LMFDB - Embedded newform 385.2.i.c.331.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 17x^14 - 28x^13 + 127x^12 - 178x^11 + 612x^10 - 527x^9 + 1556x^8 - 1065x^7 + 2812x^6 - 1224x^5 + 2359x^4 - 1154x^3 + 1351x^2 - 333*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.4
Root			$0.420010 - 0.727479i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.c.221.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.420010 + 0.727479i) q^{2} +(0.864835 + 1.49794i) q^{3} +(0.647183 + 1.12095i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.45296 q^{6} +(-2.55075 + 0.702629i) q^{7} -2.76733 q^{8} +(0.00412044 - 0.00713681i) q^{9} +O(q^{10})$	\(q+(-0.420010 + 0.727479i) q^{2} +(0.864835 + 1.49794i) q^{3} +(0.647183 + 1.12095i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.45296 q^{6} +(-2.55075 + 0.702629i) q^{7} -2.76733 q^{8} +(0.00412044 - 0.00713681i) q^{9} +(-0.420010 - 0.727479i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.11941 + 1.93888i) q^{12} -2.36441 q^{13} +(0.560192 - 2.15073i) q^{14} -1.72967 q^{15} +(-0.132059 + 0.228733i) q^{16} +(1.34414 + 2.32812i) q^{17} +(0.00346125 + 0.00599506i) q^{18} +(0.425613 - 0.737183i) q^{19} -1.29437 q^{20} +(-3.25847 - 3.21320i) q^{21} -0.840020 q^{22} +(1.71679 - 2.97356i) q^{23} +(-2.39329 - 4.14529i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.993076 - 1.72006i) q^{26} +5.20326 q^{27} +(-2.43842 - 2.40454i) q^{28} +8.27268 q^{29} +(0.726479 - 1.25830i) q^{30} +(4.32030 + 7.48298i) q^{31} +(-2.87827 - 4.98530i) q^{32} +(-0.864835 + 1.49794i) q^{33} -2.25821 q^{34} +(0.666879 - 2.56033i) q^{35} +0.0106667 q^{36} +(-5.26933 + 9.12674i) q^{37} +(0.357523 + 0.619248i) q^{38} +(-2.04482 - 3.54174i) q^{39} +(1.38367 - 2.39658i) q^{40} -8.73162 q^{41} +(3.70613 - 1.02089i) q^{42} -2.48782 q^{43} +(-0.647183 + 1.12095i) q^{44} +(0.00412044 + 0.00713681i) q^{45} +(1.44214 + 2.49785i) q^{46} +(0.618485 - 1.07125i) q^{47} -0.456837 q^{48} +(6.01262 - 3.58446i) q^{49} +0.840020 q^{50} +(-2.32492 + 4.02688i) q^{51} +(-1.53021 - 2.65040i) q^{52} +(-0.793393 - 1.37420i) q^{53} +(-2.18542 + 3.78526i) q^{54} -1.00000 q^{55} +(7.05877 - 1.94441i) q^{56} +1.47234 q^{57} +(-3.47461 + 6.01820i) q^{58} +(0.859316 + 1.48838i) q^{59} +(-1.11941 - 1.93888i) q^{60} +(-5.78286 + 10.0162i) q^{61} -7.25827 q^{62} +(-0.00549567 + 0.0210993i) q^{63} +4.30736 q^{64} +(1.18220 - 2.04764i) q^{65} +(-0.726479 - 1.25830i) q^{66} +(-1.37035 - 2.37352i) q^{67} +(-1.73981 + 3.01344i) q^{68} +5.93895 q^{69} +(1.58249 + 1.56050i) q^{70} +9.43388 q^{71} +(-0.0114026 + 0.0197499i) q^{72} +(4.18884 + 7.25529i) q^{73} +(-4.42634 - 7.66665i) q^{74} +(0.864835 - 1.49794i) q^{75} +1.10180 q^{76} +(-1.88387 - 1.85770i) q^{77} +3.43539 q^{78} +(5.35807 - 9.28045i) q^{79} +(-0.132059 - 0.228733i) q^{80} +(4.48760 + 7.77276i) q^{81} +(3.66737 - 6.35206i) q^{82} +15.4516 q^{83} +(1.49303 - 5.73213i) q^{84} -2.68828 q^{85} +(1.04491 - 1.80984i) q^{86} +(7.15450 + 12.3920i) q^{87} +(-1.38367 - 2.39658i) q^{88} +(5.66472 - 9.81158i) q^{89} -0.00692250 q^{90} +(6.03101 - 1.66130i) q^{91} +4.44431 q^{92} +(-7.47269 + 12.9431i) q^{93} +(0.519540 + 0.899869i) q^{94} +(0.425613 + 0.737183i) q^{95} +(4.97845 - 8.62293i) q^{96} -0.868386 q^{97} +(0.0822551 + 5.87956i) q^{98} +0.00824088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.420010	+	0.727479i	−0.296992	+	0.514405i	−0.975446	−	0.220237i	$-0.929317\pi$
$2$	−0.420010	+	0.727479i	−0.296992	+	0.514405i	0.678454	+	0.734643i	$0.262650\pi$
$3$	0.864835	+	1.49794i	0.499313	+	0.864835i	1.00000		0.000793342i	$-0.000252529\pi$
$3$	0.864835	+	1.49794i	0.499313	+	0.864835i	−0.500687	+	0.865628i	$0.666919\pi$
$4$	0.647183	+	1.12095i	0.323592	+	0.560477i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.45296			−0.593167
$7$	−2.55075	+	0.702629i	−0.964092	+	0.265569i
$7$	−2.55075	+	0.702629i	−0.964092	+	0.265569i
$8$	−2.76733			−0.978400
$9$	0.00412044	−	0.00713681i	0.00137348	−	0.00237894i
$10$	−0.420010	−	0.727479i	−0.132819	−	0.230049i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.11941	+	1.93888i	−0.323147	+	0.559707i
$13$	−2.36441			−0.655769			−0.327885	−	0.944718i	$-0.606336\pi$
$13$	−2.36441			−0.655769			−0.327885	+	0.944718i	$0.606336\pi$
$14$	0.560192	−	2.15073i	0.149718	−	0.574806i
$15$	−1.72967			−0.446599
$16$	−0.132059	+	0.228733i	−0.0330148	+	0.0571832i
$17$	1.34414	+	2.32812i	0.326002	+	0.564652i	0.981715	−	0.190359i	$-0.0609651\pi$
$17$	1.34414	+	2.32812i	0.326002	+	0.564652i	−0.655713	+	0.755010i	$0.727632\pi$
$18$	0.00346125	+	0.00599506i	0.000815825	+	0.00141305i
$19$	0.425613	−	0.737183i	0.0976423	−	0.169121i	−0.813066	−	0.582171i	$-0.802203\pi$
$19$	0.425613	−	0.737183i	0.0976423	−	0.169121i	0.910708	+	0.413050i	$0.135537\pi$
$20$	−1.29437			−0.289429
$21$	−3.25847	−	3.21320i	−0.711057	−	0.701179i
$22$	−0.840020			−0.179093
$23$	1.71679	−	2.97356i	0.357975	−	0.620031i	−0.629647	−	0.776881i	$-0.716801\pi$
$23$	1.71679	−	2.97356i	0.357975	−	0.620031i	0.987622	+	0.156850i	$0.0501340\pi$
$24$	−2.39329	−	4.14529i	−0.488528	−	0.846155i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.993076	−	1.72006i	0.194758	−	0.337331i
$27$	5.20326			1.00137
$28$	−2.43842	−	2.40454i	−0.460817	−	0.454416i
$29$	8.27268			1.53620			0.768099	−	0.640331i	$-0.221203\pi$
$29$	8.27268			1.53620			0.768099	+	0.640331i	$0.221203\pi$
$30$	0.726479	−	1.25830i	0.132636	−	0.229733i
$31$	4.32030	+	7.48298i	0.775949	+	1.34398i	0.934260	+	0.356593i	$0.116062\pi$
$31$	4.32030	+	7.48298i	0.775949	+	1.34398i	−0.158311	+	0.987389i	$0.550605\pi$
$32$	−2.87827	−	4.98530i	−0.508810	−	0.881285i
$33$	−0.864835	+	1.49794i	−0.150548	+	0.260758i
$34$	−2.25821			−0.387280
$35$	0.666879	−	2.56033i	0.112723	−	0.432774i
$36$	0.0106667			0.00177779
$37$	−5.26933	+	9.12674i	−0.866272	+	1.50043i	−0.000493715		1.00000i	$0.500157\pi$
$37$	−5.26933	+	9.12674i	−0.866272	+	1.50043i	−0.865778	+	0.500428i	$0.833176\pi$
$38$	0.357523	+	0.619248i	0.0579979	+	0.100455i
$39$	−2.04482	−	3.54174i	−0.327434	−	0.567132i
$40$	1.38367	−	2.39658i	0.218777	−	0.378933i
$41$	−8.73162			−1.36365			−0.681825	−	0.731516i	$-0.738813\pi$
$41$	−8.73162			−1.36365			−0.681825	+	0.731516i	$0.738813\pi$
$42$	3.70613	−	1.02089i	0.571868	−	0.157527i
$43$	−2.48782			−0.379389			−0.189695	−	0.981843i	$-0.560750\pi$
$43$	−2.48782			−0.379389			−0.189695	+	0.981843i	$0.560750\pi$
$44$	−0.647183	+	1.12095i	−0.0975666	+	0.168990i
$45$	0.00412044	+	0.00713681i	0.000614239	+	0.00106389i
$46$	1.44214	+	2.49785i	0.212631	+	0.368288i
$47$	0.618485	−	1.07125i	0.0902153	−	0.156257i	−0.817386	−	0.576090i	$-0.804578\pi$
$47$	0.618485	−	1.07125i	0.0902153	−	0.156257i	0.907602	+	0.419832i	$0.137911\pi$
$48$	−0.456837			−0.0659388
$49$	6.01262	−	3.58446i	0.858946	−	0.512066i
$50$	0.840020			0.118797
$51$	−2.32492	+	4.02688i	−0.325554	+	0.563876i
$52$	−1.53021	−	2.65040i	−0.212201	−	0.367544i
$53$	−0.793393	−	1.37420i	−0.108981	−	0.188760i	0.806377	−	0.591402i	$-0.201425\pi$
$53$	−0.793393	−	1.37420i	−0.108981	−	0.188760i	−0.915358	+	0.402642i	$0.868092\pi$
$54$	−2.18542	+	3.78526i	−0.297398	+	0.515109i
$55$	−1.00000			−0.134840
$56$	7.05877	−	1.94441i	0.943268	−	0.259833i
$57$	1.47234			0.195016
$58$	−3.47461	+	6.01820i	−0.456238	+	0.790228i
$59$	0.859316	+	1.48838i	0.111873	+	0.193770i	0.916526	−	0.399976i	$-0.130982\pi$
$59$	0.859316	+	1.48838i	0.111873	+	0.193770i	−0.804652	+	0.593746i	$0.797648\pi$
$60$	−1.11941	−	1.93888i	−0.144516	−	0.250309i
$61$	−5.78286	+	10.0162i	−0.740419	+	1.28244i	0.211885	+	0.977295i	$0.432040\pi$
$61$	−5.78286	+	10.0162i	−0.740419	+	1.28244i	−0.952304	+	0.305150i	$0.901294\pi$
$62$	−7.25827			−0.921802
$63$	−0.00549567	+	0.0210993i	−0.000692389	+	0.00265827i
$64$	4.30736			0.538421
$65$	1.18220	−	2.04764i	0.146634	−	0.253978i
$66$	−0.726479	−	1.25830i	−0.0894233	−	0.154886i
$67$	−1.37035	−	2.37352i	−0.167415	−	0.289972i	0.770095	−	0.637929i	$-0.220209\pi$
$67$	−1.37035	−	2.37352i	−0.167415	−	0.289972i	−0.937510	+	0.347957i	$0.886875\pi$
$68$	−1.73981	+	3.01344i	−0.210983	+	0.365433i
$69$	5.93895			0.714966
$70$	1.58249	+	1.56050i	0.189143	+	0.186516i
$71$	9.43388			1.11960			0.559798	−	0.828629i	$-0.310879\pi$
$71$	9.43388			1.11960			0.559798	+	0.828629i	$0.310879\pi$
$72$	−0.0114026	+	0.0197499i	−0.00134381	+	0.00232755i
$73$	4.18884	+	7.25529i	0.490267	+	0.849167i	0.999937	−	0.0112027i	$-0.00356601\pi$
$73$	4.18884	+	7.25529i	0.490267	+	0.849167i	−0.509670	+	0.860370i	$0.670233\pi$
$74$	−4.42634	−	7.66665i	−0.514552	−	0.891230i
