LMFDB - Embedded newform 51.2.h.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,2,Mod(19,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("51.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, 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:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	51.43
Dual form			51.2.h.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30656 + 1.30656i) q^{2} +(0.923880 + 0.382683i) q^{3} -1.41421i q^{4} +(-0.617317 + 1.49033i) q^{5} +(-1.70711 + 0.707107i) q^{6} +(0.0582601 + 0.140652i) q^{7} +(-0.765367 - 0.765367i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-1.14065 - 2.75378i) q^{10} +(4.64466 - 1.92388i) q^{11} +(0.541196 - 1.30656i) q^{12} -3.94495i q^{13} +(-0.259892 - 0.107651i) q^{14} +(-1.14065 + 1.14065i) q^{15} +4.82843 q^{16} +(-1.26616 - 3.92388i) q^{17} -1.84776 q^{18} +(-4.65205 + 4.65205i) q^{19} +(2.10765 + 0.873017i) q^{20} +0.152241i q^{21} +(-3.55487 + 8.58221i) q^{22} +(-3.18585 + 1.31962i) q^{23} +(-0.414214 - 1.00000i) q^{24} +(1.69552 + 1.69552i) q^{25} +(5.15432 + 5.15432i) q^{26} +(0.382683 + 0.923880i) q^{27} +(0.198912 - 0.0823922i) q^{28} +(0.858221 - 2.07193i) q^{29} -2.98067i q^{30} +(-2.37849 - 0.985204i) q^{31} +(-4.77791 + 4.77791i) q^{32} +5.02734 q^{33} +(6.78112 + 3.47247i) q^{34} -0.245584 q^{35} +(1.00000 - 1.00000i) q^{36} +(-9.86351 - 4.08560i) q^{37} -12.1564i q^{38} +(1.50967 - 3.64466i) q^{39} +(1.61313 - 0.668179i) q^{40} +(-0.105915 - 0.255701i) q^{41} +(-0.198912 - 0.198912i) q^{42} +(4.48502 + 4.48502i) q^{43} +(-2.72078 - 6.56854i) q^{44} +(-1.49033 + 0.617317i) q^{45} +(2.43835 - 5.88669i) q^{46} +9.82164i q^{47} +(4.46088 + 1.84776i) q^{48} +(4.93336 - 4.93336i) q^{49} -4.43060 q^{50} +(0.331821 - 4.10973i) q^{51} -5.57900 q^{52} +(-1.50339 + 1.50339i) q^{53} +(-1.70711 - 0.707107i) q^{54} +8.10973i q^{55} +(0.0630603 - 0.152241i) q^{56} +(-6.07820 + 2.51767i) q^{57} +(1.58579 + 3.82843i) q^{58} +(-0.936078 - 0.936078i) q^{59} +(1.61313 + 1.61313i) q^{60} +(-3.16799 - 7.64821i) q^{61} +(4.39488 - 1.82042i) q^{62} +(-0.0582601 + 0.140652i) q^{63} -2.82843i q^{64} +(5.87929 + 2.43528i) q^{65} +(-6.56854 + 6.56854i) q^{66} -7.10973 q^{67} +(-5.54920 + 1.79063i) q^{68} -3.44834 q^{69} +(0.320871 - 0.320871i) q^{70} +(6.04875 + 2.50548i) q^{71} -1.08239i q^{72} +(3.18637 - 7.69258i) q^{73} +(18.2254 - 7.54920i) q^{74} +(0.917608 + 2.21530i) q^{75} +(6.57900 + 6.57900i) q^{76} +(0.541196 + 0.541196i) q^{77} +(2.78950 + 6.73445i) q^{78} +(0.491806 - 0.203713i) q^{79} +(-2.98067 + 7.19597i) q^{80} +1.00000i q^{81} +(0.472474 + 0.195705i) q^{82} +(-1.55807 + 1.55807i) q^{83} +0.215301 q^{84} +(6.62951 + 0.535270i) q^{85} -11.7199 q^{86} +(1.58579 - 1.58579i) q^{87} +(-5.02734 - 2.08239i) q^{88} +7.64847i q^{89} +(1.14065 - 2.75378i) q^{90} +(0.554866 - 0.229833i) q^{91} +(1.86623 + 4.50548i) q^{92} +(-1.82042 - 1.82042i) q^{93} +(-12.8326 - 12.8326i) q^{94} +(-4.06132 - 9.80490i) q^{95} +(-6.24264 + 2.58579i) q^{96} +(-1.38009 + 3.33182i) q^{97} +12.8915i q^{98} +(4.64466 + 1.92388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} - 8 q^{6} + 8 q^{11} - 16 q^{14} + 16 q^{16} - 8 q^{17} - 8 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{23} + 8 q^{24} - 16 q^{25} + 16 q^{26} - 8 q^{28} + 8 q^{31} + 8 q^{33} - 8 q^{34} + 32 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^6 + 8 * q^11 - 16 * q^14 + 16 * q^16 - 8 * q^17 - 8 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^23 + 8 * q^24 - 16 * q^25 + 16 * q^26 - 8 * q^28 + 8 * q^31 + 8 * q^33 - 8 * q^34 + 32 * q^35 + 8 * q^36 - 8 * q^37 + 16 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^50 - 16 * q^52 - 32 * q^53 - 8 * q^54 - 16 * q^56 - 16 * q^57 + 24 * q^58 + 16 * q^59 - 8 * q^60 + 16 * q^61 + 16 * q^62 + 24 * q^65 - 16 * q^66 - 16 * q^67 - 24 * q^69 + 40 * q^70 - 16 * q^71 + 48 * q^73 + 64 * q^74 + 16 * q^75 + 24 * q^76 + 8 * q^78 - 16 * q^80 - 8 * q^82 + 32 * q^83 + 40 * q^85 - 32 * q^86 + 24 * q^87 - 8 * q^88 - 16 * q^91 - 32 * q^92 - 32 * q^93 - 40 * q^95 - 16 * q^96 + 8 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.30656	+	1.30656i	−0.923880	+	0.923880i	−0.997301	−	0.0734215i	$-0.976608\pi$
$2$	−1.30656	+	1.30656i	−0.923880	+	0.923880i	0.0734215	+	0.997301i	$0.476608\pi$
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$		−	1.41421i		−	0.707107i
$5$	−0.617317	+	1.49033i	−0.276072	+	0.666498i	−0.999720	−	0.0236722i	$-0.992464\pi$
$5$	−0.617317	+	1.49033i	−0.276072	+	0.666498i	0.723647	+	0.690170i	$0.242464\pi$
$6$	−1.70711	+	0.707107i	−0.696923	+	0.288675i
$7$	0.0582601	+	0.140652i	0.0220202	+	0.0531616i	0.934507	−	0.355944i	$-0.115841\pi$
$7$	0.0582601	+	0.140652i	0.0220202	+	0.0531616i	−0.912487	+	0.409106i	$0.865841\pi$
$8$	−0.765367	−	0.765367i	−0.270598	−	0.270598i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	−1.14065	−	2.75378i	−0.360706	−	0.870821i
$11$	4.64466	−	1.92388i	1.40042	−	0.580072i	0.450557	−	0.892748i	$-0.351226\pi$
$11$	4.64466	−	1.92388i	1.40042	−	0.580072i	0.949860	+	0.312676i	$0.101226\pi$
$12$	0.541196	−	1.30656i	0.156230	−	0.377172i
$13$		−	3.94495i		−	1.09413i	−0.837090	−	0.547066i	$-0.815745\pi$
$13$		−	3.94495i		−	1.09413i	0.837090	−	0.547066i	$-0.184255\pi$
$14$	−0.259892	−	0.107651i	−0.0694589	−	0.0287708i
$15$	−1.14065	+	1.14065i	−0.294515	+	0.294515i
$16$	4.82843			1.20711
$17$	−1.26616	−	3.92388i	−0.307090	−	0.951681i
$17$	−1.26616	−	3.92388i	−0.307090	−	0.951681i
$18$	−1.84776			−0.435521
$19$	−4.65205	+	4.65205i	−1.06725	+	1.06725i	−0.0696854	+	0.997569i	$0.522200\pi$
$19$	−4.65205	+	4.65205i	−1.06725	+	1.06725i	−0.997569	+	0.0696854i	$0.977800\pi$
$20$	2.10765	+	0.873017i	0.471285	+	0.195213i
$21$			0.152241i			0.0332217i
$22$	−3.55487	+	8.58221i	−0.757900	+	1.82973i
$23$	−3.18585	+	1.31962i	−0.664296	+	0.275160i	−0.689245	−	0.724528i	$-0.742058\pi$
$23$	−3.18585	+	1.31962i	−0.664296	+	0.275160i	0.0249490	+	0.999689i	$0.492058\pi$
$24$	−0.414214	−	1.00000i	−0.0845510	−	0.204124i
$25$	1.69552	+	1.69552i	0.339104	+	0.339104i
$26$	5.15432	+	5.15432i	1.01085	+	1.01085i
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$	0.198912	−	0.0823922i	0.0375909	−	0.0155707i
$29$	0.858221	−	2.07193i	0.159368	−	0.384748i	−0.823945	−	0.566669i	$-0.808232\pi$
$29$	0.858221	−	2.07193i	0.159368	−	0.384748i	0.983313	+	0.181922i	$0.0582317\pi$
$30$		−	2.98067i		−	0.544193i
$31$	−2.37849	−	0.985204i	−0.427190	−	0.176948i	0.158721	−	0.987324i	$-0.449263\pi$
$31$	−2.37849	−	0.985204i	−0.427190	−	0.176948i	−0.585911	+	0.810376i	$0.699263\pi$
$32$	−4.77791	+	4.77791i	−0.844623	+	0.844623i
$33$	5.02734			0.875147
$34$	6.78112	+	3.47247i	1.16295	+	0.595524i
$35$	−0.245584			−0.0415112
$36$	1.00000	−	1.00000i	0.166667	−	0.166667i
$37$	−9.86351	−	4.08560i	−1.62155	−	0.671668i	−0.627303	−	0.778775i	$-0.715841\pi$
$37$	−9.86351	−	4.08560i	−1.62155	−	0.671668i	−0.994248	+	0.107106i	$0.965841\pi$
$38$		−	12.1564i		−	1.97203i
$39$	1.50967	−	3.64466i	0.241740	−	0.583612i
$40$	1.61313	−	0.668179i	0.255058	−	0.105648i
$41$	−0.105915	−	0.255701i	−0.0165411	−	0.0399338i	0.915393	−	0.402561i	$-0.131880\pi$
$41$	−0.105915	−	0.255701i	−0.0165411	−	0.0399338i	−0.931934	+	0.362627i	$0.881880\pi$
$42$	−0.198912	−	0.198912i	−0.0306928	−	0.0306928i
$43$	4.48502	+	4.48502i	0.683959	+	0.683959i	0.960890	−	0.276931i	$-0.0893174\pi$
$43$	4.48502	+	4.48502i	0.683959	+	0.683959i	−0.276931	+	0.960890i	$0.589317\pi$
$44$	−2.72078	−	6.56854i	−0.410172	−	0.990244i
$45$	−1.49033	+	0.617317i	−0.222166	+	0.0920241i
$46$	2.43835	−	5.88669i	0.359514	−	0.867945i
$47$			9.82164i			1.43263i	0.697775	+	0.716317i	$0.254173\pi$
$47$			9.82164i			1.43263i	−0.697775	+	0.716317i	$0.745827\pi$
$48$	4.46088	+	1.84776i	0.643873	+	0.266701i
$49$	4.93336	−	4.93336i	0.704766	−	0.704766i
$50$	−4.43060			−0.626582
$51$	0.331821	−	4.10973i	0.0464643	−	0.575478i
$52$	−5.57900			−0.773668
$53$	−1.50339	+	1.50339i	−0.206507	+	0.206507i	−0.802781	−	0.596274i	$-0.796647\pi$
$53$	−1.50339	+	1.50339i	−0.206507	+	0.206507i	0.596274	+	0.802781i	$0.296647\pi$
$54$	−1.70711	−	0.707107i	−0.232308	−	0.0962250i
$55$			8.10973i			1.09352i
$56$	0.0630603	−	0.152241i	0.00842678	−	0.0203441i
$57$	−6.07820	+	2.51767i	−0.805077	+	0.333474i
$58$	1.58579	+	3.82843i	0.208224	+	0.502697i
$59$	−0.936078	−	0.936078i	−0.121867	−	0.121867i	0.643543	−	0.765410i	$-0.277464\pi$
$59$	−0.936078	−	0.936078i	−0.121867	−	0.121867i	−0.765410	+	0.643543i	$0.777464\pi$
$60$	1.61313	+	1.61313i	0.208254	+	0.208254i
$61$	−3.16799	−	7.64821i	−0.405620	−	0.979253i	−0.986276	−	0.165104i	$-0.947204\pi$
$61$	−3.16799	−	7.64821i	−0.405620	−	0.979253i	0.580656	−	0.814149i	$-0.302796\pi$
$62$	4.39488	−	1.82042i	0.558151	−	0.231194i
$63$	−0.0582601	+	0.140652i	−0.00734008	+	0.0177205i
$64$		−	2.82843i		−	0.353553i
$65$	5.87929	+	2.43528i	0.729236	+	0.302059i
$66$	−6.56854	+	6.56854i	−0.808531	+	0.808531i
$67$	−7.10973			−0.868592			−0.434296	−	0.900770i	$-0.643003\pi$
$67$	−7.10973			−0.868592			−0.434296	+	0.900770i	$0.643003\pi$
$68$	−5.54920	+	1.79063i	−0.672940	+	0.217145i
