LMFDB - Embedded newform 930.2.j.g.497.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.11
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.56986 + 0.731811i) q^{3} -1.00000i q^{4} +(1.45516 - 1.69779i) q^{5} +(-0.592589 + 1.62753i) q^{6} +(1.76311 + 1.76311i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.92891 - 2.29768i) q^{9} +(-0.171568 - 2.22948i) q^{10} +5.31589i q^{11} +(0.731811 + 1.56986i) q^{12} +(3.35958 - 3.35958i) q^{13} +2.49342 q^{14} +(-1.04193 + 3.73020i) q^{15} -1.00000 q^{16} +(-2.77112 + 2.77112i) q^{17} +(-0.260761 - 2.98865i) q^{18} -1.86557i q^{19} +(-1.69779 - 1.45516i) q^{20} +(-4.05810 - 1.47757i) q^{21} +(3.75890 + 3.75890i) q^{22} +(3.75550 + 3.75550i) q^{23} +(1.62753 + 0.592589i) q^{24} +(-0.765014 - 4.94113i) q^{25} -4.75116i q^{26} +(-1.34664 + 5.01862i) q^{27} +(1.76311 - 1.76311i) q^{28} +3.62239 q^{29} +(1.90089 + 3.37441i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.89023 - 8.34519i) q^{33} +3.91895i q^{34} +(5.55901 - 0.427791i) q^{35} +(-2.29768 - 1.92891i) q^{36} +(1.42681 + 1.42681i) q^{37} +(-1.31916 - 1.31916i) q^{38} +(-2.81548 + 7.73263i) q^{39} +(-2.22948 + 0.171568i) q^{40} -6.12646i q^{41} +(-3.91431 + 1.82471i) q^{42} +(6.90667 - 6.90667i) q^{43} +5.31589 q^{44} +(-1.09412 - 6.61838i) q^{45} +5.31107 q^{46} +(5.33412 - 5.33412i) q^{47} +(1.56986 - 0.731811i) q^{48} -0.782871i q^{49} +(-4.03485 - 2.95296i) q^{50} +(2.32233 - 6.37819i) q^{51} +(-3.35958 - 3.35958i) q^{52} +(7.93890 + 7.93890i) q^{53} +(2.59648 + 4.50092i) q^{54} +(9.02529 + 7.73548i) q^{55} -2.49342i q^{56} +(1.36525 + 2.92869i) q^{57} +(2.56141 - 2.56141i) q^{58} -8.98420 q^{59} +(3.73020 + 1.04193i) q^{60} -3.54388 q^{61} +(0.707107 - 0.707107i) q^{62} +(7.45194 - 0.650185i) q^{63} +1.00000i q^{64} +(-0.815147 - 10.5926i) q^{65} +(-8.65175 - 3.15014i) q^{66} +(3.66547 + 3.66547i) q^{67} +(2.77112 + 2.77112i) q^{68} +(-8.64390 - 3.14728i) q^{69} +(3.62832 - 4.23331i) q^{70} +8.57648i q^{71} +(-2.98865 + 0.260761i) q^{72} +(0.0629195 - 0.0629195i) q^{73} +2.01781 q^{74} +(4.81693 + 7.19702i) q^{75} -1.86557 q^{76} +(-9.37251 + 9.37251i) q^{77} +(3.47695 + 7.45864i) q^{78} -13.3800i q^{79} +(-1.45516 + 1.69779i) q^{80} +(-1.55864 - 8.86401i) q^{81} +(-4.33206 - 4.33206i) q^{82} +(-4.31021 - 4.31021i) q^{83} +(-1.47757 + 4.05810i) q^{84} +(0.672367 + 8.73721i) q^{85} -9.76750i q^{86} +(-5.68663 + 2.65090i) q^{87} +(3.75890 - 3.75890i) q^{88} +5.00586 q^{89} +(-5.45356 - 3.90624i) q^{90} +11.8466 q^{91} +(3.75550 - 3.75550i) q^{92} +(-1.56986 + 0.731811i) q^{93} -7.54358i q^{94} +(-3.16736 - 2.71471i) q^{95} +(0.592589 - 1.62753i) q^{96} +(7.70070 + 7.70070i) q^{97} +(-0.553574 - 0.553574i) q^{98} +(12.2142 + 10.2539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Character values

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

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

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.56986	+	0.731811i	−0.906358	+	0.422511i
$3$	−1.56986	+	0.731811i	−0.906358	+	0.422511i
$4$		−	1.00000i		−	0.500000i
$5$	1.45516	−	1.69779i	0.650768	−	0.759277i
$5$	1.45516	−	1.69779i	0.650768	−	0.759277i
$6$	−0.592589	+	1.62753i	−0.241923	+	0.664434i
$7$	1.76311	+	1.76311i	0.666394	+	0.666394i	0.956879	−	0.290486i	$-0.0938168\pi$
$7$	1.76311	+	1.76311i	0.666394	+	0.666394i	−0.290486	+	0.956879i	$0.593817\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.92891	−	2.29768i	0.642969	−	0.765892i
$10$	−0.171568	−	2.22948i	−0.0542546	−	0.705022i
$11$			5.31589i			1.60280i	0.598128	+	0.801401i	$0.295912\pi$
$11$			5.31589i			1.60280i	−0.598128	+	0.801401i	$0.704088\pi$
$12$	0.731811	+	1.56986i	0.211256	+	0.453179i
$13$	3.35958	−	3.35958i	0.931779	−	0.931779i	−0.0660382	−	0.997817i	$-0.521036\pi$
$13$	3.35958	−	3.35958i	0.931779	−	0.931779i	0.997817	+	0.0660382i	$0.0210359\pi$
$14$	2.49342			0.666394
$15$	−1.04193	+	3.73020i	−0.269025	+	0.963133i
$16$	−1.00000			−0.250000
$17$	−2.77112	+	2.77112i	−0.672095	+	0.672095i	−0.958199	−	0.286104i	$-0.907640\pi$
$17$	−2.77112	+	2.77112i	−0.672095	+	0.672095i	0.286104	+	0.958199i	$0.407640\pi$
$18$	−0.260761	−	2.98865i	−0.0614619	−	0.704431i
$19$		−	1.86557i		−	0.427992i	−0.976835	−	0.213996i	$-0.931352\pi$
$19$		−	1.86557i		−	0.427992i	0.976835	−	0.213996i	$-0.0686480\pi$
$20$	−1.69779	−	1.45516i	−0.379638	−	0.325384i
$21$	−4.05810	−	1.47757i	−0.885550	−	0.322432i
$22$	3.75890	+	3.75890i	0.801401	+	0.801401i
$23$	3.75550	+	3.75550i	0.783075	+	0.783075i	0.980348	−	0.197274i	$-0.0632087\pi$
$23$	3.75550	+	3.75550i	0.783075	+	0.783075i	−0.197274	+	0.980348i	$0.563209\pi$
$24$	1.62753	+	0.592589i	0.332217	+	0.120962i
$25$	−0.765014	−	4.94113i	−0.153003	−	0.988226i
$26$		−	4.75116i		−	0.931779i
$27$	−1.34664	+	5.01862i	−0.259162	+	0.965834i
$28$	1.76311	−	1.76311i	0.333197	−	0.333197i
$29$	3.62239			0.672660			0.336330	−	0.941744i	$-0.390814\pi$
$29$	3.62239			0.672660			0.336330	+	0.941744i	$0.390814\pi$
$30$	1.90089	+	3.37441i	0.347054	+	0.616079i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.89023	−	8.34519i	−0.677201	−	1.45271i
$34$			3.91895i			0.672095i
$35$	5.55901	−	0.427791i	0.939645	−	0.0723098i
$36$	−2.29768	−	1.92891i	−0.382946	−	0.321484i
$37$	1.42681	+	1.42681i	0.234566	+	0.234566i	0.814596	−	0.580029i	$-0.196959\pi$
$37$	1.42681	+	1.42681i	0.234566	+	0.234566i	−0.580029	+	0.814596i	$0.696959\pi$
$38$	−1.31916	−	1.31916i	−0.213996	−	0.213996i
$39$	−2.81548	+	7.73263i	−0.450838	+	1.23821i
$40$	−2.22948	+	0.171568i	−0.352511	+	0.0271273i
$41$		−	6.12646i		−	0.956792i	−0.878144	−	0.478396i	$-0.841218\pi$
$41$		−	6.12646i		−	0.956792i	0.878144	−	0.478396i	$-0.158782\pi$
$42$	−3.91431	+	1.82471i	−0.603991	+	0.281559i
$43$	6.90667	−	6.90667i	1.05326	−	1.05326i	0.0547572	−	0.998500i	$-0.482562\pi$
$43$	6.90667	−	6.90667i	1.05326	−	1.05326i	0.998500	−	0.0547572i	$-0.0174385\pi$
$44$	5.31589			0.801401
$45$	−1.09412	−	6.61838i	−0.163101	−	0.986609i
$46$	5.31107			0.783075
$47$	5.33412	−	5.33412i	0.778061	−	0.778061i	−0.201440	−	0.979501i	$-0.564562\pi$
$47$	5.33412	−	5.33412i	0.778061	−	0.778061i	0.979501	+	0.201440i	$0.0645620\pi$
$48$	1.56986	−	0.731811i	0.226589	−	0.105628i
$49$		−	0.782871i		−	0.111839i
$50$	−4.03485	−	2.95296i	−0.570614	−	0.417612i
$51$	2.32233	−	6.37819i	0.325191	−	0.893126i
$52$	−3.35958	−	3.35958i	−0.465889	−	0.465889i
$53$	7.93890	+	7.93890i	1.09049	+	1.09049i	0.995476	+	0.0950167i	$0.0302904\pi$
$53$	7.93890	+	7.93890i	1.09049	+	1.09049i	0.0950167	+	0.995476i	$0.469710\pi$
$54$	2.59648	+	4.50092i	0.353336	+	0.612498i
$55$	9.02529	+	7.73548i	1.21697	+	1.04305i
$56$		−	2.49342i		−	0.333197i
$57$	1.36525	+	2.92869i	0.180831	+	0.387914i
$58$	2.56141	−	2.56141i	0.336330	−	0.336330i
$59$	−8.98420			−1.16964			−0.584821	−	0.811162i	$-0.698835\pi$
$59$	−8.98420			−1.16964			−0.584821	+	0.811162i	$0.698835\pi$
$60$	3.73020	+	1.04193i	0.481567	+	0.134513i
$61$	−3.54388			−0.453748			−0.226874	−	0.973924i	$-0.572850\pi$
$61$	−3.54388			−0.453748			−0.226874	+	0.973924i	$0.572850\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	7.45194	−	0.650185i	0.938856	−	0.0819156i
$64$			1.00000i			0.125000i
$65$	−0.815147	−	10.5926i	−0.101107	−	1.31385i
$66$	−8.65175	−	3.15014i	−1.06496	−	0.387755i
$67$	3.66547	+	3.66547i	0.447809	+	0.447809i	0.894625	−	0.446817i	$-0.147442\pi$
$67$	3.66547	+	3.66547i	0.447809	+	0.447809i	−0.446817	+	0.894625i	$0.647442\pi$
$68$	2.77112	+	2.77112i	0.336047	+	0.336047i
$69$	−8.64390	−	3.14728i	−1.04060	−	0.378888i
$70$	3.62832	−	4.23331i	0.433668	−	0.505977i
$71$			8.57648i			1.01784i	0.860814	+	0.508920i	$0.169955\pi$
$71$			8.57648i			1.01784i	−0.860814	+	0.508920i	$0.830045\pi$
$72$	−2.98865	+	0.260761i	−0.352215	+	0.0307309i
$73$	0.0629195	−	0.0629195i	0.00736417	−	0.00736417i	−0.703415	−	0.710779i	$-0.748342\pi$
$73$	0.0629195	−	0.0629195i	0.00736417	−	0.00736417i	0.710779	+	0.703415i	$0.248342\pi$
$74$	2.01781			0.234566
$75$	4.81693	+	7.19702i	0.556212	+	0.831041i
$76$	−1.86557			−0.213996
$77$	−9.37251	+	9.37251i	−1.06810	+	1.06810i
$78$	3.47695	+	7.45864i	0.393687	+	0.844525i
$79$		−	13.3800i		−	1.50536i	−0.658385	−	0.752682i	$-0.728760\pi$
$79$		−	13.3800i		−	1.50536i	0.658385	−	0.752682i	$-0.271240\pi$
$80$	−1.45516	+	1.69779i	−0.162692	+	0.189819i
$81$	−1.55864	−	8.86401i	−0.173182	−	0.984890i
$82$	−4.33206	−	4.33206i	−0.478396	−	0.478396i
