LMFDB - Embedded newform 315.2.bh.c.169.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

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

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.6
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85508 - 1.07103i) q^{2} +(1.44646 - 0.952757i) q^{3} +(1.29422 + 2.24165i) q^{4} +(1.12216 + 1.93410i) q^{5} +(-3.70374 + 0.218235i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.26045i q^{8} +(1.18451 - 2.75626i) q^{9} +O(q^{10})$	\(q+(-1.85508 - 1.07103i) q^{2} +(1.44646 - 0.952757i) q^{3} +(1.29422 + 2.24165i) q^{4} +(1.12216 + 1.93410i) q^{5} +(-3.70374 + 0.218235i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.26045i q^{8} +(1.18451 - 2.75626i) q^{9} +(-0.0102188 - 4.78979i) q^{10} +(-0.727944 + 1.26084i) q^{11} +(4.00778 + 2.00938i) q^{12} +(4.84312 - 2.79618i) q^{13} +(1.07103 + 1.85508i) q^{14} +(3.46590 + 1.72846i) q^{15} +(1.23844 - 2.14505i) q^{16} +2.52815i q^{17} +(-5.14939 + 3.84443i) q^{18} +5.41338 q^{19} +(-2.88325 + 5.01864i) q^{20} +(-1.72905 + 0.101881i) q^{21} +(2.70079 - 1.55930i) q^{22} +(0.543577 - 0.313834i) q^{23} +(-1.20091 - 1.82320i) q^{24} +(-2.48150 + 4.34075i) q^{25} -11.9792 q^{26} +(-0.912699 - 5.11537i) q^{27} -2.58843i q^{28} +(4.23378 - 7.33312i) q^{29} +(-4.57829 - 6.91851i) q^{30} +(0.00482938 + 0.00836474i) q^{31} +(-6.77800 + 3.91328i) q^{32} +(0.148327 + 2.51731i) q^{33} +(2.70773 - 4.68993i) q^{34} +(-0.00477054 - 2.23606i) q^{35} +(7.71156 - 0.911943i) q^{36} +3.03712i q^{37} +(-10.0423 - 5.79790i) q^{38} +(4.34132 - 8.65889i) q^{39} +(2.43785 - 1.41444i) q^{40} +(-1.10021 - 1.90562i) q^{41} +(3.31665 + 1.66287i) q^{42} +(-7.84459 - 4.52908i) q^{43} -3.76846 q^{44} +(6.66009 - 0.802011i) q^{45} -1.34451 q^{46} +(-1.71151 - 0.988139i) q^{47} +(-0.252348 - 4.28267i) q^{48} +(0.500000 + 0.866025i) q^{49} +(9.25247 - 5.39468i) q^{50} +(2.40872 + 3.65688i) q^{51} +(12.5361 + 7.23771i) q^{52} +9.59662i q^{53} +(-3.78559 + 10.4669i) q^{54} +(-3.25546 + 0.00694537i) q^{55} +(-0.630227 + 1.09159i) q^{56} +(7.83025 - 5.15764i) q^{57} +(-15.7080 + 9.06902i) q^{58} +(2.11630 + 3.66555i) q^{59} +(0.611027 + 10.0063i) q^{60} +(2.78250 - 4.81944i) q^{61} -0.0206897i q^{62} +(-2.40394 + 1.79473i) q^{63} +11.8112 q^{64} +(10.8429 + 6.22933i) q^{65} +(2.42095 - 4.82867i) q^{66} +(-5.10805 + 2.94914i) q^{67} +(-5.66723 + 3.27197i) q^{68} +(0.487256 - 0.971847i) q^{69} +(-2.38604 + 4.15319i) q^{70} -12.8357 q^{71} +(-3.47414 - 1.49302i) q^{72} -0.0195652i q^{73} +(3.25285 - 5.63410i) q^{74} +(0.546289 + 8.64301i) q^{75} +(7.00608 + 12.1349i) q^{76} +(1.26084 - 0.727944i) q^{77} +(-17.3274 + 11.4133i) q^{78} +(-8.34375 + 14.4518i) q^{79} +(5.53848 - 0.0118161i) q^{80} +(-6.19389 - 6.52960i) q^{81} +4.71343i q^{82} +(12.7821 + 7.37977i) q^{83} +(-2.46615 - 3.74407i) q^{84} +(-4.88971 + 2.83700i) q^{85} +(9.70156 + 16.8036i) q^{86} +(-0.862684 - 14.6408i) q^{87} +(1.58923 + 0.917541i) q^{88} -13.5736 q^{89} +(-13.2140 - 5.64537i) q^{90} -5.59236 q^{91} +(1.40701 + 0.812339i) q^{92} +(0.0149551 + 0.00749805i) q^{93} +(2.11666 + 3.66615i) q^{94} +(6.07469 + 10.4700i) q^{95} +(-6.07571 + 12.1182i) q^{96} +(10.6278 + 6.13594i) q^{97} -2.14206i q^{98} +(2.61293 + 3.49987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.85508	−	1.07103i	−1.31174	−	0.757333i	−0.329356	−	0.944206i	$-0.606832\pi$
$2$	−1.85508	−	1.07103i	−1.31174	−	0.757333i	−0.982384	+	0.186873i	$0.940165\pi$
$3$	1.44646	−	0.952757i	0.835115	−	0.550075i
$3$	1.44646	−	0.952757i	0.835115	−	0.550075i
$4$	1.29422	+	2.24165i	0.647108	+	1.12082i
$5$	1.12216	+	1.93410i	0.501846	+	0.864957i
$5$	1.12216	+	1.93410i	0.501846	+	0.864957i
$6$	−3.70374	+	0.218235i	−1.51204	+	0.0890943i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	1.26045i		−	0.445638i
$9$	1.18451	−	2.75626i	0.394835	−	0.918752i
$10$	−0.0102188	−	4.78979i	−0.00323147	−	1.51466i
$11$	−0.727944	+	1.26084i	−0.219483	+	0.380156i	−0.954650	−	0.297730i	$-0.903771\pi$
$11$	−0.727944	+	1.26084i	−0.219483	+	0.380156i	0.735167	+	0.677886i	$0.237104\pi$
$12$	4.00778	+	2.00938i	1.15695	+	0.580059i
$13$	4.84312	−	2.79618i	1.34324	−	0.775520i	0.355959	−	0.934502i	$-0.384154\pi$
$13$	4.84312	−	2.79618i	1.34324	−	0.775520i	0.987282	+	0.158981i	$0.0508209\pi$
$14$	1.07103	+	1.85508i	0.286245	+	0.495791i
$15$	3.46590	+	1.72846i	0.894891	+	0.446286i
$16$	1.23844	−	2.14505i	0.309611	−	0.536262i
$17$			2.52815i			0.613167i	0.951844	+	0.306584i	$0.0991859\pi$
$17$			2.52815i			0.613167i	−0.951844	+	0.306584i	$0.900814\pi$
$18$	−5.14939	+	3.84443i	−1.21372	+	0.906141i
$19$	5.41338			1.24191			0.620957	−	0.783845i	$-0.286744\pi$
$19$	5.41338			1.24191			0.620957	+	0.783845i	$0.286744\pi$
$20$	−2.88325	+	5.01864i	−0.644715	+	1.12220i
$21$	−1.72905	+	0.101881i	−0.377310	+	0.0222323i
$22$	2.70079	−	1.55930i	0.575810	−	0.332444i
$23$	0.543577	−	0.313834i	0.113344	−	0.0654390i	−0.442256	−	0.896889i	$-0.645822\pi$
$23$	0.543577	−	0.313834i	0.113344	−	0.0654390i	0.555600	+	0.831450i	$0.312489\pi$
$24$	−1.20091	−	1.82320i	−0.245134	−	0.372159i
$25$	−2.48150	+	4.34075i	−0.496300	+	0.868151i
$26$	−11.9792			−2.34931
$27$	−0.912699	−	5.11537i	−0.175649	−	0.984453i
$28$		−	2.58843i		−	0.489167i
$29$	4.23378	−	7.33312i	0.786193	−	1.36173i	−0.142091	−	0.989854i	$-0.545382\pi$
$29$	4.23378	−	7.33312i	0.786193	−	1.36173i	0.928284	−	0.371873i	$-0.121284\pi$
$30$	−4.57829	−	6.91851i	−0.835877	−	1.26314i
$31$	0.00482938	+	0.00836474i	0.000867383	+	0.00150235i	0.866459	−	0.499249i	$-0.166391\pi$
$31$	0.00482938	+	0.00836474i	0.000867383	+	0.00150235i	−0.865591	+	0.500751i	$0.833057\pi$
$32$	−6.77800	+	3.91328i	−1.19819	+	0.691777i
$33$	0.148327	+	2.51731i	0.0258205	+	0.438207i
$34$	2.70773	−	4.68993i	0.464372	−	0.804316i
$35$	−0.00477054	−	2.23606i	−0.000806369	−	0.377964i
$36$	7.71156	−	0.911943i	1.28526	−	0.151991i
$37$			3.03712i			0.499299i	0.968336	+	0.249650i	$0.0803155\pi$
$37$			3.03712i			0.499299i	−0.968336	+	0.249650i	$0.919685\pi$
$38$	−10.0423	−	5.79790i	−1.62907	−	0.940543i
$39$	4.34132	−	8.65889i	0.695167	−	1.38653i
$40$	2.43785	−	1.41444i	0.385458	−	0.223642i
$41$	−1.10021	−	1.90562i	−0.171824	−	0.297607i	0.767234	−	0.641367i	$-0.221633\pi$
$41$	−1.10021	−	1.90562i	−0.171824	−	0.297607i	−0.939057	+	0.343760i	$0.888299\pi$
$42$	3.31665	+	1.66287i	0.511770	+	0.256587i
$43$	−7.84459	−	4.52908i	−1.19629	−	0.690678i	−0.236563	−	0.971616i	$-0.576021\pi$
$43$	−7.84459	−	4.52908i	−1.19629	−	0.690678i	−0.959726	+	0.280938i	$0.909354\pi$
$44$	−3.76846			−0.568117
$45$	6.66009	−	0.802011i	0.992827	−	0.119557i
$46$	−1.34451			−0.198237
$47$	−1.71151	−	0.988139i	−0.249649	−	0.144135i	0.369955	−	0.929050i	$-0.379373\pi$
$47$	−1.71151	−	0.988139i	−0.249649	−	0.144135i	−0.619604	+	0.784915i	$0.712707\pi$
$48$	−0.252348	−	4.28267i	−0.0364233	−	0.618150i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	9.25247	−	5.39468i	1.30850	−	0.762924i
$51$	2.40872	+	3.65688i	0.337288	+	0.512065i
$52$	12.5361	+	7.23771i	1.73844	+	1.00369i
$53$			9.59662i			1.31820i	0.752057	+	0.659098i	$0.229062\pi$
$53$			9.59662i			1.31820i	−0.752057	+	0.659098i	$0.770938\pi$
$54$	−3.78559	+	10.4669i	−0.515153	+	1.42437i
$55$	−3.25546	+	0.00694537i	−0.438966	+	0.000936514i
$56$	−0.630227	+	1.09159i	−0.0842177	+	0.145869i
$57$	7.83025	−	5.15764i	1.03714	−	0.683146i
$58$	−15.7080	+	9.06902i	−2.06256	+	1.19082i
$59$	2.11630	+	3.66555i	0.275519	+	0.477214i	0.970266	−	0.242041i	$-0.0778168\pi$
$59$	2.11630	+	3.66555i	0.275519	+	0.477214i	−0.694747	+	0.719255i	$0.744484\pi$
$60$	0.611027	+	10.0063i	0.0788833	+	1.29181i
$61$	2.78250	−	4.81944i	0.356263	−	0.617066i	−0.631070	−	0.775726i	$-0.717384\pi$
$61$	2.78250	−	4.81944i	0.356263	−	0.617066i	0.987333	+	0.158660i	$0.0507174\pi$
$62$		−	0.0206897i		−	0.00262759i
$63$	−2.40394	+	1.79473i	−0.302868	+	0.226115i
$64$	11.8112			1.47640
$65$	10.8429	+	6.22933i	1.34489	+	0.772653i
$66$	2.42095	−	4.82867i	0.297999	−	0.594368i
$67$	−5.10805	+	2.94914i	−0.624048	+	0.360294i	−0.778443	−	0.627715i	$-0.783990\pi$
$67$	−5.10805	+	2.94914i	−0.624048	+	0.360294i	0.154395	+	0.988009i	$0.450657\pi$
$68$	−5.66723	+	3.27197i	−0.687252	+	0.396785i
$69$	0.487256	−	0.971847i	0.0586587	−	0.116997i
$70$	−2.38604	+	4.15319i	−0.285187	+	0.496401i
$71$	−12.8357			−1.52332			−0.761661	−	0.647975i	$-0.775616\pi$
$71$	−12.8357			−1.52332			−0.761661	+	0.647975i	$0.775616\pi$
$72$	−3.47414	−	1.49302i	−0.409431	−	0.175954i
$73$		−	0.0195652i		−	0.00228994i	−0.999999	−	0.00114497i	$-0.999636\pi$
$73$		−	0.0195652i		−	0.00228994i	0.999999	−	0.00114497i	$-0.000364455\pi$
$74$	3.25285	−	5.63410i	0.378136	−	0.654951i
$75$	0.546289	+	8.64301i	0.0630800	+	0.998008i
$76$	7.00608	+	12.1349i	0.803652	+	1.39197i
$77$	1.26084	−	0.727944i	0.143686	−	0.0829569i
$78$	−17.3274	+	11.4133i	−1.96194	+	1.29230i
