LMFDB - Embedded newform 800.2.bb.b.643.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(107,800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("800.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bb (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			643.22
Character	$\chi$	$=$	800.643
Dual form			800.2.bb.b.107.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36334 + 0.375898i) q^{2} +(-1.22690 + 0.508197i) q^{3} +(1.71740 + 1.02496i) q^{4} +(-1.86371 + 0.231658i) q^{6} -0.810621 q^{7} +(1.95613 + 2.04293i) q^{8} +(-0.874309 + 0.874309i) q^{9} +(0.353731 + 0.853982i) q^{11} +(-2.62795 - 0.384736i) q^{12} +(-3.86563 + 1.60120i) q^{13} +(-1.10515 - 0.304711i) q^{14} +(1.89893 + 3.52052i) q^{16} +(4.37679 + 4.37679i) q^{17} +(-1.52063 + 0.863331i) q^{18} +(0.285895 - 0.690211i) q^{19} +(0.994548 - 0.411955i) q^{21} +(0.161246 + 1.29724i) q^{22} -5.36098 q^{23} +(-3.43818 - 1.51237i) q^{24} +(-5.87207 + 0.729895i) q^{26} +(2.15296 - 5.19770i) q^{27} +(-1.39216 - 0.830850i) q^{28} +(-1.48464 + 3.58424i) q^{29} +9.06865i q^{31} +(1.26554 + 5.51348i) q^{32} +(-0.867982 - 0.867982i) q^{33} +(4.32183 + 7.61229i) q^{34} +(-2.39767 + 0.605412i) q^{36} +(0.870467 + 0.360559i) q^{37} +(0.649221 - 0.833526i) q^{38} +(3.92901 - 3.92901i) q^{39} +(0.572180 + 0.572180i) q^{41} +(1.51076 - 0.187787i) q^{42} +(4.42382 - 10.6801i) q^{43} +(-0.267796 + 1.82919i) q^{44} +(-7.30885 - 2.01518i) q^{46} +(1.59734 - 1.59734i) q^{47} +(-4.11891 - 3.35428i) q^{48} -6.34289 q^{49} +(-7.59414 - 3.14560i) q^{51} +(-8.28000 - 1.21220i) q^{52} +(4.62712 + 1.91662i) q^{53} +(4.88902 - 6.27695i) q^{54} +(-1.58568 - 1.65604i) q^{56} +0.992109i q^{57} +(-3.37138 + 4.32846i) q^{58} +(0.996806 + 2.40650i) q^{59} +(5.76047 + 2.38607i) q^{61} +(-3.40889 + 12.3637i) q^{62} +(0.708734 - 0.708734i) q^{63} +(-0.347145 + 7.99246i) q^{64} +(-0.857084 - 1.50963i) q^{66} +(-2.34497 - 5.66126i) q^{67} +(3.03069 + 12.0027i) q^{68} +(6.57737 - 2.72444i) q^{69} +(-1.22326 - 1.22326i) q^{71} +(-3.49641 - 0.0758959i) q^{72} +11.4586i q^{73} +(1.05121 + 0.818772i) q^{74} +(1.19843 - 0.892340i) q^{76} +(-0.286742 - 0.692256i) q^{77} +(6.83349 - 3.87967i) q^{78} -17.0418i q^{79} +3.76178i q^{81} +(0.564996 + 0.995159i) q^{82} +(-3.28569 - 7.93236i) q^{83} +(2.13027 + 0.311875i) q^{84} +(10.0458 - 12.8977i) q^{86} -5.15198i q^{87} +(-1.05269 + 2.39314i) q^{88} +(7.65721 + 7.65721i) q^{89} +(3.13356 - 1.29796i) q^{91} +(-9.20696 - 5.49477i) q^{92} +(-4.60866 - 11.1263i) q^{93} +(2.77815 - 1.57728i) q^{94} +(-4.35462 - 6.12132i) q^{96} +(2.02530 - 2.02530i) q^{97} +(-8.64753 - 2.38428i) q^{98} +(-1.05591 - 0.437374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{19} - 8 q^{21} + 20 q^{22} + 8 q^{23} + 32 q^{24} - 8 q^{26} - 8 q^{27}+ \cdots - 16 q^{98}+O(q^{100}) $ 88 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 + 4 * q^13 - 16 * q^14 - 8 * q^16 + 12 * q^18 - 16 * q^19 - 8 * q^21 + 20 * q^22 + 8 * q^23 + 32 * q^24 - 8 * q^26 - 8 * q^27 + 20 * q^28 - 16 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 4 * q^37 + 4 * q^38 - 8 * q^41 + 68 * q^42 - 28 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^47 + 88 * q^48 + 40 * q^49 + 8 * q^51 - 48 * q^52 + 4 * q^53 + 56 * q^54 + 40 * q^56 + 36 * q^58 - 40 * q^61 + 32 * q^62 + 56 * q^63 - 48 * q^64 + 72 * q^66 + 28 * q^67 - 8 * q^68 - 24 * q^69 + 24 * q^71 - 88 * q^72 + 56 * q^76 + 32 * q^77 - 112 * q^78 - 68 * q^82 - 36 * q^83 - 56 * q^84 + 24 * q^86 + 24 * q^88 - 8 * q^91 - 92 * q^92 - 8 * q^93 + 32 * q^94 + 24 * q^96 + 8 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36334	+	0.375898i	0.964028	+	0.265800i
$2$	1.36334	+	0.375898i	0.964028	+	0.265800i
$3$	−1.22690	+	0.508197i	−0.708349	+	0.293408i	−0.707621	−	0.706592i	$-0.750232\pi$
$3$	−1.22690	+	0.508197i	−0.708349	+	0.293408i	−0.000727832		1.00000i	$0.500232\pi$
$4$	1.71740	+	1.02496i	0.858701	+	0.512478i
$5$		0			0
$5$		0			0
$6$	−1.86371	+	0.231658i	−0.760856	+	0.0945741i
$7$	−0.810621			−0.306386			−0.153193	−	0.988196i	$-0.548956\pi$
$7$	−0.810621			−0.306386			−0.153193	+	0.988196i	$0.548956\pi$
$8$	1.95613	+	2.04293i	0.691595	+	0.722286i
$9$	−0.874309	+	0.874309i	−0.291436	+	0.291436i
$10$		0			0
$11$	0.353731	+	0.853982i	0.106654	+	0.257485i	0.968192	−	0.250207i	$-0.0804987\pi$
$11$	0.353731	+	0.853982i	0.106654	+	0.257485i	−0.861538	+	0.507692i	$0.830499\pi$
$12$	−2.62795	−	0.384736i	−0.758625	−	0.111064i
$13$	−3.86563	+	1.60120i	−1.07213	+	0.444092i	−0.847743	−	0.530407i	$-0.822039\pi$
$13$	−3.86563	+	1.60120i	−1.07213	+	0.444092i	−0.224391	+	0.974499i	$0.572039\pi$
$14$	−1.10515	−	0.304711i	−0.295365	−	0.0814374i
$15$		0			0
$16$	1.89893	+	3.52052i	0.474733	+	0.880130i
$17$	4.37679	+	4.37679i	1.06153	+	1.06153i	0.997979	+	0.0635485i	$0.0202418\pi$
$17$	4.37679	+	4.37679i	1.06153	+	1.06153i	0.0635485	+	0.997979i	$0.479758\pi$
$18$	−1.52063	+	0.863331i	−0.358417	+	0.203489i
$19$	0.285895	−	0.690211i	0.0655888	−	0.158345i	−0.887687	−	0.460448i	$-0.847689\pi$
$19$	0.285895	−	0.690211i	0.0655888	−	0.158345i	0.953275	+	0.302103i	$0.0976887\pi$
$20$		0			0
$21$	0.994548	−	0.411955i	0.217028	−	0.0898960i
$22$	0.161246	+	1.29724i	0.0343777	+	0.276572i
$23$	−5.36098			−1.11784			−0.558921	−	0.829221i	$-0.688785\pi$
$23$	−5.36098			−1.11784			−0.558921	+	0.829221i	$0.688785\pi$
$24$	−3.43818	−	1.51237i	−0.701815	−	0.308711i
$25$		0			0
$26$	−5.87207	+	0.729895i	−1.15161	+	0.143144i
$27$	2.15296	−	5.19770i	0.414337	−	1.00030i
$28$	−1.39216	−	0.830850i	−0.263094	−	0.157016i
$29$	−1.48464	+	3.58424i	−0.275691	+	0.665576i	−0.999707	−	0.0242069i	$-0.992294\pi$
$29$	−1.48464	+	3.58424i	−0.275691	+	0.665576i	0.724016	+	0.689783i	$0.242294\pi$
$30$		0			0
$31$			9.06865i			1.62878i	0.580319	+	0.814389i	$0.302928\pi$
$31$			9.06865i			1.62878i	−0.580319	+	0.814389i	$0.697072\pi$
$32$	1.26554	+	5.51348i	0.223718	+	0.974654i
$33$	−0.867982	−	0.867982i	−0.151096	−	0.151096i
$34$	4.32183	+	7.61229i	0.741188	+	1.30550i
$35$		0			0
$36$	−2.39767	+	0.605412i	−0.399611	+	0.100902i
$37$	0.870467	+	0.360559i	0.143104	+	0.0592756i	0.453086	−	0.891467i	$-0.350323\pi$
$37$	0.870467	+	0.360559i	0.143104	+	0.0592756i	−0.309982	+	0.950742i	$0.600323\pi$
$38$	0.649221	−	0.833526i	0.105318	−	0.135216i
$39$	3.92901	−	3.92901i	0.629145	−	0.629145i
$40$		0			0
$41$	0.572180	+	0.572180i	0.0893596	+	0.0893596i	0.750374	−	0.661014i	$-0.229874\pi$
$41$	0.572180	+	0.572180i	0.0893596	+	0.0893596i	−0.661014	+	0.750374i	$0.729874\pi$
$42$	1.51076	−	0.187787i	0.233116	−	0.0289762i
$43$	4.42382	−	10.6801i	0.674627	−	1.62869i	−0.0990273	−	0.995085i	$-0.531573\pi$
$43$	4.42382	−	10.6801i	0.674627	−	1.62869i	0.773654	−	0.633608i	$-0.218427\pi$
$44$	−0.267796	+	1.82919i	−0.0403717	+	0.275760i
$45$		0			0
$46$	−7.30885	−	2.01518i	−1.07763	−	0.297123i
$47$	1.59734	−	1.59734i	0.232995	−	0.232995i	−0.580946	−	0.813942i	$-0.697317\pi$
$47$	1.59734	−	1.59734i	0.232995	−	0.232995i	0.813942	+	0.580946i	$0.197317\pi$
$48$	−4.11891	−	3.35428i	−0.594514	−	0.484149i
$49$	−6.34289			−0.906128
$50$		0			0
$51$	−7.59414	−	3.14560i	−1.06339	−	0.440471i
$52$	−8.28000	−	1.21220i	−1.14823	−	0.168102i
$53$	4.62712	+	1.91662i	0.635584	+	0.263268i	0.677124	−	0.735869i	$-0.263226\pi$
$53$	4.62712	+	1.91662i	0.635584	+	0.263268i	−0.0415393	+	0.999137i	$0.513226\pi$
$54$	4.88902	−	6.27695i	0.665312	−	0.854184i
$55$		0			0
$56$	−1.58568	−	1.65604i	−0.211895	−	0.221298i
$57$			0.992109i			0.131408i
$58$	−3.37138	+	4.32846i	−0.442684	+	0.568355i
$59$	0.996806	+	2.40650i	0.129773	+	0.313300i	0.975389	−	0.220492i	$-0.0707664\pi$
$59$	0.996806	+	2.40650i	0.129773	+	0.313300i	−0.845616	+	0.533792i	$0.820766\pi$
$60$		0			0
$61$	5.76047	+	2.38607i	0.737553	+	0.305504i	0.719652	−	0.694335i	$-0.244301\pi$
$61$	5.76047	+	2.38607i	0.737553	+	0.305504i	0.0179014	+	0.999840i	$0.494301\pi$
$62$	−3.40889	+	12.3637i	−0.432929	+	1.57019i
$63$	0.708734	−	0.708734i	0.0892920	−	0.0892920i
$64$	−0.347145	+	7.99246i	−0.0433931	+	0.999058i
$65$		0			0
$66$	−0.857084	−	1.50963i	−0.105500	−	0.185823i
$67$	−2.34497	−	5.66126i	−0.286484	−	0.691633i	0.713475	−	0.700680i	$-0.247120\pi$
$67$	−2.34497	−	5.66126i	−0.286484	−	0.691633i	−0.999959	+	0.00904731i	$0.997120\pi$
$68$	3.03069	+	12.0027i	0.367525	+	1.45554i
$69$	6.57737	−	2.72444i	0.791822	−	0.327984i
