LMFDB - Embedded newform 126.2.e.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(25,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	126.121
Dual form			126.2.e.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(-0.794182 - 1.37556i) q^{5} +(1.64400 - 0.545231i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(-0.794182 - 1.37556i) q^{5} +(1.64400 - 0.545231i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +(0.794182 + 1.37556i) q^{10} +(0.794182 - 1.37556i) q^{11} +(-1.64400 + 0.545231i) q^{12} +(2.40545 - 4.16635i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(2.05563 + 1.82841i) q^{15} +1.00000 q^{16} +(-2.69963 - 4.67589i) q^{17} +(-2.40545 + 1.79272i) q^{18} +(-3.54944 + 6.14781i) q^{19} +(-0.794182 - 1.37556i) q^{20} +(-0.761450 + 4.51887i) q^{21} +(-0.794182 + 1.37556i) q^{22} +(-0.150186 - 0.260130i) q^{23} +(1.64400 - 0.545231i) q^{24} +(1.23855 - 2.14523i) q^{25} +(-2.40545 + 4.16635i) q^{26} +(-2.97710 + 4.25874i) q^{27} +(1.23855 - 2.33795i) q^{28} +(4.13781 + 7.16689i) q^{29} +(-2.05563 - 1.82841i) q^{30} -2.71201 q^{31} -1.00000 q^{32} +(-0.555632 + 2.69443i) q^{33} +(2.69963 + 4.67589i) q^{34} +(-4.19963 + 0.153051i) q^{35} +(2.40545 - 1.79272i) q^{36} +(0.500000 - 0.866025i) q^{37} +(3.54944 - 6.14781i) q^{38} +(-1.68292 + 8.16100i) q^{39} +(0.794182 + 1.37556i) q^{40} +(2.93818 - 5.08907i) q^{41} +(0.761450 - 4.51887i) q^{42} +(-0.833104 - 1.44298i) q^{43} +(0.794182 - 1.37556i) q^{44} +(-4.37636 - 1.88510i) q^{45} +(0.150186 + 0.260130i) q^{46} +2.66621 q^{47} +(-1.64400 + 0.545231i) q^{48} +(-3.93199 - 5.79133i) q^{49} +(-1.23855 + 2.14523i) q^{50} +(6.98762 + 6.21523i) q^{51} +(2.40545 - 4.16635i) q^{52} +(2.44437 + 4.23377i) q^{53} +(2.97710 - 4.25874i) q^{54} -2.52290 q^{55} +(-1.23855 + 2.33795i) q^{56} +(2.48329 - 12.0422i) q^{57} +(-4.13781 - 7.16689i) q^{58} +6.47710 q^{59} +(2.05563 + 1.82841i) q^{60} -4.47710 q^{61} +2.71201 q^{62} +(-1.21201 - 7.84417i) q^{63} +1.00000 q^{64} -7.64145 q^{65} +(0.555632 - 2.69443i) q^{66} -10.0531 q^{67} +(-2.69963 - 4.67589i) q^{68} +(0.388736 + 0.345766i) q^{69} +(4.19963 - 0.153051i) q^{70} +12.7207 q^{71} +(-2.40545 + 1.79272i) q^{72} +(8.02654 + 13.9024i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-0.866524 + 4.20205i) q^{75} +(-3.54944 + 6.14781i) q^{76} +(-2.23236 - 3.56046i) q^{77} +(1.68292 - 8.16100i) q^{78} +8.38688 q^{79} +(-0.794182 - 1.37556i) q^{80} +(2.57234 - 8.62456i) q^{81} +(-2.93818 + 5.08907i) q^{82} +(1.18292 + 2.04887i) q^{83} +(-0.761450 + 4.51887i) q^{84} +(-4.28799 + 7.42702i) q^{85} +(0.833104 + 1.44298i) q^{86} +(-10.7101 - 9.52628i) q^{87} +(-0.794182 + 1.37556i) q^{88} +(1.60507 - 2.78007i) q^{89} +(4.37636 + 1.88510i) q^{90} +(-6.76145 - 10.7840i) q^{91} +(-0.150186 - 0.260130i) q^{92} +(4.45853 - 1.47867i) q^{93} -2.66621 q^{94} +11.2756 q^{95} +(1.64400 - 0.545231i) q^{96} +(0.712008 + 1.23323i) q^{97} +(3.93199 + 5.79133i) q^{98} +(-0.555632 - 4.73259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} - q^{10} - q^{11} + 2 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} + 6 q^{16} - 4 q^{17} - 8 q^{18} - 3 q^{19} + q^{20} - 10 q^{21} + q^{22} - 7 q^{23} - 2 q^{24} + 2 q^{25} - 8 q^{26} - 7 q^{27} + 2 q^{28} - 5 q^{29} - 12 q^{30} - 40 q^{31} - 6 q^{32} - 3 q^{33} + 4 q^{34} - 13 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 5 q^{39} - q^{40} + 10 q^{42} - 6 q^{43} - q^{44} + 9 q^{45} + 7 q^{46} + 18 q^{47} + 2 q^{48} + 12 q^{49} - 2 q^{50} + 6 q^{51} + 8 q^{52} + 15 q^{53} + 7 q^{54} - 26 q^{55} - 2 q^{56} + 22 q^{57} + 5 q^{58} + 28 q^{59} + 12 q^{60} - 16 q^{61} + 40 q^{62} - 31 q^{63} + 6 q^{64} + 24 q^{65} + 3 q^{66} - 2 q^{67} - 4 q^{68} + 3 q^{69} + 13 q^{70} + 14 q^{71} - 8 q^{72} + 19 q^{73} - 3 q^{74} + 8 q^{75} - 3 q^{76} + 10 q^{77} + 5 q^{78} - 10 q^{79} + q^{80} + 8 q^{81} + 2 q^{83} - 10 q^{84} - 2 q^{85} + 6 q^{86} - 27 q^{87} + q^{88} - 9 q^{89} - 9 q^{90} - 46 q^{91} - 7 q^{92} - 38 q^{93} - 18 q^{94} + 8 q^{95} - 2 q^{96} + 28 q^{97} - 12 q^{98} - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 - q^10 - q^11 + 2 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 - 3 * q^19 + q^20 - 10 * q^21 + q^22 - 7 * q^23 - 2 * q^24 + 2 * q^25 - 8 * q^26 - 7 * q^27 + 2 * q^28 - 5 * q^29 - 12 * q^30 - 40 * q^31 - 6 * q^32 - 3 * q^33 + 4 * q^34 - 13 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 5 * q^39 - q^40 + 10 * q^42 - 6 * q^43 - q^44 + 9 * q^45 + 7 * q^46 + 18 * q^47 + 2 * q^48 + 12 * q^49 - 2 * q^50 + 6 * q^51 + 8 * q^52 + 15 * q^53 + 7 * q^54 - 26 * q^55 - 2 * q^56 + 22 * q^57 + 5 * q^58 + 28 * q^59 + 12 * q^60 - 16 * q^61 + 40 * q^62 - 31 * q^63 + 6 * q^64 + 24 * q^65 + 3 * q^66 - 2 * q^67 - 4 * q^68 + 3 * q^69 + 13 * q^70 + 14 * q^71 - 8 * q^72 + 19 * q^73 - 3 * q^74 + 8 * q^75 - 3 * q^76 + 10 * q^77 + 5 * q^78 - 10 * q^79 + q^80 + 8 * q^81 + 2 * q^83 - 10 * q^84 - 2 * q^85 + 6 * q^86 - 27 * q^87 + q^88 - 9 * q^89 - 9 * q^90 - 46 * q^91 - 7 * q^92 - 38 * q^93 - 18 * q^94 + 8 * q^95 - 2 * q^96 + 28 * q^97 - 12 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.64400	+	0.545231i	−0.949162	+	0.314789i
$3$	−1.64400	+	0.545231i	−0.949162	+	0.314789i
$4$	1.00000			0.500000
$5$	−0.794182	−	1.37556i	−0.355169	−	0.615171i	0.631978	−	0.774986i	$-0.282243\pi$
$5$	−0.794182	−	1.37556i	−0.355169	−	0.615171i	−0.987147	+	0.159816i	$0.948910\pi$
$6$	1.64400	−	0.545231i	0.671159	−	0.222590i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$8$	−1.00000			−0.353553
$9$	2.40545	−	1.79272i	0.801815	−	0.597572i
$10$	0.794182	+	1.37556i	0.251142	+	0.434991i
$11$	0.794182	−	1.37556i	0.239455	−	0.414748i	−0.721103	−	0.692828i	$-0.756365\pi$
$11$	0.794182	−	1.37556i	0.239455	−	0.414748i	0.960558	+	0.278080i	$0.0896979\pi$
$12$	−1.64400	+	0.545231i	−0.474581	+	0.157395i
$13$	2.40545	−	4.16635i	0.667151	−	1.15554i	−0.311547	−	0.950231i	$-0.600847\pi$
$13$	2.40545	−	4.16635i	0.667151	−	1.15554i	0.978697	−	0.205308i	$-0.0658196\pi$
$14$	−1.23855	+	2.33795i	−0.331016	+	0.624843i
$15$	2.05563	+	1.82841i	0.530762	+	0.472093i
$16$	1.00000			0.250000
$17$	−2.69963	−	4.67589i	−0.654756	−	1.13407i	−0.981955	−	0.189115i	$-0.939438\pi$
$17$	−2.69963	−	4.67589i	−0.654756	−	1.13407i	0.327199	−	0.944955i	$-0.393895\pi$
$18$	−2.40545	+	1.79272i	−0.566969	+	0.422547i
$19$	−3.54944	+	6.14781i	−0.814298	+	1.41041i	0.0955331	+	0.995426i	$0.469544\pi$
$19$	−3.54944	+	6.14781i	−0.814298	+	1.41041i	−0.909831	+	0.414979i	$0.863789\pi$
$20$	−0.794182	−	1.37556i	−0.177584	−	0.307585i
$21$	−0.761450	+	4.51887i	−0.166162	+	0.986098i
$22$	−0.794182	+	1.37556i	−0.169320	+	0.293271i
$23$	−0.150186	−	0.260130i	−0.0313159	−	0.0542408i	0.849943	−	0.526875i	$-0.176636\pi$
$23$	−0.150186	−	0.260130i	−0.0313159	−	0.0542408i	−0.881259	+	0.472634i	$0.843303\pi$
$24$	1.64400	−	0.545231i	0.335579	−	0.111295i
$25$	1.23855	−	2.14523i	0.247710	−	0.429046i
$26$	−2.40545	+	4.16635i	−0.471747	+	0.817089i
$27$	−2.97710	+	4.25874i	−0.572943	+	0.819595i
$28$	1.23855	−	2.33795i	0.234064	−	0.441830i
$29$	4.13781	+	7.16689i	0.768371	+	1.33086i	0.938446	+	0.345427i	$0.112266\pi$
$29$	4.13781	+	7.16689i	0.768371	+	1.33086i	−0.170074	+	0.985431i	$0.554401\pi$
$30$	−2.05563	−	1.82841i	−0.375305	−	0.333820i
$31$	−2.71201			−0.487091			−0.243545	−	0.969889i	$-0.578311\pi$
$31$	−2.71201			−0.487091			−0.243545	+	0.969889i	$0.578311\pi$
