LMFDB - Embedded newform 875.2.bb.a.82.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			82.5
Character	$\chi$	$=$	875.82
Dual form			875.2.bb.a.843.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47859 - 0.567578i) q^{2} +(-0.936069 + 0.0490573i) q^{3} +(0.377800 + 0.340173i) q^{4} +(1.41191 + 0.458757i) q^{6} +(0.0623449 + 2.64502i) q^{7} +(1.07251 + 2.10492i) q^{8} +(-2.10975 + 0.221743i) q^{9} +(0.296290 - 2.81901i) q^{11} +(-0.370335 - 0.299891i) q^{12} +(-4.35361 - 0.689545i) q^{13} +(1.40907 - 3.94629i) q^{14} +(-0.497379 - 4.73224i) q^{16} +(-2.12183 + 3.26733i) q^{17} +(3.24531 + 0.869579i) q^{18} +(3.31747 + 3.68442i) q^{19} +(-0.188117 - 2.47286i) q^{21} +(-2.03810 + 4.00000i) q^{22} +(0.356574 - 0.928907i) q^{23} +(-1.10721 - 1.91774i) q^{24} +(6.04585 + 3.49057i) q^{26} +(4.74143 - 0.750969i) q^{27} +(-0.876209 + 1.02050i) q^{28} +(4.01849 - 1.30569i) q^{29} +(-1.19177 - 5.60686i) q^{31} +(-0.727626 + 2.71554i) q^{32} +(-0.139055 + 2.65332i) q^{33} +(4.99179 - 3.62674i) q^{34} +(-0.872494 - 0.633904i) q^{36} +(0.109682 - 0.135446i) q^{37} +(-2.81399 - 7.33069i) q^{38} +(4.10911 + 0.431885i) q^{39} +(4.52386 + 6.22657i) q^{41} +(-1.12539 + 3.76312i) q^{42} +(2.45065 - 2.45065i) q^{43} +(1.07089 - 0.964233i) q^{44} +(-1.05446 + 1.17109i) q^{46} +(3.19156 - 2.07262i) q^{47} +(0.697732 + 4.40531i) q^{48} +(-6.99223 + 0.329807i) q^{49} +(1.82589 - 3.16254i) q^{51} +(-1.41023 - 1.74149i) q^{52} +(-0.733542 - 13.9968i) q^{53} +(-7.43688 - 1.58076i) q^{54} +(-5.50068 + 2.96804i) q^{56} +(-3.28613 - 3.28613i) q^{57} +(-6.68280 - 0.350230i) q^{58} +(-9.14624 - 4.07217i) q^{59} +(-4.02106 - 9.03145i) q^{61} +(-1.42018 + 8.96669i) q^{62} +(-0.718047 - 5.56649i) q^{63} +(-2.97658 + 4.09692i) q^{64} +(1.71157 - 3.84426i) q^{66} +(-9.17658 - 5.95934i) q^{67} +(-1.91308 + 0.512609i) q^{68} +(-0.288208 + 0.887014i) q^{69} +(2.13171 + 6.56074i) q^{71} +(-2.72948 - 4.20303i) q^{72} +(4.12589 - 3.34108i) q^{73} +(-0.239051 + 0.138016i) q^{74} +2.52049i q^{76} +(7.47480 + 0.607941i) q^{77} +(-5.83057 - 2.97082i) q^{78} +(0.891037 - 4.19200i) q^{79} +(1.82357 - 0.387611i) q^{81} +(-3.15489 - 11.7742i) q^{82} +(1.82179 - 0.928247i) q^{83} +(0.770129 - 0.998239i) q^{84} +(-5.01445 + 2.23257i) q^{86} +(-3.69754 + 1.41935i) q^{87} +(6.25157 - 2.39975i) q^{88} +(6.71884 - 2.99142i) q^{89} +(1.55243 - 11.5584i) q^{91} +(0.450703 - 0.229645i) q^{92} +(1.39064 + 5.18994i) q^{93} +(-5.89539 + 1.25310i) q^{94} +(0.547892 - 2.57763i) q^{96} +(-7.31730 - 3.72835i) q^{97} +(10.5258 + 3.48099i) q^{98} +6.01310i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.47859	−	0.567578i	−1.04552	−	0.401339i	−0.225845	−	0.974163i	$-0.572514\pi$
$2$	−1.47859	−	0.567578i	−1.04552	−	0.401339i	−0.819678	+	0.572825i	$0.805848\pi$
$3$	−0.936069	+	0.0490573i	−0.540440	+	0.0283233i	−0.320603	−	0.947214i	$-0.603886\pi$
$3$	−0.936069	+	0.0490573i	−0.540440	+	0.0283233i	−0.219836	+	0.975537i	$0.570552\pi$
$4$	0.377800	+	0.340173i	0.188900	+	0.170086i
$5$		0			0
$5$		0			0
$6$	1.41191	+	0.458757i	0.576409	+	0.187287i
$7$	0.0623449	+	2.64502i	0.0235642	+	0.999722i
$7$	0.0623449	+	2.64502i	0.0235642	+	0.999722i
$8$	1.07251	+	2.10492i	0.379190	+	0.744202i
$9$	−2.10975	+	0.221743i	−0.703249	+	0.0739144i
$10$		0			0
$11$	0.296290	−	2.81901i	0.0893348	−	0.849964i	−0.854479	−	0.519486i	$-0.826123\pi$
$11$	0.296290	−	2.81901i	0.0893348	−	0.849964i	0.943814	−	0.330478i	$-0.107210\pi$
$12$	−0.370335	−	0.299891i	−0.106907	−	0.0865712i
$13$	−4.35361	−	0.689545i	−1.20748	−	0.191245i	−0.479931	−	0.877306i	$-0.659338\pi$
$13$	−4.35361	−	0.689545i	−1.20748	−	0.191245i	−0.727544	+	0.686061i	$0.759338\pi$
$14$	1.40907	−	3.94629i	0.376590	−	1.05469i
$15$		0			0
$16$	−0.497379	−	4.73224i	−0.124345	−	1.18306i
$17$	−2.12183	+	3.26733i	−0.514619	+	0.792444i	−0.996482	−	0.0838024i	$-0.973294\pi$
$17$	−2.12183	+	3.26733i	−0.514619	+	0.792444i	0.481863	+	0.876246i	$0.339960\pi$
$18$	3.24531	+	0.869579i	0.764927	+	0.204962i
$19$	3.31747	+	3.68442i	0.761080	+	0.845265i	0.991806	−	0.127754i	$-0.0407768\pi$
$19$	3.31747	+	3.68442i	0.761080	+	0.845265i	−0.230726	+	0.973019i	$0.574110\pi$
$20$		0			0
$21$	−0.188117	−	2.47286i	−0.0410504	−	0.539622i
$22$	−2.03810	+	4.00000i	−0.434525	+	0.852803i
$23$	0.356574	−	0.928907i	0.0743509	−	0.193691i	−0.891368	−	0.453280i	$-0.850254\pi$
$23$	0.356574	−	0.928907i	0.0743509	−	0.193691i	0.965719	+	0.259589i	$0.0835872\pi$
$24$	−1.10721	−	1.91774i	−0.226007	−	0.391456i
$25$		0			0
$26$	6.04585	+	3.49057i	1.18569	+	0.684558i
$27$	4.74143	−	0.750969i	0.912489	−	0.144524i
$28$	−0.876209	+	1.02050i	−0.165588	+	0.192856i
$29$	4.01849	−	1.30569i	0.746216	−	0.242460i	0.0888637	−	0.996044i	$-0.471676\pi$
$29$	4.01849	−	1.30569i	0.746216	−	0.242460i	0.657352	+	0.753584i	$0.271676\pi$
$30$		0			0
$31$	−1.19177	−	5.60686i	−0.214049	−	1.00702i	−0.945624	−	0.325261i	$-0.894548\pi$
$31$	−1.19177	−	5.60686i	−0.214049	−	1.00702i	0.731575	−	0.681761i	$-0.238785\pi$
$32$	−0.727626	+	2.71554i	−0.128627	+	0.480044i
$33$	−0.139055	+	2.65332i	−0.0242063	+	0.461884i
$34$	4.99179	−	3.62674i	0.856084	−	0.621982i
$35$		0			0
$36$	−0.872494	−	0.633904i	−0.145416	−	0.105651i
$37$	0.109682	−	0.135446i	0.0180316	−	0.0222672i	−0.768050	−	0.640389i	$-0.778773\pi$
$37$	0.109682	−	0.135446i	0.0180316	−	0.0222672i	0.786082	+	0.618122i	$0.212106\pi$
$38$	−2.81399	−	7.33069i	−0.456489	−	1.18919i
$39$	4.10911	+	0.431885i	0.657984	+	0.0691570i
$40$		0			0
$41$	4.52386	+	6.22657i	0.706509	+	0.972426i	0.999865	+	0.0164229i	$0.00522780\pi$
$41$	4.52386	+	6.22657i	0.706509	+	0.972426i	−0.293356	+	0.956003i	$0.594772\pi$
$42$	−1.12539	+	3.76312i	−0.173652	+	0.580662i
$43$	2.45065	−	2.45065i	0.373720	−	0.373720i	−0.495110	−	0.868830i	$-0.664872\pi$
$43$	2.45065	−	2.45065i	0.373720	−	0.373720i	0.868830	+	0.495110i	$0.164872\pi$
$44$	1.07089	−	0.964233i	0.161443	−	0.145364i
$45$		0			0
$46$	−1.05446	+	1.17109i	−0.155471	+	0.172668i
$47$	3.19156	−	2.07262i	0.465537	−	0.302323i	−0.290473	−	0.956883i	$-0.593813\pi$
$47$	3.19156	−	2.07262i	0.465537	−	0.302323i	0.756010	+	0.654560i	$0.227146\pi$
$48$	0.697732	+	4.40531i	0.100709	+	0.635851i
$49$	−6.99223	+	0.329807i	−0.998889	+	0.0471153i
$50$		0			0
$51$	1.82589	−	3.16254i	0.255676	−	0.442844i
$52$	−1.41023	−	1.74149i	−0.195564	−	0.241501i
$53$	−0.733542	−	13.9968i	−0.100760	−	1.92261i	−0.320848	−	0.947131i	$-0.603968\pi$
$53$	−0.733542	−	13.9968i	−0.100760	−	1.92261i	0.220088	−	0.975480i	$-0.429366\pi$
$54$	−7.43688	−	1.58076i	−1.01203	−	0.215114i
$55$		0			0
$56$	−5.50068	+	2.96804i	−0.735060	+	0.396621i
$57$	−3.28613	−	3.28613i	−0.435259	−	0.435259i
$58$	−6.68280	−	0.350230i	−0.877494	−	0.0459875i
$59$	−9.14624	−	4.07217i	−1.19074	−	0.530151i	−0.286874	−	0.957968i	$-0.592616\pi$
$59$	−9.14624	−	4.07217i	−1.19074	−	0.530151i	−0.903865	+	0.427817i	$0.859283\pi$
$60$		0			0
$61$	−4.02106	−	9.03145i	−0.514844	−	1.15636i	−0.964722	−	0.263269i	$-0.915199\pi$
$61$	−4.02106	−	9.03145i	−0.514844	−	1.15636i	0.449878	−	0.893090i	$-0.351467\pi$
$62$	−1.42018	+	8.96669i	−0.180363	+	1.13877i
$63$	−0.718047	−	5.56649i	−0.0904654	−	0.701312i
$64$	−2.97658	+	4.09692i	−0.372073	+	0.512115i
$65$		0			0
$66$	1.71157	−	3.84426i	0.210680	−	0.473196i
$67$	−9.17658	−	5.95934i	−1.12110	−	0.728050i	−0.155435	−	0.987846i	$-0.549678\pi$
$67$	−9.17658	−	5.95934i	−1.12110	−	0.728050i	−0.965663	+	0.259797i	$0.916344\pi$
$68$	−1.91308	+	0.512609i	−0.231995	+	0.0621630i
$69$	−0.288208	+	0.887014i	−0.0346962	+	0.106784i
$70$		0			0
$71$	2.13171	+	6.56074i	0.252988	+	0.778617i	0.994219	+	0.107367i	$0.0342420\pi$
$71$	2.13171	+	6.56074i	0.252988	+	0.778617i	−0.741232	+	0.671249i	$0.765758\pi$
$72$	−2.72948	−	4.20303i	−0.321672	−	0.495332i
$73$	4.12589	−	3.34108i	0.482899	−	0.391044i	−0.356727	−	0.934209i	$-0.616107\pi$
$73$	4.12589	−	3.34108i	0.482899	−	0.391044i	0.839626	+	0.543165i	$0.182774\pi$
$74$	−0.239051	+	0.138016i	−0.0277892	+	0.0160441i
$75$		0			0
$76$			2.52049i			0.289120i
$77$	7.47480	+	0.607941i	0.851833	+	0.0692813i
$78$	−5.83057	−	2.97082i	−0.660182	−	0.336380i
$79$	0.891037	−	4.19200i	0.100249	−	0.471637i	−0.899171	−	0.437597i	$-0.855830\pi$
$79$	0.891037	−	4.19200i	0.100249	−	0.471637i	0.999420	−	0.0340393i	$-0.0108371\pi$
$80$		0			0
$81$	1.82357	−	0.387611i	0.202618	−	0.0430679i
$82$	−3.15489	−	11.7742i	−0.348399	−	1.30024i
