LMFDB - Embedded newform 925.2.t.b.643.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] 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("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.12
Character	$\chi$	$=$	925.643
Dual form			925.2.t.b.82.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.723320 - 1.25283i) q^{2} +(0.791482 + 0.212077i) q^{3} +(-0.0463849 - 0.0803411i) q^{4} +(0.838191 - 0.838191i) q^{6} +(1.58905 + 0.425785i) q^{7} +2.75908 q^{8} +(-2.01661 - 1.16429i) q^{9} +4.76900i q^{11} +(-0.0196744 - 0.0734257i) q^{12} +(2.90320 + 5.02850i) q^{13} +(1.68283 - 1.68283i) q^{14} +(2.08847 - 3.61733i) q^{16} +(-1.25670 - 0.725557i) q^{17} +(-2.91731 + 1.68431i) q^{18} +(0.563197 - 2.10188i) q^{19} +(1.16741 + 0.674003i) q^{21} +(5.97473 + 3.44951i) q^{22} +4.09430 q^{23} +(2.18376 + 0.585137i) q^{24} +8.39979 q^{26} +(-3.08741 - 3.08741i) q^{27} +(-0.0395000 - 0.147416i) q^{28} +(-2.95018 + 2.95018i) q^{29} +(-1.46743 - 1.46743i) q^{31} +(-0.262184 - 0.454116i) q^{32} +(-1.01139 + 3.77458i) q^{33} +(-1.81799 + 1.04962i) q^{34} +0.216022i q^{36} +(0.827803 - 6.02617i) q^{37} +(-2.22592 - 2.22592i) q^{38} +(1.23141 + 4.59567i) q^{39} +(0.369301 - 0.213216i) q^{41} +(1.68882 - 0.975040i) q^{42} -7.53912 q^{43} +(0.383146 - 0.221210i) q^{44} +(2.96149 - 5.12945i) q^{46} +(5.55465 - 5.55465i) q^{47} +(2.42014 - 2.42014i) q^{48} +(-3.71838 - 2.14681i) q^{49} +(-0.840783 - 0.840783i) q^{51} +(0.269330 - 0.466493i) q^{52} +(10.5896 - 2.83749i) q^{53} +(-6.10117 + 1.63480i) q^{54} +(4.38432 + 1.17477i) q^{56} +(0.891520 - 1.54416i) q^{57} +(1.56214 + 5.82999i) q^{58} +(8.06779 - 2.16176i) q^{59} +(-1.52382 + 5.68696i) q^{61} +(-2.89985 + 0.777013i) q^{62} +(-2.70876 - 2.70876i) q^{63} +7.59529 q^{64} +(3.99733 + 3.99733i) q^{66} +(-2.40971 + 8.99317i) q^{67} +0.134620i q^{68} +(3.24056 + 0.868307i) q^{69} +(-6.20532 - 10.7479i) q^{71} +(-5.56398 - 3.21236i) q^{72} +(2.06563 - 2.06563i) q^{73} +(-6.95099 - 5.39595i) q^{74} +(-0.194991 + 0.0522477i) q^{76} +(-2.03057 + 7.57818i) q^{77} +(6.64828 + 1.78140i) q^{78} +(1.30294 - 4.86264i) q^{79} +(1.70401 + 2.95143i) q^{81} -0.616894i q^{82} +(-3.90229 + 1.04562i) q^{83} -0.125054i q^{84} +(-5.45320 + 9.44522i) q^{86} +(-2.96068 + 1.70935i) q^{87} +13.1580i q^{88} +(-3.97708 - 14.8427i) q^{89} +(2.47228 + 9.22669i) q^{91} +(-0.189914 - 0.328940i) q^{92} +(-0.850234 - 1.47265i) q^{93} +(-2.94123 - 10.9768i) q^{94} +(-0.111207 - 0.415028i) q^{96} +17.9332i q^{97} +(-5.37917 + 3.10566i) q^{98} +(5.55249 - 9.61720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.723320	−	1.25283i	0.511465	−	0.885883i	−0.488447	−	0.872594i	$-0.662436\pi$
$2$	0.723320	−	1.25283i	0.511465	−	0.885883i	0.999912	−	0.0132894i	$-0.00423027\pi$
$3$	0.791482	+	0.212077i	0.456962	+	0.122443i	0.479955	−	0.877293i	$-0.340653\pi$
$3$	0.791482	+	0.212077i	0.456962	+	0.122443i	−0.0229929	+	0.999736i	$0.507320\pi$
$4$	−0.0463849	−	0.0803411i	−0.0231925	−	0.0401705i
$5$		0			0
$5$		0			0
$6$	0.838191	−	0.838191i	0.342190	−	0.342190i
$7$	1.58905	+	0.425785i	0.600605	+	0.160932i	0.546296	−	0.837592i	$-0.316038\pi$
$7$	1.58905	+	0.425785i	0.600605	+	0.160932i	0.0543096	+	0.998524i	$0.482704\pi$
$8$	2.75908			0.975481
$9$	−2.01661	−	1.16429i	−0.672203	−	0.388097i
$10$		0			0
$11$			4.76900i			1.43791i	0.695059	+	0.718953i	$0.255378\pi$
$11$			4.76900i			1.43791i	−0.695059	+	0.718953i	$0.744622\pi$
$12$	−0.0196744	−	0.0734257i	−0.00567950	−	0.0211962i
$13$	2.90320	+	5.02850i	0.805204	+	1.39465i	0.916153	+	0.400828i	$0.131278\pi$
$13$	2.90320	+	5.02850i	0.805204	+	1.39465i	−0.110949	+	0.993826i	$0.535389\pi$
$14$	1.68283	−	1.68283i	0.449755	−	0.449755i
$15$		0			0
$16$	2.08847	−	3.61733i	0.522117	−	0.904333i
$17$	−1.25670	−	0.725557i	−0.304795	−	0.175973i	0.339800	−	0.940498i	$-0.389641\pi$
$17$	−1.25670	−	0.725557i	−0.304795	−	0.175973i	−0.644595	+	0.764524i	$0.722974\pi$
$18$	−2.91731	+	1.68431i	−0.687616	+	0.396995i
$19$	0.563197	−	2.10188i	0.129206	−	0.482204i	−0.870748	−	0.491729i	$-0.836365\pi$
$19$	0.563197	−	2.10188i	0.129206	−	0.482204i	0.999955	+	0.00952470i	$0.00303185\pi$
$20$		0			0
$21$	1.16741	+	0.674003i	0.254749	+	0.147079i
$22$	5.97473	+	3.44951i	1.27382	+	0.735438i
$23$	4.09430			0.853720			0.426860	−	0.904318i	$-0.359620\pi$
$23$	4.09430			0.853720			0.426860	+	0.904318i	$0.359620\pi$
$24$	2.18376	+	0.585137i	0.445758	+	0.119441i
$25$		0			0
$26$	8.39979			1.64733
$27$	−3.08741	−	3.08741i	−0.594172	−	0.594172i
$28$	−0.0395000	−	0.147416i	−0.00746480	−	0.0278590i
$29$	−2.95018	+	2.95018i	−0.547834	+	0.547834i	−0.925814	−	0.377980i	$-0.876619\pi$
$29$	−2.95018	+	2.95018i	−0.547834	+	0.547834i	0.377980	+	0.925814i	$0.376619\pi$
$30$		0			0
$31$	−1.46743	−	1.46743i	−0.263557	−	0.263557i	0.562940	−	0.826498i	$-0.309670\pi$
$31$	−1.46743	−	1.46743i	−0.263557	−	0.263557i	−0.826498	+	0.562940i	$0.809670\pi$
$32$	−0.262184	−	0.454116i	−0.0463481	−	0.0802772i
$33$	−1.01139	+	3.77458i	−0.176061	+	0.657069i
$34$	−1.81799	+	1.04962i	−0.311784	+	0.180008i
$35$		0			0
$36$			0.216022i			0.0360037i
$37$	0.827803	−	6.02617i	0.136090	−	0.990696i
$37$	0.827803	−	6.02617i	0.136090	−	0.990696i
$38$	−2.22592	−	2.22592i	−0.361092	−	0.361092i
$39$	1.23141	+	4.59567i	0.197183	+	0.735896i
$40$		0			0
$41$	0.369301	−	0.213216i	0.0576751	−	0.0332988i	−0.470885	−	0.882195i	$-0.656065\pi$
$41$	0.369301	−	0.213216i	0.0576751	−	0.0332988i	0.528560	+	0.848896i	$0.322732\pi$
$42$	1.68882	−	0.975040i	0.260590	−	0.150452i
$43$	−7.53912			−1.14971			−0.574853	−	0.818257i	$-0.694941\pi$
$43$	−7.53912			−1.14971			−0.574853	+	0.818257i	$0.694941\pi$
$44$	0.383146	−	0.221210i	0.0577615	−	0.0333486i
$45$		0			0
$46$	2.96149	−	5.12945i	0.436648	−	0.756296i
$47$	5.55465	−	5.55465i	0.810228	−	0.810228i	−0.174440	−	0.984668i	$-0.555811\pi$
$47$	5.55465	−	5.55465i	0.810228	−	0.810228i	0.984668	+	0.174440i	$0.0558114\pi$
$48$	2.42014	−	2.42014i	0.349317	−	0.349317i
$49$	−3.71838	−	2.14681i	−0.531198	−	0.306687i
$50$		0			0
$51$	−0.840783	−	0.840783i	−0.117733	−	0.117733i
$52$	0.269330	−	0.466493i	0.0373493	−	0.0646909i
$53$	10.5896	−	2.83749i	1.45460	−	0.389759i	0.556978	−	0.830527i	$-0.311961\pi$
$53$	10.5896	−	2.83749i	1.45460	−	0.389759i	0.897621	+	0.440768i	$0.145294\pi$
$54$	−6.10117	+	1.63480i	−0.830264	+	0.222469i
$55$		0			0
$56$	4.38432	+	1.17477i	0.585879	+	0.156986i
$57$	0.891520	−	1.54416i	0.118085	−	0.204529i
$58$	1.56214	+	5.82999i	0.205119	+	0.765515i
$59$	8.06779	−	2.16176i	1.05034	−	0.281437i	0.307946	−	0.951404i	$-0.400358\pi$
$59$	8.06779	−	2.16176i	1.05034	−	0.281437i	0.742391	+	0.669967i	$0.233692\pi$
$60$		0			0
$61$	−1.52382	+	5.68696i	−0.195105	+	0.728140i	0.797135	+	0.603801i	$0.206348\pi$
$61$	−1.52382	+	5.68696i	−0.195105	+	0.728140i	−0.992240	+	0.124339i	$0.960319\pi$
$62$	−2.89985	+	0.777013i	−0.368281	+	0.0986807i
$63$	−2.70876	−	2.70876i	−0.341272	−	0.341272i
$64$	7.59529			0.949412
$65$		0			0
$66$	3.99733	+	3.99733i	0.492037	+	0.492037i
$67$	−2.40971	+	8.99317i	−0.294393	+	1.09869i	0.647305	+	0.762231i	$0.275896\pi$
$67$	−2.40971	+	8.99317i	−0.294393	+	1.09869i	−0.941698	+	0.336460i	$0.890770\pi$
$68$			0.134620i			0.0163250i
$69$	3.24056	+	0.868307i	0.390118	+	0.104532i
$70$		0			0
$71$	−6.20532	−	10.7479i	−0.736436	−	1.27554i	−0.954090	−	0.299519i	$-0.903174\pi$
$71$	−6.20532	−	10.7479i	−0.736436	−	1.27554i	0.217654	−	0.976026i	$-0.430159\pi$
$72$	−5.56398	−	3.21236i	−0.655721	−	0.378581i
$73$	2.06563	−	2.06563i	0.241763	−	0.241763i	−0.575816	−	0.817579i	$-0.695316\pi$
$73$	2.06563	−	2.06563i	0.241763	−	0.241763i	0.817579	+	0.575816i	$0.195316\pi$
$74$	−6.95099	−	5.39595i	−0.808036	−	0.627266i
$75$		0			0
$76$	−0.194991	+	0.0522477i	−0.0223670	+	0.00599322i
$77$	−2.03057	+	7.57818i	−0.231405	+	0.863614i
$78$	6.64828	+	1.78140i	0.752770	+	0.201704i
$79$	1.30294	−	4.86264i	0.146592	−	0.547089i	−0.853087	−	0.521768i	$-0.825273\pi$
$79$	1.30294	−	4.86264i	0.146592	−	0.547089i	0.999679	−	0.0253210i	$-0.00806079\pi$
