LMFDB - Embedded newform 201.2.e.b.163.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 49x^{6} - 39x^{5} + 128x^{4} - 14x^{3} + 119x^{2} - 49x + 49 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 49x^6 - 39x^5 + 128x^4 - 14x^3 + 119x^2 - 49*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.5
Root			$-1.03354 + 1.79014i$ of defining polynomial
Character	$\chi$	$=$	201.163
Dual form			201.2.e.b.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03354 - 1.79014i) q^{2} -1.00000 q^{3} +(-1.13639 - 1.96829i) q^{4} -3.33986 q^{5} +(-1.03354 + 1.79014i) q^{6} +(-2.29539 - 3.97573i) q^{7} -0.563865 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.03354 - 1.79014i) q^{2} -1.00000 q^{3} +(-1.13639 - 1.96829i) q^{4} -3.33986 q^{5} +(-1.03354 + 1.79014i) q^{6} +(-2.29539 - 3.97573i) q^{7} -0.563865 q^{8} +1.00000 q^{9} +(-3.45186 + 5.97880i) q^{10} +(0.625458 + 1.08333i) q^{11} +(1.13639 + 1.96829i) q^{12} +(-0.156474 + 0.271021i) q^{13} -9.48945 q^{14} +3.33986 q^{15} +(1.69001 - 2.92718i) q^{16} +(1.78514 - 3.09195i) q^{17} +(1.03354 - 1.79014i) q^{18} +(2.95186 - 5.11277i) q^{19} +(3.79539 + 6.57380i) q^{20} +(2.29539 + 3.97573i) q^{21} +2.58573 q^{22} +(-2.56707 + 4.44630i) q^{23} +0.563865 q^{24} +6.15464 q^{25} +(0.323444 + 0.560221i) q^{26} -1.00000 q^{27} +(-5.21692 + 9.03597i) q^{28} +(4.73379 + 8.19917i) q^{29} +(3.45186 - 5.97880i) q^{30} +(-1.62546 - 2.81538i) q^{31} +(-4.05724 - 7.02734i) q^{32} +(-0.625458 - 1.08333i) q^{33} +(-3.69001 - 6.39128i) q^{34} +(7.66626 + 13.2783i) q^{35} +(-1.13639 - 1.96829i) q^{36} +(2.61310 - 4.52603i) q^{37} +(-6.10171 - 10.5685i) q^{38} +(0.156474 - 0.271021i) q^{39} +1.88323 q^{40} +(-1.63781 - 2.83677i) q^{41} +9.48945 q^{42} +6.40409 q^{43} +(1.42153 - 2.46216i) q^{44} -3.33986 q^{45} +(5.30632 + 9.19082i) q^{46} +(-5.68017 - 9.83835i) q^{47} +(-1.69001 + 2.92718i) q^{48} +(-7.03759 + 12.1895i) q^{49} +(6.36104 - 11.0176i) q^{50} +(-1.78514 + 3.09195i) q^{51} +0.711265 q^{52} -6.86493 q^{53} +(-1.03354 + 1.79014i) q^{54} +(-2.08894 - 3.61815i) q^{55} +(1.29429 + 2.24177i) q^{56} +(-2.95186 + 5.11277i) q^{57} +19.5702 q^{58} +3.85632 q^{59} +(-3.79539 - 6.57380i) q^{60} +(-2.79859 + 4.84730i) q^{61} -6.71988 q^{62} +(-2.29539 - 3.97573i) q^{63} -10.0132 q^{64} +(0.522602 - 0.905173i) q^{65} -2.58573 q^{66} +(6.32977 - 5.18980i) q^{67} -8.11447 q^{68} +(2.56707 - 4.44630i) q^{69} +31.6934 q^{70} +(5.36356 + 9.28995i) q^{71} -0.563865 q^{72} +(-3.36950 + 5.83614i) q^{73} +(-5.40147 - 9.35562i) q^{74} -6.15464 q^{75} -13.4179 q^{76} +(2.87134 - 4.97330i) q^{77} +(-0.323444 - 0.560221i) q^{78} +(-2.22355 - 3.85129i) q^{79} +(-5.64439 + 9.77637i) q^{80} +1.00000 q^{81} -6.77095 q^{82} +(5.62179 - 9.73722i) q^{83} +(5.21692 - 9.03597i) q^{84} +(-5.96211 + 10.3267i) q^{85} +(6.61885 - 11.4642i) q^{86} +(-4.73379 - 8.19917i) q^{87} +(-0.352674 - 0.610849i) q^{88} -1.04520 q^{89} +(-3.45186 + 5.97880i) q^{90} +1.43668 q^{91} +11.6688 q^{92} +(1.62546 + 2.81538i) q^{93} -23.4827 q^{94} +(-9.85879 + 17.0759i) q^{95} +(4.05724 + 7.02734i) q^{96} +(-3.31725 + 5.74565i) q^{97} +(14.5472 + 25.1965i) q^{98} +(0.625458 + 1.08333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + 3 q^{13} - 22 q^{14} - 2 q^{15} + 2 q^{17} - 2 q^{18} + 3 q^{19} + 16 q^{20} + q^{21} + 6 q^{22} - q^{23} - 12 q^{24} + 7 q^{26} - 10 q^{27} - 9 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 9 q^{32} - 2 q^{33} - 20 q^{34} + 19 q^{35} - 6 q^{36} + 27 q^{37} - 16 q^{38} - 3 q^{39} - 22 q^{40} - 7 q^{41} + 22 q^{42} + 12 q^{43} - 7 q^{44} + 2 q^{45} + 30 q^{46} - 33 q^{47} - 24 q^{49} + 21 q^{50} - 2 q^{51} - 32 q^{52} - 24 q^{53} + 2 q^{54} + 6 q^{55} - q^{56} - 3 q^{57} + 44 q^{58} + 24 q^{59} - 16 q^{60} + q^{61} + 2 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} - 6 q^{66} + 2 q^{67} - 18 q^{68} + q^{69} + 42 q^{70} - q^{71} + 12 q^{72} + 12 q^{73} + 43 q^{74} + 2 q^{76} + 40 q^{77} - 7 q^{78} + 7 q^{79} - q^{80} + 10 q^{81} - 74 q^{82} + 12 q^{83} + 9 q^{84} - 27 q^{85} - 27 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} - 80 q^{91} - 28 q^{92} + 12 q^{93} + 30 q^{94} - 12 q^{95} + 9 q^{96} - 9 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 + 6 * q^12 + 3 * q^13 - 22 * q^14 - 2 * q^15 + 2 * q^17 - 2 * q^18 + 3 * q^19 + 16 * q^20 + q^21 + 6 * q^22 - q^23 - 12 * q^24 + 7 * q^26 - 10 * q^27 - 9 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 9 * q^32 - 2 * q^33 - 20 * q^34 + 19 * q^35 - 6 * q^36 + 27 * q^37 - 16 * q^38 - 3 * q^39 - 22 * q^40 - 7 * q^41 + 22 * q^42 + 12 * q^43 - 7 * q^44 + 2 * q^45 + 30 * q^46 - 33 * q^47 - 24 * q^49 + 21 * q^50 - 2 * q^51 - 32 * q^52 - 24 * q^53 + 2 * q^54 + 6 * q^55 - q^56 - 3 * q^57 + 44 * q^58 + 24 * q^59 - 16 * q^60 + q^61 + 2 * q^62 - q^63 - 8 * q^64 - 6 * q^65 - 6 * q^66 + 2 * q^67 - 18 * q^68 + q^69 + 42 * q^70 - q^71 + 12 * q^72 + 12 * q^73 + 43 * q^74 + 2 * q^76 + 40 * q^77 - 7 * q^78 + 7 * q^79 - q^80 + 10 * q^81 - 74 * q^82 + 12 * q^83 + 9 * q^84 - 27 * q^85 - 27 * q^86 - 12 * q^87 - 10 * q^88 + 12 * q^89 - 8 * q^90 - 80 * q^91 - 28 * q^92 + 12 * q^93 + 30 * q^94 - 12 * q^95 + 9 * q^96 - 9 * q^97 + 4 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.03354	−	1.79014i	0.730820	−	1.26582i	−0.225713	−	0.974194i	$-0.572471\pi$
$2$	1.03354	−	1.79014i	0.730820	−	1.26582i	0.956533	−	0.291624i	$-0.0941955\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.13639	−	1.96829i	−0.568196	−	0.984144i
$5$	−3.33986			−1.49363			−0.746814	−	0.665032i	$-0.768418\pi$
$5$	−3.33986			−1.49363			−0.746814	+	0.665032i	$0.768418\pi$
$6$	−1.03354	+	1.79014i	−0.421939	+	0.730820i
$7$	−2.29539	−	3.97573i	−0.867574	−	1.50268i	−0.864468	−	0.502688i	$-0.832345\pi$
$7$	−2.29539	−	3.97573i	−0.867574	−	1.50268i	−0.00310622	−	0.999995i	$-0.500989\pi$
$8$	−0.563865			−0.199356
$9$	1.00000			0.333333
$10$	−3.45186	+	5.97880i	−1.09157	+	1.89066i
$11$	0.625458	+	1.08333i	0.188583	+	0.326635i	0.944778	−	0.327711i	$-0.106277\pi$
$11$	0.625458	+	1.08333i	0.188583	+	0.326635i	−0.756195	+	0.654346i	$0.772944\pi$
$12$	1.13639	+	1.96829i	0.328048	+	0.568196i
$13$	−0.156474	+	0.271021i	−0.0433982	+	0.0751678i	−0.886909	−	0.461945i	$-0.847152\pi$
$13$	−0.156474	+	0.271021i	−0.0433982	+	0.0751678i	0.843510	+	0.537113i	$0.180485\pi$
$14$	−9.48945			−2.53616
$15$	3.33986			0.862347
$16$	1.69001	−	2.92718i	0.422503	−	0.731796i
$17$	1.78514	−	3.09195i	0.432960	−	0.749908i	−0.564167	−	0.825661i	$-0.690803\pi$
$17$	1.78514	−	3.09195i	0.432960	−	0.749908i	0.997127	+	0.0757524i	$0.0241359\pi$
$18$	1.03354	−	1.79014i	0.243607	−	0.421939i
$19$	2.95186	−	5.11277i	0.677203	−	1.17295i	−0.298616	−	0.954373i	$-0.596525\pi$
$19$	2.95186	−	5.11277i	0.677203	−	1.17295i	0.975820	−	0.218577i	$-0.0701415\pi$
$20$	3.79539	+	6.57380i	0.848674	+	1.46995i
$21$	2.29539	+	3.97573i	0.500894	+	0.867574i
$22$	2.58573			0.551280
$23$	−2.56707	+	4.44630i	−0.535271	+	0.927117i	0.463879	+	0.885899i	$0.346457\pi$
$23$	−2.56707	+	4.44630i	−0.535271	+	0.927117i	−0.999150	+	0.0412186i	$0.986876\pi$
$24$	0.563865			0.115098
$25$	6.15464			1.23093
$26$	0.323444	+	0.560221i	0.0634325	+	0.109868i
$27$	−1.00000			−0.192450
$28$	−5.21692	+	9.03597i	−0.985905	+	1.70764i
$29$	4.73379	+	8.19917i	0.879043	+	1.52255i	0.852392	+	0.522903i	$0.175151\pi$
$29$	4.73379	+	8.19917i	0.879043	+	1.52255i	0.0266508	+	0.999645i	$0.491516\pi$
$30$	3.45186	−	5.97880i	0.630221	−	1.09157i
$31$	−1.62546	−	2.81538i	−0.291941	−	0.505656i	0.682328	−	0.731046i	$-0.260968\pi$
$31$	−1.62546	−	2.81538i	−0.291941	−	0.505656i	−0.974269	+	0.225390i	$0.927634\pi$
$32$	−4.05724	−	7.02734i	−0.717225	−	1.24227i
$33$	−0.625458	−	1.08333i	−0.108878	−	0.188583i
$34$	−3.69001	−	6.39128i	−0.632831	−	1.09610i
$35$	7.66626	+	13.2783i	1.29583	+	2.24445i
$36$	−1.13639	−	1.96829i	−0.189399	−	0.328048i
$37$	2.61310	−	4.52603i	0.429592	−	0.744074i	−0.567245	−	0.823549i	$-0.691991\pi$
$37$	2.61310	−	4.52603i	0.429592	−	0.744074i	0.996837	+	0.0794745i	$0.0253242\pi$
$38$	−6.10171	−	10.5685i	−0.989827	−	1.71443i
$39$	0.156474	−	0.271021i	0.0250559	−	0.0433982i
$40$	1.88323			0.297764
$41$	−1.63781	−	2.83677i	−0.255783	−	0.443030i	0.709325	−	0.704882i	$-0.249000\pi$
$41$	−1.63781	−	2.83677i	−0.255783	−	0.443030i	−0.965108	+	0.261852i	$0.915667\pi$
$42$	9.48945			1.46425
$43$	6.40409			0.976614			0.488307	−	0.872672i	$-0.337615\pi$
$43$	6.40409			0.976614			0.488307	+	0.872672i	$0.337615\pi$
$44$	1.42153	−	2.46216i	0.214304	−	0.371185i
$45$	−3.33986			−0.497876
$46$	5.30632	+	9.19082i	0.782374	+	1.35511i
$47$	−5.68017	−	9.83835i	−0.828539	−	1.43507i	−0.899185	−	0.437570i	$-0.855839\pi$
$47$	−5.68017	−	9.83835i	−0.828539	−	1.43507i	0.0706459	−	0.997501i	$-0.477494\pi$
$48$	−1.69001	+	2.92718i	−0.243932	+	0.422503i