$83$	1.82179	−	0.928247i	0.199967	−	0.101888i	−0.351140	−	0.936323i	$-0.614206\pi$
$83$	1.82179	−	0.928247i	0.199967	−	0.101888i	0.551107	+	0.834435i	$0.314206\pi$
$84$	0.770129	−	0.998239i	0.0840280	−	0.108917i
$85$		0			0
$86$	−5.01445	+	2.23257i	−0.540722	+	0.240745i
$87$	−3.69754	+	1.41935i	−0.396417	+	0.152170i
$88$	6.25157	−	2.39975i	0.666419	−	0.255814i
$89$	6.71884	−	2.99142i	0.712195	−	0.317090i	−0.0184664	−	0.999829i	$-0.505878\pi$
$89$	6.71884	−	2.99142i	0.712195	−	0.317090i	0.730662	+	0.682740i	$0.239212\pi$
$90$		0			0
$91$	1.55243	−	11.5584i	0.162739	−	1.21165i
$92$	0.450703	−	0.229645i	0.0469890	−	0.0239421i
$93$	1.39064	+	5.18994i	0.144203	+	0.538172i
$94$	−5.89539	+	1.25310i	−0.608063	+	0.129248i
$95$		0			0
$96$	0.547892	−	2.57763i	0.0559190	−	0.263078i
$97$	−7.31730	−	3.72835i	−0.742959	−	0.378556i	0.0411720	−	0.999152i	$-0.486891\pi$
$97$	−7.31730	−	3.72835i	−0.742959	−	0.378556i	−0.784131	+	0.620596i	$0.786891\pi$
$98$	10.5258	+	3.48099i	1.06327	+	0.351633i
$99$			6.01310i			0.604339i
$100$		0			0
$101$	10.1754	−	5.87479i	1.01249	−	0.584563i	0.100572	−	0.994930i	$-0.467933\pi$
$101$	10.1754	−	5.87479i	1.01249	−	0.584563i	0.911921	+	0.410367i	$0.134599\pi$
$102$	−4.49474	+	3.63977i	−0.445045	+	0.360391i
$103$	−5.97025	−	9.19339i	−0.588267	−	0.905851i	0.411718	−	0.911311i	$-0.364929\pi$
$103$	−5.97025	−	9.19339i	−0.588267	−	0.905851i	−0.999985	+	0.00545986i	$0.998262\pi$
$104$	−3.21786	−	9.90356i	−0.315537	−	0.971124i
$105$		0			0
$106$	−6.85968	+	21.1119i	−0.666271	+	2.05057i
$107$	6.90983	−	1.85148i	0.667999	−	0.178990i	0.0911455	−	0.995838i	$-0.470947\pi$
$107$	6.90983	−	1.85148i	0.667999	−	0.178990i	0.576853	+	0.816848i	$0.304280\pi$
$108$	2.04677	+	1.32919i	0.196951	+	0.127901i
$109$	5.79401	−	13.0136i	0.554965	−	1.24647i	−0.390456	−	0.920622i	$-0.627683\pi$
$109$	5.79401	−	13.0136i	0.554965	−	1.24647i	0.945421	−	0.325851i	$-0.105651\pi$
$110$		0			0
$111$	−0.0960254	+	0.132168i	−0.00911433	+	0.0125448i
$112$	12.4859	−	1.61061i	1.17980	−	0.152188i
$113$	−2.84433	+	17.9584i	−0.267572	+	1.68938i	0.378096	+	0.925766i	$0.376579\pi$
$113$	−2.84433	+	17.9584i	−0.267572	+	1.68938i	−0.645668	+	0.763618i	$0.723421\pi$
$114$	2.99371	+	6.72398i	0.280387	+	0.629759i
$115$		0			0
$116$	1.96235	+	0.873693i	0.182199	+	0.0811204i
$117$	9.33793	+	0.489380i	0.863292	+	0.0452432i
$118$	11.2123	+	11.2123i	1.03217	+	1.03217i
$119$	−8.77443	−	5.40857i	−0.804351	−	0.495803i
$120$		0			0
$121$	2.90059	+	0.616540i	0.263690	+	0.0560491i
$122$	0.819453	+	15.6361i	0.0741898	+	1.41563i
$123$	−4.54011	−	5.60657i	−0.409368	−	0.505527i
$124$	1.45705	−	2.52368i	0.130847	−	0.226633i
$125$		0			0
$126$	−2.09772	+	8.63812i	−0.186880	+	0.769545i
$127$	−2.82772	−	17.8535i	−0.250919	−	1.58424i	−0.715436	−	0.698678i	$-0.753772\pi$
$127$	−2.82772	−	17.8535i	−0.250919	−	1.58424i	0.464517	−	0.885564i	$-0.346228\pi$
$128$	11.4420	−	7.43055i	1.01134	−	0.656774i
$129$	−2.17375	+	2.41420i	−0.191388	+	0.212558i
$130$		0			0
$131$	−11.0046	+	9.90862i	−0.961480	+	0.865721i	−0.991002	−	0.133844i	$-0.957268\pi$
$131$	−11.0046	+	9.90862i	−0.961480	+	0.865721i	0.0295224	+	0.999564i	$0.490601\pi$
$132$	−0.955123	+	0.955123i	−0.0831328	+	0.0831328i
$133$	−9.53854	+	9.00447i	−0.827096	+	0.780787i
$134$	10.1860	+	14.0199i	0.879939	+	1.21113i
$135$		0			0
$136$	−9.15315	−	0.962035i	−0.784877	−	0.0824939i
$137$	−5.30092	−	13.8094i	−0.452888	−	1.17981i	−0.950034	−	0.312147i	$-0.898952\pi$
$137$	−5.30092	−	13.8094i	−0.452888	−	1.17981i	0.497145	−	0.867667i	$-0.334382\pi$
$138$	0.929593	−	1.14795i	0.0791322	−	0.0977201i
$139$	0.341041	+	0.247781i	0.0289267	+	0.0210165i	0.602155	−	0.798379i	$-0.294309\pi$
$139$	0.341041	+	0.247781i	0.0289267	+	0.0210165i	−0.573228	+	0.819396i	$0.694309\pi$
$140$		0			0
$141$	−2.88584	+	2.09669i	−0.243032	+	0.176573i
$142$	0.571799	−	10.9106i	0.0479843	−	0.915595i
$143$	−3.23377	+	12.0686i	−0.270421	+	1.00923i
$144$	2.09869	+	9.87354i	0.174891	+	0.822795i
$145$		0			0
$146$	−7.99683	+	2.59833i	−0.661823	+	0.215039i
$147$	6.52903	−	0.651742i	0.538505	−	0.0537548i
$148$	0.0875130	−	0.0138607i	0.00719352	−	0.00113934i
$149$	−5.68925	−	3.28469i	−0.466081	−	0.269092i	0.248517	−	0.968628i	$-0.420057\pi$
$149$	−5.68925	−	3.28469i	−0.466081	−	0.269092i	−0.714598	+	0.699536i	$0.753390\pi$
$150$		0			0
$151$	2.85500	+	4.94500i	0.232336	+	0.402419i	0.958495	−	0.285108i	$-0.0920296\pi$
$151$	2.85500	+	4.94500i	0.232336	+	0.402419i	−0.726159	+	0.687527i	$0.758696\pi$
$152$	−4.19740	+	10.9346i	−0.340454	+	0.886913i
$153$	3.75201	−	7.36374i	0.303332	−	0.595323i
$154$	−10.7071	−	5.14143i	−0.862805	−	0.414308i
$155$		0			0
$156$	1.40551	+	1.56097i	0.112531	+	0.124978i
$157$	8.34069	+	2.23488i	0.665660	+	0.178363i	0.575799	−	0.817591i	$-0.304691\pi$
$157$	8.34069	+	2.23488i	0.665660	+	0.178363i	0.0898608	+	0.995954i	$0.471358\pi$
$158$	−3.69677	+	5.69252i	−0.294099	+	0.452873i
$159$	1.37329	+	13.0660i	0.108909	+	1.03620i
$160$		0			0
$161$	2.47921	+	0.885232i	0.195389	+	0.0697661i
$162$	−2.91631	−	0.461898i	−0.229127	−	0.0362901i
$163$	−8.89936	−	7.20656i	−0.697051	−	0.564461i	0.213960	−	0.976842i	$-0.431364\pi$
$163$	−8.89936	−	7.20656i	−0.697051	−	0.564461i	−0.911011	+	0.412381i	$0.864697\pi$
$164$	−0.408991	+	3.89129i	−0.0319369	+	0.303859i
$165$		0			0
$166$	−3.22053	+	0.338492i	−0.249962	+	0.0262720i
$167$	4.34514	+	8.52782i	0.336237	+	0.659903i	0.995781	−	0.0917636i	$-0.0292504\pi$
$167$	4.34514	+	8.52782i	0.336237	+	0.659903i	−0.659544	+	0.751666i	$0.729250\pi$
$168$	5.00342	−	3.04814i	0.386022	−	0.235169i
$169$	6.11475	+	1.98680i	0.470366	+	0.152831i
$170$		0			0
$171$	−7.81602	−	7.03758i	−0.597706	−	0.538177i
$172$	1.75950	−	0.0922114i	0.134161	−	0.00703106i
$173$	8.24966	+	3.16675i	0.627210	+	0.240763i	0.651149	−	0.758950i	$-0.274287\pi$
$173$	8.24966	+	3.16675i	0.627210	+	0.240763i	−0.0239388	+	0.999713i	$0.507621\pi$
$174$	6.27274			0.475535
$175$		0			0
$176$	−13.4876			−1.01667
$177$	8.76129	+	3.36314i	0.658539	+	0.252789i
$178$	−11.6323	+	0.609622i	−0.871877	+	0.0456931i
$179$	9.37841	+	8.44436i	0.700975	+	0.631161i	0.940526	−	0.339723i	$-0.110333\pi$
$179$	9.37841	+	8.44436i	0.700975	+	0.631161i	−0.239550	+	0.970884i	$0.577000\pi$
$180$		0			0
$181$	20.9424	+	6.80460i	1.55664	+	0.505782i	0.955907	−	0.293670i	$-0.0948768\pi$
$181$	20.9424	+	6.80460i	1.55664	+	0.505782i	0.600730	+	0.799452i	$0.294877\pi$
$182$	−8.85570	+	16.2090i	−0.656428	+	1.20149i
$183$	4.20705	+	8.25680i	0.310994	+	0.610360i
$184$	2.33771	−	0.245703i	0.172338	−	0.0181135i
$185$		0			0
$186$	0.889509	−	8.46311i	0.0652219	−	0.620545i
$187$	8.58196	+	6.94954i	0.627575	+	0.508200i
$188$	1.91082	+	0.302644i	0.139361	+	0.0220726i
$189$	2.28193	+	12.4943i	0.165986	+	0.908830i
$190$		0			0
$191$	1.45145	+	13.8097i	0.105023	+	0.999231i	0.912429	+	0.409235i	$0.134204\pi$
$191$	1.45145	+	13.8097i	0.105023	+	0.999231i	−0.807406	+	0.589997i	$0.799129\pi$
$192$	2.58531	−	3.98102i	0.186578	−	0.287306i
$193$	−15.0896	−	4.04325i	−1.08618	−	0.291040i	−0.329052	−	0.944312i	$-0.606729\pi$
$193$	−15.0896	−	4.04325i	−1.08618	−	0.291040i	−0.757123	+	0.653272i	$0.773396\pi$
$194$	8.70317	+	9.66585i	0.624851	+	0.693967i
$195$		0			0
$196$	−2.75385	−	2.25396i	−0.196704	−	0.160997i
$197$	3.76513	−	7.38948i	0.268254	−	0.526479i	−0.717106	−	0.696964i	$-0.754534\pi$
$197$	3.76513	−	7.38948i	0.268254	−	0.526479i	0.985360	+	0.170486i	$0.0545336\pi$
$198$	3.41290	−	8.89092i	0.242545	−	0.631850i
$199$	3.90101	+	6.75675i	0.276535	+	0.478973i	0.970521	−	0.241015i	$-0.0774804\pi$
$199$	3.90101	+	6.75675i	0.276535	+	0.478973i	−0.693986	+	0.719989i	$0.744147\pi$
$200$		0			0
$201$	8.88227	+	5.12818i	0.626507	+	0.361714i
$202$	−18.3797	+	2.91106i	−1.29319	+	0.204822i
$203$	3.70410	+	10.5476i	0.259977	+	0.740295i
$204$	1.76563	−	0.573688i	0.123619	−	0.0401662i
$205$		0			0
$206$	3.60961	+	16.9819i	0.251493	+	1.18318i
$207$	−0.546302	+	2.03883i	−0.0379706	+	0.141708i
$208$	−1.09770	+	20.9453i	−0.0761117	+	1.45230i
$209$	11.3694	−	8.26033i	0.786435	−	0.571379i
$210$		0			0
$211$	−22.7260	−	16.5114i	−1.56452	−	1.13669i	−0.932176	−	0.362006i	$-0.882092\pi$
$211$	−22.7260	−	16.5114i	−1.56452	−	1.13669i	−0.632347	−	0.774686i	$-0.717908\pi$
$212$	4.48420	−	5.53753i	0.307976	−	0.380319i
$213$	−2.31728	−	6.03673i	−0.158778	−	0.413630i
$214$	−11.2677	−	1.18428i	−0.770243	−	0.0809558i
$215$		0			0
$216$	6.66597	+	9.17491i	0.453561	+	0.624274i
