LMFDB - Embedded newform 968.2.o.h.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.o (of order $10$ , degree $4$ , 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.1
Character	$\chi$	$=$	968.269
Dual form			968.2.o.h.493.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37509 - 0.330339i) q^{2} +(-1.38306 + 1.90362i) q^{3} +(1.78175 + 0.908493i) q^{4} +(3.96394 + 1.28796i) q^{5} +(2.53067 - 2.16077i) q^{6} +(0.754993 - 0.548534i) q^{7} +(-2.14996 - 1.83784i) q^{8} +(-0.783857 - 2.41246i) q^{9} +(-5.02532 - 3.08051i) q^{10} +(-4.19369 + 2.13527i) q^{12} +(-2.78966 + 0.906416i) q^{13} +(-1.21939 + 0.504881i) q^{14} +(-7.93416 + 5.76451i) q^{15} +(2.34928 + 3.23742i) q^{16} +(-0.755937 + 2.32653i) q^{17} +(0.280943 + 3.57629i) q^{18} +(-1.57693 + 2.17046i) q^{19} +(5.89266 + 5.89605i) q^{20} +2.19587i q^{21} -3.47129 q^{23} +(6.47207 - 1.55086i) q^{24} +(10.0089 + 7.27191i) q^{25} +(4.13546 - 0.324870i) q^{26} +(-1.03698 - 0.336937i) q^{27} +(1.84355 - 0.291446i) q^{28} +(2.68762 + 3.69919i) q^{29} +(12.8144 - 5.30576i) q^{30} +(-1.13033 - 3.47878i) q^{31} +(-2.16103 - 5.22781i) q^{32} +(1.80803 - 2.94948i) q^{34} +(3.69924 - 1.20196i) q^{35} +(0.795068 - 5.01054i) q^{36} +(-2.66741 - 3.67137i) q^{37} +(2.88541 - 2.46366i) q^{38} +(2.13280 - 6.56407i) q^{39} +(-6.15525 - 10.0542i) q^{40} +(3.33815 + 2.42531i) q^{41} +(0.725383 - 3.01953i) q^{42} +11.4650i q^{43} -10.5724i q^{45} +(4.77333 + 1.14670i) q^{46} +(-2.63954 - 1.91774i) q^{47} +(-9.41200 - 0.00541041i) q^{48} +(-1.89399 + 5.82912i) q^{49} +(-11.3610 - 13.3059i) q^{50} +(-3.38333 - 4.65675i) q^{51} +(-5.79396 - 0.919380i) q^{52} +(0.618312 - 0.200902i) q^{53} +(1.31464 + 0.805875i) q^{54} +(-2.63133 - 0.208231i) q^{56} +(-1.95073 - 6.00374i) q^{57} +(-2.47373 - 5.97455i) q^{58} +(1.71025 + 2.35396i) q^{59} +(-19.3737 + 3.06279i) q^{60} +(10.1820 + 3.30834i) q^{61} +(0.405122 + 5.15704i) q^{62} +(-1.91512 - 1.39142i) q^{63} +(1.24466 + 7.90258i) q^{64} -12.2255 q^{65} +5.42623i q^{67} +(-3.46053 + 3.45854i) q^{68} +(4.80099 - 6.60800i) q^{69} +(-5.48385 + 0.430795i) q^{70} +(-2.39528 + 7.37192i) q^{71} +(-2.74847 + 6.62730i) q^{72} +(10.5698 - 7.67944i) q^{73} +(2.45513 + 5.92962i) q^{74} +(-27.6859 + 8.99568i) q^{75} +(-4.78154 + 2.43459i) q^{76} +(-5.10116 + 8.32165i) q^{78} +(-1.49461 - 4.59993i) q^{79} +(5.14274 + 15.8587i) q^{80} +(8.23210 - 5.98097i) q^{81} +(-3.78909 - 4.43775i) q^{82} +(0.627378 + 0.203847i) q^{83} +(-1.99494 + 3.91250i) q^{84} +(-5.99298 + 8.24863i) q^{85} +(3.78733 - 15.7654i) q^{86} -10.7590 q^{87} -2.74629 q^{89} +(-3.49249 + 14.5381i) q^{90} +(-1.60897 + 2.21456i) q^{91} +(-6.18497 - 3.15364i) q^{92} +(8.18558 + 2.65966i) q^{93} +(2.99610 + 3.50901i) q^{94} +(-9.04633 + 6.57255i) q^{95} +(12.9406 + 3.11659i) q^{96} +(0.565208 + 1.73953i) q^{97} +(4.53000 - 7.38991i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100})$ 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$ .

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.37509	−	0.330339i	−0.972336	−	0.233585i
$2$	−1.37509	−	0.330339i	−0.972336	−	0.233585i
$3$	−1.38306	+	1.90362i	−0.798510	+	1.09905i	0.194486	+	0.980905i	$0.437696\pi$
$3$	−1.38306	+	1.90362i	−0.798510	+	1.09905i	−0.992996	+	0.118149i	$0.962304\pi$
$4$	1.78175	+	0.908493i	0.890876	+	0.454247i
$5$	3.96394	+	1.28796i	1.77273	+	0.575995i	0.998387	−	0.0567713i	$-0.0180806\pi$
$5$	3.96394	+	1.28796i	1.77273	+	0.575995i	0.774343	+	0.632766i	$0.218081\pi$
$6$	2.53067	−	2.16077i	1.03314	−	0.882130i
$7$	0.754993	−	0.548534i	0.285360	−	0.207327i	−0.435892	−	0.899999i	$-0.643567\pi$
$7$	0.754993	−	0.548534i	0.285360	−	0.207327i	0.721252	+	0.692673i	$0.243567\pi$
$8$	−2.14996	−	1.83784i	−0.760126	−	0.649776i
$9$	−0.783857	−	2.41246i	−0.261286	−	0.804154i
$10$	−5.02532	−	3.08051i	−1.58915	−	0.974144i
$11$		0			0
$11$		0			0
$12$	−4.19369	+	2.13527i	−1.21061	+	0.616401i
$13$	−2.78966	+	0.906416i	−0.773713	+	0.251394i	−0.669153	−	0.743124i	$-0.733343\pi$
$13$	−2.78966	+	0.906416i	−0.773713	+	0.251394i	−0.104559	+	0.994519i	$0.533343\pi$
$14$	−1.21939	+	0.504881i	−0.325895	+	0.134935i
$15$	−7.93416	+	5.76451i	−2.04859	+	1.48839i
$16$	2.34928	+	3.23742i	0.587320	+	0.809355i
$17$	−0.755937	+	2.32653i	−0.183342	+	0.564267i	−0.999916	−	0.0129730i	$-0.995870\pi$
$17$	−0.755937	+	2.32653i	−0.183342	+	0.564267i	0.816574	+	0.577240i	$0.195870\pi$
$18$	0.280943	+	3.57629i	0.0662190	+	0.842941i
$19$	−1.57693	+	2.17046i	−0.361772	+	0.497937i	−0.950641	−	0.310291i	$-0.899573\pi$
$19$	−1.57693	+	2.17046i	−0.361772	+	0.497937i	0.588869	+	0.808228i	$0.299573\pi$
$20$	5.89266	+	5.89605i	1.31764	+	1.31840i
$21$			2.19587i			0.479179i
$22$		0			0
$23$	−3.47129			−0.723813			−0.361907	−	0.932214i	$-0.617874\pi$
$23$	−3.47129			−0.723813			−0.361907	+	0.932214i	$0.617874\pi$
$24$	6.47207	−	1.55086i	1.32111	−	0.316567i
$25$	10.0089	+	7.27191i	2.00178	+	1.45438i
$26$	4.13546	−	0.324870i	0.811031	−	0.0637122i
$27$	−1.03698	−	0.336937i	−0.199568	−	0.0648435i
$28$	1.84355	−	0.291446i	0.348398	−	0.0550782i
$29$	2.68762	+	3.69919i	0.499078	+	0.686922i	0.982030	−	0.188725i	$-0.0604355\pi$
$29$	2.68762	+	3.69919i	0.499078	+	0.686922i	−0.482952	+	0.875647i	$0.660435\pi$
$30$	12.8144	−	5.30576i	2.33959	−	0.968694i
$31$	−1.13033	−	3.47878i	−0.203012	−	0.624808i	−0.999789	−	0.0205342i	$-0.993463\pi$
$31$	−1.13033	−	3.47878i	−0.203012	−	0.624808i	0.796777	−	0.604274i	$-0.206537\pi$
$32$	−2.16103	−	5.22781i	−0.382019	−	0.924154i
$33$		0			0
$34$	1.80803	−	2.94948i	0.310074	−	0.505832i
$35$	3.69924	−	1.20196i	0.625286	−	0.203168i
$36$	0.795068	−	5.01054i	0.132511	−	0.835090i
$37$	−2.66741	−	3.67137i	−0.438519	−	0.603570i	0.531363	−	0.847144i	$-0.321680\pi$
$37$	−2.66741	−	3.67137i	−0.438519	−	0.603570i	−0.969882	+	0.243575i	$0.921680\pi$
$38$	2.88541	−	2.46366i	0.468075	−	0.399658i
$39$	2.13280	−	6.56407i	0.341521	−	1.05109i
$40$	−6.15525	−	10.0542i	−0.973230	−	1.58971i
$41$	3.33815	+	2.42531i	0.521332	+	0.378770i	0.817105	−	0.576488i	$-0.195577\pi$
$41$	3.33815	+	2.42531i	0.521332	+	0.378770i	−0.295774	+	0.955258i	$0.595577\pi$
$42$	0.725383	−	3.01953i	0.111929	−	0.465923i
$43$			11.4650i			1.74839i	0.485573	+	0.874196i	$0.338611\pi$
$43$			11.4650i			1.74839i	−0.485573	+	0.874196i	$0.661389\pi$
$44$		0			0
$45$		−	10.5724i		−	1.57605i
$46$	4.77333	+	1.14670i	0.703790	+	0.169072i
$47$	−2.63954	−	1.91774i	−0.385016	−	0.279731i	0.378394	−	0.925645i	$-0.376477\pi$
$47$	−2.63954	−	1.91774i	−0.385016	−	0.279731i	−0.763410	+	0.645914i	$0.776477\pi$
$48$	−9.41200	−	0.00541041i	−1.35851	−	0.000780926i
$49$	−1.89399	+	5.82912i	−0.270571	+	0.832731i
$50$	−11.3610	−	13.3059i	−1.60669	−	1.88174i
$51$	−3.38333	−	4.65675i	−0.473760	−	0.652075i
$52$	−5.79396	−	0.919380i	−0.803477	−	0.127495i
$53$	0.618312	−	0.200902i	0.0849317	−	0.0275960i	−0.266243	−	0.963906i	$-0.585782\pi$
$53$	0.618312	−	0.200902i	0.0849317	−	0.0275960i	0.351175	+	0.936310i	$0.385782\pi$
$54$	1.31464	+	0.805875i	0.178901	+	0.109666i
$55$		0			0
$56$	−2.63133	−	0.208231i	−0.351626	−	0.0278261i
$57$	−1.95073	−	6.00374i	−0.258381	−	0.795215i
$58$	−2.47373	−	5.97455i	−0.324817	−	0.784496i
$59$	1.71025	+	2.35396i	0.222655	+	0.306459i	0.905701	−	0.423917i	$-0.139345\pi$
$59$	1.71025	+	2.35396i	0.222655	+	0.306459i	−0.683046	+	0.730376i	$0.739345\pi$
$60$	−19.3737	+	3.06279i	−2.50114	+	0.395404i
$61$	10.1820	+	3.30834i	1.30367	+	0.423589i	0.876858	−	0.480750i	$-0.159635\pi$
$61$	10.1820	+	3.30834i	1.30367	+	0.423589i	0.426815	+	0.904339i	$0.359635\pi$
$62$	0.405122	+	5.15704i	0.0514505	+	0.654944i
$63$	−1.91512	−	1.39142i	−0.241283	−	0.175302i
$64$	1.24466	+	7.90258i	0.155583	+	0.987823i
$65$	−12.2255			−1.51639
$66$		0			0
$67$			5.42623i			0.662919i	0.943469	+	0.331460i	$0.107541\pi$
$67$			5.42623i			0.662919i	−0.943469	+	0.331460i	$0.892459\pi$
$68$	−3.46053	+	3.45854i	−0.419651	+	0.419410i
$69$	4.80099	−	6.60800i	0.577972	−	0.795510i
$70$	−5.48385	+	0.430795i	−0.655445	+	0.0514899i
$71$	−2.39528	+	7.37192i	−0.284268	+	0.874886i	0.702350	+	0.711832i	$0.252134\pi$
$71$	−2.39528	+	7.37192i	−0.284268	+	0.874886i	−0.986617	+	0.163054i	$0.947866\pi$
$72$	−2.74847	+	6.62730i	−0.323910	+	0.781035i
$73$	10.5698	−	7.67944i	1.23711	−	0.898811i	0.239705	−	0.970846i	$-0.422949\pi$
$73$	10.5698	−	7.67944i	1.23711	−	0.898811i	0.997402	+	0.0720351i	$0.0229494\pi$
$74$	2.45513	+	5.92962i	0.285403	+	0.689304i
$75$	−27.6859	+	8.99568i	−3.19689	+	1.03873i
$76$	−4.78154	+	2.43459i	−0.548481	+	0.279266i