$49$	−7.03759	+	12.1895i	−1.00537	+	1.74135i
$50$	6.36104	−	11.0176i	0.899586	−	1.55813i
$51$	−1.78514	+	3.09195i	−0.249969	+	0.432960i
$52$	0.711265			0.0986347
$53$	−6.86493			−0.942971			−0.471485	−	0.881874i	$-0.656282\pi$
$53$	−6.86493			−0.942971			−0.471485	+	0.881874i	$0.656282\pi$
$54$	−1.03354	+	1.79014i	−0.140646	+	0.243607i
$55$	−2.08894	−	3.61815i	−0.281673	−	0.487871i
$56$	1.29429	+	2.24177i	0.172956	+	0.299569i
$57$	−2.95186	+	5.11277i	−0.390983	+	0.677203i
$58$	19.5702			2.56969
$59$	3.85632			0.502050			0.251025	−	0.967981i	$-0.419232\pi$
$59$	3.85632			0.502050			0.251025	+	0.967981i	$0.419232\pi$
$60$	−3.79539	−	6.57380i	−0.489982	−	0.848674i
$61$	−2.79859	+	4.84730i	−0.358323	+	0.620634i	−0.987681	−	0.156482i	$-0.949985\pi$
$61$	−2.79859	+	4.84730i	−0.358323	+	0.620634i	0.629358	+	0.777116i	$0.283318\pi$
$62$	−6.71988			−0.853425
$63$	−2.29539	−	3.97573i	−0.289191	−	0.500894i
$64$	−10.0132			−1.25164
$65$	0.522602	−	0.905173i	0.0648208	−	0.112273i
$66$	−2.58573			−0.318282
$67$	6.32977	−	5.18980i	0.773305	−	0.634034i
$67$	6.32977	−	5.18980i	0.773305	−	0.634034i
$68$	−8.11447			−0.984024
$69$	2.56707	−	4.44630i	0.309039	−	0.535271i
$70$	31.6934			3.78809
$71$	5.36356	+	9.28995i	0.636537	+	1.10251i	0.986187	+	0.165634i	$0.0529671\pi$
$71$	5.36356	+	9.28995i	0.636537	+	1.10251i	−0.349650	+	0.936880i	$0.613700\pi$
$72$	−0.563865			−0.0664521
$73$	−3.36950	+	5.83614i	−0.394370	+	0.683069i	−0.993021	−	0.117942i	$-0.962370\pi$
$73$	−3.36950	+	5.83614i	−0.394370	+	0.683069i	0.598651	+	0.801010i	$0.295704\pi$
$74$	−5.40147	−	9.35562i	−0.627908	−	1.08757i
$75$	−6.15464			−0.710676
$76$	−13.4179			−1.53914
$77$	2.87134	−	4.97330i	0.327219	−	0.566760i
$78$	−0.323444	−	0.560221i	−0.0366228	−	0.0634325i
$79$	−2.22355	−	3.85129i	−0.250168	−	0.433304i	0.713404	−	0.700753i	$-0.247153\pi$
$79$	−2.22355	−	3.85129i	−0.250168	−	0.433304i	−0.963572	+	0.267449i	$0.913819\pi$
$80$	−5.64439	+	9.77637i	−0.631062	+	1.09303i
$81$	1.00000			0.111111
$82$	−6.77095			−0.747727
$83$	5.62179	−	9.73722i	0.617071	−	1.06880i	−0.372946	−	0.927853i	$-0.621652\pi$
$83$	5.62179	−	9.73722i	0.617071	−	1.06880i	0.990017	−	0.140946i	$-0.0450144\pi$
$84$	5.21692	−	9.03597i	0.569212	−	0.985905i
$85$	−5.96211	+	10.3267i	−0.646681	+	1.12008i
$86$	6.61885	−	11.4642i	0.713729	−	1.23622i
$87$	−4.73379	−	8.19917i	−0.507516	−	0.879043i
$88$	−0.352674	−	0.610849i	−0.0375951	−	0.0651167i
$89$	−1.04520			−0.110791			−0.0553957	−	0.998464i	$-0.517642\pi$
$89$	−1.04520			−0.110791			−0.0553957	+	0.998464i	$0.517642\pi$
$90$	−3.45186	+	5.97880i	−0.363858	+	0.630221i
$91$	1.43668			0.150605
$92$	11.6688			1.21656
$93$	1.62546	+	2.81538i	0.168552	+	0.291941i
$94$	−23.4827			−2.42205
$95$	−9.85879	+	17.0759i	−1.01149	+	1.75195i
$96$	4.05724	+	7.02734i	0.414090	+	0.717225i
$97$	−3.31725	+	5.74565i	−0.336816	+	0.583383i	−0.983832	−	0.179094i	$-0.942683\pi$
$97$	−3.31725	+	5.74565i	−0.336816	+	0.583383i	0.647016	+	0.762477i	$0.276017\pi$
$98$	14.5472	+	25.1965i	1.46949	+	2.54523i
$99$	0.625458	+	1.08333i	0.0628609	+	0.108878i
$100$	−6.99408	−	12.1141i	−0.699408	−	1.21141i
$101$	7.45844	+	12.9184i	0.742142	+	1.28543i	0.951518	+	0.307593i	$0.0995235\pi$
$101$	7.45844	+	12.9184i	0.742142	+	1.28543i	−0.209376	+	0.977835i	$0.567143\pi$
$102$	3.69001	+	6.39128i	0.365365	+	0.632831i
$103$	8.52214	+	14.7608i	0.839711	+	1.45442i	0.890136	+	0.455695i	$0.150609\pi$
$103$	8.52214	+	14.7608i	0.839711	+	1.45442i	−0.0504249	+	0.998728i	$0.516058\pi$
$104$	0.0882303	−	0.152819i	0.00865170	−	0.0149852i
$105$	−7.66626	−	13.2783i	−0.748150	−	1.29583i
$106$	−7.09515	+	12.2892i	−0.689142	+	1.19363i
$107$	11.6491			1.12616			0.563082	−	0.826401i	$-0.309616\pi$
$107$	11.6491			1.12616			0.563082	+	0.826401i	$0.309616\pi$
$108$	1.13639	+	1.96829i	0.109349	+	0.189399i
$109$	3.98592			0.381782			0.190891	−	0.981611i	$-0.438862\pi$
$109$	3.98592			0.381782			0.190891	+	0.981611i	$0.438862\pi$
$110$	−8.63598			−0.823408
$111$	−2.61310	+	4.52603i	−0.248025	+	0.429592i
$112$	−15.5169			−1.46621
$113$	−5.70231	−	9.87670i	−0.536428	−	0.929121i	−0.999093	−	0.0425878i	$-0.986440\pi$
$113$	−5.70231	−	9.87670i	−0.536428	−	0.929121i	0.462664	−	0.886534i	$-0.346894\pi$
$114$	6.10171	+	10.5685i	0.571477	+	0.989827i
$115$	8.57365	−	14.8500i	0.799497	−	1.38477i
$116$	10.7589	−	18.6349i	0.998938	−	1.73021i
$117$	−0.156474	+	0.271021i	−0.0144661	+	0.0250559i
$118$	3.98564	−	6.90334i	0.366908	−	0.635504i
$119$	−16.3903			−1.50250
$120$	−1.88323			−0.171914
$121$	4.71760	−	8.17113i	0.428873	−	0.742830i
$122$	5.78489	+	10.0197i	0.523739	+	0.907143i
$123$	1.63781	+	2.83677i	0.147677	+	0.255783i
$124$	−3.69432	+	6.39874i	−0.331759	+	0.574624i
$125$	−3.85632			−0.344920
$126$	−9.48945			−0.845388
$127$	−3.97235	−	6.88032i	−0.352489	−	0.610530i	0.634196	−	0.773173i	$-0.281331\pi$
$127$	−3.97235	−	6.88032i	−0.352489	−	0.610530i	−0.986685	+	0.162643i	$0.947998\pi$
$128$	−2.23448	+	3.87023i	−0.197502	+	0.342083i
$129$	−6.40409			−0.563848
$130$	−1.08025	−	1.87106i	−0.0947446	−	0.164102i
$131$	−0.0342470			−0.00299218			−0.00149609	−	0.999999i	$-0.500476\pi$
$131$	−0.0342470			−0.00299218			−0.00149609	+	0.999999i	$0.500476\pi$
$132$	−1.42153	+	2.46216i	−0.123728	+	0.214304i
$133$	−27.1026			−2.35010
$134$	−2.74840	−	16.6950i	−0.237425	−	1.44223i
$135$	3.33986			0.287449
$136$	−1.00658	+	1.74344i	−0.0863133	+	0.149499i
$137$	2.47987			0.211870			0.105935	−	0.994373i	$-0.466216\pi$
$137$	2.47987			0.211870			0.105935	+	0.994373i	$0.466216\pi$
$138$	−5.30632	−	9.19082i	−0.451704	−	0.782374i
$139$	16.5170			1.40095			0.700477	−	0.713675i	$-0.252971\pi$
$139$	16.5170			1.40095			0.700477	+	0.713675i	$0.252971\pi$
$140$	17.4238	−	30.1788i	1.47258	−	2.55058i
$141$	5.68017	+	9.83835i	0.478357	+	0.828539i
$142$	22.1737			1.86078
$143$	−0.391472			−0.0327366
$144$	1.69001	−	2.92718i	0.140834	−	0.243932i
$145$	−15.8102	−	27.3840i	−1.31296	−	2.27412i
$146$	6.96499	+	12.0637i	0.576427	+	0.998401i
$147$	7.03759	−	12.1895i	0.580451	−	1.00537i
$148$	−11.8780			−0.976369
$149$	−10.5844			−0.867104			−0.433552	−	0.901128i	$-0.642740\pi$
$149$	−10.5844			−0.867104			−0.433552	+	0.901128i	$0.642740\pi$
$150$	−6.36104	+	11.0176i	−0.519376	+	0.899586i
$151$	4.35010	−	7.53460i	0.354006	−	0.613157i	−0.632941	−	0.774200i	$-0.718152\pi$
$151$	4.35010	−	7.53460i	0.354006	−	0.613157i	0.986947	+	0.161043i	$0.0514858\pi$
$152$	−1.66445	+	2.88291i	−0.135005	+	0.233835i
$153$	1.78514	−	3.09195i	0.144320	−	0.249969i
$154$	−5.93526	−	10.2802i	−0.478276	−	0.828399i
$155$	5.42880	+	9.40295i	0.436051	+	0.755263i
$156$	−0.711265			−0.0569468
$157$	−6.01189	+	10.4129i	−0.479801	+	0.831040i	−0.999732	−	0.0231686i	$-0.992625\pi$
$157$	−6.01189	+	10.4129i	−0.479801	+	0.831040i	0.519930	+	0.854209i	$0.325958\pi$
$158$	−9.19246			−0.731313
$159$	6.86493			0.544424
$160$	13.5506	+	23.4703i	1.07127	+	1.85549i
$161$	23.5697			1.85755
$162$	1.03354	−	1.79014i	0.0812022	−	0.140646i
$163$	−10.9992	−	19.0512i	−0.861527	−	1.49221i	−0.870455	−	0.492248i	$-0.836175\pi$
$163$	−10.9992	−	19.0512i	−0.861527	−	1.49221i	0.00892830	−	0.999960i	$-0.497158\pi$
$164$	−3.72240	+	6.44738i	−0.290670	+	0.503456i
$165$	2.08894	+	3.61815i	0.162624	+	0.281673i
$166$	−11.6206	−	20.1275i	−0.901936	−	1.56220i
$167$	3.28193	+	5.68447i	0.253964	+	0.439878i	0.964613	−	0.263668i	$-0.0849323\pi$
$167$	3.28193	+	5.68447i	0.253964	+	0.439878i	−0.710650	+	0.703546i	$0.751599\pi$
$168$	−1.29429	−	2.24177i	−0.0998564	−	0.172956i
$169$	6.45103	+	11.1735i	0.496233	+	0.859501i
$170$	12.3241	+	21.3460i	0.945215	+	1.63716i
$171$	2.95186	−	5.11277i	0.225734	−	0.390983i
$172$	−7.27755	−	12.6051i	−0.554908	−	0.961129i
$173$	0.292545	−	0.506702i	0.0222418	−	0.0385239i	−0.854690	−	0.519138i	$-0.826253\pi$
$173$	0.292545	−	0.506702i	0.0222418	−	0.0385239i	0.876932	+	0.480614i	$0.159586\pi$
$174$	−19.5702			−1.48361
$175$	−14.1273	−	24.4691i	−1.06792	−	1.84969i
$176$	4.22812			0.318707
$177$	−3.85632			−0.289859
$178$	−1.08025	+	1.87106i	−0.0809685	+	0.140242i
$179$	−20.1173			−1.50364			−0.751818	−	0.659371i	$-0.770823\pi$
$179$	−20.1173			−1.50364			−0.751818	+	0.659371i	$0.770823\pi$
$180$	3.79539	+	6.57380i	0.282891	+	0.489982i
$181$	2.64091	+	4.57420i	0.196298	+	0.339997i	0.947325	−	0.320274i	$-0.103775\pi$
$181$	2.64091	+	4.57420i	0.196298	+	0.339997i	−0.751028	+	0.660271i	$0.770441\pi$
$182$	1.48486	−	2.57185i	0.110065	−	0.190638i
$183$	2.79859	−	4.84730i	0.206878	−	0.358323i
$184$	1.44748	−	2.50711i	0.106710	−	0.184827i
$185$	−8.72739	+	15.1163i	−0.641650	+	1.11137i
$186$	6.71988			0.492725
$187$	4.46612			0.326595
$188$	−12.9098	+	22.3605i	−0.941545	+	1.63080i
$189$	2.29539	+	3.97573i	0.166965	+	0.289191i
$190$	20.3788	+	35.2971i	1.47843	+	2.56072i
