LMFDB - Embedded newform 930.2.s.d.439.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (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:	$7.42608738798$
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			439.1
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.16404 - 0.562979i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.759514 + 0.438506i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.16404 - 0.562979i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.759514 + 0.438506i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.562979 + 2.16404i) q^{10} +(1.33621 + 2.31438i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.519209 + 0.299765i) q^{13} +(0.438506 - 0.759514i) q^{14} +(-1.59262 - 1.56957i) q^{15} +1.00000 q^{16} +(1.86256 + 1.07535i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.673287 - 1.16617i) q^{19} +(2.16404 + 0.562979i) q^{20} +(0.438506 + 0.759514i) q^{21} +(2.31438 - 1.33621i) q^{22} +5.93547i q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.36611 + 2.43661i) q^{25} +(0.299765 + 0.519209i) q^{26} +1.00000i q^{27} +(-0.759514 - 0.438506i) q^{28} -1.51509 q^{29} +(-1.56957 + 1.59262i) q^{30} +(5.42454 + 1.25472i) q^{31} -1.00000i q^{32} +2.67242i q^{33} +(1.07535 - 1.86256i) q^{34} +(-1.39675 - 1.37653i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(9.54061 + 5.50827i) q^{37} +(-1.16617 - 0.673287i) q^{38} -0.599531 q^{39} +(0.562979 - 2.16404i) q^{40} +(-3.64807 - 6.31865i) q^{41} +(0.759514 - 0.438506i) q^{42} +(6.33621 + 3.65821i) q^{43} +(-1.33621 - 2.31438i) q^{44} +(-0.594464 - 2.15560i) q^{45} +5.93547 q^{46} +6.66299i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.11543 - 5.39608i) q^{49} +(2.43661 - 4.36611i) q^{50} +(1.07535 + 1.86256i) q^{51} +(0.519209 - 0.299765i) q^{52} +(-0.455910 + 0.263220i) q^{53} +1.00000 q^{54} +(-1.58866 - 5.76066i) q^{55} +(-0.438506 + 0.759514i) q^{56} +(1.16617 - 0.673287i) q^{57} +1.51509i q^{58} +(3.97137 - 6.87861i) q^{59} +(1.59262 + 1.56957i) q^{60} +2.40535 q^{61} +(1.25472 - 5.42454i) q^{62} +0.877011i q^{63} -1.00000 q^{64} +(1.29235 - 0.356400i) q^{65} +2.67242 q^{66} +(3.85280 - 2.22442i) q^{67} +(-1.86256 - 1.07535i) q^{68} +(-2.96774 + 5.14027i) q^{69} +(-1.37653 + 1.39675i) q^{70} +(7.57102 + 13.1134i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(1.34090 - 0.774167i) q^{73} +(5.50827 - 9.54061i) q^{74} +(2.56286 + 4.29322i) q^{75} +(-0.673287 + 1.16617i) q^{76} +2.34374i q^{77} +0.599531i q^{78} +(-3.08399 + 5.34163i) q^{79} +(-2.16404 - 0.562979i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.31865 + 3.64807i) q^{82} +(-14.7817 + 8.53423i) q^{83} +(-0.438506 - 0.759514i) q^{84} +(-3.42525 - 3.37568i) q^{85} +(3.65821 - 6.33621i) q^{86} +(-1.31211 - 0.757545i) q^{87} +(-2.31438 + 1.33621i) q^{88} -5.54809 q^{89} +(-2.15560 + 0.594464i) q^{90} -0.525795 q^{91} -5.93547i q^{92} +(4.07043 + 3.79889i) q^{93} +6.66299 q^{94} +(-2.11355 + 2.14458i) q^{95} +(0.500000 - 0.866025i) q^{96} -2.08302i q^{97} +(-5.39608 + 3.11543i) q^{98} +(-1.33621 + 2.31438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.00000			−0.500000
$5$	−2.16404	−	0.562979i	−0.967787	−	0.251772i
$5$	−2.16404	−	0.562979i	−0.967787	−	0.251772i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.759514	+	0.438506i	0.287069	+	0.165740i	0.636619	−	0.771178i	$-0.280332\pi$
$7$	0.759514	+	0.438506i	0.287069	+	0.165740i	−0.349550	+	0.936918i	$0.613666\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.562979	+	2.16404i	−0.178030	+	0.684328i
$11$	1.33621	+	2.31438i	0.402882	+	0.697812i	0.994072	−	0.108720i	$-0.0346752\pi$
$11$	1.33621	+	2.31438i	0.402882	+	0.697812i	−0.591190	+	0.806532i	$0.701342\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−0.519209	+	0.299765i	−0.144003	+	0.0831399i	−0.570270	−	0.821457i	$-0.693162\pi$
$13$	−0.519209	+	0.299765i	−0.144003	+	0.0831399i	0.426268	+	0.904597i	$0.359828\pi$
$14$	0.438506	−	0.759514i	0.117196	−	0.202989i
$15$	−1.59262	−	1.56957i	−0.411213	−	0.405262i
$16$	1.00000			0.250000
$17$	1.86256	+	1.07535i	0.451737	+	0.260811i	0.708564	−	0.705647i	$-0.249344\pi$
$17$	1.86256	+	1.07535i	0.451737	+	0.260811i	−0.256826	+	0.966458i	$0.582677\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	0.673287	−	1.16617i	0.154463	−	0.267537i	−0.778401	−	0.627768i	$-0.783969\pi$
$19$	0.673287	−	1.16617i	0.154463	−	0.267537i	0.932863	+	0.360231i	$0.117302\pi$
$20$	2.16404	+	0.562979i	0.483893	+	0.125886i
$21$	0.438506	+	0.759514i	0.0956898	+	0.165740i
$22$	2.31438	−	1.33621i	0.493428	−	0.284881i
$23$			5.93547i			1.23763i	0.785536	+	0.618816i	$0.212387\pi$
$23$			5.93547i			1.23763i	−0.785536	+	0.618816i	$0.787613\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	4.36611	+	2.43661i	0.873222	+	0.487323i
$26$	0.299765	+	0.519209i	0.0587888	+	0.101825i
$27$			1.00000i			0.192450i
$28$	−0.759514	−	0.438506i	−0.143535	−	0.0828698i
$29$	−1.51509			−0.281345			−0.140673	−	0.990056i	$-0.544926\pi$
$29$	−1.51509			−0.281345			−0.140673	+	0.990056i	$0.544926\pi$
$30$	−1.56957	+	1.59262i	−0.286563	+	0.290772i
$31$	5.42454	+	1.25472i	0.974277	+	0.225355i
$31$	5.42454	+	1.25472i	0.974277	+	0.225355i
$32$		−	1.00000i		−	0.176777i
$33$			2.67242i			0.465208i
$34$	1.07535	−	1.86256i	0.184421	−	0.319427i
$35$	−1.39675	−	1.37653i	−0.236093	−	0.232676i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.54061	+	5.50827i	1.56847	+	0.905555i	0.996348	+	0.0853838i	$0.0272116\pi$
$37$	9.54061	+	5.50827i	1.56847	+	0.905555i	0.572119	+	0.820171i	$0.306122\pi$
$38$	−1.16617	−	0.673287i	−0.189177	−	0.109222i
$39$	−0.599531			−0.0960017
$40$	0.562979	−	2.16404i	0.0890148	−	0.342164i
$41$	−3.64807	−	6.31865i	−0.569733	−	0.986807i	−0.996592	−	0.0824886i	$-0.973713\pi$
$41$	−3.64807	−	6.31865i	−0.569733	−	0.986807i	0.426859	−	0.904318i	$-0.359620\pi$
$42$	0.759514	−	0.438506i	0.117196	−	0.0676629i
$43$	6.33621	+	3.65821i	0.966262	+	0.557872i	0.898095	−	0.439802i	$-0.144951\pi$
$43$	6.33621	+	3.65821i	0.966262	+	0.557872i	0.0681676	+	0.997674i	$0.478285\pi$
$44$	−1.33621	−	2.31438i	−0.201441	−	0.348906i
$45$	−0.594464	−	2.15560i	−0.0886175	−	0.321338i
$46$	5.93547			0.875138
$47$			6.66299i			0.971898i	0.873987	+	0.485949i	$0.161526\pi$
$47$			6.66299i			0.971898i	−0.873987	+	0.485949i	$0.838474\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−3.11543	−	5.39608i	−0.445061	−	0.770868i
$50$	2.43661	−	4.36611i	0.344589	−	0.617461i
$51$	1.07535	+	1.86256i	0.150579	+	0.260811i
$52$	0.519209	−	0.299765i	0.0720013	−	0.0415700i
$53$	−0.455910	+	0.263220i	−0.0626241	+	0.0361561i	−0.530985	−	0.847381i	$-0.678178\pi$
$53$	−0.455910	+	0.263220i	−0.0626241	+	0.0361561i	0.468361	+	0.883537i	$0.344845\pi$
$54$	1.00000			0.136083
$55$	−1.58866	−	5.76066i	−0.214214	−	0.776767i
$56$	−0.438506	+	0.759514i	−0.0585978	+	0.101494i
$57$	1.16617	−	0.673287i	0.154463	−	0.0891791i
$58$			1.51509i			0.198941i
$59$	3.97137	−	6.87861i	0.517028	−	0.895519i	−0.482776	−	0.875744i	$-0.660372\pi$
$59$	3.97137	−	6.87861i	0.517028	−	0.895519i	0.999804	−	0.0197754i	$-0.00629513\pi$
$60$	1.59262	+	1.56957i	0.205607	+	0.202631i
$61$	2.40535			0.307974			0.153987	−	0.988073i	$-0.450789\pi$
$61$	2.40535			0.307974			0.153987	+	0.988073i	$0.450789\pi$
$62$	1.25472	−	5.42454i	0.159350	−	0.688918i
$63$			0.877011i			0.110493i
$64$	−1.00000			−0.125000
$65$	1.29235	−	0.356400i	0.160296	−	0.0442059i
$66$	2.67242			0.328952
$67$	3.85280	−	2.22442i	0.470695	−	0.271756i	−0.245836	−	0.969311i	$-0.579062\pi$
$67$	3.85280	−	2.22442i	0.470695	−	0.271756i	0.716530	+	0.697556i	$0.245729\pi$
$68$	−1.86256	−	1.07535i	−0.225869	−	0.130405i
$69$	−2.96774	+	5.14027i	−0.357274	+	0.618816i
$70$	−1.37653	+	1.39675i	−0.164527	+	0.166943i
$71$	7.57102	+	13.1134i	0.898515	+	1.55627i	0.829393	+	0.558665i	$0.188686\pi$
$71$	7.57102	+	13.1134i	0.898515	+	1.55627i	0.0691219	+	0.997608i	$0.477980\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	1.34090	−	0.774167i	0.156940	−	0.0906094i	−0.419473	−	0.907768i	$-0.637785\pi$
$73$	1.34090	−	0.774167i	0.156940	−	0.0906094i	0.576413	+	0.817158i	$0.304452\pi$
$74$	5.50827	−	9.54061i	0.640324	−	1.10907i
$75$	2.56286	+	4.29322i	0.295933	+	0.495739i
$76$	−0.673287	+	1.16617i	−0.0772313	+	0.133769i
$77$			2.34374i			0.267094i
$78$			0.599531i			0.0678835i
$79$	−3.08399	+	5.34163i	−0.346976	+	0.600980i	−0.985711	−	0.168447i	$-0.946125\pi$
$79$	−3.08399	+	5.34163i	−0.346976	+	0.600980i	0.638735	+	0.769427i	$0.279458\pi$
$80$	−2.16404	−	0.562979i	−0.241947	−	0.0629429i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.31865	+	3.64807i	−0.697778	+	0.402862i