$80$		0			0
$81$	1.70401	+	2.95143i	0.189334	+	0.327937i
$82$		−	0.616894i		−	0.0681246i
$83$	−3.90229	+	1.04562i	−0.428332	+	0.114771i	−0.466543	−	0.884498i	$-0.654501\pi$
$83$	−3.90229	+	1.04562i	−0.428332	+	0.114771i	0.0382109	+	0.999270i	$0.487834\pi$
$84$		−	0.125054i		−	0.0136445i
$85$		0			0
$86$	−5.45320	+	9.44522i	−0.588034	+	1.01850i
$87$	−2.96068	+	1.70935i	−0.317418	+	0.183261i
$88$			13.1580i			1.40265i
$89$	−3.97708	−	14.8427i	−0.421569	−	1.57332i	−0.771302	−	0.636469i	$-0.780394\pi$
$89$	−3.97708	−	14.8427i	−0.421569	−	1.57332i	0.349733	−	0.936849i	$-0.386272\pi$
$90$		0			0
$91$	2.47228	+	9.22669i	0.259166	+	0.967219i
$92$	−0.189914	−	0.328940i	−0.0197999	−	0.0342944i
$93$	−0.850234	−	1.47265i	−0.0881652	−	0.152707i
$94$	−2.94123	−	10.9768i	−0.303364	−	1.13217i
$95$		0			0
$96$	−0.111207	−	0.415028i	−0.0113500	−	0.0423587i
$97$			17.9332i			1.82084i	0.413689	+	0.910418i	$0.364240\pi$
$97$			17.9332i			1.82084i	−0.413689	+	0.910418i	$0.635760\pi$
$98$	−5.37917	+	3.10566i	−0.543378	+	0.313719i
$99$	5.55249	−	9.61720i	0.558046	−	0.966565i
$100$		0			0
$101$		−	6.87214i		−	0.683803i	−0.939736	−	0.341902i	$-0.888929\pi$
$101$		−	6.87214i		−	0.683803i	0.939736	−	0.341902i	$-0.111071\pi$
$102$	−1.66151	+	0.445201i	−0.164514	+	0.0440814i
$103$		−	12.6979i		−	1.25116i	−0.780159	−	0.625581i	$-0.784862\pi$
$103$		−	12.6979i		−	1.25116i	0.780159	−	0.625581i	$-0.215138\pi$
$104$	8.01017	+	13.8740i	0.785461	+	1.36046i
$105$		0			0
$106$	4.10482	−	15.3194i	0.398696	−	1.48795i
$107$	−8.86771	−	2.37610i	−0.857274	−	0.229706i	−0.196697	−	0.980464i	$-0.563022\pi$
$107$	−8.86771	−	2.37610i	−0.857274	−	0.229706i	−0.660577	+	0.750759i	$0.729688\pi$
$108$	−0.104836	+	0.391255i	−0.0100879	+	0.0376485i
$109$	−7.90182	+	2.11729i	−0.756857	+	0.202799i	−0.616557	−	0.787310i	$-0.711473\pi$
$109$	−7.90182	+	2.11729i	−0.756857	+	0.202799i	−0.140299	+	0.990109i	$0.544807\pi$
$110$		0			0
$111$	1.93320	−	4.59405i	0.183492	−	0.436048i
$112$	4.85889	−	4.85889i	0.459122	−	0.459122i
$113$	−6.41792	−	3.70539i	−0.603747	−	0.348573i	0.166767	−	0.985996i	$-0.446667\pi$
$113$	−6.41792	−	3.70539i	−0.603747	−	0.348573i	−0.770514	+	0.637423i	$0.780000\pi$
$114$	−1.28971	−	2.23384i	−0.120792	−	0.209219i
$115$		0			0
$116$	0.373864	+	0.100177i	0.0347124	+	0.00930117i
$117$		−	13.5207i		−	1.24999i
$118$	3.12729	−	11.6712i	0.287890	−	1.07442i
$119$	−1.68803	−	1.68803i	−0.154742	−	0.154742i
$120$		0			0
$121$	−11.7433			−1.06757
$122$	6.02257	+	6.02257i	0.545258	+	0.545258i
$123$	0.337514	−	0.0904365i	0.0304326	−	0.00815438i
$124$	−0.0498281	+	0.185961i	−0.00447470	+	0.0166998i
$125$		0			0
$126$	−5.35291	+	1.43431i	−0.476875	+	0.127778i
$127$	0.141304	+	0.527354i	0.0125387	+	0.0467951i	0.971912	−	0.235346i	$-0.0756222\pi$
$127$	0.141304	+	0.527354i	0.0125387	+	0.0467951i	−0.959373	+	0.282141i	$0.908956\pi$
$128$	6.01820	−	10.4238i	0.531939	−	0.921345i
$129$	−5.96708	−	1.59887i	−0.525372	−	0.140773i
$130$		0			0
$131$	−15.3752	+	4.11977i	−1.34334	+	0.359946i	−0.857671	−	0.514198i	$-0.828090\pi$
$131$	−15.3752	+	4.11977i	−1.34334	+	0.359946i	−0.485666	+	0.874144i	$0.661423\pi$
$132$	0.350167	−	0.0938269i	0.0304781	−	0.00816658i
$133$	1.78990	−	3.10019i	0.155204	−	0.268821i
$134$	9.52390	+	9.52390i	0.822740	+	0.822740i
$135$		0			0
$136$	−3.46733	−	2.00187i	−0.297322	−	0.171659i
$137$	1.35878	−	1.35878i	0.116088	−	0.116088i	−0.646676	−	0.762765i	$-0.723841\pi$
$137$	1.35878	−	1.35878i	0.116088	−	0.116088i	0.762765	+	0.646676i	$0.223841\pi$
$138$	3.43180	−	3.43180i	0.292135	−	0.292135i
$139$	−8.69989	+	15.0687i	−0.737915	+	1.27811i	0.215517	+	0.976500i	$0.430856\pi$
$139$	−8.69989	+	15.0687i	−0.737915	+	1.27811i	−0.953432	+	0.301607i	$0.902477\pi$
$140$		0			0
$141$	5.57442	−	3.21839i	0.469450	−	0.271037i
$142$	−17.9537			−1.50664
$143$	−23.9809	+	13.8454i	−2.00538	+	1.15781i
$144$	−8.42324	+	4.86316i	−0.701937	+	0.405263i
$145$		0			0
$146$	−1.09376	−	4.08198i	−0.0905206	−	0.337827i
$147$	−2.48775	−	2.48775i	−0.205186	−	0.205186i
$148$	−0.522547	+	0.213017i	−0.0429531	+	0.0175099i
$149$		−	8.07457i		−	0.661495i	−0.943719	−	0.330747i	$-0.892699\pi$
$149$		−	8.07457i		−	0.661495i	0.943719	−	0.330747i	$-0.107301\pi$
$150$		0			0
$151$	−18.1193	+	10.4612i	−1.47453	+	0.851320i	−0.999588	−	0.0286973i	$-0.990864\pi$
$151$	−18.1193	+	10.4612i	−1.47453	+	0.851320i	−0.474942	+	0.880017i	$0.657531\pi$
$152$	1.55390	−	5.79924i	0.126038	−	0.470381i
$153$	1.68952	+	2.92633i	0.136589	+	0.236580i
$154$	8.02540	+	8.02540i	0.646706	+	0.646706i
$155$		0			0
$156$	0.312102	−	0.312102i	0.0249882	−	0.0249882i
$157$	3.58307	+	13.3722i	0.285960	+	1.06722i	0.948135	+	0.317868i	$0.102967\pi$
$157$	3.58307	+	13.3722i	0.285960	+	1.06722i	−0.662175	+	0.749349i	$0.730366\pi$
$158$	−5.14960	−	5.14960i	−0.409680	−	0.409680i
$159$	8.98328			0.712420
$160$		0			0
$161$	6.50605	+	1.74329i	0.512749	+	0.137391i
$162$	4.93018			0.387351
$163$	−5.42818	−	3.13396i	−0.425168	−	0.245471i	0.272118	−	0.962264i	$-0.412276\pi$
$163$	−5.42818	−	3.13396i	−0.425168	−	0.245471i	−0.697286	+	0.716793i	$0.745609\pi$
$164$	−0.0342600	−	0.0197800i	−0.00267526	−	0.00154456i
$165$		0			0
$166$	−1.51263	+	5.64522i	−0.117403	+	0.438154i
$167$	2.71690	−	1.56860i	0.210240	−	0.121382i	−0.391183	−	0.920313i	$-0.627934\pi$
$167$	2.71690	−	1.56860i	0.210240	−	0.121382i	0.601423	+	0.798931i	$0.294601\pi$
$168$	3.22097	+	1.85963i	0.248503	+	0.143473i
$169$	−10.3572	+	17.9392i	−0.796707	+	1.37994i
$170$		0			0
$171$	−3.58294	+	3.58294i	−0.273994	+	0.273994i
$172$	0.349702	+	0.605701i	0.0266645	+	0.0461843i
$173$	−1.32677	−	4.95158i	−0.100873	−	0.376461i	0.896972	−	0.442088i	$-0.145762\pi$
$173$	−1.32677	−	4.95158i	−0.100873	−	0.376461i	−0.997844	+	0.0656265i	$0.979095\pi$
$174$			4.94563i			0.374927i
$175$		0			0
$176$	17.2510	+	9.95989i	1.30035	+	0.750755i
$177$	6.84398			0.514425
$178$	−21.4720	−	5.75340i	−1.60939	−	0.431236i
$179$	−2.46194	+	2.46194i	−0.184014	+	0.184014i	−0.793102	−	0.609088i	$-0.791536\pi$
$179$	−2.46194	+	2.46194i	−0.184014	+	0.184014i	0.609088	+	0.793102i	$0.291536\pi$
$180$		0			0
$181$	5.87198	+	10.1706i	0.436461	+	0.755972i	0.997414	−	0.0718755i	$-0.0228984\pi$
$181$	5.87198	+	10.1706i	0.436461	+	0.755972i	−0.560953	+	0.827848i	$0.689565\pi$
$182$	13.3477	+	3.57651i	0.989397	+	0.265108i
$183$	−2.41215	+	4.17796i	−0.178311	+	0.308844i
$184$	11.2965			0.832788
$185$		0			0
$186$	−2.45997			−0.180374
$187$	3.46018	−	5.99320i	0.253033	−	0.438266i
$188$	−0.703918	−	0.188614i	−0.0513385	−	0.0137561i
$189$	−3.59148	−	6.22062i	−0.261242	−	0.452484i
$190$		0			0
$191$	15.0489	−	15.0489i	1.08890	−	1.08890i	0.0932582	−	0.995642i	$-0.470272\pi$
$191$	15.0489	−	15.0489i	1.08890	−	1.08890i	0.995642	−	0.0932582i	$-0.0297282\pi$
$192$	6.01154	+	1.61079i	0.433846	+	0.116249i
$193$	12.5994			0.906924			0.453462	−	0.891276i	$-0.350189\pi$
$193$	12.5994			0.906924			0.453462	+	0.891276i	$0.350189\pi$
$194$	22.4672	+	12.9714i	1.61305	+	0.931294i
$195$		0			0
$196$			0.398319i			0.0284513i
$197$	1.45423	+	5.42726i	0.103610	+	0.386676i	0.998184	−	0.0602434i	$-0.0191877\pi$
$197$	1.45423	+	5.42726i	0.103610	+	0.386676i	−0.894574	+	0.446920i	$0.852521\pi$
$198$	−8.03246	−	13.9126i	−0.570842	−	0.988728i
$199$	11.5832	−	11.5832i	0.821108	−	0.821108i	−0.165159	−	0.986267i	$-0.552814\pi$
$199$	11.5832	−	11.5832i	0.821108	−	0.821108i	0.986267	+	0.165159i	$0.0528136\pi$
$200$		0			0
$201$	−3.81449	+	6.60689i	−0.269053	+	0.466014i
$202$	−8.60961	−	4.97076i	−0.605770	−	0.349741i
$203$	−5.94413	+	3.43184i	−0.417196	+	0.240868i
$204$	−0.0285497	+	0.106549i	−0.00199888	+	0.00745992i
$205$		0			0
$206$	−15.9083	−	9.18465i	−1.10838	−	0.639925i
$207$	−8.25660	−	4.76695i	−0.573873	−	0.331326i
$208$	24.2530			1.68164
$209$	10.0238	+	2.68588i	0.693364	+	0.185786i
$210$		0			0
$211$	17.3906			1.19722			0.598609	−	0.801042i	$-0.295720\pi$
$211$	17.3906			1.19722			0.598609	+	0.801042i	$0.295720\pi$
$212$	−0.719167	−	0.719167i	−0.0493926	−	0.0493926i