$77$		0			0
$78$	−5.10116	+	8.32165i	−0.577593	+	0.942242i
$79$	−1.49461	−	4.59993i	−0.168157	−	0.517533i	0.831098	−	0.556125i	$-0.187713\pi$
$79$	−1.49461	−	4.59993i	−0.168157	−	0.517533i	−0.999255	+	0.0385925i	$0.987713\pi$
$80$	5.14274	+	15.8587i	0.574976	+	1.77306i
$81$	8.23210	−	5.98097i	0.914678	−	0.664552i
$82$	−3.78909	−	4.43775i	−0.418435	−	0.490067i
$83$	0.627378	+	0.203847i	0.0688637	+	0.0223752i	0.343246	−	0.939245i	$-0.388473\pi$
$83$	0.627378	+	0.203847i	0.0688637	+	0.0223752i	−0.274383	+	0.961621i	$0.588473\pi$
$84$	−1.99494	+	3.91250i	−0.217665	+	0.426889i
$85$	−5.99298	+	8.24863i	−0.650030	+	0.894690i
$86$	3.78733	−	15.7654i	0.408398	−	1.70003i
$87$	−10.7590			−1.15348
$88$		0			0
$89$	−2.74629			−0.291107			−0.145553	−	0.989350i	$-0.546496\pi$
$89$	−2.74629			−0.291107			−0.145553	+	0.989350i	$0.546496\pi$
$90$	−3.49249	+	14.5381i	−0.368141	+	1.53245i
$91$	−1.60897	+	2.21456i	−0.168666	+	0.232149i
$92$	−6.18497	−	3.15364i	−0.644828	−	0.328790i
$93$	8.18558	+	2.65966i	0.848805	+	0.275794i
$94$	2.99610	+	3.50901i	0.309025	+	0.361927i
$95$	−9.04633	+	6.57255i	−0.928134	+	0.674329i
$96$	12.9406	+	3.11659i	1.32074	+	0.318086i
$97$	0.565208	+	1.73953i	0.0573882	+	0.176623i	0.975642	−	0.219371i	$-0.0704004\pi$
$97$	0.565208	+	1.73953i	0.0573882	+	0.176623i	−0.918253	+	0.395993i	$0.870400\pi$
$98$	4.53000	−	7.38991i	0.457599	−	0.746493i
$99$		0			0
$100$	11.2269	+	22.0498i	1.12269	+	2.20498i
$101$	−12.0604	+	3.91868i	−1.20006	+	0.389923i	−0.839783	−	0.542923i	$-0.817318\pi$
$101$	−12.0604	+	3.91868i	−1.20006	+	0.389923i	−0.360276	+	0.932846i	$0.617318\pi$
$102$	3.11408	+	7.52110i	0.308339	+	0.744700i
$103$	3.12802	−	2.27264i	0.308213	−	0.223930i	−0.422916	−	0.906169i	$-0.638994\pi$
$103$	3.12802	−	2.27264i	0.308213	−	0.223930i	0.731129	+	0.682239i	$0.238994\pi$
$104$	7.66351	+	3.17820i	0.751469	+	0.311648i
$105$	−2.82821	+	8.70432i	−0.276005	+	0.849455i
$106$	−0.916601	+	0.0720056i	−0.0890282	+	0.00699380i
$107$	−7.51315	+	10.3410i	−0.726324	+	0.999699i	0.272966	+	0.962024i	$0.411995\pi$
$107$	−7.51315	+	10.3410i	−0.726324	+	0.999699i	−0.999290	+	0.0376755i	$0.988005\pi$
$108$	−1.54154	−	1.54243i	−0.148335	−	0.148420i
$109$			1.85065i			0.177260i	0.996065	+	0.0886299i	$0.0282489\pi$
$109$			1.85065i			0.177260i	−0.996065	+	0.0886299i	$0.971751\pi$
$110$		0			0
$111$	10.6781			1.01352
$112$	3.54953	+	1.15557i	0.335399	+	0.109191i
$113$	−13.4956	−	9.80514i	−1.26956	−	0.922390i	−0.270376	−	0.962755i	$-0.587148\pi$
$113$	−13.4956	−	9.80514i	−1.26956	−	0.922390i	−0.999185	+	0.0403644i	$0.987148\pi$
$114$	0.699166	+	8.90010i	0.0654829	+	0.833570i
$115$	−13.7600	−	4.47089i	−1.28313	−	0.416913i
$116$	1.42798	+	9.03272i	0.132585	+	0.838667i
$117$	4.37339	+	6.01945i	0.404320	+	0.556498i
$118$	−1.57414	−	3.80187i	−0.144912	−	0.349990i
$119$	0.705457	+	2.17117i	0.0646692	+	0.199031i
$120$	27.6524	+	2.18829i	2.52431	+	0.199762i
$121$		0			0
$122$	−12.9083	−	7.91278i	−1.16866	−	0.716390i
$123$	−9.23373	+	3.00022i	−0.832577	+	0.270521i
$124$	1.14649	−	7.22522i	0.102958	−	0.648844i
$125$	18.0596	+	24.8569i	1.61530	+	2.22327i
$126$	2.17383	+	2.54597i	0.193660	+	0.226813i
$127$	2.01174	−	6.19150i	0.178513	−	0.549407i	−0.821263	−	0.570549i	$-0.806730\pi$
$127$	2.01174	−	6.19150i	0.178513	−	0.549407i	0.999776	+	0.0211425i	$0.00673036\pi$
$128$	0.899009	−	11.2779i	0.0794619	−	0.996838i
$129$	−21.8249	−	15.8567i	−1.92158	−	1.39611i
$130$	16.8112	+	4.03856i	1.47444	+	0.354205i
$131$		−	6.91569i		−	0.604227i	−0.953272	−	0.302114i	$-0.902308\pi$
$131$		−	6.91569i		−	0.604227i	0.953272	−	0.302114i	$-0.0976922\pi$
$132$		0			0
$133$			2.50368i			0.217097i
$134$	1.79250	−	7.46156i	0.154848	−	0.644580i
$135$	−3.67659	−	2.67120i	−0.316430	−	0.229900i
$136$	5.90104	−	3.61266i	0.506010	−	0.309783i
$137$	1.79833	−	5.53469i	0.153642	−	0.472861i	−0.844379	−	0.535746i	$-0.820030\pi$
$137$	1.79833	−	5.53469i	0.153642	−	0.472861i	0.998021	+	0.0628856i	$0.0200303\pi$
$138$	−8.78469	+	7.50065i	−0.747802	+	0.638498i
$139$	−5.60470	−	7.71421i	−0.475385	−	0.654311i	0.502225	−	0.864737i	$-0.332515\pi$
$139$	−5.60470	−	7.71421i	−0.475385	−	0.654311i	−0.977610	+	0.210426i	$0.932515\pi$
$140$	7.68310	+	1.21915i	0.649341	+	0.103037i
$141$	7.30128	−	2.37233i	0.614879	−	0.199786i
$142$	5.72896	−	9.34580i	0.480764	−	0.784282i
$143$		0			0
$144$	5.96865	−	8.20522i	0.497388	−	0.683769i
$145$	5.88915	+	18.1249i	0.489067	+	1.50519i
$146$	−17.0713	+	7.06830i	−1.41283	+	0.584977i
$147$	−8.47690	−	11.6675i	−0.699163	−	0.962315i
$148$	−1.41724	−	8.96479i	−0.116497	−	0.736901i
$149$	−13.2407	−	4.30218i	−1.08472	−	0.352448i	−0.288518	−	0.957474i	$-0.593162\pi$
$149$	−13.2407	−	4.30218i	−1.08472	−	0.352448i	−0.796205	+	0.605027i	$0.793162\pi$
$150$	41.0422	−	3.22416i	3.35108	−	0.263251i
$151$	12.3153	+	8.94761i	1.00221	+	0.728146i	0.962560	−	0.271068i	$-0.0873768\pi$
$151$	12.3153	+	8.94761i	1.00221	+	0.728146i	0.0396467	+	0.999214i	$0.487377\pi$
$152$	7.37930	−	1.76825i	0.598540	−	0.143424i
$153$	6.20522			0.501662
$154$		0			0
$155$		−	15.2455i		−	1.22455i
$156$	9.76353	−	9.75792i	0.781708	−	0.781259i
$157$	0.513689	−	0.707032i	0.0409969	−	0.0564273i	−0.788026	−	0.615641i	$-0.788897\pi$
$157$	0.513689	−	0.707032i	0.0409969	−	0.0564273i	0.829023	+	0.559214i	$0.188897\pi$
$158$	0.535685	+	6.81906i	0.0426168	+	0.542495i
$159$	−0.472722	+	1.45489i	−0.0374893	+	0.115380i
$160$	−1.83297	−	23.5061i	−0.144909	−	1.85832i
$161$	−2.62080	+	1.90412i	−0.206548	+	0.150066i
$162$	−13.2956	+	5.50499i	−1.04460	+	0.432513i
$163$	7.15847	−	2.32593i	0.560695	−	0.182181i	−0.0149391	−	0.999888i	$-0.504755\pi$
$163$	7.15847	−	2.32593i	0.560695	−	0.182181i	0.575634	+	0.817708i	$0.304755\pi$
$164$	3.74438	+	7.35399i	0.292387	+	0.574250i
$165$		0			0
$166$	−0.795363	−	0.487556i	−0.0617321	−	0.0378417i
$167$	−0.0441598	−	0.135910i	−0.00341719	−	0.0105170i	0.949333	−	0.314271i	$-0.101760\pi$
$167$	−0.0441598	−	0.135910i	−0.00341719	−	0.0105170i	−0.952751	+	0.303754i	$0.901760\pi$
$168$	4.03567	−	4.72104i	0.311359	−	0.364236i
$169$	−3.55661	+	2.58402i	−0.273585	+	0.198771i
$170$	10.9657	−	9.36291i	0.841034	−	0.718102i
$171$	6.47223	+	2.10296i	0.494944	+	0.160817i
$172$	−10.4158	+	20.4277i	−0.794201	+	1.55760i
$173$	−0.663666	+	0.913458i	−0.0504576	+	0.0694489i	−0.833500	−	0.552519i	$-0.813667\pi$
$173$	−0.663666	+	0.913458i	−0.0504576	+	0.0694489i	0.783043	+	0.621968i	$0.213667\pi$
$174$	14.7946	+	3.55411i	1.12157	+	0.269436i
$175$	11.5456			0.872762
$176$		0			0
$177$	−6.84641			−0.514608
$178$	3.77641	+	0.907209i	0.283054	+	0.0679982i
$179$	8.91201	−	12.2663i	0.666115	−	0.916829i	−0.333550	−	0.942733i	$-0.608246\pi$
$179$	8.91201	−	12.2663i	0.666115	−	0.916829i	0.999664	+	0.0259041i	$0.00824644\pi$
$180$	9.60500	−	18.8375i	0.715914	−	1.40406i
$181$	16.0929	+	5.22890i	1.19618	+	0.388661i	0.838353	−	0.545128i	$-0.183519\pi$
$181$	16.0929	+	5.22890i	1.19618	+	0.388661i	0.357824	+	0.933789i	$0.383519\pi$
$182$	2.94404	−	2.51372i	0.218227	−	0.186329i
$183$	−20.3801	+	14.8070i	−1.50654	+	1.09457i
$184$	7.46313	+	6.37968i	0.550189	+	0.470316i
$185$	−5.84486	−	17.9886i	−0.429723	−	1.32255i
$186$	−10.3773	−	6.36129i	−0.760903	−	0.466432i
$187$		0			0
$188$	−2.96075	−	5.81494i	−0.215935	−	0.424098i
$189$	−0.967737	+	0.314437i	−0.0703925	+	0.0228719i
$190$	14.6107	−	6.04949i	1.05997	−	0.438876i
$191$	13.4880	−	9.79958i	0.975955	−	0.709073i	0.0191543	−	0.999817i	$-0.493903\pi$
$191$	13.4880	−	9.79958i	0.975955	−	0.709073i	0.956801	+	0.290743i	$0.0939026\pi$
$192$	−16.7649	−	8.56038i	−1.20991	−	0.617792i
$193$	−0.0558394	+	0.171856i	−0.00401941	+	0.0123705i	−0.953046	−	0.302825i	$-0.902070\pi$
$193$	−0.0558394	+	0.171856i	−0.00401941	+	0.0123705i	0.949027	+	0.315196i	$0.102070\pi$
$194$	−0.202577	−	2.57873i	−0.0145442	−	0.185142i
$195$	16.9086	−	23.2727i	1.21085	−	1.66659i
$196$	−8.67034	+	8.66536i	−0.619310	+	0.618954i
$197$		−	8.38885i		−	0.597681i	−0.954303	−	0.298840i	$-0.903400\pi$
$197$		−	8.38885i		−	0.597681i	0.954303	−	0.298840i	$-0.0965998\pi$
$198$		0			0
$199$	22.0996			1.56660			0.783298	−	0.621646i	$-0.213536\pi$
$199$	22.0996			1.56660			0.783298	+	0.621646i	$0.213536\pi$
$200$	−8.15416	−	34.0292i	−0.576586	−	2.40622i
$201$	−10.3295	−	7.50479i	−0.728584	−	0.529347i
$202$	17.8787	−	1.40450i	1.25794	−	0.0988202i
$203$	4.05826	+	1.31861i	0.284834	+	0.0925482i
$204$	−1.79762	−	11.3709i	−0.125859	−	0.796122i
$205$	10.1085	+	13.9132i	0.706011	+	0.971741i