$191$	6.95406	−	12.0448i	0.503178	−	0.871530i	−0.496815	−	0.867856i	$-0.665497\pi$
$191$	6.95406	−	12.0448i	0.503178	−	0.871530i	0.999993	−	0.00367350i	$-0.00116931\pi$
$192$	10.0132			0.722637
$193$	12.8655			0.926077			0.463038	−	0.886338i	$-0.346759\pi$
$193$	12.8655			0.926077			0.463038	+	0.886338i	$0.346759\pi$
$194$	6.85700	+	11.8767i	0.492304	+	0.852696i
$195$	−0.522602	+	0.905173i	−0.0374243	+	0.0648208i
$196$	31.9899			2.28499
$197$	3.66078	+	6.34066i	0.260820	+	0.451753i	0.966460	−	0.256817i	$-0.0826738\pi$
$197$	3.66078	+	6.34066i	0.260820	+	0.451753i	−0.705640	+	0.708570i	$0.749341\pi$
$198$	2.58573			0.183760
$199$	7.86931	−	13.6300i	0.557841	−	0.966208i	−0.439836	−	0.898078i	$-0.644963\pi$
$199$	7.86931	−	13.6300i	0.557841	−	0.966208i	0.997676	−	0.0681301i	$-0.0217033\pi$
$200$	−3.47038			−0.245393
$201$	−6.32977	+	5.18980i	−0.446468	+	0.366060i
$202$	30.8342			2.16949
$203$	21.7318	−	37.6405i	1.52527	−	2.64185i
$204$	8.11447			0.568127
$205$	5.47006	+	9.47442i	0.382045	+	0.661722i
$206$	35.2317			2.45471
$207$	−2.56707	+	4.44630i	−0.178424	+	0.309039i
$208$	0.528886	+	0.916058i	0.0366717	+	0.0635172i
$209$	7.38506			0.510835
$210$	−31.6934			−2.18705
$211$	−11.1884	+	19.3789i	−0.770241	+	1.33410i	0.167190	+	0.985925i	$0.446531\pi$
$211$	−11.1884	+	19.3789i	−0.770241	+	1.33410i	−0.937431	+	0.348172i	$0.886803\pi$
$212$	7.80125	+	13.5122i	0.535792	+	0.928019i
$213$	−5.36356	−	9.28995i	−0.367505	−	0.636537i
$214$	12.0398	−	20.8535i	0.823023	−	1.42552i
$215$	−21.3887			−1.45870
$216$	0.563865			0.0383661
$217$	−7.46211	+	12.9247i	−0.506561	+	0.877389i
$218$	4.11959	−	7.13534i	0.279014	−	0.483266i
$219$	3.36950	−	5.83614i	0.227690	−	0.394370i
$220$	−4.74771	+	8.22327i	−0.320090	+	0.554413i
$221$	0.558657	+	0.967622i	0.0375793	+	0.0650893i
$222$	5.40147	+	9.35562i	0.362523	+	0.627908i
$223$	0.871719			0.0583746			0.0291873	−	0.999574i	$-0.490708\pi$
$223$	0.871719			0.0583746			0.0291873	+	0.999574i	$0.490708\pi$
$224$	−18.6258	+	32.2609i	−1.24449	+	2.15552i
$225$	6.15464			0.410309
$226$	−23.5742			−1.56813
$227$	4.03806	+	6.99412i	0.268015	+	0.464216i	0.968349	−	0.249599i	$-0.0802989\pi$
$227$	4.03806	+	6.99412i	0.268015	+	0.464216i	−0.700334	+	0.713815i	$0.746966\pi$
$228$	13.4179			0.888621
$229$	4.17477	−	7.23091i	0.275877	−	0.477832i	−0.694479	−	0.719513i	$-0.744365\pi$
$229$	4.17477	−	7.23091i	0.275877	−	0.477832i	0.970356	+	0.241680i	$0.0776986\pi$
$230$	−17.7223	−	30.6960i	−1.16858	−	2.02403i
$231$	−2.87134	+	4.97330i	−0.188920	+	0.327219i
$232$	−2.66922	−	4.62322i	−0.175243	−	0.303529i
$233$	−8.39274	−	14.5367i	−0.549827	−	0.952328i	−0.998286	−	0.0585245i	$-0.981360\pi$
$233$	−8.39274	−	14.5367i	−0.549827	−	0.952328i	0.448459	−	0.893803i	$-0.351973\pi$
$234$	0.323444	+	0.560221i	0.0211442	+	0.0366228i
$235$	18.9710	+	32.8587i	1.23753	+	2.14346i
$236$	−4.38229	−	7.59035i	−0.285263	−	0.494090i
$237$	2.22355	+	3.85129i	0.144435	+	0.250168i
$238$	−16.9400	+	29.3409i	−1.09806	+	1.90189i
$239$	−3.81459	−	6.60707i	−0.246746	−	0.427376i	0.715875	−	0.698228i	$-0.246028\pi$
$239$	−3.81459	−	6.60707i	−0.246746	−	0.427376i	−0.962621	+	0.270852i	$0.912695\pi$
$240$	5.64439	−	9.77637i	0.364344	−	0.631062i
$241$	−22.7915			−1.46813			−0.734064	−	0.679080i	$-0.762379\pi$
$241$	−22.7915			−1.46813			−0.734064	+	0.679080i	$0.762379\pi$
$242$	−9.75163	−	16.8903i	−0.626858	−	1.08575i
$243$	−1.00000			−0.0641500
$244$	12.7212			0.814391
$245$	23.5045	−	40.7111i	1.50165	−	2.60093i
$246$	6.77095			0.431700
$247$	0.923781	+	1.60003i	0.0587787	+	0.101808i
$248$	0.916538	+	1.58749i	0.0582002	+	0.100806i
$249$	−5.62179	+	9.73722i	−0.356266	+	0.617071i
$250$	−3.98564	+	6.90334i	−0.252074	+	0.436605i
$251$	7.13708	−	12.3618i	0.450488	−	0.780269i	−0.547928	−	0.836526i	$-0.684583\pi$
$251$	7.13708	−	12.3618i	0.450488	−	0.780269i	0.998416	+	0.0562567i	$0.0179165\pi$
$252$	−5.21692	+	9.03597i	−0.328635	+	0.569212i
$253$	−6.42238			−0.403772
$254$	−16.4223			−1.03043
$255$	5.96211	−	10.3267i	0.373362	−	0.646681i
$256$	−5.39432	−	9.34324i	−0.337145	−	0.583953i
$257$	0.889005	+	1.53980i	0.0554546	+	0.0960502i	0.892420	−	0.451206i	$-0.149006\pi$
$257$	0.889005	+	1.53980i	0.0554546	+	0.0960502i	−0.836965	+	0.547256i	$0.815673\pi$
$258$	−6.61885	+	11.4642i	−0.412072	+	0.713729i
$259$	−23.9923			−1.49081
$260$	−2.37552			−0.147324
$261$	4.73379	+	8.19917i	0.293014	+	0.507516i
$262$	−0.0353955	+	0.0613068i	−0.00218674	+	0.00378755i
$263$	8.97731			0.553565			0.276782	−	0.960933i	$-0.410732\pi$
$263$	8.97731			0.553565			0.276782	+	0.960933i	$0.410732\pi$
$264$	0.352674	+	0.610849i	0.0217056	+	0.0375951i
$265$	22.9279			1.40845
$266$	−28.0115	+	48.5174i	−1.71750	+	2.97479i
$267$	1.04520			0.0639654
$268$	−17.4081	−	6.56118i	−1.06337	−	0.400788i
$269$	4.39349			0.267876			0.133938	−	0.990990i	$-0.457238\pi$
$269$	4.39349			0.267876			0.133938	+	0.990990i	$0.457238\pi$
$270$	3.45186	−	5.97880i	0.210074	−	0.363858i
$271$	−17.2470			−1.04768			−0.523842	−	0.851816i	$-0.675502\pi$
$271$	−17.2470			−1.04768			−0.523842	+	0.851816i	$0.675502\pi$
$272$	−6.03381	−	10.4509i	−0.365853	−	0.633676i
$273$	−1.43668			−0.0869516
$274$	2.56304	−	4.43931i	0.154839	−	0.268188i
$275$	3.84947	+	6.66747i	0.232132	+	0.402064i
$276$	−11.6688			−0.702379
$277$	7.41504			0.445527			0.222763	−	0.974873i	$-0.428492\pi$
$277$	7.41504			0.445527			0.222763	+	0.974873i	$0.428492\pi$
$278$	17.0709	−	29.5677i	1.02385	−	1.77335i
$279$	−1.62546	−	2.81538i	−0.0973136	−	0.168552i
$280$	−4.32273	−	7.48719i	−0.258333	−	0.447445i
$281$	−12.0360	+	20.8470i	−0.718009	+	1.24363i	0.243778	+	0.969831i	$0.421613\pi$
$281$	−12.0360	+	20.8470i	−0.718009	+	1.24363i	−0.961787	+	0.273798i	$0.911720\pi$
$282$	23.4827			1.39837
$283$	12.8991			0.766773			0.383387	−	0.923588i	$-0.374758\pi$
$283$	12.8991			0.766773			0.383387	+	0.923588i	$0.374758\pi$
$284$	12.1902	−	21.1141i	0.723356	−	1.25289i
$285$	9.85879	−	17.0759i	0.583984	−	1.01149i
$286$	−0.404601	+	0.700789i	−0.0239245	+	0.0414385i
$287$	−7.51882	+	13.0230i	−0.443822	+	0.768723i
$288$	−4.05724	−	7.02734i	−0.239075	−	0.414090i
$289$	2.12656	+	3.68330i	0.125092	+	0.216665i
$290$	−65.3616			−3.83816
$291$	3.31725	−	5.74565i	0.194461	−	0.336816i
$292$	15.3163			0.896318
$293$	10.8318			0.632802			0.316401	−	0.948626i	$-0.397526\pi$
$293$	10.8318			0.632802			0.316401	+	0.948626i	$0.397526\pi$
$294$	−14.5472	−	25.1965i	−0.848410	−	1.46949i
$295$	−12.8796			−0.749876
$296$	−1.47344	+	2.55207i	−0.0856418	+	0.148336i
$297$	−0.625458	−	1.08333i	−0.0362928	−	0.0628609i
$298$	−10.9393	+	18.9474i	−0.633697	+	1.09760i
$299$	−0.803361	−	1.39146i	−0.0464596	−	0.0804704i
$300$	6.99408	+	12.1141i	0.403803	+	0.699408i
$301$	−14.6998	−	25.4609i	−0.847285	−	1.46754i
$302$	−8.99197	−	15.5746i	−0.517430	−	0.896215i
$303$	−7.45844	−	12.9184i	−0.428476	−	0.742142i
$304$	−9.97735	−	17.2813i	−0.572240	−	0.991149i
$305$	9.34690	−	16.1893i	0.535202	−	0.926997i
$306$	−3.69001	−	6.39128i	−0.210944	−	0.365365i
$307$	−16.4711	+	28.5287i	−0.940053	+	1.62822i	−0.174688	+	0.984624i	$0.555892\pi$
$307$	−16.4711	+	28.5287i	−0.940053	+	1.62822i	−0.765365	+	0.643596i	$0.777442\pi$
$308$	−13.0519			−0.743698
$309$	−8.52214	−	14.7608i	−0.484808	−	0.839711i
$310$	22.4434			1.27470
$311$	−11.7860			−0.668324			−0.334162	−	0.942516i	$-0.608453\pi$
$311$	−11.7860			−0.668324			−0.334162	+	0.942516i	$0.608453\pi$
$312$	−0.0882303	+	0.152819i	−0.00499506	+	0.00865170i
$313$	30.6039			1.72984			0.864918	−	0.501913i	$-0.167370\pi$
$313$	30.6039			1.72984			0.864918	+	0.501913i	$0.167370\pi$
$314$	12.4270	+	21.5242i	0.701297	+	1.21468i
$315$	7.66626	+	13.2783i	0.431945	+	0.748150i
$316$	−5.05364	+	8.75316i	−0.284289	+	0.492404i
$317$	−1.48655	+	2.57477i	−0.0834928	+	0.144614i	−0.904748	−	0.425947i	$-0.859941\pi$
$317$	−1.48655	+	2.57477i	−0.0834928	+	0.144614i	0.821255	+	0.570561i	$0.193274\pi$
$318$	7.09515	−	12.2892i	0.397876	−	0.689142i
$319$	−5.92158	+	10.2565i	−0.331545	+	0.574252i
$320$	33.4425			1.86949
$321$	−11.6491			−0.650191
$322$	24.3601	−	42.1929i	1.35754	−	2.35132i
$323$	−10.5390	−	18.2540i	−0.586404	−	1.01568i
$324$	−1.13639	−	1.96829i	−0.0631329	−	0.109349i
$325$	−0.963042	+	1.66804i	−0.0534200	+	0.0925261i
$326$	−45.4724			−2.51848
$327$	−3.98592			−0.220422
$328$	0.923505	+	1.59956i	0.0509920	+	0.0883208i
$329$	−26.0764	+	45.1656i	−1.43764	+	2.49006i
$330$	8.63598			0.475395
$331$	7.80361	+	13.5162i	0.428925	+	0.742920i	0.996778	−	0.0802100i	$-0.0255591\pi$
$331$	7.80361	+	13.5162i	0.428925	+	0.742920i	−0.567853	+	0.823130i	$0.692226\pi$
$332$	−25.5542			−1.40247
$333$	2.61310	−	4.52603i	0.143197	−	0.248025i
$334$	13.5680			0.742407
$335$	−21.1405	+	17.3332i	−1.15503	+	0.947012i
$336$	15.5169			0.846516
$337$	2.48435	−	4.30302i	0.135331	−	0.234400i	−0.790393	−	0.612600i	$-0.790124\pi$
