LMFDB - Embedded newform 418.2.h.b.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.b.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} +(0.397643 + 3.29270i) 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} +(6.66824 - 0.805290i) 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} +(3.05038 + 1.30198i) 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} +(-0.160812 - 1.33161i) 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} +(2.63672 - 6.17751i) 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} +(-3.35927 - 1.43382i) 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} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 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} + 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} - 2 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} - 8 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} + 3 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 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * 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 + 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 - 2 * 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 - 8 * 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 + 3 * 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	$-0.915690\pi$
$7$		−	1.38521i		−	0.523560i	0.965128	−	0.261780i	$-0.0843095\pi$
$8$	−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	0.657327	−	0.753605i	$-0.271687\pi$
$13$	−1.16812	−	2.02324i	−0.323978	−	0.561146i	−0.981305	+	0.192460i	$0.938354\pi$
$14$	−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	−0.245715	−	0.969342i	$-0.579023\pi$
$17$	−4.98091	−	2.87573i	−1.20805	−	0.697467i	−0.962333	+	0.271875i	$0.912356\pi$
$18$	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
$22$	0.397643	+	3.29270i	0.0847778	+	0.702006i
$23$	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	$-0.911305\pi$
$29$	−3.87149	−	6.70562i	−0.718917	−	1.24520i	0.242512	−	0.970149i	$-0.422029\pi$
$30$		−	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
$33$	6.66824	−	0.805290i	1.16079	−	0.140183i
$34$	−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	−0.627626	−	0.778515i	$-0.715973\pi$
$41$	2.30769	−	3.99704i	0.360401	−	0.624233i	0.988027	+	0.154282i	$0.0493065\pi$
$42$	1.40263	+	2.42943i	0.216431	+	0.374870i
$43$	−9.81686	−	5.66777i	−1.49706	−	0.864327i	−0.497063	−	0.867714i	$-0.665588\pi$
$43$	−9.81686	−	5.66777i	−1.49706	−	0.864327i	−0.999994	+	0.00338756i	$0.998922\pi$
$44$	3.05038	+	1.30198i	0.459863	+	0.196281i
$45$	−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
$55$	−0.160812	−	1.33161i	−0.0216839	−	0.179555i
$56$			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	−0.358765	−	0.933428i	$-0.616802\pi$
$61$	2.11052	−	1.21851i	0.270224	−	0.156014i	0.628990	+	0.777414i	$0.283469\pi$
$62$	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
$66$	2.63672	−	6.17751i	0.324557	−	0.760399i
$67$	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	−0.0275586	−	0.999620i	$-0.508773\pi$
$73$	−7.74970	−	4.47429i	−0.907034	−	0.523677i	−0.879476	+	0.475944i	$0.842107\pi$
$74$	−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	−0.513454	−	0.858117i	$-0.671634\pi$
$79$	4.32343	−	7.48840i	0.486424	−	0.842511i	0.999878	+	0.0156059i	$0.00496771\pi$
$80$	−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	$0.0147067\pi$
$83$			0.841550i			0.0923721i	−0.998933	+	0.0461861i	$0.985293\pi$
$84$	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
$99$	−3.35927	−	1.43382i	−0.337619	−	0.144104i
$100$	2.41822	−	4.18849i	0.241822	−	0.418849i
$101$	−2.56841	+	1.48287i	−0.255567	+	0.147551i	−0.622310	−	0.782771i	$-0.713806\pi$
$101$	−2.56841	+	1.48287i	−0.255567	+	0.147551i	0.366744	+	0.930322i	$0.380473\pi$
$102$	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	$-0.139980\pi$
