LMFDB - Embedded newform 322.2.e.a.277.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.3
Root			$0.882007 - 1.52768i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.a.93.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.0985631 - 0.170716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.154437 + 0.267494i) q^{5} -0.197126 q^{6} +(-1.71031 + 2.01862i) q^{7} +1.00000 q^{8} +(1.48057 + 2.56442i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.0985631 - 0.170716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.154437 + 0.267494i) q^{5} -0.197126 q^{6} +(-1.71031 + 2.01862i) q^{7} +1.00000 q^{8} +(1.48057 + 2.56442i) q^{9} +(0.154437 - 0.267494i) q^{10} +(-0.184881 + 0.320224i) q^{11} +(0.0985631 + 0.170716i) q^{12} +6.29639 q^{13} +(2.60333 + 0.471863i) q^{14} +0.0608874 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.30670 + 3.99533i) q^{17} +(1.48057 - 2.56442i) q^{18} +(0.176466 + 0.305648i) q^{19} -0.308875 q^{20} +(0.176038 + 0.490940i) q^{21} +0.369762 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.0985631 - 0.170716i) q^{24} +(2.45230 - 4.24750i) q^{25} +(-3.14819 - 5.45283i) q^{26} +1.17510 q^{27} +(-0.893022 - 2.49048i) q^{28} +1.74199 q^{29} +(-0.0304437 - 0.0527300i) q^{30} +(-1.46739 + 2.54159i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0364449 + 0.0631245i) q^{33} +4.61341 q^{34} +(-0.804105 - 0.145747i) q^{35} -2.96114 q^{36} +(3.18965 + 5.52464i) q^{37} +(0.176466 - 0.305648i) q^{38} +(0.620592 - 1.07490i) q^{39} +(0.154437 + 0.267494i) q^{40} -1.90213 q^{41} +(0.337147 - 0.397923i) q^{42} +6.55252 q^{43} +(-0.184881 - 0.320224i) q^{44} +(-0.457311 + 0.792086i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-5.86735 - 10.1625i) q^{47} -0.197126 q^{48} +(-1.14967 - 6.90495i) q^{49} -4.90460 q^{50} +(0.454712 + 0.787584i) q^{51} +(-3.14819 + 5.45283i) q^{52} +(-2.95230 + 5.11353i) q^{53} +(-0.587549 - 1.01766i) q^{54} -0.114210 q^{55} +(-1.71031 + 2.01862i) q^{56} +0.0695722 q^{57} +(-0.870993 - 1.50860i) q^{58} +(1.14602 - 1.98497i) q^{59} +(-0.0304437 + 0.0527300i) q^{60} +(-3.39396 - 5.87851i) q^{61} +2.93477 q^{62} +(-7.70884 - 1.39725i) q^{63} +1.00000 q^{64} +(0.972398 + 1.68424i) q^{65} +(0.0364449 - 0.0631245i) q^{66} +(-6.37212 + 11.0368i) q^{67} +(-2.30670 - 3.99533i) q^{68} +0.197126 q^{69} +(0.275832 + 0.769248i) q^{70} +0.492118 q^{71} +(1.48057 + 2.56442i) q^{72} +(-2.99976 + 5.19573i) q^{73} +(3.18965 - 5.52464i) q^{74} +(-0.483412 - 0.837295i) q^{75} -0.352932 q^{76} +(-0.330206 - 0.920887i) q^{77} -1.24118 q^{78} +(-0.333075 - 0.576902i) q^{79} +(0.154437 - 0.267494i) q^{80} +(-4.32589 + 7.49266i) q^{81} +(0.951067 + 1.64730i) q^{82} -6.44785 q^{83} +(-0.513186 - 0.0930165i) q^{84} -1.42497 q^{85} +(-3.27626 - 5.67465i) q^{86} +(0.171696 - 0.297386i) q^{87} +(-0.184881 + 0.320224i) q^{88} +(-5.81105 - 10.0650i) q^{89} +0.914622 q^{90} +(-10.7688 + 12.7100i) q^{91} -1.00000 q^{92} +(0.289260 + 0.501013i) q^{93} +(-5.86735 + 10.1625i) q^{94} +(-0.0545060 + 0.0944071i) q^{95} +(0.0985631 + 0.170716i) q^{96} +4.96548 q^{97} +(-5.40502 + 4.44811i) q^{98} -1.09492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.0985631	−	0.170716i	0.0569055	−	0.0985631i	−0.836169	−	0.548471i	$-0.815210\pi$
$3$	0.0985631	−	0.170716i	0.0569055	−	0.0985631i	0.893075	+	0.449908i	$0.148543\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.154437	+	0.267494i	0.0690665	+	0.119627i	0.898491	−	0.438993i	$-0.144665\pi$
$5$	0.154437	+	0.267494i	0.0690665	+	0.119627i	−0.829424	+	0.558619i	$0.811331\pi$
$6$	−0.197126			−0.0804765
$7$	−1.71031	+	2.01862i	−0.646437	+	0.762967i
$7$	−1.71031	+	2.01862i	−0.646437	+	0.762967i
$8$	1.00000			0.353553
$9$	1.48057	+	2.56442i	0.493524	+	0.854808i
$10$	0.154437	−	0.267494i	0.0488374	−	0.0845889i
$11$	−0.184881	+	0.320224i	−0.0557438	+	0.0965510i	−0.892551	−	0.450947i	$-0.851086\pi$
$11$	−0.184881	+	0.320224i	−0.0557438	+	0.0965510i	0.836807	+	0.547498i	$0.184420\pi$
$12$	0.0985631	+	0.170716i	0.0284527	+	0.0492816i
$13$	6.29639			1.74630			0.873152	−	0.487448i	$-0.162072\pi$
$13$	6.29639			1.74630			0.873152	+	0.487448i	$0.162072\pi$
$14$	2.60333	+	0.471863i	0.695770	+	0.126111i
$15$	0.0608874			0.0157211
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.30670	+	3.99533i	−0.559458	+	0.969009i	0.438084	+	0.898934i	$0.355657\pi$
$17$	−2.30670	+	3.99533i	−0.559458	+	0.969009i	−0.997542	+	0.0700753i	$0.977676\pi$
$18$	1.48057	−	2.56442i	0.348974	−	0.604440i
$19$	0.176466	+	0.305648i	0.0404841	+	0.0701205i	0.885557	−	0.464530i	$-0.153777\pi$
$19$	0.176466	+	0.305648i	0.0404841	+	0.0701205i	−0.845073	+	0.534650i	$0.820443\pi$
$20$	−0.308875			−0.0690665
$21$	0.176038	+	0.490940i	0.0384147	+	0.107132i
$22$	0.369762			0.0788336
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	0.0985631	−	0.170716i	0.0201191	−	0.0348473i
$25$	2.45230	−	4.24750i	0.490460	−	0.849501i
$26$	−3.14819	−	5.45283i	−0.617412	−	1.06939i
$27$	1.17510			0.226148
$28$	−0.893022	−	2.49048i	−0.168765	−	0.470657i
$29$	1.74199			0.323479			0.161739	−	0.986834i	$-0.448290\pi$
$29$	1.74199			0.323479			0.161739	+	0.986834i	$0.448290\pi$
$30$	−0.0304437	−	0.0527300i	−0.00555823	−	0.00962714i
$31$	−1.46739	+	2.54159i	−0.263550	+	0.456482i	−0.967183	−	0.254082i	$-0.918227\pi$
$31$	−1.46739	+	2.54159i	−0.263550	+	0.456482i	0.703633	+	0.710564i	$0.251560\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.0364449	+	0.0631245i	0.00634425	+	0.0109886i
$34$	4.61341			0.791193
$35$	−0.804105	−	0.145747i	−0.135918	−	0.0246357i
$36$	−2.96114			−0.493524
$37$	3.18965	+	5.52464i	0.524375	+	0.908245i	0.999597	+	0.0283789i	$0.00903451\pi$
$37$	3.18965	+	5.52464i	0.524375	+	0.908245i	−0.475222	+	0.879866i	$0.657632\pi$
$38$	0.176466	−	0.305648i	0.0286266	−	0.0495827i
$39$	0.620592	−	1.07490i	0.0993742	−	0.172121i
$40$	0.154437	+	0.267494i	0.0244187	+	0.0422944i
$41$	−1.90213			−0.297064			−0.148532	−	0.988908i	$-0.547455\pi$
$41$	−1.90213			−0.297064			−0.148532	+	0.988908i	$0.547455\pi$
$42$	0.337147	−	0.397923i	0.0520230	−	0.0614009i
$43$	6.55252			0.999250			0.499625	−	0.866242i	$-0.333471\pi$
$43$	6.55252			0.999250			0.499625	+	0.866242i	$0.333471\pi$
$44$	−0.184881	−	0.320224i	−0.0278719	−	0.0482755i
$45$	−0.457311	+	0.792086i	−0.0681719	+	0.118077i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−5.86735	−	10.1625i	−0.855841	−	1.48236i	−0.875863	−	0.482560i	$-0.839707\pi$
$47$	−5.86735	−	10.1625i	−0.855841	−	1.48236i	0.0200221	−	0.999800i	$-0.493626\pi$
$48$	−0.197126			−0.0284527
$49$	−1.14967	−	6.90495i	−0.164238	−	0.986421i
$50$	−4.90460			−0.693615
$51$	0.454712	+	0.787584i	0.0636724	+	0.110284i
$52$	−3.14819	+	5.45283i	−0.436576	+	0.756172i
$53$	−2.95230	+	5.11353i	−0.405529	+	0.702397i	−0.994383	−	0.105842i	$-0.966246\pi$
$53$	−2.95230	+	5.11353i	−0.405529	+	0.702397i	0.588854	+	0.808240i	$0.299579\pi$
$54$	−0.587549	−	1.01766i	−0.0799553	−	0.138487i
$55$	−0.114210			−0.0154001
$56$	−1.71031	+	2.01862i	−0.228550	+	0.269750i
$57$	0.0695722			0.00921506
$58$	−0.870993	−	1.50860i	−0.114367	−	0.198089i
$59$	1.14602	−	1.98497i	0.149199	−	0.258421i	−0.781732	−	0.623614i	$-0.785664\pi$
$59$	1.14602	−	1.98497i	0.149199	−	0.258421i	0.930932	+	0.365193i	$0.118997\pi$
$60$	−0.0304437	+	0.0527300i	−0.00393026	+	0.00680742i
$61$	−3.39396	−	5.87851i	−0.434552	−	0.752667i	0.562707	−	0.826657i	$-0.309760\pi$
$61$	−3.39396	−	5.87851i	−0.434552	−	0.752667i	−0.997259	+	0.0739899i	$0.976427\pi$
$62$	2.93477			0.372716
$63$	−7.70884	−	1.39725i	−0.971222	−	0.176037i
$64$	1.00000			0.125000
$65$	0.972398	+	1.68424i	0.120611	+	0.208905i
$66$	0.0364449	−	0.0631245i	0.00448606	−	0.00777009i
$67$	−6.37212	+	11.0368i	−0.778478	+	1.34836i	0.154340	+	0.988018i	$0.450675\pi$
$67$	−6.37212	+	11.0368i	−0.778478	+	1.34836i	−0.932819	+	0.360346i	$0.882659\pi$
$68$	−2.30670	−	3.99533i	−0.279729	−	0.484505i
$69$	0.197126			0.0237312
$70$	0.275832	+	0.769248i	0.0329682	+	0.0919427i
$71$	0.492118			0.0584037			0.0292018	−	0.999574i	$-0.490703\pi$
$71$	0.492118			0.0584037			0.0292018	+	0.999574i	$0.490703\pi$
$72$	1.48057	+	2.56442i	0.174487	+	0.302220i
$73$	−2.99976	+	5.19573i	−0.351095	+	0.608114i	−0.986442	−	0.164113i	$-0.947524\pi$
$73$	−2.99976	+	5.19573i	−0.351095	+	0.608114i	0.635347	+	0.772227i	$0.280857\pi$
$74$	3.18965	−	5.52464i	0.370789	−	0.642226i
$75$	−0.483412	−	0.837295i	−0.0558197	−	0.0966825i
$76$	−0.352932			−0.0404841
$77$	−0.330206	−	0.920887i	−0.0376304	−	0.104945i
$78$	−1.24118			−0.140536
$79$	−0.333075	−	0.576902i	−0.0374738	−	0.0649066i	0.846680	−	0.532102i	$-0.178598\pi$
