LMFDB - Embedded newform 630.2.t.c.311.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.14
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.13939 - 1.30453i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.63900 - 0.560056i) q^{6} +(2.26702 + 1.36404i) q^{7} +1.00000i q^{8} +(-0.403573 - 2.97273i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.13939 - 1.30453i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.63900 - 0.560056i) q^{6} +(2.26702 + 1.36404i) q^{7} +1.00000i q^{8} +(-0.403573 - 2.97273i) q^{9} +(0.866025 + 0.500000i) q^{10} -3.46745i q^{11} +(1.69945 + 0.334479i) q^{12} +(-0.584701 - 0.337577i) q^{13} +(1.28128 + 2.31480i) q^{14} +(1.13939 - 1.30453i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09222 + 3.62383i) q^{17} +(1.13686 - 2.77625i) q^{18} +(1.18312 - 0.683073i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.36245 - 1.40322i) q^{21} +(1.73372 - 3.00290i) q^{22} +2.10023i q^{23} +(1.30453 + 1.13939i) q^{24} +1.00000 q^{25} +(-0.337577 - 0.584701i) q^{26} +(-4.33783 - 2.86063i) q^{27} +(-0.0477786 + 2.64532i) q^{28} +(-4.77824 + 2.75872i) q^{29} +(1.63900 - 0.560056i) q^{30} +(-1.25425 + 0.724142i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.52337 - 3.95078i) q^{33} +(-3.62383 + 2.09222i) q^{34} +(2.26702 + 1.36404i) q^{35} +(2.37267 - 1.83587i) q^{36} +(4.59003 + 7.95017i) q^{37} +1.36615 q^{38} +(-1.10658 + 0.378125i) q^{39} +1.00000i q^{40} +(4.79244 - 8.30075i) q^{41} +(4.47960 + 0.966002i) q^{42} +(-1.38041 - 2.39094i) q^{43} +(3.00290 - 1.73372i) q^{44} +(-0.403573 - 2.97273i) q^{45} +(-1.05012 + 1.81886i) q^{46} +(2.50199 - 4.33357i) q^{47} +(0.560056 + 1.63900i) q^{48} +(3.27880 + 6.18461i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.34352 + 6.85831i) q^{51} -0.675155i q^{52} +(-6.77173 - 3.90966i) q^{53} +(-2.32636 - 4.64630i) q^{54} -3.46745i q^{55} +(-1.36404 + 2.26702i) q^{56} +(0.456948 - 2.32170i) q^{57} -5.51744 q^{58} +(-2.15707 - 3.73615i) q^{59} +(1.69945 + 0.334479i) q^{60} +(-5.15824 - 2.97811i) q^{61} -1.44828 q^{62} +(3.14001 - 7.28974i) q^{63} -1.00000 q^{64} +(-0.584701 - 0.337577i) q^{65} +(-1.94196 - 5.68316i) q^{66} +(-1.90260 - 3.29540i) q^{67} -4.18444 q^{68} +(2.73981 + 2.39299i) q^{69} +(1.28128 + 2.31480i) q^{70} +15.0448i q^{71} +(2.97273 - 0.403573i) q^{72} +(2.54435 + 1.46898i) q^{73} +9.18006i q^{74} +(1.13939 - 1.30453i) q^{75} +(1.18312 + 0.683073i) q^{76} +(4.72972 - 7.86078i) q^{77} +(-1.14739 - 0.225825i) q^{78} +(-6.65974 + 11.5350i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-8.67426 + 2.39943i) q^{81} +(8.30075 - 4.79244i) q^{82} +(-1.69398 - 2.93407i) q^{83} +(3.39645 + 3.07638i) q^{84} +(-2.09222 + 3.62383i) q^{85} -2.76082i q^{86} +(-1.84547 + 9.37660i) q^{87} +3.46745 q^{88} +(-3.11428 - 5.39408i) q^{89} +(1.13686 - 2.77625i) q^{90} +(-0.865064 - 1.56285i) q^{91} +(-1.81886 + 1.05012i) q^{92} +(-0.484421 + 2.46128i) q^{93} +(4.33357 - 2.50199i) q^{94} +(1.18312 - 0.683073i) q^{95} +(-0.334479 + 1.69945i) q^{96} +(-0.750910 + 0.433538i) q^{97} +(-0.252779 + 6.99543i) q^{98} +(-10.3078 + 1.39937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.13939	−	1.30453i	0.657828	−	0.753168i
$3$	1.13939	−	1.30453i	0.657828	−	0.753168i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.63900	−	0.560056i	0.669121	−	0.228642i
$7$	2.26702	+	1.36404i	0.856855	+	0.515558i
$7$	2.26702	+	1.36404i	0.856855	+	0.515558i
$8$			1.00000i			0.353553i
$9$	−0.403573	−	2.97273i	−0.134524	−	0.990910i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	3.46745i		−	1.04547i	−0.852494	−	0.522737i	$-0.824911\pi$
$11$		−	3.46745i		−	1.04547i	0.852494	−	0.522737i	$-0.175089\pi$
$12$	1.69945	+	0.334479i	0.490588	+	0.0965559i
$13$	−0.584701	−	0.337577i	−0.162167	−	0.0936271i	0.416720	−	0.909035i	$-0.363179\pi$
$13$	−0.584701	−	0.337577i	−0.162167	−	0.0936271i	−0.578887	+	0.815408i	$0.696513\pi$
$14$	1.28128	+	2.31480i	0.342437	+	0.618657i
$15$	1.13939	−	1.30453i	0.294190	−	0.336827i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.09222	+	3.62383i	−0.507438	+	0.878908i	0.492525	+	0.870298i	$0.336074\pi$
$17$	−2.09222	+	3.62383i	−0.507438	+	0.878908i	−0.999963	+	0.00860955i	$0.997259\pi$
$18$	1.13686	−	2.77625i	0.267961	−	0.654368i
$19$	1.18312	−	0.683073i	0.271426	−	0.156708i	−0.358110	−	0.933680i	$-0.616579\pi$
$19$	1.18312	−	0.683073i	0.271426	−	0.156708i	0.629535	+	0.776972i	$0.283245\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	4.36245	−	1.40322i	0.951965	−	0.306207i
$22$	1.73372	−	3.00290i	0.369631	−	0.640219i
$23$			2.10023i			0.437929i	0.975733	+	0.218965i	$0.0702679\pi$
$23$			2.10023i			0.437929i	−0.975733	+	0.218965i	$0.929732\pi$
$24$	1.30453	+	1.13939i	0.266285	+	0.232577i
$25$	1.00000			0.200000
$26$	−0.337577	−	0.584701i	−0.0662044	−	0.114669i
$27$	−4.33783	−	2.86063i	−0.834816	−	0.550529i
$28$	−0.0477786	+	2.64532i	−0.00902930	+	0.499918i
$29$	−4.77824	+	2.75872i	−0.887297	+	0.512281i	−0.873057	−	0.487617i	$-0.837866\pi$
$29$	−4.77824	+	2.75872i	−0.887297	+	0.512281i	−0.0142398	+	0.999899i	$0.504533\pi$
$30$	1.63900	−	0.560056i	0.299240	−	0.102252i
$31$	−1.25425	+	0.724142i	−0.225270	+	0.130060i	−0.608388	−	0.793640i	$-0.708184\pi$
$31$	−1.25425	+	0.724142i	−0.225270	+	0.130060i	0.383118	+	0.923699i	$0.374850\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.52337	−	3.95078i	−0.787418	−	0.687742i
$34$	−3.62383	+	2.09222i	−0.621482	+	0.358813i
$35$	2.26702	+	1.36404i	0.383197	+	0.230564i
$36$	2.37267	−	1.83587i	0.395446	−	0.305978i
$37$	4.59003	+	7.95017i	0.754596	+	1.30700i	0.945575	+	0.325405i	$0.105501\pi$
$37$	4.59003	+	7.95017i	0.754596	+	1.30700i	−0.190978	+	0.981594i	$0.561166\pi$
$38$	1.36615			0.221618
$39$	−1.10658	+	0.378125i	−0.177195	+	0.0605484i
$40$			1.00000i			0.158114i
$41$	4.79244	−	8.30075i	0.748454	−	1.29636i	−0.200110	−	0.979773i	$-0.564130\pi$
$41$	4.79244	−	8.30075i	0.748454	−	1.29636i	0.948564	−	0.316586i	$-0.102537\pi$
$42$	4.47960	+	0.966002i	0.691218	+	0.149057i
$43$	−1.38041	−	2.39094i	−0.210510	−	0.364614i	0.741364	−	0.671103i	$-0.234179\pi$
$43$	−1.38041	−	2.39094i	−0.210510	−	0.364614i	−0.951874	+	0.306489i	$0.900846\pi$
$44$	3.00290	−	1.73372i	0.452704	−	0.261369i
$45$	−0.403573	−	2.97273i	−0.0601612	−	0.443149i
$46$	−1.05012	+	1.81886i	−0.154831	+	0.268176i
$47$	2.50199	−	4.33357i	0.364953	−	0.632116i	−0.623816	−	0.781571i	$-0.714419\pi$
$47$	2.50199	−	4.33357i	0.364953	−	0.632116i	0.988769	+	0.149455i	$0.0477519\pi$
$48$	0.560056	+	1.63900i	0.0808372	+	0.236570i
$49$	3.27880	+	6.18461i	0.468401	+	0.883516i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	2.34352	+	6.85831i	0.328159	+	0.960356i
$52$		−	0.675155i		−	0.0936271i
$53$	−6.77173	−	3.90966i	−0.930168	−	0.537033i	−0.0433035	−	0.999062i	$-0.513788\pi$
$53$	−6.77173	−	3.90966i	−0.930168	−	0.537033i	−0.886865	+	0.462029i	$0.847122\pi$
$54$	−2.32636	−	4.64630i	−0.316577	−	0.632281i
$55$		−	3.46745i		−	0.467550i
$56$	−1.36404	+	2.26702i	−0.182277	+	0.302944i
$57$	0.456948	−	2.32170i	0.0605242	−	0.307516i
$58$	−5.51744			−0.724475
$59$	−2.15707	−	3.73615i	−0.280826	−	0.486405i	0.690762	−	0.723082i	$-0.257275\pi$
$59$	−2.15707	−	3.73615i	−0.280826	−	0.486405i	−0.971588	+	0.236677i	$0.923942\pi$
$60$	1.69945	+	0.334479i	0.219398	+	0.0431811i
$61$	−5.15824	−	2.97811i	−0.660444	−	0.381308i	0.132002	−	0.991249i	$-0.457859\pi$
$61$	−5.15824	−	2.97811i	−0.660444	−	0.381308i	−0.792446	+	0.609942i	$0.791193\pi$
$62$	−1.44828			−0.183932
$63$	3.14001	−	7.28974i	0.395603	−	0.918421i
$64$	−1.00000			−0.125000
$65$	−0.584701	−	0.337577i	−0.0725233	−	0.0418713i
$66$	−1.94196	−	5.68316i	−0.239039	−	0.699549i
$67$	−1.90260	−	3.29540i	−0.232440	−	0.402598i	0.726086	−	0.687604i	$-0.241338\pi$
$67$	−1.90260	−	3.29540i	−0.232440	−	0.402598i	−0.958526	+	0.285006i	$0.908004\pi$
$68$	−4.18444			−0.507438
$69$	2.73981	+	2.39299i	0.329834	+	0.288082i
$70$	1.28128	+	2.31480i	0.153143	+	0.276672i
$71$			15.0448i			1.78549i	0.450563	+	0.892745i	$0.351223\pi$
$71$			15.0448i			1.78549i	−0.450563	+	0.892745i	$0.648777\pi$
$72$	2.97273	−	0.403573i	0.350340	−	0.0475616i
$73$	2.54435	+	1.46898i	0.297794	+	0.171931i	0.641451	−	0.767164i	$-0.278333\pi$
$73$	2.54435	+	1.46898i	0.297794	+	0.171931i	−0.343658	+	0.939095i	$0.611666\pi$
$74$			9.18006i			1.06716i
$75$	1.13939	−	1.30453i	0.131566	−	0.150634i
$76$	1.18312	+	0.683073i	0.135713	+	0.0783539i
$77$	4.72972	−	7.86078i	0.539002	−	0.895820i
$78$	−1.14739	−	0.225825i	−0.129916	−	0.0255697i
$79$	−6.65974	+	11.5350i	−0.749280	+	1.29779i	0.198889	+	0.980022i	$0.436267\pi$
$79$	−6.65974	+	11.5350i	−0.749280	+	1.29779i	−0.948168	+	0.317768i	$0.897067\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−8.67426	+	2.39943i	−0.963806	+	0.266603i
