LMFDB - Embedded newform 325.2.s.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(32,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("325.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.s (of order $12$, degree $4$, 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:	$2.59513806569$
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			193.2
Root			$1.02262i$ of defining polynomial
Character	$\chi$	$=$	325.193
Dual form			325.2.s.b.32.2

$q$-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} +(-2.75281 + 0.737614i) q^{6} +(-0.834479 - 0.481787i) q^{7} -3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +(1.60661 + 0.430490i) q^{11} +(-1.88048 - 1.88048i) q^{12} +(-1.82127 + 3.11175i) q^{13} +0.985368i q^{14} +(0.590448 + 1.02269i) q^{16} +(7.00342 - 1.87656i) q^{17} +4.87456i q^{18} +(-0.707496 - 2.64041i) q^{19} +(-1.89884 + 1.89884i) q^{21} +(-0.440226 - 1.64295i) q^{22} +(3.72214 + 0.997344i) q^{23} +(-2.17910 + 8.13250i) q^{24} +(3.68704 + 0.0218799i) q^{26} +(-3.48159 + 3.48159i) q^{27} +(-0.796304 + 0.459747i) q^{28} +(0.253107 - 0.146132i) q^{29} +(-0.125649 - 0.125649i) q^{31} +(-2.41727 + 4.18683i) q^{32} +(2.31769 - 4.01436i) q^{33} +(-5.24282 - 5.24282i) q^{34} +(-3.93927 + 2.27434i) q^{36} +(-3.53443 + 2.04061i) q^{37} +(-1.97663 + 1.97663i) q^{38} +(7.06291 + 7.14724i) q^{39} +(-1.79277 + 6.69071i) q^{41} +(2.65254 + 0.710745i) q^{42} +(-2.05706 - 7.67707i) q^{43} +(1.12232 - 1.12232i) q^{44} +(-1.01990 - 3.80633i) q^{46} -7.84582i q^{47} +(3.17888 - 0.851780i) q^{48} +(-3.03576 - 5.25810i) q^{49} -20.2063i q^{51} +(1.70259 + 2.98981i) q^{52} +(1.99855 + 1.99855i) q^{53} +(4.86351 + 1.30317i) q^{54} +(2.52102 + 1.45551i) q^{56} -7.61811 q^{57} +(-0.258832 - 0.149437i) q^{58} +(4.87924 - 1.30739i) q^{59} +(-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} +(12.6082 - 3.37837i) q^{71} +(12.4713 + 7.20034i) q^{72} -3.22747 q^{73} +(3.61437 + 2.08676i) q^{74} +(-2.51962 - 0.675130i) q^{76} +(-1.13328 - 1.13328i) q^{77} +(2.71836 - 9.90945i) q^{78} +13.5845i q^{79} +(-0.289196 - 0.500902i) q^{81} +(6.84204 - 1.83332i) q^{82} +8.56854i q^{83} +(0.663230 + 2.47521i) q^{84} +(-5.74712 + 5.74712i) q^{86} +(-0.210809 - 0.786751i) q^{87} +(-4.85368 - 1.30054i) q^{88} +(0.134207 - 0.500868i) q^{89} +(3.01901 - 1.71922i) q^{91} +(2.60014 - 2.60014i) q^{92} +(-0.428870 + 0.247608i) q^{93} +(-6.94836 + 4.01164i) q^{94} +(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} - 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{11} - 24 q^{12} - 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} + 4 q^{21} - 16 q^{22} + 2 q^{23} - 32 q^{24} - 24 q^{26}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 + 2 * q^3 - 6 * q^4 - 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 16 * q^11 - 24 * q^12 - 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 + 4 * q^21 - 16 * q^22 + 2 * q^23 - 32 * q^24 - 24 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^32 + 18 * q^33 - 2 * q^34 + 36 * q^36 - 42 * q^37 - 8 * q^38 - 4 * q^39 + 10 * q^41 + 56 * q^42 + 22 * q^43 + 36 * q^44 + 4 * q^46 - 28 * q^48 - 18 * q^49 - 46 * q^52 + 10 * q^53 + 48 * q^54 + 12 * q^57 + 90 * q^58 + 16 * q^59 - 16 * q^61 + 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 - 28 * q^68 + 16 * q^69 - 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 64 * q^76 - 28 * q^77 - 32 * q^78 - 14 * q^81 - 22 * q^82 + 40 * q^84 + 60 * q^86 - 62 * q^87 - 50 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^93 + 48 * q^94 + 56 * q^96 + 22 * q^97 - 4 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

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	0.626666	−	0.779288i	$-0.284419\pi$
$2$	−0.511309	−	0.885613i	−0.361550	−	0.626223i	−0.988216	+	0.153065i	$0.951086\pi$
$3$	0.721300	−	2.69193i	0.416443	−	1.55418i	−0.365486	−	0.930817i	$-0.619097\pi$
$3$	0.721300	−	2.69193i	0.416443	−	1.55418i	0.781929	−	0.623368i	$-0.214236\pi$
$4$	0.477126	−	0.826407i	0.238563	−	0.413204i
$5$		0			0
$5$		0			0
$6$	−2.75281	+	0.737614i	−1.12383	+	0.301130i
$7$	−0.834479	−	0.481787i	−0.315404	−	0.182098i	0.333938	−	0.942595i	$-0.391622\pi$
$7$	−0.834479	−	0.481787i	−0.315404	−	0.182098i	−0.649342	+	0.760497i	$0.724956\pi$
$8$	−3.02107			−1.06811
$9$	−4.12812	−	2.38337i	−1.37604	−	0.794457i
$10$		0			0
$11$	1.60661	+	0.430490i	0.484411	+	0.129797i	0.492756	−	0.870168i	$-0.335990\pi$
$11$	1.60661	+	0.430490i	0.484411	+	0.129797i	−0.00834492	+	0.999965i	$0.502656\pi$
$12$	−1.88048	−	1.88048i	−0.542847	−	0.542847i
$13$	−1.82127	+	3.11175i	−0.505130	+	0.863043i
$13$	−1.82127	+	3.11175i	−0.505130	+	0.863043i
$14$			0.985368i			0.263351i
$15$		0			0
$16$	0.590448	+	1.02269i	0.147612	+	0.255671i
$17$	7.00342	−	1.87656i	1.69858	−	0.455133i	0.725998	−	0.687697i	$-0.241378\pi$
$17$	7.00342	−	1.87656i	1.69858	−	0.455133i	0.972581	+	0.232564i	$0.0747114\pi$
$18$			4.87456i			1.14894i
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	−0.998368	−	0.0571095i	$-0.981812\pi$
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	0.836057	−	0.548642i	$-0.184855\pi$
$20$		0			0
$21$	−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	$-0.285069\pi$
$23$	3.72214	+	0.997344i	0.776120	+	0.207961i	0.151046	+	0.988527i	$0.451736\pi$
$24$	−2.17910	+	8.13250i	−0.444806	+	1.66004i
$25$		0			0
$26$	3.68704	+	0.0218799i	0.723087	+	0.00429099i
$27$	−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	−0.476315	−	0.879274i	$-0.658028\pi$
$29$	0.253107	−	0.146132i	0.0470008	−	0.0271360i	0.523316	+	0.852139i	$0.324695\pi$
$30$		0			0
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	0.695733	−	0.718300i	$-0.255080\pi$
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	−0.718300	+	0.695733i	$0.755080\pi$
$32$	−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			0
$36$	−3.93927	+	2.27434i	−0.656545	+	0.379057i
$37$	−3.53443	+	2.04061i	−0.581057	+	0.335474i	−0.761553	−	0.648102i	$-0.775563\pi$
$37$	−3.53443	+	2.04061i	−0.581057	+	0.335474i	0.180496	+	0.983576i	$0.442230\pi$
$38$	−1.97663	+	1.97663i	−0.320652	+	0.320652i
$39$	7.06291	+	7.14724i	1.13097	+	1.14447i
$40$		0			0
$41$	−1.79277	+	6.69071i	−0.279984	+	1.04491i	0.672444	+	0.740148i	$0.265245\pi$
$41$	−1.79277	+	6.69071i	−0.279984	+	1.04491i	−0.952427	+	0.304765i	$0.901422\pi$
$42$	2.65254	+	0.710745i	0.409295	+	0.109670i
$43$	−2.05706	−	7.67707i	−0.313699	−	1.17074i	−0.925194	−	0.379494i	$-0.876098\pi$
$43$	−2.05706	−	7.67707i	−0.313699	−	1.17074i	0.611495	−	0.791248i	$-0.290568\pi$
$44$	1.12232	−	1.12232i	0.169195	−	0.169195i
$45$		0			0
$46$	−1.01990	−	3.80633i	−0.150376	−	0.561212i
$47$		−	7.84582i		−	1.14443i	−0.820103	−	0.572215i	$-0.806084\pi$
$47$		−	7.84582i		−	1.14443i	0.820103	−	0.572215i	$-0.193916\pi$
