LMFDB - Embedded newform 182.2.bc.a.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,2,Mod(45,182)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(182, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("182.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	182.59
Dual form			182.2.bc.a.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.0314033 - 0.0181307i) q^{3} +1.00000i q^{4} +(-3.24551 - 0.869631i) q^{5} +(-0.0350259 - 0.00938515i) q^{6} +(-2.06794 + 1.65034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.49934 + 2.59694i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.0314033 - 0.0181307i) q^{3} +1.00000i q^{4} +(-3.24551 - 0.869631i) q^{5} +(-0.0350259 - 0.00938515i) q^{6} +(-2.06794 + 1.65034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.49934 + 2.59694i) q^{9} +(1.68000 + 2.90984i) q^{10} +(-3.01261 - 0.807227i) q^{11} +(0.0181307 + 0.0314033i) q^{12} +(3.42713 - 1.12018i) q^{13} +(2.62922 + 0.295287i) q^{14} +(-0.117687 + 0.0315341i) q^{15} -1.00000 q^{16} -5.94664 q^{17} +(2.89651 - 0.776117i) q^{18} +(-0.537668 - 2.00660i) q^{19} +(0.869631 - 3.24551i) q^{20} +(-0.0350183 + 0.0893194i) q^{21} +(1.55944 + 2.70103i) q^{22} +6.51366i q^{23} +(0.00938515 - 0.0350259i) q^{24} +(5.44693 + 3.14479i) q^{25} +(-3.21543 - 1.63126i) q^{26} +0.217521i q^{27} +(-1.65034 - 2.06794i) q^{28} +(2.68213 - 4.64559i) q^{29} +(0.105515 + 0.0609191i) q^{30} +(-0.598133 - 2.23226i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.109242 + 0.0292712i) q^{33} +(4.20491 + 4.20491i) q^{34} +(8.14670 - 3.55785i) q^{35} +(-2.59694 - 1.49934i) q^{36} +(-2.12835 + 2.12835i) q^{37} +(-1.03869 + 1.79907i) q^{38} +(0.0873135 - 0.0973136i) q^{39} +(-2.90984 + 1.68000i) q^{40} +(-1.87632 - 7.00254i) q^{41} +(0.0879200 - 0.0383967i) q^{42} +(-6.96121 + 4.01906i) q^{43} +(0.807227 - 3.01261i) q^{44} +(7.12451 - 7.12451i) q^{45} +(4.60585 - 4.60585i) q^{46} +(1.37542 - 5.13313i) q^{47} +(-0.0314033 + 0.0181307i) q^{48} +(1.55275 - 6.82561i) q^{49} +(-1.62786 - 6.07527i) q^{50} +(-0.186744 + 0.107817i) q^{51} +(1.12018 + 3.42713i) q^{52} +(2.87612 - 4.98159i) q^{53} +(0.153811 - 0.153811i) q^{54} +(9.07546 + 5.23972i) q^{55} +(-0.295287 + 2.62922i) q^{56} +(-0.0532657 - 0.0532657i) q^{57} +(-5.18148 + 1.38837i) q^{58} +(8.08487 + 8.08487i) q^{59} +(-0.0315341 - 0.117687i) q^{60} +(2.82159 + 1.62905i) q^{61} +(-1.15550 + 2.00139i) q^{62} +(-1.18528 - 7.84474i) q^{63} -1.00000i q^{64} +(-12.0969 + 0.655212i) q^{65} +(0.0979433 + 0.0565476i) q^{66} +(-1.77036 + 6.60706i) q^{67} -5.94664i q^{68} +(0.118097 + 0.204550i) q^{69} +(-8.27637 - 3.24481i) q^{70} +(-4.14510 + 15.4697i) q^{71} +(0.776117 + 2.89651i) q^{72} +(-11.2497 + 3.01436i) q^{73} +3.00994 q^{74} +0.228069 q^{75} +(2.00660 - 0.537668i) q^{76} +(7.56210 - 3.30254i) q^{77} +(-0.130551 + 0.00707111i) q^{78} +(4.09800 + 7.09795i) q^{79} +(3.24551 + 0.869631i) q^{80} +(-4.49408 - 7.78398i) q^{81} +(-3.62478 + 6.27830i) q^{82} +(-9.96984 + 9.96984i) q^{83} +(-0.0893194 - 0.0350183i) q^{84} +(19.2999 + 5.17138i) q^{85} +(7.76422 + 2.08042i) q^{86} -0.194516i q^{87} +(-2.70103 + 1.55944i) q^{88} +(-8.00364 - 8.00364i) q^{89} -10.0756 q^{90} +(-5.23841 + 7.97239i) q^{91} -6.51366 q^{92} +(-0.0592559 - 0.0592559i) q^{93} +(-4.60224 + 2.65710i) q^{94} +6.98002i q^{95} +(0.0350259 + 0.00938515i) q^{96} +(-1.69806 - 0.454993i) q^{97} +(-5.92439 + 3.72848i) q^{98} +(6.61325 - 6.61325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} + 24 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 + 24 * q^9	$ 40 q - 4 q^{7} + 24 q^{9} + 4 q^{12} - 4 q^{14} - 16 q^{15} - 40 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{21} + 4 q^{22} - 8 q^{28} + 4 q^{29} + 24 q^{30} - 4 q^{31} + 36 q^{33} + 28 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{39} - 24 q^{41} - 12 q^{42} - 72 q^{43} + 12 q^{44} + 4 q^{49} - 24 q^{51} + 4 q^{52} - 4 q^{53} + 36 q^{54} - 12 q^{55} - 12 q^{56} - 12 q^{57} - 8 q^{58} - 8 q^{60} - 12 q^{61} - 36 q^{62} - 108 q^{63} - 16 q^{65} + 44 q^{67} + 84 q^{69} + 8 q^{70} + 28 q^{71} + 8 q^{72} - 44 q^{73} + 40 q^{74} + 56 q^{75} + 32 q^{76} + 8 q^{78} - 16 q^{79} + 4 q^{81} + 48 q^{82} - 108 q^{83} + 24 q^{84} + 56 q^{85} + 52 q^{86} - 12 q^{89} + 52 q^{91} + 32 q^{92} - 24 q^{93} + 48 q^{94} + 88 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 24 * q^9 + 4 * q^12 - 4 * q^14 - 16 * q^15 - 40 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^21 + 4 * q^22 - 8 * q^28 + 4 * q^29 + 24 * q^30 - 4 * q^31 + 36 * q^33 + 28 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^39 - 24 * q^41 - 12 * q^42 - 72 * q^43 + 12 * q^44 + 4 * q^49 - 24 * q^51 + 4 * q^52 - 4 * q^53 + 36 * q^54 - 12 * q^55 - 12 * q^56 - 12 * q^57 - 8 * q^58 - 8 * q^60 - 12 * q^61 - 36 * q^62 - 108 * q^63 - 16 * q^65 + 44 * q^67 + 84 * q^69 + 8 * q^70 + 28 * q^71 + 8 * q^72 - 44 * q^73 + 40 * q^74 + 56 * q^75 + 32 * q^76 + 8 * q^78 - 16 * q^79 + 4 * q^81 + 48 * q^82 - 108 * q^83 + 24 * q^84 + 56 * q^85 + 52 * q^86 - 12 * q^89 + 52 * q^91 + 32 * q^92 - 24 * q^93 + 48 * q^94 + 88 * q^97 + 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.0314033	−	0.0181307i	0.0181307	−	0.0104678i	−0.490907	−	0.871212i	$-0.663335\pi$
$3$	0.0314033	−	0.0181307i	0.0181307	−	0.0104678i	0.509038	+	0.860744i	$0.330001\pi$
$4$			1.00000i			0.500000i
$5$	−3.24551	−	0.869631i	−1.45144	−	0.388911i	−0.554912	−	0.831909i	$-0.687248\pi$
$5$	−3.24551	−	0.869631i	−1.45144	−	0.388911i	−0.896523	+	0.442998i	$0.853915\pi$
$6$	−0.0350259	−	0.00938515i	−0.0142992	−	0.00383147i
$7$	−2.06794	+	1.65034i	−0.781608	+	0.623770i
$7$	−2.06794	+	1.65034i	−0.781608	+	0.623770i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.49934	+	2.59694i	−0.499781	+	0.865646i
$10$	1.68000	+	2.90984i	0.531262	+	0.920173i
$11$	−3.01261	−	0.807227i	−0.908336	−	0.243388i	−0.225743	−	0.974187i	$-0.572481\pi$
$11$	−3.01261	−	0.807227i	−0.908336	−	0.243388i	−0.682593	+	0.730799i	$0.739148\pi$
$12$	0.0181307	+	0.0314033i	0.00523389	+	0.00906536i
$13$	3.42713	−	1.12018i	0.950514	−	0.310682i
$13$	3.42713	−	1.12018i	0.950514	−	0.310682i
$14$	2.62922	+	0.295287i	0.702689	+	0.0789187i
$15$	−0.117687	+	0.0315341i	−0.0303866	+	0.00814206i
$16$	−1.00000			−0.250000
$17$	−5.94664			−1.44227			−0.721136	−	0.692794i	$-0.756380\pi$
$17$	−5.94664			−1.44227			−0.721136	+	0.692794i	$0.756380\pi$
$18$	2.89651	−	0.776117i	0.682713	−	0.182932i
$19$	−0.537668	−	2.00660i	−0.123349	−	0.460346i	0.876426	−	0.481536i	$-0.159921\pi$
$19$	−0.537668	−	2.00660i	−0.123349	−	0.460346i	−0.999775	+	0.0211902i	$0.993254\pi$
$20$	0.869631	−	3.24551i	0.194455	−	0.725718i
$21$	−0.0350183	+	0.0893194i	−0.00764162	+	0.0194911i
$22$	1.55944	+	2.70103i	0.332474	+	0.575862i
$23$			6.51366i			1.35819i	0.734050	+	0.679096i	$0.237628\pi$
$23$			6.51366i			1.35819i	−0.734050	+	0.679096i	$0.762372\pi$
$24$	0.00938515	−	0.0350259i	0.00191574	−	0.00714962i
$25$	5.44693	+	3.14479i	1.08939	+	0.628958i
$26$	−3.21543	−	1.63126i	−0.630598	−	0.319916i
$27$			0.217521i			0.0418619i
$28$	−1.65034	−	2.06794i	−0.311885	−	0.390804i
$29$	2.68213	−	4.64559i	0.498060	−	0.862665i	−0.501938	−	0.864904i	$-0.667379\pi$
$29$	2.68213	−	4.64559i	0.498060	−	0.862665i	0.999997	+	0.00223908i	$0.000712721\pi$
$30$	0.105515	+	0.0609191i	0.0192643	+	0.0111223i
$31$	−0.598133	−	2.23226i	−0.107428	−	0.400926i	0.891181	−	0.453647i	$-0.149877\pi$
$31$	−0.598133	−	2.23226i	−0.107428	−	0.400926i	−0.998609	+	0.0527208i	$0.983211\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.109242	+	0.0292712i	−0.0190165	+	0.00509546i
$34$	4.20491	+	4.20491i	0.721136	+	0.721136i
$35$	8.14670	−	3.55785i	1.37704	−	0.601386i
$36$	−2.59694	−	1.49934i	−0.432823	−	0.249890i
$37$	−2.12835	+	2.12835i	−0.349899	+	0.349899i	−0.860072	−	0.510173i	$-0.829581\pi$
$37$	−2.12835	+	2.12835i	−0.349899	+	0.349899i	0.510173	+	0.860072i	$0.329581\pi$
$38$	−1.03869	+	1.79907i	−0.168498	+	0.291848i
$39$	0.0873135	−	0.0973136i	0.0139814	−	0.0155826i
$40$	−2.90984	+	1.68000i	−0.460086	+	0.265631i
$41$	−1.87632	−	7.00254i	−0.293033	−	1.09361i	−0.942767	−	0.333451i	$-0.891787\pi$
$41$	−1.87632	−	7.00254i	−0.293033	−	1.09361i	0.649735	−	0.760161i	$-0.274880\pi$
$42$	0.0879200	−	0.0383967i	0.0135664	−	0.00592474i
$43$	−6.96121	+	4.01906i	−1.06157	+	0.612900i	−0.925867	−	0.377849i	$-0.876664\pi$
$43$	−6.96121	+	4.01906i	−1.06157	+	0.612900i	−0.135707	+	0.990749i	$0.543331\pi$
$44$	0.807227	−	3.01261i	0.121694	−	0.454168i
$45$	7.12451	−	7.12451i	1.06206	−	1.06206i
$46$	4.60585	−	4.60585i	0.679096	−	0.679096i
$47$	1.37542	−	5.13313i	0.200625	−	0.748743i	−0.790113	−	0.612961i	$-0.789978\pi$
$47$	1.37542	−	5.13313i	0.200625	−	0.748743i	0.990739	−	0.135783i	$-0.0433549\pi$
$48$	−0.0314033	+	0.0181307i	−0.00453268	+	0.00261694i
$49$	1.55275	−	6.82561i	0.221821	−	0.975087i
$50$	−1.62786	−	6.07527i	−0.230215	−	0.859172i
$51$	−0.186744	+	0.107817i	−0.0261494	+	0.0150974i
$52$	1.12018	+	3.42713i	0.155341	+	0.475257i
$53$	2.87612	−	4.98159i	0.395066	−	0.684274i	−0.598044	−	0.801463i	$-0.704055\pi$
$53$	2.87612	−	4.98159i	0.395066	−	0.684274i	0.993110	+	0.117190i	$0.0373885\pi$
$54$	0.153811	−	0.153811i	0.0209310	−	0.0209310i
$55$	9.07546	+	5.23972i	1.22374	+	0.706524i
$56$	−0.295287	+	2.62922i	−0.0394593	+	0.351345i
$57$	−0.0532657	−	0.0532657i	−0.00705521	−	0.00705521i
$58$	−5.18148	+	1.38837i	−0.680362	+	0.182302i
$59$	8.08487	+	8.08487i	1.05256	+	1.05256i	0.998540	+	0.0540208i	$0.0172037\pi$
$59$	8.08487	+	8.08487i	1.05256	+	1.05256i	0.0540208	+	0.998540i	$0.482796\pi$