$217$	14.7559	−	3.50182i	1.00170	−	0.237719i
$218$	−15.9532	+	15.9532i	−1.08049	+	1.08049i
$219$	−3.69821	+	3.32989i	−0.249902	+	0.225013i
$220$		0			0
$221$	11.4906	−	12.7616i	0.772941	−	0.858438i
$222$	0.216998	−	0.140920i	0.0145639	−	0.00945794i
$223$	1.96762	+	12.4231i	0.131762	+	0.831912i	0.961710	+	0.274070i	$0.0883701\pi$
$223$	1.96762	+	12.4231i	0.131762	+	0.831912i	−0.829948	+	0.557841i	$0.811630\pi$
$224$	−7.22801	−	1.75528i	−0.482942	−	0.117280i
$225$		0			0
$226$	14.3984	−	24.9388i	0.957768	−	1.65890i
$227$	6.86001	+	8.47140i	0.455315	+	0.562267i	0.952171	−	0.305566i	$-0.0988457\pi$
$227$	6.86001	+	8.47140i	0.455315	+	0.562267i	−0.496856	+	0.867833i	$0.665512\pi$
$228$	−0.123648	−	2.35935i	−0.00818881	−	0.156252i
$229$	−2.71293	−	0.576652i	−0.179276	−	0.0381062i	0.117399	−	0.993085i	$-0.462544\pi$
$229$	−2.71293	−	0.576652i	−0.179276	−	0.0381062i	−0.296675	+	0.954979i	$0.595878\pi$
$230$		0			0
$231$	−7.02676	−	0.202381i	−0.462327	−	0.0133157i
$232$	7.05825	+	7.05825i	0.463397	+	0.463397i
$233$	28.2933	+	1.48279i	1.85356	+	0.0971407i	0.946271	−	0.323376i	$-0.104818\pi$
$233$	28.2933	+	1.48279i	1.85356	+	0.0971407i	0.907285	+	0.420517i	$0.138151\pi$
$234$	−13.5292	−	6.02360i	−0.884433	−	0.393775i
$235$		0			0
$236$	−2.07021	−	4.64977i	−0.134759	−	0.302674i
$237$	−0.628424	+	3.96771i	−0.0408205	+	0.257731i
$238$	9.90401	+	12.9772i	0.641982	+	0.841190i
$239$	7.39994	−	10.1851i	0.478662	−	0.658822i	−0.499585	−	0.866265i	$-0.666514\pi$
$239$	7.39994	−	10.1851i	0.478662	−	0.658822i	0.978247	+	0.207443i	$0.0665140\pi$
$240$		0			0
$241$	2.84881	−	6.39853i	0.183508	−	0.412166i	−0.798243	−	0.602335i	$-0.794237\pi$
$241$	2.84881	−	6.39853i	0.183508	−	0.412166i	0.981751	+	0.190169i	$0.0609037\pi$
$242$	−3.93886	−	2.55792i	−0.253199	−	0.164430i
$243$	−15.5988	+	4.17970i	−1.00067	+	0.268128i
$244$	1.55310	−	4.77994i	0.0994268	−	0.306004i
$245$		0			0
$246$	3.53080	+	10.8667i	0.225116	+	0.692835i
$247$	−11.9024	−	18.3281i	−0.757332	−	1.16619i
$248$	10.5238	−	8.52201i	0.668262	−	0.541148i
$249$	−1.65978	+	0.958275i	−0.105184	+	0.0607282i
$250$		0			0
$251$		−	3.04599i		−	0.192261i	−0.995369	−	0.0961305i	$-0.969353\pi$
$251$		−	3.04599i		−	0.192261i	0.995369	−	0.0961305i	$-0.0306466\pi$
$252$	1.62229	−	2.34728i	0.102195	−	0.147865i
$253$	−2.51295	−	1.28041i	−0.157988	−	0.0804988i
$254$	−5.95222	+	28.0030i	−0.373476	+	1.75706i
$255$		0			0
$256$	−11.2287	+	2.38674i	−0.701795	+	0.149171i
$257$	−1.47527	−	5.50579i	−0.0920249	−	0.343442i	0.904527	−	0.426417i	$-0.140224\pi$
$257$	−1.47527	−	5.50579i	−0.0920249	−	0.343442i	−0.996552	+	0.0829753i	$0.973558\pi$
$258$	4.58434	−	2.33584i	0.285409	−	0.145423i
$259$	0.365095	+	0.281667i	0.0226859	+	0.0175019i
$260$		0			0
$261$	−8.18848	+	3.64575i	−0.506854	+	0.225666i
$262$	21.8953	−	8.40482i	1.35270	−	0.519251i
$263$	3.73485	−	1.43367i	0.230301	−	0.0884041i	−0.240481	−	0.970654i	$-0.577305\pi$
$263$	3.73485	−	1.43367i	0.230301	−	0.0884041i	0.470782	+	0.882250i	$0.343972\pi$
$264$	−5.73417	+	2.55302i	−0.352914	+	0.157127i
$265$		0			0
$266$	19.2143	−	7.90007i	1.17811	−	0.484385i
$267$	−6.14255	+	3.12978i	−0.375918	+	0.191540i
$268$	−1.43971	−	5.37306i	−0.0879442	−	0.328212i
$269$	4.60767	−	0.979391i	0.280935	−	0.0597145i	−0.0652894	−	0.997866i	$-0.520797\pi$
$269$	4.60767	−	0.979391i	0.280935	−	0.0597145i	0.346224	+	0.938152i	$0.387464\pi$
$270$		0			0
$271$	0.456757	−	2.14887i	0.0277460	−	0.130535i	−0.962095	−	0.272716i	$-0.912078\pi$
$271$	0.456757	−	2.14887i	0.0277460	−	0.130535i	0.989841	+	0.142181i	$0.0454115\pi$
$272$	16.5172	+	8.41591i	1.00150	+	0.510290i
$273$	−0.886161	+	10.8956i	−0.0536329	+	0.659431i
$274$			23.4271i			1.41528i
$275$		0			0
$276$	−0.410623	+	0.237073i	−0.0247166	+	0.0142701i
$277$	5.31854	−	4.30687i	0.319560	−	0.258775i	−0.456096	−	0.889931i	$-0.650753\pi$
$277$	5.31854	−	4.30687i	0.319560	−	0.258775i	0.775656	+	0.631156i	$0.217419\pi$
$278$	−0.363625	−	0.559934i	−0.0218088	−	0.0335826i
$279$	3.75763	+	11.5648i	0.224963	+	0.692366i
$280$		0			0
$281$	−0.775793	+	2.38765i	−0.0462799	+	0.142435i	−0.971526	−	0.236932i	$-0.923858\pi$
$281$	−0.775793	+	2.38765i	−0.0462799	+	0.142435i	0.925246	+	0.379367i	$0.123858\pi$
$282$	5.45702	−	1.46220i	0.324961	−	0.0870730i
$283$	−6.26989	−	4.07172i	−0.372706	−	0.242038i	0.344670	−	0.938724i	$-0.387991\pi$
$283$	−6.26989	−	4.07172i	−0.372706	−	0.242038i	−0.717377	+	0.696685i	$0.754657\pi$
$284$	−1.42642	+	3.20380i	−0.0846426	+	0.190110i
$285$		0			0
$286$	11.6313	−	16.0091i	0.687772	−	0.946637i
$287$	−16.1873	+	12.3539i	−0.955508	+	0.729227i
$288$	0.932955	−	5.89045i	0.0549749	−	0.347098i
$289$	0.741235	+	1.66484i	0.0436020	+	0.0979318i
$290$		0			0
$291$	7.03240	+	3.13103i	0.412246	+	0.183544i
$292$	2.69531	+	0.141255i	0.157731	+	0.00826632i
$293$	9.76381	+	9.76381i	0.570408	+	0.570408i	0.932242	−	0.361835i	$-0.117849\pi$
$293$	9.76381	+	9.76381i	0.570408	+	0.570408i	−0.361835	+	0.932242i	$0.617849\pi$
$294$	−10.0237	−	2.74207i	−0.584593	−	0.159921i
$295$		0			0
$296$	0.402738	+	0.0856047i	0.0234087	+	0.00497567i
$297$	−0.712151	−	13.5886i	−0.0413232	−	0.788493i
$298$	6.54776	+	8.08581i	0.379301	+	0.468398i
$299$	−2.19291	+	3.79823i	−0.126819	+	0.219657i
$300$		0			0
$301$	6.63479	+	6.32922i	0.382423	+	0.364810i
$302$	−1.41470	−	8.93208i	−0.0814070	−	0.513983i
$303$	−9.23671	+	5.99839i	−0.530635	+	0.344598i
$304$	15.7856	−	17.5316i	0.905364	−	1.00551i
$305$		0			0
$306$	−9.72720	+	8.75841i	−0.556067	+	0.500685i
$307$	−1.41797	+	1.41797i	−0.0809280	+	0.0809280i	−0.746412	−	0.665484i	$-0.768225\pi$
$307$	−1.41797	+	1.41797i	−0.0809280	+	0.0809280i	0.665484	+	0.746412i	$0.268225\pi$
$308$	2.61718	+	2.77240i	0.149127	+	0.157972i
$309$	6.03957	+	8.31276i	0.343579	+	0.472896i
$310$		0			0
$311$	−9.97458	−	1.04837i	−0.565607	−	0.0594476i	−0.182590	−	0.983189i	$-0.558448\pi$
$311$	−9.97458	−	1.04837i	−0.565607	−	0.0594476i	−0.383017	+	0.923741i	$0.625115\pi$
$312$	3.49798	+	9.11255i	0.198034	+	0.515897i
$313$	11.3950	−	14.0717i	0.644086	−	0.795380i	−0.345638	−	0.938368i	$-0.612338\pi$
$313$	11.3950	−	14.0717i	0.644086	−	0.795380i	0.989724	+	0.142988i	$0.0456709\pi$
$314$	−11.0640	−	8.03848i	−0.624378	−	0.453637i
$315$		0			0
$316$	1.76264	−	1.28063i	0.0991561	−	0.0720411i
$317$	0.765274	−	14.6023i	0.0429821	−	0.820147i	−0.889059	−	0.457793i	$-0.848640\pi$
$317$	0.765274	−	14.6023i	0.0429821	−	0.820147i	0.932041	−	0.362354i	$-0.118027\pi$
$318$	5.38544	−	20.0987i	0.302001	−	1.12708i
$319$	−2.49011	−	11.7150i	−0.139419	−	0.655916i
$320$		0			0
$321$	−6.37725	+	2.07209i	−0.355943	+	0.115653i
$322$	−3.16330	−	2.71604i	−0.176284	−	0.151359i
$323$	−19.0773	+	3.02155i	−1.06149	+	0.168124i
$324$	0.820798	+	0.473888i	0.0455999	+	0.0263271i
$325$		0			0
$326$	9.06823	+	15.7066i	0.502243	+	0.869910i
$327$	−4.78518	+	12.4658i	−0.264621	+	0.689362i
$328$	−8.25453	+	16.2004i	−0.455780	+	0.894519i
$329$	5.68110	+	8.31251i	0.313209	+	0.458284i
$330$		0			0
$331$	−21.3589	−	23.7215i	−1.17399	−	1.30385i	−0.943727	−	0.330725i	$-0.892707\pi$
$331$	−21.3589	−	23.7215i	−1.17399	−	1.30385i	−0.230267	−	0.973128i	$-0.573960\pi$
$332$	1.00404	+	0.269030i	0.0551036	+	0.0147650i
$333$	−0.201367	+	0.310078i	−0.0110349	+	0.0169922i
$334$	−1.58449	−	15.0754i	−0.0866992	−	0.824888i
$335$		0			0
$336$	−11.6086	+	2.12016i	−0.633302	+	0.115664i
$337$	−22.8944	−	3.62612i	−1.24714	−	0.197527i	−0.502254	−	0.864720i	$-0.667496\pi$
$337$	−22.8944	−	3.62612i	−1.24714	−	0.197527i	−0.744885	+	0.667193i	$0.767496\pi$
$338$	−7.91356	−	6.40827i	−0.430441	−	0.348564i
$339$	1.78150	−	16.9498i	0.0967578	−	0.920589i
$340$		0			0
$341$	−16.1589	+	1.69837i	−0.875054	+	0.0919719i
$342$	7.56233	+	14.8419i	0.408924	+	0.802558i
$343$	−1.30827	−	18.4740i	−0.0706402	−	0.997502i
$344$	7.78677	+	2.53007i	0.419834	+	0.136412i
$345$		0			0
$346$	−10.4005	−	9.36466i	−0.559135	−	0.503447i
$347$	4.69537	−	0.246074i	0.252061	−	0.0132099i	0.0741128	−	0.997250i	$-0.476388\pi$
$347$	4.69537	−	0.246074i	0.252061	−	0.0132099i	0.177948	+	0.984040i	$0.443054\pi$
$348$	−1.87975	−	0.721570i	−0.100765	−	0.0386802i
$349$	18.4434			0.987251			0.493625	−	0.869675i	$-0.335671\pi$
$349$	18.4434			0.987251			0.493625	+	0.869675i	$0.335671\pi$
$350$		0			0
$351$	−21.1602			−1.12945
$352$	7.43954	+	2.85577i	0.396529	+	0.152213i
$353$	−5.16601	+	0.270739i	−0.274959	+	0.0144100i	−0.189317	−	0.981916i	$-0.560627\pi$
