LMFDB - Embedded newform 150.3.b.a.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(149,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.b (of order $2$, degree $1$, 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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.3.b.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.82843 - 1.00000i) q^{3} +2.00000 q^{4} +(4.00000 + 1.41421i) q^{6} +7.00000i q^{7} -2.82843 q^{8} +(7.00000 + 5.65685i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.82843 - 1.00000i) q^{3} +2.00000 q^{4} +(4.00000 + 1.41421i) q^{6} +7.00000i q^{7} -2.82843 q^{8} +(7.00000 + 5.65685i) q^{9} -8.48528i q^{11} +(-5.65685 - 2.00000i) q^{12} -25.0000i q^{13} -9.89949i q^{14} +4.00000 q^{16} +25.4558 q^{17} +(-9.89949 - 8.00000i) q^{18} +7.00000 q^{19} +(7.00000 - 19.7990i) q^{21} +12.0000i q^{22} +25.4558 q^{23} +(8.00000 + 2.82843i) q^{24} +35.3553i q^{26} +(-14.1421 - 23.0000i) q^{27} +14.0000i q^{28} -42.4264i q^{29} -7.00000 q^{31} -5.65685 q^{32} +(-8.48528 + 24.0000i) q^{33} -36.0000 q^{34} +(14.0000 + 11.3137i) q^{36} -2.00000i q^{37} -9.89949 q^{38} +(-25.0000 + 70.7107i) q^{39} +8.48528i q^{41} +(-9.89949 + 28.0000i) q^{42} +41.0000i q^{43} -16.9706i q^{44} -36.0000 q^{46} +(-11.3137 - 4.00000i) q^{48} +(-72.0000 - 25.4558i) q^{51} -50.0000i q^{52} +59.3970 q^{53} +(20.0000 + 32.5269i) q^{54} -19.7990i q^{56} +(-19.7990 - 7.00000i) q^{57} +60.0000i q^{58} +33.9411i q^{59} -1.00000 q^{61} +9.89949 q^{62} +(-39.5980 + 49.0000i) q^{63} +8.00000 q^{64} +(12.0000 - 33.9411i) q^{66} -17.0000i q^{67} +50.9117 q^{68} +(-72.0000 - 25.4558i) q^{69} +42.4264i q^{71} +(-19.7990 - 16.0000i) q^{72} -70.0000i q^{73} +2.82843i q^{74} +14.0000 q^{76} +59.3970 q^{77} +(35.3553 - 100.000i) q^{78} +58.0000 q^{79} +(17.0000 + 79.1960i) q^{81} -12.0000i q^{82} -118.794 q^{83} +(14.0000 - 39.5980i) q^{84} -57.9828i q^{86} +(-42.4264 + 120.000i) q^{87} +24.0000i q^{88} -135.765i q^{89} +175.000 q^{91} +50.9117 q^{92} +(19.7990 + 7.00000i) q^{93} +(16.0000 + 5.65685i) q^{96} +49.0000i q^{97} +(48.0000 - 59.3970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 16 q^{6} + 28 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 + 16 * q^6 + 28 * q^9	$ 4 q + 8 q^{4} + 16 q^{6} + 28 q^{9} + 16 q^{16} + 28 q^{19} + 28 q^{21} + 32 q^{24} - 28 q^{31} - 144 q^{34} + 56 q^{36} - 100 q^{39} - 144 q^{46} - 288 q^{51} + 80 q^{54} - 4 q^{61} + 32 q^{64} + 48 q^{66} - 288 q^{69} + 56 q^{76} + 232 q^{79} + 68 q^{81} + 56 q^{84} + 700 q^{91} + 64 q^{96} + 192 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 + 16 * q^6 + 28 * q^9 + 16 * q^16 + 28 * q^19 + 28 * q^21 + 32 * q^24 - 28 * q^31 - 144 * q^34 + 56 * q^36 - 100 * q^39 - 144 * q^46 - 288 * q^51 + 80 * q^54 - 4 * q^61 + 32 * q^64 + 48 * q^66 - 288 * q^69 + 56 * q^76 + 232 * q^79 + 68 * q^81 + 56 * q^84 + 700 * q^91 + 64 * q^96 + 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$3$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	4.00000	+	1.41421i	0.666667	+	0.235702i
$7$			7.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$7$			7.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$8$	−2.82843			−0.353553
$9$	7.00000	+	5.65685i	0.777778	+	0.628539i
$10$		0			0
$11$		−	8.48528i		−	0.771389i	−0.922627	−	0.385695i	$-0.873962\pi$
$11$		−	8.48528i		−	0.771389i	0.922627	−	0.385695i	$-0.126038\pi$
$12$	−5.65685	−	2.00000i	−0.471405	−	0.166667i
$13$		−	25.0000i		−	1.92308i	−0.274670	−	0.961538i	$-0.588569\pi$
$13$		−	25.0000i		−	1.92308i	0.274670	−	0.961538i	$-0.411431\pi$
$14$		−	9.89949i		−	0.707107i
$15$		0			0
$16$	4.00000			0.250000
$17$	25.4558			1.49740			0.748701	−	0.662908i	$-0.230678\pi$
$17$	25.4558			1.49740			0.748701	+	0.662908i	$0.230678\pi$
$18$	−9.89949	−	8.00000i	−0.549972	−	0.444444i
$19$	7.00000			0.368421			0.184211	−	0.982887i	$-0.441027\pi$
$19$	7.00000			0.368421			0.184211	+	0.982887i	$0.441027\pi$
$20$		0			0
$21$	7.00000	−	19.7990i	0.333333	−	0.942809i
$22$			12.0000i			0.545455i
$23$	25.4558			1.10678			0.553388	−	0.832924i	$-0.313335\pi$
$23$	25.4558			1.10678			0.553388	+	0.832924i	$0.313335\pi$
$24$	8.00000	+	2.82843i	0.333333	+	0.117851i
$25$		0			0
$26$			35.3553i			1.35982i
$27$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$28$			14.0000i			0.500000i
$29$		−	42.4264i		−	1.46298i	−0.681852	−	0.731490i	$-0.738825\pi$
$29$		−	42.4264i		−	1.46298i	0.681852	−	0.731490i	$-0.261175\pi$
$30$		0			0
$31$	−7.00000			−0.225806			−0.112903	−	0.993606i	$-0.536015\pi$
$31$	−7.00000			−0.225806			−0.112903	+	0.993606i	$0.536015\pi$
$32$	−5.65685			−0.176777
$33$	−8.48528	+	24.0000i	−0.257130	+	0.727273i
$34$	−36.0000			−1.05882
$35$		0			0
$36$	14.0000	+	11.3137i	0.388889	+	0.314270i
$37$		−	2.00000i		−	0.0540541i	−0.999635	−	0.0270270i	$-0.991396\pi$
$37$		−	2.00000i		−	0.0540541i	0.999635	−	0.0270270i	$-0.00860402\pi$
$38$	−9.89949			−0.260513
$39$	−25.0000	+	70.7107i	−0.641026	+	1.81309i
$40$		0			0
$41$			8.48528i			0.206958i	0.994632	+	0.103479i	$0.0329975\pi$
$41$			8.48528i			0.206958i	−0.994632	+	0.103479i	$0.967003\pi$
$42$	−9.89949	+	28.0000i	−0.235702	+	0.666667i
$43$			41.0000i			0.953488i	0.879042	+	0.476744i	$0.158183\pi$
$43$			41.0000i			0.953488i	−0.879042	+	0.476744i	$0.841817\pi$
$44$		−	16.9706i		−	0.385695i
$45$		0			0
$46$	−36.0000			−0.782609
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−11.3137	−	4.00000i	−0.235702	−	0.0833333i
$49$		0			0
$50$		0			0
$51$	−72.0000	−	25.4558i	−1.41176	−	0.499134i
$52$		−	50.0000i		−	0.961538i
$53$	59.3970			1.12070			0.560349	−	0.828257i	$-0.310667\pi$
$53$	59.3970			1.12070			0.560349	+	0.828257i	$0.310667\pi$
$54$	20.0000	+	32.5269i	0.370370	+	0.602350i
$55$		0			0
$56$		−	19.7990i		−	0.353553i
$57$	−19.7990	−	7.00000i	−0.347351	−	0.122807i
$58$			60.0000i			1.03448i
$59$			33.9411i			0.575273i	0.957740	+	0.287637i	$0.0928695\pi$
$59$			33.9411i			0.575273i	−0.957740	+	0.287637i	$0.907130\pi$
$60$		0			0
$61$	−1.00000			−0.0163934			−0.00819672	−	0.999966i	$-0.502609\pi$
$61$	−1.00000			−0.0163934			−0.00819672	+	0.999966i	$0.502609\pi$
$62$	9.89949			0.159669
$63$	−39.5980	+	49.0000i	−0.628539	+	0.777778i
$64$	8.00000			0.125000
$65$		0			0
$66$	12.0000	−	33.9411i	0.181818	−	0.514259i
$67$		−	17.0000i		−	0.253731i	−0.991920	−	0.126866i	$-0.959508\pi$
$67$		−	17.0000i		−	0.253731i	0.991920	−	0.126866i	$-0.0404917\pi$
$68$	50.9117			0.748701
$69$	−72.0000	−	25.4558i	−1.04348	−	0.368925i
$70$		0			0
$71$			42.4264i			0.597555i	0.954323	+	0.298778i	$0.0965788\pi$
$71$			42.4264i			0.597555i	−0.954323	+	0.298778i	$0.903421\pi$
$72$	−19.7990	−	16.0000i	−0.274986	−	0.222222i