$60$	−0.0315341	−	0.117687i	−0.00407103	−	0.0151933i
$61$	2.82159	+	1.62905i	0.361268	+	0.208578i	0.669637	−	0.742689i	$-0.266450\pi$
$61$	2.82159	+	1.62905i	0.361268	+	0.208578i	−0.308369	+	0.951267i	$0.599783\pi$
$62$	−1.15550	+	2.00139i	−0.146749	+	0.254177i
$63$	−1.18528	−	7.84474i	−0.149332	−	0.988344i
$64$		−	1.00000i		−	0.125000i
$65$	−12.0969	+	0.655212i	−1.50044	+	0.0812690i
$66$	0.0979433	+	0.0565476i	0.0120560	+	0.00696053i
$67$	−1.77036	+	6.60706i	−0.216284	+	0.807181i	0.769427	+	0.638735i	$0.220542\pi$
$67$	−1.77036	+	6.60706i	−0.216284	+	0.807181i	−0.985711	+	0.168447i	$0.946125\pi$
$68$		−	5.94664i		−	0.721136i
$69$	0.118097	+	0.204550i	0.0142172	+	0.0246250i
$70$	−8.27637	−	3.24481i	−0.989215	−	0.387829i
$71$	−4.14510	+	15.4697i	−0.491933	+	1.83592i	0.0546373	+	0.998506i	$0.482600\pi$
$71$	−4.14510	+	15.4697i	−0.491933	+	1.83592i	−0.546570	+	0.837413i	$0.684067\pi$
$72$	0.776117	+	2.89651i	0.0914662	+	0.341357i
$73$	−11.2497	+	3.01436i	−1.31668	+	0.352804i	−0.847734	−	0.530422i	$-0.822034\pi$
$73$	−11.2497	+	3.01436i	−1.31668	+	0.352804i	−0.468948	+	0.883226i	$0.655367\pi$
$74$	3.00994			0.349899
$75$	0.228069			0.0263352
$76$	2.00660	−	0.537668i	0.230173	−	0.0616747i
$77$	7.56210	−	3.30254i	0.861781	−	0.376359i
$78$	−0.130551	+	0.00707111i	−0.0147820	+	0.000800646i
$79$	4.09800	+	7.09795i	0.461061	+	0.798581i	0.999014	−	0.0443936i	$-0.0141356\pi$
$79$	4.09800	+	7.09795i	0.461061	+	0.798581i	−0.537953	+	0.842975i	$0.680802\pi$
$80$	3.24551	+	0.869631i	0.362859	+	0.0972277i
$81$	−4.49408	−	7.78398i	−0.499343	−	0.864887i
$82$	−3.62478	+	6.27830i	−0.400290	+	0.693323i
$83$	−9.96984	+	9.96984i	−1.09433	+	1.09433i	−0.0992713	+	0.995060i	$0.531651\pi$
$83$	−9.96984	+	9.96984i	−1.09433	+	1.09433i	−0.995060	+	0.0992713i	$0.968349\pi$
$84$	−0.0893194	−	0.0350183i	−0.00974555	−	0.00382081i
$85$	19.2999	+	5.17138i	2.09336	+	0.560915i
$86$	7.76422	+	2.08042i	0.837237	+	0.224337i
$87$		−	0.194516i		−	0.0208543i
$88$	−2.70103	+	1.55944i	−0.287931	+	0.166237i
$89$	−8.00364	−	8.00364i	−0.848384	−	0.848384i	0.141547	−	0.989931i	$-0.454792\pi$
$89$	−8.00364	−	8.00364i	−0.848384	−	0.848384i	−0.989931	+	0.141547i	$0.954792\pi$
$90$	−10.0756			−1.06206
$91$	−5.23841	+	7.97239i	−0.549135	+	0.835734i
$92$	−6.51366			−0.679096
$93$	−0.0592559	−	0.0592559i	−0.00614455	−	0.00614455i
$94$	−4.60224	+	2.65710i	−0.474684	+	0.274059i
$95$			6.98002i			0.716135i
$96$	0.0350259	+	0.00938515i	0.00357481	+	0.000957868i
$97$	−1.69806	−	0.454993i	−0.172412	−	0.0461975i	0.171580	−	0.985170i	$-0.445113\pi$
$97$	−1.69806	−	0.454993i	−0.172412	−	0.0461975i	−0.343992	+	0.938973i	$0.611779\pi$
$98$	−5.92439	+	3.72848i	−0.598454	+	0.376633i
$99$	6.61325	−	6.61325i	0.664657	−	0.664657i
$100$	−3.14479	+	5.44693i	−0.314479	+	0.544693i
$101$	−0.106227	−	0.183990i	−0.0105699	−	0.0183077i	0.860692	−	0.509126i	$-0.170031\pi$
$101$	−0.106227	−	0.183990i	−0.0105699	−	0.0183077i	−0.871262	+	0.490818i	$0.836698\pi$
$102$	0.208286	+	0.0558101i	0.0206234	+	0.00552602i
$103$	−1.25611	−	2.17565i	−0.123768	−	0.214373i	0.797482	−	0.603342i	$-0.206165\pi$
$103$	−1.25611	−	2.17565i	−0.123768	−	0.214373i	−0.921251	+	0.388969i	$0.872831\pi$
$104$	1.63126	−	3.21543i	0.159958	−	0.315299i
$105$	0.191327	−	0.259434i	0.0186716	−	0.0253182i
$106$	−5.55624	+	1.48879i	−0.539670	+	0.144604i
$107$	−6.54210			−0.632449			−0.316224	−	0.948684i	$-0.602415\pi$
$107$	−6.54210			−0.632449			−0.316224	+	0.948684i	$0.602415\pi$
$108$	−0.217521			−0.0209310
$109$	2.56326	−	0.686823i	0.245516	−	0.0657857i	−0.133963	−	0.990986i	$-0.542770\pi$
$109$	2.56326	−	0.686823i	0.245516	−	0.0657857i	0.379478	+	0.925201i	$0.376104\pi$
$110$	−2.71228	−	10.1224i	−0.258606	−	0.965129i
$111$	−0.0282488	+	0.105426i	−0.00268125	+	0.0100066i
$112$	2.06794	−	1.65034i	0.195402	−	0.155943i
$113$	5.80234	+	10.0500i	0.545839	+	0.945420i	0.998554	+	0.0537649i	$0.0171222\pi$
$113$	5.80234	+	10.0500i	0.545839	+	0.945420i	−0.452715	+	0.891655i	$0.649545\pi$
$114$			0.0753291i			0.00705521i
$115$	5.66448	−	21.1401i	0.528215	−	1.97133i
$116$	4.64559	+	2.68213i	0.431332	+	0.249030i
$117$	−2.22940	+	10.5796i	−0.206108	+	0.978081i
$118$		−	11.4337i		−	1.05256i
$119$	12.2973	−	9.81398i	1.12729	−	0.899646i
$120$	−0.0609191	+	0.105515i	−0.00556113	+	0.00963216i
$121$	−1.10207	−	0.636280i	−0.100188	−	0.0578437i
$122$	−0.843256	−	3.14708i	−0.0763448	−	0.284923i
$123$	−0.185884	−	0.185884i	−0.0167606	−	0.0167606i
$124$	2.23226	−	0.598133i	0.200463	−	0.0537139i
$125$	−3.06388	−	3.06388i	−0.274042	−	0.274042i
$126$	−4.70894	+	6.38519i	−0.419506	+	0.568838i
$127$	−5.04346	−	2.91184i	−0.447535	−	0.258384i	0.259254	−	0.965809i	$-0.416523\pi$
$127$	−5.04346	−	2.91184i	−0.447535	−	0.258384i	−0.706789	+	0.707425i	$0.749857\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.145737	+	0.252423i	−0.0128314	+	0.0222246i
$130$	9.01711	+	8.09050i	0.790853	+	0.709584i
$131$	−2.44971	+	1.41434i	−0.214032	+	0.123571i	−0.603184	−	0.797602i	$-0.706101\pi$
$131$	−2.44971	+	1.41434i	−0.214032	+	0.123571i	0.389152	+	0.921174i	$0.372768\pi$
$132$	−0.0292712	−	0.109242i	−0.00254773	−	0.00950826i
$133$	4.42344	+	3.26220i	0.383561	+	0.282868i
$134$	5.92373	−	3.42007i	0.511732	−	0.295449i
$135$	0.189163	−	0.705966i	0.0162806	−	0.0607599i
$136$	−4.20491	+	4.20491i	−0.360568	+	0.360568i
$137$	−7.55612	+	7.55612i	−0.645563	+	0.645563i	−0.951917	−	0.306355i	$-0.900891\pi$
$137$	−7.55612	+	7.55612i	−0.645563	+	0.645563i	0.306355	+	0.951917i	$0.400891\pi$
$138$	0.0611316	−	0.228146i	0.00520387	−	0.0194211i
$139$	−2.88289	+	1.66444i	−0.244524	+	0.141176i	−0.617254	−	0.786764i	$-0.711755\pi$
$139$	−2.88289	+	1.66444i	−0.244524	+	0.141176i	0.372730	+	0.927940i	$0.378422\pi$
$140$	3.55785	+	8.14670i	0.300693	+	0.688522i
$141$	−0.0498746	−	0.186135i	−0.00420020	−	0.0156754i
$142$	13.8698	−	8.00772i	1.16393	−	0.671993i
$143$	−11.2288	+	0.608194i	−0.939003	+	0.0508597i
$144$	1.49934	−	2.59694i	0.124945	−	0.216411i
$145$	−12.7448	+	12.7448i	−1.05840	+	1.05840i
$146$	10.0862	+	5.82329i	0.834743	+	0.481939i
$147$	−0.0749918	−	0.242499i	−0.00618522	−	0.0200010i
$148$	−2.12835	−	2.12835i	−0.174949	−	0.174949i
$149$	21.2613	−	5.69695i	1.74179	−	0.466712i	0.758949	−	0.651150i	$-0.225713\pi$
$149$	21.2613	−	5.69695i	1.74179	−	0.466712i	0.982844	+	0.184438i	$0.0590464\pi$
$150$	−0.161269	−	0.161269i	−0.0131676	−	0.0131676i
$151$	−1.15262	−	4.30165i	−0.0937992	−	0.350063i	0.903035	−	0.429566i	$-0.141333\pi$
$151$	−1.15262	−	4.30165i	−0.0937992	−	0.350063i	−0.996835	+	0.0795027i	$0.974667\pi$
$152$	−1.79907	−	1.03869i	−0.145924	−	0.0842492i
$153$	8.91605	−	15.4431i	0.720820	−	1.24850i
$154$	−7.68246	−	3.01196i	−0.619070	−	0.242711i
$155$			7.76498i			0.623699i
$156$	0.0973136	+	0.0873135i	0.00779132	+	0.00699068i
$157$	4.00469	+	2.31211i	0.319609	+	0.184527i	0.651218	−	0.758890i	$-0.274258\pi$
$157$	4.00469	+	2.31211i	0.319609	+	0.184527i	−0.331609	+	0.943417i	$0.607591\pi$
$158$	2.12128	−	7.91673i	0.168760	−	0.629821i
$159$		−	0.208585i		−	0.0165418i
$160$	−1.68000	−	2.90984i	−0.132816	−	0.230043i
$161$	−10.7498	−	13.4698i	−0.847199	−	1.06157i
$162$	−2.32631	+	8.68190i	−0.182772	+	0.682115i
$163$	−3.93775	−	14.6959i	−0.308429	−	1.15107i	−0.929953	−	0.367677i	$-0.880153\pi$
$163$	−3.93775	−	14.6959i	−0.308429	−	1.15107i	0.621525	−	0.783395i	$-0.286514\pi$
$164$	7.00254	−	1.87632i	0.546806	−	0.146516i
$165$	0.380000			0.0295829
$166$	14.0995			1.09433
$167$	0.814446	−	0.218230i	0.0630238	−	0.0168872i	−0.227169	−	0.973855i	$-0.572947\pi$
$167$	0.814446	−	0.218230i	0.0630238	−	0.0168872i	0.290193	+	0.956968i	$0.406280\pi$
$168$	0.0383967	+	0.0879200i	0.00296237	+	0.00678318i
$169$	10.4904	−	7.67799i	0.806954	−	0.590615i
$170$	−9.99034	−	17.3038i	−0.766224	−	1.32714i
$171$	6.01717	+	1.61230i	0.460145	+	0.123295i
$172$	−4.01906	−	6.96121i	−0.306450	−	0.530787i
$173$	−0.0804389	+	0.139324i	−0.00611566	+	0.0105926i	−0.869067	−	0.494694i	$-0.835280\pi$
$173$	−0.0804389	+	0.139324i	−0.00611566	+	0.0105926i	0.862951	+	0.505287i	$0.168613\pi$
$174$	−0.137544	+	0.137544i	−0.0104272	+	0.0104272i
$175$	−16.4539	+	2.48607i	−1.24380	+	0.187929i
$176$	3.01261	+	0.807227i	0.227084	+	0.0608470i
$177$	0.400476	+	0.107307i	0.0301016	+	0.00806571i
$178$			11.3189i			0.848384i
$179$	−0.483205	+	0.278979i	−0.0361165	+	0.0208518i	−0.517950	−	0.855411i	$-0.673304\pi$
$179$	−0.483205	+	0.278979i	−0.0361165	+	0.0208518i	0.481833	+	0.876263i	$0.339971\pi$
$180$	7.12451	+	7.12451i	0.531029	+	0.531029i
$181$	−16.3368			−1.21431			−0.607153	−	0.794585i	$-0.707689\pi$
$181$	−16.3368			−1.21431			−0.607153	+	0.794585i	$0.707689\pi$
$182$	9.34145	−	1.93321i	0.692434	−	0.143299i
$183$	0.118143			0.00873339
$184$	4.60585	+	4.60585i	0.339548	+	0.339548i
$185$	8.75846	−	5.05670i	0.643935	−	0.371776i
$186$			0.0838005i			0.00614455i
$187$	17.9149	+	4.80029i	1.31007	+	0.351032i
$188$	5.13313	+	1.37542i	0.374372	+	0.100313i
$189$	−0.358984	−	0.449820i	−0.0261122	−	0.0327196i
$190$	4.93562	−	4.93562i	0.358067	−	0.358067i
$191$	10.8954	−	18.8714i	0.788363	−	1.36548i	−0.138606	−	0.990348i	$-0.544262\pi$
$191$	10.8954	−	18.8714i	0.788363	−	1.36548i	0.926969	−	0.375137i	$-0.122404\pi$
$192$	−0.0181307	−	0.0314033i	−0.00130847	−	0.00226634i
$193$	14.8850	+	3.98842i	1.07145	+	0.287093i	0.751087	−	0.660203i	$-0.229530\pi$
$193$	14.8850	+	3.98842i	1.07145	+	0.287093i	0.320359	+	0.947296i	$0.396197\pi$
$194$	0.878979	+	1.52244i	0.0631070	+	0.109305i
$195$	−0.368004	+	0.239901i	−0.0263533	+	0.0171797i
$196$	6.82561	+	1.55275i	0.487544	+	0.110911i
