LMFDB - Embedded newform 930.2.be.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.786015 + 2.09337i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.17109 + 4.37058i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.786015 + 2.09337i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.17109 + 4.37058i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.03603 - 0.924436i) q^{10} +(1.73324 + 1.00068i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-0.612154 + 0.164026i) q^{13} +(3.91856 - 2.26238i) q^{14} +(-1.81860 - 1.30104i) q^{15} -1.00000 q^{16} +(5.31290 + 1.42359i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-1.88514 + 1.08839i) q^{19} +(-2.09337 - 0.786015i) q^{20} +(-3.91856 - 2.26238i) q^{21} +(-0.517992 - 1.93317i) q^{22} +(6.15761 + 6.15761i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.76436 - 3.29083i) q^{25} +(0.548843 + 0.316874i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.37058 - 1.17109i) q^{28} -9.68934 q^{29} +(0.365974 + 2.20592i) q^{30} +(1.69411 - 5.30377i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.41518 + 1.41518i) q^{33} +(-2.75016 - 4.76341i) q^{34} +(-8.22873 - 5.88687i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.38266 - 0.638431i) q^{37} +(2.10260 + 0.563391i) q^{38} -0.633749i q^{39} +(0.924436 + 2.03603i) q^{40} +(-4.62924 + 8.01808i) q^{41} +(1.17109 + 4.37058i) q^{42} +(2.50841 - 9.36153i) q^{43} +(-1.00068 + 1.73324i) q^{44} +(1.72739 - 1.41990i) q^{45} -8.70817i q^{46} +(-2.08728 - 2.08728i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-11.6683 - 6.73672i) q^{49} +(0.334833 + 4.98878i) q^{50} +(-2.75016 + 4.76341i) q^{51} +(-0.164026 - 0.612154i) q^{52} +(3.72577 - 0.998317i) q^{53} -1.00000 q^{54} +(-3.45715 + 2.84174i) q^{55} +(2.26238 + 3.91856i) q^{56} +(-0.563391 - 2.10260i) q^{57} +(6.85140 + 6.85140i) q^{58} +(-0.109798 + 0.0633919i) q^{59} +(1.30104 - 1.81860i) q^{60} +1.06889i q^{61} +(-4.94825 + 2.55242i) q^{62} +(3.19949 - 3.19949i) q^{63} -1.00000i q^{64} +(0.137796 - 1.41039i) q^{65} +2.00137 q^{66} +(-13.4718 + 3.60976i) q^{67} +(-1.42359 + 5.31290i) q^{68} +(-7.54150 + 4.35409i) q^{69} +(1.65594 + 9.98124i) q^{70} +(3.51615 - 6.09014i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(8.24671 - 2.20970i) q^{73} +(1.23335 + 2.13623i) q^{74} +(4.15299 - 2.78436i) q^{75} +(-1.08839 - 1.88514i) q^{76} +(-6.40335 + 6.40335i) q^{77} +(-0.448128 + 0.448128i) q^{78} +(4.85984 + 8.41749i) q^{79} +(0.786015 - 2.09337i) q^{80} +(0.500000 + 0.866025i) q^{81} +(8.94301 - 2.39627i) q^{82} +(5.11080 - 1.36944i) q^{83} +(2.26238 - 3.91856i) q^{84} +(-7.15610 + 10.0029i) q^{85} +(-8.39331 + 4.84588i) q^{86} +(2.50779 - 9.35919i) q^{87} +(1.93317 - 0.517992i) q^{88} -3.58912 q^{89} +(-2.22547 - 0.217429i) q^{90} -2.86756i q^{91} +(-6.15761 + 6.15761i) q^{92} +(4.68458 + 3.00910i) q^{93} +2.95185i q^{94} +(-0.796643 - 4.80179i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-7.94225 - 7.94225i) q^{97} +(3.48718 + 13.0143i) q^{98} +(-1.00068 - 1.73324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−0.786015	+	2.09337i	−0.351517	+	0.936182i
$5$	−0.786015	+	2.09337i	−0.351517	+	0.936182i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.17109	+	4.37058i	−0.442632	+	1.65192i	0.279482	+	0.960151i	$0.409837\pi$
$7$	−1.17109	+	4.37058i	−0.442632	+	1.65192i	−0.722114	+	0.691774i	$0.756830\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	2.03603	−	0.924436i	0.643849	−	0.292332i
$11$	1.73324	+	1.00068i	0.522590	+	0.301718i	0.737994	−	0.674808i	$-0.235773\pi$
$11$	1.73324	+	1.00068i	0.522590	+	0.301718i	−0.215404	+	0.976525i	$0.569107\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−0.612154	+	0.164026i	−0.169781	+	0.0454927i	−0.342708	−	0.939442i	$-0.611344\pi$
$13$	−0.612154	+	0.164026i	−0.169781	+	0.0454927i	0.172927	+	0.984935i	$0.444678\pi$
$14$	3.91856	−	2.26238i	1.04728	−	0.604646i
$15$	−1.81860	−	1.30104i	−0.469561	−	0.335926i
$16$	−1.00000			−0.250000
$17$	5.31290	+	1.42359i	1.28857	+	0.345270i	0.837116	−	0.547026i	$-0.184240\pi$
$17$	5.31290	+	1.42359i	1.28857	+	0.345270i	0.451451	+	0.892296i	$0.350907\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−1.88514	+	1.08839i	−0.432482	+	0.249693i	−0.700403	−	0.713747i	$-0.746997\pi$
$19$	−1.88514	+	1.08839i	−0.432482	+	0.249693i	0.267922	+	0.963441i	$0.413663\pi$
$20$	−2.09337	−	0.786015i	−0.468091	−	0.175758i
$21$	−3.91856	−	2.26238i	−0.855099	−	0.493692i
$22$	−0.517992	−	1.93317i	−0.110436	−	0.412154i
$23$	6.15761	+	6.15761i	1.28395	+	1.28395i	0.938401	+	0.345549i	$0.112307\pi$
$23$	6.15761	+	6.15761i	1.28395	+	1.28395i	0.345549	+	0.938401i	$0.387693\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.76436	−	3.29083i	−0.752872	−	0.658167i
$26$	0.548843	+	0.316874i	0.107637	+	0.0621442i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−4.37058	−	1.17109i	−0.825962	−	0.221316i
$29$	−9.68934			−1.79927			−0.899633	−	0.436647i	$-0.856166\pi$
$29$	−9.68934			−1.79927			−0.899633	+	0.436647i	$0.856166\pi$
$30$	0.365974	+	2.20592i	0.0668174	+	0.402743i
$31$	1.69411	−	5.30377i	0.304271	−	0.952586i
$31$	1.69411	−	5.30377i	0.304271	−	0.952586i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.41518	+	1.41518i	−0.246351	+	0.246351i
$34$	−2.75016	−	4.76341i	−0.471648	−	0.816918i
$35$	−8.22873	−	5.88687i	−1.39091	−	0.995063i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.38266	−	0.638431i	−0.391706	−	0.104957i	0.0575897	−	0.998340i	$-0.481658\pi$
$37$	−2.38266	−	0.638431i	−0.391706	−	0.104957i	−0.449296	+	0.893383i	$0.648325\pi$
$38$	2.10260	+	0.563391i	0.341088	+	0.0913941i
$39$		−	0.633749i		−	0.101481i
$40$	0.924436	+	2.03603i	0.146166	+	0.321925i
$41$	−4.62924	+	8.01808i	−0.722966	+	1.25221i	0.236840	+	0.971549i	$0.423888\pi$
$41$	−4.62924	+	8.01808i	−0.722966	+	1.25221i	−0.959806	+	0.280665i	$0.909445\pi$
$42$	1.17109	+	4.37058i	0.180704	+	0.674395i
$43$	2.50841	−	9.36153i	0.382529	−	1.42762i	−0.459495	−	0.888180i	$-0.651970\pi$
$43$	2.50841	−	9.36153i	0.382529	−	1.42762i	0.842025	−	0.539439i	$-0.181364\pi$
$44$	−1.00068	+	1.73324i	−0.150859	+	0.261295i
$45$	1.72739	−	1.41990i	0.257504	−	0.211666i
$46$		−	8.70817i		−	1.28395i
$47$	−2.08728	−	2.08728i	−0.304460	−	0.304460i	0.538296	−	0.842756i	$-0.319068\pi$
$47$	−2.08728	−	2.08728i	−0.304460	−	0.304460i	−0.842756	+	0.538296i	$0.819068\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	−11.6683	−	6.73672i	−1.66691	−	0.962389i
$50$	0.334833	+	4.98878i	0.0473526	+	0.705519i
$51$	−2.75016	+	4.76341i	−0.385099	+	0.667011i
$52$	−0.164026	−	0.612154i	−0.0227464	−	0.0848906i
$53$	3.72577	−	0.998317i	0.511774	−	0.137129i	0.00631492	−	0.999980i	$-0.497990\pi$
$53$	3.72577	−	0.998317i	0.511774	−	0.137129i	0.505459	+	0.862851i	$0.331323\pi$
$54$	−1.00000			−0.136083
$55$	−3.45715	+	2.84174i	−0.466162	+	0.383181i
$56$	2.26238	+	3.91856i	0.302323	+	0.523639i
$57$	−0.563391	−	2.10260i	−0.0746230	−	0.278497i
$58$	6.85140	+	6.85140i	0.899633	+	0.899633i
$59$	−0.109798	+	0.0633919i	−0.0142945	+	0.00825293i	−0.507130	−	0.861869i	$-0.669294\pi$
$59$	−0.109798	+	0.0633919i	−0.0142945	+	0.00825293i	0.492836	+	0.870122i	$0.335960\pi$
$60$	1.30104	−	1.81860i	0.167963	−	0.234780i
$61$			1.06889i			0.136857i	0.997656	+	0.0684284i	$0.0217985\pi$
$61$			1.06889i			0.136857i	−0.997656	+	0.0684284i	$0.978202\pi$
$62$	−4.94825	+	2.55242i	−0.628428	+	0.324157i
$63$	3.19949	−	3.19949i	0.403098	−	0.403098i
$64$		−	1.00000i		−	0.125000i
$65$	0.137796	−	1.41039i	0.0170915	−	0.174937i
$66$	2.00137			0.246351
$67$	−13.4718	+	3.60976i	−1.64584	+	0.441002i	−0.958445	−	0.285278i	$-0.907914\pi$
$67$	−13.4718	+	3.60976i	−1.64584	+	0.441002i	−0.687399	+	0.726280i	$0.741247\pi$
$68$	−1.42359	+	5.31290i	−0.172635	+	0.644283i
$69$	−7.54150	+	4.35409i	−0.907889	+	0.524170i
$70$	1.65594	+	9.98124i	0.197923	+	1.19299i
$71$	3.51615	−	6.09014i	0.417290	−	0.722767i	−0.578376	−	0.815770i	$-0.696313\pi$
$71$	3.51615	−	6.09014i	0.417290	−	0.722767i	0.995666	+	0.0930032i	$0.0296467\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	8.24671	−	2.20970i	0.965204	−	0.258626i	0.258403	−	0.966037i	$-0.416804\pi$
$73$	8.24671	−	2.20970i	0.965204	−	0.258626i	0.706802	+	0.707412i	$0.250137\pi$
$74$	1.23335	+	2.13623i	0.143374	+	0.248332i
$75$	4.15299	−	2.78436i	0.479546	−	0.321510i
$76$	−1.08839	−	1.88514i	−0.124847	−	0.216241i
$77$	−6.40335	+	6.40335i	−0.729730	+	0.729730i
$78$	−0.448128	+	0.448128i	−0.0507405	+	0.0507405i
$79$	4.85984	+	8.41749i	0.546775	+	0.947041i	0.998493	+	0.0548807i	$0.0174778\pi$
$79$	4.85984	+	8.41749i	0.546775	+	0.947041i	−0.451718	+	0.892161i	$0.649189\pi$
$80$	0.786015	−	2.09337i	0.0878792	−	0.234045i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	8.94301	−	2.39627i	0.987590	−	0.264624i
$83$	5.11080	−	1.36944i	0.560983	−	0.150315i	0.0328253	−	0.999461i	$-0.489549\pi$
$83$	5.11080	−	1.36944i	0.560983	−	0.150315i	0.528158	+	0.849146i	$0.322883\pi$