$83$	−14.7817	+	8.53423i	−1.62250	+	0.936753i	−0.636257	+	0.771477i	$0.719518\pi$
$83$	−14.7817	+	8.53423i	−1.62250	+	0.936753i	−0.986247	+	0.165276i	$0.947148\pi$
$84$	−0.438506	−	0.759514i	−0.0478449	−	0.0828698i
$85$	−3.42525	−	3.37568i	−0.371521	−	0.366144i
$86$	3.65821	−	6.33621i	0.394475	−	0.683251i
$87$	−1.31211	−	0.757545i	−0.140673	−	0.0812173i
$88$	−2.31438	+	1.33621i	−0.246714	+	0.142440i
$89$	−5.54809			−0.588096			−0.294048	−	0.955791i	$-0.595003\pi$
$89$	−5.54809			−0.588096			−0.294048	+	0.955791i	$0.595003\pi$
$90$	−2.15560	+	0.594464i	−0.227220	+	0.0626621i
$91$	−0.525795			−0.0551183
$92$		−	5.93547i		−	0.618816i
$93$	4.07043	+	3.79889i	0.422084	+	0.393927i
$94$	6.66299			0.687235
$95$	−2.11355	+	2.14458i	−0.216845	+	0.220030i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	2.08302i		−	0.211499i	−0.994393	−	0.105749i	$-0.966276\pi$
$97$		−	2.08302i		−	0.211499i	0.994393	−	0.105749i	$-0.0337241\pi$
$98$	−5.39608	+	3.11543i	−0.545086	+	0.314706i
$99$	−1.33621	+	2.31438i	−0.134294	+	0.232604i
$100$	−4.36611	−	2.43661i	−0.436611	−	0.243661i
$101$	2.46499			0.245275			0.122638	−	0.992452i	$-0.460865\pi$
$101$	2.46499			0.245275			0.122638	+	0.992452i	$0.460865\pi$
$102$	1.86256	−	1.07535i	0.184421	−	0.106476i
$103$	4.33292	−	2.50161i	0.426935	−	0.246491i	−0.271105	−	0.962550i	$-0.587389\pi$
$103$	4.33292	−	2.50161i	0.426935	−	0.246491i	0.698040	+	0.716059i	$0.254056\pi$
$104$	−0.299765	−	0.519209i	−0.0293944	−	0.0509126i
$105$	−0.521352	−	1.89049i	−0.0508787	−	0.184493i
$106$	0.263220	+	0.455910i	0.0255662	+	0.0442819i
$107$	−11.9204	−	6.88226i	−1.15239	−	0.665333i	−0.202922	−	0.979195i	$-0.565044\pi$
$107$	−11.9204	−	6.88226i	−1.15239	−	0.665333i	−0.949469	+	0.313862i	$0.898377\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−9.36691			−0.897188			−0.448594	−	0.893736i	$-0.648075\pi$
$109$	−9.36691			−0.897188			−0.448594	+	0.893736i	$0.648075\pi$
$110$	−5.76066	+	1.58866i	−0.549258	+	0.151472i
$111$	5.50827	+	9.54061i	0.522822	+	0.905555i
$112$	0.759514	+	0.438506i	0.0717673	+	0.0414349i
$113$	−9.38282	+	5.41717i	−0.882661	+	0.509605i	−0.871535	−	0.490333i	$-0.836875\pi$
$113$	−9.38282	+	5.41717i	−0.882661	+	0.509605i	−0.0111262	+	0.999938i	$0.503542\pi$
$114$	−0.673287	−	1.16617i	−0.0630591	−	0.109222i
$115$	3.34155	−	12.8446i	0.311601	−	1.19776i
$116$	1.51509			0.140673
$117$	−0.519209	−	0.299765i	−0.0480009	−	0.0277133i
$118$	−6.87861	−	3.97137i	−0.633228	−	0.365594i
$119$	0.943094	+	1.63349i	0.0864533	+	0.149741i
$120$	1.56957	−	1.59262i	0.143282	−	0.145386i
$121$	1.92910	−	3.34129i	0.175372	−	0.303754i
$122$		−	2.40535i		−	0.217771i
$123$		−	7.29614i		−	0.657871i
$124$	−5.42454	−	1.25472i	−0.487138	−	0.112678i
$125$	−8.07666	−	7.73095i	−0.722398	−	0.691477i
$126$	0.877011			0.0781304
$127$	10.5475	+	6.08959i	0.935937	+	0.540364i	0.888684	−	0.458519i	$-0.151620\pi$
$127$	10.5475	+	6.08959i	0.935937	+	0.540364i	0.0472528	+	0.998883i	$0.484953\pi$
$128$			1.00000i			0.0883883i
$129$	3.65821	+	6.33621i	0.322087	+	0.557872i
$130$	−0.356400	−	1.29235i	−0.0312583	−	0.113346i
$131$	8.65726	−	14.9948i	0.756388	−	1.31010i	−0.188293	−	0.982113i	$-0.560295\pi$
$131$	8.65726	−	14.9948i	0.756388	−	1.31010i	0.944681	−	0.327990i	$-0.106371\pi$
$132$		−	2.67242i		−	0.232604i
$133$	1.02274	−	0.590480i	0.0886830	−	0.0512011i
$134$	−2.22442	−	3.85280i	−0.192160	−	0.332831i
$135$	0.562979	−	2.16404i	0.0484535	−	0.186251i
$136$	−1.07535	+	1.86256i	−0.0922105	+	0.159713i
$137$	−1.68262	+	0.971459i	−0.143756	+	0.0829973i	−0.570153	−	0.821539i	$-0.693116\pi$
$137$	−1.68262	+	0.971459i	−0.143756	+	0.0829973i	0.426397	+	0.904536i	$0.359783\pi$
$138$	5.14027	+	2.96774i	0.437569	+	0.252631i
$139$	−7.28909			−0.618253			−0.309126	−	0.951021i	$-0.600037\pi$
$139$	−7.28909			−0.618253			−0.309126	+	0.951021i	$0.600037\pi$
$140$	1.39675	+	1.37653i	0.118047	+	0.116338i
$141$	−3.33150	+	5.77032i	−0.280563	+	0.485949i
$142$	13.1134	−	7.57102i	1.10045	−	0.635346i
$143$	−1.38754	−	0.801098i	−0.116032	−	0.0669912i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.27871	+	0.852963i	0.272282	+	0.0708348i
$146$	−0.774167	−	1.34090i	−0.0640705	−	0.110973i
$147$		−	6.23085i		−	0.513912i
$148$	−9.54061	−	5.50827i	−0.784233	−	0.452777i
$149$	1.92438	−	3.33313i	0.157652	−	0.273061i	−0.776370	−	0.630278i	$-0.782941\pi$
$149$	1.92438	−	3.33313i	0.157652	−	0.273061i	0.934021	+	0.357217i	$0.116274\pi$
$150$	4.29322	−	2.56286i	0.350540	−	0.209256i
$151$	−9.22330			−0.750581			−0.375291	−	0.926907i	$-0.622457\pi$
$151$	−9.22330			−0.750581			−0.375291	+	0.926907i	$0.622457\pi$
$152$	1.16617	+	0.673287i	0.0945887	+	0.0546108i
$153$			2.15070i			0.173874i
$154$	2.34374			0.188864
$155$	−11.0325	−	5.76917i	−0.886154	−	0.463391i
$156$	0.599531			0.0480009
$157$			5.51998i			0.440543i	0.975439	+	0.220271i	$0.0706943\pi$
$157$			5.51998i			0.440543i	−0.975439	+	0.220271i	$0.929306\pi$
$158$	5.34163	+	3.08399i	0.424957	+	0.245349i
$159$	−0.526440			−0.0417494
$160$	−0.562979	+	2.16404i	−0.0445074	+	0.171082i
$161$	−2.60274	+	4.50808i	−0.205125	+	0.355286i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$		−	12.8780i		−	1.00868i	−0.863504	−	0.504342i	$-0.831735\pi$
$163$		−	12.8780i		−	1.00868i	0.863504	−	0.504342i	$-0.168265\pi$
$164$	3.64807	+	6.31865i	0.284867	+	0.493403i
$165$	1.50451	−	5.78321i	0.117126	−	0.450222i
$166$	8.53423	+	14.7817i	0.662385	+	1.14728i
$167$	−11.4068	−	6.58571i	−0.882684	−	0.509618i	−0.0111413	−	0.999938i	$-0.503546\pi$
$167$	−11.4068	−	6.58571i	−0.882684	−	0.509618i	−0.871542	+	0.490320i	$0.836880\pi$
$168$	−0.759514	+	0.438506i	−0.0585978	+	0.0338314i
$169$	−6.32028	+	10.9470i	−0.486175	+	0.842081i
$170$	−3.37568	+	3.42525i	−0.258903	+	0.262705i
$171$	1.34657			0.102975
$172$	−6.33621	−	3.65821i	−0.483131	−	0.278936i
$173$	19.5288	−	11.2750i	1.48475	−	0.857220i	0.484900	−	0.874570i	$-0.338856\pi$
$173$	19.5288	−	11.2750i	1.48475	−	0.857220i	0.999849	+	0.0173492i	$0.00552269\pi$
$174$	−0.757545	+	1.31211i	−0.0574293	+	0.0994705i
$175$	2.24765	+	3.76521i	0.169907	+	0.284623i
$176$	1.33621	+	2.31438i	0.100720	+	0.174453i
$177$	6.87861	−	3.97137i	0.517028	−	0.298506i
$178$			5.54809i			0.415847i
$179$	1.05880	−	1.83389i	0.0791382	−	0.137071i	−0.823740	−	0.566968i	$-0.808116\pi$
$179$	1.05880	−	1.83389i	0.0791382	−	0.137071i	0.902878	+	0.429896i	$0.141450\pi$
$180$	0.594464	+	2.15560i	0.0443088	+	0.160669i
$181$	4.38881	+	7.60164i	0.326217	+	0.565025i	0.981758	−	0.190135i	$-0.0608925\pi$
$181$	4.38881	+	7.60164i	0.326217	+	0.565025i	−0.655541	+	0.755160i	$0.727559\pi$
$182$			0.525795i			0.0389745i
$183$	2.08310	+	1.20268i	0.153987	+	0.0889045i
$184$	−5.93547			−0.437569
$185$	−17.5452	−	17.2913i	−1.28995	−	1.27128i
$186$	3.79889	−	4.07043i	0.278548	−	0.298458i
$187$			5.74757i			0.420304i
$188$		−	6.66299i		−	0.485949i
$189$	−0.438506	+	0.759514i	−0.0318966	+	0.0552465i
$190$	2.14458	+	2.11355i	0.155584	+	0.153333i
$191$	3.81724	+	6.61165i	0.276206	+	0.478402i	0.970439	−	0.241348i	$-0.0775896\pi$
$191$	3.81724	+	6.61165i	0.276206	+	0.478402i	−0.694233	+	0.719750i	$0.744256\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−15.5042	−	8.95133i	−1.11601	−	0.644331i	−0.175634	−	0.984456i	$-0.556197\pi$
$193$	−15.5042	−	8.95133i	−1.11601	−	0.644331i	−0.940380	+	0.340125i	$0.889531\pi$
$194$	−2.08302			−0.149552
$195$	1.29741	+	0.337523i	0.0929092	+	0.0241705i
$196$	3.11543	+	5.39608i	0.222530	+	0.385434i
$197$	−8.10251	+	4.67799i	−0.577280	+	0.333293i	−0.760052	−	0.649863i	$-0.774826\pi$
$197$	−8.10251	+	4.67799i	−0.577280	+	0.333293i	0.182772	+	0.983155i	$0.441493\pi$
$198$	2.31438	+	1.33621i	0.164476	+	0.0949602i
$199$	3.26495	+	5.65506i	0.231446	+	0.400877i	0.958234	−	0.285985i	$-0.0923209\pi$
$199$	3.26495	+	5.65506i	0.231446	+	0.400877i	−0.726788	+	0.686862i	$0.758988\pi$
$200$	−2.43661	+	4.36611i	−0.172295	+	0.308731i
$201$	4.44883			0.313796
$202$		−	2.46499i		−	0.173436i
$203$	−1.15073	−	0.664375i	−0.0807656	−	0.0466300i
$204$	−1.07535	−	1.86256i	−0.0752896	−	0.130405i
$205$	4.33730	+	15.7276i	0.302930	+	1.09846i
$206$	−2.50161	−	4.33292i	−0.174296	−	0.301889i
$207$	−5.14027	+	2.96774i	−0.357274	+	0.206272i
$208$	−0.519209	+	0.299765i	−0.0360007	+	0.0207850i
$209$	3.59861			0.248921
$210$	−1.89049	+	0.521352i	−0.130456	+	0.0359767i
$211$	12.4999	−	21.6504i	0.860526	−	1.49048i	−0.0108950	−	0.999941i	$-0.503468\pi$
$211$	12.4999	−	21.6504i	0.860526	−	1.49048i	0.871422	−	0.490535i	$-0.163199\pi$