$32$	−1.00000			−0.176777
$33$	−0.555632	+	2.69443i	−0.0967231	+	0.469041i
$34$	2.69963	+	4.67589i	0.462982	+	0.801909i
$35$	−4.19963	+	0.153051i	−0.709867	+	0.0258703i
$36$	2.40545	−	1.79272i	0.400908	−	0.298786i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	3.54944	−	6.14781i	0.575796	−	0.997307i
$39$	−1.68292	+	8.16100i	−0.269483	+	1.30681i
$40$	0.794182	+	1.37556i	0.125571	+	0.217496i
$41$	2.93818	−	5.08907i	0.458866	−	0.794780i	−0.540035	−	0.841643i	$-0.681589\pi$
$41$	2.93818	−	5.08907i	0.458866	−	0.794780i	0.998901	+	0.0468628i	$0.0149223\pi$
$42$	0.761450	−	4.51887i	0.117494	−	0.697277i
$43$	−0.833104	−	1.44298i	−0.127047	−	0.220052i	0.795484	−	0.605974i	$-0.207217\pi$
$43$	−0.833104	−	1.44298i	−0.127047	−	0.220052i	−0.922531	+	0.385922i	$0.873883\pi$
$44$	0.794182	−	1.37556i	0.119727	−	0.207374i
$45$	−4.37636	−	1.88510i	−0.652389	−	0.281014i
$46$	0.150186	+	0.260130i	0.0221437	+	0.0383540i
$47$	2.66621			0.388906			0.194453	−	0.980912i	$-0.437707\pi$
$47$	2.66621			0.388906			0.194453	+	0.980912i	$0.437707\pi$
$48$	−1.64400	+	0.545231i	−0.237290	+	0.0786973i
$49$	−3.93199	−	5.79133i	−0.561713	−	0.827332i
$50$	−1.23855	+	2.14523i	−0.175157	+	0.303382i
$51$	6.98762	+	6.21523i	0.978463	+	0.870306i
$52$	2.40545	−	4.16635i	0.333575	−	0.577769i
$53$	2.44437	+	4.23377i	0.335760	+	0.581553i	0.983630	−	0.180197i	$-0.0576736\pi$
$53$	2.44437	+	4.23377i	0.335760	+	0.581553i	−0.647871	+	0.761750i	$0.724340\pi$
$54$	2.97710	−	4.25874i	0.405132	−	0.579541i
$55$	−2.52290			−0.340188
$56$	−1.23855	+	2.33795i	−0.165508	+	0.312421i
$57$	2.48329	−	12.0422i	0.328920	−	1.59503i
$58$	−4.13781	−	7.16689i	−0.543321	−	0.941059i
$59$	6.47710			0.843247			0.421623	−	0.906771i	$-0.361460\pi$
$59$	6.47710			0.843247			0.421623	+	0.906771i	$0.361460\pi$
$60$	2.05563	+	1.82841i	0.265381	+	0.236047i
$61$	−4.47710			−0.573234			−0.286617	−	0.958045i	$-0.592531\pi$
$61$	−4.47710			−0.573234			−0.286617	+	0.958045i	$0.592531\pi$
$62$	2.71201			0.344425
$63$	−1.21201	−	7.84417i	−0.152699	−	0.988273i
$64$	1.00000			0.125000
$65$	−7.64145			−0.947805
$66$	0.555632	−	2.69443i	0.0683936	−	0.331662i
$67$	−10.0531			−1.22818			−0.614090	−	0.789236i	$-0.710477\pi$
$67$	−10.0531			−1.22818			−0.614090	+	0.789236i	$0.710477\pi$
$68$	−2.69963	−	4.67589i	−0.327378	−	0.567035i
$69$	0.388736	+	0.345766i	0.0467983	+	0.0416253i
$70$	4.19963	−	0.153051i	0.501952	−	0.0182931i
$71$	12.7207			1.50967			0.754833	−	0.655917i	$-0.227718\pi$
$71$	12.7207			1.50967			0.754833	+	0.655917i	$0.227718\pi$
$72$	−2.40545	+	1.79272i	−0.283485	+	0.211274i
$73$	8.02654	+	13.9024i	0.939436	+	1.62715i	0.766527	+	0.642213i	$0.221983\pi$
$73$	8.02654	+	13.9024i	0.939436	+	1.62715i	0.172909	+	0.984938i	$0.444683\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	−0.866524	+	4.20205i	−0.100058	+	0.485211i
$76$	−3.54944	+	6.14781i	−0.407149	+	0.705203i
$77$	−2.23236	−	3.56046i	−0.254401	−	0.405752i
$78$	1.68292	−	8.16100i	0.190553	−	0.924051i
$79$	8.38688			0.943597			0.471799	−	0.881706i	$-0.343605\pi$
$79$	8.38688			0.943597			0.471799	+	0.881706i	$0.343605\pi$
$80$	−0.794182	−	1.37556i	−0.0887922	−	0.153793i
$81$	2.57234	−	8.62456i	0.285816	−	0.958285i
$82$	−2.93818	+	5.08907i	−0.324467	+	0.561994i
$83$	1.18292	+	2.04887i	0.129842	+	0.224893i	0.923615	−	0.383321i	$-0.125220\pi$
$83$	1.18292	+	2.04887i	0.129842	+	0.224893i	−0.793773	+	0.608214i	$0.791886\pi$
$84$	−0.761450	+	4.51887i	−0.0830810	+	0.493049i
$85$	−4.28799	+	7.42702i	−0.465098	+	0.805573i
$86$	0.833104	+	1.44298i	0.0898359	+	0.155600i
$87$	−10.7101	−	9.52628i	−1.14825	−	1.02132i
$88$	−0.794182	+	1.37556i	−0.0846601	+	0.146636i
$89$	1.60507	−	2.78007i	0.170138	−	0.294687i	−0.768330	−	0.640054i	$-0.778912\pi$
$89$	1.60507	−	2.78007i	0.170138	−	0.294687i	0.938468	+	0.345367i	$0.112245\pi$
$90$	4.37636	+	1.88510i	0.461308	+	0.198707i
$91$	−6.76145	−	10.7840i	−0.708793	−	1.13047i
$92$	−0.150186	−	0.260130i	−0.0156580	−	0.0271204i
$93$	4.45853	−	1.47867i	0.462328	−	0.153331i
$94$	−2.66621			−0.274998
$95$	11.2756			1.15685
$96$	1.64400	−	0.545231i	0.167790	−	0.0556474i
$97$	0.712008	+	1.23323i	0.0722934	+	0.125216i	0.899906	−	0.436084i	$-0.143635\pi$
$97$	0.712008	+	1.23323i	0.0722934	+	0.125216i	−0.827613	+	0.561300i	$0.810302\pi$
$98$	3.93199	+	5.79133i	0.397191	+	0.585012i
$99$	−0.555632	−	4.73259i	−0.0558431	−	0.475643i
$100$	1.23855	−	2.14523i	0.123855	−	0.214523i
$101$	−6.01671	+	10.4212i	−0.598685	+	1.03695i	0.394330	+	0.918969i	$0.370977\pi$
$101$	−6.01671	+	10.4212i	−0.598685	+	1.03695i	−0.993015	+	0.117984i	$0.962357\pi$
$102$	−6.98762	−	6.21523i	−0.691878	−	0.615399i
$103$	3.04944	+	5.28179i	0.300470	+	0.520430i	0.976243	−	0.216680i	$-0.0695230\pi$
$103$	3.04944	+	5.28179i	0.300470	+	0.520430i	−0.675772	+	0.737111i	$0.736190\pi$
$104$	−2.40545	+	4.16635i	−0.235873	+	0.408545i
$105$	6.82072	−	2.54138i	0.665635	−	0.248014i
$106$	−2.44437	−	4.23377i	−0.237418	−	0.411220i
$107$	−1.54325	+	2.67299i	−0.149192	+	0.258408i	−0.930929	−	0.365200i	$-0.881001\pi$
$107$	−1.54325	+	2.67299i	−0.149192	+	0.258408i	0.781737	+	0.623608i	$0.214334\pi$
$108$	−2.97710	+	4.25874i	−0.286472	+	0.409798i
$109$	1.14400	+	1.98146i	0.109575	+	0.189789i	0.915598	−	0.402095i	$-0.131718\pi$
$109$	1.14400	+	1.98146i	0.109575	+	0.189789i	−0.806023	+	0.591884i	$0.798384\pi$
$110$	2.52290			0.240549
$111$	−0.349814	+	1.69636i	−0.0332029	+	0.161011i
$112$	1.23855	−	2.33795i	0.117032	−	0.220915i
$113$	−9.73236	+	16.8569i	−0.915543	+	1.58577i	−0.109440	+	0.993993i	$0.534906\pi$
$113$	−9.73236	+	16.8569i	−0.915543	+	1.58577i	−0.806104	+	0.591774i	$0.798428\pi$
$114$	−2.48329	+	12.0422i	−0.232581	+	1.12786i
$115$	−0.238550	+	0.413181i	−0.0222449	+	0.0385293i
$116$	4.13781	+	7.16689i	0.384186	+	0.665429i
$117$	−1.68292	−	14.3342i	−0.155586	−	1.32520i
$118$	−6.47710			−0.596265
$119$	−14.2756	+	0.520259i	−1.30864	+	0.0476921i
$120$	−2.05563	−	1.82841i	−0.187653	−	0.166910i
$121$	4.23855	+	7.34138i	0.385323	+	0.667399i
$122$	4.47710			0.405338
$123$	−2.05563	+	9.96840i	−0.185350	+	0.898821i
$124$	−2.71201			−0.243545
$125$	−11.8764			−1.06225
$126$	1.21201	+	7.84417i	0.107974	+	0.698814i
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	−1.00000			−0.0883883
$129$	2.15638	+	1.91802i	0.189858	+	0.168872i
$130$	7.64145			0.670199
$131$	1.58836	+	2.75113i	0.138776	+	0.240367i	0.927034	−	0.374978i	$-0.122350\pi$
$131$	1.58836	+	2.75113i	0.138776	+	0.240367i	−0.788258	+	0.615345i	$0.789017\pi$
$132$	−0.555632	+	2.69443i	−0.0483616	+	0.234520i
$133$	9.97710	+	15.9128i	0.865124	+	1.37981i
$134$	10.0531			0.868454
$135$	8.22253	+	0.712974i	0.707683	+	0.0613631i
$136$	2.69963	+	4.67589i	0.231491	+	0.400955i
$137$	10.6316	−	18.4145i	0.908320	−	1.57326i	0.0919231	−	0.995766i	$-0.470699\pi$
$137$	10.6316	−	18.4145i	0.908320	−	1.57326i	0.816397	−	0.577491i	$-0.195968\pi$
$138$	−0.388736	−	0.345766i	−0.0330914	−	0.0294336i
$139$	6.52654	−	11.3043i	0.553574	−	0.958818i	−0.444439	−	0.895809i	$-0.646597\pi$
$139$	6.52654	−	11.3043i	0.553574	−	0.958818i	0.998013	−	0.0630092i	$-0.0200698\pi$
$140$	−4.19963	+	0.153051i	−0.354933	+	0.0129352i
$141$	−4.38323	+	1.45370i	−0.369135	+	0.122424i
$142$	−12.7207			−1.06749
$143$	−3.82072	−	6.61769i	−0.319505	−	0.553399i
$144$	2.40545	−	1.79272i	0.200454	−	0.149393i
$145$	6.57234	−	11.3836i	0.545803	−	0.945359i