$107$	18.7197			1.80971			0.904853	+	0.425724i	$0.139980\pi$
$108$	3.33008	−	1.92262i	0.320437	−	0.185004i
$109$	−0.0596970	+	0.103398i	−0.00571793	+	0.00990375i	−0.868870	−	0.495040i	$-0.835153\pi$
$109$	−0.0596970	+	0.103398i	−0.00571793	+	0.00990375i	0.863152	+	0.504944i	$0.168487\pi$
$110$	−1.23362	−	0.526539i	−0.117621	−	0.0502035i
$111$	−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	$0.00811146\pi$
$127$	5.88156	+	10.1872i	0.521904	+	0.903964i	−0.477771	+	0.878484i	$0.658555\pi$
$128$	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	−0.265128	−	0.964213i	$-0.585414\pi$
$131$	−14.1092	−	8.14594i	−1.23273	−	0.711714i	−0.967597	+	0.252499i	$0.918748\pi$
$132$	−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	−0.940783	−	0.339010i	$-0.889908\pi$
$139$	−13.1761	+	7.60723i	−1.11758	+	0.645237i	−0.176800	+	0.984247i	$0.556575\pi$
$140$		−	0.560198i		−	0.0473453i
$141$			21.3586i			1.79872i
$142$	−5.32989	+	3.07721i	−0.447274	+	0.258234i
$143$	7.12641	+	3.04173i	0.595941	+	0.254363i
$144$	−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	0.368974	−	0.929440i	$-0.379709\pi$
$149$	−3.06944	−	1.77214i	−0.251458	−	0.145179i	−0.620432	+	0.784260i	$0.713043\pi$
$150$	−8.48235	−	4.89728i	−0.692581	−	0.399862i
$151$	14.3389			1.16689			0.583443	−	0.812154i	$-0.301705\pi$
$151$	14.3389			1.16689			0.583443	+	0.812154i	$0.301705\pi$
$152$	1.88136	−	3.93198i	0.152598	−	0.318926i
$153$		−	6.33385i		−	0.512062i
$154$	4.56108	−	0.550819i	0.367542	−	0.0443863i
$155$	−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
$165$	−1.06632	+	2.49827i	−0.0830132	+	0.194490i
$166$	0.728804	+	0.420775i	0.0565662	+	0.0326585i
$167$	−2.67147	−	4.62713i	−0.206725	−	0.358058i	0.743956	−	0.668229i	$-0.232947\pi$
$167$	−2.67147	−	4.62713i	−0.206725	−	0.358058i	−0.950681	+	0.310171i	$0.899614\pi$
$168$	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	−0.857167	−	0.515039i	$-0.827777\pi$
$173$	0.229562	−	0.397614i	0.0174533	−	0.0302300i	0.874620	+	0.484809i	$0.161111\pi$
$174$	13.5799	+	7.84037i	1.02949	+	0.594377i
$175$	5.80194	−	3.34975i	0.438585	−	0.253217i
$176$	−0.397643	−	3.29270i	−0.0299735	−	0.248197i
$177$	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
$187$	18.9378	−	2.28703i	1.38487	−	0.167244i
$188$	−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	$-0.651320\pi$
$193$	7.51799	−	13.0215i	0.541157	−	0.937311i	0.998838	−	0.0481949i	$-0.0153469\pi$
$194$	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	$0.0840317\pi$
$197$			7.32487i			0.521875i	−0.965356	+	0.260938i	$0.915968\pi$
$198$	−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
$209$	−2.83672	−	14.1758i	−0.196220	−	0.980560i
$210$	−1.13449			−0.0782871
$211$	−1.12895	+	1.95540i	−0.0777201	+	0.134615i	−0.902266	−	0.431180i	$-0.858097\pi$
$211$	−1.12895	+	1.95540i	−0.0777201	+	0.134615i	0.824546	+	0.565795i	$0.191431\pi$
$212$	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	$-0.744531\pi$
$227$	−20.9381			−1.38971			−0.694854	+	0.719151i	$0.744531\pi$
$228$	−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
$231$	−1.11550	−	9.23691i	−0.0733942	−	0.607744i
$232$	3.87149	+	6.70562i	0.254176	+	0.440245i
$233$	−9.78906	−	5.65172i	−0.641303	−	0.370256i	0.143814	−	0.989605i	$-0.454063\pi$
$233$	−9.78906	−	5.65172i	−0.641303	−	0.370256i	−0.785116	+	0.619349i	$0.787397\pi$
$234$	−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	$0.0101124\pi$
$239$			0.982105i			0.0635271i	−0.999495	+	0.0317636i	$0.989888\pi$
$240$			0.819001i			0.0528663i
$241$	−1.96202	−	3.39831i	−0.126385	−	0.218905i	0.795889	−	0.605443i	$-0.207004\pi$
$241$	−1.96202	−	3.39831i	−0.126385	−	0.218905i	−0.922273	+	0.386538i	$0.873671\pi$
$242$	−7.60969	−	7.94309i	−0.489169	−	0.510601i
$243$	−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
