LMFDB - Embedded newform 847.2.e.h.485.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(485,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("847.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.e (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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} - x^{19} + 15 x^{18} - 14 x^{17} + 149 x^{16} - 131 x^{15} + 825 x^{14} - 595 x^{13} + 3197 x^{12} + \cdots + 1 $ x^20 - x^19 + 15x^18 - 14x^17 + 149x^16 - 131x^15 + 825x^14 - 595x^13 + 3197x^12 - 1997x^11 + 6915x^10 - 2406x^9 + 9021x^8 - 3913x^7 + 4916x^6 - 1317x^5 + 1429x^4 - 426x^3 + 205x^2 - 15x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			485.4
Root			$0.336982 - 0.583670i$ of defining polynomial
Character	$\chi$	$=$	847.485
Dual form			847.2.e.h.606.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.336982 + 0.583670i) q^{2} +(-1.07557 - 1.86294i) q^{3} +(0.772886 + 1.33868i) q^{4} +(-0.844546 + 1.46280i) q^{5} +1.44979 q^{6} +(2.51615 + 0.817927i) q^{7} -2.38972 q^{8} +(-0.813692 + 1.40936i) q^{9} +O(q^{10})$	\(q+(-0.336982 + 0.583670i) q^{2} +(-1.07557 - 1.86294i) q^{3} +(0.772886 + 1.33868i) q^{4} +(-0.844546 + 1.46280i) q^{5} +1.44979 q^{6} +(2.51615 + 0.817927i) q^{7} -2.38972 q^{8} +(-0.813692 + 1.40936i) q^{9} +(-0.569194 - 0.985873i) q^{10} +(1.66258 - 2.87968i) q^{12} +3.97382 q^{13} +(-1.32530 + 1.19297i) q^{14} +3.63347 q^{15} +(-0.740479 + 1.28255i) q^{16} +(-1.28446 - 2.22474i) q^{17} +(-0.548399 - 0.949855i) q^{18} +(0.167092 - 0.289411i) q^{19} -2.61095 q^{20} +(-1.18254 - 5.56716i) q^{21} +(-2.11859 + 3.66950i) q^{23} +(2.57031 + 4.45191i) q^{24} +(1.07348 + 1.85933i) q^{25} +(-1.33911 + 2.31940i) q^{26} -2.95268 q^{27} +(0.849755 + 4.00048i) q^{28} -3.11271 q^{29} +(-1.22441 + 2.12075i) q^{30} +(3.82446 + 6.62416i) q^{31} +(-2.88878 - 5.00351i) q^{32} +1.73135 q^{34} +(-3.32146 + 2.98984i) q^{35} -2.51557 q^{36} +(-5.07095 + 8.78315i) q^{37} +(0.112614 + 0.195053i) q^{38} +(-4.27412 - 7.40298i) q^{39} +(2.01823 - 3.49568i) q^{40} +10.8341 q^{41} +(3.64788 + 1.18582i) q^{42} +6.26797 q^{43} +(-1.37440 - 2.38053i) q^{45} +(-1.42785 - 2.47311i) q^{46} +(1.18203 - 2.04734i) q^{47} +3.18574 q^{48} +(5.66199 + 4.11605i) q^{49} -1.44698 q^{50} +(-2.76304 + 4.78572i) q^{51} +(3.07131 + 5.31967i) q^{52} +(2.19344 + 3.79915i) q^{53} +(0.995001 - 1.72339i) q^{54} +(-6.01289 - 1.95462i) q^{56} -0.718874 q^{57} +(1.04893 - 1.81679i) q^{58} +(0.0174953 + 0.0303028i) q^{59} +(2.80826 + 4.86404i) q^{60} +(-2.05368 + 3.55708i) q^{61} -5.15510 q^{62} +(-3.20012 + 2.88061i) q^{63} +0.931952 q^{64} +(-3.35608 + 5.81290i) q^{65} +(-2.72981 - 4.72817i) q^{67} +(1.98548 - 3.43895i) q^{68} +9.11473 q^{69} +(-0.625804 - 2.94616i) q^{70} +9.43119 q^{71} +(1.94450 - 3.36797i) q^{72} +(-0.149860 - 0.259565i) q^{73} +(-3.41764 - 5.91952i) q^{74} +(2.30921 - 3.99966i) q^{75} +0.516572 q^{76} +5.76120 q^{78} +(-7.11791 + 12.3286i) q^{79} +(-1.25074 - 2.16634i) q^{80} +(5.61689 + 9.72873i) q^{81} +(-3.65088 + 6.32351i) q^{82} +4.64425 q^{83} +(6.53867 - 5.88582i) q^{84} +4.33913 q^{85} +(-2.11219 + 3.65843i) q^{86} +(3.34793 + 5.79878i) q^{87} +(-6.99890 + 12.1225i) q^{89} +1.85259 q^{90} +(9.99872 + 3.25030i) q^{91} -6.54970 q^{92} +(8.22694 - 14.2495i) q^{93} +(0.796649 + 1.37984i) q^{94} +(0.282234 + 0.488843i) q^{95} +(-6.21416 + 10.7632i) q^{96} -3.30829 q^{97} +(-4.31040 + 1.91770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9}+O(q^{10}) $ 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9	\( 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9} - 7 q^{10} - 9 q^{12} + 2 q^{13} - 19 q^{14} - 2 q^{15} - 15 q^{16} - 19 q^{17} - 17 q^{18} - 28 q^{19} - 10 q^{20} + q^{21} - 7 q^{23} - 19 q^{24} + 8 q^{25} + 5 q^{26} + 12 q^{27} - 8 q^{28} - 30 q^{29} + 22 q^{30} + 14 q^{31} + 15 q^{32} + 24 q^{34} - 8 q^{35} + 32 q^{36} - 13 q^{37} - 24 q^{38} - 4 q^{39} - 10 q^{40} + 70 q^{41} + 25 q^{42} + 36 q^{43} - 8 q^{45} - 9 q^{46} - 16 q^{47} - 66 q^{48} - 25 q^{49} + 12 q^{50} + 21 q^{51} + 4 q^{52} + 9 q^{53} - 17 q^{54} + 12 q^{56} + 8 q^{57} + 9 q^{58} - 12 q^{59} + 21 q^{60} - 20 q^{61} + 76 q^{62} - 12 q^{63} - 58 q^{64} + 20 q^{65} - 19 q^{67} - 56 q^{68} + 18 q^{69} + 21 q^{70} + 30 q^{71} + 4 q^{72} - 3 q^{73} - 42 q^{74} + 27 q^{75} + 48 q^{76} - 50 q^{78} + 32 q^{79} + 6 q^{80} + 46 q^{81} + 18 q^{82} + 58 q^{83} - 73 q^{84} - 46 q^{85} - 9 q^{86} - 24 q^{87} - 5 q^{89} + 24 q^{90} + 28 q^{91} + 30 q^{92} + q^{93} + 19 q^{94} - q^{95} - 46 q^{96} + 8 q^{97} - 58 q^{98}+O(q^{100}) \) 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9 - 7 * q^10 - 9 * q^12 + 2 * q^13 - 19 * q^14 - 2 * q^15 - 15 * q^16 - 19 * q^17 - 17 * q^18 - 28 * q^19 - 10 * q^20 + q^21 - 7 * q^23 - 19 * q^24 + 8 * q^25 + 5 * q^26 + 12 * q^27 - 8 * q^28 - 30 * q^29 + 22 * q^30 + 14 * q^31 + 15 * q^32 + 24 * q^34 - 8 * q^35 + 32 * q^36 - 13 * q^37 - 24 * q^38 - 4 * q^39 - 10 * q^40 + 70 * q^41 + 25 * q^42 + 36 * q^43 - 8 * q^45 - 9 * q^46 - 16 * q^47 - 66 * q^48 - 25 * q^49 + 12 * q^50 + 21 * q^51 + 4 * q^52 + 9 * q^53 - 17 * q^54 + 12 * q^56 + 8 * q^57 + 9 * q^58 - 12 * q^59 + 21 * q^60 - 20 * q^61 + 76 * q^62 - 12 * q^63 - 58 * q^64 + 20 * q^65 - 19 * q^67 - 56 * q^68 + 18 * q^69 + 21 * q^70 + 30 * q^71 + 4 * q^72 - 3 * q^73 - 42 * q^74 + 27 * q^75 + 48 * q^76 - 50 * q^78 + 32 * q^79 + 6 * q^80 + 46 * q^81 + 18 * q^82 + 58 * q^83 - 73 * q^84 - 46 * q^85 - 9 * q^86 - 24 * q^87 - 5 * q^89 + 24 * q^90 + 28 * q^91 + 30 * q^92 + q^93 + 19 * q^94 - q^95 - 46 * q^96 + 8 * q^97 - 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.336982	+	0.583670i	−0.238282	+	0.412717i	−0.960221	−	0.279239i	$-0.909918\pi$
$2$	−0.336982	+	0.583670i	−0.238282	+	0.412717i	0.721939	+	0.691956i	$0.243251\pi$
$3$	−1.07557	−	1.86294i	−0.620979	−	1.07557i	−0.989304	−	0.145870i	$-0.953402\pi$
$3$	−1.07557	−	1.86294i	−0.620979	−	1.07557i	0.368324	−	0.929697i	$-0.379932\pi$
$4$	0.772886	+	1.33868i	0.386443	+	0.669339i
$5$	−0.844546	+	1.46280i	−0.377693	+	0.654183i	−0.990726	−	0.135874i	$-0.956616\pi$
$5$	−0.844546	+	1.46280i	−0.377693	+	0.654183i	0.613033	+	0.790057i	$0.289949\pi$
$6$	1.44979			0.591873
$7$	2.51615	+	0.817927i	0.951014	+	0.309147i
$7$	2.51615	+	0.817927i	0.951014	+	0.309147i
$8$	−2.38972			−0.844895
$9$	−0.813692	+	1.40936i	−0.271231	+	0.469785i
$10$	−0.569194	−	0.985873i	−0.179995	−	0.311760i
$11$		0			0
$11$		0			0
$12$	1.66258	−	2.87968i	0.479946	−	0.831292i
$13$	3.97382			1.10214			0.551070	−	0.834459i	$-0.314220\pi$
$13$	3.97382			1.10214			0.551070	+	0.834459i	$0.314220\pi$
$14$	−1.32530	+	1.19297i	−0.354200	+	0.318835i
$15$	3.63347			0.938157
$16$	−0.740479	+	1.28255i	−0.185120	+	0.320637i
$17$	−1.28446	−	2.22474i	−0.311526	−	0.539580i	0.667167	−	0.744909i	$-0.267507\pi$
$17$	−1.28446	−	2.22474i	−0.311526	−	0.539580i	−0.978693	+	0.205329i	$0.934174\pi$
$18$	−0.548399	−	0.949855i	−0.129259	−	0.223883i
$19$	0.167092	−	0.289411i	0.0383335	−	0.0663955i	−0.846222	−	0.532830i	$-0.821128\pi$
$19$	0.167092	−	0.289411i	0.0383335	−	0.0663955i	0.884556	+	0.466435i	$0.154462\pi$
$20$	−2.61095			−0.583827
$21$	−1.18254	−	5.56716i	−0.258051	−	1.21485i
$22$		0			0
$23$	−2.11859	+	3.66950i	−0.441756	+	0.765143i	−0.997820	−	0.0659962i	$-0.978977\pi$
$23$	−2.11859	+	3.66950i	−0.441756	+	0.765143i	0.556064	+	0.831139i	$0.312311\pi$
$24$	2.57031	+	4.45191i	0.524662	+	0.908742i
$25$	1.07348	+	1.85933i	0.214697	+	0.371865i
$26$	−1.33911	+	2.31940i	−0.262620	+	0.454872i
$27$	−2.95268			−0.568244
$28$	0.849755	+	4.00048i	0.160589	+	0.756019i
$29$	−3.11271			−0.578015			−0.289008	−	0.957327i	$-0.593325\pi$
$29$	−3.11271			−0.578015			−0.289008	+	0.957327i	$0.593325\pi$
$30$	−1.22441	+	2.12075i	−0.223546	+	0.387194i
$31$	3.82446	+	6.62416i	0.686894	+	1.18973i	0.972838	+	0.231488i	$0.0743595\pi$
$31$	3.82446	+	6.62416i	0.686894	+	1.18973i	−0.285944	+	0.958246i	$0.592307\pi$
$32$	−2.88878	−	5.00351i	−0.510669	−	0.884504i
$33$		0			0
$34$	1.73135			0.296925
$35$	−3.32146	+	2.98984i	−0.561430	+	0.505375i
$36$	−2.51557			−0.419261
$37$	−5.07095	+	8.78315i	−0.833659	+	1.44394i	0.0614580	+	0.998110i	$0.480425\pi$
$37$	−5.07095	+	8.78315i	−0.833659	+	1.44394i	−0.895117	+	0.445831i	$0.852908\pi$
$38$	0.112614	+	0.195053i	0.0182684	+	0.0316418i
$39$	−4.27412	−	7.40298i	−0.684406	−	1.18543i
$40$	2.01823	−	3.49568i	0.319111	−	0.552716i
$41$	10.8341			1.69200			0.845998	−	0.533186i	$-0.179006\pi$
$41$	10.8341			1.69200			0.845998	+	0.533186i	$0.179006\pi$
$42$	3.64788	+	1.18582i	0.562880	+	0.182976i
$43$	6.26797			0.955857			0.477928	−	0.878399i	$-0.341388\pi$
$43$	6.26797			0.955857			0.477928	+	0.878399i	$0.341388\pi$
$44$		0			0
$45$	−1.37440	−	2.38053i	−0.204884	−	0.354869i
$46$	−1.42785	−	2.47311i	−0.210525	−	0.364640i
$47$	1.18203	−	2.04734i	0.172417	−	0.298636i	−0.766847	−	0.641830i	$-0.778176\pi$
$47$	1.18203	−	2.04734i	0.172417	−	0.298636i	0.939265	+	0.343194i	$0.111509\pi$
