LMFDB - Embedded newform 420.2.bi.c.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(31,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("420.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	420.271
Dual form			420.2.bi.c.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41270 + 0.0654937i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.99142 - 0.185045i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.763067 + 1.19068i) q^{6} +(2.61608 + 0.395104i) q^{7} +(-2.80115 + 0.391838i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.41270 + 0.0654937i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.99142 - 0.185045i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.763067 + 1.19068i) q^{6} +(2.61608 + 0.395104i) q^{7} +(-2.80115 + 0.391838i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.25618 + 0.649629i) q^{10} +(2.76918 - 1.59879i) q^{11} +(-1.15596 - 1.63210i) q^{12} +4.22769i q^{13} +(-3.72161 - 0.386826i) q^{14} +1.00000i q^{15} +(3.93152 - 0.737006i) q^{16} +(0.0240571 - 0.0138894i) q^{17} +(0.649629 - 1.25618i) q^{18} +(2.21380 - 3.83441i) q^{19} +(-1.81714 - 0.835457i) q^{20} +(-0.965871 - 2.46315i) q^{21} +(-3.80730 + 2.43996i) q^{22} +(-3.14250 - 1.81432i) q^{23} +(1.73992 + 2.22995i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.276887 - 5.97245i) q^{26} +1.00000 q^{27} +(5.28284 + 0.302725i) q^{28} +9.93635 q^{29} +(-0.0654937 - 1.41270i) q^{30} +(-0.507143 - 0.878397i) q^{31} +(-5.50577 + 1.29866i) q^{32} +(-2.76918 - 1.59879i) q^{33} +(-0.0330758 + 0.0211971i) q^{34} +(-2.06804 - 1.65021i) q^{35} +(-0.835457 + 1.81714i) q^{36} +(2.61355 - 4.52680i) q^{37} +(-2.87629 + 5.56184i) q^{38} +(3.66129 - 2.11385i) q^{39} +(2.62179 + 1.06123i) q^{40} -7.14609i q^{41} +(1.52580 + 3.41642i) q^{42} -8.40383i q^{43} +(5.21875 - 3.69628i) q^{44} +(0.866025 - 0.500000i) q^{45} +(4.55822 + 2.35727i) q^{46} +(1.94089 - 3.36171i) q^{47} +(-2.60402 - 3.03629i) q^{48} +(6.68778 + 2.06725i) q^{49} +(-0.763067 - 1.19068i) q^{50} +(-0.0240571 - 0.0138894i) q^{51} +(0.782315 + 8.41912i) q^{52} +(2.74077 + 4.74715i) q^{53} +(-1.41270 + 0.0654937i) q^{54} -3.19757 q^{55} +(-7.48287 - 0.0816666i) q^{56} -4.42759 q^{57} +(-14.0370 + 0.650768i) q^{58} +(4.39493 + 7.61224i) q^{59} +(0.185045 + 1.99142i) q^{60} +(0.651742 + 0.376284i) q^{61} +(0.773968 + 1.20769i) q^{62} +(-1.65021 + 2.06804i) q^{63} +(7.69293 - 2.19520i) q^{64} +(2.11385 - 3.66129i) q^{65} +(4.01672 + 2.07723i) q^{66} +(14.0629 - 8.11919i) q^{67} +(0.0453377 - 0.0321113i) q^{68} +3.62864i q^{69} +(3.02959 + 2.19580i) q^{70} +9.83326i q^{71} +(1.06123 - 2.62179i) q^{72} +(-13.1339 + 7.58284i) q^{73} +(-3.39568 + 6.56617i) q^{74} +(0.500000 - 0.866025i) q^{75} +(3.69906 - 8.04558i) q^{76} +(7.87609 - 3.08844i) q^{77} +(-5.03385 + 3.22602i) q^{78} +(-12.3297 - 7.11856i) q^{79} +(-3.77330 - 1.32749i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.468024 + 10.0953i) q^{82} -9.71979 q^{83} +(-2.37925 - 4.72643i) q^{84} -0.0277788 q^{85} +(0.550397 + 11.8721i) q^{86} +(-4.96818 - 8.60513i) q^{87} +(-7.13043 + 5.56351i) q^{88} +(-8.85682 - 5.11349i) q^{89} +(-1.19068 + 0.763067i) q^{90} +(-1.67038 + 11.0600i) q^{91} +(-6.59377 - 3.03157i) q^{92} +(-0.507143 + 0.878397i) q^{93} +(-2.52171 + 4.87620i) q^{94} +(-3.83441 + 2.21380i) q^{95} +(3.87755 + 4.11881i) q^{96} +12.1010i q^{97} +(-9.58320 - 2.48239i) q^{98} +3.19757i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 14 q^{3} + 2 q^{4} + 2 q^{6} - 6 q^{7} - 4 q^{8} - 14 q^{9}+O(q^{10}) $ 28 * q - 4 * q^2 - 14 * q^3 + 2 * q^4 + 2 * q^6 - 6 * q^7 - 4 * q^8 - 14 * q^9	$ 28 q - 4 q^{2} - 14 q^{3} + 2 q^{4} + 2 q^{6} - 6 q^{7} - 4 q^{8} - 14 q^{9} - 4 q^{10} + 2 q^{12} + 28 q^{14} - 2 q^{16} - 24 q^{17} + 2 q^{18} + 14 q^{19} - 4 q^{20} + 16 q^{22} - 16 q^{24} + 14 q^{25} - 34 q^{26} + 28 q^{27} + 4 q^{28} + 8 q^{29} + 2 q^{30} + 2 q^{31} - 4 q^{32} - 4 q^{36} - 14 q^{37} - 10 q^{38} + 18 q^{39} - 2 q^{40} - 20 q^{42} + 54 q^{44} - 14 q^{46} - 16 q^{47} - 20 q^{48} + 30 q^{49} - 2 q^{50} + 24 q^{51} + 36 q^{52} + 20 q^{53} - 4 q^{54} + 8 q^{55} - 32 q^{56} - 28 q^{57} - 40 q^{58} + 16 q^{59} + 8 q^{60} + 70 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{66} - 66 q^{67} - 8 q^{68} + 6 q^{70} + 20 q^{72} + 18 q^{73} - 48 q^{74} + 14 q^{75} - 56 q^{76} + 8 q^{77} - 10 q^{78} + 6 q^{79} - 16 q^{80} - 14 q^{81} - 16 q^{82} - 24 q^{83} - 8 q^{84} - 4 q^{87} - 12 q^{88} + 36 q^{89} + 2 q^{90} + 34 q^{91} + 52 q^{92} + 2 q^{93} + 18 q^{94} - 12 q^{95} - 28 q^{96} + 2 q^{98}+O(q^{100}) $ 28 * q - 4 * q^2 - 14 * q^3 + 2 * q^4 + 2 * q^6 - 6 * q^7 - 4 * q^8 - 14 * q^9 - 4 * q^10 + 2 * q^12 + 28 * q^14 - 2 * q^16 - 24 * q^17 + 2 * q^18 + 14 * q^19 - 4 * q^20 + 16 * q^22 - 16 * q^24 + 14 * q^25 - 34 * q^26 + 28 * q^27 + 4 * q^28 + 8 * q^29 + 2 * q^30 + 2 * q^31 - 4 * q^32 - 4 * q^36 - 14 * q^37 - 10 * q^38 + 18 * q^39 - 2 * q^40 - 20 * q^42 + 54 * q^44 - 14 * q^46 - 16 * q^47 - 20 * q^48 + 30 * q^49 - 2 * q^50 + 24 * q^51 + 36 * q^52 + 20 * q^53 - 4 * q^54 + 8 * q^55 - 32 * q^56 - 28 * q^57 - 40 * q^58 + 16 * q^59 + 8 * q^60 + 70 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^66 - 66 * q^67 - 8 * q^68 + 6 * q^70 + 20 * q^72 + 18 * q^73 - 48 * q^74 + 14 * q^75 - 56 * q^76 + 8 * q^77 - 10 * q^78 + 6 * q^79 - 16 * q^80 - 14 * q^81 - 16 * q^82 - 24 * q^83 - 8 * q^84 - 4 * q^87 - 12 * q^88 + 36 * q^89 + 2 * q^90 + 34 * q^91 + 52 * q^92 + 2 * q^93 + 18 * q^94 - 12 * q^95 - 28 * q^96 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.41270	+	0.0654937i	−0.998927	+	0.0463110i
$2$	−1.41270	+	0.0654937i	−0.998927	+	0.0463110i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.99142	−	0.185045i	0.995711	−	0.0925227i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.763067	+	1.19068i	0.311521	+	0.486095i
$7$	2.61608	+	0.395104i	0.988787	+	0.149335i
$7$	2.61608	+	0.395104i	0.988787	+	0.149335i
$8$	−2.80115	+	0.391838i	−0.990357	+	0.138536i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.25618	+	0.649629i	0.397238	+	0.205431i
$11$	2.76918	−	1.59879i	0.834938	−	0.482052i	−0.0206022	−	0.999788i	$-0.506558\pi$
$11$	2.76918	−	1.59879i	0.834938	−	0.482052i	0.855541	+	0.517736i	$0.173225\pi$
$12$	−1.15596	−	1.63210i	−0.333698	−	0.471146i
$13$			4.22769i			1.17255i	0.810112	+	0.586276i	$0.199407\pi$
$13$			4.22769i			1.17255i	−0.810112	+	0.586276i	$0.800593\pi$
$14$	−3.72161	−	0.386826i	−0.994642	−	0.103384i
$15$			1.00000i			0.258199i
$16$	3.93152	−	0.737006i	0.982879	−	0.184252i
$17$	0.0240571	−	0.0138894i	0.00583472	−	0.00336867i	−0.497080	−	0.867705i	$-0.665594\pi$
$17$	0.0240571	−	0.0138894i	0.00583472	−	0.00336867i	0.502915	+	0.864336i	$0.332261\pi$
$18$	0.649629	−	1.25618i	0.153119	−	0.296084i
$19$	2.21380	−	3.83441i	0.507880	−	0.879674i	−0.492079	−	0.870551i	$-0.663763\pi$
$19$	2.21380	−	3.83441i	0.507880	−	0.879674i	0.999958	−	0.00912290i	$-0.00290395\pi$
$20$	−1.81714	−	0.835457i	−0.406326	−	0.186814i
$21$	−0.965871	−	2.46315i	−0.210770	−	0.537503i
$22$	−3.80730	+	2.43996i	−0.811718	+	0.520202i
$23$	−3.14250	−	1.81432i	−0.655256	−	0.378312i	0.135211	−	0.990817i	$-0.456829\pi$
$23$	−3.14250	−	1.81432i	−0.655256	−	0.378312i	−0.790467	+	0.612505i	$0.790162\pi$
$24$	1.73992	+	2.22995i	0.355159	+	0.455187i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.276887	−	5.97245i	−0.0543021	−	1.17129i
$27$	1.00000			0.192450
$28$	5.28284	+	0.302725i	0.998362	+	0.0572097i
$29$	9.93635			1.84513			0.922567	−	0.385836i	$-0.126087\pi$
$29$	9.93635			1.84513			0.922567	+	0.385836i	$0.126087\pi$
$30$	−0.0654937	−	1.41270i	−0.0119575	−	0.257922i
$31$	−0.507143	−	0.878397i	−0.0910855	−	0.157765i	0.816883	−	0.576804i	$-0.195700\pi$
$31$	−0.507143	−	0.878397i	−0.0910855	−	0.157765i	−0.907968	+	0.419039i	$0.862367\pi$
$32$	−5.50577	+	1.29866i	−0.973292	+	0.229572i
$33$	−2.76918	−	1.59879i	−0.482052	−	0.278313i
$34$	−0.0330758	+	0.0211971i	−0.00567245	+	0.00363527i
$35$	−2.06804	−	1.65021i	−0.349563	−	0.278937i
$36$	−0.835457	+	1.81714i	−0.139243	+	0.302857i
$37$	2.61355	−	4.52680i	0.429665	−	0.744202i	−0.567178	−	0.823595i	$-0.691965\pi$
$37$	2.61355	−	4.52680i	0.429665	−	0.744202i	0.996843	+	0.0793933i	$0.0252983\pi$
$38$	−2.87629	+	5.56184i	−0.466596	+	0.902250i
$39$	3.66129	−	2.11385i	0.586276	−	0.338486i
$40$	2.62179	+	1.06123i	0.414541	+	0.167796i
$41$		−	7.14609i		−	1.11603i	−0.829830	−	0.558016i	$-0.811563\pi$
$41$		−	7.14609i		−	1.11603i	0.829830	−	0.558016i	$-0.188437\pi$
$42$	1.52580	+	3.41642i	0.235437	+	0.527165i
$43$		−	8.40383i		−	1.28157i	−0.767720	−	0.640786i	$-0.778609\pi$
$43$		−	8.40383i		−	1.28157i	0.767720	−	0.640786i	$-0.221391\pi$
$44$	5.21875	−	3.69628i	0.786756	−	0.557235i
$45$	0.866025	−	0.500000i	0.129099	−	0.0745356i
$46$	4.55822	+	2.35727i	0.672073	+	0.347561i
$47$	1.94089	−	3.36171i	0.283107	−	0.490356i	−0.689041	−	0.724722i	$-0.741968\pi$
$47$	1.94089	−	3.36171i	0.283107	−	0.490356i	0.972148	+	0.234366i	$0.0753014\pi$
$48$	−2.60402	−	3.03629i	−0.375859	−	0.438251i
$49$	6.68778	+	2.06725i	0.955398	+	0.295322i
$50$	−0.763067	−	1.19068i	−0.107914	−	0.168388i
$51$	−0.0240571	−	0.0138894i	−0.00336867	−	0.00194491i
$52$	0.782315	+	8.41912i	0.108488	+	1.16752i
$53$	2.74077	+	4.74715i	0.376473	+	0.652071i	0.990546	−	0.137178i	$-0.0438033\pi$
$53$	2.74077	+	4.74715i	0.376473	+	0.652071i	−0.614073	+	0.789249i	$0.710470\pi$
$54$	−1.41270	+	0.0654937i	−0.192244	+	0.00891256i
$55$	−3.19757			−0.431160