$197$	−22.4365	+	6.01184i	−1.59853	+	0.428326i	−0.944599	−	0.328226i	$-0.893549\pi$
$197$	−22.4365	+	6.01184i	−1.59853	+	0.428326i	−0.653934	+	0.756552i	$0.726882\pi$
$198$	−9.35255			−0.664657
$199$	−15.1849			−1.07643			−0.538213	−	0.842809i	$-0.680901\pi$
$199$	−15.1849			−1.07643			−0.538213	+	0.842809i	$0.680901\pi$
$200$	6.07527	−	1.62786i	0.429586	−	0.115107i
$201$	0.0641957	+	0.239582i	0.00452802	+	0.0168988i
$202$	−0.0549870	+	0.205214i	−0.00386887	+	0.0144388i
$203$	2.12032	+	14.0332i	0.148817	+	0.984940i
$204$	−0.107817	−	0.186744i	−0.00754869	−	0.0130747i
$205$			24.3585i			1.70127i
$206$	−0.650211	+	2.42662i	−0.0453024	+	0.169071i
$207$	−16.9156	−	9.76620i	−1.17571	−	0.678798i
$208$	−3.42713	+	1.12018i	−0.237629	+	0.0776704i
$209$			6.47913i			0.448171i
$210$	−0.318736	+	0.0481587i	−0.0219949	+	0.00332327i
$211$	8.38309	−	14.5199i	0.577116	−	0.999593i	−0.418693	−	0.908128i	$-0.637512\pi$
$211$	8.38309	−	14.5199i	0.577116	−	0.999593i	0.995808	−	0.0914655i	$-0.0291551\pi$
$212$	4.98159	+	2.87612i	0.342137	+	0.197533i
$213$	0.150307	+	0.560955i	0.0102989	+	0.0384360i
$214$	4.62596	+	4.62596i	0.316224	+	0.316224i
$215$	26.0878	−	6.99019i	1.77917	−	0.476727i
$216$	0.153811	+	0.153811i	0.0104655	+	0.0104655i
$217$	4.92090	+	3.62906i	0.334052	+	0.246357i
$218$	−2.29816	−	1.32684i	−0.155651	−	0.0898650i
$219$	−0.298627	+	0.298627i	−0.0201793	+	0.0201793i
$220$	−5.23972	+	9.07546i	−0.353262	+	0.611868i
$221$	−20.3799	+	6.66130i	−1.37090	+	0.448087i
$222$	0.0945222	−	0.0545724i	0.00634391	−	0.00366266i
$223$	4.46691	+	16.6707i	0.299126	+	1.11635i	0.937885	+	0.346947i	$0.112782\pi$
$223$	4.46691	+	16.6707i	0.299126	+	1.11635i	−0.638759	+	0.769407i	$0.720552\pi$
$224$	−2.62922	−	0.295287i	−0.175672	−	0.0197297i
$225$	−16.3336	+	9.43023i	−1.08891	+	0.628682i
$226$	3.00351	−	11.2093i	0.199791	−	0.745629i
$227$	5.59135	−	5.59135i	0.371111	−	0.371111i	−0.496771	−	0.867882i	$-0.665481\pi$
$227$	5.59135	−	5.59135i	0.371111	−	0.371111i	0.867882	+	0.496771i	$0.165481\pi$
$228$	0.0532657	−	0.0532657i	0.00352761	−	0.00352761i
$229$	3.91734	−	14.6197i	0.258865	−	0.966097i	−0.707034	−	0.707179i	$-0.749967\pi$
$229$	3.91734	−	14.6197i	0.258865	−	0.966097i	0.965899	−	0.258918i	$-0.0833659\pi$
$230$	−18.9537	+	10.9429i	−1.24977	+	0.721555i
$231$	0.177598	−	0.240817i	0.0116851	−	0.0158446i
$232$	−1.38837	−	5.18148i	−0.0911512	−	0.340181i
$233$	0.132599	−	0.0765563i	0.00868688	−	0.00501537i	−0.495650	−	0.868522i	$-0.665070\pi$
$233$	0.132599	−	0.0765563i	0.00868688	−	0.00501537i	0.504337	+	0.863507i	$0.331737\pi$
$234$	9.05731	−	5.90446i	0.592095	−	0.385986i
$235$	−8.92785	+	15.4635i	−0.582389	+	1.00873i
$236$	−8.08487	+	8.08487i	−0.526280	+	0.526280i
$237$	0.257382	+	0.148599i	0.0167187	+	0.00965257i
$238$	−15.6350	−	1.75596i	−1.01347	−	0.113822i
$239$	−1.78437	−	1.78437i	−0.115422	−	0.115422i	0.647037	−	0.762459i	$-0.276008\pi$
$239$	−1.78437	−	1.78437i	−0.115422	−	0.115422i	−0.762459	+	0.647037i	$0.776008\pi$
$240$	0.117687	−	0.0315341i	0.00759665	−	0.00203552i
$241$	−10.9784	−	10.9784i	−0.707182	−	0.707182i	0.258760	−	0.965942i	$-0.416686\pi$
$241$	−10.9784	−	10.9784i	−0.707182	−	0.707182i	−0.965942	+	0.258760i	$0.916686\pi$
$242$	0.329363	+	1.22920i	0.0211722	+	0.0790159i
$243$	−0.847394	−	0.489243i	−0.0543604	−	0.0313850i
$244$	−1.62905	+	2.82159i	−0.104289	+	0.180634i
$245$	−10.9752	+	20.8023i	−0.701181	+	1.32901i
$246$			0.262879i			0.0167606i
$247$	−4.09041	−	6.27460i	−0.260267	−	0.399243i
$248$	−2.00139	−	1.15550i	−0.127089	−	0.0733746i
$249$	−0.132326	+	0.493846i	−0.00838580	+	0.0312962i
$250$			4.33298i			0.274042i
$251$	−0.855466	−	1.48171i	−0.0539966	−	0.0935248i	0.837764	−	0.546033i	$-0.183863\pi$
$251$	−0.855466	−	1.48171i	−0.0539966	−	0.0935248i	−0.891760	+	0.452508i	$0.850529\pi$
$252$	7.84474	−	1.18528i	0.494172	−	0.0746658i
$253$	5.25800	−	19.6231i	0.330567	−	1.23369i
$254$	1.50728	+	5.62525i	0.0945753	+	0.352960i
$255$	0.699841	−	0.187522i	0.0438257	−	0.0117431i
$256$	1.00000			0.0625000
$257$	17.6292			1.09968			0.549840	−	0.835270i	$-0.314689\pi$
$257$	17.6292			1.09968			0.549840	+	0.835270i	$0.314689\pi$
$258$	0.281542	−	0.0754389i	0.0175280	−	0.00469662i
$259$	0.888795	−	7.91380i	0.0552271	−	0.491740i
$260$	−0.655212	−	12.0969i	−0.0406345	−	0.750218i
$261$	8.04287	+	13.9307i	0.497841	+	0.862287i
$262$	2.73229	+	0.732116i	0.168802	+	0.0452303i
$263$	−4.13540	−	7.16273i	−0.255000	−	0.441673i	0.709896	−	0.704307i	$-0.248742\pi$
$263$	−4.13540	−	7.16273i	−0.255000	−	0.441673i	−0.964895	+	0.262634i	$0.915409\pi$
$264$	−0.0565476	+	0.0979433i	−0.00348026	+	0.00602800i
$265$	−13.6666	+	13.6666i	−0.839534	+	0.839534i
$266$	−0.821125	−	5.43457i	−0.0503464	−	0.333215i
$267$	−0.396453	−	0.106229i	−0.0242625	−	0.00650112i
$268$	−6.60706	−	1.77036i	−0.403591	−	0.108142i
$269$			3.77698i			0.230286i	0.993349	+	0.115143i	$0.0367327\pi$
$269$			3.77698i			0.230286i	−0.993349	+	0.115143i	$0.963267\pi$
$270$	−0.632952	+	0.365435i	−0.0385202	+	0.0222397i
$271$	6.38108	+	6.38108i	0.387623	+	0.387623i	0.873839	−	0.486216i	$-0.161623\pi$
$271$	6.38108	+	6.38108i	0.387623	+	0.387623i	−0.486216	+	0.873839i	$0.661623\pi$
$272$	5.94664			0.360568
$273$	−0.0199585	+	0.345336i	−0.00120794	+	0.0209007i
$274$	10.6860			0.645563
$275$	−13.8709	−	13.8709i	−0.836449	−	0.836449i
$276$	−0.204550	+	0.118097i	−0.0123125	+	0.00710862i
$277$		−	20.1383i		−	1.20999i	−0.796228	−	0.604997i	$-0.793174\pi$
$277$		−	20.1383i		−	1.20999i	0.796228	−	0.604997i	$-0.206826\pi$
$278$	3.21545	+	0.861576i	0.192850	+	0.0516739i
$279$	6.69386	+	1.79361i	0.400751	+	0.107381i
$280$	3.24481	−	8.27637i	0.193914	−	0.494608i
$281$	−15.3914	+	15.3914i	−0.918176	+	0.918176i	−0.996897	−	0.0787211i	$-0.974916\pi$
$281$	−15.3914	+	15.3914i	−0.918176	+	0.918176i	0.0787211	+	0.996897i	$0.474916\pi$
$282$	−0.0963503	+	0.166884i	−0.00573758	+	0.00993778i
$283$	−4.16283	−	7.21023i	−0.247455	−	0.428604i	0.715364	−	0.698752i	$-0.246261\pi$
$283$	−4.16283	−	7.21023i	−0.247455	−	0.428604i	−0.962819	+	0.270148i	$0.912927\pi$
$284$	−15.4697	−	4.14510i	−0.917960	−	0.245967i
$285$	0.126553	+	0.219196i	0.00749634	+	0.0129840i
$286$	8.37005	+	7.50993i	0.494931	+	0.444071i
$287$	15.4367	+	11.3842i	0.911200	+	0.671991i
$288$	−2.89651	+	0.776117i	−0.170678	+	0.0457331i
$289$	18.3625			1.08015
$290$	18.0239			1.05840
$291$	−0.0615740	+	0.0164987i	−0.00360953	+	0.000967171i
$292$	−3.01436	−	11.2497i	−0.176402	−	0.658341i
$293$	−1.93345	+	7.21572i	−0.112953	+	0.421547i	−0.999126	−	0.0418086i	$-0.986688\pi$
$293$	−1.93345	+	7.21572i	−0.112953	+	0.421547i	0.886172	+	0.463356i	$0.153355\pi$
$294$	−0.118446	+	0.224500i	−0.00690789	+	0.0130931i
$295$	−19.2087	−	33.2704i	−1.11837	−	1.93708i
$296$			3.00994i			0.174949i
$297$	0.175589	−	0.655306i	0.0101887	−	0.0380247i
$298$	−19.0624	−	11.0057i	−1.10425	−	0.637541i
$299$	7.29646	+	22.3231i	0.421965	+	1.29098i
$300$			0.228069i			0.0131676i
$301$	7.76254	−	19.7995i	0.447426	−	1.14123i
$302$	−2.22670	+	3.85675i	−0.128132	+	0.221931i
$303$	−0.00667174	−	0.00385193i	−0.000383281	−	0.000221288i
$304$	0.537668	+	2.00660i	0.0308374	+	0.115087i
$305$	−7.74082	−	7.74082i	−0.443238	−	0.443238i
$306$	−17.2245	+	4.61529i	−0.984658	+	0.263838i
$307$	−10.6425	−	10.6425i	−0.607397	−	0.607397i	0.334868	−	0.942265i	$-0.391308\pi$
$307$	−10.6425	−	10.6425i	−0.607397	−	0.607397i	−0.942265	+	0.334868i	$0.891308\pi$
$308$	3.30254	+	7.56210i	0.188180	+	0.430890i
$309$	−0.0788921	−	0.0455484i	−0.00448802	−	0.00259116i
$310$	5.49067	−	5.49067i	0.311849	−	0.311849i
$311$	−10.2358	+	17.7290i	−0.580421	+	1.00532i	0.415008	+	0.909818i	$0.363779\pi$
$311$	−10.2358	+	17.7290i	−0.580421	+	1.00532i	−0.995429	+	0.0955013i	$0.969555\pi$
$312$	−0.00707111	−	0.130551i	−0.000400323	−	0.00739100i
$313$	−23.6557	+	13.6576i	−1.33710	+	0.771975i	−0.986377	−	0.164503i	$-0.947398\pi$
$313$	−23.6557	+	13.6576i	−1.33710	+	0.771975i	−0.350724	+	0.936479i	$0.614064\pi$
$314$	−1.19684	−	4.46666i	−0.0675414	−	0.252068i
$315$	−2.97518	+	26.4909i	−0.167632	+	1.49259i
$316$	−7.09795	+	4.09800i	−0.399291	+	0.230531i
$317$	−2.89957	+	10.8213i	−0.162856	+	0.607787i	0.835448	+	0.549570i	$0.185208\pi$
$317$	−2.89957	+	10.8213i	−0.162856	+	0.607787i	−0.998304	+	0.0582176i	$0.981458\pi$
$318$	−0.147492	+	0.147492i	−0.00827092	+	0.00827092i
$319$	−11.8303	+	11.8303i	−0.662368	+	0.662368i
$320$	−0.869631	+	3.24551i	−0.0486139	+	0.181429i
$321$	−0.205444	+	0.118613i	−0.0114667	+	0.00662033i
$322$	−1.92339	+	17.1258i	−0.107187	+	0.954386i
$323$	3.19732	+	11.9325i	0.177903	+	0.663945i
$324$	7.78398	−	4.49408i	0.432443	−	0.249671i
$325$	22.1901	+	4.67605i	1.23088	+	0.259381i
$326$	−7.60716	+	13.1760i	−0.421321	+	0.729750i
$327$	0.0680423	−	0.0680423i	0.00376275	−	0.00376275i
$328$	−6.27830	−	3.62478i	−0.346661	−	0.200145i
$329$	5.62713	+	12.8849i	0.310234	+	0.710368i
$330$	−0.268700	−	0.268700i	−0.0147915	−	0.0147915i
$331$	−3.95228	+	1.05901i	−0.217237	+	0.0582085i	−0.365796	−	0.930695i	$-0.619203\pi$
$331$	−3.95228	+	1.05901i	−0.217237	+	0.0582085i	0.148559	+	0.988904i	$0.452537\pi$
$332$	−9.96984	−	9.96984i	−0.547166	−	0.547166i
$333$	−2.33607	−	8.71832i	−0.128016	−	0.477761i
$334$	−0.730213	−	0.421588i	−0.0399555	−	0.0230683i
$335$	11.4914	−	19.9037i	0.627843	−	1.08746i
$336$	0.0350183	−	0.0893194i	0.00191040	−	0.00487277i
$337$		−	8.73021i		−	0.475565i	−0.971318	−	0.237783i	$-0.923579\pi$
$337$		−	8.73021i		−	0.475565i	0.971318	−	0.237783i	$-0.0764205\pi$
$338$	−12.8470	−	1.98867i	−0.698784	−	0.108170i
$339$	0.364426	+	0.210401i	0.0197929	+	0.0114274i
$340$	−5.17138	+	19.2999i	−0.280458	+	1.04668i
