LMFDB - Embedded newform 175.2.n.a.169.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(29,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("175.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.n (of order $10$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.12
Character	$\chi$	$=$	175.169
Dual form			175.2.n.a.29.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99559 - 0.648406i) q^{2} +(-0.448050 - 0.616687i) q^{3} +(1.94391 - 1.41233i) q^{4} +(-0.794894 - 2.09001i) q^{5} +(-1.29399 - 0.940136i) q^{6} +1.00000i q^{7} +(0.496791 - 0.683774i) q^{8} +(0.747496 - 2.30056i) q^{9} +O(q^{10})$	\(q+(1.99559 - 0.648406i) q^{2} +(-0.448050 - 0.616687i) q^{3} +(1.94391 - 1.41233i) q^{4} +(-0.794894 - 2.09001i) q^{5} +(-1.29399 - 0.940136i) q^{6} +1.00000i q^{7} +(0.496791 - 0.683774i) q^{8} +(0.747496 - 2.30056i) q^{9} +(-2.94146 - 3.65539i) q^{10} +(1.57210 + 4.83843i) q^{11} +(-1.74193 - 0.565988i) q^{12} +(2.02755 + 0.658792i) q^{13} +(0.648406 + 1.99559i) q^{14} +(-0.932731 + 1.42663i) q^{15} +(-0.936986 + 2.88375i) q^{16} +(-1.80173 + 2.47986i) q^{17} -5.07564i q^{18} +(-1.68348 - 1.22312i) q^{19} +(-4.49699 - 2.94013i) q^{20} +(0.616687 - 0.448050i) q^{21} +(6.27453 + 8.63615i) q^{22} +(0.532883 - 0.173144i) q^{23} -0.644262 q^{24} +(-3.73629 + 3.32267i) q^{25} +4.47332 q^{26} +(-3.92852 + 1.27645i) q^{27} +(1.41233 + 1.94391i) q^{28} +(6.34885 - 4.61271i) q^{29} +(-0.936312 + 3.45175i) q^{30} +(-4.40981 - 3.20392i) q^{31} +8.05270i q^{32} +(2.27942 - 3.13735i) q^{33} +(-1.98755 + 6.11704i) q^{34} +(2.09001 - 0.794894i) q^{35} +(-1.79608 - 5.52778i) q^{36} +(-8.55379 - 2.77929i) q^{37} +(-4.15261 - 1.34926i) q^{38} +(-0.502176 - 1.54554i) q^{39} +(-1.82399 - 0.494770i) q^{40} +(1.29120 - 3.97390i) q^{41} +(0.940136 - 1.29399i) q^{42} +3.14949i q^{43} +(9.88947 + 7.18512i) q^{44} +(-5.40237 + 0.266424i) q^{45} +(0.951148 - 0.691049i) q^{46} +(5.56042 + 7.65326i) q^{47} +(2.19819 - 0.714234i) q^{48} -1.00000 q^{49} +(-5.30165 + 9.05332i) q^{50} +2.33656 q^{51} +(4.87181 - 1.58295i) q^{52} +(-5.66063 - 7.79118i) q^{53} +(-7.01204 + 5.09455i) q^{54} +(8.86271 - 7.13174i) q^{55} +(0.683774 + 0.496791i) q^{56} +1.58620i q^{57} +(9.67878 - 13.3217i) q^{58} +(2.71863 - 8.36710i) q^{59} +(0.201730 + 4.09056i) q^{60} +(2.61154 + 8.03748i) q^{61} +(-10.8776 - 3.53435i) q^{62} +(2.30056 + 0.747496i) q^{63} +(3.34744 + 10.3024i) q^{64} +(-0.234808 - 4.76128i) q^{65} +(2.51450 - 7.73884i) q^{66} +(4.99602 - 6.87643i) q^{67} +7.36526i q^{68} +(-0.345534 - 0.251045i) q^{69} +(3.65539 - 2.94146i) q^{70} +(8.39799 - 6.10149i) q^{71} +(-1.20171 - 1.65401i) q^{72} +(-11.3357 + 3.68319i) q^{73} -18.8719 q^{74} +(3.72309 + 0.815399i) q^{75} -4.99998 q^{76} +(-4.83843 + 1.57210i) q^{77} +(-2.00427 - 2.75864i) q^{78} +(-5.91108 + 4.29465i) q^{79} +(6.77186 - 0.333962i) q^{80} +(-3.32357 - 2.41471i) q^{81} -8.76749i q^{82} +(-4.59211 + 6.32050i) q^{83} +(0.565988 - 1.74193i) q^{84} +(6.61512 + 1.79440i) q^{85} +(2.04215 + 6.28509i) q^{86} +(-5.68920 - 1.84853i) q^{87} +(4.08939 + 1.32872i) q^{88} +(0.850864 + 2.61869i) q^{89} +(-10.6081 + 4.03460i) q^{90} +(-0.658792 + 2.02755i) q^{91} +(0.791338 - 1.08918i) q^{92} +4.15499i q^{93} +(16.0587 + 11.6673i) q^{94} +(-1.21814 + 4.49074i) q^{95} +(4.96600 - 3.60801i) q^{96} +(-8.25615 - 11.3636i) q^{97} +(-1.99559 + 0.648406i) q^{98} +12.3062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.99559	−	0.648406i	1.41109	−	0.458492i	0.498333	−	0.866986i	$-0.333946\pi$
$2$	1.99559	−	0.648406i	1.41109	−	0.458492i	0.912761	+	0.408494i	$0.133946\pi$
$3$	−0.448050	−	0.616687i	−0.258682	−	0.356045i	0.659846	−	0.751400i	$-0.270621\pi$
$3$	−0.448050	−	0.616687i	−0.258682	−	0.356045i	−0.918528	+	0.395356i	$0.870621\pi$
$4$	1.94391	−	1.41233i	0.971953	−	0.706165i
$5$	−0.794894	−	2.09001i	−0.355487	−	0.934681i
$5$	−0.794894	−	2.09001i	−0.355487	−	0.934681i
$6$	−1.29399	−	0.940136i	−0.528268	−	0.383809i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.496791	−	0.683774i	0.175642	−	0.241751i
$9$	0.747496	−	2.30056i	0.249165	−	0.766852i
$10$	−2.94146	−	3.65539i	−0.930170	−	1.15593i
$11$	1.57210	+	4.83843i	0.474006	+	1.45884i	0.847294	+	0.531125i	$0.178230\pi$
$11$	1.57210	+	4.83843i	0.474006	+	1.45884i	−0.373288	+	0.927716i	$0.621770\pi$
$12$	−1.74193	−	0.565988i	−0.502853	−	0.163387i
$13$	2.02755	+	0.658792i	0.562342	+	0.182716i	0.576375	−	0.817186i	$-0.304467\pi$
$13$	2.02755	+	0.658792i	0.562342	+	0.182716i	−0.0140327	+	0.999902i	$0.504467\pi$
$14$	0.648406	+	1.99559i	0.173294	+	0.533343i
$15$	−0.932731	+	1.42663i	−0.240830	+	0.368354i
$16$	−0.936986	+	2.88375i	−0.234246	+	0.720937i
$17$	−1.80173	+	2.47986i	−0.436983	+	0.601455i	−0.969538	−	0.244940i	$-0.921232\pi$
$17$	−1.80173	+	2.47986i	−0.436983	+	0.601455i	0.532555	+	0.846395i	$0.321232\pi$
$18$		−	5.07564i		−	1.19634i
$19$	−1.68348	−	1.22312i	−0.386217	−	0.280603i	0.377687	−	0.925933i	$-0.376720\pi$
$19$	−1.68348	−	1.22312i	−0.386217	−	0.280603i	−0.763903	+	0.645331i	$0.776720\pi$
$20$	−4.49699	−	2.94013i	−1.00556	−	0.657434i
$21$	0.616687	−	0.448050i	0.134572	−	0.0977724i
$22$	6.27453	+	8.63615i	1.33773	+	1.84123i
$23$	0.532883	−	0.173144i	0.111114	−	0.0361031i	−0.252932	−	0.967484i	$-0.581395\pi$
$23$	0.532883	−	0.173144i	0.111114	−	0.0361031i	0.364046	+	0.931381i	$0.381395\pi$
$24$	−0.644262			−0.131509
$25$	−3.73629	+	3.32267i	−0.747257	+	0.664535i
$26$	4.47332			0.877291
$27$	−3.92852	+	1.27645i	−0.756044	+	0.245653i
$28$	1.41233	+	1.94391i	0.266905	+	0.367364i
$29$	6.34885	−	4.61271i	1.17895	−	0.856559i	0.186899	−	0.982379i	$-0.440156\pi$
$29$	6.34885	−	4.61271i	1.17895	−	0.856559i	0.992053	+	0.125820i	$0.0401563\pi$
$30$	−0.936312	+	3.45175i	−0.170946	+	0.630201i
$31$	−4.40981	−	3.20392i	−0.792025	−	0.575440i	0.116538	−	0.993186i	$-0.462820\pi$
$31$	−4.40981	−	3.20392i	−0.792025	−	0.575440i	−0.908564	+	0.417746i	$0.862820\pi$
$32$			8.05270i			1.42353i
$33$	2.27942	−	3.13735i	0.396796	−	0.546142i
$34$	−1.98755	+	6.11704i	−0.340861	+	1.04906i
$35$	2.09001	−	0.794894i	0.353276	−	0.134362i
$36$	−1.79608	−	5.52778i	−0.299347	−	0.921296i
$37$	−8.55379	−	2.77929i	−1.40623	−	0.456913i	−0.495032	−	0.868874i	$-0.664844\pi$
$37$	−8.55379	−	2.77929i	−1.40623	−	0.456913i	−0.911201	+	0.411961i	$0.864844\pi$
$38$	−4.15261	−	1.34926i	−0.673642	−	0.218880i
$39$	−0.502176	−	1.54554i	−0.0804125	−	0.247484i
$40$	−1.82399	−	0.494770i	−0.288398	−	0.0782300i
$41$	1.29120	−	3.97390i	0.201651	−	0.620619i	−0.798183	−	0.602415i	$-0.794205\pi$
$41$	1.29120	−	3.97390i	0.201651	−	0.620619i	0.999834	−	0.0182038i	$-0.00579476\pi$
$42$	0.940136	−	1.29399i	0.145066	−	0.199666i
$43$			3.14949i			0.480293i	0.970737	+	0.240146i	$0.0771955\pi$
$43$			3.14949i			0.480293i	−0.970737	+	0.240146i	$0.922805\pi$
$44$	9.88947	+	7.18512i	1.49089	+	1.08320i
$45$	−5.40237	+	0.266424i	−0.805337	+	0.0397161i
$46$	0.951148	−	0.691049i	0.140239	−	0.101890i
$47$	5.56042	+	7.65326i	0.811071	+	1.11634i	0.991157	+	0.132692i	$0.0423622\pi$
$47$	5.56042	+	7.65326i	0.811071	+	1.11634i	−0.180087	+	0.983651i	$0.557638\pi$
$48$	2.19819	−	0.714234i	0.317281	−	0.103091i
$49$	−1.00000			−0.142857
$50$	−5.30165	+	9.05332i	−0.749766	+	1.28033i
$51$	2.33656			0.327184
$52$	4.87181	−	1.58295i	0.675598	−	0.219515i
$53$	−5.66063	−	7.79118i	−0.777547	−	1.07020i	−0.995548	−	0.0942531i	$-0.969954\pi$
$53$	−5.66063	−	7.79118i	−0.777547	−	1.07020i	0.218001	−	0.975948i	$-0.430046\pi$
$54$	−7.01204	+	5.09455i	−0.954218	+	0.693280i
$55$	8.86271	−	7.13174i	1.19505	−	0.961644i
$56$	0.683774	+	0.496791i	0.0913731	+	0.0663865i
$57$			1.58620i			0.210097i
$58$	9.67878	−	13.3217i	1.27089	−	1.74923i
$59$	2.71863	−	8.36710i	0.353936	−	1.08930i	−0.602688	−	0.797977i	$-0.705904\pi$
$59$	2.71863	−	8.36710i	0.353936	−	1.08930i	0.956624	−	0.291326i	$-0.0940964\pi$
$60$	0.201730	+	4.09056i	0.0260433	+	0.528089i
$61$	2.61154	+	8.03748i	0.334373	+	1.02909i	0.967030	+	0.254662i	$0.0819643\pi$
$61$	2.61154	+	8.03748i	0.334373	+	1.02909i	−0.632657	+	0.774432i	$0.718036\pi$
$62$	−10.8776	−	3.53435i	−1.38146	−	0.448863i
$63$	2.30056	+	0.747496i	0.289843	+	0.0941757i
$64$	3.34744	+	10.3024i	0.418430	+	1.28780i
$65$	−0.234808	−	4.76128i	−0.0291243	−	0.590564i
$66$	2.51450	−	7.73884i	0.309514	−	0.952586i
$67$	4.99602	−	6.87643i	0.610360	−	0.840089i	−0.386247	−	0.922396i	$-0.626229\pi$
$67$	4.99602	−	6.87643i	0.610360	−	0.840089i	0.996607	+	0.0823064i	$0.0262286\pi$
$68$			7.36526i			0.893169i
$69$	−0.345534	−	0.251045i	−0.0415974	−	0.0302223i
$70$	3.65539	−	2.94146i	0.436902	−	0.351571i
$71$	8.39799	−	6.10149i	0.996658	−	0.724114i	0.0352887	−	0.999377i	$-0.488765\pi$
$71$	8.39799	−	6.10149i	0.996658	−	0.724114i	0.961369	+	0.275263i	$0.0887649\pi$
$72$	−1.20171	−	1.65401i	−0.141623	−	0.194927i
$73$	−11.3357	+	3.68319i	−1.32674	+	0.431084i	−0.884805	−	0.465962i	$-0.845708\pi$
$73$	−11.3357	+	3.68319i	−1.32674	+	0.431084i	−0.441936	+	0.897046i	$0.645708\pi$