$70$		0			0
$71$	−1.22326	−	1.22326i	−0.145174	−	0.145174i	0.630784	−	0.775958i	$-0.282733\pi$
$71$	−1.22326	−	1.22326i	−0.145174	−	0.145174i	−0.775958	+	0.630784i	$0.782733\pi$
$72$	−3.49641	−	0.0758959i	−0.412056	−	0.00894442i
$73$			11.4586i			1.34113i	0.741851	+	0.670565i	$0.233948\pi$
$73$			11.4586i			1.34113i	−0.741851	+	0.670565i	$0.766052\pi$
$74$	1.05121	+	0.818772i	0.122201	+	0.0951804i
$75$		0			0
$76$	1.19843	−	0.892340i	0.137470	−	0.102358i
$77$	−0.286742	−	0.692256i	−0.0326773	−	0.0788899i
$78$	6.83349	−	3.87967i	0.773740	−	0.439287i
$79$		−	17.0418i		−	1.91736i	−0.284493	−	0.958678i	$-0.591825\pi$
$79$		−	17.0418i		−	1.91736i	0.284493	−	0.958678i	$-0.408175\pi$
$80$		0			0
$81$			3.76178i			0.417976i
$82$	0.564996	+	0.995159i	0.0623933	+	0.109897i
$83$	−3.28569	−	7.93236i	−0.360651	−	0.870689i	−0.995205	−	0.0978105i	$-0.968816\pi$
$83$	−3.28569	−	7.93236i	−0.360651	−	0.870689i	0.634554	−	0.772879i	$-0.281184\pi$
$84$	2.13027	+	0.311875i	0.232432	+	0.0340283i
$85$		0			0
$86$	10.0458	−	12.8977i	1.08327	−	1.39079i
$87$		−	5.15198i		−	0.552350i
$88$	−1.05269	+	2.39314i	−0.112217	+	0.255110i
$89$	7.65721	+	7.65721i	0.811663	+	0.811663i	0.984883	−	0.173220i	$-0.0554172\pi$
$89$	7.65721	+	7.65721i	0.811663	+	0.811663i	−0.173220	+	0.984883i	$0.555417\pi$
$90$		0			0
$91$	3.13356	−	1.29796i	0.328487	−	0.136064i
$92$	−9.20696	−	5.49477i	−0.959892	−	0.572869i
$93$	−4.60866	−	11.1263i	−0.477896	−	1.15374i
$94$	2.77815	−	1.57728i	0.286544	−	0.162684i
$95$		0			0
$96$	−4.35462	−	6.12132i	−0.444441	−	0.624755i
$97$	2.02530	−	2.02530i	0.205638	−	0.205638i	−0.596772	−	0.802411i	$-0.703550\pi$
$97$	2.02530	−	2.02530i	0.205638	−	0.205638i	0.802411	+	0.596772i	$0.203550\pi$
$98$	−8.64753	−	2.38428i	−0.873533	−	0.240849i
$99$	−1.05591	−	0.437374i	−0.106123	−	0.0439578i
$100$		0			0
$101$	0.295173	+	0.712610i	0.0293708	+	0.0709073i	0.937884	−	0.346948i	$-0.112782\pi$
$101$	0.295173	+	0.712610i	0.0293708	+	0.0709073i	−0.908514	+	0.417855i	$0.862782\pi$
$102$	−9.17098	−	7.14314i	−0.908063	−	0.707277i
$103$			9.73185i			0.958908i	0.877567	+	0.479454i	$0.159165\pi$
$103$			9.73185i			0.958908i	−0.877567	+	0.479454i	$0.840835\pi$
$104$	−10.8328	−	4.76508i	−1.06224	−	0.467255i
$105$		0			0
$106$	5.58790	+	4.35233i	0.542745	+	0.422736i
$107$	6.55453	+	2.71497i	0.633650	+	0.262466i	0.676303	−	0.736624i	$-0.263581\pi$
$107$	6.55453	+	2.71497i	0.633650	+	0.262466i	−0.0426531	+	0.999090i	$0.513581\pi$
$108$	9.02490	−	6.71985i	0.868421	−	0.646618i
$109$	10.2140	+	4.23080i	0.978328	+	0.405237i	0.813806	−	0.581137i	$-0.197392\pi$
$109$	10.2140	+	4.23080i	0.978328	+	0.405237i	0.164522	+	0.986373i	$0.447392\pi$
$110$		0			0
$111$	−1.25121			−0.118759
$112$	−1.53932	−	2.85381i	−0.145452	−	0.269659i
$113$	14.5463	−	14.5463i	1.36841	−	1.36841i	0.505690	−	0.862715i	$-0.331238\pi$
$113$	14.5463	−	14.5463i	1.36841	−	1.36841i	0.862715	−	0.505690i	$-0.168762\pi$
$114$	−0.372932	+	1.35258i	−0.0349283	+	0.126681i
$115$		0			0
$116$	−6.22340	+	4.63388i	−0.577828	+	0.430245i
$117$	1.97982	−	4.77970i	0.183034	−	0.441884i
$118$	0.454387	+	3.65558i	0.0418297	+	0.336524i
$119$	−3.54792	−	3.54792i	−0.325237	−	0.325237i
$120$		0			0
$121$	7.17401	−	7.17401i	0.652183	−	0.652183i
$122$	6.95658	+	5.41838i	0.629819	+	0.490557i
$123$	−0.992787	−	0.411226i	−0.0895166	−	0.0370790i
$124$	−9.29496	+	15.5745i	−0.834712	+	1.39863i
$125$		0			0
$126$	1.23266	−	0.699834i	0.109814	−	0.0623462i
$127$	12.0188	+	12.0188i	1.06649	+	1.06649i	0.997626	+	0.0688681i	$0.0219388\pi$
$127$	12.0188	+	12.0188i	1.06649	+	1.06649i	0.0688681	+	0.997626i	$0.478061\pi$
$128$	−3.47763	+	10.7660i	−0.307382	+	0.951586i
$129$			15.3515i			1.35162i
$130$		0			0
$131$	4.28707	−	10.3499i	0.374563	−	0.904274i	−0.618402	−	0.785862i	$-0.712220\pi$
$131$	4.28707	−	10.3499i	0.374563	−	0.904274i	0.992965	−	0.118412i	$-0.0377805\pi$
$132$	−0.601031	−	2.38032i	−0.0523130	−	0.207180i
$133$	−0.231752	+	0.559500i	−0.0200955	+	0.0485148i
$134$	−1.06894	−	8.59970i	−0.0923423	−	0.742901i
$135$		0			0
$136$	−0.379935	+	17.5030i	−0.0325791	+	1.50087i
$137$	−1.71157			−0.146229			−0.0731145	−	0.997324i	$-0.523294\pi$
$137$	−1.71157			−0.146229			−0.0731145	+	0.997324i	$0.523294\pi$
$138$	9.99132	−	1.24192i	0.850517	−	0.105719i
$139$	−1.54808	+	0.641236i	−0.131306	+	0.0543889i	−0.447369	−	0.894349i	$-0.647639\pi$
$139$	−1.54808	+	0.641236i	−0.131306	+	0.0543889i	0.316063	+	0.948738i	$0.397639\pi$
$140$		0			0
$141$	−1.14800	+	2.77153i	−0.0966794	+	0.233405i
$142$	−1.20790	−	2.12754i	−0.101365	−	0.178539i
$143$	−2.73479	−	2.73479i	−0.228694	−	0.228694i
$144$	−4.73828	−	1.41777i	−0.394857	−	0.118147i
$145$		0			0
$146$	−4.30727	+	15.6220i	−0.356473	+	1.29289i
$147$	7.78207	−	3.22344i	0.641855	−	0.265865i
$148$	1.12538	+	1.51141i	0.0925060	+	0.124238i
$149$	−7.10915	−	17.1630i	−0.582404	−	1.40605i	−0.890627	−	0.454734i	$-0.849734\pi$
$149$	−7.10915	−	17.1630i	−0.582404	−	1.40605i	0.308223	−	0.951314i	$-0.400266\pi$
$150$		0			0
$151$	7.59514	−	7.59514i	0.618083	−	0.618083i	−0.326956	−	0.945040i	$-0.606023\pi$
$151$	7.59514	−	7.59514i	0.618083	−	0.618083i	0.945040	+	0.326956i	$0.106023\pi$
$152$	1.96930	−	0.766076i	0.159731	−	0.0621370i
$153$	−7.65334			−0.618736
$154$	−0.130709	−	1.05157i	−0.0105329	−	0.0847377i
$155$		0			0
$156$	10.7747	−	2.72062i	0.862670	−	0.217824i
$157$	−13.5947	+	5.63110i	−1.08497	+	0.449411i	−0.852251	−	0.523133i	$-0.824763\pi$
$157$	−13.5947	+	5.63110i	−1.08497	+	0.449411i	−0.232722	+	0.972543i	$0.574763\pi$
$158$	6.40600	−	23.2338i	0.509634	−	1.84839i
$159$	−6.65102			−0.527460
$160$		0			0
$161$	4.34573			0.342491
$162$	−1.41405	+	5.12860i	−0.111098	+	0.402941i
$163$	4.78964	−	1.98393i	0.375154	−	0.155394i	−0.187136	−	0.982334i	$-0.559921\pi$
$163$	4.78964	−	1.98393i	0.375154	−	0.155394i	0.562290	+	0.826940i	$0.309921\pi$
$164$	0.396204	+	1.56912i	0.0309383	+	0.122528i
$165$		0			0
$166$	−1.49776	−	12.0496i	−0.116249	−	0.935230i
$167$	7.59626			0.587817			0.293908	−	0.955834i	$-0.405044\pi$
$167$	7.59626			0.587817			0.293908	+	0.955834i	$0.405044\pi$
$168$	2.78706	+	1.22596i	0.215026	+	0.0945847i
$169$	3.18690	−	3.18690i	0.245146	−	0.245146i
$170$		0			0
$171$	0.353498	+	0.853419i	0.0270326	+	0.0652626i
$172$	18.5441	−	13.8077i	1.41397	−	1.05283i
$173$	−0.0431970	+	0.0178928i	−0.00328421	+	0.00136036i	−0.384325	−	0.923198i	$-0.625566\pi$
$173$	−0.0431970	+	0.0178928i	−0.00328421	+	0.00136036i	0.381041	+	0.924558i	$0.375566\pi$
$174$	1.93662	−	7.02390i	0.146815	−	0.532481i
$175$		0			0
$176$	−2.33475	+	2.86697i	−0.175988	+	0.216106i
$177$	−2.44595	−	2.44595i	−0.183849	−	0.183849i
$178$	7.56106	+	13.3177i	0.566726	+	0.998206i
$179$	7.55581	−	18.2413i	0.564748	−	1.36342i	−0.341183	−	0.939997i	$-0.610828\pi$
$179$	7.55581	−	18.2413i	0.564748	−	1.36342i	0.905931	−	0.423425i	$-0.139172\pi$
$180$		0			0
$181$	22.1793	−	9.18697i	1.64858	−	0.682862i	0.651454	−	0.758688i	$-0.274159\pi$
$181$	22.1793	−	9.18697i	1.64858	−	0.682862i	0.997121	+	0.0758260i	$0.0241593\pi$
$182$	4.76002	−	0.591668i	0.352836	−	0.0438574i
$183$	−8.28010			−0.612082
$184$	−10.4868	−	10.9521i	−0.773094	−	0.807401i
$185$		0			0
$186$	−2.10083	−	16.9013i	−0.154040	−	1.23927i
$187$	−2.18949	+	5.28590i	−0.160112	+	0.386544i
$188$	4.38046	−	1.10607i	0.319478	−	0.0806683i
$189$	−1.74523	+	4.21336i	−0.126947	+	0.306477i
$190$		0			0
$191$			10.7326i			0.776586i	0.921536	+	0.388293i	$0.126935\pi$
$191$			10.7326i			0.776586i	−0.921536	+	0.388293i	$0.873065\pi$
$192$	−3.63584	−	9.98235i	−0.262394	−	0.720414i
$193$	13.3767	+	13.3767i	0.962880	+	0.962880i	0.999335	−	0.0364558i	$-0.0116068\pi$
$193$	13.3767	+	13.3767i	0.962880	+	0.962880i	−0.0364558	+	0.999335i	$0.511607\pi$
$194$	3.52249	−	1.99987i	0.252900	−	0.143582i
$195$		0			0
$196$	−10.8933	−	6.50118i	−0.778092	−	0.464370i
$197$	−7.08755	−	2.93576i	−0.504967	−	0.209164i	0.115632	−	0.993292i	$-0.463111\pi$
$197$	−7.08755	−	2.93576i	−0.504967	−	0.209164i	−0.620599	+	0.784128i	$0.713111\pi$
$198$	−1.27516	−	0.993207i	−0.0906220	−	0.0705841i
$199$	−15.2564	+	15.2564i	−1.08149	+	1.08149i	−0.0851236	+	0.996370i	$0.527129\pi$
$199$	−15.2564	+	15.2564i	−1.08149	+	1.08149i	−0.996370	+	0.0851236i	$0.972871\pi$
$200$		0			0
$201$	5.75407	+	5.75407i	0.405861	+	0.405861i
