LMFDB - Embedded newform 234.2.f.c.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(133,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("234.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.f (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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 4 x^{10} - 6 x^{9} + 22 x^{8} - 45 x^{7} + 75 x^{6} - 135 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 4x^10 - 6x^9 + 22x^8 - 45x^7 + 75x^6 - 135x^5 + 198x^4 - 162x^3 + 324x^2 - 729*x + 729
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			133.1
Root			$-1.26151 + 1.18685i$ of defining polynomial
Character	$\chi$	$=$	234.133
Dual form			234.2.f.c.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.65859 + 0.499074i) q^{3} +1.00000 q^{4} +(-0.102915 - 0.178255i) q^{5} +(1.65859 - 0.499074i) q^{6} +(0.779577 + 1.35027i) q^{7} -1.00000 q^{8} +(2.50185 - 1.65552i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.65859 + 0.499074i) q^{3} +1.00000 q^{4} +(-0.102915 - 0.178255i) q^{5} +(1.65859 - 0.499074i) q^{6} +(0.779577 + 1.35027i) q^{7} -1.00000 q^{8} +(2.50185 - 1.65552i) q^{9} +(0.102915 + 0.178255i) q^{10} -3.88861 q^{11} +(-1.65859 + 0.499074i) q^{12} +(-1.68162 + 3.18938i) q^{13} +(-0.779577 - 1.35027i) q^{14} +(0.259657 + 0.244289i) q^{15} +1.00000 q^{16} +(-1.84139 + 3.18938i) q^{17} +(-2.50185 + 1.65552i) q^{18} +(-3.72573 + 6.45316i) q^{19} +(-0.102915 - 0.178255i) q^{20} +(-1.96688 - 1.85047i) q^{21} +3.88861 q^{22} +(-1.68465 + 2.91790i) q^{23} +(1.65859 - 0.499074i) q^{24} +(2.47882 - 4.29344i) q^{25} +(1.68162 - 3.18938i) q^{26} +(-3.32332 + 3.99444i) q^{27} +(0.779577 + 1.35027i) q^{28} -4.87634 q^{29} +(-0.259657 - 0.244289i) q^{30} +(-1.50185 - 2.60128i) q^{31} -1.00000 q^{32} +(6.44961 - 1.94070i) q^{33} +(1.84139 - 3.18938i) q^{34} +(0.160461 - 0.277926i) q^{35} +(2.50185 - 1.65552i) q^{36} +(4.38086 + 7.58788i) q^{37} +(3.72573 - 6.45316i) q^{38} +(1.19739 - 6.12913i) q^{39} +(0.102915 + 0.178255i) q^{40} +(1.74646 - 3.02496i) q^{41} +(1.96688 + 1.85047i) q^{42} +(0.343259 + 0.594541i) q^{43} -3.88861 q^{44} +(-0.552583 - 0.275588i) q^{45} +(1.68465 - 2.91790i) q^{46} +(-1.48380 + 2.57002i) q^{47} +(-1.65859 + 0.499074i) q^{48} +(2.28452 - 3.95690i) q^{49} +(-2.47882 + 4.29344i) q^{50} +(1.46237 - 6.20887i) q^{51} +(-1.68162 + 3.18938i) q^{52} +9.52297 q^{53} +(3.32332 - 3.99444i) q^{54} +(0.400197 + 0.693162i) q^{55} +(-0.779577 - 1.35027i) q^{56} +(2.95886 - 12.5626i) q^{57} +4.87634 q^{58} +6.60057 q^{59} +(0.259657 + 0.244289i) q^{60} +(-2.67549 - 4.63408i) q^{61} +(1.50185 + 2.60128i) q^{62} +(4.18578 + 2.08756i) q^{63} +1.00000 q^{64} +(0.741586 - 0.0284788i) q^{65} +(-6.44961 + 1.94070i) q^{66} +(1.51690 - 2.62734i) q^{67} +(-1.84139 + 3.18938i) q^{68} +(1.33790 - 5.68036i) q^{69} +(-0.160461 + 0.277926i) q^{70} +(-1.39708 + 2.41982i) q^{71} +(-2.50185 + 1.65552i) q^{72} -15.3364 q^{73} +(-4.38086 - 7.58788i) q^{74} +(-1.96860 + 8.35817i) q^{75} +(-3.72573 + 6.45316i) q^{76} +(-3.03147 - 5.25066i) q^{77} +(-1.19739 + 6.12913i) q^{78} +(0.829455 - 1.43666i) q^{79} +(-0.102915 - 0.178255i) q^{80} +(3.51851 - 8.28373i) q^{81} +(-1.74646 + 3.02496i) q^{82} +(-4.34020 + 7.51744i) q^{83} +(-1.96688 - 1.85047i) q^{84} +0.758029 q^{85} +(-0.343259 - 0.594541i) q^{86} +(8.08785 - 2.43365i) q^{87} +3.88861 q^{88} +(6.25792 + 10.8390i) q^{89} +(0.552583 + 0.275588i) q^{90} +(-5.61747 + 0.215725i) q^{91} +(-1.68465 + 2.91790i) q^{92} +(3.78919 + 3.56493i) q^{93} +(1.48380 - 2.57002i) q^{94} +1.53374 q^{95} +(1.65859 - 0.499074i) q^{96} +(-3.28917 - 5.69701i) q^{97} +(-2.28452 + 3.95690i) q^{98} +(-9.72871 + 6.43767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9	\( 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9} + 3 q^{10} - 8 q^{11} - 5 q^{13} - q^{14} + 11 q^{15} + 12 q^{16} - q^{17} - 4 q^{18} + 9 q^{19} - 3 q^{20} + 8 q^{21} + 8 q^{22} + 7 q^{23} - q^{25} + 5 q^{26} - 9 q^{27} + q^{28} - 2 q^{29} - 11 q^{30} + 8 q^{31} - 12 q^{32} - 4 q^{33} + q^{34} - 3 q^{35} + 4 q^{36} + 15 q^{37} - 9 q^{38} + 18 q^{39} + 3 q^{40} - 19 q^{41} - 8 q^{42} - 2 q^{43} - 8 q^{44} - 5 q^{45} - 7 q^{46} - 23 q^{47} - 27 q^{49} + q^{50} + 8 q^{51} - 5 q^{52} - 4 q^{53} + 9 q^{54} + 24 q^{55} - q^{56} - 16 q^{57} + 2 q^{58} + 8 q^{59} + 11 q^{60} - 8 q^{61} - 8 q^{62} + 12 q^{64} + 7 q^{65} + 4 q^{66} + 14 q^{67} - q^{68} - 6 q^{69} + 3 q^{70} - 15 q^{71} - 4 q^{72} - 90 q^{73} - 15 q^{74} - 56 q^{75} + 9 q^{76} + 4 q^{77} - 18 q^{78} - 12 q^{79} - 3 q^{80} + 28 q^{81} + 19 q^{82} + 24 q^{83} + 8 q^{84} - 14 q^{85} + 2 q^{86} + 36 q^{87} + 8 q^{88} + 23 q^{89} + 5 q^{90} + 8 q^{91} + 7 q^{92} + 6 q^{93} + 23 q^{94} + 14 q^{95} - 4 q^{97} + 27 q^{98} + 31 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9 + 3 * q^10 - 8 * q^11 - 5 * q^13 - q^14 + 11 * q^15 + 12 * q^16 - q^17 - 4 * q^18 + 9 * q^19 - 3 * q^20 + 8 * q^21 + 8 * q^22 + 7 * q^23 - q^25 + 5 * q^26 - 9 * q^27 + q^28 - 2 * q^29 - 11 * q^30 + 8 * q^31 - 12 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 4 * q^36 + 15 * q^37 - 9 * q^38 + 18 * q^39 + 3 * q^40 - 19 * q^41 - 8 * q^42 - 2 * q^43 - 8 * q^44 - 5 * q^45 - 7 * q^46 - 23 * q^47 - 27 * q^49 + q^50 + 8 * q^51 - 5 * q^52 - 4 * q^53 + 9 * q^54 + 24 * q^55 - q^56 - 16 * q^57 + 2 * q^58 + 8 * q^59 + 11 * q^60 - 8 * q^61 - 8 * q^62 + 12 * q^64 + 7 * q^65 + 4 * q^66 + 14 * q^67 - q^68 - 6 * q^69 + 3 * q^70 - 15 * q^71 - 4 * q^72 - 90 * q^73 - 15 * q^74 - 56 * q^75 + 9 * q^76 + 4 * q^77 - 18 * q^78 - 12 * q^79 - 3 * q^80 + 28 * q^81 + 19 * q^82 + 24 * q^83 + 8 * q^84 - 14 * q^85 + 2 * q^86 + 36 * q^87 + 8 * q^88 + 23 * q^89 + 5 * q^90 + 8 * q^91 + 7 * q^92 + 6 * q^93 + 23 * q^94 + 14 * q^95 - 4 * q^97 + 27 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.65859	+	0.499074i	−0.957588	+	0.288141i
$3$	−1.65859	+	0.499074i	−0.957588	+	0.288141i
$4$	1.00000			0.500000
$5$	−0.102915	−	0.178255i	−0.0460251	−	0.0797179i	0.842095	−	0.539329i	$-0.181322\pi$
$5$	−0.102915	−	0.178255i	−0.0460251	−	0.0797179i	−0.888120	+	0.459611i	$0.847989\pi$
$6$	1.65859	−	0.499074i	0.677117	−	0.203746i
$7$	0.779577	+	1.35027i	0.294652	+	0.510353i	0.974904	−	0.222626i	$-0.0714628\pi$
$7$	0.779577	+	1.35027i	0.294652	+	0.510353i	−0.680252	+	0.732979i	$0.738129\pi$
$8$	−1.00000			−0.353553
$9$	2.50185	−	1.65552i	0.833950	−	0.551840i
$10$	0.102915	+	0.178255i	0.0325447	+	0.0563691i
$11$	−3.88861			−1.17246			−0.586230	−	0.810145i	$-0.699388\pi$
$11$	−3.88861			−1.17246			−0.586230	+	0.810145i	$0.699388\pi$
$12$	−1.65859	+	0.499074i	−0.478794	+	0.144070i
$13$	−1.68162	+	3.18938i	−0.466399	+	0.884575i
$13$	−1.68162	+	3.18938i	−0.466399	+	0.884575i
$14$	−0.779577	−	1.35027i	−0.208351	−	0.360874i
$15$	0.259657	+	0.244289i	0.0670431	+	0.0630752i
$16$	1.00000			0.250000
$17$	−1.84139	+	3.18938i	−0.446602	+	0.773538i	−0.998162	−	0.0605972i	$-0.980699\pi$
$17$	−1.84139	+	3.18938i	−0.446602	+	0.773538i	0.551560	+	0.834135i	$0.314033\pi$
$18$	−2.50185	+	1.65552i	−0.589692	+	0.390210i
$19$	−3.72573	+	6.45316i	−0.854741	+	1.48046i	0.0221435	+	0.999755i	$0.492951\pi$
$19$	−3.72573	+	6.45316i	−0.854741	+	1.48046i	−0.876885	+	0.480701i	$0.840382\pi$
$20$	−0.102915	−	0.178255i	−0.0230126	−	0.0398589i
$21$	−1.96688	−	1.85047i	−0.429209	−	0.403807i
$22$	3.88861			0.829054
$23$	−1.68465	+	2.91790i	−0.351273	+	0.608423i	−0.986473	−	0.163925i	$-0.947585\pi$
$23$	−1.68465	+	2.91790i	−0.351273	+	0.608423i	0.635200	+	0.772348i	$0.280918\pi$