$74$	−18.8719			−2.19382
$75$	3.72309	+	0.815399i	0.429906	+	0.0941541i
$76$	−4.99998			−0.573537
$77$	−4.83843	+	1.57210i	−0.551390	+	0.179157i
$78$	−2.00427	−	2.75864i	−0.226939	−	0.312355i
$79$	−5.91108	+	4.29465i	−0.665048	+	0.483186i	−0.868364	−	0.495927i	$-0.834828\pi$
$79$	−5.91108	+	4.29465i	−0.665048	+	0.483186i	0.203316	+	0.979113i	$0.434828\pi$
$80$	6.77186	−	0.333962i	0.757117	−	0.0373381i
$81$	−3.32357	−	2.41471i	−0.369285	−	0.268301i
$82$		−	8.76749i		−	0.968207i
$83$	−4.59211	+	6.32050i	−0.504050	+	0.693765i	−0.982902	−	0.184130i	$-0.941053\pi$
$83$	−4.59211	+	6.32050i	−0.504050	+	0.693765i	0.478852	+	0.877896i	$0.341053\pi$
$84$	0.565988	−	1.74193i	0.0617544	−	0.190060i
$85$	6.61512	+	1.79440i	0.717511	+	0.194630i
$86$	2.04215	+	6.28509i	0.220210	+	0.677738i
$87$	−5.68920	−	1.84853i	−0.609946	−	0.198184i
$88$	4.08939	+	1.32872i	0.435931	+	0.141643i
$89$	0.850864	+	2.61869i	0.0901914	+	0.277581i	0.985971	−	0.166919i	$-0.0533817\pi$
$89$	0.850864	+	2.61869i	0.0901914	+	0.277581i	−0.895779	+	0.444499i	$0.853382\pi$
$90$	−10.6081	+	4.03460i	−1.11820	+	0.425284i
$91$	−0.658792	+	2.02755i	−0.0690602	+	0.212545i
$92$	0.791338	−	1.08918i	0.0825027	−	0.113555i
$93$			4.15499i			0.430852i
$94$	16.0587	+	11.6673i	1.65633	+	1.20340i
$95$	−1.21814	+	4.49074i	−0.124979	+	0.460740i
$96$	4.96600	−	3.60801i	0.506840	−	0.368241i
$97$	−8.25615	−	11.3636i	−0.838285	−	1.15380i	−0.986324	−	0.164819i	$-0.947296\pi$
$97$	−8.25615	−	11.3636i	−0.838285	−	1.15380i	0.148039	−	0.988982i	$-0.452704\pi$
$98$	−1.99559	+	0.648406i	−0.201585	+	0.0654989i
$99$	12.3062			1.23682
$100$	−2.57028	+	11.7358i	−0.257028	+	1.17358i
$101$	13.0825			1.30176			0.650881	−	0.759180i	$-0.274400\pi$
$101$	13.0825			1.30176			0.650881	+	0.759180i	$0.274400\pi$
$102$	4.66282	−	1.51504i	0.461688	−	0.150011i
$103$	2.24756	+	3.09350i	0.221459	+	0.304812i	0.905261	−	0.424855i	$-0.139675\pi$
$103$	2.24756	+	3.09350i	0.221459	+	0.304812i	−0.683803	+	0.729667i	$0.739675\pi$
$104$	1.45773	−	1.05911i	0.142943	−	0.103854i
$105$	−1.42663	−	0.932731i	−0.139225	−	0.0910252i
$106$	−16.3481	−	11.8776i	−1.58787	−	1.15366i
$107$		−	6.20098i		−	0.599471i	−0.954022	−	0.299736i	$-0.903102\pi$
$107$		−	6.20098i		−	0.599471i	0.954022	−	0.299736i	$-0.0968984\pi$
$108$	−5.83390	+	8.02967i	−0.561367	+	0.772656i
$109$	2.61773	−	8.05654i	0.250733	−	0.771677i	−0.743907	−	0.668283i	$-0.767030\pi$
$109$	2.61773	−	8.05654i	0.250733	−	0.771677i	0.994640	−	0.103394i	$-0.0329703\pi$
$110$	13.0621	−	19.9786i	1.24542	−	1.90489i
$111$	2.11857	+	6.52027i	0.201085	+	0.618877i
$112$	−2.88375	−	0.936986i	−0.272488	−	0.0885368i
$113$	−12.6411	−	4.10733i	−1.18917	−	0.386385i	−0.353405	−	0.935471i	$-0.614976\pi$
$113$	−12.6411	−	4.10733i	−1.18917	−	0.386385i	−0.835766	+	0.549086i	$0.814976\pi$
$114$	1.02850	+	3.16540i	0.0963279	+	0.296467i
$115$	−0.785459	−	0.976100i	−0.0732444	−	0.0910218i
$116$	5.82690	−	17.9334i	0.541014	−	1.66507i
$117$	3.03118	−	4.17206i	0.280232	−	0.385707i
$118$		−	18.4601i		−	1.69939i
$119$	−2.47986	−	1.80173i	−0.227329	−	0.165164i
$120$	0.512120	+	1.34651i	0.0467499	+	0.122919i
$121$	−12.0397	+	8.74734i	−1.09452	+	0.795213i
$122$	10.4231	+	14.3462i	0.943663	+	1.29884i
$123$	−3.02917	+	0.984238i	−0.273131	+	0.0887458i
$124$	−13.0972			−1.17617
$125$	9.91437	+	5.16771i	0.886769	+	0.462214i
$126$	5.07564			0.452174
$127$	1.28960	−	0.419016i	0.114433	−	0.0371817i	−0.251241	−	0.967925i	$-0.580839\pi$
$127$	1.28960	−	0.419016i	0.114433	−	0.0371817i	0.365674	+	0.930743i	$0.380839\pi$
$128$	3.89372	+	5.35925i	0.344160	+	0.473695i
$129$	1.94225	−	1.41113i	0.171006	−	0.124243i
$130$	−3.55582	−	9.34929i	−0.311866	−	0.819987i
$131$	14.0131	+	10.1811i	1.22433	+	0.889526i	0.996452	−	0.0841637i	$-0.0268219\pi$
$131$	14.0131	+	10.1811i	1.22433	+	0.889526i	0.227876	+	0.973690i	$0.426822\pi$
$132$		−	9.31801i		−	0.811028i
$133$	1.22312	−	1.68348i	0.106058	−	0.145976i
$134$	5.51127	−	16.9620i	0.476102	−	1.46529i
$135$	5.79055	+	7.19600i	0.498372	+	0.619333i
$136$	0.800585	+	2.46395i	0.0686496	+	0.211282i
$137$	6.43589	+	2.09115i	0.549855	+	0.178659i	0.570751	−	0.821123i	$-0.306652\pi$
$137$	6.43589	+	2.09115i	0.549855	+	0.178659i	−0.0208965	+	0.999782i	$0.506652\pi$
$138$	−0.852323	−	0.276936i	−0.0725545	−	0.0235744i
$139$	0.371283	+	1.14269i	0.0314918	+	0.0969219i	0.965567	−	0.260155i	$-0.0837735\pi$
$139$	0.371283	+	1.14269i	0.0314918	+	0.0969219i	−0.934075	+	0.357077i	$0.883774\pi$
$140$	2.94013	−	4.49699i	0.248487	−	0.380065i
$141$	2.22833	−	6.85808i	0.187659	−	0.577555i
$142$	12.8027	−	17.6214i	1.07438	−	1.47875i
$143$			10.8459i			0.906976i
$144$	5.93383	+	4.31118i	0.494486	+	0.359265i
$145$	−14.6873	−	9.60255i	−1.21971	−	0.797448i
$146$	−20.2331	+	14.7002i	−1.67451	+	1.21660i
$147$	0.448050	+	0.616687i	0.0369545	+	0.0508635i
$148$	−20.5530	+	6.67809i	−1.68945	+	0.548936i
$149$	3.11700			0.255354			0.127677	−	0.991816i	$-0.459248\pi$
$149$	3.11700			0.255354			0.127677	+	0.991816i	$0.459248\pi$
$150$	7.95847	−	0.786875i	0.649806	−	0.0642481i
$151$	6.95795			0.566230			0.283115	−	0.959086i	$-0.408632\pi$
$151$	6.95795			0.566230			0.283115	+	0.959086i	$0.408632\pi$
$152$	−1.67267	+	0.543485i	−0.135672	+	0.0440824i
$153$	4.35828	+	5.99866i	0.352346	+	0.484963i
$154$	−8.63615	+	6.27453i	−0.695920	+	0.505616i
$155$	−3.19088	+	11.7633i	−0.256298	+	0.944853i
$156$	−3.15899	−	2.29514i	−0.252922	−	0.183758i
$157$			12.6429i			1.00901i	0.863407	+	0.504507i	$0.168326\pi$
$157$			12.6429i			1.00901i	−0.863407	+	0.504507i	$0.831674\pi$
$158$	−9.01140	+	12.4031i	−0.716909	+	0.986740i
$159$	−2.26848	+	6.98167i	−0.179902	+	0.553683i
$160$	16.8302	−	6.40104i	1.33055	−	0.506047i
$161$	0.173144	+	0.532883i	0.0136457	+	0.0419971i
$162$	−8.19818	−	2.66375i	−0.644110	−	0.209284i
$163$	3.39505	+	1.10312i	0.265921	+	0.0864030i	0.438943	−	0.898515i	$-0.355353\pi$
$163$	3.39505	+	1.10312i	0.265921	+	0.0864030i	−0.173022	+	0.984918i	$0.555353\pi$
$164$	−3.10249	−	9.54849i	−0.242264	−	0.745612i
$165$	−8.36899	−	2.27015i	−0.651525	−	0.176731i
$166$	−5.06572	+	15.5907i	−0.393176	+	1.21007i
$167$	−10.0579	+	13.8434i	−0.778300	+	1.07124i	0.217168	+	0.976134i	$0.430318\pi$
$167$	−10.0579	+	13.8434i	−0.778300	+	1.07124i	−0.995467	+	0.0951035i	$0.969682\pi$
$168$		−	0.644262i		−	0.0497059i
$169$	−6.84026	−	4.96974i	−0.526174	−	0.382287i
$170$	14.3646	−	0.708404i	1.10171	−	0.0543321i
$171$	−4.07225	+	2.95866i	−0.311413	+	0.226255i
$172$	4.44812	+	6.12232i	0.339166	+	0.466822i
$173$	14.5954	−	4.74232i	1.10966	−	0.360552i	0.303850	−	0.952720i	$-0.401728\pi$
$173$	14.5954	−	4.74232i	1.10966	−	0.360552i	0.805815	+	0.592168i	$0.201728\pi$
$174$	−12.5519			−0.951557
$175$	−3.32267	−	3.73629i	−0.251170	−	0.282437i
$176$	−15.4258			−1.16277
$177$	−6.37796	+	2.07233i	−0.479397	+	0.155766i
$178$	3.39595	+	4.67412i	0.254537	+	0.350340i
$179$	−6.97932	+	5.07077i	−0.521659	+	0.379007i	−0.817228	−	0.576314i	$-0.804491\pi$
$179$	−6.97932	+	5.07077i	−0.521659	+	0.379007i	0.295570	+	0.955321i	$0.404491\pi$
$180$	−10.1254	+	8.14783i	−0.754704	+	0.607304i
$181$	−5.15582	−	3.74592i	−0.383229	−	0.278432i	0.379446	−	0.925214i	$-0.376114\pi$
$181$	−5.15582	−	3.74592i	−0.383229	−	0.278432i	−0.762675	+	0.646782i	$0.776114\pi$
$182$			4.47332i			0.331585i
$183$	3.78652	−	5.21169i	0.279907	−	0.385259i
$184$	0.146340	−	0.450388i	0.0107883	−	0.0332031i
$185$	0.990600	+	20.0867i	0.0728303	+	1.47681i
$186$	2.69412	+	8.29164i	0.197542	+	0.607973i
$187$	−14.8311	−	4.81893i	−1.08456	−	0.352395i
$188$	21.6179	+	7.02407i	1.57665	+	0.512283i
$189$	−1.27645	−	3.92852i	−0.0928483	−	0.285758i
$190$	0.480907	+	9.75152i	0.0348886	+	0.707449i
$191$	−4.49520	+	13.8348i	−0.325261	+	1.00105i	0.646061	+	0.763285i	$0.276415\pi$
$191$	−4.49520	+	13.8348i	−0.325261	+	1.00105i	−0.971323	+	0.237765i	$0.923585\pi$
$192$	4.85352	−	6.68030i	0.350273	−	0.482109i
$193$			12.9376i			0.931266i	0.884978	+	0.465633i	$0.154173\pi$
$193$			12.9376i			0.931266i	−0.884978	+	0.465633i	$0.845827\pi$
$194$	−23.8441	−	17.3238i	−1.71191	−	1.24377i
$195$	−2.83101	+	2.27809i	−0.202733	+	0.163137i
$196$	−1.94391	+	1.41233i	−0.138850	+	0.100881i
$197$	11.2944	+	15.5454i	0.804692	+	1.10756i	0.992121	+	0.125285i	$0.0399845\pi$
$197$	11.2944	+	15.5454i	0.804692	+	1.10756i	−0.187429	+	0.982278i	$0.560016\pi$
$198$	24.5581	−	7.97942i	1.74527	−	0.567073i
$199$	−22.8970			−1.62312			−0.811562	−	0.584266i	$-0.801382\pi$
$199$	−22.8970			−1.62312			−0.811562	+	0.584266i	$0.801382\pi$
$200$	0.415804	+	4.20545i	0.0294018	+	0.297370i
$201$	−6.47907			−0.456998
$202$	26.1074	−	8.48279i	1.83691	−	0.596847i
$203$	4.61271	+	6.34885i	0.323749	+	0.445602i
$204$	4.54206	−	3.30000i	0.318008	−	0.231046i
$205$	−9.33186	+	0.460211i	−0.651765	+	0.0321425i
$206$	6.49105	+	4.71602i	0.452253	+	0.328581i
$207$		−	1.35535i		−	0.0942035i
$208$	−3.79958	+	5.22967i	−0.263453	+	0.362612i
$209$	3.27137	−	10.0683i	0.226286	−	0.696436i
$210$	−3.45175	−	0.936312i	−0.238194	−	0.0646117i