$84$	2.26238	−	3.91856i	0.246846	−	0.427550i
$85$	−7.15610	+	10.0029i	−0.776188	+	1.08496i
$86$	−8.39331	+	4.84588i	−0.905074	+	0.522545i
$87$	2.50779	−	9.35919i	0.268863	−	1.00341i
$88$	1.93317	−	0.517992i	0.206077	−	0.0552182i
$89$	−3.58912			−0.380446			−0.190223	−	0.981741i	$-0.560921\pi$
$89$	−3.58912			−0.380446			−0.190223	+	0.981741i	$0.560921\pi$
$90$	−2.22547	−	0.217429i	−0.234585	−	0.0229191i
$91$		−	2.86756i		−	0.300602i
$92$	−6.15761	+	6.15761i	−0.641975	+	0.641975i
$93$	4.68458	+	3.00910i	0.485769	+	0.312029i
$94$			2.95185i			0.304460i
$95$	−0.796643	−	4.80179i	−0.0817339	−	0.492653i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−7.94225	−	7.94225i	−0.806414	−	0.806414i	0.177676	−	0.984089i	$-0.443142\pi$
$97$	−7.94225	−	7.94225i	−0.806414	−	0.806414i	−0.984089	+	0.177676i	$0.943142\pi$
$98$	3.48718	+	13.0143i	0.352259	+	1.31465i
$99$	−1.00068	−	1.73324i	−0.100573	−	0.174197i
$100$	3.29083	−	3.76436i	0.329083	−	0.376436i
$101$	6.44729			0.641530			0.320765	−	0.947159i	$-0.396060\pi$
$101$	6.44729			0.641530			0.320765	+	0.947159i	$0.396060\pi$
$102$	5.31290	−	1.42359i	0.526055	−	0.140956i
$103$	−0.514240	−	1.91917i	−0.0506695	−	0.189101i	0.935952	−	0.352127i	$-0.114541\pi$
$103$	−0.514240	−	1.91917i	−0.0506695	−	0.189101i	−0.986622	+	0.163025i	$0.947875\pi$
$104$	−0.316874	+	0.548843i	−0.0310721	+	0.0538185i
$105$	7.81603	−	6.42471i	0.762767	−	0.626987i
$106$	−3.34043	−	1.92860i	−0.324452	−	0.187322i
$107$	−0.558162	+	2.08309i	−0.0539596	+	0.201380i	−0.987643	−	0.156719i	$-0.949908\pi$
$107$	−0.558162	+	2.08309i	−0.0539596	+	0.201380i	0.933684	+	0.358099i	$0.116575\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			8.92808i			0.855155i	0.903979	+	0.427578i	$0.140633\pi$
$109$			8.92808i			0.855155i	−0.903979	+	0.427578i	$0.859367\pi$
$110$	4.45399	+	0.435156i	0.424671	+	0.0414905i
$111$	1.23335	−	2.13623i	0.117065	−	0.202762i
$112$	1.17109	−	4.37058i	0.110658	−	0.412981i
$113$	4.97639	+	18.5721i	0.468140	+	1.74712i	0.646265	+	0.763113i	$0.276330\pi$
$113$	4.97639	+	18.5721i	0.468140	+	1.74712i	−0.178125	+	0.984008i	$0.557003\pi$
$114$	−1.08839	+	1.88514i	−0.101937	+	0.176560i
$115$	−17.7301	+	8.05015i	−1.65334	+	0.750680i
$116$		−	9.68934i		−	0.899633i
$117$	0.612154	+	0.164026i	0.0565937	+	0.0151642i
$118$	0.122464	+	0.0328141i	0.0112737	+	0.00302078i
$119$	−12.4438	+	21.5533i	−1.14072	+	1.97579i
$120$	−2.20592	+	0.365974i	−0.201372	+	0.0334087i
$121$	−3.49726	−	6.05744i	−0.317933	−	0.550676i
$122$	0.755816	−	0.755816i	0.0684284	−	0.0684284i
$123$	−6.54673	−	6.54673i	−0.590299	−	0.590299i
$124$	5.30377	+	1.69411i	0.476293	+	0.152136i
$125$	9.84776	−	5.29354i	0.880811	−	0.473468i
$126$	−4.52476			−0.403098
$127$	3.09610	+	0.829597i	0.274734	+	0.0736148i	0.393556	−	0.919301i	$-0.371245\pi$
$127$	3.09610	+	0.829597i	0.274734	+	0.0736148i	−0.118821	+	0.992916i	$0.537912\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	8.39331	+	4.84588i	0.738990	+	0.426656i
$130$	−1.09473	+	0.899860i	−0.0960144	+	0.0789230i
$131$	−4.00555	−	6.93781i	−0.349966	−	0.606160i	0.636277	−	0.771461i	$-0.280474\pi$
$131$	−4.00555	−	6.93781i	−0.349966	−	0.606160i	−0.986243	+	0.165301i	$0.947140\pi$
$132$	−1.41518	−	1.41518i	−0.123176	−	0.123176i
$133$	−2.54921	−	9.51378i	−0.221045	−	0.824949i
$134$	12.0785	+	6.97352i	1.04342	+	0.602421i
$135$	0.924436	+	2.03603i	0.0795628	+	0.175234i
$136$	4.76341	−	2.75016i	0.408459	−	0.235824i
$137$	0.695026	+	2.59387i	0.0593801	+	0.221609i	0.989239	−	0.146306i	$-0.0467383\pi$
$137$	0.695026	+	2.59387i	0.0593801	+	0.221609i	−0.929859	+	0.367915i	$0.880072\pi$
$138$	8.41145	+	2.25384i	0.716030	+	0.191860i
$139$	2.61284			0.221618			0.110809	−	0.993842i	$-0.464656\pi$
$139$	2.61284			0.221618			0.110809	+	0.993842i	$0.464656\pi$
$140$	5.88687	−	8.22873i	0.497531	−	0.695454i
$141$	2.55638	−	1.47593i	0.215286	−	0.124295i
$142$	−6.79267	+	1.82009i	−0.570028	+	0.152739i
$143$	−1.22515	−	0.328277i	−0.102452	−	0.0274519i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	7.61597	−	20.2833i	0.632472	−	1.68444i
$146$	−7.39380	−	4.26881i	−0.611915	−	0.353289i
$147$	9.52716	−	9.52716i	0.785787	−	0.785787i
$148$	0.638431	−	2.38266i	0.0524787	−	0.195853i
$149$	10.8385	−	6.25758i	0.887921	−	0.512641i	0.0146589	−	0.999893i	$-0.495334\pi$
$149$	10.8385	−	6.25758i	0.887921	−	0.512641i	0.873262	+	0.487251i	$0.162000\pi$
$150$	−4.90545	−	0.967766i	−0.400528	−	0.0790178i
$151$			17.0761i			1.38963i	0.719188	+	0.694815i	$0.244514\pi$
$151$			17.0761i			1.38963i	−0.719188	+	0.694815i	$0.755486\pi$
$152$	−0.563391	+	2.10260i	−0.0456971	+	0.170544i
$153$	−3.88931	−	3.88931i	−0.314432	−	0.314432i
$154$	9.05571			0.729730
$155$	9.77114	+	7.71524i	0.784837	+	0.619703i
$156$	0.633749			0.0507405
$157$	−4.34215	−	4.34215i	−0.346542	−	0.346542i	0.512278	−	0.858820i	$-0.328802\pi$
$157$	−4.34215	−	4.34215i	−0.346542	−	0.346542i	−0.858820	+	0.512278i	$0.828802\pi$
$158$	2.51564	−	9.38849i	0.200133	−	0.746908i
$159$			3.85720i			0.305896i
$160$	−2.03603	+	0.924436i	−0.160962	+	0.0730831i
$161$	−34.1235	+	19.7012i	−2.68930	+	1.55267i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	4.37277	−	4.37277i	0.342502	−	0.342502i	−0.514805	−	0.857307i	$-0.672136\pi$
$163$	4.37277	−	4.37277i	0.342502	−	0.342502i	0.857307	+	0.514805i	$0.172136\pi$
$164$	−8.01808	−	4.62924i	−0.626107	−	0.361483i
$165$	−1.85014	−	4.07485i	−0.144033	−	0.317226i
$166$	−4.58222	−	2.64555i	−0.355649	−	0.205334i
$167$	20.4029	+	5.46693i	1.57882	+	0.423044i	0.938561	−	0.345115i	$-0.112160\pi$
$167$	20.4029	+	5.46693i	1.57882	+	0.423044i	0.640260	+	0.768158i	$0.278827\pi$
$168$	−4.37058	+	1.17109i	−0.337198	+	0.0903518i
$169$	−10.9105	+	6.29918i	−0.839269	+	0.484552i
$170$	12.1332	−	2.01297i	0.930576	−	0.154388i
$171$	2.17678			0.166462
$172$	9.36153	+	2.50841i	0.713810	+	0.191265i
$173$	5.86119	+	21.8742i	0.445618	+	1.66307i	0.714301	+	0.699839i	$0.246745\pi$
$173$	5.86119	+	21.8742i	0.445618	+	1.66307i	−0.268683	+	0.963229i	$0.586588\pi$
$174$	−8.39122	+	4.84467i	−0.636136	+	0.367274i
$175$	18.7913	−	12.5986i	1.42049	−	0.952362i
$176$	−1.73324	−	1.00068i	−0.130648	−	0.0754294i
$177$	−0.0328141	−	0.122464i	−0.00246646	−	0.00920495i
$178$	2.53789	+	2.53789i	0.190223	+	0.190223i
$179$	−12.1259	−	21.0027i	−0.906334	−	1.56982i	−0.819116	−	0.573628i	$-0.805535\pi$
$179$	−12.1259	−	21.0027i	−0.906334	−	1.56982i	−0.0872187	−	0.996189i	$-0.527798\pi$
$180$	1.41990	+	1.72739i	0.105833	+	0.128752i
$181$	8.16750	+	4.71551i	0.607086	+	0.350501i	0.771824	−	0.635836i	$-0.219345\pi$
$181$	8.16750	+	4.71551i	0.607086	+	0.350501i	−0.164738	+	0.986337i	$0.552678\pi$
$182$	−2.02767	+	2.02767i	−0.150301	+	0.150301i
$183$	−1.03246	−	0.276648i	−0.0763219	−	0.0204504i
$184$	8.70817			0.641975
$185$	3.20927	−	4.48596i	0.235951	−	0.329814i
$186$	−1.18474	−	5.44026i	−0.0868696	−	0.398899i
$187$	7.78394	+	7.78394i	0.569218	+	0.569218i
$188$	2.08728	−	2.08728i	0.152230	−	0.152230i
$189$	2.26238	+	3.91856i	0.164564	+	0.285033i
$190$	−2.83206	+	3.95869i	−0.205459	+	0.287193i
$191$	8.60652	−	14.9069i	0.622746	−	1.07863i	−0.366227	−	0.930526i	$-0.619350\pi$
$191$	8.60652	−	14.9069i	0.622746	−	1.07863i	0.988972	−	0.148101i	$-0.0473162\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	2.37062	+	0.635205i	0.170641	+	0.0457231i	0.343128	−	0.939289i	$-0.388514\pi$
$193$	2.37062	+	0.635205i	0.170641	+	0.0457231i	−0.172487	+	0.985012i	$0.555180\pi$
$194$			11.2320i			0.806414i
$195$	1.32667	+	0.498136i	0.0950047	+	0.0356723i
$196$	6.73672	−	11.6683i	0.481194	−	0.833453i
$197$	3.51859	+	13.1316i	0.250689	+	0.935585i	0.970438	+	0.241351i	$0.0775904\pi$
$197$	3.51859	+	13.1316i	0.250689	+	0.935585i	−0.719749	+	0.694235i	$0.755743\pi$
$198$	−0.517992	+	1.93317i	−0.0368121	+	0.137385i
$199$	−1.14446	+	1.98226i	−0.0811284	+	0.140519i	−0.903735	−	0.428093i	$-0.859186\pi$
$199$	−1.14446	+	1.98226i	−0.0811284	+	0.140519i	0.822606	+	0.568611i	$0.192519\pi$
$200$	−4.98878	+	0.334833i	−0.352760	+	0.0236763i
$201$		−	13.9470i		−	0.983749i
$202$	−4.55892	−	4.55892i	−0.320765	−	0.320765i
$203$	11.3471	−	42.3481i	0.796412	−	2.97225i
$204$	−4.76341	−	2.75016i	−0.333506	−	0.192550i
$205$	−13.1461	−	15.9930i	−0.918165	−	1.11700i
$206$	−0.993435	+	1.72068i	−0.0692159	+	0.119885i
$207$	−2.25384	−	8.41145i	−0.156653	−	0.584636i
$208$	0.612154	−	0.164026i	0.0424453	−	0.0113732i
$209$	−4.35653			−0.301348
$210$	−10.0697	−	0.983816i	−0.694877	−	0.0678897i
$211$	−6.54758	−	11.3407i	−0.450754	−	0.780728i	0.547679	−	0.836688i	$-0.315511\pi$
$211$	−6.54758	−	11.3407i	−0.450754	−	0.780728i	−0.998433	+	0.0559600i	$0.982178\pi$
$212$	0.998317	+	3.72577i	0.0685647	+	0.255887i
$213$	4.97258	+	4.97258i	0.340716	+	0.340716i
$214$	1.86765	−	1.07829i	0.127670	−	0.0737101i
$215$	17.6254	+	12.6093i	1.20205	+	0.859949i
$216$		−	1.00000i		−	0.0680414i
$217$	21.1966	+	13.6155i	1.43892	+	0.924277i
