LMFDB - Embedded newform 700.2.p.d.551.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(451,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("700.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.6
Character	$\chi$	$=$	700.551
Dual form			700.2.p.d.451.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819270 - 1.15273i) q^{2} +(-0.878165 - 1.52103i) q^{3} +(-0.657592 + 1.88880i) q^{4} +(-1.03388 + 2.25842i) q^{6} +(-2.00509 - 1.72616i) q^{7} +(2.71603 - 0.789410i) q^{8} +(-0.0423472 + 0.0733475i) q^{9} +O(q^{10})$	\(q+(-0.819270 - 1.15273i) q^{2} +(-0.878165 - 1.52103i) q^{3} +(-0.657592 + 1.88880i) q^{4} +(-1.03388 + 2.25842i) q^{6} +(-2.00509 - 1.72616i) q^{7} +(2.71603 - 0.789410i) q^{8} +(-0.0423472 + 0.0733475i) q^{9} +(3.59956 - 2.07821i) q^{11} +(3.45039 - 0.658464i) q^{12} -4.90376i q^{13} +(-0.347088 + 3.72552i) q^{14} +(-3.13514 - 2.48412i) q^{16} +(-0.197246 + 0.113880i) q^{17} +(0.119244 - 0.0112764i) q^{18} +(-0.396093 + 0.686053i) q^{19} +(-0.864729 + 4.56564i) q^{21} +(-5.34464 - 2.44673i) q^{22} +(4.71775 + 2.72379i) q^{23} +(-3.58584 - 3.43792i) q^{24} +(-5.65273 + 4.01750i) q^{26} -5.12024 q^{27} +(4.57890 - 2.65211i) q^{28} -8.17136 q^{29} +(-2.11825 - 3.66891i) q^{31} +(-0.295003 + 5.64916i) q^{32} +(-6.32202 - 3.65002i) q^{33} +(0.292871 + 0.134074i) q^{34} +(-0.110692 - 0.128218i) q^{36} +(-2.58440 + 4.47631i) q^{37} +(1.11534 - 0.105473i) q^{38} +(-7.45874 + 4.30631i) q^{39} -5.46577i q^{41} +(5.97142 - 2.74369i) q^{42} +4.95932i q^{43} +(1.55828 + 8.16548i) q^{44} +(-0.725302 - 7.66984i) q^{46} +(-2.89353 + 5.01175i) q^{47} +(-1.02524 + 6.95011i) q^{48} +(1.04077 + 6.92220i) q^{49} +(0.346429 + 0.200011i) q^{51} +(9.26222 + 3.22467i) q^{52} +(-5.41584 - 9.38050i) q^{53} +(4.19486 + 5.90227i) q^{54} +(-6.80853 - 3.10546i) q^{56} +1.39134 q^{57} +(6.69456 + 9.41941i) q^{58} +(-3.93063 - 6.80806i) q^{59} +(11.5731 + 6.68172i) q^{61} +(-2.49386 + 5.44760i) q^{62} +(0.211519 - 0.0739705i) q^{63} +(6.75366 - 4.28813i) q^{64} +(0.971941 + 10.2780i) q^{66} +(5.62711 - 3.24881i) q^{67} +(-0.0853894 - 0.447445i) q^{68} -9.56776i q^{69} +2.03817i q^{71} +(-0.0571151 + 0.232644i) q^{72} +(-4.64359 + 2.68098i) q^{73} +(7.27732 - 0.688183i) q^{74} +(-1.03535 - 1.19928i) q^{76} +(-10.8048 - 2.04641i) q^{77} +(11.0748 + 5.06992i) q^{78} +(4.42687 + 2.55585i) q^{79} +(4.62346 + 8.00806i) q^{81} +(-6.30058 + 4.47794i) q^{82} -9.52133 q^{83} +(-8.05496 - 4.63563i) q^{84} +(5.71677 - 4.06302i) q^{86} +(7.17580 + 12.4289i) q^{87} +(8.13597 - 8.48602i) q^{88} +(-2.01542 - 1.16361i) q^{89} +(-8.46465 + 9.83247i) q^{91} +(-8.24706 + 7.11975i) q^{92} +(-3.72034 + 6.44381i) q^{93} +(8.14780 - 0.770500i) q^{94} +(8.85158 - 4.51218i) q^{96} -17.7211i q^{97} +(7.12678 - 6.87088i) q^{98} +0.352025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9	$ 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9} + 15 q^{12} - 13 q^{14} + q^{16} - 15 q^{18} + 12 q^{21} + 34 q^{22} - 18 q^{24} - 15 q^{26} + 17 q^{28} + 8 q^{29} + 14 q^{32} - 30 q^{36} - 16 q^{37} + 30 q^{38} + q^{42} + 12 q^{44} + 2 q^{46} + 20 q^{49} + 18 q^{52} - 20 q^{53} + 57 q^{54} - 31 q^{56} - 24 q^{57} - 4 q^{58} - 12 q^{61} + 40 q^{64} - 66 q^{66} + 15 q^{68} + 13 q^{72} - 72 q^{73} - q^{74} + 8 q^{77} + 60 q^{78} - 36 q^{81} - 66 q^{82} + 67 q^{84} + 4 q^{86} + 34 q^{88} - 60 q^{89} - 148 q^{92} - 20 q^{93} + 45 q^{94} + 93 q^{96}+O(q^{100}) $ 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9 + 15 * q^12 - 13 * q^14 + q^16 - 15 * q^18 + 12 * q^21 + 34 * q^22 - 18 * q^24 - 15 * q^26 + 17 * q^28 + 8 * q^29 + 14 * q^32 - 30 * q^36 - 16 * q^37 + 30 * q^38 + q^42 + 12 * q^44 + 2 * q^46 + 20 * q^49 + 18 * q^52 - 20 * q^53 + 57 * q^54 - 31 * q^56 - 24 * q^57 - 4 * q^58 - 12 * q^61 + 40 * q^64 - 66 * q^66 + 15 * q^68 + 13 * q^72 - 72 * q^73 - q^74 + 8 * q^77 + 60 * q^78 - 36 * q^81 - 66 * q^82 + 67 * q^84 + 4 * q^86 + 34 * q^88 - 60 * q^89 - 148 * q^92 - 20 * q^93 + 45 * q^94 + 93 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.819270	−	1.15273i	−0.579312	−	0.815106i
$2$	−0.819270	−	1.15273i	−0.579312	−	0.815106i
$3$	−0.878165	−	1.52103i	−0.507009	−	0.878165i	−0.999967	−	0.00811200i	$-0.997418\pi$
$3$	−0.878165	−	1.52103i	−0.507009	−	0.878165i	0.492958	−	0.870053i	$-0.335915\pi$
$4$	−0.657592	+	1.88880i	−0.328796	+	0.944401i
$5$		0			0
$5$		0			0
$6$	−1.03388	+	2.25842i	−0.422082	+	0.921997i
$7$	−2.00509	−	1.72616i	−0.757853	−	0.652426i
$7$	−2.00509	−	1.72616i	−0.757853	−	0.652426i
$8$	2.71603	−	0.789410i	0.960262	−	0.279099i
$9$	−0.0423472	+	0.0733475i	−0.0141157	+	0.0244492i
$10$		0			0
$11$	3.59956	−	2.07821i	1.08531	−	0.626604i	0.152986	−	0.988228i	$-0.451111\pi$
$11$	3.59956	−	2.07821i	1.08531	−	0.626604i	0.932324	+	0.361625i	$0.117778\pi$
$12$	3.45039	−	0.658464i	0.996042	−	0.190082i
$13$		−	4.90376i		−	1.36006i	−0.733186	−	0.680029i	$-0.761967\pi$
$13$		−	4.90376i		−	1.36006i	0.733186	−	0.680029i	$-0.238033\pi$
$14$	−0.347088	+	3.72552i	−0.0927633	+	0.995688i
$15$		0			0
$16$	−3.13514	−	2.48412i	−0.783786	−	0.621031i
$17$	−0.197246	+	0.113880i	−0.0478392	+	0.0276200i	−0.523729	−	0.851885i	$-0.675459\pi$
$17$	−0.197246	+	0.113880i	−0.0478392	+	0.0276200i	0.475890	+	0.879505i	$0.342126\pi$
$18$	0.119244	−	0.0112764i	0.0281061	−	0.00265786i
$19$	−0.396093	+	0.686053i	−0.0908700	+	0.157391i	−0.907877	−	0.419236i	$-0.862298\pi$
$19$	−0.396093	+	0.686053i	−0.0908700	+	0.157391i	0.817007	+	0.576627i	$0.195631\pi$
$20$		0			0
$21$	−0.864729	+	4.56564i	−0.188699	+	0.996305i
$22$	−5.34464	−	2.44673i	−1.13948	−	0.521644i
$23$	4.71775	+	2.72379i	0.983719	+	0.567950i	0.903391	−	0.428818i	$-0.141070\pi$
$23$	4.71775	+	2.72379i	0.983719	+	0.567950i	0.0803281	+	0.996768i	$0.474403\pi$
$24$	−3.58584	−	3.43792i	−0.731956	−	0.701763i
$25$		0			0
$26$	−5.65273	+	4.01750i	−1.10859	+	0.787897i
$27$	−5.12024			−0.985390
$28$	4.57890	−	2.65211i	0.865330	−	0.501202i
$29$	−8.17136			−1.51738			−0.758692	−	0.651449i	$-0.774161\pi$
$29$	−8.17136			−1.51738			−0.758692	+	0.651449i	$0.774161\pi$
$30$		0			0
$31$	−2.11825	−	3.66891i	−0.380448	−	0.658956i	0.610678	−	0.791879i	$-0.290897\pi$
$31$	−2.11825	−	3.66891i	−0.380448	−	0.658956i	−0.991126	+	0.132923i	$0.957564\pi$
$32$	−0.295003	+	5.64916i	−0.0521496	+	0.998639i
$33$	−6.32202	−	3.65002i	−1.10052	−	0.635387i
$34$	0.292871	+	0.134074i	0.0502270	+	0.0229934i
$35$		0			0
$36$	−0.110692	−	0.128218i	−0.0184486	−	0.0213697i
$37$	−2.58440	+	4.47631i	−0.424873	+	0.735901i	−0.996409	−	0.0846759i	$-0.973014\pi$
$37$	−2.58440	+	4.47631i	−0.424873	+	0.735901i	0.571536	+	0.820577i	$0.306348\pi$
$38$	1.11534	−	0.105473i	0.180933	−	0.0171100i
$39$	−7.45874	+	4.30631i	−1.19435	+	0.689561i
$40$		0			0
$41$		−	5.46577i		−	0.853610i	−0.904344	−	0.426805i	$-0.859639\pi$
$41$		−	5.46577i		−	0.853610i	0.904344	−	0.426805i	$-0.140361\pi$
$42$	5.97142	−	2.74369i	0.921410	−	0.423361i
$43$			4.95932i			0.756289i	0.925747	+	0.378144i	$0.123438\pi$
$43$			4.95932i			0.756289i	−0.925747	+	0.378144i	$0.876562\pi$
$44$	1.55828	+	8.16548i	0.234920	+	1.23099i
$45$		0			0
$46$	−0.725302	−	7.66984i	−0.106940	−	1.13086i
$47$	−2.89353	+	5.01175i	−0.422065	+	0.731038i	−0.996141	−	0.0877636i	$-0.972028\pi$
$47$	−2.89353	+	5.01175i	−0.422065	+	0.731038i	0.574076	+	0.818802i	$0.305361\pi$
$48$	−1.02524	+	6.95011i	−0.147981	+	1.00316i
$49$	1.04077	+	6.92220i	0.148682	+	0.988885i
$50$		0			0
$51$	0.346429	+	0.200011i	0.0485098	+	0.0280071i
$52$	9.26222	+	3.22467i	1.28444	+	0.447182i
$53$	−5.41584	−	9.38050i	−0.743922	−	1.28851i	−0.950697	−	0.310123i	$-0.899630\pi$
$53$	−5.41584	−	9.38050i	−0.743922	−	1.28851i	0.206774	−	0.978389i	$-0.433703\pi$
$54$	4.19486	+	5.90227i	0.570848	+	0.803198i
$55$		0			0
$56$	−6.80853	−	3.10546i	−0.909829	−	0.414984i
$57$	1.39134			0.184287
$58$	6.69456	+	9.41941i	0.879038	+	1.23683i
$59$	−3.93063	−	6.80806i	−0.511725	−	0.886334i	−0.999908	−	0.0135921i	$-0.995673\pi$
$59$	−3.93063	−	6.80806i	−0.511725	−	0.886334i	0.488183	−	0.872741i	$-0.337660\pi$
$60$		0			0
$61$	11.5731	+	6.68172i	1.48178	+	0.855507i	0.999786	−	0.0206676i	$-0.00657915\pi$
$61$	11.5731	+	6.68172i	1.48178	+	0.855507i	0.481995	+	0.876174i	$0.339912\pi$
$62$	−2.49386	+	5.44760i	−0.316721	+	0.691846i
$63$	0.211519	−	0.0739705i	0.0266489	−	0.00931940i
$64$	6.75366	−	4.28813i	0.844208	−	0.536016i
$65$		0			0
$66$	0.971941	+	10.2780i	0.119638	+	1.26513i
