LMFDB - Embedded newform 930.2.v.b.401.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.13
Character	$\chi$	$=$	930.401
Dual form			930.2.v.b.821.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-1.10710 + 1.33204i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.426905 + 1.67862i) q^{6} +(1.11324 + 3.42620i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.548656 - 2.94940i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-1.10710 + 1.33204i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.426905 + 1.67862i) q^{6} +(1.11324 + 3.42620i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.548656 - 2.94940i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.780462 - 2.40202i) q^{11} +(1.60896 + 0.641293i) q^{12} +(-3.06948 - 4.22477i) q^{13} +(3.42620 + 1.11324i) q^{14} +(1.33204 + 1.10710i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.50749 - 4.63957i) q^{17} +(-2.70861 - 1.28974i) q^{18} +(5.93338 + 4.31085i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-5.79631 - 2.31027i) q^{21} +(-2.40202 - 0.780462i) q^{22} +(0.996924 - 3.06822i) q^{23} +(1.46454 - 0.924732i) q^{24} -1.00000 q^{25} -5.22211 q^{26} +(4.53614 + 2.53445i) q^{27} +(2.91450 - 2.11751i) q^{28} +(5.31158 + 3.85909i) q^{29} +(1.67862 - 0.426905i) q^{30} +(2.62325 + 4.91106i) q^{31} +1.00000i q^{32} +(4.06363 + 1.61967i) q^{33} +(-2.86741 - 3.94665i) q^{34} +(3.42620 - 1.11324i) q^{35} +(-2.63550 + 1.43322i) q^{36} -9.14610i q^{37} +(6.97510 - 2.26635i) q^{38} +(9.02578 + 0.588585i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(5.51758 - 7.59430i) q^{41} +(-5.27603 + 3.33137i) q^{42} +(5.60451 - 7.71395i) q^{43} +(-2.04328 + 1.48453i) q^{44} +(-2.94940 + 0.548656i) q^{45} +(-1.89626 - 2.60998i) q^{46} +(-6.83401 - 9.40620i) q^{47} +(0.112710 - 1.72838i) q^{48} +(-4.83644 + 3.51388i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(4.51115 + 7.14450i) q^{51} +(-3.06948 + 4.22477i) q^{52} +(-0.821784 + 2.52919i) q^{53} +(4.71669 - 2.18010i) q^{54} +(-2.40202 + 0.780462i) q^{55} -3.60252i q^{56} +(-12.3111 + 3.13095i) q^{57} +(6.24414 - 2.02884i) q^{58} +(1.74341 + 2.39959i) q^{59} +(0.641293 - 1.60896i) q^{60} +3.23349i q^{61} +(5.51504 + 0.764395i) q^{62} +(9.49446 - 5.16320i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-4.22477 + 3.06948i) q^{65} +(3.69888 - 2.33553i) q^{66} -3.15833 q^{67} -4.87833 q^{68} +(2.98329 + 4.72477i) q^{69} +(1.11324 - 3.42620i) q^{70} +(-13.6854 - 4.44667i) q^{71} +(-0.389612 + 2.97459i) q^{72} +(1.99203 - 0.647248i) q^{73} +(-7.39935 - 5.37594i) q^{74} +(1.10710 - 1.33204i) q^{75} +(2.26635 - 6.97510i) q^{76} +(7.36095 - 5.34804i) q^{77} +(5.78140 - 6.95605i) q^{78} +(4.98751 + 1.62054i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-8.39795 + 3.23642i) q^{81} +(-2.90076 - 8.92763i) q^{82} +(3.06810 + 2.22910i) q^{83} +(-0.406041 + 6.22653i) q^{84} +(-4.63957 - 1.50749i) q^{85} +(-2.94647 - 9.06829i) q^{86} +(-11.0209 + 2.80283i) q^{87} +2.52563i q^{88} +(-1.84962 - 5.69255i) q^{89} +(-1.28974 + 2.70861i) q^{90} +(11.0579 - 15.2198i) q^{91} -3.22611 q^{92} +(-9.44593 - 1.94277i) q^{93} -11.6267 q^{94} +(4.31085 - 5.93338i) q^{95} +(-1.33204 - 1.10710i) q^{96} +(3.98379 + 12.2608i) q^{97} +5.97817i q^{98} +(-6.65631 + 3.61978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−1.10710	+	1.33204i	−0.639185	+	0.769053i
$3$	−1.10710	+	1.33204i	−0.639185	+	0.769053i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.426905	+	1.67862i	0.174283	+	0.685292i
$7$	1.11324	+	3.42620i	0.420765	+	1.29498i	0.906991	+	0.421150i	$0.138373\pi$
$7$	1.11324	+	3.42620i	0.420765	+	1.29498i	−0.486226	+	0.873833i	$0.661627\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.548656	−	2.94940i	−0.182885	−	0.983134i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−0.780462	−	2.40202i	−0.235318	−	0.724235i	−0.997079	−	0.0763767i	$-0.975665\pi$
$11$	−0.780462	−	2.40202i	−0.235318	−	0.724235i	0.761761	−	0.647858i	$-0.224335\pi$
$12$	1.60896	+	0.641293i	0.464466	+	0.185125i
$13$	−3.06948	−	4.22477i	−0.851320	−	1.17174i	−0.983570	−	0.180525i	$-0.942220\pi$
$13$	−3.06948	−	4.22477i	−0.851320	−	1.17174i	0.132251	−	0.991216i	$-0.457780\pi$
$14$	3.42620	+	1.11324i	0.915691	+	0.297526i
$15$	1.33204	+	1.10710i	0.343931	+	0.285852i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.50749	−	4.63957i	0.365620	−	1.12526i	−0.583973	−	0.811773i	$-0.698503\pi$
$17$	1.50749	−	4.63957i	0.365620	−	1.12526i	0.949592	−	0.313488i	$-0.101497\pi$
$18$	−2.70861	−	1.28974i	−0.638425	−	0.303995i
$19$	5.93338	+	4.31085i	1.36121	+	0.988977i	0.998367	+	0.0571271i	$0.0181940\pi$
$19$	5.93338	+	4.31085i	1.36121	+	0.988977i	0.362843	+	0.931850i	$0.381806\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	−5.79631	−	2.31027i	−1.26486	−	0.504142i
$22$	−2.40202	−	0.780462i	−0.512112	−	0.166395i
$23$	0.996924	−	3.06822i	0.207873	−	0.639768i	−0.791710	−	0.610897i	$-0.790809\pi$
$23$	0.996924	−	3.06822i	0.207873	−	0.639768i	0.999583	−	0.0288705i	$-0.00919105\pi$
$24$	1.46454	−	0.924732i	0.298948	−	0.188760i
$25$	−1.00000			−0.200000
$26$	−5.22211			−1.02414
$27$	4.53614	+	2.53445i	0.872980	+	0.487756i
$28$	2.91450	−	2.11751i	0.550789	−	0.400172i
$29$	5.31158	+	3.85909i	0.986336	+	0.716615i	0.959116	−	0.283014i	$-0.0913344\pi$
$29$	5.31158	+	3.85909i	0.986336	+	0.716615i	0.0272204	+	0.999629i	$0.491334\pi$
$30$	1.67862	−	0.426905i	0.306472	−	0.0779418i
$31$	2.62325	+	4.91106i	0.471150	+	0.882053i
$31$	2.62325	+	4.91106i	0.471150	+	0.882053i
$32$			1.00000i			0.176777i
$33$	4.06363	+	1.61967i	0.707387	+	0.281948i
$34$	−2.86741	−	3.94665i	−0.491757	−	0.676846i
$35$	3.42620	−	1.11324i	0.579134	−	0.188172i
$36$	−2.63550	+	1.43322i	−0.439251	+	0.238870i
$37$		−	9.14610i		−	1.50361i	−0.659386	−	0.751805i	$-0.729183\pi$
$37$		−	9.14610i		−	1.50361i	0.659386	−	0.751805i	$-0.270817\pi$
$38$	6.97510	−	2.26635i	1.13151	−	0.367650i
$39$	9.02578	+	0.588585i	1.44528	+	0.0942491i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	5.51758	−	7.59430i	0.861701	−	1.18603i	−0.119460	−	0.992839i	$-0.538116\pi$
$41$	5.51758	−	7.59430i	0.861701	−	1.18603i	0.981161	−	0.193191i	$-0.0618838\pi$
$42$	−5.27603	+	3.33137i	−0.814109	+	0.514041i
$43$	5.60451	−	7.71395i	0.854680	−	1.17637i	−0.128132	−	0.991757i	$-0.540898\pi$
$43$	5.60451	−	7.71395i	0.854680	−	1.17637i	0.982812	−	0.184609i	$-0.0591020\pi$
$44$	−2.04328	+	1.48453i	−0.308036	+	0.223801i
$45$	−2.94940	+	0.548656i	−0.439671	+	0.0817888i
$46$	−1.89626	−	2.60998i	−0.279589	−	0.384821i
$47$	−6.83401	−	9.40620i	−0.996842	−	1.37204i	−0.927243	−	0.374461i	$-0.877828\pi$
$47$	−6.83401	−	9.40620i	−0.996842	−	1.37204i	−0.0695994	−	0.997575i	$-0.522172\pi$
$48$	0.112710	−	1.72838i	0.0162683	−	0.249470i
$49$	−4.83644	+	3.51388i	−0.690920	+	0.501983i
$50$	−0.587785	+	0.809017i	−0.0831254	+	0.114412i
$51$	4.51115	+	7.14450i	0.631687	+	1.00043i
$52$	−3.06948	+	4.22477i	−0.425660	+	0.585870i
$53$	−0.821784	+	2.52919i	−0.112881	+	0.347411i	−0.991499	−	0.130114i	$-0.958466\pi$
$53$	−0.821784	+	2.52919i	−0.112881	+	0.347411i	0.878618	+	0.477524i	$0.158466\pi$
$54$	4.71669	−	2.18010i	0.641860	−	0.296674i
$55$	−2.40202	+	0.780462i	−0.323888	+	0.105238i
$56$		−	3.60252i		−	0.481407i
$57$	−12.3111	+	3.13095i	−1.63064	+	0.414704i
$58$	6.24414	−	2.02884i	0.819896	−	0.266400i
$59$	1.74341	+	2.39959i	0.226972	+	0.312400i	0.907281	−	0.420525i	$-0.138154\pi$
$59$	1.74341	+	2.39959i	0.226972	+	0.312400i	−0.680309	+	0.732926i	$0.738154\pi$
$60$	0.641293	−	1.60896i	0.0827905	−	0.207716i
$61$			3.23349i			0.414006i	0.978340	+	0.207003i	$0.0663710\pi$
$61$			3.23349i			0.414006i	−0.978340	+	0.207003i	$0.933629\pi$
$62$	5.51504	+	0.764395i	0.700411	+	0.0970783i
$63$	9.49446	−	5.16320i	1.19619	−	0.650502i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−4.22477	+	3.06948i	−0.524018	+	0.380722i
$66$	3.69888	−	2.33553i	0.455301	−	0.287484i
$67$	−3.15833			−0.385852			−0.192926	−	0.981213i	$-0.561798\pi$
$67$	−3.15833			−0.385852			−0.192926	+	0.981213i	$0.561798\pi$
$68$	−4.87833			−0.591585
$69$	2.98329	+	4.72477i	0.359146	+	0.568795i
$70$	1.11324	−	3.42620i	0.133058	−	0.409510i
$71$	−13.6854	−	4.44667i	−1.62416	−	0.527722i	−0.651243	−	0.758869i	$-0.725752\pi$
$71$	−13.6854	−	4.44667i	−1.62416	−	0.527722i	−0.972919	+	0.231147i	$0.925752\pi$
$72$	−0.389612	+	2.97459i	−0.0459163	+	0.350559i
$73$	1.99203	−	0.647248i	0.233149	−	0.0757547i	−0.190112	−	0.981762i	$-0.560885\pi$
$73$	1.99203	−	0.647248i	0.233149	−	0.0757547i	0.423261	+	0.906008i	$0.360885\pi$
$74$	−7.39935	−	5.37594i	−0.860157	−	0.624941i
$75$	1.10710	−	1.33204i	0.127837	−	0.153811i
$76$	2.26635	−	6.97510i	0.259968	−	0.800099i
$77$	7.36095	−	5.34804i	0.838858	−	0.609466i
$78$	5.78140	−	6.95605i	0.654614	−	0.787617i
$79$	4.98751	+	1.62054i	0.561138	+	0.182325i	0.575833	−	0.817567i	$-0.304678\pi$