$73$		−	70.0000i		−	0.958904i	−0.877568	−	0.479452i	$-0.840835\pi$
$73$		−	70.0000i		−	0.958904i	0.877568	−	0.479452i	$-0.159165\pi$
$74$			2.82843i			0.0382220i
$75$		0			0
$76$	14.0000			0.184211
$77$	59.3970			0.771389
$78$	35.3553	−	100.000i	0.453274	−	1.28205i
$79$	58.0000			0.734177			0.367089	−	0.930186i	$-0.380355\pi$
$79$	58.0000			0.734177			0.367089	+	0.930186i	$0.380355\pi$
$80$		0			0
$81$	17.0000	+	79.1960i	0.209877	+	0.977728i
$82$		−	12.0000i		−	0.146341i
$83$	−118.794			−1.43125			−0.715626	−	0.698484i	$-0.753859\pi$
$83$	−118.794			−1.43125			−0.715626	+	0.698484i	$0.753859\pi$
$84$	14.0000	−	39.5980i	0.166667	−	0.471405i
$85$		0			0
$86$		−	57.9828i		−	0.674218i
$87$	−42.4264	+	120.000i	−0.487660	+	1.37931i
$88$			24.0000i			0.272727i
$89$		−	135.765i		−	1.52544i	−0.646727	−	0.762722i	$-0.723863\pi$
$89$		−	135.765i		−	1.52544i	0.646727	−	0.762722i	$-0.276137\pi$
$90$		0			0
$91$	175.000			1.92308
$92$	50.9117			0.553388
$93$	19.7990	+	7.00000i	0.212892	+	0.0752688i
$94$		0			0
$95$		0			0
$96$	16.0000	+	5.65685i	0.166667	+	0.0589256i
$97$			49.0000i			0.505155i	0.967577	+	0.252577i	$0.0812782\pi$
$97$			49.0000i			0.505155i	−0.967577	+	0.252577i	$0.918722\pi$
$98$		0			0
$99$	48.0000	−	59.3970i	0.484848	−	0.599969i
$100$		0			0
$101$			59.3970i			0.588089i	0.955792	+	0.294044i	$0.0950014\pi$
$101$			59.3970i			0.588089i	−0.955792	+	0.294044i	$0.904999\pi$
$102$	101.823	+	36.0000i	0.998268	+	0.352941i
$103$		−	154.000i		−	1.49515i	−0.664180	−	0.747573i	$-0.731219\pi$
$103$		−	154.000i		−	1.49515i	0.664180	−	0.747573i	$-0.268781\pi$
$104$			70.7107i			0.679910i
$105$		0			0
$106$	−84.0000			−0.792453
$107$	−178.191			−1.66534			−0.832668	−	0.553773i	$-0.813188\pi$
$107$	−178.191			−1.66534			−0.832668	+	0.553773i	$0.813188\pi$
$108$	−28.2843	−	46.0000i	−0.261891	−	0.425926i
$109$	25.0000			0.229358			0.114679	−	0.993403i	$-0.463416\pi$
$109$	25.0000			0.229358			0.114679	+	0.993403i	$0.463416\pi$
$110$		0			0
$111$	−2.00000	+	5.65685i	−0.0180180	+	0.0509627i
$112$			28.0000i			0.250000i
$113$	−16.9706			−0.150182			−0.0750910	−	0.997177i	$-0.523925\pi$
$113$	−16.9706			−0.150182			−0.0750910	+	0.997177i	$0.523925\pi$
$114$	28.0000	+	9.89949i	0.245614	+	0.0868377i
$115$		0			0
$116$		−	84.8528i		−	0.731490i
$117$	141.421	−	175.000i	1.20873	−	1.49573i
$118$		−	48.0000i		−	0.406780i
$119$			178.191i			1.49740i
$120$		0			0
$121$	49.0000			0.404959
$122$	1.41421			0.0115919
$123$	8.48528	−	24.0000i	0.0689860	−	0.195122i
$124$	−14.0000			−0.112903
$125$		0			0
$126$	56.0000	−	69.2965i	0.444444	−	0.549972i
$127$			34.0000i			0.267717i	0.991000	+	0.133858i	$0.0427367\pi$
$127$			34.0000i			0.267717i	−0.991000	+	0.133858i	$0.957263\pi$
$128$	−11.3137			−0.0883883
$129$	41.0000	−	115.966i	0.317829	−	0.898957i
$130$		0			0
$131$		−	195.161i		−	1.48978i	−0.667186	−	0.744891i	$-0.732501\pi$
$131$		−	195.161i		−	1.48978i	0.667186	−	0.744891i	$-0.267499\pi$
$132$	−16.9706	+	48.0000i	−0.128565	+	0.363636i
$133$			49.0000i			0.368421i
$134$			24.0416i			0.179415i
$135$		0			0
$136$	−72.0000			−0.529412
$137$	−118.794			−0.867109			−0.433555	−	0.901127i	$-0.642741\pi$
$137$	−118.794			−0.867109			−0.433555	+	0.901127i	$0.642741\pi$
$138$	101.823	+	36.0000i	0.737851	+	0.260870i
$139$	154.000			1.10791			0.553957	−	0.832545i	$-0.313117\pi$
$139$	154.000			1.10791			0.553957	+	0.832545i	$0.313117\pi$
$140$		0			0
$141$		0			0
$142$		−	60.0000i		−	0.422535i
$143$	−212.132			−1.48344
$144$	28.0000	+	22.6274i	0.194444	+	0.157135i
$145$		0			0
$146$			98.9949i			0.678048i
$147$		0			0
$148$		−	4.00000i		−	0.0270270i
$149$			152.735i			1.02507i	0.858667	+	0.512534i	$0.171293\pi$
$149$			152.735i			1.02507i	−0.858667	+	0.512534i	$0.828707\pi$
$150$		0			0
$151$	−199.000			−1.31788			−0.658940	−	0.752195i	$-0.728995\pi$
$151$	−199.000			−1.31788			−0.658940	+	0.752195i	$0.728995\pi$
$152$	−19.7990			−0.130257
$153$	178.191	+	144.000i	1.16465	+	0.941176i
$154$	−84.0000			−0.545455
$155$		0			0
$156$	−50.0000	+	141.421i	−0.320513	+	0.906547i
$157$			145.000i			0.923567i	0.886993	+	0.461783i	$0.152790\pi$
$157$			145.000i			0.923567i	−0.886993	+	0.461783i	$0.847210\pi$
$158$	−82.0244			−0.519142
$159$	−168.000	−	59.3970i	−1.05660	−	0.373566i
$160$		0			0
$161$			178.191i			1.10678i
$162$	−24.0416	−	112.000i	−0.148405	−	0.691358i
$163$			161.000i			0.987730i	0.869539	+	0.493865i	$0.164416\pi$
$163$			161.000i			0.987730i	−0.869539	+	0.493865i	$0.835584\pi$
$164$			16.9706i			0.103479i
$165$		0			0
$166$	168.000			1.01205
$167$	110.309			0.660531			0.330265	−	0.943888i	$-0.392862\pi$
$167$	110.309			0.660531			0.330265	+	0.943888i	$0.392862\pi$
$168$	−19.7990	+	56.0000i	−0.117851	+	0.333333i
$169$	−456.000			−2.69822
$170$		0			0
$171$	49.0000	+	39.5980i	0.286550	+	0.231567i
$172$			82.0000i			0.476744i
$173$	178.191			1.03001			0.515003	−	0.857189i	$-0.327791\pi$
$173$	178.191			1.03001			0.515003	+	0.857189i	$0.327791\pi$
$174$	60.0000	−	169.706i	0.344828	−	0.975320i
$175$		0			0
$176$		−	33.9411i		−	0.192847i
$177$	33.9411	−	96.0000i	0.191758	−	0.542373i
$178$			192.000i			1.07865i
$179$			118.794i			0.663653i	0.943340	+	0.331827i	$0.107665\pi$
$179$			118.794i			0.663653i	−0.943340	+	0.331827i	$0.892335\pi$
$180$		0			0
$181$	−217.000			−1.19890			−0.599448	−	0.800414i	$-0.704613\pi$
$181$	−217.000			−1.19890			−0.599448	+	0.800414i	$0.704613\pi$
$182$	−247.487			−1.35982
$183$	2.82843	+	1.00000i	0.0154559	+	0.00546448i
$184$	−72.0000			−0.391304
$185$		0			0
$186$	−28.0000	−	9.89949i	−0.150538	−	0.0532231i
$187$		−	216.000i		−	1.15508i
$188$		0			0
$189$	161.000	−	98.9949i	0.851852	−	0.523783i
$190$		0			0
$191$		−	59.3970i		−	0.310979i	−0.987838	−	0.155489i	$-0.950305\pi$
$191$		−	59.3970i		−	0.310979i	0.987838	−	0.155489i	$-0.0496955\pi$
$192$	−22.6274	−	8.00000i	−0.117851	−	0.0416667i
$193$		−	25.0000i		−	0.129534i	−0.997900	−	0.0647668i	$-0.979370\pi$
$193$		−	25.0000i		−	0.129534i	0.997900	−	0.0647668i	$-0.0206304\pi$
$194$		−	69.2965i		−	0.357198i
$195$		0			0
$196$		0			0
$197$	135.765			0.689160			0.344580	−	0.938757i	$-0.388021\pi$
$197$	135.765			0.689160			0.344580	+	0.938757i	$0.388021\pi$
$198$	−67.8823	+	84.0000i	−0.342840	+	0.424242i
$199$	103.000			0.517588			0.258794	−	0.965933i	$-0.416675\pi$
$199$	103.000			0.517588			0.258794	+	0.965933i	$0.416675\pi$
$200$		0			0
$201$	−17.0000	+	48.0833i	−0.0845771	+	0.239220i
$202$		−	84.0000i		−	0.415842i
$203$	296.985			1.46298
$204$	−144.000	−	50.9117i	−0.705882	−	0.249567i
$205$		0			0
$206$			217.789i			1.05723i
$207$	178.191	+	144.000i	0.860826	+	0.695652i
$208$		−	100.000i		−	0.480769i
$209$		−	59.3970i		−	0.284196i
