LMFDB - Embedded newform 912.2.bo.a.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			769.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	912.769
Dual form			912.2.bo.a.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{3} +(-3.20574 - 1.16679i) q^{5} +(-2.43969 + 4.22567i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{3} +(-3.20574 - 1.16679i) q^{5} +(-2.43969 + 4.22567i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-1.70574 - 2.95442i) q^{11} +(2.08125 + 1.74638i) q^{13} +(3.20574 - 1.16679i) q^{15} +(0.205737 + 1.16679i) q^{17} +(2.52094 - 3.55596i) q^{19} +(-0.847296 - 4.80526i) q^{21} +(-3.20574 + 1.16679i) q^{23} +(5.08512 + 4.26692i) q^{25} +(0.500000 + 0.866025i) q^{27} +(0.655230 - 3.71599i) q^{29} +(3.30793 - 5.72951i) q^{31} +(3.20574 + 1.16679i) q^{33} +(12.7515 - 10.6998i) q^{35} +6.75877 q^{37} -2.71688 q^{39} +(5.02094 - 4.21307i) q^{41} +(3.91875 + 1.42631i) q^{43} +(-1.70574 + 2.95442i) q^{45} +(-0.496130 + 2.81369i) q^{47} +(-8.40420 - 14.5565i) q^{49} +(-0.907604 - 0.761570i) q^{51} +(-0.592396 + 0.215615i) q^{53} +(2.02094 + 11.4613i) q^{55} +(0.354570 + 4.34445i) q^{57} +(-2.02094 - 11.4613i) q^{59} +(-6.48545 + 2.36051i) q^{61} +(3.73783 + 3.13641i) q^{63} +(-4.63429 - 8.02682i) q^{65} +(-0.123141 + 0.698367i) q^{67} +(1.70574 - 2.95442i) q^{69} +(7.47818 + 2.72183i) q^{71} +(-9.76264 + 8.19183i) q^{73} -6.63816 q^{75} +16.6459 q^{77} +(-0.228026 + 0.191336i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(7.80200 - 13.5135i) q^{83} +(0.701867 - 3.98048i) q^{85} +(1.88666 + 3.26779i) q^{87} +(5.18866 + 4.35381i) q^{89} +(-12.4572 + 4.53406i) q^{91} +(1.14883 + 6.51536i) q^{93} +(-12.2306 + 8.45805i) q^{95} +(-1.23736 - 7.01741i) q^{97} +(-3.20574 + 1.16679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} - 9 q^{7}+O(q^{10}) $ 6 * q - 9 * q^5 - 9 * q^7	$ 6 q - 9 q^{5} - 9 q^{7} + 15 q^{13} + 9 q^{15} - 9 q^{17} + 12 q^{19} - 3 q^{21} - 9 q^{23} + 9 q^{25} + 3 q^{27} - 9 q^{29} + 9 q^{31} + 9 q^{33} + 36 q^{35} + 18 q^{37} + 27 q^{41} + 21 q^{43} - 27 q^{47} - 12 q^{49} - 9 q^{51} + 9 q^{55} + 18 q^{57} - 9 q^{59} - 3 q^{61} + 3 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{71} - 12 q^{73} - 6 q^{75} + 18 q^{77} + 21 q^{79} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 24 q^{91} + 33 q^{93} - 36 q^{95} - 54 q^{97} - 9 q^{99}+O(q^{100}) $ 6 * q - 9 * q^5 - 9 * q^7 + 15 * q^13 + 9 * q^15 - 9 * q^17 + 12 * q^19 - 3 * q^21 - 9 * q^23 + 9 * q^25 + 3 * q^27 - 9 * q^29 + 9 * q^31 + 9 * q^33 + 36 * q^35 + 18 * q^37 + 27 * q^41 + 21 * q^43 - 27 * q^47 - 12 * q^49 - 9 * q^51 + 9 * q^55 + 18 * q^57 - 9 * q^59 - 3 * q^61 + 3 * q^63 - 18 * q^65 + 3 * q^67 - 9 * q^71 - 12 * q^73 - 6 * q^75 + 18 * q^77 + 21 * q^79 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 24 * q^91 + 33 * q^93 - 36 * q^95 - 54 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$		0			0
$5$	−3.20574	−	1.16679i	−1.43365	−	0.521806i	−0.495674	−	0.868509i	$-0.665079\pi$
$5$	−3.20574	−	1.16679i	−1.43365	−	0.521806i	−0.937975	+	0.346703i	$0.887301\pi$
$6$		0			0
$7$	−2.43969	+	4.22567i	−0.922117	+	1.59715i	−0.125984	+	0.992032i	$0.540209\pi$
$7$	−2.43969	+	4.22567i	−0.922117	+	1.59715i	−0.796133	+	0.605121i	$0.793125\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$		0			0
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	0.884038	−	0.467415i	$-0.154815\pi$
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	−0.306803	+	0.951773i	$0.599259\pi$
$14$		0			0
$15$	3.20574	−	1.16679i	0.827718	−	0.301265i
$16$		0			0
$17$	0.205737	+	1.16679i	0.0498986	+	0.282989i	0.999539	−	0.0303521i	$-0.00966285\pi$
$17$	0.205737	+	1.16679i	0.0498986	+	0.282989i	−0.949641	+	0.313341i	$0.898552\pi$
$18$		0			0
$19$	2.52094	−	3.55596i	0.578344	−	0.815793i
$19$	2.52094	−	3.55596i	0.578344	−	0.815793i
$20$		0			0
$21$	−0.847296	−	4.80526i	−0.184895	−	1.04859i
$22$		0			0
$23$	−3.20574	+	1.16679i	−0.668442	+	0.243293i	−0.653877	−	0.756601i	$-0.726859\pi$
$23$	−3.20574	+	1.16679i	−0.668442	+	0.243293i	−0.0145653	+	0.999894i	$0.504636\pi$
$24$		0			0
$25$	5.08512	+	4.26692i	1.01702	+	0.853385i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	0.655230	−	3.71599i	0.121673	−	0.690043i	−0.861555	−	0.507664i	$-0.830509\pi$
$29$	0.655230	−	3.71599i	0.121673	−	0.690043i	0.983228	−	0.182379i	$-0.0583797\pi$
$30$		0			0
$31$	3.30793	−	5.72951i	0.594122	−	1.02905i	−0.399548	−	0.916712i	$-0.630833\pi$
$31$	3.30793	−	5.72951i	0.594122	−	1.02905i	0.993670	−	0.112338i	$-0.0358339\pi$
$32$		0			0
$33$	3.20574	+	1.16679i	0.558047	+	0.203113i
$34$		0			0
$35$	12.7515	−	10.6998i	2.15540	−	1.80859i
$36$		0			0
$37$	6.75877			1.11114			0.555568	−	0.831471i	$-0.312501\pi$
$37$	6.75877			1.11114			0.555568	+	0.831471i	$0.312501\pi$
$38$		0			0
$39$	−2.71688			−0.435049
$40$		0			0
$41$	5.02094	−	4.21307i	0.784140	−	0.657971i	−0.160148	−	0.987093i	$-0.551197\pi$
$41$	5.02094	−	4.21307i	0.784140	−	0.657971i	0.944288	+	0.329122i	$0.106753\pi$
$42$		0			0
$43$	3.91875	+	1.42631i	0.597603	+	0.217510i	0.623070	−	0.782166i	$-0.285885\pi$
$43$	3.91875	+	1.42631i	0.597603	+	0.217510i	−0.0254669	+	0.999676i	$0.508107\pi$
$44$		0			0
$45$	−1.70574	+	2.95442i	−0.254276	+	0.440419i
$46$		0			0
$47$	−0.496130	+	2.81369i	−0.0723679	+	0.410419i	0.927006	+	0.375046i	$0.122373\pi$
$47$	−0.496130	+	2.81369i	−0.0723679	+	0.410419i	−0.999374	+	0.0353731i	$0.988738\pi$
$48$		0			0
$49$	−8.40420	−	14.5565i	−1.20060	−	2.07950i
$50$		0			0
$51$	−0.907604	−	0.761570i	−0.127090	−	0.106641i
$52$		0			0
$53$	−0.592396	+	0.215615i	−0.0813719	+	0.0296169i	−0.382385	−	0.924003i	$-0.624897\pi$
$53$	−0.592396	+	0.215615i	−0.0813719	+	0.0296169i	0.301013	+	0.953620i	$0.402675\pi$
$54$		0			0
$55$	2.02094	+	11.4613i	0.272504	+	1.54545i
$56$		0			0
$57$	0.354570	+	4.34445i	0.0469640	+	0.575437i
$58$		0			0
$59$	−2.02094	−	11.4613i	−0.263105	−	1.49214i	−0.774379	−	0.632722i	$-0.781937\pi$
$59$	−2.02094	−	11.4613i	−0.263105	−	1.49214i	0.511274	−	0.859418i	$-0.329174\pi$
$60$		0			0
$61$	−6.48545	+	2.36051i	−0.830377	+	0.302233i	−0.722014	−	0.691879i	$-0.756783\pi$
$61$	−6.48545	+	2.36051i	−0.830377	+	0.302233i	−0.108363	+	0.994111i	$0.534561\pi$
$62$		0			0
$63$	3.73783	+	3.13641i	0.470922	+	0.395150i
$64$		0			0
$65$	−4.63429	−	8.02682i	−0.574812	−	0.995604i
$66$		0			0
$67$	−0.123141	+	0.698367i	−0.0150441	+	0.0853191i	−0.991405	−	0.130826i	$-0.958237\pi$
$67$	−0.123141	+	0.698367i	−0.0150441	+	0.0853191i	0.976361	+	0.216145i	$0.0693483\pi$
$68$		0			0
$69$	1.70574	−	2.95442i	0.205347	−	0.355671i
$70$		0			0
$71$	7.47818	+	2.72183i	0.887496	+	0.323022i	0.745231	−	0.666806i	$-0.232339\pi$
$71$	7.47818	+	2.72183i	0.887496	+	0.323022i	0.142265	+	0.989829i	$0.454561\pi$
$72$		0			0
$73$	−9.76264	+	8.19183i	−1.14263	+	0.958781i	−0.999522	−	0.0309259i	$-0.990154\pi$
$73$	−9.76264	+	8.19183i	−1.14263	+	0.958781i	−0.143109	+	0.989707i	$0.545710\pi$
