LMFDB - Embedded newform 603.2.g.h.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(37,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("603.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.g (of order $3$, degree $2$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11x^{10} + 89x^{8} + 326x^{6} + 881x^{4} + 416x^{2} + 169 $ x^12 + 11x^10 + 89x^8 + 326x^6 + 881x^4 + 416*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.5
Root			$-1.04923 - 1.81733i$ of defining polynomial
Character	$\chi$	$=$	603.37
Dual form			603.2.g.h.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04923 + 1.81733i) q^{2} +(-1.20179 + 2.08156i) q^{4} -1.25158 q^{5} +(-1.51499 + 2.62404i) q^{7} -0.846891 q^{8} +O(q^{10})$	\(q+(1.04923 + 1.81733i) q^{2} +(-1.20179 + 2.08156i) q^{4} -1.25158 q^{5} +(-1.51499 + 2.62404i) q^{7} -0.846891 q^{8} +(-1.31320 - 2.27453i) q^{10} +(-2.09847 + 3.63466i) q^{11} +(-0.798212 - 1.38254i) q^{13} -6.35831 q^{14} +(1.51499 + 2.62404i) q^{16} +(0.423446 + 0.733429i) q^{17} +(-3.21678 - 5.57162i) q^{19} +(1.50413 - 2.60523i) q^{20} -8.80715 q^{22} +(2.97681 + 5.15599i) q^{23} -3.43355 q^{25} +(1.67502 - 2.90123i) q^{26} +(-3.64139 - 6.30707i) q^{28} +(-3.60260 + 6.23989i) q^{29} +(4.02998 - 6.98012i) q^{31} +(-4.02605 + 6.97332i) q^{32} +(-0.888588 + 1.53908i) q^{34} +(1.89613 - 3.28419i) q^{35} +(1.23176 + 2.13348i) q^{37} +(6.75031 - 11.6919i) q^{38} +1.05995 q^{40} +(-2.55337 + 4.42256i) q^{41} +0.596424 q^{43} +(-5.04383 - 8.73617i) q^{44} +(-6.24675 + 10.8197i) q^{46} +(1.30179 - 2.25476i) q^{47} +(-1.09038 - 1.88859i) q^{49} +(-3.60260 - 6.23989i) q^{50} +3.83713 q^{52} +7.54699 q^{53} +(2.62640 - 4.54906i) q^{55} +(1.28303 - 2.22227i) q^{56} -15.1199 q^{58} +10.5553 q^{59} +(3.51499 + 6.08814i) q^{61} +16.9136 q^{62} -10.8371 q^{64} +(0.999025 + 1.73036i) q^{65} +(7.32819 + 3.64660i) q^{67} -2.03557 q^{68} +7.95793 q^{70} +(2.97681 - 5.15599i) q^{71} +(4.92461 + 8.52968i) q^{73} +(-2.58482 + 4.47704i) q^{74} +15.4635 q^{76} +(-6.35831 - 11.0129i) q^{77} +(4.60536 - 7.97672i) q^{79} +(-1.89613 - 3.28419i) q^{80} -10.7163 q^{82} +(1.67502 + 2.90123i) q^{83} +(-0.529975 - 0.917944i) q^{85} +(0.625789 + 1.08390i) q^{86} +(1.77718 - 3.07816i) q^{88} +8.89899 q^{89} +4.83713 q^{91} -14.3100 q^{92} +5.46353 q^{94} +(4.02605 + 6.97332i) q^{95} +(3.88859 + 6.73523i) q^{97} +(2.28812 - 3.96314i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^7	$ 12 q - 10 q^{4} + 6 q^{7} + 4 q^{10} - 14 q^{13} - 6 q^{16} - 10 q^{19} - 88 q^{22} + 16 q^{25} + 20 q^{28} - 26 q^{34} - 38 q^{37} - 84 q^{40} + 16 q^{43} + 2 q^{46} - 24 q^{49} - 20 q^{52} - 8 q^{55} + 12 q^{58} + 18 q^{61} - 64 q^{64} + 44 q^{67} + 148 q^{70} + 24 q^{73} + 80 q^{76} + 42 q^{79} + 56 q^{82} + 42 q^{85} + 52 q^{88} - 8 q^{91} - 40 q^{94} + 62 q^{97}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^7 + 4 * q^10 - 14 * q^13 - 6 * q^16 - 10 * q^19 - 88 * q^22 + 16 * q^25 + 20 * q^28 - 26 * q^34 - 38 * q^37 - 84 * q^40 + 16 * q^43 + 2 * q^46 - 24 * q^49 - 20 * q^52 - 8 * q^55 + 12 * q^58 + 18 * q^61 - 64 * q^64 + 44 * q^67 + 148 * q^70 + 24 * q^73 + 80 * q^76 + 42 * q^79 + 56 * q^82 + 42 * q^85 + 52 * q^88 - 8 * q^91 - 40 * q^94 + 62 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.04923	+	1.81733i	0.741921	+	1.28505i	0.951619	+	0.307279i	$0.0994185\pi$
$2$	1.04923	+	1.81733i	0.741921	+	1.28505i	−0.209698	+	0.977766i	$0.567248\pi$
$3$		0			0
$3$		0			0
$4$	−1.20179	+	2.08156i	−0.600894	+	1.04078i
$5$	−1.25158			−0.559723			−0.279861	−	0.960040i	$-0.590289\pi$
$5$	−1.25158			−0.559723			−0.279861	+	0.960040i	$0.590289\pi$
$6$		0			0
$7$	−1.51499	+	2.62404i	−0.572612	+	0.991792i	0.423685	+	0.905810i	$0.360736\pi$
$7$	−1.51499	+	2.62404i	−0.572612	+	0.991792i	−0.996297	+	0.0859827i	$0.972597\pi$
$8$	−0.846891			−0.299421
$9$		0			0
$10$	−1.31320	−	2.27453i	−0.415270	−	0.719269i
$11$	−2.09847	+	3.63466i	−0.632712	+	1.09589i	0.354282	+	0.935138i	$0.384725\pi$
$11$	−2.09847	+	3.63466i	−0.632712	+	1.09589i	−0.986995	+	0.160752i	$0.948608\pi$
$12$		0			0
$13$	−0.798212	−	1.38254i	−0.221384	−	0.383449i	0.733844	−	0.679318i	$-0.237724\pi$
$13$	−0.798212	−	1.38254i	−0.221384	−	0.383449i	−0.955229	+	0.295869i	$0.904391\pi$
$14$	−6.35831			−1.69933
$15$		0			0
$16$	1.51499	+	2.62404i	0.378747	+	0.656009i
$17$	0.423446	+	0.733429i	0.102701	+	0.177883i	0.912796	−	0.408415i	$-0.133918\pi$
$17$	0.423446	+	0.733429i	0.102701	+	0.177883i	−0.810096	+	0.586298i	$0.800585\pi$
$18$		0			0
$19$	−3.21678	−	5.57162i	−0.737979	−	1.27822i	−0.953404	−	0.301697i	$-0.902447\pi$
$19$	−3.21678	−	5.57162i	−0.737979	−	1.27822i	0.215425	−	0.976520i	$-0.430886\pi$
$20$	1.50413	−	2.60523i	0.336334	−	0.582548i
$21$		0			0
$22$	−8.80715			−1.87769
$23$	2.97681	+	5.15599i	0.620708	+	1.07510i	0.989354	+	0.145528i	$0.0464882\pi$
$23$	2.97681	+	5.15599i	0.620708	+	1.07510i	−0.368646	+	0.929570i	$0.620178\pi$
$24$		0			0
$25$	−3.43355			−0.686710
$26$	1.67502	−	2.90123i	0.328499	−	0.568977i
$27$		0			0
$28$	−3.64139	−	6.30707i	−0.688158	−	1.19192i
$29$	−3.60260	+	6.23989i	−0.668986	+	1.15872i	0.309202	+	0.950997i	$0.399938\pi$
$29$	−3.60260	+	6.23989i	−0.668986	+	1.15872i	−0.978188	+	0.207722i	$0.933395\pi$
$30$		0			0
$31$	4.02998	−	6.98012i	0.723805	−	1.25367i	−0.235659	−	0.971836i	$-0.575725\pi$
$31$	4.02998	−	6.98012i	0.723805	−	1.25367i	0.959464	−	0.281831i	$-0.0909418\pi$
$32$	−4.02605	+	6.97332i	−0.711711	+	1.23272i
$33$		0			0
$34$	−0.888588	+	1.53908i	−0.152392	+	0.263950i
$35$	1.89613	−	3.28419i	0.320504	−	0.555129i
$36$		0			0
$37$	1.23176	+	2.13348i	0.202501	+	0.350741i	0.949334	−	0.314270i	$-0.101760\pi$
$37$	1.23176	+	2.13348i	0.202501	+	0.350741i	−0.746833	+	0.665012i	$0.768427\pi$
$38$	6.75031	−	11.6919i	1.09504	−	1.89667i
$39$		0			0
$40$	1.05995			0.167593
$41$	−2.55337	+	4.42256i	−0.398769	+	0.690688i	−0.993574	−	0.113182i	$-0.963896\pi$
$41$	−2.55337	+	4.42256i	−0.398769	+	0.690688i	0.594805	+	0.803870i	$0.297229\pi$
$42$		0			0
$43$	0.596424			0.0909539			0.0454769	−	0.998965i	$-0.485519\pi$
$43$	0.596424			0.0909539			0.0454769	+	0.998965i	$0.485519\pi$
$44$	−5.04383	−	8.73617i	−0.760386	−	1.31703i
$45$		0			0
$46$	−6.24675	+	10.8197i	−0.921033	+	1.59528i
$47$	1.30179	−	2.25476i	0.189885	−	0.328891i	−0.755327	−	0.655349i	$-0.772522\pi$
$47$	1.30179	−	2.25476i	0.189885	−	0.328891i	0.945212	+	0.326458i	$0.105855\pi$
$48$		0			0
$49$	−1.09038	−	1.88859i	−0.155768	−	0.269798i
$50$	−3.60260	−	6.23989i	−0.509485	−	0.882454i
$51$		0			0
$52$	3.83713			0.532114
$53$	7.54699			1.03666			0.518329	−	0.855181i	$-0.326554\pi$
$53$	7.54699			1.03666			0.518329	+	0.855181i	$0.326554\pi$
$54$		0			0
$55$	2.62640	−	4.54906i	0.354144	−	0.613395i
$56$	1.28303	−	2.22227i	0.171452	−	0.296964i
$57$		0			0
$58$	−15.1199			−1.98534
$59$	10.5553			1.37418			0.687088	−	0.726574i	$-0.258889\pi$
$59$	10.5553			1.37418			0.687088	+	0.726574i	$0.258889\pi$
$60$		0			0
$61$	3.51499	+	6.08814i	0.450048	+	0.779506i	0.998388	−	0.0567491i	$-0.0180735\pi$
$61$	3.51499	+	6.08814i	0.450048	+	0.779506i	−0.548340	+	0.836255i	$0.684740\pi$