$79$	4.98751	+	1.62054i	0.561138	+	0.182325i	−0.0146950	+	0.999892i	$0.504678\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	−8.39795	+	3.23642i	−0.933106	+	0.359602i
$82$	−2.90076	−	8.92763i	−0.320336	−	0.985892i
$83$	3.06810	+	2.22910i	0.336767	+	0.244676i	0.743297	−	0.668962i	$-0.233261\pi$
$83$	3.06810	+	2.22910i	0.336767	+	0.244676i	−0.406529	+	0.913638i	$0.633261\pi$
$84$	−0.406041	+	6.22653i	−0.0443028	+	0.679370i
$85$	−4.63957	−	1.50749i	−0.503232	−	0.163510i
$86$	−2.94647	−	9.06829i	−0.317726	−	0.977859i
$87$	−11.0209	+	2.80283i	−1.18157	+	0.300495i
$88$			2.52563i			0.269233i
$89$	−1.84962	−	5.69255i	−0.196060	−	0.603410i	−0.999963	−	0.00864903i	$-0.997247\pi$
$89$	−1.84962	−	5.69255i	−0.196060	−	0.603410i	0.803903	−	0.594760i	$-0.202753\pi$
$90$	−1.28974	+	2.70861i	−0.135951	+	0.285512i
$91$	11.0579	−	15.2198i	1.15918	−	1.59547i
$92$	−3.22611			−0.336346
$93$	−9.44593	−	1.94277i	−0.979498	−	0.201456i
$94$	−11.6267			−1.19920
$95$	4.31085	−	5.93338i	0.442284	−	0.608752i
$96$	−1.33204	−	1.10710i	−0.135951	−	0.112993i
$97$	3.98379	+	12.2608i	0.404492	+	1.24490i	0.921318	+	0.388809i	$0.127113\pi$
$97$	3.98379	+	12.2608i	0.404492	+	1.24490i	−0.516826	+	0.856091i	$0.672887\pi$
$98$			5.97817i			0.603886i
$99$	−6.65631	+	3.61978i	−0.668984	+	0.363801i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	6.73937	+	2.18975i	0.670593	+	0.217889i	0.624472	−	0.781047i	$-0.285314\pi$
$101$	6.73937	+	2.18975i	0.670593	+	0.217889i	0.0461205	+	0.998936i	$0.485314\pi$
$102$	8.43161	+	0.549839i	0.834854	+	0.0544421i
$103$	−11.8781	−	8.62993i	−1.17038	−	0.850333i	−0.179328	−	0.983789i	$-0.557392\pi$
$103$	−11.8781	−	8.62993i	−1.17038	−	0.850333i	−0.991055	+	0.133457i	$0.957392\pi$
$104$	1.61372	+	4.96652i	0.158238	+	0.487007i
$105$	−2.31027	+	5.79631i	−0.225459	+	0.565661i
$106$	1.56313	+	2.15146i	0.151824	+	0.208968i
$107$	16.5893	+	5.39018i	1.60375	+	0.521089i	0.968030	−	0.250835i	$-0.0807050\pi$
$107$	16.5893	+	5.39018i	1.60375	+	0.521089i	0.635716	+	0.771923i	$0.280705\pi$
$108$	1.00867	−	5.09731i	0.0970589	−	0.490489i
$109$	7.28589	−	5.29351i	0.697862	−	0.507026i	−0.181374	−	0.983414i	$-0.558054\pi$
$109$	7.28589	−	5.29351i	0.697862	−	0.507026i	0.879235	+	0.476388i	$0.158054\pi$
$110$	−0.780462	+	2.40202i	−0.0744142	+	0.229023i
$111$	12.1830	+	10.1257i	1.15636	+	0.961085i
$112$	−2.91450	−	2.11751i	−0.275395	−	0.200086i
$113$	−7.92756	+	2.57582i	−0.745763	+	0.242313i	−0.657157	−	0.753754i	$-0.728241\pi$
$113$	−7.92756	+	2.57582i	−0.745763	+	0.242313i	−0.0886057	+	0.996067i	$0.528241\pi$
$114$	−4.70328	+	11.8002i	−0.440502	+	1.10519i
$115$	−3.06822	−	0.996924i	−0.286113	−	0.0929637i
$116$	2.02884	−	6.24414i	0.188373	−	0.579754i
$117$	−10.7765	+	11.3711i	−0.996285	+	1.05126i
$118$	2.96606			0.273048
$119$	17.5743			1.61103
$120$	−0.924732	−	1.46454i	−0.0844161	−	0.133693i
$121$	3.73863	−	2.71627i	0.339875	−	0.246934i
$122$	2.61595	+	1.90060i	0.236837	+	0.172072i
$123$	4.00739	+	15.7573i	0.361334	+	1.42079i
$124$	3.86007	−	4.01246i	0.346644	−	0.360330i
$125$			1.00000i			0.0894427i
$126$	1.40359	−	10.7160i	0.125042	−	0.954660i
$127$	−6.44644	−	8.87276i	−0.572029	−	0.787330i	0.420765	−	0.907170i	$-0.361762\pi$
$127$	−6.44644	−	8.87276i	−0.572029	−	0.787330i	−0.992793	+	0.119840i	$0.961762\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	4.07052	+	16.0056i	0.358390	+	1.40921i
$130$			5.22211i			0.458009i
$131$	−13.1889	+	4.28534i	−1.15232	+	0.374412i	−0.822017	−	0.569463i	$-0.807151\pi$
$131$	−13.1889	+	4.28534i	−1.15232	+	0.374412i	−0.330303	+	0.943875i	$0.607151\pi$
$132$	0.284664	−	4.36525i	0.0247769	−	0.379946i
$133$	−8.16457	+	25.1280i	−0.707958	+	2.17887i
$134$	−1.85642	+	2.55515i	−0.160370	+	0.220731i
$135$	2.53445	−	4.53614i	0.218131	−	0.390409i
$136$	−2.86741	+	3.94665i	−0.245879	+	0.338423i
$137$	−16.5231	+	12.0047i	−1.41166	+	1.02563i	−0.418583	+	0.908178i	$0.637473\pi$
$137$	−16.5231	+	12.0047i	−1.41166	+	1.02563i	−0.993078	+	0.117454i	$0.962527\pi$
$138$	5.57595	+	0.363616i	0.474656	+	0.0309531i
$139$	12.0315	+	16.5600i	1.02050	+	1.40460i	0.911851	+	0.410520i	$0.134653\pi$
$139$	12.0315	+	16.5600i	1.02050	+	1.40460i	0.108650	+	0.994080i	$0.465347\pi$
$140$	−2.11751	−	2.91450i	−0.178962	−	0.246320i
$141$	20.0954	+	1.31045i	1.69233	+	0.110360i
$142$	−11.6415	+	8.45806i	−0.976935	+	0.709785i
$143$	−7.75236	+	10.6702i	−0.648285	+	0.892288i
$144$	2.17749	+	2.06362i	0.181457	+	0.171969i
$145$	3.85909	−	5.31158i	0.320480	−	0.441103i
$146$	0.647248	−	1.99203i	0.0535667	−	0.164861i
$147$	0.673801	−	10.3325i	0.0555742	−	0.852214i
$148$	−8.69846	+	2.82630i	−0.715009	+	0.232321i
$149$			7.72992i			0.633260i	0.948549	+	0.316630i	$0.102551\pi$
$149$			7.72992i			0.633260i	−0.948549	+	0.316630i	$0.897449\pi$
$150$	−0.426905	−	1.67862i	−0.0348566	−	0.137058i
$151$	−14.5179	+	4.71714i	−1.18145	+	0.383876i	−0.832904	−	0.553417i	$-0.813324\pi$
$151$	−14.5179	+	4.71714i	−1.18145	+	0.383876i	−0.348543	+	0.937293i	$0.613324\pi$
$152$	−4.31085	−	5.93338i	−0.349656	−	0.481261i
$153$	−14.5111	−	1.90066i	−1.17315	−	0.153659i
$154$		−	9.09864i		−	0.733189i
$155$	4.91106	−	2.62325i	0.394466	−	0.210705i
$156$	−2.22934	−	8.76591i	−0.178490	−	0.701835i
$157$	−5.12084	−	3.72051i	−0.408688	−	0.296929i	0.364383	−	0.931249i	$-0.381280\pi$
$157$	−5.12084	−	3.72051i	−0.408688	−	0.296929i	−0.773070	+	0.634320i	$0.781280\pi$
$158$	4.24263	−	3.08245i	0.337525	−	0.245226i
$159$	−2.45918	−	3.89472i	−0.195026	−	0.308871i
$160$	1.00000			0.0790569
$161$	11.6222			0.915954
$162$	−2.31788	+	8.69640i	−0.182110	+	0.683254i
$163$	1.59199	−	4.89963i	0.124694	−	0.383768i	−0.869151	−	0.494546i	$-0.835334\pi$
$163$	1.59199	−	4.89963i	0.124694	−	0.383768i	0.993845	+	0.110778i	$0.0353342\pi$
$164$	−8.92763	−	2.90076i	−0.697131	−	0.226512i
$165$	1.61967	−	4.06363i	0.126091	−	0.316353i
$166$	3.60676	−	1.17191i	0.279939	−	0.0909577i
$167$	17.6092	+	12.7938i	1.36264	+	0.990014i	0.998272	+	0.0587575i	$0.0187139\pi$
$167$	17.6092	+	12.7938i	1.36264	+	0.990014i	0.364365	+	0.931256i	$0.381286\pi$
$168$	4.79870	+	3.98836i	0.370228	+	0.307708i
$169$	−4.40979	+	13.5719i	−0.339215	+	1.04400i
$170$	−3.94665	+	2.86741i	−0.302695	+	0.219920i
$171$	9.45905	−	19.8651i	0.723352	−	1.51912i
$172$	−9.06829	−	2.94647i	−0.691451	−	0.224666i
$173$	4.01211	+	5.52220i	0.305035	+	0.419845i	0.933825	−	0.357730i	$-0.116449\pi$
$173$	4.01211	+	5.52220i	0.305035	+	0.419845i	−0.628790	+	0.777576i	$0.716449\pi$
$174$	−4.21039	+	10.5636i	−0.319189	+	0.800822i
$175$	−1.11324	−	3.42620i	−0.0841531	−	0.258997i
$176$	2.04328	+	1.48453i	0.154018	+	0.111900i
$177$	−5.12648	−	0.334306i	−0.385330	−	0.0251279i
$178$	−5.69255	−	1.84962i	−0.426675	−	0.138635i
$179$	−0.973117	−	2.99495i	−0.0727342	−	0.223853i	0.908080	−	0.418796i	$-0.137548\pi$
$179$	−0.973117	−	2.99495i	−0.0727342	−	0.223853i	−0.980815	+	0.194943i	$0.937548\pi$
$180$	1.43322	+	2.63550i	0.106826	+	0.196439i
$181$		−	17.7543i		−	1.31967i	−0.751411	−	0.659834i	$-0.770626\pi$
$181$		−	17.7543i		−	1.31967i	0.751411	−	0.659834i	$-0.229374\pi$
$182$	−5.81346	−	17.8920i	−0.430922	−	1.32624i
$183$	−4.30714	−	3.57980i	−0.318393	−	0.264626i
$184$	−1.89626	+	2.60998i	−0.139794	+	0.192410i
$185$	−9.14610			−0.672435
$186$	−7.12391	+	6.49999i	−0.522351	+	0.476602i
$187$	−12.3209			−0.900991
$188$	−6.83401	+	9.40620i	−0.498421	+	0.686018i
$189$	−3.63374	+	18.3632i	−0.264316	+	1.33572i
$190$	−2.26635	−	6.97510i	−0.164418	−	0.506027i
$191$			20.0940i			1.45395i	0.686665	+	0.726974i	$0.259074\pi$
$191$			20.0940i			1.45395i	−0.686665	+	0.726974i	$0.740926\pi$
$192$	−1.67862	+	0.426905i	−0.121144	+	0.0308092i
$193$	−0.952181	−	2.93051i	−0.0685395	−	0.210943i	0.910920	−	0.412582i	$-0.135373\pi$
$193$	−0.952181	−	2.93051i	−0.0685395	−	0.210943i	−0.979460	+	0.201639i	$0.935373\pi$
$194$	12.2608	+	3.98379i	0.880277	+	0.286019i
$195$	0.588585	−	9.02578i	0.0421495	−	0.646350i
$196$	4.83644	+	3.51388i	0.345460	+	0.250991i
$197$	4.87074	+	14.9906i	0.347026	+	1.06803i	0.960490	+	0.278313i	$0.0897752\pi$
$197$	4.87074	+	14.9906i	0.347026	+	1.06803i	−0.613465	+	0.789722i	$0.710225\pi$
$198$	−0.984017	+	7.51272i	−0.0699310	+	0.533906i
$199$	−7.23121	−	9.95291i	−0.512607	−	0.705543i	0.471749	−	0.881733i	$-0.343623\pi$
$199$	−7.23121	−	9.95291i	−0.512607	−	0.705543i	−0.984356	+	0.176190i	$0.943623\pi$
$200$	0.951057	+	0.309017i	0.0672499	+	0.0218508i
$201$	3.49659	−	4.20702i	0.246631	−	0.296741i
$202$	5.73285	−	4.16516i	0.403362	−	0.293060i
$203$	−7.30896	+	22.4947i	−0.512988	+	1.57882i
$204$	5.40081	−	6.49813i	0.378132	−	0.454960i
$205$	−7.59430	−	5.51758i	−0.530409	−	0.385365i
$206$	−13.9635	+	4.53703i	−0.972885	+	0.316110i
$207$	−9.59638	−	1.25693i	−0.666994	−	0.0873630i
$208$	4.96652	+	1.61372i	0.344366	+	0.111891i
$209$	5.72396	−	17.6165i	0.395934	−	1.21856i
$210$	3.33137	+	5.27603i	0.229886	+	0.364081i
$211$	−25.1319			−1.73015			−0.865076	−	0.501640i	$-0.832730\pi$
$211$	−25.1319			−1.73015			−0.865076	+	0.501640i	$0.832730\pi$
$212$	2.65935			0.182645