$202$	0.134552	+	1.08249i	0.00946708	+	0.0761634i
$203$	1.20348	−	2.90546i	0.0844677	−	0.203923i
$204$	−9.81809	−	13.1859i	−0.687404	−	0.923198i
$205$		0			0
$206$	−3.65818	+	13.2678i	−0.254878	+	0.924414i
$207$	4.68716	−	4.68716i	0.325780	−	0.325780i
$208$	−12.9776	−	10.5685i	−0.899836	−	0.732791i
$209$	0.690558			0.0477669
$210$		0			0
$211$	−12.4406	−	5.15308i	−0.856449	−	0.354753i	−0.0891311	−	0.996020i	$-0.528409\pi$
$211$	−12.4406	−	5.15308i	−0.856449	−	0.354753i	−0.767318	+	0.641267i	$0.778409\pi$
$212$	5.98218	+	8.03420i	0.410858	+	0.551791i
$213$	2.12247	+	0.879155i	0.145429	+	0.0602387i
$214$	7.91550	+	6.16527i	0.541093	+	0.421449i
$215$		0			0
$216$	14.8300	−	5.76901i	1.00905	−	0.392531i
$217$		−	7.35124i		−	0.499035i
$218$	12.3349	+	9.60746i	0.835424	+	0.650699i
$219$	−5.82324	−	14.0585i	−0.393498	−	0.949988i
$220$		0			0
$221$	−23.9272	−	9.91096i	−1.60952	−	0.666683i
$222$	−1.70582	−	0.470327i	−0.114487	−	0.0315663i
$223$	−18.6893	+	18.6893i	−1.25153	+	1.25153i	−0.296495	+	0.955035i	$0.595818\pi$
$223$	−18.6893	+	18.6893i	−1.25153	+	1.25153i	−0.955035	+	0.296495i	$0.904182\pi$
$224$	−1.02587	−	4.46934i	−0.0685439	−	0.298620i
$225$		0			0
$226$	25.2996	−	14.3637i	1.68290	−	0.955459i
$227$	−8.91547	−	21.5239i	−0.591741	−	1.42859i	−0.881820	−	0.471586i	$-0.843682\pi$
$227$	−8.91547	−	21.5239i	−0.591741	−	1.42859i	0.290080	−	0.957003i	$-0.406318\pi$
$228$	−1.01687	+	1.70385i	−0.0673437	+	0.112840i
$229$	−9.93553	+	4.11543i	−0.656558	+	0.271955i	−0.685989	−	0.727612i	$-0.740630\pi$
$229$	−9.93553	+	4.11543i	−0.656558	+	0.271955i	0.0294313	+	0.999567i	$0.490630\pi$
$230$		0			0
$231$	0.703605	+	0.703605i	0.0462938	+	0.0462938i
$232$	−10.2265	+	3.97820i	−0.671402	+	0.261181i
$233$			16.9133i			1.10803i	0.832507	+	0.554014i	$0.186905\pi$
$233$			16.9133i			1.10803i	−0.832507	+	0.554014i	$0.813095\pi$
$234$	4.49585	−	5.77216i	0.293903	−	0.377338i
$235$		0			0
$236$	−0.754642	+	5.15461i	−0.0491230	+	0.335536i
$237$	8.66061	+	20.9086i	0.562567	+	1.35816i
$238$	−3.50337	−	6.17068i	−0.227090	−	0.399986i
$239$			16.3930i			1.06038i	0.847880	+	0.530189i	$0.177879\pi$
$239$			16.3930i			1.06038i	−0.847880	+	0.530189i	$0.822121\pi$
$240$		0			0
$241$		−	2.00046i		−	0.128861i	−0.997922	−	0.0644306i	$-0.979477\pi$
$241$		−	2.00046i		−	0.128861i	0.997922	−	0.0644306i	$-0.0205231\pi$
$242$	12.4773	−	7.08393i	0.802073	−	0.455373i
$243$	4.54714	+	10.9778i	0.291699	+	0.704225i
$244$	7.44743	+	10.0021i	0.476773	+	0.640316i
$245$		0			0
$246$	−1.19893	−	0.933828i	−0.0764409	−	0.0595387i
$247$			3.12588i			0.198895i
$248$	−18.5266	+	17.7394i	−1.17644	+	1.12645i
$249$	8.06240	+	8.06240i	0.510934	+	0.510934i
$250$		0			0
$251$	2.14679	−	0.889229i	0.135504	−	0.0561277i	−0.313901	−	0.949456i	$-0.601636\pi$
$251$	2.14679	−	0.889229i	0.135504	−	0.0561277i	0.449405	+	0.893328i	$0.351636\pi$
$252$	1.94360	−	0.490760i	0.122435	−	0.0309149i
$253$	−1.89635	−	4.57818i	−0.119222	−	0.287828i
$254$	11.8679	+	20.9035i	0.744656	+	1.31160i
$255$		0			0
$256$	−8.78811	+	13.3705i	−0.549257	+	0.835654i
$257$	−5.89815	+	5.89815i	−0.367916	+	0.367916i	−0.866717	−	0.498800i	$-0.833774\pi$
$257$	−5.89815	+	5.89815i	−0.367916	+	0.367916i	0.498800	+	0.866717i	$0.333774\pi$
$258$	−5.77060	+	20.9293i	−0.359262	+	1.30300i
$259$	−0.705619	−	0.292277i	−0.0438450	−	0.0181612i
$260$		0			0
$261$	−1.83570	−	4.43176i	−0.113627	−	0.274319i
$262$	9.73524	−	12.4989i	0.601445	−	0.772187i
$263$		−	6.25098i		−	0.385452i	−0.981253	−	0.192726i	$-0.938267\pi$
$263$		−	6.25098i		−	0.385452i	0.981253	−	0.192726i	$-0.0617328\pi$
$264$	0.0753467	−	3.47111i	0.00463727	−	0.213632i
$265$		0			0
$266$	−0.526273	+	0.675674i	−0.0322678	+	0.0414282i
$267$	−13.2860	−	5.50323i	−0.813089	−	0.336792i
$268$	1.77528	−	12.1261i	0.108443	−	0.740722i
$269$	−5.81666	−	2.40934i	−0.354648	−	0.146900i	0.198244	−	0.980153i	$-0.436476\pi$
$269$	−5.81666	−	2.40934i	−0.354648	−	0.146900i	−0.552893	+	0.833252i	$0.686476\pi$
$270$		0			0
$271$	−15.8408			−0.962258			−0.481129	−	0.876650i	$-0.659773\pi$
$271$	−15.8408			−0.962258			−0.481129	+	0.876650i	$0.659773\pi$
$272$	−7.09734	+	23.7198i	−0.430339	+	1.43822i
$273$	−3.18494	+	3.18494i	−0.192761	+	0.192761i
$274$	−2.33345	−	0.643375i	−0.140969	−	0.0388677i
$275$		0			0
$276$	14.0884	+	2.06256i	0.848023	+	0.124152i
$277$	−4.18090	+	10.0936i	−0.251206	+	0.606465i	−0.998302	−	0.0582513i	$-0.981448\pi$
$277$	−4.18090	+	10.0936i	−0.251206	+	0.606465i	0.747096	+	0.664716i	$0.231448\pi$
$278$	−2.35160	+	0.292303i	−0.141040	+	0.0175312i
$279$	−7.92881	−	7.92881i	−0.474685	−	0.474685i
$280$		0			0
$281$	−4.80986	+	4.80986i	−0.286932	+	0.286932i	−0.835866	−	0.548934i	$-0.815034\pi$
$281$	−4.80986	+	4.80986i	−0.286932	+	0.286932i	0.548934	+	0.835866i	$0.315034\pi$
$282$	−2.60693	+	3.34700i	−0.155241	+	0.199311i
$283$	24.3013	+	10.0659i	1.44456	+	0.598358i	0.960900	−	0.276897i	$-0.0893059\pi$
$283$	24.3013	+	10.0659i	1.44456	+	0.598358i	0.483663	+	0.875254i	$0.339306\pi$
$284$	−0.847040	−	3.35461i	−0.0502626	−	0.199060i
$285$		0			0
$286$	−2.70045	−	4.75645i	−0.159681	−	0.281255i
$287$	−0.463821	−	0.463821i	−0.0273785	−	0.0273785i
$288$	−5.92696	−	3.71401i	−0.349249	−	0.218850i
$289$			21.3126i			1.25368i
$290$		0			0
$291$	−1.45558	+	3.51409i	−0.0853278	+	0.206000i
$292$	−11.7446	+	19.6790i	−0.687299	+	1.15163i
$293$	7.47876	−	18.0553i	0.436914	−	1.05480i	−0.540095	−	0.841604i	$-0.681612\pi$
$293$	7.47876	−	18.0553i	0.436914	−	1.05480i	0.977009	−	0.213199i	$-0.0683882\pi$
$294$	11.8213	−	1.46938i	0.689433	−	0.0856962i
$295$		0			0
$296$	0.966145	+	2.48360i	0.0561560	+	0.144357i
$297$	5.20031			0.301753
$298$	−3.24066	−	26.0713i	−0.187726	−	1.51027i
$299$	20.7236	−	8.58399i	1.19848	−	0.496425i
$300$		0			0
$301$	−3.58604	+	8.65748i	−0.206696	+	0.499009i
$302$	13.2098	−	7.49977i	0.760136	−	0.431563i
$303$	−0.724293	−	0.724293i	−0.0416095	−	0.0416095i
$304$	2.97280	−	0.304167i	0.170502	−	0.0174452i
$305$		0			0
$306$	−10.4341	−	2.87688i	−0.596479	−	0.164460i
$307$	−30.3123	+	12.5558i	−1.73001	+	0.716595i	−0.730585	+	0.682822i	$0.760752\pi$
$307$	−30.3123	+	12.5558i	−1.73001	+	0.716595i	−0.999430	+	0.0337730i	$0.989248\pi$
$308$	0.217081	−	1.48278i	0.0123693	−	0.0844891i
$309$	−4.94570	−	11.9400i	−0.281351	−	0.679241i
$310$		0			0
$311$	−9.72842	+	9.72842i	−0.551648	+	0.551648i	−0.926916	−	0.375268i	$-0.877551\pi$
$311$	−9.72842	+	9.72842i	−0.551648	+	0.551648i	0.375268	+	0.926916i	$0.377551\pi$
$312$	15.7123	+	0.341064i	0.889536	+	0.0193090i
$313$	12.4426			0.703299			0.351649	−	0.936132i	$-0.385621\pi$
$313$	12.4426			0.703299			0.351649	+	0.936132i	$0.385621\pi$
$314$	−20.6509	+	2.56690i	−1.16540	+	0.144858i
$315$		0			0
$316$	17.4671	−	29.2677i	0.982602	−	1.64644i
$317$	−19.8193	+	8.20943i	−1.11316	+	0.461087i	−0.862026	−	0.506864i	$-0.830805\pi$
$317$	−19.8193	+	8.20943i	−1.11316	+	0.461087i	−0.251138	+	0.967951i	$0.580805\pi$
$318$	−9.06762	−	2.50011i	−0.508487	−	0.140199i
$319$	−3.58604			−0.200779
$320$		0			0
$321$	−9.42147			−0.525855
$322$	5.92471	+	1.63355i	0.330171	+	0.0910342i
$323$	4.27221	−	1.76961i	0.237712	−	0.0984636i
$324$	−3.85566	+	6.46049i	−0.214203	+	0.358916i
$325$		0			0
$326$	7.27567	−	0.904363i	0.402962	−	0.0500880i
$327$	−14.6817			−0.811897
$328$	−0.0496691	+	2.28818i	−0.00274252	+	0.126344i
$329$	−1.29483	+	1.29483i	−0.0713865	+	0.0713865i
$330$		0			0
$331$	8.99571	+	21.7176i	0.494449	+	1.19371i	0.952434	+	0.304746i	$0.0985714\pi$
$331$	8.99571	+	21.7176i	0.494449	+	1.19371i	−0.457985	+	0.888960i	$0.651429\pi$
$332$	2.48746	−	16.9907i	0.136517	−	0.932487i
$333$	−1.07630	+	0.445817i	−0.0589808	+	0.0244306i
$334$	10.3563	+	2.85542i	0.566672	+	0.156242i
$335$		0			0
$336$	3.33888	+	2.71905i	0.182151	+	0.148336i
$337$	−6.90744	−	6.90744i	−0.376272	−	0.376272i	0.493483	−	0.869755i	$-0.335723\pi$
$337$	−6.90744	−	6.90744i	−0.376272	−	0.376272i	−0.869755	+	0.493483i	$0.835723\pi$
$338$	5.54278	−	3.14688i	0.301488	−	0.171168i
$339$	−10.4545	+	25.2393i	−0.567808	+	1.37081i
$340$		0			0
$341$	−7.74446	+	3.20786i	−0.419386	+	0.173715i
$342$	0.161139	+	1.29638i	0.00871342	+	0.0701002i
$343$	10.8160			0.584011
$344$	30.4722	−	11.8540i	1.64295	−	0.639123i
$345$		0			0
$346$	−0.0656181	+	0.00815630i	−0.00352765	+	0.000438486i
$347$	2.89398	−	6.98669i	0.155357	−	0.375065i	−0.826968	−	0.562249i	$-0.809936\pi$