$67$	5.62711	−	3.24881i	0.687461	−	0.396906i	−0.115199	−	0.993342i	$-0.536751\pi$
$67$	5.62711	−	3.24881i	0.687461	−	0.396906i	0.802660	+	0.596437i	$0.203417\pi$
$68$	−0.0853894	−	0.447445i	−0.0103550	−	0.0542607i
$69$		−	9.56776i		−	1.15182i
$70$		0			0
$71$			2.03817i			0.241886i	0.992659	+	0.120943i	$0.0385919\pi$
$71$			2.03817i			0.241886i	−0.992659	+	0.120943i	$0.961408\pi$
$72$	−0.0571151	+	0.232644i	−0.00673108	+	0.0274173i
$73$	−4.64359	+	2.68098i	−0.543491	+	0.313785i	−0.746493	−	0.665394i	$-0.768264\pi$
$73$	−4.64359	+	2.68098i	−0.543491	+	0.313785i	0.203002	+	0.979178i	$0.434930\pi$
$74$	7.27732	−	0.688183i	0.845971	−	0.0799997i
$75$		0			0
$76$	−1.03535	−	1.19928i	−0.118763	−	0.137567i
$77$	−10.8048	−	2.04641i	−1.23132	−	0.233210i
$78$	11.0748	+	5.06992i	1.25397	+	0.574055i
$79$	4.42687	+	2.55585i	0.498062	+	0.287556i	0.727913	−	0.685670i	$-0.240491\pi$
$79$	4.42687	+	2.55585i	0.498062	+	0.287556i	−0.229851	+	0.973226i	$0.573824\pi$
$80$		0			0
$81$	4.62346	+	8.00806i	0.513717	+	0.889784i
$82$	−6.30058	+	4.47794i	−0.695783	+	0.494506i
$83$	−9.52133			−1.04510			−0.522551	−	0.852608i	$-0.675020\pi$
$83$	−9.52133			−1.04510			−0.522551	+	0.852608i	$0.675020\pi$
$84$	−8.05496	−	4.63563i	−0.878868	−	0.505789i
$85$		0			0
$86$	5.71677	−	4.06302i	0.616456	−	0.438127i
$87$	7.17580	+	12.4289i	0.769327	+	1.33251i
$88$	8.13597	−	8.48602i	0.867298	−	0.904612i
$89$	−2.01542	−	1.16361i	−0.213634	−	0.123342i	0.389365	−	0.921084i	$-0.372695\pi$
$89$	−2.01542	−	1.16361i	−0.213634	−	0.123342i	−0.602999	+	0.797742i	$0.706028\pi$
$90$		0			0
$91$	−8.46465	+	9.83247i	−0.887336	+	1.03072i
$92$	−8.24706	+	7.11975i	−0.859816	+	0.742285i
$93$	−3.72034	+	6.44381i	−0.385781	+	0.668192i
$94$	8.14780	−	0.770500i	0.840381	−	0.0794710i
$95$		0			0
$96$	8.85158	−	4.51218i	0.903410	−	0.460523i
$97$		−	17.7211i		−	1.79931i	−0.436603	−	0.899654i	$-0.643819\pi$
$97$		−	17.7211i		−	1.79931i	0.436603	−	0.899654i	$-0.356181\pi$
$98$	7.12678	−	6.87088i	0.719913	−	0.694064i
$99$			0.352025i			0.0353799i
$100$		0			0
$101$	−13.3283	+	7.69509i	−1.32621	+	0.765690i	−0.984712	−	0.174191i	$-0.944269\pi$
$101$	−13.3283	+	7.69509i	−1.32621	+	0.765690i	−0.341502	+	0.939881i	$0.610936\pi$
$102$	−0.0532596	−	0.563204i	−0.00527349	−	0.0557655i
$103$	−5.46824	+	9.47127i	−0.538801	+	0.933231i	0.460167	+	0.887832i	$0.347789\pi$
$103$	−5.46824	+	9.47127i	−0.538801	+	0.933231i	−0.998969	+	0.0453993i	$0.985544\pi$
$104$	−3.87107	−	13.3188i	−0.379590	−	1.30601i
$105$		0			0
$106$	−6.37619	+	13.9282i	−0.619311	+	1.35283i
$107$	4.08895	+	2.36075i	0.395293	+	0.228223i	0.684451	−	0.729059i	$-0.260042\pi$
$107$	4.08895	+	2.36075i	0.395293	+	0.228223i	−0.289158	+	0.957281i	$0.593375\pi$
$108$	3.36703	−	9.67112i	0.323993	−	0.930603i
$109$	−4.06945	−	7.04850i	−0.389783	−	0.675124i	0.602637	−	0.798015i	$-0.294117\pi$
$109$	−4.06945	−	7.04850i	−0.389783	−	0.675124i	−0.992420	+	0.122891i	$0.960783\pi$
$110$		0			0
$111$	9.07812			0.861657
$112$	1.99826	+	10.3926i	0.188818	+	0.982012i
$113$	9.50633			0.894280			0.447140	−	0.894464i	$-0.352443\pi$
$113$	9.50633			0.894280			0.447140	+	0.894464i	$0.352443\pi$
$114$	−1.13988	−	1.60385i	−0.106760	−	0.150214i
$115$		0			0
$116$	5.37343	−	15.4341i	0.498910	−	1.43302i
$117$	0.359678	+	0.207660i	0.0332523	+	0.0191982i
$118$	−4.62763	+	10.1086i	−0.426008	+	0.930574i
$119$	0.592071	+	0.112138i	0.0542750	+	0.0102796i
$120$		0			0
$121$	3.13791	−	5.43502i	0.285265	−	0.494093i
$122$	−1.77923	−	18.8148i	−0.161084	−	1.70341i
$123$	−8.31358	+	4.79985i	−0.749610	+	0.432788i
$124$	8.32278	−	1.58830i	0.747408	−	0.142634i
$125$		0			0
$126$	−0.258560	−	0.183224i	−0.0230343	−	0.0163229i
$127$		−	12.3200i		−	1.09322i	−0.837386	−	0.546612i	$-0.815917\pi$
$127$		−	12.3200i		−	1.09322i	0.837386	−	0.546612i	$-0.184083\pi$
$128$	−10.4761	−	4.27204i	−0.925969	−	0.377599i
$129$	7.54325	−	4.35510i	0.664146	−	0.383445i
$130$		0			0
$131$	8.32817	−	14.4248i	0.727635	−	1.26030i	−0.230245	−	0.973133i	$-0.573953\pi$
$131$	8.32817	−	14.4248i	0.727635	−	1.26030i	0.957880	−	0.287169i	$-0.0927140\pi$
$132$	11.0515	−	9.54082i	0.961908	−	0.830422i
$133$	1.97844	−	0.691880i	0.171552	−	0.0599936i
$134$	−8.35514	−	3.82491i	−0.721774	−	0.330422i
$135$		0			0
$136$	−0.445829	+	0.465010i	−0.0382295	+	0.0398743i
$137$	2.20153	+	3.81315i	0.188089	+	0.325780i	0.944613	−	0.328186i	$-0.106437\pi$
$137$	2.20153	+	3.81315i	0.188089	+	0.325780i	−0.756524	+	0.653966i	$0.773104\pi$
$138$	−11.0291	+	7.83858i	−0.938858	+	0.667265i
$139$	13.2240			1.12164			0.560822	−	0.827936i	$-0.310485\pi$
$139$	13.2240			1.12164			0.560822	+	0.827936i	$0.310485\pi$
$140$		0			0
$141$	10.1640			0.855963
$142$	2.34947	−	1.66981i	0.197163	−	0.140128i
$143$	−10.1910	−	17.6514i	−0.852217	−	1.47608i
$144$	0.314969	−	0.124759i	0.0262474	−	0.0103966i
$145$		0			0
$146$	6.89481	+	3.15638i	0.570619	+	0.261224i
$147$	9.61487	−	7.66187i	0.793021	−	0.631940i
$148$	−6.75538	−	7.82501i	−0.555289	−	0.643212i
$149$	5.77374	−	10.0004i	0.473003	−	0.819265i	−0.526520	−	0.850163i	$-0.676503\pi$
$149$	5.77374	−	10.0004i	0.473003	−	0.819265i	0.999523	+	0.0308978i	$0.00983665\pi$
$150$		0			0
$151$	−14.9095	+	8.60802i	−1.21332	+	0.700511i	−0.963481	−	0.267776i	$-0.913711\pi$
$151$	−14.9095	+	8.60802i	−1.21332	+	0.700511i	−0.249839	+	0.968287i	$0.580378\pi$
$152$	−0.534224	+	2.17602i	−0.0433313	+	0.176499i
$153$		−	0.0192900i		−	0.00155950i
$154$	6.49305	+	14.1316i	0.523225	+	1.13876i
$155$		0			0
$156$	−3.22895	−	16.9199i	−0.258523	−	1.35467i
$157$	18.0862	−	10.4421i	1.44344	−	0.833369i	0.445359	−	0.895352i	$-0.353076\pi$
$157$	18.0862	−	10.4421i	1.44344	−	0.833369i	0.998077	+	0.0619833i	$0.0197426\pi$
$158$	−0.680582	−	7.19694i	−0.0541442	−	0.572558i
$159$	−9.51200	+	16.4753i	−0.754350	+	1.30657i
$160$		0			0
$161$	−4.75782	−	13.6050i	−0.374969	−	1.07223i
$162$	5.44330	−	11.8904i	0.427666	−	0.934196i
$163$	6.24921	+	3.60798i	0.489476	+	0.282599i	0.724357	−	0.689425i	$-0.242137\pi$
$163$	6.24921	+	3.60798i	0.489476	+	0.282599i	−0.234881	+	0.972024i	$0.575470\pi$
$164$	10.3238	+	3.59425i	0.806150	+	0.280664i
$165$		0			0
$166$	7.80055	+	10.9756i	0.605440	+	0.851869i
$167$	−14.7801			−1.14372			−0.571860	−	0.820351i	$-0.693778\pi$
$167$	−14.7801			−1.14372			−0.571860	+	0.820351i	$0.693778\pi$
$168$	1.25553	+	13.0831i	0.0968665	+	1.00938i
$169$	−11.0468			−0.849756
$170$		0			0
$171$	−0.0335469	−	0.0581049i	−0.00256539	−	0.00444339i
$172$	−9.36717	−	3.26121i	−0.714240	−	0.248665i
$173$	−16.2561	−	9.38545i	−1.23593	−	0.713563i	−0.267667	−	0.963511i	$-0.586253\pi$
$173$	−16.2561	−	9.38545i	−1.23593	−	0.713563i	−0.968259	+	0.249949i	$0.919586\pi$
$174$	8.44825	−	18.4544i	0.640460	−	1.39902i
$175$		0			0
$176$	−16.4477	−	2.42627i	−1.23979	−	0.182887i
$177$	−6.90349	+	11.9572i	−0.518898	+	0.898758i
$178$	0.309849	+	3.27655i	0.0232242	+	0.245588i
$179$	11.1064	−	6.41230i	0.830134	−	0.479278i	−0.0237648	−	0.999718i	$-0.507565\pi$
$179$	11.1064	−	6.41230i	0.830134	−	0.479278i	0.853898	+	0.520440i	$0.174232\pi$
$180$		0			0
$181$		−	8.55295i		−	0.635736i	−0.948135	−	0.317868i	$-0.897033\pi$
$181$		−	8.55295i		−	0.635736i	0.948135	−	0.317868i	$-0.102967\pi$
$182$	18.2691	+	1.70204i	1.35419	+	0.126163i
$183$		−	23.4706i		−	1.73500i
$184$	14.9638	+	3.67367i	1.10314	+	0.270827i
$185$		0			0
$186$	10.4760	−	0.990665i	0.768135	−	0.0726391i
$187$	−0.473333	+	0.819837i	−0.0346135	+	0.0599524i
$188$	−7.56343	−	8.76100i	−0.551620	−	0.638961i
$189$	10.2665	+	8.83833i	0.746781	+	0.642894i
$190$		0			0
$191$	0.426822	+	0.246426i	0.0308837	+	0.0178307i	0.515362	−	0.856972i	$-0.327657\pi$
$191$	0.426822	+	0.246426i	0.0308837	+	0.0178307i	−0.484479	+	0.874803i	$0.660991\pi$
$192$	−12.4532	−	6.50682i	−0.898731	−	0.469589i
$193$	13.4878	+	23.3615i	0.970870	+	1.68160i	0.692941	+	0.720994i	$0.256314\pi$
$193$	13.4878	+	23.3615i	0.970870	+	1.68160i	0.277928	+	0.960602i	$0.410352\pi$
$194$	−20.4278	+	14.5184i	−1.46663	+	1.04236i
$195$		0			0
$196$	−13.7591	−	2.58617i	−0.982790	−	0.184727i
$197$	2.48025			0.176710			0.0883552	−	0.996089i	$-0.471839\pi$
$197$	2.48025			0.176710			0.0883552	+	0.996089i	$0.471839\pi$
$198$	0.405792	−	0.288404i	0.0288384	−	0.0204960i
$199$	−2.76798	−	4.79428i	−0.196217	−	0.339858i	0.751082	−	0.660209i	$-0.229532\pi$
$199$	−2.76798	−	4.79428i	−0.196217	−	0.339858i	−0.947299	+	0.320351i	$0.896199\pi$