$48$	3.18574			0.459822
$49$	5.66199	+	4.11605i	0.808856	+	0.588007i
$50$	−1.44698			−0.204633
$51$	−2.76304	+	4.78572i	−0.386903	+	0.670135i
$52$	3.07131	+	5.31967i	0.425914	+	0.737705i
$53$	2.19344	+	3.79915i	0.301292	+	0.521853i	0.976429	−	0.215840i	$-0.0692488\pi$
$53$	2.19344	+	3.79915i	0.301292	+	0.521853i	−0.675137	+	0.737692i	$0.735915\pi$
$54$	0.995001	−	1.72339i	0.135402	−	0.234524i
$55$		0			0
$56$	−6.01289	−	1.95462i	−0.803507	−	0.261197i
$57$	−0.718874			−0.0952172
$58$	1.04893	−	1.81679i	0.137731	−	0.238557i
$59$	0.0174953	+	0.0303028i	0.00227769	+	0.00394508i	0.867162	−	0.498026i	$-0.165942\pi$
$59$	0.0174953	+	0.0303028i	0.00227769	+	0.00394508i	−0.864884	+	0.501971i	$0.832608\pi$
$60$	2.80826	+	4.86404i	0.362544	+	0.627945i
$61$	−2.05368	+	3.55708i	−0.262947	+	0.455437i	−0.967024	−	0.254686i	$-0.918028\pi$
$61$	−2.05368	+	3.55708i	−0.262947	+	0.455437i	0.704077	+	0.710124i	$0.251361\pi$
$62$	−5.15510			−0.654698
$63$	−3.20012	+	2.88061i	−0.403177	+	0.362922i
$64$	0.931952			0.116494
$65$	−3.35608	+	5.81290i	−0.416270	+	0.721001i
$66$		0			0
$67$	−2.72981	−	4.72817i	−0.333499	−	0.577637i	0.649696	−	0.760194i	$-0.274896\pi$
$67$	−2.72981	−	4.72817i	−0.333499	−	0.577637i	−0.983195	+	0.182557i	$0.941563\pi$
$68$	1.98548	−	3.43895i	0.240774	−	0.417034i
$69$	9.11473			1.09728
$70$	−0.625804	−	2.94616i	−0.0747979	−	0.352133i
$71$	9.43119			1.11928			0.559638	−	0.828737i	$-0.310940\pi$
$71$	9.43119			1.11928			0.559638	+	0.828737i	$0.310940\pi$
$72$	1.94450	−	3.36797i	0.229161	−	0.396919i
$73$	−0.149860	−	0.259565i	−0.0175398	−	0.0303798i	0.857122	−	0.515113i	$-0.172250\pi$
$73$	−0.149860	−	0.259565i	−0.0175398	−	0.0303798i	−0.874662	+	0.484733i	$0.838917\pi$
$74$	−3.41764	−	5.91952i	−0.397292	−	0.688131i
$75$	2.30921	−	3.99966i	0.266644	−	0.461841i
$76$	0.516572			0.0592548
$77$		0			0
$78$	5.76120			0.652327
$79$	−7.11791	+	12.3286i	−0.800828	+	1.38707i	0.118244	+	0.992985i	$0.462273\pi$
$79$	−7.11791	+	12.3286i	−0.800828	+	1.38707i	−0.919072	+	0.394090i	$0.871060\pi$
$80$	−1.25074	−	2.16634i	−0.139837	−	0.242204i
$81$	5.61689	+	9.72873i	0.624099	+	1.08097i
$82$	−3.65088	+	6.32351i	−0.403173	+	0.698315i
$83$	4.64425			0.509773			0.254886	−	0.966971i	$-0.417962\pi$
$83$	4.64425			0.509773			0.254886	+	0.966971i	$0.417962\pi$
$84$	6.53867	−	5.88582i	0.713427	−	0.642196i
$85$	4.33913			0.470645
$86$	−2.11219	+	3.65843i	−0.227764	+	0.394498i
$87$	3.34793	+	5.79878i	0.358935	+	0.621694i
$88$		0			0
$89$	−6.99890	+	12.1225i	−0.741882	+	1.28498i	0.209755	+	0.977754i	$0.432733\pi$
$89$	−6.99890	+	12.1225i	−0.741882	+	1.28498i	−0.951637	+	0.307224i	$0.900600\pi$
$90$	1.85259			0.195281
$91$	9.99872	+	3.25030i	1.04815	+	0.340724i
$92$	−6.54970			−0.682854
$93$	8.22694	−	14.2495i	0.853093	−	1.47760i
$94$	0.796649	+	1.37984i	0.0821681	+	0.142319i
$95$	0.282234	+	0.488843i	0.0289566	+	0.0501542i
$96$	−6.21416	+	10.7632i	−0.634230	+	1.09852i
$97$	−3.30829			−0.335906			−0.167953	−	0.985795i	$-0.553716\pi$
$97$	−3.30829			−0.335906			−0.167953	+	0.985795i	$0.553716\pi$
$98$	−4.31040	+	1.91770i	−0.435416	+	0.193717i
$99$		0			0
$100$	−1.65936	+	2.87410i	−0.165936	+	0.287410i
$101$	4.60578	+	7.97744i	0.458292	+	0.793785i	0.998871	−	0.0475083i	$-0.0151281\pi$
$101$	4.60578	+	7.97744i	0.458292	+	0.793785i	−0.540579	+	0.841293i	$0.681795\pi$
$102$	−1.86219	−	3.22541i	−0.184384	−	0.319363i
$103$	8.33987	−	14.4451i	0.821752	−	1.42332i	−0.0826250	−	0.996581i	$-0.526330\pi$
$103$	8.33987	−	14.4451i	0.821752	−	1.42332i	0.904377	−	0.426735i	$-0.140336\pi$
$104$	−9.49634			−0.931192
$105$	9.14234	+	2.97191i	0.892201	+	0.290029i
$106$	−2.95660			−0.287170
$107$	0.670216	−	1.16085i	0.0647922	−	0.112223i	−0.831810	−	0.555061i	$-0.812695\pi$
$107$	0.670216	−	1.16085i	0.0647922	−	0.112223i	0.896602	+	0.442838i	$0.146028\pi$
$108$	−2.28209	−	3.95269i	−0.219594	−	0.380348i
$109$	−3.16671	−	5.48491i	−0.303316	−	0.525359i	0.673569	−	0.739124i	$-0.264760\pi$
$109$	−3.16671	−	5.48491i	−0.303316	−	0.525359i	−0.976885	+	0.213765i	$0.931427\pi$
$110$		0			0
$111$	21.8166			2.07074
$112$	−2.91218	+	2.62142i	−0.275175	+	0.247701i
$113$	−15.2159			−1.43139			−0.715694	−	0.698414i	$-0.753890\pi$
$113$	−15.2159			−1.43139			−0.715694	+	0.698414i	$0.753890\pi$
$114$	0.242248	−	0.419585i	0.0226886	−	0.0392978i
$115$	−3.57849	−	6.19812i	−0.333696	−	0.577978i
$116$	−2.40577	−	4.16691i	−0.223370	−	0.386888i
$117$	−3.23347	+	5.60053i	−0.298934	+	0.517769i
$118$	−0.0235824			−0.00217094
$119$	−1.41220	−	6.64837i	−0.129456	−	0.609455i
$120$	−8.68298			−0.792644
$121$		0			0
$122$	−1.38411	−	2.39734i	−0.125311	−	0.217045i
$123$	−11.6528	−	20.1832i	−1.05069	−	1.81986i
$124$	−5.91175	+	10.2394i	−0.530891	+	0.919530i
$125$	−12.0719			−1.07974
$126$	−0.602941	−	2.83853i	−0.0537143	−	0.252876i
$127$	−5.46607			−0.485035			−0.242517	−	0.970147i	$-0.577973\pi$
$127$	−5.46607			−0.485035			−0.242517	+	0.970147i	$0.577973\pi$
$128$	5.46351	−	9.46307i	0.482910	−	0.836425i
$129$	−6.74163	−	11.6768i	−0.593567	−	1.02809i
$130$	−2.26188	−	3.91768i	−0.198380	−	0.343604i
$131$	2.46819	−	4.27502i	0.215646	−	0.373510i	−0.737826	−	0.674991i	$-0.764147\pi$
$131$	2.46819	−	4.27502i	0.215646	−	0.373510i	0.953472	+	0.301481i	$0.0974808\pi$
$132$		0			0
$133$	0.657145	−	0.591533i	0.0569817	−	0.0512924i
$134$	3.67958			0.317868
$135$	2.49368	−	4.31918i	0.214622	−	0.371736i
$136$	3.06949	+	5.31652i	0.263207	+	0.455888i
$137$	−0.817669	−	1.41624i	−0.0698582	−	0.120998i	0.828981	−	0.559277i	$-0.188921\pi$
$137$	−0.817669	−	1.41624i	−0.0698582	−	0.120998i	−0.898839	+	0.438280i	$0.855588\pi$
$138$	−3.07150	+	5.31999i	−0.261463	+	0.452868i
$139$	8.85652			0.751201			0.375600	−	0.926782i	$-0.377437\pi$
$139$	8.85652			0.751201			0.375600	+	0.926782i	$0.377437\pi$
$140$	−6.56954	−	2.13557i	−0.555228	−	0.180488i
$141$	−5.08543			−0.428271
$142$	−3.17814	+	5.50470i	−0.266704	+	0.461944i
$143$		0			0
$144$	−1.20504	−	2.08720i	−0.100420	−	0.173933i
$145$	2.62883	−	4.55326i	0.218312	−	0.378128i
$146$	0.202000			0.0167177
$147$	1.57809	−	14.9750i	0.130158	−	1.23512i
$148$	−15.6771			−1.28865
$149$	−2.39581	+	4.14966i	−0.196272	+	0.339953i	−0.947317	−	0.320298i	$-0.896217\pi$
$149$	−2.39581	+	4.14966i	−0.196272	+	0.339953i	0.751045	+	0.660251i	$0.229550\pi$
$150$	1.55632	+	2.69563i	0.127073	+	0.220097i
$151$	−8.03887	−	13.9237i	−0.654194	−	1.13310i	−0.982095	−	0.188385i	$-0.939675\pi$
$151$	−8.03887	−	13.9237i	−0.654194	−	1.13310i	0.327901	−	0.944712i	$-0.393659\pi$
$152$	−0.399303	+	0.691613i	−0.0323878	+	0.0560972i
$153$	4.18061			0.337982
$154$		0			0
$155$	−12.9197			−1.03774
$156$	6.60681	−	11.4433i	0.528968	−	0.916200i
$157$	−3.40936	−	5.90519i	−0.272097	−	0.471285i	0.697302	−	0.716778i	$-0.254384\pi$
$157$	−3.40936	−	5.90519i	−0.272097	−	0.471285i	−0.969399	+	0.245492i	$0.921050\pi$
$158$	−4.79722	−	8.30902i	−0.381646	−	0.661030i
$159$	4.71838	−	8.17248i	0.374192	−	0.648120i
$160$	9.75883			0.771504
$161$	−8.33205	+	7.50015i	−0.656658	+	0.591094i
$162$	−7.57116			−0.594846
$163$	6.85970	−	11.8813i	0.537293	−	0.930619i	−0.461755	−	0.887007i	$-0.652780\pi$
$163$	6.85970	−	11.8813i	0.537293	−	0.930619i	0.999049	−	0.0436117i	$-0.0138864\pi$
$164$	8.37349	+	14.5033i	0.653860	+	1.13252i
$165$		0			0
$166$	−1.56503	+	2.71071i	−0.121470	+	0.210392i
$167$	19.5590			1.51352			0.756760	−	0.653693i	$-0.226781\pi$
$167$	19.5590			1.51352			0.756760	+	0.653693i	$0.226781\pi$
$168$	2.82594	+	13.3040i	0.218026	+	1.02642i
$169$	2.79126			0.214713
$170$	−1.46221	+	2.53262i	−0.112146	+	0.194243i
$171$	0.271923	+	0.470984i	0.0207944	+	0.0360170i
$172$	4.84443	+	8.39080i	0.369384	+	0.639792i
$173$	1.83973	−	3.18651i	0.139872	−	0.242266i	−0.787576	−	0.616218i	$-0.788664\pi$
$173$	1.83973	−	3.18651i	0.139872	−	0.242266i	0.927448	+	0.373952i	$0.121997\pi$
$174$	−4.51276			−0.342112
$175$	1.18025	+	5.55637i	0.0892183	+	0.420022i
$176$		0			0
$177$	0.0376348	−	0.0651853i	0.00282880	−	0.00489963i
$178$	−4.71701	−	8.17010i	−0.353555	−	0.612375i
$179$	−9.86780	−	17.0915i	−0.737554	−	1.27748i	−0.953594	−	0.301097i	$-0.902647\pi$
$179$	−9.86780	−	17.0915i	−0.737554	−	1.27748i	0.216039	−	0.976385i	$-0.430686\pi$
$180$	2.12451	−	3.67976i	0.158352	−	0.274273i
$181$	−2.21244			−0.164449			−0.0822246	−	0.996614i	$-0.526202\pi$
$181$	−2.21244			−0.164449			−0.0822246	+	0.996614i	$0.526202\pi$
$182$	−5.26649	+	4.74066i	−0.390378	+	0.351401i
$183$	8.83549			0.653139
$184$	5.06283	−	8.76908i	0.373237	−	0.646465i
$185$	−8.56531	−	14.8356i	−0.629734	−	1.09073i
$186$	5.54466	+	9.60363i	0.406554	+	0.704172i
$187$		0			0
$188$	3.65431			0.266518
$189$	−7.42938	−	2.41508i	−0.540408	−	0.175671i
$190$	−0.380431			−0.0275993
$191$	−4.30221	+	7.45164i	−0.311297	+	0.539182i	−0.978643	−	0.205565i	$-0.934097\pi$
$191$	−4.30221	+	7.45164i	−0.311297	+	0.539182i	0.667346	+	0.744747i	$0.267430\pi$
$192$	−1.00238	−	1.73617i	−0.0723404	−	0.125297i