$218$	6.31311	−	6.31311i	0.427578	−	0.427578i
$219$			8.53762i			0.576919i
$220$	−2.84174	−	3.45715i	−0.191590	−	0.233081i
$221$	−3.48582			−0.234482
$222$	−2.38266	+	0.638431i	−0.159913	+	0.0428487i
$223$	−5.52607	+	20.6236i	−0.370053	+	1.38106i	0.490387	+	0.871505i	$0.336856\pi$
$223$	−5.52607	+	20.6236i	−0.370053	+	1.38106i	−0.860440	+	0.509552i	$0.829811\pi$
$224$	−3.91856	+	2.26238i	−0.261820	+	0.151162i
$225$	1.61461	+	4.73213i	0.107641	+	0.315475i
$226$	9.61365	−	16.6513i	0.639491	−	1.10763i
$227$	7.88615	−	2.11309i	0.523422	−	0.140251i	0.0125731	−	0.999921i	$-0.495998\pi$
$227$	7.88615	−	2.11309i	0.523422	−	0.140251i	0.510849	+	0.859670i	$0.329331\pi$
$228$	2.10260	−	0.563391i	0.139248	−	0.0373115i
$229$	−5.33480	−	9.24015i	−0.352534	−	0.610606i	0.634159	−	0.773203i	$-0.281346\pi$
$229$	−5.33480	−	9.24015i	−0.352534	−	0.610606i	−0.986693	+	0.162597i	$0.948013\pi$
$230$	18.2294	+	6.84475i	1.20201	+	0.451330i
$231$	−4.52785	−	7.84247i	−0.297911	−	0.515997i
$232$	−6.85140	+	6.85140i	−0.449816	+	0.449816i
$233$	3.28740	−	3.28740i	0.215365	−	0.215365i	−0.591177	−	0.806542i	$-0.701337\pi$
$233$	3.28740	−	3.28740i	0.215365	−	0.215365i	0.806542	+	0.591177i	$0.201337\pi$
$234$	−0.316874	−	0.548843i	−0.0207147	−	0.0358790i
$235$	6.01006	−	2.72880i	0.392053	−	0.178007i
$236$	−0.0633919	−	0.109798i	−0.00412646	−	0.00714725i
$237$	−9.38849	+	2.51564i	−0.609848	+	0.163408i
$238$	24.0396	−	6.44138i	1.55825	−	0.417533i
$239$	−7.75429	+	13.4308i	−0.501583	+	0.868768i	0.498415	+	0.866939i	$0.333916\pi$
$239$	−7.75429	+	13.4308i	−0.501583	+	0.868768i	−0.999998	+	0.00182938i	$0.999418\pi$
$240$	1.81860	+	1.30104i	0.117390	+	0.0839815i
$241$	−10.0158	+	5.78263i	−0.645175	+	0.372492i	−0.786605	−	0.617456i	$-0.788163\pi$
$241$	−10.0158	+	5.78263i	−0.645175	+	0.372492i	0.141430	+	0.989948i	$0.454830\pi$
$242$	−1.81032	+	6.75619i	−0.116372	+	0.434305i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−1.06889			−0.0684284
$245$	23.2739	−	19.1309i	1.48692	−	1.22223i
$246$			9.25848i			0.590299i
$247$	0.975475	−	0.975475i	0.0620680	−	0.0620680i
$248$	−2.55242	−	4.94825i	−0.162079	−	0.314214i
$249$			5.29109i			0.335309i
$250$	−10.7065	−	3.22033i	−0.677140	−	0.203671i
$251$	20.8444	−	12.0345i	1.31569	−	0.759612i	0.332655	−	0.943049i	$-0.392056\pi$
$251$	20.8444	−	12.0345i	1.31569	−	0.759612i	0.983032	+	0.183437i	$0.0587222\pi$
$252$	3.19949	+	3.19949i	0.201549	+	0.201549i
$253$	4.51076	+	16.8344i	0.283589	+	1.05837i
$254$	−1.60266	−	2.77588i	−0.100560	−	0.174174i
$255$	−7.80990	−	9.50120i	−0.489075	−	0.594988i
$256$	1.00000			0.0625000
$257$	11.3043	−	3.02897i	0.705140	−	0.188942i	0.111608	−	0.993752i	$-0.464400\pi$
$257$	11.3043	−	3.02897i	0.705140	−	0.188942i	0.593532	+	0.804811i	$0.297733\pi$
$258$	−2.50841	−	9.36153i	−0.156167	−	0.582823i
$259$	5.58063	−	9.66593i	0.346763	−	0.600612i
$260$	1.41039	+	0.137796i	0.0874687	+	0.00854573i
$261$	8.39122	+	4.84467i	0.519403	+	0.299878i
$262$	−2.07342	+	7.73813i	−0.128097	+	0.478063i
$263$	−4.56820	−	4.56820i	−0.281687	−	0.281687i	0.552094	−	0.833782i	$-0.313829\pi$
$263$	−4.56820	−	4.56820i	−0.281687	−	0.281687i	−0.833782	+	0.552094i	$0.813829\pi$
$264$			2.00137i			0.123176i
$265$	−0.838669	+	8.58409i	−0.0515190	+	0.527317i
$266$	−4.92470	+	8.52982i	−0.301952	+	0.522997i
$267$	0.928932	−	3.46682i	0.0568497	−	0.212166i
$268$	−3.60976	−	13.4718i	−0.220501	−	0.822922i
$269$	−2.52782	+	4.37831i	−0.154124	+	0.266950i	−0.932740	−	0.360551i	$-0.882589\pi$
$269$	−2.52782	+	4.37831i	−0.154124	+	0.266950i	0.778616	+	0.627501i	$0.215922\pi$
$270$	0.786015	−	2.09337i	0.0478354	−	0.127398i
$271$		−	25.9633i		−	1.57716i	−0.614932	−	0.788580i	$-0.710817\pi$
$271$		−	25.9633i		−	1.57716i	0.614932	−	0.788580i	$-0.289183\pi$
$272$	−5.31290	−	1.42359i	−0.322142	−	0.0863176i
$273$	2.76985	+	0.742179i	0.167639	+	0.0449187i
$274$	1.34269	−	2.32560i	0.0811147	−	0.140495i
$275$	−3.23144	−	9.47073i	−0.194863	−	0.571106i
$276$	−4.35409	−	7.54150i	−0.262085	−	0.453945i
$277$	0.0857615	−	0.0857615i	0.00515291	−	0.00515291i	−0.704526	−	0.709679i	$-0.748840\pi$
$277$	0.0857615	−	0.0857615i	0.00515291	−	0.00515291i	0.709679	+	0.704526i	$0.248840\pi$
$278$	−1.84756	−	1.84756i	−0.110809	−	0.110809i
$279$	−4.11903	+	3.74615i	−0.246600	+	0.224276i
$280$	−9.98124	+	1.65594i	−0.596493	+	0.0989615i
$281$	−18.6572			−1.11299			−0.556496	−	0.830850i	$-0.687855\pi$
$281$	−18.6572			−1.11299			−0.556496	+	0.830850i	$0.687855\pi$
$282$	−2.85127	−	0.763996i	−0.169791	−	0.0454953i
$283$	−13.9927	+	13.9927i	−0.831779	+	0.831779i	−0.987760	−	0.155981i	$-0.950146\pi$
$283$	−13.9927	+	13.9927i	−0.831779	+	0.831779i	0.155981	+	0.987760i	$0.450146\pi$
$284$	6.09014	+	3.51615i	0.361384	+	0.208645i
$285$	4.84436	+	0.473295i	0.286955	+	0.0280356i
$286$	0.634183	+	1.09844i	0.0375000	+	0.0649519i
$287$	−29.6224	−	29.6224i	−1.74855	−	1.74855i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	11.4778	+	6.62673i	0.675167	+	0.389808i
$290$	−19.7278	+	8.95718i	−1.15846	+	0.525984i
$291$	9.72723	−	5.61602i	0.570221	−	0.329217i
$292$	2.20970	+	8.24671i	0.129313	+	0.482602i
$293$	−13.6814	−	3.66593i	−0.799278	−	0.214166i	−0.164011	−	0.986459i	$-0.552443\pi$
$293$	−13.6814	−	3.66593i	−0.799278	−	0.214166i	−0.635267	+	0.772293i	$0.719110\pi$
$294$	−13.4734			−0.785787
$295$	−0.0463996	−	0.279675i	−0.00270149	−	0.0162833i
$296$	−2.13623	+	1.23335i	−0.124166	+	0.0716872i
$297$	1.93317	−	0.517992i	0.112174	−	0.0300570i
$298$	−12.0887	−	3.23916i	−0.700281	−	0.187640i
$299$	−4.77942	−	2.75940i	−0.276401	−	0.159580i
$300$	2.78436	+	4.15299i	0.160755	+	0.239773i
$301$	37.9777	+	21.9264i	2.18900	+	1.26382i
$302$	12.0746	−	12.0746i	0.694815	−	0.694815i
$303$	−1.66868	+	6.22761i	−0.0958633	+	0.357767i
$304$	1.88514	−	1.08839i	0.108120	−	0.0624234i
$305$	−2.23757	−	0.840160i	−0.128123	−	0.0481074i
$306$			5.50031i			0.314432i
$307$	4.79894	−	17.9099i	0.273890	−	1.02217i	−0.682692	−	0.730706i	$-0.739191\pi$
$307$	4.79894	−	17.9099i	0.273890	−	1.02217i	0.956582	−	0.291464i	$-0.0941425\pi$
$308$	−6.40335	−	6.40335i	−0.364865	−	0.364865i
$309$	1.98687			0.113029
$310$	−1.45374	−	12.3647i	−0.0825670	−	0.702270i
$311$	8.97977			0.509196			0.254598	−	0.967047i	$-0.418057\pi$
$311$	8.97977			0.509196			0.254598	+	0.967047i	$0.418057\pi$
$312$	−0.448128	−	0.448128i	−0.0253703	−	0.0253703i
$313$	−0.347293	+	1.29612i	−0.0196302	+	0.0732608i	−0.975046	−	0.222002i	$-0.928741\pi$
$313$	−0.347293	+	1.29612i	−0.0196302	+	0.0732608i	0.955416	+	0.295263i	$0.0954074\pi$
$314$			6.14073i			0.346542i
$315$	4.18285	+	9.21254i	0.235677	+	0.519068i
$316$	−8.41749	+	4.85984i	−0.473521	+	0.273387i
$317$	−8.44625	+	31.5218i	−0.474389	+	1.77044i	0.149322	+	0.988789i	$0.452291\pi$
$317$	−8.44625	+	31.5218i	−0.474389	+	1.77044i	−0.623711	+	0.781655i	$0.714376\pi$
$318$	2.72745	−	2.72745i	0.152948	−	0.152948i
$319$	−16.7939	−	9.69597i	−0.940279	−	0.542870i
$320$	2.09337	+	0.786015i	0.117023	+	0.0439396i
$321$	−1.86765	−	1.07829i	−0.104242	−	0.0601841i
$322$	38.0598	+	10.1981i	2.12099	+	0.568317i
$323$	−11.5650	+	3.09883i	−0.643493	+	0.172423i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	2.84415	+	1.39705i	0.157765	+	0.0774941i
$326$	−6.18403			−0.342502
$327$	−8.62386	−	2.31076i	−0.476901	−	0.127785i
$328$	2.39627	+	8.94301i	0.132312	+	0.493795i
$329$	11.5670	−	6.67821i	0.637710	−	0.368182i
$330$	−1.57311	+	4.18960i	−0.0865966	+	0.230630i
$331$	23.2638	+	13.4314i	1.27870	+	0.738256i	0.976609	−	0.215024i	$-0.0689831\pi$
$331$	23.2638	+	13.4314i	1.27870	+	0.738256i	0.302088	+	0.953280i	$0.402316\pi$
$332$	1.36944	+	5.11080i	0.0751575	+	0.280492i
$333$	1.74423	+	1.74423i	0.0955830	+	0.0955830i
$334$	−10.5613	−	18.2927i	−0.577888	−	1.00093i
$335$	3.03250	−	31.0388i	0.165683	−	1.69583i
$336$	3.91856	+	2.26238i	0.213775	+	0.123423i
$337$	−1.28267	+	1.28267i	−0.0698716	+	0.0698716i	−0.741179	−	0.671307i	$-0.765733\pi$
$337$	−1.28267	+	1.28267i	−0.0698716	+	0.0698716i	0.671307	+	0.741179i	$0.265733\pi$
$338$	12.1691	+	3.26070i	0.661911	+	0.177358i
$339$	−19.2273			−1.04428
$340$	−10.0029	−	7.15610i	−0.542482	−	0.388094i
$341$	8.24369	−	7.49742i	0.446421	−	0.406008i
$342$	−1.53921	−	1.53921i	−0.0832311	−	0.0832311i
$343$	20.7117	−	20.7117i	1.11833	−	1.11833i
$344$	−4.84588	−	8.39331i	−0.261272	−	0.452537i
$345$	−3.18696	−	19.2095i	−0.171580	−	1.03420i
$346$	11.3229	−	19.6119i	0.608725	−	1.05434i
$347$	12.4019	+	3.32308i	0.665770	+	0.178392i	0.575848	−	0.817556i	$-0.304672\pi$
$347$	12.4019	+	3.32308i	0.665770	+	0.178392i	0.0899212	+	0.995949i	$0.471338\pi$
$348$	9.35919	+	2.50779i	0.501705	+	0.134431i
$349$		−	15.9870i		−	0.855763i	−0.903835	−	0.427881i	$-0.859260\pi$
$349$		−	15.9870i		−	0.855763i	0.903835	−	0.427881i	$-0.140740\pi$
$350$	−22.1960	−	4.37891i	−1.18642	−	0.234063i
$351$	−0.316874	+	0.548843i	−0.0169135	+	0.0292951i
$352$	0.517992	+	1.93317i	0.0276091	+	0.103038i
$353$	−5.27409	+	19.6832i	−0.280712	+	1.04763i	0.671205	+	0.741272i	$0.265777\pi$
