LMFDB - Embedded newform 845.2.o.g.357.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(258,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("845.258");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
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} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.2
Root			$-1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.357
Dual form			845.2.o.g.258.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.511309 + 0.885613i) q^{2} +(-0.721300 - 2.69193i) q^{3} +(0.477126 + 0.826407i) q^{4} +(1.69584 - 1.45744i) q^{5} +(2.75281 + 0.737614i) q^{6} +(-0.834479 + 0.481787i) q^{7} -3.02107 q^{8} +(-4.12812 + 2.38337i) q^{9} +(0.423625 + 2.24706i) q^{10} +(-1.60661 + 0.430490i) q^{11} +(1.88048 - 1.88048i) q^{12} -0.985368i q^{14} +(-5.14652 - 3.51384i) q^{15} +(0.590448 - 1.02269i) q^{16} +(-7.00342 - 1.87656i) q^{17} -4.87456i q^{18} +(0.707496 - 2.64041i) q^{19} +(2.01357 + 0.706075i) q^{20} +(1.89884 + 1.89884i) q^{21} +(0.440226 - 1.64295i) q^{22} +(-3.72214 + 0.997344i) q^{23} +(2.17910 + 8.13250i) q^{24} +(0.751762 - 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +(-0.796304 - 0.459747i) q^{28} +(0.253107 + 0.146132i) q^{29} +(5.74336 - 2.76117i) q^{30} +(0.125649 - 0.125649i) q^{31} +(-2.41727 - 4.18683i) q^{32} +(2.31769 + 4.01436i) q^{33} +(5.24282 - 5.24282i) q^{34} +(-0.712972 + 2.03323i) q^{35} +(-3.93927 - 2.27434i) q^{36} +(-3.53443 - 2.04061i) q^{37} +(1.97663 + 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(1.79277 + 6.69071i) q^{41} +(-2.65254 + 0.710745i) q^{42} +(2.05706 - 7.67707i) q^{43} +(-1.12232 - 1.12232i) q^{44} +(-3.52703 + 10.0583i) q^{45} +(1.01990 - 3.80633i) q^{46} +7.84582i q^{47} +(-3.17888 - 0.851780i) q^{48} +(-3.03576 + 5.25810i) q^{49} +(3.99335 + 3.19325i) q^{50} +20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(-4.86351 + 1.30317i) q^{54} +(-2.09714 + 3.07157i) q^{55} +(2.52102 - 1.45551i) q^{56} -7.61811 q^{57} +(-0.258832 + 0.149437i) q^{58} +(-4.87924 - 1.30739i) q^{59} +(0.448318 - 5.92967i) q^{60} +(-1.04169 - 1.80425i) q^{61} +(0.0470311 + 0.175522i) q^{62} +(2.29655 - 3.97775i) q^{63} +7.30568 q^{64} -4.74023 q^{66} +(3.64915 - 6.32050i) q^{67} +(-1.79071 - 6.68304i) q^{68} +(5.36956 + 9.30034i) q^{69} +(-1.43611 - 1.67103i) q^{70} +(-12.6082 - 3.37837i) q^{71} +(12.4713 - 7.20034i) q^{72} -3.22747 q^{73} +(3.61437 - 2.08676i) q^{74} +(-13.8489 + 1.54181i) q^{75} +(2.51962 - 0.675130i) q^{76} +(1.13328 - 1.13328i) q^{77} -13.5845i q^{79} +(-0.489192 - 2.59485i) q^{80} +(-0.289196 + 0.500902i) q^{81} +(-6.84204 - 1.83332i) q^{82} -8.56854i q^{83} +(-0.663230 + 2.47521i) q^{84} +(-14.6117 + 7.02469i) q^{85} +(5.74712 + 5.74712i) q^{86} +(0.210809 - 0.786751i) q^{87} +(4.85368 - 1.30054i) q^{88} +(-0.134207 - 0.500868i) q^{89} +(-7.10435 - 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +(-0.428870 - 0.247608i) q^{93} +(-6.94836 - 4.01164i) q^{94} +(-2.64843 - 5.50885i) q^{95} +(-9.52707 + 9.52707i) q^{96} +(3.75660 + 6.50662i) q^{97} +(-3.10442 - 5.37702i) q^{98} +(5.60626 - 5.60626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.511309	+	0.885613i	−0.361550	+	0.626223i	−0.988216	−	0.153065i	$-0.951086\pi$
$2$	−0.511309	+	0.885613i	−0.361550	+	0.626223i	0.626666	+	0.779288i	$0.284419\pi$
$3$	−0.721300	−	2.69193i	−0.416443	−	1.55418i	−0.781929	−	0.623368i	$-0.785764\pi$
$3$	−0.721300	−	2.69193i	−0.416443	−	1.55418i	0.365486	−	0.930817i	$-0.380903\pi$
$4$	0.477126	+	0.826407i	0.238563	+	0.413204i
$5$	1.69584	−	1.45744i	0.758404	−	0.651785i
$5$	1.69584	−	1.45744i	0.758404	−	0.651785i
$6$	2.75281	+	0.737614i	1.12383	+	0.301130i
$7$	−0.834479	+	0.481787i	−0.315404	+	0.182098i	−0.649342	−	0.760497i	$-0.724956\pi$
$7$	−0.834479	+	0.481787i	−0.315404	+	0.182098i	0.333938	+	0.942595i	$0.391622\pi$
$8$	−3.02107			−1.06811
$9$	−4.12812	+	2.38337i	−1.37604	+	0.794457i
$10$	0.423625	+	2.24706i	0.133962	+	0.710583i
$11$	−1.60661	+	0.430490i	−0.484411	+	0.129797i	−0.492756	−	0.870168i	$-0.664010\pi$
$11$	−1.60661	+	0.430490i	−0.484411	+	0.129797i	0.00834492	+	0.999965i	$0.497344\pi$
$12$	1.88048	−	1.88048i	0.542847	−	0.542847i
$13$		0			0
$13$		0			0
$14$		−	0.985368i		−	0.263351i
$15$	−5.14652	−	3.51384i	−1.32883	−	0.907268i
$16$	0.590448	−	1.02269i	0.147612	−	0.255671i
$17$	−7.00342	−	1.87656i	−1.69858	−	0.455133i	−0.725998	−	0.687697i	$-0.758622\pi$
$17$	−7.00342	−	1.87656i	−1.69858	−	0.455133i	−0.972581	+	0.232564i	$0.925289\pi$
$18$		−	4.87456i		−	1.14894i
$19$	0.707496	−	2.64041i	0.162311	−	0.605752i	−0.836057	−	0.548642i	$-0.815145\pi$
$19$	0.707496	−	2.64041i	0.162311	−	0.605752i	0.998368	−	0.0571095i	$-0.0181884\pi$
$20$	2.01357	+	0.706075i	0.450247	+	0.157883i
$21$	1.89884	+	1.89884i	0.414362	+	0.414362i
$22$	0.440226	−	1.64295i	0.0938565	−	0.350277i
$23$	−3.72214	+	0.997344i	−0.776120	+	0.207961i	−0.625073	−	0.780566i	$-0.714931\pi$
$23$	−3.72214	+	0.997344i	−0.776120	+	0.207961i	−0.151046	+	0.988527i	$0.548264\pi$
$24$	2.17910	+	8.13250i	0.444806	+	1.66004i
$25$	0.751762	−	4.94316i	0.150352	−	0.988632i
$26$		0			0
$27$	3.48159	+	3.48159i	0.670033	+	0.670033i
$28$	−0.796304	−	0.459747i	−0.150487	−	0.0868839i
$29$	0.253107	+	0.146132i	0.0470008	+	0.0271360i	0.523316	−	0.852139i	$-0.324695\pi$
$29$	0.253107	+	0.146132i	0.0470008	+	0.0271360i	−0.476315	+	0.879274i	$0.658028\pi$
$30$	5.74336	−	2.76117i	1.04859	−	0.504118i
$31$	0.125649	−	0.125649i	0.0225673	−	0.0225673i	−0.695733	−	0.718300i	$-0.744920\pi$
$31$	0.125649	−	0.125649i	0.0225673	−	0.0225673i	0.718300	+	0.695733i	$0.244920\pi$
$32$	−2.41727	−	4.18683i	−0.427317	−	0.740134i
$33$	2.31769	+	4.01436i	0.403458	+	0.698811i
$34$	5.24282	−	5.24282i	0.899136	−	0.899136i
$35$	−0.712972	+	2.03323i	−0.120514	+	0.343679i
$36$	−3.93927	−	2.27434i	−0.656545	−	0.379057i
$37$	−3.53443	−	2.04061i	−0.581057	−	0.335474i	0.180496	−	0.983576i	$-0.442230\pi$
$37$	−3.53443	−	2.04061i	−0.581057	−	0.335474i	−0.761553	+	0.648102i	$0.775563\pi$
$38$	1.97663	+	1.97663i	0.320652	+	0.320652i
$39$		0			0
$40$	−5.12326	+	4.40302i	−0.810059	+	0.696178i
$41$	1.79277	+	6.69071i	0.279984	+	1.04491i	0.952427	+	0.304765i	$0.0985780\pi$
$41$	1.79277	+	6.69071i	0.279984	+	1.04491i	−0.672444	+	0.740148i	$0.734755\pi$
$42$	−2.65254	+	0.710745i	−0.409295	+	0.109670i
$43$	2.05706	−	7.67707i	0.313699	−	1.17074i	−0.611495	−	0.791248i	$-0.709432\pi$
$43$	2.05706	−	7.67707i	0.313699	−	1.17074i	0.925194	−	0.379494i	$-0.123902\pi$
$44$	−1.12232	−	1.12232i	−0.169195	−	0.169195i
$45$	−3.52703	+	10.0583i	−0.525779	+	1.49940i
$46$	1.01990	−	3.80633i	0.150376	−	0.561212i
$47$			7.84582i			1.14443i	0.820103	+	0.572215i	$0.193916\pi$
$47$			7.84582i			1.14443i	−0.820103	+	0.572215i	$0.806084\pi$
$48$	−3.17888	−	0.851780i	−0.458832	−	0.122944i
$49$	−3.03576	+	5.25810i	−0.433680	+	0.751156i
$50$	3.99335	+	3.19325i	0.564744	+	0.451594i
$51$			20.2063i			2.82944i
$52$		0			0
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	−0.830918	−	0.556395i	$-0.812184\pi$
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	0.556395	+	0.830918i	$0.312184\pi$
$54$	−4.86351	+	1.30317i	−0.661840	+	0.177339i
$55$	−2.09714	+	3.07157i	−0.282779	+	0.414171i
$56$	2.52102	−	1.45551i	0.336886	−	0.194501i
$57$	−7.61811			−1.00904
$58$	−0.258832	+	0.149437i	−0.0339863	+	0.0196220i
$59$	−4.87924	−	1.30739i	−0.635223	−	0.170207i	−0.0731843	−	0.997318i	$-0.523316\pi$
$59$	−4.87924	−	1.30739i	−0.635223	−	0.170207i	−0.562039	+	0.827111i	$0.689983\pi$
$60$	0.448318	−	5.92967i	0.0578776	−	0.765517i
$61$	−1.04169	−	1.80425i	−0.133374	−	0.231011i	0.791601	−	0.611038i	$-0.209248\pi$
$61$	−1.04169	−	1.80425i	−0.133374	−	0.231011i	−0.924975	+	0.380027i	$0.875915\pi$
$62$	0.0470311	+	0.175522i	0.00597296	+	0.0222914i
$63$	2.29655	−	3.97775i	0.289339	−	0.501149i
$64$	7.30568			0.913209
$65$		0			0
$66$	−4.74023			−0.583482
$67$	3.64915	−	6.32050i	0.445814	−	0.772173i	−0.552294	−	0.833649i	$-0.686248\pi$
$67$	3.64915	−	6.32050i	0.445814	−	0.772173i	0.998109	+	0.0614765i	$0.0195809\pi$
$68$	−1.79071	−	6.68304i	−0.217156	−	0.810437i
$69$	5.36956	+	9.30034i	0.646419	+	1.11963i
$70$	−1.43611	−	1.67103i	−0.171648	−	0.199726i
$71$	−12.6082	−	3.37837i	−1.49632	−	0.400939i	−0.584457	−	0.811425i	$-0.698692\pi$
$71$	−12.6082	−	3.37837i	−1.49632	−	0.400939i	−0.911867	+	0.410486i	$0.865359\pi$
$72$	12.4713	−	7.20034i	1.46976	−	0.848568i
$73$	−3.22747			−0.377746			−0.188873	−	0.982001i	$-0.560483\pi$
$73$	−3.22747			−0.377746			−0.188873	+	0.982001i	$0.560483\pi$
$74$	3.61437	−	2.08676i	0.420163	−	0.242581i
$75$	−13.8489	+	1.54181i	−1.59913	+	0.178033i
$76$	2.51962	−	0.675130i	0.289020	−	0.0774427i
$77$	1.13328	−	1.13328i	0.129149	−	0.129149i
$78$		0			0
$79$		−	13.5845i		−	1.52838i	−0.644992	−	0.764190i	$-0.723139\pi$
$79$		−	13.5845i		−	1.52838i	0.644992	−	0.764190i	$-0.276861\pi$