$253$	−13.6878	−	5.84229i	−0.860543	−	0.367302i
$254$	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	0.263040	−	0.964785i	$-0.415275\pi$
$263$	−7.15130	−	4.12881i	−0.440968	−	0.254593i	−0.704008	+	0.710192i	$0.748608\pi$
$264$	−6.66824	+	0.805290i	−0.410402	+	0.0495622i
$265$		−	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	0.214276	−	0.976773i	$-0.431261\pi$
$271$	−8.63431	−	4.98502i	−0.524497	−	0.302819i	−0.738773	+	0.673955i	$0.764594\pi$
$272$	4.98091	−	2.87573i	0.302012	−	0.174367i
$273$	6.55376			0.396652
$274$	7.10021			0.428939
$275$	−14.7530	−	6.29697i	−0.889641	−	0.379721i
$276$	−7.86987	+	4.54367i	−0.473711	+	0.273497i
$277$			21.8927i			1.31541i	0.753277	+	0.657703i	$0.228472\pi$
$277$			21.8927i			1.31541i	−0.753277	+	0.657703i	$0.771528\pi$
$278$			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	$0.0816602\pi$
$281$	11.7908	+	20.4223i	0.703380	+	1.21829i	−0.263893	+	0.964552i	$0.585006\pi$
$282$	18.4971	+	10.6793i	1.10149	+	0.635943i
$283$	−19.8188	−	11.4424i	−1.17811	−	0.680179i	−0.222530	−	0.974926i	$-0.571431\pi$
$283$	−19.8188	−	11.4424i	−1.17811	−	0.680179i	−0.955575	+	0.294747i	$0.904765\pi$
$284$			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	$-0.541689\pi$
$293$	−4.47087			−0.261191			−0.130595	+	0.991436i	$0.541689\pi$
$294$	−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	−0.509279	−	0.860602i	$-0.670088\pi$
$307$	8.59712	−	14.8906i	0.490663	−	0.849854i	0.999942	+	0.0107475i	$0.00342111\pi$
$308$	1.80352	−	4.22542i	0.102765	−	0.240766i
$309$	−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
$319$	23.6191	+	10.0812i	1.32241	+	0.564440i
$320$	−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	−0.531629	−	0.846977i	$-0.678420\pi$
$337$	8.58563	−	14.8708i	0.467689	−	0.810062i	0.999318	+	0.0369157i	$0.0117533\pi$
$338$	−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	0.600931	−	0.799301i	$-0.294797\pi$
$347$	3.89661	+	2.24971i	0.209181	+	0.120771i	−0.391750	+	0.920072i	$0.628130\pi$
$348$	13.5799	−	7.84037i	0.727960	−	0.420288i
$349$			25.6849i			1.37488i	0.726240	+	0.687441i	$0.241266\pi$
$349$			25.6849i			1.37488i	−0.726240	+	0.687441i	$0.758734\pi$
$350$		−	6.69950i		−	0.358103i
$351$	7.77985	−	4.49170i	0.415258	−	0.239749i
$352$	−3.05038	−	1.30198i	−0.162586	−	0.0693958i
$353$	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	0.887028	−	0.461715i	$-0.152766\pi$
$359$	17.6340	+	10.1810i	0.930686	+	0.537332i	0.0436574	+	0.999047i	$0.486099\pi$
$360$	0.445365			0.0234728
$361$	−11.9210	−	14.7949i	−0.627420	−	0.778681i
$362$		−	1.59075i		−	0.0836078i
$363$	−16.0860	+	15.4108i	−0.844296	+	0.808858i
$364$	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	$-0.0870345\pi$
$373$	37.1915			1.92570			0.962851	+	0.270033i	$0.0870345\pi$
$374$	7.48829	−	17.5442i	0.387210	−	0.907187i
$375$	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
$385$	−1.84456	+	0.222759i	−0.0940077	+	0.0113528i
$386$	−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
$396$	0.437909	+	3.62612i	0.0220057	+	0.182219i
$397$	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	$0.0676496\pi$
$409$	13.5787	+	23.5190i	0.671422	+	1.16294i	−0.306079	+	0.952006i	$0.599017\pi$
$410$	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
$418$	−13.6950	−	4.63122i	−0.669842	−	0.226521i
$419$	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	$-0.986758\pi$
$431$	−11.1190	−	19.2587i	−0.535586	−	0.927661i	0.463549	−	0.886071i	$-0.346576\pi$
$432$	−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	$0.524955\pi$
$439$	−18.9100	+	32.7530i	−0.902524	+	1.56322i	−0.824207	+	0.566289i	$0.808379\pi$
$440$	0.160812	+	1.33161i	0.00766643	+	0.0634822i
$441$	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
$451$	1.83528	+	15.1971i	0.0864198	+	0.715603i