$353$	−5.27409	+	19.6832i	−0.280712	+	1.04763i	−0.951916	+	0.306358i	$0.900890\pi$
$354$	−0.0633919	+	0.109798i	−0.00336924	+	0.00583570i
$355$	9.98515	+	12.1475i	0.529957	+	0.644724i
$356$		−	3.58912i		−	0.190223i
$357$	−17.5982	−	17.5982i	−0.931395	−	0.931395i
$358$	−6.27684	+	23.4255i	−0.331741	+	1.23808i
$359$	16.9092	+	9.76253i	0.892433	+	0.515246i	0.874738	−	0.484597i	$-0.161034\pi$
$359$	16.9092	+	9.76253i	0.892433	+	0.515246i	0.0176955	+	0.999843i	$0.494367\pi$
$360$	0.217429	−	2.22547i	0.0114595	−	0.117293i
$361$	−7.13082	+	12.3509i	−0.375306	+	0.650050i
$362$	−2.44093	−	9.10967i	−0.128292	−	0.478793i
$363$	6.75619	−	1.81032i	0.354608	−	0.0950170i
$364$	2.86756			0.150301
$365$	−1.85633	+	19.0002i	−0.0971648	+	0.994518i
$366$	0.534443	+	0.925682i	0.0279358	+	0.0483862i
$367$	7.40243	+	27.6262i	0.386403	+	1.44208i	0.835943	+	0.548817i	$0.184922\pi$
$367$	7.40243	+	27.6262i	0.386403	+	1.44208i	−0.449539	+	0.893261i	$0.648412\pi$
$368$	−6.15761	−	6.15761i	−0.320987	−	0.320987i
$369$	8.01808	−	4.62924i	0.417405	−	0.240989i
$370$	−5.44135	+	0.902750i	−0.282882	+	0.0469318i
$371$			17.4529i			0.906110i
$372$	−3.00910	+	4.68458i	−0.156015	+	0.242884i
$373$	−9.40172	+	9.40172i	−0.486803	+	0.486803i	−0.907296	−	0.420493i	$-0.861857\pi$
$373$	−9.40172	+	9.40172i	−0.486803	+	0.486803i	0.420493	+	0.907296i	$0.361857\pi$
$374$		−	11.0082i		−	0.569218i
$375$	2.56437	+	10.8823i	0.132424	+	0.561958i
$376$	−2.95185			−0.152230
$377$	5.93137	−	1.58931i	0.305481	−	0.0818535i
$378$	1.17109	−	4.37058i	0.0602346	−	0.224798i
$379$	9.31091	−	5.37566i	0.478270	−	0.276129i	−0.241426	−	0.970419i	$-0.577615\pi$
$379$	9.31091	−	5.37566i	0.478270	−	0.276129i	0.719695	+	0.694290i	$0.244282\pi$
$380$	4.80179	−	0.796643i	0.246326	−	0.0408669i
$381$	−1.60266	+	2.77588i	−0.0821066	+	0.142213i
$382$	−16.6265	+	4.45506i	−0.850686	+	0.227941i
$383$	−27.9647	+	7.49311i	−1.42893	+	0.382880i	−0.888642	−	0.458601i	$-0.848351\pi$
$383$	−27.9647	+	7.49311i	−1.42893	+	0.382880i	−0.540286	+	0.841481i	$0.681684\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−8.37143	−	18.4377i	−0.426647	−	0.939672i
$386$	−1.22712	−	2.12544i	−0.0624589	−	0.108182i
$387$	−6.85311	+	6.85311i	−0.348363	+	0.348363i
$388$	7.94225	−	7.94225i	0.403207	−	0.403207i
$389$	2.03311	+	3.52145i	0.103083	+	0.178545i	0.912953	−	0.408064i	$-0.133796\pi$
$389$	2.03311	+	3.52145i	0.103083	+	0.178545i	−0.809870	+	0.586609i	$0.800463\pi$
$390$	−0.585861	−	1.29033i	−0.0296662	−	0.0653385i
$391$	23.9488	+	41.4806i	1.21114	+	2.09776i
$392$	−13.0143	+	3.48718i	−0.657324	+	0.176129i
$393$	7.73813	−	2.07342i	0.390337	−	0.104590i
$394$	6.79740	−	11.7734i	0.342448	−	0.593137i
$395$	−21.4408	+	3.55715i	−1.07880	+	0.178979i
$396$	1.73324	−	1.00068i	0.0870984	−	0.0502863i
$397$	−6.77488	+	25.2842i	−0.340021	+	1.26898i	0.558301	+	0.829639i	$0.311454\pi$
$397$	−6.77488	+	25.2842i	−0.340021	+	1.26898i	−0.898322	+	0.439338i	$0.855213\pi$
$398$	2.21092	−	0.592415i	0.110823	−	0.0296951i
$399$	9.84939			0.493086
$400$	3.76436	+	3.29083i	0.188218	+	0.164542i
$401$			30.8385i			1.54000i	0.638044	+	0.770000i	$0.279744\pi$
$401$			30.8385i			1.54000i	−0.638044	+	0.770000i	$0.720256\pi$
$402$	−9.86205	+	9.86205i	−0.491874	+	0.491874i
$403$	−0.167099	+	3.52461i	−0.00832378	+	0.175573i
$404$			6.44729i			0.320765i
$405$	−2.20592	+	0.365974i	−0.109613	+	0.0181854i
$406$	−37.9682	+	21.9210i	−1.88433	+	1.08792i
$407$	−3.49084	−	3.49084i	−0.173034	−	0.173034i
$408$	1.42359	+	5.31290i	0.0704780	+	0.263028i
$409$	−5.56971	−	9.64702i	−0.275404	−	0.477014i	0.694833	−	0.719171i	$-0.255478\pi$
$409$	−5.56971	−	9.64702i	−0.275404	−	0.477014i	−0.970237	+	0.242157i	$0.922145\pi$
$410$	−2.01307	+	20.6045i	−0.0994183	+	1.01758i
$411$	−2.68537			−0.132460
$412$	1.91917	−	0.514240i	0.0945506	−	0.0253348i
$413$	−0.148476	−	0.554119i	−0.00730602	−	0.0272664i
$414$	−4.35409	+	7.54150i	−0.213992	+	0.370644i
$415$	−1.15044	+	11.7752i	−0.0564728	+	0.578021i
$416$	−0.548843	−	0.316874i	−0.0269092	−	0.0155360i
$417$	−0.676252	+	2.52381i	−0.0331162	+	0.123591i
$418$	3.08053	+	3.08053i	0.150674	+	0.150674i
$419$			23.4277i			1.14452i	0.820072	+	0.572260i	$0.193933\pi$
$419$			23.4277i			1.14452i	−0.820072	+	0.572260i	$0.806067\pi$
$420$	6.42471	+	7.81603i	0.313494	+	0.381383i
$421$	−18.9841	+	32.8815i	−0.925230	+	1.60255i	−0.134040	+	0.990976i	$0.542795\pi$
$421$	−18.9841	+	32.8815i	−0.925230	+	1.60255i	−0.791190	+	0.611570i	$0.790538\pi$
$422$	−3.38928	+	12.6489i	−0.164987	+	0.615741i
$423$	0.763996	+	2.85127i	0.0371468	+	0.138634i
$424$	1.92860	−	3.34043i	0.0936611	−	0.162226i
$425$	−15.3149	−	22.8428i	−0.742880	−	1.10804i
$426$		−	7.03229i		−	0.340716i
$427$	−4.67165	−	1.25176i	−0.226077	−	0.0605771i
$428$	−2.08309	−	0.558162i	−0.100690	−	0.0269798i
$429$	0.634183	−	1.09844i	0.0306186	−	0.0530330i
$430$	−3.54693	−	21.3792i	−0.171048	−	1.03100i
$431$	−5.93237	−	10.2752i	−0.285752	−	0.494938i	0.687039	−	0.726621i	$-0.258910\pi$
$431$	−5.93237	−	10.2752i	−0.285752	−	0.494938i	−0.972791	+	0.231683i	$0.925577\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−6.28335	−	6.28335i	−0.301959	−	0.301959i	0.539821	−	0.841780i	$-0.318492\pi$
$433$	−6.28335	−	6.28335i	−0.301959	−	0.301959i	−0.841780	+	0.539821i	$0.818492\pi$
$434$	−5.36068	−	24.6158i	−0.257321	−	1.18160i
$435$	17.6210	+	12.6062i	0.844864	+	0.604420i
$436$	−8.92808			−0.427578
$437$	−18.3098	−	4.90611i	−0.875878	−	0.234691i
$438$	6.03701	−	6.03701i	0.288460	−	0.288460i
$439$	3.83250	+	2.21270i	0.182915	+	0.105606i	0.588662	−	0.808380i	$-0.299655\pi$
$439$	3.83250	+	2.21270i	0.182915	+	0.105606i	−0.405746	+	0.913986i	$0.632988\pi$
$440$	−0.435156	+	4.45399i	−0.0207453	+	0.212336i
$441$	6.73672	+	11.6683i	0.320796	+	0.555635i
$442$	2.46485	+	2.46485i	0.117241	+	0.117241i
$443$	7.37674	+	27.5304i	0.350479	+	1.30801i	0.886079	+	0.463534i	$0.153419\pi$
$443$	7.37674	+	27.5304i	0.350479	+	1.30801i	−0.535600	+	0.844472i	$0.679914\pi$
$444$	2.13623	+	1.23335i	0.101381	+	0.0585324i
$445$	2.82110	−	7.51334i	0.133733	−	0.356166i
$446$	18.4906	−	10.6755i	0.875555	−	0.505502i
$447$	3.23916	+	12.0887i	0.153207	+	0.571777i
$448$	4.37058	+	1.17109i	0.206491	+	0.0553290i
$449$	−2.08881			−0.0985769			−0.0492884	−	0.998785i	$-0.515695\pi$
$449$	−2.08881			−0.0985769			−0.0492884	+	0.998785i	$0.515695\pi$
$450$	2.20441	−	4.48782i	0.103917	−	0.211558i
$451$	−16.0471	+	9.26481i	−0.755630	+	0.436263i
$452$	−18.5721	+	4.97639i	−0.873560	+	0.234070i
$453$	−16.4942	−	4.41961i	−0.774966	−	0.207651i
$454$	−7.07053	−	4.08217i	−0.331836	−	0.191586i
$455$	6.00285	+	2.25395i	0.281418	+	0.105667i
$456$	−1.88514	−	1.08839i	−0.0882800	−	0.0509685i
$457$	−5.89151	+	5.89151i	−0.275593	+	0.275593i	−0.831347	−	0.555754i	$-0.812430\pi$
$457$	−5.89151	+	5.89151i	−0.275593	+	0.275593i	0.555754	+	0.831347i	$0.312430\pi$
$458$	−2.76150	+	10.3060i	−0.129036	+	0.481570i
$459$	4.76341	−	2.75016i	0.222337	−	0.128366i
$460$	−8.05015	−	17.7301i	−0.375340	−	0.826670i
$461$		−	35.0423i		−	1.63208i	−0.577994	−	0.816041i	$-0.696164\pi$
$461$		−	35.0423i		−	1.63208i	0.577994	−	0.816041i	$-0.303836\pi$
$462$	−2.34379	+	8.74714i	−0.109043	+	0.406954i
$463$	19.5007	+	19.5007i	0.906274	+	0.906274i	0.995969	−	0.0896954i	$-0.0285894\pi$
$463$	19.5007	+	19.5007i	0.906274	+	0.906274i	−0.0896954	+	0.995969i	$0.528589\pi$
$464$	9.68934			0.449816
$465$	−9.98130	+	7.44134i	−0.462872	+	0.345084i
$466$	−4.64909			−0.215365
$467$	−20.6447	−	20.6447i	−0.955321	−	0.955321i	0.0437225	−	0.999044i	$-0.486078\pi$
$467$	−20.6447	−	20.6447i	−0.955321	−	0.955321i	−0.999044	+	0.0437225i	$0.986078\pi$
$468$	−0.164026	+	0.612154i	−0.00758212	+	0.0282969i
$469$		−	63.1070i		−	2.91401i
$470$	−6.17931	−	2.32020i	−0.285030	−	0.107023i
$471$	5.31803	−	3.07037i	0.245042	−	0.141475i
$472$	−0.0328141	+	0.122464i	−0.00151039	+	0.00563686i
$473$	13.7156	−	13.7156i	0.630644	−	0.630644i
$474$	8.41749	+	4.85984i	0.386628	+	0.223220i
$475$	10.6781	+	2.10661i	0.489943	+	0.0966579i
$476$	−21.5533	−	12.4438i	−0.987893	−	0.570361i
$477$	−3.72577	−	0.998317i	−0.170591	−	0.0457098i
$478$	14.9801	−	4.01392i	0.685176	−	0.183592i
$479$	−23.9759	+	13.8425i	−1.09549	+	0.632480i	−0.935032	−	0.354563i	$-0.884630\pi$
$479$	−23.9759	+	13.8425i	−1.09549	+	0.632480i	−0.160456	+	0.987043i	$0.551296\pi$
$480$	−0.365974	−	2.20592i	−0.0167043	−	0.100686i
$481$	1.56327			0.0712791
$482$	11.1712	+	2.99331i	0.508834	+	0.136342i
$483$	−10.1981	−	38.0598i	−0.464029	−	1.73178i
$484$	6.05744	−	3.49726i	0.275338	−	0.158966i
$485$	22.8688	−	10.3833i	1.03842	−	0.471482i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	2.51314	+	9.37917i	0.113881	+	0.425011i	0.999201	−	0.0399726i	$-0.0127271\pi$
$487$	2.51314	+	9.37917i	0.113881	+	0.425011i	−0.885320	+	0.464983i	$0.846060\pi$
$488$	0.755816	+	0.755816i	0.0342142	+	0.0342142i
$489$	3.09202	+	5.35553i	0.139826	+	0.242185i