$213$	−2.63201	−	9.82280i	−0.180343	−	0.673047i
$214$	−9.39103	+	9.39103i	−0.641958	+	0.641958i
$215$		0			0
$216$	−8.51839	−	8.51839i	−0.579603	−	0.579603i
$217$	−1.70701	−	2.95662i	−0.115879	−	0.200709i
$218$	−3.06295	+	11.4311i	−0.207449	+	0.774211i
$219$	2.07298	−	1.19683i	0.140079	−	0.0808746i
$220$		0			0
$221$		−	8.42576i		−	0.566778i
$222$	−4.35723	−	5.74494i	−0.292438	−	0.385575i
$223$	7.72909	+	7.72909i	0.517578	+	0.517578i	0.916838	−	0.399260i	$-0.130733\pi$
$223$	7.72909	+	7.72909i	0.517578	+	0.517578i	−0.399260	+	0.916838i	$0.630733\pi$
$224$	−0.223268	−	0.833249i	−0.0149177	−	0.0556738i
$225$		0			0
$226$	−9.28442	+	5.36036i	−0.617591	+	0.356566i
$227$	5.73394	−	3.31049i	0.380575	−	0.219725i	−0.297493	−	0.954724i	$-0.596151\pi$
$227$	5.73394	−	3.31049i	0.380575	−	0.219725i	0.678069	+	0.734999i	$0.262817\pi$
$228$	−0.165412			−0.0109547
$229$	−9.79053	+	5.65257i	−0.646977	+	0.373532i	−0.787297	−	0.616574i	$-0.788520\pi$
$229$	−9.79053	+	5.65257i	−0.646977	+	0.373532i	0.140320	+	0.990106i	$0.455187\pi$
$230$		0			0
$231$	−3.21432	+	5.56736i	−0.211486	+	0.366305i
$232$	−8.13977	+	8.13977i	−0.534402	+	0.534402i
$233$	10.6730	−	10.6730i	0.699211	−	0.699211i	−0.265029	−	0.964240i	$-0.585382\pi$
$233$	10.6730	−	10.6730i	0.699211	−	0.699211i	0.964240	+	0.265029i	$0.0853816\pi$
$234$	−16.9391	−	9.77979i	−1.10734	−	0.639325i
$235$		0			0
$236$	−0.547902	−	0.547902i	−0.0356654	−	0.0356654i
$237$	2.06251	−	3.57237i	0.133974	−	0.232050i
$238$	−3.33580	+	0.893825i	−0.216228	+	0.0579381i
$239$	−17.2821	+	4.63073i	−1.11789	+	0.299537i	−0.770028	−	0.638010i	$-0.779758\pi$
$239$	−17.2821	+	4.63073i	−1.11789	+	0.299537i	−0.347859	+	0.937547i	$0.613091\pi$
$240$		0			0
$241$	−27.1013	−	7.26176i	−1.74575	−	0.467771i	−0.762036	−	0.647535i	$-0.775800\pi$
$241$	−27.1013	−	7.26176i	−1.74575	−	0.467771i	−0.983710	+	0.179764i	$0.942467\pi$
$242$	−8.49418	+	14.7124i	−0.546027	+	0.945746i
$243$	4.11297	+	15.3498i	0.263847	+	0.984691i
$244$	0.527578	−	0.141364i	0.0337747	−	0.00904991i
$245$		0			0
$246$	0.130829	−	0.488261i	0.00834136	−	0.0311304i
$247$	12.2044	−	3.27015i	0.776545	−	0.208075i
$248$	−4.04874	−	4.04874i	−0.257095	−	0.257095i
$249$	−3.31035			−0.209785
$250$		0			0
$251$	−1.94654	−	1.94654i	−0.122864	−	0.122864i	0.643001	−	0.765865i	$-0.277689\pi$
$251$	−1.94654	−	1.94654i	−0.122864	−	0.122864i	−0.765865	+	0.643001i	$0.777689\pi$
$252$	−0.0919790	+	0.343270i	−0.00579413	+	0.0216240i
$253$			19.5257i			1.22757i
$254$	0.762893	+	0.204416i	0.0478681	+	0.0128262i
$255$		0			0
$256$	−1.11088	−	1.92410i	−0.0694300	−	0.120256i
$257$	−5.42559	−	3.13247i	−0.338439	−	0.195398i	0.321142	−	0.947031i	$-0.395933\pi$
$257$	−5.42559	−	3.13247i	−0.338439	−	0.195398i	−0.659582	+	0.751633i	$0.729266\pi$
$258$	−6.31923	+	6.31923i	−0.393418	+	0.393418i
$259$	3.88128	−	9.22343i	0.241171	−	0.573116i
$260$		0			0
$261$	9.38422	−	2.51449i	0.580869	−	0.155643i
$262$	−5.95983	+	22.2424i	−0.368200	+	1.37414i
$263$	14.6303	+	3.92018i	0.902143	+	0.241728i	0.679936	−	0.733271i	$-0.262007\pi$
$263$	14.6303	+	3.92018i	0.902143	+	0.241728i	0.222206	+	0.975000i	$0.428674\pi$
$264$	−2.79052	+	10.4143i	−0.171744	+	0.640959i
$265$		0			0
$266$	−2.58934	−	4.48487i	−0.158763	−	0.274985i
$267$		−	12.5911i		−	0.770566i
$268$	0.834296	−	0.223549i	0.0509627	−	0.0136554i
$269$			20.5296i			1.25171i	0.779938	+	0.625856i	$0.215250\pi$
$269$			20.5296i			1.25171i	−0.779938	+	0.625856i	$0.784750\pi$
$270$		0			0
$271$	−6.43197	+	11.1405i	−0.390714	+	0.676737i	−0.992544	−	0.121888i	$-0.961105\pi$
$271$	−6.43197	+	11.1405i	−0.390714	+	0.676737i	0.601830	+	0.798624i	$0.294439\pi$
$272$	−5.24916	+	3.03060i	−0.318277	+	0.183757i
$273$			7.82707i			0.473716i
$274$	−0.719484	−	2.68515i	−0.0434656	−	0.162216i
$275$		0			0
$276$	−0.0805527	−	0.300627i	−0.00484870	−	0.0180956i
$277$	0.620061	+	1.07398i	0.0372559	+	0.0645290i	0.884052	−	0.467388i	$-0.154805\pi$
$277$	0.620061	+	1.07398i	0.0372559	+	0.0645290i	−0.846796	+	0.531917i	$0.821472\pi$
$278$	12.5856	+	21.7989i	0.754836	+	1.30741i
$279$	1.25072	+	4.66773i	0.0748784	+	0.279450i
$280$		0			0
$281$	−4.61727	−	17.2319i	−0.275443	−	1.02797i	−0.955544	−	0.294850i	$-0.904730\pi$
$281$	−4.61727	−	17.2319i	−0.275443	−	1.02797i	0.680100	−	0.733119i	$-0.261936\pi$
$282$		−	9.31171i		−	0.554504i
$283$	−14.4857	+	8.36334i	−0.861087	+	0.497149i	−0.864376	−	0.502846i	$-0.832286\pi$
$283$	−14.4857	+	8.36334i	−0.861087	+	0.497149i	0.00328885	+	0.999995i	$0.498953\pi$
$284$	−0.575667	+	0.997084i	−0.0341595	+	0.0591661i
$285$		0			0
$286$			40.0586i			2.36871i
$287$	0.677623	−	0.181569i	0.0399988	−	0.0107176i
$288$			1.22103i			0.0719501i
$289$	−7.44714	−	12.8988i	−0.438067	−	0.758754i
$290$		0			0
$291$	−3.80321	+	14.1938i	−0.222948	+	0.832054i
$292$	−0.261769	−	0.0701407i	−0.0153188	−	0.00410467i
$293$	5.30445	−	19.7965i	0.309889	−	1.15652i	−0.618765	−	0.785576i	$-0.712367\pi$
$293$	5.30445	−	19.7965i	0.309889	−	1.15652i	0.928654	−	0.370946i	$-0.120967\pi$
$294$	−4.91616	+	1.31728i	−0.286716	+	0.0768253i
$295$		0			0
$296$	2.28397	−	16.6267i	0.132753	−	0.966406i
$297$	14.7238	−	14.7238i	0.854363	−	0.854363i
$298$	−10.1160	−	5.84050i	−0.586007	−	0.338331i
$299$	11.8866	+	20.5882i	0.687419	+	1.19064i
$300$		0			0
$301$	−11.9801	−	3.21005i	−0.690519	−	0.185024i
$302$			30.2672i			1.74168i
$303$	1.45742	−	5.43918i	0.0837268	−	0.312472i
$304$	−6.42697	−	6.42697i	−0.368612	−	0.368612i
$305$		0			0
$306$	4.88825			0.279442
$307$	−4.99397	−	4.99397i	−0.285021	−	0.285021i	0.550087	−	0.835108i	$-0.314595\pi$
$307$	−4.99397	−	4.99397i	−0.285021	−	0.285021i	−0.835108	+	0.550087i	$0.814595\pi$
$308$	0.703027	−	0.188375i	0.0400587	−	0.0107337i
$309$	2.69293	−	10.0502i	0.153196	−	0.571734i
$310$		0			0
$311$	19.0548	−	5.10571i	1.08050	−	0.289518i	0.325698	−	0.945474i	$-0.394401\pi$
$311$	19.0548	−	5.10571i	1.08050	−	0.289518i	0.754800	+	0.655955i	$0.227734\pi$
$312$	3.39754	+	12.6798i	0.192348	+	0.717853i
$313$	10.3702	−	17.9617i	0.586156	−	1.01525i	−0.408574	−	0.912725i	$-0.633974\pi$
$313$	10.3702	−	17.9617i	0.586156	−	1.01525i	0.994730	−	0.102527i	$-0.0326929\pi$
$314$	19.3448	+	5.18341i	1.09169	+	0.292517i
$315$		0			0
$316$	−0.451106	+	0.120874i	−0.0253767	+	0.00679967i
$317$	−19.9739	+	5.35199i	−1.12185	+	0.300597i	−0.771630	−	0.636072i	$-0.780558\pi$
$317$	−19.9739	+	5.35199i	−1.12185	+	0.300597i	−0.350215	+	0.936669i	$0.613892\pi$
$318$	6.49779	−	11.2545i	0.364378	−	0.631121i
$319$	−14.0694	−	14.0694i	−0.787735	−	0.787735i
$320$		0			0
$321$	−6.51472	−	3.76127i	−0.363616	−	0.209934i
$322$	6.89000	−	6.89000i	0.383965	−	0.383965i
$323$	−2.23280	+	2.23280i	−0.124236	+	0.124236i
$324$	0.158081	−	0.273804i	0.00878226	−	0.0152113i
$325$		0			0
$326$	−7.85262	+	4.53371i	−0.434917	+	0.251099i
$327$	−6.70318			−0.370686
$328$	1.01893	−	0.588280i	0.0562610	−	0.0324823i
$329$	11.1917	−	6.46153i	0.617019	−	0.356236i
$330$		0			0
$331$	8.47290	+	31.6213i	0.465713	+	1.73806i	0.654515	+	0.756049i	$0.272873\pi$
$331$	8.47290	+	31.6213i	0.465713	+	1.73806i	−0.188802	+	0.982015i	$0.560460\pi$
$332$	0.265014	+	0.265014i	0.0145445	+	0.0145445i
$333$	−8.68556	+	11.1886i	−0.475966	+	0.613133i
$334$		−	4.53841i		−	0.248331i
$335$		0			0
$336$	4.87618	−	2.81526i	0.266018	−	0.153585i
$337$	2.67277	−	9.97490i	0.145595	−	0.543368i	−0.854133	−	0.520054i	$-0.825912\pi$
$337$	2.67277	−	9.97490i	0.145595	−	0.543368i	0.999728	−	0.0233134i	$-0.00742157\pi$
$338$	14.9831	+	25.9516i	0.814975	+	1.41158i
$339$	−4.29384	−	4.29384i	−0.233209	−	0.233209i
$340$		0			0
$341$	6.99815	−	6.99815i	0.378971	−	0.378971i
$342$	1.89719	+	7.08043i	0.102589	+	0.382866i
$343$	−13.1375	−	13.1375i	−0.709358	−	0.709358i
$344$	−20.8010			−1.12152
$345$		0			0
$346$	−7.16315	−	1.91936i	−0.385093	−	0.103185i
$347$	9.81456			0.526873			0.263437	−	0.964677i	$-0.415144\pi$
$347$	9.81456			0.526873			0.263437	+	0.964677i	$0.415144\pi$
$348$	0.274662	+	0.158576i	0.0147234	+	0.00850057i
$349$	11.0564	+	6.38340i	0.591834	+	0.341696i	0.765822	−	0.643052i	$-0.222332\pi$