$337$	2.48435	−	4.30302i	0.135331	−	0.234400i	0.925724	+	0.378200i	$0.123457\pi$
$338$	26.6695			1.45063
$339$	5.70231	+	9.87670i	0.309707	+	0.536428i
$340$	27.1012			1.46977
$341$	2.03331	−	3.52180i	0.110110	−	0.190716i
$342$	−6.10171	−	10.5685i	−0.329942	−	0.571477i
$343$	32.4806			1.75379
$344$	−3.61104			−0.194694
$345$	−8.57365	+	14.8500i	−0.461590	+	0.799497i
$346$	−0.604711	−	1.04739i	−0.0325094	−	0.0563080i
$347$	−4.22722	−	7.32175i	−0.226929	−	0.393052i	0.729968	−	0.683482i	$-0.239535\pi$
$347$	−4.22722	−	7.32175i	−0.226929	−	0.393052i	−0.956896	+	0.290430i	$0.906202\pi$
$348$	−10.7589	+	18.6349i	−0.576737	+	0.998938i
$349$	9.90224			0.530055			0.265027	−	0.964241i	$-0.414619\pi$
$349$	9.90224			0.530055			0.265027	+	0.964241i	$0.414619\pi$
$350$	−58.4041			−3.12183
$351$	0.156474	−	0.271021i	0.00835198	−	0.0144661i
$352$	5.07526	−	8.79061i	0.270512	−	0.468541i
$353$	−7.76437	+	13.4483i	−0.413256	+	0.715780i	−0.995244	−	0.0974176i	$-0.968942\pi$
$353$	−7.76437	+	13.4483i	−0.413256	+	0.715780i	0.581988	+	0.813197i	$0.302275\pi$
$354$	−3.98564	+	6.90334i	−0.211835	+	0.366908i
$355$	−17.9135	−	31.0271i	−0.950750	−	1.64675i
$356$	1.18776	+	2.05726i	0.0629512	+	0.109035i
$357$	16.3903			0.867468
$358$	−20.7919	+	36.0126i	−1.09889	+	1.90333i
$359$	−11.6509			−0.614913			−0.307456	−	0.951562i	$-0.599478\pi$
$359$	−11.6509			−0.614913			−0.307456	+	0.951562i	$0.599478\pi$
$360$	1.88323			0.0992548
$361$	−7.92696	−	13.7299i	−0.417208	−	0.722626i
$362$	10.9179			0.573833
$363$	−4.71760	+	8.17113i	−0.247610	+	0.428873i
$364$	−1.63263	−	2.82779i	−0.0855729	−	0.148217i
$365$	11.2536	−	19.4919i	0.589042	−	1.02025i
$366$	−5.78489	−	10.0197i	−0.302381	−	0.523739i
$367$	1.99532	+	3.45600i	0.104155	+	0.180402i	0.913393	−	0.407080i	$-0.133453\pi$
$367$	1.99532	+	3.45600i	0.104155	+	0.180402i	−0.809238	+	0.587481i	$0.800120\pi$
$368$	8.67675	+	15.0286i	0.452307	+	0.783419i
$369$	−1.63781	−	2.83677i	−0.0852611	−	0.147677i
$370$	18.0401	+	31.2464i	0.937862	+	1.62442i
$371$	15.7577	+	27.2931i	0.818097	+	1.41699i
$372$	3.69432	−	6.39874i	0.191541	−	0.331759i
$373$	2.55105	+	4.41854i	0.132088	+	0.228783i	0.924481	−	0.381227i	$-0.124498\pi$
$373$	2.55105	+	4.41854i	0.132088	+	0.228783i	−0.792393	+	0.610011i	$0.791165\pi$
$374$	4.61589	−	7.99496i	0.238682	−	0.413410i
$375$	3.85632			0.199139
$376$	3.20285	+	5.54750i	0.165174	+	0.286090i
$377$	−2.96287			−0.152595
$378$	9.48945			0.488085
$379$	−9.25045	+	16.0223i	−0.475164	+	0.823008i	−0.999595	−	0.0284447i	$-0.990945\pi$
$379$	−9.25045	+	16.0223i	−0.475164	+	0.823008i	0.524432	+	0.851453i	$0.324278\pi$
$380$	44.8138			2.29890
$381$	3.97235	+	6.88032i	0.203510	+	0.352489i
$382$	−14.3745	−	24.8974i	−0.735465	−	1.27386i
$383$	−6.56560	+	11.3720i	−0.335486	+	0.581080i	−0.983578	−	0.180483i	$-0.942234\pi$
$383$	−6.56560	+	11.3720i	−0.335486	+	0.581080i	0.648092	+	0.761562i	$0.275567\pi$
$384$	2.23448	−	3.87023i	0.114028	−	0.197502i
$385$	−9.58985	+	16.6101i	−0.488744	+	0.846529i
$386$	13.2969	−	23.0309i	0.676796	−	1.17224i
$387$	6.40409			0.325538
$388$	15.0788			0.765510
$389$	3.74722	−	6.49038i	0.189992	−	0.329075i	−0.755256	−	0.655430i	$-0.772487\pi$
$389$	3.74722	−	6.49038i	0.189992	−	0.329075i	0.945247	+	0.326355i	$0.105821\pi$
$390$	1.08025	+	1.87106i	0.0547008	+	0.0947446i
$391$	9.16516	+	15.8745i	0.463502	+	0.802809i
$392$	3.96825	−	6.87321i	0.200427	−	0.347150i
$393$	0.0342470			0.00172753
$394$	15.1342			0.762449
$395$	7.42632	+	12.8628i	0.373659	+	0.647196i
$396$	1.42153	−	2.46216i	0.0714346	−	0.123728i
$397$	−18.6595			−0.936496			−0.468248	−	0.883597i	$-0.655115\pi$
$397$	−18.6595			−0.936496			−0.468248	+	0.883597i	$0.655115\pi$
$398$	−16.2664	−	28.1743i	−0.815362	−	1.41225i
$399$	27.1026			1.35683
$400$	10.4014	−	18.0157i	0.520070	−	0.900787i
$401$	10.0722			0.502984			0.251492	−	0.967859i	$-0.419079\pi$
$401$	10.0722			0.502984			0.251492	+	0.967859i	$0.419079\pi$
$402$	2.74840	+	16.6950i	0.137078	+	0.832671i
$403$	1.01737			0.0506788
$404$	16.9514	−	29.3607i	0.843365	−	1.46075i
$405$	−3.33986			−0.165959
$406$	−44.9211	−	77.8056i	−2.22940	−	3.86143i
$407$	6.53755			0.324054
$408$	1.00658	−	1.74344i	0.0498330	−	0.0863133i
$409$	18.2488	+	31.6078i	0.902344	+	1.56291i	0.824443	+	0.565945i	$0.191488\pi$
$409$	18.2488	+	31.6078i	0.902344	+	1.56291i	0.0779007	+	0.996961i	$0.475178\pi$
$410$	22.6140			1.11683
$411$	−2.47987			−0.122323
$412$	19.3690	−	33.5481i	0.954241	−	1.65279i
$413$	−8.85174	−	15.3317i	−0.435566	−	0.754422i
$414$	5.30632	+	9.19082i	0.260791	+	0.451704i
$415$	−18.7760	+	32.5209i	−0.921676	+	1.59639i
$416$	2.53941			0.124505
$417$	−16.5170			−0.808841
$418$	7.63272	−	13.2203i	0.373329	−	0.646624i
$419$	−8.03568	+	13.9182i	−0.392569	+	0.679949i	−0.992788	−	0.119887i	$-0.961747\pi$
$419$	−8.03568	+	13.9182i	−0.392569	+	0.679949i	0.600219	+	0.799836i	$0.295080\pi$
$420$	−17.4238	+	30.1788i	−0.850192	+	1.47258i
$421$	2.18311	−	3.78126i	0.106398	−	0.184287i	−0.807910	−	0.589305i	$-0.799401\pi$
$421$	2.18311	−	3.78126i	0.106398	−	0.184287i	0.914309	+	0.405018i	$0.132735\pi$
$422$	23.1272	+	40.0575i	1.12582	+	1.94997i
$423$	−5.68017	−	9.83835i	−0.276180	−	0.478357i
$424$	3.87089			0.187987
$425$	10.9869	−	19.0298i	0.532942	−	0.923083i
$426$	−22.1737			−1.07432
$427$	25.6954			1.24349
$428$	−13.2380	−	22.9289i	−0.639882	−	1.10831i
$429$	0.391472			0.0189005
$430$	−22.1060	+	38.2887i	−1.06605	+	1.84645i
$431$	8.04812	+	13.9397i	0.387664	+	0.671454i	0.992135	−	0.125173i	$-0.0399487\pi$
$431$	8.04812	+	13.9397i	0.387664	+	0.671454i	−0.604471	+	0.796627i	$0.706615\pi$
$432$	−1.69001	+	2.92718i	−0.0813106	+	0.140834i
$433$	−11.4028	−	19.7502i	−0.547983	−	0.949135i	−0.998413	−	0.0563228i	$-0.982062\pi$
$433$	−11.4028	−	19.7502i	−0.547983	−	0.949135i	0.450429	−	0.892812i	$-0.351271\pi$
$434$	15.4247	+	26.7164i	0.740410	+	1.28243i
$435$	15.8102	+	27.3840i	0.758040	+	1.31296i
$436$	−4.52957	−	7.84544i	−0.216927	−	0.375729i
$437$	15.1553	+	26.2497i	0.724975	+	1.25569i
$438$	−6.96499	−	12.0637i	−0.332800	−	0.576427i
$439$	−8.86564	+	15.3557i	−0.423134	+	0.732889i	−0.996244	−	0.0865889i	$-0.972403\pi$
$439$	−8.86564	+	15.3557i	−0.423134	+	0.732889i	0.573110	+	0.819478i	$0.305737\pi$
$440$	1.17788	+	2.04015i	0.0561532	+	0.0972602i
$441$	−7.03759	+	12.1895i	−0.335123	+	0.580451i
$442$	2.30957			0.109855
$443$	8.25692	+	14.3014i	0.392298	+	0.679481i	0.992752	−	0.120179i	$-0.0383468\pi$
$443$	8.25692	+	14.3014i	0.392298	+	0.679481i	−0.600454	+	0.799659i	$0.705013\pi$
$444$	11.8780			0.563707
$445$	3.49083			0.165481
$446$	0.900953	−	1.56050i	0.0426614	−	0.0738916i
$447$	10.5844			0.500623
$448$	22.9841	+	39.8095i	1.08589	+	1.88082i
$449$	−18.7860	−	32.5383i	−0.886567	−	1.53558i	−0.843907	−	0.536489i	$-0.819750\pi$
$449$	−18.7860	−	32.5383i	−0.886567	−	1.53558i	−0.0426593	−	0.999090i	$-0.513583\pi$
$450$	6.36104	−	11.0176i	0.299862	−	0.519376i
$451$	2.04877	−	3.54857i	0.0964726	−	0.167096i
$452$	−12.9601	+	22.4476i	−0.609593	+	1.05585i
$453$	−4.35010	+	7.53460i	−0.204386	+	0.354006i
$454$	16.6939			0.783484
$455$	−4.79829			−0.224947
$456$	1.66445	−	2.88291i	0.0779450	−	0.135005i
$457$	8.61730	+	14.9256i	0.403100	+	0.698190i	0.994098	−	0.108483i	$-0.0345993\pi$
$457$	8.61730	+	14.9256i	0.403100	+	0.698190i	−0.590998	+	0.806673i	$0.701266\pi$
$458$	−8.62955	−	14.9468i	−0.403232	−	0.698419i
$459$	−1.78514	+	3.09195i	−0.0833232	+	0.144320i
$460$	−38.9721			−1.81708
$461$	−7.91067			−0.368437			−0.184218	−	0.982885i	$-0.558975\pi$
$461$	−7.91067			−0.368437			−0.184218	+	0.982885i	$0.558975\pi$
$462$	5.93526	+	10.2802i	0.276133	+	0.478276i
$463$	−4.72144	+	8.17777i	−0.219424	+	0.380053i	−0.954632	−	0.297788i	$-0.903751\pi$
$463$	−4.72144	+	8.17777i	−0.219424	+	0.380053i	0.735208	+	0.677841i	$0.237084\pi$
$464$	32.0006			1.48559
$465$	−5.42880	−	9.40295i	−0.251754	−	0.436051i
$466$	−34.6968			−1.60730
$467$	7.90271	−	13.6879i	0.365694	−	0.633400i	−0.623193	−	0.782068i	$-0.714165\pi$
$467$	7.90271	−	13.6879i	0.365694	−	0.633400i	0.988887	+	0.148667i	$0.0474984\pi$
$468$	0.711265			0.0328782
$469$	−35.1625	−	13.2529i	−1.62365	−	0.611960i
$470$	78.4287			3.61765
$471$	6.01189	−	10.4129i	0.277013	−	0.479801i
$472$	−2.17444			−0.100087
$473$	4.00549	+	6.93771i	0.184172	+	0.318996i
$474$	9.19246			0.422223
$475$	18.1676	−	31.4673i	0.833588	−	1.44382i
$476$	18.6258	+	32.2609i	0.853714	+	1.47868i
$477$	−6.86493			−0.314324
$478$	−15.7701			−0.721306
$479$	0.164913	−	0.285638i	0.00753507	−	0.0130511i	−0.862233	−	0.506511i	$-0.830935\pi$
$479$	0.164913	−	0.285638i	0.00753507	−	0.0130511i	0.869768	+	0.493460i	$0.164268\pi$
$480$	−13.5506	−	23.4703i	−0.618497	−	1.07127i
$481$	0.817767	+	1.41641i	0.0372870	+	0.0645829i
