LMFDB - Embedded newform 605.2.m.f.282.6

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			282.6
Character	$\chi$	$=$	605.282
Dual form			605.2.m.f.118.6

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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	−0.0940575	−	0.995567i	$-0.529984\pi$
$2$	0.175554	−	0.0278050i	0.124135	−	0.0196611i	0.218193	+	0.975906i	$0.429984\pi$
$3$	−1.06432	−	2.08884i	−0.614484	−	1.20599i	−0.963206	−	0.268766i	$-0.913384\pi$
$3$	−1.06432	−	2.08884i	−0.614484	−	1.20599i	0.348722	−	0.937226i	$-0.386616\pi$
$4$	−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	0.995451	−	0.0952786i	$-0.0303742\pi$
$7$	3.97783	+	2.02681i	1.50348	+	0.766061i	0.508029	+	0.861340i	$0.330374\pi$
$8$	−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	0.971371	+	0.237569i	$0.0763506\pi$
$13$	0.436110	+	2.75349i	0.120955	+	0.763681i	−0.850416	+	0.526112i	$0.823649\pi$
$14$	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	−0.855286	−	0.518156i	$-0.826619\pi$
$17$	0.487591	−	3.07853i	0.118258	−	0.746653i	0.973545	−	0.228497i	$-0.0733812\pi$
$18$	−0.201412	+	0.395294i	−0.0474733	+	0.0931716i
$19$	0.385927	−	1.18776i	0.0885378	−	0.272491i	−0.896978	−	0.442075i	$-0.854242\pi$
$19$	0.385927	−	1.18776i	0.0885378	−	0.272491i	0.985516	+	0.169584i	$0.0542424\pi$
$20$	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	−0.561125	−	0.827731i	$-0.689631\pi$
$23$	1.27860	−	1.27860i	0.266606	−	0.266606i	0.827731	+	0.561125i	$0.189631\pi$
$24$	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	−0.899316	−	0.437300i	$-0.855935\pi$
$29$	−2.30912	−	7.10674i	−0.428793	−	1.31969i	0.470523	−	0.882388i	$-0.344065\pi$
$30$	0.692362	+	0.623535i	0.126407	+	0.113841i
$31$	4.15416	+	3.01818i	0.746110	+	0.542081i	0.894619	−	0.446831i	$-0.147447\pi$
$31$	4.15416	+	3.01818i	0.746110	+	0.542081i	−0.148509	+	0.988911i	$0.547447\pi$
$32$	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	−0.780007	−	0.625771i	$-0.784785\pi$
$37$	1.12366	−	2.20531i	0.184729	−	0.362551i	0.964736	+	0.263220i	$0.0847845\pi$
$38$	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	0.968255	−	0.249965i	$-0.0804193\pi$
$41$	10.2749	+	3.33850i	1.60466	+	0.521387i	0.636409	+	0.771352i	$0.280419\pi$
$42$	−0.291014	−	1.83739i	−0.0449044	−	0.283515i
$43$	4.31967	+	4.31967i	0.658744	+	0.658744i	0.955083	−	0.296339i	$-0.0957657\pi$
$43$	4.31967	+	4.31967i	0.658744	+	0.658744i	−0.296339	+	0.955083i	$0.595766\pi$
$44$		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	−0.193154	−	0.981169i	$-0.561872\pi$
$47$	3.33936	−	1.70149i	0.487096	−	0.248188i	0.680249	+	0.732981i	$0.261872\pi$
$48$	−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	−0.186621	−	0.982432i	$-0.559753\pi$
$53$	−0.440586	+	0.0697819i	−0.0605191	+	0.00958528i	0.126101	+	0.992017i	$0.459753\pi$
$54$	−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	0.491157	−	0.871071i	$-0.336574\pi$
$59$	10.7575	−	3.49534i	1.40051	−	0.455054i	0.909357	+	0.416017i	$0.136574\pi$
$60$	−8.65339	−	5.62085i	−1.11715	−	0.725649i
$61$	0.811610	+	1.11709i	0.103916	+	0.143028i	0.857808	−	0.513970i	$-0.171826\pi$
$61$	0.811610	+	1.11709i	0.103916	+	0.143028i	−0.753892	+	0.656998i	$0.771826\pi$
$62$	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	0.749799	−	0.661666i	$-0.230150\pi$
$67$	0.721404	+	0.721404i	0.0881335	+	0.0881335i	−0.661666	+	0.749799i	$0.730150\pi$
$68$	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	−0.744132	−	0.668033i	$-0.767137\pi$
$71$	−2.85431	+	2.07378i	−0.338744	+	0.246112i	0.405388	+	0.914145i	$0.367137\pi$
$72$	0.275415	−	1.73890i	0.0324580	−	0.204932i
$73$	4.23102	−	8.30385i	0.495204	−	0.971892i	−0.499224	−	0.866473i	$-0.666382\pi$
$73$	4.23102	−	8.30385i	0.495204	−	0.971892i	0.994428	−	0.105419i	$-0.0336184\pi$
$74$	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	0.827060	−	0.562114i	$-0.190012\pi$