$347$	2.89398	−	6.98669i	0.155357	−	0.375065i	0.982325	+	0.187184i	$0.0599361\pi$
$348$	5.28055	−	8.84801i	0.283067	−	0.474303i
$349$	−1.31230	+	3.16817i	−0.0702457	+	0.169588i	−0.955103	−	0.296274i	$-0.904256\pi$
$349$	−1.31230	+	3.16817i	−0.0702457	+	0.169588i	0.884857	+	0.465862i	$0.154256\pi$
$350$		0			0
$351$			23.5397i			1.25646i
$352$	−4.26075	+	3.03103i	−0.227099	+	0.161555i
$353$	−7.05995	−	7.05995i	−0.375763	−	0.375763i	0.493808	−	0.869571i	$-0.335605\pi$
$353$	−7.05995	−	7.05995i	−0.375763	−	0.375763i	−0.869571	+	0.493808i	$0.835605\pi$
$354$	−2.41524	−	4.25410i	−0.128369	−	0.226103i
$355$		0			0
$356$	5.30220	+	20.9988i	0.281016	+	1.11293i
$357$	6.15597	+	2.54989i	0.325808	+	0.134954i
$358$	17.1580	−	22.0290i	0.906830	−	1.16427i
$359$	−6.96604	+	6.96604i	−0.367654	+	0.367654i	−0.866621	−	0.498967i	$-0.833713\pi$
$359$	−6.96604	+	6.96604i	−0.367654	+	0.367654i	0.498967	+	0.866621i	$0.333713\pi$
$360$		0			0
$361$	13.0404	+	13.0404i	0.686335	+	0.686335i
$362$	33.6913	−	4.18782i	1.77078	−	0.220107i
$363$	−5.15596	+	12.4476i	−0.270618	+	0.653329i
$364$	6.71194	+	0.982637i	0.351801	+	0.0515042i
$365$		0			0
$366$	−11.2886	−	3.11247i	−0.590065	−	0.162692i
$367$	10.5140	−	10.5140i	0.548826	−	0.548826i	−0.377275	−	0.926101i	$-0.623139\pi$
$367$	10.5140	−	10.5140i	0.548826	−	0.548826i	0.926101	+	0.377275i	$0.123139\pi$
$368$	−10.1801	−	18.8734i	−0.530677	−	0.983846i
$369$	−1.00053			−0.0520853
$370$		0			0
$371$	−3.75084	−	1.55365i	−0.194734	−	0.0806615i
$372$	3.48903	−	23.8320i	0.180898	−	1.23563i
$373$	−14.8828	−	6.16467i	−0.770604	−	0.319195i	−0.0374868	−	0.999297i	$-0.511935\pi$
$373$	−14.8828	−	6.16467i	−0.770604	−	0.319195i	−0.733117	+	0.680103i	$0.761935\pi$
$374$	−4.97199	+	6.38347i	−0.257095	+	0.330081i
$375$		0			0
$376$	6.38784	+	0.138659i	0.329427	+	0.00715081i
$377$		−	16.2325i		−	0.836018i
$378$	−3.96314	+	5.08822i	−0.203842	+	0.261710i
$379$	4.07716	+	9.84314i	0.209430	+	0.505608i	0.993334	−	0.115274i	$-0.0367746\pi$
$379$	4.07716	+	9.84314i	0.209430	+	0.505608i	−0.783904	+	0.620882i	$0.786775\pi$
$380$		0			0
$381$	−20.8537	−	8.63789i	−1.06837	−	0.442532i
$382$	−4.03438	+	14.6322i	−0.206417	+	0.748651i
$383$	0.245014	−	0.245014i	0.0125196	−	0.0125196i	−0.700819	−	0.713339i	$-0.747182\pi$
$383$	0.245014	−	0.245014i	0.0125196	−	0.0125196i	0.713339	+	0.700819i	$0.247182\pi$
$384$	−1.20454	−	14.9761i	−0.0614691	−	0.764243i
$385$		0			0
$386$	13.2088	+	23.2654i	0.672309	+	1.18418i
$387$	5.46988	+	13.2055i	0.278050	+	0.671271i
$388$	5.55410	−	1.40241i	0.281967	−	0.0711967i
$389$	9.70866	−	4.02146i	0.492248	−	0.203896i	−0.122730	−	0.992440i	$-0.539165\pi$
$389$	9.70866	−	4.02146i	0.492248	−	0.203896i	0.614978	+	0.788544i	$0.289165\pi$
$390$		0			0
$391$	−23.4639	−	23.4639i	−1.18662	−	1.18662i
$392$	−12.4075	−	12.9581i	−0.626673	−	0.654483i
$393$			14.8769i			0.750442i
$394$	−8.55921	−	6.66664i	−0.431207	−	0.335860i
$395$		0			0
$396$	−1.36514	−	1.83341i	−0.0686009	−	0.0921324i
$397$	5.50244	+	13.2841i	0.276159	+	0.666708i	0.999723	−	0.0235503i	$-0.00749698\pi$
$397$	5.50244	+	13.2841i	0.276159	+	0.666708i	−0.723563	+	0.690258i	$0.757497\pi$
$398$	−26.5345	+	15.0648i	−1.33005	+	0.755129i
$399$		−	0.804224i		−	0.0402616i
$400$		0			0
$401$		−	36.3553i		−	1.81550i	−0.419515	−	0.907748i	$-0.637800\pi$
$401$		−	36.3553i		−	1.81550i	0.419515	−	0.907748i	$-0.362200\pi$
$402$	5.68182	+	10.0077i	0.283384	+	0.499139i
$403$	−14.5207	−	35.0561i	−0.723328	−	1.74627i
$404$	−0.223463	+	1.52638i	−0.0111177	+	0.0759400i
$405$		0			0
$406$	2.73291	−	3.50874i	0.135632	−	0.174136i
$407$			0.870904i			0.0431691i
$408$	−8.42885	−	21.6675i	−0.417290	−	1.07270i
$409$	−1.73940	−	1.73940i	−0.0860076	−	0.0860076i	0.662794	−	0.748802i	$-0.269370\pi$
$409$	−1.73940	−	1.73940i	−0.0860076	−	0.0860076i	−0.748802	+	0.662794i	$0.769370\pi$
$410$		0			0
$411$	2.09991	−	0.869813i	0.103581	−	0.0429047i
$412$	−9.97471	+	16.7135i	−0.491419	+	0.823415i
$413$	−0.808032	−	1.95076i	−0.0397606	−	0.0959907i
$414$	8.15209	−	4.62830i	0.400653	−	0.227469i
$415$		0			0
$416$	−13.7203	−	19.2867i	−0.672692	−	0.945608i
$417$	1.57346	−	1.57346i	0.0770527	−	0.0770527i
$418$	0.941466	+	0.259579i	0.0460486	+	0.0126964i
$419$	30.4757	+	12.6234i	1.48883	+	0.616695i	0.971063	−	0.238824i	$-0.0767620\pi$
$419$	30.4757	+	12.6234i	1.48883	+	0.616695i	0.517771	+	0.855519i	$0.326762\pi$
$420$		0			0
$421$	−2.20626	−	5.32637i	−0.107526	−	0.259591i	0.860953	−	0.508684i	$-0.169868\pi$
$421$	−2.20626	−	5.32637i	−0.107526	−	0.259591i	−0.968480	+	0.249092i	$0.919868\pi$
$422$	−15.0238	−	11.7018i	−0.731347	−	0.569636i
$423$			2.79313i			0.135807i
$424$	5.13572	+	13.2020i	0.249412	+	0.641148i
$425$		0			0
$426$	2.56318	+	1.99642i	0.124186	+	0.0967269i
$427$	−4.66956	−	1.93420i	−0.225976	−	0.0936023i
$428$	8.47402	+	11.3808i	0.409607	+	0.550111i
$429$	4.74511	+	1.96549i	0.229096	+	0.0948948i
$430$		0			0
$431$	11.5520			0.556441			0.278220	−	0.960517i	$-0.410255\pi$
$431$	11.5520			0.556441			0.278220	+	0.960517i	$0.410255\pi$
$432$	22.3869	−	2.29056i	1.07709	−	0.110204i
$433$	−4.86860	+	4.86860i	−0.233970	+	0.233970i	−0.814348	−	0.580378i	$-0.802905\pi$
$433$	−4.86860	+	4.86860i	−0.233970	+	0.233970i	0.580378	+	0.814348i	$0.302905\pi$
$434$	2.76332	−	10.0223i	0.132643	−	0.481083i
$435$		0			0
$436$	13.2052	+	17.7349i	0.632416	+	0.849348i
$437$	−1.53268	+	3.70021i	−0.0733179	+	0.177005i
$438$	−2.65448	−	21.3555i	−0.126836	−	1.02041i
$439$	−12.4739	−	12.4739i	−0.595347	−	0.595347i	0.343724	−	0.939071i	$-0.388312\pi$
$439$	−12.4739	−	12.4739i	−0.595347	−	0.595347i	−0.939071	+	0.343724i	$0.888312\pi$
$440$		0			0
$441$	5.54565	−	5.54565i	0.264079	−	0.264079i
$442$	−28.8954	−	22.5062i	−1.37441	−	1.07051i
$443$	10.2113	+	4.22965i	0.485152	+	0.200957i	0.611833	−	0.790987i	$-0.290432\pi$
$443$	10.2113	+	4.22965i	0.485152	+	0.200957i	−0.126681	+	0.991944i	$0.540432\pi$
$444$	−2.14883	−	1.28243i	−0.101979	−	0.0608616i
$445$		0			0
$446$	−32.5052	+	18.4546i	−1.53917	+	0.873853i
$447$	17.4444	+	17.4444i	0.825091	+	0.825091i
$448$	0.281403	−	6.47886i	0.0132950	−	0.306097i
$449$		−	23.5370i		−	1.11078i	−0.831589	−	0.555391i	$-0.812569\pi$
$449$		−	23.5370i		−	1.11078i	0.831589	−	0.555391i	$-0.187431\pi$
$450$		0			0
$451$	−0.286234	+	0.691030i	−0.0134782	+	0.0325393i
$452$	39.8913	−	10.0726i	1.87633	−	0.473773i
$453$	−5.45862	+	13.1783i	−0.256468	+	0.619169i
$454$	−4.06406	−	32.6957i	−0.190736	−	1.53448i
$455$		0			0
$456$	−2.02681	+	1.94069i	−0.0949141	+	0.0908811i
$457$	9.83092			0.459871			0.229936	−	0.973206i	$-0.426148\pi$
$457$	9.83092			0.459871			0.229936	+	0.973206i	$0.426148\pi$
$458$	−15.0925	+	1.87599i	−0.705226	+	0.0876593i
$459$	32.1723	−	13.3262i	1.50167	−	0.622013i
$460$		0			0
$461$	−8.56757	+	20.6839i	−0.399031	+	0.963347i	0.588865	+	0.808231i	$0.299575\pi$
$461$	−8.56757	+	20.6839i	−0.399031	+	0.963347i	−0.987896	+	0.155116i	$0.950425\pi$
$462$	0.694770	+	1.22374i	0.0323236	+	0.0569334i
$463$	−10.2145	−	10.2145i	−0.474707	−	0.474707i	0.428727	−	0.903434i	$-0.358962\pi$
$463$	−10.2145	−	10.2145i	−0.474707	−	0.474707i	−0.903434	+	0.428727i	$0.858962\pi$
$464$	−15.4376	+	1.57952i	−0.716673	+	0.0733276i
$465$		0			0
$466$	−6.35769	+	23.0586i	−0.294514	+	1.06817i
$467$	−1.32214	+	0.547649i	−0.0611814	+	0.0253422i	−0.413064	−	0.910702i	$-0.635542\pi$
$467$	−1.32214	+	0.547649i	−0.0611814	+	0.0253422i	0.351883	+	0.936044i	$0.385542\pi$
$468$	8.29912	−	6.17944i	0.383627	−	0.285645i
$469$	1.90088	+	4.58914i	0.0877746	+	0.211907i
$470$		0			0
$471$	13.8176	−	13.8176i	0.636679	−	0.636679i
$472$	−2.96644	+	6.74383i	−0.136542	+	0.310410i
$473$	10.6854			0.491316
$474$	3.94788	+	31.7610i	0.181332	+	1.45883i
$475$		0			0
$476$	−2.45674	−	9.72965i	−0.112605	−	0.445958i
$477$	−5.72126	+	2.36982i	−0.261958	+	0.108507i
$478$	−6.16211	+	22.3493i	−0.281848	+	1.02223i
$479$	31.8238			1.45407			0.727033	−	0.686602i	$-0.240899\pi$
$479$	31.8238			1.45407			0.727033	+	0.686602i	$0.240899\pi$
$480$		0			0
$481$	−3.94223			−0.179750
$482$	0.751971	−	2.72732i	0.0342513	−	0.124226i
$483$	−5.33176	+	2.20849i	−0.242603	+	0.100490i
$484$	19.6737	−	4.96762i	0.894259	−	0.225801i
$485$		0			0
$486$	2.07278	+	16.6757i	0.0940234	+	0.756426i
$487$	−9.67742			−0.438526			−0.219263	−	0.975666i	$-0.570365\pi$