$353$	−5.16601	+	0.270739i	−0.274959	+	0.0144100i	−0.0856418	+	0.996326i	$0.527294\pi$
$354$	−11.0455	−	9.94543i	−0.587063	−	0.528594i
$355$		0			0
$356$	3.55598	+	1.15541i	0.188466	+	0.0612364i
$357$	8.47880	+	4.63235i	0.448746	+	0.245170i
$358$	−9.07401	−	17.8088i	−0.479576	−	0.941222i
$359$	−11.6005	+	1.21926i	−0.612251	+	0.0643502i	−0.405579	−	0.914060i	$-0.632930\pi$
$359$	−11.6005	+	1.21926i	−0.612251	+	0.0643502i	−0.206672	+	0.978410i	$0.566263\pi$
$360$		0			0
$361$	−0.583331	+	5.55002i	−0.0307016	+	0.292106i
$362$	−27.1031	−	21.9477i	−1.42451	−	1.15354i
$363$	−2.74540	−	0.434829i	−0.144096	−	0.0228226i
$364$	4.51835	−	3.83866i	0.236826	−	0.201200i
$365$		0			0
$366$	−1.53413	−	14.5963i	−0.0801903	−	0.762960i
$367$	−17.9556	+	27.6492i	−0.937274	+	1.44328i	−0.0413112	+	0.999146i	$0.513154\pi$
$367$	−17.9556	+	27.6492i	−0.937274	+	1.44328i	−0.895963	+	0.444129i	$0.853513\pi$
$368$	−4.57317	−	1.22538i	−0.238393	−	0.0638772i
$369$	−10.9249	−	12.1333i	−0.568728	−	0.631636i
$370$		0			0
$371$	36.9761	−	2.81286i	1.91970	−	0.146037i
$372$	−1.24009	+	2.43382i	−0.0642958	+	0.126188i
$373$	4.21287	−	10.9749i	0.218134	−	0.568258i	−0.780227	−	0.625497i	$-0.784896\pi$
$373$	4.21287	−	10.9749i	0.218134	−	0.568258i	0.998361	+	0.0572386i	$0.0182296\pi$
$374$	−8.74482	−	15.1465i	−0.452184	−	0.783205i
$375$		0			0
$376$	7.78569	+	4.49507i	0.401516	+	0.231816i
$377$	−18.3953	+	2.91353i	−0.947407	+	0.150054i
$378$	3.71748	−	19.7692i	0.191206	−	1.01682i
$379$	4.38145	−	1.42362i	0.225060	−	0.0731264i	−0.194316	−	0.980939i	$-0.562249\pi$
$379$	4.38145	−	1.42362i	0.225060	−	0.0731264i	0.419376	+	0.907813i	$0.362249\pi$
$380$		0			0
$381$	3.52278	+	16.5734i	0.180478	+	0.849081i
$382$	5.69195	−	21.2427i	0.291226	−	1.08687i
$383$	0.453069	−	8.64506i	0.0231507	−	0.441742i	−0.962322	−	0.271911i	$-0.912344\pi$
$383$	0.453069	−	8.64506i	0.0231507	−	0.441742i	0.985473	−	0.169831i	$-0.0543223\pi$
$384$	−10.3460	+	7.51682i	−0.527968	+	0.383591i
$385$		0			0
$386$	20.0165	+	14.5429i	1.01882	+	0.740213i
$387$	−4.62683	+	5.71366i	−0.235195	+	0.290442i
$388$	−1.49619	−	3.89771i	−0.0759577	−	0.197876i
$389$	−12.4150	−	1.30487i	−0.629465	−	0.0661594i	−0.215576	−	0.976487i	$-0.569163\pi$
$389$	−12.4150	−	1.30487i	−0.629465	−	0.0661594i	−0.413888	+	0.910328i	$0.635830\pi$
$390$		0			0
$391$	2.27846	+	3.13603i	0.115227	+	0.158596i
$392$	−8.19345	−	14.3644i	−0.413832	−	0.725510i
$393$	9.81502	−	9.81502i	0.495102	−	0.495102i
$394$	−9.76120	+	8.78902i	−0.491762	+	0.442785i
$395$		0			0
$396$	−2.04549	+	2.27175i	−0.102790	+	0.114160i
$397$	−21.7696	+	14.1374i	−1.09259	+	0.709534i	−0.959539	−	0.281576i	$-0.909143\pi$
$397$	−21.7696	+	14.1374i	−1.09259	+	0.709534i	−0.133048	+	0.991110i	$0.542476\pi$
$398$	−1.93302	−	12.2046i	−0.0968935	−	0.611762i
$399$	8.48699	−	8.89674i	0.424881	−	0.445394i
$400$		0			0
$401$	−2.67960	+	4.64121i	−0.133813	+	0.231771i	−0.925143	−	0.379618i	$-0.876055\pi$
$401$	−2.67960	+	4.64121i	−0.133813	+	0.231771i	0.791330	+	0.611389i	$0.209389\pi$
$402$	−10.2226	−	12.6239i	−0.509857	−	0.629621i
$403$	1.32235	+	25.2319i	0.0658708	+	1.25689i
$404$	5.84272	+	1.24191i	0.290686	+	0.0617873i
$405$		0			0
$406$	0.509727	−	17.6979i	0.0252973	−	0.878334i
$407$	−0.349326	−	0.349326i	−0.0173155	−	0.0173155i
$408$	8.61518	+	0.451503i	0.426515	+	0.0223527i
$409$	6.13126	+	2.72981i	0.303171	+	0.134981i	0.552684	−	0.833391i	$-0.313604\pi$
$409$	6.13126	+	2.72981i	0.303171	+	0.134981i	−0.249513	+	0.968372i	$0.580270\pi$
$410$		0			0
$411$	5.63948	+	12.6665i	0.278175	+	0.624791i
$412$	0.871776	−	5.50418i	0.0429493	−	0.271171i
$413$	10.2007	−	24.4458i	0.501945	−	1.20290i
$414$	1.96495	−	2.70453i	0.0965721	−	0.132920i
$415$		0			0
$416$	5.04029	−	11.3207i	0.247121	−	0.555042i
$417$	−0.331393	−	0.215209i	−0.0162284	−	0.0105388i
$418$	−21.4990	+	5.76065i	−1.05155	+	0.281763i
$419$	11.2169	−	34.5222i	0.547984	−	1.68652i	−0.165804	−	0.986159i	$-0.553022\pi$
$419$	11.2169	−	34.5222i	0.547984	−	1.68652i	0.713788	−	0.700362i	$-0.246978\pi$
$420$		0			0
$421$	10.0786	+	31.0186i	0.491199	+	1.51175i	0.822798	+	0.568334i	$0.192412\pi$
$421$	10.0786	+	31.0186i	0.491199	+	1.51175i	−0.331599	+	0.943421i	$0.607588\pi$
$422$	24.2310	+	37.3124i	1.17955	+	1.81634i
$423$	−6.27379	+	5.08042i	−0.305042	+	0.247018i
$424$	28.6755	−	16.5558i	1.39260	−	0.804020i
$425$		0			0
$426$			10.2411i			0.496183i
$427$	23.6377	−	11.1988i	1.14391	−	0.541950i
$428$	3.24036	+	1.65105i	0.156629	+	0.0798063i
$429$	2.43498	−	11.4557i	0.117562	−	0.553085i
$430$		0			0
$431$	−24.7337	+	5.25731i	−1.19138	+	0.253236i	−0.760600	−	0.649221i	$-0.775095\pi$
$431$	−24.7337	+	5.25731i	−1.19138	+	0.253236i	−0.430780	+	0.902457i	$0.641762\pi$
$432$	−5.91206	−	22.0641i	−0.284444	−	1.06156i
$433$	17.1376	−	8.73204i	0.823581	−	0.419635i	0.00919384	−	0.999958i	$-0.497073\pi$
$433$	17.1376	−	8.73204i	0.823581	−	0.419635i	0.814387	+	0.580322i	$0.197073\pi$
$434$	−23.8056	−	3.19738i	−1.14270	−	0.153479i
$435$		0			0
$436$	6.61583	−	2.94556i	0.316841	−	0.141067i
$437$	4.60541	−	1.76785i	0.220307	−	0.0845679i
$438$	7.35812	−	2.82452i	0.351585	−	0.134961i
$439$	−5.74961	+	2.55989i	−0.274414	+	0.122177i	−0.539330	−	0.842095i	$-0.681322\pi$
$439$	−5.74961	+	2.55989i	−0.274414	+	0.122177i	0.264916	+	0.964271i	$0.414656\pi$
$440$		0			0
$441$	14.6787	−	2.24629i	0.698985	−	0.106966i
$442$	−24.2331	+	12.3474i	−1.15265	+	0.587305i
$443$	−6.34534	−	23.6811i	−0.301476	−	1.12513i	−0.935936	−	0.352170i	$-0.885444\pi$
$443$	−6.34534	−	23.6811i	−0.301476	−	1.12513i	0.634460	−	0.772956i	$-0.281223\pi$
$444$	−0.0812382	+	0.0172677i	−0.00385540	+	0.000819490i
$445$		0			0
$446$	4.14176	−	19.4855i	0.196118	−	0.922663i
$447$	5.48667	+	2.79560i	0.259510	+	0.132227i
$448$	−11.0220	−	7.61769i	−0.520740	−	0.359902i
$449$		−	29.0905i		−	1.37286i	−0.727194	−	0.686432i	$-0.759176\pi$
$449$		−	29.0905i		−	1.37286i	0.727194	−	0.686432i	$-0.240824\pi$
$450$		0			0
$451$	18.8931	−	10.9080i	0.889643	−	0.513635i
$452$	−7.18355	+	5.81712i	−0.337886	+	0.273614i
$453$	−2.91506	−	4.48881i	−0.136962	−	0.210903i
$454$	−5.33497	−	16.4193i	−0.250382	−	0.770598i
$455$		0			0
$456$	3.39263	−	10.4415i	0.158875	−	0.488966i
$457$	−28.9363	+	7.75345i	−1.35358	+	0.362691i	−0.861456	−	0.507833i	$-0.830447\pi$
$457$	−28.9363	+	7.75345i	−1.35358	+	0.362691i	−0.492126	+	0.870524i	$0.663780\pi$
$458$	3.68403	+	2.39243i	0.172143	+	0.111791i
$459$	−7.60684	+	17.0852i	−0.355057	+	0.797471i
$460$		0			0
$461$	−7.92746	+	10.9112i	−0.369218	+	0.508186i	−0.952688	−	0.303949i	$-0.901695\pi$
$461$	−7.92746	+	10.9112i	−0.369218	+	0.508186i	0.583470	+	0.812135i	$0.301695\pi$
$462$	10.2748	+	4.28747i	0.478029	+	0.199471i
$463$	0.129975	−	0.820628i	0.00604043	−	0.0381378i	−0.984484	−	0.175474i	$-0.943854\pi$
$463$	0.129975	−	0.820628i	0.00604043	−	0.0381378i	0.990524	+	0.137336i	$0.0438541\pi$
$464$	−8.17755	−	18.3671i	−0.379633	−	0.852670i
$465$		0			0
$466$	−40.9926	−	18.2511i	−1.89895	−	0.845466i
$467$	28.4931	+	1.49326i	1.31850	+	0.0690998i	0.698562	−	0.715549i	$-0.253824\pi$
$467$	28.4931	+	1.49326i	1.31850	+	0.0690998i	0.619940	+	0.784649i	$0.287157\pi$
$468$	3.36140	+	3.36140i	0.155381	+	0.155381i
$469$	15.1904	−	24.6437i	0.701430	−	1.13794i
$470$		0			0
$471$	−7.91710	−	1.68283i	−0.364801	−	0.0775408i
$472$	−1.23785	−	23.6196i	−0.0569766	−	1.08718i
$473$	−6.18230	−	7.63451i	−0.284263	−	0.351035i
$474$	3.18117	−	5.50995i	0.146116	−	0.253080i
$475$		0			0
$476$	−1.47513	−	5.02818i	−0.0676125	−	0.230466i
$477$	4.65129	+	29.3671i	0.212968	+	1.34463i
$478$	−16.7224	+	10.8596i	−0.764863	+	0.496708i
$479$	−19.6265	+	21.7975i	−0.896759	+	0.995952i	0.103240	+	0.994657i	$0.467079\pi$
$479$	−19.6265	+	21.7975i	−0.896759	+	0.995952i	−0.999999	+	0.00129579i	$0.999588\pi$
$480$		0			0
$481$	−0.570910	+	0.514049i	−0.0260312	+	0.0234386i
$482$	−7.84390	+	7.84390i	−0.357280	+	0.357280i
$483$	−2.36414	−	0.707015i	−0.107572	−	0.0321703i
$484$	0.886114	+	1.21963i	0.0402779	+	0.0554378i
$485$		0			0
$486$	25.4366	+	2.67350i	1.15383	+	0.121272i
$487$	−1.25385	−	3.26639i	−0.0568173	−	0.148014i	0.902234	−	0.431247i	$-0.141926\pi$
$487$	−1.25385	−	3.26639i	−0.0568173	−	0.148014i	−0.959051	+	0.283233i	$0.908593\pi$
$488$	14.6979	−	18.1503i	0.665341	−	0.821628i
$489$	8.68395	+	6.30926i	0.392702	+	0.285315i
$490$		0			0
$491$	31.7981	−	23.1026i	1.43503	−	1.04261i	0.445973	−	0.895046i	$-0.352858\pi$
