LMFDB - Embedded newform 847.2.f.x.372.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.3
Root			$0.435488 - 1.34029i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.x.148.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.435488 - 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +O(q^{10})$	\(q+(0.435488 - 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} -2.58091 q^{10} +0.0302106 q^{12} +(1.43602 - 4.41961i) q^{13} +(1.14012 - 0.828347i) q^{14} +(-3.20531 - 2.32880i) q^{15} +(-1.22738 - 3.77748i) q^{16} +(1.69039 + 5.20248i) q^{17} +(-1.91565 - 1.39180i) q^{18} +(-4.69325 + 3.40985i) q^{19} +(0.00790293 - 0.0243227i) q^{20} +2.16338 q^{21} -0.719682 q^{23} +(1.89741 - 5.83962i) q^{24} +(1.33166 - 0.967509i) q^{25} +(-5.29821 - 3.84937i) q^{26} +(0.882303 + 2.71545i) q^{27} +(0.00431527 + 0.0132810i) q^{28} +(-0.948551 - 0.689163i) q^{29} +(-4.51715 + 3.28190i) q^{30} +(-0.404153 + 1.24385i) q^{31} +0.0789938 q^{32} +7.70900 q^{34} +(0.565930 - 1.74175i) q^{35} +(0.0189823 - 0.0137915i) q^{36} +(-1.69468 - 1.23126i) q^{37} +(2.52634 + 7.77528i) q^{38} +(-3.10666 - 9.56131i) q^{39} +(-4.20516 - 3.05523i) q^{40} +(-0.741582 + 0.538791i) q^{41} +(0.942126 - 2.89957i) q^{42} -8.02379 q^{43} -3.07713 q^{45} +(-0.313413 + 0.964586i) q^{46} +(-4.83455 + 3.51251i) q^{47} +(-6.95163 - 5.05065i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.716823 - 2.20615i) q^{50} +(9.57403 + 6.95594i) q^{51} +(0.0525003 - 0.0381437i) q^{52} +(3.13496 - 9.64840i) q^{53} +4.02373 q^{54} +2.83822 q^{56} +(-3.87821 + 11.9359i) q^{57} +(-1.33676 + 0.971215i) q^{58} +(6.21390 + 4.51466i) q^{59} +(-0.0170971 - 0.0526193i) q^{60} +(1.93943 + 5.96895i) q^{61} +(1.49113 + 1.08337i) q^{62} +(1.35932 - 0.987607i) q^{63} +(2.48916 - 7.66083i) q^{64} -8.51056 q^{65} -15.4673 q^{67} +(-0.0236055 + 0.0726501i) q^{68} +(-1.25960 + 0.915151i) q^{69} +(-2.08800 - 1.51702i) q^{70} +(4.29593 + 13.2215i) q^{71} +(-1.47365 - 4.53542i) q^{72} +(4.86593 + 3.53531i) q^{73} +(-2.38826 + 1.73517i) q^{74} +(1.10040 - 3.38669i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(4.83332 - 14.8754i) q^{79} +(-5.88482 + 4.27557i) q^{80} +(9.07517 + 6.59349i) q^{81} +(0.399188 + 1.22857i) q^{82} +(1.35217 + 4.16157i) q^{83} +(0.0244409 + 0.0177573i) q^{84} +(8.10479 - 5.88848i) q^{85} +(-3.49426 + 10.7542i) q^{86} -2.53651 q^{87} +15.3437 q^{89} +(-1.34005 + 4.12425i) q^{90} +(3.75955 - 2.73147i) q^{91} +(-0.00813063 - 0.00590725i) q^{92} +(0.874336 + 2.69093i) q^{93} +(2.60240 + 8.00937i) q^{94} +(8.59515 + 6.24474i) q^{95} +(0.138256 - 0.100449i) q^{96} +(0.745114 - 2.29323i) q^{97} +1.40927 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.435488	−	1.34029i	0.307936	−	0.947730i	−0.670629	−	0.741793i	$-0.733976\pi$
$2$	0.435488	−	1.34029i	0.307936	−	0.947730i	0.978565	−	0.205937i	$-0.0660243\pi$
$3$	1.75021	−	1.27160i	1.01049	−	0.734161i	0.0461746	−	0.998933i	$-0.485297\pi$
$3$	1.75021	−	1.27160i	1.01049	−	0.734161i	0.964311	+	0.264773i	$0.0852969\pi$
$4$	0.0112975	+	0.00820814i	0.00564876	+	0.00410407i
$5$	−0.565930	−	1.74175i	−0.253091	−	0.778935i	−0.994200	−	0.107550i	$-0.965700\pi$
$5$	−0.565930	−	1.74175i	−0.253091	−	0.778935i	0.741108	−	0.671385i	$-0.234300\pi$
$6$	−0.942126	−	2.89957i	−0.384621	−	1.18374i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	2.29616	−	1.66826i	0.811817	−	0.589819i
$9$	0.519216	−	1.59798i	0.173072	−	0.532661i
$10$	−2.58091			−0.816157
$11$		0			0
$11$		0			0
$12$	0.0302106			0.00872104
$13$	1.43602	−	4.41961i	0.398280	−	1.22578i	−0.528097	−	0.849184i	$-0.677094\pi$
$13$	1.43602	−	4.41961i	0.398280	−	1.22578i	0.926377	−	0.376596i	$-0.122906\pi$
$14$	1.14012	−	0.828347i	0.304710	−	0.221385i
$15$	−3.20531	−	2.32880i	−0.827609	−	0.601293i
$16$	−1.22738	−	3.77748i	−0.306844	−	0.944370i
$17$	1.69039	+	5.20248i	0.409980	+	1.26179i	0.916665	+	0.399656i	$0.130871\pi$
$17$	1.69039	+	5.20248i	0.409980	+	1.26179i	−0.506685	+	0.862131i	$0.669129\pi$
$18$	−1.91565	−	1.39180i	−0.451524	−	0.328051i
$19$	−4.69325	+	3.40985i	−1.07671	+	0.782272i	−0.977106	−	0.212755i	$-0.931756\pi$
$19$	−4.69325	+	3.40985i	−1.07671	+	0.782272i	−0.0995999	+	0.995028i	$0.531756\pi$
$20$	0.00790293	−	0.0243227i	0.00176715	−	0.00543873i
$21$	2.16338			0.472088
$22$		0			0
$23$	−0.719682			−0.150064			−0.0750321	−	0.997181i	$-0.523906\pi$
$23$	−0.719682			−0.150064			−0.0750321	+	0.997181i	$0.523906\pi$
$24$	1.89741	−	5.83962i	0.387307	−	1.19201i
$25$	1.33166	−	0.967509i	0.266332	−	0.193502i
$26$	−5.29821	−	3.84937i	−1.03906	−	0.754924i
$27$	0.882303	+	2.71545i	0.169799	+	0.522588i
$28$	0.00431527	+	0.0132810i	0.000815510	+	0.00250988i
$29$	−0.948551	−	0.689163i	−0.176142	−	0.127974i	0.496221	−	0.868196i	$-0.334720\pi$
$29$	−0.948551	−	0.689163i	−0.176142	−	0.127974i	−0.672363	+	0.740222i	$0.734720\pi$
$30$	−4.51715	+	3.28190i	−0.824714	+	0.599190i
$31$	−0.404153	+	1.24385i	−0.0725879	+	0.223403i	−0.980768	−	0.195177i	$-0.937472\pi$
$31$	−0.404153	+	1.24385i	−0.0725879	+	0.223403i	0.908180	+	0.418580i	$0.137472\pi$
$32$	0.0789938			0.0139643
$33$		0			0
$34$	7.70900			1.32208
$35$	0.565930	−	1.74175i	0.0956595	−	0.294410i
$36$	0.0189823	−	0.0137915i	0.00316372	−	0.00229858i
$37$	−1.69468	−	1.23126i	−0.278604	−	0.202417i	0.439705	−	0.898142i	$-0.355083\pi$
$37$	−1.69468	−	1.23126i	−0.278604	−	0.202417i	−0.718308	+	0.695725i	$0.755083\pi$
$38$	2.52634	+	7.77528i	0.409827	+	1.26132i
$39$	−3.10666	−	9.56131i	−0.497463	−	1.53103i
$40$	−4.20516	−	3.05523i	−0.664895	−	0.483074i
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	−0.644185	−	0.764869i	$-0.722803\pi$
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	0.528370	+	0.849014i	$0.322803\pi$
$42$	0.942126	−	2.89957i	0.145373	−	0.447413i
$43$	−8.02379			−1.22362			−0.611808	−	0.791006i	$-0.709558\pi$
$43$	−8.02379			−1.22362			−0.611808	+	0.791006i	$0.709558\pi$
$44$		0			0
$45$	−3.07713			−0.458711
$46$	−0.313413	+	0.964586i	−0.0462102	+	0.142220i
$47$	−4.83455	+	3.51251i	−0.705192	+	0.512352i	−0.881619	−	0.471962i	$-0.843546\pi$
$47$	−4.83455	+	3.51251i	−0.705192	+	0.512352i	0.176427	+	0.984314i	$0.443546\pi$
$48$	−6.95163	−	5.05065i	−1.00338	−	0.728999i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.716823	−	2.20615i	−0.101374	−	0.311997i
$51$	9.57403	+	6.95594i	1.34063	+	0.974027i
$52$	0.0525003	−	0.0381437i	0.00728048	−	0.00528958i
$53$	3.13496	−	9.64840i	0.430619	−	1.32531i	−0.466890	−	0.884315i	$-0.654626\pi$
$53$	3.13496	−	9.64840i	0.430619	−	1.32531i	0.897510	−	0.440995i	$-0.145374\pi$
$54$	4.02373			0.547560
$55$		0			0
$56$	2.83822			0.379272
$57$	−3.87821	+	11.9359i	−0.513682	+	1.58095i
$58$	−1.33676	+	0.971215i	−0.175526	+	0.127527i
$59$	6.21390	+	4.51466i	0.808981	+	0.587759i	0.913535	−	0.406760i	$-0.133341\pi$
$59$	6.21390	+	4.51466i	0.808981	+	0.587759i	−0.104554	+	0.994519i	$0.533341\pi$
$60$	−0.0170971	−	0.0526193i	−0.00220722	−	0.00679312i
$61$	1.93943	+	5.96895i	0.248318	+	0.764246i	0.995073	+	0.0991458i	$0.0316110\pi$
$61$	1.93943	+	5.96895i	0.248318	+	0.764246i	−0.746754	+	0.665100i	$0.768389\pi$
$62$	1.49113	+	1.08337i	0.189373	+	0.137588i
$63$	1.35932	−	0.987607i	0.171259	−	0.124427i
$64$	2.48916	−	7.66083i	0.311144	−	0.957604i
$65$	−8.51056			−1.05560
$66$		0			0
$67$	−15.4673			−1.88963			−0.944814	−	0.327608i	$-0.893758\pi$
$67$	−15.4673			−1.88963			−0.944814	+	0.327608i	$0.893758\pi$
$68$	−0.0236055	+	0.0726501i	−0.00286258	+	0.00881012i
$69$	−1.25960	+	0.915151i	−0.151638	+	0.110171i
$70$	−2.08800	−	1.51702i	−0.249564	−	0.181319i
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	0.792491	+	0.609883i	$0.208784\pi$
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	−0.282659	+	0.959221i	$0.591216\pi$
$72$	−1.47365	−	4.53542i	−0.173671	−	0.534504i
$73$	4.86593	+	3.53531i	0.569514	+	0.413776i	0.834929	−	0.550358i	$-0.185509\pi$
$73$	4.86593	+	3.53531i	0.569514	+	0.413776i	−0.265414	+	0.964134i	$0.585509\pi$
$74$	−2.38826	+	1.73517i	−0.277629	+	0.201709i
$75$	1.10040	−	3.38669i	0.127064	−	0.391061i
$76$	−0.0810106			−0.00929255
$77$		0			0
$78$	−14.1679			−1.60420
$79$	4.83332	−	14.8754i	0.543791	−	1.67362i	−0.180058	−	0.983656i	$-0.557628\pi$
$79$	4.83332	−	14.8754i	0.543791	−	1.67362i	0.723848	−	0.689959i	$-0.242372\pi$
$80$	−5.88482	+	4.27557i	−0.657943	+	0.478024i
$81$	9.07517	+	6.59349i	1.00835	+	0.732610i
$82$	0.399188	+	1.22857i	0.0440829	+	0.135673i
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	0.997435	−	0.0715783i	$-0.0228036\pi$
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	−0.849015	+	0.528370i	$0.822804\pi$