$79$	4.87103	+	3.53901i	0.548034	+	0.398170i	−0.279026	+	0.960284i	$0.590012\pi$
$80$	−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	−0.113983	−	0.993483i	$-0.536361\pi$
$83$	−4.82298	−	0.763885i	−0.529391	−	0.0838472i	−0.415407	+	0.909635i	$0.636361\pi$
$84$	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	$0.0436222\pi$
$89$			2.57764i			0.273229i	−0.990624	+	0.136615i	$0.956378\pi$
$90$	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	0.983615	+	0.180279i	$0.0577002\pi$
$97$	1.02281	+	6.45779i	0.103851	+	0.655689i	−0.879764	+	0.475410i	$0.842300\pi$
$98$	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	−0.287300	−	0.957841i	$-0.592758\pi$
$101$	7.15995	−	9.85482i	0.712441	−	0.980591i	0.999741	−	0.0227507i	$-0.00724240\pi$
$102$	−1.15723	+	0.589638i	−0.114583	+	0.0583828i
$103$	−11.4446	−	5.83130i	−1.12767	−	0.574575i	−0.212303	−	0.977204i	$-0.568096\pi$
$103$	−11.4446	−	5.83130i	−1.12767	−	0.574575i	−0.915363	+	0.402629i	$0.868096\pi$
$104$	−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	−0.999439	−	0.0334850i	$-0.989339\pi$
$107$	−4.54181	−	8.91381i	−0.439074	−	0.861730i	0.560366	−	0.828245i	$-0.310661\pi$
$108$	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	0.999955	+	0.00953315i	$0.00303454\pi$
$113$	4.46369	+	8.76048i	0.419908	+	0.824117i	−0.580046	+	0.814584i	$0.696965\pi$
$114$	−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	−0.874073	−	0.485794i	$-0.838530\pi$
$127$	1.20964	−	7.63739i	0.107338	−	0.677709i	0.981412	−	0.191914i	$-0.0614696\pi$
$128$	−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	$0.327206\pi$
$131$			19.6002i			1.71248i	−0.516578	+	0.856240i	$0.672794\pi$
$132$		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	0.492364	−	0.870389i	$-0.336133\pi$
$137$	8.09573	+	1.28224i	0.691665	+	0.109549i	0.199301	+	0.979938i	$0.436133\pi$
$138$	−0.744189	−	0.117868i	−0.0633496	−	0.0100336i
$139$	−3.83671	−	11.8082i	−0.325426	−	1.00156i	−0.971248	−	0.238070i	$-0.923485\pi$
$139$	−3.83671	−	11.8082i	−0.325426	−	1.00156i	0.645822	−	0.763488i	$-0.276515\pi$
$140$	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	−0.537122	−	0.843504i	$-0.680489\pi$
$149$	1.20989	−	0.879034i	0.0991177	−	0.0720133i	0.636240	+	0.771491i	$0.280489\pi$
$150$	−1.80411	−	1.04210i	−0.147305	−	0.0850874i
$151$	−5.64126	−	1.83296i	−0.459079	−	0.149164i	0.0703422	−	0.997523i	$-0.477591\pi$
$151$	−5.64126	−	1.83296i	−0.459079	−	0.149164i	−0.529421	+	0.848359i	$0.677591\pi$
$152$	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	−0.817270	−	0.576256i	$-0.804513\pi$
$157$	−10.4180	+	5.30824i	−0.831448	+	0.423644i	−0.0141784	+	0.999899i	$0.504513\pi$
$158$	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	0.114547	−	0.993418i	$-0.463458\pi$
$163$	6.77261	−	1.07268i	0.530472	−	0.0840184i	0.415924	+	0.909399i	$0.363458\pi$
$164$	−21.2659			−1.66059
$165$		0			0
$166$	−0.867933			−0.0673647
$167$	−12.3370	+	1.95399i	−0.954669	+	0.151205i	−0.614287	−	0.789083i	$-0.710556\pi$
$167$	−12.3370	+	1.95399i	−0.954669	+	0.151205i	−0.340382	+	0.940287i	$0.610556\pi$
$168$	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	−0.600350	+	0.799738i	$0.704972\pi$
$173$	−21.0477	+	10.7243i	−1.60023	+	0.815357i	−0.999878	+	0.0156192i	$0.995028\pi$
$174$	−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	0.900388	−	0.435088i	$-0.143283\pi$
$179$	18.3705	+	5.96895i	1.37308	+	0.446140i	0.472690	+	0.881229i	$0.343283\pi$
$180$	−1.14950	+	10.9259i	−0.0856790	+	0.814369i
$181$	−10.8933	+	7.91444i	−0.809692	+	0.588275i	−0.913741	−	0.406297i	$-0.866820\pi$
$181$	−10.8933	+	7.91444i	−0.809692	+	0.588275i	0.104050	+	0.994572i	$0.466820\pi$
$182$	−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	−0.982001	−	0.188873i	$-0.939516\pi$
$191$	−4.12622	−	12.6992i	−0.298562	−	0.918881i	0.683439	−	0.730008i	$-0.260484\pi$
$192$	16.7914	+	2.65949i	1.21181	+	0.191932i
$193$	−3.18937	−	0.505146i	−0.229576	−	0.0363612i	0.0405866	−	0.999176i	$-0.487077\pi$
