LMFDB - Embedded newform 147.4.e.h.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.h.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(4.50000 + 7.79423i) q^{10} +(7.50000 + 12.9904i) q^{11} +(1.50000 - 2.59808i) q^{12} +64.0000 q^{13} -9.00000 q^{15} +(35.5000 - 61.4878i) q^{16} +(42.0000 + 72.7461i) q^{17} +(13.5000 + 23.3827i) q^{18} +(-8.00000 + 13.8564i) q^{19} +3.00000 q^{20} +45.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(31.5000 + 54.5596i) q^{24} +(58.0000 + 100.459i) q^{25} +(96.0000 - 166.277i) q^{26} -27.0000 q^{27} -297.000 q^{29} +(-13.5000 + 23.3827i) q^{30} +(-126.500 - 219.104i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(-22.5000 + 38.9711i) q^{33} +252.000 q^{34} +9.00000 q^{36} +(158.000 - 273.664i) q^{37} +(24.0000 + 41.5692i) q^{38} +(96.0000 + 166.277i) q^{39} +(-31.5000 + 54.5596i) q^{40} -360.000 q^{41} +26.0000 q^{43} +(7.50000 - 12.9904i) q^{44} +(-13.5000 - 23.3827i) q^{45} +(-126.000 - 218.238i) q^{46} +(-15.0000 + 25.9808i) q^{47} +213.000 q^{48} +348.000 q^{50} +(-126.000 + 218.238i) q^{51} +(-32.0000 - 55.4256i) q^{52} +(-181.500 - 314.367i) q^{53} +(-40.5000 + 70.1481i) q^{54} -45.0000 q^{55} -48.0000 q^{57} +(-445.500 + 771.629i) q^{58} +(-7.50000 - 12.9904i) q^{59} +(4.50000 + 7.79423i) q^{60} +(-59.0000 + 102.191i) q^{61} -759.000 q^{62} +433.000 q^{64} +(-96.0000 + 166.277i) q^{65} +(67.5000 + 116.913i) q^{66} +(185.000 + 320.429i) q^{67} +(42.0000 - 72.7461i) q^{68} +252.000 q^{69} -342.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(181.000 + 313.501i) q^{73} +(-474.000 - 820.992i) q^{74} +(-174.000 + 301.377i) q^{75} +16.0000 q^{76} +576.000 q^{78} +(-233.500 + 404.434i) q^{79} +(106.500 + 184.463i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-540.000 + 935.307i) q^{82} -477.000 q^{83} -252.000 q^{85} +(39.0000 - 67.5500i) q^{86} +(-445.500 - 771.629i) q^{87} +(157.500 + 272.798i) q^{88} +(453.000 - 784.619i) q^{89} -81.0000 q^{90} -84.0000 q^{92} +(379.500 - 657.313i) q^{93} +(45.0000 + 77.9423i) q^{94} +(-24.0000 - 41.5692i) q^{95} +(67.5000 - 116.913i) q^{96} -503.000 q^{97} -135.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 - q^4 - 3 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9	\( 2 q + 3 q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9} + 9 q^{10} + 15 q^{11} + 3 q^{12} + 128 q^{13} - 18 q^{15} + 71 q^{16} + 84 q^{17} + 27 q^{18} - 16 q^{19} + 6 q^{20} + 90 q^{22} + 84 q^{23} + 63 q^{24} + 116 q^{25} + 192 q^{26} - 54 q^{27} - 594 q^{29} - 27 q^{30} - 253 q^{31} - 45 q^{32} - 45 q^{33} + 504 q^{34} + 18 q^{36} + 316 q^{37} + 48 q^{38} + 192 q^{39} - 63 q^{40} - 720 q^{41} + 52 q^{43} + 15 q^{44} - 27 q^{45} - 252 q^{46} - 30 q^{47} + 426 q^{48} + 696 q^{50} - 252 q^{51} - 64 q^{52} - 363 q^{53} - 81 q^{54} - 90 q^{55} - 96 q^{57} - 891 q^{58} - 15 q^{59} + 9 q^{60} - 118 q^{61} - 1518 q^{62} + 866 q^{64} - 192 q^{65} + 135 q^{66} + 370 q^{67} + 84 q^{68} + 504 q^{69} - 684 q^{71} - 189 q^{72} + 362 q^{73} - 948 q^{74} - 348 q^{75} + 32 q^{76} + 1152 q^{78} - 467 q^{79} + 213 q^{80} - 81 q^{81} - 1080 q^{82} - 954 q^{83} - 504 q^{85} + 78 q^{86} - 891 q^{87} + 315 q^{88} + 906 q^{89} - 162 q^{90} - 168 q^{92} + 759 q^{93} + 90 q^{94} - 48 q^{95} + 135 q^{96} - 1006 q^{97} - 270 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 - q^4 - 3 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9 + 9 * q^10 + 15 * q^11 + 3 * q^12 + 128 * q^13 - 18 * q^15 + 71 * q^16 + 84 * q^17 + 27 * q^18 - 16 * q^19 + 6 * q^20 + 90 * q^22 + 84 * q^23 + 63 * q^24 + 116 * q^25 + 192 * q^26 - 54 * q^27 - 594 * q^29 - 27 * q^30 - 253 * q^31 - 45 * q^32 - 45 * q^33 + 504 * q^34 + 18 * q^36 + 316 * q^37 + 48 * q^38 + 192 * q^39 - 63 * q^40 - 720 * q^41 + 52 * q^43 + 15 * q^44 - 27 * q^45 - 252 * q^46 - 30 * q^47 + 426 * q^48 + 696 * q^50 - 252 * q^51 - 64 * q^52 - 363 * q^53 - 81 * q^54 - 90 * q^55 - 96 * q^57 - 891 * q^58 - 15 * q^59 + 9 * q^60 - 118 * q^61 - 1518 * q^62 + 866 * q^64 - 192 * q^65 + 135 * q^66 + 370 * q^67 + 84 * q^68 + 504 * q^69 - 684 * q^71 - 189 * q^72 + 362 * q^73 - 948 * q^74 - 348 * q^75 + 32 * q^76 + 1152 * q^78 - 467 * q^79 + 213 * q^80 - 81 * q^81 - 1080 * q^82 - 954 * q^83 - 504 * q^85 + 78 * q^86 - 891 * q^87 + 315 * q^88 + 906 * q^89 - 162 * q^90 - 168 * q^92 + 759 * q^93 + 90 * q^94 - 48 * q^95 + 135 * q^96 - 1006 * q^97 - 270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$5$	−1.50000	+	2.59808i	−0.134164	+	0.232379i	−0.925278	−	0.379290i	$-0.876168\pi$
$5$	−1.50000	+	2.59808i	−0.134164	+	0.232379i	0.791114	+	0.611669i	$0.209502\pi$
$6$	9.00000			0.612372
$7$		0			0
$7$		0			0
$8$	21.0000			0.928078
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	4.50000	+	7.79423i	0.142302	+	0.246475i
$11$	7.50000	+	12.9904i	0.205576	+	0.356068i	0.950316	−	0.311287i	$-0.100760\pi$
$11$	7.50000	+	12.9904i	0.205576	+	0.356068i	−0.744740	+	0.667355i	$0.767427\pi$
$12$	1.50000	−	2.59808i	0.0360844	−	0.0625000i
$13$	64.0000			1.36542			0.682708	−	0.730691i	$-0.260802\pi$
$13$	64.0000			1.36542			0.682708	+	0.730691i	$0.260802\pi$
$14$		0			0
$15$	−9.00000			−0.154919
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	0.992939	+	0.118630i	$0.0378502\pi$
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	−0.393733	+	0.919225i	$0.628817\pi$
$18$	13.5000	+	23.3827i	0.176777	+	0.306186i
$19$	−8.00000	+	13.8564i	−0.0965961	+	0.167309i	−0.910274	−	0.414007i	$-0.864129\pi$
$19$	−8.00000	+	13.8564i	−0.0965961	+	0.167309i	0.813678	+	0.581317i	$0.197462\pi$
$20$	3.00000			0.0335410
$21$		0			0
$22$	45.0000			0.436092
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	−0.610406	−	0.792088i	$-0.708994\pi$
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	0.991172	+	0.132583i	$0.0423272\pi$
$24$	31.5000	+	54.5596i	0.267913	+	0.464039i
$25$	58.0000	+	100.459i	0.464000	+	0.803672i
$26$	96.0000	−	166.277i	0.724121	−	1.25421i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−297.000			−1.90178			−0.950888	−	0.309535i	$-0.899827\pi$
$29$	−297.000			−1.90178			−0.950888	+	0.309535i	$0.899827\pi$
$30$	−13.5000	+	23.3827i	−0.0821584	+	0.142302i
$31$	−126.500	−	219.104i	−0.732906	−	1.26943i	−0.955636	−	0.294550i	$-0.904830\pi$
$31$	−126.500	−	219.104i	−0.732906	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$32$	−22.5000	−	38.9711i	−0.124296	−	0.215287i
$33$	−22.5000	+	38.9711i	−0.118689	+	0.205576i
$34$	252.000			1.27111
$35$		0			0
$36$	9.00000			0.0416667
$37$	158.000	−	273.664i	0.702028	−	1.21595i	−0.265725	−	0.964049i	$-0.585611\pi$