$83$	−4.31021	−	4.31021i	−0.473107	−	0.473107i	0.429812	−	0.902919i	$-0.358580\pi$
$83$	−4.31021	−	4.31021i	−0.473107	−	0.473107i	−0.902919	+	0.429812i	$0.858580\pi$
$84$	−1.47757	+	4.05810i	−0.161216	+	0.442775i
$85$	0.672367	+	8.73721i	0.0729284	+	0.947683i
$86$		−	9.76750i		−	1.05326i
$87$	−5.68663	+	2.65090i	−0.609671	+	0.284207i
$88$	3.75890	−	3.75890i	0.400700	−	0.400700i
$89$	5.00586			0.530620			0.265310	−	0.964163i	$-0.414526\pi$
$89$	5.00586			0.530620			0.265310	+	0.964163i	$0.414526\pi$
$90$	−5.45356	−	3.90624i	−0.574855	−	0.411754i
$91$	11.8466			1.24186
$92$	3.75550	−	3.75550i	0.391537	−	0.391537i
$93$	−1.56986	+	0.731811i	−0.162787	+	0.0758852i
$94$		−	7.54358i		−	0.778061i
$95$	−3.16736	−	2.71471i	−0.324965	−	0.278523i
$96$	0.592589	−	1.62753i	0.0604808	−	0.166109i
$97$	7.70070	+	7.70070i	0.781888	+	0.781888i	0.980149	−	0.198261i	$-0.0635294\pi$
$97$	7.70070	+	7.70070i	0.781888	+	0.781888i	−0.198261	+	0.980149i	$0.563529\pi$
$98$	−0.553574	−	0.553574i	−0.0559194	−	0.0559194i
$99$	12.2142	+	10.2539i	1.22757	+	1.03055i
$100$	−4.94113	+	0.765014i	−0.494113	+	0.0765014i
$101$		−	6.10793i		−	0.607762i	−0.952710	−	0.303881i	$-0.901717\pi$
$101$		−	6.10793i		−	0.607762i	0.952710	−	0.303881i	$-0.0982825\pi$
$102$	−2.86793	−	6.15220i	−0.283967	−	0.609158i
$103$	−7.86523	+	7.86523i	−0.774984	+	0.774984i	−0.978973	−	0.203989i	$-0.934609\pi$
$103$	−7.86523	+	7.86523i	−0.774984	+	0.774984i	0.203989	+	0.978973i	$0.434609\pi$
$104$	−4.75116			−0.465889
$105$	−8.41380	+	4.73972i	−0.821103	+	0.462549i
$106$	11.2273			1.09049
$107$	−2.79803	+	2.79803i	−0.270496	+	0.270496i	−0.829300	−	0.558804i	$-0.811260\pi$
$107$	−2.79803	+	2.79803i	−0.270496	+	0.270496i	0.558804	+	0.829300i	$0.311260\pi$
$108$	5.01862	+	1.34664i	0.482917	+	0.129581i
$109$			5.73010i			0.548844i	0.961609	+	0.274422i	$0.0884865\pi$
$109$			5.73010i			0.548844i	−0.961609	+	0.274422i	$0.911513\pi$
$110$	11.8517	−	0.912037i	1.13001	−	0.0869593i
$111$	−3.28404	−	1.19573i	−0.311708	−	0.113494i
$112$	−1.76311	−	1.76311i	−0.166598	−	0.166598i
$113$	0.541653	+	0.541653i	0.0509544	+	0.0509544i	0.732125	−	0.681170i	$-0.238529\pi$
$113$	0.541653	+	0.541653i	0.0509544	+	0.0509544i	−0.681170	+	0.732125i	$0.738529\pi$
$114$	3.03627	+	1.10552i	0.284373	+	0.103541i
$115$	11.8409	−	0.911210i	1.10417	−	0.0849708i
$116$		−	3.62239i		−	0.336330i
$117$	−1.23892	−	14.1995i	−0.114538	−	1.31275i
$118$	−6.35279	+	6.35279i	−0.584821	+	0.584821i
$119$	−9.77158			−0.895759
$120$	3.37441	−	1.90089i	0.308040	−	0.173527i
$121$	−17.2587			−1.56897
$122$	−2.50590	+	2.50590i	−0.226874	+	0.226874i
$123$	4.48341	+	9.61767i	0.404255	+	0.867196i
$124$		−	1.00000i		−	0.0898027i
$125$	−9.50224	−	5.89130i	−0.849906	−	0.526934i
$126$	4.80957	−	5.72907i	0.428470	−	0.510386i
$127$	−13.3408	−	13.3408i	−1.18380	−	1.18380i	−0.978751	−	0.205051i	$-0.934264\pi$
$127$	−13.3408	−	13.3408i	−1.18380	−	1.18380i	−0.205051	−	0.978751i	$-0.565736\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.78811	+	15.8969i	−0.509615	+	1.39964i
$130$	−8.06649	−	6.91370i	−0.707478	−	0.606372i
$131$			0.255148i			0.0222924i	0.999938	+	0.0111462i	$0.00354801\pi$
$131$			0.255148i			0.0222924i	−0.999938	+	0.0111462i	$0.996452\pi$
$132$	−8.34519	+	3.89023i	−0.726356	+	0.338601i
$133$	3.28922	−	3.28922i	0.285211	−	0.285211i
$134$	5.18376			0.447809
$135$	6.56100	+	9.58922i	0.564681	+	0.825309i
$136$	3.91895			0.336047
$137$	−7.91747	+	7.91747i	−0.676435	+	0.676435i	−0.959192	−	0.282756i	$-0.908751\pi$
$137$	−7.91747	+	7.91747i	−0.676435	+	0.676435i	0.282756	+	0.959192i	$0.408751\pi$
$138$	−8.33763	+	3.88670i	−0.709746	+	0.330858i
$139$			1.09893i			0.0932096i	0.998913	+	0.0466048i	$0.0148401\pi$
$139$			1.09893i			0.0932096i	−0.998913	+	0.0466048i	$0.985160\pi$
$140$	−0.427791	−	5.55901i	−0.0361549	−	0.469822i
$141$	−4.47024	+	12.2774i	−0.376462	+	1.03394i
$142$	6.06448	+	6.06448i	0.508920	+	0.508920i
$143$	17.8591	+	17.8591i	1.49346	+	1.49346i
$144$	−1.92891	+	2.29768i	−0.160742	+	0.191473i
$145$	5.27116	−	6.15007i	0.437746	−	0.510736i
$146$		−	0.0889817i		−	0.00736417i
$147$	0.572914	+	1.22900i	0.0472531	+	0.101366i
$148$	1.42681	−	1.42681i	0.117283	−	0.117283i
$149$	−16.7070			−1.36869			−0.684347	−	0.729156i	$-0.739913\pi$
$149$	−16.7070			−1.36869			−0.684347	+	0.729156i	$0.739913\pi$
$150$	8.49515	+	1.68298i	0.693626	+	0.137415i
$151$	−22.2992			−1.81469			−0.907343	−	0.420391i	$-0.861893\pi$
$151$	−22.2992			−1.81469			−0.907343	+	0.420391i	$0.861893\pi$
$152$	−1.31916	+	1.31916i	−0.106998	+	0.106998i
$153$	1.02191	+	11.7124i	0.0826164	+	0.946888i
$154$			13.2547i			1.06810i
$155$	1.45516	−	1.69779i	0.116881	−	0.136370i
$156$	7.73263	+	2.81548i	0.619106	+	0.225419i
$157$	13.3935	+	13.3935i	1.06892	+	1.06892i	0.997442	+	0.0714780i	$0.0227716\pi$
$157$	13.3935	+	13.3935i	1.06892	+	1.06892i	0.0714780	+	0.997442i	$0.477228\pi$
$158$	−9.46106	−	9.46106i	−0.752682	−	0.752682i
$159$	−18.2727	−	6.65317i	−1.44912	−	0.527631i
$160$	0.171568	+	2.22948i	0.0135636	+	0.176256i
$161$			13.2427i			1.04367i
$162$	−7.36993	−	5.16567i	−0.579036	−	0.405854i
$163$	−2.50082	+	2.50082i	−0.195880	+	0.195880i	−0.798231	−	0.602351i	$-0.794231\pi$
$163$	−2.50082	+	2.50082i	−0.195880	+	0.195880i	0.602351	+	0.798231i	$0.294231\pi$
$164$	−6.12646			−0.478396
$165$	−19.8293	−	5.53879i	−1.54371	−	0.431194i
$166$	−6.09556			−0.473107
$167$	−5.03410	+	5.03410i	−0.389551	+	0.389551i	−0.874527	−	0.484977i	$-0.838828\pi$
$167$	−5.03410	+	5.03410i	−0.389551	+	0.389551i	0.484977	+	0.874527i	$0.338828\pi$
$168$	1.82471	+	3.91431i	0.140779	+	0.301996i
$169$		−	9.57351i		−	0.736424i
$170$	6.65357	+	5.70270i	0.510306	+	0.437378i
$171$	−4.28649	−	3.59852i	−0.327796	−	0.275186i
$172$	−6.90667	−	6.90667i	−0.526628	−	0.526628i
$173$	3.30244	+	3.30244i	0.251080	+	0.251080i	0.821413	−	0.570334i	$-0.193186\pi$
$173$	3.30244	+	3.30244i	0.251080	+	0.251080i	−0.570334	+	0.821413i	$0.693186\pi$
$174$	−2.14659	+	5.89553i	−0.162732	+	0.446939i
$175$	7.36296	−	10.0606i	0.556587	−	0.760508i
$176$		−	5.31589i		−	0.400700i
$177$	14.1039	−	6.57473i	1.06011	−	0.494187i
$178$	3.53968	−	3.53968i	0.265310	−	0.265310i
$179$	−9.97200			−0.745342			−0.372671	−	0.927963i	$-0.621558\pi$
$179$	−9.97200			−0.745342			−0.372671	+	0.927963i	$0.621558\pi$
$180$	−6.61838	+	1.09412i	−0.493305	+	0.0815506i
$181$	−16.2713			−1.20944			−0.604718	−	0.796439i	$-0.706714\pi$
$181$	−16.2713			−1.20944			−0.604718	+	0.796439i	$0.706714\pi$
$182$	8.37683	−	8.37683i	0.620932	−	0.620932i
$183$	5.56339	−	2.59345i	0.411258	−	0.191713i
$184$		−	5.31107i		−	0.391537i
$185$	4.49867	−	0.346192i	0.330749	−	0.0254526i
$186$	−0.592589	+	1.62753i	−0.0434507	+	0.119336i
$187$	−14.7310	−	14.7310i	−1.07723	−	1.07723i
$188$	−5.33412	−	5.33412i	−0.389031	−	0.389031i
$189$	−11.2227	+	6.47411i	−0.816329	+	0.470922i
$190$	−4.15925	+	0.320073i	−0.301744	+	0.0232205i
$191$			14.4761i			1.04745i	0.851886	+	0.523727i	$0.175459\pi$
$191$			14.4761i			1.04745i	−0.851886	+	0.523727i	$0.824541\pi$
$192$	−0.731811	−	1.56986i	−0.0528139	−	0.113295i
$193$	6.75153	−	6.75153i	0.485985	−	0.485985i	−0.421051	−	0.907037i	$-0.638339\pi$
$193$	6.75153	−	6.75153i	0.485985	−	0.485985i	0.907037	+	0.421051i	$0.138339\pi$
$194$	10.8904			0.781888
$195$	9.03144	+	16.0323i	0.646755	+	1.14810i
$196$	−0.782871			−0.0559194
$197$	−14.0237	+	14.0237i	−0.999150	+	0.999150i	−1.00000		0.000850008i	$-0.999729\pi$
$197$	−14.0237	+	14.0237i	−0.999150	+	0.999150i	0.000850008		1.00000i	$0.499729\pi$
$198$	15.8873	−	1.38618i	1.12906	−	0.0985112i
$199$		−	11.1677i		−	0.791660i	−0.918324	−	0.395830i	$-0.870457\pi$
$199$		−	11.1677i		−	0.791660i	0.918324	−	0.395830i	$-0.129543\pi$
$200$	−2.95296	+	4.03485i	−0.208806	+	0.285307i
$201$	−8.43670	−	3.07184i	−0.595079	−	0.216671i
$202$	−4.31896	−	4.31896i	−0.303881	−	0.303881i
$203$	6.38668	+	6.38668i	0.448257	+	0.448257i
$204$	−6.37819	−	2.32233i	−0.446563	−	0.162595i
$205$	−10.4015	−	8.91498i	−0.726470	−	0.622650i
$206$			11.1231i			0.774984i
$207$	15.8729	−	1.38492i	1.10324	−	0.0962585i
$208$	−3.35958	+	3.35958i	−0.232945	+	0.232945i
$209$	9.91719			0.685986
$210$	−2.59797	+	9.30094i	−0.179277	+	0.641826i
$211$	−4.26926			−0.293908			−0.146954	−	0.989143i	$-0.546947\pi$
$211$	−4.26926			−0.293908			−0.146954	+	0.989143i	$0.546947\pi$
$212$	7.93890	−	7.93890i	0.545246	−	0.545246i
$213$	−6.27636	−	13.4638i	−0.430049	−	0.922527i