$212$	0.455910	−	0.263220i	0.0313121	−	0.0180780i
$213$			15.1420i			1.03752i
$214$	−6.88226	+	11.9204i	−0.470461	+	0.814863i
$215$	−11.6523	−	11.4837i	−0.794679	−	0.783179i
$216$	−1.00000			−0.0680414
$217$	3.56981	+	3.33167i	0.242335	+	0.226169i
$218$			9.36691i			0.634408i
$219$	1.54833			0.104627
$220$	1.58866	+	5.76066i	0.107107	+	0.388384i
$221$	−1.28941			−0.0867351
$222$	9.54061	−	5.50827i	0.640324	−	0.369691i
$223$	−2.44055	−	1.40905i	−0.163431	−	0.0943572i	0.416053	−	0.909340i	$-0.363413\pi$
$223$	−2.44055	−	1.40905i	−0.163431	−	0.0943572i	−0.579485	+	0.814983i	$0.696746\pi$
$224$	0.438506	−	0.759514i	0.0292989	−	0.0507472i
$225$	0.0728857	+	4.99947i	0.00485905	+	0.333298i
$226$	5.41717	+	9.38282i	0.360345	+	0.624136i
$227$	−9.39580	+	5.42467i	−0.623621	+	0.360048i	−0.778277	−	0.627921i	$-0.783906\pi$
$227$	−9.39580	+	5.42467i	−0.623621	+	0.360048i	0.154656	+	0.987968i	$0.450573\pi$
$228$	−1.16617	+	0.673287i	−0.0772313	+	0.0445895i
$229$	−0.964039	+	1.66976i	−0.0637055	+	0.110341i	−0.896119	−	0.443814i	$-0.853625\pi$
$229$	−0.964039	+	1.66976i	−0.0637055	+	0.110341i	0.832414	+	0.554155i	$0.186958\pi$
$230$	−12.8446	−	3.34155i	−0.846947	−	0.220335i
$231$	−1.17187	+	2.02974i	−0.0771034	+	0.133547i
$232$		−	1.51509i		−	0.0994705i
$233$			9.56183i			0.626416i	0.949684	+	0.313208i	$0.101404\pi$
$233$			9.56183i			0.626416i	−0.949684	+	0.313208i	$0.898596\pi$
$234$	−0.299765	+	0.519209i	−0.0195963	+	0.0339417i
$235$	3.75112	−	14.4190i	0.244696	−	0.940590i
$236$	−3.97137	+	6.87861i	−0.258514	+	0.447760i
$237$	−5.34163	+	3.08399i	−0.346976	+	0.200327i
$238$	1.63349	−	0.943094i	0.105883	−	0.0611317i
$239$	−3.66276	−	6.34409i	−0.236924	−	0.410365i	0.722906	−	0.690947i	$-0.242806\pi$
$239$	−3.66276	−	6.34409i	−0.236924	−	0.410365i	−0.959830	+	0.280582i	$0.909473\pi$
$240$	−1.59262	−	1.56957i	−0.102803	−	0.101315i
$241$	−6.48181	+	11.2268i	−0.417530	+	0.723183i	−0.995690	−	0.0927402i	$-0.970437\pi$
$241$	−6.48181	+	11.2268i	−0.417530	+	0.723183i	0.578161	+	0.815923i	$0.303771\pi$
$242$	−3.34129	−	1.92910i	−0.214786	−	0.124007i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.40535			−0.153987
$245$	3.70402	+	13.4312i	0.236641	+	0.858089i
$246$	−7.29614			−0.465185
$247$			0.807313i			0.0513681i
$248$	−1.25472	+	5.42454i	−0.0796751	+	0.344459i
$249$	−17.0685			−1.08167
$250$	−7.73095	+	8.07666i	−0.488948	+	0.510813i
$251$	1.46547	−	2.53827i	0.0924997	−	0.160214i	−0.816063	−	0.577963i	$-0.803848\pi$
$251$	1.46547	−	2.53827i	0.0924997	−	0.160214i	0.908562	+	0.417749i	$0.137181\pi$
$252$		−	0.877011i		−	0.0552465i
$253$	−13.7369	+	7.93103i	−0.863634	+	0.498619i
$254$	6.08959	−	10.5475i	0.382095	−	0.661808i
$255$	−1.27851	−	4.63605i	−0.0800637	−	0.290321i
$256$	1.00000			0.0625000
$257$	8.77809	−	5.06803i	0.547562	−	0.316135i	−0.200576	−	0.979678i	$-0.564281\pi$
$257$	8.77809	−	5.06803i	0.547562	−	0.316135i	0.748138	+	0.663543i	$0.230948\pi$
$258$	6.33621	−	3.65821i	0.394475	−	0.227750i
$259$	4.83082	+	8.36722i	0.300172	+	0.519914i
$260$	−1.29235	+	0.356400i	−0.0801481	+	0.0221030i
$261$	−0.757545	−	1.31211i	−0.0468908	−	0.0812173i
$262$	−14.9948	−	8.65726i	−0.926383	−	0.534847i
$263$		−	12.1600i		−	0.749816i	−0.927062	−	0.374908i	$-0.877674\pi$
$263$		−	12.1600i		−	0.749816i	0.927062	−	0.374908i	$-0.122326\pi$
$264$	−2.67242			−0.164476
$265$	1.13479	−	0.312950i	0.0697099	−	0.0192244i
$266$	−0.590480	−	1.02274i	−0.0362047	−	0.0627083i
$267$	−4.80479	−	2.77404i	−0.294048	−	0.169769i
$268$	−3.85280	+	2.22442i	−0.235347	+	0.135878i
$269$	1.25688	+	2.17698i	0.0766333	+	0.132733i	0.901795	−	0.432163i	$-0.142250\pi$
$269$	1.25688	+	2.17698i	0.0766333	+	0.132733i	−0.825162	+	0.564896i	$0.808916\pi$
$270$	−2.16404	−	0.562979i	−0.131699	−	0.0342618i
$271$	15.0754			0.915764			0.457882	−	0.889013i	$-0.348608\pi$
$271$	15.0754			0.915764			0.457882	+	0.889013i	$0.348608\pi$
$272$	1.86256	+	1.07535i	0.112934	+	0.0652027i
$273$	−0.455352	−	0.262898i	−0.0275592	−	0.0159113i
$274$	0.971459	+	1.68262i	0.0586880	+	0.101651i
$275$	0.194781	+	13.3607i	0.0117457	+	0.805678i
$276$	2.96774	−	5.14027i	0.178637	−	0.309408i
$277$			10.8759i			0.653470i	0.945116	+	0.326735i	$0.105949\pi$
$277$			10.8759i			0.653470i	−0.945116	+	0.326735i	$0.894051\pi$
$278$			7.28909i			0.437171i
$279$	1.62565	+	5.32515i	0.0973250	+	0.318809i
$280$	1.37653	−	1.39675i	0.0822636	−	0.0834716i
$281$	2.48469			0.148224			0.0741120	−	0.997250i	$-0.476388\pi$
$281$	2.48469			0.148224			0.0741120	+	0.997250i	$0.476388\pi$
$282$	5.77032	+	3.33150i	0.343618	+	0.198388i
$283$		−	19.3416i		−	1.14974i	−0.818246	−	0.574869i	$-0.805053\pi$
$283$		−	19.3416i		−	1.14974i	0.818246	−	0.574869i	$-0.194947\pi$
$284$	−7.57102	−	13.1134i	−0.449258	−	0.778137i
$285$	−2.90268	+	0.800490i	−0.171940	+	0.0474170i
$286$	−0.801098	+	1.38754i	−0.0473699	+	0.0820471i
$287$		−	6.39880i		−	0.377709i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−6.18725	−	10.7166i	−0.363956	−	0.630390i
$290$	0.852963	−	3.27871i	0.0500877	−	0.192532i
$291$	1.04151	−	1.80395i	0.0610544	−	0.105749i
$292$	−1.34090	+	0.774167i	−0.0784701	+	0.0453047i
$293$	−2.65290	−	1.53165i	−0.154984	−	0.0894802i	0.420502	−	0.907292i	$-0.361854\pi$
$293$	−2.65290	−	1.53165i	−0.154984	−	0.0894802i	−0.575486	+	0.817811i	$0.695187\pi$
$294$	−6.23085			−0.363391
$295$	−12.4667	+	12.6498i	−0.725839	+	0.736498i
$296$	−5.50827	+	9.54061i	−0.320162	+	0.554537i
$297$	−2.31438	+	1.33621i	−0.134294	+	0.0775347i
$298$	−3.33313	−	1.92438i	−0.193083	−	0.111477i
$299$	−1.77925	−	3.08175i	−0.102897	−	0.178222i
$300$	−2.56286	−	4.29322i	−0.147967	−	0.247869i
$301$	3.20829	+	5.55692i	0.184923	+	0.320296i
$302$			9.22330i			0.530741i
$303$	2.13474	+	1.23249i	0.122638	+	0.0708049i
$304$	0.673287	−	1.16617i	0.0386157	−	0.0668843i
$305$	−5.20528	−	1.35416i	−0.298053	−	0.0775392i
$306$	2.15070			0.122947
$307$	−13.0911	−	7.55815i	−0.747149	−	0.431366i	0.0775141	−	0.996991i	$-0.475302\pi$
$307$	−13.0911	−	7.55815i	−0.747149	−	0.431366i	−0.824663	+	0.565625i	$0.808635\pi$
$308$		−	2.34374i		−	0.133547i
$309$	5.00323			0.284624
$310$	−5.76917	+	11.0325i	−0.327667	+	0.626605i
$311$	−10.2157			−0.579282			−0.289641	−	0.957135i	$-0.593536\pi$
$311$	−10.2157			−0.579282			−0.289641	+	0.957135i	$0.593536\pi$
$312$		−	0.599531i		−	0.0339417i
$313$	−4.54437	−	2.62369i	−0.256863	−	0.148300i	0.366040	−	0.930599i	$-0.380713\pi$
$313$	−4.54437	−	2.62369i	−0.256863	−	0.148300i	−0.622903	+	0.782299i	$0.714047\pi$
$314$	5.51998			0.311511
$315$	0.493739	−	1.89788i	0.0278190	−	0.106934i
$316$	3.08399	−	5.34163i	0.173488	−	0.300490i
$317$	−9.94450	−	5.74146i	−0.558539	−	0.322472i	0.194020	−	0.980998i	$-0.437847\pi$
$317$	−9.94450	−	5.74146i	−0.558539	−	0.322472i	−0.752559	+	0.658525i	$0.771181\pi$
$318$			0.526440i			0.0295213i
$319$	−2.02448	−	3.50649i	−0.113349	−	0.196326i
$320$	2.16404	+	0.562979i	0.120973	+	0.0314715i
$321$	−6.88226	−	11.9204i	−0.384130	−	0.665333i
$322$	4.50808	+	2.60274i	0.251225	+	0.145045i
$323$	2.50808	−	1.44804i	0.139553	−	0.0805710i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−2.99734	+	0.0436972i	−0.166262	+	0.00242389i
$326$	−12.8780			−0.713247
$327$	−8.11199	−	4.68346i	−0.448594	−	0.258996i
$328$	6.31865	−	3.64807i	0.348889	−	0.201431i
$329$	−2.92176	+	5.06064i	−0.161082	+	0.279002i
$330$	−5.78321	−	1.50451i	−0.318355	−	0.0828208i
$331$	10.9140	+	18.9037i	0.599890	+	1.03904i	0.992837	+	0.119479i	$0.0381225\pi$
$331$	10.9140	+	18.9037i	0.599890	+	1.03904i	−0.392946	+	0.919561i	$0.628544\pi$
$332$	14.7817	−	8.53423i	0.811252	−	0.468377i
$333$			11.0165i			0.603703i
$334$	−6.58571	+	11.4068i	−0.360354	+	0.624152i
$335$	−9.58990	+	2.64467i	−0.523952	+	0.144494i
$336$	0.438506	+	0.759514i	0.0239224	+	0.0414349i
$337$			29.7385i			1.61996i	0.586460	+	0.809978i	$0.300521\pi$
$337$			29.7385i			1.61996i	−0.586460	+	0.809978i	$0.699479\pi$
$338$	10.9470	+	6.32028i	0.595441	+	0.343778i
$339$	−10.8343			−0.588441
$340$	3.42525	+	3.37568i	0.185760	+	0.183072i
$341$	4.34441	+	14.2310i	0.235263	+	0.770653i
$342$		−	1.34657i		−	0.0728144i
$343$		−	11.6036i		−	0.626536i
$344$	−3.65821	+	6.33621i	−0.197237	+	0.341625i
$345$	9.31615	−	9.45296i	0.501565	−	0.508930i
$346$	−11.2750	−	19.5288i	−0.606146	−	1.04988i
$347$	−10.8455	−	6.26166i	−0.582218	−	0.336143i	0.179797	−	0.983704i	$-0.442456\pi$
$347$	−10.8455	−	6.26166i	−0.582218	−	0.336143i	−0.762014	+	0.647560i	$0.775789\pi$
$348$	1.31211	+	0.757545i	0.0703363	+	0.0406087i
$349$	28.4817			1.52459			0.762296	−	0.647228i	$-0.224072\pi$
$349$	28.4817			1.52459			0.762296	+	0.647228i	$0.224072\pi$