$211$	−4.27858	−	13.1681i	−0.294550	−	0.906531i	−0.983372	−	0.181601i	$-0.941872\pi$
$211$	−4.27858	−	13.1681i	−0.294550	−	0.906531i	0.688823	−	0.724930i	$-0.258128\pi$
$212$	−22.0075	−	7.15066i	−1.51148	−	0.491109i
$213$	−7.52543	−	2.44516i	−0.515634	−	0.167540i
$214$	−4.02075	−	12.3746i	−0.274853	−	0.845910i
$215$	6.58247	−	2.50351i	0.448921	−	0.170738i
$216$	−1.07885	+	3.32035i	−0.0734062	+	0.225921i
$217$	3.20392	−	4.40981i	0.217496	−	0.299357i
$218$		−	17.7749i		−	1.20387i
$219$	7.35032	+	5.34032i	0.496689	+	0.360865i
$220$	7.15590	−	26.3805i	0.482451	−	1.77857i
$221$	−5.28681	+	3.84109i	−0.355629	+	0.258380i
$222$	8.45557	+	11.6381i	0.567500	+	0.781097i
$223$	24.3036	−	7.89673i	1.62749	−	0.528804i	0.653799	−	0.756668i	$-0.273174\pi$
$223$	24.3036	−	7.89673i	1.62749	−	0.528804i	0.973693	+	0.227864i	$0.0731742\pi$
$224$	−8.05270			−0.538043
$225$	4.85114	+	11.0792i	0.323409	+	0.738615i
$226$	−27.8896			−1.85519
$227$	6.65680	−	2.16293i	0.441827	−	0.143558i	−0.0796512	−	0.996823i	$-0.525381\pi$
$227$	6.65680	−	2.16293i	0.441827	−	0.143558i	0.521479	+	0.853264i	$0.325381\pi$
$228$	2.24024	+	3.08342i	0.148363	+	0.204205i
$229$	19.8275	−	14.4055i	1.31024	−	0.951943i	0.310238	−	0.950659i	$-0.399591\pi$
$229$	19.8275	−	14.4055i	1.31024	−	0.951943i	0.999999	−	0.00128444i	$-0.000408851\pi$
$230$	−2.20036	−	1.43860i	−0.145088	−	0.0948583i
$231$	3.13735	+	2.27942i	0.206422	+	0.149975i
$232$		−	6.63273i		−	0.435460i
$233$	0.115446	−	0.158898i	0.00756311	−	0.0104097i	−0.805219	−	0.592978i	$-0.797952\pi$
$233$	0.115446	−	0.158898i	0.00756311	−	0.0104097i	0.812782	+	0.582568i	$0.197952\pi$
$234$	3.34379	−	10.2911i	0.218591	−	0.672753i
$235$	11.5755	−	17.7049i	0.755099	−	1.15494i
$236$	−6.53234	−	20.1045i	−0.425219	−	1.30869i
$237$	5.29691	+	1.72107i	0.344072	+	0.111796i
$238$	−6.11704	−	1.98755i	−0.396509	−	0.128833i
$239$	−0.161524	−	0.497118i	−0.0104481	−	0.0321559i	0.945697	−	0.325051i	$-0.105381\pi$
$239$	−0.161524	−	0.497118i	−0.0104481	−	0.0321559i	−0.956145	+	0.292895i	$0.905381\pi$
$240$	−3.24008	−	4.02649i	−0.209146	−	0.259909i
$241$	1.33713	−	4.11526i	0.0861321	−	0.265087i	−0.898709	−	0.438545i	$-0.855494\pi$
$241$	1.33713	−	4.11526i	0.0861321	−	0.265087i	0.984841	+	0.173458i	$0.0554940\pi$
$242$	−18.3544	+	25.2627i	−1.17987	+	1.62395i
$243$			15.5236i			0.995838i
$244$	16.4282	+	11.9358i	1.05171	+	0.764109i
$245$	0.794894	+	2.09001i	0.0507839	+	0.133526i
$246$	−5.40680	+	3.92827i	−0.344725	+	0.250457i
$247$	−2.60756	−	3.58900i	−0.165915	−	0.228363i
$248$	−4.38151	+	1.42364i	−0.278226	+	0.0904011i
$249$	5.95527			0.377400
$250$	23.1358	+	3.88408i	1.46323	+	0.245651i
$251$	28.6966			1.81131			0.905657	−	0.424011i	$-0.139378\pi$
$251$	28.6966			1.81131			0.905657	+	0.424011i	$0.139378\pi$
$252$	5.52778	−	1.79608i	0.348217	−	0.113143i
$253$	1.67549	+	2.30612i	0.105337	+	0.144984i
$254$	2.30181	−	1.67237i	0.144429	−	0.104934i
$255$	−1.85732	−	4.88344i	−0.116310	−	0.305813i
$256$	−6.28221	−	4.56429i	−0.392638	−	0.285268i
$257$		−	17.1777i		−	1.07152i	−0.844371	−	0.535759i	$-0.820026\pi$
$257$		−	17.1777i		−	1.07152i	0.844371	−	0.535759i	$-0.179974\pi$
$258$	2.96095	−	4.07540i	0.184341	−	0.253723i
$259$	2.77929	−	8.55379i	0.172697	−	0.531506i
$260$	−7.18094	−	8.92385i	−0.445343	−	0.553434i
$261$	−5.86606	−	18.0539i	−0.363100	−	1.11751i
$262$	34.5658	+	11.2311i	2.13548	+	0.693860i
$263$	−0.287845	−	0.0935265i	−0.0177493	−	0.00576709i	0.300129	−	0.953899i	$-0.402970\pi$
$263$	−0.287845	−	0.0935265i	−0.0177493	−	0.00576709i	−0.317878	+	0.948132i	$0.602970\pi$
$264$	−1.01284	−	3.11721i	−0.0623362	−	0.191851i
$265$	−11.7841	+	18.0239i	−0.723889	+	1.10720i
$266$	1.34926	−	4.15261i	0.0827287	−	0.254613i
$267$	1.23368	−	1.69802i	0.0755002	−	0.103917i
$268$		−	20.4232i		−	1.24754i
$269$	−20.7615	−	15.0841i	−1.26585	−	0.919694i	−0.266821	−	0.963746i	$-0.585973\pi$
$269$	−20.7615	−	15.0841i	−1.26585	−	0.919694i	−0.999029	+	0.0440518i	$0.985973\pi$
$270$	16.2215	+	10.6056i	0.987208	+	0.645437i
$271$	−17.0467	+	12.3851i	−1.03551	+	0.752344i	−0.969405	−	0.245468i	$-0.921058\pi$
$271$	−17.0467	+	12.3851i	−1.03551	+	0.752344i	−0.0661082	+	0.997812i	$0.521058\pi$
$272$	−5.46311	−	7.51932i	−0.331249	−	0.455926i
$273$	1.54554	−	0.502176i	0.0935402	−	0.0303931i
$274$	14.1993			0.857810
$275$	−21.9503	−	12.8542i	−1.32365	−	0.775136i
$276$	−1.02624			−0.0617727
$277$	16.7041	−	5.42749i	1.00365	−	0.326106i	0.239327	−	0.970939i	$-0.423073\pi$
$277$	16.7041	−	5.42749i	1.00365	−	0.326106i	0.764324	+	0.644833i	$0.223073\pi$
$278$	1.48186	+	2.03960i	0.0888758	+	0.122327i
$279$	−10.6671	+	7.75011i	−0.638623	+	0.463987i
$280$	0.494770	−	1.82399i	0.0295682	−	0.109004i
$281$	14.0099	+	10.1788i	0.835761	+	0.607216i	0.921183	−	0.389129i	$-0.127224\pi$
$281$	14.0099	+	10.1788i	0.835761	+	0.607216i	−0.0854224	+	0.996345i	$0.527224\pi$
$282$		−	15.1308i		−	0.901024i
$283$	6.34789	−	8.73712i	0.377343	−	0.519368i	−0.577535	−	0.816366i	$-0.695985\pi$
$283$	6.34789	−	8.73712i	0.377343	−	0.519368i	0.954878	+	0.296998i	$0.0959854\pi$
$284$	7.70757	−	23.7215i	0.457360	−	1.40761i
$285$	3.31517	−	1.26086i	0.196374	−	0.0746869i
$286$	7.03251	+	21.6438i	0.415841	+	1.27983i
$287$	3.97390	+	1.29120i	0.234572	+	0.0762170i
$288$	18.5257	+	6.01936i	1.09164	+	0.354694i
$289$	2.34978	+	7.23189i	0.138222	+	0.425405i
$290$	−35.5361	−	9.63942i	−2.08675	−	0.566046i
$291$	−3.30863	+	10.1829i	−0.193956	+	0.596934i
$292$	−16.8336	+	23.1695i	−0.985114	+	1.35589i
$293$		−	0.803822i		−	0.0469598i	−0.999724	−	0.0234799i	$-0.992525\pi$
$293$		−	0.803822i		−	0.0469598i	0.999724	−	0.0234799i	$-0.00747457\pi$
$294$	1.29399	+	0.940136i	0.0754668	+	0.0548298i
$295$	−19.6483	+	0.968979i	−1.14397	+	0.0564162i
$296$	−6.14985	+	4.46813i	−0.357453	+	0.259705i
$297$	−12.3520	−	17.0011i	−0.716738	−	0.986506i
$298$	6.22024	−	2.02108i	0.360329	−	0.117078i
$299$	1.19452			0.0690806
$300$	8.38896	−	3.67318i	0.484337	−	0.212071i
$301$	−3.14949			−0.181534
$302$	13.8852	−	4.51158i	0.799004	−	0.259612i
$303$	−5.86163	−	8.06784i	−0.336742	−	0.463485i
$304$	5.10456	−	3.70868i	0.292767	−	0.212707i
$305$	14.7225	−	11.8471i	0.843010	−	0.678362i
$306$	12.5869	+	9.14492i	0.719545	+	0.522780i
$307$		−	15.0801i		−	0.860666i	−0.902670	−	0.430333i	$-0.858396\pi$
$307$		−	15.0801i		−	0.860666i	0.902670	−	0.430333i	$-0.141604\pi$
$308$	−7.18512	+	9.88947i	−0.409410	+	0.563505i
$309$	0.900705	−	2.77208i	0.0512393	−	0.157698i
$310$	1.25972	+	25.5437i	0.0715471	+	1.45079i
$311$	−5.15835	−	15.8758i	−0.292503	−	0.900233i	−0.984049	−	0.177900i	$-0.943070\pi$
$311$	−5.15835	−	15.8758i	−0.292503	−	0.900233i	0.691545	−	0.722333i	$-0.256930\pi$
$312$	−1.30627	−	0.424434i	−0.0739532	−	0.0240289i
$313$	−18.0513	−	5.86522i	−1.02032	−	0.331522i	−0.249363	−	0.968410i	$-0.580221\pi$
$313$	−18.0513	−	5.86522i	−1.02032	−	0.331522i	−0.770956	+	0.636888i	$0.780221\pi$
$314$	8.19774	+	25.2301i	0.462625	+	1.42381i
$315$	−0.266424	−	5.40237i	−0.0150113	−	0.304389i
$316$	−5.42512	+	16.6968i	−0.305187	+	0.939268i
$317$	6.79757	−	9.35605i	0.381790	−	0.525488i	−0.574268	−	0.818667i	$-0.694713\pi$
$317$	6.79757	−	9.35605i	0.381790	−	0.525488i	0.956058	+	0.293179i	$0.0947132\pi$
$318$			15.4034i			0.863782i
$319$	32.2993	+	23.4668i	1.80841	+	1.31389i
$320$	18.8712	−	15.1855i	1.05493	−	0.848894i
$321$	−3.82406	+	2.77834i	−0.213438	+	0.155072i
$322$	0.691049	+	0.951148i	0.0385107	+	0.0530054i
$323$	6.06634	−	1.97107i	0.337540	−	0.109673i
$324$	−9.87108			−0.548393
$325$	−9.76447	+	4.27546i	−0.541635	+	0.237160i
$326$	7.49040			0.414855
$327$	−6.14124	+	1.99541i	−0.339611	+	0.110346i
$328$	−2.07579	−	2.85708i	−0.114616	−	0.157756i
$329$	−7.65326	+	5.56042i	−0.421938	+	0.306556i
$330$	−18.1730	+	0.896223i	−1.00039	+	0.0493354i
$331$	4.03727	+	2.93325i	0.221909	+	0.161226i	0.693185	−	0.720759i	$-0.256207\pi$
$331$	4.03727	+	2.93325i	0.221909	+	0.161226i	−0.471277	+	0.881985i	$0.656207\pi$
$332$			18.7721i			1.03025i
$333$	−12.7878	+	17.6010i	−0.700770	+	0.964526i
$334$	−11.0952	+	34.1474i	−0.607100	+	1.86846i
$335$	−18.3431	−	4.97570i	−1.00219	−	0.271851i
$336$	0.714234	+	2.19819i	0.0389647	+	0.119921i
$337$	1.34280	+	0.436302i	0.0731469	+	0.0237669i	0.345362	−	0.938470i	$-0.387756\pi$
$337$	1.34280	+	0.436302i	0.0731469	+	0.0237669i	−0.272215	+	0.962236i	$0.587756\pi$
$338$	−16.8727	−	5.48229i	−0.917756	−	0.298197i
$339$	3.13088	+	9.63587i	0.170046	+	0.523348i
$340$	15.3935	−	5.85460i	0.834828	−	0.317510i
$341$	8.56924	−	26.3734i	0.464051	−	1.42820i
$342$	−6.20812	+	8.54474i	−0.335697	+	0.462047i
$343$		−	1.00000i		−	0.0539949i
$344$	2.15354	+	1.56464i	0.116111	+	0.0843596i
$345$	−0.250024	+	0.921724i	−0.0134608	+	0.0496240i
$346$	26.0514	−	18.9274i	1.40053	−	1.01755i
$347$	−15.3640	−	21.1467i	−0.824782	−	1.13521i	−0.988872	−	0.148769i	$-0.952469\pi$
$347$	−15.3640	−	21.1467i	−0.824782	−	1.13521i	0.164090	−	0.986445i	$-0.447531\pi$
$348$	−13.6700	+	4.44166i	−0.732790	+	0.238098i