$214$			3.95701i			0.270496i
$215$	−1.67579	−	21.7764i	−0.114288	−	1.48514i
$216$	4.50092	−	2.59648i	0.306249	−	0.176668i
$217$	1.76311	+	1.76311i	0.119688	+	0.119688i
$218$	4.05179	+	4.05179i	0.274422	+	0.274422i
$219$	−0.0527295	+	0.144820i	−0.00356313	+	0.00978602i
$220$	7.73548	−	9.02529i	0.521526	−	0.608485i
$221$			18.6196i			1.25249i
$222$	−3.16768	+	1.47666i	−0.212601	+	0.0991068i
$223$	18.4359	−	18.4359i	1.23456	−	1.23456i	0.272365	−	0.962194i	$-0.412194\pi$
$223$	18.4359	−	18.4359i	1.23456	−	1.23456i	0.962194	−	0.272365i	$-0.0878057\pi$
$224$	−2.49342			−0.166598
$225$	−12.8288	−	7.77322i	−0.855251	−	0.518215i
$226$	0.766013			0.0509544
$227$	−6.34333	+	6.34333i	−0.421021	+	0.421021i	−0.885555	−	0.464534i	$-0.846222\pi$
$227$	−6.34333	+	6.34333i	−0.421021	+	0.421021i	0.464534	+	0.885555i	$0.346222\pi$
$228$	2.92869	−	1.36525i	0.193957	−	0.0904157i
$229$			11.9922i			0.792465i	0.918150	+	0.396232i	$0.129683\pi$
$229$			11.9922i			0.792465i	−0.918150	+	0.396232i	$0.870317\pi$
$230$	7.72846	−	9.01711i	0.509600	−	0.594571i
$231$	7.85461	−	21.5724i	0.516795	−	1.41936i
$232$	−2.56141	−	2.56141i	−0.168165	−	0.168165i
$233$	−13.0981	−	13.0981i	−0.858087	−	0.858087i	0.133026	−	0.991113i	$-0.457531\pi$
$233$	−13.0981	−	13.0981i	−0.858087	−	0.858087i	−0.991113	+	0.133026i	$0.957531\pi$
$234$	−10.9166	−	9.16454i	−0.713642	−	0.599105i
$235$	−1.29424	−	16.8182i	−0.0844267	−	1.09710i
$236$			8.98420i			0.584821i
$237$	9.79160	+	21.0046i	0.636033	+	1.36440i
$238$	−6.90955	+	6.90955i	−0.447880	+	0.447880i
$239$	13.8215			0.894036			0.447018	−	0.894525i	$-0.352486\pi$
$239$	13.8215			0.894036			0.447018	+	0.894525i	$0.352486\pi$
$240$	1.04193	−	3.73020i	0.0672564	−	0.240783i
$241$	−20.8975			−1.34613			−0.673063	−	0.739585i	$-0.735022\pi$
$241$	−20.8975			−1.34613			−0.673063	+	0.739585i	$0.735022\pi$
$242$	−12.2037	+	12.2037i	−0.784486	+	0.784486i
$243$	8.93362	+	12.7746i	0.573092	+	0.819491i
$244$			3.54388i			0.226874i
$245$	−1.32915	−	1.13920i	−0.0849166	−	0.0727811i
$246$	9.97097	+	3.63047i	0.635726	+	0.231470i
$247$	−6.26754	−	6.26754i	−0.398794	−	0.398794i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	9.92068	+	3.61216i	0.628697	+	0.228911i
$250$	−10.8849	+	2.55332i	−0.688420	+	0.161486i
$251$			8.88807i			0.561010i	0.959853	+	0.280505i	$0.0905019\pi$
$251$			8.88807i			0.561010i	−0.959853	+	0.280505i	$0.909498\pi$
$252$	−0.650185	−	7.45194i	−0.0409578	−	0.469428i
$253$	−19.9638	+	19.9638i	−1.25511	+	1.25511i
$254$	−18.8667			−1.18380
$255$	−7.44950	−	13.2241i	−0.466506	−	0.828127i
$256$	1.00000			0.0625000
$257$	11.3584	−	11.3584i	0.708519	−	0.708519i	−0.257704	−	0.966224i	$-0.582966\pi$
$257$	11.3584	−	11.3584i	0.708519	−	0.708519i	0.966224	+	0.257704i	$0.0829661\pi$
$258$	7.14796	+	15.3336i	0.445013	+	0.954628i
$259$			5.03125i			0.312627i
$260$	−10.5926	+	0.815147i	−0.656925	+	0.0505533i
$261$	6.98725	−	8.32308i	0.432500	−	0.515186i
$262$	0.180417	+	0.180417i	0.0111462	+	0.0111462i
$263$	22.8829	+	22.8829i	1.41102	+	1.41102i	0.752996	+	0.658025i	$0.228608\pi$
$263$	22.8829	+	22.8829i	1.41102	+	1.41102i	0.658025	+	0.752996i	$0.271392\pi$
$264$	−3.15014	+	8.65175i	−0.193878	+	0.532478i
$265$	25.0310	−	1.92625i	1.53764	−	0.118328i
$266$		−	4.65165i		−	0.285211i
$267$	−7.85849	+	3.66334i	−0.480932	+	0.224193i
$268$	3.66547	−	3.66547i	0.223904	−	0.223904i
$269$	−0.122472			−0.00746727			−0.00373364	−	0.999993i	$-0.501188\pi$
$269$	−0.122472			−0.00746727			−0.00373364	+	0.999993i	$0.501188\pi$
$270$	11.4199	+	2.14127i	0.694995	+	0.130314i
$271$	−18.0601			−1.09707			−0.548535	−	0.836127i	$-0.684814\pi$
$271$	−18.0601			−1.09707			−0.548535	+	0.836127i	$0.684814\pi$
$272$	2.77112	−	2.77112i	0.168024	−	0.168024i
$273$	−18.5975	+	8.66948i	−1.12557	+	0.524701i
$274$			11.1970i			0.676435i
$275$	26.2665	−	4.06673i	1.58393	−	0.245233i
$276$	−3.14728	+	8.64390i	−0.189444	+	0.520302i
$277$	18.5836	+	18.5836i	1.11658	+	1.11658i	0.992240	+	0.124338i	$0.0396808\pi$
$277$	18.5836	+	18.5836i	1.11658	+	1.11658i	0.124338	+	0.992240i	$0.460319\pi$
$278$	0.777057	+	0.777057i	0.0466048	+	0.0466048i
$279$	1.92891	−	2.29768i	0.115481	−	0.137558i
$280$	−4.23331	−	3.62832i	−0.252989	−	0.216834i
$281$		−	26.1152i		−	1.55790i	−0.627083	−	0.778952i	$-0.715751\pi$
$281$		−	26.1152i		−	1.55790i	0.627083	−	0.778952i	$-0.284249\pi$
$282$	5.52047	+	11.8423i	0.328739	+	0.705202i
$283$	0.365636	−	0.365636i	0.0217348	−	0.0217348i	−0.696156	−	0.717891i	$-0.745108\pi$
$283$	0.365636	−	0.365636i	0.0217348	−	0.0217348i	0.717891	+	0.696156i	$0.245108\pi$
$284$	8.57648			0.508920
$285$	6.95896	+	1.94380i	0.412213	+	0.115141i
$286$	25.2566			1.49346
$287$	10.8016	−	10.8016i	0.637600	−	0.637600i
$288$	0.260761	+	2.98865i	0.0153655	+	0.176108i
$289$			1.64182i			0.0965776i
$290$	−0.621486	−	8.07603i	−0.0364949	−	0.474241i
$291$	−17.7245	−	6.45355i	−1.03903	−	0.378314i
$292$	−0.0629195	−	0.0629195i	−0.00368209	−	0.00368209i
$293$	−5.81410	−	5.81410i	−0.339663	−	0.339663i	0.516577	−	0.856241i	$-0.327206\pi$
$293$	−5.81410	−	5.81410i	−0.339663	−	0.339663i	−0.856241	+	0.516577i	$0.827206\pi$
$294$	1.27414	+	0.463921i	0.0743095	+	0.0270564i
$295$	−13.0735	+	15.2533i	−0.761166	+	0.888083i
$296$		−	2.01781i		−	0.117283i
$297$	−26.6784	−	7.15861i	−1.54804	−	0.415385i
$298$	−11.8137	+	11.8137i	−0.684347	+	0.684347i
$299$	25.2337			1.45931
$300$	7.19702	−	4.81693i	0.415520	−	0.278106i
$301$	24.3545			1.40377
$302$	−15.7679	+	15.7679i	−0.907343	+	0.907343i
$303$	4.46985	+	9.58859i	0.256786	+	0.550850i
$304$			1.86557i			0.106998i
$305$	−5.15692	+	6.01678i	−0.295284	+	0.344520i
$306$	9.00449	+	7.55929i	0.514752	+	0.432136i
$307$	0.562256	+	0.562256i	0.0320896	+	0.0320896i	0.722970	−	0.690880i	$-0.242777\pi$
$307$	0.562256	+	0.562256i	0.0320896	+	0.0320896i	−0.690880	+	0.722970i	$0.742777\pi$
$308$	9.37251	+	9.37251i	0.534048	+	0.534048i
$309$	6.59143	−	18.1031i	0.374973	−	1.02985i
$310$	−0.171568	−	2.22948i	−0.00974441	−	0.126626i
$311$			15.0371i			0.852674i	0.904564	+	0.426337i	$0.140196\pi$
$311$			15.0371i			0.852674i	−0.904564	+	0.426337i	$0.859804\pi$
$312$	7.45864	−	3.47695i	0.422263	−	0.196843i
$313$	23.4317	−	23.4317i	1.32444	−	1.32444i	0.414291	−	0.910144i	$-0.364029\pi$
$313$	23.4317	−	23.4317i	1.32444	−	1.32444i	0.910144	−	0.414291i	$-0.135971\pi$
$314$	18.9413			1.06892
$315$	9.73989	−	13.5980i	0.548781	−	0.766160i
$316$	−13.3800			−0.752682
$317$	13.0369	−	13.0369i	0.732227	−	0.732227i	−0.238833	−	0.971061i	$-0.576765\pi$
$317$	13.0369	−	13.0369i	0.732227	−	0.732227i	0.971061	+	0.238833i	$0.0767649\pi$
$318$	−17.6253	+	8.21626i	−0.988376	+	0.460745i
$319$			19.2562i			1.07814i
$320$	1.69779	+	1.45516i	0.0949096	+	0.0813460i
$321$	2.34488	−	6.44014i	0.130878	−	0.359453i
$322$	9.36402	+	9.36402i	0.521836	+	0.521836i
$323$	5.16973	+	5.16973i	0.287651	+	0.287651i
$324$	−8.86401	+	1.55864i	−0.492445	+	0.0865912i
$325$	−19.1702	−	14.0300i	−1.06337	−	0.778243i
$326$			3.53670i			0.195880i
$327$	−4.19335	−	8.99544i	−0.231893	−	0.497449i
$328$	−4.33206	+	4.33206i	−0.239198	+	0.239198i
$329$	18.8093			1.03699
$330$	−17.9380	+	10.1049i	−0.987453	+	0.556258i
$331$	22.3579			1.22890			0.614450	−	0.788956i	$-0.289378\pi$
$331$	22.3579			1.22890			0.614450	+	0.788956i	$0.289378\pi$
$332$	−4.31021	+	4.31021i	−0.236554	+	0.236554i
$333$	6.03053	−	0.526166i	0.330471	−	0.0288337i
$334$			7.11930i			0.389551i
$335$	11.5571	−	0.889367i	0.631430	−	0.0485913i
$336$	4.05810	+	1.47757i	0.221387	+	0.0806081i
$337$	14.4378	+	14.4378i	0.786479	+	0.786479i	0.980915	−	0.194436i	$-0.0622877\pi$
$337$	14.4378	+	14.4378i	0.786479	+	0.786479i	−0.194436	+	0.980915i	$0.562288\pi$
$338$	−6.76949	−	6.76949i	−0.368212	−	0.368212i
$339$	−1.24671	−	0.453931i	−0.0677117	−	0.0246541i
$340$	8.73721	−	0.672367i	0.473842	−	0.0364642i
$341$			5.31589i			0.287872i
$342$	−5.57554	+	0.486468i	−0.301491	+	0.0263052i
$343$	13.7221	−	13.7221i	0.740922	−	0.740922i
$344$	−9.76750			−0.526628
$345$	−17.9217	+	10.0958i	−0.964872	+	0.543538i
$346$	4.67035			0.251080
$347$	−15.0026	+	15.0026i	−0.805384	+	0.805384i	−0.983931	−	0.178548i	$-0.942860\pi$
$347$	−15.0026	+	15.0026i	−0.805384	+	0.805384i	0.178548	+	0.983931i	$0.442860\pi$
$348$	2.65090	+	5.68663i	0.142103	+	0.304836i
$349$		−	4.46110i		−	0.238797i	−0.992846	−	0.119398i	$-0.961903\pi$
$349$		−	4.46110i		−	0.238797i	0.992846	−	0.119398i	$-0.0380966\pi$