$200$		0			0
$201$	−9.88306	−	5.70599i	−0.697097	−	0.402469i
$202$	19.7899	+	9.05961i	1.39241	+	0.637432i
$203$	16.3843	+	14.1050i	1.14995	+	0.989980i
$204$	−0.605590	+	0.522810i	−0.0423998	+	0.0366040i
$205$		0			0
$206$	15.3978	−	1.45610i	1.07282	−	0.101451i
$207$	−0.399567	+	0.230690i	−0.0277718	+	0.0160341i
$208$	−12.1815	+	15.3740i	−0.844637	+	1.06599i
$209$			3.29266i			0.227758i
$210$		0			0
$211$		−	21.7260i		−	1.49568i	−0.663879	−	0.747840i	$-0.731091\pi$
$211$		−	21.7260i		−	1.49568i	0.663879	−	0.747840i	$-0.268909\pi$
$212$	21.2793	−	4.06089i	1.46147	−	0.278903i
$213$	3.10011	−	1.78985i	0.212416	−	0.122638i
$214$	−0.628630	−	6.64756i	−0.0429723	−	0.454418i
$215$		0			0
$216$	−13.9067	+	4.04197i	−0.946233	+	0.275021i
$217$	−2.08584	+	11.0129i	−0.141596	+	0.747605i
$218$	−4.79106	+	10.4656i	−0.324492	+	0.708822i
$219$	8.15568	+	4.70868i	0.551110	+	0.318183i
$220$		0			0
$221$	0.558440	+	0.967246i	0.0375647	+	0.0650640i
$222$	−7.43743	−	10.4647i	−0.499168	−	0.702342i
$223$	24.6124			1.64817			0.824084	−	0.566467i	$-0.191690\pi$
$223$	24.6124			1.64817			0.824084	+	0.566467i	$0.191690\pi$
$224$	10.3428	−	10.8178i	0.691060	−	0.722798i
$225$		0			0
$226$	−7.78825	−	10.9583i	−0.518067	−	0.728933i
$227$	−4.09988	−	7.10120i	−0.272119	−	0.471323i	0.697286	−	0.716793i	$-0.254391\pi$
$227$	−4.09988	−	7.10120i	−0.272119	−	0.471323i	−0.969404	+	0.245470i	$0.921058\pi$
$228$	−0.914934	+	2.62797i	−0.0605930	+	0.174041i
$229$	−4.20964	−	2.43044i	−0.278181	−	0.160608i	0.354419	−	0.935087i	$-0.384679\pi$
$229$	−4.20964	−	2.43044i	−0.278181	−	0.160608i	−0.632600	+	0.774479i	$0.718012\pi$
$230$		0			0
$231$	6.37572	+	18.2314i	0.419491	+	1.19954i
$232$	−22.1937	+	6.45056i	−1.45709	+	0.423500i
$233$	−10.5793	+	18.3238i	−0.693071	+	1.20043i	0.277755	+	0.960652i	$0.410410\pi$
$233$	−10.5793	+	18.3238i	−0.693071	+	1.20043i	−0.970827	+	0.239783i	$0.922924\pi$
$234$	−0.0552965	−	0.584743i	−0.00361485	−	0.0382259i
$235$		0			0
$236$	15.4438	−	2.94726i	1.00531	−	0.191850i
$237$		−	8.97784i		−	0.583174i
$238$	−0.355801	−	0.774371i	−0.0230632	−	0.0501950i
$239$		−	2.45963i		−	0.159100i	−0.996831	−	0.0795500i	$-0.974652\pi$
$239$		−	2.45963i		−	0.159100i	0.996831	−	0.0795500i	$-0.0253483\pi$
$240$		0			0
$241$	−1.36901	+	0.790395i	−0.0881854	+	0.0509138i	−0.543444	−	0.839445i	$-0.682880\pi$
$241$	−1.36901	+	0.790395i	−0.0881854	+	0.0509138i	0.455259	+	0.890359i	$0.349547\pi$
$242$	−8.83593	+	0.835574i	−0.567995	+	0.0537127i
$243$	0.439955	−	0.762024i	0.0282231	−	0.0488839i
$244$	−20.2308	+	17.4654i	−1.29515	+	1.11811i
$245$		0			0
$246$	12.3440	+	5.65098i	0.787026	+	0.360293i
$247$	3.36424	+	1.94234i	0.214061	+	0.123588i
$248$	−8.64950	−	8.29271i	−0.549244	−	0.526588i
$249$	8.36130	+	14.4822i	0.529876	+	0.917772i
$250$		0			0
$251$	26.3036			1.66027			0.830135	−	0.557562i	$-0.188263\pi$
$251$	26.3036			1.66027			0.830135	+	0.557562i	$0.188263\pi$
$252$	0.000622162		0.448160i	3.91925e−5		0.0282314i
$253$	22.6425			1.42352
$254$	−14.2017	+	10.0934i	−0.891093	+	0.633317i
$255$		0			0
$256$	3.65826	+	15.5762i	0.228642	+	0.973511i
$257$	10.3912	+	5.99938i	0.648187	+	0.374231i	0.787761	−	0.615981i	$-0.211240\pi$
$257$	10.3912	+	5.99938i	0.648187	+	0.374231i	−0.139574	+	0.990212i	$0.544573\pi$
$258$	−11.2002	−	5.12736i	−0.697296	−	0.319216i
$259$	12.9088	−	4.51433i	0.802112	−	0.280507i
$260$		0			0
$261$	0.346034	−	0.599349i	0.0214190	−	0.0370988i
$262$	−23.4510	+	2.21765i	−1.44881	+	0.137007i
$263$	−8.41133	+	4.85628i	−0.518665	+	0.299451i	−0.736388	−	0.676559i	$-0.763470\pi$
$263$	−8.41133	+	4.85628i	−0.518665	+	0.299451i	0.217723	+	0.976011i	$0.430137\pi$
$264$	−20.0522	−	4.92291i	−1.23413	−	0.302984i
$265$		0			0
$266$	−2.41843	−	1.71378i	−0.148283	−	0.105078i
$267$			4.08735i			0.250142i
$268$	2.43602	+	12.7649i	0.148804	+	0.779740i
$269$	2.91623	−	1.68369i	0.177806	−	0.102656i	−0.408456	−	0.912778i	$-0.633933\pi$
$269$	2.91623	−	1.68369i	0.177806	−	0.102656i	0.586261	+	0.810122i	$0.300599\pi$
$270$		0			0
$271$	4.96774	−	8.60437i	0.301768	−	0.522678i	−0.674768	−	0.738030i	$-0.735756\pi$
$271$	4.96774	−	8.60437i	0.301768	−	0.522678i	0.976537	+	0.215352i	$0.0690897\pi$
$272$	0.901287	+	0.132953i	0.0546485	+	0.00806146i
$273$	22.3888	+	4.24042i	1.35503	+	0.256642i
$274$	2.59191	−	5.66178i	0.156583	−	0.342041i
$275$		0			0
$276$	18.0716	+	6.29169i	1.08778	+	0.378715i
$277$	0.200391	+	0.347087i	0.0120403	+	0.0208544i	0.871983	−	0.489537i	$-0.162834\pi$
$277$	0.200391	+	0.347087i	0.0120403	+	0.0208544i	−0.859942	+	0.510391i	$0.829501\pi$
$278$	−10.8340	−	15.2438i	−0.649782	−	0.914260i
$279$	0.358807			0.0214812
$280$		0			0
$281$	−21.4548			−1.27988			−0.639942	−	0.768423i	$-0.721042\pi$
$281$	−21.4548			−1.27988			−0.639942	+	0.768423i	$0.721042\pi$
$282$	−8.32706	−	11.7164i	−0.495869	−	0.697701i
$283$	−10.2131	−	17.6896i	−0.607106	−	1.05154i	−0.991715	−	0.128459i	$-0.958997\pi$
$283$	−10.2131	−	17.6896i	−0.607106	−	1.05154i	0.384609	−	0.923080i	$-0.374336\pi$
$284$	−3.84970	−	1.34029i	−0.228438	−	0.0795313i
$285$		0			0
$286$	−11.9981	+	26.2088i	−0.709465	+	1.54976i
$287$	−9.43477	+	10.9594i	−0.556917	+	0.646911i
$288$	−0.401859	−	0.260864i	−0.0236798	−	0.0153715i
$289$	−8.47406	+	14.6775i	−0.498474	+	0.863383i
$290$		0			0
$291$	−26.9543	+	15.5621i	−1.58009	+	0.912265i
$292$	−2.01025	−	10.5338i	−0.117641	−	0.616445i
$293$		−	4.64138i		−	0.271152i	−0.990767	−	0.135576i	$-0.956711\pi$
$293$		−	4.64138i		−	0.271152i	0.990767	−	0.135576i	$-0.0432885\pi$
$294$	−16.7093	−	4.80625i	−0.974505	−	0.280306i
$295$		0			0
$296$	−3.48567	+	14.1980i	−0.202600	+	0.825240i
$297$	−18.4306	+	10.6409i	−1.06945	+	0.617449i
$298$	−16.2581	+	1.53745i	−0.941804	+	0.0890622i
$299$	13.3568	−	23.1347i	0.772445	−	1.33791i
$300$		0			0
$301$	8.56055	−	9.94388i	0.493422	−	0.573155i
$302$	22.1377	+	10.1344i	1.27388	+	0.583171i
$303$	23.4089	+	13.5151i	1.34480	+	0.776423i
$304$	2.94605	−	1.16693i	0.168968	−	0.0669282i
$305$		0			0
$306$	−0.0222362	+	0.0158037i	−0.00127116	+	0.000903439i
$307$	6.02430			0.343825			0.171912	−	0.985112i	$-0.445005\pi$
$307$	6.02430			0.343825			0.171912	+	0.985112i	$0.445005\pi$
$308$	10.9704	−	19.0624i	0.625096	−	1.08618i
$309$	19.2081			1.09271
$310$		0			0
$311$	−11.5074	−	19.9313i	−0.652522	−	1.13020i	−0.982509	−	0.186216i	$-0.940378\pi$
$311$	−11.5074	−	19.9313i	−0.652522	−	1.13020i	0.329987	−	0.943986i	$-0.392956\pi$
$312$	−16.8587	+	17.5841i	−0.954438	+	0.995502i
$313$	7.37980	+	4.26073i	0.417131	+	0.240831i	0.693849	−	0.720120i	$-0.255913\pi$
$313$	7.37980	+	4.26073i	0.417131	+	0.240831i	−0.276718	+	0.960951i	$0.589247\pi$
$314$	−26.8544	−	12.2937i	−1.51548	−	0.693774i
$315$		0			0
$316$	−7.73857	+	6.68077i	−0.435329	+	0.375822i
$317$	−2.10140	+	3.63973i	−0.118026	+	0.204428i	−0.918985	−	0.394291i	$-0.870990\pi$
$317$	−2.10140	+	3.63973i	−0.118026	+	0.204428i	0.800959	+	0.598719i	$0.204323\pi$
$318$	26.7845	−	2.53289i	1.50200	−	0.142037i
$319$	−29.4133	+	16.9818i	−1.64683	+	0.950799i
$320$		0			0
$321$		−	8.29252i		−	0.462844i
$322$	−11.7850	+	16.6307i	−0.656755	+	0.926792i
$323$		−	0.180428i		−	0.0100393i
$324$	−18.1660	+	3.46675i	−1.00922	+	0.192597i
$325$		0			0
$326$	−0.960746	−	10.1596i	−0.0532108	−	0.562687i
$327$	−7.14730	+	12.3795i	−0.395247	+	0.684587i
$328$	−4.31474	−	14.8452i	−0.238241	−	0.819690i
$329$	14.4528	−	5.05431i	0.796811	−	0.278653i
$330$		0			0
$331$	9.27412	+	5.35442i	0.509752	+	0.294305i	0.732732	−	0.680518i	$-0.238245\pi$
$331$	9.27412	+	5.35442i	0.509752	+	0.294305i	−0.222980	+	0.974823i	$0.571578\pi$
$332$	6.26116	−	17.9839i	0.343626	−	0.986995i
$333$	−0.218884	−	0.379119i	−0.0119948	−	0.0207756i
$334$	12.1089	+	17.0376i	0.662570	+	0.932253i
$335$		0			0
$336$	14.0527	−	12.1659i	0.766636	−	0.663702i
$337$	28.6850			1.56257			0.781286	−	0.624173i	$-0.214564\pi$
$337$	28.6850			1.56257			0.781286	+	0.624173i	$0.214564\pi$
$338$	9.05034	+	12.7341i	0.492273	+	0.692641i
$339$	−8.34812	−	14.4594i	−0.453408	−	0.785326i
$340$		0			0
$341$	−15.2495	−	8.80432i	−0.825808	−	0.476780i
$342$	−0.0394955	+	0.0862742i	−0.00213567	+	0.00466517i
$343$	9.86195	−	15.6762i	0.532495	−	0.846433i
$344$	3.91493	+	13.4697i	0.211079	+	0.726236i
$345$		0			0
$346$	2.49919	+	26.4282i	0.134357	+	1.42079i
$347$	20.2775	−	11.7072i	1.08855	−	0.628475i	0.155361	−	0.987858i	$-0.450346\pi$
$347$	20.2775	−	11.7072i	1.08855	−	0.628475i	0.933190	+	0.359383i	$0.117013\pi$