$24$	1.65859	−	0.499074i	0.338559	−	0.101873i
$25$	2.47882	−	4.29344i	0.495763	−	0.858687i
$26$	1.68162	−	3.18938i	0.329794	−	0.625489i
$27$	−3.32332	+	3.99444i	−0.639573	+	0.768730i
$28$	0.779577	+	1.35027i	0.147326	+	0.255176i
$29$	−4.87634			−0.905513			−0.452756	−	0.891634i	$-0.649559\pi$
$29$	−4.87634			−0.905513			−0.452756	+	0.891634i	$0.649559\pi$
$30$	−0.259657	−	0.244289i	−0.0474066	−	0.0446009i
$31$	−1.50185	−	2.60128i	−0.269740	−	0.467204i	0.699054	−	0.715068i	$-0.253604\pi$
$31$	−1.50185	−	2.60128i	−0.269740	−	0.467204i	−0.968795	+	0.247865i	$0.920271\pi$
$32$	−1.00000			−0.176777
$33$	6.44961	−	1.94070i	1.12273	−	0.337833i
$34$	1.84139	−	3.18938i	0.315796	−	0.546974i
$35$	0.160461	−	0.277926i	0.0271228	−	0.0469781i
$36$	2.50185	−	1.65552i	0.416975	−	0.275920i
$37$	4.38086	+	7.58788i	0.720210	+	1.24744i	0.960916	+	0.276842i	$0.0892877\pi$
$37$	4.38086	+	7.58788i	0.720210	+	1.24744i	−0.240706	+	0.970598i	$0.577379\pi$
$38$	3.72573	−	6.45316i	0.604393	−	1.04684i
$39$	1.19739	−	6.12913i	0.191736	−	0.981447i
$40$	0.102915	+	0.178255i	0.0162723	+	0.0281845i
$41$	1.74646	−	3.02496i	0.272751	−	0.472419i	−0.696814	−	0.717252i	$-0.745400\pi$
$41$	1.74646	−	3.02496i	0.272751	−	0.472419i	0.969565	+	0.244833i	$0.0787331\pi$
$42$	1.96688	+	1.85047i	0.303497	+	0.285534i
$43$	0.343259	+	0.594541i	0.0523464	+	0.0906667i	0.891011	−	0.453981i	$-0.149997\pi$
$43$	0.343259	+	0.594541i	0.0523464	+	0.0906667i	−0.838665	+	0.544648i	$0.816663\pi$
$44$	−3.88861			−0.586230
$45$	−0.552583	−	0.275588i	−0.0823742	−	0.0410822i
$46$	1.68465	−	2.91790i	0.248388	−	0.430220i
$47$	−1.48380	+	2.57002i	−0.216434	+	0.374875i	−0.953715	−	0.300711i	$-0.902776\pi$
$47$	−1.48380	+	2.57002i	−0.216434	+	0.374875i	0.737281	+	0.675586i	$0.236109\pi$
$48$	−1.65859	+	0.499074i	−0.239397	+	0.0720352i
$49$	2.28452	−	3.95690i	0.326360	−	0.565272i
$50$	−2.47882	+	4.29344i	−0.350558	+	0.607184i
$51$	1.46237	−	6.20887i	0.204773	−	0.869415i
$52$	−1.68162	+	3.18938i	−0.233199	+	0.442287i
$53$	9.52297			1.30808			0.654041	−	0.756460i	$-0.273073\pi$
$53$	9.52297			1.30808			0.654041	+	0.756460i	$0.273073\pi$
$54$	3.32332	−	3.99444i	0.452246	−	0.543574i
$55$	0.400197	+	0.693162i	0.0539626	+	0.0934660i
$56$	−0.779577	−	1.35027i	−0.104175	−	0.180437i
$57$	2.95886	−	12.5626i	0.391911	−	1.66395i
$58$	4.87634			0.640294
$59$	6.60057			0.859321			0.429661	−	0.902990i	$-0.358633\pi$
$59$	6.60057			0.859321			0.429661	+	0.902990i	$0.358633\pi$
$60$	0.259657	+	0.244289i	0.0335215	+	0.0315376i
$61$	−2.67549	−	4.63408i	−0.342561	−	0.593333i	0.642346	−	0.766414i	$-0.277961\pi$
$61$	−2.67549	−	4.63408i	−0.342561	−	0.593333i	−0.984908	+	0.173081i	$0.944628\pi$
$62$	1.50185	+	2.60128i	0.190735	+	0.330363i
$63$	4.18578	+	2.08756i	0.527359	+	0.263008i
$64$	1.00000			0.125000
$65$	0.741586	−	0.0284788i	0.0919825	−	0.00353236i
$66$	−6.44961	+	1.94070i	−0.793892	+	0.238884i
$67$	1.51690	−	2.62734i	0.185318	−	0.320981i	−0.758365	−	0.651830i	$-0.774002\pi$
$67$	1.51690	−	2.62734i	0.185318	−	0.320981i	0.943684	+	0.330849i	$0.107335\pi$
$68$	−1.84139	+	3.18938i	−0.223301	+	0.386769i
$69$	1.33790	−	5.68036i	0.161064	−	0.683835i
$70$	−0.160461	+	0.277926i	−0.0191787	+	0.0332186i
$71$	−1.39708	+	2.41982i	−0.165803	+	0.287180i	−0.936940	−	0.349489i	$-0.886355\pi$
$71$	−1.39708	+	2.41982i	−0.165803	+	0.287180i	0.771137	+	0.636669i	$0.219688\pi$
$72$	−2.50185	+	1.65552i	−0.294846	+	0.195105i
$73$	−15.3364			−1.79499			−0.897493	−	0.441028i	$-0.854614\pi$
$73$	−15.3364			−1.79499			−0.897493	+	0.441028i	$0.854614\pi$
$74$	−4.38086	−	7.58788i	−0.509265	−	0.882073i
$75$	−1.96860	+	8.35817i	−0.227314	+	0.965118i
$76$	−3.72573	+	6.45316i	−0.427371	+	0.740228i
$77$	−3.03147	−	5.25066i	−0.345468	−	0.598368i
$78$	−1.19739	+	6.12913i	−0.135578	+	0.693988i
$79$	0.829455	−	1.43666i	0.0933210	−	0.161637i	−0.815586	−	0.578636i	$-0.803585\pi$
$79$	0.829455	−	1.43666i	0.0933210	−	0.161637i	0.908907	+	0.417000i	$0.136918\pi$
$80$	−0.102915	−	0.178255i	−0.0115063	−	0.0199295i
$81$	3.51851	−	8.28373i	0.390945	−	0.920414i
$82$	−1.74646	+	3.02496i	−0.192864	+	0.334051i
$83$	−4.34020	+	7.51744i	−0.476398	+	0.825146i	−0.999634	−	0.0270417i	$-0.991391\pi$
$83$	−4.34020	+	7.51744i	−0.476398	+	0.825146i	0.523236	+	0.852188i	$0.324725\pi$
$84$	−1.96688	−	1.85047i	−0.214605	−	0.201903i
$85$	0.758029			0.0822198
$86$	−0.343259	−	0.594541i	−0.0370145	−	0.0641110i
$87$	8.08785	−	2.43365i	0.867108	−	0.260915i
$88$	3.88861			0.414527
$89$	6.25792	+	10.8390i	0.663339	+	1.14894i	0.979733	+	0.200308i	$0.0641944\pi$
$89$	6.25792	+	10.8390i	0.663339	+	1.14894i	−0.316394	+	0.948628i	$0.602472\pi$
$90$	0.552583	+	0.275588i	0.0582473	+	0.0290495i
$91$	−5.61747	+	0.215725i	−0.588871	+	0.0226141i
$92$	−1.68465	+	2.91790i	−0.175637	+	0.304212i
$93$	3.78919	+	3.56493i	0.392920	+	0.369666i
$94$	1.48380	−	2.57002i	0.153042	−	0.265077i
$95$	1.53374			0.157358
$96$	1.65859	−	0.499074i	0.169279	−	0.0509366i
$97$	−3.28917	−	5.69701i	−0.333965	−	0.578444i	0.649321	−	0.760515i	$-0.275053\pi$
$97$	−3.28917	−	5.69701i	−0.333965	−	0.578444i	−0.983285	+	0.182071i	$0.941720\pi$
$98$	−2.28452	+	3.95690i	−0.230771	+	0.399708i
$99$	−9.72871	+	6.43767i	−0.977773	+	0.647010i
$100$	2.47882	−	4.29344i	0.247882	−	0.429344i
$101$	11.3049			1.12488			0.562440	−	0.826838i	$-0.309863\pi$
$101$	11.3049			1.12488			0.562440	+	0.826838i	$0.309863\pi$
$102$	−1.46237	+	6.20887i	−0.144797	+	0.614769i
$103$	9.34320	+	16.1829i	0.920613	+	1.59455i	0.798469	+	0.602036i	$0.205644\pi$
$103$	9.34320	+	16.1829i	0.920613	+	1.59455i	0.122144	+	0.992512i	$0.461023\pi$
$104$	1.68162	−	3.18938i	0.164897	−	0.312744i
$105$	−0.127433	+	0.541048i	−0.0124362	+	0.0528009i
$106$	−9.52297			−0.924953
$107$	−5.71380	−	9.89659i	−0.552374	−	0.956739i	−0.998103	−	0.0615712i	$-0.980389\pi$
$107$	−5.71380	−	9.89659i	−0.552374	−	0.956739i	0.445729	−	0.895168i	$-0.352944\pi$
$108$	−3.32332	+	3.99444i	−0.319786	+	0.384365i
$109$	−6.39848			−0.612863			−0.306432	−	0.951893i	$-0.599135\pi$
$109$	−6.39848			−0.612863			−0.306432	+	0.951893i	$0.599135\pi$
$110$	−0.400197	−	0.693162i	−0.0381573	−	0.0660904i
$111$	−11.0530	−	10.3988i	−1.04910	−	0.987012i
$112$	0.779577	+	1.35027i	0.0736631	+	0.127588i
$113$	12.9768			1.22076			0.610378	−	0.792110i	$-0.291017\pi$
$113$	12.9768			1.22076			0.610378	+	0.792110i	$0.291017\pi$
$114$	−2.95886	+	12.5626i	−0.277123	+	1.17659i
$115$	0.693504			0.0646696
$116$	−4.87634			−0.452756
$117$	1.07291	+	10.7633i	0.0991907	+	0.995068i
$118$	−6.60057			−0.607632
$119$	−5.74202			−0.526370
$120$	−0.259657	−	0.244289i	−0.0237033	−	0.0223004i
$121$	4.12128			0.374662
$122$	2.67549	+	4.63408i	0.242227	+	0.419550i
$123$	−1.38698	+	5.88878i	−0.125060	+	0.530973i
$124$	−1.50185	−	2.60128i	−0.134870	−	0.233602i
$125$	−2.04959			−0.183321
$126$	−4.18578	−	2.08756i	−0.372899	−	0.185975i
$127$	−5.60948	−	9.71591i	−0.497761	−	0.862147i	0.502236	−	0.864731i	$-0.332511\pi$
$127$	−5.60948	−	9.71591i	−0.497761	−	0.862147i	−0.999997	+	0.00258339i	$0.999178\pi$
$128$	−1.00000			−0.0883883
$129$	−0.866046	−	0.814789i	−0.0762511	−	0.0717382i
$130$	−0.741586	+	0.0284788i	−0.0650414	+	0.00249776i
$131$	0.232322	+	0.402393i	0.0202980	+	0.0351572i	0.875996	−	0.482318i	$-0.160205\pi$
$131$	0.232322	+	0.402393i	0.0202980	+	0.0351572i	−0.855698	+	0.517476i	$0.826872\pi$
$132$	6.44961	−	1.94070i	0.561367	−	0.168917i
$133$	−11.6180			−1.00741
$134$	−1.51690	+	2.62734i	−0.131040	+	0.226968i
