LMFDB - Embedded newform 150.3.d.a.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(101,150)]

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, 0]))

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

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

chi := DirichletCharacter("150.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Embedding invariants

Embedding label			101.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	150.101
Dual form			150.3.d.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +(-1.00000 + 2.82843i) q^{3} -2.00000 q^{4} +(4.00000 + 1.41421i) q^{6} -7.00000 q^{7} +2.82843i q^{8} +(-7.00000 - 5.65685i) q^{9} -8.48528i q^{11} +(2.00000 - 5.65685i) q^{12} -25.0000 q^{13} +9.89949i q^{14} +4.00000 q^{16} +25.4558i q^{17} +(-8.00000 + 9.89949i) q^{18} -7.00000 q^{19} +(7.00000 - 19.7990i) q^{21} -12.0000 q^{22} -25.4558i q^{23} +(-8.00000 - 2.82843i) q^{24} +35.3553i q^{26} +(23.0000 - 14.1421i) q^{27} +14.0000 q^{28} +42.4264i q^{29} -7.00000 q^{31} -5.65685i q^{32} +(24.0000 + 8.48528i) q^{33} +36.0000 q^{34} +(14.0000 + 11.3137i) q^{36} +2.00000 q^{37} +9.89949i q^{38} +(25.0000 - 70.7107i) q^{39} +8.48528i q^{41} +(-28.0000 - 9.89949i) q^{42} +41.0000 q^{43} +16.9706i q^{44} -36.0000 q^{46} +(-4.00000 + 11.3137i) q^{48} +(-72.0000 - 25.4558i) q^{51} +50.0000 q^{52} -59.3970i q^{53} +(-20.0000 - 32.5269i) q^{54} -19.7990i q^{56} +(7.00000 - 19.7990i) q^{57} +60.0000 q^{58} -33.9411i q^{59} -1.00000 q^{61} +9.89949i q^{62} +(49.0000 + 39.5980i) q^{63} -8.00000 q^{64} +(12.0000 - 33.9411i) q^{66} +17.0000 q^{67} -50.9117i q^{68} +(72.0000 + 25.4558i) q^{69} +42.4264i q^{71} +(16.0000 - 19.7990i) q^{72} -70.0000 q^{73} -2.82843i q^{74} +14.0000 q^{76} +59.3970i q^{77} +(-100.000 - 35.3553i) q^{78} -58.0000 q^{79} +(17.0000 + 79.1960i) q^{81} +12.0000 q^{82} +118.794i q^{83} +(-14.0000 + 39.5980i) q^{84} -57.9828i q^{86} +(-120.000 - 42.4264i) q^{87} +24.0000 q^{88} +135.765i q^{89} +175.000 q^{91} +50.9117i q^{92} +(7.00000 - 19.7990i) q^{93} +(16.0000 + 5.65685i) q^{96} -49.0000 q^{97} +(-48.0000 + 59.3970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{4} + 8 q^{6} - 14 q^{7} - 14 q^{9} + 4 q^{12} - 50 q^{13} + 8 q^{16} - 16 q^{18} - 14 q^{19} + 14 q^{21} - 24 q^{22} - 16 q^{24} + 46 q^{27} + 28 q^{28} - 14 q^{31} + 48 q^{33} + 72 q^{34}+ \cdots - 96 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^6 - 14 * q^7 - 14 * q^9 + 4 * q^12 - 50 * q^13 + 8 * q^16 - 16 * q^18 - 14 * q^19 + 14 * q^21 - 24 * q^22 - 16 * q^24 + 46 * q^27 + 28 * q^28 - 14 * q^31 + 48 * q^33 + 72 * q^34 + 28 * q^36 + 4 * q^37 + 50 * q^39 - 56 * q^42 + 82 * q^43 - 72 * q^46 - 8 * q^48 - 144 * q^51 + 100 * q^52 - 40 * q^54 + 14 * q^57 + 120 * q^58 - 2 * q^61 + 98 * q^63 - 16 * q^64 + 24 * q^66 + 34 * q^67 + 144 * q^69 + 32 * q^72 - 140 * q^73 + 28 * q^76 - 200 * q^78 - 116 * q^79 + 34 * q^81 + 24 * q^82 - 28 * q^84 - 240 * q^87 + 48 * q^88 + 350 * q^91 + 14 * q^93 + 32 * q^96 - 98 * q^97 - 96 * q^99