$56$	−7.48287	−	0.0816666i	−0.999940	−	0.0109132i
$57$	−4.42759			−0.586449
$58$	−14.0370	+	0.650768i	−1.84315	+	0.0854501i
$59$	4.39493	+	7.61224i	0.572171	+	0.991030i	0.996343	+	0.0854477i	$0.0272320\pi$
$59$	4.39493	+	7.61224i	0.572171	+	0.991030i	−0.424171	+	0.905582i	$0.639435\pi$
$60$	0.185045	+	1.99142i	0.0238892	+	0.257091i
$61$	0.651742	+	0.376284i	0.0834471	+	0.0481782i	0.541143	−	0.840931i	$-0.317992\pi$
$61$	0.651742	+	0.376284i	0.0834471	+	0.0481782i	−0.457696	+	0.889109i	$0.651325\pi$
$62$	0.773968	+	1.20769i	0.0982941	+	0.153377i
$63$	−1.65021	+	2.06804i	−0.207907	+	0.260549i
$64$	7.69293	−	2.19520i	0.961616	−	0.274400i
$65$	2.11385	−	3.66129i	0.262191	−	0.454127i
$66$	4.01672	+	2.07723i	0.494424	+	0.255690i
$67$	14.0629	−	8.11919i	1.71805	−	0.991917i	0.795583	−	0.605844i	$-0.207165\pi$
$67$	14.0629	−	8.11919i	1.71805	−	0.991917i	0.922468	−	0.386073i	$-0.126169\pi$
$68$	0.0453377	−	0.0321113i	0.00549801	−	0.00389407i
$69$			3.62864i			0.436837i
$70$	3.02959	+	2.19580i	0.362106	+	0.262449i
$71$			9.83326i			1.16699i	0.812116	+	0.583497i	$0.198316\pi$
$71$			9.83326i			1.16699i	−0.812116	+	0.583497i	$0.801684\pi$
$72$	1.06123	−	2.62179i	0.125068	−	0.308981i
$73$	−13.1339	+	7.58284i	−1.53720	+	0.887504i	−0.538201	+	0.842816i	$0.680896\pi$
$73$	−13.1339	+	7.58284i	−1.53720	+	0.887504i	−0.999001	+	0.0446878i	$0.985771\pi$
$74$	−3.39568	+	6.56617i	−0.394739	+	0.763302i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	3.69906	−	8.04558i	0.424312	−	0.922891i
$77$	7.87609	−	3.08844i	0.897563	−	0.351961i
$78$	−5.03385	+	3.22602i	−0.569971	+	0.365274i
$79$	−12.3297	−	7.11856i	−1.38720	−	0.800901i	−0.394202	−	0.919024i	$-0.628979\pi$
$79$	−12.3297	−	7.11856i	−1.38720	−	0.800901i	−0.992999	+	0.118123i	$0.962312\pi$
$80$	−3.77330	−	1.32749i	−0.421867	−	0.148418i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.468024	+	10.0953i	0.0516846	+	1.11483i
$83$	−9.71979			−1.06689			−0.533443	−	0.845836i	$-0.679102\pi$
$83$	−9.71979			−1.06689			−0.533443	+	0.845836i	$0.679102\pi$
$84$	−2.37925	−	4.72643i	−0.259597	−	0.515696i
$85$	−0.0277788			−0.00301303
$86$	0.550397	+	11.8721i	0.0593509	+	1.28020i
$87$	−4.96818	−	8.60513i	−0.532644	−	0.922567i
$88$	−7.13043	+	5.56351i	−0.760106	+	0.593072i
$89$	−8.85682	−	5.11349i	−0.938821	−	0.542029i	−0.0492308	−	0.998787i	$-0.515677\pi$
$89$	−8.85682	−	5.11349i	−0.938821	−	0.542029i	−0.889591	+	0.456759i	$0.849010\pi$
$90$	−1.19068	+	0.763067i	−0.125509	+	0.0804344i
$91$	−1.67038	+	11.0600i	−0.175104	+	1.15940i
$92$	−6.59377	−	3.03157i	−0.687448	−	0.316064i
$93$	−0.507143	+	0.878397i	−0.0525883	+	0.0910855i
$94$	−2.52171	+	4.87620i	−0.260095	+	0.502941i
$95$	−3.83441	+	2.21380i	−0.393402	+	0.227131i
$96$	3.87755	+	4.11881i	0.395751	+	0.420374i
$97$			12.1010i			1.22867i	0.789044	+	0.614337i	$0.210576\pi$
$97$			12.1010i			1.22867i	−0.789044	+	0.614337i	$0.789424\pi$
$98$	−9.58320	−	2.48239i	−0.968049	−	0.250759i
$99$			3.19757i			0.321368i
$100$	1.15596	+	1.63210i	0.115596	+	0.163210i
$101$	−7.55848	+	4.36389i	−0.752097	+	0.434223i	−0.826451	−	0.563009i	$-0.809644\pi$
$101$	−7.55848	+	4.36389i	−0.752097	+	0.434223i	0.0743544	+	0.997232i	$0.476310\pi$
$102$	0.0348951	+	0.0180459i	0.00345513	+	0.00178681i
$103$	−1.15713	+	2.00421i	−0.114016	+	0.197481i	−0.917386	−	0.397999i	$-0.869705\pi$
$103$	−1.15713	+	2.00421i	−0.114016	+	0.197481i	0.803370	+	0.595480i	$0.203038\pi$
$104$	−1.65657	−	11.8424i	−0.162440	−	1.16125i
$105$	−0.395104	+	2.61608i	−0.0385582	+	0.255304i
$106$	−4.18278	−	6.52677i	−0.406267	−	0.633936i
$107$	2.45435	+	1.41702i	0.237271	+	0.136989i	0.613922	−	0.789367i	$-0.289591\pi$
$107$	2.45435	+	1.41702i	0.237271	+	0.136989i	−0.376651	+	0.926355i	$0.622924\pi$
$108$	1.99142	−	0.185045i	0.191625	−	0.0178060i
$109$	2.63306	+	4.56059i	0.252201	+	0.436826i	0.964132	−	0.265425i	$-0.0855121\pi$
$109$	2.63306	+	4.56059i	0.252201	+	0.436826i	−0.711930	+	0.702250i	$0.752179\pi$
$110$	4.51720	−	0.209421i	0.430698	−	0.0199675i
$111$	−5.22710			−0.496135
$112$	10.5764	−	0.374710i	0.999373	−	0.0354068i
$113$	7.58034			0.713098			0.356549	−	0.934277i	$-0.383953\pi$
$113$	7.58034			0.713098			0.356549	+	0.934277i	$0.383953\pi$
$114$	6.25485	−	0.289979i	0.585820	−	0.0271591i
$115$	1.81432	+	3.14250i	0.169186	+	0.293039i
$116$	19.7875	−	1.83868i	1.83722	−	0.170717i
$117$	−3.66129	−	2.11385i	−0.338486	−	0.195425i
$118$	−6.70726	−	10.4659i	−0.617453	−	0.963468i
$119$	0.0684233	−	0.0268307i	0.00627235	−	0.00245957i
$120$	−0.391838	−	2.80115i	−0.0357698	−	0.255709i
$121$	−0.387772	+	0.671641i	−0.0352520	+	0.0610582i
$122$	−0.945358	−	0.488890i	−0.0855887	−	0.0442620i
$123$	−6.18869	+	3.57304i	−0.558016	+	0.322171i
$124$	−1.17248	−	1.65541i	−0.105292	−	0.148661i
$125$		−	1.00000i		−	0.0894427i
$126$	2.19580	−	3.02959i	0.195618	−	0.269898i
$127$			10.8340i			0.961359i	0.876896	+	0.480680i	$0.159610\pi$
$127$			10.8340i			0.961359i	−0.876896	+	0.480680i	$0.840390\pi$
$128$	−10.7240	+	3.60499i	−0.947876	+	0.318639i
$129$	−7.27793	+	4.20191i	−0.640786	+	0.369958i
$130$	−2.74643	+	5.31074i	−0.240878	+	0.465782i
$131$	−2.44953	+	4.24271i	−0.214017	+	0.370688i	−0.952968	−	0.303071i	$-0.901988\pi$
$131$	−2.44953	+	4.24271i	−0.214017	+	0.370688i	0.738951	+	0.673759i	$0.235321\pi$
$132$	−5.81045	−	2.67143i	−0.505734	−	0.232518i
$133$	7.30647	−	9.15645i	0.633551	−	0.793965i
$134$	−19.3348	+	12.3910i	−1.67027	+	1.07042i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	−0.0619454	+	0.0483329i	−0.00531177	+	0.00414451i
$137$	5.20079	+	9.00803i	0.444333	+	0.769608i	0.998006	−	0.0631268i	$-0.0201073\pi$
$137$	5.20079	+	9.00803i	0.444333	+	0.769608i	−0.553672	+	0.832735i	$0.686774\pi$
$138$	−0.237653	−	5.12617i	−0.0202304	−	0.436369i
$139$	−1.79231			−0.152022			−0.0760108	−	0.997107i	$-0.524218\pi$
$139$	−1.79231			−0.152022			−0.0760108	+	0.997107i	$0.524218\pi$
$140$	−4.42371	−	2.90359i	−0.373872	−	0.245398i
$141$	−3.88177			−0.326904
$142$	−0.644016	−	13.8914i	−0.0540446	−	1.16574i
$143$	6.75918	+	11.7072i	0.565231	+	0.979008i
$144$	−1.32749	+	3.77330i	−0.110624	+	0.314441i
$145$	−8.60513	−	4.96818i	−0.714618	−	0.412585i
$146$	18.0575	−	11.5724i	1.49445	−	0.957741i
$147$	−1.55360	−	6.82542i	−0.128139	−	0.562951i
$148$	4.36702	−	9.49840i	0.358967	−	0.780763i
$149$	1.68786	−	2.92346i	0.138275	−	0.239499i	−0.788569	−	0.614946i	$-0.789178\pi$
$149$	1.68786	−	2.92346i	0.138275	−	0.239499i	0.926844	+	0.375447i	$0.122511\pi$
$150$	−0.649629	+	1.25618i	−0.0530420	+	0.102566i
$151$	−2.50213	+	1.44461i	−0.203621	+	0.117560i	−0.598343	−	0.801240i	$-0.704174\pi$
$151$	−2.50213	+	1.44461i	−0.203621	+	0.117560i	0.394723	+	0.918800i	$0.370841\pi$
$152$	−4.69872	+	11.6082i	−0.381116	+	0.941551i
$153$			0.0277788i			0.00224578i
$154$	−10.9242	+	4.87886i	−0.880301	+	0.393150i
$155$			1.01429i			0.0814694i
$156$	6.90002	−	4.88707i	0.552443	−	0.391278i
$157$	−0.544422	+	0.314322i	−0.0434496	+	0.0250856i	−0.521567	−	0.853210i	$-0.674653\pi$
$157$	−0.544422	+	0.314322i	−0.0434496	+	0.0250856i	0.478118	+	0.878296i	$0.341319\pi$
$158$	17.8844	+	9.24885i	1.42280	+	0.735799i
$159$	2.74077	−	4.74715i	0.217357	−	0.376473i
$160$	5.41746	+	1.62822i	0.428288	+	0.128722i
$161$	−7.50419	−	5.98803i	−0.591413	−	0.471923i
$162$	0.763067	+	1.19068i	0.0599522	+	0.0935490i
$163$	−17.3413	−	10.0120i	−1.35828	−	0.784201i	−0.368885	−	0.929475i	$-0.620260\pi$
$163$	−17.3413	−	10.0120i	−1.35828	−	0.784201i	−0.989391	+	0.145274i	$0.953594\pi$
$164$	−1.32235	−	14.2309i	−0.103258	−	1.11124i
$165$	1.59879	+	2.76918i	0.124465	+	0.215580i
$166$	13.7311	−	0.636585i	1.06574	−	0.0494085i
$167$	15.1640			1.17343			0.586713	−	0.809795i	$-0.300422\pi$
$167$	15.1640			1.17343			0.586713	+	0.809795i	$0.300422\pi$
$168$	3.67071	+	6.52119i	0.283201	+	0.503121i
$169$	−4.87340			−0.374877
$170$	0.0392430	−	0.00181934i	0.00300980	−	0.000139537i
$171$	2.21380	+	3.83441i	0.169293	+	0.293225i
$172$	−1.55509	−	16.7356i	−0.118574	−	1.27607i
$173$	17.7806	+	10.2656i	1.35183	+	0.780481i	0.988506	−	0.151181i	$-0.0483078\pi$
$173$	17.7806	+	10.2656i	1.35183	+	0.780481i	0.363326	+	0.931662i	$0.381641\pi$
$174$	7.58211	+	11.8311i	0.574798	+	0.896910i
$175$	0.965871	+	2.46315i	0.0730130	+	0.186196i
$176$	9.70875	−	8.32655i	0.731825	−	0.627637i
$177$	4.39493	−	7.61224i	0.330343	−	0.572171i
$178$	12.8469	+	6.64374i	0.962916	+	0.497969i
$179$	−0.618263	+	0.356954i	−0.0462111	+	0.0266800i	−0.522928	−	0.852377i	$-0.675160\pi$
$179$	−0.618263	+	0.356954i	−0.0462111	+	0.0266800i	0.476716	+	0.879057i	$0.341827\pi$
$180$	1.63210	−	1.15596i	0.121649	−	0.0861605i
$181$		−	11.0448i		−	0.820955i	−0.911871	−	0.410478i	$-0.865362\pi$
$181$		−	11.0448i		−	0.820955i	0.911871	−	0.410478i	$-0.134638\pi$
$182$	1.63538	−	15.7338i	0.121222	−	1.16627i
$183$		−	0.752567i		−	0.0556314i
$184$	9.51354	+	3.85084i	0.701348	+	0.283888i
$185$	−4.52680	+	2.61355i	−0.332817	+	0.192152i
$186$	0.658909	−	1.27412i	0.0483136	−	0.0934232i
$187$	0.0444123	−	0.0769244i	0.00324775	−	0.00562527i
$188$	3.24305	−	7.05374i	0.236524	−	0.514447i
$189$	2.61608	+	0.395104i	0.190292	+	0.0287396i
$190$	5.27187	−	3.37855i	0.382461	−	0.245106i
$191$	6.85537	+	3.95795i	0.496037	+	0.286387i	0.727075	−	0.686558i	$-0.240879\pi$
$191$	6.85537	+	3.95795i	0.496037	+	0.286387i	−0.231039	+	0.972945i	$0.574212\pi$
$192$	−5.74756	−	5.56467i	−0.414794	−	0.401595i
$193$	−12.8280	−	22.2187i	−0.923377	−	1.59934i	−0.794151	−	0.607720i	$-0.792084\pi$
$193$	−12.8280	−	22.2187i	−0.923377	−	1.59934i	−0.129226	−	0.991615i	$-0.541249\pi$
