LMFDB - Embedded newform 418.2.h.a.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.3
Root			$-2.02516i$ of defining polynomial
Character	$\chi$	$=$	418.65
Dual form			418.2.h.a.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.75384 - 1.01258i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.202207 + 0.350232i) q^{5} +(1.75384 - 1.01258i) q^{6} +1.38521i q^{7} +1.00000 q^{8} +(0.550630 + 0.953720i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.75384 - 1.01258i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.202207 + 0.350232i) q^{5} +(1.75384 - 1.01258i) q^{6} +1.38521i q^{7} +1.00000 q^{8} +(0.550630 + 0.953720i) q^{9} +(-0.202207 - 0.350232i) q^{10} +(-2.65274 - 1.99072i) q^{11} +2.02516i q^{12} +(1.16812 + 2.02324i) q^{13} +(-1.19963 - 0.692605i) q^{14} +(0.709276 - 0.409500i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.98091 + 2.87573i) q^{17} -1.10126 q^{18} +(1.88136 - 3.93198i) q^{19} +0.404414 q^{20} +(1.40263 - 2.42943i) q^{21} +(3.05038 - 1.30198i) q^{22} +(2.24362 + 3.88606i) q^{23} +(-1.75384 - 1.01258i) q^{24} +(2.41822 + 4.18849i) q^{25} -2.33624 q^{26} +3.84525i q^{27} +(1.19963 - 0.692605i) q^{28} +(3.87149 + 6.70562i) q^{29} +0.819001i q^{30} +6.93179i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.63672 + 6.17751i) q^{33} +(-4.98091 + 2.87573i) q^{34} +(-0.485145 - 0.280099i) q^{35} +(0.550630 - 0.953720i) q^{36} -10.8902i q^{37} +(2.46452 + 3.59530i) q^{38} -4.73124i q^{39} +(-0.202207 + 0.350232i) q^{40} +(-2.30769 + 3.99704i) q^{41} +(1.40263 + 2.42943i) q^{42} +(9.81686 + 5.66777i) q^{43} +(-0.397643 + 3.29270i) q^{44} -0.445365 q^{45} -4.48723 q^{46} +(-5.27332 - 9.13366i) q^{47} +(1.75384 - 1.01258i) q^{48} +5.08119 q^{49} -4.83645 q^{50} +(-5.82380 - 10.0871i) q^{51} +(1.16812 - 2.02324i) q^{52} +(-3.60309 + 2.08025i) q^{53} +(-3.33008 - 1.92262i) q^{54} +(1.23362 - 0.526539i) q^{55} +1.38521i q^{56} +(-7.28104 + 4.99104i) q^{57} -7.74298 q^{58} +(-1.94176 - 1.12108i) q^{59} +(-0.709276 - 0.409500i) q^{60} +(-2.11052 + 1.21851i) q^{61} +(-6.00310 - 3.46589i) q^{62} +(-1.32110 + 0.762739i) q^{63} +1.00000 q^{64} -0.944805 q^{65} +(-6.66824 - 0.805290i) q^{66} +(7.42746 - 4.28824i) q^{67} -5.75146i q^{68} -9.08735i q^{69} +(0.485145 - 0.280099i) q^{70} +(-5.32989 - 3.07721i) q^{71} +(0.550630 + 0.953720i) q^{72} +(7.74970 + 4.47429i) q^{73} +(9.43122 + 5.44512i) q^{74} -9.79457i q^{75} +(-4.34588 + 0.336688i) q^{76} +(2.75756 - 3.67460i) q^{77} +(4.09738 + 2.36562i) q^{78} +(-4.32343 + 7.48840i) q^{79} +(-0.202207 - 0.350232i) q^{80} +(5.54550 - 9.60509i) q^{81} +(-2.30769 - 3.99704i) q^{82} -0.841550i q^{83} -2.80527 q^{84} +(-2.01435 + 1.16298i) q^{85} +(-9.81686 + 5.66777i) q^{86} -15.6807i q^{87} +(-2.65274 - 1.99072i) q^{88} +(-12.4450 + 7.18512i) q^{89} +(0.222682 - 0.385697i) q^{90} +(-2.80261 + 1.61809i) q^{91} +(2.24362 - 3.88606i) q^{92} +(7.01898 - 12.1572i) q^{93} +10.5466 q^{94} +(0.996684 + 1.45399i) q^{95} +2.02516i q^{96} +(13.2024 + 7.62242i) q^{97} +(-2.54060 + 4.40044i) q^{98} +(0.437909 - 3.62612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} - 3 q^{6} + 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q - 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 - 3 * q^6 + 20 * q^8 + 11 * q^9	$ 20 q - 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} - 3 q^{6} + 20 q^{8} + 11 q^{9} + 2 q^{10} + q^{11} - 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} - 6 q^{17} - 22 q^{18} + 18 q^{19} - 4 q^{20} + 14 q^{21} + q^{22} - 4 q^{23} + 3 q^{24} - 20 q^{25} + 10 q^{26} + 6 q^{28} - 5 q^{29} - 10 q^{32} - 8 q^{33} + 6 q^{34} + 12 q^{35} + 11 q^{36} - 12 q^{38} + 2 q^{40} + q^{41} + 14 q^{42} - 3 q^{43} - 2 q^{44} + 12 q^{45} + 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} + 40 q^{50} + 12 q^{51} - 5 q^{52} - 24 q^{53} - 27 q^{54} - 20 q^{55} - 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} - 27 q^{61} - 12 q^{63} + 20 q^{64} + 8 q^{65} + 13 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} + 11 q^{72} + 9 q^{73} + 12 q^{74} - 6 q^{76} - 22 q^{77} + 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} - 28 q^{84} + 12 q^{85} + 3 q^{86} + q^{88} + 21 q^{89} - 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} - 2 q^{94} + 24 q^{95} + 24 q^{97} - 4 q^{98} + 21 q^{99}+O(q^{100}) $ 20 * q - 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 - 3 * q^6 + 20 * q^8 + 11 * q^9 + 2 * q^10 + q^11 - 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 - 6 * q^17 - 22 * q^18 + 18 * q^19 - 4 * q^20 + 14 * q^21 + q^22 - 4 * q^23 + 3 * q^24 - 20 * q^25 + 10 * q^26 + 6 * q^28 - 5 * q^29 - 10 * q^32 - 8 * q^33 + 6 * q^34 + 12 * q^35 + 11 * q^36 - 12 * q^38 + 2 * q^40 + q^41 + 14 * q^42 - 3 * q^43 - 2 * q^44 + 12 * q^45 + 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 + 40 * q^50 + 12 * q^51 - 5 * q^52 - 24 * q^53 - 27 * q^54 - 20 * q^55 - 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 - 27 * q^61 - 12 * q^63 + 20 * q^64 + 8 * q^65 + 13 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 + 11 * q^72 + 9 * q^73 + 12 * q^74 - 6 * q^76 - 22 * q^77 + 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 - 28 * q^84 + 12 * q^85 + 3 * q^86 + q^88 + 21 * q^89 - 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 - 2 * q^94 + 24 * q^95 + 24 * q^97 - 4 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.75384	−	1.01258i	−1.01258	−	0.584612i	−0.100633	−	0.994924i	$-0.532087\pi$
$3$	−1.75384	−	1.01258i	−1.01258	−	0.584612i	−0.911946	+	0.410311i	$0.865420\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.202207	+	0.350232i	−0.0904296	+	0.156629i	−0.907692	−	0.419637i	$-0.862157\pi$
$5$	−0.202207	+	0.350232i	−0.0904296	+	0.156629i	0.817262	+	0.576266i	$0.195491\pi$
$6$	1.75384	−	1.01258i	0.716001	−	0.413383i
$7$			1.38521i			0.523560i	0.965128	+	0.261780i	$0.0843095\pi$
$7$			1.38521i			0.523560i	−0.965128	+	0.261780i	$0.915690\pi$
$8$	1.00000			0.353553
$9$	0.550630	+	0.953720i	0.183543	+	0.317907i
$10$	−0.202207	−	0.350232i	−0.0639434	−	0.110753i
$11$	−2.65274	−	1.99072i	−0.799832	−	0.600225i
$11$	−2.65274	−	1.99072i	−0.799832	−	0.600225i
$12$			2.02516i			0.584612i
$13$	1.16812	+	2.02324i	0.323978	+	0.561146i	0.981305	−	0.192460i	$-0.0616464\pi$
$13$	1.16812	+	2.02324i	0.323978	+	0.561146i	−0.657327	+	0.753605i	$0.728313\pi$
$14$	−1.19963	−	0.692605i	−0.320614	−	0.185106i
$15$	0.709276	−	0.409500i	0.183134	−	0.105733i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.98091	+	2.87573i	1.20805	+	0.697467i	0.962333	−	0.271875i	$-0.0876438\pi$
$17$	4.98091	+	2.87573i	1.20805	+	0.697467i	0.245715	+	0.969342i	$0.420977\pi$
$18$	−1.10126			−0.259570
$19$	1.88136	−	3.93198i	0.431613	−	0.902059i
$19$	1.88136	−	3.93198i	0.431613	−	0.902059i
$20$	0.404414			0.0904296
$21$	1.40263	−	2.42943i	0.306080	−	0.530146i
$22$	3.05038	−	1.30198i	0.650344	−	0.277583i
$23$	2.24362	+	3.88606i	0.467826	+	0.810299i	0.999324	−	0.0367609i	$-0.0117040\pi$
$23$	2.24362	+	3.88606i	0.467826	+	0.810299i	−0.531498	+	0.847060i	$0.678371\pi$
$24$	−1.75384	−	1.01258i	−0.358001	−	0.206692i
$25$	2.41822	+	4.18849i	0.483645	+	0.837698i
$26$	−2.33624			−0.458173
$27$			3.84525i			0.740018i
$28$	1.19963	−	0.692605i	0.226708	−	0.130890i
$29$	3.87149	+	6.70562i	0.718917	+	1.24520i	0.961429	+	0.275053i	$0.0886954\pi$
$29$	3.87149	+	6.70562i	0.718917	+	1.24520i	−0.242512	+	0.970149i	$0.577971\pi$
$30$			0.819001i			0.149528i
$31$			6.93179i			1.24499i	0.782625	+	0.622493i	$0.213880\pi$
$31$			6.93179i			1.24499i	−0.782625	+	0.622493i	$0.786120\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.63672	+	6.17751i	0.458993	+	1.07537i
$34$	−4.98091	+	2.87573i	−0.854219	+	0.493183i
$35$	−0.485145	−	0.280099i	−0.0820045	−	0.0473453i
$36$	0.550630	−	0.953720i	0.0917717	−	0.158953i
$37$		−	10.8902i		−	1.79034i	−0.445722	−	0.895171i	$-0.647053\pi$
$37$		−	10.8902i		−	1.79034i	0.445722	−	0.895171i	$-0.352947\pi$
$38$	2.46452	+	3.59530i	0.399798	+	0.583234i
$39$		−	4.73124i		−	0.757605i
$40$	−0.202207	+	0.350232i	−0.0319717	+	0.0553766i
$41$	−2.30769	+	3.99704i	−0.360401	+	0.624233i	−0.988027	−	0.154282i	$-0.950693\pi$
$41$	−2.30769	+	3.99704i	−0.360401	+	0.624233i	0.627626	+	0.778515i	$0.284027\pi$
$42$	1.40263	+	2.42943i	0.216431	+	0.374870i
$43$	9.81686	+	5.66777i	1.49706	+	0.864327i	0.999994	−	0.00338756i	$-0.00107830\pi$
$43$	9.81686	+	5.66777i	1.49706	+	0.864327i	0.497063	+	0.867714i	$0.334412\pi$
$44$	−0.397643	+	3.29270i	−0.0599470	+	0.496393i
$45$	−0.445365			−0.0663910
$46$	−4.48723			−0.661606
$47$	−5.27332	−	9.13366i	−0.769193	−	1.33228i	−0.938001	−	0.346633i	$-0.887325\pi$
$47$	−5.27332	−	9.13366i	−0.769193	−	1.33228i	0.168808	−	0.985649i	$-0.446008\pi$
$48$	1.75384	−	1.01258i	0.253145	−	0.146153i
$49$	5.08119			0.725885
$50$	−4.83645			−0.683977
$51$	−5.82380	−	10.0871i	−0.815496	−	1.41248i
$52$	1.16812	−	2.02324i	0.161989	−	0.280573i
$53$	−3.60309	+	2.08025i	−0.494923	+	0.285744i	−0.726614	−	0.687045i	$-0.758907\pi$
$53$	−3.60309	+	2.08025i	−0.494923	+	0.285744i	0.231692	+	0.972789i	$0.425574\pi$