$74$		0			0
$75$	−6.63816			−0.766508
$76$		0			0
$77$	16.6459			1.89698
$78$		0			0
$79$	−0.228026	+	0.191336i	−0.0256549	+	0.0215270i	−0.655525	−	0.755174i	$-0.727553\pi$
$79$	−0.228026	+	0.191336i	−0.0256549	+	0.0215270i	0.629870	+	0.776701i	$0.283108\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	7.80200	−	13.5135i	0.856381	−	1.48330i	−0.0189766	−	0.999820i	$-0.506041\pi$
$83$	7.80200	−	13.5135i	0.856381	−	1.48330i	0.875358	−	0.483476i	$-0.160626\pi$
$84$		0			0
$85$	0.701867	−	3.98048i	0.0761281	−	0.431744i
$86$		0			0
$87$	1.88666	+	3.26779i	0.202271	+	0.350344i
$88$		0			0
$89$	5.18866	+	4.35381i	0.549997	+	0.461502i	0.874940	−	0.484231i	$-0.160901\pi$
$89$	5.18866	+	4.35381i	0.549997	+	0.461502i	−0.324943	+	0.945734i	$0.605345\pi$
$90$		0			0
$91$	−12.4572	+	4.53406i	−1.30587	+	0.475299i
$92$		0			0
$93$	1.14883	+	6.51536i	0.119128	+	0.675611i
$94$		0			0
$95$	−12.2306	+	8.45805i	−1.25483	+	0.867777i
$96$		0			0
$97$	−1.23736	−	7.01741i	−0.125635	−	0.712510i	−0.980929	−	0.194367i	$-0.937735\pi$
$97$	−1.23736	−	7.01741i	−0.125635	−	0.712510i	0.855294	−	0.518143i	$-0.173376\pi$
$98$		0			0
$99$	−3.20574	+	1.16679i	−0.322189	+	0.117267i
$100$		0			0
$101$	−3.55896	−	2.98632i	−0.354130	−	0.297150i	0.448316	−	0.893875i	$-0.352024\pi$
$101$	−3.55896	−	2.98632i	−0.354130	−	0.297150i	−0.802446	+	0.596725i	$0.796468\pi$
$102$		0			0
$103$	−6.19119	−	10.7235i	−0.610036	−	1.05661i	−0.991234	−	0.132120i	$-0.957822\pi$
$103$	−6.19119	−	10.7235i	−0.610036	−	1.05661i	0.381198	−	0.924494i	$-0.375512\pi$
$104$		0			0
$105$	−2.89053	+	16.3930i	−0.282087	+	1.59979i
$106$		0			0
$107$	1.94949	−	3.37662i	0.188465	−	0.326430i	−0.756274	−	0.654255i	$-0.772982\pi$
$107$	1.94949	−	3.37662i	0.188465	−	0.326430i	0.944739	+	0.327825i	$0.106316\pi$
$108$		0			0
$109$	10.8969	+	3.96616i	1.04374	+	0.379889i	0.806295	−	0.591513i	$-0.201469\pi$
$109$	10.8969	+	3.96616i	1.04374	+	0.379889i	0.237441	+	0.971402i	$0.423691\pi$
$110$		0			0
$111$	−5.17752	+	4.34445i	−0.491428	+	0.412357i
$112$		0			0
$113$	1.94087			0.182582			0.0912911	−	0.995824i	$-0.470901\pi$
$113$	1.94087			0.182582			0.0912911	+	0.995824i	$0.470901\pi$
$114$		0			0
$115$	11.6382			1.08526
$116$		0			0
$117$	2.08125	−	1.74638i	0.192412	−	0.161453i
$118$		0			0
$119$	−5.43242	−	1.97724i	−0.497989	−	0.181253i
$120$		0			0
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$		0			0
$123$	−1.13816	+	6.45480i	−0.102624	+	0.582010i
$124$		0			0
$125$	−2.79426	−	4.83981i	−0.249926	−	0.432885i
$126$		0			0
$127$	4.66044	+	3.91058i	0.413548	+	0.347008i	0.825702	−	0.564106i	$-0.190779\pi$
$127$	4.66044	+	3.91058i	0.413548	+	0.347008i	−0.412155	+	0.911114i	$0.635224\pi$
$128$		0			0
$129$	−3.91875	+	1.42631i	−0.345027	+	0.125579i
$130$		0			0
$131$	3.23055	+	18.3214i	0.282255	+	1.60075i	0.714930	+	0.699196i	$0.246458\pi$
$131$	3.23055	+	18.3214i	0.282255	+	1.60075i	−0.432676	+	0.901550i	$0.642430\pi$
$132$		0			0
$133$	8.87598	+	19.3281i	0.769645	+	1.67596i
$134$		0			0
$135$	−0.592396	−	3.35965i	−0.0509854	−	0.289152i
$136$		0			0
$137$	−4.27244	+	1.55504i	−0.365019	+	0.132856i	−0.518017	−	0.855370i	$-0.673330\pi$
$137$	−4.27244	+	1.55504i	−0.365019	+	0.132856i	0.152998	+	0.988227i	$0.451107\pi$
$138$		0			0
$139$	2.30928	+	1.93771i	0.195870	+	0.164355i	0.735448	−	0.677581i	$-0.236972\pi$
$139$	2.30928	+	1.93771i	0.195870	+	0.164355i	−0.539578	+	0.841936i	$0.681416\pi$
$140$		0			0
$141$	−1.42855	−	2.47432i	−0.120305	−	0.208375i
$142$		0			0
$143$	1.60947	−	9.12776i	0.134591	−	0.763302i
$144$		0			0
$145$	−6.43629	+	11.1480i	−0.534505	+	0.925789i
$146$		0			0
$147$	15.7947	+	5.74881i	1.30273	+	0.474154i
$148$		0			0
$149$	0.907604	−	0.761570i	0.0743538	−	0.0623902i	−0.604853	−	0.796337i	$-0.706768\pi$
$149$	0.907604	−	0.761570i	0.0743538	−	0.0623902i	0.679207	+	0.733947i	$0.262324\pi$
$150$		0			0
$151$	3.63816			0.296069			0.148034	−	0.988982i	$-0.452705\pi$
$151$	3.63816			0.296069			0.148034	+	0.988982i	$0.452705\pi$
$152$		0			0
$153$	1.18479			0.0957848
$154$		0			0
$155$	−17.2895	+	14.5076i	−1.38873	+	1.16528i
$156$		0			0
$157$	−5.89306	−	2.14490i	−0.470317	−	0.171181i	0.0959789	−	0.995383i	$-0.469402\pi$
$157$	−5.89306	−	2.14490i	−0.470317	−	0.171181i	−0.566296	+	0.824202i	$0.691624\pi$
$158$		0			0
$159$	0.315207	−	0.545955i	0.0249976	−	0.0432971i
$160$		0			0
$161$	2.89053	−	16.3930i	0.227806	−	1.29195i
$162$		0			0
$163$	−9.64930	−	16.7131i	−0.755792	−	1.30907i	−0.944980	−	0.327128i	$-0.893919\pi$
$163$	−9.64930	−	16.7131i	−0.755792	−	1.30907i	0.189188	−	0.981941i	$-0.439414\pi$
$164$		0			0
$165$	−8.91534	−	7.48086i	−0.694059	−	0.582384i
$166$		0			0
$167$	−7.25624	+	2.64106i	−0.561505	+	0.204371i	−0.607151	−	0.794587i	$-0.707688\pi$
$167$	−7.25624	+	2.64106i	−0.561505	+	0.204371i	0.0456458	+	0.998958i	$0.485465\pi$
$168$		0			0
$169$	−0.975652	−	5.53320i	−0.0750501	−	0.425631i
$170$		0			0
$171$	−3.06418	−	3.10013i	−0.234324	−	0.237073i
$172$		0			0
$173$	−2.51707	−	14.2750i	−0.191370	−	1.08531i	−0.917495	−	0.397748i	$-0.869792\pi$
$173$	−2.51707	−	14.2750i	−0.191370	−	1.08531i	0.726125	−	0.687563i	$-0.241319\pi$
$174$		0			0
$175$	−30.4368	+	11.0781i	−2.30080	+	0.837424i
$176$		0			0
$177$	8.91534	+	7.48086i	0.670118	+	0.562296i
$178$		0			0
$179$	−4.91147	−	8.50692i	−0.367101	−	0.635837i	0.622010	−	0.783009i	$-0.286316\pi$
$179$	−4.91147	−	8.50692i	−0.367101	−	0.635837i	−0.989111	+	0.147172i	$0.952983\pi$
$180$		0			0
$181$	3.28446	−	18.6271i	0.244132	−	1.38454i	−0.578367	−	0.815777i	$-0.696310\pi$
$181$	3.28446	−	18.6271i	0.244132	−	1.38454i	0.822499	−	0.568766i	$-0.192579\pi$
$182$		0			0
$183$	3.45084	−	5.97702i	0.255093	−	0.441834i
$184$		0			0
$185$	−21.6668	−	7.88609i	−1.59298	−	0.579797i
$186$		0			0
$187$	3.09627	−	2.59808i	0.226421	−	0.189990i
$188$		0			0
$189$	−4.87939			−0.354923
$190$		0			0
$191$	10.0915			0.730197			0.365098	−	0.930969i	$-0.381035\pi$
$191$	10.0915			0.730197			0.365098	+	0.930969i	$0.381035\pi$
$192$		0			0
$193$	1.93376	−	1.62262i	0.139195	−	0.116799i	−0.570532	−	0.821276i	$-0.693263\pi$
$193$	1.93376	−	1.62262i	0.139195	−	0.116799i	0.709727	+	0.704477i	$0.248818\pi$
$194$		0			0
$195$	8.70961	+	3.17004i	0.623708	+	0.227011i
$196$		0			0
$197$	−7.42855	+	12.8666i	−0.529262	+	0.916709i	0.470155	+	0.882584i	$0.344198\pi$
$197$	−7.42855	+	12.8666i	−0.529262	+	0.916709i	−0.999418	+	0.0341253i	$0.989135\pi$
$198$		0			0
$199$	−1.40121	+	7.94664i	−0.0993289	+	0.563322i	0.894006	+	0.448056i	$0.147883\pi$
$199$	−1.40121	+	7.94664i	−0.0993289	+	0.563322i	−0.993335	+	0.115267i	$0.963228\pi$
$200$		0			0
$201$	−0.354570	−	0.614134i	−0.0250095	−	0.0433177i
$202$		0			0
$203$	14.1040	+	11.8347i	0.989907	+	0.830631i
$204$		0			0
$205$	−21.0116	+	7.64760i	−1.46751	+	0.534132i
$206$		0			0
$207$	0.592396	+	3.35965i	0.0411744	+	0.233512i
$208$		0			0