$37$	158.000	−	273.664i	0.702028	−	1.21595i	0.967753	−	0.251900i	$-0.0810553\pi$
$38$	24.0000	+	41.5692i	0.102456	+	0.177458i
$39$	96.0000	+	166.277i	0.394162	+	0.682708i
$40$	−31.5000	+	54.5596i	−0.124515	+	0.215666i
$41$	−360.000			−1.37128			−0.685641	−	0.727940i	$-0.740478\pi$
$41$	−360.000			−1.37128			−0.685641	+	0.727940i	$0.740478\pi$
$42$		0			0
$43$	26.0000			0.0922084			0.0461042	−	0.998937i	$-0.485319\pi$
$43$	26.0000			0.0922084			0.0461042	+	0.998937i	$0.485319\pi$
$44$	7.50000	−	12.9904i	0.0256970	−	0.0445085i
$45$	−13.5000	−	23.3827i	−0.0447214	−	0.0774597i
$46$	−126.000	−	218.238i	−0.403863	−	0.699511i
$47$	−15.0000	+	25.9808i	−0.0465527	+	0.0806316i	−0.888363	−	0.459142i	$-0.848157\pi$
$47$	−15.0000	+	25.9808i	−0.0465527	+	0.0806316i	0.841810	+	0.539774i	$0.181490\pi$
$48$	213.000			0.640498
$49$		0			0
$50$	348.000			0.984293
$51$	−126.000	+	218.238i	−0.345952	+	0.599206i
$52$	−32.0000	−	55.4256i	−0.0853385	−	0.147811i
$53$	−181.500	−	314.367i	−0.470395	−	0.814748i	0.529032	−	0.848602i	$-0.322555\pi$
$53$	−181.500	−	314.367i	−0.470395	−	0.814748i	−0.999427	+	0.0338538i	$0.989222\pi$
$54$	−40.5000	+	70.1481i	−0.102062	+	0.176777i
$55$	−45.0000			−0.110324
$56$		0			0
$57$	−48.0000			−0.111540
$58$	−445.500	+	771.629i	−1.00857	+	1.74689i
$59$	−7.50000	−	12.9904i	−0.0165494	−	0.0286645i	0.857632	−	0.514264i	$-0.171935\pi$
$59$	−7.50000	−	12.9904i	−0.0165494	−	0.0286645i	−0.874182	+	0.485599i	$0.838601\pi$
$60$	4.50000	+	7.79423i	0.00968246	+	0.0167705i
$61$	−59.0000	+	102.191i	−0.123839	+	0.214495i	−0.921279	−	0.388903i	$-0.872854\pi$
$61$	−59.0000	+	102.191i	−0.123839	+	0.214495i	0.797440	+	0.603399i	$0.206187\pi$
$62$	−759.000			−1.55473
$63$		0			0
$64$	433.000			0.845703
$65$	−96.0000	+	166.277i	−0.183190	+	0.317294i
$66$	67.5000	+	116.913i	0.125889	+	0.218046i
$67$	185.000	+	320.429i	0.337334	+	0.584279i	0.983930	−	0.178553i	$-0.0571417\pi$
$67$	185.000	+	320.429i	0.337334	+	0.584279i	−0.646597	+	0.762832i	$0.723808\pi$
$68$	42.0000	−	72.7461i	0.0749007	−	0.129732i
$69$	252.000			0.439670
$70$		0			0
$71$	−342.000			−0.571661			−0.285831	−	0.958280i	$-0.592269\pi$
$71$	−342.000			−0.571661			−0.285831	+	0.958280i	$0.592269\pi$
$72$	−94.5000	+	163.679i	−0.154680	+	0.267913i
$73$	181.000	+	313.501i	0.290198	+	0.502638i	0.973856	−	0.227165i	$-0.0729455\pi$
$73$	181.000	+	313.501i	0.290198	+	0.502638i	−0.683658	+	0.729802i	$0.739612\pi$
$74$	−474.000	−	820.992i	−0.744613	−	1.28971i
$75$	−174.000	+	301.377i	−0.267891	+	0.464000i
$76$	16.0000			0.0241490
$77$		0			0
$78$	576.000			0.836143
$79$	−233.500	+	404.434i	−0.332542	+	0.575979i	−0.983010	−	0.183555i	$-0.941240\pi$
$79$	−233.500	+	404.434i	−0.332542	+	0.575979i	0.650468	+	0.759534i	$0.274573\pi$
$80$	106.500	+	184.463i	0.148838	+	0.257795i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−540.000	+	935.307i	−0.727232	+	1.25960i
$83$	−477.000			−0.630814			−0.315407	−	0.948957i	$-0.602141\pi$
$83$	−477.000			−0.630814			−0.315407	+	0.948957i	$0.602141\pi$
$84$		0			0
$85$	−252.000			−0.321568
$86$	39.0000	−	67.5500i	0.0489009	−	0.0846989i
$87$	−445.500	−	771.629i	−0.548996	−	0.950888i
$88$	157.500	+	272.798i	0.190790	+	0.330459i
$89$	453.000	−	784.619i	0.539527	−	0.934488i	−0.459402	−	0.888228i	$-0.651936\pi$
$89$	453.000	−	784.619i	0.539527	−	0.934488i	0.998929	−	0.0462600i	$-0.0147303\pi$
$90$	−81.0000			−0.0948683
$91$		0			0
$92$	−84.0000			−0.0951914
$93$	379.500	−	657.313i	0.423143	−	0.732906i
$94$	45.0000	+	77.9423i	0.0493765	+	0.0855227i
$95$	−24.0000	−	41.5692i	−0.0259195	−	0.0448938i
$96$	67.5000	−	116.913i	0.0717624	−	0.124296i
$97$	−503.000			−0.526515			−0.263257	−	0.964726i	$-0.584797\pi$
$97$	−503.000			−0.526515			−0.263257	+	0.964726i	$0.584797\pi$
$98$		0			0
$99$	−135.000			−0.137051
$100$	58.0000	−	100.459i	0.0580000	−	0.100459i
$101$	−543.000	−	940.504i	−0.534956	−	0.926570i	−0.999165	−	0.0408451i	$-0.986995\pi$
$101$	−543.000	−	940.504i	−0.534956	−	0.926570i	0.464210	−	0.885725i	$-0.346338\pi$
$102$	378.000	+	654.715i	0.366937	+	0.635554i
$103$	868.000	−	1503.42i	0.830355	−	1.43822i	−0.0674017	−	0.997726i	$-0.521471\pi$
$103$	868.000	−	1503.42i	0.830355	−	1.43822i	0.897757	−	0.440491i	$-0.145196\pi$
$104$	1344.00			1.26721
$105$		0			0
$106$	−1089.00			−0.997859
$107$	676.500	−	1171.73i	0.611212	−	1.05865i	−0.379824	−	0.925059i	$-0.624015\pi$
$107$	676.500	−	1171.73i	0.611212	−	1.05865i	0.991036	−	0.133592i	$-0.0426512\pi$
$108$	13.5000	+	23.3827i	0.0120281	+	0.0208333i
$109$	185.000	+	320.429i	0.162567	+	0.281574i	0.935789	−	0.352562i	$-0.114689\pi$
$109$	185.000	+	320.429i	0.162567	+	0.281574i	−0.773222	+	0.634136i	$0.781356\pi$
$110$	−67.5000	+	116.913i	−0.0585079	+	0.101339i
$111$	948.000			0.810632
$112$		0			0
$113$	−648.000			−0.539458			−0.269729	−	0.962936i	$-0.586934\pi$
$113$	−648.000			−0.539458			−0.269729	+	0.962936i	$0.586934\pi$
$114$	−72.0000	+	124.708i	−0.0591528	+	0.102456i
$115$	126.000	+	218.238i	0.102170	+	0.176964i
$116$	148.500	+	257.210i	0.118861	+	0.205873i
$117$	−288.000	+	498.831i	−0.227569	+	0.394162i
$118$	−45.0000			−0.0351067
$119$		0			0
$120$	−189.000			−0.143777
$121$	553.000	−	957.824i	0.415477	−	0.719627i
$122$	177.000	+	306.573i	0.131351	+	0.227507i
$123$	−540.000	−	935.307i	−0.395855	−	0.685641i
$124$	−126.500	+	219.104i	−0.0916132	+	0.158679i
$125$	−723.000			−0.517337
$126$		0			0
$127$	377.000			0.263412			0.131706	−	0.991289i	$-0.457954\pi$
$127$	377.000			0.263412			0.131706	+	0.991289i	$0.457954\pi$
$128$	829.500	−	1436.74i	0.572798	−	0.992115i
$129$	39.0000	+	67.5500i	0.0266183	+	0.0461042i
$130$	288.000	+	498.831i	0.194302	+	0.336541i
$131$	−325.500	+	563.783i	−0.217092	+	0.376015i	−0.953918	−	0.300068i	$-0.902991\pi$
$131$	−325.500	+	563.783i	−0.217092	+	0.376015i	0.736826	+	0.676083i	$0.236324\pi$
$132$	45.0000			0.0296723
$133$		0			0
$134$	1110.00			0.715593
$135$	40.5000	−	70.1481i	0.0258199	−	0.0447214i
$136$	882.000	+	1527.67i	0.556109	+	0.963210i
$137$	885.000	+	1532.86i	0.551903	+	0.955923i	0.998137	+	0.0610074i	$0.0194313\pi$
$137$	885.000	+	1532.86i	0.551903	+	0.955923i	−0.446235	+	0.894916i	$0.647235\pi$
$138$	378.000	−	654.715i	0.233170	−	0.403863i
$139$	1558.00			0.950704			0.475352	−	0.879796i	$-0.342321\pi$
$139$	1558.00			0.950704			0.475352	+	0.879796i	$0.342321\pi$
$140$		0			0
$141$	−90.0000			−0.0537544
$142$	−513.000	+	888.542i	−0.303169	+	0.525104i
$143$	480.000	+	831.384i	0.280697	+	0.486181i
$144$	319.500	+	553.390i	0.184896	+	0.320249i
$145$	445.500	−	771.629i	0.255150	−	0.441933i