$349$	21.3865			1.14479			0.572395	−	0.819978i	$-0.306014\pi$
$349$	21.3865			1.14479			0.572395	+	0.819978i	$0.306014\pi$
$350$	−9.05332	−	5.30165i	−0.483920	−	0.283385i
$351$	−8.80619			−0.470040
$352$	−38.9624	+	12.6596i	−2.07670	+	0.674761i
$353$	−6.97666	−	9.60254i	−0.371330	−	0.511092i	0.581932	−	0.813238i	$-0.302297\pi$
$353$	−6.97666	−	9.60254i	−0.371330	−	0.511092i	−0.953262	+	0.302146i	$0.902297\pi$
$354$	−11.3841	+	8.27102i	−0.605057	+	0.439600i
$355$	−19.4277	−	12.7018i	−1.03111	−	0.674144i
$356$	5.35246	+	3.88879i	0.283680	+	0.206105i
$357$			2.33656i			0.123664i
$358$	−10.6399	+	14.6446i	−0.562337	+	0.773991i
$359$	8.20092	−	25.2398i	0.432828	−	1.33211i	−0.462468	−	0.886636i	$-0.653036\pi$
$359$	8.20092	−	25.2398i	0.432828	−	1.33211i	0.895296	−	0.445471i	$-0.146964\pi$
$360$	−2.50167	+	3.82635i	−0.131850	+	0.201667i
$361$	−4.53324	−	13.9519i	−0.238592	−	0.734310i
$362$	−12.7178	−	4.13225i	−0.668431	−	0.217186i
$363$	10.7887	+	3.50548i	0.566262	+	0.183990i
$364$	1.58295	+	4.87181i	0.0829689	+	0.255352i
$365$	16.7086	+	20.7639i	0.874566	+	1.08683i
$366$	4.17703	−	12.8556i	0.218337	−	0.671972i
$367$	−1.86707	+	2.56980i	−0.0974600	+	0.134142i	−0.854962	−	0.518691i	$-0.826420\pi$
$367$	−1.86707	+	2.56980i	−0.0974600	+	0.134142i	0.757502	+	0.652833i	$0.226420\pi$
$368$			1.69893i			0.0885630i
$369$	−8.17701	−	5.94095i	−0.425678	−	0.309273i
$370$	15.0012	+	39.4426i	0.779875	+	2.05052i
$371$	7.79118	−	5.66063i	0.404498	−	0.293885i
$372$	5.86822	+	8.07691i	0.304253	+	0.418768i
$373$	4.43961	−	1.44252i	0.229874	−	0.0746906i	−0.191815	−	0.981431i	$-0.561437\pi$
$373$	4.43961	−	1.44252i	0.229874	−	0.0746906i	0.421689	+	0.906740i	$0.361437\pi$
$374$	−32.7214			−1.69199
$375$	−1.25527	−	8.42946i	−0.0648219	−	0.435295i
$376$	7.99547			0.412335
$377$	15.9114	−	5.16994i	0.819481	−	0.266266i
$378$	−5.09455	−	7.01204i	−0.262035	−	0.360661i
$379$	−26.9427	+	19.5750i	−1.38395	+	1.00550i	−0.387456	+	0.921888i	$0.626646\pi$
$379$	−26.9427	+	19.5750i	−1.38395	+	1.00550i	−0.996498	+	0.0836139i	$0.973354\pi$
$380$	3.97445	+	10.4500i	0.203885	+	0.536074i
$381$	−0.836206	−	0.607539i	−0.0428401	−	0.0311252i
$382$			30.5233i			1.56171i
$383$	−7.56494	+	10.4123i	−0.386551	+	0.532041i	−0.957305	−	0.289080i	$-0.906651\pi$
$383$	−7.56494	+	10.4123i	−0.386551	+	0.532041i	0.570755	+	0.821121i	$0.306651\pi$
$384$	1.56040	−	4.80242i	0.0796289	−	0.245072i
$385$	7.13174	+	8.86271i	0.363467	+	0.451685i
$386$	8.38879	+	25.8180i	0.426978	+	1.31410i
$387$	7.24558	+	2.35423i	0.368314	+	0.119672i
$388$	−32.0984	−	10.4294i	−1.62955	−	0.529472i
$389$	10.1390	+	31.2046i	0.514067	+	1.58214i	0.784973	+	0.619529i	$0.212677\pi$
$389$	10.1390	+	31.2046i	0.514067	+	1.58214i	−0.270907	+	0.962606i	$0.587323\pi$
$390$	−4.17241	+	6.38178i	−0.211278	+	0.323154i
$391$	−0.530736	+	1.63344i	−0.0268405	+	0.0826064i
$392$	−0.496791	+	0.683774i	−0.0250917	+	0.0345358i
$393$		−	13.2033i		−	0.666020i
$394$	32.6187	+	23.6988i	1.64330	+	1.19393i
$395$	13.6745	+	8.94043i	0.688041	+	0.449842i
$396$	23.9221	−	17.3804i	1.20213	−	0.873400i
$397$	18.2482	+	25.1165i	0.915852	+	1.26056i	0.965128	+	0.261777i	$0.0843086\pi$
$397$	18.2482	+	25.1165i	0.915852	+	1.26056i	−0.0492761	+	0.998785i	$0.515691\pi$
$398$	−45.6929	+	14.8465i	−2.29038	+	0.744189i
$399$	−1.58620			−0.0794093
$400$	−6.08090	−	13.8878i	−0.304045	−	0.694390i
$401$	−20.8535			−1.04138			−0.520688	−	0.853747i	$-0.674324\pi$
$401$	−20.8535			−1.04138			−0.520688	+	0.853747i	$0.674324\pi$
$402$	−12.9295	+	4.20107i	−0.644867	+	0.209530i
$403$	−6.83041	−	9.40126i	−0.340247	−	0.468310i
$404$	25.4312	−	18.4769i	1.26525	−	0.919259i
$405$	−2.40489	+	8.86573i	−0.119500	+	0.440542i
$406$	13.3217	+	9.67878i	0.661145	+	0.480350i
$407$		−	45.7562i		−	2.26805i
$408$	1.16078	−	1.59768i	0.0574673	−	0.0790970i
$409$	−3.28498	+	10.1101i	−0.162432	+	0.499913i	−0.998838	−	0.0481967i	$-0.984653\pi$
$409$	−3.28498	+	10.1101i	−0.162432	+	0.499913i	0.836406	+	0.548110i	$0.184653\pi$
$410$	−18.3241	+	6.96922i	−0.904965	+	0.344185i
$411$	−1.59401	−	4.90587i	−0.0786268	−	0.241989i
$412$	8.73810	+	2.83918i	0.430495	+	0.139876i
$413$	8.36710	+	2.71863i	0.411718	+	0.133775i
$414$	−0.878819	−	2.70473i	−0.0431916	−	0.132930i
$415$	16.8602	+	4.57344i	0.827633	+	0.224501i
$416$	−5.30505	+	16.3273i	−0.260102	+	0.800510i
$417$	0.538330	−	0.740948i	0.0263622	−	0.0362844i
$418$		−	22.2133i		−	1.08649i
$419$	−22.7230	−	16.5092i	−1.11009	−	0.806528i	−0.127412	−	0.991850i	$-0.540667\pi$
$419$	−22.7230	−	16.5092i	−1.11009	−	0.806528i	−0.982678	+	0.185322i	$0.940667\pi$
$420$	−4.09056	+	0.201730i	−0.199599	+	0.00984344i
$421$	23.2381	−	16.8835i	1.13256	−	0.822852i	0.146493	−	0.989212i	$-0.453201\pi$
$421$	23.2381	−	16.8835i	1.13256	−	0.822852i	0.986065	+	0.166360i	$0.0532014\pi$
$422$	−17.0766	−	23.5039i	−0.831274	−	1.14415i
$423$	21.7632	−	7.07128i	1.05816	−	0.343817i
$424$	−8.13956			−0.395292
$425$	−1.50801	−	15.2520i	−0.0731492	−	0.739832i
$426$	−16.6031			−0.804423
$427$	−8.03748	+	2.61154i	−0.388961	+	0.126381i
$428$	−8.75783	−	12.0541i	−0.423326	−	0.582658i
$429$	6.68850	−	4.85948i	0.322924	−	0.234618i
$430$	11.5126	−	9.26409i	0.555187	−	0.446754i
$431$	6.14542	+	4.46491i	0.296014	+	0.215067i	0.725872	−	0.687830i	$-0.241436\pi$
$431$	6.14542	+	4.46491i	0.296014	+	0.215067i	−0.429858	+	0.902897i	$0.641436\pi$
$432$		−	12.5249i		−	0.602603i
$433$	10.0598	−	13.8461i	0.483442	−	0.665400i	−0.495720	−	0.868482i	$-0.665096\pi$
$433$	10.0598	−	13.8461i	0.483442	−	0.665400i	0.979162	+	0.203082i	$0.0650958\pi$
$434$	3.53435	−	10.8776i	0.169654	−	0.522142i
$435$	0.658857	+	13.3599i	0.0315898	+	0.640557i
$436$	−6.28988	−	19.3583i	−0.301231	−	0.927093i
$437$	−1.10887	−	0.360295i	−0.0530446	−	0.0172352i
$438$	18.1309	+	5.89109i	0.866328	+	0.281487i
$439$	2.61473	+	8.04730i	0.124794	+	0.384077i	0.993864	−	0.110613i	$-0.0352815\pi$
$439$	2.61473	+	8.04730i	0.124794	+	0.384077i	−0.869069	+	0.494690i	$0.835282\pi$
$440$	−0.473586	−	9.60307i	−0.0225773	−	0.457808i
$441$	−0.747496	+	2.30056i	−0.0355951	+	0.109550i
$442$	−8.05971	+	11.0932i	−0.383361	+	0.527651i
$443$			21.1766i			1.00613i	0.864249	+	0.503064i	$0.167794\pi$
$443$			21.1766i			1.00613i	−0.864249	+	0.503064i	$0.832206\pi$
$444$	13.3271	+	9.68269i	0.632475	+	0.459520i
$445$	4.79674	−	3.85990i	0.227387	−	0.182977i
$446$	43.3798	−	31.5172i	2.05409	−	1.49238i
$447$	−1.39657	−	1.92221i	−0.0660555	−	0.0909176i
$448$	−10.3024	+	3.34744i	−0.486741	+	0.158152i
$449$	−5.40545			−0.255099			−0.127549	−	0.991832i	$-0.540711\pi$
$449$	−5.40545			−0.255099			−0.127549	+	0.991832i	$0.540711\pi$
$450$	16.8647	+	18.9641i	0.795010	+	0.893974i
$451$	21.2573			1.00097
$452$	−30.3739	+	9.86909i	−1.42867	+	0.464203i
$453$	−3.11751	−	4.29088i	−0.146473	−	0.201603i
$454$	11.8818	−	8.63261i	0.557639	−	0.405149i
$455$	4.76128	−	0.234808i	0.223212	−	0.0110079i
$456$	1.08460	+	0.788009i	0.0507911	+	0.0369019i
$457$			13.6769i			0.639779i	0.947455	+	0.319890i	$0.103646\pi$
$457$			13.6769i			0.639779i	−0.947455	+	0.319890i	$0.896354\pi$
$458$	30.2269	−	41.6037i	1.41241	−	1.94401i
$459$	3.91269	−	12.0420i	0.182629	−	0.562073i
$460$	−2.90544	−	0.788120i	−0.135467	−	0.0367463i
$461$	−10.6262	−	32.7042i	−0.494913	−	1.52319i	−0.817092	−	0.576508i	$-0.804415\pi$
$461$	−10.6262	−	32.7042i	−0.494913	−	1.52319i	0.322178	−	0.946679i	$-0.395585\pi$
$462$	7.73884	+	2.51450i	0.360044	+	0.116985i
$463$	17.7747	+	5.77536i	0.826061	+	0.268404i	0.691385	−	0.722486i	$-0.257001\pi$
$463$	17.7747	+	5.77536i	0.826061	+	0.268404i	0.134676	+	0.990890i	$0.457001\pi$
$464$	7.35310	+	22.6305i	0.341359	+	1.05060i
$465$	8.68397	−	3.30277i	0.402709	−	0.153162i
$466$	0.127352	−	0.391950i	0.00589948	−	0.0181567i
$467$	−15.8678	+	21.8402i	−0.734275	+	1.01064i	0.264653	+	0.964344i	$0.414743\pi$
$467$	−15.8678	+	21.8402i	−0.734275	+	1.01064i	−0.998928	+	0.0462990i	$0.985257\pi$
$468$		−	12.3911i		−	0.572779i
$469$	6.87643	+	4.99602i	0.317524	+	0.230695i
$470$	11.6199	−	42.8372i	0.535986	−	1.97593i
$471$	7.79673	−	5.66465i	0.359254	−	0.261013i
$472$	−4.37061	−	6.01563i	−0.201174	−	0.276892i
$473$	−15.2386	+	4.95131i	−0.700671	+	0.227662i
$474$	11.6864			0.536775
$475$	10.3540	−	1.02373i	0.475074	−	0.0469718i
$476$	−7.36526			−0.337586
$477$	−22.1554	+	7.19871i	−1.01442	+	0.329606i
$478$	−0.644669	−	0.887311i	−0.0294865	−	0.0405847i
$479$	−20.8267	+	15.1315i	−0.951598	+	0.691376i	−0.951184	−	0.308623i	$-0.900132\pi$
$479$	−20.8267	+	15.1315i	−0.951598	+	0.691376i	−0.000413797		1.00000i	$0.500132\pi$
$480$	−11.4882	−	7.51100i	−0.524363	−	0.342829i
$481$	−15.5123	−	11.2703i	−0.707299	−	0.513883i
$482$		−	9.07937i		−	0.413554i
$483$	0.251045	−	0.345534i	0.0114230	−	0.0157223i
$484$	−11.0499	+	34.0080i	−0.502267	+	1.54582i
$485$	−17.1873	+	26.2883i	−0.780436	+	1.19369i
$486$	10.0656	+	30.9787i	0.456584	+	1.40522i
$487$	33.0010	+	10.7227i	1.49542	+	0.485891i	0.938678	−	0.344796i	$-0.112052\pi$