$350$	−1.90750	−	12.3203i	−0.101960	−	0.658547i
$351$	12.3363	+	21.3846i	0.658462	+	1.14143i
$352$	−3.75890	−	3.75890i	−0.200350	−	0.200350i
$353$	−21.4307	−	21.4307i	−1.14064	−	1.14064i	−0.988333	−	0.152310i	$-0.951329\pi$
$353$	−21.4307	−	21.4307i	−1.14064	−	1.14064i	−0.152310	−	0.988333i	$-0.548671\pi$
$354$	5.32393	−	14.6220i	0.282964	−	0.777151i
$355$	14.5611	+	12.4802i	0.772823	+	0.662378i
$356$		−	5.00586i		−	0.265310i
$357$	15.3400	−	7.15095i	0.811878	−	0.378468i
$358$	−7.05127	+	7.05127i	−0.372671	+	0.372671i
$359$	−4.46782			−0.235803			−0.117901	−	0.993025i	$-0.537617\pi$
$359$	−4.46782			−0.235803			−0.117901	+	0.993025i	$0.537617\pi$
$360$	−3.90624	+	5.45356i	−0.205877	+	0.287428i
$361$	15.5196			0.816823
$362$	−11.5056	+	11.5056i	−0.604718	+	0.604718i
$363$	27.0937	−	12.6301i	1.42205	−	0.662909i
$364$		−	11.8466i		−	0.620932i
$365$	−0.0152664	−	0.198383i	−0.000799080	−	0.0103838i
$366$	2.10006	−	5.76776i	0.109772	−	0.301486i
$367$	19.9206	+	19.9206i	1.03985	+	1.03985i	0.999172	+	0.0406769i	$0.0129514\pi$
$367$	19.9206	+	19.9206i	1.03985	+	1.03985i	0.0406769	+	0.999172i	$0.487049\pi$
$368$	−3.75550	−	3.75550i	−0.195769	−	0.195769i
$369$	−14.0766	−	11.8174i	−0.732800	−	0.615187i
$370$	2.93624	−	3.42583i	0.152648	−	0.178101i
$371$			27.9944i			1.45339i
$372$	0.731811	+	1.56986i	0.0379426	+	0.0813933i
$373$	0.326405	−	0.326405i	0.0169006	−	0.0169006i	−0.698606	−	0.715507i	$-0.746196\pi$
$373$	0.326405	−	0.326405i	0.0169006	−	0.0169006i	0.715507	+	0.698606i	$0.246196\pi$
$374$	−20.8327			−1.07723
$375$	19.2285	+	2.29466i	0.992955	+	0.118496i
$376$	−7.54358			−0.389031
$377$	12.1697	−	12.1697i	0.626771	−	0.626771i
$378$	−3.35774	+	12.5135i	−0.172704	+	0.643626i
$379$			6.15747i			0.316288i	0.987416	+	0.158144i	$0.0505510\pi$
$379$			6.15747i			0.316288i	−0.987416	+	0.158144i	$0.949449\pi$
$380$	−2.71471	+	3.16736i	−0.139262	+	0.162482i
$381$	30.7060	+	11.1802i	1.57312	+	0.572779i
$382$	10.2361	+	10.2361i	0.523727	+	0.523727i
$383$	−24.9090	−	24.9090i	−1.27279	−	1.27279i	−0.944618	−	0.328171i	$-0.893568\pi$
$383$	−24.9090	−	24.9090i	−1.27279	−	1.27279i	−0.328171	−	0.944618i	$-0.606432\pi$
$384$	−1.62753	−	0.592589i	−0.0830543	−	0.0302404i
$385$	2.27409	+	29.5511i	0.115898	+	1.50606i
$386$		−	9.54810i		−	0.485985i
$387$	−2.54698	−	29.1916i	−0.129470	−	1.48389i
$388$	7.70070	−	7.70070i	0.390944	−	0.390944i
$389$	−22.1377			−1.12243			−0.561214	−	0.827671i	$-0.689665\pi$
$389$	−22.1377			−1.12243			−0.561214	+	0.827671i	$0.689665\pi$
$390$	17.7228	+	4.95038i	0.897427	+	0.250672i
$391$	−20.8138			−1.05260
$392$	−0.553574	+	0.553574i	−0.0279597	+	0.0279597i
$393$	−0.186720	−	0.400546i	−0.00941877	−	0.0202049i
$394$			19.8326i			0.999150i
$395$	−22.7164	−	19.4700i	−1.14299	−	0.979642i
$396$	10.2539	−	12.2142i	0.515276	−	0.613787i
$397$	−24.1567	−	24.1567i	−1.21239	−	1.21239i	−0.970238	−	0.242154i	$-0.922146\pi$
$397$	−24.1567	−	24.1567i	−1.21239	−	1.21239i	−0.242154	−	0.970238i	$-0.577854\pi$
$398$	−7.89679	−	7.89679i	−0.395830	−	0.395830i
$399$	−2.75652	+	7.57069i	−0.137999	+	0.379008i
$400$	0.765014	+	4.94113i	0.0382507	+	0.247056i
$401$		−	31.1190i		−	1.55401i	−0.629495	−	0.777004i	$-0.716738\pi$
$401$		−	31.1190i		−	1.55401i	0.629495	−	0.777004i	$-0.283262\pi$
$402$	−8.13776	+	3.79353i	−0.405875	+	0.189204i
$403$	3.35958	−	3.35958i	0.167352	−	0.167352i
$404$	−6.10793			−0.303881
$405$	−17.3173	−	10.2523i	−0.860506	−	0.509441i
$406$	9.03212			0.448257
$407$	−7.58477	+	7.58477i	−0.375963	+	0.375963i
$408$	−6.15220	+	2.86793i	−0.304579	+	0.141984i
$409$		−	22.2078i		−	1.09811i	−0.835788	−	0.549053i	$-0.814989\pi$
$409$		−	22.2078i		−	1.09811i	0.835788	−	0.549053i	$-0.185011\pi$
$410$	−13.6588	+	1.05110i	−0.674560	+	0.0519103i
$411$	6.63522	−	18.2234i	0.327291	−	0.898894i
$412$	7.86523	+	7.86523i	0.387492	+	0.387492i
$413$	−15.8401	−	15.8401i	−0.779443	−	0.779443i
$414$	10.2446	−	12.2031i	0.503493	−	0.599751i
$415$	−13.5899	+	1.04580i	−0.667102	+	0.0513364i
$416$			4.75116i			0.232945i
$417$	−0.804205	−	1.72516i	−0.0393821	−	0.0844813i
$418$	7.01251	−	7.01251i	0.342993	−	0.342993i
$419$	−24.1596			−1.18027			−0.590136	−	0.807304i	$-0.700926\pi$
$419$	−24.1596			−1.18027			−0.590136	+	0.807304i	$0.700926\pi$
$420$	4.73972	+	8.41380i	0.231274	+	0.410551i
$421$	−33.4804			−1.63173			−0.815867	−	0.578239i	$-0.803740\pi$
$421$	−33.4804			−1.63173			−0.815867	+	0.578239i	$0.803740\pi$
$422$	−3.01882	+	3.01882i	−0.146954	+	0.146954i
$423$	−1.96707	−	22.5451i	−0.0956422	−	1.09618i
$424$		−	11.2273i		−	0.545246i
$425$	15.8124	+	11.5725i	0.767014	+	0.561349i
$426$	−13.9584	−	5.08232i	−0.676288	−	0.246239i
$427$	−6.24826	−	6.24826i	−0.302375	−	0.302375i
$428$	2.79803	+	2.79803i	0.135248	+	0.135248i
$429$	−41.1058	−	14.9668i	−1.98461	−	0.722604i
$430$	−16.5832	−	14.2133i	−0.799714	−	0.685426i
$431$		−	11.1430i		−	0.536739i	−0.963316	−	0.268370i	$-0.913515\pi$
$431$		−	11.1430i		−	0.536739i	0.963316	−	0.268370i	$-0.0864848\pi$
$432$	1.34664	−	5.01862i	0.0647904	−	0.241458i
$433$	−27.0728	+	27.0728i	−1.30104	+	1.30104i	−0.373346	+	0.927692i	$0.621790\pi$
$433$	−27.0728	+	27.0728i	−1.30104	+	1.30104i	−0.927692	+	0.373346i	$0.878210\pi$
$434$	2.49342			0.119688
$435$	−3.77428	+	13.5122i	−0.180963	+	0.647862i
$436$	5.73010			0.274422
$437$	7.00616	−	7.00616i	0.335150	−	0.335150i
$438$	0.0651177	+	0.139689i	0.00311145	+	0.00667458i
$439$		−	31.9187i		−	1.52340i	−0.647933	−	0.761698i	$-0.724366\pi$
$439$		−	31.9187i		−	1.52340i	0.647933	−	0.761698i	$-0.275634\pi$
$440$	−0.912037	−	11.8517i	−0.0434797	−	0.565005i
$441$	−1.79879	−	1.51009i	−0.0856565	−	0.0719088i
$442$	13.1660	+	13.1660i	0.626244	+	0.626244i
$443$	−21.4595	−	21.4595i	−1.01957	−	1.01957i	−0.999805	−	0.0197682i	$-0.993707\pi$
$443$	−21.4595	−	21.4595i	−1.01957	−	1.01957i	−0.0197682	−	0.999805i	$-0.506293\pi$
$444$	−1.19573	+	3.28404i	−0.0567470	+	0.155854i
$445$	7.28433	−	8.49893i	0.345311	−	0.402888i
$446$		−	26.0723i		−	1.23456i
$447$	26.2277	−	12.2264i	1.24053	−	0.578289i
$448$	−1.76311	+	1.76311i	−0.0832992	+	0.0832992i
$449$	−9.97274			−0.470643			−0.235321	−	0.971918i	$-0.575614\pi$
$449$	−9.97274			−0.470643			−0.235321	+	0.971918i	$0.575614\pi$
$450$	−14.5678	+	3.57481i	−0.686733	+	0.168518i
$451$	32.5676			1.53355
$452$	0.541653	−	0.541653i	0.0254772	−	0.0254772i
$453$	35.0066	−	16.3188i	1.64475	−	0.766725i
$454$			8.97082i			0.421021i
$455$	17.2387	−	20.1131i	0.808165	−	0.942918i
$456$	1.10552	−	3.03627i	0.0517706	−	0.142186i
$457$	−15.4251	−	15.4251i	−0.721554	−	0.721554i	0.247367	−	0.968922i	$-0.420435\pi$
$457$	−15.4251	−	15.4251i	−0.721554	−	0.721554i	−0.968922	+	0.247367i	$0.920435\pi$
$458$	8.47974	+	8.47974i	0.396232	+	0.396232i
$459$	−10.1755	−	17.6389i	−0.474951	−	0.823313i
$460$	−0.911210	−	11.8409i	−0.0424854	−	0.552085i
$461$			26.3536i			1.22741i	0.789535	+	0.613705i	$0.210322\pi$
$461$			26.3536i			1.22741i	−0.789535	+	0.613705i	$0.789678\pi$
$462$	−9.69996	−	20.8080i	−0.451283	−	0.968078i
$463$	−21.2390	+	21.2390i	−0.987060	+	0.987060i	−0.999917	−	0.0128574i	$-0.995907\pi$
$463$	−21.2390	+	21.2390i	−0.987060	+	0.987060i	0.0128574	+	0.999917i	$0.495907\pi$
$464$	−3.62239			−0.168165
$465$	−1.04193	+	3.73020i	−0.0483184	+	0.172984i
$466$	−18.5235			−0.858087
$467$	−12.0325	+	12.0325i	−0.556798	+	0.556798i	−0.928394	−	0.371596i	$-0.878810\pi$
$467$	−12.0325	+	12.0325i	−0.556798	+	0.556798i	0.371596	+	0.928394i	$0.378810\pi$
$468$	−14.1995	+	1.23892i	−0.656374	+	0.0572689i
$469$			12.9253i			0.596834i
$470$	−12.8075	−	10.9771i	−0.590764	−	0.506337i
$471$	−30.8275	−	11.2244i	−1.42045	−	0.517193i
$472$	6.35279	+	6.35279i	0.292411	+	0.292411i
$473$	36.7151	+	36.7151i	1.68816	+	1.68816i
$474$	21.7762	+	7.92881i	1.00022	+	0.364182i
$475$	−9.21804	+	1.42719i	−0.422953	+	0.0654840i
$476$			9.77158i			0.447880i
$477$	33.5544	−	2.92764i	1.53635	−	0.134047i
$478$	9.77324	−	9.77324i	0.447018	−	0.447018i
$479$	9.47779			0.433051			0.216526	−	0.976277i	$-0.430528\pi$
$479$	9.47779			0.433051			0.216526	+	0.976277i	$0.430528\pi$
$480$	−1.90089	−	3.37441i	−0.0867635	−	0.154020i
$481$	9.58695			0.437128
$482$	−14.7768	+	14.7768i	−0.673063	+	0.673063i
$483$	−9.69116	−	20.7892i	−0.440963	−	0.945941i
$484$			17.2587i			0.784486i
$485$	24.2800	−	1.86845i	1.10250	−	0.0848420i
$486$	15.3500	+	2.71598i	0.696292	+	0.123199i
$487$	13.2910	+	13.2910i	0.602271	+	0.602271i	0.940915	−	0.338644i	$-0.109968\pi$