$82$	8.30075	−	4.79244i	0.916665	−	0.529237i
$83$	−1.69398	−	2.93407i	−0.185939	−	0.322056i	0.757954	−	0.652308i	$-0.226199\pi$
$83$	−1.69398	−	2.93407i	−0.185939	−	0.322056i	−0.943893	+	0.330253i	$0.892866\pi$
$84$	3.39645	+	3.07638i	0.370583	+	0.335661i
$85$	−2.09222	+	3.62383i	−0.226933	+	0.393059i
$86$		−	2.76082i		−	0.297706i
$87$	−1.84547	+	9.37660i	−0.197855	+	1.00528i
$88$	3.46745			0.369631
$89$	−3.11428	−	5.39408i	−0.330113	−	0.571772i	0.652421	−	0.757857i	$-0.273753\pi$
$89$	−3.11428	−	5.39408i	−0.330113	−	0.571772i	−0.982534	+	0.186085i	$0.940420\pi$
$90$	1.13686	−	2.77625i	0.119836	−	0.292642i
$91$	−0.865064	−	1.56285i	−0.0906834	−	0.163831i
$92$	−1.81886	+	1.05012i	−0.189629	+	0.109482i
$93$	−0.484421	+	2.46128i	−0.0502321	+	0.255223i
$94$	4.33357	−	2.50199i	0.446974	−	0.258060i
$95$	1.18312	−	0.683073i	0.121385	−	0.0700819i
$96$	−0.334479	+	1.69945i	−0.0341377	+	0.173449i
$97$	−0.750910	+	0.433538i	−0.0762433	+	0.0440191i	−0.537637	−	0.843176i	$-0.680683\pi$
$97$	−0.750910	+	0.433538i	−0.0762433	+	0.0440191i	0.461394	+	0.887196i	$0.347350\pi$
$98$	−0.252779	+	6.99543i	−0.0255346	+	0.706646i
$99$	−10.3078	+	1.39937i	−1.03597	+	0.140642i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−14.7480			−1.46748			−0.733741	−	0.679429i	$-0.762227\pi$
$101$	−14.7480			−1.46748			−0.733741	+	0.679429i	$0.762227\pi$
$102$	−1.39961	+	7.11123i	−0.138582	+	0.704117i
$103$			12.9350i			1.27453i	0.770646	+	0.637263i	$0.219934\pi$
$103$			12.9350i			1.27453i	−0.770646	+	0.637263i	$0.780066\pi$
$104$	0.337577	−	0.584701i	0.0331022	−	0.0573347i
$105$	4.36245	−	1.40322i	0.425732	−	0.136940i
$106$	−3.90966	−	6.77173i	−0.379740	−	0.657728i
$107$	−9.12788	+	5.26998i	−0.882425	+	0.509468i	−0.871457	−	0.490472i	$-0.836825\pi$
$107$	−9.12788	+	5.26998i	−0.882425	+	0.509468i	−0.0109678	+	0.999940i	$0.503491\pi$
$108$	0.308465	−	5.18699i	0.0296821	−	0.499118i
$109$	−4.94221	+	8.56016i	−0.473378	+	0.819915i	−0.999536	−	0.0304723i	$-0.990299\pi$
$109$	−4.94221	+	8.56016i	−0.473378	+	0.819915i	0.526158	+	0.850387i	$0.323632\pi$
$110$	1.73372	−	3.00290i	0.165304	−	0.286315i
$111$	15.6010	+	3.07054i	1.48078	+	0.291443i
$112$	−2.31480	+	1.28128i	−0.218728	+	0.121070i
$113$	−11.0811	−	6.39765i	−1.04242	−	0.601841i	−0.121901	−	0.992542i	$-0.538899\pi$
$113$	−11.0811	−	6.39765i	−1.04242	−	0.601841i	−0.920517	+	0.390702i	$0.872232\pi$
$114$	1.55658	−	1.78217i	0.145787	−	0.166916i
$115$			2.10023i			0.195848i
$116$	−4.77824	−	2.75872i	−0.443649	−	0.256141i
$117$	−0.767557	+	1.87440i	−0.0709607	+	0.173288i
$118$		−	4.31413i		−	0.397148i
$119$	−9.68615	+	5.36145i	−0.887928	+	0.491483i
$120$	1.30453	+	1.13939i	0.119086	+	0.104012i
$121$	−1.02317			−0.0930159
$122$	−2.97811	−	5.15824i	−0.269625	−	0.467005i
$123$	−5.36807	−	15.7097i	−0.484023	−	1.41649i
$124$	−1.25425	−	0.724142i	−0.112635	−	0.0650299i
$125$	1.00000			0.0894427
$126$	6.36420	−	4.74310i	0.566968	−	0.422549i
$127$	18.2495			1.61938			0.809689	−	0.586859i	$-0.199636\pi$
$127$	18.2495			1.61938			0.809689	+	0.586859i	$0.199636\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−4.69186	−	0.923436i	−0.413096	−	0.0813040i
$130$	−0.337577	−	0.584701i	−0.0296075	−	0.0512817i
$131$	12.1291			1.05972			0.529861	−	0.848085i	$-0.322244\pi$
$131$	12.1291			1.05972			0.529861	+	0.848085i	$0.322244\pi$
$132$	1.15979	−	5.89274i	0.100947	−	0.512897i
$133$	3.61390	+	0.0652726i	0.313364	+	0.00565985i
$134$		−	3.80521i		−	0.328720i
$135$	−4.33783	−	2.86063i	−0.373341	−	0.246204i
$136$	−3.62383	−	2.09222i	−0.310741	−	0.179406i
$137$			2.98492i			0.255019i	0.991837	+	0.127509i	$0.0406983\pi$
$137$			2.98492i			0.255019i	−0.991837	+	0.127509i	$0.959302\pi$
$138$	1.17625	+	3.44229i	0.100129	+	0.293028i
$139$	−1.16435	−	0.672235i	−0.0987585	−	0.0570182i	0.449807	−	0.893126i	$-0.351493\pi$
$139$	−1.16435	−	0.672235i	−0.0987585	−	0.0570182i	−0.548566	+	0.836107i	$0.684826\pi$
$140$	−0.0477786	+	2.64532i	−0.00403803	+	0.223570i
$141$	−2.80251	−	8.20154i	−0.236014	−	0.690695i
$142$	−7.52240	+	13.0292i	−0.631266	+	1.09338i
$143$	−1.17053	+	2.02742i	−0.0978847	+	0.169541i
$144$	2.77625	+	1.13686i	0.231354	+	0.0947384i
$145$	−4.77824	+	2.75872i	−0.396811	+	0.229099i
$146$	1.46898	+	2.54435i	0.121574	+	0.210572i
$147$	11.8038	+	2.76941i	0.973563	+	0.228417i
$148$	−4.59003	+	7.95017i	−0.377298	+	0.653500i
$149$		−	16.7400i		−	1.37140i	−0.727886	−	0.685699i	$-0.759497\pi$
$149$		−	16.7400i		−	1.37140i	0.727886	−	0.685699i	$-0.240503\pi$
$150$	1.63900	−	0.560056i	0.133824	−	0.0457284i
$151$	4.73194			0.385080			0.192540	−	0.981289i	$-0.438328\pi$
$151$	4.73194			0.385080			0.192540	+	0.981289i	$0.438328\pi$
$152$	0.683073	+	1.18312i	0.0554046	+	0.0959635i
$153$	11.6170	+	4.75712i	0.939181	+	0.384591i
$154$	8.02645	−	4.44278i	0.646790	−	0.358009i
$155$	−1.25425	+	0.724142i	−0.100744	+	0.0581645i
$156$	−0.880757	−	0.769266i	−0.0705170	−	0.0615906i
$157$	5.94513	−	3.43242i	0.474473	−	0.273937i	−0.243637	−	0.969866i	$-0.578341\pi$
$157$	5.94513	−	3.43242i	0.474473	−	0.273937i	0.718110	+	0.695929i	$0.245007\pi$
$158$	−11.5350	+	6.65974i	−0.917676	+	0.529821i
$159$	−12.8159	+	4.37926i	−1.01637	+	0.347298i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−2.86480	+	4.76128i	−0.225778	+	0.375242i
$162$	−8.71184	−	2.25916i	−0.684467	−	0.177496i
$163$	9.44821	+	16.3648i	0.740041	+	1.28179i	0.952476	+	0.304613i	$0.0985272\pi$
$163$	9.44821	+	16.3648i	0.740041	+	1.28179i	−0.212435	+	0.977175i	$0.568139\pi$
$164$	9.58488			0.748454
$165$	−4.52337	−	3.95078i	−0.352144	−	0.307568i
$166$		−	3.38797i		−	0.262957i
$167$	8.90365	−	15.4216i	0.688985	−	1.19336i	−0.283182	−	0.959066i	$-0.591390\pi$
$167$	8.90365	−	15.4216i	0.688985	−	1.19336i	0.972167	−	0.234291i	$-0.0752768\pi$
$168$	1.40322	+	4.36245i	0.108261	+	0.336570i
$169$	−6.27208	−	10.8636i	−0.482468	−	0.835659i
$170$	−3.62383	+	2.09222i	−0.277935	+	0.160466i
$171$	−2.50807	−	3.24142i	−0.191797	−	0.247878i
$172$	1.38041	−	2.39094i	0.105255	−	0.182307i
$173$	−3.22610	+	5.58778i	−0.245276	+	0.424831i	−0.962209	−	0.272311i	$-0.912212\pi$
$173$	−3.22610	+	5.58778i	−0.245276	+	0.424831i	0.716933	+	0.697142i	$0.245545\pi$
$174$	−6.28652	+	7.19764i	−0.476580	+	0.545652i
$175$	2.26702	+	1.36404i	0.171371	+	0.103112i
$176$	3.00290	+	1.73372i	0.226352	+	0.130684i
$177$	−7.33165	−	1.44299i	−0.551080	−	0.108462i
$178$		−	6.22855i		−	0.466850i
$179$	−19.4958	−	11.2559i	−1.45718	−	0.841305i	−0.458311	−	0.888792i	$-0.651546\pi$
$179$	−19.4958	−	11.2559i	−1.45718	−	0.841305i	−0.998872	+	0.0474866i	$0.984879\pi$
$180$	2.37267	−	1.83587i	0.176849	−	0.136838i
$181$		−	3.72966i		−	0.277223i	−0.990347	−	0.138612i	$-0.955736\pi$
$181$		−	3.72966i		−	0.277223i	0.990347	−	0.138612i	$-0.0442640\pi$
$182$	0.0322579	−	1.78600i	0.00239112	−	0.132387i
$183$	−9.76227	+	3.33582i	−0.721648	+	0.246591i
$184$	−2.10023			−0.154831
$185$	4.59003	+	7.95017i	0.337466	+	0.584508i
$186$	−1.65016	+	1.88932i	−0.120996	+	0.138532i
$187$	12.5654	+	7.25465i	0.918875	+	0.530513i
$188$	5.00398			0.364953
$189$	−5.93196	−	12.4021i	−0.431487	−	0.902119i
$190$	1.36615			0.0991107
$191$	20.2669	+	11.7011i	1.46646	+	0.846663i	0.999296	−	0.0375069i	$-0.0119416\pi$
$191$	20.2669	+	11.7011i	1.46646	+	0.846663i	0.467166	+	0.884170i	$0.345275\pi$
$192$	−1.13939	+	1.30453i	−0.0822285	+	0.0941460i
$193$	2.35052	+	4.07122i	0.169194	+	0.293053i	0.938137	−	0.346265i	$-0.112550\pi$
$193$	2.35052	+	4.07122i	0.169194	+	0.293053i	−0.768943	+	0.639318i	$0.779217\pi$
$194$	−0.867076			−0.0622524
$195$	−1.10658	+	0.378125i	−0.0792440	+	0.0270781i
$196$	−3.71663	+	5.93183i	−0.265474	+	0.423702i
$197$		−	16.2139i		−	1.15519i	−0.816323	−	0.577595i	$-0.803991\pi$
$197$		−	16.2139i		−	1.15519i	0.816323	−	0.577595i	$-0.196009\pi$
$198$	−9.62648	−	3.94200i	−0.684124	−	0.280146i
$199$	−6.39208	−	3.69047i	−0.453123	−	0.261610i	0.256025	−	0.966670i	$-0.417587\pi$
$199$	−6.39208	−	3.69047i	−0.453123	−	0.261610i	−0.709148	+	0.705060i	$0.750920\pi$
$200$			1.00000i			0.0707107i
$201$	−6.46675	−	1.27276i	−0.456129	−	0.0897738i
$202$	−12.7722	−	7.37400i	−0.898645	−	0.518833i
$203$	−14.5954	−	0.263615i	−1.02440	−	0.0185022i
$204$	−4.76771	+	5.45870i	−0.333807	+	0.382186i
$205$	4.79244	−	8.30075i	0.334719	−	0.579750i
$206$	−6.46751	+	11.2021i	−0.450613	+	0.780485i
$207$	6.24343	−	0.847599i	0.433949	−	0.0589122i
$208$	0.584701	−	0.337577i	0.0405417	−	0.0234068i
$209$	−2.36852	−	4.10240i	−0.163834	−	0.283769i
$210$	4.47960	+	0.966002i	0.309122	+	0.0666605i
$211$	−5.42793	+	9.40146i	−0.373674	+	0.647223i	−0.990128	−	0.140168i	$-0.955236\pi$
$211$	−5.42793	+	9.40146i	−0.373674	+	0.647223i	0.616453	+	0.787392i	$0.288569\pi$
$212$		−	7.81932i		−	0.537033i
$213$	19.6263	+	17.1419i	1.34477	+	1.17454i
$214$	−10.5400			−0.720497