$487$	−9.67742			−0.438526			−0.219263	+	0.975666i	$0.570365\pi$
$488$	6.39364	+	16.4357i	0.289426	+	0.744009i
$489$	−4.86816	+	4.86816i	−0.220146	+	0.220146i
$490$		0			0
$491$	−9.42241	−	22.7477i	−0.425227	−	1.02659i	−0.980781	−	0.195109i	$-0.937494\pi$
$491$	−9.42241	−	22.7477i	−0.425227	−	1.02659i	0.555554	−	0.831480i	$-0.312506\pi$
$492$	−1.28352	−	1.72380i	−0.0578658	−	0.0777150i
$493$	−22.1854	+	9.18949i	−0.999180	+	0.413874i
$494$	−1.17501	+	4.26164i	−0.0528663	+	0.191740i
$495$		0			0
$496$	−31.9264	+	17.2208i	−1.43354	+	0.773235i
$497$	0.991599	+	0.991599i	0.0444793	+	0.0444793i
$498$	7.96117	+	14.0225i	0.356748	+	0.628361i
$499$	−7.85461	+	18.9627i	−0.351621	+	0.848887i	0.644800	+	0.764351i	$0.276941\pi$
$499$	−7.85461	+	18.9627i	−0.351621	+	0.848887i	−0.996420	+	0.0845356i	$0.973059\pi$
$500$		0			0
$501$	−9.31983	+	3.86040i	−0.416379	+	0.172470i
$502$	3.26107	−	0.405349i	0.145549	−	0.0180916i
$503$	20.3583			0.907731			0.453865	−	0.891070i	$-0.350045\pi$
$503$	20.3583			0.907731			0.453865	+	0.891070i	$0.350045\pi$
$504$	2.83427	+	0.0615228i	0.126248	+	0.00274044i
$505$		0			0
$506$	−0.864436	−	6.95446i	−0.0384289	−	0.309163i
$507$	−2.29042	+	5.52957i	−0.101721	+	0.245577i
$508$	8.32235	+	32.9598i	0.369245	+	1.46235i
$509$	1.82470	−	4.40522i	0.0808785	−	0.195258i	−0.878267	−	0.478170i	$-0.841300\pi$
$509$	1.82470	−	4.40522i	0.0808785	−	0.195258i	0.959146	+	0.282912i	$0.0913004\pi$
$510$		0			0
$511$		−	9.28860i		−	0.410903i
$512$	−17.0071	+	14.9251i	−0.751616	+	0.659601i
$513$	−2.97199	−	2.97199i	−0.131217	−	0.131217i
$514$	−10.2583	+	5.82409i	−0.452474	+	0.256890i
$515$		0			0
$516$	−15.7346	+	26.3647i	−0.692677	+	1.16064i
$517$	1.92912	+	0.799069i	0.0848427	+	0.0351430i
$518$	−0.852133	−	0.663714i	−0.0374406	−	0.0291619i
$519$	0.0439052	−	0.0439052i	0.00192722	−	0.00192722i
$520$		0			0
$521$	7.13106	+	7.13106i	0.312417	+	0.312417i	0.845845	−	0.533428i	$-0.179097\pi$
$521$	7.13106	+	7.13106i	0.312417	+	0.312417i	−0.533428	+	0.845845i	$0.679097\pi$
$522$	−0.836790	−	6.73205i	−0.0366253	−	0.294654i
$523$	−5.75338	+	13.8899i	−0.251578	+	0.607363i	−0.998332	−	0.0577377i	$-0.981611\pi$
$523$	−5.75338	+	13.8899i	−0.251578	+	0.607363i	0.746754	+	0.665100i	$0.231611\pi$
$524$	17.9708	−	13.3809i	0.785058	−	0.584546i
$525$		0			0
$526$	2.34973	−	8.52222i	0.102453	−	0.371586i
$527$	−39.6916	+	39.6916i	−1.72899	+	1.72899i
$528$	1.40751	−	4.70399i	0.0612539	−	0.204715i
$529$	5.74014			0.249571
$530$		0			0
$531$	−2.97554	−	1.23251i	−0.129128	−	0.0534864i
$532$	−0.971474	+	0.723349i	−0.0421187	+	0.0313612i
$533$	−3.12801	−	1.29567i	−0.135489	−	0.0561215i
$534$	−16.0447	−	12.4970i	−0.694321	−	0.540797i
$535$		0			0
$536$	6.97852	−	15.8648i	0.301426	−	0.685253i
$537$			26.2201i			1.13148i
$538$	−7.02443	−	5.47123i	−0.302845	−	0.235881i
$539$	−2.24368	−	5.41672i	−0.0966420	−	0.233315i
$540$		0			0
$541$	16.0301	+	6.63988i	0.689187	+	0.285471i	0.699662	−	0.714474i	$-0.253334\pi$
$541$	16.0301	+	6.63988i	0.689187	+	0.285471i	−0.0104742	+	0.999945i	$0.503334\pi$
$542$	−21.5964	−	5.95451i	−0.927644	−	0.255768i
$543$	−22.5429	+	22.5429i	−0.967410	+	0.967410i
$544$	−18.5923	+	29.6703i	−0.797139	+	1.27210i
$545$		0			0
$546$	−5.53937	+	3.14494i	−0.237063	+	0.134591i
$547$	7.54852	+	18.2237i	0.322751	+	0.779191i	0.999092	+	0.0426017i	$0.0135647\pi$
$547$	7.54852	+	18.2237i	0.322751	+	0.779191i	−0.676341	+	0.736589i	$0.736435\pi$
$548$	−2.93945	−	1.75428i	−0.125567	−	0.0749391i
$549$	−7.12260	+	2.95028i	−0.303985	+	0.125915i
$550$		0			0
$551$	2.04943	+	2.04943i	0.0873086	+	0.0873086i
$552$	18.4320	+	8.10778i	0.784518	+	0.345090i
$553$			13.8145i			0.587451i
$554$	−9.49416	+	12.1894i	−0.403368	+	0.517879i
$555$		0			0
$556$	−3.31591	−	0.485454i	−0.140626	−	0.0205878i
$557$	−9.98481	−	24.1055i	−0.423070	−	1.02138i	−0.981437	−	0.191787i	$-0.938572\pi$
$557$	−9.98481	−	24.1055i	−0.423070	−	1.02138i	0.558367	−	0.829594i	$-0.311428\pi$
$558$	−7.82925	−	13.7901i	−0.331439	−	0.583781i
$559$			48.3686i			2.04577i
$560$		0			0
$561$		−	7.59795i		−	0.320786i
$562$	−8.36550	+	4.74946i	−0.352877	+	0.200344i
$563$	−8.21473	−	19.8321i	−0.346210	−	0.835824i	−0.997060	−	0.0766186i	$-0.975588\pi$
$563$	−8.21473	−	19.8321i	−0.346210	−	0.835824i	0.650851	−	0.759206i	$-0.274412\pi$
$564$	−4.81227	+	3.58317i	−0.202633	+	0.150879i
$565$		0			0
$566$	29.3472	+	22.8581i	1.23356	+	0.960799i
$567$		−	3.04938i		−	0.128062i
$568$	0.106187	−	4.89188i	0.00445551	−	0.205259i
$569$	−14.8979	−	14.8979i	−0.624551	−	0.624551i	0.322141	−	0.946692i	$-0.395597\pi$
$569$	−14.8979	−	14.8979i	−0.624551	−	0.624551i	−0.946692	+	0.322141i	$0.895597\pi$
$570$		0			0
$571$	6.23047	−	2.58075i	0.260737	−	0.108001i	−0.248486	−	0.968636i	$-0.579933\pi$
$571$	6.23047	−	2.58075i	0.260737	−	0.108001i	0.509223	+	0.860635i	$0.329933\pi$
$572$	−1.89369	−	7.49976i	−0.0791793	−	0.313581i
$573$	−5.45429	−	13.1678i	−0.227856	−	0.550094i
$574$	−0.457997	−	0.806697i	−0.0191164	−	0.0336709i
$575$		0			0
$576$	−6.68438	−	7.29140i	−0.278516	−	0.303808i
$577$	18.1617	−	18.1617i	0.756080	−	0.756080i	−0.219526	−	0.975607i	$-0.570451\pi$
$577$	18.1617	−	18.1617i	0.756080	−	0.756080i	0.975607	+	0.219526i	$0.0704512\pi$
$578$	−8.01135	+	29.0563i	−0.333228	+	1.20858i
$579$	−23.2099	−	9.61386i	−0.964571	−	0.399538i
$580$		0			0
$581$	2.66345	+	6.43014i	0.110498	+	0.266767i
$582$	−3.30540	+	4.24375i	−0.137013	+	0.175909i
$583$			4.62945i			0.191732i
$584$	−23.4092	+	22.4145i	−0.968679	+	0.927519i
$585$		0			0
$586$	16.9831	−	21.8043i	0.701564	−	0.900728i
$587$	22.7897	+	9.43980i	0.940631	+	0.389622i	0.799702	−	0.600398i	$-0.204991\pi$
$587$	22.7897	+	9.43980i	0.940631	+	0.389622i	0.140929	+	0.990020i	$0.454991\pi$
$588$	16.6688	+	2.44034i	0.687411	+	0.100638i
$589$	6.25928	+	2.59268i	0.257909	+	0.106830i
$590$		0			0
$591$	10.1876			0.419063
$592$	0.383603	+	3.74917i	0.0157660	+	0.154090i
$593$	6.73738	−	6.73738i	0.276671	−	0.276671i	−0.555107	−	0.831779i	$-0.687323\pi$
$593$	6.73738	−	6.73738i	0.276671	−	0.276671i	0.831779	+	0.555107i	$0.187323\pi$
$594$	7.08980	+	1.95479i	0.290898	+	0.0802059i
$595$		0			0
$596$	5.38205	−	36.7623i	0.220457	−	1.50584i
$597$	10.9647	−	26.4712i	0.448757	−	1.08339i
$598$	31.4800	−	3.91295i	1.28731	−	0.160013i
$599$	−17.9363	−	17.9363i	−0.732856	−	0.732856i	0.238328	−	0.971185i	$-0.423401\pi$
$599$	−17.9363	−	17.9363i	−0.732856	−	0.732856i	−0.971185	+	0.238328i	$0.923401\pi$
$600$		0			0
$601$	−29.0033	+	29.0033i	−1.18307	+	1.18307i	−0.204126	+	0.978945i	$0.565435\pi$
$601$	−29.0033	+	29.0033i	−1.18307	+	1.18307i	−0.978945	+	0.204126i	$0.934565\pi$
$602$	−8.14333	+	10.4551i	−0.331897	+	0.426119i
$603$	6.99992	+	2.89946i	0.285059	+	0.118075i
$604$	20.8286	−	5.25922i	0.847502	−	0.213995i
$605$		0			0
$606$	−0.715198	−	1.25972i	−0.0290529	−	0.0511726i
$607$	−9.76508	−	9.76508i	−0.396352	−	0.396352i	0.480592	−	0.876944i	$-0.340422\pi$
$607$	−9.76508	−	9.76508i	−0.396352	−	0.396352i	−0.876944	+	0.480592i	$0.840422\pi$
$608$	4.16727	+	0.702786i	0.169005	+	0.0285017i
$609$			4.17630i			0.169232i
$610$		0			0
$611$	−3.61706	+	8.73236i	−0.146331	+	0.353274i
$612$	−13.1438	−	7.84433i	−0.531309	−	0.317088i
$613$	2.09885	−	5.06707i	0.0847717	−	0.204657i	−0.875809	−	0.482657i	$-0.839672\pi$
$613$	2.09885	−	5.06707i	0.0847717	−	0.204657i	0.960581	+	0.278000i	$0.0896716\pi$
$614$	−46.0457	+	5.72346i	−1.85825	+	0.230980i
$615$		0			0
$616$	0.853329	−	1.93993i	0.0343816	−	0.0781621i
$617$	27.5407			1.10875			0.554374	−	0.832268i	$-0.312958\pi$
$617$	27.5407			1.10875			0.554374	+	0.832268i	$0.312958\pi$
$618$	−2.25446	−	18.1373i	−0.0906878	−	0.729591i
$619$	−18.0221	+	7.46500i	−0.724370	+	0.300044i	−0.714236	−	0.699905i	$-0.753226\pi$
$619$	−18.0221	+	7.46500i	−0.724370	+	0.300044i	−0.0101336	+	0.999949i	$0.503226\pi$
$620$		0			0
$621$	−11.5420	+	27.8648i	−0.463163	+	1.11817i
$622$	−16.9201	+	9.60627i	−0.678433	+	0.385176i
$623$	−6.20710	−	6.20710i	−0.248682	−	0.248682i
$624$	21.2931	+	6.37122i	0.852405	+	0.255053i
$625$		0			0
$626$	16.9636	+	4.67716i	0.678000	+	0.186937i
$627$	−0.847243	+	0.350939i	−0.0338356	+	0.0140152i
$628$	−29.1191	−	4.26308i	−1.16198	−	0.170115i
$629$	2.23176	+	5.38794i	0.0889861	+	0.214831i
$630$		0			0
$631$	25.8413	−	25.8413i	1.02873	−	1.02873i	0.0291526	−	0.999575i	$-0.490719\pi$