$193$	0.127767	+	0.221299i	0.00919689	+	0.0159295i	0.870587	−	0.492014i	$-0.163739\pi$
$193$	0.127767	+	0.221299i	0.00919689	+	0.0159295i	−0.861390	+	0.507944i	$0.830406\pi$
$194$	1.11483	−	1.93095i	0.0800404	−	0.138634i
$195$	14.4388			1.03398
$196$	−1.13399	+	10.7608i	−0.0809991	+	0.768630i
$197$	9.76587			0.695789			0.347895	−	0.937534i	$-0.386897\pi$
$197$	9.76587			0.695789			0.347895	+	0.937534i	$0.386897\pi$
$198$		0			0
$199$	0.176993	+	0.306561i	0.0125467	+	0.0217315i	0.872231	−	0.489095i	$-0.162673\pi$
$199$	0.176993	+	0.306561i	0.0125467	+	0.0217315i	−0.859684	+	0.510826i	$0.829339\pi$
$200$	−2.56533	−	4.44328i	−0.181396	−	0.314187i
$201$	−5.87219	+	10.1709i	−0.414192	+	0.717402i
$202$	−6.20826			−0.436811
$203$	−7.83203	−	2.54597i	−0.549701	−	0.178692i
$204$	−8.54206			−0.598064
$205$	−9.14987	+	15.8480i	−0.639054	+	1.10687i
$206$	5.62077	+	9.73546i	0.391618	+	0.678302i
$207$	−3.44775	−	5.97168i	−0.239635	−	0.415061i
$208$	−2.94253	+	5.09661i	−0.204028	+	0.353386i
$209$		0			0
$210$	−4.81542	+	4.33463i	−0.332295	+	0.299118i
$211$	−14.9065			−1.02620			−0.513102	−	0.858327i	$-0.671504\pi$
$211$	−14.9065			−1.02620			−0.513102	+	0.858327i	$0.671504\pi$
$212$	−3.39056	+	5.87262i	−0.232864	+	0.403333i
$213$	−10.1439	−	17.5697i	−0.695047	−	1.20386i
$214$	0.451702	+	0.782370i	0.0308777	+	0.0534817i
$215$	−5.29359	+	9.16878i	−0.361020	+	0.625305i
$216$	7.05609			0.480106
$217$	4.20483	+	19.7955i	0.285442	+	1.34381i
$218$	4.26850			0.289099
$219$	−0.322369	+	0.558359i	−0.0217837	+	0.0377304i
$220$		0			0
$221$	−5.10420	−	8.84073i	−0.343346	−	0.594692i
$222$	−7.35181	+	12.7337i	−0.493421	+	0.854630i
$223$	28.6542			1.91883			0.959415	−	0.281999i	$-0.0909975\pi$
$223$	28.6542			1.91883			0.959415	+	0.281999i	$0.0909975\pi$
$224$	−3.17609	−	14.9524i	−0.212211	−	0.999048i
$225$	−3.49394			−0.232929
$226$	5.12748	−	8.88105i	0.341075	−	0.590759i
$227$	−10.5329	−	18.2436i	−0.699095	−	1.21087i	−0.968780	−	0.247920i	$-0.920253\pi$
$227$	−10.5329	−	18.2436i	−0.699095	−	1.21087i	0.269685	−	0.962949i	$-0.413080\pi$
$228$	−0.555608	−	0.962341i	−0.0367960	−	0.0637326i
$229$	3.60887	−	6.25074i	0.238481	−	0.413061i	−0.721798	−	0.692104i	$-0.756684\pi$
$229$	3.60887	−	6.25074i	0.238481	−	0.413061i	0.960279	+	0.279043i	$0.0900173\pi$
$230$	4.82354			0.318055
$231$		0			0
$232$	7.43851			0.488362
$233$	12.8420	−	22.2430i	0.841309	−	1.45719i	−0.0474801	−	0.998872i	$-0.515119\pi$
$233$	12.8420	−	22.2430i	0.841309	−	1.45719i	0.888789	−	0.458317i	$-0.151548\pi$
$234$	−2.17924	−	3.77456i	−0.142461	−	0.246750i
$235$	1.99657	+	3.45815i	0.130242	+	0.225585i
$236$	−0.0270438	+	0.0468412i	−0.00176040	+	0.00304910i
$237$	30.6232			1.98919
$238$	4.35634	+	1.41612i	0.282380	+	0.0917935i
$239$	8.67528			0.561157			0.280579	−	0.959831i	$-0.409474\pi$
$239$	8.67528			0.561157			0.280579	+	0.959831i	$0.409474\pi$
$240$	−2.69051	+	4.66009i	−0.173671	+	0.300808i
$241$	−11.0355	−	19.1141i	−0.710862	−	1.23125i	−0.964534	−	0.263959i	$-0.914972\pi$
$241$	−11.0355	−	19.1141i	−0.710862	−	1.23125i	0.253672	−	0.967290i	$-0.418362\pi$
$242$		0			0
$243$	7.65366	−	13.2565i	0.490983	−	0.850407i
$244$	−6.34905			−0.406456
$245$	−10.8028	+	4.80615i	−0.690163	+	0.307054i
$246$	15.7071			1.00145
$247$	0.663993	−	1.15007i	0.0422489	−	0.0731772i
$248$	−9.13941	−	15.8299i	−0.580353	−	1.00520i
$249$	−4.99521	−	8.65195i	−0.316558	−	0.548295i
$250$	4.06801	−	7.04600i	0.257284	−	0.445628i
$251$	17.2343			1.08782			0.543910	−	0.839144i	$-0.316943\pi$
$251$	17.2343			1.08782			0.543910	+	0.839144i	$0.316943\pi$
$252$	−6.32953	−	2.05755i	−0.398723	−	0.129613i
$253$		0			0
$254$	1.84197	−	3.19038i	0.115575	−	0.200182i
$255$	−4.66703	−	8.08353i	−0.292261	−	0.506211i
$256$	4.61416	+	7.99196i	0.288385	+	0.499497i
$257$	2.86735	−	4.96639i	0.178860	−	0.309795i	−0.762630	−	0.646835i	$-0.776092\pi$
$257$	2.86735	−	4.96639i	0.178860	−	0.309795i	0.941490	+	0.337040i	$0.109426\pi$
$258$	9.08723			0.565746
$259$	−19.9432	+	17.9520i	−1.23921	+	1.11548i
$260$	−10.3755			−0.643459
$261$	2.53278	−	4.38691i	0.156775	−	0.271543i
$262$	1.66347	+	2.88121i	0.102769	+	0.178002i
$263$	11.2982	+	19.5691i	0.696679	+	1.20668i	0.969612	+	0.244650i	$0.0786729\pi$
$263$	11.2982	+	19.5691i	0.696679	+	1.20668i	−0.272933	+	0.962033i	$0.587994\pi$
$264$		0			0
$265$	−7.40984			−0.455183
$266$	0.123814	+	0.582892i	0.00759153	+	0.0357394i
$267$	30.1112			1.84277
$268$	4.21966	−	7.30867i	0.257757	−	0.446448i
$269$	8.13015	+	14.0818i	0.495704	+	0.858585i	0.999988	−	0.00495328i	$-0.00157668\pi$
$269$	8.13015	+	14.0818i	0.495704	+	0.858585i	−0.504284	+	0.863538i	$0.668243\pi$
$270$	1.68065	+	2.91097i	0.102281	+	0.177156i
$271$	3.53313	−	6.11956i	0.214622	−	0.371737i	−0.738533	−	0.674217i	$-0.764481\pi$
$271$	3.53313	−	6.11956i	0.214622	−	0.371737i	0.953156	+	0.302480i	$0.0978146\pi$
$272$	3.80445			0.230679
$273$	−4.69920	−	22.1229i	−0.284409	−	1.33894i
$274$	1.10216			0.0665839
$275$		0			0
$276$	7.04465	+	12.2017i	0.424038	+	0.734455i
$277$	5.94494	+	10.2969i	0.357197	+	0.618683i	0.987491	−	0.157673i	$-0.0503992\pi$
$277$	5.94494	+	10.2969i	0.357197	+	0.618683i	−0.630294	+	0.776356i	$0.717066\pi$
$278$	−2.98449	+	5.16929i	−0.178998	+	0.310033i
$279$	−12.4477			−0.745227
$280$	7.93738	−	7.14488i	0.474349	−	0.426988i
$281$	−10.3912			−0.619886			−0.309943	−	0.950755i	$-0.600310\pi$
$281$	−10.3912			−0.619886			−0.309943	+	0.950755i	$0.600310\pi$
$282$	1.71370	−	2.96822i	0.102049	−	0.176755i
$283$	−10.1502	−	17.5806i	−0.603366	−	1.04506i	−0.992307	−	0.123798i	$-0.960492\pi$
$283$	−10.1502	−	17.5806i	−0.603366	−	1.04506i	0.388941	−	0.921263i	$-0.372841\pi$
$284$	7.28923	+	12.6253i	0.432537	+	0.749175i
$285$	0.607123	−	1.05157i	0.0359628	−	0.0622895i
$286$		0			0
$287$	27.2601	+	8.86146i	1.60911	+	0.523076i
$288$	9.40231			0.554036
$289$	5.20034	−	9.00726i	0.305903	−	0.529839i
$290$	1.77173	+	3.06873i	0.104040	+	0.180202i
$291$	3.55829	+	6.16314i	0.208591	+	0.361289i
$292$	0.231649	−	0.401228i	0.0135562	−	0.0234801i
$293$	−23.8756			−1.39483			−0.697415	−	0.716668i	$-0.745666\pi$
$293$	−23.8756			−1.39483			−0.697415	+	0.716668i	$0.745666\pi$
$294$	8.20869	+	5.96740i	0.478740	+	0.348026i
$295$	−0.0591024			−0.00344107
$296$	12.1182	−	20.9893i	0.704354	−	1.21998i
$297$		0			0
$298$	−1.61469	−	2.79672i	−0.0935364	−	0.162010i
$299$	−8.41888	+	14.5819i	−0.486877	+	0.843295i
$300$	7.13902			0.412171
$301$	15.7711	+	5.12674i	0.909034	+	0.295501i
$302$	10.8358			0.623531
$303$	9.90765	−	17.1606i	0.569180	−	0.985848i
$304$	0.247456	+	0.428606i	0.0141926	+	0.0245822i
$305$	−3.46886	−	6.00824i	−0.198626	−	0.344031i
$306$	−1.40879	+	2.44010i	−0.0805351	+	0.139491i
$307$	−8.73868			−0.498743			−0.249372	−	0.968408i	$-0.580224\pi$
$307$	−8.73868			−0.498743			−0.249372	+	0.968408i	$0.580224\pi$
$308$		0			0
$309$	−35.8804			−2.04116
$310$	4.35372	−	7.54087i	0.247275	−	0.428292i
$311$	−1.30908	−	2.26738i	−0.0742308	−	0.128572i	0.826521	−	0.562906i	$-0.190317\pi$
$311$	−1.30908	−	2.26738i	−0.0742308	−	0.128572i	−0.900752	+	0.434335i	$0.856983\pi$
$312$	10.2140	+	17.6911i	0.578251	+	1.00156i
$313$	11.3768	−	19.7052i	0.643054	−	1.11380i	−0.341694	−	0.939811i	$-0.611001\pi$
$313$	11.3768	−	19.7052i	0.643054	−	1.11380i	0.984747	−	0.173990i	$-0.0556662\pi$
$314$	4.59557			0.259343
$315$	−1.51109	−	7.11393i	−0.0851405	−	0.400825i
$316$	−22.0053			−1.23790
$317$	−2.24407	+	3.88684i	−0.126039	+	0.218307i	−0.922139	−	0.386859i	$-0.873560\pi$
$317$	−2.24407	+	3.88684i	−0.126039	+	0.218307i	0.796099	+	0.605166i	$0.206893\pi$
$318$	3.18002	+	5.50796i	0.178327	+	0.308871i
$319$		0			0
$320$	−0.787077	+	1.36326i	−0.0439989	+	0.0762084i
$321$	−2.88345			−0.160939
$322$	−1.56986	−	7.39058i	−0.0874848	−	0.411861i
$323$	−0.858488			−0.0477676
$324$	−8.68243	+	15.0384i	−0.482357	+	0.835467i
$325$	4.26583	+	7.38863i	0.236626	+	0.409848i
$326$	4.62319	+	8.00760i	0.256055	+	0.443500i
$327$	−6.81203	+	11.7988i	−0.376706	+	0.652474i
$328$	−25.8904			−1.42956
$329$	4.64875	−	4.18460i	0.256294	−	0.230705i
$330$		0			0
$331$	6.90068	−	11.9523i	0.379296	−	0.656960i	−0.611664	−	0.791118i	$-0.709500\pi$
$331$	6.90068	−	11.9523i	0.379296	−	0.656960i	0.990960	+	0.134158i	$0.0428330\pi$
$332$	3.58948	+	6.21716i	0.196998	+	0.341211i
$333$	−8.25239	−	14.2936i	−0.452228	−	0.783282i
$334$	−6.59103	+	11.4160i	−0.360645	+	0.624655i
$335$	9.22180			0.503841
$336$	8.01579	+	2.60570i	0.437297	+	0.142153i
$337$	11.2551			0.613106			0.306553	−	0.951854i	$-0.400824\pi$
$337$	11.2551			0.613106			0.306553	+	0.951854i	$0.400824\pi$
$338$	−0.940606	+	1.62918i	−0.0511622	+	0.0886155i
$339$	16.3657	+	28.3462i	0.888863	+	1.53956i
$340$	3.35366	+	5.80870i	0.181877	+	0.315021i
$341$		0			0
$342$	−0.366532			−0.0198198
$343$	10.8798	+	14.9877i	0.587453	+	0.809258i
$344$	−14.9787			−0.807599
$345$	−7.69781	+	13.3330i	−0.414436	+	0.717825i
$346$	1.23991	+	2.14759i	0.0666581	+	0.115455i