$79$	−8.34375	+	14.4518i	−0.938745	+	1.62595i	−0.170929	+	0.985283i	$0.554677\pi$
$79$	−8.34375	+	14.4518i	−0.938745	+	1.62595i	−0.767816	+	0.640671i	$0.778656\pi$
$80$	5.53848	−	0.0118161i	0.619221	−	0.00132108i
$81$	−6.19389	−	6.52960i	−0.688210	−	0.725512i
$82$			4.71343i			0.520511i
$83$	12.7821	+	7.37977i	1.40302	+	0.810035i	0.994702	−	0.102803i	$-0.0327811\pi$
$83$	12.7821	+	7.37977i	1.40302	+	0.810035i	0.408321	+	0.912838i	$0.366114\pi$
$84$	−2.46615	−	3.74407i	−0.269079	−	0.408511i
$85$	−4.88971	+	2.83700i	−0.530363	+	0.307716i
$86$	9.70156	+	16.8036i	1.04615	+	1.81198i
$87$	−0.862684	−	14.6408i	−0.0924894	−	1.56966i
$88$	1.58923	+	0.917541i	0.169412	+	0.0978101i
$89$	−13.5736			−1.43879			−0.719397	−	0.694599i	$-0.755582\pi$
$89$	−13.5736			−1.43879			−0.719397	+	0.694599i	$0.755582\pi$
$90$	−13.2140	−	5.64537i	−1.39288	−	0.595074i
$91$	−5.59236			−0.586238
$92$	1.40701	+	0.812339i	0.146691	+	0.0846922i
$93$	0.0149551	+	0.00749805i	0.00155077	+	0.000777511i
$94$	2.11666	+	3.66615i	0.218316	+	0.378135i
$95$	6.07469	+	10.4700i	0.623250	+	1.07420i
$96$	−6.07571	+	12.1182i	−0.620100	+	1.23681i
$97$	10.6278	+	6.13594i	1.07909	+	0.623011i	0.930650	−	0.365911i	$-0.119243\pi$
$97$	10.6278	+	6.13594i	1.07909	+	0.623011i	0.148436	+	0.988922i	$0.452576\pi$
$98$		−	2.14206i		−	0.216381i
$99$	2.61293	+	3.49987i	0.262610	+	0.351750i
$100$	−12.9420	+	0.0552228i	−1.29420	+	0.00552228i
$101$	0.983472	−	1.70342i	0.0978591	−	0.169497i	−0.812939	−	0.582349i	$-0.802134\pi$
$101$	0.983472	−	1.70342i	0.0978591	−	0.169497i	0.910798	+	0.412852i	$0.135467\pi$
$102$	−0.551733	−	9.36361i	−0.0546297	−	0.927136i
$103$	−8.61087	+	4.97149i	−0.848454	+	0.489855i	−0.860129	−	0.510077i	$-0.829617\pi$
$103$	−8.61087	+	4.97149i	−0.848454	+	0.489855i	0.0116750	+	0.999932i	$0.496284\pi$
$104$	−3.52446	−	6.10454i	−0.345601	−	0.598599i
$105$	−2.13733	−	3.22984i	−0.208582	−	0.315200i
$106$	10.2783	−	17.8025i	0.998315	−	1.72913i
$107$		−	16.8968i		−	1.63347i	−0.577011	−	0.816736i	$-0.695781\pi$
$107$		−	16.8968i		−	1.63347i	0.577011	−	0.816736i	$-0.304219\pi$
$108$	10.2856	−	8.66634i	0.989734	−	0.833918i
$109$	8.64269			0.827820			0.413910	−	0.910318i	$-0.364163\pi$
$109$	8.64269			0.827820			0.413910	+	0.910318i	$0.364163\pi$
$110$	6.04657	+	3.47381i	0.576518	+	0.331215i
$111$	2.89364	+	4.39308i	0.274652	+	0.416973i
$112$	−2.14505	+	1.23844i	−0.202688	+	0.117022i
$113$	11.3009	−	6.52460i	1.06310	−	0.613783i	0.136814	−	0.990597i	$-0.456314\pi$
$113$	11.3009	−	6.52460i	1.06310	−	0.613783i	0.926289	+	0.376814i	$0.122980\pi$
$114$	−20.0497	+	1.18139i	−1.87783	+	0.110647i
$115$	1.21697	+	0.699160i	0.113483	+	0.0651971i
$116$	21.9177			2.03501
$117$	−1.97027	−	16.6610i	−0.182152	−	1.54031i
$118$		−	9.06651i		−	0.834640i
$119$	1.26408	−	2.18944i	0.115878	−	0.200706i
$120$	2.17864	−	4.36861i	0.198882	−	0.398797i
$121$	4.44020	+	7.69064i	0.403654	+	0.699149i
$122$	−10.3235	+	5.96029i	−0.934649	+	0.539620i
$123$	−3.40700	−	1.70817i	−0.307199	−	0.154021i
$124$	−0.0125005	+	0.0216515i	−0.00112258	+	0.00194437i
$125$	−11.1801	+	0.0715577i	−0.999980	+	0.00640031i
$126$	6.38172	−	0.754681i	0.568529	−	0.0672323i
$127$			3.62083i			0.321297i	0.987012	+	0.160648i	$0.0513585\pi$
$127$			3.62083i			0.321297i	−0.987012	+	0.160648i	$0.948642\pi$
$128$	−8.35473	−	4.82360i	−0.738460	−	0.426350i
$129$	−15.6620	+	0.922854i	−1.37896	+	0.0812528i
$130$	−13.4426	−	23.1689i	−1.17899	−	2.03205i
$131$	−7.03266	−	12.1809i	−0.614447	−	1.06425i	−0.990481	−	0.137647i	$-0.956046\pi$
$131$	−7.03266	−	12.1809i	−0.614447	−	1.06425i	0.376035	−	0.926606i	$-0.377287\pi$
$132$	−5.45094	+	3.59043i	−0.474444	+	0.312507i
$133$	−4.68812	−	2.70669i	−0.406512	−	0.234700i
$134$	12.6345			1.09145
$135$	8.86944	−	7.50553i	0.763360	−	0.645973i
$136$	3.18662			0.273251
$137$	2.70676	+	1.56275i	0.231254	+	0.133515i	0.611151	−	0.791514i	$-0.290707\pi$
$137$	2.70676	+	1.56275i	0.231254	+	0.133515i	−0.379896	+	0.925029i	$0.624040\pi$
$138$	−1.94478	+	1.28099i	−0.165550	+	0.109045i
$139$	−3.09586	−	5.36219i	−0.262587	−	0.454815i	0.704341	−	0.709861i	$-0.251242\pi$
$139$	−3.09586	−	5.36219i	−0.262587	−	0.454815i	−0.966929	+	0.255047i	$0.917909\pi$
$140$	5.00629	−	2.90464i	0.423109	−	0.245487i
$141$	−3.41709	+	0.201345i	−0.287771	+	0.0169563i
$142$	23.8113	+	13.7475i	1.99820	+	1.15366i
$143$			8.14185i			0.680855i
$144$	−4.44536	−	5.95429i	−0.370446	−	0.496191i
$145$	18.9340	−	0.0403948i	1.57238	−	0.00335461i
$146$	−0.0209550	+	0.0362950i	−0.00173424	+	0.00300380i
$147$	1.54834	+	0.776294i	0.127705	+	0.0640277i
$148$	−6.80815	+	3.93069i	−0.559626	+	0.323100i
$149$	−1.03632	−	1.79496i	−0.0848985	−	0.147049i	0.820449	−	0.571719i	$-0.193723\pi$
$149$	−1.03632	−	1.79496i	−0.0848985	−	0.147049i	−0.905348	+	0.424671i	$0.860390\pi$
$150$	8.24352	−	16.6186i	0.673081	−	1.35690i
$151$	−5.55913	+	9.62870i	−0.452396	+	0.783572i	−0.998534	−	0.0541226i	$-0.982764\pi$
$151$	−5.55913	+	9.62870i	−0.452396	+	0.783572i	0.546139	+	0.837695i	$0.316097\pi$
$152$		−	6.82332i		−	0.553444i
$153$	6.96824	+	2.99461i	0.563348	+	0.242100i
$154$	−3.11860			−0.251304
$155$	−0.0107589	+	0.0187271i	−0.000864176	+	0.00150420i
$156$	25.0288	−	1.47477i	2.00390	−	0.118076i
$157$	−13.8622	+	8.00336i	−1.10633	+	0.638737i	−0.937875	−	0.346973i	$-0.887210\pi$
$157$	−13.8622	+	8.00336i	−1.10633	+	0.638737i	−0.168450	+	0.985710i	$0.553876\pi$
$158$	30.9566	−	17.8728i	2.46278	−	1.42189i
$159$	9.14325	+	13.8811i	0.725107	+	1.10085i
$160$	−15.1747	−	8.71800i	−1.19967	−	0.689219i
$161$	−0.627669			−0.0494672
$162$	4.49675	+	18.7468i	0.353298	+	1.47289i
$163$		−	7.28015i		−	0.570225i	−0.958494	−	0.285113i	$-0.907969\pi$
$163$		−	7.28015i		−	0.570225i	0.958494	−	0.285113i	$-0.0920310\pi$
$164$	2.84781	−	4.93255i	0.222377	−	0.385168i
$165$	−4.70228	+	3.11171i	−0.366072	+	0.242246i
$166$	−15.8079	−	27.3801i	−1.22693	−	2.12511i
$167$	−16.5513	+	9.55592i	−1.28078	+	0.739459i	−0.976991	−	0.213280i	$-0.931585\pi$
$167$	−16.5513	+	9.55592i	−1.28078	+	0.739459i	−0.303790	+	0.952739i	$0.598252\pi$
$168$	0.128416	+	2.17939i	0.00990754	+	0.168144i
$169$	9.13723	−	15.8261i	0.702864	−	1.21740i
$170$	12.1093	−	0.0258347i	0.928742	−	0.00198143i
$171$	6.41218	−	14.9207i	0.490352	−	1.14101i
$172$		−	23.4464i		−	1.78777i
$173$	−7.67769	−	4.43271i	−0.583724	−	0.337013i	0.178888	−	0.983869i	$-0.442750\pi$
$173$	−7.67769	−	4.43271i	−0.583724	−	0.337013i	−0.762612	+	0.646856i	$0.776083\pi$
$174$	−14.0805	+	28.0839i	−1.06744	+	2.12904i
$175$	4.31942	−	2.51845i	0.326517	−	0.190377i
$176$	1.80304	+	3.12295i	0.135909	+	0.235401i
$177$	6.55353	+	3.28575i	0.492594	+	0.246972i
$178$	25.1800	+	14.5377i	1.88732	+	1.08965i
$179$	−7.79822			−0.582867			−0.291433	−	0.956591i	$-0.594132\pi$
$179$	−7.79822			−0.582867			−0.291433	+	0.956591i	$0.594132\pi$
$180$	10.4174	+	13.8916i	0.776468	+	1.03542i
$181$	−26.2856			−1.95379			−0.976896	−	0.213716i	$-0.931443\pi$
$181$	−26.2856			−1.95379			−0.976896	+	0.213716i	$0.931443\pi$
$182$	10.3743	+	5.98959i	0.768992	+	0.443978i
$183$	−0.566968	−	9.62218i	−0.0419115	−	0.711292i
$184$	−0.395574	−	0.685155i	−0.0291621	−	0.0505103i
$185$	−5.87410	+	3.40814i	−0.431872	+	0.250572i
$186$	−0.0197123	−	0.0299268i	−0.00144537	−	0.00219434i
$187$	−3.18759	−	1.84035i	−0.233099	−	0.134580i
$188$		−	5.11546i		−	0.373083i
$189$	−1.76726	+	4.88639i	−0.128549	+	0.355432i
$190$	−0.0553182	−	25.9289i	−0.00401320	−	1.88108i
$191$	6.43582	−	11.1472i	0.465679	−	0.806580i	−0.533553	−	0.845767i	$-0.679143\pi$
$191$	6.43582	−	11.1472i	0.465679	−	0.806580i	0.999232	+	0.0391867i	$0.0124767\pi$
$192$	17.0845	−	11.2532i	1.23296	−	0.812130i
$193$	13.6973	−	7.90812i	0.985951	−	0.569239i	0.0818894	−	0.996641i	$-0.473905\pi$
$193$	13.6973	−	7.90812i	0.985951	−	0.569239i	0.904061	+	0.427402i	$0.140571\pi$
$194$	−13.1436	−	22.7653i	−0.943653	−	1.63446i
$195$	21.6188	−	1.32014i	1.54816	−	0.0945370i
$196$	−1.29422	+	2.24165i	−0.0924439	+	0.160118i
$197$			7.18825i			0.512142i	0.966658	+	0.256071i	$0.0824281\pi$
$197$			7.18825i			0.512142i	−0.966658	+	0.256071i	$0.917572\pi$
$198$	−1.09873	−	9.29107i	−0.0780834	−	0.660287i
$199$	−16.9190			−1.19936			−0.599678	−	0.800241i	$-0.704705\pi$
$199$	−16.9190			−1.19936			−0.599678	+	0.800241i	$0.704705\pi$
$200$	5.47133	+	3.12782i	0.386881	+	0.221170i
$201$	−4.57879	+	9.13255i	−0.322963	+	0.644160i
$202$	−3.64884	+	2.10666i	−0.256731	+	0.148224i
$203$	−7.33312	+	4.23378i	−0.514684	+	0.297153i
$204$	−5.08003	+	10.1323i	−0.355673	+	0.709401i
$205$	2.45104	−	4.26632i	0.171188	−	0.297973i
$206$	21.2985			1.48393
$207$	−0.221137	−	1.86998i	−0.0153701	−	0.129972i
$208$		−	13.8516i		−	0.960439i
$209$	−3.94064	+	6.82538i	−0.272579	+	0.472122i
$210$	0.505657	+	8.28075i	0.0348937	+	0.571426i
$211$	6.90565	+	11.9609i	0.475404	+	0.823424i	0.999603	−	0.0281715i	$-0.00896845\pi$