$54$	−3.33008	−	1.92262i	−0.453167	−	0.261636i
$55$	1.23362	−	0.526539i	0.166341	−	0.0709985i
$56$			1.38521i			0.185106i
$57$	−7.28104	+	4.99104i	−0.964397	+	0.661079i
$58$	−7.74298			−1.01670
$59$	−1.94176	−	1.12108i	−0.252796	−	0.145952i	0.368248	−	0.929728i	$-0.379958\pi$
$59$	−1.94176	−	1.12108i	−0.252796	−	0.145952i	−0.621044	+	0.783776i	$0.713291\pi$
$60$	−0.709276	−	0.409500i	−0.0915671	−	0.0528663i
$61$	−2.11052	+	1.21851i	−0.270224	+	0.156014i	−0.628990	−	0.777414i	$-0.716531\pi$
$61$	−2.11052	+	1.21851i	−0.270224	+	0.156014i	0.358765	+	0.933428i	$0.383198\pi$
$62$	−6.00310	−	3.46589i	−0.762395	−	0.440169i
$63$	−1.32110	+	0.762739i	−0.166443	+	0.0960960i
$64$	1.00000			0.125000
$65$	−0.944805			−0.117189
$66$	−6.66824	−	0.805290i	−0.820803	−	0.0991243i
$67$	7.42746	−	4.28824i	0.907408	−	0.523892i	0.0278119	−	0.999613i	$-0.491146\pi$
$67$	7.42746	−	4.28824i	0.907408	−	0.523892i	0.879596	+	0.475721i	$0.157813\pi$
$68$		−	5.75146i		−	0.697467i
$69$		−	9.08735i		−	1.09399i
$70$	0.485145	−	0.280099i	0.0579860	−	0.0334782i
$71$	−5.32989	−	3.07721i	−0.632541	−	0.365198i	0.149195	−	0.988808i	$-0.452332\pi$
$71$	−5.32989	−	3.07721i	−0.632541	−	0.365198i	−0.781735	+	0.623610i	$0.785665\pi$
$72$	0.550630	+	0.953720i	0.0648924	+	0.112397i
$73$	7.74970	+	4.47429i	0.907034	+	0.523677i	0.879476	−	0.475944i	$-0.157893\pi$
$73$	7.74970	+	4.47429i	0.907034	+	0.523677i	0.0275586	+	0.999620i	$0.491227\pi$
$74$	9.43122	+	5.44512i	1.09636	+	0.632982i
$75$		−	9.79457i		−	1.13098i
$76$	−4.34588	+	0.336688i	−0.498506	+	0.0386207i
$77$	2.75756	−	3.67460i	0.314254	−	0.418760i
$78$	4.09738	+	2.36562i	0.463937	+	0.267854i
$79$	−4.32343	+	7.48840i	−0.486424	+	0.842511i	−0.999878	−	0.0156059i	$-0.995032\pi$
$79$	−4.32343	+	7.48840i	−0.486424	+	0.842511i	0.513454	+	0.858117i	$0.328366\pi$
$80$	−0.202207	−	0.350232i	−0.0226074	−	0.0391572i
$81$	5.54550	−	9.60509i	0.616167	−	1.06723i
$82$	−2.30769	−	3.99704i	−0.254842	−	0.441399i
$83$		−	0.841550i		−	0.0923721i	−0.998933	−	0.0461861i	$-0.985293\pi$
$83$		−	0.841550i		−	0.0923721i	0.998933	−	0.0461861i	$-0.0147067\pi$
$84$	−2.80527			−0.306080
$85$	−2.01435	+	1.16298i	−0.218487	+	0.126143i
$86$	−9.81686	+	5.66777i	−1.05858	+	0.611171i
$87$		−	15.6807i		−	1.68115i
$88$	−2.65274	−	1.99072i	−0.282783	−	0.212211i
$89$	−12.4450	+	7.18512i	−1.31917	+	0.761621i	−0.983595	−	0.180393i	$-0.942263\pi$
$89$	−12.4450	+	7.18512i	−1.31917	+	0.761621i	−0.335572	+	0.942014i	$0.608930\pi$
$90$	0.222682	−	0.385697i	0.0234728	−	0.0406560i
$91$	−2.80261	+	1.61809i	−0.293793	+	0.169622i
$92$	2.24362	−	3.88606i	0.233913	−	0.405149i
$93$	7.01898	−	12.1572i	0.727834	−	1.26065i
$94$	10.5466			1.08780
$95$	0.996684	+	1.45399i	0.102258	+	0.149176i
$96$			2.02516i			0.206692i
$97$	13.2024	+	7.62242i	1.34050	+	0.773940i	0.986881	−	0.161448i	$-0.0516165\pi$
$97$	13.2024	+	7.62242i	1.34050	+	0.773940i	0.353622	+	0.935388i	$0.384950\pi$
$98$	−2.54060	+	4.40044i	−0.256639	+	0.444512i
$99$	0.437909	−	3.62612i	0.0440115	−	0.364439i
$100$	2.41822	−	4.18849i	0.241822	−	0.418849i
$101$	2.56841	−	1.48287i	0.255567	−	0.147551i	−0.366744	−	0.930322i	$-0.619527\pi$
$101$	2.56841	−	1.48287i	0.255567	−	0.147551i	0.622310	+	0.782771i	$0.286194\pi$
$102$	11.6476			1.15328
$103$		−	14.5804i		−	1.43665i	−0.695706	−	0.718327i	$-0.744908\pi$
$103$		−	14.5804i		−	1.43665i	0.695706	−	0.718327i	$-0.255092\pi$
$104$	1.16812	+	2.02324i	0.114543	+	0.198395i
$105$	0.567244	+	0.982496i	0.0553574	+	0.0958818i
$106$		−	4.16049i		−	0.404103i
$107$	−18.7197			−1.80971			−0.904853	−	0.425724i	$-0.860020\pi$
$107$	−18.7197			−1.80971			−0.904853	+	0.425724i	$0.860020\pi$
$108$	3.33008	−	1.92262i	0.320437	−	0.185004i
$109$	0.0596970	−	0.103398i	0.00571793	−	0.00990375i	−0.863152	−	0.504944i	$-0.831513\pi$
$109$	0.0596970	−	0.103398i	0.00571793	−	0.00990375i	0.868870	+	0.495040i	$0.164847\pi$
$110$	−0.160812	+	1.33161i	−0.0153329	+	0.126964i
$111$	−11.0272	+	19.0997i	−1.04666	+	1.81286i
$112$	−1.19963	−	0.692605i	−0.113354	−	0.0654450i
$113$			1.58084i			0.148713i	0.997232	+	0.0743564i	$0.0236902\pi$
$113$			1.58084i			0.148713i	−0.997232	+	0.0743564i	$0.976310\pi$
$114$	−0.681845	−	8.80108i	−0.0638606	−	0.824297i
$115$	−1.81470			−0.169221
$116$	3.87149	−	6.70562i	0.359459	−	0.622601i
$117$	−1.28640	+	2.22811i	−0.118928	+	0.205989i
$118$	1.94176	−	1.12108i	0.178754	−	0.103204i
$119$	−3.98349	+	6.89961i	−0.365166	+	0.632486i
$120$	0.709276	−	0.409500i	0.0647477	−	0.0373821i
$121$	3.07407	+	10.5617i	0.279461	+	0.960157i
$122$		−	2.43702i		−	0.220637i
$123$	8.09463	−	4.67344i	0.729869	−	0.421390i
$124$	6.00310	−	3.46589i	0.539095	−	0.311246i
$125$	−3.97799			−0.355803
$126$		−	1.52548i		−	0.135900i
$127$	−5.88156	−	10.1872i	−0.521904	−	0.903964i	−0.999675	−	0.0254801i	$-0.991889\pi$
$127$	−5.88156	−	10.1872i	−0.521904	−	0.903964i	0.477771	−	0.878484i	$-0.341445\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−11.4781	−	19.8807i	−1.01059	−	1.75040i
$130$	0.472403	−	0.818225i	0.0414324	−	0.0717631i
$131$	14.1092	+	8.14594i	1.23273	+	0.711714i	0.967597	−	0.252499i	$-0.0812525\pi$
$131$	14.1092	+	8.14594i	1.23273	+	0.711714i	0.265128	+	0.964213i	$0.414586\pi$
$132$	4.03152	−	5.37222i	0.350899	−	0.467591i
$133$	5.44662	+	2.60608i	0.472282	+	0.225975i
$134$			8.57649i			0.740896i
$135$	−1.34673	−	0.777535i	−0.115908	−	0.0669195i
$136$	4.98091	+	2.87573i	0.427109	+	0.246592i
$137$	3.55011	+	6.14896i	0.303306	+	0.525341i	0.976883	−	0.213776i	$-0.0685762\pi$
$137$	3.55011	+	6.14896i	0.303306	+	0.525341i	−0.673577	+	0.739117i	$0.735243\pi$
$138$	7.86987	+	4.54367i	0.669928	+	0.386783i
$139$	13.1761	−	7.60723i	1.11758	−	0.645237i	0.176800	−	0.984247i	$-0.443425\pi$
$139$	13.1761	−	7.60723i	1.11758	−	0.645237i	0.940783	+	0.339010i	$0.110092\pi$
$140$			0.560198i			0.0473453i
$141$			21.3586i			1.79872i
$142$	5.32989	−	3.07721i	0.447274	−	0.258234i
$143$	0.928988	−	7.69252i	0.0776859	−	0.643281i
$144$	−1.10126			−0.0917717
$145$	−3.13137			−0.260046
$146$	−7.74970	+	4.47429i	−0.641370	+	0.370295i
$147$	−8.91159	−	5.14511i	−0.735015	−	0.424361i
$148$	−9.43122	+	5.44512i	−0.775241	+	0.447586i
$149$	3.06944	+	1.77214i	0.251458	+	0.145179i	0.620432	−	0.784260i	$-0.286957\pi$
$149$	3.06944	+	1.77214i	0.251458	+	0.145179i	−0.368974	+	0.929440i	$0.620291\pi$
$150$	8.48235	+	4.89728i	0.692581	+	0.399862i
$151$	−14.3389			−1.16689			−0.583443	−	0.812154i	$-0.698295\pi$
$151$	−14.3389			−1.16689			−0.583443	+	0.812154i	$0.698295\pi$
$152$	1.88136	−	3.93198i	0.152598	−	0.318926i
$153$			6.33385i			0.512062i
$154$	1.80352	+	4.22542i	0.145332	+	0.340494i
$155$	−2.42774	−	1.40165i	−0.195001	−	0.112584i
$156$	−4.09738	+	2.36562i	−0.328053	+	0.189401i
$157$	0.290152	−	0.502558i	0.0231566	−	0.0401085i	−0.854215	−	0.519920i	$-0.825962\pi$
$157$	0.290152	−	0.502558i	0.0231566	−	0.0401085i	0.877371	+	0.479812i	$0.159295\pi$
$158$	−4.32343	−	7.48840i	−0.343954	−	0.595745i
$159$	8.42565			0.668198
$160$	0.404414			0.0319717
$161$	−5.38300	+	3.10788i	−0.424240	+	0.244935i
$162$	5.54550	+	9.60509i	0.435696	+	0.754647i
$163$	−17.1636			−1.34435			−0.672177	−	0.740391i	$-0.734640\pi$
$163$	−17.1636			−1.34435			−0.672177	+	0.740391i	$0.734640\pi$
$164$	4.61539			0.360401
$165$	−2.69672	−	0.325670i	−0.209940	−	0.0253534i
$166$	0.728804	+	0.420775i	0.0565662	+	0.0326585i
$167$	2.67147	+	4.62713i	0.206725	+	0.358058i	0.950681	−	0.310171i	$-0.100386\pi$
$167$	2.67147	+	4.62713i	0.206725	+	0.358058i	−0.743956	+	0.668229i	$0.767053\pi$
$168$	1.40263	−	2.42943i	0.108216	−	0.187435i
$169$	3.77100	−	6.53157i	0.290077	−	0.502428i
$170$		−	2.32597i		−	0.178394i
$171$	4.78594	−	0.370781i	0.365990	−	0.0283543i
$172$		−	11.3355i		−	0.864327i
$173$	−0.229562	+	0.397614i	−0.0174533	+	0.0302300i	−0.874620	−	0.484809i	$-0.838889\pi$
$173$	−0.229562	+	0.397614i	−0.0174533	+	0.0302300i	0.857167	+	0.515039i	$0.172223\pi$
$174$	13.5799	+	7.84037i	1.02949	+	0.594377i
$175$	−5.80194	+	3.34975i	−0.438585	+	0.253217i
$176$	3.05038	−	1.30198i	0.229931	−	0.0981405i
$177$	2.27036	+	3.93238i	0.170651	+	0.295576i
$178$		−	14.3702i		−	1.07710i
$179$			18.4706i			1.38056i	0.723542	+	0.690280i	$0.242513\pi$
$179$			18.4706i			1.38056i	−0.723542	+	0.690280i	$0.757487\pi$
$180$	0.222682	+	0.385697i	0.0165978	+	0.0287482i
$181$	1.37763	−	0.795374i	0.102398	−	0.0591197i	−0.447926	−	0.894070i	$-0.647837\pi$
$181$	1.37763	−	0.795374i	0.102398	−	0.0591197i	0.550325	+	0.834951i	$0.314504\pi$
$182$		−	3.23618i		−	0.239881i
$183$	4.93535			0.364831
$184$	2.24362	+	3.88606i	0.165402	+	0.286484i
$185$	3.81411	+	2.20208i	0.280419	+	0.161900i
$186$	7.01898	+	12.1572i	0.514657	+	0.891411i
$187$	−7.48829	−	17.5442i	−0.547598	−	1.28296i
$188$	−5.27332	+	9.13366i	−0.384597	+	0.666141i
$189$	−5.32647			−0.387444
$190$	−1.75753	+	0.136161i	−0.127505	+	0.00987816i
$191$	−3.57810			−0.258902			−0.129451	−	0.991586i	$-0.541322\pi$
$191$	−3.57810			−0.258902			−0.129451	+	0.991586i	$0.541322\pi$
$192$	−1.75384	−	1.01258i	−0.126572	−	0.0730766i