$347$	−7.71949	−	13.3705i	−0.414404	−	0.717769i	0.580962	−	0.813931i	$-0.302677\pi$
$347$	−7.71949	−	13.3705i	−0.414404	−	0.717769i	−0.995366	+	0.0961623i	$0.969343\pi$
$348$	−5.17513	+	8.96359i	−0.277416	+	0.480499i
$349$	9.90224			0.530055			0.265027	−	0.964241i	$-0.414619\pi$
$349$	9.90224			0.530055			0.265027	+	0.964241i	$0.414619\pi$
$350$	−3.64081	−	1.18352i	−0.194609	−	0.0632619i
$351$	−11.7334			−0.626285
$352$		0			0
$353$	−4.91732	−	8.51704i	−0.261722	−	0.453316i	0.704977	−	0.709230i	$-0.250957\pi$
$353$	−4.91732	−	8.51704i	−0.261722	−	0.453316i	−0.966700	+	0.255913i	$0.917624\pi$
$354$	0.0253645	+	0.0439326i	0.00134811	+	0.00233499i
$355$	−7.96508	+	13.7959i	−0.422742	+	0.732211i
$356$	−21.6374			−1.14678
$357$	−10.8666	+	9.78162i	−0.575121	+	0.517698i
$358$	13.3011			0.702985
$359$	1.52968	−	2.64948i	0.0807332	−	0.139834i	−0.822832	−	0.568285i	$-0.807607\pi$
$359$	1.52968	−	2.64948i	0.0807332	−	0.139834i	0.903565	+	0.428451i	$0.140940\pi$
$360$	3.28444	+	5.68882i	0.173105	+	0.299827i
$361$	9.44416	+	16.3578i	0.497061	+	0.860935i
$362$	0.745552	−	1.29133i	0.0391853	−	0.0678710i
$363$		0			0
$364$	3.37677	+	15.8972i	0.176991	+	0.833239i
$365$	0.506254			0.0264986
$366$	−2.97740	+	5.15701i	−0.155631	+	0.269561i
$367$	3.83999	+	6.65106i	0.200446	+	0.347182i	0.948672	−	0.316261i	$-0.102428\pi$
$367$	3.83999	+	6.65106i	0.200446	+	0.347182i	−0.748226	+	0.663444i	$0.769094\pi$
$368$	−3.13753	−	5.43437i	−0.163555	−	0.283286i
$369$	−8.81559	+	15.2690i	−0.458921	+	0.794875i
$370$	11.5454			0.600218
$371$	2.41159	+	11.3533i	0.125204	+	0.589433i
$372$	25.4339			1.31869
$373$	−3.34422	+	5.79236i	−0.173157	+	0.299917i	−0.939522	−	0.342488i	$-0.888730\pi$
$373$	−3.34422	+	5.79236i	−0.173157	+	0.299917i	0.766365	+	0.642406i	$0.222064\pi$
$374$		0			0
$375$	12.9841	+	22.4892i	0.670498	+	1.16134i
$376$	−2.82474	+	4.89259i	−0.145675	+	0.252316i
$377$	−12.3693			−0.637054
$378$	3.91318	−	3.52247i	0.201272	−	0.181176i
$379$	−13.5095			−0.693937			−0.346968	−	0.937877i	$-0.612789\pi$
$379$	−13.5095			−0.693937			−0.346968	+	0.937877i	$0.612789\pi$
$380$	−0.436269	+	0.755640i	−0.0223801	+	0.0387635i
$381$	5.87912	+	10.1829i	0.301197	+	0.521688i
$382$	−2.89953	−	5.02214i	−0.148353	−	0.256955i
$383$	−0.250604	+	0.434059i	−0.0128053	+	0.0221794i	−0.872357	−	0.488869i	$-0.837409\pi$
$383$	−0.250604	+	0.434059i	−0.0128053	+	0.0221794i	0.859552	+	0.511049i	$0.170743\pi$
$384$	−23.5055			−1.19951
$385$		0			0
$386$	−0.172221			−0.00876582
$387$	−5.10020	+	8.83381i	−0.259258	+	0.449048i
$388$	−2.55693	−	4.42873i	−0.129808	−	0.224835i
$389$	9.35329	+	16.2004i	0.474231	+	0.821392i	0.999565	−	0.0295044i	$-0.00939290\pi$
$389$	9.35329	+	16.2004i	0.474231	+	0.821392i	−0.525334	+	0.850896i	$0.676060\pi$
$390$	−4.86560	+	8.42747i	−0.246379	+	0.426741i
$391$	10.8849			0.550474
$392$	−13.5306	−	9.83621i	−0.683398	−	0.496804i
$393$	−10.6188			−0.535648
$394$	−3.29092	+	5.70004i	−0.165794	+	0.287164i
$395$	−12.0228	−	20.8241i	−0.604934	−	1.04778i
$396$		0			0
$397$	−2.36033	+	4.08821i	−0.118461	+	0.205181i	−0.919158	−	0.393889i	$-0.871130\pi$
$397$	−2.36033	+	4.08821i	−0.118461	+	0.205181i	0.800697	+	0.599070i	$0.204463\pi$
$398$	−0.238574			−0.0119586
$399$	−1.80879	−	0.587986i	−0.0905529	−	0.0294361i
$400$	−3.17956			−0.158978
$401$	−8.45382	+	14.6425i	−0.422164	+	0.731209i	−0.996151	−	0.0876552i	$-0.972063\pi$
$401$	−8.45382	+	14.6425i	−0.422164	+	0.731209i	0.573987	+	0.818864i	$0.305396\pi$
$402$	−3.95764	−	6.85484i	−0.197389	−	0.341888i
$403$	15.1977	+	26.3232i	0.757053	+	1.31125i
$404$	−7.11948	+	12.3313i	−0.354208	+	0.613506i
$405$	−18.9749			−0.942870
$406$	4.12526	−	3.71337i	0.204733	−	0.184292i
$407$		0			0
$408$	6.60290	−	11.4366i	0.326892	−	0.566194i
$409$	−12.7469	−	22.0782i	−0.630293	−	1.09170i	−0.987492	−	0.157671i	$-0.949602\pi$
$409$	−12.7469	−	22.0782i	−0.630293	−	1.09170i	0.357199	−	0.934028i	$-0.383732\pi$
$410$	−6.16668	−	10.6810i	−0.304551	−	0.527497i
$411$	−1.75892	+	3.04653i	−0.0867610	+	0.150274i
$412$	25.7831			1.27024
$413$	0.0192353	+	0.0905561i	0.000946508	+	0.00445597i
$414$	4.64732			0.228403
$415$	−3.92229	+	6.79360i	−0.192537	+	0.333485i
$416$	−11.4795	−	19.8831i	−0.562829	−	0.974848i
$417$	−9.52579	−	16.4992i	−0.466480	−	0.807967i
$418$		0			0
$419$	−22.6624			−1.10713			−0.553565	−	0.832806i	$-0.686733\pi$
$419$	−22.6624			−1.10713			−0.553565	+	0.832806i	$0.686733\pi$
$420$	3.08756	+	14.5356i	0.150657	+	0.709265i
$421$	−18.7875			−0.915648			−0.457824	−	0.889043i	$-0.651371\pi$
$421$	−18.7875			−0.915648			−0.457824	+	0.889043i	$0.651371\pi$
$422$	5.02322	−	8.70047i	0.244526	−	0.423532i
$423$	1.92362	+	3.33182i	0.0935298	+	0.161998i
$424$	−5.24171	−	9.07891i	−0.254560	−	0.440911i
$425$	2.75768	−	4.77645i	0.133767	−	0.231692i
$426$	13.6732			0.662470
$427$	−8.07680	+	7.27038i	−0.390864	+	0.351838i
$428$	2.07200			0.100154
$429$		0			0
$430$	−3.56769	−	6.17942i	−0.172049	−	0.297998i
$431$	17.1479	+	29.7010i	0.825985	+	1.43065i	0.901164	+	0.433477i	$0.142714\pi$
$431$	17.1479	+	29.7010i	0.825985	+	1.43065i	−0.0751798	+	0.997170i	$0.523953\pi$
$432$	2.18640	−	3.78695i	0.105193	−	0.182200i
$433$	3.18662			0.153139			0.0765696	−	0.997064i	$-0.475603\pi$
$433$	3.18662			0.153139			0.0765696	+	0.997064i	$0.475603\pi$
$434$	−12.9710	−	4.21649i	−0.622627	−	0.202398i
$435$	−11.3099			−0.542269
$436$	4.89502	−	8.47842i	0.234429	−	0.406043i
$437$	0.707996	+	1.22629i	0.0338681	+	0.0586612i
$438$	−0.217265	−	0.376314i	−0.0103813	−	0.0179810i
$439$	6.18390	−	10.7108i	0.295141	−	0.511200i	−0.679877	−	0.733327i	$-0.737967\pi$
$439$	6.18390	−	10.7108i	0.295141	−	0.511200i	0.975018	+	0.222127i	$0.0713000\pi$
$440$		0			0
$441$	−10.4081	+	4.63057i	−0.495624	+	0.220503i
$442$	6.88010			0.327253
$443$	2.55149	−	4.41931i	0.121225	−	0.209968i	−0.799026	−	0.601297i	$-0.794651\pi$
$443$	2.55149	−	4.41931i	0.121225	−	0.209968i	0.920251	+	0.391329i	$0.127984\pi$
$444$	16.8618	+	29.2054i	0.800224	+	1.38603i
$445$	−11.8218	−	20.4760i	−0.560407	−	0.970653i
$446$	−9.65596	+	16.7246i	−0.457223	+	0.791934i
$447$	10.3074			0.487524
$448$	2.34493	+	0.762269i	0.110787	+	0.0360138i
$449$	−1.22330			−0.0577313			−0.0288657	−	0.999583i	$-0.509190\pi$
$449$	−1.22330			−0.0577313			−0.0288657	+	0.999583i	$0.509190\pi$
$450$	1.17739	−	2.03931i	0.0555029	−	0.0961338i
$451$		0			0
$452$	−11.7601	−	20.3692i	−0.553150	−	0.958085i
$453$	−17.2927	+	29.9518i	−0.812482	+	1.40726i
$454$	14.1976			0.666328
$455$	−13.1989	+	11.8811i	−0.618774	+	0.556994i
$456$	1.71791			0.0804485
$457$	2.56699	−	4.44616i	0.120079	−	0.207983i	−0.799720	−	0.600374i	$-0.795019\pi$
$457$	2.56699	−	4.44616i	0.120079	−	0.207983i	0.919799	+	0.392391i	$0.128352\pi$
$458$	2.43225	+	4.21278i	0.113651	+	0.196850i
$459$	3.79259	+	6.56896i	0.177023	+	0.306613i
$460$	5.53153	−	9.58089i	0.257909	−	0.446711i
$461$	−22.7757			−1.06077			−0.530386	−	0.847757i	$-0.677953\pi$
$461$	−22.7757			−1.06077			−0.530386	+	0.847757i	$0.677953\pi$
$462$		0			0
$463$	29.8445			1.38699			0.693496	−	0.720460i	$-0.256069\pi$
$463$	29.8445			1.38699			0.693496	+	0.720460i	$0.256069\pi$
$464$	2.30489	−	3.99219i	0.107002	−	0.185333i
$465$	13.8961	+	24.0687i	0.644414	+	1.11616i
$466$	8.65506	+	14.9910i	0.400938	+	0.694445i
$467$	−0.774998	+	1.34234i	−0.0358626	+	0.0621159i	−0.883400	−	0.468620i	$-0.844751\pi$
$467$	−0.774998	+	1.34234i	−0.0358626	+	0.0621159i	0.847537	+	0.530736i	$0.178085\pi$
$468$	−9.99641			−0.462084
$469$	−3.00130	−	14.1295i	−0.138587	−	0.652442i
$470$	−2.69123			−0.124137
$471$	−7.33400	+	12.7029i	−0.337933	+	0.585317i
$472$	−0.0418089	−	0.0724152i	−0.00192441	−	0.00333318i
$473$		0			0
$474$	−10.3195	+	17.8738i	−0.473989	+	0.820973i
$475$	0.717480			0.0329203
$476$	7.80856	−	7.02892i	0.357905	−	0.322170i
$477$	−7.13913			−0.326878
$478$	−2.92341	+	5.06350i	−0.133714	+	0.231599i
$479$	−5.87274	−	10.1719i	−0.268332	−	0.464765i	0.700099	−	0.714046i	$-0.253139\pi$
$479$	−5.87274	−	10.1719i	−0.268332	−	0.464765i	−0.968431	+	0.249281i	$0.919806\pi$
$480$	−10.4963	−	18.1801i	−0.479088	−	0.829804i
$481$	−20.1511	+	34.9027i	−0.918809	+	1.59142i
$482$	14.8751			0.677543
$483$	22.9340	+	7.45518i	1.04353	+	0.339222i
$484$		0			0
$485$	2.79400	−	4.83936i	0.126869	−	0.219744i
$486$	5.15829	+	8.93442i	0.233985	+	0.405274i
$487$	−3.67196	−	6.36002i	−0.166392	−	0.288200i	0.770757	−	0.637130i	$-0.219878\pi$
$487$	−3.67196	−	6.36002i	−0.166392	−	0.288200i	−0.937149	+	0.348930i	$0.886545\pi$
$488$	4.90773	−	8.50044i	0.222163	−	0.384797i
$489$	−29.5123			−1.33459
$490$	0.835128	−	7.92483i	0.0377272	−	0.358007i
$491$	12.9613			0.584935			0.292467	−	0.956276i	$-0.405524\pi$
$491$	12.9613			0.584935			0.292467	+	0.956276i	$0.405524\pi$
$492$	18.0125	−	31.1986i	0.812067	−	1.40654i
$493$	3.99813	+	6.92497i	0.180067	+	0.311885i
$494$	0.447507	+	0.775106i	0.0201343	+	0.0348737i
$495$		0			0
$496$	−11.3277			−0.508630
$497$	23.7303	+	7.71402i	1.06445	+	0.346021i