$75$	0.864835	−	1.49794i	0.0998626	−	0.172967i
$76$	1.10180			0.126385
$77$	−1.88387	−	1.85770i	−0.214687	−	0.211704i
$78$	3.43539			0.388981
$79$	5.35807	−	9.28045i	0.602830	−	1.04413i	−0.389560	−	0.921001i	$-0.627373\pi$
$79$	5.35807	−	9.28045i	0.602830	−	1.04413i	0.992390	−	0.123131i	$-0.0392937\pi$
$80$	−0.132059	−	0.228733i	−0.0147646	−	0.0255731i
$81$	4.48760	+	7.77276i	0.498623	+	0.863640i
$82$	3.66737	−	6.35206i	0.404993	−	0.701468i
$83$	15.4516			1.69603			0.848016	−	0.529971i	$-0.177797\pi$
$83$	15.4516			1.69603			0.848016	+	0.529971i	$0.177797\pi$
$84$	1.49303	−	5.73213i	0.162903	−	0.625427i
$85$	−2.68828			−0.291585
$86$	1.04491	−	1.80984i	0.112676	−	0.195160i
$87$	7.15450	+	12.3920i	0.767043	+	1.32856i
$88$	−1.38367	−	2.39658i	−0.147499	−	0.255476i
$89$	5.66472	−	9.81158i	0.600459	−	1.04002i	−0.392293	−	0.919840i	$-0.628318\pi$
$89$	5.66472	−	9.81158i	0.600459	−	1.04002i	0.992752	−	0.120185i	$-0.0383486\pi$
$90$	−0.00692250			−0.000729696
$91$	6.03101	−	1.66130i	0.632222	−	0.174152i
$92$	4.44431			0.463351
$93$	−7.47269	+	12.9431i	−0.774882	+	1.34214i
$94$	0.519540	+	0.899869i	0.0535864	+	0.0928144i
$95$	0.425613	+	0.737183i	0.0436669	+	0.0756334i
$96$	4.97845	−	8.62293i	0.508111	−	0.880074i
$97$	−0.868386			−0.0881712			−0.0440856	−	0.999028i	$-0.514037\pi$
$97$	−0.868386			−0.0881712			−0.0440856	+	0.999028i	$0.514037\pi$
$98$	0.0822551	+	5.87956i	0.00830902	+	0.593926i
$99$	0.00824088			0.000828239
$100$	0.647183	−	1.12095i	0.0647183	−	0.112095i
$101$	−3.08827	−	5.34905i	−0.307295	−	0.532250i	0.670475	−	0.741932i	$-0.266090\pi$
$101$	−3.08827	−	5.34905i	−0.307295	−	0.532250i	−0.977770	+	0.209682i	$0.932757\pi$
$102$	−1.95298	−	3.38266i	−0.193374	−	0.334933i
$103$	−8.57424	+	14.8510i	−0.844845	+	1.46331i	0.0409112	+	0.999163i	$0.486974\pi$
$103$	−8.57424	+	14.8510i	−0.844845	+	1.46331i	−0.885756	+	0.464151i	$0.846359\pi$
$104$	6.54311			0.641605
$105$	4.41195	−	1.21532i	0.430562	−	0.118603i
$106$	1.33293			0.129466
$107$	−0.0362443	+	0.0627770i	−0.00350387	+	0.00606888i	−0.867772	−	0.496962i	$-0.834449\pi$
$107$	−0.0362443	+	0.0627770i	−0.00350387	+	0.00606888i	0.864268	+	0.503031i	$0.167782\pi$
$108$	3.36747	+	5.83262i	0.324035	+	0.561244i
$109$	−6.99922	−	12.1230i	−0.670404	−	1.16117i	−0.977790	−	0.209589i	$-0.932788\pi$
$109$	−6.99922	−	12.1230i	−0.670404	−	1.16117i	0.307386	−	0.951585i	$-0.400546\pi$
$110$	0.420010	−	0.727479i	0.0400464	−	0.0693624i
$111$	−18.2284			−1.73016
$112$	0.176135	−	0.676228i	0.0166432	−	0.0638976i
$113$	19.2148			1.80758			0.903788	−	0.427980i	$-0.140775\pi$
$113$	19.2148			1.80758			0.903788	+	0.427980i	$0.140775\pi$
$114$	−0.618397	+	1.07110i	−0.0579182	+	0.100317i
$115$	1.71679	+	2.97356i	0.160091	+	0.277286i
$116$	5.35394	+	9.27330i	0.497101	+	0.861004i
$117$	−0.00974241	+	0.0168743i	−0.000900686	+	0.00156003i
$118$	−1.44368			−0.132902
$119$	−5.06437	−	4.99401i	−0.464250	−	0.457800i
$120$	4.78657			0.436952
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−4.85772	−	8.41382i	−0.439797	−	0.761751i
$123$	−7.55141	−	13.0794i	−0.680888	−	1.17933i
$124$	−5.59205	+	9.68572i	−0.502181	+	0.869803i
$125$	1.00000			0.0894427
$126$	−0.0130411	−	0.0128599i	−0.00116179	−	0.00114565i
$127$	4.31313			0.382728			0.191364	−	0.981519i	$-0.438709\pi$
$127$	4.31313			0.382728			0.191364	+	0.981519i	$0.438709\pi$
$128$	3.94740	−	6.83709i	0.348904	−	0.604319i
$129$	−2.15156	−	3.72661i	−0.189434	−	0.328109i
$130$	0.993076	+	1.72006i	0.0870985	+	0.150859i
$131$	1.86569	−	3.23147i	0.163006	−	0.282334i	−0.772939	−	0.634480i	$-0.781214\pi$
$131$	1.86569	−	3.23147i	0.163006	−	0.282334i	0.935945	+	0.352145i	$0.114548\pi$
$132$	−2.23883			−0.194865
$133$	−0.567664	+	2.17942i	−0.0492227	+	0.188979i
$134$	2.30225			0.198884
$135$	−2.60163	+	4.50616i	−0.223913	+	0.387828i
$136$	−3.71968	−	6.44268i	−0.318960	−	0.552455i
$137$	−7.29235	−	12.6307i	−0.623028	−	1.07912i	−0.988919	−	0.148458i	$-0.952569\pi$
$137$	−7.29235	−	12.6307i	−0.623028	−	1.07912i	0.365891	−	0.930658i	$-0.380764\pi$
$138$	−2.49442	+	4.32046i	−0.212339	+	0.367782i
$139$	21.5533			1.82813			0.914064	−	0.405569i	$-0.132927\pi$
$139$	21.5533			1.82813			0.914064	+	0.405569i	$0.132927\pi$
$140$	3.30160	−	0.909460i	0.279036	−	0.0768634i
$141$	2.13955			0.180183
$142$	−3.96232	+	6.86294i	−0.332511	+	0.575925i
$143$	−1.18220	−	2.04764i	−0.0988609	−	0.171232i
$144$	0.00108828	+	0.00188496i	9.06902e−5	+	0.000157080i
$145$	−4.13634	+	7.16435i	−0.343504	+	0.594967i
$146$	−7.03742			−0.582421
$147$	10.5692	+	5.90657i	0.871735	+	0.487166i
$148$	−13.6409			−1.12127
$149$	−5.97456	+	10.3482i	−0.489455	+	0.847761i	−0.999926	−	0.0121340i	$-0.996138\pi$
$149$	−5.97456	+	10.3482i	−0.489455	+	0.847761i	0.510472	+	0.859895i	$0.329471\pi$
$150$	0.726479	+	1.25830i	0.0593167	+	0.102740i
$151$	−4.04305	−	7.00277i	−0.329019	−	0.569877i	0.653299	−	0.757100i	$-0.273385\pi$
$151$	−4.04305	−	7.00277i	−0.329019	−	0.569877i	−0.982317	+	0.187223i	$0.940051\pi$
$152$	−1.17781	+	2.04003i	−0.0955332	+	0.165468i
$153$	0.0221538			0.00179103
$154$	2.14268	−	0.590222i	0.172662	−	0.0475615i
$155$	−8.64060			−0.694029
$156$	2.64675	−	4.58431i	0.211910	−	0.367039i
$157$	1.29519	+	2.24333i	0.103367	+	0.179038i	0.913070	−	0.407803i	$-0.133705\pi$
$157$	1.29519	+	2.24333i	0.103367	+	0.179038i	−0.809703	+	0.586840i	$0.800372\pi$
$158$	4.50089	+	7.79576i	0.358071	+	0.620198i
$159$	1.37231	−	2.37691i	0.108831	−	0.188501i
$160$	5.75653			0.455094
$161$	−2.28978	+	8.79107i	−0.180460	+	0.692834i
$162$	−7.53935			−0.592348
$163$	9.63489	−	16.6881i	0.754663	−	1.30711i	−0.190879	−	0.981613i	$-0.561134\pi$
$163$	9.63489	−	16.6881i	0.754663	−	1.30711i	0.945542	−	0.325500i	$-0.105533\pi$
$164$	−5.65096	−	9.78774i	−0.441266	−	0.764294i
$165$	−0.864835	−	1.49794i	−0.0673273	−	0.116614i
$166$	−6.48982	+	11.2407i	−0.503708	+	0.872447i
$167$	−1.24666			−0.0964692			−0.0482346	−	0.998836i	$-0.515360\pi$
$167$	−1.24666			−0.0964692			−0.0482346	+	0.998836i	$0.515360\pi$
$168$	9.01728	+	8.89201i	0.695698	+	0.686033i
$169$	−7.40957			−0.569967
$170$	1.12910	−	1.95567i	0.0865984	−	0.149993i
$171$	−0.00350742	−	0.00607503i	−0.000268219	−	0.000464569i
$172$	−1.61008	−	2.78874i	−0.122767	−	0.212639i
$173$	−5.41909	+	9.38614i	−0.412006	+	0.713615i	−0.995109	−	0.0987833i	$-0.968505\pi$
$173$	−5.41909	+	9.38614i	−0.412006	+	0.713615i	0.583103	+	0.812398i	$0.301838\pi$
$174$	−12.0199			−0.911223
$175$	1.88387	+	1.85770i	0.142407	+	0.140429i
$176$	−0.264118			−0.0199086
$177$	−1.48633	+	2.57440i	−0.111720	+	0.193504i
$178$	4.75847	+	8.24192i	0.356663	+	0.617758i
$179$	−0.770313	−	1.33422i	−0.0575759	−	0.0997244i	0.835801	−	0.549033i	$-0.185004\pi$
$179$	−0.770313	−	1.33422i	−0.0575759	−	0.0997244i	−0.893377	+	0.449308i	$0.851670\pi$
$180$	−0.00533336	+	0.00923765i	−0.000397525	+	0.000688534i
$181$	−10.3832			−0.771777			−0.385888	−	0.922545i	$-0.626105\pi$
$181$	−10.3832			−0.771777			−0.385888	+	0.922545i	$0.626105\pi$
$182$	−1.32452	+	5.08520i	−0.0981801	+	0.376940i
$183$	−20.0049			−1.47880
$184$	−4.75092	+	8.22884i	−0.350243	+	0.606638i
$185$	−5.26933	−	9.12674i	−0.387409	−	0.671012i
$186$	−6.27721	−	10.8724i	−0.460267	−	0.797206i
$187$	−1.34414	+	2.32812i	−0.0982933	+	0.170249i
$188$	1.60109			0.116772
$189$	−13.2722	+	3.65597i	−0.965412	+	0.265932i
$190$	−0.715046			−0.0518749
$191$	4.05221	−	7.01863i	0.293208	−	0.507851i	−0.681359	−	0.731950i	$-0.738611\pi$
$191$	4.05221	−	7.01863i	0.293208	−	0.507851i	0.974566	+	0.224099i	$0.0719439\pi$
$192$	3.72516	+	6.45217i	0.268840	+	0.465645i
$193$	−6.15348	−	10.6581i	−0.442937	−	0.767190i	0.554969	−	0.831871i	$-0.312730\pi$
$193$	−6.15348	−	10.6581i	−0.442937	−	0.767190i	−0.997906	+	0.0646814i	$0.979397\pi$
$194$	0.364731	−	0.631732i	0.0261861	−	0.0453557i
$195$	4.08965			0.292866
$196$	7.90929	+	4.42008i	0.564949	+	0.315720i
$197$	8.59720			0.612525			0.306262	−	0.951947i	$-0.400921\pi$
$197$	8.59720			0.612525			0.306262	+	0.951947i	$0.400921\pi$
$198$	−0.00346125	+	0.00599506i	−0.000245980	+	0.000426050i
$199$	−6.49991	−	11.2582i	−0.460767	−	0.798071i	0.538233	−	0.842796i	$-0.319092\pi$
$199$	−6.49991	−	11.2582i	−0.460767	−	0.798071i	−0.998999	+	0.0447251i	$0.985759\pi$
$200$	1.38367	+	2.39658i	0.0978400	+	0.169464i
$201$	2.37026	−	4.10541i	0.167185	−	0.289574i
$202$	5.18842			0.365056
$203$	−21.1015	+	5.81263i	−1.48104	+	0.407966i
$204$	−6.01860			−0.421386
$205$	4.36581	−	7.56180i	0.304921	−	0.528139i
$206$	−7.20253	−	12.4751i	−0.501824	−	0.869185i
$207$	−0.0141478	−	0.0245048i	−0.000983343	−	0.00170320i