$210$		0			0
$211$	−7.00000			−0.0331754			−0.0165877	−	0.999862i	$-0.505280\pi$
$211$	−7.00000			−0.0331754			−0.0165877	+	0.999862i	$0.505280\pi$
$212$	118.794			0.560349
$213$	42.4264	−	120.000i	0.199185	−	0.563380i
$214$	252.000			1.17757
$215$		0			0
$216$	40.0000	+	65.0538i	0.185185	+	0.301175i
$217$		−	49.0000i		−	0.225806i
$218$	−35.3553			−0.162180
$219$	−70.0000	+	197.990i	−0.319635	+	0.904063i
$220$		0			0
$221$		−	636.396i		−	2.87962i
$222$	2.82843	−	8.00000i	0.0127407	−	0.0360360i
$223$			161.000i			0.721973i	0.932571	+	0.360987i	$0.117560\pi$
$223$			161.000i			0.721973i	−0.932571	+	0.360987i	$0.882440\pi$
$224$		−	39.5980i		−	0.176777i
$225$		0			0
$226$	24.0000			0.106195
$227$	−59.3970			−0.261661			−0.130830	−	0.991405i	$-0.541764\pi$
$227$	−59.3970			−0.261661			−0.130830	+	0.991405i	$0.541764\pi$
$228$	−39.5980	−	14.0000i	−0.173675	−	0.0614035i
$229$	97.0000			0.423581			0.211790	−	0.977315i	$-0.432071\pi$
$229$	97.0000			0.423581			0.211790	+	0.977315i	$0.432071\pi$
$230$		0			0
$231$	−168.000	−	59.3970i	−0.727273	−	0.257130i
$232$			120.000i			0.517241i
$233$	−263.044			−1.12894			−0.564472	−	0.825453i	$-0.690920\pi$
$233$	−263.044			−1.12894			−0.564472	+	0.825453i	$0.690920\pi$
$234$	−200.000	+	247.487i	−0.854701	+	1.05764i
$235$		0			0
$236$			67.8823i			0.287637i
$237$	−164.049	−	58.0000i	−0.692189	−	0.244726i
$238$		−	252.000i		−	1.05882i
$239$		−	59.3970i		−	0.248523i	−0.992250	−	0.124261i	$-0.960344\pi$
$239$		−	59.3970i		−	0.248523i	0.992250	−	0.124261i	$-0.0396562\pi$
$240$		0			0
$241$	119.000			0.493776			0.246888	−	0.969044i	$-0.420592\pi$
$241$	119.000			0.493776			0.246888	+	0.969044i	$0.420592\pi$
$242$	−69.2965			−0.286349
$243$	31.1127	−	241.000i	0.128036	−	0.991770i
$244$	−2.00000			−0.00819672
$245$		0			0
$246$	−12.0000	+	33.9411i	−0.0487805	+	0.137972i
$247$		−	175.000i		−	0.708502i
$248$	19.7990			0.0798346
$249$	336.000	+	118.794i	1.34940	+	0.477084i
$250$		0			0
$251$			288.500i			1.14940i	0.818364	+	0.574700i	$0.194881\pi$
$251$			288.500i			1.14940i	−0.818364	+	0.574700i	$0.805119\pi$
$252$	−79.1960	+	98.0000i	−0.314270	+	0.388889i
$253$		−	216.000i		−	0.853755i
$254$		−	48.0833i		−	0.189304i
$255$		0			0
$256$	16.0000			0.0625000
$257$	118.794			0.462233			0.231117	−	0.972926i	$-0.425762\pi$
$257$	118.794			0.462233			0.231117	+	0.972926i	$0.425762\pi$
$258$	−57.9828	+	164.000i	−0.224739	+	0.635659i
$259$	14.0000			0.0540541
$260$		0			0
$261$	240.000	−	296.985i	0.919540	−	1.13787i
$262$			276.000i			1.05344i
$263$	8.48528			0.0322634			0.0161317	−	0.999870i	$-0.494865\pi$
$263$	8.48528			0.0322634			0.0161317	+	0.999870i	$0.494865\pi$
$264$	24.0000	−	67.8823i	0.0909091	−	0.257130i
$265$		0			0
$266$		−	69.2965i		−	0.260513i
$267$	−135.765	+	384.000i	−0.508481	+	1.43820i
$268$		−	34.0000i		−	0.126866i
$269$		−	59.3970i		−	0.220807i	−0.993887	−	0.110403i	$-0.964786\pi$
$269$		−	59.3970i		−	0.220807i	0.993887	−	0.110403i	$-0.0352142\pi$
$270$		0			0
$271$	470.000			1.73432			0.867159	−	0.498032i	$-0.165944\pi$
$271$	470.000			1.73432			0.867159	+	0.498032i	$0.165944\pi$
$272$	101.823			0.374351
$273$	−494.975	−	175.000i	−1.81309	−	0.641026i
$274$	168.000			0.613139
$275$		0			0
$276$	−144.000	−	50.9117i	−0.521739	−	0.184463i
$277$			217.000i			0.783394i	0.920094	+	0.391697i	$0.128112\pi$
$277$			217.000i			0.783394i	−0.920094	+	0.391697i	$0.871888\pi$
$278$	−217.789			−0.783413
$279$	−49.0000	−	39.5980i	−0.175627	−	0.141928i
$280$		0			0
$281$			517.602i			1.84200i	0.389562	+	0.921000i	$0.372626\pi$
$281$			517.602i			1.84200i	−0.389562	+	0.921000i	$0.627374\pi$
$282$		0			0
$283$			65.0000i			0.229682i	0.993384	+	0.114841i	$0.0366359\pi$
$283$			65.0000i			0.229682i	−0.993384	+	0.114841i	$0.963364\pi$
$284$			84.8528i			0.298778i
$285$		0			0
$286$	300.000			1.04895
$287$	−59.3970			−0.206958
$288$	−39.5980	−	32.0000i	−0.137493	−	0.111111i
$289$	359.000			1.24221
$290$		0			0
$291$	49.0000	−	138.593i	0.168385	−	0.476264i
$292$		−	140.000i		−	0.479452i
$293$	169.706			0.579200			0.289600	−	0.957148i	$-0.406478\pi$
$293$	169.706			0.579200			0.289600	+	0.957148i	$0.406478\pi$
$294$		0			0
$295$		0			0
$296$			5.65685i			0.0191110i
$297$	−195.161	+	120.000i	−0.657109	+	0.404040i
$298$		−	216.000i		−	0.724832i
$299$		−	636.396i		−	2.12842i
$300$		0			0
$301$	−287.000			−0.953488
$302$	281.428			0.931882
$303$	59.3970	−	168.000i	0.196030	−	0.554455i
$304$	28.0000			0.0921053
$305$		0			0
$306$	−252.000	−	203.647i	−0.823529	−	0.665512i
$307$		−	521.000i		−	1.69707i	−0.529141	−	0.848534i	$-0.677486\pi$
$307$		−	521.000i		−	1.69707i	0.529141	−	0.848534i	$-0.322514\pi$
$308$	118.794			0.385695
$309$	−154.000	+	435.578i	−0.498382	+	1.40964i
$310$		0			0
$311$		−	33.9411i		−	0.109135i	−0.998510	−	0.0545677i	$-0.982622\pi$
$311$		−	33.9411i		−	0.109135i	0.998510	−	0.0545677i	$-0.0173781\pi$
$312$	70.7107	−	200.000i	0.226637	−	0.641026i
$313$			119.000i			0.380192i	0.981766	+	0.190096i	$0.0608799\pi$
$313$			119.000i			0.380192i	−0.981766	+	0.190096i	$0.939120\pi$
$314$		−	205.061i		−	0.653060i
$315$		0			0
$316$	116.000			0.367089
$317$	152.735			0.481814			0.240907	−	0.970548i	$-0.422555\pi$
$317$	152.735			0.481814			0.240907	+	0.970548i	$0.422555\pi$
$318$	237.588	+	84.0000i	0.747132	+	0.264151i
$319$	−360.000			−1.12853
$320$		0			0
$321$	504.000	+	178.191i	1.57009	+	0.555112i
$322$		−	252.000i		−	0.782609i
$323$	178.191			0.551675
$324$	34.0000	+	158.392i	0.104938	+	0.488864i
$325$		0			0
$326$		−	227.688i		−	0.698431i
$327$	−70.7107	−	25.0000i	−0.216241	−	0.0764526i
$328$		−	24.0000i		−	0.0731707i
$329$		0			0
$330$		0			0
$331$	−418.000			−1.26284			−0.631420	−	0.775441i	$-0.717528\pi$
$331$	−418.000			−1.26284			−0.631420	+	0.775441i	$0.717528\pi$
$332$	−237.588			−0.715626
$333$	11.3137	−	14.0000i	0.0339751	−	0.0420420i
$334$	−156.000			−0.467066
$335$		0			0
$336$	28.0000	−	79.1960i	0.0833333	−	0.235702i
$337$			553.000i			1.64095i	0.571683	+	0.820475i	$0.306291\pi$
$337$			553.000i			1.64095i	−0.571683	+	0.820475i	$0.693709\pi$
$338$	644.881			1.90793
$339$	48.0000	+	16.9706i	0.141593	+	0.0500607i
$340$		0			0
$341$			59.3970i			0.174185i
$342$	−69.2965	−	56.0000i	−0.202621	−	0.163743i
$343$			343.000i			1.00000i
$344$		−	115.966i		−	0.337109i
$345$		0			0
$346$	−252.000			−0.728324
$347$	644.881			1.85845			0.929224	−	0.369517i	$-0.120477\pi$
$347$	644.881			1.85845			0.929224	+	0.369517i	$0.120477\pi$
$348$	−84.8528	+	240.000i	−0.243830	+	0.689655i
$349$	−266.000			−0.762178			−0.381089	−	0.924538i	$-0.624451\pi$
$349$	−266.000			−0.762178			−0.381089	+	0.924538i	$0.624451\pi$
$350$		0			0