$194$	−0.792541	−	17.0951i	−0.0569011	−	1.22736i
$195$	−4.22769			−0.302752
$196$	13.7007	+	2.87923i	0.978624	+	0.205659i
$197$	17.3494			1.23610			0.618048	−	0.786140i	$-0.287924\pi$
$197$	17.3494			1.23610			0.618048	+	0.786140i	$0.287924\pi$
$198$	−0.209421	−	4.51720i	−0.0148829	−	0.321023i
$199$	2.46002	+	4.26088i	0.174386	+	0.302046i	0.939949	−	0.341316i	$-0.110873\pi$
$199$	2.46002	+	4.26088i	0.174386	+	0.302046i	−0.765562	+	0.643362i	$0.777539\pi$
$200$	−1.73992	−	2.22995i	−0.123031	−	0.157681i
$201$	−14.0629	−	8.11919i	−0.991917	−	0.572684i
$202$	10.3920	−	6.65988i	0.731180	−	0.468588i
$203$	25.9943	+	3.92590i	1.82444	+	0.275544i
$204$	−0.0504781	−	0.0232080i	−0.00353417	−	0.00162488i
$205$	−3.57304	+	6.18869i	−0.249552	+	0.432237i
$206$	1.50342	−	2.90713i	0.104748	−	0.202549i
$207$	3.14250	−	1.81432i	0.218419	−	0.126104i
$208$	3.11584	+	16.6213i	0.216044	+	1.15248i
$209$		−	14.1575i		−	0.979298i
$210$	0.386826	−	3.72161i	0.0266935	−	0.256815i
$211$			10.8887i			0.749607i	0.927104	+	0.374804i	$0.122290\pi$
$211$			10.8887i			0.749607i	−0.927104	+	0.374804i	$0.877710\pi$
$212$	6.33646	+	8.94640i	0.435190	+	0.614441i
$213$	8.51585	−	4.91663i	0.583497	−	0.336882i
$214$	−3.56006	−	1.84108i	−0.243361	−	0.125853i
$215$	−4.20191	+	7.27793i	−0.286568	+	0.496351i
$216$	−2.80115	+	0.391838i	−0.190594	+	0.0266612i
$217$	−0.979669	−	2.49833i	−0.0665043	−	0.169598i
$218$	−4.01840	−	6.27028i	−0.272161	−	0.424677i
$219$	13.1339	+	7.58284i	0.887504	+	0.512401i
$220$	−6.36771	+	0.591695i	−0.429311	+	0.0398921i
$221$	0.0587201	+	0.101706i	0.00394994	+	0.00684150i
$222$	7.38431	−	0.342342i	0.495602	−	0.0229765i
$223$	8.27502			0.554136			0.277068	−	0.960850i	$-0.410637\pi$
$223$	8.27502			0.554136			0.277068	+	0.960850i	$0.410637\pi$
$224$	−14.9167	+	1.22204i	−0.996661	+	0.0816508i
$225$	−1.00000			−0.0666667
$226$	−10.7087	+	0.496464i	−0.712333	+	0.0330243i
$227$	−3.88652	−	6.73165i	−0.257957	−	0.446795i	0.707737	−	0.706476i	$-0.249716\pi$
$227$	−3.88652	−	6.73165i	−0.257957	−	0.446795i	−0.965695	+	0.259681i	$0.916383\pi$
$228$	−8.81720	+	0.819306i	−0.583934	+	0.0542598i
$229$	−8.90049	−	5.13870i	−0.588161	−	0.339575i	0.176209	−	0.984353i	$-0.443617\pi$
$229$	−8.90049	−	5.13870i	−0.588161	−	0.339575i	−0.764370	+	0.644778i	$0.776950\pi$
$230$	−2.76890	−	4.32057i	−0.182576	−	0.284890i
$231$	−6.61271	−	5.27667i	−0.435084	−	0.347179i
$232$	−27.8333	+	3.89344i	−1.82734	+	0.255617i
$233$	−6.55168	+	11.3478i	−0.429215	+	0.743422i	−0.996804	−	0.0798902i	$-0.974543\pi$
$233$	−6.55168	+	11.3478i	−0.429215	+	0.743422i	0.567589	+	0.823312i	$0.307876\pi$
$234$	5.31074	+	2.74643i	0.347174	+	0.179540i
$235$	−3.36171	+	1.94089i	−0.219294	+	0.126609i
$236$	10.1608	+	14.3459i	0.661410	+	0.933840i
$237$			14.2371i			0.924801i
$238$	−0.0949040	+	0.0423850i	−0.00615172	+	0.00274741i
$239$			2.13869i			0.138341i	0.997605	+	0.0691703i	$0.0220352\pi$
$239$			2.13869i			0.138341i	−0.997605	+	0.0691703i	$0.977965\pi$
$240$	0.737006	+	3.93152i	0.0475736	+	0.253778i
$241$	−4.08113	+	2.35624i	−0.262889	+	0.151779i	−0.625652	−	0.780103i	$-0.715167\pi$
$241$	−4.08113	+	2.35624i	−0.262889	+	0.151779i	0.362763	+	0.931881i	$0.381833\pi$
$242$	0.503816	−	0.974221i	0.0323865	−	0.0626253i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.36752	+	0.628737i	0.0875467	+	0.0402508i
$245$	−4.75817	−	5.13419i	−0.303988	−	0.328011i
$246$	8.50873	−	5.45295i	0.542497	−	0.347667i
$247$	16.2107	+	9.35926i	1.03146	+	0.595515i
$248$	1.76477	+	2.26181i	0.112063	+	0.143625i
$249$	4.85989	+	8.41758i	0.307983	+	0.533443i
$250$	0.0654937	+	1.41270i	0.00414218	+	0.0893468i
$251$	−15.4935			−0.977941			−0.488970	−	0.872300i	$-0.662627\pi$
$251$	−15.4935			−0.977941			−0.488970	+	0.872300i	$0.662627\pi$
$252$	−2.90359	+	4.42371i	−0.182909	+	0.278667i
$253$	−11.6028			−0.729465
$254$	−0.709556	−	15.3051i	−0.0445215	−	0.960328i
$255$	0.0138894	+	0.0240571i	0.000869788	+	0.00150652i
$256$	14.9136	−	5.79511i	0.932103	−	0.362194i
$257$	−26.2832	−	15.1746i	−1.63950	−	0.946565i	−0.981006	−	0.193979i	$-0.937860\pi$
$257$	−26.2832	−	15.1746i	−1.63950	−	0.946565i	−0.658494	−	0.752586i	$-0.728806\pi$
$258$	10.0063	−	6.41268i	0.622965	−	0.399236i
$259$	8.62583	−	10.8099i	0.535983	−	0.671693i
$260$	3.53206	−	7.68233i	0.219049	−	0.476438i
$261$	−4.96818	+	8.60513i	−0.307522	+	0.532644i
$262$	3.18257	−	6.15409i	0.196620	−	0.380201i
$263$	−8.99063	+	5.19074i	−0.554386	+	0.320075i	−0.750889	−	0.660428i	$-0.770375\pi$
$263$	−8.99063	+	5.19074i	−0.554386	+	0.320075i	0.196503	+	0.980503i	$0.437041\pi$
$264$	8.38336	+	3.39337i	0.515960	+	0.208848i
$265$		−	5.48153i		−	0.336728i
$266$	−9.72213	+	13.4138i	−0.596102	+	0.822454i
$267$			10.2270i			0.625881i
$268$	26.5027	−	18.7710i	1.61891	−	1.14662i
$269$	−9.29283	+	5.36522i	−0.566594	+	0.327123i	−0.755788	−	0.654817i	$-0.772746\pi$
$269$	−9.29283	+	5.36522i	−0.566594	+	0.327123i	0.189194	+	0.981940i	$0.439413\pi$
$270$	1.25618	+	0.649629i	0.0764485	+	0.0395352i
$271$	−14.7596	+	25.5644i	−0.896584	+	1.55293i	−0.0647528	+	0.997901i	$0.520626\pi$
$271$	−14.7596	+	25.5644i	−0.896584	+	1.55293i	−0.831832	+	0.555028i	$0.812707\pi$
$272$	0.0843445	−	0.0723367i	0.00511414	−	0.00438606i
$273$	10.4134	−	4.08341i	0.630250	−	0.247139i
$274$	−7.93710	−	12.3850i	−0.479498	−	0.748205i
$275$	2.76918	+	1.59879i	0.166988	+	0.0964104i
$276$	0.671464	+	7.22616i	0.0404174	+	0.434964i
$277$	7.27017	+	12.5923i	0.436822	+	0.756598i	0.997442	−	0.0714748i	$-0.0227705\pi$
$277$	7.27017	+	12.5923i	0.436822	+	0.756598i	−0.560620	+	0.828073i	$0.689437\pi$
$278$	2.53199	−	0.117385i	0.151859	−	0.00704028i
$279$	1.01429			0.0607237
$280$	6.43952	+	3.81216i	0.384835	+	0.227820i
$281$	24.3453			1.45232			0.726159	−	0.687527i	$-0.241304\pi$
$281$	24.3453			1.45232			0.726159	+	0.687527i	$0.241304\pi$
$282$	5.48377	−	0.254232i	0.326553	−	0.0151393i
$283$	−8.20436	−	14.2104i	−0.487698	−	0.844718i	0.512202	−	0.858865i	$-0.328830\pi$
$283$	−8.20436	−	14.2104i	−0.487698	−	0.844718i	−0.999900	+	0.0141469i	$0.995497\pi$
$284$	1.81960	+	19.5822i	0.107973	+	1.16199i
$285$	3.83441	+	2.21380i	0.227131	+	0.131134i
$286$	−10.3154	−	16.0961i	−0.609963	−	0.951781i
$287$	2.82345	−	18.6948i	0.166663	−	1.10352i
$288$	1.62822	−	5.41746i	0.0959435	−	0.319227i
$289$	−8.49961	+	14.7218i	−0.499977	+	0.865986i
$290$	12.4818	+	6.45494i	0.732958	+	0.379047i
$291$	10.4798	−	6.05052i	0.614337	−	0.354688i
$292$	−24.7519	+	17.5310i	−1.44849	+	1.02592i
$293$			11.5810i			0.676568i	0.941044	+	0.338284i	$0.109846\pi$
$293$			11.5810i			0.676568i	−0.941044	+	0.338284i	$0.890154\pi$
$294$	2.64179	+	9.54049i	0.154072	+	0.556413i
$295$		−	8.78986i		−	0.511765i
$296$	−5.54718	+	13.7044i	−0.322423	+	0.796550i
$297$	2.76918	−	1.59879i	0.160684	−	0.0927709i
$298$	−2.19297	+	4.24050i	−0.127035	+	0.245646i
$299$	7.67040	−	13.2855i	0.443591	−	0.768322i
$300$	0.835457	−	1.81714i	0.0482351	−	0.104913i
$301$	3.32039	−	21.9851i	0.191384	−	1.26720i
$302$	3.44014	−	2.20466i	0.197958	−	0.126864i
$303$	7.55848	+	4.36389i	0.434223	+	0.250699i
$304$	5.87760	−	16.7066i	0.337103	−	0.958191i
$305$	−0.376284	−	0.651742i	−0.0215459	−	0.0373187i
$306$	−0.00181934	−	0.0392430i	−0.000104004	−	0.00224337i
$307$	−24.3468			−1.38954			−0.694771	−	0.719231i	$-0.744494\pi$
$307$	−24.3468			−1.38954			−0.694771	+	0.719231i	$0.744494\pi$
$308$	15.1131	−	7.60782i	0.861149	−	0.433496i
$309$	2.31427			0.131654
$310$	−0.0664293	−	1.43288i	−0.00377293	−	0.0813820i
$311$	−9.11504	−	15.7877i	−0.516866	−	0.895239i	−0.999808	−	0.0195862i	$-0.993765\pi$
$311$	−9.11504	−	15.7877i	−0.516866	−	0.895239i	0.482942	−	0.875652i	$-0.339568\pi$
$312$	−9.42755	+	7.35585i	−0.533730	+	0.416443i
$313$	−14.5701	−	8.41208i	−0.823553	−	0.475479i	0.0280870	−	0.999605i	$-0.491058\pi$
$313$	−14.5701	−	8.41208i	−0.823553	−	0.475479i	−0.851640	+	0.524127i	$0.824392\pi$
$314$	0.748517	−	0.479698i	0.0422412	−	0.0270709i
$315$	2.46315	−	0.965871i	0.138783	−	0.0544207i
$316$	−25.8709	−	11.8945i	−1.45535	−	0.669118i
$317$	3.35948	−	5.81879i	0.188687	−	0.326816i	−0.756126	−	0.654427i	$-0.772910\pi$
$317$	3.35948	−	5.81879i	0.188687	−	0.326816i	0.944813	+	0.327611i	$0.106243\pi$
$318$	−3.56096	+	6.88578i	−0.199689	+	0.386135i
$319$	27.5155	−	15.8861i	1.54057	−	0.889451i
$320$	−7.75987	−	1.94536i	−0.433790	−	0.108749i
$321$		−	2.83404i		−	0.158181i
$322$	10.9933	+	7.96779i	0.612634	+	0.444028i
$323$		−	0.122993i		−	0.00684353i
$324$	−1.15596	−	1.63210i	−0.0642203	−	0.0906721i
$325$	−3.66129	+	2.11385i	−0.203092	+	0.117255i
$326$	25.1537	+	13.0082i	1.39314	+	0.720456i
$327$	2.63306	−	4.56059i	0.145609	−	0.252201i
$328$	2.80011	+	20.0173i	0.154610	+	1.10527i
$329$	6.40575	−	8.02767i	0.353160	−	0.442580i
$330$	−2.43996	−	3.80730i	−0.134315	−	0.209585i
$331$	−7.44073	−	4.29591i	−0.408980	−	0.236125i	0.281372	−	0.959599i	$-0.409211\pi$
$331$	−7.44073	−	4.29591i	−0.408980	−	0.236125i	−0.690351	+	0.723474i	$0.742544\pi$
$332$	−19.3562	+	1.79860i	−1.06231	+	0.0987111i
$333$	2.61355	+	4.52680i	0.143222	+	0.248067i
$334$	−21.4221	+	0.993147i	−1.17217	+	0.0543426i
$335$	−16.2384			−0.887198
$336$	−5.61269	−	8.97205i	−0.306198	−	0.489465i
$337$	2.67946			0.145960			0.0729798	−	0.997333i	$-0.476749\pi$
$337$	2.67946			0.145960			0.0729798	+	0.997333i	$0.476749\pi$
$338$	6.88464	−	0.319177i	0.374475	−	0.0173609i
$339$	−3.79017	−	6.56477i	−0.205854	−	0.356549i
$340$	−0.0553193	+	0.00514034i	−0.00300011	+	0.000278774i