$482$	−23.5558	+	40.7999i	−1.07294	+	1.85838i
$483$	−23.5697			−1.07246
$484$	−21.4442			−0.974736
$485$	11.0792	−	19.1897i	0.503078	−	0.871357i
$486$	−1.03354	+	1.79014i	−0.0468821	+	0.0812022i
$487$	5.64503	−	9.77747i	0.255801	−	0.443059i	−0.709312	−	0.704895i	$-0.750994\pi$
$487$	5.64503	−	9.77747i	0.255801	−	0.443059i	0.965113	+	0.261835i	$0.0843276\pi$
$488$	1.57803	−	2.73322i	0.0714340	−	0.123727i
$489$	10.9992	+	19.0512i	0.497403	+	0.861527i
$490$	−48.5856	−	84.1527i	−2.19487	−	3.80163i
$491$	−12.0275			−0.542792			−0.271396	−	0.962468i	$-0.587485\pi$
$491$	−12.0275			−0.542792			−0.271396	+	0.962468i	$0.587485\pi$
$492$	3.72240	−	6.44738i	0.167819	−	0.290670i
$493$	33.8019			1.52236
$494$	3.81904			0.171827
$495$	−2.08894	−	3.61815i	−0.0938909	−	0.162624i
$496$	−10.9882			−0.493383
$497$	24.6229	−	42.6480i	1.10449	−	1.91303i
$498$	11.6206	+	20.1275i	0.520733	+	0.901936i
$499$	11.9785	−	20.7473i	0.536230	−	0.928777i	−0.462873	−	0.886425i	$-0.653181\pi$
$499$	11.9785	−	20.7473i	0.536230	−	0.928777i	0.999103	−	0.0423527i	$-0.0134853\pi$
$500$	4.38229	+	7.59035i	0.195982	+	0.339451i
$501$	−3.28193	−	5.68447i	−0.146626	−	0.253964i
$502$	−14.7529	−	25.5527i	−0.658452	−	1.14047i
$503$	−19.2961	−	33.4218i	−0.860370	−	1.49020i	−0.871572	−	0.490267i	$-0.836899\pi$
$503$	−19.2961	−	33.4218i	−0.860370	−	1.49020i	0.0112021	−	0.999937i	$-0.496434\pi$
$504$	1.29429	+	2.24177i	0.0576521	+	0.0998564i
$505$	−24.9101	−	43.1456i	−1.10849	−	1.91995i
$506$	−6.63776	+	11.4969i	−0.295084	+	0.511101i
$507$	−6.45103	−	11.1735i	−0.286500	−	0.496233i
$508$	−9.02830	+	15.6375i	−0.400566	+	0.693801i
$509$	15.0496			0.667060			0.333530	−	0.942740i	$-0.391760\pi$
$509$	15.0496			0.667060			0.333530	+	0.942740i	$0.391760\pi$
$510$	−12.3241	−	21.3460i	−0.545720	−	0.945215i
$511$	30.9372			1.36858
$512$	−31.2388			−1.38057
$513$	−2.95186	+	5.11277i	−0.130328	+	0.225734i
$514$	3.67527			0.162109
$515$	−28.4627	−	49.2989i	−1.25422	−	2.17237i
$516$	7.27755	+	12.6051i	0.320376	+	0.554908i
$517$	7.10542	−	12.3070i	0.312496	−	0.541259i
$518$	−24.7969	+	42.9495i	−1.08951	+	1.88709i
$519$	−0.292545	+	0.506702i	−0.0128413	+	0.0222418i
$520$	−0.294677	+	0.510395i	−0.0129224	+	0.0223823i
$521$	17.1192			0.750008			0.375004	−	0.927023i	$-0.377641\pi$
$521$	17.1192			0.750008			0.375004	+	0.927023i	$0.377641\pi$
$522$	19.5702			0.856563
$523$	−6.81799	+	11.8091i	−0.298130	+	0.516376i	−0.975708	−	0.219075i	$-0.929696\pi$
$523$	−6.81799	+	11.8091i	−0.298130	+	0.516376i	0.677578	+	0.735451i	$0.263029\pi$
$524$	0.0389180	+	0.0674080i	0.00170014	+	0.00294473i
$525$	14.1273	+	24.4691i	0.616564	+	1.06792i
$526$	9.27837	−	16.0706i	0.404556	−	0.700712i
$527$	−11.6067			−0.505595
$528$	−4.22812			−0.184005
$529$	−1.67971	−	2.90935i	−0.0730309	−	0.126493i
$530$	23.6968	−	41.0440i	1.02932	−	1.78284i
$531$	3.85632			0.167350
$532$	30.7992	+	53.3458i	1.33532	+	2.31283i
$533$	1.02510			0.0444021
$534$	1.08025	−	1.87106i	0.0467472	−	0.0809685i
$535$	−38.9064			−1.68207
$536$	−3.56914	+	2.92634i	−0.154163	+	0.126399i
$537$	20.1173			0.868124
$538$	4.54083	−	7.86495i	0.195769	−	0.339082i
$539$	−17.6069			−0.758382
$540$	−3.79539	−	6.57380i	−0.163327	−	0.282891i
$541$	19.9674			0.858467			0.429234	−	0.903194i	$-0.358784\pi$
$541$	19.9674			0.858467			0.429234	+	0.903194i	$0.358784\pi$
$542$	−17.8254	+	30.8746i	−0.765668	+	1.32618i
$543$	−2.64091	−	4.57420i	−0.113332	−	0.196298i
$544$	−28.9709			−1.24212
$545$	−13.3124			−0.570240
$546$	−1.48486	+	2.57185i	−0.0635460	+	0.110065i
$547$	1.76830	+	3.06278i	0.0756070	+	0.130955i	0.901350	−	0.433091i	$-0.142577\pi$
$547$	1.76830	+	3.06278i	0.0756070	+	0.130955i	−0.825743	+	0.564046i	$0.809244\pi$
$548$	−2.81811	−	4.88110i	−0.120384	−	0.208510i
$549$	−2.79859	+	4.84730i	−0.119441	+	0.206878i
$550$	15.9142			0.678586
$551$	55.8940			2.38116
$552$	−1.44748	+	2.50711i	−0.0616089	+	0.106710i
$553$	−10.2078	+	17.6804i	−0.434079	+	0.751848i
$554$	7.66371	−	13.2739i	0.325600	−	0.563956i
$555$	8.72739	−	15.1163i	0.370457	−	0.641650i
$556$	−18.7698	−	32.5102i	−0.796017	−	1.37874i
$557$	5.64762	+	9.78197i	0.239297	+	0.414475i	0.960513	−	0.278236i	$-0.0897496\pi$
$557$	5.64762	+	9.78197i	0.239297	+	0.414475i	−0.721216	+	0.692711i	$0.756416\pi$
$558$	−6.71988			−0.284475
$559$	−1.00207	+	1.73564i	−0.0423833	+	0.0734099i
$560$	51.8242			2.18997
$561$	−4.46612			−0.188560
$562$	24.8793	+	43.0923i	1.04947	+	1.81774i
$563$	−17.7756			−0.749152			−0.374576	−	0.927196i	$-0.622212\pi$
$563$	−17.7756			−0.749152			−0.374576	+	0.927196i	$0.622212\pi$
$564$	12.9098	−	22.3605i	0.543601	−	0.941545i
$565$	19.0449	+	32.9867i	0.801225	+	1.38776i
$566$	13.3317	−	23.0912i	0.560373	−	0.970595i
$567$	−2.29539	−	3.97573i	−0.0963971	−	0.166965i
$568$	−3.02432	−	5.23828i	−0.126898	−	0.219793i
$569$	−9.53612	−	16.5170i	−0.399775	−	0.692431i	0.593923	−	0.804522i	$-0.297578\pi$
$569$	−9.53612	−	16.5170i	−0.399775	−	0.692431i	−0.993698	+	0.112091i	$0.964245\pi$
$570$	−20.3788	−	35.2971i	−0.853575	−	1.47843i
$571$	10.0860	+	17.4695i	0.422086	+	0.731075i	0.996143	−	0.0877406i	$-0.0279647\pi$
$571$	10.0860	+	17.4695i	0.422086	+	0.731075i	−0.574057	+	0.818815i	$0.694631\pi$
$572$	0.444866	+	0.770531i	0.0186008	+	0.0322175i
$573$	−6.95406	+	12.0448i	−0.290510	+	0.503178i
$574$	15.5419	+	26.9194i	0.648708	+	1.12360i
$575$	−15.7994	+	27.3653i	−0.658880	+	1.14121i
$576$	−10.0132			−0.417215
$577$	22.2069	+	38.4635i	0.924485	+	1.60125i	0.792388	+	0.610018i	$0.208838\pi$
$577$	22.2069	+	38.4635i	0.924485	+	1.60125i	0.132097	+	0.991237i	$0.457829\pi$
$578$	8.79149			0.365678
$579$	−12.8655			−0.534671
$580$	−35.9331	+	62.2380i	−1.49204	+	2.58429i
$581$	−51.6167			−2.14142
$582$	−6.85700	−	11.8767i	−0.284232	−	0.492304i
$583$	−4.29373	−	7.43695i	−0.177828	−	0.308007i
$584$	1.89994	−	3.29079i	0.0786201	−	0.136174i
$585$	0.522602	−	0.905173i	0.0216069	−	0.0374243i
$586$	11.1951	−	19.3904i	0.462464	−	0.801012i
$587$	−14.0683	+	24.3670i	−0.580661	+	1.00573i	0.414740	+	0.909940i	$0.363873\pi$
$587$	−14.0683	+	24.3670i	−0.580661	+	1.00573i	−0.995401	+	0.0957948i	$0.969461\pi$
$588$	−31.9899			−1.31924
$589$	−19.1925			−0.790813
$590$	−13.3115	+	23.0562i	−0.548025	+	0.949207i
$591$	−3.66078	−	6.34066i	−0.150584	−	0.260820i
$592$	−8.83234	−	15.2981i	−0.363007	−	0.628747i
$593$	−9.59039	+	16.6110i	−0.393830	+	0.682134i	−0.992951	−	0.118525i	$-0.962183\pi$
$593$	−9.59039	+	16.6110i	−0.393830	+	0.682134i	0.599121	+	0.800658i	$0.295517\pi$
$594$	−2.58573			−0.106094
$595$	54.7413			2.24418
$596$	12.0280	+	20.8331i	0.492685	+	0.853356i
$597$	−7.86931	+	13.6300i	−0.322069	+	0.557841i
$598$	−3.32121			−0.135814
$599$	14.5622	+	25.2225i	0.594996	+	1.03056i	0.993547	+	0.113418i	$0.0361798\pi$
$599$	14.5622	+	25.2225i	0.594996	+	1.03056i	−0.398551	+	0.917146i	$0.630487\pi$
$600$	3.47038			0.141678
$601$	9.71384	−	16.8249i	0.396236	−	0.686300i	−0.597022	−	0.802225i	$-0.703650\pi$
$601$	9.71384	−	16.8249i	0.396236	−	0.686300i	0.993258	+	0.115924i	$0.0369830\pi$
$602$	−60.7713			−2.47685
$603$	6.32977	−	5.18980i	0.257768	−	0.211345i
$604$	−19.7737			−0.804580
$605$	−15.7561	+	27.2904i	−0.640577	+	1.10951i
$606$	−30.8342			−1.25256
$607$	−2.66582	−	4.61734i	−0.108202	−	0.187412i	0.806840	−	0.590771i	$-0.201176\pi$
$607$	−2.66582	−	4.61734i	−0.108202	−	0.187412i	−0.915042	+	0.403358i	$0.867843\pi$
$608$	−47.9056			−1.94283
$609$	−21.7318	+	37.6405i	−0.880615	+	1.52527i
$610$	−19.3207	−	33.4644i	−0.782272	−	1.35494i
$611$	3.55521			0.143828
$612$	−8.11447			−0.328008
$613$	14.2852	−	24.7427i	0.576974	−	0.999348i	−0.418850	−	0.908055i	$-0.637567\pi$
$613$	14.2852	−	24.7427i	0.576974	−	0.999348i	0.995824	−	0.0912929i	$-0.0290999\pi$
$614$	34.0469	+	58.9709i	1.37402	+	2.37987i
$615$	−5.47006	−	9.47442i	−0.220574	−	0.382045i
$616$	−1.61904	+	2.80427i	−0.0652332	+	0.112987i
$617$	4.40114			0.177183			0.0885916	−	0.996068i	$-0.471763\pi$
$617$	4.40114			0.177183			0.0885916	+	0.996068i	$0.471763\pi$
$618$	−35.2317			−1.41723
$619$	−5.28074	+	9.14650i	−0.212251	+	0.367629i	−0.952419	−	0.304793i	$-0.901413\pi$
$619$	−5.28074	+	9.14650i	−0.212251	+	0.367629i	0.740168	+	0.672422i	$0.234746\pi$
$620$	12.3385	−	21.3709i	0.495525	−	0.858275i
$621$	2.56707	−	4.44630i	0.103013	−	0.178424i
$622$	−12.1813	+	21.0986i	−0.488425	+	0.845976i
$623$	2.39914	+	4.15544i	0.0961197	+	0.166484i
$624$	−0.528886	−	0.916058i	−0.0211724	−	0.0366717i
$625$	−17.8936			−0.715745
$626$	31.6303	−	54.7852i	1.26420	−	2.18966i
$627$	−7.38506			−0.294931
$628$	27.3275			1.09048
$629$	−9.32951	−	16.1592i	−0.371992	−	0.644309i
$630$	31.6934			1.26270
$631$	22.1816	−	38.4197i	0.883037	−	1.52946i	0.0350890	−	0.999384i	$-0.488829\pi$
$631$	22.1816	−	38.4197i	0.883037	−	1.52946i	0.847948	−	0.530080i	$-0.177838\pi$