$135$	1.05405	+	0.181308i	0.0907180	+	0.0156045i
$136$	1.84139	−	3.18938i	0.157898	−	0.273487i
$137$	7.69850	+	13.3342i	0.657727	+	1.13922i	0.981203	+	0.192981i	$0.0618154\pi$
$137$	7.69850	+	13.3342i	0.657727	+	1.13922i	−0.323475	+	0.946237i	$0.604851\pi$
$138$	−1.33790	+	5.68036i	−0.113889	+	0.483544i
$139$	4.81710			0.408581			0.204290	−	0.978910i	$-0.434511\pi$
$139$	4.81710			0.408581			0.204290	+	0.978910i	$0.434511\pi$
$140$	0.160461	−	0.277926i	0.0135614	−	0.0234891i
$141$	1.17839	−	5.00313i	0.0992382	−	0.421340i
$142$	1.39708	−	2.41982i	0.117241	−	0.203067i
$143$	6.53918	−	12.4022i	0.546834	−	1.03713i
$144$	2.50185	−	1.65552i	0.208487	−	0.137960i
$145$	0.501850	+	0.869229i	0.0416764	+	0.0721856i
$146$	15.3364			1.26925
$147$	−1.81430	+	7.70303i	−0.149641	+	0.635335i
$148$	4.38086	+	7.58788i	0.360105	+	0.623720i
$149$	−16.7978			−1.37613			−0.688064	−	0.725650i	$-0.741539\pi$
$149$	−16.7978			−1.37613			−0.688064	+	0.725650i	$0.741539\pi$
$150$	1.96860	−	8.35817i	0.160736	−	0.682442i
$151$	−0.315574	+	0.546591i	−0.0256811	+	0.0444809i	−0.878580	−	0.477595i	$-0.841509\pi$
$151$	−0.315574	+	0.546591i	−0.0256811	+	0.0444809i	0.852899	+	0.522076i	$0.174842\pi$
$152$	3.72573	−	6.45316i	0.302197	−	0.523420i
$153$	0.673203	+	11.0278i	0.0544253	+	0.891545i
$154$	3.03147	+	5.25066i	0.244283	+	0.423110i
$155$	−0.309127	+	0.535423i	−0.0248297	+	0.0430062i
$156$	1.19739	−	6.12913i	0.0958679	−	0.490723i
$157$	−8.62325	−	14.9359i	−0.688210	−	1.19202i	−0.972416	−	0.233252i	$-0.925063\pi$
$157$	−8.62325	−	14.9359i	−0.688210	−	1.19202i	0.284206	−	0.958763i	$-0.408270\pi$
$158$	−0.829455	+	1.43666i	−0.0659879	+	0.114294i
$159$	−15.7947	+	4.75267i	−1.25260	+	0.376911i
$160$	0.102915	+	0.178255i	0.00813617	+	0.0140923i
$161$	−5.25325			−0.414014
$162$	−3.51851	+	8.28373i	−0.276440	+	0.650831i
$163$	1.67055	−	2.89347i	0.130847	−	0.226634i	−0.793156	−	0.609018i	$-0.791564\pi$
$163$	1.67055	−	2.89347i	0.130847	−	0.226634i	0.924003	+	0.382384i	$0.124897\pi$
$164$	1.74646	−	3.02496i	0.136376	−	0.236209i
$165$	−1.00970	−	0.949945i	−0.0786053	−	0.0739531i
$166$	4.34020	−	7.51744i	0.336865	−	0.583466i
$167$	10.5805	−	18.3260i	0.818744	−	1.41811i	−0.0878642	−	0.996132i	$-0.528004\pi$
$167$	10.5805	−	18.3260i	0.818744	−	1.41811i	0.906608	−	0.421974i	$-0.138663\pi$
$168$	1.96688	+	1.85047i	0.151748	+	0.142767i
$169$	−7.34428	−	10.7267i	−0.564945	−	0.825129i
$170$	−0.758029			−0.0581381
$171$	1.36211	+	22.3128i	0.104163	+	1.70631i
$172$	0.343259	+	0.594541i	0.0261732	+	0.0453333i
$173$	11.2917	+	19.5577i	0.858489	+	1.48695i	0.873370	+	0.487057i	$0.161930\pi$
$173$	11.2917	+	19.5577i	0.858489	+	1.48695i	−0.0148813	+	0.999889i	$0.504737\pi$
$174$	−8.08785	+	2.43365i	−0.613138	+	0.184495i
$175$	7.72971			0.584311
$176$	−3.88861			−0.293115
$177$	−10.9476	+	3.29418i	−0.822876	+	0.247605i
$178$	−6.25792	−	10.8390i	−0.469051	−	0.812421i
$179$	5.40388	+	9.35979i	0.403905	+	0.699584i	0.994193	−	0.107609i	$-0.0343194\pi$
$179$	5.40388	+	9.35979i	0.403905	+	0.699584i	−0.590289	+	0.807192i	$0.700986\pi$
$180$	−0.552583	−	0.275588i	−0.0411871	−	0.0205411i
$181$	13.6295			1.01307			0.506536	−	0.862219i	$-0.330926\pi$
$181$	13.6295			1.01307			0.506536	+	0.862219i	$0.330926\pi$
$182$	5.61747	−	0.215725i	0.416394	−	0.0159906i
$183$	6.75029	+	6.35078i	0.498996	+	0.469463i
$184$	1.68465	−	2.91790i	0.124194	−	0.215110i
$185$	0.901716	−	1.56182i	0.0662955	−	0.114827i
$186$	−3.78919	−	3.56493i	−0.277837	−	0.261393i
$187$	7.16044	−	12.4022i	0.523623	−	0.906942i
$188$	−1.48380	+	2.57002i	−0.108217	+	0.187438i
$189$	−7.98434	−	1.37339i	−0.580775	−	0.0998997i
$190$	−1.53374			−0.111269
$191$	−5.95622	−	10.3165i	−0.430977	−	0.746474i	0.565981	−	0.824418i	$-0.308498\pi$
$191$	−5.95622	−	10.3165i	−0.430977	−	0.746474i	−0.996958	+	0.0779446i	$0.975164\pi$
$192$	−1.65859	+	0.499074i	−0.119699	+	0.0360176i
$193$	−11.9054	+	20.6208i	−0.856973	+	1.48432i	0.0178300	+	0.999841i	$0.494324\pi$
$193$	−11.9054	+	20.6208i	−0.856973	+	1.48432i	−0.874803	+	0.484479i	$0.839009\pi$
$194$	3.28917	+	5.69701i	0.236149	+	0.409022i
$195$	−1.21578	+	0.417341i	−0.0870635	+	0.0298864i
$196$	2.28452	−	3.95690i	0.163180	−	0.282636i
$197$	−3.84864	−	6.66603i	−0.274204	−	0.474935i	0.695730	−	0.718303i	$-0.255081\pi$
$197$	−3.84864	−	6.66603i	−0.274204	−	0.474935i	−0.969934	+	0.243368i	$0.921748\pi$
$198$	9.72871	−	6.43767i	0.691390	−	0.457505i
$199$	3.23845	−	5.60917i	0.229568	−	0.397623i	−0.728112	−	0.685458i	$-0.759602\pi$
$199$	3.23845	−	5.60917i	0.229568	−	0.397623i	0.957680	+	0.287835i	$0.0929354\pi$
$200$	−2.47882	+	4.29344i	−0.175279	+	0.303592i
$201$	−1.20467	+	5.11473i	−0.0849711	+	0.360765i
$202$	−11.3049			−0.795411
$203$	−3.80148	−	6.58435i	−0.266812	−	0.462131i
$204$	1.46237	−	6.20887i	0.102387	−	0.434708i
$205$	−0.718950			−0.0502136
$206$	−9.34320	−	16.1829i	−0.650972	−	1.12752i
$207$	0.615900	+	10.0891i	0.0428080	+	0.701241i
$208$	−1.68162	+	3.18938i	−0.116600	+	0.221144i
$209$	14.4879	−	25.0938i	1.00215	−	1.73577i
$210$	0.127433	−	0.541048i	0.00879372	−	0.0373359i
$211$	6.90747	−	11.9641i	0.475530	−	0.823642i	−0.524077	−	0.851671i	$-0.675590\pi$
$211$	6.90747	−	11.9641i	0.475530	−	0.823642i	0.999607	+	0.0280291i	$0.00892309\pi$
$212$	9.52297			0.654041
$213$	1.10952	−	4.71074i	0.0760232	−	0.322775i
$214$	5.71380	+	9.89659i	0.390587	+	0.676517i
$215$	0.0706531	−	0.122375i	0.00481850	−	0.00834590i
$216$	3.32332	−	3.99444i	0.226123	−	0.271787i
$217$	2.34161	−	4.05580i	0.158959	−	0.275325i
$218$	6.39848			0.433360
$219$	25.4368	−	7.65399i	1.71886	−	0.517209i
$220$	0.400197	+	0.693162i	0.0269813	+	0.0467330i
$221$	−7.07562	−	11.2362i	−0.475957	−	0.755830i
$222$	11.0530	+	10.3988i	0.741827	+	0.697923i
$223$	11.8684			0.794767			0.397383	−	0.917653i	$-0.369918\pi$
$223$	11.8684			0.794767			0.397383	+	0.917653i	$0.369918\pi$
$224$	−0.779577	−	1.35027i	−0.0520877	−	0.0902185i
$225$	−0.906244	−	14.8453i	−0.0604163	−	0.989684i
$226$	−12.9768			−0.863205
$227$	−4.91697	−	8.51644i	−0.326351	−	0.565256i	0.655434	−	0.755252i	$-0.272486\pi$
$227$	−4.91697	−	8.51644i	−0.326351	−	0.565256i	−0.981785	+	0.189996i	$0.939152\pi$
$228$	2.95886	−	12.5626i	0.195955	−	0.831976i
$229$	8.65591	+	14.9925i	0.571999	+	0.990731i	0.996361	+	0.0852383i	$0.0271652\pi$
$229$	8.65591	+	14.9925i	0.571999	+	0.990731i	−0.424362	+	0.905493i	$0.639502\pi$
$230$	−0.693504			−0.0457283
$231$	7.64844	+	7.19577i	0.503230	+	0.473447i
$232$	4.87634			0.320147
$233$	17.6548			1.15660			0.578301	−	0.815823i	$-0.303716\pi$
$233$	17.6548			1.15660			0.578301	+	0.815823i	$0.303716\pi$
$234$	−1.07291	−	10.7633i	−0.0701384	−	0.703620i
$235$	0.610823			0.0398457
$236$	6.60057			0.429661
$237$	−0.658728	+	2.79679i	−0.0427890	+	0.181671i
$238$	5.74202			0.372200
$239$	−0.631256	−	1.09337i	−0.0408326	−	0.0707241i	0.844887	−	0.534945i	$-0.179668\pi$
$239$	−0.631256	−	1.09337i	−0.0408326	−	0.0707241i	−0.885719	+	0.464221i	$0.846334\pi$
$240$	0.259657	+	0.244289i	0.0167608	+	0.0157688i
$241$	5.44455	+	9.43023i	0.350714	+	0.607455i	0.986375	−	0.164514i	$-0.0526056\pi$
$241$	5.44455	+	9.43023i	0.350714	+	0.607455i	−0.635661	+	0.771969i	$0.719272\pi$
$242$	−4.12128			−0.264926
$243$	−1.70157	+	15.4953i	−0.109156	+	0.994025i
$244$	−2.67549	−	4.63408i	−0.171281	−	0.296667i
$245$	−0.940449			−0.0600831
$246$	1.38698	−	5.88878i	0.0884309	−	0.375455i
$247$	−14.3163	−	22.7346i	−0.910923	−	1.44656i
$248$	1.50185	+	2.60128i	0.0953676	+	0.165181i
$249$	3.44685	−	14.6344i	0.218435	−	0.927420i