$487$	33.0010	+	10.7227i	1.49542	+	0.485891i	0.556741	+	0.830686i	$0.312052\pi$
$488$	6.79321	+	2.20725i	0.307514	+	0.0999174i
$489$	−0.840872	−	2.58794i	−0.0380256	−	0.117031i
$490$	2.94146	+	3.65539i	0.132881	+	0.165133i
$491$	−4.61728	+	14.2105i	−0.208375	+	0.641312i	0.791183	+	0.611579i	$0.209466\pi$
$491$	−4.61728	+	14.2105i	−0.208375	+	0.641312i	−0.999558	+	0.0297324i	$0.990534\pi$
$492$	−4.49836	+	6.19146i	−0.202802	+	0.279133i
$493$			24.0551i			1.08339i
$494$	−7.53075	−	5.47141i	−0.338824	−	0.246170i
$495$	−9.78213	−	25.7201i	−0.439674	−	1.15603i
$496$	13.3712	−	9.71475i	0.600385	−	0.436205i
$497$	6.10149	+	8.39799i	0.273689	+	0.376701i
$498$	11.8843	−	3.86143i	0.532546	−	0.173035i
$499$	−18.9886			−0.850045			−0.425022	−	0.905183i	$-0.639734\pi$
$499$	−18.9886			−0.850045			−0.425022	+	0.905183i	$0.639734\pi$
$500$	26.5711	−	3.95684i	1.18830	−	0.176955i
$501$	13.0435			0.582740
$502$	57.2666	−	18.6070i	2.55593	−	0.830473i
$503$	−8.51429	−	11.7189i	−0.379633	−	0.522521i	0.575854	−	0.817553i	$-0.304670\pi$
$503$	−8.51429	−	11.7189i	−0.379633	−	0.522521i	−0.955487	+	0.295032i	$0.904670\pi$
$504$	1.65401	−	1.20171i	0.0736756	−	0.0535285i
$505$	−10.3992	−	27.3426i	−0.462760	−	1.21673i
$506$	4.83889	+	3.51566i	0.215115	+	0.156290i
$507$			6.44499i			0.286232i
$508$	1.91507	−	2.63587i	0.0849675	−	0.116948i
$509$	−10.4251	+	32.0851i	−0.462083	+	1.42215i	0.400531	+	0.916283i	$0.368826\pi$
$509$	−10.4251	+	32.0851i	−0.462083	+	1.42215i	−0.862614	+	0.505862i	$0.831174\pi$
$510$	−6.87290	−	8.54104i	−0.304337	−	0.378204i
$511$	−3.68319	−	11.3357i	−0.162935	−	0.501461i
$512$	−28.0966	−	9.12913i	−1.24170	−	0.403454i
$513$	8.17483	+	2.65616i	0.360928	+	0.117273i
$514$	−11.1381	−	34.2797i	−0.491283	−	1.51201i
$515$	4.67888	−	7.15643i	0.206176	−	0.315350i
$516$	1.78258	−	5.48620i	0.0784735	−	0.241517i
$517$	−28.2882	+	38.9354i	−1.24411	+	1.71238i
$518$		−	18.8719i		−	0.829185i
$519$	−9.46398	−	6.87598i	−0.415422	−	0.301822i
$520$	−3.37229	−	2.20480i	−0.147885	−	0.0966870i
$521$	−3.65848	+	2.65804i	−0.160281	+	0.116451i	−0.665035	−	0.746812i	$-0.731583\pi$
$521$	−3.65848	+	2.65804i	−0.160281	+	0.116451i	0.504754	+	0.863263i	$0.331583\pi$
$522$	−23.4125	−	32.2245i	−1.02474	−	1.41043i
$523$	−23.4977	+	7.63485i	−1.02748	+	0.333849i	−0.773794	−	0.633438i	$-0.781643\pi$
$523$	−23.4977	+	7.63485i	−1.02748	+	0.333849i	−0.253687	+	0.967286i	$0.581643\pi$
$524$	41.6192			1.81814
$525$	−0.815399	+	3.72309i	−0.0355869	+	0.162489i
$526$	−0.635063			−0.0276901
$527$	15.8905	−	5.16315i	0.692203	−	0.224910i
$528$	6.91154	+	9.51291i	0.300786	+	0.413996i
$529$	−18.3534	+	13.3345i	−0.797974	+	0.579762i
$530$	−11.8293	+	43.6092i	−0.513832	+	1.89426i
$531$	−17.2168	−	12.5087i	−0.747146	−	0.542833i
$532$		−	4.99998i		−	0.216776i
$533$	5.23595	−	7.20666i	0.226794	−	0.312155i
$534$	1.36092	−	4.18848i	0.0588927	−	0.181253i
$535$	−12.9601	+	4.92912i	−0.560314	+	0.213104i
$536$	−2.21995	−	6.83229i	−0.0958870	−	0.295110i
$537$	6.25416	+	2.03210i	0.269887	+	0.0876916i
$538$	−51.2120	−	16.6398i	−2.20791	−	0.717392i
$539$	−1.57210	−	4.83843i	−0.0677151	−	0.208406i
$540$	21.4194	+	5.81017i	0.921745	+	0.250030i
$541$	−4.02156	+	12.3771i	−0.172900	+	0.532133i	−0.999531	−	0.0306115i	$-0.990255\pi$
$541$	−4.02156	+	12.3771i	−0.172900	+	0.532133i	0.826631	+	0.562745i	$0.190255\pi$
$542$	−25.9876	+	35.7688i	−1.11626	+	1.53640i
$543$			4.85789i			0.208472i
$544$	−19.9696	−	14.5088i	−0.856189	−	0.622058i
$545$	−18.9191	+	0.933015i	−0.810404	+	0.0399660i
$546$	2.75864	−	2.00427i	0.118059	−	0.0857749i
$547$	−13.2746	−	18.2709i	−0.567581	−	0.781209i	0.424684	−	0.905342i	$-0.360385\pi$
$547$	−13.2746	−	18.2709i	−0.567581	−	0.781209i	−0.992266	+	0.124133i	$0.960385\pi$
$548$	15.4642	−	5.02461i	0.660596	−	0.214641i
$549$	20.4428			0.872477
$550$	−52.1385	−	11.4189i	−2.22319	−	0.486904i
$551$	−16.3301			−0.695684
$552$	−0.343316	+	0.111550i	−0.0146125	+	0.00474789i
$553$	−4.29465	−	5.91108i	−0.182627	−	0.251365i
$554$	29.8153	−	21.6620i	1.26673	−	0.920332i
$555$	11.9434	−	9.61075i	0.506969	−	0.407954i
$556$	2.33560	+	1.69691i	0.0990515	+	0.0719651i
$557$		−	14.6267i		−	0.619752i	−0.950777	−	0.309876i	$-0.899713\pi$
$557$		−	14.6267i		−	0.619752i	0.950777	−	0.309876i	$-0.100287\pi$
$558$	−16.2619	+	22.3826i	−0.688422	+	0.947532i
$559$	−2.07486	+	6.38576i	−0.0877572	+	0.270089i
$560$	0.333962	+	6.77186i	0.0141125	+	0.286163i
$561$	3.67331	+	11.3053i	0.155087	+	0.477310i
$562$	34.5580	+	11.2286i	1.45774	+	0.473649i
$563$	10.6446	+	3.45864i	0.448616	+	0.145764i	0.524608	−	0.851344i	$-0.324212\pi$
$563$	10.6446	+	3.45864i	0.448616	+	0.145764i	−0.0759911	+	0.997108i	$0.524212\pi$
$564$	−5.35422	−	16.4786i	−0.225453	−	0.693874i
$565$	1.46394	+	29.6848i	0.0615884	+	1.24885i
$566$	7.00257	−	21.5517i	0.294340	−	0.905885i
$567$	2.41471	−	3.32357i	0.101408	−	0.139577i
$568$		−	8.77349i		−	0.368127i
$569$	33.1605	+	24.0925i	1.39016	+	1.01001i	0.995848	+	0.0910338i	$0.0290171\pi$
$569$	33.1605	+	24.0925i	1.39016	+	1.01001i	0.394312	+	0.918977i	$0.370983\pi$
$570$	5.79817	−	4.66573i	0.242859	−	0.195426i
$571$	−24.6784	+	17.9299i	−1.03276	+	0.750344i	−0.968859	−	0.247613i	$-0.920354\pi$
$571$	−24.6784	+	17.9299i	−1.03276	+	0.750344i	−0.0639003	+	0.997956i	$0.520354\pi$
$572$	15.3179	+	21.0833i	0.640475	+	0.881538i
$573$	10.5458	−	3.42654i	0.440558	−	0.143146i
$574$	8.76749			0.365948
$575$	−1.41570	+	2.41751i	−0.0590389	+	0.100817i
$576$	26.2034			1.09181
$577$	3.09645	−	1.00610i	0.128907	−	0.0418844i	−0.243853	−	0.969812i	$-0.578411\pi$
$577$	3.09645	−	1.00610i	0.128907	−	0.0418844i	0.372760	+	0.927928i	$0.378411\pi$
$578$	9.37839	+	12.9083i	0.390090	+	0.536912i
$579$	7.97843	−	5.79667i	0.331572	−	0.240901i
$580$	−42.1127	+	2.07683i	−1.74863	+	0.0862358i
$581$	−6.32050	−	4.59211i	−0.262219	−	0.190513i
$582$			22.4663i			0.931257i
$583$	28.7980	−	39.6370i	1.19269	−	1.64160i
$584$	−3.11300	+	9.58081i	−0.128817	+	0.396457i
$585$	−11.1291	−	3.01885i	−0.460132	−	0.124814i
$586$	−0.521203	−	1.60410i	−0.0215307	−	0.0662647i
$587$	23.3752	+	7.59508i	0.964800	+	0.313482i	0.748715	−	0.662892i	$-0.230671\pi$
$587$	23.3752	+	7.59508i	0.964800	+	0.313482i	0.216085	+	0.976375i	$0.430671\pi$
$588$	1.74193	+	0.565988i	0.0718361	+	0.0233410i
$589$	3.50506	+	10.7875i	0.144423	+	0.444489i
$590$	−38.5817	+	14.6738i	−1.58838	+	0.604110i
$591$	4.52620	−	13.9302i	0.186183	−	0.573012i
$592$	16.0296	−	22.0628i	0.658811	−	0.906775i
$593$			3.91382i			0.160721i	0.996766	+	0.0803606i	$0.0256072\pi$
$593$			3.91382i			0.160721i	−0.996766	+	0.0803606i	$0.974393\pi$
$594$	−35.6732	−	25.9181i	−1.46369	−	1.06343i
$595$	−1.79440	+	6.61512i	−0.0735632	+	0.271194i
$596$	6.05915	−	4.40223i	0.248193	−	0.180322i
$597$	10.2590	+	14.1203i	0.419872	+	0.577904i
$598$	2.38376	−	0.774531i	0.0974792	−	0.0316729i
$599$	3.79938			0.155239			0.0776193	−	0.996983i	$-0.475268\pi$
$599$	3.79938			0.155239			0.0776193	+	0.996983i	$0.475268\pi$
$600$	2.40715	−	2.14067i	0.0982713	−	0.0873925i
$601$	−3.58328			−0.146165			−0.0730825	−	0.997326i	$-0.523284\pi$
$601$	−3.58328			−0.146165			−0.0730825	+	0.997326i	$0.523284\pi$
$602$	−6.28509	+	2.04215i	−0.256161	+	0.0832317i
$603$	−12.0851	−	16.6337i	−0.492143	−	0.677377i
$604$	13.5256	−	9.82693i	0.550349	−	0.399852i
$605$	27.8523	+	18.2099i	1.13236	+	0.740336i
$606$	−16.9286	−	12.2994i	−0.687678	−	0.499627i
$607$			23.3873i			0.949260i	0.880185	+	0.474630i	$0.157418\pi$
$607$			23.3873i			0.949260i	−0.880185	+	0.474630i	$0.842582\pi$
$608$	9.84941	−	13.5565i	0.399446	−	0.549791i
$609$	1.84853	−	5.68920i	0.0749064	−	0.230538i
$610$	21.6984	−	33.1881i	0.878542	−	1.34375i
$611$	6.23214	+	19.1806i	0.252125	+	0.775962i
$612$	16.9442	+	5.50550i	0.684928	+	0.222547i
$613$	−21.7483	−	7.06645i	−0.878405	−	0.285411i	−0.165110	−	0.986275i	$-0.552798\pi$
$613$	−21.7483	−	7.06645i	−0.878405	−	0.285411i	−0.713295	+	0.700864i	$0.752798\pi$
$614$	−9.77802	−	30.0936i	−0.394609	−	1.21448i
$615$	4.46494	+	5.54864i	0.180044	+	0.223743i
$616$	−1.32872	+	4.08939i	−0.0535358	+	0.164766i
$617$	7.01660	−	9.65752i	0.282478	−	0.388797i	−0.644075	−	0.764962i	$-0.722758\pi$
$617$	7.01660	−	9.65752i	0.282478	−	0.388797i	0.926553	+	0.376165i	$0.122758\pi$
$618$		−	6.11596i		−	0.246020i
$619$	23.3385	+	16.9564i	0.938055	+	0.681537i	0.947952	−	0.318414i	$-0.103150\pi$
$619$	23.3385	+	16.9564i	0.938055	+	0.681537i	−0.00989695	+	0.999951i	$0.503150\pi$
$620$	10.4109	+	27.3734i	0.418113	+	1.09934i
$621$	−1.87243	+	1.36040i	−0.0751381	+	0.0545910i
$622$	−20.5879	−	28.3368i	−0.825499	−	1.13620i
$623$	−2.61869	+	0.850864i	−0.104916	+	0.0340891i
$624$	4.92747			0.197257
$625$	2.91969	−	24.8289i	0.116787	−	0.993157i
$626$	−39.8260			−1.59177
$627$	−7.67470	+	2.49366i	−0.306498	+	0.0995873i
$628$	17.8560	+	24.5767i	0.712531	+	0.980715i
$629$	22.3039	−	16.2047i	0.889313	−	0.646124i
$630$	−4.03460	−	10.6081i	−0.160742	−	0.422639i
$631$	20.1801	+	14.6617i	0.803357	+	0.583673i	0.911897	−	0.410419i	$-0.134618\pi$