$348$	−28.1944	+	5.38055i	−1.51138	+	0.288428i
$349$			19.7474i			1.05706i	0.848916	+	0.528528i	$0.177256\pi$
$349$			19.7474i			1.05706i	−0.848916	+	0.528528i	$0.822744\pi$
$350$		0			0
$351$			25.1084i			1.34019i
$352$	10.6782	+	20.9476i	0.569153	+	1.11651i
$353$	18.6720	−	10.7803i	0.993809	−	0.573776i	0.0873982	−	0.996173i	$-0.472145\pi$
$353$	18.6720	−	10.7803i	0.993809	−	0.573776i	0.906411	+	0.422398i	$0.138811\pi$
$354$	19.4393	−	1.83829i	1.03319	−	0.0977038i
$355$		0			0
$356$	3.52315	−	3.04156i	0.186726	−	0.161202i
$357$	−0.349371	−	0.999030i	−0.0184907	−	0.0528743i
$358$	−16.4908	−	7.54936i	−0.871568	−	0.398996i
$359$	−6.74629	−	3.89497i	−0.356056	−	0.205569i	0.311294	−	0.950314i	$-0.399238\pi$
$359$	−6.74629	−	3.89497i	−0.356056	−	0.205569i	−0.667349	+	0.744745i	$0.732571\pi$
$360$		0			0
$361$	9.18622	+	15.9110i	0.483485	+	0.837421i
$362$	−9.85928	+	7.00718i	−0.518192	+	0.368289i
$363$	−11.0224			−0.578526
$364$	−13.0053	−	22.4538i	−0.681663	−	1.17690i
$365$		0			0
$366$	−27.0554	+	19.2288i	−1.41421	+	1.00510i
$367$	−2.76679	−	4.79223i	−0.144425	−	0.250152i	0.784733	−	0.619834i	$-0.212800\pi$
$367$	−2.76679	−	4.79223i	−0.144425	−	0.250152i	−0.929158	+	0.369682i	$0.879467\pi$
$368$	−8.02459	−	20.2590i	−0.418311	−	1.05607i
$369$	0.400901	+	0.231460i	0.0208701	+	0.0120493i
$370$		0			0
$371$	−5.33297	+	28.1573i	−0.276874	+	1.46186i
$372$	−9.72462	−	11.2644i	−0.504198	−	0.584031i
$373$	4.73689	−	8.20453i	0.245267	−	0.424814i	−0.716940	−	0.697135i	$-0.754458\pi$
$373$	4.73689	−	8.20453i	0.245267	−	0.424814i	0.962207	+	0.272321i	$0.0877911\pi$
$374$	1.33284	−	0.126041i	0.0689196	−	0.00651742i
$375$		0			0
$376$	−3.90261	+	15.8962i	−0.201262	+	0.819786i
$377$			40.0704i			2.06373i
$378$	1.77718	−	19.0756i	0.0914080	−	0.981141i
$379$		−	23.6212i		−	1.21334i	−0.794954	−	0.606670i	$-0.792505\pi$
$379$		−	23.6212i		−	1.21334i	0.794954	−	0.606670i	$-0.207495\pi$
$380$		0			0
$381$	−18.7390	+	10.8190i	−0.960030	+	0.554274i
$382$	−0.0656191	−	0.693901i	−0.00335737	−	0.0355031i
$383$	8.43407	−	14.6082i	0.430961	−	0.746446i	−0.565996	−	0.824408i	$-0.691508\pi$
$383$	8.43407	−	14.6082i	0.430961	−	0.746446i	0.996956	+	0.0779625i	$0.0248415\pi$
$384$	2.70189	+	19.6861i	0.137880	+	1.00460i
$385$		0			0
$386$	15.8795	−	34.6872i	0.808243	−	1.76553i
$387$	−0.363754	−	0.210013i	−0.0184906	−	0.0106756i
$388$	33.4717	+	11.6533i	1.69927	+	0.591606i
$389$	5.17328	+	8.96039i	0.262296	+	0.454310i	0.966852	−	0.255339i	$-0.0821871\pi$
$389$	5.17328	+	8.96039i	0.262296	+	0.454310i	−0.704556	+	0.709649i	$0.748854\pi$
$390$		0			0
$391$	−1.24074			−0.0627471
$392$	8.29122	+	17.9793i	0.418770	+	0.908092i
$393$	−29.2540			−1.47567
$394$	−2.03199	−	2.85907i	−0.102370	−	0.144038i
$395$		0			0
$396$	−0.664906	−	0.231489i	−0.0334128	−	0.0116328i
$397$	−2.23880	−	1.29257i	−0.112362	−	0.0648724i	0.442766	−	0.896637i	$-0.353997\pi$
$397$	−2.23880	−	1.29257i	−0.112362	−	0.0648724i	−0.555128	+	0.831765i	$0.687331\pi$
$398$	−3.25881	+	7.11856i	−0.163349	+	0.356821i
$399$	−2.78976	−	2.40167i	−0.139663	−	0.120234i
$400$		0			0
$401$	−3.98844	+	6.90819i	−0.199173	+	0.344978i	−0.948261	−	0.317493i	$-0.897159\pi$
$401$	−3.98844	+	6.90819i	−0.199173	+	0.344978i	0.749087	+	0.662471i	$0.230492\pi$
$402$	1.51941	+	16.0673i	0.0757813	+	0.801364i
$403$	−17.9914	+	10.3874i	−0.896217	+	0.517431i
$404$	−5.76992	−	30.2347i	−0.287064	−	1.50423i
$405$		0			0
$406$	2.83619	−	30.4426i	0.140758	−	1.51084i
$407$			21.4837i			1.06491i
$408$	1.09880	+	0.269762i	0.0543989	+	0.0133552i
$409$	−5.63217	+	3.25173i	−0.278493	+	0.160788i	−0.632741	−	0.774364i	$-0.718070\pi$
$409$	−5.63217	+	3.25173i	−0.278493	+	0.160788i	0.354248	+	0.935151i	$0.384737\pi$
$410$		0			0
$411$	3.86661	−	6.69716i	0.190726	−	0.330346i
$412$	−14.2935	−	16.5566i	−0.704189	−	0.815688i
$413$	−3.87049	+	20.4357i	−0.190455	+	1.00557i
$414$	0.593278	+	0.271597i	0.0291580	+	0.0133483i
$415$		0			0
$416$	27.7021	+	1.44662i	1.35821	+	0.0709265i
$417$	−11.6128	−	20.1140i	−0.568684	−	0.984989i
$418$	3.79556	−	2.69758i	0.185647	−	0.131943i
$419$	−29.4385			−1.43817			−0.719083	−	0.694924i	$-0.755438\pi$
$419$	−29.4385			−1.43817			−0.719083	+	0.694924i	$0.755438\pi$
$420$		0			0
$421$	−11.3233			−0.551863			−0.275932	−	0.961177i	$-0.588986\pi$
$421$	−11.3233			−0.551863			−0.275932	+	0.961177i	$0.588986\pi$
$422$	−25.0443	+	17.7995i	−1.21914	+	0.866465i
$423$	−0.245066	−	0.424467i	−0.0119155	−	0.0206383i
$424$	−22.1147	−	21.2024i	−1.07398	−	1.02968i
$425$		0			0
$426$	−4.60305	−	2.10723i	−0.223018	−	0.102096i
$427$	−11.6714	−	33.3744i	−0.564817	−	1.61510i
$428$	−7.14785	+	6.17079i	−0.345505	+	0.298277i
$429$	−17.8988	+	31.0017i	−0.864163	+	1.49677i
$430$		0			0
$431$	−28.5918	+	16.5075i	−1.37722	+	0.795136i	−0.991824	−	0.127616i	$-0.959267\pi$
$431$	−28.5918	+	16.5075i	−1.37722	+	0.795136i	−0.385393	+	0.922753i	$0.625934\pi$
$432$	16.0527	+	12.7193i	0.772335	+	0.611958i
$433$		−	18.9367i		−	0.910041i	−0.890481	−	0.455021i	$-0.849632\pi$
$433$		−	18.9367i		−	0.910041i	0.890481	−	0.455021i	$-0.150368\pi$
$434$	14.4038	−	6.61814i	0.691406	−	0.317681i
$435$		0			0
$436$	15.9893	−	3.05135i	0.765747	−	0.146133i
$437$	−3.73734	+	2.15775i	−0.178781	+	0.103219i
$438$	−1.25384	−	13.2590i	−0.0599110	−	0.633540i
$439$	−12.1486	+	21.0420i	−0.579820	+	1.00428i	0.415680	+	0.909511i	$0.363544\pi$
$439$	−12.1486	+	21.0420i	−0.579820	+	1.00428i	−0.995500	+	0.0947665i	$0.969790\pi$
$440$		0			0
$441$	−0.551800	−	0.216798i	−0.0262762	−	0.0103237i
$442$	0.657465	−	1.43617i	0.0312724	−	0.0683116i
$443$	12.9956	+	7.50299i	0.617438	+	0.356478i	0.775871	−	0.630892i	$-0.217311\pi$
$443$	12.9956	+	7.50299i	0.617438	+	0.356478i	−0.158433	+	0.987370i	$0.550644\pi$
$444$	−5.96970	+	17.1468i	−0.283309	+	0.813749i
$445$		0			0
$446$	−20.1642	−	28.3716i	−0.954803	−	1.34343i
$447$	−20.2812			−0.959267
$448$	−20.9437	−	3.05980i	−0.989496	−	0.144562i
$449$	10.9965			0.518957			0.259479	−	0.965749i	$-0.416449\pi$
$449$	10.9965			0.518957			0.259479	+	0.965749i	$0.416449\pi$
$450$		0			0
$451$	−11.3590	−	19.6744i	−0.534875	−	0.926431i
$452$	−6.25129	+	17.9556i	−0.294036	+	0.844559i
$453$	26.1861	+	15.1185i	1.23033	+	0.710330i
$454$	−4.82689	+	10.5439i	−0.226537	+	0.494848i
$455$		0			0
$456$	3.77892	−	1.09834i	0.176964	−	0.0514344i
$457$	8.29835	−	14.3732i	0.388180	−	0.672348i	−0.604024	−	0.796966i	$-0.706437\pi$
$457$	8.29835	−	14.3732i	0.388180	−	0.672348i	0.992205	+	0.124618i	$0.0397704\pi$
$458$	0.647186	+	6.84379i	0.0302410	+	0.319789i
$459$	1.00995	−	0.583093i	0.0471403	−	0.0272164i
$460$		0			0
$461$		−	6.62872i		−	0.308730i	−0.988014	−	0.154365i	$-0.950667\pi$
$461$		−	6.62872i		−	0.308730i	0.988014	−	0.154365i	$-0.0493332\pi$
$462$	15.7925	−	22.2860i	0.734736	−	1.03684i
$463$			2.10944i			0.0980341i	0.998798	+	0.0490170i	$0.0156089\pi$
$463$			2.10944i			0.0980341i	−0.998798	+	0.0490170i	$0.984391\pi$
$464$	25.6184	+	20.2987i	1.18930	+	0.942342i
$465$		0			0
$466$	29.7898	−	2.81709i	1.37999	−	0.130499i
$467$	5.68790	−	9.85173i	0.263204	−	0.455883i	−0.703887	−	0.710312i	$-0.748554\pi$
$467$	5.68790	−	9.85173i	0.263204	−	0.455883i	0.967092	+	0.254428i	$0.0818873\pi$
$468$	−0.628751	+	0.542805i	−0.0290640	+	0.0250912i
$469$	−16.8908	−	3.19911i	−0.779946	−	0.147721i
$470$		0			0
$471$	−31.7653	−	18.3397i	−1.46367	−	0.845050i
$472$	−16.0501	−	15.3880i	−0.738765	−	0.708291i
$473$	10.3065	+	17.8514i	0.473893	+	0.820807i
$474$	−10.3491	+	7.35528i	−0.475348	+	0.337839i
$475$		0			0
$476$	−0.601147	+	1.04456i	−0.0275535	+	0.0478775i
$477$	0.917382			0.0420040
$478$	−2.83530	+	2.01510i	−0.129683	+	0.0921685i
$479$	5.01824	+	8.69185i	0.229289	+	0.397141i	0.957598	−	0.288109i	$-0.0930265\pi$
$479$	5.01824	+	8.69185i	0.229289	+	0.397141i	−0.728308	+	0.685250i	$0.759693\pi$
$480$		0			0
$481$	21.9507	+	12.6733i	1.00087	+	0.577851i
$482$	2.03270	+	0.930551i	0.0925870	+	0.0423855i
$483$	−16.5155	+	19.1842i	−0.751479	+	0.872913i
$484$	8.20221	+	9.50092i	0.372828	+	0.431860i
$485$		0			0
$486$	−1.23885	+	0.117153i	−0.0561955	+	0.00531416i
$487$	22.6852	−	13.0973i	1.02796	−	0.593495i	0.111563	−	0.993757i	$-0.464414\pi$
$487$	22.6852	−	13.0973i	1.02796	−	0.593495i	0.916401	+	0.400262i	$0.131081\pi$
$488$	36.7075	+	9.01186i	1.66167	+	0.407948i
$489$		−	12.6736i		−	0.573120i
$490$		0			0
$491$		−	26.0472i		−	1.17549i	−0.809045	−	0.587747i	$-0.800015\pi$