$69$	−3.44834			−0.415132
$70$	0.320871	−	0.320871i	0.0383514	−	0.0383514i
$71$	6.04875	+	2.50548i	0.717855	+	0.297345i	0.711551	−	0.702635i	$-0.247993\pi$
$71$	6.04875	+	2.50548i	0.717855	+	0.297345i	0.00630431	+	0.999980i	$0.497993\pi$
$72$		−	1.08239i		−	0.127561i
$73$	3.18637	−	7.69258i	0.372936	−	0.900348i	−0.620314	−	0.784354i	$-0.712995\pi$
$73$	3.18637	−	7.69258i	0.372936	−	0.900348i	0.993250	−	0.115994i	$-0.0370053\pi$
$74$	18.2254	−	7.54920i	2.11866	−	0.877577i
$75$	0.917608	+	2.21530i	0.105956	+	0.255801i
$76$	6.57900	+	6.57900i	0.754663	+	0.754663i
$77$	0.541196	+	0.541196i	0.0616750	+	0.0616750i
$78$	2.78950	+	6.73445i	0.315849	+	0.762526i
$79$	0.491806	−	0.203713i	0.0553325	−	0.0229195i	−0.354846	−	0.934925i	$-0.615467\pi$
$79$	0.491806	−	0.203713i	0.0553325	−	0.0229195i	0.410178	+	0.912005i	$0.365467\pi$
$80$	−2.98067	+	7.19597i	−0.333249	+	0.804534i
$81$			1.00000i			0.111111i
$82$	0.472474	+	0.195705i	0.0521760	+	0.0216120i
$83$	−1.55807	+	1.55807i	−0.171021	+	0.171021i	−0.787428	−	0.616407i	$-0.788588\pi$
$83$	−1.55807	+	1.55807i	−0.171021	+	0.171021i	0.616407	+	0.787428i	$0.288588\pi$
$84$	0.215301			0.0234913
$85$	6.62951	+	0.535270i	0.719072	+	0.0580581i
$86$	−11.7199			−1.26379
$87$	1.58579	−	1.58579i	0.170014	−	0.170014i
$88$	−5.02734	−	2.08239i	−0.535916	−	0.221984i
$89$			7.64847i			0.810737i	0.914153	+	0.405368i	$0.132857\pi$
$89$			7.64847i			0.810737i	−0.914153	+	0.405368i	$0.867143\pi$
$90$	1.14065	−	2.75378i	0.120235	−	0.290274i
$91$	0.554866	−	0.229833i	0.0581657	−	0.0240930i
$92$	1.86623	+	4.50548i	0.194568	+	0.469728i
$93$	−1.82042	−	1.82042i	−0.188769	−	0.188769i
$94$	−12.8326	−	12.8326i	−1.32358	−	1.32358i
$95$	−4.06132	−	9.80490i	−0.416683	−	1.00596i
$96$	−6.24264	+	2.58579i	−0.637137	+	0.263911i
$97$	−1.38009	+	3.33182i	−0.140126	+	0.338295i	−0.978327	−	0.207067i	$-0.933608\pi$
$97$	−1.38009	+	3.33182i	−0.140126	+	0.338295i	0.838200	+	0.545363i	$0.183608\pi$
$98$			12.8915i			1.30224i
$99$	4.64466	+	1.92388i	0.466805	+	0.193357i
$100$	2.39782	−	2.39782i	0.239782	−	0.239782i
$101$	−9.13707			−0.909173			−0.454586	−	0.890703i	$-0.650213\pi$
$101$	−9.13707			−0.909173			−0.454586	+	0.890703i	$0.650213\pi$
$102$	4.93608	+	5.80317i	0.488745	+	0.574599i
$103$	7.57862			0.746744			0.373372	−	0.927682i	$-0.378202\pi$
$103$	7.57862			0.746744			0.373372	+	0.927682i	$0.378202\pi$
$104$	−3.01933	+	3.01933i	−0.296070	+	0.296070i
$105$	−0.226890	−	0.0939809i	−0.0221422	−	0.00917159i
$106$		−	3.92856i		−	0.381575i
$107$	7.06688	−	17.0610i	0.683181	−	1.64934i	−0.0749059	−	0.997191i	$-0.523866\pi$
$107$	7.06688	−	17.0610i	0.683181	−	1.64934i	0.758087	−	0.652154i	$-0.226134\pi$
$108$	1.30656	−	0.541196i	0.125724	−	0.0520766i
$109$	4.10973	+	9.92177i	0.393641	+	0.950333i	0.989140	+	0.146977i	$0.0469544\pi$
$109$	4.10973	+	9.92177i	0.393641	+	0.950333i	−0.595499	+	0.803356i	$0.703046\pi$
$110$	−10.5959	−	10.5959i	−1.01028	−	1.01028i
$111$	−7.54920	−	7.54920i	−0.716539	−	0.716539i
$112$	0.281305	+	0.679129i	0.0265808	+	0.0641717i
$113$	1.54747	−	0.640982i	0.145574	−	0.0602985i	−0.308707	−	0.951157i	$-0.599896\pi$
$113$	1.54747	−	0.640982i	0.145574	−	0.0602985i	0.454281	+	0.890859i	$0.349896\pi$
$114$	4.65205	−	11.2311i	0.435705	−	1.05188i
$115$		−	5.56261i		−	0.518716i
$116$	−2.93015	−	1.21371i	−0.272058	−	0.112690i
$117$	2.78950	−	2.78950i	0.257889	−	0.257889i
$118$	2.44609			0.225181
$119$	0.478136	−	0.406694i	0.0438306	−	0.0372816i
$120$	1.74603			0.159390
$121$	10.0933	−	10.0933i	0.917577	−	0.917577i
$122$	14.1320	+	5.85369i	1.27946	+	0.529968i
$123$		−	0.276769i		−	0.0249554i
$124$	−1.39329	+	3.36370i	−0.125121	+	0.302069i
$125$	−11.0252	+	4.56680i	−0.986127	+	0.408467i
$126$	−0.107651	−	0.259892i	−0.00959028	−	0.0231530i
$127$	8.61339	+	8.61339i	0.764315	+	0.764315i	0.977099	−	0.212784i	$-0.0682532\pi$
$127$	8.61339	+	8.61339i	0.764315	+	0.764315i	−0.212784	+	0.977099i	$0.568253\pi$
$128$	−5.86030	−	5.86030i	−0.517982	−	0.517982i
$129$	2.42727	+	5.85996i	0.213710	+	0.515940i
$130$	−10.8635	+	4.49981i	−0.952793	+	0.394660i
$131$	−3.99948	+	9.65561i	−0.349436	+	0.843614i	0.647250	+	0.762278i	$0.275919\pi$
$131$	−3.99948	+	9.65561i	−0.349436	+	0.843614i	−0.996687	+	0.0813367i	$0.974081\pi$
$132$		−	7.10973i		−	0.618823i
$133$	−0.925351	−	0.383293i	−0.0802381	−	0.0332357i
$134$	9.28931	−	9.28931i	0.802474	−	0.802474i
$135$	−1.61313			−0.138836
$136$	−2.03413	+	3.97229i	−0.174425	+	0.340621i
$137$	13.4928			1.15276			0.576382	−	0.817180i	$-0.304464\pi$
$137$	13.4928			1.15276			0.576382	+	0.817180i	$0.304464\pi$
$138$	4.50548	−	4.50548i	0.383532	−	0.383532i
$139$	−4.92241	−	2.03893i	−0.417513	−	0.172940i	0.164030	−	0.986455i	$-0.447551\pi$
$139$	−4.92241	−	2.03893i	−0.417513	−	0.172940i	−0.581543	+	0.813516i	$0.697551\pi$
$140$			0.347308i			0.0293529i
$141$	−3.75858	+	9.07401i	−0.316529	+	0.764170i
$142$	−11.1766	+	4.62951i	−0.937923	+	0.388500i
$143$	−7.58960	−	18.3229i	−0.634675	−	1.53224i
$144$	3.41421	+	3.41421i	0.284518	+	0.284518i
$145$	2.55807	+	2.55807i	0.212436	+	0.212436i
$146$	5.88764	+	14.2140i	0.487265	+	1.17636i
$147$	6.44574	−	2.66991i	0.531636	−	0.220211i
$148$	−5.77791	+	13.9491i	−0.474941	+	1.14661i
$149$			9.31890i			0.763434i	0.924279	+	0.381717i	$0.124667\pi$
$149$			9.31890i			0.763434i	−0.924279	+	0.381717i	$0.875333\pi$
$150$	−4.09334	−	1.69552i	−0.334220	−	0.138438i
$151$	−8.45929	+	8.45929i	−0.688407	+	0.688407i	−0.961880	−	0.273472i	$-0.911828\pi$
$151$	−8.45929	+	8.45929i	−0.688407	+	0.688407i	0.273472	+	0.961880i	$0.411828\pi$
$152$	7.12106			0.577594
$153$	1.87929	−	3.66991i	0.151932	−	0.296695i
$154$	−1.41421			−0.113961
$155$	2.93657	−	2.93657i	0.235871	−	0.235871i
$156$	−5.15432	−	2.13499i	−0.412676	−	0.170936i
$157$			18.1548i			1.44891i	0.689321	+	0.724456i	$0.257909\pi$
$157$			18.1548i			1.44891i	−0.689321	+	0.724456i	$0.742091\pi$
$158$	−0.376412	+	0.908738i	−0.0299457	+	0.0722953i
$159$	−1.96428	+	0.813631i	−0.155777	+	0.0645251i
$160$	−4.17120	−	10.0702i	−0.329762	−	0.796116i
$161$	−0.371216	−	0.371216i	−0.0292559	−	0.0292559i
$162$	−1.30656	−	1.30656i	−0.102653	−	0.102653i
$163$	7.93015	+	19.1451i	0.621137	+	1.49956i	0.850369	+	0.526186i	$0.176379\pi$
$163$	7.93015	+	19.1451i	0.621137	+	1.49956i	−0.229232	+	0.973372i	$0.573621\pi$
$164$	−0.361616	+	0.149786i	−0.0282374	+	0.0116963i
$165$	−3.10346	+	7.49242i	−0.241604	+	0.583284i
$166$		−	4.07144i		−	0.316005i
$167$	−7.47308	−	3.09545i	−0.578285	−	0.239533i	0.0743169	−	0.997235i	$-0.476322\pi$
$167$	−7.47308	−	3.09545i	−0.578285	−	0.239533i	−0.652601	+	0.757701i	$0.726322\pi$
$168$	0.116520	−	0.116520i	0.00898973	−	0.00898973i
$169$	−2.56261			−0.197124
$170$	−9.36124	+	7.96251i	−0.717974	+	0.610697i
$171$	−6.57900			−0.503109
$172$	6.34277	−	6.34277i	0.483632	−	0.483632i
$173$	−1.07228	−	0.444151i	−0.0815236	−	0.0337682i	0.341549	−	0.939864i	$-0.389048\pi$
$173$	−1.07228	−	0.444151i	−0.0815236	−	0.0337682i	−0.423073	+	0.906096i	$0.639048\pi$
$174$			4.14386i			0.314145i
$175$	−0.139697	+	0.337260i	−0.0105601	+	0.0254944i
$176$	22.4264	−	9.28931i	1.69045	−	0.700208i
$177$	−0.506602	−	1.22304i	−0.0380785	−	0.0919297i
$178$	−9.99321	−	9.99321i	−0.749023	−	0.749023i
$179$	2.04826	+	2.04826i	0.153094	+	0.153094i	0.779499	−	0.626404i	$-0.215474\pi$
$179$	2.04826	+	2.04826i	0.153094	+	0.153094i	−0.626404	+	0.779499i	$0.715474\pi$
$180$	0.873017	+	2.10765i	0.0650709	+	0.157095i
$181$	0.778548	−	0.322485i	0.0578690	−	0.0239701i	−0.353561	−	0.935411i	$-0.615029\pi$
$181$	0.778548	−	0.322485i	0.0578690	−	0.0239701i	0.411430	+	0.911441i	$0.365029\pi$
$182$	−0.424676	+	1.02526i	−0.0314791	+	0.0759972i
$183$		−	8.27836i		−	0.611954i
$184$	3.44834	+	1.42835i	0.254215	+	0.105299i
$185$	12.1778	−	12.1778i	0.895331	−	0.895331i
$186$	4.75699			0.348799
$187$	−13.4300	−	15.7891i	−0.982096	−	1.15462i
$188$	13.8899			1.01302
$189$	−0.107651	+	0.107651i	−0.00783043	+	0.00783043i
$190$	18.1171	+	7.50435i	1.31435	+	0.544423i
$191$		−	9.97069i		−	0.721454i	−0.932671	−	0.360727i	$-0.882529\pi$
$191$		−	9.97069i		−	0.721454i	0.932671	−	0.360727i	$-0.117471\pi$
$192$	1.08239	−	2.61313i	0.0781149	−	0.188586i
$193$	3.44993	−	1.42901i	0.248332	−	0.102862i	−0.255046	−	0.966929i	$-0.582091\pi$
$193$	3.44993	−	1.42901i	0.248332	−	0.102862i	0.503377	+	0.864067i	$0.332091\pi$
$194$	−2.55007	−	6.15640i	−0.183084	−	0.442004i
$195$	4.49981	+	4.49981i	0.322238	+	0.322238i
$196$	−6.97682	−	6.97682i	−0.498344	−	0.498344i
$197$	−6.20151	−	14.9718i	−0.441839	−	1.06669i	−0.975303	−	0.220871i	$-0.929110\pi$
$197$	−6.20151	−	14.9718i	−0.441839	−	1.06669i	0.533464	−	0.845823i	$-0.320890\pi$
$198$	−8.58221	+	3.55487i	−0.609911	+	0.252633i
$199$	6.30411	−	15.2195i	0.446886	−	1.07888i	−0.526596	−	0.850116i	$-0.676532\pi$
$199$	6.30411	−	15.2195i	0.446886	−	1.07888i	0.973482	−	0.228763i	$-0.0734682\pi$
$200$		−	2.59539i		−	0.183522i
$201$	−6.56854	−	2.72078i	−0.463309	−	0.191909i
$202$	11.9382	−	11.9382i	0.839966	−	0.839966i
$203$	0.341422			0.0239631
$204$	−5.81204	−	0.469266i	−0.406924	−	0.0328552i