$209$	−14.8059	−	1.38241i	−1.02414	−	0.0956231i
$210$		0			0
$211$	−1.37939	−	7.82288i	−0.0949608	−	0.538549i	−0.994759	−	0.102244i	$-0.967398\pi$
$211$	−1.37939	−	7.82288i	−0.0949608	−	0.538549i	0.899799	−	0.436306i	$-0.143713\pi$
$212$		0			0
$213$	−7.47818	+	2.72183i	−0.512396	+	0.186497i
$214$		0			0
$215$	−10.8983	−	9.14473i	−0.743256	−	0.623666i
$216$		0			0
$217$	16.1407	+	27.9565i	1.09570	+	1.89781i
$218$		0			0
$219$	2.21301	−	12.5506i	0.149541	−	0.848092i
$220$		0			0
$221$	−1.60947	+	2.78768i	−0.108265	+	0.187520i
$222$		0			0
$223$	11.2464	+	4.09337i	0.753118	+	0.274112i	0.689917	−	0.723888i	$-0.257647\pi$
$223$	11.2464	+	4.09337i	0.753118	+	0.274112i	0.0632006	+	0.998001i	$0.479869\pi$
$224$		0			0
$225$	5.08512	−	4.26692i	0.339008	−	0.284462i
$226$		0			0
$227$	−26.5945			−1.76514			−0.882570	−	0.470181i	$-0.844189\pi$
$227$	−26.5945			−1.76514			−0.882570	+	0.470181i	$0.844189\pi$
$228$		0			0
$229$	−19.9026			−1.31520			−0.657601	−	0.753367i	$-0.728429\pi$
$229$	−19.9026			−1.31520			−0.657601	+	0.753367i	$0.728429\pi$
$230$		0			0
$231$	−12.7515	+	10.6998i	−0.838987	+	0.703994i
$232$		0			0
$233$	4.05051	+	1.47426i	0.265358	+	0.0965822i	0.471273	−	0.881988i	$-0.343795\pi$
$233$	4.05051	+	1.47426i	0.265358	+	0.0965822i	−0.205915	+	0.978570i	$0.566017\pi$
$234$		0			0
$235$	4.87346	−	8.44107i	0.317909	−	0.550635i
$236$		0			0
$237$	0.0516892	−	0.293144i	0.00335758	−	0.0190418i
$238$		0			0
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	0.870610	−	0.491973i	$-0.163724\pi$
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	−0.861367	+	0.507984i	$0.830391\pi$
$240$		0			0
$241$	7.32816	+	6.14906i	0.472048	+	0.396096i	0.847541	−	0.530730i	$-0.178082\pi$
$241$	7.32816	+	6.14906i	0.472048	+	0.396096i	−0.375493	+	0.926825i	$0.622526\pi$
$242$		0			0
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$		0			0
$245$	9.95723	+	56.4703i	0.636144	+	3.60775i
$246$		0			0
$247$	11.4568	−	2.99832i	0.728977	−	0.190779i
$248$		0			0
$249$	2.70961	+	15.3669i	0.171714	+	0.973841i
$250$		0			0
$251$	27.8974	−	10.1538i	1.76087	−	0.640903i	0.760900	−	0.648870i	$-0.224758\pi$
$251$	27.8974	−	10.1538i	1.76087	−	0.640903i	0.999968	+	0.00796619i	$0.00253575\pi$
$252$		0			0
$253$	8.91534	+	7.48086i	0.560503	+	0.470318i
$254$		0			0
$255$	2.02094	+	3.50038i	0.126556	+	0.219202i
$256$		0			0
$257$	2.74304	−	15.5566i	0.171106	−	0.970391i	−0.771437	−	0.636306i	$-0.780462\pi$
$257$	2.74304	−	15.5566i	0.171106	−	0.970391i	0.942543	−	0.334085i	$-0.108427\pi$
$258$		0			0
$259$	−16.4893	+	28.5603i	−1.02460	+	1.77465i
$260$		0			0
$261$	−3.54576	−	1.29055i	−0.219477	−	0.0798831i
$262$		0			0
$263$	−8.32295	+	6.98378i	−0.513215	+	0.430638i	−0.862259	−	0.506468i	$-0.830951\pi$
$263$	−8.32295	+	6.98378i	−0.513215	+	0.430638i	0.349044	+	0.937106i	$0.386506\pi$
$264$		0			0
$265$	2.15064			0.132113
$266$		0			0
$267$	−6.77332			−0.414520
$268$		0			0
$269$	−13.2476	+	11.1161i	−0.807722	+	0.677759i	−0.950063	−	0.312058i	$-0.898982\pi$
$269$	−13.2476	+	11.1161i	−0.807722	+	0.677759i	0.142341	+	0.989818i	$0.454537\pi$
$270$		0			0
$271$	1.35844	+	0.494432i	0.0825194	+	0.0300346i	0.382950	−	0.923769i	$-0.374908\pi$
$271$	1.35844	+	0.494432i	0.0825194	+	0.0300346i	−0.300431	+	0.953804i	$0.597130\pi$
$272$		0			0
$273$	6.62836	−	11.4806i	0.401166	−	0.694840i
$274$		0			0
$275$	3.93242	−	22.3019i	0.237134	−	1.34485i
$276$		0			0
$277$	−10.5954	−	18.3518i	−0.636615	−	1.10265i	−0.986170	−	0.165734i	$-0.947001\pi$
$277$	−10.5954	−	18.3518i	−0.636615	−	1.10265i	0.349555	−	0.936916i	$-0.386333\pi$
$278$		0			0
$279$	−5.06805	−	4.25260i	−0.303416	−	0.254596i
$280$		0			0
$281$	22.8983	−	8.33429i	1.36600	−	0.497182i	0.448093	−	0.893987i	$-0.352103\pi$
$281$	22.8983	−	8.33429i	1.36600	−	0.497182i	0.917903	+	0.396805i	$0.129881\pi$
$282$		0			0
$283$	0.716415	+	4.06299i	0.0425864	+	0.241520i	0.998669	−	0.0515779i	$-0.0164250\pi$
$283$	0.716415	+	4.06299i	0.0425864	+	0.241520i	−0.956083	+	0.293098i	$0.905314\pi$
$284$		0			0
$285$	3.93242	−	14.3409i	0.232936	−	0.849481i
$286$		0			0
$287$	5.55350	+	31.4955i	0.327813	+	1.85912i
$288$		0			0
$289$	14.6557	−	5.33424i	0.862100	−	0.313779i
$290$		0			0
$291$	5.45858	+	4.58029i	0.319987	+	0.268501i
$292$		0			0
$293$	−1.39053	−	2.40847i	−0.0812356	−	0.140704i	0.822545	−	0.568700i	$-0.192553\pi$
$293$	−1.39053	−	2.40847i	−0.0812356	−	0.140704i	−0.903781	+	0.427995i	$0.859220\pi$
$294$		0			0
$295$	−6.89440	+	39.1001i	−0.401407	+	2.27649i
$296$		0			0
$297$	1.70574	−	2.95442i	0.0989769	−	0.171433i
$298$		0			0
$299$	−8.70961	−	3.17004i	−0.503690	−	0.183328i
$300$		0			0
$301$	−15.5876	+	13.0796i	−0.898457	+	0.753895i
$302$		0			0
$303$	4.64590			0.266900
$304$		0			0
$305$	23.5449			1.34818
$306$		0			0
$307$	19.1689	−	16.0846i	1.09403	−	0.917998i	0.0970179	−	0.995283i	$-0.469070\pi$
$307$	19.1689	−	16.0846i	1.09403	−	0.917998i	0.997009	+	0.0772850i	$0.0246251\pi$
$308$		0			0
$309$	11.6356	+	4.23502i	0.661928	+	0.240922i
$310$		0			0
$311$	11.9868	−	20.7617i	0.679709	−	1.17729i	−0.295360	−	0.955386i	$-0.595439\pi$
$311$	11.9868	−	20.7617i	0.679709	−	1.17729i	0.975068	−	0.221904i	$-0.0712272\pi$
$312$		0			0
$313$	−2.19459	+	12.4462i	−0.124046	+	0.703498i	0.857824	+	0.513943i	$0.171816\pi$
$313$	−2.19459	+	12.4462i	−0.124046	+	0.703498i	−0.981870	+	0.189555i	$0.939295\pi$
$314$		0			0
$315$	−8.32295	−	14.4158i	−0.468945	−	0.812237i
$316$		0			0
$317$	−10.8268	−	9.08478i	−0.608095	−	0.510252i	0.285941	−	0.958247i	$-0.407694\pi$
$317$	−10.8268	−	9.08478i	−0.608095	−	0.510252i	−0.894036	+	0.447995i	$0.852138\pi$
$318$		0			0
$319$	−12.0963	+	4.40268i	−0.677261	+	0.246503i
$320$		0			0
$321$	0.677052	+	3.83975i	0.0377893	+	0.214314i
$322$		0			0
$323$	4.66772	+	2.20983i	0.259719	+	0.122958i
$324$		0			0
$325$	3.13176	+	17.7611i	0.173719	+	0.985208i
$326$		0			0
$327$	−10.8969	+	3.96616i	−0.602601	+	0.219329i
$328$		0			0
$329$	−10.6793	−	8.96102i	−0.588770	−	0.494037i
$330$		0			0
$331$	14.7490	+	25.5460i	0.810677	+	1.40413i	0.912391	+	0.409320i	$0.134234\pi$
$331$	14.7490	+	25.5460i	0.810677	+	1.40413i	−0.101714	+	0.994814i	$0.532433\pi$
$332$		0			0
$333$	1.17365	−	6.65609i	0.0643155	−	0.364751i
$334$		0			0
$335$	1.20961	−	2.09510i	0.0660879	−	0.114468i
$336$		0			0
$337$	20.9072	+	7.60960i	1.13889	+	0.414521i	0.841511	−	0.540239i	$-0.181666\pi$
$337$	20.9072	+	7.60960i	1.13889	+	0.414521i	0.297376	+	0.954760i	$0.403889\pi$
$338$		0			0
$339$	−1.48680	+	1.24757i	−0.0807517	+	0.0677587i
$340$		0			0
$341$	−22.5699			−1.22223
$342$		0			0
$343$	47.8590			2.58414
$344$		0			0
$345$	−8.91534	+	7.48086i	−0.479986	+	0.402756i
$346$		0			0
$347$	−13.1792	−	4.79682i	−0.707495	−	0.257507i	−0.0368873	−	0.999319i	$-0.511744\pi$
$347$	−13.1792	−	4.79682i	−0.707495	−	0.257507i	−0.670607	+	0.741812i	$0.733966\pi$
$348$		0			0
$349$	17.0560	−	29.5419i	0.912988	−	1.58134i	0.103168	−	0.994664i	$-0.467102\pi$