$208$	0.312242	−	0.540818i	0.0216501	−	0.0374990i
$209$	0.851225			0.0588805
$210$	−0.968947	+	3.72005i	−0.0668637	+	0.256708i
$211$	4.91456			0.338332			0.169166	−	0.985588i	$-0.445893\pi$
$211$	4.91456			0.338332			0.169166	+	0.985588i	$0.445893\pi$
$212$	1.02694	−	1.77871i	0.0705306	−	0.122163i
$213$	8.15875	+	14.1314i	0.559028	+	0.968265i
$214$	−0.0304459	−	0.0527339i	−0.00208124	−	0.00360482i
$215$	1.24391	−	2.15452i	0.0848341	−	0.146937i
$216$	−14.3992			−0.979739
$217$	−16.2777	−	16.0516i	−1.10501	−	1.08965i
$218$	11.7590			0.796418
$219$	−7.24531	+	12.5493i	−0.489593	+	0.848000i
$220$	−0.647183	−	1.12095i	−0.0436331	−	0.0755747i
$221$	−3.17810	−	5.50463i	−0.213782	−	0.370281i
$222$	7.65611	−	13.2608i	0.513844	−	0.890005i
$223$	−11.4523			−0.766900			−0.383450	−	0.923562i	$-0.625264\pi$
$223$	−11.4523			−0.766900			−0.383450	+	0.923562i	$0.625264\pi$
$224$	10.8445	+	10.6939i	0.724582	+	0.714516i
$225$	−0.00824088			−0.000549392
$226$	−8.07041	+	13.9784i	−0.536835	+	0.929826i
$227$	7.50117	+	12.9924i	0.497870	+	0.862337i	0.999997	−	0.00245739i	$-0.000782214\pi$
$227$	7.50117	+	12.9924i	0.497870	+	0.862337i	−0.502127	+	0.864794i	$0.667449\pi$
$228$	0.952873	+	1.65043i	0.0631056	+	0.109302i
$229$	−10.9958	+	19.0453i	−0.726622	+	1.25855i	0.231681	+	0.972792i	$0.425577\pi$
$229$	−10.9958	+	19.0453i	−0.726622	+	1.25855i	−0.958303	+	0.285754i	$0.907756\pi$
$230$	−2.88427			−0.190183
$231$	1.15348	−	4.42852i	0.0758935	−	0.291375i
$232$	−22.8933			−1.50302
$233$	11.3589	−	19.6742i	0.744146	−	1.28890i	−0.206447	−	0.978458i	$-0.566190\pi$
$233$	11.3589	−	19.6742i	0.744146	−	1.28890i	0.950593	−	0.310441i	$-0.100477\pi$
$234$	−0.00818382	−	0.0141748i	−0.000534993	−	0.000926635i
$235$	0.618485	+	1.07125i	0.0403455	+	0.0698805i
$236$	−1.11227	+	1.92651i	−0.0724026	+	0.125405i
$237$	18.5354			1.20400
$238$	5.76012	−	1.58668i	0.373373	−	0.102849i
$239$	9.17361			0.593392			0.296696	−	0.954972i	$-0.404115\pi$
$239$	9.17361			0.593392			0.296696	+	0.954972i	$0.404115\pi$
$240$	0.228419	−	0.395633i	0.0147444	−	0.0255380i
$241$	10.4319	+	18.0686i	0.671978	+	1.16390i	0.977342	+	0.211665i	$0.0678886\pi$
$241$	10.4319	+	18.0686i	0.671978	+	1.16390i	−0.305364	+	0.952236i	$0.598778\pi$
$242$	−0.420010	−	0.727479i	−0.0269993	−	0.0467641i
$243$	0.0428207	−	0.0741677i	0.00274695	−	0.00475786i
$244$	−14.9703			−0.958374
$245$	0.0979204	+	6.99932i	0.00625591	+	0.447170i
$246$	12.6867			0.808872
$247$	−1.00632	+	1.74300i	−0.0640308	+	0.110905i
$248$	−11.9557	−	20.7079i	−0.759188	−	1.31495i
$249$	13.3631	+	23.1455i	0.846850	+	1.46679i
$250$	−0.420010	+	0.727479i	−0.0265638	+	0.0460098i
$251$	−14.2324			−0.898341			−0.449170	−	0.893446i	$-0.648280\pi$
$251$	−14.2324			−0.898341			−0.449170	+	0.893446i	$0.648280\pi$
$252$	−0.0272081	+	0.00749475i	−0.00171395	+	0.000472125i
$253$	3.43358			0.215867
$254$	−1.81156	+	3.13771i	−0.113667	+	0.196877i
$255$	−2.32492	−	4.02688i	−0.145592	−	0.252173i
$256$	7.62326	+	13.2039i	0.476453	+	0.825242i
$257$	0.0297923	−	0.0516017i	0.00185839	−	0.00321883i	−0.865095	−	0.501609i	$-0.832742\pi$
$257$	0.0297923	−	0.0516017i	0.00185839	−	0.00321883i	0.866953	+	0.498390i	$0.166075\pi$
$258$	3.61470			0.225041
$259$	7.02801	−	26.9824i	0.436699	−	1.67660i
$260$	3.06041			0.189799
$261$	0.0340871	−	0.0590405i	0.00210994	−	0.00365452i
$262$	1.56721	+	2.71450i	0.0968228	+	0.167702i
$263$	−12.0899	−	20.9403i	−0.745493	−	1.29123i	−0.949964	−	0.312359i	$-0.898881\pi$
$263$	−12.0899	−	20.9403i	−0.745493	−	1.29123i	0.204471	−	0.978873i	$-0.434452\pi$
$264$	2.39329	−	4.14529i	0.147297	−	0.255125i
$265$	1.58679			0.0974755
$266$	−1.34705	−	1.32834i	−0.0825931	−	0.0814457i
$267$	19.5962			1.19927
$268$	1.77374	−	3.07221i	0.108348	−	0.187665i
$269$	−3.12889	−	5.41940i	−0.190772	−	0.330426i	0.754734	−	0.656030i	$-0.227766\pi$
$269$	−3.12889	−	5.41940i	−0.190772	−	0.330426i	−0.945506	+	0.325604i	$0.894432\pi$
$270$	−2.18542	−	3.78526i	−0.133001	−	0.230364i
$271$	1.71151	−	2.96443i	0.103967	−	0.180076i	−0.809349	−	0.587329i	$-0.800180\pi$
$271$	1.71151	−	2.96443i	0.103967	−	0.180076i	0.913316	+	0.407252i	$0.133513\pi$
$272$	−0.710023			−0.0430515
$273$	7.70436	+	7.59733i	0.466289	+	0.459811i
$274$	12.2514			0.740136
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	3.84359	+	6.65730i	0.231357	+	0.400722i
$277$	0.584052	+	1.01161i	0.0350923	+	0.0607816i	0.883038	−	0.469301i	$-0.155494\pi$
$277$	0.584052	+	1.01161i	0.0350923	+	0.0607816i	−0.847946	+	0.530083i	$0.822161\pi$
$278$	−9.05261	+	15.6796i	−0.542939	+	0.940399i
$279$	0.0712061			0.00426300
$280$	−1.84548	+	7.08528i	−0.110288	+	0.423426i
$281$	−22.5561			−1.34558			−0.672792	−	0.739831i	$-0.734905\pi$
$281$	−22.5561			−1.34558			−0.672792	+	0.739831i	$0.734905\pi$
$282$	−0.898632	+	1.55648i	−0.0535128	+	0.0926868i
$283$	−2.28545	−	3.95852i	−0.135856	−	0.235310i	0.790068	−	0.613019i	$-0.210045\pi$
$283$	−2.28545	−	3.95852i	−0.135856	−	0.235310i	−0.925924	+	0.377709i	$0.876712\pi$
$284$	6.10545	+	10.5749i	0.362292	+	0.627508i
$285$	−0.736170	+	1.27508i	−0.0436069	+	0.0755294i
$286$	1.98615			0.117444
$287$	22.2722	−	6.13509i	1.31468	−	0.362143i
$288$	−0.0474389			−0.00279536
$289$	4.88657	−	8.46379i	0.287446	−	0.497870i
$290$	−3.47461	−	6.01820i	−0.204036	−	0.353401i
$291$	−0.751010	−	1.30079i	−0.0440250	−	0.0762536i
$292$	−5.42190	+	9.39100i	−0.317292	+	0.549567i
$293$	−0.140907			−0.00823186			−0.00411593	−	0.999992i	$-0.501310\pi$
$293$	−0.140907			−0.00823186			−0.00411593	+	0.999992i	$0.501310\pi$
$294$	−8.73609	+	5.20807i	−0.509499	+	0.303741i
$295$	−1.71863			−0.100063
$296$	14.5820	−	25.2567i	0.847561	−	1.46802i
$297$	2.60163	+	4.50616i	0.150962	+	0.261474i
$298$	−5.01875	−	8.69273i	−0.290728	−	0.503556i
$299$	−4.05919	+	7.03072i	−0.234749	+	0.406597i
$300$	2.23883			0.129259
$301$	6.34581	−	1.74802i	0.365766	−	0.100754i
$302$	6.79249			0.390864
$303$	5.34169	−	9.25208i	0.306872	−	0.531518i
$304$	0.112412	+	0.194703i	0.00644727	+	0.0111670i
$305$	−5.78286	−	10.0162i	−0.331126	−	0.573526i
$306$	−0.00930481	+	0.0161164i	−0.000531921	+	0.000921314i
$307$	2.62990			0.150097			0.0750483	−	0.997180i	$-0.476089\pi$
$307$	2.62990			0.150097			0.0750483	+	0.997180i	$0.476089\pi$
$308$	0.863186	−	3.31400i	0.0491846	−	0.188833i
$309$	−29.6612			−1.68737
$310$	3.62914	−	6.28585i	0.206121	−	0.357012i
$311$	0.735539	+	1.27399i	0.0417086	+	0.0722414i	0.886126	−	0.463444i	$-0.153387\pi$
$311$	0.735539	+	1.27399i	0.0417086	+	0.0722414i	−0.844418	+	0.535686i	$0.820053\pi$
$312$	5.65871	+	9.80118i	0.320361	+	0.554882i
$313$	2.65110	−	4.59185i	0.149849	−	0.259547i	−0.781322	−	0.624128i	$-0.785454\pi$
$313$	2.65110	−	4.59185i	0.149849	−	0.259547i	0.931172	+	0.364581i	$0.118788\pi$
$314$	−2.17597			−0.122797
$315$	−0.0155247	−	0.0153091i	−0.000874719	−	0.000862568i
$316$	13.8706			0.780283
$317$	−5.84844	+	10.1298i	−0.328481	+	0.568946i	−0.982211	−	0.187782i	$-0.939870\pi$
$317$	−5.84844	+	10.1298i	−0.328481	+	0.568946i	0.653729	+	0.756728i	$0.273203\pi$
$318$	1.15277	+	1.99665i	0.0646439	+	0.111967i
$319$	4.13634	+	7.16435i	0.231591	+	0.401127i
$320$	−2.15368	+	3.73029i	−0.120395	+	0.208529i
$321$	−0.125381			−0.00699811
$322$	−5.43359	−	5.35810i	−0.302802	−	0.298595i
$323$	2.28833			0.127326
$324$	−5.80861	+	10.0608i	−0.322700	+	0.558933i
$325$	1.18220	+	2.04764i	0.0655769	+	0.113583i
$326$	8.09350	+	14.0183i	0.448257	+	0.776404i
$327$	12.1063	−	20.9688i	0.669482	−	1.15958i
$328$	24.1633			1.33419
$329$	−0.824909	+	3.16705i	−0.0454787	+	0.174605i
$330$	1.45296			0.0799827
$331$	13.4141	−	23.2340i	0.737307	−	1.27705i	−0.216396	−	0.976306i	$-0.569430\pi$
$331$	13.4141	−	23.2340i	0.737307	−	1.27705i	0.953704	−	0.300748i	$-0.0972363\pi$
$332$	10.0000	+	17.3205i	0.548822	+	0.950587i
$333$	0.0434239	+	0.0752124i	0.00237961	+	0.00412161i
$334$	0.523608	−	0.906916i	0.0286506	−	0.0496242i
$335$	2.74071			0.149741
$336$	1.16528	−	0.320987i	0.0635710	−	0.0175113i
$337$	17.0846			0.930657			0.465328	−	0.885138i	$-0.345936\pi$
$337$	17.0846			0.930657			0.465328	+	0.885138i	$0.345936\pi$
$338$	3.11209	−	5.39030i	0.169275	−	0.293194i
$339$	16.6176	+	28.7826i	0.902546	+	1.56326i
$340$	−1.73981	−	3.01344i	−0.0943545	−	0.163427i
$341$	−4.32030	+	7.48298i	−0.233957	+	0.405226i
$342$	0.00589261			0.000318636
$343$	−12.8181	+	13.3677i	−0.692115	+	0.721788i
$344$	6.88464			0.371195
$345$	−2.96948	+	5.14328i	−0.159871	+	0.276905i
$346$	−4.55214	−	7.88454i	−0.244725	−	0.423876i
$347$	0.195382	+	0.338412i	0.0104887	+	0.0181669i	0.871222	−	0.490889i	$-0.163328\pi$