$349$	11.0564	+	6.38340i	0.591834	+	0.341696i	−0.173988	+	0.984748i	$0.555665\pi$
$350$		0			0
$351$	6.56164	−	24.4884i	0.350235	−	1.30709i
$352$	2.16568	−	1.25036i	0.115431	−	0.0666442i
$353$	2.95032	+	1.70337i	0.157030	+	0.0906610i	0.576456	−	0.817128i	$-0.304435\pi$
$353$	2.95032	+	1.70337i	0.157030	+	0.0906610i	−0.419426	+	0.907789i	$0.637769\pi$
$354$	4.95039	−	8.57432i	0.263110	−	0.455720i
$355$		0			0
$356$	−1.00800	+	1.00800i	−0.0534238	+	0.0534238i
$357$	−0.978054	−	1.69404i	−0.0517641	−	0.0896581i
$358$	1.30362	+	4.86517i	0.0688983	+	0.257132i
$359$			4.52436i			0.238787i	0.992847	+	0.119393i	$0.0380949\pi$
$359$			4.52436i			0.238787i	−0.992847	+	0.119393i	$0.961905\pi$
$360$		0			0
$361$	12.3538	+	7.13246i	0.650199	+	0.375393i
$362$	16.9893			0.892937
$363$	−9.29463	−	2.49049i	−0.487841	−	0.130717i
$364$	0.626605	−	0.626605i	0.0328430	−	0.0328430i
$365$		0			0
$366$	3.48951	+	6.04401i	0.182400	+	0.315925i
$367$	−10.4390	−	2.79712i	−0.544912	−	0.146009i	−0.0241463	−	0.999708i	$-0.507687\pi$
$367$	−10.4390	−	2.79712i	−0.544912	−	0.146009i	−0.520766	+	0.853700i	$0.674353\pi$
$368$	8.55081	−	14.8104i	0.445742	−	0.772047i
$369$	−0.992981			−0.0516925
$370$		0			0
$371$	18.0357			0.936364
$372$	−0.0788761	+	0.136617i	−0.00408954	+	0.00708328i
$373$	−18.9102	−	5.06699i	−0.979135	−	0.262359i	−0.266455	−	0.963847i	$-0.585852\pi$
$373$	−18.9102	−	5.06699i	−0.979135	−	0.262359i	−0.712680	+	0.701489i	$0.752519\pi$
$374$	−5.00563	−	8.67001i	−0.258835	−	0.448316i
$375$		0			0
$376$	15.3257	−	15.3257i	0.790362	−	0.790362i
$377$	−23.3999	−	6.27000i	−1.20516	−	0.322921i
$378$	−10.3912			−0.534463
$379$	4.24970	+	2.45356i	0.218292	+	0.126031i	0.605159	−	0.796104i	$-0.293109\pi$
$379$	4.24970	+	2.45356i	0.218292	+	0.126031i	−0.386867	+	0.922136i	$0.626443\pi$
$380$		0			0
$381$			0.447359i			0.0229189i
$382$	−7.96850	−	29.7389i	−0.407704	−	1.52157i
$383$	3.23997	+	5.61179i	0.165555	+	0.286749i	0.936852	−	0.349726i	$-0.113725\pi$
$383$	3.23997	+	5.61179i	0.165555	+	0.286749i	−0.771298	+	0.636475i	$0.780392\pi$
$384$	6.97395	−	6.97395i	0.355888	−	0.355888i
$385$		0			0
$386$	9.11340	−	15.7849i	0.463860	−	0.803429i
$387$	15.2035	+	8.77772i	0.772835	+	0.446197i
$388$	1.44077	−	0.831829i	0.0731440	−	0.0422297i
$389$	2.23101	−	8.32624i	0.113117	−	0.422157i	−0.886022	−	0.463642i	$-0.846542\pi$
$389$	2.23101	−	8.32624i	0.113117	−	0.422157i	0.999139	+	0.0414853i	$0.0132090\pi$
$390$		0			0
$391$	−5.14531	−	2.97065i	−0.260209	−	0.150232i
$392$	−10.2593	−	5.92322i	−0.518173	−	0.299168i
$393$	−13.0429			−0.657928
$394$	7.85130	+	2.10375i	0.395543	+	0.105985i
$395$		0			0
$396$	−1.03021			−0.0517699
$397$	0.770578	+	0.770578i	0.0386742	+	0.0386742i	0.726179	−	0.687505i	$-0.241294\pi$
$397$	0.770578	+	0.770578i	0.0386742	+	0.0386742i	−0.687505	+	0.726179i	$0.741294\pi$
$398$	−6.13337	−	22.8900i	−0.307438	−	1.14737i
$399$	2.07415	−	2.07415i	0.103837	−	0.103837i
$400$		0			0
$401$	−17.3804	−	17.3804i	−0.867936	−	0.867936i	0.124308	−	0.992244i	$-0.460329\pi$
$401$	−17.3804	−	17.3804i	−0.867936	−	0.867936i	−0.992244	+	0.124308i	$0.960329\pi$
$402$	5.51820	+	9.55780i	0.275223	+	0.476700i
$403$	3.11871	−	11.6392i	0.155354	−	0.579789i
$404$	−0.552115	+	0.318764i	−0.0274687	+	0.0158591i
$405$		0			0
$406$			9.92929i			0.492783i
$407$	28.7388	+	3.94779i	1.42453	+	0.195685i
$408$	−2.31978	−	2.31978i	−0.114846	−	0.114846i
$409$	−2.48177	−	9.26208i	−0.122715	−	0.457980i	0.877033	−	0.480431i	$-0.159520\pi$
$409$	−2.48177	−	9.26208i	−0.122715	−	0.457980i	−0.999748	+	0.0224508i	$0.992853\pi$
$410$		0			0
$411$	1.36362	−	0.787285i	0.0672623	−	0.0388339i
$412$	−1.02016	+	0.588991i	−0.0502598	+	0.0290175i
$413$	13.7406			0.676130
$414$	−11.9443	+	6.89606i	−0.587032	+	0.338923i
$415$		0			0
$416$	1.52235	−	2.63679i	0.0746393	−	0.129279i
$417$	−10.0815	+	10.0815i	−0.493695	+	0.493695i
$418$	10.6154	−	10.6154i	0.519216	−	0.519216i
$419$	14.2802	+	8.24465i	0.697631	+	0.402778i	0.806465	−	0.591282i	$-0.201378\pi$
$419$	14.2802	+	8.24465i	0.697631	+	0.402778i	−0.108833	+	0.994060i	$0.534711\pi$
$420$		0			0
$421$	0.456713	+	0.456713i	0.0222588	+	0.0222588i	0.718149	−	0.695890i	$-0.244990\pi$
$421$	0.456713	+	0.456713i	0.0222588	+	0.0222588i	−0.695890	+	0.718149i	$0.744990\pi$
$422$	12.5790	−	21.7874i	0.612335	−	1.06059i
$423$	−17.6688	+	4.73433i	−0.859085	+	0.230191i
$424$	29.2176	−	7.82884i	1.41893	−	0.380202i
$425$		0			0
$426$	−14.2101	−	3.80758i	−0.688480	−	0.184478i
$427$	−4.84284	+	8.38805i	−0.234362	+	0.405926i
$428$	0.220430	+	0.822656i	0.0106549	+	0.0397646i
$429$	−21.9167	+	5.87257i	−1.05815	+	0.283530i
$430$		0			0
$431$	−3.57129	+	13.3283i	−0.172023	+	0.641999i	0.825016	+	0.565109i	$0.191166\pi$
$431$	−3.57129	+	13.3283i	−0.172023	+	0.641999i	−0.997040	+	0.0768905i	$0.975501\pi$
$432$	−17.6161	+	4.72022i	−0.847556	+	0.227102i
$433$	16.0407	+	16.0407i	0.770868	+	0.770868i	0.978258	−	0.207391i	$-0.0664971\pi$
$433$	16.0407	+	16.0407i	0.770868	+	0.770868i	−0.207391	+	0.978258i	$0.566497\pi$
$434$	−4.93885			−0.237073
$435$		0			0
$436$	0.536630	+	0.536630i	0.0256999	+	0.0256999i
$437$	2.30589	−	8.60572i	0.110306	−	0.411667i
$438$		−	3.46278i		−	0.165458i
$439$	10.9533	+	2.93493i	0.522774	+	0.140077i	0.510549	−	0.859849i	$-0.329442\pi$
$439$	10.9533	+	2.93493i	0.522774	+	0.140077i	0.0122243	+	0.999925i	$0.496109\pi$
$440$		0			0
$441$	4.99902	+	8.65855i	0.238048	+	0.412312i
$442$	−10.5560	−	6.09452i	−0.502099	−	0.289887i
$443$	18.6448	−	18.6448i	0.885840	−	0.885840i	−0.108280	−	0.994120i	$-0.534534\pi$
$443$	18.6448	−	18.6448i	0.885840	−	0.885840i	0.994120	+	0.108280i	$0.0345344\pi$
$444$	−0.458762	+	0.0577790i	−0.0217719	+	0.00274207i
$445$		0			0
$446$	15.2738	−	4.09261i	0.723237	−	0.193791i
$447$	1.71243	−	6.39088i	0.0809952	−	0.302278i
$448$	12.0693	+	3.23396i	0.570222	+	0.152790i
$449$	9.44296	−	35.2416i	0.445641	−	1.66315i	−0.268598	−	0.963252i	$-0.586560\pi$
$449$	9.44296	−	35.2416i	0.445641	−	1.66315i	0.714239	−	0.699902i	$-0.246773\pi$
$450$		0			0
$451$	1.01683	+	1.76120i	0.0478805	+	0.0829314i
$452$			0.687496i			0.0323371i
$453$	−16.5597	+	4.43716i	−0.778043	+	0.208476i
$454$		−	9.57819i		−	0.449527i
$455$		0			0
$456$	2.45977	−	4.26045i	0.115189	−	0.199514i
$457$	35.7289	−	20.6281i	1.67133	−	0.964941i	0.704430	−	0.709773i	$-0.251203\pi$
$457$	35.7289	−	20.6281i	1.67133	−	0.964941i	0.966897	−	0.255168i	$-0.0821307\pi$
$458$			16.3545i			0.764194i
$459$	1.63986	+	6.12004i	0.0765420	+	0.285659i
$460$		0			0
$461$	7.84179	+	29.2660i	0.365229	+	1.36305i	0.867111	+	0.498115i	$0.165974\pi$
$461$	7.84179	+	29.2660i	0.365229	+	1.36305i	−0.501882	+	0.864936i	$0.667359\pi$
$462$	4.64996	+	8.05397i	0.216336	+	0.374705i
$463$	−2.12165	−	3.67480i	−0.0986013	−	0.170783i	0.812505	−	0.582955i	$-0.198104\pi$
$463$	−2.12165	−	3.67480i	−0.0986013	−	0.170783i	−0.911106	+	0.412172i	$0.864770\pi$
$464$	4.51042	+	16.8331i	0.209391	+	0.781458i
$465$		0			0
$466$	−5.65143	−	21.0914i	−0.261797	−	0.977041i
$467$			9.79517i			0.453266i	0.973980	+	0.226633i	$0.0727718\pi$
$467$			9.79517i			0.453266i	−0.973980	+	0.226633i	$0.927228\pi$
$468$	−1.08627	+	0.627156i	−0.0502127	+	0.0289903i
$469$	−7.65832	+	13.2646i	−0.353628	+	0.612502i
$470$		0			0
$471$			11.3437i			0.522692i
$472$	22.2597	−	5.96446i	1.02458	−	0.274537i
$473$		−	35.9540i		−	1.65317i
$474$	−2.98371	−	5.16793i	−0.137046	−	0.237371i
$475$		0			0
$476$	−0.0573190	+	0.213917i	−0.00262721	+	0.00980489i
$477$	−24.6588	−	6.60731i	−1.12905	−	0.302528i
$478$	−6.69901	+	25.0010i	−0.306405	+	1.14352i
$479$	−29.0918	+	7.79512i	−1.32924	+	0.356168i	−0.852431	−	0.522840i	$-0.824873\pi$
$479$	−29.0918	+	7.79512i	−1.32924	+	0.356168i	−0.476807	+	0.879008i	$0.658206\pi$
$480$		0			0
$481$	32.7059	−	13.3326i	1.49126	−	0.607914i
$482$	−28.7006	+	28.7006i	−1.30728	+	1.30728i
$483$	4.77971	+	2.75957i	0.217484	+	0.125565i
$484$	0.544713	+	0.943471i	0.0247597	+	0.0428850i
$485$		0			0
$486$	22.2057	+	5.94999i	1.00727	+	0.269897i