$146$	1086.00			0.615603
$147$		0			0
$148$	−316.000			−0.175507
$149$	−1227.00	+	2125.23i	−0.674629	+	1.16849i	0.301948	+	0.953324i	$0.402363\pi$
$149$	−1227.00	+	2125.23i	−0.674629	+	1.16849i	−0.976577	+	0.215168i	$0.930970\pi$
$150$	522.000	+	904.131i	0.284141	+	0.492146i
$151$	−629.500	−	1090.33i	−0.339258	−	0.587612i	0.645035	−	0.764153i	$-0.276843\pi$
$151$	−629.500	−	1090.33i	−0.339258	−	0.587612i	−0.984293	+	0.176540i	$0.943509\pi$
$152$	−168.000	+	290.985i	−0.0896487	+	0.155276i
$153$	−756.000			−0.399470
$154$		0			0
$155$	759.000			0.393318
$156$	96.0000	−	166.277i	0.0492702	−	0.0853385i
$157$	−98.0000	−	169.741i	−0.0498169	−	0.0862854i	0.840042	−	0.542522i	$-0.182530\pi$
$157$	−98.0000	−	169.741i	−0.0498169	−	0.0862854i	−0.889859	+	0.456236i	$0.849197\pi$
$158$	700.500	+	1213.30i	0.352714	+	0.610918i
$159$	544.500	−	943.102i	0.271583	−	0.470395i
$160$	135.000			0.0667043
$161$		0			0
$162$	−243.000			−0.117851
$163$	626.000	−	1084.26i	0.300810	−	0.521019i	−0.675509	−	0.737351i	$-0.736076\pi$
$163$	626.000	−	1084.26i	0.300810	−	0.521019i	0.976320	+	0.216332i	$0.0694095\pi$
$164$	180.000	+	311.769i	0.0857051	+	0.148446i
$165$	−67.5000	−	116.913i	−0.0318477	−	0.0551618i
$166$	−715.500	+	1239.28i	−0.334540	+	0.579440i
$167$	2646.00			1.22607			0.613035	−	0.790056i	$-0.289949\pi$
$167$	2646.00			1.22607			0.613035	+	0.790056i	$0.289949\pi$
$168$		0			0
$169$	1899.00			0.864360
$170$	−378.000	+	654.715i	−0.170537	+	0.295379i
$171$	−72.0000	−	124.708i	−0.0321987	−	0.0557698i
$172$	−13.0000	−	22.5167i	−0.00576303	−	0.00998186i
$173$	−393.000	+	680.696i	−0.172712	+	0.299147i	−0.939367	−	0.342913i	$-0.888586\pi$
$173$	−393.000	+	680.696i	−0.172712	+	0.299147i	0.766655	+	0.642059i	$0.221920\pi$
$174$	−2673.00			−1.16460
$175$		0			0
$176$	1065.00			0.456122
$177$	22.5000	−	38.9711i	0.00955482	−	0.0165494i
$178$	−1359.00	−	2353.86i	−0.572255	−	0.991174i
$179$	−1446.00	−	2504.55i	−0.603794	−	1.04580i	−0.992241	−	0.124331i	$-0.960322\pi$
$179$	−1446.00	−	2504.55i	−0.603794	−	1.04580i	0.388447	−	0.921471i	$-0.373012\pi$
$180$	−13.5000	+	23.3827i	−0.00559017	+	0.00968246i
$181$	−1352.00			−0.555212			−0.277606	−	0.960695i	$-0.589541\pi$
$181$	−1352.00			−0.555212			−0.277606	+	0.960695i	$0.589541\pi$
$182$		0			0
$183$	−354.000			−0.142997
$184$	882.000	−	1527.67i	0.353380	−	0.612072i
$185$	474.000	+	820.992i	0.188374	+	0.326273i
$186$	−1138.50	−	1971.94i	−0.448811	−	0.777364i
$187$	−630.000	+	1091.19i	−0.246365	+	0.426716i
$188$	30.0000			0.0116382
$189$		0			0
$190$	−144.000			−0.0549835
$191$	−1956.00	+	3387.89i	−0.741001	+	1.28345i	0.211039	+	0.977478i	$0.432315\pi$
$191$	−1956.00	+	3387.89i	−0.741001	+	1.28345i	−0.952040	+	0.305974i	$0.901018\pi$
$192$	649.500	+	1124.97i	0.244133	+	0.422852i
$193$	−746.500	−	1292.98i	−0.278416	−	0.482230i	0.692575	−	0.721345i	$-0.256476\pi$
$193$	−746.500	−	1292.98i	−0.278416	−	0.482230i	−0.970991	+	0.239115i	$0.923143\pi$
$194$	−754.500	+	1306.83i	−0.279227	+	0.483635i
$195$	−576.000			−0.211529
$196$		0			0
$197$	−4086.00			−1.47774			−0.738872	−	0.673846i	$-0.764641\pi$
$197$	−4086.00			−1.47774			−0.738872	+	0.673846i	$0.764641\pi$
$198$	−202.500	+	350.740i	−0.0726821	+	0.125889i
$199$	−1778.00	−	3079.59i	−0.633362	−	1.09702i	−0.986860	−	0.161580i	$-0.948341\pi$
$199$	−1778.00	−	3079.59i	−0.633362	−	1.09702i	0.353497	−	0.935436i	$-0.384992\pi$
$200$	1218.00	+	2109.64i	0.430628	+	0.745870i
$201$	−555.000	+	961.288i	−0.194760	+	0.337334i
$202$	−3258.00			−1.13481
$203$		0			0
$204$	252.000			0.0864879
$205$	540.000	−	935.307i	0.183977	−	0.318657i
$206$	−2604.00	−	4510.26i	−0.880725	−	1.52546i
$207$	378.000	+	654.715i	0.126922	+	0.219835i
$208$	2272.00	−	3935.22i	0.757379	−	1.31182i
$209$	−240.000			−0.0794313
$210$		0			0
$211$	1250.00			0.407837			0.203918	−	0.978988i	$-0.434632\pi$
$211$	1250.00			0.407837			0.203918	+	0.978988i	$0.434632\pi$
$212$	−181.500	+	314.367i	−0.0587994	+	0.101844i
$213$	−513.000	−	888.542i	−0.165024	−	0.285831i
$214$	−2029.50	−	3515.20i	−0.648289	−	1.12287i
$215$	−39.0000	+	67.5500i	−0.0123711	+	0.0214273i
$216$	−567.000			−0.178609
$217$		0			0
$218$	1110.00			0.344856
$219$	−543.000	+	940.504i	−0.167546	+	0.290198i
$220$	22.5000	+	38.9711i	0.00689523	+	0.0119429i
$221$	2688.00	+	4655.75i	0.818165	+	1.41710i
$222$	1422.00	−	2462.98i	0.429903	−	0.744613i
$223$	−425.000			−0.127624			−0.0638119	−	0.997962i	$-0.520326\pi$
$223$	−425.000			−0.127624			−0.0638119	+	0.997962i	$0.520326\pi$
$224$		0			0
$225$	−1044.00			−0.309333
$226$	−972.000	+	1683.55i	−0.286091	+	0.495523i
$227$	1927.50	+	3338.53i	0.563580	+	0.976149i	0.997180	+	0.0750439i	$0.0239097\pi$
$227$	1927.50	+	3338.53i	0.563580	+	0.976149i	−0.433600	+	0.901105i	$0.642757\pi$
$228$	24.0000	+	41.5692i	0.00697122	+	0.0120745i
$229$	−1094.00	+	1894.86i	−0.315692	+	0.546795i	−0.979584	−	0.201033i	$-0.935570\pi$
$229$	−1094.00	+	1894.86i	−0.315692	+	0.546795i	0.663892	+	0.747828i	$0.268903\pi$
$230$	756.000			0.216735
$231$		0			0
$232$	−6237.00			−1.76500
$233$	−426.000	+	737.854i	−0.119778	+	0.207461i	−0.919679	−	0.392670i	$-0.871551\pi$
$233$	−426.000	+	737.854i	−0.119778	+	0.207461i	0.799902	+	0.600131i	$0.204885\pi$
$234$	864.000	+	1496.49i	0.241374	+	0.418072i
$235$	−45.0000	−	77.9423i	−0.0124914	−	0.0216357i
$236$	−7.50000	+	12.9904i	−0.00206868	+	0.00358306i
$237$	−1401.00			−0.383986
$238$		0			0
$239$	5508.00			1.49072			0.745362	−	0.666660i	$-0.232277\pi$
$239$	5508.00			1.49072			0.745362	+	0.666660i	$0.232277\pi$
$240$	−319.500	+	553.390i	−0.0859318	+	0.148838i
$241$	395.500	+	685.026i	0.105711	+	0.183097i	0.914029	−	0.405650i	$-0.132955\pi$
$241$	395.500	+	685.026i	0.105711	+	0.183097i	−0.808317	+	0.588747i	$0.799621\pi$
$242$	−1659.00	−	2873.47i	−0.440680	−	0.763280i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	118.000			0.0309597
$245$		0			0
$246$	−3240.00			−0.839735
$247$	−512.000	+	886.810i	−0.131894	+	0.228447i
$248$	−2656.50	−	4601.19i	−0.680193	−	1.17813i
$249$	−715.500	−	1239.28i	−0.182100	−	0.315407i
$250$	−1084.50	+	1878.41i	−0.274359	+	0.475204i
$251$	−5265.00			−1.32400			−0.662000	−	0.749504i	$-0.730292\pi$
$251$	−5265.00			−1.32400			−0.662000	+	0.749504i	$0.730292\pi$
$252$		0			0
$253$	1260.00			0.313105
$254$	565.500	−	979.475i	0.139695	−	0.241959i
$255$	−378.000	−	654.715i	−0.0928285	−	0.160784i
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	−3435.00	+	5949.59i	−0.833733	+	1.44407i	0.0613246	+	0.998118i	$0.480468\pi$
$257$	−3435.00	+	5949.59i	−0.833733	+	1.44407i	−0.895058	+	0.445950i	$0.852866\pi$