$48$	3.17888	−	0.851780i	0.458832	−	0.122944i
$49$	−3.03576	−	5.25810i	−0.433680	−	0.751156i
$50$		0			0
$51$		−	20.2063i		−	2.82944i
$52$	1.70259	+	2.98981i	0.236107	+	0.414612i
$53$	1.99855	+	1.99855i	0.274522	+	0.274522i	0.830918	−	0.556395i	$-0.187816\pi$
$53$	1.99855	+	1.99855i	0.274522	+	0.274522i	−0.556395	+	0.830918i	$0.687816\pi$
$54$	4.86351	+	1.30317i	0.661840	+	0.177339i
$55$		0			0
$56$	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	$-0.476684\pi$
$59$	4.87924	−	1.30739i	0.635223	−	0.170207i	0.562039	+	0.827111i	$0.310017\pi$
$60$		0			0
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	−0.924975	−	0.380027i	$-0.875915\pi$
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	0.791601	+	0.611038i	$0.209248\pi$
$62$	−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	0.998109	−	0.0614765i	$-0.0195809\pi$
$67$	3.64915	+	6.32050i	0.445814	+	0.772173i	−0.552294	+	0.833649i	$0.686248\pi$
$68$	1.79071	−	6.68304i	0.217156	−	0.810437i
$69$	5.36956	−	9.30034i	0.646419	−	1.11963i
$70$		0			0
$71$	12.6082	−	3.37837i	1.49632	−	0.400939i	0.584457	−	0.811425i	$-0.301308\pi$
$71$	12.6082	−	3.37837i	1.49632	−	0.400939i	0.911867	+	0.410486i	$0.134641\pi$
$72$	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
$75$		0			0
$76$	−2.51962	−	0.675130i	−0.289020	−	0.0774427i
$77$	−1.13328	−	1.13328i	−0.129149	−	0.129149i
$78$	2.71836	−	9.90945i	0.307793	−	1.12202i
$79$			13.5845i			1.52838i	0.644992	+	0.764190i	$0.276861\pi$
$79$			13.5845i			1.52838i	−0.644992	+	0.764190i	$0.723139\pi$
$80$		0			0
$81$	−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	$0.155840\pi$
$83$			8.56854i			0.940519i	−0.882528	+	0.470260i	$0.844160\pi$
$84$	0.663230	+	2.47521i	0.0723643	+	0.270067i
$85$		0			0
$86$	−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	$-0.907918\pi$
$89$	0.134207	−	0.500868i	0.0142259	−	0.0530919i	0.972674	+	0.232175i	$0.0745843\pi$
$90$		0			0
$91$	3.01901	−	1.71922i	0.316479	−	0.180223i
$92$	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
$95$		0			0
$96$	9.52707	+	9.52707i	0.972353	+	0.972353i
$97$	3.75660	−	6.50662i	0.381425	−	0.660648i	−0.609841	−	0.792524i	$-0.708767\pi$
$97$	3.75660	−	6.50662i	0.381425	−	0.660648i	0.991266	+	0.131876i	$0.0421001\pi$
$98$	−3.10442	+	5.37702i	−0.313594	+	0.543161i
$99$	−5.60626	−	5.60626i	−0.563450	−	0.563450i
$100$		0			0
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	−0.0169388	−	0.999857i	$-0.505392\pi$
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	0.857432	+	0.514598i	$0.172059\pi$
$102$	−17.8949	+	10.3316i	−1.77186	+	1.02298i
$103$	2.52321	−	2.52321i	0.248619	−	0.248619i	−0.571784	−	0.820404i	$-0.693749\pi$
$103$	2.52321	−	2.52321i	0.248619	−	0.248619i	0.820404	+	0.571784i	$0.193749\pi$
$104$	5.50220	−	9.40081i	0.539535	−	0.921825i
$105$		0			0
$106$	0.748066	−	2.79182i	0.0726586	−	0.271166i
$107$	−0.429359	−	0.115046i	−0.0415077	−	0.0111220i	0.238005	−	0.971264i	$-0.423506\pi$
$107$	−0.429359	−	0.115046i	−0.0415077	−	0.0111220i	−0.279513	+	0.960142i	$0.590173\pi$
$108$	1.21605	+	4.53837i	0.117015	+	0.436705i
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	−0.944258	−	0.329206i	$-0.893219\pi$
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	0.329206	+	0.944258i	$0.393219\pi$
$110$		0			0
$111$	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	$-0.554329\pi$
$113$	1.86865	−	0.500704i	0.175788	−	0.0471023i	0.345639	+	0.938367i	$0.387662\pi$
$114$	3.89521	+	6.74670i	0.364820	+	0.631886i
$115$		0			0
$116$		−	0.278893i		−	0.0258946i
$117$	14.9349	−	8.50489i	1.38073	−	0.786277i
$118$	−3.65264	−	3.65264i	−0.336253	−	0.336253i
$119$	−6.74831	−	1.80821i	−0.618617	−	0.165758i
$120$		0			0
$121$	−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
$125$		0			0
$126$	2.34850	−	4.06772i	0.209221	−	0.362381i
$127$	0.562967	−	2.10102i	0.0499553	−	0.186436i	−0.936440	−	0.350829i	$-0.885900\pi$
$127$	0.562967	−	2.10102i	0.0499553	−	0.186436i	0.986395	+	0.164393i	$0.0525666\pi$
$128$	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
$135$		0			0
$136$	−21.1578	+	5.66923i	−1.81427	+	0.486132i
$137$	3.82564	+	2.20873i	0.326846	+	0.188705i	0.654440	−	0.756114i	$-0.272904\pi$
$137$	3.82564	+	2.20873i	0.326846	+	0.188705i	−0.327594	+	0.944819i	$0.606238\pi$
$138$	−10.9820			−0.934850
$139$	11.9066	+	6.87430i	1.00991	+	0.583070i	0.911165	−	0.412043i	$-0.135184\pi$
$139$	11.9066	+	6.87430i	1.00991	+	0.583070i	0.0987430	+	0.995113i	$0.468518\pi$
$140$		0			0
$141$	−21.1204	−	5.65919i	−1.77866	−	0.476590i
$142$	−9.43864	−	9.43864i	−0.792073	−	0.792073i
$143$	−4.26565	+	4.21532i	−0.356711	+	0.352503i
$144$		−	5.62903i		−	0.469085i
$145$		0			0
$146$	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	$-0.140121\pi$
$149$	−1.12129	−	4.18471i	−0.0918596	−	0.342825i	−0.996525	+	0.0832987i	$0.973454\pi$
$150$		0			0
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	−0.486910	−	0.873452i	$-0.661876\pi$
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	0.873452	+	0.486910i	$0.161876\pi$
$152$	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			0
$156$	9.27643	−	2.42670i	0.742709	−	0.194292i
$157$	−14.4488	+	14.4488i	−1.15314	+	1.15314i	−0.167218	+	0.985920i	$0.553478\pi$
$157$	−14.4488	+	14.4488i	−1.15314	+	1.15314i	−0.985920	+	0.167218i	$0.946522\pi$
$158$	12.0306	−	6.94589i	0.957106	−	0.552586i
$159$	6.82151	−	3.93840i	0.540981	−	0.312336i
$160$		0			0
$161$	−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	−0.0544633	−	0.998516i	$-0.517345\pi$
$163$	10.6926	−	18.5201i	0.837508	−	1.45061i	0.891972	−	0.452091i	$-0.149322\pi$
$164$	4.67387	+	4.67387i	0.364968	+	0.364968i
$165$		0			0
$166$	7.58841	−	4.38117i	0.588975	−	0.340045i
$167$	−1.48475	+	0.857220i	−0.114893	+	0.0663337i	−0.556345	−	0.830951i	$-0.687797\pi$
$167$	−1.48475	+	0.857220i	−0.114893	+	0.0663337i	0.441452	+	0.897285i	$0.354464\pi$
$168$	5.73655	−	5.73655i	0.442584	−	0.442584i
$169$	−6.36593	−	11.3347i	−0.489687	−	0.871898i
$170$		0			0
$171$	−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	0.938281	+	0.345875i	$0.112418\pi$
$173$	3.92804	+	14.6596i	0.298643	+	1.11455i	−0.639638	+	0.768677i	$0.720916\pi$
$174$	−0.588968	+	0.588968i	−0.0446496	+	0.0446496i
$175$		0			0
$176$	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	0.912967	−	0.408033i	$-0.133785\pi$
$179$	1.37961	+	2.38956i	0.103117	+	0.178604i	−0.809850	+	0.586637i	$0.800452\pi$
$180$		0			0
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$	−3.06621	−	1.79462i	−0.227283	−	0.133026i
$183$	4.10555	+	4.10555i	0.303491	+	0.303491i
$184$	−11.2449	−	3.01305i	−0.828981	−	0.222125i
$185$		0			0
$186$	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
$190$		0			0