$193$	−7.51799	+	13.0215i	−0.541157	+	0.937311i	0.457681	+	0.889116i	$0.348680\pi$
$193$	−7.51799	+	13.0215i	−0.541157	+	0.937311i	−0.998838	+	0.0481949i	$0.984653\pi$
$194$	−13.2024	+	7.62242i	−0.947879	+	0.547258i
$195$	1.65703	+	0.956689i	0.118663	+	0.0685099i
$196$	−2.54060	−	4.40044i	−0.181471	−	0.314317i
$197$		−	7.32487i		−	0.521875i	−0.965356	−	0.260938i	$-0.915968\pi$
$197$		−	7.32487i		−	0.521875i	0.965356	−	0.260938i	$-0.0840317\pi$
$198$	2.92136	+	2.19230i	0.207612	+	0.155800i
$199$	4.94502	+	8.56503i	0.350543	+	0.607159i	0.986345	−	0.164694i	$-0.0526636\pi$
$199$	4.94502	+	8.56503i	0.350543	+	0.607159i	−0.635801	+	0.771853i	$0.719330\pi$
$200$	2.41822	+	4.18849i	0.170994	+	0.296171i
$201$	−17.3687			−1.22510
$202$			2.96575i			0.208669i
$203$	−9.28869	+	5.36283i	−0.651938	+	0.376397i
$204$	−5.82380	+	10.0871i	−0.407748	+	0.706240i
$205$	−0.933262	−	1.61646i	−0.0651819	−	0.112898i
$206$	12.6270	+	7.29022i	0.879767	+	0.507934i
$207$	−2.47081	+	4.27956i	−0.171733	+	0.297450i
$208$	−2.33624			−0.161989
$209$	−12.8182	+	6.68528i	−0.886656	+	0.462430i
$210$	−1.13449			−0.0782871
$211$	1.12895	−	1.95540i	0.0777201	−	0.134615i	−0.824546	−	0.565795i	$-0.808569\pi$
$211$	1.12895	−	1.95540i	0.0777201	−	0.134615i	0.902266	+	0.431180i	$0.141903\pi$
$212$	3.60309	+	2.08025i	0.247461	+	0.142872i
$213$	6.23183	+	10.7939i	0.426998	+	0.739583i
$214$	9.35987	−	16.2118i	0.639828	−	1.10821i
$215$	−3.97007	+	2.29212i	−0.270757	+	0.156321i
$216$			3.84525i			0.261636i
$217$	−9.60198			−0.651825
$218$	0.0596970	+	0.103398i	0.00404319	+	0.00700301i
$219$	−9.06115	−	15.6944i	−0.612296	−	1.06053i
$220$	−1.07280	−	0.805074i	−0.0723285	−	0.0542781i
$221$			13.4368i			0.903854i
$222$	−11.0272	−	19.0997i	−0.740098	−	1.28189i
$223$	22.6010	+	13.0487i	1.51347	+	0.873804i	0.999876	+	0.0157724i	$0.00502071\pi$
$223$	22.6010	+	13.0487i	1.51347	+	0.873804i	0.513597	+	0.858031i	$0.328313\pi$
$224$	1.19963	−	0.692605i	0.0801535	−	0.0462766i
$225$	−2.66310	+	4.61262i	−0.177540	+	0.307508i
$226$	−1.36905	−	0.790419i	−0.0910676	−	0.0525779i
$227$	20.9381			1.38971			0.694854	−	0.719151i	$-0.255469\pi$
$227$	20.9381			1.38971			0.694854	+	0.719151i	$0.255469\pi$
$228$	7.96288	+	3.81005i	0.527355	+	0.252326i
$229$	−16.1268			−1.06569			−0.532845	−	0.846213i	$-0.678877\pi$
$229$	−16.1268			−1.06569			−0.532845	+	0.846213i	$0.678877\pi$
$230$	0.907348	−	1.57157i	0.0598288	−	0.103626i
$231$	−8.55714	+	3.65241i	−0.563019	+	0.240311i
$232$	3.87149	+	6.70562i	0.254176	+	0.440245i
$233$	9.78906	+	5.65172i	0.641303	+	0.370256i	0.785116	−	0.619349i	$-0.212603\pi$
$233$	9.78906	+	5.65172i	0.641303	+	0.370256i	−0.143814	+	0.989605i	$0.545937\pi$
$234$	−1.28640	−	2.22811i	−0.0840947	−	0.145656i
$235$	4.26521			0.278231
$236$			2.24216i			0.145952i
$237$	15.1652	−	8.75563i	0.985085	−	0.568739i
$238$	−3.98349	−	6.89961i	−0.258211	−	0.447235i
$239$		−	0.982105i		−	0.0635271i	−0.999495	−	0.0317636i	$-0.989888\pi$
$239$		−	0.982105i		−	0.0635271i	0.999495	−	0.0317636i	$-0.0101124\pi$
$240$			0.819001i			0.0528663i
$241$	1.96202	+	3.39831i	0.126385	+	0.218905i	0.922273	−	0.386538i	$-0.126329\pi$
$241$	1.96202	+	3.39831i	0.126385	+	0.218905i	−0.795889	+	0.605443i	$0.792996\pi$
$242$	−10.6838	−	2.61864i	−0.686778	−	0.168333i
$243$	−9.46158	+	5.46265i	−0.606961	+	0.350429i
$244$	2.11052	+	1.21851i	0.135112	+	0.0780071i
$245$	−1.02745	+	1.77960i	−0.0656415	+	0.113694i
$246$			9.34688i			0.595935i
$247$	10.1530	−	0.786581i	0.646019	−	0.0500490i
$248$			6.93179i			0.440169i
$249$	−0.852136	+	1.47594i	−0.0540019	+	0.0935340i
$250$	1.98900	−	3.44504i	0.125795	−	0.217884i
$251$	3.97448	+	6.88401i	0.250867	+	0.434515i	0.963765	−	0.266753i	$-0.0859509\pi$
$251$	3.97448	+	6.88401i	0.250867	+	0.434515i	−0.712898	+	0.701268i	$0.752618\pi$
$252$	1.32110	+	0.762739i	0.0832216	+	0.0480480i
$253$	1.78432	−	14.7751i	0.112179	−	0.928903i
$254$	11.7631			0.738084
$255$	4.71045			0.294980
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.1422	−	6.43298i	0.695034	−	0.401278i	−0.110461	−	0.993880i	$-0.535233\pi$
$257$	11.1422	−	6.43298i	0.695034	−	0.401278i	0.805495	+	0.592602i	$0.201899\pi$
$258$	22.9562			1.42919
$259$	15.0853			0.937352
$260$	0.472403	+	0.818225i	0.0292972	+	0.0507442i
$261$	−4.26352	+	7.38463i	−0.263905	+	0.457097i
$262$	−14.1092	+	8.14594i	−0.871668	+	0.503258i
$263$	7.15130	+	4.12881i	0.440968	+	0.254593i	0.704008	−	0.710192i	$-0.251392\pi$
$263$	7.15130	+	4.12881i	0.440968	+	0.254593i	−0.263040	+	0.964785i	$0.584725\pi$
$264$	2.63672	+	6.17751i	0.162279	+	0.380199i
$265$		−	1.68256i		−	0.103359i
$266$	−4.98024	+	3.41388i	−0.305358	+	0.209318i
$267$	29.1020			1.78101
$268$	−7.42746	−	4.28824i	−0.453704	−	0.261946i
$269$	−22.4442	−	12.9582i	−1.36845	−	0.790074i	−0.377719	−	0.925920i	$-0.623291\pi$
$269$	−22.4442	−	12.9582i	−1.36845	−	0.790074i	−0.990730	+	0.135846i	$0.956625\pi$
$270$	1.34673	−	0.777535i	0.0819593	−	0.0473193i
$271$	8.63431	+	4.98502i	0.524497	+	0.302819i	0.738773	−	0.673955i	$-0.235406\pi$
$271$	8.63431	+	4.98502i	0.524497	+	0.302819i	−0.214276	+	0.976773i	$0.568739\pi$
$272$	−4.98091	+	2.87573i	−0.302012	+	0.174367i
$273$	6.55376			0.396652
$274$	−7.10021			−0.428939
$275$	1.92318	−	15.9250i	0.115972	−	0.960313i
$276$	−7.86987	+	4.54367i	−0.473711	+	0.273497i
$277$		−	21.8927i		−	1.31541i	−0.753277	−	0.657703i	$-0.771528\pi$
$277$		−	21.8927i		−	1.31541i	0.753277	−	0.657703i	$-0.228472\pi$
$278$			15.2145i			0.912503i
$279$	−6.61098	+	3.81685i	−0.395789	+	0.228509i
$280$	−0.485145	−	0.280099i	−0.0289930	−	0.0167391i
$281$	−11.7908	−	20.4223i	−0.703380	−	1.21829i	−0.967273	−	0.253738i	$-0.918340\pi$
$281$	−11.7908	−	20.4223i	−0.703380	−	1.21829i	0.263893	−	0.964552i	$-0.414994\pi$
$282$	−18.4971	−	10.6793i	−1.10149	−	0.635943i
$283$	19.8188	+	11.4424i	1.17811	+	0.680179i	0.955575	−	0.294747i	$-0.0952352\pi$
$283$	19.8188	+	11.4424i	1.17811	+	0.680179i	0.222530	+	0.974926i	$0.428569\pi$
$284$			6.15442i			0.365198i
$285$	−0.275747	−	3.55928i	−0.0163339	−	0.210833i
$286$	6.19743	+	4.65079i	0.366462	+	0.275007i
$287$	−5.53674	−	3.19664i	−0.326823	−	0.188692i
$288$	0.550630	−	0.953720i	0.0324462	−	0.0561985i
$289$	8.03964	+	13.9251i	0.472920	+	0.819121i
$290$	1.56568	−	2.71184i	0.0919400	−	0.159245i
$291$	−15.4366	−	26.7370i	−0.904910	−	1.56735i
$292$		−	8.94859i		−	0.523677i
$293$	4.47087			0.261191			0.130595	−	0.991436i	$-0.458311\pi$
$293$	4.47087			0.261191			0.130595	+	0.991436i	$0.458311\pi$
$294$	8.91159	−	5.14511i	0.519734	−	0.300069i
$295$	0.785276	−	0.453379i	0.0457205	−	0.0263967i
$296$		−	10.8902i		−	0.632982i
$297$	7.65481	−	10.2004i	0.444177	−	0.591890i
$298$	−3.06944	+	1.77214i	−0.177808	+	0.102657i
$299$	−5.24161	+	9.07874i	−0.303130	+	0.525037i
$300$	−8.48235	+	4.89728i	−0.489728	+	0.282745i
$301$	−7.85105	+	13.5984i	−0.452527	+	0.783800i
$302$	7.16946	−	12.4179i	0.412556	−	0.714569i
$303$	−6.00610			−0.345042
$304$	2.46452	+	3.59530i	0.141350	+	0.206204i
$305$		−	0.985563i		−	0.0564332i
$306$	−5.48528	−	3.16693i	−0.313573	−	0.181041i
$307$	−8.59712	+	14.8906i	−0.490663	+	0.849854i	−0.999942	−	0.0107475i	$-0.996579\pi$
$307$	−8.59712	+	14.8906i	−0.490663	+	0.849854i	0.509279	+	0.860602i	$0.329912\pi$
$308$	−4.56108	−	0.550819i	−0.259892	−	0.0313858i
$309$	−14.7638	+	25.5717i	−0.839885	+	1.45472i
$310$	2.42774	−	1.40165i	0.137886	−	0.0796086i
$311$	−18.7483			−1.06312			−0.531560	−	0.847020i	$-0.678394\pi$
$311$	−18.7483			−1.06312			−0.531560	+	0.847020i	$0.678394\pi$
$312$		−	4.73124i		−	0.267854i
$313$	1.93035	+	3.34346i	0.109110	+	0.188983i	0.915410	−	0.402523i	$-0.131867\pi$
$313$	1.93035	+	3.34346i	0.109110	+	0.188983i	−0.806300	+	0.591507i	$0.798533\pi$
$314$	0.290152	+	0.502558i	0.0163742	+	0.0283610i
$315$		−	0.616924i		−	0.0347597i
$316$	8.64686			0.486424
$317$	18.3112	−	10.5720i	1.02846	−	0.593782i	0.111917	−	0.993718i	$-0.464301\pi$
$317$	18.3112	−	10.5720i	1.02846	−	0.593782i	0.916543	+	0.399936i	$0.130968\pi$
$318$	−4.21283	+	7.29683i	−0.236244	+	0.409186i
$319$	3.07894	−	25.4953i	0.172388	−	1.42746i
$320$	−0.202207	+	0.350232i	−0.0113037	+	0.0195786i
$321$	32.8314	+	18.9552i	1.83247	+	1.05798i
$322$		−	6.21576i		−	0.346391i
$323$	20.6782	−	14.1746i	1.15057	−	0.788694i
$324$	−11.0910			−0.616167
$325$	−5.64954	+	9.78529i	−0.313380	+	0.542790i
$326$	8.58178	−	14.8641i	0.475301	−	0.823245i
$327$	−0.209397	+	0.120896i	−0.0115797	+	0.00668555i
$328$	−2.30769	+	3.99704i	−0.127421	+	0.220700i
$329$	12.6520	−	7.30466i	0.697530	−	0.402719i
$330$	1.63040	−	2.17260i	0.0897506	−	0.119598i
$331$			2.79682i			0.153727i	0.997042	+	0.0768634i	$0.0244906\pi$
$331$			2.79682i			0.153727i	−0.997042	+	0.0768634i	$0.975509\pi$
$332$	−0.728804	+	0.420775i	−0.0399983	+	0.0230930i
$333$	10.3862	−	5.99649i	0.569162	−	0.328606i
$334$	−5.34295			−0.292353
$335$			3.46845i			0.189502i
$336$	1.40263	+	2.42943i	0.0765199	+	0.132536i
$337$	−8.58563	+	14.8708i	−0.467689	+	0.810062i	−0.999318	−	0.0369157i	$-0.988247\pi$
$337$	−8.58563	+	14.8708i	−0.467689	+	0.810062i	0.531629	+	0.846977i	$0.321580\pi$