$258$	234.000			0.0564659
$259$		0			0
$260$	192.000			0.0457974
$261$	1336.50	−	2314.89i	0.316963	−	0.548996i
$262$	976.500	+	1691.35i	0.230261	+	0.398824i
$263$	111.000	+	192.258i	0.0260249	+	0.0450765i	0.878745	−	0.477292i	$-0.158382\pi$
$263$	111.000	+	192.258i	0.0260249	+	0.0450765i	−0.852720	+	0.522369i	$0.825048\pi$
$264$	−472.500	+	818.394i	−0.110153	+	0.190790i
$265$	1089.00			0.252441
$266$		0			0
$267$	2718.00			0.622992
$268$	185.000	−	320.429i	0.0421667	−	0.0730349i
$269$	3925.50	+	6799.17i	0.889747	+	1.54109i	0.840174	+	0.542317i	$0.182453\pi$
$269$	3925.50	+	6799.17i	0.889747	+	1.54109i	0.0495729	+	0.998771i	$0.484214\pi$
$270$	−121.500	−	210.444i	−0.0273861	−	0.0474342i
$271$	2591.50	−	4488.61i	0.580895	−	1.00614i	−0.414479	−	0.910059i	$-0.636036\pi$
$271$	2591.50	−	4488.61i	0.580895	−	1.00614i	0.995374	−	0.0960800i	$-0.0306305\pi$
$272$	5964.00			1.32949
$273$		0			0
$274$	5310.00			1.17076
$275$	−870.000	+	1506.88i	−0.190774	+	0.330431i
$276$	−126.000	−	218.238i	−0.0274794	−	0.0475957i
$277$	2480.00	+	4295.49i	0.537938	+	0.931736i	0.999015	+	0.0443755i	$0.0141298\pi$
$277$	2480.00	+	4295.49i	0.537938	+	0.931736i	−0.461077	+	0.887360i	$0.652537\pi$
$278$	2337.00	−	4047.80i	0.504187	−	0.873277i
$279$	2277.00			0.488604
$280$		0			0
$281$	−774.000			−0.164317			−0.0821583	−	0.996619i	$-0.526181\pi$
$281$	−774.000			−0.164317			−0.0821583	+	0.996619i	$0.526181\pi$
$282$	−135.000	+	233.827i	−0.0285076	+	0.0493765i
$283$	1849.00	+	3202.56i	0.388380	+	0.672695i	0.992232	−	0.124402i	$-0.0397013\pi$
$283$	1849.00	+	3202.56i	0.388380	+	0.672695i	−0.603852	+	0.797097i	$0.706368\pi$
$284$	171.000	+	296.181i	0.0357288	+	0.0618841i
$285$	72.0000	−	124.708i	0.0149646	−	0.0259195i
$286$	2880.00			0.595447
$287$		0			0
$288$	405.000			0.0828641
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$	−1336.50	−	2314.89i	−0.270628	−	0.468741i
$291$	−754.500	−	1306.83i	−0.151992	−	0.263257i
$292$	181.000	−	313.501i	0.0362747	−	0.0628297i
$293$	6273.00			1.25076			0.625380	−	0.780321i	$-0.284944\pi$
$293$	6273.00			1.25076			0.625380	+	0.780321i	$0.284944\pi$
$294$		0			0
$295$	45.0000			0.00888136
$296$	3318.00	−	5746.94i	0.651537	−	1.12849i
$297$	−202.500	−	350.740i	−0.0395631	−	0.0685253i
$298$	3681.00	+	6375.68i	0.715552	+	1.23937i
$299$	2688.00	−	4655.75i	0.519903	−	0.900499i
$300$	348.000			0.0669726
$301$		0			0
$302$	−3777.00			−0.719675
$303$	1629.00	−	2821.51i	0.308857	−	0.534956i
$304$	568.000	+	983.805i	0.107161	+	0.185609i
$305$	−177.000	−	306.573i	−0.0332295	−	0.0575551i
$306$	−1134.00	+	1964.15i	−0.211851	+	0.366937i
$307$	1684.00			0.313065			0.156533	−	0.987673i	$-0.449968\pi$
$307$	1684.00			0.313065			0.156533	+	0.987673i	$0.449968\pi$
$308$		0			0
$309$	5208.00			0.958812
$310$	1138.50	−	1971.94i	0.208589	−	0.361286i
$311$	−660.000	−	1143.15i	−0.120338	−	0.208432i	0.799563	−	0.600582i	$-0.205065\pi$
$311$	−660.000	−	1143.15i	−0.120338	−	0.208432i	−0.919901	+	0.392151i	$0.871731\pi$
$312$	2016.00	+	3491.81i	0.365813	+	0.633606i
$313$	−4251.50	+	7363.81i	−0.767760	+	1.32980i	0.171014	+	0.985269i	$0.445296\pi$
$313$	−4251.50	+	7363.81i	−0.767760	+	1.32980i	−0.938775	+	0.344531i	$0.888038\pi$
$314$	−588.000			−0.105678
$315$		0			0
$316$	467.000			0.0831355
$317$	1288.50	−	2231.75i	0.228295	−	0.395418i	−0.729008	−	0.684505i	$-0.760018\pi$
$317$	1288.50	−	2231.75i	0.228295	−	0.395418i	0.957303	+	0.289087i	$0.0933517\pi$
$318$	−1633.50	−	2829.30i	−0.288057	−	0.498929i
$319$	−2227.50	−	3858.14i	−0.390959	−	0.677162i
$320$	−649.500	+	1124.97i	−0.113463	+	0.196524i
$321$	4059.00			0.705767
$322$		0			0
$323$	−1344.00			−0.231524
$324$	−40.5000	+	70.1481i	−0.00694444	+	0.0120281i
$325$	3712.00	+	6429.37i	0.633553	+	1.09735i
$326$	−1878.00	−	3252.79i	−0.319058	−	0.552624i
$327$	−555.000	+	961.288i	−0.0938580	+	0.162567i
$328$	−7560.00			−1.27266
$329$		0			0
$330$	−405.000			−0.0675591
$331$	242.000	−	419.156i	0.0401859	−	0.0696040i	−0.845233	−	0.534398i	$-0.820538\pi$
$331$	242.000	−	419.156i	0.0401859	−	0.0696040i	0.885419	+	0.464794i	$0.153872\pi$
$332$	238.500	+	413.094i	0.0394259	+	0.0682876i
$333$	1422.00	+	2462.98i	0.234009	+	0.405316i
$334$	3969.00	−	6874.51i	0.650222	−	1.12622i
$335$	−1110.00			−0.181032
$336$		0			0
$337$	−8359.00			−1.35117			−0.675584	−	0.737283i	$-0.736109\pi$
$337$	−8359.00			−1.35117			−0.675584	+	0.737283i	$0.736109\pi$
$338$	2848.50	−	4933.75i	0.458396	−	0.793966i
$339$	−972.000	−	1683.55i	−0.155728	−	0.269729i
$340$	126.000	+	218.238i	0.0200980	+	0.0348107i
$341$	1897.50	−	3286.57i	0.301335	−	0.521928i
$342$	−432.000			−0.0683038
$343$		0			0
$344$	546.000			0.0855766
$345$	−378.000	+	654.715i	−0.0589879	+	0.102170i
$346$	1179.00	+	2042.09i	0.183189	+	0.317293i
$347$	930.000	+	1610.81i	0.143876	+	0.249201i	0.928953	−	0.370197i	$-0.120710\pi$
$347$	930.000	+	1610.81i	0.143876	+	0.249201i	−0.785077	+	0.619398i	$0.787377\pi$
$348$	−445.500	+	771.629i	−0.0686244	+	0.118861i
$349$	1918.00			0.294178			0.147089	−	0.989123i	$-0.453010\pi$
$349$	1918.00			0.294178			0.147089	+	0.989123i	$0.453010\pi$
$350$		0			0
$351$	−1728.00			−0.262774
$352$	337.500	−	584.567i	0.0511046	−	0.0885157i
$353$	−1524.00	−	2639.65i	−0.229786	−	0.398000i	0.727959	−	0.685621i	$-0.240469\pi$
$353$	−1524.00	−	2639.65i	−0.229786	−	0.398000i	−0.957744	+	0.287620i	$0.907136\pi$
$354$	−67.5000	−	116.913i	−0.0101344	−	0.0175533i
$355$	513.000	−	888.542i	0.0766964	−	0.132842i
$356$	−906.000			−0.134882
$357$		0			0
$358$	−8676.00			−1.28084
$359$	15.0000	−	25.9808i	0.00220521	−	0.00381953i	−0.864921	−	0.501909i	$-0.832631\pi$
$359$	15.0000	−	25.9808i	0.00220521	−	0.00381953i	0.867126	+	0.498089i	$0.165965\pi$
$360$	−283.500	−	491.036i	−0.0415049	−	0.0718886i
$361$	3301.50	+	5718.37i	0.481338	+	0.833703i
$362$	−2028.00	+	3512.60i	−0.294446	+	0.509995i
$363$	3318.00			0.479752
$364$		0			0
$365$	−1086.00			−0.155737
$366$	−531.000	+	919.719i	−0.0758356	+	0.131351i
$367$	−5655.50	−	9795.61i	−0.804400	−	1.39326i	−0.916696	−	0.399586i	$-0.869154\pi$
$367$	−5655.50	−	9795.61i	−0.804400	−	1.39326i	0.112296	−	0.993675i	$-0.464180\pi$
$368$	−2982.00	−	5164.98i	−0.422412	−	0.731638i
$369$	1620.00	−	2805.92i	0.228547	−	0.395855i
$370$	2844.00			0.399601
$371$		0			0
$372$	−759.000			−0.105786
$373$	−604.000	+	1046.16i	−0.0838443	+	0.145223i	−0.904898	−	0.425628i	$-0.860053\pi$
$373$	−604.000	+	1046.16i	−0.0838443	+	0.145223i	0.821054	+	0.570851i	$0.193387\pi$
$374$	1890.00	+	3273.58i	0.261309	+	0.452600i