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	0.305093	+	0.952322i	$0.401312\pi$
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	−0.977282	+	0.211943i	$0.932021\pi$
$192$	5.26958	−	19.6663i	0.380299	−	1.41930i
$193$	6.28576	+	10.8872i	0.452459	+	0.783681i	0.998538	−	0.0540520i	$-0.0172137\pi$
$193$	6.28576	+	10.8872i	0.452459	+	0.783681i	−0.546079	+	0.837733i	$0.683880\pi$
$194$	−7.68313			−0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	7.14308	+	12.3722i	0.508924	+	0.881481i	0.999947	+	0.0103349i	$0.00328975\pi$
$197$	7.14308	+	12.3722i	0.508924	+	0.881481i	−0.491023	+	0.871147i	$0.663377\pi$
$198$	−2.09845	+	7.83150i	−0.149130	+	0.556561i
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	0.477373	+	0.878701i	$0.341589\pi$
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	−0.999664	+	0.0259331i	$0.991744\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−3.52473	−	0.944449i	−0.245580	−	0.0658029i
$207$	−12.9884	−	12.9884i	−0.902756	−	0.902756i
$208$	−4.25770	−	0.0252664i	−0.295219	−	0.00175191i
$209$		−	4.54668i		−	0.314500i
$210$		0			0
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	0.974678	−	0.223611i	$-0.0717845\pi$
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	−0.680992	+	0.732291i	$0.738451\pi$
$212$	2.60518	−	0.698056i	0.178925	−	0.0479427i
$213$		−	36.3773i		−	2.49253i
$214$	0.117649	+	0.439070i	0.00804229	+	0.0300142i
$215$		0			0
$216$	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
$220$		0			0
$221$	−6.91576	+	25.2106i	−0.465205	+	1.69585i
$222$	8.22445	−	8.22445i	0.551989	−	0.551989i
$223$	−6.11483	+	3.53040i	−0.409479	+	0.236413i	−0.690566	−	0.723269i	$-0.742638\pi$
$223$	−6.11483	+	3.53040i	−0.409479	+	0.236413i	0.281087	+	0.959682i	$0.409305\pi$
$224$	4.03432	−	2.32922i	0.269555	−	0.155627i
$225$		0			0
$226$	−1.39889	−	1.39889i	−0.0930527	−	0.0930527i
$227$	−8.58775	+	14.8744i	−0.569989	+	0.987249i	0.426578	+	0.904451i	$0.359719\pi$
$227$	−8.58775	+	14.8744i	−0.569989	+	0.987249i	−0.996566	+	0.0827985i	$0.973614\pi$
$228$	−3.63480	+	6.29566i	−0.240721	+	0.416940i
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	0.937240	−	0.348684i	$-0.113371\pi$
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	−0.348684	+	0.937240i	$0.613371\pi$
$230$		0			0
$231$	−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	−0.165666	+	0.986182i	$0.552977\pi$
$233$	−17.5822	+	17.5822i	−1.15185	+	1.15185i	−0.986182	+	0.165666i	$0.947023\pi$
$234$	−15.1684	−	8.87790i	−0.991588	−	0.580366i
$235$		0			0
$236$	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	$-0.717405\pi$
$239$	2.23488	−	2.23488i	0.144562	−	0.144562i	0.775684	+	0.631122i	$0.217405\pi$
$240$		0			0
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	−0.936825	−	0.349797i	$-0.886250\pi$
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	0.636416	−	0.771346i	$-0.280416\pi$
$242$			8.41971i			0.541239i
$243$	−15.8248	+	4.24025i	−1.01516	+	0.272012i
$244$	0.994033	+	1.72172i	0.0636364	+	0.110222i
$245$		0			0
$246$		−	19.7406i		−	1.25862i
$247$	9.50483	+	2.60736i	0.604778	+	0.165902i
$248$	0.379596	+	0.379596i	0.0241044	+	0.0241044i
$249$	23.0659	+	6.18048i	1.46174	+	0.391672i
$250$		0			0
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	0.830658	−	0.556782i	$-0.187964\pi$
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	−0.0668586	+	0.997762i	$0.521298\pi$
$252$	4.38299			0.276102
$253$	5.55068	+	3.20468i	0.348968	+	0.201477i
$254$	−2.14854	+	0.575700i	−0.134812	+	0.0361227i
$255$		0			0
$256$	8.42962	−	14.6005i	0.526851	−	0.912533i
$257$	5.99887	−	22.3881i	0.374199	−	1.39653i	−0.480312	−	0.877098i	$-0.659476\pi$
$257$	5.99887	−	22.3881i	0.374199	−	1.39653i	0.854511	−	0.519433i	$-0.173857\pi$
$258$	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	$-0.929438\pi$
$263$	−0.336737	+	1.25672i	−0.0207641	+	0.0774926i	0.954766	+	0.297357i	$0.0961052\pi$
$264$	−7.00191	+	12.1277i	−0.430938	+	0.746407i
$265$		0			0
$266$	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	0.694706	−	0.719294i	$-0.255534\pi$
$269$	6.87429	+	3.96887i	0.419133	+	0.241986i	−0.275574	+	0.961280i	$0.588868\pi$
$270$		0			0
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	0.232450	−	0.972608i	$-0.425326\pi$
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	−0.284997	+	0.958528i	$0.591993\pi$
$272$	6.05429	+	6.05429i	0.367095	+	0.367095i
$273$	−2.45041	−	9.36704i	−0.148305	−	0.566919i
$274$		−	4.51738i		−	0.272905i
$275$		0			0
$276$	−5.12391	−	8.87488i	−0.308423	−	0.534205i
$277$	−9.22930	+	2.47298i	−0.554535	+	0.148587i	−0.525194	−	0.850982i	$-0.676007\pi$
$277$	−9.22930	+	2.47298i	−0.554535	+	0.148587i	−0.0293404	+	0.999569i	$0.509341\pi$
$278$		−	14.0596i		−	0.843236i
$279$	0.219227	+	0.818165i	0.0131248	+	0.0489823i
$280$		0			0
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	−0.520651	−	0.853769i	$-0.674311\pi$
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	0.853769	+	0.520651i	$0.174311\pi$
$282$	5.78719	+	21.5981i	0.344622	+	1.28615i
$283$	20.3851	+	5.46218i	1.21177	+	0.324693i	0.807457	−	0.589927i	$-0.200843\pi$
$283$	20.3851	+	5.46218i	1.21177	+	0.324693i	0.404314	+	0.914620i	$0.367510\pi$
$284$	3.22382	−	12.0315i	0.191298	−	0.713936i
$285$		0			0
$286$	5.91420	+	1.62238i	0.349714	+	0.0959335i
$287$	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			0
$291$	−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	−0.801293	−	0.598272i	$-0.795854\pi$
$293$	2.01079	−	3.48280i	0.117472	−	0.203467i	0.918765	+	0.394805i	$0.129188\pi$
$294$	12.2353	+	12.2353i	0.713579	+	0.713579i
$295$		0			0
$296$	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
$299$	−9.88252	+	9.76592i	−0.571521	+	0.564778i
$300$		0			0
$301$	−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
$305$		0			0
$306$	9.14740	+	34.1386i	0.522922	+	1.95157i
$307$			24.2191i			1.38226i	0.722732	+	0.691128i	$0.242886\pi$
$307$			24.2191i			1.38226i	−0.722732	+	0.691128i	$0.757114\pi$
$308$	−1.47727	+	0.395832i	−0.0841750	+	0.0225546i
$309$	−4.97231	−	8.61229i	−0.282865	−	0.489936i
$310$		0			0
$311$		−	7.87243i		−	0.446405i	−0.974772	−	0.223202i	$-0.928349\pi$
$311$		−	7.87243i		−	0.446405i	0.974772	−	0.223202i	$-0.0716511\pi$
$312$	−21.3376	−	21.5923i	−1.20800	−	1.22242i
$313$	−3.39121	−	3.39121i	−0.191683	−	0.191683i	0.604740	−	0.796423i	$-0.293277\pi$
$313$	−3.39121	−	3.39121i	−0.191683	−	0.191683i	−0.796423	+	0.604740i	$0.793277\pi$
$314$	20.1838	+	5.40824i	1.13904	+	0.305204i
$315$		0			0
$316$	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
$320$		0			0
$321$	−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
$330$		0			0
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.990858	−	0.134910i	$-0.956925\pi$
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.790653	+	0.612264i	$0.790259\pi$