$338$	3.77100	+	6.53157i	0.205116	+	0.355270i
$339$	1.60072	−	2.77253i	0.0869394	−	0.150583i
$340$	2.01435	+	1.16298i	0.109243	+	0.0630717i
$341$	13.7992	−	18.3882i	0.747271	−	0.995779i
$342$	−2.07187	+	4.33014i	−0.112034	+	0.234147i
$343$			16.7350i			0.903605i
$344$	9.81686	+	5.66777i	0.529290	+	0.305586i
$345$	3.18268	+	1.83752i	0.171350	+	0.0989289i
$346$	−0.229562	−	0.397614i	−0.0123413	−	0.0213758i
$347$	−3.89661	−	2.24971i	−0.209181	−	0.120771i	0.391750	−	0.920072i	$-0.371870\pi$
$347$	−3.89661	−	2.24971i	−0.209181	−	0.120771i	−0.600931	+	0.799301i	$0.705203\pi$
$348$	−13.5799	+	7.84037i	−0.727960	+	0.420288i
$349$		−	25.6849i		−	1.37488i	−0.726240	−	0.687441i	$-0.758734\pi$
$349$		−	25.6849i		−	1.37488i	0.726240	−	0.687441i	$-0.241266\pi$
$350$		−	6.69950i		−	0.358103i
$351$	−7.77985	+	4.49170i	−0.415258	+	0.239749i
$352$	−0.397643	+	3.29270i	−0.0211945	+	0.175502i
$353$	3.56000			0.189480			0.0947400	−	0.995502i	$-0.469798\pi$
$353$	3.56000			0.189480			0.0947400	+	0.995502i	$0.469798\pi$
$354$	−4.54072			−0.241336
$355$	2.15548	−	1.24447i	0.114401	−	0.0660494i
$356$	12.4450	+	7.18512i	0.659583	+	0.380811i
$357$	13.9728	−	8.06719i	0.739518	−	0.426961i
$358$	−15.9960	−	9.23532i	−0.845417	−	0.488102i
$359$	−17.6340	−	10.1810i	−0.930686	−	0.537332i	−0.0436574	−	0.999047i	$-0.513901\pi$
$359$	−17.6340	−	10.1810i	−0.930686	−	0.537332i	−0.887028	+	0.461715i	$0.847234\pi$
$360$	−0.445365			−0.0234728
$361$	−11.9210	−	14.7949i	−0.627420	−	0.778681i
$362$			1.59075i			0.0836078i
$363$	5.30316	−	21.6363i	0.278344	−	1.13561i
$364$	2.80261	+	1.61809i	0.146897	+	0.0848109i
$365$	−3.13409	+	1.80947i	−0.164046	+	0.0947117i
$366$	−2.46767	+	4.27413i	−0.128987	+	0.223413i
$367$	11.1850	+	19.3729i	0.583851	+	1.01126i	0.995018	+	0.0996989i	$0.0317880\pi$
$367$	11.1850	+	19.3729i	0.583851	+	1.01126i	−0.411167	+	0.911560i	$0.634879\pi$
$368$	−4.48723			−0.233913
$369$	−5.08274			−0.264597
$370$	−3.81411	+	2.20208i	−0.198286	+	0.114481i
$371$	−2.88158	−	4.99104i	−0.149604	−	0.259122i
$372$	−14.0380			−0.727834
$373$	−37.1915			−1.92570			−0.962851	−	0.270033i	$-0.912965\pi$
$373$	−37.1915			−1.92570			−0.962851	+	0.270033i	$0.912965\pi$
$374$	18.9378	+	2.28703i	0.979252	+	0.118259i
$375$	6.97675	+	4.02803i	0.360278	+	0.208007i
$376$	−5.27332	−	9.13366i	−0.271951	−	0.471033i
$377$	−9.04471	+	15.6659i	−0.465826	+	0.806835i
$378$	2.66324	−	4.61286i	0.136982	−	0.237260i
$379$		−	23.5259i		−	1.20844i	−0.796816	−	0.604222i	$-0.793484\pi$
$379$		−	23.5259i		−	1.20844i	0.796816	−	0.604222i	$-0.206516\pi$
$380$	0.760847	−	1.59015i	0.0390306	−	0.0815728i
$381$			23.8222i			1.22045i
$382$	1.78905	−	3.09873i	0.0915358	−	0.158545i
$383$	−6.71609	−	3.87754i	−0.343176	−	0.198133i	0.318499	−	0.947923i	$-0.396821\pi$
$383$	−6.71609	−	3.87754i	−0.343176	−	0.198133i	−0.661676	+	0.749790i	$0.730154\pi$
$384$	1.75384	−	1.01258i	0.0895001	−	0.0516729i
$385$	0.729367	+	1.70882i	0.0371720	+	0.0870894i
$386$	−7.51799	−	13.0215i	−0.382656	−	0.662779i
$387$			12.4834i			0.634566i
$388$		−	15.2448i		−	0.773940i
$389$	−4.49405	−	7.78393i	−0.227858	−	0.394661i	0.729315	−	0.684178i	$-0.239839\pi$
$389$	−4.49405	−	7.78393i	−0.227858	−	0.394661i	−0.957173	+	0.289517i	$0.906505\pi$
$390$	−1.65703	+	0.956689i	−0.0839072	+	0.0484438i
$391$			25.8081i			1.30517i
$392$	5.08119			0.256639
$393$	−16.4968	−	28.5733i	−0.832154	−	1.44133i
$394$	6.34352	+	3.66243i	0.319582	+	0.184511i
$395$	−1.74845	−	3.02841i	−0.0879743	−	0.152376i
$396$	−3.35927	+	1.43382i	−0.168810	+	0.0720522i
$397$	19.4077	−	33.6150i	0.974042	−	1.68709i	0.290982	−	0.956729i	$-0.406018\pi$
$397$	19.4077	−	33.6150i	0.974042	−	1.68709i	0.683060	−	0.730362i	$-0.260649\pi$
$398$	−9.89005			−0.495743
$399$	−6.91363	−	10.0858i	−0.346115	−	0.504920i
$400$	−4.83645			−0.241822
$401$	−5.77833	−	3.33612i	−0.288556	−	0.166598i	0.348734	−	0.937222i	$-0.386612\pi$
$401$	−5.77833	−	3.33612i	−0.288556	−	0.166598i	−0.637290	+	0.770624i	$0.719945\pi$
$402$	8.68437	−	15.0418i	0.433137	−	0.750215i
$403$	−14.0247	+	8.09714i	−0.698618	+	0.403347i
$404$	−2.56841	−	1.48287i	−0.127783	−	0.0737757i
$405$	2.24268	+	3.88443i	0.111439	+	0.193019i
$406$		−	10.7257i		−	0.532305i
$407$	−21.6794	+	28.8890i	−1.07461	+	1.43197i
$408$	−5.82380	−	10.0871i	−0.288321	−	0.499387i
$409$	−13.5787	−	23.5190i	−0.671422	−	1.16294i	−0.977501	−	0.210931i	$-0.932350\pi$
$409$	−13.5787	−	23.5190i	−0.671422	−	1.16294i	0.306079	−	0.952006i	$-0.400983\pi$
$410$	1.86652			0.0921811
$411$		−	14.3790i		−	0.709266i
$412$	−12.6270	+	7.29022i	−0.622089	+	0.359163i
$413$	1.55293	−	2.68975i	0.0764146	−	0.132354i
$414$	−2.47081	−	4.27956i	−0.121433	−	0.210329i
$415$	0.294738	+	0.170167i	0.0144681	+	0.00835318i
$416$	1.16812	−	2.02324i	0.0572717	−	0.0991974i
$417$	−30.8117			−1.50885
$418$	0.619497	−	14.4436i	0.0303006	−	0.706457i
$419$	6.33615			0.309541			0.154770	−	0.987950i	$-0.450536\pi$
$419$	6.33615			0.309541			0.154770	+	0.987950i	$0.450536\pi$
$420$	0.567244	−	0.982496i	0.0276787	−	0.0479409i
$421$	0.755454	+	0.436162i	0.0368186	+	0.0212572i	0.518296	−	0.855201i	$-0.326566\pi$
$421$	0.755454	+	0.436162i	0.0368186	+	0.0212572i	−0.481478	+	0.876458i	$0.659900\pi$
$422$	1.12895	+	1.95540i	0.0549564	+	0.0951873i
$423$	5.80730	−	10.0585i	0.282361	−	0.489063i
$424$	−3.60309	+	2.08025i	−0.174982	+	0.101026i
$425$			27.8166i			1.34931i
$426$	−12.4637			−0.603867
$427$	−1.68789	−	2.92351i	−0.0816828	−	0.141479i
$428$	9.35987	+	16.2118i	0.452427	+	0.783626i
$429$	−9.41858	+	12.5508i	−0.454733	+	0.605956i
$430$		−	4.58424i		−	0.221072i
$431$	11.1190	+	19.2587i	0.535586	+	0.927661i	0.999135	+	0.0415901i	$0.0132424\pi$
$431$	11.1190	+	19.2587i	0.535586	+	0.927661i	−0.463549	+	0.886071i	$0.653424\pi$
$432$	−3.33008	−	1.92262i	−0.160219	−	0.0925022i
$433$	−1.62992	+	0.941037i	−0.0783291	+	0.0452233i	−0.538653	−	0.842528i	$-0.681067\pi$
$433$	−1.62992	+	0.941037i	−0.0783291	+	0.0452233i	0.460324	+	0.887751i	$0.347733\pi$
$434$	4.80099	−	8.31556i	0.230455	−	0.399160i
$435$	5.49190	+	3.17075i	0.263317	+	0.152026i
$436$	−0.119394			−0.00571793
$437$	19.5010	−	1.51079i	0.932857	−	0.0722711i
$438$	18.1223			0.865917
$439$	18.9100	−	32.7530i	0.902524	−	1.56322i	0.0783174	−	0.996928i	$-0.475045\pi$
$439$	18.9100	−	32.7530i	0.902524	−	1.56322i	0.824207	−	0.566289i	$-0.191621\pi$
$440$	1.23362	−	0.526539i	0.0588104	−	0.0251018i
$441$	2.79786	+	4.84603i	0.133231	+	0.230764i
$442$	−11.6366	−	6.71838i	−0.553495	−	0.319561i
$443$	−6.54099	−	11.3293i	−0.310772	−	0.538273i	0.667758	−	0.744379i	$-0.267254\pi$
$443$	−6.54099	−	11.3293i	−0.310772	−	0.538273i	−0.978530	+	0.206106i	$0.933921\pi$
$444$	22.0544			1.04666
$445$		−	5.81152i		−	0.275492i
$446$	−22.6010	+	13.0487i	−1.07019	+	0.617873i
$447$	−3.58886	−	6.21609i	−0.169747	−	0.294011i
$448$			1.38521i			0.0654450i
$449$		−	30.3180i		−	1.43079i	−0.698718	−	0.715397i	$-0.746246\pi$
$449$		−	30.3180i		−	1.43079i	0.698718	−	0.715397i	$-0.253754\pi$
$450$	−2.66310	−	4.61262i	−0.125540	−	0.217441i
$451$	14.0787	−	6.00915i	0.662940	−	0.282960i
$452$	1.36905	−	0.790419i	0.0643945	−	0.0371782i
$453$	25.1481	+	14.5193i	1.18156	+	0.682176i
$454$	−10.4690	+	18.1329i	−0.491336	+	0.851019i
$455$		−	1.30875i		−	0.0613553i
$456$	−7.28104	+	4.99104i	−0.340966	+	0.233727i
$457$			13.0841i			0.612050i	0.952023	+	0.306025i	$0.0989991\pi$
$457$			13.0841i			0.612050i	−0.952023	+	0.306025i	$0.901001\pi$
$458$	8.06341	−	13.9662i	0.376779	−	0.652600i
$459$	−11.0579	+	19.1528i	−0.516138	+	0.893977i
$460$	0.907348	+	1.57157i	0.0423053	+	0.0732750i
$461$	−1.37713	−	0.795087i	−0.0641393	−	0.0370309i	0.467587	−	0.883947i	$-0.345123\pi$
$461$	−1.37713	−	0.795087i	−0.0641393	−	0.0370309i	−0.531727	+	0.846916i	$0.678457\pi$
$462$	1.11550	−	9.23691i	0.0518976	−	0.429740i
$463$	−20.3009			−0.943464			−0.471732	−	0.881742i	$-0.656371\pi$
$463$	−20.3009			−0.943464			−0.471732	+	0.881742i	$0.656371\pi$
$464$	−7.74298			−0.359459
$465$	2.83857	+	4.91655i	0.131636	+	0.227999i
$466$	−9.78906	+	5.65172i	−0.453469	+	0.261811i
$467$	11.8553			0.548597			0.274299	−	0.961645i	$-0.411554\pi$
$467$	11.8553			0.548597			0.274299	+	0.961645i	$0.411554\pi$
$468$	2.57280			0.118928
$469$	5.94012	+	10.2886i	0.274289	+	0.475083i
$470$	−2.13260	+	3.69378i	−0.0983696	+	0.170381i
$471$	−1.01776	+	0.587603i	−0.0468958	+	0.0270753i
$472$	−1.94176	−	1.12108i	−0.0893769	−	0.0516018i
$473$	−14.7587	−	34.5777i	−0.678604	−	1.58989i
$474$			17.5113i			0.804318i
$475$	21.0186	−	1.62837i	0.964400	−	0.0747148i
$476$	7.96698			0.365166
$477$	−3.96794	−	2.29089i	−0.181680	−	0.104893i
$478$	0.850528	+	0.491053i	0.0389023	+	0.0224602i
$479$	−30.4870	+	17.6017i	−1.39299	+	0.804242i	−0.993645	−	0.112559i	$-0.964095\pi$
$479$	−30.4870	+	17.6017i	−1.39299	+	0.804242i	−0.399344	+	0.916801i	$0.630762\pi$
$480$	−0.709276	−	0.409500i	−0.0323739	−	0.0186911i
$481$	22.0335	−	12.7211i	1.00464	−	0.580031i
$482$	−3.92403			−0.178735
$483$	12.5879			0.572769
$484$	7.60969	−	7.94309i	0.345895	−	0.361049i
$485$	−5.33924	+	3.08261i	−0.242442	+	0.139974i
$486$		−	10.9253i		−	0.495581i