$206$	−5.05205	+	2.09178i	−0.351993	+	0.145741i
$207$	2.72099	+	8.37435i	0.189122	+	0.582057i
$208$	−9.48814	−	6.90187i	−0.657884	−	0.478559i
$209$		0			0
$210$	6.76442	−	11.0350i	0.466789	−	0.761485i
$211$	14.3029	−	4.64730i	0.984653	−	0.319933i	0.227937	−	0.973676i	$-0.426802\pi$
$211$	14.3029	−	4.64730i	0.984653	−	0.319933i	0.756717	+	0.653743i	$0.226802\pi$
$212$	1.28420	+	0.203775i	0.0881990	+	0.0139953i
$213$	−10.7205	−	14.7555i	−0.734556	−	1.01103i
$214$	13.7473	−	11.7379i	0.939746	−	0.802385i
$215$	−14.7665	+	45.4465i	−1.00706	+	3.09943i
$216$	1.61024	+	2.63022i	0.109563	+	0.178964i
$217$	−2.76162	−	2.00643i	−0.187471	−	0.136206i
$218$	0.611341	−	2.54481i	0.0414053	−	0.172356i
$219$			30.7421i			2.07736i
$220$		0			0
$221$		−	7.17543i		−	0.482672i
$222$	−14.6833	−	3.52738i	−0.985480	−	0.236743i
$223$	8.31394	+	6.04043i	0.556743	+	0.404497i	0.830265	−	0.557368i	$-0.188189\pi$
$223$	8.31394	+	6.04043i	0.556743	+	0.404497i	−0.273523	+	0.961866i	$0.588189\pi$
$224$	−4.49919	−	2.76156i	−0.300615	−	0.184514i
$225$	9.69765	−	29.8463i	0.646510	−	1.98975i
$226$	15.3187	+	17.9411i	1.01898	+	1.19342i
$227$	−9.20991	−	12.6764i	−0.611283	−	0.841360i	0.385399	−	0.922750i	$-0.374064\pi$
$227$	−9.20991	−	12.6764i	−0.611283	−	0.841360i	−0.996682	+	0.0813906i	$0.974064\pi$
$228$	1.97863	−	12.4694i	0.131038	−	0.825807i
$229$	13.3858	−	4.34932i	0.884561	−	0.287411i	0.168711	−	0.985666i	$-0.446039\pi$
$229$	13.3858	−	4.34932i	0.884561	−	0.287411i	0.715850	+	0.698254i	$0.246039\pi$
$230$	17.4443	+	10.6933i	1.15024	+	0.705098i
$231$		0			0
$232$	1.02026	−	12.8925i	0.0669831	−	0.846436i
$233$	3.73889	+	11.5071i	0.244943	+	0.753857i	0.995646	+	0.0932169i	$0.0297150\pi$
$233$	3.73889	+	11.5071i	0.244943	+	0.753857i	−0.750703	+	0.660640i	$0.770285\pi$
$234$	−4.02535	−	9.72200i	−0.263145	−	0.635547i
$235$	−7.99301	−	11.0014i	−0.521407	−	0.717655i
$236$	0.908687	+	5.74792i	0.0591505	+	0.374157i
$237$	10.8236	+	3.51682i	0.703071	+	0.228442i
$238$	−0.252844	−	3.21860i	−0.0163895	−	0.208631i
$239$	−17.5944	−	12.7831i	−1.13809	−	0.826869i	−0.151236	−	0.988498i	$-0.548325\pi$
$239$	−17.5944	−	12.7831i	−1.13809	−	0.826869i	−0.986852	+	0.161629i	$0.948325\pi$
$240$	−37.3017	−	12.1438i	−2.40781	−	0.783877i
$241$	6.93967			0.447024			0.223512	−	0.974701i	$-0.428248\pi$
$241$	6.93967			0.447024			0.223512	+	0.974701i	$0.428248\pi$
$242$		0			0
$243$			20.6718i			1.32609i
$244$	15.1362	+	15.1449i	0.968997	+	0.969554i
$245$	−15.0154	+	20.6669i	−0.959298	+	1.32036i
$246$	13.6883	−	1.07531i	0.872734	−	0.0685595i
$247$	2.43176	−	7.48419i	0.154729	−	0.476208i
$248$	−3.96331	+	9.55661i	−0.251670	+	0.606845i
$249$	−1.25575	+	0.912354i	−0.0795798	+	0.0578181i
$250$	−16.6224	−	40.1463i	−1.05129	−	2.53908i
$251$	−16.8602	+	5.47821i	−1.06421	+	0.345781i	−0.788229	−	0.615383i	$-0.789001\pi$
$251$	−16.8602	+	5.47821i	−1.06421	+	0.345781i	−0.275977	+	0.961164i	$0.589001\pi$
$252$	−2.14818	−	4.21904i	−0.135323	−	0.265775i
$253$		0			0
$254$	−4.81162	+	7.84932i	−0.301908	+	0.492510i
$255$	−7.41360	−	22.8167i	−0.464257	−	1.42884i
$256$	−4.96176	+	15.2112i	−0.310110	+	0.950701i
$257$	−14.3637	+	10.4358i	−0.895983	+	0.650970i	−0.937431	−	0.348171i	$-0.886803\pi$
$257$	−14.3637	+	10.4358i	−0.895983	+	0.650970i	0.0414480	+	0.999141i	$0.486803\pi$
$258$	24.7732	+	29.0141i	1.54231	+	1.80634i
$259$	−4.02775	−	1.30869i	−0.250272	−	0.0813183i
$260$	−21.7828	−	11.1068i	−1.35091	−	0.688813i
$261$	6.81744	−	9.38341i	0.421989	−	0.580818i
$262$	−2.28453	+	9.50971i	−0.141138	+	0.587512i
$263$	27.6424			1.70450			0.852252	−	0.523132i	$-0.175237\pi$
$263$	27.6424			1.70450			0.852252	+	0.523132i	$0.175237\pi$
$264$		0			0
$265$	2.70971			0.166456
$266$	0.827064	−	3.44279i	0.0507105	−	0.211091i
$267$	3.79829	−	5.22789i	0.232451	−	0.319942i
$268$	−4.92969	+	9.66819i	−0.301129	+	0.590579i
$269$	−10.1081	−	3.28433i	−0.616304	−	0.200249i	−0.0158051	−	0.999875i	$-0.505031\pi$
$269$	−10.1081	−	3.28433i	−0.616304	−	0.200249i	−0.600498	+	0.799626i	$0.705031\pi$
$270$	4.17324	+	4.88766i	0.253975	+	0.297454i
$271$	15.9765	−	11.6076i	0.970504	−	0.705113i	0.0149379	−	0.999888i	$-0.495245\pi$
$271$	15.9765	−	11.6076i	0.970504	−	0.705113i	0.955566	+	0.294776i	$0.0952449\pi$
$272$	−9.30787	+	3.01840i	−0.564373	+	0.183017i
$273$	−1.99037	−	6.12574i	−0.120463	−	0.370747i
$274$	−4.30120	+	7.01665i	−0.259845	+	0.423891i
$275$		0			0
$276$	14.5575	−	7.41215i	0.876259	−	0.446159i
$277$	−11.9218	+	3.87361i	−0.716309	+	0.232743i	−0.644422	−	0.764670i	$-0.722902\pi$
$277$	−11.9218	+	3.87361i	−0.716309	+	0.232743i	−0.0718867	+	0.997413i	$0.522902\pi$
$278$	5.15867	+	12.4592i	0.309396	+	0.747253i
$279$	−7.50642	+	5.45374i	−0.449398	+	0.326507i
$280$	−10.1622	−	4.21447i	−0.607310	−	0.251863i
$281$	7.35576	−	22.6387i	0.438808	−	1.35051i	−0.450325	−	0.892864i	$-0.648692\pi$
$281$	7.35576	−	22.6387i	0.438808	−	1.35051i	0.889134	−	0.457648i	$-0.151308\pi$
$282$	−10.8236	+	0.850271i	−0.644536	+	0.0506329i
$283$	−16.2989	+	22.4336i	−0.968872	+	1.33354i	−0.0262574	+	0.999655i	$0.508359\pi$
$283$	−16.2989	+	22.4336i	−0.968872	+	1.33354i	−0.942615	+	0.333883i	$0.891641\pi$
$284$	−10.9651	+	10.9588i	−0.650661	+	0.650287i
$285$		−	26.3110i		−	1.55853i
$286$		0			0
$287$	3.85065			0.227297
$288$	−10.9179	+	9.31125i	−0.643346	+	0.548671i
$289$	8.91197	+	6.47492i	0.524233	+	0.380878i
$290$	−2.11074	−	26.8688i	−0.123947	−	1.57779i
$291$	−4.09312	−	1.32994i	−0.239943	−	0.0779622i
$292$	25.8096	−	4.08023i	1.51039	−	0.238777i
$293$	−3.29976	−	4.54174i	−0.192774	−	0.265331i	0.701678	−	0.712494i	$-0.252434\pi$
$293$	−3.29976	−	4.54174i	−0.192774	−	0.265331i	−0.894453	+	0.447163i	$0.852434\pi$
$294$	7.80230	+	18.8441i	0.455039	+	1.09901i
$295$	3.74752	+	11.5337i	0.218189	+	0.671518i
$296$	−1.01258	+	12.7956i	−0.0588553	+	0.743728i
$297$		0			0
$298$	16.7860	+	10.2898i	0.972389	+	0.596073i
$299$	9.68371	−	3.14643i	0.560023	−	0.181963i
$300$	−57.5019	−	9.12434i	−3.31987	−	0.526794i
$301$	6.28893	+	8.65597i	0.362488	+	0.498922i
$302$	−13.9789	−	16.3720i	−0.804398	−	0.942103i
$303$	9.22065	−	28.3782i	0.529712	−	1.63029i
$304$	−10.7313	−	0.00616882i	−0.615484	−	0.000353806i
$305$	36.0999	+	26.2281i	2.06708	+	1.50182i
$306$	−8.53275	−	2.04983i	−0.487785	−	0.117181i
$307$		−	27.8554i		−	1.58979i	−0.606747	−	0.794895i	$-0.707526\pi$
$307$		−	27.8554i		−	1.58979i	0.606747	−	0.794895i	$-0.292474\pi$
$308$		0			0
$309$			9.09775i			0.517553i
$310$	−5.03620	+	20.9640i	−0.286037	+	1.19067i
$311$	19.7461	+	14.3464i	1.11970	+	0.813509i	0.984164	−	0.177263i	$-0.0567243\pi$
$311$	19.7461	+	14.3464i	1.11970	+	0.813509i	0.135536	+	0.990772i	$0.456724\pi$
$312$	−16.6492	+	10.1928i	−0.942574	+	0.577051i
$313$	2.82291	−	8.68803i	0.159561	−	0.491077i	−0.839034	−	0.544079i	$-0.816879\pi$
$313$	2.82291	−	8.68803i	0.159561	−	0.491077i	0.998594	+	0.0530024i	$0.0168791\pi$
$314$	−0.939930	+	0.802542i	−0.0530433	+	0.0452901i
$315$	−5.79935	−	7.98212i	−0.326756	−	0.449742i
$316$	1.51599	−	9.55378i	0.0852808	−	0.537442i
$317$	−17.0715	+	5.54688i	−0.958833	+	0.311544i	−0.746299	−	0.665610i	$-0.768171\pi$
$317$	−17.0715	+	5.54688i	−0.958833	+	0.311544i	−0.212533	+	0.977154i	$0.568171\pi$
$318$	1.13064	−	1.84445i	0.0634033	−	0.103431i
$319$		0			0
$320$	−5.24447	+	32.9285i	−0.293175	+	1.84076i
$321$	−9.29411	−	28.6043i	−0.518747	−	1.59654i
$322$	4.23284	−	1.75259i	0.235887	−	0.0976678i
$323$	−3.85758	−	5.30951i	−0.214642	−	0.295429i
$324$	20.1012	−	3.17780i	1.11673	−	0.176544i
$325$	−34.5129	−	11.2139i	−1.91443	−	0.622036i
$326$	−10.6119	+	0.833640i	−0.587738	+	0.0461710i
$327$	−3.52293	−	2.55955i	−0.194818	−	0.141544i
$328$	−2.71956	−	11.3493i	−0.150162	−	0.626662i
$329$	−3.04478			−0.167864
$330$		0			0
$331$			13.1934i			0.725173i	0.931950	+	0.362586i	$0.118106\pi$
$331$			13.1934i			0.725173i	−0.931950	+	0.362586i	$0.881894\pi$
$332$	0.932638	+	0.933174i	0.0511851	+	0.0512146i
$333$	−6.76618	+	9.31285i	−0.370784	+	0.510341i
$334$	0.0158274	+	0.201476i	0.000866036	+	0.0110243i
$335$	−6.98878	+	21.5093i	−0.381838	+	1.17518i
$336$	−7.10896	+	5.15872i	−0.387826	+	0.281431i
$337$	19.3122	−	14.0311i	1.05200	−	0.764324i	0.0794093	−	0.996842i	$-0.474697\pi$
$337$	19.3122	−	14.0311i	1.05200	−	0.764324i	0.972592	+	0.232518i	$0.0746966\pi$
$338$	5.74426	−	2.37838i	0.312447	−	0.129367i
$339$	37.3305	−	12.1294i	2.02751	−	0.658779i
$340$	−18.1718	+	9.25244i	−0.985506	+	0.501784i
$341$		0			0
$342$	−8.20522	−	5.02979i	−0.443688	−	0.271980i