$205$	0.446463			0.0311823
$206$	−9.90195	+	9.90195i	−0.689902	+	0.689902i
$207$	−3.18585	−	1.31962i	−0.221432	−	0.0917202i
$208$		−	19.0479i		−	1.32073i
$209$	−12.6572	+	30.5572i	−0.875517	+	2.11368i
$210$	0.419238	−	0.173654i	0.0289302	−	0.0119833i
$211$	−4.09040	−	9.87510i	−0.281595	−	0.679830i	0.718278	−	0.695756i	$-0.244930\pi$
$211$	−4.09040	−	9.87510i	−0.281595	−	0.679830i	−0.999873	+	0.0159259i	$0.994930\pi$
$212$	2.12612	+	2.12612i	0.146023	+	0.146023i
$213$	4.62951	+	4.62951i	0.317209	+	0.317209i
$214$	13.0579	+	31.5245i	0.892619	+	2.15497i
$215$	−9.45285	+	3.91550i	−0.644679	+	0.267035i
$216$	0.414214	−	1.00000i	0.0281837	−	0.0680414i
$217$		−	0.391939i		−	0.0266065i
$218$	−18.3330	−	7.59379i	−1.24167	−	0.514317i
$219$	5.88764	−	5.88764i	0.397850	−	0.397850i
$220$	11.4689			0.773233
$221$	−15.4795	+	4.99495i	−1.04126	+	0.335997i
$222$	19.7270			1.32399
$223$	3.83004	−	3.83004i	0.256479	−	0.256479i	−0.567142	−	0.823620i	$-0.691951\pi$
$223$	3.83004	−	3.83004i	0.256479	−	0.256479i	0.823620	+	0.567142i	$0.191951\pi$
$224$	−0.950385	−	0.393663i	−0.0635003	−	0.0263027i
$225$			2.39782i			0.159855i
$226$	−1.18438	+	2.85935i	−0.0787838	+	0.190201i
$227$	−11.3625	+	4.70650i	−0.754155	+	0.312381i	−0.726436	−	0.687235i	$-0.758824\pi$
$227$	−11.3625	+	4.70650i	−0.754155	+	0.312381i	−0.0277193	+	0.999616i	$0.508824\pi$
$228$	3.56053	+	8.59588i	0.235802	+	0.569276i
$229$	−21.2951	−	21.2951i	−1.40722	−	1.40722i	−0.773856	−	0.633362i	$-0.781674\pi$
$229$	−21.2951	−	21.2951i	−1.40722	−	1.40722i	−0.633362	−	0.773856i	$-0.718326\pi$
$230$	7.26790	+	7.26790i	0.479231	+	0.479231i
$231$	0.292893	+	0.707107i	0.0192710	+	0.0465242i
$232$	−2.24264	+	0.928932i	−0.147237	+	0.0609874i
$233$	−3.36196	+	8.11649i	−0.220249	+	0.531729i	−0.994924	−	0.100631i	$-0.967914\pi$
$233$	−3.36196	+	8.11649i	−0.220249	+	0.531729i	0.774674	+	0.632360i	$0.217914\pi$
$234$			7.28931i			0.476517i
$235$	−14.6375	−	6.06306i	−0.954847	−	0.395510i
$236$	−1.32381	+	1.32381i	−0.0861729	+	0.0861729i
$237$	0.532327			0.0345783
$238$	−0.0933429	+	1.15609i	−0.00605052	+	0.0749379i
$239$	14.6501			0.947634			0.473817	−	0.880623i	$-0.342876\pi$
$239$	14.6501			0.947634			0.473817	+	0.880623i	$0.342876\pi$
$240$	−5.50756	+	5.50756i	−0.355511	+	0.355511i
$241$	15.6646	+	6.48849i	1.00905	+	0.417960i	0.825106	−	0.564977i	$-0.191115\pi$
$241$	15.6646	+	6.48849i	1.00905	+	0.417960i	0.183939	+	0.982938i	$0.441115\pi$
$242$			26.3752i			1.69546i
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$	−10.8162	+	4.48022i	−0.692436	+	0.286816i
$245$	4.30691	+	10.3978i	0.275158	+	0.664291i
$246$	0.361616	+	0.361616i	0.0230558	+	0.0230558i
$247$	18.3521	+	18.3521i	1.16772	+	1.16772i
$248$	1.06638	+	2.57446i	0.0677150	+	0.163479i
$249$	−2.03572	+	0.843223i	−0.129009	+	0.0534371i
$250$	8.43835	−	20.3720i	0.533688	−	1.28844i
$251$		−	13.9453i		−	0.880217i	−0.897945	−	0.440109i	$-0.854940\pi$
$251$		−	13.9453i		−	0.880217i	0.897945	−	0.440109i	$-0.145060\pi$
$252$	0.198912	+	0.0823922i	0.0125303	+	0.00519022i
$253$	−12.2584	+	12.2584i	−0.770678	+	0.770678i
$254$	−22.5079			−1.41227
$255$	5.92003	+	3.03153i	0.370727	+	0.189842i
$256$	20.9706			1.31066
$257$	13.9019	−	13.9019i	0.867180	−	0.867180i	−0.124980	−	0.992159i	$-0.539887\pi$
$257$	13.9019	−	13.9019i	0.867180	−	0.867180i	0.992159	+	0.124980i	$0.0398865\pi$
$258$	−10.8278	−	4.48502i	−0.674109	−	0.279225i
$259$		−	1.62535i		−	0.100994i
$260$	3.44401	−	8.31457i	0.213588	−	0.515648i
$261$	2.07193	−	0.858221i	0.128249	−	0.0531226i
$262$	−7.39008	−	17.8412i	−0.456561	−	1.10224i
$263$	19.7085	+	19.7085i	1.21528	+	1.21528i	0.969266	+	0.246015i	$0.0791213\pi$
$263$	19.7085	+	19.7085i	1.21528	+	1.21528i	0.246015	+	0.969266i	$0.420879\pi$
$264$	−3.84776	−	3.84776i	−0.236813	−	0.236813i
$265$	−1.31249	−	3.16863i	−0.0806256	−	0.194647i
$266$	1.70983	−	0.708233i	0.104836	−	0.0434246i
$267$	−2.92694	+	7.06627i	−0.179126	+	0.432449i
$268$			10.0547i			0.614187i
$269$	0.189698	+	0.0785753i	0.0115661	+	0.00479082i	0.388459	−	0.921466i	$-0.373008\pi$
$269$	0.189698	+	0.0785753i	0.0115661	+	0.00479082i	−0.376893	+	0.926257i	$0.623008\pi$
$270$	2.10765	−	2.10765i	0.128268	−	0.128268i
$271$	8.21077			0.498768			0.249384	−	0.968405i	$-0.419772\pi$
$271$	8.21077			0.498768			0.249384	+	0.968405i	$0.419772\pi$
$272$	−6.11358	−	18.9462i	−0.370690	−	1.14878i
$273$	0.600582			0.0363489
$274$	−17.6291	+	17.6291i	−1.06502	+	1.06502i
$275$	11.1371	+	4.61313i	0.671591	+	0.278182i
$276$			4.87669i			0.293542i
$277$	9.01896	−	21.7737i	0.541897	−	1.30825i	−0.381486	−	0.924374i	$-0.624588\pi$
$277$	9.01896	−	21.7737i	0.541897	−	1.30825i	0.923383	−	0.383880i	$-0.125412\pi$
$278$	9.09542	−	3.76745i	0.545507	−	0.225957i
$279$	−0.985204	−	2.37849i	−0.0589826	−	0.142397i
$280$	0.187962	+	0.187962i	0.0112329	+	0.0112329i
$281$	−7.17941	−	7.17941i	−0.428288	−	0.428288i	0.459757	−	0.888045i	$-0.347936\pi$
$281$	−7.17941	−	7.17941i	−0.428288	−	0.428288i	−0.888045	+	0.459757i	$0.847936\pi$
$282$	−6.94495	−	16.7666i	−0.413566	−	0.998436i
$283$	−8.75762	+	3.62753i	−0.520587	+	0.215634i	−0.627475	−	0.778637i	$-0.715911\pi$
$283$	−8.75762	+	3.62753i	−0.520587	+	0.215634i	0.106888	+	0.994271i	$0.465911\pi$
$284$	3.54328	−	8.55423i	0.210255	−	0.507600i
$285$		−	10.6128i		−	0.628645i
$286$	33.8563	+	14.0238i	2.00197	+	0.829242i
$287$	0.0297943	−	0.0297943i	0.00175870	−	0.00175870i
$288$	−6.75699			−0.398159
$289$	−13.7937	+	9.93654i	−0.811392	+	0.584503i
$290$	−6.68457			−0.392531
$291$	−2.55007	+	2.55007i	−0.149487	+	0.149487i
$292$	−10.8789	−	4.50621i	−0.636642	−	0.263706i
$293$		−	9.28515i		−	0.542444i	−0.962517	−	0.271222i	$-0.912572\pi$
$293$		−	9.28515i		−	0.542444i	0.962517	−	0.271222i	$-0.0874278\pi$
$294$	−4.93336	+	11.9102i	−0.287719	+	0.694616i
$295$	1.97292	−	0.817212i	0.114868	−	0.0475799i
$296$	4.42222	+	10.6762i	0.257036	+	0.620541i
$297$	3.55487	+	3.55487i	0.206274	+	0.206274i
$298$	−12.1757	−	12.1757i	−0.705321	−	0.705321i
$299$	5.20584	+	12.5680i	0.301062	+	0.726827i
$300$	3.13291	−	1.29769i	0.180879	−	0.0749224i
$301$	−0.369530	+	0.892125i	−0.0212994	+	0.0514213i
$302$		−	22.1052i		−	1.27201i
$303$	−8.44155	−	3.49661i	−0.484955	−	0.200875i
$304$	−22.4621	+	22.4621i	−1.28829	+	1.28829i
$305$	13.3540			0.764650
$306$	2.33956	+	7.25038i	0.133744	+	0.414477i
$307$	−27.1418			−1.54906			−0.774531	−	0.632536i	$-0.782014\pi$
$307$	−27.1418			−1.54906			−0.774531	+	0.632536i	$0.782014\pi$
$308$	0.765367	−	0.765367i	0.0436108	−	0.0436108i
$309$	7.00174	+	2.90021i	0.398315	+	0.164987i
$310$			7.67362i			0.435832i
$311$	−0.989538	+	2.38896i	−0.0561115	+	0.135465i	−0.949449	−	0.313921i	$-0.898357\pi$
$311$	−0.989538	+	2.38896i	−0.0561115	+	0.135465i	0.893338	+	0.449386i	$0.148357\pi$
$312$	−3.94495	+	1.63405i	−0.223339	+	0.0925099i
$313$	9.80071	+	23.6610i	0.553969	+	1.33740i	0.914475	+	0.404643i	$0.132604\pi$
$313$	9.80071	+	23.6610i	0.553969	+	1.33740i	−0.360506	+	0.932757i	$0.617396\pi$
$314$	−23.7204	−	23.7204i	−1.33862	−	1.33862i
$315$	−0.173654	−	0.173654i	−0.00978429	−	0.00978429i
$316$	−0.288093	−	0.695518i	−0.0162065	−	0.0391260i
$317$	23.6497	−	9.79601i	1.32830	−	0.550199i	0.398128	−	0.917330i	$-0.369660\pi$
$317$	23.6497	−	9.79601i	1.32830	−	0.550199i	0.930169	+	0.367131i	$0.119660\pi$
$318$	1.50339	−	3.62951i	0.0843062	−	0.203533i
$319$		−	11.2745i		−	0.631252i
$320$	4.21530	+	1.74603i	0.235643	+	0.0976063i
$321$	13.0579	−	13.0579i	0.728820	−	0.728820i
$322$	0.970034			0.0540579
$323$	24.1444	+	12.3638i	1.34343	+	0.687942i
$324$	1.41421			0.0785674
$325$	6.68873	−	6.68873i	0.371024	−	0.371024i
$326$	−35.3755	−	14.6530i	−1.95927	−	0.811555i
$327$			10.7392i			0.593882i
$328$	−0.114641	+	0.276769i	−0.00633001	+	0.0152820i
$329$	−1.38144	+	0.572209i	−0.0761610	+	0.0315469i
$330$	−5.73445	−	13.8442i	−0.315671	−	0.762097i
$331$	0.235588	+	0.235588i	0.0129491	+	0.0129491i	0.713552	−	0.700603i	$-0.247085\pi$
$331$	0.235588	+	0.235588i	0.0129491	+	0.0129491i	−0.700603	+	0.713552i	$0.747085\pi$
$332$	2.20345	+	2.20345i	0.120930	+	0.120930i
$333$	−4.08560	−	9.86351i	−0.223889	−	0.540517i
$334$	13.8085	−	5.71965i	0.755565	−	0.312965i
$335$	4.38896	−	10.5959i	0.239794	−	0.578914i
$336$			0.735084i			0.0401021i
$337$	−3.46953	−	1.43713i	−0.188997	−	0.0782853i	0.286178	−	0.958177i	$-0.407615\pi$
$337$	−3.46953	−	1.43713i	−0.188997	−	0.0782853i	−0.475175	+	0.879891i	$0.657615\pi$
$338$	3.34821	−	3.34821i	0.182119	−	0.182119i
$339$	1.67497			0.0909717
$340$	0.756986	−	9.37555i	0.0410533	−	0.508461i
$341$	−12.9427			−0.700886
$342$	8.59588	−	8.59588i	0.464812	−	0.464812i
$343$	1.96587	+	0.814291i	0.106147	+	0.0439676i
$344$		−	6.86537i		−	0.370156i
$345$	2.12872	−	5.13918i	0.114606	−	0.276684i
$346$	1.98131	−	0.820684i	0.106516	−	0.0441202i
$347$	1.26668	+	3.05804i	0.0679989	+	0.164164i	0.954225	−	0.299088i	$-0.0966825\pi$
$347$	1.26668	+	3.05804i	0.0679989	+	0.164164i	−0.886227	+	0.463252i	$0.846682\pi$
$348$	−2.24264	−	2.24264i	−0.120218	−	0.120218i
$349$	1.82779	+	1.82779i	0.0978393	+	0.0978393i	0.754332	−	0.656493i	$-0.227961\pi$