$84$	0.0244409	+	0.0177573i	0.00266672	+	0.00193748i
$85$	8.10479	−	5.88848i	0.879088	−	0.638695i
$86$	−3.49426	+	10.7542i	−0.376796	+	1.15966i
$87$	−2.53651			−0.271942
$88$		0			0
$89$	15.3437			1.62643			0.813215	−	0.581963i	$-0.197715\pi$
$89$	15.3437			1.62643			0.813215	+	0.581963i	$0.197715\pi$
$90$	−1.34005	+	4.12425i	−0.141254	+	0.434735i
$91$	3.75955	−	2.73147i	0.394108	−	0.286336i
$92$	−0.00813063	−	0.00590725i	−0.000847677	−	0.000615873i
$93$	0.874336	+	2.69093i	0.0906644	+	0.279036i
$94$	2.60240	+	8.00937i	0.268417	+	0.826104i
$95$	8.59515	+	6.24474i	0.881844	+	0.640697i
$96$	0.138256	−	0.100449i	0.0141107	−	0.0102520i
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	−0.906077	−	0.423114i	$-0.860937\pi$
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	0.981731	+	0.190272i	$0.0609370\pi$
$98$	1.40927			0.142358
$99$		0			0
$100$	0.0229859			0.00229859
$101$	−3.67603	+	11.3136i	−0.365778	+	1.12575i	0.583714	+	0.811959i	$0.301599\pi$
$101$	−3.67603	+	11.3136i	−0.365778	+	1.12575i	−0.949492	+	0.313790i	$0.898401\pi$
$102$	13.4924	−	9.80279i	1.33594	−	0.970620i
$103$	−0.320625	−	0.232947i	−0.0315921	−	0.0229530i	0.571877	−	0.820339i	$-0.306215\pi$
$103$	−0.320625	−	0.232947i	−0.0315921	−	0.0229530i	−0.603469	+	0.797386i	$0.706215\pi$
$104$	−4.07573	−	12.5438i	−0.399658	−	1.23002i
$105$	−1.22432	−	3.76807i	−0.119482	−	0.367726i
$106$	−11.5665	−	8.40352i	−1.12343	−	0.816222i
$107$	−2.64496	+	1.92168i	−0.255698	+	0.185776i	−0.708248	−	0.705963i	$-0.750514\pi$
$107$	−2.64496	+	1.92168i	−0.255698	+	0.185776i	0.452550	+	0.891739i	$0.350514\pi$
$108$	−0.0123209	+	0.0379199i	−0.00118558	+	0.00364885i
$109$	2.84638			0.272634			0.136317	−	0.990665i	$-0.456473\pi$
$109$	2.84638			0.272634			0.136317	+	0.990665i	$0.456473\pi$
$110$		0			0
$111$	−4.53172			−0.430132
$112$	1.22738	−	3.77748i	0.115976	−	0.356938i
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.982177	−	0.187961i	$-0.939812\pi$
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.124748	+	0.992188i	$0.539812\pi$
$114$	14.3087	+	10.3959i	1.34013	+	0.973663i
$115$	0.407290	+	1.25351i	0.0379799	+	0.116890i
$116$	−0.00505954	−	0.0155717i	−0.000469767	−	0.00144579i
$117$	−6.31686	−	4.58947i	−0.583994	−	0.424296i
$118$	8.75705	−	6.36237i	0.806152	−	0.585704i
$119$	−1.69039	+	5.20248i	−0.154958	+	0.476911i
$120$	−11.2450			−1.02652
$121$		0			0
$122$	8.84474			0.800765
$123$	−0.612797	+	1.88600i	−0.0552541	+	0.170054i
$124$	−0.0147756	+	0.0107351i	−0.00132689	+	0.000964044i
$125$	−9.84690	−	7.15419i	−0.880734	−	0.639890i
$126$	−0.731714	−	2.25198i	−0.0651863	−	0.200623i
$127$	−1.55524	−	4.78655i	−0.138006	−	0.424737i	0.858040	−	0.513583i	$-0.171682\pi$
$127$	−1.55524	−	4.78655i	−0.138006	−	0.424737i	−0.996045	+	0.0888458i	$0.971682\pi$
$128$	−9.05595	−	6.57953i	−0.800440	−	0.581554i
$129$	−14.0433	+	10.2031i	−1.23645	+	0.898331i
$130$	−3.70624	+	11.4066i	−0.325059	+	1.00043i
$131$	0.180053			0.0157313			0.00786565	−	0.999969i	$-0.497496\pi$
$131$	0.180053			0.0157313			0.00786565	+	0.999969i	$0.497496\pi$
$132$		0			0
$133$	−5.80118			−0.503026
$134$	−6.73581	+	20.7307i	−0.581885	+	1.79086i
$135$	4.23032	−	3.07350i	0.364088	−	0.264525i
$136$	12.5605	+	9.12574i	1.07705	+	0.782526i
$137$	2.57224	+	7.91655i	0.219762	+	0.676357i	0.998781	+	0.0493570i	$0.0157172\pi$
$137$	2.57224	+	7.91655i	0.219762	+	0.676357i	−0.779020	+	0.627000i	$0.784283\pi$
$138$	0.678031	+	2.08677i	0.0577179	+	0.177637i
$139$	−5.63172	−	4.09169i	−0.477677	−	0.347052i	0.322749	−	0.946485i	$-0.395393\pi$
$139$	−5.63172	−	4.09169i	−0.477677	−	0.347052i	−0.800425	+	0.599432i	$0.795393\pi$
$140$	0.0206901	−	0.0150323i	0.00174864	−	0.00127046i
$141$	−3.99497	+	12.2953i	−0.336438	+	1.03545i
$142$	19.5915			1.64408
$143$		0			0
$144$	−6.67362			−0.556135
$145$	−0.663538	+	2.04216i	−0.0551038	+	0.169592i
$146$	6.85740	−	4.98219i	0.567523	−	0.412329i
$147$	1.75021	+	1.27160i	0.144355	+	0.104880i
$148$	−0.00903937	−	0.0278203i	−0.000743031	−	0.00228682i
$149$	0.993277	+	3.05699i	0.0813724	+	0.250439i	0.983463	−	0.181108i	$-0.0579682\pi$
$149$	0.993277	+	3.05699i	0.0813724	+	0.250439i	−0.902091	+	0.431546i	$0.857968\pi$
$150$	−4.05995	−	2.94972i	−0.331493	−	0.240844i
$151$	18.0144	−	13.0882i	1.46599	−	1.06510i	0.484239	−	0.874936i	$-0.339097\pi$
$151$	18.0144	−	13.0882i	1.46599	−	1.06510i	0.981752	−	0.190168i	$-0.0609034\pi$
$152$	−5.08796	+	15.6591i	−0.412688	+	1.27012i
$153$	9.19115			0.743061
$154$		0			0
$155$	2.39521			0.192388
$156$	0.0433830	−	0.133519i	0.00347342	−	0.0106901i
$157$	−10.7233	+	7.79096i	−0.855816	+	0.621786i	−0.926743	−	0.375695i	$-0.877404\pi$
$157$	−10.7233	+	7.79096i	−0.855816	+	0.621786i	0.0709277	+	0.997481i	$0.477404\pi$
$158$	−17.8326	−	12.9561i	−1.41868	−	1.03073i
$159$	−6.78211	−	20.8732i	−0.537856	−	1.65535i
$160$	−0.0447049	−	0.137588i	−0.00353423	−	0.0108773i
$161$	−0.582235	−	0.423019i	−0.0458866	−	0.0333385i
$162$	12.7893	−	9.29200i	1.00483	−	0.730048i
$163$	4.23920	−	13.0469i	0.332040	−	1.02191i	−0.636122	−	0.771589i	$-0.719462\pi$
$163$	4.23920	−	13.0469i	0.332040	−	1.02191i	0.968162	−	0.250325i	$-0.0805375\pi$
$164$	−0.0128005			−0.000999552
$165$		0			0
$166$	6.16657			0.478619
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	0.775936	+	0.630812i	$0.217278\pi$
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	−0.998527	+	0.0542539i	$0.982722\pi$
$168$	4.96748	−	3.60908i	0.383249	−	0.278447i
$169$	−6.95361	−	5.05209i	−0.534893	−	0.388623i
$170$	−4.36275	−	13.4272i	−0.334608	−	1.02982i
$171$	3.01206	+	9.27018i	0.230338	+	0.708908i
$172$	−0.0906490	−	0.0658604i	−0.00691192	−	0.00502181i
$173$	8.49927	−	6.17508i	0.646188	−	0.469483i	−0.215783	−	0.976441i	$-0.569230\pi$
$173$	8.49927	−	6.17508i	0.646188	−	0.469483i	0.861970	+	0.506959i	$0.169230\pi$
$174$	−1.10462	+	3.39966i	−0.0837409	+	0.257728i
$175$	1.64602			0.124428
$176$		0			0
$177$	16.6165			1.24897
$178$	6.68200	−	20.5651i	0.500837	−	1.54142i
$179$	6.73370	−	4.89232i	0.503300	−	0.365669i	−0.306976	−	0.951717i	$-0.599317\pi$
$179$	6.73370	−	4.89232i	0.503300	−	0.365669i	0.810276	+	0.586048i	$0.199317\pi$
$180$	−0.0347639	−	0.0252575i	−0.00259115	−	0.00188258i
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	−0.964201	−	0.265172i	$-0.914571\pi$
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	0.624191	−	0.781272i	$-0.285429\pi$
$182$	−2.02374	−	6.22842i	−0.150009	−	0.461681i
$183$	10.9845	+	7.98074i	0.812001	+	0.589953i
$184$	−1.65251	+	1.20062i	−0.121825	+	0.0885107i
$185$	−1.18547	+	3.64852i	−0.0871578	+	0.268244i
$186$	3.98740			0.292370
$187$		0			0
$188$	−0.0834496			−0.00608619
$189$	−0.882303	+	2.71545i	−0.0641781	+	0.197520i
$190$	12.1129	−	8.80052i	0.878760	−	0.638457i
$191$	7.77203	+	5.64671i	0.562364	+	0.408582i	0.832324	−	0.554290i	$-0.187010\pi$
$191$	7.77203	+	5.64671i	0.562364	+	0.408582i	−0.269959	+	0.962872i	$0.587010\pi$
$192$	−5.38499	−	16.5733i	−0.388628	−	1.19607i
$193$	0.459758	+	1.41499i	0.0330941	+	0.101853i	0.966239	−	0.257647i	$-0.0829472\pi$
$193$	0.459758	+	1.41499i	0.0330941	+	0.101853i	−0.933145	+	0.359500i	$0.882947\pi$
$194$	−2.74911	−	1.99734i	−0.197374	−	0.143401i
$195$	−14.8953	+	10.8221i	−1.06667	+	0.774983i
$196$	−0.00431527	+	0.0132810i	−0.000308234	+	0.000948646i
$197$	14.0434			1.00055			0.500274	−	0.865867i	$-0.333233\pi$
$197$	14.0434			1.00055			0.500274	+	0.865867i	$0.333233\pi$
$198$		0			0
$199$	−4.28729			−0.303918			−0.151959	−	0.988387i	$-0.548558\pi$
$199$	−4.28729			−0.303918			−0.151959	+	0.988387i	$0.548558\pi$
$200$	1.44366	−	4.44312i	0.102082	−	0.314176i
$201$	−27.0710	+	19.6682i	−1.90944	+	1.38729i
$202$	13.5627	+	9.85391i	0.954271	+	0.693318i
$203$	−0.362314	−	1.11509i	−0.0254295	−	0.0782639i
$204$	0.0510676	+	0.157170i	0.00357545	+	0.0110041i
$205$	1.35812	+	0.986734i	0.0948554	+	0.0689165i
$206$	−0.451846	+	0.328285i	−0.0314816	+	0.0228727i
$207$	−0.373671	+	1.15004i	−0.0259719	+	0.0799333i
$208$	−18.4575			−1.27980
$209$		0			0
$210$	−5.58350			−0.385298
$211$	0.449704	−	1.38405i	0.0309589	−	0.0952816i	−0.934383	−	0.356270i	$-0.884048\pi$
$211$	0.449704	−	1.38405i	0.0309589	−	0.0952816i	0.965342	+	0.260988i	$0.0840484\pi$
$212$	0.114613	−	0.0832710i	0.00787163	−	0.00571907i
$213$	24.3313	+	17.6777i	1.66715	+	1.21126i
$214$	1.42376	+	4.38189i	0.0973264	+	0.299540i
$215$	4.54090	+	13.9755i	0.309687	+	0.953118i
$216$	6.55599	+	4.76320i	0.446079	+	0.324095i
$217$	−1.05809	+	0.768744i	−0.0718275	+	0.0521857i
$218$	1.23957	−	3.81499i	0.0839540	−	0.258384i