$343$	3.78619	+	11.6527i	0.204435	+	0.629186i
$344$	21.0708	−	24.6492i	1.13606	−	1.32900i
$345$	27.5417	−	20.0102i	1.48280	−	1.07732i
$346$	1.21435	−	1.03685i	0.0652840	−	0.0557416i
$347$	35.3993	+	11.5019i	1.90033	+	0.617456i	0.963528	+	0.267607i	$0.0862328\pi$
$347$	35.3993	+	11.5019i	1.90033	+	0.617456i	0.936806	+	0.349849i	$0.113767\pi$
$348$	−19.1698	−	9.77445i	−1.02761	−	0.523966i
$349$	16.7013	−	22.9874i	0.894001	−	1.23049i	−0.0783407	−	0.996927i	$-0.524962\pi$
$349$	16.7013	−	22.9874i	0.894001	−	1.23049i	0.972342	−	0.233561i	$-0.0750378\pi$
$350$	−15.8762	−	3.81395i	−0.848618	−	0.203864i
$351$	3.19824			0.170709
$352$		0			0
$353$	−6.72158			−0.357754			−0.178877	−	0.983871i	$-0.557246\pi$
$353$	−6.72158			−0.357754			−0.178877	+	0.983871i	$0.557246\pi$
$354$	9.41444	+	2.26164i	0.500372	+	0.120205i
$355$	−18.9895	+	26.1368i	−1.00786	+	1.38720i
$356$	−4.89322	−	2.49499i	−0.259340	−	0.132234i
$357$	−5.10877	−	1.65994i	−0.270385	−	0.0878534i
$358$	−16.3069	+	13.9233i	−0.861845	+	0.735871i
$359$	16.0396	−	11.6534i	0.846536	−	0.615044i	−0.0776527	−	0.996980i	$-0.524743\pi$
$359$	16.0396	−	11.6534i	0.846536	−	0.615044i	0.924189	+	0.381936i	$0.124743\pi$
$360$	−19.4305	+	22.7303i	−1.02408	+	1.19799i
$361$	3.64714	+	11.2248i	0.191955	+	0.590777i
$362$	−20.4019	−	12.5063i	−1.07230	−	0.657319i
$363$		0			0
$364$	−4.87871	+	2.48406i	−0.255714	+	0.130200i
$365$	51.7891	−	16.8273i	2.71077	−	0.880782i
$366$	32.9159	−	13.6287i	1.72054	−	0.712382i
$367$	−3.67959	+	2.67338i	−0.192073	+	0.139549i	−0.679666	−	0.733522i	$-0.737875\pi$
$367$	−3.67959	+	2.67338i	−0.192073	+	0.139549i	0.487593	+	0.873071i	$0.337875\pi$
$368$	−8.15502	−	11.2380i	−0.425110	−	0.585822i
$369$	3.23434	−	9.95426i	0.168373	−	0.518198i
$370$	2.09487	+	26.6668i	0.108907	+	1.38634i
$371$	0.356620	−	0.490845i	0.0185148	−	0.0254834i
$372$	12.1684	+	12.1754i	0.630902	+	0.631265i
$373$			33.3992i			1.72934i	0.502336	+	0.864672i	$0.332474\pi$
$373$			33.3992i			1.72934i	−0.502336	+	0.864672i	$0.667526\pi$
$374$		0			0
$375$	−72.2956			−3.73333
$376$	2.15040	+	8.97412i	0.110899	+	0.462805i
$377$	−10.8505	−	7.88338i	−0.558831	−	0.406015i
$378$	1.43460	−	0.112698i	0.0737878	−	0.00579655i
$379$	−8.79578	−	2.85792i	−0.451809	−	0.146802i	0.0742686	−	0.997238i	$-0.476338\pi$
$379$	−8.79578	−	2.85792i	−0.451809	−	0.146802i	−0.526077	+	0.850437i	$0.676338\pi$
$380$	−22.0894	+	3.49211i	−1.13316	+	0.179142i
$381$	9.00389	+	12.3928i	0.461283	+	0.634902i
$382$	−21.7844	+	9.01972i	−1.11459	+	0.461489i
$383$	9.76741	+	30.0610i	0.499091	+	1.53605i	0.810482	+	0.585764i	$0.199205\pi$
$383$	9.76741	+	30.0610i	0.499091	+	1.53605i	−0.311390	+	0.950282i	$0.600795\pi$
$384$	20.2255	+	17.3094i	1.03213	+	0.883318i
$385$		0			0
$386$	0.133555	−	0.217872i	0.00679777	−	0.0110894i
$387$	27.6588	−	8.98689i	1.40598	−	0.456829i
$388$	−0.573292	+	3.61290i	−0.0291045	+	0.183417i
$389$	2.93624	+	4.04139i	0.148873	+	0.204906i	0.876940	−	0.480600i	$-0.159581\pi$
$389$	2.93624	+	4.04139i	0.148873	+	0.204906i	−0.728067	+	0.685506i	$0.759581\pi$
$390$	−30.9387	+	26.4165i	−1.56664	+	1.33765i
$391$	2.62407	−	8.07607i	0.132705	−	0.408424i
$392$	14.7850	−	9.05151i	0.746756	−	0.457170i
$393$	13.1648	+	9.56482i	0.664078	+	0.482481i
$394$	−2.77116	+	11.5354i	−0.139609	+	0.581147i
$395$		−	20.1589i		−	1.01430i
$396$		0			0
$397$		−	17.7950i		−	0.893107i	−0.894757	−	0.446553i	$-0.852651\pi$
$397$		−	17.7950i		−	0.893107i	0.894757	−	0.446553i	$-0.147349\pi$
$398$	−30.3889	−	7.30035i	−1.52326	−	0.365933i
$399$	−4.76605	−	3.46274i	−0.238601	−	0.173354i
$400$	−0.0284471	+	49.4868i	−0.00142235	+	2.47434i
$401$	−3.76193	+	11.5780i	−0.187862	+	0.578180i	−0.999986	−	0.00530515i	$-0.998311\pi$
$401$	−3.76193	+	11.5780i	−0.187862	+	0.578180i	0.812124	+	0.583485i	$0.198311\pi$
$402$	11.7248	+	13.7320i	0.584781	+	0.684890i
$403$	6.30645	+	8.68008i	0.314147	+	0.432386i
$404$	−25.0488	−	3.97472i	−1.24623	−	0.197750i
$405$	40.3349	−	13.1056i	2.00426	−	0.651222i
$406$	−5.14489	−	3.15381i	−0.255337	−	0.156521i
$407$		0			0
$408$	−1.28436	+	16.2299i	−0.0635852	+	0.803497i
$409$	−0.181701	−	0.559218i	−0.00898453	−	0.0276516i	0.946464	−	0.322810i	$-0.104628\pi$
$409$	−0.181701	−	0.559218i	−0.00898453	−	0.0276516i	−0.955448	+	0.295159i	$0.904628\pi$
$410$	−9.30409	−	22.4712i	−0.459496	−	1.10977i
$411$	8.04874	+	11.0781i	0.397015	+	0.546444i
$412$	7.63803	−	1.20750i	0.376299	−	0.0594890i
$413$	2.58245	+	0.839090i	0.127074	+	0.0412889i
$414$	−0.975235	−	12.4143i	−0.0479302	−	0.610132i
$415$	2.22434	+	1.61608i	0.109189	+	0.0793302i
$416$	10.7671	+	12.6250i	0.527901	+	0.618992i
$417$	22.4365			1.09872
$418$		0			0
$419$			11.1507i			0.544748i	0.962191	+	0.272374i	$0.0878088\pi$
$419$			11.1507i			0.544748i	−0.962191	+	0.272374i	$0.912191\pi$
$420$	−12.9470	+	12.9395i	−0.631748	+	0.631385i
$421$	20.4783	−	28.1860i	0.998053	−	1.37370i	0.0715408	−	0.997438i	$-0.477208\pi$
$421$	20.4783	−	28.1860i	0.998053	−	1.37370i	0.926512	−	0.376265i	$-0.122792\pi$
$422$	−21.2030	+	1.66565i	−1.03215	+	0.0810824i
$423$	−2.55745	+	7.87102i	−0.124347	+	0.382702i
$424$	−1.69857	−	0.704430i	−0.0824900	−	0.0342101i
$425$	−24.4845	+	17.7890i	−1.18767	+	0.862893i
$426$	9.86734	+	23.8316i	0.478074	+	1.15464i
$427$	9.50208	−	3.08741i	0.459838	−	0.149410i
$428$	−22.7813	+	11.5994i	−1.10117	+	0.560678i
$429$		0			0
$430$	35.3180	−	57.6152i	1.70319	−	2.77845i
$431$	7.68362	+	23.6478i	0.370107	+	1.13907i	0.946721	+	0.322056i	$0.104374\pi$
$431$	7.68362	+	23.6478i	0.370107	+	1.13907i	−0.576614	+	0.817017i	$0.695626\pi$
$432$	−1.34536	−	4.14871i	−0.0647288	−	0.199605i
$433$	0.443102	−	0.321932i	0.0212941	−	0.0154711i	−0.577087	−	0.816682i	$-0.695811\pi$
$433$	0.443102	−	0.321932i	0.0212941	−	0.0154711i	0.598381	+	0.801211i	$0.295811\pi$
$434$	3.13468	+	3.67130i	0.150469	+	0.176228i
$435$	−42.6480	−	13.8572i	−2.04481	−	0.664400i
$436$	−1.68130	+	3.29739i	−0.0805197	+	0.157917i
$437$	5.47397	−	7.53428i	0.261856	−	0.360413i
$438$	10.1553	−	42.2731i	0.485240	−	2.01989i
$439$	−27.5308			−1.31397			−0.656987	−	0.753902i	$-0.728169\pi$
$439$	−27.5308			−1.31397			−0.656987	+	0.753902i	$0.728169\pi$
$440$		0			0
$441$	15.5471			0.740340
$442$	−2.37033	+	9.86688i	−0.112745	+	0.469319i
$443$	4.73434	−	6.51626i	0.224935	−	0.309597i	−0.681602	−	0.731724i	$-0.738716\pi$
$443$	4.73434	−	6.51626i	0.224935	−	0.309597i	0.906537	+	0.422127i	$0.138716\pi$
$444$	19.0257	+	9.70095i	0.902918	+	0.460387i
$445$	−10.8862	−	3.53713i	−0.516054	−	0.167676i
$446$	−9.43703	−	11.0526i	−0.446857	−	0.523354i
$447$	26.5024	−	19.2551i	1.25352	−	0.910737i
$448$	5.27455	+	5.28365i	0.249199	+	0.249629i
$449$	−10.4357	−	32.1177i	−0.492490	−	1.51573i	−0.820833	−	0.571169i	$-0.806490\pi$
$449$	−10.4357	−	32.1177i	−0.492490	−	1.51573i	0.328343	−	0.944559i	$-0.393510\pi$
$450$	−23.1945	+	37.8379i	−1.09340	+	1.78369i
$451$		0			0
$452$	−15.1379	−	29.7310i	−0.712029	−	1.39843i
$453$	−34.0656	+	11.0686i	−1.60054	+	0.520048i
$454$	8.47697	+	20.4735i	0.397844	+	0.960871i
$455$	−9.23016	+	6.70610i	−0.432716	+	0.314387i
$456$	−6.83994	+	16.4930i	−0.320309	+	0.772353i
$457$	1.18421	−	3.64464i	0.0553952	−	0.170489i	−0.919531	−	0.393018i	$-0.871431\pi$
$457$	1.18421	−	3.64464i	0.0553952	−	0.170489i	0.974926	+	0.222529i	$0.0714311\pi$
$458$	−19.8435	+	1.55885i	−0.927226	+	0.0728402i
$459$	1.56779	−	2.15788i	0.0731781	−	0.100721i
$460$	−20.4551	−	20.4669i	−0.953724	−	0.954273i
$461$		−	15.8380i		−	0.737649i	−0.929499	−	0.368825i	$-0.879760\pi$
$461$		−	15.8380i		−	0.737649i	0.929499	−	0.368825i	$-0.120240\pi$
$462$		0			0
$463$	30.4131			1.41341			0.706707	−	0.707506i	$-0.250180\pi$
$463$	30.4131			1.41341			0.706707	+	0.707506i	$0.250180\pi$
$464$	−5.66185	+	17.3914i	−0.262845	+	0.807374i
$465$	29.0217	+	21.0855i	1.34585	+	0.977815i
$466$	−1.34006	−	17.0584i	−0.0620772	−	0.790217i
$467$	−19.1937	−	6.23642i	−0.888179	−	0.288587i	−0.170830	−	0.985301i	$-0.554645\pi$
$467$	−19.1937	−	6.23642i	−0.888179	−	0.288587i	−0.717349	+	0.696714i	$0.754645\pi$
$468$	2.32366	+	14.6984i	0.107411	+	0.679432i
$469$	2.97647	+	4.09676i	0.137441	+	0.189171i
$470$	7.35692	+	17.7684i	0.339349	+	0.819595i
$471$	0.635457	+	1.95574i	0.0292803	+	0.0901155i
$472$	0.649234	−	8.20408i	0.0298834	−	0.377624i
$473$		0			0
$474$	−13.7218	−	8.41142i	−0.630261	−	0.386349i
$475$	−31.5667	+	10.2567i	−1.44838	+	0.470608i
$476$	−0.715547	+	4.50940i	−0.0327970	+	0.206688i
$477$	−0.969336	−	1.33418i	−0.0443828	−	0.0610878i
$478$	19.9712	+	23.3900i	0.913460	+	1.06983i