$146$	−8.02654	−	13.9024i	−0.664281	−	1.15057i
$147$	9.62178	+	7.37708i	0.793591	+	0.608451i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−2.60439	−	4.51093i	−0.213360	−	0.369550i	0.739404	−	0.673262i	$-0.235107\pi$
$149$	−2.60439	−	4.51093i	−0.213360	−	0.369550i	−0.952764	+	0.303712i	$0.901774\pi$
$150$	0.866524	−	4.20205i	0.0707514	−	0.343096i
$151$	0.261450	−	0.452845i	0.0212765	−	0.0368520i	−0.855191	−	0.518313i	$-0.826560\pi$
$151$	0.261450	−	0.452845i	0.0212765	−	0.0368520i	0.876468	+	0.481461i	$0.159894\pi$
$152$	3.54944	−	6.14781i	0.287898	−	0.498654i
$153$	−14.8764	−	6.40794i	−1.20268	−	0.518052i
$154$	2.23236	+	3.56046i	0.179889	+	0.286910i
$155$	2.15383	+	3.73054i	0.173000	+	0.299644i
$156$	−1.68292	+	8.16100i	−0.134741	+	0.653403i
$157$	8.86398			0.707422			0.353711	−	0.935355i	$-0.384920\pi$
$157$	8.86398			0.707422			0.353711	+	0.935355i	$0.384920\pi$
$158$	−8.38688			−0.667224
$159$	−6.32691	−	5.62755i	−0.501757	−	0.446294i
$160$	0.794182	+	1.37556i	0.0627856	+	0.108748i
$161$	−0.794182	+	0.0289431i	−0.0625903	+	0.00228104i
$162$	−2.57234	+	8.62456i	−0.202102	+	0.677610i
$163$	10.9814	−	19.0204i	0.860132	−	1.48979i	−0.0116689	−	0.999932i	$-0.503714\pi$
$163$	10.9814	−	19.0204i	0.860132	−	1.48979i	0.871801	−	0.489860i	$-0.162952\pi$
$164$	2.93818	−	5.08907i	0.229433	−	0.397390i
$165$	4.14764	−	1.37556i	0.322893	−	0.107087i
$166$	−1.18292	−	2.04887i	−0.0918122	−	0.159023i
$167$	1.65019	−	2.85821i	0.127695	−	0.221175i	−0.795088	−	0.606494i	$-0.792575\pi$
$167$	1.65019	−	2.85821i	0.127695	−	0.221175i	0.922783	+	0.385319i	$0.125909\pi$
$168$	0.761450	−	4.51887i	0.0587471	−	0.348638i
$169$	−5.07234	−	8.78555i	−0.390180	−	0.675812i
$170$	4.28799	−	7.42702i	0.328874	−	0.569626i
$171$	2.48329	+	21.1514i	0.189902	+	1.61749i
$172$	−0.833104	−	1.44298i	−0.0635236	−	0.110026i
$173$	19.1075			1.45272			0.726360	−	0.687315i	$-0.241211\pi$
$173$	19.1075			1.45272			0.726360	+	0.687315i	$0.241211\pi$
$174$	10.7101	+	9.52628i	0.811934	+	0.722185i
$175$	−3.48143	−	5.55264i	−0.263171	−	0.419740i
$176$	0.794182	−	1.37556i	0.0598637	−	0.103687i
$177$	−10.6483	+	3.53152i	−0.800377	+	0.265445i
$178$	−1.60507	+	2.78007i	−0.120305	+	0.208375i
$179$	−8.03706	−	13.9206i	−0.600718	−	1.04047i	−0.992712	−	0.120507i	$-0.961548\pi$
$179$	−8.03706	−	13.9206i	−0.600718	−	1.04047i	0.391994	−	0.919968i	$-0.371785\pi$
$180$	−4.37636	−	1.88510i	−0.326194	−	0.140507i
$181$	8.05308			0.598581			0.299291	−	0.954162i	$-0.403250\pi$
$181$	8.05308			0.598581			0.299291	+	0.954162i	$0.403250\pi$
$182$	6.76145	+	10.7840i	0.501192	+	0.799366i
$183$	7.36033	−	2.44105i	0.544092	−	0.180448i
$184$	0.150186	+	0.260130i	0.0110719	+	0.0191770i
$185$	−1.58836			−0.116779
$186$	−4.45853	+	1.47867i	−0.326915	+	0.108421i
$187$	−8.57598			−0.627138
$188$	2.66621			0.194453
$189$	6.26942	+	12.2350i	0.456033	+	0.889963i
$190$	−11.2756			−0.818019
$191$	−23.9629			−1.73389			−0.866946	−	0.498402i	$-0.833920\pi$
$191$	−23.9629			−1.73389			−0.866946	+	0.498402i	$0.833920\pi$
$192$	−1.64400	+	0.545231i	−0.118645	+	0.0393487i
$193$	9.76509			0.702907			0.351453	−	0.936205i	$-0.385688\pi$
$193$	9.76509			0.702907			0.351453	+	0.936205i	$0.385688\pi$
$194$	−0.712008	−	1.23323i	−0.0511192	−	0.0885410i
$195$	12.5625	−	4.16635i	0.899620	−	0.298359i
$196$	−3.93199	−	5.79133i	−0.280856	−	0.413666i
$197$	−18.2436			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$197$	−18.2436			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$198$	0.555632	+	4.73259i	0.0394871	+	0.336330i
$199$	9.04944	+	15.6741i	0.641498	+	1.11111i	0.985098	+	0.171991i	$0.0550200\pi$
$199$	9.04944	+	15.6741i	0.641498	+	1.11111i	−0.343601	+	0.939116i	$0.611647\pi$
$200$	−1.23855	+	2.14523i	−0.0875787	+	0.151691i
$201$	16.5272	−	5.48125i	1.16574	−	0.386618i
$202$	6.01671	−	10.4212i	0.423334	−	0.733236i
$203$	21.8807	−	0.797418i	1.53572	−	0.0559678i
$204$	6.98762	+	6.21523i	0.489231	+	0.435153i
$205$	−9.33379			−0.651900
$206$	−3.04944	−	5.28179i	−0.212465	−	0.368000i
$207$	−0.827603	−	0.356487i	−0.0575224	−	0.0247776i
$208$	2.40545	−	4.16635i	0.166788	−	0.288885i
$209$	5.63781	+	9.76497i	0.389975	+	0.675457i
$210$	−6.82072	+	2.54138i	−0.470675	+	0.175372i
$211$	0.166208	−	0.287880i	0.0114422	−	0.0198185i	−0.860248	−	0.509877i	$-0.829691\pi$
$211$	0.166208	−	0.287880i	0.0114422	−	0.0198185i	0.871690	+	0.490058i	$0.163024\pi$
$212$	2.44437	+	4.23377i	0.167880	+	0.290776i
$213$	−20.9127	+	6.93570i	−1.43292	+	0.475227i
$214$	1.54325	−	2.67299i	0.105495	−	0.182722i
$215$	−1.32327	+	2.29197i	−0.0902464	+	0.156311i
$216$	2.97710	−	4.25874i	0.202566	−	0.289771i
$217$	−3.35896	+	6.34053i	−0.228021	+	0.430423i
$218$	−1.14400	−	1.98146i	−0.0774812	−	0.134201i
$219$	−20.7756	−	18.4791i	−1.40389	−	1.24870i
$220$	−2.52290			−0.170094
$221$	−25.9752			−1.74728
$222$	0.349814	−	1.69636i	0.0234780	−	0.113852i
$223$	3.16621	+	5.48403i	0.212025	+	0.367238i	0.952348	−	0.305013i	$-0.0986609\pi$
$223$	3.16621	+	5.48403i	0.212025	+	0.367238i	−0.740323	+	0.672251i	$0.765328\pi$
$224$	−1.23855	+	2.33795i	−0.0827541	+	0.156211i
$225$	−0.866524	−	7.38061i	−0.0577683	−	0.492040i
$226$	9.73236	−	16.8569i	0.647387	−	1.12131i
$227$	11.6545	−	20.1862i	0.773537	−	1.33981i	−0.162075	−	0.986778i	$-0.551819\pi$
$227$	11.6545	−	20.1862i	0.773537	−	1.33981i	0.935613	−	0.353028i	$-0.114848\pi$
$228$	2.48329	−	12.0422i	0.164460	−	0.797517i
$229$	2.47710	+	4.29046i	0.163691	+	0.283522i	0.936190	−	0.351495i	$-0.114327\pi$
$229$	2.47710	+	4.29046i	0.163691	+	0.283522i	−0.772498	+	0.635017i	$0.780993\pi$
$230$	0.238550	−	0.413181i	0.0157295	−	0.0272443i
$231$	5.61126	+	4.63623i	0.369194	+	0.305041i
$232$	−4.13781	−	7.16689i	−0.271660	−	0.470529i
$233$	−7.13781	+	12.3630i	−0.467613	+	0.809930i	−0.999315	−	0.0370017i	$-0.988219\pi$
$233$	−7.13781	+	12.3630i	−0.467613	+	0.809930i	0.531702	+	0.846932i	$0.321553\pi$
$234$	1.68292	+	14.3342i	0.110016	+	0.937057i
$235$	−2.11745	−	3.66754i	−0.138127	−	0.239244i
$236$	6.47710			0.421623
$237$	−13.7880	+	4.57279i	−0.895626	+	0.297034i
$238$	14.2756	−	0.520259i	0.925351	−	0.0337234i
$239$	2.48762	−	4.30868i	0.160911	−	0.278706i	−0.774285	−	0.632837i	$-0.781890\pi$
$239$	2.48762	−	4.30868i	0.160911	−	0.278706i	0.935196	+	0.354132i	$0.115224\pi$
$240$	2.05563	+	1.82841i	0.132690	+	0.118023i
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	−0.577107	−	0.816668i	$-0.695819\pi$
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	0.995809	+	0.0914555i	$0.0291519\pi$
$242$	−4.23855	−	7.34138i	−0.272464	−	0.471922i
$243$	0.473458	+	15.5813i	0.0303723	+	0.999539i
$244$	−4.47710			−0.286617
$245$	−4.84362	+	10.0081i	−0.309448	+	0.639392i
$246$	2.05563	−	9.96840i	0.131062	−	0.635562i
$247$	17.0760	+	29.5765i	1.08652	+	1.88191i
$248$	2.71201			0.172213
$249$	−3.06182	−	2.72338i	−0.194035	−	0.172587i
$250$	11.8764			0.751127
$251$	2.43268			0.153549			0.0767746	−	0.997048i	$-0.475538\pi$
$251$	2.43268			0.153549			0.0767746	+	0.997048i	$0.475538\pi$
$252$	−1.21201	−	7.84417i	−0.0763493	−	0.494136i
$253$	−0.477100			−0.0299950
$254$	13.4400			0.843298
$255$	3.00000	−	14.5479i	0.187867	−	0.911027i
$256$	1.00000			0.0625000
$257$	0.493810	+	0.855304i	0.0308030	+	0.0533524i	0.881016	−	0.473087i	$-0.156860\pi$
$257$	0.493810	+	0.855304i	0.0308030	+	0.0533524i	−0.850213	+	0.526439i	$0.823527\pi$