$632$	1.25378	+	2.17161i	0.0498726	+	0.0863820i
$633$	11.1884	−	19.3789i	0.444699	−	0.770241i
$634$	3.07280	+	5.32224i	0.122036	+	0.211373i
$635$	13.2671	+	22.9793i	0.526488	+	0.911905i
$636$	−7.80125	−	13.5122i	−0.309340	−	0.535792i
$637$	−2.20240	−	3.81468i	−0.0872625	−	0.151143i
$638$	12.2403	+	21.2009i	0.484599	+	0.839350i
$639$	5.36356	+	9.28995i	0.212179	+	0.367505i
$640$	7.46284	−	12.9260i	0.294995	−	0.510946i
$641$	−19.3700	−	33.5499i	−0.765070	−	1.32514i	−0.940209	−	0.340597i	$-0.889371\pi$
$641$	−19.3700	−	33.5499i	−0.765070	−	1.32514i	0.175139	−	0.984544i	$-0.443963\pi$
$642$	−12.0398	+	20.8535i	−0.475173	+	0.823023i
$643$	−8.35195			−0.329369			−0.164684	−	0.986346i	$-0.552661\pi$
$643$	−8.35195			−0.329369			−0.164684	+	0.986346i	$0.552661\pi$
$644$	−26.7844	−	46.3919i	−1.05545	−	1.82810i
$645$	21.3887			0.842180
$646$	−43.5696			−1.71422
$647$	14.0986	−	24.4194i	0.554272	−	0.960027i	−0.443688	−	0.896181i	$-0.646330\pi$
$647$	14.0986	−	24.4194i	0.554272	−	0.960027i	0.997960	−	0.0638453i	$-0.0203364\pi$
$648$	−0.563865			−0.0221507
$649$	2.41197	+	4.17765i	0.0946780	+	0.163987i
$650$	1.99068	+	3.44795i	0.0780808	+	0.135240i
$651$	7.46211	−	12.9247i	0.292463	−	0.506561i
$652$	−24.9989	+	43.2994i	−0.979032	+	1.69573i
$653$	−12.8044	+	22.1779i	−0.501076	+	0.867889i	0.498923	+	0.866646i	$0.333729\pi$
$653$	−12.8044	+	22.1779i	−0.501076	+	0.867889i	−0.999999	+	0.00124301i	$0.999604\pi$
$654$	−4.11959	+	7.13534i	−0.161089	+	0.279014i
$655$	0.114380			0.00446920
$656$	−11.0717			−0.432276
$657$	−3.36950	+	5.83614i	−0.131457	+	0.227690i
$658$	53.9018	+	93.3606i	2.10131	+	3.63957i
$659$	25.0194	+	43.3349i	0.974617	+	1.68809i	0.681192	+	0.732105i	$0.261462\pi$
$659$	25.0194	+	43.3349i	0.974617	+	1.68809i	0.293425	+	0.955982i	$0.405205\pi$
$660$	4.74771	−	8.22327i	0.184804	−	0.320090i
$661$	14.0595			0.546850			0.273425	−	0.961893i	$-0.411844\pi$
$661$	14.0595			0.546850			0.273425	+	0.961893i	$0.411844\pi$
$662$	32.2612			1.25387
$663$	−0.558657	−	0.967622i	−0.0216964	−	0.0375793i
$664$	−3.16993	+	5.49048i	−0.123017	+	0.213072i
$665$	90.5189			3.51017
$666$	−5.40147	−	9.35562i	−0.209303	−	0.362523i
$667$	−48.6079			−1.88211
$668$	7.45912	−	12.9196i	0.288602	−	0.499874i
$669$	−0.871719			−0.0337026
$670$	9.17925	+	55.7589i	0.354625	+	2.15415i
$671$	−7.00161			−0.270294
$672$	18.6258	−	32.2609i	0.718508	−	1.24449i
$673$	−34.3350			−1.32352			−0.661758	−	0.749717i	$-0.730190\pi$
$673$	−34.3350			−1.32352			−0.661758	+	0.749717i	$0.730190\pi$
$674$	−5.13533	−	8.89465i	−0.197805	−	0.342609i
$675$	−6.15464			−0.236892
$676$	14.6618	−	25.3950i	0.563916	−	0.976730i
$677$	−12.0753	−	20.9150i	−0.464091	−	0.803830i	0.535069	−	0.844809i	$-0.320286\pi$
$677$	−12.0753	−	20.9150i	−0.464091	−	0.803830i	−0.999160	+	0.0409786i	$0.986952\pi$
$678$	23.5742			0.905361
$679$	30.4575			1.16885
$680$	3.36182	−	5.82285i	0.128920	−	0.223296i
$681$	−4.03806	−	6.99412i	−0.154739	−	0.268015i
$682$	−4.20300	−	7.27981i	−0.160941	−	0.278758i
$683$	3.21623	−	5.57067i	0.123066	−	0.213156i	−0.797910	−	0.602777i	$-0.794061\pi$
$683$	3.21623	−	5.57067i	0.123066	−	0.213156i	0.920975	+	0.389621i	$0.127394\pi$
$684$	−13.4179			−0.513046
$685$	−8.28241			−0.316455
$686$	33.5698	−	58.1446i	1.28170	−	2.21997i
$687$	−4.17477	+	7.23091i	−0.159277	+	0.275877i
$688$	10.8230	−	18.7459i	0.412622	−	0.714682i
$689$	1.07419	−	1.86054i	0.0409232	−	0.0708811i
$690$	17.7223	+	30.6960i	0.674678	+	1.16858i
$691$	−14.3739	−	24.8963i	−0.546809	−	0.947101i	−0.998491	−	0.0549222i	$-0.982509\pi$
$691$	−14.3739	−	24.8963i	−0.546809	−	0.947101i	0.451681	−	0.892179i	$-0.350824\pi$
$692$	−1.32978			−0.0505507
$693$	2.87134	−	4.97330i	0.109073	−	0.188920i
$694$	−17.4759			−0.663377
$695$	−55.1644			−2.09251
$696$	2.66922	+	4.62322i	0.101176	+	0.175243i
$697$	−11.6949			−0.442976
$698$	10.2343	−	17.7264i	0.387375	−	0.670953i
$699$	8.39274	+	14.5367i	0.317443	+	0.549827i
$700$	−32.1082	+	55.6131i	−1.21358	+	2.10198i
$701$	−15.8328	−	27.4233i	−0.597998	−	1.03576i	−0.993116	−	0.117133i	$-0.962630\pi$
$701$	−15.8328	−	27.4233i	−0.597998	−	1.03576i	0.395118	−	0.918630i	$-0.370704\pi$
$702$	−0.323444	−	0.560221i	−0.0122076	−	0.0211442i
$703$	−15.4270	−	26.7204i	−0.581842	−	1.00778i
$704$	−6.26281	−	10.8475i	−0.236038	−	0.408831i
$705$	−18.9710	−	32.8587i	−0.714488	−	1.23753i
$706$	16.0495	+	27.7986i	0.604031	+	1.04621i
$707$	34.2400	−	59.3054i	1.28773	−	2.23041i
$708$	4.38229	+	7.59035i	0.164697	+	0.285263i
$709$	5.50090	−	9.52783i	0.206591	−	0.357825i	−0.744048	−	0.668126i	$-0.767097\pi$
$709$	5.50090	−	9.52783i	0.206591	−	0.357825i	0.950638	+	0.310301i	$0.100430\pi$
$710$	−74.0570			−2.77931
$711$	−2.22355	−	3.85129i	−0.0833895	−	0.144435i
$712$	0.589353			0.0220869
$713$	16.6907			0.625070
$714$	16.9400	−	29.3409i	0.633963	−	1.09806i
$715$	1.30746			0.0488963
$716$	22.8611	+	39.5966i	0.854360	+	1.47979i
$717$	3.81459	+	6.60707i	0.142459	+	0.246746i
$718$	−12.0417	+	20.8568i	−0.449391	+	0.778367i
$719$	1.79747	−	3.11331i	0.0670343	−	0.116107i	−0.830560	−	0.556929i	$-0.811980\pi$
$719$	1.79747	−	3.11331i	0.0670343	−	0.116107i	0.897595	+	0.440822i	$0.145313\pi$
$720$	−5.64439	+	9.77637i	−0.210354	+	0.364344i
$721$	39.1232	−	67.7634i	1.45702	−	2.52364i
$722$	−32.7712			−1.21962
$723$	22.7915			0.847625
$724$	6.00223	−	10.3962i	0.223071	−	0.386370i
$725$	29.1348	+	50.4629i	1.08204	+	1.87415i
$726$	9.75163	+	16.8903i	0.361917	+	0.626858i
$727$	1.23023	−	2.13083i	0.0456269	−	0.0790281i	−0.842310	−	0.538993i	$-0.818805\pi$
$727$	1.23023	−	2.13083i	0.0456269	−	0.0790281i	0.887937	+	0.459965i	$0.152138\pi$
$728$	−0.810091			−0.0300240
$729$	1.00000			0.0370370
$730$	−23.2621	−	40.2911i	−0.860968	−	1.49124i
$731$	11.4322	−	19.8011i	0.422835	−	0.732371i
$732$	−12.7212			−0.470189
$733$	21.1873	+	36.6975i	0.782571	+	1.35545i	0.930440	+	0.366445i	$0.119425\pi$
$733$	21.1873	+	36.6975i	0.782571	+	1.35545i	−0.147869	+	0.989007i	$0.547241\pi$
$734$	8.24894			0.304474
$735$	−23.5045	+	40.7111i	−0.866978	+	1.50165i
$736$	41.6609			1.53564
$737$	9.58124	+	3.61120i	0.352930	+	0.133020i
$738$	−6.77095			−0.249242
$739$	13.0916	−	22.6753i	0.481582	−	0.834125i	−0.518194	−	0.855263i	$-0.673396\pi$
$739$	13.0916	−	22.6753i	0.481582	−	0.834125i	0.999777	+	0.0211382i	$0.00672898\pi$
$740$	39.6709			1.45833
$741$	−0.923781	−	1.60003i	−0.0339359	−	0.0587787i
$742$	65.1444			2.39153
$743$	13.1783	−	22.8256i	0.483466	−	0.837389i	−0.516353	−	0.856376i	$-0.672711\pi$
$743$	13.1783	−	22.8256i	0.483466	−	0.837389i	0.999820	+	0.0189872i	$0.00604417\pi$
$744$	−0.916538	−	1.58749i	−0.0336019	−	0.0582002i
$745$	35.3502			1.29513
$746$	10.5464			0.386131
$747$	5.62179	−	9.73722i	0.205690	−	0.356266i
$748$	−5.07526	−	8.79061i	−0.185570	−	0.321417i
$749$	−26.7392	−	46.3137i	−0.977031	−	1.69227i
$750$	3.98564	−	6.90334i	0.145535	−	0.252074i
$751$	−50.4002			−1.83913			−0.919564	−	0.392940i	$-0.871458\pi$
$751$	−50.4002			−1.83913			−0.919564	+	0.392940i	$0.871458\pi$
$752$	−38.3982			−1.40024
$753$	−7.13708	+	12.3618i	−0.260090	+	0.450488i
$754$	−3.06223	+	5.30394i	−0.111520	+	0.193158i
$755$	−14.5287	+	25.1645i	−0.528754	+	0.915829i
$756$	5.21692	−	9.03597i	0.189737	−	0.328635i
$757$	20.6986	+	35.8511i	0.752304	+	1.30303i	0.946704	+	0.322106i	$0.104391\pi$
$757$	20.6986	+	35.8511i	0.752304	+	1.30303i	−0.194400	+	0.980922i	$0.562276\pi$
$758$	19.1213	+	33.1191i	0.694519	+	1.20294i
$759$	6.42238			0.233118
$760$	5.55902	−	9.62851i	0.201647	−	0.349263i
$761$	−28.7610			−1.04259			−0.521293	−	0.853378i	$-0.674550\pi$
$761$	−28.7610			−1.04259			−0.521293	+	0.853378i	$0.674550\pi$
$762$	16.4223			0.594916
$763$	−9.14922	−	15.8469i	−0.331224	−	0.573697i
$764$	−31.6101			−1.14362
$765$	−5.96211	+	10.3267i	−0.215560	+	0.373362i
$766$	13.5716	+	23.5066i	0.490360	+	0.849329i
$767$	−0.603415	+	1.04515i	−0.0217881	+	0.0377380i
$768$	5.39432	+	9.34324i	0.194651	+	0.337145i
$769$	3.85449	+	6.67617i	0.138996	+	0.240749i	0.927117	−	0.374772i	$-0.122279\pi$
$769$	3.85449	+	6.67617i	0.138996	+	0.240749i	−0.788121	+	0.615521i	$0.788946\pi$
$770$	19.8229	+	34.3343i	0.714368	+	1.23732i
$771$	−0.889005	−	1.53980i	−0.0320167	−	0.0554546i
$772$	−14.6202	−	25.3230i	−0.526193	−	0.911393i
$773$	−3.50421	−	6.06947i	−0.126038	−	0.218304i	0.796100	−	0.605165i	$-0.206893\pi$
$773$	−3.50421	−	6.06947i	−0.126038	−	0.218304i	−0.922138	+	0.386861i	$0.873559\pi$
$774$	6.61885	−	11.4642i	0.237910	−	0.412072i
$775$	−10.0041	−	17.3276i	−0.359358	−	0.622426i
$776$	1.87048	−	3.23977i	0.0671464	−	0.116301i
$777$	23.9923			0.860720
$778$	−7.74578	−	13.4161i	−0.277700	−	0.480990i
$779$	−19.3384			−0.692869
$780$	2.37552			0.0850573
$781$	−6.70936	+	11.6210i	−0.240080	+	0.415830i
$782$	37.8901			1.35495
$783$	−4.73379	−	8.19917i	−0.169172	−	0.293014i