$487$	13.2910	+	13.2910i	0.602271	+	0.602271i	−0.338644	+	0.940915i	$0.609968\pi$
$488$	2.50590	+	2.50590i	0.113437	+	0.113437i
$489$	2.09581	−	5.75607i	0.0947757	−	0.260298i
$490$	−1.74539	+	0.134316i	−0.0788488	+	0.00606776i
$491$			6.99037i			0.315471i	0.987481	+	0.157736i	$0.0504194\pi$
$491$			6.99037i			0.315471i	−0.987481	+	0.157736i	$0.949581\pi$
$492$	9.61767	−	4.48341i	0.433598	−	0.202128i
$493$	−10.0381	+	10.0381i	−0.452091	+	0.452091i
$494$	−8.86364			−0.398794
$495$	35.1826	−	5.81620i	1.58134	−	0.261419i
$496$	−1.00000			−0.0449013
$497$	−15.1213	+	15.1213i	−0.678282	+	0.678282i
$498$	9.56916	−	4.46080i	0.428804	−	0.199893i
$499$			37.1388i			1.66256i	0.555855	+	0.831280i	$0.312391\pi$
$499$			37.1388i			1.66256i	−0.555855	+	0.831280i	$0.687609\pi$
$500$	−5.89130	+	9.50224i	−0.263467	+	0.424953i
$501$	4.21881	−	11.5868i	0.188483	−	0.517662i
$502$	6.28481	+	6.28481i	0.280505	+	0.280505i
$503$	9.45292	+	9.45292i	0.421485	+	0.421485i	0.885715	−	0.464230i	$-0.153669\pi$
$503$	9.45292	+	9.45292i	0.421485	+	0.421485i	−0.464230	+	0.885715i	$0.653669\pi$
$504$	−5.72907	−	4.80957i	−0.255193	−	0.214235i
$505$	−10.3700	−	8.88803i	−0.461460	−	0.395512i
$506$			28.2331i			1.25511i
$507$	7.00600	+	15.0290i	0.311147	+	0.667463i
$508$	−13.3408	+	13.3408i	−0.591901	+	0.591901i
$509$	1.81871			0.0806127			0.0403064	−	0.999187i	$-0.487167\pi$
$509$	1.81871			0.0806127			0.0403064	+	0.999187i	$0.487167\pi$
$510$	−14.6185	−	4.08328i	−0.647317	−	0.180811i
$511$	0.221868			0.00981488
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	9.36261	+	2.51226i	0.413369	+	0.110919i
$514$		−	16.0632i		−	0.708519i
$515$	1.90837	+	24.7987i	0.0840928	+	1.09276i
$516$	15.8969	+	5.78811i	0.699820	+	0.254807i
$517$	28.3556	+	28.3556i	1.24708	+	1.24708i
$518$	3.55763	+	3.55763i	0.156313	+	0.156313i
$519$	−7.60111	−	2.76760i	−0.333652	−	0.121484i
$520$	−6.91370	+	8.06649i	−0.303186	+	0.353739i
$521$		−	1.54036i		−	0.0674844i	−0.999431	−	0.0337422i	$-0.989257\pi$
$521$		−	1.54036i		−	0.0674844i	0.999431	−	0.0337422i	$-0.0107425\pi$
$522$	−0.944576	−	10.8260i	−0.0413430	−	0.473843i
$523$	−13.0285	+	13.0285i	−0.569695	+	0.569695i	−0.932043	−	0.362348i	$-0.881975\pi$
$523$	−13.0285	+	13.0285i	−0.569695	+	0.569695i	0.362348	+	0.932043i	$0.381975\pi$
$524$	0.255148			0.0111462
$525$	−4.19637	+	21.1820i	−0.183144	+	0.924456i
$526$	32.3613			1.41102
$527$	−2.77112	+	2.77112i	−0.120712	+	0.120712i
$528$	3.89023	+	8.34519i	0.169300	+	0.363178i
$529$			5.20749i			0.226412i
$530$	16.3375	−	19.0617i	0.709657	−	0.827986i
$531$	−17.3297	+	20.6428i	−0.752044	+	0.895821i
$532$	−3.28922	−	3.28922i	−0.142606	−	0.142606i
$533$	−20.5823	−	20.5823i	−0.891519	−	0.891519i
$534$	−2.96642	+	8.14717i	−0.128369	+	0.352562i
$535$	0.678896	+	8.82206i	0.0293513	+	0.381411i
$536$		−	5.18376i		−	0.223904i
$537$	15.6546	−	7.29762i	0.675547	−	0.314915i
$538$	−0.0866010	+	0.0866010i	−0.00373364	+	0.00373364i
$539$	4.16166			0.179255
$540$	9.58922	−	6.56100i	0.412654	−	0.282341i
$541$	41.2666			1.77419			0.887095	−	0.461587i	$-0.152720\pi$
$541$	41.2666			1.77419			0.887095	+	0.461587i	$0.152720\pi$
$542$	−12.7704	+	12.7704i	−0.548535	+	0.548535i
$543$	25.5436	−	11.9075i	1.09618	−	0.511001i
$544$		−	3.91895i		−	0.168024i
$545$	9.72853	+	8.33822i	0.416725	+	0.357170i
$546$	−7.02017	+	19.2807i	−0.300436	+	0.825137i
$547$	−26.3308	−	26.3308i	−1.12582	−	1.12582i	−0.990849	−	0.134972i	$-0.956905\pi$
$547$	−26.3308	−	26.3308i	−1.12582	−	1.12582i	−0.134972	−	0.990849i	$-0.543095\pi$
$548$	7.91747	+	7.91747i	0.338218	+	0.338218i
$549$	−6.83582	+	8.14270i	−0.291745	+	0.347522i
$550$	15.6976	−	21.4488i	0.669348	−	0.914581i
$551$		−	6.75783i		−	0.287893i
$552$	3.88670	+	8.33763i	0.165429	+	0.354873i
$553$	23.5904	−	23.5904i	1.00316	−	1.00316i
$554$	26.2811			1.11658
$555$	−6.80892	+	3.83565i	−0.289023	+	0.162814i
$556$	1.09893			0.0466048
$557$	14.8040	−	14.8040i	0.627268	−	0.627268i	−0.320112	−	0.947380i	$-0.603721\pi$
$557$	14.8040	−	14.8040i	0.627268	−	0.627268i	0.947380	+	0.320112i	$0.103721\pi$
$558$	−0.260761	−	2.98865i	−0.0110389	−	0.126519i
$559$		−	46.4070i		−	1.96281i
$560$	−5.55901	+	0.427791i	−0.234911	+	0.0180775i
$561$	33.9058	+	12.3452i	1.43150	+	0.521216i
$562$	−18.4663	−	18.4663i	−0.778952	−	0.778952i
$563$	−29.7240	−	29.7240i	−1.25272	−	1.25272i	−0.954497	−	0.298219i	$-0.903607\pi$
$563$	−29.7240	−	29.7240i	−1.25272	−	1.25272i	−0.298219	−	0.954497i	$-0.596393\pi$
$564$	12.2774	+	4.47024i	0.516971	+	0.188231i
$565$	1.70781	−	0.131423i	0.0718480	−	0.00552902i
$566$		−	0.517087i		−	0.0217348i
$567$	12.8802	−	18.3763i	0.540917	−	0.771732i
$568$	6.06448	−	6.06448i	0.254460	−	0.254460i
$569$	36.1254			1.51446			0.757228	−	0.653150i	$-0.226553\pi$
$569$	36.1254			1.51446			0.757228	+	0.653150i	$0.226553\pi$
$570$	6.29520	−	3.54626i	0.263677	−	0.148536i
$571$	24.6288			1.03068			0.515341	−	0.856985i	$-0.327665\pi$
$571$	24.6288			1.03068			0.515341	+	0.856985i	$0.327665\pi$
$572$	17.8591	−	17.8591i	0.746728	−	0.746728i
$573$	−10.5938	−	22.7254i	−0.442561	−	0.949368i
$574$		−	15.2758i		−	0.637600i
$575$	15.6834	−	21.4294i	0.654042	−	0.893667i
$576$	2.29768	+	1.92891i	0.0957366	+	0.0803711i
$577$	−11.7196	−	11.7196i	−0.487893	−	0.487893i	0.419748	−	0.907641i	$-0.362119\pi$
$577$	−11.7196	−	11.7196i	−0.487893	−	0.487893i	−0.907641	+	0.419748i	$0.862119\pi$
$578$	1.16094	+	1.16094i	0.0482888	+	0.0482888i
$579$	−5.65810	+	15.5398i	−0.235142	+	0.645811i
$580$	−6.15007	−	5.27116i	−0.255368	−	0.218873i
$581$		−	15.1988i		−	0.630551i
$582$	−17.0964	+	7.96974i	−0.708670	+	0.330356i
$583$	−42.2024	+	42.2024i	−1.74784	+	1.74784i
$584$	−0.0889817			−0.00368209
$585$	−25.9107	−	18.5592i	−1.07128	−	0.767328i
$586$	−8.22238			−0.339663
$587$	−10.6912	+	10.6912i	−0.441275	+	0.441275i	−0.892440	−	0.451166i	$-0.851008\pi$
$587$	−10.6912	+	10.6912i	−0.441275	+	0.441275i	0.451166	+	0.892440i	$0.351008\pi$
$588$	1.22900	−	0.572914i	0.0506830	−	0.0236266i
$589$		−	1.86557i		−	0.0768697i
$590$	1.54140	+	20.0301i	0.0634585	+	0.824624i
$591$	11.7525	−	32.2780i	0.483435	−	1.32774i
$592$	−1.42681	−	1.42681i	−0.0586415	−	0.0586415i
$593$	23.5587	+	23.5587i	0.967441	+	0.967441i	0.999486	−	0.0320459i	$-0.0102023\pi$
$593$	23.5587	+	23.5587i	0.967441	+	0.967441i	−0.0320459	+	0.999486i	$0.510202\pi$
$594$	−23.9264	+	13.8026i	−0.981712	+	0.566328i
$595$	−14.2192	+	16.5901i	−0.582931	+	0.680129i
$596$			16.7070i			0.684347i
$597$	8.17267	+	17.5318i	0.334485	+	0.717527i
$598$	17.8430	−	17.8430i	0.729653	−	0.729653i
$599$	−0.0185367			−0.000757390			−0.000378695	−	1.00000i	$-0.500121\pi$
$599$	−0.0185367			−0.000757390			−0.000378695		1.00000i	$0.500121\pi$
$600$	1.68298	−	8.49515i	0.0687073	−	0.346813i
$601$	−8.10421			−0.330578			−0.165289	−	0.986245i	$-0.552856\pi$
$601$	−8.10421			−0.330578			−0.165289	+	0.986245i	$0.552856\pi$
$602$	17.2212	−	17.2212i	0.701884	−	0.701884i
$603$	15.4924	−	1.35172i	0.630900	−	0.0550463i
$604$			22.2992i			0.907343i
$605$	−25.1142	+	29.3017i	−1.02104	+	1.19128i
$606$	9.94082	+	3.61949i	0.403818	+	0.147032i
$607$	5.34558	+	5.34558i	0.216970	+	0.216970i	0.807220	−	0.590250i	$-0.200971\pi$
$607$	5.34558	+	5.34558i	0.216970	+	0.216970i	−0.590250	+	0.807220i	$0.700971\pi$
$608$	1.31916	+	1.31916i	0.0534990	+	0.0534990i
$609$	−14.7000	−	5.35233i	−0.595674	−	0.216888i
$610$	0.608017	+	7.90100i	0.0246179	+	0.319902i
$611$		−	35.8408i		−	1.44996i
$612$	11.7124	−	1.02191i	0.473444	−	0.0413082i
$613$	−30.9751	+	30.9751i	−1.25107	+	1.25107i	−0.295833	+	0.955240i	$0.595597\pi$
$613$	−30.9751	+	30.9751i	−1.25107	+	1.25107i	−0.955240	+	0.295833i	$0.904403\pi$
$614$	0.795149			0.0320896
$615$	22.8529	+	6.38335i	0.921518	+	0.257401i
$616$	13.2547			0.534048
$617$	−20.6041	+	20.6041i	−0.829491	+	0.829491i	−0.987446	−	0.157956i	$-0.949510\pi$
$617$	−20.6041	+	20.6041i	−0.829491	+	0.829491i	0.157956	+	0.987446i	$0.449510\pi$
$618$	−8.14001	−	17.4617i	−0.327439	−	0.702413i
$619$		−	29.7973i		−	1.19765i	−0.800879	−	0.598827i	$-0.795634\pi$
$619$		−	29.7973i		−	1.19765i	0.800879	−	0.598827i	$-0.204366\pi$
$620$	−1.69779	−	1.45516i	−0.0681851	−	0.0584407i
$621$	−23.9047	+	13.7901i	−0.959263	+	0.553377i
$622$	10.6328	+	10.6328i	0.426337	+	0.426337i
$623$	8.82590	+	8.82590i	0.353602	+	0.353602i
$624$	2.81548	−	7.73263i	0.112710	−	0.309553i
$625$	−23.8295	+	7.56006i	−0.953180	+	0.302402i
$626$		−	33.1374i		−	1.32444i