$487$		−	8.80800i		−	0.399129i	−0.979885	−	0.199564i	$-0.936047\pi$
$487$		−	8.80800i		−	0.399129i	0.979885	−	0.199564i	$-0.0639527\pi$
$488$	−4.20433	+	15.6908i	−0.190321	+	0.710287i
$489$	−3.63166	−	3.63166i	−0.164230	−	0.164230i
$490$		0			0
$491$	−37.2665			−1.68181			−0.840907	−	0.541179i	$-0.817978\pi$
$491$	−37.2665			−1.68181			−0.840907	+	0.541179i	$0.817978\pi$
$492$	−0.0229213	−	0.0229213i	−0.00103337	−	0.00103337i
$493$	5.84801	−	1.56697i	0.263381	−	0.0705728i
$494$	4.73073	−	17.6553i	0.212846	−	0.794351i
$495$		0			0
$496$	−8.37284	+	2.24349i	−0.375951	+	0.100736i
$497$	−5.28427	−	19.7212i	−0.237032	−	0.884615i
$498$	−2.39444	+	4.14729i	−0.107297	+	0.185845i
$499$	3.52008	+	0.943201i	0.157580	+	0.0422235i	0.336747	−	0.941595i	$-0.390673\pi$
$499$	3.52008	+	0.943201i	0.157580	+	0.0422235i	−0.179166	+	0.983819i	$0.557340\pi$
$500$		0			0
$501$	2.48305	−	0.665330i	0.110934	−	0.0297248i
$502$	−3.84664	+	1.03071i	−0.171684	+	0.0460026i
$503$	−12.2071	+	21.1433i	−0.544287	+	0.942732i	0.454365	+	0.890816i	$0.349866\pi$
$503$	−12.2071	+	21.1433i	−0.544287	+	0.942732i	−0.998651	+	0.0519165i	$0.983467\pi$
$504$	−7.47367	−	7.47367i	−0.332904	−	0.332904i
$505$		0			0
$506$	24.4623	+	14.1233i	1.08748	+	0.627859i
$507$	−12.0020	+	12.0020i	−0.533029	+	0.533029i
$508$	0.0358138	−	0.0358138i	0.00158898	−	0.00158898i
$509$	21.1376	−	36.6113i	0.936906	−	1.62277i	0.165708	−	0.986175i	$-0.447009\pi$
$509$	21.1376	−	36.6113i	0.936906	−	1.62277i	0.771199	−	0.636595i	$-0.219657\pi$
$510$		0			0
$511$	4.16190	−	2.40287i	0.184112	−	0.106297i
$512$	20.8587			0.921833
$513$	−8.22817	+	4.75054i	−0.363283	+	0.209741i
$514$	−7.84888	+	4.53155i	−0.346199	+	0.199878i
$515$		0			0
$516$	0.148327	+	0.553565i	0.00652975	+	0.0243694i
$517$	26.4901	+	26.4901i	1.16503	+	1.16503i
$518$	−8.74797	−	11.5341i	−0.384364	−	0.506778i
$519$		−	4.20046i		−	0.184380i
$520$		0			0
$521$	20.8093	−	12.0143i	0.911672	−	0.526354i	0.0307035	−	0.999529i	$-0.490225\pi$
$521$	20.8093	−	12.0143i	0.911672	−	0.526354i	0.880969	+	0.473174i	$0.156892\pi$
$522$	3.63757	−	13.5756i	0.159212	−	0.594188i
$523$	−7.40563	−	12.8269i	−0.323825	−	0.560882i	0.657448	−	0.753500i	$-0.271636\pi$
$523$	−7.40563	−	12.8269i	−0.323825	−	0.560882i	−0.981274	+	0.192617i	$0.938302\pi$
$524$	1.04416	+	1.04416i	0.0456145	+	0.0456145i
$525$		0			0
$526$	15.4937	−	15.4937i	0.675557	−	0.675557i
$527$	0.779415	+	2.90882i	0.0339518	+	0.126710i
$528$	11.5416	+	11.5416i	0.502285	+	0.502285i
$529$	−6.23672			−0.271162
$530$		0			0
$531$	−18.7865	−	5.03383i	−0.815265	−	0.218449i
$532$	−0.332097			−0.0143982
$533$	2.14431	+	1.23802i	0.0928805	+	0.0536246i
$534$	−15.7745	−	9.10743i	−0.682631	−	0.394117i
$535$		0			0
$536$	−6.64859	+	24.8129i	−0.287175	+	1.07175i
$537$	−2.47071	+	1.42646i	−0.106619	+	0.0615564i
$538$	25.7201	+	14.8495i	1.10887	+	0.640207i
$539$	10.2381	−	17.7330i	0.440987	−	0.763813i
$540$		0			0
$541$	11.8805	−	11.8805i	0.510784	−	0.510784i	−0.403983	−	0.914767i	$-0.632374\pi$
$541$	11.8805	−	11.8805i	0.510784	−	0.510784i	0.914767	+	0.403983i	$0.132374\pi$
$542$	9.30474	+	16.1163i	0.399673	+	0.692254i
$543$	2.49062	+	9.29514i	0.106883	+	0.398892i
$544$			0.760918i			0.0326241i
$545$		0			0
$546$	9.80597	+	5.66148i	0.419657	+	0.242289i
$547$	−17.4832			−0.747526			−0.373763	−	0.927524i	$-0.621933\pi$
$547$	−17.4832			−0.747526			−0.373763	+	0.927524i	$0.621933\pi$
$548$	−0.172193	−	0.0461389i	−0.00735571	−	0.00197096i
$549$	9.69421	−	9.69421i	0.413739	−	0.413739i
$550$		0			0
$551$	4.53939	+	7.86245i	0.193384	+	0.334952i
$552$	8.94097	+	2.39572i	0.380553	+	0.101969i
$553$	4.14088	−	7.17221i	0.176088	−	0.304993i
$554$	1.79401			0.0762202
$555$		0			0
$556$	1.61418			0.0684563
$557$	15.7212	−	27.2299i	0.666129	−	1.15377i	−0.312849	−	0.949803i	$-0.601283\pi$
$557$	15.7212	−	27.2299i	0.666129	−	1.15377i	0.978978	−	0.203967i	$-0.0653834\pi$
$558$	6.75253	+	1.80934i	0.285858	+	0.0765953i
$559$	−21.8876	−	37.9105i	−0.925747	−	1.60344i
$560$		0			0
$561$	4.00969	−	4.00969i	0.169289	−	0.169289i
$562$	−24.9284	−	6.67954i	−1.05154	−	0.281759i
$563$	17.3599			0.731633			0.365816	−	0.930687i	$-0.380790\pi$
$563$	17.3599			0.731633			0.365816	+	0.930687i	$0.380790\pi$
$564$	−0.517138	−	0.298570i	−0.0217754	−	0.0125720i
$565$		0			0
$566$			24.1975i			1.01710i
$567$	1.45108	+	5.41552i	0.0609398	+	0.227430i
$568$	−17.1210	−	29.6544i	−0.718380	−	1.24427i
$569$	−13.2625	+	13.2625i	−0.555994	+	0.555994i	−0.928165	−	0.372170i	$-0.878614\pi$
$569$	−13.2625	+	13.2625i	−0.555994	+	0.555994i	0.372170	+	0.928165i	$0.378614\pi$
$570$		0			0
$571$	−13.5109	+	23.4016i	−0.565415	+	0.979327i	0.431596	+	0.902067i	$0.357951\pi$
$571$	−13.5109	+	23.4016i	−0.565415	+	0.979327i	−0.997011	+	0.0772604i	$0.975383\pi$
$572$	2.22470	+	1.28443i	0.0930195	+	0.0537048i
$573$	15.1025	−	8.71941i	0.630914	−	0.364259i
$574$	0.262664	−	0.980277i	0.0109634	−	0.0409160i
$575$		0			0
$576$	−15.3167	−	8.84312i	−0.638197	−	0.368463i
$577$	−21.9876	−	12.6946i	−0.915357	−	0.528482i	−0.0332064	−	0.999449i	$-0.510572\pi$
$577$	−21.9876	−	12.6946i	−0.915357	−	0.528482i	−0.882151	+	0.470967i	$0.843905\pi$
$578$	−21.5467			−0.896223
$579$	9.97220	+	2.67204i	0.414430	+	0.111046i
$580$		0			0
$581$	−6.64615			−0.275729
$582$	15.0314	+	15.0314i	0.623072	+	0.623072i
$583$	13.5320	+	50.5020i	0.560436	+	2.09158i
$584$	5.69922	−	5.69922i	0.235836	−	0.235836i
$585$		0			0
$586$	−20.9648	−	20.9648i	−0.866046	−	0.866046i
$587$	21.1677	+	36.6636i	0.873686	+	1.51327i	0.858156	+	0.513389i	$0.171610\pi$
$587$	21.1677	+	36.6636i	0.873686	+	1.51327i	0.0155295	+	0.999879i	$0.495057\pi$
$588$	−0.0844742	+	0.315262i	−0.00348366	+	0.0130012i
$589$	−3.91080	+	2.25790i	−0.161142	+	0.0930352i
$590$		0			0
$591$			4.60399i			0.189383i
$592$	−20.0698	−	15.5799i	−0.824864	−	0.640330i
$593$	22.5131	+	22.5131i	0.924503	+	0.924503i	0.997344	−	0.0728403i	$-0.0232063\pi$
$593$	22.5131	+	22.5131i	0.924503	+	0.924503i	−0.0728403	+	0.997344i	$0.523206\pi$
$594$	−7.79637	−	29.0965i	−0.319889	−	1.19384i
$595$		0			0
$596$	−0.648720	+	0.374539i	−0.0265726	+	0.0153417i
$597$	11.6244	−	6.71134i	0.475754	−	0.274677i
$598$	34.3912			1.40636
$599$	13.9673	−	8.06402i	0.570688	−	0.329487i	−0.186736	−	0.982410i	$-0.559791\pi$
$599$	13.9673	−	8.06402i	0.570688	−	0.329487i	0.757424	+	0.652923i	$0.226458\pi$
$600$		0			0
$601$	12.0579	−	20.8849i	0.491852	−	0.851912i	−0.508104	−	0.861296i	$-0.669654\pi$
$601$	12.0579	−	20.8849i	0.491852	−	0.851912i	0.999956	+	0.00938333i	$0.00298685\pi$
$602$	−12.6871	+	12.6871i	−0.517086	+	0.517086i
$603$	15.3301	−	15.3301i	0.624290	−	0.624290i
$604$	1.68093	+	0.970484i	0.0683960	+	0.0394884i
$605$		0			0
$606$	−5.76017	−	5.76017i	−0.233991	−	0.233991i
$607$	−2.36675	+	4.09934i	−0.0960635	+	0.166387i	−0.910052	−	0.414494i	$-0.863959\pi$
$607$	−2.36675	+	4.09934i	−0.0960635	+	0.166387i	0.813988	+	0.580881i	$0.197292\pi$
$608$	−1.10216	+	0.295323i	−0.0446984	+	0.0119769i
$609$	−5.43249	+	1.45563i	−0.220136	+	0.0589851i
$610$		0			0
$611$	44.0578	+	11.8053i	1.78239	+	0.477589i
$612$	0.156736	−	0.271475i	0.00633568	−	0.0109737i
$613$	5.33493	+	19.9102i	0.215476	+	0.804167i	0.985999	+	0.166754i	$0.0533286\pi$
$613$	5.33493	+	19.9102i	0.215476	+	0.804167i	−0.770523	+	0.637413i	$0.780005\pi$
$614$	−9.86883	+	2.64434i	−0.398273	+	0.106717i
$615$		0			0
$616$	−5.60249	+	20.9088i	−0.225731	+	0.842439i
$617$	−14.7457	+	3.95109i	−0.593638	+	0.159065i	−0.543115	−	0.839658i	$-0.682755\pi$
$617$	−14.7457	+	3.95109i	−0.593638	+	0.159065i	−0.0505225	+	0.998723i	$0.516089\pi$
$618$	−10.6433	−	10.6433i	−0.428135	−	0.428135i
$619$	−6.80631			−0.273569			−0.136784	−	0.990601i	$-0.543677\pi$
$619$	−6.80631			−0.273569			−0.136784	+	0.990601i	$0.543677\pi$
$620$		0			0
$621$	−12.6408	−	12.6408i	−0.507256	−	0.507256i
$622$	7.38613	−	27.5654i	0.296157	−	1.10527i
$623$		−	25.2791i		−	1.01279i
$624$	19.1958	+	5.14350i	0.768447	+	0.205905i
$625$		0			0
$626$	−15.0019	−	25.9841i	−0.599597	−	1.03853i