$219$	13.0119			0.879264
$220$		0			0
$221$	25.4204			1.70996
$222$	−1.97351	+	6.07383i	−0.132453	+	0.407649i
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	−0.448412	−	0.893827i	$-0.648010\pi$
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	0.711513	+	0.702673i	$0.248010\pi$
$224$	0.0639073	+	0.0464314i	0.00426999	+	0.00310233i
$225$	−0.854642	−	2.63032i	−0.0569761	−	0.175354i
$226$	6.33396	+	19.4939i	0.421329	+	1.29672i
$227$	0.321296	+	0.233435i	0.0213252	+	0.0154936i	0.598397	−	0.801200i	$-0.295805\pi$
$227$	0.321296	+	0.233435i	0.0213252	+	0.0154936i	−0.577072	+	0.816694i	$0.695805\pi$
$228$	−0.141786	+	0.103013i	−0.00938999	+	0.00682223i
$229$	0.676634	−	2.08246i	0.0447132	−	0.137613i	−0.926208	−	0.377014i	$-0.876951\pi$
$229$	0.676634	−	2.08246i	0.0447132	−	0.137613i	0.970921	+	0.239401i	$0.0769509\pi$
$230$	1.85744			0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	0.389410	−	1.19848i	0.0255111	−	0.0785150i	−0.937490	−	0.348011i	$-0.886857\pi$
$233$	0.389410	−	1.19848i	0.0255111	−	0.0785150i	0.963001	+	0.269496i	$0.0868571\pi$
$234$	−8.90215	+	6.46779i	−0.581952	+	0.422813i
$235$	8.85393	+	6.43276i	0.577567	+	0.419627i
$236$	0.0331448	+	0.102009i	0.00215754	+	0.00664023i
$237$	−10.4563	−	32.1812i	−0.679210	−	2.09039i
$238$	6.23671	+	4.53123i	0.404266	+	0.293716i
$239$	−9.02997	+	6.56066i	−0.584100	+	0.424374i	−0.840200	−	0.542277i	$-0.817562\pi$
$239$	−9.02997	+	6.56066i	−0.584100	+	0.424374i	0.256100	+	0.966650i	$0.417562\pi$
$240$	−4.86285	+	14.9663i	−0.313896	+	0.966072i
$241$	21.4843			1.38392			0.691962	−	0.721934i	$-0.256746\pi$
$241$	21.4843			1.38392			0.691962	+	0.721934i	$0.256746\pi$
$242$		0			0
$243$	15.7022			1.00730
$244$	−0.0270832	+	0.0833535i	−0.00173382	+	0.00533616i
$245$	1.48162	−	1.07646i	0.0946574	−	0.0687726i
$246$	2.26092	+	1.64266i	0.144151	+	0.104732i
$247$	8.33060	+	25.6390i	0.530063	+	1.63137i
$248$	1.14707	+	3.53032i	0.0728391	+	0.224176i
$249$	7.65846	+	5.56419i	0.485335	+	0.352616i
$250$	−13.8769	+	10.0822i	−0.877653	+	0.637652i
$251$	−0.130968	+	0.403077i	−0.00826660	+	0.0254420i	−0.955105	−	0.296268i	$-0.904258\pi$
$251$	−0.130968	+	0.403077i	−0.00826660	+	0.0254420i	0.946838	+	0.321710i	$0.104258\pi$
$252$	0.0234634			0.00147806
$253$		0			0
$254$	−7.09267			−0.445033
$255$	6.69730	−	20.6122i	0.419401	−	1.29078i
$256$	0.271127	−	0.196986i	0.0169455	−	0.0123116i
$257$	−14.1093	−	10.2510i	−0.880115	−	0.639441i	0.0531672	−	0.998586i	$-0.483068\pi$
$257$	−14.1093	−	10.2510i	−0.880115	−	0.639441i	−0.933282	+	0.359145i	$0.883068\pi$
$258$	7.55942	+	23.2655i	0.470629	+	1.44845i
$259$	−0.647310	−	1.99221i	−0.0402219	−	0.123790i
$260$	−0.0961483	−	0.0698558i	−0.00596286	−	0.00433227i
$261$	−1.59377	+	1.15794i	−0.0986521	+	0.0716749i
$262$	0.0784109	−	0.241324i	0.00484424	−	0.0149090i
$263$	−1.51519			−0.0934307			−0.0467153	−	0.998908i	$-0.514875\pi$
$263$	−1.51519			−0.0934307			−0.0467153	+	0.998908i	$0.514875\pi$
$264$		0			0
$265$	−18.5793			−1.14132
$266$	−2.52634	+	7.77528i	−0.154900	+	0.476733i
$267$	26.8548	−	19.5111i	1.64348	−	1.19406i
$268$	−0.174742	−	0.126957i	−0.0106741	−	0.00775516i
$269$	−0.627622	−	1.93162i	−0.0382668	−	0.117773i	0.930098	−	0.367311i	$-0.119721\pi$
$269$	−0.627622	−	1.93162i	−0.0382668	−	0.117773i	−0.968365	+	0.249538i	$0.919721\pi$
$270$	−2.27715	−	7.00834i	−0.138583	−	0.426514i
$271$	6.15212	+	4.46978i	0.373715	+	0.271520i	0.758750	−	0.651382i	$-0.225811\pi$
$271$	6.15212	+	4.46978i	0.373715	+	0.271520i	−0.385035	+	0.922902i	$0.625811\pi$
$272$	17.5775	−	12.7708i	1.06579	−	0.774344i
$273$	3.10666	−	9.56131i	0.188023	−	0.578677i
$274$	11.7307			0.708676
$275$		0			0
$276$	−0.0217420			−0.00130872
$277$	−4.45813	+	13.7207i	−0.267863	+	0.824398i	0.723157	+	0.690684i	$0.242690\pi$
$277$	−4.45813	+	13.7207i	−0.267863	+	0.824398i	−0.991020	+	0.133714i	$0.957310\pi$
$278$	−7.93661	+	5.76628i	−0.476006	+	0.345839i
$279$	1.77781	+	1.29166i	0.106435	+	0.0773295i
$280$	−1.60623	−	4.94347i	−0.0959906	−	0.295429i
$281$	−5.48494	−	16.8809i	−0.327204	−	1.00703i	−0.970436	−	0.241359i	$-0.922407\pi$
$281$	−5.48494	−	16.8809i	−0.327204	−	1.00703i	0.643232	−	0.765672i	$-0.277593\pi$
$282$	14.7395	+	10.7089i	0.877725	+	0.637704i
$283$	−25.1897	+	18.3014i	−1.49737	+	1.08790i	−0.525956	+	0.850512i	$0.676292\pi$
$283$	−25.1897	+	18.3014i	−1.49737	+	1.08790i	−0.971414	+	0.237392i	$0.923708\pi$
$284$	−0.0599905	+	0.184632i	−0.00355978	+	0.0109559i
$285$	22.9842			1.36147
$286$		0			0
$287$	−0.916645			−0.0541079
$288$	0.0410148	−	0.126231i	0.00241682	−	0.00743821i
$289$	−10.4551	+	7.59609i	−0.615007	+	0.446829i
$290$	2.44813	+	1.77867i	0.143759	+	0.104447i
$291$	−1.61197	−	4.96112i	−0.0944951	−	0.290826i
$292$	0.0259547	+	0.0798805i	0.00151889	+	0.00467465i
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.149229	−	0.988803i	$-0.547679\pi$
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.986522	+	0.163632i	$0.947679\pi$
$294$	2.46652	−	1.79203i	0.143850	−	0.104513i
$295$	4.34679	−	13.3781i	0.253080	−	0.778901i
$296$	−5.94532			−0.345565
$297$		0			0
$298$	4.52983			0.262406
$299$	−1.03348	+	3.18072i	−0.0597676	+	0.183946i
$300$	0.0402302	−	0.0292290i	0.00232269	−	0.00168754i
$301$	−6.49138	−	4.71627i	−0.374157	−	0.271841i
$302$	−9.69701	−	29.8443i	−0.558000	−	1.71735i
$303$	7.95265	+	24.4757i	0.456868	+	1.40609i
$304$	18.6410	+	13.5435i	1.06914	+	0.776772i
$305$	9.29885	−	6.75601i	0.532450	−	0.386848i
$306$	4.00263	−	12.3188i	0.228815	−	0.704221i
$307$	5.46298			0.311789			0.155894	−	0.987774i	$-0.450174\pi$
$307$	5.46298			0.311789			0.155894	+	0.987774i	$0.450174\pi$
$308$		0			0
$309$	−0.857378			−0.0487745
$310$	1.04308	−	3.21028i	0.0592431	−	0.182332i
$311$	−11.2360	+	8.16342i	−0.637134	+	0.462905i	−0.858864	−	0.512203i	$-0.828830\pi$
$311$	−11.2360	+	8.16342i	−0.637134	+	0.462905i	0.221730	+	0.975108i	$0.428830\pi$
$312$	−23.0842	−	16.7716i	−1.30688	−	0.949506i
$313$	8.48207	+	26.1051i	0.479435	+	1.47555i	0.839882	+	0.542770i	$0.182624\pi$
$313$	8.48207	+	26.1051i	0.479435	+	1.47555i	−0.360447	+	0.932780i	$0.617376\pi$
$314$	5.77229	+	17.7653i	0.325749	+	1.00255i
$315$	−2.48945	−	1.80869i	−0.140265	−	0.101908i
$316$	0.176704	−	0.128383i	0.00994038	−	0.00722211i
$317$	2.41828	−	7.44269i	0.135824	−	0.418023i	−0.859893	−	0.510474i	$-0.829470\pi$
$317$	2.41828	−	7.44269i	0.135824	−	0.418023i	0.995717	+	0.0924507i	$0.0294701\pi$
$318$	−30.9297			−1.73445
$319$		0			0
$320$	−14.7520			−0.824659
$321$	−2.18563	+	6.72669i	−0.121990	+	0.375447i
$322$	−0.820525	+	0.596147i	−0.0457261	+	0.0332220i
$323$	−25.6731	−	18.6526i	−1.42849	−	1.03786i
$324$	0.0484067	+	0.148980i	0.00268926	+	0.00827669i
$325$	−2.36372	−	7.27479i	−0.131116	−	0.403533i
$326$	−15.6406	−	11.3635i	−0.866252	−	0.629369i
$327$	4.98178	−	3.61947i	0.275493	−	0.200157i
$328$	−0.803950	+	2.47430i	−0.0443907	+	0.136621i
$329$	−5.97584			−0.329458
$330$		0			0
$331$	−28.1462			−1.54705			−0.773527	−	0.633764i	$-0.781509\pi$
$331$	−28.1462			−1.54705			−0.773527	+	0.633764i	$0.781509\pi$
$332$	−0.0188825	+	0.0581143i	−0.00103631	+	0.00318943i
$333$	−2.84743	+	2.06878i	−0.156038	+	0.113368i
$334$	10.6129	+	7.71075i	0.580714	+	0.421913i
$335$	8.75338	+	26.9401i	0.478248	+	1.47190i
$336$	−2.65528	−	8.17213i	−0.144858	−	0.445826i
$337$	−20.2084	−	14.6823i	−1.10082	−	0.799793i	−0.119628	−	0.992819i	$-0.538170\pi$
$337$	−20.2084	−	14.6823i	−1.10082	−	0.799793i	−0.981194	+	0.193025i	$0.938170\pi$
$338$	−9.79950	+	7.11975i	−0.533022	+	0.387263i
$339$	−9.72333	+	29.9253i	−0.528099	+	1.62532i
$340$	0.139898			0.00758701
$341$		0			0
$342$	13.7365			0.742783
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−18.4239	+	13.3858i	−0.993352	+	0.721713i
$345$	2.30681	+	1.67599i	0.124194	+	0.0902325i
$346$	−4.57509	−	14.0807i	−0.245959	−	0.756983i
$347$	−6.38096	−	19.6386i	−0.342548	−	1.05425i	−0.962883	−	0.269918i	$-0.913003\pi$
$347$	−6.38096	−	19.6386i	−0.342548	−	1.05425i	0.620335	−	0.784337i	$-0.286997\pi$
$348$	−0.0286563	−	0.0208200i	−0.00153614	−	0.00111607i
$349$	−4.85185	+	3.52507i	−0.259713	+	0.188693i	−0.710021	−	0.704181i	$-0.751314\pi$
$349$	−4.85185	+	3.52507i	−0.259713	+	0.188693i	0.450307	+	0.892874i	$0.351314\pi$
$350$	0.716823	−	2.20615i	0.0383158	−	0.117924i
$351$	13.2682			0.708206
$352$		0			0
$353$	24.0382			1.27942			0.639712	−	0.768615i	$-0.279054\pi$
$353$	24.0382			1.27942			0.639712	+	0.768615i	$0.279054\pi$
$354$	7.23629	−	22.2710i	0.384604	−	1.18369i
$355$	20.5974	−	14.9649i	1.09320	−	0.794253i
$356$	0.173346	+	0.125943i	0.00918732	+	0.00667498i