$347$	0.195382	+	0.338412i	0.0104887	+	0.0181669i	−0.860733	+	0.509056i	$0.829995\pi$
$348$	−9.26055	+	16.0397i	−0.496418	+	0.859821i
$349$	4.79546			0.256695			0.128348	−	0.991729i	$-0.459033\pi$
$349$	4.79546			0.256695			0.128348	+	0.991729i	$0.459033\pi$
$350$	−2.14268	+	0.590222i	−0.114531	+	0.0315487i
$351$	−12.3027			−0.656667
$352$	2.87827	−	4.98530i	0.153412	−	0.265718i
$353$	−14.3776	−	24.9027i	−0.765242	−	1.32544i	−0.940119	−	0.340848i	$-0.889286\pi$
$353$	−14.3776	−	24.9027i	−0.765242	−	1.32544i	0.174876	−	0.984590i	$-0.444047\pi$
$354$	−1.24855	−	2.16255i	−0.0663596	−	0.114938i
$355$	−4.71694	+	8.16998i	−0.250349	+	0.433617i
$356$	14.6644			0.777214
$357$	3.10088	−	11.9051i	0.164116	−	0.630085i
$358$	1.29416			0.0683983
$359$	6.06575	−	10.5062i	0.320138	−	0.554495i	−0.660378	−	0.750933i	$-0.729604\pi$
$359$	6.06575	−	10.5062i	0.320138	−	0.554495i	0.980516	+	0.196438i	$0.0629375\pi$
$360$	−0.0114026	−	0.0197499i	−0.000600971	−	0.00104091i
$361$	9.13771	+	15.8270i	0.480932	+	0.832999i
$362$	4.36105	−	7.55355i	0.229211	−	0.397006i
$363$	−1.72967			−0.0907841
$364$	5.76542	+	5.68532i	0.302190	+	0.297992i
$365$	−8.37768			−0.438508
$366$	8.40225	−	14.5531i	0.439193	−	0.760704i
$367$	−13.3908	−	23.1936i	−0.698995	−	1.21069i	−0.968815	−	0.247784i	$-0.920298\pi$
$367$	−13.3908	−	23.1936i	−0.698995	−	1.21069i	0.269820	−	0.962911i	$-0.413036\pi$
$368$	0.453435	+	0.785372i	0.0236369	+	0.0409403i
$369$	−0.0359781	+	0.0623159i	−0.00187294	+	0.00324404i
$370$	8.85268			0.460229
$371$	2.98930	+	2.94777i	0.155197	+	0.153040i
$372$	−19.3448			−1.00298
$373$	−3.10304	+	5.37461i	−0.160669	+	0.278287i	−0.935109	−	0.354361i	$-0.884699\pi$
$373$	−3.10304	+	5.37461i	−0.160669	+	0.278287i	0.774440	+	0.632648i	$0.218032\pi$
$374$	−1.12910	−	1.95567i	−0.0583846	−	0.101125i
$375$	0.864835	+	1.49794i	0.0446599	+	0.0773532i
$376$	−1.71155	+	2.96450i	−0.0882666	+	0.152882i
$377$	−19.5600			−1.00739
$378$	2.91483	−	11.1908i	0.149922	−	0.575592i
$379$	7.15513			0.367535			0.183767	−	0.982970i	$-0.441171\pi$
$379$	7.15513			0.367535			0.183767	+	0.982970i	$0.441171\pi$
$380$	−0.550899	+	0.954185i	−0.0282605	+	0.0489486i
$381$	3.73015	+	6.46080i	0.191101	+	0.330997i
$382$	3.40394	+	5.89579i	0.174161	+	0.301655i
$383$	14.9727	−	25.9334i	0.765067	−	1.32513i	−0.175144	−	0.984543i	$-0.556039\pi$
$383$	14.9727	−	25.9334i	0.765067	−	1.32513i	0.940211	−	0.340592i	$-0.110627\pi$
$384$	13.6554			0.696848
$385$	2.55075	−	0.702629i	0.129998	−	0.0358093i
$386$	10.3381			0.526195
$387$	−0.0102509	+	0.0177551i	−0.000521084	+	0.000902543i
$388$	−0.562005	−	0.973421i	−0.0285315	−	0.0494180i
$389$	6.60039	+	11.4322i	0.334653	+	0.579636i	0.983418	−	0.181353i	$-0.0580476\pi$
$389$	6.60039	+	11.4322i	0.334653	+	0.579636i	−0.648765	+	0.760989i	$0.724714\pi$
$390$	−1.71769	+	2.97513i	−0.0869788	+	0.150652i
$391$	9.23041			0.466802
$392$	−16.6389	+	9.91939i	−0.840393	+	0.501005i
$393$	6.45405			0.325564
$394$	−3.61091	+	6.25428i	−0.181915	+	0.315086i
$395$	5.35807	+	9.28045i	0.269594	+	0.466950i
$396$	0.00533336	+	0.00923765i	0.000268011	+	0.000464209i
$397$	0.327124	−	0.566595i	0.0164179	−	0.0284366i	−0.857700	−	0.514151i	$-0.828107\pi$
$397$	0.327124	−	0.566595i	0.0164179	−	0.0284366i	0.874118	+	0.485714i	$0.161440\pi$
$398$	10.9201			0.547376
$399$	−3.75557	+	1.03451i	−0.188013	+	0.0517902i
$400$	0.264118			0.0132059
$401$	−16.0271	+	27.7597i	−0.800355	+	1.38626i	0.119027	+	0.992891i	$0.462022\pi$
$401$	−16.0271	+	27.7597i	−0.800355	+	1.38626i	−0.919383	+	0.393365i	$0.871311\pi$
$402$	1.99107	+	3.44863i	0.0993054	+	0.172002i
$403$	−10.2150	−	17.6928i	−0.508843	−	0.881342i
$404$	3.99736	−	6.92363i	0.198876	−	0.344463i
$405$	−8.97521			−0.445982
$406$	4.63429	−	17.7923i	0.229996	−	0.883015i
$407$	−10.5387			−0.522382
$408$	6.43383	−	11.1437i	0.318522	−	0.551696i
$409$	1.89398	+	3.28047i	0.0936513	+	0.162209i	0.909045	−	0.416698i	$-0.136813\pi$
$409$	1.89398	+	3.28047i	0.0936513	+	0.162209i	−0.815394	+	0.578907i	$0.803479\pi$
$410$	3.66737	+	6.35206i	0.181118	+	0.313706i
$411$	12.6134	−	21.8470i	0.622171	−	1.07763i
$412$	−22.1964			−1.09354
$413$	−3.23768	−	3.19270i	−0.159316	−	0.157102i
$414$	0.0237689			0.00116818
$415$	−7.72579	+	13.3815i	−0.379244	+	0.656870i
$416$	6.80540	+	11.7873i	0.333662	+	0.577920i
$417$	18.6401	+	32.2855i	0.912808	+	1.58103i
$418$	−0.357523	+	0.619248i	−0.0174870	+	0.0302884i
$419$	−23.5925			−1.15257			−0.576284	−	0.817249i	$-0.695498\pi$
$419$	−23.5925			−1.15257			−0.576284	+	0.817249i	$0.695498\pi$
$420$	4.21766	+	4.15906i	0.205801	+	0.202942i
$421$	5.64210			0.274979			0.137490	−	0.990503i	$-0.456097\pi$
$421$	5.64210			0.274979			0.137490	+	0.990503i	$0.456097\pi$
$422$	−2.06416	+	3.57524i	−0.100482	+	0.174040i
$423$	−0.00509686	−	0.00882802i	−0.000247818	−	0.000429233i
$424$	2.19558	+	3.80286i	0.106627	+	0.184683i
$425$	1.34414	−	2.32812i	0.0652004	−	0.112930i
$426$	−13.7070			−0.664107
$427$	7.71294	−	29.6120i	0.373255	−	1.43303i
$428$	−0.0938268			−0.00453529
$429$	2.04482	−	3.54174i	0.0987251	−	0.170997i
$430$	1.04491	+	1.80984i	0.0503901	+	0.0872781i
$431$	5.54362	+	9.60184i	0.267027	+	0.462504i	0.968093	−	0.250592i	$-0.0806254\pi$
$431$	5.54362	+	9.60184i	0.267027	+	0.462504i	−0.701066	+	0.713097i	$0.747292\pi$
$432$	−0.687138	+	1.19016i	−0.0330599	+	0.0572615i
$433$	32.2725			1.55092			0.775459	−	0.631398i	$-0.217518\pi$
$433$	32.2725			1.55092			0.775459	+	0.631398i	$0.217518\pi$
$434$	18.5140	−	5.09987i	0.888702	−	0.244802i
$435$	−14.3090			−0.686064
$436$	9.05956	−	15.6916i	0.433874	−	0.751492i
$437$	−1.46137	−	2.53117i	−0.0699070	−	0.121082i
$438$	−6.08621	−	10.5416i	−0.290810	−	0.503698i
$439$	3.51504	−	6.08823i	0.167764	−	0.290575i	−0.769870	−	0.638201i	$-0.779679\pi$
$439$	3.51504	−	6.08823i	0.167764	−	0.290575i	0.937633	+	0.347626i	$0.113012\pi$
$440$	2.76733			0.131927
$441$	−0.000806950	−	0.0576805i	−3.84262e−5	−	0.00274669i
$442$	5.33933			0.253966
$443$	2.08099	−	3.60438i	0.0988707	−	0.171249i	−0.812347	−	0.583175i	$-0.801810\pi$
$443$	2.08099	−	3.60438i	0.0988707	−	0.171249i	0.911217	+	0.411926i	$0.135144\pi$
$444$	−11.7971	−	20.4332i	−0.559866	−	0.969717i
$445$	5.66472	+	9.81158i	0.268533	+	0.465113i
$446$	4.81006	−	8.33128i	0.227763	−	0.394497i
$447$	−20.6680			−0.977564
$448$	−10.9870	+	3.02648i	−0.519087	+	0.142988i
$449$	−32.7979			−1.54783			−0.773915	−	0.633289i	$-0.781704\pi$
$449$	−32.7979			−1.54783			−0.773915	+	0.633289i	$0.781704\pi$
$450$	0.00346125	−	0.00599506i	0.000163165	−	0.000282610i
$451$	−4.36581	−	7.56180i	−0.205578	−	0.356071i
$452$	12.4355	+	21.5389i	0.584916	+	1.01311i
$453$	6.99314	−	12.1125i	0.328567	−	0.569094i
$454$	−12.6023			−0.591454
$455$	−1.57678	+	6.05366i	−0.0739204	+	0.283800i
$456$	−4.07445			−0.190804
$457$	−9.87570	+	17.1052i	−0.461966	+	0.800148i	−0.999059	−	0.0433748i	$-0.986189\pi$
$457$	−9.87570	+	17.1052i	−0.461966	+	0.800148i	0.537093	+	0.843523i	$0.319522\pi$
$458$	−9.23668	−	15.9984i	−0.431602	−	0.747556i
$459$	6.99392	+	12.1138i	0.326448	+	0.565425i
$460$	−2.22215	+	3.84888i	−0.103608	+	0.179455i
$461$	−11.1721			−0.520336			−0.260168	−	0.965563i	$-0.583778\pi$
$461$	−11.1721			−0.520336			−0.260168	+	0.965563i	$0.583778\pi$
$462$	2.73718	+	2.69916i	0.127345	+	0.125576i
$463$	2.49062			0.115749			0.0578744	−	0.998324i	$-0.481568\pi$
$463$	2.49062			0.115749			0.0578744	+	0.998324i	$0.481568\pi$
$464$	−1.09248	+	1.89223i	−0.0507172	+	0.0878448i
$465$	−7.47269	−	12.9431i	−0.346538	−	0.600221i
$466$	9.54170	+	16.5267i	0.442011	+	0.765585i
$467$	5.57025	−	9.64796i	0.257761	−	0.446454i	−0.707881	−	0.706332i	$-0.750349\pi$
$467$	5.57025	−	9.64796i	0.257761	−	0.446454i	0.965642	+	0.259877i	$0.0836821\pi$
$468$	−0.0252205			−0.00116582
$469$	5.16313	+	5.09141i	0.238411	+	0.235099i
$470$	−1.03908			−0.0479291
$471$	−2.24025	+	3.88023i	−0.103225	+	0.178792i
$472$	−2.37801	−	4.11884i	−0.109457	−	0.189585i
$473$	−1.24391	−	2.15452i	−0.0571951	−	0.0990648i
$474$	−7.78505	+	13.4841i	−0.357579	+	0.619345i
$475$	−0.851225			−0.0390569
$476$	2.32049	−	8.90897i	0.106359	−	0.408342i
$477$	−0.0130765			−0.000598732
$478$	−3.85301	+	6.67361i	−0.176232	+	0.305244i
$479$	8.87708	+	15.3755i	0.405604	+	0.702527i	0.994392	−	0.105761i	$-0.0337279\pi$
$479$	8.87708	+	15.3755i	0.405604	+	0.702527i	−0.588788	+	0.808288i	$0.700395\pi$
$480$	4.97845	+	8.62293i	0.227234	+	0.393581i
$481$	12.4589	−	21.5794i	0.568075	−	0.983934i
$482$	−17.5260			−0.798288
$483$	−15.1488	+	4.17288i	−0.689293	+	0.189873i