$213$	21.0743	−	13.3066i	1.44399	−	0.911755i
$214$	14.1117	−	10.2527i	0.964655	−	0.700863i
$215$	−7.71395	−	5.60451i	−0.526087	−	0.382225i
$216$	−3.53093	−	3.81215i	−0.240250	−	0.259384i
$217$	−13.9060	+	14.4550i	−0.944000	+	0.981269i
$218$		−	9.00585i		−	0.609953i
$219$	−1.34321	+	3.37003i	−0.0907659	+	0.227725i
$220$	1.48453	+	2.04328i	0.100087	+	0.137758i
$221$	−24.2283	+	7.87226i	−1.62977	+	0.529546i
$222$	15.3528	−	3.90452i	1.03041	−	0.262054i
$223$		−	0.941387i		−	0.0630399i	−0.999503	−	0.0315200i	$-0.989965\pi$
$223$		−	0.941387i		−	0.0630399i	0.999503	−	0.0315200i	$-0.0100348\pi$
$224$	−3.42620	+	1.11324i	−0.228923	+	0.0743815i
$225$	0.548656	+	2.94940i	0.0365771	+	0.196627i
$226$	−2.57582	+	7.92756i	−0.171341	+	0.527334i
$227$	5.52910	−	7.61015i	0.366979	−	0.505104i	−0.585097	−	0.810963i	$-0.698944\pi$
$227$	5.52910	−	7.61015i	0.366979	−	0.505104i	0.952077	+	0.305859i	$0.0989437\pi$
$228$	6.78204	+	10.7410i	0.449151	+	0.711341i
$229$	10.0899	−	13.8876i	0.666762	−	0.917719i	−0.332919	−	0.942955i	$-0.608034\pi$
$229$	10.0899	−	13.8876i	0.666762	−	0.917719i	0.999682	+	0.0252359i	$0.00803368\pi$
$230$	−2.60998	+	1.89626i	−0.172097	+	0.125036i
$231$	−1.02551	+	15.7259i	−0.0674736	+	1.03469i
$232$	−3.85909	−	5.31158i	−0.253362	−	0.348722i
$233$	−2.27849	−	3.13607i	−0.149269	−	0.205451i	0.727834	−	0.685753i	$-0.240527\pi$
$233$	−2.27849	−	3.13607i	−0.149269	−	0.205451i	−0.877103	+	0.480302i	$0.840527\pi$
$234$	2.86514	+	15.4021i	0.187300	+	1.00687i
$235$	−9.40620	+	6.83401i	−0.613593	+	0.445801i
$236$	1.74341	−	2.39959i	0.113486	−	0.156200i
$237$	−7.68029	+	4.84945i	−0.498889	+	0.315006i
$238$	10.3299	−	14.2179i	0.669589	−	0.921610i
$239$	0.405238	−	1.24719i	0.0262127	−	0.0806743i	−0.937094	−	0.349076i	$-0.886495\pi$
$239$	0.405238	−	1.24719i	0.0262127	−	0.0806743i	0.963307	+	0.268402i	$0.0864955\pi$
$240$	−1.72838	−	0.112710i	−0.111566	−	0.00727542i
$241$	2.40774	−	0.782323i	0.155096	−	0.0503938i	−0.230440	−	0.973087i	$-0.574017\pi$
$241$	2.40774	−	0.782323i	0.155096	−	0.0503938i	0.385536	+	0.922693i	$0.374017\pi$
$242$		−	4.62120i		−	0.297062i
$243$	4.98635	−	14.7694i	0.319874	−	0.947460i
$244$	3.07523	−	0.999204i	0.196872	−	0.0639675i
$245$	3.51388	+	4.83644i	0.224494	+	0.308989i
$246$	15.1034	+	6.01986i	0.962957	+	0.383812i
$247$		−	38.2992i		−	2.43692i
$248$	−0.977259	−	5.48133i	−0.0620560	−	0.348065i
$249$	−6.36594	+	1.61898i	−0.403425	+	0.102599i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−8.37769	+	6.08675i	−0.528795	+	0.384192i	−0.819907	−	0.572497i	$-0.805975\pi$
$251$	−8.37769	+	6.08675i	−0.528795	+	0.384192i	0.291112	+	0.956689i	$0.405975\pi$
$252$	−7.84445	−	7.43425i	−0.494154	−	0.468314i
$253$	−8.14797			−0.512258
$254$	−10.9673			−0.688152
$255$	7.14450	−	4.51115i	0.447406	−	0.282499i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−11.0461	−	3.58911i	−0.689040	−	0.223883i	−0.0564910	−	0.998403i	$-0.517991\pi$
$257$	−11.0461	−	3.58911i	−0.689040	−	0.223883i	−0.632549	+	0.774521i	$0.717991\pi$
$258$	15.3414	+	6.11470i	0.955111	+	0.380685i
$259$	31.3364	−	10.1818i	1.94715	−	0.632667i
$260$	4.22477	+	3.06948i	0.262009	+	0.190361i
$261$	8.46778	−	17.7833i	0.524142	−	1.10076i
$262$	−4.28534	+	13.1889i	−0.264749	+	0.814813i
$263$	−0.125874	+	0.0914531i	−0.00776175	+	0.00563924i	−0.591659	−	0.806188i	$-0.701527\pi$
$263$	−0.125874	+	0.0914531i	−0.00776175	+	0.00563924i	0.583898	+	0.811827i	$0.301527\pi$
$264$	−3.36424	−	2.79613i	−0.207054	−	0.172090i
$265$	2.52919	+	0.821784i	0.155367	+	0.0504818i
$266$	15.5299	+	21.3751i	0.952202	+	1.31059i
$267$	9.63042	+	3.83846i	0.589372	+	0.234910i
$268$	0.975979	+	3.00375i	0.0596174	+	0.183483i
$269$	−7.69843	−	5.59324i	−0.469382	−	0.341026i	0.327819	−	0.944741i	$-0.393686\pi$
$269$	−7.69843	−	5.59324i	−0.469382	−	0.341026i	−0.797200	+	0.603715i	$0.793686\pi$
$270$	−2.18010	−	4.71669i	−0.132677	−	0.287049i
$271$	18.1390	+	5.89373i	1.10187	+	0.358019i	0.802821	−	0.596220i	$-0.203331\pi$
$271$	18.1390	+	5.89373i	1.10187	+	0.358019i	0.299047	+	0.954238i	$0.403331\pi$
$272$	1.50749	+	4.63957i	0.0914049	+	0.281315i
$273$	8.03125	+	31.5794i	0.486074	+	1.91127i
$274$			20.4236i			1.23384i
$275$	0.780462	+	2.40202i	0.0470637	+	0.144847i
$276$	3.57163	−	4.29731i	0.214987	−	0.258668i
$277$	−3.64207	+	5.01289i	−0.218831	+	0.301195i	−0.904292	−	0.426914i	$-0.859601\pi$
$277$	−3.64207	+	5.01289i	−0.218831	+	0.301195i	0.685461	+	0.728109i	$0.259601\pi$
$278$	20.4693			1.22767
$279$	13.0454	−	10.4315i	0.781010	−	0.624518i
$280$	−3.60252			−0.215292
$281$	−8.58490	+	11.8161i	−0.512132	+	0.704890i	−0.984277	−	0.176631i	$-0.943480\pi$
$281$	−8.58490	+	11.8161i	−0.512132	+	0.704890i	0.472145	+	0.881521i	$0.343480\pi$
$282$	12.8719	−	15.4872i	0.766512	−	0.922251i
$283$	3.97740	+	12.2412i	0.236432	+	0.727663i	0.996928	+	0.0783208i	$0.0249558\pi$
$283$	3.97740	+	12.2412i	0.236432	+	0.727663i	−0.760496	+	0.649343i	$0.775044\pi$
$284$			14.3897i			0.853873i
$285$	3.13095	+	12.3111i	0.185461	+	0.729245i
$286$	4.07566	+	12.5436i	0.240999	+	0.741717i
$287$	32.1620	+	10.4501i	1.89846	+	0.616848i
$288$	2.94940	−	0.548656i	0.173795	−	0.0323299i
$289$	−5.49981	−	3.99584i	−0.323518	−	0.235050i
$290$	−2.02884	−	6.24414i	−0.119138	−	0.366668i
$291$	−20.7424	−	8.26742i	−1.21594	−	0.484645i
$292$	−1.23114	−	1.69452i	−0.0720470	−	0.0991642i
$293$	14.0101	+	4.55215i	0.818477	+	0.265939i	0.688184	−	0.725536i	$-0.258408\pi$
$293$	14.0101	+	4.55215i	0.818477	+	0.265939i	0.130293	+	0.991476i	$0.458408\pi$
$294$	−7.96315	−	6.61843i	−0.464421	−	0.385995i
$295$	2.39959	−	1.74341i	0.139710	−	0.101505i
$296$	−2.82630	+	8.69846i	−0.164275	+	0.505588i
$297$	2.54752	−	12.8739i	0.147822	−	0.747021i
$298$	6.25364	+	4.54353i	0.362264	+	0.263200i
$299$	−16.0226	+	5.20604i	−0.926608	+	0.301073i
$300$	−1.60896	−	0.641293i	−0.0928932	−	0.0370250i
$301$	32.6687	+	10.6147i	1.88299	+	0.611822i
$302$	−4.71714	+	14.5179i	−0.271441	+	0.835410i
$303$	−10.3780	+	6.55283i	−0.596201	+	0.376450i
$304$	−7.33406			−0.420637
$305$	3.23349			0.185149
$306$	−10.0670	+	10.6225i	−0.575495	+	0.607248i
$307$	8.00163	−	5.81352i	0.456677	−	0.331795i	−0.335549	−	0.942023i	$-0.608922\pi$
$307$	8.00163	−	5.81352i	0.456677	−	0.331795i	0.792226	+	0.610227i	$0.208922\pi$
$308$	−7.36095	−	5.34804i	−0.419429	−	0.304733i
$309$	24.6456	−	6.26787i	1.40204	−	0.356567i
$310$	0.764395	−	5.51504i	0.0434147	−	0.313233i
$311$			14.8586i			0.842553i	0.906932	+	0.421277i	$0.138418\pi$
$311$			14.8586i			0.842553i	−0.906932	+	0.421277i	$0.861582\pi$
$312$	−8.40214	−	3.34890i	−0.475678	−	0.189594i
$313$	−7.69371	−	10.5895i	−0.434874	−	0.598553i	0.534189	−	0.845365i	$-0.320617\pi$
$313$	−7.69371	−	10.5895i	−0.434874	−	0.598553i	−0.969063	+	0.246812i	$0.920617\pi$
$314$	−6.01991	+	1.95599i	−0.339723	+	0.110383i
$315$	−5.16320	−	9.49446i	−0.290913	−	0.534952i
$316$		−	5.24417i		−	0.295008i
$317$	−1.84596	+	0.599789i	−0.103679	+	0.0336875i	−0.360397	−	0.932799i	$-0.617359\pi$
$317$	−1.84596	+	0.599789i	−0.103679	+	0.0336875i	0.256718	+	0.966486i	$0.417359\pi$
$318$	−4.59636	−	0.299736i	−0.257751	−	0.0168084i
$319$	5.12411	−	15.7704i	0.286895	−	0.882972i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	−25.5459	+	16.1301i	−1.42583	+	0.900294i
$322$	6.83133	−	9.40252i	0.380695	−	0.523982i
$323$	28.9450	−	21.0298i	1.61054	−	1.17013i
$324$	5.67312	+	6.98682i	0.315174	+	0.388157i
$325$	3.06948	+	4.22477i	0.170264	+	0.234348i
$326$	−3.02814	−	4.16787i	−0.167713	−	0.230837i
$327$	−1.01505	+	15.5655i	−0.0561325	+	0.860776i
$328$	−7.59430	+	5.51758i	−0.419325	+	0.304657i
$329$	24.6197	−	33.8861i	1.35733	−	1.86820i
$330$	−2.33553	−	3.69888i	−0.128567	−	0.203617i
$331$	16.0602	−	22.1050i	0.882748	−	1.21500i	−0.0929044	−	0.995675i	$-0.529615\pi$
$331$	16.0602	−	22.1050i	0.882748	−	1.21500i	0.975652	−	0.219323i	$-0.0703849\pi$
$332$	1.17191	−	3.60676i	0.0643168	−	0.197947i
$333$	−26.9755	+	5.01807i	−1.47825	+	0.274988i
$334$	20.7008	−	6.72610i	1.13270	−	0.368036i
$335$			3.15833i			0.172558i
$336$	6.04725	−	1.53793i	0.329905	−	0.0839012i
$337$	0.219987	−	0.0714781i	0.0119835	−	0.00389366i	−0.303019	−	0.952984i	$-0.597995\pi$
$337$	0.219987	−	0.0714781i	0.0119835	−	0.00389366i	0.315003	+	0.949091i	$0.397995\pi$
$338$	8.38792	+	11.5450i	0.456243	+	0.627964i
$339$	5.34552	−	13.4115i	0.290329	−	0.728414i
$340$			4.87833i			0.264565i
$341$	9.74910	−	10.1340i	0.527944	−	0.548787i
$342$	−10.5113	−	19.3289i	−0.568387	−	1.04519i
$343$	2.97813	+	2.16374i	0.160804	+	0.116831i
$344$	−7.71395	+	5.60451i	−0.415908	+	0.302175i
$345$	4.72477	−	2.98329i	0.254373	−	0.160615i
$346$	6.82582			0.366958
$347$	7.43086			0.398909			0.199455	−	0.979907i	$-0.436083\pi$
$347$	7.43086			0.398909			0.199455	+	0.979907i	$0.436083\pi$
$348$	6.07130	+	9.61539i	0.325456	+	0.515439i
$349$	−7.70147	+	23.7027i	−0.412250	+	1.26878i	0.502437	+	0.864614i	$0.332437\pi$
$349$	−7.70147	+	23.7027i	−0.412250	+	1.26878i	−0.914687	+	0.404162i	$0.867563\pi$