$631$	25.8413	−	25.8413i	1.02873	−	1.02873i	0.999575	−	0.0291526i	$-0.00928088\pi$
$632$	34.8153	−	33.3360i	1.38488	−	1.32603i
$633$	17.8822			0.710752
$634$	−30.1064	+	3.74221i	−1.19568	+	0.148622i
$635$		0			0
$636$	−11.4225	−	6.81700i	−0.452931	−	0.270312i
$637$	24.5193	−	10.1562i	0.971490	−	0.402404i
$638$	−4.88899	−	1.34798i	−0.193557	−	0.0533672i
$639$	2.13901			0.0846180
$640$		0			0
$641$	10.5781			0.417809			0.208904	−	0.977936i	$-0.433010\pi$
$641$	10.5781			0.417809			0.208904	+	0.977936i	$0.433010\pi$
$642$	−12.8447	−	3.54151i	−0.506939	−	0.139772i
$643$	37.7706	−	15.6451i	1.48953	−	0.616982i	0.518312	−	0.855192i	$-0.326561\pi$
$643$	37.7706	−	15.6451i	1.48953	−	0.616982i	0.971214	+	0.238210i	$0.0765606\pi$
$644$	7.46335	+	4.45417i	0.294097	+	0.175519i
$645$		0			0
$646$	6.48967	−	0.806663i	0.255333	−	0.0317377i
$647$	2.74049			0.107740			0.0538699	−	0.998548i	$-0.482844\pi$
$647$	2.74049			0.107740			0.0538699	+	0.998548i	$0.482844\pi$
$648$	−7.68507	+	7.35852i	−0.301898	+	0.289070i
$649$	−1.70251	+	1.70251i	−0.0668293	+	0.0668293i
$650$		0			0
$651$	3.73588	+	9.01921i	0.146421	+	0.353491i
$652$	10.2592	+	1.50196i	0.401780	+	0.0588212i
$653$	−18.0867	+	7.49175i	−0.707787	+	0.293175i	−0.707388	−	0.706825i	$-0.750127\pi$
$653$	−18.0867	+	7.49175i	−0.707787	+	0.293175i	−0.000398301		1.00000i	$0.500127\pi$
$654$	−20.0161	−	5.51881i	−0.782692	−	0.215802i
$655$		0			0
$656$	−0.927840	+	3.10090i	−0.0362261	+	0.121070i
$657$	−10.0184	−	10.0184i	−0.390854	−	0.390854i
$658$	−2.25203	+	1.27857i	−0.0877931	+	0.0498440i
$659$	−12.5791	+	30.3686i	−0.490012	+	1.18299i	0.464702	+	0.885467i	$0.346161\pi$
$659$	−12.5791	+	30.3686i	−0.490012	+	1.18299i	−0.954714	+	0.297526i	$0.903839\pi$
$660$		0			0
$661$	23.3971	−	9.69138i	0.910041	−	0.376951i	0.121968	−	0.992534i	$-0.461079\pi$
$661$	23.3971	−	9.69138i	0.910041	−	0.376951i	0.788072	+	0.615583i	$0.211079\pi$
$662$	4.10063	+	32.9899i	0.159376	+	1.28219i
$663$	34.3929			1.33571
$664$	9.77805	−	22.2291i	0.379462	−	0.862657i
$665$		0			0
$666$	−1.63494	+	0.203223i	−0.0633528	+	0.00787472i
$667$	7.95912	−	19.2150i	0.308179	−	0.744009i
$668$	13.0458	+	7.78583i	0.504758	+	0.301243i
$669$	13.4320	−	32.4277i	0.519311	−	1.25373i
$670$		0			0
$671$			5.76337i			0.222492i
$672$	3.52994	+	4.96207i	0.136171	+	0.191416i
$673$	20.6746	+	20.6746i	0.796946	+	0.796946i	0.982613	−	0.185667i	$-0.0594446\pi$
$673$	20.6746	+	20.6746i	0.796946	+	0.796946i	−0.185667	+	0.982613i	$0.559445\pi$
$674$	−6.82070	−	12.0137i	−0.262724	−	0.462750i
$675$		0			0
$676$	8.73961	−	2.20675i	0.336139	−	0.0848752i
$677$	−34.6696	−	14.3606i	−1.33246	−	0.551924i	−0.401106	−	0.916032i	$-0.631374\pi$
$677$	−34.6696	−	14.3606i	−1.33246	−	0.551924i	−0.931357	+	0.364107i	$0.881374\pi$
$678$	−23.7404	+	30.4800i	−0.911744	+	1.17058i
$679$	−1.64175	+	1.64175i	−0.0630047	+	0.0630047i
$680$		0			0
$681$	21.8767	+	21.8767i	0.838318	+	0.838318i
$682$	−11.7642	+	1.46228i	−0.450474	+	0.0559937i
$683$	−7.42928	+	17.9359i	−0.284274	+	0.686297i	−0.999926	−	0.0121593i	$-0.996129\pi$
$683$	−7.42928	+	17.9359i	−0.284274	+	0.686297i	0.715652	+	0.698457i	$0.246129\pi$
$684$	−0.267619	+	1.82798i	−0.0102327	+	0.0698946i
$685$		0			0
$686$	14.7459	+	4.06573i	0.563003	+	0.155230i
$687$	10.0984	−	10.0984i	0.385279	−	0.385279i
$688$	45.9999	−	4.70655i	1.75373	−	0.179436i
$689$	−20.9557			−0.798347
$690$		0			0
$691$	−10.7885	−	4.46873i	−0.410413	−	0.169999i	0.167918	−	0.985801i	$-0.446296\pi$
$691$	−10.7885	−	4.46873i	−0.410413	−	0.169999i	−0.578331	+	0.815802i	$0.696296\pi$
$692$	−0.0925259	−	0.0135459i	−0.00351731	−	0.000514938i
$693$	0.855947	+	0.354545i	0.0325147	+	0.0134680i
$694$	6.57177	−	8.43740i	0.249461	−	0.320279i
$695$		0			0
$696$	10.5251	−	10.0779i	0.398954	−	0.382002i
$697$			5.00863i			0.189715i
$698$	−2.98002	+	3.82601i	−0.112795	+	0.144816i
$699$	−8.59530	−	20.7509i	−0.325104	−	0.784871i
$700$		0			0
$701$	−47.2867	−	19.5868i	−1.78599	−	0.739782i	−0.991114	−	0.133014i	$-0.957535\pi$
$701$	−47.2867	−	19.5868i	−1.78599	−	0.739782i	−0.794879	−	0.606769i	$-0.792465\pi$
$702$	−8.84853	+	32.0927i	−0.333966	+	1.21126i
$703$	0.497724	−	0.497724i	0.0187720	−	0.0187720i
$704$	−6.94822	+	2.53073i	−0.261871	+	0.0953803i
$705$		0			0
$706$	−6.97130	−	12.2790i	−0.262369	−	0.462124i
$707$	−0.239273	−	0.577657i	−0.00899879	−	0.0217250i
$708$	−1.69369	−	6.70768i	−0.0636528	−	0.252090i
$709$	−0.906566	+	0.375512i	−0.0340468	+	0.0141027i	−0.399642	−	0.916671i	$-0.630866\pi$
$709$	−0.906566	+	0.375512i	−0.0340468	+	0.0141027i	0.365595	+	0.930774i	$0.380866\pi$
$710$		0			0
$711$	14.8998	+	14.8998i	0.558788	+	0.558788i
$712$	−0.664697	+	30.6216i	−0.0249106	+	1.14759i
$713$		−	48.6169i		−	1.82072i
$714$	7.43419	+	5.79038i	0.278218	+	0.216700i
$715$		0			0
$716$	31.6729	−	23.5833i	1.18367	−	0.881350i
$717$	−8.33090	−	20.1126i	−0.311123	−	0.751117i
$718$	−12.1156	+	6.87857i	−0.452151	+	0.256706i
$719$		−	42.1446i		−	1.57173i	−0.618399	−	0.785864i	$-0.712218\pi$
$719$		−	42.1446i		−	1.57173i	0.618399	−	0.785864i	$-0.287782\pi$
$720$		0			0
$721$		−	7.88884i		−	0.293796i
$722$	12.8766	+	22.6803i	0.479219	+	0.844075i
$723$	1.01663	+	2.45436i	0.0378089	+	0.0912787i
$724$	47.5070	+	6.95509i	1.76558	+	0.258484i
$725$		0			0
$726$	−11.7084	+	15.0322i	−0.434538	+	0.557897i
$727$			17.3527i			0.643576i	0.946812	+	0.321788i	$0.104284\pi$
$727$			17.3527i			0.643576i	−0.946812	+	0.321788i	$0.895716\pi$
$728$	8.78130	+	3.86268i	0.325457	+	0.143160i
$729$	−19.1377	−	19.1377i	−0.708804	−	0.708804i
$730$		0			0
$731$	66.1065	−	27.3822i	2.44504	−	1.01277i
$732$	−14.2202	−	8.48673i	−0.525596	−	0.313679i
$733$	1.67662	+	4.04772i	0.0619273	+	0.149506i	0.951814	−	0.306676i	$-0.0992167\pi$
$733$	1.67662	+	4.04772i	0.0619273	+	0.149506i	−0.889887	+	0.456182i	$0.849217\pi$
$734$	18.2864	−	10.3820i	0.674962	−	0.383206i
$735$		0			0
$736$	−6.78453	−	29.5576i	−0.250081	−	1.08951i
$737$	4.00513	−	4.00513i	0.147531	−	0.147531i
$738$	−1.36406	−	0.376096i	−0.0502117	−	0.0138443i
$739$	27.4135	+	11.3551i	1.00842	+	0.417703i	0.824879	−	0.565309i	$-0.191243\pi$
$739$	27.4135	+	11.3551i	1.00842	+	0.417703i	0.183544	+	0.983011i	$0.441243\pi$
$740$		0			0
$741$	−1.58856	−	3.83513i	−0.0583573	−	0.140887i
$742$	−4.52967	−	3.52809i	−0.166289	−	0.129520i
$743$		−	23.9173i		−	0.877440i	−0.898624	−	0.438720i	$-0.855432\pi$
$743$		−	23.9173i		−	0.877440i	0.898624	−	0.438720i	$-0.144568\pi$
$744$	13.7151	−	31.1796i	0.502822	−	1.14310i
$745$		0			0
$746$	−17.9731	−	13.9990i	−0.658042	−	0.512539i
$747$	9.80804	+	4.06262i	0.358858	+	0.148644i
$748$	−9.17805	+	6.83389i	−0.335583	+	0.249872i
$749$	−5.31324	−	2.20081i	−0.194141	−	0.0804160i
$750$		0			0
$751$	−22.5603			−0.823236			−0.411618	−	0.911357i	$-0.635036\pi$
$751$	−22.5603			−0.823236			−0.411618	+	0.911357i	$0.635036\pi$
$752$	8.65668	+	2.59022i	0.315677	+	0.0944555i
$753$	−2.18198	+	2.18198i	−0.0795159	+	0.0795159i
$754$	6.10178	−	22.1305i	0.222214	−	0.805945i
$755$		0			0
$756$	−7.31577	+	5.44725i	−0.266072	+	0.198115i
$757$	9.21573	−	22.2487i	0.334951	−	0.808644i	−0.663233	−	0.748413i	$-0.730816\pi$
$757$	9.21573	−	22.2487i	0.334951	−	0.808644i	0.998184	−	0.0602313i	$-0.0191838\pi$
$758$	1.85855	+	14.9522i	0.0675054	+	0.543087i
$759$	4.65324	+	4.65324i	0.168902	+	0.168902i
$760$		0			0
$761$	−8.29763	+	8.29763i	−0.300789	+	0.300789i	−0.841322	−	0.540534i	$-0.818222\pi$
$761$	−8.29763	+	8.29763i	−0.300789	+	0.300789i	0.540534	+	0.841322i	$0.318222\pi$
$762$	−25.1838	−	19.6153i	−0.912311	−	0.710586i
$763$	−8.27972	−	3.42957i	−0.299746	−	0.124159i
$764$	−11.0005	+	18.4322i	−0.397983	+	0.666855i
$765$		0			0
$766$	0.426137	−	0.241937i	0.0153970	−	0.00874154i
$767$	−7.70657	−	7.70657i	−0.278268	−	0.278268i
$768$	3.98727	−	20.8703i	0.143878	−	0.753091i
$769$		−	22.7180i		−	0.819233i	−0.912258	−	0.409616i	$-0.865663\pi$
$769$		−	22.7180i		−	0.819233i	0.912258	−	0.409616i	$-0.134337\pi$
$770$		0			0
$771$	4.23900	−	10.2338i	0.152664	−	0.368563i
$772$	9.26267	+	36.6838i	0.333371	+	1.32028i
$773$	1.94650	−	4.69925i	0.0700106	−	0.169020i	−0.885001	−	0.465589i	$-0.845842\pi$
$773$	1.94650	−	4.69925i	0.0700106	−	0.169020i	0.955011	+	0.296569i	$0.0958424\pi$
$774$	2.49341	+	20.0597i	0.0896237	+	0.721030i
$775$		0			0
$776$	8.09930	+	0.175810i	0.290748	+	0.00631120i