$627$	7.36408	+	4.25166i	0.294093	+	0.169795i
$628$	0.908136	−	0.908136i	0.0362386	−	0.0362386i
$629$	−5.41263	+	6.97248i	−0.215816	+	0.278011i
$630$		0			0
$631$	24.9840	−	6.69444i	0.994597	−	0.266501i	0.275416	−	0.961325i	$-0.411184\pi$
$631$	24.9840	−	6.69444i	0.994597	−	0.266501i	0.719180	+	0.694824i	$0.244518\pi$
$632$	3.59491	−	13.4164i	0.142998	−	0.533675i
$633$	13.7643	+	3.68814i	0.547083	+	0.146591i
$634$	−7.74240	+	28.8950i	−0.307490	+	1.14757i
$635$		0			0
$636$	−0.416689	−	0.721726i	−0.0165228	−	0.0286183i
$637$		−	24.9305i		−	0.987783i
$638$	−27.8032	+	7.44984i	−1.10074	+	0.294942i
$639$			28.8992i			1.14323i
$640$		0			0
$641$	17.3223	−	30.0031i	0.684190	−	1.18505i	−0.289501	−	0.957178i	$-0.593489\pi$
$641$	17.3223	−	30.0031i	0.684190	−	1.18505i	0.973691	−	0.227874i	$-0.0731773\pi$
$642$	−9.42446	+	5.44121i	−0.371954	+	0.214748i
$643$		−	22.9695i		−	0.905827i	−0.891555	−	0.452913i	$-0.850385\pi$
$643$		−	22.9695i		−	0.905827i	0.891555	−	0.452913i	$-0.149615\pi$
$644$	−0.161725	−	0.603566i	−0.00637285	−	0.0237838i
$645$		0			0
$646$	1.18228	+	4.41235i	0.0465164	+	0.173601i
$647$	7.12196	+	12.3356i	0.279993	+	0.484962i	0.971383	−	0.237520i	$-0.0763344\pi$
$647$	7.12196	+	12.3356i	0.279993	+	0.484962i	−0.691389	+	0.722482i	$0.743001\pi$
$648$	4.70149	+	8.14323i	0.184692	+	0.319896i
$649$	10.3094	+	38.4753i	0.404680	+	1.51029i
$650$		0			0
$651$	−0.724034	−	2.70213i	−0.0283771	−	0.105905i
$652$			0.581474i			0.0227723i
$653$	9.03552	−	5.21666i	0.353587	−	0.204144i	−0.312677	−	0.949860i	$-0.601226\pi$
$653$	9.03552	−	5.21666i	0.353587	−	0.204144i	0.666264	+	0.745716i	$0.267892\pi$
$654$	−4.84854	+	8.39792i	−0.189593	+	0.328385i
$655$		0			0
$656$		−	1.78118i		−	0.0695434i
$657$	−6.57055	+	1.76057i	−0.256341	+	0.0686865i
$658$		−	18.6950i		−	0.728808i
$659$	9.90312	+	17.1527i	0.385771	+	0.668174i	0.991876	−	0.127210i	$-0.0406023\pi$
$659$	9.90312	+	17.1527i	0.385771	+	0.668174i	−0.606105	+	0.795385i	$0.707269\pi$
$660$		0			0
$661$	−5.73632	+	21.4082i	−0.223117	+	0.832683i	0.760033	+	0.649884i	$0.225183\pi$
$661$	−5.73632	+	21.4082i	−0.223117	+	0.832683i	−0.983150	+	0.182799i	$0.941484\pi$
$662$	45.7447	+	12.2572i	1.77792	+	0.476391i
$663$	1.78691	−	6.66884i	0.0693978	−	0.258996i
$664$	−10.7667	+	2.88494i	−0.417830	+	0.111957i
$665$		0			0
$666$	7.73498	+	18.9745i	0.299724	+	0.735246i
$667$	−12.0789	+	12.0789i	−0.467697	+	0.467697i
$668$	−0.252047	−	0.145519i	−0.00975198	−	0.00563031i
$669$	4.47828	+	7.75660i	0.173140	+	0.299888i
$670$		0			0
$671$	−27.1211	−	7.26707i	−1.04700	−	0.280542i
$672$		−	0.706852i		−	0.0272674i
$673$	−12.6606	+	47.2502i	−0.488032	+	1.82136i	0.0779695	+	0.996956i	$0.475156\pi$
$673$	−12.6606	+	47.2502i	−0.488032	+	1.82136i	−0.566001	+	0.824404i	$0.691510\pi$
$674$	−10.5636	−	10.5636i	−0.406893	−	0.406893i
$675$		0			0
$676$	1.92167			0.0739104
$677$	8.62241	+	8.62241i	0.331386	+	0.331386i	0.853113	−	0.521727i	$-0.174712\pi$
$677$	8.62241	+	8.62241i	0.331386	+	0.331386i	−0.521727	+	0.853113i	$0.674712\pi$
$678$	−8.48527	+	2.27362i	−0.325875	+	0.0873179i
$679$	−7.63567	+	28.4967i	−0.293030	+	1.09360i
$680$		0			0
$681$	5.24039	−	1.40416i	0.200812	−	0.0538075i
$682$	−3.70557	−	13.8294i	−0.141894	−	0.529554i
$683$	−7.97715	+	13.8168i	−0.305237	+	0.528686i	−0.977314	−	0.211795i	$-0.932069\pi$
$683$	−7.97715	+	13.8168i	−0.305237	+	0.528686i	0.672077	+	0.740481i	$0.265402\pi$
$684$	0.454052	+	0.121663i	0.0173611	+	0.00465190i
$685$		0			0
$686$	−25.9616	+	6.95640i	−0.991220	+	0.265597i
$687$	−8.94781	+	2.39756i	−0.341380	+	0.0914726i
$688$	−15.7452	+	27.2715i	−0.600280	+	1.03972i
$689$	45.0122	+	45.0122i	1.71483	+	1.71483i
$690$		0			0
$691$	−16.8398	−	9.72247i	−0.640617	−	0.369860i	0.144235	−	0.989543i	$-0.453928\pi$
$691$	−16.8398	−	9.72247i	−0.640617	−	0.369860i	−0.784852	+	0.619683i	$0.787261\pi$
$692$	−0.336273	+	0.336273i	−0.0127832	+	0.0127832i
$693$	12.9181	−	12.9181i	0.490716	−	0.490716i
$694$	7.09907	−	12.2960i	0.269477	−	0.466748i
$695$		0			0
$696$	−8.16874	+	4.71623i	−0.309635	+	0.178768i
$697$	−0.618801			−0.0234388
$698$	15.9946	−	9.23449i	0.605405	−	0.349531i
$699$	10.7110	−	6.18399i	0.405127	−	0.233900i
$700$		0			0
$701$	−11.0896	−	41.3868i	−0.418847	−	1.56316i	−0.777003	−	0.629497i	$-0.783261\pi$
$701$	−11.0896	−	41.3868i	−0.418847	−	1.56316i	0.358155	−	0.933662i	$-0.383406\pi$
$702$	−25.9336	−	25.9336i	−0.978799	−	0.978799i
$703$	−12.2001	−	5.13386i	−0.460134	−	0.193627i
$704$			36.2219i			1.36517i
$705$		0			0
$706$	4.26805	−	2.46416i	0.160630	−	0.0927399i
$707$	2.92605	−	10.9202i	0.110046	−	0.410696i
$708$	−0.317457	−	0.549852i	−0.0119308	−	0.0206647i
$709$	−11.6125	−	11.6125i	−0.436116	−	0.436116i	0.454586	−	0.890703i	$-0.349787\pi$
$709$	−11.6125	−	11.6125i	−0.436116	−	0.436116i	−0.890703	+	0.454586i	$0.849787\pi$
$710$		0			0
$711$	−8.28904	+	8.28904i	−0.310863	+	0.310863i
$712$	−10.9731	−	40.9520i	−0.411233	−	1.53474i
$713$	−6.00808	−	6.00808i	−0.225004	−	0.225004i
$714$	−2.82979			−0.105902
$715$		0			0
$716$	0.311992	+	0.0835981i	0.0116597	+	0.00312421i
$717$	−14.6606			−0.547509
$718$	5.66824	+	3.27256i	0.211537	+	0.122131i
$719$	28.4138	+	16.4047i	1.05966	+	0.611794i	0.925337	−	0.379144i	$-0.123782\pi$
$719$	28.4138	+	16.4047i	1.05966	+	0.611794i	0.134320	+	0.990938i	$0.457115\pi$
$720$		0			0
$721$	5.40658	−	20.1776i	0.201352	−	0.751454i
$722$	17.8715	−	10.3181i	0.665108	−	0.384000i
$723$	−19.9101	−	11.4951i	−0.740465	−	0.427508i
$724$	0.544743	−	0.943522i	0.0202452	−	0.0350657i
$725$		0			0
$726$	−9.84315	+	9.84315i	−0.365313	+	0.365313i
$727$	19.7125	+	34.1431i	0.731097	+	1.26630i	0.956415	+	0.292011i	$0.0943245\pi$
$727$	19.7125	+	34.1431i	0.731097	+	1.26630i	−0.225318	+	0.974285i	$0.572342\pi$
$728$	6.82122	+	25.4571i	0.252811	+	0.943504i
$729$			2.79732i			0.103604i
$730$		0			0
$731$	9.47442	+	5.47006i	0.350424	+	0.202317i
$732$	0.447549			0.0165419
$733$	−40.8538	−	10.9468i	−1.50897	−	0.404328i	−0.592878	−	0.805293i	$-0.702008\pi$
$733$	−40.8538	−	10.9468i	−1.50897	−	0.404328i	−0.916093	+	0.400965i	$0.868675\pi$
$734$	−11.0551	+	11.0551i	−0.408050	+	0.408050i
$735$		0			0
$736$	−1.07346	−	1.85929i	−0.0395683	−	0.0685343i
$737$	−42.8884	−	11.4919i	−1.57981	−	0.423310i
$738$	−0.718244	+	1.24403i	−0.0264389	+	0.0457935i
$739$	−32.4999			−1.19553			−0.597764	−	0.801672i	$-0.703944\pi$
$739$	−32.4999			−1.19553			−0.597764	+	0.801672i	$0.703944\pi$
$740$		0			0
$741$	10.3531			0.380329
$742$	13.0456	−	22.5956i	0.478917	−	0.829509i
$743$	11.0864	+	2.97059i	0.406720	+	0.108980i	0.456378	−	0.889786i	$-0.349146\pi$
$743$	11.0864	+	2.97059i	0.406720	+	0.108980i	−0.0496580	+	0.998766i	$0.515813\pi$
$744$	−2.34586	−	4.06315i	−0.0860035	−	0.148962i
$745$		0			0
$746$	−20.0262	+	20.0262i	−0.733212	+	0.733212i
$747$	9.08680	+	2.43480i	0.332469	+	0.0890847i
$748$	−0.642000			−0.0234739
$749$	−13.0795	−	7.55148i	−0.477916	−	0.275925i
$750$		0			0
$751$			35.5418i			1.29694i	0.761240	+	0.648470i	$0.224591\pi$
$751$			35.5418i			1.29694i	−0.761240	+	0.648470i	$0.775409\pi$
$752$	−8.49230	−	31.6937i	−0.309682	−	1.15575i
$753$	−1.12783	−	1.95346i	−0.0411005	−	0.0711882i
$754$	−24.7809	+	24.7809i	−0.902466	+	0.902466i
$755$		0			0
$756$	−0.333181	+	0.577086i	−0.0121177	+	0.0209884i
$757$	31.7438	+	18.3273i	1.15375	+	0.666117i	0.949798	−	0.312864i	$-0.101288\pi$
$757$	31.7438	+	18.3273i	1.15375	+	0.666117i	0.203951	+	0.978981i	$0.434622\pi$
$758$	6.14778	−	3.54943i	0.223298	−	0.128921i
$759$	−4.14095	+	15.4542i	−0.150307	+	0.560953i
$760$		0			0
$761$	18.5429	+	10.7058i	0.672180	+	0.388083i	0.796902	−	0.604109i	$-0.206471\pi$
$761$	18.5429	+	10.7058i	0.672180	+	0.388083i	−0.124722	+	0.992192i	$0.539804\pi$
$762$	0.560464	+	0.323584i	0.0203035	+	0.0117222i
$763$	−13.4579			−0.487209
$764$	−1.90709	−	0.511002i	−0.0689960	−	0.0184874i
$765$		0			0
$766$	9.37414			0.338701
$767$	34.2929	+	34.2929i	1.23824	+	1.23824i
$768$	−0.471184	−	1.75848i	−0.0170024	−	0.0634538i
$769$	23.2703	−	23.2703i	0.839147	−	0.839147i	−0.149599	−	0.988747i	$-0.547798\pi$