$491$	31.7981	−	23.1026i	1.43503	−	1.04261i	0.989053	−	0.147561i	$-0.0471424\pi$
$492$	0.191948	−	3.66258i	0.00865368	−	0.165122i
$493$	−4.26044	+	15.9002i	−0.191881	+	0.716109i
$494$	7.19618	+	33.8553i	0.323771	+	1.52322i
$495$		0			0
$496$	−25.9403	+	8.42850i	−1.16475	+	0.378451i
$497$	−17.2204	+	6.04745i	−0.772439	+	0.271265i
$498$	2.99804	−	0.474842i	0.134345	−	0.0212782i
$499$	−25.9919	−	15.0064i	−1.16356	−	0.671780i	−0.211403	−	0.977399i	$-0.567803\pi$
$499$	−25.9919	−	15.0064i	−1.16356	−	0.671780i	−0.952154	+	0.305619i	$0.901137\pi$
$500$		0			0
$501$	−4.48571	−	7.76947i	−0.200407	−	0.347114i
$502$	−1.72884	+	4.50377i	−0.0771617	+	0.201013i
$503$	−19.0522	+	37.3921i	−0.849497	+	1.66723i	−0.110142	+	0.993916i	$0.535131\pi$
$503$	−19.0522	+	37.3921i	−0.849497	+	1.66723i	−0.739355	+	0.673316i	$0.764869\pi$
$504$	10.9469	−	7.48155i	0.487614	−	0.333255i
$505$		0			0
$506$	2.98889	+	3.31950i	0.132873	+	0.147570i
$507$	−5.82130	−	1.55981i	−0.258533	−	0.0692737i
$508$	5.00496	−	7.70697i	0.222059	−	0.341941i
$509$	0.302860	+	2.88152i	0.0134240	+	0.127721i	0.999181	−	0.0404521i	$-0.0128798\pi$
$509$	0.302860	+	2.88152i	0.0134240	+	0.127721i	−0.985757	+	0.168173i	$0.946213\pi$
$510$		0			0
$511$	9.09444	+	10.7047i	0.402314	+	0.473550i
$512$	−8.99285	−	1.42433i	−0.397431	−	0.0629470i
$513$	18.4964	+	14.9781i	0.816638	+	0.661300i
$514$	−0.943642	+	8.97815i	−0.0416222	+	0.396009i
$515$		0			0
$516$	−1.64249	+	0.172633i	−0.0723066	+	0.00759973i
$517$	−4.89712	−	9.61114i	−0.215375	−	0.422697i
$518$	−0.379959	−	0.623690i	−0.0166944	−	0.0274034i
$519$	−7.87760	−	2.55959i	−0.345788	−	0.112353i
$520$		0			0
$521$	−17.9718	−	16.1818i	−0.787357	−	0.708939i	0.173849	−	0.984772i	$-0.444380\pi$
$521$	−17.9718	−	16.1818i	−0.787357	−	0.708939i	−0.961206	+	0.275833i	$0.911046\pi$
$522$	14.1767	−	0.742968i	0.620496	−	0.0325188i
$523$	35.8325	+	13.7548i	1.56684	+	0.601455i	0.978334	−	0.207034i	$-0.0663812\pi$
$523$	35.8325	+	13.7548i	1.56684	+	0.601455i	0.588511	+	0.808489i	$0.299715\pi$
$524$	−7.52820			−0.328871
$525$		0			0
$526$	−6.33604			−0.276264
$527$	20.8482	+	8.00288i	0.908162	+	0.348611i
$528$	12.6253	−	0.661666i	0.549447	−	0.0287953i
$529$	16.3566	+	14.7276i	0.711157	+	0.640328i
$530$		0			0
$531$	20.1992	+	6.56313i	0.876572	+	0.284815i
$532$	−6.66673	+	0.157140i	−0.289040	+	0.00681287i
$533$	−15.4017	−	30.2275i	−0.667120	−	1.30930i
$534$	10.8587	−	1.14130i	0.469903	−	0.0493888i
$535$		0			0
$536$	2.70196	−	25.7074i	0.116707	−	1.11039i
$537$	−9.19310	−	7.44443i	−0.396712	−	0.321251i
$538$	−7.36875	−	1.16709i	−0.317689	−	0.0503170i
$539$	−1.14200	+	19.8089i	−0.0491893	+	0.853229i
$540$		0			0
$541$	2.65634	+	25.2734i	0.114205	+	1.08659i	0.890113	+	0.455740i	$0.150625\pi$
$541$	2.65634	+	25.2734i	0.114205	+	1.08659i	−0.775908	+	0.630846i	$0.782708\pi$
$542$	−1.89501	+	2.91806i	−0.0813976	+	0.125341i
$543$	−19.9374	−	5.34220i	−0.855594	−	0.229256i
$544$	−7.32866	−	8.13930i	−0.314214	−	0.348970i
$545$		0			0
$546$	7.49437	−	15.6072i	0.320730	−	0.667925i
$547$	−6.68428	+	13.1186i	−0.285799	+	0.560912i	−0.988616	−	0.150458i	$-0.951925\pi$
$547$	−6.68428	+	13.1186i	−0.285799	+	0.560912i	0.702817	+	0.711370i	$0.251925\pi$
$548$	2.69488	−	7.02041i	0.115120	−	0.299897i
$549$	10.4861	+	18.1624i	0.447535	+	0.775154i
$550$		0			0
$551$	18.1419	+	10.4743i	0.772873	+	0.446218i
$552$	−2.17620	+	0.344676i	−0.0926253	+	0.0146704i
$553$	11.1435	+	2.09546i	0.473868	+	0.0891079i
$554$	−10.3084	+	3.34942i	−0.437964	+	0.142303i
$555$		0			0
$556$	0.0445570	+	0.209624i	0.00188964	+	0.00889005i
$557$	3.28809	−	12.2713i	0.139321	−	0.519952i	−0.860622	−	0.509245i	$-0.829925\pi$
$557$	3.28809	−	12.2713i	0.139321	−	0.519952i	0.999943	−	0.0107078i	$-0.00340848\pi$
$558$	1.00792	−	19.2324i	0.0426689	−	0.814170i
$559$	−12.3590	+	8.97935i	−0.522730	+	0.379786i
$560$		0			0
$561$	−8.37424	−	6.08424i	−0.353560	−	0.256877i
$562$	2.50226	−	3.09003i	0.105551	−	0.130345i
$563$	7.12783	+	18.5686i	0.300402	+	0.782574i	0.997825	+	0.0659147i	$0.0209965\pi$
$563$	7.12783	+	18.5686i	0.300402	+	0.782574i	−0.697423	+	0.716660i	$0.745670\pi$
$564$	−1.80351	−	0.189556i	−0.0759414	−	0.00798176i
$565$		0			0
$566$	6.95960	+	9.57906i	0.292534	+	0.402638i
$567$	1.13893	+	4.79920i	0.0478304	+	0.201547i
$568$	−11.5236	+	11.5236i	−0.483517	+	0.483517i
$569$	−0.969506	+	0.872947i	−0.0406438	+	0.0365958i	−0.689202	−	0.724569i	$-0.742039\pi$
$569$	−0.969506	+	0.872947i	−0.0406438	+	0.0365958i	0.648558	+	0.761165i	$0.275372\pi$
$570$		0			0
$571$	−13.9499	+	15.4929i	−0.583786	+	0.648360i	−0.960602	−	0.277929i	$-0.910352\pi$
$571$	−13.9499	+	15.4929i	−0.583786	+	0.648360i	0.376816	+	0.926288i	$0.377019\pi$
$572$	−5.32712	+	3.45947i	−0.222738	+	0.144648i
$573$	−2.03612	−	12.8556i	−0.0850603	−	0.537050i
$574$	30.9463	−	9.07879i	1.29167	−	0.378941i
$575$		0			0
$576$	5.37138	−	9.30350i	0.223807	−	0.387646i
$577$	−20.0007	−	24.6988i	−0.832640	−	1.02822i	−0.999110	−	0.0421780i	$-0.986570\pi$
$577$	−20.0007	−	24.6988i	−0.832640	−	1.02822i	0.166470	−	0.986046i	$-0.446763\pi$
$578$	−0.151056	−	2.88233i	−0.00628312	−	0.119889i
$579$	14.3233	+	3.04451i	0.595256	+	0.126525i
$580$		0			0
$581$	2.56881	+	4.76078i	0.106572	+	0.197511i
$582$	−8.62095	−	8.62095i	−0.357350	−	0.357350i
$583$	−39.6745	−	2.07925i	−1.64315	−	0.0861139i
$584$	11.4578	+	5.10133i	0.474126	+	0.211094i
$585$		0			0
$586$	−8.89496	−	19.9784i	−0.367448	−	0.825301i
$587$	−0.789333	+	4.98365i	−0.0325793	+	0.205697i	−0.998609	−	0.0527353i	$-0.983206\pi$
$587$	−0.789333	+	4.98365i	−0.0325793	+	0.205697i	0.966029	+	0.258433i	$0.0832060\pi$
$588$	2.68837	+	1.97477i	0.110867	+	0.0814381i
$589$	16.7044	−	22.9916i	0.688292	−	0.947352i
$590$		0			0
$591$	−3.16191	+	7.10177i	−0.130064	+	0.292128i
$592$	−0.695517	−	0.451674i	−0.0285856	−	0.0185637i
$593$	9.79820	−	2.62542i	0.402364	−	0.107813i	−0.0519610	−	0.998649i	$-0.516547\pi$
$593$	9.79820	−	2.62542i	0.402364	−	0.107813i	0.454325	+	0.890836i	$0.349880\pi$
$594$	−6.65964	+	20.4963i	−0.273248	+	0.840972i
$595$		0			0
$596$	−1.03204	−	3.17628i	−0.0422739	−	0.130106i
$597$	−3.98308	−	6.13341i	−0.163017	−	0.251024i
$598$	5.39821	−	4.37139i	0.220749	−	0.178759i
$599$	−35.8204	+	20.6809i	−1.46358	+	0.844999i	−0.999175	−	0.0406237i	$-0.987066\pi$
$599$	−35.8204	+	20.6809i	−1.46358	+	0.844999i	−0.464406	+	0.885622i	$0.653732\pi$
$600$		0			0
$601$		−	42.8734i		−	1.74884i	−0.485169	−	0.874420i	$-0.661242\pi$
$601$		−	42.8734i		−	1.74884i	0.485169	−	0.874420i	$-0.338758\pi$
$602$	−6.21782	−	13.1241i	−0.253420	−	0.534898i
$603$	20.6817	+	10.5379i	0.842224	+	0.429135i
$604$	−0.603536	+	2.83942i	−0.0245575	+	0.115534i
$605$		0			0
$606$	17.0619	−	3.62661i	0.693091	−	0.147321i
$607$	4.97957	+	18.5840i	0.202115	+	0.754302i	0.990310	+	0.138876i	$0.0443491\pi$
$607$	4.97957	+	18.5840i	0.202115	+	0.754302i	−0.788195	+	0.615425i	$0.788984\pi$
$608$	−12.4191	+	6.32784i	−0.503660	+	0.256628i
$609$	−3.98473	−	9.69155i	−0.161469	−	0.392722i
$610$		0			0
$611$	−15.3240	+	6.82268i	−0.619942	+	0.276016i
$612$	3.92245	−	1.50569i	0.158556	−	0.0608639i
$613$	−11.6319	+	4.46508i	−0.469809	+	0.180343i	−0.581743	−	0.813373i	$-0.697629\pi$
$613$	−11.6319	+	4.46508i	−0.469809	+	0.180343i	0.111934	+	0.993716i	$0.464296\pi$
$614$	2.90142	−	1.29179i	0.117092	−	0.0521326i
$615$		0			0
$616$	6.73714	+	16.3859i	0.271447	+	0.660206i
$617$	16.0963	−	8.20148i	0.648013	−	0.330179i	−0.0989034	−	0.995097i	$-0.531533\pi$
$617$	16.0963	−	8.20148i	0.648013	−	0.330179i	0.746916	+	0.664918i	$0.231533\pi$
$618$	−4.21192	−	15.7191i	−0.169428	−	0.632316i
$619$	8.74147	−	1.85806i	0.351349	−	0.0746816i	−0.0288563	−	0.999584i	$-0.509187\pi$
$619$	8.74147	−	1.85806i	0.351349	−	0.0746816i	0.380206	+	0.924902i	$0.375853\pi$
$620$		0			0
$621$	0.993091	−	4.67213i	0.0398514	−	0.187486i
$622$	14.1533	+	7.21147i	0.567496	+	0.289154i
$623$	8.33124	+	17.5849i	0.333784	+	0.704526i
$624$		−	19.6601i		−	0.787035i
$625$		0			0
$626$	−24.8354	+	14.3387i	−0.992624	+	0.573091i
$627$	−10.2373	+	8.28999i	−0.408838	+	0.331070i
$628$	2.39087	+	3.68161i	0.0954060	+	0.146912i
$629$	0.209820	+	0.645761i	0.00836609	+	0.0257482i
$630$		0			0
$631$	14.0918	−	43.3700i	0.560984	−	1.72653i	−0.118608	−	0.992941i	$-0.537843\pi$
$631$	14.0918	−	43.3700i	0.560984	−	1.72653i	0.679592	−	0.733590i	$-0.262157\pi$
$632$	9.77947	−	2.62040i	0.389006	−	0.104234i