$350$	3.76521	−	2.24765i	0.201259	−	0.120142i
$351$	−0.299765	−	0.519209i	−0.0160003	−	0.0277133i
$352$	2.31438	−	1.33621i	0.123357	−	0.0712201i
$353$	19.7484	+	11.4018i	1.05110	+	0.606855i	0.922958	−	0.384900i	$-0.125764\pi$
$353$	19.7484	+	11.4018i	1.05110	+	0.606855i	0.128146	+	0.991755i	$0.459098\pi$
$354$	−3.97137	−	6.87861i	−0.211076	−	0.365594i
$355$	−9.00141	−	32.6402i	−0.477745	−	1.73236i
$356$	5.54809			0.294048
$357$			1.88619i			0.0998277i
$358$	−1.83389	−	1.05880i	−0.0969241	−	0.0559592i
$359$	2.51607	+	4.35796i	0.132793	+	0.230004i	0.924752	−	0.380570i	$-0.124272\pi$
$359$	2.51607	+	4.35796i	0.132793	+	0.230004i	−0.791959	+	0.610574i	$0.790939\pi$
$360$	2.15560	−	0.594464i	0.113610	−	0.0313310i
$361$	8.59337	+	14.8842i	0.452283	+	0.783376i
$362$	7.60164	−	4.38881i	0.399533	−	0.230671i
$363$	3.34129	−	1.92910i	0.175372	−	0.101251i
$364$	0.525795			0.0275592
$365$	−3.33759	+	0.920430i	−0.174697	+	0.0481775i
$366$	1.20268	−	2.08310i	0.0628650	−	0.108885i
$367$	−1.74905	+	1.00981i	−0.0912996	+	0.0527119i	−0.544955	−	0.838465i	$-0.683453\pi$
$367$	−1.74905	+	1.00981i	−0.0912996	+	0.0527119i	0.453655	+	0.891177i	$0.350120\pi$
$368$			5.93547i			0.309408i
$369$	3.64807	−	6.31865i	0.189911	−	0.328936i
$370$	−17.2913	+	17.5452i	−0.898930	+	0.912131i
$371$	−0.461694			−0.0239700
$372$	−4.07043	−	3.79889i	−0.211042	−	0.196964i
$373$		−	3.18649i		−	0.164990i	−0.996591	−	0.0824952i	$-0.973711\pi$
$373$		−	3.18649i		−	0.164990i	0.996591	−	0.0824952i	$-0.0262889\pi$
$374$	5.74757			0.297200
$375$	−3.12912	−	10.7335i	−0.161587	−	0.554277i
$376$	−6.66299			−0.343618
$377$	0.786648	−	0.454171i	0.0405144	−	0.0233910i
$378$	0.759514	+	0.438506i	0.0390652	+	0.0225543i
$379$	17.9536	−	31.0966i	0.922217	−	1.59733i	0.126240	−	0.992000i	$-0.459709\pi$
$379$	17.9536	−	31.0966i	0.922217	−	1.59733i	0.795977	−	0.605327i	$-0.206958\pi$
$380$	2.11355	−	2.14458i	0.108423	−	0.110015i
$381$	6.08959	+	10.5475i	0.311979	+	0.540364i
$382$	6.61165	−	3.81724i	0.338281	−	0.195307i
$383$	26.5713	−	15.3409i	1.35773	−	0.783885i	0.368411	−	0.929663i	$-0.379902\pi$
$383$	26.5713	−	15.3409i	1.35773	−	0.783885i	0.989317	+	0.145778i	$0.0465685\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	1.31948	−	5.07194i	0.0672467	−	0.258490i
$386$	−8.95133	+	15.5042i	−0.455611	+	0.789141i
$387$			7.31642i			0.371915i
$388$			2.08302i			0.105749i
$389$	5.84318	−	10.1207i	0.296261	−	0.513139i	−0.679017	−	0.734123i	$-0.737594\pi$
$389$	5.84318	−	10.1207i	0.296261	−	0.513139i	0.975277	+	0.220984i	$0.0709269\pi$
$390$	0.337523	−	1.29741i	0.0170911	−	0.0656967i
$391$	−6.38271	+	11.0552i	−0.322788	+	0.559084i
$392$	5.39608	−	3.11543i	0.272543	−	0.157353i
$393$	14.9948	−	8.65726i	0.756388	−	0.436701i
$394$	4.67799	+	8.10251i	0.235674	+	0.408199i
$395$	9.68110	−	9.82326i	0.487109	−	0.494262i
$396$	1.33621	−	2.31438i	0.0671470	−	0.116302i
$397$	−13.2338	−	7.64053i	−0.664185	−	0.383467i	0.129685	−	0.991555i	$-0.458603\pi$
$397$	−13.2338	−	7.64053i	−0.664185	−	0.383467i	−0.793870	+	0.608088i	$0.791937\pi$
$398$	5.65506	−	3.26495i	0.283463	−	0.163657i
$399$	1.18096			0.0591220
$400$	4.36611	+	2.43661i	0.218305	+	0.121831i
$401$	32.3288			1.61442			0.807211	−	0.590263i	$-0.200976\pi$
$401$	32.3288			1.61442			0.807211	+	0.590263i	$0.200976\pi$
$402$		−	4.44883i		−	0.221888i
$403$	−3.19259	+	0.974626i	−0.159034	+	0.0485496i
$404$	−2.46499			−0.122638
$405$	1.56957	−	1.59262i	0.0779927	−	0.0791380i
$406$	−0.664375	+	1.15073i	−0.0329724	+	0.0571099i
$407$			29.4408i			1.45933i
$408$	−1.86256	+	1.07535i	−0.0922105	+	0.0532378i
$409$	−13.4323	+	23.2654i	−0.664183	+	1.15040i	0.315323	+	0.948985i	$0.397887\pi$
$409$	−13.4323	+	23.2654i	−0.664183	+	1.15040i	−0.979506	+	0.201415i	$0.935446\pi$
$410$	15.7276	−	4.33730i	0.776729	−	0.214204i
$411$	−1.94292			−0.0958371
$412$	−4.33292	+	2.50161i	−0.213468	+	0.123246i
$413$	6.03262	−	3.48294i	0.296846	−	0.171384i
$414$	2.96774	+	5.14027i	0.145856	+	0.252631i
$415$	36.7928	−	10.1466i	1.80609	−	0.498077i
$416$	0.299765	+	0.519209i	0.0146972	+	0.0254563i
$417$	−6.31254	−	3.64455i	−0.309126	−	0.178474i
$418$		−	3.59861i		−	0.176014i
$419$	39.9208			1.95026			0.975130	−	0.221635i	$-0.0711394\pi$
$419$	39.9208			1.95026			0.975130	+	0.221635i	$0.0711394\pi$
$420$	0.521352	+	1.89049i	0.0254394	+	0.0922463i
$421$	−14.8483	−	25.7180i	−0.723662	−	1.25342i	−0.959522	−	0.281632i	$-0.909124\pi$
$421$	−14.8483	−	25.7180i	−0.723662	−	1.25342i	0.235861	−	0.971787i	$-0.424209\pi$
$422$	−21.6504	−	12.4999i	−1.05393	−	0.608484i
$423$	−5.77032	+	3.33150i	−0.280563	+	0.161983i
$424$	−0.263220	−	0.455910i	−0.0127831	−	0.0221410i
$425$	5.51193	+	9.23344i	0.267368	+	0.447887i
$426$	15.1420			0.733634
$427$	1.82690	+	1.05476i	0.0884099	+	0.0510435i
$428$	11.9204	+	6.88226i	0.576195	+	0.332666i
$429$	−0.801098	−	1.38754i	−0.0386774	−	0.0669912i
$430$	−11.4837	+	11.6523i	−0.553791	+	0.561923i
$431$	12.3013	−	21.3065i	0.592534	−	1.02630i	−0.401356	−	0.915922i	$-0.631461\pi$
$431$	12.3013	−	21.3065i	0.592534	−	1.02630i	0.993890	−	0.110377i	$-0.0352057\pi$
$432$			1.00000i			0.0481125i
$433$		−	27.2004i		−	1.30717i	−0.756855	−	0.653583i	$-0.773265\pi$
$433$		−	27.2004i		−	1.30717i	0.756855	−	0.653583i	$-0.226735\pi$
$434$	3.33167	−	3.56981i	0.159925	−	0.171357i
$435$	2.41296	+	2.37804i	0.115693	+	0.114018i
$436$	9.36691			0.448594
$437$	6.92176	+	3.99628i	0.331112	+	0.191168i
$438$		−	1.54833i		−	0.0739823i
$439$	−11.3367	−	19.6357i	−0.541069	−	0.937159i	−0.998843	−	0.0480903i	$-0.984686\pi$
$439$	−11.3367	−	19.6357i	−0.541069	−	0.937159i	0.457774	−	0.889069i	$-0.348647\pi$
$440$	5.76066	−	1.58866i	0.274629	−	0.0757362i
$441$	3.11543	−	5.39608i	0.148354	−	0.256956i
$442$			1.28941i			0.0613310i
$443$	22.4644	−	12.9698i	1.06732	−	0.616215i	0.139869	−	0.990170i	$-0.455332\pi$
$443$	22.4644	−	12.9698i	1.06732	−	0.616215i	0.927447	+	0.373955i	$0.121999\pi$
$444$	−5.50827	−	9.54061i	−0.261411	−	0.452777i
$445$	12.0063	+	3.12346i	0.569152	+	0.148066i
$446$	−1.40905	+	2.44055i	−0.0667206	+	0.115563i
$447$	3.33313	−	1.92438i	0.157652	−	0.0910203i
$448$	−0.759514	−	0.438506i	−0.0358837	−	0.0207174i
$449$	−29.7946			−1.40610			−0.703048	−	0.711143i	$-0.748178\pi$
$449$	−29.7946			−1.40610			−0.703048	+	0.711143i	$0.748178\pi$
$450$	4.99947	−	0.0728857i	0.235677	−	0.00343587i
$451$	9.74917	−	16.8861i	0.459070	−	0.795133i
$452$	9.38282	−	5.41717i	0.441331	−	0.254802i
$453$	−7.98761	−	4.61165i	−0.375291	−	0.216674i
$454$	5.42467	+	9.39580i	0.254592	+	0.440967i
$455$	1.13784	+	0.296012i	0.0533428	+	0.0138772i
$456$	0.673287	+	1.16617i	0.0315296	+	0.0546108i
$457$			21.8147i			1.02045i	0.860041	+	0.510225i	$0.170438\pi$
$457$			21.8147i			1.02045i	−0.860041	+	0.510225i	$0.829562\pi$
$458$	1.66976	+	0.964039i	0.0780230	+	0.0450466i
$459$	−1.07535	+	1.86256i	−0.0501930	+	0.0869369i
$460$	−3.34155	+	12.8446i	−0.155800	+	0.598882i
$461$	30.4071			1.41620			0.708099	−	0.706113i	$-0.249553\pi$
$461$	30.4071			1.41620			0.708099	+	0.706113i	$0.249553\pi$
$462$	2.02974	+	1.17187i	0.0944320	+	0.0545203i
$463$		−	16.0722i		−	0.746938i	−0.927643	−	0.373469i	$-0.878168\pi$
$463$		−	16.0722i		−	0.746938i	0.927643	−	0.373469i	$-0.121832\pi$
$464$	−1.51509			−0.0703363
$465$	−6.66986	−	10.5125i	−0.309307	−	0.487506i
$466$	9.56183			0.442943
$467$			31.7383i			1.46867i	0.678785	+	0.734337i	$0.262507\pi$
$467$			31.7383i			1.46867i	−0.678785	+	0.734337i	$0.737493\pi$
$468$	0.519209	+	0.299765i	0.0240004	+	0.0138567i
$469$	3.90168			0.180163
$470$	−14.4190	−	3.75112i	−0.665097	−	0.173026i
$471$	−2.75999	+	4.78045i	−0.127174	+	0.220271i
$472$	6.87861	+	3.97137i	0.316614	+	0.182797i
$473$			19.5525i			0.899026i
$474$	3.08399	+	5.34163i	0.141652	+	0.245349i
$475$	5.78114	−	3.45107i	0.265257	−	0.158346i
$476$	−0.943094	−	1.63349i	−0.0432266	−	0.0748707i
$477$	−0.455910	−	0.263220i	−0.0208747	−	0.0120520i
$478$	−6.34409	+	3.66276i	−0.290172	+	0.167531i
$479$	−2.85865	+	4.95133i	−0.130615	+	0.226232i	−0.923914	−	0.382600i	$-0.875029\pi$
$479$	−2.85865	+	4.95133i	−0.130615	+	0.226232i	0.793299	+	0.608833i	$0.208362\pi$
$480$	−1.56957	+	1.59262i	−0.0716408	+	0.0726929i
$481$	−6.60476			−0.301151
$482$	11.2268	+	6.48181i	0.511367	+	0.295238i
$483$	−4.50808	+	2.60274i	−0.205125	+	0.118429i
$484$	−1.92910	+	3.34129i	−0.0876861	+	0.151877i
$485$	−1.17270	+	4.50773i	−0.0532494	+	0.204686i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	20.4207	−	11.7899i	0.925352	−	0.534252i	0.0400136	−	0.999199i	$-0.487260\pi$
$487$	20.4207	−	11.7899i	0.925352	−	0.534252i	0.885339	+	0.464947i	$0.153927\pi$