$250$	2.04959			0.129627
$251$	−12.3336	+	21.3624i	−0.778489	+	1.34838i	0.154323	+	0.988020i	$0.450680\pi$
$251$	−12.3336	+	21.3624i	−0.778489	+	1.34838i	−0.932812	+	0.360362i	$0.882653\pi$
$252$	4.18578	+	2.08756i	0.263679	+	0.131504i
$253$	6.55094	−	11.3466i	0.411854	−	0.713352i
$254$	5.60948	+	9.71591i	0.351970	+	0.609630i
$255$	−1.25726	+	0.378313i	−0.0787327	+	0.0236909i
$256$	1.00000			0.0625000
$257$	−12.7687	+	22.1161i	−0.796492	+	1.37956i	0.125396	+	0.992107i	$0.459980\pi$
$257$	−12.7687	+	22.1161i	−0.796492	+	1.37956i	−0.921888	+	0.387457i	$0.873353\pi$
$258$	0.866046	+	0.814789i	0.0539177	+	0.0507266i
$259$	−6.83044	+	11.8307i	−0.424423	+	0.735122i
$260$	0.741586	−	0.0284788i	0.0459912	−	0.00176618i
$261$	−12.1999	+	8.07287i	−0.755152	+	0.499698i
$262$	−0.232322	−	0.402393i	−0.0143529	−	0.0248599i
$263$	−12.4022			−0.764751			−0.382376	−	0.924007i	$-0.624894\pi$
$263$	−12.4022			−0.764751			−0.382376	+	0.924007i	$0.624894\pi$
$264$	−6.44961	+	1.94070i	−0.396946	+	0.119442i
$265$	−0.980060	−	1.69751i	−0.0602046	−	0.104277i
$266$	11.6180			0.712344
$267$	−15.7888	−	14.8544i	−0.966260	−	0.909073i
$268$	1.51690	−	2.62734i	0.0926592	−	0.160490i
$269$	2.46813	−	4.27492i	0.150484	−	0.260646i	−0.780921	−	0.624629i	$-0.785250\pi$
$269$	2.46813	−	4.27492i	0.150484	−	0.260646i	0.931406	+	0.363983i	$0.118583\pi$
$270$	−1.05405	−	0.181308i	−0.0641473	−	0.0110340i
$271$	13.7565	+	23.8269i	0.835647	+	1.44738i	0.893503	+	0.449058i	$0.148240\pi$
$271$	13.7565	+	23.8269i	0.835647	+	1.44738i	−0.0578557	+	0.998325i	$0.518426\pi$
$272$	−1.84139	+	3.18938i	−0.111651	+	0.193385i
$273$	9.20942	−	3.16133i	0.557379	−	0.191333i
$274$	−7.69850	−	13.3342i	−0.465083	−	0.805548i
$275$	−9.63915	+	16.6955i	−0.581263	+	1.00678i
$276$	1.33790	−	5.68036i	0.0805318	−	0.341917i
$277$	1.33384	+	2.31027i	0.0801425	+	0.138811i	0.903311	−	0.428986i	$-0.141129\pi$
$277$	1.33384	+	2.31027i	0.0801425	+	0.138811i	−0.823168	+	0.567797i	$0.807796\pi$
$278$	−4.81710			−0.288910
$279$	−8.06387	−	4.02167i	−0.482772	−	0.240771i
$280$	−0.160461	+	0.277926i	−0.00958937	+	0.0166093i
$281$	−5.51262	+	9.54813i	−0.328855	+	0.569594i	−0.982285	−	0.187393i	$-0.939996\pi$
$281$	−5.51262	+	9.54813i	−0.328855	+	0.569594i	0.653430	+	0.756987i	$0.273329\pi$
$282$	−1.17839	+	5.00313i	−0.0701720	+	0.297932i
$283$	−2.43391	+	4.21565i	−0.144681	+	0.250595i	−0.929254	−	0.369442i	$-0.879549\pi$
$283$	−2.43391	+	4.21565i	−0.144681	+	0.250595i	0.784573	+	0.620036i	$0.212882\pi$
$284$	−1.39708	+	2.41982i	−0.0829017	+	0.143590i
$285$	−2.54385	+	0.765450i	−0.150684	+	0.0453413i
$286$	−6.53918	+	12.4022i	−0.386670	+	0.733360i
$287$	5.44600			0.321467
$288$	−2.50185	+	1.65552i	−0.147423	+	0.0975525i
$289$	1.71857	+	2.97666i	0.101093	+	0.175097i
$290$	−0.501850	−	0.869229i	−0.0294696	−	0.0510429i
$291$	8.29862	+	7.80747i	0.486474	+	0.457682i
$292$	−15.3364			−0.897493
$293$	−8.49447			−0.496252			−0.248126	−	0.968728i	$-0.579815\pi$
$293$	−8.49447			−0.496252			−0.248126	+	0.968728i	$0.579815\pi$
$294$	1.81430	−	7.70303i	0.105812	−	0.449250i
$295$	−0.679300	−	1.17658i	−0.0395504	−	0.0685033i
$296$	−4.38086	−	7.58788i	−0.254633	−	0.441037i
$297$	12.9231	−	15.5328i	0.749873	−	0.901305i
$298$	16.7978			0.973070
$299$	−6.47333	−	10.2798i	−0.374362	−	0.594495i
$300$	−1.96860	+	8.35817i	−0.113657	+	0.482559i
$301$	−0.535193	+	0.926981i	−0.0308480	+	0.0534303i
$302$	0.315574	−	0.546591i	0.0181593	−	0.0314528i
$303$	−18.7502	+	5.64199i	−1.07717	+	0.324124i
$304$	−3.72573	+	6.45316i	−0.213685	+	0.370114i
$305$	−0.550698	+	0.953836i	−0.0315328	+	0.0546165i
$306$	−0.673203	−	11.0278i	−0.0384845	−	0.630418i
$307$	−14.0572			−0.802285			−0.401142	−	0.916016i	$-0.631387\pi$
$307$	−14.0572			−0.802285			−0.401142	+	0.916016i	$0.631387\pi$
$308$	−3.03147	−	5.25066i	−0.172734	−	0.299184i
$309$	−23.5730	−	22.1779i	−1.34102	−	1.26165i
$310$	0.309127	−	0.535423i	0.0175572	−	0.0304100i
$311$	−4.74354	−	8.21605i	−0.268981	−	0.465890i	0.699618	−	0.714517i	$-0.253354\pi$
$311$	−4.74354	−	8.21605i	−0.268981	−	0.465890i	−0.968599	+	0.248628i	$0.920020\pi$
$312$	−1.19739	+	6.12913i	−0.0677889	+	0.346994i
$313$	−16.9273	+	29.3190i	−0.956790	+	1.65721i	−0.226573	+	0.973994i	$0.572752\pi$
$313$	−16.9273	+	29.3190i	−0.956790	+	1.65721i	−0.730217	+	0.683215i	$0.760581\pi$
$314$	8.62325	+	14.9359i	0.486638	+	0.842882i
$315$	−0.0586638	−	0.960976i	−0.00330533	−	0.0541449i
$316$	0.829455	−	1.43666i	0.0466605	−	0.0808183i
$317$	−3.53923	+	6.13013i	−0.198783	+	0.344302i	−0.948134	−	0.317871i	$-0.897032\pi$
$317$	−3.53923	+	6.13013i	−0.198783	+	0.344302i	0.749351	+	0.662173i	$0.230366\pi$
$318$	15.7947	−	4.75267i	0.885724	−	0.266517i
$319$	18.9622			1.06168
$320$	−0.102915	−	0.178255i	−0.00575314	−	0.00996474i
$321$	14.4160	+	13.5628i	0.804622	+	0.757001i
$322$	5.25325			0.292752
$323$	−13.7210	−	23.7655i	−0.763459	−	1.32235i
$324$	3.51851	−	8.28373i	0.195473	−	0.460207i
$325$	9.52496	+	15.1258i	0.528350	+	0.839030i
$326$	−1.67055	+	2.89347i	−0.0925229	+	0.160254i
$327$	10.6125	−	3.19332i	0.586871	−	0.176591i
$328$	−1.74646	+	3.02496i	−0.0964321	+	0.167025i
$329$	−4.62694			−0.255092
$330$	1.00970	+	0.949945i	0.0555824	+	0.0522927i
$331$	6.47693	+	11.2184i	0.356004	+	0.616618i	0.987289	−	0.158933i	$-0.0508055\pi$
$331$	6.47693	+	11.2184i	0.356004	+	0.616618i	−0.631285	+	0.775551i	$0.717472\pi$
$332$	−4.34020	+	7.51744i	−0.238199	+	0.412573i
$333$	23.5222	+	11.7311i	1.28901	+	0.642862i
$334$	−10.5805	+	18.3260i	−0.578939	+	1.00275i
$335$	−0.624448			−0.0341172
$336$	−1.96688	−	1.85047i	−0.107302	−	0.100952i
$337$	9.11943	+	15.7953i	0.496767	+	0.860425i	0.999993	−	0.00372930i	$-0.00118707\pi$
$337$	9.11943	+	15.7953i	0.496767	+	0.860425i	−0.503226	+	0.864155i	$0.667854\pi$
$338$	7.34428	+	10.7267i	0.399476	+	0.583454i
$339$	−21.5232	+	6.47640i	−1.16898	+	0.351750i
$340$	0.758029			0.0411099
$341$	5.84011	+	10.1154i	0.316259	+	0.547777i
$342$	−1.36211	−	22.3128i	−0.0736545	−	1.20654i
$343$	18.0379			0.973956
$344$	−0.343259	−	0.594541i	−0.0185073	−	0.0320555i
$345$	−1.15024	+	0.346110i	−0.0619269	+	0.0186339i
$346$	−11.2917	−	19.5577i	−0.607043	−	1.05143i
$347$	−12.4970			−0.670877			−0.335438	−	0.942062i	$-0.608884\pi$
$347$	−12.4970			−0.670877			−0.335438	+	0.942062i	$0.608884\pi$
$348$	8.08785	−	2.43365i	0.433554	−	0.130458i
$349$	2.01307			0.107757			0.0538787	−	0.998547i	$-0.482842\pi$
$349$	2.01307			0.107757			0.0538787	+	0.998547i	$0.482842\pi$
$350$	−7.72971			−0.413171
$351$	−7.15121	−	17.3165i	−0.381703	−	0.924285i
$352$	3.88861			0.207264
$353$	−36.1145			−1.92218			−0.961091	−	0.276233i	$-0.910914\pi$
$353$	−36.1145			−1.92218			−0.961091	+	0.276233i	$0.910914\pi$
$354$	10.9476	−	3.29418i	0.581861	−	0.175083i
$355$	0.575126			0.0305245
$356$	6.25792	+	10.8390i	0.331669	+	0.574468i
$357$	9.52366	−	2.86569i	0.504046	−	0.151669i
$358$	−5.40388	−	9.35979i	−0.285604	−	0.494680i
$359$	34.3296			1.81185			0.905923	−	0.423442i	$-0.139178\pi$
$359$	34.3296			1.81185			0.905923	+	0.423442i	$0.139178\pi$
$360$	0.552583	+	0.275588i	0.0291237	+	0.0145248i
$361$	−18.2621	−	31.6310i	−0.961165	−	1.66479i
$362$	−13.6295			−0.716350
$363$	−6.83551	+	2.05682i	−0.358771	+	0.107955i
$364$	−5.61747	+	0.215725i	−0.294435	+	0.0113071i
$365$	1.57835	+	2.73378i	0.0826145	+	0.143093i
$366$	−6.75029	−	6.35078i	−0.352843	−	0.331961i
$367$	−5.05771			−0.264010			−0.132005	−	0.991249i	$-0.542142\pi$
$367$	−5.05771			−0.264010			−0.132005	+	0.991249i	$0.542142\pi$