$193$	−3.18937	−	0.505146i	−0.229576	−	0.0363612i	−0.270162	+	0.962815i	$0.587077\pi$
$194$	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	−0.566337	−	0.824174i	$-0.691640\pi$
$197$	3.61891	−	3.61891i	0.257837	−	0.257837i	0.824174	+	0.566337i	$0.191640\pi$
$198$		0			0
$199$		−	7.26740i		−	0.515173i	−0.966255	−	0.257586i	$-0.917073\pi$
$199$		−	7.26740i		−	0.515173i	0.966255	−	0.257586i	$-0.0829272\pi$
$200$	−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	−0.993896	−	0.110324i	$-0.964811\pi$
$211$	−8.45172	+	11.6328i	−0.581840	+	0.800835i	0.412055	+	0.911159i	$0.364811\pi$
$212$	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	0.664853	−	0.746974i	$-0.268494\pi$
$223$	−4.93173	−	9.67906i	−0.330253	−	0.648158i	−0.995106	+	0.0988167i	$0.968494\pi$
$224$	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	0.847931	−	0.530107i	$-0.177848\pi$
$227$	13.8230	+	7.04318i	0.917467	+	0.467473i	0.0695357	+	0.997579i	$0.477848\pi$
$228$	5.13503	−	2.61643i	0.340076	−	0.173277i
$229$	−12.1528	+	16.7269i	−0.803081	+	1.10535i	0.189273	+	0.981924i	$0.439387\pi$
$229$	−12.1528	+	16.7269i	−0.803081	+	1.10535i	−0.992354	+	0.123422i	$0.960613\pi$
$230$	−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	−0.880657	−	0.473755i	$-0.842898\pi$
$233$	−2.89260	−	18.2632i	−0.189501	−	1.19646i	0.691156	−	0.722705i	$-0.257102\pi$
$234$	−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	−0.636229	−	0.771500i	$-0.719507\pi$
$239$	5.13209	−	15.7950i	0.331967	−	1.02169i	0.968197	−	0.250190i	$-0.0804932\pi$
$240$	19.2988	+	5.17324i	1.24573	+	0.333931i
$241$		−	13.5493i		−	0.872789i	−0.899755	−	0.436395i	$-0.856255\pi$
$241$		−	13.5493i		−	0.872789i	0.899755	−	0.436395i	$-0.143745\pi$
$242$		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	0.743206	−	0.669062i	$-0.233304\pi$
$251$	5.33201	+	3.87393i	0.336554	+	0.244521i	−0.406653	+	0.913583i	$0.633304\pi$
$252$	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	0.550541	+	0.834808i	$0.314422\pi$
$257$	−7.18893	+	14.1091i	−0.448433	+	0.880099i	−0.998974	+	0.0452910i	$0.985578\pi$
$258$	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	−0.931541	−	0.363637i	$-0.881535\pi$
$263$	−21.0043	−	21.0043i	−1.29518	−	1.29518i	−0.363637	−	0.931541i	$-0.618465\pi$
$264$		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	0.725027	−	0.688721i	$-0.241827\pi$
$269$	−2.52630	−	3.47716i	−0.154031	−	0.212006i	−0.879058	+	0.476715i	$0.841827\pi$
$270$	0.459333	−	0.0975845i	0.0279541	−	0.00593881i
$271$	19.8046	−	6.43490i	1.20304	−	0.390892i	0.362163	−	0.932115i	$-0.382038\pi$
$271$	19.8046	−	6.43490i	1.20304	−	0.390892i	0.840879	+	0.541222i	$0.182038\pi$
$272$	−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	0.138811	−	0.990319i	$-0.455672\pi$
$277$	9.60074	−	1.52061i	0.576853	−	0.0913645i	0.438042	+	0.898954i	$0.355672\pi$
$278$	−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	0.793791	−	0.608191i	$-0.208104\pi$
$281$	−0.501682	−	0.690506i	−0.0299278	−	0.0411921i	−0.823719	+	0.566999i	$0.808104\pi$
$282$	−1.39148	−	0.708997i	−0.0828617	−	0.0422201i
$283$	8.65761	−	4.41127i	0.514642	−	0.262223i	−0.177325	−	0.984152i	$-0.556744\pi$
$283$	8.65761	−	4.41127i	0.514642	−	0.262223i	0.691967	+	0.721929i	$0.256744\pi$
$284$	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	0.204107	+	0.978949i	$0.434571\pi$
$293$	−12.1164	+	23.7799i	−0.707850	+	1.38923i	−0.911957	+	0.410286i	$0.865429\pi$
$294$	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	−0.580929	−	0.813954i	$-0.697311\pi$
$307$	4.08294	−	4.08294i	0.233026	−	0.233026i	0.813954	+	0.580929i	$0.197311\pi$
$308$		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	−0.957550	−	0.288268i	$-0.906921\pi$
$311$	−0.236944	+	0.729239i	−0.0134359	+	0.0413514i	0.944114	+	0.329620i	$0.106921\pi$
$312$	−2.09287	+	4.10748i	−0.118485	+	0.232540i