$80$	−0.489192	−	2.59485i	−0.0546934	−	0.290113i
$81$	−0.289196	+	0.500902i	−0.0321329	+	0.0556558i
$82$	−6.84204	−	1.83332i	−0.755577	−	0.202456i
$83$		−	8.56854i		−	0.940519i	−0.882528	−	0.470260i	$-0.844160\pi$
$83$		−	8.56854i		−	0.940519i	0.882528	−	0.470260i	$-0.155840\pi$
$84$	−0.663230	+	2.47521i	−0.0723643	+	0.270067i
$85$	−14.6117	+	7.02469i	−1.58486	+	0.761934i
$86$	5.74712	+	5.74712i	0.619728	+	0.619728i
$87$	0.210809	−	0.786751i	0.0226011	−	0.0843486i
$88$	4.85368	−	1.30054i	0.517404	−	0.138638i
$89$	−0.134207	−	0.500868i	−0.0142259	−	0.0530919i	0.958448	−	0.285267i	$-0.0920823\pi$
$89$	−0.134207	−	0.500868i	−0.0142259	−	0.0530919i	−0.972674	+	0.232175i	$0.925416\pi$
$90$	−7.10435	−	8.26648i	−0.748864	−	0.871363i
$91$		0			0
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$	−0.428870	−	0.247608i	−0.0444718	−	0.0256758i
$94$	−6.94836	−	4.01164i	−0.716669	−	0.413769i
$95$	−2.64843	−	5.50885i	−0.271723	−	0.565196i
$96$	−9.52707	+	9.52707i	−0.972353	+	0.972353i
$97$	3.75660	+	6.50662i	0.381425	+	0.660648i	0.991266	−	0.131876i	$-0.0421001\pi$
$97$	3.75660	+	6.50662i	0.381425	+	0.660648i	−0.609841	+	0.792524i	$0.708767\pi$
$98$	−3.10442	−	5.37702i	−0.313594	−	0.543161i
$99$	5.60626	−	5.60626i	0.563450	−	0.563450i
$100$	4.44375	−	1.73725i	0.444375	−	0.173725i
$101$	8.44685	+	4.87679i	0.840493	+	0.485259i	0.857432	−	0.514598i	$-0.172059\pi$
$101$	8.44685	+	4.87679i	0.840493	+	0.485259i	−0.0169388	+	0.999857i	$0.505392\pi$
$102$	−17.8949	−	10.3316i	−1.77186	−	1.02298i
$103$	−2.52321	−	2.52321i	−0.248619	−	0.248619i	0.571784	−	0.820404i	$-0.306251\pi$
$103$	−2.52321	−	2.52321i	−0.248619	−	0.248619i	−0.820404	+	0.571784i	$0.806251\pi$
$104$		0			0
$105$	5.98759	+	0.452697i	0.584329	+	0.0441787i
$106$	−0.748066	−	2.79182i	−0.0726586	−	0.271166i
$107$	0.429359	−	0.115046i	0.0415077	−	0.0111220i	−0.238005	−	0.971264i	$-0.576494\pi$
$107$	0.429359	−	0.115046i	0.0415077	−	0.0111220i	0.279513	+	0.960142i	$0.409827\pi$
$108$	−1.21605	+	4.53837i	−0.117015	+	0.436705i
$109$	6.42134	+	6.42134i	0.615053	+	0.615053i	0.944258	−	0.329206i	$-0.106781\pi$
$109$	6.42134	+	6.42134i	0.615053	+	0.615053i	−0.329206	+	0.944258i	$0.606781\pi$
$110$	−1.64793	−	3.42778i	−0.157124	−	0.326826i
$111$	−2.94378	+	10.9863i	−0.279411	+	1.04278i
$112$			1.13788i			0.107520i
$113$	−1.86865	−	0.500704i	−0.175788	−	0.0471023i	0.169851	−	0.985470i	$-0.445671\pi$
$113$	−1.86865	−	0.500704i	−0.175788	−	0.0471023i	−0.345639	+	0.938367i	$0.612338\pi$
$114$	3.89521	−	6.74670i	0.364820	−	0.631886i
$115$	−4.85860	+	7.11612i	−0.453066	+	0.663581i
$116$			0.278893i			0.0258946i
$117$		0			0
$118$	3.65264	−	3.65264i	0.336253	−	0.336253i
$119$	6.74831	−	1.80821i	0.618617	−	0.165758i
$120$	15.5480	+	10.6155i	1.41933	+	0.969062i
$121$	−7.13041	+	4.11674i	−0.648219	+	0.374249i
$122$	2.13050			0.192886
$123$	16.7178	−	9.65202i	1.50739	−	0.870293i
$124$	0.163788	+	0.0438869i	0.0147086	+	0.00394116i
$125$	−5.92947	−	9.47847i	−0.530348	−	0.847780i
$126$	2.34850	+	4.06772i	0.209221	+	0.362381i
$127$	−0.562967	−	2.10102i	−0.0499553	−	0.186436i	0.936440	−	0.350829i	$-0.114100\pi$
$127$	−0.562967	−	2.10102i	−0.0499553	−	0.186436i	−0.986395	+	0.164393i	$0.947433\pi$
$128$	1.09908	−	1.90366i	0.0971460	−	0.168262i
$129$	−22.1499			−1.95019
$130$		0			0
$131$	−0.0622493			−0.00543874			−0.00271937	−	0.999996i	$-0.500866\pi$
$131$	−0.0622493			−0.00543874			−0.00271937	+	0.999996i	$0.500866\pi$
$132$	−2.21166	+	3.83072i	−0.192501	+	0.333421i
$133$	0.681725	+	2.54423i	0.0591130	+	0.220613i
$134$	3.73168	+	6.46346i	0.322368	+	0.558358i
$135$	10.9784	+	0.830034i	0.944872	+	0.0714380i
$136$	21.1578	+	5.66923i	1.81427	+	0.486132i
$137$	3.82564	−	2.20873i	0.326846	−	0.188705i	−0.327594	−	0.944819i	$-0.606238\pi$
$137$	3.82564	−	2.20873i	0.326846	−	0.188705i	0.654440	+	0.756114i	$0.272904\pi$
$138$	−10.9820			−0.934850
$139$	11.9066	−	6.87430i	1.00991	−	0.583070i	0.0987430	−	0.995113i	$-0.468518\pi$
$139$	11.9066	−	6.87430i	1.00991	−	0.583070i	0.911165	+	0.412043i	$0.135184\pi$
$140$	−2.02046	+	0.380905i	−0.170760	+	0.0321923i
$141$	21.1204	−	5.65919i	1.77866	−	0.476590i
$142$	9.43864	−	9.43864i	0.792073	−	0.792073i
$143$		0			0
$144$			5.62903i			0.469085i
$145$	0.642207	−	0.121072i	0.0533324	−	0.0100544i
$146$	1.65023	−	2.85829i	0.136574	−	0.236553i
$147$	16.3441	+	4.37939i	1.34804	+	0.361206i
$148$		−	3.89451i		−	0.320127i
$149$	1.12129	−	4.18471i	0.0918596	−	0.342825i	−0.904665	−	0.426124i	$-0.859879\pi$
$149$	1.12129	−	4.18471i	0.0918596	−	0.342825i	0.996525	+	0.0832987i	$0.0265456\pi$
$150$	5.71560	−	13.0531i	0.466677	−	1.06578i
$151$	−4.74990	−	4.74990i	−0.386542	−	0.386542i	0.486910	−	0.873452i	$-0.338124\pi$
$151$	−4.74990	−	4.74990i	−0.386542	−	0.386542i	−0.873452	+	0.486910i	$0.838124\pi$
$152$	−2.13740	+	7.97687i	−0.173366	+	0.647010i
$153$	33.3835	−	8.94508i	2.69890	−	0.723167i
$154$	0.424190	+	1.58310i	0.0341822	+	0.127570i
$155$	0.0299556	−	0.396208i	0.00240610	−	0.0318242i
$156$		0			0
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.985920	+	0.167218i	$0.0534784\pi$
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.167218	+	0.985920i	$0.446522\pi$
$158$	12.0306	+	6.94589i	0.957106	+	0.552586i
$159$	6.82151	+	3.93840i	0.540981	+	0.312336i
$160$	−10.2013	−	3.57719i	−0.806487	−	0.282802i
$161$	2.62554	−	2.62554i	0.206922	−	0.206922i
$162$	−0.295737	−	0.512231i	−0.0232353	−	0.0402447i
$163$	10.6926	+	18.5201i	0.837508	+	1.45061i	0.891972	+	0.452091i	$0.149322\pi$
$163$	10.6926	+	18.5201i	0.837508	+	1.45061i	−0.0544633	+	0.998516i	$0.517345\pi$
$164$	−4.67387	+	4.67387i	−0.364968	+	0.364968i
$165$	9.78111	+	3.42984i	0.761459	+	0.267012i
$166$	7.58841	+	4.38117i	0.588975	+	0.340045i
$167$	−1.48475	−	0.857220i	−0.114893	−	0.0663337i	0.441452	−	0.897285i	$-0.354464\pi$
$167$	−1.48475	−	0.857220i	−0.114893	−	0.0663337i	−0.556345	+	0.830951i	$0.687797\pi$
$168$	−5.73655	−	5.73655i	−0.442584	−	0.442584i
$169$		0			0
$170$	1.24992	−	16.5321i	0.0958646	−	1.26795i
$171$	3.37245	+	12.5862i	0.257898	+	0.962488i
$172$	7.32587	−	1.96296i	0.558592	−	0.149674i
$173$	−3.92804	+	14.6596i	−0.298643	+	1.11455i	0.639638	+	0.768677i	$0.279084\pi$
$173$	−3.92804	+	14.6596i	−0.298643	+	1.11455i	−0.938281	+	0.345875i	$0.887582\pi$
$174$	0.588968	+	0.588968i	0.0446496	+	0.0446496i
$175$	1.75422	+	4.48716i	0.132607	+	0.339197i
$176$	−0.508363	+	1.89724i	−0.0383193	+	0.143010i
$177$			14.0776i			1.05814i
$178$	0.512196	+	0.137243i	0.0383907	+	0.0102868i
$179$	1.37961	−	2.38956i	0.103117	−	0.178604i	−0.809850	−	0.586637i	$-0.800452\pi$
$179$	1.37961	−	2.38956i	0.103117	−	0.178604i	0.912967	+	0.408033i	$0.133785\pi$
$180$	−9.99508	+	1.88431i	−0.744990	+	0.140448i
$181$		−	10.3568i		−	0.769818i	−0.922954	−	0.384909i	$-0.874233\pi$
$181$		−	10.3568i		−	0.769818i	0.922954	−	0.384909i	$-0.125767\pi$
$182$		0			0
$183$	−4.10555	+	4.10555i	−0.303491	+	0.303491i
$184$	11.2449	−	3.01305i	0.828981	−	0.222125i
$185$	−8.96789	+	1.69066i	−0.659333	+	0.124300i
$186$	0.438570	−	0.253209i	0.0321575	−	0.0185662i
$187$	12.0596			0.881885
$188$	−6.48384	+	3.74345i	−0.472883	+	0.273019i
$189$	−4.58270	−	1.22793i	−0.333342	−	0.0893188i
$190$	6.23287	+	0.471242i	0.452180	+	0.0341875i
$191$	−9.28983	−	16.0905i	−0.672189	−	1.16427i	−0.977282	−	0.211943i	$-0.932021\pi$
$191$	−9.28983	−	16.0905i	−0.672189	−	1.16427i	0.305093	−	0.952322i	$-0.401312\pi$
$192$	−5.26958	−	19.6663i	−0.380299	−	1.41930i
$193$	6.28576	−	10.8872i	0.452459	−	0.783681i	−0.546079	−	0.837733i	$-0.683880\pi$
$193$	6.28576	−	10.8872i	0.452459	−	0.783681i	0.998538	+	0.0540520i	$0.0172137\pi$
$194$	−7.68313			−0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	7.14308	−	12.3722i	0.508924	−	0.881481i	−0.491023	−	0.871147i	$-0.663377\pi$
$197$	7.14308	−	12.3722i	0.508924	−	0.881481i	0.999947	−	0.0103349i	$-0.00328975\pi$
$198$	2.09845	+	7.83150i	0.149130	+	0.556561i
$199$	−7.36781	−	12.7614i	−0.522291	−	0.904634i	−0.999664	−	0.0259331i	$-0.991744\pi$
$199$	−7.36781	−	12.7614i	−0.522291	−	0.904634i	0.477373	−	0.878701i	$-0.341589\pi$
$200$	−2.27113	+	14.9336i	−0.160593	+	1.05597i
$201$	−19.6465	−	5.26425i	−1.38575	−	0.371312i
$202$	−8.63790	+	4.98709i	−0.607760	+	0.350891i
$203$	−0.281617			−0.0197656
$204$	−16.6986	+	9.64094i	−1.16914	+	0.675001i
$205$	12.7915	+	8.73354i	0.893400	+	0.609977i
$206$	3.52473	−	0.944449i	0.245580	−	0.0658029i
$207$	12.9884	−	12.9884i	0.902756	−	0.902756i
$208$		0			0
$209$			4.54668i			0.314500i
$210$	−3.46242	+	5.07122i	−0.238930	+	0.349947i
$211$	4.26604	−	7.38900i	0.293686	−	0.508680i	−0.680992	−	0.732291i	$-0.738451\pi$
$211$	4.26604	−	7.38900i	0.293686	−	0.508680i	0.974678	+	0.223611i	$0.0717845\pi$
$212$	−2.60518	−	0.698056i	−0.178925	−	0.0479427i
$213$			36.3773i			2.49253i
$214$	−0.117649	+	0.439070i	−0.00804229	+	0.0300142i
$215$	−7.70038	−	16.0171i	−0.525161	−	1.09236i