$627$	−15.5686	+	7.25751i	−0.621749	+	0.289837i
$628$	13.3935	−	13.3935i	0.534460	−	0.534460i
$629$	−7.90772			−0.315301
$630$	−2.72809	−	16.5024i	−0.108690	−	0.657470i
$631$	−14.0062			−0.557577			−0.278789	−	0.960352i	$-0.589933\pi$
$631$	−14.0062			−0.557577			−0.278789	+	0.960352i	$0.589933\pi$
$632$	−9.46106	+	9.46106i	−0.376341	+	0.376341i
$633$	6.70213	−	3.12429i	0.266386	−	0.124179i
$634$		−	18.4370i		−	0.732227i
$635$	−42.0629	+	3.23692i	−1.66921	+	0.128453i
$636$	−6.65317	+	18.2727i	−0.263816	+	0.724561i
$637$	−2.63012	−	2.63012i	−0.104209	−	0.104209i
$638$	13.6162	+	13.6162i	0.539071	+	0.539071i
$639$	19.7060	+	16.5432i	0.779556	+	0.654439i
$640$	2.22948	−	0.171568i	0.0881278	−	0.00678182i
$641$			11.0951i			0.438231i	0.975699	+	0.219116i	$0.0703172\pi$
$641$			11.0951i			0.438231i	−0.975699	+	0.219116i	$0.929683\pi$
$642$	−2.89578	−	6.21194i	−0.114287	−	0.245166i
$643$	5.70015	−	5.70015i	0.224792	−	0.224792i	−0.585721	−	0.810513i	$-0.699188\pi$
$643$	5.70015	−	5.70015i	0.224792	−	0.224792i	0.810513	+	0.585721i	$0.199188\pi$
$644$	13.2427			0.521836
$645$	18.5670	+	32.9595i	0.731074	+	1.29778i
$646$	7.31110			0.287651
$647$	−7.49872	+	7.49872i	−0.294805	+	0.294805i	−0.838975	−	0.544170i	$-0.816845\pi$
$647$	−7.49872	+	7.49872i	−0.294805	+	0.294805i	0.544170	+	0.838975i	$0.316845\pi$
$648$	−5.16567	+	7.36993i	−0.202927	+	0.289518i
$649$		−	47.7590i		−	1.87471i
$650$	−23.4761	+	3.63470i	−0.920808	+	0.142565i
$651$	−4.05810	−	1.47757i	−0.159049	−	0.0579106i
$652$	2.50082	+	2.50082i	0.0979398	+	0.0979398i
$653$	−16.8945	−	16.8945i	−0.661133	−	0.661133i	0.294514	−	0.955647i	$-0.404842\pi$
$653$	−16.8945	−	16.8945i	−0.661133	−	0.661133i	−0.955647	+	0.294514i	$0.904842\pi$
$654$	−9.32588	−	3.39559i	−0.364671	−	0.132778i
$655$	0.433189	+	0.371281i	0.0169261	+	0.0145072i
$656$			6.12646i			0.239198i
$657$	−0.0232029	−	0.265935i	−0.000905232	−	0.0103751i
$658$	13.3002	−	13.3002i	0.518495	−	0.518495i
$659$	45.2653			1.76329			0.881643	−	0.471917i	$-0.156438\pi$
$659$	45.2653			1.76329			0.881643	+	0.471917i	$0.156438\pi$
$660$	−5.53879	+	19.8293i	−0.215597	+	0.771856i
$661$	−6.67439			−0.259604			−0.129802	−	0.991540i	$-0.541434\pi$
$661$	−6.67439			−0.259604			−0.129802	+	0.991540i	$0.541434\pi$
$662$	15.8094	−	15.8094i	0.614450	−	0.614450i
$663$	−13.6260	−	29.2301i	−0.529190	−	1.13520i
$664$			6.09556i			0.236554i
$665$	−0.798075	−	10.3708i	−0.0309480	−	0.402161i
$666$	3.89217	−	4.63629i	0.150819	−	0.179652i
$667$	13.6039	+	13.6039i	0.526743	+	0.526743i
$668$	5.03410	+	5.03410i	0.194775	+	0.194775i
$669$	−15.4501	+	42.4333i	−0.597337	+	1.64057i
$670$	7.54320	−	8.80096i	0.291419	−	0.340011i
$671$		−	18.8389i		−	0.727267i
$672$	3.91431	−	1.82471i	0.150998	−	0.0703897i
$673$	13.5402	−	13.5402i	0.521935	−	0.521935i	−0.396220	−	0.918155i	$-0.629678\pi$
$673$	13.5402	−	13.5402i	0.521935	−	0.521935i	0.918155	+	0.396220i	$0.129678\pi$
$674$	20.4182			0.786479
$675$	25.8279	+	2.81462i	0.994114	+	0.108335i
$676$	−9.57351			−0.368212
$677$	16.0012	−	16.0012i	0.614976	−	0.614976i	−0.329262	−	0.944238i	$-0.606800\pi$
$677$	16.0012	−	16.0012i	0.614976	−	0.614976i	0.944238	+	0.329262i	$0.106800\pi$
$678$	−1.20253	+	0.560576i	−0.0461829	+	0.0215288i
$679$			27.1544i			1.04209i
$680$	5.70270	−	6.65357i	0.218689	−	0.255153i
$681$	5.31600	−	14.6002i	0.203710	−	0.559482i
$682$	3.75890	+	3.75890i	0.143936	+	0.143936i
$683$	−3.42852	−	3.42852i	−0.131189	−	0.131189i	0.638463	−	0.769652i	$-0.279570\pi$
$683$	−3.42852	−	3.42852i	−0.131189	−	0.131189i	−0.769652	+	0.638463i	$0.779570\pi$
$684$	−3.59852	+	4.28649i	−0.137593	+	0.163898i
$685$	1.92105	+	24.9634i	0.0733994	+	0.953804i
$686$		−	19.4059i		−	0.740922i
$687$	−8.77600	−	18.8260i	−0.334825	−	0.718257i
$688$	−6.90667	+	6.90667i	−0.263314	+	0.263314i
$689$	53.3427			2.03220
$690$	−5.53377	+	19.8114i	−0.210667	+	0.754205i
$691$	−13.9403			−0.530316			−0.265158	−	0.964205i	$-0.585424\pi$
$691$	−13.9403			−0.530316			−0.265158	+	0.964205i	$0.585424\pi$
$692$	3.30244	−	3.30244i	0.125540	−	0.125540i
$693$	3.45631	+	39.6137i	0.131294	+	1.50480i
$694$			21.2169i			0.805384i
$695$	1.86575	+	1.59911i	0.0707719	+	0.0606578i
$696$	5.89553	+	2.14659i	0.223469	+	0.0813661i
$697$	16.9771	+	16.9771i	0.643055	+	0.643055i
$698$	−3.15447	−	3.15447i	−0.119398	−	0.119398i
$699$	30.1475	+	10.9768i	1.14028	+	0.415182i
$700$	−10.0606	−	7.36296i	−0.380254	−	0.278294i
$701$		−	17.0635i		−	0.644480i	−0.946658	−	0.322240i	$-0.895564\pi$
$701$		−	17.0635i		−	0.644480i	0.946658	−	0.322240i	$-0.104436\pi$
$702$	23.8443	+	6.39812i	0.899944	+	0.241481i
$703$	2.66182	−	2.66182i	0.100392	−	0.100392i
$704$	−5.31589			−0.200350
$705$	14.3395	+	25.4551i	0.540058	+	0.958695i
$706$	−30.3076			−1.14064
$707$	10.7690	−	10.7690i	0.405009	−	0.405009i
$708$	−6.57473	−	14.1039i	−0.247094	−	0.530057i
$709$			21.8486i			0.820541i	0.911964	+	0.410270i	$0.134566\pi$
$709$			21.8486i			0.820541i	−0.911964	+	0.410270i	$0.865434\pi$
$710$	19.1210	−	1.47145i	0.717600	−	0.0552225i
$711$	−30.7428	−	25.8087i	−1.15295	−	0.967901i
$712$	−3.53968	−	3.53968i	−0.132655	−	0.132655i
$713$	3.75550	+	3.75550i	0.140644	+	0.140644i
$714$	5.79053	−	15.9035i	0.216705	−	0.595173i
$715$	56.3091	−	4.33323i	2.10584	−	0.162054i
$716$			9.97200i			0.372671i
$717$	−21.6977	+	10.1147i	−0.810316	+	0.377740i
$718$	−3.15923	+	3.15923i	−0.117901	+	0.117901i
$719$	6.72001			0.250614			0.125307	−	0.992118i	$-0.460008\pi$
$719$	6.72001			0.250614			0.125307	+	0.992118i	$0.460008\pi$
$720$	1.09412	+	6.61838i	0.0407753	+	0.246652i
$721$	−27.7346			−1.03289
$722$	10.9740	−	10.9740i	0.408411	−	0.408411i
$723$	32.8061	−	15.2930i	1.22007	−	0.568754i
$724$			16.2713i			0.604718i
$725$	−2.77118	−	17.8987i	−0.102919	−	0.664740i
$726$	10.2273	−	28.0890i	0.379571	−	1.04248i
$727$	−2.57592	−	2.57592i	−0.0955356	−	0.0955356i	0.657724	−	0.753259i	$-0.271519\pi$
$727$	−2.57592	−	2.57592i	−0.0955356	−	0.0955356i	−0.753259	+	0.657724i	$0.771519\pi$
$728$	−8.37683	−	8.37683i	−0.310466	−	0.310466i
$729$	−23.3731	−	13.5166i	−0.865671	−	0.500614i
$730$	−0.151073	−	0.129483i	−0.00559145	−	0.00479237i
$731$			38.2784i			1.41578i
$732$	−2.59345	−	5.56339i	−0.0958567	−	0.205629i
$733$	12.8296	−	12.8296i	0.473870	−	0.473870i	−0.429294	−	0.903165i	$-0.641238\pi$
$733$	12.8296	−	12.8296i	0.473870	−	0.473870i	0.903165	+	0.429294i	$0.141238\pi$
$734$	28.1720			1.03985
$735$	2.92027	+	0.815698i	0.107716	+	0.0300875i
$736$	−5.31107			−0.195769
$737$	−19.4852	+	19.4852i	−0.717748	+	0.717748i
$738$	−18.3098	+	1.59754i	−0.673994	+	0.0588062i
$739$			5.13226i			0.188793i	0.995535	+	0.0943966i	$0.0300922\pi$
$739$			5.13226i			0.188793i	−0.995535	+	0.0943966i	$0.969908\pi$
$740$	−0.346192	−	4.49867i	−0.0127263	−	0.165374i
$741$	14.4258	+	5.25249i	0.529945	+	0.192955i
$742$	19.7950	+	19.7950i	0.726697	+	0.726697i
$743$	−11.8016	−	11.8016i	−0.432961	−	0.432961i	0.456674	−	0.889634i	$-0.349041\pi$
$743$	−11.8016	−	11.8016i	−0.432961	−	0.432961i	−0.889634	+	0.456674i	$0.849041\pi$
$744$	1.62753	+	0.592589i	0.0596680	+	0.0217254i
$745$	−24.3114	+	28.3651i	−0.890702	+	1.03922i
$746$		−	0.461607i		−	0.0169006i
$747$	−18.2175	+	1.58948i	−0.666542	+	0.0581561i
$748$	−14.7310	+	14.7310i	−0.538617	+	0.538617i
$749$	−9.86648			−0.360513
$750$	15.2192	−	11.9740i	0.555725	−	0.437229i
$751$	11.9892			0.437493			0.218747	−	0.975782i	$-0.429803\pi$
$751$	11.9892			0.437493			0.218747	+	0.975782i	$0.429803\pi$
$752$	−5.33412	+	5.33412i	−0.194515	+	0.194515i
$753$	−6.50438	−	13.9530i	−0.237033	−	0.508476i
$754$		−	17.2105i		−	0.626771i
$755$	−32.4490	+	37.8595i	−1.18094	+	1.37785i
$756$	6.47411	+	11.2227i	0.235461	+	0.408165i
$757$	29.9624	+	29.9624i	1.08900	+	1.08900i	0.995631	+	0.0933711i	$0.0297643\pi$
$757$	29.9624	+	29.9624i	1.08900	+	1.08900i	0.0933711	+	0.995631i	$0.470236\pi$
$758$	4.35399	+	4.35399i	0.158144	+	0.158144i
$759$	16.7306	−	45.9501i	0.607282	−	1.66788i
$760$	0.320073	+	4.15925i	0.0116103	+	0.150872i
$761$		−	23.2384i		−	0.842393i	−0.906969	−	0.421196i	$-0.861610\pi$
$761$		−	23.2384i		−	0.842393i	0.906969	−	0.421196i	$-0.138390\pi$
$762$	29.6180	−	13.8069i	1.07295	−	0.500170i
$763$	−10.1028	+	10.1028i	−0.365746	+	0.365746i
$764$	14.4761			0.523727
$765$	21.3722	+	15.3084i	0.772714	+	0.553475i
$766$	−35.2266			−1.27279
$767$	−30.1831	+	30.1831i	−1.08985	+	1.08985i
$768$	−1.56986	+	0.731811i	−0.0566474	+	0.0264069i