$79$	−0.333075	−	0.576902i	−0.0374738	−	0.0649066i	−0.884154	+	0.467196i	$0.845264\pi$
$80$	0.154437	−	0.267494i	0.0172666	−	0.0299067i
$81$	−4.32589	+	7.49266i	−0.480655	+	0.832518i
$82$	0.951067	+	1.64730i	0.105028	+	0.181914i
$83$	−6.44785			−0.707744			−0.353872	−	0.935294i	$-0.615135\pi$
$83$	−6.44785			−0.707744			−0.353872	+	0.935294i	$0.615135\pi$
$84$	−0.513186	−	0.0930165i	−0.0559931	−	0.0101489i
$85$	−1.42497			−0.154559
$86$	−3.27626	−	5.67465i	−0.353288	−	0.611913i
$87$	0.171696	−	0.297386i	0.0184077	−	0.0318831i
$88$	−0.184881	+	0.320224i	−0.0197084	+	0.0341359i
$89$	−5.81105	−	10.0650i	−0.615970	−	1.06689i	−0.990214	−	0.139560i	$-0.955431\pi$
$89$	−5.81105	−	10.0650i	−0.615970	−	1.06689i	0.374244	−	0.927330i	$-0.377902\pi$
$90$	0.914622			0.0964097
$91$	−10.7688	+	12.7100i	−1.12888	+	1.33237i
$92$	−1.00000			−0.104257
$93$	0.289260	+	0.501013i	0.0299949	+	0.0519527i
$94$	−5.86735	+	10.1625i	−0.605171	+	1.04819i
$95$	−0.0545060	+	0.0944071i	−0.00559219	+	0.00968596i
$96$	0.0985631	+	0.170716i	0.0100596	+	0.0174237i
$97$	4.96548			0.504168			0.252084	−	0.967705i	$-0.418884\pi$
$97$	4.96548			0.504168			0.252084	+	0.967705i	$0.418884\pi$
$98$	−5.40502	+	4.44811i	−0.545990	+	0.449327i
$99$	−1.09492			−0.110043
$100$	2.45230	+	4.24750i	0.245230	+	0.424750i
$101$	6.67745	−	11.5657i	0.664432	−	1.15083i	−0.315008	−	0.949089i	$-0.602007\pi$
$101$	6.67745	−	11.5657i	0.664432	−	1.15083i	0.979439	−	0.201740i	$-0.0646596\pi$
$102$	0.454712	−	0.787584i	0.0450232	−	0.0779825i
$103$	−0.439355	−	0.760986i	−0.0432910	−	0.0749821i	0.843568	−	0.537022i	$-0.180451\pi$
$103$	−0.439355	−	0.760986i	−0.0432910	−	0.0749821i	−0.886859	+	0.462040i	$0.847118\pi$
$104$	6.29639			0.617412
$105$	−0.104136	+	0.122909i	−0.0101627	+	0.0119946i
$106$	5.90460			0.573505
$107$	−7.15055	−	12.3851i	−0.691270	−	1.19731i	−0.971422	−	0.237359i	$-0.923718\pi$
$107$	−7.15055	−	12.3851i	−0.691270	−	1.19731i	0.280152	−	0.959956i	$-0.409615\pi$
$108$	−0.587549	+	1.01766i	−0.0565369	+	0.0979248i
$109$	7.56040	−	13.0950i	0.724155	−	1.25427i	−0.235166	−	0.971955i	$-0.575563\pi$
$109$	7.56040	−	13.0950i	0.724155	−	1.25427i	0.959321	−	0.282318i	$-0.0911034\pi$
$110$	0.0571052	+	0.0989090i	0.00544476	+	0.00943061i
$111$	1.25753			0.119359
$112$	2.60333	+	0.471863i	0.245992	+	0.0445868i
$113$	7.57075			0.712196			0.356098	−	0.934449i	$-0.384107\pi$
$113$	7.57075			0.712196			0.356098	+	0.934449i	$0.384107\pi$
$114$	−0.0347861	−	0.0602513i	−0.00325802	−	0.00564305i
$115$	−0.154437	+	0.267494i	−0.0144014	+	0.0249439i
$116$	−0.870993	+	1.50860i	−0.0808697	+	0.140070i
$117$	9.32225	+	16.1466i	0.861842	+	1.49275i
$118$	−2.29204			−0.211000
$119$	−4.11987	−	11.4896i	−0.377668	−	1.05325i
$120$	0.0608874			0.00555823
$121$	5.43164	+	9.40787i	0.493785	+	0.855261i
$122$	−3.39396	+	5.87851i	−0.307275	+	0.532216i
$123$	−0.187480	+	0.324726i	−0.0169045	+	0.0292795i
$124$	−1.46739	−	2.54159i	−0.131775	−	0.228241i
$125$	3.05928			0.273630
$126$	2.64436	+	7.37468i	0.235579	+	0.656988i
$127$	16.0215			1.42168			0.710841	−	0.703353i	$-0.248315\pi$
$127$	16.0215			1.42168			0.710841	+	0.703353i	$0.248315\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.645837	−	1.11862i	0.0568628	−	0.0984892i
$130$	0.972398	−	1.68424i	0.0852850	−	0.147718i
$131$	−9.15897	−	15.8638i	−0.800223	−	1.38603i	−0.919469	−	0.393161i	$-0.871381\pi$
$131$	−9.15897	−	15.8638i	−0.800223	−	1.38603i	0.119247	−	0.992865i	$-0.461952\pi$
$132$	−0.0728899			−0.00634425
$133$	−0.918800	−	0.166535i	−0.0796701	−	0.0144405i
$134$	12.7442			1.10093
$135$	0.181479	+	0.314331i	0.0156192	+	0.0270533i
$136$	−2.30670	+	3.99533i	−0.197798	+	0.342597i
$137$	4.61681	−	7.99655i	0.394441	−	0.683191i	−0.598589	−	0.801056i	$-0.704272\pi$
$137$	4.61681	−	7.99655i	0.394441	−	0.683191i	0.993030	+	0.117865i	$0.0376050\pi$
$138$	−0.0985631	−	0.170716i	−0.00839025	−	0.0145323i
$139$	−17.2940			−1.46686			−0.733430	−	0.679765i	$-0.762082\pi$
$139$	−17.2940			−1.46686			−0.733430	+	0.679765i	$0.762082\pi$
$140$	0.528272	−	0.623502i	0.0446472	−	0.0526955i
$141$	−2.31322			−0.194808
$142$	−0.246059	−	0.426187i	−0.0206488	−	0.0357648i
$143$	−1.16408	+	2.01625i	−0.0973455	+	0.168607i
$144$	1.48057	−	2.56442i	0.123381	−	0.213702i
$145$	0.269028	+	0.465970i	0.0223416	+	0.0386967i
$146$	5.99951			0.496523
$147$	−1.29210	−	0.484306i	−0.106571	−	0.0399449i
$148$	−6.37930			−0.524375
$149$	7.37742	+	12.7781i	0.604382	+	1.04682i	0.992149	+	0.125063i	$0.0399132\pi$
$149$	7.37742	+	12.7781i	0.604382	+	1.04682i	−0.387767	+	0.921757i	$0.626753\pi$
$150$	−0.483412	+	0.837295i	−0.0394705	+	0.0683648i
$151$	10.6213	−	18.3966i	0.864348	−	1.49710i	−0.00334456	−	0.999994i	$-0.501065\pi$
$151$	10.6213	−	18.3966i	0.864348	−	1.49710i	0.867693	−	0.497101i	$-0.165602\pi$
$152$	0.176466	+	0.305648i	0.0143133	+	0.0247913i
$153$	−13.6610			−1.10442
$154$	−0.632409	+	0.746410i	−0.0509610	+	0.0601475i
$155$	−0.906477			−0.0728100
$156$	0.620592	+	1.07490i	0.0496871	+	0.0860606i
$157$	6.82206	−	11.8162i	0.544460	−	0.943032i	−0.454181	−	0.890909i	$-0.650068\pi$
$157$	6.82206	−	11.8162i	0.544460	−	0.943032i	0.998641	−	0.0521224i	$-0.0165986\pi$
$158$	−0.333075	+	0.576902i	−0.0264980	+	0.0458959i
$159$	0.581976	+	1.00801i	0.0461537	+	0.0799405i
$160$	−0.308875			−0.0244187
$161$	−2.60333	−	0.471863i	−0.205171	−	0.0371880i
$162$	8.65178			0.679748
$163$	9.56734	+	16.5711i	0.749372	+	1.29795i	0.948124	+	0.317901i	$0.102978\pi$
$163$	9.56734	+	16.5711i	0.749372	+	1.29795i	−0.198752	+	0.980050i	$0.563689\pi$
$164$	0.951067	−	1.64730i	0.0742659	−	0.128632i
$165$	−0.0112569	+	0.0194976i	−0.000876351	+	0.00151788i
$166$	3.22393	+	5.58400i	0.250225	+	0.433403i
$167$	5.31322			0.411149			0.205575	−	0.978641i	$-0.434094\pi$
$167$	5.31322			0.411149			0.205575	+	0.978641i	$0.434094\pi$
$168$	0.176038	+	0.490940i	0.0135816	+	0.0378768i
$169$	26.6445			2.04958
$170$	0.712483	+	1.23406i	0.0546450	+	0.0946478i
$171$	−0.522541	+	0.905068i	−0.0399597	+	0.0692122i
$172$	−3.27626	+	5.67465i	−0.249812	+	0.432688i
$173$	2.61269	+	4.52531i	0.198639	+	0.344053i	0.948087	−	0.318010i	$-0.103015\pi$
$173$	2.61269	+	4.52531i	0.198639	+	0.344053i	−0.749448	+	0.662063i	$0.769681\pi$
$174$	−0.343391			−0.0260324
$175$	4.37991	+	12.2148i	0.331090	+	0.923354i
$176$	0.369762			0.0278719
$177$	−0.225911	−	0.391290i	−0.0169805	−	0.0294111i
$178$	−5.81105	+	10.0650i	−0.435556	+	0.754406i
$179$	5.20161	−	9.00945i	0.388786	−	0.673398i	−0.603500	−	0.797363i	$-0.706228\pi$
$179$	5.20161	−	9.00945i	0.388786	−	0.673398i	0.992287	+	0.123965i	$0.0395611\pi$
$180$	−0.457311	−	0.792086i	−0.0340860	−	0.0590386i
$181$	7.39945			0.549997			0.274998	−	0.961445i	$-0.411323\pi$
$181$	7.39945			0.549997			0.274998	+	0.961445i	$0.411323\pi$
$182$	16.3916	+	2.97103i	1.21503	+	0.220227i
$183$	−1.33808			−0.0989136
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−0.985203	+	1.70642i	−0.0724336	+	0.125459i
$186$	0.289260	−	0.501013i	0.0212096	−	0.0367361i
$187$	−0.852932	−	1.47732i	−0.0623726	−	0.108032i
$188$	11.7347			0.855841
$189$	−2.00978	+	2.37208i	−0.146190	+	0.172543i
$190$	0.109012			0.00790855
$191$	1.99976	+	3.46368i	0.144697	+	0.250623i	0.929260	−	0.369426i	$-0.120446\pi$
$191$	1.99976	+	3.46368i	0.144697	+	0.250623i	−0.784563	+	0.620050i	$0.787112\pi$
$192$	0.0985631	−	0.170716i	0.00711318	−	0.0123204i
$193$	−0.226630	+	0.392534i	−0.0163132	+	0.0282552i	−0.874067	−	0.485806i	$-0.838526\pi$
$193$	−0.226630	+	0.392534i	−0.0163132	+	0.0282552i	0.857754	+	0.514061i	$0.171860\pi$
$194$	−2.48274	−	4.30023i	−0.178250	−	0.308739i
$195$	0.383370			0.0274537
$196$	6.55469	+	2.45683i	0.468192	+	0.175488i
$197$	−6.07584			−0.432885			−0.216443	−	0.976295i	$-0.569445\pi$
$197$	−6.07584			−0.432885			−0.216443	+	0.976295i	$0.569445\pi$
$198$	0.547459	+	0.948227i	0.0389062	+	0.0673876i
$199$	12.9633	−	22.4530i	0.918941	−	1.59165i	0.117914	−	0.993024i	$-0.462379\pi$
$199$	12.9633	−	22.4530i	0.918941	−	1.59165i	0.801027	−	0.598628i	$-0.204287\pi$
$200$	2.45230	−	4.24750i	0.173404	−	0.300344i
$201$	1.25611	+	2.17565i	0.0885993	+	0.153459i
$202$	−13.3549			−0.939648
$203$	−2.97934	+	3.51641i	−0.209109	+	0.246804i
$204$	−0.909424			−0.0636724
$205$	−0.293761	−	0.508809i	−0.0205171	−	0.0355367i
$206$	−0.439355	+	0.760986i	−0.0306113	+	0.0530204i
$207$	−1.48057	+	2.56442i	−0.102907	+	0.178240i
$208$	−3.14819	−	5.45283i	−0.218288	−	0.378086i
$209$	−0.130501			−0.00902694
$210$	0.158510	+	0.0287305i	0.0109382	+	0.00198259i