$313$	−4.19579	+	26.4912i	−0.237160	+	1.49737i	0.525624	+	0.850717i	$0.323832\pi$
$313$	−4.19579	+	26.4912i	−0.237160	+	1.49737i	−0.762784	+	0.646653i	$0.776168\pi$
$314$	−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	−0.918895	−	0.394501i	$-0.870917\pi$
$317$	−2.97124	−	18.7597i	−0.166881	−	1.05365i	0.752014	−	0.659147i	$-0.229083\pi$
$318$	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	0.793384	−	0.608722i	$-0.208317\pi$
$337$	14.0850	+	7.17665i	0.767257	+	0.390937i	−0.0261269	+	0.999659i	$0.508317\pi$
$338$	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	−0.707259	−	0.706955i	$-0.750068\pi$
$347$	3.42466	−	21.6225i	0.183845	−	1.16075i	0.891104	−	0.453799i	$-0.149932\pi$
$348$	15.6549	−	30.7244i	0.839190	−	1.64700i
$349$	−8.64803	+	26.6159i	−0.462919	+	1.42472i	0.398663	+	0.917098i	$0.369474\pi$
$349$	−8.64803	+	26.6159i	−0.462919	+	1.42472i	−0.861581	+	0.507620i	$0.830526\pi$
$350$	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	−0.911030	−	0.412340i	$-0.864711\pi$
$353$	−9.36952	+	9.36952i	−0.498689	+	0.498689i	0.412340	+	0.911030i	$0.364711\pi$
$354$	−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	0.936253	−	0.351326i	$-0.114269\pi$
$359$	−0.524759	−	1.61504i	−0.0276957	−	0.0852386i	−0.963949	+	0.266087i	$0.914269\pi$
$360$	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	0.484804	+	0.874623i	$0.338891\pi$
$367$	−9.72692	+	19.0902i	−0.507741	+	0.996498i	−0.992545	+	0.121875i	$0.961109\pi$
$368$	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	0.525154	−	0.851007i	$-0.324008\pi$
$373$	−6.29327	−	6.29327i	−0.325853	−	0.325853i	−0.851007	+	0.525154i	$0.824008\pi$
$374$		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	0.938732	+	0.344648i	$0.112002\pi$
$379$	19.0090	+	26.1637i	0.976427	+	1.34394i	0.0376952	+	0.999289i	$0.487998\pi$
$380$	−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	−0.707789	−	0.706424i	$-0.750307\pi$
$383$	−22.7533	+	3.60377i	−1.16264	+	0.184144i	−0.454851	+	0.890568i	$0.650307\pi$
$384$	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	0.0582550	−	0.998302i	$-0.481446\pi$
$389$	13.6518	−	4.43572i	0.692171	−	0.224900i	0.633916	+	0.773402i	$0.281446\pi$
$390$	−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	0.475321	−	0.879812i	$-0.342332\pi$
$397$	−8.05942	−	8.05942i	−0.404491	−	0.404491i	−0.879812	+	0.475321i	$0.842332\pi$
$398$	−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	−0.0370655	−	0.999313i	$-0.511801\pi$
$401$	18.0602	−	13.1215i	0.901884	−	0.655257i	0.938949	+	0.344056i	$0.111801\pi$
$402$	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	0.529980	−	0.848010i	$-0.322200\pi$
$409$	−2.28030	−	1.65673i	−0.112753	−	0.0819202i	−0.642733	+	0.766090i	$0.722200\pi$
$410$	−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	$-0.793214\pi$
$419$		−	24.7639i		−	1.20980i	0.796303	−	0.604898i	$-0.206786\pi$
$420$	−23.0294	−	39.8976i	−1.12372	−	1.94680i
$421$	8.84136	−	27.2109i	0.430902	−	1.32618i	−0.466327	−	0.884612i	$-0.654423\pi$
$421$	8.84136	−	27.2109i	0.430902	−	1.32618i	0.897229	−	0.441566i	$-0.145577\pi$
$422$	−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	0.0122178	−	0.999925i	$-0.496111\pi$
$431$	19.9182	−	27.4151i	0.959428	−	1.32054i	0.947210	−	0.320614i	$-0.103889\pi$
$432$	−4.01244	+	2.04444i	−0.193048	+	0.0983631i
$433$	−2.37765	−	1.21148i	−0.114263	−	0.0582198i	0.395925	−	0.918283i	$-0.370424\pi$
$433$	−2.37765	−	1.21148i	−0.114263	−	0.0582198i	−0.510188	+	0.860063i	$0.670424\pi$
$434$	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	0.715706	−	0.698401i	$-0.246105\pi$
$443$	−5.68271	−	11.1530i	−0.269994	−	0.529893i	−0.985700	+	0.168509i	$0.946105\pi$
$444$	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	−0.943975	−	0.330017i	$-0.892946\pi$
$449$	−7.17069	+	9.86961i	−0.338406	+	0.465776i	0.605569	+	0.795793i	$0.292946\pi$
$450$	−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	0.588370	+	0.808592i	$0.299770\pi$