$216$	−10.5181	−	10.5181i	−0.715669	−	0.715669i
$217$	−0.0443156	+	0.165388i	−0.00300834	+	0.0112273i
$218$	−8.97011	+	2.40353i	−0.607532	+	0.162788i
$219$	2.32797	+	8.68810i	0.157310	+	0.587087i
$220$	−3.53897	−	0.267567i	−0.238597	−	0.0180394i
$221$		0			0
$222$	−8.22445	−	8.22445i	−0.551989	−	0.551989i
$223$	−6.11483	−	3.53040i	−0.409479	−	0.236413i	0.281087	−	0.959682i	$-0.409305\pi$
$223$	−6.11483	−	3.53040i	−0.409479	−	0.236413i	−0.690566	+	0.723269i	$0.742638\pi$
$224$	4.03432	+	2.32922i	0.269555	+	0.155627i
$225$	8.67803	+	22.1977i	0.578535	+	1.47985i
$226$	1.39889	−	1.39889i	0.0930527	−	0.0930527i
$227$	−8.58775	−	14.8744i	−0.569989	−	0.987249i	−0.996566	−	0.0827985i	$-0.973614\pi$
$227$	−8.58775	−	14.8744i	−0.569989	−	0.987249i	0.426578	−	0.904451i	$-0.359719\pi$
$228$	−3.63480	−	6.29566i	−0.240721	−	0.416940i
$229$	−8.90647	+	8.90647i	−0.588556	+	0.588556i	−0.937240	−	0.348684i	$-0.886629\pi$
$229$	−8.90647	+	8.90647i	−0.588556	+	0.588556i	0.348684	+	0.937240i	$0.386629\pi$
$230$	−3.81788	−	7.94137i	−0.251744	−	0.523638i
$231$	−3.86813	−	2.23327i	−0.254504	−	0.146938i
$232$	−0.764655	−	0.441474i	−0.0502021	−	0.0289842i
$233$	17.5822	+	17.5822i	1.15185	+	1.15185i	0.986182	+	0.165666i	$0.0529773\pi$
$233$	17.5822	+	17.5822i	1.15185	+	1.15185i	0.165666	+	0.986182i	$0.447023\pi$
$234$		0			0
$235$	11.4348	+	13.3053i	0.745923	+	0.867940i
$236$	−1.24758	−	4.65603i	−0.0812105	−	0.303082i
$237$	−36.5686	+	9.79852i	−2.37538	+	0.636482i
$238$	−1.84910	+	6.90095i	−0.119860	+	0.447322i
$239$	−2.23488	−	2.23488i	−0.144562	−	0.144562i	0.631122	−	0.775684i	$-0.282595\pi$
$239$	−2.23488	−	2.23488i	−0.144562	−	0.144562i	−0.775684	+	0.631122i	$0.782595\pi$
$240$	−6.63230	+	3.18854i	−0.428113	+	0.205819i
$241$	4.66361	−	17.4048i	0.300409	−	1.12114i	−0.636416	−	0.771346i	$-0.719584\pi$
$241$	4.66361	−	17.4048i	0.300409	−	1.12114i	0.936825	−	0.349797i	$-0.113750\pi$
$242$		−	8.41971i		−	0.541239i
$243$	15.8248	+	4.24025i	1.01516	+	0.272012i
$244$	0.994033	−	1.72172i	0.0636364	−	0.110222i
$245$	2.51516	+	13.3413i	0.160688	+	0.852346i
$246$			19.7406i			1.25862i
$247$		0			0
$248$	−0.379596	+	0.379596i	−0.0241044	+	0.0241044i
$249$	−23.0659	+	6.18048i	−1.46174	+	0.391672i
$250$	11.4260	−	0.404792i	0.722647	−	0.0256013i
$251$	12.1009	−	6.98644i	0.763800	−	0.440980i	−0.0668586	−	0.997762i	$-0.521298\pi$
$251$	12.1009	−	6.98644i	0.763800	−	0.440980i	0.830658	+	0.556782i	$0.187964\pi$
$252$	4.38299			0.276102
$253$	5.55068	−	3.20468i	0.348968	−	0.201477i
$254$	2.14854	+	0.575700i	0.134812	+	0.0361227i
$255$	29.4493	+	34.2666i	1.84419	+	2.14586i
$256$	8.42962	+	14.6005i	0.526851	+	0.912533i
$257$	−5.99887	−	22.3881i	−0.374199	−	1.39653i	−0.854511	−	0.519433i	$-0.826143\pi$
$257$	−5.99887	−	22.3881i	−0.374199	−	1.39653i	0.480312	−	0.877098i	$-0.340524\pi$
$258$	11.3254	−	19.6162i	0.705090	−	1.22125i
$259$	3.93255			0.244357
$260$		0			0
$261$	−1.39314			−0.0862334
$262$	0.0318286	−	0.0551288i	0.00196638	−	0.00340587i
$263$	0.336737	+	1.25672i	0.0207641	+	0.0774926i	0.975530	−	0.219864i	$-0.0705615\pi$
$263$	0.336737	+	1.25672i	0.0207641	+	0.0774926i	−0.954766	+	0.297357i	$0.903895\pi$
$264$	−7.00191	−	12.1277i	−0.430938	−	0.746407i
$265$	−0.476468	+	6.30199i	−0.0292692	+	0.387128i
$266$	−2.60178	−	0.697144i	−0.159525	−	0.0427446i
$267$	−1.25150	+	0.722551i	−0.0765903	+	0.0442194i
$268$	6.96441			0.425419
$269$	6.87429	−	3.96887i	0.419133	−	0.241986i	−0.275574	−	0.961280i	$-0.588868\pi$
$269$	6.87429	−	3.96887i	0.419133	−	0.241986i	0.694706	+	0.719294i	$0.255534\pi$
$270$	−6.34846	+	9.29823i	−0.386355	+	0.565872i
$271$	0.865041	−	0.231787i	0.0525475	−	0.0140801i	−0.232450	−	0.972608i	$-0.574674\pi$
$271$	0.865041	−	0.231787i	0.0525475	−	0.0140801i	0.284997	+	0.958528i	$0.408007\pi$
$272$	−6.05429	+	6.05429i	−0.367095	+	0.367095i
$273$		0			0
$274$			4.51738i			0.272905i
$275$	0.920192	+	8.26535i	0.0554897	+	0.498420i
$276$	−5.12391	+	8.87488i	−0.308423	+	0.534205i
$277$	9.22930	+	2.47298i	0.554535	+	0.148587i	0.525194	−	0.850982i	$-0.323993\pi$
$277$	9.22930	+	2.47298i	0.554535	+	0.148587i	0.0293404	+	0.999569i	$0.490659\pi$
$278$			14.0596i			0.843236i
$279$	−0.219227	+	0.818165i	−0.0131248	+	0.0489823i
$280$	2.15394	−	6.14255i	0.128723	−	0.367087i
$281$	−5.58408	−	5.58408i	−0.333118	−	0.333118i	0.520651	−	0.853769i	$-0.325689\pi$
$281$	−5.58408	−	5.58408i	−0.333118	−	0.333118i	−0.853769	+	0.520651i	$0.825689\pi$
$282$	−5.78719	+	21.5981i	−0.344622	+	1.28615i
$283$	−20.3851	+	5.46218i	−1.21177	+	0.324693i	−0.807457	−	0.589927i	$-0.799157\pi$
$283$	−20.3851	+	5.46218i	−1.21177	+	0.324693i	−0.404314	+	0.914620i	$0.632490\pi$
$284$	−3.22382	−	12.0315i	−0.191298	−	0.713936i
$285$	−12.9191	+	11.1029i	−0.765262	+	0.657679i
$286$		0			0
$287$	−4.71953	−	4.71953i	−0.278585	−	0.278585i
$288$	19.9576	+	11.5225i	1.17601	+	0.678970i
$289$	30.8040	+	17.7847i	1.81200	+	1.04616i
$290$	−0.221144	+	0.630652i	−0.0129860	+	0.0370332i
$291$	14.8057	−	14.8057i	0.867927	−	0.867927i
$292$	−1.53991	−	2.66720i	−0.0901164	−	0.156086i
$293$	2.01079	+	3.48280i	0.117472	+	0.203467i	0.918765	−	0.394805i	$-0.129188\pi$
$293$	2.01079	+	3.48280i	0.117472	+	0.203467i	−0.801293	+	0.598272i	$0.795854\pi$
$294$	−12.2353	+	12.2353i	−0.713579	+	0.713579i
$295$	−10.1799	+	4.89405i	−0.592694	+	0.284943i
$296$	10.6778	+	6.16482i	0.620633	+	0.358323i
$297$	−7.09234	−	4.09477i	−0.411539	−	0.237602i
$298$	3.13271	+	3.13271i	0.181473	+	0.181473i
$299$		0			0
$300$	−7.88183	−	10.7092i	−0.455058	−	0.618294i
$301$	1.98213	+	7.39742i	0.114248	+	0.426380i
$302$	6.63524	−	1.77791i	0.381815	−	0.102307i
$303$	7.03525	−	26.2559i	0.404165	−	1.50836i
$304$	−2.28257	−	2.28257i	−0.130914	−	0.130914i
$305$	−4.39612	−	1.54154i	−0.251721	−	0.0882683i
$306$	−9.14740	+	34.1386i	−0.522922	+	1.95157i
$307$		−	24.2191i		−	1.38226i	−0.722732	−	0.691128i	$-0.757114\pi$
$307$		−	24.2191i		−	1.38226i	0.722732	−	0.691128i	$-0.242886\pi$
$308$	1.47727	+	0.395832i	0.0841750	+	0.0225546i
$309$	−4.97231	+	8.61229i	−0.282865	+	0.489936i
$310$	0.335570	+	0.229114i	0.0190591	+	0.0130128i
$311$			7.87243i			0.446405i	0.974772	+	0.223202i	$0.0716511\pi$
$311$			7.87243i			0.446405i	−0.974772	+	0.223202i	$0.928349\pi$
$312$		0			0
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	−0.604740	−	0.796423i	$-0.706723\pi$
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	0.796423	+	0.604740i	$0.206723\pi$
$314$	−20.1838	+	5.40824i	−1.13904	+	0.305204i
$315$	−1.90272	−	10.0927i	−0.107206	−	0.568660i
$316$	11.2264	−	6.48154i	0.631532	−	0.364615i
$317$	−22.9255			−1.28762			−0.643812	−	0.765184i	$-0.722648\pi$
$317$	−22.9255			−1.28762			−0.643812	+	0.765184i	$0.722648\pi$
$318$	−6.97580	+	4.02748i	−0.391183	+	0.225850i
$319$	−0.469553	−	0.125816i	−0.0262899	−	0.00704436i
$320$	12.3893	−	10.6476i	0.692581	−	0.595216i
$321$	−0.619393	−	1.07282i	−0.0345712	−	0.0598790i
$322$	0.982751	+	3.66768i	0.0547666	+	0.204392i
$323$	−9.90979	+	17.1643i	−0.551395	+	0.955044i
$324$	−0.551932			−0.0306629
$325$		0			0
$326$	−21.8689			−1.21120
$327$	12.6541	−	21.9175i	0.699771	−	1.21204i
$328$	−5.41609	−	20.2131i	−0.299053	−	1.11608i
$329$	−3.78001	−	6.54718i	−0.208399	−	0.360958i
$330$	−8.03868	+	6.90858i	−0.442515	+	0.380305i
$331$	32.4118	+	8.68470i	1.78151	+	0.477354i	0.990858	−	0.134910i	$-0.0430745\pi$
$331$	32.4118	+	8.68470i	1.78151	+	0.477354i	0.790653	+	0.612264i	$0.209741\pi$
$332$	7.08110	−	4.08828i	0.388626	−	0.224373i
$333$	19.4541			1.06608
$334$	1.51833	−	0.876609i	0.0830794	−	0.0479659i
$335$	−3.02336	−	16.0370i	−0.165184	−	0.876194i
$336$	3.06309	−	0.820752i	0.167105	−	0.0447757i
$337$	14.5544	−	14.5544i	0.792826	−	0.792826i	−0.189126	−	0.981953i	$-0.560566\pi$
$337$	14.5544	−	14.5544i	0.792826	−	0.792826i	0.981953	+	0.189126i	$0.0605656\pi$
$338$		0			0
$339$			5.39143i			0.292822i
$340$	−12.7769	−	8.72352i	−0.692923	−	0.473099i
$341$	−0.147779	+	0.255960i	−0.00800267	+	0.0138610i
$342$	−12.8708	−	3.44873i	−0.695975	−	0.186486i
$343$		−	12.5954i		−	0.680087i
$344$	−6.21454	+	23.1930i	−0.335065	+	1.25048i
$345$	22.6606	+	7.94613i	1.22000	+	0.427805i
$346$	−10.9743	−	10.9743i	−0.589983	−	0.589983i
$347$	5.90442	−	22.0356i	0.316966	−	1.18293i	−0.605179	−	0.796089i	$-0.706899\pi$
$347$	5.90442	−	22.0356i	0.316966	−	1.18293i	0.922145	−	0.386844i	$-0.126435\pi$
$348$	0.750759	−	0.201165i	0.0402449	−	0.0107836i
$349$	−2.68798	−	10.0317i	−0.143884	−	0.536983i	−0.999803	−	0.0198718i	$-0.993674\pi$
$349$	−2.68798	−	10.0317i	−0.143884	−	0.536983i	0.855918	−	0.517111i	$-0.172992\pi$
$350$	−4.87083	−	0.740762i	−0.260357	−	0.0395954i
$351$		0			0
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$	−3.72420	−	2.15017i	−0.198219	−	0.114442i	0.397605	−	0.917556i	$-0.369841\pi$
$353$	−3.72420	−	2.15017i	−0.198219	−	0.114442i	−0.595825	+	0.803115i	$0.703175\pi$