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$3$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	4.00000	+	1.41421i	0.666667	+	0.235702i
$7$	−7.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$7$	−7.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$8$			2.82843i			0.353553i
$9$	−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	$-0.126038\pi$
$12$	2.00000	−	5.65685i	0.166667	−	0.471405i
$13$	−25.0000			−1.92308			−0.961538	−	0.274670i	$-0.911431\pi$
$13$	−25.0000			−1.92308			−0.961538	+	0.274670i	$0.911431\pi$
$14$			9.89949i			0.707107i
$15$		0			0
$16$	4.00000			0.250000
$17$			25.4558i			1.49740i	0.662908	+	0.748701i	$0.269322\pi$
$17$			25.4558i			1.49740i	−0.662908	+	0.748701i	$0.730678\pi$
$18$	−8.00000	+	9.89949i	−0.444444	+	0.549972i
$19$	−7.00000			−0.368421			−0.184211	−	0.982887i	$-0.558973\pi$
$19$	−7.00000			−0.368421			−0.184211	+	0.982887i	$0.558973\pi$
$20$		0			0
$21$	7.00000	−	19.7990i	0.333333	−	0.942809i
$22$	−12.0000			−0.545455
$23$		−	25.4558i		−	1.10678i	−0.832924	−	0.553388i	$-0.813335\pi$
$23$		−	25.4558i		−	1.10678i	0.832924	−	0.553388i	$-0.186665\pi$
$24$	−8.00000	−	2.82843i	−0.333333	−	0.117851i
$25$		0			0
$26$			35.3553i			1.35982i
$27$	23.0000	−	14.1421i	0.851852	−	0.523783i
$28$	14.0000			0.500000
$29$			42.4264i			1.46298i	0.681852	+	0.731490i	$0.261175\pi$
$29$			42.4264i			1.46298i	−0.681852	+	0.731490i	$0.738825\pi$
$30$		0			0
$31$	−7.00000			−0.225806			−0.112903	−	0.993606i	$-0.536015\pi$
$31$	−7.00000			−0.225806			−0.112903	+	0.993606i	$0.536015\pi$
$32$		−	5.65685i		−	0.176777i
$33$	24.0000	+	8.48528i	0.727273	+	0.257130i
$34$	36.0000			1.05882
$35$		0			0
$36$	14.0000	+	11.3137i	0.388889	+	0.314270i
$37$	2.00000			0.0540541			0.0270270	−	0.999635i	$-0.491396\pi$
$37$	2.00000			0.0540541			0.0270270	+	0.999635i	$0.491396\pi$
$38$			9.89949i			0.260513i
$39$	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	$0.967003\pi$
$42$	−28.0000	−	9.89949i	−0.666667	−	0.235702i
$43$	41.0000			0.953488			0.476744	−	0.879042i	$-0.341817\pi$
$43$	41.0000			0.953488			0.476744	+	0.879042i	$0.341817\pi$
$44$			16.9706i			0.385695i
$45$		0			0
$46$	−36.0000			−0.782609
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−4.00000	+	11.3137i	−0.0833333	+	0.235702i
$49$		0			0
$50$		0			0
$51$	−72.0000	−	25.4558i	−1.41176	−	0.499134i
$52$	50.0000			0.961538
$53$		−	59.3970i		−	1.12070i	−0.828257	−	0.560349i	$-0.810667\pi$
$53$		−	59.3970i		−	1.12070i	0.828257	−	0.560349i	$-0.189333\pi$
$54$	−20.0000	−	32.5269i	−0.370370	−	0.602350i
$55$		0			0
$56$		−	19.7990i		−	0.353553i
$57$	7.00000	−	19.7990i	0.122807	−	0.347351i
$58$	60.0000			1.03448
$59$		−	33.9411i		−	0.575273i	−0.957740	−	0.287637i	$-0.907130\pi$
$59$		−	33.9411i		−	0.575273i	0.957740	−	0.287637i	$-0.0928695\pi$
$60$		0			0