$491$		−	26.0472i		−	1.17549i	0.809045	−	0.587747i	$-0.199985\pi$
$492$	−3.59902	−	18.8591i	−0.162256	−	0.850232i
$493$	1.61177	−	0.930555i	0.0725904	−	0.0419101i
$494$	−0.517214	−	5.46938i	−0.0232706	−	0.246079i
$495$		0			0
$496$	−2.47302	+	16.7645i	−0.111042	+	0.752750i
$497$	3.51820	−	4.08671i	0.157813	−	0.183314i
$498$	9.84396	−	21.5032i	0.441118	−	0.963581i
$499$	15.0374	+	8.68187i	0.673169	+	0.388654i	0.797276	−	0.603615i	$-0.206273\pi$
$499$	15.0374	+	8.68187i	0.673169	+	0.388654i	−0.124108	+	0.992269i	$0.539607\pi$
$500$		0			0
$501$	12.9794	+	22.4810i	0.579876	+	1.00437i
$502$	−21.5498	−	30.3211i	−0.961814	−	1.35330i
$503$	31.7491			1.41562			0.707810	−	0.706403i	$-0.249683\pi$
$503$	31.7491			1.41562			0.707810	+	0.706403i	$0.249683\pi$
$504$	0.516100	−	0.367882i	0.0229889	−	0.0163867i
$505$		0			0
$506$	−18.5503	−	26.1007i	−0.824661	−	1.16032i
$507$	9.70093	+	16.8025i	0.430834	+	0.746226i
$508$	23.2700	+	8.10154i	1.03244	+	0.359448i
$509$	−8.90601	−	5.14189i	−0.394752	−	0.227910i	0.289465	−	0.957189i	$-0.406523\pi$
$509$	−8.90601	−	5.14189i	−0.394752	−	0.227910i	−0.684217	+	0.729278i	$0.739856\pi$
$510$		0			0
$511$	13.9386	+	2.63996i	0.616607	+	0.116785i
$512$	14.9581	−	16.9781i	0.661060	−	0.750333i
$513$	2.02809	−	3.51276i	0.0895424	−	0.155092i
$514$	−1.59754	−	16.8934i	−0.0704643	−	0.745138i
$515$		0			0
$516$	3.26553	+	17.1116i	0.143757	+	0.753296i
$517$			24.0535i			1.05787i
$518$	−15.7796	−	11.1819i	−0.693316	−	0.491305i
$519$			32.9679i			1.44713i
$520$		0			0
$521$	13.7812	−	7.95657i	0.603764	−	0.348584i	−0.166757	−	0.985998i	$-0.553329\pi$
$521$	13.7812	−	7.95657i	0.603764	−	0.348584i	0.770521	+	0.637415i	$0.219996\pi$
$522$	−0.974386	+	0.0921433i	−0.0426477	+	0.00403300i
$523$	−1.17655	+	2.03784i	−0.0514470	+	0.0891087i	−0.890602	−	0.454783i	$-0.849717\pi$
$523$	−1.17655	+	2.03784i	−0.0514470	+	0.0891087i	0.839155	+	0.543892i	$0.183050\pi$
$524$	21.7691	+	25.2159i	0.950986	+	1.10156i
$525$		0			0
$526$	12.4892	+	5.71742i	0.544553	+	0.249291i
$527$	0.835631	+	0.482452i	0.0364007	+	0.0210159i
$528$	10.7534	+	27.1480i	0.467980	+	1.18147i
$529$	3.33811	+	5.78178i	0.145135	+	0.251382i
$530$		0			0
$531$	0.665805			0.0288935
$532$	0.00581937	+	4.19185i	0.000252302	+	0.181740i
$533$	−26.8028			−1.16096
$534$	4.71163	−	3.34864i	0.203892	−	0.144910i
$535$		0			0
$536$	12.7188	−	13.2660i	0.549367	−	0.573003i
$537$	−19.5066	−	11.2621i	−0.841770	−	0.485996i
$538$	−4.33003	−	1.98225i	−0.186681	−	0.0854607i
$539$	18.1321	+	22.7539i	0.781005	+	0.980082i
$540$		0			0
$541$	23.1217	−	40.0480i	0.994081	−	1.72180i	0.402955	−	0.915220i	$-0.367983\pi$
$541$	23.1217	−	40.0480i	0.994081	−	1.72180i	0.591126	−	0.806579i	$-0.298683\pi$
$542$	−13.9885	+	1.32283i	−0.600856	+	0.0568203i
$543$	−13.0093	+	7.51090i	−0.558281	+	0.322324i
$544$	−0.585138	−	1.14787i	−0.0250876	−	0.0492145i
$545$		0			0
$546$	−13.4544	−	29.2824i	−0.575795	−	1.25317i
$547$		−	0.635487i		−	0.0271715i	−0.999908	−	0.0135857i	$-0.995675\pi$
$547$		−	0.635487i		−	0.0271715i	0.999908	−	0.0135857i	$-0.00432461\pi$
$548$	−8.65000	+	1.65074i	−0.369510	+	0.0705163i
$549$	−0.980175	+	0.565904i	−0.0418329	+	0.0241522i
$550$		0			0
$551$	3.23662	−	5.60599i	0.137885	−	0.238823i
$552$	−7.55289	−	25.9864i	−0.321472	−	1.10605i
$553$	−4.46447	−	12.7662i	−0.189848	−	0.542873i
$554$	0.235925	−	0.515355i	0.0100235	−	0.0218953i
$555$		0			0
$556$	−8.69600	+	24.9775i	−0.368792	+	1.05928i
$557$	−15.2995	−	26.4995i	−0.648260	−	1.12282i	−0.983538	−	0.180700i	$-0.942164\pi$
$557$	−15.2995	−	26.4995i	−0.648260	−	1.12282i	0.335279	−	0.942119i	$-0.391170\pi$
$558$	−0.293960	−	0.413609i	−0.0124443	−	0.0175095i
$559$	24.3193			1.02860
$560$		0			0
$561$	1.66266			0.0701975
$562$	17.5773	+	24.7317i	0.741452	+	1.04324i
$563$	−5.08940	−	8.81511i	−0.214493	−	0.371512i	0.738623	−	0.674119i	$-0.235477\pi$
$563$	−5.08940	−	8.81511i	−0.214493	−	0.371512i	−0.953116	+	0.302607i	$0.902143\pi$
$564$	−6.68377	+	19.1978i	−0.281437	+	0.808372i
$565$		0			0
$566$	−12.0241	+	26.2656i	−0.505412	+	1.10402i
$567$	4.55272	−	24.0377i	0.191196	−	1.00949i
$568$	1.60895	+	5.53574i	0.0675101	+	0.232274i
$569$	19.6151	−	33.9744i	0.822308	−	1.42428i	−0.0816516	−	0.996661i	$-0.526019\pi$
$569$	19.6151	−	33.9744i	0.822308	−	1.42428i	0.903959	−	0.427618i	$-0.140647\pi$
$570$		0			0
$571$	19.0886	−	11.0208i	0.798833	−	0.461206i	−0.0442302	−	0.999021i	$-0.514083\pi$
$571$	19.0886	−	11.0208i	0.798833	−	0.461206i	0.843063	+	0.537815i	$0.180750\pi$
$572$	40.0415	−	7.64142i	1.67422	−	0.319504i
$573$		−	0.865610i		−	0.0361614i
$574$	20.3629	+	1.89711i	0.849930	+	0.0791837i
$575$		0			0
$576$	0.0285246	+	0.676955i	0.00118853	+	0.0282064i
$577$	35.8168	−	20.6789i	1.49107	−	0.860872i	0.491127	−	0.871088i	$-0.336585\pi$
$577$	35.8168	−	20.6789i	1.49107	−	0.860872i	0.999948	+	0.0102160i	$0.00325192\pi$
$578$	23.8618	−	2.25650i	0.992521	−	0.0938582i
$579$	23.6889	−	41.0305i	0.984479	−	1.70517i
$580$		0			0
$581$	19.0911	+	16.4353i	0.792033	+	0.681851i
$582$	40.0218	+	18.3216i	1.65896	+	0.759455i
$583$	−38.9893	−	22.5105i	−1.61477	−	0.932289i
$584$	−10.4958	+	10.9473i	−0.434317	+	0.453003i
$585$		0			0
$586$	−5.35028	+	3.80254i	−0.221018	+	0.157082i
$587$	0.600496			0.0247851			0.0123926	−	0.999923i	$-0.496055\pi$
$587$	0.600496			0.0247851			0.0123926	+	0.999923i	$0.496055\pi$
$588$	8.14909	+	23.1990i	0.336063	+	0.956710i
$589$	3.35609			0.138285
$590$		0			0
$591$	−2.17807	−	3.77252i	−0.0895938	−	0.155181i
$592$	19.2222	−	7.61392i	0.790027	−	0.312930i
$593$	−31.2425	−	18.0379i	−1.28298	−	0.740727i	−0.305586	−	0.952165i	$-0.598852\pi$
$593$	−31.2425	−	18.0379i	−1.28298	−	0.740727i	−0.977392	+	0.211437i	$0.932186\pi$
$594$	27.3658	+	12.5278i	1.12283	+	0.514023i
$595$		0			0
$596$	15.0920	+	17.4816i	0.618193	+	0.716076i
$597$	−4.86149	+	8.42034i	−0.198967	+	0.344622i
$598$	−37.6110	+	3.55670i	−1.53803	+	0.145444i
$599$	−4.57779	+	2.64299i	−0.187043	+	0.107989i	−0.590598	−	0.806966i	$-0.701108\pi$
$599$	−4.57779	+	2.64299i	−0.187043	+	0.107989i	0.403554	+	0.914956i	$0.367775\pi$
$600$		0			0
$601$			34.2340i			1.39643i	0.715886	+	0.698217i	$0.246023\pi$
$601$			34.2340i			1.39643i	−0.715886	+	0.698217i	$0.753977\pi$
$602$	−18.4761	−	1.72132i	−0.753028	−	0.0701558i
$603$			0.550313i			0.0224105i
$604$	−6.45445	−	33.8217i	−0.262628	−	1.37619i
$605$		0			0
$606$	−3.59885	−	38.0567i	−0.146193	−	1.54595i
$607$	−15.1918	+	26.3130i	−0.616618	+	1.06801i	0.373481	+	0.927638i	$0.378164\pi$
$607$	−15.1918	+	26.3130i	−0.616618	+	1.06801i	−0.990098	+	0.140375i	$0.955169\pi$
$608$	−3.75877	−	2.43998i	−0.152438	−	0.0989542i
$609$	7.06601	−	37.3075i	0.286329	−	1.51178i
$610$		0			0
$611$	24.5764	+	14.1892i	0.994254	+	0.574033i
$612$	0.0364350	+	0.0126850i	0.00147280	+	0.000512759i
$613$	−1.27473	−	2.20790i	−0.0514859	−	0.0891763i	0.839134	−	0.543925i	$-0.183062\pi$
$613$	−1.27473	−	2.20790i	−0.0514859	−	0.0891763i	−0.890620	+	0.454749i	$0.849729\pi$
$614$	−4.93553	−	6.94442i	−0.199182	−	0.280254i
$615$		0			0
$616$	−30.9615	+	2.97127i	−1.24748	+	0.119716i
$617$	−30.0546			−1.20995			−0.604976	−	0.796243i	$-0.706817\pi$
$617$	−30.0546			−1.20995			−0.604976	+	0.796243i	$0.706817\pi$
$618$	−15.7366	−	22.1418i	−0.633019	−	0.890673i
$619$	−5.95465	−	10.3137i	−0.239337	−	0.414545i	0.721187	−	0.692741i	$-0.243597\pi$
$619$	−5.95465	−	10.3137i	−0.239337	−	0.414545i	−0.960524	+	0.278196i	$0.910264\pi$
$620$		0			0
$621$	−24.1560	−	13.9465i	−0.969347	−	0.559653i
$622$	−13.5479	+	29.5941i	−0.543220	+	1.18661i
$623$	2.03254	+	5.81207i	0.0814320	+	0.232856i
$624$	34.0816	+	5.02754i	1.36436	+	0.201263i
$625$		0			0
$626$	−1.13456	−	11.9976i	−0.0453462	−	0.479522i
$627$	5.00822	−	2.89150i	0.200009	−	0.115475i
$628$	7.82966	+	41.0279i	0.312438	+	1.63719i
$629$		−	1.17725i		−	0.0469399i
$630$		0			0
$631$			25.8722i			1.02996i	0.857203	+	0.514979i	$0.172200\pi$
$631$			25.8722i			1.02996i	−0.857203	+	0.514979i	$0.827800\pi$
$632$	14.0411	+	3.44717i	0.558526	+	0.137121i
$633$	−33.0458	+	19.0790i	−1.31345	+	0.758323i
$634$	5.91726	−	0.559568i	0.235004	−	0.0222233i
$635$		0			0
$636$	−24.8635	−	28.8003i	−0.985901	−	1.14201i
$637$	33.9448	−	5.10369i	1.34494	−	0.202215i
$638$	43.6730	+	19.9931i	1.72903	+	0.791534i
$639$	−0.149495	−	0.0863108i	−0.00591392	−	0.00341440i
$640$		0			0
$641$	−17.7104	−	30.6754i	−0.699520	−	1.21160i	−0.968633	−	0.248496i	$-0.920064\pi$