$368$	−1.68465	+	2.91790i	−0.0878183	+	0.152106i
$369$	−0.638498	−	10.4593i	−0.0332389	−	0.544489i
$370$	−0.901716	+	1.56182i	−0.0468780	+	0.0811951i
$371$	7.42389	+	12.8586i	0.385429	+	0.667583i
$372$	3.78919	+	3.56493i	0.196460	+	0.184833i
$373$	−27.0459			−1.40038			−0.700191	−	0.713955i	$-0.746902\pi$
$373$	−27.0459			−1.40038			−0.700191	+	0.713955i	$0.746902\pi$
$374$	−7.16044	+	12.4022i	−0.370258	+	0.641305i
$375$	3.39943	−	1.02290i	0.175546	−	0.0528221i
$376$	1.48380	−	2.57002i	0.0765211	−	0.132538i
$377$	8.20017	−	15.5525i	0.422330	−	0.800994i
$378$	7.98434	+	1.37339i	0.410670	+	0.0706397i
$379$	3.71240	+	6.43007i	0.190693	+	0.330290i	0.945480	−	0.325680i	$-0.105593\pi$
$379$	3.71240	+	6.43007i	0.190693	+	0.330290i	−0.754787	+	0.655970i	$0.772260\pi$
$380$	1.53374			0.0786792
$381$	14.1528	+	13.3152i	0.725070	+	0.682157i
$382$	5.95622	+	10.3165i	0.304747	+	0.527837i
$383$	30.9084			1.57935			0.789673	−	0.613528i	$-0.210250\pi$
$383$	30.9084			1.57935			0.789673	+	0.613528i	$0.210250\pi$
$384$	1.65859	−	0.499074i	0.0846396	−	0.0254683i
$385$	−0.623969	+	1.08075i	−0.0318004	+	0.0550800i
$386$	11.9054	−	20.6208i	0.605971	−	1.04957i
$387$	1.84306	+	0.919181i	0.0936878	+	0.0467246i
$388$	−3.28917	−	5.69701i	−0.166982	−	0.289222i
$389$	−4.51699	+	7.82366i	−0.229020	+	0.396675i	−0.957518	−	0.288373i	$-0.906886\pi$
$389$	−4.51699	+	7.82366i	−0.229020	+	0.396675i	0.728498	+	0.685048i	$0.240219\pi$
$390$	1.21578	−	0.417341i	0.0615632	−	0.0211329i
$391$	−6.20418	−	10.7460i	−0.313759	−	0.543447i
$392$	−2.28452	+	3.95690i	−0.115386	+	0.199854i
$393$	−0.586151	−	0.551460i	−0.0295674	−	0.0278175i
$394$	3.84864	+	6.66603i	0.193891	+	0.335830i
$395$	−0.341455			−0.0171804
$396$	−9.72871	+	6.43767i	−0.488886	+	0.323505i
$397$	7.41951	−	12.8510i	0.372374	−	0.644971i	−0.617556	−	0.786527i	$-0.711877\pi$
$397$	7.41951	−	12.8510i	0.372374	−	0.644971i	0.989930	+	0.141556i	$0.0452104\pi$
$398$	−3.23845	+	5.60917i	−0.162329	+	0.281162i
$399$	19.2695	−	5.79823i	0.964680	−	0.290275i
$400$	2.47882	−	4.29344i	0.123941	−	0.214672i
$401$	−8.08912	+	14.0108i	−0.403951	+	0.699664i	−0.994199	−	0.107558i	$-0.965697\pi$
$401$	−8.08912	+	14.0108i	−0.403951	+	0.699664i	0.590247	+	0.807222i	$0.299030\pi$
$402$	1.20467	−	5.11473i	0.0600836	−	0.255100i
$403$	10.8220	−	0.415593i	0.539083	−	0.0207022i
$404$	11.3049			0.562440
$405$	−1.83872	+	0.225333i	−0.0913668	+	0.0111969i
$406$	3.80148	+	6.58435i	0.188664	+	0.326776i
$407$	−17.0355	−	29.5063i	−0.844417	−	1.46257i
$408$	−1.46237	+	6.20887i	−0.0723983	+	0.307385i
$409$	1.94673			0.0962595			0.0481298	−	0.998841i	$-0.484674\pi$
$409$	1.94673			0.0962595			0.0481298	+	0.998841i	$0.484674\pi$
$410$	0.718950			0.0355064
$411$	−19.4234	−	18.2739i	−0.958087	−	0.901383i
$412$	9.34320	+	16.1829i	0.460306	+	0.797274i
$413$	5.14565	+	8.91253i	0.253201	+	0.438557i
$414$	−0.615900	−	10.0891i	−0.0302698	−	0.495852i
$415$	1.78669			0.0877052
$416$	1.68162	−	3.18938i	0.0824484	−	0.156372i
$417$	−7.98960	+	2.40409i	−0.391252	+	0.117729i
$418$	−14.4879	+	25.0938i	−0.708627	+	1.22738i
$419$	−11.7449	+	20.3428i	−0.573778	+	0.993812i	0.422396	+	0.906412i	$0.361189\pi$
$419$	−11.7449	+	20.3428i	−0.573778	+	0.993812i	−0.996173	+	0.0874004i	$0.972144\pi$
$420$	−0.127433	+	0.541048i	−0.00621810	+	0.0264004i
$421$	1.97408	−	3.41921i	0.0962108	−	0.166642i	−0.813903	−	0.581001i	$-0.802661\pi$
$421$	1.97408	−	3.41921i	0.0962108	−	0.166642i	0.910113	+	0.414360i	$0.135994\pi$
$422$	−6.90747	+	11.9641i	−0.336250	+	0.582403i
$423$	0.542470	+	8.88625i	0.0263758	+	0.432064i
$424$	−9.52297			−0.462476
$425$	9.12893	+	15.8118i	0.442818	+	0.766984i
$426$	−1.10952	+	4.71074i	−0.0537565	+	0.228236i
$427$	4.17150	−	7.22525i	0.201873	−	0.349654i
$428$	−5.71380	−	9.89659i	−0.276187	−	0.478370i
$429$	−4.65618	+	23.8338i	−0.224803	+	1.15071i
$430$	−0.0706531	+	0.122375i	−0.00340720	+	0.00590144i
$431$	−14.3356	−	24.8300i	−0.690522	−	1.19602i	−0.971667	−	0.236354i	$-0.924047\pi$
$431$	−14.3356	−	24.8300i	−0.690522	−	1.19602i	0.281145	−	0.959665i	$-0.409286\pi$
$432$	−3.32332	+	3.99444i	−0.159893	+	0.192183i
$433$	−2.86328	+	4.95934i	−0.137600	+	0.238331i	−0.926588	−	0.376079i	$-0.877272\pi$
$433$	−2.86328	+	4.95934i	−0.137600	+	0.238331i	0.788988	+	0.614409i	$0.210606\pi$
$434$	−2.34161	+	4.05580i	−0.112401	+	0.194684i
$435$	−1.26617	−	1.19124i	−0.0607084	−	0.0571154i
$436$	−6.39848			−0.306432
$437$	−12.5531	−	21.7426i	−0.600496	−	1.04009i
$438$	−25.4368	+	7.65399i	−1.21542	+	0.365722i
$439$	38.9982			1.86128			0.930642	−	0.365931i	$-0.119249\pi$
$439$	38.9982			1.86128			0.930642	+	0.365931i	$0.119249\pi$
$440$	−0.400197	−	0.693162i	−0.0190787	−	0.0330452i
$441$	−0.835210	−	13.6816i	−0.0397719	−	0.651507i
$442$	7.07562	+	11.2362i	0.336553	+	0.534453i
$443$	19.4094	−	33.6180i	0.922167	−	1.59724i	0.126112	−	0.992016i	$-0.459750\pi$
$443$	19.4094	−	33.6180i	0.922167	−	1.59724i	0.796055	−	0.605224i	$-0.206917\pi$
$444$	−11.0530	−	10.3988i	−0.524551	−	0.493506i
$445$	1.28807	−	2.23101i	0.0610605	−	0.105760i
$446$	−11.8684			−0.561985
$447$	27.8607	−	8.38334i	1.31776	−	0.396519i
$448$	0.779577	+	1.35027i	0.0368315	+	0.0637941i
$449$	−13.3263	+	23.0818i	−0.628907	+	1.08930i	0.358865	+	0.933390i	$0.383164\pi$
$449$	−13.3263	+	23.0818i	−0.628907	+	1.08930i	−0.987771	+	0.155909i	$0.950169\pi$
$450$	0.906244	+	14.8453i	0.0427208	+	0.699813i
$451$	−6.79130	+	11.7629i	−0.319790	+	0.553892i
$452$	12.9768			0.610378
$453$	0.250619	−	1.06407i	0.0117751	−	0.0499941i
$454$	4.91697	+	8.51644i	0.230765	+	0.399696i
$455$	0.616578	+	0.979138i	0.0289056	+	0.0459027i
$456$	−2.95886	+	12.5626i	−0.138561	+	0.588296i
$457$	11.2829			0.527790			0.263895	−	0.964551i	$-0.414993\pi$
$457$	11.2829			0.527790			0.263895	+	0.964551i	$0.414993\pi$
$458$	−8.65591	−	14.9925i	−0.404464	−	0.700553i
$459$	−6.62026	−	17.9546i	−0.309007	−	0.838051i
$460$	0.693504			0.0323348
$461$	3.88317	+	6.72585i	0.180857	+	0.313254i	0.942173	−	0.335128i	$-0.108779\pi$
$461$	3.88317	+	6.72585i	0.180857	+	0.313254i	−0.761316	+	0.648382i	$0.775446\pi$
$462$	−7.64844	−	7.19577i	−0.355838	−	0.334777i
$463$	0.105633	+	0.182962i	0.00490918	+	0.00850295i	0.868470	−	0.495742i	$-0.165104\pi$
$463$	0.105633	+	0.182962i	0.00490918	+	0.00850295i	−0.863560	+	0.504245i	$0.831771\pi$
$464$	−4.87634			−0.226378
$465$	0.245499	−	1.04233i	0.0113847	−	0.0483367i
$466$	−17.6548			−0.817841
$467$	−34.8916			−1.61459			−0.807294	−	0.590149i	$-0.799069\pi$
$467$	−34.8916			−1.61459			−0.807294	+	0.590149i	$0.799069\pi$
$468$	1.07291	+	10.7633i	0.0495953	+	0.497534i
$469$	4.73015			0.218418
$470$	−0.610823			−0.0281752
$471$	21.7566	+	20.4689i	1.00249	+	0.943158i
$472$	−6.60057			−0.303816
$473$	−1.33480	−	2.31194i	−0.0613741	−	0.106303i
$474$	0.658728	−	2.79679i	0.0302564	−	0.128461i
$475$	18.4708	+	31.9924i	0.847499	+	1.46791i
$476$	−5.74202			−0.263185
$477$	23.8250	−	15.7655i	1.09087	−	0.721852i
$478$	0.631256	+	1.09337i	0.0288730	+	0.0500095i
$479$	−7.45915			−0.340817			−0.170409	−	0.985373i	$-0.554509\pi$
$479$	−7.45915			−0.340817			−0.170409	+	0.985373i	$0.554509\pi$
$480$	−0.259657	−	0.244289i	−0.0118517	−	0.0111502i
$481$	−31.5676	+	1.21228i	−1.43936	+	0.0552750i
$482$	−5.44455	−	9.43023i	−0.247992	−	0.429535i
$483$	8.71299	−	2.62176i	0.396455	−	0.119294i
$484$	4.12128			0.187331
$485$	−0.677012	+	1.17262i	−0.0307415	+	0.0532459i
$486$	1.70157	−	15.4953i	0.0771847	−	0.702882i