$349$	1.82779	+	1.82779i	0.0978393	+	0.0978393i	−0.656493	+	0.754332i	$0.727961\pi$
$350$	−0.258127	−	0.623174i	−0.0137975	−	0.0333101i
$351$	3.64466	−	1.50967i	0.194537	−	0.0805800i
$352$	−12.9996	+	31.3839i	−0.692882	+	1.67277i
$353$			13.2848i			0.707079i	0.935420	+	0.353539i	$0.115022\pi$
$353$			13.2848i			0.707079i	−0.935420	+	0.353539i	$0.884978\pi$
$354$	2.25989	+	0.936078i	0.120112	+	0.0497520i
$355$	−7.46799	+	7.46799i	−0.396360	+	0.396360i
$356$	10.8166			0.573277
$357$	0.597375	−	0.192762i	0.0316164	−	0.0102020i
$358$	−5.35237			−0.282882
$359$	−10.4143	+	10.4143i	−0.549647	+	0.549647i	−0.926339	−	0.376692i	$-0.877062\pi$
$359$	−10.4143	+	10.4143i	−0.549647	+	0.549647i	0.376692	+	0.926339i	$0.377062\pi$
$360$	1.61313	+	0.668179i	0.0850192	+	0.0352161i
$361$		−	24.2832i		−	1.27806i
$362$	−0.595875	+	1.43857i	−0.0313185	+	0.0756095i
$363$	13.1876	−	5.46248i	0.692169	−	0.286706i
$364$	−0.325033	−	0.784699i	−0.0170364	−	0.0411294i
$365$	9.49751	+	9.49751i	0.497122	+	0.497122i
$366$	10.8162	+	10.8162i	0.565372	+	0.565372i
$367$	−0.168365	−	0.406470i	−0.00878861	−	0.0212176i	0.919424	−	0.393267i	$-0.128655\pi$
$367$	−0.168365	−	0.406470i	−0.00878861	−	0.0212176i	−0.928213	+	0.372049i	$0.878655\pi$
$368$	−15.3827	+	6.37170i	−0.801876	+	0.332148i
$369$	0.105915	−	0.255701i	0.00551370	−	0.0133113i
$370$			31.8222i			1.65436i
$371$	−0.299044	−	0.123868i	−0.0155256	−	0.00643090i
$372$	−2.57446	+	2.57446i	−0.133480	+	0.133480i
$373$	0.827899			0.0428670			0.0214335	−	0.999770i	$-0.493177\pi$
$373$	0.827899			0.0428670			0.0214335	+	0.999770i	$0.493177\pi$
$374$	38.1766	+	3.08239i	1.97406	+	0.159387i
$375$	−11.9336			−0.616250
$376$	7.51716	−	7.51716i	0.387668	−	0.387668i
$377$	−8.17365	−	3.38564i	−0.420965	−	0.174369i
$378$		−	0.281305i		−	0.0144687i
$379$	7.58033	−	18.3005i	0.389375	−	0.940035i	−0.600697	−	0.799477i	$-0.705110\pi$
$379$	7.58033	−	18.3005i	0.389375	−	0.940035i	0.990072	−	0.140558i	$-0.0448897\pi$
$380$	−13.8662	+	5.74358i	−0.711323	+	0.294639i
$381$	4.66153	+	11.2539i	0.238818	+	0.576557i
$382$	13.0273	+	13.0273i	0.666537	+	0.666537i
$383$	−11.7966	−	11.7966i	−0.602776	−	0.602776i	0.338273	−	0.941048i	$-0.390157\pi$
$383$	−11.7966	−	11.7966i	−0.602776	−	0.602776i	−0.941048	+	0.338273i	$0.890157\pi$
$384$	−3.17157	−	7.65685i	−0.161849	−	0.390737i
$385$	−1.14065	+	0.472474i	−0.0581330	+	0.0240795i
$386$	−2.64047	+	6.37465i	−0.134396	+	0.324461i
$387$			6.34277i			0.322421i
$388$	4.71191	+	1.95174i	0.239211	+	0.0990844i
$389$	−12.2315	+	12.2315i	−0.620163	+	0.620163i	−0.945573	−	0.325410i	$-0.894498\pi$
$389$	−12.2315	+	12.2315i	−0.620163	+	0.620163i	0.325410	+	0.945573i	$0.394498\pi$
$390$	−11.7586			−0.595419
$391$	9.21185	+	10.8300i	0.465863	+	0.547699i
$392$	−7.55166			−0.381416
$393$	−7.39008	+	7.39008i	−0.372780	+	0.372780i
$394$	27.6642	+	11.4589i	1.39370	+	0.577291i
$395$			0.858710i			0.0432064i
$396$	2.72078	−	6.56854i	0.136724	−	0.330081i
$397$	−5.95039	+	2.46473i	−0.298641	+	0.123701i	−0.526973	−	0.849882i	$-0.676673\pi$
$397$	−5.95039	+	2.46473i	−0.298641	+	0.123701i	0.228331	+	0.973583i	$0.426673\pi$
$398$	11.6485	+	28.1219i	0.583885	+	1.40962i
$399$	−0.708233	−	0.708233i	−0.0354560	−	0.0354560i
$400$	8.18669	+	8.18669i	0.409334	+	0.409334i
$401$	−8.06407	−	19.4684i	−0.402700	−	0.972204i	−0.987008	−	0.160672i	$-0.948634\pi$
$401$	−8.06407	−	19.4684i	−0.402700	−	0.972204i	0.584308	−	0.811532i	$-0.301366\pi$
$402$	12.1371	−	5.02734i	0.605342	−	0.250741i
$403$	−3.88658	+	9.38303i	−0.193604	+	0.467402i
$404$			12.9218i			0.642882i
$405$	−1.49033	−	0.617317i	−0.0740553	−	0.0306747i
$406$	−0.446089	+	0.446089i	−0.0221390	+	0.0221390i
$407$	−53.6728			−2.66046
$408$	−3.39942	+	2.89149i	−0.168296	+	0.143150i
$409$	−27.6232			−1.36588			−0.682939	−	0.730475i	$-0.739299\pi$
$409$	−27.6232			−1.36588			−0.682939	+	0.730475i	$0.739299\pi$
$410$	−0.583332	+	0.583332i	−0.0288087	+	0.0288087i
$411$	12.4657	+	5.16346i	0.614887	+	0.254694i
$412$		−	10.7178i		−	0.528028i
$413$	0.0771255	−	0.186197i	0.00379510	−	0.00916218i
$414$	5.88669	−	2.43835i	0.289315	−	0.119838i
$415$	−1.36023	−	3.28387i	−0.0667708	−	0.161199i
$416$	18.8486	+	18.8486i	0.924129	+	0.924129i
$417$	−3.76745	−	3.76745i	−0.184493	−	0.184493i
$418$	−23.3875	−	56.4623i	−1.14392	−	2.76166i
$419$	−11.1336	+	4.61170i	−0.543914	+	0.225297i	−0.637685	−	0.770297i	$-0.720108\pi$
$419$	−11.1336	+	4.61170i	−0.543914	+	0.225297i	0.0937711	+	0.995594i	$0.470108\pi$
$420$	−0.132909	+	0.320871i	−0.00648529	+	0.0156569i
$421$			14.0183i			0.683210i	0.939844	+	0.341605i	$0.110971\pi$
$421$			14.0183i			0.683210i	−0.939844	+	0.341605i	$0.889029\pi$
$422$	18.2468	+	7.55807i	0.888240	+	0.367921i
$423$	−6.94495	+	6.94495i	−0.337675	+	0.337675i
$424$	2.30130			0.111761
$425$	4.50621	−	8.79981i	0.218583	−	0.426854i
$426$	−12.0975			−0.586126
$427$	0.891171	−	0.891171i	0.0431268	−	0.0431268i
$428$	−24.1278	−	9.99407i	−1.16626	−	0.483082i
$429$		−	19.8326i		−	0.957526i
$430$	7.23490	−	17.4666i	0.348898	−	0.842314i
$431$	3.18166	−	1.31789i	0.153255	−	0.0634804i	−0.304737	−	0.952436i	$-0.598569\pi$
$431$	3.18166	−	1.31789i	0.153255	−	0.0634804i	0.457992	+	0.888956i	$0.348569\pi$
$432$	1.84776	+	4.46088i	0.0889003	+	0.214624i
$433$	−3.93561	−	3.93561i	−0.189133	−	0.189133i	0.606188	−	0.795321i	$-0.292698\pi$
$433$	−3.93561	−	3.93561i	−0.189133	−	0.189133i	−0.795321	+	0.606188i	$0.792698\pi$
$434$	0.512092	+	0.512092i	0.0245812	+	0.0245812i
$435$	1.38442	+	3.34228i	0.0663778	+	0.160250i
$436$	14.0315	−	5.81204i	0.671987	−	0.278346i
$437$	8.68180	−	20.9597i	0.415307	−	1.00264i
$438$			15.3852i			0.735131i
$439$	16.2477	+	6.73002i	0.775461	+	0.321206i	0.735082	−	0.677978i	$-0.237144\pi$
$439$	16.2477	+	6.73002i	0.775461	+	0.321206i	0.0403786	+	0.999184i	$0.487144\pi$
$440$	6.20692	−	6.20692i	0.295903	−	0.295903i
$441$	6.97682			0.332230
$442$	13.6987	−	26.7512i	0.651582	−	1.27242i
$443$	5.87632			0.279192			0.139596	−	0.990209i	$-0.455420\pi$
$443$	5.87632			0.279192			0.139596	+	0.990209i	$0.455420\pi$
$444$	−10.6762	+	10.6762i	−0.506669	+	0.506669i
$445$	−11.3988	−	4.72153i	−0.540354	−	0.223822i
$446$			10.0084i			0.473911i
$447$	−3.56619	+	8.60954i	−0.168675	+	0.407217i
$448$	0.397825	−	0.164784i	0.0187955	−	0.00778533i
$449$	−15.3001	−	36.9378i	−0.722058	−	1.74320i	−0.667403	−	0.744697i	$-0.732594\pi$
$449$	−15.3001	−	36.9378i	−0.722058	−	1.74320i	−0.0546546	−	0.998505i	$-0.517406\pi$
$450$	−3.13291	−	3.13291i	−0.147687	−	0.147687i
$451$	−0.983875	−	0.983875i	−0.0463289	−	0.0463289i
$452$	−0.906486	−	2.18845i	−0.0426375	−	0.102936i
$453$	−11.0526	+	4.57814i	−0.519296	+	0.215100i
$454$	8.69647	−	20.9951i	0.408146	−	0.985351i
$455$			0.968815i			0.0454188i
$456$	6.57900	+	2.72511i	0.308090	+	0.127615i
$457$	12.5092	−	12.5092i	0.585154	−	0.585154i	−0.351161	−	0.936315i	$-0.614213\pi$
$457$	12.5092	−	12.5092i	0.585154	−	0.585154i	0.936315	+	0.351161i	$0.114213\pi$
$458$	55.6467			2.60020
$459$	3.14065	−	2.67139i	0.146593	−	0.124690i
$460$	−7.86672			−0.366788
$461$	21.1186	−	21.1186i	0.983591	−	0.983591i	−0.0162762	−	0.999868i	$-0.505181\pi$
$461$	21.1186	−	21.1186i	0.983591	−	0.983591i	0.999868	+	0.0162762i	$0.00518111\pi$
$462$	−1.30656	−	0.541196i	−0.0607868	−	0.0251787i
$463$		−	9.45213i		−	0.439278i	−0.975581	−	0.219639i	$-0.929512\pi$
$463$		−	9.45213i		−	0.439278i	0.975581	−	0.219639i	$-0.0704879\pi$
$464$	4.14386	−	10.0042i	0.192374	−	0.464432i
$465$	3.83681	−	1.58926i	0.177928	−	0.0737001i
$466$	−6.21209	−	14.9973i	−0.287770	−	0.694737i
$467$	14.1488	+	14.1488i	0.654726	+	0.654726i	0.954127	−	0.299401i	$-0.0967869\pi$
$467$	14.1488	+	14.1488i	0.654726	+	0.654726i	−0.299401	+	0.954127i	$0.596787\pi$
$468$	−3.94495	−	3.94495i	−0.182355	−	0.182355i
$469$	−0.414214	−	1.00000i	−0.0191266	−	0.0461757i
$470$	27.0466	−	11.2031i	1.24757	−	0.516759i
$471$	−6.94755	+	16.7729i	−0.320126	+	0.772852i
$472$			1.43289i			0.0659539i
$473$	29.4600	+	12.2027i	1.35457	+	0.561082i
$474$	−0.695518	+	0.695518i	−0.0319462	+	0.0319462i
$475$	−15.7753			−0.723820
$476$	−0.575153	−	0.676186i	−0.0263621	−	0.0309929i
$477$	−2.12612			−0.0973484
$478$	−19.1412	+	19.1412i	−0.875500	+	0.875500i
$479$	1.11392	+	0.461402i	0.0508964	+	0.0210820i	0.407986	−	0.912988i	$-0.366231\pi$
$479$	1.11392	+	0.461402i	0.0508964	+	0.0210820i	−0.357090	+	0.934070i	$0.616231\pi$
$480$		−	10.8999i		−	0.497509i
$481$	−16.1175	+	38.9110i	−0.734894	+	1.77419i
$482$	−28.9444	+	11.9892i	−1.31838	+	0.546091i
$483$	−0.200901	−	0.485017i	−0.00914130	−	0.0220690i
$484$	−14.2741	−	14.2741i	−0.648825	−	0.648825i
$485$	−4.11358	−	4.11358i	−0.186788	−	0.186788i
$486$	−0.707107	−	1.70711i	−0.0320750	−	0.0774359i
$487$	11.0508	−	4.57738i	0.500759	−	0.207421i	−0.117983	−	0.993016i	$-0.537643\pi$
$487$	11.0508	−	4.57738i	0.500759	−	0.207421i	0.618742	+	0.785595i	$0.287643\pi$
$488$	−3.42901	+	8.27836i	−0.155224	+	0.374744i
$489$			20.7225i			0.937103i
$490$	−19.2126	−	7.95813i	−0.867938	−	0.359512i
$491$	−22.1064	+	22.1064i	−0.997649	+	0.997649i	−0.999997	−	0.00234871i	$-0.999252\pi$