$211$	−14.9365			−1.02827			−0.514137	−	0.857708i	$-0.671888\pi$
$211$	−14.9365			−1.02827			−0.514137	+	0.857708i	$0.671888\pi$
$212$	−2.95230	−	5.11353i	−0.202765	−	0.351199i
$213$	0.0485047	−	0.0840126i	0.00332349	−	0.00575645i
$214$	−7.15055	+	12.3851i	−0.488802	+	0.846629i
$215$	1.01195	+	1.75276i	0.0690147	+	0.119537i
$216$	1.17510			0.0799553
$217$	−2.62081	−	7.30900i	−0.177912	−	0.496167i
$218$	−15.1208			−1.02411
$219$	0.591331	+	1.02422i	0.0399585	+	0.0692101i
$220$	0.0571052	−	0.0989090i	0.00385003	−	0.00666845i
$221$	−14.5239	+	25.1561i	−0.976983	+	1.69218i
$222$	−0.628764	−	1.08905i	−0.0421999	−	0.0730924i
$223$	−5.36408			−0.359205			−0.179603	−	0.983739i	$-0.557481\pi$
$223$	−5.36408			−0.359205			−0.179603	+	0.983739i	$0.557481\pi$
$224$	−0.893022	−	2.49048i	−0.0596675	−	0.166402i
$225$	14.5232			0.968213
$226$	−3.78537	−	6.55646i	−0.251799	−	0.436129i
$227$	−14.0894	+	24.4035i	−0.935146	+	1.61972i	−0.160772	+	0.986992i	$0.551398\pi$
$227$	−14.0894	+	24.4035i	−0.935146	+	1.61972i	−0.774374	+	0.632729i	$0.781935\pi$
$228$	−0.0347861	+	0.0602513i	−0.00230377	+	0.00399024i
$229$	−7.91864	−	13.7155i	−0.523278	−	0.906345i	−0.999633	−	0.0270914i	$-0.991375\pi$
$229$	−7.91864	−	13.7155i	−0.523278	−	0.906345i	0.476355	−	0.879253i	$-0.341958\pi$
$230$	0.308875			0.0203666
$231$	−0.189757	−	0.0343940i	−0.0124851	−	0.00226296i
$232$	1.74199			0.114367
$233$	−12.7090	−	22.0127i	−0.832596	−	1.44210i	−0.895973	−	0.444109i	$-0.853520\pi$
$233$	−12.7090	−	22.0127i	−0.832596	−	1.44210i	0.0633771	−	0.997990i	$-0.479813\pi$
$234$	9.32225	−	16.1466i	0.609414	−	1.05554i
$235$	1.81228	−	3.13896i	0.118220	−	0.204763i
$236$	1.14602	+	1.98497i	0.0745997	+	0.129210i
$237$	−0.131316			−0.00852986
$238$	−7.89037	+	9.31272i	−0.511456	+	0.603654i
$239$	8.59412			0.555907			0.277954	−	0.960595i	$-0.410344\pi$
$239$	8.59412			0.555907			0.277954	+	0.960595i	$0.410344\pi$
$240$	−0.0304437	−	0.0527300i	−0.00196513	−	0.00340371i
$241$	−4.69442	+	8.13098i	−0.302394	+	0.523762i	−0.976678	−	0.214710i	$-0.931119\pi$
$241$	−4.69442	+	8.13098i	−0.302394	+	0.523762i	0.674283	+	0.738473i	$0.264453\pi$
$242$	5.43164	−	9.40787i	0.349159	−	0.604761i
$243$	2.61539	+	4.52999i	0.167778	+	0.290599i
$244$	6.78792			0.434552
$245$	1.66948	−	1.37391i	0.106659	−	0.0877759i
$246$	0.374961			0.0239066
$247$	1.11110	+	1.92448i	0.0706975	+	0.122452i
$248$	−1.46739	+	2.54159i	−0.0931790	+	0.161391i
$249$	−0.635520	+	1.10075i	−0.0402745	+	0.0697574i
$250$	−1.52964	−	2.64942i	−0.0967430	−	0.167564i
$251$	−3.13763			−0.198046			−0.0990229	−	0.995085i	$-0.531572\pi$
$251$	−3.13763			−0.198046			−0.0990229	+	0.995085i	$0.531572\pi$
$252$	5.06447	−	5.97742i	0.319032	−	0.376542i
$253$	−0.369762			−0.0232468
$254$	−8.01077	−	13.8751i	−0.502641	−	0.870599i
$255$	−0.140449	+	0.243265i	−0.00879527	+	0.0152338i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.4913	+	23.3677i	0.841567	+	1.45764i	0.888570	+	0.458742i	$0.151700\pi$
$257$	13.4913	+	23.3677i	0.841567	+	1.45764i	−0.0470028	+	0.998895i	$0.514967\pi$
$258$	−1.29167			−0.0804161
$259$	−16.6075	−	3.01015i	−1.03194	−	0.187042i
$260$	−1.94480			−0.120611
$261$	2.57913	+	4.46719i	0.159644	+	0.276512i
$262$	−9.15897	+	15.8638i	−0.565843	+	0.980068i
$263$	5.36612	−	9.29439i	0.330889	−	0.573117i	−0.651797	−	0.758393i	$-0.725985\pi$
$263$	5.36612	−	9.29439i	0.330889	−	0.573117i	0.982686	+	0.185277i	$0.0593181\pi$
$264$	0.0364449	+	0.0631245i	0.00224303	+	0.00388504i
$265$	−1.82378			−0.112034
$266$	0.315176	+	0.878972i	0.0193247	+	0.0538932i
$267$	−2.29102			−0.140208
$268$	−6.37212	−	11.0368i	−0.389239	−	0.674182i
$269$	7.93807	−	13.7491i	0.483992	−	0.838300i	−0.515838	−	0.856686i	$-0.672520\pi$
$269$	7.93807	−	13.7491i	0.483992	−	0.838300i	0.999831	+	0.0183863i	$0.00585286\pi$
$270$	0.181479	−	0.314331i	0.0110445	−	0.0191296i
$271$	−7.19021	−	12.4538i	−0.436774	−	0.756515i	0.560664	−	0.828043i	$-0.310546\pi$
$271$	−7.19021	−	12.4538i	−0.436774	−	0.756515i	−0.997439	+	0.0715280i	$0.977212\pi$
$272$	4.61341			0.279729
$273$	1.10840	+	3.09115i	0.0670837	+	0.187085i
$274$	−9.23362			−0.557823
$275$	0.906767	+	1.57057i	0.0546801	+	0.0947088i
$276$	−0.0985631	+	0.170716i	−0.00593280	+	0.0102759i
$277$	−5.81799	+	10.0771i	−0.349569	+	0.605471i	−0.986173	−	0.165720i	$-0.947005\pi$
$277$	−5.81799	+	10.0771i	−0.349569	+	0.605471i	0.636604	+	0.771191i	$0.280339\pi$
$278$	8.64701	+	14.9771i	0.518613	+	0.898264i
$279$	−8.69027			−0.520273
$280$	−0.804105	−	0.145747i	−0.0480544	−	0.00871002i
$281$	−25.2062			−1.50367			−0.751837	−	0.659349i	$-0.770832\pi$
$281$	−25.2062			−1.50367			−0.751837	+	0.659349i	$0.770832\pi$
$282$	1.15661	+	2.00331i	0.0688750	+	0.119295i
$283$	1.78808	−	3.09704i	0.106290	−	0.184100i	−0.807974	−	0.589218i	$-0.799436\pi$
$283$	1.78808	−	3.09704i	0.106290	−	0.184100i	0.914265	+	0.405118i	$0.132769\pi$
$284$	−0.246059	+	0.426187i	−0.0146009	+	0.0252895i
$285$	0.0107446	+	0.0186101i	0.000636453	+	0.00110237i
$286$	2.32817			0.137667
$287$	3.25324	−	3.83969i	0.192033	−	0.226650i
$288$	−2.96114			−0.174487
$289$	−2.14176	−	3.70964i	−0.125986	−	0.218214i
$290$	0.269028	−	0.465970i	0.0157979	−	0.0273627i
$291$	0.489414	−	0.847689i	0.0286899	−	0.0496924i
$292$	−2.99976	−	5.19573i	−0.175548	−	0.304057i
$293$	−4.03243			−0.235577			−0.117788	−	0.993039i	$-0.537580\pi$
$293$	−4.03243			−0.235577			−0.117788	+	0.993039i	$0.537580\pi$
$294$	0.226630	+	1.36115i	0.0132173	+	0.0793837i
$295$	0.707955			0.0412187
$296$	3.18965	+	5.52464i	0.185395	+	0.321113i
$297$	−0.217253	+	0.376294i	−0.0126063	+	0.0218348i
$298$	7.37742	−	12.7781i	0.427363	−	0.740214i
$299$	3.14819	+	5.45283i	0.182065	+	0.315345i
$300$	0.966825			0.0558197
$301$	−11.2069	+	13.2271i	−0.645952	+	0.762395i
$302$	−21.2426			−1.22237
$303$	−1.31630	−	2.27990i	−0.0756196	−	0.130977i
$304$	0.176466	−	0.305648i	0.0101210	−	0.0175301i
$305$	1.04831	−	1.81573i	0.0600261	−	0.103968i
$306$	6.83048	+	11.8307i	0.390472	+	0.676318i
$307$	−1.35937			−0.0775831			−0.0387915	−	0.999247i	$-0.512351\pi$
$307$	−1.35937			−0.0775831			−0.0387915	+	0.999247i	$0.512351\pi$
$308$	0.962615	+	0.174477i	0.0548501	+	0.00994175i
$309$	−0.173217			−0.00985397
$310$	0.453239	+	0.785032i	0.0257422	+	0.0445868i
$311$	−7.38172	+	12.7855i	−0.418579	+	0.725000i	−0.995797	−	0.0915904i	$-0.970805\pi$
$311$	−7.38172	+	12.7855i	−0.418579	+	0.725000i	0.577218	+	0.816590i	$0.304138\pi$
$312$	0.620592	−	1.07490i	0.0351341	−	0.0608540i
$313$	11.6470	+	20.1732i	0.658328	+	1.14026i	0.981048	+	0.193763i	$0.0620693\pi$
$313$	11.6470	+	20.1732i	0.658328	+	1.14026i	−0.322720	+	0.946494i	$0.604597\pi$
$314$	−13.6441			−0.769982
$315$	−0.816778	−	2.27785i	−0.0460202	−	0.128342i
$316$	0.666150			0.0374738
$317$	−9.66087	−	16.7331i	−0.542608	−	0.939825i	−0.998753	−	0.0499197i	$-0.984103\pi$
$317$	−9.66087	−	16.7331i	−0.542608	−	0.939825i	0.456145	−	0.889906i	$-0.349230\pi$
$318$	0.581976	−	1.00801i	0.0326356	−	0.0565265i
$319$	−0.322060	+	0.557825i	−0.0180319	+	0.0312322i
$320$	0.154437	+	0.267494i	0.00863332	+	0.0149533i
$321$	−2.81912			−0.157348
$322$	0.893022	+	2.49048i	0.0497662	+	0.138789i
$323$	−1.62822			−0.0905966
$324$	−4.32589	−	7.49266i	−0.240327	−	0.416259i
$325$	15.4406	−	26.7439i	0.856491	−	1.48349i
$326$	9.56734	−	16.5711i	0.529886	−	0.917790i
$327$	−1.49035	−	2.58137i	−0.0824168	−	0.142750i
$328$	−1.90213			−0.105028
$329$	30.5493	+	5.53716i	1.68424	+	0.305274i
$330$	0.0225139			0.00123935
$331$	2.00407	+	3.47116i	0.110154	+	0.190792i	0.915832	−	0.401561i	$-0.131532\pi$
$331$	2.00407	+	3.47116i	0.110154	+	0.190792i	−0.805678	+	0.592353i	$0.798199\pi$
$332$	3.22393	−	5.58400i	0.176936	−	0.306462i
$333$	−9.44501	+	16.3592i	−0.517583	+	0.896481i
$334$	−2.65661	−	4.60138i	−0.145363	−	0.251776i
$335$	−3.93638			−0.215067
$336$	0.337147	−	0.397923i	0.0183929	−	0.0217085i
$337$	−18.7242			−1.01997			−0.509986	−	0.860183i	$-0.670349\pi$
$337$	−18.7242			−1.01997			−0.509986	+	0.860183i	$0.670349\pi$
$338$	−13.3222	−	23.0748i	−0.724635	−	1.25510i
$339$	0.746197	−	1.29245i	0.0405278	−	0.0701963i
$340$	0.712483	−	1.23406i	0.0386398	−	0.0669261i
$341$	−0.542584	−	0.939783i	−0.0293826	−	0.0508921i
$342$	1.04508			0.0565116
$343$	15.9048	+	9.48887i	0.858776	+	0.512351i
$344$	6.55252			0.353288
$345$	0.0304437	+	0.0527300i	0.00163903	+	0.00283889i
$346$	2.61269	−	4.52531i	0.140459	−	0.243282i
$347$	−2.62469	+	4.54610i	−0.140901	+	0.244047i	−0.927836	−	0.372988i	$-0.878333\pi$
$347$	−2.62469	+	4.54610i	−0.140901	+	0.244047i	0.786935	+	0.617036i	$0.211667\pi$