$498$	6.73318			0.301721
$499$	−2.18677	+	3.78760i	−0.0978933	+	0.169556i	−0.910812	−	0.412820i	$-0.864544\pi$
$499$	−2.18677	+	3.78760i	−0.0978933	+	0.169556i	0.812919	+	0.582377i	$0.197877\pi$
$500$	−9.33020	−	16.1604i	−0.417259	−	0.722714i
$501$	−21.0370	−	36.4372i	−0.939864	−	1.62789i
$502$	−5.80765	+	10.0592i	−0.259208	+	0.448962i
$503$	−32.0104			−1.42727			−0.713637	−	0.700515i	$-0.752954\pi$
$503$	−32.0104			−1.42727			−0.713637	+	0.700515i	$0.752954\pi$
$504$	7.64740	−	6.88385i	0.340642	−	0.306631i
$505$	−15.5592			−0.692374
$506$		0			0
$507$	−3.00219	−	5.19995i	−0.133332	−	0.230938i
$508$	−4.22465	−	7.31730i	−0.187438	−	0.324653i
$509$	10.8109	−	18.7251i	0.479186	−	0.829974i	−0.520529	−	0.853844i	$-0.674265\pi$
$509$	10.8109	−	18.7251i	0.479186	−	0.829974i	0.999715	+	0.0238698i	$0.00759870\pi$
$510$	6.29082			0.278562
$511$	−0.164764	−	0.775678i	−0.00728875	−	0.0343140i
$512$	15.6345			0.690953
$513$	−0.493369	+	0.854540i	−0.0217828	+	0.0377289i
$514$	1.93249	+	3.34717i	0.0852385	+	0.147637i
$515$	14.0868	+	24.3991i	0.620739	+	1.07515i
$516$	10.4210	−	18.0497i	0.458760	−	0.794596i
$517$		0			0
$518$	−3.75755	−	17.6898i	−0.165097	−	0.777244i
$519$	−7.91502			−0.347431
$520$	8.02010	−	13.8912i	0.351704	−	0.609170i
$521$	−0.735723	−	1.27431i	−0.0322326	−	0.0558285i	0.849459	−	0.527654i	$-0.176928\pi$
$521$	−0.735723	−	1.27431i	−0.0322326	−	0.0558285i	−0.881692	+	0.471826i	$0.843595\pi$
$522$	1.70701	+	2.95662i	0.0747136	+	0.129408i
$523$	17.2638	−	29.9018i	0.754894	−	1.30752i	−0.190532	−	0.981681i	$-0.561021\pi$
$523$	17.2638	−	29.9018i	0.754894	−	1.30752i	0.945427	−	0.325835i	$-0.105645\pi$
$524$	7.63051			0.333340
$525$	9.08173	−	8.17498i	0.396359	−	0.356785i
$526$	−15.2292			−0.664025
$527$	9.82471	−	17.0169i	0.427971	−	0.741267i
$528$		0			0
$529$	2.52319	+	4.37030i	0.109704	+	0.190013i
$530$	2.49698	−	4.32490i	0.108462	−	0.187862i
$531$	−0.0569432			−0.00247112
$532$	1.29977	+	0.422518i	0.0563522	+	0.0183185i
$533$	43.0526			1.86482
$534$	−10.1469	+	17.5750i	−0.439100	+	0.760544i
$535$	1.13206	+	1.96078i	0.0489431	+	0.0847719i
$536$	6.52348	+	11.2990i	0.281772	+	0.488043i
$537$	−21.2270	+	36.7662i	−0.916012	+	1.58658i
$538$	−10.9589			−0.472470
$539$		0			0
$540$	7.70932			0.331756
$541$	−3.05888	+	5.29814i	−0.131512	+	0.227785i	−0.924259	−	0.381765i	$-0.875316\pi$
$541$	−3.05888	+	5.29814i	−0.131512	+	0.227785i	0.792748	+	0.609550i	$0.208650\pi$
$542$	2.38120	+	4.12437i	0.102281	+	0.177157i
$543$	2.37963	+	4.12163i	0.102120	+	0.176876i
$544$	−7.42102	+	12.8536i	−0.318174	+	0.551093i
$545$	10.6977			0.458241
$546$	14.4960	+	4.71224i	0.620373	+	0.201665i
$547$	25.0809			1.07238			0.536191	−	0.844097i	$-0.319863\pi$
$547$	25.0809			1.07238			0.536191	+	0.844097i	$0.319863\pi$
$548$	1.26393	−	2.18919i	0.0539924	−	0.0935176i
$549$	−3.34213	−	5.78874i	−0.142639	−	0.247057i
$550$		0			0
$551$	−0.520108	+	0.900853i	−0.0221573	+	0.0383776i
$552$	−21.7817			−0.927090
$553$	−27.9936	+	25.1986i	−1.19041	+	1.07155i
$554$	−8.01335			−0.340455
$555$	−18.4251	+	31.9133i	−0.782104	+	1.35464i
$556$	6.84509	+	11.8560i	0.290296	+	0.502808i
$557$	−15.3483	−	26.5840i	−0.650327	−	1.12640i	−0.983044	−	0.183372i	$-0.941299\pi$
$557$	−15.3483	−	26.5840i	−0.650327	−	1.12640i	0.332717	−	0.943027i	$-0.392035\pi$
$558$	4.19466	−	7.26537i	0.177574	−	0.307568i
$559$	24.9078			1.05349
$560$	−1.37513	−	6.47384i	−0.0581099	−	0.273570i
$561$		0			0
$562$	3.50164	−	6.06502i	0.147708	−	0.255838i
$563$	−8.73624	−	15.1316i	−0.368189	−	0.637722i	0.621094	−	0.783736i	$-0.286689\pi$
$563$	−8.73624	−	15.1316i	−0.368189	−	0.637722i	−0.989282	+	0.146015i	$0.953355\pi$
$564$	−3.93046	−	6.80776i	−0.165502	−	0.286658i
$565$	12.8505	−	22.2577i	0.540625	−	0.936390i
$566$	13.6817			0.575086
$567$	6.17552	+	29.0731i	0.259348	+	1.22096i
$568$	−22.5379			−0.945670
$569$	11.6724	−	20.2172i	0.489333	−	0.847549i	−0.510592	−	0.859823i	$-0.670574\pi$
$569$	11.6724	−	20.2172i	0.489333	−	0.847549i	0.999925	+	0.0122741i	$0.00390706\pi$
$570$	0.409179	+	0.708719i	0.0171386	+	0.0296850i
$571$	7.38432	+	12.7900i	0.309024	+	0.535245i	0.978149	−	0.207905i	$-0.0666643\pi$
$571$	7.38432	+	12.7900i	0.309024	+	0.535245i	−0.669125	+	0.743150i	$0.733331\pi$
$572$		0			0
$573$	18.5093			0.773236
$574$	−14.3583	+	12.9247i	−0.599305	+	0.539468i
$575$	−9.09706			−0.379374
$576$	−0.758322	+	1.31345i	−0.0315968	+	0.0547272i
$577$	18.1174	+	31.3802i	0.754237	+	1.30638i	0.945753	+	0.324887i	$0.105326\pi$
$577$	18.1174	+	31.3802i	0.754237	+	1.30638i	−0.191516	+	0.981489i	$0.561340\pi$
$578$	3.50485	+	6.07057i	0.145782	+	0.252502i
$579$	0.274845	−	0.476045i	0.0114222	−	0.0197837i
$580$	8.12713			0.337461
$581$	11.6856	+	3.79866i	0.484801	+	0.157595i
$582$	−4.79632			−0.198814
$583$		0			0
$584$	0.358123	+	0.620288i	0.0148193	+	0.0256677i
$585$	−5.46163	−	9.45982i	−0.225811	−	0.391115i
$586$	8.04566	−	13.9355i	0.332363	−	0.575670i
$587$	−18.1920			−0.750863			−0.375432	−	0.926850i	$-0.622506\pi$
$587$	−18.1920			−0.750863			−0.375432	+	0.926850i	$0.622506\pi$
$588$	21.2664	−	9.46144i	0.877013	−	0.390183i
$589$	2.55614			0.105324
$590$	0.0199164	−	0.0344963i	0.000819947	−	0.00142019i
$591$	−10.5039	−	18.1932i	−0.432071	−	0.748369i
$592$	−7.50986	−	13.0075i	−0.308653	−	0.534603i
$593$	−21.2413	+	36.7910i	−0.872276	+	1.51083i	−0.0126393	+	0.999920i	$0.504023\pi$
$593$	−21.2413	+	36.7910i	−0.872276	+	1.51083i	−0.859637	+	0.510906i	$0.829310\pi$
$594$		0			0
$595$	10.9179	+	3.54909i	0.447590	+	0.145499i
$596$	−7.40675			−0.303392
$597$	0.380736	−	0.659454i	0.0155825	−	0.0269897i
$598$	−5.67402	−	9.82770i	−0.232028	−	0.401884i
$599$	8.79406	+	15.2318i	0.359315	+	0.622353i	0.987847	−	0.155432i	$-0.0496769\pi$
$599$	8.79406	+	15.2318i	0.359315	+	0.622353i	−0.628531	+	0.777784i	$0.716344\pi$
$600$	−5.51836	+	9.55809i	−0.225286	+	0.390207i
$601$	−30.6943			−1.25204			−0.626022	−	0.779805i	$-0.715318\pi$
$601$	−30.6943			−1.25204			−0.626022	+	0.779805i	$0.715318\pi$
$602$	−8.30692	+	7.47752i	−0.338565	+	0.304761i
$603$	8.88489			0.361821
$604$	12.4263	−	21.5229i	0.505617	−	0.875755i
$605$		0			0
$606$	6.67740	+	11.5656i	0.271251	+	0.469820i
$607$	17.7358	−	30.7194i	0.719875	−	1.24686i	−0.241174	−	0.970482i	$-0.577532\pi$
$607$	17.7358	−	30.7194i	0.719875	−	1.24686i	0.961049	−	0.276378i	$-0.0891342\pi$
$608$	−1.93077			−0.0783029
$609$	3.68090	+	17.3289i	0.149158	+	0.702204i
$610$	4.67577			0.189316
$611$	4.69720	−	8.13578i	0.190028	−	0.329138i
$612$	3.23113	+	5.59649i	0.130611	+	0.226225i
$613$	6.87104	+	11.9010i	0.277519	+	0.480677i	0.970767	−	0.240022i	$-0.0771546\pi$
$613$	6.87104	+	11.9010i	0.277519	+	0.480677i	−0.693249	+	0.720698i	$0.743821\pi$
$614$	2.94478	−	5.10051i	0.118842	−	0.205840i
$615$	39.3652			1.58736
$616$		0			0
$617$	2.42135			0.0974798			0.0487399	−	0.998812i	$-0.484479\pi$
$617$	2.42135			0.0974798			0.0487399	+	0.998812i	$0.484479\pi$
$618$	12.0910	−	20.9423i	0.486373	−	0.842423i
$619$	6.95609	+	12.0483i	0.279589	+	0.484262i	0.971283	−	0.237929i	$-0.0764686\pi$
$619$	6.95609	+	12.0483i	0.279589	+	0.484262i	−0.691694	+	0.722191i	$0.743135\pi$
$620$	−9.98549	−	17.2954i	−0.401027	−	0.694599i
$621$	6.25551	−	10.8349i	0.251025	−	0.434788i
$622$	1.76454			0.0707516
$623$	−27.5256	+	24.7773i	−1.10279	+	0.992681i
$624$	12.6596			0.506788
$625$	4.82786	−	8.36210i	0.193114	−	0.334484i
$626$	7.66754	+	13.2806i	0.306457	+	0.530798i
$627$		0			0
$628$	5.27010	−	9.12808i	0.210300	−	0.364250i
$629$	26.0537			1.03883
$630$	4.66140	+	1.51529i	0.185715	+	0.0603705i
$631$	38.7883			1.54414			0.772068	−	0.635540i	$-0.219222\pi$
$631$	38.7883			1.54414			0.772068	+	0.635540i	$0.219222\pi$
$632$	17.0098	−	29.4619i	0.676615	−	1.17193i
$633$	16.0329	+	27.7699i	0.637252	+	1.10375i
$634$	−1.51242	−	2.61959i	−0.0600659	−	0.104037i
$635$	4.61635	−	7.99575i	0.183194	−	0.317302i
$636$	14.5871			0.578416
$637$	22.4997	+	16.3564i	0.891473	+	0.648066i
$638$		0			0
$639$	−7.67408	+	13.2919i	−0.303582	+	0.525819i
$640$	9.22837	+	15.9840i	0.364783	+	0.631823i
$641$	12.6465	+	21.9044i	0.499508	+	0.865173i	1.00000		0.000568132i	$-0.000180842\pi$
$641$	12.6465	+	21.9044i	0.499508	+	0.865173i	−0.500492	+	0.865741i	$0.666848\pi$
$642$	0.971671	−	1.68298i	0.0383488	−	0.0664221i
$643$	−0.0897008			−0.00353745			−0.00176873	−	0.999998i	$-0.500563\pi$
$643$	−0.0897008			−0.00353745			−0.00176873	+	0.999998i	$0.500563\pi$
$644$	−16.4800	−	5.35718i	−0.649403	−	0.211102i
$645$	22.7745			0.896744
$646$	0.289295	−	0.501074i	0.0113822	−	0.0197145i
$647$	2.16992	+	3.75841i	0.0853083	+	0.147758i	0.905523	−	0.424298i	$-0.139479\pi$
$647$	2.16992	+	3.75841i	0.0853083	+	0.147758i	−0.820214	+	0.572056i	$0.806146\pi$
$648$	−13.4228	−	23.2490i	−0.527298	−	0.913306i
$649$		0			0
$650$	−5.75003			−0.225535
$651$	32.3552	−	29.1247i	1.26810	−	1.14149i
$652$	21.2071			0.830533
$653$	10.6123	−	18.3810i	0.415291	−	0.719305i	−0.580168	−	0.814497i	$-0.697013\pi$