$488$			2.40535i			0.108885i
$489$	6.43900	−	11.1527i	0.291182	−	0.504342i
$490$	13.4312	−	3.70402i	0.606761	−	0.167331i
$491$	14.1985	+	24.5925i	0.640768	+	1.10984i	0.985262	+	0.171054i	$0.0547172\pi$
$491$	14.1985	+	24.5925i	0.640768	+	1.10984i	−0.344494	+	0.938789i	$0.611949\pi$
$492$			7.29614i			0.328936i
$493$	−2.82195	−	1.62925i	−0.127094	−	0.0733778i
$494$	0.807313			0.0363227
$495$	4.19455	−	4.25615i	0.188531	−	0.191300i
$496$	5.42454	+	1.25472i	0.243569	+	0.0563388i
$497$			13.2797i			0.595678i
$498$			17.0685i			0.764856i
$499$	14.6696	−	25.4084i	0.656700	−	1.13744i	−0.324765	−	0.945795i	$-0.605285\pi$
$499$	14.6696	−	25.4084i	0.656700	−	1.13744i	0.981465	−	0.191643i	$-0.0613814\pi$
$500$	8.07666	+	7.73095i	0.361199	+	0.345739i
$501$	−6.58571	−	11.4068i	−0.294228	−	0.509618i
$502$	−2.53827	−	1.46547i	−0.113289	−	0.0654072i
$503$	−22.8668	−	13.2022i	−1.01958	−	0.588655i	−0.105598	−	0.994409i	$-0.533676\pi$
$503$	−22.8668	−	13.2022i	−1.01958	−	0.588655i	−0.913982	+	0.405754i	$0.867009\pi$
$504$	−0.877011			−0.0390652
$505$	−5.33432	−	1.38774i	−0.237374	−	0.0617534i
$506$	7.93103	+	13.7369i	0.352577	+	0.610682i
$507$	−10.9470	+	6.32028i	−0.486175	+	0.280694i
$508$	−10.5475	−	6.08959i	−0.467969	−	0.270182i
$509$	−4.77269	−	8.26655i	−0.211546	−	0.366408i	0.740653	−	0.671888i	$-0.234516\pi$
$509$	−4.77269	−	8.26655i	−0.211546	−	0.366408i	−0.952199	+	0.305480i	$0.901183\pi$
$510$	−4.63605	+	1.27851i	−0.205288	+	0.0566136i
$511$	1.35791			0.0600703
$512$		−	1.00000i		−	0.0441942i
$513$	1.16617	+	0.673287i	0.0514876	+	0.0297264i
$514$	−5.06803	−	8.77809i	−0.223541	−	0.387185i
$515$	−10.7850	+	2.97424i	−0.475242	+	0.131061i
$516$	−3.65821	−	6.33621i	−0.161044	−	0.278936i
$517$	−15.4207	+	8.90315i	−0.678202	+	0.391560i
$518$	8.36722	−	4.83082i	0.367635	−	0.212254i
$519$	22.5500			0.989833
$520$	0.356400	+	1.29235i	0.0156292	+	0.0566732i
$521$	10.6051	−	18.3686i	0.464619	−	0.804744i	−0.534565	−	0.845127i	$-0.679525\pi$
$521$	10.6051	−	18.3686i	0.464619	−	0.804744i	0.999184	+	0.0403834i	$0.0128579\pi$
$522$	−1.31211	+	0.757545i	−0.0574293	+	0.0331568i
$523$		−	14.1342i		−	0.618044i	−0.951055	−	0.309022i	$-0.899998\pi$
$523$		−	14.1342i		−	0.618044i	0.951055	−	0.309022i	$-0.100002\pi$
$524$	−8.65726	+	14.9948i	−0.378194	+	0.655052i
$525$	0.0639216	+	4.38459i	0.00278977	+	0.191359i
$526$	−12.1600			−0.530200
$527$	8.75427	+	8.17028i	0.381342	+	0.355903i
$528$			2.67242i			0.116302i
$529$	−12.2298			−0.531732
$530$	−0.312950	−	1.13479i	−0.0135937	−	0.0492923i
$531$	7.94274			0.344686
$532$	−1.02274	+	0.590480i	−0.0443415	+	0.0256006i
$533$	3.78822	+	2.18713i	0.164086	+	0.0947352i
$534$	−2.77404	+	4.80479i	−0.120045	+	0.207923i
$535$	21.9217	+	21.6044i	0.947756	+	0.934040i
$536$	2.22442	+	3.85280i	0.0960801	+	0.166416i
$537$	1.83389	−	1.05880i	0.0791382	−	0.0456905i
$538$	2.17698	−	1.25688i	0.0938562	−	0.0541879i
$539$	8.32571	−	14.4206i	0.358614	−	0.621138i
$540$	−0.562979	+	2.16404i	−0.0242267	+	0.0931253i
$541$	2.79145	−	4.83493i	0.120014	−	0.207870i	−0.799759	−	0.600321i	$-0.795039\pi$
$541$	2.79145	−	4.83493i	0.120014	−	0.207870i	0.919773	+	0.392451i	$0.128373\pi$
$542$		−	15.0754i		−	0.647543i
$543$			8.77761i			0.376683i
$544$	1.07535	−	1.86256i	0.0461052	−	0.0798566i
$545$	20.2703	+	5.27337i	0.868286	+	0.225887i
$546$	−0.262898	+	0.455352i	−0.0112510	+	0.0194873i
$547$	−17.8380	+	10.2988i	−0.762696	+	0.440343i	−0.830263	−	0.557372i	$-0.811810\pi$
$547$	−17.8380	+	10.2988i	−0.762696	+	0.440343i	0.0675669	+	0.997715i	$0.478476\pi$
$548$	1.68262	−	0.971459i	0.0718778	−	0.0414987i
$549$	1.20268	+	2.08310i	0.0513290	+	0.0889045i
$550$	13.3607	−	0.194781i	0.569701	−	0.00830549i
$551$	−1.02009	+	1.76685i	−0.0434573	+	0.0752703i
$552$	−5.14027	−	2.96774i	−0.218784	−	0.126315i
$553$	−4.68467	+	2.70470i	−0.199212	+	0.115015i
$554$	10.8759			0.462073
$555$	−6.54895	−	23.7473i	−0.277987	−	1.00802i
$556$	7.28909			0.309126
$557$		−	26.0926i		−	1.10558i	−0.833321	−	0.552789i	$-0.813564\pi$
$557$		−	26.0926i		−	1.10558i	0.833321	−	0.552789i	$-0.186436\pi$
$558$	5.32515	−	1.62565i	0.225432	−	0.0688192i
$559$	−4.38642			−0.185526
$560$	−1.39675	−	1.37653i	−0.0590233	−	0.0581691i
$561$	−2.87378	+	4.97754i	−0.121331	+	0.210152i
$562$		−	2.48469i		−	0.104810i
$563$	5.16733	−	2.98336i	0.217777	−	0.125734i	−0.387143	−	0.922019i	$-0.626538\pi$
$563$	5.16733	−	2.98336i	0.217777	−	0.125734i	0.604921	+	0.796286i	$0.293205\pi$
$564$	3.33150	−	5.77032i	0.140281	−	0.242974i
$565$	23.3545	−	6.44063i	0.982532	−	0.270959i
$566$	−19.3416			−0.812987
$567$	−0.759514	+	0.438506i	−0.0318966	+	0.0184155i
$568$	−13.1134	+	7.57102i	−0.550226	+	0.317673i
$569$	12.7252	+	22.0408i	0.533470	+	0.923997i	0.999236	+	0.0390888i	$0.0124455\pi$
$569$	12.7252	+	22.0408i	0.533470	+	0.923997i	−0.465766	+	0.884908i	$0.654221\pi$
$570$	0.800490	+	2.90268i	0.0335289	+	0.121580i
$571$	−13.6796	−	23.6938i	−0.572475	−	0.991556i	−0.996311	−	0.0858168i	$-0.972650\pi$
$571$	−13.6796	−	23.6938i	−0.572475	−	0.991556i	0.423836	−	0.905739i	$-0.360683\pi$
$572$	1.38754	+	0.801098i	0.0580161	+	0.0334956i
$573$			7.63447i			0.318935i
$574$	−6.39880			−0.267081
$575$	−14.4625	+	25.9149i	−0.603126	+	1.08073i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	2.02727	+	1.17044i	0.0843962	+	0.0487262i	0.541604	−	0.840634i	$-0.317817\pi$
$577$	2.02727	+	1.17044i	0.0843962	+	0.0487262i	−0.457208	+	0.889360i	$0.651151\pi$
$578$	−10.7166	+	6.18725i	−0.445753	+	0.257355i
$579$	−8.95133	−	15.5042i	−0.372005	−	0.644331i
$580$	−3.27871	−	0.852963i	−0.136141	−	0.0354174i
$581$	−14.9692			−0.621028
$582$	−1.80395	−	1.04151i	−0.0747761	−	0.0431720i
$583$	−1.21838	−	0.703434i	−0.0504603	−	0.0291332i
$584$	0.774167	+	1.34090i	0.0320353	+	0.0554867i
$585$	0.954825	+	0.941007i	0.0394772	+	0.0389058i
$586$	−1.53165	+	2.65290i	−0.0632720	+	0.109590i
$587$		−	31.5154i		−	1.30078i	−0.759601	−	0.650389i	$-0.774606\pi$
$587$		−	31.5154i		−	1.30078i	0.759601	−	0.650389i	$-0.225394\pi$
$588$			6.23085i			0.256956i
$589$	5.11549	−	5.48114i	0.210780	−	0.225846i
$590$	12.6498	+	12.4667i	0.520783	+	0.513246i
$591$	−9.35597			−0.384853
$592$	9.54061	+	5.50827i	0.392117	+	0.226389i
$593$			8.79133i			0.361017i	0.983573	+	0.180508i	$0.0577743\pi$
$593$			8.79133i			0.361017i	−0.983573	+	0.180508i	$0.942226\pi$
$594$	1.33621	+	2.31438i	0.0548253	+	0.0949602i
$595$	−1.12127	−	4.06587i	−0.0459677	−	0.166684i
$596$	−1.92438	+	3.33313i	−0.0788259	+	0.136530i
$597$			6.52991i			0.267251i
$598$	−3.08175	+	1.77925i	−0.126022	+	0.0727589i
$599$	−9.05942	−	15.6914i	−0.370158	−	0.641132i	0.619432	−	0.785051i	$-0.287363\pi$
$599$	−9.05942	−	15.6914i	−0.370158	−	0.641132i	−0.989590	+	0.143918i	$0.954030\pi$
$600$	−4.29322	+	2.56286i	−0.175270	+	0.104628i
$601$	−8.35145	+	14.4651i	−0.340663	+	0.590045i	−0.984556	−	0.175070i	$-0.943985\pi$
$601$	−8.35145	+	14.4651i	−0.340663	+	0.590045i	0.643893	+	0.765115i	$0.277318\pi$
$602$	5.55692	−	3.20829i	0.226483	−	0.130760i
$603$	3.85280	+	2.22442i	0.156898	+	0.0905852i
$604$	9.22330			0.375291
$605$	−6.05571	+	6.14464i	−0.246200	+	0.249815i
$606$	1.23249	−	2.13474i	0.0500666	−	0.0867179i
$607$	4.48711	−	2.59063i	0.182126	−	0.105151i	−0.406165	−	0.913800i	$-0.633134\pi$
$607$	4.48711	−	2.59063i	0.182126	−	0.105151i	0.588291	+	0.808649i	$0.299801\pi$
$608$	−1.16617	−	0.673287i	−0.0472943	−	0.0273054i
$609$	−0.664375	−	1.15073i	−0.0269219	−	0.0466300i
$610$	−1.35416	+	5.20528i	−0.0548285	+	0.210755i
$611$	−1.99734	−	3.45949i	−0.0808035	−	0.139956i
$612$		−	2.15070i		−	0.0869369i
$613$	−3.25012	−	1.87646i	−0.131271	−	0.0757894i	0.432926	−	0.901429i	$-0.357481\pi$
$613$	−3.25012	−	1.87646i	−0.131271	−	0.0757894i	−0.564198	+	0.825640i	$0.690814\pi$
$614$	−7.55815	+	13.0911i	−0.305022	+	0.528314i
$615$	−4.10757	+	15.7891i	−0.165633	+	0.636679i
$616$	−2.34374			−0.0944320
$617$	19.4604	+	11.2355i	0.783446	+	0.452323i	0.837650	−	0.546207i	$-0.183929\pi$
$617$	19.4604	+	11.2355i	0.783446	+	0.452323i	−0.0542044	+	0.998530i	$0.517262\pi$
$618$		−	5.00323i		−	0.201259i
$619$	−36.6090			−1.47144			−0.735721	−	0.677285i	$-0.763156\pi$
$619$	−36.6090			−1.47144			−0.735721	+	0.677285i	$0.763156\pi$
$620$	11.0325	+	5.76917i	0.443077	+	0.231696i
$621$	−5.93547			−0.238182
$622$			10.2157i			0.409614i
$623$	−4.21385	−	2.43287i	−0.168824	−	0.0974708i
$624$	−0.599531			−0.0240004
$625$	13.1258	+	21.2770i	0.525033	+	0.851082i
$626$	−2.62369	+	4.54437i	−0.104864	+	0.181629i
$627$	3.11649	+	1.79930i	0.124460	+	0.0718573i
$628$		−	5.51998i		−	0.220271i