$341$	−2.80874	−	1.62163i	−0.152102	−	0.0878159i
$342$	−3.37855	−	5.27187i	−0.182691	−	0.285070i
$343$	16.6790	+	8.05048i	0.900583	+	0.434685i
$344$	3.29294	+	23.5404i	0.177543	+	1.26921i
$345$	1.81432	−	3.14250i	0.0976798	−	0.169186i
$346$	−25.7909	−	13.3377i	−1.38653	−	0.717038i
$347$	−26.7086	+	15.4202i	−1.43379	+	0.827802i	−0.997408	−	0.0719571i	$-0.977076\pi$
$347$	−26.7086	+	15.4202i	−1.43379	+	0.827802i	−0.436387	+	0.899759i	$0.643742\pi$
$348$	−11.4861	−	16.2171i	−0.615718	−	0.869328i
$349$			28.5179i			1.52653i	0.646087	+	0.763264i	$0.276404\pi$
$349$			28.5179i			1.52653i	−0.646087	+	0.763264i	$0.723596\pi$
$350$	−1.52580	−	3.41642i	−0.0815576	−	0.182615i
$351$			4.22769i			0.225658i
$352$	−13.1702	+	12.3987i	−0.701973	+	0.660856i
$353$	9.48618	−	5.47685i	0.504899	−	0.291503i	−0.225836	−	0.974165i	$-0.572511\pi$
$353$	9.48618	−	5.47685i	0.504899	−	0.291503i	0.730734	+	0.682662i	$0.239178\pi$
$354$	−5.71015	+	11.0416i	−0.303491	+	0.586856i
$355$	4.91663	−	8.51585i	0.260948	−	0.451975i
$356$	−18.5839	−	8.54420i	−0.984944	−	0.452842i
$357$	−0.0574477	−	0.0458409i	−0.00304046	−	0.00242616i
$358$	0.850039	−	0.544760i	0.0449260	−	0.0287915i
$359$	−12.4283	−	7.17550i	−0.655942	−	0.378709i	0.134787	−	0.990875i	$-0.456965\pi$
$359$	−12.4283	−	7.17550i	−0.655942	−	0.378709i	−0.790729	+	0.612166i	$0.790298\pi$
$360$	−2.22995	+	1.73992i	−0.117529	+	0.0917018i
$361$	−0.301794	−	0.522722i	−0.0158839	−	0.0275117i
$362$	0.723366	+	15.6030i	0.0380193	+	0.820074i
$363$	0.775544			0.0407055
$364$	−1.27983	+	22.3342i	−0.0670813	+	1.17063i
$365$	15.1657			0.793808
$366$	0.0492884	+	1.06315i	0.00257635	+	0.0555717i
$367$	−7.52235	−	13.0291i	−0.392664	−	0.680113i	0.600136	−	0.799898i	$-0.295113\pi$
$367$	−7.52235	−	13.0291i	−0.392664	−	0.680113i	−0.992800	+	0.119785i	$0.961780\pi$
$368$	−13.6919	−	4.81700i	−0.713742	−	0.251103i
$369$	6.18869	+	3.57304i	0.322171	+	0.186005i
$370$	6.22383	−	3.98863i	0.323561	−	0.207359i
$371$	5.29446	+	13.5018i	0.274874	+	0.700980i
$372$	−0.847392	+	1.84310i	−0.0439352	+	0.0955605i
$373$	2.93260	−	5.07941i	0.151844	−	0.263002i	−0.780061	−	0.625703i	$-0.784812\pi$
$373$	2.93260	−	5.07941i	0.151844	−	0.263002i	0.931905	+	0.362701i	$0.118146\pi$
$374$	−0.0577031	+	0.111580i	−0.00298375	+	0.00576964i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$	−4.11947	+	10.1772i	−0.212446	+	0.524849i
$377$			42.0079i			2.16352i
$378$	−3.72161	−	0.386826i	−0.191419	−	0.0198962i
$379$			19.1854i			0.985487i	0.870175	+	0.492743i	$0.164006\pi$
$379$			19.1854i			0.985487i	−0.870175	+	0.492743i	$0.835994\pi$
$380$	−7.22627	+	5.11814i	−0.370700	+	0.262555i
$381$	9.38249	−	5.41698i	0.480680	−	0.277520i
$382$	−9.94377	−	5.14239i	−0.508768	−	0.263108i
$383$	14.6655	−	25.4013i	0.749370	−	1.29795i	−0.198754	−	0.980049i	$-0.563690\pi$
$383$	14.6655	−	25.4013i	0.749370	−	1.29795i	0.948125	−	0.317898i	$-0.102977\pi$
$384$	8.48401	+	7.48476i	0.432948	+	0.381955i
$385$	−8.36511	−	1.26337i	−0.426326	−	0.0643875i
$386$	19.5772	+	30.5481i	0.996453	+	1.55486i
$387$	7.27793	+	4.20191i	0.369958	+	0.213595i
$388$	2.23924	+	24.0983i	0.113680	+	1.22340i
$389$	−15.9762	−	27.6716i	−0.810025	−	1.40300i	−0.912846	−	0.408304i	$-0.866120\pi$
$389$	−15.9762	−	27.6716i	−0.810025	−	1.40300i	0.102821	−	0.994700i	$-0.467213\pi$
$390$	5.97245	−	0.276887i	0.302427	−	0.0140207i
$391$	−0.100799			−0.00509764
$392$	−19.5435	−	3.17016i	−0.987098	−	0.160117i
$393$	4.89906			0.247125
$394$	−24.5095	+	1.13628i	−1.23477	+	0.0572449i
$395$	7.11856	+	12.3297i	0.358174	+	0.620375i
$396$	0.591695	+	6.36771i	0.0297338	+	0.319989i
$397$	18.6817	+	10.7859i	0.937608	+	0.541328i	0.889210	−	0.457500i	$-0.151255\pi$
$397$	18.6817	+	10.7859i	0.937608	+	0.541328i	0.0483981	+	0.998828i	$0.484588\pi$
$398$	−3.75432	−	5.85822i	−0.188187	−	0.293646i
$399$	−11.5830	−	1.74936i	−0.579873	−	0.0875776i
$400$	2.60402	+	3.03629i	0.130201	+	0.151814i
$401$	−12.3096	+	21.3208i	−0.614711	+	1.06471i	0.375724	+	0.926732i	$0.377394\pi$
$401$	−12.3096	+	21.3208i	−0.614711	+	1.06471i	−0.990435	+	0.137980i	$0.955939\pi$
$402$	20.3983	+	10.5489i	1.01737	+	0.526133i
$403$	3.71360	−	2.14405i	0.184987	−	0.106803i
$404$	−14.2446	+	10.0890i	−0.708695	+	0.501947i
$405$			1.00000i			0.0496904i
$406$	−36.9792	−	3.84364i	−1.83525	−	0.190756i
$407$		−	16.7140i		−	0.828483i
$408$	0.0728302	+	0.0294798i	0.00360563	+	0.00145947i
$409$	17.4951	−	10.1008i	0.865077	−	0.499453i	−0.000632036	−	1.00000i	$-0.500201\pi$
$409$	17.4951	−	10.1008i	0.865077	−	0.499453i	0.865709	+	0.500547i	$0.166868\pi$
$410$	4.64231	−	8.97676i	0.229267	−	0.443330i
$411$	5.20079	−	9.00803i	0.256536	−	0.444333i
$412$	−1.93347	+	4.20536i	−0.0952552	+	0.207183i
$413$	8.48987	+	21.6507i	0.417759	+	1.06536i
$414$	−4.32057	+	2.76890i	−0.212344	+	0.136084i
$415$	8.41758	+	4.85989i	0.413203	+	0.238563i
$416$	−5.49032	−	23.2767i	−0.269185	−	1.14123i
$417$	0.896154	+	1.55218i	0.0438849	+	0.0760108i
$418$	0.927229	+	20.0003i	0.0453523	+	0.978247i
$419$	−32.1735			−1.57178			−0.785889	−	0.618367i	$-0.787794\pi$
$419$	−32.1735			−1.57178			−0.785889	+	0.618367i	$0.787794\pi$
$420$	−0.302725	+	5.28284i	−0.0147715	+	0.257776i
$421$	33.6148			1.63828			0.819142	−	0.573591i	$-0.194450\pi$
$421$	33.6148			1.63828			0.819142	+	0.573591i	$0.194450\pi$
$422$	−0.713139	−	15.3824i	−0.0347151	−	0.748803i
$423$	1.94089	+	3.36171i	0.0943691	+	0.163452i
$424$	−9.53742	−	12.2236i	−0.463178	−	0.593628i
$425$	0.0240571	+	0.0138894i	0.00116694	+	0.000673735i
$426$	−11.7083	+	7.50344i	−0.567269	+	0.363543i
$427$	1.55634	+	1.24190i	0.0753166	+	0.0600996i
$428$	5.14986	+	2.36772i	0.248928	+	0.114448i
$429$	6.75918	−	11.7072i	0.326336	−	0.565231i
$430$	5.45937	−	10.5567i	0.263274	−	0.509089i
$431$	−16.6974	+	9.64022i	−0.804283	+	0.464353i	−0.844967	−	0.534819i	$-0.820380\pi$
$431$	−16.6974	+	9.64022i	−0.804283	+	0.464353i	0.0406835	+	0.999172i	$0.487046\pi$
$432$	3.93152	−	0.737006i	0.189155	−	0.0354592i
$433$			1.49261i			0.0717302i	0.999357	+	0.0358651i	$0.0114187\pi$
$433$			1.49261i			0.0717302i	−0.999357	+	0.0358651i	$0.988581\pi$
$434$	1.54760	+	3.46523i	0.0742872	+	0.166336i
$435$			9.93635i			0.476412i
$436$	6.08745	+	8.59483i	0.291536	+	0.411618i
$437$	−13.9137	+	8.03308i	−0.665583	+	0.384274i
$438$	−19.0508	−	9.85206i	−0.910282	−	0.470750i
$439$	−14.7632	+	25.5707i	−0.704610	+	1.22042i	0.262222	+	0.965008i	$0.415545\pi$
$439$	−14.7632	+	25.5707i	−0.704610	+	1.22042i	−0.966832	+	0.255413i	$0.917789\pi$
$440$	8.95689	−	1.25293i	0.427003	−	0.0597311i
$441$	−5.13419	+	4.75817i	−0.244485	+	0.226579i
$442$	−0.0896148	−	0.139834i	−0.00426254	−	0.00665124i
$443$	0.729211	+	0.421010i	0.0346458	+	0.0200028i	0.517223	−	0.855851i	$-0.326966\pi$
$443$	0.729211	+	0.421010i	0.0346458	+	0.0200028i	−0.482577	+	0.875854i	$0.660299\pi$
$444$	−10.4094	+	0.967251i	−0.494006	+	0.0459037i
$445$	5.11349	+	8.85682i	0.242403	+	0.419854i
$446$	−11.6901	+	0.541961i	−0.553542	+	0.0256626i
$447$	−3.37572			−0.159666
$448$	20.9927	−	2.70331i	0.991810	−	0.127720i
$449$	−28.9426			−1.36588			−0.682942	−	0.730473i	$-0.739300\pi$
$449$	−28.9426			−1.36588			−0.682942	+	0.730473i	$0.739300\pi$
$450$	1.41270	−	0.0654937i	0.0665951	−	0.00308740i
$451$	−11.4251	−	19.7888i	−0.537985	−	0.931818i
$452$	15.0957	−	1.40271i	0.710040	−	0.0659778i
$453$	2.50213	+	1.44461i	0.117560	+	0.0678735i
$454$	5.93135	+	9.25523i	0.278372	+	0.434369i
$455$	6.97659	−	8.74305i	0.327068	−	0.409881i
$456$	12.4024	−	1.73490i	0.580794	−	0.0812442i
$457$	8.41476	−	14.5748i	0.393626	−	0.681780i	−0.599299	−	0.800525i	$-0.704554\pi$
$457$	8.41476	−	14.5748i	0.393626	−	0.681780i	0.992925	+	0.118746i	$0.0378873\pi$
$458$	12.9102	+	6.67650i	0.603256	+	0.311972i
$459$	0.0240571	−	0.0138894i	0.00112289	−	0.000648302i
$460$	4.19458	+	5.92231i	0.195573	+	0.276129i
$461$		−	2.64310i		−	0.123101i	−0.998104	−	0.0615507i	$-0.980395\pi$
$461$		−	2.64310i		−	0.123101i	0.998104	−	0.0615507i	$-0.0196046\pi$
$462$	9.68734	+	7.02124i	0.450696	+	0.326658i
$463$		−	4.31256i		−	0.200422i	−0.994966	−	0.100211i	$-0.968048\pi$
$463$		−	4.31256i		−	0.200422i	0.994966	−	0.100211i	$-0.0319517\pi$
$464$	39.0649	−	7.32316i	1.81354	−	0.339969i
$465$	0.878397	−	0.507143i	0.0407347	−	0.0235182i
$466$	8.51232	−	16.4602i	0.394326	−	0.762502i
$467$	14.5185	−	25.1468i	0.671836	−	1.16365i	−0.305547	−	0.952177i	$-0.598839\pi$
$467$	14.5185	−	25.1468i	0.671836	−	1.16365i	0.977383	−	0.211477i	$-0.0678275\pi$
$468$	−7.68233	−	3.53206i	−0.355116	−	0.163269i
$469$	39.9975	−	15.6842i	1.84691	−	0.724229i
$470$	4.62196	−	2.96205i	0.213195	−	0.136629i
$471$	0.544422	+	0.314322i	0.0250856	+	0.0144832i
$472$	−15.2936	−	19.6010i	−0.703947	−	0.902207i
$473$	−13.4359	−	23.2717i	−0.617784	−	1.07003i
$474$	−0.932441	−	20.1127i	−0.0428285	−	0.923808i
$475$	4.42759			0.203152
$476$	0.131295	−	0.0660927i	0.00601788	−	0.00302935i
$477$	−5.48153			−0.250982
$478$	−0.140071	−	3.02132i	−0.00640669	−	0.138192i
$479$	−3.16961	−	5.48993i	−0.144823	−	0.250841i	0.784484	−	0.620149i	$-0.212928\pi$
$479$	−3.16961	−	5.48993i	−0.144823	−	0.250841i	−0.929307	+	0.369308i	$0.879595\pi$
$480$	−1.29866	−	5.50577i	−0.0592752	−	0.251303i
$481$	19.1379	+	11.0493i	0.872615	+	0.503805i
$482$	5.61108	−	3.59594i	0.255578	−	0.163791i
$483$	−1.43369	+	9.49284i	−0.0652353	+	0.431939i
$484$	−0.647933	+	1.40927i	−0.0294515	+	0.0640580i
$485$	6.05052	−	10.4798i	0.274740	−	0.475863i
$486$	0.649629	−	1.25618i	0.0294678	−	0.0569814i