$490$	−29.9848	−	2.92952i	−1.35457	−	0.132342i
$491$	1.40735	+	0.812533i	0.0635128	+	0.0366691i	0.531420	−	0.847108i	$-0.321659\pi$
$491$	1.40735	+	0.812533i	0.0635128	+	0.0366691i	−0.467907	+	0.883778i	$0.654992\pi$
$492$	6.54673	−	6.54673i	0.295150	−	0.295150i
$493$	−51.4785	−	13.7936i	−2.31847	−	0.621233i
$494$	−1.37953			−0.0620680
$495$	4.41485	−	0.732448i	0.198433	−	0.0329211i
$496$	−1.69411	+	5.30377i	−0.0760678	+	0.238146i
$497$	22.4997	+	22.4997i	1.00925	+	1.00925i
$498$	3.74137	−	3.74137i	0.167655	−	0.167655i
$499$	−5.36266	−	9.28841i	−0.240066	−	0.415806i	0.720667	−	0.693281i	$-0.243836\pi$
$499$	−5.36266	−	9.28841i	−0.240066	−	0.415806i	−0.960733	+	0.277475i	$0.910502\pi$
$500$	5.29354	+	9.84776i	0.236734	+	0.440405i
$501$	−10.5613	+	18.2927i	−0.471844	+	0.817258i
$502$	−23.2489	−	6.22952i	−1.03765	−	0.278037i
$503$	15.0705	+	4.03812i	0.671958	+	0.180051i	0.578637	−	0.815585i	$-0.303585\pi$
$503$	15.0705	+	4.03812i	0.671958	+	0.180051i	0.0933216	+	0.995636i	$0.470252\pi$
$504$		−	4.52476i		−	0.201549i
$505$	−5.06767	+	13.4965i	−0.225508	+	0.600588i
$506$	8.71413	−	15.0933i	0.387390	−	0.670980i
$507$	−3.26070	−	12.1691i	−0.144813	−	0.540448i
$508$	−0.829597	+	3.09610i	−0.0368074	+	0.137367i
$509$	−12.0489	+	20.8693i	−0.534057	+	0.925014i	0.465151	+	0.885231i	$0.346000\pi$
$509$	−12.0489	+	20.8693i	−0.534057	+	0.925014i	−0.999208	+	0.0397827i	$0.987333\pi$
$510$	−1.19593	+	12.2408i	−0.0529567	+	0.542031i
$511$			38.6307i			1.70892i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.563391	+	2.10260i	−0.0248743	+	0.0928323i
$514$	−10.1351	−	5.85151i	−0.447041	−	0.258099i
$515$	4.42172	+	0.432004i	0.194844	+	0.0190364i
$516$	−4.84588	+	8.39331i	−0.213328	+	0.369495i
$517$	−1.52904	−	5.70645i	−0.0672470	−	0.250969i
$518$	−10.7809	+	2.88875i	−0.473688	+	0.126924i
$519$	−22.6459			−0.994044
$520$	−0.899860	−	1.09473i	−0.0394615	−	0.0480072i
$521$	−16.3097	−	28.2492i	−0.714540	−	1.23762i	−0.963137	−	0.269012i	$-0.913303\pi$
$521$	−16.3097	−	28.2492i	−0.714540	−	1.23762i	0.248597	−	0.968607i	$-0.420031\pi$
$522$	−2.50779	−	9.35919i	−0.109763	−	0.409640i
$523$	20.1931	+	20.1931i	0.882981	+	0.882981i	0.993837	−	0.110856i	$-0.0353592\pi$
$523$	20.1931	+	20.1931i	0.882981	+	0.882981i	−0.110856	+	0.993837i	$0.535359\pi$
$524$	6.93781	−	4.00555i	0.303080	−	0.174983i
$525$	7.30574	+	21.4117i	0.318849	+	0.934485i
$526$			6.46041i			0.281687i
$527$	16.5510	−	25.7667i	0.720973	−	1.12241i
$528$	1.41518	−	1.41518i	0.0615879	−	0.0615879i
$529$			52.8322i			2.29705i
$530$	6.66290	−	5.47684i	0.289418	−	0.237899i
$531$	0.126784			0.00550195
$532$	9.51378	−	2.54921i	0.412475	−	0.110522i
$533$	1.51863	−	5.66762i	0.0657794	−	0.245492i
$534$	−3.10827	+	1.79456i	−0.134508	+	0.0776582i
$535$	−3.92194	−	2.80578i	−0.169560	−	0.121304i
$536$	−6.97352	+	12.0785i	−0.301210	+	0.521712i
$537$	23.4255	−	6.27684i	1.01088	−	0.270866i
$538$	4.88337	−	1.30850i	0.210537	−	0.0564132i
$539$	−13.4827	−	23.3527i	−0.580739	−	1.00587i
$540$	−2.03603	+	0.924436i	−0.0876168	+	0.0397814i
$541$	2.55948	+	4.43314i	0.110040	+	0.190596i	0.915786	−	0.401666i	$-0.131569\pi$
$541$	2.55948	+	4.43314i	0.110040	+	0.190596i	−0.805746	+	0.592261i	$0.798235\pi$
$542$	−18.3588	+	18.3588i	−0.788580	+	0.788580i
$543$	−6.66874	+	6.66874i	−0.286183	+	0.286183i
$544$	2.75016	+	4.76341i	0.117912	+	0.204230i
$545$	−18.6897	−	7.01761i	−0.800580	−	0.300601i
$546$	−1.43378	−	2.48338i	−0.0613601	−	0.106279i
$547$	11.7442	−	3.14686i	0.502147	−	0.134550i	0.00115083	−	0.999999i	$-0.499634\pi$
$547$	11.7442	−	3.14686i	0.502147	−	0.134550i	0.500996	+	0.865449i	$0.332967\pi$
$548$	−2.59387	+	0.695026i	−0.110805	+	0.0296900i
$549$	0.534443	−	0.925682i	0.0228095	−	0.0395071i
$550$	−4.41184	+	8.98179i	−0.188122	+	0.382985i
$551$	18.2658	−	10.5458i	0.778149	−	0.449265i
$552$	−2.25384	+	8.41145i	−0.0959298	+	0.358015i
$553$	−42.4806	+	11.3827i	−1.80646	+	0.484040i
$554$	−0.121285			−0.00515291
$555$	3.50248	+	4.26097i	0.148672	+	0.180868i
$556$			2.61284i			0.110809i
$557$	21.4988	−	21.4988i	0.910935	−	0.910935i	−0.0854108	−	0.996346i	$-0.527220\pi$
$557$	21.4988	−	21.4988i	0.910935	−	0.910935i	0.996346	+	0.0854108i	$0.0272203\pi$
$558$	5.56152	+	0.263667i	0.235438	+	0.0111619i
$559$			6.14215i			0.259785i
$560$	8.22873	+	5.88687i	0.347727	+	0.248766i
$561$	−9.53334	+	5.50408i	−0.402498	+	0.232382i
$562$	13.1926	+	13.1926i	0.556496	+	0.556496i
$563$	−5.32386	−	19.8689i	−0.224374	−	0.837375i	−0.982654	−	0.185447i	$-0.940627\pi$
$563$	−5.32386	−	19.8689i	−0.224374	−	0.837375i	0.758280	−	0.651929i	$-0.226040\pi$
$564$	1.47593	+	2.55638i	0.0621477	+	0.107643i
$565$	−42.7898	−	4.18058i	−1.80018	−	0.175878i
$566$	19.7886			0.831779
$567$	−4.37058	+	1.17109i	−0.183547	+	0.0491813i
$568$	−1.82009	−	6.79267i	−0.0763693	−	0.285014i
$569$	14.1565	−	24.5198i	0.593471	−	1.02792i	−0.400289	−	0.916389i	$-0.631090\pi$
$569$	14.1565	−	24.5198i	0.593471	−	1.02792i	0.993761	−	0.111534i	$-0.0355763\pi$
$570$	−3.09081	−	3.76015i	−0.129460	−	0.157495i
$571$	−41.2315	−	23.8050i	−1.72548	−	0.996208i	−0.906243	−	0.422757i	$-0.861063\pi$
$571$	−41.2315	−	23.8050i	−1.72548	−	0.996208i	−0.819240	−	0.573451i	$-0.805604\pi$
$572$	0.328277	−	1.22515i	0.0137260	−	0.0512259i
$573$	12.1715	+	12.1715i	0.508470	+	0.508470i
$574$			41.8924i			1.74855i
$575$	−2.91578	−	43.4431i	−0.121597	−	1.81170i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.0178	+	41.1189i	−0.458676	+	1.71180i	0.218373	+	0.975865i	$0.429925\pi$
$577$	−11.0178	+	41.1189i	−0.458676	+	1.71180i	−0.677049	+	0.735938i	$0.736742\pi$
$578$	−3.43025	−	12.8019i	−0.142679	−	0.532487i
$579$	−1.22712	+	2.12544i	−0.0509975	+	0.0883302i
$580$	20.2833	+	7.61597i	0.842220	+	0.316236i
$581$			23.9409i			0.993237i
$582$	−10.8493	−	2.90707i	−0.449719	−	0.120502i
$583$	7.45664	+	1.99800i	0.308822	+	0.0827487i
$584$	4.26881	−	7.39380i	0.176645	−	0.305958i
$585$	−0.824530	+	1.15254i	−0.0340901	+	0.0476515i
$586$	7.08203	+	12.2664i	0.292556	+	0.506722i
$587$	−1.49878	+	1.49878i	−0.0618612	+	0.0618612i	−0.737361	−	0.675499i	$-0.763928\pi$
$587$	−1.49878	+	1.49878i	−0.0618612	+	0.0618612i	0.675499	+	0.737361i	$0.263928\pi$
$588$	9.52716	+	9.52716i	0.392894	+	0.392894i
$589$	2.57892	+	11.8422i	0.106263	+	0.487950i
$590$	−0.164950	+	0.230569i	−0.00679090	+	0.00949239i
$591$	−13.5948			−0.559215
$592$	2.38266	+	0.638431i	0.0979266	+	0.0262394i
$593$	19.0726	−	19.0726i	0.783216	−	0.783216i	−0.197156	−	0.980372i	$-0.563170\pi$
$593$	19.0726	−	19.0726i	0.783216	−	0.783216i	0.980372	+	0.197156i	$0.0631705\pi$
$594$	−1.73324	−	1.00068i	−0.0711155	−	0.0410586i
$595$	−35.3379	−	42.9906i	−1.44871	−	1.76244i
$596$	6.25758	+	10.8385i	0.256321	+	0.443960i
$597$	−1.61851	−	1.61851i	−0.0662411	−	0.0662411i
$598$	1.42837	+	5.33075i	0.0584103	+	0.217990i
$599$	37.9772	+	21.9261i	1.55170	+	0.895877i	0.998003	+	0.0631616i	$0.0201184\pi$
$599$	37.9772	+	21.9261i	1.55170	+	0.895877i	0.553701	+	0.832715i	$0.313215\pi$
$600$	0.967766	−	4.90545i	0.0395089	−	0.200264i
$601$	41.8274	−	24.1491i	1.70618	−	0.985062i	0.766987	−	0.641663i	$-0.221755\pi$
$601$	41.8274	−	24.1491i	1.70618	−	0.985062i	0.939190	−	0.343399i	$-0.111578\pi$
$602$	−11.3500	−	42.3586i	−0.462590	−	1.72641i
$603$	13.4718	+	3.60976i	0.548615	+	0.147001i
$604$	−17.0761			−0.694815
$605$	15.4293	−	2.55981i	0.627292	−	0.104071i
$606$	5.58352	−	3.22365i	0.226815	−	0.130952i
$607$	36.4447	−	9.76534i	1.47925	−	0.396363i	0.573156	−	0.819446i	$-0.305719\pi$
$607$	36.4447	−	9.76534i	1.47925	−	0.396363i	0.906091	+	0.423083i	$0.139052\pi$
$608$	−2.10260	−	0.563391i	−0.0852719	−	0.0228485i
$609$	37.9682	+	21.9210i	1.53855	+	0.888283i
$610$	0.988116	+	2.17628i	0.0400077	+	0.0881151i
$611$	1.62010	+	0.935367i	0.0655424	+	0.0378409i
$612$	3.88931	−	3.88931i	0.157216	−	0.157216i
$613$	−3.53763	+	13.2026i	−0.142884	+	0.533249i	0.856957	+	0.515388i	$0.172352\pi$
$613$	−3.53763	+	13.2026i	−0.142884	+	0.533249i	−0.999840	+	0.0178610i	$0.994314\pi$
$614$	−16.0576	+	9.27083i	−0.648030	+	0.374140i
$615$	18.8505	−	8.55888i	0.760127	−	0.345127i
$616$			9.05571i			0.364865i
$617$	−6.67801	+	24.9227i	−0.268846	+	1.00335i	0.691007	+	0.722848i	$0.257167\pi$
$617$	−6.67801	+	24.9227i	−0.268846	+	1.00335i	−0.959854	+	0.280501i	$0.909499\pi$
$618$	−1.40493	−	1.40493i	−0.0565145	−	0.0565145i
$619$	−6.80166			−0.273382			−0.136691	−	0.990614i	$-0.543647\pi$
$619$	−6.80166			−0.273382			−0.136691	+	0.990614i	$0.543647\pi$
$620$	−7.71524	+	9.77114i	−0.309851	+	0.392418i
$621$	8.70817			0.349447
$622$	−6.34965	−	6.34965i	−0.254598	−	0.254598i
$623$	4.20319	−	15.6865i	0.168397	−	0.628468i
$624$			0.633749i			0.0253703i
$625$	3.34082	+	24.7758i	0.133633	+	0.991031i
$626$	1.16207	−	0.670919i	0.0464455	−	0.0268153i
$627$	1.12755	−	4.20809i	0.0450301	−	0.168055i
$628$	4.34215	−	4.34215i	0.173271	−	0.173271i
$629$	−11.7499	−	6.78383i	−0.468501	−	0.270489i
$630$	3.55653	−	9.47198i	0.141696	−	0.377373i