$215$	−1.38041	−	2.39094i	−0.0941431	−	0.163061i
$216$	2.86063	−	4.33783i	0.194641	−	0.295152i
$217$	−3.83117	−	0.0691969i	−0.260077	−	0.00469739i
$218$	−8.56016	+	4.94221i	−0.579767	+	0.334729i
$219$	4.81533	−	1.64542i	0.325390	−	0.111187i
$220$	3.00290	−	1.73372i	0.202455	−	0.116888i
$221$	2.44665	−	1.41257i	0.164579	−	0.0950198i
$222$	11.9756	+	10.4597i	0.803751	+	0.702008i
$223$	18.2083	−	10.5126i	1.21932	−	0.703973i	0.254545	−	0.967061i	$-0.418074\pi$
$223$	18.2083	−	10.5126i	1.21932	−	0.703973i	0.964772	+	0.263088i	$0.0847410\pi$
$224$	−2.64532	−	0.0477786i	−0.176748	−	0.00319234i
$225$	−0.403573	−	2.97273i	−0.0269049	−	0.198182i
$226$	−6.39765	−	11.0811i	−0.425566	−	0.737101i
$227$	18.6494			1.23781			0.618903	−	0.785468i	$-0.287578\pi$
$227$	18.6494			1.23781			0.618903	+	0.785468i	$0.287578\pi$
$228$	2.23912	−	0.765119i	0.148289	−	0.0506713i
$229$		−	21.2832i		−	1.40644i	−0.710975	−	0.703218i	$-0.751746\pi$
$229$		−	21.2832i		−	1.40644i	0.710975	−	0.703218i	$-0.248254\pi$
$230$	−1.05012	+	1.81886i	−0.0692427	+	0.119932i
$231$	−4.86558	−	15.1266i	−0.320132	−	0.995254i
$232$	−2.75872	−	4.77824i	−0.181119	−	0.313707i
$233$	−7.31621	+	4.22401i	−0.479301	+	0.276724i	−0.720125	−	0.693844i	$-0.755916\pi$
$233$	−7.31621	+	4.22401i	−0.479301	+	0.276724i	0.240824	+	0.970569i	$0.422582\pi$
$234$	−1.60192	+	1.23950i	−0.104721	+	0.0810284i
$235$	2.50199	−	4.33357i	0.163212	−	0.282691i
$236$	2.15707	−	3.73615i	0.140413	−	0.243203i
$237$	7.45966	+	21.8307i	0.484557	+	1.41806i
$238$	−11.0692	−	0.199926i	−0.717508	−	0.0129593i
$239$	−13.2764	−	7.66511i	−0.858777	−	0.495815i	0.00482569	−	0.999988i	$-0.498464\pi$
$239$	−13.2764	−	7.66511i	−0.858777	−	0.495815i	−0.863602	+	0.504173i	$0.831797\pi$
$240$	0.560056	+	1.63900i	0.0361515	+	0.105797i
$241$		−	23.3601i		−	1.50475i	−0.658732	−	0.752377i	$-0.728907\pi$
$241$		−	23.3601i		−	1.50475i	0.658732	−	0.752377i	$-0.271093\pi$
$242$	−0.886095	−	0.511587i	−0.0569604	−	0.0328861i
$243$	−6.75326	+	14.0497i	−0.433222	+	0.901287i
$244$		−	5.95622i		−	0.381308i
$245$	3.27880	+	6.18461i	0.209475	+	0.395120i
$246$	3.20595	−	16.2890i	0.204404	−	1.03855i
$247$	−0.922361			−0.0586884
$248$	−0.724142	−	1.25425i	−0.0459830	−	0.0796450i
$249$	−5.75768	−	1.13321i	−0.364878	−	0.0718140i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	1.34222			0.0847203			0.0423601	−	0.999102i	$-0.486512\pi$
$251$	1.34222			0.0847203			0.0423601	+	0.999102i	$0.486512\pi$
$252$	7.88311	−	0.925548i	0.496589	−	0.0583040i
$253$	7.28245			0.457844
$254$	15.8045	+	9.12473i	0.991662	+	0.572537i
$255$	2.34352	+	6.85831i	0.146757	+	0.429484i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.31498			−0.581052			−0.290526	−	0.956867i	$-0.593830\pi$
$257$	−9.31498			−0.581052			−0.290526	+	0.956867i	$0.593830\pi$
$258$	−3.60156	−	3.14565i	−0.224223	−	0.195840i
$259$	−0.438610	+	24.2842i	−0.0272539	+	1.50895i
$260$		−	0.675155i		−	0.0418713i
$261$	10.1293	+	13.0911i	0.626988	+	0.810318i
$262$	10.5041	+	6.06454i	0.648945	+	0.374668i
$263$			4.56924i			0.281752i	0.990027	+	0.140876i	$0.0449918\pi$
$263$			4.56924i			0.281752i	−0.990027	+	0.140876i	$0.955008\pi$
$264$	3.95078	−	4.52337i	0.243154	−	0.278394i
$265$	−6.77173	−	3.90966i	−0.415984	−	0.240168i
$266$	3.09709	+	1.86348i	0.189895	+	0.114257i
$267$	−10.5851	−	2.08332i	−0.647797	−	0.127497i
$268$	1.90260	−	3.29540i	0.116220	−	0.201299i
$269$	−6.36975	+	11.0327i	−0.388370	+	0.672677i	−0.992230	−	0.124413i	$-0.960295\pi$
$269$	−6.36975	+	11.0327i	−0.388370	+	0.672677i	0.603860	+	0.797090i	$0.293629\pi$
$270$	−2.32636	−	4.64630i	−0.141577	−	0.282765i
$271$	−25.4368	+	14.6860i	−1.54518	+	0.892109i	−0.546678	+	0.837343i	$0.684108\pi$
$271$	−25.4368	+	14.6860i	−1.54518	+	0.892109i	−0.998499	+	0.0547661i	$0.982559\pi$
$272$	−2.09222	−	3.62383i	−0.126859	−	0.219727i
$273$	−3.02443	−	0.652201i	−0.183047	−	0.0394730i
$274$	−1.49246	+	2.58501i	−0.0901627	+	0.156166i
$275$		−	3.46745i		−	0.209095i
$276$	−0.702485	+	3.56924i	−0.0422846	+	0.214843i
$277$	28.9078			1.73690			0.868449	−	0.495778i	$-0.165117\pi$
$277$	28.9078			1.73690			0.868449	+	0.495778i	$0.165117\pi$
$278$	−0.672235	−	1.16435i	−0.0403180	−	0.0698328i
$279$	2.65886	+	3.43630i	0.159182	+	0.205726i
$280$	−1.36404	+	2.26702i	−0.0815168	+	0.135481i
$281$	27.6524	−	15.9651i	1.64960	−	0.952400i	0.672377	−	0.740209i	$-0.265274\pi$
$281$	27.6524	−	15.9651i	1.64960	−	0.952400i	0.977228	−	0.212191i	$-0.0680598\pi$
$282$	1.67373	−	8.50400i	0.0996690	−	0.506406i
$283$	25.4788	−	14.7102i	1.51456	−	0.874429i	0.514701	−	0.857370i	$-0.327903\pi$
$283$	25.4788	−	14.7102i	1.51456	−	0.874429i	0.999854	−	0.0170589i	$-0.00543027\pi$
$284$	−13.0292	+	7.52240i	−0.773139	+	0.446372i
$285$	0.456948	−	2.32170i	0.0270673	−	0.137525i
$286$	−2.02742	+	1.17053i	−0.119884	+	0.0692150i
$287$	22.1871	−	12.2809i	1.30966	−	0.724921i
$288$	1.83587	+	2.37267i	0.108180	+	0.139811i
$289$	−0.254758	−	0.441253i	−0.0149857	−	0.0259561i
$290$	−5.51744			−0.323995
$291$	−0.290019	+	1.47355i	−0.0170012	+	0.0863811i
$292$			2.93796i			0.171931i
$293$	6.52531	−	11.3022i	0.381213	−	0.660280i	−0.610023	−	0.792384i	$-0.708840\pi$
$293$	6.52531	−	11.3022i	0.381213	−	0.660280i	0.991236	+	0.132104i	$0.0421732\pi$
$294$	8.83771	+	8.30030i	0.515426	+	0.484083i
$295$	−2.15707	−	3.73615i	−0.125589	−	0.217527i
$296$	−7.95017	+	4.59003i	−0.462094	+	0.266790i
$297$	−9.91909	+	15.0412i	−0.575564	+	0.872778i
$298$	8.37002	−	14.4973i	0.484862	−	0.839806i
$299$	0.708992	−	1.22801i	0.0410021	−	0.0710176i
$300$	1.69945	+	0.334479i	0.0981177	+	0.0193112i
$301$	0.131908	−	7.30324i	0.00760304	−	0.420952i
$302$	4.09798	+	2.36597i	0.235812	+	0.136146i
$303$	−16.8038	+	19.2392i	−0.965351	+	1.10526i
$304$			1.36615i			0.0783539i
$305$	−5.15824	−	2.97811i	−0.295360	−	0.170526i
$306$	7.68208	+	9.92830i	0.439155	+	0.567563i
$307$		−	11.9979i		−	0.684754i	−0.939563	−	0.342377i	$-0.888768\pi$
$307$		−	11.9979i		−	0.684754i	0.939563	−	0.342377i	$-0.111232\pi$
$308$	9.17250	+	0.165670i	0.522652	+	0.00943990i
$309$	16.8741	+	14.7381i	0.959932	+	0.838419i
$310$	−1.44828			−0.0822570
$311$	16.8171	+	29.1281i	0.953612	+	1.65170i	0.737513	+	0.675333i	$0.236000\pi$
$311$	16.8171	+	29.1281i	0.953612	+	1.65170i	0.216099	+	0.976371i	$0.430666\pi$
$312$	−0.378125	−	1.10658i	−0.0214071	−	0.0626479i
$313$	7.57807	+	4.37520i	0.428338	+	0.247301i	0.698638	−	0.715475i	$-0.253790\pi$
$313$	7.57807	+	4.37520i	0.428338	+	0.247301i	−0.270301	+	0.962776i	$0.587123\pi$
$314$	6.86484			0.387406
$315$	3.14001	−	7.28974i	0.176919	−	0.410731i
$316$	−13.3195			−0.749280
$317$	4.61804	+	2.66623i	0.259375	+	0.149750i	0.624050	−	0.781385i	$-0.285486\pi$
$317$	4.61804	+	2.66623i	0.259375	+	0.149750i	−0.364674	+	0.931135i	$0.618820\pi$
$318$	−13.2885	−	2.61540i	−0.745183	−	0.146664i
$319$	9.56571	+	16.5683i	0.535577	+	0.927646i
$320$	−1.00000			−0.0559017
$321$	−3.52540	+	17.9121i	−0.196769	+	0.999757i
$322$	−4.86163	+	2.69099i	−0.270928	+	0.149963i
$323$			5.71656i			0.318078i
$324$	−6.41510	−	6.31241i	−0.356394	−	0.350690i
$325$	−0.584701	−	0.337577i	−0.0324334	−	0.0187254i
$326$			18.8964i			1.04658i
$327$	5.53583	+	16.2006i	0.306132	+	0.895896i
$328$	8.30075	+	4.79244i	0.458332	+	0.264618i
$329$	11.5832	−	6.41151i	0.638604	−	0.353478i
$330$	−1.94196	−	5.68316i	−0.106902	−	0.312848i
$331$	−17.3319	+	30.0198i	−0.952650	+	1.65004i	−0.212992	+	0.977054i	$0.568321\pi$
$331$	−17.3319	+	30.0198i	−0.952650	+	1.65004i	−0.739657	+	0.672984i	$0.765012\pi$
$332$	1.69398	−	2.93407i	0.0929695	−	0.161028i
$333$	21.7813	−	16.8534i	1.19361	−	0.923561i
$334$	15.4216	−	8.90365i	0.843831	−	0.487186i
$335$	−1.90260	−	3.29540i	−0.103950	−	0.180047i
$336$	−0.966002	+	4.47960i	−0.0526997	+	0.244382i
$337$	16.5226	−	28.6180i	0.900044	−	1.55892i	0.0726093	−	0.997360i	$-0.476867\pi$
$337$	16.5226	−	28.6180i	0.900044	−	1.55892i	0.827435	−	0.561562i	$-0.189799\pi$
$338$		−	12.5442i		−	0.682313i
$339$	−20.9716	+	7.16609i	−1.13902	+	0.389209i
$340$	−4.18444			−0.226933
$341$	2.51092	+	4.34904i	0.135974	+	0.235514i
$342$	−0.551340	−	4.06119i	−0.0298131	−	0.219604i
$343$	−1.00291	+	18.4931i	−0.0541523	+	0.998533i
$344$	2.39094	−	1.38041i	0.128911	−	0.0744266i
$345$	2.73981	+	2.39299i	0.147506	+	0.128834i
$346$	−5.58778	+	3.22610i	−0.300401	+	0.173436i
$347$	−18.2272	+	10.5235i	−0.978489	+	0.564931i	−0.901813	−	0.432126i	$-0.857764\pi$
$347$	−18.2272	+	10.5235i	−0.978489	+	0.564931i	−0.0766750	+	0.997056i	$0.524430\pi$
$348$	−9.04311	+	3.09008i	−0.484761	+	0.165645i
$349$	20.0559	−	11.5793i	1.07357	−	0.619824i	0.144413	−	0.989518i	$-0.453871\pi$
$349$	20.0559	−	11.5793i	1.07357	−	0.619824i	0.929154	+	0.369694i	$0.120537\pi$
$350$	1.28128	+	2.31480i	0.0684874	+	0.123731i
$351$	1.57065	+	3.13697i	0.0838351	+	0.167439i