$354$	−12.4673	−	7.19799i	−0.662629	−	0.382569i
$355$	−26.3054	+	12.6465i	−1.39614	+	0.671208i
$356$	0.349887	−	0.349887i	0.0185440	−	0.0185440i
$357$	−9.73511	−	16.8617i	−0.515237	−	0.892416i
$358$	1.41082	+	2.44361i	0.0745640	+	0.129149i
$359$	−10.4273	+	10.4273i	−0.550333	+	0.550333i	−0.926537	−	0.376204i	$-0.877229\pi$
$359$	−10.4273	+	10.4273i	−0.550333	+	0.550333i	0.376204	+	0.926537i	$0.377229\pi$
$360$	10.6554	−	30.3868i	0.561589	−	1.60153i
$361$	9.98326	+	5.76384i	0.525435	+	0.303360i
$362$	9.17216	+	5.29555i	0.482078	+	0.278328i
$363$	16.2251	+	16.2251i	0.851599	+	0.851599i
$364$		0			0
$365$	−5.47327	+	4.70382i	−0.286484	+	0.246209i
$366$	−1.53673	−	5.73514i	−0.0803259	−	0.299780i
$367$	−11.0341	+	2.95657i	−0.575973	+	0.154331i	−0.535034	−	0.844830i	$-0.679701\pi$
$367$	−11.0341	+	2.95657i	−0.575973	+	0.154331i	−0.0409383	+	0.999162i	$0.513035\pi$
$368$	−1.17776	+	4.39546i	−0.0613950	+	0.229129i
$369$	−23.3472	−	23.3472i	−1.21541	−	1.21541i
$370$	3.08809	−	8.80653i	0.160542	−	0.457830i
$371$	0.704874	−	2.63063i	0.0365953	−	0.136575i
$372$		−	0.472562i		−	0.0245012i
$373$	−27.1975	−	7.28755i	−1.40823	−	0.377335i	−0.526939	−	0.849903i	$-0.676661\pi$
$373$	−27.1975	−	7.28755i	−1.40823	−	0.377335i	−0.881294	+	0.472568i	$0.843327\pi$
$374$	−6.16618	+	10.6801i	−0.318846	+	0.552257i
$375$	−21.2384	+	22.7985i	−1.09675	+	1.17731i
$376$		−	23.7028i		−	1.22238i
$377$		0			0
$378$	3.43065	−	3.43065i	0.176453	−	0.176453i
$379$	16.3551	−	4.38232i	0.840103	−	0.225105i	0.186987	−	0.982362i	$-0.440128\pi$
$379$	16.3551	−	4.38232i	0.840103	−	0.225105i	0.653116	+	0.757258i	$0.273461\pi$
$380$	3.28892	−	4.81710i	0.168718	−	0.247112i
$381$	−5.24973	+	3.03093i	−0.268952	+	0.155279i
$382$	18.9999			0.972119
$383$	5.71918	−	3.30197i	0.292236	−	0.168723i	−0.346714	−	0.937971i	$-0.612702\pi$
$383$	5.71918	−	3.30197i	0.292236	−	0.168723i	0.638950	+	0.769248i	$0.279369\pi$
$384$	−5.91729	−	1.58553i	−0.301966	−	0.0809114i
$385$	0.270181	−	3.57354i	0.0137697	−	0.182124i
$386$	6.42793	+	11.1335i	0.327173	+	0.566680i
$387$	9.80550	+	36.5946i	0.498441	+	1.86021i
$388$	−3.58475	+	6.20897i	−0.181988	+	0.315212i
$389$	−33.6949			−1.70840			−0.854199	−	0.519946i	$-0.825952\pi$
$389$	−33.6949			−1.70840			−0.854199	+	0.519946i	$0.825952\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$	9.17126	−	15.8851i	0.463218	−	0.802318i
$393$	0.0449004	+	0.167570i	0.00226492	+	0.00845281i
$394$	7.30464	+	12.6520i	0.368003	+	0.637399i
$395$	−19.7986	−	23.0372i	−0.996175	−	1.15913i
$396$	7.30795	+	1.95816i	0.367238	+	0.0984012i
$397$	−5.04104	+	2.91045i	−0.253002	+	0.146071i	−0.621138	−	0.783701i	$-0.713329\pi$
$397$	−5.04104	+	2.91045i	−0.253002	+	0.146071i	0.368136	+	0.929772i	$0.379996\pi$
$398$	15.0689			0.755337
$399$	6.35716	−	3.67031i	0.318256	−	0.183745i
$400$	−4.61142	−	3.68750i	−0.230571	−	0.184375i
$401$	−0.255004	+	0.0683280i	−0.0127343	+	0.00341214i	−0.265181	−	0.964199i	$-0.585432\pi$
$401$	−0.255004	+	0.0683280i	−0.0127343	+	0.00341214i	0.252446	+	0.967611i	$0.418765\pi$
$402$	14.7075	−	14.7075i	0.733544	−	0.733544i
$403$		0			0
$404$			9.30738i			0.463060i
$405$	0.239602	+	1.27094i	0.0119059	+	0.0631533i
$406$	0.143993	−	0.249404i	0.00714627	−	0.0123777i
$407$	6.55691	+	1.75692i	0.325014	+	0.0870872i
$408$		−	61.0446i		−	3.02216i
$409$	−9.61872	+	35.8975i	−0.475615	+	1.77502i	0.143427	+	0.989661i	$0.454188\pi$
$409$	−9.61872	+	35.8975i	−0.475615	+	1.77502i	−0.619042	+	0.785358i	$0.712479\pi$
$410$	−14.2750	+	6.86281i	−0.704990	+	0.338930i
$411$	−8.70518	−	8.70518i	−0.429395	−	0.429395i
$412$	0.881310	−	3.28909i	0.0434190	−	0.162042i
$413$	4.70151	−	1.25977i	0.231346	−	0.0619890i
$414$	4.86161	+	18.1438i	0.238935	+	0.891718i
$415$	−12.4881	−	14.5309i	−0.613016	−	0.713293i
$416$		0			0
$417$	−27.0934	−	27.0934i	−1.32677	−	1.32677i
$418$	−4.02660	−	2.32476i	−0.196947	−	0.113708i
$419$	−29.3721	−	16.9580i	−1.43492	−	0.828451i	−0.437428	−	0.899253i	$-0.644111\pi$
$419$	−29.3721	−	16.9580i	−1.43492	−	0.828451i	−0.997490	+	0.0708027i	$0.977444\pi$
$420$	2.48272	+	5.16418i	0.121145	+	0.251986i
$421$	21.5599	−	21.5599i	1.05076	−	1.05076i	0.0521230	−	0.998641i	$-0.483401\pi$
$421$	21.5599	−	21.5599i	1.05076	−	1.05076i	0.998641	−	0.0521230i	$-0.0165988\pi$
$422$	4.36253	+	7.55613i	0.212365	+	0.367826i
$423$	−18.6995	−	32.3885i	−0.909201	−	1.57478i
$424$	6.03777	−	6.03777i	0.293220	−	0.293220i
$425$	−14.5411	+	33.2083i	−0.705345	+	1.61084i
$426$	−32.2162	−	18.6000i	−1.56088	−	0.901175i
$427$	1.73853	+	1.00374i	0.0841335	+	0.0485745i
$428$	0.299934	+	0.299934i	0.0144979	+	0.0144979i
$429$		0			0
$430$	18.1223	+	1.37015i	0.873933	+	0.0660745i
$431$	−1.19014	−	4.44167i	−0.0573271	−	0.213948i	0.931320	−	0.364201i	$-0.118658\pi$
$431$	−1.19014	−	4.44167i	−0.0573271	−	0.213948i	−0.988648	+	0.150253i	$0.951991\pi$
$432$	5.61627	−	1.50488i	0.270213	−	0.0724033i
$433$	−1.03596	+	3.86627i	−0.0497853	+	0.185801i	−0.986341	−	0.164719i	$-0.947328\pi$
$433$	−1.03596	+	3.86627i	−0.0497853	+	0.185801i	0.936555	+	0.350520i	$0.113995\pi$
$434$	−0.123811	−	0.123811i	−0.00594311	−	0.00594311i
$435$	−0.789140	−	1.64145i	−0.0378364	−	0.0787013i
$436$	−2.24285	+	8.37043i	−0.107413	+	0.400871i
$437$			10.5336i			0.503890i
$438$	−8.88461	−	2.38062i	−0.424523	−	0.113751i
$439$	−11.3618	+	19.6793i	−0.542271	+	0.939242i	0.456502	+	0.889723i	$0.349102\pi$
$439$	−11.3618	+	19.6793i	−0.542271	+	0.939242i	−0.998773	+	0.0495192i	$0.984231\pi$
$440$	6.33562	−	9.27944i	0.302039	−	0.442380i
$441$		−	28.9414i		−	1.37816i
$442$		0			0
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	−0.661824	−	0.749660i	$-0.730217\pi$
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	0.749660	+	0.661824i	$0.230217\pi$
$444$	−10.4837	+	2.80911i	−0.497536	+	0.133314i
$445$	−0.957576	−	0.653794i	−0.0453935	−	0.0309928i
$446$	6.25313	−	3.61025i	0.296094	−	0.170950i
$447$	−12.0737			−0.571067
$448$	−6.09644	+	3.51978i	−0.288030	+	0.166294i
$449$	31.0770	+	8.32705i	1.46661	+	0.392978i	0.901769	−	0.432219i	$-0.142269\pi$
$449$	31.0770	+	8.32705i	1.46661	+	0.392978i	0.564845	+	0.825197i	$0.308936\pi$
$450$	−24.0957	−	3.66451i	−1.13588	−	0.172746i
$451$	−5.76056	−	9.97759i	−0.271254	−	0.469826i
$452$	−0.477798	−	1.78317i	−0.0224737	−	0.0838731i
$453$	−9.36029	+	16.2125i	−0.439785	+	0.761729i
$454$	17.5640			0.824318
$455$		0			0
$456$	23.0149			1.07777
$457$	−14.1837	+	24.5669i	−0.663486	+	1.14919i	0.316208	+	0.948690i	$0.397590\pi$
$457$	−14.1837	+	24.5669i	−0.663486	+	1.14919i	−0.979693	+	0.200501i	$0.935743\pi$
$458$	−3.33373	−	12.4416i	−0.155775	−	0.581360i
$459$	−17.8496	−	30.9165i	−0.833149	−	1.44306i
$460$	−8.19898	−	0.619891i	−0.382279	−	0.0289026i
$461$	11.1174	+	2.97890i	0.517790	+	0.138741i	0.508244	−	0.861213i	$-0.330295\pi$
$461$	11.1174	+	2.97890i	0.517790	+	0.138741i	0.00954570	+	0.999954i	$0.496961\pi$
$462$	3.95562	−	2.28378i	0.184032	−	0.106251i
$463$	−29.9456			−1.39169			−0.695845	−	0.718192i	$-0.744970\pi$
$463$	−29.9456			−1.39169			−0.695845	+	0.718192i	$0.744970\pi$
$464$	0.298893	−	0.172566i	0.0138758	−	0.00801118i
$465$	−1.08817	+	0.205146i	−0.0504626	+	0.00951342i
$466$	−24.5609	+	6.58109i	−1.13776	+	0.304863i
$467$	−16.1332	+	16.1332i	−0.746557	+	0.746557i	−0.973831	−	0.227274i	$-0.927019\pi$
$467$	−16.1332	+	16.1332i	−0.746557	+	0.746557i	0.227274	+	0.973831i	$0.427019\pi$
$468$		0			0
$469$			7.03244i			0.324728i
$470$	−17.6300	+	3.32368i	−0.813213	+	0.153310i
$471$	28.4732	−	49.3170i	1.31197	−	2.27241i
$472$	14.7405	+	3.94971i	0.678488	+	0.181800i
$473$			13.2196i			0.607837i
$474$	10.0201	−	37.3957i	0.460240	−	1.71764i
$475$	−12.5201	−	5.48223i	−0.574462	−	0.251542i
$476$	4.71411	+	4.71411i	0.216071	+	0.216071i
$477$	3.48697	−	13.0136i	0.159657	−	0.595850i
$478$	3.12195	−	0.836524i	0.142795	−	0.0382617i
$479$	−10.0493	−	37.5043i	−0.459162	−	1.71362i	−0.675555	−	0.737309i	$-0.736096\pi$
$479$	−10.0493	−	37.5043i	−0.459162	−	1.71362i	0.216393	−	0.976306i	$-0.430571\pi$
$480$	−2.27132	+	30.0415i	−0.103671	+	1.37120i
$481$		0			0
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$	−8.96157	−	5.17396i	−0.407765	−	0.235424i
$484$	−6.80421	−	3.92841i	−0.309282	−	0.178564i
$485$	15.8536	+	5.55920i	0.719874	+	0.252430i
$486$	−11.8466	+	11.8466i	−0.537372	+	0.537372i
$487$	14.4718	+	25.0660i	0.655782	+	1.13585i	0.981697	+	0.190448i	$0.0609941\pi$
$487$	14.4718	+	25.0660i	0.655782	+	1.13585i	−0.325916	+	0.945399i	$0.605673\pi$
$488$	3.14701	+	5.45078i	0.142458	+	0.246745i
$489$	42.1422	−	42.1422i	1.90574	−	1.90574i
$490$	−13.1013	−	4.59408i	−0.591855	−	0.207539i
$491$	6.30003	+	3.63733i	0.284317	+	0.164150i	0.635376	−	0.772203i	$-0.280845\pi$
$491$	6.30003	+	3.63733i	0.284317	+	0.164150i	−0.351059	+	0.936353i	$0.614178\pi$
$492$	15.9530	+	9.21046i	0.719216	+	0.415240i
$493$	−1.49839	−	1.49839i	−0.0674842	−	0.0674842i
$494$		0			0