$633$	22.0831	+	14.3409i	0.877725	+	0.570001i
$634$	−9.41948	+	21.1565i	−0.374095	+	0.840232i
$635$		0			0
$636$	−3.92587	+	5.40349i	−0.155671	+	0.214263i
$637$	30.6689	+	3.38560i	1.21515	+	0.134142i
$638$	−2.96735	+	18.7351i	−0.117478	+	0.741730i
$639$	−5.95218	−	13.3688i	−0.235464	−	0.528862i
$640$		0			0
$641$	−1.95689	−	0.871265i	−0.0772926	−	0.0344129i	0.367726	−	0.929934i	$-0.380136\pi$
$641$	−1.95689	−	0.871265i	−0.0772926	−	0.0344129i	−0.445019	+	0.895521i	$0.646803\pi$
$642$	10.6054	+	0.555807i	0.418563	+	0.0219360i
$643$	−6.86315	−	6.86315i	−0.270656	−	0.270656i	0.558708	−	0.829364i	$-0.311297\pi$
$643$	−6.86315	−	6.86315i	−0.270656	−	0.270656i	−0.829364	+	0.558708i	$0.811297\pi$
$644$	0.635513	+	1.17780i	0.0250427	+	0.0464118i
$645$		0			0
$646$	29.9226	+	6.36024i	1.17729	+	0.250240i
$647$	−1.46165	−	27.8899i	−0.0574632	−	1.09646i	−0.863419	−	0.504488i	$-0.831681\pi$
$647$	−1.46165	−	27.8899i	−0.0574632	−	1.09646i	0.805956	−	0.591976i	$-0.201652\pi$
$648$	2.77168	+	3.42274i	0.108882	+	0.134458i
$649$	−14.1894	+	24.5768i	−0.556984	+	0.964724i
$650$		0			0
$651$	−13.6408	+	4.00184i	−0.534625	+	0.156844i
$652$	−0.910704	−	5.74996i	−0.0356659	−	0.225186i
$653$	10.4839	−	6.80832i	0.410267	−	0.266430i	−0.322963	−	0.946412i	$-0.604679\pi$
$653$	10.4839	−	6.80832i	0.410267	−	0.266430i	0.733229	+	0.679981i	$0.238012\pi$
$654$	14.1507	−	15.7159i	0.553335	−	0.614541i
$655$		0			0
$656$	27.2155	−	24.5050i	1.06259	−	0.956759i
$657$	−7.96372	+	7.96372i	−0.310694	+	0.310694i
$658$	−3.68203	−	15.5153i	−0.143540	−	0.604849i
$659$	−4.46660	−	6.14775i	−0.173994	−	0.239482i	0.713109	−	0.701053i	$-0.247286\pi$
$659$	−4.46660	−	6.14775i	−0.173994	−	0.239482i	−0.887104	+	0.461570i	$0.847286\pi$
$660$		0			0
$661$	45.2845	+	4.75959i	1.76136	+	0.185127i	0.929243	−	0.369469i	$-0.120461\pi$
$661$	45.2845	+	4.75959i	1.76136	+	0.185127i	0.832120	+	0.554596i	$0.187127\pi$
$662$	18.1174	+	47.1973i	0.704151	+	1.83438i
$663$	−10.1299	+	12.5094i	−0.393414	+	0.485826i
$664$	3.90777	+	2.83916i	0.151651	+	0.110181i
$665$		0			0
$666$	0.473734	−	0.344188i	0.0183568	−	0.0133370i
$667$	0.220028	−	4.19838i	0.00851952	−	0.162562i
$668$	−1.25934	+	4.69991i	−0.0487252	+	0.181845i
$669$	−2.45128	−	11.5323i	−0.0947718	−	0.445866i
$670$		0			0
$671$	−26.6512	+	8.65949i	−1.02886	+	0.334296i
$672$	6.85203	+	1.28848i	0.264323	+	0.0497042i
$673$	−23.7602	+	3.76325i	−0.915888	+	0.145062i	−0.596548	−	0.802578i	$-0.703461\pi$
$673$	−23.7602	+	3.76325i	−0.915888	+	0.145062i	−0.319341	+	0.947640i	$0.603461\pi$
$674$	31.7934	+	18.3559i	1.22464	+	0.707044i
$675$		0			0
$676$	1.63430	+	2.83069i	0.0628576	+	0.108873i
$677$	−2.81453	+	7.33211i	−0.108171	+	0.281796i	−0.976973	−	0.213365i	$-0.931558\pi$
$677$	−2.81453	+	7.33211i	−0.108171	+	0.281796i	0.868801	+	0.495161i	$0.164891\pi$
$678$	−12.2545	+	24.0508i	−0.470630	+	0.923664i
$679$	9.40535	−	19.5868i	0.360944	−	0.751673i
$680$		0			0
$681$	−6.83702	−	7.59328i	−0.261995	−	0.290975i
$682$	24.8564	+	6.66025i	0.951800	+	0.255034i
$683$	−9.45109	+	14.5534i	−0.361636	+	0.556870i	−0.971920	−	0.235312i	$-0.924389\pi$
$683$	−9.45109	+	14.5534i	−0.361636	+	0.556870i	0.610284	+	0.792183i	$0.291055\pi$
$684$	−0.558902	−	5.31759i	−0.0213701	−	0.203323i
$685$		0			0
$686$	−8.55103	+	28.0581i	−0.326480	+	1.07126i
$687$	2.56778	+	0.406697i	0.0979670	+	0.0155164i
$688$	−12.8160	−	10.3782i	−0.488604	−	0.395664i
$689$	−6.45787	+	61.4426i	−0.246025	+	2.34078i
$690$		0			0
$691$	−38.0413	+	3.99830i	−1.44716	+	0.152103i	−0.795290	−	0.606229i	$-0.792681\pi$
$691$	−38.0413	+	3.99830i	−1.44716	+	0.152103i	−0.651869	+	0.758332i	$0.726015\pi$
$692$	2.03948	+	4.00271i	0.0775294	+	0.152160i
$693$	−15.9047	+	0.374886i	−0.604171	+	0.0142407i
$694$	−7.08220	−	2.30115i	−0.268837	−	0.0873503i
$695$		0			0
$696$	−6.95327	−	6.26075i	−0.263563	−	0.237313i
$697$	−29.9431	+	1.56925i	−1.13418	+	0.0594397i
$698$	−27.2702	−	10.4681i	−1.03219	−	0.396222i
$699$	−26.5572			−1.00449
$700$		0			0
$701$	−38.6073			−1.45818			−0.729088	−	0.684420i	$-0.760056\pi$
$701$	−38.6073			−1.45818			−0.729088	+	0.684420i	$0.760056\pi$
$702$	31.2873	+	12.0101i	1.18086	+	0.453291i
$703$	0.862908	−	0.0452231i	0.0325452	−	0.00170562i
$704$	10.6673	+	9.60490i	0.402040	+	0.361998i
$705$		0			0
$706$	7.79209	+	2.53180i	0.293259	+	0.0952856i
$707$	16.1733	+	26.5479i	0.608259	+	0.998437i
$708$	2.16597	+	4.25095i	0.0814020	+	0.159760i
$709$	0.0584804	−	0.00614654i	0.00219628	−	0.000230838i	−0.103430	−	0.994637i	$-0.532982\pi$
$709$	0.0584804	−	0.00614654i	0.00219628	−	0.000230838i	0.105627	+	0.994406i	$0.466315\pi$
$710$		0			0
$711$	−0.950314	+	9.04164i	−0.0356396	+	0.339088i
$712$	13.5027	+	10.9343i	0.506036	+	0.409780i
$713$	−5.63321	−	0.892213i	−0.210965	−	0.0334136i
$714$	−9.90747	−	11.6617i	−0.370778	−	0.436430i
$715$		0			0
$716$	0.670624	+	6.38056i	0.0250624	+	0.238453i
$717$	−6.42720	+	9.89702i	−0.240028	+	0.369611i
$718$	17.8444	+	4.78140i	0.665949	+	0.178440i
$719$	−7.15755	−	7.94927i	−0.266932	−	0.296458i	0.594746	−	0.803914i	$-0.297253\pi$
$719$	−7.15755	−	7.94927i	−0.266932	−	0.296458i	−0.861678	+	0.507456i	$0.830586\pi$
$720$		0			0
$721$	23.9444	−	16.3646i	0.891738	−	0.609449i
$722$	4.01258	−	7.87513i	0.149333	−	0.293082i
$723$	−2.35279	+	6.12923i	−0.0875012	+	0.227948i
$724$	5.59730	+	9.69481i	0.208022	+	0.360305i
$725$		0			0
$726$	3.81253	+	2.20116i	0.141496	+	0.0816929i
$727$	34.2911	−	5.43117i	1.27179	−	0.201431i	0.516193	−	0.856472i	$-0.327349\pi$
$727$	34.2911	−	5.43117i	1.27179	−	0.201431i	0.755593	+	0.655041i	$0.227349\pi$
$728$	25.9945	−	9.12873i	0.963419	−	0.338333i
$729$	9.07738	−	2.94942i	0.336199	−	0.109238i
$730$		0			0
$731$	2.80722	+	13.2069i	0.103829	+	0.488476i
$732$	−1.21931	+	4.55054i	−0.0450672	+	0.168193i
$733$	−1.13757	+	21.7061i	−0.0420171	+	0.801734i	0.893632	+	0.448801i	$0.148149\pi$
$733$	−1.13757	+	21.7061i	−0.0420171	+	0.801734i	−0.935649	+	0.352933i	$0.885184\pi$
$734$	42.2421	−	30.6907i	1.55918	−	1.13281i
$735$		0			0
$736$	2.26303	+	1.64419i	0.0834164	+	0.0606056i
$737$	−19.5184	+	24.1032i	−0.718969	+	0.887852i
$738$	9.26686	+	24.1410i	0.341118	+	0.888643i
$739$	−32.9995	−	3.46839i	−1.21391	−	0.127587i	−0.524149	−	0.851627i	$-0.675616\pi$
$739$	−32.9995	−	3.46839i	−1.21391	−	0.127587i	−0.689758	+	0.724040i	$0.742283\pi$
$740$		0			0
$741$	12.0406	+	16.5725i	0.442323	+	0.608805i
$742$	−56.2691	−	16.8278i	−2.06570	−	0.617766i
$743$	28.3572	−	28.3572i	1.04033	−	1.04033i	0.0411733	−	0.999152i	$-0.486890\pi$
$743$	28.3572	−	28.3572i	1.04033	−	1.04033i	0.999152	−	0.0411733i	$-0.0131096\pi$
$744$	−9.43294	+	8.49346i	−0.345828	+	0.311385i
$745$		0			0
$746$	−12.4582	+	13.8363i	−0.456128	+	0.506581i
$747$	−3.63768	+	2.36233i	−0.133096	+	0.0864333i
$748$	0.878223	+	5.54488i	0.0321110	+	0.202741i
$749$	5.32800	+	18.1612i	0.194681	+	0.663595i
$750$		0			0
$751$	5.40198	−	9.35651i	0.197121	−	0.341424i	−0.750473	−	0.660901i	$-0.770174\pi$
$751$	5.40198	−	9.35651i	0.197121	−	0.341424i	0.947594	+	0.319478i	$0.103507\pi$
$752$	−11.3956	−	14.0724i	−0.415554	−	0.513166i
$753$	0.149428	+	2.85125i	0.00544545	+	0.103905i
$754$	28.8528	+	6.13286i	1.05076	+	0.223345i
$755$		0			0
$756$	−3.38812	+	5.49661i	−0.123225	+	0.199910i
$757$	8.08043	+	8.08043i	0.293688	+	0.293688i	0.838535	−	0.544847i	$-0.183412\pi$
$757$	8.08043	+	8.08043i	0.293688	+	0.293688i	−0.544847	+	0.838535i	$0.683412\pi$
$758$	−7.28639	−	0.381863i	−0.264654	−	0.0138699i
$759$	2.41511	+	1.07528i	0.0876629	+	0.0390300i
$760$		0			0
$761$	−3.77414	−	8.47685i	−0.136812	−	0.307285i	0.832127	−	0.554586i	$-0.187123\pi$
$761$	−3.77414	−	8.47685i	−0.136812	−	0.307285i	−0.968939	+	0.247300i	$0.920457\pi$
$762$	4.19794	−	26.5047i	0.152075	−	0.960166i
$763$	34.7823	+	14.5139i	1.25920	+	0.525439i
$764$	−4.14931	+	5.71103i	−0.150117	+	0.206618i
$765$		0			0
$766$	−5.57666	+	12.5254i	−0.201493	+	0.452560i
$767$	37.0113	+	24.0354i	1.33640	+	0.867868i
$768$	10.3938	−	2.78500i	0.375053	−	0.100495i
$769$	−0.767310	+	2.36154i	−0.0276699	+	0.0851592i	−0.963938	−	0.266128i	$-0.914256\pi$
$769$	−0.767310	+	2.36154i	−0.0276699	+	0.0851592i	0.936268	+	0.351287i	$0.114256\pi$
$770$		0			0
$771$	1.65106	+	5.08143i	0.0594613	+	0.183003i
$772$	−4.32546	−	6.66062i	−0.155677	−	0.239721i
$773$	18.3094	−	14.8267i	0.658544	−	0.533279i	−0.240770	−	0.970582i	$-0.577400\pi$
$773$	18.3094	−	14.8267i	0.658544	−	0.533279i	0.899314	+	0.437304i	$0.144066\pi$