$487$	3.10457	−	1.79242i	0.140681	−	0.0812224i	−0.428007	−	0.903775i	$-0.640784\pi$
$487$	3.10457	−	1.79242i	0.140681	−	0.0812224i	0.568689	+	0.822553i	$0.307451\pi$
$488$	−1.97307	−	0.798651i	−0.0893168	−	0.0361532i
$489$			20.0240i			0.905517i
$490$	7.05810	+	6.94141i	0.318852	+	0.313581i
$491$		−	29.5967i		−	1.33568i	−0.744304	−	0.667840i	$-0.767219\pi$
$491$		−	29.5967i		−	1.33568i	0.744304	−	0.667840i	$-0.232781\pi$
$492$	−11.6631	+	8.26063i	−0.525814	+	0.372418i
$493$	0.239040	−	0.138010i	0.0107658	−	0.00621566i
$494$	−23.5138	−	12.1601i	−1.05794	−	0.547108i
$495$	1.59879	−	2.76918i	0.0718600	−	0.124465i
$496$	−2.64122	−	3.07967i	−0.118594	−	0.138281i
$497$	−3.88516	+	25.7246i	−0.174273	+	1.15391i
$498$	−7.41685	−	11.5732i	−0.332357	−	0.518607i
$499$	−3.43398	−	1.98261i	−0.153726	−	0.0887537i	0.421164	−	0.906985i	$-0.361622\pi$
$499$	−3.43398	−	1.98261i	−0.153726	−	0.0887537i	−0.574890	+	0.818231i	$0.694955\pi$
$500$	−0.185045	−	1.99142i	−0.00827548	−	0.0890591i
$501$	−7.58201	−	13.1324i	−0.338739	−	0.586713i
$502$	21.8876	−	1.01473i	0.976891	−	0.0452894i
$503$	9.43672			0.420762			0.210381	−	0.977619i	$-0.432529\pi$
$503$	9.43672			0.420762			0.210381	+	0.977619i	$0.432529\pi$
$504$	3.81216	−	6.43952i	0.169807	−	0.286839i
$505$	8.72778			0.388381
$506$	16.3913	−	0.759913i	0.728682	−	0.0337823i
$507$	2.43670	+	4.22049i	0.108218	+	0.187439i
$508$	2.00477	+	21.5750i	0.0889475	+	0.957235i
$509$	31.6978	+	18.3007i	1.40498	+	0.811165i	0.994898	−	0.100885i	$-0.0321673\pi$
$509$	31.6978	+	18.3007i	1.40498	+	0.811165i	0.410080	+	0.912049i	$0.365501\pi$
$510$	−0.0211971	−	0.0330758i	−0.000938623	−	0.00146462i
$511$	−37.3553	+	14.6481i	−1.65250	+	0.647993i
$512$	−20.6889	+	9.16347i	−0.914329	+	0.404972i
$513$	2.21380	−	3.83441i	0.0977415	−	0.169293i
$514$	38.1240	+	19.7157i	1.68158	+	0.869623i
$515$	2.00421	−	1.15713i	0.0883163	−	0.0509894i
$516$	−13.7159	+	9.71453i	−0.603808	+	0.427658i
$517$		−	12.4122i		−	0.545890i
$518$	−11.4777	+	15.8360i	−0.504301	+	0.695794i
$519$		−	20.5312i		−	0.901221i
$520$	−4.48658	+	11.0841i	−0.196749	+	0.486071i
$521$	−30.9170	+	17.8500i	−1.35450	+	0.782021i	−0.988876	−	0.148742i	$-0.952478\pi$
$521$	−30.9170	+	17.8500i	−1.35450	+	0.782021i	−0.365624	+	0.930763i	$0.619144\pi$
$522$	6.45494	−	12.4818i	0.282525	−	0.546315i
$523$	9.62874	−	16.6775i	0.421035	−	0.729255i	−0.575006	−	0.818149i	$-0.695000\pi$
$523$	9.62874	−	16.6775i	0.421035	−	0.729255i	0.996041	+	0.0888947i	$0.0283335\pi$
$524$	−4.09296	+	8.90230i	−0.178802	+	0.388899i
$525$	1.65021	−	2.06804i	0.0720212	−	0.0902568i
$526$	12.3611	−	7.92177i	0.538968	−	0.345406i
$527$	−0.0244008	−	0.0140878i	−0.00106292	−	0.000613675i
$528$	−12.0654	−	4.24475i	−0.525078	−	0.184729i
$529$	−4.91647	−	8.51558i	−0.213760	−	0.370242i
$530$	0.359006	+	7.74374i	0.0155942	+	0.336367i
$531$	−8.78986			−0.381447
$532$	12.8559	−	19.5864i	0.557374	−	0.849177i
$533$	30.2115			1.30860
$534$	−0.669802	−	14.4476i	−0.0289852	−	0.625209i
$535$	−1.41702	−	2.45435i	−0.0612632	−	0.106111i
$536$	−36.2108	+	28.2535i	−1.56407	+	1.22036i
$537$	0.618263	+	0.356954i	0.0266800	+	0.0154037i
$538$	12.7766	−	8.18805i	0.550837	−	0.353012i
$539$	21.8248	−	4.96774i	0.940059	−	0.213976i
$540$	−1.81714	−	0.835457i	−0.0781974	−	0.0359523i
$541$	−18.2488	+	31.6078i	−0.784577	+	1.35893i	0.144675	+	0.989479i	$0.453786\pi$
$541$	−18.2488	+	31.6078i	−0.784577	+	1.35893i	−0.929252	+	0.369448i	$0.879547\pi$
$542$	19.1766	−	37.0815i	0.823705	−	1.59279i
$543$	−9.56510	+	5.52241i	−0.410478	+	0.236989i
$544$	−0.114416	+	0.107714i	−0.00490553	+	0.00461819i
$545$		−	5.26612i		−	0.225576i
$546$	−14.4436	+	6.45063i	−0.618128	+	0.276061i
$547$			16.2090i			0.693048i	0.938041	+	0.346524i	$0.112638\pi$
$547$			16.2090i			0.693048i	−0.938041	+	0.346524i	$0.887362\pi$
$548$	12.0239	+	16.9764i	0.513634	+	0.725196i
$549$	−0.651742	+	0.376284i	−0.0278157	+	0.0160594i
$550$	−4.01672	−	2.07723i	−0.171273	−	0.0885736i
$551$	21.9971	−	38.1000i	0.937107	−	1.62312i
$552$	−1.42184	−	10.1644i	−0.0605176	−	0.432625i
$553$	−29.4430	−	23.4943i	−1.25204	−	0.999078i
$554$	−11.0953	−	17.3130i	−0.471392	−	0.735557i
$555$	4.52680	+	2.61355i	0.192152	+	0.110939i
$556$	−3.56924	+	0.331658i	−0.151370	+	0.0140654i
$557$	−17.8697	−	30.9512i	−0.757162	−	1.31144i	−0.944292	−	0.329108i	$-0.893252\pi$
$557$	−17.8697	−	30.9512i	−0.757162	−	1.31144i	0.187131	−	0.982335i	$-0.440081\pi$
$558$	−1.43288	+	0.0664293i	−0.0606585	+	0.00281218i
$559$	35.5288			1.50271
$560$	−9.34676	−	4.96368i	−0.394973	−	0.209754i
$561$	−0.0888247			−0.00375018
$562$	−34.3925	+	1.59446i	−1.45076	+	0.0672583i
$563$	21.8929	+	37.9196i	0.922674	+	1.59812i	0.795260	+	0.606269i	$0.207335\pi$
$563$	21.8929	+	37.9196i	0.922674	+	1.59812i	0.127415	+	0.991850i	$0.459332\pi$
$564$	−7.73024	+	0.718304i	−0.325502	+	0.0302460i
$565$	−6.56477	−	3.79017i	−0.276182	−	0.159454i
$566$	12.5210	+	19.5376i	0.526295	+	0.821226i
$567$	−0.965871	−	2.46315i	−0.0405628	−	0.103442i
$568$	−3.85305	−	27.5445i	−0.161670	−	1.15574i
$569$	7.81716	−	13.5397i	0.327712	−	0.567614i	−0.654345	−	0.756196i	$-0.727056\pi$
$569$	7.81716	−	13.5397i	0.327712	−	0.567614i	0.982058	+	0.188582i	$0.0603890\pi$
$570$	−5.56184	−	2.87629i	−0.232960	−	0.120475i
$571$	26.6205	−	15.3693i	1.11403	−	0.643187i	0.174161	−	0.984717i	$-0.444279\pi$
$571$	26.6205	−	15.3693i	1.11403	−	0.643187i	0.939871	+	0.341531i	$0.110945\pi$
$572$	15.6267	+	22.0633i	0.653387	+	0.922512i
$573$		−	7.91589i		−	0.330691i
$574$	−2.76429	+	26.5949i	−0.115379	+	1.11005i
$575$		−	3.62864i		−	0.151325i
$576$	−1.94536	+	7.75987i	−0.0810569	+	0.323328i
$577$	35.4040	−	20.4405i	1.47389	−	0.850950i	0.474321	−	0.880352i	$-0.342694\pi$
$577$	35.4040	−	20.4405i	1.47389	−	0.850950i	0.999568	+	0.0294019i	$0.00936025\pi$
$578$	11.0432	−	21.3541i	0.459336	−	0.888211i
$579$	−12.8280	+	22.2187i	−0.533112	+	0.923377i
$580$	−18.0558	−	8.30139i	−0.749726	−	0.344697i
$581$	−25.4278	−	3.84033i	−1.05492	−	0.159324i
$582$	−14.4085	+	9.23390i	−0.597252	+	0.382758i
$583$	15.1793	+	8.76379i	0.628664	+	0.362959i
$584$	33.8187	−	26.3870i	1.39943	−	1.09190i
$585$	2.11385	+	3.66129i	0.0873968	+	0.151376i
$586$	−0.758481	−	16.3604i	−0.0313326	−	0.675842i
$587$	17.9678			0.741610			0.370805	−	0.928711i	$-0.379082\pi$
$587$	17.9678			0.741610			0.370805	+	0.928711i	$0.379082\pi$
$588$	−4.35688	−	13.3048i	−0.179675	−	0.548681i
$589$	−4.49085			−0.185042
$590$	0.575680	+	12.4174i	0.0237004	+	0.511216i
$591$	−8.67472	−	15.0251i	−0.356830	−	0.618048i
$592$	6.93894	−	19.7234i	0.285188	−	0.810627i
$593$	−21.6912	−	12.5234i	−0.890750	−	0.514275i	−0.0165621	−	0.999863i	$-0.505272\pi$
$593$	−21.6912	−	12.5234i	−0.890750	−	0.514275i	−0.874188	+	0.485588i	$0.838605\pi$
$594$	−3.80730	+	2.43996i	−0.156215	+	0.100113i
$595$	−0.0726717	−	0.0109755i	−0.00297925	−	0.000449953i
$596$	2.82027	−	6.13417i	0.115523	−	0.251265i
$597$	2.46002	−	4.26088i	0.100682	−	0.174386i
$598$	−9.96583	+	19.2708i	−0.407533	+	0.788040i
$599$	−0.143636	+	0.0829281i	−0.00586879	+	0.00338835i	−0.502932	−	0.864326i	$-0.667745\pi$
$599$	−0.143636	+	0.0829281i	−0.00586879	+	0.00338835i	0.497063	+	0.867715i	$0.334412\pi$
$600$	−1.06123	+	2.62179i	−0.0433247	+	0.107034i
$601$			33.3152i			1.35895i	0.733697	+	0.679477i	$0.237793\pi$
$601$			33.3152i			1.35895i	−0.733697	+	0.679477i	$0.762207\pi$
$602$	−3.25082	+	31.2757i	−0.132493	+	1.27470i
$603$			16.2384i			0.661278i
$604$	−4.71548	+	3.33983i	−0.191870	+	0.135896i
$605$	0.671641	−	0.387772i	0.0273061	−	0.0157652i
$606$	−10.9636	−	5.66982i	−0.445367	−	0.230321i
$607$	−2.73180	+	4.73162i	−0.110880	+	0.192051i	−0.916125	−	0.400892i	$-0.868700\pi$
$607$	−2.73180	+	4.73162i	−0.110880	+	0.192051i	0.805245	+	0.592942i	$0.202034\pi$
$608$	−7.20908	+	23.9863i	−0.292367	+	0.972774i
$609$	−9.59724	−	24.4747i	−0.388900	−	0.991765i
$610$	0.574260	+	0.896070i	0.0232511	+	0.0362808i
$611$	14.2123	+	8.20547i	0.574968	+	0.331958i
$612$	0.00514034	+	0.0553193i	0.000207786	+	0.00223615i
$613$	−4.82341	−	8.35438i	−0.194816	−	0.337430i	0.752024	−	0.659135i	$-0.229077\pi$
$613$	−4.82341	−	8.35438i	−0.194816	−	0.337430i	−0.946840	+	0.321705i	$0.895744\pi$
$614$	34.3946	−	1.59456i	1.38805	−	0.0643511i
$615$	7.14609			0.288158
$616$	−20.8520	+	11.7374i	−0.840149	+	0.472911i
$617$	−7.87750			−0.317136			−0.158568	−	0.987348i	$-0.550688\pi$
$617$	−7.87750			−0.317136			−0.158568	+	0.987348i	$0.550688\pi$
$618$	−3.26936	+	0.151570i	−0.131513	+	0.00609704i
$619$	−10.1448	−	17.5712i	−0.407752	−	0.706247i	0.586885	−	0.809670i	$-0.300354\pi$
$619$	−10.1448	−	17.5712i	−0.407752	−	0.706247i	−0.994637	+	0.103423i	$0.967021\pi$
$620$	0.187689	+	2.01987i	0.00753776	+	0.0811199i
$621$	−3.14250	−	1.81432i	−0.126104	−	0.0728062i
$622$	13.9108	+	21.7063i	0.557771	+	0.870341i
$623$	−21.1498	−	16.8767i	−0.847350	−	0.676150i
$624$	12.8365	−	11.0090i	0.513872	−	0.440714i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	21.1341	+	10.9295i	0.844689	+	0.436829i
$627$	−12.2608	+	7.07877i	−0.489649	+	0.282699i
$628$	−1.02601	+	0.726691i	−0.0409422	+	0.0289981i
$629$		−	0.145203i		−	0.00578961i
$630$	−3.41642	+	1.52580i	−0.136113	+	0.0607895i
$631$		−	0.774240i		−	0.0308220i	−0.999881	−	0.0154110i	$-0.995094\pi$
$631$		−	0.774240i		−	0.0308220i	0.999881	−	0.0154110i	$-0.00490567\pi$
$632$	37.3267	+	15.1089i	1.48478	+	0.601001i
$633$	9.42987	−	5.44434i	0.374804	−	0.216393i
$634$	−4.36483	+	8.44021i	−0.173350	+	0.335204i
$635$	5.41698	−	9.38249i	0.214966	−	0.372333i