$452$	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	$-0.901001\pi$
$457$		−	13.0841i		−	0.612050i	0.952023	−	0.306025i	$-0.0989991\pi$
$458$	−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	0.531727	−	0.846916i	$-0.321543\pi$
$461$	1.37713	+	0.795087i	0.0641393	+	0.0370309i	−0.467587	+	0.883947i	$0.654877\pi$
$462$	−8.55714	−	3.65241i	−0.398114	−	0.169925i
$463$	−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
$473$	37.3245	−	4.50750i	1.71618	−	0.207255i
$474$			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	0.399344	−	0.916801i	$-0.369238\pi$
$479$	30.4870	−	17.6017i	1.39299	−	0.804242i	0.993645	+	0.112559i	$0.0359047\pi$
$480$	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
$484$	−10.6838	+	2.61864i	−0.485625	+	0.119029i
$485$	−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	0.989811	−	0.142385i	$-0.0454772\pi$
$491$	30.1668	+	17.4168i	1.36141	+	0.786009i	0.371596	+	0.928394i	$0.378811\pi$
$492$	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	−0.768439	−	0.639923i	$-0.778966\pi$
$503$	−13.4222	+	7.74934i	−0.598468	+	0.345526i	0.169970	+	0.985449i	$0.445633\pi$
$504$	−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
$517$	32.1713	+	13.7315i	1.41489	+	0.603912i
$518$	−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	0.930991	−	0.365042i	$-0.118945\pi$
$523$	3.41574	+	5.91624i	0.149360	+	0.258699i	−0.781631	+	0.623741i	$0.785612\pi$
$524$			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
$528$	−2.63672	+	6.17751i	−0.114748	+	0.268841i
$529$	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	0.00295633	−	0.999996i	$-0.499059\pi$
$541$	20.2463	−	11.6892i	0.870456	−	0.502558i	0.867500	+	0.497438i	$0.165726\pi$
$542$	−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	0.616881	−	0.787056i	$-0.288396\pi$
$547$	−8.72771	−	15.1168i	−0.373170	−	0.646349i	−0.990051	+	0.140707i	$0.955063\pi$
$548$	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	−0.994777	−	0.102076i	$-0.967451\pi$
$557$	−33.1300	+	19.1276i	−1.40376	+	0.810464i	−0.408988	+	0.912540i	$0.634118\pi$
$558$			7.63370i			0.323160i
$559$			26.4825i			1.12009i
$560$	−0.485145	+	0.280099i	−0.0205011	+	0.0118363i
$561$	−35.5297	−	15.1650i	−1.50006	−	0.640265i
$562$	23.5816			0.994730
$563$	−18.5879			−0.783388			−0.391694	−	0.920096i	$-0.628111\pi$
$563$	−18.5879			−0.783388			−0.391694	+	0.920096i	$0.628111\pi$
$564$	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	$-0.620182\pi$
$569$	−17.5877			−0.737313			−0.368656	+	0.929566i	$0.620182\pi$
$570$	3.22030	+	1.54083i	0.134883	+	0.0645384i
$571$			4.34134i			0.181680i	0.995866	+	0.0908398i	$0.0289551\pi$
$571$			4.34134i			0.181680i	−0.995866	+	0.0908398i	$0.971045\pi$
$572$	−0.928988	−	7.69252i	−0.0388429	−	0.321641i
$573$	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
$583$	5.41688	−	12.6911i	0.224344	−	0.525612i
$584$	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	−0.863631	−	0.504124i	$-0.831815\pi$
$593$	−20.9147	+	12.0751i	−0.858862	+	0.495864i	0.00476879	+	0.999989i	$0.498482\pi$
$594$	−12.6612	+	1.52904i	−0.519497	+	0.0627371i
$595$	−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	$-0.645911\pi$
$601$	−21.6964			−0.885013			−0.442506	+	0.896765i	$0.645911\pi$
$602$	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
$605$	3.07746	+	3.21229i	0.125117	+	0.130598i
$606$	3.00305	−	5.20144i	0.121991	−	0.211294i
$607$	8.28171			0.336144			0.168072	−	0.985775i	$-0.446246\pi$
$607$	8.28171			0.336144			0.168072	+	0.985775i	$0.446246\pi$
$608$	−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	0.986098	−	0.166162i	$-0.0531376\pi$
$613$	33.0592	+	19.0867i	1.33525	+	0.770905i	0.349148	+	0.937067i	$0.386471\pi$
$614$	−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
$627$	−9.37895	+	27.7344i	−0.374559	+	1.10761i
$628$	−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