$774$	10.0842	−	5.82209i	0.362467	−	0.209271i
$775$		0			0
$776$		−	19.4010i		−	0.696456i
$777$	−0.355572	−	0.245749i	−0.0127561	−	0.00881619i
$778$	17.6161	+	8.97584i	0.631567	+	0.321800i
$779$	−7.93352	+	37.3243i	−0.284248	+	1.33728i
$780$		0			0
$781$	19.1264	−	4.06544i	0.684396	−	0.145473i
$782$	−1.58897	−	5.93011i	−0.0568214	−	0.212060i
$783$	18.0729	−	9.20860i	0.645872	−	0.329088i
$784$	5.03851	+	32.9249i	0.179947	+	1.17589i
$785$		0			0
$786$	−20.0832	+	8.94162i	−0.716344	+	0.318937i
$787$	27.2461	−	10.4588i	0.971219	−	0.372816i	0.179538	−	0.983751i	$-0.442540\pi$
$787$	27.2461	−	10.4588i	0.971219	−	0.372816i	0.791681	+	0.610935i	$0.209206\pi$
$788$	3.93617	−	1.51095i	0.140220	−	0.0538255i
$789$	−3.42574	+	1.52524i	−0.121960	+	0.0543000i
$790$		0			0
$791$	−47.6776	−	6.40369i	−1.69522	−	0.227689i
$792$	−12.6571	+	6.44911i	−0.449750	+	0.229159i
$793$	11.2786	+	42.0922i	0.400513	+	1.49474i
$794$	40.2125	−	8.54742i	1.42709	−	0.303337i
$795$		0			0
$796$	−0.824660	+	3.87972i	−0.0292293	+	0.137513i
$797$	−27.4174	−	13.9698i	−0.971172	−	0.494837i	−0.104940	−	0.994479i	$-0.533465\pi$
$797$	−27.4174	−	13.9698i	−0.971172	−	0.494837i	−0.866232	+	0.499641i	$0.833465\pi$
$798$	−17.5984	+	8.33762i	−0.622977	+	0.295148i
$799$			14.8256i			0.524493i
$800$		0			0
$801$	−13.5117	+	7.80099i	−0.477413	+	0.275635i
$802$	6.59629	−	5.34157i	0.232923	−	0.188617i
$803$	−8.19608	−	12.6209i	−0.289233	−	0.445380i
$804$	1.61125	+	4.95893i	0.0568246	+	0.174888i
$805$		0			0
$806$	12.3659	−	38.0582i	0.435569	−	1.34054i
$807$	−4.26505	+	1.14282i	−0.150137	+	0.0402291i
$808$	23.2792	+	15.1177i	0.818960	+	0.531839i
$809$	5.57231	−	12.5156i	0.195912	−	0.440026i	−0.788700	−	0.614778i	$-0.789246\pi$
$809$	5.57231	−	12.5156i	0.195912	−	0.440026i	0.984612	+	0.174752i	$0.0559123\pi$
$810$		0			0
$811$	0.902857	−	1.24268i	0.0317036	−	0.0436363i	−0.792871	−	0.609390i	$-0.791415\pi$
$811$	0.902857	−	1.24268i	0.0317036	−	0.0436363i	0.824575	+	0.565753i	$0.191415\pi$
$812$	−2.18859	+	5.24491i	−0.0768045	+	0.184060i
$813$	−0.322138	+	2.03390i	−0.0112979	+	0.0713319i
$814$	0.318241	+	0.714781i	0.0111543	+	0.0250531i
$815$		0			0
$816$	−15.8741	−	7.06759i	−0.555703	−	0.247415i
$817$	17.1592	+	0.899275i	0.600324	+	0.0314616i
$818$	−7.51625	−	7.51625i	−0.262799	−	0.262799i
$819$	−0.712246	+	24.7295i	−0.0248879	+	0.864118i
$820$		0			0
$821$	−5.93836	−	1.26224i	−0.207250	−	0.0440524i	0.103117	−	0.994669i	$-0.467118\pi$
$821$	−5.93836	−	1.26224i	−0.207250	−	0.0440524i	−0.310367	+	0.950617i	$0.600452\pi$
$822$	−1.14927	−	21.9294i	−0.0400854	−	0.764876i
$823$	−11.1440	−	13.7617i	−0.388456	−	0.479703i	0.544979	−	0.838449i	$-0.316537\pi$
$823$	−11.1440	−	13.7617i	−0.388456	−	0.479703i	−0.933435	+	0.358747i	$0.883204\pi$
$824$	12.9482	−	22.4269i	0.451071	−	0.781279i
$825$		0			0
$826$	−28.9577	+	30.3557i	−1.00757	+	1.05621i
$827$	−6.34498	−	40.0606i	−0.220637	−	1.39304i	−0.810593	−	0.585609i	$-0.800855\pi$
$827$	−6.34498	−	40.0606i	−0.220637	−	1.39304i	0.589957	−	0.807435i	$-0.299145\pi$
$828$	−0.899946	+	0.584432i	−0.0312753	+	0.0203104i
$829$	−19.9634	+	22.1716i	−0.693357	+	0.770051i	−0.982304	−	0.187294i	$-0.940028\pi$
$829$	−19.9634	+	22.1716i	−0.693357	+	0.770051i	0.288947	+	0.957345i	$0.406695\pi$
$830$		0			0
$831$	−4.76724	+	4.29244i	−0.165374	+	0.148903i
$832$	15.7839	−	15.7839i	0.547209	−	0.547209i
$833$	13.7587	−	23.5457i	0.476711	−	0.815810i
$834$	0.367847	+	0.506298i	0.0127375	+	0.0175317i
$835$		0			0
$836$	7.10528	+	0.746795i	0.245741	+	0.0258285i
$837$	−9.86130	−	25.6896i	−0.340856	−	0.887961i
$838$	−36.1794	+	44.6778i	−1.24979	+	1.54337i
$839$	−11.0058	−	7.99616i	−0.379961	−	0.276058i	0.381368	−	0.924423i	$-0.375453\pi$
$839$	−11.0058	−	7.99616i	−0.379961	−	0.276058i	−0.761330	+	0.648365i	$0.775453\pi$
$840$		0			0
$841$	−9.01801	+	6.55197i	−0.310966	+	0.225930i
$842$	2.70342	−	51.5843i	0.0931659	−	1.77771i
$843$	0.609065	−	2.27306i	0.0209773	−	0.0782884i
$844$	−2.96915	−	13.9688i	−0.102203	−	0.480825i
$845$		0			0
$846$	12.1599	−	3.95100i	0.418067	−	0.135838i
$847$	−1.44992	+	7.71055i	−0.0498199	+	0.264938i
$848$	−65.8715	+	10.4330i	−2.26204	+	0.358271i
$849$	6.06880	+	3.50382i	0.208281	+	0.120251i
$850$		0			0
$851$	−0.0867071	−	0.150181i	−0.00297228	−	0.00514814i
$852$	1.17806	−	3.06895i	0.0403597	−	0.105141i
$853$	13.5441	−	26.5819i	0.463743	−	0.910146i	−0.534158	−	0.845384i	$-0.679371\pi$
$853$	13.5441	−	26.5819i	0.463743	−	0.910146i	0.997901	−	0.0647614i	$-0.0206286\pi$
$854$	−41.3067	+	3.14230i	−1.41349	+	0.107527i
$855$		0			0
$856$	11.3081	+	12.5589i	0.386503	+	0.429255i
$857$	15.0324	+	4.02791i	0.513496	+	0.137591i	0.506256	−	0.862383i	$-0.331029\pi$
$857$	15.0324	+	4.02791i	0.513496	+	0.137591i	0.00723941	+	0.999974i	$0.497696\pi$
$858$	−10.1023	+	15.5562i	−0.344888	+	0.531080i
$859$	0.670849	+	6.38270i	0.0228891	+	0.217775i	0.999988	+	0.00498739i	$0.00158754\pi$
$859$	0.670849	+	6.38270i	0.0228891	+	0.217775i	−0.977098	+	0.212788i	$0.931746\pi$
$860$		0			0
$861$	14.5464	−	12.3582i	0.495740	−	0.421166i
$862$	39.5550	+	6.26489i	1.34725	+	0.213383i
$863$	4.49800	+	3.64241i	0.153114	+	0.123989i	0.702816	−	0.711371i	$-0.251926\pi$
$863$	4.49800	+	3.64241i	0.153114	+	0.123989i	−0.549702	+	0.835361i	$0.685259\pi$
$864$	−1.41071	+	13.4220i	−0.0479932	+	0.456625i
$865$		0			0
$866$	−30.2956	+	3.18420i	−1.02949	+	0.108204i
$867$	−0.775519	−	1.52204i	−0.0263380	−	0.0516913i
$868$	6.76602	+	3.69658i	0.229654	+	0.125470i
$869$	−11.5533	−	3.75389i	−0.391918	−	0.127342i
$870$		0			0
$871$	35.8421	+	32.2723i	1.21446	+	1.09351i
$872$	33.6066	−	1.76125i	1.13806	−	0.0596434i
$873$	16.2644	+	6.24331i	0.550466	+	0.211304i
$874$	−7.81292			−0.264276
$875$		0			0
$876$	−2.52992			−0.0854782
$877$	0.275229	+	0.105651i	0.00929383	+	0.00356757i	0.363010	−	0.931785i	$-0.381749\pi$
$877$	0.275229	+	0.105651i	0.00929383	+	0.00356757i	−0.353717	+	0.935353i	$0.615082\pi$
$878$	9.95426	−	0.521681i	0.335940	−	0.0176059i
$879$	−9.61859	−	8.66061i	−0.324427	−	0.292115i
$880$		0			0
$881$	−12.4276	−	4.03797i	−0.418696	−	0.136043i	0.0920894	−	0.995751i	$-0.470645\pi$
$881$	−12.4276	−	4.03797i	−0.418696	−	0.136043i	−0.510786	+	0.859708i	$0.670645\pi$
$882$	−22.9787	−	5.00997i	−0.773735	−	0.168694i
$883$	−2.90787	−	5.70702i	−0.0978577	−	0.192057i	0.836888	−	0.547374i	$-0.184373\pi$
$883$	−2.90787	−	5.70702i	−0.0978577	−	0.192057i	−0.934746	+	0.355318i	$0.884373\pi$
$884$	8.68230	−	0.912546i	0.292017	−	0.0306922i
$885$		0			0
$886$	−4.05873	+	38.6162i	−0.136356	+	1.29734i
$887$	−34.8560	−	28.2259i	−1.17035	−	0.947732i	−0.171056	−	0.985261i	$-0.554718\pi$
$887$	−34.8560	−	28.2259i	−1.17035	−	0.947732i	−0.999296	+	0.0375294i	$0.988051\pi$
$888$	−0.381191	−	0.0603747i	−0.0127919	−	0.00202604i
$889$	47.0465	−	8.59243i	1.57789	−	0.288181i
$890$		0			0
$891$	−0.552375	−	5.25549i	−0.0185053	−	0.176066i
$892$	−3.48263	+	5.36278i	−0.116607	+	0.179559i
$893$	18.2243	+	4.88319i	0.609854	+	0.163410i
$894$	−6.52582	−	7.24766i	−0.218256	−	0.242398i
$895$		0			0
$896$	20.3673	+	29.8011i	0.680423	+	0.995586i
$897$	1.86638	−	3.66299i	0.0623168	−	0.122304i
$898$	−16.5111	+	43.0129i	−0.550983	+	1.43536i
$899$	−12.1100	−	20.9751i	−0.403889	−	0.699557i
$900$		0			0
$901$	47.2887	+	27.3021i	1.57541	+	0.909566i
$902$	−34.1263	+	5.40508i	−1.13628	+	0.179970i
$903$	−6.52112	−	5.59910i	−0.217009	−	0.186327i
$904$	−40.8516	+	13.2735i	−1.35870	+	0.441470i
$905$		0			0
$906$	1.76244	+	8.29164i	0.0585532	+	0.275471i
$907$	0.997046	−	3.72103i	0.0331064	−	0.123555i	−0.947395	−	0.320067i	$-0.896295\pi$
$907$	0.997046	−	3.72103i	0.0331064	−	0.123555i	0.980501	+	0.196512i	$0.0629614\pi$
$908$	−0.290029	+	5.53408i	−0.00962495	+	0.183655i
$909$	−20.1649	+	14.6506i	−0.668827	+	0.485931i
$910$		0			0
$911$	27.1055	+	19.6933i	0.898046	+	0.652469i	0.937963	−	0.346734i	$-0.112709\pi$
$911$	27.1055	+	19.6933i	0.898046	+	0.652469i	−0.0399171	+	0.999203i	$0.512709\pi$
$912$	−13.9163	+	17.1852i	−0.460815	+	0.569059i
$913$	−2.07696	−	5.41067i	−0.0687373	−	0.179067i
$914$	47.1857	+	4.95941i	1.56076	+	0.164043i
$915$		0			0
$916$	−0.828785	−	1.14072i	−0.0273838	−	0.0376906i
$917$	−26.8946	−	28.4897i	−0.888137	−	0.940813i
$918$	20.9446	−	20.9446i	0.691276	−	0.691276i
$919$	−5.63331	+	5.07226i	−0.185826	+	0.167318i	−0.756793	−	0.653654i	$-0.773235\pi$