$211$	6.90565	+	11.9609i	0.475404	+	0.823424i	−0.524199	+	0.851596i	$0.675635\pi$
$212$	−21.5122	+	12.4201i	−1.47747	+	0.853015i
$213$	−18.5664	+	12.2294i	−1.27215	+	0.837941i
$214$	−18.0970	+	31.3449i	−1.23708	+	2.14269i
$215$	−0.0432123	−	20.2546i	−0.00294705	−	1.38135i
$216$	−6.44769	+	1.15042i	−0.438710	+	0.0782759i
$217$		−	0.00965877i		−	0.000655680i
$218$	−16.0329	−	9.25659i	−1.08588	−	0.626936i
$219$	−0.0186409	−	0.0283003i	−0.00125964	−	0.00191236i
$220$	−4.22883	−	7.28860i	−0.285108	−	0.491397i
$221$	7.06917	+	12.2442i	0.475524	+	0.823631i
$222$	−0.662807	−	11.2487i	−0.0444847	−	0.754963i
$223$	−0.910234	−	0.525524i	−0.0609538	−	0.0351917i	0.469213	−	0.883085i	$-0.344538\pi$
$223$	−0.910234	−	0.525524i	−0.0609538	−	0.0351917i	−0.530167	+	0.847893i	$0.677871\pi$
$224$	7.82656			0.522934
$225$	9.02488	+	11.9813i	0.601658	+	0.798754i
$226$	−27.9522			−1.85935
$227$	−9.66608	−	5.58072i	−0.641561	−	0.370405i	0.143655	−	0.989628i	$-0.454114\pi$
$227$	−9.66608	−	5.58072i	−0.641561	−	0.370405i	−0.785215	+	0.619223i	$0.787448\pi$
$228$	21.6956	+	10.8776i	1.43683	+	0.720384i
$229$	10.5131	+	18.2092i	0.694724	+	1.20330i	0.970274	+	0.242010i	$0.0778068\pi$
$229$	10.5131	+	18.2092i	0.694724	+	1.20330i	−0.275550	+	0.961287i	$0.588860\pi$
$230$	−1.50875	−	2.60041i	−0.0994843	−	0.171466i
$231$	1.13020	−	2.25421i	0.0743615	−	0.148316i
$232$	−9.24307	−	5.33649i	−0.606837	−	0.350358i
$233$			15.9935i			1.04777i	0.851789	+	0.523885i	$0.175518\pi$
$233$			15.9935i			1.04777i	−0.851789	+	0.523885i	$0.824482\pi$
$234$	−14.1894	+	33.0177i	−0.927591	+	2.15843i
$235$	−0.00942792	−	4.41908i	−0.000615009	−	0.288269i
$236$	−5.47791	+	9.48801i	−0.356581	+	0.617617i
$237$	1.70014	+	28.8535i	0.110436	+	1.87424i
$238$	−4.68993	+	2.70773i	−0.304003	+	0.175516i
$239$	−9.17807	−	15.8969i	−0.593680	−	1.02828i	−0.993732	−	0.111791i	$-0.964341\pi$
$239$	−9.17807	−	15.8969i	−0.593680	−	1.02828i	0.400052	−	0.916492i	$-0.368992\pi$
$240$	7.99994	−	5.29392i	0.516394	−	0.341721i
$241$	−6.14120	+	10.6369i	−0.395590	+	0.685182i	−0.993176	−	0.116623i	$-0.962793\pi$
$241$	−6.14120	+	10.6369i	−0.395590	+	0.685182i	0.597586	+	0.801804i	$0.296126\pi$
$242$		−	19.0223i		−	1.22280i
$243$	−15.1804	−	3.54355i	−0.973820	−	0.227319i
$244$	14.4046			0.922162
$245$	−1.11390	+	1.93887i	−0.0711645	+	0.123870i
$246$	4.49075	+	6.81779i	0.286320	+	0.434687i
$247$	26.2177	−	15.1368i	1.66819	−	0.963130i
$248$	0.0105434	−	0.00608722i	0.000669505	−	0.000386539i
$249$	25.5200	−	1.50372i	1.61727	−	0.0952942i
$250$	20.8166	+	11.8415i	1.31656	+	0.748922i
$251$	8.96476			0.565851			0.282925	−	0.959142i	$-0.408695\pi$
$251$	8.96476			0.565851			0.282925	+	0.959142i	$0.408695\pi$
$252$	−7.13438	−	3.06601i	−0.449423	−	0.193141i
$253$			0.913816i			0.0574511i
$254$	3.87802	−	6.71693i	0.243329	−	0.421457i
$255$	−4.36980	+	8.76232i	−0.273648	+	0.548718i
$256$	−1.47874	−	2.56126i	−0.0924213	−	0.160078i
$257$	−16.7998	+	9.69937i	−1.04794	+	0.605030i	−0.922073	−	0.387017i	$-0.873506\pi$
$257$	−16.7998	+	9.69937i	−1.04794	+	0.605030i	−0.125870	+	0.992047i	$0.540172\pi$
$258$	30.0427	+	15.0625i	1.87038	+	0.937753i
$259$	1.51856	−	2.63022i	0.0943587	−	0.163434i
$260$	0.0690556	+	32.3680i	0.00428265	+	2.00738i
$261$	−15.1970	−	20.3555i	−0.940672	−	1.25997i
$262$			30.1288i			1.86136i
$263$	−4.76318	−	2.75003i	−0.293711	−	0.169574i	0.345903	−	0.938270i	$-0.387572\pi$
$263$	−4.76318	−	2.75003i	−0.293711	−	0.169574i	−0.639614	+	0.768696i	$0.720906\pi$
$264$	3.17295	−	0.186960i	0.195282	−	0.0115066i
$265$	−18.5608	+	10.7690i	−1.14018	+	0.661533i
$266$	5.79790	+	10.0423i	0.355492	+	0.615730i
$267$	−19.6336	+	12.9323i	−1.20156	+	0.791445i
$268$	−13.2218	−	7.63363i	−0.807652	−	0.466298i
$269$	4.70095			0.286622			0.143311	−	0.989678i	$-0.454225\pi$
$269$	4.70095			0.286622			0.143311	+	0.989678i	$0.454225\pi$
$270$	−24.4922	+	4.42391i	−1.49055	+	0.269230i
$271$	−3.67634			−0.223322			−0.111661	−	0.993746i	$-0.535617\pi$
$271$	−3.67634			−0.223322			−0.111661	+	0.993746i	$0.535617\pi$
$272$	5.42301	+	3.13098i	0.328818	+	0.189843i
$273$	−8.08913	+	5.32816i	−0.489577	+	0.322475i
$274$	−3.34751	−	5.79805i	−0.202230	−	0.350273i
$275$	−3.66659	−	6.28859i	−0.221103	−	0.379216i
$276$	2.80915	−	0.165524i	0.169091	−	0.00996336i
$277$	−21.6668	−	12.5093i	−1.30183	−	0.751612i	−0.321112	−	0.947041i	$-0.604057\pi$
$277$	−21.6668	−	12.5093i	−1.30183	−	0.751612i	−0.980718	+	0.195429i	$0.937390\pi$
$278$			13.2630i			0.795465i
$279$	0.0287758	−	0.00340293i	0.00172276	−	0.000203728i
$280$	−2.81846	+	0.00601305i	−0.168435	+	0.000359349i
$281$	2.28536	−	3.95836i	0.136333	−	0.236136i	−0.789773	−	0.613399i	$-0.789802\pi$
$281$	2.28536	−	3.95836i	0.136333	−	0.236136i	0.926106	+	0.377264i	$0.123135\pi$
$282$	6.55462	+	3.28630i	0.390322	+	0.195696i
$283$	13.6707	−	7.89280i	0.812640	−	0.469178i	−0.0352316	−	0.999379i	$-0.511217\pi$
$283$	13.6707	−	7.89280i	0.812640	−	0.469178i	0.847872	+	0.530201i	$0.177884\pi$
$284$	−16.6122	−	28.7732i	−0.985754	−	1.70738i
$285$	18.7622	+	9.35679i	1.11138	+	0.554248i
$286$	8.72017	−	15.1038i	0.515634	−	0.893105i
$287$			2.20042i			0.129886i
$288$	2.75742	+	23.3172i	0.162482	+	1.37398i
$289$	10.6084			0.624026
$290$	−35.1673	−	20.2040i	−2.06510	−	1.18642i
$291$	21.2187	−	1.25027i	1.24386	−	0.0732923i
$292$	0.0438583	−	0.0253216i	0.00256661	−	0.00148183i
$293$	17.1463	−	9.89943i	1.00170	−	0.578331i	0.0929482	−	0.995671i	$-0.470371\pi$
$293$	17.1463	−	9.89943i	1.00170	−	0.578331i	0.908750	+	0.417340i	$0.137038\pi$
$294$	−2.04087	−	3.09841i	−0.119026	−	0.180703i
$295$	−4.71470	+	8.20649i	−0.274501	+	0.477800i
$296$	3.82815			0.222507
$297$	7.11403	+	2.57294i	0.412798	+	0.149297i
$298$			4.43972i			0.257186i
$299$	1.75507	−	3.03988i	0.101499	−	0.175801i
$300$	−18.6676	+	12.4105i	−1.07777	+	0.716520i
$301$	4.52908	+	7.84459i	0.261052	+	0.452155i
$302$	20.6253	−	11.9080i	1.18685	−	0.685229i
$303$	−0.200394	−	3.40095i	−0.0115123	−	0.195379i
$304$	6.70417	−	11.6120i	0.384510	−	0.665991i
$305$	12.4437	−	0.0265481i	0.712524	−	0.00152014i
$306$	−9.71931	−	13.0184i	−0.555616	−	0.744215i
$307$		−	5.71932i		−	0.326419i	−0.986591	−	0.163209i	$-0.947815\pi$
$307$		−	5.71932i		−	0.326419i	0.986591	−	0.163209i	$-0.0521846\pi$
$308$	3.26359	+	1.88423i	0.185960	+	0.107364i
$309$	−7.71867	+	15.3951i	−0.439100	+	0.875799i
$310$	0.0400160	−	0.0232172i	0.00227275	−	0.00131865i
$311$	−1.21595	−	2.10609i	−0.0689504	−	0.119426i	0.829489	−	0.558523i	$-0.188632\pi$
$311$	−1.21595	−	2.10609i	−0.0689504	−	0.119426i	−0.898440	+	0.439097i	$0.855298\pi$
$312$	−10.9141	−	5.47203i	−0.617891	−	0.309793i
$313$	9.23829	+	5.33373i	0.522179	+	0.301480i	0.737826	−	0.674991i	$-0.235853\pi$
$313$	9.23829	+	5.33373i	0.522179	+	0.301480i	−0.215647	+	0.976471i	$0.569186\pi$
$314$	34.2874			1.93495
$315$	−6.16881	−	2.63548i	−0.347573	−	0.148493i
$316$	−43.1944			−2.42988
$317$	−15.8994	−	9.17953i	−0.893000	−	0.515574i	−0.0180777	−	0.999837i	$-0.505755\pi$
$317$	−15.8994	−	9.17953i	−0.893000	−	0.515574i	−0.874923	+	0.484263i	$0.839088\pi$
$318$	−2.09432	−	35.5433i	−0.117444	−	1.99317i
$319$	6.16391	+	10.6762i	0.345113	+	0.597753i
$320$	13.2541	+	22.8441i	0.740926	+	1.27702i
$321$	−16.0985	−	24.4405i	−0.898532	−	1.36414i
$322$	1.16438	+	0.672253i	0.0648882	+	0.0374632i
$323$			13.6858i			0.761501i
$324$	6.62084	−	22.3352i	0.367824	−	1.24085i
$325$	0.119310	+	27.9615i	0.00661812	+	1.55103i
$326$	−7.79726	+	13.5053i	−0.431850	+	0.747987i
$327$	12.5013	−	8.23439i	0.691325	−	0.455363i
$328$	−2.40194	+	1.38676i	−0.132625	+	0.0765711i
$329$	0.988139	+	1.71151i	0.0544779	+	0.0943584i
$330$	12.0558	−	0.736180i	0.663652	−	0.0405254i
$331$	10.0383	−	17.3868i	0.551752	−	0.955663i	−0.446396	−	0.894835i	$-0.647293\pi$
$331$	10.0383	−	17.3868i	0.551752	−	0.955663i	0.998148	−	0.0608273i	$-0.0193739\pi$
$332$			38.2041i			2.09672i
$333$	8.37108	+	3.59749i	0.458732	+	0.197141i
$334$	40.9387			2.24007
$335$	−11.4360	−	6.57008i	−0.624815	−	0.358962i
$336$	−1.92279	+	3.83507i	−0.104897	+	0.209220i
$337$	11.5496	−	6.66818i	0.629148	−	0.363239i	−0.151274	−	0.988492i	$-0.548338\pi$
$337$	11.5496	−	6.66818i	0.629148	−	0.363239i	0.780422	+	0.625253i	$0.215004\pi$
$338$	−33.9006	+	19.5725i	−1.84395	+	1.06460i
$339$	10.1300	−	20.2046i	0.550187	−	1.09737i
$340$	−12.6879	−	7.28930i	−0.688097	−	0.395318i
$341$	−0.0140621			−0.000761505
$342$	−27.8756	+	20.8114i	−1.50734	+	1.12535i
$343$		−	1.00000i		−	0.0539949i
$344$	−5.70870	+	9.88775i	−0.307792	+	0.533112i
$345$	2.42643	−	0.148168i	0.130635	−	0.00797710i
$346$	9.49515	+	16.4461i	0.510462	+	0.884147i
$347$	21.9229	−	12.6572i	1.17688	−	0.679474i	0.221592	−	0.975139i	$-0.428875\pi$
$347$	21.9229	−	12.6572i	1.17688	−	0.679474i	0.955292	+	0.295665i	$0.0955412\pi$
$348$	31.7031	−	20.8822i	1.69947	−	1.11941i
$349$	14.0984	−	24.4191i	0.754668	−	1.30712i	−0.190871	−	0.981615i	$-0.561131\pi$