$341$			7.20777i			0.390323i
$342$	−3.11472	−	5.39485i	−0.168425	−	0.291720i
$343$	8.05360	+	16.6775i	0.434854	+	0.900501i
$344$	−2.08042	+	7.76422i	−0.112169	+	0.418619i
$345$	−0.205402	−	0.766571i	−0.0110585	−	0.0412708i
$346$	0.155396	−	0.0416383i	0.00835415	−	0.00223849i
$347$	12.5972			0.676253			0.338127	−	0.941101i	$-0.390207\pi$
$347$	12.5972			0.676253			0.338127	+	0.941101i	$0.390207\pi$
$348$	0.194516			0.0104272
$349$	29.0996	−	7.79722i	1.55767	−	0.417376i	0.625743	−	0.780029i	$-0.284796\pi$
$349$	29.0996	−	7.79722i	1.55767	−	0.417376i	0.931924	+	0.362654i	$0.118129\pi$
$350$	13.3926	+	9.87675i	0.715864	+	0.527935i
$351$	0.243662	+	0.745472i	0.0130057	+	0.0397903i
$352$	−1.55944	−	2.70103i	−0.0831185	−	0.143966i
$353$	15.1839	+	4.06850i	0.808155	+	0.216544i	0.639161	−	0.769073i	$-0.279282\pi$
$353$	15.1839	+	4.06850i	0.808155	+	0.216544i	0.168994	+	0.985617i	$0.445948\pi$
$354$	−0.207302	−	0.359057i	−0.0110180	−	0.0190837i
$355$	26.9059	−	46.6024i	1.42802	−	2.47340i
$356$	8.00364	−	8.00364i	0.424192	−	0.424192i
$357$	0.208241	−	0.531150i	0.0110213	−	0.0281115i
$358$	0.538945	+	0.144410i	0.0284842	+	0.00763231i
$359$	−4.48128	−	1.20075i	−0.236513	−	0.0633734i	0.138616	−	0.990346i	$-0.455735\pi$
$359$	−4.48128	−	1.20075i	−0.236513	−	0.0633734i	−0.375128	+	0.926973i	$0.622401\pi$
$360$		−	10.0756i		−	0.531029i
$361$	12.7171	−	7.34223i	0.669322	−	0.386433i
$362$	11.5519	+	11.5519i	0.607153	+	0.607153i
$363$	−0.0461449			−0.00242198
$364$	−7.97239	−	5.23841i	−0.417867	−	0.274568i
$365$	39.1325			2.04829
$366$	−0.0835398	−	0.0835398i	−0.00436669	−	0.00436669i
$367$	−18.7078	+	10.8010i	−0.976539	+	0.563805i	−0.901223	−	0.433355i	$-0.857330\pi$
$367$	−18.7078	+	10.8010i	−0.976539	+	0.563805i	−0.0753157	+	0.997160i	$0.523996\pi$
$368$		−	6.51366i		−	0.339548i
$369$	20.9984	+	5.62650i	1.09313	+	0.292904i
$370$	−9.76879	−	2.61754i	−0.507855	−	0.136079i
$371$	2.27368	+	15.0482i	0.118043	+	0.781264i
$372$	0.0592559	−	0.0592559i	0.00307228	−	0.00307228i
$373$	8.63845	−	14.9622i	0.447282	−	0.774715i	−0.550926	−	0.834554i	$-0.685725\pi$
$373$	8.63845	−	14.9622i	0.447282	−	0.774715i	0.998208	+	0.0598389i	$0.0190587\pi$
$374$	−9.27344	−	16.0621i	−0.479518	−	0.830550i
$375$	−0.151766	−	0.0406656i	−0.00783717	−	0.00209996i
$376$	−2.65710	−	4.60224i	−0.137030	−	0.237342i
$377$	3.98812	−	18.9255i	0.205399	−	0.974713i
$378$	−0.0642310	+	0.571911i	−0.00330369	+	0.0294159i
$379$	22.8334	−	6.11818i	1.17287	−	0.314270i	0.380776	−	0.924667i	$-0.375657\pi$
$379$	22.8334	−	6.11818i	1.17287	−	0.314270i	0.792095	+	0.610398i	$0.208990\pi$
$380$	−6.98002			−0.358067
$381$	−0.211175			−0.0108188
$382$	−21.0483	+	5.63987i	−1.07692	+	0.288561i
$383$	9.30271	+	34.7182i	0.475346	+	1.77402i	0.620072	+	0.784545i	$0.287103\pi$
$383$	9.30271	+	34.7182i	0.475346	+	1.77402i	−0.144725	+	0.989472i	$0.546230\pi$
$384$	−0.00938515	+	0.0350259i	−0.000478934	+	0.00178741i
$385$	−27.4148	+	4.14218i	−1.39719	+	0.211105i
$386$	−7.70504	−	13.3455i	−0.392176	−	0.679269i
$387$		−	24.1038i		−	1.22526i
$388$	0.454993	−	1.69806i	0.0230988	−	0.0862058i
$389$	6.53051	+	3.77039i	0.331110	+	0.191167i	0.656334	−	0.754471i	$-0.272106\pi$
$389$	6.53051	+	3.77039i	0.331110	+	0.191167i	−0.325224	+	0.945637i	$0.605440\pi$
$390$	0.429854	+	0.0905819i	0.0217665	+	0.00458680i
$391$		−	38.7344i		−	1.95888i
$392$	−3.72848	−	5.92439i	−0.188317	−	0.299227i
$393$	−0.0512860	+	0.0888299i	−0.00258703	+	0.00448087i
$394$	20.1160	+	11.6140i	1.01343	+	0.585104i
$395$	−7.12750	−	26.6002i	−0.358623	−	1.33840i
$396$	6.61325	+	6.61325i	0.332328	+	0.332328i
$397$	−22.4554	+	6.01690i	−1.12700	+	0.301979i	−0.773714	−	0.633535i	$-0.781603\pi$
$397$	−22.4554	+	6.01690i	−1.12700	+	0.301979i	−0.353288	+	0.935515i	$0.614937\pi$
$398$	10.7373	+	10.7373i	0.538213	+	0.538213i
$399$	0.198057	+	0.0222437i	0.00991524	+	0.00111358i
$400$	−5.44693	−	3.14479i	−0.272347	−	0.157239i
$401$	−21.2343	+	21.2343i	−1.06039	+	1.06039i	−0.0623344	+	0.998055i	$0.519855\pi$
$401$	−21.2343	+	21.2343i	−1.06039	+	1.06039i	−0.998055	+	0.0623344i	$0.980145\pi$
$402$	0.124017	−	0.214803i	0.00618538	−	0.0107134i
$403$	−4.55041	−	6.98023i	−0.226672	−	0.347710i
$404$	0.183990	−	0.106227i	0.00915384	−	0.00528497i
$405$	7.81639	+	29.1712i	0.388400	+	1.44953i
$406$	8.42370	−	11.4223i	0.418061	−	0.566879i
$407$	8.12995	−	4.69383i	0.402987	−	0.232665i
$408$	−0.0558101	+	0.208286i	−0.00276301	+	0.0103117i
$409$	−7.03688	+	7.03688i	−0.347951	+	0.347951i	−0.859346	−	0.511395i	$-0.829129\pi$
$409$	−7.03688	+	7.03688i	−0.347951	+	0.347951i	0.511395	+	0.859346i	$0.329129\pi$
$410$	17.2241	−	17.2241i	0.850636	−	0.850636i
$411$	−0.100289	+	0.374285i	−0.00494691	+	0.0184621i
$412$	2.17565	−	1.25611i	0.107187	−	0.0618842i
$413$	−30.0618	−	3.37623i	−1.47925	−	0.166133i
$414$	5.05536	+	18.8669i	0.248457	+	0.927255i
$415$	41.0273	−	23.6871i	2.01395	−	1.16275i
$416$	3.21543	+	1.63126i	0.157649	+	0.0799790i
$417$	−0.0603549	+	0.104538i	−0.00295559	+	0.00511923i
$418$	4.58144	−	4.58144i	0.224086	−	0.224086i
$419$	−7.37453	−	4.25769i	−0.360269	−	0.208002i	0.308929	−	0.951085i	$-0.400029\pi$
$419$	−7.37453	−	4.25769i	−0.360269	−	0.208002i	−0.669199	+	0.743083i	$0.733363\pi$
$420$	0.259434	+	0.191327i	0.0126591	+	0.00933581i
$421$	−0.546952	−	0.546952i	−0.0266568	−	0.0266568i	0.693653	−	0.720310i	$-0.256000\pi$
$421$	−0.546952	−	0.546952i	−0.0266568	−	0.0266568i	−0.720310	+	0.693653i	$0.756000\pi$
$422$	−16.1949	+	4.33941i	−0.788355	+	0.211239i
$423$	11.2682	+	11.2682i	0.547878	+	0.547878i
$424$	−1.48879	−	5.55624i	−0.0723020	−	0.269835i
$425$	−32.3910	−	18.7009i	−1.57119	−	0.907128i
$426$	0.290371	−	0.502938i	0.0140685	−	0.0243674i
$427$	−8.52336	+	1.28782i	−0.412474	+	0.0623219i
$428$		−	6.54210i		−	0.316224i
$429$	−0.341596	+	0.222686i	−0.0164924	+	0.0107514i
$430$	−23.3896	−	13.5040i	−1.12795	−	0.651221i
$431$	1.58679	−	5.92198i	0.0764329	−	0.285252i	−0.917121	−	0.398608i	$-0.869493\pi$
$431$	1.58679	−	5.92198i	0.0764329	−	0.285252i	0.993554	+	0.113356i	$0.0361601\pi$
$432$		−	0.217521i		−	0.0104655i
$433$	17.2645	+	29.9029i	0.829677	+	1.43704i	0.898292	+	0.439400i	$0.144809\pi$
$433$	17.2645	+	29.9029i	0.829677	+	1.43704i	−0.0686146	+	0.997643i	$0.521858\pi$
$434$	−0.913467	−	6.04574i	−0.0438478	−	0.290205i
$435$	−0.169157	+	0.631303i	−0.00811047	+	0.0302687i
$436$	0.686823	+	2.56326i	0.0328929	+	0.122758i
$437$	13.0703	−	3.50218i	0.625238	−	0.167532i
$438$	0.422322			0.0201793
$439$	−11.8992			−0.567920			−0.283960	−	0.958836i	$-0.591648\pi$
$439$	−11.8992			−0.567920			−0.283960	+	0.958836i	$0.591648\pi$
$440$	10.1224	−	2.71228i	0.482565	−	0.129303i
$441$	15.3976	+	14.2663i	0.733218	+	0.679348i
$442$	19.1210	+	9.70051i	0.909494	+	0.461406i
$443$	−17.0068	−	29.4566i	−0.808016	−	1.39952i	−0.914236	−	0.405182i	$-0.867208\pi$
$443$	−17.0068	−	29.4566i	−0.808016	−	1.39952i	0.106220	−	0.994343i	$-0.466125\pi$
$444$	−0.105426	−	0.0282488i	−0.00500329	−	0.00134063i
$445$	19.0157	+	32.9361i	0.901429	+	1.56132i
$446$	8.62940	−	14.9466i	0.408614	−	0.707740i
$447$	0.564386	−	0.564386i	0.0266945	−	0.0266945i
$448$	1.65034	+	2.06794i	0.0779713	+	0.0977010i
$449$	−33.5708	−	8.99527i	−1.58430	−	0.424513i	−0.644049	−	0.764984i	$-0.722747\pi$
$449$	−33.5708	−	8.99527i	−1.58430	−	0.424513i	−0.940255	+	0.340471i	$0.889414\pi$
$450$	18.2178	+	4.88145i	0.858796	+	0.230114i
$451$			22.6105i			1.06469i
$452$	−10.0500	+	5.80234i	−0.472710	+	0.272919i
$453$	−0.114188	−	0.114188i	−0.00536503	−	0.00536503i
$454$	−7.90736			−0.371111
$455$	23.9344	−	21.3190i	1.12206	−	0.999449i
$456$	−0.0753291			−0.00352761
$457$	−10.1448	−	10.1448i	−0.474553	−	0.474553i	0.428831	−	0.903385i	$-0.358925\pi$
$457$	−10.1448	−	10.1448i	−0.474553	−	0.474553i	−0.903385	+	0.428831i	$0.858925\pi$
$458$	−13.1077	+	7.56771i	−0.612481	+	0.353616i
$459$		−	1.29352i		−	0.0603763i
$460$	21.1401	+	5.66448i	0.985663	+	0.264108i
$461$	−0.649382	−	0.174001i	−0.0302447	−	0.00810405i	0.243665	−	0.969859i	$-0.421650\pi$
$461$	−0.649382	−	0.174001i	−0.0302447	−	0.00810405i	−0.273910	+	0.961755i	$0.588317\pi$
$462$	−0.295864	+	0.0447029i	−0.0137648	+	0.00207977i
$463$	−5.94052	+	5.94052i	−0.276079	+	0.276079i	−0.831542	−	0.555462i	$-0.812541\pi$
$463$	−5.94052	+	5.94052i	−0.276079	+	0.276079i	0.555462	+	0.831542i	$0.312541\pi$
$464$	−2.68213	+	4.64559i	−0.124515	+	0.215666i
$465$	0.140785	+	0.243846i	0.00652874	+	0.0113081i
$466$	−0.147895	−	0.0396285i	−0.00685113	−	0.00183575i
$467$	−13.3169	−	23.0656i	−0.616234	−	1.06735i	−0.990167	−	0.139893i	$-0.955324\pi$
$467$	−13.3169	−	23.0656i	−0.616234	−	1.06735i	0.373932	−	0.927456i	$-0.378009\pi$
$468$	−10.5796	−	2.22940i	−0.489041	−	0.103054i
$469$	−7.24292	−	16.5847i	−0.334447	−	0.765810i
$470$	17.2473	−	4.62140i	0.795558	−	0.213169i
$471$	0.167681			0.00772633
$472$	11.4337			0.526280
$473$	24.2157	−	6.48858i	1.11344	−	0.298345i
$474$	−0.0769207	−	0.287072i	−0.00353308	−	0.0131857i
$475$	3.38170	−	12.6207i	0.155163	−	0.579077i
$476$	9.81398	+	12.2973i	0.449823	+	0.563645i
$477$	8.62458	+	14.9382i	0.394892	+	0.683974i
$478$			2.52349i			0.115422i
$479$	3.03767	−	11.3368i	0.138795	−	0.517989i	−0.861159	−	0.508336i	$-0.830261\pi$
$479$	3.03767	−	11.3368i	0.138795	−	0.517989i	0.999953	−	0.00965294i	$-0.00307268\pi$
$480$	−0.105515	−	0.0609191i	−0.00481608	−	0.00278057i
$481$	−4.90999	+	9.67826i	−0.223876	+	0.441291i
$482$			15.5258i			0.707182i
$483$	−0.581796	−	0.228097i	−0.0264726	−	0.0103788i
$484$	0.636280	−	1.10207i	0.0289218	−	0.0500941i
$485$	5.11538	+	2.95337i	0.232278	+	0.134105i