$629$	11.8466	+	20.5190i	0.472357	+	0.818146i
$630$	−1.89788	−	0.493739i	−0.0756135	−	0.0196710i
$631$	−11.0962	−	19.2191i	−0.441732	−	0.765102i	0.556086	−	0.831124i	$-0.312302\pi$
$631$	−11.0962	−	19.2191i	−0.441732	−	0.765102i	−0.997818	+	0.0660227i	$0.978969\pi$
$632$	−5.34163	−	3.08399i	−0.212479	−	0.122675i
$633$	21.6504	−	12.4999i	0.860526	−	0.496825i
$634$	−5.74146	+	9.94450i	−0.228022	+	0.394946i
$635$	−19.3968	−	19.1161i	−0.769739	−	0.758599i
$636$	0.526440			0.0208747
$637$	3.23511	+	1.86779i	0.128180	+	0.0740047i
$638$	−3.50649	+	2.02448i	−0.138823	+	0.0801497i
$639$	−7.57102	+	13.1134i	−0.299505	+	0.518758i
$640$	0.562979	−	2.16404i	0.0222537	−	0.0855411i
$641$	−21.6944	−	37.5759i	−0.856879	−	1.48416i	−0.874891	−	0.484320i	$-0.839067\pi$
$641$	−21.6944	−	37.5759i	−0.856879	−	1.48416i	0.0180124	−	0.999838i	$-0.494266\pi$
$642$	−11.9204	+	6.88226i	−0.470461	+	0.271621i
$643$		−	25.7188i		−	1.01425i	−0.861872	−	0.507126i	$-0.830708\pi$
$643$		−	25.7188i		−	1.01425i	0.861872	−	0.507126i	$-0.169292\pi$
$644$	2.60274	−	4.50808i	0.102562	−	0.177643i
$645$	−4.34935	−	15.7713i	−0.171256	−	0.620993i
$646$	−1.44804	−	2.50808i	−0.0569723	−	0.0986789i
$647$			26.2047i			1.03021i	0.857126	+	0.515106i	$0.172248\pi$
$647$			26.2047i			1.03021i	−0.857126	+	0.515106i	$0.827752\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	21.2263			0.833205
$650$	0.0436972	+	2.99734i	0.00171395	+	0.117565i
$651$	1.42571	+	4.67022i	0.0558781	+	0.183040i
$652$			12.8780i			0.504342i
$653$			49.5922i			1.94069i	0.241719	+	0.970346i	$0.422289\pi$
$653$			49.5922i			1.94069i	−0.241719	+	0.970346i	$0.577711\pi$
$654$	−4.68346	+	8.11199i	−0.183138	+	0.317204i
$655$	−27.1764	+	27.5755i	−1.06187	+	1.07746i
$656$	−3.64807	−	6.31865i	−0.142433	−	0.246702i
$657$	1.34090	+	0.774167i	0.0523134	+	0.0302031i
$658$	5.06064	+	2.92176i	0.197284	+	0.113902i
$659$	−6.60687			−0.257367			−0.128684	−	0.991686i	$-0.541075\pi$
$659$	−6.60687			−0.257367			−0.128684	+	0.991686i	$0.541075\pi$
$660$	−1.50451	+	5.78321i	−0.0585631	+	0.225111i
$661$	−5.39524	−	9.34483i	−0.209850	−	0.363472i	0.741817	−	0.670603i	$-0.233964\pi$
$661$	−5.39524	−	9.34483i	−0.209850	−	0.363472i	−0.951667	+	0.307131i	$0.900631\pi$
$662$	18.9037	−	10.9140i	0.734713	−	0.424187i
$663$	−1.11666	−	0.644705i	−0.0433676	−	0.0250383i
$664$	−8.53423	−	14.7817i	−0.331192	−	0.573642i
$665$	−2.54568	+	0.702039i	−0.0987172	+	0.0272239i
$666$	11.0165			0.426883
$667$		−	8.99277i		−	0.348202i
$668$	11.4068	+	6.58571i	0.441342	+	0.254809i
$669$	−1.40905	−	2.44055i	−0.0544771	−	0.0943572i
$670$	2.64467	+	9.58990i	0.102173	+	0.370490i
$671$	3.21405	+	5.56691i	0.124077	+	0.214908i
$672$	0.759514	−	0.438506i	0.0292989	−	0.0169157i
$673$	20.8669	−	12.0475i	0.804359	−	0.464397i	−0.0406344	−	0.999174i	$-0.512938\pi$
$673$	20.8669	−	12.0475i	0.804359	−	0.464397i	0.844993	+	0.534777i	$0.179605\pi$
$674$	29.7385			1.14548
$675$	−2.43661	+	4.36611i	−0.0937853	+	0.168052i
$676$	6.32028	−	10.9470i	0.243088	−	0.421040i
$677$	6.69957	−	3.86800i	0.257485	−	0.148659i	−0.365702	−	0.930732i	$-0.619171\pi$
$677$	6.69957	−	3.86800i	0.257485	−	0.148659i	0.623187	+	0.782073i	$0.285838\pi$
$678$			10.8343i			0.416090i
$679$	0.913417	−	1.58208i	0.0350537	−	0.0607148i
$680$	3.37568	−	3.42525i	0.129451	−	0.131352i
$681$	−10.8493			−0.415747
$682$	14.2310	−	4.34441i	0.544934	−	0.166356i
$683$		−	32.7226i		−	1.25210i	−0.779784	−	0.626048i	$-0.784671\pi$
$683$		−	32.7226i		−	1.25210i	0.779784	−	0.626048i	$-0.215329\pi$
$684$	−1.34657			−0.0514876
$685$	4.18815	−	1.15500i	0.160021	−	0.0441301i
$686$	−11.6036			−0.443028
$687$	−1.66976	+	0.964039i	−0.0637055	+	0.0367804i
$688$	6.33621	+	3.65821i	0.241566	+	0.139468i
$689$	0.157808	−	0.273332i	0.00601202	−	0.0104131i
$690$	−9.45296	−	9.31615i	−0.359868	−	0.354660i
$691$	1.39068	+	2.40873i	0.0529039	+	0.0916323i	0.891265	−	0.453484i	$-0.149819\pi$
$691$	1.39068	+	2.40873i	0.0529039	+	0.0916323i	−0.838361	+	0.545116i	$0.816486\pi$
$692$	−19.5288	+	11.2750i	−0.742375	+	0.428610i
$693$	−2.02974	+	1.17187i	−0.0771034	+	0.0445156i
$694$	−6.26166	+	10.8455i	−0.237689	+	0.411690i
$695$	15.7739	+	4.10360i	0.598337	+	0.155659i
$696$	0.757545	−	1.31211i	0.0287147	−	0.0497353i
$697$		−	15.6918i		−	0.594370i
$698$		−	28.4817i		−	1.07805i
$699$	−4.78092	+	8.28079i	−0.180831	+	0.313208i
$700$	−2.24765	−	3.76521i	−0.0849533	−	0.142311i
$701$	−8.57416	+	14.8509i	−0.323841	+	0.560910i	−0.981277	−	0.192601i	$-0.938308\pi$
$701$	−8.57416	+	14.8509i	−0.323841	+	0.560910i	0.657436	+	0.753511i	$0.271641\pi$
$702$	−0.519209	+	0.299765i	−0.0195963	+	0.0113139i
$703$	12.8471	−	7.41730i	0.484539	−	0.279749i
$704$	−1.33621	−	2.31438i	−0.0503602	−	0.0872265i
$705$	10.4581	−	10.6116i	0.393873	−	0.399657i
$706$	11.4018	−	19.7484i	0.429111	−	0.743243i
$707$	1.87219	+	1.08091i	0.0704110	+	0.0406518i
$708$	−6.87861	+	3.97137i	−0.258514	+	0.149253i
$709$	−41.3508			−1.55296			−0.776482	−	0.630140i	$-0.782998\pi$
$709$	−41.3508			−1.55296			−0.776482	+	0.630140i	$0.782998\pi$
$710$	−32.6402	+	9.00141i	−1.22496	+	0.337817i
$711$	−6.16798			−0.231317
$712$		−	5.54809i		−	0.207923i
$713$	−7.44738	+	32.1972i	−0.278907	+	1.20580i
$714$	1.88619			0.0705888
$715$	2.55169	+	2.51476i	0.0954278	+	0.0940468i
$716$	−1.05880	+	1.83389i	−0.0395691	+	0.0685357i
$717$		−	7.32552i		−	0.273577i
$718$	4.35796	−	2.51607i	0.162638	−	0.0938989i
$719$	−20.0362	+	34.7037i	−0.747224	+	1.29423i	0.201925	+	0.979401i	$0.435280\pi$
$719$	−20.0362	+	34.7037i	−0.747224	+	1.29423i	−0.949148	+	0.314829i	$0.898053\pi$
$720$	−0.594464	−	2.15560i	−0.0221544	−	0.0803345i
$721$	4.38789			0.163413
$722$	14.8842	−	8.59337i	0.553931	−	0.319812i
$723$	−11.2268	+	6.48181i	−0.417530	+	0.241061i
$724$	−4.38881	−	7.60164i	−0.163109	−	0.282513i
$725$	−6.61505	−	3.69169i	−0.245677	−	0.137106i
$726$	−1.92910	−	3.34129i	−0.0715954	−	0.124007i
$727$	5.62697	+	3.24873i	0.208693	+	0.120489i	0.600704	−	0.799472i	$-0.294887\pi$
$727$	5.62697	+	3.24873i	0.208693	+	0.120489i	−0.392011	+	0.919961i	$0.628220\pi$
$728$		−	0.525795i		−	0.0194873i
$729$	−1.00000			−0.0370370
$730$	0.920430	+	3.33759i	0.0340666	+	0.123530i
$731$	7.86771	+	13.6273i	0.290998	+	0.504023i
$732$	−2.08310	−	1.20268i	−0.0769935	−	0.0444522i
$733$	−33.2676	+	19.2070i	−1.22877	+	0.709428i	−0.966772	−	0.255641i	$-0.917713\pi$
$733$	−33.2676	+	19.2070i	−1.22877	+	0.709428i	−0.261994	+	0.965069i	$0.584380\pi$
$734$	1.00981	+	1.74905i	0.0372729	+	0.0645586i
$735$	−3.50784	+	13.4838i	−0.129389	+	0.497357i
$736$	5.93547			0.218784
$737$	10.2963	+	5.94456i	0.379269	+	0.218971i
$738$	−6.31865	−	3.64807i	−0.232593	−	0.134287i
$739$	10.9846	+	19.0258i	0.404074	+	0.699876i	0.994213	−	0.107425i	$-0.0342607\pi$
$739$	10.9846	+	19.0258i	0.404074	+	0.699876i	−0.590140	+	0.807301i	$0.700927\pi$
$740$	17.5452	+	17.2913i	0.644974	+	0.635640i
$741$	−0.403656	+	0.699153i	−0.0148287	+	0.0256840i
$742$			0.461694i			0.0169493i
$743$			17.8112i			0.653431i	0.945123	+	0.326715i	$0.105942\pi$
$743$			17.8112i			0.653431i	−0.945123	+	0.326715i	$0.894058\pi$
$744$	−3.79889	+	4.07043i	−0.139274	+	0.149229i
$745$	−6.04092	+	6.12963i	−0.221322	+	0.224572i
$746$	−3.18649			−0.116666
$747$	−14.7817	−	8.53423i	−0.540835	−	0.312251i
$748$		−	5.74757i		−	0.210152i
$749$	−6.03582	−	10.4543i	−0.220544	−	0.381993i
$750$	−10.7335	+	3.12912i	−0.391933	+	0.114259i
$751$	−14.2351	+	24.6559i	−0.519445	+	0.899705i	0.480300	+	0.877105i	$0.340528\pi$
$751$	−14.2351	+	24.6559i	−0.519445	+	0.899705i	−0.999745	+	0.0226006i	$0.992805\pi$
$752$			6.66299i			0.242974i
$753$	2.53827	−	1.46547i	0.0924997	−	0.0534047i
$754$	−0.454171	−	0.786648i	−0.0165399	−	0.0286480i
$755$	19.9596	+	5.19252i	0.726403	+	0.188975i
$756$	0.438506	−	0.759514i	0.0159483	−	0.0276233i
$757$	−17.8550	+	10.3086i	−0.648951	+	0.374672i	−0.788054	−	0.615606i	$-0.788911\pi$
$757$	−17.8550	+	10.3086i	−0.648951	+	0.374672i	0.139103	+	0.990278i	$0.455578\pi$
$758$	−31.0966	−	17.9536i	−1.12948	−	0.652106i
$759$	−15.8621			−0.575756
$760$	−2.14458	−	2.11355i	−0.0777922	−	0.0766664i
$761$	−5.87697	+	10.1792i	−0.213040	+	0.368996i	−0.952664	−	0.304024i	$-0.901670\pi$
$761$	−5.87697	+	10.1792i	−0.213040	+	0.368996i	0.739624	+	0.673020i	$0.235003\pi$
$762$	10.5475	−	6.08959i	0.382095	−	0.220603i
$763$	−7.11430	−	4.10745i	−0.257555	−	0.148699i
$764$	−3.81724	−	6.61165i	−0.138103	−	0.239201i
$765$	1.21080	−	4.65419i	0.0437765	−	0.168273i
$766$	−15.3409	−	26.5713i	−0.554290	−	0.960059i