$61$	−1.00000			−0.0163934			−0.00819672	−	0.999966i	$-0.502609\pi$
$61$	−1.00000			−0.0163934			−0.00819672	+	0.999966i	$0.502609\pi$
$62$			9.89949i			0.159669i
$63$	49.0000	+	39.5980i	0.777778	+	0.628539i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	12.0000	−	33.9411i	0.181818	−	0.514259i
$67$	17.0000			0.253731			0.126866	−	0.991920i	$-0.459508\pi$
$67$	17.0000			0.253731			0.126866	+	0.991920i	$0.459508\pi$
$68$		−	50.9117i		−	0.748701i
$69$	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	$0.903421\pi$
$72$	16.0000	−	19.7990i	0.222222	−	0.274986i
$73$	−70.0000			−0.958904			−0.479452	−	0.877568i	$-0.659165\pi$
$73$	−70.0000			−0.958904			−0.479452	+	0.877568i	$0.659165\pi$
$74$		−	2.82843i		−	0.0382220i
$75$		0			0
$76$	14.0000			0.184211
$77$			59.3970i			0.771389i
$78$	−100.000	−	35.3553i	−1.28205	−	0.453274i
$79$	−58.0000			−0.734177			−0.367089	−	0.930186i	$-0.619645\pi$
$79$	−58.0000			−0.734177			−0.367089	+	0.930186i	$0.619645\pi$
$80$		0			0
$81$	17.0000	+	79.1960i	0.209877	+	0.977728i
$82$	12.0000			0.146341
$83$			118.794i			1.43125i	0.698484	+	0.715626i	$0.253859\pi$
$83$			118.794i			1.43125i	−0.698484	+	0.715626i	$0.746141\pi$
$84$	−14.0000	+	39.5980i	−0.166667	+	0.471405i
$85$		0			0
$86$		−	57.9828i		−	0.674218i
$87$	−120.000	−	42.4264i	−1.37931	−	0.487660i
$88$	24.0000			0.272727
$89$			135.765i			1.52544i	0.646727	+	0.762722i	$0.276137\pi$
$89$			135.765i			1.52544i	−0.646727	+	0.762722i	$0.723863\pi$
$90$		0			0
$91$	175.000			1.92308
$92$			50.9117i			0.553388i
$93$	7.00000	−	19.7990i	0.0752688	−	0.212892i
$94$		0			0
$95$		0			0
$96$	16.0000	+	5.65685i	0.166667	+	0.0589256i
$97$	−49.0000			−0.505155			−0.252577	−	0.967577i	$-0.581278\pi$
$97$	−49.0000			−0.505155			−0.252577	+	0.967577i	$0.581278\pi$
$98$		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	$0.904999\pi$
$102$	−36.0000	+	101.823i	−0.352941	+	0.998268i
$103$	−154.000			−1.49515			−0.747573	−	0.664180i	$-0.768781\pi$
$103$	−154.000			−1.49515			−0.747573	+	0.664180i	$0.768781\pi$
$104$		−	70.7107i		−	0.679910i
$105$		0			0
$106$	−84.0000			−0.792453
$107$		−	178.191i		−	1.66534i	−0.553773	−	0.832668i	$-0.686812\pi$
$107$		−	178.191i		−	1.66534i	0.553773	−	0.832668i	$-0.313188\pi$
$108$	−46.0000	+	28.2843i	−0.425926	+	0.261891i
$109$	−25.0000			−0.229358			−0.114679	−	0.993403i	$-0.536584\pi$
$109$	−25.0000			−0.229358			−0.114679	+	0.993403i	$0.536584\pi$
$110$		0			0
$111$	−2.00000	+	5.65685i	−0.0180180	+	0.0509627i
$112$	−28.0000			−0.250000
$113$			16.9706i			0.150182i	0.997177	+	0.0750910i	$0.0239247\pi$
$113$			16.9706i			0.150182i	−0.997177	+	0.0750910i	$0.976075\pi$
$114$	−28.0000	−	9.89949i	−0.245614	−	0.0868377i
$115$		0			0
$116$		−	84.8528i		−	0.731490i
$117$	175.000	+	141.421i	1.49573	+	1.20873i
$118$	−48.0000			−0.406780
$119$		−	178.191i		−	1.49740i
$120$		0			0
$121$	49.0000			0.404959
$122$			1.41421i			0.0115919i