$486$	0.253251	+	0.945145i	0.0114877	+	0.0428727i
$487$	0.680244	+	0.680244i	0.0308248	+	0.0308248i	0.722351	−	0.691526i	$-0.243061\pi$
$487$	0.680244	+	0.680244i	0.0308248	+	0.0308248i	−0.691526	+	0.722351i	$0.743061\pi$
$488$	3.14708	−	0.843256i	0.142461	−	0.0381724i
$489$	−0.390106	−	0.390106i	−0.0176412	−	0.0176412i
$490$	22.4701	−	6.94877i	1.01509	−	0.313913i
$491$	−18.4654	−	10.6610i	−0.833331	−	0.481124i	0.0216605	−	0.999765i	$-0.493105\pi$
$491$	−18.4654	−	10.6610i	−0.833331	−	0.481124i	−0.854992	+	0.518641i	$0.826438\pi$
$492$	0.185884	−	0.185884i	0.00838029	−	0.00838029i
$493$	−15.9497	+	27.6257i	−0.718337	+	1.24420i
$494$	−1.54446	+	7.32917i	−0.0694884	+	0.329755i
$495$	−27.2145	+	15.7123i	−1.22320	+	0.706214i
$496$	0.598133	+	2.23226i	0.0268570	+	0.100232i
$497$	−16.9585	−	38.8313i	−0.760693	−	1.74182i
$498$	0.442770	−	0.255634i	0.0198410	−	0.0114552i
$499$	−10.3098	+	38.4768i	−0.461531	+	1.72246i	0.206611	+	0.978423i	$0.433757\pi$
$499$	−10.3098	+	38.4768i	−0.461531	+	1.72246i	−0.668142	+	0.744034i	$0.732910\pi$
$500$	3.06388	−	3.06388i	0.137021	−	0.137021i
$501$	0.0216197	−	0.0216197i	0.000965895	−	0.000965895i
$502$	−0.442822	+	1.65263i	−0.0197641	+	0.0737607i
$503$	−13.8697	+	8.00769i	−0.618421	+	0.357045i	−0.776254	−	0.630420i	$-0.782883\pi$
$503$	−13.8697	+	8.00769i	−0.618421	+	0.357045i	0.157833	+	0.987466i	$0.449549\pi$
$504$	−6.38519	−	4.70894i	−0.284419	−	0.209753i
$505$	0.184756	+	0.689519i	0.00822153	+	0.0306832i
$506$	−17.5936	+	10.1577i	−0.782131	+	0.451563i
$507$	0.190226	−	0.431313i	0.00844823	−	0.0191553i
$508$	2.91184	−	5.04346i	0.129192	−	0.223767i
$509$	0.350846	−	0.350846i	0.0155510	−	0.0155510i	−0.699289	−	0.714840i	$-0.746500\pi$
$509$	0.350846	−	0.350846i	0.0155510	−	0.0155510i	0.714840	+	0.699289i	$0.246500\pi$
$510$	−0.627460	−	0.362264i	−0.0277844	−	0.0160413i
$511$	18.2891	−	24.7994i	0.809060	−	1.09706i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.436478	−	0.116954i	0.0192710	−	0.00516364i
$514$	−12.4657	−	12.4657i	−0.549840	−	0.549840i
$515$	2.18471	+	8.15344i	0.0962697	+	0.359283i
$516$	−0.252423	−	0.145737i	−0.0111123	−	0.00641570i
$517$	−8.28719	+	14.3538i	−0.364470	+	0.631281i
$518$	−6.22438	+	4.96743i	−0.273483	+	0.218256i
$519$			0.00583366i			0.000256069i
$520$	−8.09050	+	9.01711i	−0.354792	+	0.395426i
$521$	4.72213	+	2.72632i	0.206880	+	0.119442i	0.599861	−	0.800104i	$-0.295223\pi$
$521$	4.72213	+	2.72632i	0.206880	+	0.119442i	−0.392980	+	0.919547i	$0.628556\pi$
$522$	4.16330	−	15.5376i	0.182223	−	0.680064i
$523$		−	2.58729i		−	0.113134i	−0.998399	−	0.0565672i	$-0.981984\pi$
$523$		−	2.58729i		−	0.113134i	0.998399	−	0.0565672i	$-0.0180155\pi$
$524$	−1.41434	−	2.44971i	−0.0617857	−	0.107016i
$525$	−0.471633	+	0.376392i	−0.0205838	+	0.0164271i
$526$	−2.14064	+	7.98898i	−0.0933364	+	0.348336i
$527$	3.55688	+	13.2745i	0.154940	+	0.578245i
$528$	0.109242	−	0.0292712i	0.00475413	−	0.00127387i
$529$	−19.4277			−0.844683
$530$	19.3275			0.839534
$531$	−33.1179	+	8.87391i	−1.43719	+	0.385095i
$532$	−3.26220	+	4.42344i	−0.141434	+	0.191781i
$533$	−14.2745	−	21.8968i	−0.618297	−	0.948454i
$534$	0.205219	+	0.355450i	0.00888069	+	0.0153818i
$535$	21.2324	+	5.68921i	0.917958	+	0.245966i
$536$	3.42007	+	5.92373i	0.147724	+	0.255866i
$537$	−0.0101162	+	0.0175217i	−0.000436545	+	0.000756118i
$538$	2.67073	−	2.67073i	0.115143	−	0.115143i
$539$	−10.1876	+	19.3095i	−0.438813	+	0.831719i
$540$	0.705966	+	0.189163i	0.0303799	+	0.00814028i
$541$	9.63470	+	2.58161i	0.414228	+	0.110992i	0.459913	−	0.887964i	$-0.347880\pi$
$541$	9.63470	+	2.58161i	0.414228	+	0.110992i	−0.0456852	+	0.998956i	$0.514547\pi$
$542$		−	9.02421i		−	0.387623i
$543$	−0.513031	+	0.296198i	−0.0220163	+	0.0127111i
$544$	−4.20491	−	4.20491i	−0.180284	−	0.180284i
$545$	−8.91636			−0.381935
$546$	0.258302	−	0.230077i	0.0110543	−	0.00984637i
$547$	−3.43305			−0.146787			−0.0733934	−	0.997303i	$-0.523383\pi$
$547$	−3.43305			−0.146787			−0.0733934	+	0.997303i	$0.523383\pi$
$548$	−7.55612	−	7.55612i	−0.322781	−	0.322781i
$549$	−8.46106	+	4.88500i	−0.361109	+	0.208487i
$550$			19.6165i			0.836449i
$551$	−10.7640	−	2.88419i	−0.458560	−	0.122871i
$552$	0.228146	+	0.0611316i	0.00971055	+	0.00260194i
$553$	−20.1884	−	7.91502i	−0.858500	−	0.336581i
$554$	−14.2399	+	14.2399i	−0.604997	+	0.604997i
$555$	0.183363	−	0.317594i	0.00778333	−	0.0134811i
$556$	−1.66444	−	2.88289i	−0.0705879	−	0.122262i
$557$	24.1247	+	6.46418i	1.02219	+	0.273896i	0.730716	−	0.682681i	$-0.239186\pi$
$557$	24.1247	+	6.46418i	1.02219	+	0.273896i	0.291478	+	0.956577i	$0.405853\pi$
$558$	−3.46499	−	6.00155i	−0.146685	−	0.254066i
$559$	−19.3549	+	21.5716i	−0.818624	+	0.912382i
$560$	−8.14670	+	3.55785i	−0.344261	+	0.150347i
$561$	0.649620	−	0.174065i	0.0274270	−	0.00734904i
$562$	21.7668			0.918176
$563$	30.5761			1.28863			0.644315	−	0.764760i	$-0.277143\pi$
$563$	30.5761			1.28863			0.644315	+	0.764760i	$0.277143\pi$
$564$	0.186135	−	0.0498746i	0.00783768	−	0.00210010i
$565$	−10.0918	−	37.6631i	−0.424565	−	1.58450i
$566$	−2.15484	+	8.04197i	−0.0905747	+	0.338029i
$567$	22.1397	+	8.68003i	0.929781	+	0.364527i
$568$	8.00772	+	13.8698i	0.335997	+	0.581963i
$569$			39.4671i			1.65455i	0.561799	+	0.827274i	$0.310109\pi$
$569$			39.4671i			1.65455i	−0.561799	+	0.827274i	$0.689891\pi$
$570$	0.0655085	−	0.244481i	0.00274385	−	0.0102402i
$571$	33.3332	+	19.2449i	1.39495	+	0.805375i	0.993858	−	0.110663i	$-0.0352975\pi$
$571$	33.3332	+	19.2449i	1.39495	+	0.805375i	0.401092	+	0.916038i	$0.368631\pi$
$572$	−0.608194	−	11.2288i	−0.0254299	−	0.469501i
$573$		−	0.790165i		−	0.0330096i
$574$	−2.86552	−	18.9653i	−0.119604	−	0.791595i
$575$	−20.4841	+	35.4795i	−0.854245	+	1.47960i
$576$	2.59694	+	1.49934i	0.108206	+	0.0624726i
$577$	9.45242	+	35.2769i	0.393509	+	1.46860i	0.824304	+	0.566147i	$0.191567\pi$
$577$	9.45242	+	35.2769i	0.393509	+	1.46860i	−0.430795	+	0.902450i	$0.641767\pi$
$578$	−12.9843	−	12.9843i	−0.540074	−	0.540074i
$579$	0.539751	−	0.144626i	0.0224313	−	0.00601045i
$580$	−12.7448	−	12.7448i	−0.529200	−	0.529200i
$581$	4.16339	−	37.0706i	0.172726	−	1.53795i
$582$	0.0552057	+	0.0318730i	0.00228835	+	0.00132118i
$583$	−12.6859	+	12.6859i	−0.525396	+	0.525396i
$584$	−5.82329	+	10.0862i	−0.240970	+	0.417372i
$585$	16.4359	−	32.3973i	0.679539	−	1.33946i
$586$	6.46944	−	3.73513i	0.267250	−	0.154297i
$587$	7.73131	+	28.8537i	0.319105	+	1.19092i	0.920106	+	0.391669i	$0.128102\pi$
$587$	7.73131	+	28.8537i	0.319105	+	1.19092i	−0.601001	+	0.799249i	$0.705231\pi$
$588$	0.242499	−	0.0749918i	0.0100005	−	0.00309261i
$589$	−4.15767	+	2.40043i	−0.171314	+	0.0989081i
$590$	−9.94313	+	37.1083i	−0.409352	+	1.52772i
$591$	−0.595581	+	0.595581i	−0.0244989	+	0.0244989i
$592$	2.12835	−	2.12835i	0.0874747	−	0.0874747i
$593$	−1.37140	+	5.11813i	−0.0563166	+	0.210176i	−0.988351	−	0.152194i	$-0.951366\pi$
$593$	−1.37140	+	5.11813i	−0.0563166	+	0.210176i	0.932034	+	0.362371i	$0.118033\pi$
$594$	−0.587531	+	0.339211i	−0.0241067	+	0.0139180i
$595$	−48.4455	+	21.1573i	−1.98607	+	0.867363i
$596$	5.69695	+	21.2613i	0.233356	+	0.870897i
$597$	−0.476855	+	0.275313i	−0.0195164	+	0.0112678i
$598$	10.6255	−	20.9442i	0.434507	−	0.856472i
$599$	−8.34264	+	14.4499i	−0.340871	+	0.590406i	−0.984595	−	0.174852i	$-0.944055\pi$
$599$	−8.34264	+	14.4499i	−0.340871	+	0.590406i	0.643724	+	0.765258i	$0.277389\pi$
$600$	0.161269	−	0.161269i	0.00658379	−	0.00658379i
$601$	−21.4409	−	12.3789i	−0.874593	−	0.504947i	−0.00572138	−	0.999984i	$-0.501821\pi$
$601$	−21.4409	−	12.3789i	−0.874593	−	0.504947i	−0.868872	+	0.495037i	$0.835155\pi$
$602$	−19.4893	+	8.51144i	−0.794326	+	0.346900i
$603$	−14.5038	−	14.5038i	−0.590639	−	0.590639i
$604$	4.30165	−	1.15262i	0.175032	−	0.0468996i
$605$	3.02345	+	3.02345i	0.122921	+	0.122921i
$606$	0.00199391	+	0.00744136i	8.09969e−5	+	0.000302284i
$607$	6.93580	+	4.00439i	0.281515	+	0.162533i	0.634109	−	0.773243i	$-0.281367\pi$
$607$	6.93580	+	4.00439i	0.281515	+	0.162533i	−0.352594	+	0.935776i	$0.614700\pi$
$608$	1.03869	−	1.79907i	0.0421246	−	0.0729620i
$609$	0.321018	+	0.402247i	0.0130083	+	0.0162999i
$610$			10.9472i			0.443238i
$611$	−1.03629	−	19.1326i	−0.0419238	−	0.774022i
$612$	15.4431	+	8.91605i	0.624248	+	0.360410i
$613$	4.32553	−	16.1431i	0.174706	−	0.652013i	−0.821895	−	0.569639i	$-0.807083\pi$
$613$	4.32553	−	16.1431i	0.174706	−	0.652013i	0.996601	−	0.0823743i	$-0.0262503\pi$
$614$			15.0507i			0.607397i
$615$	0.441637	+	0.764938i	0.0178085	+	0.0308453i
$616$	3.01196	−	7.68246i	0.121355	−	0.309535i
$617$	0.776717	−	2.89875i	0.0312694	−	0.116699i	−0.948527	−	0.316696i	$-0.897427\pi$
$617$	0.776717	−	2.89875i	0.0312694	−	0.116699i	0.979797	+	0.199997i	$0.0640932\pi$
$618$	0.0235776	+	0.0879928i	0.000948430	+	0.00353959i
$619$	−41.9559	+	11.2421i	−1.68635	+	0.451856i	−0.969444	−	0.245313i	$-0.921109\pi$
$619$	−41.9559	+	11.2421i	−1.68635	+	0.451856i	−0.716906	+	0.697169i	$0.754443\pi$
$620$	−7.76498			−0.311849
$621$	−1.41686			−0.0568565
$622$	19.7741	−	5.29846i	0.792870	−	0.212449i
$623$	29.7598	+	3.34231i	1.19230	+	0.133907i
$624$	−0.0873135	+	0.0973136i	−0.00349534	+	0.00389566i
$625$	−8.44455	−	14.6264i	−0.337782	−	0.585056i
$626$	26.3845	+	7.06971i	1.05454	+	0.282563i
$627$	0.117471	+	0.203466i	0.00469135	+	0.00812566i
$628$	−2.31211	+	4.00469i	−0.0922633	+	0.159805i
$629$	12.6565	−	12.6565i	0.504649	−	0.504649i
$630$	20.8357	−	16.6281i	0.830113	−	0.662481i
$631$	−20.0767	−	5.37953i	−0.799239	−	0.214156i	−0.163989	−	0.986462i	$-0.552436\pi$
$631$	−20.0767	−	5.37953i	−0.799239	−	0.214156i	−0.635250	+	0.772307i	$0.719103\pi$