$487$			2.53576i			0.114906i	0.998348	+	0.0574532i	$0.0182980\pi$
$487$			2.53576i			0.114906i	−0.998348	+	0.0574532i	$0.981702\pi$
$488$	−2.11052	+	1.21851i	−0.0955388	+	0.0551593i
$489$	30.1021	+	17.3794i	1.36126	+	0.785926i
$490$	−1.02745	−	1.77960i	−0.0464155	−	0.0803941i
$491$	−30.1668	−	17.4168i	−1.36141	−	0.786009i	−0.371596	−	0.928394i	$-0.621189\pi$
$491$	−30.1668	−	17.4168i	−1.36141	−	0.786009i	−0.989811	+	0.142385i	$0.954523\pi$
$492$	−8.09463	−	4.67344i	−0.364934	−	0.210695i
$493$			44.5334i			2.00568i
$494$	−4.39530	+	9.18604i	−0.197754	+	0.413299i
$495$	1.18144	+	0.886596i	0.0531017	+	0.0398495i
$496$	−6.00310	−	3.46589i	−0.269547	−	0.155623i
$497$	4.26258	−	7.38301i	0.191203	−	0.331173i
$498$	−0.852136	−	1.47594i	−0.0381851	−	0.0661386i
$499$	−3.64732	+	6.31734i	−0.163276	+	0.282803i	−0.936042	−	0.351889i	$-0.885540\pi$
$499$	−3.64732	+	6.31734i	−0.163276	+	0.282803i	0.772765	+	0.634692i	$0.218873\pi$
$500$	1.98900	+	3.44504i	0.0889506	+	0.154067i
$501$		−	10.8203i		−	0.483416i
$502$	−7.94897			−0.354780
$503$	13.4222	−	7.74934i	0.598468	−	0.345526i	−0.169970	−	0.985449i	$-0.554367\pi$
$503$	13.4222	−	7.74934i	0.598468	−	0.345526i	0.768439	+	0.639923i	$0.221034\pi$
$504$	−1.32110	+	0.762739i	−0.0588466	+	0.0339751i
$505$			1.19939i			0.0533721i
$506$	11.9035	+	8.93282i	0.529173	+	0.397112i
$507$	−13.2275	+	7.63687i	−0.587452	+	0.339165i
$508$	−5.88156	+	10.1872i	−0.260952	+	0.451982i
$509$	10.9432	−	6.31806i	0.485049	−	0.280043i	−0.237469	−	0.971395i	$-0.576318\pi$
$509$	10.9432	−	6.31806i	0.485049	−	0.280043i	0.722518	+	0.691352i	$0.242985\pi$
$510$	−2.35522	+	4.07937i	−0.104291	+	0.180637i
$511$	−6.19784	+	10.7350i	−0.274176	+	0.474887i
$512$	1.00000			0.0441942
$513$	15.1194	+	7.23428i	0.667540	+	0.319401i
$514$			12.8660i			0.567493i
$515$	5.10654	+	2.94826i	0.225021	+	0.129916i
$516$	−11.4781	+	19.8807i	−0.505296	+	0.875199i
$517$	−4.19380	+	34.7270i	−0.184443	+	1.52729i
$518$	−7.54263	+	13.0642i	−0.331404	+	0.574009i
$519$	0.805230	−	0.464900i	0.0353457	−	0.0204068i
$520$	−0.944805			−0.0414324
$521$			5.88154i			0.257675i	0.991666	+	0.128838i	$0.0411246\pi$
$521$			5.88154i			0.257675i	−0.991666	+	0.128838i	$0.958875\pi$
$522$	−4.26352	−	7.38463i	−0.186609	−	0.323216i
$523$	−3.41574	−	5.91624i	−0.149360	−	0.258699i	0.781631	−	0.623741i	$-0.214388\pi$
$523$	−3.41574	−	5.91624i	−0.149360	−	0.258699i	−0.930991	+	0.365042i	$0.881055\pi$
$524$		−	16.2919i		−	0.711714i
$525$	13.5675			0.592136
$526$	−7.15130	+	4.12881i	−0.311812	+	0.180024i
$527$	−19.9339	+	34.5266i	−0.868336	+	1.50400i
$528$	−6.66824	−	0.805290i	−0.290198	−	0.0350457i
$529$	1.43238	−	2.48095i	0.0622773	−	0.107868i
$530$	1.45714	+	0.841280i	0.0632941	+	0.0365429i
$531$		−	2.46920i		−	0.107154i
$532$	−0.466383	−	6.01995i	−0.0202203	−	0.260998i
$533$	−10.7826			−0.467047
$534$	−14.5510	+	25.2031i	−0.629683	+	1.09064i
$535$	3.78526	−	6.55626i	0.163651	−	0.283452i
$536$	7.42746	−	4.28824i	0.320817	−	0.185224i
$537$	18.7030	−	32.3945i	0.807093	−	1.39793i
$538$	22.4442	−	12.9582i	0.967639	−	0.558667i
$539$	−13.4791	−	10.1152i	−0.580586	−	0.435694i
$540$			1.55507i			0.0669195i
$541$	−20.2463	+	11.6892i	−0.870456	+	0.502558i	−0.867500	−	0.497438i	$-0.834274\pi$
$541$	−20.2463	+	11.6892i	−0.870456	+	0.502558i	−0.00295633	+	0.999996i	$0.500941\pi$
$542$	−8.63431	+	4.98502i	−0.370876	+	0.214125i
$543$	−3.22151			−0.138248
$544$		−	5.75146i		−	0.246592i
$545$	0.0241423	+	0.0418156i	0.00103414	+	0.00179118i
$546$	−3.27688	+	5.67573i	−0.140238	+	0.242899i
$547$	8.72771	+	15.1168i	0.373170	+	0.646349i	0.990051	−	0.140707i	$-0.0449375\pi$
$547$	8.72771	+	15.1168i	0.373170	+	0.646349i	−0.616881	+	0.787056i	$0.711604\pi$
$548$	3.55011	−	6.14896i	0.151653	−	0.262671i
$549$	−2.32423	−	1.34190i	−0.0991958	−	0.0572707i
$550$	12.8298	+	9.62802i	0.547067	+	0.410540i
$551$	33.6500	−	2.60696i	1.43354	−	0.111060i
$552$		−	9.08735i		−	0.386783i
$553$	−10.3730	−	5.98886i	−0.441105	−	0.254672i
$554$	18.9597	+	10.9464i	0.805519	+	0.465066i
$555$	−4.45955	−	7.72417i	−0.189298	−	0.327873i
$556$	−13.1761	−	7.60723i	−0.558792	−	0.322619i
$557$	33.1300	−	19.1276i	1.40376	−	0.810464i	0.408988	−	0.912540i	$-0.365882\pi$
$557$	33.1300	−	19.1276i	1.40376	−	0.810464i	0.994777	+	0.102076i	$0.0325486\pi$
$558$		−	7.63370i		−	0.323160i
$559$			26.4825i			1.12009i
$560$	0.485145	−	0.280099i	0.0205011	−	0.0118363i
$561$	−4.63159	+	38.3521i	−0.195546	+	1.61923i
$562$	23.5816			0.994730
$563$	18.5879			0.783388			0.391694	−	0.920096i	$-0.371889\pi$
$563$	18.5879			0.783388			0.391694	+	0.920096i	$0.371889\pi$
$564$	18.4971	−	10.6793i	0.778868	−	0.449680i
$565$	−0.553661	−	0.319656i	−0.0232927	−	0.0134480i
$566$	−19.8188	+	11.4424i	−0.833046	+	0.480959i
$567$	13.3051	+	7.68169i	0.558760	+	0.322601i
$568$	−5.32989	−	3.07721i	−0.223637	−	0.129117i
$569$	17.5877			0.737313			0.368656	−	0.929566i	$-0.379818\pi$
$569$	17.5877			0.737313			0.368656	+	0.929566i	$0.379818\pi$
$570$	3.22030	+	1.54083i	0.134883	+	0.0645384i
$571$		−	4.34134i		−	0.181680i	−0.995866	−	0.0908398i	$-0.971045\pi$
$571$		−	4.34134i		−	0.181680i	0.995866	−	0.0908398i	$-0.0289551\pi$
$572$	−7.12641	+	3.04173i	−0.297970	+	0.127181i
$573$	6.27541	+	3.62311i	0.262159	+	0.151358i
$574$	5.53674	−	3.19664i	0.231099	−	0.133425i
$575$	−10.8511	+	18.7947i	−0.452524	+	0.783794i
$576$	0.550630	+	0.953720i	0.0229429	+	0.0397383i
$577$	−36.2549			−1.50931			−0.754655	−	0.656121i	$-0.772196\pi$
$577$	−36.2549			−1.50931			−0.754655	+	0.656121i	$0.772196\pi$
$578$	−16.0793			−0.668810
$579$	26.3707	−	15.2251i	1.09593	−	0.632734i
$580$	1.56568	+	2.71184i	0.0650114	+	0.112603i
$581$	1.16572			0.0483624
$582$	30.8732			1.27974
$583$	13.6993	+	1.65439i	0.567365	+	0.0685179i
$584$	7.74970	+	4.47429i	0.320685	+	0.185148i
$585$	−0.520238	−	0.901079i	−0.0215092	−	0.0372550i
$586$	−2.23543	+	3.87188i	−0.0923449	+	0.159946i
$587$	−12.5745	+	21.7796i	−0.519004	+	0.898941i	0.480752	+	0.876857i	$0.340364\pi$
$587$	−12.5745	+	21.7796i	−0.519004	+	0.898941i	−0.999756	+	0.0220847i	$0.992970\pi$
$588$			10.2902i			0.424361i
$589$	27.2557	+	13.0412i	1.12305	+	0.537352i
$590$			0.906758i			0.0373306i
$591$	−7.41700	+	12.8466i	−0.305095	+	0.528439i
$592$	9.43122	+	5.44512i	0.387621	+	0.223793i
$593$	20.9147	−	12.0751i	0.858862	−	0.495864i	−0.00476879	−	0.999989i	$-0.501518\pi$
$593$	20.9147	−	12.0751i	0.858862	−	0.495864i	0.863631	+	0.504124i	$0.168185\pi$
$594$	5.00644	+	11.7295i	0.205417	+	0.481266i
$595$	−1.61098	−	2.79029i	−0.0660436	−	0.114391i
$596$		−	3.54428i		−	0.145179i
$597$		−	20.0289i		−	0.819728i
$598$	−5.24161	−	9.07874i	−0.214346	−	0.371257i
$599$	−3.29316	+	1.90131i	−0.134555	+	0.0776853i	−0.565766	−	0.824566i	$-0.691420\pi$
$599$	−3.29316	+	1.90131i	−0.134555	+	0.0776853i	0.431212	+	0.902251i	$0.358086\pi$
$600$		−	9.79457i		−	0.399862i
$601$	21.6964			0.885013			0.442506	−	0.896765i	$-0.354089\pi$
$601$	21.6964			0.885013			0.442506	+	0.896765i	$0.354089\pi$
$602$	−7.85105	−	13.5984i	−0.319985	−	0.554230i
$603$	8.17956	+	4.72247i	0.333098	+	0.192314i
$604$	7.16946	+	12.4179i	0.291721	+	0.505276i
$605$	−4.32066	−	1.05901i	−0.175660	−	0.0430550i
$606$	3.00305	−	5.20144i	0.121991	−	0.211294i
$607$	−8.28171			−0.336144			−0.168072	−	0.985775i	$-0.553754\pi$
$607$	−8.28171			−0.336144			−0.168072	+	0.985775i	$0.553754\pi$
$608$	−4.34588	+	0.336688i	−0.176249	+	0.0136545i
$609$	21.7211			0.880184
$610$	0.853523	+	0.492782i	0.0345581	+	0.0199521i
$611$	12.3197	−	21.3384i	0.498403	−	0.863259i
$612$	5.48528	−	3.16693i	0.221729	−	0.128015i
$613$	−33.0592	−	19.0867i	−1.33525	−	0.770905i	−0.349148	−	0.937067i	$-0.613529\pi$
$613$	−33.0592	−	19.0867i	−1.33525	−	0.770905i	−0.986098	+	0.166162i	$0.946862\pi$
$614$	−8.59712	−	14.8906i	−0.346951	−	0.600938i
$615$			3.78000i			0.152424i
$616$	2.75756	−	3.67460i	0.111105	−	0.148054i
$617$	6.63494	+	11.4921i	0.267113	+	0.462653i	0.968115	−	0.250506i	$-0.0805971\pi$
$617$	6.63494	+	11.4921i	0.267113	+	0.462653i	−0.701002	+	0.713159i	$0.747264\pi$
$618$	−14.7638	−	25.5717i	−0.593889	−	1.02865i
$619$	−15.9422			−0.640771			−0.320386	−	0.947287i	$-0.603812\pi$
$619$	−15.9422			−0.640771			−0.320386	+	0.947287i	$0.603812\pi$
$620$			2.80331i			0.112584i
$621$	−14.9428	+	8.62725i	−0.599635	+	0.346200i
$622$	9.37417	−	16.2365i	0.375870	−	0.651026i
$623$	−9.95290	−	17.2389i	−0.398755	−	0.690663i
$624$	4.09738	+	2.36562i	0.164026	+	0.0947006i
$625$	−11.2867	+	19.5492i	−0.451470	+	0.781969i
$626$	−3.86069			−0.154304
$627$	29.2505	+	1.25458i	1.16815	+	0.0501030i
$628$	−0.580304			−0.0231566
$629$	31.3174	−	54.2432i	1.24870	−	2.16282i
$630$	0.534272	+	0.308462i	0.0212859	+	0.0122894i
$631$	−11.1339	−	19.2845i	−0.443234	−	0.767704i	0.554693	−	0.832055i	$-0.312836\pi$
$631$	−11.1339	−	19.2845i	−0.443234	−	0.767704i	−0.997927	+	0.0643507i	$0.979502\pi$
$632$	−4.32343	+	7.48840i	−0.171977	+	0.297873i
$633$	−3.95999	+	2.28630i	−0.157395	+	0.0908722i
$634$			21.1440i			0.839734i
$635$	4.75717			0.188782
$636$	−4.21283	−	7.29683i	−0.167049	−	0.289338i