$258$	−2.15638	−	1.91802i	−0.134250	−	0.119410i
$259$	−1.40545	−	2.24159i	−0.0873302	−	0.139286i
$260$	−7.64145			−0.473902
$261$	22.8015	+	9.82166i	1.41138	+	0.607946i
$262$	−1.58836	−	2.75113i	−0.0981295	−	0.169965i
$263$	−8.59269	+	14.8830i	−0.529848	+	0.917724i	0.469545	+	0.882908i	$0.344418\pi$
$263$	−8.59269	+	14.8830i	−0.529848	+	0.917724i	−0.999394	+	0.0348158i	$0.988916\pi$
$264$	0.555632	−	2.69443i	0.0341968	−	0.165831i
$265$	3.88255	−	6.72477i	0.238503	−	0.413099i
$266$	−9.97710	−	15.9128i	−0.611735	−	0.975675i
$267$	−1.12296	+	5.44556i	−0.0687237	+	0.333263i
$268$	−10.0531			−0.614090
$269$	11.4523	+	19.8360i	0.698262	+	1.20942i	0.969069	+	0.246791i	$0.0793761\pi$
$269$	11.4523	+	19.8360i	0.698262	+	1.20942i	−0.270807	+	0.962634i	$0.587291\pi$
$270$	−8.22253	−	0.712974i	−0.500407	−	0.0433902i
$271$	7.00364	−	12.1307i	0.425441	−	0.736885i	−0.571021	−	0.820936i	$-0.693452\pi$
$271$	7.00364	−	12.1307i	0.425441	−	0.736885i	0.996462	+	0.0840504i	$0.0267857\pi$
$272$	−2.69963	−	4.67589i	−0.163689	−	0.283518i
$273$	16.9956	+	14.0424i	1.02862	+	0.849883i
$274$	−10.6316	+	18.4145i	−0.642279	+	1.11246i
$275$	−1.96727	−	3.40741i	−0.118631	−	0.205474i
$276$	0.388736	+	0.345766i	0.0233991	+	0.0208127i
$277$	−14.1476	+	24.5044i	−0.850049	+	1.47233i	0.0311139	+	0.999516i	$0.490095\pi$
$277$	−14.1476	+	24.5044i	−0.850049	+	1.47233i	−0.881163	+	0.472813i	$0.843239\pi$
$278$	−6.52654	+	11.3043i	−0.391436	+	0.677987i
$279$	−6.52359	+	4.86186i	−0.390557	+	0.291072i
$280$	4.19963	−	0.153051i	0.250976	−	0.00914654i
$281$	−8.79782	−	15.2383i	−0.524834	−	0.909039i	−0.999582	−	0.0289175i	$-0.990794\pi$
$281$	−8.79782	−	15.2383i	−0.524834	−	0.909039i	0.474748	−	0.880122i	$-0.342539\pi$
$282$	4.38323	−	1.45370i	0.261018	−	0.0865665i
$283$	−18.5229			−1.10107			−0.550536	−	0.834811i	$-0.685577\pi$
$283$	−18.5229			−1.10107			−0.550536	+	0.834811i	$0.685577\pi$
$284$	12.7207			0.754833
$285$	−18.5371	+	6.14781i	−1.09804	+	0.364165i
$286$	3.82072	+	6.61769i	0.225924	+	0.391312i
$287$	−8.25890	−	13.1724i	−0.487508	−	0.777541i
$288$	−2.40545	+	1.79272i	−0.141742	+	0.105637i
$289$	−6.07598	+	10.5239i	−0.357411	+	0.619054i
$290$	−6.57234	+	11.3836i	−0.385941	+	0.668470i
$291$	−1.84294	−	1.63922i	−0.108035	−	0.0960929i
$292$	8.02654	+	13.9024i	0.469718	+	0.813575i
$293$	−7.04256	+	12.1981i	−0.411431	+	0.712619i	−0.995046	−	0.0994108i	$-0.968304\pi$
$293$	−7.04256	+	12.1981i	−0.411431	+	0.712619i	0.583616	+	0.812030i	$0.301638\pi$
$294$	−9.62178	−	7.37708i	−0.561154	−	0.430240i
$295$	−5.14400	−	8.90966i	−0.299495	−	0.518741i
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	3.49381	+	7.47741i	0.202731	+	0.433883i
$298$	2.60439	+	4.51093i	0.150868	+	0.261311i
$299$	−1.44506			−0.0835698
$300$	−0.866524	+	4.20205i	−0.0500288	+	0.242605i
$301$	−4.40545	+	0.160552i	−0.253926	+	0.00925405i
$302$	−0.261450	+	0.452845i	−0.0150448	+	0.0260583i
$303$	4.20946	−	20.4130i	0.241827	−	1.17270i
$304$	−3.54944	+	6.14781i	−0.203574	+	0.352601i
$305$	3.55563	+	6.15854i	0.203595	+	0.352637i
$306$	14.8764	+	6.40794i	0.850425	+	0.366318i
$307$	−5.85532			−0.334180			−0.167090	−	0.985942i	$-0.553437\pi$
$307$	−5.85532			−0.334180			−0.167090	+	0.985942i	$0.553437\pi$
$308$	−2.23236	−	3.56046i	−0.127201	−	0.202876i
$309$	−7.89307	−	7.02059i	−0.449021	−	0.399387i
$310$	−2.15383	−	3.73054i	−0.122329	−	0.211880i
$311$	0.810892			0.0459815			0.0229907	−	0.999736i	$-0.492681\pi$
$311$	0.810892			0.0459815			0.0229907	+	0.999736i	$0.492681\pi$
$312$	1.68292	−	8.16100i	0.0952765	−	0.462025i
$313$	10.5760			0.597790			0.298895	−	0.954286i	$-0.403382\pi$
$313$	10.5760			0.597790			0.298895	+	0.954286i	$0.403382\pi$
$314$	−8.86398			−0.500223
$315$	−9.82760	+	7.89689i	−0.553723	+	0.444940i
$316$	8.38688			0.471799
$317$	12.1964			0.685018			0.342509	−	0.939515i	$-0.388723\pi$
$317$	12.1964			0.685018			0.342509	+	0.939515i	$0.388723\pi$
$318$	6.32691	+	5.62755i	0.354796	+	0.315578i
$319$	13.1447			0.735961
$320$	−0.794182	−	1.37556i	−0.0443961	−	0.0768963i
$321$	1.07970	−	5.23582i	0.0602631	−	0.292235i
$322$	0.794182	−	0.0289431i	0.0442580	−	0.00161294i
$323$	38.3287			2.13267
$324$	2.57234	−	8.62456i	0.142908	−	0.479142i
$325$	−5.95853	−	10.3205i	−0.330520	−	0.572477i
$326$	−10.9814	+	19.0204i	−0.608205	+	1.05344i
$327$	−2.96108	−	2.63377i	−0.163748	−	0.145648i
$328$	−2.93818	+	5.08907i	−0.162234	+	0.280997i
$329$	3.30223	−	6.23345i	0.182058	−	0.343661i
$330$	−4.14764	+	1.37556i	−0.228320	+	0.0757223i
$331$	−15.6662			−0.861093			−0.430546	−	0.902568i	$-0.641679\pi$
$331$	−15.6662			−0.861093			−0.430546	+	0.902568i	$0.641679\pi$
$332$	1.18292	+	2.04887i	0.0649211	+	0.112447i
$333$	−0.349814	−	2.97954i	−0.0191697	−	0.163278i
$334$	−1.65019	+	2.85821i	−0.0902942	+	0.156394i
$335$	7.98398	+	13.8287i	0.436211	+	0.755540i
$336$	−0.761450	+	4.51887i	−0.0415405	+	0.246525i
$337$	−4.21201	+	7.29541i	−0.229443	+	0.397406i	−0.957643	−	0.287958i	$-0.907024\pi$
$337$	−4.21201	+	7.29541i	−0.229443	+	0.397406i	0.728200	+	0.685364i	$0.240357\pi$
$338$	5.07234	+	8.78555i	0.275899	+	0.477871i
$339$	6.80903	−	33.0191i	0.369816	−	1.79335i
$340$	−4.28799	+	7.42702i	−0.232549	+	0.402787i
$341$	−2.15383	+	3.73054i	−0.116636	+	0.202020i
$342$	−2.48329	−	21.1514i	−0.134281	−	1.14374i
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$	0.833104	+	1.44298i	0.0449179	+	0.0778002i
$345$	0.166896	−	0.809332i	0.00898539	−	0.0435730i
$346$	−19.1075			−1.02723
$347$	0.567323			0.0304555			0.0152277	−	0.999884i	$-0.495153\pi$
$347$	0.567323			0.0304555			0.0152277	+	0.999884i	$0.495153\pi$
$348$	−10.7101	−	9.52628i	−0.574124	−	0.510662i
$349$	−0.00364189	−	0.00630794i	−0.000194946	−	0.000337656i	0.865928	−	0.500169i	$-0.166729\pi$
$349$	−0.00364189	−	0.00630794i	−0.000194946	−	0.000337656i	−0.866123	+	0.499831i	$0.833395\pi$
$350$	3.48143	+	5.55264i	0.186090	+	0.296801i
$351$	10.5822	+	22.6478i	0.564835	+	1.20885i
$352$	−0.794182	+	1.37556i	−0.0423300	+	0.0733178i
$353$	−3.32691	+	5.76238i	−0.177074	+	0.306701i	−0.940877	−	0.338748i	$-0.889996\pi$
$353$	−3.32691	+	5.76238i	−0.177074	+	0.306701i	0.763803	+	0.645449i	$0.223330\pi$
$354$	10.6483	−	3.53152i	0.565952	−	0.187698i
$355$	−10.1025	−	17.4981i	−0.536186	−	0.928702i
$356$	1.60507	−	2.78007i	0.0850688	−	0.147343i
$357$	23.1854	−	8.63881i	1.22710	−	0.457214i
$358$	8.03706	+	13.9206i	0.424772	+	0.735727i
$359$	−0.398568	+	0.690339i	−0.0210356	+	0.0364347i	−0.876352	−	0.481672i	$-0.840030\pi$
$359$	−0.398568	+	0.690339i	−0.0210356	+	0.0364347i	0.855316	+	0.518107i	$0.173363\pi$
$360$	4.37636	+	1.88510i	0.230654	+	0.0993536i
$361$	−15.6971	−	27.1881i	−0.826162	−	1.43095i
$362$	−8.05308			−0.423261
$363$	−10.9709	−	9.75822i	−0.575823	−	0.512174i
$364$	−6.76145	−	10.7840i	−0.354396	−	0.565237i
$365$	12.7491	−	22.0820i	0.667317	−	1.15583i
$366$	−7.36033	+	2.44105i	−0.384731	+	0.127596i
$367$	7.71634	−	13.3651i	0.402790	−	0.697652i	−0.591272	−	0.806472i	$-0.701374\pi$
$367$	7.71634	−	13.3651i	0.402790	−	0.697652i	0.994061	+	0.108820i	$0.0347073\pi$
$368$	−0.150186	−	0.260130i	−0.00782898	−	0.0135602i
$369$	−2.05563	−	17.5088i	−0.107012	−	0.911472i
$370$	1.58836			0.0825751
$371$	12.9258	−	0.471067i	0.671074	−	0.0244566i
$372$	4.45853	−	1.47867i	0.231164	−	0.0766655i
$373$	−5.12110	−	8.87000i	−0.265160	−	0.459271i	0.702445	−	0.711738i	$-0.252092\pi$