$636$	4.57958	−	9.96074i	0.181592	−	0.394969i
$637$	−8.73971	+	28.2739i	−0.346280	+	1.12025i
$638$	−37.8306	+	24.2443i	−1.49773	+	0.959842i
$639$	−8.51585	−	4.91663i	−0.336882	−	0.194499i
$640$	11.0897	+	2.23999i	0.438361	+	0.0885433i
$641$	2.19404	+	3.80019i	0.0866595	+	0.150099i	0.906097	−	0.423070i	$-0.139047\pi$
$641$	2.19404	+	3.80019i	0.0866595	+	0.150099i	−0.819438	+	0.573168i	$0.805714\pi$
$642$	0.185612	+	4.00364i	0.00732552	+	0.158011i
$643$	24.8993			0.981933			0.490967	−	0.871178i	$-0.336644\pi$
$643$	24.8993			0.981933			0.490967	+	0.871178i	$0.336644\pi$
$644$	−16.0521	−	10.5361i	−0.632540	−	0.415180i
$645$	8.40383			0.330900
$646$	0.00805528	+	0.173752i	0.000316931	+	0.00683618i
$647$	13.2837	+	23.0081i	0.522237	+	0.904541i	0.999665	+	0.0258706i	$0.00823578\pi$
$647$	13.2837	+	23.0081i	0.522237	+	0.904541i	−0.477428	+	0.878671i	$0.658431\pi$
$648$	1.73992	+	2.22995i	0.0683505	+	0.0876008i
$649$	24.3407	+	14.0531i	0.955455	+	0.551632i
$650$	5.03385	−	3.22602i	0.197444	−	0.126535i
$651$	−1.67379	+	2.09759i	−0.0656009	+	0.0822109i
$652$	−36.3865	−	16.7292i	−1.42501	−	0.655166i
$653$	−13.6578	+	23.6560i	−0.534471	+	0.925732i	0.464717	+	0.885459i	$0.346156\pi$
$653$	−13.6578	+	23.6560i	−0.534471	+	0.925732i	−0.999189	+	0.0402726i	$0.987177\pi$
$654$	−3.42102	+	6.61518i	−0.133773	+	0.258674i
$655$	4.24271	−	2.44953i	0.165777	−	0.0957111i
$656$	−5.26671	−	28.0950i	−0.205631	−	1.09692i
$657$		−	15.1657i		−	0.591669i
$658$	−8.52361	+	11.7602i	−0.332285	+	0.458460i
$659$			10.7939i			0.420469i	0.977651	+	0.210235i	$0.0674228\pi$
$659$			10.7939i			0.420469i	−0.977651	+	0.210235i	$0.932577\pi$
$660$	3.69628	+	5.21875i	0.143877	+	0.203140i
$661$	31.7769	−	18.3464i	1.23598	−	0.713591i	0.267707	−	0.963500i	$-0.413734\pi$
$661$	31.7769	−	18.3464i	1.23598	−	0.713591i	0.968269	+	0.249909i	$0.0804006\pi$
$662$	10.7929	+	5.58149i	0.419476	+	0.216931i
$663$	0.0587201	−	0.101706i	0.00228050	−	0.00394994i
$664$	27.2266	−	3.80858i	1.05660	−	0.147802i
$665$	−10.9058	+	4.27649i	−0.422909	+	0.165835i
$666$	−3.98863	−	6.22383i	−0.154556	−	0.241168i
$667$	−31.2250	−	18.0277i	−1.20904	−	0.698037i
$668$	30.1979	−	2.80603i	1.16839	−	0.108569i
$669$	−4.13751	−	7.16638i	−0.159965	−	0.277068i
$670$	22.9399	−	1.06351i	0.886246	−	0.0410870i
$671$	2.40639			0.0928975
$672$	8.51664	+	12.3072i	0.328537	+	0.474760i
$673$	−39.3008			−1.51493			−0.757467	−	0.652873i	$-0.773563\pi$
$673$	−39.3008			−1.51493			−0.757467	+	0.652873i	$0.773563\pi$
$674$	−3.78527	+	0.175488i	−0.145803	+	0.00675954i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−9.70500	+	0.901801i	−0.373269	+	0.0346846i
$677$	−39.6904	−	22.9153i	−1.52543	−	0.880705i	−0.999545	−	0.0301465i	$-0.990403\pi$
$677$	−39.6904	−	22.9153i	−1.52543	−	0.880705i	−0.525880	−	0.850559i	$-0.676264\pi$
$678$	5.78431	+	9.02579i	0.222145	+	0.346633i
$679$	−4.78117	+	31.6573i	−0.183485	+	1.21490i
$680$	0.0778127	−	0.0108848i	0.00298398	−	0.000417413i
$681$	−3.88652	+	6.73165i	−0.148932	+	0.257957i
$682$	4.07410	+	2.10691i	0.156005	+	0.0806777i
$683$	−7.86053	+	4.53828i	−0.300775	+	0.173652i	−0.642791	−	0.766042i	$-0.722224\pi$
$683$	−7.86053	+	4.53828i	−0.300775	+	0.173652i	0.342016	+	0.939694i	$0.388890\pi$
$684$	5.11814	+	7.22627i	0.195697	+	0.276303i
$685$		−	10.4016i		−	0.397424i
$686$	−24.0896	−	10.2805i	−0.919747	−	0.392512i
$687$			10.2774i			0.392107i
$688$	−6.19367	−	33.0398i	−0.236132	−	1.25963i
$689$	−20.0695	+	11.5871i	−0.764587	+	0.441434i
$690$	−2.35727	+	4.55822i	−0.0897398	+	0.173529i
$691$	−0.592762	+	1.02669i	−0.0225497	+	0.0390573i	−0.877080	−	0.480344i	$-0.840512\pi$
$691$	−0.592762	+	1.02669i	−0.0225497	+	0.0390573i	0.854530	+	0.519402i	$0.173845\pi$
$692$	37.3082	+	17.1530i	1.41825	+	0.652058i
$693$	−1.26337	+	8.36511i	−0.0479916	+	0.317764i
$694$	36.7213	−	23.5334i	1.39392	−	0.893314i
$695$	1.55218	+	0.896154i	0.0588777	+	0.0339931i
$696$	17.2884	+	22.1576i	0.655317	+	0.839881i
$697$	−0.0992549	−	0.171915i	−0.00375955	−	0.00651173i
$698$	−1.86774	−	40.2871i	−0.0706951	−	1.52489i
$699$	13.1034			0.495615
$700$	2.37925	+	4.72643i	0.0899272	+	0.178642i
$701$	−33.7877			−1.27614			−0.638072	−	0.769976i	$-0.720268\pi$
$701$	−33.7877			−1.27614			−0.638072	+	0.769976i	$0.720268\pi$
$702$	−0.276887	−	5.97245i	−0.0104504	−	0.225416i
$703$	−11.5717	−	20.0428i	−0.436436	−	0.755930i
$704$	17.7934	−	18.3782i	0.670615	−	0.692656i
$705$	3.36171	+	1.94089i	0.126609	+	0.0730980i
$706$	−13.0424	+	8.35841i	−0.490857	+	0.314573i
$707$	−21.4978	+	8.42991i	−0.808508	+	0.317039i
$708$	7.34355	−	15.9724i	0.275987	−	0.600281i
$709$	−23.5654	+	40.8164i	−0.885017	+	1.53289i	−0.0393218	+	0.999227i	$0.512520\pi$
$709$	−23.5654	+	40.8164i	−0.885017	+	1.53289i	−0.845695	+	0.533667i	$0.820814\pi$
$710$	−6.38797	+	12.3523i	−0.239736	+	0.463574i
$711$	12.3297	−	7.11856i	0.462400	−	0.266967i
$712$	26.8130	+	10.8532i	1.00486	+	0.406742i
$713$			3.68048i			0.137835i
$714$	0.0841585	+	0.0609968i	0.00314955	+	0.00228275i
$715$		−	13.5184i		−	0.505558i
$716$	−1.16517	+	0.825253i	−0.0435444	+	0.0308411i
$717$	1.85216	−	1.06935i	0.0691703	−	0.0399355i
$718$	18.0274	+	9.32283i	0.672777	+	0.347925i
$719$	−13.0972	+	22.6850i	−0.488443	+	0.846009i	−0.999912	−	0.0132934i	$-0.995768\pi$
$719$	−13.0972	+	22.6850i	−0.488443	+	0.846009i	0.511468	+	0.859302i	$0.329102\pi$
$720$	3.03629	−	2.60402i	0.113156	−	0.0970463i
$721$	−3.81903	+	4.78600i	−0.142228	+	0.178240i
$722$	0.460578	+	0.718682i	0.0171409	+	0.0267466i
$723$	4.08113	+	2.35624i	0.151779	+	0.0876296i
$724$	−2.04379	−	21.9949i	−0.0759570	−	0.817434i
$725$	4.96818	+	8.60513i	0.184513	+	0.319587i
$726$	−1.09561	+	0.0507932i	−0.0406618	+	0.00188511i
$727$	−13.1713			−0.488497			−0.244248	−	0.969713i	$-0.578541\pi$
$727$	−13.1713			−0.488497			−0.244248	+	0.969713i	$0.578541\pi$
$728$	0.345262	−	31.6353i	0.0127962	−	1.17248i
$729$	1.00000			0.0370370
$730$	−21.4245	+	0.993256i	−0.792956	+	0.0367621i
$731$	−0.116724	−	0.202172i	−0.00431720	−	0.00747760i
$732$	−0.139259	−	1.49868i	−0.00514716	−	0.0553928i
$733$	34.2539	+	19.7765i	1.26520	+	0.730462i	0.974075	−	0.226223i	$-0.0726379\pi$
$733$	34.2539	+	19.7765i	1.26520	+	0.730462i	0.291123	+	0.956686i	$0.405971\pi$
$734$	11.4801	+	17.9135i	0.423739	+	0.661199i
$735$	−2.06725	+	6.68778i	−0.0762518	+	0.246683i
$736$	19.6580	+	5.90822i	0.724605	+	0.217780i
$737$	25.9617	−	44.9670i	0.956311	−	1.65638i
$738$	−8.97676	−	4.64231i	−0.330439	−	0.170886i
$739$	6.91877	−	3.99455i	0.254511	−	0.146942i	−0.367317	−	0.930096i	$-0.619724\pi$
$739$	6.91877	−	3.99455i	0.254511	−	0.146942i	0.621828	+	0.783154i	$0.286390\pi$
$740$	−8.53115	+	6.04234i	−0.313611	+	0.222121i
$741$		−	18.7185i		−	0.687642i
$742$	−8.36374	−	18.7272i	−0.307043	−	0.687498i
$743$		−	21.5075i		−	0.789034i	−0.918889	−	0.394517i	$-0.870912\pi$
$743$		−	21.5075i		−	0.789034i	0.918889	−	0.394517i	$-0.129088\pi$
$744$	1.07640	−	2.65924i	0.0394626	−	0.0974926i
$745$	−2.92346	+	1.68786i	−0.107107	+	0.0618384i
$746$	−3.81020	+	7.36772i	−0.139501	+	0.269752i
$747$	4.85989	−	8.41758i	0.177814	−	0.307983i
$748$	0.0742092	−	0.161407i	0.00271336	−	0.00590163i
$749$	5.86092	+	4.67677i	0.214153	+	0.170886i
$750$	1.19068	−	0.763067i	0.0434776	−	0.0278633i
$751$	31.2634	+	18.0499i	1.14082	+	0.658651i	0.946633	−	0.322314i	$-0.104461\pi$
$751$	31.2634	+	18.0499i	1.14082	+	0.658651i	0.194185	+	0.980965i	$0.437794\pi$
$752$	5.15302	−	14.6471i	0.187911	−	0.534124i
$753$	7.74675	+	13.4178i	0.282307	+	0.488970i
$754$	−2.75125	−	59.3444i	−0.100195	−	2.16119i
$755$	2.88921			0.105149
$756$	5.28284	+	0.302725i	0.192135	+	0.0110100i
$757$	−35.3900			−1.28627			−0.643136	−	0.765752i	$-0.722367\pi$
$757$	−35.3900			−1.28627			−0.643136	+	0.765752i	$0.722367\pi$
$758$	−1.25652	−	27.1031i	−0.0456389	−	0.984429i
$759$	5.80142	+	10.0484i	0.210578	+	0.364732i
$760$	9.87332	−	7.70365i	0.358143	−	0.279441i
$761$	16.8825	+	9.74712i	0.611990	+	0.353333i	0.773744	−	0.633498i	$-0.218382\pi$
$761$	16.8825	+	9.74712i	0.611990	+	0.353333i	−0.161754	+	0.986831i	$0.551715\pi$
$762$	−12.8998	+	8.26705i	−0.467312	+	0.299483i
$763$	5.08639	+	12.9712i	0.184140	+	0.469590i
$764$	14.3843	+	6.61339i	0.520406	+	0.239264i
$765$	0.0138894	−	0.0240571i	0.000502172	−	0.000869788i
$766$	−19.0542	+	36.8449i	−0.688457	+	1.33126i
$767$	−32.1822	+	18.5804i	−1.16203	+	0.670900i
$768$	−12.4755	−	10.0180i	−0.450172	−	0.361495i
$769$		−	37.9994i		−	1.37029i	−0.728405	−	0.685147i	$-0.759738\pi$
$769$		−	37.9994i		−	1.37029i	0.728405	−	0.685147i	$-0.240262\pi$
$770$	11.9001	+	1.23690i	0.428850	+	0.0445749i
$771$			30.3492i			1.09300i
$772$	−29.6573	−	41.8730i	−1.06739	−	1.50704i
$773$	11.8112	−	6.81921i	0.424820	−	0.245270i	−0.272318	−	0.962207i	$-0.587790\pi$
$773$	11.8112	−	6.81921i	0.424820	−	0.245270i	0.697137	+	0.716938i	$0.254457\pi$
$774$	−10.5567	−	5.45937i	−0.379453	−	0.196233i
$775$	0.507143	−	0.878397i	0.0182171	−	0.0315530i
$776$	−4.74165	−	33.8969i	−0.170215	−	1.21683i
$777$	−13.6745	−	2.06525i	−0.490571	−	0.0740905i
$778$	24.3818	+	38.0452i	0.874130	+	1.36399i
$779$	−27.4010	−	15.8200i	−0.981744	−	0.566810i
$780$	−8.41912	+	0.782315i	−0.301453	+	0.0280114i
$781$	15.7213	+	27.2300i	0.562551	+	0.974367i
$782$	0.142399	−	0.00660172i	0.00509217	−	0.000236077i
$783$	9.93635			0.355096
$784$	27.8167	+	3.19850i	0.993454	+	0.114232i
$785$	0.628644			0.0224373
$786$	−6.92089	+	0.320858i	−0.246860	+	0.0114446i
$787$	−0.838461	−	1.45226i	−0.0298879	−	0.0517674i	0.850695	−	0.525660i	$-0.176182\pi$