$352$	1.73372	+	3.00290i	0.0924077	+	0.160055i
$353$	30.9907			1.64947			0.824735	−	0.565520i	$-0.191324\pi$
$353$	30.9907			1.64947			0.824735	+	0.565520i	$0.191324\pi$
$354$	−5.62790	−	4.91549i	−0.299119	−	0.261255i
$355$			15.0448i			0.798495i
$356$	3.11428	−	5.39408i	0.165056	−	0.285886i
$357$	−4.04218	+	18.7446i	−0.213935	+	0.992070i
$358$	−11.2559	−	19.4958i	−0.594893	−	1.03038i
$359$	14.9578	−	8.63586i	0.789440	−	0.455783i	−0.0503254	−	0.998733i	$-0.516026\pi$
$359$	14.9578	−	8.63586i	0.789440	−	0.455783i	0.839765	+	0.542949i	$0.182693\pi$
$360$	2.97273	−	0.403573i	0.156677	−	0.0212702i
$361$	−8.56682	+	14.8382i	−0.450885	+	0.780956i
$362$	1.86483	−	3.22998i	0.0980132	−	0.169764i
$363$	−1.16580	+	1.33476i	−0.0611885	+	0.0700566i
$364$	0.920936	−	1.53059i	0.0482702	−	0.0802249i
$365$	2.54435	+	1.46898i	0.133177	+	0.0768900i
$366$	−10.1223	−	1.99223i	−0.529100	−	0.104136i
$367$		−	8.59688i		−	0.448753i	−0.974503	−	0.224377i	$-0.927965\pi$
$367$		−	8.59688i		−	0.448753i	0.974503	−	0.224377i	$-0.0720346\pi$
$368$	−1.81886	−	1.05012i	−0.0948145	−	0.0547411i
$369$	−26.6100	−	10.8967i	−1.38526	−	0.567258i
$370$			9.18006i			0.477249i
$371$	−10.0188	−	18.1002i	−0.520148	−	0.939715i
$372$	−2.37374	+	0.811120i	−0.123073	+	0.0420546i
$373$	−22.5066			−1.16535			−0.582674	−	0.812706i	$-0.697994\pi$
$373$	−22.5066			−1.16535			−0.582674	+	0.812706i	$0.697994\pi$
$374$	7.25465	+	12.5654i	0.375129	+	0.649743i
$375$	1.13939	−	1.30453i	0.0588379	−	0.0673654i
$376$	4.33357	+	2.50199i	0.223487	+	0.129030i
$377$	3.72513			0.191854
$378$	1.06382	−	13.7065i	0.0547168	−	0.704987i
$379$	5.83453			0.299700			0.149850	−	0.988709i	$-0.452121\pi$
$379$	5.83453			0.299700			0.149850	+	0.988709i	$0.452121\pi$
$380$	1.18312	+	0.683073i	0.0606927	+	0.0350409i
$381$	20.7933	−	23.8069i	1.06527	−	1.21966i
$382$	11.7011	+	20.2669i	0.598681	+	1.03695i
$383$	19.9636			1.02009			0.510047	−	0.860146i	$-0.329628\pi$
$383$	19.9636			1.02009			0.510047	+	0.860146i	$0.329628\pi$
$384$	−1.63900	+	0.560056i	−0.0836401	+	0.0285803i
$385$	4.72972	−	7.86078i	0.241049	−	0.400623i
$386$			4.70104i			0.239277i
$387$	−6.55052	+	5.06850i	−0.332981	+	0.257646i
$388$	−0.750910	−	0.433538i	−0.0381217	−	0.0220096i
$389$		−	2.36254i		−	0.119786i	−0.998205	−	0.0598929i	$-0.980924\pi$
$389$		−	2.36254i		−	0.119786i	0.998205	−	0.0598929i	$-0.0190759\pi$
$390$	−1.14739	−	0.225825i	−0.0581004	−	0.0114351i
$391$	−7.61089	−	4.39415i	−0.384899	−	0.222222i
$392$	−6.18461	+	3.27880i	−0.312370	+	0.165605i
$393$	13.8198	−	15.8227i	0.697115	−	0.798149i
$394$	8.10693	−	14.0416i	0.408421	−	0.707407i
$395$	−6.65974	+	11.5350i	−0.335088	+	0.580390i
$396$	−6.36578	−	8.22712i	−0.319892	−	0.413428i
$397$	−9.86892	+	5.69782i	−0.495307	+	0.285966i	−0.726773	−	0.686877i	$-0.758981\pi$
$397$	−9.86892	+	5.69782i	−0.495307	+	0.285966i	0.231467	+	0.972843i	$0.425648\pi$
$398$	−3.69047	−	6.39208i	−0.184987	−	0.320406i
$399$	4.20279	−	4.64005i	0.210403	−	0.232293i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			24.7854i			1.23773i	0.785499	+	0.618863i	$0.212406\pi$
$401$			24.7854i			1.23773i	−0.785499	+	0.618863i	$0.787594\pi$
$402$	−4.96399	−	4.33562i	−0.247581	−	0.216241i
$403$	0.977816			0.0487085
$404$	−7.37400	−	12.7722i	−0.366870	−	0.635438i
$405$	−8.67426	+	2.39943i	−0.431027	+	0.119229i
$406$	−12.5082	−	7.52599i	−0.620770	−	0.373509i
$407$	27.5668	−	15.9157i	1.36643	−	0.788911i
$408$	−6.85831	+	2.34352i	−0.339537	+	0.116022i
$409$	6.90095	−	3.98426i	0.341230	−	0.197009i	−0.319586	−	0.947557i	$-0.603544\pi$
$409$	6.90095	−	3.98426i	0.341230	−	0.197009i	0.660816	+	0.750548i	$0.270210\pi$
$410$	8.30075	−	4.79244i	0.409945	−	0.236682i
$411$	3.89390	+	3.40099i	0.192072	+	0.167758i
$412$	−11.2021	+	6.46751i	−0.551886	+	0.318632i
$413$	0.206123	−	11.4123i	0.0101427	−	0.561561i
$414$	5.83077	+	2.38767i	0.286567	+	0.117348i
$415$	−1.69398	−	2.93407i	−0.0831544	−	0.144028i
$416$	0.675155			0.0331022
$417$	−2.20359	+	0.752979i	−0.107910	+	0.0368736i
$418$		−	4.73704i		−	0.231696i
$419$	6.65561	−	11.5279i	0.325148	−	0.563173i	−0.656394	−	0.754418i	$-0.727919\pi$
$419$	6.65561	−	11.5279i	0.325148	−	0.563173i	0.981542	+	0.191245i	$0.0612526\pi$
$420$	3.39645	+	3.07638i	0.165730	+	0.150112i
$421$	−9.33082	−	16.1615i	−0.454757	−	0.787661i	0.543918	−	0.839139i	$-0.316940\pi$
$421$	−9.33082	−	16.1615i	−0.454757	−	0.787661i	−0.998674	+	0.0514772i	$0.983607\pi$
$422$	−9.40146	+	5.42793i	−0.457656	+	0.264228i
$423$	−13.8923	−	5.68882i	−0.675466	−	0.276600i
$424$	3.90966	−	6.77173i	0.189870	−	0.328864i
$425$	−2.09222	+	3.62383i	−0.101488	+	0.175782i
$426$	8.42594	+	24.6585i	0.408238	+	1.19471i
$427$	−7.63160	−	13.7875i	−0.369319	−	0.667223i
$428$	−9.12788	−	5.26998i	−0.441212	−	0.254734i
$429$	1.31113	+	3.83701i	0.0633018	+	0.185253i
$430$		−	2.76082i		−	0.133138i
$431$	34.0791	+	19.6756i	1.64153	+	0.947740i	0.980289	+	0.197571i	$0.0633053\pi$
$431$	34.0791	+	19.6756i	1.64153	+	0.947740i	0.661246	+	0.750169i	$0.270028\pi$
$432$	4.64630	−	2.32636i	0.223545	−	0.111927i
$433$			13.9220i			0.669047i	0.942387	+	0.334523i	$0.108575\pi$
$433$			13.9220i			0.669047i	−0.942387	+	0.334523i	$0.891425\pi$
$434$	−3.28329	−	1.97551i	−0.157603	−	0.0948277i
$435$	−1.84547	+	9.37660i	−0.0884835	+	0.449574i
$436$	−9.88442			−0.473378
$437$	1.43461	+	2.48483i	0.0686269	+	0.118865i
$438$	4.99291	+	0.982688i	0.238571	+	0.0469546i
$439$	−23.1659	−	13.3748i	−1.10565	−	0.638346i	−0.167949	−	0.985796i	$-0.553714\pi$
$439$	−23.1659	−	13.3748i	−1.10565	−	0.638346i	−0.937699	+	0.347450i	$0.887048\pi$
$440$	3.46745			0.165304
$441$	17.0620	−	12.2429i	0.812474	−	0.582997i
$442$	2.82514			0.134378
$443$	16.0098	+	9.24324i	0.760647	+	0.439160i	0.829528	−	0.558465i	$-0.188610\pi$
$443$	16.0098	+	9.24324i	0.760647	+	0.439160i	−0.0688810	+	0.997625i	$0.521943\pi$
$444$	5.14135	+	15.0462i	0.243998	+	0.714059i
$445$	−3.11428	−	5.39408i	−0.147631	−	0.255704i
$446$	21.0251			0.995568
$447$	−21.8378	−	19.0735i	−1.03289	−	0.902144i
$448$	−2.26702	−	1.36404i	−0.107107	−	0.0644447i
$449$			20.3882i			0.962178i	0.876672	+	0.481089i	$0.159759\pi$
$449$			20.3882i			0.962178i	−0.876672	+	0.481089i	$0.840241\pi$
$450$	1.13686	−	2.77625i	0.0535921	−	0.130874i
$451$	−28.7824	−	16.6175i	−1.35531	−	0.782489i
$452$		−	12.7953i		−	0.601841i
$453$	5.39153	−	6.17293i	0.253316	−	0.290030i
$454$	16.1509	+	9.32471i	0.757998	+	0.437630i
$455$	−0.865064	−	1.56285i	−0.0405548	−	0.0732676i
$456$	2.32170	+	0.456948i	0.108723	+	0.0213985i
$457$	3.76798	−	6.52634i	0.176259	−	0.305289i	−0.764337	−	0.644816i	$-0.776934\pi$
$457$	3.76798	−	6.52634i	0.176259	−	0.305289i	0.940596	+	0.339527i	$0.110267\pi$
$458$	10.6416	−	18.4318i	0.497250	−	0.861262i
$459$	19.4421	−	9.73449i	0.907481	−	0.454367i
$460$	−1.81886	+	1.05012i	−0.0848046	+	0.0489620i
$461$	−9.46493	−	16.3937i	−0.440826	−	0.763532i	0.556925	−	0.830563i	$-0.311981\pi$
$461$	−9.46493	−	16.3937i	−0.440826	−	0.763532i	−0.997751	+	0.0670302i	$0.978648\pi$
$462$	3.34956	−	15.5328i	0.155836	−	0.722650i
$463$	−2.49274	+	4.31755i	−0.115847	+	0.200653i	−0.918118	−	0.396307i	$-0.870292\pi$
$463$	−2.49274	+	4.31755i	−0.115847	+	0.200653i	0.802271	+	0.596960i	$0.203625\pi$
$464$		−	5.51744i		−	0.256141i
$465$	−0.484421	+	2.46128i	−0.0224645	+	0.114139i
$466$	−8.44803			−0.391347
$467$	−8.76741	−	15.1856i	−0.405707	−	0.702706i	0.588696	−	0.808354i	$-0.299641\pi$
$467$	−8.76741	−	15.1856i	−0.405707	−	0.702706i	−0.994404	+	0.105649i	$0.966308\pi$
$468$	−2.00705	+	0.272475i	−0.0927761	+	0.0125951i
$469$	0.181807	−	10.0660i	0.00839508	−	0.464804i
$470$	4.33357	−	2.50199i	0.199893	−	0.115408i
$471$	2.29615	−	11.6664i	0.105801	−	0.537561i
$472$	3.73615	−	2.15707i	0.171970	−	0.0992870i
$473$	−8.29044	+	4.78649i	−0.381195	+	0.220083i
$474$	−4.45509	+	22.6358i	−0.204629	+	1.03970i
$475$	1.18312	−	0.683073i	0.0542852	−	0.0313416i
$476$	−9.48622	−	5.70773i	−0.434800	−	0.261613i
$477$	−8.88947	+	21.7084i	−0.407021	+	0.993957i
$478$	−7.66511	−	13.2764i	−0.350594	−	0.607247i
$479$	5.84145			0.266903			0.133451	−	0.991055i	$-0.457394\pi$
$479$	5.84145			0.266903			0.133451	+	0.991055i	$0.457394\pi$
$480$	−0.334479	+	1.69945i	−0.0152668	+	0.0775688i
$481$		−	6.19796i		−	0.282603i
$482$	11.6800	−	20.2304i	0.532011	−	0.921470i
$483$	2.94709	+	9.16217i	0.134097	+	0.416893i
$484$	−0.511587	−	0.886095i	−0.0232540	−	0.0402771i
$485$	−0.750910	+	0.433538i	−0.0340971	+	0.0196859i
$486$	−12.8733	+	8.79075i	−0.583946	+	0.398757i
$487$	1.14434	−	1.98205i	0.0518548	−	0.0898151i	−0.838933	−	0.544235i	$-0.816820\pi$
$487$	1.14434	−	1.98205i	0.0518548	−	0.0898151i	0.890788	+	0.454420i	$0.150153\pi$
$488$	2.97811	−	5.15824i	0.134813	−	0.233502i
$489$	32.1135	+	6.32046i	1.45222	+	0.285821i
$490$	−0.252779	+	6.99543i	−0.0114194	+	0.316022i