$769$	23.2703	−	23.2703i	0.839147	−	0.839147i	0.988747	+	0.149599i	$0.0477984\pi$
$770$		0			0
$771$	−3.62993	−	3.62993i	−0.130729	−	0.130729i
$772$	−0.584422	−	1.01225i	−0.0210338	−	0.0364316i
$773$	−8.99634	+	33.5748i	−0.323576	+	1.20760i	0.592160	+	0.805821i	$0.298275\pi$
$773$	−8.99634	+	33.5748i	−0.323576	+	1.20760i	−0.915736	+	0.401781i	$0.868391\pi$
$774$	21.9939	−	12.6982i	0.790556	−	0.456428i
$775$		0			0
$776$			49.4790i			1.77619i
$777$	5.02804	−	6.47705i	0.180380	−	0.232363i
$778$	−8.81761	−	8.81761i	−0.316127	−	0.316127i
$779$	−0.240165	−	0.896309i	−0.00860481	−	0.0321136i
$780$		0			0
$781$	51.2568	−	29.5931i	1.83411	−	1.05893i
$782$	−7.44341	+	4.29746i	−0.266176	+	0.153677i
$783$	18.2168			0.651015
$784$	−15.5314	+	8.96708i	−0.554695	+	0.320253i
$785$		0			0
$786$	−9.43420	+	16.3405i	−0.336507	+	0.582847i
$787$	1.73887	−	1.73887i	0.0619839	−	0.0619839i	−0.675435	−	0.737419i	$-0.736044\pi$
$787$	1.73887	−	1.73887i	0.0619839	−	0.0619839i	0.737419	+	0.675435i	$0.236044\pi$
$788$	0.368577	−	0.368577i	0.0131300	−	0.0131300i
$789$	10.7482	+	6.20550i	0.382647	+	0.220922i
$790$		0			0
$791$	−8.62071	−	8.62071i	−0.306517	−	0.306517i
$792$	15.3198	−	26.5346i	0.544364	−	0.942866i
$793$	−33.0208	+	8.84790i	−1.17260	+	0.314198i
$794$	1.52278	−	0.408027i	0.0540413	−	0.0144803i
$795$		0			0
$796$	−1.46789	−	0.393319i	−0.0520279	−	0.0139408i
$797$	−15.6728	+	27.1461i	−0.555160	+	0.961566i	0.442731	+	0.896655i	$0.354010\pi$
$797$	−15.6728	+	27.1461i	−0.555160	+	0.961566i	−0.997891	+	0.0649113i	$0.979324\pi$
$798$	−1.09828	−	4.09883i	−0.0388786	−	0.145097i
$799$	−11.0107	+	2.95032i	−0.389532	+	0.104375i
$800$		0			0
$801$	−9.26094	+	34.5623i	−0.327219	+	1.22120i
$802$	−34.3462	+	9.20305i	−1.21281	+	0.324971i
$803$	9.85096	+	9.85096i	0.347633	+	0.347633i
$804$	0.707740			0.0249601
$805$		0			0
$806$	−12.3261	−	12.3261i	−0.434167	−	0.434167i
$807$	−4.35386	+	16.2488i	−0.153263	+	0.571986i
$808$		−	18.9608i		−	0.667037i
$809$	−0.121396	−	0.0325280i	−0.00426806	−	0.00114362i	0.256684	−	0.966495i	$-0.417370\pi$
$809$	−0.121396	−	0.0325280i	−0.00426806	−	0.00114362i	−0.260952	+	0.965352i	$0.584037\pi$
$810$		0			0
$811$	−7.32474	−	12.6868i	−0.257207	−	0.445495i	0.708286	−	0.705926i	$-0.249469\pi$
$811$	−7.32474	−	12.6868i	−0.257207	−	0.445495i	−0.965492	+	0.260431i	$0.916135\pi$
$812$	0.551436	+	0.318372i	0.0193516	+	0.0111727i
$813$	−7.45343	+	7.45343i	−0.261403	+	0.261403i
$814$	25.7332	−	33.1492i	0.901950	−	1.16188i
$815$		0			0
$816$	−4.79733	+	1.28544i	−0.167940	+	0.0449995i
$817$	−4.24601	+	15.8463i	−0.148549	+	0.554393i
$818$	−13.3989	−	3.59022i	−0.468482	−	0.125529i
$819$	5.75691	−	21.4851i	0.201163	−	0.750749i
$820$		0			0
$821$	−7.54707	−	13.0719i	−0.263394	−	0.456213i	0.703747	−	0.710450i	$-0.251509\pi$
$821$	−7.54707	−	13.0719i	−0.263394	−	0.456213i	−0.967142	+	0.254238i	$0.918175\pi$
$822$		−	2.27784i		−	0.0794487i
$823$	−15.2859	+	4.09584i	−0.532832	+	0.142772i	−0.515196	−	0.857073i	$-0.672281\pi$
$823$	−15.2859	+	4.09584i	−0.532832	+	0.142772i	−0.0176363	+	0.999844i	$0.505614\pi$
$824$		−	35.0345i		−	1.22048i
$825$		0			0
$826$	9.93885	−	17.2146i	0.345817	−	0.598972i
$827$	−20.0903	+	11.5992i	−0.698610	+	0.403343i	−0.806829	−	0.590784i	$-0.798818\pi$
$827$	−20.0903	+	11.5992i	−0.698610	+	0.403343i	0.108220	+	0.994127i	$0.465485\pi$
$828$			0.884458i			0.0307371i
$829$	−6.63771	−	24.7723i	−0.230537	−	0.860377i	−0.980110	−	0.198455i	$-0.936408\pi$
$829$	−6.63771	−	24.7723i	−0.230537	−	0.860377i	0.749573	−	0.661922i	$-0.230259\pi$
$830$		0			0
$831$	0.263001	+	0.981534i	0.00912342	+	0.0340491i
$832$	22.0507	+	38.1929i	0.764470	+	1.32410i
$833$	3.11527	+	5.39580i	0.107938	+	0.186953i
$834$	5.33824	+	19.9226i	0.184848	+	0.689863i
$835$		0			0
$836$	−0.249169	−	0.929911i	−0.00861769	−	0.0321616i
$837$			9.06108i			0.313197i
$838$	20.6583	−	11.9270i	0.713628	−	0.412013i
$839$	−28.4964	+	49.3573i	−0.983806	+	1.70400i	−0.336681	+	0.941619i	$0.609304\pi$
$839$	−28.4964	+	49.3573i	−0.983806	+	1.70400i	−0.647125	+	0.762384i	$0.724029\pi$
$840$		0			0
$841$			11.5929i			0.399755i
$842$	0.902532	−	0.241833i	0.0311033	−	0.00833410i
$843$		−	14.6180i		−	0.503469i
$844$	−0.806661	−	1.39718i	−0.0277664	−	0.0480929i
$845$		0			0
$846$	−6.84888	+	25.5604i	−0.235469	+	0.878783i
$847$	−18.6607	−	5.00013i	−0.641191	−	0.171807i
$848$	11.8520	−	44.2322i	0.406999	−	1.51894i
$849$	−13.2389	+	3.54735i	−0.454357	+	0.121745i
$850$		0			0
$851$	3.38927	−	24.6729i	0.116183	−	0.845778i
$852$	−0.667089	+	0.667089i	−0.0228541	+	0.0228541i
$853$	21.1492	+	12.2105i	0.724135	+	0.418079i	0.816273	−	0.577667i	$-0.196037\pi$
$853$	21.1492	+	12.2105i	0.724135	+	0.418079i	−0.0921378	+	0.995746i	$0.529370\pi$
$854$	7.00586	+	12.1345i	0.239735	+	0.415234i
$855$		0			0
$856$	−24.4667	−	6.55583i	−0.836254	−	0.224074i
$857$			23.7142i			0.810060i	0.914303	+	0.405030i	$0.132739\pi$
$857$			23.7142i			0.810060i	−0.914303	+	0.405030i	$0.867261\pi$
$858$	−8.49550	+	31.7056i	−0.290032	+	1.08241i
$859$	1.55152	+	1.55152i	0.0529373	+	0.0529373i	0.733080	−	0.680143i	$-0.238082\pi$
$859$	1.55152	+	1.55152i	0.0529373	+	0.0529373i	−0.680143	+	0.733080i	$0.738082\pi$
$860$		0			0
$861$	0.574833			0.0195903
$862$	14.1148	+	14.1148i	0.480753	+	0.480753i
$863$	−38.9434	+	10.4349i	−1.32565	+	0.355207i	−0.851091	−	0.525018i	$-0.824059\pi$
$863$	−38.9434	+	10.4349i	−1.32565	+	0.355207i	−0.474558	+	0.880224i	$0.657392\pi$
$864$	−0.592573	+	2.21151i	−0.0201597	+	0.0752372i
$865$		0			0
$866$	31.6988	−	8.49368i	1.07717	−	0.288627i
$867$	−3.15873	−	11.7886i	−0.107276	−	0.400360i
$868$	−0.158359	+	0.274286i	−0.00537505	+	0.00930986i
$869$	23.1899	+	6.21371i	0.786663	+	0.210786i
$870$		0			0
$871$	−52.2180	+	13.9918i	−1.76934	+	0.474094i
$872$	−21.8017	+	5.84175i	−0.738299	+	0.197827i
$873$	20.8794	−	36.1642i	0.706660	−	1.22397i
$874$	−9.11358	−	9.11358i	−0.308271	−	0.308271i
$875$		0			0
$876$	−0.192310	−	0.111030i	−0.00649755	−	0.00375136i
$877$	−5.84034	+	5.84034i	−0.197214	+	0.197214i	−0.798805	−	0.601590i	$-0.794534\pi$
$877$	−5.84034	+	5.84034i	−0.197214	+	0.197214i	0.601590	+	0.798805i	$0.294534\pi$
$878$	11.5997	−	11.5997i	0.391472	−	0.391472i
$879$	8.39676	−	14.5436i	0.283216	−	0.490544i
$880$		0			0
$881$	−32.5692	+	18.8038i	−1.09728	+	0.633517i	−0.935506	−	0.353311i	$-0.885056\pi$
$881$	−32.5692	+	18.8038i	−1.09728	+	0.633517i	−0.161777	+	0.986827i	$0.551723\pi$
$882$	14.4636			0.487014
$883$	20.7143	−	11.9594i	0.697091	−	0.402466i	−0.109172	−	0.994023i	$-0.534820\pi$
$883$	20.7143	−	11.9594i	0.697091	−	0.402466i	0.806263	+	0.591557i	$0.201487\pi$
$884$	−0.676934	+	0.390828i	−0.0227678	+	0.0131450i
$885$		0			0
$886$	−9.87255	−	36.8448i	−0.331675	−	1.23783i
$887$	−21.5121	−	21.5121i	−0.722305	−	0.722305i	0.246769	−	0.969074i	$-0.420631\pi$
$887$	−21.5121	−	21.5121i	−0.722305	−	0.722305i	−0.969074	+	0.246769i	$0.920631\pi$
$888$	5.33386	−	12.6753i	0.178993	−	0.425356i
$889$			0.898159i			0.0301233i
$890$		0			0
$891$	−14.0754	+	8.12641i	−0.471542	+	0.272245i
$892$	0.262450	−	0.979477i	0.00878748	−	0.0327953i
$893$	−8.54683	−	14.8035i	−0.286009	−	0.495382i
$894$	−6.76804	−	6.76804i	−0.226357	−	0.226357i
$895$		0			0
$896$	14.0015	−	14.0015i	0.467759	−	0.467759i
$897$	5.04174	+	18.8160i	0.168339	+	0.628249i
$898$	−37.3214	−	37.3214i	−1.24543	−	1.24543i
$899$	8.65834			0.288772
$900$		0			0
$901$	−15.3668	−	4.11751i	−0.511941	−	0.137174i
$902$	2.94197			0.0979567
$903$	−8.80122	−	5.08139i	−0.292886	−	0.169098i
$904$	−17.7075	−	10.2234i	−0.588944	−	0.340027i
$905$		0			0
$906$	−6.41898	+	23.9559i	−0.213256	+	0.795883i
$907$	26.5778	−	15.3447i	0.882500	−	0.509512i	0.0110183	−	0.999939i	$-0.496493\pi$
$907$	26.5778	−	15.3447i	0.882500	−	0.509512i	0.871482	+	0.490428i	$0.163159\pi$
$908$	−0.531937	−	0.307114i	−0.0176530	−	0.0101919i
$909$	−8.00116	+	13.8584i	−0.265382	+	0.459655i
$910$		0			0
$911$	−2.31494	+	2.31494i	−0.0766975	+	0.0766975i	−0.744415	−	0.667717i	$-0.767271\pi$