$62$	16.9136			2.14802
$63$		0			0
$64$	−10.8371			−1.35464
$65$	0.999025	+	1.73036i	0.123914	+	0.214625i
$66$		0			0
$67$	7.32819	+	3.64660i	0.895281	+	0.445503i
$67$	7.32819	+	3.64660i	0.895281	+	0.445503i
$68$	−2.03557			−0.246849
$69$		0			0
$70$	7.95793			0.951154
$71$	2.97681	−	5.15599i	0.353283	−	0.611903i	−0.633540	−	0.773710i	$-0.718399\pi$
$71$	2.97681	−	5.15599i	0.353283	−	0.611903i	0.986822	+	0.161807i	$0.0517321\pi$
$72$		0			0
$73$	4.92461	+	8.52968i	0.576382	+	0.998323i	0.995890	+	0.0905716i	$0.0288694\pi$
$73$	4.92461	+	8.52968i	0.576382	+	0.998323i	−0.419508	+	0.907752i	$0.637797\pi$
$74$	−2.58482	+	4.47704i	−0.300479	+	0.520445i
$75$		0			0
$76$	15.4635			1.77379
$77$	−6.35831	−	11.0129i	−0.724597	−	1.25504i
$78$		0			0
$79$	4.60536	−	7.97672i	0.518144	−	0.897452i	−0.481634	−	0.876372i	$-0.659957\pi$
$79$	4.60536	−	7.97672i	0.518144	−	0.897452i	0.999778	−	0.0210790i	$-0.00671016\pi$
$80$	−1.89613	−	3.28419i	−0.211993	−	0.367183i
$81$		0			0
$82$	−10.7163			−1.18342
$83$	1.67502	+	2.90123i	0.183858	+	0.318451i	0.943191	−	0.332251i	$-0.107808\pi$
$83$	1.67502	+	2.90123i	0.183858	+	0.318451i	−0.759333	+	0.650702i	$0.774475\pi$
$84$		0			0
$85$	−0.529975	−	0.917944i	−0.0574839	−	0.0995651i
$86$	0.625789	+	1.08390i	0.0674806	+	0.116880i
$87$		0			0
$88$	1.77718	−	3.07816i	0.189448	−	0.328133i
$89$	8.89899			0.943291			0.471645	−	0.881788i	$-0.343660\pi$
$89$	8.89899			0.943291			0.471645	+	0.881788i	$0.343660\pi$
$90$		0			0
$91$	4.83713			0.507069
$92$	−14.3100			−1.49192
$93$		0			0
$94$	5.46353			0.563520
$95$	4.02605	+	6.97332i	0.413064	+	0.715447i
$96$		0			0
$97$	3.88859	+	6.73523i	0.394826	+	0.683859i	0.993079	−	0.117448i	$-0.0374714\pi$
$97$	3.88859	+	6.73523i	0.394826	+	0.683859i	−0.598253	+	0.801307i	$0.704138\pi$
$98$	2.28812	−	3.96314i	0.231135	−	0.400338i
$99$		0			0
$100$	4.12640	−	7.14713i	0.412640	−	0.714713i
$101$	−2.18013	+	3.77610i	−0.216931	+	0.375736i	−0.953868	−	0.300226i	$-0.902938\pi$
$101$	−2.18013	+	3.77610i	−0.216931	+	0.375736i	0.736937	+	0.675961i	$0.236271\pi$
$102$		0			0
$103$	6.62035	−	11.4668i	0.652323	−	1.12986i	−0.330235	−	0.943899i	$-0.607128\pi$
$103$	6.62035	−	11.4668i	0.652323	−	1.12986i	0.982558	−	0.185957i	$-0.0595386\pi$
$104$	0.675999	+	1.17086i	0.0662871	+	0.114813i
$105$		0			0
$106$	7.91856	+	13.7154i	0.769119	+	1.33215i
$107$	−14.8526			−1.43586			−0.717928	−	0.696117i	$-0.754909\pi$
$107$	−14.8526			−1.43586			−0.717928	+	0.696117i	$0.754909\pi$
$108$		0			0
$109$	−11.6264			−1.11361			−0.556804	−	0.830644i	$-0.687972\pi$
$109$	−11.6264			−1.11361			−0.556804	+	0.830644i	$0.687972\pi$
$110$	11.0228			1.05099
$111$		0			0
$112$	−9.18075			−0.867499
$113$	1.03048	−	1.78484i	0.0969391	−	0.167903i	−0.813477	−	0.581597i	$-0.802428\pi$
$113$	1.03048	−	1.78484i	0.0969391	−	0.167903i	0.910416	+	0.413693i	$0.135761\pi$
$114$		0			0
$115$	−3.72571	−	6.45313i	−0.347425	−	0.601757i
$116$	−8.65913	−	14.9980i	−0.803980	−	1.39253i
$117$		0			0
$118$	11.0749	+	19.1824i	1.01953	+	1.76588i
$119$	−2.56606			−0.235230
$120$		0			0
$121$	−3.30715	−	5.72815i	−0.300650	−	0.520741i
$122$	−7.37610	+	12.7758i	−0.667800	+	1.15666i
$123$		0			0
$124$	9.68635	+	16.7773i	0.869860	+	1.50664i
$125$	10.5553			0.944090
$126$		0			0
$127$	1.81320	−	3.14055i	0.160895	−	0.278679i	−0.774295	−	0.632825i	$-0.781895\pi$
$127$	1.81320	−	3.14055i	0.160895	−	0.278679i	0.935190	+	0.354146i	$0.115228\pi$
$128$	−3.31860	−	5.74798i	−0.293325	−	0.508054i
$129$		0			0
$130$	−2.09642	+	3.63111i	−0.183869	+	0.318470i
$131$	−16.3456			−1.42812			−0.714059	−	0.700086i	$-0.753145\pi$
$131$	−16.3456			−1.42812			−0.714059	+	0.700086i	$0.753145\pi$
$132$		0			0
$133$	19.4935			1.69030
$134$	1.06193	+	17.1439i	0.0917366	+	1.48100i
$135$		0			0
$136$	−0.358612	−	0.621135i	−0.0307508	−	0.0532619i
$137$	6.80052			0.581007			0.290504	−	0.956874i	$-0.406177\pi$
$137$	6.80052			0.581007			0.290504	+	0.956874i	$0.406177\pi$
$138$		0			0
$139$	−4.58433			−0.388838			−0.194419	−	0.980919i	$-0.562282\pi$
$139$	−4.58433			−0.388838			−0.194419	+	0.980919i	$0.562282\pi$
$140$	4.55748	+	7.89379i	0.385178	+	0.667147i
$141$		0			0
$142$	12.4935			1.04843
$143$	6.70010			0.560290
$144$		0			0
$145$	4.50894	−	7.80971i	0.374447	−	0.648561i
$146$	−10.3341	+	17.8993i	−0.855260	+	1.48135i
$147$		0			0
$148$	−5.92127			−0.486726
$149$	−9.70836			−0.795340			−0.397670	−	0.917529i	$-0.630181\pi$
$149$	−9.70836			−0.795340			−0.397670	+	0.917529i	$0.630181\pi$
$150$		0			0
$151$	−5.55390	−	9.61964i	−0.451970	−	0.782835i	0.546538	−	0.837434i	$-0.315945\pi$
$151$	−5.55390	−	9.61964i	−0.451970	−	0.782835i	−0.998508	+	0.0545989i	$0.982612\pi$
$152$	2.72426	+	4.71856i	0.220967	+	0.382725i
$153$		0			0
$154$	13.3427	−	23.1103i	1.07519	−	1.86228i
$155$	−5.04383	+	8.73617i	−0.405130	+	0.701706i
$156$		0			0
$157$	−5.43355	−	9.41119i	−0.433645	−	0.751094i	0.563539	−	0.826089i	$-0.309439\pi$
$157$	−5.43355	−	9.41119i	−0.433645	−	0.751094i	−0.997184	+	0.0749948i	$0.976106\pi$
$158$	19.3284			1.53769
$159$		0			0
$160$	5.03891	−	8.72766i	0.398361	−	0.689982i
$161$	−18.0393			−1.42170
$162$		0			0
$163$	−6.25569	+	10.8352i	−0.489983	+	0.848676i	−0.999934	−	0.0115277i	$-0.996331\pi$
$163$	−6.25569	+	10.8352i	−0.489983	+	0.848676i	0.509950	+	0.860204i	$0.329664\pi$
$164$	−6.13721	−	10.6300i	−0.479236	−	0.830060i
$165$		0			0
$166$	−3.51499	+	6.08814i	−0.272816	+	0.472531i
$167$	−9.62670	+	16.6739i	−0.744936	+	1.29027i	0.205288	+	0.978702i	$0.434187\pi$
$167$	−9.62670	+	16.6739i	−0.744936	+	1.29027i	−0.950224	+	0.311566i	$0.899146\pi$
$168$		0			0
$169$	5.22571	−	9.05120i	0.401978	−	0.696246i
$170$	1.11214	−	1.92628i	0.0852971	−	0.147739i
$171$		0			0
$172$	−0.716776	+	1.24149i	−0.0546536	+	0.0946629i
$173$	−10.7764	−	18.6652i	−0.819311	−	1.41909i	−0.906191	−	0.422869i	$-0.861023\pi$
$173$	−10.7764	−	18.6652i	−0.819311	−	1.41909i	0.0868796	−	0.996219i	$-0.472310\pi$
$174$		0			0
$175$	5.20179	−	9.00976i	0.393218	−	0.681074i
$176$	−12.7166			−0.958552
$177$		0			0
$178$	9.33713	+	16.1724i	0.699847	+	1.21217i
$179$	9.70836			0.725637			0.362818	−	0.931860i	$-0.381815\pi$
$179$	9.70836			0.725637			0.362818	+	0.931860i	$0.381815\pi$
$180$		0			0
$181$	−10.0300	+	17.3724i	−0.745522	+	1.29128i	0.204428	+	0.978882i	$0.434467\pi$
$181$	−10.0300	+	17.3724i	−0.745522	+	1.29128i	−0.949950	+	0.312401i	$0.898867\pi$
$182$	5.07528	+	8.79065i	0.376205	+	0.651606i
$183$		0			0
$184$	−2.52104	−	4.36656i	−0.185853	−	0.321907i
$185$	−1.54165	−	2.67021i	−0.113344	−	0.196318i
$186$		0			0
$187$	−3.55435			−0.259920
$188$	3.12895	+	5.41949i	0.228202	+	0.395257i
$189$		0			0
$190$	−8.44854	+	14.6333i	−0.612921	+	1.06161i
$191$	10.7951	+	18.6977i	0.781107	+	1.35292i	0.931297	+	0.364260i	$0.118678\pi$
$191$	10.7951	+	18.6977i	0.781107	+	1.35292i	−0.150190	+	0.988657i	$0.547989\pi$
$192$		0			0
$193$	12.8371			0.924037			0.462018	−	0.886870i	$-0.347125\pi$
$193$	12.8371			0.924037			0.462018	+	0.886870i	$0.347125\pi$
$194$	−8.16008	+	14.1337i	−0.585860	+	1.01474i
$195$		0			0
$196$	5.24160			0.374400