$491$	−19.2005	−	11.0854i	−0.866507	−	0.500278i	−0.000321242	−	1.00000i	$-0.500102\pi$
$491$	−19.2005	−	11.0854i	−0.866507	−	0.500278i	−0.866186	+	0.499722i	$0.833436\pi$
$492$	10.9209	−	12.5037i	0.492354	−	0.563711i
$493$		−	23.0874i		−	1.03980i
$494$	−0.798788	−	0.461180i	−0.0359392	−	0.0207495i
$495$	−10.3078	+	1.39937i	−0.463300	+	0.0628969i
$496$		−	1.44828i		−	0.0650299i
$497$	−20.5217	+	34.1069i	−0.920523	+	1.52991i
$498$	−4.41969	−	3.86022i	−0.198051	−	0.172981i
$499$	2.87655			0.128772			0.0643860	−	0.997925i	$-0.479491\pi$
$499$	2.87655			0.128772			0.0643860	+	0.997925i	$0.479491\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−9.97309	−	29.1862i	−0.445565	−	1.30395i
$502$	1.16240	+	0.671111i	0.0518804	+	0.0299531i
$503$	−4.73597			−0.211166			−0.105583	−	0.994410i	$-0.533671\pi$
$503$	−4.73597			−0.211166			−0.105583	+	0.994410i	$0.533671\pi$
$504$	7.28974	+	3.14001i	0.324711	+	0.139867i
$505$	−14.7480			−0.656278
$506$	6.30679	+	3.64122i	0.280371	+	0.161872i
$507$	−21.3182	−	4.19576i	−0.946773	−	0.186340i
$508$	9.12473	+	15.8045i	0.404845	+	0.701211i
$509$	9.29802			0.412127			0.206064	−	0.978539i	$-0.433935\pi$
$509$	9.29802			0.412127			0.206064	+	0.978539i	$0.433935\pi$
$510$	−1.39961	+	7.11123i	−0.0619757	+	0.314891i
$511$	3.76436	+	6.80081i	0.166525	+	0.300850i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.08619	−	0.421409i	−0.312863	−	0.0186057i
$514$	−8.06701	−	4.65749i	−0.355820	−	0.205433i
$515$			12.9350i			0.569985i
$516$	−1.54621	−	4.52499i	−0.0680682	−	0.199202i
$517$	−15.0264	−	8.67551i	−0.660861	−	0.381548i
$518$	−12.5219	+	20.8114i	−0.550183	+	0.914402i
$519$	3.61360	+	10.5752i	0.158619	+	0.464200i
$520$	0.337577	−	0.584701i	0.0148037	−	0.0256408i
$521$	−16.9641	+	29.3827i	−0.743210	+	1.28728i	0.207816	+	0.978168i	$0.433364\pi$
$521$	−16.9641	+	29.3827i	−0.743210	+	1.28728i	−0.951026	+	0.309110i	$0.899969\pi$
$522$	2.22669	+	16.4019i	0.0974596	+	0.717890i
$523$	13.5175	−	7.80435i	0.591080	−	0.341260i	−0.174444	−	0.984667i	$-0.555813\pi$
$523$	13.5175	−	7.80435i	0.591080	−	0.341260i	0.765524	+	0.643407i	$0.222480\pi$
$524$	6.06454	+	10.5041i	0.264930	+	0.458873i
$525$	4.36245	−	1.40322i	0.190393	−	0.0612415i
$526$	−2.28462	+	3.95708i	−0.0996142	+	0.172537i
$527$		−	6.06025i		−	0.263989i
$528$	5.68316	−	1.94196i	0.247328	−	0.0845132i
$529$	18.5890			0.808218
$530$	−3.90966	−	6.77173i	−0.169825	−	0.294145i
$531$	−10.2360	+	7.92019i	−0.444206	+	0.343707i
$532$	1.75042	+	3.16236i	0.0758903	+	0.137106i
$533$	−5.60429	+	3.23564i	−0.242749	+	0.140151i
$534$	−8.12530	−	7.09676i	−0.351616	−	0.307107i
$535$	−9.12788	+	5.26998i	−0.394632	+	0.227841i
$536$	3.29540	−	1.90260i	0.142340	−	0.0821799i
$537$	−36.8969	+	12.6079i	−1.59222	+	0.544070i
$538$	−11.0327	+	6.36975i	−0.475654	+	0.274619i
$539$	21.4448	−	11.3691i	0.923693	−	0.489701i
$540$	0.308465	−	5.18699i	0.0132742	−	0.223212i
$541$	−18.3723	−	31.8218i	−0.789887	−	1.36812i	−0.926036	−	0.377436i	$-0.876806\pi$
$541$	−18.3723	−	31.8218i	−0.789887	−	1.36812i	0.136149	−	0.990688i	$-0.456528\pi$
$542$	−29.3719			−1.26163
$543$	−4.86543	−	4.24954i	−0.208796	−	0.182365i
$544$		−	4.18444i		−	0.179406i
$545$	−4.94221	+	8.56016i	−0.211701	+	0.366677i
$546$	−2.29313	−	2.07704i	−0.0981369	−	0.0888889i
$547$	5.55216	+	9.61662i	0.237393	+	0.411177i	0.959965	−	0.280118i	$-0.0903737\pi$
$547$	5.55216	+	9.61662i	0.237393	+	0.411177i	−0.722572	+	0.691295i	$0.757040\pi$
$548$	−2.58501	+	1.49246i	−0.110426	+	0.0637547i
$549$	−6.77139	+	16.5359i	−0.288996	+	0.705736i
$550$	1.73372	−	3.00290i	0.0739262	−	0.128044i
$551$	−3.76882	+	6.52778i	−0.160557	+	0.278093i
$552$	−2.39299	+	2.73981i	−0.101852	+	0.116614i
$553$	−30.8320	+	17.0660i	−1.31111	+	0.725721i
$554$	25.0348	+	14.4539i	1.06363	+	0.614086i
$555$	15.6010	+	3.07054i	0.662227	+	0.130337i
$556$		−	1.34447i		−	0.0570182i
$557$	0.516410	+	0.298150i	0.0218810	+	0.0126330i	0.510901	−	0.859640i	$-0.329312\pi$
$557$	0.516410	+	0.298150i	0.0218810	+	0.0126330i	−0.489020	+	0.872273i	$0.662645\pi$
$558$	0.584489	+	4.30536i	0.0247434	+	0.182260i
$559$			1.86398i			0.0788379i
$560$	−2.31480	+	1.28128i	−0.0978183	+	0.0541441i
$561$	23.7808	−	8.12603i	1.00403	−	0.343081i
$562$	31.9303			1.34690
$563$	4.43803	+	7.68690i	0.187041	+	0.323964i	0.944262	−	0.329194i	$-0.106777\pi$
$563$	4.43803	+	7.68690i	0.187041	+	0.323964i	−0.757222	+	0.653158i	$0.773444\pi$
$564$	5.70149	−	6.52782i	0.240076	−	0.274871i
$565$	−11.0811	−	6.39765i	−0.466184	−	0.269151i
$566$	29.4203			1.23663
$567$	−22.9377	−	6.39244i	−0.963292	−	0.268457i
$568$	−15.0448			−0.631266
$569$	1.07436	+	0.620281i	0.0450395	+	0.0260036i	0.522351	−	0.852731i	$-0.325055\pi$
$569$	1.07436	+	0.620281i	0.0450395	+	0.0260036i	−0.477311	+	0.878734i	$0.658389\pi$
$570$	1.55658	−	1.78217i	0.0651978	−	0.0746470i
$571$	7.48105	+	12.9576i	0.313072	+	0.542257i	0.979026	−	0.203736i	$-0.0653085\pi$
$571$	7.48105	+	12.9576i	0.313072	+	0.542257i	−0.665954	+	0.745993i	$0.731975\pi$
$572$	−2.34106			−0.0978847
$573$	38.3564	−	13.1066i	1.60236	−	0.547534i
$574$	25.3551	+	0.457952i	1.05830	+	0.0191146i
$575$			2.10023i			0.0875858i
$576$	0.403573	+	2.97273i	0.0168156	+	0.123864i
$577$	−39.9391	−	23.0589i	−1.66269	−	0.959953i	−0.971424	−	0.237349i	$-0.923721\pi$
$577$	−39.9391	−	23.0589i	−1.66269	−	0.959953i	−0.691263	−	0.722604i	$-0.742945\pi$
$578$		−	0.509515i		−	0.0211930i
$579$	7.98918	+	1.57240i	0.332019	+	0.0653468i
$580$	−4.77824	−	2.75872i	−0.198406	−	0.114550i
$581$	0.161872	−	8.96226i	0.00671560	−	0.371817i
$582$	−0.987939	+	1.13112i	−0.0409514	+	0.0468865i
$583$	−13.5565	+	23.4806i	−0.561454	+	0.972467i
$584$	−1.46898	+	2.54435i	−0.0607869	+	0.105286i
$585$	−0.767557	+	1.87440i	−0.0317346	+	0.0774968i
$586$	11.3022	−	6.52531i	0.466888	−	0.269558i
$587$	18.2697	+	31.6441i	0.754072	+	1.30609i	0.945834	+	0.324649i	$0.105246\pi$
$587$	18.2697	+	31.6441i	0.754072	+	1.30609i	−0.191763	+	0.981441i	$0.561420\pi$
$588$	3.50353	+	11.6071i	0.144483	+	0.478670i
$589$	−0.989284	+	1.71349i	−0.0407627	+	0.0706031i
$590$		−	4.31413i		−	0.177610i
$591$	−21.1514	−	18.4739i	−0.870052	−	0.759916i
$592$	−9.18006			−0.377298
$593$	0.871192	+	1.50895i	0.0357756	+	0.0619651i	0.883359	−	0.468697i	$-0.155277\pi$
$593$	0.871192	+	1.50895i	0.0357756	+	0.0619651i	−0.847583	+	0.530662i	$0.821943\pi$
$594$	−16.1108	+	8.06651i	−0.661033	+	0.330973i
$595$	−9.68615	+	5.36145i	−0.397093	+	0.219798i
$596$	14.4973	−	8.37002i	0.593832	−	0.342849i
$597$	−12.0974	+	4.13374i	−0.495113	+	0.169183i
$598$	1.22801	−	0.708992i	0.0502171	−	0.0289928i
$599$	6.40629	−	3.69868i	0.261754	−	0.151124i	−0.363380	−	0.931641i	$-0.618377\pi$
$599$	6.40629	−	3.69868i	0.261754	−	0.151124i	0.625134	+	0.780517i	$0.285044\pi$
$600$	1.30453	+	1.13939i	0.0532570	+	0.0465155i
$601$	−18.7412	+	10.8202i	−0.764469	+	0.441367i	−0.830898	−	0.556425i	$-0.812173\pi$
$601$	−18.7412	+	10.8202i	−0.764469	+	0.441367i	0.0664288	+	0.997791i	$0.478839\pi$
$602$	3.76586	−	6.25884i	0.153485	−	0.255091i
$603$	−9.02851	+	6.98586i	−0.367669	+	0.284486i
$604$	2.36597	+	4.09798i	0.0962699	+	0.166744i
$605$	−1.02317			−0.0415980
$606$	−24.1721	+	8.25972i	−0.981923	+	0.335528i
$607$		−	20.3118i		−	0.824432i	−0.911086	−	0.412216i	$-0.864755\pi$
$607$		−	20.3118i		−	0.824432i	0.911086	−	0.412216i	$-0.135245\pi$
$608$	−0.683073	+	1.18312i	−0.0277023	+	0.0479818i
$609$	−16.9738	+	18.7397i	−0.687811	+	0.759371i
$610$	−2.97811	−	5.15824i	−0.120580	−	0.208851i
$611$	−2.92583	+	1.68923i	−0.118366	+	0.0683389i
$612$	1.68873	+	12.4392i	0.0682628	+	0.502825i
$613$	1.63069	−	2.82444i	0.0658630	−	0.114078i	−0.831213	−	0.555953i	$-0.812353\pi$
$613$	1.63069	−	2.82444i	0.0658630	−	0.114078i	0.897077	+	0.441875i	$0.145687\pi$
$614$	5.99893	−	10.3904i	0.242097	−	0.419324i
$615$	−5.36807	−	15.7097i	−0.216462	−	0.633475i
$616$	7.86078	+	4.72972i	0.316720	+	0.190566i
$617$	−16.3813	−	9.45777i	−0.659488	−	0.380755i	0.132594	−	0.991170i	$-0.457669\pi$
$617$	−16.3813	−	9.45777i	−0.659488	−	0.380755i	−0.792082	+	0.610415i	$0.791003\pi$
$618$	7.24434	+	21.2006i	0.291410	+	0.852812i
$619$			38.7030i			1.55561i	0.628508	+	0.777803i	$0.283666\pi$
$619$			38.7030i			1.55561i	−0.628508	+	0.777803i	$0.716334\pi$
$620$	−1.25425	−	0.724142i	−0.0503719	−	0.0290822i
$621$	6.00800	−	9.11046i	0.241093	−	0.365590i
$622$			33.6343i			1.34861i
$623$	0.297591	−	16.4765i	0.0119227	−	0.660117i
$624$	0.225825	−	1.14739i	0.00904025	−	0.0459324i
$625$	1.00000			0.0400000
$626$	4.37520	+	7.57807i	0.174868	+	0.302880i
$627$	−8.05035	−	1.58444i	−0.321500	−	0.0632765i
$628$	5.94513	+	3.43242i	0.237236	+	0.136969i
$629$	−38.4134			−1.53164
$630$	6.36420	−	4.74310i	0.253556	−	0.188970i
$631$	−29.2398			−1.16402			−0.582010	−	0.813182i	$-0.697734\pi$