$641$	−17.7104	−	30.6754i	−0.699520	−	1.21160i	0.269113	−	0.963109i	$-0.413270\pi$
$642$	−9.55908	+	6.79382i	−0.377267	+	0.268131i
$643$	−23.1771			−0.914017			−0.457008	−	0.889462i	$-0.651079\pi$
$643$	−23.1771			−0.914017			−0.457008	+	0.889462i	$0.651079\pi$
$644$	28.8259	−	0.0400178i	1.13590	−	0.00157692i
$645$		0			0
$646$	−0.207986	+	0.147820i	−0.00818310	+	0.00581588i
$647$	16.6735	+	28.8793i	0.655501	+	1.13536i	0.981768	+	0.190083i	$0.0608758\pi$
$647$	16.6735	+	28.8793i	0.655501	+	1.13536i	−0.326267	+	0.945278i	$0.605791\pi$
$648$	18.8791	+	18.1003i	0.741641	+	0.711049i
$649$	−28.2971	−	16.3374i	−1.11076	−	0.641298i
$650$		0			0
$651$	18.5826	−	6.49854i	0.728311	−	0.254698i
$652$	−10.9242	+	9.43093i	−0.427824	+	0.369344i
$653$	5.69556	−	9.86500i	0.222884	−	0.386047i	−0.732798	−	0.680446i	$-0.761786\pi$
$653$	5.69556	−	9.86500i	0.222884	−	0.386047i	0.955683	+	0.294399i	$0.0951194\pi$
$654$	20.1258	−	1.90321i	0.786982	−	0.0744214i
$655$		0			0
$656$	−13.5777	+	17.1360i	−0.530118	+	0.669048i
$657$		−	0.454128i		−	0.0177172i
$658$	−17.6671	−	12.5194i	−0.688734	−	0.488059i
$659$		−	9.33865i		−	0.363782i	−0.983319	−	0.181891i	$-0.941778\pi$
$659$		−	9.33865i		−	0.363782i	0.983319	−	0.181891i	$-0.0582218\pi$
$660$		0			0
$661$	−8.88871	+	5.13190i	−0.345731	+	0.199608i	−0.662803	−	0.748793i	$-0.730633\pi$
$661$	−8.88871	+	5.13190i	−0.345731	+	0.199608i	0.317072	+	0.948401i	$0.397300\pi$
$662$	−1.42579	−	15.0773i	−0.0554150	−	0.585996i
$663$	0.980805	−	1.69880i	0.0380913	−	0.0659761i
$664$	−25.8602	+	7.51624i	−1.00357	+	0.291687i
$665$		0			0
$666$	−0.257698	+	0.562916i	−0.00998558	+	0.0218125i
$667$	−38.5505	−	22.2571i	−1.49268	−	0.861799i
$668$	9.71929	−	27.9167i	0.376051	−	1.08013i
$669$	−21.6137	−	37.4361i	−0.835636	−	1.44736i
$670$		0			0
$671$	55.5441			2.14425
$672$	−25.5369	−	6.23187i	−0.985109	−	0.240400i
$673$	−14.1636			−0.545967			−0.272983	−	0.962019i	$-0.588010\pi$
$673$	−14.1636			−0.545967			−0.272983	+	0.962019i	$0.588010\pi$
$674$	−23.5008	−	33.0662i	−0.905216	−	1.27366i
$675$		0			0
$676$	7.26431	−	20.8653i	0.279396	−	0.802510i
$677$	−13.4853	−	7.78573i	−0.518281	−	0.299230i	0.217950	−	0.975960i	$-0.430063\pi$
$677$	−13.4853	−	7.78573i	−0.518281	−	0.299230i	−0.736231	+	0.676730i	$0.763396\pi$
$678$	−9.82845	+	21.4693i	−0.377459	+	0.824524i
$679$	−30.5894	+	35.5325i	−1.17392	+	1.36361i
$680$		0			0
$681$	−7.20074	+	12.4720i	−0.275933	+	0.477930i
$682$	2.34445	+	24.7918i	0.0897734	+	0.949326i
$683$	−0.0816759	+	0.0471556i	−0.00312524	+	0.00180436i	−0.501562	−	0.865122i	$-0.667241\pi$
$683$	−0.0816759	+	0.0471556i	−0.00312524	+	0.00180436i	0.498437	+	0.866926i	$0.333908\pi$
$684$	0.131809	−	0.0251541i	0.00503983	−	0.000961789i
$685$		0			0
$686$	−26.1500	+	1.47480i	−0.998413	+	0.0563083i
$687$			8.53730i			0.325718i
$688$	12.3196	−	15.5482i	0.469679	−	0.592769i
$689$	−45.9997	+	26.5579i	−1.75245	+	1.01178i
$690$		0			0
$691$	3.68824	−	6.38822i	0.140307	−	0.243019i	−0.787305	−	0.616564i	$-0.788524\pi$
$691$	3.68824	−	6.38822i	0.140307	−	0.243019i	0.927612	+	0.373544i	$0.121858\pi$
$692$	28.4171	−	24.5327i	1.08026	−	0.932594i
$693$	0.607651	−	0.705843i	0.0230827	−	0.0268127i
$694$	−30.1080	−	13.7832i	−1.14288	−	0.523202i
$695$		0			0
$696$	29.3012	+	28.0925i	1.11066	+	1.06484i
$697$	0.622442	+	1.07810i	0.0235767	+	0.0408360i
$698$	22.7636	−	16.1785i	0.861613	−	0.612365i
$699$	37.1614			1.40557
$700$		0			0
$701$	3.40837			0.128732			0.0643661	−	0.997926i	$-0.479497\pi$
$701$	3.40837			0.128732			0.0643661	+	0.997926i	$0.479497\pi$
$702$	28.9433	−	20.5706i	1.09239	−	0.776386i
$703$	−2.04733	−	3.54607i	−0.0772163	−	0.133743i
$704$	15.3986	−	29.4709i	0.580357	−	1.11073i
$705$		0			0
$706$	−27.7242	−	12.6919i	−1.04341	−	0.477665i
$707$	40.0073	+	7.57735i	1.50463	+	0.284976i
$708$	−18.0451	−	20.9023i	−0.678176	−	0.785556i
$709$	13.4643	−	23.3209i	0.505663	−	0.875834i	−0.494315	−	0.869283i	$-0.664581\pi$
$709$	13.4643	−	23.3209i	0.505663	−	0.875834i	0.999979	−	0.00655175i	$-0.00208550\pi$
$710$		0			0
$711$	−0.374931	+	0.216466i	−0.0140610	+	0.00811813i
$712$	−6.39252	−	1.56939i	−0.239570	−	0.0588155i
$713$		−	23.0787i		−	0.864303i
$714$	−0.865387	+	1.22121i	−0.0323863	+	0.0457026i
$715$		0			0
$716$	4.80806	+	25.1945i	0.179686	+	0.941564i
$717$	−3.74116	+	2.15996i	−0.139716	+	0.0806651i
$718$	1.03717	+	10.9677i	0.0387067	+	0.409311i
$719$	−0.995916	+	1.72498i	−0.0371414	+	0.0643308i	−0.883999	−	0.467490i	$-0.845159\pi$
$719$	−0.995916	+	1.72498i	−0.0371414	+	0.0643308i	0.846857	+	0.531820i	$0.178492\pi$
$720$		0			0
$721$	27.3132	−	9.55171i	1.01720	−	0.355724i
$722$	10.8152	−	23.6247i	0.402498	−	0.879220i
$723$	2.40442	+	1.38820i	0.0894215	+	0.0516275i
$724$	16.1548	+	5.62436i	0.600390	+	0.209028i
$725$		0			0
$726$	9.03033	+	12.7059i	0.335147	+	0.471560i
$727$	−26.2307			−0.972843			−0.486422	−	0.873724i	$-0.661698\pi$
$727$	−26.2307			−0.972843			−0.486422	+	0.873724i	$0.661698\pi$
$728$	−15.2284	+	33.3874i	−0.564402	+	1.23742i
$729$	26.1953			0.970197
$730$		0			0
$731$	−0.564767	−	0.978205i	−0.0208887	−	0.0361802i
$732$	44.3313	+	15.4341i	1.63853	+	0.570460i
$733$	−2.67432	−	1.54402i	−0.0987782	−	0.0570296i	0.449797	−	0.893131i	$-0.351496\pi$
$733$	−2.67432	−	1.54402i	−0.0987782	−	0.0570296i	−0.548575	+	0.836101i	$0.684830\pi$
$734$	−3.25741	+	7.11551i	−0.120233	+	0.262638i
$735$		0			0
$736$	−16.7789	+	25.8478i	−0.618478	+	0.952762i
$737$	13.5034	−	23.3886i	0.497405	−	0.861531i
$738$	−0.0616340	−	0.651760i	−0.00226878	−	0.0239916i
$739$	10.1238	−	5.84500i	0.372411	−	0.215012i	−0.302100	−	0.953276i	$-0.597688\pi$
$739$	10.1238	−	5.84500i	0.372411	−	0.215012i	0.674511	+	0.738264i	$0.264354\pi$
$740$		0			0
$741$		−	6.82279i		−	0.250642i
$742$	36.8271	−	16.9210i	1.35196	−	0.621188i
$743$			12.3264i			0.452214i	0.974103	+	0.226107i	$0.0725998\pi$
$743$			12.3264i			0.452214i	−0.974103	+	0.226107i	$0.927400\pi$
$744$	−5.01775	+	20.4385i	−0.183960	+	0.749311i
$745$		0			0
$746$	−13.3384	+	1.26136i	−0.488355	+	0.0461815i
$747$	0.403202	−	0.698366i	0.0147524	−	0.0255519i
$748$	−1.23725	−	1.43315i	−0.0452383	−	0.0524012i
$749$	−4.12367	−	11.7917i	−0.150676	−	0.430859i
$750$		0			0
$751$	23.8338	+	13.7605i	0.869709	+	0.502127i	0.867252	−	0.497870i	$-0.165884\pi$
$751$	23.8338	+	13.7605i	0.869709	+	0.502127i	0.00245756	+	0.999997i	$0.499218\pi$
$752$	21.5214	−	8.52466i	0.784806	−	0.310862i
$753$	−23.0989	−	40.0085i	−0.841772	−	1.45799i
$754$	46.1905	−	32.8285i	1.68216	−	1.19554i
$755$		0			0
$756$	−23.4450	+	13.5794i	−0.852688	+	0.493879i
$757$	−20.5776			−0.747904			−0.373952	−	0.927448i	$-0.621998\pi$
$757$	−20.5776			−0.747904			−0.373952	+	0.927448i	$0.621998\pi$
$758$	−27.2290	+	19.3521i	−0.989001	+	0.702902i
$759$	−19.8838	−	34.4398i	−0.721737	−	1.25008i
$760$		0			0
$761$	2.16571	+	1.25037i	0.0785069	+	0.0453260i	0.538740	−	0.842472i	$-0.318901\pi$
$761$	2.16571	+	1.25037i	0.0785069	+	0.0453260i	−0.460233	+	0.887798i	$0.652234\pi$
$762$	27.8238	+	12.7375i	1.00795	+	0.461429i
$763$	−4.00719	+	21.1574i	−0.145070	+	0.765949i
$764$	−0.746124	+	0.644134i	−0.0269938	+	0.0233040i
$765$		0			0
$766$	−23.7492	+	2.24585i	−0.858093	+	0.0811460i
$767$	−33.3851	+	19.2749i	−1.20546	+	0.695975i
$768$	20.4792	−	19.2428i	0.738980	−	0.694363i
$769$		−	36.2043i		−	1.30556i	−0.757548	−	0.652779i	$-0.773603\pi$
$769$		−	36.2043i		−	1.30556i	0.757548	−	0.652779i	$-0.226397\pi$
$770$		0			0
$771$		−	21.0738i		−	0.758953i
$772$	−52.9946	+	10.1134i	−1.90732	+	0.363988i
$773$	−9.73087	+	5.61812i	−0.349995	+	0.202070i	−0.664683	−	0.747125i	$-0.731433\pi$
$773$	−9.73087	+	5.61812i	−0.349995	+	0.202070i	0.314688	+	0.949195i	$0.398100\pi$
$774$	0.0559231	+	0.591369i	0.00201011	+	0.0212563i
$775$		0			0
$776$	−13.9892	−	48.1312i	−0.502185	−	1.72781i
$777$	−18.2024	−	15.6702i	−0.653009	−	0.562167i
$778$	6.09063	−	13.3044i	0.218360	−	0.476986i
$779$	3.74981	+	2.16495i	0.134351	+	0.0775675i
$780$		0			0
$781$	4.23574	+	7.33653i	0.151567	+	0.262522i
$782$	1.01650	+	1.43025i	0.0363501	+	0.0511455i
$783$	41.8393			1.49522
$784$	13.9326	−	24.2875i	0.497594	−	0.867410i
$785$		0			0
$786$	23.9669	+	33.7221i	0.854873	+	1.20283i
$787$	19.1837	+	33.2271i	0.683825	+	1.18442i	0.973805	+	0.227387i	$0.0730181\pi$
$787$	19.1837	+	33.2271i	0.683825	+	1.18442i	−0.289980	+	0.957033i	$0.593649\pi$