$123$	−24.0000	−	8.48528i	−0.195122	−	0.0689860i
$124$	14.0000			0.112903
$125$		0			0
$126$	56.0000	−	69.2965i	0.444444	−	0.549972i
$127$	−34.0000			−0.267717			−0.133858	−	0.991000i	$-0.542737\pi$
$127$	−34.0000			−0.267717			−0.133858	+	0.991000i	$0.542737\pi$
$128$			11.3137i			0.0883883i
$129$	−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	$-0.267499\pi$
$132$	−48.0000	−	16.9706i	−0.363636	−	0.128565i
$133$	49.0000			0.368421
$134$		−	24.0416i		−	0.179415i
$135$		0			0
$136$	−72.0000			−0.529412
$137$		−	118.794i		−	0.867109i	−0.901127	−	0.433555i	$-0.857259\pi$
$137$		−	118.794i		−	0.867109i	0.901127	−	0.433555i	$-0.142741\pi$
$138$	36.0000	−	101.823i	0.260870	−	0.737851i
$139$	−154.000			−1.10791			−0.553957	−	0.832545i	$-0.686883\pi$
$139$	−154.000			−1.10791			−0.553957	+	0.832545i	$0.686883\pi$
$140$		0			0
$141$		0			0
$142$	60.0000			0.422535
$143$			212.132i			1.48344i
$144$	−28.0000	−	22.6274i	−0.194444	−	0.157135i
$145$		0			0
$146$			98.9949i			0.678048i
$147$		0			0
$148$	−4.00000			−0.0270270
$149$		−	152.735i		−	1.02507i	−0.858667	−	0.512534i	$-0.828707\pi$
$149$		−	152.735i		−	1.02507i	0.858667	−	0.512534i	$-0.171293\pi$
$150$		0			0
$151$	−199.000			−1.31788			−0.658940	−	0.752195i	$-0.728995\pi$
$151$	−199.000			−1.31788			−0.658940	+	0.752195i	$0.728995\pi$
$152$		−	19.7990i		−	0.130257i
$153$	144.000	−	178.191i	0.941176	−	1.16465i
$154$	84.0000			0.545455
$155$		0			0
$156$	−50.0000	+	141.421i	−0.320513	+	0.906547i
$157$	−145.000			−0.923567			−0.461783	−	0.886993i	$-0.652790\pi$
$157$	−145.000			−0.923567			−0.461783	+	0.886993i	$0.652790\pi$
$158$			82.0244i			0.519142i
$159$	168.000	+	59.3970i	1.05660	+	0.373566i
$160$		0			0
$161$			178.191i			1.10678i
$162$	112.000	−	24.0416i	0.691358	−	0.148405i
$163$	161.000			0.987730			0.493865	−	0.869539i	$-0.335584\pi$
$163$	161.000			0.987730			0.493865	+	0.869539i	$0.335584\pi$
$164$		−	16.9706i		−	0.103479i
$165$		0			0
$166$	168.000			1.01205
$167$			110.309i			0.660531i	0.943888	+	0.330265i	$0.107138\pi$
$167$			110.309i			0.660531i	−0.943888	+	0.330265i	$0.892862\pi$
$168$	56.0000	+	19.7990i	0.333333	+	0.117851i
$169$	456.000			2.69822
$170$		0			0
$171$	49.0000	+	39.5980i	0.286550	+	0.231567i
$172$	−82.0000			−0.476744
$173$		−	178.191i		−	1.03001i	−0.857189	−	0.515003i	$-0.827791\pi$
$173$		−	178.191i		−	1.03001i	0.857189	−	0.515003i	$-0.172209\pi$
$174$	−60.0000	+	169.706i	−0.344828	+	0.975320i
$175$		0			0
$176$		−	33.9411i		−	0.192847i
$177$	96.0000	+	33.9411i	0.542373	+	0.191758i
$178$	192.000			1.07865
$179$		−	118.794i		−	0.663653i	−0.943340	−	0.331827i	$-0.892335\pi$
$179$		−	118.794i		−	0.663653i	0.943340	−	0.331827i	$-0.107665\pi$
$180$		0			0
$181$	−217.000			−1.19890			−0.599448	−	0.800414i	$-0.704613\pi$
$181$	−217.000			−1.19890			−0.599448	+	0.800414i	$0.704613\pi$
$182$		−	247.487i		−	1.35982i
$183$	1.00000	−	2.82843i	0.00546448	−	0.0154559i