$487$	21.2844	−	36.8657i	0.964489	−	1.67054i	0.253509	−	0.967333i	$-0.418415\pi$
$487$	21.2844	−	36.8657i	0.964489	−	1.67054i	0.710981	−	0.703211i	$-0.248251\pi$
$488$	2.67549	+	4.63408i	0.121114	+	0.209775i
$489$	−1.32670	+	5.63281i	−0.0599953	+	0.254724i
$490$	0.940449			0.0424851
$491$	16.7098	−	28.9423i	0.754103	−	1.30615i	−0.191715	−	0.981451i	$-0.561405\pi$
$491$	16.7098	−	28.9423i	0.754103	−	1.30615i	0.945819	−	0.324695i	$-0.105262\pi$
$492$	−1.38698	+	5.88878i	−0.0625301	+	0.265487i
$493$	8.97923	−	15.5525i	0.404404	−	0.700449i
$494$	14.3163	+	22.7346i	0.644120	+	1.02288i
$495$	2.14878	+	1.07165i	0.0965804	+	0.0481672i
$496$	−1.50185	−	2.60128i	−0.0674350	−	0.116801i
$497$	−4.35654			−0.195418
$498$	−3.44685	+	14.6344i	−0.154457	+	0.655785i
$499$	3.44081	+	5.95966i	0.154032	+	0.266791i	0.932706	−	0.360637i	$-0.117441\pi$
$499$	3.44081	+	5.95966i	0.154032	+	0.266791i	−0.778674	+	0.627428i	$0.784107\pi$
$500$	−2.04959			−0.0916603
$501$	−8.40271	+	35.6757i	−0.375405	+	1.59387i
$502$	12.3336	−	21.3624i	0.550475	−	0.953450i
$503$	−13.4441	+	23.2858i	−0.599441	+	1.03826i	0.393463	+	0.919340i	$0.371277\pi$
$503$	−13.4441	+	23.2858i	−0.599441	+	1.03826i	−0.992904	+	0.118921i	$0.962056\pi$
$504$	−4.18578	−	2.08756i	−0.186449	−	0.0929873i
$505$	−1.16345	−	2.01515i	−0.0517728	−	0.0896731i
$506$	−6.55094	+	11.3466i	−0.291225	+	0.504416i
$507$	17.5346	+	14.1258i	0.778737	+	0.627350i
$508$	−5.60948	−	9.71591i	−0.248881	−	0.431074i
$509$	17.0186	−	29.4770i	0.754335	−	1.30655i	−0.191370	−	0.981518i	$-0.561293\pi$
$509$	17.0186	−	29.4770i	0.754335	−	1.30655i	0.945704	−	0.325028i	$-0.105374\pi$
$510$	1.25726	−	0.378313i	0.0556724	−	0.0167520i
$511$	−11.9559	−	20.7082i	−0.528897	−	0.916076i
$512$	−1.00000			−0.0441942
$513$	−13.3950	−	36.3281i	−0.591402	−	1.60392i
$514$	12.7687	−	22.1161i	0.563205	−	0.975499i
$515$	1.92312	−	3.33094i	0.0847427	−	0.146779i
$516$	−0.866046	−	0.814789i	−0.0381255	−	0.0358691i
$517$	5.76991	−	9.99379i	0.253761	−	0.439526i
$518$	6.83044	−	11.8307i	0.300112	−	0.519810i
$519$	−28.4890	−	26.8029i	−1.25053	−	1.17652i
$520$	−0.741586	+	0.0284788i	−0.0325207	+	0.00124888i
$521$	28.8015			1.26182			0.630909	−	0.775857i	$-0.282682\pi$
$521$	28.8015			1.26182			0.630909	+	0.775857i	$0.282682\pi$
$522$	12.1999	−	8.07287i	0.533973	−	0.353340i
$523$	11.0647	+	19.1647i	0.483827	+	0.838013i	0.999827	−	0.0185751i	$-0.00591297\pi$
$523$	11.0647	+	19.1647i	0.483827	+	0.838013i	−0.516000	+	0.856588i	$0.672580\pi$
$524$	0.232322	+	0.402393i	0.0101490	+	0.0175786i
$525$	−12.8204	+	3.85770i	−0.559530	+	0.168364i
$526$	12.4022			0.540761
$527$	11.0620			0.481866
$528$	6.44961	−	1.94070i	0.280683	−	0.0844583i
$529$	5.82393	+	10.0873i	0.253214	+	0.438580i
$530$	0.980060	+	1.69751i	0.0425711	+	0.0737353i
$531$	16.5136	−	10.9274i	0.716631	−	0.474208i
$532$	−11.6180			−0.503703
$533$	6.71085	+	10.6570i	0.290679	+	0.461604i
$534$	15.7888	+	14.8544i	0.683249	+	0.642811i
$535$	−1.17607	+	2.03702i	−0.0508461	+	0.0880681i
$536$	−1.51690	+	2.62734i	−0.0655200	+	0.113484i
$537$	−13.6341	−	12.8271i	−0.588353	−	0.553532i
$538$	−2.46813	+	4.27492i	−0.106408	+	0.184305i
$539$	−8.88360	+	15.3869i	−0.382644	+	0.662759i
$540$	1.05405	+	0.181308i	0.0453590	+	0.00780224i
$541$	20.1937			0.868196			0.434098	−	0.900866i	$-0.357067\pi$
$541$	20.1937			0.868196			0.434098	+	0.900866i	$0.357067\pi$
$542$	−13.7565	−	23.8269i	−0.590892	−	1.02345i
$543$	−22.6058	+	6.80213i	−0.970106	+	0.291907i
$544$	1.84139	−	3.18938i	0.0789489	−	0.136744i
$545$	0.658502	+	1.14056i	0.0282071	+	0.0488562i
$546$	−9.20942	+	3.16133i	−0.394127	+	0.135293i
$547$	−2.75008	+	4.76328i	−0.117585	+	0.203663i	−0.918810	−	0.394700i	$-0.870849\pi$
$547$	−2.75008	+	4.76328i	−0.117585	+	0.203663i	0.801225	+	0.598363i	$0.204182\pi$
$548$	7.69850	+	13.3342i	0.328864	+	0.569609i
$549$	−14.3655	−	7.16445i	−0.613104	−	0.305771i
$550$	9.63915	−	16.6955i	0.411015	−	0.711898i
$551$	18.1679	−	31.4678i	0.773979	−	1.34057i
$552$	−1.33790	+	5.68036i	−0.0569446	+	0.241772i
$553$	2.58650			0.109989
$554$	−1.33384	−	2.31027i	−0.0566693	−	0.0981542i
$555$	−0.716115	+	3.04044i	−0.0303974	+	0.129060i
$556$	4.81710			0.204290
$557$	−12.6702	−	21.9455i	−0.536856	−	0.929861i	−0.999071	−	0.0430936i	$-0.986279\pi$
$557$	−12.6702	−	21.9455i	−0.536856	−	0.929861i	0.462215	−	0.886768i	$-0.347055\pi$
$558$	8.06387	+	4.02167i	0.341371	+	0.170251i
$559$	−2.47345	+	0.0949868i	−0.104616	+	0.00401751i
$560$	0.160461	−	0.277926i	0.00678071	−	0.0117445i
$561$	−5.68660	+	24.1439i	−0.240089	+	1.01935i
$562$	5.51262	−	9.54813i	0.232536	−	0.402764i
$563$	21.5657			0.908884			0.454442	−	0.890776i	$-0.349839\pi$
$563$	21.5657			0.908884			0.454442	+	0.890776i	$0.349839\pi$
$564$	1.17839	−	5.00313i	0.0496191	−	0.210670i
$565$	−1.33551	−	2.31318i	−0.0561855	−	0.0973161i
$566$	2.43391	−	4.21565i	0.102305	−	0.177197i
$567$	13.9282	−	1.70688i	0.584929	−	0.0716823i
$568$	1.39708	−	2.41982i	0.0586204	−	0.101533i
$569$	−0.571838			−0.0239727			−0.0119864	−	0.999928i	$-0.503815\pi$
$569$	−0.571838			−0.0239727			−0.0119864	+	0.999928i	$0.503815\pi$
$570$	2.54385	−	0.765450i	0.106550	−	0.0320612i
$571$	−5.02115	−	8.69689i	−0.210129	−	0.363953i	0.741626	−	0.670814i	$-0.234055\pi$
$571$	−5.02115	−	8.69689i	−0.210129	−	0.363953i	−0.951755	+	0.306860i	$0.900722\pi$
$572$	6.53918	−	12.4022i	0.273417	−	0.518564i
$573$	15.0276	+	14.1382i	0.627788	+	0.590632i
$574$	−5.44600			−0.227312
$575$	8.35187	+	14.4659i	0.348297	+	0.603268i
$576$	2.50185	−	1.65552i	0.104244	−	0.0689800i
$577$	−16.7133			−0.695785			−0.347892	−	0.937534i	$-0.613103\pi$
$577$	−16.7133			−0.695785			−0.347892	+	0.937534i	$0.613103\pi$
$578$	−1.71857	−	2.97666i	−0.0714832	−	0.123813i
$579$	9.45494	−	40.1432i	0.392934	−	1.66830i
$580$	0.501850	+	0.869229i	0.0208382	+	0.0360928i
$581$	−13.5341			−0.561488
$582$	−8.29862	−	7.80747i	−0.343989	−	0.323630i
$583$	−37.0311			−1.53367
$584$	15.3364			0.634624
$585$	1.80819	−	1.29896i	0.0747595	−	0.0537054i
$586$	8.49447			0.350903
$587$	1.93733			0.0799620			0.0399810	−	0.999200i	$-0.487270\pi$
$587$	1.93733			0.0799620			0.0399810	+	0.999200i	$0.487270\pi$
$588$	−1.81430	+	7.70303i	−0.0748203	+	0.317668i
$589$	22.3820			0.922232
$590$	0.679300	+	1.17658i	0.0279663	+	0.0484391i
$591$	9.71016	+	9.13547i	0.399423	+	0.375783i
$592$	4.38086	+	7.58788i	0.180052	+	0.311860i
$593$	45.4544			1.86659			0.933294	−	0.359113i	$-0.116921\pi$
$593$	45.4544			1.86659			0.933294	+	0.359113i	$0.116921\pi$
$594$	−12.9231	+	15.5328i	−0.530241	+	0.637319i
$595$	0.590942	+	1.02354i	0.0242262	+	0.0419611i
$596$	−16.7978			−0.688064
$597$	−2.57188	+	10.9195i	−0.105260	+	0.446907i
$598$	6.47333	+	10.2798i	0.264714	+	0.420372i
$599$	11.8317	+	20.4932i	0.483431	+	0.837327i	0.999819	−	0.0190274i	$-0.00605698\pi$
$599$	11.8317	+	20.4932i	0.483431	+	0.837327i	−0.516388	+	0.856355i	$0.672724\pi$
$600$	1.96860	−	8.35817i	0.0803678	−	0.341221i
$601$	−33.3662			−1.36104			−0.680519	−	0.732731i	$-0.738246\pi$
$601$	−33.3662			−1.36104			−0.680519	+	0.732731i	$0.738246\pi$
$602$	0.535193	−	0.926981i	0.0218128	−	0.0377809i
$603$	−0.554571	−	9.08447i	−0.0225839	−	0.369948i
$604$	−0.315574	+	0.546591i	−0.0128405	+	0.0222405i
$605$	−0.424143	−	0.734637i	−0.0172439	−	0.0298672i
$606$	18.7502	−	5.64199i	0.761676	−	0.229190i
$607$	−29.0036			−1.17722			−0.588610	−	0.808417i	$-0.700324\pi$
$607$	−29.0036			−1.17722			−0.588610	+	0.808417i	$0.700324\pi$
$608$	3.72573	−	6.45316i	0.151098	−	0.261710i