$350$	−3.42620	−	1.11324i	−0.183138	−	0.0595052i
$351$	−3.21608	−	26.9436i	−0.171661	−	1.43814i
$352$	2.40202	−	0.780462i	0.128028	−	0.0415988i
$353$	8.19201	+	5.95185i	0.436017	+	0.316785i	0.784050	−	0.620697i	$-0.213150\pi$
$353$	8.19201	+	5.95185i	0.436017	+	0.316785i	−0.348033	+	0.937482i	$0.613150\pi$
$354$	−3.28373	+	3.95091i	−0.174528	+	0.209988i
$355$	−4.44667	+	13.6854i	−0.236005	+	0.726347i
$356$	−4.84238	+	3.51819i	−0.256645	+	0.186464i
$357$	−19.4565	+	23.4097i	−1.02975	+	1.23897i
$358$	−2.99495	−	0.973117i	−0.158288	−	0.0514309i
$359$	−1.42856	−	1.96625i	−0.0753967	−	0.103775i	0.769653	−	0.638462i	$-0.220429\pi$
$359$	−1.42856	−	1.96625i	−0.0753967	−	0.103775i	−0.845050	+	0.534688i	$0.820429\pi$
$360$	2.97459	+	0.389612i	0.156775	+	0.0205344i
$361$	10.7502	+	33.0858i	0.565801	+	1.74136i
$362$	−14.3636	−	10.4357i	−0.754932	−	0.548490i
$363$	−0.520857	+	7.98718i	−0.0273379	+	0.419218i
$364$	−17.8920	−	5.81346i	−0.937795	−	0.304708i
$365$	−0.647248	−	1.99203i	−0.0338785	−	0.104267i
$366$	−5.42779	+	1.38039i	−0.283715	+	0.0721543i
$367$		−	13.6746i		−	0.713807i	−0.934141	−	0.356903i	$-0.883833\pi$
$367$		−	13.6746i		−	0.713807i	0.934141	−	0.356903i	$-0.116167\pi$
$368$	0.996924	+	3.06822i	0.0519683	+	0.159942i
$369$	−25.4259	−	12.1069i	−1.32362	−	0.630261i
$370$	−5.37594	+	7.39935i	−0.279482	+	0.384674i
$371$	−9.58036			−0.497387
$372$	1.07127	+	9.58396i	0.0555429	+	0.496905i
$373$	−17.7758			−0.920394			−0.460197	−	0.887817i	$-0.652221\pi$
$373$	−17.7758			−0.920394			−0.460197	+	0.887817i	$0.652221\pi$
$374$	−7.24202	+	9.96779i	−0.374476	+	0.515422i
$375$	−1.33204	−	1.10710i	−0.0687862	−	0.0571704i
$376$	3.59285	+	11.0577i	0.185287	+	0.570255i
$377$		−	34.2856i		−	1.76580i
$378$	12.7203	+	13.7334i	0.654260	+	0.706368i
$379$	7.95100	+	24.4707i	0.408415	+	1.25697i	0.918010	+	0.396558i	$0.129796\pi$
$379$	7.95100	+	24.4707i	0.408415	+	1.25697i	−0.509594	+	0.860415i	$0.670204\pi$
$380$	−6.97510	−	2.26635i	−0.357815	−	0.116261i
$381$	18.9557	+	1.23613i	0.971131	+	0.0633289i
$382$	16.2564	+	11.8109i	0.831748	+	0.604300i
$383$	−7.09569	−	21.8383i	−0.362573	−	1.11588i	−0.951487	−	0.307689i	$-0.900444\pi$
$383$	−7.09569	−	21.8383i	−0.362573	−	1.11588i	0.588914	−	0.808195i	$-0.299556\pi$
$384$	−0.641293	+	1.60896i	−0.0327258	+	0.0821068i
$385$	−5.34804	−	7.36095i	−0.272562	−	0.375149i
$386$	−2.93051	−	0.952181i	−0.149159	−	0.0484648i
$387$	−25.8265	−	12.2977i	−1.31283	−	0.625125i
$388$	10.4297	−	7.57762i	0.529488	−	0.384695i
$389$	3.37039	−	10.3730i	0.170885	−	0.525931i	−0.828536	−	0.559935i	$-0.810826\pi$
$389$	3.37039	−	10.3730i	0.170885	−	0.525931i	0.999422	+	0.0340042i	$0.0108260\pi$
$390$	−6.95605	−	5.78140i	−0.352233	−	0.292752i
$391$	−12.7324	−	9.25060i	−0.643903	−	0.467823i
$392$	5.68558	−	1.84736i	0.287165	−	0.0933055i
$393$	8.89321	−	22.3124i	0.448603	−	1.12551i
$394$	14.9906	+	4.87074i	0.755215	+	0.245384i
$395$	1.62054	−	4.98751i	0.0815382	−	0.250949i
$396$	5.49953	+	5.21195i	0.276362	+	0.261910i
$397$	15.8285			0.794409			0.397204	−	0.917730i	$-0.369980\pi$
$397$	15.8285			0.794409			0.397204	+	0.917730i	$0.369980\pi$
$398$	−12.3025			−0.616667
$399$	−24.4324	−	38.6947i	−1.22315	−	1.93716i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	16.3239	+	11.8600i	0.815178	+	0.592261i	0.915327	−	0.402711i	$-0.131932\pi$
$401$	16.3239	+	11.8600i	0.815178	+	0.592261i	−0.100150	+	0.994972i	$0.531932\pi$
$402$	−1.34831	−	5.30163i	−0.0672475	−	0.264421i
$403$	12.6961	−	26.1570i	0.632438	−	1.30297i
$404$		−	7.08619i		−	0.352551i
$405$	3.23642	+	8.39795i	0.160819	+	0.417298i
$406$	13.9025	+	19.1351i	0.689967	+	0.949659i
$407$	−21.9691	+	7.13819i	−1.08897	+	0.353827i
$408$	−2.08258	−	8.18885i	−0.103103	−	0.405408i
$409$		−	24.0606i		−	1.18972i	−0.803829	−	0.594860i	$-0.797208\pi$
$409$		−	24.0606i		−	1.18972i	0.803829	−	0.594860i	$-0.202792\pi$
$410$	−8.92763	+	2.90076i	−0.440904	+	0.143259i
$411$	2.30196	−	35.2998i	0.113547	−	1.74121i
$412$	−4.53703	+	13.9635i	−0.223523	+	0.687934i
$413$	−6.28066	+	8.64459i	−0.309051	+	0.425372i
$414$	−6.65749	+	7.02482i	−0.327198	+	0.345251i
$415$	2.22910	−	3.06810i	0.109422	−	0.150607i
$416$	4.22477	−	3.06948i	0.207136	−	0.150493i
$417$	−35.3787	−	2.30710i	−1.73250	−	0.112979i
$418$	−10.8876	−	14.9855i	−0.532531	−	0.732965i
$419$	6.11017	+	8.40992i	0.298501	+	0.410852i	0.931752	−	0.363095i	$-0.118280\pi$
$419$	6.11017	+	8.40992i	0.298501	+	0.410852i	−0.633251	+	0.773946i	$0.718280\pi$
$420$	6.22653	+	0.406041i	0.303823	+	0.0198128i
$421$	−19.0024	+	13.8061i	−0.926123	+	0.672868i	−0.945040	−	0.326954i	$-0.893978\pi$
$421$	−19.0024	+	13.8061i	−0.926123	+	0.672868i	0.0189177	+	0.999821i	$0.493978\pi$
$422$	−14.7722	+	20.3321i	−0.719098	+	0.989754i
$423$	−23.9932	+	25.3170i	−1.16659	+	1.23096i
$424$	1.56313	−	2.15146i	0.0759121	−	0.104484i
$425$	−1.50749	+	4.63957i	−0.0731239	+	0.225052i
$426$	1.62187	−	24.8709i	0.0785798	−	1.20500i
$427$	−11.0786	+	3.59965i	−0.536131	+	0.174199i
$428$		−	17.4430i		−	0.843139i
$429$	−5.63049	−	22.1394i	−0.271843	−	1.06890i
$430$	−9.06829	+	2.94647i	−0.437312	+	0.142091i
$431$	−14.4740	−	19.9218i	−0.697188	−	0.959597i	−0.999979	−	0.00654002i	$-0.997918\pi$
$431$	−14.4740	−	19.9218i	−0.697188	−	0.959597i	0.302790	−	0.953057i	$-0.402082\pi$
$432$	−5.15953	+	0.615858i	−0.248238	+	0.0296305i
$433$			10.2774i			0.493898i	0.969028	+	0.246949i	$0.0794280\pi$
$433$			10.2774i			0.493898i	−0.969028	+	0.246949i	$0.920572\pi$
$434$	3.52060	+	19.7466i	0.168994	+	0.947868i
$435$	2.80283	+	11.0209i	0.134386	+	0.528412i
$436$	−7.28589	−	5.29351i	−0.348931	−	0.253513i
$437$	19.1418	−	13.9073i	0.915674	−	0.665276i
$438$	1.93689	+	3.06753i	0.0925481	+	0.146572i
$439$	29.3863			1.40253			0.701267	−	0.712899i	$-0.252618\pi$
$439$	29.3863			1.40253			0.701267	+	0.712899i	$0.252618\pi$
$440$	2.52563			0.120405
$441$	13.0174	+	12.3367i	0.619876	+	0.587462i
$442$	−7.87226	+	24.2283i	−0.374445	+	1.15242i
$443$	6.79771	+	2.20871i	0.322969	+	0.104939i	0.466014	−	0.884777i	$-0.345689\pi$
$443$	6.79771	+	2.20871i	0.322969	+	0.104939i	−0.143045	+	0.989716i	$0.545689\pi$
$444$	5.86533	−	14.7157i	0.278356	−	0.698376i
$445$	−5.69255	+	1.84962i	−0.269853	+	0.0876805i
$446$	−0.761598	−	0.553333i	−0.0360627	−	0.0262011i
$447$	−10.2966	−	8.55780i	−0.487011	−	0.404770i
$448$	−1.11324	+	3.42620i	−0.0525957	+	0.161873i
$449$	9.73818	−	7.07520i	0.459573	−	0.333899i	−0.333791	−	0.942647i	$-0.608328\pi$
$449$	9.73818	−	7.07520i	0.459573	−	0.333899i	0.793364	+	0.608748i	$0.208328\pi$
$450$	2.70861	+	1.28974i	0.127685	+	0.0607991i
$451$	−22.5479	−	7.32625i	−1.06174	−	0.344980i
$452$	4.89950	+	6.74359i	0.230453	+	0.317192i
$453$	9.78933	−	24.5607i	0.459943	−	1.15396i
$454$	−2.90682	−	8.94627i	−0.136424	−	0.419869i
$455$	−15.2198	−	11.0579i	−0.713517	−	0.518400i
$456$	12.6760	+	0.826624i	0.593610	+	0.0387102i
$457$	−3.74313	−	1.21622i	−0.175096	−	0.0568922i	0.220157	−	0.975464i	$-0.429343\pi$
$457$	−3.74313	−	1.21622i	−0.175096	−	0.0568922i	−0.395253	+	0.918572i	$0.629343\pi$
$458$	−5.30460	−	16.3259i	−0.247868	−	0.762858i
$459$	18.5970	−	17.2251i	0.868031	−	0.803997i
$460$			3.22611i			0.150418i
$461$	−1.58409	−	4.87532i	−0.0737784	−	0.227066i	0.907366	−	0.420340i	$-0.138089\pi$
$461$	−1.58409	−	4.87532i	−0.0737784	−	0.227066i	−0.981145	+	0.193274i	$0.938089\pi$
$462$	12.1197	+	10.0731i	0.563861	+	0.468643i
$463$	−24.5401	+	33.7765i	−1.14047	+	1.56973i	−0.374026	+	0.927418i	$0.622023\pi$
$463$	−24.5401	+	33.7765i	−1.14047	+	1.56973i	−0.766446	+	0.642308i	$0.777977\pi$
$464$	−6.56548			−0.304795
$465$	−1.94277	+	9.44593i	−0.0900937	+	0.438045i
$466$	−3.87640			−0.179571
$467$	−2.33079	+	3.20806i	−0.107856	+	0.148451i	−0.859533	−	0.511081i	$-0.829245\pi$
$467$	−2.33079	+	3.20806i	−0.107856	+	0.148451i	0.751677	+	0.659532i	$0.229245\pi$
$468$	14.1446	+	6.73517i	0.653836	+	0.311334i
$469$	−3.51599	−	10.8211i	−0.162353	−	0.499672i
$470$			11.6267i			0.536300i
$471$	10.6252	−	2.70218i	0.489581	−	0.124510i
$472$	−0.916563	−	2.82089i	−0.0421882	−	0.129842i
$473$	−22.9031	−	7.44168i	−1.05309	−	0.342169i
$474$	−0.591073	+	9.06393i	−0.0271489	+	0.416320i
$475$	−5.93338	−	4.31085i	−0.272242	−	0.197795i
$476$	−5.43076	−	16.7142i	−0.248918	−	0.766092i
$477$	7.91048	+	1.03611i	0.362196	+	0.0474404i
$478$	−0.770809	−	1.06093i	−0.0352560	−	0.0485257i
$479$	9.73097	+	3.16178i	0.444619	+	0.144466i	0.522766	−	0.852476i	$-0.324900\pi$
$479$	9.73097	+	3.16178i	0.444619	+	0.144466i	−0.0781466	+	0.996942i	$0.524900\pi$
$480$	−1.10710	+	1.33204i	−0.0505320	+	0.0607990i
$481$	−38.6402	+	28.0737i	−1.76184	+	1.28005i
$482$	0.782323	−	2.40774i	0.0356338	−	0.109670i
$483$	−12.8669	+	15.4812i	−0.585464	+	0.704417i
$484$	−3.73863	−	2.71627i	−0.169938	−	0.123467i
$485$	12.2608	−	3.98379i	0.556736	−	0.180895i
$486$	−9.01783	−	12.7153i	−0.409057	−	0.576778i
$487$	−7.67274	−	2.49302i	−0.347685	−	0.112970i	0.129968	−	0.991518i	$-0.458512\pi$