$777$	1.01426			0.0363862
$778$	14.7479	−	1.83315i	0.528737	−	0.0657217i
$779$	0.558509	−	0.231342i	0.0200106	−	0.00828868i
$780$		0			0
$781$	0.611936	−	1.47735i	0.0218968	−	0.0528636i
$782$	−23.1693	−	40.8093i	−0.828531	−	1.45934i
$783$	15.4334	+	15.4334i	0.551545	+	0.551545i
$784$	−12.0447	−	22.3303i	−0.430169	−	0.797510i
$785$		0			0
$786$	−5.59221	+	20.2823i	−0.199468	+	0.723447i
$787$	29.8282	−	12.3552i	1.06326	−	0.440417i	0.218653	−	0.975803i	$-0.429834\pi$
$787$	29.8282	−	12.3552i	1.06326	−	0.440417i	0.844608	+	0.535386i	$0.179834\pi$
$788$	−9.16314	−	12.3063i	−0.326423	−	0.438394i
$789$	3.17673	+	7.66930i	0.113095	+	0.273034i
$790$		0			0
$791$	−11.7916	+	11.7916i	−0.419260	+	0.419260i
$792$	−1.17198	−	3.01272i	−0.0416444	−	0.107052i
$793$	−26.0884			−0.926428
$794$	2.50825	+	20.1791i	0.0890144	+	0.716128i
$795$		0			0
$796$	−41.8384	+	10.5642i	−1.48292	+	0.374438i
$797$	14.4591	−	5.98915i	0.512167	−	0.212147i	−0.111605	−	0.993753i	$-0.535599\pi$
$797$	14.4591	−	5.98915i	0.512167	−	0.212147i	0.623772	+	0.781606i	$0.285599\pi$
$798$	0.302306	−	1.09643i	0.0107015	−	0.0388133i
$799$	13.9824			0.494662
$800$		0			0
$801$	−13.3895			−0.473096
$802$	13.6659	−	49.5647i	0.482559	−	1.75019i
$803$	−9.78546	+	4.05327i	−0.345321	+	0.143037i
$804$	3.98438	+	15.7797i	0.140518	+	0.556508i
$805$		0			0
$806$	−6.61916	−	53.2517i	−0.233150	−	1.87571i
$807$	8.36087			0.294316
$808$	−0.878419	+	1.99697i	−0.0309027	+	0.0702532i
$809$	36.9823	−	36.9823i	1.30023	−	1.30023i	0.371991	−	0.928236i	$-0.378675\pi$
$809$	36.9823	−	36.9823i	1.30023	−	1.30023i	0.928236	−	0.371991i	$-0.121325\pi$
$810$		0			0
$811$	16.7840	+	40.5201i	0.589365	+	1.42285i	0.884111	+	0.467278i	$0.154765\pi$
$811$	16.7840	+	40.5201i	0.589365	+	1.42285i	−0.294745	+	0.955576i	$0.595235\pi$
$812$	5.04482	−	3.75632i	0.177038	−	0.131821i
$813$	19.4350	−	8.05023i	0.681614	−	0.282334i
$814$	−0.327371	+	1.18734i	−0.0114744	+	0.0416162i
$815$		0			0
$816$	−3.34663	−	32.7086i	−0.117156	−	1.14503i
$817$	−6.10674	−	6.10674i	−0.213648	−	0.213648i
$818$	−1.71756	−	3.02523i	−0.0600529	−	0.105775i
$819$	−1.60488	+	3.87453i	−0.0560791	+	0.135387i
$820$		0			0
$821$	41.4829	−	17.1828i	1.44776	−	0.599682i	0.486095	−	0.873906i	$-0.338421\pi$
$821$	41.4829	−	17.1828i	1.44776	−	0.599682i	0.961666	+	0.274223i	$0.0884207\pi$
$822$	3.18986	−	0.396498i	0.111259	−	0.0138295i
$823$	−5.15995			−0.179865			−0.0899323	−	0.995948i	$-0.528665\pi$
$823$	−5.15995			−0.179865			−0.0899323	+	0.995948i	$0.528665\pi$
$824$	−19.8815	+	19.0367i	−0.692605	+	0.663176i
$825$		0			0
$826$	−0.368336	−	2.96329i	−0.0128160	−	0.103106i
$827$	1.85424	−	4.47653i	0.0644782	−	0.155664i	−0.888356	−	0.459155i	$-0.848152\pi$
$827$	1.85424	−	4.47653i	0.0644782	−	0.155664i	0.952834	+	0.303491i	$0.0981522\pi$
$828$	12.8539	−	3.24560i	0.446702	−	0.112792i
$829$	7.40324	−	17.8730i	0.257125	−	0.620755i	−0.741621	−	0.670819i	$-0.765943\pi$
$829$	7.40324	−	17.8730i	0.257125	−	0.620755i	0.998746	+	0.0500640i	$0.0159425\pi$
$830$		0			0
$831$		−	14.5085i		−	0.503295i
$832$	−11.4556	−	31.4518i	−0.397151	−	1.09039i
$833$	−27.7615	−	27.7615i	−0.961879	−	0.961879i
$834$	2.73662	−	1.55370i	0.0947616	−	0.0538003i
$835$		0			0
$836$	1.18596	+	0.707791i	0.0410174	+	0.0244795i
$837$	47.1361	+	19.5244i	1.62926	+	0.674863i
$838$	36.8036	+	28.6658i	1.27136	+	0.990244i
$839$	11.2001	−	11.2001i	0.386669	−	0.386669i	−0.486828	−	0.873498i	$-0.661846\pi$
$839$	11.2001	−	11.2001i	0.386669	−	0.386669i	0.873498	+	0.486828i	$0.161846\pi$
$840$		0			0
$841$	9.86351	+	9.86351i	0.340121	+	0.340121i
$842$	−1.00571	−	8.09099i	−0.0346589	−	0.278834i
$843$	3.45684	−	8.34556i	0.119060	−	0.287436i
$844$	−16.0839	−	21.6010i	−0.553630	−	0.743537i
$845$		0			0
$846$	−1.04993	+	3.80799i	−0.0360974	+	0.130921i
$847$	−5.81541	+	5.81541i	−0.199820	+	0.199820i
$848$	2.03911	+	19.9294i	0.0700234	+	0.684379i
$849$	−34.9307			−1.19882
$850$		0			0
$851$	−4.66656	−	1.93295i	−0.159968	−	0.0662607i
$852$	2.74403	+	3.68530i	0.0940091	+	0.126256i
$853$	1.97932	+	0.819862i	0.0677707	+	0.0280715i	0.416311	−	0.909222i	$-0.363323\pi$
$853$	1.97932	+	0.819862i	0.0677707	+	0.0280715i	−0.348541	+	0.937294i	$0.613323\pi$
$854$	−5.63915	−	4.39225i	−0.192968	−	0.150300i
$855$		0			0
$856$	7.27497	+	18.7013i	0.248653	+	0.639197i
$857$		−	15.5286i		−	0.530448i	−0.964187	−	0.265224i	$-0.914554\pi$
$857$		−	15.5286i		−	0.530448i	0.964187	−	0.265224i	$-0.0854460\pi$
$858$	5.73039	+	4.46331i	0.195632	+	0.152375i
$859$	14.0088	+	33.8203i	0.477974	+	1.15393i	0.960557	+	0.278082i	$0.0896987\pi$
$859$	14.0088	+	33.8203i	0.477974	+	1.15393i	−0.482583	+	0.875850i	$0.660301\pi$
$860$		0			0
$861$	0.804774	+	0.333348i	0.0274266	+	0.0113605i
$862$	15.7493	+	4.34238i	0.536425	+	0.147902i
$863$	−13.2837	+	13.2837i	−0.452182	+	0.452182i	−0.896078	−	0.443896i	$-0.853596\pi$
$863$	−13.2837	+	13.2837i	−0.452182	+	0.452182i	0.443896	+	0.896078i	$0.353596\pi$
$864$	31.3820	+	5.29239i	1.06764	+	0.180051i
$865$		0			0
$866$	−8.46766	+	4.80747i	−0.287743	+	0.163364i
$867$	−10.8310	−	26.1483i	−0.367840	−	0.888043i
$868$	7.53469	−	12.6250i	0.255744	−	0.428521i
$869$	14.5534	−	6.02822i	0.493691	−	0.204494i
$870$		0			0
$871$	18.1296	+	18.1296i	0.614298	+	0.614298i
$872$	11.3367	+	29.1426i	0.383910	+	0.986892i
$873$			3.54148i			0.119861i
$874$	−3.48046	+	4.46852i	−0.117728	+	0.151150i
$875$		0			0
$876$	4.40854	−	30.1127i	0.148951	−	1.01741i
$877$	1.17244	+	2.83052i	0.0395905	+	0.0955799i	0.942438	−	0.334381i	$-0.108527\pi$
$877$	1.17244	+	2.83052i	0.0395905	+	0.0955799i	−0.902847	+	0.429961i	$0.858527\pi$
$878$	−12.3173	−	21.6951i	−0.415688	−	0.732175i
$879$			25.9527i			0.875362i
$880$		0			0
$881$		−	32.6206i		−	1.09902i	−0.835488	−	0.549508i	$-0.814815\pi$
$881$		−	32.6206i		−	1.09902i	0.835488	−	0.549508i	$-0.185185\pi$
$882$	9.64522	−	5.47602i	0.324771	−	0.184387i
$883$	−5.81184	−	14.0310i	−0.195584	−	0.472181i	0.795413	−	0.606068i	$-0.207254\pi$
$883$	−5.81184	−	14.0310i	−0.195584	−	0.472181i	−0.990997	+	0.133887i	$0.957254\pi$
$884$	−30.9343	−	41.5454i	−1.04043	−	1.39732i
$885$		0			0
$886$	12.3315	+	9.60485i	0.414286	+	0.322681i
$887$		−	26.0808i		−	0.875708i	−0.899046	−	0.437854i	$-0.855739\pi$
$887$		−	26.0808i		−	0.875708i	0.899046	−	0.437854i	$-0.144261\pi$
$888$	−2.44752	−	2.55613i	−0.0821334	−	0.0857782i
$889$	−9.74267	−	9.74267i	−0.326759	−	0.326759i
$890$		0			0
$891$	−3.21250	+	1.33066i	−0.107623	+	0.0445788i
$892$	−51.2528	+	12.9413i	−1.71607	+	0.433308i
$893$	−0.645829	−	1.55917i	−0.0216118	−	0.0521756i
$894$	17.2253	+	30.3400i	0.576101	+	1.01472i
$895$		0			0
$896$	2.81904	−	8.72712i	0.0941775	−	0.291553i
$897$	−21.0633	+	21.0633i	−0.703285	+	0.703285i
$898$	8.84753	−	32.0890i	0.295246	−	1.07082i
$899$	−32.5042	−	13.4637i	−1.08408	−	0.449039i
$900$		0			0
$901$	11.8633	+	28.6406i	0.395224	+	0.954156i
$902$	−0.649991	+	0.834515i	−0.0216423	+	0.0277863i
$903$		−	12.4442i		−	0.414119i
$904$	58.1717	+	1.26272i	1.93476	+	0.0419974i
$905$		0			0
$906$	−12.3957	+	15.9146i	−0.411818	+	0.528727i
$907$	−22.6408	−	9.37811i	−0.751774	−	0.311395i	−0.0263091	−	0.999654i	$-0.508375\pi$
$907$	−22.6408	−	9.37811i	−0.751774	−	0.311395i	−0.725465	+	0.688259i	$0.758375\pi$
$908$	6.74955	−	46.1031i	0.223992	−	1.52998i
$909$	−0.881114	−	0.364969i	−0.0292247	−	0.0121053i
$910$		0			0
$911$	19.6911			0.652395			0.326198	−	0.945302i	$-0.394233\pi$
$911$	19.6911			0.652395			0.326198	+	0.945302i	$0.394233\pi$
$912$	−3.49274	+	1.88395i	−0.115656	+	0.0623837i
$913$	5.61184	−	5.61184i	0.185725	−	0.185725i
$914$	13.4029	+	3.69542i	0.443329	+	0.122234i
$915$		0			0
$916$	−21.2814	−	3.11563i	−0.703158	−	0.102943i
$917$	−3.47519	+	8.38984i	−0.114761	+	0.277057i
$918$	48.8711	−	6.07465i	1.61299	−	0.200493i
$919$	14.8097	+	14.8097i	0.488526	+	0.488526i	0.907841	−	0.419315i	$-0.137730\pi$
$919$	14.8097	+	14.8097i	0.488526	+	0.488526i	−0.419315	+	0.907841i	$0.637730\pi$
$920$		0			0
$921$	30.8092	−	30.8092i	1.01520	−	1.01520i
$922$	−19.4556	+	24.9787i	−0.640735	+	0.822631i
$923$	6.68735	+	2.76999i	0.220117	+	0.0911753i
$924$	0.487208	+	1.92954i	0.0160280	+	0.0634771i
$925$		0			0
$926$	−10.0862	−	17.7654i	−0.331454	−	0.583808i
$927$	−8.50865	−	8.50865i	−0.279461	−	0.279461i
$928$	−21.6405	−	3.64953i	−0.710383	−	0.119802i