$351$	−575.000	+	353.553i	−1.63818	+	1.00727i
$352$			48.0000i			0.136364i
$353$	−415.779			−1.17784			−0.588922	−	0.808190i	$-0.700447\pi$
$353$	−415.779			−1.17784			−0.588922	+	0.808190i	$0.700447\pi$
$354$	−48.0000	+	135.765i	−0.135593	+	0.383516i
$355$		0			0
$356$		−	271.529i		−	0.762722i
$357$	178.191	−	504.000i	0.499134	−	1.41176i
$358$		−	168.000i		−	0.469274i
$359$		−	330.926i		−	0.921799i	−0.887452	−	0.460900i	$-0.847527\pi$
$359$		−	330.926i		−	0.921799i	0.887452	−	0.460900i	$-0.152473\pi$
$360$		0			0
$361$	−312.000			−0.864266
$362$	306.884			0.847747
$363$	−138.593	−	49.0000i	−0.381799	−	0.134986i
$364$	350.000			0.961538
$365$		0			0
$366$	−4.00000	−	1.41421i	−0.0109290	−	0.00386397i
$367$			103.000i			0.280654i	0.990105	+	0.140327i	$0.0448154\pi$
$367$			103.000i			0.280654i	−0.990105	+	0.140327i	$0.955185\pi$
$368$	101.823			0.276694
$369$	−48.0000	+	59.3970i	−0.130081	+	0.160967i
$370$		0			0
$371$			415.779i			1.12070i
$372$	39.5980	+	14.0000i	0.106446	+	0.0376344i
$373$			359.000i			0.962466i	0.876593	+	0.481233i	$0.159811\pi$
$373$			359.000i			0.962466i	−0.876593	+	0.481233i	$0.840189\pi$
$374$			305.470i			0.816765i
$375$		0			0
$376$		0			0
$377$	−1060.66			−2.81342
$378$	−227.688	+	140.000i	−0.602350	+	0.370370i
$379$	−377.000			−0.994723			−0.497361	−	0.867543i	$-0.665698\pi$
$379$	−377.000			−0.994723			−0.497361	+	0.867543i	$0.665698\pi$
$380$		0			0
$381$	34.0000	−	96.1665i	0.0892388	−	0.252406i
$382$			84.0000i			0.219895i
$383$	610.940			1.59514			0.797572	−	0.603224i	$-0.206117\pi$
$383$	610.940			1.59514			0.797572	+	0.603224i	$0.206117\pi$
$384$	32.0000	+	11.3137i	0.0833333	+	0.0294628i
$385$		0			0
$386$			35.3553i			0.0915941i
$387$	−231.931	+	287.000i	−0.599305	+	0.741602i
$388$			98.0000i			0.252577i
$389$			347.897i			0.894336i	0.894450	+	0.447168i	$0.147567\pi$
$389$			347.897i			0.894336i	−0.894450	+	0.447168i	$0.852433\pi$
$390$		0			0
$391$	648.000			1.65729
$392$		0			0
$393$	−195.161	+	552.000i	−0.496594	+	1.40458i
$394$	−192.000			−0.487310
$395$		0			0
$396$	96.0000	−	118.794i	0.242424	−	0.299985i
$397$		−	239.000i		−	0.602015i	−0.953622	−	0.301008i	$-0.902677\pi$
$397$		−	239.000i		−	0.602015i	0.953622	−	0.301008i	$-0.0973229\pi$
$398$	−145.664			−0.365990
$399$	49.0000	−	138.593i	0.122807	−	0.347351i
$400$		0			0
$401$		−	93.3381i		−	0.232763i	−0.993205	−	0.116382i	$-0.962870\pi$
$401$		−	93.3381i		−	0.232763i	0.993205	−	0.116382i	$-0.0371296\pi$
$402$	24.0416	−	68.0000i	0.0598051	−	0.169154i
$403$			175.000i			0.434243i
$404$			118.794i			0.294044i
$405$		0			0
$406$	−420.000			−1.03448
$407$	−16.9706			−0.0416967
$408$	203.647	+	72.0000i	0.499134	+	0.176471i
$409$	−455.000			−1.11247			−0.556235	−	0.831025i	$-0.687754\pi$
$409$	−455.000			−1.11247			−0.556235	+	0.831025i	$0.687754\pi$
$410$		0			0
$411$	336.000	+	118.794i	0.817518	+	0.289036i
$412$		−	308.000i		−	0.747573i
$413$	−237.588			−0.575273
$414$	−252.000	−	203.647i	−0.608696	−	0.491900i
$415$		0			0
$416$			141.421i			0.339955i
$417$	−435.578	−	154.000i	−1.04455	−	0.369305i
$418$			84.0000i			0.200957i
$419$			296.985i			0.708794i	0.935095	+	0.354397i	$0.115314\pi$
$419$			296.985i			0.708794i	−0.935095	+	0.354397i	$0.884686\pi$
$420$		0			0
$421$	−526.000			−1.24941			−0.624703	−	0.780862i	$-0.714780\pi$
$421$	−526.000			−1.24941			−0.624703	+	0.780862i	$0.714780\pi$
$422$	9.89949			0.0234585
$423$		0			0
$424$	−168.000			−0.396226
$425$		0			0
$426$	−60.0000	+	169.706i	−0.140845	+	0.398370i
$427$		−	7.00000i		−	0.0163934i
$428$	−356.382			−0.832668
$429$	600.000	+	212.132i	1.39860	+	0.494480i
$430$		0			0
$431$			280.014i			0.649685i	0.945768	+	0.324843i	$0.105311\pi$
$431$			280.014i			0.649685i	−0.945768	+	0.324843i	$0.894689\pi$
$432$	−56.5685	−	92.0000i	−0.130946	−	0.212963i
$433$			119.000i			0.274827i	0.990514	+	0.137413i	$0.0438789\pi$
$433$			119.000i			0.274827i	−0.990514	+	0.137413i	$0.956121\pi$
$434$			69.2965i			0.159669i
$435$		0			0
$436$	50.0000			0.114679
$437$	178.191			0.407760
$438$	98.9949	−	280.000i	0.226016	−	0.639269i
$439$	727.000			1.65604			0.828018	−	0.560701i	$-0.189468\pi$
$439$	727.000			1.65604			0.828018	+	0.560701i	$0.189468\pi$
$440$		0			0
$441$		0			0
$442$			900.000i			2.03620i
$443$	−526.087			−1.18756			−0.593778	−	0.804629i	$-0.702364\pi$
$443$	−526.087			−1.18756			−0.593778	+	0.804629i	$0.702364\pi$
$444$	−4.00000	+	11.3137i	−0.00900901	+	0.0254813i
$445$		0			0
$446$		−	227.688i		−	0.510512i
$447$	152.735	−	432.000i	0.341689	−	0.966443i
$448$			56.0000i			0.125000i
$449$			254.558i			0.566945i	0.958980	+	0.283473i	$0.0914865\pi$
$449$			254.558i			0.566945i	−0.958980	+	0.283473i	$0.908513\pi$
$450$		0			0
$451$	72.0000			0.159645
$452$	−33.9411			−0.0750910
$453$	562.857	+	199.000i	1.24251	+	0.439294i
$454$	84.0000			0.185022
$455$		0			0
$456$	56.0000	+	19.7990i	0.122807	+	0.0434188i
$457$			310.000i			0.678337i	0.940726	+	0.339168i	$0.110146\pi$
$457$			310.000i			0.678337i	−0.940726	+	0.339168i	$0.889854\pi$
$458$	−137.179			−0.299517
$459$	−360.000	−	585.484i	−0.784314	−	1.27557i
$460$		0			0
$461$		−	721.249i		−	1.56453i	−0.622945	−	0.782266i	$-0.714064\pi$
$461$		−	721.249i		−	1.56453i	0.622945	−	0.782266i	$-0.285936\pi$
$462$	237.588	+	84.0000i	0.514259	+	0.181818i
$463$		−	730.000i		−	1.57667i	−0.615244	−	0.788337i	$-0.710942\pi$
$463$		−	730.000i		−	1.57667i	0.615244	−	0.788337i	$-0.289058\pi$
$464$		−	169.706i		−	0.365745i
$465$		0			0
$466$	372.000			0.798283
$467$	195.161			0.417905			0.208952	−	0.977926i	$-0.432995\pi$
$467$	195.161			0.417905			0.208952	+	0.977926i	$0.432995\pi$
$468$	282.843	−	350.000i	0.604365	−	0.747863i
$469$	119.000			0.253731
$470$		0			0
$471$	145.000	−	410.122i	0.307856	−	0.870747i
$472$		−	96.0000i		−	0.203390i
$473$	347.897			0.735511
$474$	232.000	+	82.0244i	0.489451	+	0.173047i
$475$		0			0
$476$			356.382i			0.748701i
$477$	415.779	+	336.000i	0.871654	+	0.704403i
$478$			84.0000i			0.175732i
$479$		−	390.323i		−	0.814870i	−0.913234	−	0.407435i	$-0.866423\pi$
$479$		−	390.323i		−	0.814870i	0.913234	−	0.407435i	$-0.133577\pi$
$480$		0			0
$481$	−50.0000			−0.103950
$482$	−168.291			−0.349152
$483$	178.191	−	504.000i	0.368925	−	1.04348i
$484$	98.0000			0.202479
$485$		0			0
$486$	−44.0000	+	340.825i	−0.0905350	+	0.701287i
$487$		−	473.000i		−	0.971253i	−0.874167	−	0.485626i	$-0.838592\pi$
$487$		−	473.000i		−	0.971253i	0.874167	−	0.485626i	$-0.161408\pi$
$488$	2.82843			0.00579596
$489$	161.000	−	455.377i	0.329243	−	0.931241i
$490$		0			0
$491$		−	814.587i		−	1.65904i	−0.558479	−	0.829518i	$-0.688615\pi$
$491$		−	814.587i		−	1.65904i	0.558479	−	0.829518i	$-0.311385\pi$