$348$	0.171696	+	0.297386i	0.00920385	+	0.0159415i
$349$	−29.3789			−1.57262			−0.786309	−	0.617834i	$-0.788010\pi$
$349$	−29.3789			−1.57262			−0.786309	+	0.617834i	$0.788010\pi$
$350$	8.38839	−	9.90052i	0.448378	−	0.529205i
$351$	7.39887			0.394922
$352$	−0.184881	−	0.320224i	−0.00985420	−	0.0170680i
$353$	−1.88815	+	3.27037i	−0.100496	+	0.174064i	−0.911889	−	0.410437i	$-0.865376\pi$
$353$	−1.88815	+	3.27037i	−0.100496	+	0.174064i	0.811393	+	0.584501i	$0.198710\pi$
$354$	−0.225911	+	0.391290i	−0.0120070	+	0.0207968i
$355$	0.0760015	+	0.131638i	0.00403374	+	0.00698664i
$356$	11.6221			0.615970
$357$	−2.36753	−	0.429123i	−0.125303	−	0.0227116i
$358$	−10.4032			−0.549827
$359$	9.28414	+	16.0806i	0.489998	+	0.848702i	0.999934	−	0.0115107i	$-0.00366406\pi$
$359$	9.28414	+	16.0806i	0.489998	+	0.848702i	−0.509935	+	0.860213i	$0.670331\pi$
$360$	−0.457311	+	0.792086i	−0.0241024	+	0.0417466i
$361$	9.43772	−	16.3466i	0.496722	−	0.860348i
$362$	−3.69973	−	6.40811i	−0.194453	−	0.336803i
$363$	2.14144			0.112396
$364$	−5.62281	−	15.6811i	−0.294715	−	0.821911i
$365$	−1.85310			−0.0969957
$366$	0.669039	+	1.15881i	0.0349712	+	0.0605720i
$367$	−7.66138	+	13.2699i	−0.399921	+	0.692683i	−0.993716	−	0.111933i	$-0.964296\pi$
$367$	−7.66138	+	13.2699i	−0.399921	+	0.692683i	0.593795	+	0.804616i	$0.297629\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−2.81624	−	4.87788i	−0.146608	−	0.253932i
$370$	1.97041			0.102437
$371$	−5.27293	−	14.7053i	−0.273757	−	0.763461i
$372$	−0.578520			−0.0299949
$373$	−2.03891	−	3.53149i	−0.105571	−	0.182854i	0.808401	−	0.588633i	$-0.200334\pi$
$373$	−2.03891	−	3.53149i	−0.105571	−	0.182854i	−0.913971	+	0.405779i	$0.867000\pi$
$374$	−0.852932	+	1.47732i	−0.0441041	+	0.0763905i
$375$	0.301532	−	0.522270i	0.0155711	−	0.0269699i
$376$	−5.86735	−	10.1625i	−0.302585	−	0.524093i
$377$	10.9682			0.564892
$378$	3.05917	+	0.554485i	0.157347	+	0.0285196i
$379$	27.4392			1.40946			0.704729	−	0.709477i	$-0.251069\pi$
$379$	27.4392			1.40946			0.704729	+	0.709477i	$0.251069\pi$
$380$	−0.0545060	−	0.0944071i	−0.00279610	−	0.00484298i
$381$	1.57913	−	2.73514i	0.0809015	−	0.140125i
$382$	1.99976	−	3.46368i	0.102316	−	0.177217i
$383$	0.302361	+	0.523705i	0.0154499	+	0.0267601i	0.873647	−	0.486560i	$-0.161749\pi$
$383$	0.302361	+	0.523705i	0.0154499	+	0.0267601i	−0.858197	+	0.513320i	$0.828415\pi$
$384$	−0.197126			−0.0100596
$385$	0.195335	−	0.230547i	0.00995521	−	0.0117498i
$386$	0.453259			0.0230703
$387$	9.70147	+	16.8034i	0.493153	+	0.854167i
$388$	−2.48274	+	4.30023i	−0.126042	+	0.218311i
$389$	4.05062	−	7.01588i	0.205375	−	0.355719i	−0.744877	−	0.667201i	$-0.767492\pi$
$389$	4.05062	−	7.01588i	0.205375	−	0.355719i	0.950252	+	0.311482i	$0.100825\pi$
$390$	−0.191685	−	0.332009i	−0.00970636	−	0.0168119i
$391$	−4.61341			−0.233310
$392$	−1.14967	−	6.90495i	−0.0580670	−	0.348752i
$393$	−3.61095			−0.182148
$394$	3.03792	+	5.26183i	0.153048	+	0.265087i
$395$	0.102878	−	0.178191i	0.00517638	−	0.00896575i
$396$	0.547459	−	0.948227i	0.0275109	−	0.0476502i
$397$	6.42365	+	11.1261i	0.322394	+	0.558402i	0.980981	−	0.194102i	$-0.0621791\pi$
$397$	6.42365	+	11.1261i	0.322394	+	0.558402i	−0.658588	+	0.752504i	$0.728846\pi$
$398$	−25.9265			−1.29958
$399$	−0.118990	+	0.140440i	−0.00595696	+	0.00703079i
$400$	−4.90460			−0.245230
$401$	−4.03550	−	6.98970i	−0.201523	−	0.349049i	0.747496	−	0.664266i	$-0.231256\pi$
$401$	−4.03550	−	6.98970i	−0.201523	−	0.349049i	−0.949019	+	0.315217i	$0.897923\pi$
$402$	1.25611	−	2.17565i	0.0626492	−	0.108512i
$403$	−9.23922	+	16.0028i	−0.460239	+	0.797157i
$404$	6.67745	+	11.5657i	0.332216	+	0.575415i
$405$	−2.67232			−0.132789
$406$	4.53497	+	0.821978i	0.225067	+	0.0407941i
$407$	−2.35883			−0.116923
$408$	0.454712	+	0.787584i	0.0225116	+	0.0389912i
$409$	8.67087	−	15.0184i	0.428747	−	0.742612i	−0.568015	−	0.823018i	$-0.692289\pi$
$409$	8.67087	−	15.0184i	0.428747	−	0.742612i	0.996762	+	0.0804065i	$0.0256218\pi$
$410$	−0.293761	+	0.508809i	−0.0145078	+	0.0251283i
$411$	−0.910095	−	1.57633i	−0.0448917	−	0.0777546i
$412$	0.878711			0.0432910
$413$	2.04685	+	5.70830i	0.100719	+	0.280887i
$414$	2.96114			0.145532
$415$	−0.995790	−	1.72476i	−0.0488814	−	0.0846651i
$416$	−3.14819	+	5.45283i	−0.154353	+	0.267347i
$417$	−1.70455	+	2.95237i	−0.0834723	+	0.144578i
$418$	0.0652505	+	0.113017i	0.00319151	+	0.00552785i
$419$	15.7626			0.770054			0.385027	−	0.922905i	$-0.374192\pi$
$419$	15.7626			0.770054			0.385027	+	0.922905i	$0.374192\pi$
$420$	−0.0543738	−	0.151639i	−0.00265317	−	0.00739923i
$421$	−16.4898			−0.803661			−0.401831	−	0.915714i	$-0.631626\pi$
$421$	−16.4898			−0.803661			−0.401831	+	0.915714i	$0.631626\pi$
$422$	7.46827	+	12.9354i	0.363550	+	0.629686i
$423$	17.3740	−	30.0927i	0.844755	−	1.46316i
$424$	−2.95230	+	5.11353i	−0.143376	+	0.248335i
$425$	11.3135	+	19.5955i	0.548783	+	0.950520i
$426$	−0.0970094			−0.00470012
$427$	17.6712	+	3.20297i	0.855171	+	0.155002i
$428$	14.3011			0.691270
$429$	0.229471	+	0.397456i	0.0110790	+	0.0191894i
$430$	1.01195	−	1.75276i	0.0488008	−	0.0845254i
$431$	−5.47285	+	9.47926i	−0.263618	+	0.456600i	−0.967201	−	0.254014i	$-0.918249\pi$
$431$	−5.47285	+	9.47926i	−0.263618	+	0.456600i	0.703583	+	0.710614i	$0.251583\pi$
$432$	−0.587549	−	1.01766i	−0.0282685	−	0.0489624i
$433$	−28.0699			−1.34896			−0.674478	−	0.738295i	$-0.735631\pi$
$433$	−28.0699			−1.34896			−0.674478	+	0.738295i	$0.735631\pi$
$434$	−5.01937	+	5.92419i	−0.240938	+	0.284370i
$435$	0.106065			0.00508543
$436$	7.56040	+	13.0950i	0.362078	+	0.627137i
$437$	−0.176466	+	0.305648i	−0.00844152	+	0.0146211i
$438$	0.591331	−	1.02422i	0.0282549	−	0.0489389i
$439$	4.54122	+	7.86562i	0.216740	+	0.375405i	0.953810	−	0.300412i	$-0.0971242\pi$
$439$	4.54122	+	7.86562i	0.216740	+	0.375405i	−0.737069	+	0.675817i	$0.763791\pi$
$440$	−0.114210			−0.00544476
$441$	16.0050	−	13.1715i	0.762145	−	0.627214i
$442$	29.0478			1.38166
$443$	15.3899	+	26.6560i	0.731194	+	1.26647i	0.956373	+	0.292148i	$0.0943699\pi$
$443$	15.3899	+	26.6560i	0.731194	+	1.26647i	−0.225179	+	0.974317i	$0.572297\pi$
$444$	−0.628764	+	1.08905i	−0.0298398	+	0.0516841i
$445$	1.79489	−	3.10883i	0.0850858	−	0.147373i
$446$	2.68204	+	4.64543i	0.126998	+	0.219967i
$447$	2.90857			0.137571
$448$	−1.71031	+	2.01862i	−0.0808046	+	0.0953709i
$449$	−30.9015			−1.45833			−0.729166	−	0.684337i	$-0.760092\pi$
$449$	−30.9015			−1.45833			−0.729166	+	0.684337i	$0.760092\pi$
$450$	−7.26160	−	12.5775i	−0.342315	−	0.592907i
$451$	0.351669	−	0.609108i	0.0165594	−	0.0286818i
$452$	−3.78537	+	6.55646i	−0.178049	+	0.308390i
$453$	−2.09374	−	3.62646i	−0.0983723	−	0.170386i
$454$	28.1788			1.32250
$455$	−5.06295	−	0.917677i	−0.237355	−	0.0430213i
$456$	0.0695722			0.00325802
$457$	−20.3512	−	35.2492i	−0.951987	−	1.64889i	−0.741117	−	0.671376i	$-0.765704\pi$
$457$	−20.3512	−	35.2492i	−0.951987	−	1.64889i	−0.210870	−	0.977514i	$-0.567630\pi$
$458$	−7.91864	+	13.7155i	−0.370014	+	0.640882i
$459$	−2.71060	+	4.69490i	−0.126520	+	0.219139i
$460$	−0.154437	−	0.267494i	−0.00720068	−	0.0124720i
$461$	22.0792			1.02833			0.514166	−	0.857691i	$-0.328102\pi$
$461$	22.0792			1.02833			0.514166	+	0.857691i	$0.328102\pi$
$462$	0.0650922	+	0.181531i	0.00302837	+	0.00844559i
$463$	16.3672			0.760648			0.380324	−	0.924853i	$-0.375813\pi$
$463$	16.3672			0.760648			0.380324	+	0.924853i	$0.375813\pi$
$464$	−0.870993	−	1.50860i	−0.0404348	−	0.0700352i
$465$	−0.0893452	+	0.154750i	−0.00414329	+	0.00717638i
$466$	−12.7090	+	22.0127i	−0.588734	+	1.01972i
$467$	15.0234	+	26.0213i	0.695201	+	1.20412i	0.970113	+	0.242654i	$0.0780181\pi$
$467$	15.0234	+	26.0213i	0.695201	+	1.20412i	−0.274912	+	0.961469i	$0.588649\pi$
$468$	−18.6445			−0.861842
$469$	−11.3809	−	31.7393i	−0.525520	−	1.46559i
$470$	−3.62455			−0.167188
$471$	−1.34481	−	2.32927i	−0.0619655	−	0.107327i
$472$	1.14602	−	1.98497i	0.0527500	−	0.0913656i
$473$	−1.21144	+	2.09827i	−0.0557020	+	0.0964786i
$474$	0.0656578	+	0.113723i	0.00301576	+	0.00522345i
$475$	1.73099			0.0794233
$476$	12.0102	+	2.17689i	0.550488	+	0.0997778i
$477$	−17.4843			−0.800553
$478$	−4.29706	−	7.44272i	−0.196543	−	0.340422i
$479$	4.04609	−	7.00803i	0.184871	−	0.320205i	−0.758662	−	0.651484i	$-0.774147\pi$
$479$	4.04609	−	7.00803i	0.184871	−	0.320205i	0.943533	+	0.331279i	$0.107480\pi$
$480$	−0.0304437	+	0.0527300i	−0.00138956	+	0.00240678i
$481$	20.0833	+	34.7853i	0.915719	+	1.58607i
$482$	9.38884			0.427650
$483$	−0.337147	+	0.397923i	−0.0153407	+	0.0181061i
$484$	−10.8633			−0.493785
$485$	0.766857	+	1.32823i	0.0348212	+	0.0603120i