$484$	−1.29437			−0.0588348
$485$	0.434193	−	0.752044i	0.0197157	−	0.0341486i
$486$	0.0359703	+	0.0623023i	0.00163164	+	0.00282609i
$487$	−10.6364	−	18.4227i	−0.481979	−	0.834812i	0.517807	−	0.855497i	$-0.326749\pi$
$487$	−10.6364	−	18.4227i	−0.481979	−	0.834812i	−0.999786	+	0.0206852i	$0.993415\pi$
$488$	16.0031	−	27.7182i	0.724427	−	1.25474i
$489$	33.3304			1.50725
$490$	−5.13298	−	2.86855i	−0.231884	−	0.129588i
$491$	−21.5966			−0.974639			−0.487320	−	0.873224i	$-0.662025\pi$
$491$	−21.5966			−0.974639			−0.487320	+	0.873224i	$0.662025\pi$
$492$	9.77429	−	16.9296i	0.440659	−	0.763244i
$493$	11.1196	+	19.2598i	0.500804	+	0.867417i
$494$	−0.845331	−	1.46416i	−0.0380333	−	0.0658755i
$495$	−0.00412044	+	0.00713681i	−0.000185200	+	0.000320776i
$496$	−2.28214			−0.102471
$497$	−24.0634	+	6.62852i	−1.07939	+	0.297330i
$498$	−22.4505			−1.00603
$499$	−16.1173	+	27.9160i	−0.721511	+	1.24969i	0.238883	+	0.971048i	$0.423219\pi$
$499$	−16.1173	+	27.9160i	−0.721511	+	1.24969i	−0.960394	+	0.278645i	$0.910115\pi$
$500$	0.647183	+	1.12095i	0.0289429	+	0.0501306i
$501$	−1.07815	−	1.86741i	−0.0481683	−	0.0834299i
$502$	5.97775	−	10.3538i	0.266800	−	0.462111i
$503$	13.3675			0.596028			0.298014	−	0.954561i	$-0.403676\pi$
$503$	13.3675			0.596028			0.298014	+	0.954561i	$0.403676\pi$
$504$	0.0152083	−	0.0583889i	0.000677434	−	0.00260085i
$505$	6.17655			0.274853
$506$	−1.44214	+	2.49785i	−0.0641108	+	0.111043i
$507$	−6.40805	−	11.0991i	−0.284592	−	0.492927i
$508$	2.79139	+	4.83482i	0.123848	+	0.214511i
$509$	0.658092	−	1.13985i	0.0291694	−	0.0505229i	−0.851072	−	0.525049i	$-0.824047\pi$
$509$	0.658092	−	1.13985i	0.0291694	−	0.0505229i	0.880242	+	0.474526i	$0.157380\pi$
$510$	3.90596			0.172959
$511$	−15.7825	−	15.5632i	−0.698175	−	0.688475i
$512$	2.98221			0.131796
$513$	2.21458	−	3.83576i	0.0977759	−	0.169353i
$514$	0.0250261	+	0.0433465i	0.00110385	+	0.00191193i
$515$	−8.57424	−	14.8510i	−0.377826	−	0.654414i
$516$	2.78490	−	4.82359i	0.122599	−	0.212347i
$517$	1.23697			0.0544019
$518$	16.6773	+	16.4456i	0.732758	+	0.722578i
$519$	−18.7465			−0.822879
$520$	−3.27156	+	5.66650i	−0.143467	+	0.248492i
$521$	−16.0681	−	27.8308i	−0.703958	−	1.21929i	−0.967066	−	0.254524i	$-0.918081\pi$
$521$	−16.0681	−	27.8308i	−0.703958	−	1.21929i	0.263109	−	0.964766i	$-0.415252\pi$
$522$	0.0286338	+	0.0495952i	0.00125327	+	0.00217072i
$523$	17.6993	−	30.6561i	0.773936	−	1.34050i	−0.161455	−	0.986880i	$-0.551619\pi$
$523$	17.6993	−	30.6561i	0.773936	−	1.34050i	0.935391	−	0.353616i	$-0.115048\pi$
$524$	4.82977			0.210989
$525$	−1.15348	+	4.42852i	−0.0503420	+	0.193276i
$526$	20.3114			0.885621
$527$	−11.6142	+	20.1163i	−0.505921	+	0.876282i
$528$	−0.228419	−	0.395633i	−0.00994064	−	0.0172177i
$529$	5.60528	+	9.70863i	0.243708	+	0.422114i
$530$	−0.666466	+	1.15435i	−0.0289494	+	0.0501419i
$531$	0.0141630			0.000614623
$532$	−2.81041	+	0.774155i	−0.121847	+	0.0335639i
$533$	20.6451			0.894240
$534$	−8.23059	+	14.2558i	−0.356173	+	0.616909i
$535$	−0.0362443	−	0.0627770i	−0.00156698	−	0.00271409i
$536$	3.79223	+	6.56833i	0.163799	+	0.283709i
$537$	1.33239	−	2.30776i	0.0574968	−	0.0995873i
$538$	5.25666			0.226631
$539$	6.11054	+	3.41486i	0.263200	+	0.147088i
$540$	−6.73493			−0.289825
$541$	−13.4898	+	23.3649i	−0.579970	+	1.00454i	0.415512	+	0.909588i	$0.363602\pi$
$541$	−13.4898	+	23.3649i	−0.579970	+	1.00454i	−0.995482	+	0.0949498i	$0.969731\pi$
$542$	1.43771	+	2.49018i	0.0617548	+	0.106962i
$543$	−8.97975	−	15.5534i	−0.385358	−	0.667460i
$544$	7.73759	−	13.4019i	0.331746	−	0.574601i
$545$	13.9984			0.599627
$546$	−8.76280	+	2.41380i	−0.375013	+	0.103301i
$547$	−25.7359			−1.10039			−0.550193	−	0.835037i	$-0.685446\pi$
$547$	−25.7359			−1.10039			−0.550193	+	0.835037i	$0.685446\pi$
$548$	9.43897	−	16.3488i	0.403213	−	0.698385i
$549$	0.0476559	+	0.0825424i	0.00203390	+	0.00352282i
$550$	0.420010	+	0.727479i	0.0179093	+	0.0310198i
$551$	3.52096	−	6.09848i	0.149998	−	0.259804i
$552$	−16.4351			−0.699523
$553$	−7.14637	+	27.4368i	−0.303895	+	1.16673i
$554$	−0.981231			−0.0416885
$555$	9.11420	−	15.7863i	0.386876	−	0.670089i
$556$	13.9489	+	24.1603i	0.591567	+	1.02462i
$557$	16.3365	+	28.2956i	0.692198	+	1.19892i	0.971116	+	0.238607i	$0.0766909\pi$
$557$	16.3365	+	28.2956i	0.692198	+	1.19892i	−0.278918	+	0.960315i	$0.589976\pi$
$558$	−0.0299073	+	0.0518009i	−0.00126608	+	0.00219291i
$559$	5.88223			0.248792
$560$	0.497564	+	0.490651i	0.0210259	+	0.0207338i
$561$	−4.64984			−0.196316
$562$	9.47379	−	16.4091i	0.399628	−	0.692176i
$563$	4.48362	+	7.76585i	0.188962	+	0.327292i	0.944904	−	0.327346i	$-0.106154\pi$
$563$	4.48362	+	7.76585i	0.188962	+	0.327292i	−0.755942	+	0.654638i	$0.772821\pi$
$564$	1.38468	+	2.39834i	0.0583056	+	0.100988i
$565$	−9.60740	+	16.6405i	−0.404186	+	0.700071i
$566$	3.83965			0.161393
$567$	−16.9081	−	16.6732i	−0.710074	−	0.700210i
$568$	−26.1067			−1.09541
$569$	−18.1772	+	31.4839i	−0.762029	+	1.31987i	0.179774	+	0.983708i	$0.442464\pi$
$569$	−18.1772	+	31.4839i	−0.762029	+	1.31987i	−0.941803	+	0.336166i	$0.890870\pi$
$570$	−0.618397	−	1.07110i	−0.0259018	−	0.0448632i
$571$	9.92870	+	17.1970i	0.415503	+	0.719673i	0.995481	−	0.0949594i	$-0.0302721\pi$
$571$	9.92870	+	17.1970i	0.415503	+	0.719673i	−0.579978	+	0.814632i	$0.696939\pi$
$572$	1.53021	−	2.65040i	0.0639812	−	0.110819i
$573$	14.0180			0.585609
$574$	−4.89138	+	18.7793i	−0.204162	+	0.783833i
$575$	−3.43358			−0.143190
$576$	0.0177482	−	0.0307408i	0.000739510	−	0.00128087i
$577$	−17.9249	−	31.0468i	−0.746222	−	1.29249i	−0.949622	−	0.313398i	$-0.898533\pi$
$577$	−17.9249	−	31.0468i	−0.746222	−	1.29249i	0.203400	−	0.979096i	$-0.434801\pi$
$578$	4.10482	+	7.10976i	0.170738	+	0.295727i
$579$	10.6435	−	18.4351i	0.442328	−	0.766135i
$580$	−10.7079			−0.444621
$581$	−39.4131	+	10.8567i	−1.63513	+	0.450413i
$582$	1.26173			0.0523003
$583$	0.793393	−	1.37420i	0.0328590	−	0.0569134i
$584$	−11.5919	−	20.0778i	−0.479677	−	0.830825i
$585$	−0.00974241	−	0.0168743i	−0.000402799	−	0.000697668i
$586$	0.0591822	−	0.102507i	0.00244479	−	0.00423451i
$587$	18.5271			0.764694			0.382347	−	0.924019i	$-0.375116\pi$
$587$	18.5271			0.764694			0.382347	+	0.924019i	$0.375116\pi$
$588$	0.219227	+	15.6703i	0.00904077	+	0.646231i
$589$	7.35510			0.303061
$590$	0.721842	−	1.25027i	0.0297178	−	0.0514727i
$591$	7.43516	+	12.8781i	0.305842	+	0.529733i
$592$	−1.39172	−	2.41054i	−0.0571995	−	0.0990725i
$593$	−18.6166	+	32.2449i	−0.764492	+	1.32414i	0.176022	+	0.984386i	$0.443677\pi$
$593$	−18.6166	+	32.2449i	−0.764492	+	1.32414i	−0.940515	+	0.339753i	$0.889656\pi$
$594$	−4.37085			−0.179338
$595$	6.85712	−	1.88886i	0.281115	−	0.0774359i
$596$	−15.4665			−0.633534
$597$	11.2427	−	19.4729i	0.460133	−	0.796974i
$598$	−3.40980	−	5.90595i	−0.139437	−	0.241512i
$599$	10.2346	+	17.7268i	0.418173	+	0.724297i	0.995756	−	0.0920355i	$-0.0293373\pi$
$599$	10.2346	+	17.7268i	0.418173	+	0.724297i	−0.577583	+	0.816332i	$0.696004\pi$
$600$	−2.39329	+	4.14529i	−0.0977055	+	0.169231i
$601$	−29.6018			−1.20748			−0.603741	−	0.797180i	$-0.706324\pi$
$601$	−29.6018			−1.20748			−0.603741	+	0.797180i	$0.706324\pi$
$602$	−1.39366	+	5.35062i	−0.0568012	+	0.218075i
$603$	−0.0225858			−0.000919767
$604$	5.23319	−	9.06415i	0.212935	−	0.368815i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	4.48713	+	7.77194i	0.182277	+	0.315713i
$607$	−4.91559	+	8.51406i	−0.199518	+	0.345575i	−0.948372	−	0.317160i	$-0.897271\pi$
$607$	−4.91559	+	8.51406i	−0.199518	+	0.345575i	0.748854	+	0.662735i	$0.230604\pi$
$608$	−4.90011			−0.198726
$609$	−26.9563	−	26.5818i	−1.09232	−	1.07715i
$610$	9.71544			0.393367
$611$	−1.46235	+	2.53287i	−0.0591604	+	0.102469i
$612$	0.0143376	+	0.0248334i	0.000579562	+	0.00100383i
$613$	10.3781	+	17.9753i	0.419166	+	0.726017i	0.995856	−	0.0909460i	$-0.0289891\pi$
$613$	10.3781	+	17.9753i	0.419166	+	0.726017i	−0.576689	+	0.816963i	$0.695656\pi$
$614$	−1.10459	+	1.91320i	−0.0445774	+	0.0772104i
$615$	15.1028			0.609004
$616$	5.21329	+	5.14087i	0.210050	+	0.207131i
$617$	43.5900			1.75487			0.877434	−	0.479697i	$-0.159253\pi$
$617$	43.5900			1.75487			0.877434	+	0.479697i	$0.159253\pi$
$618$	12.4580	−	21.5779i	0.501134	−	0.867990i
$619$	5.65989	+	9.80321i	0.227490	+	0.394024i	0.957064	−	0.289878i	$-0.0936147\pi$
$619$	5.65989	+	9.80321i	0.227490	+	0.394024i	−0.729574	+	0.683902i	$0.760281\pi$
$620$	−5.59205	−	9.68572i	−0.224582	−	0.388988i
$621$	8.93290	−	15.4722i	0.358465	−	0.620880i
$622$	−1.23573			−0.0495484
$623$	−7.55536	+	29.0070i	−0.302699	+	1.16214i