$349$	14.0984	−	24.4191i	0.754668	−	1.30712i	0.945539	−	0.325508i	$-0.105535\pi$
$350$	−10.7102	+	0.0456997i	−0.572485	+	0.00244275i
$351$	−18.7238	−	22.2223i	−0.999402	−	1.18614i
$352$		−	11.3946i		−	0.607334i
$353$	3.10079	+	1.79024i	0.165038	+	0.0952850i	0.580244	−	0.814443i	$-0.302957\pi$
$353$	3.10079	+	1.79024i	0.165038	+	0.0952850i	−0.415206	+	0.909728i	$0.636290\pi$
$354$	−8.63819	−	13.1144i	−0.459114	−	0.697021i
$355$	−14.4038	−	24.8256i	−0.764474	−	1.31761i
$356$	−17.5671	−	30.4271i	−0.931055	−	1.61263i
$357$	−0.257571	−	4.37131i	−0.0136321	−	0.231354i
$358$	14.4663	+	8.35214i	0.764569	+	0.441424i
$359$	−2.31414			−0.122136			−0.0610678	−	0.998134i	$-0.519451\pi$
$359$	−2.31414			−0.122136			−0.0610678	+	0.998134i	$0.519451\pi$
$360$	−1.01090	−	8.39474i	−0.0532791	−	0.442442i
$361$	10.3047			0.542351
$362$	48.7619	+	28.1527i	2.56287	+	1.47967i
$363$	13.7499	+	6.89380i	0.721682	+	0.361831i
$364$	−7.23771	−	12.5361i	−0.379359	−	0.657070i
$365$	0.0378411	−	0.0219554i	0.00198070	−	0.00114920i
$366$	−9.25389	+	18.4572i	−0.483708	+	0.964771i
$367$	−28.6771	−	16.5567i	−1.49693	−	0.864254i	−0.496938	−	0.867786i	$-0.665542\pi$
$367$	−28.6771	−	16.5567i	−1.49693	−	0.864254i	−0.999994	+	0.00353190i	$0.998876\pi$
$368$		−	1.55467i		−	0.0810426i
$369$	−6.55557	+	0.775240i	−0.341269	+	0.0403574i
$370$	14.5472	−	0.0310357i	0.756270	−	0.00161347i
$371$	4.79831	−	8.31092i	0.249116	−	0.431481i
$372$	0.00254713	+	0.0432281i	0.000132063	+	0.00224127i
$373$	20.2943	−	11.7169i	1.05080	−	0.606678i	0.127924	−	0.991784i	$-0.459168\pi$
$373$	20.2943	−	11.7169i	1.05080	−	0.606678i	0.922872	+	0.385106i	$0.125835\pi$
$374$	3.94215	+	6.82801i	0.203844	+	0.353068i
$375$	−16.1034	+	10.7554i	−0.831578	+	0.555409i
$376$	−1.24550	+	2.15728i	−0.0642320	+	0.111253i
$377$		−	47.3536i		−	2.43884i
$378$	8.51189	−	7.17185i	0.437804	−	0.368880i
$379$	2.33427			0.119904			0.0599518	−	0.998201i	$-0.480905\pi$
$379$	2.33427			0.119904			0.0599518	+	0.998201i	$0.480905\pi$
$380$	−15.6081	+	27.1678i	−0.800681	+	1.39368i
$381$	3.44977	+	5.23739i	0.176737	+	0.268320i
$382$	−23.8779	+	13.7859i	−1.22170	+	0.705349i
$383$	−6.56559	+	3.79065i	−0.335486	+	0.193693i	−0.658274	−	0.752778i	$-0.728713\pi$
$383$	−6.56559	+	3.79065i	−0.335486	+	0.193693i	0.322788	+	0.946471i	$0.395380\pi$
$384$	−16.6805	+	0.982867i	−0.851224	+	0.0501567i
$385$	2.82278	+	1.62171i	0.143862	+	0.0826502i
$386$	−33.8794			−1.72441
$387$	−21.7753	+	16.2570i	−1.10690	+	0.826389i
$388$			31.7649i			1.61262i
$389$	−4.04380	+	7.00407i	−0.205029	+	0.355121i	−0.950142	−	0.311818i	$-0.899062\pi$
$389$	−4.04380	+	7.00407i	−0.205029	+	0.355121i	0.745113	+	0.666938i	$0.232396\pi$
$390$	−41.5186	−	20.7055i	−2.10238	−	1.04846i
$391$	0.793422	+	1.37425i	0.0401251	+	0.0694986i
$392$	1.09159	−	0.630227i	0.0551334	−	0.0318313i
$393$	−21.7780	−	10.9188i	−1.09855	−	0.550782i
$394$	7.69884	−	13.3348i	0.387862	−	0.671797i
$395$	−37.3143	+	0.0796084i	−1.87749	+	0.00400553i
$396$	−4.46377	+	10.3869i	−0.224313	+	0.521959i
$397$			17.4642i			0.876505i	0.898852	+	0.438253i	$0.144402\pi$
$397$			17.4642i			0.876505i	−0.898852	+	0.438253i	$0.855598\pi$
$398$	31.3861	+	18.1208i	1.57324	+	0.908313i
$399$	−9.36001	+	0.551520i	−0.468587	+	0.0276106i
$400$	6.23793	+	10.6987i	0.311896	+	0.534936i
$401$	6.08616	+	10.5415i	0.303928	+	0.526419i	0.977022	−	0.213138i	$-0.0683683\pi$
$401$	6.08616	+	10.5415i	0.303928	+	0.526419i	−0.673094	+	0.739557i	$0.735035\pi$
$402$	18.2753	−	12.0376i	0.911488	−	0.600380i
$403$	0.0467786	+	0.0270076i	0.00233021	+	0.00134535i
$404$	5.09130			0.253302
$405$	5.67837	−	19.3069i	0.282160	−	0.959367i
$406$	18.1380			0.900176
$407$	−3.82931	−	2.21085i	−0.189812	−	0.109588i
$408$	4.60933	−	3.03608i	0.228196	−	0.150308i
$409$	−13.0476	−	22.5991i	−0.645161	−	1.11745i	−0.984264	−	0.176703i	$-0.943457\pi$
$409$	−13.0476	−	22.5991i	−0.645161	−	1.11745i	0.339103	−	0.940749i	$-0.389876\pi$
$410$	−9.11625	+	5.28923i	−0.450219	+	0.261217i
$411$	5.40415	−	0.318429i	0.266567	−	0.0157069i
$412$	−22.2886	−	12.8683i	−1.09808	−	0.633978i
$413$		−	4.23261i		−	0.208273i
$414$	−1.59258	+	3.70580i	−0.0782708	+	0.182130i
$415$	0.0704110	+	33.0033i	0.00345634	+	1.62007i
$416$	−21.8845	+	37.9050i	−1.07297	+	1.85844i
$417$	−9.58691	−	4.80660i	−0.469473	−	0.235380i
$418$	14.6204	−	8.44109i	0.715107	−	0.412867i
$419$	10.1361	+	17.5562i	0.495179	+	0.857676i	0.999985	−	0.00555740i	$-0.00176898\pi$
$419$	10.1361	+	17.5562i	0.495179	+	0.857676i	−0.504805	+	0.863233i	$0.668436\pi$
$420$	4.47399	−	8.97123i	0.218308	−	0.437751i
$421$	−10.1781	+	17.6290i	−0.496051	+	0.859185i	−0.999990	−	0.00455429i	$-0.998550\pi$
$421$	−10.1781	+	17.6290i	−0.496051	+	0.859185i	0.503939	+	0.863739i	$0.331884\pi$
$422$		−	29.5847i		−	1.44016i
$423$	−4.75085	+	3.54689i	−0.230994	+	0.172456i
$424$	12.0961			0.587439
$425$	−10.9741	−	6.27361i	−0.532322	−	0.304315i
$426$	47.5402	−	2.80121i	2.30333	−	0.135719i
$427$	−4.81944	+	2.78250i	−0.233229	+	0.134655i
$428$	37.8766	−	21.8681i	1.83083	−	1.05703i
$429$	7.75720	+	11.7769i	0.374521	+	0.568593i
$430$	−21.6131	+	37.6202i	−1.04228	+	1.81421i
$431$	34.7941			1.67597			0.837986	−	0.545692i	$-0.183733\pi$
$431$	34.7941			1.67597			0.837986	+	0.545692i	$0.183733\pi$
$432$	−12.1030	−	4.37731i	−0.582308	−	0.210604i
$433$		−	7.74464i		−	0.372184i	−0.982532	−	0.186092i	$-0.940418\pi$
$433$		−	7.74464i		−	0.372184i	0.982532	−	0.186092i	$-0.0595822\pi$
$434$	−0.0103448	+	0.0179178i	−0.000496568	+	0.000860082i
$435$	27.3488	−	18.0979i	1.31128	−	0.867730i
$436$	11.1855	+	19.3739i	0.535689	+	0.927840i
$437$	2.94259	−	1.69890i	0.140763	−	0.0812696i
$438$	0.00426982	+	0.0724644i	0.000204020	+	0.00346248i
$439$	−9.65328	+	16.7200i	−0.460726	+	0.798001i	−0.998997	−	0.0447710i	$-0.985744\pi$
$439$	−9.65328	+	16.7200i	−0.460726	+	0.798001i	0.538271	+	0.842772i	$0.319078\pi$
$440$	0.00875433	+	4.10336i	0.000417346	+	0.195620i
$441$	2.97924	−	0.352315i	0.141869	−	0.0167769i
$442$		−	30.2852i		−	1.44052i
$443$	10.5867	+	6.11225i	0.502990	+	0.290402i	0.729948	−	0.683503i	$-0.239544\pi$
$443$	10.5867	+	6.11225i	0.502990	+	0.290402i	−0.226957	+	0.973905i	$0.572878\pi$
$444$	−6.10274	+	12.1721i	−0.289623	+	0.577663i
$445$	−15.2317	−	26.2527i	−0.722054	−	1.24450i
$446$	1.12570	+	1.94978i	0.0533037	+	0.0923247i
$447$	−3.20915	−	1.60898i	−0.151788	−	0.0761020i
$448$	−10.2288	−	5.90560i	−0.483265	−	0.279013i
$449$	3.15996			0.149128			0.0745639	−	0.997216i	$-0.476244\pi$
$449$	3.15996			0.149128			0.0745639	+	0.997216i	$0.476244\pi$
$450$	−3.90952	−	31.8922i	−0.184297	−	1.50341i
$451$	3.20356			0.150850
$452$	29.2517	+	16.8885i	1.37588	+	0.794367i
$453$	1.13274	+	19.2241i	0.0532208	+	0.903225i
$454$	11.9542	+	20.7054i	0.561040	+	0.971750i
$455$	−6.27554	−	10.8162i	−0.294202	−	0.507071i
$456$	−6.50097	−	9.86967i	−0.304436	−	0.462190i
$457$	8.02079	+	4.63081i	0.375197	+	0.216620i	0.675726	−	0.737153i	$-0.263830\pi$
$457$	8.02079	+	4.63081i	0.375197	+	0.216620i	−0.300530	+	0.953772i	$0.597163\pi$
$458$		−	45.0393i		−	2.10455i
$459$	12.9324	−	2.30744i	0.603634	−	0.107702i
$460$	0.00775059	+	3.63288i	0.000361373	+	0.169384i
$461$	−19.5604	+	33.8797i	−0.911021	+	1.57793i	−0.0983955	+	0.995147i	$0.531371\pi$
$461$	−19.5604	+	33.8797i	−0.911021	+	1.57793i	−0.812625	+	0.582787i	$0.801962\pi$
$462$	−4.51094	+	2.97127i	−0.209868	+	0.138236i
$463$	−7.64051	+	4.41125i	−0.355085	+	0.205008i	−0.666922	−	0.745127i	$-0.732389\pi$
$463$	−7.64051	+	4.41125i	−0.355085	+	0.205008i	0.311838	+	0.950135i	$0.399055\pi$
$464$	−10.4866	−	18.1633i	−0.486828	−	0.843211i
$465$	0.00228006	+	0.0373387i	0.000105735	+	0.00173154i
$466$	17.1295	−	29.6692i	0.793511	−	1.37440i
$467$		−	24.3474i		−	1.12666i	−0.826232	−	0.563331i	$-0.809520\pi$
$467$		−	24.3474i		−	1.12666i	0.826232	−	0.563331i	$-0.190480\pi$
$468$	34.7981	−	25.9795i	1.60854	−	1.20090i
$469$	5.89827			0.272357
$470$	−4.71549	+	8.20785i	−0.217509	+	0.378600i
$471$	−12.4259	+	24.7839i	−0.572556	+	1.14198i
$472$	4.62026	−	2.66751i	0.212665	−	0.122782i
$473$	11.4208	−	6.59383i	0.525131	−	0.303185i
$474$	27.7492	−	55.3465i	1.27456	−	2.54215i
$475$	−13.4333	+	23.4981i	−0.616362	+	1.07817i
$476$	6.54395			0.299941
$477$	26.4507	+	11.3673i	1.21110	+	0.520471i
$478$			39.3200i			1.79845i
$479$	10.3849	−	17.9871i	0.474496	−	0.821851i	−0.525078	−	0.851054i	$-0.675964\pi$
$479$	10.3849	−	17.9871i	0.474496	−	0.821851i	0.999573	+	0.0292033i	$0.00929703\pi$
$480$	−30.2558	+	1.84754i	−1.38098	+	0.0843285i
$481$	8.49233	+	14.7091i	0.387217	+	0.670679i
$482$	22.7849	−	13.1548i	1.03782	−	0.599187i
$483$	−0.907900	+	0.598016i	−0.0413109	+	0.0272107i
$484$	−11.4931	+	19.9067i	−0.522415	+	0.904850i
$485$	0.0585435	+	27.4407i	0.00265833	+	1.24602i
$486$	24.3655	+	22.8322i	1.10524	+	1.03569i
$487$			15.1713i			0.687476i	0.939066	+	0.343738i	$0.111693\pi$