$631$	20.1801	+	14.6617i	0.803357	+	0.583673i	−0.108540	+	0.994092i	$0.534618\pi$
$632$			6.17538i			0.245644i
$633$	−6.20360	+	8.53852i	−0.246571	+	0.339376i
$634$	7.49863	−	23.0784i	0.297809	−	0.916561i
$635$	−1.90084	−	2.36220i	−0.0754326	−	0.0937411i
$636$	5.45071	+	16.7756i	0.216135	+	0.665195i
$637$	−2.02755	−	0.658792i	−0.0803346	−	0.0261023i
$638$	79.6721	+	25.8870i	3.15425	+	1.02488i
$639$	−7.75937	−	23.8809i	−0.306956	−	0.944713i
$640$	8.10579	−	12.3980i	0.320410	−	0.490072i
$641$	−7.32921	+	22.5570i	−0.289487	+	0.890948i	0.695531	+	0.718496i	$0.255169\pi$
$641$	−7.32921	+	22.5570i	−0.289487	+	0.890948i	−0.985018	+	0.172452i	$0.944831\pi$
$642$	−5.82976	+	8.02398i	−0.230082	+	0.316681i
$643$			1.92797i			0.0760317i	0.999277	+	0.0380158i	$0.0121037\pi$
$643$			1.92797i			0.0760317i	−0.999277	+	0.0380158i	$0.987896\pi$
$644$	1.08918	+	0.791338i	0.0429199	+	0.0311831i
$645$	−4.49316	−	2.93763i	−0.176918	−	0.115669i
$646$	10.8279	−	7.86690i	0.426016	−	0.309519i
$647$	−10.6274	−	14.6274i	−0.417806	−	0.575061i	0.547295	−	0.836940i	$-0.315658\pi$
$647$	−10.6274	−	14.6274i	−0.417806	−	0.575061i	−0.965101	+	0.261879i	$0.915658\pi$
$648$	−3.30224	+	1.07296i	−0.129724	+	0.0421499i
$649$	44.7575			1.75689
$650$	−16.7136	+	14.8634i	−0.655562	+	0.582990i
$651$	−4.15499			−0.162847
$652$	8.15764	−	2.65058i	0.319478	−	0.103805i
$653$	−5.05076	−	6.95177i	−0.197651	−	0.272044i	0.698674	−	0.715440i	$-0.253774\pi$
$653$	−5.05076	−	6.95177i	−0.197651	−	0.272044i	−0.896326	+	0.443396i	$0.853774\pi$
$654$	−10.9616	+	7.96403i	−0.428631	+	0.311418i
$655$	10.1397	−	37.3804i	0.396190	−	1.46057i
$656$	10.2499	+	7.44698i	0.400191	+	0.290756i
$657$			28.8315i			1.12483i
$658$	−11.6673	+	16.0587i	−0.454841	+	0.626034i
$659$	−14.5013	+	44.6304i	−0.564890	+	1.73855i	0.103388	+	0.994641i	$0.467032\pi$
$659$	−14.5013	+	44.6304i	−0.564890	+	1.73855i	−0.668278	+	0.743912i	$0.732968\pi$
$660$	−19.4747	+	7.40683i	−0.758053	+	0.288310i
$661$	6.78308	+	20.8762i	0.263831	+	0.811989i	0.991960	+	0.126549i	$0.0403901\pi$
$661$	6.78308	+	20.8762i	0.263831	+	0.811989i	−0.728129	+	0.685440i	$0.759610\pi$
$662$	9.95867	+	3.23577i	0.387055	+	0.125762i
$663$	4.73751	+	1.53931i	0.183990	+	0.0597818i
$664$	2.04047	+	6.27993i	0.0791858	+	0.243709i
$665$	−4.49074	−	1.21814i	−0.174143	−	0.0472376i
$666$	−14.1067	+	43.4160i	−0.546624	+	1.68233i
$667$	2.58453	−	3.55730i	0.100073	−	0.137739i
$668$			41.1154i			1.59080i
$669$	−15.7590	−	11.4496i	−0.609280	−	0.442668i
$670$	−39.8315	+	1.96434i	−1.53883	+	0.0758889i
$671$	−34.7832	+	25.2715i	−1.34279	+	0.975594i
$672$	3.60801	+	4.96600i	0.139182	+	0.191567i
$673$	−27.0248	+	8.78089i	−1.04173	+	0.338478i	−0.779418	−	0.626505i	$-0.784485\pi$
$673$	−27.0248	+	8.78089i	−1.04173	+	0.338478i	−0.262312	+	0.964983i	$0.584485\pi$
$674$	2.96257			0.114114
$675$	10.4368	−	17.8224i	0.401714	−	0.685984i
$676$	−20.3157			−0.781374
$677$	36.3076	−	11.7970i	1.39541	−	0.453397i	0.487709	−	0.873007i	$-0.337833\pi$
$677$	36.3076	−	11.7970i	1.39541	−	0.453397i	0.907705	+	0.419609i	$0.137833\pi$
$678$	12.4959	+	17.1991i	0.479902	+	0.660529i
$679$	11.3636	−	8.25615i	0.436096	−	0.316842i
$680$	4.51329	−	3.63181i	0.173077	−	0.139273i
$681$	−4.31642	−	3.13607i	−0.165406	−	0.120174i
$682$		−	58.1868i		−	2.22809i
$683$	15.9953	−	22.0156i	0.612042	−	0.842404i	−0.384701	−	0.923041i	$-0.625695\pi$
$683$	15.9953	−	22.0156i	0.612042	−	0.842404i	0.996744	+	0.0806370i	$0.0256955\pi$
$684$	−3.73746	+	11.5027i	−0.142905	+	0.439818i
$685$	−0.745329	−	15.1133i	−0.0284776	−	0.577450i
$686$	−0.648406	−	1.99559i	−0.0247562	−	0.0761919i
$687$	−17.7674	−	5.77298i	−0.677869	−	0.220253i
$688$	−9.08233	−	2.95103i	−0.346261	−	0.112507i
$689$	−6.34445	−	19.5262i	−0.241704	−	0.743890i
$690$	0.0987061	+	2.00150i	0.00375768	+	0.0761957i
$691$	−7.89476	+	24.2976i	−0.300331	+	0.924323i	0.681048	+	0.732239i	$0.261525\pi$
$691$	−7.89476	+	24.2976i	−0.300331	+	0.924323i	−0.981378	+	0.192084i	$0.938475\pi$
$692$	21.6743	−	29.8321i	0.823933	−	1.13405i
$693$			12.3062i			0.467474i
$694$	−44.3718	−	32.2380i	−1.68433	−	1.22374i
$695$	2.09311	−	1.68430i	0.0793961	−	0.0638893i
$696$	−4.09032	+	2.97179i	−0.155043	+	0.112645i
$697$	7.52834	+	10.3619i	0.285156	+	0.392484i
$698$	42.6785	−	13.8671i	1.61541	−	0.524877i
$699$	−0.149716			−0.00566276
$700$	−11.7358	−	2.57028i	−0.443573	−	0.0971475i
$701$	−2.89917			−0.109500			−0.0547500	−	0.998500i	$-0.517436\pi$
$701$	−2.89917			−0.109500			−0.0547500	+	0.998500i	$0.517436\pi$
$702$	−17.5735	+	5.70999i	−0.663270	+	0.215510i
$703$	11.0007	+	15.1412i	0.414900	+	0.571061i
$704$	−44.5848	+	32.3927i	−1.68035	+	1.22085i
$705$	−16.1047	+	0.794223i	−0.606540	+	0.0299122i
$706$	−20.1489	−	14.6390i	−0.758313	−	0.550947i
$707$			13.0825i			0.492019i
$708$	−9.47136	+	13.0362i	−0.355955	+	0.489931i
$709$	−0.249448	+	0.767723i	−0.00936823	+	0.0288324i	−0.955631	−	0.294565i	$-0.904825\pi$
$709$	−0.249448	+	0.767723i	−0.00936823	+	0.0288324i	0.946263	+	0.323398i	$0.104825\pi$
$710$	−47.0056	−	12.7506i	−1.76409	−	0.478522i
$711$	5.46158	+	16.8090i	0.204825	+	0.630387i
$712$	2.21329	+	0.719142i	0.0829467	+	0.0269510i
$713$	−2.90465	−	0.943779i	−0.108780	−	0.0353448i
$714$	1.51504	+	4.66282i	0.0566990	+	0.174502i
$715$	22.6679	−	8.62130i	0.847733	−	0.322418i
$716$	−6.40554	+	19.7142i	−0.239386	+	0.736755i
$717$	−0.234196	+	0.322343i	−0.00874621	+	0.0120381i
$718$		−	55.6858i		−	2.07818i
$719$	−27.6311	−	20.0752i	−1.03047	−	0.748677i	−0.0620635	−	0.998072i	$-0.519768\pi$
$719$	−27.6311	−	20.0752i	−1.03047	−	0.748677i	−0.968402	+	0.249395i	$0.919768\pi$
$720$	4.29364	−	15.8287i	0.160015	−	0.589900i
$721$	−3.09350	+	2.24756i	−0.115208	+	0.0837035i
$722$	−18.0930	−	24.9028i	−0.673350	−	0.926787i
$723$	−3.13693	+	1.01925i	−0.116664	+	0.0379063i
$724$	−15.3129			−0.569100
$725$	−8.39460	+	38.3296i	−0.311768	+	1.42352i
$726$	23.8029			0.883407
$727$	−21.6939	+	7.04879i	−0.804584	+	0.261425i	−0.682302	−	0.731070i	$-0.739021\pi$
$727$	−21.6939	+	7.04879i	−0.804584	+	0.261425i	−0.122282	+	0.992495i	$0.539021\pi$
$728$	1.05911	+	1.45773i	0.0392531	+	0.0540272i
$729$	−0.397508	+	0.288807i	−0.0147225	+	0.0106965i
$730$	46.8069	+	30.6024i	1.73240	+	1.13264i
$731$	−7.81031	−	5.67452i	−0.288875	−	0.209880i
$732$		−	15.4789i		−	0.572115i
$733$	20.7953	−	28.6222i	0.768091	−	1.05719i	−0.228406	−	0.973566i	$-0.573352\pi$
$733$	20.7953	−	28.6222i	0.768091	−	1.05719i	0.996498	−	0.0836209i	$-0.0266485\pi$
$734$	−2.05962	+	6.33887i	−0.0760221	+	0.233972i
$735$	0.932731	−	1.42663i	0.0344043	−	0.0526220i
$736$	1.39428	+	4.29115i	0.0513938	+	0.158174i
$737$	41.1253	+	13.3624i	1.51487	+	0.492211i
$738$	−20.1701	−	6.55366i	−0.742471	−	0.241244i
$739$	−3.97566	−	12.2358i	−0.146247	−	0.450102i	0.850922	−	0.525292i	$-0.176044\pi$
$739$	−3.97566	−	12.2358i	−0.146247	−	0.450102i	−0.997169	+	0.0751895i	$0.976044\pi$
$740$	30.2948	+	37.6477i	1.11366	+	1.38396i
$741$	−1.04497	+	3.21610i	−0.0383881	+	0.118146i
$742$	11.8776	−	16.3481i	0.436041	−	0.600159i
$743$			35.2855i			1.29450i	0.762279	+	0.647249i	$0.224081\pi$
$743$			35.2855i			1.29450i	−0.762279	+	0.647249i	$0.775919\pi$
$744$	2.84107	+	2.06416i	0.104159	+	0.0756758i
$745$	−2.47768	−	6.51456i	−0.0907753	−	0.238675i
$746$	7.92429	−	5.75733i	0.290129	−	0.210791i
$747$	11.1081	+	15.2890i	0.406424	+	0.559394i
$748$	−35.6363	+	11.5789i	−1.30299	+	0.423367i
$749$	6.20098			0.226579
$750$	−7.97071	−	16.0078i	−0.291049	−	0.584522i
$751$	−32.0474			−1.16943			−0.584713	−	0.811240i	$-0.698793\pi$
$751$	−32.0474			−1.16943			−0.584713	+	0.811240i	$0.698793\pi$
$752$	−27.2801	+	8.86384i	−0.994803	+	0.323231i
$753$	−12.8575	−	17.6968i	−0.468554	−	0.644909i
$754$	28.4005	−	20.6342i	1.03428	−	0.751451i
$755$	−5.53084	−	14.5422i	−0.201288	−	0.529245i
$756$	−8.02967	−	5.83390i	−0.292036	−	0.212177i
$757$		−	9.20649i		−	0.334616i	−0.985905	−	0.167308i	$-0.946493\pi$
$757$		−	9.20649i		−	0.334616i	0.985905	−	0.167308i	$-0.0535074\pi$
$758$	−41.0740	+	56.5335i	−1.49187	+	2.05339i
$759$	0.671449	−	2.06651i	0.0243721	−	0.0750095i
$760$	2.46549	+	3.06389i	0.0894326	+	0.111139i
$761$	−5.36150	−	16.5010i	−0.194354	−	0.598161i	−0.999984	−	0.00574104i	$-0.998173\pi$
$761$	−5.36150	−	16.5010i	−0.194354	−	0.598161i	0.805629	−	0.592420i	$-0.201827\pi$
$762$	−2.06265	−	0.670197i	−0.0747221	−	0.0242787i
$763$	8.05654	+	2.61773i	0.291666	+	0.0947682i
$764$	10.8011	+	33.2423i	0.390769	+	1.20266i
$765$	9.07289	−	13.8772i	0.328031	−	0.501730i
$766$	−8.34514	+	25.6837i	−0.301522	+	0.927990i
$767$	11.0243	−	15.1737i	0.398066	−	0.547891i
$768$			5.91919i			0.213590i
$769$	−9.38772	−	6.82058i	−0.338530	−	0.245956i	0.405511	−	0.914090i	$-0.367093\pi$
$769$	−9.38772	−	6.82058i	−0.338530	−	0.245956i	−0.744041	+	0.668134i	$0.767093\pi$
$770$	19.9786	+	13.0621i	0.719980	+	0.470724i
$771$	−10.5933	+	7.69648i	−0.381508	+	0.277182i
$772$	18.2721	+	25.1494i	0.657628	+	0.905147i