$624$	1.08015			0.0432406
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.22698	+	3.85724i	0.0890080	+	0.154166i
$627$	0.736170	+	1.27508i	0.0293998	+	0.0509219i
$628$	−1.67645	+	2.90370i	−0.0668976	+	0.115870i
$629$	−28.3309			−1.12963
$630$	0.0176576	−	0.00486395i	0.000703494	−	0.000193784i
$631$	−42.6894			−1.69944			−0.849719	−	0.527235i	$-0.823229\pi$
$631$	−42.6894			−1.69944			−0.849719	+	0.527235i	$0.823229\pi$
$632$	−14.8276	+	25.6821i	−0.589809	+	1.02158i
$633$	4.25028	+	7.36171i	0.168934	+	0.292602i
$634$	−4.91281	−	8.50923i	−0.195113	−	0.337945i
$635$	−2.15657	+	3.73528i	−0.0855807	+	0.148230i
$636$	3.55254			0.140867
$637$	−14.2163	+	8.47513i	−0.563271	+	0.335797i
$638$	−6.94922			−0.275122
$639$	0.0388717	−	0.0673278i	0.00153774	−	0.00266345i
$640$	3.94740	+	6.83709i	0.156034	+	0.270260i
$641$	−13.6037	−	23.5623i	−0.537313	−	0.930654i	−0.999048	−	0.0436353i	$-0.986106\pi$
$641$	−13.6037	−	23.5623i	−0.537313	−	0.930654i	0.461734	−	0.887018i	$-0.347227\pi$
$642$	0.0526614	−	0.0912123i	0.00207838	−	0.00359986i
$643$	−6.24495			−0.246277			−0.123138	−	0.992389i	$-0.539296\pi$
$643$	−6.24495			−0.246277			−0.123138	+	0.992389i	$0.539296\pi$
$644$	−11.3363	+	3.12270i	−0.446713	+	0.123052i
$645$	4.30311			0.169435
$646$	−0.961123	+	1.66471i	−0.0378149	+	0.0654973i
$647$	2.54355	+	4.40555i	0.0999972	+	0.173200i	0.911683	−	0.410894i	$-0.134783\pi$
$647$	2.54355	+	4.40555i	0.0999972	+	0.173200i	−0.811686	+	0.584094i	$0.801450\pi$
$648$	−12.4187	−	21.5098i	−0.487853	−	0.844985i
$649$	−0.859316	+	1.48838i	−0.0337311	+	0.0584240i
$650$	−1.98615			−0.0779033
$651$	9.96676	−	38.2651i	0.390628	−	1.49973i
$652$	24.9421			0.976810
$653$	−10.9592	+	18.9819i	−0.428866	+	0.742818i	−0.996773	−	0.0802747i	$-0.974420\pi$
$653$	−10.9592	+	18.9819i	−0.428866	+	0.742818i	0.567906	+	0.823093i	$0.307754\pi$
$654$	10.1696	+	17.6142i	0.397662	+	0.688770i
$655$	1.86569	+	3.23147i	0.0728984	+	0.126264i
$656$	1.15309	−	1.99721i	0.0450206	−	0.0779779i
$657$	0.0690395			0.00269349
$658$	−1.95749	−	1.93029i	−0.0763108	−	0.0752507i
$659$	15.5957			0.607521			0.303761	−	0.952748i	$-0.401758\pi$
$659$	15.5957			0.607521			0.303761	+	0.952748i	$0.401758\pi$
$660$	1.11941	−	1.93888i	0.0435731	−	0.0754709i
$661$	9.87202	+	17.0988i	0.383977	+	0.665068i	0.991627	−	0.129137i	$-0.0412208\pi$
$661$	9.87202	+	17.0988i	0.383977	+	0.665068i	−0.607650	+	0.794205i	$0.707887\pi$
$662$	11.2681	+	19.5170i	0.437948	+	0.758549i
$663$	5.49706	−	9.52119i	0.213488	−	0.369772i
$664$	−42.7597			−1.65940
$665$	−1.60360	−	1.58132i	−0.0621848	−	0.0613209i
$666$	−0.0729539			−0.00282690
$667$	14.2024	−	24.5993i	0.549921	−	0.952490i
$668$	−0.806815	−	1.39744i	−0.0312166	−	0.0540688i
$669$	−9.90432	−	17.1548i	−0.382923	−	0.663242i
$670$	−1.15112	+	1.99381i	−0.0444718	+	0.0770275i
$671$	−11.5657			−0.446490
$672$	−6.64005	+	25.4929i	−0.256145	+	0.983411i
$673$	40.4291			1.55843			0.779215	−	0.626757i	$-0.215618\pi$
$673$	40.4291			1.55843			0.779215	+	0.626757i	$0.215618\pi$
$674$	−7.17570	+	12.4287i	−0.276397	+	0.478734i
$675$	−2.60163	−	4.50616i	−0.100137	−	0.173442i
$676$	−4.79535	−	8.30579i	−0.184436	−	0.319453i
$677$	3.44357	−	5.96444i	0.132347	−	0.229232i	−0.792234	−	0.610218i	$-0.791082\pi$
$677$	3.44357	−	5.96444i	0.132347	−	0.229232i	0.924581	+	0.380986i	$0.124415\pi$
$678$	−27.9183			−1.07220
$679$	2.21503	−	0.610153i	0.0850051	−	0.0234155i
$680$	7.43937			0.285287
$681$	−12.9746	+	22.4726i	−0.497186	+	0.861151i
$682$	−3.62914	−	6.28585i	−0.138967	−	0.240698i
$683$	16.6643	+	28.8634i	0.637641	+	1.10443i	0.985949	+	0.167047i	$0.0534231\pi$
$683$	16.6643	+	28.8634i	0.637641	+	1.10443i	−0.348308	+	0.937380i	$0.613244\pi$
$684$	0.00453989	−	0.00786332i	0.000173587	−	0.000300662i
$685$	14.5847			0.557253
$686$	−4.34097	−	14.9395i	−0.165739	−	0.570392i
$687$	−38.0382			−1.45125
$688$	0.328539	−	0.569047i	0.0125254	−	0.0216947i
$689$	1.87591	+	3.24916i	0.0714663	+	0.123783i
$690$	−2.49442	−	4.32046i	−0.0949609	−	0.164477i
$691$	19.8303	−	34.3470i	0.754379	−	1.30662i	−0.191303	−	0.981531i	$-0.561271\pi$
$691$	19.8303	−	34.3470i	0.754379	−	1.30662i	0.945682	−	0.325092i	$-0.105395\pi$
$692$	−14.0286			−0.533286
$693$	−0.0210204	+	0.00579028i	−0.000798499	+	0.000219955i
$694$	−0.328250			−0.0124602
$695$	−10.7767	+	18.6657i	−0.408782	+	0.708031i
$696$	−19.7989	−	34.2927i	−0.750475	−	1.29986i
$697$	−11.7365	−	20.3282i	−0.444552	−	0.769987i
$698$	−2.01414	+	3.48860i	−0.0762364	+	0.132045i
$699$	39.2943			1.48625
$700$	−0.863186	+	3.31400i	−0.0326254	+	0.125257i
$701$	49.1276			1.85552			0.927761	−	0.373174i	$-0.121731\pi$
$701$	49.1276			1.85552			0.927761	+	0.373174i	$0.121731\pi$
$702$	5.16724	−	8.94991i	0.195025	−	0.337793i
$703$	4.48539	+	7.76892i	0.169170	+	0.293010i
$704$	2.15368	+	3.73029i	0.0811700	+	0.140590i
$705$	−1.06977	+	1.85290i	−0.0402900	+	0.0697844i
$706$	24.1549			0.909083
$707$	11.6358	+	11.4742i	0.437609	+	0.431530i
$708$	−3.84772			−0.144606
$709$	19.1470	−	33.1637i	0.719082	−	1.24549i	−0.242281	−	0.970206i	$-0.577896\pi$
$709$	19.1470	−	33.1637i	0.719082	−	1.24549i	0.961364	−	0.275281i	$-0.0887709\pi$
$710$	−3.96232	−	6.86294i	−0.148703	−	0.257562i
$711$	−0.0441552	−	0.0764791i	−0.00165595	−	0.00286819i
$712$	−15.6762	+	27.1519i	−0.587489	+	1.01756i
$713$	29.6681			1.11108
$714$	7.35831	+	7.25609i	0.275378	+	0.271552i
$715$	2.36441			0.0884239
$716$	0.997067	−	1.72697i	0.0372622	−	0.0645400i
$717$	7.93366	+	13.7415i	0.296288	+	0.513186i
$718$	5.09535	+	8.82540i	0.190157	+	0.329361i
$719$	−14.8986	+	25.8051i	−0.555622	+	0.962366i	0.442232	+	0.896901i	$0.354187\pi$
$719$	−14.8986	+	25.8051i	−0.555622	+	0.962366i	−0.997855	+	0.0654658i	$0.979147\pi$
$720$	−0.00217656			−8.11158e−5
$721$	11.4360	−	43.9057i	0.425897	−	1.63513i
$722$	−15.3517			−0.571332
$723$	−18.0438	+	31.2527i	−0.671055	+	1.16230i
$724$	−6.71983	−	11.6391i	−0.249741	−	0.432563i
$725$	−4.13634	−	7.16435i	−0.153620	−	0.266077i
$726$	0.726479	−	1.25830i	0.0269622	−	0.0466998i
$727$	41.2443			1.52967			0.764833	−	0.644229i	$-0.222822\pi$
$727$	41.2443			1.52967			0.764833	+	0.644229i	$0.222822\pi$
$728$	−16.6898	+	4.59738i	−0.618566	+	0.170390i
$729$	27.0738			1.00273
$730$	3.51871	−	6.09458i	0.130233	−	0.225571i
$731$	−3.34398	−	5.79195i	−0.123682	−	0.214223i
$732$	−12.9468	−	22.4246i	−0.478529	−	0.828836i
$733$	−13.0849	+	22.6637i	−0.483302	+	0.837104i	−0.999816	−	0.0191750i	$-0.993896\pi$
$733$	−13.0849	+	22.6637i	−0.483302	+	0.837104i	0.516514	+	0.856279i	$0.327229\pi$
$734$	22.4971			0.830383
$735$	−10.3999	+	6.19993i	−0.383605	+	0.228688i
$736$	−19.7655			−0.728565
$737$	1.37035	−	2.37352i	0.0504777	−	0.0874299i
$738$	−0.0302223	−	0.0523466i	−0.00111250	−	0.00192690i
$739$	−13.3032	−	23.0418i	−0.489365	−	0.847605i	0.510560	−	0.859842i	$-0.329438\pi$
$739$	−13.3032	−	23.0418i	−0.489365	−	0.847605i	−0.999925	+	0.0122373i	$0.996105\pi$
$740$	6.82044	−	11.8134i	0.250724	−	0.434267i
$741$	−3.48121			−0.127886
$742$	−3.39997	+	0.936557i	−0.124817	+	0.0343821i
$743$	−53.2152			−1.95228			−0.976138	−	0.217153i	$-0.930323\pi$
$743$	−53.2152			−1.95228			−0.976138	+	0.217153i	$0.930323\pi$
$744$	20.6794	−	35.8178i	0.758145	−	1.31315i
$745$	−5.97456	−	10.3482i	−0.218891	−	0.379130i
$746$	−2.60661	−	4.51478i	−0.0954348	−	0.165298i
$747$	0.0636673	−	0.110275i	0.00232946	−	0.00403475i
$748$	−3.47962			−0.127228
$749$	0.0483411	−	0.185595i	0.00176635	−	0.00678148i
$750$	−1.45296			−0.0530545
$751$	−22.1544	+	38.3725i	−0.808425	+	1.40023i	0.105529	+	0.994416i	$0.466347\pi$
$751$	−22.1544	+	38.3725i	−0.808425	+	1.40023i	−0.913954	+	0.405818i	$0.866987\pi$
$752$	0.163353	+	0.282936i	0.00595687	+	0.0103176i
$753$	−12.3087	−	21.3193i	−0.448553	−	0.776917i
$754$	8.21540	−	14.2295i	0.299187	−	0.518207i
$755$	8.08610			0.294283
$756$	−12.6877	−	12.5115i	−0.461448	−	0.455038i
$757$	−12.4743			−0.453385			−0.226693	−	0.973966i	$-0.572791\pi$
$757$	−12.4743			−0.453385			−0.226693	+	0.973966i	$0.572791\pi$
$758$	−3.00523	+	5.20521i	−0.109155	+	0.189062i
$759$	2.96948	+	5.14328i	0.107785	+	0.186689i
$760$	−1.17781	−	2.04003i	−0.0427237	−	0.0739997i
$761$	−7.49235	+	12.9771i	−0.271598	+	0.470421i	−0.969271	−	0.245995i	$-0.920885\pi$
$761$	−7.49235	+	12.9771i	−0.271598	+	0.470421i	0.697674	+	0.716416i	$0.254219\pi$
$762$	−6.26679			−0.227022
$763$	26.3712	+	26.0049i	0.954702	+	0.941440i
$764$	10.4901			0.379518
$765$	−0.0110769	+	0.0191857i	−0.000400486	+	0.000693662i
$766$	12.5773	+	21.7846i	0.454437	+	0.787108i
$767$	−2.03177	−	3.51914i	−0.0733631	−	0.127069i