$487$	−7.67274	−	2.49302i	−0.347685	−	0.112970i	−0.477653	+	0.878548i	$0.658512\pi$
$488$	0.999204	−	3.07523i	0.0452318	−	0.139209i
$489$	4.76401	+	7.54497i	0.215436	+	0.341195i
$490$	5.97817			0.270066
$491$	13.4302			0.606097			0.303049	−	0.952975i	$-0.401995\pi$
$491$	13.4302			0.606097			0.303049	+	0.952975i	$0.401995\pi$
$492$	13.7477	−	8.68052i	0.619795	−	0.391348i
$493$	25.9117	−	18.8259i	1.16700	−	0.847877i
$494$	−30.9847	−	22.5117i	−1.39407	−	1.01285i
$495$	3.61978	+	6.65631i	0.162697	+	0.299179i
$496$	−5.00891	−	2.43123i	−0.224907	−	0.109165i
$497$		−	51.8393i		−	2.32531i
$498$	−2.43202	+	6.10177i	−0.108982	+	0.273427i
$499$	1.35042	+	1.85870i	0.0604532	+	0.0832067i	0.838173	−	0.545404i	$-0.183624\pi$
$499$	1.35042	+	1.85870i	0.0604532	+	0.0832067i	−0.777720	+	0.628611i	$0.783624\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	−36.5369	+	9.29206i	−1.63235	+	0.415138i
$502$			10.3554i			0.462184i
$503$	1.60486	−	0.521451i	0.0715573	−	0.0232504i	−0.273020	−	0.962008i	$-0.588022\pi$
$503$	1.60486	−	0.521451i	0.0715573	−	0.0232504i	0.344577	+	0.938758i	$0.388022\pi$
$504$	−10.6253	+	1.97655i	−0.473288	+	0.0880424i
$505$	2.18975	−	6.73937i	0.0974428	−	0.299898i
$506$	−4.78926	+	6.59185i	−0.212908	+	0.293043i
$507$	−13.1963	−	20.8995i	−0.586067	−	0.928180i
$508$	−6.44644	+	8.87276i	−0.286014	+	0.393665i
$509$	19.8620	−	14.4306i	0.880368	−	0.639625i	−0.0529809	−	0.998596i	$-0.516872\pi$
$509$	19.8620	−	14.4306i	0.880368	−	0.639625i	0.933349	+	0.358971i	$0.116872\pi$
$510$	0.549839	−	8.43161i	0.0243473	−	0.373358i
$511$	4.43521	+	6.10454i	0.196202	+	0.270049i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	15.9890	+	34.5925i	0.705930	+	1.52730i
$514$	−9.39642	+	6.82690i	−0.414458	+	0.301121i
$515$	−8.62993	+	11.8781i	−0.380280	+	0.523411i
$516$	13.9643	−	8.81728i	0.614745	−	0.388159i
$517$	−17.2602	+	23.7566i	−0.759101	+	1.04481i
$518$	10.1818	−	31.3364i	0.447363	−	1.37684i
$519$	−11.7976	−	0.769340i	−0.517857	−	0.0337703i
$520$	4.96652	−	1.61372i	0.217796	−	0.0707663i
$521$			10.7064i			0.469056i	0.972109	+	0.234528i	$0.0753544\pi$
$521$			10.7064i			0.469056i	−0.972109	+	0.234528i	$0.924646\pi$
$522$	−9.40976	−	17.3033i	−0.411854	−	0.757347i
$523$	18.9636	−	6.16163i	0.829218	−	0.269429i	0.136502	−	0.990640i	$-0.456414\pi$
$523$	18.9636	−	6.16163i	0.829218	−	0.269429i	0.692716	+	0.721210i	$0.256414\pi$
$524$	8.15119	+	11.2192i	0.356087	+	0.490111i
$525$	5.79631	+	2.31027i	0.252971	+	0.100828i
$526$			0.155589i			0.00678402i
$527$	26.7397	−	4.76739i	1.16480	−	0.207671i
$528$	−4.23956	+	1.07820i	−0.184503	+	0.0469228i
$529$	10.1873	+	7.40150i	0.442926	+	0.321804i
$530$	2.15146	−	1.56313i	0.0934533	−	0.0678978i
$531$	6.12084	−	6.45856i	0.265622	−	0.280278i
$532$	26.4211			1.14550
$533$	−49.0203			−2.12330
$534$	8.76600	−	5.53499i	0.379342	−	0.239522i
$535$	5.39018	−	16.5893i	0.233038	−	0.717217i
$536$	3.00375	+	0.975979i	0.129742	+	0.0421559i
$537$	5.06673	+	2.01948i	0.218645	+	0.0871469i
$538$	−9.05005	+	2.94054i	−0.390175	+	0.126776i
$539$	12.2151	+	8.87476i	0.526140	+	0.382263i
$540$	−5.09731	−	1.00867i	−0.219353	−	0.0434061i
$541$	−0.129646	+	0.399009i	−0.00557392	+	0.0171547i	−0.953805	−	0.300427i	$-0.902871\pi$
$541$	−0.129646	+	0.399009i	−0.00557392	+	0.0171547i	0.948231	+	0.317582i	$0.102871\pi$
$542$	15.4300	−	11.2105i	0.662775	−	0.481534i
$543$	23.6495	+	19.6558i	1.01490	+	0.843512i
$544$	4.63957	+	1.50749i	0.198920	+	0.0646330i
$545$	−5.29351	−	7.28589i	−0.226749	−	0.312093i
$546$	30.2689	+	12.0645i	1.29539	+	0.516312i
$547$	0.957076	+	2.94558i	0.0409216	+	0.125944i	0.969430	−	0.245367i	$-0.0789084\pi$
$547$	0.957076	+	2.94558i	0.0409216	+	0.125944i	−0.928509	+	0.371311i	$0.878908\pi$
$548$	16.5231	+	12.0047i	0.705831	+	0.512816i
$549$	9.53687	−	1.77408i	0.407024	−	0.0757157i
$550$	2.40202	+	0.780462i	0.102422	+	0.0332790i
$551$	14.8797	+	45.7949i	0.633895	+	1.95093i
$552$	−1.37724	−	5.41541i	−0.0586194	−	0.230495i
$553$			18.8923i			0.803381i
$554$	1.91475	+	5.89300i	0.0813500	+	0.250370i
$555$	10.1257	−	12.1830i	0.429810	−	0.517138i
$556$	12.0315	−	16.5600i	0.510251	−	0.702300i
$557$	20.2783			0.859218			0.429609	−	0.903015i	$-0.358651\pi$
$557$	20.2783			0.859218			0.429609	+	0.903015i	$0.358651\pi$
$558$	−0.771353	−	16.6855i	−0.0326540	−	0.706352i
$559$	−49.7926			−2.10600
$560$	−2.11751	+	2.91450i	−0.0894811	+	0.123160i
$561$	13.6404	−	16.4119i	0.575900	−	0.692910i
$562$	4.51335	+	13.8907i	0.190384	+	0.585942i
$563$		−	7.84526i		−	0.330638i	−0.986240	−	0.165319i	$-0.947135\pi$
$563$		−	7.84526i		−	0.330638i	0.986240	−	0.165319i	$-0.0528654\pi$
$564$	−4.96350	−	19.5168i	−0.209001	−	0.821805i
$565$	2.57582	+	7.92756i	0.108366	+	0.333515i
$566$	12.2412	+	3.97740i	0.514536	+	0.167183i
$567$	−20.4376	−	25.1702i	−0.858297	−	1.05705i
$568$	11.6415	+	8.45806i	0.488468	+	0.354892i
$569$	−3.22418	−	9.92299i	−0.135165	−	0.415994i	0.860451	−	0.509533i	$-0.170182\pi$
$569$	−3.22418	−	9.92299i	−0.135165	−	0.415994i	−0.995616	+	0.0935395i	$0.970182\pi$
$570$	11.8002	+	4.70328i	0.494255	+	0.196999i
$571$	24.1540	+	33.2451i	1.01081	+	1.39126i	0.918450	+	0.395537i	$0.129441\pi$
$571$	24.1540	+	33.2451i	1.01081	+	1.39126i	0.0923613	+	0.995726i	$0.470559\pi$
$572$	12.5436	+	4.07566i	0.524473	+	0.170412i
$573$	−26.7660	−	22.2460i	−1.11816	−	0.929342i
$574$	27.3586	−	19.8772i	1.14193	−	0.829659i
$575$	−0.996924	+	3.06822i	−0.0415746	+	0.127954i
$576$	1.28974	−	2.70861i	0.0537393	−	0.112859i
$577$	20.3564	+	14.7898i	0.847448	+	0.615707i	0.924441	−	0.381325i	$-0.124532\pi$
$577$	20.3564	+	14.7898i	0.847448	+	0.615707i	−0.0769934	+	0.997032i	$0.524532\pi$
$578$	−6.46541	+	2.10074i	−0.268926	+	0.0873792i
$579$	4.95772	+	1.97603i	0.206036	+	0.0821210i
$580$	−6.24414	−	2.02884i	−0.259274	−	0.0842432i
$581$	−4.22183	+	12.9934i	−0.175151	+	0.539059i
$582$	−18.8805	+	11.9215i	−0.782624	+	0.494161i
$583$	6.71653			0.278170
$584$	−2.09454			−0.0866727
$585$	11.3711	+	10.7765i	0.470136	+	0.445552i
$586$	11.9177	−	8.65869i	0.492314	−	0.357687i
$587$	−24.5217	−	17.8160i	−1.01212	−	0.735347i	−0.0474660	−	0.998873i	$-0.515115\pi$
$587$	−24.5217	−	17.8160i	−1.01212	−	0.735347i	−0.964652	+	0.263526i	$0.915115\pi$
$588$	−10.0350	+	2.55211i	−0.413838	+	0.105247i
$589$	−5.60612	+	40.4477i	−0.230996	+	1.66662i
$590$		−	2.96606i		−	0.122111i
$591$	−25.3604	−	10.1081i	−1.04319	−	0.415791i
$592$	5.37594	+	7.39935i	0.220950	+	0.304112i
$593$	21.1130	−	6.86004i	0.867008	−	0.281708i	0.158456	−	0.987366i	$-0.449349\pi$
$593$	21.1130	−	6.86004i	0.867008	−	0.281708i	0.708553	+	0.705658i	$0.249349\pi$
$594$	−8.91783	−	9.62808i	−0.365903	−	0.395045i
$595$		−	17.5743i		−	0.720476i
$596$	7.35159	−	2.38868i	0.301133	−	0.0978440i
$597$	21.2633	+	1.38662i	0.870251	+	0.0567504i
$598$	−5.20604	+	16.0226i	−0.212891	+	0.655211i
$599$	−12.1947	+	16.7845i	−0.498261	+	0.685797i	−0.981885	−	0.189479i	$-0.939320\pi$
$599$	−12.1947	+	16.7845i	−0.498261	+	0.685797i	0.483624	+	0.875276i	$0.339320\pi$
$600$	−1.46454	+	0.924732i	−0.0597895	+	0.0377520i
$601$	20.3647	−	28.0296i	0.830693	−	1.14335i	−0.157100	−	0.987583i	$-0.550215\pi$
$601$	20.3647	−	28.0296i	0.830693	−	1.14335i	0.987794	−	0.155768i	$-0.0497854\pi$
$602$	27.7897	−	20.1904i	1.13262	−	0.822899i
$603$	1.73284	+	9.31520i	0.0705667	+	0.379344i
$604$	8.97254	+	12.3496i	0.365087	+	0.502500i
$605$	−2.71627	−	3.73863i	−0.110432	−	0.151997i
$606$	−0.798687	+	12.2476i	−0.0324445	+	0.497526i
$607$	−1.98934	+	1.44534i	−0.0807449	+	0.0586646i	−0.627425	−	0.778677i	$-0.715891\pi$
$607$	−1.98934	+	1.44534i	−0.0807449	+	0.0586646i	0.546680	+	0.837341i	$0.315891\pi$
$608$	−4.31085	+	5.93338i	−0.174828	+	0.240630i
$609$	−21.8720	−	34.6397i	−0.886298	−	1.40367i
$610$	1.90060	−	2.61595i	0.0769530	−	0.105917i
$611$	−18.7622	+	57.7442i	−0.759039	+	2.33608i
$612$	2.67653	+	14.3882i	0.108192	+	0.581607i
$613$	−14.4267	+	4.68752i	−0.582689	+	0.189327i	−0.585505	−	0.810669i	$-0.699104\pi$
$613$	−14.4267	+	4.68752i	−0.582689	+	0.189327i	0.00281562	+	0.999996i	$0.499104\pi$
$614$		−	9.89056i		−	0.399150i
$615$	15.7573	−	4.00739i	0.635395	−	0.161593i
$616$	−8.65332	+	2.81163i	−0.348652	+	0.113284i
$617$	−24.1950	−	33.3016i	−0.974055	−	1.34067i	−0.939971	−	0.341253i	$-0.889149\pi$
$617$	−24.1950	−	33.3016i	−0.974055	−	1.34067i	−0.0340840	−	0.999419i	$-0.510851\pi$
$618$	9.41554	−	23.6229i	0.378748	−	0.950253i
$619$			15.5870i			0.626494i	0.949672	+	0.313247i	$0.101417\pi$
$619$			15.5870i			0.626494i	−0.949672	+	0.313247i	$0.898583\pi$
$620$	−4.01246	−	3.86007i	−0.161144	−	0.155024i
$621$	12.2984	−	11.3912i	0.493519	−	0.457113i
$622$	12.0208	+	8.73366i	0.481992	+	0.350188i
$623$	17.4448	−	12.6744i	0.698910	−	0.507788i
$624$	−7.64797	+	4.82905i	−0.306164	+	0.193317i
$625$	1.00000			0.0400000
$626$	−13.0893			−0.523154
$627$	17.1289	+	27.1278i	0.684063	+	1.08338i
$628$	−1.95599	+	6.01991i	−0.0780524	+	0.240221i