$487$			15.1713i			0.687476i	−0.939066	+	0.343738i	$0.888307\pi$
$488$	−6.07468	−	3.50722i	−0.274988	−	0.158764i
$489$	−6.93621	−	10.5305i	−0.313666	−	0.476204i
$490$	4.14297	−	2.40374i	0.187160	−	0.108590i
$491$	−2.44664	−	4.23771i	−0.110415	−	0.191245i	0.805522	−	0.592565i	$-0.201885\pi$
$491$	−2.44664	−	4.23771i	−0.110415	−	0.191245i	−0.915938	+	0.401320i	$0.868551\pi$
$492$	−0.580276	−	9.84803i	−0.0261609	−	0.443983i
$493$	18.5393	+	10.7036i	0.834966	+	0.482068i
$494$	−64.8478			−2.91764
$495$	−3.83697	+	8.98110i	−0.172459	+	0.403670i
$496$	0.0239237			0.00107421
$497$	11.1161	+	6.41787i	0.498624	+	0.287881i
$498$	−48.9522	−	24.5432i	−2.19360	−	1.09981i
$499$	16.3239	+	28.2739i	0.730759	+	1.26571i	0.956559	+	0.291539i	$0.0941672\pi$
$499$	16.3239	+	28.2739i	0.730759	+	1.26571i	−0.225800	+	0.974174i	$0.572499\pi$
$500$	−14.6299	−	24.9692i	−0.654268	−	1.11666i
$501$	−14.8364	+	29.5917i	−0.662842	+	1.32206i
$502$	−16.6303	−	9.60154i	−0.742249	−	0.428538i
$503$		−	5.42978i		−	0.242102i	−0.992646	−	0.121051i	$-0.961374\pi$
$503$		−	5.42978i		−	0.242102i	0.992646	−	0.121051i	$-0.0386265\pi$
$504$	2.26218	+	3.03006i	0.100766	+	0.134970i
$505$	4.39821	−	0.00938339i	0.195718	−	0.000417555i
$506$	0.978725	−	1.69520i	0.0435096	−	0.0753609i
$507$	−1.86182	−	31.5975i	−0.0826863	−	1.40329i
$508$	−8.11662	+	4.68613i	−0.360117	+	0.207913i
$509$	10.8200	+	18.7408i	0.479588	+	0.830670i	0.999726	−	0.0234118i	$-0.00745288\pi$
$509$	10.8200	+	18.7408i	0.479588	+	0.830670i	−0.520138	+	0.854082i	$0.674120\pi$
$510$	17.4910	−	11.5746i	0.774517	−	0.512532i
$511$	−0.00978261	+	0.0169440i	−0.000432757	+	0.000749557i
$512$			25.6295i			1.13268i
$513$	−4.94079	−	27.6914i	−0.218141	−	1.22261i
$514$	41.5533			1.83284
$515$	−19.2782	−	11.0755i	−0.849497	−	0.488044i
$516$	−22.3387	−	33.9143i	−0.983408	−	1.49300i
$517$	2.49176	−	1.43862i	0.109588	−	0.0632704i
$518$	−5.63410	+	3.25285i	−0.247548	+	0.142922i
$519$	−15.3288	+	0.903219i	−0.672859	+	0.0396469i
$520$	7.85179	−	13.6669i	0.344324	−	0.599335i
$521$	−15.6968			−0.687690			−0.343845	−	0.939026i	$-0.611729\pi$
$521$	−15.6968			−0.687690			−0.343845	+	0.939026i	$0.611729\pi$
$522$	6.39031	+	54.0376i	0.279696	+	2.36516i
$523$			12.0014i			0.524785i	0.964961	+	0.262392i	$0.0845115\pi$
$523$			12.0014i			0.524785i	−0.964961	+	0.262392i	$0.915489\pi$
$524$	18.2036	−	31.5295i	0.795226	−	1.37737i
$525$	3.84840	−	7.75821i	0.167958	−	0.338596i
$526$	5.89073	+	10.2030i	0.256848	+	0.444874i
$527$	−0.0211473	+	0.0122094i	−0.000921193	+	0.000531851i
$528$	5.58344	+	2.79937i	0.242988	+	0.121827i
$529$	−11.3030	+	19.5774i	−0.491435	+	0.851191i
$530$	45.9657	−	0.0980659i	1.99662	−	0.00425971i
$531$	12.6100	−	1.49121i	0.547226	−	0.0647131i
$532$		−	14.0122i		−	0.607504i
$533$	−10.6569	−	6.15275i	−0.461601	−	0.266505i
$534$	50.2729	−	2.96223i	2.17552	−	0.128188i
$535$	32.6801	−	18.9609i	1.41288	−	0.819752i
$536$	3.71725	+	6.43847i	0.160561	+	0.278100i
$537$	−11.2798	+	7.42981i	−0.486761	+	0.320620i
$538$	−8.72063	−	5.03486i	−0.375973	−	0.217068i
$539$	−1.45589			−0.0627095
$540$	28.3037	+	10.1684i	1.21800	+	0.437578i
$541$	26.5969			1.14349			0.571745	−	0.820431i	$-0.306267\pi$
$541$	26.5969			1.14349			0.571745	+	0.820431i	$0.306267\pi$
$542$	6.81991	+	3.93747i	0.292940	+	0.169129i
$543$	−38.0211	+	25.0438i	−1.63164	+	1.07473i
$544$	−9.89337	−	17.1358i	−0.424175	−	0.734692i
$545$	9.69851	+	16.7159i	0.415439	+	0.716028i
$546$	20.7126	−	1.22045i	0.886418	−	0.0522305i
$547$	−9.24609	−	5.33823i	−0.395334	−	0.228246i	0.289135	−	0.957288i	$-0.406633\pi$
$547$	−9.24609	−	5.33823i	−0.395334	−	0.228246i	−0.684469	+	0.729042i	$0.739966\pi$
$548$			8.09014i			0.345594i
$549$	−9.98771	−	13.3779i	−0.426265	−	0.570957i
$550$	0.0665337	+	15.5929i	0.00283701	+	0.664882i
$551$	22.9190	−	39.6970i	0.976384	−	1.69115i
$552$	−1.22497	−	0.614164i	−0.0521382	−	0.0261406i
$553$	14.4518	−	8.34375i	0.614553	−	0.354812i
$554$	26.7957	+	46.4116i	1.13844	+	1.97184i
$555$	−5.24953	+	10.5263i	−0.222830	+	0.446818i
$556$	8.01342	−	13.8796i	0.339845	−	0.588628i
$557$			35.5632i			1.50686i	0.657528	+	0.753430i	$0.271602\pi$
$557$			35.5632i			1.50686i	−0.657528	+	0.753430i	$0.728398\pi$
$558$	−0.0570261	−	0.0245071i	−0.00241411	−	0.00103747i
$559$	−50.6564			−2.14254
$560$	−4.80237	−	2.75901i	−0.202937	−	0.116589i
$561$	−6.36413	+	0.374994i	−0.268694	+	0.0158323i
$562$	−8.47905	+	4.89538i	−0.357667	+	0.206499i
$563$	−8.88629	+	5.13050i	−0.374512	+	0.216225i	−0.675428	−	0.737426i	$-0.736041\pi$
$563$	−8.88629	+	5.13050i	−0.374512	+	0.216225i	0.300916	+	0.953651i	$0.402708\pi$
$564$	−4.87379	−	7.39932i	−0.205224	−	0.311568i
$565$	25.3007	+	14.5355i	1.06441	+	0.611513i
$566$	−33.8137			−1.42130
$567$	2.09926	+	8.75175i	0.0881608	+	0.367539i
$568$			16.1789i			0.678851i
$569$	2.47812	−	4.29223i	0.103888	−	0.179940i	−0.809395	−	0.587264i	$-0.800205\pi$
$569$	2.47812	−	4.29223i	0.103888	−	0.179940i	0.913283	+	0.407325i	$0.133538\pi$
$570$	−24.7840	−	37.4525i	−1.03809	−	1.56871i
$571$	−6.08012	−	10.5311i	−0.254445	−	0.440712i	0.710300	−	0.703899i	$-0.248559\pi$
$571$	−6.08012	−	10.5311i	−0.254445	−	0.440712i	−0.964745	+	0.263188i	$0.915226\pi$
$572$	−18.2511	+	10.5373i	−0.763118	+	0.440587i
$573$	−1.31137	−	22.2557i	−0.0547835	−	0.929746i
$574$	2.35671	−	4.08195i	0.0983673	−	0.170377i
$575$	0.0133910	+	3.13832i	0.000558442	+	0.130877i
$576$	13.9904	−	32.5547i	0.582935	−	1.35645i
$577$		−	42.0218i		−	1.74939i	−0.484675	−	0.874694i	$-0.661062\pi$
$577$		−	42.0218i		−	1.74939i	0.484675	−	0.874694i	$-0.338938\pi$
$578$	−19.6795	−	11.3620i	−0.818560	−	0.472596i
$579$	12.2781	−	24.4890i	0.510259	−	1.01773i
$580$	24.5952	+	42.3910i	1.02126	+	1.76019i
$581$	−7.37977	−	12.7821i	−0.306165	−	0.530293i
$582$	−40.7015	−	20.4066i	−1.68713	−	0.845879i
$583$	−12.0998	−	6.98580i	−0.501121	−	0.289322i
$584$	−0.0246611			−0.00102048
$585$	30.0131	−	22.5070i	1.24089	−	0.930551i
$586$	−42.4104			−1.75196
$587$	12.0914	+	6.98095i	0.499064	+	0.288135i	0.728327	−	0.685230i	$-0.240298\pi$
$587$	12.0914	+	6.98095i	0.499064	+	0.288135i	−0.229263	+	0.973365i	$0.573632\pi$
$588$	0.263712	+	4.47553i	0.0108753	+	0.184568i
$589$	0.0261433	+	0.0452815i	0.00107722	+	0.00186579i
$590$	17.5356	−	10.1741i	0.721928	−	0.418861i
$591$	6.84866	+	10.3975i	0.281716	+	0.427698i
$592$	6.51477	+	3.76130i	0.267755	+	0.154589i
$593$			5.19704i			0.213417i	0.994290	+	0.106708i	$0.0340311\pi$
$593$			5.19704i			0.213417i	−0.994290	+	0.106708i	$0.965969\pi$
$594$	−10.4414	−	12.3924i	−0.428416	−	0.508464i
$595$	5.65311	−	0.0120607i	0.231755	−	0.000494439i
$596$	2.68244	−	4.64612i	0.109877	−	0.190312i
$597$	−24.4727	+	16.1197i	−1.00160	+	0.659736i
$598$	−6.51161	+	3.75948i	−0.266279	+	0.153737i
$599$	−19.6755	−	34.0790i	−0.803920	−	1.39243i	−0.917018	−	0.398846i	$-0.869411\pi$
$599$	−19.6755	−	34.0790i	−0.803920	−	1.39243i	0.113099	−	0.993584i	$-0.463922\pi$
$600$	10.8941	−	0.688572i	0.444751	−	0.0281109i
$601$	7.50220	−	12.9942i	0.306021	−	0.530044i	−0.671467	−	0.741034i	$-0.734336\pi$
$601$	7.50220	−	12.9942i	0.306021	−	0.530044i	0.977488	+	0.210990i	$0.0676689\pi$
$602$		−	19.4031i		−	0.790812i
$603$	2.07805	+	17.5724i	0.0846247	+	0.715602i
$604$	−28.7788			−1.17099
$605$	−9.89187	+	17.2179i	−0.402162	+	0.700009i
$606$	−3.27077	+	6.52366i	−0.132866	+	0.265006i
$607$	1.91151	−	1.10361i	0.0775856	−	0.0447941i	−0.460705	−	0.887553i	$-0.652403\pi$
$607$	1.91151	−	1.10361i	0.0775856	−	0.0447941i	0.538291	+	0.842759i	$0.319070\pi$
$608$	−36.6919	+	21.1841i	−1.48805	+	0.859127i
$609$	−6.57332	+	13.1107i	−0.266364	+	0.531272i
$610$	−23.1125	−	13.2783i	−0.935798	−	0.537624i
$611$	−11.0521			−0.447118
$612$	2.30553	+	19.4960i	0.0931956	+	0.788079i
$613$		−	19.3498i		−	0.781530i	−0.920491	−	0.390765i	$-0.872211\pi$
$613$		−	19.3498i		−	0.781530i	0.920491	−	0.390765i	$-0.127789\pi$
$614$	−6.12557	+	10.6098i	−0.247208	+	0.428177i
$615$	−0.519432	−	8.50633i	−0.0209455	−	0.343008i
$616$	−0.917541	−	1.58923i	−0.0369688	−	0.0640318i
$617$	10.0662	−	5.81175i	0.405252	−	0.233972i	−0.283496	−	0.958973i	$-0.591494\pi$
$617$	10.0662	−	5.81175i	0.405252	−	0.233972i	0.688747	+	0.725001i	$0.258161\pi$
$618$	30.8074	−	20.2923i	1.23926	−	0.816275i
$619$	7.75111	−	13.4253i	0.311543	−	0.539609i	−0.667153	−	0.744920i	$-0.732487\pi$
$619$	7.75111	−	13.4253i	0.311543	−	0.539609i	0.978697	+	0.205312i	$0.0658208\pi$
$620$	−0.0559039		0.000119269i	−0.00224516		4.78994e-6i
$621$	−2.10150	−	2.49416i	−0.0843303	−	0.100087i
$622$			5.20930i			0.208874i
$623$	11.7551	+	6.78678i	0.470956	+	0.271907i
$624$	−13.1973	−	20.0359i	−0.528313	−	0.802077i
$625$	−12.6843	−	21.5432i	−0.507372	−	0.861727i
$626$	−11.4252	−	19.7890i	−0.456642	−	0.790927i
$627$	0.802952	+	13.6271i	0.0320668	+	0.544215i
$628$	−35.8814	−	20.7161i	−1.43182	−	0.826664i
$629$	−7.67830			−0.306154