$769$		−	33.2909i		−	1.20050i	−0.799812	−	0.600251i	$-0.795067\pi$
$769$		−	33.2909i		−	1.20050i	0.799812	−	0.600251i	$-0.204933\pi$
$770$	22.5038	+	19.2878i	0.810981	+	0.695083i
$771$	−9.51890	+	26.1433i	−0.342815	+	0.941529i
$772$	−6.75153	−	6.75153i	−0.242993	−	0.242993i
$773$	4.90985	+	4.90985i	0.176595	+	0.176595i	0.789870	−	0.613275i	$-0.210148\pi$
$773$	4.90985	+	4.90985i	0.176595	+	0.176595i	−0.613275	+	0.789870i	$0.710148\pi$
$774$	−22.4426	−	18.8406i	−0.806682	−	0.677211i
$775$	−0.765014	−	4.94113i	−0.0274801	−	0.177491i
$776$		−	10.8904i		−	0.390944i
$777$	−3.68192	−	7.89835i	−0.132088	−	0.283352i
$778$	−15.6537	+	15.6537i	−0.561214	+	0.561214i
$779$	−11.4294			−0.409500
$780$	16.0323	−	9.03144i	0.574050	−	0.323377i
$781$	−45.5916			−1.63140
$782$	−14.7176	+	14.7176i	−0.526300	+	0.526300i
$783$	−4.87806	+	18.1794i	−0.174328	+	0.649678i
$784$			0.782871i			0.0279597i
$785$	42.2292	−	3.24972i	1.50723	−	0.115988i
$786$	−0.415260	−	0.151198i	−0.0148118	−	0.00539304i
$787$	29.7522	+	29.7522i	1.06055	+	1.06055i	0.998045	+	0.0625074i	$0.0199097\pi$
$787$	29.7522	+	29.7522i	1.06055	+	1.06055i	0.0625074	+	0.998045i	$0.480090\pi$
$788$	14.0237	+	14.0237i	0.499575	+	0.499575i
$789$	−52.6689	−	19.1770i	−1.87506	−	0.682718i
$790$	−29.8303	+	2.29557i	−1.06131	+	0.0816728i
$791$			1.90999i			0.0679114i
$792$	−1.38618	−	15.8873i	−0.0492556	−	0.564531i
$793$	−11.9059	+	11.9059i	−0.422792	+	0.422792i
$794$	−34.1628			−1.21239
$795$	−37.8855	+	21.3419i	−1.34366	+	0.756919i
$796$	−11.1677			−0.395830
$797$	25.8025	−	25.8025i	0.913971	−	0.913971i	−0.0826107	−	0.996582i	$-0.526326\pi$
$797$	25.8025	−	25.8025i	0.913971	−	0.913971i	0.996582	+	0.0826107i	$0.0263258\pi$
$798$	3.40413	+	7.30244i	0.120505	+	0.258503i
$799$			29.5629i			1.04586i
$800$	4.03485	+	2.95296i	0.142654	+	0.104403i
$801$	9.65584	−	11.5019i	0.341172	−	0.406398i
$802$	−22.0044	−	22.0044i	−0.777004	−	0.777004i
$803$	0.334473	+	0.334473i	0.0118033	+	0.0118033i
$804$	−3.07184	+	8.43670i	−0.108335	+	0.297539i
$805$	22.4834	+	19.2703i	0.792436	+	0.679188i
$806$		−	4.75116i		−	0.167352i
$807$	0.192264	−	0.0896266i	0.00676802	−	0.00315501i
$808$	−4.31896	+	4.31896i	−0.151941	+	0.151941i
$809$	−30.9649			−1.08867			−0.544334	−	0.838869i	$-0.683218\pi$
$809$	−30.9649			−1.08867			−0.544334	+	0.838869i	$0.683218\pi$
$810$	−19.4947	+	4.99574i	−0.684973	+	0.175532i
$811$	28.5123			1.00120			0.500602	−	0.865678i	$-0.333112\pi$
$811$	28.5123			1.00120			0.500602	+	0.865678i	$0.333112\pi$
$812$	6.38668	−	6.38668i	0.224128	−	0.224128i
$813$	28.3517	−	13.2165i	0.994339	−	0.463525i
$814$			10.7265i			0.375963i
$815$	0.606784	+	7.88499i	0.0212547	+	0.276199i
$816$	−2.32233	+	6.37819i	−0.0812977	+	0.223281i
$817$	−12.8849	−	12.8849i	−0.450786	−	0.450786i
$818$	−15.7033	−	15.7033i	−0.549053	−	0.549053i
$819$	22.8510	−	27.2197i	0.798479	−	0.951134i
$820$	−8.91498	+	10.4015i	−0.311325	+	0.363235i
$821$			17.0697i			0.595736i	0.954607	+	0.297868i	$0.0962755\pi$
$821$			17.0697i			0.595736i	−0.954607	+	0.297868i	$0.903724\pi$
$822$	−8.19408	−	17.5777i	−0.285802	−	0.613093i
$823$	−38.0364	+	38.0364i	−1.32586	+	1.32586i	−0.416922	+	0.908942i	$0.636891\pi$
$823$	−38.0364	+	38.0364i	−1.32586	+	1.32586i	−0.908942	+	0.416922i	$0.863109\pi$
$824$	11.1231			0.387492
$825$	−38.2586	+	25.6063i	−1.33199	+	0.891497i
$826$	−22.4014			−0.779443
$827$	−12.7698	+	12.7698i	−0.444048	+	0.444048i	−0.893370	−	0.449322i	$-0.851666\pi$
$827$	−12.7698	+	12.7698i	−0.444048	+	0.444048i	0.449322	+	0.893370i	$0.351666\pi$
$828$	−1.38492	−	15.8729i	−0.0481292	−	0.551622i
$829$		−	32.6869i		−	1.13526i	−0.823283	−	0.567631i	$-0.807860\pi$
$829$		−	32.6869i		−	1.13526i	0.823283	−	0.567631i	$-0.192140\pi$
$830$	−8.87002	+	10.3490i	−0.307883	+	0.359219i
$831$	−42.7732	−	15.5739i	−1.48379	−	0.540253i
$832$	3.35958	+	3.35958i	0.116472	+	0.116472i
$833$	2.16943	+	2.16943i	0.0751662	+	0.0751662i
$834$	−1.78853	−	0.651211i	−0.0619317	−	0.0225496i
$835$	1.22144	+	15.8723i	0.0422698	+	0.549284i
$836$		−	9.91719i		−	0.342993i
$837$	−1.34664	+	5.01862i	−0.0465468	+	0.173469i
$838$	−17.0834	+	17.0834i	−0.590136	+	0.590136i
$839$	49.2199			1.69926			0.849630	−	0.527379i	$-0.176825\pi$
$839$	49.2199			1.69926			0.849630	+	0.527379i	$0.176825\pi$
$840$	9.30094	+	2.59797i	0.320913	+	0.0896384i
$841$	−15.8783			−0.547528
$842$	−23.6742	+	23.6742i	−0.815867	+	0.815867i
$843$	19.1114	+	40.9972i	0.658232	+	1.41202i
$844$			4.26926i			0.146954i
$845$	−16.2539	−	13.9310i	−0.559150	−	0.479241i
$846$	−17.3327	−	14.5509i	−0.595911	−	0.500269i
$847$	−30.4290	−	30.4290i	−1.04555	−	1.04555i
$848$	−7.93890	−	7.93890i	−0.272623	−	0.272623i
$849$	−0.306420	+	0.841573i	−0.0105163	+	0.0288827i
$850$	19.3640	−	2.99805i	0.664181	−	0.102832i
$851$			10.7168i			0.367366i
$852$	−13.4638	+	6.27636i	−0.461264	+	0.215024i
$853$	−3.00535	+	3.00535i	−0.102901	+	0.102901i	−0.756683	−	0.653782i	$-0.773181\pi$
$853$	−3.00535	+	3.00535i	−0.102901	+	0.102901i	0.653782	+	0.756683i	$0.273181\pi$
$854$	−8.83638			−0.302375
$855$	−12.3471	+	2.04115i	−0.422261	+	0.0698060i
$856$	3.95701			0.135248
$857$	4.52371	−	4.52371i	0.154527	−	0.154527i	−0.625609	−	0.780136i	$-0.715150\pi$
$857$	4.52371	−	4.52371i	0.154527	−	0.154527i	0.780136	+	0.625609i	$0.215150\pi$
$858$	−39.6493	+	18.4831i	−1.35361	+	0.631002i
$859$		−	13.8864i		−	0.473799i	−0.971534	−	0.236899i	$-0.923869\pi$
$859$		−	13.8864i		−	0.473799i	0.971534	−	0.236899i	$-0.0761312\pi$
$860$	−21.7764	+	1.67579i	−0.742570	+	0.0571440i
$861$	−9.05228	+	24.8618i	−0.308501	+	0.847287i
$862$	−7.87929	−	7.87929i	−0.268370	−	0.268370i
$863$	19.1746	+	19.1746i	0.652712	+	0.652712i	0.953645	−	0.300933i	$-0.0972980\pi$
$863$	19.1746	+	19.1746i	0.652712	+	0.652712i	−0.300933	+	0.953645i	$0.597298\pi$
$864$	−2.59648	−	4.50092i	−0.0883340	−	0.153124i
$865$	10.4124	−	0.801283i	0.354033	−	0.0272444i
$866$			38.2868i			1.30104i
$867$	−1.20150	−	2.57742i	−0.0408051	−	0.0875339i
$868$	1.76311	−	1.76311i	0.0598439	−	0.0598439i
$869$	71.1264			2.41280
$870$	6.88577	+	12.2234i	0.233449	+	0.414412i
$871$	24.6289			0.834517
$872$	4.05179	−	4.05179i	0.137211	−	0.137211i
$873$	32.5477	−	2.83980i	1.10157	−	0.0961126i
$874$		−	9.90820i		−	0.335150i
$875$	−6.36649	−	27.1405i	−0.215227	−	0.917518i
$876$	0.144820	+	0.0527295i	0.00489301	+	0.00178157i
$877$	−9.57875	−	9.57875i	−0.323452	−	0.323452i	0.526638	−	0.850090i	$-0.323452\pi$
$877$	−9.57875	−	9.57875i	−0.323452	−	0.323452i	−0.850090	+	0.526638i	$0.823452\pi$
$878$	−22.5699	−	22.5699i	−0.761698	−	0.761698i
$879$	13.3821	+	4.87249i	0.451368	+	0.164345i
$880$	−9.02529	−	7.73548i	−0.304243	−	0.260763i
$881$		−	34.9896i		−	1.17883i	−0.807831	−	0.589414i	$-0.799359\pi$
$881$		−	34.9896i		−	1.17883i	0.807831	−	0.589414i	$-0.200641\pi$
$882$	−2.33972	+	0.204142i	−0.0787826	+	0.00687382i
$883$	−24.3320	+	24.3320i	−0.818836	+	0.818836i	−0.985939	−	0.167103i	$-0.946559\pi$
$883$	−24.3320	+	24.3320i	−0.818836	+	0.818836i	0.167103	+	0.985939i	$0.446559\pi$
$884$	18.6196			0.626244
$885$	9.36091	−	33.5128i	0.314664	−	1.12652i
$886$	−30.3484			−1.01957
$887$	34.5491	−	34.5491i	1.16005	−	1.16005i	0.175582	−	0.984465i	$-0.443819\pi$
$887$	34.5491	−	34.5491i	1.16005	−	1.16005i	0.984465	−	0.175582i	$-0.0561806\pi$
$888$	1.47666	+	3.16768i	0.0495534	+	0.106300i
$889$		−	47.0426i		−	1.57776i
$890$	−0.858846	−	11.1605i	−0.0287886	−	0.374099i
$891$	47.1201	−	8.28557i	1.57858	−	0.277577i
$892$	−18.4359	−	18.4359i	−0.617279	−	0.617279i
$893$	−9.95119	−	9.95119i	−0.333004	−	0.333004i
$894$	9.90041	−	27.1911i	0.331119	−	0.909408i
$895$	−14.5109	+	16.9304i	−0.485045	+	0.565921i
$896$			2.49342i			0.0832992i
$897$	−39.6134	+	18.4663i	−1.32265	+	0.616573i
$898$	−7.05179	+	7.05179i	−0.235321	+	0.235321i
$899$	3.62239			0.120813
$900$	−7.77322	+	12.8288i	−0.259107	+	0.427625i
$901$	−43.9993			−1.46583
$902$	23.0288	−	23.0288i	0.766774	−	0.766774i
$903$	−38.2330	+	17.8229i	−1.27232	+	0.593107i
$904$		−	0.766013i		−	0.0254772i
$905$	−23.6774	+	27.6253i	−0.787063	+	0.918297i
$906$	13.2143	−	36.2926i	0.439015	−	1.20574i
$907$	−25.5536	−	25.5536i	−0.848493	−	0.848493i	0.141452	−	0.989945i	$-0.454823\pi$
$907$	−25.5536	−	25.5536i	−0.848493	−	0.848493i	−0.989945	+	0.141452i	$0.954823\pi$
$908$	6.34333	+	6.34333i	0.210511	+	0.210511i
$909$	−14.0341	−	11.7816i	−0.465480	−	0.390772i
$910$	−2.03250	−	26.4118i	−0.0673768	−	0.875541i