$919$	−5.63331	+	5.07226i	−0.185826	+	0.167318i	0.570967	+	0.820973i	$0.306568\pi$
$920$		0			0
$921$	1.25776	−	1.39688i	0.0414446	−	0.0460289i
$922$	17.9144	−	11.6338i	0.589981	−	0.383138i
$923$	−4.75673	−	30.0328i	−0.156570	−	0.988543i
$924$	−2.58586	−	2.46677i	−0.0850687	−	0.0811508i
$925$		0			0
$926$	−0.657950	+	1.13960i	−0.0216216	+	0.0374497i
$927$	14.6343	+	18.0719i	0.480653	+	0.593558i
$928$	0.621684	+	11.8624i	0.0204078	+	0.389403i
$929$	−43.1332	−	9.16824i	−1.41515	−	0.300800i	−0.564025	−	0.825758i	$-0.690748\pi$
$929$	−43.1332	−	9.16824i	−1.41515	−	0.300800i	−0.851128	+	0.524958i	$0.824081\pi$
$930$		0			0
$931$	−24.4117	−	24.6682i	−0.800060	−	0.808468i
$932$	10.1848	+	10.1848i	0.333614	+	0.333614i
$933$	9.38833	+	0.492021i	0.307360	+	0.0161081i
$934$	−41.2821	−	18.3800i	−1.35079	−	0.601411i
$935$		0			0
$936$	8.98492	+	20.1805i	0.293681	+	0.659619i
$937$	0.491029	−	3.10024i	0.0160412	−	0.101280i	−0.978369	−	0.206869i	$-0.933673\pi$
$937$	0.491029	−	3.10024i	0.0160412	−	0.101280i	0.994410	+	0.105589i	$0.0336727\pi$
$938$	−36.4477	+	27.8163i	−1.19006	+	0.908234i
$939$	−9.97623	+	13.7311i	−0.325562	+	0.448098i
$940$		0			0
$941$	−15.9548	+	35.8350i	−0.520111	+	1.16819i	0.442368	+	0.896833i	$0.354138\pi$
$941$	−15.9548	+	35.8350i	−0.520111	+	1.16819i	−0.962479	+	0.271355i	$0.912528\pi$
$942$	10.7510	+	6.98180i	0.350287	+	0.227479i
$943$	7.39700	−	1.98202i	0.240879	−	0.0645434i
$944$	−14.7213	+	45.3077i	−0.479139	+	1.47464i
$945$		0			0
$946$	4.80792	+	14.7973i	0.156319	+	0.481100i
$947$	13.1592	+	20.2634i	0.427617	+	0.658473i	0.985153	−	0.171680i	$-0.0549196\pi$
$947$	13.1592	+	20.2634i	0.427617	+	0.658473i	−0.557535	+	0.830153i	$0.688253\pi$
$948$	−1.58713	+	1.28523i	−0.0515475	+	0.0417423i
$949$	−20.2664	+	11.7008i	−0.657874	+	0.379824i
$950$		0			0
$951$			13.7063i			0.444458i
$952$	1.97395	−	24.2702i	0.0639760	−	0.786603i
$953$	14.2501	+	7.26077i	0.461605	+	0.235199i	0.669297	−	0.742995i	$-0.266595\pi$
$953$	14.2501	+	7.26077i	0.461605	+	0.235199i	−0.207692	+	0.978194i	$0.566595\pi$
$954$	9.79076	−	46.0619i	0.316988	−	1.49131i
$955$		0			0
$956$	6.26041	−	1.33069i	0.202476	−	0.0430376i
$957$	2.90562	+	10.8439i	0.0939254	+	0.350535i
$958$	41.3914	−	21.0900i	1.33730	−	0.681387i
$959$	36.1955	−	14.8820i	1.16881	−	0.480564i
$960$		0			0
$961$	−1.69664	+	0.755393i	−0.0547304	+	0.0243675i
$962$	1.13591	−	0.436033i	0.0366231	−	0.0140583i
$963$	−14.1674	+	5.43837i	−0.456539	+	0.175249i
$964$	3.25289	−	1.44828i	0.104768	−	0.0466459i
$965$		0			0
$966$	3.09431	+	2.38722i	0.0995577	+	0.0768075i
$967$	−19.6328	+	10.0034i	−0.631349	+	0.321688i	−0.740217	−	0.672368i	$-0.765277\pi$
$967$	−19.6328	+	10.0034i	−0.631349	+	0.321688i	0.108868	+	0.994056i	$0.465277\pi$
$968$	1.81315	+	6.76676i	0.0582768	+	0.217492i
$969$	17.7095	−	3.76427i	0.568910	−	0.120926i
$970$		0			0
$971$	−5.66095	+	26.6327i	−0.181669	+	0.854684i	0.789025	+	0.614362i	$0.210586\pi$
$971$	−5.66095	+	26.6327i	−0.181669	+	0.854684i	−0.970693	+	0.240322i	$0.922747\pi$
$972$	−7.31506	−	3.72721i	−0.234631	−	0.119550i
$973$	−0.634122	+	0.917507i	−0.0203290	+	0.0294139i
$974$			5.54132i			0.177555i
$975$		0			0
$976$	−40.7390	+	23.5207i	−1.30402	+	0.752879i
$977$	9.28858	−	7.52175i	0.297168	−	0.240642i	−0.469127	−	0.883131i	$-0.655431\pi$
$977$	9.28858	−	7.52175i	0.297168	−	0.240642i	0.766295	+	0.642489i	$0.222098\pi$
$978$	−9.25902	−	14.2576i	−0.296071	−	0.455909i
$979$	−6.44212	−	19.8268i	−0.205891	−	0.633667i
$980$		0			0
$981$	−9.33822	+	28.7401i	−0.298146	+	0.917600i
$982$	−60.1289	+	16.1115i	−1.91879	+	0.514138i
$983$	−25.0107	−	16.2421i	−0.797718	−	0.518044i	0.0802436	−	0.996775i	$-0.474430\pi$
$983$	−25.0107	−	16.2421i	−0.797718	−	0.518044i	−0.877962	+	0.478731i	$0.841097\pi$
$984$	6.93206	−	15.5697i	0.220986	−	0.496343i
$985$		0			0
$986$	15.3241	−	21.0918i	0.488018	−	0.671699i
$987$	−5.72569	−	7.50239i	−0.182251	−	0.238804i
$988$	1.73799	−	10.9732i	0.0552928	−	0.349105i
$989$	−1.40259	−	3.15026i	−0.0445997	−	0.100173i
$990$		0			0
$991$	−19.2720	−	8.58044i	−0.612195	−	0.272567i	0.0771278	−	0.997021i	$-0.475425\pi$
$991$	−19.2720	−	8.58044i	−0.612195	−	0.272567i	−0.689323	+	0.724455i	$0.742092\pi$
$992$	16.0928	+	0.843389i	0.510947	+	0.0267776i
$993$	21.1572	+	21.1572i	0.671402	+	0.671402i
$994$	28.8943	+	0.832199i	0.916471	+	0.0263957i
$995$		0			0
$996$	−0.953044	−	0.202576i	−0.0301984	−	0.00641886i
$997$	2.35804	+	44.9940i	0.0746798	+	1.42497i	0.737070	+	0.675816i	$0.236209\pi$
$997$	2.35804	+	44.9940i	0.0746798	+	1.42497i	−0.662391	+	0.749159i	$0.730458\pi$
$998$	29.9141	+	36.9408i	0.946914	+	1.16934i
$999$	0.418334	−	0.724576i	0.0132355	−	0.0229246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.82.5		288
5.2	odd	4		175.2.x.a.138.14	yes	288
5.3	odd	4		875.2.bb.c.418.5		288
5.4	even	2		875.2.bb.b.82.14		288
7.3	odd	6	inner	875.2.bb.a.332.14		288
25.2	odd	20		875.2.bb.b.593.5		288
25.11	even	5		875.2.bb.c.782.5		288
25.14	even	10		175.2.x.a.152.14	yes	288
25.23	odd	20	inner	875.2.bb.a.593.14		288
35.3	even	12		875.2.bb.c.668.5		288
35.17	even	12		175.2.x.a.38.14	✓	288
35.24	odd	6		875.2.bb.b.332.5		288
175.52	even	60		875.2.bb.b.843.14		288
175.73	even	60	inner	875.2.bb.a.843.5		288
175.136	odd	30		875.2.bb.c.157.5		288
175.164	odd	30		175.2.x.a.52.14	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.14	✓	288	35.17	even	12
175.2.x.a.52.14	yes	288	175.164	odd	30
175.2.x.a.138.14	yes	288	5.2	odd	4
175.2.x.a.152.14	yes	288	25.14	even	10
875.2.bb.a.82.5		288	1.1	even	1	trivial
875.2.bb.a.332.14		288	7.3	odd	6	inner
875.2.bb.a.593.14		288	25.23	odd	20	inner
875.2.bb.a.843.5		288	175.73	even	60	inner
875.2.bb.b.82.14		288	5.4	even	2
875.2.bb.b.332.5		288	35.24	odd	6
875.2.bb.b.593.5		288	25.2	odd	20
875.2.bb.b.843.14		288	175.52	even	60
875.2.bb.c.157.5		288	175.136	odd	30
875.2.bb.c.418.5		288	5.3	odd	4
875.2.bb.c.668.5		288	35.3	even	12
875.2.bb.c.782.5		288	25.11	even	5

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.47859 - 0.567578i) q^{2} +(-0.936069 + 0.0490573i) q^{3} +(0.377800 + 0.340173i) q^{4} +(1.41191 + 0.458757i) q^{6} +(0.0623449 + 2.64502i) q^{7} +(1.07251 + 2.10492i) q^{8} +(-2.10975 + 0.221743i) q^{9} +(0.296290 - 2.81901i) q^{11} +(-0.370335 - 0.299891i) q^{12} +(-4.35361 - 0.689545i) q^{13} +(1.40907 - 3.94629i) q^{14} +(-0.497379 - 4.73224i) q^{16} +(-2.12183 + 3.26733i) q^{17} +(3.24531 + 0.869579i) q^{18} +(3.31747 + 3.68442i) q^{19} +(-0.188117 - 2.47286i) q^{21} +(-2.03810 + 4.00000i) q^{22} +(0.356574 - 0.928907i) q^{23} +(-1.10721 - 1.91774i) q^{24} +(6.04585 + 3.49057i) q^{26} +(4.74143 - 0.750969i) q^{27} +(-0.876209 + 1.02050i) q^{28} +(4.01849 - 1.30569i) q^{29} +(-1.19177 - 5.60686i) q^{31} +(-0.727626 + 2.71554i) q^{32} +(-0.139055 + 2.65332i) q^{33} +(4.99179 - 3.62674i) q^{34} +(-0.872494 - 0.633904i) q^{36} +(0.109682 - 0.135446i) q^{37} +(-2.81399 - 7.33069i) q^{38} +(4.10911 + 0.431885i) q^{39} +(4.52386 + 6.22657i) q^{41} +(-1.12539 + 3.76312i) q^{42} +(2.45065 - 2.45065i) q^{43} +(1.07089 - 0.964233i) q^{44} +(-1.05446 + 1.17109i) q^{46} +(3.19156 - 2.07262i) q^{47} +(0.697732 + 4.40531i) q^{48} +(-6.99223 + 0.329807i) q^{49} +(1.82589 - 3.16254i) q^{51} +(-1.41023 - 1.74149i) q^{52} +(-0.733542 - 13.9968i) q^{53} +(-7.43688 - 1.58076i) q^{54} +(-5.50068 + 2.96804i) q^{56} +(-3.28613 - 3.28613i) q^{57} +(-6.68280 - 0.350230i) q^{58} +(-9.14624 - 4.07217i) q^{59} +(-4.02106 - 9.03145i) q^{61} +(-1.42018 + 8.96669i) q^{62} +(-0.718047 - 5.56649i) q^{63} +(-2.97658 + 4.09692i) q^{64} +(1.71157 - 3.84426i) q^{66} +(-9.17658 - 5.95934i) q^{67} +(-1.91308 + 0.512609i) q^{68} +(-0.288208 + 0.887014i) q^{69} +(2.13171 + 6.56074i) q^{71} +(-2.72948 - 4.20303i) q^{72} +(4.12589 - 3.34108i) q^{73} +(-0.239051 + 0.138016i) q^{74} +2.52049i q^{76} +(7.47480 + 0.607941i) q^{77} +(-5.83057 - 2.97082i) q^{78} +(0.891037 - 4.19200i) q^{79} +(1.82357 - 0.387611i) q^{81} +(-3.15489 - 11.7742i) q^{82} +(1.82179 - 0.928247i) q^{83} +(0.770129 - 0.998239i) q^{84} +(-5.01445 + 2.23257i) q^{86} +(-3.69754 + 1.41935i) q^{87} +(6.25157 - 2.39975i) q^{88} +(6.71884 - 2.99142i) q^{89} +(1.55243 - 11.5584i) q^{91} +(0.450703 - 0.229645i) q^{92} +(1.39064 + 5.18994i) q^{93} +(-5.89539 + 1.25310i) q^{94} +(0.547892 - 2.57763i) q^{96} +(-7.31730 - 3.72835i) q^{97} +(10.5258 + 3.48099i) q^{98} +6.01310i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more