$197$	−1.55434	+	2.69220i	−0.110742	+	0.191811i	−0.916070	−	0.401019i	$-0.868656\pi$
$197$	−1.55434	+	2.69220i	−0.110742	+	0.191811i	0.805327	+	0.592830i	$0.201989\pi$
$198$		0			0
$199$	−9.01499	−	15.6144i	−0.639056	−	1.10688i	−0.985640	−	0.168858i	$-0.945992\pi$
$199$	−9.01499	−	15.6144i	−0.639056	−	1.10688i	0.346585	−	0.938019i	$-0.387341\pi$
$200$	2.90784			0.205616
$201$		0			0
$202$	−9.14988			−0.643783
$203$	−10.9158	−	18.9067i	−0.766139	−	1.32699i
$204$		0			0
$205$	3.19574	−	5.53518i	0.223200	−	0.386594i
$206$	27.7852			1.93589
$207$		0			0
$208$	2.41856	−	4.18907i	0.167697	−	0.290460i
$209$	27.0012			1.86771
$210$		0			0
$211$	9.65638	+	16.7253i	0.664772	+	1.15142i	0.979347	+	0.202187i	$0.0648048\pi$
$211$	9.65638	+	16.7253i	0.664772	+	1.15142i	−0.314575	+	0.949233i	$0.601862\pi$
$212$	−9.06988	+	15.7095i	−0.622922	+	1.07893i
$213$		0			0
$214$	−15.5839	−	26.9921i	−1.06529	−	1.84514i
$215$	−0.746472			−0.0509090
$216$		0			0
$217$	12.2107	+	21.1496i	0.828918	+	1.43573i
$218$	−12.1988	−	21.1290i	−0.826209	−	1.43104i
$219$		0			0
$220$	6.31275	+	10.9340i	0.425606	+	0.737170i
$221$	0.675999	−	1.17086i	0.0454726	−	0.0787609i
$222$		0			0
$223$	−20.9570			−1.40339			−0.701693	−	0.712479i	$-0.747572\pi$
$223$	−20.9570			−1.40339			−0.701693	+	0.712479i	$0.747572\pi$
$224$	−12.1988	−	21.1290i	−0.815068	−	1.41174i
$225$		0			0
$226$	4.32485			0.287685
$227$	6.47899	−	11.2219i	0.430026	−	0.744827i	−0.566849	−	0.823822i	$-0.691838\pi$
$227$	6.47899	−	11.2219i	0.430026	−	0.744827i	0.996875	+	0.0789948i	$0.0251711\pi$
$228$		0			0
$229$	10.8461	+	18.7859i	0.716728	+	1.24141i	0.962289	+	0.272029i	$0.0876945\pi$
$229$	10.8461	+	18.7859i	0.716728	+	1.24141i	−0.245561	+	0.969381i	$0.578972\pi$
$230$	7.81830	−	13.5417i	0.515523	−	0.892913i
$231$		0			0
$232$	3.05101	−	5.28451i	0.200309	−	0.346945i
$233$	8.47554	−	14.6801i	0.555251	−	0.961723i	−0.442633	−	0.896703i	$-0.645955\pi$
$233$	8.47554	−	14.6801i	0.555251	−	0.961723i	0.997884	−	0.0650202i	$-0.0207112\pi$
$234$		0			0
$235$	−1.62929	+	2.82201i	−0.106283	+	0.184088i
$236$	−12.6852	+	21.9714i	−0.825734	+	1.43021i
$237$		0			0
$238$	−2.69240	−	4.66337i	−0.174522	−	0.302282i
$239$	9.00091	−	15.5900i	0.582220	−	1.00844i	−0.412995	−	0.910733i	$-0.635517\pi$
$239$	9.00091	−	15.5900i	0.582220	−	1.00844i	0.995216	−	0.0977023i	$-0.0311493\pi$
$240$		0			0
$241$	21.5535			1.38838			0.694190	−	0.719792i	$-0.255763\pi$
$241$	21.5535			1.38838			0.694190	+	0.719792i	$0.255763\pi$
$242$	6.93996	−	12.0204i	0.446117	−	0.772698i
$243$		0			0
$244$	−16.8971			−1.08172
$245$	1.36469	+	2.36371i	0.0871869	+	0.151012i
$246$		0			0
$247$	−5.13534	+	8.89467i	−0.326754	+	0.565954i
$248$	−3.41295	+	5.91140i	−0.216723	+	0.375375i
$249$		0			0
$250$	11.0749	+	19.1824i	0.700441	+	1.21320i
$251$	−0.202344	−	0.350469i	−0.0127718	−	0.0221214i	0.859569	−	0.511020i	$-0.170732\pi$
$251$	−0.202344	−	0.350469i	−0.0127718	−	0.0221214i	−0.872341	+	0.488898i	$0.837399\pi$
$252$		0			0
$253$	−24.9870			−1.57092
$254$	7.60989			0.477487
$255$		0			0
$256$	−3.87315	+	6.70849i	−0.242072	+	0.419281i
$257$	−1.49144	+	2.58325i	−0.0930334	+	0.161139i	−0.908786	−	0.417262i	$-0.862990\pi$
$257$	−1.49144	+	2.58325i	−0.0930334	+	0.161139i	0.815753	+	0.578401i	$0.196323\pi$
$258$		0			0
$259$	−7.46443			−0.463817
$260$	−4.80247			−0.297836
$261$		0			0
$262$	−17.1503	−	29.7052i	−1.05955	−	1.83520i
$263$	−10.3139			−0.635981			−0.317991	−	0.948094i	$-0.603008\pi$
$263$	−10.3139			−0.635981			−0.317991	+	0.948094i	$0.603008\pi$
$264$		0			0
$265$	−9.44565			−0.580242
$266$	20.4533	+	35.4261i	1.25407	+	2.17211i
$267$		0			0
$268$	−16.3975	+	10.8716i	−1.00164	+	0.664089i
$269$	−25.2445			−1.53919			−0.769593	−	0.638534i	$-0.779541\pi$
$269$	−25.2445			−1.53919			−0.769593	+	0.638534i	$0.779541\pi$
$270$		0			0
$271$	2.55435			0.155166			0.0775829	−	0.996986i	$-0.475280\pi$
$271$	2.55435			0.155166			0.0775829	+	0.996986i	$0.475280\pi$
$272$	−1.28303	+	2.22227i	−0.0777951	+	0.134745i
$273$		0			0
$274$	7.13534	+	12.3588i	0.431062	+	0.746621i
$275$	7.20520	−	12.4798i	0.434490	−	0.752559i
$276$		0			0
$277$	1.65638			0.0995219			0.0497610	−	0.998761i	$-0.484154\pi$
$277$	1.65638			0.0995219			0.0497610	+	0.998761i	$0.484154\pi$
$278$	−4.81004	−	8.33123i	−0.288487	−	0.499674i
$279$		0			0
$280$	−1.60581	+	2.78135i	−0.0959657	+	0.166217i
$281$	−8.08355	−	14.0011i	−0.482224	−	0.835236i	0.517568	−	0.855642i	$-0.326838\pi$
$281$	−8.08355	−	14.0011i	−0.482224	−	0.835236i	−0.999792	+	0.0204058i	$0.993504\pi$
$282$		0			0
$283$	13.8792			0.825033			0.412516	−	0.910950i	$-0.364650\pi$
$283$	13.8792			0.825033			0.412516	+	0.910950i	$0.364650\pi$
$284$	7.15499	+	12.3928i	0.424571	+	0.735378i
$285$		0			0
$286$	7.02998	+	12.1763i	0.415691	+	0.719998i
$287$	−7.73664	−	13.4003i	−0.456679	−	0.790992i
$288$		0			0
$289$	8.14139	−	14.1013i	0.478905	−	0.829488i
$290$	18.9237			1.11124
$291$		0			0
$292$	−23.6734			−1.38538
$293$	10.5553			0.616644			0.308322	−	0.951282i	$-0.400233\pi$
$293$	10.5553			0.616644			0.308322	+	0.951282i	$0.400233\pi$
$294$		0			0
$295$	−13.2107			−0.769158
$296$	−1.04317	−	1.80682i	−0.0606330	−	0.105019i
$297$		0			0
$298$	−10.1864	−	17.6433i	−0.590079	−	1.02205i
$299$	4.75226	−	8.23115i	0.274830	−	0.476020i
$300$		0			0
$301$	−0.903576	+	1.56504i	−0.0520812	+	0.0902073i
$302$	11.6547	−	20.1865i	0.670652	−	1.16160i
$303$		0			0
$304$	9.74675	−	16.8819i	0.559015	−	0.968242i
$305$	−4.39928	−	7.61978i	−0.251902	−	0.436307i
$306$		0			0
$307$	−12.8432	−	22.2450i	−0.732999	−	1.26959i	−0.955596	−	0.294681i	$-0.904787\pi$
$307$	−12.8432	−	22.2450i	−0.732999	−	1.26959i	0.222597	−	0.974911i	$-0.428547\pi$
$308$	30.5654			1.74162
$309$		0			0
$310$	−21.1687			−1.20230
$311$	−9.84630			−0.558332			−0.279166	−	0.960243i	$-0.590058\pi$
$311$	−9.84630			−0.558332			−0.279166	+	0.960243i	$0.590058\pi$
$312$		0			0
$313$	9.03576			0.510731			0.255366	−	0.966845i	$-0.417804\pi$
$313$	9.03576			0.510731			0.255366	+	0.966845i	$0.417804\pi$
$314$	11.4021	−	19.7491i	0.643460	−	1.11451i
$315$		0			0
$316$	11.0693	+	19.1727i	0.622699	+	1.07855i
$317$	−3.92563	−	6.79939i	−0.220485	−	0.381892i	0.734470	−	0.678641i	$-0.237431\pi$
$317$	−3.92563	−	6.79939i	−0.220485	−	0.381892i	−0.954955	+	0.296749i	$0.904097\pi$
$318$		0			0
$319$	−15.1199	−	26.1884i	−0.846552	−	1.46627i
$320$	13.5635			0.758224
$321$		0			0
$322$	−18.9275	−	32.7834i	−1.05479	−	1.82695i
$323$	2.72426	−	4.71856i	0.151582	−	0.262547i
$324$		0			0
$325$	2.74070	+	4.74704i	0.152027	+	0.263318i
$326$	−26.2548			−1.45412
$327$		0			0
$328$	2.16242	−	3.74543i	0.119400	−	0.206807i
$329$	3.94439	+	6.83188i	0.217461	+	0.376654i
$330$		0			0
$331$	15.7646	−	27.3051i	0.866502	−	1.50083i	0.000954748	−	1.00000i	$-0.499696\pi$
$331$	15.7646	−	27.3051i	0.866502	−	1.50083i	0.865548	−	0.500827i	$-0.166971\pi$
$332$	−8.05209			−0.441916
$333$		0			0
$334$	−40.4027			−2.21074
$335$	−9.17180	−	4.56400i	−0.501109	−	0.249358i
$336$		0			0
$337$	9.15033	+	15.8488i	0.498450	+	0.863341i	0.999998	−	0.00178880i	$-0.000569393\pi$
$337$	9.15033	+	15.8488i	0.498450	+	0.863341i	−0.501548	+	0.865130i	$0.667236\pi$