$479$	−3.88139	+	11.9457i	−0.177345	+	0.545813i	−0.999733	−	0.0231151i	$-0.992642\pi$
$479$	−3.88139	+	11.9457i	−0.177345	+	0.545813i	0.822388	+	0.568928i	$0.192642\pi$
$480$	47.2817	+	29.0210i	2.15810	+	1.32462i
$481$	10.7689	+	7.82410i	0.491022	+	0.356748i
$482$	−9.54268	−	2.29245i	−0.434657	−	0.104418i
$483$		−	7.62250i		−	0.346836i
$484$		0			0
$485$			7.62338i			0.346160i
$486$	6.82869	−	28.4255i	0.309756	−	1.28941i
$487$	−11.5300	−	8.37704i	−0.522475	−	0.379600i	0.295061	−	0.955479i	$-0.404660\pi$
$487$	−11.5300	−	8.37704i	−0.522475	−	0.379600i	−0.817535	+	0.575878i	$0.804660\pi$
$488$	−15.8107	−	25.8257i	−0.715718	−	1.16908i
$489$	−5.47291	+	16.8439i	−0.247494	+	0.761707i
$490$	27.4746	−	23.4587i	1.24118	−	1.05976i
$491$	11.9935	+	16.5077i	0.541261	+	0.744982i	0.988794	−	0.149285i	$-0.0476973\pi$
$491$	11.9935	+	16.5077i	0.541261	+	0.744982i	−0.447533	+	0.894267i	$0.647697\pi$
$492$	−19.1779	−	3.04313i	−0.864606	−	0.137195i
$493$	−10.6380	+	3.45648i	−0.479109	+	0.155672i
$494$	−5.81622	+	9.48814i	−0.261684	+	0.426892i
$495$		0			0
$496$	8.60683	−	11.8320i	0.386458	−	0.531271i
$497$	2.23533	+	6.87964i	0.100268	+	0.308594i
$498$	2.02815	−	0.839748i	0.0908838	−	0.0376300i
$499$	19.6174	+	27.0010i	0.878195	+	1.20873i	0.976918	+	0.213617i	$0.0685244\pi$
$499$	19.6174	+	27.0010i	0.878195	+	1.20873i	−0.0987224	+	0.995115i	$0.531476\pi$
$500$	9.59540	+	60.6959i	0.429119	+	2.71440i
$501$	0.319796	+	0.103908i	0.0142874	+	0.00464227i
$502$	24.9940	−	1.96345i	1.11554	−	0.0876332i
$503$	11.9855	+	8.70794i	0.534405	+	0.388268i	0.822003	−	0.569483i	$-0.192857\pi$
$503$	11.9855	+	8.70794i	0.534405	+	0.388268i	−0.287598	+	0.957751i	$0.592857\pi$
$504$	1.56023	+	6.51120i	0.0694982	+	0.290032i
$505$	−52.8541			−2.35197
$506$		0			0
$507$		−	10.3443i		−	0.459405i
$508$	9.20936	−	9.20407i	0.408599	−	0.408364i
$509$	14.0753	−	19.3730i	0.623877	−	0.858694i	−0.373751	−	0.927529i	$-0.621928\pi$
$509$	14.0753	−	19.3730i	0.623877	−	0.858694i	0.997628	+	0.0688356i	$0.0219284\pi$
$510$	2.65712	+	33.8240i	0.117659	+	1.49775i
$511$	3.76772	−	11.5958i	0.166674	−	0.512970i
$512$	11.8477	−	19.2777i	0.523601	−	0.851964i
$513$	2.36656	−	1.71941i	0.104486	−	0.0759136i
$514$	23.1988	−	9.60534i	1.02325	−	0.423673i
$515$	15.3264	−	4.97984i	0.675361	−	0.219438i
$516$	−24.4809	−	48.0806i	−1.07771	−	2.11663i
$517$		0			0
$518$	5.10621	+	3.13010i	0.224354	+	0.137529i
$519$	−0.820985	−	2.52673i	−0.0360372	−	0.110911i
$520$	26.2843	+	22.4685i	1.15264	+	0.985311i
$521$	−16.6784	+	12.1176i	−0.730695	+	0.530881i	−0.889783	−	0.456383i	$-0.849145\pi$
$521$	−16.6784	+	12.1176i	−0.730695	+	0.530881i	0.159088	+	0.987264i	$0.449145\pi$
$522$	−12.4743	+	10.6510i	−0.545986	+	0.466180i
$523$	−21.4952	−	6.98423i	−0.939922	−	0.305399i	−0.201308	−	0.979528i	$-0.564519\pi$
$523$	−21.4952	−	6.98423i	−0.939922	−	0.305399i	−0.738614	+	0.674129i	$0.764519\pi$
$524$	6.28286	−	12.3221i	0.274468	−	0.538291i
$525$	−15.9682	+	21.9783i	−0.696909	+	0.959213i
$526$	−38.0108	−	9.13137i	−1.65735	−	0.398147i
$527$	8.94797			0.389779
$528$		0			0
$529$	−10.9502			−0.476095
$530$	−3.72610	−	0.895123i	−0.161851	−	0.0388817i
$531$	4.33824	−	5.97108i	0.188264	−	0.259123i
$532$	−2.27458	+	4.46094i	−0.0986154	+	0.193406i
$533$	−11.5107	−	3.74004i	−0.498582	−	0.161999i
$534$	−6.94997	+	5.93411i	−0.300755	+	0.256794i
$535$	−43.1005	+	31.3144i	−1.86340	+	1.35384i
$536$	9.97256	−	11.6662i	0.430749	−	0.503902i
$537$	11.0246	+	33.9301i	0.475745	+	1.46419i
$538$	12.8147	+	7.85537i	0.552479	+	0.338669i
$539$		0			0
$540$	−4.12400	−	8.09956i	−0.177469	−	0.348550i
$541$	−4.99695	+	1.62361i	−0.214836	+	0.0698044i	−0.414458	−	0.910069i	$-0.636029\pi$
$541$	−4.99695	+	1.62361i	−0.214836	+	0.0698044i	0.199622	+	0.979873i	$0.436029\pi$
$542$	−25.8036	+	10.6839i	−1.10836	+	0.458911i
$543$	−32.2113	+	23.4029i	−1.38232	+	1.00431i
$544$	13.7963	−	1.07582i	0.591510	−	0.0461252i
$545$	−2.38357	+	7.33586i	−0.102101	+	0.314234i
$546$	0.713373	+	9.08095i	0.0305296	+	0.388629i
$547$	18.4779	−	25.4327i	0.790059	−	1.08742i	−0.204042	−	0.978962i	$-0.565408\pi$
$547$	18.4779	−	25.4327i	0.790059	−	1.08742i	0.994101	−	0.108461i	$-0.0345922\pi$
$548$	8.23241	−	8.22768i	0.351671	−	0.351469i
$549$		−	27.1570i		−	1.15903i
$550$		0			0
$551$	−12.2671			−0.522596
$552$	−22.4664	+	5.38347i	−0.956234	+	0.229136i
$553$	−3.65164	−	2.65307i	−0.155284	−	0.112820i
$554$	17.6731	−	1.38835i	0.750858	−	0.0589853i
$555$	42.3273	+	13.7530i	1.79669	+	0.583781i
$556$	−2.97788	−	18.8366i	−0.126290	−	0.798851i
$557$	8.16465	+	11.2377i	0.345947	+	0.476156i	0.946167	−	0.323680i	$-0.104920\pi$
$557$	8.16465	+	11.2377i	0.345947	+	0.476156i	−0.600219	+	0.799835i	$0.704920\pi$
$558$	12.1236	−	5.01972i	0.513233	−	0.212502i
$559$	−10.3920	−	31.9834i	−0.439536	−	1.35275i
$560$	12.5818	+	9.15226i	0.531678	+	0.386754i
$561$		0			0
$562$	−17.5933	+	28.7004i	−0.742129	+	1.21065i
$563$	−19.5119	+	6.33980i	−0.822328	+	0.267191i	−0.689810	−	0.723990i	$-0.742306\pi$
$563$	−19.5119	+	6.33980i	−0.822328	+	0.267191i	−0.132518	+	0.991181i	$0.542306\pi$
$564$	15.1643	+	2.40626i	0.638533	+	0.101322i
$565$	−40.8672	−	56.2489i	−1.71930	−	2.36641i
$566$	29.8232	−	25.4640i	1.25356	−	1.07033i
$567$	2.93441	−	9.03118i	0.123234	−	0.379274i
$568$	18.6982	−	11.4472i	0.784559	−	0.480313i
$569$	−16.9333	−	12.3028i	−0.709882	−	0.515760i	0.173253	−	0.984877i	$-0.444572\pi$
$569$	−16.9333	−	12.3028i	−0.709882	−	0.515760i	−0.883136	+	0.469118i	$0.844572\pi$
$570$	−8.69155	+	36.1800i	−0.364049	+	1.51541i
$571$			6.00582i			0.251336i	0.992072	+	0.125668i	$0.0401074\pi$
$571$			6.00582i			0.251336i	−0.992072	+	0.125668i	$0.959893\pi$
$572$		0			0
$573$			39.2293i			1.63883i
$574$	−5.29499	−	1.27202i	−0.221009	−	0.0530931i
$575$	−34.7438	−	25.2429i	−1.44892	−	1.05270i
$576$	18.0890	−	9.19719i	0.753710	−	0.383216i
$577$	−14.0359	+	43.1981i	−0.584323	+	1.79836i	0.0176474	+	0.999844i	$0.494382\pi$
$577$	−14.0359	+	43.1981i	−0.584323	+	1.79836i	−0.601971	+	0.798518i	$0.705618\pi$
$578$	−10.1158	−	11.8476i	−0.420764	−	0.492794i
$579$	−0.249919	−	0.343984i	−0.0103863	−	0.0142955i
$580$	−5.97337	+	37.6444i	−0.248031	+	1.56310i
$581$	0.585483	−	0.190235i	0.0242899	−	0.00789228i
$582$	5.18909	+	3.18090i	0.215095	+	0.131853i
$583$		0			0
$584$	−36.8384	−	2.91522i	−1.52438	−	0.120633i
$585$	9.58303	+	29.4935i	0.396210	+	1.21941i
$586$	3.03716	+	7.33534i	0.125464	+	0.303020i
$587$	−2.91089	−	4.00649i	−0.120145	−	0.165366i	0.744708	−	0.667390i	$-0.232589\pi$
$587$	−2.91089	−	4.00649i	−0.120145	−	0.165366i	−0.864853	+	0.502025i	$0.832589\pi$
$588$	−4.50393	−	28.4897i	−0.185739	−	1.17490i
$589$	9.33300	+	3.03247i	0.384559	+	0.124951i
$590$	−1.34316	−	17.0978i	−0.0552969	−	0.703907i
$591$	15.9692	+	11.6023i	0.656883	+	0.477254i
$592$	5.61928	−	17.2606i	0.230951	−	0.709406i
$593$	17.6332			0.724110			0.362055	−	0.932157i	$-0.382075\pi$
$593$	17.6332			0.724110			0.362055	+	0.932157i	$0.382075\pi$
$594$		0			0
$595$			9.51502i			0.390078i
$596$	−19.6832	−	19.6945i	−0.806256	−	0.806719i
$597$	−30.5650	+	42.0691i	−1.25094	+	1.72177i
$598$	−14.3554	+	1.12772i	−0.587035	+	0.0461158i
$599$	13.9531	−	42.9433i	0.570109	−	1.75462i	−0.0821494	−	0.996620i	$-0.526178\pi$
$599$	13.9531	−	42.9433i	0.570109	−	1.75462i	0.652259	−	0.757996i	$-0.273822\pi$
$600$	76.0562	+	31.5419i	3.10498	+	1.28769i
$601$	−12.6510	+	9.19149i	−0.516045	+	0.374929i	−0.815112	−	0.579304i	$-0.803325\pi$
$601$	−12.6510	+	9.19149i	−0.516045	+	0.374929i	0.299067	+	0.954232i	$0.403325\pi$
$602$	−5.78845	−	13.9802i	−0.235920	−	0.569792i
$603$	13.0906	−	4.25338i	0.533089	−	0.173211i
$604$	13.8140	+	27.1308i	0.562084	+	1.10394i
$605$		0			0
$606$	−22.0537	+	35.9767i	−0.895869	+	1.46145i
$607$	12.9576	+	39.8795i	0.525934	+	1.61866i	0.762462	+	0.647033i	$0.223990\pi$
$607$	12.9576	+	39.8795i	0.525934	+	1.61866i	−0.236528	+	0.971625i	$0.576010\pi$
$608$	14.7545	+	3.55346i	0.598375	+	0.144112i
$609$	−8.12295	+	5.90167i	−0.329158	+	0.239148i
$610$	−40.9765	−	47.9913i	−1.65909	−	1.94311i
$611$	9.10169	+	2.95732i	0.368215	+	0.119640i
$612$	11.0562	+	5.63740i	0.446919	+	0.227878i
$613$	16.3942	−	22.5646i	0.662154	−	0.911377i	−0.337396	−	0.941363i	$-0.609546\pi$
$613$	16.3942	−	22.5646i	0.662154	−	0.911377i	0.999550	+	0.0299855i	$0.00954612\pi$
$614$	−9.20172	+	38.3037i	−0.371351	+	1.54581i
$615$	−40.4662			−1.63175
$616$		0			0
$617$	−14.7471			−0.593697			−0.296849	−	0.954925i	$-0.595936\pi$