$457$	−4.72598	+	29.8386i	−0.221072	+	1.39579i	−0.809441	+	0.587201i	$0.800230\pi$
$458$	−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	$-0.872416\pi$
$461$		−	16.7546i		−	0.780340i	0.920743	−	0.390170i	$-0.127584\pi$
$462$		0			0
$463$	−15.7524	+	15.7524i	−0.732077	+	0.732077i	−0.971031	−	0.238954i	$-0.923195\pi$
$463$	−15.7524	+	15.7524i	−0.732077	+	0.732077i	0.238954	+	0.971031i	$0.423195\pi$
$464$	−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	−0.634891	−	0.772602i	$-0.718955\pi$
$467$	−31.9281	−	5.05691i	−1.47745	−	0.234006i	−0.842564	+	0.538596i	$0.818955\pi$
$468$	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	−0.881583	−	0.472030i	$-0.843521\pi$
$479$	−15.4314	+	11.2116i	−0.705079	+	0.512270i	0.176503	+	0.984300i	$0.443521\pi$
$480$	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	−0.911239	−	0.411879i	$-0.864873\pi$
$487$	−24.5758	+	12.5220i	−1.11363	+	0.567425i	−0.202396	+	0.979304i	$0.564873\pi$
$488$	−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	−0.967708	−	0.252075i	$-0.918887\pi$
$491$	−35.5076	+	11.5371i	−1.60243	+	0.520662i	−0.634726	+	0.772737i	$0.718887\pi$
$492$	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	−0.593714	−	0.804676i	$-0.702339\pi$
$499$	−13.4267	+	4.36259i	−0.601061	+	0.195297i	−0.00734745	+	0.999973i	$0.502339\pi$
$500$	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	−0.684512	−	0.729001i	$-0.739985\pi$
$503$	−11.1484	+	5.68041i	−0.497084	+	0.253277i	0.187428	+	0.982278i	$0.439985\pi$
$504$	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	0.263844	−	0.964565i	$-0.415009\pi$
$509$	−2.02279	−	0.657243i	−0.0896585	−	0.0291318i	−0.353503	+	0.935433i	$0.615009\pi$
$510$	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	0.965901	+	0.258910i	$0.0833633\pi$
$521$	7.68427	+	23.6498i	0.336654	+	1.03612i	−0.629247	+	0.777205i	$0.716637\pi$
$522$	3.27433	+	0.518603i	0.143314	+	0.0226987i
$523$	−19.0167	−	3.01195i	−0.831541	−	0.131703i	−0.273872	−	0.961766i	$-0.588304\pi$
$523$	−19.0167	−	3.01195i	−0.831541	−	0.131703i	−0.557670	+	0.830063i	$0.688304\pi$
$524$	−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	−0.140492	−	0.990082i	$-0.544868\pi$
$541$	19.6436	−	27.0372i	0.844546	−	1.16242i	0.985038	−	0.172337i	$-0.0551317\pi$
$542$	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	−0.980686	−	0.195586i	$-0.937339\pi$
$547$	−13.1554	−	25.8190i	−0.562486	−	1.10394i	0.418200	−	0.908355i	$-0.362661\pi$
$548$	−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	0.778566	−	0.627562i	$-0.215947\pi$
$557$	17.1929	+	8.76023i	0.728487	+	0.371183i	−0.0500790	+	0.998745i	$0.515947\pi$
$558$	−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	0.990961	−	0.134152i	$-0.0428310\pi$
$563$	0.167182	+	1.05554i	0.00704587	+	0.0444859i	−0.983915	+	0.178638i	$0.942831\pi$
$564$	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	−0.886860	−	0.462039i	$-0.847118\pi$
$569$	2.43796	−	7.50327i	0.102205	−	0.314553i	0.989064	+	0.147486i	$0.0471180\pi$
$570$	1.00781	−	0.581722i	0.0422126	−	0.0243657i
$571$			12.2418i			0.512302i	0.966637	+	0.256151i	$0.0824544\pi$
$571$			12.2418i			0.512302i	−0.966637	+	0.256151i	$0.917546\pi$
$572$		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	−0.916670	−	0.399644i	$-0.869134\pi$
$577$	−45.9272	−	7.27415i	−1.91197	−	0.302827i	−0.995302	+	0.0968174i	$0.969134\pi$
$578$	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	−0.834189	−	0.551479i	$-0.814064\pi$
$587$	2.47831	−	4.86395i	0.102291	−	0.200757i	0.936480	+	0.350722i	$0.114064\pi$
$588$	−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	0.982376	+	0.186913i	$0.0598483\pi$
$593$	28.4741	+	28.4741i	1.16929	+	1.16929i	0.186913	+	0.982376i	$0.440152\pi$
$594$		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	0.884243	−	0.467027i	$-0.154675\pi$
$599$	4.08303	+	5.61980i	0.166828	+	0.229619i	−0.717415	+	0.696646i	$0.754675\pi$