$784$	23.7872	+	41.2006i	0.849543	+	1.47145i
$785$	20.0789	−	34.7776i	0.716645	−	1.24127i
$786$	0.0353955	−	0.0613068i	0.00126252	−	0.00218674i
$787$	−4.30791	+	7.46152i	−0.153561	+	0.265975i	−0.932534	−	0.361082i	$-0.882407\pi$
$787$	−4.30791	+	7.46152i	−0.153561	+	0.265975i	0.778973	+	0.627057i	$0.215741\pi$
$788$	8.32016	−	14.4109i	0.296394	−	0.513369i
$789$	−8.97731			−0.319601
$790$	30.7015			1.09231
$791$	−26.1780	+	45.3417i	−0.930783	+	1.61216i
$792$	−0.352674	−	0.610849i	−0.0125317	−	0.0217056i
$793$	−0.875816	−	1.51696i	−0.0311011	−	0.0538687i
$794$	−19.2853	+	33.4031i	−0.684410	+	1.18543i
$795$	−22.9279			−0.813168
$796$	−35.7705			−1.26785
$797$	−17.6433	−	30.5591i	−0.624959	−	1.08246i	−0.988549	−	0.150901i	$-0.951782\pi$
$797$	−17.6433	−	30.5591i	−0.624959	−	1.08246i	0.363590	−	0.931559i	$-0.381551\pi$
$798$	28.0115	−	48.5174i	0.991598	−	1.71750i
$799$	−40.5596			−1.43490
$800$	−24.9708	−	43.2507i	−0.882852	−	1.52914i
$801$	−1.04520			−0.0369304
$802$	10.4100	−	18.0307i	0.367591	−	0.636686i
$803$	−8.42992			−0.297485
$804$	17.4081	+	6.56118i	0.613937	+	0.231395i
$805$	−78.7193			−2.77449
$806$	1.05149	−	1.82123i	0.0370371	−	0.0641501i
$807$	−4.39349			−0.154658
$808$	−4.20555	−	7.28423i	−0.147951	−	0.256258i
$809$	13.4420			0.472594			0.236297	−	0.971681i	$-0.424066\pi$
$809$	13.4420			0.472594			0.236297	+	0.971681i	$0.424066\pi$
$810$	−3.45186	+	5.97880i	−0.121286	+	0.210074i
$811$	−3.31678	−	5.74483i	−0.116468	−	0.201728i	0.801898	−	0.597461i	$-0.203824\pi$
$811$	−3.31678	−	5.74483i	−0.116468	−	0.201728i	−0.918366	+	0.395733i	$0.870491\pi$
$812$	−98.7832			−3.46661
$813$	17.2470			0.604880
$814$	6.75679	−	11.7031i	0.236825	−	0.410193i
$815$	36.7359	+	63.6284i	1.28680	+	2.22881i
$816$	6.03381	+	10.4509i	0.211225	+	0.365853i
$817$	18.9040	−	32.7426i	0.661366	−	1.14552i
$818$	75.4431			2.63780
$819$	1.43668			0.0502015
$820$	12.4323	−	21.5333i	0.434153	−	0.751976i
$821$	13.3383	−	23.1026i	0.465511	−	0.806288i	−0.533714	−	0.845665i	$-0.679204\pi$
$821$	13.3383	−	23.1026i	0.465511	−	0.806288i	0.999224	+	0.0393773i	$0.0125374\pi$
$822$	−2.56304	+	4.43931i	−0.0893961	+	0.154839i
$823$	9.80031	−	16.9746i	0.341617	−	0.591699i	−0.643116	−	0.765769i	$-0.722359\pi$
$823$	9.80031	−	16.9746i	0.341617	−	0.591699i	0.984733	+	0.174070i	$0.0556920\pi$
$824$	−4.80533	−	8.32308i	−0.167402	−	0.289948i
$825$	−3.84947	−	6.66747i	−0.134021	−	0.232132i
$826$	−36.5944			−1.27328
$827$	−28.4148	+	49.2160i	−0.988081	+	1.71141i	−0.360729	+	0.932671i	$0.617472\pi$
$827$	−28.4148	+	49.2160i	−0.988081	+	1.71141i	−0.627352	+	0.778736i	$0.715861\pi$
$828$	11.6688			0.405519
$829$	33.0130			1.14659			0.573294	−	0.819350i	$-0.305665\pi$
$829$	33.0130			1.14659			0.573294	+	0.819350i	$0.305665\pi$
$830$	38.8113	+	67.2231i	1.34716	+	2.33335i
$831$	−7.41504			−0.257225
$832$	1.56680	−	2.71378i	0.0543191	−	0.0940834i
$833$	25.1262	+	43.5198i	0.870570	+	1.50787i
$834$	−17.0709	+	29.5677i	−0.591117	+	1.02385i
$835$	−10.9612	−	18.9853i	−0.379327	−	0.657014i
$836$	−8.39232	−	14.5359i	−0.290255	−	0.502736i
$837$	1.62546	+	2.81538i	0.0561840	+	0.0973136i
$838$	16.6103	+	28.7699i	0.573794	+	0.993841i
$839$	−20.6511	−	35.7688i	−0.712957	−	1.23488i	−0.963742	−	0.266835i	$-0.914022\pi$
$839$	−20.6511	−	35.7688i	−0.712957	−	1.23488i	0.250786	−	0.968043i	$-0.419311\pi$
$840$	4.32273	+	7.48719i	0.149148	+	0.258333i
$841$	−30.3176	+	52.5116i	−1.04543	+	1.81074i
$842$	−4.51265	−	7.81613i	−0.155516	−	0.269362i
$843$	12.0360	−	20.8470i	0.414543	−	0.718009i
$844$	50.8576			1.75059
$845$	−21.5455	−	37.3179i	−0.741188	−	1.28378i
$846$	−23.4827			−0.807350
$847$	−43.3149			−1.48832
$848$	−11.6018	+	20.0949i	−0.398408	+	0.690062i
$849$	−12.8991			−0.442697
$850$	−22.7107	−	39.3360i	−0.778970	−	1.34921i
$851$	13.4160	+	23.2373i	0.459896	+	0.796563i
$852$	−12.1902	+	21.1141i	−0.417630	+	0.723356i
$853$	27.8005	−	48.1518i	0.951870	−	1.64869i	0.210496	−	0.977595i	$-0.432492\pi$
$853$	27.8005	−	48.1518i	0.951870	−	1.64869i	0.741374	−	0.671092i	$-0.234175\pi$
$854$	26.5571	−	45.9983i	0.908766	−	1.57403i
$855$	−9.85879	+	17.0759i	−0.337163	+	0.583984i
$856$	−6.56853			−0.224508
$857$	26.5305			0.906264			0.453132	−	0.891443i	$-0.350307\pi$
$857$	26.5305			0.906264			0.453132	+	0.891443i	$0.350307\pi$
$858$	0.404601	−	0.700789i	0.0138128	−	0.0239245i
$859$	−1.70883	−	2.95978i	−0.0583045	−	0.100986i	0.835400	−	0.549643i	$-0.185236\pi$
$859$	−1.70883	−	2.95978i	−0.0583045	−	0.100986i	−0.893704	+	0.448656i	$0.851903\pi$
$860$	24.3060	+	42.0992i	0.828827	+	1.43557i
$861$	7.51882	−	13.0230i	0.256241	−	0.443822i
$862$	33.2721			1.13325
$863$	−46.2407			−1.57405			−0.787026	−	0.616920i	$-0.788380\pi$
$863$	−46.2407			−1.57405			−0.787026	+	0.616920i	$0.788380\pi$
$864$	4.05724	+	7.02734i	0.138030	+	0.239075i
$865$	−0.977057	+	1.69231i	−0.0332209	+	0.0575403i
$866$	−47.1408			−1.60191
$867$	−2.12656	−	3.68330i	−0.0722217	−	0.125092i
$868$	33.9195			1.15130
$869$	2.78147	−	4.81765i	0.0943549	−	0.163427i
$870$	65.3616			2.21596
$871$	0.416099	+	2.52757i	0.0140990	+	0.0856436i
$872$	−2.24752			−0.0761106
$873$	−3.31725	+	5.74565i	−0.112272	+	0.194461i
$874$	62.6541			2.11931
$875$	8.85174	+	15.3317i	0.299243	+	0.518305i
$876$	−15.3163			−0.517489
$877$	−5.98748	+	10.3706i	−0.202183	+	0.350191i	−0.949231	−	0.314579i	$-0.898137\pi$
$877$	−5.98748	+	10.3706i	−0.202183	+	0.350191i	0.747049	+	0.664769i	$0.231470\pi$
$878$	18.3259	+	31.7414i	0.618470	+	1.07122i
$879$	−10.8318			−0.365348
$880$	−14.1213			−0.476029
$881$	3.05463	−	5.29077i	0.102913	−	0.178251i	−0.809971	−	0.586470i	$-0.800517\pi$
$881$	3.05463	−	5.29077i	0.102913	−	0.178251i	0.912884	+	0.408220i	$0.133850\pi$
$882$	14.5472	+	25.1965i	0.489830	+	0.848410i
$883$	22.9344	+	39.7235i	0.771802	+	1.33680i	0.936574	+	0.350469i	$0.113978\pi$
$883$	22.9344	+	39.7235i	0.771802	+	1.33680i	−0.164772	+	0.986332i	$0.552689\pi$
$884$	1.26971	−	2.19920i	0.0427048	−	0.0739670i
$885$	12.8796			0.432941
$886$	34.1353			1.14680
$887$	−12.0402	+	20.8543i	−0.404271	+	0.700218i	−0.994236	−	0.107210i	$-0.965808\pi$
$887$	−12.0402	+	20.8543i	−0.404271	+	0.700218i	0.589965	+	0.807429i	$0.299141\pi$
$888$	1.47344	−	2.55207i	0.0494453	−	0.0856418i
$889$	−18.2362	+	31.5860i	−0.611622	+	1.05936i
$890$	3.60790	−	6.24906i	0.120937	−	0.209469i
$891$	0.625458	+	1.08333i	0.0209536	+	0.0362928i
$892$	−0.990615	−	1.71580i	−0.0331682	−	0.0574491i
$893$	−67.0683			−2.24436
$894$	10.9393	−	18.9474i	0.365865	−	0.633697i
$895$	67.1888			2.24587
$896$	20.5160			0.685391
$897$	0.803361	+	1.39146i	0.0268235	+	0.0464596i
$898$	−77.6641			−2.59168
$899$	15.3892	−	26.6548i	0.513257	−	0.888988i
$900$	−6.99408	−	12.1141i	−0.233136	−	0.403803i
$901$	−12.2549	+	21.2260i	−0.408268	+	0.707142i
$902$	−4.23495	−	7.33514i	−0.141008	−	0.244234i
$903$	14.6998	+	25.4609i	0.489180	+	0.847285i
$904$	3.21533	+	5.56912i	0.106940	+	0.185226i
$905$	−8.82027	−	15.2772i	−0.293196	−	0.507830i
$906$	8.99197	+	15.5746i	0.298738	+	0.517430i
$907$	−8.50135	−	14.7248i	−0.282283	−	0.488928i	0.689664	−	0.724130i	$-0.257758\pi$
$907$	−8.50135	−	14.7248i	−0.282283	−	0.488928i	−0.971947	+	0.235202i	$0.924425\pi$
$908$	9.17763	−	15.8961i	0.304570	−	0.527531i
$909$	7.45844	+	12.9184i	0.247381	+	0.428476i
$910$	−4.95920	+	8.58959i	−0.164396	+	0.284742i
$911$	25.5080			0.845117			0.422559	−	0.906336i	$-0.361132\pi$
$911$	25.5080			0.845117			0.422559	+	0.906336i	$0.361132\pi$
$912$	9.97735	+	17.2813i	0.330383	+	0.572240i
$913$	14.0648			0.465476
$914$	35.6251			1.17837
$915$	−9.34690	+	16.1893i	−0.308999	+	0.535202i
$916$	−18.9767			−0.627008
$917$	0.0786101	+	0.136157i	0.00259594	+	0.00449629i
$918$	3.69001	+	6.39128i	0.121788	+	0.210944i
$919$	4.03888	−	6.99554i	0.133230	−	0.230762i	−0.791690	−	0.610923i	$-0.790798\pi$
$919$	4.03888	−	6.99554i	0.133230	−	0.230762i	0.924920	+	0.380162i	$0.124132\pi$
$920$	−4.83438	+	8.37339i	−0.159385	+	0.276062i
$921$	16.4711	−	28.5287i	0.542740	−	0.940053i
$922$	−8.17596	+	14.1612i	−0.269261	+	0.466374i
$923$	−3.35703			−0.110498
$924$	13.0519			0.429374
$925$	16.0827	−	27.8561i	0.528796	−	0.915901i
$926$	9.75955	+	16.9040i	0.320719	+	0.555501i
$927$	8.52214	+	14.7608i	0.279904	+	0.484808i
$928$	38.4122	−	66.5319i	1.26094	−	2.18402i
$929$	15.0624			0.494180			0.247090	−	0.968993i	$-0.420526\pi$
$929$	15.0624			0.494180			0.247090	+	0.968993i	$0.420526\pi$
$930$	−22.4434			−0.735949
$931$	41.5480	+	71.9632i	1.36168	+	2.35850i
$932$	−19.0749	+	33.0387i	−0.624819	+	1.08222i
$933$	11.7860			0.385857
$934$	−16.3355	−	28.2939i	−0.534513	−	0.925803i
$935$	−14.9162			−0.487812
$936$	0.0882303	−	0.152819i	0.00288390	−	0.00499506i
$937$	−36.2108			−1.18296			−0.591478	−	0.806321i	$-0.701455\pi$
$937$	−36.2108			−1.18296			−0.591478	+	0.806321i	$0.701455\pi$