$373$	−5.12110	−	8.87000i	−0.265160	−	0.459271i	−0.967606	+	0.252467i	$0.918758\pi$
$374$	8.57598			0.443454
$375$	19.5247	−	6.47536i	1.00825	−	0.334386i
$376$	−2.66621			−0.137499
$377$	39.8131			2.05048
$378$	−6.26942	−	12.2350i	−0.322464	−	0.629299i
$379$	25.0087			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$379$	25.0087			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$380$	11.2756			0.578427
$381$	22.0952	−	7.32788i	1.13197	−	0.375419i
$382$	23.9629			1.22605
$383$	3.13348	+	5.42734i	0.160113	+	0.277324i	0.934909	−	0.354887i	$-0.115481\pi$
$383$	3.13348	+	5.42734i	0.160113	+	0.277324i	−0.774796	+	0.632211i	$0.782147\pi$
$384$	1.64400	−	0.545231i	0.0838948	−	0.0278237i
$385$	−3.12474	+	5.89841i	−0.159251	+	0.300611i
$386$	−9.76509			−0.497030
$387$	−4.59084	−	1.97749i	−0.233365	−	0.100521i
$388$	0.712008	+	1.23323i	0.0361467	+	0.0626080i
$389$	10.8171	−	18.7357i	0.548448	−	0.949940i	−0.449933	−	0.893062i	$-0.648552\pi$
$389$	10.8171	−	18.7357i	0.548448	−	0.949940i	0.998381	−	0.0568774i	$-0.0181144\pi$
$390$	−12.5625	+	4.16635i	−0.636127	+	0.210972i
$391$	−0.810892	+	1.40451i	−0.0410086	+	0.0710290i
$392$	3.93199	+	5.79133i	0.198595	+	0.292506i
$393$	−4.11126	−	3.65682i	−0.207386	−	0.184462i
$394$	18.2436			0.919098
$395$	−6.66071	−	11.5367i	−0.335137	−	0.580473i
$396$	−0.555632	−	4.73259i	−0.0279216	−	0.237821i
$397$	2.05308	−	3.55605i	0.103041	−	0.178473i	−0.809895	−	0.586575i	$-0.800476\pi$
$397$	2.05308	−	3.55605i	0.103041	−	0.178473i	0.912936	+	0.408102i	$0.133809\pi$
$398$	−9.04944	−	15.6741i	−0.453608	−	0.785671i
$399$	−25.0785	−	20.7207i	−1.25549	−	1.03733i
$400$	1.23855	−	2.14523i	0.0619275	−	0.107262i
$401$	−8.37085	−	14.4987i	−0.418021	−	0.724033i	0.577720	−	0.816235i	$-0.303943\pi$
$401$	−8.37085	−	14.4987i	−0.418021	−	0.724033i	−0.995740	+	0.0922024i	$0.970609\pi$
$402$	−16.5272	+	5.48125i	−0.824303	+	0.273380i
$403$	−6.52359	+	11.2992i	−0.324963	+	0.562853i
$404$	−6.01671	+	10.4212i	−0.299343	+	0.518476i
$405$	−13.9065	+	3.31105i	−0.691022	+	0.164527i
$406$	−21.8807	+	0.797418i	−1.08592	+	0.0395752i
$407$	−0.794182	−	1.37556i	−0.0393661	−	0.0681842i
$408$	−6.98762	−	6.21523i	−0.345939	−	0.307700i
$409$	−8.76509			−0.433406			−0.216703	−	0.976238i	$-0.569530\pi$
$409$	−8.76509			−0.433406			−0.216703	+	0.976238i	$0.569530\pi$
$410$	9.33379			0.460963
$411$	−7.43818	+	36.0701i	−0.366898	+	1.77920i
$412$	3.04944	+	5.28179i	0.150235	+	0.260215i
$413$	8.02221	−	15.1431i	0.394747	−	0.745144i
$414$	0.827603	+	0.356487i	0.0406744	+	0.0175204i
$415$	1.87890	−	3.25436i	0.0922318	−	0.159750i
$416$	−2.40545	+	4.16635i	−0.117937	+	0.204272i
$417$	−4.56615	+	22.1427i	−0.223605	+	1.08433i
$418$	−5.63781	−	9.76497i	−0.275754	−	0.477620i
$419$	−0.210149	+	0.363988i	−0.0102664	+	0.0177820i	−0.871113	−	0.491083i	$-0.836601\pi$
$419$	−0.210149	+	0.363988i	−0.0102664	+	0.0177820i	0.860847	+	0.508865i	$0.169935\pi$
$420$	6.82072	−	2.54138i	0.332817	−	0.124007i
$421$	3.28799	+	5.69497i	0.160247	+	0.277556i	0.934957	−	0.354761i	$-0.115438\pi$
$421$	3.28799	+	5.69497i	0.160247	+	0.277556i	−0.774710	+	0.632316i	$0.782104\pi$
$422$	−0.166208	+	0.287880i	−0.00809086	+	0.0140138i
$423$	6.41342	−	4.77975i	0.311831	−	0.232399i
$424$	−2.44437	−	4.23377i	−0.118709	−	0.205610i
$425$	−13.3745			−0.648758
$426$	20.9127	−	6.93570i	1.01323	−	0.336036i
$427$	−5.54511	+	10.4672i	−0.268347	+	0.506544i
$428$	−1.54325	+	2.67299i	−0.0745959	+	0.129204i
$429$	9.88942	+	8.79628i	0.477466	+	0.424688i
$430$	1.32327	−	2.29197i	0.0638138	−	0.110529i
$431$	11.0439	+	19.1287i	0.531968	+	0.921395i	0.999304	+	0.0373155i	$0.0118806\pi$
$431$	11.0439	+	19.1287i	0.531968	+	0.921395i	−0.467336	+	0.884080i	$0.654786\pi$
$432$	−2.97710	+	4.25874i	−0.143236	+	0.204899i
$433$	−9.43268			−0.453306			−0.226653	−	0.973976i	$-0.572778\pi$
$433$	−9.43268			−0.453306			−0.226653	+	0.973976i	$0.572778\pi$
$434$	3.35896	−	6.34053i	0.161235	−	0.304355i
$435$	−4.59820	+	22.2981i	−0.220467	+	1.06911i
$436$	1.14400	+	1.98146i	0.0547875	+	0.0948947i
$437$	2.13231			0.102002
$438$	20.7756	+	18.4791i	0.992697	+	0.882967i
$439$	−31.2064			−1.48940			−0.744701	−	0.667398i	$-0.767408\pi$
$439$	−31.2064			−1.48940			−0.744701	+	0.667398i	$0.767408\pi$
$440$	2.52290			0.120275
$441$	−19.8404	−	6.88179i	−0.944780	−	0.327704i
$442$	25.9752			1.23552
$443$	13.0545			0.620236			0.310118	−	0.950698i	$-0.399631\pi$
$443$	13.0545			0.620236			0.310118	+	0.950698i	$0.399631\pi$
$444$	−0.349814	+	1.69636i	−0.0166014	+	0.0805056i
$445$	−5.09888			−0.241710
$446$	−3.16621	−	5.48403i	−0.149924	−	0.259676i
$447$	6.74110	+	5.99596i	0.318843	+	0.283599i
$448$	1.23855	−	2.33795i	0.0585160	−	0.110458i
$449$	−9.91706			−0.468015			−0.234008	−	0.972235i	$-0.575184\pi$
$449$	−9.91706			−0.468015			−0.234008	+	0.972235i	$0.575184\pi$
$450$	0.866524	+	7.38061i	0.0408484	+	0.347925i
$451$	−4.66690	−	8.08330i	−0.219756	−	0.380628i
$452$	−9.73236	+	16.8569i	−0.457772	+	0.792884i
$453$	−0.182918	+	0.887026i	−0.00859423	+	0.0416761i
$454$	−11.6545	+	20.1862i	−0.546974	+	0.947386i
$455$	−9.46431	+	17.8653i	−0.443694	+	0.837538i
$456$	−2.48329	+	12.0422i	−0.116291	+	0.563930i
$457$	−24.5229			−1.14713			−0.573566	−	0.819159i	$-0.694441\pi$
$457$	−24.5229			−1.14713			−0.573566	+	0.819159i	$0.694441\pi$
$458$	−2.47710	−	4.29046i	−0.115747	−	0.200480i
$459$	27.9505	+	2.42358i	1.30462	+	0.113123i
$460$	−0.238550	+	0.413181i	−0.0111224	+	0.0192646i
$461$	1.75526	+	3.04020i	0.0817506	+	0.141596i	0.904002	−	0.427528i	$-0.140616\pi$
$461$	1.75526	+	3.04020i	0.0817506	+	0.141596i	−0.822251	+	0.569125i	$0.807282\pi$
$462$	−5.61126	−	4.63623i	−0.261060	−	0.215697i
$463$	8.69413	−	15.0587i	0.404050	−	0.699836i	−0.590160	−	0.807286i	$-0.700935\pi$
$463$	8.69413	−	15.0587i	0.404050	−	0.699836i	0.994210	+	0.107451i	$0.0342687\pi$
$464$	4.13781	+	7.16689i	0.192093	+	0.332715i
$465$	−5.57489	−	4.95866i	−0.258529	−	0.229952i
$466$	7.13781	−	12.3630i	0.330652	−	0.572707i
$467$	6.69894	−	11.6029i	0.309990	−	0.536918i	−0.668370	−	0.743829i	$-0.733008\pi$
$467$	6.69894	−	11.6029i	0.309990	−	0.536918i	0.978360	+	0.206911i	$0.0663410\pi$
$468$	−1.68292	−	14.3342i	−0.0777929	−	0.662600i
$469$	−12.4512	+	23.5036i	−0.574945	+	1.08529i
$470$	2.11745	+	3.66754i	0.0976709	+	0.169171i
$471$	−14.5723	+	4.83292i	−0.671458	+	0.222689i
$472$	−6.47710			−0.298133
$473$	−2.64654			−0.121688
$474$	13.7880	−	4.57279i	0.633303	−	0.210035i
$475$	8.79232	+	15.2287i	0.403419	+	0.698743i
$476$	−14.2756	+	0.520259i	−0.654322	+	0.0238460i
$477$	13.4697	+	5.80205i	0.616737	+	0.265658i
$478$	−2.48762	+	4.30868i	−0.113781	+	0.197075i
$479$	−10.4029	+	18.0183i	−0.475321	+	0.823279i	−0.999600	−	0.0282667i	$-0.991001\pi$
$479$	−10.4029	+	18.0183i	−0.475321	+	0.823279i	0.524280	+	0.851546i	$0.324335\pi$
$480$	−2.05563	−	1.82841i	−0.0938263	−	0.0834550i
$481$	−2.40545	−	4.16635i	−0.109679	−	0.189969i
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$	1.28985	−	0.480595i	0.0586903	−	0.0218678i
$484$	4.23855	+	7.34138i	0.192661	+	0.333699i
$485$	1.13093	−	1.95882i	0.0513528	−	0.0889456i
$486$	−0.473458	−	15.5813i	−0.0214765	−	0.706781i
$487$	16.2472	+	28.1410i	0.736231	+	1.27519i	0.954181	+	0.299230i	$0.0967298\pi$
$487$	16.2472	+	28.1410i	0.736231	+	1.27519i	−0.217950	+	0.975960i	$0.569937\pi$
$488$	4.47710			0.202669