$911$		−	2.98577i		−	0.0989231i	−0.998776	−	0.0494615i	$-0.984249\pi$
$911$		−	2.98577i		−	0.0989231i	0.998776	−	0.0494615i	$-0.0157505\pi$
$912$	−1.36525	−	2.92869i	−0.0452079	−	0.0969785i
$913$	22.9126	−	22.9126i	0.758297	−	0.758297i
$914$	−21.8143			−0.721554
$915$	3.69248	−	13.2194i	0.122070	−	0.437019i
$916$	11.9922			0.396232
$917$	−0.449854	+	0.449854i	−0.0148555	+	0.0148555i
$918$	−19.6677	−	5.27743i	−0.649132	−	0.174181i
$919$		−	15.7119i		−	0.518289i	−0.965839	−	0.259144i	$-0.916559\pi$
$919$		−	15.7119i		−	0.518289i	0.965839	−	0.259144i	$-0.0834406\pi$
$920$	−9.01711	−	7.72846i	−0.297285	−	0.254800i
$921$	−1.29413	−	0.471197i	−0.0426429	−	0.0155265i
$922$	18.6348	+	18.6348i	0.613705	+	0.613705i
$923$	28.8133	+	28.8133i	0.948402	+	0.948402i
$924$	−21.5724	−	7.85461i	−0.709680	−	0.258398i
$925$	5.95852	−	8.14158i	0.195915	−	0.267694i
$926$			30.0365i			0.987060i
$927$	2.90047	+	33.2430i	0.0952639	+	1.09184i
$928$	−2.56141	+	2.56141i	−0.0840826	+	0.0840826i
$929$	−27.0438			−0.887278			−0.443639	−	0.896206i	$-0.646313\pi$
$929$	−27.0438			−0.887278			−0.443639	+	0.896206i	$0.646313\pi$
$930$	1.90089	+	3.37441i	0.0623327	+	0.110651i
$931$	−1.46050			−0.0478661
$932$	−13.0981	+	13.0981i	−0.429043	+	0.429043i
$933$	−11.0043	−	23.6061i	−0.360264	−	0.772828i
$934$			17.0165i			0.556798i
$935$	−46.4461	+	3.57423i	−1.51895	+	0.116890i
$936$	−9.16454	+	10.9166i	−0.299552	+	0.356821i
$937$	−4.59656	−	4.59656i	−0.150163	−	0.150163i	0.628028	−	0.778191i	$-0.283862\pi$
$937$	−4.59656	−	4.59656i	−0.150163	−	0.150163i	−0.778191	+	0.628028i	$0.783862\pi$
$938$	9.13955	+	9.13955i	0.298417	+	0.298417i
$939$	−19.6368	+	53.9319i	−0.640824	+	1.76000i
$940$	−16.8182	+	1.29424i	−0.548550	+	0.0422134i
$941$			26.6136i			0.867580i	0.901014	+	0.433790i	$0.142824\pi$
$941$			26.6136i			0.867580i	−0.901014	+	0.433790i	$0.857176\pi$
$942$	−29.7352	+	13.8615i	−0.968824	+	0.451631i
$943$	23.0079	−	23.0079i	0.749240	−	0.749240i
$944$	8.98420			0.292411
$945$	−5.33909	+	28.4747i	−0.173681	+	0.926281i
$946$	51.9230			1.68816
$947$	−11.3623	+	11.3623i	−0.369225	+	0.369225i	−0.867194	−	0.497970i	$-0.834079\pi$
$947$	−11.3623	+	11.3623i	−0.369225	+	0.369225i	0.497970	+	0.867194i	$0.334079\pi$
$948$	21.0046	−	9.79160i	0.682199	−	0.318016i
$949$		−	0.422766i		−	0.0137236i
$950$	−5.50897	+	7.52732i	−0.178734	+	0.244218i
$951$	−10.9256	+	30.0067i	−0.354286	+	0.973034i
$952$	6.90955	+	6.90955i	0.223940	+	0.223940i
$953$	−1.11734	−	1.11734i	−0.0361943	−	0.0361943i	0.688778	−	0.724972i	$-0.258147\pi$
$953$	−1.11734	−	1.11734i	−0.0361943	−	0.0361943i	−0.724972	+	0.688778i	$0.758147\pi$
$954$	21.6564	−	25.7967i	0.701152	−	0.835200i
$955$	24.5774	+	21.0651i	0.795307	+	0.681649i
$956$		−	13.8215i		−	0.447018i
$957$	−14.0919	−	30.2295i	−0.455527	−	0.977182i
$958$	6.70181	−	6.70181i	0.216526	−	0.216526i
$959$	−27.9188			−0.901545
$960$	−3.73020	−	1.04193i	−0.120392	−	0.0336282i
$961$	1.00000			0.0322581
$962$	6.77900	−	6.77900i	0.218564	−	0.218564i
$963$	1.03183	+	11.8261i	0.0332503	+	0.381091i
$964$			20.8975i			0.673063i
$965$	−1.63815	−	21.2873i	−0.0527339	−	0.685261i
$966$	−21.5529	−	7.84748i	−0.693452	−	0.252489i
$967$	−25.4252	−	25.4252i	−0.817618	−	0.817618i	0.168144	−	0.985762i	$-0.446223\pi$
$967$	−25.4252	−	25.4252i	−0.817618	−	0.817618i	−0.985762	+	0.168144i	$0.946223\pi$
$968$	12.2037	+	12.2037i	0.392243	+	0.392243i
$969$	−11.8990	−	4.33247i	−0.382251	−	0.139179i
$970$	15.8473	−	18.4897i	0.508827	−	0.593669i
$971$			61.8055i			1.98343i	0.128452	+	0.991716i	$0.458999\pi$
$971$			61.8055i			1.98343i	−0.128452	+	0.991716i	$0.541001\pi$
$972$	12.7746	−	8.93362i	0.409745	−	0.286546i
$973$	−1.93753	+	1.93753i	−0.0621143	+	0.0621143i
$974$	18.7962			0.602271
$975$	40.3618	+	7.99610i	1.29261	+	0.256080i
$976$	3.54388			0.113437
$977$	5.25621	−	5.25621i	0.168161	−	0.168161i	−0.618010	−	0.786171i	$-0.712061\pi$
$977$	5.25621	−	5.25621i	0.168161	−	0.168161i	0.786171	+	0.618010i	$0.212061\pi$
$978$	−2.58819	−	5.55212i	−0.0827613	−	0.177537i
$979$			26.6106i			0.850479i
$980$	−1.13920	+	1.32915i	−0.0363905	+	0.0424583i
$981$	13.1659	+	11.0528i	0.420355	+	0.352890i
$982$	4.94294	+	4.94294i	0.157736	+	0.157736i
$983$	−17.7765	−	17.7765i	−0.566983	−	0.566983i	0.364299	−	0.931282i	$-0.381309\pi$
$983$	−17.7765	−	17.7765i	−0.566983	−	0.566983i	−0.931282	+	0.364299i	$0.881309\pi$
$984$	3.63047	−	9.97097i	0.115735	−	0.317863i
$985$	3.40263	+	44.2162i	0.108417	+	1.40885i
$986$			14.1960i			0.452091i
$987$	−29.5279	+	13.7648i	−0.939884	+	0.438140i
$988$	−6.26754	+	6.26754i	−0.199397	+	0.199397i
$989$	51.8759			1.64956
$990$	20.7652	−	28.9905i	0.659960	−	0.921379i
$991$	−28.3639			−0.901008			−0.450504	−	0.892774i	$-0.648756\pi$
$991$	−28.3639			−0.901008			−0.450504	+	0.892774i	$0.648756\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	−35.0987	+	16.3617i	−1.11382	+	0.519224i
$994$			21.3847i			0.678282i
$995$	−18.9605	−	16.2509i	−0.601089	−	0.515187i
$996$	3.61216	−	9.92068i	0.114456	−	0.314349i
$997$	−7.52405	−	7.52405i	−0.238289	−	0.238289i	0.577852	−	0.816141i	$-0.303891\pi$
$997$	−7.52405	−	7.52405i	−0.238289	−	0.238289i	−0.816141	+	0.577852i	$0.803891\pi$
$998$	26.2611	+	26.2611i	0.831280	+	0.831280i
$999$	−9.08202	+	5.23921i	−0.287342	+	0.165761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.11	yes	40
3.2	odd	2	inner	930.2.j.g.497.4	✓	40
5.3	odd	4	inner	930.2.j.g.683.4	yes	40
15.8	even	4	inner	930.2.j.g.683.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.4	✓	40	3.2	odd	2	inner
930.2.j.g.497.11	yes	40	1.1	even	1	trivial
930.2.j.g.683.4	yes	40	5.3	odd	4	inner
930.2.j.g.683.11	yes	40	15.8	even	4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.56986 + 0.731811i) q^{3} -1.00000i q^{4} +(1.45516 - 1.69779i) q^{5} +(-0.592589 + 1.62753i) q^{6} +(1.76311 + 1.76311i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.92891 - 2.29768i) q^{9} +(-0.171568 - 2.22948i) q^{10} +5.31589i q^{11} +(0.731811 + 1.56986i) q^{12} +(3.35958 - 3.35958i) q^{13} +2.49342 q^{14} +(-1.04193 + 3.73020i) q^{15} -1.00000 q^{16} +(-2.77112 + 2.77112i) q^{17} +(-0.260761 - 2.98865i) q^{18} -1.86557i q^{19} +(-1.69779 - 1.45516i) q^{20} +(-4.05810 - 1.47757i) q^{21} +(3.75890 + 3.75890i) q^{22} +(3.75550 + 3.75550i) q^{23} +(1.62753 + 0.592589i) q^{24} +(-0.765014 - 4.94113i) q^{25} -4.75116i q^{26} +(-1.34664 + 5.01862i) q^{27} +(1.76311 - 1.76311i) q^{28} +3.62239 q^{29} +(1.90089 + 3.37441i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.89023 - 8.34519i) q^{33} +3.91895i q^{34} +(5.55901 - 0.427791i) q^{35} +(-2.29768 - 1.92891i) q^{36} +(1.42681 + 1.42681i) q^{37} +(-1.31916 - 1.31916i) q^{38} +(-2.81548 + 7.73263i) q^{39} +(-2.22948 + 0.171568i) q^{40} -6.12646i q^{41} +(-3.91431 + 1.82471i) q^{42} +(6.90667 - 6.90667i) q^{43} +5.31589 q^{44} +(-1.09412 - 6.61838i) q^{45} +5.31107 q^{46} +(5.33412 - 5.33412i) q^{47} +(1.56986 - 0.731811i) q^{48} -0.782871i q^{49} +(-4.03485 - 2.95296i) q^{50} +(2.32233 - 6.37819i) q^{51} +(-3.35958 - 3.35958i) q^{52} +(7.93890 + 7.93890i) q^{53} +(2.59648 + 4.50092i) q^{54} +(9.02529 + 7.73548i) q^{55} -2.49342i q^{56} +(1.36525 + 2.92869i) q^{57} +(2.56141 - 2.56141i) q^{58} -8.98420 q^{59} +(3.73020 + 1.04193i) q^{60} -3.54388 q^{61} +(0.707107 - 0.707107i) q^{62} +(7.45194 - 0.650185i) q^{63} +1.00000i q^{64} +(-0.815147 - 10.5926i) q^{65} +(-8.65175 - 3.15014i) q^{66} +(3.66547 + 3.66547i) q^{67} +(2.77112 + 2.77112i) q^{68} +(-8.64390 - 3.14728i) q^{69} +(3.62832 - 4.23331i) q^{70} +8.57648i q^{71} +(-2.98865 + 0.260761i) q^{72} +(0.0629195 - 0.0629195i) q^{73} +2.01781 q^{74} +(4.81693 + 7.19702i) q^{75} -1.86557 q^{76} +(-9.37251 + 9.37251i) q^{77} +(3.47695 + 7.45864i) q^{78} -13.3800i q^{79} +(-1.45516 + 1.69779i) q^{80} +(-1.55864 - 8.86401i) q^{81} +(-4.33206 - 4.33206i) q^{82} +(-4.31021 - 4.31021i) q^{83} +(-1.47757 + 4.05810i) q^{84} +(0.672367 + 8.73721i) q^{85} -9.76750i q^{86} +(-5.68663 + 2.65090i) q^{87} +(3.75890 - 3.75890i) q^{88} +5.00586 q^{89} +(-5.45356 - 3.90624i) q^{90} +11.8466 q^{91} +(3.75550 - 3.75550i) q^{92} +(-1.56986 + 0.731811i) q^{93} -7.54358i q^{94} +(-3.16736 - 2.71471i) q^{95} +(0.592589 - 1.62753i) q^{96} +(7.70070 + 7.70070i) q^{97} +(-0.553574 - 0.553574i) q^{98} +(12.2142 + 10.2539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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