$338$	21.9320			1.19294
$339$		0			0
$340$	2.54767			0.138167
$341$	16.9136	+	29.2952i	0.915921	+	1.58642i
$342$		0			0
$343$	−14.6022			−0.788445
$344$	−0.505107			−0.0272335
$345$		0			0
$346$	22.6139	−	39.1683i	1.21573	−	2.10570i
$347$	18.1337	−	31.4085i	0.973468	−	1.68610i	0.288565	−	0.957460i	$-0.406822\pi$
$347$	18.1337	−	31.4085i	0.973468	−	1.68610i	0.684902	−	0.728635i	$-0.259845\pi$
$348$		0			0
$349$	−26.1199			−1.39817			−0.699083	−	0.715040i	$-0.746408\pi$
$349$	−26.1199			−1.39817			−0.699083	+	0.715040i	$0.746408\pi$
$350$	21.8316			1.16695
$351$		0			0
$352$	−16.8971	−	29.2666i	−0.900617	−	1.55991i
$353$	−1.18111	−	2.04573i	−0.0628639	−	0.108883i	0.832881	−	0.553453i	$-0.186690\pi$
$353$	−1.18111	−	2.04573i	−0.0628639	−	0.108883i	−0.895744	+	0.444569i	$0.853357\pi$
$354$		0			0
$355$	−3.72571	+	6.45313i	−0.197740	+	0.342496i
$356$	−10.6947	+	18.5238i	−0.566818	+	0.981757i
$357$		0			0
$358$	10.1864	+	17.6433i	0.538365	+	0.932476i
$359$	−6.55915			−0.346179			−0.173089	−	0.984906i	$-0.555375\pi$
$359$	−6.55915			−0.346179			−0.173089	+	0.984906i	$0.555375\pi$
$360$		0			0
$361$	−11.1953	+	19.3908i	−0.589226	+	1.02057i
$362$	−42.0952			−2.21247
$363$		0			0
$364$	−5.81320	+	10.0688i	−0.304694	+	0.527746i
$365$	−6.16354	−	10.6756i	−0.322614	−	0.558784i
$366$		0			0
$367$	1.36466	−	2.36366i	0.0712347	−	0.123382i	−0.828208	−	0.560421i	$-0.810639\pi$
$367$	1.36466	−	2.36366i	0.0712347	−	0.123382i	0.899443	+	0.437039i	$0.143973\pi$
$368$	−9.01967	+	15.6225i	−0.470183	+	0.814380i
$369$		0			0
$370$	3.23510	−	5.60336i	0.168185	−	0.291305i
$371$	−11.4336	+	19.8036i	−0.593603	+	1.02815i
$372$		0			0
$373$	9.65638	−	16.7253i	0.499988	−	0.866005i	−0.500012	−	0.866019i	$-0.666671\pi$
$373$	9.65638	−	16.7253i	0.499988	−	0.866005i	1.00000		1.36691e-5i	$4.35101e-6\pi$
$374$	−3.72935	−	6.45942i	−0.192840	−	0.334009i
$375$		0			0
$376$	−1.10247	+	1.90954i	−0.0568557	+	0.0984770i
$377$	11.5026			0.592412
$378$		0			0
$379$	17.0689	+	29.5642i	0.876770	+	1.51861i	0.854865	+	0.518850i	$0.173640\pi$
$379$	17.0689	+	29.5642i	0.876770	+	1.51861i	0.0219048	+	0.999760i	$0.493027\pi$
$380$	−19.3538			−0.992830
$381$		0			0
$382$	−22.6532	+	39.2365i	−1.15904	+	2.00752i
$383$	5.05652	+	8.75816i	0.258376	+	0.447521i	0.965807	−	0.259262i	$-0.0834792\pi$
$383$	5.05652	+	8.75816i	0.258376	+	0.447521i	−0.707431	+	0.706783i	$0.750146\pi$
$384$		0			0
$385$	7.95793	+	13.7835i	0.405574	+	0.702474i
$386$	13.4692	+	23.3293i	0.685562	+	1.18743i
$387$		0			0
$388$	−18.6930			−0.948995
$389$	13.4002	+	23.2098i	0.679417	+	1.17678i	0.975157	+	0.221516i	$0.0711005\pi$
$389$	13.4002	+	23.2098i	0.679417	+	1.17678i	−0.295740	+	0.955268i	$0.595566\pi$
$390$		0			0
$391$	−2.52104	+	4.36656i	−0.127494	+	0.220827i
$392$	0.923430	+	1.59943i	0.0466402	+	0.0807833i
$393$		0			0
$394$	−6.52348			−0.328648
$395$	−5.76397	+	9.98350i	−0.290017	+	0.502324i
$396$		0			0
$397$	20.0049			1.00402			0.502008	−	0.864863i	$-0.332595\pi$
$397$	20.0049			1.00402			0.502008	+	0.864863i	$0.332595\pi$
$398$	18.9177	−	32.7664i	0.948258	−	1.64243i
$399$		0			0
$400$	−5.20179	−	9.00976i	−0.260089	−	0.450488i
$401$	−27.1797			−1.35729			−0.678644	−	0.734467i	$-0.737432\pi$
$401$	−27.1797			−1.35729			−0.678644	+	0.734467i	$0.737432\pi$
$402$		0			0
$403$	−12.8671			−0.640956
$404$	−5.24011	−	9.07614i	−0.260705	−	0.451555i
$405$		0			0
$406$	22.9065	−	39.6752i	1.13683	−	1.96905i
$407$	−10.3393			−0.512499
$408$		0			0
$409$	−4.28567	+	7.42299i	−0.211913	+	0.367043i	−0.952313	−	0.305123i	$-0.901303\pi$
$409$	−4.28567	+	7.42299i	−0.211913	+	0.367043i	0.740401	+	0.672166i	$0.234636\pi$
$410$	13.4123			0.662387
$411$		0			0
$412$	15.9125	+	27.5613i	0.783953	+	1.35785i
$413$	−15.9911	+	27.6974i	−0.786869	+	1.36290i
$414$		0			0
$415$	−2.09642	−	3.63111i	−0.102909	−	0.178244i
$416$	12.8546			0.630247
$417$		0			0
$418$	28.3306	+	49.0701i	1.38570	+	2.40010i
$419$	1.94634	+	3.37115i	0.0950847	+	0.164692i	0.909644	−	0.415389i	$-0.136354\pi$
$419$	1.94634	+	3.37115i	0.0950847	+	0.164692i	−0.814559	+	0.580080i	$0.803021\pi$
$420$		0			0
$421$	3.88859	+	6.73523i	0.189518	+	0.328255i	0.945090	−	0.326811i	$-0.105974\pi$
$421$	3.88859	+	6.73523i	0.189518	+	0.328255i	−0.755572	+	0.655066i	$0.772641\pi$
$422$	−20.2636	+	35.0976i	−0.986417	+	1.70852i
$423$		0			0
$424$	−6.39148			−0.310398
$425$	−1.45392	−	2.51827i	−0.0705256	−	0.122154i
$426$		0			0
$427$	−21.3007			−1.03081
$428$	17.8497	−	30.9166i	0.862797	−	1.49441i
$429$		0			0
$430$	−0.783224	−	1.35658i	−0.0377704	−	0.0654203i
$431$	−11.4914	+	19.9036i	−0.553520	+	0.958725i	0.444497	+	0.895780i	$0.353382\pi$
$431$	−11.4914	+	19.9036i	−0.553520	+	0.958725i	−0.998017	+	0.0629445i	$0.979951\pi$
$432$		0			0
$433$	−10.3371	+	17.9044i	−0.496771	+	0.860432i	−0.999993	−	0.00372498i	$-0.998814\pi$
$433$	−10.3371	+	17.9044i	−0.496771	+	0.860432i	0.503222	+	0.864157i	$0.332148\pi$
$434$	−25.6238	+	44.3818i	−1.22998	+	2.13039i
$435$		0			0
$436$	13.9725	−	24.2010i	0.669160	−	1.15902i
$437$	19.1515	−	33.1713i	0.916139	−	1.58680i
$438$		0			0
$439$	16.1503	+	27.9732i	0.770813	+	1.33509i	0.937118	+	0.349013i	$0.113483\pi$
$439$	16.1503	+	27.9732i	0.770813	+	1.33509i	−0.166305	+	0.986074i	$0.553184\pi$
$440$	−2.22428	+	3.85256i	−0.106038	+	0.183663i
$441$		0			0
$442$	2.83713			0.134948
$443$	16.2878	−	28.2113i	0.773856	−	1.34036i	−0.161580	−	0.986860i	$-0.551659\pi$
$443$	16.2878	−	28.2113i	0.773856	−	1.34036i	0.935435	−	0.353497i	$-0.115008\pi$
$444$		0			0
$445$	−11.1378			−0.527981
$446$	−21.9888	−	38.0858i	−1.04120	−	1.80341i
$447$		0			0
$448$	16.4181	−	28.4370i	0.775683	−	1.34352i
$449$	−17.1924	+	29.7782i	−0.811362	+	1.40532i	0.100549	+	0.994932i	$0.467940\pi$
$449$	−17.1924	+	29.7782i	−0.811362	+	1.40532i	−0.911911	+	0.410388i	$0.865393\pi$
$450$		0			0
$451$	−10.7163	−	18.5612i	−0.504612	−	0.874014i
$452$	2.47683	+	4.28999i	0.116500	+	0.201784i
$453$		0			0
$454$	27.1920			1.27618
$455$	−6.05404			−0.283818
$456$		0			0
$457$	−2.22282	+	3.85004i	−0.103979	+	0.180097i	−0.913321	−	0.407241i	$-0.866491\pi$
$457$	−2.22282	+	3.85004i	−0.103979	+	0.180097i	0.809341	+	0.587338i	$0.199824\pi$
$458$	−22.7601	+	39.4217i	−1.06351	+	1.84206i
$459$		0			0
$460$	17.9101			0.835061
$461$	22.6785			1.05624			0.528121	−	0.849169i	$-0.322897\pi$
$461$	22.6785			1.05624			0.528121	+	0.849169i	$0.322897\pi$
$462$		0			0
$463$	−2.39753	−	4.15264i	−0.111423	−	0.192989i	0.804922	−	0.593381i	$-0.202207\pi$
$463$	−2.39753	−	4.15264i	−0.111423	−	0.192989i	−0.916344	+	0.400392i	$0.868874\pi$
$464$	−21.8316			−1.01351
$465$		0			0
$466$	35.5713			1.64781
$467$	9.27222	+	16.0600i	0.429067	+	0.743166i	0.996791	−	0.0800531i	$-0.0255090\pi$
$467$	9.27222	+	16.0600i	0.429067	+	0.743166i	−0.567723	+	0.823219i	$0.692176\pi$
$468$		0			0
$469$	−20.6709	+	13.7049i	−0.954494	+	0.632832i
$470$	−6.83803			−0.315415
$471$		0			0
$472$	−8.93915			−0.411458
$473$	−1.25158	+	2.16780i	−0.0575476	+	0.0996754i
$474$		0			0
$475$	11.0450	+	19.1304i	0.506778	+	0.877765i
$476$	3.08386	−	5.34140i	0.141348	−	0.244823i
$477$		0			0
$478$	37.7763			1.72785