$489$	−7.68292	+	37.2569i	−0.347434	+	1.68481i
$490$	4.84362	−	10.0081i	0.218813	−	0.452118i
$491$	−9.66071	+	16.7328i	−0.435982	+	0.755142i	−0.997375	−	0.0724067i	$-0.976932\pi$
$491$	−9.66071	+	16.7328i	−0.435982	+	0.755142i	0.561394	+	0.827549i	$0.310265\pi$
$492$	−2.05563	+	9.96840i	−0.0926751	+	0.449410i
$493$	22.3411	−	38.6959i	1.00619	−	1.74277i
$494$	−17.0760	−	29.5765i	−0.768285	−	1.33071i
$495$	−6.06870	+	4.52284i	−0.272768	+	0.203287i
$496$	−2.71201			−0.121773
$497$	15.7552	−	29.7402i	0.706717	−	1.33403i
$498$	3.06182	+	2.72338i	0.137204	+	0.122037i
$499$	5.57530	+	9.65670i	0.249585	+	0.432293i	0.963411	−	0.268030i	$-0.0863726\pi$
$499$	5.57530	+	9.65670i	0.249585	+	0.432293i	−0.713826	+	0.700323i	$0.753039\pi$
$500$	−11.8764			−0.531127
$501$	−1.15452	+	5.59861i	−0.0515800	+	0.250128i
$502$	−2.43268			−0.108576
$503$	−40.7651			−1.81763			−0.908813	−	0.417204i	$-0.863010\pi$
$503$	−40.7651			−1.81763			−0.908813	+	0.417204i	$0.863010\pi$
$504$	1.21201	+	7.84417i	0.0539871	+	0.349407i
$505$	19.1135			0.850537
$506$	0.477100			0.0212097
$507$	13.1291	+	11.6778i	0.583082	+	0.518630i
$508$	−13.4400			−0.596302
$509$	−0.722528	−	1.25146i	−0.0320255	−	0.0554698i	0.849568	−	0.527478i	$-0.176862\pi$
$509$	−0.722528	−	1.25146i	−0.0320255	−	0.0554698i	−0.881594	+	0.472009i	$0.843529\pi$
$510$	−3.00000	+	14.5479i	−0.132842	+	0.644194i
$511$	42.4443	−	1.54684i	1.87762	−	0.0684280i
$512$	−1.00000			−0.0441942
$513$	−15.6149	−	33.4188i	−0.689415	−	1.47548i
$514$	−0.493810	−	0.855304i	−0.0217810	−	0.0377259i
$515$	4.84362	−	8.38940i	0.213436	−	0.369681i
$516$	2.15638	+	1.91802i	0.0949292	+	0.0844360i
$517$	2.11745	−	3.66754i	0.0931255	−	0.161298i
$518$	1.40545	+	2.24159i	0.0617518	+	0.0984898i
$519$	−31.4127	+	10.4180i	−1.37887	+	0.457301i
$520$	7.64145			0.335100
$521$	9.64214	+	16.7007i	0.422430	+	0.731670i	0.996177	−	0.0873630i	$-0.0278440\pi$
$521$	9.64214	+	16.7007i	0.422430	+	0.731670i	−0.573747	+	0.819033i	$0.694511\pi$
$522$	−22.8015	−	9.82166i	−0.997993	−	0.429882i
$523$	−18.3454	+	31.7752i	−0.802189	+	1.38943i	0.115984	+	0.993251i	$0.462998\pi$
$523$	−18.3454	+	31.7752i	−0.802189	+	1.38943i	−0.918173	+	0.396180i	$0.870335\pi$
$524$	1.58836	+	2.75113i	0.0693880	+	0.120184i
$525$	8.75093	+	7.23033i	0.381922	+	0.315558i
$526$	8.59269	−	14.8830i	0.374659	−	0.648929i
$527$	7.32141	+	12.6811i	0.318926	+	0.552396i
$528$	−0.555632	+	2.69443i	−0.0241808	+	0.117260i
$529$	11.4549	−	19.8404i	0.498039	−	0.862628i
$530$	−3.88255	+	6.72477i	−0.168647	+	0.292105i
$531$	15.5803	−	11.6116i	0.676128	−	0.503900i
$532$	9.97710	+	15.9128i	0.432562	+	0.689907i
$533$	−14.1353	−	24.4830i	−0.612266	−	1.06048i
$534$	1.12296	−	5.44556i	0.0485950	−	0.235652i
$535$	4.90249			0.211953
$536$	10.0531			0.434227
$537$	20.8028	+	18.5034i	0.897709	+	0.798479i
$538$	−11.4523	−	19.8360i	−0.493745	−	0.855192i
$539$	−11.0891	+	0.809332i	−0.477639	+	0.0348604i
$540$	8.22253	+	0.712974i	0.353841	+	0.0306815i
$541$	−1.62543	+	2.81532i	−0.0698825	+	0.121040i	−0.898849	−	0.438258i	$-0.855596\pi$
$541$	−1.62543	+	2.81532i	−0.0698825	+	0.121040i	0.828967	+	0.559298i	$0.188929\pi$
$542$	−7.00364	+	12.1307i	−0.300832	+	0.521057i
$543$	−13.2392	+	4.39079i	−0.568150	+	0.188427i
$544$	2.69963	+	4.67589i	0.115746	+	0.200477i
$545$	1.81708	−	3.14728i	0.0778352	−	0.134815i
$546$	−16.9956	−	14.0424i	−0.727344	−	0.600958i
$547$	−2.95853	−	5.12432i	−0.126498	−	0.219100i	0.795820	−	0.605534i	$-0.207040\pi$
$547$	−2.95853	−	5.12432i	−0.126498	−	0.219100i	−0.922317	+	0.386433i	$0.873707\pi$
$548$	10.6316	−	18.4145i	0.454160	−	0.786628i
$549$	−10.7694	+	8.02617i	−0.459628	+	0.342548i
$550$	1.96727	+	3.40741i	0.0838846	+	0.145292i
$551$	−58.7476			−2.50273
$552$	−0.388736	−	0.345766i	−0.0165457	−	0.0147168i
$553$	10.3876	−	19.6081i	0.441724	−	0.833820i
$554$	14.1476	−	24.5044i	0.601076	−	1.04109i
$555$	2.61126	−	0.866025i	0.110842	−	0.0367607i
$556$	6.52654	−	11.3043i	0.276787	−	0.479409i
$557$	12.8040	+	22.1772i	0.542523	+	0.939678i	0.998758	+	0.0498188i	$0.0158644\pi$
$557$	12.8040	+	22.1772i	0.542523	+	0.939678i	−0.456235	+	0.889859i	$0.650802\pi$
$558$	6.52359	−	4.86186i	0.276166	−	0.205819i
$559$	−8.01594			−0.339038
$560$	−4.19963	+	0.153051i	−0.177467	+	0.00646758i
$561$	14.0989	−	4.67589i	0.595255	−	0.197416i
$562$	8.79782	+	15.2383i	0.371114	+	0.642788i
$563$	−46.6377			−1.96555			−0.982773	−	0.184817i	$-0.940831\pi$
$563$	−46.6377			−1.96555			−0.982773	+	0.184817i	$0.940831\pi$
$564$	−4.38323	+	1.45370i	−0.184567	+	0.0612118i
$565$	30.9171			1.30069
$566$	18.5229			0.778576
$567$	−16.9778	−	16.6959i	−0.713000	−	0.701164i
$568$	−12.7207			−0.533747
$569$	31.1978			1.30788			0.653939	−	0.756547i	$-0.273115\pi$
$569$	31.1978			1.30788			0.653939	+	0.756547i	$0.273115\pi$
$570$	18.5371	−	6.14781i	0.776432	−	0.257504i
$571$	−15.6762			−0.656030			−0.328015	−	0.944672i	$-0.606380\pi$
$571$	−15.6762			−0.656030			−0.328015	+	0.944672i	$0.606380\pi$
$572$	−3.82072	−	6.61769i	−0.159752	−	0.276699i
$573$	39.3948	−	13.0653i	1.64574	−	0.545811i
$574$	8.25890	+	13.1724i	0.344720	+	0.549804i
$575$	−0.744051			−0.0310291
$576$	2.40545	−	1.79272i	0.100227	−	0.0746965i
$577$	6.99567	+	12.1169i	0.291234	+	0.504431i	0.974102	−	0.226110i	$-0.0726010\pi$
$577$	6.99567	+	12.1169i	0.291234	+	0.504431i	−0.682868	+	0.730542i	$0.739268\pi$
$578$	6.07598	−	10.5239i	0.252728	−	0.437737i
$579$	−16.0538	+	5.32423i	−0.667172	+	0.221268i
$580$	6.57234	−	11.3836i	0.272902	−	0.472680i
$581$	6.25526	−	0.227966i	0.259512	−	0.00945763i
$582$	1.84294	+	1.63922i	0.0763921	+	0.0679480i
$583$	7.76509			0.321597
$584$	−8.02654	−	13.9024i	−0.332141	−	0.575285i
$585$	−18.3811	+	13.6989i	−0.759965	+	0.566382i
$586$	7.04256	−	12.1981i	0.290926	−	0.503898i
$587$	1.44801	+	2.50803i	0.0597658	+	0.103517i	0.894360	−	0.447348i	$-0.147631\pi$
$587$	1.44801	+	2.50803i	0.0597658	+	0.103517i	−0.834594	+	0.550865i	$0.814298\pi$
$588$	9.62178	+	7.37708i	0.396796	+	0.304226i
$589$	9.62612	−	16.6729i	0.396637	−	0.686996i
$590$	5.14400	+	8.90966i	0.211775	+	0.366805i
$591$	29.9924	−	9.94696i	1.23372	−	0.409163i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−2.04394	+	3.54021i	−0.0839346	+	0.145379i	−0.904937	−	0.425546i	$-0.860082\pi$
$593$	−2.04394	+	3.54021i	−0.0839346	+	0.145379i	0.821002	+	0.570925i	$0.193415\pi$
$594$	−3.49381	−	7.47741i	−0.143353	−	0.306802i
$595$	12.0531	+	19.2238i	0.494128	+	0.788100i
$596$	−2.60439	−	4.51093i	−0.106680	−	0.184775i
$597$	−23.4233	−	20.8341i	−0.958650	−	0.852683i
$598$	1.44506			0.0590928
$599$	−19.7651			−0.807580			−0.403790	−	0.914852i	$-0.632307\pi$
$599$	−19.7651			−0.807580			−0.403790	+	0.914852i	$0.632307\pi$
$600$	0.866524	−	4.20205i	0.0353757	−	0.171548i
$601$	−13.4320	−	23.2649i	−0.547902	−	0.948994i	−0.998418	−	0.0562261i	$-0.982093\pi$
$601$	−13.4320	−	23.2649i	−0.547902	−	0.948994i	0.450516	−	0.892768i	$-0.351240\pi$
$602$	4.40545	−	0.160552i	0.179553	−	0.00654360i
$603$	−24.1822	+	18.0223i	−0.984773	+	0.733926i
$604$	0.261450	−	0.452845i	0.0106383	−	0.0184260i
$605$	6.73236	−	11.6608i	0.273709	−	0.474079i
$606$	−4.20946	+	20.4130i	−0.170998	+	0.829221i
$607$	7.62110	+	13.2001i	0.309331	+	0.535777i	0.978216	−	0.207589i	$-0.0665617\pi$
$607$	7.62110	+	13.2001i	0.309331	+	0.535777i	−0.668885	+	0.743366i	$0.733228\pi$
$608$	3.54944	−	6.14781i	0.143949	−	0.249327i