$332$	7.08110	+	4.08828i	0.388626	+	0.224373i
$333$	19.4541			1.06608
$334$	1.51833	+	0.876609i	0.0830794	+	0.0479659i
$335$		0			0
$336$	−3.06309	−	0.820752i	−0.167105	−	0.0447757i
$337$	−14.5544	−	14.5544i	−0.792826	−	0.792826i	0.189126	−	0.981953i	$-0.439434\pi$
$337$	−14.5544	−	14.5544i	−0.792826	−	0.792826i	−0.981953	+	0.189126i	$0.939434\pi$
$338$	−6.78318	+	11.4333i	−0.368957	+	0.621888i
$339$		−	5.39143i		−	0.292822i
$340$		0			0
$341$	−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
$345$		0			0
$346$	10.9743	−	10.9743i	0.589983	−	0.589983i
$347$	−5.90442	−	22.0356i	−0.316966	−	1.18293i	−0.922145	−	0.386844i	$-0.873565\pi$
$347$	−5.90442	−	22.0356i	−0.316966	−	1.18293i	0.605179	−	0.796089i	$-0.293101\pi$
$348$	−0.750759	−	0.201165i	−0.0402449	−	0.0107836i
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	−0.855918	−	0.517111i	$-0.827008\pi$
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	0.999803	−	0.0198718i	$-0.00632581\pi$
$350$		0			0
$351$	−4.49290	−	17.1748i	−0.239813	−	0.916721i
$352$	−5.68599	+	5.68599i	−0.303064	+	0.303064i
$353$	−3.72420	+	2.15017i	−0.198219	+	0.114442i	−0.595825	−	0.803115i	$-0.703175\pi$
$353$	−3.72420	+	2.15017i	−0.198219	+	0.114442i	0.397605	+	0.917556i	$0.369841\pi$
$354$	−12.4673	+	7.19799i	−0.662629	+	0.382569i
$355$		0			0
$356$	−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	$-0.122771\pi$
$359$	10.4273	+	10.4273i	0.550333	+	0.550333i	−0.376204	+	0.926537i	$0.622771\pi$
$360$		0			0
$361$	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
$364$	0.0196734	−	3.31522i	0.00103117	−	0.173765i
$365$		0			0
$366$	1.53673	−	5.73514i	0.0803259	−	0.299780i
$367$	11.0341	+	2.95657i	0.575973	+	0.154331i	0.535034	−	0.844830i	$-0.320299\pi$
$367$	11.0341	+	2.95657i	0.575973	+	0.154331i	0.0409383	+	0.999162i	$0.486965\pi$
$368$	1.17776	+	4.39546i	0.0613950	+	0.229129i
$369$	23.3472	−	23.3472i	1.21541	−	1.21541i
$370$		0			0
$371$	−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	$-0.323339\pi$
$373$	27.1975	−	7.28755i	1.40823	−	0.377335i	0.881294	+	0.472568i	$0.156673\pi$
$374$	−6.16618	−	10.6801i	−0.318846	−	0.552257i
$375$		0			0
$376$			23.7028i			1.22238i
$377$	−0.00625324	+	1.05375i	−0.000322058	+	0.0542709i
$378$	−3.43065	−	3.43065i	−0.176453	−	0.176453i
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.186987	−	0.982362i	$-0.559872\pi$
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.653116	+	0.757258i	$0.726539\pi$
$380$		0			0
$381$	−5.24973	−	3.03093i	−0.268952	−	0.155279i
$382$	18.9999			0.972119
$383$	5.71918	+	3.30197i	0.292236	+	0.168723i	0.638950	−	0.769248i	$-0.279369\pi$
$383$	5.71918	+	3.30197i	0.292236	+	0.168723i	−0.346714	+	0.937971i	$0.612702\pi$
$384$	5.91729	−	1.58553i	0.301966	−	0.0809114i
$385$		0			0
$386$	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
$395$		0			0
$396$	−7.30795	+	1.95816i	−0.367238	+	0.0984012i
$397$	−5.04104	−	2.91045i	−0.253002	−	0.146071i	0.368136	−	0.929772i	$-0.379996\pi$
$397$	−5.04104	−	2.91045i	−0.253002	−	0.146071i	−0.621138	+	0.783701i	$0.713329\pi$
$398$	15.0689			0.755337
$399$	6.35716	+	3.67031i	0.318256	+	0.183745i
$400$		0			0
$401$	0.255004	+	0.0683280i	0.0127343	+	0.00341214i	0.265181	−	0.964199i	$-0.414568\pi$
$401$	0.255004	+	0.0683280i	0.0127343	+	0.00341214i	−0.252446	+	0.967611i	$0.581235\pi$
$402$	−14.7075	−	14.7075i	−0.733544	−	0.733544i
$403$	0.619831	−	0.162147i	0.0308760	−	0.00807713i
$404$		−	9.30738i		−	0.463060i
$405$		0			0
$406$	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	0.619042	+	0.785358i	$0.287521\pi$
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	−0.143427	+	0.989661i	$0.545812\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	−8.62585	−	15.1473i	−0.422917	−	0.742657i
$417$	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	−0.997490	−	0.0708027i	$-0.977444\pi$
$419$	−29.3721	+	16.9580i	−1.43492	+	0.828451i	−0.437428	+	0.899253i	$0.644111\pi$
$420$		0			0
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.998641	−	0.0521230i	$-0.983401\pi$
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.0521230	−	0.998641i	$-0.516599\pi$
$422$	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
$425$		0			0
$426$	−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
$429$	8.27052	+	14.5233i	0.399305	+	0.701192i
$430$		0			0
$431$	1.19014	−	4.44167i	0.0573271	−	0.213948i	−0.931320	−	0.364201i	$-0.881342\pi$
$431$	1.19014	−	4.44167i	0.0573271	−	0.213948i	0.988648	+	0.150253i	$0.0480089\pi$
$432$	−5.61627	−	1.50488i	−0.270213	−	0.0724033i
$433$	1.03596	+	3.86627i	0.0497853	+	0.185801i	0.986341	−	0.164719i	$-0.0526716\pi$
$433$	1.03596	+	3.86627i	0.0497853	+	0.185801i	−0.936555	+	0.350520i	$0.886005\pi$
$434$	0.123811	−	0.123811i	0.00594311	−	0.00594311i
$435$		0			0
$436$	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	−0.998773	−	0.0495192i	$-0.984231\pi$
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	0.456502	−	0.889723i	$-0.349102\pi$
$440$		0			0
$441$			28.9414i			1.37816i
$442$	25.8629	−	6.76571i	1.23017	−	0.321812i
$443$	−1.84874	−	1.84874i	−0.0878361	−	0.0878361i	0.661824	−	0.749660i	$-0.269783\pi$
$443$	−1.84874	−	1.84874i	−0.0878361	−	0.0878361i	−0.749660	+	0.661824i	$0.769783\pi$
$444$	10.4837	+	2.80911i	0.497536	+	0.133314i
$445$		0			0
$446$	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	$-0.857731\pi$
$449$	−31.0770	+	8.32705i	−1.46661	+	0.392978i	−0.564845	+	0.825197i	$0.691064\pi$
$450$		0			0
$451$	−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	−0.979693	−	0.200501i	$-0.935743\pi$
$457$	−14.1837	−	24.5669i	−0.663486	−	1.14919i	0.316208	−	0.948690i	$-0.397590\pi$
$458$	3.33373	−	12.4416i	0.155775	−	0.581360i
$459$	−17.8496	+	30.9165i	−0.833149	+	1.44306i
$460$		0			0
$461$	−11.1174	+	2.97890i	−0.517790	+	0.138741i	−0.508244	−	0.861213i	$-0.669705\pi$
$461$	−11.1174	+	2.97890i	−0.517790	+	0.138741i	−0.00954570	+	0.999954i	$0.503039\pi$
$462$	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
$465$		0			0
$466$	24.5609	+	6.58109i	1.13776	+	0.304863i
$467$	16.1332	+	16.1332i	0.746557	+	0.746557i	0.973831	−	0.227274i	$-0.0729812\pi$
$467$	16.1332	+	16.1332i	0.746557	+	0.746557i	−0.227274	+	0.973831i	$0.572981\pi$
$468$	0.0973232	−	16.4002i	0.00449877	−	0.758100i
$469$		−	7.03244i		−	0.324728i
$470$		0			0
$471$	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
$475$		0			0
$476$	−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	−0.216393	−	0.976306i	$-0.569429\pi$
$479$	10.0493	−	37.5043i	0.459162	−	1.71362i	0.675555	−	0.737309i	$-0.263904\pi$
$480$		0			0
$481$	0.0873213	−	14.7148i	0.00398151	−	0.670935i
$482$	−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