$767$			4.76192i			0.171943i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	19.5081	−	33.7890i	0.703480	−	1.21846i	−0.263757	−	0.964589i	$-0.584962\pi$
$769$	19.5081	−	33.7890i	0.703480	−	1.21846i	0.967237	−	0.253875i	$-0.0817051\pi$
$770$	−5.07194	−	1.31948i	−0.182780	−	0.0475506i
$771$	10.1361			0.365041
$772$	15.5042	+	8.95133i	0.558007	+	0.322165i
$773$		−	27.3458i		−	0.983559i	−0.870720	−	0.491779i	$-0.836347\pi$
$773$		−	27.3458i		−	0.983559i	0.870720	−	0.491779i	$-0.163653\pi$
$774$	7.31642			0.262983
$775$	20.6269	+	18.6958i	0.740939	+	0.671572i
$776$	2.08302			0.0747761
$777$			9.66164i			0.346609i
$778$	−10.1207	−	5.84318i	−0.362844	−	0.209488i
$779$	−9.82480			−0.352010
$780$	−1.29741	−	0.337523i	−0.0464546	−	0.0120853i
$781$	−20.2329	+	35.0445i	−0.723991	+	1.25399i
$782$	11.0552	+	6.38271i	0.395332	+	0.228245i
$783$		−	1.51509i		−	0.0541449i
$784$	−3.11543	−	5.39608i	−0.111265	−	0.192717i
$785$	3.10763	−	11.9454i	0.110916	−	0.426351i
$786$	−8.65726	−	14.9948i	−0.308794	−	0.534847i
$787$	27.8018	+	16.0514i	0.991027	+	0.572169i	0.905581	−	0.424173i	$-0.139435\pi$
$787$	27.8018	+	16.0514i	0.991027	+	0.572169i	0.0854455	+	0.996343i	$0.472769\pi$
$788$	8.10251	−	4.67799i	0.288640	−	0.166646i
$789$	6.07999	−	10.5308i	0.216453	−	0.374908i
$790$	−9.82326	−	9.68110i	−0.349496	−	0.344438i
$791$	−9.50184			−0.337847
$792$	−2.31438	−	1.33621i	−0.0822379	−	0.0474801i
$793$	−1.24888	+	0.721042i	−0.0443491	+	0.0256050i
$794$	−7.64053	+	13.2338i	−0.271152	+	0.469650i
$795$	1.13924	+	0.296375i	0.0404045	+	0.0105113i
$796$	−3.26495	−	5.65506i	−0.115723	−	0.200438i
$797$	1.32198	−	0.763246i	0.0468270	−	0.0270356i	−0.476404	−	0.879227i	$-0.658060\pi$
$797$	1.32198	−	0.763246i	0.0468270	−	0.0270356i	0.523231	+	0.852191i	$0.324727\pi$
$798$		−	1.18096i		−	0.0418056i
$799$	−7.16505	+	12.4102i	−0.253481	+	0.439042i
$800$	2.43661	−	4.36611i	0.0861473	−	0.154365i
$801$	−2.77404	−	4.80479i	−0.0980160	−	0.169769i
$802$		−	32.3288i		−	1.14157i
$803$	3.58343	+	2.06890i	0.126457	+	0.0730098i
$804$	−4.44883			−0.156898
$805$	8.17037	−	8.29035i	0.287968	−	0.292197i
$806$	0.974626	+	3.19259i	0.0343297	+	0.112454i
$807$			2.51376i			0.0884885i
$808$			2.46499i			0.0867179i
$809$	−11.3180	+	19.6033i	−0.397919	+	0.689216i	−0.993469	−	0.114102i	$-0.963601\pi$
$809$	−11.3180	+	19.6033i	−0.397919	+	0.689216i	0.595550	+	0.803318i	$0.296934\pi$
$810$	−1.59262	−	1.56957i	−0.0559590	−	0.0551491i
$811$	−0.743060	−	1.28702i	−0.0260924	−	0.0451933i	0.852684	−	0.522426i	$-0.174973\pi$
$811$	−0.743060	−	1.28702i	−0.0260924	−	0.0451933i	−0.878777	+	0.477233i	$0.841640\pi$
$812$	1.15073	+	0.664375i	0.0403828	+	0.0233150i
$813$	13.0557	+	7.53769i	0.457882	+	0.264358i
$814$	29.4408			1.03190
$815$	−7.25004	+	27.8685i	−0.253958	+	0.976190i
$816$	1.07535	+	1.86256i	0.0376448	+	0.0652027i
$817$	8.53217	−	4.92605i	0.298503	−	0.172341i
$818$	23.2654	+	13.4323i	0.813455	+	0.469649i
$819$	−0.262898	−	0.455352i	−0.00918639	−	0.0159113i
$820$	−4.33730	−	15.7276i	−0.151465	−	0.549231i
$821$	−38.2894			−1.33631			−0.668155	−	0.744022i	$-0.732916\pi$
$821$	−38.2894			−1.33631			−0.668155	+	0.744022i	$0.732916\pi$
$822$			1.94292i			0.0677670i
$823$	−9.41190	−	5.43397i	−0.328078	−	0.189416i	0.326909	−	0.945056i	$-0.393993\pi$
$823$	−9.41190	−	5.43397i	−0.328078	−	0.189416i	−0.654988	+	0.755640i	$0.727326\pi$
$824$	2.50161	+	4.33292i	0.0871478	+	0.150944i
$825$	−6.51165	+	11.6681i	−0.226706	+	0.406230i
$826$	−3.48294	−	6.03262i	−0.121187	−	0.209902i
$827$	3.01180	−	1.73886i	0.104731	−	0.0604662i	−0.446720	−	0.894674i	$-0.647408\pi$
$827$	3.01180	−	1.73886i	0.104731	−	0.0604662i	0.551450	+	0.834208i	$0.314075\pi$
$828$	5.14027	−	2.96774i	0.178637	−	0.103136i
$829$	31.7488			1.10268			0.551341	−	0.834280i	$-0.314116\pi$
$829$	31.7488			1.10268			0.551341	+	0.834280i	$0.314116\pi$
$830$	−10.1466	−	36.7928i	−0.352193	−	1.27710i
$831$	−5.43796	+	9.41882i	−0.188641	+	0.326735i
$832$	0.519209	−	0.299765i	0.0180003	−	0.0103925i
$833$		−	13.4007i		−	0.464306i
$834$	−3.64455	+	6.31254i	−0.126200	+	0.218585i
$835$	20.9771	+	20.6735i	0.725942	+	0.715436i
$836$	−3.59861			−0.124460
$837$	−1.25472	+	5.42454i	−0.0433696	+	0.187500i
$838$		−	39.9208i		−	1.37904i
$839$	44.3158			1.52995			0.764975	−	0.644060i	$-0.222751\pi$
$839$	44.3158			1.52995			0.764975	+	0.644060i	$0.222751\pi$
$840$	1.89049	−	0.521352i	0.0652280	−	0.0179884i
$841$	−26.7045			−0.920845
$842$	−25.7180	+	14.8483i	−0.886301	+	0.511706i
$843$	2.15180	+	1.24234i	0.0741120	+	0.0427886i
$844$	−12.4999	+	21.6504i	−0.430263	+	0.745238i
$845$	19.8403	−	20.1316i	0.682526	−	0.692549i
$846$	3.33150	+	5.77032i	0.114539	+	0.198388i
$847$	2.93035	−	1.69184i	0.100688	−	0.0581323i
$848$	−0.455910	+	0.263220i	−0.0156560	+	0.00903901i
$849$	9.67079	−	16.7503i	0.331901	−	0.574869i
$850$	9.23344	−	5.51193i	0.316704	−	0.189058i
$851$	−32.6942	+	56.6280i	−1.12074	+	1.94118i
$852$		−	15.1420i		−	0.518758i
$853$			24.6295i			0.843299i	0.906759	+	0.421650i	$0.138549\pi$
$853$			24.6295i			0.843299i	−0.906759	+	0.421650i	$0.861451\pi$
$854$	1.05476	−	1.82690i	0.0360932	−	0.0625153i
$855$	−2.91404	−	0.758093i	−0.0996579	−	0.0259262i
$856$	6.88226	−	11.9204i	0.235231	−	0.407432i
$857$	5.96837	−	3.44584i	0.203876	−	0.117708i	−0.394586	−	0.918859i	$-0.629112\pi$
$857$	5.96837	−	3.44584i	0.203876	−	0.117708i	0.598462	+	0.801151i	$0.295779\pi$
$858$	−1.38754	+	0.801098i	−0.0473699	+	0.0273490i
$859$	13.4278	+	23.2577i	0.458151	+	0.793541i	0.998863	−	0.0476668i	$-0.0151786\pi$
$859$	13.4278	+	23.2577i	0.458151	+	0.793541i	−0.540712	+	0.841208i	$0.681845\pi$
$860$	11.6523	+	11.4837i	0.397340	+	0.391589i
$861$	3.19940	−	5.54152i	0.109035	−	0.188855i
$862$	−21.3065	−	12.3013i	−0.725703	−	0.418985i
$863$	−8.59725	+	4.96363i	−0.292654	+	0.168964i	−0.639138	−	0.769092i	$-0.720709\pi$
$863$	−8.59725	+	4.96363i	−0.292654	+	0.168964i	0.346484	+	0.938056i	$0.387375\pi$
$864$	1.00000			0.0340207
$865$	−48.6087	+	13.4051i	−1.65274	+	0.455789i
$866$	−27.2004			−0.924306
$867$		−	12.3745i		−	0.420260i
$868$	−3.56981	−	3.33167i	−0.121167	−	0.113084i
$869$	−16.4834			−0.559162
$870$	2.37804	−	2.41296i	0.0806232	−	0.0818072i
$871$	−1.33361	+	2.30987i	−0.0451875	+	0.0782670i
$872$		−	9.36691i		−	0.317204i
$873$	1.80395	−	1.04151i	0.0610544	−	0.0352498i
$874$	3.99628	−	6.92176i	0.135176	−	0.234132i
$875$	−2.74427	−	9.41343i	−0.0927733	−	0.318232i
$876$	−1.54833			−0.0523134
$877$	−1.16758	+	0.674102i	−0.0394263	+	0.0227628i	−0.519584	−	0.854420i	$-0.673913\pi$
$877$	−1.16758	+	0.674102i	−0.0394263	+	0.0227628i	0.480157	+	0.877182i	$0.340580\pi$
$878$	−19.6357	+	11.3367i	−0.662671	+	0.382594i
$879$	−1.53165	−	2.65290i	−0.0516614	−	0.0894802i
$880$	−1.58866	−	5.76066i	−0.0535536	−	0.194192i
$881$	−23.8662	−	41.3374i	−0.804071	−	1.39269i	−0.916916	−	0.399080i	$-0.869330\pi$
$881$	−23.8662	−	41.3374i	−0.804071	−	1.39269i	0.112845	−	0.993613i	$-0.464004\pi$
$882$	−5.39608	−	3.11543i	−0.181695	−	0.104902i
$883$		−	40.3342i		−	1.35735i	−0.734437	−	0.678677i	$-0.762553\pi$
$883$		−	40.3342i		−	1.35735i	0.734437	−	0.678677i	$-0.237447\pi$
$884$	1.28941			0.0433676
$885$	−17.1214	+	4.72168i	−0.575529	+	0.158717i
$886$	−12.9698	−	22.4644i	−0.435730	−	0.754706i
$887$	−17.7783	−	10.2643i	−0.596935	−	0.344641i	0.170900	−	0.985288i	$-0.445333\pi$
$887$	−17.7783	−	10.2643i	−0.596935	−	0.344641i	−0.767835	+	0.640648i	$0.778666\pi$
$888$	−9.54061	+	5.50827i	−0.320162	+	0.184846i
$889$	5.34064	+	9.25026i	0.179119	+	0.310244i
$890$	3.12346	−	12.0063i	0.104698	−	0.402451i
$891$	−2.67242			−0.0895293
$892$	2.44055	+	1.40905i	0.0817157	+	0.0471786i
$893$	7.77017	+	4.48611i	0.260019	+	0.150122i
$894$	−1.92438	−	3.33313i	−0.0643610	−	0.111477i
$895$	−3.32372	+	3.37253i	−0.111100	+	0.112731i
$896$	−0.438506	+	0.759514i	−0.0146494	+	0.0253736i
$897$		−	3.55850i		−	0.118815i
$898$			29.7946i			0.994259i
$899$	−8.21867	−	1.90102i	−0.274108	−	0.0634026i
$900$	−0.0728857	−	4.99947i	−0.00242952	−	0.166649i
$901$	−1.13221			−0.0377195
$902$	−16.8861	−	9.74917i	−0.562244	−	0.324612i
$903$			6.41658i			0.213531i
$904$	−5.41717	−	9.38282i	−0.180172	−	0.312068i
$905$	−5.21798	−	18.9210i	−0.173452	−	0.628956i
$906$	−4.61165	+	7.98761i	−0.153212	+	0.265371i
$907$			46.1232i			1.53150i	0.643141	+	0.765748i	$0.277631\pi$
$907$			46.1232i			1.53150i	−0.643141	+	0.765748i	$0.722369\pi$
$908$	9.39580	−	5.42467i	0.311810	−	0.180024i
$909$	1.23249	+	2.13474i	0.0408792	+	0.0708049i
$910$	0.296012	−	1.13784i	0.00981269	−	0.0377190i
$911$	16.3813	−	28.3733i	0.542737	−	0.940048i	−0.456008	−	0.889975i	$-0.650721\pi$