$617$	−14.7471			−0.593697			−0.296849	+	0.954925i	$0.595936\pi$
$618$	3.00534	−	12.5102i	0.120893	−	0.503235i
$619$	3.01034	−	4.14338i	0.120996	−	0.166537i	−0.744222	−	0.667932i	$-0.767180\pi$
$619$	3.01034	−	4.14338i	0.120996	−	0.166537i	0.865218	+	0.501395i	$0.167180\pi$
$620$	13.8505	−	27.1637i	0.556248	−	1.09092i
$621$	3.59967	+	1.16960i	0.144450	+	0.0469346i
$622$	−22.4135	−	26.2505i	−0.898701	−	1.05255i
$623$	−2.07343	+	1.50644i	−0.0830703	+	0.0603541i
$624$	26.2612	−	8.51609i	1.05129	−	0.340917i
$625$	20.4571	+	62.9606i	0.818285	+	2.51842i
$626$	−6.75176	+	11.0143i	−0.269855	+	0.440221i
$627$		0			0
$628$	1.55760	−	0.793073i	0.0621550	−	0.0316471i
$629$	10.5580	−	3.43049i	0.420973	−	0.136783i
$630$	5.33783	+	12.8919i	0.212664	+	0.513626i
$631$	39.2452	−	28.5133i	1.56233	−	1.13510i	0.628255	−	0.778007i	$-0.283769\pi$
$631$	39.2452	−	28.5133i	1.56233	−	1.13510i	0.934070	−	0.357089i	$-0.116231\pi$
$632$	−5.24061	+	12.6365i	−0.208460	+	0.502654i
$633$	−10.9351	+	33.6548i	−0.434631	+	1.33766i
$634$	25.3073	−	1.98807i	1.00508	−	0.0789562i
$635$	15.9489	−	21.9517i	0.632911	−	0.871127i
$636$	−2.16403	+	2.16279i	−0.0858094	+	0.0857601i
$637$		−	17.9780i		−	0.712314i
$638$		0			0
$639$	19.6620			0.777818
$640$	18.0892	−	43.5472i	0.715038	−	1.72135i
$641$	5.84236	+	4.24472i	0.230759	+	0.167656i	0.697156	−	0.716919i	$-0.254448\pi$
$641$	5.84236	+	4.24472i	0.230759	+	0.167656i	−0.466397	+	0.884575i	$0.654448\pi$
$642$	3.33112	+	42.4038i	0.131469	+	1.67354i
$643$	11.3753	+	3.69606i	0.448598	+	0.145758i	0.524599	−	0.851349i	$-0.324215\pi$
$643$	11.3753	+	3.69606i	0.448598	+	0.145758i	−0.0760011	+	0.997108i	$0.524215\pi$
$644$	−6.39949	+	1.01169i	−0.252175	+	0.0398663i
$645$	−66.0899	−	90.9649i	−2.60229	−	3.58174i
$646$	3.55059	+	8.57537i	0.139696	+	0.337393i
$647$	−8.09476	−	24.9131i	−0.318238	−	0.979436i	−0.974401	−	0.224817i	$-0.927822\pi$
$647$	−8.09476	−	24.9131i	−0.318238	−	0.979436i	0.656163	−	0.754619i	$-0.272178\pi$
$648$	−28.6908	−	2.27046i	−1.12708	−	0.0891921i
$649$		0			0
$650$	43.7540	+	26.8211i	1.71617	+	1.05201i
$651$	7.63897	−	2.48205i	0.299395	−	0.0972793i
$652$	14.8677	+	2.35919i	0.582264	+	0.0923932i
$653$	20.1129	+	27.6830i	0.787077	+	1.08332i	0.994466	+	0.105060i	$0.0335034\pi$
$653$	20.1129	+	27.6830i	0.787077	+	1.08332i	−0.207389	+	0.978259i	$0.566497\pi$
$654$	3.99882	+	4.68338i	0.156366	+	0.183135i
$655$	8.90716	−	27.4134i	0.348032	−	1.07113i
$656$	−0.00948761	+	16.5047i	−0.000370429	+	0.644402i
$657$	−26.8116	−	19.4798i	−1.04602	−	0.759978i
$658$	4.18685	+	1.00581i	0.163220	+	0.0392106i
$659$		−	2.73052i		−	0.106366i	−0.998585	−	0.0531831i	$-0.983063\pi$
$659$		−	2.73052i		−	0.106366i	0.998585	−	0.0531831i	$-0.0169367\pi$
$660$		0			0
$661$			11.2478i			0.437488i	0.975782	+	0.218744i	$0.0701959\pi$
$661$			11.2478i			0.437488i	−0.975782	+	0.218744i	$0.929804\pi$
$662$	4.35829	−	18.1421i	0.169390	−	0.705112i
$663$	13.6593	+	9.92405i	0.530483	+	0.385418i
$664$	−0.974198	−	1.59129i	−0.0378062	−	0.0617539i
$665$	−3.22465	+	9.92445i	−0.125047	+	0.384854i
$666$	12.3805	−	10.5709i	0.479735	−	0.409613i
$667$	−9.32949	−	12.8409i	−0.361239	−	0.497203i
$668$	0.0447914	−	0.282277i	0.00173303	−	0.0109216i
$669$	−22.9973	+	7.47229i	−0.889129	+	0.288895i
$670$	16.7156	−	27.2685i	0.645779	−	1.05348i
$671$		0			0
$672$	11.4796	−	4.74534i	0.442835	−	0.183056i
$673$	6.19370	+	19.0622i	0.238749	+	0.734795i	0.996602	+	0.0823692i	$0.0262487\pi$
$673$	6.19370	+	19.0622i	0.238749	+	0.734795i	−0.757852	+	0.652426i	$0.773751\pi$
$674$	−31.1910	+	12.9145i	−1.20143	+	0.497448i
$675$	−7.92893	−	10.9132i	−0.305185	−	0.420050i
$676$	−8.68456	+	1.37294i	−0.334021	+	0.0528054i
$677$	25.8130	+	8.38714i	0.992073	+	0.322344i	0.759694	−	0.650281i	$-0.225349\pi$
$677$	25.8130	+	8.38714i	0.992073	+	0.322344i	0.232380	+	0.972625i	$0.425349\pi$
$678$	−55.3396	+	4.34732i	−2.12531	+	0.166958i
$679$	1.38092	+	1.00330i	0.0529949	+	0.0385031i
$680$	28.0444	−	6.72007i	1.07545	−	0.257703i
$681$	36.8688			1.41282
$682$		0			0
$683$		−	41.8019i		−	1.59951i	−0.600330	−	0.799753i	$-0.704964\pi$
$683$		−	41.8019i		−	1.59951i	0.600330	−	0.799753i	$-0.295036\pi$
$684$	9.62139	+	9.62693i	0.367883	+	0.368095i
$685$	14.2570	−	19.6230i	0.544731	−	0.749758i
$686$	−1.35701	−	17.2742i	−0.0518111	−	0.659534i
$687$	−10.2340	+	31.4969i	−0.390450	+	1.20168i
$688$	−37.1169	+	26.9344i	−1.41507	+	1.02687i
$689$	−1.54278	+	1.12090i	−0.0587753	+	0.0427027i
$690$	−44.4826	+	18.4178i	−1.69342	+	0.701154i
$691$	−27.3669	+	8.89205i	−1.04109	+	0.338270i	−0.779165	−	0.626819i	$-0.784356\pi$
$691$	−27.3669	+	8.89205i	−1.04109	+	0.338270i	−0.261922	+	0.965089i	$0.584356\pi$
$692$	−2.01236	+	1.02462i	−0.0764984	+	0.0389502i
$693$		0			0
$694$	−44.8777	−	27.5100i	−1.70354	−	1.04426i
$695$	−12.2811	−	37.7974i	−0.465849	−	1.43374i
$696$	23.1314	+	19.7733i	0.876792	+	0.749505i
$697$	−8.16600	+	5.93295i	−0.309309	+	0.224726i
$698$	−30.5595	+	26.0927i	−1.15669	+	0.987622i
$699$	−27.0763	−	8.79761i	−1.02412	−	0.332756i
$700$	20.5713	+	10.4891i	0.777523	+	0.396449i
$701$	−13.2737	+	18.2697i	−0.501342	+	0.690037i	−0.982429	−	0.186635i	$-0.940242\pi$
$701$	−13.2737	+	18.2697i	−0.501342	+	0.690037i	0.481088	+	0.876672i	$0.340242\pi$
$702$	−4.39787	−	1.05650i	−0.165987	−	0.0398752i
$703$	12.1749			0.459184
$704$		0			0
$705$	31.9973			1.20509
$706$	9.24278	+	2.22040i	0.347857	+	0.0835659i
$707$	−6.95602	+	9.57414i	−0.261608	+	0.360073i
$708$	−12.1986	−	6.21992i	−0.458452	−	0.233759i
$709$	−13.8303	−	4.49374i	−0.519408	−	0.168766i	0.0375687	−	0.999294i	$-0.488039\pi$
$709$	−13.8303	−	4.49374i	−0.519408	−	0.168766i	−0.556977	+	0.830528i	$0.688039\pi$
$710$	34.7464	−	29.6676i	1.30401	−	1.11340i
$711$	−9.92561	+	7.21138i	−0.372239	+	0.270448i
$712$	5.90443	+	5.04726i	0.221278	+	0.189154i
$713$	3.92368	+	12.0759i	0.146943	+	0.452244i
$714$	6.47669	+	3.97020i	0.242384	+	0.148581i
$715$		0			0
$716$	27.0229	−	13.7591i	1.00989	−	0.514200i
$717$	48.6682	−	15.8133i	1.81755	−	0.590557i
$718$	−25.9055	+	10.7260i	−0.966783	+	0.400292i
$719$	4.84126	−	3.51738i	0.180549	−	0.131176i	−0.493840	−	0.869553i	$-0.664407\pi$
$719$	4.84126	−	3.51738i	0.180549	−	0.131176i	0.674389	+	0.738376i	$0.264407\pi$
$720$	34.2274	−	24.8376i	1.27558	−	0.925644i
$721$	1.11501	−	3.43165i	0.0415252	−	0.127801i
$722$	−1.30718	−	16.6399i	−0.0486482	−	0.619271i
$723$	−9.59798	+	13.2105i	−0.356953	+	0.491303i
$724$	23.9231	+	23.9369i	0.889097	+	0.889608i
$725$			56.5690i			2.10092i
$726$		0			0
$727$	−13.7234			−0.508973			−0.254486	−	0.967076i	$-0.581906\pi$
$727$	−13.7234			−0.508973			−0.254486	+	0.967076i	$0.581906\pi$
$728$	7.52925	−	1.80418i	0.279053	−	0.0668674i
$729$	−14.6548	−	10.6473i	−0.542771	−	0.394346i
$730$	−76.7735	+	6.03110i	−2.84151	+	0.223221i
$731$	−26.6737	−	8.66679i	−0.986561	−	0.320553i
$732$	−49.7644	+	7.86725i	−1.83935	+	0.290782i
$733$	−27.3103	−	37.5894i	−1.00873	−	1.38840i	−0.919813	−	0.392358i	$-0.871660\pi$
$733$	−27.3103	−	37.5894i	−1.00873	−	1.38840i	−0.0889165	−	0.996039i	$-0.528340\pi$
$734$	5.94289	−	2.46062i	0.219356	−	0.0908233i
$735$	−18.5747	−	57.1671i	−0.685139	−	2.10864i
$736$	7.50155	+	18.1472i	0.276511	+	0.668915i
$737$		0			0
$738$	−7.73579	+	12.6196i	−0.284758	+	0.464534i
$739$	11.9623	−	3.88679i	0.440040	−	0.142978i	−0.0806139	−	0.996745i	$-0.525688\pi$
$739$	11.9623	−	3.88679i	0.440040	−	0.142978i	0.520654	+	0.853768i	$0.325688\pi$
$740$	5.92846	−	37.3613i	0.217934	−	1.37343i
$741$	10.8838	+	14.9802i	0.399825	+	0.550312i
$742$	−0.652530	+	0.557151i	−0.0239551	+	0.0204537i
$743$	2.89308	−	8.90399i	0.106137	−	0.326656i	−0.883859	−	0.467754i	$-0.845063\pi$
$743$	2.89308	−	8.90399i	0.106137	−	0.326656i	0.989996	+	0.141098i	$0.0450634\pi$
$744$	−12.7106	−	20.7620i	−0.465995	−	0.761171i
$745$	−46.9445	−	34.1072i	−1.71991	−	1.24959i
$746$	11.0331	−	45.9269i	0.403949	−	1.68150i
$747$		−	1.67331i		−	0.0612233i
$748$		0			0
$749$			11.9286i			0.435861i
$750$	99.4130	+	23.8821i	3.63005	+	0.872050i
$751$	−3.20540	−	2.32886i	−0.116967	−	0.0849813i	0.527764	−	0.849391i	$-0.323031\pi$
$751$	−3.20540	−	2.32886i	−0.116967	−	0.0849813i	−0.644731	+	0.764410i	$0.723031\pi$
$752$	0.00750203	−	13.0506i	0.000273571	−	0.475906i
$753$	12.8902	−	39.6720i	0.469746	−	1.44573i
$754$	12.3163	+	14.4247i	0.448533	+	0.525317i
$755$	37.2931	+	51.3295i	1.35723	+	1.86807i
$756$	−2.00993	−	0.318934i	−0.0731005	−	0.0115995i
$757$	−3.39413	+	1.10282i	−0.123362	+	0.0400826i	−0.370047	−	0.929013i	$-0.620658\pi$