$631$	−29.2398			−1.16402			−0.582010	+	0.813182i	$0.697734\pi$
$632$	−11.5350	−	6.65974i	−0.458838	−	0.264910i
$633$	6.07990	+	17.7928i	0.241654	+	0.707201i
$634$	2.66623	+	4.61804i	0.105889	+	0.183406i
$635$	18.2495			0.724208
$636$	−10.2005	−	8.90926i	−0.404476	−	0.353275i
$637$	0.170665	−	4.72300i	0.00676200	−	0.187132i
$638$			19.1314i			0.757420i
$639$	44.7241	−	6.07168i	1.76926	−	0.240192i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	3.24063i		−	0.127997i	−0.997950	−	0.0639985i	$-0.979615\pi$
$641$		−	3.24063i		−	0.127997i	0.997950	−	0.0639985i	$-0.0203853\pi$
$642$	−12.0091	+	13.7496i	−0.473963	+	0.542655i
$643$	−34.0743	−	19.6728i	−1.34376	−	0.775820i	−0.356402	−	0.934333i	$-0.615997\pi$
$643$	−34.0743	−	19.6728i	−1.34376	−	0.775820i	−0.987357	+	0.158513i	$0.949330\pi$
$644$	−5.55579	−	0.100346i	−0.218929	−	0.00395420i
$645$	−4.69186	−	0.923436i	−0.184742	−	0.0363603i
$646$	−2.85828	+	4.95068i	−0.112457	+	0.194782i
$647$	12.0788	−	20.9212i	0.474869	−	0.822496i	−0.524717	−	0.851277i	$-0.675829\pi$
$647$	12.0788	−	20.9212i	0.474869	−	0.822496i	0.999586	+	0.0287802i	$0.00916227\pi$
$648$	−2.39943	−	8.67426i	−0.0942585	−	0.340757i
$649$	−12.9549	+	7.47951i	−0.508524	+	0.293596i
$650$	−0.337577	−	0.584701i	−0.0132409	−	0.0229339i
$651$	−4.45548	+	4.91902i	−0.174624	+	0.192792i
$652$	−9.44821	+	16.3648i	−0.370020	+	0.640894i
$653$		−	20.6769i		−	0.809150i	−0.914505	−	0.404575i	$-0.867419\pi$
$653$		−	20.6769i		−	0.809150i	0.914505	−	0.404575i	$-0.132581\pi$
$654$	−3.30614	+	16.7981i	−0.129280	+	0.656856i
$655$	12.1291			0.473922
$656$	4.79244	+	8.30075i	0.187113	+	0.324090i
$657$	3.34005	−	8.15651i	0.130308	−	0.318216i
$658$	13.2371	+	0.239083i	0.516037	+	0.00932042i
$659$	−19.6364	+	11.3371i	−0.764927	+	0.441631i	−0.831062	−	0.556180i	$-0.812267\pi$
$659$	−19.6364	+	11.3371i	−0.764927	+	0.441631i	0.0661347	+	0.997811i	$0.478933\pi$
$660$	1.15979	−	5.89274i	0.0451447	−	0.229375i
$661$	41.0554	−	23.7034i	1.59687	−	0.921954i	0.604786	−	0.796388i	$-0.293259\pi$
$661$	41.0554	−	23.7034i	1.59687	−	0.921954i	0.992085	−	0.125565i	$-0.0400745\pi$
$662$	−30.0198	+	17.3319i	−1.16675	+	0.673625i
$663$	0.944952	−	4.80118i	0.0366989	−	0.186463i
$664$	2.93407	−	1.69398i	0.113864	−	0.0657393i
$665$	3.61390	+	0.0652726i	0.140141	+	0.00253116i
$666$	27.2899	−	3.70483i	1.05746	−	0.143559i
$667$	−5.79396	−	10.0354i	−0.224343	−	0.388573i
$668$	17.8073			0.688985
$669$	7.03247	−	35.7311i	0.271891	−	1.38144i
$670$		−	3.80521i		−	0.147008i
$671$	−10.3264	+	17.8859i	−0.398647	+	0.690477i
$672$	−3.07638	+	3.39645i	−0.118674	+	0.131021i
$673$	−4.41029	−	7.63884i	−0.170004	−	0.294456i	0.768417	−	0.639950i	$-0.221045\pi$
$673$	−4.41029	−	7.63884i	−0.170004	−	0.294456i	−0.938421	+	0.345494i	$0.887711\pi$
$674$	28.6180	−	16.5226i	1.10232	−	0.636427i
$675$	−4.33783	−	2.86063i	−0.166963	−	0.110106i
$676$	6.27208	−	10.8636i	0.241234	−	0.417829i
$677$	−6.42305	+	11.1251i	−0.246858	+	0.427571i	−0.962652	−	0.270741i	$-0.912731\pi$
$677$	−6.42305	+	11.1251i	−0.246858	+	0.427571i	0.715794	+	0.698311i	$0.246065\pi$
$678$	−21.7450	−	4.27977i	−0.835110	−	0.164363i
$679$	−2.29369	−	0.0414277i	−0.0880239	−	0.00158985i
$680$	−3.62383	−	2.09222i	−0.138967	−	0.0802329i
$681$	21.2490	−	24.3286i	0.814263	−	0.932275i
$682$			5.02184i			0.192296i
$683$	15.4843	+	8.93988i	0.592491	+	0.342075i	0.766082	−	0.642743i	$-0.222204\pi$
$683$	15.4843	+	8.93988i	0.592491	+	0.342075i	−0.173591	+	0.984818i	$0.555537\pi$
$684$	1.55312	−	3.79276i	0.0593850	−	0.145020i
$685$			2.98492i			0.114048i
$686$	−10.1151	+	15.5140i	−0.386196	+	0.592328i
$687$	−27.7645	−	24.2499i	−1.05928	−	0.925193i
$688$	2.76082			0.105255
$689$	2.63963	+	4.57196i	0.100562	+	0.174178i
$690$	1.17625	+	3.44229i	0.0447791	+	0.131046i
$691$	14.1029	+	8.14232i	0.536500	+	0.309749i	0.743659	−	0.668559i	$-0.233088\pi$
$691$	14.1029	+	8.14232i	0.536500	+	0.309749i	−0.207159	+	0.978307i	$0.566422\pi$
$692$	−6.45221			−0.245276
$693$	−25.2768	−	10.8878i	−0.960186	−	0.413593i
$694$	−21.0470			−0.798933
$695$	−1.16435	−	0.672235i	−0.0441661	−	0.0254993i
$696$	−9.37660	−	1.84547i	−0.355419	−	0.0699523i
$697$	20.0537	+	34.7340i	0.759587	+	1.31564i
$698$	23.1585			0.876563
$699$	−2.82569	+	14.3570i	−0.106877	+	0.543031i
$700$	−0.0477786	+	2.64532i	−0.00180586	+	0.0999837i
$701$			14.7886i			0.558559i	0.960210	+	0.279279i	$0.0900955\pi$
$701$			14.7886i			0.558559i	−0.960210	+	0.279279i	$0.909904\pi$
$702$	−0.208262	+	3.50202i	−0.00786034	+	0.132175i
$703$	10.8611	+	6.27066i	0.409634	+	0.236502i
$704$			3.46745i			0.130684i
$705$	−2.80251	−	8.20154i	−0.105549	−	0.308888i
$706$	26.8387	+	15.4954i	1.01009	+	0.583175i
$707$	−33.4341	−	20.1168i	−1.25742	−	0.756572i
$708$	−2.41616	−	7.07089i	−0.0908048	−	0.265740i
$709$	−1.77684	+	3.07758i	−0.0667308	+	0.115581i	−0.897460	−	0.441095i	$-0.854590\pi$
$709$	−1.77684	+	3.07758i	−0.0667308	+	0.115581i	0.830730	+	0.556676i	$0.187924\pi$
$710$	−7.52240	+	13.0292i	−0.282311	+	0.488976i
$711$	36.9782	+	15.1424i	1.38679	+	0.567884i
$712$	5.39408	−	3.11428i	0.202152	−	0.116712i
$713$	−1.52087	−	2.63422i	−0.0569569	−	0.0986523i
$714$	−12.8729	+	14.2122i	−0.481757	+	0.531879i
$715$	−1.17053	+	2.02742i	−0.0437754	+	0.0758212i
$716$		−	22.5118i		−	0.841305i
$717$	−25.1263	+	8.58579i	−0.938360	+	0.320642i
$718$	17.2717			0.644575
$719$	−18.0431	−	31.2515i	−0.672892	−	1.16548i	−0.977080	−	0.212872i	$-0.931718\pi$
$719$	−18.0431	−	31.2515i	−0.672892	−	1.16548i	0.304188	−	0.952612i	$-0.401615\pi$
$720$	2.77625	+	1.13686i	0.103465	+	0.0423683i
$721$	−17.6439	+	29.3240i	−0.657092	+	1.09208i
$722$	−14.8382	+	8.56682i	−0.552219	+	0.318824i
$723$	−30.4738	−	26.6163i	−1.13333	−	0.989870i
$724$	3.22998	−	1.86483i	0.120041	−	0.0693058i
$725$	−4.77824	+	2.75872i	−0.177459	+	0.102456i
$726$	−1.67699	+	0.573036i	−0.0622389	+	0.0212673i
$727$	−29.7027	+	17.1489i	−1.10161	+	0.636017i	−0.936644	−	0.350282i	$-0.886086\pi$
$727$	−29.7027	+	17.1489i	−1.10161	+	0.636017i	−0.164969	+	0.986299i	$0.552752\pi$
$728$	1.56285	−	0.865064i	0.0579231	−	0.0320614i
$729$	10.6336	+	24.8179i	0.393835	+	0.919181i
$730$	1.46898	+	2.54435i	0.0543694	+	0.0941706i
$731$	11.5525			0.427283
$732$	−7.77004	−	6.78646i	−0.287189	−	0.250835i
$733$			5.89064i			0.217576i	0.994065	+	0.108788i	$0.0346969\pi$
$733$			5.89064i			0.217576i	−0.994065	+	0.108788i	$0.965303\pi$
$734$	4.29844	−	7.44511i	0.158658	−	0.274804i
$735$	11.8038	+	2.76941i	0.435391	+	0.102151i
$736$	−1.05012	−	1.81886i	−0.0387078	−	0.0670439i
$737$	−11.4266	+	6.59717i	−0.420905	+	0.243010i
$738$	−17.5966	−	22.7418i	−0.647740	−	0.837137i
$739$	7.90804	−	13.6971i	0.290902	−	0.503857i	−0.683121	−	0.730305i	$-0.739378\pi$
$739$	7.90804	−	13.6971i	0.290902	−	0.503857i	0.974023	+	0.226448i	$0.0727114\pi$
$740$	−4.59003	+	7.95017i	−0.168733	+	0.292254i
$741$	−1.05093	+	1.20324i	−0.0386069	+	0.0442022i
$742$	0.373596	−	20.6846i	0.0137151	−	0.759355i
$743$	14.2025	+	8.19980i	0.521038	+	0.300821i	0.737359	−	0.675501i	$-0.236073\pi$
$743$	14.2025	+	8.19980i	0.521038	+	0.300821i	−0.216321	+	0.976322i	$0.569406\pi$
$744$	−2.46128	−	0.484421i	−0.0902350	−	0.0177597i
$745$		−	16.7400i		−	0.613308i
$746$	−19.4913	−	11.2533i	−0.713627	−	0.412013i
$747$	−8.03854	+	6.21987i	−0.294115	+	0.227573i
$748$			14.5093i			0.530513i
$749$	−27.8816	−	0.503584i	−1.01877	−	0.0184006i
$750$	1.63900	−	0.560056i	0.0598480	−	0.0204504i
$751$	18.2063			0.664357			0.332179	−	0.943216i	$-0.392216\pi$
$751$	18.2063			0.664357			0.332179	+	0.943216i	$0.392216\pi$
$752$	2.50199	+	4.33357i	0.0912381	+	0.158029i
$753$	1.52932	−	1.75096i	0.0557314	−	0.0638086i
$754$	3.22605	+	1.86256i	0.117486	+	0.0678305i
$755$	4.73194			0.172213
$756$	7.77454	−	11.3383i	0.282757	−	0.412369i
$757$	29.2189			1.06198			0.530990	−	0.847378i	$-0.321820\pi$
$757$	29.2189			1.06198			0.530990	+	0.847378i	$0.321820\pi$
$758$	5.05285	+	2.91727i	0.183528	+	0.105960i
$759$	8.29756	−	9.50014i	0.301182	−	0.344833i
$760$	0.683073	+	1.18312i	0.0247777	+	0.0429162i
$761$	−13.4591			−0.487893			−0.243946	−	0.969789i	$-0.578442\pi$
$761$	−13.4591			−0.487893			−0.243946	+	0.969789i	$0.578442\pi$
$762$	29.9110	−	10.2207i	1.08356	−	0.370258i
$763$	−22.8805	+	12.6647i	−0.828330	+	0.458494i
$764$			23.4022i			0.846663i
$765$	11.6170	+	4.75712i	0.420015	+	0.171994i
$766$	17.2890	+	9.98182i	0.624678	+	0.360658i
$767$			2.91271i			0.105172i
$768$	−1.69945	−	0.334479i	−0.0613235	−	0.0120695i
$769$	−32.3572	−	18.6814i	−1.16683	−	0.673670i	−0.213899	−	0.976856i	$-0.568616\pi$
$769$	−32.3572	−	18.6814i	−1.16683	−	0.673670i	−0.952931	+	0.303186i	$0.901950\pi$
$770$	8.02645	−	4.44278i	0.289253	−	0.160107i
$771$	−10.6134	+	12.1516i	−0.382232	+	0.437630i
$772$	−2.35052	+	4.07122i	−0.0845971	+	0.146526i