$491$	−22.1064	+	22.1064i	−0.997649	+	0.997649i	0.00234871	+	0.999997i	$0.499252\pi$
$492$	−0.391410			−0.0176461
$493$	−9.21665	−	0.744156i	−0.415097	−	0.0335151i
$494$	−47.9564			−2.15766
$495$	−5.73445	+	5.73445i	−0.257744	+	0.257744i
$496$	−11.4844	−	4.75699i	−0.515664	−	0.213595i
$497$			0.996740i			0.0447099i
$498$	1.55807	−	3.76152i	0.0698189	−	0.168558i
$499$	38.2107	−	15.8274i	1.71055	−	0.708531i	0.710558	−	0.703638i	$-0.248442\pi$
$499$	38.2107	−	15.8274i	1.71055	−	0.708531i	0.999988	−	0.00489302i	$-0.00155750\pi$
$500$	6.45843	+	15.5920i	0.288830	+	0.697297i
$501$	−5.71965	−	5.71965i	−0.255535	−	0.255535i
$502$	18.2204	+	18.2204i	0.813215	+	0.813215i
$503$	−1.17972	−	2.84810i	−0.0526013	−	0.126991i	0.895394	−	0.445274i	$-0.146894\pi$
$503$	−1.17972	−	2.84810i	−0.0526013	−	0.126991i	−0.947996	+	0.318283i	$0.896894\pi$
$504$	0.152241	−	0.0630603i	0.00678135	−	0.00280893i
$505$	5.64047	−	13.6173i	0.250997	−	0.605961i
$506$		−	32.0327i		−	1.42403i
$507$	−2.36754	−	0.980668i	−0.105146	−	0.0435530i
$508$	12.1812	−	12.1812i	0.540452	−	0.540452i
$509$	33.8077			1.49850			0.749249	−	0.662288i	$-0.230415\pi$
$509$	33.8077			1.49850			0.749249	+	0.662288i	$0.230415\pi$
$510$	−11.6958	+	3.77401i	−0.517898	+	0.167116i
$511$	1.26762			0.0560760
$512$	−15.6788	+	15.6788i	−0.692910	+	0.692910i
$513$	−6.07820	−	2.51767i	−0.268359	−	0.111158i
$514$			36.3275i			1.60234i
$515$	−4.67841	+	11.2947i	−0.206155	+	0.497703i
$516$	8.28723	−	3.43268i	0.364825	−	0.151115i
$517$	18.8956	+	45.6181i	0.831030	+	2.00628i
$518$	2.12363	+	2.12363i	0.0933067	+	0.0933067i
$519$	−0.820684	−	0.820684i	−0.0360240	−	0.0360240i
$520$	−2.63593	−	6.36370i	−0.115593	−	0.279067i
$521$	−37.8381	+	15.6731i	−1.65772	+	0.686649i	−0.997900	−	0.0647762i	$-0.979367\pi$
$521$	−37.8381	+	15.6731i	−1.65772	+	0.686649i	−0.659818	+	0.751425i	$0.729367\pi$
$522$	−1.58579	+	3.82843i	−0.0694080	+	0.167566i
$523$		−	9.06788i		−	0.396511i	−0.980150	−	0.198255i	$-0.936472\pi$
$523$		−	9.06788i		−	0.396511i	0.980150	−	0.198255i	$-0.0635275\pi$
$524$	13.6551	+	5.65612i	0.596525	+	0.247089i
$525$	−0.258127	+	0.258127i	−0.0112656	+	0.0112656i
$526$	−51.5009			−2.24555
$527$	−0.854262	+	10.5803i	−0.0372122	+	0.460887i
$528$	24.2741			1.05640
$529$	−7.85521	+	7.85521i	−0.341531	+	0.341531i
$530$	5.85486	+	2.42516i	0.254319	+	0.105342i
$531$		−	1.32381i		−	0.0574486i
$532$	−0.542058	+	1.30864i	−0.0235012	+	0.0567369i
$533$	−1.00873	+	0.417828i	−0.0436928	+	0.0180981i
$534$	−5.40829	−	13.0568i	−0.234039	−	0.565021i
$535$	21.0640	+	21.0640i	0.910677	+	0.910677i
$536$	5.44155	+	5.44155i	0.235039	+	0.235039i
$537$	1.10851	+	2.67619i	0.0478359	+	0.115486i
$538$	−0.350515	+	0.145188i	−0.0151118	+	0.00625951i
$539$	13.4226	−	32.4049i	0.578151	−	1.39578i
$540$			2.28130i			0.0981717i
$541$	11.9569	+	4.95269i	0.514065	+	0.212933i	0.624608	−	0.780939i	$-0.285259\pi$
$541$	11.9569	+	4.95269i	0.514065	+	0.212933i	−0.110543	+	0.993871i	$0.535259\pi$
$542$	−10.7279	+	10.7279i	−0.460802	+	0.460802i
$543$	0.842695			0.0361635
$544$	24.7976	+	12.6983i	1.06319	+	0.544436i
$545$	−17.3238			−0.742068
$546$	−0.784699	+	0.784699i	−0.0335820	+	0.0335820i
$547$	9.84840	+	4.07934i	0.421087	+	0.174420i	0.583157	−	0.812359i	$-0.301817\pi$
$547$	9.84840	+	4.07934i	0.421087	+	0.174420i	−0.162070	+	0.986779i	$0.551817\pi$
$548$		−	19.0816i		−	0.815127i
$549$	3.16799	−	7.64821i	0.135207	−	0.326418i
$550$	−20.5786	+	8.52395i	−0.877475	+	0.363462i
$551$	5.64624	+	13.6312i	0.240538	+	0.580710i
$552$	2.63925	+	2.63925i	0.112334	+	0.112334i
$553$	0.0573053	+	0.0573053i	0.00243687	+	0.00243687i
$554$	16.6649	+	40.2325i	0.708022	+	1.70932i
$555$	15.9111	−	6.59059i	0.675388	−	0.279755i
$556$	−2.88348	+	6.96134i	−0.122287	+	0.295226i
$557$		−	30.1933i		−	1.27933i	−0.768653	−	0.639667i	$-0.779072\pi$
$557$		−	30.1933i		−	1.27933i	0.768653	−	0.639667i	$-0.220928\pi$
$558$	4.39488	+	1.82042i	0.186050	+	0.0770645i
$559$	17.6932	−	17.6932i	0.748341	−	0.748341i
$560$	−1.18578			−0.0501085
$561$	−6.36543	−	19.7267i	−0.268749	−	0.832861i
$562$	18.7607			0.791372
$563$	−21.1592	+	21.1592i	−0.891755	+	0.891755i	−0.994688	−	0.102934i	$-0.967177\pi$
$563$	−21.1592	+	21.1592i	−0.891755	+	0.891755i	0.102934	+	0.994688i	$0.467177\pi$
$564$	12.8326	+	5.31543i	0.540349	+	0.223820i
$565$			2.70193i			0.113671i
$566$	6.70279	−	16.1820i	0.281739	−	0.680179i
$567$	−0.140652	+	0.0582601i	−0.00590684	+	0.00244669i
$568$	−2.71191	−	6.54712i	−0.113789	−	0.274711i
$569$	−18.1692	−	18.1692i	−0.761694	−	0.761694i	0.214935	−	0.976628i	$-0.431046\pi$
$569$	−18.1692	−	18.1692i	−0.761694	−	0.761694i	−0.976628	+	0.214935i	$0.931046\pi$
$570$	13.8662	+	13.8662i	0.580792	+	0.580792i
$571$	−10.7206	−	25.8818i	−0.448643	−	1.08312i	−0.972831	−	0.231518i	$-0.925631\pi$
$571$	−10.7206	−	25.8818i	−0.448643	−	1.08312i	0.524187	−	0.851603i	$-0.324369\pi$
$572$	−25.9125	+	10.7333i	−1.08346	+	0.448783i
$573$	3.81562	−	9.21172i	0.159400	−	0.384825i
$574$			0.0778563i			0.00324966i
$575$	−7.63912	−	3.16423i	−0.318573	−	0.131957i
$576$	2.00000	−	2.00000i	0.0833333	−	0.0833333i
$577$	11.8072			0.491538			0.245769	−	0.969328i	$-0.420959\pi$
$577$	11.8072			0.491538			0.245769	+	0.969328i	$0.420959\pi$
$578$	5.03957	−	31.0050i	0.209618	−	1.28964i
$579$	3.73418			0.155187
$580$	3.61766	−	3.61766i	0.150215	−	0.150215i
$581$	−0.309920	−	0.128373i	−0.0128576	−	0.00532581i
$582$		−	6.66364i		−	0.276217i
$583$	−4.09040	+	9.87510i	−0.169407	+	0.408985i
$584$	−8.32638	+	3.44890i	−0.344548	+	0.142717i
$585$	2.43528	+	5.87929i	0.100686	+	0.243079i
$586$	12.1316	+	12.1316i	0.501153	+	0.501153i
$587$	5.26250	+	5.26250i	0.217207	+	0.217207i	0.807320	−	0.590114i	$-0.200917\pi$
$587$	5.26250	+	5.26250i	0.217207	+	0.217207i	−0.590114	+	0.807320i	$0.700917\pi$
$588$	−3.77583	−	9.11566i	−0.155713	−	0.375923i
$589$	15.6481	−	6.48165i	0.644769	−	0.267072i
$590$	−1.51001	+	3.64549i	−0.0621662	+	0.150082i
$591$		−	16.2053i		−	0.666598i
$592$	−47.6252	−	19.7270i	−1.95739	−	0.810776i
$593$	−5.41074	+	5.41074i	−0.222193	+	0.222193i	−0.809421	−	0.587229i	$-0.800219\pi$
$593$	−5.41074	+	5.41074i	−0.222193	+	0.222193i	0.587229	+	0.809421i	$0.300219\pi$
$594$	−9.28931			−0.381145
$595$	0.310949	+	0.963641i	0.0127477	+	0.0395054i
$596$	13.1789			0.539830
$597$	11.6485	−	11.6485i	0.476740	−	0.476740i
$598$	−23.2227	−	9.61915i	−0.949646	−	0.393356i
$599$		−	16.1547i		−	0.660062i	−0.943970	−	0.330031i	$-0.892941\pi$
$599$		−	16.1547i		−	0.660062i	0.943970	−	0.330031i	$-0.107059\pi$
$600$	0.993212	−	2.39782i	0.0405477	−	0.0978908i
$601$	−26.5316	+	10.9897i	−1.08225	+	0.448281i	−0.851296	−	0.524685i	$-0.824183\pi$
$601$	−26.5316	+	10.9897i	−1.08225	+	0.448281i	−0.230949	+	0.972966i	$0.574183\pi$
$602$	−0.682803	−	1.64843i	−0.0278290	−	0.0671851i
$603$	−5.02734	−	5.02734i	−0.204729	−	0.204729i
$604$	11.9632	+	11.9632i	0.486778	+	0.486778i
$605$	8.81166	+	21.2732i	0.358245	+	0.864880i
$606$	15.5980	−	6.46088i	0.633624	−	0.262456i
$607$	−9.87815	+	23.8480i	−0.400942	+	0.967959i	0.586496	+	0.809952i	$0.300507\pi$
$607$	−9.87815	+	23.8480i	−0.400942	+	0.967959i	−0.987438	+	0.158007i	$0.949493\pi$
$608$		−	44.4542i		−	1.80286i
$609$	0.315433	+	0.130656i	0.0127820	+	0.00529447i
$610$	−17.4479	+	17.4479i	−0.706445	+	0.706445i
$611$	38.7458			1.56749
$612$	−5.19004	−	2.65772i	−0.209795	−	0.107432i
$613$	49.1769			1.98623			0.993117	−	0.117123i	$-0.0373670\pi$
$613$	49.1769			1.98623			0.993117	+	0.117123i	$0.0373670\pi$
$614$	35.4624	−	35.4624i	1.43115	−	1.43115i
$615$	0.412478	+	0.170854i	0.0166327	+	0.00688949i
$616$		−	0.828427i		−	0.0333783i
$617$	1.35880	−	3.28044i	0.0547034	−	0.132066i	−0.894165	−	0.447738i	$-0.852230\pi$
$617$	1.35880	−	3.28044i	0.0547034	−	0.132066i	0.948868	+	0.315672i	$0.102230\pi$
$618$	−12.9375	+	5.35890i	−0.520423	+	0.215566i
$619$	−13.4709	−	32.5216i	−0.541440	−	1.30715i	−0.923707	−	0.383101i	$-0.874856\pi$
$619$	−13.4709	−	32.5216i	−0.541440	−	1.30715i	0.382266	−	0.924052i	$-0.375144\pi$
$620$	−4.15293	−	4.15293i	−0.166786	−	0.166786i
$621$	−2.43835	−	2.43835i	−0.0978474	−	0.0978474i
$622$	−1.82843	−	4.41421i	−0.0733132	−	0.176994i
$623$	−1.07578	+	0.445601i	−0.0431000	+	0.0178526i
$624$	7.28931	−	17.5980i	0.291806	−	0.704482i
$625$		−	7.26131i		−	0.290453i
$626$	−43.7199	−	18.1094i	−1.74740	−	0.723796i
$627$	−23.3875	+	23.3875i	−0.934005	+	0.934005i
$628$	25.6748			1.02454
$629$	−3.54259	+	43.8763i	−0.141252	+	1.74946i
$630$	0.453780			0.0180790
$631$	−22.2124	+	22.2124i	−0.884262	+	0.884262i	−0.993964	−	0.109702i	$-0.965010\pi$
$631$	−22.2124	+	22.2124i	−0.884262	+	0.884262i	0.109702	+	0.993964i	$0.465010\pi$
$632$	−0.532327	−	0.220497i	−0.0211748	−	0.00877089i
$633$		−	10.6887i		−	0.424839i
$634$	−18.1007	+	43.6989i	−0.718869	+	1.73550i
$635$	−18.1540	+	7.51964i	−0.720420	+	0.298408i
$636$	1.15065	+	2.77791i	0.0456262	+	0.110151i
$637$	−19.4618	−	19.4618i	−0.771106	−	0.771106i
$638$	14.7309	+	14.7309i	0.583201	+	0.583201i
$639$	2.50548	+	6.04875i	0.0991151	+	0.239285i
$640$	12.3515	−	5.11615i	0.488235	−	0.202233i