$788$	−1.63099	+	4.68470i	−0.0581017	+	0.166886i
$789$	14.7731	+	8.52923i	0.525935	+	0.303649i
$790$		0			0
$791$	−19.0610	−	16.4094i	−0.677733	−	0.583451i
$792$	0.277892	+	0.956112i	0.00987448	+	0.0339740i
$793$	32.7655	−	56.7516i	1.16354	−	2.01531i
$794$	0.344191	+	3.63971i	0.0122149	+	0.129168i
$795$		0			0
$796$	10.8757	−	2.07548i	0.385477	−	0.0735636i
$797$			35.5238i			1.25832i	0.777276	+	0.629159i	$0.216601\pi$
$797$			35.5238i			1.25832i	−0.777276	+	0.629159i	$0.783399\pi$
$798$	−0.482918	+	5.18347i	−0.0170951	+	0.183493i
$799$		−	1.31806i		−	0.0466297i
$800$		0			0
$801$	0.170695	−	0.0985508i	0.00603121	−	0.00348212i
$802$	11.2309	−	1.06206i	0.396577	−	0.0375025i
$803$	−11.1433	+	19.3007i	−0.393237	+	0.681107i
$804$	17.2765	−	14.9149i	0.609295	−	0.526009i
$805$		0			0
$806$	26.7137	+	12.2293i	0.940951	+	0.430758i
$807$	−5.12186	−	2.95711i	−0.180298	−	0.104095i
$808$	−30.1255	+	31.4216i	−1.05981	+	1.10541i
$809$	1.74646	+	3.02495i	0.0614022	+	0.106352i	0.895092	−	0.445881i	$-0.147109\pi$
$809$	1.74646	+	3.02495i	0.0614022	+	0.106352i	−0.833690	+	0.552232i	$0.813776\pi$
$810$		0			0
$811$	−16.6986			−0.586367			−0.293184	−	0.956056i	$-0.594715\pi$
$811$	−16.6986			−0.586367			−0.293184	+	0.956056i	$0.594715\pi$
$812$	−37.4158	+	21.6714i	−1.31304	+	0.760516i
$813$	−17.4500			−0.611997
$814$	24.7650	−	17.6010i	0.868013	−	0.616913i
$815$		0			0
$816$	−0.589253	−	1.48764i	−0.0206280	−	0.0520777i
$817$	−3.40235	−	1.96435i	−0.119033	−	0.0687239i
$818$	8.36265	+	3.82834i	0.292393	+	0.133855i
$819$	−0.362733	−	1.03724i	−0.0126749	−	0.0362440i
$820$		0			0
$821$	−14.5330	+	25.1719i	−0.507206	+	0.878506i	0.492760	+	0.870165i	$0.335988\pi$
$821$	−14.5330	+	25.1719i	−0.507206	+	0.878506i	−0.999965	+	0.00834036i	$0.997345\pi$
$822$	−10.8878	+	1.02961i	−0.379757	+	0.0359119i
$823$	2.55264	−	1.47377i	0.0889796	−	0.0513724i	−0.454850	−	0.890568i	$-0.650307\pi$
$823$	2.55264	−	1.47377i	0.0889796	−	0.0513724i	0.543830	+	0.839196i	$0.316974\pi$
$824$	−7.37520	+	30.0409i	−0.256927	+	1.04653i
$825$		0			0
$826$	26.7279	−	12.2807i	0.929981	−	0.427299i
$827$			17.2803i			0.600896i	0.953798	+	0.300448i	$0.0971361\pi$
$827$			17.2803i			0.600896i	−0.953798	+	0.300448i	$0.902864\pi$
$828$	−0.172976	−	0.906403i	−0.00601132	−	0.0314997i
$829$	−1.71627	+	0.990889i	−0.0596085	+	0.0344150i	−0.529508	−	0.848305i	$-0.677623\pi$
$829$	−1.71627	+	0.990889i	−0.0596085	+	0.0344150i	0.469900	+	0.882720i	$0.344290\pi$
$830$		0			0
$831$	0.351952	−	0.609599i	0.0122091	−	0.0211468i
$832$	−21.0279	−	33.1183i	−0.729012	−	1.14817i
$833$	−0.993588	−	1.24685i	−0.0344258	−	0.0432009i
$834$	−13.6721	+	29.8654i	−0.473426	+	1.03415i
$835$		0			0
$836$	−6.21918	−	2.16523i	−0.215095	−	0.0748859i
$837$	10.8459	+	18.7857i	0.374890	+	0.649328i
$838$	24.1181	+	33.9348i	0.833146	+	1.17226i
$839$	−28.7538			−0.992693			−0.496346	−	0.868125i	$-0.665325\pi$
$839$	−28.7538			−0.992693			−0.496346	+	0.868125i	$0.665325\pi$
$840$		0			0
$841$	37.7712			1.30245
$842$	9.27683	+	13.0527i	0.319701	+	0.449827i
$843$	18.8408	+	32.6333i	0.648913	+	1.12395i
$844$	41.0361	+	14.2869i	1.41252	+	0.491774i
$845$		0			0
$846$	−0.288522	+	0.630249i	−0.00991959	+	0.0216684i
$847$	−15.6735	+	5.48118i	−0.538547	+	0.188336i
$848$	−6.32290	+	42.8628i	−0.217129	+	1.47192i
$849$	−17.9376	+	31.0688i	−0.615616	+	1.06628i
$850$		0			0
$851$	−24.3851	+	14.0788i	−0.835911	+	0.482613i
$852$	1.34206	+	7.03249i	0.0459783	+	0.240929i
$853$			54.2406i			1.85716i	0.371127	+	0.928582i	$0.378972\pi$
$853$			54.2406i			1.85716i	−0.371127	+	0.928582i	$0.621028\pi$
$854$	−28.9098	+	40.7966i	−0.989273	+	1.39603i
$855$		0			0
$856$	12.9693	+	3.18403i	0.443282	+	0.108828i
$857$	4.30041	−	2.48284i	0.146899	−	0.0848123i	−0.424749	−	0.905311i	$-0.639638\pi$
$857$	4.30041	−	2.48284i	0.146899	−	0.0848123i	0.571648	+	0.820499i	$0.306304\pi$
$858$	50.4006	−	4.76616i	1.72065	−	0.162714i
$859$	−17.3837	+	30.1095i	−0.593125	+	1.02732i	0.400684	+	0.916216i	$0.368772\pi$
$859$	−17.3837	+	30.1095i	−0.593125	+	1.02732i	−0.993809	+	0.111106i	$0.964561\pi$
$860$		0			0
$861$	24.9548	+	4.72641i	0.850456	+	0.161076i
$862$	42.4531	+	19.4346i	1.44596	+	0.661946i
$863$	−28.5637	−	16.4912i	−0.972319	−	0.561369i	−0.0723765	−	0.997377i	$-0.523058\pi$
$863$	−28.5637	−	16.4912i	−0.972319	−	0.561369i	−0.899942	+	0.436009i	$0.856392\pi$
$864$	1.51048	−	28.9250i	0.0513877	−	0.984049i
$865$		0			0
$866$	−21.8290	+	15.5143i	−0.741780	+	0.527197i
$867$	29.7665			1.01092
$868$	−19.4296	−	11.1817i	−0.659483	−	0.379533i
$869$	21.2464			0.720735
$870$		0			0
$871$	−15.9314	−	27.5940i	−0.539815	−	0.934986i
$872$	−16.6169	−	15.9315i	−0.562720	−	0.539508i
$873$	1.29980	+	0.750440i	0.0439916	+	0.0253986i
$874$	5.54920	+	2.54037i	0.187705	+	0.0859294i
$875$		0			0
$876$	−14.2569	+	12.3081i	−0.481695	+	0.415851i
$877$	15.7899	−	27.3489i	0.533187	−	0.923507i	−0.466062	−	0.884752i	$-0.654328\pi$
$877$	15.7899	−	27.3489i	0.533187	−	0.923507i	0.999249	−	0.0387545i	$-0.0123390\pi$
$878$	34.2087	−	3.23497i	1.15449	−	0.109175i
$879$	−7.05966	+	4.07590i	−0.238116	+	0.137477i
$880$		0			0
$881$			31.0031i			1.04452i	0.852786	+	0.522261i	$0.174911\pi$
$881$			31.0031i			1.04452i	−0.852786	+	0.522261i	$0.825089\pi$
$882$	0.202163	+	0.813694i	0.00680718	+	0.0273985i
$883$		−	1.05418i		−	0.0354759i	−0.999843	−	0.0177380i	$-0.994354\pi$
$883$		−	1.05418i		−	0.0354759i	0.999843	−	0.0177380i	$-0.00564647\pi$
$884$	−2.19416	+	0.418729i	−0.0737977	+	0.0140834i
$885$		0			0
$886$	−1.99792	−	21.1274i	−0.0671215	−	0.709789i
$887$	9.82722	−	17.0213i	0.329966	−	0.571518i	−0.652539	−	0.757755i	$-0.726296\pi$
$887$	9.82722	−	17.0213i	0.329966	−	0.571518i	0.982505	+	0.186238i	$0.0596294\pi$
$888$	24.6565	−	7.16636i	0.827417	−	0.240487i
$889$	−21.2662	+	24.7027i	−0.713247	+	0.828502i
$890$		0			0
$891$	33.2848	+	19.2170i	1.11508	+	0.643794i
$892$	−16.1849	+	46.4879i	−0.541911	+	1.55653i
$893$	−2.29222	−	3.97023i	−0.0767061	−	0.132859i
$894$	16.6158	+	23.3788i	0.555714	+	0.781904i
$895$		0			0
$896$	13.6314	+	26.6493i	0.455393	+	0.890290i
$897$	−46.9180			−1.56655
$898$	−9.00911	−	12.6761i	−0.300638	−	0.423005i
$899$	17.3090	+	29.9800i	0.577286	+	0.999889i
$900$		0			0
$901$	2.13650	+	1.23351i	0.0711773	+	0.0410942i
$902$	−13.3732	+	29.2126i	−0.445280	+	0.972673i
$903$	−22.6425	−	4.28846i	−0.753494	−	0.142711i
$904$	25.8195	−	7.50439i	0.858744	−	0.249592i
$905$		0			0
$906$	−4.02582	−	42.5717i	−0.133749	−	1.41435i
$907$	11.1493	−	6.43706i	0.370207	−	0.213739i	−0.303342	−	0.952882i	$-0.598102\pi$
$907$	11.1493	−	6.43706i	0.370207	−	0.213739i	0.673549	+	0.739143i	$0.264769\pi$
$908$	16.1088	−	3.07417i	0.534590	−	0.102020i
$909$		−	1.30346i		−	0.0432331i
$910$		0			0
$911$			15.4628i			0.512306i	0.966636	+	0.256153i	$0.0824551\pi$
$911$			15.4628i			0.512306i	−0.966636	+	0.256153i	$0.917545\pi$
$912$	−4.36205	−	3.45626i	−0.144442	−	0.114448i
$913$	−34.2727	+	19.7873i	−1.13426	+	0.654865i
$914$	−23.3670	+	2.20971i	−0.772913	+	0.0730909i
$915$		0			0
$916$	7.35885	−	6.35294i	0.243143	−	0.209907i
$917$	−41.5982	+	14.5473i	−1.37369	+	0.480395i
$918$	−1.49957	−	0.686489i	−0.0494932	−	0.0226575i
$919$	−13.7399	−	7.93272i	−0.453236	−	0.261676i	0.255960	−	0.966687i	$-0.417609\pi$
$919$	−13.7399	−	7.93272i	−0.453236	−	0.261676i	−0.709196	+	0.705011i	$0.750942\pi$
$920$		0			0
$921$	−5.29033	−	9.16312i	−0.174322	−	0.301935i
$922$	−7.64115	+	5.43071i	−0.251648	+	0.178851i
$923$	9.99469			0.328979
$924$	−38.6282	+	0.0536258i	−1.27077	+	0.00176416i
$925$		0			0
$926$	2.43163	−	1.72820i	0.0799082	−	0.0567923i
$927$	−0.463129	−	0.802163i	−0.0152112	−	0.0263465i
$928$	2.41058	−	46.1613i	0.0791310	−	1.51532i
$929$	0.835215	+	0.482212i	0.0274025	+	0.0158209i	0.513639	−	0.858007i	$-0.328297\pi$
$929$	0.835215	+	0.482212i	0.0274025	+	0.0158209i	−0.486236	+	0.873827i	$0.661631\pi$
$930$		0			0
$931$	−5.16124	−	2.02781i	−0.169153	−	0.0664588i
$932$	−27.6533	−	32.0318i	−0.905813	−	1.04924i
$933$	−20.2107	+	35.0060i	−0.661669	+	1.14604i
$934$	−16.0163	+	1.51459i	−0.524071	+	0.0495590i
$935$		0			0
$936$	1.14083	+	0.280079i	0.0372891	+	0.00915465i
$937$		−	24.0110i		−	0.784404i	−0.919879	−	0.392202i	$-0.871713\pi$
$937$		−	24.0110i		−	0.784404i	0.919879	−	0.392202i	$-0.128287\pi$
$938$	10.1504	+	22.0916i	0.331423	+	0.721315i
$939$		−	14.9665i		−	0.488413i
$940$		0			0