$485$		0			0
$486$	11.8466	+	11.8466i	0.537372	+	0.537372i
$487$	14.4718	−	25.0660i	0.655782	−	1.13585i	−0.325916	−	0.945399i	$-0.605673\pi$
$487$	14.4718	−	25.0660i	0.655782	−	1.13585i	0.981697	−	0.190448i	$-0.0609941\pi$
$488$	3.14701	−	5.45078i	0.142458	−	0.246745i
$489$	−42.1422	−	42.1422i	−1.90574	−	1.90574i
$490$		0			0
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	−0.351059	−	0.936353i	$-0.614178\pi$
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	0.635376	+	0.772203i	$0.280845\pi$
$492$	15.9530	−	9.21046i	0.719216	−	0.415240i
$493$	1.49839	−	1.49839i	0.0674842	−	0.0674842i
$494$	−2.55079	−	9.75077i	−0.114766	−	0.438708i
$495$		0			0
$496$	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	$-0.792872\pi$
$499$	−4.24201	+	4.24201i	−0.189899	+	0.189899i	0.605754	+	0.795652i	$0.292872\pi$
$500$		0			0
$501$	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	$-0.557542\pi$
$503$	3.50677	−	0.939636i	0.156359	−	0.0418963i	0.336149	+	0.941809i	$0.390875\pi$
$504$	−6.93805	−	12.0171i	−0.309046	−	0.535283i
$505$		0			0
$506$		−	6.55433i		−	0.291376i
$507$	−35.1039	+	8.96091i	−1.55902	+	0.397968i
$508$	−1.46769	−	1.46769i	−0.0651184	−	0.0651184i
$509$	22.5037	+	6.02986i	0.997460	+	0.267269i	0.720381	−	0.693578i	$-0.243967\pi$
$509$	22.5037	+	6.02986i	0.997460	+	0.267269i	0.277079	+	0.960847i	$0.410634\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	−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	0.800243	+	0.599677i	$0.204704\pi$
$523$	−4.40520	+	16.4404i	−0.192626	+	0.718890i	−0.992869	+	0.119214i	$0.961963\pi$
$524$	−0.0297008	+	0.0514432i	−0.00129748	+	0.00224731i
$525$		0			0
$526$	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
$530$		0			0
$531$	−23.2581	−	6.23198i	−1.00931	−	0.270445i
$532$	1.77730	+	1.77730i	0.0770558	+	0.0770558i
$533$	−17.5547	−	17.7643i	−0.760377	−	0.769456i
$534$			1.47779i			0.0639501i
$535$		0			0
$536$	−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
$540$		0			0
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	−0.902483	−	0.430727i	$-0.858257\pi$
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	0.430727	+	0.902483i	$0.358257\pi$
$542$	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
$545$		0			0
$546$	−7.04266	+	6.95956i	−0.301398	+	0.297842i
$547$	20.4450	−	20.4450i	0.874167	−	0.874167i	−0.118756	−	0.992923i	$-0.537891\pi$
$547$	20.4450	−	20.4450i	0.874167	−	0.874167i	0.992923	+	0.118756i	$0.0378908\pi$
$548$	3.65063	−	2.10769i	0.155947	−	0.0900361i
$549$	8.60042	−	4.96545i	0.367057	−	0.211920i
$550$		0			0
$551$	−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
$555$		0			0
$556$	11.3619	−	6.55982i	0.481854	−	0.278198i
$557$	−11.7609	+	6.79015i	−0.498324	+	0.287708i	−0.728021	−	0.685555i	$-0.759560\pi$
$557$	−11.7609	+	6.79015i	−0.498324	+	0.287708i	0.229697	+	0.973262i	$0.426226\pi$
$558$	0.612485	−	0.612485i	0.0259286	−	0.0259286i
$559$	27.6356	+	7.58098i	1.16886	+	0.320641i
$560$		0			0
$561$	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	$-0.115925\pi$
$563$	−1.25538	−	4.68514i	−0.0529080	−	0.197455i	−0.987321	+	0.158736i	$0.949258\pi$
$564$	−14.7539	+	14.7539i	−0.621251	+	0.621251i
$565$		0			0
$566$	−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	0.863406	−	0.504509i	$-0.168327\pi$
$569$	−0.124396	−	0.215461i	−0.00521497	−	0.00903259i	−0.868621	+	0.495477i	$0.834993\pi$
$570$		0			0
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$	1.44832	+	5.53640i	0.0605572	+	0.231489i
$573$	36.6136	+	36.6136i	1.52955	+	1.52955i
$574$	−6.59281	−	1.76654i	−0.275179	−	0.0737339i
$575$		0			0
$576$	−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			0
$581$	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	−0.945937	−	0.324351i	$-0.894854\pi$
$587$	−18.2647	−	31.6354i	−0.753865	−	1.30573i	0.192072	−	0.981381i	$-0.438479\pi$
$588$	−4.17904	+	15.5964i	−0.172341	+	0.643185i
$589$	−0.242870	+	0.420663i	−0.0100073	+	0.0173331i
$590$		0			0
$591$	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
$595$		0			0
$596$	−3.99327	−	1.06999i	−0.163571	−	0.0438287i
$597$	29.0384	+	29.0384i	1.18846	+	1.18846i
$598$	13.7018	+	3.75868i	0.560310	+	0.153704i
$599$			13.2549i			0.541579i	0.962639	+	0.270789i	$0.0872847\pi$
$599$			13.2549i			0.541579i	−0.962639	+	0.270789i	$0.912715\pi$
$600$		0			0
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	0.854662	−	0.519185i	$-0.173764\pi$
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	−0.876958	+	0.480566i	$0.840431\pi$
$602$	7.56474	−	2.02696i	0.308316	−	0.0826129i
$603$		−	34.7891i		−	1.41672i
$604$	−1.65905	−	6.19166i	−0.0675058	−	0.251935i
$605$		0			0
$606$	−19.6554	+	19.6554i	−0.798446	+	0.798446i
$607$	10.8348	+	40.4361i	0.439771	+	1.64125i	0.729384	+	0.684105i	$0.239807\pi$
$607$	10.8348	+	40.4361i	0.439771	+	1.64125i	−0.289612	+	0.957144i	$0.593526\pi$
$608$	12.7652	+	3.42042i	0.517696	+	0.138716i
$609$	−0.203130	+	0.758093i	−0.00823126	+	0.0307195i
$610$		0			0
$611$	24.4142	+	14.2894i	0.987693	+	0.578087i
$612$	−23.3204	+	23.3204i	−0.942673	+	0.942673i
$613$	−24.1705	+	13.9548i	−0.976235	+	0.563630i	−0.901131	−	0.433546i	$-0.857262\pi$
$613$	−24.1705	+	13.9548i	−0.976235	+	0.563630i	−0.0751039	+	0.997176i	$0.523929\pi$
$614$	21.4487	−	12.3834i	0.865601	−	0.499755i
$615$		0			0
$616$	3.42371	+	3.42371i	0.137945	+	0.137945i
$617$	2.19132	−	3.79548i	0.0882193	−	0.152800i	−0.818539	−	0.574451i	$-0.805216\pi$
$617$	2.19132	−	3.79548i	0.0882193	−	0.152800i	0.906758	+	0.421650i	$0.138549\pi$
$618$	−5.08477	+	8.80708i	−0.204540	+	0.354273i
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	0.510998	−	0.859582i	$-0.329276\pi$
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	−0.859582	+	0.510998i	$0.829276\pi$
$620$		0			0
$621$	−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
$624$	−3.13910	+	11.4432i	−0.125664	+	0.458095i
$625$		0			0
$626$	−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
$630$		0			0
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	−0.964612	−	0.263673i	$-0.915066\pi$
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	0.703542	−	0.710653i	$-0.251601\pi$
$632$		−	41.0398i		−	1.63248i
$633$	22.9677	−	6.15419i	0.912886	−	0.244607i
$634$	11.7220	+	20.3031i	0.465540	+	0.806340i
$635$		0			0
$636$		−	7.51646i		−	0.298047i
$637$	21.8908	+	0.129906i	0.867345	+	0.00514706i
$638$	−0.351511	−	0.351511i	−0.0139164	−	0.0139164i
$639$	−60.1003	−	16.1038i	−2.37753	−	0.637057i
$640$		0			0
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	0.471760	−	0.881727i	$-0.343619\pi$
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	−0.527718	+	0.849420i	$0.676952\pi$
$642$	1.26681			0.0499968
$643$	−34.3541	−	19.8344i	−1.35479	−	0.782191i	−0.365878	−	0.930663i	$-0.619231\pi$