$479$	4.56261	+	7.90266i	0.208471	+	0.361082i	0.951233	−	0.308473i	$-0.0998181\pi$
$479$	4.56261	+	7.90266i	0.208471	+	0.361082i	−0.742762	+	0.669555i	$0.766485\pi$
$480$		0			0
$481$	1.96642	−	3.40593i	0.0896609	−	0.155297i
$482$	22.6146	+	39.1697i	1.03007	+	1.78413i
$483$		0			0
$484$	15.8980			0.722635
$485$	−4.86687	−	8.42967i	−0.220993	−	0.382772i
$486$		0			0
$487$	−5.22282	−	9.04620i	−0.236669	−	0.409922i	0.723088	−	0.690756i	$-0.242722\pi$
$487$	−5.22282	−	9.04620i	−0.236669	−	0.409922i	−0.959756	+	0.280834i	$0.909389\pi$
$488$	−2.97681	−	5.15599i	−0.134754	−	0.233401i
$489$		0			0
$490$	−2.86376	+	4.96018i	−0.129372	+	0.224078i
$491$	−36.4307			−1.64409			−0.822047	−	0.569419i	$-0.807168\pi$
$491$	−36.4307			−1.64409			−0.822047	+	0.569419i	$0.807168\pi$
$492$		0			0
$493$	−6.10202			−0.274821
$494$	−21.5527			−0.969702
$495$		0			0
$496$	24.4215			1.09656
$497$	9.01967	+	15.6225i	0.404587	+	0.700766i
$498$		0			0
$499$	13.4756	+	23.3405i	0.603252	+	1.04486i	0.992325	+	0.123656i	$0.0394619\pi$
$499$	13.4756	+	23.3405i	0.603252	+	1.04486i	−0.389073	+	0.921207i	$0.627205\pi$
$500$	−12.6852	+	21.9714i	−0.567298	+	0.982589i
$501$		0			0
$502$	0.424612	−	0.735450i	0.0189514	−	0.0328247i
$503$	19.5435	−	33.8503i	0.871400	−	1.50931i	0.0108516	−	0.999941i	$-0.496546\pi$
$503$	19.5435	−	33.8503i	0.871400	−	1.50931i	0.860549	−	0.509368i	$-0.170121\pi$
$504$		0			0
$505$	2.72860	−	4.72608i	0.121421	−	0.210308i
$506$	−26.2172	−	45.4096i	−1.16550	−	2.01870i
$507$		0			0
$508$	4.35816	+	7.54856i	0.193362	+	0.334913i
$509$	−28.4161			−1.25952			−0.629761	−	0.776789i	$-0.716847\pi$
$509$	−28.4161			−1.25952			−0.629761	+	0.776789i	$0.716847\pi$
$510$		0			0
$511$	−29.8429			−1.32017
$512$	−29.5298			−1.30504
$513$		0			0
$514$	−6.25948			−0.276094
$515$	−8.28589	+	14.3516i	−0.365120	+	0.632406i
$516$		0			0
$517$	5.46353	+	9.46311i	0.240286	+	0.416187i
$518$	−7.83194	−	13.5653i	−0.344115	−	0.596026i
$519$		0			0
$520$	−0.846066	−	1.46543i	−0.0371024	−	0.0642633i
$521$	30.4892			1.33576			0.667878	−	0.744271i	$-0.267203\pi$
$521$	30.4892			1.33576			0.667878	+	0.744271i	$0.267203\pi$
$522$		0			0
$523$	−14.9036	−	25.8138i	−0.651688	−	1.12876i	−0.982713	−	0.185135i	$-0.940728\pi$
$523$	−14.9036	−	25.8138i	−0.651688	−	1.12876i	0.331025	−	0.943622i	$-0.392605\pi$
$524$	19.6439	−	34.0242i	0.858147	−	1.48635i
$525$		0			0
$526$	−10.8217	−	18.7437i	−0.471848	−	0.817265i
$527$	6.82590			0.297341
$528$		0			0
$529$	−6.22282	+	10.7782i	−0.270558	+	0.468619i
$530$	−9.91070	−	17.1658i	−0.430493	−	0.745637i
$531$		0			0
$532$	−23.4271	+	40.5768i	−1.01569	+	1.75923i
$533$	8.15251			0.353125
$534$		0			0
$535$	18.5892			0.803682
$536$	−6.20618	−	3.08827i	−0.268066	−	0.133393i
$537$		0			0
$538$	−26.4875	−	45.8776i	−1.14196	−	1.97792i
$539$	9.15248			0.394225
$540$		0			0
$541$	−4.17497			−0.179496			−0.0897480	−	0.995965i	$-0.528606\pi$
$541$	−4.17497			−0.179496			−0.0897480	+	0.995965i	$0.528606\pi$
$542$	2.68011	+	4.64210i	0.115121	+	0.199395i
$543$		0			0
$544$	−6.81925			−0.292373
$545$	14.5514			0.623311
$546$		0			0
$547$	9.22887	−	15.9849i	0.394598	−	0.683464i	−0.598452	−	0.801159i	$-0.704217\pi$
$547$	9.22887	−	15.9849i	0.394598	−	0.683464i	0.993050	+	0.117695i	$0.0375505\pi$
$548$	−8.17278	+	14.1557i	−0.349124	+	0.604700i
$549$		0			0
$550$	30.2398			1.28943
$551$	46.3550			1.97479
$552$		0			0
$553$	13.9541	+	24.1693i	0.593390	+	1.02778i
$554$	1.73793	+	3.01018i	0.0738374	+	0.127890i
$555$		0			0
$556$	5.50939	−	9.54254i	0.233650	−	0.404694i
$557$	−5.56920	+	9.64614i	−0.235975	+	0.408720i	−0.959555	−	0.281520i	$-0.909162\pi$
$557$	−5.56920	+	9.64614i	−0.235975	+	0.408720i	0.723581	+	0.690240i	$0.242495\pi$
$558$		0			0
$559$	−0.476073	−	0.824583i	−0.0201358	−	0.0348761i
$560$	11.4904			0.485559
$561$		0			0
$562$	16.9631	−	29.3809i	0.715544	−	1.23936i
$563$	20.4015			0.859823			0.429911	−	0.902871i	$-0.358545\pi$
$563$	20.4015			0.859823			0.429911	+	0.902871i	$0.358545\pi$
$564$		0			0
$565$	−1.28972	+	2.23386i	−0.0542590	+	0.0939794i
$566$	14.5625	+	25.2231i	0.612109	+	1.06020i
$567$		0			0
$568$	−2.52104	+	4.36656i	−0.105780	+	0.183217i
$569$	−17.8811	+	30.9710i	−0.749616	+	1.29837i	0.198390	+	0.980123i	$0.436429\pi$
$569$	−17.8811	+	30.9710i	−0.749616	+	1.29837i	−0.948007	+	0.318250i	$0.896905\pi$
$570$		0			0
$571$	21.7702	−	37.7071i	0.911056	−	1.57799i	0.0984801	−	0.995139i	$-0.468602\pi$
$571$	21.7702	−	37.7071i	0.911056	−	1.57799i	0.812576	−	0.582856i	$-0.198065\pi$
$572$	−8.05209	+	13.9466i	−0.336675	+	0.583138i
$573$		0			0
$574$	16.2351	−	28.1200i	0.677640	−	1.17371i
$575$	−10.2210	−	17.7034i	−0.426247	−	0.738281i
$576$		0			0
$577$	17.1139	−	29.6421i	0.712459	−	1.23402i	−0.251472	−	0.967864i	$-0.580915\pi$
$577$	17.1139	−	29.6421i	0.712459	−	1.23402i	0.963931	−	0.266151i	$-0.0857519\pi$
$578$	34.1689			1.42124
$579$		0			0
$580$	10.8376	+	18.7712i	0.450006	+	0.779433i
$581$	−10.1506			−0.421116
$582$		0			0
$583$	−15.8371	+	27.4307i	−0.655907	+	1.13606i
$584$	−4.17061	−	7.22371i	−0.172581	−	0.298919i
$585$		0			0
$586$	11.0749	+	19.1824i	0.457502	+	0.792416i
$587$	21.8068	+	37.7704i	0.900062	+	1.55895i	0.827412	+	0.561595i	$0.189812\pi$
$587$	21.8068	+	37.7704i	0.900062	+	1.55895i	0.0726491	+	0.997358i	$0.476855\pi$
$588$		0			0
$589$	−51.8541			−2.13661
$590$	−13.8612	−	24.0082i	−0.570655	−	0.988403i
$591$		0			0
$592$	−3.73221	+	6.46438i	−0.153393	+	0.265684i
$593$	7.48409	+	12.9628i	0.307335	+	0.532319i	0.977778	−	0.209641i	$-0.0672296\pi$
$593$	7.48409	+	12.9628i	0.307335	+	0.532319i	−0.670444	+	0.741960i	$0.733896\pi$
$594$		0			0
$595$	3.21163			0.131664
$596$	11.6674	−	20.2085i	0.477915	−	0.827773i
$597$		0			0
$598$	19.9449			0.815609
$599$	17.1661	−	29.7326i	0.701389	−	1.21484i	−0.266591	−	0.963810i	$-0.585897\pi$
$599$	17.1661	−	29.7326i	0.701389	−	1.21484i	0.967979	−	0.251031i	$-0.0807695\pi$
$600$		0			0
$601$	11.8342	+	20.4975i	0.482729	+	0.836110i	0.999803	−	0.0198298i	$-0.00631244\pi$
$601$	11.8342	+	20.4975i	0.482729	+	0.836110i	−0.517075	+	0.855940i	$0.672979\pi$
$602$	−3.79225			−0.154561
$603$		0			0
$604$	26.6984			1.08634
$605$	4.13916	+	7.16923i	0.168281	+	0.291471i
$606$		0			0
$607$	16.6049	−	28.7606i	0.673973	−	1.16735i	−0.302795	−	0.953056i	$-0.597920\pi$
$607$	16.6049	−	28.7606i	0.673973	−	1.16735i	0.976768	−	0.214299i	$-0.0687468\pi$
$608$	51.8036			2.10091
$609$		0			0
$610$	9.23176	−	15.9899i	0.373783	−	0.647411i
$611$	−4.15641			−0.168150
$612$		0			0
$613$	7.05146	+	12.2135i	0.284806	+	0.493298i	0.972562	−	0.232644i	$-0.0747375\pi$
$613$	7.05146	+	12.2135i	0.284806	+	0.493298i	−0.687756	+	0.725942i	$0.741404\pi$
$614$	26.9510	−	46.6805i	1.08765	−	1.88387i
$615$		0			0
$616$	5.38480	+	9.32675i	0.216960	+	0.375785i
$617$	−2.57819			−0.103794			−0.0518970	−	0.998652i	$-0.516527\pi$
$617$	−2.57819			−0.103794			−0.0518970	+	0.998652i	$0.516527\pi$
$618$		0			0
$619$	−3.23781	−	5.60805i	−0.130139	−	0.225407i	0.793591	−	0.608451i	$-0.208209\pi$
$619$	−3.23781	−	5.60805i	−0.130139	−	0.225407i	−0.923730	+	0.383045i	$0.874876\pi$