$632$	7.91673	+	2.12128i	0.314911	+	0.0843800i
$633$		−	0.607966i		−	0.0241645i
$634$	9.70216	−	5.60154i	0.385322	−	0.222466i
$635$	13.8364	+	13.8364i	0.549079	+	0.549079i
$636$	0.208585			0.00827092
$637$	−2.32444	−	25.1316i	−0.0920977	−	0.995750i
$638$	16.7305			0.662368
$639$	−33.9590	−	33.9590i	−1.34340	−	1.34340i
$640$	2.90984	−	1.68000i	0.115022	−	0.0664078i
$641$		−	29.1428i		−	1.15107i	−0.817777	−	0.575536i	$-0.804794\pi$
$641$		−	29.1428i		−	1.15107i	0.817777	−	0.575536i	$-0.195206\pi$
$642$	0.229143	+	0.0613986i	0.00904354	+	0.00242321i
$643$	38.0380	+	10.1922i	1.50007	+	0.401943i	0.913124	−	0.407682i	$-0.133663\pi$
$643$	38.0380	+	10.1922i	1.50007	+	0.401943i	0.586947	+	0.809625i	$0.300330\pi$
$644$	13.4698	−	10.7498i	0.530786	−	0.423600i
$645$	0.692505	−	0.692505i	0.0272674	−	0.0272674i
$646$	6.17674	−	10.6984i	0.243021	−	0.420924i
$647$	−14.1647	−	24.5339i	−0.556870	−	0.964528i	−0.997755	−	0.0669643i	$-0.978669\pi$
$647$	−14.1647	−	24.5339i	−0.556870	−	0.964528i	0.440885	−	0.897564i	$-0.354665\pi$
$648$	−8.68190	−	2.32631i	−0.341057	−	0.0913860i
$649$	−17.8302	−	30.8829i	−0.699898	−	1.21226i
$650$	−12.3843	−	18.9972i	−0.485751	−	0.745132i
$651$	0.220330	+	0.0247452i	0.00863542	+	0.000969839i
$652$	14.6959	−	3.93775i	0.575536	−	0.154214i
$653$	5.38429			0.210704			0.105352	−	0.994435i	$-0.466403\pi$
$653$	5.38429			0.210704			0.105352	+	0.994435i	$0.466403\pi$
$654$	−0.0962263			−0.00376275
$655$	9.18049	−	2.45991i	0.358712	−	0.0961165i
$656$	1.87632	+	7.00254i	0.0732581	+	0.273403i
$657$	9.03911	−	33.7344i	0.352649	−	1.31611i
$658$	5.13202	−	13.0900i	0.200067	−	0.510301i
$659$	7.17647	+	12.4300i	0.279556	+	0.484205i	0.971274	−	0.237962i	$-0.0764795\pi$
$659$	7.17647	+	12.4300i	0.279556	+	0.484205i	−0.691719	+	0.722167i	$0.743146\pi$
$660$			0.380000i			0.0147915i
$661$	0.295866	−	1.10419i	0.0115079	−	0.0429479i	−0.959933	−	0.280229i	$-0.909590\pi$
$661$	0.295866	−	1.10419i	0.0115079	−	0.0429479i	0.971441	+	0.237281i	$0.0762562\pi$
$662$	3.54352	+	2.04585i	0.137723	+	0.0795143i
$663$	−0.519222	+	0.578689i	−0.0201649	+	0.0224744i
$664$			14.0995i			0.547166i
$665$	−11.5194	−	14.4343i	−0.446704	−	0.559736i
$666$	−4.51293	+	7.81663i	−0.174873	+	0.302888i
$667$	30.2598	+	17.4705i	1.17166	+	0.676460i
$668$	0.218230	+	0.814446i	0.00844358	+	0.0315119i
$669$	0.442528	+	0.442528i	0.0171091	+	0.0171091i
$670$	−22.1997	+	5.94839i	−0.857650	+	0.229807i
$671$	−7.18535	−	7.18535i	−0.277387	−	0.277387i
$672$	−0.0879200	+	0.0383967i	−0.00339159	+	0.00148118i
$673$	37.0049	+	21.3648i	1.42643	+	0.823552i	0.996837	−	0.0794689i	$-0.0253225\pi$
$673$	37.0049	+	21.3648i	1.42643	+	0.823552i	0.429597	+	0.903021i	$0.358656\pi$
$674$	−6.17319	+	6.17319i	−0.237783	+	0.237783i
$675$	−0.684057	+	1.18482i	−0.0263294	+	0.0456038i
$676$	7.67799	+	10.4904i	0.295307	+	0.403477i
$677$	19.5414	−	11.2822i	0.751038	−	0.433612i	−0.0750310	−	0.997181i	$-0.523906\pi$
$677$	19.5414	−	11.2822i	0.751038	−	0.433612i	0.826069	+	0.563569i	$0.190572\pi$
$678$	−0.108912	−	0.406464i	−0.00418273	−	0.0156102i
$679$	4.26237	−	1.86148i	0.163575	−	0.0714369i
$680$	17.3038	−	9.99034i	0.663570	−	0.383112i
$681$	0.0742118	−	0.276962i	0.00284380	−	0.0106132i
$682$	5.09666	−	5.09666i	0.195161	−	0.195161i
$683$	−7.53795	+	7.53795i	−0.288432	+	0.288432i	−0.836460	−	0.548028i	$-0.815379\pi$
$683$	−7.53795	+	7.53795i	−0.288432	+	0.288432i	0.548028	+	0.836460i	$0.315379\pi$
$684$	−1.61230	+	6.01717i	−0.0616477	+	0.230072i
$685$	31.0945	−	17.9524i	1.18806	−	0.685926i
$686$	6.09803	−	17.4875i	0.232824	−	0.667677i
$687$	−0.142048	−	0.530131i	−0.00541948	−	0.0202258i
$688$	6.96121	−	4.01906i	0.265394	−	0.153225i
$689$	4.27656	−	20.2943i	0.162924	−	0.773151i
$690$	−0.396806	+	0.687289i	−0.0151062	+	0.0261646i
$691$	−11.4728	+	11.4728i	−0.436445	+	0.436445i	−0.890814	−	0.454369i	$-0.849865\pi$
$691$	−11.4728	+	11.4728i	−0.436445	+	0.436445i	0.454369	+	0.890814i	$0.349865\pi$
$692$	−0.139324	−	0.0804389i	−0.00529632	−	0.00305783i
$693$	−2.76168	+	24.5899i	−0.104908	+	0.934094i
$694$	−8.90757	−	8.90757i	−0.338127	−	0.338127i
$695$	10.8039	−	2.89489i	0.409815	−	0.109810i
$696$	−0.137544	−	0.137544i	−0.00521358	−	0.00521358i
$697$	11.1578	+	41.6416i	0.422633	+	1.57729i
$698$	−26.0900	−	15.0631i	−0.987521	−	0.570146i
$699$	0.00277604	−	0.00480825i	0.000105000	−	0.000181865i
$700$	−2.48607	−	16.4539i	−0.0939645	−	0.621899i
$701$			16.2812i			0.614931i	0.951559	+	0.307466i	$0.0994809\pi$
$701$			16.2812i			0.614931i	−0.951559	+	0.307466i	$0.900519\pi$
$702$	0.354833	−	0.699423i	0.0133923	−	0.0263980i
$703$	5.41510	+	3.12641i	0.204234	+	0.117915i
$704$	−0.807227	+	3.01261i	−0.0304235	+	0.113542i
$705$			0.647473i			0.0243853i
$706$	−7.85974	−	13.6135i	−0.295805	−	0.512350i
$707$	0.523316	+	0.205170i	0.0196813	+	0.00771621i
$708$	−0.107307	+	0.400476i	−0.00403286	+	0.0150508i
$709$	−5.37477	−	20.0589i	−0.201854	−	0.753328i	−0.990386	−	0.138334i	$-0.955825\pi$
$709$	−5.37477	−	20.0589i	−0.201854	−	0.753328i	0.788532	−	0.614994i	$-0.210841\pi$
$710$	−51.9782	+	13.9275i	−1.95071	+	0.522691i
$711$	−24.5772			−0.921718
$712$	−11.3189			−0.424192
$713$	14.5402	−	3.89603i	0.544535	−	0.145908i
$714$	−0.522829	+	0.228331i	−0.0195664	+	0.00854508i
$715$	36.9722	+	7.79105i	1.38268	+	0.291369i
$716$	−0.278979	−	0.483205i	−0.0104259	−	0.0180582i
$717$	−0.0883872	−	0.0236833i	−0.00330088	−	0.000884469i
$718$	2.31968	+	4.01780i	0.0865697	+	0.149943i
$719$	−3.06885	+	5.31540i	−0.114449	+	0.198231i	−0.917559	−	0.397599i	$-0.869843\pi$
$719$	−3.06885	+	5.31540i	−0.114449	+	0.198231i	0.803111	+	0.595830i	$0.203177\pi$
$720$	−7.12451	+	7.12451i	−0.265515	+	0.265515i
$721$	6.18813	+	2.42610i	0.230458	+	0.0903526i
$722$	−14.1841	−	3.80062i	−0.527877	−	0.141444i
$723$	−0.543805	−	0.145712i	−0.0202243	−	0.00541909i
$724$		−	16.3368i		−	0.607153i
$725$	29.2188	−	16.8695i	1.08516	−	0.626517i
$726$	0.0326293	+	0.0326293i	0.00121099	+	0.00121099i
$727$	−11.7366			−0.435286			−0.217643	−	0.976028i	$-0.569837\pi$
$727$	−11.7366			−0.435286			−0.217643	+	0.976028i	$0.569837\pi$
$728$	1.93321	+	9.34145i	0.0716496	+	0.346217i
$729$	26.9290			0.997371
$730$	−27.6708	−	27.6708i	−1.02414	−	1.02414i
$731$	41.3958	−	23.8999i	1.53108	−	0.883969i
$732$			0.118143i			0.00436669i
$733$	−4.99579	−	1.33862i	−0.184524	−	0.0494430i	0.165374	−	0.986231i	$-0.447117\pi$
$733$	−4.99579	−	1.33862i	−0.184524	−	0.0494430i	−0.349898	+	0.936788i	$0.613784\pi$
$734$	20.8658	+	5.59098i	0.770172	+	0.206367i
$735$	0.0325015	+	0.852249i	0.00119884	+	0.0314357i
$736$	−4.60585	+	4.60585i	−0.169774	+	0.169774i
$737$	10.6668	−	18.4754i	0.392916	−	0.680551i
$738$	−10.8696	−	18.8267i	−0.400114	−	0.693019i
$739$	30.3962	+	8.14464i	1.11814	+	0.299606i	0.770132	−	0.637885i	$-0.220190\pi$
$739$	30.3962	+	8.14464i	1.11814	+	0.299606i	0.348011	+	0.937490i	$0.386857\pi$
$740$	5.05670	+	8.75846i	0.185888	+	0.321967i
$741$	−0.242215	−	0.122881i	−0.00889801	−	0.00451415i
$742$	9.03296	−	12.2484i	0.331610	−	0.449654i
$743$	43.3322	−	11.6108i	1.58970	−	0.425960i	0.647791	−	0.761818i	$-0.275693\pi$
$743$	43.3322	−	11.6108i	1.58970	−	0.425960i	0.941912	+	0.335859i	$0.109026\pi$
$744$	−0.0838005			−0.00307228
$745$	−73.9579			−2.70961
$746$	−16.6882	+	4.47159i	−0.610999	+	0.163717i
$747$	−10.9428	−	40.8392i	−0.400378	−	1.49423i
$748$	−4.80029	+	17.9149i	−0.175516	+	0.655034i
$749$	13.5287	−	10.7967i	0.494327	−	0.394503i
$750$	0.0785600	+	0.136070i	0.00286860	+	0.00496857i
$751$			36.8107i			1.34324i	0.740896	+	0.671620i	$0.234401\pi$
$751$			36.8107i			1.34324i	−0.740896	+	0.671620i	$0.765599\pi$
$752$	−1.37542	+	5.13313i	−0.0501563	+	0.187186i
$753$	−0.0537290	−	0.0310204i	−0.00195799	−	0.00113045i
$754$	−16.2024	+	10.5623i	−0.590056	+	0.384657i
$755$			14.9634i			0.544574i
$756$	0.449820	−	0.358984i	0.0163598	−	0.0130561i
$757$	−15.5608	+	26.9521i	−0.565567	+	0.979591i	0.431429	+	0.902147i	$0.358009\pi$
$757$	−15.5608	+	26.9521i	−0.565567	+	0.979591i	−0.996997	+	0.0774445i	$0.975324\pi$
$758$	−20.4718	−	11.8194i	−0.743570	−	0.429300i
$759$	−0.190662	−	0.711562i	−0.00692061	−	0.0258281i
$760$	4.93562	+	4.93562i	0.179034	+	0.179034i
$761$	−16.6980	+	4.47422i	−0.605302	+	0.162190i	−0.548437	−	0.836192i	$-0.684777\pi$
$761$	−16.6980	+	4.47422i	−0.605302	+	0.162190i	−0.0568650	+	0.998382i	$0.518110\pi$
$762$	0.149324	+	0.149324i	0.00540942	+	0.00540942i
$763$	−4.16717	+	5.65056i	−0.150862	+	0.204564i
$764$	18.8714	+	10.8954i	0.682742	+	0.394181i
$765$	−42.3669	+	42.3669i	−1.53178	+	1.53178i
$766$	17.9715	−	31.1275i	0.649335	−	1.12468i
$767$	36.7644	+	18.6514i	1.32748	+	0.673462i
$768$	0.0314033	−	0.0181307i	0.00113317	−	0.000654236i
$769$	−4.28846	−	16.0047i	−0.154646	−	0.577146i	−0.999135	−	0.0415739i	$-0.986763\pi$
$769$	−4.28846	−	16.0047i	−0.154646	−	0.577146i	0.844490	−	0.535572i	$-0.179904\pi$
$770$	22.3142	+	16.4562i	0.804147	+	0.593042i
$771$	0.553616	−	0.319630i	0.0199380	−	0.0115112i
$772$	−3.98842	+	14.8850i	−0.143547	+	0.535723i
$773$	16.6143	−	16.6143i	0.597575	−	0.597575i	−0.342092	−	0.939667i	$-0.611135\pi$
$773$	16.6143	−	16.6143i	0.597575	−	0.597575i	0.939667	+	0.342092i	$0.111135\pi$
$774$	−17.0439	+	17.0439i	−0.612632	+	0.612632i
$775$	3.76201	−	14.0400i	0.135135	−	0.504332i
$776$	−1.52244	+	0.878979i	−0.0546523	+	0.0315535i
$777$	−0.115572	−	0.264634i	−0.00414612	−	0.00949370i
$778$	−1.95170	−	7.28384i	−0.0699718	−	0.261138i
$779$	−13.0425	+	7.53007i	−0.467295	+	0.269793i
$780$	−0.239901	−	0.368004i	−0.00858985	−	0.0131766i
$781$	24.9752	−	43.2582i	0.893681	−	1.54790i
