−	0.0640849i
$961$	−1.43184	+	4.40675i	−0.0461884	+	0.142153i
$962$	1.21133	−	0.191856i	0.0390549	−	0.00618569i
$963$	24.6632	−	3.90627i	0.794762	−	0.125878i
$964$	8.24167	−	25.3653i	0.265446	−	0.816960i
$965$	7.21068	+	0.377147i	0.232120	+	0.0121408i
$966$	−2.72137	+	1.97719i	−0.0875585	+	0.0636150i
$967$	1.28318	+	1.28318i	0.0412643	+	0.0412643i	0.727438	−	0.686174i	$-0.240711\pi$
$967$	1.28318	+	1.28318i	0.0412643	+	0.0412643i	−0.686174	+	0.727438i	$0.740711\pi$
$968$		0			0
$969$		−	9.12579i		−	0.293163i
$970$	−1.29907	+	2.25059i	−0.0417106	+	0.0722621i
$971$	−10.8413	−	33.3660i	−0.347913	−	1.07076i	−0.960006	−	0.279979i	$-0.909672\pi$
$971$	−10.8413	−	33.3660i	−0.347913	−	1.07076i	0.612093	−	0.790785i	$-0.290328\pi$
$972$	−18.3230	−	35.9608i	−0.587709	−	1.15344i
$973$	8.67112	+	54.7473i	0.277983	+	1.75512i
$974$	−3.96620	−	2.88162i	−0.127085	−	0.0923329i
$975$	16.3449	+	28.2967i	0.523457	+	0.906221i
$976$	5.00524	−	1.62630i	0.160214	−	0.0520566i
$977$	8.11108	−	51.2113i	0.259496	−	1.63840i	−0.422016	−	0.906588i	$-0.638677\pi$
$977$	8.11108	−	51.2113i	0.259496	−	1.63840i	0.681512	−	0.731807i	$-0.261323\pi$
$978$	−2.02039	+	2.02039i	−0.0646051	+	0.0646051i
$979$		0			0
$980$	51.9931	−	23.1553i	1.66086	−	0.739669i
$981$	−12.9057	−	17.7632i	−0.412048	−	0.567135i
$982$	−5.91271	−	3.01268i	−0.188682	−	0.0961383i
$983$	0.696229	−	0.354746i	0.0222063	−	0.0113147i	−0.442852	−	0.896595i	$-0.646033\pi$
$983$	0.696229	−	0.354746i	0.0222063	−	0.0113147i	0.465058	+	0.885280i	$0.346033\pi$
$984$	10.5007	−	14.4530i	0.334751	−	0.460745i
$985$	−6.23385	−	9.59711i	−0.198627	−	0.305789i
$986$	−3.93717	−	1.27927i	−0.125385	−	0.0407401i
$987$	−17.8082	+	34.9505i	−0.566840	+	1.11249i
$988$	−6.76896	−	1.07210i	−0.215349	−	0.0341080i
$989$	11.0462			0.351250
$990$		0			0
$991$	−27.7886			−0.882735			−0.441368	−	0.897326i	$-0.645507\pi$
$991$	−27.7886			−0.882735			−0.441368	+	0.897326i	$0.645507\pi$
$992$	10.5904	+	1.67735i	0.336244	+	0.0532558i
$993$	0.0217602	−	0.0427067i	0.000690538	−	0.00135526i
$994$	−2.66260	−	0.865132i	−0.0844526	−	0.0274403i
$995$	3.37700	−	15.8956i	0.107058	−	0.503926i
$996$	−13.2450	+	18.2302i	−0.419685	+	0.577647i
$997$	42.1867	−	21.4952i	1.33606	−	0.680759i	0.367618	−	0.929977i	$-0.380174\pi$
$997$	42.1867	−	21.4952i	1.33606	−	0.680759i	0.968447	+	0.249218i	$0.0801736\pi$
$998$	−2.23581	−	1.13920i	−0.0707733	−	0.0360608i
$999$	−1.71888	−	2.36583i	−0.0543829	−	0.0748517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.f.118.6		80
5.2	odd	4	inner	605.2.m.f.602.5		80
11.2	odd	10		605.2.e.a.483.6	yes	20
11.3	even	5	inner	605.2.m.f.578.6		80
11.4	even	5	inner	605.2.m.f.403.6		80
11.5	even	5	inner	605.2.m.f.233.5		80
11.6	odd	10	inner	605.2.m.f.233.6		80
11.7	odd	10	inner	605.2.m.f.403.5		80
11.8	odd	10	inner	605.2.m.f.578.5		80
11.9	even	5		605.2.e.a.483.5	yes	20
11.10	odd	2	inner	605.2.m.f.118.5		80
55.2	even	20		605.2.e.a.362.5	✓	20
55.7	even	20	inner	605.2.m.f.282.6		80
55.17	even	20	inner	605.2.m.f.112.6		80
55.27	odd	20	inner	605.2.m.f.112.5		80
55.32	even	4	inner	605.2.m.f.602.6		80
55.37	odd	20	inner	605.2.m.f.282.5		80
55.42	odd	20		605.2.e.a.362.6	yes	20
55.47	odd	20	inner	605.2.m.f.457.6		80
55.52	even	20	inner	605.2.m.f.457.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.5	✓	20	55.2	even	20
605.2.e.a.362.6	yes	20	55.42	odd	20
605.2.e.a.483.5	yes	20	11.9	even	5
605.2.e.a.483.6	yes	20	11.2	odd	10
605.2.m.f.112.5		80	55.27	odd	20	inner
605.2.m.f.112.6		80	55.17	even	20	inner
605.2.m.f.118.5		80	11.10	odd	2	inner
605.2.m.f.118.6		80	1.1	even	1	trivial