$631$	10.9166	+	6.30267i	0.434581	+	0.250905i	0.701296	−	0.712870i	$-0.252605\pi$
$631$	10.9166	+	6.30267i	0.434581	+	0.250905i	−0.266715	+	0.963775i	$0.585938\pi$
$632$	9.38849	+	2.51564i	0.373454	+	0.100067i
$633$	12.6489	−	3.38928i	0.502750	−	0.134712i
$634$	28.2617	−	16.3169i	1.12242	−	0.648027i
$635$	−4.17023	+	5.82919i	−0.165490	+	0.231324i
$636$	−3.85720			−0.152948
$637$	8.24783	+	2.21000i	0.326791	+	0.0875634i
$638$	5.01900	+	18.7312i	0.198704	+	0.741574i
$639$	−6.09014	+	3.51615i	−0.240922	+	0.139097i
$640$	−0.924436	−	2.03603i	−0.0365416	−	0.0804811i
$641$	−8.85154	−	5.11044i	−0.349615	−	0.201850i	0.314901	−	0.949125i	$-0.398029\pi$
$641$	−8.85154	−	5.11044i	−0.349615	−	0.201850i	−0.664516	+	0.747274i	$0.731362\pi$
$642$	0.558162	+	2.08309i	0.0220289	+	0.0822130i
$643$	−28.1904	−	28.1904i	−1.11172	−	1.11172i	−0.992918	−	0.118803i	$-0.962094\pi$
$643$	−28.1904	−	28.1904i	−1.11172	−	1.11172i	−0.118803	−	0.992918i	$-0.537906\pi$
$644$	−19.7012	−	34.1235i	−0.776335	−	1.34465i
$645$	−16.7415	+	13.7613i	−0.659195	+	0.541852i
$646$	10.3689	+	5.98648i	0.407958	+	0.235535i
$647$	13.1314	−	13.1314i	0.516249	−	0.516249i	−0.400185	−	0.916434i	$-0.631054\pi$
$647$	13.1314	−	13.1314i	0.516249	−	0.516249i	0.916434	+	0.400185i	$0.131054\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−0.253741			−0.00996022
$650$	−1.02326	−	2.99898i	−0.0401356	−	0.117630i
$651$	−18.6376	+	16.9504i	−0.730465	+	0.664339i
$652$	4.37277	+	4.37277i	0.171251	+	0.171251i
$653$	−4.32278	+	4.32278i	−0.169164	+	0.169164i	−0.786612	−	0.617448i	$-0.788167\pi$
$653$	−4.32278	+	4.32278i	−0.169164	+	0.169164i	0.617448	+	0.786612i	$0.288167\pi$
$654$	4.46404	+	7.73194i	0.174558	+	0.302343i
$655$	17.6718	−	2.93185i	0.690495	−	0.114557i
$656$	4.62924	−	8.01808i	0.180741	−	0.313053i
$657$	−8.24671	−	2.20970i	−0.321735	−	0.0862086i
$658$	−12.9013	−	3.45690i	−0.502946	−	0.134764i
$659$			35.8022i			1.39466i	0.716752	+	0.697328i	$0.245628\pi$
$659$			35.8022i			1.39466i	−0.716752	+	0.697328i	$0.754372\pi$
$660$	4.07485	−	1.85014i	0.158613	−	0.0720165i
$661$	15.1749	−	26.2837i	0.590235	−	1.02232i	−0.403965	−	0.914774i	$-0.632368\pi$
$661$	15.1749	−	26.2837i	0.590235	−	1.02232i	0.994200	−	0.107543i	$-0.0342984\pi$
$662$	−6.95260	−	25.9474i	−0.270220	−	1.00848i
$663$	0.902196	−	3.36704i	0.0350384	−	0.130765i
$664$	2.64555	−	4.58222i	0.102667	−	0.177825i
$665$	21.9195	+	2.14155i	0.850003	+	0.0830457i
$666$		−	2.46671i		−	0.0955830i
$667$	−59.6632	−	59.6632i	−2.31017	−	2.31017i
$668$	−5.46693	+	20.4029i	−0.211522	+	0.789410i
$669$	−18.4906	−	10.6755i	−0.714888	−	0.412741i
$670$	−24.0920	+	19.8034i	−0.930756	+	0.765073i
$671$	−1.06962	+	1.85263i	−0.0412921	+	0.0715200i
$672$	−1.17109	−	4.37058i	−0.0451759	−	0.168599i
$673$	4.28764	−	1.14887i	0.165276	−	0.0442857i	−0.175232	−	0.984527i	$-0.556068\pi$
$673$	4.28764	−	1.14887i	0.165276	−	0.0442857i	0.340508	+	0.940242i	$0.389401\pi$
$674$	1.81397			0.0698716
$675$	−4.98878	+	0.334833i	−0.192018	+	0.0128877i
$676$	−6.29918	−	10.9105i	−0.242276	−	0.419635i
$677$	1.49956	+	5.59643i	0.0576327	+	0.215088i	0.988737	−	0.149666i	$-0.0478198\pi$
$677$	1.49956	+	5.59643i	0.0576327	+	0.215088i	−0.931104	+	0.364754i	$0.881153\pi$
$678$	13.5958	+	13.5958i	0.522142	+	0.522142i
$679$	44.0134	−	25.4111i	1.68908	−	0.975190i
$680$	2.01297	+	12.1332i	0.0771939	+	0.465288i
$681$			8.16434i			0.312858i
$682$	−11.1306	−	0.527695i	−0.426214	−	0.0202065i
$683$	3.86806	−	3.86806i	0.148007	−	0.148007i	−0.629220	−	0.777227i	$-0.716626\pi$
$683$	3.86806	−	3.86806i	0.148007	−	0.148007i	0.777227	+	0.629220i	$0.216626\pi$
$684$			2.17678i			0.0832311i
$685$	−5.97622	−	0.583879i	−0.228340	−	0.0223089i
$686$	−29.2908			−1.11833
$687$	10.3060	−	2.76150i	0.393200	−	0.105358i
$688$	−2.50841	+	9.36153i	−0.0956324	+	0.356905i
$689$	−2.11700	+	1.22225i	−0.0806511	+	0.0465640i
$690$	−11.3296	+	15.8367i	−0.431312	+	0.602892i
$691$	6.14386	−	10.6415i	0.233723	−	0.404821i	−0.725178	−	0.688562i	$-0.758242\pi$
$691$	6.14386	−	10.6415i	0.233723	−	0.404821i	0.958901	+	0.283741i	$0.0915757\pi$
$692$	−21.8742	+	5.86119i	−0.831534	+	0.222809i
$693$	8.74714	−	2.34379i	0.332276	−	0.0890332i
$694$	−6.41970	−	11.1193i	−0.243689	−	0.422081i
$695$	−2.05373	+	5.46963i	−0.0779024	+	0.207475i
$696$	−4.84467	−	8.39122i	−0.183637	−	0.318068i
$697$	−36.0091	+	36.0091i	−1.36394	+	1.36394i
$698$	−11.3045	+	11.3045i	−0.427881	+	0.427881i
$699$	2.32454	+	4.02623i	0.0879223	+	0.152286i
$700$	12.5986	+	18.7913i	0.476181	+	0.710244i
$701$	−2.95267	−	5.11417i	−0.111521	−	0.193159i	0.804863	−	0.593461i	$-0.202239\pi$
$701$	−2.95267	−	5.11417i	−0.111521	−	0.193159i	−0.916384	+	0.400301i	$0.868905\pi$
$702$	0.612154	−	0.164026i	0.0231043	−	0.00619077i
$703$	5.18651	−	1.38972i	0.195613	−	0.0524143i
$704$	1.00068	−	1.73324i	0.0377147	−	0.0653238i
$705$	1.08030	+	6.51154i	0.0406865	+	0.245239i
$706$	17.6475	−	10.1888i	0.664171	−	0.383459i
$707$	−7.55038	+	28.1784i	−0.283961	+	1.05976i
$708$	0.122464	−	0.0328141i	0.00460247	−	0.00123323i
$709$	−2.20227			−0.0827079			−0.0413539	−	0.999145i	$-0.513167\pi$
$709$	−2.20227			−0.0827079			−0.0413539	+	0.999145i	$0.513167\pi$
$710$	1.52903	−	15.6502i	0.0573834	−	0.587340i
$711$		−	9.71968i		−	0.364516i
$712$	−2.53789	+	2.53789i	−0.0951115	+	0.0951115i
$713$	43.0902	−	22.2269i	1.61374	−	0.832403i
$714$			24.8876i			0.931395i
$715$	1.65019	−	2.30665i	0.0617135	−	0.0862638i
$716$	21.0027	−	12.1259i	0.784909	−	0.453167i
$717$	−10.9662	−	10.9662i	−0.409541	−	0.409541i
$718$	−5.05346	−	18.8598i	−0.188593	−	0.703840i
$719$	22.2144	+	38.4764i	0.828457	+	1.43493i	0.899249	+	0.437438i	$0.144114\pi$
$719$	22.2144	+	38.4764i	0.828457	+	1.43493i	−0.0707918	+	0.997491i	$0.522553\pi$
$720$	−1.72739	+	1.41990i	−0.0643761	+	0.0529166i
$721$	8.99011			0.334809
$722$	13.7757	−	3.69118i	0.512678	−	0.137372i
$723$	−2.99331	−	11.1712i	−0.111322	−	0.415461i
$724$	−4.71551	+	8.16750i	−0.175251	+	0.303543i
$725$	36.4742	+	31.8860i	1.35462	+	1.18422i
$726$	−6.05744	−	3.49726i	−0.224813	−	0.129796i
$727$	5.38507	−	20.0973i	0.199721	−	0.745369i	−0.791273	−	0.611463i	$-0.790581\pi$
$727$	5.38507	−	20.0973i	0.199721	−	0.745369i	0.990994	−	0.133906i	$-0.0427520\pi$
$728$	−2.02767	−	2.02767i	−0.0751505	−	0.0751505i
$729$		−	1.00000i		−	0.0370370i
$730$	14.7478	−	12.1226i	0.545841	−	0.448677i
$731$	26.6539	−	46.1659i	0.985829	−	1.70751i
$732$	0.276648	−	1.03246i	0.0102252	−	0.0381610i
$733$	0.772400	+	2.88263i	0.0285292	+	0.106473i	0.978722	−	0.205189i	$-0.0657810\pi$
$733$	0.772400	+	2.88263i	0.0285292	+	0.106473i	−0.950193	+	0.311662i	$0.899114\pi$
$734$	14.3004	−	24.7690i	0.527837	−	0.914240i
$735$	12.4553	+	27.4323i	0.459422	+	1.01186i
$736$			8.70817i			0.320987i
$737$	−26.9621	−	7.22446i	−0.993160	−	0.266116i
$738$	−8.94301	−	2.39627i	−0.329197	−	0.0882080i
$739$	12.5828	−	21.7940i	0.462865	−	0.801705i	−0.536238	−	0.844067i	$-0.680155\pi$
$739$	12.5828	−	21.7940i	0.462865	−	0.801705i	0.999102	+	0.0423618i	$0.0134882\pi$
$740$	4.48596	+	3.20927i	0.164907	+	0.117975i
$741$	0.689765	+	1.19471i	0.0253392	+	0.0438887i
$742$	12.3411	−	12.3411i	0.453055	−	0.453055i
$743$	−36.0824	−	36.0824i	−1.32374	−	1.32374i	−0.910728	−	0.413008i	$-0.864478\pi$
$743$	−36.0824	−	36.0824i	−1.32374	−	1.32374i	−0.413008	−	0.910728i	$-0.635522\pi$
$744$	5.44026	−	1.18474i	0.199449	−	0.0434348i
$745$	4.58022	+	27.6074i	0.167806	+	1.01146i
$746$	13.2960			0.486803
$747$	−5.11080	−	1.36944i	−0.186994	−	0.0501050i
$748$	−7.78394	+	7.78394i	−0.284609	+	0.284609i
$749$	−8.45065	−	4.87899i	−0.308780	−	0.178274i
$750$	5.88165	−	9.50822i	0.214767	−	0.347191i
$751$	10.5492	+	18.2717i	0.384944	+	0.666743i	0.991761	−	0.128098i	$-0.0408874\pi$
$751$	10.5492	+	18.2717i	0.384944	+	0.666743i	−0.606817	+	0.794841i	$0.707554\pi$
$752$	2.08728	+	2.08728i	0.0761151	+	0.0761151i
$753$	6.22952	+	23.2489i	0.227017	+	0.847237i
$754$	−5.31792	−	3.07031i	−0.193667	−	0.111814i
$755$	−35.7465	−	13.4221i	−1.30095	−	0.488478i
$756$	−3.91856	+	2.26238i	−0.142517	+	0.0822819i
$757$	−13.0336	−	48.6421i	−0.473715	−	1.76793i	−0.626243	−	0.779628i	$-0.715408\pi$
$757$	−13.0336	−	48.6421i	−0.473715	−	1.76793i	0.152528	−	0.988299i	$-0.451259\pi$
$758$	−10.3850	−	2.78265i	−0.377199	−	0.101070i
$759$	−17.4283			−0.632606
$760$	−3.95869	−	2.83206i	−0.143597	−	0.102730i
$761$	−14.2825	+	8.24599i	−0.517739	+	0.298917i	−0.736009	−	0.676972i	$-0.763292\pi$
$761$	−14.2825	+	8.24599i	−0.517739	+	0.298917i	0.218270	+	0.975888i	$0.429959\pi$
$762$	3.09610	−	0.829597i	0.112160	−	0.0300531i
$763$	−39.0209	−	10.4556i	−1.41265	−	0.378519i
$764$	14.9069	+	8.60652i	0.539314	+	0.311373i
$765$	11.1988	−	5.08469i	0.404894	−	0.183837i
$766$	25.0725	+	14.4756i	0.905904	+	0.523024i
$767$	0.0568154	−	0.0568154i	0.00205149	−	0.00205149i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	33.7812	−	19.5036i	1.21818	−	0.703317i	0.253653	−	0.967295i	$-0.418368\pi$