$773$	−17.6040	+	30.4911i	−0.633173	+	1.09669i	0.353727	+	0.935349i	$0.384914\pi$
$773$	−17.6040	+	30.4911i	−0.633173	+	1.09669i	−0.986899	+	0.161338i	$0.948419\pi$
$774$	−8.20716	+	1.11419i	−0.295000	+	0.0400488i
$775$	−1.25425	+	0.724142i	−0.0450540	+	0.0260119i
$776$	−0.433538	−	0.750910i	−0.0155631	−	0.0269561i
$777$	31.1796	+	28.2414i	1.11856	+	1.01315i
$778$	1.18127	−	2.04602i	0.0423507	−	0.0733535i
$779$		−	13.0944i		−	0.469154i
$780$	−0.880757	−	0.769266i	−0.0315361	−	0.0275441i
$781$	52.1670			1.86668
$782$	−4.39415	−	7.61089i	−0.157134	−	0.272165i
$783$	28.6189	+	1.70194i	1.02276	+	0.0608223i
$784$	−6.99543	−	0.252779i	−0.249837	−	0.00902783i
$785$	5.94513	−	3.43242i	0.212191	−	0.122508i
$786$	19.8796	−	6.79296i	0.709082	−	0.242297i
$787$	19.4460	−	11.2272i	0.693176	−	0.400205i	−0.111625	−	0.993750i	$-0.535606\pi$
$787$	19.4460	−	11.2272i	0.693176	−	0.400205i	0.804801	+	0.593545i	$0.202272\pi$
$788$	14.0416	−	8.10693i	0.500212	−	0.288797i
$789$	5.96069	+	5.20616i	0.212206	+	0.185344i
$790$	−11.5350	+	6.65974i	−0.410397	+	0.236943i
$791$	−16.3944	−	29.6186i	−0.582918	−	1.05312i
$792$	−1.39937	−	10.3078i	−0.0497244	−	0.366271i
$793$	2.01068	+	3.48261i	0.0714015	+	0.123671i
$794$	−11.3956			−0.404416
$795$	−12.8159	+	4.37926i	−0.454533	+	0.155316i
$796$		−	7.38094i		−	0.261610i
$797$	−20.1411	+	34.8854i	−0.713435	+	1.23571i	0.250125	+	0.968213i	$0.419528\pi$
$797$	−20.1411	+	34.8854i	−0.713435	+	1.23571i	−0.963560	+	0.267492i	$0.913805\pi$
$798$	5.95975	−	1.91700i	0.210973	−	0.0678612i
$799$	10.4694	+	18.1336i	0.370381	+	0.641519i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−14.7783	+	11.4348i	−0.522166	+	0.404029i
$802$	−12.3927	+	21.4648i	−0.437602	+	0.757949i
$803$	5.09361	−	8.82239i	0.179750	−	0.311336i
$804$	−2.13113	−	6.23675i	−0.0751591	−	0.219953i
$805$	−2.86480	+	4.76128i	−0.100971	+	0.167813i
$806$	0.846813	+	0.488908i	0.0298277	+	0.0172210i
$807$	7.13483	+	20.8801i	0.251158	+	0.735014i
$808$		−	14.7480i		−	0.518833i
$809$	−24.4523	−	14.1175i	−0.859696	−	0.496345i	0.00421477	−	0.999991i	$-0.498658\pi$
$809$	−24.4523	−	14.1175i	−0.859696	−	0.496345i	−0.863910	+	0.503646i	$0.831992\pi$
$810$	−8.71184	−	2.25916i	−0.306103	−	0.0793788i
$811$		−	20.3324i		−	0.713969i	−0.934110	−	0.356984i	$-0.883805\pi$
$811$		−	20.3324i		−	0.713969i	0.934110	−	0.356984i	$-0.116195\pi$
$812$	−7.06940	−	12.7718i	−0.248087	−	0.448202i
$813$	−9.82430	+	49.9161i	−0.344553	+	1.75063i
$814$	31.8314			1.11569
$815$	9.44821	+	16.3648i	0.330956	+	0.573233i
$816$	−7.11123	−	1.39961i	−0.248943	−	0.0489961i
$817$	−3.26637	−	1.88584i	−0.114276	−	0.0659772i
$818$	7.96853			0.278613
$819$	−4.29682	+	3.20233i	−0.150143	+	0.111898i
$820$	9.58488			0.334719
$821$	−13.6725	−	7.89380i	−0.477172	−	0.275496i	0.242065	−	0.970260i	$-0.422175\pi$
$821$	−13.6725	−	7.89380i	−0.477172	−	0.275496i	−0.719237	+	0.694764i	$0.755509\pi$
$822$	1.67172	+	4.89229i	0.0583080	+	0.170638i
$823$	−17.4709	−	30.2605i	−0.608998	−	1.05481i	−0.991406	−	0.130821i	$-0.958239\pi$
$823$	−17.4709	−	30.2605i	−0.608998	−	1.05481i	0.382408	−	0.923993i	$-0.375095\pi$
$824$	−12.9350			−0.450613
$825$	−4.52337	−	3.95078i	−0.157484	−	0.137548i
$826$	5.88464	−	9.78025i	0.204753	−	0.340298i
$827$		−	39.2335i		−	1.36428i	−0.731220	−	0.682142i	$-0.761049\pi$
$827$		−	39.2335i		−	1.36428i	0.731220	−	0.682142i	$-0.238951\pi$
$828$	3.85576	+	4.98317i	0.133997	+	0.173177i
$829$	39.3335	+	22.7092i	1.36611	+	0.788723i	0.990428	−	0.138027i	$-0.0440761\pi$
$829$	39.3335	+	22.7092i	1.36611	+	0.788723i	0.375679	+	0.926750i	$0.377409\pi$
$830$		−	3.38797i		−	0.117598i
$831$	32.9373	−	37.7109i	1.14258	−	1.30818i
$832$	0.584701	+	0.337577i	0.0202709	+	0.0117034i
$833$	−29.2720	−	1.05774i	−1.01421	−	0.0366485i
$834$	−2.28486	−	0.449698i	−0.0791181	−	0.0155718i
$835$	8.90365	−	15.4216i	0.308123	−	0.533685i
$836$	2.36852	−	4.10240i	0.0819170	−	0.141884i
$837$	7.51223	+	0.446745i	0.259661	+	0.0154418i
$838$	11.5279	−	6.65561i	0.398223	−	0.229914i
$839$	−13.9179	−	24.1066i	−0.480500	−	0.832251i	0.519249	−	0.854623i	$-0.326212\pi$
$839$	−13.9179	−	24.1066i	−0.480500	−	0.832251i	−0.999750	+	0.0223717i	$0.992878\pi$
$840$	1.40322	+	4.36245i	0.0484157	+	0.150519i
$841$	0.721064	−	1.24892i	0.0248643	−	0.0430662i
$842$		−	18.6616i		−	0.643123i
$843$	10.6800	−	54.2638i	0.367839	−	1.86895i
$844$	−10.8559			−0.373674
$845$	−6.27208	−	10.8636i	−0.215766	−	0.373718i
$846$	−9.18665	−	11.8728i	−0.315844	−	0.408195i
$847$	−2.31956	−	1.39565i	−0.0797011	−	0.0479551i
$848$	6.77173	−	3.90966i	0.232542	−	0.134258i
$849$	9.84050	−	49.9983i	0.337725	−	1.71594i
$850$	−3.62383	+	2.09222i	−0.124296	+	0.0717625i
$851$	−16.6972	+	9.64014i	−0.572373	+	0.330460i
$852$	−5.03217	+	25.5679i	−0.172399	+	0.875940i
$853$	7.24010	−	4.18007i	0.247896	−	0.143123i	−0.370904	−	0.928671i	$-0.620952\pi$
$853$	7.24010	−	4.18007i	0.247896	−	0.143123i	0.618801	+	0.785548i	$0.287619\pi$
$854$	0.284580	−	15.7561i	0.00973811	−	0.539163i
$855$	−2.50807	−	3.24142i	−0.0857741	−	0.110854i
$856$	−5.26998	−	9.12788i	−0.180124	−	0.311984i
$857$	−30.4710			−1.04087			−0.520435	−	0.853901i	$-0.674230\pi$
$857$	−30.4710			−1.04087			−0.520435	+	0.853901i	$0.674230\pi$
$858$	−0.783037	+	3.97851i	−0.0267324	+	0.135824i
$859$		−	49.8661i		−	1.70141i	−0.525644	−	0.850705i	$-0.676176\pi$
$859$		−	49.8661i		−	1.70141i	0.525644	−	0.850705i	$-0.323824\pi$
$860$	1.38041	−	2.39094i	0.0470715	−	0.0815303i
$861$	9.25902	−	42.9365i	0.315546	−	1.46327i
$862$	19.6756	+	34.0791i	0.670154	+	1.16074i
$863$	−17.7519	+	10.2491i	−0.604282	+	0.348882i	−0.770724	−	0.637169i	$-0.780105\pi$
$863$	−17.7519	+	10.2491i	−0.604282	+	0.348882i	0.166442	+	0.986051i	$0.446772\pi$
$864$	5.18699	+	0.308465i	0.176465	+	0.0104942i
$865$	−3.22610	+	5.58778i	−0.109691	+	0.189990i
$866$	−6.96098	+	12.0568i	−0.236544	+	0.409706i
$867$	−0.865895	−	0.170422i	−0.0294073	−	0.00578785i
$868$	−1.85566	−	3.35249i	−0.0629852	−	0.113791i
$869$	39.9970	+	23.0923i	1.35681	+	0.783352i
$870$	−6.28652	+	7.19764i	−0.213133	+	0.244023i
$871$			2.56910i			0.0870507i
$872$	−8.56016	−	4.94221i	−0.289884	−	0.167364i
$873$	1.59184	+	2.05729i	0.0538756	+	0.0696287i
$874$			2.86923i			0.0970531i
$875$	2.26702	+	1.36404i	0.0766394	+	0.0461129i
$876$	3.83265	+	3.34749i	0.129493	+	0.113101i
$877$	−14.4898			−0.489285			−0.244642	−	0.969613i	$-0.578671\pi$
$877$	−14.4898			−0.489285			−0.244642	+	0.969613i	$0.578671\pi$
$878$	−13.3748	−	23.1659i	−0.451379	−	0.781811i
$879$	−7.30908	−	21.3900i	−0.246529	−	0.721468i
$880$	3.00290	+	1.73372i	0.101228	+	0.0584438i
$881$	−14.9789			−0.504653			−0.252327	−	0.967642i	$-0.581196\pi$
$881$	−14.9789			−0.504653			−0.252327	+	0.967642i	$0.581196\pi$
$882$	20.8976	−	2.07173i	0.703657	−	0.0697586i
$883$	58.2660			1.96081			0.980404	−	0.196998i	$-0.0631191\pi$
$883$	58.2660			1.96081			0.980404	+	0.196998i	$0.0631191\pi$
$884$	2.44665	+	1.41257i	0.0822896	+	0.0475099i
$885$	−7.33165	−	1.44299i	−0.246451	−	0.0485055i
$886$	9.24324	+	16.0098i	0.310533	+	0.537859i
$887$	10.2904			0.345518			0.172759	−	0.984964i	$-0.444732\pi$
$887$	10.2904			0.345518			0.172759	+	0.984964i	$0.444732\pi$
$888$	−3.07054	+	15.6010i	−0.103041	+	0.523537i
$889$	41.3720	+	24.8930i	1.38757	+	0.834883i
$890$		−	6.22855i		−	0.208781i
$891$	8.31989	+	30.0775i	0.278727	+	1.00763i
$892$	18.2083	+	10.5126i	0.609658	+	0.351986i
$893$		−	6.83617i		−	0.228764i
$894$	−9.37536	−	27.4370i	−0.313559	−	0.917631i
$895$	−19.4958	−	11.2559i	−0.651672	−	0.376243i
$896$	−1.28128	−	2.31480i	−0.0428046	−	0.0773322i
$897$	−0.794151	−	2.32408i	−0.0265159	−	0.0775988i
$898$	−10.1941	+	17.6567i	−0.340181	+	0.589211i
$899$	3.99541	−	6.92025i	0.133254	−	0.230803i
$900$	2.37267	−	1.83587i	0.0790891	−	0.0611957i
$901$	28.3359	−	16.3597i	0.944005	−	0.545021i
$902$	−16.6175	−	28.7824i	−0.553303	−	0.958349i
$903$	−9.37697	−	8.49333i	−0.312046	−	0.282640i
$904$	6.39765	−	11.0811i	0.212783	−	0.368551i
$905$		−	3.72966i		−	0.123978i
$906$	7.75567	−	2.65015i	0.257665	−	0.0880454i
$907$	−11.7857			−0.391339			−0.195670	−	0.980670i	$-0.562688\pi$
$907$	−11.7857			−0.391339			−0.195670	+	0.980670i	$0.562688\pi$
$908$	9.32471	+	16.1509i	0.309451	+	0.535985i
$909$	5.95190	+	43.8419i	0.197412	+	1.45414i
$910$	0.0322579	−	1.78600i	0.00106934	−	0.0592053i
$911$	−10.6516	+	6.14972i	−0.352904	+	0.203749i	−0.665964	−	0.745984i	$-0.731979\pi$
$911$	−10.6516	+	6.14972i	−0.352904	+	0.203749i	0.313059	+	0.949734i	$0.398646\pi$
$912$	1.78217	+	1.55658i	0.0590137	+	0.0515434i
$913$	−10.1737	+	5.87380i	−0.336701	+	0.194394i
$914$	6.52634	−	3.76798i	0.215872	−	0.124634i
$915$	−9.76227	+	3.33582i	−0.322731	+	0.110279i
$916$	18.4318	−	10.6416i	0.609004	−	0.351609i
$917$	27.4969	+	16.5445i	0.908028	+	0.546348i
$918$	21.7046	+	1.29075i	0.716359	+	0.0426012i