$600$	8.08699	+	1.72069i	0.330150	+	0.0702470i
$601$	23.1053	−	7.50735i	0.942483	−	0.306231i	0.202826	−	0.979215i	$-0.434988\pi$
$601$	23.1053	−	7.50735i	0.942483	−	0.306231i	0.739657	+	0.672984i	$0.234988\pi$
$602$	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	−0.0752535	−	0.997164i	$-0.523977\pi$
$607$	3.97442	−	0.629487i	0.161317	−	0.0255501i	0.236570	+	0.971614i	$0.423977\pi$
$608$	−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	0.663431	−	0.748238i	$-0.269100\pi$
$613$	41.0680	−	20.9252i	1.65872	−	0.845161i	0.995292	−	0.0969234i	$-0.0309002\pi$
$614$	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	0.833021	−	0.553242i	$-0.186610\pi$
$617$	6.94955	+	6.94955i	0.279778	+	0.279778i	−0.553242	+	0.833021i	$0.686610\pi$
$618$	0.837271	+	5.28632i	0.0336800	+	0.212647i
$619$	−19.8128	−	6.43756i	−0.796343	−	0.258747i	−0.117540	−	0.993068i	$-0.537501\pi$
$619$	−19.8128	−	6.43756i	−0.796343	−	0.258747i	−0.678803	+	0.734321i	$0.737501\pi$
$620$	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	−0.944910	−	0.327332i	$-0.893851\pi$
$631$	−9.36619	−	28.8262i	−0.372862	−	1.14755i	0.572047	−	0.820221i	$-0.306149\pi$
$632$	−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	0.501480	+	0.865169i	$0.332789\pi$
$641$	−10.4502	+	32.1625i	−0.412759	+	1.27034i	−0.914240	+	0.405174i	$0.867211\pi$
$642$	−1.89254	+	3.71431i	−0.0746925	+	0.146592i
$643$	1.97627	−	12.4777i	0.0779364	−	0.492071i	−0.917585	−	0.397539i	$-0.869864\pi$
$643$	1.97627	−	12.4777i	0.0779364	−	0.492071i	0.995522	−	0.0945322i	$-0.0301355\pi$
$644$	−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	−0.999669	−	0.0257267i	$-0.991810\pi$
$647$	−1.44674	−	9.13437i	−0.0568773	−	0.359109i	0.942792	−	0.333382i	$-0.108190\pi$
$648$	−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	0.379656	−	0.925128i	$-0.376042\pi$
$653$	−3.72144	−	1.89617i	−0.145631	−	0.0742027i	−0.525287	+	0.850925i	$0.676042\pi$
$654$	−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	0.960796	−	0.277258i	$-0.0894255\pi$
$673$	−1.00274	−	6.33102i	−0.0386526	−	0.244043i	−0.999448	+	0.0332145i	$0.989426\pi$
$674$	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	0.753755	+	0.657155i	$0.228240\pi$
$677$	−4.32390	+	27.3000i	−0.166181	+	1.04922i	−0.919936	+	0.392069i	$0.871760\pi$
$678$	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	−0.802814	−	0.596230i	$-0.796665\pi$
$683$	−5.39890	+	5.39890i	−0.206583	+	0.206583i	0.596230	+	0.802814i	$0.296665\pi$
$684$	−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	0.905328	−	0.424714i	$-0.139625\pi$
$691$	20.5343	+	14.9191i	0.781162	+	0.567548i	−0.124165	+	0.992262i	$0.539625\pi$
$692$	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	−0.307084	−	0.951682i	$-0.599353\pi$
$701$	−29.5187	−	9.59120i	−1.11491	−	0.362255i	−0.807821	+	0.589428i	$0.799353\pi$
$702$	−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	−0.836975	−	0.547241i	$-0.815678\pi$
$709$	−29.2576	−	40.2696i	−1.09879	−	1.51236i	−0.261817	−	0.965117i	$-0.584322\pi$
$710$	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	−0.873502	−	0.486820i	$-0.838157\pi$
$719$	−34.6985	+	11.2742i	−1.29403	+	0.420457i	−0.420532	+	0.907278i	$0.638157\pi$
$720$	−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	0.305050	−	0.952336i	$-0.401327\pi$
$727$	−17.4528	−	17.4528i	−0.647287	−	0.647287i	−0.952336	+	0.305050i	$0.901327\pi$
$728$	−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	−0.799572	−	0.600570i	$-0.794940\pi$
$733$	4.23102	−	8.30385i	0.156276	−	0.306710i	0.955848	+	0.293861i	$0.0949402\pi$
$734$	−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	−0.101590	−	0.994826i	$-0.532393\pi$
$739$	−29.3354	−	21.3134i	−1.07912	−	0.784026i	−0.977529	+	0.210800i	$0.932393\pi$
$740$	−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	0.859872	−	0.510510i	$-0.170543\pi$
$743$	41.4295	+	6.56179i	1.51990	+	0.240729i	0.660030	+	0.751239i	$0.270543\pi$