$357$	3.65696	+	11.2550i	0.193547	+	0.595675i
$358$	−3.62470	−	11.1557i	−0.191571	−	0.589596i
$359$	−8.85883	−	6.43632i	−0.467551	−	0.339696i	0.328935	−	0.944353i	$-0.393310\pi$
$359$	−8.85883	−	6.43632i	−0.467551	−	0.339696i	−0.796486	+	0.604657i	$0.793310\pi$
$360$	−7.06559	+	5.13345i	−0.372389	+	0.270557i
$361$	4.52822	−	13.9364i	0.238328	−	0.733497i
$362$	−20.8613			−1.09645
$363$		0			0
$364$	0.0648939			0.00340136
$365$	3.40385	−	10.4760i	0.178166	−	0.548338i
$366$	15.4802	−	11.2470i	0.809161	−	0.587890i
$367$	−8.58995	−	6.24096i	−0.448392	−	0.325776i	0.340569	−	0.940220i	$-0.389380\pi$
$367$	−8.58995	−	6.24096i	−0.448392	−	0.325776i	−0.788960	+	0.614444i	$0.789380\pi$
$368$	0.883322	+	2.71859i	0.0460463	+	0.141716i
$369$	0.475937	+	1.46478i	0.0247763	+	0.0762535i
$370$	4.37382	+	3.17777i	0.227384	+	0.165204i
$371$	8.20742	−	5.96304i	0.426108	−	0.309586i
$372$	−0.0122097	+	0.0375775i	−0.000633042	+	0.00194830i
$373$	−36.6036			−1.89526			−0.947631	−	0.319367i	$-0.896530\pi$
$373$	−36.6036			−1.89526			−0.947631	+	0.319367i	$0.896530\pi$
$374$		0			0
$375$	−26.3315			−1.35975
$376$	−5.24115	+	16.1306i	−0.270292	+	0.831872i
$377$	−4.40797	+	3.20258i	−0.227022	+	0.164941i
$378$	3.25527	+	2.36509i	0.167433	+	0.121647i
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	−0.999856	−	0.0169501i	$-0.994604\pi$
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	0.798938	−	0.601414i	$-0.205396\pi$
$380$	0.0458463	+	0.141100i	0.00235187	+	0.00723830i
$381$	−8.80860	−	6.39982i	−0.451278	−	0.327873i
$382$	10.9529	−	7.95773i	0.560398	−	0.407153i
$383$	−4.77984	+	14.7108i	−0.244238	+	0.751688i	0.751522	+	0.659708i	$0.229320\pi$
$383$	−4.77984	+	14.7108i	−0.244238	+	0.751688i	−0.995761	+	0.0919809i	$0.970680\pi$
$384$	−24.2164			−1.23579
$385$		0			0
$386$	2.09672			0.106720
$387$	−4.16608	+	12.8219i	−0.211774	+	0.651773i
$388$	0.0272411	−	0.0197918i	0.00138296	−	0.00100478i
$389$	10.2850	+	7.47249i	0.521470	+	0.378870i	0.817157	−	0.576415i	$-0.195549\pi$
$389$	10.2850	+	7.47249i	0.521470	+	0.378870i	−0.295687	+	0.955285i	$0.595549\pi$
$390$	8.01801	+	24.6769i	0.406008	+	1.24956i
$391$	−1.21654	−	3.74414i	−0.0615232	−	0.189349i
$392$	2.29616	+	1.66826i	0.115974	+	0.0842599i
$393$	0.315131	−	0.228956i	0.0158963	−	0.0115493i
$394$	6.11571	−	18.8222i	0.308105	−	0.948250i
$395$	−28.6446			−1.44127
$396$		0			0
$397$	−18.9574			−0.951445			−0.475722	−	0.879596i	$-0.657813\pi$
$397$	−18.9574			−0.951445			−0.475722	+	0.879596i	$0.657813\pi$
$398$	−1.86706	+	5.74622i	−0.0935873	+	0.288032i
$399$	−10.1533	+	7.37680i	−0.508300	+	0.369302i
$400$	−5.28919	−	3.84282i	−0.264460	−	0.192141i
$401$	−2.68291	−	8.25715i	−0.133978	−	0.412343i	0.861451	−	0.507840i	$-0.169556\pi$
$401$	−2.68291	−	8.25715i	−0.133978	−	0.412343i	−0.995430	+	0.0954974i	$0.969556\pi$
$402$	14.5721	+	44.8484i	0.726791	+	2.23683i
$403$	4.91698	+	3.57240i	0.244932	+	0.177954i
$404$	−0.134394	+	0.0976429i	−0.00668635	+	0.00485792i
$405$	6.34833	−	19.5381i	0.315451	−	0.970858i
$406$	−1.65233			−0.0820037
$407$		0			0
$408$	33.5879			1.66285
$409$	−1.76574	+	5.43440i	−0.0873104	+	0.268714i	−0.985173	−	0.171561i	$-0.945119\pi$
$409$	−1.76574	+	5.43440i	−0.0873104	+	0.268714i	0.897863	+	0.440275i	$0.145119\pi$
$410$	1.91396	−	1.39057i	0.0945237	−	0.0686755i
$411$	14.5687	+	10.5848i	0.718620	+	0.522108i
$412$	−0.00171020	−	0.00526346i	−8.42556e−5	−	0.000259312i
$413$	2.37350	+	7.30488i	0.116792	+	0.359450i
$414$	1.37866	+	1.00166i	0.0677575	+	0.0492287i
$415$	6.48318	−	4.71031i	0.318247	−	0.231220i
$416$	0.113437	−	0.349122i	0.00556169	−	0.0171171i
$417$	−15.0597			−0.737477
$418$		0			0
$419$	−27.1909			−1.32836			−0.664181	−	0.747571i	$-0.731220\pi$
$419$	−27.1909			−1.32836			−0.664181	+	0.747571i	$0.731220\pi$
$420$	0.0170971	−	0.0526193i	0.000834251	−	0.00256756i
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	−0.00467947	−	0.999989i	$-0.501490\pi$
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	0.949600	+	0.313464i	$0.101490\pi$
$422$	−1.65919	−	1.20547i	−0.0807679	−	0.0586813i
$423$	3.10275	+	9.54928i	0.150861	+	0.464302i
$424$	−8.89768	−	27.3842i	−0.432110	−	1.32990i
$425$	7.28447	+	5.29248i	0.353349	+	0.256723i
$426$	34.2893	−	24.9126i	1.66132	−	1.20702i
$427$	−1.93943	+	5.96895i	−0.0938555	+	0.288858i
$428$	−0.0456549			−0.00220681
$429$		0			0
$430$	20.7087			0.998663
$431$	−5.09049	+	15.6669i	−0.245200	+	0.754649i	0.750403	+	0.660980i	$0.229859\pi$
$431$	−5.09049	+	15.6669i	−0.245200	+	0.754649i	−0.995603	+	0.0936683i	$0.970141\pi$
$432$	9.17463	−	6.66576i	0.441415	−	0.320706i
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	0.124200	−	0.992257i	$-0.460364\pi$
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	−0.905313	+	0.424745i	$0.860364\pi$
$434$	0.569559	+	1.75292i	0.0273397	+	0.0841430i
$435$	1.43548	+	4.41797i	0.0688262	+	0.211825i
$436$	0.0321571	+	0.0233635i	0.00154005	+	0.00111891i
$437$	3.37765	−	2.45401i	0.161575	−	0.117391i
$438$	5.66653	−	17.4398i	0.270757	−	0.833306i
$439$	−26.7682			−1.27758			−0.638788	−	0.769383i	$-0.720564\pi$
$439$	−26.7682			−1.27758			−0.638788	+	0.769383i	$0.720564\pi$
$440$		0			0
$441$	1.68022			0.0800104
$442$	11.0703	−	34.0708i	0.526559	−	1.62058i
$443$	−21.2086	+	15.4090i	−1.00765	+	0.732103i	−0.963716	−	0.266931i	$-0.913990\pi$
$443$	−21.2086	+	15.4090i	−1.00765	+	0.732103i	−0.0439378	+	0.999034i	$0.513990\pi$
$444$	−0.0511972	−	0.0371970i	−0.00242971	−	0.00176529i
$445$	−8.68346	−	26.7249i	−0.411635	−	1.26688i
$446$	−2.11491	−	6.50903i	−0.100144	−	0.308212i
$447$	5.62573	+	4.08733i	0.266088	+	0.193324i
$448$	6.51669	−	4.73465i	0.307885	−	0.223691i
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	−0.854483	−	0.519479i	$-0.826126\pi$
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	0.996634	+	0.0819851i	$0.0261260\pi$
$450$	−3.89758			−0.183734
$451$		0			0
$452$	−0.203107			−0.00955336
$453$	14.8860	−	45.8143i	0.699404	−	2.15254i
$454$	0.452792	−	0.328973i	0.0212506	−	0.0154395i
$455$	−6.88518	−	5.00238i	−0.322782	−	0.234515i
$456$	11.0072	+	33.8767i	0.515459	+	1.58642i
$457$	−3.67276	−	11.3036i	−0.171805	−	0.528760i	0.827669	−	0.561217i	$-0.189667\pi$
$457$	−3.67276	−	11.3036i	−0.171805	−	0.528760i	−0.999473	+	0.0324572i	$0.989667\pi$
$458$	−2.49645	−	1.81378i	−0.116651	−	0.0847522i
$459$	−12.6356	+	9.18033i	−0.589781	+	0.428501i
$460$	−0.00568760	+	0.0175046i	−0.000265186	+	0.000816158i
$461$	−9.14737			−0.426035			−0.213018	−	0.977048i	$-0.568329\pi$
$461$	−9.14737			−0.426035			−0.213018	+	0.977048i	$0.568329\pi$
$462$		0			0
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	−1.43907	+	4.42899i	−0.0668070	+	0.205611i
$465$	4.19212	−	3.04575i	0.194405	−	0.141243i
$466$	−1.43673	−	1.04385i	−0.0665553	−	0.0483552i
$467$	−6.42243	−	19.7662i	−0.297195	−	0.914671i	−0.982475	−	0.186392i	$-0.940320\pi$
$467$	−6.42243	−	19.7662i	−0.297195	−	0.914671i	0.685281	−	0.728279i	$-0.259680\pi$
$468$	−0.0336939	−	0.103699i	−0.00155750	−	0.00479350i
$469$	−12.5133	−	9.09143i	−0.577810	−	0.419803i
$470$	12.4776	−	9.06548i	0.575547	−	0.418159i
$471$	−8.86110	+	27.2717i	−0.408298	+	1.25661i
$472$	21.7998			1.00342
$473$		0			0
$474$	−47.6858			−2.19028
$475$	−2.95076	+	9.08152i	−0.135390	+	0.416689i
$476$	−0.0617999	+	0.0449003i	−0.00283259	+	0.00205800i
$477$	−13.7903	−	10.0192i	−0.631413	−	0.458748i
$478$	4.86076	+	14.9599i	0.222326	+	0.684249i
$479$	7.58214	+	23.3354i	0.346437	+	1.06622i	0.960810	+	0.277207i	$0.0894088\pi$
$479$	7.58214	+	23.3354i	0.346437	+	1.06622i	−0.614374	+	0.789015i	$0.710591\pi$
$480$	−0.253200	−	0.183960i	−0.0115569	−	0.00839661i
$481$	−7.87527	+	5.72172i	−0.359081	+	0.260888i
$482$	9.35614	−	28.7952i	0.426161	−	1.31159i
$483$	−1.55695			−0.0708436
$484$		0			0
$485$	−4.41591			−0.200516
$486$	6.83811	−	21.0456i	0.310183	−	0.954646i
$487$	10.0086	−	7.27168i	0.453533	−	0.329511i	−0.337456	−	0.941341i	$-0.609566\pi$
$487$	10.0086	−	7.27168i	0.453533	−	0.329511i	0.790989	+	0.611830i	$0.209566\pi$
$488$	14.4110	+	10.4702i	0.652356	+	0.473964i
$489$	−9.17101	−	28.2255i	−0.414727	−	1.27640i
$490$	−0.797546	−	2.45459i	−0.0360295	−	0.110887i
$491$	13.3691	+	9.71320i	0.603338	+	0.438350i	0.847062	−	0.531494i	$-0.178369\pi$
$491$	13.3691	+	9.71320i	0.603338	+	0.438350i	−0.243724	+	0.969845i	$0.578369\pi$
$492$	−0.0224036	+	0.0162772i	−0.00101003	+	0.000733831i
$493$	1.98194	−	6.09977i	0.0892620	−	0.274720i
$494$	37.9916			1.70932
$495$		0			0
$496$	5.19468			0.233248
$497$	−4.29593	+	13.2215i	−0.192699	+	0.593065i