$919$	16.1298	+	27.9377i	0.532074	+	0.921579i	0.999299	+	0.0374404i	$0.0119204\pi$
$919$	16.1298	+	27.9377i	0.532074	+	0.921579i	−0.467225	+	0.884138i	$0.654746\pi$
$920$	−2.10023			−0.0692427
$921$	−15.6515	−	13.6703i	−0.515735	−	0.450450i
$922$		−	18.9299i		−	0.623422i
$923$	5.07878	−	8.79671i	0.167170	−	0.289547i
$924$	10.6672	−	11.7770i	0.350925	−	0.387435i
$925$	4.59003	+	7.95017i	0.150919	+	0.261400i
$926$	−4.31755	+	2.49274i	−0.141883	+	0.0819164i
$927$	38.4524	−	5.22023i	1.26294	−	0.171455i
$928$	2.75872	−	4.77824i	0.0905594	−	0.156853i
$929$	−10.7705	+	18.6551i	−0.353369	+	0.612053i	−0.986837	−	0.161715i	$-0.948297\pi$
$929$	−10.7705	+	18.6551i	−0.353369	+	0.612053i	0.633468	+	0.773769i	$0.281631\pi$
$930$	−1.65016	+	1.88932i	−0.0541109	+	0.0619533i
$931$	8.10376	+	5.07746i	0.265590	+	0.166407i
$932$	−7.31621	−	4.22401i	−0.239650	−	0.138362i
$933$	57.1597	+	11.2500i	1.87132	+	0.368307i
$934$		−	17.5348i		−	0.573757i
$935$	12.5654	+	7.25465i	0.410933	+	0.237253i
$936$	−1.87440	−	0.767557i	−0.0612666	−	0.0250884i
$937$			30.1471i			0.984864i	0.870351	+	0.492432i	$0.163892\pi$
$937$			30.1471i			0.984864i	−0.870351	+	0.492432i	$0.836108\pi$
$938$	5.19044	−	8.62650i	0.169474	−	0.281665i
$939$	14.3419	−	4.90072i	0.468032	−	0.159929i
$940$	5.00398			0.163212
$941$	6.63748	+	11.4965i	0.216376	+	0.374774i	0.953697	−	0.300768i	$-0.0972430\pi$
$941$	6.63748	+	11.4965i	0.216376	+	0.374774i	−0.737321	+	0.675542i	$0.763910\pi$
$942$	7.82175	−	8.95536i	0.254846	−	0.291782i
$943$	17.4335	+	10.0653i	0.567714	+	0.327770i
$944$	4.31413			0.140413
$945$	−5.93196	−	12.4021i	−0.192967	−	0.403440i
$946$	−9.57298			−0.311244
$947$	16.7669	+	9.68035i	0.544849	+	0.314569i	0.747042	−	0.664777i	$-0.231473\pi$
$947$	16.7669	+	9.68035i	0.544849	+	0.314569i	−0.202193	+	0.979346i	$0.564807\pi$
$948$	−15.1761	+	17.3756i	−0.492897	+	0.564334i
$949$	−0.991790	−	1.71783i	−0.0321949	−	0.0557631i
$950$	1.36615			0.0443237
$951$	8.73993	−	2.98648i	0.283411	−	0.0968432i
$952$	−5.36145	−	9.68615i	−0.173765	−	0.313930i
$953$		−	7.70584i		−	0.249617i	−0.992181	−	0.124808i	$-0.960168\pi$
$953$		−	7.70584i		−	0.249617i	0.992181	−	0.124808i	$-0.0398316\pi$
$954$	−18.5527	+	14.3553i	−0.600665	+	0.464768i
$955$	20.2669	+	11.7011i	0.655822	+	0.378639i
$956$		−	15.3302i		−	0.495815i
$957$	32.5128	+	6.39906i	1.05099	+	0.206852i
$958$	5.05885	+	2.92073i	0.163444	+	0.0943644i
$959$	−4.07154	+	6.76688i	−0.131477	+	0.218514i
$960$	−1.13939	+	1.30453i	−0.0367737	+	0.0421034i
$961$	−14.4512	+	25.0303i	−0.466169	+	0.807428i
$962$	3.09898	−	5.36759i	0.0999152	−	0.173058i
$963$	19.3500	+	25.0079i	0.623545	+	0.805868i
$964$	20.2304	−	11.6800i	0.651578	−	0.376189i
$965$	2.35052	+	4.07122i	0.0756660	+	0.131057i
$966$	−2.02883	+	9.40822i	−0.0652766	+	0.302704i
$967$	−5.91203	+	10.2399i	−0.190118	+	0.329294i	−0.945289	−	0.326233i	$-0.894220\pi$
$967$	−5.91203	+	10.2399i	−0.190118	+	0.329294i	0.755171	+	0.655528i	$0.227554\pi$
$968$		−	1.02317i		−	0.0328861i
$969$	7.45739	+	6.51340i	0.239566	+	0.209240i
$970$	−0.867076			−0.0278401
$971$	14.4654	+	25.0548i	0.464216	+	0.804046i	0.999166	−	0.0408377i	$-0.0130027\pi$
$971$	14.4654	+	25.0548i	0.464216	+	0.804046i	−0.534949	+	0.844884i	$0.679669\pi$
$972$	−15.5440	+	1.17635i	−0.498574	+	0.0377313i
$973$	−1.72265	−	3.11218i	−0.0552255	−	0.0997721i
$974$	1.98205	−	1.14434i	0.0635089	−	0.0366669i
$975$	−1.10658	+	0.378125i	−0.0354390	+	0.0121097i
$976$	5.15824	−	2.97811i	0.165111	−	0.0953269i
$977$	−6.29169	+	3.63251i	−0.201289	+	0.116214i	−0.597257	−	0.802050i	$-0.703743\pi$
$977$	−6.29169	+	3.63251i	−0.201289	+	0.116214i	0.395968	+	0.918264i	$0.370409\pi$
$978$	24.6509	+	21.5304i	0.788247	+	0.688467i
$979$	−18.7037	+	10.7986i	−0.597772	+	0.345124i
$980$	−3.71663	+	5.93183i	−0.118723	+	0.189485i
$981$	27.4416	+	11.2372i	0.876143	+	0.358777i
$982$	−11.0854	−	19.2005i	−0.353750	−	0.612713i
$983$	−17.7284			−0.565448			−0.282724	−	0.959201i	$-0.591238\pi$
$983$	−17.7284			−0.565448			−0.282724	+	0.959201i	$0.591238\pi$
$984$	15.7097	−	5.36807i	0.500806	−	0.171128i
$985$		−	16.2139i		−	0.516617i
$986$	11.5437	−	19.9943i	0.367626	−	0.636747i
$987$	4.83385	−	22.4158i	0.153863	−	0.713504i
$988$	−0.461180	−	0.798788i	−0.0146721	−	0.0254128i
$989$	5.02153	−	2.89918i	0.159675	−	0.0921886i
$990$	−9.62648	−	3.94200i	−0.305950	−	0.125285i
$991$	5.01544	−	8.68699i	0.159321	−	0.275951i	−0.775303	−	0.631589i	$-0.782403\pi$
$991$	5.01544	−	8.68699i	0.159321	−	0.275951i	0.934624	+	0.355638i	$0.115736\pi$
$992$	0.724142	−	1.25425i	0.0229915	−	0.0398225i
$993$	19.4137	+	56.8143i	0.616076	+	1.80295i
$994$	−34.8258	+	19.2766i	−1.10461	+	0.611418i
$995$	−6.39208	−	3.69047i	−0.202643	−	0.116996i
$996$	−1.89745	−	5.55290i	−0.0601231	−	0.175950i
$997$			3.42378i			0.108432i	0.998529	+	0.0542161i	$0.0172660\pi$
$997$			3.42378i			0.108432i	−0.998529	+	0.0542161i	$0.982734\pi$
$998$	2.49116	+	1.43827i	0.0788564	+	0.0455278i
$999$	2.83173	−	47.6169i	0.0895920	−	1.50653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.14	✓	32
3.2	odd	2		1890.2.t.c.1151.7		32
7.5	odd	6		630.2.bk.c.131.4	yes	32
9.2	odd	6		630.2.bk.c.101.12	yes	32
9.7	even	3		1890.2.bk.c.521.15		32
21.5	even	6		1890.2.bk.c.341.15		32
63.47	even	6	inner	630.2.t.c.551.14	yes	32
63.61	odd	6		1890.2.t.c.1601.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.14	✓	32	1.1	even	1	trivial
630.2.t.c.551.14	yes	32	63.47	even	6	inner
630.2.bk.c.101.12	yes	32	9.2	odd	6
630.2.bk.c.131.4	yes	32	7.5	odd	6
1890.2.t.c.1151.7		32	3.2	odd	2
1890.2.t.c.1601.7		32	63.61	odd	6
1890.2.bk.c.341.15		32	21.5	even	6
1890.2.bk.c.521.15		32	9.7	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.13939 - 1.30453i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.63900 - 0.560056i) q^{6} +(2.26702 + 1.36404i) q^{7} +1.00000i q^{8} +(-0.403573 - 2.97273i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.13939 - 1.30453i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.63900 - 0.560056i) q^{6} +(2.26702 + 1.36404i) q^{7} +1.00000i q^{8} +(-0.403573 - 2.97273i) q^{9} +(0.866025 + 0.500000i) q^{10} -3.46745i q^{11} +(1.69945 + 0.334479i) q^{12} +(-0.584701 - 0.337577i) q^{13} +(1.28128 + 2.31480i) q^{14} +(1.13939 - 1.30453i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09222 + 3.62383i) q^{17} +(1.13686 - 2.77625i) q^{18} +(1.18312 - 0.683073i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.36245 - 1.40322i) q^{21} +(1.73372 - 3.00290i) q^{22} +2.10023i q^{23} +(1.30453 + 1.13939i) q^{24} +1.00000 q^{25} +(-0.337577 - 0.584701i) q^{26} +(-4.33783 - 2.86063i) q^{27} +(-0.0477786 + 2.64532i) q^{28} +(-4.77824 + 2.75872i) q^{29} +(1.63900 - 0.560056i) q^{30} +(-1.25425 + 0.724142i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.52337 - 3.95078i) q^{33} +(-3.62383 + 2.09222i) q^{34} +(2.26702 + 1.36404i) q^{35} +(2.37267 - 1.83587i) q^{36} +(4.59003 + 7.95017i) q^{37} +1.36615 q^{38} +(-1.10658 + 0.378125i) q^{39} +1.00000i q^{40} +(4.79244 - 8.30075i) q^{41} +(4.47960 + 0.966002i) q^{42} +(-1.38041 - 2.39094i) q^{43} +(3.00290 - 1.73372i) q^{44} +(-0.403573 - 2.97273i) q^{45} +(-1.05012 + 1.81886i) q^{46} +(2.50199 - 4.33357i) q^{47} +(0.560056 + 1.63900i) q^{48} +(3.27880 + 6.18461i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.34352 + 6.85831i) q^{51} -0.675155i q^{52} +(-6.77173 - 3.90966i) q^{53} +(-2.32636 - 4.64630i) q^{54} -3.46745i q^{55} +(-1.36404 + 2.26702i) q^{56} +(0.456948 - 2.32170i) q^{57} -5.51744 q^{58} +(-2.15707 - 3.73615i) q^{59} +(1.69945 + 0.334479i) q^{60} +(-5.15824 - 2.97811i) q^{61} -1.44828 q^{62} +(3.14001 - 7.28974i) q^{63} -1.00000 q^{64} +(-0.584701 - 0.337577i) q^{65} +(-1.94196 - 5.68316i) q^{66} +(-1.90260 - 3.29540i) q^{67} -4.18444 q^{68} +(2.73981 + 2.39299i) q^{69} +(1.28128 + 2.31480i) q^{70} +15.0448i q^{71} +(2.97273 - 0.403573i) q^{72} +(2.54435 + 1.46898i) q^{73} +9.18006i q^{74} +(1.13939 - 1.30453i) q^{75} +(1.18312 + 0.683073i) q^{76} +(4.72972 - 7.86078i) q^{77} +(-1.14739 - 0.225825i) q^{78} +(-6.65974 + 11.5350i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-8.67426 + 2.39943i) q^{81} +(8.30075 - 4.79244i) q^{82} +(-1.69398 - 2.93407i) q^{83} +(3.39645 + 3.07638i) q^{84} +(-2.09222 + 3.62383i) q^{85} -2.76082i q^{86} +(-1.84547 + 9.37660i) q^{87} +3.46745 q^{88} +(-3.11428 - 5.39408i) q^{89} +(1.13686 - 2.77625i) q^{90} +(-0.865064 - 1.56285i) q^{91} +(-1.81886 + 1.05012i) q^{92} +(-0.484421 + 2.46128i) q^{93} +(4.33357 - 2.50199i) q^{94} +(1.18312 - 0.683073i) q^{95} +(-0.334479 + 1.69945i) q^{96} +(-0.750910 + 0.433538i) q^{97} +(-0.252779 + 6.99543i) q^{98} +(-10.3078 + 1.39937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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