$609$	9.59118	+	9.02353i	0.388654	+	0.365652i
$610$	0.550698	−	0.953836i	0.0222971	−	0.0386197i
$611$	−5.70156	−	9.05420i	−0.230661	−	0.366294i
$612$	0.673203	+	11.0278i	0.0272126	+	0.445773i
$613$	−2.55168	−	4.41964i	−0.103061	−	0.178507i	0.809883	−	0.586591i	$-0.199530\pi$
$613$	−2.55168	−	4.41964i	−0.103061	−	0.178507i	−0.912944	+	0.408084i	$0.866197\pi$
$614$	14.0572			0.567301
$615$	1.19244	−	0.358809i	0.0480840	−	0.0144686i
$616$	3.03147	+	5.25066i	0.122141	+	0.211555i
$617$	9.12456			0.367341			0.183671	−	0.982988i	$-0.441202\pi$
$617$	9.12456			0.367341			0.183671	+	0.982988i	$0.441202\pi$
$618$	23.5730	+	22.1779i	0.948246	+	0.892124i
$619$	4.97487	−	8.61673i	0.199957	−	0.346336i	−0.748557	−	0.663070i	$-0.769253\pi$
$619$	4.97487	−	8.61673i	0.199957	−	0.346336i	0.948514	+	0.316734i	$0.102586\pi$
$620$	−0.309127	+	0.535423i	−0.0124148	+	0.0215031i
$621$	−6.05674	−	16.4263i	−0.243048	−	0.659165i
$622$	4.74354	+	8.21605i	0.190199	+	0.329434i
$623$	−9.75707	+	16.8997i	−0.390909	+	0.677073i
$624$	1.19739	−	6.12913i	0.0479340	−	0.245362i
$625$	−12.1832	−	21.1018i	−0.487326	−	0.844073i
$626$	16.9273	−	29.3190i	0.676553	−	1.17182i
$627$	−11.5059	+	48.8509i	−0.459500	+	1.95092i
$628$	−8.62325	−	14.9359i	−0.344105	−	0.596008i
$629$	−32.2675			−1.28659
$630$	0.0586638	+	0.960976i	0.00233722	+	0.0382862i
$631$	22.5331	−	39.0284i	0.897027	−	1.55370i	0.0657504	−	0.997836i	$-0.479056\pi$
$631$	22.5331	−	39.0284i	0.897027	−	1.55370i	0.831276	−	0.555860i	$-0.187611\pi$
$632$	−0.829455	+	1.43666i	−0.0329939	+	0.0571472i
$633$	−5.48570	+	23.2909i	−0.218037	+	0.925729i
$634$	3.53923	−	6.13013i	0.140561	−	0.243458i
$635$	−1.15460	+	1.99983i	−0.0458190	+	0.0793609i
$636$	−15.7947	+	4.75267i	−0.626301	+	0.188456i
$637$	8.77836	+	13.9402i	0.347811	+	0.552332i
$638$	−18.9622			−0.750719
$639$	0.510768	+	8.36693i	0.0202057	+	0.330991i
$640$	0.102915	+	0.178255i	0.00406809	+	0.00704613i
$641$	18.2836	+	31.6682i	0.722160	+	1.25082i	0.960132	+	0.279546i	$0.0901841\pi$
$641$	18.2836	+	31.6682i	0.722160	+	1.25082i	−0.237972	+	0.971272i	$0.576483\pi$
$642$	−14.4160	−	13.5628i	−0.568954	−	0.535280i
$643$	−25.2155			−0.994402			−0.497201	−	0.867635i	$-0.665639\pi$
$643$	−25.2155			−0.994402			−0.497201	+	0.867635i	$0.665639\pi$
$644$	−5.25325			−0.207007
$645$	−0.0561106	+	0.238231i	−0.00220935	+	0.00938034i
$646$	13.7210	+	23.7655i	0.539847	+	0.935043i
$647$	0.159617	+	0.276465i	0.00627519	+	0.0108689i	0.869146	−	0.494556i	$-0.164669\pi$
$647$	0.159617	+	0.276465i	0.00627519	+	0.0108689i	−0.862871	+	0.505425i	$0.831336\pi$
$648$	−3.51851	+	8.28373i	−0.138220	+	0.325416i
$649$	−25.6670			−1.00752
$650$	−9.52496	−	15.1258i	−0.373600	−	0.593284i
$651$	−1.85964	+	7.89555i	−0.0728850	+	0.309451i
$652$	1.67055	−	2.89347i	0.0654236	−	0.113317i
$653$	19.7365	−	34.1847i	0.772350	−	1.33775i	−0.163922	−	0.986473i	$-0.552414\pi$
$653$	19.7365	−	34.1847i	0.772350	−	1.33775i	0.936272	−	0.351276i	$-0.114252\pi$
$654$	−10.6125	+	3.19332i	−0.414980	+	0.124869i
$655$	0.0478189	−	0.0828248i	0.00186844	−	0.00323623i
$656$	1.74646	−	3.02496i	0.0681878	−	0.118105i
$657$	−38.3693	+	25.3897i	−1.49693	+	0.990546i
$658$	4.62694			0.180377
$659$	21.0981	+	36.5430i	0.821866	+	1.42351i	0.904291	+	0.426917i	$0.140400\pi$
$659$	21.0981	+	36.5430i	0.821866	+	1.42351i	−0.0824246	+	0.996597i	$0.526266\pi$
$660$	−1.00970	−	0.949945i	−0.0393027	−	0.0369766i
$661$	−14.6644	+	25.3995i	−0.570380	+	0.987928i	0.426146	+	0.904654i	$0.359871\pi$
$661$	−14.6644	+	25.3995i	−0.570380	+	0.987928i	−0.996527	+	0.0832736i	$0.973462\pi$
$662$	−6.47693	−	11.2184i	−0.251733	−	0.436015i
$663$	17.3433	+	15.1050i	0.673557	+	0.586631i
$664$	4.34020	−	7.51744i	0.168432	−	0.291733i
$665$	1.19567	+	2.07096i	0.0463660	+	0.0803083i
$666$	−23.5222	−	11.7311i	−0.911465	−	0.454572i
$667$	8.21491	−	14.2286i	0.318083	−	0.550935i
$668$	10.5805	−	18.3260i	0.409372	−	0.709053i
$669$	−19.6848	+	5.92321i	−0.761059	+	0.229005i
$670$	0.624448			0.0241245
$671$	10.4039	+	18.0201i	0.401639	+	0.695659i
$672$	1.96688	+	1.85047i	0.0758741	+	0.0713836i
$673$	−44.3927			−1.71121			−0.855607	−	0.517627i	$-0.826816\pi$
$673$	−44.3927			−1.71121			−0.855607	+	0.517627i	$0.826816\pi$
$674$	−9.11943	−	15.7953i	−0.351267	−	0.608413i
$675$	8.91198	+	24.1699i	0.343022	+	0.930302i
$676$	−7.34428	−	10.7267i	−0.282472	−	0.412564i
$677$	−0.870301	+	1.50741i	−0.0334484	+	0.0579343i	−0.882265	−	0.470753i	$-0.843982\pi$
$677$	−0.870301	+	1.50741i	−0.0334484	+	0.0579343i	0.848817	+	0.528687i	$0.177316\pi$
$678$	21.5232	−	6.47640i	0.826595	−	0.248725i
$679$	5.12832	−	8.88252i	0.196807	−	0.340880i
$680$	−0.758029			−0.0290691
$681$	12.4056	+	11.6714i	0.475383	+	0.447248i
$682$	−5.84011	−	10.1154i	−0.223629	−	0.387337i
$683$	7.31521	−	12.6703i	0.279909	−	0.484816i	−0.691453	−	0.722421i	$-0.743029\pi$
$683$	7.31521	−	12.6703i	0.279909	−	0.484816i	0.971362	+	0.237605i	$0.0763625\pi$
$684$	1.36211	+	22.3128i	0.0520816	+	0.853153i
$685$	1.58459	−	2.74459i	0.0605440	−	0.104865i
$686$	−18.0379			−0.688691
$687$	−21.8390	−	20.5465i	−0.833209	−	0.783896i
$688$	0.343259	+	0.594541i	0.0130866	+	0.0226667i
$689$	−16.0141	+	30.3724i	−0.610087	+	1.15710i
$690$	1.15024	−	0.346110i	0.0437889	−	0.0131762i
$691$	−18.0550			−0.686844			−0.343422	−	0.939181i	$-0.611586\pi$
$691$	−18.0550			−0.686844			−0.343422	+	0.939181i	$0.611586\pi$
$692$	11.2917	+	19.5577i	0.429244	+	0.743473i
$693$	−16.2769	−	8.11770i	−0.618307	−	0.308366i
$694$	12.4970			0.474381
$695$	−0.495753	−	0.858670i	−0.0188050	−	0.0325712i
$696$	−8.08785	+	2.43365i	−0.306569	+	0.0922474i
$697$	6.43182	+	11.1402i	0.243623	+	0.421967i
$698$	−2.01307			−0.0761960
$699$	−29.2820	+	8.81104i	−1.10755	+	0.333264i
$700$	7.72971			0.292156
$701$	−20.6019			−0.778122			−0.389061	−	0.921212i	$-0.627201\pi$
$701$	−20.6019			−0.778122			−0.389061	+	0.921212i	$0.627201\pi$
$702$	7.15121	+	17.3165i	0.269905	+	0.653568i
$703$	−65.2877			−2.46237
$704$	−3.88861			−0.146557
$705$	−1.01311	+	0.304846i	−0.0381558	+	0.0114812i
$706$	36.1145			1.35919
$707$	8.81305	+	15.2646i	0.331449	+	0.574086i
$708$	−10.9476	+	3.29418i	−0.411438	+	0.123803i
$709$	9.83614	+	17.0367i	0.369404	+	0.639826i	0.989472	−	0.144721i	$-0.0462286\pi$
$709$	9.83614	+	17.0367i	0.369404	+	0.639826i	−0.620069	+	0.784548i	$0.712895\pi$
$710$	−0.575126			−0.0215841
$711$	−0.303245	−	4.96748i	−0.0113726	−	0.186295i
$712$	−6.25792	−	10.8390i	−0.234526	−	0.406210i
$713$	10.1204			0.379010
$714$	−9.52366	+	2.86569i	−0.356414	+	0.107246i
$715$	−2.88374	+	0.110743i	−0.107846	+	0.00414155i
$716$	5.40388	+	9.35979i	0.201952	+	0.349792i
$717$	1.59267	+	1.49841i	0.0594793	+	0.0559590i
$718$	−34.3296			−1.28117
$719$	−15.9912	+	27.6975i	−0.596370	+	1.03294i	0.396982	+	0.917827i	$0.370058\pi$
$719$	−15.9912	+	27.6975i	−0.596370	+	1.03294i	−0.993352	+	0.115117i	$0.963276\pi$
$720$	−0.552583	−	0.275588i	−0.0205935	−	0.0102706i
$721$	−14.5675	+	25.2316i	−0.542521	+	0.939675i
$722$	18.2621	+	31.6310i	0.679647	+	1.17718i
$723$	−13.7367	−	12.9237i	−0.510872	−	0.480636i
$724$	13.6295			0.506536
$725$	−12.0875	+	20.9362i	−0.448920	+	0.777552i
$726$	6.83551	−	2.05682i	0.253690	−	0.0763359i
$727$	−3.26856	+	5.66131i	−0.121224	+	0.209966i	−0.920251	−	0.391329i	$-0.872015\pi$
$727$	−3.26856	+	5.66131i	−0.121224	+	0.209966i	0.799027	+	0.601296i	$0.205349\pi$
$728$	5.61747	−	0.215725i	0.208197	−	0.00799530i
$729$	−4.91111	−	26.5496i	−0.181893	−	0.983318i
$730$	−1.57835	−	2.73378i	−0.0584173	−	0.101182i