$375$	−1084.50	−	1878.41i	−0.149342	−	0.258668i
$376$	−315.000	+	545.596i	−0.0432045	+	0.0748324i
$377$	−19008.0			−2.59672
$378$		0			0
$379$	7640.00			1.03546			0.517731	−	0.855543i	$-0.326777\pi$
$379$	7640.00			1.03546			0.517731	+	0.855543i	$0.326777\pi$
$380$	−24.0000	+	41.5692i	−0.00323993	+	0.00561173i
$381$	565.500	+	979.475i	0.0760405	+	0.131706i
$382$	5868.00	+	10163.7i	0.785950	+	1.36131i
$383$	6375.00	−	11041.8i	0.850515	−	1.47314i	−0.0302291	−	0.999543i	$-0.509624\pi$
$383$	6375.00	−	11041.8i	0.850515	−	1.47314i	0.880744	−	0.473592i	$-0.157043\pi$
$384$	4977.00			0.661410
$385$		0			0
$386$	−4479.00			−0.590609
$387$	−117.000	+	202.650i	−0.0153681	+	0.0266183i
$388$	251.500	+	435.611i	0.0329072	+	0.0569969i
$389$	−1563.00	−	2707.20i	−0.203720	−	0.352854i	0.746004	−	0.665942i	$-0.231970\pi$
$389$	−1563.00	−	2707.20i	−0.203720	−	0.352854i	−0.949724	+	0.313087i	$0.898637\pi$
$390$	−864.000	+	1496.49i	−0.112180	+	0.194302i
$391$	7056.00			0.912627
$392$		0			0
$393$	−1953.00			−0.250676
$394$	−6129.00	+	10615.7i	−0.783692	+	1.35739i
$395$	−700.500	−	1213.30i	−0.0892303	−	0.154551i
$396$	67.5000	+	116.913i	0.00856566	+	0.0148362i
$397$	−2966.00	+	5137.26i	−0.374960	+	0.649450i	−0.990321	−	0.138795i	$-0.955677\pi$
$397$	−2966.00	+	5137.26i	−0.374960	+	0.649450i	0.615361	+	0.788246i	$0.289010\pi$
$398$	−10668.0			−1.34356
$399$		0			0
$400$	8236.00			1.02950
$401$	−804.000	+	1392.57i	−0.100124	+	0.173420i	−0.911736	−	0.410777i	$-0.865257\pi$
$401$	−804.000	+	1392.57i	−0.100124	+	0.173420i	0.811611	+	0.584198i	$0.198591\pi$
$402$	1665.00	+	2883.86i	0.206574	+	0.357796i
$403$	−8096.00	−	14022.7i	−1.00072	−	1.73330i
$404$	−543.000	+	940.504i	−0.0668695	+	0.115821i
$405$	243.000			0.0298142
$406$		0			0
$407$	4740.00			0.577280
$408$	−2646.00	+	4583.01i	−0.321070	+	0.556109i
$409$	−2232.50	−	3866.80i	−0.269902	−	0.467484i	0.698934	−	0.715186i	$-0.253658\pi$
$409$	−2232.50	−	3866.80i	−0.269902	−	0.467484i	−0.968836	+	0.247702i	$0.920325\pi$
$410$	−1620.00	−	2805.92i	−0.195137	−	0.337987i
$411$	−2655.00	+	4598.59i	−0.318641	+	0.551903i
$412$	−1736.00			−0.207589
$413$		0			0
$414$	2268.00			0.269242
$415$	715.500	−	1239.28i	0.0846326	−	0.146588i
$416$	−1440.00	−	2494.15i	−0.169716	−	0.293957i
$417$	2337.00	+	4047.80i	0.274445	+	0.475352i
$418$	−360.000	+	623.538i	−0.0421248	+	0.0729623i
$419$	1584.00			0.184686			0.0923430	−	0.995727i	$-0.470564\pi$
$419$	1584.00			0.184686			0.0923430	+	0.995727i	$0.470564\pi$
$420$		0			0
$421$	−1330.00			−0.153967			−0.0769837	−	0.997032i	$-0.524529\pi$
$421$	−1330.00			−0.153967			−0.0769837	+	0.997032i	$0.524529\pi$
$422$	1875.00	−	3247.60i	0.216288	−	0.374622i
$423$	−135.000	−	233.827i	−0.0155176	−	0.0268772i
$424$	−3811.50	−	6601.71i	−0.436563	−	0.756150i
$425$	−4872.00	+	8438.55i	−0.556063	+	0.963129i
$426$	−3078.00			−0.350069
$427$		0			0
$428$	−1353.00			−0.152803
$429$	−1440.00	+	2494.15i	−0.162060	+	0.280697i
$430$	117.000	+	202.650i	0.0131215	+	0.0227271i
$431$	−4794.00	−	8303.45i	−0.535775	−	0.927989i	−0.999125	−	0.0418139i	$-0.986686\pi$
$431$	−4794.00	−	8303.45i	−0.535775	−	0.927989i	0.463351	−	0.886175i	$-0.346647\pi$
$432$	−958.500	+	1660.17i	−0.106750	+	0.184896i
$433$	−494.000			−0.0548271			−0.0274135	−	0.999624i	$-0.508727\pi$
$433$	−494.000			−0.0548271			−0.0274135	+	0.999624i	$0.508727\pi$
$434$		0			0
$435$	2673.00			0.294622
$436$	185.000	−	320.429i	0.0203209	−	0.0351968i
$437$	672.000	+	1163.94i	0.0735609	+	0.127411i
$438$	1629.00	+	2821.51i	0.177709	+	0.307801i
$439$	−8004.50	+	13864.2i	−0.870237	+	1.50729i	−0.00848508	+	0.999964i	$0.502701\pi$
$439$	−8004.50	+	13864.2i	−0.870237	+	1.50729i	−0.861752	+	0.507330i	$0.830632\pi$
$440$	−945.000			−0.102389
$441$		0			0
$442$	16128.0			1.73559
$443$	−3886.50	+	6731.62i	−0.416824	+	0.721961i	−0.995618	−	0.0935130i	$-0.970190\pi$
$443$	−3886.50	+	6731.62i	−0.416824	+	0.721961i	0.578794	+	0.815474i	$0.303524\pi$
$444$	−474.000	−	820.992i	−0.0506645	−	0.0877535i
$445$	1359.00	+	2353.86i	0.144770	+	0.250749i
$446$	−637.500	+	1104.18i	−0.0676827	+	0.117230i
$447$	−7362.00			−0.778995
$448$		0			0
$449$	864.000			0.0908122			0.0454061	−	0.998969i	$-0.485542\pi$
$449$	864.000			0.0908122			0.0454061	+	0.998969i	$0.485542\pi$
$450$	−1566.00	+	2712.39i	−0.164049	+	0.284141i
$451$	−2700.00	−	4676.54i	−0.281903	−	0.488269i
$452$	324.000	+	561.184i	0.0337161	+	0.0583980i
$453$	1888.50	−	3270.98i	0.195871	−	0.339258i
$454$	11565.0			1.19553
$455$		0			0
$456$	−1008.00			−0.103517
$457$	−1259.50	+	2181.52i	−0.128921	+	0.223298i	−0.923259	−	0.384179i	$-0.874485\pi$
$457$	−1259.50	+	2181.52i	−0.128921	+	0.223298i	0.794338	+	0.607476i	$0.207818\pi$
$458$	3282.00	+	5684.59i	0.334842	+	0.579964i
$459$	−1134.00	−	1964.15i	−0.115317	−	0.199735i
$460$	126.000	−	218.238i	0.0127713	−	0.0221205i
$461$	342.000			0.0345521			0.0172761	−	0.999851i	$-0.494501\pi$
$461$	342.000			0.0345521			0.0172761	+	0.999851i	$0.494501\pi$
$462$		0			0
$463$	−4336.00			−0.435229			−0.217614	−	0.976035i	$-0.569828\pi$
$463$	−4336.00			−0.435229			−0.217614	+	0.976035i	$0.569828\pi$
$464$	−10543.5	+	18261.9i	−1.05489	+	1.82713i
$465$	1138.50	+	1971.94i	0.113541	+	0.196659i
$466$	1278.00	+	2213.56i	0.127043	+	0.220046i
$467$	9318.00	−	16139.2i	0.923310	−	1.59922i	0.129052	−	0.991638i	$-0.458806\pi$
$467$	9318.00	−	16139.2i	0.923310	−	1.59922i	0.794257	−	0.607581i	$-0.207860\pi$
$468$	576.000			0.0568923
$469$		0			0
$470$	−270.000			−0.0264982
$471$	294.000	−	509.223i	0.0287618	−	0.0498169i
$472$	−157.500	−	272.798i	−0.0153592	−	0.0266029i
$473$	195.000	+	337.750i	0.0189558	+	0.0328325i
$474$	−2101.50	+	3639.90i	−0.203639	+	0.352714i
$475$	−1856.00			−0.179282
$476$		0			0
$477$	3267.00			0.313597
$478$	8262.00	−	14310.2i	0.790575	−	1.36932i
$479$	7539.00	+	13057.9i	0.719135	+	1.24558i	0.961343	+	0.275354i	$0.0887951\pi$
$479$	7539.00	+	13057.9i	0.719135	+	1.24558i	−0.242208	+	0.970224i	$0.577872\pi$
$480$	202.500	+	350.740i	0.0192559	+	0.0333521i
$481$	10112.0	−	17514.5i	0.958560	−	1.66028i
$482$	2373.00			0.224247
$483$		0			0
$484$	−1106.00			−0.103869
$485$	754.500	−	1306.83i	0.0706393	−	0.122351i
$486$	−364.500	−	631.333i	−0.0340207	−	0.0589256i
$487$	−3110.50	−	5387.54i	−0.289425	−	0.501300i	0.684247	−	0.729250i	$-0.260131\pi$
$487$	−3110.50	−	5387.54i	−0.289425	−	0.501300i	−0.973673	+	0.227950i	$0.926798\pi$
$488$	−1239.00	+	2146.01i	−0.114932	+	0.199068i
$489$	3756.00			0.347346
$490$		0			0
$491$	−7371.00			−0.677492			−0.338746	−	0.940878i	$-0.610003\pi$
$491$	−7371.00			−0.677492			−0.338746	+	0.940878i	$0.610003\pi$