$492$	16.9706	−	48.0000i	0.0344930	−	0.0975610i
$493$		−	1080.00i		−	2.19067i
$494$			247.487i			0.500987i
$495$		0			0
$496$	−28.0000			−0.0564516
$497$	−296.985			−0.597555
$498$	−475.176	−	168.000i	−0.954168	−	0.337349i
$499$	175.000			0.350701			0.175351	−	0.984506i	$-0.443894\pi$
$499$	175.000			0.350701			0.175351	+	0.984506i	$0.443894\pi$
$500$		0			0
$501$	−312.000	−	110.309i	−0.622754	−	0.220177i
$502$		−	408.000i		−	0.812749i
$503$	−347.897			−0.691643			−0.345822	−	0.938300i	$-0.612400\pi$
$503$	−347.897			−0.691643			−0.345822	+	0.938300i	$0.612400\pi$
$504$	112.000	−	138.593i	0.222222	−	0.274986i
$505$		0			0
$506$			305.470i			0.603696i
$507$	1289.76	+	456.000i	2.54391	+	0.899408i
$508$			68.0000i			0.133858i
$509$			729.734i			1.43366i	0.697247	+	0.716831i	$0.254408\pi$
$509$			729.734i			1.43366i	−0.697247	+	0.716831i	$0.745592\pi$
$510$		0			0
$511$	490.000			0.958904
$512$	−22.6274			−0.0441942
$513$	−98.9949	−	161.000i	−0.192973	−	0.313840i
$514$	−168.000			−0.326848
$515$		0			0
$516$	82.0000	−	231.931i	0.158915	−	0.449479i
$517$		0			0
$518$	−19.7990			−0.0382220
$519$	−504.000	−	178.191i	−0.971098	−	0.343335i
$520$		0			0
$521$			568.514i			1.09120i	0.838047	+	0.545599i	$0.183698\pi$
$521$			568.514i			1.09120i	−0.838047	+	0.545599i	$0.816302\pi$
$522$	−339.411	+	420.000i	−0.650213	+	0.804598i
$523$		−	175.000i		−	0.334608i	−0.985905	−	0.167304i	$-0.946494\pi$
$523$		−	175.000i		−	0.334608i	0.985905	−	0.167304i	$-0.0535061\pi$
$524$		−	390.323i		−	0.744891i
$525$		0			0
$526$	−12.0000			−0.0228137
$527$	−178.191			−0.338123
$528$	−33.9411	+	96.0000i	−0.0642824	+	0.181818i
$529$	119.000			0.224953
$530$		0			0
$531$	−192.000	+	237.588i	−0.361582	+	0.447435i
$532$			98.0000i			0.184211i
$533$	212.132			0.397996
$534$	192.000	−	543.058i	0.359551	−	1.01696i
$535$		0			0
$536$			48.0833i			0.0897076i
$537$	118.794	−	336.000i	0.221218	−	0.625698i
$538$			84.0000i			0.156134i
$539$		0			0
$540$		0			0
$541$	863.000			1.59519			0.797597	−	0.603191i	$-0.206104\pi$
$541$	863.000			1.59519			0.797597	+	0.603191i	$0.206104\pi$
$542$	−664.680			−1.22635
$543$	613.769	+	217.000i	1.13033	+	0.399632i
$544$	−144.000			−0.264706
$545$		0			0
$546$	700.000	+	247.487i	1.28205	+	0.453274i
$547$			778.000i			1.42230i	0.703039	+	0.711152i	$0.251826\pi$
$547$			778.000i			1.42230i	−0.703039	+	0.711152i	$0.748174\pi$
$548$	−237.588			−0.433555
$549$	−7.00000	−	5.65685i	−0.0127505	−	0.0103039i
$550$		0			0
$551$		−	296.985i		−	0.538992i
$552$	203.647	+	72.0000i	0.368925	+	0.130435i
$553$			406.000i			0.734177i
$554$		−	306.884i		−	0.553943i
$555$		0			0
$556$	308.000			0.553957
$557$	424.264			0.761695			0.380847	−	0.924638i	$-0.375632\pi$
$557$	424.264			0.761695			0.380847	+	0.924638i	$0.375632\pi$
$558$	69.2965	+	56.0000i	0.124187	+	0.100358i
$559$	1025.00			1.83363
$560$		0			0
$561$	−216.000	+	610.940i	−0.385027	+	1.08902i
$562$		−	732.000i		−	1.30249i
$563$	−381.838			−0.678220			−0.339110	−	0.940747i	$-0.610126\pi$
$563$	−381.838			−0.678220			−0.339110	+	0.940747i	$0.610126\pi$
$564$		0			0
$565$		0			0
$566$		−	91.9239i		−	0.162410i
$567$	−554.372	+	119.000i	−0.977728	+	0.209877i
$568$		−	120.000i		−	0.211268i
$569$			381.838i			0.671068i	0.942028	+	0.335534i	$0.108917\pi$
$569$			381.838i			0.671068i	−0.942028	+	0.335534i	$0.891083\pi$
$570$		0			0
$571$	−535.000			−0.936953			−0.468476	−	0.883476i	$-0.655197\pi$
$571$	−535.000			−0.936953			−0.468476	+	0.883476i	$0.655197\pi$
$572$	−424.264			−0.741720
$573$	−59.3970	+	168.000i	−0.103660	+	0.293194i
$574$	84.0000			0.146341
$575$		0			0
$576$	56.0000	+	45.2548i	0.0972222	+	0.0785674i
$577$			49.0000i			0.0849220i	0.999098	+	0.0424610i	$0.0135198\pi$
$577$			49.0000i			0.0849220i	−0.999098	+	0.0424610i	$0.986480\pi$
$578$	−507.703			−0.878378
$579$	−25.0000	+	70.7107i	−0.0431779	+	0.122126i
$580$		0			0
$581$		−	831.558i		−	1.43125i
$582$	−69.2965	+	196.000i	−0.119066	+	0.336770i
$583$		−	504.000i		−	0.864494i
$584$			197.990i			0.339024i
$585$		0			0
$586$	−240.000			−0.409556
$587$	−415.779			−0.708311			−0.354156	−	0.935186i	$-0.615232\pi$
$587$	−415.779			−0.708311			−0.354156	+	0.935186i	$0.615232\pi$
$588$		0			0
$589$	−49.0000			−0.0831919
$590$		0			0
$591$	−384.000	−	135.765i	−0.649746	−	0.229720i
$592$		−	8.00000i		−	0.0135135i
$593$	−772.161			−1.30213			−0.651063	−	0.759024i	$-0.725677\pi$
$593$	−772.161			−1.30213			−0.651063	+	0.759024i	$0.725677\pi$
$594$	276.000	−	169.706i	0.464646	−	0.285700i
$595$		0			0
$596$			305.470i			0.512534i
$597$	−291.328	−	103.000i	−0.487987	−	0.172529i
$598$			900.000i			1.50502i
$599$			644.881i			1.07660i	0.842754	+	0.538298i	$0.180933\pi$
$599$			644.881i			1.07660i	−0.842754	+	0.538298i	$0.819067\pi$
$600$		0			0
$601$	455.000			0.757072			0.378536	−	0.925587i	$-0.376428\pi$
$601$	455.000			0.757072			0.378536	+	0.925587i	$0.376428\pi$
$602$	405.879			0.674218
$603$	96.1665	−	119.000i	0.159480	−	0.197347i
$604$	−398.000			−0.658940
$605$		0			0
$606$	−84.0000	+	237.588i	−0.138614	+	0.392059i
$607$		−	566.000i		−	0.932455i	−0.884665	−	0.466227i	$-0.845613\pi$
$607$		−	566.000i		−	0.932455i	0.884665	−	0.466227i	$-0.154387\pi$
$608$	−39.5980			−0.0651283
$609$	−840.000	−	296.985i	−1.37931	−	0.487660i
$610$		0			0
$611$		0			0
$612$	356.382	+	288.000i	0.582323	+	0.470588i
$613$			578.000i			0.942904i	0.881892	+	0.471452i	$0.156270\pi$
$613$			578.000i			0.942904i	−0.881892	+	0.471452i	$0.843730\pi$
$614$			736.805i			1.20001i
$615$		0			0
$616$	−168.000			−0.272727
$617$	636.396			1.03144			0.515718	−	0.856758i	$-0.327525\pi$
$617$	636.396			1.03144			0.515718	+	0.856758i	$0.327525\pi$
$618$	217.789	−	616.000i	0.352409	−	0.996764i
$619$	−593.000			−0.957997			−0.478998	−	0.877816i	$-0.659000\pi$
$619$	−593.000			−0.957997			−0.478998	+	0.877816i	$0.659000\pi$
$620$		0			0
$621$	−360.000	−	585.484i	−0.579710	−	0.942809i
$622$			48.0000i			0.0771704i
$623$	950.352			1.52544
$624$	−100.000	+	282.843i	−0.160256	+	0.453274i
$625$		0			0
$626$		−	168.291i		−	0.268836i
$627$	−59.3970	+	168.000i	−0.0947320	+	0.267943i
$628$			290.000i			0.461783i
$629$		−	50.9117i		−	0.0809407i
$630$		0			0
$631$	−559.000			−0.885895			−0.442948	−	0.896547i	$-0.646067\pi$
$631$	−559.000			−0.885895			−0.442948	+	0.896547i	$0.646067\pi$
$632$	−164.049			−0.259571
$633$	19.7990	+	7.00000i	0.0312780	+	0.0110585i
$634$	−216.000			−0.340694
$635$		0			0
$636$	−336.000	−	118.794i	−0.528302	−	0.186783i
$637$		0			0
$638$	509.117			0.797989
$639$	−240.000	+	296.985i	−0.375587	+	0.464765i
$640$		0			0
$641$			543.058i			0.847204i	0.905848	+	0.423602i	$0.139235\pi$