$782$	−27.3893	+	27.3893i	−0.979440	+	0.979440i
$783$	1.01051	+	0.583420i	0.0361128	+	0.0208497i
$784$	−1.55275	+	6.82561i	−0.0554553	+	0.243772i
$785$	−10.9866	−	10.9866i	−0.392128	−	0.392128i
$786$	0.0990769	−	0.0265476i	0.00353395	−	0.000946920i
$787$	−2.61667	−	2.61667i	−0.0932741	−	0.0932741i	0.658930	−	0.752204i	$-0.271009\pi$
$787$	−2.61667	−	2.61667i	−0.0932741	−	0.0932741i	−0.752204	+	0.658930i	$0.771009\pi$
$788$	−6.01184	−	22.4365i	−0.214163	−	0.799266i
$789$	−0.259731	−	0.149956i	−0.00924666	−	0.00533856i
$790$	−13.7693	+	23.8491i	−0.489889	+	0.848512i
$791$	−28.5847	−	11.2068i	−1.01636	−	0.398470i
$792$		−	9.35255i		−	0.332328i
$793$	11.4948	+	2.42226i	0.408191	+	0.0860171i
$794$	20.1329	+	11.6237i	0.714491	+	0.412511i
$795$	−0.181392	+	0.676963i	−0.00643330	+	0.0240094i
$796$		−	15.1849i		−	0.538213i
$797$	−11.6148	−	20.1173i	−0.411416	−	0.712593i	0.583629	−	0.812020i	$-0.301632\pi$
$797$	−11.6148	−	20.1173i	−0.411416	−	0.712593i	−0.995045	+	0.0994274i	$0.968299\pi$
$798$	−0.124319	−	0.155776i	−0.00440083	−	0.00551441i
$799$	−8.17911	+	30.5249i	−0.289356	+	1.07989i
$800$	1.62786	+	6.07527i	0.0575536	+	0.214793i
$801$	32.7852	−	8.78475i	1.15841	−	0.310394i
$802$	30.0298			1.06039
$803$	36.3244			1.28186
$804$	−0.239582	+	0.0641957i	−0.00844939	+	0.00226401i
$805$	23.1746	+	53.0648i	0.816798	+	1.87029i
$806$	−1.71814	+	8.15340i	−0.0605190	+	0.287191i
$807$	0.0684793	+	0.118610i	0.00241059	+	0.00417526i
$808$	−0.205214	−	0.0549870i	−0.00721941	−	0.00193443i
$809$	−1.92272	−	3.33024i	−0.0675991	−	0.117085i	0.830245	−	0.557399i	$-0.188201\pi$
$809$	−1.92272	−	3.33024i	−0.0675991	−	0.117085i	−0.897844	+	0.440314i	$0.854867\pi$
$810$	15.1001	−	26.1542i	0.530564	−	0.918963i
$811$	31.0031	−	31.0031i	1.08866	−	1.08866i	0.0929980	−	0.995666i	$-0.470355\pi$
$811$	31.0031	−	31.0031i	1.08866	−	1.08866i	0.995666	−	0.0929980i	$-0.0296450\pi$
$812$	−14.0332	+	2.12032i	−0.492470	+	0.0744087i
$813$	0.316081	+	0.0846936i	0.0110854	+	0.00297033i
$814$	−9.06778	−	2.42971i	−0.317826	−	0.0851611i
$815$			51.1200i			1.79066i
$816$	0.186744	−	0.107817i	0.00653736	−	0.00377434i
$817$	11.8075	+	11.8075i	0.413091	+	0.413091i
$818$	9.95165			0.347951
$819$	−12.8496	−	25.5572i	−0.449002	−	0.893040i
$820$	−24.3585			−0.850636
$821$	20.7691	+	20.7691i	0.724845	+	0.724845i	0.969588	−	0.244743i	$-0.0787035\pi$
$821$	20.7691	+	20.7691i	0.724845	+	0.724845i	−0.244743	+	0.969588i	$0.578703\pi$
$822$	0.335575	−	0.193744i	0.0117045	−	0.00675760i
$823$			0.950311i			0.0331258i	0.999863	+	0.0165629i	$0.00527237\pi$
$823$			0.950311i			0.0331258i	−0.999863	+	0.0165629i	$0.994728\pi$
$824$	−2.42662	−	0.650211i	−0.0845353	−	0.0226512i
$825$	−0.687083	−	0.184103i	−0.0239212	−	0.00640966i
$826$	18.8696	+	23.6443i	0.656556	+	0.822689i
$827$	−1.05849	+	1.05849i	−0.0368074	+	0.0368074i	−0.725271	−	0.688464i	$-0.758286\pi$
$827$	−1.05849	+	1.05849i	−0.0368074	+	0.0368074i	0.688464	+	0.725271i	$0.258286\pi$
$828$	9.76620	−	16.9156i	0.339399	−	0.587856i
$829$	−5.94525	−	10.2975i	−0.206487	−	0.357646i	0.744118	−	0.668048i	$-0.232870\pi$
$829$	−5.94525	−	10.2975i	−0.206487	−	0.357646i	−0.950606	+	0.310401i	$0.899537\pi$
$830$	−45.7600	−	12.2613i	−1.58835	−	0.425597i
$831$	−0.365122	−	0.632410i	−0.0126659	−	0.0219381i
$832$	−1.12018	−	3.42713i	−0.0388352	−	0.118814i
$833$	−9.23363	+	40.5895i	−0.319926	+	1.40634i
$834$	0.116597	−	0.0312420i	0.00403741	−	0.00108182i
$835$	−2.83307			−0.0980425
$836$	−6.47913			−0.224086
$837$	0.485564	−	0.130106i	0.0167835	−	0.00449714i
$838$	2.20394	+	8.22522i	0.0761339	+	0.284136i
$839$	7.53618	−	28.1254i	0.260178	−	0.970997i	−0.704959	−	0.709249i	$-0.749034\pi$
$839$	7.53618	−	28.1254i	0.260178	−	0.970997i	0.965136	−	0.261748i	$-0.0842989\pi$
$840$	−0.0481587	−	0.318736i	−0.00166163	−	0.0109974i
$841$	0.112322	+	0.194547i	0.00387317	+	0.00670853i
$842$			0.773506i			0.0266568i
$843$	−0.204284	+	0.762400i	−0.00703593	+	0.0262584i
$844$	14.5199	+	8.38309i	0.499797	+	0.288558i
$845$	−40.7237	+	15.7962i	−1.40094	+	0.543406i
$846$		−	15.9356i		−	0.547878i
$847$	3.32909	−	0.503002i	0.114389	−	0.0172834i
$848$	−2.87612	+	4.98159i	−0.0987664	+	0.171068i
$849$	−0.261453	−	0.150950i	−0.00897306	−	0.00518060i
$850$	9.68031	+	36.1274i	0.332032	+	1.23916i
$851$	−13.8633	−	13.8633i	−0.475229	−	0.475229i
$852$	−0.560955	+	0.150307i	−0.0192180	+	0.00514944i
$853$	−6.89225	−	6.89225i	−0.235986	−	0.235986i	0.579200	−	0.815186i	$-0.303365\pi$
$853$	−6.89225	−	6.89225i	−0.235986	−	0.235986i	−0.815186	+	0.579200i	$0.803365\pi$
$854$	6.93755	+	5.11630i	0.237398	+	0.175076i
$855$	−18.1267	−	10.4654i	−0.619919	−	0.357910i
$856$	−4.62596	+	4.62596i	−0.158112	+	0.158112i
$857$	−20.6808	+	35.8201i	−0.706441	+	1.22359i	0.259727	+	0.965682i	$0.416367\pi$
$857$	−20.6808	+	35.8201i	−0.706441	+	1.22359i	−0.966169	+	0.257910i	$0.916966\pi$
$858$	0.399008	+	0.0840818i	0.0136219	+	0.00287051i
$859$	−26.7947	+	15.4699i	−0.914222	+	0.527827i	−0.881787	−	0.471647i	$-0.843660\pi$
$859$	−26.7947	+	15.4699i	−0.914222	+	0.527827i	−0.0324351	+	0.999474i	$0.510326\pi$
$860$	6.99019	+	26.0878i	0.238364	+	0.889585i
$861$	0.691168	+	0.0776248i	0.0235549	+	0.00264544i
$862$	−5.30950	+	3.06544i	−0.180842	+	0.104409i
$863$	−3.23782	+	12.0837i	−0.110217	+	0.411334i	−0.998885	−	0.0472170i	$-0.984965\pi$
$863$	−3.23782	+	12.0837i	−0.110217	+	0.411334i	0.888668	+	0.458551i	$0.151631\pi$
$864$	−0.153811	+	0.153811i	−0.00523274	+	0.00523274i
$865$	0.382226	−	0.382226i	0.0129961	−	0.0129961i
$866$	8.93674	−	33.3524i	0.303683	−	1.13336i
$867$	0.576644	−	0.332926i	0.0195839	−	0.0113067i
$868$	−3.62906	+	4.92090i	−0.123178	+	0.167026i
$869$	−6.61603	−	24.6914i	−0.224433	−	0.837597i
$870$	0.566011	−	0.326787i	0.0191896	−	0.0110791i
$871$	1.33385	+	24.6264i	0.0451958	+	0.834432i
$872$	1.32684	−	2.29816i	0.0449325	−	0.0778254i
$873$	3.72756	−	3.72756i	0.126159	−	0.126159i
$874$	−11.7185	−	6.76570i	−0.396385	−	0.228853i
$875$	11.3924	+	1.27947i	0.385132	+	0.0432540i
$876$	−0.298627	−	0.298627i	−0.0100897	−	0.0100897i
$877$	−50.2252	+	13.4578i	−1.69598	+	0.454438i	−0.971923	−	0.235299i	$-0.924393\pi$
$877$	−50.2252	+	13.4578i	−1.69598	+	0.454438i	−0.724061	+	0.689736i	$0.757727\pi$
$878$	8.41404	+	8.41404i	0.283960	+	0.283960i
$879$	0.0701096	+	0.261652i	0.00236474	+	0.00882532i
$880$	−9.07546	−	5.23972i	−0.305934	−	0.176631i
$881$	−3.74394	+	6.48469i	−0.126137	+	0.218475i	−0.922177	−	0.386769i	$-0.873591\pi$
$881$	−3.74394	+	6.48469i	−0.126137	+	0.218475i	0.796040	+	0.605244i	$0.206924\pi$
$882$	−0.799927	−	20.9755i	−0.0269350	−	0.706283i
$883$		−	42.5577i		−	1.43218i	−0.698007	−	0.716091i	$-0.745930\pi$
$883$		−	42.5577i		−	1.43218i	0.698007	−	0.716091i	$-0.254070\pi$
$884$	−6.66130	−	20.3799i	−0.224044	−	0.685450i
$885$	−1.20643	−	0.696533i	−0.0405537	−	0.0234137i
$886$	−8.80335	+	32.8545i	−0.295754	+	1.10377i
$887$		−	38.1956i		−	1.28248i	−0.767339	−	0.641242i	$-0.778419\pi$
$887$		−	38.1956i		−	1.28248i	0.767339	−	0.641242i	$-0.221581\pi$
$888$	0.0545724	+	0.0945222i	0.00183133	+	0.00317196i
$889$	15.2351	−	2.30192i	0.510969	−	0.0772038i
$890$	9.84323	−	36.7354i	0.329946	−	1.23137i
$891$	7.25549	+	27.0779i	0.243068	+	0.907142i
$892$	−16.6707	+	4.46691i	−0.558177	+	0.149563i
$893$	−11.0397			−0.369428
$894$	−0.798162			−0.0266945
$895$	1.81085	−	0.485217i	0.0605302	−	0.0162190i
$896$	0.295287	−	2.62922i	0.00986483	−	0.0878361i
$897$	0.633867	+	0.568730i	0.0211642	+	0.0189894i
$898$	17.3775	+	30.0988i	0.579896	+	1.00441i
$899$	−11.9745	−	3.20855i	−0.399371	−	0.107011i
$900$	−9.43023	−	16.3336i	−0.314341	−	0.544455i
$901$	−17.1033	+	29.6237i	−0.569792	+	0.986909i
$902$	15.9881	−	15.9881i	0.532344	−	0.532344i
$903$	−0.115210	−	0.762512i	−0.00383395	−	0.0253748i
$904$	11.2093	+	3.00351i	0.372815	+	0.0998954i
$905$	53.0213	+	14.2070i	1.76249	+	0.472257i
$906$			0.161486i			0.00536503i
$907$	−48.4838	+	27.9921i	−1.60988	+	0.929463i	−0.620482	+	0.784221i	$0.713063\pi$
$907$	−48.4838	+	27.9921i	−1.60988	+	0.929463i	−0.989396	+	0.145242i	$0.953604\pi$
$908$	5.59135	+	5.59135i	0.185555	+	0.185555i
$909$	0.637080			0.0211306
$910$	−31.9989	−	1.84936i	−1.06075	−	0.0613056i
$911$	−48.1896			−1.59659			−0.798297	−	0.602264i	$-0.794265\pi$
$911$	−48.1896			−1.59659			−0.798297	+	0.602264i	$0.794265\pi$
$912$	0.0532657	+	0.0532657i	0.00176380	+	0.00176380i
$913$	38.0832	−	21.9873i	1.26037	−	0.727674i
$914$			14.3469i			0.474553i
$915$	−0.383434	−	0.102741i	−0.0126759	−	0.00339651i
$916$	14.6197	+	3.91734i	0.483049	+	0.129432i
$917$	2.73170	−	6.96762i	0.0902088	−	0.230091i
$918$	−0.914656	+	0.914656i	−0.0301881	+	0.0301881i
$919$	−10.0151	+	17.3466i	−0.330367	+	0.572212i	−0.982584	−	0.185820i	$-0.940506\pi$
$919$	−10.0151	+	17.3466i	−0.330367	+	0.572212i	0.652217	+	0.758032i	$0.273839\pi$
$920$	−10.9429	−	18.9537i	−0.360778	−	0.624885i
$921$	−0.527164	−	0.141253i	−0.0173706	−	0.00465445i
$922$	0.336145	+	0.582220i	0.0110703	+	0.0191744i
$923$	3.12307	+	57.6600i	0.102797	+	1.89790i
$924$	0.240817	+	0.177598i	0.00792230	+	0.00584253i
$925$	−18.2862	+	4.89977i	−0.601246	+	0.161103i
$926$	8.40116			0.276079
$927$	7.53337			0.247428
$928$	5.18148	−	1.38837i	0.170091	−	0.0455756i
$929$	5.32643	+	19.8785i	0.174755	+	0.652193i	0.996593	+	0.0824728i	$0.0262817\pi$
$929$	5.32643	+	19.8785i	0.174755	+	0.652193i	−0.821839	+	0.569720i	$0.807052\pi$
$930$	0.0728755	−	0.271975i	0.00238968	−	0.00891842i
$931$	−14.5312	+	0.554163i	−0.476239	+	0.0181620i
$932$	0.0765563	+	0.132599i	0.00250769	+	0.00434344i
$933$			0.742332i			0.0243029i