$643$	−34.3541	−	19.8344i	−1.35479	−	0.782191i	−0.988917	+	0.148472i	$0.952565\pi$
$644$	−3.42248	+	0.917051i	−0.134865	+	0.0361369i
$645$		0			0
$646$	−10.1339	+	17.5525i	−0.398714	+	0.690593i
$647$	3.84742	−	14.3588i	0.151258	−	0.564501i	−0.848139	−	0.529773i	$-0.822277\pi$
$647$	3.84742	−	14.3588i	0.151258	−	0.564501i	0.999397	−	0.0347277i	$-0.0110564\pi$
$648$	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	$-0.997601\pi$
$653$	−3.32718	+	12.4172i	−0.130203	+	0.485922i	0.869769	+	0.493459i	$0.164268\pi$
$654$	12.9403	−	22.4132i	0.506005	−	0.876426i
$655$		0			0
$656$	−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	0.0349025	−	0.999391i	$-0.488888\pi$
$659$	−20.8742	−	12.0517i	−0.813144	−	0.469469i	−0.848047	+	0.529922i	$0.822221\pi$
$660$		0			0
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.903217	−	0.429185i	$-0.141199\pi$
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.567616	+	0.823293i	$0.307866\pi$
$662$	24.2637	+	24.2637i	0.943036	+	0.943036i
$663$	62.8768	+	36.8011i	2.44193	+	1.42924i
$664$		−	25.8862i		−	1.00458i
$665$		0			0
$666$	−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
$670$		0			0
$671$	−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	$-0.353519\pi$
$673$	9.87723	+	2.64660i	0.380739	+	0.102019i	−0.0633730	+	0.997990i	$0.520186\pi$
$674$	−5.44776	+	20.3313i	−0.209840	+	0.783132i
$675$		0			0
$676$	−12.4044	−	0.147227i	−0.477093	−	0.00566259i
$677$	−29.8933	+	29.8933i	−1.14889	+	1.14889i	−0.162121	+	0.986771i	$0.551833\pi$
$677$	−29.8933	+	29.8933i	−1.14889	+	1.14889i	−0.986771	+	0.162121i	$0.948167\pi$
$678$	−4.77472	+	2.75669i	−0.183372	+	0.105870i
$679$	−6.26961	+	3.61976i	−0.240606	+	0.138914i
$680$		0			0
$681$	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	−0.608459	−	0.793585i	$-0.708212\pi$
$683$	10.0103	−	17.3384i	0.383035	−	0.663436i	0.991494	+	0.130149i	$0.0415455\pi$
$684$	8.79221	+	8.79221i	0.336178	+	0.336178i
$685$		0			0
$686$	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
$689$	−9.85890	+	2.57908i	−0.375594	+	0.0982550i
$690$		0			0
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	0.540147	+	0.841571i	$0.318369\pi$
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	−0.888566	+	0.458749i	$0.848298\pi$
$692$	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
$695$		0			0
$696$	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
$700$		0			0
$701$			37.1781i			1.40420i	0.712080	+	0.702098i	$0.247753\pi$
$701$			37.1781i			1.40420i	−0.712080	+	0.702098i	$0.752247\pi$
$702$	−12.9129	+	12.7606i	−0.487367	+	0.481617i
$703$	7.88864	+	7.88864i	0.297526	+	0.297526i
$704$	11.7374	+	3.14502i	0.442368	+	0.118532i
$705$		0			0
$706$	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	$-0.223236\pi$
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.984250	+	0.176783i	$0.0565692\pi$
$710$		0			0
$711$	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	−0.366190	−	0.930540i	$-0.619338\pi$
$719$	16.6992	−	28.9239i	0.622777	−	1.07868i	0.988966	−	0.148141i	$-0.0473288\pi$
$720$		0			0
$721$	−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			0
$726$	22.6652	+	6.07313i	0.841186	+	0.225395i
$727$	23.6487	+	23.6487i	0.877083	+	0.877083i	0.993232	−	0.116149i	$-0.0370549\pi$
$727$	23.6487	+	23.6487i	0.877083	+	0.877083i	−0.116149	+	0.993232i	$0.537055\pi$
$728$	−9.12066	+	5.19389i	−0.338034	+	0.192499i
$729$			43.9226i			1.62676i
$730$		0			0
$731$	−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	$0.0875424\pi$
$733$			14.7049i			0.543138i	−0.962419	+	0.271569i	$0.912458\pi$
$734$	−3.02344	−	11.2836i	−0.111597	−	0.416486i
$735$		0			0
$736$	−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	−0.796185	−	0.605054i	$-0.793152\pi$
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	0.992043	−	0.125900i	$-0.0401817\pi$
$740$		0			0
$741$	13.8747	−	23.7056i	0.509698	−	0.870848i
$742$	−1.96931	+	1.96931i	−0.0722956	+	0.0722956i
$743$	38.6601	−	22.3204i	1.41830	−	0.818856i	0.422151	−	0.906526i	$-0.361275\pi$
$743$	38.6601	−	22.3204i	1.41830	−	0.818856i	0.996150	+	0.0876692i	$0.0279419\pi$
$744$	1.29565	−	0.748042i	0.0475007	−	0.0274246i
$745$		0			0
$746$	−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
$750$		0			0
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	−0.195804	−	0.980643i	$-0.562732\pi$
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	0.751360	+	0.659893i	$0.229398\pi$
$752$	8.02381	−	4.63255i	0.292598	−	0.168932i
$753$	27.5353	−	27.5353i	1.00344	−	1.00344i
$754$	0.936413	−	0.533254i	0.0341022	−	0.0194200i
$755$		0			0
$756$	1.17176	−	4.37306i	0.0426164	−	0.159047i
$757$	−33.9933	−	9.10848i	−1.23551	−	0.331053i	−0.418786	−	0.908085i	$-0.637544\pi$
$757$	−33.9933	−	9.10848i	−1.23551	−	0.331053i	−0.816722	+	0.577032i	$0.804211\pi$
$758$	4.48144	+	16.7250i	0.162773	+	0.607478i
$759$	12.6305	−	12.6305i	0.458457	−	0.458457i
$760$		0			0
$761$	−3.03122	−	11.3127i	−0.109882	−	0.410084i	0.888972	−	0.457962i	$-0.151421\pi$
$761$	−3.03122	−	11.3127i	−0.109882	−	0.410084i	−0.998853	+	0.0478787i	$0.984754\pi$
$762$			6.19897i			0.224565i
$763$	8.45219	−	2.26476i	0.305990	−	0.0819897i
$764$	8.86485	+	15.3544i	0.320719	+	0.555502i
$765$		0			0
$766$		−	6.75331i		−	0.244007i
$767$	−4.81817	+	17.5641i	−0.173974	+	0.634202i
$768$	−33.2233	−	33.2233i	−1.19884	−	1.19884i
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.0871555	−	0.996195i	$-0.527778\pi$
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.573576	+	0.819152i	$0.694444\pi$
$770$		0			0
$771$	−55.9401	−	32.2971i	−2.01463	−	1.16315i
$772$	11.9964			0.431760
$773$	14.2114	+	8.20497i	0.511149	+	0.295112i	0.733306	−	0.679899i	$-0.237976\pi$
$773$	14.2114	+	8.20497i	0.511149	+	0.295112i	−0.222157	+	0.975011i	$0.571310\pi$
$774$	37.4223	−	10.0273i	1.34512	−	0.360423i
$775$		0			0
$776$	−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
$785$		0			0
$786$	0.171361	−	0.0459159i	0.00611223	−	0.00163777i
$787$	11.7781	+	6.80008i	0.419844	+	0.242397i	0.695010	−	0.719000i	$-0.255400\pi$
$787$	11.7781	+	6.80008i	0.419844	+	0.242397i	−0.275167	+	0.961396i	$0.588733\pi$
$788$	13.6326			0.485642
$789$	3.14011	+	1.81294i	0.111791	+	0.0645424i
$790$		0			0
$791$	−1.80058	−	0.482465i	−0.0640214	−	0.0171545i
$792$	16.9369	+	16.9369i	0.601827	+	0.601827i
$793$	−3.71719	−	6.52751i	−0.132001	−	0.231799i
$794$			5.95255i			0.211248i
$795$		0			0
$796$	7.03076	+	12.1776i	0.249199	+	0.431625i
$797$	28.9148	−	7.74769i	1.02421	−	0.274437i	0.292657	−	0.956218i	$-0.405461\pi$
$797$	28.9148	−	7.74769i	1.02421	−	0.274437i	0.731557	+	0.681780i	$0.238794\pi$
$798$		−	7.50664i		−	0.265732i
$799$	−14.7232	−	54.9476i	−0.520868	−	1.94391i
$800$		0			0