$486$	2.61539	−	4.52999i	0.118637	−	0.205485i
$487$	−3.29781	+	5.71198i	−0.149438	+	0.258834i	−0.931020	−	0.364968i	$-0.881080\pi$
$487$	−3.29781	+	5.71198i	−0.149438	+	0.258834i	0.781582	+	0.623803i	$0.214413\pi$
$488$	−3.39396	−	5.87851i	−0.153637	−	0.266108i
$489$	3.77195			0.170573
$490$	−2.02458	−	0.758854i	−0.0914612	−	0.0342815i
$491$	−12.7040			−0.573323			−0.286661	−	0.958032i	$-0.592545\pi$
$491$	−12.7040			−0.573323			−0.286661	+	0.958032i	$0.592545\pi$
$492$	−0.187480	−	0.324726i	−0.00845227	−	0.0146398i
$493$	−4.01825	+	6.95981i	−0.180973	+	0.313454i
$494$	1.11110	−	1.92448i	0.0499907	−	0.0865864i
$495$	−0.169096	−	0.292884i	−0.00760032	−	0.0131641i
$496$	2.93477			0.131775
$497$	−0.841675	+	0.993400i	−0.0377543	+	0.0445601i
$498$	1.27104			0.0569567
$499$	3.34489	+	5.79352i	0.149738	+	0.259354i	0.931131	−	0.364686i	$-0.118824\pi$
$499$	3.34489	+	5.79352i	0.149738	+	0.259354i	−0.781393	+	0.624040i	$0.785490\pi$
$500$	−1.52964	+	2.64942i	−0.0684076	+	0.118485i
$501$	0.523687	−	0.907053i	0.0233966	−	0.0405242i
$502$	1.56882	+	2.71727i	0.0700197	+	0.121278i
$503$	42.8269			1.90956			0.954779	−	0.297316i	$-0.0960913\pi$
$503$	42.8269			1.90956			0.954779	+	0.297316i	$0.0960913\pi$
$504$	−7.70884	−	1.39725i	−0.343379	−	0.0622385i
$505$	4.12500			0.183560
$506$	0.184881	+	0.320224i	0.00821897	+	0.0142357i
$507$	2.62616	−	4.54865i	0.116632	−	0.202013i
$508$	−8.01077	+	13.8751i	−0.355421	+	0.615606i
$509$	13.9892	+	24.2300i	0.620059	+	1.07397i	0.989474	+	0.144709i	$0.0462247\pi$
$509$	13.9892	+	24.2300i	0.620059	+	1.07397i	−0.369415	+	0.929264i	$0.620442\pi$
$510$	0.280898			0.0124384
$511$	−5.35770	−	14.9417i	−0.237011	−	0.660982i
$512$	1.00000			0.0441942
$513$	0.207365	+	0.359167i	0.00915538	+	0.0158576i
$514$	13.4913	−	23.3677i	0.595078	−	1.03070i
$515$	0.135706	−	0.235049i	0.00597991	−	0.0103575i
$516$	0.645837	+	1.11862i	0.0284314	+	0.0492446i
$517$	4.33905			0.190831
$518$	5.69686	+	15.8876i	0.250306	+	0.698059i
$519$	1.03006			0.0452146
$520$	0.972398	+	1.68424i	0.0426425	+	0.0738589i
$521$	2.01361	−	3.48768i	0.0882180	−	0.152798i	−0.818540	−	0.574450i	$-0.805216\pi$
$521$	2.01361	−	3.48768i	0.0882180	−	0.152798i	0.906758	+	0.421652i	$0.138549\pi$
$522$	2.57913	−	4.46719i	0.112886	−	0.195524i
$523$	−17.3396	−	30.0331i	−0.758209	−	1.31326i	−0.943763	−	0.330623i	$-0.892741\pi$
$523$	−17.3396	−	30.0331i	−0.758209	−	1.31326i	0.185554	−	0.982634i	$-0.440592\pi$
$524$	18.3179			0.800223
$525$	2.51697	+	0.456209i	0.109849	+	0.0199106i
$526$	−10.7322			−0.467948
$527$	−6.76965	−	11.7254i	−0.294890	−	0.510765i
$528$	0.0364449	−	0.0631245i	0.00158606	−	0.00274714i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	0.911891	+	1.57944i	0.0396100	+	0.0686066i
$531$	6.78707			0.294534
$532$	0.603624	−	0.712436i	0.0261704	−	0.0308880i
$533$	−11.9766			−0.518763
$534$	1.14551	+	1.98408i	0.0495711	+	0.0858596i
$535$	2.20863	−	3.82545i	0.0954872	−	0.165389i
$536$	−6.37212	+	11.0368i	−0.275234	+	0.476719i
$537$	−1.02537	−	1.77600i	−0.0442481	−	0.0766400i
$538$	−15.8761			−0.684469
$539$	2.42368	+	0.908444i	0.104395	+	0.0391294i
$540$	−0.362958			−0.0156192
$541$	13.3296	+	23.0875i	0.573084	+	0.992610i	0.996247	+	0.0865564i	$0.0275863\pi$
$541$	13.3296	+	23.0875i	0.573084	+	0.992610i	−0.423163	+	0.906053i	$0.639080\pi$
$542$	−7.19021	+	12.4538i	−0.308846	+	0.534937i
$543$	0.729313	−	1.26321i	0.0312978	−	0.0542094i
$544$	−2.30670	−	3.99533i	−0.0988991	−	0.171298i
$545$	4.67044			0.200060
$546$	2.12281	−	2.50548i	0.0908479	−	0.107225i
$547$	−5.21015			−0.222770			−0.111385	−	0.993777i	$-0.535529\pi$
$547$	−5.21015			−0.222770			−0.111385	+	0.993777i	$0.535529\pi$
$548$	4.61681	+	7.99655i	0.197220	+	0.341596i
$549$	10.0500	−	17.4071i	0.428924	−	0.742917i
$550$	0.906767	−	1.57057i	0.0386647	−	0.0669692i
$551$	0.307401	+	0.532435i	0.0130957	+	0.0226825i
$552$	0.197126			0.00839025
$553$	1.73421	+	0.314331i	0.0737461	+	0.0133667i
$554$	11.6360			0.494365
$555$	0.194210	+	0.336381i	0.00824373	+	0.0142786i
$556$	8.64701	−	14.9771i	0.366715	−	0.635169i
$557$	−23.3278	+	40.4050i	−0.988431	+	1.71201i	−0.362867	+	0.931841i	$0.618202\pi$
$557$	−23.3278	+	40.4050i	−0.988431	+	1.71201i	−0.625564	+	0.780172i	$0.715131\pi$
$558$	4.34513	+	7.52599i	0.183944	+	0.318601i
$559$	41.2572			1.74499
$560$	0.275832	+	0.769248i	0.0116560	+	0.0325067i
$561$	−0.336271			−0.0141974
$562$	12.6031	+	21.8292i	0.531629	+	0.920809i
$563$	−20.9007	+	36.2010i	−0.880859	+	1.52569i	−0.0304709	+	0.999536i	$0.509701\pi$
$563$	−20.9007	+	36.2010i	−0.880859	+	1.52569i	−0.850388	+	0.526156i	$0.823633\pi$
$564$	1.15661	−	2.00331i	0.0487020	−	0.0843544i
$565$	1.16921	+	2.02513i	0.0491889	+	0.0851977i
$566$	−3.57615			−0.150317
$567$	−7.72623	−	21.5471i	−0.324471	−	0.904894i
$568$	0.492118			0.0206488
$569$	5.68959	+	9.85467i	0.238520	+	0.413129i	0.960290	−	0.279004i	$-0.0900043\pi$
$569$	5.68959	+	9.85467i	0.238520	+	0.413129i	−0.721770	+	0.692133i	$0.756671\pi$
$570$	0.0107446	−	0.0186101i	0.000450040	−	0.000779492i
$571$	−10.6530	+	18.4516i	−0.445815	+	0.772174i	−0.998109	−	0.0614758i	$-0.980419\pi$
$571$	−10.6530	+	18.4516i	−0.445815	+	0.772174i	0.552294	+	0.833649i	$0.313753\pi$
$572$	−1.16408	−	2.01625i	−0.0486728	−	0.0843037i
$573$	0.788410			0.0329363
$574$	−4.95189	−	0.897546i	−0.206688	−	0.0374629i
$575$	4.90460			0.204536
$576$	1.48057	+	2.56442i	0.0616904	+	0.106851i
$577$	8.62124	−	14.9324i	0.358907	−	0.621645i	−0.628872	−	0.777509i	$-0.716483\pi$
$577$	8.62124	−	14.9324i	0.358907	−	0.621645i	0.987779	+	0.155864i	$0.0498162\pi$
$578$	−2.14176	+	3.70964i	−0.0890857	+	0.154301i
$579$	0.0446747	+	0.0773788i	0.00185662	+	0.00321575i
$580$	−0.538056			−0.0223416
$581$	11.0278	−	13.0158i	0.457512	−	0.539985i
$582$	−0.978827			−0.0405737
$583$	−1.09165	−	1.89079i	−0.0452115	−	0.0783086i
$584$	−2.99976	+	5.19573i	−0.124131	+	0.215001i
$585$	−2.87941	+	4.98728i	−0.119049	+	0.206199i
$586$	2.01621	+	3.49218i	0.0832890	+	0.144261i
$587$	−3.94485			−0.162821			−0.0814107	−	0.996681i	$-0.525943\pi$
$587$	−3.94485			−0.162821			−0.0814107	+	0.996681i	$0.525943\pi$
$588$	1.06547	−	0.876840i	0.0439393	−	0.0361603i
$589$	−1.03577			−0.0426784
$590$	−0.353978	−	0.613107i	−0.0145730	−	0.0252412i
$591$	−0.598854	+	1.03724i	−0.0246335	+	0.0426666i
$592$	3.18965	−	5.52464i	0.131094	−	0.227061i
$593$	−4.52179	−	7.83196i	−0.185687	−	0.321620i	0.758120	−	0.652115i	$-0.226118\pi$
$593$	−4.52179	−	7.83196i	−0.185687	−	0.321620i	−0.943808	+	0.330494i	$0.892785\pi$
$594$	0.434507			0.0178280
$595$	2.43714	−	2.87647i	0.0999128	−	0.117924i
$596$	−14.7548			−0.604382
$597$	−2.55540	−	4.42608i	−0.104585	−	0.181147i
$598$	3.14819	−	5.45283i	0.128739	−	0.222983i
$599$	15.0419	−	26.0534i	0.614597	−	1.06451i	−0.375858	−	0.926677i	$-0.622652\pi$
$599$	15.0419	−	26.0534i	0.614597	−	1.06451i	0.990455	−	0.137836i	$-0.0440147\pi$
$600$	−0.483412	−	0.837295i	−0.0197352	−	0.0341824i
$601$	−25.0873			−1.02333			−0.511665	−	0.859185i	$-0.670971\pi$
$601$	−25.0873			−1.02333			−0.511665	+	0.859185i	$0.670971\pi$
$602$	17.0584	+	3.09189i	0.695248	+	0.126016i
$603$	−37.7375			−1.53679
$604$	10.6213	+	18.3966i	0.432174	+	0.748548i
$605$	−1.67770	+	2.90586i	−0.0682081	+	0.118140i
$606$	−1.31630	+	2.27990i	−0.0534711	+	0.0926147i
$607$	−19.0622	−	33.0168i	−0.773713	−	1.34011i	−0.935515	−	0.353287i	$-0.885064\pi$
$607$	−19.0622	−	33.0168i	−0.773713	−	1.34011i	0.161802	−	0.986823i	$-0.448269\pi$
$608$	−0.352932			−0.0143133
$609$	0.306656	+	0.855211i	0.0124263	+	0.0346549i
$610$	−2.09662			−0.0848897
$611$	−36.9431	−	63.9873i	−1.49456	−	2.58865i
$612$	6.83048	−	11.8307i	0.276106	−	0.478229i
$613$	15.8375	−	27.4314i	0.639670	−	1.10794i	−0.345835	−	0.938296i	$-0.612404\pi$
$613$	15.8375	−	27.4314i	0.639670	−	1.10794i	0.985505	−	0.169646i	$-0.0542625\pi$
$614$	0.679683	+	1.17725i	0.0274298	+	0.0475097i
$615$	−0.115816			−0.00467015
$616$	−0.330206	−	0.920887i	−0.0133044	−	0.0371036i
$617$	−39.9083			−1.60665			−0.803324	−	0.595543i	$-0.796937\pi$
$617$	−39.9083			−1.60665			−0.803324	+	0.595543i	$0.796937\pi$
$618$	0.0866085	+	0.150010i	0.00348390	+	0.00603430i
$619$	5.69093	−	9.85698i	0.228738	−	0.396185i	−0.728696	−	0.684837i	$-0.759873\pi$
$619$	5.69093	−	9.85698i	0.228738	−	0.396185i	0.957434	+	0.288651i	$0.0932068\pi$
$620$	0.453239	−	0.785032i	0.0182025	−	0.0315276i
$621$	0.587549	+	1.01766i	0.0235775	+	0.0408375i
$622$	14.7634			0.591960
$623$	30.2562	+	5.48403i	1.21219	+	0.219713i
$624$	−1.24118			−0.0496871
$625$	−11.7890	−	20.4192i	−0.471561	−	0.816767i