$492$	−540.000	+	935.307i	−0.0494819	+	0.0857051i
$493$	−12474.0	−	21605.6i	−1.13956	−	1.97377i
$494$	1536.00	+	2660.43i	0.139895	+	0.242304i
$495$	202.500	−	350.740i	0.0183873	−	0.0318477i
$496$	−17963.0			−1.62613
$497$		0			0
$498$	−4293.00			−0.386293
$499$	−2137.00	+	3701.39i	−0.191714	+	0.332058i	−0.945818	−	0.324696i	$-0.894738\pi$
$499$	−2137.00	+	3701.39i	−0.191714	+	0.332058i	0.754104	+	0.656755i	$0.228071\pi$
$500$	361.500	+	626.136i	0.0323335	+	0.0560033i
$501$	3969.00	+	6874.51i	0.353936	+	0.613035i
$502$	−7897.50	+	13678.9i	−0.702157	+	1.21617i
$503$	2520.00			0.223382			0.111691	−	0.993743i	$-0.464373\pi$
$503$	2520.00			0.223382			0.111691	+	0.993743i	$0.464373\pi$
$504$		0			0
$505$	3258.00			0.287087
$506$	1890.00	−	3273.58i	0.166049	−	0.287605i
$507$	2848.50	+	4933.75i	0.249519	+	0.432180i
$508$	−188.500	−	326.492i	−0.0164633	−	0.0285152i
$509$	−7138.50	+	12364.2i	−0.621628	+	1.07669i	0.367555	+	0.930002i	$0.380195\pi$
$509$	−7138.50	+	12364.2i	−0.621628	+	1.07669i	−0.989183	+	0.146689i	$0.953138\pi$
$510$	−2268.00			−0.196919
$511$		0			0
$512$	8733.00			0.753804
$513$	216.000	−	374.123i	0.0185899	−	0.0321987i
$514$	10305.0	+	17848.8i	0.884308	+	1.53167i
$515$	2604.00	+	4510.26i	0.222808	+	0.385914i
$516$	39.0000	−	67.5500i	0.00332729	−	0.00576303i
$517$	−450.000			−0.0382804
$518$		0			0
$519$	−2358.00			−0.199431
$520$	−2016.00	+	3491.81i	−0.170014	+	0.294473i
$521$	−3153.00	−	5461.16i	−0.265135	−	0.459228i	0.702464	−	0.711719i	$-0.252083\pi$
$521$	−3153.00	−	5461.16i	−0.265135	−	0.459228i	−0.967599	+	0.252492i	$0.918750\pi$
$522$	−4009.50	−	6944.66i	−0.336190	−	0.582298i
$523$	4036.00	−	6990.56i	0.337442	−	0.584466i	−0.646509	−	0.762906i	$-0.723772\pi$
$523$	4036.00	−	6990.56i	0.337442	−	0.584466i	0.983951	+	0.178440i	$0.0571051\pi$
$524$	651.000			0.0542730
$525$		0			0
$526$	666.000			0.0552072
$527$	10626.0	−	18404.8i	0.878322	−	1.52130i
$528$	1597.50	+	2766.95i	0.131671	+	0.228061i
$529$	2555.50	+	4426.26i	0.210035	+	0.363792i
$530$	1633.50	−	2829.30i	0.133877	−	0.231881i
$531$	135.000			0.0110330
$532$		0			0
$533$	−23040.0			−1.87237
$534$	4077.00	−	7061.57i	0.330391	−	0.572255i
$535$	2029.50	+	3515.20i	0.164005	+	0.284066i
$536$	3885.00	+	6729.02i	0.313072	+	0.542256i
$537$	4338.00	−	7513.64i	0.348601	−	0.603794i
$538$	23553.0			1.88744
$539$		0			0
$540$	−81.0000			−0.00645497
$541$	11429.0	−	19795.6i	0.908264	−	1.57316i	0.0917903	−	0.995778i	$-0.470741\pi$
$541$	11429.0	−	19795.6i	0.908264	−	1.57316i	0.816474	−	0.577382i	$-0.195926\pi$
$542$	−7774.50	−	13465.8i	−0.616132	−	1.06717i
$543$	−2028.00	−	3512.60i	−0.160276	−	0.277606i
$544$	1890.00	−	3273.58i	0.148958	−	0.258003i
$545$	−1110.00			−0.0872425
$546$		0			0
$547$	−24724.0			−1.93258			−0.966291	−	0.257454i	$-0.917116\pi$
$547$	−24724.0			−1.93258			−0.966291	+	0.257454i	$0.917116\pi$
$548$	885.000	−	1532.86i	0.0689878	−	0.119490i
$549$	−531.000	−	919.719i	−0.0412796	−	0.0714985i
$550$	2610.00	+	4520.65i	0.202347	+	0.350475i
$551$	2376.00	−	4115.35i	0.183704	−	0.318185i
$552$	5292.00			0.408048
$553$		0			0
$554$	14880.0			1.14114
$555$	−1422.00	+	2462.98i	−0.108758	+	0.188374i
$556$	−779.000	−	1349.27i	−0.0594190	−	0.102917i
$557$	4921.50	+	8524.29i	0.374382	+	0.648448i	0.990234	−	0.139413i	$-0.0445216\pi$
$557$	4921.50	+	8524.29i	0.374382	+	0.648448i	−0.615853	+	0.787861i	$0.711188\pi$
$558$	3415.50	−	5915.82i	0.259121	−	0.448811i
$559$	1664.00			0.125903
$560$		0			0
$561$	−3780.00			−0.284477
$562$	−1161.00	+	2010.91i	−0.0871420	+	0.150934i
$563$	−6685.50	−	11579.6i	−0.500462	−	0.866826i	−1.00000		0.000533812i	$-0.999830\pi$
$563$	−6685.50	−	11579.6i	−0.500462	−	0.866826i	0.499538	−	0.866292i	$-0.333503\pi$
$564$	45.0000	+	77.9423i	0.00335965	+	0.00581908i
$565$	972.000	−	1683.55i	0.0723758	−	0.125359i
$566$	11094.0			0.823879
$567$		0			0
$568$	−7182.00			−0.530546
$569$	2616.00	−	4531.04i	0.192739	−	0.333834i	−0.753418	−	0.657542i	$-0.771596\pi$
$569$	2616.00	−	4531.04i	0.192739	−	0.333834i	0.946157	+	0.323708i	$0.104930\pi$
$570$	−216.000	−	374.123i	−0.0158724	−	0.0274917i
$571$	7199.00	+	12469.0i	0.527616	+	0.913858i	0.999482	+	0.0321874i	$0.0102474\pi$
$571$	7199.00	+	12469.0i	0.527616	+	0.913858i	−0.471866	+	0.881670i	$0.656419\pi$
$572$	480.000	−	831.384i	0.0350871	−	0.0607726i
$573$	−11736.0			−0.855634
$574$		0			0
$575$	9744.00			0.706701
$576$	−1948.50	+	3374.90i	−0.140951	+	0.244133i
$577$	9935.50	+	17208.8i	0.716846	+	1.24161i	0.962243	+	0.272191i	$0.0877484\pi$
$577$	9935.50	+	17208.8i	0.716846	+	1.24161i	−0.245397	+	0.969423i	$0.578918\pi$
$578$	3214.50	+	5567.68i	0.231325	+	0.400666i
$579$	2239.50	−	3878.93i	0.160743	−	0.278416i
$580$	−891.000			−0.0637875
$581$		0			0
$582$	−4527.00			−0.322423
$583$	2722.50	−	4715.51i	0.193404	−	0.334985i
$584$	3801.00	+	6583.53i	0.269326	+	0.466487i
$585$	−864.000	−	1496.49i	−0.0610633	−	0.105765i
$586$	9409.50	−	16297.7i	0.663315	−	1.14890i
$587$	16137.0			1.13466			0.567330	−	0.823491i	$-0.307976\pi$
$587$	16137.0			1.13466			0.567330	+	0.823491i	$0.307976\pi$
$588$		0			0
$589$	4048.00			0.283183
$590$	67.5000	−	116.913i	0.00471005	−	0.00815805i
$591$	−6129.00	−	10615.7i	−0.426588	−	0.738872i
$592$	−11218.0	−	19430.1i	−0.778812	−	1.34894i
$593$	−10662.0	+	18467.1i	−0.738340	+	1.27884i	0.214902	+	0.976636i	$0.431057\pi$
$593$	−10662.0	+	18467.1i	−0.738340	+	1.27884i	−0.953242	+	0.302207i	$0.902276\pi$
$594$	−1215.00			−0.0839260
$595$		0			0
$596$	2454.00			0.168657
$597$	5334.00	−	9238.76i	0.365672	−	0.633362i
$598$	−8064.00	−	13967.3i	−0.551441	−	0.955123i
$599$	4323.00	+	7487.66i	0.294880	+	0.510747i	0.974957	−	0.222394i	$-0.0713871\pi$
$599$	4323.00	+	7487.66i	0.294880	+	0.510747i	−0.680077	+	0.733141i	$0.738054\pi$
$600$	−3654.00	+	6328.91i	−0.248623	+	0.430628i
$601$	−11195.0			−0.759823			−0.379911	−	0.925023i	$-0.624046\pi$
$601$	−11195.0			−0.759823			−0.379911	+	0.925023i	$0.624046\pi$
$602$		0			0
$603$	−3330.00			−0.224889
$604$	−629.500	+	1090.33i	−0.0424073	+	0.0734515i
$605$	1659.00	+	2873.47i	0.111484	+	0.193096i
$606$	−4887.00	−	8464.53i	−0.327592	−	0.567406i
$607$	−4485.50	+	7769.11i	−0.299935	+	0.519503i	−0.976121	−	0.217228i	$-0.930298\pi$
$607$	−4485.50	+	7769.11i	−0.299935	+	0.519503i	0.676185	+	0.736731i	$0.263632\pi$
$608$	720.000			0.0480261
$609$		0			0
$610$	−1062.00			−0.0704904
$611$	−960.000	+	1662.77i	−0.0635637	+	0.110096i
$612$	378.000	+	654.715i	0.0249669	+	0.0432439i
$613$	6386.00	+	11060.9i	0.420764	+	0.728784i	0.996014	−	0.0891932i	$-0.0284288\pi$