$653$	10.6123	−	18.3810i	0.415291	−	0.719305i	0.995459	+	0.0951916i	$0.0303464\pi$
$654$	−4.59106	−	7.95196i	−0.179525	−	0.310946i
$655$	4.16899	+	7.22091i	0.162896	+	0.282144i
$656$	−8.02239	+	13.8952i	−0.313222	+	0.542516i
$657$	0.487759			0.0190293
$658$	0.875881	+	4.12347i	0.0341454	+	0.160750i
$659$	25.4606			0.991805			0.495902	−	0.868378i	$-0.334837\pi$
$659$	25.4606			0.991805			0.495902	+	0.868378i	$0.334837\pi$
$660$		0			0
$661$	−4.77124	−	8.26403i	−0.185580	−	0.321433i	0.758192	−	0.652031i	$-0.226083\pi$
$661$	−4.77124	−	8.26403i	−0.185580	−	0.321433i	−0.943772	+	0.330598i	$0.892750\pi$
$662$	4.65081	+	8.05544i	0.180759	+	0.313084i
$663$	−10.9798	+	19.0176i	−0.426421	+	0.738583i
$664$	−11.0985			−0.430704
$665$	0.310304	+	1.46085i	0.0120331	+	0.0566492i
$666$	11.1236			0.431032
$667$	6.59453	−	11.4221i	0.255341	−	0.442264i
$668$	15.1169	+	26.1832i	0.584889	+	1.01306i
$669$	−30.8196	−	53.3811i	−1.19155	−	2.06383i
$670$	−3.10758	+	5.38249i	−0.120056	+	0.207944i
$671$		0			0
$672$	−24.4393	+	21.9992i	−0.942765	+	0.848636i
$673$	−16.5396			−0.637554			−0.318777	−	0.947830i	$-0.603272\pi$
$673$	−16.5396			−0.637554			−0.318777	+	0.947830i	$0.603272\pi$
$674$	−3.79278	+	6.56928i	−0.146092	+	0.253039i
$675$	−3.16965	−	5.49000i	−0.122000	−	0.211310i
$676$	2.15733	+	3.73660i	0.0829742	+	0.143716i
$677$	−1.21682	+	2.10759i	−0.0467660	+	0.0810011i	−0.888461	−	0.458952i	$-0.848225\pi$
$677$	−1.21682	+	2.10759i	−0.0467660	+	0.0810011i	0.841695	+	0.539954i	$0.181558\pi$
$678$	−22.0598			−0.847201
$679$	−8.32414	−	2.70594i	−0.319451	−	0.103844i
$680$	−10.3693			−0.397645
$681$	−22.6578	+	39.2444i	−0.868248	+	1.50385i
$682$		0			0
$683$	2.64045	+	4.57339i	0.101034	+	0.174996i	0.912111	−	0.409944i	$-0.134452\pi$
$683$	2.64045	+	4.57339i	0.101034	+	0.174996i	−0.811077	+	0.584939i	$0.801118\pi$
$684$	−0.420330	+	0.728034i	−0.0160717	+	0.0278371i
$685$	2.76224			0.105540
$686$	−12.4141	+	1.29962i	−0.473974	+	0.0496198i
$687$	−15.5263			−0.592366
$688$	−4.64130	+	8.03897i	−0.176948	+	0.306483i
$689$	8.71633	+	15.0971i	0.332066	+	0.575155i
$690$	−5.18805	−	8.98596i	−0.197506	−	0.342090i
$691$	10.5490	−	18.2714i	0.401304	−	0.695079i	−0.592580	−	0.805512i	$-0.701890\pi$
$691$	10.5490	−	18.2714i	0.401304	−	0.695079i	0.993884	+	0.110433i	$0.0352238\pi$
$692$	5.68761			0.216211
$693$		0			0
$694$	10.4053			0.394980
$695$	−7.47975	+	12.9553i	−0.283723	+	0.491423i
$696$	−8.00062	−	13.8575i	−0.303263	−	0.525266i
$697$	−13.9159	−	24.1030i	−0.527101	−	0.912966i
$698$	−3.33688	+	5.77964i	−0.126303	+	0.218763i
$699$	−55.2498			−2.08974
$700$	−6.52599	+	5.87441i	−0.246659	+	0.222032i
$701$	−28.0933			−1.06107			−0.530535	−	0.847663i	$-0.678009\pi$
$701$	−28.0933			−1.06107			−0.530535	+	0.847663i	$0.678009\pi$
$702$	3.95396	−	6.84845i	0.149233	−	0.258478i
$703$	1.69463	+	2.93518i	0.0639141	+	0.110703i
$704$		0			0
$705$	4.29489	−	7.43896i	0.161755	−	0.280167i
$706$	6.62819			0.249455
$707$	5.06385	+	23.8396i	0.190446	+	0.896581i
$708$	0.116350			0.00437268
$709$	2.54978	−	4.41634i	0.0957589	−	0.165859i	−0.814166	−	0.580632i	$-0.802806\pi$
$709$	2.54978	−	4.41634i	0.0957589	−	0.165859i	0.909925	+	0.414773i	$0.136139\pi$
$710$	−5.36818	−	9.29795i	−0.201464	−	0.348946i
$711$	−11.5836	−	20.0633i	−0.434418	−	0.752434i
$712$	16.7254	−	28.9693i	0.626812	−	1.08567i
$713$	−32.4098			−1.21376
$714$	−2.04740	−	9.63873i	−0.0766219	−	0.360720i
$715$		0			0
$716$	15.2534	−	26.4196i	0.570046	−	0.987348i
$717$	−9.33085	−	16.1615i	−0.348467	−	0.603563i
$718$	1.03095	+	1.78565i	0.0384746	+	0.0666399i
$719$	−12.0198	+	20.8189i	−0.448262	+	0.776412i	−0.998273	−	0.0587450i	$-0.981290\pi$
$719$	−12.0198	+	20.8189i	−0.448262	+	0.776412i	0.550011	+	0.835157i	$0.314623\pi$
$720$	4.07086			0.151712
$721$	32.7994	−	29.5245i	1.22151	−	1.09955i
$722$	−12.7300			−0.473763
$723$	−23.7390	+	41.1171i	−0.882862	+	1.52916i
$724$	−1.70996	−	2.96174i	−0.0635502	−	0.110072i
$725$	−3.34144	−	5.78754i	−0.124098	−	0.214944i
$726$		0			0
$727$	14.6738			0.544221			0.272111	−	0.962266i	$-0.412278\pi$
$727$	14.6738			0.544221			0.272111	+	0.962266i	$0.412278\pi$
$728$	−23.8942	−	7.76731i	−0.885577	−	0.287876i
$729$	0.773198			0.0286370
$730$	−0.170599	+	0.295485i	−0.00631414	+	0.0109364i
$731$	−8.05094	−	13.9446i	−0.297775	−	0.515761i
$732$	6.82883	+	11.8279i	0.252401	+	0.437171i
$733$	24.2626	−	42.0240i	0.896159	−	1.55219i	0.0637950	−	0.997963i	$-0.479680\pi$
$733$	24.2626	−	42.0240i	0.896159	−	1.55219i	0.832364	−	0.554230i	$-0.186987\pi$
$734$	−5.17603			−0.191051
$735$	20.5727	+	14.9555i	0.758834	+	0.551643i
$736$	24.4805			0.902363
$737$		0			0
$738$	−5.94139	−	10.2908i	−0.218706	−	0.378809i
$739$	−5.64178	−	9.77184i	−0.207536	−	0.359463i	0.743402	−	0.668845i	$-0.233211\pi$
$739$	−5.64178	−	9.77184i	−0.207536	−	0.359463i	−0.950938	+	0.309382i	$0.899878\pi$
$740$	13.2400	−	22.9324i	0.486713	−	0.843011i
$741$	−2.85668			−0.104943
$742$	−7.43923	−	2.41828i	−0.273103	−	0.0887778i
$743$	−3.46274			−0.127036			−0.0635179	−	0.997981i	$-0.520232\pi$
$743$	−3.46274			−0.127036			−0.0635179	+	0.997981i	$0.520232\pi$
$744$	−19.6601	+	34.0523i	−0.720774	+	1.24842i
$745$	−4.04674	−	7.00916i	−0.148261	−	0.256796i
$746$	−2.25389	−	3.90384i	−0.0825206	−	0.142930i
$747$	−3.77899	+	6.54540i	−0.138266	+	0.239484i
$748$		0			0
$749$	2.63585	−	2.37268i	0.0963119	−	0.0866957i
$750$	−17.5017			−0.639071
$751$	−1.07037	+	1.85393i	−0.0390583	+	0.0676509i	−0.884894	−	0.465793i	$-0.845769\pi$
$751$	−1.07037	+	1.85393i	−0.0390583	+	0.0676509i	0.845835	+	0.533444i	$0.179102\pi$
$752$	1.75054	+	3.03203i	0.0638357	+	0.110567i
$753$	−18.5367	−	32.1065i	−0.675514	−	1.17002i
$754$	4.16825	−	7.21961i	0.151799	−	0.262923i
$755$	27.1568			0.988337
$756$	−2.50906	−	11.8121i	−0.0912535	−	0.429603i
$757$	−36.7958			−1.33737			−0.668683	−	0.743548i	$-0.733142\pi$
$757$	−36.7958			−1.33737			−0.668683	+	0.743548i	$0.733142\pi$
$758$	4.55246	−	7.88509i	0.165353	−	0.286399i
$759$		0			0
$760$	−0.674460	−	1.16820i	−0.0244652	−	0.0423750i
$761$	14.6993	−	25.4600i	0.532850	−	0.922923i	−0.466414	−	0.884566i	$-0.654454\pi$
$761$	14.6993	−	25.4600i	0.532850	−	0.922923i	0.999264	−	0.0383563i	$-0.0122122\pi$
$762$	−7.92464			−0.287079
$763$	−3.48166	−	16.3910i	−0.126045	−	0.593393i
$764$	−13.3005			−0.481194
$765$	−3.53072	+	6.11538i	−0.127653	+	0.221102i
$766$	−0.168898	−	0.292540i	−0.00610254	−	0.0105699i
$767$	0.0695232	+	0.120418i	0.00251034	+	0.00434803i
$768$	9.92568	−	17.1918i	0.358162	−	0.620355i
$769$	1.47798			0.0532972			0.0266486	−	0.999645i	$-0.491516\pi$
$769$	1.47798			0.0532972			0.0266486	+	0.999645i	$0.491516\pi$
$770$		0			0
$771$	−12.3361			−0.444274
$772$	−0.197499	+	0.342078i	−0.00710815	+	0.0123117i
$773$	−9.38075	−	16.2479i	−0.337402	−	0.584398i	0.646541	−	0.762879i	$-0.276215\pi$
$773$	−9.38075	−	16.2479i	−0.337402	−	0.584398i	−0.983943	+	0.178481i	$0.942882\pi$
$774$	−3.43735	−	5.95367i	−0.123553	−	0.214000i
$775$	−8.21099	+	14.2218i	−0.294947	+	0.510864i
$776$	7.90589			0.283805
$777$	54.8938	+	17.8444i	1.96930	+	0.640164i
$778$	−12.6076			−0.452003
$779$	1.81028	−	3.13550i	0.0648601	−	0.112341i
$780$	11.1595	+	19.3288i	0.399575	+	0.692084i
$781$		0			0
$782$	−3.66802	+	6.35320i	−0.131168	+	0.227190i
$783$	9.19083			0.328454
$784$	−9.47161	+	4.21392i	−0.338272	+	0.150497i
$785$	11.5175			0.411076
$786$	3.57835	−	6.19788i	0.127635	−	0.221071i
$787$	−9.47805	−	16.4165i	−0.337856	−	0.585184i	0.646173	−	0.763191i	$-0.276368\pi$
$787$	−9.47805	−	16.4165i	−0.337856	−	0.585184i	−0.984029	+	0.178007i	$0.943035\pi$
$788$	7.54791	+	13.0734i	0.268883	+	0.465719i
$789$	24.3040	−	42.0958i	0.865246	−	1.49865i
$790$	16.2059			0.576580
$791$	−38.2854	−	12.4455i	−1.36127	−	0.442510i
$792$		0			0
$793$	−8.16096	+	14.1352i	−0.289804	+	0.501956i
$794$	−1.59078	−	2.75530i	−0.0564545	−	0.0977821i
$795$	7.96979	+	13.8041i	0.282659	+	0.489580i
$796$	−0.273591	+	0.473873i	−0.00969717	+	0.0167960i
$797$	−39.7729			−1.40883			−0.704414	−	0.709789i	$-0.748790\pi$
$797$	−39.7729			−1.40883			−0.704414	+	0.709789i	$0.748790\pi$
$798$	0.952721	−	0.857597i	0.0337260	−	0.0303586i
$799$	−6.07309			−0.214850
$800$	6.20211	−	10.7424i	0.219278	−	0.379800i
$801$	−11.3899	−	19.7279i	−0.402442	−	0.697051i
$802$	−5.69757	−	9.86849i	−0.201188	−	0.348468i
$803$		0			0
$804$	−18.1541			−0.640247
$805$	−3.93439	−	18.5223i	−0.138669	−	0.652826i
$806$	−20.4854			−0.721569
$807$	17.4891	−	30.2919i	0.615644	−	1.06633i
$808$	−11.0065	−	19.0639i	−0.387209	−	0.670665i
$809$	28.0211	+	48.5340i	0.985170	+	1.70636i	0.641179	+	0.767391i	$0.278445\pi$
$809$	28.0211	+	48.5340i	0.985170	+	1.70636i	0.343990	+	0.938973i	$0.388221\pi$
$810$	6.39420	−	11.0751i	0.224669	−	0.389138i
$811$	20.9980			0.737341			0.368670	−	0.929560i	$-0.379813\pi$
$811$	20.9980			0.737341			0.368670	+	0.929560i	$0.379813\pi$
$812$	−2.64504	−	12.4523i	−0.0928226	−	0.436990i