$184$	72.0000			0.391304
$185$		0			0
$186$	−28.0000	−	9.89949i	−0.150538	−	0.0532231i
$187$	216.000			1.15508
$188$		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	$-0.0496955\pi$
$192$	8.00000	−	22.6274i	0.0416667	−	0.117851i
$193$	−25.0000			−0.129534			−0.0647668	−	0.997900i	$-0.520630\pi$
$193$	−25.0000			−0.129534			−0.0647668	+	0.997900i	$0.520630\pi$
$194$			69.2965i			0.357198i
$195$		0			0
$196$		0			0
$197$			135.765i			0.689160i	0.938757	+	0.344580i	$0.111979\pi$
$197$			135.765i			0.689160i	−0.938757	+	0.344580i	$0.888021\pi$
$198$	84.0000	+	67.8823i	0.424242	+	0.342840i
$199$	−103.000			−0.517588			−0.258794	−	0.965933i	$-0.583325\pi$
$199$	−103.000			−0.517588			−0.258794	+	0.965933i	$0.583325\pi$
$200$		0			0
$201$	−17.0000	+	48.0833i	−0.0845771	+	0.239220i
$202$	84.0000			0.415842
$203$		−	296.985i		−	1.46298i
$204$	144.000	+	50.9117i	0.705882	+	0.249567i
$205$		0			0
$206$			217.789i			1.05723i
$207$	−144.000	+	178.191i	−0.695652	+	0.860826i
$208$	−100.000			−0.480769
$209$			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	$0.505280\pi$
$212$			118.794i			0.560349i
$213$	−120.000	−	42.4264i	−0.563380	−	0.199185i
$214$	−252.000			−1.17757
$215$		0			0
$216$	40.0000	+	65.0538i	0.185185	+	0.301175i
$217$	49.0000			0.225806
$218$			35.3553i			0.162180i
$219$	70.0000	−	197.990i	0.319635	−	0.904063i
$220$		0			0
$221$		−	636.396i		−	2.87962i
$222$	8.00000	+	2.82843i	0.0360360	+	0.0127407i
$223$	161.000			0.721973			0.360987	−	0.932571i	$-0.382440\pi$
$223$	161.000			0.721973			0.360987	+	0.932571i	$0.382440\pi$
$224$			39.5980i			0.176777i
$225$		0			0
$226$	24.0000			0.106195
$227$		−	59.3970i		−	0.261661i	−0.991405	−	0.130830i	$-0.958236\pi$
$227$		−	59.3970i		−	0.261661i	0.991405	−	0.130830i	$-0.0417643\pi$
$228$	−14.0000	+	39.5980i	−0.0614035	+	0.173675i
$229$	−97.0000			−0.423581			−0.211790	−	0.977315i	$-0.567929\pi$
$229$	−97.0000			−0.423581			−0.211790	+	0.977315i	$0.567929\pi$
$230$		0			0
$231$	−168.000	−	59.3970i	−0.727273	−	0.257130i
$232$	−120.000			−0.517241
$233$			263.044i			1.12894i	0.825453	+	0.564472i	$0.190920\pi$
$233$			263.044i			1.12894i	−0.825453	+	0.564472i	$0.809080\pi$
$234$	200.000	−	247.487i	0.854701	−	1.05764i
$235$		0			0
$236$			67.8823i			0.287637i
$237$	58.0000	−	164.049i	0.244726	−	0.692189i
$238$	−252.000			−1.05882
$239$			59.3970i			0.248523i	0.992250	+	0.124261i	$0.0396562\pi$
$239$			59.3970i			0.248523i	−0.992250	+	0.124261i	$0.960344\pi$
$240$		0			0
$241$	119.000			0.493776			0.246888	−	0.969044i	$-0.420592\pi$
$241$	119.000			0.493776			0.246888	+	0.969044i	$0.420592\pi$
$242$		−	69.2965i		−	0.286349i
$243$	−241.000	−	31.1127i	−0.991770	−	0.128036i
$244$	2.00000			0.00819672
$245$		0			0
$246$	−12.0000	+	33.9411i	−0.0487805	+	0.137972i
$247$	175.000			0.708502
$248$		−	19.7990i		−	0.0798346i
$249$	−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	$0.805119\pi$