$498$	10.7928	−	7.84144i	0.483638	−	0.351383i
$499$	11.1167	+	8.07673i	0.497650	+	0.361564i	0.808119	−	0.589020i	$-0.200486\pi$
$499$	11.1167	+	8.07673i	0.497650	+	0.361564i	−0.310469	+	0.950584i	$0.600486\pi$
$500$	−0.0525231	−	0.161649i	−0.00234890	−	0.00722918i
$501$	6.22300	+	19.1524i	0.278023	+	0.855667i
$502$	0.483206	+	0.351070i	0.0215665	+	0.0156690i
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	−0.915310	−	0.402751i	$-0.868054\pi$
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	0.100193	+	0.994968i	$0.468054\pi$
$504$	1.47365	−	4.53542i	0.0656414	−	0.202024i
$505$	21.7859			0.969461
$506$		0			0
$507$	−18.5946			−0.825813
$508$	0.0217182	−	0.0668418i	0.000963590	−	0.00296563i
$509$	17.3644	−	12.6160i	0.769664	−	0.559194i	−0.132195	−	0.991224i	$-0.542202\pi$
$509$	17.3644	−	12.6160i	0.769664	−	0.559194i	0.901859	+	0.432030i	$0.142202\pi$
$510$	−24.7098	−	17.9527i	−1.09417	−	0.794958i
$511$	1.85862	+	5.72025i	0.0822206	+	0.253049i
$512$	−7.06408	−	21.7410i	−0.312191	−	0.960825i
$513$	−13.4001	−	9.73576i	−0.591630	−	0.429844i
$514$	−19.8838	+	14.4464i	−0.877037	+	0.637204i
$515$	−0.224286	+	0.690280i	−0.00988321	+	0.0304174i
$516$	−0.242403			−0.0106712
$517$		0			0
$518$	−2.95205			−0.129706
$519$	7.02327	−	21.6154i	0.308287	−	0.948811i
$520$	−19.5416	+	14.1978i	−0.856957	+	0.622616i
$521$	−28.0822	−	20.4029i	−1.23031	−	0.893869i	−0.233393	−	0.972383i	$-0.574983\pi$
$521$	−28.0822	−	20.4029i	−1.23031	−	0.893869i	−0.996913	+	0.0785132i	$0.974983\pi$
$522$	0.857916	+	2.64039i	0.0375500	+	0.115567i
$523$	−6.09633	−	18.7626i	−0.266574	−	0.820430i	−0.991327	−	0.131421i	$-0.958046\pi$
$523$	−6.09633	−	18.7626i	−0.266574	−	0.820430i	0.724753	−	0.689009i	$-0.241954\pi$
$524$	0.00203415	+	0.00147790i	8.88624e−5	+	6.45623e-5i
$525$	2.88089	−	2.09309i	0.125732	−	0.0913499i
$526$	−0.659847	+	2.03080i	−0.0287707	+	0.0885471i
$527$	−7.15430			−0.311646
$528$		0			0
$529$	−22.4821			−0.977481
$530$	−8.09105	+	24.9017i	−0.351453	+	1.08166i
$531$	10.4407	−	7.58562i	0.453088	−	0.329188i
$532$	−0.0655390	−	0.0476168i	−0.00284147	−	0.00206445i
$533$	1.31632	+	4.05122i	0.0570162	+	0.175478i
$534$	−14.4557	−	44.4901i	−0.625560	−	1.92527i
$535$	4.84395	+	3.51933i	0.209422	+	0.152154i
$536$	−35.5154	+	25.8034i	−1.53403	+	1.11454i
$537$	5.56431	−	17.1252i	0.240118	−	0.739006i
$538$	−2.86226			−0.123401
$539$		0			0
$540$	0.0730199			0.00314227
$541$	1.71487	−	5.27782i	0.0737279	−	0.226911i	−0.907401	−	0.420266i	$-0.861937\pi$
$541$	1.71487	−	5.27782i	0.0737279	−	0.226911i	0.981129	+	0.193355i	$0.0619368\pi$
$542$	8.66998	−	6.29911i	0.372408	−	0.270570i
$543$	−25.9083	−	18.8235i	−1.11183	−	0.807794i
$544$	0.133530	+	0.410964i	0.00572506	+	0.0176199i
$545$	−1.61085	−	4.95770i	−0.0690014	−	0.212364i
$546$	−11.4620	−	8.32766i	−0.490530	−	0.356391i
$547$	−6.83353	+	4.96485i	−0.292181	+	0.212282i	−0.724213	−	0.689576i	$-0.757797\pi$
$547$	−6.83353	+	4.96485i	−0.292181	+	0.212282i	0.432032	+	0.901858i	$0.357797\pi$
$548$	−0.0359201	+	0.110551i	−0.00153443	+	0.00472250i
$549$	10.5453			0.450061
$550$		0			0
$551$	6.80173			0.289763
$552$	−1.36553	+	4.20267i	−0.0581209	+	0.178878i
$553$	12.6538	−	9.19351i	0.538094	−	0.390948i
$554$	16.4483	+	11.9504i	0.698822	+	0.507724i
$555$	2.56463	+	7.89313i	0.108863	+	0.335045i
$556$	−0.0300394	−	0.0924519i	−0.00127396	−	0.00392083i
$557$	−9.85665	−	7.16128i	−0.417640	−	0.303433i	0.359048	−	0.933319i	$-0.383102\pi$
$557$	−9.85665	−	7.16128i	−0.417640	−	0.303433i	−0.776687	+	0.629886i	$0.783102\pi$
$558$	2.50542	−	1.82029i	0.106063	−	0.0770591i
$559$	−11.5223	+	35.4620i	−0.487342	+	1.49988i
$560$	−7.27404			−0.307384
$561$		0			0
$562$	−25.0140			−1.05515
$563$	8.45270	−	26.0147i	0.356239	−	1.09639i	−0.599049	−	0.800713i	$-0.704454\pi$
$563$	8.45270	−	26.0147i	0.356239	−	1.09639i	0.955288	−	0.295678i	$-0.0955456\pi$
$564$	−0.146055	+	0.106115i	−0.00615001	+	0.00446824i
$565$	21.5495	+	15.6566i	0.906594	+	0.658679i
$566$	13.5594	+	41.7316i	0.569944	+	1.75411i
$567$	3.46640	+	10.6685i	0.145575	+	0.448035i
$568$	31.9211	+	23.1920i	1.33938	+	0.973115i
$569$	5.77253	−	4.19399i	0.241997	−	0.175821i	−0.460176	−	0.887828i	$-0.652214\pi$
$569$	5.77253	−	4.19399i	0.241997	−	0.175821i	0.702173	+	0.712007i	$0.252214\pi$
$570$	10.0093	−	30.8055i	0.419245	−	1.29030i
$571$	−32.4839			−1.35941			−0.679705	−	0.733486i	$-0.737892\pi$
$571$	−32.4839			−1.35941			−0.679705	+	0.733486i	$0.737892\pi$
$572$		0			0
$573$	20.7831			0.868226
$574$	−0.399188	+	1.22857i	−0.0166618	+	0.0512797i
$575$	−0.958373	+	0.696299i	−0.0399669	+	0.0290377i
$576$	−10.9495	−	7.95525i	−0.456228	−	0.331469i
$577$	10.7482	+	33.0795i	0.447453	+	1.37712i	0.879771	+	0.475398i	$0.157696\pi$
$577$	10.7482	+	33.0795i	0.447453	+	1.37712i	−0.432317	+	0.901721i	$0.642304\pi$
$578$	5.62791	+	17.3209i	0.234090	+	0.720456i
$579$	2.60398	+	1.89190i	0.108218	+	0.0786248i
$580$	−0.0242587	+	0.0176249i	−0.00100729	+	0.000731836i
$581$	−1.35217	+	4.16157i	−0.0560977	+	0.172651i
$582$	−7.35135			−0.304723
$583$		0			0
$584$	17.0708			0.706395
$585$	−4.41882	+	13.5997i	−0.182696	+	0.562279i
$586$	−27.3975	+	19.9054i	−1.13178	+	0.822285i
$587$	11.7105	+	8.50816i	0.483343	+	0.351169i	0.802618	−	0.596493i	$-0.203440\pi$
$587$	11.7105	+	8.50816i	0.483343	+	0.351169i	−0.319276	+	0.947662i	$0.603440\pi$
$588$	0.00933558	+	0.0287320i	0.000384993	+	0.00118489i
$589$	−2.34456	−	7.21581i	−0.0966059	−	0.297322i
$590$	−16.0375	−	11.6520i	−0.660255	−	0.479704i
$591$	24.5789	−	17.8576i	1.01104	−	0.734563i
$592$	−2.57103	+	7.91283i	−0.105669	+	0.325215i
$593$	15.0291			0.617169			0.308585	−	0.951197i	$-0.400145\pi$
$593$	15.0291			0.617169			0.308585	+	0.951197i	$0.400145\pi$
$594$		0			0
$595$	10.0181			0.410701
$596$	−0.0138706	+	0.0426894i	−0.000568163	+	0.00174863i
$597$	−7.50366	+	5.45173i	−0.307104	+	0.223124i
$598$	3.81303	+	2.77033i	0.155926	+	0.113287i
$599$	0.544010	+	1.67429i	0.0222276	+	0.0684097i	0.961555	−	0.274612i	$-0.0885495\pi$
$599$	0.544010	+	1.67429i	0.0222276	+	0.0684097i	−0.939327	+	0.343022i	$0.888549\pi$
$600$	−3.12318	−	9.61216i	−0.127503	−	0.392415i
$601$	18.9605	+	13.7756i	0.773415	+	0.561919i	0.902995	−	0.429650i	$-0.141363\pi$
$601$	18.9605	+	13.7756i	0.773415	+	0.561919i	−0.129581	+	0.991569i	$0.541363\pi$
$602$	−9.14810	+	6.64648i	−0.372849	+	0.270890i
$603$	−8.03085	+	24.7164i	−0.327042	+	1.00653i
$604$	0.310948			0.0126523
$605$		0			0
$606$	36.2679			1.47328
$607$	7.81149	−	24.0413i	0.317059	−	0.975806i	−0.657840	−	0.753158i	$-0.728530\pi$
$607$	7.81149	−	24.0413i	0.317059	−	0.975806i	0.974899	−	0.222649i	$-0.0714703\pi$
$608$	−0.370738	+	0.269357i	−0.0150354	+	0.0109239i
$609$	−2.05208	−	1.49092i	−0.0831544	−	0.0604152i
$610$	−5.00550	−	15.4053i	−0.202667	−	0.623744i
$611$	8.58142	+	26.4109i	0.347167	+	1.06847i
$612$	0.103837	+	0.0754422i	0.00419737	+	0.00304957i
$613$	0.939222	−	0.682385i	0.0379348	−	0.0275613i	−0.568656	−	0.822575i	$-0.692537\pi$
$613$	0.939222	−	0.682385i	0.0379348	−	0.0275613i	0.606591	+	0.795014i	$0.292537\pi$
$614$	2.37906	−	7.32199i	0.0960110	−	0.295492i
$615$	3.63174			0.146446
$616$		0			0
$617$	12.9711			0.522197			0.261098	−	0.965312i	$-0.415915\pi$
$617$	12.9711			0.522197			0.261098	+	0.965312i	$0.415915\pi$
$618$	−0.373377	+	1.14914i	−0.0150194	+	0.0462251i
$619$	−37.0465	+	26.9158i	−1.48902	+	1.08184i	−0.514517	+	0.857480i	$0.672029\pi$
$619$	−37.0465	+	26.9158i	−1.48902	+	1.08184i	−0.974507	+	0.224358i	$0.927971\pi$
$620$	0.0270599	+	0.0196602i	0.00108675	+	0.000789572i
$621$	−0.634978	−	1.95426i	−0.0254808	−	0.0784218i
$622$	6.04824	+	18.6146i	0.242512	+	0.746377i
$623$	12.4133	+	9.01881i	0.497329	+	0.361331i
$624$	−32.3046	+	23.4707i	−1.29322	+	0.939578i
$625$	−4.34493	+	13.3723i	−0.173797	+	0.534893i
$626$	38.6824			1.54606
$627$		0			0
$628$	−0.185097			−0.00738615
$629$	3.54092	−	10.8978i	0.141186	−	0.434525i
$630$	−3.50830	+	2.54893i	−0.139774	+	0.101552i
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	0.772170	−	0.635416i	$-0.219171\pi$
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	−0.365703	+	0.930732i	$0.619171\pi$
$632$	−13.7180	−	42.2196i	−0.545672	−	1.67941i
$633$	−0.972881	−	2.99422i	−0.0386685	−	0.119009i
$634$	−8.92225	−	6.48240i	−0.354348	−	0.257449i
$635$	−7.45682	+	5.41770i	−0.295915	+	0.214995i
$636$	0.0947088	−	0.291484i	0.00375545	−	0.0115581i
$637$	4.64706			0.184123
$638$		0			0
$639$	23.3582			0.924038
$640$	−6.33488	+	19.4968i	−0.250408	+	0.770678i
$641$	−22.6175	+	16.4326i	−0.893336	+	0.649047i	−0.936746	−	0.350011i	$-0.886178\pi$