$744$	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	0.794008	+	0.607907i	$0.207991\pi$
$751$	−5.63645	+	17.3472i	−0.205677	+	0.633008i	−0.999685	+	0.0251010i	$0.992009\pi$
$752$	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	−0.978044	−	0.208400i	$-0.933174\pi$
$757$	−3.08890	−	19.5025i	−0.112268	−	0.708832i	0.865776	−	0.500432i	$-0.166826\pi$
$758$	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	0.0141864	+	0.999899i	$0.495484\pi$
$761$	−25.9630	+	35.7350i	−0.941158	+	1.29539i	−0.955345	+	0.295494i	$0.904516\pi$
$762$	−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	0.997441	+	0.0714986i	$0.0227781\pi$
$773$	13.0396	+	25.5917i	0.469003	+	0.920471i	−0.528437	+	0.848972i	$0.677222\pi$
$774$	−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	−0.518312	−	0.855192i	$-0.673439\pi$
$787$	6.70201	−	42.3148i	0.238901	−	1.50836i	0.757213	−	0.653168i	$-0.226561\pi$
$788$	−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	0.295983	−	0.955193i	$-0.404353\pi$
$797$	7.96988	+	1.26231i	0.282308	+	0.0447132i	−0.0136748	+	0.999906i	$0.504353\pi$
$798$	−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	−0.156948	−	0.987607i	$-0.550166\pi$
$809$	20.8720	−	15.1644i	0.733822	−	0.533153i	0.890770	+	0.454454i	$0.150166\pi$
$810$	−2.56539	−	3.16866i	−0.0901385	−	0.111335i
$811$	5.06847	+	1.64685i	0.177978	+	0.0578286i	0.396650	−	0.917970i	$-0.370173\pi$
$811$	5.06847	+	1.64685i	0.177978	+	0.0578286i	−0.218672	+	0.975798i	$0.570173\pi$
$812$	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	−0.291056	−	0.956706i	$-0.594007\pi$
$821$	1.02612	−	0.333406i	0.0358118	−	0.0116360i	0.326868	+	0.945070i	$0.394007\pi$
$822$	−1.55059	−	3.04321i	−0.0540832	−	0.106144i
$823$	39.5254	−	6.26021i	1.37777	−	0.218217i	0.576782	−	0.816898i	$-0.304308\pi$
$823$	39.5254	−	6.26021i	1.37777	−	0.218217i	0.800988	+	0.598681i	$0.204308\pi$
$824$	9.05995			0.315618
$825$		0			0
$826$	8.97561			0.312301
$827$	2.85794	−	0.452654i	0.0993805	−	0.0157403i	−0.106546	−	0.994308i	$-0.533979\pi$
$827$	2.85794	−	0.452654i	0.0993805	−	0.0157403i	0.205927	+	0.978567i	$0.433979\pi$
$828$	−4.03328	−	7.91575i	−0.140166	−	0.275091i
$829$	38.5306	−	12.5193i	1.33822	−	0.434815i	0.449507	−	0.893277i	$-0.351600\pi$
$829$	38.5306	−	12.5193i	1.33822	−	0.434815i	0.888714	+	0.458462i	$0.151600\pi$
$830$	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	−0.478081	−	0.878316i	$-0.658667\pi$
$839$	−40.0048	−	12.9983i	−1.38112	−	0.448752i	−0.903037	+	0.429564i	$0.858667\pi$
$840$	−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	−0.322877	−	0.946441i	$-0.604650\pi$
$853$	−26.9403	−	4.26692i	−0.922418	−	0.146097i	−0.599541	+	0.800344i	$0.704650\pi$
$854$	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	−0.183608	−	0.982999i	$-0.558778\pi$
$857$	23.4018	−	23.4018i	0.799391	−	0.799391i	0.982999	+	0.183608i	$0.0587778\pi$
$858$		0			0
$859$			31.9233i			1.08921i	0.838693	+	0.544605i	$0.183321\pi$
$859$			31.9233i			1.08921i	−0.838693	+	0.544605i	$0.816679\pi$
$860$	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	0.782519	+	0.622627i	$0.213935\pi$
$863$	−4.52707	+	28.5828i	−0.154103	+	0.972969i	−0.936622	+	0.350342i	$0.886065\pi$
$864$	−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	0.875317	−	0.483550i	$-0.160653\pi$
$877$	−0.899725	−	1.76581i	−0.0303816	−	0.0596272i	−0.905698	+	0.423923i	$0.860653\pi$
$878$	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	0.857616	−	0.514291i	$-0.171945\pi$
$883$	−1.85864	−	3.64779i	−0.0625482	−	0.122758i	−0.920164	+	0.391533i	$0.871945\pi$
$884$	−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	0.127744	−	0.991807i	$-0.459227\pi$
$887$	−17.8564	−	9.09830i	−0.599560	−	0.305491i	−0.727303	+	0.686316i	$0.759227\pi$
$888$	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	−0.0513496	−	0.998681i	$-0.516352\pi$
$907$	−12.3115	−	1.94994i	−0.408795	−	0.0647468i	−0.357446	+	0.933934i	$0.616352\pi$