$649$	7.38275	−	0.891578i	0.289798	−	0.0349975i
$650$	−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	0.654018	−	0.756479i	$-0.273082\pi$
$659$	−8.42320	−	14.5894i	−0.328121	−	0.568323i	−0.982139	+	0.188156i	$0.939749\pi$
$660$	2.69672	−	0.325670i	0.104970	−	0.0126767i
$661$	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
$671$	−3.17295	+	7.43384i	−0.122490	+	0.286980i
$672$	−2.80527			−0.108216
$673$	−30.6912			−1.18306			−0.591530	−	0.806283i	$-0.701476\pi$
$673$	−30.6912			−1.18306			−0.591530	+	0.806283i	$0.701476\pi$
$674$	−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	$-0.424846\pi$
$677$	12.1726			0.467830			0.233915	+	0.972257i	$0.424846\pi$
$678$	−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
$682$	−22.8243	+	2.75638i	−0.873988	+	0.105547i
$683$		−	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
$693$	−1.98614	+	4.65329i	−0.0754473	+	0.176764i
$694$	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	0.776784	−	0.629767i	$-0.216849\pi$
$701$	16.4096	+	9.47410i	0.619783	+	0.357832i	−0.157002	+	0.987598i	$0.550183\pi$
$702$		−	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
$726$	5.30316	+	21.6363i	0.196819	+	0.802998i
$727$	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	$-0.766922\pi$
$733$		−	36.1998i		−	1.33707i	0.743680	−	0.668535i	$-0.233078\pi$
$734$	22.3699			0.825689
$735$	3.60397	−	2.08075i	0.132934	−	0.0767497i
$736$	−2.24362	+	3.88606i	−0.0827008	+	0.143242i
$737$	−11.1664	+	26.1616i	−0.411321	+	0.963674i
$738$	2.54137	−	4.40178i	0.0935491	−	0.162032i
$739$	−16.7486	−	9.66982i	−0.616108	−	0.355710i	0.159244	−	0.987239i	$-0.449094\pi$
$739$	−16.7486	−	9.66982i	−0.616108	−	0.355710i	−0.775352	+	0.631529i	$0.782428\pi$
$740$		−	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	$-0.660691\pi$
$743$	14.0698	−	24.3695i	0.516170	−	0.894032i	0.999824	−	0.0187728i	$-0.00597591\pi$
$744$	−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	$-0.982445\pi$
$761$		−	3.04124i		−	0.110245i	0.998480	−	0.0551224i	$-0.0175549\pi$
$762$	−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	−0.234513	−	0.972113i	$-0.575350\pi$
$769$	13.5910	−	7.84678i	0.490105	−	0.282962i	0.724618	+	0.689151i	$0.242016\pi$
$770$	−0.729367	+	1.70882i	−0.0262846	+	0.0615815i
$771$	−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
$781$	20.2647	−	2.44726i	0.725127	−	0.0875700i
$782$	−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	$-0.755190\pi$
$787$	−40.3153			−1.43708			−0.718542	+	0.695483i	$0.755190\pi$
$788$	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
$792$	3.35927	+	1.43382i	0.119366	+	0.0509486i
$793$	−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
$803$	29.4650	−	3.55835i	1.03980	−	0.125571i
$804$	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	$0.251474\pi$
$809$			40.4103i			1.42075i	−0.703824	+	0.710375i	$0.748526\pi$
$810$	4.48535			0.157599
$811$	−8.21365	−	14.2265i	−0.288420	−	0.499558i	0.685013	−	0.728531i	$-0.259797\pi$
$811$	−8.21365	−	14.2265i	−0.288420	−	0.499558i	−0.973433	+	0.228973i	$0.926463\pi$
$812$	9.28869	+	5.36283i	0.325969	+	0.188198i
$813$	10.0955	+	17.4858i	0.354063	+	0.613255i
$814$	35.8583	−	4.33043i	1.25683	−	0.151781i
$815$	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	0.127435	−	0.991847i	$-0.459326\pi$
$821$	30.0891	−	17.3720i	1.05012	−	0.606285i	0.922682	+	0.385562i	$0.125992\pi$
$822$	−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	0.854636	−	0.519227i	$-0.173780\pi$
$827$	−0.642603	−	1.11302i	−0.0223455	−	0.0387036i	−0.876982	+	0.480523i	$0.840447\pi$
$828$	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
$836$	−10.8582	+	9.54457i	−0.375540	+	0.330106i
$837$	−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	0.960210	−	0.279280i	$-0.0900958\pi$