$813$	−15.2005			−0.533105
$814$		0			0
$815$	11.5867	+	20.0687i	0.405863	+	0.702976i
$816$	−4.09194	−	7.08745i	−0.143247	−	0.248111i
$817$	1.04733	−	1.81402i	0.0366413	−	0.0634646i
$818$	17.1819			0.600750
$819$	−12.7167	+	11.4470i	−0.444358	+	0.399991i
$820$	−28.2872			−0.987833
$821$	16.2147	−	28.0846i	0.565896	−	0.980161i	−0.431070	−	0.902319i	$-0.641864\pi$
$821$	16.2147	−	28.0846i	0.565896	−	0.980161i	0.996966	−	0.0778419i	$-0.0248030\pi$
$822$	−1.18545	−	2.05325i	−0.0413472	−	0.0716155i
$823$	−0.877291	−	1.51951i	−0.0305804	−	0.0529669i	0.850330	−	0.526250i	$-0.176402\pi$
$823$	−0.877291	−	1.51951i	−0.0305804	−	0.0529669i	−0.880911	+	0.473283i	$0.843069\pi$
$824$	−19.9300	+	34.5197i	−0.694294	+	1.20255i
$825$		0			0
$826$	−0.0593368	−	0.0192887i	−0.00206459	−	0.000671139i
$827$	−11.6503			−0.405121			−0.202560	−	0.979270i	$-0.564926\pi$
$827$	−11.6503			−0.405121			−0.202560	+	0.979270i	$0.564926\pi$
$828$	5.32944	−	9.23086i	0.185211	−	0.320795i
$829$	−9.81943	−	17.0077i	−0.341043	−	0.590703i	0.643584	−	0.765376i	$-0.277447\pi$
$829$	−9.81943	−	17.0077i	−0.341043	−	0.590703i	−0.984627	+	0.174672i	$0.944113\pi$
$830$	−2.64348	−	4.57864i	−0.0917565	−	0.158927i
$831$	12.7884	−	22.1501i	0.443624	−	0.768379i
$832$	3.70341			0.128393
$833$	1.88457	−	17.8834i	0.0652965	−	0.619622i
$834$	12.8401			0.444616
$835$	−16.5185	+	28.6108i	−0.571645	+	0.990119i
$836$		0			0
$837$	−11.2924	−	19.5590i	−0.390323	−	0.676060i
$838$	7.63682	−	13.2274i	0.263810	−	0.456932i
$839$	−44.3104			−1.52976			−0.764882	−	0.644171i	$-0.777203\pi$
$839$	−44.3104			−1.52976			−0.764882	+	0.644171i	$0.777203\pi$
$840$	−21.8477	−	7.10204i	−0.753816	−	0.245044i
$841$	−19.3111			−0.665899
$842$	6.33106	−	10.9657i	0.218183	−	0.377903i
$843$	11.1764	+	19.3581i	0.384937	+	0.666730i
$844$	−11.5210	−	19.9550i	−0.396570	−	0.686879i
$845$	−2.35735	+	4.08305i	−0.0810954	+	0.140461i
$846$	−2.59291			−0.0891460
$847$		0			0
$848$	−6.49678			−0.223100
$849$	−21.8344	+	37.8184i	−0.749356	+	1.29792i
$850$	1.85858	+	3.21915i	0.0637487	+	0.110416i
$851$	−21.4865	−	37.2157i	−0.736547	−	1.27574i
$852$	15.6801	−	27.1588i	0.537192	−	0.930445i
$853$	−19.7584			−0.676516			−0.338258	−	0.941053i	$-0.609838\pi$
$853$	−19.7584			−0.676516			−0.338258	+	0.941053i	$0.609838\pi$
$854$	−1.52177	−	7.16417i	−0.0520738	−	0.245153i
$855$	−0.918605			−0.0314156
$856$	−1.60163	+	2.77411i	−0.0547426	+	0.0948170i
$857$	−1.69370	−	2.93357i	−0.0578556	−	0.100209i	0.835647	−	0.549267i	$-0.185093\pi$
$857$	−1.69370	−	2.93357i	−0.0578556	−	0.100209i	−0.893503	+	0.449058i	$0.851760\pi$
$858$		0			0
$859$	−8.04855	+	13.9405i	−0.274613	+	0.475643i	−0.970037	−	0.242956i	$-0.921883\pi$
$859$	−8.04855	+	13.9405i	−0.274613	+	0.475643i	0.695425	+	0.718599i	$0.255216\pi$
$860$	−16.3654			−0.558055
$861$	−12.8117	−	60.3149i	−0.436622	−	2.05553i
$862$	−23.1141			−0.787270
$863$	22.5420	−	39.0439i	0.767340	−	1.32907i	−0.171661	−	0.985156i	$-0.554913\pi$
$863$	22.5420	−	39.0439i	0.767340	−	1.32907i	0.939001	−	0.343915i	$-0.111753\pi$
$864$	8.52965	+	14.7738i	0.290185	+	0.502614i
$865$	3.10748	+	5.38231i	0.105657	+	0.183004i
$866$	−1.07383	+	1.85993i	−0.0364904	+	0.0632032i
$867$	−22.3733			−0.759837
$868$	−23.2499	+	20.9286i	−0.789154	+	0.710362i
$869$		0			0
$870$	3.81124	−	6.60126i	0.129213	−	0.223804i
$871$	−10.8478	−	18.7889i	−0.367563	−	0.636637i
$872$	7.56757	+	13.1074i	0.256270	+	0.443873i
$873$	2.69193	−	4.66256i	0.0911080	−	0.157804i
$874$	−0.954328			−0.0322806
$875$	−30.3746	−	9.87392i	−1.02685	−	0.333799i
$876$	−0.996617			−0.0336726
$877$	−28.0768	+	48.6304i	−0.948085	+	1.64213i	−0.198630	+	0.980074i	$0.563649\pi$
$877$	−28.0768	+	48.6304i	−0.948085	+	1.64213i	−0.749454	+	0.662056i	$0.769684\pi$
$878$	4.16772	+	7.21871i	0.140654	+	0.243620i
$879$	25.6799	+	44.4788i	0.866160	+	1.50023i
$880$		0			0
$881$	20.4943			0.690469			0.345235	−	0.938516i	$-0.387799\pi$
$881$	20.4943			0.690469			0.345235	+	0.938516i	$0.387799\pi$
$882$	0.804618	−	7.63531i	0.0270929	−	0.257094i
$883$	18.1224			0.609867			0.304934	−	0.952374i	$-0.401366\pi$
$883$	18.1224			0.609867			0.304934	+	0.952374i	$0.401366\pi$
$884$	7.88993	−	13.6658i	0.265367	−	0.459629i
$885$	0.0635686	+	0.110104i	0.00213684	+	0.00370111i
$886$	1.71961	+	2.97846i	0.0577716	+	0.100063i
$887$	−7.53589	+	13.0525i	−0.253030	+	0.438261i	−0.964359	−	0.264599i	$-0.914761\pi$
$887$	−7.53589	+	13.0525i	−0.253030	+	0.438261i	0.711328	+	0.702860i	$0.248094\pi$
$888$	−52.1357			−1.74956
$889$	−13.7534	−	4.47084i	−0.461275	−	0.149947i
$890$	15.9349			0.534140
$891$		0			0
$892$	22.1465	+	38.3588i	0.741518	+	1.28435i
$893$	−0.395017	−	0.684189i	−0.0132187	−	0.0228955i
$894$	−3.47341	+	6.01613i	−0.116168	+	0.201209i
$895$	33.3353			1.11428
$896$	21.4871	−	19.3417i	0.717833	−	0.646162i
$897$	36.2203			1.20936
$898$	0.412232	−	0.714006i	0.0137564	−	0.0238267i
$899$	−11.9044	−	20.6191i	−0.397035	−	0.687685i
$900$	−2.70042	−	4.67726i	−0.0900139	−	0.155909i
$901$	5.63475	−	9.75967i	0.187721	−	0.325142i
$902$		0			0
$903$	−7.41213	−	34.8948i	−0.246660	−	1.16123i
$904$	36.3617			1.20937
$905$	1.86851	−	3.23635i	0.0621112	−	0.107580i
$906$	−11.6547	−	20.1865i	−0.387200	−	0.670650i
$907$	−8.13854	−	14.0964i	−0.270236	−	0.468062i	0.698686	−	0.715428i	$-0.253768\pi$
$907$	−8.13854	−	14.0964i	−0.270236	−	0.468062i	−0.968922	+	0.247366i	$0.920435\pi$
$908$	16.2815	−	28.2004i	0.540321	−	0.935864i
$909$	−14.9907			−0.497211
$910$	−2.48683	−	11.7075i	−0.0824377	−	0.388100i
$911$	−8.25789			−0.273596			−0.136798	−	0.990599i	$-0.543681\pi$
$911$	−8.25789			−0.273596			−0.136798	+	0.990599i	$0.543681\pi$
$912$	0.532311	−	0.921990i	0.0176266	−	0.0305301i
$913$		0			0
$914$	1.73006	+	2.99655i	0.0572253	+	0.0991172i
$915$	−7.46199	+	12.9245i	−0.246686	+	0.427272i
$916$	11.1570			0.368637
$917$	9.70697	−	8.73779i	0.320552	−	0.288547i
$918$	−5.11214			−0.168726
$919$	−18.7181	+	32.4208i	−0.617455	+	1.06946i	0.372494	+	0.928035i	$0.378503\pi$
$919$	−18.7181	+	32.4208i	−0.617455	+	1.06946i	−0.989948	+	0.141428i	$0.954831\pi$
$920$	8.55159	+	14.8118i	0.281938	+	0.488330i
$921$	9.39905	+	16.2796i	0.309709	+	0.536432i
$922$	7.67501	−	13.2935i	0.252763	−	0.437798i
$923$	37.4779			1.23360
$924$		0			0
$925$	−21.7743			−0.715935
$926$	−10.0571	+	17.4194i	−0.330496	+	0.572436i
$927$	13.5722	+	23.5077i	0.445769	+	0.772094i
$928$	8.99192	+	15.5745i	0.295174	+	0.511257i
$929$	−27.1069	+	46.9504i	−0.889347	+	1.54039i	−0.0486981	+	0.998814i	$0.515507\pi$
$929$	−27.1069	+	46.9504i	−0.889347	+	1.54039i	−0.840649	+	0.541581i	$0.817826\pi$
$930$	−18.7309			−0.614210
$931$	2.13730	−	0.950888i	0.0700473	−	0.0311641i
$932$	39.7017			1.30047
$933$	−2.81600	+	4.87745i	−0.0921916	+	0.159681i
$934$	−0.522321	−	0.904686i	−0.0170909	−	0.0296022i
$935$		0			0
$936$	7.72709	−	13.3837i	0.252568	−	0.437460i
$937$	−23.4647			−0.766560			−0.383280	−	0.923632i	$-0.625206\pi$
$937$	−23.4647			−0.766560			−0.383280	+	0.923632i	$0.625206\pi$
$938$	9.25838	+	3.00963i	0.302297	+	0.0982679i
$939$	−48.9460			−1.59729
$940$	−3.08624	+	5.34552i	−0.100662	+	0.174352i
$941$	21.4563	+	37.1634i	0.699455	+	1.21149i	0.968656	+	0.248407i	$0.0799070\pi$
$941$	21.4563	+	37.1634i	0.699455	+	1.21149i	−0.269201	+	0.963084i	$0.586760\pi$
$942$	−4.94285	−	8.56127i	−0.161047	−	0.278941i
$943$	−22.9529	+	39.7555i	−0.747448	+	1.29462i
$944$	−0.0518196			−0.00168658
$945$	9.80723	−	8.82804i	0.319029	−	0.287176i
$946$		0			0
$947$	−26.8719	+	46.5435i	−0.873219	+	1.51246i	−0.0145710	+	0.999894i	$0.504638\pi$
$947$	−26.8719	+	46.5435i	−0.873219	+	1.51246i	−0.858648	+	0.512566i	$0.828695\pi$
$948$	23.6682	+	40.9946i	0.768709	+	1.33144i
$949$	−0.595516	−	1.03146i	−0.0193313	−	0.0334828i
$950$	−0.241778	+	0.418772i	−0.00784432	+	0.0135868i
$951$	9.65459			0.313071
$952$	3.37478	+	15.8878i	0.109377	+	0.514926i
$953$	−9.56288			−0.309772			−0.154886	−	0.987932i	$-0.549501\pi$
$953$	−9.56288			−0.309772			−0.154886	+	0.987932i	$0.549501\pi$
$954$	2.40576	−	4.16690i	0.0778893	−	0.134908i
$955$	−7.26683	−	12.5865i	−0.235149	−	0.407290i
$956$	6.70500	+	11.6134i	0.216855	+	0.375604i
$957$		0			0
$958$	7.91603			0.255755
$959$	−0.898991	−	4.23227i	−0.0290299	−	0.136667i
$960$	3.38622			0.109290
$961$	−13.7530	+	23.8209i	−0.443646	+	0.768417i
$962$	−13.5811	−	23.5231i	−0.437872	−	0.758416i
$963$	1.09070	+	1.88915i	0.0351473	+	0.0608769i
$964$	17.0584	−	29.5461i	0.549416	−	0.951616i
$965$	−0.431621			−0.0138944
$966$	−12.0797	+	10.8736i	−0.388658	+	0.349853i
$967$	−34.7245			−1.11666			−0.558332	−	0.829618i	$-0.688558\pi$
$967$	−34.7245			−1.11666			−0.558332	+	0.829618i	$0.688558\pi$
$968$		0			0
$969$	0.923362	+	1.59931i	0.0296627	+	0.0513773i
$970$	1.88306	+	3.26155i	0.0604613	+	0.104722i
$971$	4.09888	−	7.09947i	0.131539	−	0.227833i	−0.792731	−	0.609572i	$-0.791341\pi$
$971$	4.09888	−	7.09947i	0.131539	−	0.227833i	0.924270	+	0.381739i	$0.124675\pi$
$972$	23.6616			0.758947