$620$	−12.1232	−	20.9980i	−0.486881	−	0.843302i
$621$		0			0
$622$	−10.3311	−	17.8940i	−0.414238	−	0.717482i
$623$	−13.4819	+	23.3513i	−0.540139	+	0.935548i
$624$		0			0
$625$	3.95703			0.158281
$626$	9.48063	+	16.4209i	0.378922	+	0.656313i
$627$		0			0
$628$	26.1199			1.04230
$629$	−1.04317	+	1.80682i	−0.0415939	+	0.0720427i
$630$		0			0
$631$	14.9036	+	25.8138i	0.593302	+	1.02763i	0.993784	+	0.111325i	$0.0355093\pi$
$631$	14.9036	+	25.8138i	0.593302	+	1.02763i	−0.400482	+	0.916305i	$0.631157\pi$
$632$	−3.90024	+	6.75542i	−0.155143	+	0.268716i
$633$		0			0
$634$	8.23781	−	14.2683i	0.327165	−	0.566667i
$635$	−2.26936	+	3.93065i	−0.0900569	+	0.155983i
$636$		0			0
$637$	−1.74070	+	3.01498i	−0.0689691	+	0.119458i
$638$	31.7287	−	54.9556i	1.25615	−	2.17571i
$639$		0			0
$640$	4.15348	+	7.19405i	0.164181	+	0.284370i
$641$	15.1756	−	26.2850i	0.599402	−	1.03819i	−0.393508	−	0.919321i	$-0.628739\pi$
$641$	15.1756	−	26.2850i	0.599402	−	1.03819i	0.992909	−	0.118873i	$-0.0379281\pi$
$642$		0			0
$643$	−6.97002			−0.274871			−0.137435	−	0.990511i	$-0.543886\pi$
$643$	−6.97002			−0.274871			−0.137435	+	0.990511i	$0.543886\pi$
$644$	21.6795	−	37.5499i	0.854290	−	1.47967i
$645$		0			0
$646$	11.4336			0.449847
$647$	−19.8275	−	34.3422i	−0.779498	−	1.35013i	−0.932231	−	0.361863i	$-0.882141\pi$
$647$	−19.8275	−	34.3422i	−0.779498	−	1.35013i	0.152733	−	0.988268i	$-0.451193\pi$
$648$		0			0
$649$	−22.1499	+	38.3647i	−0.869459	+	1.50595i
$650$	−5.75128	+	9.96151i	−0.225584	+	0.390723i
$651$		0			0
$652$	−15.0360	−	26.0432i	−0.588856	−	1.01993i
$653$	−20.0673	−	34.7576i	−0.785295	−	1.36017i	−0.928822	−	0.370525i	$-0.879178\pi$
$653$	−20.0673	−	34.7576i	−0.785295	−	1.36017i	0.143527	−	0.989646i	$-0.454156\pi$
$654$		0			0
$655$	20.4577			0.799350
$656$	−15.4733			−0.604130
$657$		0			0
$658$	−8.27718	+	14.3365i	−0.322678	+	0.558895i
$659$	−14.9860	+	25.9565i	−0.583771	+	1.01112i	0.411256	+	0.911520i	$0.365090\pi$
$659$	−14.9860	+	25.9565i	−0.583771	+	1.01112i	−0.995027	+	0.0996015i	$0.968243\pi$
$660$		0			0
$661$	−17.6622			−0.686978			−0.343489	−	0.939157i	$-0.611609\pi$
$661$	−17.6622			−0.686978			−0.343489	+	0.939157i	$0.611609\pi$
$662$	66.1632			2.57151
$663$		0			0
$664$	−1.41856	−	2.45702i	−0.0550509	−	0.0953510i
$665$	−24.3976			−0.946100
$666$		0			0
$667$	−42.8971			−1.66098
$668$	−23.1385	−	40.0771i	−0.895255	−	1.55063i
$669$		0			0
$670$	−1.32909	−	21.4569i	−0.0513471	−	0.828952i
$671$	−29.5044			−1.13900
$672$		0			0
$673$	25.0657			0.966213			0.483106	−	0.875562i	$-0.339508\pi$
$673$	25.0657			0.966213			0.483106	+	0.875562i	$0.339508\pi$
$674$	−19.2017	+	33.2583i	−0.739621	+	1.28106i
$675$		0			0
$676$	12.5604	+	21.7553i	0.483092	+	0.836740i
$677$	−17.5267	+	30.3571i	−0.673604	+	1.16672i	0.303270	+	0.952905i	$0.401921\pi$
$677$	−17.5267	+	30.3571i	−0.673604	+	1.16672i	−0.976875	+	0.213812i	$0.931412\pi$
$678$		0			0
$679$	−23.5647			−0.904328
$680$	0.448832	+	0.777399i	0.0172119	+	0.0298119i
$681$		0			0
$682$	−35.4926	+	61.4750i	−1.35908	+	2.35400i
$683$	18.5444	+	32.1199i	0.709583	+	1.22903i	0.965012	+	0.262207i	$0.0844502\pi$
$683$	18.5444	+	32.1199i	0.709583	+	1.22903i	−0.255428	+	0.966828i	$0.582216\pi$
$684$		0			0
$685$	−8.51138			−0.325203
$686$	−15.3211	−	26.5370i	−0.584964	−	1.01319i
$687$		0			0
$688$	0.903576	+	1.56504i	0.0344485	+	0.0596665i
$689$	−6.02410	−	10.4340i	−0.229500	−	0.397505i
$690$		0			0
$691$	8.11141	−	14.0494i	0.308573	−	0.534464i	−0.669478	−	0.742832i	$-0.733482\pi$
$691$	8.11141	−	14.0494i	0.308573	−	0.534464i	0.978050	+	0.208369i	$0.0668154\pi$
$692$	51.8036			1.96928
$693$		0			0
$694$	76.1060			2.88894
$695$	5.73765			0.217641
$696$		0			0
$697$	−4.32485			−0.163815
$698$	−27.4059	−	47.4684i	−1.03733	−	1.79671i
$699$		0			0
$700$	12.5029	+	21.6556i	0.472565	+	0.818506i
$701$	−13.0645	+	22.6283i	−0.493438	+	0.854660i	−0.999971	−	0.00756020i	$-0.997593\pi$
$701$	−13.0645	+	22.6283i	−0.493438	+	0.854660i	0.506533	+	0.862221i	$0.330927\pi$
$702$		0			0
$703$	7.92461	−	13.7258i	0.298882	−	0.517680i
$704$	22.7414	−	39.3892i	0.857098	−	1.48454i
$705$		0			0
$706$	2.47851	−	4.29291i	0.0932801	−	0.161566i
$707$	−6.60574	−	11.4415i	−0.248435	−	0.430301i
$708$		0			0
$709$	19.5114	+	33.7947i	0.732765	+	1.26919i	0.955697	+	0.294353i	$0.0951040\pi$
$709$	19.5114	+	33.7947i	0.732765	+	1.26919i	−0.222932	+	0.974834i	$0.571563\pi$
$710$	−15.6366			−0.586831
$711$		0			0
$712$	−7.53647			−0.282441
$713$	47.9859			1.79709
$714$		0			0
$715$	−8.38570			−0.313607
$716$	−11.6674	+	20.2085i	−0.436031	+	0.755228i
$717$		0			0
$718$	−6.88209	−	11.9201i	−0.256837	−	0.444855i
$719$	8.47554	+	14.6801i	0.316084	+	0.547474i	0.979667	−	0.200629i	$-0.0642984\pi$
$719$	8.47554	+	14.6801i	0.316084	+	0.547474i	−0.663583	+	0.748103i	$0.730965\pi$
$720$		0			0
$721$	20.0595	+	34.7441i	0.747055	+	1.29394i
$722$	−46.9860			−1.74864
$723$		0			0
$724$	−24.1078	−	41.7559i	−0.895959	−	1.55185i
$725$	12.3697	−	21.4250i	0.459400	−	0.795704i
$726$		0			0
$727$	−5.16892	−	8.95284i	−0.191705	−	0.332042i	0.754111	−	0.656747i	$-0.228068\pi$
$727$	−5.16892	−	8.95284i	−0.191705	−	0.332042i	−0.945815	+	0.324705i	$0.894735\pi$
$728$	−4.09652			−0.151827
$729$		0			0
$730$	12.9340	−	22.4023i	0.478709	−	0.829148i
$731$	0.252553	+	0.437435i	0.00934102	+	0.0161791i
$732$		0			0
$733$	9.44854	−	16.3653i	0.348990	−	0.604468i	−0.637081	−	0.770797i	$-0.719858\pi$
$733$	9.44854	−	16.3653i	0.348990	−	0.604468i	0.986070	+	0.166329i	$0.0531915\pi$
$734$	5.72740			0.211402
$735$		0			0
$736$	−47.9392			−1.76706
$737$	−28.6321	+	18.9832i	−1.05468	+	0.699254i
$738$		0			0
$739$	−8.37920	−	14.5132i	−0.308234	−	0.533877i	0.669742	−	0.742594i	$-0.266405\pi$
$739$	−8.37920	−	14.5132i	−0.308234	−	0.533877i	−0.977976	+	0.208717i	$0.933071\pi$
$740$	7.41094			0.272431
$741$		0			0
$742$	−47.9861			−1.76163
$743$	21.0978	+	36.5425i	0.774004	+	1.34061i	0.935353	+	0.353716i	$0.115082\pi$
$743$	21.0978	+	36.5425i	0.774004	+	1.34061i	−0.161349	+	0.986897i	$0.551585\pi$
$744$		0			0
$745$	12.1508			0.445170
$746$	40.5272			1.48381
$747$		0			0
$748$	4.27158	−	7.39859i	0.156184	−	0.270519i
$749$	22.5015	−	38.9738i	0.822188	−	1.42407i
$750$		0			0
$751$	9.95215			0.363159			0.181579	−	0.983376i	$-0.441879\pi$
$751$	9.95215			0.363159			0.181579	+	0.983376i	$0.441879\pi$
$752$	7.88877			0.287674
$753$		0			0
$754$	12.0689	+	20.9039i	0.439523	+	0.761276i
$755$	6.95115	+	12.0397i	0.252978	+	0.438171i
$756$		0			0
$757$	−16.3910	+	28.3901i	−0.595742	+	1.03186i	0.397700	+	0.917516i	$0.369809\pi$
$757$	−16.3910	+	28.3901i	−0.595742	+	1.03186i	−0.993442	+	0.114340i	$0.963525\pi$
$758$	−35.8186	+	62.0395i	−1.30099	+	2.25338i
$759$		0			0
$760$	−3.40962	−	5.90564i	−0.123680	−	0.214220i
$761$	51.3360			1.86093			0.930464	−	0.366384i	$-0.119404\pi$
$761$	51.3360			1.86093			0.930464	+	0.366384i	$0.119404\pi$
$762$		0			0
$763$	17.6139	−	30.5081i	0.637664	−	1.10447i
$764$	−51.8937			−1.87745
$765$		0			0
$766$	−10.6110	+	18.3787i	−0.383390	+	0.664050i
$767$	−8.42533	−	14.5931i	−0.304221	−	0.526926i
$768$		0			0