$641$			543.058i			0.847204i	−0.905848	+	0.423602i	$0.860765\pi$
$642$	−712.764	−	252.000i	−1.11022	−	0.392523i
$643$			854.000i			1.32815i	0.747666	+	0.664075i	$0.231174\pi$
$643$			854.000i			1.32815i	−0.747666	+	0.664075i	$0.768826\pi$
$644$			356.382i			0.553388i
$645$		0			0
$646$	−252.000			−0.390093
$647$	−322.441			−0.498363			−0.249181	−	0.968457i	$-0.580162\pi$
$647$	−322.441			−0.498363			−0.249181	+	0.968457i	$0.580162\pi$
$648$	−48.0833	−	224.000i	−0.0742026	−	0.345679i
$649$	288.000			0.443760
$650$		0			0
$651$	−49.0000	+	138.593i	−0.0752688	+	0.212892i
$652$			322.000i			0.493865i
$653$	356.382			0.545761			0.272880	−	0.962048i	$-0.412024\pi$
$653$	356.382			0.545761			0.272880	+	0.962048i	$0.412024\pi$
$654$	100.000	+	35.3553i	0.152905	+	0.0540602i
$655$		0			0
$656$			33.9411i			0.0517395i
$657$	395.980	−	490.000i	0.602709	−	0.745814i
$658$		0			0
$659$			890.955i			1.35198i	0.736911	+	0.675990i	$0.236284\pi$
$659$			890.955i			1.35198i	−0.736911	+	0.675990i	$0.763716\pi$
$660$		0			0
$661$	−910.000			−1.37670			−0.688351	−	0.725378i	$-0.741665\pi$
$661$	−910.000			−1.37670			−0.688351	+	0.725378i	$0.741665\pi$
$662$	591.141			0.892963
$663$	−636.396	+	1800.00i	−0.959873	+	2.71493i
$664$	336.000			0.506024
$665$		0			0
$666$	−16.0000	+	19.7990i	−0.0240240	+	0.0297282i
$667$		−	1080.00i		−	1.61919i
$668$	220.617			0.330265
$669$	161.000	−	455.377i	0.240658	−	0.680683i
$670$		0			0
$671$			8.48528i			0.0126457i
$672$	−39.5980	+	112.000i	−0.0589256	+	0.166667i
$673$		−	742.000i		−	1.10253i	−0.834332	−	0.551263i	$-0.814146\pi$
$673$		−	742.000i		−	1.10253i	0.834332	−	0.551263i	$-0.185854\pi$
$674$		−	782.060i		−	1.16033i
$675$		0			0
$676$	−912.000			−1.34911
$677$	−432.749			−0.639216			−0.319608	−	0.947550i	$-0.603551\pi$
$677$	−432.749			−0.639216			−0.319608	+	0.947550i	$0.603551\pi$
$678$	−67.8823	−	24.0000i	−0.100121	−	0.0353982i
$679$	−343.000			−0.505155
$680$		0			0
$681$	168.000	+	59.3970i	0.246696	+	0.0872202i
$682$		−	84.0000i		−	0.123167i
$683$	661.852			0.969037			0.484518	−	0.874781i	$-0.338995\pi$
$683$	661.852			0.969037			0.484518	+	0.874781i	$0.338995\pi$
$684$	98.0000	+	79.1960i	0.143275	+	0.115784i
$685$		0			0
$686$		−	485.075i		−	0.707107i
$687$	−274.357	−	97.0000i	−0.399356	−	0.141194i
$688$			164.000i			0.238372i
$689$		−	1484.92i		−	2.15519i
$690$		0			0
$691$	302.000			0.437048			0.218524	−	0.975832i	$-0.429876\pi$
$691$	302.000			0.437048			0.218524	+	0.975832i	$0.429876\pi$
$692$	356.382			0.515003
$693$	415.779	+	336.000i	0.599969	+	0.484848i
$694$	−912.000			−1.31412
$695$		0			0
$696$	120.000	−	339.411i	0.172414	−	0.487660i
$697$			216.000i			0.309900i
$698$	376.181			0.538941
$699$	744.000	+	263.044i	1.06438	+	0.376314i
$700$		0			0
$701$			178.191i			0.254195i	0.991890	+	0.127098i	$0.0405662\pi$
$701$			178.191i			0.254195i	−0.991890	+	0.127098i	$0.959434\pi$
$702$	813.173	−	500.000i	1.15837	−	0.712251i
$703$		−	14.0000i		−	0.0199147i
$704$		−	67.8823i		−	0.0964237i
$705$		0			0
$706$	588.000			0.832861
$707$	−415.779			−0.588089
$708$	67.8823	−	192.000i	0.0958789	−	0.271186i
$709$	−95.0000			−0.133992			−0.0669958	−	0.997753i	$-0.521341\pi$
$709$	−95.0000			−0.133992			−0.0669958	+	0.997753i	$0.521341\pi$
$710$		0			0
$711$	406.000	+	328.098i	0.571027	+	0.461459i
$712$			384.000i			0.539326i
$713$	−178.191			−0.249917
$714$	−252.000	+	712.764i	−0.352941	+	0.998268i
$715$		0			0
$716$			237.588i			0.331827i
$717$	−59.3970	+	168.000i	−0.0828410	+	0.234310i
$718$			468.000i			0.651811i
$719$		−	873.984i		−	1.21555i	−0.794107	−	0.607777i	$-0.792061\pi$
$719$		−	873.984i		−	1.21555i	0.794107	−	0.607777i	$-0.207939\pi$
$720$		0			0
$721$	1078.00			1.49515
$722$	441.235			0.611128
$723$	−336.583	−	119.000i	−0.465536	−	0.164592i
$724$	−434.000			−0.599448
$725$		0			0
$726$	196.000	+	69.2965i	0.269972	+	0.0954497i
$727$			871.000i			1.19807i	0.800721	+	0.599037i	$0.204450\pi$
$727$			871.000i			1.19807i	−0.800721	+	0.599037i	$0.795550\pi$
$728$	−494.975			−0.679910
$729$	−329.000	+	650.538i	−0.451303	+	0.892371i
$730$		0			0
$731$			1043.69i			1.42776i
$732$	5.65685	+	2.00000i	0.00772794	+	0.00273224i
$733$		−	406.000i		−	0.553888i	−0.960886	−	0.276944i	$-0.910678\pi$
$733$		−	406.000i		−	0.553888i	0.960886	−	0.276944i	$-0.0893217\pi$
$734$		−	145.664i		−	0.198452i
$735$		0			0
$736$	−144.000			−0.195652
$737$	−144.250			−0.195726
$738$	67.8823	−	84.0000i	0.0919814	−	0.113821i
$739$	−830.000			−1.12314			−0.561570	−	0.827429i	$-0.689802\pi$
$739$	−830.000			−1.12314			−0.561570	+	0.827429i	$0.689802\pi$
$740$		0			0
$741$	−175.000	+	494.975i	−0.236167	+	0.667982i
$742$		−	588.000i		−	0.792453i
$743$	−1306.73			−1.75873			−0.879363	−	0.476152i	$-0.842031\pi$
$743$	−1306.73			−1.75873			−0.879363	+	0.476152i	$0.842031\pi$
$744$	−56.0000	−	19.7990i	−0.0752688	−	0.0266115i
$745$		0			0
$746$		−	507.703i		−	0.680567i
$747$	−831.558	−	672.000i	−1.11320	−	0.899598i
$748$		−	432.000i		−	0.577540i
$749$		−	1247.34i		−	1.66534i
$750$		0			0
$751$	350.000			0.466045			0.233023	−	0.972471i	$-0.425138\pi$
$751$	350.000			0.466045			0.233023	+	0.972471i	$0.425138\pi$
$752$		0			0
$753$	288.500	−	816.000i	0.383134	−	1.08367i
$754$	1500.00			1.98939
$755$		0			0
$756$	322.000	−	197.990i	0.425926	−	0.261891i
$757$			265.000i			0.350066i	0.984563	+	0.175033i	$0.0560032\pi$
$757$			265.000i			0.350066i	−0.984563	+	0.175033i	$0.943997\pi$
$758$	533.159			0.703375
$759$	−216.000	+	610.940i	−0.284585	+	0.804928i
$760$		0			0
$761$			1069.15i			1.40492i	0.711722	+	0.702461i	$0.247915\pi$
$761$			1069.15i			1.40492i	−0.711722	+	0.702461i	$0.752085\pi$
$762$	−48.0833	+	136.000i	−0.0631014	+	0.178478i
$763$			175.000i			0.229358i
$764$		−	118.794i		−	0.155489i
$765$		0			0
$766$	−864.000			−1.12794
$767$	848.528			1.10629
$768$	−45.2548	−	16.0000i	−0.0589256	−	0.0208333i
$769$	529.000			0.687906			0.343953	−	0.938987i	$-0.388234\pi$
$769$	529.000			0.687906			0.343953	+	0.938987i	$0.388234\pi$
$770$		0			0
$771$	−336.000	−	118.794i	−0.435798	−	0.154078i
$772$		−	50.0000i		−	0.0647668i
$773$	1009.75			1.30627			0.653136	−	0.757240i	$-0.273453\pi$
$773$	1009.75			1.30627			0.653136	+	0.757240i	$0.273453\pi$
$774$	328.000	−	405.879i	0.423773	−	0.524392i
$775$		0			0
$776$		−	138.593i		−	0.178599i
$777$	−39.5980	−	14.0000i	−0.0509627	−	0.0180180i
$778$		−	492.000i		−	0.632391i
$779$			59.3970i			0.0762477i
$780$		0			0
$781$	360.000			0.460948
$782$	−916.410			−1.17188
$783$	−975.807	+	600.000i	−1.24624	+	0.766284i
$784$		0			0
$785$		0			0
$786$	276.000	−	780.646i	0.351145	−	0.993188i
$787$			1519.00i			1.93011i	0.262039	+	0.965057i	$0.415605\pi$