$495$	1.33657	−	17.6781i	0.0600743	−	0.794571i
$496$	−0.0543104	−	0.202689i	−0.00243861	−	0.00910102i
$497$	12.1490	−	3.25531i	0.544956	−	0.146021i
$498$	6.32027	−	23.5876i	0.283218	−	1.05698i
$499$	4.24201	+	4.24201i	0.189899	+	0.189899i	0.795652	−	0.605754i	$-0.207128\pi$
$499$	4.24201	+	4.24201i	0.189899	+	0.189899i	−0.605754	+	0.795652i	$0.707128\pi$
$500$	5.00397	−	9.42259i	0.223784	−	0.421391i
$501$	−1.23663	+	4.61515i	−0.0552483	+	0.206190i
$502$			14.2889i			0.637745i
$503$	−3.50677	−	0.939636i	−0.156359	−	0.0418963i	0.179790	−	0.983705i	$-0.442458\pi$
$503$	−3.50677	−	0.939636i	−0.156359	−	0.0418963i	−0.336149	+	0.941809i	$0.609125\pi$
$504$	−6.93805	+	12.0171i	−0.309046	+	0.535283i
$505$	21.4321	−	4.04047i	0.953717	−	0.179799i
$506$			6.55433i			0.291376i
$507$		0			0
$508$	1.46769	−	1.46769i	0.0651184	−	0.0651184i
$509$	−22.5037	+	6.02986i	−0.997460	+	0.267269i	−0.720381	−	0.693578i	$-0.756033\pi$
$509$	−22.5037	+	6.02986i	−0.997460	+	0.267269i	−0.277079	+	0.960847i	$0.589366\pi$
$510$	−45.4047	+	8.55987i	−2.01055	+	0.379038i
$511$	2.69325	−	1.55495i	0.119143	−	0.0687870i
$512$	−12.8442			−0.567640
$513$	11.6560	−	6.72962i	0.514627	−	0.297120i
$514$	22.8945	+	6.13455i	1.00983	+	0.270584i
$515$	−7.95639	−	0.601550i	−0.350600	−	0.0265075i
$516$	−10.5683	−	18.3048i	−0.465243	−	0.805824i
$517$	−3.37754	−	12.6052i	−0.148544	−	0.554375i
$518$	−2.01075	+	3.48272i	−0.0883472	+	0.153022i
$519$	42.2960			1.85659
$520$		0			0
$521$	−13.0530			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$521$	−13.0530			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$522$	0.712327	−	1.23379i	0.0311777	−	0.0540013i
$523$	4.40520	+	16.4404i	0.192626	+	0.718890i	0.992869	+	0.119214i	$0.0380374\pi$
$523$	4.40520	+	16.4404i	0.192626	+	0.718890i	−0.800243	+	0.599677i	$0.795296\pi$
$524$	−0.0297008	−	0.0514432i	−0.00129748	−	0.00224731i
$525$	10.8138	−	7.95882i	0.471952	−	0.347351i
$526$	−1.28514	−	0.344353i	−0.0560349	−	0.0150145i
$527$	−1.11577	+	0.644187i	−0.0486035	+	0.0280612i
$528$	5.47391			0.238221
$529$	−7.05896	+	4.07549i	−0.306911	+	0.177195i
$530$	−5.33750	−	3.64423i	−0.231846	−	0.158295i
$531$	23.2581	−	6.23198i	1.00931	−	0.270445i
$532$	−1.77730	+	1.77730i	−0.0770558	+	0.0770558i
$533$		0			0
$534$		−	1.47779i		−	0.0639501i
$535$	0.560453	−	0.820864i	0.0242305	−	0.0354891i
$536$	−11.0243	+	19.0947i	−0.476178	+	0.824765i
$537$	−7.42764	−	1.99023i	−0.320526	−	0.0858847i
$538$			8.11728i			0.349961i
$539$	2.61373	−	9.75457i	0.112581	−	0.420159i
$540$	4.55215	+	9.46868i	0.195893	+	0.407467i
$541$	10.9728	+	10.9728i	0.471756	+	0.471756i	0.902483	−	0.430727i	$-0.141743\pi$
$541$	10.9728	+	10.9728i	0.471756	+	0.471756i	−0.430727	+	0.902483i	$0.641743\pi$
$542$	−0.237029	+	0.884606i	−0.0101813	+	0.0379971i
$543$	−27.8799	+	7.47039i	−1.19644	+	0.320585i
$544$	9.07231	+	33.8583i	0.388972	+	1.45166i
$545$	20.2483	+	1.53089i	0.867340	+	0.0655761i
$546$		0			0
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	0.118756	−	0.992923i	$-0.462109\pi$
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	−0.992923	+	0.118756i	$0.962109\pi$
$548$	3.65063	+	2.10769i	0.155947	+	0.0900361i
$549$	8.60042	+	4.96545i	0.367057	+	0.211920i
$550$	−7.79041	−	3.41121i	−0.332184	−	0.145455i
$551$	0.564920	−	0.564920i	0.0240664	−	0.0240664i
$552$	−16.2218	−	28.0970i	−0.690446	−	1.19589i
$553$	6.54485	+	11.3360i	0.278315	+	0.482056i
$554$	−6.90913	+	6.90913i	−0.293541	+	0.293541i
$555$	11.0197	+	22.9214i	0.467759	+	0.972961i
$556$	11.3619	+	6.55982i	0.481854	+	0.278198i
$557$	−11.7609	−	6.79015i	−0.498324	−	0.287708i	0.229697	−	0.973262i	$-0.426226\pi$
$557$	−11.7609	−	6.79015i	−0.498324	−	0.287708i	−0.728021	+	0.685555i	$0.759560\pi$
$558$	−0.612485	−	0.612485i	−0.0259286	−	0.0259286i
$559$		0			0
$560$	1.65839	+	1.92967i	0.0700797	+	0.0815432i
$561$	−8.69858	−	32.4636i	−0.367254	−	1.37061i
$562$	7.80052	−	2.09014i	0.329045	−	0.0881673i
$563$	1.25538	−	4.68514i	0.0529080	−	0.197455i	−0.934413	−	0.356191i	$-0.884075\pi$
$563$	1.25538	−	4.68514i	0.0529080	−	0.197455i	0.987321	+	0.158736i	$0.0507418\pi$
$564$	14.7539	+	14.7539i	0.621251	+	0.621251i
$565$	−3.89868	+	1.87433i	−0.164019	+	0.0788535i
$566$	5.58573	−	20.8462i	0.234786	−	0.876232i
$567$		−	0.557323i		−	0.0234054i
$568$	38.0904	+	10.2063i	1.59824	+	0.428247i
$569$	−0.124396	+	0.215461i	−0.00521497	+	0.00903259i	−0.868621	−	0.495477i	$-0.834993\pi$
$569$	−0.124396	+	0.215461i	−0.00521497	+	0.00903259i	0.863406	+	0.504509i	$0.168327\pi$
$570$	−3.22722	−	17.1183i	−0.135173	−	0.717009i
$571$			7.72842i			0.323424i	0.986838	+	0.161712i	$0.0517016\pi$
$571$			7.72842i			0.323424i	−0.986838	+	0.161712i	$0.948298\pi$
$572$		0			0
$573$	−36.6136	+	36.6136i	−1.52955	+	1.52955i
$574$	6.59281	−	1.76654i	0.275179	−	0.0737339i
$575$	2.13187	+	19.1489i	0.0889052	+	0.798565i
$576$	−30.1587	+	17.4121i	−1.25661	+	0.725506i
$577$	12.1339			0.505141			0.252570	−	0.967578i	$-0.418724\pi$
$577$	12.1339			0.505141			0.252570	+	0.967578i	$0.418724\pi$
$578$	−31.5007	+	18.1869i	−1.31026	+	0.756477i
$579$	−33.8416	−	9.06783i	−1.40641	−	0.376846i
$580$	0.406469	+	0.472958i	0.0168777	+	0.0196385i
$581$	4.12821	+	7.15027i	0.171267	+	0.296643i
$582$	5.54184	+	20.6824i	0.229717	+	0.857315i
$583$	2.35054	−	4.07125i	0.0973492	−	0.168614i
$584$	9.75040			0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$	−18.2647	+	31.6354i	−0.753865	+	1.30573i	0.192072	+	0.981381i	$0.438479\pi$
$587$	−18.2647	+	31.6354i	−0.753865	+	1.30573i	−0.945937	+	0.324351i	$0.894854\pi$
$588$	4.17904	+	15.5964i	0.172341	+	0.643185i
$589$	−0.242870	−	0.420663i	−0.0100073	−	0.0173331i
$590$	0.870813	−	11.5178i	0.0358508	−	0.474180i
$591$	−38.4573	−	10.3046i	−1.58192	−	0.423875i
$592$	−4.17380	+	2.40974i	−0.171542	+	0.0990398i
$593$	16.6936			0.685525			0.342762	−	0.939422i	$-0.388637\pi$
$593$	16.6936			0.685525			0.342762	+	0.939422i	$0.388637\pi$
$594$	7.25276	−	4.18738i	0.297584	−	0.171810i
$595$	8.80873	−	12.9017i	0.361123	−	0.528917i
$596$	3.99327	−	1.06999i	0.163571	−	0.0438287i
$597$	−29.0384	+	29.0384i	−1.18846	+	1.18846i
$598$		0			0
$599$		−	13.2549i		−	0.541579i	−0.962639	−	0.270789i	$-0.912715\pi$
$599$		−	13.2549i		−	0.541579i	0.962639	−	0.270789i	$-0.0872847\pi$
$600$	41.8384	−	4.65793i	1.70805	−	0.190159i
$601$	−0.546605	+	0.946748i	−0.0222965	+	0.0386187i	−0.876958	−	0.480566i	$-0.840431\pi$
$601$	−0.546605	+	0.946748i	−0.0222965	+	0.0386187i	0.854662	+	0.519185i	$0.173764\pi$
$602$	−7.56474	−	2.02696i	−0.308316	−	0.0826129i
$603$			34.7891i			1.41672i
$604$	1.65905	−	6.19166i	0.0675058	−	0.251935i
$605$	−6.09216	+	17.3735i	−0.247682	+	0.706332i
$606$	19.6554	+	19.6554i	0.798446	+	0.798446i
$607$	−10.8348	+	40.4361i	−0.439771	+	1.64125i	0.289612	+	0.957144i	$0.406474\pi$
$607$	−10.8348	+	40.4361i	−0.439771	+	1.64125i	−0.729384	+	0.684105i	$0.760193\pi$
$608$	−12.7652	+	3.42042i	−0.517696	+	0.138716i
$609$	0.203130	+	0.758093i	0.00823126	+	0.0307195i
$610$	3.61298	−	3.10506i	0.146285	−	0.125720i
$611$		0			0
$612$	23.3204	+	23.3204i	0.942673	+	0.942673i
$613$	−24.1705	−	13.9548i	−0.976235	−	0.563630i	−0.0751039	−	0.997176i	$-0.523929\pi$
$613$	−24.1705	−	13.9548i	−0.976235	−	0.563630i	−0.901131	+	0.433546i	$0.857262\pi$
$614$	21.4487	+	12.3834i	0.865601	+	0.499755i
$615$	14.2835	−	40.7334i	0.575967	−	1.64253i
$616$	−3.42371	+	3.42371i	−0.137945	+	0.137945i
$617$	2.19132	+	3.79548i	0.0882193	+	0.152800i	0.906758	−	0.421650i	$-0.138549\pi$
$617$	2.19132	+	3.79548i	0.0882193	+	0.152800i	−0.818539	+	0.574451i	$0.805216\pi$
$618$	−5.08477	−	8.80708i	−0.204540	−	0.354273i
$619$	8.67268	−	8.67268i	0.348584	−	0.348584i	−0.510998	−	0.859582i	$-0.670724\pi$
$619$	8.67268	−	8.67268i	0.348584	−	0.348584i	0.859582	+	0.510998i	$0.170724\pi$
$620$	0.341722	−	0.164286i	0.0137239	−	0.00659787i
$621$	−16.4313	−	9.48662i	−0.659366	−	0.380685i
$622$	−6.97193	−	4.02525i	−0.279549	−	0.161398i
$623$	0.353304	+	0.353304i	0.0141548	+	0.0141548i
$624$		0			0
$625$	−23.8697	−	7.43216i	−0.954788	−	0.297287i
$626$	1.26934	+	4.73726i	0.0507332	+	0.189339i
$627$	12.2393	−	3.27952i	0.488791	−	0.130971i
$628$	−5.04668	+	18.8345i	−0.201385	+	0.751577i
$629$	20.9238	+	20.9238i	0.834287	+	0.834287i
$630$	9.91112	+	3.47542i	0.394868	+	0.138464i
$631$	6.55800	−	24.4748i	0.261070	−	0.974326i	−0.703542	−	0.710653i	$-0.748399\pi$
$631$	6.55800	−	24.4748i	0.261070	−	0.974326i	0.964612	−	0.263673i	$-0.0849339\pi$
$632$			41.0398i			1.63248i
$633$	−22.9677	−	6.15419i	−0.912886	−	0.244607i
$634$	11.7220	−	20.3031i	0.465540	−	0.806340i
$635$	−4.01681	−	2.74251i	−0.159402	−	0.108833i
$636$			7.51646i			0.298047i
$637$		0			0
$638$	0.351511	−	0.351511i	0.0139164	−	0.0139164i
$639$	60.1003	−	16.1038i	2.37753	−	0.637057i
$640$	−0.910600	−	4.83016i	−0.0359946	−	0.190929i
$641$	−1.41675	+	0.817961i	−0.0559582	+	0.0323075i	−0.527718	−	0.849420i	$-0.676952\pi$