$731$	−2.52829			−0.0935122
$732$	6.75029	+	6.35078i	0.249498	+	0.234732i
$733$	−2.15768	−	3.73721i	−0.0796956	−	0.138037i	0.823423	−	0.567428i	$-0.192062\pi$
$733$	−2.15768	−	3.73721i	−0.0796956	−	0.138037i	−0.903119	+	0.429391i	$0.858728\pi$
$734$	5.05771			0.186683
$735$	1.55982	−	0.469354i	0.0575348	−	0.0173124i
$736$	1.68465	−	2.91790i	0.0620969	−	0.107555i
$737$	−5.89862	+	10.2167i	−0.217278	+	0.376337i
$738$	0.638498	+	10.4593i	0.0235034	+	0.385012i
$739$	−4.64539	−	8.04606i	−0.170884	−	0.295979i	0.767845	−	0.640635i	$-0.221329\pi$
$739$	−4.64539	−	8.04606i	−0.170884	−	0.295979i	−0.938729	+	0.344656i	$0.887996\pi$
$740$	0.901716	−	1.56182i	0.0331477	−	0.0574136i
$741$	35.0911	+	30.5624i	1.28910	+	1.12274i
$742$	−7.42389	−	12.8586i	−0.272540	−	0.472052i
$743$	1.47826	−	2.56043i	0.0542322	−	0.0939329i	−0.837635	−	0.546231i	$-0.816062\pi$
$743$	1.47826	−	2.56043i	0.0542322	−	0.0939329i	0.891867	+	0.452298i	$0.149396\pi$
$744$	−3.78919	−	3.56493i	−0.138918	−	0.130697i
$745$	1.72875	+	2.99428i	0.0633365	+	0.109702i
$746$	27.0459			0.990220
$747$	1.58676	+	25.9928i	0.0580564	+	0.951026i
$748$	7.16044	−	12.4022i	0.261812	−	0.453471i
$749$	8.90869	−	15.4303i	0.325516	−	0.563811i
$750$	−3.39943	+	1.02290i	−0.124129	+	0.0373509i
$751$	−9.89013	+	17.1302i	−0.360896	+	0.625090i	−0.988109	−	0.153758i	$-0.950862\pi$
$751$	−9.89013	+	17.1302i	−0.360896	+	0.625090i	0.627213	+	0.778848i	$0.284196\pi$
$752$	−1.48380	+	2.57002i	−0.0541086	+	0.0937188i
$753$	9.79495	−	41.5869i	0.356948	−	1.51551i
$754$	−8.20017	+	15.5525i	−0.298632	+	0.566388i
$755$	0.129910			0.00472790
$756$	−7.98434	−	1.37339i	−0.290388	−	0.0499498i
$757$	17.1539	+	29.7115i	0.623470	+	1.07988i	0.988835	+	0.149017i	$0.0476109\pi$
$757$	17.1539	+	29.7115i	0.623470	+	1.07988i	−0.365365	+	0.930864i	$0.619056\pi$
$758$	−3.71240	−	6.43007i	−0.134840	−	0.233551i
$759$	−5.20255	+	22.0887i	−0.188841	+	0.801769i
$760$	−1.53374			−0.0556346
$761$	−6.16063			−0.223323			−0.111661	−	0.993746i	$-0.535617\pi$
$761$	−6.16063			−0.223323			−0.111661	+	0.993746i	$0.535617\pi$
$762$	−14.1528	−	13.3152i	−0.512702	−	0.482358i
$763$	−4.98811	−	8.63965i	−0.180582	−	0.312777i
$764$	−5.95622	−	10.3165i	−0.215488	−	0.373237i
$765$	1.89647	−	1.25493i	0.0685672	−	0.0453722i
$766$	−30.9084			−1.11677
$767$	−11.0997	+	21.0517i	−0.400786	+	0.760134i
$768$

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.65859 + 0.499074i) q^{3} +1.00000 q^{4} +(-0.102915 - 0.178255i) q^{5} +(1.65859 - 0.499074i) q^{6} +(0.779577 + 1.35027i) q^{7} -1.00000 q^{8} +(2.50185 - 1.65552i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.65859 + 0.499074i) q^{3} +1.00000 q^{4} +(-0.102915 - 0.178255i) q^{5} +(1.65859 - 0.499074i) q^{6} +(0.779577 + 1.35027i) q^{7} -1.00000 q^{8} +(2.50185 - 1.65552i) q^{9} +(0.102915 + 0.178255i) q^{10} -3.88861 q^{11} +(-1.65859 + 0.499074i) q^{12} +(-1.68162 + 3.18938i) q^{13} +(-0.779577 - 1.35027i) q^{14} +(0.259657 + 0.244289i) q^{15} +1.00000 q^{16} +(-1.84139 + 3.18938i) q^{17} +(-2.50185 + 1.65552i) q^{18} +(-3.72573 + 6.45316i) q^{19} +(-0.102915 - 0.178255i) q^{20} +(-1.96688 - 1.85047i) q^{21} +3.88861 q^{22} +(-1.68465 + 2.91790i) q^{23} +(1.65859 - 0.499074i) q^{24} +(2.47882 - 4.29344i) q^{25} +(1.68162 - 3.18938i) q^{26} +(-3.32332 + 3.99444i) q^{27} +(0.779577 + 1.35027i) q^{28} -4.87634 q^{29} +(-0.259657 - 0.244289i) q^{30} +(-1.50185 - 2.60128i) q^{31} -1.00000 q^{32} +(6.44961 - 1.94070i) q^{33} +(1.84139 - 3.18938i) q^{34} +(0.160461 - 0.277926i) q^{35} +(2.50185 - 1.65552i) q^{36} +(4.38086 + 7.58788i) q^{37} +(3.72573 - 6.45316i) q^{38} +(1.19739 - 6.12913i) q^{39} +(0.102915 + 0.178255i) q^{40} +(1.74646 - 3.02496i) q^{41} +(1.96688 + 1.85047i) q^{42} +(0.343259 + 0.594541i) q^{43} -3.88861 q^{44} +(-0.552583 - 0.275588i) q^{45} +(1.68465 - 2.91790i) q^{46} +(-1.48380 + 2.57002i) q^{47} +(-1.65859 + 0.499074i) q^{48} +(2.28452 - 3.95690i) q^{49} +(-2.47882 + 4.29344i) q^{50} +(1.46237 - 6.20887i) q^{51} +(-1.68162 + 3.18938i) q^{52} +9.52297 q^{53} +(3.32332 - 3.99444i) q^{54} +(0.400197 + 0.693162i) q^{55} +(-0.779577 - 1.35027i) q^{56} +(2.95886 - 12.5626i) q^{57} +4.87634 q^{58} +6.60057 q^{59} +(0.259657 + 0.244289i) q^{60} +(-2.67549 - 4.63408i) q^{61} +(1.50185 + 2.60128i) q^{62} +(4.18578 + 2.08756i) q^{63} +1.00000 q^{64} +(0.741586 - 0.0284788i) q^{65} +(-6.44961 + 1.94070i) q^{66} +(1.51690 - 2.62734i) q^{67} +(-1.84139 + 3.18938i) q^{68} +(1.33790 - 5.68036i) q^{69} +(-0.160461 + 0.277926i) q^{70} +(-1.39708 + 2.41982i) q^{71} +(-2.50185 + 1.65552i) q^{72} -15.3364 q^{73} +(-4.38086 - 7.58788i) q^{74} +(-1.96860 + 8.35817i) q^{75} +(-3.72573 + 6.45316i) q^{76} +(-3.03147 - 5.25066i) q^{77} +(-1.19739 + 6.12913i) q^{78} +(0.829455 - 1.43666i) q^{79} +(-0.102915 - 0.178255i) q^{80} +(3.51851 - 8.28373i) q^{81} +(-1.74646 + 3.02496i) q^{82} +(-4.34020 + 7.51744i) q^{83} +(-1.96688 - 1.85047i) q^{84} +0.758029 q^{85} +(-0.343259 - 0.594541i) q^{86} +(8.08785 - 2.43365i) q^{87} +3.88861 q^{88} +(6.25792 + 10.8390i) q^{89} +(0.552583 + 0.275588i) q^{90} +(-5.61747 + 0.215725i) q^{91} +(-1.68465 + 2.91790i) q^{92} +(3.78919 + 3.56493i) q^{93} +(1.48380 - 2.57002i) q^{94} +1.53374 q^{95} +(1.65859 - 0.499074i) q^{96} +(-3.28917 - 5.69701i) q^{97} +(-2.28452 + 3.95690i) q^{98} +(-9.72871 + 6.43767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9	\( 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9} + 3 q^{10} - 8 q^{11} - 5 q^{13} - q^{14} + 11 q^{15} + 12 q^{16} - q^{17} - 4 q^{18} + 9 q^{19} - 3 q^{20} + 8 q^{21} + 8 q^{22} + 7 q^{23} - q^{25} + 5 q^{26} - 9 q^{27} + q^{28} - 2 q^{29} - 11 q^{30} + 8 q^{31} - 12 q^{32} - 4 q^{33} + q^{34} - 3 q^{35} + 4 q^{36} + 15 q^{37} - 9 q^{38} + 18 q^{39} + 3 q^{40} - 19 q^{41} - 8 q^{42} - 2 q^{43} - 8 q^{44} - 5 q^{45} - 7 q^{46} - 23 q^{47} - 27 q^{49} + q^{50} + 8 q^{51} - 5 q^{52} - 4 q^{53} + 9 q^{54} + 24 q^{55} - q^{56} - 16 q^{57} + 2 q^{58} + 8 q^{59} + 11 q^{60} - 8 q^{61} - 8 q^{62} + 12 q^{64} + 7 q^{65} + 4 q^{66} + 14 q^{67} - q^{68} - 6 q^{69} + 3 q^{70} - 15 q^{71} - 4 q^{72} - 90 q^{73} - 15 q^{74} - 56 q^{75} + 9 q^{76} + 4 q^{77} - 18 q^{78} - 12 q^{79} - 3 q^{80} + 28 q^{81} + 19 q^{82} + 24 q^{83} + 8 q^{84} - 14 q^{85} + 2 q^{86} + 36 q^{87} + 8 q^{88} + 23 q^{89} + 5 q^{90} + 8 q^{91} + 7 q^{92} + 6 q^{93} + 23 q^{94} + 14 q^{95} - 4 q^{97} + 27 q^{98} + 31 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9 + 3 * q^10 - 8 * q^11 - 5 * q^13 - q^14 + 11 * q^15 + 12 * q^16 - q^17 - 4 * q^18 + 9 * q^19 - 3 * q^20 + 8 * q^21 + 8 * q^22 + 7 * q^23 - q^25 + 5 * q^26 - 9 * q^27 + q^28 - 2 * q^29 - 11 * q^30 + 8 * q^31 - 12 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 4 * q^36 + 15 * q^37 - 9 * q^38 + 18 * q^39 + 3 * q^40 - 19 * q^41 - 8 * q^42 - 2 * q^43 - 8 * q^44 - 5 * q^45 - 7 * q^46 - 23 * q^47 - 27 * q^49 + q^50 + 8 * q^51 - 5 * q^52 - 4 * q^53 + 9 * q^54 + 24 * q^55 - q^56 - 16 * q^57 + 2 * q^58 + 8 * q^59 + 11 * q^60 - 8 * q^61 - 8 * q^62 + 12 * q^64 + 7 * q^65 + 4 * q^66 + 14 * q^67 - q^68 - 6 * q^69 + 3 * q^70 - 15 * q^71 - 4 * q^72 - 90 * q^73 - 15 * q^74 - 56 * q^75 + 9 * q^76 + 4 * q^77 - 18 * q^78 - 12 * q^79 - 3 * q^80 + 28 * q^81 + 19 * q^82 + 24 * q^83 + 8 * q^84 - 14 * q^85 + 2 * q^86 + 36 * q^87 + 8 * q^88 + 23 * q^89 + 5 * q^90 + 8 * q^91 + 7 * q^92 + 6 * q^93 + 23 * q^94 + 14 * q^95 - 4 * q^97 + 27 * q^98 + 31 * q^99

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