$941$	2.18480	−	1.26140i	0.0712225	−	0.0411203i	−0.463966	−	0.885853i	$-0.653574\pi$
$941$	2.18480	−	1.26140i	0.0712225	−	0.0411203i	0.535188	+	0.844733i	$0.320241\pi$
$942$	4.88357	+	51.6422i	0.159115	+	1.68259i
$943$	14.8876	−	25.7861i	0.484808	−	0.839713i
$944$	−4.58895	+	31.1084i	−0.149358	+	1.01249i
$945$		0			0
$946$	12.1341	−	26.5058i	0.394513	−	0.861777i
$947$	−17.0478	−	9.84254i	−0.553978	−	0.319840i	0.196747	−	0.980454i	$-0.436962\pi$
$947$	−17.0478	−	9.84254i	−0.553978	−	0.319840i	−0.750725	+	0.660615i	$0.770296\pi$
$948$	16.9574	+	5.90376i	0.550750	+	0.191745i
$949$	13.1469	+	22.7710i	0.426765	+	0.739179i
$950$		0			0
$951$	7.38150			0.239362
$952$	1.69661	−	0.162817i	0.0549873	−	0.00527693i
$953$	26.9765			0.873856			0.436928	−	0.899496i	$-0.356066\pi$
$953$	26.9765			0.873856			0.436928	+	0.899496i	$0.356066\pi$
$954$	−0.751584	−	1.05750i	−0.0243334	−	0.0342378i
$955$		0			0
$956$	4.64575	+	1.61743i	0.150254	+	0.0523115i
$957$	51.6595	+	29.8257i	1.66992	+	0.964126i
$958$	5.90810	−	12.9057i	0.190882	−	0.416963i
$959$	2.16784	−	11.4459i	0.0700033	−	0.369607i
$960$		0			0
$961$	6.52607	−	11.3035i	0.210518	−	0.364629i
$962$	−3.37468	−	35.6862i	−0.108804	−	1.15057i
$963$	−0.346311	+	0.199943i	−0.0111597	+	0.00644306i
$964$	−0.592653	−	3.10554i	−0.0190881	−	0.100023i
$965$		0			0
$966$	35.6449	+	3.32086i	1.14686	+	0.106847i
$967$		−	22.8186i		−	0.733797i	−0.930261	−	0.366898i	$-0.880420\pi$
$967$		−	22.8186i		−	0.733797i	0.930261	−	0.366898i	$-0.119580\pi$
$968$	4.23221	−	17.2388i	0.136028	−	0.554076i
$969$	−0.274436	+	0.158446i	−0.00881616	+	0.00509001i
$970$		0			0
$971$	−12.7360	+	22.0594i	−0.408718	+	0.707921i	−0.994746	−	0.102370i	$-0.967357\pi$
$971$	−12.7360	+	22.0594i	−0.408718	+	0.707921i	0.586028	+	0.810291i	$0.300691\pi$
$972$	1.15000	+	1.33209i	0.0368863	+	0.0427268i
$973$	−26.5153	−	22.8267i	−0.850042	−	0.731790i
$974$	−33.6830	−	15.4198i	−1.07927	−	0.494081i
$975$		0			0
$976$	−19.6851	−	49.6971i	−0.630103	−	1.59077i
$977$	−6.10223	−	10.5694i	−0.195228	−	0.338144i	0.751748	−	0.659451i	$-0.229211\pi$
$977$	−6.10223	−	10.5694i	−0.195228	−	0.338144i	−0.946975	+	0.321307i	$0.895878\pi$
$978$	−14.6093	+	10.3831i	−0.467154	+	0.332015i
$979$	−9.67286			−0.309146
$980$		0			0
$981$	0.689320			0.0220083
$982$	−30.0255	+	21.3397i	−0.958152	+	0.680977i
$983$	−3.70841	−	6.42315i	−0.118280	−	0.204867i	0.800806	−	0.598923i	$-0.204405\pi$
$983$	−3.70841	−	6.42315i	−0.118280	−	0.204867i	−0.919086	+	0.394057i	$0.871071\pi$
$984$	−18.7909	+	19.5994i	−0.599032	+	0.624805i
$985$		0			0
$986$	−2.39316	−	1.09556i	−0.0762137	−	0.0348899i
$987$	−20.3797	−	17.5446i	−0.648694	−	0.558452i
$988$	−5.88100	+	5.07711i	−0.187099	+	0.161524i
$989$	−13.5082	+	23.3968i	−0.429535	+	0.743976i
$990$		0			0
$991$	−22.8598	+	13.1981i	−0.726164	+	0.419251i	−0.817017	−	0.576613i	$-0.804374\pi$
$991$	−22.8598	+	13.1981i	−0.726164	+	0.419251i	0.0908531	+	0.995864i	$0.471041\pi$
$992$	21.3511	−	10.8840i	0.677899	−	0.345566i
$993$		−	18.8082i		−	0.596862i
$994$	−7.59325	−	0.707425i	−0.240843	−	0.0224382i
$995$		0			0
$996$	−32.8523	+	6.26946i	−1.04097	+	0.198655i
$997$	7.20245	−	4.15834i	0.228104	−	0.131696i	−0.381593	−	0.924330i	$-0.624624\pi$
$997$	7.20245	−	4.15834i	0.228104	−	0.131696i	0.609697	+	0.792635i	$0.291291\pi$
$998$	−2.31184	−	24.4470i	−0.0731800	−	0.773856i
$999$	13.2327	−	22.9198i	0.418665	−	0.725150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.d.551.6	yes	32
4.3	odd	2	inner	700.2.p.d.551.16	yes	32
5.2	odd	4		700.2.t.e.299.26		64
5.3	odd	4		700.2.t.e.299.7		64
5.4	even	2		700.2.p.f.551.11	yes	32
7.3	odd	6	inner	700.2.p.d.451.16	yes	32
20.3	even	4		700.2.t.e.299.18		64
20.7	even	4		700.2.t.e.299.15		64
20.19	odd	2		700.2.p.f.551.1	yes	32
28.3	even	6	inner	700.2.p.d.451.6	✓	32
35.3	even	12		700.2.t.e.199.15		64
35.17	even	12		700.2.t.e.199.18		64
35.24	odd	6		700.2.p.f.451.1	yes	32
140.3	odd	12		700.2.t.e.199.26		64
140.59	even	6		700.2.p.f.451.11	yes	32
140.87	odd	12		700.2.t.e.199.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.p.d.451.6	✓	32	28.3	even	6	inner
700.2.p.d.451.16	yes	32	7.3	odd	6	inner
700.2.p.d.551.6	yes	32	1.1	even	1	trivial
700.2.p.d.551.16	yes	32	4.3	odd	2	inner
700.2.p.f.451.1	yes	32	35.24	odd	6
700.2.p.f.451.11	yes	32	140.59	even	6
700.2.p.f.551.1	yes	32	20.19	odd	2
700.2.p.f.551.11	yes	32	5.4	even	2
700.2.t.e.199.7		64	140.87	odd	12
700.2.t.e.199.15		64	35.3	even	12
700.2.t.e.199.18		64	35.17	even	12
700.2.t.e.199.26		64	140.3	odd	12
700.2.t.e.299.7		64	5.3	odd	4
700.2.t.e.299.15		64	20.7	even	4
700.2.t.e.299.18		64	20.3	even	4
700.2.t.e.299.26		64	5.2	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819270 - 1.15273i) q^{2} +(-0.878165 - 1.52103i) q^{3} +(-0.657592 + 1.88880i) q^{4} +(-1.03388 + 2.25842i) q^{6} +(-2.00509 - 1.72616i) q^{7} +(2.71603 - 0.789410i) q^{8} +(-0.0423472 + 0.0733475i) q^{9} +O(q^{10})\)	\(q+(-0.819270 - 1.15273i) q^{2} +(-0.878165 - 1.52103i) q^{3} +(-0.657592 + 1.88880i) q^{4} +(-1.03388 + 2.25842i) q^{6} +(-2.00509 - 1.72616i) q^{7} +(2.71603 - 0.789410i) q^{8} +(-0.0423472 + 0.0733475i) q^{9} +(3.59956 - 2.07821i) q^{11} +(3.45039 - 0.658464i) q^{12} -4.90376i q^{13} +(-0.347088 + 3.72552i) q^{14} +(-3.13514 - 2.48412i) q^{16} +(-0.197246 + 0.113880i) q^{17} +(0.119244 - 0.0112764i) q^{18} +(-0.396093 + 0.686053i) q^{19} +(-0.864729 + 4.56564i) q^{21} +(-5.34464 - 2.44673i) q^{22} +(4.71775 + 2.72379i) q^{23} +(-3.58584 - 3.43792i) q^{24} +(-5.65273 + 4.01750i) q^{26} -5.12024 q^{27} +(4.57890 - 2.65211i) q^{28} -8.17136 q^{29} +(-2.11825 - 3.66891i) q^{31} +(-0.295003 + 5.64916i) q^{32} +(-6.32202 - 3.65002i) q^{33} +(0.292871 + 0.134074i) q^{34} +(-0.110692 - 0.128218i) q^{36} +(-2.58440 + 4.47631i) q^{37} +(1.11534 - 0.105473i) q^{38} +(-7.45874 + 4.30631i) q^{39} -5.46577i q^{41} +(5.97142 - 2.74369i) q^{42} +4.95932i q^{43} +(1.55828 + 8.16548i) q^{44} +(-0.725302 - 7.66984i) q^{46} +(-2.89353 + 5.01175i) q^{47} +(-1.02524 + 6.95011i) q^{48} +(1.04077 + 6.92220i) q^{49} +(0.346429 + 0.200011i) q^{51} +(9.26222 + 3.22467i) q^{52} +(-5.41584 - 9.38050i) q^{53} +(4.19486 + 5.90227i) q^{54} +(-6.80853 - 3.10546i) q^{56} +1.39134 q^{57} +(6.69456 + 9.41941i) q^{58} +(-3.93063 - 6.80806i) q^{59} +(11.5731 + 6.68172i) q^{61} +(-2.49386 + 5.44760i) q^{62} +(0.211519 - 0.0739705i) q^{63} +(6.75366 - 4.28813i) q^{64} +(0.971941 + 10.2780i) q^{66} +(5.62711 - 3.24881i) q^{67} +(-0.0853894 - 0.447445i) q^{68} -9.56776i q^{69} +2.03817i q^{71} +(-0.0571151 + 0.232644i) q^{72} +(-4.64359 + 2.68098i) q^{73} +(7.27732 - 0.688183i) q^{74} +(-1.03535 - 1.19928i) q^{76} +(-10.8048 - 2.04641i) q^{77} +(11.0748 + 5.06992i) q^{78} +(4.42687 + 2.55585i) q^{79} +(4.62346 + 8.00806i) q^{81} +(-6.30058 + 4.47794i) q^{82} -9.52133 q^{83} +(-8.05496 - 4.63563i) q^{84} +(5.71677 - 4.06302i) q^{86} +(7.17580 + 12.4289i) q^{87} +(8.13597 - 8.48602i) q^{88} +(-2.01542 - 1.16361i) q^{89} +(-8.46465 + 9.83247i) q^{91} +(-8.24706 + 7.11975i) q^{92} +(-3.72034 + 6.44381i) q^{93} +(8.14780 - 0.770500i) q^{94} +(8.85158 - 4.51218i) q^{96} -17.7211i q^{97} +(7.12678 - 6.87088i) q^{98} +0.352025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9	\( 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9} + 15 q^{12} - 13 q^{14} + q^{16} - 15 q^{18} + 12 q^{21} + 34 q^{22} - 18 q^{24} - 15 q^{26} + 17 q^{28} + 8 q^{29} + 14 q^{32} - 30 q^{36} - 16 q^{37} + 30 q^{38} + q^{42} + 12 q^{44} + 2 q^{46} + 20 q^{49} + 18 q^{52} - 20 q^{53} + 57 q^{54} - 31 q^{56} - 24 q^{57} - 4 q^{58} - 12 q^{61} + 40 q^{64} - 66 q^{66} + 15 q^{68} + 13 q^{72} - 72 q^{73} - q^{74} + 8 q^{77} + 60 q^{78} - 36 q^{81} - 66 q^{82} + 67 q^{84} + 4 q^{86} + 34 q^{88} - 60 q^{89} - 148 q^{92} - 20 q^{93} + 45 q^{94} + 93 q^{96}+O(q^{100}) \) 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9 + 15 * q^12 - 13 * q^14 + q^16 - 15 * q^18 + 12 * q^21 + 34 * q^22 - 18 * q^24 - 15 * q^26 + 17 * q^28 + 8 * q^29 + 14 * q^32 - 30 * q^36 - 16 * q^37 + 30 * q^38 + q^42 + 12 * q^44 + 2 * q^46 + 20 * q^49 + 18 * q^52 - 20 * q^53 + 57 * q^54 - 31 * q^56 - 24 * q^57 - 4 * q^58 - 12 * q^61 + 40 * q^64 - 66 * q^66 + 15 * q^68 + 13 * q^72 - 72 * q^73 - q^74 + 8 * q^77 + 60 * q^78 - 36 * q^81 - 66 * q^82 + 67 * q^84 + 4 * q^86 + 34 * q^88 - 60 * q^89 - 148 * q^92 - 20 * q^93 + 45 * q^94 + 93 * q^96

Introduction

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