$349$	17.0560	−	29.5419i	0.912988	−	1.58134i	0.809820	−	0.586678i	$-0.199565\pi$
$350$		0			0
$351$	−0.471782	+	2.67561i	−0.0251818	+	0.142813i
$352$		0			0
$353$	−15.2219	−	26.3652i	−0.810182	−	1.40328i	−0.912737	−	0.408549i	$-0.866035\pi$
$353$	−15.2219	−	26.3652i	−0.810182	−	1.40328i	0.102555	−	0.994727i	$-0.467298\pi$
$354$		0			0
$355$	−20.7973	−	17.4510i	−1.10380	−	0.926201i
$356$		0			0
$357$	5.43242	−	1.97724i	0.287514	−	0.104647i
$358$		0			0
$359$	−2.36959	−	13.4386i	−0.125062	−	0.709261i	−0.981271	−	0.192632i	$-0.938298\pi$
$359$	−2.36959	−	13.4386i	−0.125062	−	0.709261i	0.856209	−	0.516629i	$-0.172813\pi$
$360$		0			0
$361$	−6.28968	−	17.9287i	−0.331036	−	0.943618i
$362$		0			0
$363$	−0.110815	−	0.628461i	−0.00581626	−	0.0329856i
$364$		0			0
$365$	40.8546	−	14.8699i	2.13843	−	0.778324i
$366$		0			0
$367$	−18.2062	−	15.2768i	−0.950356	−	0.797443i	0.0290014	−	0.999579i	$-0.490767\pi$
$367$	−18.2062	−	15.2768i	−0.950356	−	0.797443i	−0.979357	+	0.202136i	$0.935212\pi$
$368$		0			0
$369$	−3.27719	−	5.67626i	−0.170604	−	0.295494i
$370$		0			0
$371$	0.534148	−	3.02931i	0.0277316	−	0.157274i
$372$		0			0
$373$	11.6172	−	20.1216i	0.601516	−	1.04186i	−0.391075	−	0.920359i	$-0.627897\pi$
$373$	11.6172	−	20.1216i	0.601516	−	1.04186i	0.992592	−	0.121498i	$-0.0387699\pi$
$374$		0			0
$375$	5.25150	+	1.91139i	0.271186	+	0.0987037i
$376$		0			0
$377$	7.85323	−	6.58964i	0.404462	−	0.339384i
$378$		0			0
$379$	4.50030			0.231165			0.115583	−	0.993298i	$-0.463127\pi$
$379$	4.50030			0.231165			0.115583	+	0.993298i	$0.463127\pi$
$380$		0			0
$381$	−6.08378			−0.311681
$382$		0			0
$383$	−3.34002	+	2.80261i	−0.170667	+	0.143207i	−0.724121	−	0.689673i	$-0.757754\pi$
$383$	−3.34002	+	2.80261i	−0.170667	+	0.143207i	0.553453	+	0.832880i	$0.313310\pi$
$384$		0			0
$385$	−53.3624	−	19.4223i	−2.71960	−	0.989853i
$386$		0			0
$387$	2.08512	−	3.61154i	0.105993	−	0.183585i
$388$		0			0
$389$	−0.227559	+	1.29055i	−0.0115377	+	0.0654335i	−0.990033	−	0.140836i	$-0.955021\pi$
$389$	−0.227559	+	1.29055i	−0.0115377	+	0.0654335i	0.978495	+	0.206269i	$0.0661322\pi$
$390$		0			0
$391$	−2.02094	−	3.50038i	−0.102204	−	0.177022i
$392$		0			0
$393$	−14.2515	−	11.9584i	−0.718893	−	0.603223i
$394$		0			0
$395$	0.954241	−	0.347315i	0.0480131	−	0.0174753i
$396$		0			0
$397$	−3.30154	−	18.7239i	−0.165699	−	0.939728i	−0.948340	−	0.317255i	$-0.897239\pi$
$397$	−3.30154	−	18.7239i	−0.165699	−	0.939728i	0.782641	−	0.622473i	$-0.213872\pi$
$398$		0			0
$399$	−19.2233	−	9.10083i	−0.962368	−	0.455612i
$400$		0			0
$401$	6.22756	+	35.3182i	0.310989	+	1.76371i	0.593877	+	0.804556i	$0.297597\pi$
$401$	6.22756	+	35.3182i	0.310989	+	1.76371i	−0.282888	+	0.959153i	$0.591292\pi$
$402$		0			0
$403$	16.8905	−	6.14765i	0.841377	−	0.306236i
$404$		0			0
$405$	2.61334	+	2.19285i	0.129858	+	0.108964i
$406$		0			0
$407$	−11.5287	−	19.9683i	−0.571456	−	0.989790i
$408$		0			0
$409$	−5.05468	+	28.6665i	−0.249938	+	1.41747i	0.558801	+	0.829301i	$0.311261\pi$
$409$	−5.05468	+	28.6665i	−0.249938	+	1.41747i	−0.808739	+	0.588167i	$0.799850\pi$
$410$		0			0
$411$	2.27332	−	3.93750i	0.112135	−	0.194223i
$412$		0			0
$413$	53.3624	+	19.4223i	2.62579	+	0.955710i
$414$		0			0
$415$	−40.7786	+	34.2173i	−2.00174	+	1.67966i
$416$		0			0
$417$	−3.01455			−0.147623
$418$		0			0
$419$	−13.1584			−0.642829			−0.321415	−	0.946939i	$-0.604158\pi$
$419$	−13.1584			−0.642829			−0.321415	+	0.946939i	$0.604158\pi$
$420$		0			0
$421$	−0.115400	+	0.0968323i	−0.00562426	+	0.00471932i	−0.645595	−	0.763680i	$-0.723391\pi$
$421$	−0.115400	+	0.0968323i	−0.00562426	+	0.00471932i	0.639971	+	0.768399i	$0.278946\pi$
$422$		0			0
$423$	2.68479	+	0.977185i	0.130539	+	0.0475123i
$424$		0			0
$425$	−3.93242	+	6.81115i	−0.190750	+	0.330389i
$426$		0			0
$427$	5.84776	−	33.1643i	0.282993	−	1.60493i
$428$		0			0
$429$	4.63429	+	8.02682i	0.223745	+	0.387538i
$430$		0			0
$431$	23.5915	+	19.7956i	1.13636	+	0.953522i	0.999314	−	0.0370420i	$-0.0117935\pi$
$431$	23.5915	+	19.7956i	1.13636	+	0.953522i	0.137050	+	0.990564i	$0.456238\pi$
$432$		0			0
$433$	27.6587	−	10.0669i	1.32919	−	0.483786i	0.422800	−	0.906223i	$-0.361047\pi$
$433$	27.6587	−	10.0669i	1.32919	−	0.483786i	0.906392	+	0.422437i	$0.138825\pi$
$434$		0			0
$435$	−2.23530	−	12.6770i	−0.107174	−	0.607816i
$436$		0			0
$437$	−3.93242	+	14.3409i	−0.188113	+	0.686018i
$438$		0			0
$439$	−3.43835	−	19.4998i	−0.164103	−	0.930677i	−0.949984	−	0.312298i	$-0.898901\pi$
$439$	−3.43835	−	19.4998i	−0.164103	−	0.930677i	0.785881	−	0.618378i	$-0.212210\pi$
$440$		0			0
$441$	−15.7947	+	5.74881i	−0.752130	+	0.273753i
$442$		0			0
$443$	14.2383	+	11.9473i	0.676482	+	0.567636i	0.914976	−	0.403508i	$-0.132209\pi$
$443$	14.2383	+	11.9473i	0.676482	+	0.567636i	−0.238494	+	0.971144i	$0.576654\pi$
$444$		0			0
$445$	−11.5535	−	20.0112i	−0.547688	−	0.948624i
$446$		0			0
$447$	−0.205737	+	1.16679i	−0.00973103	+	0.0551874i
$448$		0			0
$449$	−1.68954	+	2.92637i	−0.0797343	+	0.138104i	−0.903135	−	0.429356i	$-0.858741\pi$
$449$	−1.68954	+	2.92637i	−0.0797343	+	0.138104i	0.823401	+	0.567460i	$0.192074\pi$
$450$		0			0
$451$	−21.0116	−	7.64760i	−0.989398	−	0.360111i
$452$		0			0
$453$	−2.78699	+	2.33856i	−0.130944	+	0.109875i
$454$		0			0
$455$	45.2249			2.12018
$456$		0			0
$457$	21.7912			1.01935			0.509674	−	0.860368i	$-0.329766\pi$
$457$	21.7912			1.01935			0.509674	+	0.860368i	$0.329766\pi$
$458$		0			0
$459$	−0.907604	+	0.761570i	−0.0423633	+	0.0355470i
$460$		0			0
$461$	−11.0544	−	4.02346i	−0.514854	−	0.187391i	0.0715092	−	0.997440i	$-0.477218\pi$
$461$	−11.0544	−	4.02346i	−0.514854	−	0.187391i	−0.586363	+	0.810049i	$0.699441\pi$
$462$		0			0
$463$	8.49660	−	14.7165i	0.394870	−	0.683935i	−0.598214	−	0.801336i	$-0.704123\pi$
$463$	8.49660	−	14.7165i	0.394870	−	0.683935i	0.993085	+	0.117401i	$0.0374562\pi$
$464$		0			0
$465$	3.91921	−	22.2270i	0.181749	−	1.03075i
$466$		0			0
$467$	−5.85251	−	10.1368i	−0.270822	−	0.469077i	0.698251	−	0.715853i	$-0.253962\pi$
$467$	−5.85251	−	10.1368i	−0.270822	−	0.469077i	−0.969073	+	0.246776i	$0.920629\pi$
$468$		0			0
$469$	−2.65064	−	2.22415i	−0.122395	−	0.102702i
$470$		0			0
$471$	5.89306	−	2.14490i	0.271538	−	0.0988316i
$472$		0			0
$473$	−2.47044	−	14.0105i	−0.113591	−	0.644206i
$474$		0			0
$475$	27.9923	−	7.32580i	1.28438	−	0.336131i
$476$		0			0
$477$	0.109470	+	0.620838i	0.00501231	+	0.0284262i
$478$		0			0
$479$	28.1716	−	10.2536i	1.28719	−	0.468500i	0.394388	−	0.918944i	$-0.370957\pi$
$479$	28.1716	−	10.2536i	1.28719	−	0.468500i	0.892805	+	0.450444i	$0.148734\pi$
$480$		0			0
$481$	14.0667	+	11.8034i	0.641386	+	0.538187i
$482$		0			0
$483$	8.32295	+	14.4158i	0.378707	+	0.655940i
$484$		0			0
$485$	−4.22122	+	23.9397i	−0.191676	+	1.08705i
$486$		0			0
$487$	7.25537	−	12.5667i	0.328772	−	0.569450i	−0.653496	−	0.756930i	$-0.726699\pi$