$613$	6386.00	+	11060.9i	0.420764	+	0.728784i	−0.575251	+	0.817977i	$0.695096\pi$
$614$	2526.00	−	4375.16i	0.166028	−	0.287569i
$615$	3240.00			0.212438
$616$		0			0
$617$	12762.0			0.832705			0.416352	−	0.909203i	$-0.363308\pi$
$617$	12762.0			0.832705			0.416352	+	0.909203i	$0.363308\pi$
$618$	7812.00	−	13530.8i	0.508487	−	0.880725i
$619$	6421.00	+	11121.5i	0.416933	+	0.722150i	0.995629	−	0.0933936i	$-0.0297715\pi$
$619$	6421.00	+	11121.5i	0.416933	+	0.722150i	−0.578696	+	0.815543i	$0.696438\pi$
$620$	−379.500	−	657.313i	−0.0245824	−	0.0425780i
$621$	−1134.00	+	1964.15i	−0.0732783	+	0.126922i
$622$	−3960.00			−0.255276
$623$		0			0
$624$	13632.0			0.874546
$625$	−6165.50	+	10679.0i	−0.394592	+	0.683453i
$626$	12754.5	+	22091.4i	0.814333	+	1.41047i
$627$	−360.000	−	623.538i	−0.0229298	−	0.0397157i
$628$	−98.0000	+	169.741i	−0.00622711	+	0.0107857i
$629$	26544.0			1.68264
$630$		0			0
$631$	21365.0			1.34790			0.673952	−	0.738775i	$-0.264596\pi$
$631$	21365.0			1.34790			0.673952	+	0.738775i	$0.264596\pi$
$632$	−4903.50	+	8493.11i	−0.308625	+	0.534554i
$633$	1875.00	+	3247.60i	0.117732	+	0.203918i
$634$	−3865.50	−	6695.24i	−0.242143	−	0.419404i
$635$	−565.500	+	979.475i	−0.0353404	+	0.0612114i
$636$	−1089.00			−0.0678957
$637$		0			0
$638$	−13365.0			−0.829350
$639$	1539.00	−	2665.63i	0.0952768	−	0.165024i
$640$	2488.50	+	4310.21i	0.153698	+	0.266212i
$641$	−4137.00	−	7165.49i	−0.254917	−	0.441529i	0.709956	−	0.704246i	$-0.248715\pi$
$641$	−4137.00	−	7165.49i	−0.254917	−	0.441529i	−0.964873	+	0.262717i	$0.915381\pi$
$642$	6088.50	−	10545.6i	0.374290	−	0.648289i
$643$	−27998.0			−1.71716			−0.858580	−	0.512680i	$-0.828653\pi$
$643$	−27998.0			−1.71716			−0.858580	+	0.512680i	$0.828653\pi$
$644$		0			0
$645$	−234.000			−0.0142849
$646$	−2016.00	+	3491.81i	−0.122784	+	0.212668i
$647$	−8733.00	−	15126.0i	−0.530649	−	0.919110i	−0.999360	−	0.0357592i	$-0.988615\pi$
$647$	−8733.00	−	15126.0i	−0.530649	−	0.919110i	0.468712	−	0.883351i	$-0.344718\pi$
$648$	−850.500	−	1473.11i	−0.0515599	−	0.0893043i
$649$	112.500	−	194.856i	0.00680433	−	0.0117854i
$650$	22272.0			1.34397
$651$		0			0
$652$	−1252.00			−0.0752026
$653$	−1078.50	+	1868.02i	−0.0646324	+	0.111947i	−0.896531	−	0.442981i	$-0.853921\pi$
$653$	−1078.50	+	1868.02i	−0.0646324	+	0.111947i	0.831898	+	0.554928i	$0.187254\pi$
$654$	1665.00	+	2883.86i	0.0995515	+	0.172428i
$655$	−976.500	−	1691.35i	−0.0582519	−	0.100895i
$656$	−12780.0	+	22135.6i	−0.760633	+	1.31745i
$657$	−3258.00			−0.193465
$658$		0			0
$659$	19944.0			1.17892			0.589460	−	0.807798i	$-0.299341\pi$
$659$	19944.0			1.17892			0.589460	+	0.807798i	$0.299341\pi$
$660$	−67.5000	+	116.913i	−0.00398096	+	0.00689523i
$661$	13753.0	+	23820.9i	0.809273	+	1.40170i	0.913368	+	0.407135i	$0.133472\pi$
$661$	13753.0	+	23820.9i	0.809273	+	1.40170i	−0.104095	+	0.994567i	$0.533194\pi$
$662$	−726.000	−	1257.47i	−0.0426236	−	0.0738262i
$663$	−8064.00	+	13967.3i	−0.472368	+	0.818165i
$664$	−10017.0			−0.585444
$665$		0			0
$666$	8532.00			0.496409
$667$	−12474.0	+	21605.6i	−0.724131	+	1.25423i
$668$	−1323.00	−	2291.50i	−0.0766294	−	0.132726i
$669$	−637.500	−	1104.18i	−0.0368418	−	0.0638119i
$670$	−1665.00	+	2883.86i	−0.0960068	+	0.166289i
$671$	−1770.00			−0.101833
$672$		0			0
$673$	−19123.0			−1.09530			−0.547650	−	0.836707i	$-0.684478\pi$
$673$	−19123.0			−1.09530			−0.547650	+	0.836707i	$0.684478\pi$
$674$	−12538.5	+	21717.3i	−0.716565	+	1.24113i
$675$	−1566.00	−	2712.39i	−0.0892968	−	0.154667i
$676$	−949.500	−	1644.58i	−0.0540225	−	0.0935698i
$677$	6928.50	−	12000.5i	0.393329	−	0.681266i	−0.599557	−	0.800332i	$-0.704657\pi$
$677$	6928.50	−	12000.5i	0.393329	−	0.681266i	0.992886	+	0.119066i	$0.0379899\pi$
$678$	−5832.00			−0.330349
$679$		0			0
$680$	−5292.00			−0.298440
$681$	−5782.50	+	10015.6i	−0.325383	+	0.563580i
$682$	−5692.50	−	9859.70i	−0.319615	−	0.553589i
$683$	11122.5	+	19264.7i	0.623120	+	1.07927i	0.988901	+	0.148574i	$0.0474683\pi$
$683$	11122.5	+	19264.7i	0.623120	+	1.07927i	−0.365782	+	0.930701i	$0.619198\pi$
$684$	−72.0000	+	124.708i	−0.00402484	+	0.00697122i
$685$	−5310.00			−0.296182
$686$		0			0
$687$	−6564.00			−0.364530
$688$	923.000	−	1598.68i	0.0511469	−	0.0885890i
$689$	−11616.0	−	20119.5i	−0.642285	−	1.11247i
$690$	1134.00	+	1964.15i	0.0625661	+	0.108368i
$691$	−320.000	+	554.256i	−0.0176170	+	0.0305136i	−0.874700	−	0.484666i	$-0.838941\pi$
$691$	−320.000	+	554.256i	−0.0176170	+	0.0305136i	0.857082	+	0.515179i	$0.172275\pi$
$692$	786.000			0.0431781
$693$		0			0
$694$	5580.00			0.305207
$695$	−2337.00	+	4047.80i	−0.127550	+	0.220924i
$696$	−9355.50	−	16204.2i	−0.509511	−	0.882498i
$697$	−15120.0	−	26188.6i	−0.821680	−	1.42319i
$698$	2877.00	−	4983.11i	0.156012	−	0.270220i
$699$	−2556.00			−0.138307
$700$		0			0
$701$	−15561.0			−0.838418			−0.419209	−	0.907890i	$-0.637693\pi$
$701$	−15561.0			−0.838418			−0.419209	+	0.907890i	$0.637693\pi$
$702$	−2592.00	+	4489.48i	−0.139357	+	0.241374i
$703$	2528.00	+	4378.62i	0.135626	+	0.234912i
$704$	3247.50	+	5624.83i	0.173856	+	0.301128i
$705$	135.000	−	233.827i	0.00721191	−	0.0124914i
$706$	−9144.00			−0.487449
$707$		0			0
$708$	−45.0000			−0.00238871
$709$	−2767.00	+	4792.58i	−0.146568	+	0.253864i	−0.929957	−	0.367668i	$-0.880156\pi$
$709$	−2767.00	+	4792.58i	−0.146568	+	0.253864i	0.783389	+	0.621532i	$0.213489\pi$
$710$	−1539.00	−	2665.63i	−0.0813488	−	0.140900i
$711$	−2101.50	−	3639.90i	−0.110847	−	0.191993i
$712$	9513.00	−	16477.0i	0.500723	−	0.867278i
$713$	−21252.0			−1.11626
$714$		0			0
$715$	−2880.00			−0.150638
$716$	−1446.00	+	2504.55i	−0.0754742	+	0.130725i
$717$	8262.00	+	14310.2i	0.430335	+	0.745362i
$718$	−45.0000	−	77.9423i	−0.00233898	−	0.00405123i
$719$	−10923.0	+	18919.2i	−0.566564	+	0.981317i	0.430339	+	0.902667i	$0.358394\pi$
$719$	−10923.0	+	18919.2i	−0.566564	+	0.981317i	−0.996902	+	0.0786494i	$0.974939\pi$
$720$	−1917.00			−0.0992255
$721$		0			0
$722$	19809.0			1.02107
$723$	−1186.50	+	2055.08i	−0.0610324	+	0.105711i
$724$	676.000	+	1170.87i	0.0347007	+	0.0601035i
$725$	−17226.0	−	29836.3i	−0.882424	−	1.52840i
$726$	4977.00	−	8620.42i	0.254427	−	0.440680i
$727$	11089.0			0.565706			0.282853	−	0.959163i	$-0.408719\pi$
$727$	11089.0			0.565706			0.282853	+	0.959163i	$0.408719\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−1629.00	+	2821.51i	−0.0825918	+	0.143053i
$731$	1092.00	+	1891.40i	0.0552518	+	0.0956990i
$732$	177.000	+	306.573i	0.00893731	+	0.0154799i
$733$	5881.00	−	10186.2i	0.296343	−	0.513282i	−0.678953	−	0.734182i	$-0.737566\pi$