$641$	−22.6175	+	16.4326i	−0.893336	+	0.649047i	0.0434095	+	0.999057i	$0.486178\pi$
$642$	8.06392	+	5.85878i	0.318257	+	0.231228i
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.492313	−	0.870418i	$-0.663848\pi$
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.113330	−	0.993557i	$-0.536152\pi$
$644$	−0.00310563	−	0.00955813i	−0.000122379	−	0.000376643i
$645$	25.7188	+	18.6858i	1.01268	+	0.735752i
$646$	−36.1802	+	26.2865i	−1.42349	+	1.03423i
$647$	−3.40125	+	10.4680i	−0.133717	+	0.411539i	−0.995388	−	0.0959281i	$-0.969418\pi$
$647$	−3.40125	+	10.4680i	−0.133717	+	0.411539i	0.861671	+	0.507467i	$0.169418\pi$
$648$	31.8377			1.25070
$649$		0			0
$650$	−10.7797			−0.422816
$651$	−0.874336	+	2.69093i	−0.0342679	+	0.105466i
$652$	0.154983	−	0.112602i	0.00606962	−	0.00440984i
$653$	−23.4100	−	17.0084i	−0.916106	−	0.665590i	0.0264458	−	0.999650i	$-0.491581\pi$
$653$	−23.4100	−	17.0084i	−0.916106	−	0.665590i	−0.942552	+	0.334060i	$0.891581\pi$
$654$	−2.68165	−	8.25328i	−0.104861	−	0.322729i
$655$	−0.101897	−	0.313608i	−0.00398146	−	0.0122537i
$656$	2.94547	+	2.14001i	0.115001	+	0.0835533i
$657$	8.17583	−	5.94009i	0.318969	−	0.231745i
$658$	−2.60240	+	8.00937i	−0.101452	+	0.312238i
$659$	−10.8405			−0.422288			−0.211144	−	0.977455i	$-0.567719\pi$
$659$	−10.8405			−0.422288			−0.211144	+	0.977455i	$0.567719\pi$
$660$		0			0
$661$	20.3444			0.791305			0.395652	−	0.918400i	$-0.370519\pi$
$661$	20.3444			0.791305			0.395652	+	0.918400i	$0.370519\pi$
$662$	−12.2573	+	37.7241i	−0.476394	+	1.46619i
$663$	44.4911	−	32.3247i	1.72789	−	1.25539i
$664$	10.0474	+	7.29986i	0.389915	+	0.283289i
$665$	3.28306	+	10.1042i	0.127311	+	0.391824i
$666$	1.53275	+	4.71732i	0.0593929	+	0.182792i
$667$	0.682656	+	0.495978i	0.0264325	+	0.0192044i
$668$	−0.105164	+	0.0764062i	−0.00406892	+	0.00295625i
$669$	3.24662	−	9.99208i	0.125522	−	0.386316i
$670$	39.9197			1.54223
$671$		0			0
$672$	0.170894			0.00659237
$673$	3.73255	−	11.4876i	0.143879	−	0.442815i	−0.852986	−	0.521934i	$-0.825211\pi$
$673$	3.73255	−	11.4876i	0.143879	−	0.442815i	0.996865	+	0.0791188i	$0.0252107\pi$
$674$	−28.4790	+	20.6912i	−1.09697	+	0.796996i
$675$	3.80215	+	2.76242i	0.146345	+	0.106326i
$676$	−0.0370903	−	0.114152i	−0.00142655	−	0.00439047i
$677$	−1.04951	−	3.23007i	−0.0403361	−	0.124142i	0.928861	−	0.370429i	$-0.120789\pi$
$677$	−1.04951	−	3.23007i	−0.0403361	−	0.124142i	−0.969197	+	0.246287i	$0.920789\pi$
$678$	35.8743	+	26.0642i	1.37775	+	1.00099i
$679$	1.95073	−	1.41729i	0.0748623	−	0.0543906i
$680$	8.78642	−	27.0418i	0.336944	−	1.03701i
$681$	0.859173			0.0329236
$682$		0			0
$683$	−4.75643			−0.182000			−0.0909999	−	0.995851i	$-0.529006\pi$
$683$	−4.75643			−0.182000			−0.0909999	+	0.995851i	$0.529006\pi$
$684$	−0.0420620	+	0.129454i	−0.00160828	+	0.00494978i
$685$	12.3330	−	8.96042i	0.471218	−	0.342360i
$686$	1.14012	+	0.828347i	0.0435300	+	0.0316264i
$687$	−1.46382	−	4.50516i	−0.0558481	−	0.171883i
$688$	9.84822	+	30.3097i	0.375460	+	1.15555i
$689$	−38.1404	−	27.7106i	−1.45303	−	1.05569i
$690$	3.25091	−	2.36193i	0.123760	−	0.0899170i
$691$	2.04998	−	6.30920i	0.0779850	−	0.240013i	−0.904462	−	0.426554i	$-0.859728\pi$
$691$	2.04998	−	6.30920i	0.0779850	−	0.240013i	0.982447	+	0.186540i	$0.0597275\pi$
$692$	0.146707			0.00557695
$693$		0			0
$694$	−29.1003			−1.10463
$695$	−3.93955	+	12.1247i	−0.149435	+	0.459915i
$696$	−5.82424	+	4.23156i	−0.220767	+	0.160397i
$697$	−4.05661	−	2.94730i	−0.153655	−	0.111637i
$698$	2.61171	+	8.03802i	0.0988547	+	0.304244i
$699$	−0.842441	−	2.59277i	−0.0318641	−	0.0980675i
$700$	0.0185960	+	0.0135108i	0.000702863	+	0.000510660i
$701$	2.45134	−	1.78101i	0.0925860	−	0.0672677i	−0.540529	−	0.841325i	$-0.681776\pi$
$701$	2.45134	−	1.78101i	0.0925860	−	0.0672677i	0.633115	+	0.774058i	$0.281776\pi$
$702$	5.77815	−	17.7833i	0.218082	−	0.671188i
$703$	12.1519			0.458319
$704$		0			0
$705$	23.6762			0.891697
$706$	10.4683	−	32.2182i	0.393981	−	1.21255i
$707$	−9.62396	+	6.99222i	−0.361946	+	0.262969i
$708$	0.187726	+	0.136391i	0.00705516	+	0.00512587i
$709$	−4.22026	−	12.9886i	−0.158495	−	0.487798i	0.840003	−	0.542582i	$-0.182553\pi$
$709$	−4.22026	−	12.9886i	−0.158495	−	0.487798i	−0.998498	+	0.0547836i	$0.982553\pi$
$710$	−11.0874	−	34.1236i	−0.416103	−	1.28063i
$711$	−21.2611	−	15.4471i	−0.797354	−	0.579312i
$712$	35.2317	−	25.5973i	1.32036	−	0.959300i
$713$	0.290862	−	0.895180i	0.0108928	−	0.0335247i
$714$	16.6775			0.624140
$715$		0			0
$716$	0.116231			0.00434376
$717$	−7.46181	+	22.9651i	−0.278666	+	0.857647i
$718$	−12.4845	+	9.07050i	−0.465916	+	0.338508i
$719$	1.53737	+	1.11696i	0.0573341	+	0.0416557i	0.616083	−	0.787681i	$-0.288719\pi$
$719$	1.53737	+	1.11696i	0.0573341	+	0.0416557i	−0.558749	+	0.829337i	$0.688719\pi$
$720$	3.77680	+	11.6238i	0.140753	+	0.433193i
$721$	−0.122468	−	0.376917i	−0.00456094	−	0.0140371i
$722$	−16.7069	−	12.1383i	−0.621768	−	0.451741i
$723$	37.6021	−	27.3195i	1.39844	−	1.01602i
$724$	0.0638788	−	0.196599i	0.00237404	−	0.00730654i
$725$	−1.92992			−0.0716754
$726$		0			0
$727$	−13.8211			−0.512595			−0.256298	−	0.966598i	$-0.582503\pi$
$727$	−13.8211			−0.512595			−0.256298	+	0.966598i	$0.582503\pi$
$728$	4.07573	−	12.5438i	0.151057	−	0.464905i
$729$	0.256684	−	0.186492i	0.00950682	−	0.00690711i
$730$	−12.5586	−	9.12432i	−0.464813	−	0.337706i
$731$	−13.5633	−	41.7436i	−0.501658	−	1.54394i
$732$	0.0585912	+	0.180325i	0.00216559	+	0.00666502i
$733$	39.1357	+	28.4337i	1.44551	+	1.05022i	0.986855	+	0.161610i	$0.0516685\pi$
$733$	39.1357	+	28.4337i	1.44551	+	1.05022i	0.458655	+	0.888615i	$0.348331\pi$
$734$	−12.1055	+	8.79519i	−0.446824	+	0.324636i
$735$	1.22432	−	3.76807i	0.0451598	−	0.138987i
$736$	−0.0568504			−0.00209553
$737$		0			0
$738$	2.17050			0.0798973
$739$	−7.17170	+	22.0722i	−0.263815	+	0.811939i	0.728149	+	0.685419i	$0.240381\pi$
$739$	−7.17170	+	22.0722i	−0.263815	+	0.811939i	−0.991964	+	0.126520i	$0.959619\pi$
$740$	−0.0433404	+	0.0314887i	−0.00159323	+	0.00115755i
$741$	47.1829	+	34.2804i	1.73331	+	1.25932i
$742$	−4.41799	−	13.5972i	−0.162190	−	0.499168i
$743$	13.8536	+	42.6369i	0.508238	+	1.56420i	0.795257	+	0.606272i	$0.207336\pi$
$743$	13.8536	+	42.6369i	0.508238	+	1.56420i	−0.287019	+	0.957925i	$0.592664\pi$
$744$	6.49679	+	4.72020i	0.238184	+	0.173051i
$745$	4.76240	−	3.46009i	0.174481	−	0.126768i
$746$	−15.9404	+	49.0596i	−0.583620	+	1.79620i
$747$	7.35218			0.269002
$748$		0			0
$749$	−3.26935			−0.119460
$750$	−11.4670	+	35.2919i	−0.418717	+	1.28868i
$751$	33.3199	−	24.2083i	1.21586	−	0.883373i	0.220109	−	0.975475i	$-0.429359\pi$
$751$	33.3199	−	24.2083i	1.21586	−	0.883373i	0.995750	+	0.0921022i	$0.0293587\pi$
$752$	19.2022	+	13.9512i	0.700234	+	0.508750i
$753$	0.283333	+	0.872008i	0.0103252	+	0.0317777i
$754$	2.37278	+	7.30266i	0.0864115	+	0.265947i
$755$	−32.9913	−	23.9696i	−1.20068	−	0.872343i
$756$	−0.0322566	+	0.0234358i	−0.00117316	+	0.000852352i
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	0.749655	+	0.661829i	$0.230219\pi$
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	−0.995497	+	0.0947948i	$0.969781\pi$
$758$	−17.8382			−0.647912
$759$		0			0
$760$	30.1537			1.09379
$761$	11.0367	−	33.9673i	0.400078	−	1.23131i	−0.524857	−	0.851190i	$-0.675881\pi$
$761$	11.0367	−	33.9673i	0.400078	−	1.23131i	0.924935	−	0.380124i	$-0.124119\pi$
$762$	−12.4137	+	9.01906i	−0.449700	+	0.326726i
$763$	2.30277	+	1.67306i	0.0833660	+	0.0605690i
$764$	0.0414558	+	0.127588i	0.00149982	+	0.00461596i
$765$	−5.20154	−	16.0087i	−0.188062	−	0.578796i
$766$	17.6353	+	12.8128i	0.637188	+	0.462944i
$767$	28.8764	−	20.9799i	1.04266	−	0.757540i
$768$	0.224043	−	0.689533i	0.00808445	−	0.0248814i
$769$	−5.30246			−0.191212			−0.0956058	−	0.995419i	$-0.530479\pi$
$769$	−5.30246			−0.191212			−0.0956058	+	0.995419i	$0.530479\pi$
$770$		0			0
$771$	−37.7295			−1.35880
$772$	−0.00642030	+	0.0197596i	−0.000231072	+	0.000711165i
$773$	40.3628	−	29.3253i	1.45175	−	1.05476i	0.466332	−	0.884610i	$-0.345575\pi$
$773$	40.3628	−	29.3253i	1.45175	−	1.05476i	0.985418	−	0.170149i	$-0.0544248\pi$
$774$	15.3708	+	11.1675i	0.552492	+	0.401409i
$775$	0.665245	+	2.04741i	0.0238963	+	0.0735452i
$776$	−2.11479	−	6.50867i	−0.0759167	−	0.233648i
$777$	−3.66624	−	2.66368i	−0.131526	−	0.0955589i
$778$	14.4943	−	10.5307i	0.519646	−	0.377545i
$779$	1.64324	−	5.05736i	0.0588750	−	0.181199i
$780$	−0.257109			−0.00920597
$781$		0			0
$782$	−5.54803			−0.198397
$783$	1.03448	−	3.18379i	0.0369692	−	0.113779i
$784$	3.21332	−	2.33461i	0.114761	−	0.0833789i
$785$	19.6386	+	14.2683i	0.700931	+	0.509256i