$252$	−98.0000	−	79.1960i	−0.388889	−	0.314270i
$253$	−216.000			−0.853755
$254$			48.0833i			0.189304i
$255$		0			0
$256$	16.0000			0.0625000
$257$			118.794i			0.462233i	0.972926	+	0.231117i	$0.0742379\pi$
$257$			118.794i			0.462233i	−0.972926	+	0.231117i	$0.925762\pi$
$258$	164.000	+	57.9828i	0.635659	+	0.224739i
$259$	−14.0000			−0.0540541
$260$		0			0
$261$	240.000	−	296.985i	0.919540	−	1.13787i
$262$	−276.000			−1.05344
$263$		−	8.48528i		−	0.0322634i	−0.999870	−	0.0161317i	$-0.994865\pi$
$263$		−	8.48528i		−	0.0322634i	0.999870	−	0.0161317i	$-0.00513511\pi$
$264$	−24.0000	+	67.8823i	−0.0909091	+	0.257130i
$265$		0			0
$266$		−	69.2965i		−	0.260513i
$267$	−384.000	−	135.765i	−1.43820	−	0.508481i
$268$	−34.0000			−0.126866
$269$			59.3970i			0.220807i	0.993887	+	0.110403i	$0.0352142\pi$
$269$			59.3970i			0.220807i	−0.993887	+	0.110403i	$0.964786\pi$
$270$		0			0
$271$	470.000			1.73432			0.867159	−	0.498032i	$-0.165944\pi$
$271$	470.000			1.73432			0.867159	+	0.498032i	$0.165944\pi$
$272$			101.823i			0.374351i
$273$	−175.000	+	494.975i	−0.641026	+	1.81309i
$274$	−168.000			−0.613139
$275$		0			0
$276$	−144.000	−	50.9117i	−0.521739	−	0.184463i
$277$	−217.000			−0.783394			−0.391697	−	0.920094i	$-0.628112\pi$
$277$	−217.000			−0.783394			−0.391697	+	0.920094i	$0.628112\pi$
$278$			217.789i			0.783413i
$279$	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
$283$	65.0000			0.229682			0.114841	−	0.993384i	$-0.463364\pi$
$283$	65.0000			0.229682			0.114841	+	0.993384i	$0.463364\pi$
$284$		−	84.8528i		−	0.298778i
$285$		0			0
$286$	300.000			1.04895
$287$		−	59.3970i		−	0.206958i
$288$	−32.0000	+	39.5980i	−0.111111	+	0.137493i
$289$	−359.000			−1.24221
$290$		0			0
$291$	49.0000	−	138.593i	0.168385	−	0.476264i
$292$	140.000			0.479452
$293$		−	169.706i		−	0.579200i	−0.957148	−	0.289600i	$-0.906478\pi$
$293$		−	169.706i		−	0.579200i	0.957148	−	0.289600i	$-0.0935223\pi$
$294$		0			0
$295$		0			0
$296$			5.65685i			0.0191110i
$297$	−120.000	−	195.161i	−0.404040	−	0.657109i
$298$	−216.000			−0.724832
$299$			636.396i			2.12842i
$300$		0			0
$301$	−287.000			−0.953488
$302$			281.428i			0.931882i
$303$	−168.000	−	59.3970i	−0.554455	−	0.196030i
$304$	−28.0000			−0.0921053
$305$		0			0
$306$	−252.000	−	203.647i	−0.823529	−	0.665512i
$307$	521.000			1.69707			0.848534	−	0.529141i	$-0.177486\pi$
$307$	521.000			1.69707			0.848534	+	0.529141i	$0.177486\pi$
$308$		−	118.794i		−	0.385695i
$309$	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	$-0.0173781\pi$
$312$	200.000	+	70.7107i	0.641026	+	0.226637i
$313$	119.000			0.380192			0.190096	−	0.981766i	$-0.439120\pi$
$313$	119.000			0.380192			0.190096	+	0.981766i	$0.439120\pi$
$314$			205.061i			0.653060i
$315$		0			0
$316$	116.000			0.367089
$317$			152.735i			0.481814i	0.970548	+	0.240907i	$0.0774449\pi$
$317$			152.735i			0.481814i	−0.970548	+	0.240907i	$0.922555\pi$