$641$	−1.41675	+	0.817961i	−0.0559582	+	0.0323075i	0.471760	+	0.881727i	$0.343619\pi$
$642$	1.26681			0.0499968
$643$	−34.3541	+	19.8344i	−1.35479	+	0.782191i	−0.988917	−	0.148472i	$-0.952565\pi$
$643$	−34.3541	+	19.8344i	−1.35479	+	0.782191i	−0.365878	+	0.930663i	$0.619231\pi$
$644$	3.42248	+	0.917051i	0.134865	+	0.0361369i
$645$	−37.5627	+	32.2820i	−1.47903	+	1.27110i
$646$	−10.1339	−	17.5525i	−0.398714	−	0.690593i
$647$	−3.84742	−	14.3588i	−0.151258	−	0.564501i	−0.999397	−	0.0347277i	$-0.988944\pi$
$647$	−3.84742	−	14.3588i	−0.151258	−	0.564501i	0.848139	−	0.529773i	$-0.177723\pi$
$648$	0.873682	−	1.51326i	0.0343215	−	0.0594465i
$649$	8.40185			0.329801
$650$		0			0
$651$	0.477178			0.0187021
$652$	−10.2034	+	17.6729i	−0.399597	+	0.692123i
$653$	3.32718	+	12.4172i	0.130203	+	0.485922i	0.999972	−	0.00753655i	$-0.00239898\pi$
$653$	3.32718	+	12.4172i	0.130203	+	0.485922i	−0.869769	+	0.493459i	$0.835732\pi$
$654$	12.9403	+	22.4132i	0.506005	+	0.876426i
$655$	−0.105565	+	0.0907243i	−0.00412476	+	0.00354489i
$656$	7.90103	+	2.11708i	0.308483	+	0.0826579i
$657$	13.3234	−	7.69225i	0.519794	−	0.300103i
$658$	7.73102			0.301387
$659$	−20.8742	+	12.0517i	−0.813144	+	0.469469i	−0.848047	−	0.529922i	$-0.822221\pi$
$659$	−20.8742	+	12.0517i	−0.813144	+	0.469469i	0.0349025	+	0.999391i	$0.488888\pi$
$660$	1.83239	+	9.71965i	0.0713256	+	0.378337i
$661$	−37.8150	+	10.1325i	−1.47083	+	0.394108i	−0.903217	−	0.429185i	$-0.858801\pi$
$661$	−37.8150	+	10.1325i	−1.47083	+	0.394108i	−0.567616	+	0.823293i	$0.692134\pi$
$662$	−24.2637	+	24.2637i	−0.943036	+	0.943036i
$663$		0			0
$664$			25.8862i			1.00458i
$665$	4.86415	+	3.32104i	0.188624	+	0.128785i
$666$	−9.94705	+	17.2288i	−0.385440	+	0.667602i
$667$	−1.08784	−	0.291487i	−0.0421215	−	0.0112864i
$668$		−	1.63601i		−	0.0632991i
$669$	−5.09295	+	19.0071i	−0.196905	+	0.734858i
$670$	15.7484	+	5.52232i	0.608415	+	0.213346i
$671$	2.45030	+	2.45030i	0.0945926	+	0.0945926i
$672$	3.36013	−	12.5402i	0.129620	−	0.483747i
$673$	−9.87723	+	2.64660i	−0.380739	+	0.102019i	−0.444112	−	0.895971i	$-0.646481\pi$
$673$	−9.87723	+	2.64660i	−0.380739	+	0.102019i	0.0633730	+	0.997990i	$0.479814\pi$
$674$	5.44776	+	20.3313i	0.209840	+	0.783132i
$675$	19.8274	−	14.5927i	0.763157	−	0.561675i
$676$		0			0
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.986771	+	0.162121i	$0.0518333\pi$
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.162121	+	0.986771i	$0.448167\pi$
$678$	−4.77472	−	2.75669i	−0.183372	−	0.105870i
$679$	−6.26961	−	3.61976i	−0.240606	−	0.138914i
$680$	44.1429	−	21.2221i	1.69280	−	0.813829i
$681$	−33.8465	+	33.8465i	−1.29700	+	1.29700i
$682$	−0.151121	−	0.261750i	−0.00578673	−	0.0100229i
$683$	10.0103	+	17.3384i	0.383035	+	0.663436i	0.991494	−	0.130149i	$-0.0415455\pi$
$683$	10.0103	+	17.3384i	0.383035	+	0.663436i	−0.608459	+	0.793585i	$0.708212\pi$
$684$	−8.79221	+	8.79221i	−0.336178	+	0.336178i
$685$	3.26859	−	9.32129i	0.124886	−	0.356148i
$686$	11.1546	+	6.44013i	0.425886	+	0.245885i
$687$	30.3998	+	17.5513i	1.15983	+	0.669625i
$688$	−6.63664	−	6.63664i	−0.253019	−	0.253019i
$689$		0			0
$690$	−18.6238	+	16.0056i	−0.708994	+	0.609322i
$691$	9.15886	+	34.1813i	0.348420	+	1.30032i	0.888566	+	0.458749i	$0.151702\pi$
$691$	9.15886	+	34.1813i	0.348420	+	1.30032i	−0.540147	+	0.841571i	$0.681631\pi$
$692$	−13.9890	+	3.74834i	−0.531782	+	0.142491i
$693$	−1.97729	+	7.37933i	−0.0751109	+	0.280318i
$694$	16.4960	+	16.4960i	0.626181	+	0.626181i
$695$	10.1729	−	29.0109i	0.385881	−	1.10045i
$696$	−0.636870	+	2.37683i	−0.0241405	+	0.0900935i
$697$		−	50.2221i		−	1.90230i
$698$	10.2586	+	2.74877i	0.388292	+	0.104043i
$699$	34.6479	−	60.0120i	1.31051	−	2.26986i
$700$	−2.87123	+	3.59064i	−0.108522	+	0.135714i
$701$		−	37.1781i		−	1.40420i	−0.712080	−	0.702098i	$-0.752247\pi$
$701$		−	37.1781i		−	1.40420i	0.712080	−	0.702098i	$-0.247753\pi$
$702$		0			0
$703$	−7.88864	+	7.88864i	−0.297526	+	0.297526i
$704$	−11.7374	+	3.14502i	−0.442368	+	0.118532i
$705$	27.5689	−	40.3787i	1.03831	−	1.52075i
$706$	3.80843	−	2.19880i	0.143332	−	0.0827529i
$707$	−9.39830			−0.353459
$708$	−11.6338	+	6.71678i	−0.437225	+	0.252432i
$709$	−46.5506	−	12.4732i	−1.74824	−	0.468440i	−0.763994	−	0.645224i	$-0.776764\pi$
$709$	−46.5506	−	12.4732i	−1.74824	−	0.468440i	−0.984250	+	0.176783i	$0.943431\pi$
$710$	2.25023	−	29.7626i	0.0844497	−	1.11697i
$711$	32.3770	+	56.0786i	1.21423	+	2.10311i
$712$	0.405449	+	1.51316i	0.0151948	+	0.0567079i
$713$	−0.342369	+	0.593001i	−0.0128218	+	0.0222080i
$714$	19.9106			0.745135
$715$		0			0
$716$	2.63300			0.0983998
$717$	−4.40411	+	7.62814i	−0.164474	+	0.284878i
$718$	−3.90299	−	14.5662i	−0.145658	−	0.543604i
$719$	16.6992	+	28.9239i	0.622777	+	1.07868i	0.988966	+	0.148141i	$0.0473288\pi$
$719$	16.6992	+	28.9239i	0.622777	+	1.07868i	−0.366190	+	0.930540i	$0.619338\pi$
$720$	8.20394	+	9.54594i	0.305743	+	0.355756i
$721$	3.32122	+	0.889918i	0.123689	+	0.0331423i
$722$	−10.2091	+	5.89421i	−0.379942	+	0.219360i
$723$	−50.2164			−1.86757
$724$	8.55897	−	4.94153i	0.318092	−	0.183650i
$725$	0.912629	−	1.14129i	0.0338942	−	0.0423866i
$726$	−22.6652	+	6.07313i	−0.841186	+	0.225395i
$727$	−23.6487	+	23.6487i	−0.877083	+	0.877083i	−0.993232	−	0.116149i	$-0.962945\pi$
$727$	−23.6487	+	23.6487i	−0.877083	+	0.877083i	0.116149	+	0.993232i	$0.462945\pi$
$728$		0			0
$729$		−	43.9226i		−	1.62676i
$730$	−1.36723	−	7.25231i	−0.0506036	−	0.268420i
$731$	−28.8130	+	49.9055i	−1.06569	+	1.84582i
$732$	−5.35173	−	1.43399i	−0.197806	−	0.0530018i
$733$		−	14.7049i		−	0.543138i	−0.962419	−	0.271569i	$-0.912458\pi$
$733$		−	14.7049i		−	0.543138i	0.962419	−	0.271569i	$-0.0875424\pi$
$734$	3.02344	−	11.2836i	0.111597	−	0.416486i
$735$	34.0997	−	16.3937i	1.25779	−	0.604692i
$736$	13.1731	+	13.1731i	0.485568	+	0.485568i
$737$	−3.14184	+	11.7255i	−0.115731	+	0.431914i
$738$	32.6142	−	8.73896i	1.20055	−	0.321686i
$739$	−5.32432	−	19.8706i	−0.195858	−	0.730953i	−0.992043	−	0.125900i	$-0.959818\pi$
$739$	−5.32432	−	19.8706i	−0.195858	−	0.730953i	0.796185	−	0.605054i	$-0.206848\pi$
$740$	−5.67600	−	6.60447i	−0.208654	−	0.242785i
$741$		0			0
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$	38.6601	+	22.3204i	1.41830	+	0.818856i	0.996150	−	0.0876692i	$-0.0279419\pi$
$743$	38.6601	+	22.3204i	1.41830	+	0.818856i	0.422151	+	0.906526i	$0.361275\pi$
$744$	1.29565	+	0.748042i	0.0475007	+	0.0274246i
$745$	−4.19742	−	8.73082i	−0.153781	−	0.319872i
$746$	20.3603	−	20.3603i	0.745443	−	0.745443i
$747$	20.4220	+	35.3720i	0.747202	+	1.29419i
$748$	5.75395	+	9.96614i	0.210385	+	0.364398i
$749$	−0.302864	+	0.302864i	−0.0110664	+	0.0110664i
$750$	−9.33127	−	30.4661i	−0.340730	−	1.11246i
$751$	15.2247	+	8.78996i	0.555555	+	0.320750i	0.751360	−	0.659893i	$-0.229398\pi$
$751$	15.2247	+	8.78996i	0.555555	+	0.320750i	−0.195804	+	0.980643i	$0.562732\pi$
$752$	8.02381	+	4.63255i	0.292598	+	0.168932i
$753$	−27.5353	−	27.5353i	−1.00344	−	1.00344i
$754$		0			0
$755$	−14.9778	−	1.13241i	−0.545097	−	0.0412125i
$756$	−1.17176	−	4.37306i	−0.0426164	−	0.159047i
$757$	33.9933	−	9.10848i	1.23551	−	0.331053i	0.418786	−	0.908085i	$-0.362456\pi$
$757$	33.9933	−	9.10848i	1.23551	−	0.331053i	0.816722	+	0.577032i	$0.195789\pi$
$758$	−4.48144	+	16.7250i	−0.162773	+	0.607478i
$759$	−12.6305	−	12.6305i	−0.458457	−	0.458457i
$760$	8.00109	+	16.6426i	0.290230	+	0.603692i
$761$	3.03122	−	11.3127i	0.109882	−	0.410084i	−0.888972	−	0.457962i	$-0.848579\pi$
$761$	3.03122	−	11.3127i	0.109882	−	0.410084i	0.998853	+	0.0478787i	$0.0152461\pi$
$762$		−	6.19897i		−	0.224565i
$763$	−8.45219	−	2.26476i	−0.305990	−	0.0819897i
$764$	8.86485	−	15.3544i	0.320719	−	0.555502i
$765$	43.5763	−	63.8238i	1.57550	−	2.30755i
$766$			6.75331i			0.244007i
$767$		0			0
$768$	33.2233	−	33.2233i	1.19884	−	1.19884i
$769$	18.3227	−	4.90954i	0.660732	−	0.177043i	0.0871555	−	0.996195i	$-0.472222\pi$
$769$	18.3227	−	4.90954i	0.660732	−	0.177043i	0.573576	+	0.819152i	$0.305556\pi$
$770$	3.02663	+	2.06646i	0.109072	+	0.0744700i
$771$	−55.9401	+	32.2971i	−2.01463	+	1.16315i
$772$	11.9964			0.431760
$773$	14.2114	−	8.20497i	0.511149	−	0.295112i	−0.222157	−	0.975011i	$-0.571310\pi$
$773$	14.2114	−	8.20497i	0.511149	−	0.295112i	0.733306	+	0.679899i	$0.237976\pi$
$774$	−37.4223	−	10.0273i	−1.34512	−	0.360423i
$775$	−0.526647	−	0.715564i	−0.0189177	−	0.0257038i
$776$	−11.3490	−	19.6570i	−0.407404	−	0.705644i
$777$	−2.83655	−	10.5861i	−0.101761	−	0.379775i
$778$	17.2285	−	29.8406i	0.617671	−	1.06984i
$779$	18.9346			0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$	−14.2856	+	24.7434i	−0.510852	+	0.884822i
$783$	0.372446	+	1.38999i	0.0133101	+	0.0496741i
$784$	3.58492	+	6.20926i	0.128033	+	0.221759i
$785$	45.5610	+	3.44468i	1.62614	+	0.122946i
$786$	−0.171361	−	0.0459159i	−0.00611223	−	0.00163777i