$911$	−2.31494	+	2.31494i	−0.0766975	+	0.0766975i	0.667717	+	0.744415i	$0.267271\pi$
$912$	−3.72382	−	6.44985i	−0.123308	−	0.213576i
$913$	−4.98654	−	18.6100i	−0.165030	−	0.615902i
$914$		−	59.6829i		−	1.97413i
$915$		0			0
$916$	0.908266	+	0.524388i	0.0300100	+	0.0173263i
$917$	−26.1861			−0.864742
$918$	8.85349	+	2.37229i	0.292209	+	0.0782971i
$919$	−19.7684	+	19.7684i	−0.652098	+	0.652098i	−0.953498	−	0.301400i	$-0.902546\pi$
$919$	−19.7684	+	19.7684i	−0.652098	+	0.652098i	0.301400	+	0.953498i	$0.402546\pi$
$920$		0			0
$921$	−2.89353	−	5.01175i	−0.0953452	−	0.165143i
$922$	42.3373	+	11.3443i	1.39431	+	0.373603i
$923$	36.0306	−	62.4069i	1.18596	−	2.05415i
$924$	0.596383			0.0196196
$925$		0			0
$926$	−6.13852			−0.201724
$927$	−14.7840	+	25.6067i	−0.485571	+	0.841034i
$928$	2.11322	+	0.566234i	0.0693697	+	0.0185876i
$929$	9.70159	+	16.8036i	0.318299	+	0.551310i	0.980133	−	0.198340i	$-0.0635552\pi$
$929$	9.70159	+	16.8036i	0.318299	+	0.551310i	−0.661834	+	0.749650i	$0.730222\pi$
$930$		0			0
$931$	−6.60652	+	6.60652i	−0.216520	+	0.216520i
$932$	−1.35255	−	0.362414i	−0.0443041	−	0.0118713i
$933$	16.1643			0.529196
$934$	12.2717	+	7.08504i	0.401541	+	0.231830i
$935$		0			0
$936$		−	37.3046i		−	1.21934i
$937$	−5.29178	−	19.7492i	−0.172875	−	0.645178i	−0.996904	−	0.0786302i	$-0.974945\pi$
$937$	−5.29178	−	19.7492i	−0.172875	−	0.645178i	0.824029	−	0.566548i	$-0.191721\pi$
$938$	11.0788	+	19.1891i	0.361737	+	0.626547i
$939$	12.0171	−	12.0171i	0.392162	−	0.392162i
$940$		0			0
$941$	0.662999	−	1.14835i	0.0216131	−	0.0374351i	−0.855017	−	0.518601i	$-0.826453\pi$
$941$	0.662999	−	1.14835i	0.0216131	−	0.0374351i	0.876630	+	0.481166i	$0.159786\pi$
$942$	14.2118	+	8.20516i	0.463044	+	0.267339i
$943$	1.51203	−	0.872970i	0.0492384	−	0.0284278i
$944$	9.02952	−	33.6986i	0.293886	−	1.09680i
$945$		0			0
$946$	−45.0442	−	26.0063i	−1.46451	−	0.845537i
$947$	−12.6269	−	7.29012i	−0.410318	−	0.236897i	0.280608	−	0.959822i	$-0.409464\pi$
$947$	−12.6269	−	7.29012i	−0.410318	−	0.236897i	−0.690926	+	0.722925i	$0.742797\pi$
$948$	−0.382677			−0.0124288
$949$	16.3839	+	4.39006i	0.531845	+	0.142507i
$950$		0			0
$951$	−16.9440			−0.549447
$952$	−4.65741	−	4.65741i	−0.150948	−	0.150948i
$953$	−6.41629	−	23.9459i	−0.207844	−	0.775684i	−0.988564	−	0.150803i	$-0.951814\pi$
$953$	−6.41629	−	23.9459i	−0.207844	−	0.775684i	0.780720	−	0.624881i	$-0.214853\pi$
$954$	−26.1141	+	26.1141i	−0.845474	+	0.845474i
$955$		0			0
$956$	1.17367	+	1.17367i	0.0379591	+	0.0379591i
$957$	−8.15188	−	14.1195i	−0.263513	−	0.456418i
$958$	−11.2767	+	42.0854i	−0.364335	+	1.35972i
$959$	2.73772	−	1.58062i	0.0884057	−	0.0510410i
$960$		0			0
$961$		−	26.6933i		−	0.861075i
$962$	6.95337	−	50.6186i	0.224186	−	1.63201i
$963$	15.1162	+	15.1162i	0.487114	+	0.487114i
$964$	0.673673	+	2.51418i	0.0216975	+	0.0809763i
$965$		0			0
$966$	6.91453	−	3.99210i	0.222471	−	0.128444i
$967$	−28.8077	+	16.6321i	−0.926393	+	0.534853i	−0.885669	−	0.464317i	$-0.846300\pi$
$967$	−28.8077	+	16.6321i	−0.926393	+	0.534853i	−0.0407238	+	0.999170i	$0.512966\pi$
$968$	−32.4007			−1.04140
$969$	−2.24075	+	1.29370i	−0.0719832	+	0.0415595i
$970$		0			0
$971$	−6.82047	+	11.8134i	−0.218879	+	0.379110i	−0.954466	−	0.298321i	$-0.903573\pi$
$971$	−6.82047	+	11.8134i	−0.218879	+	0.379110i	0.735586	+	0.677431i	$0.236907\pi$
$972$	1.04244	−	1.04244i	0.0334363	−	0.0334363i
$973$	−20.2406	+	20.2406i	−0.648884	+	0.648884i
$974$	−11.0349	−	6.37101i	−0.353581	−	0.204140i
$975$		0			0
$976$	17.3892	+	17.3892i	0.556614	+	0.556614i
$977$	3.68372	−	6.38040i	0.117853	−	0.204127i	−0.801064	−	0.598579i	$-0.795732\pi$
$977$	3.68372	−	6.38040i	0.117853	−	0.204127i	0.918917	+	0.394452i	$0.129066\pi$
$978$	−7.17671	+	1.92299i	−0.229486	+	0.0614905i
$979$	70.7846	−	18.9667i	2.26228	−	0.606177i
$980$		0			0
$981$	18.4000	+	4.93027i	0.587467	+	0.157411i
$982$	−26.9556	+	46.6885i	−0.860189	+	1.48989i
$983$	9.94128	+	37.1014i	0.317078	+	1.18335i	0.922040	+	0.387095i	$0.126522\pi$
$983$	9.94128	+	37.1014i	0.317078	+	1.18335i	−0.604962	+	0.796254i	$0.706812\pi$
$984$	0.931226	−	0.249521i	0.0296864	−	0.00795445i
$985$		0			0
$986$	2.26684	−	8.45998i	0.0721910	−	0.269421i
$987$	10.2284	−	2.74069i	0.325573	−	0.0872370i
$988$	−0.828826	−	0.828826i	−0.0263685	−	0.0263685i
$989$	−30.8674			−0.981527
$990$		0			0
$991$	−10.4917	−	10.4917i	−0.333278	−	0.333278i	0.520552	−	0.853830i	$-0.325726\pi$
$991$	−10.4917	−	10.4917i	−0.333278	−	0.333278i	−0.853830	+	0.520552i	$0.825726\pi$
$992$	−0.281646	+	1.05112i	−0.00894228	+	0.0333730i
$993$			26.8246i			0.851253i
$994$	−28.5294	−	7.64444i	−0.904899	−	0.242467i
$995$		0			0
$996$	0.153550	+	0.265957i	0.00486542	+	0.00842716i
$997$	21.4627	+	12.3915i	0.679731	+	0.392443i	0.799754	−	0.600328i	$-0.204963\pi$
$997$	21.4627	+	12.3915i	0.679731	+	0.392443i	−0.120023	+	0.992771i	$0.538297\pi$
$998$	3.72781	−	3.72781i	0.118002	−	0.118002i
$999$	−21.1610	+	16.0495i	−0.669505	+	0.507783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.t.b.643.12		68
5.2	odd	4		925.2.y.b.532.12		68
5.3	odd	4		185.2.u.a.162.6	yes	68
5.4	even	2		185.2.p.a.88.6	yes	68
37.8	odd	12		925.2.y.b.193.12		68
185.8	even	12		185.2.p.a.82.6	✓	68
185.82	even	12	inner	925.2.t.b.82.12		68
185.119	odd	12		185.2.u.a.8.6	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.6	✓	68	185.8	even	12
185.2.p.a.88.6	yes	68	5.4	even	2
185.2.u.a.8.6	yes	68	185.119	odd	12
185.2.u.a.162.6	yes	68	5.3	odd	4
925.2.t.b.82.12		68	185.82	even	12	inner
925.2.t.b.643.12		68	1.1	even	1	trivial
925.2.y.b.193.12		68	37.8	odd	12
925.2.y.b.532.12		68	5.2	odd	4

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.723320 - 1.25283i) q^{2} +(0.791482 + 0.212077i) q^{3} +(-0.0463849 - 0.0803411i) q^{4} +(0.838191 - 0.838191i) q^{6} +(1.58905 + 0.425785i) q^{7} +2.75908 q^{8} +(-2.01661 - 1.16429i) q^{9} +4.76900i q^{11} +(-0.0196744 - 0.0734257i) q^{12} +(2.90320 + 5.02850i) q^{13} +(1.68283 - 1.68283i) q^{14} +(2.08847 - 3.61733i) q^{16} +(-1.25670 - 0.725557i) q^{17} +(-2.91731 + 1.68431i) q^{18} +(0.563197 - 2.10188i) q^{19} +(1.16741 + 0.674003i) q^{21} +(5.97473 + 3.44951i) q^{22} +4.09430 q^{23} +(2.18376 + 0.585137i) q^{24} +8.39979 q^{26} +(-3.08741 - 3.08741i) q^{27} +(-0.0395000 - 0.147416i) q^{28} +(-2.95018 + 2.95018i) q^{29} +(-1.46743 - 1.46743i) q^{31} +(-0.262184 - 0.454116i) q^{32} +(-1.01139 + 3.77458i) q^{33} +(-1.81799 + 1.04962i) q^{34} +0.216022i q^{36} +(0.827803 - 6.02617i) q^{37} +(-2.22592 - 2.22592i) q^{38} +(1.23141 + 4.59567i) q^{39} +(0.369301 - 0.213216i) q^{41} +(1.68882 - 0.975040i) q^{42} -7.53912 q^{43} +(0.383146 - 0.221210i) q^{44} +(2.96149 - 5.12945i) q^{46} +(5.55465 - 5.55465i) q^{47} +(2.42014 - 2.42014i) q^{48} +(-3.71838 - 2.14681i) q^{49} +(-0.840783 - 0.840783i) q^{51} +(0.269330 - 0.466493i) q^{52} +(10.5896 - 2.83749i) q^{53} +(-6.10117 + 1.63480i) q^{54} +(4.38432 + 1.17477i) q^{56} +(0.891520 - 1.54416i) q^{57} +(1.56214 + 5.82999i) q^{58} +(8.06779 - 2.16176i) q^{59} +(-1.52382 + 5.68696i) q^{61} +(-2.89985 + 0.777013i) q^{62} +(-2.70876 - 2.70876i) q^{63} +7.59529 q^{64} +(3.99733 + 3.99733i) q^{66} +(-2.40971 + 8.99317i) q^{67} +0.134620i q^{68} +(3.24056 + 0.868307i) q^{69} +(-6.20532 - 10.7479i) q^{71} +(-5.56398 - 3.21236i) q^{72} +(2.06563 - 2.06563i) q^{73} +(-6.95099 - 5.39595i) q^{74} +(-0.194991 + 0.0522477i) q^{76} +(-2.03057 + 7.57818i) q^{77} +(6.64828 + 1.78140i) q^{78} +(1.30294 - 4.86264i) q^{79} +(1.70401 + 2.95143i) q^{81} -0.616894i q^{82} +(-3.90229 + 1.04562i) q^{83} -0.125054i q^{84} +(-5.45320 + 9.44522i) q^{86} +(-2.96068 + 1.70935i) q^{87} +13.1580i q^{88} +(-3.97708 - 14.8427i) q^{89} +(2.47228 + 9.22669i) q^{91} +(-0.189914 - 0.328940i) q^{92} +(-0.850234 - 1.47265i) q^{93} +(-2.94123 - 10.9768i) q^{94} +(-0.111207 - 0.415028i) q^{96} +17.9332i q^{97} +(-5.37917 + 3.10566i) q^{98} +(5.55249 - 9.61720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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