$768$	−13.1857	+	22.8383i	−0.475799	+	0.824107i
$769$	0.798745			0.0288035			0.0144017	−	0.999896i	$-0.495416\pi$
$769$	0.798745			0.0288035			0.0144017	+	0.999896i	$0.495416\pi$
$770$	−0.560192	+	2.15073i	−0.0201879	+	0.0775068i
$771$	0.103062			0.00371167
$772$	7.96486	−	13.7955i	0.286662	−	0.496512i
$773$	−21.0878	−	36.5251i	−0.758474	−	1.31372i	−0.943628	−	0.331007i	$-0.892612\pi$
$773$	−21.0878	−	36.5251i	−0.758474	−	1.31372i	0.185154	−	0.982710i	$-0.440722\pi$
$774$	−0.00861098	−	0.0149147i	−0.000309515	−	0.000536096i
$775$	4.32030	−	7.48298i	0.155190	−	0.268796i
$776$	2.40311			0.0862667
$777$	46.4960	−	12.8078i	1.66804	−	0.459477i
$778$	−11.0889			−0.397557
$779$	−3.71629	+	6.43680i	−0.133150	+	0.230622i
$780$	2.64675	+	4.58431i	0.0947690	+	0.164145i
$781$	4.71694	+	8.16998i	0.168785	+	0.292345i
$782$	−3.87687	+	6.71493i	−0.138636	+	0.240125i
$783$	43.0449			1.53830
$784$	0.0258625	+	1.84865i	0.000923662	+	0.0660230i
$785$	−2.59038			−0.0924546
$786$	−2.71076	+	4.69518i	−0.0966898	+	0.167472i
$787$	9.83851	+	17.0408i	0.350705	+	0.607439i	0.986373	−	0.164524i	$-0.0526087\pi$
$787$	9.83851	+	17.0408i	0.350705	+	0.607439i	−0.635668	+	0.771962i	$0.719275\pi$
$788$	5.56396	+	9.63706i	0.198208	+	0.343306i
$789$	20.9115	−	36.2197i	0.744468	−	1.28946i
$790$	−9.00177			−0.320269
$791$	−49.0121	+	13.5009i	−1.74267	+	0.480036i
$792$	−0.0228053			−0.000810350
$793$	13.6731	−	23.6824i	0.485544	−	0.840988i
$794$	0.274790	+	0.475951i	0.00975195	+	0.0168909i
$795$	1.37231	+	2.37691i	0.0486708	+	0.0843002i
$796$	8.41327	−	14.5722i	0.298200	−	0.516498i
$797$	44.8687			1.58933			0.794666	−	0.607048i	$-0.207646\pi$
$797$	44.8687			1.58933			0.794666	+	0.607048i	$0.207646\pi$
$798$	0.824792	−	3.16660i	0.0291973	−	0.112096i
$799$	3.32532			0.117641
$800$	−2.87827	+	4.98530i	−0.101762	+	0.176257i
$801$	−0.0466822	−	0.0808560i	−0.00164944	−	0.00285691i
$802$	−13.4631	−	23.3187i	−0.475398	−	0.823413i
$803$	−4.18884	+	7.25529i	−0.147821	+	0.256033i
$804$	6.13597			0.216399
$805$	−6.46840	−	6.37854i	−0.227981	−	0.224814i
$806$	17.1615			0.604489
$807$	5.41195	−	9.37377i	0.190510	−	0.329972i
$808$	8.54628	+	14.8026i	0.300657	+	0.520753i
$809$	−6.09963	−	10.5649i	−0.214451	−	0.371441i	0.738651	−	0.674088i	$-0.235463\pi$
$809$	−6.09963	−	10.5649i	−0.214451	−	0.371441i	−0.953103	+	0.302647i	$0.902130\pi$
$810$	3.76968	−	6.52927i	0.132453	−	0.229415i
$811$	29.6563			1.04137			0.520687	−	0.853748i	$-0.325676\pi$
$811$	29.6563			1.04137			0.520687	+	0.853748i	$0.325676\pi$
$812$	−20.1722	−	19.8920i	−0.707907	−	0.698072i
$813$	5.92071			0.207648
$814$	4.42634	−	7.66665i	0.155143	−	0.268716i
$815$	9.63489	+	16.6881i	0.337495	+	0.584559i
$816$	−0.614053	−	1.06357i	−0.0214962	−	0.0372324i
$817$	−1.05885	+	1.83398i	−0.0370444	+	0.0641629i
$818$	−3.18196			−0.111255
$819$	0.0129940	−	0.0498875i	0.000454048	−	0.00174321i
$820$	11.3019			0.394680
$821$	13.5002	−	23.3831i	0.471161	−	0.816074i	−0.528295	−	0.849061i	$-0.677169\pi$
$821$	13.5002	−	23.3831i	0.471161	−	0.816074i	0.999456	+	0.0329866i	$0.0105019\pi$
$822$	10.5955	+	18.3519i	0.369560	+	0.640096i
$823$	−6.12479	−	10.6084i	−0.213497	−	0.369787i	0.739310	−	0.673365i	$-0.235152\pi$
$823$	−6.12479	−	10.6084i	−0.213497	−	0.369787i	−0.952806	+	0.303578i	$0.901819\pi$
$824$	23.7278	−	41.0977i	0.826596	−	1.43171i
$825$	1.72967			0.0602194
$826$	3.68248	−	1.01438i	0.128130	−	0.0352946i
$827$	48.8330			1.69809			0.849044	−	0.528322i	$-0.177178\pi$
$827$	48.8330			1.69809			0.849044	+	0.528322i	$0.177178\pi$
$828$	0.0183125	−	0.0317182i	0.000636403	−	0.00110228i
$829$	−25.4753	−	44.1245i	−0.884794	−	1.53251i	−0.845950	−	0.533262i	$-0.820966\pi$
$829$	−25.4753	−	44.1245i	−0.884794	−	1.53251i	−0.0388436	−	0.999245i	$-0.512367\pi$
$830$	−6.48982	−	11.2407i	−0.225265	−	0.390170i
$831$	−1.01022	+	1.74975i	−0.0350441	+	0.0606981i
$832$	−10.1844			−0.353080
$833$	16.4269	+	9.18009i	0.569157	+	0.318071i
$834$	−31.3161			−1.08439
$835$	0.623328	−	1.07964i	0.0215712	−	0.0373623i
$836$	0.550899	+	0.954185i	0.0190532	+	0.0330012i
$837$	22.4797	+	38.9359i	0.777011	+	1.34582i
$838$	9.90908	−	17.1630i	0.342304	−	0.592887i
$839$	−3.97731			−0.137312			−0.0686559	−	0.997640i	$-0.521871\pi$
$839$	−3.97731			−0.137312			−0.0686559	+	0.997640i	$0.521871\pi$
$840$	−12.2093	+	3.36319i	−0.421262	+	0.116041i
$841$	39.4372			1.35990
$842$	−2.36974	+	4.10451i	−0.0816666	+	0.141451i
$843$	−19.5073	−	33.7877i	−0.671868	−	1.16371i
$844$	3.18062	+	5.50900i	0.109481	+	0.189627i
$845$	3.70478	−	6.41687i	0.127448	−	0.220747i
$846$	0.00856292			0.000294399
$847$	0.666879	−	2.56033i	0.0229142	−	0.0879739i
$848$	0.419099			0.0143919
$849$	3.95308	−	6.84694i	0.135669	−	0.234986i
$850$	1.12910	+	1.95567i	0.0387280	+	0.0670788i
$851$	18.0926	+	31.3374i	0.620208	+	1.07423i
$852$	−10.5604	+	18.2912i	−0.361794	+	0.626645i
$853$	38.4264			1.31570			0.657848	−	0.753151i	$-0.271467\pi$
$853$	38.4264			1.31570			0.657848	+	0.753151i	$0.271467\pi$
$854$	18.3026	+	18.0483i	0.626302	+	0.617602i
$855$	0.00701484			0.000239903
$856$	0.100300	−	0.173725i	0.00342819	−	0.00593779i
$857$	−24.8493	−	43.0402i	−0.848836	−	1.47023i	−0.882248	−	0.470785i	$-0.843971\pi$
$857$	−24.8493	−	43.0402i	−0.848836	−	1.47023i	0.0334125	−	0.999442i	$-0.489363\pi$
$858$	1.71769	+	2.97513i	0.0586411	+	0.101569i
$859$	−3.48818	+	6.04170i	−0.119015	+	0.206140i	−0.919378	−	0.393376i	$-0.871307\pi$
$859$	−3.48818	+	6.04170i	−0.119015	+	0.206140i	0.800363	+	0.599516i	$0.204640\pi$
$860$	3.22015			0.109806
$861$	28.4517	+	28.0565i	0.969632	+	0.956162i
$862$	−9.31351			−0.317219
$863$	5.10681	−	8.84525i	0.173838	−	0.301096i	−0.765921	−	0.642935i	$-0.777717\pi$
$863$	5.10681	−	8.84525i	0.173838	−	0.301096i	0.939758	+	0.341839i	$0.111050\pi$
$864$	−14.9764	−	25.9398i	−0.509507	−	0.882492i
$865$	−5.41909	−	9.38614i	−0.184255	−	0.319138i
$866$	−13.5548	+	23.4776i	−0.460610	+	0.797800i
$867$	16.9043			0.574101
$868$	7.45844	−	28.6350i	0.253156	−	0.971934i
$869$	10.7161			0.363520
$870$	6.00993	−	10.4095i	0.203756	−	0.352915i
$871$	3.24008	+	5.61198i	0.109786	+	0.190155i
$872$	19.3692	+	33.5484i	0.655923	+	1.13609i
$873$	−0.00357813	+	0.00619750i	−0.000121101	+	0.000209754i
$874$	2.45517			0.0830472
$875$	−2.55075	+	0.702629i	−0.0862310	+	0.0237532i
$876$	−18.7562			−0.633713
$877$	−5.92083	+	10.2552i	−0.199932	+	0.346293i	−0.948506	−	0.316759i	$-0.897406\pi$
$877$	−5.92083	+	10.2552i	−0.199932	+	0.346293i	0.748574	+	0.663051i	$0.230739\pi$
$878$	2.95271	+	5.11424i	0.0996490	+	0.172597i
$879$	−0.121861	−	0.211069i	−0.00411027	−	0.00711920i
$880$	0.132059	−	0.228733i	0.00445171	−	0.00771058i
$881$	−19.7987			−0.667036			−0.333518	−	0.942744i	$-0.608236\pi$
$881$	−19.7987			−0.667036			−0.333518	+	0.942744i	$0.608236\pi$
$882$	0.0423003	+	0.0236393i	0.00142432	+	0.000795978i
$883$	−49.1745			−1.65485			−0.827426	−	0.561574i	$-0.810196\pi$
$883$	−49.1745			−1.65485			−0.827426	+	0.561574i	$0.810196\pi$
$884$	4.11362	−	7.12501i	0.138356	−	0.239640i
$885$	−1.48633	−	2.57440i	−0.0499625	−	0.0865377i
$886$	1.74807	+	3.02775i	0.0587276	+	0.101719i
$887$	−16.0511	+	27.8012i	−0.538942	+	0.933475i	0.460020	+	0.887909i	$0.347842\pi$
$887$	−16.0511	+	27.8012i	−0.538942	+	0.933475i	−0.998961	+	0.0455658i	$0.985491\pi$
$888$	50.4441			1.69279
$889$	−11.0017	+	3.03053i	−0.368985	+	0.101641i
$890$	−9.51695			−0.319009
$891$	−4.48760	+	7.77276i	−0.150340	+	0.260397i
$892$	−7.41171	−	12.8375i	−0.248163	−	0.429830i
$893$	−0.526470	−	0.911873i	−0.0176176	−	0.0305147i
$894$	8.68078	−	15.0355i	0.290329	−	0.502864i
$895$	1.54063			0.0514975
$896$	−5.26487	+	20.2132i	−0.175887	+	0.675277i
$897$	−14.0421			−0.468853
$898$	13.7755	−	23.8598i	0.459693	−	0.796212i
$899$	35.7405	+	61.9043i	1.19201	+	2.06462i
$900$	−0.00533336	−	0.00923765i	−0.000177779	−	0.000307922i
$901$	2.13286	−	3.69423i	0.0710560	−	0.123073i
$902$	7.33473			0.244220
$903$	8.10650	+	7.99388i	0.269767	+	0.266020i
$904$	−53.1737			−1.76853
$905$	5.19160	−	8.99211i	0.172575	−	0.298908i
$906$	5.87438	+	10.1747i	0.195163	+	0.338033i
$907$	10.3096	+	17.8568i	0.342325	+	0.592924i	0.984864	−	0.173329i	$-0.0554523\pi$
$907$	10.3096	+	17.8568i	0.342325	+	0.592924i	−0.642539	+	0.766253i	$0.722119\pi$
$908$	−9.70927	+	16.8169i	−0.322213	+	0.558090i
$909$	−0.0509002			−0.00168825
$910$	−3.74165	−	3.68967i	−0.124034	−	0.122311i
$911$	48.7546			1.61531			0.807656	−	0.589654i	$-0.200736\pi$
$911$	48.7546			1.61531			0.807656	+	0.589654i	$0.200736\pi$
$912$	−0.194436	+	0.336772i	−0.00643841	+	0.0111516i