$637$	5.93543	+	10.2805i	0.235170	+	0.407327i
$638$	20.5401	+	15.4141i	0.813191	+	0.610250i
$639$		−	6.77762i		−	0.268119i
$640$	−0.202207	−	0.350232i	−0.00799292	−	0.0138442i
$641$	−15.7602	−	9.09915i	−0.622490	−	0.359395i	0.155348	−	0.987860i	$-0.450350\pi$
$641$	−15.7602	−	9.09915i	−0.622490	−	0.359395i	−0.777838	+	0.628465i	$0.783684\pi$
$642$	−32.8314	+	18.9552i	−1.29575	+	0.748103i
$643$	6.13428	−	10.6249i	0.241913	−	0.419005i	−0.719347	−	0.694651i	$-0.755559\pi$
$643$	6.13428	−	10.6249i	0.241913	−	0.419005i	0.961259	+	0.275647i	$0.0888920\pi$
$644$	5.38300	+	3.10788i	0.212120	+	0.122468i
$645$	9.28382			0.365550
$646$	1.93644	+	24.9951i	0.0761884	+	0.983420i
$647$	44.1577			1.73602			0.868010	−	0.496548i	$-0.165399\pi$
$647$	44.1577			1.73602			0.868010	+	0.496548i	$0.165399\pi$
$648$	5.54550	−	9.60509i	0.217848	−	0.377324i
$649$	2.91924	+	6.83944i	0.114590	+	0.268471i
$650$	−5.64954	−	9.78529i	−0.221593	−	0.383811i
$651$	16.8403	+	9.72276i	0.660024	+	0.381065i
$652$	8.58178	+	14.8641i	0.336088	+	0.582122i
$653$	8.65426			0.338667			0.169334	−	0.985559i	$-0.445838\pi$
$653$	8.65426			0.338667			0.169334	+	0.985559i	$0.445838\pi$
$654$		−	0.241791i		−	0.00945479i
$655$	−5.70594	+	3.29433i	−0.222950	+	0.128720i
$656$	−2.30769	−	3.99704i	−0.0901003	−	0.156058i
$657$			9.85473i			0.384470i
$658$			14.6093i			0.569531i
$659$	8.42320	+	14.5894i	0.328121	+	0.568323i	0.982139	−	0.188156i	$-0.0602512\pi$
$659$	8.42320	+	14.5894i	0.328121	+	0.568323i	−0.654018	+	0.756479i	$0.726918\pi$
$660$	1.06632	+	2.49827i	0.0415066	+	0.0972449i
$661$	6.06493	−	3.50159i	0.235899	−	0.136196i	−0.377392	−	0.926054i	$-0.623179\pi$
$661$	6.06493	−	3.50159i	0.235899	−	0.136196i	0.613290	+	0.789858i	$0.289846\pi$
$662$	−2.42211	−	1.39841i	−0.0941381	−	0.0543507i
$663$	13.6058	−	23.5659i	0.528404	−	0.915223i
$664$		−	0.841550i		−	0.0326585i
$665$	−2.01408	+	1.38062i	−0.0781025	+	0.0535380i
$666$			11.9930i			0.464719i
$667$	−17.3723	+	30.0896i	−0.672657	+	1.16508i
$668$	2.67147	−	4.62713i	0.103362	−	0.179029i
$669$	−26.4256	−	45.7705i	−1.02167	−	1.76959i
$670$	−3.00376	−	1.73422i	−0.116046	−	0.0669989i
$671$	8.02437	+	0.969064i	0.309778	+	0.0374103i
$672$	−2.80527			−0.108216
$673$	30.6912			1.18306			0.591530	−	0.806283i	$-0.298524\pi$
$673$	30.6912			1.18306			0.591530	+	0.806283i	$0.298524\pi$
$674$	−8.58563	−	14.8708i	−0.330706	−	0.572800i
$675$	−16.1058	+	9.29867i	−0.619911	+	0.357906i
$676$	−7.54201			−0.290077
$677$	−12.1726			−0.467830			−0.233915	−	0.972257i	$-0.575154\pi$
$677$	−12.1726			−0.467830			−0.233915	+	0.972257i	$0.575154\pi$
$678$	1.60072	+	2.77253i	0.0614754	+	0.106479i
$679$	−10.5587	+	18.2881i	−0.405204	+	0.701834i
$680$	−2.01435	+	1.16298i	−0.0772467	+	0.0445984i
$681$	−36.7220	−	21.2014i	−1.40719	−	0.812441i
$682$	9.02506	+	21.1446i	0.345587	+	0.809669i
$683$		−	26.9552i		−	1.03141i	−0.856766	−	0.515706i	$-0.827530\pi$
$683$		−	26.9552i		−	1.03141i	0.856766	−	0.515706i	$-0.172470\pi$
$684$	−2.71408	−	3.95936i	−0.103775	−	0.151390i
$685$	−2.87142			−0.109711
$686$	−14.4929	−	8.36749i	−0.553342	−	0.319472i
$687$	28.2838	+	16.3297i	1.07910	+	0.623016i
$688$	−9.81686	+	5.66777i	−0.374264	+	0.216082i
$689$	−8.41767	−	4.85995i	−0.320688	−	0.185149i
$690$	−3.18268	+	1.83752i	−0.121163	+	0.0699533i
$691$	−22.1203			−0.841496			−0.420748	−	0.907177i	$-0.638232\pi$
$691$	−22.1203			−0.841496			−0.420748	+	0.907177i	$0.638232\pi$
$692$	0.459125			0.0174533
$693$	5.02294	+	0.606596i	0.190806	+	0.0230427i
$694$	3.89661	−	2.24971i	0.147913	−	0.0853977i
$695$			6.15294i			0.233394i
$696$		−	15.6807i		−	0.594377i
$697$	−22.9888	+	13.2726i	−0.870763	+	0.502735i
$698$	22.2438	+	12.8425i	0.841940	+	0.486094i
$699$	−11.4456	−	19.8244i	−0.432913	−	0.749827i
$700$	5.80194	+	3.34975i	0.219293	+	0.126609i
$701$	−16.4096	−	9.47410i	−0.619783	−	0.357832i	0.157002	−	0.987598i	$-0.449817\pi$
$701$	−16.4096	−	9.47410i	−0.619783	−	0.357832i	−0.776784	+	0.629767i	$0.783151\pi$
$702$		−	8.98340i		−	0.339056i
$703$	−42.8202	−	20.4884i	−1.61499	−	0.772736i
$704$	−2.65274	−	1.99072i	−0.0999789	−	0.0750281i
$705$	−7.48048	−	4.31886i	−0.281731	−	0.162658i
$706$	−1.78000	+	3.08305i	−0.0669913	+	0.116032i
$707$	2.05409	+	3.55779i	0.0772520	+	0.133804i
$708$	2.27036	−	3.93238i	0.0853253	−	0.147788i
$709$	19.2204	+	33.2906i	0.721835	+	1.25026i	0.960263	+	0.279096i	$0.0900346\pi$
$709$	19.2204	+	33.2906i	0.721835	+	1.25026i	−0.238428	+	0.971160i	$0.576632\pi$
$710$			2.48893i			0.0934079i
$711$	−9.52245			−0.357120
$712$	−12.4450	+	7.18512i	−0.466396	+	0.269274i
$713$	−26.9373	+	15.5523i	−1.00881	+	0.582437i
$714$			16.1344i			0.603814i
$715$	2.50632	+	1.88084i	0.0937312	+	0.0703395i
$716$	15.9960	−	9.23532i	0.597800	−	0.345140i
$717$	−0.994459	+	1.72245i	−0.0371387	+	0.0643262i
$718$	17.6340	−	10.1810i	0.658094	−	0.379951i
$719$	3.41998	−	5.92358i	0.127544	−	0.220912i	−0.795181	−	0.606373i	$-0.792624\pi$
$719$	3.41998	−	5.92358i	0.127544	−	0.220912i	0.922724	+	0.385460i	$0.125957\pi$
$720$	0.222682	−	0.385697i	0.00829888	−	0.0143741i
$721$	20.1970			0.752174
$722$	18.7733	−	2.92640i	0.698669	−	0.108910i
$723$		−	7.94678i		−	0.295544i
$724$	−1.37763	−	0.795374i	−0.0511991	−	0.0295598i
$725$	−18.7243	+	32.4314i	−0.695402	+	1.20447i
$726$	16.0860	+	15.4108i	0.597007	+	0.571949i
$727$	9.37417	−	16.2365i	0.347669	−	0.602180i	−0.638166	−	0.769899i	$-0.720307\pi$
$727$	9.37417	−	16.2365i	0.347669	−	0.602180i	0.985835	+	0.167719i	$0.0536400\pi$
$728$	−2.80261	+	1.61809i	−0.103872	+	0.0599703i
$729$	−11.1476			−0.412874
$730$		−	3.61893i		−	0.133943i
$731$	32.5979	+	56.4613i	1.20568	+	2.08830i
$732$	−2.46767	−	4.27413i	−0.0912078	−	0.157977i
$733$			36.1998i			1.33707i	0.743680	+	0.668535i	$0.233078\pi$
$733$			36.1998i			1.33707i	−0.743680	+	0.668535i	$0.766922\pi$
$734$	−22.3699			−0.825689
$735$	3.60397	−	2.08075i	0.132934	−	0.0767497i
$736$	2.24362	−	3.88606i	0.0827008	−	0.143242i
$737$	−28.2398	−	3.41038i	−1.04023	−	0.125623i
$738$	2.54137	−	4.40178i	0.0935491	−	0.162032i
$739$	16.7486	+	9.66982i	0.616108	+	0.355710i	0.775352	−	0.631529i	$-0.217572\pi$
$739$	16.7486	+	9.66982i	0.616108	+	0.355710i	−0.159244	+	0.987239i	$0.550906\pi$
$740$		−	4.40416i		−	0.161900i
$741$	−18.6032	−	8.90116i	−0.683404	−	0.326992i
$742$	5.76316			0.211572
$743$	−14.0698	+	24.3695i	−0.516170	+	0.894032i	0.483654	+	0.875259i	$0.339309\pi$
$743$	−14.0698	+	24.3695i	−0.516170	+	0.894032i	−0.999824	+	0.0187728i	$0.994024\pi$
$744$	7.01898	−	12.1572i	0.257328	−	0.445706i
$745$	−1.24132	+	0.716678i	−0.0454785	+	0.0262570i
$746$	18.5957	−	32.2088i	0.680839	−	1.17925i
$747$	0.802603	−	0.463383i	0.0293657	−	0.0169543i
$748$	−11.4495	+	15.2571i	−0.418637	+	0.557856i
$749$		−	25.9308i		−	0.947490i
$750$	−6.97675	+	4.02803i	−0.254755	+	0.147083i
$751$	−8.78702	+	5.07319i	−0.320643	+	0.185123i	−0.651679	−	0.758495i	$-0.725935\pi$
$751$	−8.78702	+	5.07319i	−0.320643	+	0.185123i	0.331036	+	0.943618i	$0.392602\pi$
$752$	10.5466			0.384597
$753$		−	16.0979i		−	0.586640i
$754$	−9.04471	−	15.6659i	−0.329389	−	0.570518i
$755$	2.89943	−	5.02196i	0.105521	−	0.182768i
$756$	2.66324	+	4.61286i	0.0968610	+	0.167768i
$757$	−7.30677	+	12.6557i	−0.265569	+	0.459979i	−0.967713	−	0.252056i	$-0.918893\pi$
$757$	−7.30677	+	12.6557i	−0.265569	+	0.459979i	0.702143	+	0.712036i	$0.252227\pi$
$758$	20.3740	+	11.7630i	0.740018	+	0.427250i
$759$	−18.0904	+	24.1064i	−0.656638	+	0.875006i
$760$	0.996684	+	1.45399i	0.0361535	+	0.0527416i
$761$			3.04124i			0.110245i	0.998480	+	0.0551224i	$0.0175549\pi$
$761$			3.04124i			0.110245i	−0.998480	+	0.0551224i	$0.982445\pi$
$762$	−20.6306	−	11.9111i	−0.747368	−	0.431493i
$763$	0.143228	+	0.0826928i	0.00518521	+	0.00299368i
$764$	1.78905	+	3.09873i	0.0647256	+	0.112108i
$765$	−2.21832	−	1.28075i	−0.0802036	−	0.0463055i
$766$	6.71609	−	3.87754i	0.242662	−	0.140101i
$767$		−	5.23820i		−	0.189141i
$768$			2.02516i			0.0730766i
$769$	−13.5910	+	7.84678i	−0.490105	+	0.282962i	−0.724618	−	0.689151i	$-0.757984\pi$
$769$	−13.5910	+	7.84678i	−0.490105	+	0.282962i	0.234513	+	0.972113i	$0.424650\pi$
$770$	−1.84456	−	0.222759i	−0.0664735	−	0.00802767i
$771$	−26.0556			−0.938369
$772$	15.0360			0.541157
$773$	−11.4627	+	6.61797i	−0.412284	+	0.238032i	−0.691770	−	0.722118i	$-0.743169\pi$
$773$	−11.4627	+	6.61797i	−0.412284	+	0.238032i	0.279487	+	0.960150i	$0.409836\pi$
$774$	−10.8109	−	6.24169i	−0.388591	−	0.224353i
$775$	−29.0337	+	16.7626i	−1.04292	+	0.602131i
$776$	13.2024	+	7.62242i	0.473940	+	0.273629i
$777$	−26.4571	−	15.2750i	−0.949143	−	0.547988i
$778$	8.98811			0.322239
$779$	11.3747	+	16.5937i	0.407541	+	0.594530i
$780$		−	1.91338i		−	0.0685099i
$781$	8.01294	+	18.7733i	0.286726	+	0.671763i
$782$	−22.3505	−	12.9041i	−0.799252	−	0.461448i
$783$	−25.7847	+	14.8868i	−0.921471	+	0.532012i
$784$	−2.54060	+	4.40044i	−0.0907356	+	0.157159i
$785$	0.117341	+	0.203241i	0.00418809	+	0.00725399i
$786$	32.9936			1.17684
$787$	40.3153			1.43708			0.718542	−	0.695483i	$-0.244810\pi$
$787$	40.3153			1.43708			0.718542	+	0.695483i	$0.244810\pi$