$757$	−3.39413	+	1.10282i	−0.123362	+	0.0400826i	0.246686	+	0.969096i	$0.420658\pi$
$758$	11.1509	+	6.83549i	0.405019	+	0.248276i
$759$		0			0
$760$	31.5286	+	2.49503i	1.14366	+	0.0905042i
$761$	−15.3896	−	47.3644i	−0.557873	−	1.71696i	−0.688233	−	0.725490i	$-0.741613\pi$
$761$	−15.3896	−	47.3644i	−0.557873	−	1.71696i	0.130360	−	0.991467i	$-0.458387\pi$
$762$	−8.28735	−	20.0156i	−0.300219	−	0.725087i
$763$	1.01514	+	1.39723i	0.0367507	+	0.0505830i
$764$	32.9351	−	5.20670i	1.19155	−	0.188372i
$765$	24.5972	+	7.99210i	0.889312	+	0.288955i
$766$	−3.50076	−	44.5632i	−0.126487	−	1.61013i
$767$	−6.90468	−	5.01654i	−0.249313	−	0.181137i
$768$	−22.0939	−	30.4833i	−0.797246	−	1.09997i
$769$	−30.5772			−1.10264			−0.551321	−	0.834293i	$-0.685876\pi$
$769$	−30.5772			−1.10264			−0.551321	+	0.834293i	$0.685876\pi$
$770$		0			0
$771$		−	41.7764i		−	1.50454i
$772$	−0.255622	+	0.255475i	−0.00920003	+	0.00919475i
$773$	14.0666	−	19.3610i	0.505940	−	0.696367i	−0.477288	−	0.878747i	$-0.658380\pi$
$773$	14.0666	−	19.3610i	0.505940	−	0.696367i	0.983228	+	0.182380i	$0.0583802\pi$
$774$	−41.0021	+	3.22101i	−1.47379	+	0.115777i
$775$	13.9841	−	43.0385i	0.502322	−	1.54599i
$776$	1.98181	−	4.77869i	0.0711429	−	0.171545i
$777$	8.06186	−	5.85729i	0.289218	−	0.210129i
$778$	−2.70257	−	6.52723i	−0.0968918	−	0.234013i
$779$	−10.5281	+	3.42078i	−0.377207	+	0.122562i
$780$	51.2699	−	26.1048i	1.83576	−	0.934701i
$781$		0			0
$782$	−6.27618	+	10.2385i	−0.224436	+	0.366128i
$783$	−1.54063	−	4.74156i	−0.0550574	−	0.169449i
$784$	−23.3208	+	7.56257i	−0.832886	+	0.270092i
$785$	2.94687	−	2.14102i	0.105178	−	0.0764164i
$786$	−14.9432	−	17.5014i	−0.533007	−	0.624253i
$787$	12.8385	+	4.17150i	0.457645	+	0.148698i	0.528762	−	0.848770i	$-0.322656\pi$
$787$	12.8385	+	4.17150i	0.457645	+	0.148698i	−0.0711172	+	0.997468i	$0.522656\pi$
$788$	7.62121	−	14.9468i	0.271494	−	0.532459i
$789$	−38.2311	+	52.6206i	−1.36106	+	1.87334i
$790$	−6.65927	+	27.7203i	−0.236926	+	0.986244i
$791$	−15.5676			−0.553519
$792$		0			0
$793$	−31.4031			−1.11516
$794$	−5.87839	+	24.4698i	−0.208616	+	0.868400i
$795$	−3.74769	+	5.15825i	−0.132917	+	0.182944i
$796$	39.3759	+	20.0773i	1.39564	+	0.711621i
$797$	22.7188	+	7.38178i	0.804740	+	0.261476i	0.682368	−	0.731008i	$-0.260950\pi$
$797$	22.7188	+	7.38178i	0.804740	+	0.261476i	0.122372	+	0.992484i	$0.460950\pi$
$798$	5.40987	+	6.33599i	0.191507	+	0.224292i
$799$	6.45701	−	4.69129i	0.228433	−	0.165966i
$800$	16.3866	−	68.0395i	0.579352	−	2.40556i
$801$	2.15270	+	6.62533i	0.0760619	+	0.234095i
$802$	8.99768	−	14.6782i	0.317719	−	0.518304i
$803$		0			0
$804$	−11.5865	−	22.7559i	−0.408624	−	0.802540i
$805$	−12.8411	+	4.17234i	−0.452590	+	0.147056i
$806$	−5.80457	−	14.0192i	−0.204457	−	0.493804i
$807$	20.2323	−	14.6996i	0.712209	−	0.517450i
$808$	33.1314	+	13.7402i	1.16556	+	0.483379i
$809$	−6.23775	+	19.1978i	−0.219308	+	0.674959i	0.779512	+	0.626387i	$0.215467\pi$
$809$	−6.23775	+	19.1978i	−0.219308	+	0.674959i	−0.998820	+	0.0485722i	$0.984533\pi$
$810$	−59.7934	+	4.69720i	−2.10093	+	0.165043i
$811$	−2.22185	+	3.05811i	−0.0780197	+	0.107385i	−0.846243	−	0.532797i	$-0.821141\pi$
$811$	−2.22185	+	3.05811i	−0.0780197	+	0.107385i	0.768223	+	0.640182i	$0.221141\pi$
$812$	6.03287	+	6.03634i	0.211712	+	0.211834i
$813$			46.4672i			1.62968i
$814$		0			0
$815$	31.3715			1.09890
$816$	7.12747	−	21.8933i	0.249511	−	0.766417i
$817$	−24.8842	−	18.0795i	−0.870589	−	0.632520i
$818$	0.0651237	+	0.828999i	0.00227700	+	0.0289853i
$819$	6.60375	+	2.14569i	0.230754	+	0.0749764i
$820$	5.37086	+	33.9734i	0.187558	+	1.18640i
$821$	19.1100	+	26.3027i	0.666943	+	0.917969i	0.999686	−	0.0250487i	$-0.00797408\pi$
$821$	19.1100	+	26.3027i	0.666943	+	0.917969i	−0.332743	+	0.943018i	$0.607974\pi$
$822$	−7.40821	−	17.8923i	−0.258391	−	0.624065i
$823$	6.41677	+	19.7488i	0.223674	+	0.688399i	0.998423	+	0.0561302i	$0.0178762\pi$
$823$	6.41677	+	19.7488i	0.223674	+	0.688399i	−0.774749	+	0.632269i	$0.782124\pi$
$824$	−10.9019	−	0.862726i	−0.379785	−	0.0300545i
$825$		0			0
$826$	−3.27392	−	2.00691i	−0.113914	−	0.0698293i
$827$	10.6651	−	3.46530i	0.370862	−	0.120500i	−0.117655	−	0.993054i	$-0.537538\pi$
$827$	10.6651	−	3.46530i	0.370862	−	0.120500i	0.488518	+	0.872554i	$0.337538\pi$
$828$	−2.75991	+	17.3930i	−0.0959134	+	0.604449i
$829$	−4.00990	−	5.51915i	−0.139270	−	0.191688i	0.733685	−	0.679490i	$-0.237799\pi$
$829$	−4.00990	−	5.51915i	−0.139270	−	0.191688i	−0.872954	+	0.487802i	$0.837799\pi$
$830$	−2.52482	−	2.95704i	−0.0876378	−	0.102641i
$831$	9.11461	−	28.0519i	0.316182	−	0.973110i
$832$	−10.6352	−	20.9173i	−0.368710	−	0.725178i
$833$	−12.1299	−	8.81289i	−0.420276	−	0.305348i
$834$	−30.8523	−	7.41167i	−1.06833	−	0.256645i
$835$		−	0.595616i		−	0.0206121i
$836$		0			0
$837$			3.98829i			0.137856i
$838$	3.68352	−	15.3333i	0.127245	−	0.529678i
$839$	15.6723	+	11.3866i	0.541067	+	0.393108i	0.824481	−	0.565889i	$-0.191467\pi$
$839$	15.6723	+	11.3866i	0.541067	+	0.393108i	−0.283414	+	0.958998i	$0.591467\pi$
$840$	22.0777	−	13.5161i	0.761753	−	0.466351i
$841$	2.50079	−	7.69664i	0.0862342	−	0.265402i
$842$	−37.4705	+	31.9935i	−1.29132	+	1.10257i
$843$	32.9220	+	45.3132i	1.13389	+	1.56067i
$844$	29.7063	+	4.71377i	1.02253	+	0.162255i
$845$	−17.4263	+	5.66215i	−0.599484	+	0.194784i
$846$	6.11683	−	9.97855i	0.210301	−	0.343070i
$847$		0			0
$848$	2.10299	+	1.52976i	0.0722170	+	0.0525322i
$849$	−20.1625	−	62.0539i	−0.691977	−	2.12969i
$850$	39.5448	−	16.3733i	1.35637	−	0.561600i
$851$	9.25933	+	12.7444i	0.317406	+	0.436872i
$852$	−5.69600	−	36.0301i	−0.195142	−	1.23437i
$853$	−10.6051	−	3.44582i	−0.363113	−	0.117983i	0.121777	−	0.992557i	$-0.461141\pi$
$853$	−10.6051	−	3.44582i	−0.363113	−	0.117983i	−0.484891	+	0.874575i	$0.661141\pi$
$854$	−14.0861	+	1.10657i	−0.482017	+	0.0378659i
$855$	22.9470	+	16.6720i	0.784772	+	0.570171i
$856$	35.1581	−	8.42468i	1.20168	−	0.287949i
$857$	30.4078			1.03871			0.519355	−	0.854558i	$-0.326172\pi$
$857$	30.4078			1.03871			0.519355	+	0.854558i	$0.326172\pi$
$858$		0			0
$859$			27.7908i			0.948210i	0.880468	+	0.474105i	$0.157228\pi$
$859$			27.7908i			0.948210i	−0.880468	+	0.474105i	$0.842772\pi$
$860$	−67.5980	+	67.5592i	−2.30507	+	2.30375i
$861$	−5.32567	+	7.33016i	−0.181498	+	0.249811i
$862$	−2.75390	−	35.0560i	−0.0937982	−	1.19401i
$863$	0.0685484	−	0.210970i	0.00233341	−	0.00718151i	−0.949883	−	0.312606i	$-0.898798\pi$
$863$	0.0685484	−	0.210970i	0.00233341	−	0.00718151i	0.952216	+	0.305424i	$0.0987982\pi$
$864$	0.479513	+	6.14928i	0.0163134	+	0.209203i
$865$	−3.80724	+	2.76612i	−0.129450	+	0.0940508i
$866$	−0.715652	+	0.296312i	−0.0243188	+	0.0100691i
$867$	−24.6516	+	8.00978i	−0.837211	+	0.272026i
$868$	−3.09769	−	6.08388i	−0.105142	−	0.206500i
$869$		0			0
$870$	54.0673	+	33.1432i	1.83305	+	1.12366i
$871$	−4.91842	−	15.1373i	−0.166654	−	0.512909i
$872$	3.40120	−	3.97882i	0.115179	−	0.134740i
$873$	3.75351	−	2.72709i	0.127037	−	0.0922979i
$874$	−10.0161	+	8.55205i	−0.338799	+	0.289277i
$875$	27.2697	+	8.86048i	0.921886	+	0.299539i
$876$	−27.9290	+	54.7747i	−0.943632	+	1.85067i
$877$	9.13829	−	12.5778i	0.308578	−	0.424721i	−0.626359	−	0.779535i	$-0.715456\pi$
$877$	9.13829	−	12.5778i	0.308578	−	0.424721i	0.934937	+	0.354813i	$0.115456\pi$
$878$	37.8574	+	9.09451i	1.27762	+	0.306925i
$879$	13.2095			0.445545
$880$		0			0
$881$	21.4338			0.722125			0.361062	−	0.932542i	$-0.382414\pi$
$881$	21.4338			0.722125			0.361062	+	0.932542i	$0.382414\pi$
$882$	−21.3787	−	5.13583i	−0.719860	−	0.172932i
$883$	8.38770	−	11.5447i	0.282269	−	0.388509i	−0.644215	−	0.764844i	$-0.722816\pi$
$883$	8.38770	−	11.5447i	0.282269	−	0.388509i	0.926484	+	0.376335i	$0.122816\pi$
$884$	6.51883	−	12.7848i	0.219252	−	0.430001i
$885$	−27.1388	−	8.81793i	−0.912260	−	0.296411i
$886$	−8.66273	+	7.39652i	−0.291030	+	0.248491i
$887$	19.1016	−	13.8781i	0.641369	−	0.465982i	−0.218951	−	0.975736i	$-0.570264\pi$
$887$	19.1016	−	13.8781i	0.641369	−	0.465982i	0.860320	+	0.509754i	$0.170264\pi$
$888$	−22.9574	−	19.6246i	−0.770401	−	0.658559i
$889$	−1.87740	−	5.77805i	−0.0629660	−	0.193789i
$890$	13.8010	+	8.46000i	0.462611	+	0.283580i
$891$		0			0
$892$	9.32569	+	18.3157i	0.312247	+	0.613255i
$893$	8.32474	−	2.70487i	0.278577	−	0.0905151i
$894$	−42.8040	+	17.7228i	−1.43158	+	0.592738i
$895$	51.1253	−	37.1447i	1.70893	−	1.24161i
$896$	−5.50759	−	9.00790i	−0.183996	−	0.300933i
$897$	−7.40355	+	22.7858i	−0.247197	+	0.760795i
$898$	3.74027	+	47.6121i	0.124814	+	1.58883i