$487$	7.25537	−	12.5667i	0.328772	−	0.569450i	0.982268	+	0.187480i	$0.0600319\pi$
$488$		0			0
$489$	18.1348	+	6.60051i	0.820082	+	0.298485i
$490$		0			0
$491$	8.92855	−	7.49194i	0.402940	−	0.338107i	−0.418689	−	0.908130i	$-0.637510\pi$
$491$	8.92855	−	7.49194i	0.402940	−	0.338107i	0.821629	+	0.570023i	$0.193066\pi$
$492$		0			0
$493$	4.47060			0.201346
$494$		0			0
$495$	11.6382			0.523096
$496$		0			0
$497$	−29.7460	+	24.9599i	−1.33429	+	1.11960i
$498$		0			0
$499$	−1.58512	−	0.576937i	−0.0709598	−	0.0258273i	0.306296	−	0.951936i	$-0.400910\pi$
$499$	−1.58512	−	0.576937i	−0.0709598	−	0.0258273i	−0.377256	+	0.926109i	$0.623132\pi$
$500$		0			0
$501$	3.86097	−	6.68739i	0.172495	−	0.298771i
$502$		0			0
$503$	−3.00299	+	17.0308i	−0.133897	+	0.759367i	0.841725	+	0.539907i	$0.181541\pi$
$503$	−3.00299	+	17.0308i	−0.133897	+	0.759367i	−0.975622	+	0.219460i	$0.929571\pi$
$504$		0			0
$505$	7.92468	+	13.7259i	0.352644	+	0.610797i
$506$		0			0
$507$	4.30406	+	3.61154i	0.191150	+	0.160394i
$508$		0			0
$509$	−30.4859	+	11.0960i	−1.35126	+	0.491820i	−0.913342	−	0.407193i	$-0.866508\pi$
$509$	−30.4859	+	11.0960i	−1.35126	+	0.491820i	−0.437922	+	0.899013i	$0.644286\pi$
$510$		0			0
$511$	−10.7981	−	61.2393i	−0.477681	−	2.70907i
$512$		0			0
$513$	4.34002	+	0.405223i	0.191617	+	0.0178910i
$514$		0			0
$515$	7.33527	+	41.6004i	0.323231	+	1.83313i
$516$		0			0
$517$	9.15910	−	3.33364i	0.402817	−	0.146613i
$518$		0			0
$519$	11.1040	+	9.31737i	0.487412	+	0.408987i
$520$		0			0
$521$	−15.5822	−	26.9891i	−0.682668	−	1.18242i	−0.974164	−	0.225843i	$-0.927486\pi$
$521$	−15.5822	−	26.9891i	−0.682668	−	1.18242i	0.291496	−	0.956572i	$-0.405847\pi$
$522$		0			0
$523$	2.89306	−	16.4073i	0.126504	−	0.717443i	−0.853898	−	0.520440i	$-0.825768\pi$
$523$	2.89306	−	16.4073i	0.126504	−	0.717443i	0.980403	−	0.197003i	$-0.0631208\pi$
$524$		0			0
$525$	16.1951	−	28.0507i	0.706810	−	1.22423i
$526$		0			0
$527$	7.36571	+	2.68090i	0.320856	+	0.116782i
$528$		0			0
$529$	−8.70368	+	7.30325i	−0.378421	+	0.317533i
$530$		0			0
$531$	−11.6382			−0.505053
$532$		0			0
$533$	17.8075			0.771327
$534$		0			0
$535$	−10.1894	+	8.54990i	−0.440525	+	0.369645i
$536$		0			0
$537$	9.23055	+	3.35965i	0.398328	+	0.144979i
$538$		0			0
$539$	−28.6707	+	49.6591i	−1.23493	+	2.13897i
$540$		0			0
$541$	6.29385	−	35.6942i	0.270594	−	1.53461i	−0.482025	−	0.876157i	$-0.660099\pi$
$541$	6.29385	−	35.6942i	0.270594	−	1.53461i	0.752619	−	0.658456i	$-0.228790\pi$
$542$		0			0
$543$	9.45723	+	16.3804i	0.405849	+	0.702951i
$544$		0			0
$545$	−30.3050	−	25.4289i	−1.29812	−	1.08925i
$546$		0			0
$547$	−16.1604	+	5.88192i	−0.690971	+	0.251493i	−0.663551	−	0.748131i	$-0.730951\pi$
$547$	−16.1604	+	5.88192i	−0.690971	+	0.251493i	−0.0274199	+	0.999624i	$0.508729\pi$
$548$		0			0
$549$	1.19846	+	6.79682i	0.0511492	+	0.290081i
$550$		0			0
$551$	−11.5621	−	11.6978i	−0.492563	−	0.498342i
$552$		0			0
$553$	−0.252212	−	1.43036i	−0.0107251	−	0.0608253i
$554$		0			0
$555$	21.6668	−	7.88609i	0.919706	−	0.334746i
$556$		0			0
$557$	−12.6932	−	10.6509i	−0.537830	−	0.451293i	0.332965	−	0.942939i	$-0.391951\pi$
$557$	−12.6932	−	10.6509i	−0.537830	−	0.451293i	−0.870795	+	0.491646i	$0.836395\pi$
$558$		0			0
$559$	5.66503	+	9.81212i	0.239605	+	0.415008i
$560$		0			0
$561$	−0.701867	+	3.98048i	−0.0296328	+	0.168056i
$562$		0			0
$563$	−15.3486	+	26.5846i	−0.646868	+	1.12041i	0.336999	+	0.941505i	$0.390588\pi$
$563$	−15.3486	+	26.5846i	−0.646868	+	1.12041i	−0.983867	+	0.178903i	$0.942745\pi$
$564$		0			0
$565$	−6.22193	−	2.26460i	−0.261759	−	0.0952724i
$566$		0			0
$567$	3.73783	−	3.13641i	0.156974	−	0.131717i
$568$		0			0
$569$	13.4534			0.563994			0.281997	−	0.959415i	$-0.409003\pi$
$569$	13.4534			0.563994			0.281997	+	0.959415i	$0.409003\pi$
$570$		0			0
$571$	9.47565			0.396544			0.198272	−	0.980147i	$-0.436467\pi$
$571$	9.47565			0.396544			0.198272	+	0.980147i	$0.436467\pi$
$572$		0			0
$573$	−7.73055	+	6.48670i	−0.322948	+	0.270986i
$574$		0			0
$575$	−21.2802	−	7.74535i	−0.887445	−	0.323004i
$576$		0			0
$577$	9.38191	−	16.2499i	0.390574	−	0.676494i	−0.601951	−	0.798533i	$-0.705610\pi$
$577$	9.38191	−	16.2499i	0.390574	−	0.676494i	0.992525	+	0.122039i	$0.0389432\pi$
$578$		0			0
$579$	−0.438348	+	2.48600i	−0.0182171	+	0.103315i
$580$		0			0
$581$	38.0690	+	65.9374i	1.57937	+	2.73554i
$582$		0			0
$583$	1.64749	+	1.38241i	0.0682320	+	0.0572535i
$584$		0			0
$585$	−8.70961	+	3.17004i	−0.360098	+	0.131065i
$586$		0			0
$587$	3.15611	+	17.8992i	0.130266	+	0.738778i	0.978040	+	0.208419i	$0.0668317\pi$
$587$	3.15611	+	17.8992i	0.130266	+	0.738778i	−0.847773	+	0.530359i	$0.822057\pi$
$588$		0			0
$589$	−12.0348	−	26.2066i	−0.495884	−	1.07983i
$590$		0			0
$591$	−2.57991	−	14.6314i	−0.106123	−	0.601855i
$592$		0			0
$593$	30.7221	−	11.1819i	1.26161	−	0.459187i	0.377298	−	0.926092i	$-0.376853\pi$
$593$	30.7221	−	11.1819i	1.26161	−	0.459187i	0.884307	+	0.466905i	$0.154631\pi$
$594$		0			0
$595$	15.1079	+	12.6770i	0.619363	+	0.519707i
$596$		0			0
$597$	−4.03462	−	6.98816i	−0.165126	−	0.286006i
$598$		0			0
$599$	−1.53343	+	8.69653i	−0.0626544	+	0.355331i	0.937322	+	0.348464i	$0.113297\pi$
$599$	−1.53343	+	8.69653i	−0.0626544	+	0.355331i	−0.999976	+	0.00686632i	$0.997814\pi$
$600$		0			0
$601$	−16.5262	+	28.6241i	−0.674116	+	1.16760i	0.302610	+	0.953114i	$0.402142\pi$
$601$	−16.5262	+	28.6241i	−0.674116	+	1.16760i	−0.976726	+	0.214489i	$0.931191\pi$
$602$		0			0
$603$	0.666374	+	0.242540i	0.0271369	+	0.00987701i
$604$		0			0
$605$	1.66772	−	1.39938i	0.0678024	−	0.0568930i
$606$		0			0
$607$	−5.16250			−0.209540			−0.104770	−	0.994497i	$-0.533411\pi$
$607$	−5.16250			−0.209540			−0.104770	+	0.994497i	$0.533411\pi$
$608$		0			0
$609$	−18.4115			−0.746071
$610$		0			0
$611$	−5.94634	+	4.98957i	−0.240563	+	0.201856i
$612$		0			0
$613$	44.2486	+	16.1052i	1.78718	+	0.650481i	0.999404	+	0.0345227i	$0.0109911\pi$
$613$	44.2486	+	16.1052i	1.78718	+	0.650481i	0.787779	+	0.615959i	$0.211231\pi$
$614$		0			0
$615$	11.1800	−	19.3644i	0.450823	−	0.780848i
$616$		0			0
$617$	−7.36009	+	41.7411i	−0.296306	+	1.68044i	0.365540	+	0.930796i	$0.380884\pi$
$617$	−7.36009	+	41.7411i	−0.296306	+	1.68044i	−0.661846	+	0.749640i	$0.730227\pi$
$618$		0			0
$619$	−0.928081	−	1.60748i	−0.0373027	−	0.0646102i	0.846771	−	0.531957i	$-0.178543\pi$
$619$	−0.928081	−	1.60748i	−0.0373027	−	0.0646102i	−0.884074	+	0.467347i	$0.845210\pi$
$620$		0			0
$621$	−2.61334	−	2.19285i	−0.104870	−	0.0879962i
$622$		0			0
$623$	−31.0565	+	11.3036i	−1.24425	+	0.452871i
$624$		0			0
$625$	−2.45290	−	13.9111i	−0.0981159	−	0.556443i
$626$		0			0
$627$	12.2306	−	8.45805i	0.488441	−	0.337782i
$628$		0			0
$629$	1.39053	+	7.88609i	0.0554440	+	0.314439i
$630$		0			0
$631$	23.1618	−	8.43020i	0.922056	−	0.335601i	0.163000	−	0.986626i	$-0.447883\pi$
$631$	23.1618	−	8.43020i	0.922056	−	0.335601i	0.759056	+	0.651025i	$0.225661\pi$
$632$		0			0