605.2.m.f.233.5		80	11.5	even	5	inner
605.2.m.f.233.6		80	11.6	odd	10	inner
605.2.m.f.282.5		80	55.37	odd	20	inner
605.2.m.f.282.6		80	55.7	even	20	inner
605.2.m.f.403.5		80	11.7	odd	10	inner
605.2.m.f.403.6		80	11.4	even	5	inner
605.2.m.f.457.5		80	55.52	even	20	inner
605.2.m.f.457.6		80	55.47	odd	20	inner
605.2.m.f.578.5		80	11.8	odd	10	inner
605.2.m.f.578.6		80	11.3	even	5	inner
605.2.m.f.602.5		80	5.2	odd	4	inner
605.2.m.f.602.6		80	55.32	even	4	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.175554 + 0.0278050i) q^{2} +(-1.06432 + 2.08884i) q^{3} +(-1.87207 - 0.608271i) q^{4} +(-2.18725 - 0.464678i) q^{5} +(-0.244925 + 0.337111i) q^{6} +(3.97783 - 2.02681i) q^{7} +(-0.628475 - 0.320224i) q^{8} +(-1.46712 - 2.01932i) q^{9} +O(q^{10})\)	\(q+(0.175554 + 0.0278050i) q^{2} +(-1.06432 + 2.08884i) q^{3} +(-1.87207 - 0.608271i) q^{4} +(-2.18725 - 0.464678i) q^{5} +(-0.244925 + 0.337111i) q^{6} +(3.97783 - 2.02681i) q^{7} +(-0.628475 - 0.320224i) q^{8} +(-1.46712 - 2.01932i) q^{9} +(-0.371061 - 0.142393i) q^{10} +(3.26305 - 3.26305i) q^{12} +(0.436110 - 2.75349i) q^{13} +(0.754680 - 0.245211i) q^{14} +(3.29857 - 4.07425i) q^{15} +(3.08352 + 2.24031i) q^{16} +(0.487591 + 3.07853i) q^{17} +(-0.201412 - 0.395294i) q^{18} +(0.385927 + 1.18776i) q^{19} +(3.81203 + 2.20035i) q^{20} +10.4662i q^{21} +(1.27860 + 1.27860i) q^{23} +(1.33779 - 0.971964i) q^{24} +(4.56815 + 2.03274i) q^{25} +(0.153122 - 0.471260i) q^{26} +(-1.16696 + 0.184829i) q^{27} +(-8.67962 + 1.37472i) q^{28} +(-2.30912 + 7.10674i) q^{29} +(0.692362 - 0.623535i) q^{30} +(4.15416 - 3.01818i) q^{31} +(1.47655 + 1.47655i) q^{32} +0.554006i q^{34} +(-9.64234 + 2.58473i) q^{35} +(1.51826 + 4.67272i) q^{36} +(1.12366 + 2.20531i) q^{37} +(0.0347254 + 0.219247i) q^{38} +(5.28744 + 3.84155i) q^{39} +(1.22583 + 0.992450i) q^{40} +(10.2749 - 3.33850i) q^{41} +(-0.291014 + 1.83739i) q^{42} +(4.31967 - 4.31967i) q^{43} +(2.27064 + 5.09851i) q^{45} +(0.188911 + 0.260014i) q^{46} +(3.33936 + 1.70149i) q^{47} +(-7.96149 + 4.05658i) q^{48} +(7.60072 - 10.4615i) q^{49} +(0.745437 + 0.483873i) q^{50} +(-6.94950 - 2.25803i) q^{51} +(-2.49130 + 4.88944i) q^{52} +(-0.440586 - 0.0697819i) q^{53} -0.210005 q^{54} -3.14900 q^{56} +(-2.89179 - 0.458015i) q^{57} +(-0.602978 + 1.18341i) q^{58} +(10.7575 + 3.49534i) q^{59} +(-8.65339 + 5.62085i) q^{60} +(0.811610 - 1.11709i) q^{61} +(0.813201 - 0.414347i) q^{62} +(-9.92875 - 5.05895i) q^{63} +(-4.26246 - 5.86677i) q^{64} +(-2.23337 + 5.81993i) q^{65} +(0.721404 - 0.721404i) q^{67} +(0.959778 - 6.05980i) q^{68} +(-4.03161 + 1.30995i) q^{69} +(-1.76462 + 0.185654i) q^{70} +(-2.85431 - 2.07378i) q^{71} +(0.275415 + 1.73890i) q^{72} +(4.23102 + 8.30385i) q^{73} +(0.135945 + 0.418395i) q^{74} +(-9.10802 + 7.37865i) q^{75} -2.45832i q^{76} +(0.821417 + 0.821417i) q^{78} +(4.87103 - 3.53901i) q^{79} +(-5.70342 - 6.33297i) q^{80} +(3.16988 - 9.75589i) q^{81} +(1.89662 - 0.300395i) q^{82} +(-4.82298 + 0.763885i) q^{83} +(6.36630 - 19.5935i) q^{84} +(0.364040 - 6.96009i) q^{85} +(0.878445 - 0.638228i) q^{86} +(-12.3872 - 12.3872i) q^{87} -2.57764i q^{89} +(0.256855 + 0.958199i) q^{90} +(-3.84602 - 11.8368i) q^{91} +(-1.61588 - 3.17135i) q^{92} +(1.88314 + 11.8897i) q^{93} +(0.538928 + 0.391554i) q^{94} +(-0.292194 - 2.77727i) q^{95} +(-4.65581 + 1.51276i) q^{96} +(1.02281 - 6.45779i) q^{97} +(1.62522 - 1.62522i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^5	\( 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Introduction

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