$786$	−0.169633	−	0.522075i	−0.00605059	−	0.0186218i
$787$	−11.0804	−	34.1020i	−0.394974	−	1.21560i	−0.928982	−	0.370125i	$-0.879315\pi$
$787$	−11.0804	−	34.1020i	−0.394974	−	1.21560i	0.534008	−	0.845479i	$-0.320685\pi$
$788$	0.158655	+	0.115270i	0.00565186	+	0.00410632i
$789$	−2.65191	+	1.92672i	−0.0944103	+	0.0685931i
$790$	−12.4744	+	38.3922i	−0.443818	+	1.36593i
$791$	−14.5445			−0.517144
$792$		0			0
$793$	29.1655			1.03570
$794$	−8.25571	+	25.4085i	−0.292984	+	0.901713i
$795$	−32.5177	+	23.6255i	−1.15328	+	0.837910i
$796$	−0.0484357	−	0.0351906i	−0.00171676	−	0.00124730i
$797$	4.55530	+	14.0198i	0.161357	+	0.496606i	0.998749	−	0.0499962i	$-0.0159209\pi$
$797$	4.55530	+	14.0198i	0.161357	+	0.496606i	−0.837392	+	0.546602i	$0.815921\pi$
$798$	5.46544	+	16.8209i	0.193474	+	0.595453i
$799$	−26.4460	−	19.2142i	−0.935593	−	0.679748i
$800$	0.105193	−	0.0764272i	0.00371913	−	0.00270211i
$801$	7.96670	−	24.5190i	0.281489	−	0.866336i
$802$	−12.2354			−0.432046
$803$		0			0
$804$	−0.467275			−0.0164795
$805$	−0.407290	+	1.25351i	−0.0143551	+	0.0441804i
$806$	6.92934	−	5.03446i	0.244076	−	0.177331i
$807$	−3.55473	−	2.58266i	−0.125132	−	0.0909140i
$808$	10.4334	+	32.1106i	0.367044	+	1.12965i
$809$	8.33599	+	25.6556i	0.293078	+	0.902001i	0.983860	+	0.178938i	$0.0572663\pi$
$809$	8.33599	+	25.6556i	0.293078	+	0.902001i	−0.690782	+	0.723063i	$0.742734\pi$
$810$	−23.4222	−	17.0172i	−0.822973	−	0.597925i
$811$	1.18472	−	0.860750i	0.0416012	−	0.0302250i	−0.566790	−	0.823862i	$-0.691815\pi$
$811$	1.18472	−	0.860750i	0.0416012	−	0.0302250i	0.608392	+	0.793637i	$0.291815\pi$
$812$	0.00505954	−	0.0155717i	0.000177555	−	0.000546459i
$813$	16.4513			0.576972
$814$		0			0
$815$	−25.1236			−0.880041
$816$	14.5250	−	44.7033i	0.508476	−	1.56493i
$817$	37.6577	−	27.3599i	1.31747	−	0.957201i
$818$	6.51473	+	4.73323i	0.227782	+	0.165493i
$819$	−2.41283	−	7.42591i	−0.0843110	−	0.259482i
$820$	0.00724418	+	0.0222953i	0.000252978	+	0.000778586i
$821$	24.7791	+	18.0031i	0.864797	+	0.628312i	0.929186	−	0.369613i	$-0.120510\pi$
$821$	24.7791	+	18.0031i	0.864797	+	0.628312i	−0.0643886	+	0.997925i	$0.520510\pi$
$822$	20.5312	−	14.9168i	0.716107	−	0.520282i
$823$	−7.58137	+	23.3330i	−0.264270	+	0.813339i	0.727591	+	0.686011i	$0.240640\pi$
$823$	−7.58137	+	23.3330i	−0.264270	+	0.813339i	−0.991861	+	0.127328i	$0.959360\pi$
$824$	−1.12482			−0.0391851
$825$		0			0
$826$	10.8243			0.376626
$827$	2.02927	−	6.24545i	0.0705646	−	0.217176i	−0.909555	−	0.415584i	$-0.863577\pi$
$827$	2.02927	−	6.24545i	0.0705646	−	0.217176i	0.980119	+	0.198408i	$0.0635772\pi$
$828$	−0.0136612	+	0.00992547i	−0.000474761	+	0.000344934i
$829$	16.0543	+	11.6642i	0.557590	+	0.405113i	0.830576	−	0.556905i	$-0.188011\pi$
$829$	16.0543	+	11.6642i	0.557590	+	0.405113i	−0.272986	+	0.962018i	$0.588011\pi$
$830$	−3.48985	−	10.7406i	−0.121134	−	0.372813i
$831$	9.64463	+	29.6831i	0.334569	+	1.02970i
$832$	−30.2834	−	22.0022i	−1.04989	−	0.762789i
$833$	−4.42550	+	3.21531i	−0.153334	+	0.111404i
$834$	−6.55832	+	20.1844i	−0.227096	+	0.698930i
$835$	17.0476			0.589958
$836$		0			0
$837$	−3.73421			−0.129073
$838$	−11.8413	+	36.4438i	−0.409051	+	1.25893i
$839$	6.44019	−	4.67907i	0.222340	−	0.161539i	−0.471039	−	0.882112i	$-0.656121\pi$
$839$	6.44019	−	4.67907i	0.222340	−	0.161539i	0.693379	+	0.720573i	$0.256121\pi$
$840$	−9.09737	−	6.60963i	−0.313889	−	0.228054i
$841$	−8.53669	−	26.2732i	−0.294369	−	0.905973i
$842$	−10.4365	−	32.1202i	−0.359665	−	1.10694i
$843$	−31.0656	−	22.5705i	−1.06996	−	0.777370i
$844$	0.0164410	−	0.0119451i	0.000565922	−	0.000411166i
$845$	−4.86424	+	14.9706i	−0.167335	+	0.515004i
$846$	14.1500			0.486489
$847$		0			0
$848$	−40.2944			−1.38372
$849$	−20.8152	+	64.0625i	−0.714375	+	2.19862i
$850$	10.2658	−	7.45852i	0.352113	−	0.255825i
$851$	1.21963	+	0.886114i	0.0418084	+	0.0303756i
$852$	0.129782	+	0.399429i	0.00444627	+	0.0136842i
$853$	−10.5292	−	32.4055i	−0.360513	−	1.10954i	−0.952744	−	0.303776i	$-0.901753\pi$
$853$	−10.5292	−	32.4055i	−0.360513	−	1.10954i	0.592231	−	0.805768i	$-0.298247\pi$
$854$	7.15554	+	5.19881i	0.244858	+	0.177900i
$855$	14.4417	−	10.4925i	0.493897	−	0.358837i
$856$	−2.86741	+	8.82497i	−0.0980060	+	0.301631i
$857$	−24.8539			−0.848992			−0.424496	−	0.905430i	$-0.639549\pi$
$857$	−24.8539			−0.848992			−0.424496	+	0.905430i	$0.639549\pi$
$858$		0			0
$859$	2.05654			0.0701683			0.0350841	−	0.999384i	$-0.488830\pi$
$859$	2.05654			0.0701683			0.0350841	+	0.999384i	$0.488830\pi$
$860$	−0.0634115	+	0.195160i	−0.00216231	+	0.00665491i
$861$	−1.60432	+	1.16561i	−0.0546752	+	0.0397239i
$862$	18.7814	+	13.6455i	0.639697	+	0.464767i
$863$	−0.0801824	−	0.246776i	−0.00272944	−	0.00840035i	0.949683	−	0.313214i	$-0.101406\pi$
$863$	−0.0801824	−	0.246776i	−0.00272944	−	0.00840035i	−0.952412	+	0.304814i	$0.901406\pi$
$864$	0.0696964	+	0.214504i	0.00237112	+	0.00729756i
$865$	−15.5655	−	11.3090i	−0.529241	−	0.384516i
$866$	−22.9061	+	16.6423i	−0.778381	+	0.565527i
$867$	−8.63946	+	26.5895i	−0.293412	+	0.903028i
$868$	−0.0182637			−0.000619910
$869$		0			0
$870$	6.54651			0.221947
$871$	−22.2113	+	68.3593i	−0.752601	+	2.31627i
$872$	6.53577	−	4.74851i	0.221329	−	0.160805i
$873$	−3.27766	−	2.38136i	−0.110932	−	0.0805968i
$874$	−1.81816	−	5.59573i	−0.0615003	−	0.189278i
$875$	−3.76118	−	11.5757i	−0.127151	−	0.391331i
$876$	0.147003	+	0.106804i	0.00496676	+	0.00360856i
$877$	15.0420	−	10.9287i	0.507934	−	0.369035i	−0.304106	−	0.952638i	$-0.598358\pi$
$877$	15.0420	−	10.9287i	0.507934	−	0.369035i	0.812039	+	0.583603i	$0.198358\pi$
$878$	−11.6572	+	35.8772i	−0.393412	+	1.21080i
$879$	−51.9867			−1.75347
$880$		0			0
$881$	6.45292			0.217404			0.108702	−	0.994074i	$-0.465330\pi$
$881$	6.45292			0.217404			0.108702	+	0.994074i	$0.465330\pi$
$882$	0.731714	−	2.25198i	0.0246381	−	0.0758283i
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	−0.583988	−	0.811762i	$-0.698508\pi$
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	0.591570	+	0.806254i	$0.298508\pi$
$884$	0.287188	+	0.208654i	0.00965917	+	0.00701779i
$885$	−9.40377	−	28.9418i	−0.316104	−	0.972869i
$886$	11.4165	+	35.1362i	0.383543	+	1.18042i
$887$	24.7211	+	17.9609i	0.830054	+	0.603069i	0.919575	−	0.392916i	$-0.128534\pi$
$887$	24.7211	+	17.9609i	0.830054	+	0.603069i	−0.0895209	+	0.995985i	$0.528534\pi$
$888$	−10.4056	+	7.56009i	−0.349188	+	0.253700i
$889$	1.55524	−	4.78655i	0.0521612	−	0.160536i
$890$	−39.6008			−1.32742
$891$		0			0
$892$	0.0678176			0.00227070
$893$	10.7127	−	32.9702i	0.358485	−	1.10330i
$894$	7.92816	−	5.76014i	0.265157	−	0.192648i
$895$	−12.3320	−	8.95972i	−0.412213	−	0.299491i
$896$	−3.45907	−	10.6459i	−0.115559	−	0.355655i
$897$	2.23581	+	6.88111i	0.0746514	+	0.229753i
$898$	−11.1132	−	8.07423i	−0.370853	−	0.269441i
$899$	1.24058	−	0.901332i	0.0413756	−	0.0300611i
$900$	0.0119347	−	0.0367311i	0.000397822	−	0.00122437i
$901$	55.4949			1.84880
$902$		0			0
$903$	−17.3585			−0.577655
$904$	−12.7564	+	39.2601i	−0.424271	+	1.30577i
$905$	−21.9324	+	15.9348i	−0.729058	+	0.529692i
$906$	−54.9220	−	39.9031i	−1.82466	−	1.32569i
$907$	9.86836	+	30.3717i	0.327674	+	1.00848i	0.970219	+	0.242228i	$0.0778782\pi$
$907$	9.86836	+	30.3717i	0.327674	+	1.00848i	−0.642546	+	0.766247i	$0.722122\pi$
$908$	0.00171378	+	0.00527448i	5.68739e−5	+	0.000175040i
$909$	16.1704	+	11.7484i	0.536337	+	0.389671i
$910$	−9.70307	+	7.04969i	−0.321654	+	0.233695i
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	−0.935697	−	0.352805i	$-0.885228\pi$
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	0.964368	+	0.264564i	$0.0852280\pi$
$912$	49.8477			1.65062
$913$		0			0
$914$	−16.7496			−0.554027
$915$	7.68399	−	23.6489i	0.254025	−	0.781808i
$916$	0.0247374	−	0.0179728i	0.000817348	−	0.000593838i
$917$	0.145666	+	0.105832i	0.00481031	+	0.00349490i
$918$	6.80167	+	20.9334i	0.224488	+	0.690904i
$919$	4.89293	+	15.0589i	0.161403	+	0.496747i	0.998753	−	0.0499194i	$-0.0158965\pi$
$919$	4.89293	+	15.0589i	0.161403	+	0.496747i	−0.837350	+	0.546667i	$0.815896\pi$
$920$	3.02638	+	2.19880i	0.0997769	+	0.0724922i
$921$	9.56137	−	6.94674i	0.315058	−	0.228903i
$922$	−3.98356	+	12.2602i	−0.131192	+	0.403767i
$923$	64.6030			2.12643
$924$		0			0
$925$	−3.44799			−0.113369
$926$	16.9554	−	52.1833i	0.557188	−	1.71485i
$927$	−0.538719	+	0.391402i	−0.0176939	+	0.0128553i
$928$	−0.0749296	−	0.0544396i	−0.00245969	−	0.00178707i
$929$	−8.49282	−	26.1382i	−0.278640	−	0.857567i	−0.988233	−	0.152955i	$-0.951121\pi$
$929$	−8.49282	−	26.1382i	−0.278640	−	0.857567i	0.709593	−	0.704612i	$-0.248879\pi$