$633$	6.08512	+	5.10602i	0.241862	+	0.202946i
$634$		0			0
$635$	−10.3773	−	17.9741i	−0.411812	−	0.713279i
$636$		0			0
$637$	7.92989	−	44.9727i	0.314194	−	1.78188i
$638$		0			0
$639$	3.97906	−	6.89193i	0.157409	−	0.272640i
$640$		0			0
$641$	−16.5744	−	6.03260i	−0.654651	−	0.238274i	−0.00672584	−	0.999977i	$-0.502141\pi$
$641$	−16.5744	−	6.03260i	−0.654651	−	0.238274i	−0.647925	+	0.761704i	$0.724363\pi$
$642$		0			0
$643$	−22.8653	+	19.1863i	−0.901720	+	0.756633i	−0.970526	−	0.240997i	$-0.922525\pi$
$643$	−22.8653	+	19.1863i	−0.901720	+	0.756633i	0.0688062	+	0.997630i	$0.478081\pi$
$644$		0			0
$645$	14.2267			0.560175
$646$		0			0
$647$	−23.9391			−0.941144			−0.470572	−	0.882362i	$-0.655952\pi$
$647$	−23.9391			−0.941144			−0.470572	+	0.882362i	$0.655952\pi$
$648$		0			0
$649$	−30.4145	+	25.5208i	−1.19387	+	1.00178i
$650$		0			0
$651$	−30.3346	−	11.0409i	−1.18891	−	0.432726i
$652$		0			0
$653$	13.2430	−	22.9376i	0.518240	−	0.897618i	−0.481535	−	0.876427i	$-0.659921\pi$
$653$	13.2430	−	22.9376i	0.518240	−	0.897618i	0.999775	−	0.0211916i	$-0.00674602\pi$
$654$		0			0
$655$	11.0209	−	62.5029i	0.430624	−	2.44219i
$656$		0			0
$657$	6.37211	+	11.0368i	0.248600	+	0.430587i
$658$		0			0
$659$	4.05509	+	3.40263i	0.157964	+	0.132548i	0.718344	−	0.695688i	$-0.244900\pi$
$659$	4.05509	+	3.40263i	0.157964	+	0.132548i	−0.560380	+	0.828236i	$0.689345\pi$
$660$		0			0
$661$	−43.3264	+	15.7695i	−1.68520	+	0.613363i	−0.994008	−	0.109306i	$-0.965137\pi$
$661$	−43.3264	+	15.7695i	−1.68520	+	0.613363i	−0.691194	+	0.722669i	$0.742915\pi$
$662$		0			0
$663$	−0.558963	−	3.17004i	−0.0217083	−	0.123114i
$664$		0			0
$665$	−5.90214	−	72.3173i	−0.228875	−	2.80435i
$666$		0			0
$667$	2.23530	+	12.6770i	0.0865512	+	0.490856i
$668$		0			0
$669$	−11.2464	+	4.09337i	−0.434813	+	0.158259i
$670$		0			0
$671$	18.0364	+	15.1344i	0.696289	+	0.584255i
$672$		0			0
$673$	−1.19072	−	2.06239i	−0.0458990	−	0.0794994i	0.842163	−	0.539223i	$-0.181282\pi$
$673$	−1.19072	−	2.06239i	−0.0458990	−	0.0794994i	−0.888062	+	0.459723i	$0.847949\pi$
$674$		0			0
$675$	−1.15270	+	6.53731i	−0.0443676	+	0.251621i
$676$		0			0
$677$	−7.97431	+	13.8119i	−0.306478	+	0.530835i	−0.977589	−	0.210522i	$-0.932484\pi$
$677$	−7.97431	+	13.8119i	−0.306478	+	0.530835i	0.671112	+	0.741356i	$0.265817\pi$
$678$		0			0
$679$	32.6721	+	11.8917i	1.25384	+	0.456360i
$680$		0			0
$681$	20.3726	−	17.0946i	0.780679	−	0.655067i
$682$		0			0
$683$	1.26083			0.0482443			0.0241222	−	0.999709i	$-0.492321\pi$
$683$	1.26083			0.0482443			0.0241222	+	0.999709i	$0.492321\pi$
$684$		0			0
$685$	15.5107			0.592635
$686$		0			0
$687$	15.2463	−	12.7931i	0.581682	−	0.488089i
$688$		0			0
$689$	−1.60947	−	0.585799i	−0.0613159	−	0.0223172i
$690$		0			0
$691$	−4.05438	+	7.02239i	−0.154236	+	0.267144i	−0.932780	−	0.360445i	$-0.882625\pi$
$691$	−4.05438	+	7.02239i	−0.154236	+	0.267144i	0.778545	+	0.627589i	$0.215958\pi$
$692$		0			0
$693$	2.89053	−	16.3930i	0.109802	−	0.622719i
$694$		0			0
$695$	−5.14203	−	8.90625i	−0.195048	−	0.337833i
$696$		0			0
$697$	5.94878	+	4.99162i	0.225326	+	0.189071i
$698$		0			0
$699$	−4.05051	+	1.47426i	−0.153204	+	0.0557618i
$700$		0			0
$701$	1.77615	+	10.0730i	0.0670842	+	0.380454i	0.999803	+	0.0198489i	$0.00631853\pi$
$701$	1.77615	+	10.0730i	0.0670842	+	0.380454i	−0.932719	+	0.360605i	$0.882570\pi$
$702$		0			0
$703$	17.0385	−	24.0339i	0.642619	−	0.906456i
$704$		0			0
$705$	1.69253	+	9.59883i	0.0637445	+	0.361513i
$706$		0			0
$707$	21.3020	−	7.75330i	0.801144	−	0.291593i
$708$		0			0
$709$	0.156574	+	0.131381i	0.00588026	+	0.00493413i	0.645723	−	0.763572i	$-0.276556\pi$
$709$	0.156574	+	0.131381i	0.00588026	+	0.00493413i	−0.639843	+	0.768506i	$0.721001\pi$
$710$		0			0
$711$	0.148833	+	0.257787i	0.00558168	+	0.00966776i
$712$		0			0
$713$	−3.91921	+	22.2270i	−0.146776	+	0.832407i
$714$		0			0
$715$	−15.8097	+	27.3833i	−0.591251	+	1.02408i
$716$		0			0
$717$	−0.268571	−	0.0977517i	−0.0100300	−	0.00365061i
$718$		0			0
$719$	−12.2103	+	10.2457i	−0.455368	+	0.382099i	−0.841423	−	0.540376i	$-0.818282\pi$
$719$	−12.2103	+	10.2457i	−0.455368	+	0.382099i	0.386055	+	0.922476i	$0.373837\pi$
$720$		0			0
$721$	60.4184			2.25010
$722$		0			0
$723$	−9.56624			−0.355772
$724$		0			0
$725$	19.1878	−	16.1005i	0.712616	−	0.597956i
$726$		0			0
$727$	−29.0959	−	10.5900i	−1.07911	−	0.392762i	−0.259531	−	0.965735i	$-0.583568\pi$
$727$	−29.0959	−	10.5900i	−1.07911	−	0.392762i	−0.819575	+	0.572972i	$0.805790\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−0.857974	+	4.86581i	−0.0317333	+	0.179969i
$732$		0			0
$733$	−1.97906	−	3.42782i	−0.0730981	−	0.126610i	0.827160	−	0.561967i	$-0.189955\pi$
$733$	−1.97906	−	3.42782i	−0.0730981	−	0.126610i	−0.900258	+	0.435358i	$0.856622\pi$
$734$		0			0
$735$	−43.9261	−	36.8584i	−1.62024	−	1.35954i
$736$		0			0
$737$	2.27332	−	0.827420i	0.0837388	−	0.0304784i
$738$		0			0
$739$	4.48070	+	25.4113i	0.164825	+	0.934771i	0.949244	+	0.314540i	$0.101850\pi$
$739$	4.48070	+	25.4113i	0.164825	+	0.934771i	−0.784419	+	0.620231i	$0.787039\pi$
$740$		0			0
$741$	−6.84911	+	9.66112i	−0.251608	+	0.354910i
$742$		0			0
$743$	−5.54189	−	31.4296i	−0.203312	−	1.15304i	−0.900074	−	0.435738i	$-0.856487\pi$
$743$	−5.54189	−	31.4296i	−0.203312	−	1.15304i	0.696761	−	0.717303i	$-0.254624\pi$
$744$		0			0
$745$	−3.79813	+	1.38241i	−0.139153	+	0.0506475i
$746$		0			0
$747$	−11.9534	−	10.0301i	−0.437351	−	0.366981i
$748$		0			0
$749$	9.51233	+	16.4758i	0.347573	+	0.602014i
$750$		0			0
$751$	0.0882212	−	0.500327i	0.00321924	−	0.0182572i	−0.983156	−	0.182769i	$-0.941494\pi$
$751$	0.0882212	−	0.500327i	0.00321924	−	0.0182572i	0.986375	+	0.164512i	$0.0526050\pi$
$752$		0			0
$753$	−14.8439	+	25.7104i	−0.540942	+	0.936938i
$754$		0			0
$755$	−11.6630	−	4.24497i	−0.424459	−	0.154490i
$756$		0			0
$757$	−36.8999	+	30.9627i	−1.34115	+	1.12536i	−0.359822	+	0.933021i	$0.617162\pi$
$757$	−36.8999	+	30.9627i	−1.34115	+	1.12536i	−0.981329	+	0.192338i	$0.938393\pi$
$758$		0			0
$759$	−11.6382			−0.422438
$760$		0			0
$761$	5.15064			0.186711			0.0933554	−	0.995633i	$-0.470241\pi$
$761$	5.15064			0.186711			0.0933554	+	0.995633i	$0.470241\pi$
$762$		0			0
$763$	−43.3448	+	36.3706i	−1.56919	+	1.31671i
$764$		0			0
$765$	−3.79813	−	1.38241i	−0.137322	−	0.0499810i
$766$		0			0
$767$	15.8097	−	27.3833i	0.570857	−	0.988753i
$768$		0			0
$769$	3.39874	−	19.2752i	0.122562	−	0.695081i	−0.860165	−	0.510016i	$-0.829639\pi$
$769$	3.39874	−	19.2752i	0.122562	−	0.695081i	0.982726	−	0.185065i	$-0.0592496\pi$
$770$		0			0
$771$	7.89827	+	13.6802i	0.284449	+	0.492681i
$772$		0			0
$773$	17.1552	+	14.3949i	0.617031	+	0.517750i	0.896869	−	0.442297i	$-0.145836\pi$
$773$	17.1552	+	14.3949i	0.617031	+	0.517750i	−0.279838	+	0.960047i	$0.590281\pi$
$774$		0			0
$775$	41.2686	−	15.0206i	1.48241	−	0.539554i
$776$		0			0
$777$	−5.72668	−	32.4776i	−0.205444	−	1.16513i