$641$	10.1700	−	24.5525i	0.401691	−	0.969767i	−0.585565	−	0.810625i	$-0.699127\pi$
$641$	10.1700	−	24.5525i	0.401691	−	0.969767i	0.987256	−	0.159141i	$-0.0508726\pi$
$642$			34.1219i			1.34668i
$643$	−14.8049	−	6.13238i	−0.583847	−	0.241837i	0.0711538	−	0.997465i	$-0.477332\pi$
$643$	−14.8049	−	6.13238i	−0.583847	−	0.241837i	−0.655001	+	0.755628i	$0.727332\pi$
$644$	−0.524979	+	0.524979i	−0.0206871	+	0.0206871i
$645$	−10.2317			−0.402872
$646$	−47.7003	+	15.3920i	−1.87674	+	0.605590i
$647$	41.6554			1.63764			0.818822	−	0.574048i	$-0.194628\pi$
$647$	41.6554			1.63764			0.818822	+	0.574048i	$0.194628\pi$
$648$	0.765367	−	0.765367i	0.0300665	−	0.0300665i
$649$	−6.14866	−	2.54686i	−0.241356	−	0.0999729i
$650$			17.4785i			0.685563i
$651$	0.149988	−	0.362104i	0.00587851	−	0.0141920i
$652$	27.0752	−	11.2149i	1.06035	−	0.439210i
$653$	−4.71711	−	11.3881i	−0.184595	−	0.445652i	0.804308	−	0.594212i	$-0.202536\pi$
$653$	−4.71711	−	11.3881i	−0.184595	−	0.445652i	−0.988903	+	0.148560i	$0.952536\pi$
$654$	−14.0315	−	14.0315i	−0.548675	−	0.548675i
$655$	−11.9211	−	11.9211i	−0.465797	−	0.465797i
$656$	−0.511402	−	1.23463i	−0.0199669	−	0.0482043i
$657$	7.69258	−	3.18637i	0.300116	−	0.124312i
$658$	1.05731	−	2.55256i	0.0412181	−	0.0995092i
$659$			3.46449i			0.134957i	0.997721	+	0.0674786i	$0.0214955\pi$
$659$			3.46449i			0.134957i	−0.997721	+	0.0674786i	$0.978505\pi$
$660$	10.5959	+	4.38896i	0.412444	+	0.170840i
$661$	20.0276	−	20.0276i	0.778984	−	0.778984i	−0.200674	−	0.979658i	$-0.564313\pi$
$661$	20.0276	−	20.0276i	0.778984	−	0.778984i	0.979658	+	0.200674i	$0.0643134\pi$
$662$	−0.615621			−0.0239268
$663$	−16.2127	−	1.30902i	−0.629648	−	0.0508380i
$664$	2.38500			0.0925558
$665$	1.14247	−	1.14247i	0.0443031	−	0.0443031i
$666$	18.2254	+	7.54920i	0.706220	+	0.292526i
$667$			7.73339i			0.299438i
$668$	−4.37763	+	10.5685i	−0.169376	+	0.408909i
$669$	5.00419	−	2.07280i	0.193473	−	0.0801392i
$670$	8.10973	+	19.5786i	0.313306	+	0.756388i
$671$	−29.4285	−	29.4285i	−1.13607	−	1.13607i
$672$	−0.727394	−	0.727394i	−0.0280598	−	0.0280598i
$673$	10.8715	+	26.2461i	0.419065	+	1.01171i	0.982619	+	0.185634i	$0.0594338\pi$
$673$	10.8715	+	26.2461i	0.419065	+	1.01171i	−0.563554	+	0.826079i	$0.690566\pi$
$674$	6.41086	−	2.65546i	0.246937	−	0.102285i
$675$	−0.917608	+	2.21530i	−0.0353187	+	0.0852670i
$676$			3.62408i			0.139388i
$677$	17.8293	+	7.38512i	0.685234	+	0.283833i	0.698013	−	0.716085i	$-0.254068\pi$
$677$	17.8293	+	7.38512i	0.685234	+	0.283833i	−0.0127789	+	0.999918i	$0.504068\pi$
$678$	−2.18845	+	2.18845i	−0.0840469	+	0.0840469i
$679$	−0.549032			−0.0210699
$680$	−4.66433	−	5.48369i	−0.178869	−	0.210290i
$681$	−12.2987			−0.471286
$682$	16.9104	−	16.9104i	0.647534	−	0.647534i
$683$	17.9965	+	7.45441i	0.688618	+	0.285235i	0.699424	−	0.714707i	$-0.253440\pi$
$683$	17.9965	+	7.45441i	0.688618	+	0.285235i	−0.0108060	+	0.999942i	$0.503440\pi$
$684$			9.30411i			0.355751i
$685$	−8.32930	+	20.1087i	−0.318246	+	0.768315i
$686$	−3.63246	+	1.50461i	−0.138688	+	0.0574464i
$687$	−11.5248	−	27.8233i	−0.439699	−	1.06153i
$688$	21.6556	+	21.6556i	0.825611	+	0.825611i
$689$	5.93081	+	5.93081i	0.225946	+	0.225946i
$690$	3.93336	+	9.49597i	0.149740	+	0.361505i
$691$	−6.96550	+	2.88520i	−0.264980	+	0.109758i	−0.511218	−	0.859451i	$-0.670806\pi$
$691$	−6.96550	+	2.88520i	−0.264980	+	0.109758i	0.246238	+	0.969209i	$0.420806\pi$
$692$	−0.628124	+	1.51643i	−0.0238777	+	0.0576459i
$693$			0.765367i			0.0290739i
$694$	−5.65051	−	2.34052i	−0.214491	−	0.0888449i
$695$	6.07737	−	6.07737i	0.230528	−	0.230528i
$696$	−2.42742			−0.0920110
$697$	−0.869234	+	0.739356i	−0.0329246	+	0.0280051i
$698$	−4.77624			−0.180783
$699$	−6.21209	+	6.21209i	−0.234963	+	0.234963i
$700$	0.476957	+	0.197562i	0.0180273	+	0.00746714i
$701$			39.0875i			1.47632i	0.674628	+	0.738158i	$0.264304\pi$
$701$			39.0875i			1.47632i	−0.674628	+	0.738158i	$0.735696\pi$
$702$	−2.78950	+	6.73445i	−0.105283	+	0.254175i
$703$	64.8920	−	26.8792i	2.44745	−	1.01377i
$704$	−5.44155	−	13.1371i	−0.205086	−	0.495122i
$705$	−11.2031	−	11.2031i	−0.421932	−	0.421932i
$706$	−17.3574	−	17.3574i	−0.653256	−	0.653256i
$707$	−0.532327	−	1.28515i	−0.0200202	−	0.0483330i
$708$	−1.72965	+	0.716443i	−0.0650041	+	0.0269256i
$709$	−2.56889	+	6.20186i	−0.0964768	+	0.232916i	−0.964749	−	0.263173i	$-0.915231\pi$
$709$	−2.56889	+	6.20186i	−0.0964768	+	0.232916i	0.868272	+	0.496089i	$0.165231\pi$
$710$		−	19.5148i		−	0.732377i
$711$	0.491806	+	0.203713i	0.0184442	+	0.00763982i
$712$	5.85389	−	5.85389i	0.219384	−	0.219384i
$713$	8.87762			0.332470
$714$	−0.528653	+	1.03236i	−0.0197843	+	0.0386352i
$715$	31.9925			1.19645
$716$	2.89668	−	2.89668i	0.108254	−	0.108254i
$717$	13.5349	+	5.60634i	0.505470	+	0.209373i
$718$		−	27.2140i		−	1.01562i
$719$	2.83424	−	6.84246i	0.105699	−	0.255181i	−0.862177	−	0.506607i	$-0.830900\pi$
$719$	2.83424	−	6.84246i	0.105699	−	0.255181i	0.967876	+	0.251426i	$0.0808995\pi$
$720$	−7.19597	+	2.98067i	−0.268178	+	0.111083i
$721$	0.441531	+	1.06595i	0.0164435	+	0.0396981i
$722$	31.7275	+	31.7275i	1.18078	+	1.18078i
$723$	11.9892	+	11.9892i	0.445882	+	0.445882i
$724$	−0.456063	−	1.10103i	−0.0169494	−	0.0409196i
$725$	4.96812	−	2.05786i	0.184512	−	0.0764272i
$726$	−10.0933	+	24.3675i	−0.374599	+	0.904362i
$727$		−	6.36054i		−	0.235899i	−0.993020	−	0.117950i	$-0.962368\pi$
$727$		−	6.36054i		−	0.235899i	0.993020	−	0.117950i	$-0.0376322\pi$
$728$	−0.600582	−	0.248769i	−0.0222591	−	0.00922001i
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$	−24.8182			−0.918562
$731$	11.9199	−	23.2774i	0.440874	−	0.860947i
$732$	−11.7074			−0.432717
$733$	−29.2273	+	29.2273i	−1.07954	+	1.07954i	−0.0829857	+	0.996551i	$0.526446\pi$
$733$	−29.2273	+	29.2273i	−1.07954	+	1.07954i	−0.996551	+	0.0829857i	$0.973554\pi$
$734$	0.751059	+	0.311099i	0.0277221	+	0.0114829i
$735$			11.2545i			0.415128i
$736$	8.91667	−	21.5268i	0.328673	−	0.793487i
$737$	−33.0223	+	13.6783i	−1.21639	+	0.503845i
$738$	0.195705	+	0.472474i	0.00720400	+	0.0173920i
$739$	−16.3803	−	16.3803i	−0.602561	−	0.602561i	0.338430	−	0.940991i	$-0.390104\pi$
$739$	−16.3803	−	16.3803i	−0.602561	−	0.602561i	−0.940991	+	0.338430i	$0.890104\pi$
$740$	−17.2220	−	17.2220i	−0.633095	−	0.633095i
$741$	9.93209	+	23.9782i	0.364864	+	0.880861i
$742$	0.552561	−	0.228878i	0.0202851	−	0.00840238i
$743$	−14.5995	+	35.2464i	−0.535606	+	1.29307i	0.392158	+	0.919898i	$0.371729\pi$
$743$	−14.5995	+	35.2464i	−0.535606	+	1.29307i	−0.927764	+	0.373168i	$0.878271\pi$
$744$			2.78658i			0.102161i
$745$	−13.8883	−	5.75271i	−0.508827	−	0.210763i
$746$	−1.08170	+	1.08170i	−0.0396039	+	0.0396039i
$747$	−2.20345			−0.0806200
$748$	−22.3292	+	18.9928i	−0.816436	+	0.694447i
$749$	2.81138			0.102726
$750$	15.5920	−	15.5920i	0.569340	−	0.569340i
$751$	−31.6034	−	13.0906i	−1.15322	−	0.477681i	−0.277611	−	0.960694i	$-0.589543\pi$
$751$	−31.6034	−	13.0906i	−1.15322	−	0.477681i	−0.875613	+	0.483013i	$0.839543\pi$
$752$			47.4231i			1.72934i
$753$	5.33662	−	12.8837i	0.194477	−	0.469510i
$754$	15.1029	−	6.25584i	0.550017	−	0.227824i
$755$	−7.38511	−	17.8292i	−0.268772	−	0.648872i
$756$	0.152241	+	0.152241i	0.00553695	+	0.00553695i
$757$	−4.96523	−	4.96523i	−0.180465	−	0.180465i	0.611094	−	0.791558i	$-0.290730\pi$
$757$	−4.96523	−	4.96523i	−0.180465	−	0.180465i	−0.791558	+	0.611094i	$0.790730\pi$
$758$	14.0066	+	33.8150i	0.508743	+	1.22821i
$759$	−16.0164	+	6.63419i	−0.581357	+	0.240806i
$760$	−4.39595	+	10.6128i	−0.159458	+	0.384965i
$761$			47.2917i			1.71432i	0.515048	+	0.857161i	$0.327774\pi$
$761$			47.2917i			1.71432i	−0.515048	+	0.857161i	$0.672226\pi$
$762$	−20.7946	−	8.61339i	−0.753308	−	0.312030i
$763$	−1.15609	+	1.15609i	−0.0418531	+	0.0418531i
$764$	−14.1007			−0.510145
$765$	4.30928	+	5.06627i	0.155802	+	0.183171i
$766$	30.8259			1.11378
$767$	−3.69278	+	3.69278i	−0.133338	+	0.133338i
$768$	19.3743	+	8.02509i	0.699109	+	0.289580i
$769$		−	6.39156i		−	0.230486i	−0.993337	−	0.115243i	$-0.963235\pi$
$769$		−	6.39156i		−	0.230486i	0.993337	−	0.115243i	$-0.0367646\pi$
$770$	0.873017	−	2.10765i	0.0314614	−	0.0759545i
$771$	18.1638	−	7.52368i	0.654152	−	0.270959i
$772$	−2.02092	−	4.87894i	−0.0727347	−	0.175597i
$773$	−2.60024	−	2.60024i	−0.0935241	−	0.0935241i	0.658797	−	0.752321i	$-0.271066\pi$
$773$	−2.60024	−	2.60024i	−0.0935241	−	0.0935241i	−0.752321	+	0.658797i	$0.771066\pi$
$774$	−8.28723	−	8.28723i	−0.297878	−	0.297878i
$775$	−2.36235	−	5.70321i	−0.0848580	−	0.204865i
$776$	3.60634	−	1.49379i	0.129460	−	0.0536241i
$777$	0.621995	−	1.50163i	0.0223140	−	0.0538707i
$778$		−	31.9625i		−	1.14591i
$779$	1.68226	+	0.696813i	0.0602731	+	0.0249659i
$780$	6.36370	−	6.36370i	0.227857	−	0.227857i
$781$	32.9146			1.17778
$782$	−26.1860	−	2.11427i	−0.936409	−	0.0756061i
$783$	2.24264			0.0801454
$784$	23.8204	−	23.8204i	0.850727	−	0.850727i
$785$	−27.0567	−	11.2073i	−0.965696	−	0.400004i
$786$		−	19.3112i		−	0.688808i
$787$	−1.55526	+	3.75473i	−0.0554391	+	0.133842i	−0.949172	−	0.314757i	$-0.898077\pi$
$787$	−1.55526	+	3.75473i	−0.0554391	+	0.133842i	0.893733	+	0.448599i	$0.148077\pi$