$626$	11.6470	−	20.1732i	0.465508	−	0.806284i
$627$	−0.0128626	+	0.0222787i	−0.000513682	+	0.000889724i
$628$	6.82206	+	11.8162i	0.272230	+	0.471516i
$629$	−29.4303			−1.17346
$630$	−1.56429	+	1.84628i	−0.0623228	+	0.0735574i
$631$	28.3119			1.12708			0.563539	−	0.826089i	$-0.309439\pi$
$631$	28.3119			1.12708			0.563539	+	0.826089i	$0.309439\pi$
$632$	−0.333075	−	0.576902i	−0.0132490	−	0.0229479i
$633$	−1.47219	+	2.54991i	−0.0585144	+	0.101350i
$634$	−9.66087	+	16.7331i	−0.383682	+	0.664557i
$635$	2.47433	+	4.28566i	0.0981907	+	0.170071i
$636$	−1.16395			−0.0461537
$637$	−7.23875	−	43.4762i	−0.286810	−	1.72259i
$638$	0.644121			0.0255010
$639$	0.728615	+	1.26200i	0.0288236	+	0.0499239i
$640$	0.154437	−	0.267494i	0.00610468	−	0.0105736i
$641$	1.16446	−	2.01691i	0.0459935	−	0.0796632i	−0.842112	−	0.539302i	$-0.818688\pi$
$641$	1.16446	−	2.01691i	0.0459935	−	0.0796632i	0.888106	+	0.459639i	$0.152021\pi$
$642$	1.40956	+	2.44143i	0.0556310	+	0.0963556i
$643$	−5.03301			−0.198482			−0.0992412	−	0.995063i	$-0.531642\pi$
$643$	−5.03301			−0.198482			−0.0992412	+	0.995063i	$0.531642\pi$
$644$	1.71031	−	2.01862i	0.0673957	−	0.0795448i
$645$	0.398966			0.0157093
$646$	0.814110	+	1.41008i	0.0320307	+	0.0554788i
$647$	17.9635	−	31.1137i	0.706218	−	1.22321i	−0.260032	−	0.965600i	$-0.583733\pi$
$647$	17.9635	−	31.1137i	0.706218	−	1.22321i	0.966250	−	0.257605i	$-0.0829335\pi$
$648$	−4.32589	+	7.49266i	−0.169937	+	0.294340i
$649$	0.423756	+	0.733967i	0.0166339	+	0.0288107i
$650$	−30.8812			−1.21126
$651$	−1.50608	−	0.272982i	−0.0590280	−	0.0106990i
$652$	−19.1347			−0.749372
$653$	11.9554	+	20.7073i	0.467849	+	0.810338i	0.999325	−	0.0367350i	$-0.0116957\pi$
$653$	11.9554	+	20.7073i	0.467849	+	0.810338i	−0.531476	+	0.847073i	$0.678362\pi$
$654$	−1.49035	+	2.58137i	−0.0582775	+	0.100940i
$655$	2.82897	−	4.89993i	0.110537	−	0.191456i
$656$	0.951067	+	1.64730i	0.0371329	+	0.0643161i
$657$	−17.7654			−0.693095
$658$	−10.4793	−	29.2251i	−0.408527	−	1.13931i
$659$	25.6645			0.999749			0.499874	−	0.866098i	$-0.333380\pi$
$659$	25.6645			0.999749			0.499874	+	0.866098i	$0.333380\pi$
$660$	−0.0112569	−	0.0194976i	−0.000438175	−	0.000758942i
$661$	−0.221521	+	0.383685i	−0.00861616	+	0.0149236i	−0.870301	−	0.492520i	$-0.836076\pi$
$661$	−0.221521	+	0.383685i	−0.00861616	+	0.0149236i	0.861685	+	0.507443i	$0.169409\pi$
$662$	2.00407	−	3.47116i	0.0778905	−	0.134910i
$663$	2.86304	+	4.95894i	0.111191	+	0.192589i
$664$	−6.44785			−0.250225
$665$	−0.0973500	−	0.271492i	−0.00377507	−	0.0105280i
$666$	18.8900			0.731973
$667$	0.870993	+	1.50860i	0.0337250	+	0.0584134i
$668$	−2.65661	+	4.60138i	−0.102787	+	0.178033i
$669$	−0.528700	+	0.915736i	−0.0204407	+	0.0354044i
$670$	1.96819	+	3.40900i	0.0760377	+	0.131701i
$671$	2.50992			0.0968943
$672$	−0.513186	−	0.0930165i	−0.0197966	−	0.00358819i
$673$	27.3836			1.05556			0.527781	−	0.849381i	$-0.323024\pi$
$673$	27.3836			1.05556			0.527781	+	0.849381i	$0.323024\pi$
$674$	9.36209	+	16.2156i	0.360614	+	0.624602i
$675$	2.88169	−	4.99123i	0.110916	−	0.192113i
$676$	−13.3222	+	23.0748i	−0.512394	+	0.887493i
$677$	−19.3292	−	33.4792i	−0.742882	−	1.28671i	−0.951178	−	0.308644i	$-0.900125\pi$
$677$	−19.3292	−	33.4792i	−0.742882	−	1.28671i	0.208296	−	0.978066i	$-0.433208\pi$
$678$	−1.49239			−0.0573150
$679$	−8.49253	+	10.0234i	−0.325913	+	0.384664i
$680$	−1.42497			−0.0546450
$681$	2.77739	+	4.81058i	0.106430	+	0.184342i
$682$	−0.542584	+	0.939783i	−0.0207766	+	0.0359861i
$683$	−19.0423	+	32.9822i	−0.728633	+	1.26203i	0.228828	+	0.973467i	$0.426511\pi$
$683$	−19.0423	+	32.9822i	−0.728633	+	1.26203i	−0.957461	+	0.288562i	$0.906823\pi$
$684$	−0.522541	−	0.905068i	−0.0199799	−	0.0346061i
$685$	2.85203			0.108971
$686$	0.265219	−	18.5184i	0.0101261	−	0.707034i
$687$	−3.12194			−0.119110
$688$	−3.27626	−	5.67465i	−0.124906	−	0.216344i
$689$	−18.5888	+	32.1968i	−0.708177	+	1.22660i
$690$	0.0304437	−	0.0527300i	0.00115897	−	0.00200740i
$691$	10.0832	+	17.4646i	0.383582	+	0.664384i	0.991571	−	0.129562i	$-0.0413570\pi$
$691$	10.0832	+	17.4646i	0.383582	+	0.664384i	−0.607989	+	0.793945i	$0.708024\pi$
$692$	−5.22538			−0.198639
$693$	1.87265	−	2.21023i	0.0711362	−	0.0839596i
$694$	5.24938			0.199264
$695$	−2.67084	−	4.62604i	−0.101311	−	0.175476i
$696$	0.171696	−	0.297386i	0.00650811	−	0.0112724i
$697$	4.38766	−	7.59965i	0.166195	−	0.287857i
$698$	14.6895	+	25.4429i	0.556004	+	0.963027i
$699$	−5.01057			−0.189517
$700$	−12.7683	−	2.31430i	−0.482596	−	0.0874722i
$701$	−21.0182			−0.793847			−0.396924	−	0.917852i	$-0.629922\pi$
$701$	−21.0182			−0.793847			−0.396924	+	0.917852i	$0.629922\pi$
$702$	−3.69944	−	6.40761i	−0.139626	−	0.241840i
$703$	−1.12573	+	1.94982i	−0.0424577	+	0.0735390i
$704$	−0.184881	+	0.320224i	−0.00696797	+	0.0120689i
$705$	−0.357247	−	0.618771i	−0.0134547	−	0.0233043i
$706$	3.77629			0.142123
$707$	11.9262	+	33.2602i	0.448532	+	1.25088i
$708$	0.451822			0.0169805
$709$	−4.15409	−	7.19509i	−0.156010	−	0.270217i	0.777416	−	0.628986i	$-0.216530\pi$
$709$	−4.15409	−	7.19509i	−0.156010	−	0.270217i	−0.933426	+	0.358769i	$0.883197\pi$
$710$	0.0760015	−	0.131638i	0.00285228	−	0.00494030i
$711$	0.986281	−	1.70829i	0.0369884	−	0.0640659i
$712$	−5.81105	−	10.0650i	−0.217778	−	0.377203i
$713$	−2.93477			−0.109908
$714$	0.812135	+	2.26491i	0.0303934	+	0.0847620i
$715$	−0.719112			−0.0268933
$716$	5.20161	+	9.00945i	0.194393	+	0.336699i
$717$	0.847063	−	1.46716i	0.0316342	−	0.0547920i
$718$	9.28414	−	16.0806i	0.346481	−	0.600123i
$719$	−16.2182	−	28.0908i	−0.604838	−	1.04761i	−0.992077	−	0.125631i	$-0.959904\pi$
$719$	−16.2182	−	28.0908i	−0.604838	−	1.04761i	0.387239	−	0.921980i	$-0.373429\pi$
$720$	0.914622			0.0340860
$721$	2.28758	+	0.414631i	0.0851938	+	0.0154417i
$722$	−18.8754			−0.702471
$723$	0.925394	+	1.60283i	0.0344158	+	0.0596099i
$724$	−3.69973	+	6.40811i	−0.137499	+	0.238156i
$725$	4.27187	−	7.39910i	0.158653	−	0.274796i
$726$	−1.07072	−	1.85454i	−0.0397381	−	0.0688284i
$727$	−17.1339			−0.635460			−0.317730	−	0.948181i	$-0.602921\pi$
$727$	−17.1339			−0.635460			−0.317730	+	0.948181i	$0.602921\pi$
$728$	−10.7688	+	12.7100i	−0.399118	+	0.471065i
$729$	−24.9242			−0.923119
$730$	0.926550	+	1.60483i	0.0342932	+	0.0593975i
$731$	−15.1147	+	26.1795i	−0.559038	+	0.968283i
$732$	0.669039	−	1.15881i	0.0247284	−	0.0428308i
$733$	3.43584	+	5.95105i	0.126906	+	0.219807i	0.922476	−	0.386054i	$-0.126162\pi$
$733$	3.43584	+	5.95105i	0.126906	+	0.219807i	−0.795571	+	0.605861i	$0.792829\pi$
$734$	15.3228			0.565573
$735$	−0.0700002	−	0.420424i	−0.00258200	−	0.0155076i
$736$	−1.00000			−0.0368605
$737$	−2.35617	−	4.08101i	−0.0867906	−	0.150326i
$738$	−2.81624	+	4.87788i	−0.103667	+	0.179557i
$739$	5.63174	−	9.75446i	0.207167	−	0.358823i	−0.743654	−	0.668565i	$-0.766909\pi$
$739$	5.63174	−	9.75446i	0.207167	−	0.358823i	0.950821	+	0.309741i	$0.100242\pi$
$740$	−0.985203	−	1.70642i	−0.0362168	−	0.0627293i
$741$	0.438054			0.0160923
$742$	−10.0987	+	11.9191i	−0.370735	+	0.437566i
$743$	−23.7565			−0.871540			−0.435770	−	0.900058i	$-0.643524\pi$
$743$	−23.7565			−0.871540			−0.435770	+	0.900058i	$0.643524\pi$
$744$	0.289260	+	0.501013i	0.0106048	+	0.0183680i
$745$	−2.27870	+	3.94683i	−0.0834851	+	0.144601i
$746$	−2.03891	+	3.53149i	−0.0746497	+	0.129297i
$747$	−9.54650	−	16.5350i	−0.349288	−	0.604985i
$748$	1.70586			0.0623726
$749$	37.2305	+	6.74815i	1.36037	+	0.246572i
$750$	−0.603065			−0.0220208
$751$	16.9977	+	29.4409i	0.620256	+	1.07431i	0.989438	+	0.144957i	$0.0463045\pi$
$751$	16.9977	+	29.4409i	0.620256	+	1.07431i	−0.369182	+	0.929357i	$0.620362\pi$
$752$	−5.86735	+	10.1625i	−0.213960	+	0.370590i
$753$	−0.309255	+	0.535646i	−0.0112699	+	0.0195200i
$754$	−5.48411	−	9.49876i	−0.199720	−	0.345924i
$755$	6.56130			0.238790
$756$	−1.04939	−	2.92656i	−0.0381659	−	0.106438i
$757$	−40.7166			−1.47987			−0.739935	−	0.672679i	$-0.765144\pi$
$757$	−40.7166			−1.47987			−0.739935	+	0.672679i	$0.765144\pi$
$758$	−13.7196	−	23.7631i	−0.498319	−	0.863113i
$759$	−0.0364449	+	0.0631245i	−0.00132287	+	0.00229127i
$760$	−0.0545060	+	0.0944071i	−0.00197714	+	0.00342450i
$761$	−19.0121	−	32.9300i	−0.689189	−	1.19371i	−0.972101	−	0.234565i	$-0.924634\pi$
$761$	−19.0121	−	32.9300i	−0.689189	−	1.19371i	0.282911	−	0.959146i	$-0.408700\pi$
$762$	−3.15827			−0.114412
$763$	13.5032	+	37.6581i	0.488849	+	1.36332i
$764$	−3.99951			−0.144697
$765$	−2.10976	−	3.65422i	−0.0762786	−	0.132118i
$766$	0.302361	−	0.523705i	0.0109248	−	0.0189222i
$767$	7.21580	−	12.4981i	0.260547	−	0.451281i
$768$	0.0985631	+	0.170716i	0.00355659	+	0.00616020i