$930$	−2.25659	−	6.94506i	−0.0739964	−	0.227737i
$931$	−4.69325	−	3.40985i	−0.153815	−	0.111753i
$932$	0.0142366	−	0.0103435i	0.000466337	−	0.000338814i
$933$	−9.28472	+	28.5754i	−0.303968	+	0.935517i
$934$	−29.2894			−0.958379
$935$		0			0
$936$	−22.1610			−0.724354
$937$	3.80357	−	11.7062i	0.124257	−	0.382425i	−0.869508	−	0.493919i	$-0.835564\pi$
$937$	3.80357	−	11.7062i	0.124257	−	0.382425i	0.993765	+	0.111495i	$0.0355638\pi$
$938$	−17.6346	+	12.8123i	−0.575789	+	0.418335i
$939$	48.0408	+	34.9037i	1.56775	+	1.13904i
$940$	0.0472266	+	0.145349i	0.00154036	+	0.00474075i
$941$	−0.451208	−	1.38867i	−0.0147089	−	0.0452695i	0.943433	−	0.331564i	$-0.107576\pi$
$941$	−0.451208	−	1.38867i	−0.0147089	−	0.0452695i	−0.958142	+	0.286295i	$0.907576\pi$
$942$	32.6931	+	23.7530i	1.06520	+	0.773913i
$943$	0.533703	−	0.387758i	0.0173798	−	0.0126271i
$944$	9.42725	−	29.0141i	0.306831	−	0.944328i
$945$	5.22896			0.170098
$946$		0			0
$947$	11.0714			0.359771			0.179885	−	0.983688i	$-0.442427\pi$
$947$	11.0714			0.359771			0.179885	+	0.983688i	$0.442427\pi$
$948$	0.146017	−	0.449395i	0.00474242	−	0.0145957i
$949$	22.6123	−	16.4288i	0.734025	−	0.533301i
$950$	10.8869	+	7.90978i	0.353217	+	0.256627i
$951$	−5.23165	−	16.1014i	−0.169648	−	0.522123i
$952$	4.79769	+	14.7658i	0.155494	+	0.478561i
$953$	−11.9924	−	8.71296i	−0.388471	−	0.282240i	0.376358	−	0.926474i	$-0.377176\pi$
$953$	−11.9924	−	8.71296i	−0.388471	−	0.282240i	−0.764828	+	0.644234i	$0.777176\pi$
$954$	−19.4342	+	14.1197i	−0.629204	+	0.457144i
$955$	5.43675	−	16.7326i	0.175929	−	0.541454i
$956$	−0.155867			−0.00504110
$957$		0			0
$958$	34.5782			1.11717
$959$	−2.57224	+	7.91655i	−0.0830621	+	0.255639i
$960$	−25.8191	+	18.7586i	−0.833306	+	0.605432i
$961$	23.6957	+	17.2159i	0.764377	+	0.555353i
$962$	4.23920	+	13.0469i	0.136677	+	0.420649i
$963$	1.69750	+	5.22437i	0.0547012	+	0.168353i
$964$	0.242719	+	0.176346i	0.00781746	+	0.00567972i
$965$	2.20437	−	1.60157i	0.0709612	−	0.0515563i
$966$	−0.678031	+	2.08677i	−0.0218153	+	0.0671406i
$967$	−16.5193			−0.531224			−0.265612	−	0.964080i	$-0.585574\pi$
$967$	−16.5193			−0.531224			−0.265612	+	0.964080i	$0.585574\pi$
$968$		0			0
$969$	−68.6520			−2.20542
$970$	−1.92308	+	5.91862i	−0.0617462	+	0.190035i
$971$	−33.0073	+	23.9812i	−1.05926	+	0.769595i	−0.973951	−	0.226760i	$-0.927187\pi$
$971$	−33.0073	+	23.9812i	−1.05926	+	0.769595i	−0.0853055	+	0.996355i	$0.527187\pi$
$972$	0.177396	+	0.128886i	0.00568998	+	0.00413401i
$973$	−2.15113	−	6.62049i	−0.0689620	−	0.212243i
$974$	−5.38755	−	16.5812i	−0.172628	−	0.531296i
$975$	−13.3877	−	9.72671i	−0.428748	−	0.311504i
$976$	20.1672	−	14.6523i	0.645535	−	0.469009i
$977$	15.1772	−	46.7107i	0.485562	−	1.49441i	−0.345603	−	0.938381i	$-0.612326\pi$
$977$	15.1772	−	46.7107i	0.485562	−	1.49441i	0.831165	−	0.556025i	$-0.187674\pi$
$978$	−41.8243			−1.33739
$979$		0			0
$980$	0.0255744			0.000816945
$981$	1.47789	−	4.54847i	0.0471853	−	0.145222i
$982$	18.8406	−	13.6885i	0.601228	−	0.436817i
$983$	−0.895411	−	0.650554i	−0.0285592	−	0.0207495i	0.573414	−	0.819266i	$-0.305619\pi$
$983$	−0.895411	−	0.650554i	−0.0285592	−	0.0207495i	−0.601973	+	0.798516i	$0.705619\pi$
$984$	1.73925	+	5.35286i	0.0554453	+	0.170643i
$985$	−7.94756	−	24.4601i	−0.253230	−	0.779362i
$986$	−7.31238	−	5.31275i	−0.232874	−	0.169193i
$987$	−10.4590	+	7.59889i	−0.332913	+	0.241875i
$988$	−0.116333	+	0.358036i	−0.00370104	+	0.0113906i
$989$	5.77458			0.183621
$990$		0			0
$991$	41.7851			1.32735			0.663674	−	0.748022i	$-0.268996\pi$
$991$	41.7851			1.32735			0.663674	+	0.748022i	$0.268996\pi$
$992$	−0.0319255	+	0.0982567i	−0.00101364	+	0.00311965i
$993$	−49.2618	+	35.7908i	−1.56328	+	1.13579i
$994$	15.8499	+	11.5156i	0.502727	+	0.365253i
$995$	2.42630	+	7.46739i	0.0769189	+	0.236732i
$996$	0.0408500	+	0.125723i	0.00129438	+	0.00398369i
$997$	35.7541	+	25.9769i	1.13234	+	0.822695i	0.986034	−	0.166543i	$-0.0532606\pi$
$997$	35.7541	+	25.9769i	1.13234	+	0.822695i	0.146309	+	0.989239i	$0.453261\pi$
$998$	15.6664	−	11.3823i	0.495910	−	0.360300i
$999$	1.84819	−	5.68816i	0.0584743	−	0.179965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.x.372.3		16
11.2	odd	10		847.2.f.w.729.3		16
11.3	even	5		847.2.f.v.323.2		16
11.4	even	5		847.2.a.o.1.6		8
11.5	even	5	inner	847.2.f.x.148.3		16
11.6	odd	10		77.2.f.b.71.2	yes	16
11.7	odd	10		847.2.a.p.1.3		8
11.8	odd	10		847.2.f.w.323.3		16
11.9	even	5		847.2.f.v.729.2		16
11.10	odd	2		77.2.f.b.64.2	✓	16
33.17	even	10		693.2.m.i.379.3		16
33.26	odd	10		7623.2.a.cw.1.3		8
33.29	even	10		7623.2.a.ct.1.6		8
33.32	even	2		693.2.m.i.64.3		16
77.6	even	10		539.2.f.e.148.2		16
77.10	even	6		539.2.q.f.471.2		32
77.17	even	30		539.2.q.f.324.3		32
77.32	odd	6		539.2.q.g.471.2		32
77.39	odd	30		539.2.q.g.324.3		32
77.48	odd	10		5929.2.a.bs.1.6		8
77.54	even	6		539.2.q.f.361.3		32
77.61	even	30		539.2.q.f.214.2		32
77.62	even	10		5929.2.a.bt.1.3		8
77.65	odd	6		539.2.q.g.361.3		32
77.72	odd	30		539.2.q.g.214.2		32
77.76	even	2		539.2.f.e.295.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	11.10	odd	2
77.2.f.b.71.2	yes	16	11.6	odd	10
539.2.f.e.148.2		16	77.6	even	10
539.2.f.e.295.2		16	77.76	even	2
539.2.q.f.214.2		32	77.61	even	30
539.2.q.f.324.3		32	77.17	even	30
539.2.q.f.361.3		32	77.54	even	6
539.2.q.f.471.2		32	77.10	even	6
539.2.q.g.214.2		32	77.72	odd	30
539.2.q.g.324.3		32	77.39	odd	30
539.2.q.g.361.3		32	77.65	odd	6
539.2.q.g.471.2		32	77.32	odd	6
693.2.m.i.64.3		16	33.32	even	2
693.2.m.i.379.3		16	33.17	even	10
847.2.a.o.1.6		8	11.4	even	5
847.2.a.p.1.3		8	11.7	odd	10
847.2.f.v.323.2		16	11.3	even	5
847.2.f.v.729.2		16	11.9	even	5
847.2.f.w.323.3		16	11.8	odd	10
847.2.f.w.729.3		16	11.2	odd	10
847.2.f.x.148.3		16	11.5	even	5	inner
847.2.f.x.372.3		16	1.1	even	1	trivial
5929.2.a.bs.1.6		8	77.48	odd	10
5929.2.a.bt.1.3		8	77.62	even	10
7623.2.a.ct.1.6		8	33.29	even	10
7623.2.a.cw.1.3		8	33.26	odd	10

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.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.435488 - 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +O(q^{10})\)	\(q+(0.435488 - 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} -2.58091 q^{10} +0.0302106 q^{12} +(1.43602 - 4.41961i) q^{13} +(1.14012 - 0.828347i) q^{14} +(-3.20531 - 2.32880i) q^{15} +(-1.22738 - 3.77748i) q^{16} +(1.69039 + 5.20248i) q^{17} +(-1.91565 - 1.39180i) q^{18} +(-4.69325 + 3.40985i) q^{19} +(0.00790293 - 0.0243227i) q^{20} +2.16338 q^{21} -0.719682 q^{23} +(1.89741 - 5.83962i) q^{24} +(1.33166 - 0.967509i) q^{25} +(-5.29821 - 3.84937i) q^{26} +(0.882303 + 2.71545i) q^{27} +(0.00431527 + 0.0132810i) q^{28} +(-0.948551 - 0.689163i) q^{29} +(-4.51715 + 3.28190i) q^{30} +(-0.404153 + 1.24385i) q^{31} +0.0789938 q^{32} +7.70900 q^{34} +(0.565930 - 1.74175i) q^{35} +(0.0189823 - 0.0137915i) q^{36} +(-1.69468 - 1.23126i) q^{37} +(2.52634 + 7.77528i) q^{38} +(-3.10666 - 9.56131i) q^{39} +(-4.20516 - 3.05523i) q^{40} +(-0.741582 + 0.538791i) q^{41} +(0.942126 - 2.89957i) q^{42} -8.02379 q^{43} -3.07713 q^{45} +(-0.313413 + 0.964586i) q^{46} +(-4.83455 + 3.51251i) q^{47} +(-6.95163 - 5.05065i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.716823 - 2.20615i) q^{50} +(9.57403 + 6.95594i) q^{51} +(0.0525003 - 0.0381437i) q^{52} +(3.13496 - 9.64840i) q^{53} +4.02373 q^{54} +2.83822 q^{56} +(-3.87821 + 11.9359i) q^{57} +(-1.33676 + 0.971215i) q^{58} +(6.21390 + 4.51466i) q^{59} +(-0.0170971 - 0.0526193i) q^{60} +(1.93943 + 5.96895i) q^{61} +(1.49113 + 1.08337i) q^{62} +(1.35932 - 0.987607i) q^{63} +(2.48916 - 7.66083i) q^{64} -8.51056 q^{65} -15.4673 q^{67} +(-0.0236055 + 0.0726501i) q^{68} +(-1.25960 + 0.915151i) q^{69} +(-2.08800 - 1.51702i) q^{70} +(4.29593 + 13.2215i) q^{71} +(-1.47365 - 4.53542i) q^{72} +(4.86593 + 3.53531i) q^{73} +(-2.38826 + 1.73517i) q^{74} +(1.10040 - 3.38669i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(4.83332 - 14.8754i) q^{79} +(-5.88482 + 4.27557i) q^{80} +(9.07517 + 6.59349i) q^{81} +(0.399188 + 1.22857i) q^{82} +(1.35217 + 4.16157i) q^{83} +(0.0244409 + 0.0177573i) q^{84} +(8.10479 - 5.88848i) q^{85} +(-3.49426 + 10.7542i) q^{86} -2.53651 q^{87} +15.3437 q^{89} +(-1.34005 + 4.12425i) q^{90} +(3.75955 - 2.73147i) q^{91} +(-0.00813063 - 0.00590725i) q^{92} +(0.874336 + 2.69093i) q^{93} +(2.60240 + 8.00937i) q^{94} +(8.59515 + 6.24474i) q^{95} +(0.138256 - 0.100449i) q^{96} +(0.745114 - 2.29323i) q^{97} +1.40927 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

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