$629$	−42.4340	−	13.7876i	−1.69195	−	0.549749i
$630$	−10.7160	−	1.40359i	−0.426937	−	0.0559203i
$631$	8.73356	−	2.83770i	0.347677	−	0.112967i	−0.129972	−	0.991518i	$-0.541489\pi$
$631$	8.73356	−	2.83770i	0.347677	−	0.112967i	0.477650	+	0.878550i	$0.341489\pi$
$632$	−4.24263	−	3.08245i	−0.168763	−	0.122613i
$633$	27.8236	−	33.4767i	1.10589	−	1.33058i
$634$	−0.599789	+	1.84596i	−0.0238207	+	0.0733124i
$635$	−8.87276	+	6.44644i	−0.352105	+	0.255819i
$636$	−2.94417	+	3.54235i	−0.116744	+	0.140464i
$637$	29.6907	+	9.64709i	1.17639	+	0.382231i
$638$	−9.74663	−	13.4151i	−0.385873	−	0.531108i
$639$	−5.60641	+	42.8035i	−0.221786	+	1.69328i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−25.4904	−	18.5199i	−1.00681	−	0.731492i	−0.0432741	−	0.999063i	$-0.513779\pi$
$641$	−25.4904	−	18.5199i	−1.00681	−	0.731492i	−0.963538	+	0.267571i	$0.913779\pi$
$642$	−1.96601	+	30.1481i	−0.0775921	+	1.18985i
$643$	5.23733	+	1.70171i	0.206540	+	0.0671090i	0.410460	−	0.911879i	$-0.365368\pi$
$643$	5.23733	+	1.70171i	0.206540	+	0.0671090i	−0.203920	+	0.978988i	$0.565368\pi$
$644$	−3.59144	−	11.0533i	−0.141523	−	0.435562i
$645$	16.0056	−	4.07052i	0.630218	−	0.160277i
$646$		−	35.7780i		−	1.40767i
$647$	1.36654	+	4.20578i	0.0537242	+	0.165346i	0.974319	−	0.225174i	$-0.0722951\pi$
$647$	1.36654	+	4.20578i	0.0537242	+	0.165346i	−0.920594	+	0.390520i	$0.872295\pi$
$648$	8.98704	−	0.482905i	0.353044	−	0.0189703i
$649$	4.40320	−	6.06048i	0.172841	−	0.237895i
$650$	5.22211			0.204828
$651$	−3.85928	−	34.5264i	−0.151257	−	1.35320i
$652$	−5.15177			−0.201759
$653$	−22.2370	+	30.6066i	−0.870201	+	1.19773i	0.108838	+	0.994059i	$0.465287\pi$
$653$	−22.2370	+	30.6066i	−0.870201	+	1.19773i	−0.979040	+	0.203670i	$0.934713\pi$
$654$	11.9961	+	9.97039i	0.469087	+	0.389873i
$655$	4.28534	+	13.1889i	0.167442	+	0.515333i
$656$			9.38707i			0.366504i
$657$	−3.00193	−	5.52017i	−0.117117	−	0.215362i
$658$	−12.9433	−	39.8354i	−0.504583	−	1.55295i
$659$	21.9362	+	7.12749i	0.854512	+	0.277648i	0.703335	−	0.710859i	$-0.251694\pi$
$659$	21.9362	+	7.12749i	0.854512	+	0.277648i	0.151177	+	0.988507i	$0.451694\pi$
$660$	−4.36525	−	0.284664i	−0.169917	−	0.0110806i
$661$	−29.0871	−	21.1330i	−1.13136	−	0.821979i	−0.145465	−	0.989363i	$-0.546468\pi$
$661$	−29.0871	−	21.1330i	−1.13136	−	0.821979i	−0.985892	+	0.167384i	$0.946468\pi$
$662$	−8.44334	−	25.9859i	−0.328160	−	1.00997i
$663$	16.3370	−	40.9885i	0.634478	−	1.59186i
$664$	−2.22910	−	3.06810i	−0.0865059	−	0.119065i
$665$	25.1280	+	8.16457i	0.974421	+	0.316609i
$666$	−11.7961	+	24.7732i	−0.457091	+	0.959943i
$667$	17.1358	−	12.4499i	0.663500	−	0.482061i
$668$	6.72610	−	20.7008i	0.260241	−	0.800938i
$669$	1.25396	+	1.04221i	0.0484810	+	0.0402942i
$670$	2.55515	+	1.85642i	0.0987139	+	0.0717198i
$671$	7.76690	−	2.52362i	0.299838	−	0.0974232i
$672$	2.31027	−	5.79631i	0.0891206	−	0.223597i
$673$	−13.3751	−	4.34583i	−0.515572	−	0.167520i	0.0396627	−	0.999213i	$-0.487372\pi$
$673$	−13.3751	−	4.34583i	−0.515572	−	0.167520i	−0.555235	+	0.831694i	$0.687372\pi$
$674$	0.0714781	−	0.219987i	0.00275323	−	0.00847358i
$675$	−4.53614	−	2.53445i	−0.174596	−	0.0975512i
$676$	14.2704			0.548861
$677$	−9.96267			−0.382896			−0.191448	−	0.981503i	$-0.561318\pi$
$677$	−9.96267			−0.382896			−0.191448	+	0.981503i	$0.561318\pi$
$678$	−7.70813	−	12.2077i	−0.296029	−	0.468834i
$679$	−37.5732	+	27.2985i	−1.44193	+	1.04762i
$680$	3.94665	+	2.86741i	0.151347	+	0.109960i
$681$	4.01575	+	15.7902i	0.153884	+	0.605081i
$682$	−2.46819	−	13.8438i	−0.0945120	−	0.530107i
$683$			11.7724i			0.450457i	0.974306	+	0.225229i	$0.0723129\pi$
$683$			11.7724i			0.450457i	−0.974306	+	0.225229i	$0.927687\pi$
$684$	−21.8158	−	2.85744i	−0.834149	−	0.109257i
$685$	12.0047	+	16.5231i	0.458677	+	0.631314i
$686$	3.50100	−	1.13754i	0.133669	−	0.0434317i
$687$	7.32826	+	28.8152i	0.279591	+	1.09937i
$688$			9.53497i			0.363517i
$689$	13.2077	−	4.29144i	0.503173	−	0.163491i
$690$	0.363616	−	5.57595i	0.0138426	−	0.212273i
$691$	1.15975	−	3.56935i	0.0441191	−	0.135785i	−0.926571	−	0.376121i	$-0.877258\pi$
$691$	1.15975	−	3.56935i	0.0441191	−	0.135785i	0.970690	+	0.240336i	$0.0772577\pi$
$692$	4.01211	−	5.52220i	0.152518	−	0.209923i
$693$	−19.8122	−	18.7762i	−0.752602	−	0.713248i
$694$	4.36775	−	6.01169i	0.165798	−	0.228201i
$695$	16.5600	−	12.0315i	0.628156	−	0.456382i
$696$	11.3476	+	0.739997i	0.430131	+	0.0280495i
$697$	−26.9166	−	37.0475i	−1.01954	−	1.40327i
$698$	14.6491	+	20.1627i	0.554476	+	0.763170i
$699$	6.69988	+	0.436910i	0.253413	+	0.0165255i
$700$	−2.91450	+	2.11751i	−0.110158	+	0.0800343i
$701$	−3.29124	+	4.53000i	−0.124308	+	0.171096i	−0.866635	−	0.498942i	$-0.833722\pi$
$701$	−3.29124	+	4.53000i	−0.124308	+	0.171096i	0.742327	+	0.670038i	$0.233722\pi$
$702$	−23.6882	−	13.2352i	−0.894053	−	0.499530i
$703$	39.4275	−	54.2673i	1.48704	−	2.04673i
$704$	0.780462	−	2.40202i	0.0294148	−	0.0905294i
$705$	1.31045	−	20.0954i	0.0493544	−	0.756835i
$706$	9.63029	−	3.12907i	0.362441	−	0.117764i
$707$			25.5282i			0.960086i
$708$	1.26623	+	4.97888i	0.0475877	+	0.187118i
$709$	−29.4812	+	9.57901i	−1.10719	+	0.359747i	−0.804865	−	0.593458i	$-0.797762\pi$
$709$	−29.4812	+	9.57901i	−1.10719	+	0.359747i	−0.302324	+	0.953205i	$0.597762\pi$
$710$	8.45806	+	11.6415i	0.317425	+	0.436899i
$711$	2.04320	−	15.5993i	0.0766258	−	0.585019i
$712$			5.98551i			0.224316i
$713$	17.6834	−	3.15275i	0.662248	−	0.118071i
$714$	7.50256	+	29.5005i	0.280776	+	1.10403i
$715$	10.6702	+	7.75236i	0.399043	+	0.289922i
$716$	−2.54765	+	1.85098i	−0.0952103	+	0.0691743i
$717$	1.21267	+	1.92056i	0.0452881	+	0.0717247i
$718$	−2.43042			−0.0907024
$719$	32.3176			1.20524			0.602621	−	0.798028i	$-0.294123\pi$
$719$	32.3176			1.20524			0.602621	+	0.798028i	$0.294123\pi$
$720$	2.06362	−	2.17749i	0.0769068	−	0.0811502i
$721$	16.3447	−	50.3039i	0.608710	−	1.87342i
$722$	33.0858	+	10.7502i	1.23132	+	0.400082i
$723$	−1.62353	+	4.07332i	−0.0603796	+	0.151488i
$724$	−16.8854	+	5.48639i	−0.627540	+	0.203900i
$725$	−5.31158	−	3.85909i	−0.197267	−	0.143323i
$726$	6.15562	+	5.11613i	0.228456	+	0.189877i
$727$	6.71844	−	20.6772i	0.249173	−	0.766876i	−0.745749	−	0.666227i	$-0.767908\pi$
$727$	6.71844	−	20.6772i	0.249173	−	0.766876i	0.994922	−	0.100649i	$-0.0320919\pi$
$728$	−15.2198	+	11.0579i	−0.564085	+	0.409831i
$729$	14.1531	+	22.9933i	0.524188	+	0.851602i
$730$	−1.99203	−	0.647248i	−0.0737282	−	0.0239557i
$731$	−27.3407	−	37.6312i	−1.01123	−	1.39184i
$732$	−2.07361	+	5.20255i	−0.0766430	+	0.192292i
$733$	3.75379	+	11.5530i	0.138650	+	0.426719i	0.996140	−	0.0877808i	$-0.0279775\pi$
$733$	3.75379	+	11.5530i	0.138650	+	0.426719i	−0.857490	+	0.514500i	$0.827978\pi$
$734$	−11.0630	−	8.03771i	−0.408341	−	0.296677i
$735$	−10.3325	−	0.673801i	−0.381122	−	0.0248535i
$736$	3.06822	+	0.996924i	0.113096	+	0.0367471i
$737$	2.46496	+	7.58637i	0.0907980	+	0.279448i
$738$	−24.7397	+	13.4537i	−0.910680	+	0.495238i
$739$			20.6589i			0.759949i	0.924997	+	0.379975i	$0.124067\pi$
$739$			20.6589i			0.759949i	−0.924997	+	0.379975i	$0.875933\pi$
$740$	2.82630	+	8.69846i	0.103897	+	0.319762i
$741$	51.0161	+	42.4011i	1.87412	+	1.55764i
$742$	−5.63119	+	7.75067i	−0.206728	+	0.284536i
$743$	−21.8022			−0.799846			−0.399923	−	0.916549i	$-0.630963\pi$
$743$	−21.8022			−0.799846			−0.399923	+	0.916549i	$0.630963\pi$
$744$	8.38327	+	4.76664i	0.307346	+	0.174753i
$745$	7.72992			0.283202
$746$	−10.4483	+	14.3809i	−0.382540	+	0.526522i
$747$	4.89119	−	10.2721i	0.178959	−	0.375835i
$748$	3.80736	+	11.7178i	0.139211	+	0.428446i
$749$			62.8388i			2.29608i
$750$	−1.67862	+	0.426905i	−0.0612944	+	0.0155884i
$751$	9.39795	+	28.9239i	0.342936	+	1.05545i	0.962679	+	0.270644i	$0.0872368\pi$
$751$	9.39795	+	28.9239i	0.342936	+	1.05545i	−0.619743	+	0.784805i	$0.712763\pi$
$752$	11.0577	+	3.59285i	0.403231	+	0.131018i
$753$	1.16716	−	17.8981i	0.0425337	−	0.652241i
$754$	−27.7376	−	20.1526i	−1.01015	−	0.733913i
$755$	4.71714	+	14.5179i	0.171674	+	0.528359i
$756$	18.5873	−	2.21864i	0.676014	−	0.0806913i
$757$	18.6557	+	25.6774i	0.678054	+	0.933262i	0.999908	−	0.0135277i	$-0.00430612\pi$
$757$	18.6557	+	25.6774i	0.678054	+	0.933262i	−0.321854	+	0.946789i	$0.604306\pi$
$758$	24.4707	+	7.95100i	0.888814	+	0.288793i
$759$	9.02062	−	10.8534i	0.327428	−	0.393954i
$760$	−5.93338	+	4.31085i	−0.215226	+	0.156371i
$761$	−8.77146	+	26.9958i	−0.317965	+	0.978596i	0.656552	+	0.754281i	$0.272014\pi$
$761$	−8.77146	+	26.9958i	−0.317965	+	0.978596i	−0.974517	+	0.224315i	$0.927986\pi$
$762$	12.1419	−	14.6089i	0.439856	−	0.529225i
$763$	26.2476	+	19.0700i	0.950226	+	0.690380i
$764$	19.1105	−	6.20938i	0.691394	−	0.224647i
$765$	−1.90066	+	14.5111i	−0.0687185	+	0.524648i
$766$	−21.8383	−	7.09569i	−0.789049	−	0.256378i
$767$	4.78639	−	14.7310i	0.172826	−	0.531905i
$768$	0.924732	+	1.46454i	0.0333684	+	0.0528470i
$769$	10.1925			0.367550			0.183775	−	0.982968i	$-0.441168\pi$
$769$	10.1925			0.367550			0.183775	+	0.982968i	$0.441168\pi$