$787$	−0.838461	−	1.45226i	−0.0298879	−	0.0517674i	−0.880582	+	0.473893i	$0.842848\pi$
$788$	34.5501	−	3.21043i	1.23079	−	0.114367i
$789$	8.99063	+	5.19074i	0.320075	+	0.184795i
$790$	−10.8639	−	16.9519i	−0.386520	−	0.603122i
$791$	19.8308	+	2.99503i	0.705102	+	0.106491i
$792$	−1.25293	−	8.95689i	−0.0445209	−	0.318269i
$793$	−1.59081	+	2.75537i	−0.0564914	+	0.0978460i
$794$	−27.0980	−	14.0136i	−0.961671	−	0.497326i
$795$	−4.74715	+	2.74077i	−0.168364	+	0.0972050i
$796$	5.68739	+	8.02999i	0.201584	+	0.284616i
$797$			5.57115i			0.197340i	0.995120	+	0.0986702i	$0.0314589\pi$
$797$			5.57115i			0.197340i	−0.995120	+	0.0986702i	$0.968541\pi$
$798$	16.4778	+	1.71271i	0.583307	+	0.0606292i
$799$		−	0.107831i		−	0.00381479i
$800$	−3.87755	−	4.11881i	−0.137092	−	0.145622i
$801$	8.85682	−	5.11349i	0.312940	−	0.180676i
$802$	15.9933	−	30.9261i	0.564744	−	1.09204i
$803$	−24.2467	+	41.9964i	−0.855646	+	1.48202i
$804$	−29.5075	−	13.5665i	−1.04065	−	0.478452i
$805$	3.50480	+	8.93788i	0.123528	+	0.315019i
$806$	−5.10576	+	3.27210i	−0.179843	+	0.115255i
$807$	9.29283	+	5.36522i	0.327123	+	0.188865i
$808$	19.4625	−	15.1856i	0.684689	−	0.534228i
$809$	1.85470	+	3.21244i	0.0652078	+	0.112943i	0.896786	−	0.442464i	$-0.145896\pi$
$809$	1.85470	+	3.21244i	0.0652078	+	0.112943i	−0.831578	+	0.555408i	$0.812562\pi$
$810$	−0.0654937	−	1.41270i	−0.00230121	−	0.0496371i
$811$	11.6337			0.408513			0.204256	−	0.978917i	$-0.434522\pi$
$811$	11.6337			0.408513			0.204256	+	0.978917i	$0.434522\pi$
$812$	52.4921	+	3.00799i	1.84211	+	0.105560i
$813$	29.5193			1.03529
$814$	1.09466	+	23.6118i	0.0383679	+	0.827595i
$815$	10.0120	+	17.3413i	0.350705	+	0.607439i
$816$	−0.104818	−	0.0368761i	−0.00366935	−	0.00129092i
$817$	−32.2237	−	18.6044i	−1.12736	−	0.650884i
$818$	−24.0537	+	15.4152i	−0.841019	+	0.538979i
$819$	−8.74305	−	6.97659i	−0.305507	−	0.243782i
$820$	−5.97025	+	12.9855i	−0.208490	+	0.453472i
$821$	11.2992	−	19.5709i	0.394346	−	0.683028i	−0.598671	−	0.800995i	$-0.704304\pi$
$821$	11.2992	−	19.5709i	0.394346	−	0.683028i	0.993018	+	0.117967i	$0.0376377\pi$
$822$	−6.75717	+	13.0662i	−0.235683	+	0.455737i
$823$	−13.1260	+	7.57829i	−0.457543	+	0.264162i	−0.711010	−	0.703181i	$-0.751762\pi$
$823$	−13.1260	+	7.57829i	−0.457543	+	0.264162i	0.253468	+	0.967344i	$0.418429\pi$
$824$	2.45598	−	6.06752i	0.0855582	−	0.211372i
$825$		−	3.19757i		−	0.111325i
$826$	−13.4116	−	30.0299i	−0.466649	−	1.04487i
$827$			33.0850i			1.15048i	0.817986	+	0.575238i	$0.195091\pi$
$827$			33.0850i			1.15048i	−0.817986	+	0.575238i	$0.804909\pi$
$828$	5.92231	−	4.19458i	0.205814	−	0.145772i
$829$	3.54057	−	2.04415i	0.122969	−	0.0709962i	−0.437254	−	0.899338i	$-0.644049\pi$
$829$	3.54057	−	2.04415i	0.122969	−	0.0709962i	0.560223	+	0.828342i	$0.310716\pi$
$830$	−12.2098	−	6.31425i	−0.423808	−	0.219171i
$831$	7.27017	−	12.5923i	0.252199	−	0.436822i
$832$	9.28063	+	32.5233i	0.321748	+	1.12754i
$833$	0.189602	−	0.0431571i	0.00656932	−	0.00149531i
$834$	−1.36765	−	2.13407i	−0.0473579	−	0.0738969i
$835$	−13.1324	−	7.58201i	−0.454466	−	0.262386i
$836$	−2.61979	−	28.1936i	−0.0906072	−	0.975097i
$837$	−0.507143	−	0.878397i	−0.0175294	−	0.0303618i
$838$	45.4514	−	2.10716i	1.57009	−	0.0727907i
$839$	13.0124			0.449237			0.224618	−	0.974447i	$-0.427886\pi$
$839$	13.0124			0.449237			0.224618	+	0.974447i	$0.427886\pi$
$840$	0.0816666	−	7.48287i	0.00281777	−	0.258184i
$841$	69.7311			2.40452
$842$	−47.4874	+	2.20155i	−1.63653	+	0.0758706i
$843$	−12.1726	−	21.0836i	−0.419248	−	0.726159i
$844$	2.01490	+	21.6839i	0.0693557	+	0.746392i
$845$	4.22049	+	2.43670i	0.145189	+	0.0838251i
$846$	−2.96205	−	4.62196i	−0.101837	−	0.158906i
$847$	−1.27981	+	1.60386i	−0.0439749	+	0.0551092i
$848$	14.2740	+	16.6435i	0.490173	+	0.571541i
$849$	−8.20436	+	14.2104i	−0.281573	+	0.487698i
$850$	−0.0348951	−	0.0180459i	−0.00119689	−	0.000618970i
$851$	−16.4262	+	9.48365i	−0.563081	+	0.325095i
$852$	16.0488	−	11.3669i	0.549825	−	0.389424i
$853$			7.09037i			0.242770i	0.992606	+	0.121385i	$0.0387335\pi$
$853$			7.09037i			0.242770i	−0.992606	+	0.121385i	$0.961266\pi$
$854$	−2.27997	−	1.65249i	−0.0780191	−	0.0565471i
$855$		−	4.42759i		−	0.151421i
$856$	−7.43027	−	3.00759i	−0.253961	−	0.102797i
$857$	13.9093	−	8.03052i	0.475131	−	0.274317i	−0.243254	−	0.969963i	$-0.578215\pi$
$857$	13.9093	−	8.03052i	0.475131	−	0.274317i	0.718385	+	0.695645i	$0.244881\pi$
$858$	−8.78191	+	16.9815i	−0.299810	+	0.579737i
$859$	−22.5677	+	39.0884i	−0.770000	+	1.33368i	0.167562	+	0.985861i	$0.446410\pi$
$859$	−22.5677	+	39.0884i	−0.770000	+	1.33368i	−0.937562	+	0.347817i	$0.886923\pi$
$860$	−7.02103	+	15.2710i	−0.239415	+	0.520735i
$861$	−17.6019	+	6.90220i	−0.599870	+	0.235226i
$862$	22.9569	−	14.7123i	0.781916	−	0.501102i
$863$	−40.3873	−	23.3176i	−1.37480	−	0.793741i	−0.383271	−	0.923636i	$-0.625203\pi$
$863$	−40.3873	−	23.3176i	−1.37480	−	0.793741i	−0.991528	+	0.129895i	$0.958536\pi$
$864$	−5.50577	+	1.29866i	−0.187310	+	0.0441812i
$865$	−10.2656	−	17.7806i	−0.349042	−	0.604558i
$866$	−0.0977564	−	2.10860i	−0.00332190	−	0.0716532i
$867$	16.9992			0.577324
$868$	−2.41324	−	4.79395i	−0.0819107	−	0.162717i
$869$	−45.5242			−1.54430
$870$	−0.650768	−	14.0370i	−0.0220631	−	0.475901i
$871$	34.3255	+	59.4535i	1.16307	+	2.01450i
$872$	−9.16262	−	11.7432i	−0.310286	−	0.397675i
$873$	−10.4798	−	6.05052i	−0.354688	−	0.204779i
$874$	19.1297	−	12.2596i	0.647073	−	0.414686i
$875$	0.395104	−	2.61608i	0.0133570	−	0.0884398i
$876$	27.5582	+	12.6703i	0.931106	+	0.428089i
$877$	24.0692	−	41.6891i	0.812760	−	1.40774i	−0.0981648	−	0.995170i	$-0.531297\pi$
$877$	24.0692	−	41.6891i	0.812760	−	1.40774i	0.910925	−	0.412572i	$-0.135369\pi$
$878$	19.1812	−	37.0905i	0.647335	−	1.25174i
$879$	10.0294	−	5.79049i	0.338284	−	0.195308i
$880$	−12.5713	+	2.35663i	−0.423778	+	0.0794420i
$881$		−	33.1071i		−	1.11541i	−0.830040	−	0.557703i	$-0.811683\pi$
$881$		−	33.1071i		−	1.11541i	0.830040	−	0.557703i	$-0.188317\pi$
$882$	6.94141	−	7.05810i	0.233730	−	0.237659i
$883$		−	8.32751i		−	0.280243i	−0.990134	−	0.140121i	$-0.955251\pi$
$883$		−	8.32751i		−	0.280243i	0.990134	−	0.140121i	$-0.0447493\pi$
$884$	0.135757	+	0.191674i	0.00456600	+	0.00644670i
$885$	−7.61224	+	4.39493i	−0.255883	+	0.147734i
$886$	−1.05773	−	0.547000i	−0.0355350	−	0.0183768i
$887$	−17.7729	+	30.7835i	−0.596754	+	1.03361i	0.396543	+	0.918016i	$0.370210\pi$
$887$	−17.7729	+	30.7835i	−0.596754	+	1.03361i	−0.993297	+	0.115592i	$0.963124\pi$
$888$	14.6419	−	2.04818i	0.491351	−	0.0687324i
$889$	−4.28055	+	28.3426i	−0.143565	+	0.950579i
$890$	−7.80387	−	12.1771i	−0.261586	−	0.408177i
$891$	−2.76918	−	1.59879i	−0.0927709	−	0.0535613i
$892$	16.4791	−	1.53125i	0.551759	−	0.0512702i
$893$	−8.59346	−	14.8843i	−0.287569	−	0.498084i
$894$	4.76887	−	0.221088i	0.159495	−	0.00739430i
$895$	0.713908			0.0238633
$896$	−29.4792	+	5.19385i	−0.984831	+	0.173514i
$897$	−15.3408			−0.512214
$898$	40.8870	−	1.89555i	1.36442	−	0.0632555i
$899$	−5.03915	−	8.72807i	−0.168065	−	0.291097i
$900$	−1.99142	+	0.185045i	−0.0663807	+	0.00616818i
$901$	0.131870	+	0.0761352i	0.00439323	+	0.00253643i
$902$	17.4362	+	27.2073i	0.580561	+	0.905903i
$903$	−20.6999	+	8.11701i	−0.688848	+	0.270117i
$904$	−21.2337	+	2.97027i	−0.706222	+	0.0987896i
$905$	−5.52241	+	9.56510i	−0.183571	+	0.317955i
$906$	−3.62936	−	1.87692i	−0.120578	−	0.0623564i
$907$	−36.0434	+	20.8097i	−1.19680	+	0.690973i	−0.959841	−	0.280546i	$-0.909484\pi$
$907$	−36.0434	+	20.8097i	−1.19680	+	0.690973i	−0.236960	+	0.971519i	$0.576151\pi$
$908$	−8.98535	−	12.6864i	−0.298189	−	0.421012i
$909$		−	8.72778i		−	0.289482i
$910$	−9.28319	+	12.8082i	−0.307735	+	0.424588i
$911$		−	45.1916i		−	1.49726i	−0.662986	−	0.748632i	$-0.730711\pi$
$911$		−	45.1916i		−	1.49726i	0.662986	−	0.748632i	$-0.269289\pi$
$912$	−17.4072	+	3.26316i	−0.576409	+	0.108054i
$913$	−26.9158	+	15.5399i	−0.890783	+	0.514294i
$914$	−10.9329	+	21.1409i	−0.361629	+	0.699277i
$915$	−0.376284	+	0.651742i	−0.0124396	+	0.0215459i
$916$	−18.6755	−	8.58632i	−0.617057	−	0.283700i
$917$	−8.08449	+	10.1315i	−0.266974	+	0.334571i
$918$	−0.0330758	+	0.0211971i	−0.00109166	+	0.000699608i
$919$	−18.8981	−	10.9108i	−0.623390	−	0.359915i	0.154797	−	0.987946i	$-0.450528\pi$
$919$	−18.8981	−	10.9108i	−0.623390	−	0.359915i	−0.778188	+	0.628032i	$0.783861\pi$
$920$	−6.31355	−	8.09170i	−0.208151	−	0.266775i
$921$	12.1734	+	21.0849i	0.401126	+	0.694771i
$922$	0.173106	+	3.73390i	0.00570095	+	0.122969i
$923$	−41.5720			−1.36836
$924$	−14.1451	−	9.28442i	−0.465340	−	0.305435i
$925$	5.22710			0.171866
$926$	0.282445	+	6.09234i	0.00928173	+	0.200207i
$927$	−1.15713	−	2.00421i	−0.0380053	−	0.0658270i
$928$	−54.7073	+	12.9039i	−1.79585	+	0.423591i
$929$	28.3350	+	16.3592i	0.929641	+	0.536728i	0.886698	−	0.462349i	$-0.152993\pi$
$929$	28.3350	+	16.3592i	0.929641	+	0.536728i	0.0429428	+	0.999078i	$0.486327\pi$
$930$	−1.20769	+	0.773968i	−0.0396018	+	0.0253794i
$931$	22.7321	−	21.0672i	0.745014	−	0.690450i
$932$	−10.9473	+	23.8107i	−0.358590	+	0.779945i
$933$	−9.11504	+	15.7877i	−0.298413	+	0.516866i
$934$	−18.8633	+	36.4756i	−0.617225	+	1.19352i
$935$	−0.0769244	+	0.0444123i	−0.00251570	+	0.00145244i
$936$	11.0841	+	4.48658i	0.362296	+	0.146648i
$937$			48.2229i			1.57537i	0.616075	+	0.787687i	$0.288722\pi$
$937$			48.2229i			1.57537i	−0.616075	+	0.787687i	$0.711278\pi$
$938$	−55.4772	+	24.7766i	−1.81139	+	0.808984i
$939$			16.8242i			0.549035i
$940$	−6.33544	+	4.48719i	−0.206639	+	0.146356i