$929$		−	2.48749i		−	0.0816119i	−0.999167	−	0.0408059i	$-0.987007\pi$
$929$		−	2.48749i		−	0.0816119i	0.999167	−	0.0408059i	$-0.0129925\pi$
$930$		0			0
$931$	−1.81340	+	4.37794i	−0.0594318	+	0.143481i
$932$	−17.3354	+	29.0469i	−0.567840	+	0.951464i
$933$	6.99181	−	16.8797i	0.228902	−	0.552618i
$934$	−2.00839	+	0.249642i	−0.0657166	+	0.00816854i
$935$		0			0
$936$	13.6374	−	5.30506i	0.445752	−	0.173401i
$937$	29.6925			0.970013			0.485006	−	0.874511i	$-0.338817\pi$
$937$	29.6925			0.970013			0.485006	+	0.874511i	$0.338817\pi$
$938$	0.866504	+	6.97110i	0.0282924	+	0.227614i
$939$	−15.2658	+	6.32331i	−0.498181	+	0.206353i
$940$		0			0
$941$	15.1479	−	36.5702i	0.493807	−	1.19215i	−0.458962	−	0.888456i	$-0.651778\pi$
$941$	15.1479	−	36.5702i	0.493807	−	1.19215i	0.952768	−	0.303698i	$-0.0982215\pi$
$942$	24.0320	−	13.6440i	0.783006	−	0.444547i
$943$	−3.06745	−	3.06745i	−0.0998899	−	0.0998899i
$944$	−6.57927	+	8.07906i	−0.214137	+	0.262951i
$945$		0			0
$946$	14.5679	+	4.01663i	0.473642	+	0.130592i
$947$	−35.1138	+	14.5446i	−1.14104	+	0.472636i	−0.871521	−	0.490358i	$-0.836866\pi$
$947$	−35.1138	+	14.5446i	−1.14104	+	0.472636i	−0.269523	+	0.962994i	$0.586866\pi$
$948$	−6.55660	+	44.7851i	−0.212949	+	1.45455i
$949$	−18.3475	−	44.2948i	−0.595586	−	1.43787i
$950$		0			0
$951$	20.1442	−	20.1442i	0.653222	−	0.653222i
$952$	0.307983	−	14.1883i	0.00998178	−	0.459846i
$953$	−34.9734			−1.13290			−0.566450	−	0.824096i	$-0.691684\pi$
$953$	−34.9734			−1.13290			−0.566450	+	0.824096i	$0.691684\pi$
$954$	−8.69084	+	1.08027i	−0.281376	+	0.0349749i
$955$		0			0
$956$	−16.8021	+	28.1534i	−0.543420	+	0.910547i
$957$	4.39969	−	1.82241i	0.142222	−	0.0589102i
$958$	43.3867	+	11.9625i	1.40176	+	0.386491i
$959$	1.38743			0.0448025
$960$		0			0
$961$	−51.2404			−1.65292
$962$	−5.37461	−	1.48188i	−0.173284	−	0.0477777i
$963$	−8.10441	+	3.35696i	−0.261161	+	0.108176i
$964$	2.05039	−	3.43560i	0.0660385	−	0.110653i
$965$		0			0
$966$	−8.09917	+	1.00672i	−0.260587	+	0.0323908i
$967$	11.5019			0.369876			0.184938	−	0.982750i	$-0.440792\pi$
$967$	11.5019			0.369876			0.184938	+	0.982750i	$0.440792\pi$
$968$	28.6893	+	0.622752i	0.922109	+	0.0200160i
$969$	−4.34225	+	4.34225i	−0.139493	+	0.139493i
$970$		0			0
$971$	−12.3780	−	29.8832i	−0.397230	−	0.958998i	−0.988320	−	0.152393i	$-0.951302\pi$
$971$	−12.3780	−	29.8832i	−0.397230	−	0.958998i	0.591090	−	0.806606i	$-0.298698\pi$
$972$	−3.44246	+	23.5139i	−0.110417	+	0.754207i
$973$	1.25491	−	0.519799i	0.0402305	−	0.0166640i
$974$	−13.1936	−	3.63772i	−0.422751	−	0.116560i
$975$		0			0
$976$	2.53856	+	24.8108i	0.0812574	+	0.794176i
$977$	−13.9126	−	13.9126i	−0.445104	−	0.445104i	0.448619	−	0.893723i	$-0.351916\pi$
$977$	−13.9126	−	13.9126i	−0.445104	−	0.445104i	−0.893723	+	0.448619i	$0.851916\pi$
$978$	−8.46690	+	4.80704i	−0.270742	+	0.153712i
$979$	−3.83053	+	9.24771i	−0.122424	+	0.295558i
$980$		0			0
$981$	−12.6293	+	5.23121i	−0.403221	+	0.167020i
$982$	−4.29514	−	34.5548i	−0.137063	−	1.10269i
$983$	29.1931			0.931115			0.465557	−	0.885018i	$-0.345854\pi$
$983$	29.1931			0.931115			0.465557	+	0.885018i	$0.345854\pi$
$984$	−1.10191	−	2.83261i	−0.0351276	−	0.0903002i
$985$		0			0
$986$	−33.7006	+	4.18897i	−1.07325	+	0.133404i
$987$	0.930596	−	2.24666i	0.0296212	−	0.0715119i
$988$	−3.20388	+	5.36838i	−0.101929	+	0.170791i
$989$	−23.7160	+	57.2556i	−0.754126	+	1.82062i
$990$		0			0
$991$			16.1180i			0.512006i	0.966676	+	0.256003i	$0.0824057\pi$
$991$			16.1180i			0.512006i	−0.966676	+	0.256003i	$0.917594\pi$
$992$	−49.9998	+	11.4767i	−1.58749	+	0.364386i
$993$	−22.0736	−	22.0736i	−0.700485	−	0.700485i
$994$	0.979148	+	1.72463i	0.0310567	+	0.0547019i
$995$		0			0
$996$	5.58278	+	22.1100i	0.176897	+	0.700582i
$997$	4.69692	+	1.94553i	0.148753	+	0.0616154i	0.455818	−	0.890073i	$-0.349347\pi$
$997$	4.69692	+	1.94553i	0.148753	+	0.0616154i	−0.307065	+	0.951689i	$0.599347\pi$
$998$	−17.8366	+	22.9001i	−0.564606	+	0.724890i
$999$	3.74816	−	3.74816i	0.118586	−	0.118586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bb.b.643.22		88
5.2	odd	4		800.2.v.b.707.10		88
5.3	odd	4		160.2.u.a.67.13	yes	88
5.4	even	2		160.2.ba.a.3.1	yes	88
20.3	even	4		640.2.u.a.47.16		88
20.19	odd	2		640.2.ba.a.303.7		88
32.11	odd	8		800.2.v.b.43.10		88
160.43	even	8		160.2.ba.a.107.1	yes	88
160.53	odd	8		640.2.ba.a.207.7		88
160.107	even	8	inner	800.2.bb.b.107.22		88
160.139	odd	8		160.2.u.a.43.13	✓	88
160.149	even	8		640.2.u.a.463.16		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.13	✓	88	160.139	odd	8
160.2.u.a.67.13	yes	88	5.3	odd	4
160.2.ba.a.3.1	yes	88	5.4	even	2
160.2.ba.a.107.1	yes	88	160.43	even	8
640.2.u.a.47.16		88	20.3	even	4
640.2.u.a.463.16		88	160.149	even	8
640.2.ba.a.207.7		88	160.53	odd	8
640.2.ba.a.303.7		88	20.19	odd	2
800.2.v.b.43.10		88	32.11	odd	8
800.2.v.b.707.10		88	5.2	odd	4
800.2.bb.b.107.22		88	160.107	even	8	inner
800.2.bb.b.643.22		88	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bb (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36334 + 0.375898i) q^{2} +(-1.22690 + 0.508197i) q^{3} +(1.71740 + 1.02496i) q^{4} +(-1.86371 + 0.231658i) q^{6} -0.810621 q^{7} +(1.95613 + 2.04293i) q^{8} +(-0.874309 + 0.874309i) q^{9} +(0.353731 + 0.853982i) q^{11} +(-2.62795 - 0.384736i) q^{12} +(-3.86563 + 1.60120i) q^{13} +(-1.10515 - 0.304711i) q^{14} +(1.89893 + 3.52052i) q^{16} +(4.37679 + 4.37679i) q^{17} +(-1.52063 + 0.863331i) q^{18} +(0.285895 - 0.690211i) q^{19} +(0.994548 - 0.411955i) q^{21} +(0.161246 + 1.29724i) q^{22} -5.36098 q^{23} +(-3.43818 - 1.51237i) q^{24} +(-5.87207 + 0.729895i) q^{26} +(2.15296 - 5.19770i) q^{27} +(-1.39216 - 0.830850i) q^{28} +(-1.48464 + 3.58424i) q^{29} +9.06865i q^{31} +(1.26554 + 5.51348i) q^{32} +(-0.867982 - 0.867982i) q^{33} +(4.32183 + 7.61229i) q^{34} +(-2.39767 + 0.605412i) q^{36} +(0.870467 + 0.360559i) q^{37} +(0.649221 - 0.833526i) q^{38} +(3.92901 - 3.92901i) q^{39} +(0.572180 + 0.572180i) q^{41} +(1.51076 - 0.187787i) q^{42} +(4.42382 - 10.6801i) q^{43} +(-0.267796 + 1.82919i) q^{44} +(-7.30885 - 2.01518i) q^{46} +(1.59734 - 1.59734i) q^{47} +(-4.11891 - 3.35428i) q^{48} -6.34289 q^{49} +(-7.59414 - 3.14560i) q^{51} +(-8.28000 - 1.21220i) q^{52} +(4.62712 + 1.91662i) q^{53} +(4.88902 - 6.27695i) q^{54} +(-1.58568 - 1.65604i) q^{56} +0.992109i q^{57} +(-3.37138 + 4.32846i) q^{58} +(0.996806 + 2.40650i) q^{59} +(5.76047 + 2.38607i) q^{61} +(-3.40889 + 12.3637i) q^{62} +(0.708734 - 0.708734i) q^{63} +(-0.347145 + 7.99246i) q^{64} +(-0.857084 - 1.50963i) q^{66} +(-2.34497 - 5.66126i) q^{67} +(3.03069 + 12.0027i) q^{68} +(6.57737 - 2.72444i) q^{69} +(-1.22326 - 1.22326i) q^{71} +(-3.49641 - 0.0758959i) q^{72} +11.4586i q^{73} +(1.05121 + 0.818772i) q^{74} +(1.19843 - 0.892340i) q^{76} +(-0.286742 - 0.692256i) q^{77} +(6.83349 - 3.87967i) q^{78} -17.0418i q^{79} +3.76178i q^{81} +(0.564996 + 0.995159i) q^{82} +(-3.28569 - 7.93236i) q^{83} +(2.13027 + 0.311875i) q^{84} +(10.0458 - 12.8977i) q^{86} -5.15198i q^{87} +(-1.05269 + 2.39314i) q^{88} +(7.65721 + 7.65721i) q^{89} +(3.13356 - 1.29796i) q^{91} +(-9.20696 - 5.49477i) q^{92} +(-4.60866 - 11.1263i) q^{93} +(2.77815 - 1.57728i) q^{94} +(-4.35462 - 6.12132i) q^{96} +(2.02530 - 2.02530i) q^{97} +(-8.64753 - 2.38428i) q^{98} +(-1.05591 - 0.437374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{19} - 8 q^{21} + 20 q^{22} + 8 q^{23} + 32 q^{24} - 8 q^{26} - 8 q^{27}+ \cdots - 16 q^{98}+O(q^{100}) \) 88 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 + 4 * q^13 - 16 * q^14 - 8 * q^16 + 12 * q^18 - 16 * q^19 - 8 * q^21 + 20 * q^22 + 8 * q^23 + 32 * q^24 - 8 * q^26 - 8 * q^27 + 20 * q^28 - 16 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 4 * q^37 + 4 * q^38 - 8 * q^41 + 68 * q^42 - 28 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^47 + 88 * q^48 + 40 * q^49 + 8 * q^51 - 48 * q^52 + 4 * q^53 + 56 * q^54 + 40 * q^56 + 36 * q^58 - 40 * q^61 + 32 * q^62 + 56 * q^63 - 48 * q^64 + 72 * q^66 + 28 * q^67 - 8 * q^68 - 24 * q^69 + 24 * q^71 - 88 * q^72 + 56 * q^76 + 32 * q^77 - 112 * q^78 - 68 * q^82 - 36 * q^83 - 56 * q^84 + 24 * q^86 + 24 * q^88 - 8 * q^91 - 92 * q^92 - 8 * q^93 + 32 * q^94 + 24 * q^96 + 8 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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