$609$	−35.5370	+	13.2410i	−1.44003	+	0.536552i
$610$	−3.55563	−	6.15854i	−0.143963	−	0.249352i
$611$	6.41342	−	11.1084i	0.259459	−	0.449396i
$612$	−14.8764	−	6.40794i	−0.601341	−	0.259026i
$613$	−1.36033	−	2.35617i	−0.0549434	−	0.0951648i	0.837246	−	0.546827i	$-0.184165\pi$
$613$	−1.36033	−	2.35617i	−0.0549434	−	0.0951648i	−0.892189	+	0.451662i	$0.850831\pi$
$614$	5.85532			0.236301
$615$	15.3447	−	5.08907i	0.618759	−	0.205211i
$616$	2.23236	+	3.56046i	0.0899444	+	0.143455i
$617$	−9.21812	+	15.9663i	−0.371108	+	0.642777i	−0.989736	−	0.142906i	$-0.954355\pi$
$617$	−9.21812	+	15.9663i	−0.371108	+	0.642777i	0.618629	+	0.785684i	$0.287689\pi$
$618$	7.89307	+	7.02059i	0.317506	+	0.282410i
$619$	−0.0537728	+	0.0931373i	−0.00216131	+	0.00374350i	−0.867104	−	0.498127i	$-0.834021\pi$
$619$	−0.0537728	+	0.0931373i	−0.00216131	+	0.00374350i	0.864943	+	0.501871i	$0.167355\pi$
$620$	2.15383	+	3.73054i	0.0864998	+	0.149822i
$621$	1.55494	+	0.134829i	0.0623977	+	0.00541050i
$622$	−0.810892			−0.0325138
$623$	−4.51169	−	7.19583i	−0.180757	−	0.288295i
$624$	−1.68292	+	8.16100i	−0.0673706	+	0.326701i
$625$	3.23924	+	5.61053i	0.129570	+	0.224421i
$626$	−10.5760			−0.422701
$627$	−14.5927	−	12.9797i	−0.582776	−	0.518358i
$628$	8.86398			0.353711
$629$	−5.39926			−0.215282
$630$	9.82760	−	7.89689i	0.391541	−	0.314620i
$631$	35.7266			1.42225			0.711126	−	0.703064i	$-0.248185\pi$
$631$	35.7266			1.42225			0.711126	+	0.703064i	$0.248185\pi$
$632$	−8.38688			−0.333612
$633$	−0.116283	+	0.563895i	−0.00462185	+	0.0224128i
$634$	−12.1964			−0.484381
$635$	10.6738	+	18.4875i	0.423576	+	0.733655i
$636$	−6.32691	−	5.62755i	−0.250878	−	0.223147i
$637$	−33.5869	+	2.45133i	−1.33076	+	0.0971254i
$638$	−13.1447			−0.520403
$639$	30.5989	−	22.8045i	1.21047	−	0.902134i
$640$	0.794182	+	1.37556i	0.0313928	+	0.0543739i
$641$	−8.65638	+	14.9933i	−0.341906	+	0.592199i	−0.984787	−	0.173767i	$-0.944406\pi$
$641$	−8.65638	+	14.9933i	−0.341906	+	0.592199i	0.642880	+	0.765967i	$0.277739\pi$
$642$	−1.07970	+	5.23582i	−0.0426125	+	0.206641i
$643$	14.4821	−	25.0838i	0.571119	−	0.989207i	−0.425332	−	0.905037i	$-0.639843\pi$
$643$	14.4821	−	25.0838i	0.571119	−	0.989207i	0.996451	−	0.0841700i	$-0.0268239\pi$
$644$	−0.794182	+	0.0289431i	−0.0312952	+	0.00114052i
$645$	0.925798	−	4.48949i	0.0364533	−	0.176773i
$646$	−38.3287			−1.50802
$647$	1.27816	+	2.21384i	0.0502497	+	0.0870350i	0.890056	−	0.455851i	$-0.150665\pi$
$647$	1.27816	+	2.21384i	0.0502497	+	0.0870350i	−0.839807	+	0.542886i	$0.817332\pi$
$648$	−2.57234	+	8.62456i	−0.101051	+	0.338805i
$649$	5.14400	−	8.90966i	0.201920	−	0.349735i
$650$	5.95853	+	10.3205i	0.233713	+	0.404802i
$651$	2.06506	−	12.2552i	0.0809360	−	0.480320i
$652$	10.9814	−	19.0204i	0.430066	−	0.744896i
$653$	−14.9883	−	25.9605i	−0.586538	−	1.01591i	−0.994682	−	0.102996i	$-0.967157\pi$
$653$	−14.9883	−	25.9605i	−0.586538	−	1.01591i	0.408144	−	0.912918i	$-0.366176\pi$
$654$	2.96108	+	2.63377i	0.115787	+	0.102989i
$655$	2.52290	−	4.36979i	0.0985779	−	0.170742i
$656$	2.93818	−	5.08907i	0.114717	−	0.198695i
$657$	44.2304	+	19.0521i	1.72559	+	0.743294i
$658$	−3.30223	+	6.23345i	−0.128734	+	0.243005i
$659$	−7.63162	−	13.2183i	−0.297286	−	0.514914i	0.678228	−	0.734851i	$-0.262748\pi$
$659$	−7.63162	−	13.2183i	−0.297286	−	0.514914i	−0.975514	+	0.219937i	$0.929415\pi$
$660$	4.14764	−	1.37556i	0.161447	−	0.0535437i
$661$	−27.2522			−1.05999			−0.529994	−	0.848001i	$-0.677806\pi$
$661$	−27.2522			−1.05999			−0.529994	+	0.848001i	$0.677806\pi$
$662$	15.6662			0.608884
$663$	42.7032	−	14.1625i	1.65845	−	0.550026i
$664$	−1.18292	−	2.04887i	−0.0459061	−	0.0795117i
$665$	13.9654	−	26.3618i	0.541555	−	1.02227i
$666$	0.349814	+	2.97954i	0.0135550	+	0.115455i
$667$	1.24288	−	2.15273i	0.0481245	−	0.0833541i
$668$	1.65019	−	2.85821i	0.0638476	−	0.110587i
$669$	−8.19530	−	7.28941i	−0.316849	−	0.281825i
$670$	−7.98398	−	13.8287i	−0.308448	−	0.534248i
$671$	−3.55563	+	6.15854i	−0.137264	+	0.237748i
$672$	0.761450	−	4.51887i	0.0293736	−	0.174319i
$673$	23.2280	+	40.2320i	0.895372	+	1.55083i	0.833344	+	0.552755i	$0.186423\pi$
$673$	23.2280	+	40.2320i	0.895372	+	1.55083i	0.0620280	+	0.998074i	$0.480243\pi$
$674$	4.21201	−	7.29541i	0.162240	−	0.281009i
$675$	5.44870	+	11.6612i	0.209721	+	0.448841i
$676$	−5.07234	−	8.78555i	−0.195090	−	0.337906i
$677$	5.09888			0.195966			0.0979830	−	0.995188i	$-0.468761\pi$
$677$	5.09888			0.195966			0.0979830	+	0.995188i	$0.468761\pi$
$678$	−6.80903	+	33.0191i	−0.261499	+	1.26809i
$679$	3.76509	−	0.137215i	0.144491	−	0.00526582i
$680$	4.28799	−	7.42702i	0.164437	−	0.284813i
$681$	−8.15383	+	39.5405i	−0.312455	+	1.51519i
$682$	2.15383	−	3.73054i	0.0824743	−	0.142850i
$683$	−7.77197	−	13.4614i	−0.297386	−	0.515088i	0.678151	−	0.734923i	$-0.262782\pi$
$683$	−7.77197	−	13.4614i	−0.297386	−	0.515088i	−0.975537	+	0.219835i	$0.929448\pi$
$684$	2.48329	+	21.1514i	0.0949510	+	0.808743i
$685$	−33.7738			−1.29043
$686$	18.4098	−	2.01993i	0.702889	−	0.0771213i
$687$	−6.41164	−	5.70291i	−0.244619	−	0.217580i
$688$	−0.833104	−	1.44298i	−0.0317618	−	0.0550130i
$689$	23.5192			0.896009
$690$	−0.166896	+	0.809332i	−0.00635363	+	0.0308107i
$691$	23.2967			0.886246			0.443123	−	0.896461i	$-0.353870\pi$
$691$	23.2967			0.886246			0.443123	+	0.896461i	$0.353870\pi$
$692$	19.1075			0.726360
$693$	−11.7527	−	4.56251i	−0.446449	−	0.173315i
$694$	−0.567323			−0.0215353
$695$	−20.7330			−0.786449
$696$	10.7101	+	9.52628i	0.405967	+	0.361093i
$697$	−31.7280			−1.20178
$698$	0.00364189	+	0.00630794i	0.000137848	+	0.000238759i
$699$	4.99381	−	24.2165i	0.188883	−	0.915954i
$700$	−3.48143	−	5.55264i	−0.131586	−	0.209870i
$701$	−45.6464			−1.72404			−0.862020	−	0.506874i	$-0.830801\pi$
$701$	−45.6464			−1.72404			−0.862020	+	0.506874i	$0.830801\pi$
$702$	−10.5822	−	22.6478i	−0.399398	−	0.854787i
$703$	3.54944	+	6.14781i	0.133870	+	0.231869i
$704$	0.794182	−	1.37556i	0.0299319	−	0.0518435i
$705$	5.48074	+	4.87492i	0.206417	+	0.183600i
$706$	3.32691	−	5.76238i	0.125210	−	0.216870i
$707$	16.9123	+	26.9740i	0.636053	+	1.01446i
$708$	−10.6483	+	3.53152i	−0.400189	+	0.132723i
$709$	18.0014			0.676056			0.338028	−	0.941136i	$-0.390240\pi$
$709$	18.0014			0.676056			0.338028	+	0.941136i	$0.390240\pi$
$710$	10.1025	+	17.4981i	0.379141	+	0.656692i
$711$	20.1742	−	15.0353i	0.756591	−	0.563867i
$712$	−1.60507	+	2.78007i	−0.0601527	+	0.104188i
$713$	0.407305	+	0.705474i	0.0152537	+	0.0264202i
$714$	−23.1854	+	8.63881i	−0.867691	+	0.323299i
$715$	−6.06870	+	10.5113i	−0.226957	+	0.393100i
$716$	−8.03706	−	13.9206i	−0.300359	−	0.520237i
$717$	−1.74041	+	8.43979i	−0.0649968	+	0.315190i
$718$	0.398568	−	0.690339i	0.0148744	−	0.0257632i
$719$	18.4389	−	31.9371i	0.687654	−	1.19105i	−0.284941	−	0.958545i	$-0.591974\pi$
$719$	18.4389	−	31.9371i	0.687654	−	1.19105i	0.972595	−	0.232506i	$-0.0746926\pi$
$720$	−4.37636	−	1.88510i	−0.163097	−	0.0702536i
$721$	16.1254	−	0.587674i	0.600542	−	0.0218861i
$722$	15.6971	+	27.1881i	0.584185	+	1.01184i
$723$	−4.54758	+	22.0527i	−0.169126	+	0.820147i
$724$	8.05308			0.299291
$725$	20.4995			0.761333
$726$	10.9709	+	9.75822i	0.407169	+	0.362161i
$727$	15.2429	+	26.4014i	0.565327	+	0.979175i	0.997019	+	0.0771543i	$0.0245834\pi$
$727$	15.2429	+	26.4014i	0.565327	+	0.979175i	−0.431692	+	0.902021i	$0.642083\pi$
$728$	6.76145	+	10.7840i	0.250596	+	0.399683i