$941$	12.0821	−	6.97562i	0.393866	−	0.227399i	−0.289968	−	0.957036i	$-0.593645\pi$
$941$	12.0821	−	6.97562i	0.393866	−	0.227399i	0.683834	+	0.729638i	$0.260311\pi$
$942$	−0.789689	−	0.408386i	−0.0257295	−	0.0133059i
$943$	−12.9653	+	22.4566i	−0.422209	+	0.731287i
$944$	22.8890	+	26.6886i	0.744974	+	0.868639i
$945$	−2.06804	−	1.65021i	−0.0672734	−	0.0536814i
$946$	20.5050	+	31.9959i	0.666675	+	1.04027i
$947$	8.02322	+	4.63221i	0.260720	+	0.150527i	0.624663	−	0.780895i	$-0.285236\pi$
$947$	8.02322	+	4.63221i	0.260720	+	0.150527i	−0.363943	+	0.931421i	$0.618570\pi$
$948$	2.63451	+	28.3521i	0.0855650	+	0.920834i
$949$	−32.0579	−	55.5260i	−1.04064	−	1.80245i
$950$	−6.25485	+	0.289979i	−0.202934	+	0.00940817i
$951$	−6.71896			−0.217877
$952$	−0.181151	+	0.101968i	−0.00587113	+	0.00330480i
$953$	−11.7847			−0.381744			−0.190872	−	0.981615i	$-0.561132\pi$
$953$	−11.7847			−0.381744			−0.190872	+	0.981615i	$0.561132\pi$
$954$	7.74374	−	0.359006i	0.250713	−	0.0116232i
$955$	−3.95795	−	6.85537i	−0.128076	−	0.221834i
$956$	0.395755	+	4.25904i	0.0127996	+	0.137747i
$957$	−27.5155	−	15.8861i	−0.889451	−	0.513525i
$958$	4.83726	+	7.54802i	0.156285	+	0.243865i
$959$	10.0466	+	25.6206i	0.324421	+	0.827333i
$960$	2.19520	+	7.69293i	0.0708497	+	0.248288i
$961$	14.9856	−	25.9558i	0.483407	−	0.837285i
$962$	−27.7598	−	14.3559i	−0.895010	−	0.462852i
$963$	−2.45435	+	1.41702i	−0.0790904	+	0.0456629i
$964$	−7.69124	+	5.44746i	−0.247718	+	0.175451i
$965$			25.6559i			0.825893i
$966$	1.40365	−	13.5044i	0.0451618	−	0.434497i
$967$			45.1186i			1.45092i	0.688266	+	0.725458i	$0.258372\pi$
$967$			45.1186i			1.45092i	−0.688266	+	0.725458i	$0.741628\pi$
$968$	0.823034	−	2.03331i	0.0264533	−	0.0653532i
$969$	−0.106515	+	0.0614966i	−0.00342176	+	0.00197556i
$970$	−7.86118	+	15.2011i	−0.252407	+	0.488076i
$971$	16.9470	−	29.3531i	0.543855	−	0.941984i	−0.454823	−	0.890582i	$-0.650298\pi$
$971$	16.9470	−	29.3531i	0.543855	−	0.941984i	0.998678	−	0.0514026i	$-0.0163692\pi$
$972$	−0.835457	+	1.81714i	−0.0267973	+	0.0582849i
$973$	−4.68883	−	0.708149i	−0.150317	−	0.0227022i
$974$	−4.26842	+	2.73548i	−0.136769	+	0.0876503i
$975$	3.66129	+	2.11385i	0.117255	+	0.0676973i
$976$	2.83966	+	0.999027i	0.0908953	+	0.0319781i
$977$	3.23551	+	5.60406i	0.103513	+	0.179290i	0.913130	−	0.407669i	$-0.133658\pi$
$977$	3.23551	+	5.60406i	0.103513	+	0.179290i	−0.809617	+	0.586959i	$0.800325\pi$
$978$	−1.31145	−	28.2879i	−0.0419354	−	0.904546i
$979$	−32.7015			−1.04514
$980$	−10.4256	−	9.34385i	−0.333033	−	0.298478i
$981$	−5.26612			−0.168134
$982$	1.93840	+	41.8112i	0.0618567	+	1.33425i
$983$	3.75124	+	6.49734i	0.119646	+	0.207233i	0.919627	−	0.392792i	$-0.128491\pi$
$983$	3.75124	+	6.49734i	0.119646	+	0.207233i	−0.799981	+	0.600025i	$0.795157\pi$
$984$	15.9354	−	12.4336i	0.508003	−	0.396369i
$985$	−15.0251	−	8.67472i	−0.478738	−	0.276400i
$986$	−0.328653	+	0.210622i	−0.0104664	+	0.00670757i
$987$	−10.1550	−	1.53371i	−0.323238	−	0.0488184i
$988$	34.0142	+	15.6385i	1.08214	+	0.497527i
$989$	−15.2472	+	26.4090i	−0.484834	+	0.839758i
$990$	−2.07723	+	4.01672i	−0.0660188	+	0.127660i
$991$	10.3882	−	5.99760i	0.329991	−	0.190520i	−0.325846	−	0.945423i	$-0.605649\pi$
$991$	10.3882	−	5.99760i	0.329991	−	0.190520i	0.655837	+	0.754903i	$0.272316\pi$
$992$	3.93295	+	4.17765i	0.124871	+	0.132640i
$993$			8.59182i			0.272653i
$994$	3.80376	−	36.5955i	0.120648	−	1.16074i
$995$		−	4.92004i		−	0.155976i
$996$	11.2357	+	15.8637i	0.356018	+	0.502659i
$997$	6.46216	−	3.73093i	0.204659	−	0.118160i	−0.394168	−	0.919038i	$-0.628967\pi$
$997$	6.46216	−	3.73093i	0.204659	−	0.118160i	0.598827	+	0.800879i	$0.295634\pi$
$998$	4.98101	+	2.57592i	0.157671	+	0.0815393i
$999$	2.61355	−	4.52680i	0.0826891	−	0.143222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bi.c.271.1	yes	28
4.3	odd	2		420.2.bi.d.271.9	yes	28
7.3	odd	6		420.2.bi.d.31.9	yes	28
28.3	even	6	inner	420.2.bi.c.31.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bi.c.31.1	✓	28	28.3	even	6	inner
420.2.bi.c.271.1	yes	28	1.1	even	1	trivial
420.2.bi.d.31.9	yes	28	7.3	odd	6
420.2.bi.d.271.9	yes	28	4.3	odd	2

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41270 + 0.0654937i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.99142 - 0.185045i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.763067 + 1.19068i) q^{6} +(2.61608 + 0.395104i) q^{7} +(-2.80115 + 0.391838i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.41270 + 0.0654937i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.99142 - 0.185045i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.763067 + 1.19068i) q^{6} +(2.61608 + 0.395104i) q^{7} +(-2.80115 + 0.391838i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.25618 + 0.649629i) q^{10} +(2.76918 - 1.59879i) q^{11} +(-1.15596 - 1.63210i) q^{12} +4.22769i q^{13} +(-3.72161 - 0.386826i) q^{14} +1.00000i q^{15} +(3.93152 - 0.737006i) q^{16} +(0.0240571 - 0.0138894i) q^{17} +(0.649629 - 1.25618i) q^{18} +(2.21380 - 3.83441i) q^{19} +(-1.81714 - 0.835457i) q^{20} +(-0.965871 - 2.46315i) q^{21} +(-3.80730 + 2.43996i) q^{22} +(-3.14250 - 1.81432i) q^{23} +(1.73992 + 2.22995i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.276887 - 5.97245i) q^{26} +1.00000 q^{27} +(5.28284 + 0.302725i) q^{28} +9.93635 q^{29} +(-0.0654937 - 1.41270i) q^{30} +(-0.507143 - 0.878397i) q^{31} +(-5.50577 + 1.29866i) q^{32} +(-2.76918 - 1.59879i) q^{33} +(-0.0330758 + 0.0211971i) q^{34} +(-2.06804 - 1.65021i) q^{35} +(-0.835457 + 1.81714i) q^{36} +(2.61355 - 4.52680i) q^{37} +(-2.87629 + 5.56184i) q^{38} +(3.66129 - 2.11385i) q^{39} +(2.62179 + 1.06123i) q^{40} -7.14609i q^{41} +(1.52580 + 3.41642i) q^{42} -8.40383i q^{43} +(5.21875 - 3.69628i) q^{44} +(0.866025 - 0.500000i) q^{45} +(4.55822 + 2.35727i) q^{46} +(1.94089 - 3.36171i) q^{47} +(-2.60402 - 3.03629i) q^{48} +(6.68778 + 2.06725i) q^{49} +(-0.763067 - 1.19068i) q^{50} +(-0.0240571 - 0.0138894i) q^{51} +(0.782315 + 8.41912i) q^{52} +(2.74077 + 4.74715i) q^{53} +(-1.41270 + 0.0654937i) q^{54} -3.19757 q^{55} +(-7.48287 - 0.0816666i) q^{56} -4.42759 q^{57} +(-14.0370 + 0.650768i) q^{58} +(4.39493 + 7.61224i) q^{59} +(0.185045 + 1.99142i) q^{60} +(0.651742 + 0.376284i) q^{61} +(0.773968 + 1.20769i) q^{62} +(-1.65021 + 2.06804i) q^{63} +(7.69293 - 2.19520i) q^{64} +(2.11385 - 3.66129i) q^{65} +(4.01672 + 2.07723i) q^{66} +(14.0629 - 8.11919i) q^{67} +(0.0453377 - 0.0321113i) q^{68} +3.62864i q^{69} +(3.02959 + 2.19580i) q^{70} +9.83326i q^{71} +(1.06123 - 2.62179i) q^{72} +(-13.1339 + 7.58284i) q^{73} +(-3.39568 + 6.56617i) q^{74} +(0.500000 - 0.866025i) q^{75} +(3.69906 - 8.04558i) q^{76} +(7.87609 - 3.08844i) q^{77} +(-5.03385 + 3.22602i) q^{78} +(-12.3297 - 7.11856i) q^{79} +(-3.77330 - 1.32749i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.468024 + 10.0953i) q^{82} -9.71979 q^{83} +(-2.37925 - 4.72643i) q^{84} -0.0277788 q^{85} +(0.550397 + 11.8721i) q^{86} +(-4.96818 - 8.60513i) q^{87} +(-7.13043 + 5.56351i) q^{88} +(-8.85682 - 5.11349i) q^{89} +(-1.19068 + 0.763067i) q^{90} +(-1.67038 + 11.0600i) q^{91} +(-6.59377 - 3.03157i) q^{92} +(-0.507143 + 0.878397i) q^{93} +(-2.52171 + 4.87620i) q^{94} +(-3.83441 + 2.21380i) q^{95} +(3.87755 + 4.11881i) q^{96} +12.1010i q^{97} +(-9.58320 - 2.48239i) q^{98} +3.19757i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 14 q^{3} + 2 q^{4} + 2 q^{6} - 6 q^{7} - 4 q^{8} - 14 q^{9}+O(q^{10}) \) 28 * q - 4 * q^2 - 14 * q^3 + 2 * q^4 + 2 * q^6 - 6 * q^7 - 4 * q^8 - 14 * q^9	\( 28 q - 4 q^{2} - 14 q^{3} + 2 q^{4} + 2 q^{6} - 6 q^{7} - 4 q^{8} - 14 q^{9} - 4 q^{10} + 2 q^{12} + 28 q^{14} - 2 q^{16} - 24 q^{17} + 2 q^{18} + 14 q^{19} - 4 q^{20} + 16 q^{22} - 16 q^{24} + 14 q^{25} - 34 q^{26} + 28 q^{27} + 4 q^{28} + 8 q^{29} + 2 q^{30} + 2 q^{31} - 4 q^{32} - 4 q^{36} - 14 q^{37} - 10 q^{38} + 18 q^{39} - 2 q^{40} - 20 q^{42} + 54 q^{44} - 14 q^{46} - 16 q^{47} - 20 q^{48} + 30 q^{49} - 2 q^{50} + 24 q^{51} + 36 q^{52} + 20 q^{53} - 4 q^{54} + 8 q^{55} - 32 q^{56} - 28 q^{57} - 40 q^{58} + 16 q^{59} + 8 q^{60} + 70 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{66} - 66 q^{67} - 8 q^{68} + 6 q^{70} + 20 q^{72} + 18 q^{73} - 48 q^{74} + 14 q^{75} - 56 q^{76} + 8 q^{77} - 10 q^{78} + 6 q^{79} - 16 q^{80} - 14 q^{81} - 16 q^{82} - 24 q^{83} - 8 q^{84} - 4 q^{87} - 12 q^{88} + 36 q^{89} + 2 q^{90} + 34 q^{91} + 52 q^{92} + 2 q^{93} + 18 q^{94} - 12 q^{95} - 28 q^{96} + 2 q^{98}+O(q^{100}) \) 28 * q - 4 * q^2 - 14 * q^3 + 2 * q^4 + 2 * q^6 - 6 * q^7 - 4 * q^8 - 14 * q^9 - 4 * q^10 + 2 * q^12 + 28 * q^14 - 2 * q^16 - 24 * q^17 + 2 * q^18 + 14 * q^19 - 4 * q^20 + 16 * q^22 - 16 * q^24 + 14 * q^25 - 34 * q^26 + 28 * q^27 + 4 * q^28 + 8 * q^29 + 2 * q^30 + 2 * q^31 - 4 * q^32 - 4 * q^36 - 14 * q^37 - 10 * q^38 + 18 * q^39 - 2 * q^40 - 20 * q^42 + 54 * q^44 - 14 * q^46 - 16 * q^47 - 20 * q^48 + 30 * q^49 - 2 * q^50 + 24 * q^51 + 36 * q^52 + 20 * q^53 - 4 * q^54 + 8 * q^55 - 32 * q^56 - 28 * q^57 - 40 * q^58 + 16 * q^59 + 8 * q^60 + 70 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^66 - 66 * q^67 - 8 * q^68 + 6 * q^70 + 20 * q^72 + 18 * q^73 - 48 * q^74 + 14 * q^75 - 56 * q^76 + 8 * q^77 - 10 * q^78 + 6 * q^79 - 16 * q^80 - 14 * q^81 - 16 * q^82 - 24 * q^83 - 8 * q^84 - 4 * q^87 - 12 * q^88 + 36 * q^89 + 2 * q^90 + 34 * q^91 + 52 * q^92 + 2 * q^93 + 18 * q^94 - 12 * q^95 - 28 * q^96 + 2 * q^98

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