$787$			1519.00i			1.93011i	−0.262039	+	0.965057i	$0.584395\pi$
$788$	271.529			0.344580
$789$	−24.0000	−	8.48528i	−0.0304183	−	0.0107545i
$790$		0			0
$791$		−	118.794i		−	0.150182i
$792$	−135.765	+	168.000i	−0.171420	+	0.212121i
$793$			25.0000i			0.0315259i
$794$			337.997i			0.425689i
$795$		0			0
$796$	206.000			0.258794
$797$	526.087			0.660085			0.330042	−	0.943966i	$-0.392937\pi$
$797$	526.087			0.660085			0.330042	+	0.943966i	$0.392937\pi$
$798$	−69.2965	+	196.000i	−0.0868377	+	0.245614i
$799$		0			0
$800$		0			0
$801$	768.000	−	950.352i	0.958801	−	1.18646i
$802$			132.000i			0.164589i
$803$	−593.970			−0.739688
$804$	−34.0000	+	96.1665i	−0.0422886	+	0.119610i
$805$		0			0
$806$		−	247.487i		−	0.307056i
$807$	−59.3970	+	168.000i	−0.0736022	+	0.208178i
$808$		−	168.000i		−	0.207921i
$809$		−	823.072i		−	1.01739i	−0.860945	−	0.508697i	$-0.830127\pi$
$809$		−	823.072i		−	1.01739i	0.860945	−	0.508697i	$-0.169873\pi$
$810$		0			0
$811$	−319.000			−0.393342			−0.196671	−	0.980470i	$-0.563013\pi$
$811$	−319.000			−0.393342			−0.196671	+	0.980470i	$0.563013\pi$
$812$	593.970			0.731490
$813$	−1329.36	−	470.000i	−1.63513	−	0.578106i
$814$	24.0000			0.0294840
$815$		0			0
$816$	−288.000	−	101.823i	−0.352941	−	0.124784i
$817$			287.000i			0.351285i
$818$	643.467			0.786635
$819$	1225.00	+	989.949i	1.49573	+	1.20873i
$820$		0			0
$821$			118.794i			0.144694i	0.997380	+	0.0723471i	$0.0230489\pi$
$821$			118.794i			0.144694i	−0.997380	+	0.0723471i	$0.976951\pi$
$822$	−475.176	−	168.000i	−0.578073	−	0.204380i
$823$		−	1375.00i		−	1.67072i	−0.549706	−	0.835358i	$-0.685260\pi$
$823$		−	1375.00i		−	1.67072i	0.549706	−	0.835358i	$-0.314740\pi$
$824$			435.578i			0.528614i
$825$		0			0
$826$	336.000			0.406780
$827$	280.014			0.338590			0.169295	−	0.985565i	$-0.445851\pi$
$827$	280.014			0.338590			0.169295	+	0.985565i	$0.445851\pi$
$828$	356.382	+	288.000i	0.430413	+	0.347826i
$829$	142.000			0.171291			0.0856454	−	0.996326i	$-0.472705\pi$
$829$	142.000			0.171291			0.0856454	+	0.996326i	$0.472705\pi$
$830$		0			0
$831$	217.000	−	613.769i	0.261131	−	0.738590i
$832$		−	200.000i		−	0.240385i
$833$		0			0
$834$	616.000	+	217.789i	0.738609	+	0.261138i
$835$		0			0
$836$		−	118.794i		−	0.142098i
$837$	98.9949	+	161.000i	0.118274	+	0.192354i
$838$		−	420.000i		−	0.501193i
$839$			1247.34i			1.48669i	0.668906	+	0.743347i	$0.266763\pi$
$839$			1247.34i			1.48669i	−0.668906	+	0.743347i	$0.733237\pi$
$840$		0			0
$841$	−959.000			−1.14031
$842$	743.876			0.883464
$843$	517.602	−	1464.00i	0.614000	−	1.73665i
$844$	−14.0000			−0.0165877
$845$		0			0
$846$		0			0
$847$			343.000i			0.404959i
$848$	237.588			0.280174
$849$	65.0000	−	183.848i	0.0765607	−	0.216546i
$850$		0			0
$851$		−	50.9117i		−	0.0598257i
$852$	84.8528	−	240.000i	0.0995925	−	0.281690i
$853$		−	1057.00i		−	1.23916i	−0.784935	−	0.619578i	$-0.787304\pi$
$853$		−	1057.00i		−	1.23916i	0.784935	−	0.619578i	$-0.212696\pi$
$854$			9.89949i			0.0115919i
$855$		0			0
$856$	504.000			0.588785
$857$	627.911			0.732685			0.366342	−	0.930480i	$-0.380610\pi$
$857$	627.911			0.732685			0.366342	+	0.930480i	$0.380610\pi$
$858$	−848.528	−	300.000i	−0.988961	−	0.349650i
$859$	946.000			1.10128			0.550640	−	0.834743i	$-0.314384\pi$
$859$	946.000			1.10128			0.550640	+	0.834743i	$0.314384\pi$
$860$		0			0
$861$	168.000	+	59.3970i	0.195122	+	0.0689860i
$862$		−	396.000i		−	0.459397i
$863$	−390.323			−0.452286			−0.226143	−	0.974094i	$-0.572612\pi$
$863$	−390.323			−0.452286			−0.226143	+	0.974094i	$0.572612\pi$
$864$	80.0000	+	130.108i	0.0925926	+	0.150588i
$865$		0			0
$866$		−	168.291i		−	0.194332i
$867$	−1015.41	−	359.000i	−1.17117	−	0.414072i
$868$		−	98.0000i		−	0.112903i
$869$		−	492.146i		−	0.566336i
$870$		0			0
$871$	−425.000			−0.487945
$872$	−70.7107			−0.0810902
$873$	−277.186	+	343.000i	−0.317510	+	0.392898i
$874$	−252.000			−0.288330
$875$		0			0
$876$	−140.000	+	395.980i	−0.159817	+	0.452032i
$877$		−	1463.00i		−	1.66819i	−0.551623	−	0.834094i	$-0.685991\pi$
$877$		−	1463.00i		−	1.66819i	0.551623	−	0.834094i	$-0.314009\pi$
$878$	−1028.13			−1.17099
$879$	−480.000	−	169.706i	−0.546075	−	0.193067i
$880$		0			0
$881$		−	1069.15i		−	1.21356i	−0.794870	−	0.606779i	$-0.792461\pi$
$881$		−	1069.15i		−	1.21356i	0.794870	−	0.606779i	$-0.207539\pi$
$882$		0			0
$883$			1289.00i			1.45980i	0.683556	+	0.729898i	$0.260432\pi$
$883$			1289.00i			1.45980i	−0.683556	+	0.729898i	$0.739568\pi$
$884$		−	1272.79i		−	1.43981i
$885$		0			0
$886$	744.000			0.839729
$887$	−1289.76			−1.45407			−0.727037	−	0.686599i	$-0.759103\pi$
$887$	−1289.76			−1.45407			−0.727037	+	0.686599i	$0.759103\pi$
$888$	5.65685	−	16.0000i	0.00637033	−	0.0180180i
$889$	−238.000			−0.267717
$890$		0			0
$891$	672.000	−	144.250i	0.754209	−	0.161897i
$892$			322.000i			0.360987i
$893$		0			0
$894$	−216.000	+	610.940i	−0.241611	+	0.683378i
$895$		0			0
$896$		−	79.1960i		−	0.0883883i
$897$	−636.396	+	1800.00i	−0.709472	+	2.00669i
$898$		−	360.000i		−	0.400891i
$899$			296.985i			0.330350i
$900$		0			0
$901$	1512.00			1.67814
$902$	−101.823			−0.112886
$903$	811.759	+	287.000i	0.898957	+	0.317829i
$904$	48.0000			0.0530973
$905$		0			0
$906$	−796.000	−	281.428i	−0.878587	−	0.310627i
$907$		−	14.0000i		−	0.0154355i	−0.999970	−	0.00771775i	$-0.997543\pi$
$907$		−	14.0000i		−	0.0154355i	0.999970	−	0.00771775i	$-0.00245666\pi$
$908$	−118.794			−0.130830
$909$	−336.000	+	415.779i	−0.369637	+	0.457402i
$910$		0			0
$911$		−	695.793i		−	0.763768i	−0.924210	−	0.381884i	$-0.875275\pi$
$911$		−	695.793i		−	0.763768i	0.924210	−	0.381884i	$-0.124725\pi$
$912$	−79.1960	−	28.0000i	−0.0868377	−	0.0307018i
$913$			1008.00i			1.10405i
$914$		−	438.406i		−	0.479657i
$915$		0			0
$916$	194.000			0.211790
$917$	1366.13			1.48978
$918$	509.117	+	828.000i	0.554594	+	0.901961i
$919$	1423.00			1.54842			0.774211	−	0.632927i	$-0.218147\pi$
$919$	1423.00			1.54842			0.774211	+	0.632927i	$0.218147\pi$
$920$		0			0
$921$	−521.000	+	1473.61i	−0.565689	+	1.60001i
$922$			1020.00i			1.10629i
$923$	1060.66			1.14914
$924$	−336.000	−	118.794i	−0.363636	−	0.128565i
$925$		0			0
$926$			1032.38i			1.11488i
$927$	871.156	−	1078.00i	0.939758	−	1.16289i
$928$			240.000i			0.258621i
$929$		−	415.779i		−	0.447555i	−0.974640	−	0.223778i	$-0.928161\pi$
$929$		−	415.779i		−	0.447555i	0.974640	−	0.223778i	$-0.0718389\pi$
$930$		0			0
$931$		0			0
$932$	−526.087			−0.564472
$933$	−33.9411	+	96.0000i	−0.0363785	+	0.102894i
$934$	−276.000			−0.295503
$935$		0			0
$936$	−400.000	+	494.975i	−0.427350	+	0.528819i
$937$		−	1655.00i		−	1.76628i	−0.469114	−	0.883138i	$-0.655427\pi$
$937$		−	1655.00i		−	1.76628i	0.469114	−	0.883138i	$-0.344573\pi$