$630$	8.62096	+	11.4960i	0.343467	+	0.458012i
$631$	21.2472			0.845839			0.422919	−	0.906167i	$-0.361005\pi$
$631$	21.2472			0.845839			0.422919	+	0.906167i	$0.361005\pi$
$632$	18.2158	+	10.5169i	0.724587	+	0.418341i
$633$	21.3846	+	10.7216i	0.849963	+	0.426147i
$634$	19.6631	+	34.0575i	0.780923	+	1.35260i
$635$	−7.00305	+	4.06316i	−0.277908	+	0.161242i
$636$	−19.2833	+	38.4611i	−0.764632	+	1.52508i
$637$	4.84312	+	2.79618i	0.191892	+	0.110789i
$638$		−	26.4070i		−	1.04546i
$639$	−15.2040	+	35.3786i	−0.601462	+	1.39956i
$640$	−0.0460224	−	21.5718i	−0.00181919	−	0.852699i
$641$	−1.02155	+	1.76938i	−0.0403489	+	0.0698863i	−0.885495	−	0.464650i	$-0.846180\pi$
$641$	−1.02155	+	1.76938i	−0.0403489	+	0.0698863i	0.845146	+	0.534536i	$0.179514\pi$
$642$	3.68747	+	62.5812i	0.145533	+	2.46988i
$643$	18.4711	−	10.6643i	0.728427	−	0.420558i	−0.0894192	−	0.995994i	$-0.528501\pi$
$643$	18.4711	−	10.6643i	0.728427	−	0.420558i	0.817847	+	0.575436i	$0.195168\pi$
$644$	−0.812339	−	1.40701i	−0.0320106	−	0.0554440i
$645$	−19.3602	−	29.2563i	−0.762308	−	1.15197i
$646$	14.6580	−	25.3883i	0.576710	−	0.998891i
$647$		−	8.72076i		−	0.342849i	−0.985197	−	0.171424i	$-0.945163\pi$
$647$		−	8.72076i		−	0.342849i	0.985197	−	0.171424i	$-0.0548369\pi$
$648$	−8.23027	+	7.80712i	−0.323316	+	0.306693i
$649$	−6.16220			−0.241888
$650$	29.7263	−	51.9987i	1.16596	−	2.03956i
$651$	−0.00920246	−	0.0139710i	−0.000360673	−	0.000547568i
$652$	16.3195	−	9.42208i	0.639121	−	0.368997i
$653$	6.49487	−	3.74981i	0.254164	−	0.146742i	−0.367506	−	0.930021i	$-0.619788\pi$
$653$	6.49487	−	3.74981i	0.254164	−	0.146742i	0.621669	+	0.783280i	$0.286455\pi$
$654$	−32.0103	+	1.88614i	−1.25170	+	0.0737540i
$655$	15.6674	−	27.2709i	0.612175	−	1.06556i
$656$	−5.45018			−0.212794
$657$	−0.0539267	−	0.0231751i	−0.00210388	−	0.000904148i
$658$		−	4.23331i		−	0.165032i
$659$	−23.7539	+	41.1429i	−0.925319	+	1.60270i	−0.134272	+	0.990945i	$0.542870\pi$
$659$	−23.7539	+	41.1429i	−0.925319	+	1.60270i	−0.791047	+	0.611755i	$0.790464\pi$
$660$	−13.0611	−	6.51363i	−0.508403	−	0.253543i
$661$	3.02051	+	5.23168i	0.117484	+	0.203489i	0.918770	−	0.394793i	$-0.129184\pi$
$661$	3.02051	+	5.23168i	0.117484	+	0.203489i	−0.801286	+	0.598282i	$0.795850\pi$
$662$	−37.2435	+	21.5026i	−1.44751	+	0.835721i
$663$	21.8910	+	10.9755i	0.850176	+	0.426253i
$664$	9.30187	−	16.1113i	0.360983	−	0.625240i
$665$	−0.0258247	−	12.1047i	−0.00100144	−	0.469398i
$666$	−11.6760	−	15.6393i	−0.452436	−	0.606011i
$667$		−	5.31482i		−	0.205791i
$668$	−42.8420	−	24.7348i	−1.65761	−	0.957019i
$669$	−1.81732	+	0.107082i	−0.0702615	+	0.00414002i
$670$	14.1779	+	24.4363i	0.547741	+	0.944058i
$671$	4.05101	+	7.01656i	0.156388	+	0.270871i
$672$	11.3208	−	7.45681i	0.436710	−	0.287653i
$673$	15.2870	+	8.82597i	0.589271	+	0.340216i	0.764809	−	0.644257i	$-0.222833\pi$
$673$	15.2870	+	8.82597i	0.589271	+	0.340216i	−0.175538	+	0.984473i	$0.556166\pi$
$674$	−28.5673			−1.10037
$675$	24.4694	+	8.73199i	0.941828	+	0.336094i
$676$	47.3022			1.81931
$677$	0.170656	+	0.0985280i	0.00655882	+	0.00378674i	0.503276	−	0.864126i	$-0.332128\pi$
$677$	0.170656	+	0.0985280i	0.00655882	+	0.00378674i	−0.496717	+	0.867913i	$0.665461\pi$
$678$	−40.4318	+	26.6317i	−1.55277	+	1.02278i
$679$	−6.13594	−	10.6278i	−0.235476	−	0.407856i
$680$	3.57591	+	6.16325i	0.137130	+	0.236350i
$681$	−19.2987	+	1.13714i	−0.739528	+	0.0435752i
$682$	0.0260863	+	0.0150609i	0.000998896	+	0.000576713i
$683$			26.9951i			1.03294i	0.856305	+	0.516470i	$0.172754\pi$
$683$			26.9951i			1.03294i	−0.856305	+	0.516470i	$0.827246\pi$
$684$	41.7456	−	4.93669i	1.59618	−	0.188759i
$685$	0.0149103	+	6.98881i	0.000569694	+	0.267029i
$686$	−1.07103	+	1.85508i	−0.0408922	+	0.0708273i
$687$	32.5557	+	16.3225i	1.24208	+	0.622742i
$688$	−19.4302	+	11.2180i	−0.740769	+	0.427683i
$689$	26.8339	+	46.4776i	1.02229	+	1.77066i
$690$	−4.65992	−	2.32392i	−0.177400	−	0.0884701i
$691$	−5.67304	+	9.82600i	−0.215813	+	0.373798i	−0.953524	−	0.301318i	$-0.902573\pi$
$691$	−5.67304	+	9.82600i	−0.215813	+	0.373798i	0.737711	+	0.675117i	$0.235907\pi$
$692$		−	22.9475i		−	0.872335i
$693$	−0.512931	−	4.33744i	−0.0194847	−	0.164766i
$694$	−54.2250			−2.05835
$695$	6.89696	−	12.0050i	0.261616	−	0.455374i
$696$	−18.4541	+	1.08737i	−0.699502	+	0.0412168i
$697$	4.81769	−	2.78149i	0.182483	−	0.105357i
$698$	−52.3072	+	30.1996i	−1.97986	+	1.14307i
$699$	15.2379	+	23.1340i	0.576352	+	0.875009i
$700$	11.2357	+	6.42319i	0.424671	+	0.242774i
$701$	22.6364			0.854966			0.427483	−	0.904023i	$-0.359400\pi$
$701$	22.6364			0.854966			0.427483	+	0.904023i	$0.359400\pi$
$702$	10.9334	+	61.2779i	0.412654	+	2.31278i
$703$			16.4411i			0.620087i
$704$	−8.59789	+	14.8920i	−0.324045	+	0.561263i
$705$	−4.22395	−	6.38305i	−0.159083	−	0.240400i
$706$	−3.83481	−	6.64209i	−0.144325	−	0.249978i
$707$	−1.70342	+	0.983472i	−0.0640638	+	0.0369873i
$708$	1.11619	+	18.9432i	0.0419490	+	0.711928i
$709$	19.6379	−	34.0138i	0.737516	−	1.27741i	−0.216095	−	0.976372i	$-0.569332\pi$
$709$	19.6379	−	34.0138i	0.737516	−	1.27741i	0.953611	−	0.301042i	$-0.0973346\pi$
$710$	0.131166	+	61.4805i	0.00492257	+	2.30732i
$711$	29.9496	+	40.1157i	1.12320	+	1.50446i
$712$			17.1089i			0.641182i
$713$	0.00525029	+	0.00303125i	0.000196625	+	0.000113521i
$714$	−4.20399	+	8.38499i	−0.157330	+	0.313800i
$715$	−15.7472	+	9.13648i	−0.588910	+	0.341685i
$716$	−10.0926	−	17.4809i	−0.377177	−	0.653290i
$717$	−28.4216	−	14.2498i	−1.06142	−	0.532167i
$718$	4.29292	+	2.47852i	0.160210	+	0.0924974i
$719$	26.1683			0.975912			0.487956	−	0.872868i	$-0.337743\pi$
$719$	26.1683			0.975912			0.487956	+	0.872868i	$0.337743\pi$
$720$	6.52779	−	15.2795i	0.243277	−	0.569432i
$721$	9.94297			0.370296
$722$	−19.1160	−	11.0366i	−0.711423	−	0.410740i
$723$	1.25134	+	21.2369i	0.0465380	+	0.789810i
$724$	−34.0192	−	58.9230i	−1.26431	−	2.18986i
$725$	21.3252	+	36.5749i	0.791996	+	1.35836i
$726$	−18.1237	−	27.5151i	−0.672633	−	1.02118i
$727$	−1.91041	−	1.10297i	−0.0708530	−	0.0409070i	0.464155	−	0.885754i	$-0.346358\pi$
$727$	−1.91041	−	1.10297i	−0.0708530	−	0.0409070i	−0.535008	+	0.844847i	$0.679691\pi$
$728$			7.04891i			0.261250i
$729$	−25.3340	+	9.33758i	−0.938295	+	0.345836i
$730$	−0.0937132		0.000199933i	−0.00346848		7.39985e-6i
$731$	11.4502	−	19.8323i	0.423501	−	0.733525i
$732$	20.8358	−	13.7241i	0.770112	−	0.507258i
$733$	−18.7963	+	10.8520i	−0.694257	+	0.400830i	−0.805205	−	0.592997i	$-0.797945\pi$
$733$	−18.7963	+	10.8520i	−0.694257	+	0.400830i	0.110948	+	0.993826i	$0.464611\pi$
$734$	35.4655	+	61.4281i	1.30906	+	2.26735i
$735$	0.236061	+	3.86578i	0.00870724	+	0.142592i
$736$	−2.45624	+	4.25434i	−0.0905384	+	0.156817i
$737$		−	8.58722i		−	0.316314i
$738$	12.9914	+	5.58308i	0.478220	+	0.205516i
$739$	−12.7449			−0.468830			−0.234415	−	0.972137i	$-0.575317\pi$
$739$	−12.7449			−0.468830			−0.234415	+	0.972137i	$0.575317\pi$
$740$	−15.2422	−	8.75678i	−0.560314	−	0.321906i
$741$	23.5012	−	46.8738i	0.863337	−	1.72195i
$742$	−17.8025	+	10.2783i	−0.653550	+	0.377327i
$743$	16.3810	−	9.45756i	0.600960	−	0.346964i	−0.168459	−	0.985709i	$-0.553879\pi$
$743$	16.3810	−	9.45756i	0.600960	−	0.346964i	0.769419	+	0.638744i	$0.220546\pi$
$744$	0.00945095	−	0.0188502i	0.000346489	−	0.000691082i
$745$	2.30871	−	4.01858i	0.0845846	−	0.147229i
$746$	−50.1966			−1.83783
$747$	35.4811	−	26.4895i	1.29818	−	0.969199i
$748$		−	9.52726i		−	0.348351i
$749$	−8.44838	+	14.6330i	−0.308697	+	0.534679i
$750$	41.3926	−	2.70493i	1.51144	−	0.0987700i
$751$	18.9825	+	32.8787i	0.692683	+	1.19976i	0.970956	+	0.239260i	$0.0769047\pi$
$751$	18.9825	+	32.8787i	0.692683	+	1.19976i	−0.278273	+	0.960502i	$0.589762\pi$
$752$	−4.23921	+	2.44751i	−0.154588	+	0.0892515i
$753$	12.9672	−	8.54124i	0.472551	−	0.311260i
$754$	−50.7172	+	87.8448i	−1.84701	+	3.19912i
$755$	−24.8611	+	0.0530401i	−0.904789	+	0.00193033i
$756$	−13.2408	+	2.36246i	−0.481562	+	0.0859218i
$757$			22.2742i			0.809568i	0.914412	+	0.404784i	$0.132653\pi$
$757$			22.2742i			0.809568i	−0.914412	+	0.404784i	$0.867347\pi$
$758$	−4.33027	−	2.50008i	−0.157282	−	0.0908070i
$759$	0.870645	+	1.32180i	0.0316024	+	0.0479783i
$760$	13.1970	−	7.65687i	0.478705	−	0.277744i
$761$	17.0593	+	29.5475i	0.618399	+	1.07110i	0.989778	+	0.142617i	$0.0455516\pi$
$761$	17.0593	+	29.5475i	0.618399	+	1.07110i	−0.371379	+	0.928481i	$0.621115\pi$
$762$	−0.790193	−	13.4106i	−0.0286257	−	0.485815i
$763$	−7.48479	−	4.32135i	−0.270968	−	0.156443i
$764$	33.3173			1.20538
$765$	2.02761	+	16.8377i	0.0733083	+	0.608769i
$766$	16.2396			0.586761
$767$	20.4990	+	11.8351i	0.740178	+	0.427342i
$768$	−4.57920	−	2.29588i	−0.165238	−	0.0828453i
$769$	−27.1565	−	47.0365i	−0.979290	−	1.69618i	−0.664983	−	0.746858i	$-0.731561\pi$
$769$	−27.1565	−	47.0365i	−0.979290	−	1.69618i	−0.314306	−	0.949322i	$-0.601772\pi$
$770$	−3.49958	−	6.03170i	−0.126116	−	0.217367i