$908$	−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	0.0880004	−	0.996120i	$-0.471952\pi$
$911$	−25.1173	−	18.2488i	−0.832173	−	0.604609i	−0.920173	+	0.391512i	$0.871952\pi$
$912$	−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	−0.841614	−	0.540079i	$-0.818394\pi$
$919$	−17.8265	+	12.9517i	−0.588041	+	0.427237i	0.253573	+	0.967316i	$0.418394\pi$
$920$	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	0.572840	−	0.819667i	$-0.305841\pi$
$929$	−11.6958	−	16.0979i	−0.383727	−	0.528154i	−0.956567	+	0.291513i	$0.905841\pi$
$930$	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	−0.341666	−	0.939822i	$-0.610991\pi$
$937$	−11.5153	+	1.82384i	−0.376188	+	0.0595824i	−0.0345227	+	0.999404i	$0.510991\pi$
$938$	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	0.807795	−	0.589464i	$-0.200661\pi$
$941$	−0.0748640	−	0.103042i	−0.00244050	−	0.00335906i	−0.810236	+	0.586104i	$0.800661\pi$
$942$	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	0.882718	+	0.469903i	$0.155711\pi$
$947$	41.6247	+	41.6247i	1.35262	+	1.35262i	0.469903	+	0.882718i	$0.344289\pi$
$948$	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	−0.339990	−	0.940429i	$-0.610424\pi$
$953$	19.1607	−	37.6049i	0.620674	−	1.21814i	0.960664	−	0.277713i	$-0.0895765\pi$
$954$	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	−0.686174	−	0.727438i	$-0.740711\pi$
$967$	1.28318	−	1.28318i	0.0412643	−	0.0412643i	0.727438	+	0.686174i	$0.240711\pi$
$968$		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	0.612093	+	0.790785i	$0.290328\pi$
$971$	−10.8413	+	33.3660i	−0.347913	+	1.07076i	−0.960006	+	0.279979i	$0.909672\pi$
$972$	−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	0.681512	+	0.731807i	$0.261323\pi$
$977$	8.11108	+	51.2113i	0.259496	+	1.63840i	−0.422016	+	0.906588i	$0.638677\pi$
$978$	−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	0.465058	−	0.885280i	$-0.346033\pi$
$983$	0.696229	+	0.354746i	0.0222063	+	0.0113147i	−0.442852	+	0.896595i	$0.646033\pi$
$984$	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	0.968447	−	0.249218i	$-0.0801736\pi$
$997$	42.1867	+	21.4952i	1.33606	+	0.680759i	0.367618	+	0.929977i	$0.380174\pi$
$998$	−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.282.6		80
5.3	odd	4	inner	605.2.m.f.403.5		80
11.2	odd	10	inner	605.2.m.f.457.6		80
11.3	even	5	inner	605.2.m.f.602.6		80
11.4	even	5	inner	605.2.m.f.112.6		80
11.5	even	5		605.2.e.a.362.5	✓	20
11.6	odd	10		605.2.e.a.362.6	yes	20
11.7	odd	10	inner	605.2.m.f.112.5		80
11.8	odd	10	inner	605.2.m.f.602.5		80
11.9	even	5	inner	605.2.m.f.457.5		80
11.10	odd	2	inner	605.2.m.f.282.5		80
55.3	odd	20	inner	605.2.m.f.118.5		80
55.8	even	20	inner	605.2.m.f.118.6		80
55.13	even	20	inner	605.2.m.f.578.6		80
55.18	even	20	inner	605.2.m.f.233.5		80
55.28	even	20		605.2.e.a.483.5	yes	20
55.38	odd	20		605.2.e.a.483.6	yes	20
55.43	even	4	inner	605.2.m.f.403.6		80
55.48	odd	20	inner	605.2.m.f.233.6		80
55.53	odd	20	inner	605.2.m.f.578.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.5	✓	20	11.5	even	5
605.2.e.a.362.6	yes	20	11.6	odd	10
605.2.e.a.483.5	yes	20	55.28	even	20
605.2.e.a.483.6	yes	20	55.38	odd	20
605.2.m.f.112.5		80	11.7	odd	10	inner
605.2.m.f.112.6		80	11.4	even	5	inner
605.2.m.f.118.5		80	55.3	odd	20	inner
605.2.m.f.118.6		80	55.8	even	20	inner
605.2.m.f.233.5		80	55.18	even	20	inner
605.2.m.f.233.6		80	55.48	odd	20	inner
605.2.m.f.282.5		80	11.10	odd	2	inner
605.2.m.f.282.6		80	1.1	even	1	trivial
605.2.m.f.403.5		80	5.3	odd	4	inner
605.2.m.f.403.6		80	55.43	even	4	inner
605.2.m.f.457.5		80	11.9	even	5	inner
605.2.m.f.457.6		80	11.2	odd	10	inner
605.2.m.f.578.5		80	55.53	odd	20	inner
605.2.m.f.578.6		80	55.13	even	20	inner
605.2.m.f.602.5		80	11.8	odd	10	inner
605.2.m.f.602.6		80	11.3	even	5	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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