$769$	33.7812	−	19.5036i	1.21818	−	0.703317i	0.964529	+	0.263978i	$0.0850347\pi$
$770$	−7.11792	+	18.9569i	−0.256512	+	0.683160i
$771$			11.7030i			0.421474i
$772$	−0.635205	+	2.37062i	−0.0228615	+	0.0853204i
$773$	−26.6513	−	26.6513i	−0.958581	−	0.958581i	0.0405950	−	0.999176i	$-0.487075\pi$
$773$	−26.6513	−	26.6513i	−0.958581	−	0.958581i	−0.999176	+	0.0405950i	$0.987075\pi$
$774$	9.69176			0.348363
$775$	−23.8311	+	14.3903i	−0.856037	+	0.516914i
$776$	−11.2320			−0.403207
$777$	7.89220	+	7.89220i	0.283131	+	0.283131i
$778$	1.05242	−	3.92767i	0.0377309	−	0.140814i
$779$		−	20.1536i		−	0.722079i
$780$	−0.498136	+	1.32667i	−0.0178361	+	0.0475023i
$781$	12.1886	−	7.03710i	0.436143	−	0.251807i
$782$	12.3968	−	46.2656i	0.443310	−	1.65445i
$783$	−6.85140	+	6.85140i	−0.244849	+	0.244849i
$784$	11.6683	+	6.73672i	0.416727	+	0.240597i
$785$	12.5027	−	5.67672i	0.446241	−	0.202611i
$786$	−6.93781	−	4.00555i	−0.247464	−	0.142873i
$787$	11.1452	+	2.98634i	0.397283	+	0.106452i	0.451928	−	0.892054i	$-0.350736\pi$
$787$	11.1452	+	2.98634i	0.397283	+	0.106452i	−0.0546456	+	0.998506i	$0.517403\pi$
$788$	−13.1316	+	3.51859i	−0.467793	+	0.125345i
$789$	5.59488	−	3.23020i	0.199183	−	0.114998i
$790$	17.6762	+	12.6456i	0.628891	+	0.449912i
$791$	−86.9989			−3.09333
$792$	−1.93317	−	0.517992i	−0.0686923	−	0.0184061i
$793$	−0.175325	−	0.654323i	−0.00622598	−	0.0232357i
$794$	22.6692	−	13.0881i	0.804499	−	0.464478i
$795$	−8.07453	−	3.03182i	−0.286374	−	0.107528i
$796$	−1.98226	−	1.14446i	−0.0702593	−	0.0405642i
$797$	−2.64292	−	9.86351i	−0.0936170	−	0.349383i	0.903189	−	0.429243i	$-0.141220\pi$
$797$	−2.64292	−	9.86351i	−0.0936170	−	0.349383i	−0.996806	+	0.0798594i	$0.974553\pi$
$798$	−6.96457	−	6.96457i	−0.246543	−	0.246543i
$799$	−8.11806	−	14.0609i	−0.287196	−	0.497439i
$800$	−0.334833	−	4.98878i	−0.0118381	−	0.176380i
$801$	3.10827	+	1.79456i	0.109825	+	0.0634076i
$802$	21.8061	−	21.8061i	0.770000	−	0.770000i
$803$	16.5047	+	4.42242i	0.582438	+	0.156064i
$804$	13.9470			0.491874
$805$	−14.4202	−	86.9183i	−0.508246	−	3.06347i
$806$	2.61043	−	2.37412i	0.0919485	−	0.0836247i
$807$	−3.57488	−	3.57488i	−0.125842	−	0.125842i
$808$	4.55892	−	4.55892i	0.160382	−	0.160382i
$809$	2.65041	+	4.59064i	0.0931834	+	0.161398i	0.908849	−	0.417125i	$-0.136962\pi$
$809$	2.65041	+	4.59064i	0.0931834	+	0.161398i	−0.815666	+	0.578524i	$0.803629\pi$
$810$	1.81860	+	1.30104i	0.0638991	+	0.0457137i
$811$	−7.46058	+	12.9221i	−0.261977	+	0.453757i	−0.966767	−	0.255659i	$-0.917708\pi$
$811$	−7.46058	+	12.9221i	−0.261977	+	0.453757i	0.704791	+	0.709415i	$0.251041\pi$
$812$	42.3481	+	11.3471i	1.48613	+	0.398206i
$813$	25.0787	+	6.71980i	0.879547	+	0.235674i
$814$			4.93679i			0.173034i
$815$	5.71675	+	12.5909i	0.200249	+	0.441039i
$816$	2.75016	−	4.76341i	0.0962748	−	0.166753i
$817$	5.46026	+	20.3780i	0.191030	+	0.712934i
$818$	−2.88309	+	10.7598i	−0.100805	+	0.376209i
$819$	−1.43378	+	2.48338i	−0.0501003	+	0.0867764i
$820$	15.9930	−	13.1461i	0.558501	−	0.459082i
$821$			41.6817i			1.45470i	0.686265	+	0.727351i	$0.259249\pi$
$821$			41.6817i			1.45470i	−0.686265	+	0.727351i	$0.740751\pi$
$822$	1.89885	+	1.89885i	0.0662299	+	0.0662299i
$823$	6.76475	−	25.2464i	0.235804	−	0.880034i	−0.741980	−	0.670422i	$-0.766113\pi$
$823$	6.76475	−	25.2464i	0.235804	−	0.880034i	0.977785	−	0.209612i	$-0.0672202\pi$
$824$	−1.72068	−	0.993435i	−0.0599427	−	0.0346079i
$825$	9.98438	−	0.670124i	0.347611	−	0.0233307i
$826$	−0.286833	+	0.496810i	−0.00998021	+	0.0172862i
$827$	9.21104	+	34.3761i	0.320299	+	1.19537i	0.918954	+	0.394365i	$0.129036\pi$
$827$	9.21104	+	34.3761i	0.320299	+	1.19537i	−0.598655	+	0.801007i	$0.704298\pi$
$828$	8.41145	−	2.25384i	0.292318	−	0.0783264i
$829$	27.0408			0.939165			0.469582	−	0.882889i	$-0.344405\pi$
$829$	27.0408			0.939165			0.469582	+	0.882889i	$0.344405\pi$
$830$	9.13979	−	7.51282i	0.317247	−	0.260774i
$831$	0.0606425	+	0.105036i	0.00210367	+	0.00364366i
$832$	0.164026	+	0.612154i	0.00568659	+	0.0212226i
$833$	−52.4024	−	52.4024i	−1.81564	−	1.81564i
$834$	2.26278	−	1.30642i	0.0783538	−	0.0452376i
$835$	−27.4812	+	38.4136i	−0.951028	+	1.32936i
$836$		−	4.35653i		−	0.150674i
$837$	−2.55242	−	4.94825i	−0.0882244	−	0.171037i
$838$	16.5659	−	16.5659i	0.572260	−	0.572260i
$839$		−	9.07745i		−	0.313389i	−0.987647	−	0.156694i	$-0.949916\pi$
$839$		−	9.07745i		−	0.313389i	0.987647	−	0.156694i	$-0.0500837\pi$
$840$	0.983816	−	10.0697i	0.0339449	−	0.347438i
$841$	64.8834			2.23736
$842$	36.6745	−	9.82691i	1.26389	−	0.338658i
$843$	4.82883	−	18.0214i	0.166314	−	0.620691i
$844$	11.3407	−	6.54758i	0.390364	−	0.225377i
$845$	−4.61067	−	27.7909i	−0.158612	−	0.956037i
$846$	1.47593	−	2.55638i	0.0507434	−	0.0878902i
$847$	30.5701	−	8.19125i	1.05040	−	0.281455i
$848$	−3.72577	+	0.998317i	−0.127943	+	0.0342823i
$849$	−9.89432	−	17.1375i	−0.339572	−	0.588156i
$850$	−5.32302	+	26.9815i	−0.182578	+	0.925458i
$851$	−10.7403	−	18.6027i	−0.368171	−	0.637691i
$852$	−4.97258	+	4.97258i	−0.170358	+	0.170358i
$853$	−6.78866	+	6.78866i	−0.232439	+	0.232439i	−0.813710	−	0.581271i	$-0.802556\pi$
$853$	−6.78866	+	6.78866i	−0.232439	+	0.232439i	0.581271	+	0.813710i	$0.302556\pi$
$854$	2.41822	+	4.18849i	0.0827499	+	0.143327i
$855$	−1.71098	+	4.55679i	−0.0585143	+	0.155839i
$856$	1.07829	+	1.86765i	0.0368551	+	0.0638348i
$857$	−6.12417	+	1.64097i	−0.209198	+	0.0560544i	−0.361896	−	0.932219i	$-0.617870\pi$
$857$	−6.12417	+	1.64097i	−0.209198	+	0.0560544i	0.152698	+	0.988273i	$0.451204\pi$
$858$	−1.22515	+	0.328277i	−0.0418258	+	0.0112072i
$859$	5.07391	−	8.78826i	0.173119	−	0.299852i	−0.766389	−	0.642376i	$-0.777949\pi$
$859$	5.07391	−	8.78826i	0.173119	−	0.299852i	0.939509	+	0.342525i	$0.111282\pi$
$860$	−12.6093	+	17.6254i	−0.429974	+	0.601023i
$861$	36.2799	−	20.9462i	1.23641	−	0.713844i
$862$	−3.07082	+	11.4605i	−0.104593	+	0.390345i
$863$	−6.41369	+	1.71854i	−0.218325	+	0.0584999i	−0.366323	−	0.930488i	$-0.619384\pi$
$863$	−6.41369	+	1.71854i	−0.218325	+	0.0584999i	0.147999	+	0.988988i	$0.452717\pi$
$864$	1.00000			0.0340207
$865$	−50.3978	−	4.92388i	−1.71358	−	0.167417i
$866$			8.88600i			0.301959i
$867$	−9.37161	+	9.37161i	−0.318277	+	0.318277i
$868$	−13.6155	+	21.1966i	−0.462139	+	0.719460i
$869$			19.4527i			0.659886i
$870$	−3.54604	−	21.3739i	−0.120222	−	0.724642i
$871$	7.65473	−	4.41946i	0.259371	−	0.149748i
$872$	6.31311	+	6.31311i	0.213789	+	0.213789i
$873$	2.90707	+	10.8493i	0.0983893	+	0.367194i
$874$	9.47787	+	16.4162i	0.320594	+	0.555285i
$875$	11.6032	+	49.2397i	0.392259	+	1.66461i
$876$	−8.53762			−0.288460
$877$	31.2933	−	8.38501i	1.05670	−	0.283142i	0.311682	−	0.950187i	$-0.399108\pi$
$877$	31.2933	−	8.38501i	1.05670	−	0.283142i	0.745017	+	0.667045i	$0.232441\pi$
$878$	−1.14538	−	4.27460i	−0.0386546	−	0.144261i
$879$	7.08203	−	12.2664i	0.238871	−	0.413737i
$880$	3.45715	−	2.84174i	0.116540	−	0.0957951i
$881$	13.5843	+	7.84292i	0.457668	+	0.264235i	0.711063	−	0.703128i	$-0.248214\pi$
$881$	13.5843	+	7.84292i	0.457668	+	0.264235i	−0.253395	+	0.967363i	$0.581547\pi$
$882$	3.48718	−	13.0143i	0.117420	−	0.438216i
$883$	−2.89289	−	2.89289i	−0.0973536	−	0.0973536i	0.656753	−	0.754106i	$-0.271930\pi$
$883$	−2.89289	−	2.89289i	−0.0973536	−	0.0973536i	−0.754106	+	0.656753i	$0.771930\pi$
$884$		−	3.48582i		−	0.117241i
$885$	0.282154	+	0.0275666i	0.00948450	+	0.000926640i
$886$	14.2508	−	24.6830i	0.478764	−	0.829243i
$887$	3.11362	−	11.6202i	0.104545	−	0.390167i	−0.893748	−	0.448569i	$-0.851934\pi$
$887$	3.11362	−	11.6202i	0.104545	−	0.390167i	0.998293	+	0.0584018i	$0.0186004\pi$
$888$	−0.638431	−	2.38266i	−0.0214243	−	0.0799567i
$889$	−7.25164	+	12.5602i	−0.243212	+	0.421256i
$890$	−7.30755	+	3.31791i	−0.244950	+	0.111217i
$891$			2.00137i			0.0670484i
$892$	−20.6236	−	5.52607i	−0.690528	−	0.185027i
$893$	6.20658	+	1.66305i	0.207695	+	0.0556518i
$894$	6.25758	−	10.8385i	0.209285	−	0.362492i
$895$	53.4976	−	8.87554i	1.78823	−	0.296677i
$896$	−2.26238	−	3.91856i	−0.0755808	−	0.130910i
$897$	3.90238	−	3.90238i	0.130297	−	0.130297i
$898$	1.47701	+	1.47701i	0.0492884	+	0.0492884i
$899$	−16.4148	+	51.3901i	−0.547464	+	1.71395i
$900$	−4.73213	+	1.61461i	−0.157738	+	0.0538205i
$901$	21.2158			0.706801
$902$	17.8982	+	4.79582i	0.595946	+	0.159683i
$903$	−31.0087	+	31.0087i	−1.03190	+	1.03190i
$904$	16.6513	+	9.61365i	0.553815	+	0.319745i
$905$	−16.2911	+	13.3911i	−0.541533	+	0.445136i
$906$	8.53803	+	14.7883i	0.283657	+	0.491309i
$907$	21.0026	+	21.0026i	0.697380	+	0.697380i	0.963845	−	0.266465i	$-0.0858556\pi$
$907$	21.0026	+	21.0026i	0.697380	+	0.697380i	−0.266465	+	0.963845i	$0.585856\pi$
$908$	2.11309	+	7.88615i	0.0701253	+	0.261711i
$909$	−5.58352	−	3.22365i	−0.185194	−	0.106922i
$910$	−2.65088	−	5.83844i	−0.0878758	−	0.193542i
$911$	−4.32122	+	2.49485i	−0.143168	+	0.0826582i	−0.569873	−	0.821733i	$-0.693008\pi$
$911$	−4.32122	+	2.49485i	−0.143168	+	0.0826582i	0.426705	+	0.904391i	$0.359674\pi$