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$	−12.7491	+	22.0820i	−0.471864	+	0.817293i
$731$	−4.49814	+	7.79101i	−0.166370	+	0.288161i
$732$	7.36033	−	2.44105i	0.272046	−	0.0902240i
$733$	−3.07530	−	5.32657i	−0.113589	−	0.196741i	0.803626	−	0.595135i	$-0.202901\pi$
$733$	−3.07530	−	5.32657i	−0.113589	−	0.196741i	−0.917215	+	0.398393i	$0.869568\pi$
$734$	−7.71634	+	13.3651i	−0.284815	+	0.493314i
$735$	2.50619	−	19.0941i	0.0924422	−	0.704297i
$736$	0.150186	+	0.260130i	0.00553593	+	0.00958851i
$737$	−7.98398	+	13.8287i	−0.294094	+	0.509385i
$738$	2.05563	+	17.5088i	0.0756689	+	0.644508i
$739$	−20.3912	−	35.3186i	−0.750103	−	1.29922i	−0.947772	−	0.318947i	$-0.896671\pi$
$739$	−20.3912	−	35.3186i	−0.750103	−	1.29922i	0.197670	−	0.980269i	$-0.436663\pi$
$740$	−1.58836			−0.0583894
$741$	−44.1989	−	39.3132i	−1.62369	−	1.44421i
$742$	−12.9258	+	0.471067i	−0.474521	+	0.0172934i
$743$	7.25271	−	12.5621i	0.266076	−	0.460858i	−0.701769	−	0.712405i	$-0.747606\pi$
$743$	7.25271	−	12.5621i	0.266076	−	0.460858i	0.967845	+	0.251547i	$0.0809394\pi$
$744$	−4.45853	+	1.47867i	−0.163458	+	0.0542107i
$745$	−4.13671	+	7.16500i	−0.151557	+	0.262505i
$746$	5.12110	+	8.87000i	0.187497	+	0.324754i
$747$	6.51849	+	2.80782i	0.238499	+	0.102733i
$748$	−8.57598			−0.313569
$749$	4.33792	+	6.91867i	0.158504	+	0.252803i
$750$	−19.5247	+	6.47536i	−0.712941	+	0.236447i
$751$	−2.09455	−	3.62787i	−0.0764314	−	0.132383i	0.825276	−	0.564729i	$-0.191019\pi$
$751$	−2.09455	−	3.62787i	−0.0764314	−	0.132383i	−0.901708	+	0.432346i	$0.857686\pi$
$752$	2.66621			0.0972266
$753$	−3.99931	+	1.32637i	−0.145743	+	0.0483356i
$754$	−39.8131			−1.44991
$755$	−0.830556			−0.0302270
$756$	6.26942	+	12.2350i	0.228017	+	0.444981i
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$	−25.0087			−0.908355
$759$	0.784350	−	0.260130i	0.0284701	−	0.00944211i
$760$	−11.2756			−0.409009
$761$	−1.81708	−	3.14728i	−0.0658692	−	0.114089i	0.831210	−	0.555959i	$-0.187649\pi$
$761$	−1.81708	−	3.14728i	−0.0658692	−	0.114089i	−0.897079	+	0.441870i	$0.854315\pi$
$762$	−22.0952	+	7.32788i	−0.800426	+	0.265461i
$763$	6.04944	−	0.220465i	0.219005	−	0.00798138i
$764$	−23.9629			−0.866946
$765$	3.00000	+	25.5524i	0.108465	+	0.923851i
$766$	−3.13348	−	5.42734i	−0.113217	−	0.196098i
$767$	15.5803	−	26.9859i	0.562573	−

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(-0.794182 - 1.37556i) q^{5} +(1.64400 - 0.545231i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(-0.794182 - 1.37556i) q^{5} +(1.64400 - 0.545231i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.40545 - 1.79272i) q^{9} +(0.794182 + 1.37556i) q^{10} +(0.794182 - 1.37556i) q^{11} +(-1.64400 + 0.545231i) q^{12} +(2.40545 - 4.16635i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(2.05563 + 1.82841i) q^{15} +1.00000 q^{16} +(-2.69963 - 4.67589i) q^{17} +(-2.40545 + 1.79272i) q^{18} +(-3.54944 + 6.14781i) q^{19} +(-0.794182 - 1.37556i) q^{20} +(-0.761450 + 4.51887i) q^{21} +(-0.794182 + 1.37556i) q^{22} +(-0.150186 - 0.260130i) q^{23} +(1.64400 - 0.545231i) q^{24} +(1.23855 - 2.14523i) q^{25} +(-2.40545 + 4.16635i) q^{26} +(-2.97710 + 4.25874i) q^{27} +(1.23855 - 2.33795i) q^{28} +(4.13781 + 7.16689i) q^{29} +(-2.05563 - 1.82841i) q^{30} -2.71201 q^{31} -1.00000 q^{32} +(-0.555632 + 2.69443i) q^{33} +(2.69963 + 4.67589i) q^{34} +(-4.19963 + 0.153051i) q^{35} +(2.40545 - 1.79272i) q^{36} +(0.500000 - 0.866025i) q^{37} +(3.54944 - 6.14781i) q^{38} +(-1.68292 + 8.16100i) q^{39} +(0.794182 + 1.37556i) q^{40} +(2.93818 - 5.08907i) q^{41} +(0.761450 - 4.51887i) q^{42} +(-0.833104 - 1.44298i) q^{43} +(0.794182 - 1.37556i) q^{44} +(-4.37636 - 1.88510i) q^{45} +(0.150186 + 0.260130i) q^{46} +2.66621 q^{47} +(-1.64400 + 0.545231i) q^{48} +(-3.93199 - 5.79133i) q^{49} +(-1.23855 + 2.14523i) q^{50} +(6.98762 + 6.21523i) q^{51} +(2.40545 - 4.16635i) q^{52} +(2.44437 + 4.23377i) q^{53} +(2.97710 - 4.25874i) q^{54} -2.52290 q^{55} +(-1.23855 + 2.33795i) q^{56} +(2.48329 - 12.0422i) q^{57} +(-4.13781 - 7.16689i) q^{58} +6.47710 q^{59} +(2.05563 + 1.82841i) q^{60} -4.47710 q^{61} +2.71201 q^{62} +(-1.21201 - 7.84417i) q^{63} +1.00000 q^{64} -7.64145 q^{65} +(0.555632 - 2.69443i) q^{66} -10.0531 q^{67} +(-2.69963 - 4.67589i) q^{68} +(0.388736 + 0.345766i) q^{69} +(4.19963 - 0.153051i) q^{70} +12.7207 q^{71} +(-2.40545 + 1.79272i) q^{72} +(8.02654 + 13.9024i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-0.866524 + 4.20205i) q^{75} +(-3.54944 + 6.14781i) q^{76} +(-2.23236 - 3.56046i) q^{77} +(1.68292 - 8.16100i) q^{78} +8.38688 q^{79} +(-0.794182 - 1.37556i) q^{80} +(2.57234 - 8.62456i) q^{81} +(-2.93818 + 5.08907i) q^{82} +(1.18292 + 2.04887i) q^{83} +(-0.761450 + 4.51887i) q^{84} +(-4.28799 + 7.42702i) q^{85} +(0.833104 + 1.44298i) q^{86} +(-10.7101 - 9.52628i) q^{87} +(-0.794182 + 1.37556i) q^{88} +(1.60507 - 2.78007i) q^{89} +(4.37636 + 1.88510i) q^{90} +(-6.76145 - 10.7840i) q^{91} +(-0.150186 - 0.260130i) q^{92} +(4.45853 - 1.47867i) q^{93} -2.66621 q^{94} +11.2756 q^{95} +(1.64400 - 0.545231i) q^{96} +(0.712008 + 1.23323i) q^{97} +(3.93199 + 5.79133i) q^{98} +(-0.555632 - 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 6 q^{8} + 8 q^{9} - q^{10} - q^{11} + 2 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} + 6 q^{16} - 4 q^{17} - 8 q^{18} - 3 q^{19} + q^{20} - 10 q^{21} + q^{22} - 7 q^{23} - 2 q^{24} + 2 q^{25} - 8 q^{26} - 7 q^{27} + 2 q^{28} - 5 q^{29} - 12 q^{30} - 40 q^{31} - 6 q^{32} - 3 q^{33} + 4 q^{34} - 13 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 5 q^{39} - q^{40} + 10 q^{42} - 6 q^{43} - q^{44} + 9 q^{45} + 7 q^{46} + 18 q^{47} + 2 q^{48} + 12 q^{49} - 2 q^{50} + 6 q^{51} + 8 q^{52} + 15 q^{53} + 7 q^{54} - 26 q^{55} - 2 q^{56} + 22 q^{57} + 5 q^{58} + 28 q^{59} + 12 q^{60} - 16 q^{61} + 40 q^{62} - 31 q^{63} + 6 q^{64} + 24 q^{65} + 3 q^{66} - 2 q^{67} - 4 q^{68} + 3 q^{69} + 13 q^{70} + 14 q^{71} - 8 q^{72} + 19 q^{73} - 3 q^{74} + 8 q^{75} - 3 q^{76} + 10 q^{77} + 5 q^{78} - 10 q^{79} + q^{80} + 8 q^{81} + 2 q^{83} - 10 q^{84} - 2 q^{85} + 6 q^{86} - 27 q^{87} + q^{88} - 9 q^{89} - 9 q^{90} - 46 q^{91} - 7 q^{92} - 38 q^{93} - 18 q^{94} + 8 q^{95} - 2 q^{96} + 28 q^{97} - 12 q^{98} - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 6 * q^8 + 8 * q^9 - q^10 - q^11 + 2 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 - 3 * q^19 + q^20 - 10 * q^21 + q^22 - 7 * q^23 - 2 * q^24 + 2 * q^25 - 8 * q^26 - 7 * q^27 + 2 * q^28 - 5 * q^29 - 12 * q^30 - 40 * q^31 - 6 * q^32 - 3 * q^33 + 4 * q^34 - 13 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 5 * q^39 - q^40 + 10 * q^42 - 6 * q^43 - q^44 + 9 * q^45 + 7 * q^46 + 18 * q^47 + 2 * q^48 + 12 * q^49 - 2 * q^50 + 6 * q^51 + 8 * q^52 + 15 * q^53 + 7 * q^54 - 26 * q^55 - 2 * q^56 + 22 * q^57 + 5 * q^58 + 28 * q^59 + 12 * q^60 - 16 * q^61 + 40 * q^62 - 31 * q^63 + 6 * q^64 + 24 * q^65 + 3 * q^66 - 2 * q^67 - 4 * q^68 + 3 * q^69 + 13 * q^70 + 14 * q^71 - 8 * q^72 + 19 * q^73 - 3 * q^74 + 8 * q^75 - 3 * q^76 + 10 * q^77 + 5 * q^78 - 10 * q^79 + q^80 + 8 * q^81 + 2 * q^83 - 10 * q^84 - 2 * q^85 + 6 * q^86 - 27 * q^87 + q^88 - 9 * q^89 - 9 * q^90 - 46 * q^91 - 7 * q^92 - 38 * q^93 - 18 * q^94 + 8 * q^95 - 2 * q^96 + 28 * q^97 - 12 * q^98 - 3 * q^99

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