$934$	−6.89335	+	25.7263i	−0.225557	+	0.841792i
$935$	−53.9685	−	31.1587i	−1.76496	−	1.01900i
$936$	5.90446	+	9.05731i	0.192993	+	0.296047i
$937$			36.7487i			1.20053i	0.799803	+	0.600263i	$0.204938\pi$
$937$			36.7487i			1.20053i	−0.799803	+	0.600263i	$0.795062\pi$
$938$	−6.60564	+	16.8487i	−0.215682	+	0.550129i
$939$	−0.495246	+	0.857790i	−0.0161617	+	0.0279929i
$940$	−15.4635	−	8.92785i	−0.504364	−	0.291194i
$941$	−5.79068	−	21.6111i	−0.188771	−	0.704502i	−0.993792	−	0.111256i	$-0.964513\pi$
$941$	−5.79068	−	21.6111i	−0.188771	−	0.704502i	0.805021	−	0.593246i	$-0.202154\pi$
$942$	−0.118568	−	0.118568i	−0.00386317	−	0.00386317i
$943$	45.6121	−	12.2217i	1.48533	−	0.397994i
$944$	−8.08487	−	8.08487i	−0.263140	−	0.263140i
$945$	0.773907	+	1.77208i	0.0251752	+	0.0576457i
$946$	−21.7112	−	12.5350i	−0.705892	−	0.407547i
$947$	31.2820	−	31.2820i	1.01653	−	1.01653i	0.0166681	−	0.999861i	$-0.494694\pi$
$947$	31.2820	−	31.2820i	1.01653	−	1.01653i	0.999861	−	0.0166681i	$-0.00530588\pi$
$948$	−0.148599	+	0.257382i	−0.00482628	+	0.00835937i
$949$	−35.1777	+	22.9323i	−1.14192	+	0.744414i
$950$	−11.3154	+	6.53295i	−0.367120	+	0.211957i
$951$	0.105143	+	0.392398i	0.00340948	+	0.0127244i
$952$	1.75596	−	15.6350i	0.0569111	−	0.506734i
$953$	27.9551	−	16.1399i	0.905553	−	0.522821i	0.0265556	−	0.999647i	$-0.491546\pi$
$953$	27.9551	−	16.1399i	0.905553	−	0.522821i	0.878998	+	0.476826i	$0.158213\pi$
$954$	4.46441	−	16.6614i	0.144541	−	0.539433i
$955$	−51.7722	+	51.7722i	−1.67531	+	1.67531i
$956$	1.78437	−	1.78437i	0.0577108	−	0.0577108i
$957$	−0.157018	+	0.586001i	−0.00507569	+	0.0189427i
$958$	−10.1643	+	5.86833i	−0.328392	+	0.189597i
$959$	3.15542	−	28.0958i	0.101894	−	0.907260i
$960$	0.0315341	+	0.117687i	0.00101776	+	0.00379832i
$961$	22.2216	−	12.8296i	0.716824	−	0.413859i
$962$	10.3155	−	3.37167i	0.332584	−	0.108707i
$963$	9.80885	−	16.9894i	0.316086	−	0.547477i
$964$	10.9784	−	10.9784i	0.353591	−	0.353591i
$965$	−44.8409	−	25.8889i	−1.44348	−	0.833394i
$966$	0.250103	+	0.572681i	0.00804693	+	0.0184257i
$967$	−42.5240	−	42.5240i	−1.36748	−	1.36748i	−0.864018	−	0.503462i	$-0.832060\pi$
$967$	−42.5240	−	42.5240i	−1.36748	−	1.36748i	−0.503462	−	0.864018i	$-0.667940\pi$
$968$	−1.22920	+	0.329363i	−0.0395080	+	0.0105861i
$969$	0.316752	+	0.316752i	0.0101755	+	0.0101755i
$970$	−1.52878	−	5.70547i	−0.0490860	−	0.183192i
$971$	11.3861	+	6.57378i	0.365398	+	0.210963i	0.671446	−	0.741053i	$-0.265673\pi$
$971$	11.3861	+	6.57378i	0.365398	+	0.210963i	−0.306048	+	0.952016i	$0.599007\pi$
$972$	0.489243	−	0.847394i	0.0156925	−	0.0271802i
$973$	3.21475	−	8.19971i	0.103060	−	0.262871i
$974$		−	0.962010i		−	0.0308248i
$975$	0.781622	−	0.255478i	0.0250319	−	0.00818185i
$976$	−2.82159	−	1.62905i	−0.0903169	−	0.0521445i
$977$	0.0701847	−	0.261933i	0.00224541	−	0.00837997i	−0.964794	−	0.263007i	$-0.915286\pi$
$977$	0.0701847	−	0.261933i	0.00224541	−	0.00837997i	0.967039	+	0.254627i	$0.0819526\pi$
$978$			0.551693i			0.0176412i
$979$	17.6511	+	30.5726i	0.564132	+	0.977105i
$980$	−20.8023	−	10.9752i	−0.664504	−	0.350590i
$981$	−2.05957	+	7.68641i	−0.0657569	+	0.245408i
$982$	5.51854	+	20.5955i	0.176104	+	0.657228i
$983$	22.3914	−	5.99977i	0.714176	−	0.191363i	0.116604	−	0.993178i	$-0.462799\pi$
$983$	22.3914	−	5.99977i	0.714176	−	0.191363i	0.597571	+	0.801816i	$0.296132\pi$
$984$	−0.262879			−0.00838029
$985$	78.0458			2.48675
$986$	30.8124	−	8.25616i	0.981267	−	0.262930i
$987$	0.410323	+	0.302605i	0.0130607	+	0.00963202i
$988$	6.27460	−	4.09041i	0.199622	−	0.130133i
$989$	−26.1787	−	45.3429i	−0.832436	−	1.44182i
$990$	30.3538	+	8.13327i	0.964706	+	0.258492i
$991$	19.7653	+	34.2345i	0.627865	+	1.08749i	0.987979	+	0.154586i	$0.0494043\pi$
$991$	19.7653	+	34.2345i	0.627865	+	1.08749i	−0.360114	+	0.932908i	$0.617262\pi$
$992$	1.15550	−	2.00139i	0.0366873	−	0.0635443i
$993$	−0.104914	+	0.104914i	−0.00332935	+	0.00332935i
$994$	−15.4664	+	39.4494i	−0.490564	+	1.25126i
$995$	49.2826	+	13.2052i	1.56236	+	0.418634i
$996$	−0.493846	−	0.132326i	−0.0156481	−	0.00419290i
$997$			34.4292i			1.09038i	0.838311	+	0.545192i	$0.183543\pi$
$997$			34.4292i			1.09038i	−0.838311	+	0.545192i	$0.816457\pi$
$998$	34.4973	−	19.9170i	1.09199	−	0.630463i
$999$	−0.462961	−	0.462961i	−0.0146474	−	0.0146474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.bc.a.59.3	yes	40
7.5	odd	6		182.2.w.a.33.3	✓	40
13.2	odd	12		182.2.w.a.171.3	yes	40
91.54	even	12	inner	182.2.bc.a.145.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.w.a.33.3	✓	40	7.5	odd	6
182.2.w.a.171.3	yes	40	13.2	odd	12
182.2.bc.a.59.3	yes	40	1.1	even	1	trivial
182.2.bc.a.145.3	yes	40	91.54	even	12	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:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.0314033 - 0.0181307i) q^{3} +1.00000i q^{4} +(-3.24551 - 0.869631i) q^{5} +(-0.0350259 - 0.00938515i) q^{6} +(-2.06794 + 1.65034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.49934 + 2.59694i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.0314033 - 0.0181307i) q^{3} +1.00000i q^{4} +(-3.24551 - 0.869631i) q^{5} +(-0.0350259 - 0.00938515i) q^{6} +(-2.06794 + 1.65034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.49934 + 2.59694i) q^{9} +(1.68000 + 2.90984i) q^{10} +(-3.01261 - 0.807227i) q^{11} +(0.0181307 + 0.0314033i) q^{12} +(3.42713 - 1.12018i) q^{13} +(2.62922 + 0.295287i) q^{14} +(-0.117687 + 0.0315341i) q^{15} -1.00000 q^{16} -5.94664 q^{17} +(2.89651 - 0.776117i) q^{18} +(-0.537668 - 2.00660i) q^{19} +(0.869631 - 3.24551i) q^{20} +(-0.0350183 + 0.0893194i) q^{21} +(1.55944 + 2.70103i) q^{22} +6.51366i q^{23} +(0.00938515 - 0.0350259i) q^{24} +(5.44693 + 3.14479i) q^{25} +(-3.21543 - 1.63126i) q^{26} +0.217521i q^{27} +(-1.65034 - 2.06794i) q^{28} +(2.68213 - 4.64559i) q^{29} +(0.105515 + 0.0609191i) q^{30} +(-0.598133 - 2.23226i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.109242 + 0.0292712i) q^{33} +(4.20491 + 4.20491i) q^{34} +(8.14670 - 3.55785i) q^{35} +(-2.59694 - 1.49934i) q^{36} +(-2.12835 + 2.12835i) q^{37} +(-1.03869 + 1.79907i) q^{38} +(0.0873135 - 0.0973136i) q^{39} +(-2.90984 + 1.68000i) q^{40} +(-1.87632 - 7.00254i) q^{41} +(0.0879200 - 0.0383967i) q^{42} +(-6.96121 + 4.01906i) q^{43} +(0.807227 - 3.01261i) q^{44} +(7.12451 - 7.12451i) q^{45} +(4.60585 - 4.60585i) q^{46} +(1.37542 - 5.13313i) q^{47} +(-0.0314033 + 0.0181307i) q^{48} +(1.55275 - 6.82561i) q^{49} +(-1.62786 - 6.07527i) q^{50} +(-0.186744 + 0.107817i) q^{51} +(1.12018 + 3.42713i) q^{52} +(2.87612 - 4.98159i) q^{53} +(0.153811 - 0.153811i) q^{54} +(9.07546 + 5.23972i) q^{55} +(-0.295287 + 2.62922i) q^{56} +(-0.0532657 - 0.0532657i) q^{57} +(-5.18148 + 1.38837i) q^{58} +(8.08487 + 8.08487i) q^{59} +(-0.0315341 - 0.117687i) q^{60} +(2.82159 + 1.62905i) q^{61} +(-1.15550 + 2.00139i) q^{62} +(-1.18528 - 7.84474i) q^{63} -1.00000i q^{64} +(-12.0969 + 0.655212i) q^{65} +(0.0979433 + 0.0565476i) q^{66} +(-1.77036 + 6.60706i) q^{67} -5.94664i q^{68} +(0.118097 + 0.204550i) q^{69} +(-8.27637 - 3.24481i) q^{70} +(-4.14510 + 15.4697i) q^{71} +(0.776117 + 2.89651i) q^{72} +(-11.2497 + 3.01436i) q^{73} +3.00994 q^{74} +0.228069 q^{75} +(2.00660 - 0.537668i) q^{76} +(7.56210 - 3.30254i) q^{77} +(-0.130551 + 0.00707111i) q^{78} +(4.09800 + 7.09795i) q^{79} +(3.24551 + 0.869631i) q^{80} +(-4.49408 - 7.78398i) q^{81} +(-3.62478 + 6.27830i) q^{82} +(-9.96984 + 9.96984i) q^{83} +(-0.0893194 - 0.0350183i) q^{84} +(19.2999 + 5.17138i) q^{85} +(7.76422 + 2.08042i) q^{86} -0.194516i q^{87} +(-2.70103 + 1.55944i) q^{88} +(-8.00364 - 8.00364i) q^{89} -10.0756 q^{90} +(-5.23841 + 7.97239i) q^{91} -6.51366 q^{92} +(-0.0592559 - 0.0592559i) q^{93} +(-4.60224 + 2.65710i) q^{94} +6.98002i q^{95} +(0.0350259 + 0.00938515i) q^{96} +(-1.69806 - 0.454993i) q^{97} +(-5.92439 + 3.72848i) q^{98} +(6.61325 - 6.61325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} + 24 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 + 24 * q^9	\( 40 q - 4 q^{7} + 24 q^{9} + 4 q^{12} - 4 q^{14} - 16 q^{15} - 40 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{21} + 4 q^{22} - 8 q^{28} + 4 q^{29} + 24 q^{30} - 4 q^{31} + 36 q^{33} + 28 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{39} - 24 q^{41} - 12 q^{42} - 72 q^{43} + 12 q^{44} + 4 q^{49} - 24 q^{51} + 4 q^{52} - 4 q^{53} + 36 q^{54} - 12 q^{55} - 12 q^{56} - 12 q^{57} - 8 q^{58} - 8 q^{60} - 12 q^{61} - 36 q^{62} - 108 q^{63} - 16 q^{65} + 44 q^{67} + 84 q^{69} + 8 q^{70} + 28 q^{71} + 8 q^{72} - 44 q^{73} + 40 q^{74} + 56 q^{75} + 32 q^{76} + 8 q^{78} - 16 q^{79} + 4 q^{81} + 48 q^{82} - 108 q^{83} + 24 q^{84} + 56 q^{85} + 52 q^{86} - 12 q^{89} + 52 q^{91} + 32 q^{92} - 24 q^{93} + 48 q^{94} + 88 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 24 * q^9 + 4 * q^12 - 4 * q^14 - 16 * q^15 - 40 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^21 + 4 * q^22 - 8 * q^28 + 4 * q^29 + 24 * q^30 - 4 * q^31 + 36 * q^33 + 28 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^39 - 24 * q^41 - 12 * q^42 - 72 * q^43 + 12 * q^44 + 4 * q^49 - 24 * q^51 + 4 * q^52 - 4 * q^53 + 36 * q^54 - 12 * q^55 - 12 * q^56 - 12 * q^57 - 8 * q^58 - 8 * q^60 - 12 * q^61 - 36 * q^62 - 108 * q^63 - 16 * q^65 + 44 * q^67 + 84 * q^69 + 8 * q^70 + 28 * q^71 + 8 * q^72 - 44 * q^73 + 40 * q^74 + 56 * q^75 + 32 * q^76 + 8 * q^78 - 16 * q^79 + 4 * q^81 + 48 * q^82 - 108 * q^83 + 24 * q^84 + 56 * q^85 + 52 * q^86 - 12 * q^89 + 52 * q^91 + 32 * q^92 - 24 * q^93 + 48 * q^94 + 88 * q^97 + 88 * q^98 + 28 * q^99

Introduction

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