$787$	11.7781	−	6.80008i	0.419844	−	0.242397i	−0.275167	−	0.961396i	$-0.588733\pi$
$787$	11.7781	−	6.80008i	0.419844	−	0.242397i	0.695010	+	0.719000i	$0.255400\pi$
$788$	13.6326			0.485642
$789$	3.14011	−	1.81294i	0.111791	−	0.0645424i
$790$	30.5253	−	5.75474i	1.08604	−	0.204745i
$791$	1.80058	−	0.482465i	0.0640214	−	0.0171545i
$792$	−16.9369	+	16.9369i	−0.601827	+	0.601827i
$793$		0			0
$794$		−	5.95255i		−	0.211248i
$795$	17.3082	−	3.26301i	0.613858	−	0.115727i
$796$	7.03076	−	12.1776i	0.249199	−	0.431625i
$797$	−28.9148	−	7.74769i	−1.02421	−	0.274437i	−0.292657	−	0.956218i	$-0.594539\pi$
$797$	−28.9148	−	7.74769i	−1.02421	−	0.274437i	−0.731557	+	0.681780i	$0.761206\pi$
$798$			7.50664i			0.265732i
$799$	14.7232	−	54.9476i	0.520868	−	1.94391i
$800$	−22.5134	+	8.80145i	−0.795969	+	0.311178i
$801$	1.74778	+	1.74778i	0.0617546	+	0.0617546i
$802$	0.0698734	−	0.260771i	0.00246732	−	0.00920815i
$803$	5.18527	−	1.38939i	0.182984	−	0.0490305i
$804$	−5.02343	−	18.7477i	−0.177163	−	0.661180i
$805$	0.625946	−	8.27906i	0.0220617	−	0.291799i
$806$		0			0
$807$	−15.6423	−	15.6423i	−0.550636	−	0.550636i
$808$	−25.5185	−	14.7331i	−0.897739	−	0.518310i
$809$	2.54661	+	1.47029i	0.0895342	+	0.0516926i	0.544099	−	0.839021i	$-0.316872\pi$
$809$	2.54661	+	1.47029i	0.0895342	+	0.0516926i	−0.454564	+	0.890714i	$0.650205\pi$
$810$	−1.24807	−	0.437646i	−0.0438526	−	0.0153773i
$811$	−16.3366	+	16.3366i	−0.573657	+	0.573657i	−0.933148	−	0.359492i	$-0.882950\pi$
$811$	−16.3366	+	16.3366i	−0.573657	+	0.573657i	0.359492	+	0.933148i	$0.382950\pi$
$812$	−0.134367	−	0.232730i	−0.00471536	−	0.00816724i
$813$	−1.24791	−	2.16144i	−0.0437660	−	0.0758050i
$814$	−4.90856	+	4.90856i	−0.172045	+	0.172045i
$815$	45.1248	+	15.8234i	1.58065	+	0.554270i
$816$	20.6647	+	11.9307i	0.723408	+	0.417660i
$817$	−18.8153	−	10.8630i	−0.658262	−	0.380048i
$818$	−26.8732	−	26.8732i	−0.939599	−	0.939599i
$819$		0			0
$820$	−1.11428	+	14.7380i	−0.0389124	+	0.514674i
$821$	−11.8735	−	44.3125i	−0.414388	−	1.54652i	−0.786059	−	0.618151i	$-0.787882\pi$
$821$	−11.8735	−	44.3125i	−0.414388	−	1.54652i	0.371672	−	0.928364i	$-0.378785\pi$
$822$	12.1605	−	3.25838i	0.424145	−	0.113649i
$823$	−4.58752	+	17.1209i	−0.159911	+	0.596796i	0.838724	+	0.544557i	$0.183302\pi$
$823$	−4.58752	+	17.1209i	−0.159911	+	0.596796i	−0.998635	+	0.0522385i	$0.983364\pi$
$824$	7.62280	+	7.62280i	0.265553	+	0.265553i
$825$	21.5860	−	8.43889i	0.751528	−	0.293804i
$826$	−1.28826	+	4.80785i	−0.0448242	+	0.167286i
$827$		−	5.79276i		−	0.201434i	−0.994915	−	0.100717i	$-0.967886\pi$
$827$		−	5.79276i		−	0.201434i	0.994915	−	0.100717i	$-0.0321137\pi$
$828$	16.9308	+	4.53660i	0.588387	+	0.157658i
$829$	−16.8799	+	29.2368i	−0.586262	+	1.01544i	0.408454	+	0.912779i	$0.366068\pi$
$829$	−16.8799	+	29.2368i	−0.586262	+	1.01544i	−0.994717	+	0.102657i	$0.967265\pi$
$830$	19.2540	−	3.62985i	0.668317	−	0.125994i
$831$		−	26.6284i		−	0.923727i
$832$		0			0
$833$	31.1279	−	31.1279i	1.07852	−	1.07852i
$834$	37.8473	−	10.1412i	1.31055	−	0.351160i
$835$	−3.76724	+	0.710216i	−0.130371	+	0.0245780i
$836$	−3.75741	+	2.16934i	−0.129953	+	0.0750282i
$837$	0.874920			0.0302417
$838$	30.0364	−	17.3415i	1.03759	−	0.599053i
$839$	37.8626	+	10.1452i	1.30716	+	0.350253i	0.844154	−	0.536101i	$-0.180103\pi$
$839$	37.8626	+	10.1452i	1.30716	+	0.350253i	0.463008	+	0.886354i	$0.346770\pi$
$840$	−18.0889	−	1.36763i	−0.624127	−	0.0471877i
$841$	−14.4573	−	25.0408i	−0.498527	−	0.863475i
$842$	8.06995	+	30.1175i	0.278109	+	1.03792i
$843$	−11.0041	+	19.0597i	−0.379002	+	0.656451i
$844$	8.14177			0.280251
$845$		0			0
$846$	38.2449			1.31489
$847$	3.96679	−	6.87068i	0.136300	−	0.236079i
$848$	0.863850	+	3.22393i	0.0296647	+	0.110710i
$849$	29.4076	+	50.9354i	1.00927	+	1.74810i
$850$	−21.9748	−	29.8575i	−0.753728	−	1.02410i
$851$	15.1908	+	4.07037i	0.520735	+	0.139531i
$852$	−30.0625	+	17.3566i	−1.02992	+	0.594626i
$853$	−40.6417			−1.39154			−0.695772	−	0.718262i	$-0.744938\pi$
$853$	−40.6417			−1.39154			−0.695772	+	0.718262i	$0.744938\pi$
$854$	−1.77785	+	1.02644i	−0.0608369	+	0.0351242i
$855$	24.0627	+	16.4290i	0.822926	+	0.561860i
$856$	−1.29713	+	0.347564i	−0.0443348	+	0.0118795i
$857$	27.2327	−	27.2327i	0.930252	−	0.930252i	−0.0674695	−	0.997721i	$-0.521493\pi$
$857$	27.2327	−	27.2327i	0.930252	−	0.930252i	0.997721	+	0.0674695i	$0.0214925\pi$
$858$		0			0
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	9.56262	−	14.0058i	0.326083	−	0.477595i
$861$	−9.30043	+	16.1088i	−0.316958	+	0.548987i
$862$	4.54213	+	1.21706i	0.154706	+	0.0414532i
$863$			55.4497i			1.88753i	0.330615	+	0.943766i	$0.392744\pi$
$863$			55.4497i			1.88753i	−0.330615	+	0.943766i	$0.607256\pi$
$864$	6.16090	−	22.9928i	0.209598	−	0.782230i
$865$	14.7041	+	30.5853i	0.499956	+	1.03993i
$866$	−2.89432	−	2.89432i	−0.0983531	−	0.0983531i
$867$	25.6562	−	95.7502i	0.871330	−	3.25185i
$868$	−0.157822	+	0.0422883i	−0.00535683	+	0.00143536i
$869$	5.84800	+	21.8250i	0.198380	+	0.740363i
$870$	1.85718	+	0.140414i	0.0629643	+	0.00476048i
$871$		0			0
$872$	−19.3993	−	19.3993i	−0.656944	−	0.656944i
$873$	−31.0154	−	17.9068i	−1.04971	−	0.606052i
$874$	−9.32869	−	5.38592i	−0.315548	−	0.182181i
$875$	9.51462	+	5.05285i	0.321653	+	0.170817i
$876$	−6.06917	+	6.06917i	−0.205058	+	0.205058i
$877$	2.68849	+	4.65661i	0.0907839	+	0.157242i	0.907841	−	0.419314i	$-0.137729\pi$
$877$	2.68849	+	4.65661i	0.0907839	+	0.157242i	−0.817057	+	0.576557i	$0.804396\pi$
$878$	−11.6188	−	20.1244i	−0.392116	−	0.679166i
$879$	7.92505	−	7.92505i	0.267305	−	0.267305i
$880$	1.90300	+	3.95832i	0.0641500	+	0.133435i
$881$	−37.0890	−	21.4133i	−1.24956	−	0.721434i	−0.278538	−	0.960425i	$-0.589850\pi$
$881$	−37.0890	−	21.4133i	−1.24956	−	0.721434i	−0.971022	+	0.238992i	$0.923183\pi$
$882$	25.6309	+	14.7980i	0.863037	+	0.498274i
$883$	−32.9568	−	32.9568i	−1.10908	−	1.10908i	−0.993271	−	0.115813i	$-0.963053\pi$
$883$	−32.9568	−	32.9568i	−1.10908	−	1.10908i	−0.115813	−	0.993271i	$-0.536947\pi$
$884$		0			0
$885$	20.5172	+	23.8733i	0.689677	+	0.802494i
$886$	0.691990	+	2.58254i	0.0232478	+	0.0867622i
$887$	20.4194	−	5.47136i	0.685616	−	0.183710i	0.100837	−	0.994903i	$-0.467848\pi$
$887$	20.4194	−	5.47136i	0.685616	−	0.183710i	0.584779	+	0.811193i	$0.301181\pi$
$888$	8.89336	−	33.1905i	0.298442	−	1.11380i
$889$	1.48203	+	1.48203i	0.0497057	+	0.0497057i
$890$	1.06863	−	0.513751i	0.0358204	−	0.0172210i
$891$	0.248992	−	0.929249i	0.00834153	−	0.0311310i
$892$		−	6.73778i		−	0.225598i
$893$	20.7162	+	5.55089i	0.693241	+	0.185753i
$894$	6.17340	−	10.6926i	0.206469	−	0.357616i
$895$	−1.14302	−	6.06302i	−0.0382071	−	0.202664i
$896$			2.11809i			0.0707605i
$897$		0			0
$898$	−23.2645	+	23.2645i	−0.776346	+	0.776346i
$899$	0.0501642	−	0.0134414i	0.00167307	−	0.000448297i
$900$	−14.2038	+	17.7627i	−0.473461	+	0.592090i
$901$	17.7471	−	10.2463i	0.591242	−	0.341354i
$902$	11.7817			0.392288
$903$	18.4836	−	10.6715i	0.615096	−	0.355126i
$904$	5.64533	+	1.51266i	0.187761	+	0.0503104i
$905$	−15.0944	−	17.5636i	−0.501756	−	0.583833i
$906$	−9.57200	−	16.5792i	−0.318008	−	0.550807i
$907$	2.86355	+	10.6869i	0.0950825	+	0.354853i	0.997032	−	0.0769889i	$-0.0245306\pi$
$907$	2.86355	+	10.6869i	0.0950825	+	0.354853i	−0.901949	+	0.431842i	$0.857864\pi$
$908$	8.19488	−	14.1940i	0.271957	−	0.471043i
$909$	−46.4928			−1.54207
$910$		0			0
$911$	−15.0479			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$911$	−15.0479			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$912$	−4.49810	+	7.79093i	−0.148947	+	0.257983i
$913$	3.68867	+	13.7663i	0.122077	+	0.455598i
$914$	−14.5045	−	25.1226i	−0.479767	−	0.830980i
$915$	−0.978791	+	12.9459i	−0.0323578	+	0.427980i
$916$	−11.6099	−	3.11086i	−0.383602	−	0.102786i
$917$	0.0519457	−	0.0299909i	0.00171540	−	0.000990386i
$918$	36.5067			1.20490
$919$	10.8342	−	6.25513i	0.357388	−	0.206338i	−0.310547	−	0.950558i	$-0.600512\pi$
$919$	10.8342	−	6.25513i	0.357388	−	0.206338i	0.667934	+	0.744220i	$0.267179\pi$
$920$	14.6782	−	21.4983i	0.483925	−	0.708778i
$921$	−65.1960	+	17.4692i	−2.14828	+	0.575630i
$922$	−8.32259	+	8.32259i	−0.274090	+	0.274090i
$923$		0			0
$924$		−	4.26220i		−	0.140216i
$925$	−12.7441	+	15.9372i	−0.419023	+	0.524013i
$926$	15.3114	−	26.5202i	0.503165	−	0.871508i
$927$	16.4299	+	4.40237i	0.539628	+	0.144593i
$928$		−	1.41296i		−	0.0463826i
$929$	−12.6170	+	47.0874i	−0.413952	+	1.54489i	0.372975	+	0.927841i	$0.378338\pi$
$929$	−12.6170	+	47.0874i	−0.413952	+	1.54489i	−0.786926	+	0.617047i	$0.788329\pi$
$930$	0.374711	−	1.06859i	0.0122872	−	0.0350404i
$931$	11.7357	+	11.7357i	0.384623	+	0.384623i
$932$	−6.14112	+	22.9190i	−0.201159	+	0.750736i
$933$	21.1920	−	5.67838i	0.693795	−	0.185902i
$934$	−6.03874	−	22.5369i	−0.197594	−	0.737429i
$935$	20.4512	−	17.5761i	0.668825	−	0.574800i
$936$		0			0
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	0.817306	−	0.576203i	$-0.195466\pi$