$788$	−6.34352	+	3.66243i	−0.225979	+	0.130469i
$789$	−8.36148	−	14.4825i	−0.297677	−	0.515591i
$790$	3.49691			0.124414
$791$	−2.18979			−0.0778601
$792$	0.437909	−	3.62612i	0.0155604	−	0.128849i
$793$	−4.93067	−	2.84672i	−0.175093	−	0.101090i
$794$	19.4077	+	33.6150i	0.688752	+	1.19295i
$795$	−1.70372	+	2.95094i	−0.0604249	+	0.104659i
$796$	4.94502	−	8.56503i	0.175272	−	0.303579i
$797$		−	5.26939i		−	0.186651i	−0.995636	−	0.0933256i	$-0.970250\pi$
$797$		−	5.26939i		−	0.186651i	0.995636	−	0.0933256i	$-0.0297498\pi$
$798$	12.1913	−	0.944499i	0.431569	−	0.0334349i
$799$		−	60.6586i		−	2.14595i
$800$	2.41822	−	4.18849i	0.0854972	−	0.148085i
$801$	−13.7052	−	7.91269i	−0.484249	−	0.279581i
$802$	5.77833	−	3.33612i	0.204040	−	0.117803i
$803$	−11.6509	−	27.2966i	−0.411151	−	0.963277i
$804$	8.68437	+	15.0418i	0.306274	+	0.530482i
$805$		−	2.51374i		−	0.0885976i
$806$		−	16.1943i		−	0.570419i
$807$	26.2423	+	45.4531i	0.923774	+	1.60002i
$808$	2.56841	−	1.48287i	0.0903564	−	0.0521673i
$809$		−	40.4103i		−	1.42075i	−0.703824	−	0.710375i	$-0.748526\pi$
$809$		−	40.4103i		−	1.42075i	0.703824	−	0.710375i	$-0.251474\pi$
$810$	−4.48535			−0.157599
$811$	8.21365	+	14.2265i	0.288420	+	0.499558i	0.973433	−	0.228973i	$-0.0735367\pi$
$811$	8.21365	+	14.2265i	0.288420	+	0.499558i	−0.685013	+	0.728531i	$0.740203\pi$
$812$	9.28869	+	5.36283i	0.325969	+	0.188198i
$813$	−10.0955	−	17.4858i	−0.354063	−	0.613255i
$814$	−14.1789	−	33.2194i	−0.496969	−	1.16434i
$815$	3.47059	−	6.01123i	0.121569	−	0.210564i
$816$	11.6476			0.407748
$817$	40.7546	−	27.9366i	1.42582	−	0.977379i
$818$	27.1574			0.949534
$819$	−3.08640	−	1.78194i	−0.107848	−	0.0622659i
$820$	−0.933262	+	1.61646i	−0.0325909	+	0.0564491i
$821$	−30.0891	+	17.3720i	−1.05012	+	0.606285i	−0.922682	−	0.385562i	$-0.874008\pi$
$821$	−30.0891	+	17.3720i	−1.05012	+	0.606285i	−0.127435	+	0.991847i	$0.540674\pi$
$822$	12.4526	+	7.18952i	0.434335	+	0.250763i
$823$	−17.9459	−	31.0831i	−0.625553	−	1.08349i	−0.988434	−	0.151654i	$-0.951540\pi$
$823$	−17.9459	−	31.0831i	−0.625553	−	1.08349i	0.362880	−	0.931836i	$-0.381793\pi$
$824$		−	14.5804i		−	0.507934i
$825$	−19.4982	+	25.9825i	−0.678842	+	0.904593i
$826$	1.55293	+	2.68975i	0.0540333	+	0.0935884i
$827$	0.642603	+	1.11302i	0.0223455	+	0.0387036i	0.876982	−	0.480523i	$-0.159553\pi$
$827$	0.642603	+	1.11302i	0.0223455	+	0.0387036i	−0.854636	+	0.519227i	$0.826220\pi$
$828$	4.94161			0.171733
$829$		−	5.24829i		−	0.182281i	−0.995838	−	0.0911403i	$-0.970949\pi$
$829$		−	5.24829i		−	0.182281i	0.995838	−	0.0911403i	$-0.0290512\pi$
$830$	−0.294738	+	0.170167i	−0.0102305	+	0.00590659i
$831$	−22.1681	+	38.3963i	−0.769003	+	1.33195i
$832$	1.16812	+	2.02324i	0.0404972	+	0.0701432i
$833$	25.3090	+	14.6121i	0.876904	+	0.506281i
$834$	15.4058	−	26.6837i	0.533461	−	0.923981i
$835$	−2.16076			−0.0747762
$836$	12.1987	+	7.75828i	0.421902	+	0.268326i
$837$	−26.6544			−0.921312
$838$	−3.16807	+	5.48726i	−0.109439	+	0.189554i
$839$	12.2462	+	7.07037i	0.422787	+	0.244096i	0.696269	−	0.717781i	$-0.254842\pi$
$839$	12.2462	+	7.07037i	0.422787	+	0.244096i	−0.273482	+	0.961877i	$0.588175\pi$
$840$	0.567244	+	0.982496i	0.0195718	+	0.0338993i
$841$	−15.4769	+	26.8067i	−0.533685	+	0.924369i
$842$	−0.755454	+	0.436162i	−0.0260347	+	0.0150311i
$843$			47.7565i			1.64482i
$844$	−2.25790			−0.0777201
$845$	1.52504	+	2.64145i	0.0524631	+	0.0908688i
$846$	5.80730	+	10.0585i	0.199659	+	0.345820i
$847$	−14.6302	+	4.25823i	−0.502700	+	0.146315i
$848$		−	4.16049i		−	0.142872i
$849$	−23.1726	−	40.1362i	−0.795283	−	1.37747i
$850$	−24.0899	−	13.9083i	−0.826277	−	0.477051i
$851$	42.3200	−	24.4335i	1.45071	−	0.837569i
$852$	6.23183	−	10.7939i	0.213499	−	0.369791i
$853$	−35.0022	−	20.2085i	−1.19845	−	0.691926i	−0.238241	−	0.971206i	$-0.576571\pi$
$853$	−35.0022	−	20.2085i	−1.19845	−	0.691926i	−0.960210	+	0.279280i	$0.909904\pi$
$854$	3.37578			0.115517
$855$	−0.837890	+	1.75117i	−0.0286553	+	0.0598886i
$856$	−18.7197			−0.639828
$857$	29.0044	−	50.2370i	0.990770	−	1.71606i	0.377994	−	0.925808i	$-0.376614\pi$
$857$	29.0044	−	50.2370i	0.990770	−	1.71606i	0.612776	−	0.790256i	$-0.290053\pi$
$858$	−6.15999	−	14.4321i	−0.210299	−	0.492704i
$859$	−7.89116	−	13.6679i	−0.269243	−	0.466342i	0.699424	−	0.714707i	$-0.253440\pi$
$859$	−7.89116	−	13.6679i	−0.269243	−	0.466342i	−0.968667	+	0.248365i	$0.920107\pi$
$860$	3.97007	+	2.29212i	0.135378	+	0.0781607i
$861$	6.47370	+	11.2128i	0.220623	+	0.382130i
$862$	−22.2381			−0.757432
$863$			31.7531i			1.08089i	0.841380	+	0.540445i	$0.181744\pi$
$863$			31.7531i			1.08089i	−0.841380	+	0.540445i	$0.818256\pi$
$864$	3.33008	−	1.92262i	0.113292	−	0.0654090i
$865$	−0.0928381	−	0.160800i	−0.00315659	−	0.00546737i
$866$		−	1.88207i		−	0.0639555i
$867$		−	32.5631i		−	1.10590i
$868$	4.80099	+	8.31556i	0.162956	+	0.282249i
$869$	26.3763	−	11.2581i	0.894753	−	0.381903i
$870$	−5.49190	+	3.17075i	−0.186193	+	0.107499i
$871$	17.3523	+	10.0183i	0.587960	+	0.339459i
$872$	0.0596970	−	0.103398i	0.00202159	−	0.00350150i
$873$			16.7886i			0.568206i
$874$	−8.44209	+	17.6437i	−0.285558	+	0.596808i
$875$		−	5.51036i		−	0.186284i
$876$	−9.06115	+	15.6944i	−0.306148	+	0.530264i
$877$	22.4242	−	38.8399i	0.757212	−	1.31153i	−0.187055	−	0.982350i	$-0.559894\pi$
$877$	22.4242	−	38.8399i	0.757212	−	1.31153i	0.944267	−	0.329181i	$-0.106773\pi$
$878$	18.9100	+	32.7530i	0.638181	+	1.10536i
$879$	−7.84117	−	4.52710i	−0.264476	−	0.152695i
$880$	−0.160812	+	1.33161i	−0.00542098	+	0.0448887i
$881$	11.6579			0.392765			0.196383	−	0.980527i	$-0.437080\pi$
$881$	11.6579			0.392765			0.196383	+	0.980527i	$0.437080\pi$
$882$	−5.59572			−0.188418
$883$	−17.6335	−	30.5421i	−0.593414	−	1.02782i	−0.993769	−	0.111463i	$-0.964446\pi$
$883$	−17.6335	−	30.5421i	−0.593414	−	1.02782i	0.400354	−	0.916360i	$-0.368887\pi$
$884$	11.6366	−	6.71838i	0.391380	−	0.225964i
$885$	−1.83633			−0.0617275
$886$	13.0820			0.439498
$887$	2.18760	+	3.78904i	0.0734525	+	0.127224i	0.900412	−	0.435038i	$-0.143265\pi$
$887$	2.18760	+	3.78904i	0.0734525	+	0.127224i	−0.826960	+	0.562261i	$0.809932\pi$
$888$	−11.0272	+	19.0997i	−0.370049	+	0.640944i
$889$	14.1114	−	8.14720i	0.473280	−	0.273248i
$890$	5.03292	+	2.90576i	0.168704	+	0.0974013i
$891$	−33.8318	+	14.4403i	−1.13341	+	0.483768i
$892$		−	26.0973i		−	0.873804i
$893$	−45.8344	+	3.55092i	−1.53379	+	0.118827i
$894$	7.17772			0.240059
$895$	−6.46902	−	3.73489i	−0.216235	−	0.124844i
$896$	−1.19963	−	0.692605i	−0.0400767	−	0.0231383i
$897$	18.3859	−	10.6151i	0.613886	−	0.354428i
$898$	26.2561	+	15.1590i	0.876179	+	0.505862i
$899$	−46.4819	+	26.8363i	−1.55026	+	0.895042i
$900$	5.32619			0.177540
$901$	−23.9289			−0.797187
$902$	−1.83528	+	15.1971i	−0.0611080	+	0.506008i
$903$	27.5389	−	15.8996i	0.916438	−	0.529106i
$904$			1.58084i			0.0525779i
$905$			0.643320i			0.0213847i
$906$	−25.1481	+	14.5193i	−0.835491	+	0.482371i
$907$	4.89800	+	2.82786i	0.162635	+	0.0938975i	0.579109	−	0.815250i	$-0.303401\pi$
$907$	4.89800	+	2.82786i	0.162635	+	0.0938975i	−0.416473	+	0.909148i	$0.636734\pi$
$908$	−10.4690	−	18.1329i	−0.347427	−	0.601761i
$909$	2.82849	+	1.63303i	0.0938151	+	0.0541642i
$910$	1.13341	+	0.654377i	0.0375723	+	0.0216924i
$911$			12.8640i			0.426202i	0.977030	+	0.213101i	$0.0683564\pi$
$911$			12.8640i			0.426202i	−0.977030	+	0.213101i	$0.931644\pi$
$912$	−0.681845	−	8.80108i	−0.0225781	−	0.291433i
$913$	−1.67529	+	2.23242i	−0.0554440	+	0.0738822i
$914$	−11.3312	−	6.54207i	−0.374802	−	0.216392i
$915$	−0.997960	+	1.72852i	−0.0329915	+	0.0571430i
$916$	8.06341	+	13.9662i	0.266423	+	0.461458i
$917$	−11.2838	+	19.5442i	−0.372625	+	0.645406i
$918$	−11.0579	−	19.1528i	−0.364965	−	0.632137i
$919$			21.0002i			0.692732i	0.938099	+	0.346366i	$0.112584\pi$
$919$			21.0002i			0.692732i	−0.938099	+	0.346366i	$0.887416\pi$
$920$	−1.81470			−0.0598288
$921$	30.1559	−	17.4105i	0.993671	−	0.573696i
$922$	1.37713	−	0.795087i	0.0453534	−	0.0261848i
$923$		−	14.3782i		−	0.473263i
$924$	7.44165	+	5.58450i	0.244812	+	0.183717i
$925$	45.6136	−	26.3350i	1.49977	−	0.865890i
$926$	10.1505	−	17.5811i	0.333565	−	0.577752i
$927$	13.9057	−	8.02843i	0.456722	−	0.263688i
$928$	3.87149	−	6.70562i	0.127088	−	0.220123i
$929$	22.6122	−	39.1654i	0.741881	−	1.28497i	−0.209757	−	0.977753i	$-0.567267\pi$
$929$	22.6122	−	39.1654i	0.741881	−	1.28497i	0.951638	−	0.307222i	$-0.0993993\pi$
$930$	−5.67714			−0.186161
$931$	9.55954	−	19.9792i	0.313301	−	0.654791i
$932$		−	11.3034i		−	0.370256i
$933$	32.8815	+	18.9842i	1.07649	+	0.621514i
$934$	−5.92764	+	10.2670i	−0.193958	+	0.335946i
$935$	7.65872	+	0.924905i	0.250467	+	0.0302476i
$936$	−1.28640	+	2.22811i	−0.0420474	+	0.0728282i
$937$	−12.4120	+	7.16608i	−0.405483	+	0.234106i	−0.688847	−	0.724907i	$-0.741883\pi$
$937$	−12.4120	+	7.16608i	−0.405483	+	0.234106i	0.283364	+	0.959012i	$0.408549\pi$
$938$	−11.8802			−0.387903
$939$		−	7.81851i		−	0.255147i
$940$	−2.13260	−	3.69378i	−0.0695578	−	0.120478i
$941$	6.47291	+	11.2114i	0.211011	+	0.365481i	0.952031	−	0.306001i	$-0.0989912\pi$