$771$	−15.0591	+	30.0359i	−0.542342	+	1.08172i
$772$	35.4544	+	20.4696i	1.27603	+	0.736718i
$773$			11.9021i			0.428088i	0.976824	+	0.214044i	$0.0686637\pi$
$773$			11.9021i			0.428088i	−0.976824	+	0.214044i	$0.931336\pi$
$774$	57.8066	−	6.83602i	2.07781	−	0.245716i
$775$	−0.0482934		0.000206065i	−0.00173475		7.40206e-6i
$776$	7.73408	−	13.3958i	0.277637	−	0.480882i
$777$	−0.309425	−	5.25134i	−0.0111006	−	0.188391i
$778$	15.0032	−	8.66208i	0.537889	−	0.310551i
$779$	−5.95584	−	10.3158i	−0.213390	−	0.369603i
$780$	30.9387	+	46.7533i	1.10778	+	1.67403i
$781$	9.34370	−	16.1838i	0.334344	−	0.579101i
$782$		−	3.39912i		−	0.121552i
$783$	−41.3758	−	14.9644i	−1.47865	−	0.534784i
$784$	2.47689			0.0884603
$785$	−31.0350	−	17.8299i	−1.10769	−	0.636376i
$786$	28.7054	+	43.5802i	1.02389	+	1.55445i
$787$	17.2183	−	9.94097i	0.613765	−	0.354357i	−0.160673	−	0.987008i	$-0.551366\pi$
$787$	17.2183	−	9.94097i	0.613765	−	0.354357i	0.774437	+	0.632651i	$0.218033\pi$
$788$	−16.1135	+	9.30315i	−0.574021	+	0.331411i
$789$	−9.50988	+	0.560351i	−0.338561	+	0.0199490i
$790$	69.3063	+	39.8171i	2.46581	+	1.41663i
$791$	−13.0492			−0.463976
$792$	4.41143	−	3.29348i	0.156753	−	0.117029i
$793$		−	31.1215i		−	1.10516i
$794$	18.7047	−	32.3976i	0.663807	−	1.14975i
$795$	−16.5873	+	33.2609i	−0.588292	+	1.17964i
$796$	−21.8968	−	37.9264i	−0.776113	−	1.34427i
$797$	−26.9569	+	15.5636i	−0.954862	+	0.551290i	−0.894588	−	0.446892i	$-0.852531\pi$
$797$	−26.9569	+	15.5636i	−0.954862	+	0.551290i	−0.0602741	+	0.998182i	$0.519197\pi$
$798$	17.9543	+	9.00175i	0.635574	+	0.318658i
$799$	2.49817	−	4.32695i	0.0883788	−	0.153077i
$800$	−0.166975	−	39.1324i	−0.00590347	−	1.38354i
$801$	−16.0780	+	37.4122i	−0.568087	+	1.32190i
$802$		−	26.0739i		−	0.920700i
$803$	0.0246685	+	0.0142424i	0.000870534	+	0.000502603i
$804$	−26.3979	+	1.55544i	−0.930982	+	0.0548563i
$805$	−0.704347	−	1.21398i	−0.0248250	−	0.0427870i
$806$	−0.0578520	−	0.100203i	−0.00203775	−	0.00352949i
$807$	6.79974	−	4.47886i	0.239362	−	0.157663i
$808$	−2.14709	−	1.23962i	−0.0755343	−	0.0436098i
$809$	−40.2288			−1.41437			−0.707184	−	0.707029i	$-0.750035\pi$
$809$	−40.2288			−1.41437			−0.707184	+	0.707029i	$0.750035\pi$
$810$	−31.2121	+	29.7341i	−1.09668	+	1.04475i
$811$	7.10610			0.249529			0.124764	−	0.992186i	$-0.460182\pi$
$811$	7.10610			0.249529			0.124764	+	0.992186i	$0.460182\pi$
$812$	−18.9813	−	10.9588i	−0.666112	−	0.384580i
$813$	−5.31769	+	3.50266i	−0.186499	+	0.122844i
$814$	4.73578	+	8.20262i	0.165989	+	0.287502i
$815$	14.0805	−	8.16951i	0.493220	−	0.286165i
$816$	10.8272	−	0.637974i	0.379029	−	0.0223336i
$817$	−42.4657	−	24.5176i	−1.48569	−	0.857762i
$818$			55.8974i			1.95441i
$819$	−6.62418	+	15.4140i	−0.231468	+	0.538608i
$820$	12.7358	−	0.0271712i	0.444752	−	0.000948860i
$821$	13.4546	−	23.3041i	0.469570	−	0.813320i	−0.529824	−	0.848107i	$-0.677742\pi$
$821$	13.4546	−	23.3041i	0.469570	−	0.813320i	0.999395	+	0.0347875i	$0.0110755\pi$
$822$	−10.3662	−	5.19730i	−0.361562	−	0.181277i
$823$	26.1427	−	15.0935i	0.911277	−	0.526126i	0.0304355	−	0.999537i	$-0.490311\pi$
$823$	26.1427	−	15.0935i	0.911277	−	0.526126i	0.880842	+	0.473410i	$0.156977\pi$
$824$	6.26633	+	10.8536i	0.218298	+	0.378103i
$825$	−11.2951	−	5.60284i	−0.393244	−	0.195066i
$826$	−4.53326	+	7.85183i	−0.157732	+	0.273200i
$827$		−	17.0246i		−	0.592003i	−0.955187	−	0.296002i	$-0.904347\pi$
$827$		−	17.0246i		−	0.592003i	0.955187	−	0.296002i	$-0.0956534\pi$
$828$	3.90563	−	2.91586i	0.135730	−	0.101333i
$829$	22.8488			0.793570			0.396785	−	0.917912i	$-0.370126\pi$
$829$	22.8488			0.793570			0.396785	+	0.917912i	$0.370126\pi$
$830$	35.2169	−	61.2991i	1.22240	−	2.12772i
$831$	−43.2585	+	2.54892i	−1.50062	+	0.0884212i
$832$	57.2031	−	33.0262i	1.98316	−	1.14498i
$833$	−2.18944	+	1.26408i	−0.0758598	+	0.0437977i
$834$	12.6365	+	19.1845i	0.437565	+	0.664305i
$835$	−37.0554	−	21.2887i	−1.28236	−	0.736725i
$836$	−20.4001			−0.705553
$837$	0.0383809	−	0.0323386i	0.00132664	−	0.00111778i
$838$		−	43.4242i		−	1.50006i
$839$	6.93195	−	12.0065i	0.239317	−	0.414510i	−0.721201	−	0.692726i	$-0.756410\pi$
$839$	6.93195	−	12.0065i	0.239317	−	0.414510i	0.960519	+	0.278216i	$0.0897430\pi$
$840$	−4.07106	+	2.69400i	−0.140465	+	0.0929519i
$841$	−21.3498	−	36.9789i	−0.736199	−	1.27513i
$842$	37.7624	−	21.8021i	1.30138	−	0.751351i
$843$	−0.465670	−	7.90301i	−0.0160385	−	0.272194i
$844$	−17.8748	+	30.9600i	−0.615276	+	1.06569i
$845$	40.8628	−	0.0871791i	1.40572	−	0.00299905i
$846$	12.6121	−	1.49146i	0.433611	−	0.0512774i
$847$		−	8.88039i		−	0.305134i
$848$	20.5852	+	11.8849i	0.706899	+	0.408128i
$849$	12.2543	−	24.4415i	0.420565	−	0.838831i
$850$	13.6386	+	23.3917i	0.467800	+	0.802327i
$851$	0.953153	+	1.65091i	0.0326737	+	0.0565924i
$852$	−51.4428	−	25.7919i	−1.76240	−	0.883617i
$853$	−40.2246	−	23.2237i	−1.37726	−	0.795164i	−0.385435	−	0.922735i	$-0.625949\pi$
$853$	−40.2246	−	23.2237i	−1.37726	−	0.795164i	−0.991829	+	0.127571i	$0.959282\pi$
$854$	11.9206			0.407914
$855$	36.0536	−	4.34159i	1.23301	−	0.148479i
$856$	−21.2976			−0.727937
$857$	7.01164	+	4.04817i	0.239513	+	0.138283i	0.614953	−	0.788564i	$-0.289175\pi$
$857$	7.01164	+	4.04817i	0.239513	+	0.138283i	−0.375440	+	0.926847i	$0.622508\pi$
$858$	−1.77684	−	30.1553i	−0.0606603	−	1.02948i
$859$	12.0057	+	20.7945i	0.409630	+	0.709500i	0.994848	−	0.101376i	$-0.0323245\pi$
$859$	12.0057	+	20.7945i	0.409630	+	0.709500i	−0.585218	+	0.810876i	$0.698991\pi$
$860$	45.3477	−	26.3107i	1.54634	−	0.897187i
$861$	2.09646	+	3.18282i	0.0714472	+	0.108470i
$862$	−64.5458	−	37.2655i	−2.19844	−	1.26927i
$863$			0.211875i			0.00721231i	0.999993	+	0.00360615i	$0.00114788\pi$
$863$			0.211875i			0.00721231i	−0.999993	+	0.00360615i	$0.998852\pi$
$864$	26.2041	+	31.1003i	0.891483	+	1.05805i
$865$	−0.0422929	−	19.8237i	−0.00143800	−	0.674025i
$866$	−8.29475	+	14.3669i	−0.281867	+	0.488208i
$867$	15.3447	−	10.1073i	0.521134	−	0.343261i
$868$	0.0216515	−	0.0125005i	0.000734901	−	0.000424295i
$869$	−12.1476	−	21.0402i	−0.412078	−	0.713740i
$870$	−70.1177	+	4.28168i	−2.37721	+	0.145163i
$871$	−16.4926	+	28.5661i	−0.558831	+	0.967924i
$872$		−	10.8937i		−	0.368908i
$873$	29.5009	−	22.0248i	0.998454	−	0.745426i
$874$	−7.27832			−0.246193
$875$	9.71804	+	5.52808i	0.328530	+	0.186883i
$876$	0.0393140	−	0.0784131i	0.00132830	−	0.00264933i
$877$	−44.8007	+	25.8657i	−1.51281	+	0.873423i	−0.512926	+	0.858433i	$0.671438\pi$
$877$	−44.8007	+	25.8657i	−1.51281	+	0.873423i	−0.999888	+	0.0149901i	$0.995228\pi$
$878$	35.8152	−	20.6779i	1.20870	−	0.697846i
$879$	15.3697	−	30.6554i	0.518409	−	1.03398i
$880$	−4.01680	+	6.99171i	−0.135406	+	0.235691i
$881$	55.2598			1.86175			0.930875	−	0.365337i	$-0.119046\pi$
$881$	55.2598			1.86175			0.930875	+	0.365337i	$0.119046\pi$
$882$	−5.90407	−	2.53729i	−0.198800	−	0.0854349i
$883$			33.4030i			1.12410i	0.827103	+	0.562050i	$0.189987\pi$
$883$			33.4030i			1.12410i	−0.827103	+	0.562050i	$0.810013\pi$
$884$	−18.2980	+	31.6932i	−0.615430	+	1.06596i
$885$	0.999153	+	16.3623i	0.0335862	+	0.550014i
$886$	−13.0928	−	22.6774i	−0.439862	−	0.761863i
$887$	43.6743	−	25.2154i	1.46644	−	0.846650i	0.467146	−	0.884180i	$-0.345282\pi$
$887$	43.6743	−	25.2154i	1.46644	−	0.846650i	0.999295	+	0.0375303i	$0.0119491\pi$
$888$	5.53728	−	3.64730i	0.185819	−	0.122395i
$889$	1.81041	−	3.13573i	0.0607193	−	0.105169i
$890$	0.138705	+	65.0145i	0.00464942	+	2.17929i
$891$	12.7416	−	3.05629i	0.426858	−	0.102390i
$892$		−	2.72056i		−	0.0910912i
$893$	−9.26503	−	5.34917i	−0.310043	−	0.179003i
$894$	4.22997	+	6.42188i	0.141471	+	0.214780i
$895$	−8.75088	−	15.0826i	−0.292510	−	0.504154i
$896$	4.82360	+	8.35473i	0.161145	+	0.279112i
$897$	−0.357618	−	6.06923i	−0.0119405	−	0.202646i
$898$	−5.86198	−	3.38442i	−0.195617	−	0.112940i
$899$	0.0817862			0.00272772
$900$	−15.1777	+	35.7370i	−0.505924	+	1.19123i
$901$	−24.2617			−0.808275
$902$	−5.94286	−	3.43111i	−0.197876	−	0.114243i
$903$	14.0251	+	7.03179i	0.466727	+	0.234003i
$904$	−8.22396	−	14.2443i	−0.273525	−	0.473759i
$905$	−29.4967	−	50.8390i	−0.980503	−	1.68995i
$906$	18.4882	−	36.8754i	0.614230	−	1.22510i
$907$	51.7321	+	29.8676i	1.71774	+	0.991736i	0.923016	+	0.384761i	$0.125716\pi$
$907$	51.7321	+	29.8676i	1.71774	+	0.991736i	0.794721	+	0.606975i	$0.207617\pi$
$908$		−	28.8906i		−	0.958768i
$909$	−3.53014	−	4.72842i	−0.117087	−	0.156832i
$910$	0.0571472	+	26.7862i	0.00189441	+	0.887954i
$911$	29.2670	−	50.6919i	0.969659	−	1.67950i	0.273118	−	0.961981i	$-0.411945\pi$
$911$	29.2670	−	50.6919i	0.969659	−	1.67950i	0.696541	−	0.717517i	$-0.254722\pi$
$912$	−1.36605	−	23.1837i	−0.0452346	−	0.767689i
$913$	−18.6094	+	10.7441i	−0.615880	+	0.355579i
$914$	−9.91948	−	17.1810i	−0.328107	−	0.568298i
$915$	17.9741	−	11.8942i	0.594204	−	0.393211i
$916$	−27.2124	+	47.1332i	−0.899122	+	1.55733i