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	−0.576203	+	0.817306i	$0.695466\pi$
$938$	−6.22802	−	3.59575i	−0.203352	−	0.117405i
$939$	−11.5750	−	6.68281i	−0.377735	−	0.218085i
$940$	−5.53974	+	15.7981i	−0.180686	+	0.515277i
$941$	1.54410	−	1.54410i	0.0503363	−	0.0503363i	−0.681491	−	0.731827i	$-0.738668\pi$
$941$	1.54410	−	1.54410i	0.0503363	−	0.0503363i	0.731827	+	0.681491i	$0.238668\pi$
$942$	29.1172	+	50.4324i	0.948688	+	1.64318i
$943$	−13.3459	−	23.1158i	−0.434602	−	0.752753i
$944$	−4.21798	+	4.21798i	−0.137284	+	0.137284i
$945$	−9.56117	+	4.59662i	−0.311025	+	0.149528i
$946$	−11.7074	−	6.75929i	−0.380642	−	0.219764i
$947$	−5.81670	−	3.35827i	−0.189017	−	0.109129i	0.402505	−	0.915418i	$-0.368140\pi$
$947$	−5.81670	−	3.35827i	−0.189017	−	0.109129i	−0.591522	+	0.806289i	$0.701473\pi$
$948$	−25.5454	−	25.5454i	−0.829676	−	0.829676i
$949$		0			0
$950$	11.2568	−	8.28486i	0.365218	−	0.268796i
$951$	16.5361	+	61.7137i	0.536221	+	2.00121i
$952$	−20.3871	+	5.46272i	−0.660751	+	0.177048i
$953$	−4.67309	+	17.4402i	−0.151376	+	0.564944i	0.848012	+	0.529977i	$0.177799\pi$
$953$	−4.67309	+	17.4402i	−0.151376	+	0.564944i	−0.999388	+	0.0349673i	$0.988867\pi$
$954$	9.74205	+	9.74205i	0.315411	+	0.315411i
$955$	−39.2049	−	13.7476i	−1.26864	−	0.444860i
$956$	0.780600	−	2.91324i	0.0252464	−	0.0942208i
$957$			1.35475i			0.0437929i
$958$	38.3526	+	10.2765i	1.23912	+	0.332020i
$959$	−2.12828	+	3.68629i	−0.0687257	+	0.119036i
$960$	−37.5988	−	25.6709i	−1.21350	−	0.828526i
$961$			30.9684i			0.998981i
$962$		0			0
$963$	−1.49825	+	1.49825i	−0.0482804	+	0.0482804i
$964$	16.6086	−	4.45026i	0.534927	−	0.143333i
$965$	−5.20782	−	27.6241i	−0.167646	−	0.889253i
$966$	9.16426	−	5.29099i	0.294855	−	0.170235i
$967$	−60.0570			−1.93130			−0.965651	−	0.259841i	$-0.916330\pi$
$967$	−60.0570			−1.93130			−0.965651	+	0.259841i	$0.916330\pi$
$968$	21.5415	−	12.4370i	0.692369	−	0.399740i
$969$	53.3528	+	14.2958i	1.71394	+	0.459249i
$970$	−13.0294	+	11.1977i	−0.418348	+	0.359536i
$971$	20.4589	+	35.4359i	0.656558	+	1.13719i	0.981501	+	0.191459i	$0.0613218\pi$
$971$	20.4589	+	35.4359i	0.656558	+	1.13719i	−0.324942	+	0.945734i	$0.605345\pi$
$972$	4.04627	+	15.1009i	0.129784	+	0.484361i
$973$	−6.62390	+	11.4729i	−0.212352	+	0.367805i
$974$	−29.5983			−0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$	18.7479	−	32.4724i	0.599800	−	1.03888i	−0.393050	−	0.919517i	$-0.628580\pi$
$977$	18.7479	−	32.4724i	0.599800	−	1.03888i	0.992850	−	0.119367i	$-0.0380865\pi$
$978$	15.7740	+	58.8694i	0.504397	+	1.88244i
$979$	0.431236	+	0.746923i	0.0137824	+	0.0238718i
$980$	−9.82532	+	8.44405i	−0.313858	+	0.269735i
$981$	−41.8125	−	11.2036i	−1.33497	−	0.357704i
$982$	−6.44253	+	3.71959i	−0.205589	+	0.118697i
$983$	46.1176			1.47092			0.735461	−	0.677567i	$-0.236966\pi$
$983$	46.1176			1.47092			0.735461	+	0.677567i	$0.236966\pi$
$984$	−50.5056	+	29.1594i	−1.61006	+	0.929569i
$985$	−5.91812	−	31.3919i	−0.188567	−	1.00023i
$986$	2.09314	−	0.560854i	0.0666591	−	0.0178612i
$987$	−14.8980	+	14.8980i	−0.474208	+	0.474208i
$988$		0			0
$989$			30.6267i			0.973873i
$990$	14.9725	+	10.2226i	0.475859	+	0.324897i
$991$	−0.401099	+	0.694724i	−0.0127413	+	0.0220686i	−0.872326	−	0.488925i	$-0.837389\pi$
$991$	−0.401099	+	0.694724i	−0.0127413	+	0.0220686i	0.859584	+	0.510994i	$0.170722\pi$
$992$	−0.829802	−	0.222345i	−0.0263462	−	0.00705945i
$993$		−	93.5143i		−	2.96759i
$994$	−3.32894	+	12.4238i	−0.105587	+	0.394058i
$995$	−31.0936	−	10.9033i	−0.985734	−	0.345656i
$996$	−16.1129	−	16.1129i	−0.510558	−	0.510558i
$997$	4.04012	−	15.0779i	0.127952	−	0.477522i	−0.871976	−	0.489549i	$-0.837162\pi$
$997$	4.04012	−	15.0779i	0.127952	−	0.477522i	0.999928	+	0.0120264i	$0.00382820\pi$
$998$	−5.92576	+	1.58780i	−0.187577	+	0.0502610i
$999$	−5.20090	−	19.4100i	−0.164549	−	0.614106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.g.357.2		20
5.3	odd	4		845.2.t.g.188.4		20
13.2	odd	12		65.2.t.a.37.2	yes	20
13.3	even	3		845.2.o.f.587.2		20
13.4	even	6		845.2.k.e.577.3		20
13.5	odd	4		845.2.t.f.657.4		20
13.6	odd	12		845.2.f.e.437.3		20
13.7	odd	12		845.2.f.d.437.8		20
13.8	odd	4		845.2.t.e.657.2		20
13.9	even	3		845.2.k.d.577.8		20
13.10	even	6		845.2.o.e.587.4		20
13.11	odd	12		845.2.t.g.427.4		20
13.12	even	2		65.2.o.a.32.4	✓	20
39.2	even	12		585.2.dp.a.37.4		20
39.38	odd	2		585.2.cf.a.487.2		20
65.2	even	12		325.2.s.b.193.2		20
65.3	odd	12		845.2.t.e.418.2		20
65.8	even	4		845.2.o.f.488.2		20
65.12	odd	4		325.2.x.b.318.4		20
65.18	even	4		845.2.o.e.488.4		20
65.23	odd	12		845.2.t.f.418.4		20
65.28	even	12		65.2.o.a.63.4	yes	20
65.33	even	12		845.2.k.d.268.8		20
65.38	odd	4		65.2.t.a.58.2	yes	20
65.43	odd	12		845.2.f.e.408.8		20
65.48	odd	12		845.2.f.d.408.3		20
65.54	odd	12		325.2.x.b.232.4		20
65.58	even	12		845.2.k.e.268.3		20
65.63	even	12	inner	845.2.o.g.258.2		20
65.64	even	2		325.2.s.b.32.2		20
195.38	even	4		585.2.dp.a.253.4		20
195.158	odd	12		585.2.cf.a.388.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	13.12	even	2
65.2.o.a.63.4	yes	20	65.28	even	12
65.2.t.a.37.2	yes	20	13.2	odd	12
65.2.t.a.58.2	yes	20	65.38	odd	4
325.2.s.b.32.2		20	65.64	even	2
325.2.s.b.193.2		20	65.2	even	12
325.2.x.b.232.4		20	65.54	odd	12
325.2.x.b.318.4		20	65.12	odd	4
585.2.cf.a.388.2		20	195.158	odd	12
585.2.cf.a.487.2		20	39.38	odd	2
585.2.dp.a.37.4		20	39.2	even	12
585.2.dp.a.253.4		20	195.38	even	4
845.2.f.d.408.3		20	65.48	odd	12
845.2.f.d.437.8		20	13.7	odd	12
845.2.f.e.408.8		20	65.43	odd	12
845.2.f.e.437.3		20	13.6	odd	12
845.2.k.d.268.8		20	65.33	even	12
845.2.k.d.577.8		20	13.9	even	3
845.2.k.e.268.3		20	65.58	even	12
845.2.k.e.577.3		20	13.4	even	6
845.2.o.e.488.4		20	65.18	even	4
845.2.o.e.587.4		20	13.10	even	6
845.2.o.f.488.2		20	65.8	even	4
845.2.o.f.587.2		20	13.3	even	3
845.2.o.g.258.2		20	65.63	even	12	inner
845.2.o.g.357.2		20	1.1	even	1	trivial
845.2.t.e.418.2		20	65.3	odd	12
845.2.t.e.657.2		20	13.8	odd	4
845.2.t.f.418.4		20	65.23	odd	12
845.2.t.f.657.4		20	13.5	odd	4
845.2.t.g.188.4		20	5.3	odd	4
845.2.t.g.427.4		20	13.11	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.511309 + 0.885613i) q^{2} +(-0.721300 - 2.69193i) q^{3} +(0.477126 + 0.826407i) q^{4} +(1.69584 - 1.45744i) q^{5} +(2.75281 + 0.737614i) q^{6} +(-0.834479 + 0.481787i) q^{7} -3.02107 q^{8} +(-4.12812 + 2.38337i) q^{9} +(0.423625 + 2.24706i) q^{10} +(-1.60661 + 0.430490i) q^{11} +(1.88048 - 1.88048i) q^{12} -0.985368i q^{14} +(-5.14652 - 3.51384i) q^{15} +(0.590448 - 1.02269i) q^{16} +(-7.00342 - 1.87656i) q^{17} -4.87456i q^{18} +(0.707496 - 2.64041i) q^{19} +(2.01357 + 0.706075i) q^{20} +(1.89884 + 1.89884i) q^{21} +(0.440226 - 1.64295i) q^{22} +(-3.72214 + 0.997344i) q^{23} +(2.17910 + 8.13250i) q^{24} +(0.751762 - 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +(-0.796304 - 0.459747i) q^{28} +(0.253107 + 0.146132i) q^{29} +(5.74336 - 2.76117i) q^{30} +(0.125649 - 0.125649i) q^{31} +(-2.41727 - 4.18683i) q^{32} +(2.31769 + 4.01436i) q^{33} +(5.24282 - 5.24282i) q^{34} +(-0.712972 + 2.03323i) q^{35} +(-3.93927 - 2.27434i) q^{36} +(-3.53443 - 2.04061i) q^{37} +(1.97663 + 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(1.79277 + 6.69071i) q^{41} +(-2.65254 + 0.710745i) q^{42} +(2.05706 - 7.67707i) q^{43} +(-1.12232 - 1.12232i) q^{44} +(-3.52703 + 10.0583i) q^{45} +(1.01990 - 3.80633i) q^{46} +7.84582i q^{47} +(-3.17888 - 0.851780i) q^{48} +(-3.03576 + 5.25810i) q^{49} +(3.99335 + 3.19325i) q^{50} +20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(-4.86351 + 1.30317i) q^{54} +(-2.09714 + 3.07157i) q^{55} +(2.52102 - 1.45551i) q^{56} -7.61811 q^{57} +(-0.258832 + 0.149437i) q^{58} +(-4.87924 - 1.30739i) q^{59} +(0.448318 - 5.92967i) q^{60} +(-1.04169 - 1.80425i) q^{61} +(0.0470311 + 0.175522i) q^{62} +(2.29655 - 3.97775i) q^{63} +7.30568 q^{64} -4.74023 q^{66} +(3.64915 - 6.32050i) q^{67} +(-1.79071 - 6.68304i) q^{68} +(5.36956 + 9.30034i) q^{69} +(-1.43611 - 1.67103i) q^{70} +(-12.6082 - 3.37837i) q^{71} +(12.4713 - 7.20034i) q^{72} -3.22747 q^{73} +(3.61437 - 2.08676i) q^{74} +(-13.8489 + 1.54181i) q^{75} +(2.51962 - 0.675130i) q^{76} +(1.13328 - 1.13328i) q^{77} -13.5845i q^{79} +(-0.489192 - 2.59485i) q^{80} +(-0.289196 + 0.500902i) q^{81} +(-6.84204 - 1.83332i) q^{82} -8.56854i q^{83} +(-0.663230 + 2.47521i) q^{84} +(-14.6117 + 7.02469i) q^{85} +(5.74712 + 5.74712i) q^{86} +(0.210809 - 0.786751i) q^{87} +(4.85368 - 1.30054i) q^{88} +(-0.134207 - 0.500868i) q^{89} +(-7.10435 - 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +(-0.428870 - 0.247608i) q^{93} +(-6.94836 - 4.01164i) q^{94} +(-2.64843 - 5.50885i) q^{95} +(-9.52707 + 9.52707i) q^{96} +(3.75660 + 6.50662i) q^{97} +(-3.10442 - 5.37702i) q^{98} +(5.60626 - 5.60626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

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