$911$	16.3813	−	28.3733i	0.542737	−	0.940048i	0.998746	−	0.0500729i	$-0.0159454\pi$
$912$	1.16617	−	0.673287i	0.0386157	−	0.0222948i
$913$	−39.5029	−	22.8070i	−1.30736	−	0.754802i
$914$	21.8147			0.721567
$915$	−3.83082	−	3.77538i	−0.126643	−	0.124810i
$916$	0.964039	−	1.66976i	0.0318527	−	0.0551706i
$917$	13.1506	−	7.59252i	0.434272	−	0.250727i
$918$	1.86256	+	1.07535i	0.0614737	+	0.0354918i
$919$	5.10293	+	8.83854i	0.168330	+	0.291556i	0.937833	−	0.347087i	$-0.112829\pi$
$919$	5.10293	+	8.83854i	0.168330	+	0.291556i	−0.769503	+	0.638644i	$0.779496\pi$
$920$	12.8446	+	3.34155i	0.423473	+	0.110167i
$921$	−7.55815	−	13.0911i	−0.249050	−	0.431366i
$922$		−	30.4071i		−	1.00140i
$923$	−7.86188	−	4.53906i	−0.258777	−	0.149405i
$924$	1.17187	−	2.02974i	0.0385517	−	0.0667735i
$925$	28.2338	+	47.2965i	0.928322	+	1.55510i
$926$	−16.0722			−0.528165
$927$	4.33292	+	2.50161i	0.142312	+	0.0821638i
$928$			1.51509i			0.0497353i
$929$	−1.03028			−0.0338025			−0.0169012	−	0.999857i	$-0.505380\pi$
$929$	−1.03028			−0.0338025			−0.0169012	+	0.999857i	$0.505380\pi$
$930$	−10.5125	+	6.66986i	−0.344719	+	0.218713i
$931$	−8.39030			−0.274981
$932$		−	9.56183i		−	0.313208i
$933$	−8.84710	−	5.10787i	−0.289641	−	0.167224i
$934$	31.7383			1.03851
$935$	3.23576	−	12.4379i	0.105821	−	0.406764i
$936$	0.299765	−	0.519209i	0.00979814	−	0.0169709i
$937$	−39.9284	−	23.0527i	−1.30441	−	0.753099i	−0.323249	−	0.946314i	$-0.604775\pi$
$937$	−39.9284	−	23.0527i	−1.30441	−	0.753099i	−0.981156	+	0.193215i	$0.938108\pi$
$938$		−	3.90168i		−	0.127394i
$939$	−2.62369	−	4.54437i	−0.0856209	−	0.148300i
$940$	−3.75112	+	14.4190i	−0.122348	+	0.470295i
$941$	3.00405	+	5.20318i	0.0979294	+	0.169619i	0.910827	−	0.412787i	$-0.135445\pi$
$941$	3.00405	+	5.20318i	0.0979294	+	0.169619i	−0.812898	+	0.582406i	$0.802111\pi$
$942$	4.78045	+	2.75999i	0.155755	+	0.0899254i
$943$	37.5042	−	21.6530i	1.22130	−	0.705120i
$944$	3.97137	−	6.87861i	0.129257	−	0.223880i
$945$	1.37653	−	1.39675i	0.0447786	−	0.0454362i
$946$	19.5525			0.635707
$947$	2.11532	+	1.22128i	0.0687387	+	0.0396863i	0.533975	−	0.845500i	$-0.320697\pi$
$947$	2.11532	+	1.22128i	0.0687387	+	0.0396863i	−0.465237	+	0.885186i	$0.654031\pi$
$948$	5.34163	−	3.08399i	0.173488	−	0.100163i
$949$	−0.464137	+	0.803909i	−0.0150665	+	0.0260960i
$950$	−3.45107	−	5.78114i	−0.111968	−	0.187565i
$951$	−5.74146	−	9.94450i	−0.186180	−	0.322472i
$952$	−1.63349	+	0.943094i	−0.0529416	+	0.0305659i
$953$			53.0968i			1.71997i	0.510316	+	0.859987i	$0.329529\pi$
$953$			53.0968i			1.71997i	−0.510316	+	0.859987i	$0.670471\pi$
$954$	−0.263220	+	0.455910i	−0.00852206	+	0.0147606i
$955$	−4.53842	−	16.4569i	−0.146860	−	0.532532i
$956$	3.66276	+	6.34409i	0.118462	+	0.205183i
$957$		−	4.04895i		−	0.130884i
$958$	4.95133	+	2.85865i	0.159970	+	0.0923589i
$959$	−1.70396			−0.0550238
$960$	1.59262	+	1.56957i	0.0514016	+	0.0506577i
$961$	27.8513	+	13.6126i	0.898430	+	0.439117i
$962$			6.60476i			0.212946i
$963$		−	13.7645i		−	0.443555i
$964$	6.48181	−	11.2268i	0.208765	−	0.361591i
$965$	28.5122	+	28.0995i	0.917839	+	0.904556i
$966$	2.60274	+	4.50808i	0.0837417	+	0.145045i
$967$	−37.3413	−	21.5590i	−1.20082	−	0.693292i	−0.240079	−	0.970753i	$-0.577173\pi$
$967$	−37.3413	−	21.5590i	−1.20082	−	0.693292i	−0.960737	+	0.277462i	$0.910507\pi$
$968$	3.34129	+	1.92910i	0.107393	+	0.0620035i
$969$	2.89608			0.0930354
$970$	4.50773	+	1.17270i	0.144735	+	0.0376530i
$971$	3.55058	+	6.14979i	0.113944	+	0.197356i	0.917357	−	0.398066i	$-0.130318\pi$
$971$	3.55058	+	6.14979i	0.113944	+	0.197356i	−0.803413	+	0.595422i	$0.796985\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−5.53617	−	3.19631i	−0.177481	−	0.102469i
$974$	−11.7899	−	20.4207i	−0.377773	−	0.654323i
$975$	−2.61762	−	1.46082i	−0.0838308	−	0.0467838i
$976$	2.40535			0.0769935
$977$		−	55.6044i		−	1.77894i	−0.456992	−	0.889471i	$-0.651073\pi$
$977$		−	55.6044i		−	1.77894i	0.456992	−	0.889471i	$-0.348927\pi$
$978$	−11.1527	−	6.43900i	−0.356623	−	0.205897i
$979$	−7.41340	−	12.8404i	−0.236933	−	0.410381i
$980$	−3.70402	−	13.4312i	−0.118321	−	0.429045i
$981$	−4.68346	−	8.11199i	−0.149531	−	0.258996i
$982$	24.5925	−	14.1985i	0.784777	−	0.453091i
$983$	30.8200	−	17.7939i	0.983006	−	0.567539i	0.0798294	−	0.996809i	$-0.474562\pi$
$983$	30.8200	−	17.7939i	0.983006	−	0.567539i	0.903176	+	0.429270i	$0.141229\pi$
$984$	7.29614			0.232593
$985$	20.1677	−	5.56179i	0.642597	−	0.177213i
$986$	−1.62925	+	2.82195i	−0.0518859	+	0.0898691i
$987$	−5.06064	+	2.92176i	−0.161082	+	0.0930007i
$988$		−	0.807313i		−	0.0256840i
$989$	−21.7132	+	37.6084i	−0.690440	+	1.19588i
$990$	−4.25615	−	4.19455i	−0.135269	−	0.133312i
$991$	−50.2480			−1.59618			−0.798089	−	0.602539i	$-0.794156\pi$
$991$	−50.2480			−1.59618			−0.798089	+	0.602539i	$0.794156\pi$
$992$	1.25472	−	5.42454i	0.0398375	−	0.172229i
$993$			21.8281i			0.692694i
$994$	13.2797			0.421208
$995$	−3.88180	−	14.0759i	−0.123061	−	0.446235i
$996$	17.0685			0.540835
$997$	35.0819	−	20.2545i	1.11106	−	0.641468i	0.171953	−	0.985105i	$-0.444992\pi$
$997$	35.0819	−	20.2545i	1.11106	−	0.641468i	0.939102	+	0.343637i	$0.111659\pi$
$998$	−25.4084	−	14.6696i	−0.804290	−	0.464357i
$999$	−5.50827	+	9.54061i	−0.174274	+	0.301852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.d.439.1	✓	28
5.4	even	2	inner	930.2.s.d.439.11	yes	28
31.25	even	3	inner	930.2.s.d.769.4	yes	28
155.149	even	6	inner	930.2.s.d.769.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.d.439.1	✓	28	1.1	even	1	trivial
930.2.s.d.439.11	yes	28	5.4	even	2	inner
930.2.s.d.769.4	yes	28	31.25	even	3	inner
930.2.s.d.769.8	yes	28	155.149	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.16404 - 0.562979i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.759514 + 0.438506i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.16404 - 0.562979i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.759514 + 0.438506i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.562979 + 2.16404i) q^{10} +(1.33621 + 2.31438i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.519209 + 0.299765i) q^{13} +(0.438506 - 0.759514i) q^{14} +(-1.59262 - 1.56957i) q^{15} +1.00000 q^{16} +(1.86256 + 1.07535i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.673287 - 1.16617i) q^{19} +(2.16404 + 0.562979i) q^{20} +(0.438506 + 0.759514i) q^{21} +(2.31438 - 1.33621i) q^{22} +5.93547i q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.36611 + 2.43661i) q^{25} +(0.299765 + 0.519209i) q^{26} +1.00000i q^{27} +(-0.759514 - 0.438506i) q^{28} -1.51509 q^{29} +(-1.56957 + 1.59262i) q^{30} +(5.42454 + 1.25472i) q^{31} -1.00000i q^{32} +2.67242i q^{33} +(1.07535 - 1.86256i) q^{34} +(-1.39675 - 1.37653i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(9.54061 + 5.50827i) q^{37} +(-1.16617 - 0.673287i) q^{38} -0.599531 q^{39} +(0.562979 - 2.16404i) q^{40} +(-3.64807 - 6.31865i) q^{41} +(0.759514 - 0.438506i) q^{42} +(6.33621 + 3.65821i) q^{43} +(-1.33621 - 2.31438i) q^{44} +(-0.594464 - 2.15560i) q^{45} +5.93547 q^{46} +6.66299i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.11543 - 5.39608i) q^{49} +(2.43661 - 4.36611i) q^{50} +(1.07535 + 1.86256i) q^{51} +(0.519209 - 0.299765i) q^{52} +(-0.455910 + 0.263220i) q^{53} +1.00000 q^{54} +(-1.58866 - 5.76066i) q^{55} +(-0.438506 + 0.759514i) q^{56} +(1.16617 - 0.673287i) q^{57} +1.51509i q^{58} +(3.97137 - 6.87861i) q^{59} +(1.59262 + 1.56957i) q^{60} +2.40535 q^{61} +(1.25472 - 5.42454i) q^{62} +0.877011i q^{63} -1.00000 q^{64} +(1.29235 - 0.356400i) q^{65} +2.67242 q^{66} +(3.85280 - 2.22442i) q^{67} +(-1.86256 - 1.07535i) q^{68} +(-2.96774 + 5.14027i) q^{69} +(-1.37653 + 1.39675i) q^{70} +(7.57102 + 13.1134i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(1.34090 - 0.774167i) q^{73} +(5.50827 - 9.54061i) q^{74} +(2.56286 + 4.29322i) q^{75} +(-0.673287 + 1.16617i) q^{76} +2.34374i q^{77} +0.599531i q^{78} +(-3.08399 + 5.34163i) q^{79} +(-2.16404 - 0.562979i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.31865 + 3.64807i) q^{82} +(-14.7817 + 8.53423i) q^{83} +(-0.438506 - 0.759514i) q^{84} +(-3.42525 - 3.37568i) q^{85} +(3.65821 - 6.33621i) q^{86} +(-1.31211 - 0.757545i) q^{87} +(-2.31438 + 1.33621i) q^{88} -5.54809 q^{89} +(-2.15560 + 0.594464i) q^{90} -0.525795 q^{91} -5.93547i q^{92} +(4.07043 + 3.79889i) q^{93} +6.66299 q^{94} +(-2.11355 + 2.14458i) q^{95} +(0.500000 - 0.866025i) q^{96} -2.08302i q^{97} +(-5.39608 + 3.11543i) q^{98} +(-1.33621 + 2.31438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Introduction

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