$938$	−168.291			−0.179415
$939$	119.000	−	336.583i	0.126731	−	0.358448i
$940$		0			0
$941$			1663.12i			1.76739i	0.468062	+	0.883696i	$0.344952\pi$
$941$			1663.12i			1.76739i	−0.468062	+	0.883696i	$0.655048\pi$
$942$	−205.061	+	580.000i	−0.217687	+	0.615711i
$943$			216.000i			0.229056i
$944$			135.765i			0.143818i
$945$		0			0
$946$	−492.000			−0.520085
$947$	−415.779			−0.439048			−0.219524	−	0.975607i	$-0.570450\pi$
$947$	−415.779			−0.439048			−0.219524	+	0.975607i	$0.570450\pi$
$948$	−328.098	−	116.000i	−0.346094	−	0.122363i
$949$	−1750.00			−1.84405
$950$		0			0
$951$	−432.000	−	152.735i	−0.454259	−	0.160605i
$952$		−	504.000i		−	0.529412i
$953$	1680.09			1.76294			0.881472	−	0.472236i	$-0.156553\pi$
$953$	1680.09			1.76294			0.881472	+	0.472236i	$0.156553\pi$
$954$	−588.000	−	475.176i	−0.616352	−	0.498088i
$955$		0			0
$956$		−	118.794i		−	0.124261i
$957$	1018.23	+	360.000i	1.06399	+	0.376176i
$958$			552.000i			0.576200i
$959$		−	831.558i		−	0.867109i
$960$		0			0
$961$	−912.000			−0.949011
$962$	70.7107			0.0735038
$963$	−1247.34	−	1008.00i	−1.29526	−	1.04673i
$964$	238.000			0.246888
$965$		0			0
$966$	−252.000	+	712.764i	−0.260870	+	0.737851i
$967$			1162.00i			1.20165i	0.799379	+	0.600827i	$0.205162\pi$
$967$			1162.00i			1.20165i	−0.799379	+	0.600827i	$0.794838\pi$
$968$	−138.593			−0.143175
$969$	−504.000	−	178.191i	−0.520124	−	0.183892i
$970$		0			0
$971$		−	712.764i		−	0.734051i	−0.930211	−	0.367026i	$-0.880376\pi$
$971$		−	712.764i		−	0.734051i	0.930211	−	0.367026i	$-0.119624\pi$
$972$	62.2254	−	482.000i	0.0640179	−	0.495885i
$973$			1078.00i			1.10791i
$974$			668.923i			0.686779i
$975$		0			0
$976$	−4.00000			−0.00409836
$977$	−899.440			−0.920614			−0.460307	−	0.887760i	$-0.652261\pi$
$977$	−899.440			−0.920614			−0.460307	+	0.887760i	$0.652261\pi$
$978$	−227.688	+	644.000i	−0.232810	+	0.658487i
$979$	−1152.00			−1.17671
$980$		0			0
$981$	175.000	+	141.421i	0.178389	+	0.144160i
$982$			1152.00i			1.17312i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	−24.0000	+	67.8823i	−0.0243902	+	0.0689860i
$985$		0			0
$986$			1527.35i			1.54904i
$987$		0			0
$988$		−	350.000i		−	0.354251i
$989$			1043.69i			1.05530i
$990$		0			0
$991$	−535.000			−0.539859			−0.269929	−	0.962880i	$-0.587000\pi$
$991$	−535.000			−0.539859			−0.269929	+	0.962880i	$0.587000\pi$
$992$	39.5980			0.0399173
$993$	1182.28	+	418.000i	1.19062	+	0.420947i
$994$	420.000			0.422535
$995$		0			0
$996$	672.000	+	237.588i	0.674699	+	0.238542i
$997$		−	1274.00i		−	1.27783i	−0.769276	−	0.638917i	$-0.779383\pi$
$997$		−	1274.00i		−	1.27783i	0.769276	−	0.638917i	$-0.220617\pi$
$998$	−247.487			−0.247983
$999$	−46.0000	+	28.2843i	−0.0460460	+	0.0283126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.b.a.149.1		4
3.2	odd	2	inner	150.3.b.a.149.3		4
4.3	odd	2		1200.3.c.h.449.4		4
5.2	odd	4		150.3.d.a.101.1	✓	2
5.3	odd	4		150.3.d.b.101.2	yes	2
5.4	even	2	inner	150.3.b.a.149.4		4
12.11	even	2		1200.3.c.h.449.2		4
15.2	even	4		150.3.d.a.101.2	yes	2
15.8	even	4		150.3.d.b.101.1	yes	2
15.14	odd	2	inner	150.3.b.a.149.2		4
20.3	even	4		1200.3.l.i.401.2		2
20.7	even	4		1200.3.l.p.401.1		2
20.19	odd	2		1200.3.c.h.449.1		4
60.23	odd	4		1200.3.l.i.401.1		2
60.47	odd	4		1200.3.l.p.401.2		2
60.59	even	2		1200.3.c.h.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.b.a.149.1		4	1.1	even	1	trivial
150.3.b.a.149.2		4	15.14	odd	2	inner
150.3.b.a.149.3		4	3.2	odd	2	inner
150.3.b.a.149.4		4	5.4	even	2	inner
150.3.d.a.101.1	✓	2	5.2	odd	4
150.3.d.a.101.2	yes	2	15.2	even	4
150.3.d.b.101.1	yes	2	15.8	even	4
150.3.d.b.101.2	yes	2	5.3	odd	4
1200.3.c.h.449.1		4	20.19	odd	2
1200.3.c.h.449.2		4	12.11	even	2
1200.3.c.h.449.3		4	60.59	even	2
1200.3.c.h.449.4		4	4.3	odd	2
1200.3.l.i.401.1		2	60.23	odd	4
1200.3.l.i.401.2		2	20.3	even	4
1200.3.l.p.401.1		2	20.7	even	4
1200.3.l.p.401.2		2	60.47	odd	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.82843 - 1.00000i) q^{3} +2.00000 q^{4} +(4.00000 + 1.41421i) q^{6} +7.00000i q^{7} -2.82843 q^{8} +(7.00000 + 5.65685i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.82843 - 1.00000i) q^{3} +2.00000 q^{4} +(4.00000 + 1.41421i) q^{6} +7.00000i q^{7} -2.82843 q^{8} +(7.00000 + 5.65685i) q^{9} -8.48528i q^{11} +(-5.65685 - 2.00000i) q^{12} -25.0000i q^{13} -9.89949i q^{14} +4.00000 q^{16} +25.4558 q^{17} +(-9.89949 - 8.00000i) q^{18} +7.00000 q^{19} +(7.00000 - 19.7990i) q^{21} +12.0000i q^{22} +25.4558 q^{23} +(8.00000 + 2.82843i) q^{24} +35.3553i q^{26} +(-14.1421 - 23.0000i) q^{27} +14.0000i q^{28} -42.4264i q^{29} -7.00000 q^{31} -5.65685 q^{32} +(-8.48528 + 24.0000i) q^{33} -36.0000 q^{34} +(14.0000 + 11.3137i) q^{36} -2.00000i q^{37} -9.89949 q^{38} +(-25.0000 + 70.7107i) q^{39} +8.48528i q^{41} +(-9.89949 + 28.0000i) q^{42} +41.0000i q^{43} -16.9706i q^{44} -36.0000 q^{46} +(-11.3137 - 4.00000i) q^{48} +(-72.0000 - 25.4558i) q^{51} -50.0000i q^{52} +59.3970 q^{53} +(20.0000 + 32.5269i) q^{54} -19.7990i q^{56} +(-19.7990 - 7.00000i) q^{57} +60.0000i q^{58} +33.9411i q^{59} -1.00000 q^{61} +9.89949 q^{62} +(-39.5980 + 49.0000i) q^{63} +8.00000 q^{64} +(12.0000 - 33.9411i) q^{66} -17.0000i q^{67} +50.9117 q^{68} +(-72.0000 - 25.4558i) q^{69} +42.4264i q^{71} +(-19.7990 - 16.0000i) q^{72} -70.0000i q^{73} +2.82843i q^{74} +14.0000 q^{76} +59.3970 q^{77} +(35.3553 - 100.000i) q^{78} +58.0000 q^{79} +(17.0000 + 79.1960i) q^{81} -12.0000i q^{82} -118.794 q^{83} +(14.0000 - 39.5980i) q^{84} -57.9828i q^{86} +(-42.4264 + 120.000i) q^{87} +24.0000i q^{88} -135.765i q^{89} +175.000 q^{91} +50.9117 q^{92} +(19.7990 + 7.00000i) q^{93} +(16.0000 + 5.65685i) q^{96} +49.0000i q^{97} +(48.0000 - 59.3970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 16 q^{6} + 28 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 + 16 * q^6 + 28 * q^9	\( 4 q + 8 q^{4} + 16 q^{6} + 28 q^{9} + 16 q^{16} + 28 q^{19} + 28 q^{21} + 32 q^{24} - 28 q^{31} - 144 q^{34} + 56 q^{36} - 100 q^{39} - 144 q^{46} - 288 q^{51} + 80 q^{54} - 4 q^{61} + 32 q^{64} + 48 q^{66} - 288 q^{69} + 56 q^{76} + 232 q^{79} + 68 q^{81} + 56 q^{84} + 700 q^{91} + 64 q^{96} + 192 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 + 16 * q^6 + 28 * q^9 + 16 * q^16 + 28 * q^19 + 28 * q^21 + 32 * q^24 - 28 * q^31 - 144 * q^34 + 56 * q^36 - 100 * q^39 - 144 * q^46 - 288 * q^51 + 80 * q^54 - 4 * q^61 + 32 * q^64 + 48 * q^66 - 288 * q^69 + 56 * q^76 + 232 * q^79 + 68 * q^81 + 56 * q^84 + 700 * q^91 + 64 * q^96 + 192 * q^99

Introduction

L-functions

Modular forms

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Database

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