$773$	30.6397	−	9.95543i	1.10203	−	0.358072i	0.299148	−	0.954207i	$-0.403298\pi$
$773$	30.6397	−	9.95543i	1.10203	−	0.358072i	0.802884	+	0.596135i	$0.203298\pi$
$774$	15.9857			0.574594
$775$	27.1219	−	2.68161i	0.974247	−	0.0963264i
$776$	−11.8717			−0.426170
$777$	−6.52027	+	2.11857i	−0.233913	+	0.0760031i
$778$	40.4665	+	55.6973i	1.45079	+	1.99685i
$779$	−7.03426	+	5.11069i	−0.252028	+	0.183109i
$780$	−2.28581	+	8.42672i	−0.0818451	+	0.301725i
$781$	42.7241	+	31.0409i	1.52879	+	1.11073i
$782$			3.60380i			0.128872i
$783$	−19.0537	+	26.2251i	−0.680923	+	0.937210i
$784$	0.936986	−	2.88375i	0.0334638	−	0.102991i
$785$	26.4238	−	10.0498i	0.943107	−	0.358692i
$786$	−8.56111	−	26.3484i	−0.305365	−	0.939816i
$787$	−31.8660	−	10.3539i	−1.13590	−	0.369077i	−0.320086	−	0.947389i	$-0.603712\pi$
$787$	−31.8660	−	10.3539i	−1.13590	−	0.369077i	−0.815816	+	0.578312i	$0.803712\pi$
$788$	43.9105	+	14.2674i	1.56425	+	0.508254i
$789$	0.0712922	+	0.219415i	0.00253807	+	0.00781138i
$790$	33.0858	+	8.97475i	1.17714	+	0.319307i
$791$	4.10733	−	12.6411i	0.146040	−	0.449464i
$792$	6.11361	−	8.41466i	0.217238	−	0.299002i
$793$			18.0169i			0.639798i
$794$	52.7016	+	38.2900i	1.87031	+	1.35886i
$795$	16.3950	−	0.808536i	0.581470	−	0.0286758i
$796$	−44.5096	+	32.3381i	−1.57760	+	1.14619i
$797$	6.93392	+	9.54373i	0.245612	+	0.338056i	0.913969	−	0.405785i	$-0.133002\pi$
$797$	6.93392	+	9.54373i	0.245612	+	0.338056i	−0.668356	+	0.743841i	$0.733002\pi$
$798$	−3.16540	+	1.02850i	−0.112054	+	0.0364085i
$799$	−28.9974			−1.02585
$800$	−26.7565	−	30.0872i	−0.945984	−	1.06374i
$801$	6.66046			0.235336
$802$	−41.6150	+	13.5215i	−1.46948	+	0.477462i
$803$	−35.6416	−	49.0565i	−1.25777	−	1.73117i
$804$	−12.5947	+	9.15059i	−0.444181	+	0.322716i
$805$	0.976100	−	0.785459i	0.0344030	−	0.0276838i
$806$	−19.7265	−	14.3322i	−0.694837	−	0.504829i
$807$			19.5618i			0.688607i
$808$	6.49928	−	8.94550i	0.228644	−	0.314701i
$809$	3.58641	−	11.0378i	0.126091	−	0.388070i	−0.868007	−	0.496552i	$-0.834599\pi$
$809$	3.58641	−	11.0378i	0.126091	−	0.388070i	0.994098	+	0.108483i	$0.0345992\pi$
$810$	0.949418	+	19.2517i	0.0333592	+	0.676436i
$811$	−16.8669	−	51.9110i	−0.592277	−	1.82284i	−0.567837	−	0.823141i	$-0.692220\pi$
$811$	−16.8669	−	51.9110i	−0.592277	−	1.82284i	−0.0244404	−	0.999701i	$-0.507780\pi$
$812$	17.9334	+	5.82690i	0.629337	+	0.204484i
$813$	15.2755	+	4.96332i	0.535736	+	0.174071i
$814$	−29.6686	−	91.3105i	−1.03988	−	3.20043i
$815$	−0.393176	−	7.97256i	−0.0137723	−	0.279267i
$816$	−2.18933	+	6.73806i	−0.0766418	+	0.235879i
$817$	3.85220	−	5.30210i	0.134772	−	0.185497i
$818$			22.3056i			0.779898i
$819$	4.17206	+	3.03118i	0.145783	+	0.105918i
$820$	−17.4903	+	14.0743i	−0.610787	+	0.491495i
$821$	2.30922	−	1.67774i	0.0805922	−	0.0585537i	−0.546760	−	0.837290i	$-0.684139\pi$
$821$	2.30922	−	1.67774i	0.0805922	−	0.0585537i	0.627352	+	0.778736i	$0.284139\pi$
$822$	−6.36198	−	8.75652i	−0.221900	−	0.305419i
$823$	2.76091	−	0.897075i	0.0962393	−	0.0312701i	−0.260502	−	0.965473i	$-0.583888\pi$
$823$	2.76091	−	0.897075i	0.0962393	−	0.0312701i	0.356741	+	0.934203i	$0.383888\pi$
$824$	3.23182			0.112586
$825$	1.90783	+	19.2958i	0.0664220	+	0.671793i
$826$	18.4601			0.642307
$827$	−18.8810	+	6.13482i	−0.656558	+	0.213329i	−0.618304	−	0.785939i	$-0.712180\pi$
$827$	−18.8810	+	6.13482i	−0.656558	+	0.213329i	−0.0382546	+	0.999268i	$0.512180\pi$
$828$	−1.91421	−	2.63468i	−0.0665233	−	0.0915614i
$829$	−8.71760	+	6.33371i	−0.302775	+	0.219979i	−0.728790	−	0.684737i	$-0.759917\pi$
$829$	−8.71760	+	6.33371i	−0.302775	+	0.219979i	0.426015	+	0.904716i	$0.359917\pi$
$830$	36.6114	−	1.80553i	1.27080	−	0.0626709i
$831$	−10.8313	−	7.86941i	−0.375734	−	0.272987i
$832$			23.0939i			0.800636i
$833$	1.80173	−	2.47986i	0.0624261	−	0.0859222i
$834$	0.593850	−	1.82768i	0.0205634	−	0.0632875i
$835$	36.9279	+	10.0169i	1.27794	+	0.346651i
$836$	−7.86046	−	24.1920i	−0.271860	−	0.836698i
$837$	21.4137	+	6.95772i	0.740165	+	0.240494i
$838$	−56.0504	−	18.2119i	−1.93623	−	0.629118i
$839$	−0.512063	−	1.57597i	−0.0176784	−	0.0544084i	0.941828	−	0.336095i	$-0.109106\pi$
$839$	−0.512063	−	1.57597i	−0.0176784	−	0.0544084i	−0.959507	+	0.281686i	$0.909106\pi$
$840$	−1.34651	+	0.512120i	−0.0464591	+	0.0176698i
$841$	10.0693	−	30.9902i	0.347218	−	1.06863i
$842$	35.4264	−	48.7603i	1.22087	−	1.68039i
$843$		−	13.2003i		−	0.454644i
$844$	−26.9149	−	19.5548i	−0.926449	−	0.673105i
$845$	−4.94952	+	18.2466i	−0.170269	+	0.627703i
$846$	38.8452	−	28.2227i	1.33553	−	0.970317i
$847$	−8.74734	−	12.0397i	−0.300562	−	0.413688i
$848$	27.7717	−	9.02358i	0.953685	−	0.309871i
$849$	−8.23224			−0.282530
$850$	−12.8989	−	29.4590i	−0.442428	−	1.01043i
$851$	−5.03939			−0.172748
$852$	−18.0821	+	5.87523i	−0.619483	+	0.201282i
$853$	14.5010	+	19.9589i	0.496505	+	0.683381i	0.981571	−	0.191097i	$-0.0612044\pi$
$853$	14.5010	+	19.9589i	0.496505	+	0.683381i	−0.485066	+	0.874478i	$0.661204\pi$
$854$	−14.3462	+	10.4231i	−0.490916	+	0.356671i
$855$	9.42064	+	6.15922i	0.322179	+	0.210641i
$856$	−4.24007	−	3.08059i	−0.144922	−	0.105292i
$857$			20.2120i			0.690428i	0.938524	+	0.345214i	$0.112194\pi$
$857$			20.2120i			0.690428i	−0.938524	+	0.345214i	$0.887806\pi$
$858$	10.1966	−	14.0344i	0.348105	−	0.479126i
$859$	1.44560	−	4.44910i	0.0493233	−	0.151801i	−0.923361	−	0.383932i	$-0.874570\pi$
$859$	1.44560	−	4.44910i	0.0493233	−	0.151801i	0.972685	+	0.232131i	$0.0745697\pi$
$860$	9.25992	−	14.1632i	0.315761	−	0.482962i
$861$	−0.984238	−	3.02917i	−0.0335428	−	0.103234i
$862$	15.1588	+	4.92539i	0.516310	+	0.167759i
$863$	−35.4003	−	11.5023i	−1.20504	−	0.391542i	−0.363428	−	0.931622i	$-0.618394\pi$
$863$	−35.4003	−	11.5023i	−1.20504	−	0.391542i	−0.841613	+	0.540081i	$0.818394\pi$
$864$	−10.2789	−	31.6352i	−0.349695	−	1.07625i
$865$	−21.5133	−	26.7348i	−0.731473	−	0.909011i
$866$	11.0973	−	34.1539i	0.377101	−	1.16060i
$867$	3.40699	−	4.68932i	0.115708	−	0.159258i
$868$		−	13.0972i		−	0.444550i
$869$	−30.0722	−	21.8487i	−1.02013	−	0.741167i
$870$	9.97743	+	26.2336i	0.338267	+	0.889402i
$871$	14.6598	−	10.6510i	0.496729	−	0.360895i
$872$	−4.20839	−	5.79235i	−0.142514	−	0.196154i
$873$	−32.3141	+	10.4995i	−1.09367	+	0.355354i
$874$	−2.44647			−0.0827532
$875$	−5.16771	+	9.91437i	−0.174700	+	0.335167i
$876$	21.8306			0.737589
$877$	−4.55100	+	1.47871i	−0.153676	+	0.0499325i	−0.384845	−	0.922981i	$-0.625745\pi$
$877$	−4.55100	+	1.47871i	−0.153676	+	0.0499325i	0.231169	+	0.972914i	$0.425745\pi$
$878$	10.4358	+	14.3637i	0.352192	+	0.484751i
$879$	−0.495707	+	0.360152i	−0.0167198	+	0.0121476i
$880$	12.2619	+	32.2401i	0.413348	+	1.08681i
$881$	19.3095	+	14.0292i	0.650555	+	0.472656i	0.863460	−	0.504417i	$-0.168293\pi$
$881$	19.3095	+	14.0292i	0.650555	+	0.472656i	−0.212905	+	0.977073i	$0.568293\pi$
$882$			5.07564i			0.170906i
$883$	8.81516	−	12.1330i	0.296654	−	0.408309i	−0.634507	−	0.772917i	$-0.718797\pi$
$883$	8.81516	−	12.1330i	0.296654	−	0.408309i	0.931161	+	0.364608i	$0.118797\pi$
$884$	−4.85217	+	14.9335i	−0.163196	+	0.502266i
$885$	9.40099	+	11.6827i	0.316011	+	0.392711i
$886$	13.7310	+	42.2597i	0.461302	+	1.41974i
$887$	−20.8759	−	6.78299i	−0.700944	−	0.227750i	−0.0632021	−	0.998001i	$-0.520131\pi$
$887$	−20.8759	−	6.78299i	−0.700944	−	0.227750i	−0.637742	+	0.770250i	$0.720131\pi$
$888$	5.51088	+	1.79059i	0.184933	+	0.0600883i
$889$	0.419016	+	1.28960i	0.0140533	+	0.0432517i
$890$	7.06954	−	10.8130i	0.236972	−	0.362452i
$891$	6.45843	−	19.8770i	0.216366	−	0.665905i
$892$	36.0912	−	49.6753i	1.20842	−	1.66325i
$893$		−	19.6852i		−	0.658739i
$894$	−4.03335	−	2.93040i	−0.134895	−	0.0980073i
$895$	16.1458	+	10.5561i	0.539694	+	0.352852i
$896$	−5.35925	+	3.89372i	−0.179040	+	0.130080i
$897$	−0.535202	−	0.736642i	−0.0178699	−	0.0245958i
$898$	−10.7870	+	3.50492i	−0.359968	+	0.116961i
$899$	−42.7760			−1.42666
$900$	25.0777	+	14.6856i	0.835923	+	0.489519i
$901$	29.5200			0.983453
$902$	42.4208	−	13.7834i	1.41246	−	0.458936i
$903$	1.41113	+	1.94225i	0.0469594	+	0.0646341i
$904$	−9.08844	+	6.60314i	−0.302277	+	0.219617i
$905$	−3.73069	+	13.7533i	−0.124012	+	0.457176i
$906$	−9.00350	−	6.54142i	−0.299121	−	0.217324i
$907$			10.0942i			0.335172i	0.985857	+	0.167586i	$0.0535972\pi$
$907$			10.0942i			0.335172i	−0.985857	+	0.167586i	$0.946403\pi$
$908$	9.88543	−	13.6061i	0.328060	−	0.451535i
$909$	9.77915	−	30.0971i	0.324354	−	0.998258i
$910$	9.34929	−	3.55582i	0.309926	−	0.117874i
$911$	4.71082	+	14.4984i	0.156076	+	0.480353i	0.998268	−	0.0588242i	$-0.0187351\pi$
$911$	4.71082	+	14.4984i	0.156076	+	0.480353i	−0.842192	+	0.539178i	$0.818735\pi$
$912$	−4.57419	−	1.48625i	−0.151467	−	0.0492145i
$913$	−37.8005	−	12.2821i	−1.25102	−	0.406480i
$914$	8.86819	+	27.2935i	0.293334	+	0.902788i
$915$	−13.9024	−	3.77112i	−0.459598	−	0.124669i
$916$	18.1974	−	56.0060i	0.601260	−	1.85049i
$917$	−10.1811	+	14.0131i	−0.336209	+	0.462753i
$918$		−	26.5679i		−	0.876871i