$769$	8.15638	−	14.1273i	0.294126	−	0.509442i	−0.680655	−	0.732604i	$-0.738305\pi$
$769$	8.15638	−	14.1273i	0.294126	−	0.509442i	0.974781	+	0.223162i	$0.0716380\pi$
$770$	−16.6995	+	28.9243i	−0.601807	+	1.04236i
$771$		0			0
$772$	−15.4275	+	26.7212i	−0.555248	+	0.961718i
$773$	0.492414	−	0.852885i	0.0177109	−	0.0306762i	−0.857034	−	0.515260i	$-0.827695\pi$
$773$	0.492414	−	0.852885i	0.0177109	−	0.0306762i	0.874745	+	0.484583i	$0.161029\pi$
$774$		0			0
$775$	−13.8371	+	23.9666i	−0.497044	+	0.860906i
$776$	−3.29321	−	5.70401i	−0.118219	−	0.204762i
$777$		0			0
$778$	−28.1199	+	48.7051i	−1.00815	+	1.74616i
$779$	32.8544			1.17713
$780$		0			0
$781$	12.4935	+	21.6394i	0.447053	+	0.774318i
$782$	−10.5806			−0.378363
$783$		0			0
$784$	3.30381	−	5.72237i	0.117993	−	0.204370i
$785$	6.80052	+	11.7788i	0.242721	+	0.420405i
$786$		0			0
$787$	−4.52104	−	7.83066i	−0.161158	−	0.279133i	0.774127	−	0.633031i	$-0.218189\pi$
$787$	−4.52104	−	7.83066i	−0.161158	−	0.279133i	−0.935284	+	0.353898i	$0.884856\pi$
$788$	−3.73598	−	6.47090i	−0.133089	−	0.230516i
$789$		0			0
$790$	−24.1911			−0.860679
$791$	3.12232	+	5.40801i	0.111017	+	0.192287i
$792$		0			0
$793$	5.61141	−	9.71925i	0.199267	−	0.345141i
$794$	20.9898	+	36.3554i	0.744901	+	1.29021i
$795$		0			0
$796$	43.3364			1.53602
$797$	−9.45581	+	16.3779i	−0.334942	+	0.580136i	−0.983474	−	0.181051i	$-0.942050\pi$
$797$	−9.45581	+	16.3779i	−0.334942	+	0.580136i	0.648532	+	0.761188i	$0.275383\pi$
$798$		0			0
$799$	2.20495			0.0780054
$800$	13.8236	−	23.9432i	0.488739	−	0.846522i
$801$		0			0
$802$	−28.5179	−	49.3944i	−1.00700	−	1.74418i
$803$	−41.3366			−1.45874
$804$		0			0
$805$	22.5776			0.795758
$806$	−13.5006	−	23.3837i	−0.475539	−	0.823657i
$807$		0			0
$808$	1.84633	−	3.19794i	0.0649538	−	0.112503i
$809$	18.0647			0.635122			0.317561	−	0.948238i	$-0.397136\pi$
$809$	18.0647			0.635122			0.317561	+	0.948238i	$0.397136\pi$
$810$		0			0
$811$	−3.87965	+	6.71975i	−0.136233	+	0.235962i	−0.926068	−	0.377357i	$-0.876833\pi$
$811$	−3.87965	+	6.71975i	−0.136233	+	0.235962i	0.789835	+	0.613320i	$0.210166\pi$
$812$	52.4739			1.84147
$813$		0			0
$814$	−10.8483	−	18.7899i	−0.380234	−	0.658584i
$815$	7.82949	−	13.5611i	0.274255	−	0.475024i
$816$		0			0
$817$	−1.91856	−	3.32305i	−0.0671220	−	0.116259i
$818$	−17.9867			−0.628890
$819$		0			0
$820$	7.68120	+	13.3042i	0.268239	+	0.464604i
$821$	−18.6966	−	32.3834i	−0.652515	−	1.13019i	−0.982511	−	0.186207i	$-0.940381\pi$
$821$	−18.6966	−	32.3834i	−0.652515	−	1.13019i	0.329996	−	0.943982i	$-0.392953\pi$
$822$		0			0
$823$	−16.0928	−	27.8736i	−0.560960	−	0.971612i	−0.997413	−	0.0718846i	$-0.977099\pi$
$823$	−16.0928	−	27.8736i	−0.560960	−	0.971612i	0.436453	−	0.899727i	$-0.356235\pi$
$824$	−5.60672	+	9.71112i	−0.195319	+	0.338303i
$825$		0			0
$826$	−67.1136			−2.33518
$827$	−16.4070	−	28.4177i	−0.570526	−	0.988179i	−0.996512	−	0.0834498i	$-0.973406\pi$
$827$	−16.4070	−	28.4177i	−0.570526	−	0.988179i	0.425986	−	0.904730i	$-0.359927\pi$
$828$		0			0
$829$	−10.0121			−0.347735			−0.173867	−	0.984769i	$-0.555626\pi$
$829$	−10.0121			−0.347735			−0.173867	+	0.984769i	$0.555626\pi$
$830$	4.39928	−	7.61978i	0.152701	−	0.264487i
$831$		0			0
$832$	8.65033	+	14.9828i	0.299896	+	0.519435i
$833$	0.923430	−	1.59943i	0.0319949	−	0.0554169i
$834$		0			0
$835$	12.0486	−	20.8687i	0.416958	−	0.722192i
$836$	−32.4497	+	56.2046i	−1.12230	+	1.94388i
$837$		0			0
$838$	−4.08433	+	7.07426i	−0.141091	+	0.244376i
$839$	−12.0279	+	20.8330i	−0.415250	+	0.719235i	−0.995455	−	0.0952362i	$-0.969639\pi$
$839$	−12.0279	+	20.8330i	−0.415250	+	0.719235i	0.580204	+	0.814471i	$0.302973\pi$
$840$		0			0
$841$	−11.4575	−	19.8449i	−0.395085	−	0.684308i
$842$	−8.16008	+	14.1337i	−0.281215	+	0.487079i
$843$		0			0
$844$	−46.4197			−1.59783
$845$	−6.54039	+	11.3283i	−0.224996	+	0.389705i
$846$		0			0
$847$	20.0412			0.688623
$848$	11.4336	+	19.8036i	0.392631	+	0.680057i
$849$		0			0
$850$	3.05101	−	5.28451i	0.104649	−	0.181257i
$851$	−7.33346	+	12.7019i	−0.251388	+	0.435416i
$852$		0			0
$853$	−19.3792	−	33.5658i	−0.663531	−	1.14927i	−0.979681	−	0.200561i	$-0.935724\pi$
$853$	−19.3792	−	33.5658i	−0.663531	−	1.14927i	0.316150	−	0.948709i	$-0.397610\pi$
$854$	−22.3494	−	38.7103i	−0.764780	−	1.32464i
$855$		0			0
$856$	12.5785			0.429926
$857$	−34.0177			−1.16202			−0.581012	−	0.813895i	$-0.697343\pi$
$857$	−34.0177			−1.16202			−0.581012	+	0.813895i	$0.697343\pi$
$858$		0			0
$859$	3.09931	−	5.36817i	0.105747	−	0.183160i	−0.808296	−	0.588776i	$-0.799610\pi$
$859$	3.09931	−	5.36817i	0.105747	−	0.183160i	0.914043	+	0.405617i	$0.132943\pi$
$860$	0.897101	−	1.55382i	0.0305909	−	0.0529850i
$861$		0			0
$862$	−48.2286			−1.64267
$863$	−12.8546			−0.437574			−0.218787	−	0.975773i	$-0.570210\pi$
$863$	−12.8546			−0.437574			−0.218787	+	0.975773i	$0.570210\pi$
$864$		0			0
$865$	13.4875	+	23.3610i	0.458587	+	0.794296i
$866$	−43.3843			−1.47426
$867$		0			0
$868$	−58.6988			−1.99237
$869$	19.3284	+	33.4778i	0.655672	+	1.13566i
$870$		0			0
$871$	−0.807868	−	13.0423i	−0.0273736	−	0.441921i
$872$	9.84630			0.333438
$873$		0			0
$874$	80.3776			2.71881
$875$	−15.9911	+	27.6974i	−0.540597	+	0.936342i
$876$		0			0
$877$	−3.90647	−	6.76620i	−0.131912	−	0.228478i	0.792502	−	0.609870i	$-0.208778\pi$
$877$	−3.90647	−	6.76620i	−0.131912	−	0.228478i	−0.924414	+	0.381392i	$0.875445\pi$
$878$	−33.8910	+	58.7009i	−1.14376	+	1.98106i
$879$		0			0
$880$	15.9159			0.536523
$881$	−7.47652	−	12.9497i	−0.251890	−	0.436287i	0.712156	−	0.702021i	$-0.247719\pi$
$881$	−7.47652	−	12.9497i	−0.251890	−	0.436287i	−0.964046	+	0.265735i	$0.914386\pi$
$882$		0			0
$883$	−6.31031	+	10.9298i	−0.212359	+	0.367816i	−0.952452	−	0.304688i	$-0.901448\pi$
$883$	−6.31031	+	10.9298i	−0.212359	+	0.367816i	0.740093	+	0.672504i	$0.234781\pi$
$884$	1.62481	+	2.81426i	0.0546484	+	0.0946539i
$885$		0			0
$886$	68.3588			2.29656
$887$	−19.2017	−	33.2583i	−0.644729	−	1.11670i	−0.984364	−	0.176147i	$-0.943637\pi$
$887$	−19.2017	−	33.2583i	−0.644729	−	1.11670i	0.339634	−	0.940558i	$-0.389697\pi$
$888$		0			0
$889$	5.49395	+	9.51580i	0.184261	+	0.319150i
$890$	−11.6861	−	20.2410i	−0.391721	−	0.678480i
$891$		0			0
$892$	25.1859	−	43.6233i	0.843286	−	1.46061i
$893$	−16.7502			−0.560525
$894$		0			0
$895$	−12.1508			−0.406156
$896$	20.1105			0.671846
$897$		0			0
$898$	−72.1557			−2.40787
$899$	29.0368	+	50.2932i	0.968431	+	1.67737i
$900$		0			0
$901$	3.19574	+	5.53518i	0.106466	+	0.184404i
$902$	22.4879	−	38.9502i	0.748765	−	1.29690i
$903$		0			0
$904$	−0.872702	+	1.51156i	−0.0290256	+	0.0502739i
$905$	12.5533	−	21.7430i	0.417286	−	0.722760i
$906$		0			0
$907$	−20.7188	+	35.8860i	−0.687955	+	1.19157i	0.284543	+	0.958663i	$0.408158\pi$
$907$	−20.7188	+	35.8860i	−0.687955	+	1.19157i	−0.972498	+	0.232910i	$0.925175\pi$
$908$	15.5728	+	26.9728i	0.516800	+	0.895124i
$909$		0			0
$910$	−6.35211	−	11.0022i	−0.210571	−	0.364719i
$911$	−8.21843			−0.272289			−0.136144	−	0.990689i	$-0.543471\pi$
$911$	−8.21843			−0.272289			−0.136144	+	0.990689i	$0.543471\pi$
$912$		0			0
$913$	−14.0600			−0.465316
$914$	−9.32906			−0.308578
$915$		0			0
$916$	−52.1387			−1.72271