$770$	−9.09864			−0.327892
$771$	17.0100	−	10.7404i	0.612601	−	0.386806i
$772$	−2.49284	+	1.81116i	−0.0897194	+	0.0651849i
$773$	17.4839	+	12.7028i	0.628853	+	0.456888i	0.856003	−	0.516972i	$-0.172941\pi$
$773$	17.4839	+	12.7028i	0.628853	+	0.456888i	−0.227150	+	0.973860i	$0.572941\pi$
$774$	−25.1295	+	13.6657i	−0.903259	+	0.491203i
$775$	−2.62325	−	4.91106i	−0.0942300	−	0.176411i
$776$		−	12.8918i		−	0.462789i
$777$	−21.1300	+	53.0136i	−0.758034	+	1.90185i
$778$	−6.41086	−	8.82379i	−0.229840	−	0.316348i
$779$	65.4758	−	21.2744i	2.34591	−	0.762234i
$780$	−8.76591	+	2.22934i	−0.313870	+	0.0798232i
$781$			36.3431i			1.30046i
$782$	−14.9678	+	4.86333i	−0.535247	+	0.173912i
$783$	14.3134	+	30.9673i	0.511518	+	1.10668i
$784$	1.84736	−	5.68558i	0.0659770	−	0.203056i
$785$	−3.72051	+	5.12084i	−0.132791	+	0.182771i
$786$	−12.8238	−	20.3097i	−0.457411	−	0.724422i
$787$	−19.6224	+	27.0079i	−0.699461	+	0.962726i	0.300499	+	0.953782i	$0.402847\pi$
$787$	−19.6224	+	27.0079i	−0.699461	+	0.962726i	−0.999960	+	0.00894383i	$0.997153\pi$
$788$	12.7518	−	9.26469i	0.454262	−	0.330041i
$789$	0.0175365	−	0.268917i	0.000624317	−	0.00957371i
$790$	−3.08245	−	4.24263i	−0.109669	−	0.150946i
$791$	−17.6506	−	24.2939i	−0.627582	−	0.863793i
$792$	7.44910	−	1.38570i	0.264692	−	0.0492388i
$793$	13.6608	−	9.92513i	0.485108	−	0.352452i
$794$	9.30375	−	12.8055i	0.330178	−	0.454451i
$795$	−3.89472	+	2.45918i	−0.138131	+	0.0872182i
$796$	−7.23121	+	9.95291i	−0.256304	+	0.352772i
$797$	−15.7099	+	48.3500i	−0.556473	+	1.71265i	0.135550	+	0.990771i	$0.456720\pi$
$797$	−15.7099	+	48.3500i	−0.556473	+	1.71265i	−0.692022	+	0.721876i	$0.743280\pi$
$798$	−45.6657	−	2.97793i	−1.61655	−	0.105418i
$799$	−53.9429	+	17.5271i	−1.90836	+	0.620065i
$800$		−	1.00000i		−	0.0353553i
$801$	−15.7748	+	8.57854i	−0.557376	+	0.303108i
$802$	19.1899	−	6.23518i	0.677619	−	0.220172i
$803$	−3.10940	−	4.27973i	−0.109728	−	0.151028i
$804$	−5.08163	−	2.02542i	−0.179215	−	0.0714309i
$805$		−	11.6222i		−	0.409627i
$806$	−13.6989	−	25.6461i	−0.482523	−	0.903345i
$807$	15.9733	−	4.06233i	0.562288	−	0.143001i
$808$	−5.73285	−	4.16516i	−0.201681	−	0.146530i
$809$	5.44904	−	3.95896i	0.191578	−	0.139190i	−0.487862	−	0.872921i	$-0.662223\pi$
$809$	5.44904	−	3.95896i	0.191578	−	0.139190i	0.679440	+	0.733731i	$0.262223\pi$
$810$	8.69640	+	2.31788i	0.305560	+	0.0814419i
$811$	11.8014			0.414403			0.207201	−	0.978298i	$-0.433564\pi$
$811$	11.8014			0.414403			0.207201	+	0.978298i	$0.433564\pi$
$812$	23.6523			0.830032
$813$	−27.9324	+	17.6370i	−0.979633	+	0.618555i
$814$	−7.13819	+	21.9691i	−0.250193	+	0.770016i
$815$	−4.89963	−	1.59199i	−0.171626	−	0.0557648i
$816$	−7.84903	−	3.12844i	−0.274771	−	0.109517i
$817$	66.5074	−	21.6096i	2.32680	−	0.756023i
$818$	−19.4654	−	14.1425i	−0.680593	−	0.494480i
$819$	−50.9564	−	24.2636i	−1.78056	−	0.847839i
$820$	−2.90076	+	8.92763i	−0.101299	+	0.311766i
$821$	19.8260	−	14.4044i	0.691932	−	0.502718i	−0.185363	−	0.982670i	$-0.559346\pi$
$821$	19.8260	−	14.4044i	0.691932	−	0.502718i	0.877295	+	0.479952i	$0.159346\pi$
$822$	−27.2051	−	22.6110i	−0.948887	−	0.788650i
$823$	−48.3625	−	15.7139i	−1.68581	−	0.547753i	−0.699785	−	0.714354i	$-0.746721\pi$
$823$	−48.3625	−	15.7139i	−1.68581	−	0.547753i	−0.986024	+	0.166601i	$0.946721\pi$
$824$	8.62993	+	11.8781i	0.300638	+	0.413793i
$825$	−4.06363	−	1.61967i	−0.141477	−	0.0563896i
$826$	3.30194	+	10.1623i	0.114889	+	0.353592i
$827$	22.3344	+	16.2269i	0.776643	+	0.564264i	0.903970	−	0.427597i	$-0.140640\pi$
$827$	22.3344	+	16.2269i	0.776643	+	0.564264i	−0.127327	+	0.991861i	$0.540640\pi$
$828$	1.77003	+	9.51511i	0.0615127	+	0.330673i
$829$	3.09066	+	1.00422i	0.107343	+	0.0348779i	0.362196	−	0.932102i	$-0.382027\pi$
$829$	3.09066	+	1.00422i	0.107343	+	0.0348779i	−0.254853	+	0.966980i	$0.582027\pi$
$830$	−1.17191	−	3.60676i	−0.0406775	−	0.125193i
$831$	−2.64522	−	10.4012i	−0.0917615	−	0.360812i
$832$		−	5.22211i		−	0.181044i
$833$	9.01202	+	27.7361i	0.312248	+	0.961000i
$834$	−22.6616	+	27.2659i	−0.784705	+	0.944140i
$835$	12.7938	−	17.6092i	0.442748	−	0.609390i
$836$	−18.5231			−0.640635
$837$	−0.547434	+	28.9258i	−0.0189221	+	0.999821i
$838$	10.3952			0.359097
$839$	6.12415	−	8.42916i	0.211429	−	0.291007i	−0.690110	−	0.723704i	$-0.742438\pi$
$839$	6.12415	−	8.42916i	0.211429	−	0.291007i	0.901539	+	0.432697i	$0.142438\pi$
$840$	3.98836	−	4.79870i	0.137611	−	0.165571i
$841$	4.35883	+	13.4151i	0.150305	+	0.462590i
$842$			23.4883i			0.809461i
$843$	−6.23516	−	24.5170i	−0.214750	−	0.844412i
$844$	7.76619	+	23.9019i	0.267323	+	0.822736i
$845$	13.5719	+	4.40979i	0.466889	+	0.151701i
$846$	6.37906	+	34.2918i	0.219317	+	1.17898i
$847$	13.4685	+	9.78543i	0.462783	+	0.336231i
$848$	−0.821784	−	2.52919i	−0.0282202	−	0.0868527i
$849$	−20.7091	−	8.25417i	−0.710736	−	0.283283i
$850$	2.86741	+	3.94665i	0.0983514	+	0.135369i
$851$	−28.0622	−	9.11797i	−0.961961	−	0.312560i
$852$	−19.1677	−	15.9309i	−0.656673	−	0.545782i
$853$	−16.1377	+	11.7247i	−0.552544	+	0.401446i	−0.828722	−	0.559660i	$-0.810932\pi$
$853$	−16.1377	+	11.7247i	−0.552544	+	0.401446i	0.276179	+	0.961106i	$0.410932\pi$
$854$	−3.59965	+	11.0786i	−0.123178	+	0.379102i
$855$	−19.8651	−	9.45905i	−0.679372	−	0.323493i
$856$	−14.1117	−	10.2527i	−0.482327	−	0.350431i
$857$	−9.64710	+	3.13453i	−0.329539	+	0.107074i	−0.469113	−	0.883138i	$-0.655426\pi$
$857$	−9.64710	+	3.13453i	−0.329539	+	0.107074i	0.139575	+	0.990212i	$0.455426\pi$
$858$	−21.2207	−	8.45807i	−0.724463	−	0.288754i
$859$	−11.9038	−	3.86779i	−0.406154	−	0.131967i	0.0988133	−	0.995106i	$-0.468495\pi$
$859$	−11.9038	−	3.86779i	−0.406154	−	0.131967i	−0.504967	+	0.863139i	$0.668495\pi$
$860$	−2.94647	+	9.06829i	−0.100474	+	0.309226i
$861$	−49.5265	+	31.2718i	−1.68786	+	1.06574i
$862$	−24.6246			−0.838719
$863$	−41.7185			−1.42011			−0.710057	−	0.704144i	$-0.751331\pi$
$863$	−41.7185			−1.42011			−0.710057	+	0.704144i	$0.751331\pi$
$864$	−2.53445	+	4.53614i	−0.0862239	+	0.154323i
$865$	5.52220	−	4.01211i	0.187760	−	0.136416i
$866$	8.31455	+	6.04088i	0.282540	+	0.205277i
$867$	11.4115	−	2.90216i	0.387553	−	0.0985624i
$868$	18.0447	+	8.75854i	0.612477	+	0.297284i
$869$		−	13.2448i		−	0.449300i
$870$	10.5636	+	4.21039i	0.358139	+	0.142746i
$871$	9.69443	+	13.3432i	0.328483	+	0.452118i
$872$	−8.56508	+	2.78296i	−0.290050	+	0.0942430i
$873$	33.9764	−	18.4768i	1.14993	−	0.625344i
$874$		−	23.6605i		−	0.800329i
$875$	−3.42620	+	1.11324i	−0.115827	+	0.0376344i
$876$	3.62016	+	0.236076i	0.122314	+	0.00797628i
$877$	5.36124	−	16.5002i	0.181036	−	0.557172i	−0.818821	−	0.574048i	$-0.805372\pi$
$877$	5.36124	−	16.5002i	0.181036	−	0.557172i	0.999858	+	0.0168761i	$0.00537209\pi$
$878$	17.2729	−	23.7740i	0.582931	−	0.802335i
$879$	−21.5742	+	13.6223i	−0.727679	+	0.459468i
$880$	1.48453	−	2.04328i	0.0500434	−	0.0688789i
$881$	15.4281	−	11.2092i	0.519786	−	0.377647i	−0.296737	−	0.954959i	$-0.595898\pi$
$881$	15.4281	−	11.2092i	0.519786	−	0.377647i	0.816523	+	0.577312i	$0.195898\pi$
$882$	17.6320	−	3.27996i	0.593701	−	0.110442i
$883$	26.1961	+	36.0559i	0.881570	+	1.21338i	0.975984	+	0.217844i	$0.0699024\pi$
$883$	26.1961	+	36.0559i	0.881570	+	1.21338i	−0.0944135	+	0.995533i	$0.530098\pi$
$884$	14.9739	+	20.6098i	0.503628	+	0.693184i
$885$	−0.334306	+	5.12648i	−0.0112376	+	0.172325i
$886$	5.78248	−	4.20122i	0.194266	−	0.141143i
$887$	10.5272	−	14.4895i	0.353469	−	0.486508i	−0.594846	−	0.803840i	$-0.702787\pi$
$887$	10.5272	−	14.4895i	0.353469	−	0.486508i	0.948315	+	0.317332i	$0.102787\pi$
$888$	−8.45769	−	13.3948i	−0.283821	−	0.449501i
$889$	23.2234	−	31.9643i	0.778889	−	1.07205i
$890$	−1.84962	+	5.69255i	−0.0619995	+	0.190815i
$891$	14.3282	+	17.6461i	0.480013	+	0.591167i
$892$	−0.895312	+	0.290905i	−0.0299773	+	0.00974020i
$893$		−	85.2709i		−	2.85348i
$894$	−12.9756	+	3.29994i	−0.433968	+	0.110367i
$895$	−2.99495	+	0.973117i	−0.100110	+	0.0325277i
$896$	2.11751	+	2.91450i	0.0707410	+	0.0973667i
$897$	10.8039	−	27.1063i	0.360733	−	0.905052i
$898$		−	12.0370i		−	0.401681i
$899$	−5.01862	+	36.2089i	−0.167380	+	1.20763i
$900$	2.63550	−	1.43322i	0.0878502	−	0.0477740i
$901$	10.4955	+	7.62545i	0.349657	+	0.254040i
$902$	−19.1804	+	13.9354i	−0.638637	+	0.463997i
$903$	−50.3068	+	31.7645i	−1.67410	+	1.05706i
$904$	8.33553			0.277236
$905$	−17.7543			−0.590174
$906$	−14.1160	−	22.3562i	−0.468973	−	0.742734i
$907$	14.5472	−	44.7716i	0.483031	−	1.48662i	−0.351782	−	0.936082i	$-0.614424\pi$
$907$	14.5472	−	44.7716i	0.483031	−	1.48662i	0.834813	−	0.550534i	$-0.185576\pi$
$908$	−8.94627	−	2.90682i	−0.296892	−	0.0964662i
$909$	2.76087	−	21.0785i	0.0915723	−	0.699131i
$910$	−17.8920	+	5.81346i	−0.593114	+	0.192714i
$911$	−31.8303	−	23.1260i	−1.05458	−	0.766200i	−0.0815050	−	0.996673i	$-0.525973\pi$
$911$	−31.8303	−	23.1260i	−1.05458	−	0.766200i	−0.973079	+	0.230473i	$0.925973\pi$
$912$	8.11954	−	9.76925i	0.268865	−	0.323492i
$913$	2.95981	−	9.10935i	0.0979553	−	0.301475i