$973$	22.2843	+	7.24399i	0.714402	+	0.232232i
$974$	4.94953			0.158593
$975$	9.17638	−	15.8939i	0.293879	−	0.509014i
$976$	−3.04141	−	5.26788i	−0.0973533	−	0.168621i
$977$	−0.945220	−	1.63717i	−0.0302403	−	0.0523777i	0.850509	−	0.525960i	$-0.176294\pi$
$977$	−0.945220	−	1.63717i	−0.0302403	−	0.0523777i	−0.880749	+	0.473582i	$0.842961\pi$
$978$	9.94511	−	17.2254i	0.318010	−	0.550809i
$979$		0			0
$980$	−14.7832	−	10.7468i	−0.472232	−	0.343294i
$981$	10.3069			0.329075
$982$	−4.36772	+	7.56511i	−0.139380	+	0.241412i
$983$	20.1163	+	34.8424i	0.641610	+	1.11130i	0.985073	+	0.172135i	$0.0550665\pi$
$983$	20.1163	+	34.8424i	0.641610	+	1.11130i	−0.343463	+	0.939166i	$0.611600\pi$
$984$	27.8469	+	48.2322i	0.887726	+	1.53759i
$985$	−8.24773	+	14.2855i	−0.262795	+	0.455173i
$986$	−5.38920			−0.171627
$987$	−12.7957	−	4.15951i	−0.407292	−	0.132399i
$988$	2.05276			0.0653071
$989$	−13.2792	+	23.0003i	−0.422255	+	0.731367i
$990$		0			0
$991$	−12.7333	−	22.0548i	−0.404487	−	0.700592i	0.589774	−	0.807568i	$-0.299217\pi$
$991$	−12.7333	−	22.0548i	−0.404487	−	0.700592i	−0.994262	+	0.106976i	$0.965883\pi$
$992$	22.0961	−	38.2715i	0.701550	−	1.21512i
$993$	−29.6886			−0.942139
$994$	−12.4991	+	11.2512i	−0.396448	+	0.356865i
$995$	−0.597915			−0.0189552
$996$	7.72145	−	13.3739i	0.244664	−	0.423770i
$997$	−8.24651	−	14.2834i	−0.261170	−	0.452359i	0.705383	−	0.708826i	$-0.250775\pi$
$997$	−8.24651	−	14.2834i	−0.261170	−	0.452359i	−0.966553	+	0.256467i	$0.917442\pi$
$998$	−1.47380	−	2.55270i	−0.0466525	−	0.0808044i
$999$	14.9729	−	25.9338i	0.473722	−	0.820511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.e.h.485.4		20
7.2	even	3		5929.2.a.by.1.7		10
7.4	even	3	inner	847.2.e.h.606.4		20
7.5	odd	6		5929.2.a.bz.1.7		10
11.2	odd	10		847.2.n.i.807.2		40
11.3	even	5		847.2.n.j.9.4		40
11.4	even	5		847.2.n.j.632.2		40
11.5	even	5		847.2.n.h.366.2		40
11.6	odd	10		847.2.n.i.366.4		40
11.7	odd	10		77.2.m.b.16.4	yes	40
11.8	odd	10		77.2.m.b.9.2	✓	40
11.9	even	5		847.2.n.h.807.4		40
11.10	odd	2		847.2.e.i.485.7		20
33.8	even	10		693.2.by.b.163.4		40
33.29	even	10		693.2.by.b.478.2		40
77.4	even	15		847.2.n.j.753.4		40
77.18	odd	30		77.2.m.b.60.2	yes	40
77.19	even	30		539.2.f.g.295.2		20
77.25	even	15		847.2.n.j.130.2		40
77.30	odd	30		539.2.f.h.295.2		20
77.32	odd	6		847.2.e.i.606.7		20
77.39	odd	30		847.2.n.i.487.2		40
77.40	even	30		539.2.f.g.148.2		20
77.41	even	10		539.2.q.h.471.2		40
77.46	odd	30		847.2.n.i.81.4		40
77.51	odd	30		539.2.f.h.148.2		20
77.52	even	30		539.2.q.h.361.4		40
77.53	even	15		847.2.n.h.81.2		40
77.54	even	6		5929.2.a.bx.1.4		10
77.60	even	15		847.2.n.h.487.4		40
77.62	even	10		539.2.q.h.324.4		40
77.65	odd	6		5929.2.a.bw.1.4		10
77.73	even	30		539.2.q.h.214.2		40
77.74	odd	30		77.2.m.b.53.4	yes	40
231.74	even	30		693.2.by.b.361.2		40
231.95	even	30		693.2.by.b.676.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.2	✓	40	11.8	odd	10
77.2.m.b.16.4	yes	40	11.7	odd	10
77.2.m.b.53.4	yes	40	77.74	odd	30
77.2.m.b.60.2	yes	40	77.18	odd	30
539.2.f.g.148.2		20	77.40	even	30
539.2.f.g.295.2		20	77.19	even	30
539.2.f.h.148.2		20	77.51	odd	30
539.2.f.h.295.2		20	77.30	odd	30
539.2.q.h.214.2		40	77.73	even	30
539.2.q.h.324.4		40	77.62	even	10
539.2.q.h.361.4		40	77.52	even	30
539.2.q.h.471.2		40	77.41	even	10
693.2.by.b.163.4		40	33.8	even	10
693.2.by.b.361.2		40	231.74	even	30
693.2.by.b.478.2		40	33.29	even	10
693.2.by.b.676.4		40	231.95	even	30
847.2.e.h.485.4		20	1.1	even	1	trivial
847.2.e.h.606.4		20	7.4	even	3	inner
847.2.e.i.485.7		20	11.10	odd	2
847.2.e.i.606.7		20	77.32	odd	6
847.2.n.h.81.2		40	77.53	even	15
847.2.n.h.366.2		40	11.5	even	5
847.2.n.h.487.4		40	77.60	even	15
847.2.n.h.807.4		40	11.9	even	5
847.2.n.i.81.4		40	77.46	odd	30
847.2.n.i.366.4		40	11.6	odd	10
847.2.n.i.487.2		40	77.39	odd	30
847.2.n.i.807.2		40	11.2	odd	10
847.2.n.j.9.4		40	11.3	even	5
847.2.n.j.130.2		40	77.25	even	15
847.2.n.j.632.2		40	11.4	even	5
847.2.n.j.753.4		40	77.4	even	15
5929.2.a.bw.1.4		10	77.65	odd	6
5929.2.a.bx.1.4		10	77.54	even	6
5929.2.a.by.1.7		10	7.2	even	3
5929.2.a.bz.1.7		10	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.336982 + 0.583670i) q^{2} +(-1.07557 - 1.86294i) q^{3} +(0.772886 + 1.33868i) q^{4} +(-0.844546 + 1.46280i) q^{5} +1.44979 q^{6} +(2.51615 + 0.817927i) q^{7} -2.38972 q^{8} +(-0.813692 + 1.40936i) q^{9} +O(q^{10})\)	\(q+(-0.336982 + 0.583670i) q^{2} +(-1.07557 - 1.86294i) q^{3} +(0.772886 + 1.33868i) q^{4} +(-0.844546 + 1.46280i) q^{5} +1.44979 q^{6} +(2.51615 + 0.817927i) q^{7} -2.38972 q^{8} +(-0.813692 + 1.40936i) q^{9} +(-0.569194 - 0.985873i) q^{10} +(1.66258 - 2.87968i) q^{12} +3.97382 q^{13} +(-1.32530 + 1.19297i) q^{14} +3.63347 q^{15} +(-0.740479 + 1.28255i) q^{16} +(-1.28446 - 2.22474i) q^{17} +(-0.548399 - 0.949855i) q^{18} +(0.167092 - 0.289411i) q^{19} -2.61095 q^{20} +(-1.18254 - 5.56716i) q^{21} +(-2.11859 + 3.66950i) q^{23} +(2.57031 + 4.45191i) q^{24} +(1.07348 + 1.85933i) q^{25} +(-1.33911 + 2.31940i) q^{26} -2.95268 q^{27} +(0.849755 + 4.00048i) q^{28} -3.11271 q^{29} +(-1.22441 + 2.12075i) q^{30} +(3.82446 + 6.62416i) q^{31} +(-2.88878 - 5.00351i) q^{32} +1.73135 q^{34} +(-3.32146 + 2.98984i) q^{35} -2.51557 q^{36} +(-5.07095 + 8.78315i) q^{37} +(0.112614 + 0.195053i) q^{38} +(-4.27412 - 7.40298i) q^{39} +(2.01823 - 3.49568i) q^{40} +10.8341 q^{41} +(3.64788 + 1.18582i) q^{42} +6.26797 q^{43} +(-1.37440 - 2.38053i) q^{45} +(-1.42785 - 2.47311i) q^{46} +(1.18203 - 2.04734i) q^{47} +3.18574 q^{48} +(5.66199 + 4.11605i) q^{49} -1.44698 q^{50} +(-2.76304 + 4.78572i) q^{51} +(3.07131 + 5.31967i) q^{52} +(2.19344 + 3.79915i) q^{53} +(0.995001 - 1.72339i) q^{54} +(-6.01289 - 1.95462i) q^{56} -0.718874 q^{57} +(1.04893 - 1.81679i) q^{58} +(0.0174953 + 0.0303028i) q^{59} +(2.80826 + 4.86404i) q^{60} +(-2.05368 + 3.55708i) q^{61} -5.15510 q^{62} +(-3.20012 + 2.88061i) q^{63} +0.931952 q^{64} +(-3.35608 + 5.81290i) q^{65} +(-2.72981 - 4.72817i) q^{67} +(1.98548 - 3.43895i) q^{68} +9.11473 q^{69} +(-0.625804 - 2.94616i) q^{70} +9.43119 q^{71} +(1.94450 - 3.36797i) q^{72} +(-0.149860 - 0.259565i) q^{73} +(-3.41764 - 5.91952i) q^{74} +(2.30921 - 3.99966i) q^{75} +0.516572 q^{76} +5.76120 q^{78} +(-7.11791 + 12.3286i) q^{79} +(-1.25074 - 2.16634i) q^{80} +(5.61689 + 9.72873i) q^{81} +(-3.65088 + 6.32351i) q^{82} +4.64425 q^{83} +(6.53867 - 5.88582i) q^{84} +4.33913 q^{85} +(-2.11219 + 3.65843i) q^{86} +(3.34793 + 5.79878i) q^{87} +(-6.99890 + 12.1225i) q^{89} +1.85259 q^{90} +(9.99872 + 3.25030i) q^{91} -6.54970 q^{92} +(8.22694 - 14.2495i) q^{93} +(0.796649 + 1.37984i) q^{94} +(0.282234 + 0.488843i) q^{95} +(-6.21416 + 10.7632i) q^{96} -3.30829 q^{97} +(-4.31040 + 1.91770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9}+O(q^{10}) \) 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9	\( 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9} - 7 q^{10} - 9 q^{12} + 2 q^{13} - 19 q^{14} - 2 q^{15} - 15 q^{16} - 19 q^{17} - 17 q^{18} - 28 q^{19} - 10 q^{20} + q^{21} - 7 q^{23} - 19 q^{24} + 8 q^{25} + 5 q^{26} + 12 q^{27} - 8 q^{28} - 30 q^{29} + 22 q^{30} + 14 q^{31} + 15 q^{32} + 24 q^{34} - 8 q^{35} + 32 q^{36} - 13 q^{37} - 24 q^{38} - 4 q^{39} - 10 q^{40} + 70 q^{41} + 25 q^{42} + 36 q^{43} - 8 q^{45} - 9 q^{46} - 16 q^{47} - 66 q^{48} - 25 q^{49} + 12 q^{50} + 21 q^{51} + 4 q^{52} + 9 q^{53} - 17 q^{54} + 12 q^{56} + 8 q^{57} + 9 q^{58} - 12 q^{59} + 21 q^{60} - 20 q^{61} + 76 q^{62} - 12 q^{63} - 58 q^{64} + 20 q^{65} - 19 q^{67} - 56 q^{68} + 18 q^{69} + 21 q^{70} + 30 q^{71} + 4 q^{72} - 3 q^{73} - 42 q^{74} + 27 q^{75} + 48 q^{76} - 50 q^{78} + 32 q^{79} + 6 q^{80} + 46 q^{81} + 18 q^{82} + 58 q^{83} - 73 q^{84} - 46 q^{85} - 9 q^{86} - 24 q^{87} - 5 q^{89} + 24 q^{90} + 28 q^{91} + 30 q^{92} + q^{93} + 19 q^{94} - q^{95} - 46 q^{96} + 8 q^{97} - 58 q^{98}+O(q^{100}) \) 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9 - 7 * q^10 - 9 * q^12 + 2 * q^13 - 19 * q^14 - 2 * q^15 - 15 * q^16 - 19 * q^17 - 17 * q^18 - 28 * q^19 - 10 * q^20 + q^21 - 7 * q^23 - 19 * q^24 + 8 * q^25 + 5 * q^26 + 12 * q^27 - 8 * q^28 - 30 * q^29 + 22 * q^30 + 14 * q^31 + 15 * q^32 + 24 * q^34 - 8 * q^35 + 32 * q^36 - 13 * q^37 - 24 * q^38 - 4 * q^39 - 10 * q^40 + 70 * q^41 + 25 * q^42 + 36 * q^43 - 8 * q^45 - 9 * q^46 - 16 * q^47 - 66 * q^48 - 25 * q^49 + 12 * q^50 + 21 * q^51 + 4 * q^52 + 9 * q^53 - 17 * q^54 + 12 * q^56 + 8 * q^57 + 9 * q^58 - 12 * q^59 + 21 * q^60 - 20 * q^61 + 76 * q^62 - 12 * q^63 - 58 * q^64 + 20 * q^65 - 19 * q^67 - 56 * q^68 + 18 * q^69 + 21 * q^70 + 30 * q^71 + 4 * q^72 - 3 * q^73 - 42 * q^74 + 27 * q^75 + 48 * q^76 - 50 * q^78 + 32 * q^79 + 6 * q^80 + 46 * q^81 + 18 * q^82 + 58 * q^83 - 73 * q^84 - 46 * q^85 - 9 * q^86 - 24 * q^87 - 5 * q^89 + 24 * q^90 + 28 * q^91 + 30 * q^92 + q^93 + 19 * q^94 - q^95 - 46 * q^96 + 8 * q^97 - 58 * q^98

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