$917$	24.7633	−	42.8913i	0.817757	−	1.41640i
$918$		0			0
$919$	2.62324	+	4.54359i	0.0865328	+	0.149879i	0.906043	−	0.423185i	$-0.139088\pi$
$919$	2.62324	+	4.54359i	0.0865328	+	0.149879i	−0.819511	+	0.573064i	$0.805755\pi$
$920$	3.15528	+	5.46510i	0.104026	+	0.180179i
$921$		0			0
$922$	23.7951	+	41.2142i	0.783648	+	1.35732i
$923$	−9.50451			−0.312845
$924$		0			0
$925$	−4.22932	−	7.32540i	−0.139059	−	0.240858i
$926$	5.03114	−	8.71419i	0.165333	−	0.286366i
$927$		0			0
$928$	−29.0085	−	50.2442i	−0.952250	−	1.64935i
$929$	−21.6785			−0.711249			−0.355624	−	0.934629i	$-0.615732\pi$
$929$	−21.6785			−0.711249			−0.355624	+	0.934629i	$0.615732\pi$
$930$		0			0
$931$	−7.01499	+	12.1503i	−0.229907	+	0.398210i
$932$	20.3716	+	35.2846i	0.667294	+	1.15579i
$933$		0			0
$934$	−19.4575	+	33.7013i	−0.636668	+	1.10274i
$935$	4.44855			0.145483
$936$		0			0
$937$	35.9319			1.17385			0.586923	−	0.809643i	$-0.300339\pi$
$937$	35.9319			1.17385			0.586923	+	0.809643i	$0.300339\pi$
$938$	−46.5949	−	23.1862i	−1.52138	−	0.757056i
$939$		0			0
$940$	−3.91612	−	6.78292i	−0.127730	−	0.221235i
$941$	56.3048			1.83548			0.917742	−	0.397178i	$-0.130011\pi$
$941$	56.3048			1.83548			0.917742	+	0.397178i	$0.130011\pi$
$942$		0			0
$943$	−30.4036			−0.990077
$944$	15.9911	+	27.6974i	0.520465	+	0.901472i
$945$		0			0
$946$	−5.25280			−0.170783
$947$	−16.8658			−0.548065			−0.274032	−	0.961720i	$-0.588358\pi$
$947$	−16.8658			−0.548065			−0.274032	+	0.961720i	$0.588358\pi$
$948$		0			0
$949$	7.86177	−	13.6170i	0.255204	−	0.442026i
$950$	−23.1775	+	40.1446i	−0.751978	+	1.30246i
$951$		0			0
$952$	2.17317			0.0704330
$953$	−6.35831			−0.205966			−0.102983	−	0.994683i	$-0.532839\pi$
$953$	−6.35831			−0.205966			−0.102983	+	0.994683i	$0.532839\pi$
$954$		0			0
$955$	−13.5109	−	23.4016i	−0.437203	−	0.757259i
$956$	21.6344	+	37.4718i	0.699705	+	1.21193i
$957$		0			0
$958$	−9.57449	+	16.5835i	−0.309338	+	0.535789i
$959$	−10.3027	+	17.8448i	−0.332691	+	0.576239i
$960$		0			0
$961$	−16.9814	−	29.4127i	−0.547787	−	0.948795i
$962$	8.25293			0.266085
$963$		0			0
$964$	−25.9027	+	44.8648i	−0.834269	+	1.44500i
$965$	−16.0667			−0.517204
$966$		0			0
$967$	7.70179	−	13.3399i	0.247673	−	0.428982i	−0.715207	−	0.698913i	$-0.753668\pi$
$967$	7.70179	−	13.3399i	0.247673	−	0.428982i	0.962880	+	0.269931i	$0.0870009\pi$
$968$	2.80080	+	4.85112i	0.0900210	+	0.155921i
$969$		0			0
$970$	10.2130	−	17.6894i	0.327919	−	0.567973i
$971$	3.16040	−	5.47397i	0.101422	−	0.175668i	−0.810849	−	0.585256i	$-0.800994\pi$
$971$	3.16040	−	5.47397i	0.101422	−	0.175668i	0.912271	+	0.409588i	$0.134327\pi$
$972$		0			0
$973$	6.94520	−	12.0294i	0.222653	−	0.385646i
$974$	10.9599	−	18.9832i	0.351179	−	0.608260i
$975$		0			0
$976$	−10.6503	+	18.4469i	−0.340909	+	0.590471i
$977$	4.09502	+	7.09277i	0.131011	+	0.226918i	0.924067	−	0.382231i	$-0.124844\pi$
$977$	4.09502	+	7.09277i	0.131011	+	0.226918i	−0.793055	+	0.609149i	$0.791511\pi$
$978$		0			0
$979$	−18.6743	+	32.3448i	−0.596832	+	1.03374i
$980$	−6.56028			−0.209560
$981$		0			0
$982$	−38.2244	−	66.2065i	−1.21979	−	2.11274i
$983$	39.9217			1.27330			0.636652	−	0.771151i	$-0.280319\pi$
$983$	39.9217			1.27330			0.636652	+	0.771151i	$0.280319\pi$
$984$		0			0
$985$	1.94538	−	3.36950i	0.0619850	−	0.107361i
$986$	−6.40246	−	11.0894i	−0.203896	−	0.353158i
$987$		0			0
$988$	−12.3432	−	21.3790i	−0.392689	−	0.680157i
$989$	1.77544	+	3.07516i	0.0564558	+	0.0977843i
$990$		0			0
$991$	33.8841			1.07636			0.538182	−	0.842829i	$-0.319111\pi$
$991$	33.8841			1.07636			0.538182	+	0.842829i	$0.319111\pi$
$992$	32.4497	+	56.2046i	1.03028	+	1.78450i
$993$		0			0
$994$	−18.9275	+	32.7834i	−0.600344	+	1.03983i
$995$	11.2830	+	19.5427i	0.357694	+	0.619544i
$996$		0			0
$997$	−34.0527			−1.07846			−0.539230	−	0.842158i	$-0.681285\pi$
$997$	−34.0527			−1.07846			−0.539230	+	0.842158i	$0.681285\pi$
$998$	−28.2782	+	48.9793i	−0.895130	+	1.55041i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.g.h.37.5	yes	12
3.2	odd	2	inner	603.2.g.h.37.2	✓	12
67.29	even	3	inner	603.2.g.h.163.5	yes	12
201.29	odd	6	inner	603.2.g.h.163.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.g.h.37.2	✓	12	3.2	odd	2	inner
603.2.g.h.37.5	yes	12	1.1	even	1	trivial
603.2.g.h.163.2	yes	12	201.29	odd	6	inner
603.2.g.h.163.5	yes	12	67.29	even	3	inner

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04923 + 1.81733i) q^{2} +(-1.20179 + 2.08156i) q^{4} -1.25158 q^{5} +(-1.51499 + 2.62404i) q^{7} -0.846891 q^{8} +O(q^{10})\)	\(q+(1.04923 + 1.81733i) q^{2} +(-1.20179 + 2.08156i) q^{4} -1.25158 q^{5} +(-1.51499 + 2.62404i) q^{7} -0.846891 q^{8} +(-1.31320 - 2.27453i) q^{10} +(-2.09847 + 3.63466i) q^{11} +(-0.798212 - 1.38254i) q^{13} -6.35831 q^{14} +(1.51499 + 2.62404i) q^{16} +(0.423446 + 0.733429i) q^{17} +(-3.21678 - 5.57162i) q^{19} +(1.50413 - 2.60523i) q^{20} -8.80715 q^{22} +(2.97681 + 5.15599i) q^{23} -3.43355 q^{25} +(1.67502 - 2.90123i) q^{26} +(-3.64139 - 6.30707i) q^{28} +(-3.60260 + 6.23989i) q^{29} +(4.02998 - 6.98012i) q^{31} +(-4.02605 + 6.97332i) q^{32} +(-0.888588 + 1.53908i) q^{34} +(1.89613 - 3.28419i) q^{35} +(1.23176 + 2.13348i) q^{37} +(6.75031 - 11.6919i) q^{38} +1.05995 q^{40} +(-2.55337 + 4.42256i) q^{41} +0.596424 q^{43} +(-5.04383 - 8.73617i) q^{44} +(-6.24675 + 10.8197i) q^{46} +(1.30179 - 2.25476i) q^{47} +(-1.09038 - 1.88859i) q^{49} +(-3.60260 - 6.23989i) q^{50} +3.83713 q^{52} +7.54699 q^{53} +(2.62640 - 4.54906i) q^{55} +(1.28303 - 2.22227i) q^{56} -15.1199 q^{58} +10.5553 q^{59} +(3.51499 + 6.08814i) q^{61} +16.9136 q^{62} -10.8371 q^{64} +(0.999025 + 1.73036i) q^{65} +(7.32819 + 3.64660i) q^{67} -2.03557 q^{68} +7.95793 q^{70} +(2.97681 - 5.15599i) q^{71} +(4.92461 + 8.52968i) q^{73} +(-2.58482 + 4.47704i) q^{74} +15.4635 q^{76} +(-6.35831 - 11.0129i) q^{77} +(4.60536 - 7.97672i) q^{79} +(-1.89613 - 3.28419i) q^{80} -10.7163 q^{82} +(1.67502 + 2.90123i) q^{83} +(-0.529975 - 0.917944i) q^{85} +(0.625789 + 1.08390i) q^{86} +(1.77718 - 3.07816i) q^{88} +8.89899 q^{89} +4.83713 q^{91} -14.3100 q^{92} +5.46353 q^{94} +(4.02605 + 6.97332i) q^{95} +(3.88859 + 6.73523i) q^{97} +(2.28812 - 3.96314i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^7	\( 12 q - 10 q^{4} + 6 q^{7} + 4 q^{10} - 14 q^{13} - 6 q^{16} - 10 q^{19} - 88 q^{22} + 16 q^{25} + 20 q^{28} - 26 q^{34} - 38 q^{37} - 84 q^{40} + 16 q^{43} + 2 q^{46} - 24 q^{49} - 20 q^{52} - 8 q^{55} + 12 q^{58} + 18 q^{61} - 64 q^{64} + 44 q^{67} + 148 q^{70} + 24 q^{73} + 80 q^{76} + 42 q^{79} + 56 q^{82} + 42 q^{85} + 52 q^{88} - 8 q^{91} - 40 q^{94} + 62 q^{97}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^7 + 4 * q^10 - 14 * q^13 - 6 * q^16 - 10 * q^19 - 88 * q^22 + 16 * q^25 + 20 * q^28 - 26 * q^34 - 38 * q^37 - 84 * q^40 + 16 * q^43 + 2 * q^46 - 24 * q^49 - 20 * q^52 - 8 * q^55 + 12 * q^58 + 18 * q^61 - 64 * q^64 + 44 * q^67 + 148 * q^70 + 24 * q^73 + 80 * q^76 + 42 * q^79 + 56 * q^82 + 42 * q^85 + 52 * q^88 - 8 * q^91 - 40 * q^94 + 62 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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