$941$	6.47291	+	11.2114i	0.211011	+	0.365481i	−0.741020	+	0.671483i	$0.765658\pi$
$942$		−	1.17521i		−	0.0382903i
$943$	−20.7103			−0.674420
$944$	1.94176	−	1.12108i	0.0631990	−	0.0364880i
$945$	1.07705	−	1.86550i	0.0350364	−	0.0606848i
$946$	37.3245	+	4.50750i	1.21353	+	0.146551i
$947$	25.3923	−	43.9807i	0.825137	−	1.42918i	−0.0766769	−	0.997056i	$-0.524431\pi$
$947$	25.3923	−	43.9807i	0.825137	−	1.42918i	0.901814	−	0.432124i	$-0.142236\pi$
$948$	−15.1652	−	8.75563i	−0.492542	−	0.284370i
$949$			20.9060i			0.678638i
$950$	−9.09909	+	19.0168i	−0.295214	+	0.616988i
$951$	−42.8198			−1.38853
$952$	−3.98349	+	6.89961i	−0.129106	+	0.223617i
$953$	2.26365	−	3.92075i	0.0733267	−	0.127006i	−0.827031	−	0.562157i	$-0.809972\pi$
$953$	2.26365	−	3.92075i	0.0733267	−	0.127006i	0.900357	+	0.435151i	$0.143305\pi$
$954$	3.96794	−	2.29089i	0.128467	−	0.0741704i
$955$	0.723517	−	1.25317i	0.0234124	−	0.0405515i
$956$	−0.850528	+	0.491053i	−0.0275080	+	0.0158818i
$957$	−31.2160	+	41.5970i	−1.00907	+	1.34464i
$958$		−	35.2034i		−	1.13737i
$959$	−8.51761	+	4.91764i	−0.275048	+	0.158799i
$960$	0.709276	−	0.409500i	0.0228918	−	0.0132166i
$961$	−17.0497			−0.549990
$962$			25.4421i			0.820287i
$963$	−10.3077	−	17.8534i	−0.332160	−	0.575318i
$964$	1.96202	−	3.39831i	0.0631923	−	0.109452i
$965$	−3.04038	−	5.26609i	−0.0978732	−	0.169521i
$966$	−6.29394	+	10.9014i	−0.202504	+	0.350748i
$967$	41.4064	+	23.9060i	1.33154	+	0.768765i	0.985536	−	0.169467i	$-0.0542048\pi$
$967$	41.4064	+	23.9060i	1.33154	+	0.768765i	0.346005	+	0.938233i	$0.387538\pi$
$968$	3.07407	+	10.5617i	0.0988044	+	0.339467i
$969$	−50.6191	+	3.92160i	−1.62612	+	0.125980i
$970$		−	6.16522i		−	0.197953i
$971$	−29.2651	−	16.8962i	−0.939161	−	0.542225i	−0.0494637	−	0.998776i	$-0.515751\pi$
$971$	−29.2651	−	16.8962i	−0.939161	−	0.542225i	−0.889697	+	0.456551i	$0.849085\pi$
$972$	9.46158	+	5.46265i	0.303480	+	0.175214i
$973$	10.5376	+	18.2517i	0.337820	+	0.585122i
$974$	−2.19604	−	1.26788i	−0.0703656	−	0.0406256i
$975$	19.8168	−	11.4412i	0.634644	−	0.366412i
$976$		−	2.43702i		−	0.0780071i
$977$		−	41.9876i		−	1.34330i	−0.740867	−	0.671652i	$-0.765585\pi$
$977$		−	41.9876i		−	1.34330i	0.740867	−	0.671652i	$-0.234415\pi$
$978$	−30.1021	+	17.3794i	−0.962558	+	0.555733i
$979$	47.3169	+	5.71423i	1.51226	+	0.182628i
$980$	2.05490			0.0656415
$981$	0.131484			0.00419795
$982$	30.1668	−	17.4168i	0.962661	−	0.555792i
$983$	−19.7456	−	11.4001i	−0.629786	−	0.363607i	0.150883	−	0.988552i	$-0.451788\pi$
$983$	−19.7456	−	11.4001i	−0.629786	−	0.363607i	−0.780669	+	0.624945i	$0.785122\pi$
$984$	8.09463	−	4.67344i	0.258048	−	0.148984i
$985$	2.56541	+	1.48114i	0.0817406	+	0.0471930i
$986$	−38.5671	−	22.2667i	−1.22823	−	0.709116i
$987$	−29.5862			−0.941738
$988$	−5.75769	−	8.39946i	−0.183177	−	0.267222i
$989$			50.8652i			1.61742i
$990$	−1.35853	+	0.579857i	−0.0431770	+	0.0184290i
$991$	16.4206	+	9.48042i	0.521616	+	0.301155i	0.737596	−	0.675243i	$-0.235961\pi$
$991$	16.4206	+	9.48042i	0.521616	+	0.301155i	−0.215979	+	0.976398i	$0.569294\pi$
$992$	6.00310	−	3.46589i	0.190599	−	0.110042i
$993$	2.83200	−	4.90516i	0.0898707	−	0.155661i
$994$	4.26258	+	7.38301i	0.135201	+	0.234175i
$995$	−3.99967			−0.126798
$996$	1.70427			0.0540019
$997$	0.671992	−	0.387975i	0.0212822	−	0.0122873i	−0.489321	−	0.872104i	$-0.662755\pi$
$997$	0.671992	−	0.387975i	0.0212822	−	0.0122873i	0.510603	+	0.859816i	$0.329422\pi$
$998$	−3.64732	−	6.31734i	−0.115454	−	0.199972i
$999$	41.8756			1.32489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.a.65.3	✓	20
11.10	odd	2		418.2.h.b.65.3	yes	20
19.12	odd	6		418.2.h.b.373.3	yes	20
209.164	even	6	inner	418.2.h.a.373.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.3	✓	20	1.1	even	1	trivial
418.2.h.a.373.3	yes	20	209.164	even	6	inner
418.2.h.b.65.3	yes	20	11.10	odd	2
418.2.h.b.373.3	yes	20	19.12	odd	6

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.75384 - 1.01258i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.202207 + 0.350232i) q^{5} +(1.75384 - 1.01258i) q^{6} +1.38521i q^{7} +1.00000 q^{8} +(0.550630 + 0.953720i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.75384 - 1.01258i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.202207 + 0.350232i) q^{5} +(1.75384 - 1.01258i) q^{6} +1.38521i q^{7} +1.00000 q^{8} +(0.550630 + 0.953720i) q^{9} +(-0.202207 - 0.350232i) q^{10} +(-2.65274 - 1.99072i) q^{11} +2.02516i q^{12} +(1.16812 + 2.02324i) q^{13} +(-1.19963 - 0.692605i) q^{14} +(0.709276 - 0.409500i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.98091 + 2.87573i) q^{17} -1.10126 q^{18} +(1.88136 - 3.93198i) q^{19} +0.404414 q^{20} +(1.40263 - 2.42943i) q^{21} +(3.05038 - 1.30198i) q^{22} +(2.24362 + 3.88606i) q^{23} +(-1.75384 - 1.01258i) q^{24} +(2.41822 + 4.18849i) q^{25} -2.33624 q^{26} +3.84525i q^{27} +(1.19963 - 0.692605i) q^{28} +(3.87149 + 6.70562i) q^{29} +0.819001i q^{30} +6.93179i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.63672 + 6.17751i) q^{33} +(-4.98091 + 2.87573i) q^{34} +(-0.485145 - 0.280099i) q^{35} +(0.550630 - 0.953720i) q^{36} -10.8902i q^{37} +(2.46452 + 3.59530i) q^{38} -4.73124i q^{39} +(-0.202207 + 0.350232i) q^{40} +(-2.30769 + 3.99704i) q^{41} +(1.40263 + 2.42943i) q^{42} +(9.81686 + 5.66777i) q^{43} +(-0.397643 + 3.29270i) q^{44} -0.445365 q^{45} -4.48723 q^{46} +(-5.27332 - 9.13366i) q^{47} +(1.75384 - 1.01258i) q^{48} +5.08119 q^{49} -4.83645 q^{50} +(-5.82380 - 10.0871i) q^{51} +(1.16812 - 2.02324i) q^{52} +(-3.60309 + 2.08025i) q^{53} +(-3.33008 - 1.92262i) q^{54} +(1.23362 - 0.526539i) q^{55} +1.38521i q^{56} +(-7.28104 + 4.99104i) q^{57} -7.74298 q^{58} +(-1.94176 - 1.12108i) q^{59} +(-0.709276 - 0.409500i) q^{60} +(-2.11052 + 1.21851i) q^{61} +(-6.00310 - 3.46589i) q^{62} +(-1.32110 + 0.762739i) q^{63} +1.00000 q^{64} -0.944805 q^{65} +(-6.66824 - 0.805290i) q^{66} +(7.42746 - 4.28824i) q^{67} -5.75146i q^{68} -9.08735i q^{69} +(0.485145 - 0.280099i) q^{70} +(-5.32989 - 3.07721i) q^{71} +(0.550630 + 0.953720i) q^{72} +(7.74970 + 4.47429i) q^{73} +(9.43122 + 5.44512i) q^{74} -9.79457i q^{75} +(-4.34588 + 0.336688i) q^{76} +(2.75756 - 3.67460i) q^{77} +(4.09738 + 2.36562i) q^{78} +(-4.32343 + 7.48840i) q^{79} +(-0.202207 - 0.350232i) q^{80} +(5.54550 - 9.60509i) q^{81} +(-2.30769 - 3.99704i) q^{82} -0.841550i q^{83} -2.80527 q^{84} +(-2.01435 + 1.16298i) q^{85} +(-9.81686 + 5.66777i) q^{86} -15.6807i q^{87} +(-2.65274 - 1.99072i) q^{88} +(-12.4450 + 7.18512i) q^{89} +(0.222682 - 0.385697i) q^{90} +(-2.80261 + 1.61809i) q^{91} +(2.24362 - 3.88606i) q^{92} +(7.01898 - 12.1572i) q^{93} +10.5466 q^{94} +(0.996684 + 1.45399i) q^{95} +2.02516i q^{96} +(13.2024 + 7.62242i) q^{97} +(-2.54060 + 4.40044i) q^{98} +(0.437909 - 3.62612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} - 3 q^{6} + 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q - 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 - 3 * q^6 + 20 * q^8 + 11 * q^9	\( 20 q - 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} - 3 q^{6} + 20 q^{8} + 11 q^{9} + 2 q^{10} + q^{11} - 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} - 6 q^{17} - 22 q^{18} + 18 q^{19} - 4 q^{20} + 14 q^{21} + q^{22} - 4 q^{23} + 3 q^{24} - 20 q^{25} + 10 q^{26} + 6 q^{28} - 5 q^{29} - 10 q^{32} - 8 q^{33} + 6 q^{34} + 12 q^{35} + 11 q^{36} - 12 q^{38} + 2 q^{40} + q^{41} + 14 q^{42} - 3 q^{43} - 2 q^{44} + 12 q^{45} + 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} + 40 q^{50} + 12 q^{51} - 5 q^{52} - 24 q^{53} - 27 q^{54} - 20 q^{55} - 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} - 27 q^{61} - 12 q^{63} + 20 q^{64} + 8 q^{65} + 13 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} + 11 q^{72} + 9 q^{73} + 12 q^{74} - 6 q^{76} - 22 q^{77} + 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} - 28 q^{84} + 12 q^{85} + 3 q^{86} + q^{88} + 21 q^{89} - 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} - 2 q^{94} + 24 q^{95} + 24 q^{97} - 4 q^{98} + 21 q^{99}+O(q^{100}) \) 20 * q - 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 - 3 * q^6 + 20 * q^8 + 11 * q^9 + 2 * q^10 + q^11 - 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 - 6 * q^17 - 22 * q^18 + 18 * q^19 - 4 * q^20 + 14 * q^21 + q^22 - 4 * q^23 + 3 * q^24 - 20 * q^25 + 10 * q^26 + 6 * q^28 - 5 * q^29 - 10 * q^32 - 8 * q^33 + 6 * q^34 + 12 * q^35 + 11 * q^36 - 12 * q^38 + 2 * q^40 + q^41 + 14 * q^42 - 3 * q^43 - 2 * q^44 + 12 * q^45 + 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 + 40 * q^50 + 12 * q^51 - 5 * q^52 - 24 * q^53 - 27 * q^54 - 20 * q^55 - 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 - 27 * q^61 - 12 * q^63 + 20 * q^64 + 8 * q^65 + 13 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 + 11 * q^72 + 9 * q^73 + 12 * q^74 - 6 * q^76 - 22 * q^77 + 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 - 28 * q^84 + 12 * q^85 + 3 * q^86 + q^88 + 21 * q^89 - 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 - 2 * q^94 + 24 * q^95 + 24 * q^97 - 4 * q^98 + 21 * q^99

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