$778$		0			0
$779$	−2.32399	−	28.4752i	−0.0832655	−	1.02023i
$780$		0			0
$781$	−4.71436	−	26.7364i	−0.168693	−	0.956705i
$782$		0			0
$783$	3.54576	−	1.29055i	0.126715	−	0.0461205i
$784$		0			0
$785$	16.3889	+	13.7520i	0.584946	+	0.490828i
$786$		0			0
$787$	16.8444	+	29.1753i	0.600437	+	1.03999i	0.992755	+	0.120157i	$0.0383398\pi$
$787$	16.8444	+	29.1753i	0.600437	+	1.03999i	−0.392318	+	0.919830i	$0.628327\pi$
$788$		0			0
$789$	1.88666	−	10.6998i	0.0671668	−	0.380922i
$790$		0			0
$791$	−4.73514	+	8.20150i	−0.168362	+	0.291612i
$792$		0			0
$793$	−17.6202	−	6.41323i	−0.625712	−	0.227740i
$794$		0			0
$795$	−1.64749	+	1.38241i	−0.0584304	+	0.0490289i
$796$		0			0
$797$	−47.8631			−1.69540			−0.847699	−	0.530478i	$-0.822012\pi$
$797$	−47.8631			−1.69540			−0.847699	+	0.530478i	$0.822012\pi$
$798$		0			0
$799$	−3.38507			−0.119755
$800$		0			0
$801$	5.18866	−	4.35381i	0.183332	−	0.153834i
$802$		0			0
$803$	40.8546	+	14.8699i	1.44173	+	0.524746i
$804$		0			0
$805$	−28.3935	+	49.1790i	−1.00074	+	1.73333i
$806$		0			0
$807$	3.00299	−	17.0308i	0.105710	−	0.599513i
$808$		0			0
$809$	1.83703	+	3.18183i	0.0645865	+	0.111867i	0.896510	−	0.443022i	$-0.146094\pi$
$809$	1.83703	+	3.18183i	0.0645865	+	0.111867i	−0.831924	+	0.554890i	$0.812760\pi$
$810$		0			0
$811$	14.3289	+	12.0234i	0.503155	+	0.422197i	0.858713	−	0.512457i	$-0.171265\pi$
$811$	14.3289	+	12.0234i	0.503155	+	0.422197i	−0.355558	+	0.934654i	$0.615709\pi$
$812$		0			0
$813$	−1.35844	+	0.494432i	−0.0476426	+	0.0173405i
$814$		0			0
$815$	11.4324	+	64.8365i	0.400460	+	2.27112i
$816$		0			0
$817$	14.9508	−	10.3393i	0.523064	−	0.361725i
$818$		0			0
$819$	2.30200	+	13.0553i	0.0804385	+	0.456190i
$820$		0			0
$821$	20.9706	−	7.63267i	0.731879	−	0.266382i	0.0509190	−	0.998703i	$-0.483785\pi$
$821$	20.9706	−	7.63267i	0.731879	−	0.266382i	0.680960	+	0.732321i	$0.261563\pi$
$822$		0			0
$823$	20.2264	+	16.9720i	0.705049	+	0.591606i	0.923205	−	0.384307i	$-0.125560\pi$
$823$	20.2264	+	16.9720i	0.705049	+	0.591606i	−0.218156	+	0.975914i	$0.570004\pi$
$824$		0			0
$825$	11.3229	+	19.6119i	0.394214	+	0.682799i
$826$		0			0
$827$	−5.15224	+	29.2198i	−0.179161	+	1.01607i	0.754070	+	0.656794i	$0.228088\pi$
$827$	−5.15224	+	29.2198i	−0.179161	+	1.01607i	−0.933231	+	0.359277i	$0.883023\pi$
$828$		0			0
$829$	−0.884133	+	1.53136i	−0.0307072	+	0.0531864i	−0.880971	−	0.473171i	$-0.843109\pi$
$829$	−0.884133	+	1.53136i	−0.0307072	+	0.0531864i	0.850263	+	0.526357i	$0.176443\pi$
$830$		0			0
$831$	19.9128	+	7.24767i	0.690768	+	0.251419i
$832$		0			0
$833$	15.2554	−	12.8008i	0.528567	−	0.443520i
$834$		0			0
$835$	26.3432			0.911643
$836$		0			0
$837$	6.61587			0.228678
$838$		0			0
$839$	−20.4643	+	17.1716i	−0.706505	+	0.592828i	−0.923616	−	0.383319i	$-0.874781\pi$
$839$	−20.4643	+	17.1716i	−0.706505	+	0.592828i	0.217111	+	0.976147i	$0.430337\pi$
$840$		0			0
$841$	13.8718	+	5.04892i	0.478338	+	0.174101i
$842$		0			0
$843$	−12.1839	+	21.1032i	−0.419636	+	0.726831i
$844$		0			0
$845$	−3.32841	+	18.8764i	−0.114501	+	0.649366i
$846$		0			0
$847$	−1.55690	−	2.69664i	−0.0534958	−	0.0926575i
$848$		0			0
$849$	−3.16044	−	2.65193i	−0.108466	−	0.0910139i
$850$		0			0
$851$	−21.6668	+	7.88609i	−0.742730	+	0.270332i
$852$		0			0
$853$	2.41828	+	13.7148i	0.0828004	+	0.469584i	0.997810	+	0.0661513i	$0.0210720\pi$
$853$	2.41828	+	13.7148i	0.0828004	+	0.469584i	−0.915009	+	0.403433i	$0.867817\pi$
$854$		0			0
$855$	6.20574	+	13.5135i	0.212232	+	0.462151i
$856$		0			0
$857$	−3.41551	−	19.3703i	−0.116671	−	0.661677i	−0.985909	−	0.167282i	$-0.946501\pi$
$857$	−3.41551	−	19.3703i	−0.116671	−	0.661677i	0.869238	−	0.494395i	$-0.164610\pi$
$858$		0			0
$859$	−40.7806	+	14.8429i	−1.39142	+	0.506435i	−0.925619	−	0.378456i	$-0.876455\pi$
$859$	−40.7806	+	14.8429i	−1.39142	+	0.506435i	−0.465799	+	0.884891i	$0.654233\pi$
$860$		0			0
$861$	−24.4991	−	20.5572i	−0.834928	−	0.700588i
$862$		0			0
$863$	−14.7096	−	25.4778i	−0.500721	−	0.867274i	−1.00000		0.000832579i	$-0.999735\pi$
$863$	−14.7096	−	25.4778i	−0.500721	−	0.867274i	0.499279	−	0.866441i	$-0.333598\pi$
$864$		0			0
$865$	−8.58693	+	48.6989i	−0.291964	+	1.65581i
$866$		0			0
$867$	−7.79813	+	13.5068i	−0.264838	+	0.458714i
$868$		0			0
$869$	0.954241	+	0.347315i	0.0323704	+	0.0117819i
$870$		0			0
$871$	−1.47590	+	1.23843i	−0.0500090	+	0.0419625i
$872$		0			0
$873$	−7.12567			−0.241167
$874$		0			0
$875$	27.2686			0.921846
$876$		0			0
$877$	−20.0437	+	16.8187i	−0.676828	+	0.567926i	−0.915077	−	0.403278i	$-0.867871\pi$
$877$	−20.0437	+	16.8187i	−0.676828	+	0.567926i	0.238250	+	0.971204i	$0.423426\pi$
$878$		0			0
$879$	2.61334	+	0.951178i	0.0881458	+	0.0320824i
$880$		0			0
$881$	−11.3143	+	19.5970i	−0.381189	+	0.660240i	−0.991233	−	0.132129i	$-0.957819\pi$
$881$	−11.3143	+	19.5970i	−0.381189	+	0.660240i	0.610043	+	0.792368i	$0.291152\pi$
$882$		0			0
$883$	1.43810	−	8.15587i	0.0483959	−	0.274467i	−0.951001	−	0.309187i	$-0.899943\pi$
$883$	1.43810	−	8.15587i	0.0483959	−	0.274467i	0.999397	+	0.0347205i	$0.0110541\pi$
$884$		0			0
$885$	−19.8516	−	34.3840i	−0.667305	−	1.15581i
$886$		0			0
$887$	−30.9152	−	25.9409i	−1.03803	−	0.871011i	−0.0462457	−	0.998930i	$-0.514726\pi$
$887$	−30.9152	−	25.9409i	−1.03803	−	0.871011i	−0.991785	+	0.127919i	$0.959170\pi$
$888$		0			0
$889$	−27.8949	+	10.1529i	−0.935564	+	0.340517i
$890$		0			0
$891$	0.592396	+	3.35965i	0.0198460	+	0.112552i
$892$		0			0
$893$	8.75465	+	8.85737i	0.292963	+	0.296401i
$894$		0			0
$895$	5.81908	+	33.0016i	0.194510	+	1.10312i
$896$		0			0
$897$	8.70961	−	3.17004i	0.290805	−	0.105844i
$898$		0			0
$899$	−19.1234	−	16.0464i	−0.637800	−	0.535178i
$900$		0			0
$901$	−0.373455	−	0.646844i	−0.0124416	−	0.0215495i
$902$		0			0
$903$	3.53343	−	20.0391i	0.117585	−	0.666859i
$904$		0			0
$905$	−32.2631	+	55.8813i	−1.07246	+	1.85756i
$906$		0			0
$907$	−18.0903	−	6.58434i	−0.600680	−	0.218630i	0.0237404	−	0.999718i	$-0.492442\pi$
$907$	−18.0903	−	6.58434i	−0.600680	−	0.218630i	−0.624420	+	0.781089i	$0.714665\pi$
$908$		0			0
$909$	−3.55896	+	2.98632i	−0.118043	+	0.0990501i
$910$		0			0
$911$	58.7684			1.94708			0.973542	−	0.228510i	$-0.0733853\pi$
$911$	58.7684			1.94708			0.973542	+	0.228510i	$0.0733853\pi$
$912$		0			0
$913$	−53.2327			−1.76174
$914$		0			0
$915$	−18.0364	+	15.1344i	−0.596266	+	0.500326i
$916$		0			0
$917$	−85.3016	−	31.0473i	−2.81691	−	1.02527i
$918$		0			0
$919$	−26.8714	+	46.5426i	−0.886406	+	1.53530i	−0.0423114	+	0.999104i	$0.513472\pi$
$919$	−26.8714	+	46.5426i	−0.886406	+	1.53530i	−0.844094	+	0.536195i	$0.819861\pi$
$920$		0			0
$921$	−4.34524	+	24.6431i	−0.143180	+	0.812017i
$922$		0			0
$923$	10.8106	+	18.7245i	0.355836	+	0.616326i
$924$		0			0
$925$	34.3692	+	28.8392i	1.13005	+	0.948226i
$926$		0			0
$927$	−11.6356	+	4.23502i	−0.382164	+	0.139096i
$928$		0			0
$929$	−5.38981	−	30.5672i	−0.176834	−	1.00288i	−0.936006	−	0.351985i	$-0.885507\pi$