$914$	−3.18410	+	2.31338i	−0.105321	+	0.0765198i
$915$	−3.57980	+	4.30714i	−0.118345	+	0.142390i
$916$	−16.3259	−	5.30460i	−0.539422	−	0.175269i
$917$	−29.3649	−	40.4173i	−0.969713	−	1.33470i
$918$	−3.00436	−	25.1699i	−0.0991587	−	0.830730i
$919$	11.6521	+	35.8614i	0.384367	+	1.18296i	0.936938	+	0.349494i	$0.113647\pi$
$919$	11.6521	+	35.8614i	0.384367	+	1.18296i	−0.552572	+	0.833465i	$0.686353\pi$
$920$	2.60998	+	1.89626i	0.0860485	+	0.0625179i
$921$	−1.11477	+	17.0946i	−0.0367328	+	0.563287i
$922$	−4.87532	−	1.58409i	−0.160560	−	0.0521692i
$923$	23.2210	+	71.4668i	0.764327	+	2.35236i
$924$	15.2731	−	3.88425i	0.502449	−	0.127782i
$925$			9.14610i			0.300722i
$926$	12.9015	+	39.7066i	0.423969	+	1.30484i
$927$	−18.9362	+	39.7681i	−0.621945	+	1.30616i
$928$	−3.85909	+	5.31158i	−0.126681	+	0.174361i
$929$	−0.562548			−0.0184566			−0.00922830	−	0.999957i	$-0.502938\pi$
$929$	−0.562548			−0.0184566			−0.00922830	+	0.999957i	$0.502938\pi$
$930$	6.49999	+	7.12391i	0.213143	+	0.233602i
$931$	−43.8442			−1.43694
$932$	−2.27849	+	3.13607i	−0.0746344	+	0.102725i
$933$	−19.7922	−	16.4499i	−0.647968	−	0.538547i
$934$	1.22537	+	3.77130i	0.0400953	+	0.123401i
$935$			12.3209i			0.402935i
$936$	13.7629	−	7.48442i	0.449854	−	0.244636i
$937$	14.1653	+	43.5962i	0.462759	+	1.42423i	0.861779	+	0.507283i	$0.169350\pi$
$937$	14.1653	+	43.5962i	0.462759	+	1.42423i	−0.399020	+	0.916942i	$0.630650\pi$
$938$	−10.8211	−	3.51599i	−0.353321	−	0.114801i
$939$	22.6233	+	1.47530i	0.738284	+	0.0481446i
$940$	9.40620	+	6.83401i	0.306796	+	0.222901i
$941$	−4.74278	−	14.5968i	−0.154610	−	0.475841i	0.843511	−	0.537112i	$-0.180485\pi$
$941$	−4.74278	−	14.5968i	−0.154610	−	0.475841i	−0.998121	+	0.0612707i	$0.980485\pi$
$942$	4.05920	−	10.1842i	0.132256	−	0.331820i
$943$	−17.8003	−	24.5001i	−0.579659	−	0.797832i
$944$	−2.82089	−	0.916563i	−0.0918122	−	0.0298316i
$945$	18.3632	+	3.63374i	0.597354	+	0.118206i
$946$	−19.4826	+	14.1549i	−0.633433	+	0.460216i
$947$	−4.76957	+	14.6792i	−0.154990	+	0.477011i	−0.998160	−	0.0606366i	$-0.980687\pi$
$947$	−4.76957	+	14.6792i	−0.154990	+	0.477011i	0.843170	+	0.537648i	$0.180687\pi$
$948$	6.98545	+	5.80583i	0.226877	+	0.188565i
$949$	−8.84895	−	6.42914i	−0.287249	−	0.208699i
$950$	−6.97510	+	2.26635i	−0.226302	+	0.0735301i
$951$	1.24472	−	3.12292i	0.0403629	−	0.101268i
$952$	−16.7142	−	5.43076i	−0.541709	−	0.176012i
$953$	2.96647	−	9.12985i	0.0960934	−	0.295745i	−0.891444	−	0.453131i	$-0.850307\pi$
$953$	2.96647	−	9.12985i	0.0960934	−	0.295745i	0.987537	+	0.157386i	$0.0503068\pi$
$954$	5.48790	−	5.79070i	0.177677	−	0.187481i
$955$	20.0940			0.650226
$956$	−1.31138			−0.0424130
$957$	15.3339	+	24.2849i	0.495673	+	0.785020i
$958$	8.27766	−	6.01407i	0.267439	−	0.194306i
$959$	−59.5247	−	43.2473i	−1.92215	−	1.39653i
$960$	0.426905	+	1.67862i	0.0137783	+	0.0541771i
$961$	−17.2371	+	25.7659i	−0.556035	+	0.831159i
$962$			47.7619i			1.53991i
$963$	6.79601	−	51.8858i	0.218998	−	1.67200i
$964$	−1.48807	−	2.04815i	−0.0479274	−	0.0659664i
$965$	−2.93051	+	0.952181i	−0.0943365	+	0.0306518i
$966$	4.96155	+	19.5091i	0.159635	+	0.627696i
$967$			47.6976i			1.53385i	0.641736	+	0.766926i	$0.278215\pi$
$967$			47.6976i			1.53385i	−0.641736	+	0.766926i	$0.721785\pi$
$968$	−4.39502	+	1.42803i	−0.141261	+	0.0458986i
$969$	−4.03255	+	61.8379i	−0.129544	+	1.98652i
$970$	3.98379	−	12.2608i	0.127912	−	0.393672i
$971$	16.3664	−	22.5264i	0.525223	−	0.722907i	−0.461170	−	0.887312i	$-0.652570\pi$
$971$	16.3664	−	22.5264i	0.525223	−	0.722907i	0.986393	+	0.164405i	$0.0525703\pi$
$972$	−15.5874	−	0.178289i	−0.499967	−	0.00571862i
$973$	−43.3439	+	59.6577i	−1.38954	+	1.91254i
$974$	−6.52682	+	4.74201i	−0.209133	+	0.151944i
$975$	−9.02578	−	0.588585i	−0.289056	−	0.0188498i
$976$	−1.90060	−	2.61595i	−0.0608367	−	0.0837345i
$977$	19.0530	+	26.2242i	0.609559	+	0.838986i	0.996541	−	0.0831011i	$-0.0264824\pi$
$977$	19.0530	+	26.2242i	0.609559	+	0.838986i	−0.386982	+	0.922087i	$0.626482\pi$
$978$	8.90422	+	0.580658i	0.284726	+	0.0185674i
$979$	−12.2300	+	8.88565i	−0.390874	+	0.283987i
$980$	3.51388	−	4.83644i	0.112247	−	0.154494i
$981$	−19.6101	−	18.5847i	−0.626103	−	0.593364i
$982$	7.89409	−	10.8653i	0.251910	−	0.346725i
$983$	−8.57799	+	26.4003i	−0.273595	+	0.842040i	0.715992	+	0.698108i	$0.245974\pi$
$983$	−8.57799	+	26.4003i	−0.273595	+	0.842040i	−0.989588	+	0.143932i	$0.954026\pi$
$984$	1.05802	−	16.2244i	0.0337284	−	0.517216i
$985$	14.9906	−	4.87074i	0.477640	−	0.155195i
$986$		−	32.0286i		−	1.02000i
$987$	17.8811	+	70.3096i	0.569162	+	2.23798i
$988$	−36.4247	+	11.8351i	−1.15883	+	0.376525i
$989$	−18.0808	−	24.8861i	−0.574936	−	0.791332i
$990$	7.51272	+	0.984017i	0.238770	+	0.0312741i
$991$			6.11587i			0.194277i	0.995271	+	0.0971385i	$0.0309690\pi$
$991$			6.11587i			0.194277i	−0.995271	+	0.0971385i	$0.969031\pi$
$992$	−4.91106	+	2.62325i	−0.155926	+	0.0832883i
$993$	11.6644	+	45.8652i	0.370159	+	1.45549i
$994$	−41.9389	−	30.4704i	−1.33022	−	0.966461i
$995$	−9.95291	+	7.23121i	−0.315528	+	0.229245i
$996$	3.50693	+	5.55408i	0.111121	+	0.175988i
$997$	43.6220			1.38152			0.690762	−	0.723082i	$-0.257275\pi$
$997$	43.6220			1.38152			0.690762	+	0.723082i	$0.257275\pi$
$998$	2.29748			0.0727253
$999$	23.1804	−	41.4880i	0.733395	−	1.31262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.b.401.13	yes	80
3.2	odd	2	inner	930.2.v.b.401.9	✓	80
31.15	odd	10	inner	930.2.v.b.821.9	yes	80
93.77	even	10	inner	930.2.v.b.821.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.b.401.9	✓	80	3.2	odd	2	inner
930.2.v.b.401.13	yes	80	1.1	even	1	trivial
930.2.v.b.821.9	yes	80	31.15	odd	10	inner
930.2.v.b.821.13	yes	80	93.77	even	10	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-1.10710 + 1.33204i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.426905 + 1.67862i) q^{6} +(1.11324 + 3.42620i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.548656 - 2.94940i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-1.10710 + 1.33204i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.426905 + 1.67862i) q^{6} +(1.11324 + 3.42620i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.548656 - 2.94940i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.780462 - 2.40202i) q^{11} +(1.60896 + 0.641293i) q^{12} +(-3.06948 - 4.22477i) q^{13} +(3.42620 + 1.11324i) q^{14} +(1.33204 + 1.10710i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.50749 - 4.63957i) q^{17} +(-2.70861 - 1.28974i) q^{18} +(5.93338 + 4.31085i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-5.79631 - 2.31027i) q^{21} +(-2.40202 - 0.780462i) q^{22} +(0.996924 - 3.06822i) q^{23} +(1.46454 - 0.924732i) q^{24} -1.00000 q^{25} -5.22211 q^{26} +(4.53614 + 2.53445i) q^{27} +(2.91450 - 2.11751i) q^{28} +(5.31158 + 3.85909i) q^{29} +(1.67862 - 0.426905i) q^{30} +(2.62325 + 4.91106i) q^{31} +1.00000i q^{32} +(4.06363 + 1.61967i) q^{33} +(-2.86741 - 3.94665i) q^{34} +(3.42620 - 1.11324i) q^{35} +(-2.63550 + 1.43322i) q^{36} -9.14610i q^{37} +(6.97510 - 2.26635i) q^{38} +(9.02578 + 0.588585i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(5.51758 - 7.59430i) q^{41} +(-5.27603 + 3.33137i) q^{42} +(5.60451 - 7.71395i) q^{43} +(-2.04328 + 1.48453i) q^{44} +(-2.94940 + 0.548656i) q^{45} +(-1.89626 - 2.60998i) q^{46} +(-6.83401 - 9.40620i) q^{47} +(0.112710 - 1.72838i) q^{48} +(-4.83644 + 3.51388i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(4.51115 + 7.14450i) q^{51} +(-3.06948 + 4.22477i) q^{52} +(-0.821784 + 2.52919i) q^{53} +(4.71669 - 2.18010i) q^{54} +(-2.40202 + 0.780462i) q^{55} -3.60252i q^{56} +(-12.3111 + 3.13095i) q^{57} +(6.24414 - 2.02884i) q^{58} +(1.74341 + 2.39959i) q^{59} +(0.641293 - 1.60896i) q^{60} +3.23349i q^{61} +(5.51504 + 0.764395i) q^{62} +(9.49446 - 5.16320i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-4.22477 + 3.06948i) q^{65} +(3.69888 - 2.33553i) q^{66} -3.15833 q^{67} -4.87833 q^{68} +(2.98329 + 4.72477i) q^{69} +(1.11324 - 3.42620i) q^{70} +(-13.6854 - 4.44667i) q^{71} +(-0.389612 + 2.97459i) q^{72} +(1.99203 - 0.647248i) q^{73} +(-7.39935 - 5.37594i) q^{74} +(1.10710 - 1.33204i) q^{75} +(2.26635 - 6.97510i) q^{76} +(7.36095 - 5.34804i) q^{77} +(5.78140 - 6.95605i) q^{78} +(4.98751 + 1.62054i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-8.39795 + 3.23642i) q^{81} +(-2.90076 - 8.92763i) q^{82} +(3.06810 + 2.22910i) q^{83} +(-0.406041 + 6.22653i) q^{84} +(-4.63957 - 1.50749i) q^{85} +(-2.94647 - 9.06829i) q^{86} +(-11.0209 + 2.80283i) q^{87} +2.52563i q^{88} +(-1.84962 - 5.69255i) q^{89} +(-1.28974 + 2.70861i) q^{90} +(11.0579 - 15.2198i) q^{91} -3.22611 q^{92} +(-9.44593 - 1.94277i) q^{93} -11.6267 q^{94} +(4.31085 - 5.93338i) q^{95} +(-1.33204 - 1.10710i) q^{96} +(3.98379 + 12.2608i) q^{97} +5.97817i q^{98} +(-6.65631 + 3.61978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Introduction

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