$938$	−60.0661	+	49.2483i	−1.96123	+	1.60801i
$939$	−30.6039			−0.998721
$940$	43.1169	−	74.6807i	1.40632	−	2.43582i
$941$	0.00732878			0.000238911			0.000119456	−	1.00000i	$-0.499962\pi$
$941$	0.00732878			0.000238911			0.000119456		1.00000i	$0.499962\pi$
$942$	−12.4270	−	21.5242i	−0.404894	−	0.701297i
$943$	16.8175			0.547654
$944$	6.51722	−	11.2882i	0.212117	−	0.367398i
$945$	−7.66626	−	13.2783i	−0.249383	−	0.431945i
$946$	16.5593			0.538388
$947$	−21.7746			−0.707581			−0.353790	−	0.935325i	$-0.615107\pi$
$947$	−21.7746			−0.707581			−0.353790	+	0.935325i	$0.615107\pi$
$948$	5.05364	−	8.75316i	0.164135	−	0.284289i
$949$	−1.05448	−	1.82641i	−0.0342299	−	0.0592878i
$950$	−37.5538	−	65.0451i	−1.21841	−	2.11034i
$951$	1.48655	−	2.57477i	0.0482046	−	0.0834928i
$952$	9.24193			0.299533
$953$	47.2450			1.53042			0.765208	−	0.643784i	$-0.222636\pi$
$953$	47.2450			1.53042			0.765208	+	0.643784i	$0.222636\pi$
$954$	−7.09515	+	12.2892i	−0.229714	+	0.397876i
$955$	−23.2256	+	40.2278i	−0.751561	+	1.30174i
$956$	−8.66975	+	15.0164i	−0.280400	+	0.485667i
$957$	5.92158	−	10.2565i	0.191417	−	0.331545i
$958$	−0.340887	−	0.590433i	−0.0110136	−	0.0190760i
$959$	−5.69226	−	9.85929i	−0.183813	−	0.318373i
$960$	−33.4425			−1.07935
$961$	10.2158	−	17.6942i	0.329541	−	0.570782i
$962$	3.38077			0.109000
$963$	11.6491			0.375388
$964$	25.9001	+	44.8602i	0.834185	+	1.44485i
$965$	−42.9688			−1.38322
$966$	−24.3601	+	42.1929i	−0.783774	+	1.35754i
$967$	3.99150	+	6.91347i	0.128358	+	0.222322i	0.923040	−	0.384703i	$-0.125696\pi$
$967$	3.99150	+	6.91347i	0.128358	+	0.222322i	−0.794683	+	0.607025i	$0.792363\pi$
$968$	−2.66009	+	4.60741i	−0.0854986	+	0.148088i
$969$	10.5390	+	18.2540i	0.338560	+	0.586404i
$970$	−22.9014	−	39.6664i	−0.735319	−	1.27361i
$971$	29.2476	+	50.6583i	0.938599	+	1.62570i	0.768087	+	0.640346i	$0.221209\pi$
$971$	29.2476	+	50.6583i	0.938599	+	1.62570i	0.170513	+	0.985356i	$0.445458\pi$
$972$	1.13639	+	1.96829i	0.0364498	+	0.0631329i
$973$	−37.9129	−	65.6671i	−1.21543	−	2.10519i
$974$	−11.6687	−	20.2107i	−0.373888	−	0.647594i
$975$	0.963042	−	1.66804i	0.0308420	−	0.0534200i
$976$	9.45930	+	16.3840i	0.302785	+	0.524439i
$977$	15.9807	−	27.6794i	0.511267	−	0.885541i	−0.488647	−	0.872481i	$-0.662510\pi$
$977$	15.9807	−	27.6794i	0.511267	−	0.885541i	0.999915	−	0.0130596i	$-0.00415712\pi$
$978$	45.4724			1.45405
$979$	−0.653731	−	1.13229i	−0.0208933	−	0.0361883i
$980$	−106.842			−3.41293
$981$	3.98592			0.127261
$982$	−12.4308	+	21.5308i	−0.396683	+	0.687075i
$983$	19.4566			0.620569			0.310284	−	0.950644i	$-0.399576\pi$
$983$	19.4566			0.620569			0.310284	+	0.950644i	$0.399576\pi$
$984$	−0.923505	−	1.59956i	−0.0294403	−	0.0509920i
$985$	−12.2265	−	21.1769i	−0.389568	−	0.674751i
$986$	34.9355	−	60.5100i	1.11257	−	1.92703i
$987$	26.0764	−	45.1656i	0.830021	−	1.43764i
$988$	2.09955	−	3.63653i	0.0667957	−	0.115694i
$989$	−16.4397	+	28.4745i	−0.522754	+	0.905436i
$990$	−8.63598			−0.274469
$991$	52.3607			1.66329			0.831646	−	0.555306i	$-0.187399\pi$
$991$	52.3607			1.66329			0.831646	+	0.555306i	$0.187399\pi$
$992$	−13.1897	+	22.8453i	−0.418774	+	0.725339i
$993$	−7.80361	−	13.5162i	−0.247640	−	0.428925i
$994$	−50.8972	−	88.1566i	−1.61436	−	2.79616i
$995$	−26.2824	+	45.5224i	−0.833207	+	1.44316i
$996$	25.5542			0.809717
$997$	−20.2985			−0.642860			−0.321430	−	0.946933i	$-0.604163\pi$
$997$	−20.2985			−0.642860			−0.321430	+	0.946933i	$0.604163\pi$
$998$	−24.7603	−	42.8862i	−0.783775	−	1.35754i
$999$	−2.61310	+	4.52603i	−0.0826749	+	0.143197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.e.b.163.5	yes	10
3.2	odd	2		603.2.g.g.163.1		10
67.37	even	3	inner	201.2.e.b.37.5	✓	10
201.104	odd	6		603.2.g.g.37.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.e.b.37.5	✓	10	67.37	even	3	inner
201.2.e.b.163.5	yes	10	1.1	even	1	trivial
603.2.g.g.37.1		10	201.104	odd	6
603.2.g.g.163.1		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03354 - 1.79014i) q^{2} -1.00000 q^{3} +(-1.13639 - 1.96829i) q^{4} -3.33986 q^{5} +(-1.03354 + 1.79014i) q^{6} +(-2.29539 - 3.97573i) q^{7} -0.563865 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.03354 - 1.79014i) q^{2} -1.00000 q^{3} +(-1.13639 - 1.96829i) q^{4} -3.33986 q^{5} +(-1.03354 + 1.79014i) q^{6} +(-2.29539 - 3.97573i) q^{7} -0.563865 q^{8} +1.00000 q^{9} +(-3.45186 + 5.97880i) q^{10} +(0.625458 + 1.08333i) q^{11} +(1.13639 + 1.96829i) q^{12} +(-0.156474 + 0.271021i) q^{13} -9.48945 q^{14} +3.33986 q^{15} +(1.69001 - 2.92718i) q^{16} +(1.78514 - 3.09195i) q^{17} +(1.03354 - 1.79014i) q^{18} +(2.95186 - 5.11277i) q^{19} +(3.79539 + 6.57380i) q^{20} +(2.29539 + 3.97573i) q^{21} +2.58573 q^{22} +(-2.56707 + 4.44630i) q^{23} +0.563865 q^{24} +6.15464 q^{25} +(0.323444 + 0.560221i) q^{26} -1.00000 q^{27} +(-5.21692 + 9.03597i) q^{28} +(4.73379 + 8.19917i) q^{29} +(3.45186 - 5.97880i) q^{30} +(-1.62546 - 2.81538i) q^{31} +(-4.05724 - 7.02734i) q^{32} +(-0.625458 - 1.08333i) q^{33} +(-3.69001 - 6.39128i) q^{34} +(7.66626 + 13.2783i) q^{35} +(-1.13639 - 1.96829i) q^{36} +(2.61310 - 4.52603i) q^{37} +(-6.10171 - 10.5685i) q^{38} +(0.156474 - 0.271021i) q^{39} +1.88323 q^{40} +(-1.63781 - 2.83677i) q^{41} +9.48945 q^{42} +6.40409 q^{43} +(1.42153 - 2.46216i) q^{44} -3.33986 q^{45} +(5.30632 + 9.19082i) q^{46} +(-5.68017 - 9.83835i) q^{47} +(-1.69001 + 2.92718i) q^{48} +(-7.03759 + 12.1895i) q^{49} +(6.36104 - 11.0176i) q^{50} +(-1.78514 + 3.09195i) q^{51} +0.711265 q^{52} -6.86493 q^{53} +(-1.03354 + 1.79014i) q^{54} +(-2.08894 - 3.61815i) q^{55} +(1.29429 + 2.24177i) q^{56} +(-2.95186 + 5.11277i) q^{57} +19.5702 q^{58} +3.85632 q^{59} +(-3.79539 - 6.57380i) q^{60} +(-2.79859 + 4.84730i) q^{61} -6.71988 q^{62} +(-2.29539 - 3.97573i) q^{63} -10.0132 q^{64} +(0.522602 - 0.905173i) q^{65} -2.58573 q^{66} +(6.32977 - 5.18980i) q^{67} -8.11447 q^{68} +(2.56707 - 4.44630i) q^{69} +31.6934 q^{70} +(5.36356 + 9.28995i) q^{71} -0.563865 q^{72} +(-3.36950 + 5.83614i) q^{73} +(-5.40147 - 9.35562i) q^{74} -6.15464 q^{75} -13.4179 q^{76} +(2.87134 - 4.97330i) q^{77} +(-0.323444 - 0.560221i) q^{78} +(-2.22355 - 3.85129i) q^{79} +(-5.64439 + 9.77637i) q^{80} +1.00000 q^{81} -6.77095 q^{82} +(5.62179 - 9.73722i) q^{83} +(5.21692 - 9.03597i) q^{84} +(-5.96211 + 10.3267i) q^{85} +(6.61885 - 11.4642i) q^{86} +(-4.73379 - 8.19917i) q^{87} +(-0.352674 - 0.610849i) q^{88} -1.04520 q^{89} +(-3.45186 + 5.97880i) q^{90} +1.43668 q^{91} +11.6688 q^{92} +(1.62546 + 2.81538i) q^{93} -23.4827 q^{94} +(-9.85879 + 17.0759i) q^{95} +(4.05724 + 7.02734i) q^{96} +(-3.31725 + 5.74565i) q^{97} +(14.5472 + 25.1965i) q^{98} +(0.625458 + 1.08333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + 3 q^{13} - 22 q^{14} - 2 q^{15} + 2 q^{17} - 2 q^{18} + 3 q^{19} + 16 q^{20} + q^{21} + 6 q^{22} - q^{23} - 12 q^{24} + 7 q^{26} - 10 q^{27} - 9 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 9 q^{32} - 2 q^{33} - 20 q^{34} + 19 q^{35} - 6 q^{36} + 27 q^{37} - 16 q^{38} - 3 q^{39} - 22 q^{40} - 7 q^{41} + 22 q^{42} + 12 q^{43} - 7 q^{44} + 2 q^{45} + 30 q^{46} - 33 q^{47} - 24 q^{49} + 21 q^{50} - 2 q^{51} - 32 q^{52} - 24 q^{53} + 2 q^{54} + 6 q^{55} - q^{56} - 3 q^{57} + 44 q^{58} + 24 q^{59} - 16 q^{60} + q^{61} + 2 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} - 6 q^{66} + 2 q^{67} - 18 q^{68} + q^{69} + 42 q^{70} - q^{71} + 12 q^{72} + 12 q^{73} + 43 q^{74} + 2 q^{76} + 40 q^{77} - 7 q^{78} + 7 q^{79} - q^{80} + 10 q^{81} - 74 q^{82} + 12 q^{83} + 9 q^{84} - 27 q^{85} - 27 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} - 80 q^{91} - 28 q^{92} + 12 q^{93} + 30 q^{94} - 12 q^{95} + 9 q^{96} - 9 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 + 6 * q^12 + 3 * q^13 - 22 * q^14 - 2 * q^15 + 2 * q^17 - 2 * q^18 + 3 * q^19 + 16 * q^20 + q^21 + 6 * q^22 - q^23 - 12 * q^24 + 7 * q^26 - 10 * q^27 - 9 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 9 * q^32 - 2 * q^33 - 20 * q^34 + 19 * q^35 - 6 * q^36 + 27 * q^37 - 16 * q^38 - 3 * q^39 - 22 * q^40 - 7 * q^41 + 22 * q^42 + 12 * q^43 - 7 * q^44 + 2 * q^45 + 30 * q^46 - 33 * q^47 - 24 * q^49 + 21 * q^50 - 2 * q^51 - 32 * q^52 - 24 * q^53 + 2 * q^54 + 6 * q^55 - q^56 - 3 * q^57 + 44 * q^58 + 24 * q^59 - 16 * q^60 + q^61 + 2 * q^62 - q^63 - 8 * q^64 - 6 * q^65 - 6 * q^66 + 2 * q^67 - 18 * q^68 + q^69 + 42 * q^70 - q^71 + 12 * q^72 + 12 * q^73 + 43 * q^74 + 2 * q^76 + 40 * q^77 - 7 * q^78 + 7 * q^79 - q^80 + 10 * q^81 - 74 * q^82 + 12 * q^83 + 9 * q^84 - 27 * q^85 - 27 * q^86 - 12 * q^87 - 10 * q^88 + 12 * q^89 - 8 * q^90 - 80 * q^91 - 28 * q^92 + 12 * q^93 + 30 * q^94 - 12 * q^95 + 9 * q^96 - 9 * q^97 + 4 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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