$912$	0.563391	+	2.10260i	0.0186557	+	0.0696242i
$913$	10.2286	+	2.74074i	0.338517	+	0.0907054i
$914$	8.33185			0.275593
$915$	1.39066	−	1.94387i	0.0459737	−	0.0642625i
$916$	9.24015	−	5.33480i	0.305303	−	0.176267i
$917$	35.0132	−	9.38175i	1.15624	−	0.309813i
$918$	−5.31290	−	1.42359i	−0.175352	−	0.0469853i
$919$	−3.65848	−	2.11222i	−0.120682	−	0.0696758i	0.438444	−	0.898759i	$-0.355530\pi$
$919$	−3.65848	−	2.11222i	−0.120682	−	0.0696758i	−0.559126	+	0.829083i	$0.688863\pi$
$920$	−6.84475	+	18.2294i	−0.225665	+	0.601005i
$921$	16.0576	+	9.27083i	0.529114	+	0.305484i
$922$	−24.7786	+	24.7786i	−0.816041	+	0.816041i
$923$	−1.15348	+	4.30485i	−0.0379673	+	0.141696i
$924$	7.84247	−	4.52785i	0.257998	−	0.148955i
$925$	6.86821	+	10.2442i	0.225825	+	0.336828i
$926$		−	27.5781i		−	0.906274i
$927$	−0.514240	+	1.91917i	−0.0168898	+	0.0630338i
$928$	−6.85140	−	6.85140i	−0.224908	−	0.224908i
$929$	10.4568			0.343077			0.171539	−	0.985177i	$-0.445126\pi$
$929$	10.4568			0.343077			0.171539	+	0.985177i	$0.445126\pi$
$930$	12.3197	+	1.79602i	0.403978	+	0.0588939i
$931$	29.3287			0.961209
$932$	3.28740	+	3.28740i	0.107682	+	0.107682i
$933$	−2.32413	+	8.67379i	−0.0760888	+	0.283967i
$934$			29.1960i			0.955321i
$935$	−22.4129	+	10.1763i	−0.732981	+	0.332802i
$936$	0.548843	−	0.316874i	0.0179395	−	0.0103574i
$937$	−5.19421	+	19.3851i	−0.169687	+	0.633282i	0.827708	+	0.561159i	$0.189644\pi$
$937$	−5.19421	+	19.3851i	−0.169687	+	0.633282i	−0.997396	+	0.0721236i	$0.977022\pi$
$938$	−44.6234	+	44.6234i	−1.45701	+	1.45701i
$939$	−1.16207	−	0.670919i	−0.0379226	−	0.0218946i
$940$	2.72880	+	6.01006i	0.0890037	+	0.196027i
$941$	−25.4771	−	14.7092i	−0.830529	−	0.479506i	0.0235047	−	0.999724i	$-0.492518\pi$
$941$	−25.4771	−	14.7092i	−0.830529	−	0.479506i	−0.854034	+	0.520218i	$0.825851\pi$
$942$	−5.93149	−	1.58934i	−0.193258	−	0.0517834i
$943$	−77.8772	+	20.8671i	−2.53603	+	0.679527i
$944$	0.109798	−	0.0633919i	0.00357362	−	0.00206323i
$945$	−9.98124	+	1.65594i	−0.324690	+	0.0538678i
$946$	−19.3968			−0.630644
$947$	−4.99942	−	1.33959i	−0.162459	−	0.0435309i	0.176673	−	0.984270i	$-0.443467\pi$
$947$	−4.99942	−	1.33959i	−0.162459	−	0.0435309i	−0.339132	+	0.940739i	$0.610133\pi$
$948$	−2.51564	−	9.38849i	−0.0817041	−	0.304924i
$949$	−4.68581	+	2.70535i	−0.152108	+	0.0878195i
$950$	−6.06093	−	9.04013i	−0.196643	−	0.293301i
$951$	−28.2617	−	16.3169i	−0.916449	−	0.529112i
$952$	6.44138	+	24.0396i	0.208766	+	0.779127i
$953$	22.3911	+	22.3911i	0.725320	+	0.725320i	0.969684	−	0.244363i	$-0.0785790\pi$
$953$	22.3911	+	22.3911i	0.725320	+	0.725320i	−0.244363	+	0.969684i	$0.578579\pi$
$954$	1.92860	+	3.34043i	0.0624407	+	0.108151i
$955$	24.4408	+	29.7337i	0.790885	+	0.962158i
$956$	−13.4308	−	7.75429i	−0.434384	−	0.250792i
$957$	13.7122	−	13.7122i	0.443252	−	0.443252i
$958$	26.7417	+	7.16541i	0.863984	+	0.231504i
$959$	−12.1507			−0.392366
$960$	−1.30104	+	1.81860i	−0.0419907	+	0.0586951i
$961$	−25.2600	−	17.9703i	−0.814838	−	0.579688i
$962$	−1.10540	−	1.10540i	−0.0356396	−	0.0356396i
$963$	1.52493	−	1.52493i	0.0491401	−	0.0491401i
$964$	−5.78263	−	10.0158i	−0.186246	−	0.322588i
$965$	−3.19306	+	4.46329i	−0.102788	+	0.143678i
$966$	−19.7012	+	34.1235i	−0.633875	+	1.09790i
$967$	26.1059	+	6.99504i	0.839508	+	0.224945i	0.652857	−	0.757481i	$-0.273570\pi$
$967$	26.1059	+	6.99504i	0.839508	+	0.224945i	0.186651	+	0.982426i	$0.440237\pi$
$968$	−6.75619	−	1.81032i	−0.217152	−	0.0581858i
$969$		−	11.9730i		−	0.384627i
$970$	−23.5128	−	8.82856i	−0.754950	−	0.283468i
$971$	−9.57266	+	16.5803i	−0.307201	+	0.532088i	−0.977749	−	0.209778i	$-0.932726\pi$
$971$	−9.57266	+	16.5803i	−0.307201	+	0.532088i	0.670548	+	0.741866i	$0.266059\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−3.05988	+	11.4196i	−0.0980952	+	0.366096i
$974$	4.85501	−	8.40913i	0.155565	−	0.269446i
$975$	−2.08556	+	2.38566i	−0.0667915	+	0.0764022i
$976$		−	1.06889i		−	0.0342142i
$977$	−2.38346	−	2.38346i	−0.0762535	−	0.0762535i	0.667951	−	0.744205i	$-0.267171\pi$
$977$	−2.38346	−	2.38346i	−0.0762535	−	0.0762535i	−0.744205	+	0.667951i	$0.767171\pi$
$978$	1.60055	−	5.97332i	0.0511798	−	0.191006i
$979$	−6.22079	−	3.59157i	−0.198817	−	0.114787i
$980$	19.1309	+	23.2739i	0.611116	+	0.743458i
$981$	4.46404	−	7.73194i	0.142526	−	0.246862i
$982$	−0.420598	−	1.56969i	−0.0134218	−	0.0500909i
$983$	7.70080	−	2.06342i	0.245617	−	0.0658130i	−0.133910	−	0.990994i	$-0.542753\pi$
$983$	7.70080	−	2.06342i	0.245617	−	0.0658130i	0.379527	+	0.925181i	$0.376087\pi$
$984$	−9.25848			−0.295150
$985$	−30.2548	−	2.95591i	−0.963999	−	0.0941831i
$986$	26.6472	+	46.1543i	0.848620	+	1.46985i
$987$	3.45690	+	12.9013i	0.110034	+	0.410654i
$988$	0.975475	+	0.975475i	0.0310340	+	0.0310340i
$989$	73.0904	−	42.1988i	2.32414	−	1.34184i
$990$	−3.63969	−	2.60385i	−0.115677	−	0.0827558i
$991$		−	13.4354i		−	0.426789i	−0.976966	−	0.213394i	$-0.931548\pi$
$991$		−	13.4354i		−	0.426789i	0.976966	−	0.213394i	$-0.0684519\pi$
$992$	4.94825	−	2.55242i	0.157107	−	0.0810393i
$993$	−18.9948	+	18.9948i	−0.602783	+	0.602783i
$994$		−	31.8194i		−	1.00925i
$995$	−3.25003	−	3.95385i	−0.103033	−	0.125346i
$996$	−5.29109			−0.167655
$997$	33.7498	−	9.04324i	1.06887	−	0.286402i	0.318840	−	0.947809i	$-0.396707\pi$
$997$	33.7498	−	9.04324i	1.06887	−	0.286402i	0.750028	+	0.661406i	$0.230040\pi$
$998$	−2.77592	+	10.3599i	−0.0878702	+	0.327936i
$999$	−2.13623	+	1.23335i	−0.0675874	+	0.0390216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.4	✓	64
5.3	odd	4		930.2.be.b.223.3	yes	64
31.26	odd	6		930.2.be.b.367.3	yes	64
155.88	even	12	inner	930.2.be.a.553.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.4	✓	64	1.1	even	1	trivial
930.2.be.a.553.4	yes	64	155.88	even	12	inner
930.2.be.b.223.3	yes	64	5.3	odd	4
930.2.be.b.367.3	yes	64	31.26	odd	6

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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.786015 + 2.09337i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.17109 + 4.37058i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.786015 + 2.09337i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.17109 + 4.37058i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.03603 - 0.924436i) q^{10} +(1.73324 + 1.00068i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-0.612154 + 0.164026i) q^{13} +(3.91856 - 2.26238i) q^{14} +(-1.81860 - 1.30104i) q^{15} -1.00000 q^{16} +(5.31290 + 1.42359i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-1.88514 + 1.08839i) q^{19} +(-2.09337 - 0.786015i) q^{20} +(-3.91856 - 2.26238i) q^{21} +(-0.517992 - 1.93317i) q^{22} +(6.15761 + 6.15761i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.76436 - 3.29083i) q^{25} +(0.548843 + 0.316874i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.37058 - 1.17109i) q^{28} -9.68934 q^{29} +(0.365974 + 2.20592i) q^{30} +(1.69411 - 5.30377i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.41518 + 1.41518i) q^{33} +(-2.75016 - 4.76341i) q^{34} +(-8.22873 - 5.88687i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.38266 - 0.638431i) q^{37} +(2.10260 + 0.563391i) q^{38} -0.633749i q^{39} +(0.924436 + 2.03603i) q^{40} +(-4.62924 + 8.01808i) q^{41} +(1.17109 + 4.37058i) q^{42} +(2.50841 - 9.36153i) q^{43} +(-1.00068 + 1.73324i) q^{44} +(1.72739 - 1.41990i) q^{45} -8.70817i q^{46} +(-2.08728 - 2.08728i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-11.6683 - 6.73672i) q^{49} +(0.334833 + 4.98878i) q^{50} +(-2.75016 + 4.76341i) q^{51} +(-0.164026 - 0.612154i) q^{52} +(3.72577 - 0.998317i) q^{53} -1.00000 q^{54} +(-3.45715 + 2.84174i) q^{55} +(2.26238 + 3.91856i) q^{56} +(-0.563391 - 2.10260i) q^{57} +(6.85140 + 6.85140i) q^{58} +(-0.109798 + 0.0633919i) q^{59} +(1.30104 - 1.81860i) q^{60} +1.06889i q^{61} +(-4.94825 + 2.55242i) q^{62} +(3.19949 - 3.19949i) q^{63} -1.00000i q^{64} +(0.137796 - 1.41039i) q^{65} +2.00137 q^{66} +(-13.4718 + 3.60976i) q^{67} +(-1.42359 + 5.31290i) q^{68} +(-7.54150 + 4.35409i) q^{69} +(1.65594 + 9.98124i) q^{70} +(3.51615 - 6.09014i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(8.24671 - 2.20970i) q^{73} +(1.23335 + 2.13623i) q^{74} +(4.15299 - 2.78436i) q^{75} +(-1.08839 - 1.88514i) q^{76} +(-6.40335 + 6.40335i) q^{77} +(-0.448128 + 0.448128i) q^{78} +(4.85984 + 8.41749i) q^{79} +(0.786015 - 2.09337i) q^{80} +(0.500000 + 0.866025i) q^{81} +(8.94301 - 2.39627i) q^{82} +(5.11080 - 1.36944i) q^{83} +(2.26238 - 3.91856i) q^{84} +(-7.15610 + 10.0029i) q^{85} +(-8.39331 + 4.84588i) q^{86} +(2.50779 - 9.35919i) q^{87} +(1.93317 - 0.517992i) q^{88} -3.58912 q^{89} +(-2.22547 - 0.217429i) q^{90} -2.86756i q^{91} +(-6.15761 + 6.15761i) q^{92} +(4.68458 + 3.00910i) q^{93} +2.95185i q^{94} +(-0.796643 - 4.80179i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-7.94225 - 7.94225i) q^{97} +(3.48718 + 13.0143i) q^{98} +(-1.00068 - 1.73324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more