$733$	5881.00	−	10186.2i	0.296343	−	0.513282i	0.975296	+	0.220900i	$0.0708994\pi$
$734$	−33933.0			−1.70639
$735$		0			0
$736$	−3780.00			−0.189311
$737$	−2775.00	+	4806.44i	−0.138695	+	0.240227i
$738$	−4860.00	−	8417.77i	−0.242411	−	0.419868i
$739$	11363.0	+	19681.3i	0.565622	+	0.979686i	0.996992	+	0.0775108i	$0.0246972\pi$
$739$	11363.0	+	19681.3i	0.565622	+	0.979686i	−0.431369	+	0.902175i	$0.641969\pi$
$740$	474.000	−	820.992i	0.0235467	−	0.0407841i
$741$	−3072.00			−0.152298
$742$		0			0
$743$	6678.00			0.329734			0.164867	−	0.986316i	$-0.447281\pi$
$743$	6678.00			0.329734			0.164867	+	0.986316i	$0.447281\pi$
$744$	7969.50	−	13803.6i	0.392710	−	0.680193i
$745$	−3681.00	−	6375.68i	−0.181022	−	0.313539i
$746$	1812.00	+	3138.48i	0.0889303	+	0.154032i
$747$	2146.50	−	3717.85i	0.105136	−	0.182100i
$748$	1260.00			0.0615911
$749$		0			0
$750$	−6507.00			−0.316803
$751$	9993.50	−	17309.2i	0.485577	−	0.841043i	−0.514286	−	0.857619i	$-0.671943\pi$
$751$	9993.50	−	17309.2i	0.485577	−	0.841043i	0.999863	+	0.0165754i	$0.00527637\pi$
$752$	1065.00	+	1844.63i	0.0516444	+	0.0894506i
$753$	−7897.50	−	13678.9i	−0.382206	−	0.662000i
$754$	−28512.0	+	49384.2i	−1.37712	+	2.38524i
$755$	3777.00			0.182065
$756$		0			0
$757$	314.000			0.0150760			0.00753799	−	0.999972i	$-0.497601\pi$
$757$	314.000			0.0150760			0.00753799	+	0.999972i	$0.497601\pi$
$758$	11460.0	−	19849.3i	0.549137	−	0.951133i
$759$	1890.00	+	3273.58i	0.0903856	+	0.156552i
$760$	−504.000	−	872.954i	−0.0240553	−	0.0416649i
$761$	−5748.00	+	9955.83i	−0.273804	+	0.474242i	−0.969833	−	0.243772i	$-0.921615\pi$
$761$	−5748.00	+	9955.83i	−0.273804	+	0.474242i	0.696029	+	0.718014i	$0.254949\pi$
$762$	3393.00			0.161306
$763$		0			0
$764$	3912.00			0.185250
$765$	1134.00	−	1964.15i	0.0535946	−	0.0928285i
$766$	−19125.0	−	33125.5i	−0.902107	−	1.56250i
$767$	−480.000	−	831.384i	−0.0225969	−	0.0391389i
$768$	2269.50	−	3930.89i	0.106632	−	0.184692i
$769$	−2765.00			−0.129660			−0.0648299	−	0.997896i	$-0.520650\pi$
$769$	−2765.00			−0.129660			−0.0648299	+	0.997896i	$0.520650\pi$
$770$		0			0
$771$	−20610.0			−0.962712
$772$	−746.500	+	1292.98i	−0.0348020	+	0.0602

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(4.50000 + 7.79423i) q^{10} +(7.50000 + 12.9904i) q^{11} +(1.50000 - 2.59808i) q^{12} +64.0000 q^{13} -9.00000 q^{15} +(35.5000 - 61.4878i) q^{16} +(42.0000 + 72.7461i) q^{17} +(13.5000 + 23.3827i) q^{18} +(-8.00000 + 13.8564i) q^{19} +3.00000 q^{20} +45.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(31.5000 + 54.5596i) q^{24} +(58.0000 + 100.459i) q^{25} +(96.0000 - 166.277i) q^{26} -27.0000 q^{27} -297.000 q^{29} +(-13.5000 + 23.3827i) q^{30} +(-126.500 - 219.104i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(-22.5000 + 38.9711i) q^{33} +252.000 q^{34} +9.00000 q^{36} +(158.000 - 273.664i) q^{37} +(24.0000 + 41.5692i) q^{38} +(96.0000 + 166.277i) q^{39} +(-31.5000 + 54.5596i) q^{40} -360.000 q^{41} +26.0000 q^{43} +(7.50000 - 12.9904i) q^{44} +(-13.5000 - 23.3827i) q^{45} +(-126.000 - 218.238i) q^{46} +(-15.0000 + 25.9808i) q^{47} +213.000 q^{48} +348.000 q^{50} +(-126.000 + 218.238i) q^{51} +(-32.0000 - 55.4256i) q^{52} +(-181.500 - 314.367i) q^{53} +(-40.5000 + 70.1481i) q^{54} -45.0000 q^{55} -48.0000 q^{57} +(-445.500 + 771.629i) q^{58} +(-7.50000 - 12.9904i) q^{59} +(4.50000 + 7.79423i) q^{60} +(-59.0000 + 102.191i) q^{61} -759.000 q^{62} +433.000 q^{64} +(-96.0000 + 166.277i) q^{65} +(67.5000 + 116.913i) q^{66} +(185.000 + 320.429i) q^{67} +(42.0000 - 72.7461i) q^{68} +252.000 q^{69} -342.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(181.000 + 313.501i) q^{73} +(-474.000 - 820.992i) q^{74} +(-174.000 + 301.377i) q^{75} +16.0000 q^{76} +576.000 q^{78} +(-233.500 + 404.434i) q^{79} +(106.500 + 184.463i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-540.000 + 935.307i) q^{82} -477.000 q^{83} -252.000 q^{85} +(39.0000 - 67.5500i) q^{86} +(-445.500 - 771.629i) q^{87} +(157.500 + 272.798i) q^{88} +(453.000 - 784.619i) q^{89} -81.0000 q^{90} -84.0000 q^{92} +(379.500 - 657.313i) q^{93} +(45.0000 + 77.9423i) q^{94} +(-24.0000 - 41.5692i) q^{95} +(67.5000 - 116.913i) q^{96} -503.000 q^{97} -135.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 - q^4 - 3 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9	\( 2 q + 3 q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + 18 q^{6} + 42 q^{8} - 9 q^{9} + 9 q^{10} + 15 q^{11} + 3 q^{12} + 128 q^{13} - 18 q^{15} + 71 q^{16} + 84 q^{17} + 27 q^{18} - 16 q^{19} + 6 q^{20} + 90 q^{22} + 84 q^{23} + 63 q^{24} + 116 q^{25} + 192 q^{26} - 54 q^{27} - 594 q^{29} - 27 q^{30} - 253 q^{31} - 45 q^{32} - 45 q^{33} + 504 q^{34} + 18 q^{36} + 316 q^{37} + 48 q^{38} + 192 q^{39} - 63 q^{40} - 720 q^{41} + 52 q^{43} + 15 q^{44} - 27 q^{45} - 252 q^{46} - 30 q^{47} + 426 q^{48} + 696 q^{50} - 252 q^{51} - 64 q^{52} - 363 q^{53} - 81 q^{54} - 90 q^{55} - 96 q^{57} - 891 q^{58} - 15 q^{59} + 9 q^{60} - 118 q^{61} - 1518 q^{62} + 866 q^{64} - 192 q^{65} + 135 q^{66} + 370 q^{67} + 84 q^{68} + 504 q^{69} - 684 q^{71} - 189 q^{72} + 362 q^{73} - 948 q^{74} - 348 q^{75} + 32 q^{76} + 1152 q^{78} - 467 q^{79} + 213 q^{80} - 81 q^{81} - 1080 q^{82} - 954 q^{83} - 504 q^{85} + 78 q^{86} - 891 q^{87} + 315 q^{88} + 906 q^{89} - 162 q^{90} - 168 q^{92} + 759 q^{93} + 90 q^{94} - 48 q^{95} + 135 q^{96} - 1006 q^{97} - 270 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 - q^4 - 3 * q^5 + 18 * q^6 + 42 * q^8 - 9 * q^9 + 9 * q^10 + 15 * q^11 + 3 * q^12 + 128 * q^13 - 18 * q^15 + 71 * q^16 + 84 * q^17 + 27 * q^18 - 16 * q^19 + 6 * q^20 + 90 * q^22 + 84 * q^23 + 63 * q^24 + 116 * q^25 + 192 * q^26 - 54 * q^27 - 594 * q^29 - 27 * q^30 - 253 * q^31 - 45 * q^32 - 45 * q^33 + 504 * q^34 + 18 * q^36 + 316 * q^37 + 48 * q^38 + 192 * q^39 - 63 * q^40 - 720 * q^41 + 52 * q^43 + 15 * q^44 - 27 * q^45 - 252 * q^46 - 30 * q^47 + 426 * q^48 + 696 * q^50 - 252 * q^51 - 64 * q^52 - 363 * q^53 - 81 * q^54 - 90 * q^55 - 96 * q^57 - 891 * q^58 - 15 * q^59 + 9 * q^60 - 118 * q^61 - 1518 * q^62 + 866 * q^64 - 192 * q^65 + 135 * q^66 + 370 * q^67 + 84 * q^68 + 504 * q^69 - 684 * q^71 - 189 * q^72 + 362 * q^73 - 948 * q^74 - 348 * q^75 + 32 * q^76 + 1152 * q^78 - 467 * q^79 + 213 * q^80 - 81 * q^81 - 1080 * q^82 - 954 * q^83 - 504 * q^85 + 78 * q^86 - 891 * q^87 + 315 * q^88 + 906 * q^89 - 162 * q^90 - 168 * q^92 + 759 * q^93 + 90 * q^94 - 48 * q^95 + 135 * q^96 - 1006 * q^97 - 270 * q^99

Introduction

L-functions

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