$919$	9.66583	+	7.02264i	0.318846	+	0.231655i	0.735683	−	0.677326i	$-0.236861\pi$
$919$	9.66583	+	7.02264i	0.318846	+	0.231655i	−0.416837	+	0.908981i	$0.636861\pi$
$920$	−1.05764	+	0.0521587i	−0.0348694	+	0.00171962i
$921$	−9.29970	+	6.75663i	−0.306436	+	0.222638i
$922$	−42.4112	−	58.3740i	−1.39674	−	1.92245i
$923$	21.0470	−	6.83858i	0.692770	−	0.225095i
$924$	9.31801			0.306540
$925$	41.1941	−	18.0372i	1.35445	−	0.593059i
$926$	39.2158			1.28871
$927$	8.79682	−	2.85826i	0.288925	−	0.0938776i
$928$	37.1448	+	51.1254i	1.21934	+	1.67827i
$929$	33.0992	−	24.0480i	1.08595	−	0.788989i	0.107240	−	0.994233i	$-0.465799\pi$
$929$	33.0992	−	24.0480i	1.08595	−	0.788989i	0.978711	+	0.205244i	$0.0657988\pi$
$930$	15.1881	−	12.2217i	0.498037	−	0.400766i
$931$	1.68348	+	1.22312i	0.0551738	+	0.0400861i
$932$		−	0.471930i		−	0.0154586i
$933$	−7.47919	+	10.2942i	−0.244858	+	0.337018i
$934$	−17.5043	+	53.8728i	−0.572759	+	1.76277i
$935$	1.71757	+	34.8278i	0.0561705	+	1.13899i
$936$	−1.34688	−	4.14528i	−0.0440242	−	0.135493i
$937$	−36.2468	−	11.7773i	−1.18413	−	0.384748i	−0.350232	−	0.936663i	$-0.613897\pi$
$937$	−36.2468	−	11.7773i	−1.18413	−	0.384748i	−0.833900	+	0.551915i	$0.813897\pi$
$938$	16.9620	+	5.51127i	0.553828	+	0.179949i
$939$	4.47087	+	13.7599i	0.145901	+	0.449038i
$940$	−2.50353	−	50.7650i	−0.0816562	−	1.65577i
$941$	10.5644	−	32.5140i	0.344391	−	1.05993i	−0.617518	−	0.786557i	$-0.711862\pi$
$941$	10.5644	−	32.5140i	0.344391	−	1.05993i	0.961909	−	0.273370i	$-0.0881384\pi$
$942$	11.8861	−	16.3598i	0.387269	−	0.533030i
$943$		−	2.34119i		−	0.0762396i
$944$	21.5813	+	15.6797i	0.702410	+	0.510331i
$945$	−7.19600	+	5.79055i	−0.234086	+	0.188367i
$946$	−27.1995	+	19.7616i	−0.884331	+	0.642504i
$947$	−27.1052	−	37.3071i	−0.880802	−	1.21232i	−0.976198	−	0.216880i	$-0.930412\pi$
$947$	−27.1052	−	37.3071i	−0.880802	−	1.21232i	0.0953967	−	0.995439i	$-0.469588\pi$
$948$	12.7274	−	4.13539i	0.413368	−	0.134311i
$949$	−25.4101			−0.824848
$950$	19.9985	−	8.75652i	0.648837	−	0.284099i
$951$	−8.81541			−0.285859
$952$	−2.46395	+	0.800585i	−0.0798570	+	0.0259471i
$953$	−24.8979	−	34.2690i	−0.806521	−	1.11008i	−0.991851	−	0.127405i	$-0.959335\pi$
$953$	−24.8979	−	34.2690i	−0.806521	−	1.11008i	0.185330	−	0.982676i	$-0.440665\pi$
$954$	−39.5453	+	28.7313i	−1.28033	+	0.930211i
$955$	32.4881	−	1.60219i	1.05129	−	0.0518455i
$956$	−1.01608	−	0.738227i	−0.0328625	−	0.0238760i
$957$		−	30.4329i		−	0.983755i
$958$	−31.7502	+	43.7004i	−1.02580	+	1.41190i
$959$	−2.09115	+	6.43589i	−0.0675266	+	0.207826i
$960$	−17.8199	−	4.83378i	−0.575136	−	0.156010i
$961$	−0.398166	−	1.22543i	−0.0128441	−	0.0395300i
$962$	−38.2639	−	12.4327i	−1.23368	−	0.400846i
$963$	−14.2657	−	4.63521i	−0.459706	−	0.149367i
$964$	−3.21286	−	9.88816i	−0.103479	−	0.318476i
$965$	27.0396	−	10.2840i	0.870437	−	0.331053i
$966$	0.276936	−	0.852323i	0.00891028	−	0.0274230i
$967$	1.04219	−	1.43445i	0.0335145	−	0.0461288i	−0.791931	−	0.610611i	$-0.790924\pi$
$967$	1.04219	−	1.43445i	0.0335145	−	0.0461288i	0.825445	+	0.564482i	$0.190924\pi$
$968$			12.5780i			0.404273i
$969$	−3.93356	−	2.85790i	−0.126364	−	0.0918089i
$970$	−17.2533	+	63.6050i	−0.553970	+	2.04223i
$971$	−25.6221	+	18.6155i	−0.822252	+	0.597401i	−0.917357	−	0.398066i	$-0.869681\pi$
$971$	−25.6221	+	18.6155i	−0.822252	+	0.597401i	0.0951050	+	0.995467i	$0.469681\pi$
$972$	21.9244	+	30.1764i	0.703226	+	0.967908i
$973$	−1.14269	+	0.371283i	−0.0366330	+	0.0119028i
$974$	72.8091			2.33295
$975$	7.01159	+	4.10601i	0.224551	+	0.131497i
$976$	−25.6250			−0.820237
$977$	23.5057	−	7.63748i	0.752015	−	0.244345i	0.0921670	−	0.995744i	$-0.470621\pi$
$977$	23.5057	−	7.63748i	0.752015	−	0.244345i	0.659848	+	0.751399i	$0.270621\pi$
$978$	−3.35607	−	4.61923i	−0.107315	−	0.147707i
$979$	−11.3327	+	8.23368i	−0.362194	+	0.263150i
$980$	4.49699	+	2.94013i	0.143651	+	0.0939191i
$981$	−16.5778	−	12.0445i	−0.529288	−	0.384550i
$982$			31.3522i			1.00049i
$983$	18.0929	−	24.9027i	0.577074	−	0.794274i	−0.416297	−	0.909229i	$-0.636672\pi$
$983$	18.0929	−	24.9027i	0.577074	−	0.794274i	0.993371	+	0.114955i	$0.0366723\pi$
$984$	−0.831869	+	2.56023i	−0.0265190	+	0.0816172i
$985$	23.5122	−	35.9623i	0.749160	−	1.14585i
$986$	15.5975	+	48.0041i	0.496725	+	1.52876i
$987$	6.85808	+	2.22833i	0.218295	+	0.0709284i
$988$	−10.1377	−	3.29394i	−0.322524	−	0.104794i
$989$	0.545316	+	1.67831i	0.0173400	+	0.0533672i
$990$	−36.1982	−	44.9839i	−1.15045	−	1.42968i
$991$	−7.49337	+	23.0622i	−0.238035	+	0.732596i	0.758669	+	0.651476i	$0.225850\pi$
$991$	−7.49337	+	23.0622i	−0.238035	+	0.732596i	−0.996704	+	0.0811202i	$0.974150\pi$
$992$	25.8002	−	35.5109i	0.819156	−	1.12747i
$993$		−	3.80398i		−	0.120716i
$994$	17.6214	+	12.8027i	0.558916	+	0.406076i
$995$	18.2007	+	47.8549i	0.577000	+	1.51710i
$996$	11.5765	−	8.41081i	0.366815	−	0.266507i
$997$	3.75052	+	5.16215i	0.118780	+	0.163487i	0.864267	−	0.503034i	$-0.167783\pi$
$997$	3.75052	+	5.16215i	0.118780	+	0.163487i	−0.745487	+	0.666521i	$0.767783\pi$
$998$	−37.8933	+	12.3123i	−1.19949	+	0.389739i
$999$	37.1513			1.17542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.n.a.169.12	yes	56
5.2	odd	4		875.2.h.d.526.12		56
5.3	odd	4		875.2.h.e.526.3		56
5.4	even	2		875.2.n.c.99.3		56
25.2	odd	20		4375.2.a.p.1.23		28
25.3	odd	20		875.2.h.e.351.3		56
25.4	even	10	inner	175.2.n.a.29.12	✓	56
25.21	even	5		875.2.n.c.274.3		56
25.22	odd	20		875.2.h.d.351.12		56
25.23	odd	20		4375.2.a.o.1.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.12	✓	56	25.4	even	10	inner
175.2.n.a.169.12	yes	56	1.1	even	1	trivial
875.2.h.d.351.12		56	25.22	odd	20
875.2.h.d.526.12		56	5.2	odd	4
875.2.h.e.351.3		56	25.3	odd	20
875.2.h.e.526.3		56	5.3	odd	4
875.2.n.c.99.3		56	5.4	even	2
875.2.n.c.274.3		56	25.21	even	5
4375.2.a.o.1.6		28	25.23	odd	20
4375.2.a.p.1.23		28	25.2	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99559 - 0.648406i) q^{2} +(-0.448050 - 0.616687i) q^{3} +(1.94391 - 1.41233i) q^{4} +(-0.794894 - 2.09001i) q^{5} +(-1.29399 - 0.940136i) q^{6} +1.00000i q^{7} +(0.496791 - 0.683774i) q^{8} +(0.747496 - 2.30056i) q^{9} +O(q^{10})\)	\(q+(1.99559 - 0.648406i) q^{2} +(-0.448050 - 0.616687i) q^{3} +(1.94391 - 1.41233i) q^{4} +(-0.794894 - 2.09001i) q^{5} +(-1.29399 - 0.940136i) q^{6} +1.00000i q^{7} +(0.496791 - 0.683774i) q^{8} +(0.747496 - 2.30056i) q^{9} +(-2.94146 - 3.65539i) q^{10} +(1.57210 + 4.83843i) q^{11} +(-1.74193 - 0.565988i) q^{12} +(2.02755 + 0.658792i) q^{13} +(0.648406 + 1.99559i) q^{14} +(-0.932731 + 1.42663i) q^{15} +(-0.936986 + 2.88375i) q^{16} +(-1.80173 + 2.47986i) q^{17} -5.07564i q^{18} +(-1.68348 - 1.22312i) q^{19} +(-4.49699 - 2.94013i) q^{20} +(0.616687 - 0.448050i) q^{21} +(6.27453 + 8.63615i) q^{22} +(0.532883 - 0.173144i) q^{23} -0.644262 q^{24} +(-3.73629 + 3.32267i) q^{25} +4.47332 q^{26} +(-3.92852 + 1.27645i) q^{27} +(1.41233 + 1.94391i) q^{28} +(6.34885 - 4.61271i) q^{29} +(-0.936312 + 3.45175i) q^{30} +(-4.40981 - 3.20392i) q^{31} +8.05270i q^{32} +(2.27942 - 3.13735i) q^{33} +(-1.98755 + 6.11704i) q^{34} +(2.09001 - 0.794894i) q^{35} +(-1.79608 - 5.52778i) q^{36} +(-8.55379 - 2.77929i) q^{37} +(-4.15261 - 1.34926i) q^{38} +(-0.502176 - 1.54554i) q^{39} +(-1.82399 - 0.494770i) q^{40} +(1.29120 - 3.97390i) q^{41} +(0.940136 - 1.29399i) q^{42} +3.14949i q^{43} +(9.88947 + 7.18512i) q^{44} +(-5.40237 + 0.266424i) q^{45} +(0.951148 - 0.691049i) q^{46} +(5.56042 + 7.65326i) q^{47} +(2.19819 - 0.714234i) q^{48} -1.00000 q^{49} +(-5.30165 + 9.05332i) q^{50} +2.33656 q^{51} +(4.87181 - 1.58295i) q^{52} +(-5.66063 - 7.79118i) q^{53} +(-7.01204 + 5.09455i) q^{54} +(8.86271 - 7.13174i) q^{55} +(0.683774 + 0.496791i) q^{56} +1.58620i q^{57} +(9.67878 - 13.3217i) q^{58} +(2.71863 - 8.36710i) q^{59} +(0.201730 + 4.09056i) q^{60} +(2.61154 + 8.03748i) q^{61} +(-10.8776 - 3.53435i) q^{62} +(2.30056 + 0.747496i) q^{63} +(3.34744 + 10.3024i) q^{64} +(-0.234808 - 4.76128i) q^{65} +(2.51450 - 7.73884i) q^{66} +(4.99602 - 6.87643i) q^{67} +7.36526i q^{68} +(-0.345534 - 0.251045i) q^{69} +(3.65539 - 2.94146i) q^{70} +(8.39799 - 6.10149i) q^{71} +(-1.20171 - 1.65401i) q^{72} +(-11.3357 + 3.68319i) q^{73} -18.8719 q^{74} +(3.72309 + 0.815399i) q^{75} -4.99998 q^{76} +(-4.83843 + 1.57210i) q^{77} +(-2.00427 - 2.75864i) q^{78} +(-5.91108 + 4.29465i) q^{79} +(6.77186 - 0.333962i) q^{80} +(-3.32357 - 2.41471i) q^{81} -8.76749i q^{82} +(-4.59211 + 6.32050i) q^{83} +(0.565988 - 1.74193i) q^{84} +(6.61512 + 1.79440i) q^{85} +(2.04215 + 6.28509i) q^{86} +(-5.68920 - 1.84853i) q^{87} +(4.08939 + 1.32872i) q^{88} +(0.850864 + 2.61869i) q^{89} +(-10.6081 + 4.03460i) q^{90} +(-0.658792 + 2.02755i) q^{91} +(0.791338 - 1.08918i) q^{92} +4.15499i q^{93} +(16.0587 + 11.6673i) q^{94} +(-1.21814 + 4.49074i) q^{95} +(4.96600 - 3.60801i) q^{96} +(-8.25615 - 11.3636i) q^{97} +(-1.99559 + 0.648406i) q^{98} +12.3062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

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