$788$	−21.1733	+	8.77026i	−0.754267	+	0.312428i
$789$	10.6662	+	25.7505i	0.379726	+	0.916741i
$790$	−1.12196	−	1.12196i	−0.0399175	−	0.0399175i
$791$	0.180311	+	0.180311i	0.00641113	+	0.00641113i
$792$	−2.08239	−	5.02734i	−0.0739946	−	0.178639i
$793$	−30.1718	+	12.4976i	−1.07143	+	0.443801i
$794$	4.55423	−	10.9949i	0.161623	−	0.390194i
$795$		−	3.42970i		−	0.121639i
$796$	−21.5236	−	8.91536i	−0.762883	−	0.315996i
$797$	9.76205	−	9.76205i	0.345790	−	0.345790i	−0.512749	−	0.858539i	$-0.671373\pi$
$797$	9.76205	−	9.76205i	0.345790	−	0.345790i	0.858539	+	0.512749i	$0.171373\pi$
$798$	1.85070			0.0655141
$799$	38.5389	−	12.4358i	1.36341	−	0.439947i
$800$	−16.2021			−0.572830
$801$	−5.40829	+	5.40829i	−0.191092	+	0.191092i
$802$	35.9729	+	14.9004i	1.27025	+	0.526153i
$803$		−	41.8596i		−	1.47719i
$804$	−3.84776	+	9.28931i	−0.135700	+	0.327609i
$805$	0.782394	−	0.324078i	0.0275758	−	0.0114223i
$806$	−7.18146	−	17.3376i	−0.252956	−	0.610690i
$807$	0.145188	+	0.145188i	0.00511087	+	0.00511087i
$808$	6.99321	+	6.99321i	0.246020	+	0.246020i
$809$	7.21319	+	17.4142i	0.253602	+	0.612250i	0.998490	−	0.0549401i	$-0.0174968\pi$
$809$	7.21319	+	17.4142i	0.253602	+	0.612250i	−0.744887	+	0.667190i	$0.767497\pi$
$810$	2.75378	−	1.14065i	0.0967579	−	0.0400784i
$811$	−0.994804	+	2.40167i	−0.0349323	+	0.0843340i	−0.940383	−	0.340118i	$-0.889533\pi$
$811$	−0.994804	+	2.40167i	−0.0349323	+	0.0843340i	0.905451	+	0.424452i	$0.139533\pi$
$812$		−	0.482843i		−	0.0169445i
$813$	7.58576	+	3.14212i	0.266044	+	0.110199i
$814$	70.1269	−	70.1269i	2.45795	−	2.45795i
$815$	−33.4280			−1.17093
$816$	1.60218	−	19.8435i	0.0560874	−	0.694663i
$817$	−41.7291			−1.45992
$818$	36.0914	−	36.0914i	1.26191	−	1.26191i
$819$	0.554866	+	0.229833i	0.0193886	+	0.00803101i
$820$		−	0.631394i		−	0.0220492i
$821$	4.97770	−	12.0172i	0.173723	−	0.419404i	−0.812904	−	0.582397i	$-0.802115\pi$
$821$	4.97770	−	12.0172i	0.173723	−	0.419404i	0.986627	+	0.162993i	$0.0521149\pi$
$822$	−23.0336	+	9.54082i	−0.803388	+	0.332774i
$823$	−8.28676	−	20.0060i	−0.288858	−	0.697366i	0.711125	−	0.703065i	$-0.248186\pi$
$823$	−8.28676	−	20.0060i	−0.288858	−	0.697366i	−0.999984	+	0.00569929i	$0.998186\pi$
$824$	−5.80043	−	5.80043i	−0.202067	−	0.202067i
$825$	8.52395	+	8.52395i	0.296766	+	0.296766i
$826$	0.142509	+	0.344048i	0.00495853	+	0.0119710i
$827$	−44.2300	+	18.3207i	−1.53803	+	0.637072i	−0.981102	−	0.193490i	$-0.938019\pi$
$827$	−44.2300	+	18.3207i	−1.53803	+	0.637072i	−0.556926	+	0.830562i	$0.688019\pi$
$828$	−1.86623	+	4.50548i	−0.0648559	+	0.156576i
$829$			12.9906i			0.451181i	0.974222	+	0.225590i	$0.0724311\pi$
$829$			12.9906i			0.451181i	−0.974222	+	0.225590i	$0.927569\pi$
$830$	6.06781	+	2.51337i	0.210617	+	0.0872403i
$831$	16.6649	−	16.6649i	0.578098	−	0.578098i
$832$	−11.1580			−0.386834
$833$	−25.6043	−	13.1115i	−0.887138	−	0.454285i
$834$	9.84482			0.340898
$835$	9.22652	−	9.22652i	0.319297	−	0.319297i
$836$	43.2144	+	17.9000i	1.49460	+	0.619084i
$837$		−	2.57446i		−	0.0889864i
$838$	8.52132	−	20.5723i	0.294364	−	0.710658i
$839$	17.4361	−	7.22226i	0.601961	−	0.249340i	−0.0608263	−	0.998148i	$-0.519374\pi$
$839$	17.4361	−	7.22226i	0.601961	−	0.249340i	0.662787	+	0.748808i	$0.269374\pi$
$840$	0.101724	+	0.245584i	0.00350982	+	0.00847345i
$841$	16.9497	+	16.9497i	0.584474	+	0.584474i
$842$	−18.3158	−	18.3158i	−0.631204	−	0.631204i
$843$	−3.88547	−	9.38035i	−0.133823	−	0.323076i
$844$	−13.9655	+	5.78470i	−0.480712	+	0.199118i
$845$	1.58194	−	3.81914i	0.0544204	−	0.131383i
$846$		−	18.1480i		−	0.623942i
$847$	2.00769	+	0.831613i	0.0689851	+	0.0285746i
$848$	−7.25903	+	7.25903i	−0.249276	+	0.249276i
$849$	−9.47918			−0.325325
$850$	5.60987	+	17.3852i	0.192417	+	0.596306i
$851$	36.8151			1.26201
$852$	6.54712	−	6.54712i	0.224301	−	0.224301i
$853$	5.57645	+	2.30984i	0.190934	+	0.0790875i	0.476102	−	0.879390i	$-0.342049\pi$
$853$	5.57645	+	2.30984i	0.190934	+	0.0790875i	−0.285168	+	0.958478i	$0.592049\pi$
$854$			2.32874i			0.0796879i
$855$	4.06132	−	9.80490i	0.138894	−	0.335321i
$856$	−18.4666	+	7.64913i	−0.631177	+	0.261442i
$857$	6.15488	+	14.8592i	0.210247	+	0.507581i	0.993461	−	0.114171i	$-0.0364213\pi$
$857$	6.15488	+	14.8592i	0.210247	+	0.507581i	−0.783214	+	0.621752i	$0.786421\pi$
$858$	25.9125	+	25.9125i	0.884639	+	0.884639i
$859$	−40.9101	−	40.9101i	−1.39583	−	1.39583i	−0.811548	−	0.584285i	$-0.801375\pi$
$859$	−40.9101	−	40.9101i	−1.39583	−	1.39583i	−0.584285	−	0.811548i	$-0.698625\pi$
$860$	5.53735	+	13.3683i	0.188822	+	0.455857i
$861$	0.0389281	−	0.0161246i	0.00132667	−	0.000549524i
$862$	−2.43514	+	5.87894i	−0.0829411	+	0.200238i
$863$		−	7.56067i		−	0.257368i	−0.991686	−	0.128684i	$-0.958925\pi$
$863$		−	7.56067i		−	0.257368i	0.991686	−	0.128684i	$-0.0410753\pi$
$864$	−6.24264	−	2.58579i	−0.212379	−	0.0879702i
$865$	1.32387	−	1.32387i	0.0450128	−	0.0450128i
$866$	10.2842			0.349473
$867$	−16.5462	+	3.90156i	−0.561940	+	0.132504i
$868$	−0.554285			−0.0188137
$869$	1.89235	−	1.89235i	0.0641936	−	0.0641936i
$870$	−6.17574	−	2.55807i	−0.209377	−	0.0867268i
$871$			28.0475i			0.950354i
$872$	4.44834	−	10.7392i	0.150640	−	0.363677i
$873$	−3.33182	+	1.38009i	−0.112765	+	0.0467088i
$874$	16.0419	+	38.7285i	0.542624	+	1.31001i
$875$	−1.28466	−	1.28466i	−0.0434295	−	0.0434295i
$876$	−8.32638	−	8.32638i	−0.281322	−	0.281322i
$877$	6.64567	+	16.0441i	0.224408	+	0.541770i	0.995479	−	0.0949797i	$-0.0302786\pi$
$877$	6.64567	+	16.0441i	0.224408	+	0.541770i	−0.771071	+	0.636749i	$0.780279\pi$
$878$	−30.0218	+	12.4355i	−1.01319	+	0.419676i
$879$	3.55327	−	8.57836i	0.119849	−	0.289341i
$880$			39.1572i			1.31999i
$881$	37.9731	+	15.7290i	1.27935	+	0.529923i	0.915793	−	0.401650i	$-0.131563\pi$
$881$	37.9731	+	15.7290i	1.27935	+	0.529923i	0.363554	+	0.931573i	$0.381563\pi$
$882$	−9.11566	+	9.11566i	−0.306940	+	0.306940i
$883$	−28.3729			−0.954824			−0.477412	−	0.878680i	$-0.658425\pi$
$883$	−28.3729			−0.954824			−0.477412	+	0.878680i	$0.658425\pi$
$884$	7.06392	+	21.8913i	0.237585	+	0.736285i
$885$	2.13548			0.0717833
$886$	−7.67778	+	7.67778i	−0.257940	+	0.257940i
$887$	−19.8638	−	8.22786i	−0.666961	−	0.276264i	0.0234033	−	0.999726i	$-0.492550\pi$
$887$	−19.8638	−	8.22786i	−0.666961	−	0.276264i	−0.690364	+	0.723462i	$0.742550\pi$
$888$			11.5558i			0.387788i
$889$	−0.709676	+	1.71331i	−0.0238018	+	0.0574626i
$890$	21.0622	−	8.72425i	0.706006	−	0.292437i
$891$	1.92388	+	4.64466i	0.0644524	+	0.155602i
$892$	−5.41650	−	5.41650i	−0.181358	−	0.181358i
$893$	−45.6908	−	45.6908i	−1.52898	−	1.52898i
$894$	−6.58946	−	15.9084i	−0.220385	−	0.532055i
$895$	−4.31703	+	1.78817i	−0.144302	+	0.0597719i
$896$	0.482843	−	1.16569i	0.0161307	−	0.0389429i
$897$			13.6035i			0.454208i
$898$	68.2521	+	28.2710i	2.27760	+	0.943414i
$899$	−4.08255	+	4.08255i	−0.136161	+	0.136161i
$900$	3.39104			0.113035
$901$	7.80268	+	3.99560i	0.259945	+	0.133113i
$902$	2.57099			0.0856046
$903$	−0.682803	+	0.682803i	−0.0227223	+	0.0227223i
$904$	−1.67497	−	0.693794i	−0.0557086	−	0.0230752i
$905$			1.35937i			0.0451871i
$906$	8.45929	−	20.4225i	0.281041	−	0.678493i
$907$	−13.6798	+	5.66635i	−0.454229	+	0.188148i	−0.598055	−	0.801455i	$-0.704060\pi$
$907$	−13.6798	+	5.66635i	−0.454229	+	0.188148i	0.143826	+	0.989603i	$0.454060\pi$
$908$	6.65599	+	16.0690i	0.220887	+	0.533268i
$909$	−6.46088	−	6.46088i	−0.214294	−	0.214294i
$910$	−1.26582	−	1.26582i	−0.0419615	−	0.0419615i
$911$	18.1855	+	43.9036i	0.602512	+	1.45459i	0.870987	+	0.491306i	$0.163480\pi$
$911$	18.1855	+	43.9036i	0.602512	+	1.45459i	−0.268475	+	0.963287i	$0.586520\pi$
$912$	−29.3482	+	12.1564i	−0.971814	+	0.402539i
$913$	−4.23917	+	10.2343i	−0.140296	+	0.338705i
$914$			32.6880i			1.08122i
$915$	12.3375	+	5.11037i	0.407866	+	0.168944i
$916$	−30.1158	+	30.1158i	−0.995053	+	0.995053i
$917$	−1.59109			−0.0525425
$918$	−0.613126	+	7.59379i	−0.0202362	+	0.250633i
$919$	−52.4090			−1.72881			−0.864407	−	0.502793i	$-0.832306\pi$
$919$	−52.4090			−1.72881			−0.864407	+	0.502793i	$0.832306\pi$
$920$	−4.25744	+	4.25744i	−0.140364	+	0.140364i
$921$	−25.0757	−	10.3867i	−0.826273	−	0.342253i
$922$			55.1856i			1.81744i
$923$	9.88397	−	23.8620i	0.325335	−	0.785428i
$924$	1.00000	−	0.414214i	0.0328976	−	0.0136266i
$925$	−9.79655	−	23.6510i	−0.322109	−	0.777639i
$926$	12.3498	+	12.3498i	0.405840	+	0.405840i
$927$	5.35890	+	5.35890i	0.176009	+	0.176009i
$928$	5.79899	+	14.0000i	0.190361	+	0.459573i
$929$	42.4038	−	17.5642i	1.39122	−	0.576263i	0.443764	−	0.896143i	$-0.353643\pi$
$929$	42.4038	−	17.5642i	1.39122	−	0.576263i	0.947458	+	0.319880i	$0.103643\pi$
$930$	−2.93657	+	7.08950i	−0.0962938	+	0.232474i
$931$			45.9005i			1.50433i
$932$	11.4785	+	4.75453i	0.375989	+	0.155740i
$933$	−1.82843	+	1.82843i	−0.0598600	+	0.0598600i
$934$	−36.9725			−1.20978
$935$	31.8216	−	10.2682i	1.04068	−	0.335807i
$936$	−4.26998			−0.139569
$937$	15.3852	−	15.3852i	0.502611	−	0.502611i	−0.409637	−	0.912248i	$-0.634345\pi$
$937$	15.3852	−	15.3852i	0.502611	−	0.502611i	0.912248	+	0.409637i	$0.134345\pi$
$938$	1.84776	+	0.765367i	0.0603315	+	0.0249901i