$899$	9.83079	−	13.5309i	0.327875	−	0.451282i
$900$	44.3939	−	44.3684i	1.47980	−	1.47895i
$901$			1.59039i			0.0529837i
$902$		0			0
$903$	−25.1756			−0.837792
$904$	10.9947	+	45.8835i	0.365680	+	1.52606i
$905$	57.0568	+	41.4542i	1.89663	+	1.37798i
$906$	50.4998	−	3.96712i	1.67774	−	0.131799i
$907$	43.0717	+	13.9948i	1.43017	+	0.464691i	0.918819	−	0.394680i	$-0.129145\pi$
$907$	43.0717	+	13.9948i	1.43017	+	0.464691i	0.511353	+	0.859371i	$0.329145\pi$
$908$	−4.89340	−	30.9533i	−0.162393	−	1.02722i
$909$	18.9073	+	26.0237i	0.627116	+	0.863151i
$910$	14.9076	−	6.17242i	0.494182	−	0.204614i
$911$	−6.93864	−	21.3549i	−0.229887	−	0.707520i	−0.997759	−	0.0669163i	$-0.978684\pi$
$911$	−6.93864	−	21.3549i	−0.229887	−	0.707520i	0.767871	−	0.640604i	$-0.221316\pi$
$912$	14.8538	−	20.4198i	0.491859	−	0.676168i
$913$		0			0
$914$	−2.83237	+	4.62051i	−0.0936864	+	0.152833i
$915$	−99.8567	+	32.4454i	−3.30116	+	1.07261i
$916$	27.8016	+	4.41153i	0.918590	+	0.145761i
$917$	−3.79350	−	5.22130i	−0.125272	−	0.172423i
$918$	−2.86869	+	2.44938i	−0.0946807	+	0.0808414i
$919$	−12.8344	+	39.5001i	−0.423367	+	1.30299i	0.481182	+	0.876621i	$0.340207\pi$
$919$	−12.8344	+	39.5001i	−0.423367	+	1.30299i	−0.904549	+	0.426369i	$0.859793\pi$
$920$	21.3666	+	34.9009i	0.704437	+	1.15065i
$921$	53.0260	+	38.5256i	1.74727	+	1.26946i
$922$	−5.23191	+	21.7787i	−0.172304	+	0.717243i
$923$		−	22.7363i		−	0.748373i
$924$		0			0
$925$		−	56.1436i		−	1.84599i
$926$	−41.8207	−	10.0466i	−1.37431	−	0.330153i
$927$	−7.93458	−	5.76481i	−0.260606	−	0.189341i
$928$	13.5306	−	22.0444i	0.444164	−	0.723642i
$929$	−11.5262	+	35.4741i	−0.378164	+	1.16387i	0.563156	+	0.826351i	$0.309587\pi$
$929$	−11.5262	+	35.4741i	−0.378164	+	1.16387i	−0.941319	+	0.337517i	$0.890413\pi$
$930$	−32.9421	−	38.5814i	−1.08021	−	1.26513i
$931$	−9.66515	−	13.3029i	−0.316763	−	0.435986i
$932$	−3.79237	+	23.8996i	−0.124223	+	0.782857i
$933$	−54.6201	+	17.7471i	−1.78818	+	0.581015i
$934$	24.3330	+	14.9161i	0.796199	+	0.488069i
$935$		0			0
$936$	1.66020	−	20.9792i	0.0542653	−	0.685726i
$937$	−4.07584	−	12.5441i	−0.133152	−	0.409799i	0.862146	−	0.506660i	$-0.169120\pi$
$937$	−4.07584	−	12.5441i	−0.133152	−	0.409799i	−0.995298	+	0.0968606i	$0.969120\pi$
$938$	−2.73960	−	6.61667i	−0.0894511	−	0.216042i
$939$	12.6344	+	17.3898i	0.412309	+	0.567495i
$940$	−4.24684	−	26.8634i	−0.138517	−	0.876189i
$941$	23.4640	+	7.62393i	0.764906	+	0.248533i	0.665383	−	0.746502i	$-0.268268\pi$
$941$	23.4640	+	7.62393i	0.764906	+	0.248533i	0.0995231	+	0.995035i	$0.468268\pi$
$942$	−0.227755	−	2.89923i	−0.00742067	−	0.0944620i
$943$	−11.5877	−	8.41894i	−0.377347	−	0.274159i
$944$	−3.60289	+	11.0669i	−0.117264	+	0.360197i
$945$	−4.24104			−0.137961
$946$		0			0
$947$		−	38.8667i		−	1.26300i	−0.775376	−	0.631500i	$-0.782440\pi$
$947$		−	38.8667i		−	1.26300i	0.775376	−	0.631500i	$-0.217560\pi$
$948$	16.0901	+	16.0993i	0.522581	+	0.522881i
$949$	−22.5255	+	31.0037i	−0.731209	+	1.00642i
$950$	46.7953	−	3.67610i	1.51824	−	0.119269i
$951$	13.0518	−	40.1693i	0.423234	−	1.30258i
$952$	2.47357	−	5.96446i	0.0801690	−	0.193309i
$953$	42.5387	−	30.9061i	1.37796	−	1.00115i	0.380895	−	0.924618i	$-0.375616\pi$
$953$	42.5387	−	30.9061i	1.37796	−	1.00115i	0.997067	−	0.0765301i	$-0.0243841\pi$
$954$	0.892195	+	2.15482i	0.0288859	+	0.0697650i
$955$	66.0871	−	21.4730i	2.13853	−	0.694850i
$956$	−19.7355	−	38.7607i	−0.638292	−	1.25361i
$957$		0			0
$958$	9.28340	−	15.1442i	0.299933	−	0.489288i
$959$	−1.67824	−	5.16510i	−0.0541933	−	0.166790i
$960$	−55.4298	−	55.5255i	−1.78899	−	1.79208i
$961$	14.2552	−	10.3570i	0.459846	−	0.334098i
$962$	−12.2237	−	14.3163i	−0.394107	−	0.461575i
$963$	30.8364	+	10.0194i	0.993690	+	0.322869i
$964$	12.3648	+	6.30464i	0.398243	+	0.203059i
$965$	−0.442689	+	0.609309i	−0.0142506	+	0.0196143i
$966$	−2.51801	+	10.4816i	−0.0810157	+	0.337241i
$967$	2.98370			0.0959493			0.0479746	−	0.998849i	$-0.484723\pi$
$967$	2.98370			0.0959493			0.0479746	+	0.998849i	$0.484723\pi$
$968$		0			0
$969$	15.4425			0.496086
$970$	2.51830	−	10.4828i	0.0808578	−	0.336584i
$971$	−8.84279	+	12.1711i	−0.283779	+	0.390588i	−0.926981	−	0.375108i	$-0.877605\pi$
$971$	−8.84279	+	12.1711i	−0.283779	+	0.390588i	0.643202	+	0.765696i	$0.277605\pi$
$972$	−18.7801	+	36.8319i	−0.602373	+	1.18138i
$973$	−8.46302	−	2.74980i	−0.271312	−	0.0881546i
$974$	13.0876	+	15.3280i	0.419352	+	0.491141i
$975$	69.0803	−	50.1898i	2.21234	−	1.60736i
$976$	13.2099	+	40.7357i	0.422840	+	1.30392i
$977$	−3.53247	−	10.8718i	−0.113014	−	0.347820i	0.878514	−	0.477717i	$-0.158536\pi$
$977$	−3.53247	−	10.8718i	−0.113014	−	0.347820i	−0.991528	+	0.129896i	$0.958536\pi$
$978$	13.0899	−	21.3540i	0.418570	−	0.682824i
$979$		0			0
$980$	−45.5294	+	23.1819i	−1.45438	+	0.740519i
$981$	4.46462	−	1.45064i	0.142544	−	0.0463154i
$982$	−11.0391	−	26.6615i	−0.352271	−	0.850804i
$983$	−47.0065	+	34.1522i	−1.49927	+	1.08929i	−0.528606	+	0.848868i	$0.677285\pi$
$983$	−47.0065	+	34.1522i	−1.49927	+	1.08929i	−0.970669	+	0.240419i	$0.922715\pi$
$984$	25.3661	+	10.5198i	0.808641	+	0.335359i
$985$	10.8045	−	33.2529i	0.344261	−	1.05953i
$986$	15.7700	−	1.23884i	0.502218	−	0.0394528i
$987$	4.21111	−	5.79610i	0.134041	−	0.184492i
$988$	11.1321	−	11.1257i	0.354160	−	0.353957i
$989$		−	39.7982i		−	1.26551i
$990$		0			0
$991$	30.2307			0.960311			0.480156	−	0.877183i	$-0.340580\pi$
$991$	30.2307			0.960311			0.480156	+	0.877183i	$0.340580\pi$
$992$	−15.7437	+	13.4269i	−0.499864	+	0.426304i
$993$	−25.1151	−	18.2472i	−0.797004	−	0.579058i
$994$	−0.801169	−	10.1985i	−0.0254115	−	0.323478i
$995$	87.6014	+	28.4634i	2.77715	+	0.902351i
$996$	−3.06630	+	0.484751i	−0.0971594	+	0.0153599i
$997$	−7.87606	−	10.8405i	−0.249437	−	0.343321i	0.665877	−	0.746062i	$-0.268058\pi$
$997$	−7.87606	−	10.8405i	−0.249437	−	0.343321i	−0.915314	+	0.402741i	$0.868058\pi$
$998$	−18.0562	−	43.6093i	−0.571559	−	1.38043i
$999$	1.52904	+	4.70590i	0.0483767	+	0.148888i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.h.269.1		40
8.5	even	2	inner	968.2.o.h.269.7		40
11.2	odd	10		968.2.o.g.493.4		40
11.3	even	5		968.2.c.d.485.4		10
11.4	even	5	inner	968.2.o.h.245.5		40
11.5	even	5	inner	968.2.o.h.565.9		40
11.6	odd	10		968.2.o.g.565.2		40
11.7	odd	10		968.2.o.g.245.6		40
11.8	odd	10		88.2.c.a.45.7	✓	10
11.9	even	5	inner	968.2.o.h.493.7		40
11.10	odd	2		968.2.o.g.269.10		40
33.8	even	10		792.2.f.g.397.4		10
44.3	odd	10		3872.2.c.f.1937.9		10
44.19	even	10		352.2.c.a.177.9		10
88.3	odd	10		3872.2.c.f.1937.2		10
88.5	even	10	inner	968.2.o.h.565.5		40
88.13	odd	10		968.2.o.g.493.10		40
88.19	even	10		352.2.c.a.177.2		10
88.21	odd	2		968.2.o.g.269.4		40
88.29	odd	10		968.2.o.g.245.2		40
88.37	even	10	inner	968.2.o.h.245.9		40
88.53	even	10	inner	968.2.o.h.493.1		40
88.61	odd	10		968.2.o.g.565.6		40
88.69	even	10		968.2.c.d.485.3		10
88.85	odd	10		88.2.c.a.45.8	yes	10
132.107	odd	10		3168.2.f.g.1585.1		10
176.19	even	20		2816.2.a.q.1.1		5
176.85	odd	20		2816.2.a.o.1.1		5
176.107	even	20		2816.2.a.p.1.5		5
176.173	odd	20		2816.2.a.r.1.5		5
264.107	odd	10		3168.2.f.g.1585.10		10
264.173	even	10		792.2.f.g.397.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.7	✓	10	11.8	odd	10
88.2.c.a.45.8	yes	10	88.85	odd	10
352.2.c.a.177.2		10	88.19	even	10
352.2.c.a.177.9		10	44.19	even	10
792.2.f.g.397.3		10	264.173	even	10
792.2.f.g.397.4		10	33.8	even	10
968.2.c.d.485.3		10	88.69	even	10
968.2.c.d.485.4		10	11.3	even	5
968.2.o.g.245.2		40	88.29	odd	10
968.2.o.g.245.6		40	11.7	odd	10
968.2.o.g.269.4		40	88.21	odd	2
968.2.o.g.269.10		40	11.10	odd	2
968.2.o.g.493.4		40	11.2	odd	10
968.2.o.g.493.10		40	88.13	odd	10
968.2.o.g.565.2		40	11.6	odd	10
968.2.o.g.565.6		40	88.61	odd	10
968.2.o.h.245.5		40	11.4	even	5	inner
968.2.o.h.245.9		40	88.37	even	10	inner
968.2.o.h.269.1		40	1.1	even	1	trivial
968.2.o.h.269.7		40	8.5	even	2	inner
968.2.o.h.493.1		40	88.53	even	10	inner
968.2.o.h.493.7		40	11.9	even	5	inner
968.2.o.h.565.5		40	88.5	even	10	inner
968.2.o.h.565.9		40	11.5	even	5	inner
2816.2.a.o.1.1		5	176.85	odd	20
2816.2.a.p.1.5		5	176.107	even	20
2816.2.a.q.1.1		5	176.19	even	20
2816.2.a.r.1.5		5	176.173	odd	20
3168.2.f.g.1585.1		10	132.107	odd	10
3168.2.f.g.1585.10		10	264.107	odd	10
3872.2.c.f.1937.2		10	88.3	odd	10
3872.2.c.f.1937.9		10	44.3	odd	10

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	968.2.o.h.269.1

Level	$968$
Weight	$2$
Character	968.269
Analytic conductor	$7.730$
Analytic rank	$0$
Dimension	$40$
Inner twists	$8$