$769$	−18.1567			−0.654746			−0.327373	−	0.944895i	$-0.606163\pi$
$769$	−18.1567			−0.654746			−0.327373	+	0.944895i	$0.606163\pi$
$770$	−0.297328	−	0.0538916i	−0.0107149	−	0.00194212i
$771$	5.31900			0.191559
$772$	−0.226630	−	0.392534i	−0.00815658	−	0.0141276i
$773$	−12.8258	+	22.2150i	−0.461313	+	0.799018i	−0.999027	−	0.0441098i	$-0.985955\pi$
$773$	−12.8258	+	22.2150i	−0.461313	+	0.799018i	0.537714	+	0.843128i	$0.319288\pi$
$774$	9.70147	−	16.8034i	0.348712	−	0.603987i
$775$	7.19693	+	12.4655i	0.258521	+	0.447772i
$776$	4.96548			0.178250
$777$	−2.15077	+	2.53847i	−0.0771583	+	0.0910673i
$778$	−8.10124			−0.290443
$779$	−0.335662	−	0.581384i	−0.0120263	−	0.0208302i
$780$	−0.191685	+	0.332009i	−0.00686343	+	0.0118878i
$781$	−0.0909833	+	0.157588i	−0.00325564	+	0.00563893i
$782$	2.30670	+	3.99533i	0.0824876	+	0.142873i
$783$	2.04700			0.0731540
$784$	−5.40502	+	4.44811i	−0.193037	+	0.158861i
$785$	4.21433			0.150416
$786$	1.80547	+	3.12717i	0.0643991	+	0.111542i
$787$	−13.5264	+	23.4284i	−0.482165	+	0.835134i	−0.999790	−	0.0204733i	$-0.993483\pi$
$787$	−13.5264	+	23.4284i	−0.482165	+	0.835134i	0.517626	+	0.855607i	$0.326816\pi$
$788$	3.03792	−	5.26183i	0.108221	−	0.187445i
$789$	−1.05780	−	1.83217i	−0.0376588	−	0.0652269i
$790$	−0.205757			−0.00732050
$791$	−12.9483	+	15.2825i	−0.460390	+	0.543382i
$792$	−1.09492			−0.0389062
$793$	−21.3697	−	37.0134i	−0.758860	−	1.31438i
$794$	6.42365	−	11.1261i	0.227967	−	0.394850i
$795$	−0.179758	+	0.311349i	−0.00637535	+	0.0110424i
$796$	12.9633	+	22.4530i	0.459470	+	0.795826i
$797$	28.6420			1.01455			0.507276	−	0.861783i	$-0.330652\pi$
$797$	28.6420			1.01455			0.507276	+	0.861783i	$0.330652\pi$
$798$	0.181120	+	0.0328285i	0.00641157	+	0.00116212i
$799$	54.1369			1.91523
$800$	2.45230	+	4.24750i	0.0867018	+	0.150172i
$801$	17.2073	−	29.8040i	0.607991	−	1.05307i
$802$	−4.03550	+	6.98970i	−0.142499	+	0.246815i
$803$	−1.10920	−	1.92119i	−0.0391427	−	0.0677972i
$804$	−2.51222			−0.0885993
$805$	−0.275832	−	0.769248i	−0.00972180	−	0.0271124i
$806$	18.4784			0.650876
$807$	−1.56480	−	2.71032i	−0.0550836	−	0.0954076i
$808$	6.67745	−	11.5657i	0.234912	−	0.406880i
$809$	−21.0580	+	36.4736i	−0.740360	+	1.28234i	0.211971	+	0.977276i	$0.432012\pi$
$809$	−21.0580	+	36.4736i	−0.740360	+	1.28234i	−0.952331	+	0.305066i	$0.901322\pi$
$810$	1.33616	+	2.31430i	0.0469478	+	0.0813161i
$811$	3.28555			0.115371			0.0576856	−	0.998335i	$-0.481628\pi$
$811$	3.28555			0.115371			0.0576856	+	0.998335i	$0.481628\pi$
$812$	−1.55563	−	4.33839i	−0.0545920	−	0.152248i
$813$	−2.83476			−0.0994194
$814$	1.17941	+	2.04280i	0.0413384	+	0.0716002i
$815$	−2.95511	+	5.11841i	−0.103513	+	0.179290i
$816$	0.454712	−	0.787584i	0.0159181	−	0.0275710i
$817$	1.15630	+	2.00277i	0.0404537	+	0.0700679i
$818$	−17.3417			−0.606340
$819$	−48.5378	−	8.79764i	−1.69605	−	0.307414i
$820$	0.587522			0.0205171
$821$	−16.4529	−	28.4973i	−0.574211	−	0.994562i	−0.996127	−	0.0879271i	$-0.971976\pi$
$821$	−16.4529	−	28.4973i	−0.574211	−	0.994562i	0.421916	−	0.906635i	$-0.361358\pi$
$822$	−0.910095	+	1.57633i	−0.0317432	+	0.0549808i
$823$	20.6346	−	35.7402i	0.719278	−	1.24583i	−0.242008	−	0.970274i	$-0.577806\pi$
$823$	20.6346	−	35.7402i	0.719278	−	1.24583i	0.961286	−	0.275552i	$-0.0888605\pi$
$824$	−0.439355	−	0.760986i	−0.0153057	−	0.0265102i
$825$	0.357495			0.0124464
$826$	3.92011	−	4.62677i	0.136398	−	0.160986i
$827$	8.07826			0.280909			0.140454	−	0.990087i	$-0.455144\pi$
$827$	8.07826			0.280909			0.140454	+	0.990087i	$0.455144\pi$
$828$	−1.48057	−	2.56442i	−0.0514534	−	0.0891199i
$829$	−8.07798	+	13.9915i	−0.280560	+	0.485944i	−0.971523	−	0.236946i	$-0.923853\pi$
$829$	−8.07798	+	13.9915i	−0.280560	+	0.485944i	0.690963	+	0.722890i	$0.257187\pi$
$830$	−0.995790	+	1.72476i	−0.0345644	+	0.0598672i
$831$	1.14688	+	1.98645i	0.0397848	+	0.0689092i
$832$	6.29639			0.218288
$833$	30.2395	+	11.3344i	1.04774	+	0.392712i
$834$	3.40911			0.118048
$835$	0.820560	+	1.42125i	0.0283966	+	0.0491844i
$836$	0.0652505	−	0.113017i	0.00225674	−	0.00390878i
$837$	−1.72432	+	2.98661i	−0.0596012	+	0.103232i
$838$	−7.88131	−	13.6508i	−0.272255	−	0.471560i
$839$	28.5777			0.986613			0.493306	−	0.869856i	$-0.335788\pi$
$839$	28.5777			0.986613			0.493306	+	0.869856i	$0.335788\pi$
$840$	−0.104136	+	0.122909i	−0.00359305	+	0.00424075i
$841$	−25.9655			−0.895362
$842$	8.24488	+	14.2805i	0.284137	+	0.492140i
$843$	−2.48440	+	4.30311i	−0.0855673	+	0.148207i
$844$	7.46827	−	12.9354i	0.257068	−	0.445256i
$845$	4.11491	+	7.12723i	0.141557	+	0.245184i
$846$	−34.7481			−1.19466
$847$	−28.2807	−	5.12597i	−0.971737	−	0.176131i
$848$	5.90460			0.202765
$849$	−0.352477	−	0.610508i	−0.0120970	−	0.0209526i
$850$	11.3135	−	19.5955i	0.388048	−	0.672119i
$851$	−3.18965	+	5.52464i	−0.109340	+	0.189382i
$852$	0.0485047	+	0.0840126i	0.00166174	+	0.00287822i
$853$	−11.7746			−0.403154			−0.201577	−	0.979473i	$-0.564607\pi$
$853$	−11.7746			−0.403154			−0.201577	+	0.979473i	$0.564607\pi$
$854$	−6.06176	−	16.9052i	−0.207429	−	0.578485i
$855$	−0.322800			−0.0110395
$856$	−7.15055	−	12.3851i	−0.244401	−	0.423315i
$857$	16.4006	−	28.4066i	0.560232	−	0.970351i	−0.437243	−	0.899343i	$-0.644045\pi$
$857$	16.4006	−	28.4066i	0.560232	−	0.970351i	0.997476	−	0.0710077i	$-0.0226215\pi$
$858$	0.229471	−	0.397456i	0.00783403	−	0.0135689i
$859$	12.3157	+	21.3315i	0.420207	+	0.727820i	0.995959	−	0.0898038i	$-0.0286240\pi$
$859$	12.3157	+	21.3315i	0.420207	+	0.727820i	−0.575752	+	0.817624i	$0.695291\pi$
$860$	−2.02391			−0.0690147
$861$	−0.334848	−	0.933834i	−0.0114116	−	0.0318250i
$862$	10.9457			0.372812
$863$	−15.2591	−	26.4296i	−0.519426	−	0.899673i	−0.999745	−	0.0225789i	$-0.992812\pi$
$863$	−15.2591	−	26.4296i	−0.519426	−	0.899673i	0.480319	−	0.877094i	$-0.340521\pi$
$864$	−0.587549	+	1.01766i	−0.0199888	+	0.0346216i
$865$	−0.806994	+	1.39775i	−0.0274386	+	0.0475251i
$866$	14.0350	+	24.3093i	0.476928	+	0.826063i
$867$	−0.844396			−0.0286772
$868$	7.64019	+	1.38481i	0.259325	+	0.0470035i
$869$	0.246317			0.00835573
$870$	−0.0530325	−	0.0918550i	−0.00179797	−	0.00311417i
$871$	−40.1213	+	69.4922i	−1.35946	+	2.35465i
$872$	7.56040	−	13.0950i	0.256028	−	0.443453i
$873$	7.35175	+	12.7336i	0.248819	+	0.430967i
$874$	0.352932			0.0119381
$875$	−5.23233	+	6.17553i	−0.176885	+	0.208771i
$876$	−1.18266			−0.0399585
$877$	20.9763	+	36.3320i	0.708319	+	1.22684i	0.965480	+	0.260476i	$0.0838795\pi$
$877$	20.9763	+	36.3320i	0.708319	+	1.22684i	−0.257161	+	0.966368i	$0.582787\pi$
$878$	4.54122	−	7.86562i	0.153259	−	0.265452i
$879$	−0.397449	+	0.688401i	−0.0134056	+	0.0232192i
$880$	0.0571052	+	0.0989090i	0.00192501	+	0.00333422i
$881$	38.4289			1.29470			0.647352	−	0.762192i	$-0.275877\pi$
$881$	38.4289			1.29470			0.647352	+	0.762192i	$0.275877\pi$
$882$	−19.4094	−	7.27503i	−0.653547	−	0.244963i
$883$	44.5679			1.49983			0.749914	−	0.661536i	$-0.230095\pi$
$883$	44.5679			1.49983			0.749914	+	0.661536i	$0.230095\pi$
$884$	−14.5239	−	25.1561i	−0.488492	−	0.846092i
$885$	0.0697783	−	0.120860i	0.00234557	−	0.00406265i
$886$	15.3899	−	26.6560i	0.517032	−	0.895526i
$887$	4.21548	+	7.30142i	0.141542	+	0.245158i	0.928077	−	0.372387i	$-0.121461\pi$
$887$	4.21548	+	7.30142i	0.141542	+	0.245158i	−0.786536	+	0.617545i	$0.788127\pi$
$888$	1.25753			0.0421999
$889$	−27.4018	+	32.3414i	−0.919028	+	1.08470i
$890$	−3.58977			−0.120329
$891$	−1.59955	−	2.77050i	−0.0535870	−	0.0928154i
$892$	2.68204	−	4.64543i	0.0898013	−	0.155540i
$893$	2.07078	−	3.58669i	0.0692959	−	0.120024i
$894$	−1.45428	−	2.51889i	−0.0486385	−	0.0842444i
$895$	3.21329			0.107408
$896$	2.60333	+	0.471863i	0.0869713	+	0.0157638i
$897$	1.24118			0.0414419
$898$	15.4507	+	26.7615i	0.515598	+	0.893042i
$899$	−2.55616	+	4.42741i	−0.0852529	+	0.147662i
$900$	−7.26160	+	12.5775i	−0.242053	+	0.419249i
$901$	−13.6202	−	23.5908i	−0.453753	−	0.785923i
$902$	−0.703338			−0.0234186
$903$	1.15349	+	3.21689i	0.0383858	+	0.107052i
$904$	7.57075			0.251799
$905$	1.14275	+	1.97931i	0.0379864	+	0.0657943i
$906$	−2.09374	+	3.62646i	−0.0695597	+	0.120481i
$907$	5.55314	−	9.61832i	0.184389	−	0.319371i	−0.758982	−	0.651112i	$-0.774303\pi$
$907$	5.55314	−	9.61832i	0.184389	−	0.319371i	0.943370	+	0.331741i	$0.107636\pi$
$908$	−14.0894	−	24.4035i	−0.467573	−	0.809860i
$909$	39.5458			1.31165
$910$	1.73675	+	4.84348i	0.0575726	+	0.160560i
$911$	18.4884			0.612548			0.306274	−	0.951943i	$-0.400918\pi$
$911$	18.4884			0.612548			0.306274	+	0.951943i	$0.400918\pi$
$912$	−0.0347861	−	0.0602513i	−0.00115188	−	0.00199512i