$801$	−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			0
$806$	−0.460525	−	0.466023i	−0.0162213	−	0.0164150i
$807$	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	−0.454564	−	0.890714i	$-0.650205\pi$
$809$	2.54661	−	1.47029i	0.0895342	−	0.0516926i	0.544099	+	0.839021i	$0.316872\pi$
$810$		0			0
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	0.933148	−	0.359492i	$-0.117050\pi$
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	−0.359492	+	0.933148i	$0.617050\pi$
$812$	−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
$815$		0			0
$816$	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
$819$	−16.5604	−	0.0982738i	−0.578667	−	0.00343397i
$820$		0			0
$821$	11.8735	−	44.3125i	0.414388	−	1.54652i	−0.371672	−	0.928364i	$-0.621215\pi$
$821$	11.8735	−	44.3125i	0.414388	−	1.54652i	0.786059	−	0.618151i	$-0.212118\pi$
$822$	−12.1605	−	3.25838i	−0.424145	−	0.113649i
$823$	4.58752	+	17.1209i	0.159911	+	0.596796i	0.998635	+	0.0522385i	$0.0166356\pi$
$823$	4.58752	+	17.1209i	0.159911	+	0.596796i	−0.838724	+	0.544557i	$0.816698\pi$
$824$	−7.62280	+	7.62280i	−0.265553	+	0.265553i
$825$		0			0
$826$	1.28826	+	4.80785i	0.0448242	+	0.167286i
$827$			5.79276i			0.201434i	0.994915	+	0.100717i	$0.0321137\pi$
$827$			5.79276i			0.201434i	−0.994915	+	0.100717i	$0.967886\pi$
$828$	−16.9308	+	4.53660i	−0.588387	+	0.157658i
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	−0.994717	−	0.102657i	$-0.967265\pi$
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	0.408454	−	0.912779i	$-0.366068\pi$
$830$		0			0
$831$			26.6284i			0.923727i
$832$	−13.3056	+	22.7334i	−0.461290	+	0.788139i
$833$	−31.1279	−	31.1279i	−1.07852	−	1.07852i
$834$	−37.8473	−	10.1412i	−1.31055	−	0.351160i
$835$		0			0
$836$	−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	$-0.819897\pi$
$839$	−37.8626	+	10.1452i	−1.30716	+	0.350253i	−0.463008	+	0.886354i	$0.653230\pi$
$840$		0			0
$841$	−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
$850$		0			0
$851$	−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
$855$		0			0
$856$	1.29713	+	0.347564i	0.0443348	+	0.0118795i
$857$	−27.2327	−	27.2327i	−0.930252	−	0.930252i	0.0674695	−	0.997721i	$-0.478507\pi$
$857$	−27.2327	−	27.2327i	−0.930252	−	0.930252i	−0.997721	+	0.0674695i	$0.978507\pi$
$858$	8.63325	−	14.7504i	0.294734	−	0.503570i
$859$			44.5502i			1.52003i	0.649904	+	0.760016i	$0.274809\pi$
$859$			44.5502i			1.52003i	−0.649904	+	0.760016i	$0.725191\pi$
$860$		0			0
$861$	−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	$-0.607256\pi$
$863$		−	55.4497i		−	1.88753i	0.330615	−	0.943766i	$-0.392744\pi$
$864$	−6.16090	−	22.9928i	−0.209598	−	0.782230i
$865$		0			0
$866$	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
$870$		0			0
$871$	−26.3139	−	0.156154i	−0.891612	−	0.00529107i
$872$	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
$875$		0			0
$876$	6.06917	+	6.06917i	0.205058	+	0.205058i
$877$	2.68849	−	4.65661i	0.0907839	−	0.157242i	−0.817057	−	0.576557i	$-0.804396\pi$
$877$	2.68849	−	4.65661i	0.0907839	−	0.157242i	0.907841	+	0.419314i	$0.137729\pi$
$878$	−11.6188	+	20.1244i	−0.392116	+	0.679166i
$879$	−7.92505	−	7.92505i	−0.267305	−	0.267305i
$880$		0			0
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.971022	−	0.238992i	$-0.923183\pi$
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.278538	+	0.960425i	$0.589850\pi$
$882$	25.6309	−	14.7980i	0.863037	−	0.498274i
$883$	32.9568	−	32.9568i	1.10908	−	1.10908i	0.115813	−	0.993271i	$-0.463053\pi$
$883$	32.9568	−	32.9568i	1.10908	−	1.10908i	0.993271	−	0.115813i	$-0.0369473\pi$
$884$	17.5345	+	17.7439i	0.589750	+	0.596791i
$885$		0			0
$886$	−0.691990	+	2.58254i	−0.0232478	+	0.0867622i
$887$	−20.4194	−	5.47136i	−0.685616	−	0.183710i	−0.100837	−	0.994903i	$-0.532152\pi$
$887$	−20.4194	−	5.47136i	−0.685616	−	0.183710i	−0.584779	+	0.811193i	$0.698819\pi$
$888$	−8.89336	−	33.1905i	−0.298442	−	1.11380i
$889$	−1.48203	+	1.48203i	−0.0497057	+	0.0497057i
$890$		0			0
$891$	−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
$895$		0			0
$896$		−	2.11809i		−	0.0707605i
$897$	19.1609	+	33.6472i	0.639763	+	1.12345i
$898$	23.2645	+	23.2645i	0.776346	+	0.776346i
$899$	−0.0501642	−	0.0134414i	−0.00167307	−	0.000448297i
$900$		0			0
$901$	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
$905$		0			0
$906$	−9.57200	+	16.5792i	−0.318008	+	0.550807i
$907$	−2.86355	+	10.6869i	−0.0950825	+	0.354853i	−0.997032	−	0.0769889i	$-0.975469\pi$
$907$	−2.86355	+	10.6869i	−0.0950825	+	0.354853i	0.901949	+	0.431842i	$0.142136\pi$
$908$	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			0
$916$	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	0.667934	−	0.744220i	$-0.267179\pi$
$919$	10.8342	+	6.25513i	0.357388	+	0.206338i	−0.310547	+	0.950558i	$0.600512\pi$
$920$		0			0
$921$	65.1960	+	17.4692i	2.14828	+	0.575630i
$922$	8.32259	+	8.32259i	0.274090	+	0.274090i
$923$	−12.4504	+	45.3866i	−0.409811	+	1.49392i
$924$			4.26220i			0.140216i
$925$		0			0
$926$	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	0.786926	+	0.617047i	$0.211671\pi$
$929$	12.6170	+	47.0874i	0.413952	+	1.54489i	−0.372975	+	0.927841i	$0.621662\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−45.1193	+	25.6939i	−1.47477	+	0.839831i
$937$	−7.38027	+	7.38027i	−0.241103	+	0.241103i	−0.817306	−	0.576203i	$-0.804534\pi$
$937$	−7.38027	+	7.38027i	−0.241103	+	0.241103i	0.576203	+	0.817306i	$0.304534\pi$
$938$	−6.22802	+	3.59575i	−0.203352	+	0.117405i
$939$	−11.5750	+	6.68281i	−0.377735	+	0.218085i
$940$		0			0
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	0.681491	−	0.731827i	$-0.261332\pi$
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	−0.731827	+	0.681491i	$0.761332\pi$
$942$	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
$945$		0			0
$946$	−11.7074	+	6.75929i	−0.380642	+	0.219764i
$947$	−5.81670	+	3.35827i	−0.189017	+	0.109129i	−0.591522	−	0.806289i	$-0.701473\pi$
$947$	−5.81670	+	3.35827i	−0.189017	+	0.109129i	0.402505	+	0.915418i	$0.368140\pi$
$948$	25.5454	−	25.5454i	0.829676	−	0.829676i
$949$	5.87810	−	10.0431i	0.190811	−	0.326011i
$950$		0			0
$951$	−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	0.999388	+	0.0349673i	$0.0111327\pi$
$953$	4.67309	+	17.4402i	0.151376	+	0.564944i	−0.848012	+	0.529977i	$0.822201\pi$
$954$	−9.74205	+	9.74205i	−0.315411	+	0.315411i
$955$		0			0
$956$	−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
$960$		0			0
$961$		−	30.9684i		−	0.998981i
$962$	−13.0762	+	7.44646i	−0.421595	+	0.240083i
$963$	1.49825	+	1.49825i	0.0482804	+	0.0482804i
$964$	−16.6086	−	4.45026i	−0.534927	−	0.143333i
$965$		0			0
$966$	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
$970$		0			0
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	−0.324942	−	0.945734i	$-0.605345\pi$