$939$			25.6105i			0.835767i
$940$	−8.57446	+	20.7006i	−0.279668	+	0.675179i
$941$	49.9839	−	20.7040i	1.62943	−	0.674932i	0.634261	−	0.773119i	$-0.281304\pi$
$941$	49.9839	−	20.7040i	1.62943	−	0.674932i	0.995168	+	0.0981874i	$0.0313045\pi$
$942$	−12.8374	−	30.9922i	−0.418265	−	1.00978i
$943$	0.674858	+	0.674858i	0.0219764	+	0.0219764i
$944$	−4.51978	−	4.51978i	−0.147106	−	0.147106i
$945$	−0.0939809	−	0.226890i	−0.00305720	−	0.00738073i
$946$	−54.4350	+	22.5477i	−1.76983	+	0.733089i
$947$	2.21041	−	5.33640i	0.0718286	−	0.173410i	−0.883888	−	0.467699i	$-0.845083\pi$
$947$	2.21041	−	5.33640i	0.0718286	−	0.173410i	0.955716	+	0.294290i	$0.0950830\pi$
$948$		−	0.752823i		−	0.0244506i
$949$	−30.3468	−	12.5701i	−0.985099	−	0.408041i
$950$	20.6114	−	20.6114i	0.668722	−	0.668722i
$951$	25.5982			0.830078
$952$	−0.677220	−	0.0546790i	−0.0219488	−	0.00177216i
$953$	−31.4698			−1.01941			−0.509704	−	0.860350i	$-0.670245\pi$
$953$	−31.4698			−1.01941			−0.509704	+	0.860350i	$0.670245\pi$
$954$	2.77791	−	2.77791i	0.0899382	−	0.0899382i
$955$	14.8597	+	6.15507i	0.480847	+	0.199174i
$956$		−	20.7183i		−	0.670078i
$957$	4.31457	−	10.4163i	0.139470	−	0.336711i
$958$	−2.05826	+	0.852559i	−0.0664994	+	0.0275449i
$959$	0.786089	+	1.89779i	0.0253841	+	0.0612828i
$960$	3.22625	+	3.22625i	0.104127	+	0.104127i
$961$	−17.2337	−	17.2337i	−0.555926	−	0.555926i
$962$	−29.7812	−	71.8982i	−0.960185	−	2.31809i
$963$	17.0610	−	7.06688i	0.549781	−	0.227727i
$964$	9.17611	−	22.1531i	0.295543	−	0.713503i
$965$			6.02371i			0.193910i
$966$	0.896195	+	0.371216i	0.0288346	+	0.0119437i
$967$	4.11626	−	4.11626i	0.132370	−	0.132370i	−0.637818	−	0.770187i	$-0.720163\pi$
$967$	4.11626	−	4.11626i	0.132370	−	0.132370i	0.770187	+	0.637818i	$0.220163\pi$
$968$	−15.4502			−0.496589
$969$	17.5750	+	20.6623i	0.564592	+	0.663770i
$970$	10.7493			0.345139
$971$	15.4891	−	15.4891i	0.497070	−	0.497070i	−0.413455	−	0.910525i	$-0.635678\pi$
$971$	15.4891	−	15.4891i	0.497070	−	0.497070i	0.910525	+	0.413455i	$0.135678\pi$
$972$	1.30656	+	0.541196i	0.0419080	+	0.0173589i
$973$		−	0.811136i		−	0.0260038i
$974$	−8.45790	+	20.4192i	−0.271009	+	0.654273i
$975$	8.73925	−	3.61991i	0.279880	−	0.115930i
$976$	−15.2964	−	36.9288i	−0.489626	−	1.18206i
$977$	19.8324	+	19.8324i	0.634495	+	0.634495i	0.949192	−	0.314697i	$-0.101903\pi$
$977$	19.8324	+	19.8324i	0.634495	+	0.634495i	−0.314697	+	0.949192i	$0.601903\pi$
$978$	−27.0752	−	27.0752i	−0.865770	−	0.865770i
$979$	14.7147	+	35.5245i	0.470285	+	1.13537i
$980$	14.7047	−	6.09089i	0.469725	−	0.194566i
$981$	−4.10973	+	9.92177i	−0.131214	+	0.316778i
$982$		−	57.7668i		−	1.84341i
$983$	−28.9425	−	11.9884i	−0.923121	−	0.382369i	−0.130056	−	0.991507i	$-0.541516\pi$
$983$	−28.9425	−	11.9884i	−0.923121	−	0.382369i	−0.793065	+	0.609137i	$0.791516\pi$
$984$	−0.211830	+	0.211830i	−0.00675288	+	0.00675288i
$985$	26.1412			0.832929
$986$	13.0144	−	11.0698i	0.414464	−	0.352536i
$987$	−1.49526			−0.0475945
$988$	25.9538	−	25.9538i	0.825700	−	0.825700i
$989$	−20.2071	−	8.37007i	−0.642549	−	0.266153i
$990$		−	14.9848i		−	0.476249i
$991$	6.88802	−	16.6291i	0.218805	−	0.528242i	−0.775919	−	0.630833i	$-0.782713\pi$
$991$	6.88802	−	16.6291i	0.218805	−	0.528242i	0.994724	+	0.102591i	$0.0327133\pi$
$992$	16.0714	−	6.65701i	0.510269	−	0.211360i
$993$	0.127499	+	0.307810i	0.00404607	+	0.00976807i
$994$	−1.30230	−	1.30230i	−0.0413066	−	0.0413066i
$995$	18.7905	+	18.7905i	0.595697	+	0.595697i
$996$	1.19250	+	2.87894i	0.0377857	+	0.0912228i
$997$	51.3369	−	21.2644i	1.62586	−	0.673451i	0.631097	−	0.775704i	$-0.282605\pi$
$997$	51.3369	−	21.2644i	1.62586	−	0.673451i	0.994758	+	0.102253i	$0.0326050\pi$
$998$	−29.2452	+	70.6042i	−0.925741	+	2.23494i
$999$		−	10.6762i		−	0.337780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.h.a.43.1	yes	8
3.2	odd	2		153.2.l.e.145.2		8
4.3	odd	2		816.2.bq.a.145.1		8
17.2	even	8	inner	51.2.h.a.19.1	✓	8
17.3	odd	16		867.2.e.i.829.4		8
17.4	even	4		867.2.h.f.688.2		8
17.5	odd	16		867.2.e.h.616.1		8
17.6	odd	16		867.2.a.n.1.1		4
17.7	odd	16		867.2.d.e.577.7		8
17.8	even	8		867.2.h.b.712.2		8
17.9	even	8		867.2.h.f.712.2		8
17.10	odd	16		867.2.d.e.577.8		8
17.11	odd	16		867.2.a.m.1.1		4
17.12	odd	16		867.2.e.i.616.1		8
17.13	even	4		867.2.h.b.688.2		8
17.14	odd	16		867.2.e.h.829.4		8
17.15	even	8		867.2.h.g.733.1		8
17.16	even	2		867.2.h.g.757.1		8
51.2	odd	8		153.2.l.e.19.2		8
51.11	even	16		2601.2.a.bc.1.4		4
51.23	even	16		2601.2.a.bd.1.4		4
68.19	odd	8		816.2.bq.a.529.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.1	✓	8	17.2	even	8	inner
51.2.h.a.43.1	yes	8	1.1	even	1	trivial
153.2.l.e.19.2		8	51.2	odd	8
153.2.l.e.145.2		8	3.2	odd	2
816.2.bq.a.145.1		8	4.3	odd	2
816.2.bq.a.529.1		8	68.19	odd	8
867.2.a.m.1.1		4	17.11	odd	16
867.2.a.n.1.1		4	17.6	odd	16
867.2.d.e.577.7		8	17.7	odd	16
867.2.d.e.577.8		8	17.10	odd	16
867.2.e.h.616.1		8	17.5	odd	16
867.2.e.h.829.4		8	17.14	odd	16
867.2.e.i.616.1		8	17.12	odd	16
867.2.e.i.829.4		8	17.3	odd	16
867.2.h.b.688.2		8	17.13	even	4
867.2.h.b.712.2		8	17.8	even	8
867.2.h.f.688.2		8	17.4	even	4
867.2.h.f.712.2		8	17.9	even	8
867.2.h.g.733.1		8	17.15	even	8
867.2.h.g.757.1		8	17.16	even	2
2601.2.a.bc.1.4		4	51.11	even	16
2601.2.a.bd.1.4		4	51.23	even	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30656 + 1.30656i) q^{2} +(0.923880 + 0.382683i) q^{3} -1.41421i q^{4} +(-0.617317 + 1.49033i) q^{5} +(-1.70711 + 0.707107i) q^{6} +(0.0582601 + 0.140652i) q^{7} +(-0.765367 - 0.765367i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-1.14065 - 2.75378i) q^{10} +(4.64466 - 1.92388i) q^{11} +(0.541196 - 1.30656i) q^{12} -3.94495i q^{13} +(-0.259892 - 0.107651i) q^{14} +(-1.14065 + 1.14065i) q^{15} +4.82843 q^{16} +(-1.26616 - 3.92388i) q^{17} -1.84776 q^{18} +(-4.65205 + 4.65205i) q^{19} +(2.10765 + 0.873017i) q^{20} +0.152241i q^{21} +(-3.55487 + 8.58221i) q^{22} +(-3.18585 + 1.31962i) q^{23} +(-0.414214 - 1.00000i) q^{24} +(1.69552 + 1.69552i) q^{25} +(5.15432 + 5.15432i) q^{26} +(0.382683 + 0.923880i) q^{27} +(0.198912 - 0.0823922i) q^{28} +(0.858221 - 2.07193i) q^{29} -2.98067i q^{30} +(-2.37849 - 0.985204i) q^{31} +(-4.77791 + 4.77791i) q^{32} +5.02734 q^{33} +(6.78112 + 3.47247i) q^{34} -0.245584 q^{35} +(1.00000 - 1.00000i) q^{36} +(-9.86351 - 4.08560i) q^{37} -12.1564i q^{38} +(1.50967 - 3.64466i) q^{39} +(1.61313 - 0.668179i) q^{40} +(-0.105915 - 0.255701i) q^{41} +(-0.198912 - 0.198912i) q^{42} +(4.48502 + 4.48502i) q^{43} +(-2.72078 - 6.56854i) q^{44} +(-1.49033 + 0.617317i) q^{45} +(2.43835 - 5.88669i) q^{46} +9.82164i q^{47} +(4.46088 + 1.84776i) q^{48} +(4.93336 - 4.93336i) q^{49} -4.43060 q^{50} +(0.331821 - 4.10973i) q^{51} -5.57900 q^{52} +(-1.50339 + 1.50339i) q^{53} +(-1.70711 - 0.707107i) q^{54} +8.10973i q^{55} +(0.0630603 - 0.152241i) q^{56} +(-6.07820 + 2.51767i) q^{57} +(1.58579 + 3.82843i) q^{58} +(-0.936078 - 0.936078i) q^{59} +(1.61313 + 1.61313i) q^{60} +(-3.16799 - 7.64821i) q^{61} +(4.39488 - 1.82042i) q^{62} +(-0.0582601 + 0.140652i) q^{63} -2.82843i q^{64} +(5.87929 + 2.43528i) q^{65} +(-6.56854 + 6.56854i) q^{66} -7.10973 q^{67} +(-5.54920 + 1.79063i) q^{68} -3.44834 q^{69} +(0.320871 - 0.320871i) q^{70} +(6.04875 + 2.50548i) q^{71} -1.08239i q^{72} +(3.18637 - 7.69258i) q^{73} +(18.2254 - 7.54920i) q^{74} +(0.917608 + 2.21530i) q^{75} +(6.57900 + 6.57900i) q^{76} +(0.541196 + 0.541196i) q^{77} +(2.78950 + 6.73445i) q^{78} +(0.491806 - 0.203713i) q^{79} +(-2.98067 + 7.19597i) q^{80} +1.00000i q^{81} +(0.472474 + 0.195705i) q^{82} +(-1.55807 + 1.55807i) q^{83} +0.215301 q^{84} +(6.62951 + 0.535270i) q^{85} -11.7199 q^{86} +(1.58579 - 1.58579i) q^{87} +(-5.02734 - 2.08239i) q^{88} +7.64847i q^{89} +(1.14065 - 2.75378i) q^{90} +(0.554866 - 0.229833i) q^{91} +(1.86623 + 4.50548i) q^{92} +(-1.82042 - 1.82042i) q^{93} +(-12.8326 - 12.8326i) q^{94} +(-4.06132 - 9.80490i) q^{95} +(-6.24264 + 2.58579i) q^{96} +(-1.38009 + 3.33182i) q^{97} +12.8915i q^{98} +(4.64466 + 1.92388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} - 8 q^{6} + 8 q^{11} - 16 q^{14} + 16 q^{16} - 8 q^{17} - 8 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{23} + 8 q^{24} - 16 q^{25} + 16 q^{26} - 8 q^{28} + 8 q^{31} + 8 q^{33} - 8 q^{34} + 32 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^6 + 8 * q^11 - 16 * q^14 + 16 * q^16 - 8 * q^17 - 8 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^23 + 8 * q^24 - 16 * q^25 + 16 * q^26 - 8 * q^28 + 8 * q^31 + 8 * q^33 - 8 * q^34 + 32 * q^35 + 8 * q^36 - 8 * q^37 + 16 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^50 - 16 * q^52 - 32 * q^53 - 8 * q^54 - 16 * q^56 - 16 * q^57 + 24 * q^58 + 16 * q^59 - 8 * q^60 + 16 * q^61 + 16 * q^62 + 24 * q^65 - 16 * q^66 - 16 * q^67 - 24 * q^69 + 40 * q^70 - 16 * q^71 + 48 * q^73 + 64 * q^74 + 16 * q^75 + 24 * q^76 + 8 * q^78 - 16 * q^80 - 8 * q^82 + 32 * q^83 + 40 * q^85 - 32 * q^86 + 24 * q^87 - 8 * q^88 - 16 * q^91 - 32 * q^92 - 32 * q^93 - 40 * q^95 - 16 * q^96 + 8 * q^97 + 8 * q^99

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