$913$	1.19209	−	2.06475i	0.0394523	−	0.0683334i
$914$	−20.3512	+	35.2492i	−0.673157	+	1.16594i
$915$	−0.206649	−	0.357927i	−0.00683162	−	0.0118327i
$916$	15.8373			0.523278
$917$	47.6877	+	8.64355i	1.57479	+	0.285435i
$918$	5.42120			0.178926
$919$	−2.91435	−	5.04781i	−0.0961356	−	0.166512i	0.813946	−	0.580940i	$-0.197315\pi$
$919$	−2.91435	−	5.04781i	−0.0961356	−	0.166512i	−0.910082	+	0.414428i	$0.863982\pi$
$920$	−0.154437	+	0.267494i	−0.00509165	+	0.00881900i
$921$	−0.133983	+	0.232066i	−0.00441490	+	0.00764683i
$922$	−11.0396	−	19.1212i	−0.363570	−	0.629722i
$923$	3.09857			0.101991
$924$	0.124664	−	0.147137i	0.00410116	−	0.00484045i
$925$	31.2879			1.02874
$926$	−8.18359	−	14.1744i	−0.268930	−	0.465800i
$927$	1.30099	−	2.25339i	0.0427302	−	0.0740109i
$928$	−0.870993	+	1.50860i	−0.0285918	+	0.0495224i
$929$	12.6140	+	21.8481i	0.413852	+	0.716813i	0.995307	−	0.0967658i	$-0.0308498\pi$
$929$	12.6140	+	21.8481i	0.413852	+	0.716813i	−0.581455	+	0.813578i	$0.697516\pi$
$930$	0.178690			0.00585949
$931$	1.90761	−	1.56988i	0.0625193	−	0.0514508i
$932$	25.4180			0.832596
$933$	1.45513	+	2.52036i	0.0476388	+	0.0825129i
$934$	15.0234	−	26.0213i	0.491581	−	0.851444i
$935$	0.263449	−	0.456308i	0.00861572	−	0.0149229i
$936$	9.32225	+	16.1466i	0.304707	+	0.527768i
$937$	31.9205			1.04280			0.521399	−	0.853313i	$-0.325410\pi$
$937$	31.9205			1.04280			0.521399	+	0.853313i	$0.325410\pi$
$938$	−21.7966	+	25.7258i	−0.711685	+	0.839977i
$939$	4.59186			0.149850
$940$	1.81228	+	3.13896i	0.0591100	+	0.102381i
$941$	−26.0129	+	45.0557i	−0.847998	+	1.46878i	0.0349945	+	0.999388i	$0.488859\pi$
$941$	−26.0129	+	45.0557i	−0.847998	+	1.46878i	−0.882992	+	0.469388i	$0.844475\pi$
$942$	−1.34481	+	2.32927i	−0.0438162	+	0.0758919i
$943$	−0.951067	−	1.64730i	−0.0309710	−	0.0536434i
$944$	−2.29204			−0.0745997
$945$	−0.944901	−	0.171266i	−0.0307376	−	0.00557130i
$946$	2.42288			0.0787745
$947$	12.2772	+	21.2647i	0.398955	+	0.691011i	0.993597	−	0.112980i	$-0.0360396\pi$
$947$	12.2772	+	21.2647i	0.398955	+	0.691011i	−0.594642	+	0.803990i	$0.702706\pi$
$948$	0.0656578	−	0.113723i	0.00213247	−	0.00369354i
$949$	−18.8876	+	32.7143i	−0.613119	+	1.06195i
$950$	−0.865495	−	1.49908i	−0.0280804	−	0.0486366i
$951$	−3.80882			−0.123510
$952$	−4.11987	−	11.4896i	−0.133526	−	0.372381i
$953$	37.5355			1.21589			0.607947	−	0.793977i	$-0.291993\pi$
$953$	37.5355			1.21589			0.607947	+	0.793977i	$0.291993\pi$
$954$	8.74217	+	15.1419i	0.283038	+	0.490237i
$955$	−0.617675	+	1.06984i	−0.0199875	+	0.0346194i
$956$	−4.29706	+	7.44272i	−0.138977	+	0.240715i
$957$	0.0634866	+	0.109962i	0.00205223	+	0.00355457i
$958$	−8.09218			−0.261447
$959$	8.24582	+	22.9962i	0.266272	+	0.742585i
$960$	0.0608874			0.00196513
$961$	11.1936	+	19.3878i	0.361083	+	0.625413i
$962$	20.0833	−	34.7853i	0.647511	−	1.12152i
$963$	21.1738	−	36.6741i	0.682316	−	1.18181i
$964$	−4.69442	−	8.13098i	−0.151197	−	0.261881i
$965$	−0.140000			−0.00450677
$966$	0.513186	+	0.0930165i	0.0165115	+	0.00299276i
$967$	−25.6889			−0.826100			−0.413050	−	0.910708i	$-0.635537\pi$
$967$	−25.6889			−0.826100			−0.413050	+	0.910708i	$0.635537\pi$
$968$	5.43164	+	9.40787i	0.174579	+	0.302380i
$969$	−0.160482	+	0.277964i	−0.00515544	+	0.00892948i
$970$	0.766857	−	1.32823i	0.0246223	−	0.0426471i
$971$	−26.4915	−	45.8847i	−0.850154	−	1.47251i	−0.881069	−	0.472987i	$-0.843176\pi$
$971$	−26.4915	−	45.8847i	−0.850154	−	1.47251i	0.0309157	−	0.999522i	$-0.490158\pi$
$972$	−5.23079			−0.167778
$973$	29.5782	−	34.9101i	0.948233	−	1.11917i
$974$	6.59563			0.211337
$975$	−3.04375	−	5.27193i	−0.0974781	−	0.168837i
$976$	−3.39396	+	5.87851i	−0.108638	+	0.188167i
$977$	25.6548	−	44.4355i	0.820771	−	1.42162i	−0.0843381	−	0.996437i	$-0.526878\pi$
$977$	25.6548	−	44.4355i	0.820771	−	1.42162i	0.905109	−	0.425180i	$-0.139789\pi$
$978$	−1.88598	−	3.26660i	−0.0603068	−	0.104454i
$979$	4.29741			0.137346
$980$	0.355103	+	2.13276i	0.0113434	+	0.0681287i
$981$	44.7748			1.42955
$982$	6.35199	+	11.0020i	0.202700	+	0.351087i
$983$	−0.842694	+	1.45959i	−0.0268778	+	0.0465536i	−0.879151	−	0.476543i	$-0.841890\pi$
$983$	−0.842694	+	1.45959i	−0.0268778	+	0.0465536i	0.852274	+	0.523096i	$0.175223\pi$
$984$	−0.187480	+	0.324726i	−0.00597666	+	0.0103519i
$985$	−0.938337	−	1.62525i	−0.0298979	−	0.0517847i
$986$	8.03649			0.255934
$987$	3.95632	−	4.66951i	0.125931	−	0.148632i
$988$	−2.22220			−0.0706975
$989$	3.27626	+	5.67465i	0.104179	+	0.180443i
$990$	−0.169096	+	0.292884i	−0.00537424	+	0.00930845i
$991$	−9.49397	+	16.4440i	−0.301586	+	0.522362i	−0.976495	−	0.215539i	$-0.930849\pi$
$991$	−9.49397	+	16.4440i	−0.301586	+	0.522362i	0.674909	+	0.737901i	$0.264183\pi$
$992$	−1.46739	−	2.54159i	−0.0465895	−	0.0806954i
$993$	0.790111			0.0250734
$994$	1.28115	+	0.232212i	0.0406355	+	0.00736532i
$995$	8.00805			0.253872
$996$	−0.635520	−	1.10075i	−0.0201372	−	0.0348787i
$997$	24.5349	−	42.4957i	0.777029	−	1.34585i	−0.156619	−	0.987659i	$-0.550059\pi$
$997$	24.5349	−	42.4957i	0.777029	−	1.34585i	0.933647	−	0.358194i	$-0.116607\pi$
$998$	3.34489	−	5.79352i	0.105881	−	0.183391i
$999$	3.74815	+	6.49199i	0.118586	+	0.205397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.a.277.3	yes	8
7.2	even	3	inner	322.2.e.a.93.3	✓	8
7.3	odd	6		2254.2.a.x.1.3		4
7.4	even	3		2254.2.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.a.93.3	✓	8	7.2	even	3	inner
322.2.e.a.277.3	yes	8	1.1	even	1	trivial
2254.2.a.x.1.3		4	7.3	odd	6
2254.2.a.z.1.2		4	7.4	even	3

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.0985631 - 0.170716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.154437 + 0.267494i) q^{5} -0.197126 q^{6} +(-1.71031 + 2.01862i) q^{7} +1.00000 q^{8} +(1.48057 + 2.56442i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.0985631 - 0.170716i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.154437 + 0.267494i) q^{5} -0.197126 q^{6} +(-1.71031 + 2.01862i) q^{7} +1.00000 q^{8} +(1.48057 + 2.56442i) q^{9} +(0.154437 - 0.267494i) q^{10} +(-0.184881 + 0.320224i) q^{11} +(0.0985631 + 0.170716i) q^{12} +6.29639 q^{13} +(2.60333 + 0.471863i) q^{14} +0.0608874 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.30670 + 3.99533i) q^{17} +(1.48057 - 2.56442i) q^{18} +(0.176466 + 0.305648i) q^{19} -0.308875 q^{20} +(0.176038 + 0.490940i) q^{21} +0.369762 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.0985631 - 0.170716i) q^{24} +(2.45230 - 4.24750i) q^{25} +(-3.14819 - 5.45283i) q^{26} +1.17510 q^{27} +(-0.893022 - 2.49048i) q^{28} +1.74199 q^{29} +(-0.0304437 - 0.0527300i) q^{30} +(-1.46739 + 2.54159i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0364449 + 0.0631245i) q^{33} +4.61341 q^{34} +(-0.804105 - 0.145747i) q^{35} -2.96114 q^{36} +(3.18965 + 5.52464i) q^{37} +(0.176466 - 0.305648i) q^{38} +(0.620592 - 1.07490i) q^{39} +(0.154437 + 0.267494i) q^{40} -1.90213 q^{41} +(0.337147 - 0.397923i) q^{42} +6.55252 q^{43} +(-0.184881 - 0.320224i) q^{44} +(-0.457311 + 0.792086i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-5.86735 - 10.1625i) q^{47} -0.197126 q^{48} +(-1.14967 - 6.90495i) q^{49} -4.90460 q^{50} +(0.454712 + 0.787584i) q^{51} +(-3.14819 + 5.45283i) q^{52} +(-2.95230 + 5.11353i) q^{53} +(-0.587549 - 1.01766i) q^{54} -0.114210 q^{55} +(-1.71031 + 2.01862i) q^{56} +0.0695722 q^{57} +(-0.870993 - 1.50860i) q^{58} +(1.14602 - 1.98497i) q^{59} +(-0.0304437 + 0.0527300i) q^{60} +(-3.39396 - 5.87851i) q^{61} +2.93477 q^{62} +(-7.70884 - 1.39725i) q^{63} +1.00000 q^{64} +(0.972398 + 1.68424i) q^{65} +(0.0364449 - 0.0631245i) q^{66} +(-6.37212 + 11.0368i) q^{67} +(-2.30670 - 3.99533i) q^{68} +0.197126 q^{69} +(0.275832 + 0.769248i) q^{70} +0.492118 q^{71} +(1.48057 + 2.56442i) q^{72} +(-2.99976 + 5.19573i) q^{73} +(3.18965 - 5.52464i) q^{74} +(-0.483412 - 0.837295i) q^{75} -0.352932 q^{76} +(-0.330206 - 0.920887i) q^{77} -1.24118 q^{78} +(-0.333075 - 0.576902i) q^{79} +(0.154437 - 0.267494i) q^{80} +(-4.32589 + 7.49266i) q^{81} +(0.951067 + 1.64730i) q^{82} -6.44785 q^{83} +(-0.513186 - 0.0930165i) q^{84} -1.42497 q^{85} +(-3.27626 - 5.67465i) q^{86} +(0.171696 - 0.297386i) q^{87} +(-0.184881 + 0.320224i) q^{88} +(-5.81105 - 10.0650i) q^{89} +0.914622 q^{90} +(-10.7688 + 12.7100i) q^{91} -1.00000 q^{92} +(0.289260 + 0.501013i) q^{93} +(-5.86735 + 10.1625i) q^{94} +(-0.0545060 + 0.0944071i) q^{95} +(0.0985631 + 0.170716i) q^{96} +4.96548 q^{97} +(-5.40502 + 4.44811i) q^{98} -1.09492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

Introduction

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