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	0.981501	−	0.191459i	$-0.0613218\pi$
$972$	−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	0.992850	+	0.119367i	$0.0380865\pi$
$977$	18.7479	+	32.4724i	0.599800	+	1.03888i	−0.393050	+	0.919517i	$0.628580\pi$
$978$	−15.7740	+	58.8694i	−0.504397	+	1.88244i
$979$	0.431236	−	0.746923i	0.0137824	−	0.0238718i
$980$		0			0
$981$	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
$985$		0			0
$986$	−2.09314	−	0.560854i	−0.0666591	−	0.0178612i
$987$	14.8980	+	14.8980i	0.474208	+	0.474208i
$988$	6.68975	−	6.61082i	0.212829	−	0.210318i
$989$		−	30.6267i		−	0.973873i
$990$		0			0
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	0.859584	−	0.510994i	$-0.170722\pi$
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	−0.872326	+	0.488925i	$0.837389\pi$
$992$	0.829802	−	0.222345i	0.0263462	−	0.00705945i
$993$			93.5143i			2.96759i
$994$	3.32894	+	12.4238i	0.105587	+	0.394058i
$995$		0			0
$996$	16.1129	−	16.1129i	0.510558	−	0.510558i
$997$	−4.04012	−	15.0779i	−0.127952	−	0.477522i	0.871976	−	0.489549i	$-0.162838\pi$
$997$	−4.04012	−	15.0779i	−0.127952	−	0.477522i	−0.999928	+	0.0120264i	$0.996172\pi$
$998$	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	325.2.s.b.193.2		20
5.2	odd	4		325.2.x.b.232.4		20
5.3	odd	4		65.2.t.a.37.2	yes	20
5.4	even	2		65.2.o.a.63.4	yes	20
13.6	odd	12		325.2.x.b.318.4		20
15.8	even	4		585.2.dp.a.37.4		20
15.14	odd	2		585.2.cf.a.388.2		20
65.3	odd	12		845.2.f.e.437.3		20
65.4	even	6		845.2.o.f.488.2		20
65.8	even	4		845.2.o.f.587.2		20
65.9	even	6		845.2.o.e.488.4		20
65.18	even	4		845.2.o.e.587.4		20
65.19	odd	12		65.2.t.a.58.2	yes	20
65.23	odd	12		845.2.f.d.437.8		20
65.24	odd	12		845.2.f.d.408.3		20
65.28	even	12		845.2.k.e.577.3		20
65.29	even	6		845.2.k.e.268.3		20
65.32	even	12	inner	325.2.s.b.32.2		20
65.33	even	12		845.2.o.g.357.2		20
65.34	odd	4		845.2.t.e.418.2		20
65.38	odd	4		845.2.t.g.427.4		20
65.43	odd	12		845.2.t.e.657.2		20
65.44	odd	4		845.2.t.f.418.4		20
65.48	odd	12		845.2.t.f.657.4		20
65.49	even	6		845.2.k.d.268.8		20
65.54	odd	12		845.2.f.e.408.8		20
65.58	even	12		65.2.o.a.32.4	✓	20
65.59	odd	12		845.2.t.g.188.4		20
65.63	even	12		845.2.k.d.577.8		20
65.64	even	2		845.2.o.g.258.2		20
195.149	even	12		585.2.dp.a.253.4		20
195.188	odd	12		585.2.cf.a.487.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	65.58	even	12
65.2.o.a.63.4	yes	20	5.4	even	2
65.2.t.a.37.2	yes	20	5.3	odd	4
65.2.t.a.58.2	yes	20	65.19	odd	12
325.2.s.b.32.2		20	65.32	even	12	inner
325.2.s.b.193.2		20	1.1	even	1	trivial
325.2.x.b.232.4		20	5.2	odd	4
325.2.x.b.318.4		20	13.6	odd	12
585.2.cf.a.388.2		20	15.14	odd	2
585.2.cf.a.487.2		20	195.188	odd	12
585.2.dp.a.37.4		20	15.8	even	4
585.2.dp.a.253.4		20	195.149	even	12
845.2.f.d.408.3		20	65.24	odd	12
845.2.f.d.437.8		20	65.23	odd	12
845.2.f.e.408.8		20	65.54	odd	12
845.2.f.e.437.3		20	65.3	odd	12
845.2.k.d.268.8		20	65.49	even	6
845.2.k.d.577.8		20	65.63	even	12
845.2.k.e.268.3		20	65.29	even	6
845.2.k.e.577.3		20	65.28	even	12
845.2.o.e.488.4		20	65.9	even	6
845.2.o.e.587.4		20	65.18	even	4
845.2.o.f.488.2		20	65.4	even	6
845.2.o.f.587.2		20	65.8	even	4
845.2.o.g.258.2		20	65.64	even	2
845.2.o.g.357.2		20	65.33	even	12
845.2.t.e.418.2		20	65.34	odd	4
845.2.t.e.657.2		20	65.43	odd	12
845.2.t.f.418.4		20	65.44	odd	4
845.2.t.f.657.4		20	65.48	odd	12
845.2.t.g.188.4		20	65.59	odd	12
845.2.t.g.427.4		20	65.38	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.511309 - 0.885613i) q^{2} +(0.721300 - 2.69193i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-2.75281 + 0.737614i) q^{6} +(-0.834479 - 0.481787i) q^{7} -3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +(1.60661 + 0.430490i) q^{11} +(-1.88048 - 1.88048i) q^{12} +(-1.82127 + 3.11175i) q^{13} +0.985368i q^{14} +(0.590448 + 1.02269i) q^{16} +(7.00342 - 1.87656i) q^{17} +4.87456i q^{18} +(-0.707496 - 2.64041i) q^{19} +(-1.89884 + 1.89884i) q^{21} +(-0.440226 - 1.64295i) q^{22} +(3.72214 + 0.997344i) q^{23} +(-2.17910 + 8.13250i) q^{24} +(3.68704 + 0.0218799i) q^{26} +(-3.48159 + 3.48159i) q^{27} +(-0.796304 + 0.459747i) q^{28} +(0.253107 - 0.146132i) q^{29} +(-0.125649 - 0.125649i) q^{31} +(-2.41727 + 4.18683i) q^{32} +(2.31769 - 4.01436i) q^{33} +(-5.24282 - 5.24282i) q^{34} +(-3.93927 + 2.27434i) q^{36} +(-3.53443 + 2.04061i) q^{37} +(-1.97663 + 1.97663i) q^{38} +(7.06291 + 7.14724i) q^{39} +(-1.79277 + 6.69071i) q^{41} +(2.65254 + 0.710745i) q^{42} +(-2.05706 - 7.67707i) q^{43} +(1.12232 - 1.12232i) q^{44} +(-1.01990 - 3.80633i) q^{46} -7.84582i q^{47} +(3.17888 - 0.851780i) q^{48} +(-3.03576 - 5.25810i) q^{49} -20.2063i q^{51} +(1.70259 + 2.98981i) q^{52} +(1.99855 + 1.99855i) q^{53} +(4.86351 + 1.30317i) q^{54} +(2.52102 + 1.45551i) q^{56} -7.61811 q^{57} +(-0.258832 - 0.149437i) q^{58} +(4.87924 - 1.30739i) q^{59} +(-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} +(12.6082 - 3.37837i) q^{71} +(12.4713 + 7.20034i) q^{72} -3.22747 q^{73} +(3.61437 + 2.08676i) q^{74} +(-2.51962 - 0.675130i) q^{76} +(-1.13328 - 1.13328i) q^{77} +(2.71836 - 9.90945i) q^{78} +13.5845i q^{79} +(-0.289196 - 0.500902i) q^{81} +(6.84204 - 1.83332i) q^{82} +8.56854i q^{83} +(0.663230 + 2.47521i) q^{84} +(-5.74712 + 5.74712i) q^{86} +(-0.210809 - 0.786751i) q^{87} +(-4.85368 - 1.30054i) q^{88} +(0.134207 - 0.500868i) q^{89} +(3.01901 - 1.71922i) q^{91} +(2.60014 - 2.60014i) q^{92} +(-0.428870 + 0.247608i) q^{93} +(-6.94836 + 4.01164i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 2 q^{3} - 6 q^{4} - 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{11} - 24 q^{12} - 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} + 4 q^{21} - 16 q^{22} + 2 q^{23} - 32 q^{24} - 24 q^{26}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 2 * q^3 - 6 * q^4 - 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 16 * q^11 - 24 * q^12 - 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 + 4 * q^21 - 16 * q^22 + 2 * q^23 - 32 * q^24 - 24 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^32 + 18 * q^33 - 2 * q^34 + 36 * q^36 - 42 * q^37 - 8 * q^38 - 4 * q^39 + 10 * q^41 + 56 * q^42 + 22 * q^43 + 36 * q^44 + 4 * q^46 - 28 * q^48 - 18 * q^49 - 46 * q^52 + 10 * q^53 + 48 * q^54 + 12 * q^57 + 90 * q^58 + 16 * q^59 - 16 * q^61 + 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 - 28 * q^68 + 16 * q^69 - 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 64 * q^76 - 28 * q^77 - 32 * q^78 - 14 * q^81 - 22 * q^82 + 40 * q^84 + 60 * q^86 - 62 * q^87 - 50 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^93 + 48 * q^94 + 56 * q^96 + 22 * q^97 - 4 * q^98 - 60 * q^99

Introduction

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