$929$	−5.38981	−	30.5672i	−0.176834	−	1.00288i	0.759171	−	0.650891i	$-0.225604\pi$
$930$		0			0
$931$	−72.9488	−	6.81115i	−2.39080	−	0.223226i
$932$		0			0
$933$	4.16297	+	23.6094i	0.136290	+	0.772936i
$934$		0			0
$935$	−12.9572	+	4.71605i	−0.423747	+	0.154231i
$936$		0			0
$937$	−15.8899	−	13.3332i	−0.519100	−	0.435577i	0.345218	−	0.938523i	$-0.387805\pi$
$937$	−15.8899	−	13.3332i	−0.519100	−	0.435577i	−0.864318	+	0.502946i	$0.832250\pi$
$938$		0			0
$939$	−6.31908	−	10.9450i	−0.206215	−	0.357175i
$940$		0			0
$941$	−2.58095	+	14.6373i	−0.0841365	+	0.477162i	0.913403	+	0.407056i	$0.133445\pi$
$941$	−2.58095	+	14.6373i	−0.0841365	+	0.477162i	−0.997540	+	0.0701055i	$0.977666\pi$
$942$		0			0
$943$	−11.1800	+	19.3644i	−0.364072	+	0.630592i
$944$		0			0
$945$	15.6420	+	5.69323i	0.508835	+	0.185201i
$946$		0			0
$947$	19.3043	−	16.1982i	0.627305	−	0.526371i	−0.272785	−	0.962075i	$-0.587945\pi$
$947$	19.3043	−	16.1982i	0.627305	−	0.526371i	0.900090	+	0.435704i	$0.143500\pi$
$948$		0			0
$949$	−34.6245			−1.12396
$950$		0			0
$951$	14.1334			0.458307
$952$		0			0
$953$	−9.48751	+	7.96097i	−0.307331	+	0.257881i	−0.783388	−	0.621533i	$-0.786510\pi$
$953$	−9.48751	+	7.96097i	−0.307331	+	0.257881i	0.476057	+	0.879414i	$0.342066\pi$
$954$		0			0
$955$	−32.3508	−	11.7747i	−1.04685	−	0.381021i
$956$		0			0
$957$	6.43629	−	11.1480i	0.208056	−	0.360363i
$958$		0			0
$959$	3.85235	−	21.8478i	0.124399	−	0.705501i
$960$		0			0
$961$	−6.38485	−	11.0589i	−0.205963	−	0.356738i
$962$		0			0
$963$	−2.98680	−	2.50622i	−0.0962482	−	0.0807618i
$964$		0			0
$965$	−8.09240	+	2.94539i	−0.260503	+	0.0948155i
$966$		0			0
$967$	0.591929	+	3.35700i	0.0190352	+	0.107954i	0.992845	−	0.119410i	$-0.0381004\pi$
$967$	0.591929	+	3.35700i	0.0190352	+	0.107954i	−0.973810	+	0.227364i	$0.926989\pi$
$968$		0			0
$969$	−4.99613	+	1.30753i	−0.160499	+	0.0420038i
$970$		0			0
$971$	2.41323	+	13.6861i	0.0774442	+	0.439208i	0.998733	+	0.0503282i	$0.0160267\pi$
$971$	2.41323	+	13.6861i	0.0774442	+	0.439208i	−0.921289	+	0.388880i	$0.872862\pi$
$972$		0			0
$973$	−13.8221	+	5.03082i	−0.443115	+	0.161281i
$974$		0			0
$975$	−13.8157	−	11.5927i	−0.442456	−	0.371264i
$976$		0			0
$977$	−6.42009	−	11.1199i	−0.205397	−	0.355758i	0.744862	−	0.667218i	$-0.232515\pi$
$977$	−6.42009	−	11.1199i	−0.205397	−	0.355758i	−0.950259	+	0.311460i	$0.899182\pi$
$978$		0			0
$979$	4.01249	−	22.7560i	0.128240	−	0.727283i
$980$		0			0
$981$	5.79813	−	10.0427i	0.185120	−	0.320638i
$982$		0			0
$983$	−0.814330	−	0.296392i	−0.0259731	−	0.00945343i	0.329001	−	0.944330i	$-0.393288\pi$
$983$	−0.814330	−	0.296392i	−0.0259731	−	0.00945343i	−0.354974	+	0.934876i	$0.615510\pi$
$984$		0			0
$985$	38.8267	−	32.5794i	1.23712	−	1.03807i
$986$		0			0
$987$	13.9409			0.443743
$988$		0			0
$989$	−14.2267			−0.452382
$990$		0			0
$991$	16.0646	−	13.4798i	0.510310	−	0.428201i	−0.350928	−	0.936402i	$-0.614134\pi$
$991$	16.0646	−	13.4798i	0.510310	−	0.428201i	0.861238	+	0.508201i	$0.169689\pi$
$992$		0			0
$993$	−27.7190	−	10.0889i	−0.879636	−	0.320161i
$994$		0			0
$995$	13.7640	−	23.8399i	0.436348	−	0.755776i
$996$		0			0
$997$	6.90208	−	39.1437i	0.218591	−	1.23969i	−0.655974	−	0.754784i	$-0.727742\pi$
$997$	6.90208	−	39.1437i	0.218591	−	1.23969i	0.874565	−	0.484909i	$-0.161147\pi$
$998$		0			0
$999$	3.37939	+	5.85327i	0.106919	+	0.185189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.a.769.1		6
4.3	odd	2		114.2.i.a.85.1	yes	6
12.11	even	2		342.2.u.e.199.1		6
19.17	even	9	inner	912.2.bo.a.625.1		6
76.51	even	18		2166.2.a.s.1.3		3
76.55	odd	18		114.2.i.a.55.1	✓	6
76.63	odd	18		2166.2.a.q.1.3		3
228.131	even	18		342.2.u.e.55.1		6
228.203	odd	18		6498.2.a.bm.1.1		3
228.215	even	18		6498.2.a.br.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.55.1	✓	6	76.55	odd	18
114.2.i.a.85.1	yes	6	4.3	odd	2
342.2.u.e.55.1		6	228.131	even	18
342.2.u.e.199.1		6	12.11	even	2
912.2.bo.a.625.1		6	19.17	even	9	inner
912.2.bo.a.769.1		6	1.1	even	1	trivial
2166.2.a.q.1.3		3	76.63	odd	18
2166.2.a.s.1.3		3	76.51	even	18
6498.2.a.bm.1.1		3	228.203	odd	18
6498.2.a.br.1.1		3	228.215	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{3} +(-3.20574 - 1.16679i) q^{5} +(-2.43969 + 4.22567i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{3} +(-3.20574 - 1.16679i) q^{5} +(-2.43969 + 4.22567i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-1.70574 - 2.95442i) q^{11} +(2.08125 + 1.74638i) q^{13} +(3.20574 - 1.16679i) q^{15} +(0.205737 + 1.16679i) q^{17} +(2.52094 - 3.55596i) q^{19} +(-0.847296 - 4.80526i) q^{21} +(-3.20574 + 1.16679i) q^{23} +(5.08512 + 4.26692i) q^{25} +(0.500000 + 0.866025i) q^{27} +(0.655230 - 3.71599i) q^{29} +(3.30793 - 5.72951i) q^{31} +(3.20574 + 1.16679i) q^{33} +(12.7515 - 10.6998i) q^{35} +6.75877 q^{37} -2.71688 q^{39} +(5.02094 - 4.21307i) q^{41} +(3.91875 + 1.42631i) q^{43} +(-1.70574 + 2.95442i) q^{45} +(-0.496130 + 2.81369i) q^{47} +(-8.40420 - 14.5565i) q^{49} +(-0.907604 - 0.761570i) q^{51} +(-0.592396 + 0.215615i) q^{53} +(2.02094 + 11.4613i) q^{55} +(0.354570 + 4.34445i) q^{57} +(-2.02094 - 11.4613i) q^{59} +(-6.48545 + 2.36051i) q^{61} +(3.73783 + 3.13641i) q^{63} +(-4.63429 - 8.02682i) q^{65} +(-0.123141 + 0.698367i) q^{67} +(1.70574 - 2.95442i) q^{69} +(7.47818 + 2.72183i) q^{71} +(-9.76264 + 8.19183i) q^{73} -6.63816 q^{75} +16.6459 q^{77} +(-0.228026 + 0.191336i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(7.80200 - 13.5135i) q^{83} +(0.701867 - 3.98048i) q^{85} +(1.88666 + 3.26779i) q^{87} +(5.18866 + 4.35381i) q^{89} +(-12.4572 + 4.53406i) q^{91} +(1.14883 + 6.51536i) q^{93} +(-12.2306 + 8.45805i) q^{95} +(-1.23736 - 7.01741i) q^{97} +(-3.20574 + 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} - 9 q^{7}+O(q^{10}) \) 6 * q - 9 * q^5 - 9 * q^7	\( 6 q - 9 q^{5} - 9 q^{7} + 15 q^{13} + 9 q^{15} - 9 q^{17} + 12 q^{19} - 3 q^{21} - 9 q^{23} + 9 q^{25} + 3 q^{27} - 9 q^{29} + 9 q^{31} + 9 q^{33} + 36 q^{35} + 18 q^{37} + 27 q^{41} + 21 q^{43} - 27 q^{47} - 12 q^{49} - 9 q^{51} + 9 q^{55} + 18 q^{57} - 9 q^{59} - 3 q^{61} + 3 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{71} - 12 q^{73} - 6 q^{75} + 18 q^{77} + 21 q^{79} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 24 q^{91} + 33 q^{93} - 36 q^{95} - 54 q^{97} - 9 q^{99}+O(q^{100}) \) 6 * q - 9 * q^5 - 9 * q^7 + 15 * q^13 + 9 * q^15 - 9 * q^17 + 12 * q^19 - 3 * q^21 - 9 * q^23 + 9 * q^25 + 3 * q^27 - 9 * q^29 + 9 * q^31 + 9 * q^33 + 36 * q^35 + 18 * q^37 + 27 * q^41 + 21 * q^43 - 27 * q^47 - 12 * q^49 - 9 * q^51 + 9 * q^55 + 18 * q^57 - 9 * q^59 - 3 * q^61 + 3 * q^63 - 18 * q^65 + 3 * q^67 - 9 * q^71 - 12 * q^73 - 6 * q^75 + 18 * q^77 + 21 * q^79 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 24 * q^91 + 33 * q^93 - 36 * q^95 - 54 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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