$917$			14.0653i			0.464478i
$918$	−26.4620	−	9.57054i	−0.873378	−	0.315875i
$919$	−49.0265			−1.61724			−0.808618	−	0.588334i	$-0.799784\pi$
$919$	−49.0265			−1.61724			−0.808618	+	0.588334i	$0.799784\pi$
$920$	0.881260	−	1.53394i	0.0290543	−	0.0505724i
$921$	−5.44913	−	8.27278i	−0.179555	−	0.272597i
$922$	72.5724	−	41.8997i	2.39004	−	1.37989i
$923$	−62.1651	+	35.8910i	−2.04619	+	1.18137i
$924$	6.51587	−	0.383935i	0.214356	−	0.0126305i
$925$	−13.1834	−	7.53662i	−0.433467	−	0.247802i
$926$	18.8984			0.621038
$927$	3.50306	+	29.6225i	0.115056	+	0.972931i
$928$			66.2718i			2.17548i
$929$	1.59218	−	2.75774i	0.0522378	−	0.0904785i	−0.838724	−	0.544557i	$-0.816698\pi$
$929$	1.59218	−	2.75774i	0.0522378	−	0.0904785i	0.890962	+	0.454078i	$0.150031\pi$
$930$	0.0357612	−	0.0717083i	0.00117266	−	0.00235141i
$931$	2.70669	+	4.68812i	0.0887081	+	0.153647i
$932$	−35.8518	+	20.6990i	−1.17436	+	0.678020i
$933$	−3.76543	−	1.88788i	−0.123275	−	0.0618063i
$934$	−26.0768	+	45.1663i	−0.853258	+	1.47789i
$935$	−0.0175590	−	8.23029i	−0.000574240	−	0.269159i
$936$	−21.0004	+	2.48344i	−0.686420	+	0.0811737i
$937$			32.2257i			1.05277i	0.850247	+	0.526384i	$0.176453\pi$
$937$			32.2257i			1.05277i	−0.850247	+	0.526384i	$0.823547\pi$
$938$	−10.9418	−	6.31723i	−0.357261	−	0.206265i
$939$	18.4446	−	1.08681i	0.601916	−	0.0354668i
$940$	9.89382	−	5.74038i	0.322701	−	0.187230i
$941$	−8.95697	−	15.5139i	−0.291989	−	0.505740i	0.682291	−	0.731081i	$-0.260984\pi$
$941$	−8.95697	−	15.5139i	−0.291989	−	0.505740i	−0.974280	+	0.225341i	$0.927650\pi$
$942$	49.5954	−	32.6676i	1.61591	−	1.06437i
$943$	−1.19610	−	0.690566i	−0.0389502	−	0.0224879i
$944$	10.4837			0.341215
$945$	−11.4339	+	2.06526i	−0.371946	+	0.0671828i
$946$	−28.2488			−0.918447
$947$	21.3043	+	12.3001i	0.692297	+	0.399698i	0.804472	−	0.593990i	$-0.202448\pi$
$947$	21.3043	+	12.3001i	0.692297	+	0.399698i	−0.112175	+	0.993688i	$0.535782\pi$
$948$	−62.4791	+	41.1538i	−2.02923	+	1.33661i
$949$	−0.0547078	−	0.0947568i	−0.00177589	−	0.00307593i
$950$	50.0871	−	29.2035i	1.62504	−	0.947485i
$951$	−31.7438	+	1.87044i	−1.02936	+	0.0606532i
$952$	−2.75970	−	1.59331i	−0.0894423	−	0.0516395i
$953$		−	32.8119i		−	1.06288i	−0.847095	−	0.531442i	$-0.821650\pi$
$953$		−	32.8119i		−	1.06288i	0.847095	−	0.531442i	$-0.178350\pi$
$954$	−36.8935	−	49.4167i	−1.19447	−	1.59993i
$955$	28.7818	−	0.0614046i	0.931356	−	0.00198701i
$956$	23.7568	−	41.1480i	0.768349	−	1.33082i
$957$	19.0877	+	9.57002i	0.617018	+	0.309355i
$958$	−38.5295	+	22.2450i	−1.24483	+	0.718703i
$959$	−1.56275	−	2.70676i	−0.0504638	−	0.0874059i
$960$	40.9364	+	20.4151i	1.32122	+	0.658896i
$961$	15.5000	−	26.8467i	0.499998	−	0.866023i
$962$		−	36.3822i		−	1.17301i
$963$	−46.5718	−	20.0143i	−1.50076	−	0.644953i
$964$	−31.7922			−1.02396
$965$	30.6657	+	17.6177i	0.987163	+	0.567134i
$966$	2.32472	−	0.136980i	0.0747967	−	0.00440725i
$967$	−24.9148	+	14.3846i	−0.801206	+	0.462576i	−0.843893	−	0.536512i	$-0.819742\pi$
$967$	−24.9148	+	14.3846i	−0.801206	+	0.462576i	0.0426868	+	0.999089i	$0.486408\pi$
$968$	9.69371	−	5.59667i	0.311568	−	0.179884i
$969$	13.0393	+	19.7961i	0.418882	+	0.635941i
$970$	29.2813	−	50.9674i	0.940164	−	1.63647i
$971$	5.74531			0.184376			0.0921879	−	0.995742i	$-0.470614\pi$
$971$	5.74531			0.184376			0.0921879	+	0.995742i	$0.470614\pi$
$972$	−11.7033	−	38.6151i	−0.375382	−	1.23858i
$973$			6.19172i			0.198497i
$974$	16.2489	−	28.1439i	0.520648	−	0.901789i
$975$	26.8131	+	40.3316i	0.858708	+	1.29165i
$976$	−6.89195	−	11.9372i	−0.220606	−	0.382101i
$977$	16.7887	−	9.69294i	0.537117	−	0.310105i	−0.206793	−	0.978385i	$-0.566303\pi$
$977$	16.7887	−	9.69294i	0.537117	−	0.310105i	0.743910	+	0.668280i	$0.232969\pi$
$978$	1.58879	+	26.9637i	0.0508038	+	0.862205i
$979$	9.88079	−	17.1140i	0.315792	−	0.546967i
$980$	−5.78789	+	0.0123482i	−0.184887	+	0.000394449i
$981$	10.2373	−	23.8215i	0.326853	−	0.760561i
$982$			10.4817i			0.334485i
$983$	38.1620	+	22.0328i	1.21718	+	0.702738i	0.964313	−	0.264763i	$-0.0852938\pi$
$983$	38.1620	+	22.0328i	1.21718	+	0.702738i	0.252865	+	0.967502i	$0.418627\pi$
$984$	−2.15307	+	4.29437i	−0.0686374	+	0.136899i
$985$	−13.9028	+	8.06639i	−0.442981	+	0.257017i
$986$	−22.9279	−	39.7122i	−0.730172	−	1.26470i
$987$	3.05996	+	1.53417i	0.0973995	+	0.0488333i
$988$	67.8626	+	39.1805i	2.15900	+	1.24650i
$989$	−5.68552			−0.180789
$990$	16.7369	−	12.5511i	0.531934	−	0.398902i
$991$	−30.7311			−0.976206			−0.488103	−	0.872786i	$-0.662311\pi$
$991$	−30.7311			−0.976206			−0.488103	+	0.872786i	$0.662311\pi$
$992$	−0.0654671	−	0.0377975i	−0.00207858	−	0.00120007i
$993$	−2.04541	−	34.7133i	−0.0649093	−	1.10159i
$994$	−13.7475	−	23.8113i	−0.436044	−	0.755250i
$995$	−18.9859	−	32.7231i	−0.601893	−	1.03739i
$996$	36.3992	+	55.2607i	1.15335	+	1.75100i
$997$	25.3797	+	14.6530i	0.803784	+	0.464065i	0.844793	−	0.535094i	$-0.179724\pi$
$997$	25.3797	+	14.6530i	0.803784	+	0.464065i	−0.0410084	+	0.999159i	$0.513057\pi$
$998$		−	69.9337i		−	2.21371i
$999$	15.5360	−	2.77198i	0.491537	−	0.0877015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.c.169.6	✓	64
3.2	odd	2		945.2.bh.c.694.27		64
5.4	even	2	inner	315.2.bh.c.169.27	yes	64
9.4	even	3	inner	315.2.bh.c.274.27	yes	64
9.5	odd	6		945.2.bh.c.64.6		64
15.14	odd	2		945.2.bh.c.694.6		64
45.4	even	6	inner	315.2.bh.c.274.6	yes	64
45.14	odd	6		945.2.bh.c.64.27		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.6	✓	64	1.1	even	1	trivial
315.2.bh.c.169.27	yes	64	5.4	even	2	inner
315.2.bh.c.274.6	yes	64	45.4	even	6	inner
315.2.bh.c.274.27	yes	64	9.4	even	3	inner
945.2.bh.c.64.6		64	9.5	odd	6
945.2.bh.c.64.27		64	45.14	odd	6
945.2.bh.c.694.6		64	15.14	odd	2
945.2.bh.c.694.27		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85508 - 1.07103i) q^{2} +(1.44646 - 0.952757i) q^{3} +(1.29422 + 2.24165i) q^{4} +(1.12216 + 1.93410i) q^{5} +(-3.70374 + 0.218235i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.26045i q^{8} +(1.18451 - 2.75626i) q^{9} +O(q^{10})\)	\(q+(-1.85508 - 1.07103i) q^{2} +(1.44646 - 0.952757i) q^{3} +(1.29422 + 2.24165i) q^{4} +(1.12216 + 1.93410i) q^{5} +(-3.70374 + 0.218235i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.26045i q^{8} +(1.18451 - 2.75626i) q^{9} +(-0.0102188 - 4.78979i) q^{10} +(-0.727944 + 1.26084i) q^{11} +(4.00778 + 2.00938i) q^{12} +(4.84312 - 2.79618i) q^{13} +(1.07103 + 1.85508i) q^{14} +(3.46590 + 1.72846i) q^{15} +(1.23844 - 2.14505i) q^{16} +2.52815i q^{17} +(-5.14939 + 3.84443i) q^{18} +5.41338 q^{19} +(-2.88325 + 5.01864i) q^{20} +(-1.72905 + 0.101881i) q^{21} +(2.70079 - 1.55930i) q^{22} +(0.543577 - 0.313834i) q^{23} +(-1.20091 - 1.82320i) q^{24} +(-2.48150 + 4.34075i) q^{25} -11.9792 q^{26} +(-0.912699 - 5.11537i) q^{27} -2.58843i q^{28} +(4.23378 - 7.33312i) q^{29} +(-4.57829 - 6.91851i) q^{30} +(0.00482938 + 0.00836474i) q^{31} +(-6.77800 + 3.91328i) q^{32} +(0.148327 + 2.51731i) q^{33} +(2.70773 - 4.68993i) q^{34} +(-0.00477054 - 2.23606i) q^{35} +(7.71156 - 0.911943i) q^{36} +3.03712i q^{37} +(-10.0423 - 5.79790i) q^{38} +(4.34132 - 8.65889i) q^{39} +(2.43785 - 1.41444i) q^{40} +(-1.10021 - 1.90562i) q^{41} +(3.31665 + 1.66287i) q^{42} +(-7.84459 - 4.52908i) q^{43} -3.76846 q^{44} +(6.66009 - 0.802011i) q^{45} -1.34451 q^{46} +(-1.71151 - 0.988139i) q^{47} +(-0.252348 - 4.28267i) q^{48} +(0.500000 + 0.866025i) q^{49} +(9.25247 - 5.39468i) q^{50} +(2.40872 + 3.65688i) q^{51} +(12.5361 + 7.23771i) q^{52} +9.59662i q^{53} +(-3.78559 + 10.4669i) q^{54} +(-3.25546 + 0.00694537i) q^{55} +(-0.630227 + 1.09159i) q^{56} +(7.83025 - 5.15764i) q^{57} +(-15.7080 + 9.06902i) q^{58} +(2.11630 + 3.66555i) q^{59} +(0.611027 + 10.0063i) q^{60} +(2.78250 - 4.81944i) q^{61} -0.0206897i q^{62} +(-2.40394 + 1.79473i) q^{63} +11.8112 q^{64} +(10.8429 + 6.22933i) q^{65} +(2.42095 - 4.82867i) q^{66} +(-5.10805 + 2.94914i) q^{67} +(-5.66723 + 3.27197i) q^{68} +(0.487256 - 0.971847i) q^{69} +(-2.38604 + 4.15319i) q^{70} -12.8357 q^{71} +(-3.47414 - 1.49302i) q^{72} -0.0195652i q^{73} +(3.25285 - 5.63410i) q^{74} +(0.546289 + 8.64301i) q^{75} +(7.00608 + 12.1349i) q^{76} +(1.26084 - 0.727944i) q^{77} +(-17.3274 + 11.4133i) q^{78} +(-8.34375 + 14.4518i) q^{79} +(5.53848 - 0.0118161i) q^{80} +(-6.19389 - 6.52960i) q^{81} +4.71343i q^{82} +(12.7821 + 7.37977i) q^{83} +(-2.46615 - 3.74407i) q^{84} +(-4.88971 + 2.83700i) q^{85} +(9.70156 + 16.8036i) q^{86} +(-0.862684 - 14.6408i) q^{87} +(1.58923 + 0.917541i) q^{88} -13.5736 q^{89} +(-13.2140 - 5.64537i) q^{90} -5.59236 q^{91} +(1.40701 + 0.812339i) q^{92} +(0.0149551 + 0.00749805i) q^{93} +(2.11666 + 3.66615i) q^{94} +(6.07469 + 10.4700i) q^{95} +(-6.07571 + 12.1182i) q^{96} +(10.6278 + 6.13594i) q^{97} -2.14206i q^{98} +(2.61293 + 3.49987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

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