$913$	7.72579	+	13.3815i	0.255686	+	0.442862i
$914$	−8.29578	−	14.3687i	−0.274400	−	0.475275i
$915$	10.0024	−	17.3247i	0.330671	−	0.572738i
$916$	−28.4652			−0.940515
$917$	−2.48838	+	9.55354i	−0.0821734	+	0.315486i
$918$	−11.7501			−0.387810
$919$	17.2150	−	29.8173i	0.567872	−	0.983583i	−0.428904	−	0.903350i	$-0.641100\pi$
$919$	17.2150	−	29.8173i	0.567872	−	0.983583i	0.996776	−	0.0802329i	$-0.0255664\pi$
$920$	−4.75092	−	8.22884i	−0.156633	−	0.271297i
$921$	2.27443	+	3.93943i	0.0749451	+	0.129809i
$922$	4.69239	−	8.12745i	0.154535	−	0.267663i
$923$	−22.3056			−0.734196
$924$	5.71068	−	1.57307i	0.187868	−	0.0517501i
$925$	10.5387			0.346509
$926$	−1.04608	+	1.81187i	−0.0343765	+	0.0595418i
$927$	0.0706592	+	0.122385i	0.00232075	+	0.00401966i
$928$	−23.8110	−	41.2418i	−0.781633	−	1.35383i
$929$	3.87101	−	6.70479i	0.127004	−	0.219977i	−0.795511	−	0.605940i	$-0.792797\pi$
$929$	3.87101	−	6.70479i	0.127004	−	0.219977i	0.922514	+	0.385963i	$0.126131\pi$
$930$	12.5544			0.411676
$931$	−0.0833524	−	5.95799i	−0.00273176	−	0.195265i
$932$	29.4051			0.963197
$933$	−1.27224	+	2.20358i	−0.0416512	+	0.0721421i
$934$	4.67912	+	8.10448i	0.153106	+	0.265187i
$935$	−1.34414	−	2.32812i	−0.0439581	−	0.0761376i
$936$	0.0269605	−	0.0466969i	0.000881231	−	0.00152634i
$937$	−25.6711			−0.838639			−0.419319	−	0.907839i	$-0.637731\pi$
$937$	−25.6711			−0.838639			−0.419319	+	0.907839i	$0.637731\pi$
$938$	−5.87246	+	1.61763i	−0.191743	+	0.0528174i
$939$	9.17107			0.299287
$940$	−0.800546	+	1.38659i	−0.0261109	+	0.0452255i
$941$	7.19213	+	12.4571i	0.234457	+	0.406091i	0.959115	−	0.283018i	$-0.0913356\pi$
$941$	7.19213	+	12.4571i	0.234457	+	0.406091i	−0.724658	+	0.689109i	$0.758002\pi$
$942$	−1.88186	−	3.25947i	−0.0613142	−	0.106199i
$943$	−14.9903	+	25.9640i	−0.488152	+	0.845505i
$944$	−0.453922			−0.0147739
$945$	3.46995	−	13.3221i	0.112877	−	0.433367i
$946$	2.08982			0.0679459
$947$	−7.96998	+	13.8044i	−0.258990	+	0.448583i	−0.965972	−	0.258648i	$-0.916723\pi$
$947$	−7.96998	+	13.8044i	−0.258990	+	0.448583i	0.706982	+	0.707232i	$0.250056\pi$
$948$	11.9958	+	20.7773i	0.389605	+	0.674816i
$949$	−9.90414	−	17.1545i	−0.321502	−	0.556858i
$950$	0.357523	−	0.619248i	0.0115996	−	0.0200911i
$951$	−20.2318			−0.656059
$952$	14.0148	+	13.8201i	0.454222	+	0.447912i
$953$	−19.0478			−0.617018			−0.308509	−	0.951221i	$-0.599830\pi$
$953$	−19.0478			−0.617018			−0.308509	+	0.951221i	$0.599830\pi$
$954$	0.00549226	−	0.00951288i	0.000177819	−	0.000307991i
$955$	4.05221	+	7.01863i	0.131126	+	0.227118i
$956$	5.93701	+	10.2832i	0.192017	+	0.332582i
$957$	−7.15450	+	12.3920i	−0.231272	+	0.400575i
$958$	−14.9138			−0.481844
$959$	27.4757	+	27.0940i	0.887235	+	0.874910i
$960$	−7.45032			−0.240458
$961$	−21.8300	+	37.8106i	−0.704192	+	1.21970i
$962$	10.4657	+	18.1271i	0.337427	+	0.584441i
$963$	0.000298685	0	0.000517337i	9.62499e−6	0	1.66710e-5i
$964$	−13.5027	+	23.3874i	−0.434893	+	0.753257i
$965$	12.3070			0.396175
$966$	3.32695	−	12.7731i	0.107043	−	0.410966i
$967$	31.6656			1.01830			0.509148	−	0.860679i	$-0.329961\pi$
$967$	31.6656			1.01830			0.509148	+	0.860679i	$0.329961\pi$
$968$	1.38367	−	2.39658i	0.0444727	−	0.0770290i
$969$	1.97903	+	3.42778i	0.0635756	+	0.110116i
$970$	0.364731	+	0.631732i	0.0117108	+	0.0202837i
$971$	17.4419	−	30.2103i	0.559738	−	0.969495i	−0.437780	−	0.899082i	$-0.644235\pi$
$971$	17.4419	−	30.2103i	0.559738	−	0.969495i	0.997518	−	0.0704128i	$-0.0224317\pi$
$972$	0.110851			0.00355556
$973$	−54.9771	+	15.1440i	−1.76248	+	0.485494i
$974$	17.8695			0.572575
$975$	−2.04482	+	3.54174i	−0.0654868	+	0.113426i
$976$	−1.52736	−	2.64546i	−0.0488895	−	0.0846792i
$977$	8.29367	+	14.3651i	0.265338	+	0.459579i	0.967652	−	0.252288i	$-0.0811831\pi$
$977$	8.29367	+	14.3651i	0.265338	+	0.459579i	−0.702314	+	0.711867i	$0.747850\pi$
$978$	−13.9991	+	24.2471i	−0.447641	+	0.775337i
$979$	11.3294			0.362090
$980$	−7.78254	+	4.63960i	−0.248604	+	0.148207i
$981$	−0.115359			−0.00368314
$982$	9.07077	−	15.7110i	0.289460	−	0.501359i
$983$	1.04107	+	1.80318i	0.0332049	+	0.0575125i	0.882150	−	0.470968i	$-0.156095\pi$
$983$	1.04107	+	1.80318i	0.0332049	+	0.0575125i	−0.848945	+	0.528481i	$0.822762\pi$
$984$	20.8973	+	36.1951i	0.666181	+	1.15386i
$985$	−4.29860	+	7.44539i	−0.136965	+	0.237230i
$986$	−18.6814			−0.594938
$987$	−5.45745	+	1.50331i	−0.173713	+	0.0478509i
$988$	−2.60510			−0.0828793
$989$	−4.27106	+	7.39770i	−0.135812	+	0.235233i
$990$	−0.00346125	−	0.00599506i	−0.000110006	−	0.000190536i
$991$	12.1021	+	20.9614i	0.384435	+	0.665862i	0.991691	−	0.128645i	$-0.0410628\pi$
$991$	12.1021	+	20.9614i	0.384435	+	0.665862i	−0.607255	+	0.794507i	$0.707729\pi$
$992$	24.8699	−	43.0760i	0.789621	−	1.36766i
$993$	46.4040			1.47259
$994$	5.28478	−	20.2897i	0.167623	−	0.643549i
$995$	12.9998			0.412122
$996$	−17.2967	+	29.9588i	−0.548067	+	0.949280i
$997$	−30.0524	−	52.0523i	−0.951769	−	1.64851i	−0.741595	−	0.670848i	$-0.765930\pi$
$997$	−30.0524	−	52.0523i	−0.951769	−	1.64851i	−0.210174	−	0.977664i	$-0.567403\pi$
$998$	−13.5389	−	23.4500i	−0.428566	−	0.742298i
$999$	−27.4177	+	47.4889i	−0.867458	+	1.50248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.c.331.4	yes	16
7.2	even	3		2695.2.a.t.1.5		8
7.4	even	3	inner	385.2.i.c.221.4	✓	16
7.5	odd	6		2695.2.a.s.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.4	✓	16	7.4	even	3	inner
385.2.i.c.331.4	yes	16	1.1	even	1	trivial
2695.2.a.s.1.5		8	7.5	odd	6
2695.2.a.t.1.5		8	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.420010 + 0.727479i) q^{2} +(0.864835 + 1.49794i) q^{3} +(0.647183 + 1.12095i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.45296 q^{6} +(-2.55075 + 0.702629i) q^{7} -2.76733 q^{8} +(0.00412044 - 0.00713681i) q^{9} +O(q^{10})\)	\(q+(-0.420010 + 0.727479i) q^{2} +(0.864835 + 1.49794i) q^{3} +(0.647183 + 1.12095i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.45296 q^{6} +(-2.55075 + 0.702629i) q^{7} -2.76733 q^{8} +(0.00412044 - 0.00713681i) q^{9} +(-0.420010 - 0.727479i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.11941 + 1.93888i) q^{12} -2.36441 q^{13} +(0.560192 - 2.15073i) q^{14} -1.72967 q^{15} +(-0.132059 + 0.228733i) q^{16} +(1.34414 + 2.32812i) q^{17} +(0.00346125 + 0.00599506i) q^{18} +(0.425613 - 0.737183i) q^{19} -1.29437 q^{20} +(-3.25847 - 3.21320i) q^{21} -0.840020 q^{22} +(1.71679 - 2.97356i) q^{23} +(-2.39329 - 4.14529i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.993076 - 1.72006i) q^{26} +5.20326 q^{27} +(-2.43842 - 2.40454i) q^{28} +8.27268 q^{29} +(0.726479 - 1.25830i) q^{30} +(4.32030 + 7.48298i) q^{31} +(-2.87827 - 4.98530i) q^{32} +(-0.864835 + 1.49794i) q^{33} -2.25821 q^{34} +(0.666879 - 2.56033i) q^{35} +0.0106667 q^{36} +(-5.26933 + 9.12674i) q^{37} +(0.357523 + 0.619248i) q^{38} +(-2.04482 - 3.54174i) q^{39} +(1.38367 - 2.39658i) q^{40} -8.73162 q^{41} +(3.70613 - 1.02089i) q^{42} -2.48782 q^{43} +(-0.647183 + 1.12095i) q^{44} +(0.00412044 + 0.00713681i) q^{45} +(1.44214 + 2.49785i) q^{46} +(0.618485 - 1.07125i) q^{47} -0.456837 q^{48} +(6.01262 - 3.58446i) q^{49} +0.840020 q^{50} +(-2.32492 + 4.02688i) q^{51} +(-1.53021 - 2.65040i) q^{52} +(-0.793393 - 1.37420i) q^{53} +(-2.18542 + 3.78526i) q^{54} -1.00000 q^{55} +(7.05877 - 1.94441i) q^{56} +1.47234 q^{57} +(-3.47461 + 6.01820i) q^{58} +(0.859316 + 1.48838i) q^{59} +(-1.11941 - 1.93888i) q^{60} +(-5.78286 + 10.0162i) q^{61} -7.25827 q^{62} +(-0.00549567 + 0.0210993i) q^{63} +4.30736 q^{64} +(1.18220 - 2.04764i) q^{65} +(-0.726479 - 1.25830i) q^{66} +(-1.37035 - 2.37352i) q^{67} +(-1.73981 + 3.01344i) q^{68} +5.93895 q^{69} +(1.58249 + 1.56050i) q^{70} +9.43388 q^{71} +(-0.0114026 + 0.0197499i) q^{72} +(4.18884 + 7.25529i) q^{73} +(-4.42634 - 7.66665i) q^{74} +(0.864835 - 1.49794i) q^{75} +1.10180 q^{76} +(-1.88387 - 1.85770i) q^{77} +3.43539 q^{78} +(5.35807 - 9.28045i) q^{79} +(-0.132059 - 0.228733i) q^{80} +(4.48760 + 7.77276i) q^{81} +(3.66737 - 6.35206i) q^{82} +15.4516 q^{83} +(1.49303 - 5.73213i) q^{84} -2.68828 q^{85} +(1.04491 - 1.80984i) q^{86} +(7.15450 + 12.3920i) q^{87} +(-1.38367 - 2.39658i) q^{88} +(5.66472 - 9.81158i) q^{89} -0.00692250 q^{90} +(6.03101 - 1.66130i) q^{91} +4.44431 q^{92} +(-7.47269 + 12.9431i) q^{93} +(0.519540 + 0.899869i) q^{94} +(0.425613 + 0.737183i) q^{95} +(4.97845 - 8.62293i) q^{96} -0.868386 q^{97} +(0.0822551 + 5.87956i) q^{98} +0.00824088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Introduction

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