$853$	35.0022	+	20.2085i	1.19845	+	0.691926i	0.238241	+	0.971206i	$0.423429\pi$
$854$	−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	$0.623386\pi$
$857$	−29.0044	+	50.2370i	−0.990770	+	1.71606i	−0.612776	+	0.790256i	$0.709947\pi$
$858$	−15.5786	+	1.88135i	−0.531844	+	0.0642281i
$859$	−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
$869$	3.43837	+	28.4715i	0.116639	+	0.965831i
$870$	−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	$0.440106\pi$
$877$	−22.4242	+	38.8399i	−0.757212	+	1.31153i	−0.944267	+	0.329181i	$0.893227\pi$
$878$	18.9100	+	32.7530i	0.638181	+	1.10536i
$879$	7.84117	+	4.52710i	0.264476	+	0.152695i
$880$	1.23362	+	0.526539i	0.0415852	+	0.0177496i
$881$	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	0.826960	−	0.562261i	$-0.190068\pi$
$887$	−2.18760	−	3.78904i	−0.0734525	−	0.127224i	−0.900412	+	0.435038i	$0.856735\pi$
$888$	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
$891$	4.41026	+	36.5194i	0.147749	+	1.22344i
$892$		−	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
$902$	14.0787	+	6.00915i	0.468769	+	0.200083i
$903$	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	$-0.887416\pi$
$919$		−	21.0002i		−	0.692732i	0.938099	−	0.346366i	$-0.112584\pi$
$920$	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
$935$	−3.02837	+	7.09510i	−0.0990382	+	0.232034i
$936$	−1.28640	+	2.22811i	−0.0420474	+	0.0728282i
$937$	12.4120	−	7.16608i	0.405483	−	0.234106i	−0.283364	−	0.959012i	$-0.591451\pi$
$937$	12.4120	−	7.16608i	0.405483	−	0.234106i	0.688847	+	0.724907i	$0.258117\pi$
$938$	−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	0.741020	−	0.671483i	$-0.234342\pi$
$941$	−6.47291	−	11.2114i	−0.211011	−	0.365481i	−0.952031	+	0.306001i	$0.901009\pi$
$942$			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
$946$	14.7587	−	34.5777i	0.479845	−	1.12422i
$947$	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	−0.900357	−	0.435151i	$-0.856695\pi$
$953$	−2.26365	+	3.92075i	−0.0733267	+	0.127006i	0.827031	+	0.562157i	$0.190028\pi$
$954$	−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	−0.346005	−	0.938233i	$-0.612462\pi$
$967$	−41.4064	−	23.9060i	−1.33154	−	0.768765i	−0.985536	+	0.169467i	$0.945795\pi$
$968$	−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
$979$	18.7098	−	43.8348i	0.597967	−	1.40097i
$980$	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
$990$	−0.177096	−	1.46645i	−0.00562849	−	0.0466069i
$991$	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	−0.510603	−	0.859816i	$-0.670578\pi$
$997$	−0.671992	+	0.387975i	−0.0212822	+	0.0122873i	0.489321	+	0.872104i	$0.337245\pi$
$998$	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.b.65.3	yes	20
11.10	odd	2		418.2.h.a.65.3	✓	20
19.12	odd	6		418.2.h.a.373.3	yes	20
209.164	even	6	inner	418.2.h.b.373.3	yes	20

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
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} +(0.397643 + 3.29270i) 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} +(6.66824 - 0.805290i) 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} +(3.05038 + 1.30198i) 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} +(-0.160812 - 1.33161i) 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} +(2.63672 - 6.17751i) 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} +(-3.35927 - 1.43382i) 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	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 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 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * 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 + 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 - 2 * 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 - 8 * 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 + 3 * q^99

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