$318$	84.0000	−	237.588i	0.264151	−	0.747132i
$319$	360.000			1.12853
$320$		0			0
$321$	504.000	+	178.191i	1.57009	+	0.555112i
$322$	252.000			0.782609
$323$		−	178.191i		−	0.551675i
$324$	−34.0000	−	158.392i	−0.104938	−	0.488864i
$325$		0			0
$326$		−	227.688i		−	0.698431i
$327$	25.0000	−	70.7107i	0.0764526	−	0.216241i
$328$	−24.0000			−0.0731707
$329$		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	$0.717528\pi$
$332$		−	237.588i		−	0.715626i
$333$	−14.0000	−	11.3137i	−0.0420420	−	0.0339751i
$334$	156.000			0.467066
$335$		0			0
$336$	28.0000	−	79.1960i	0.0833333	−	0.235702i
$337$	−553.000			−1.64095			−0.820475	−	0.571683i	$-0.806291\pi$
$337$	−553.000			−1.64095			−0.820475	+	0.571683i	$0.806291\pi$
$338$		−	644.881i		−	1.90793i
$339$	−48.0000	−	16.9706i	−0.141593	−	0.0500607i
$340$		0			0
$341$			59.3970i			0.174185i
$342$	56.0000	−	69.2965i	0.163743	−	0.202621i
$343$	343.000			1.00000
$344$			115.966i			0.337109i
$345$		0			0
$346$	−252.000			−0.728324
$347$			644.881i			1.85845i	0.369517	+	0.929224i	$0.379523\pi$
$347$			644.881i			1.85845i	−0.369517	+	0.929224i	$0.620477\pi$
$348$	240.000	+	84.8528i	0.689655	+	0.243830i
$349$	266.000			0.762178			0.381089	−	0.924538i	$-0.375549\pi$
$349$	266.000			0.762178			0.381089	+	0.924538i	$0.375549\pi$
$350$		0			0
$351$	−575.000	+	353.553i	−1.63818	+	1.00727i
$352$	−48.0000			−0.136364
$353$			415.779i			1.17784i	0.808190	+	0.588922i	$0.200447\pi$
$353$			415.779i			1.17784i	−0.808190	+	0.588922i	$0.799553\pi$
$354$	48.0000	−	135.765i	0.135593	−	0.383516i
$355$		0			0
$356$		−	271.529i		−	0.762722i
$357$	504.000	+	178.191i	1.41176	+	0.499134i
$358$	−168.000			−0.469274
$359$			330.926i			0.921799i	0.887452	+	0.460900i	$0.152473\pi$
$359$			330.926i			0.921799i	−0.887452	+	0.460900i	$0.847527\pi$
$360$		0			0
$361$	−312.000			−0.864266
$362$			306.884i			0.847747i
$363$	−49.0000	+	138.593i	−0.134986	+	0.381799i
$364$	−350.000			−0.961538
$365$		0			0
$366$	−4.00000	−	1.41421i	−0.0109290	−	0.00386397i
$367$	−103.000			−0.280654			−0.140327	−	0.990105i	$-0.544815\pi$
$367$	−103.000			−0.280654			−0.140327	+	0.990105i	$0.544815\pi$
$368$		−	101.823i		−	0.276694i
$369$	48.0000	−	59.3970i	0.130081	−	0.160967i
$370$		0			0
$371$			415.779i			1.12070i
$372$	−14.0000	+	39.5980i	−0.0376344	+	0.106446i
$373$	359.000			0.962466			0.481233	−	0.876593i	$-0.340189\pi$
$373$	359.000			0.962466			0.481233	+	0.876593i	$0.340189\pi$
$374$		−	305.470i		−	0.816765i
$375$		0			0
$376$		0			0
$377$		−	1060.66i		−	2.81342i
$378$	140.000	+	227.688i	0.370370	+	0.602350i
$379$	377.000			0.994723			0.497361	−	0.867543i	$-0.334302\pi$
$379$	377.000			0.994723			0.497361	+	0.867543i	$0.334302\pi$
$380$		0			0
$381$	34.0000	−	96.1665i	0.0892388	−	0.252406i
$382$	−84.0000			−0.219895
$383$		−	610.940i		−	1.59514i	−0.603224	−	0.797572i	$-0.706117\pi$
$383$		−	610.940i		−	1.59514i	0.603224	−	0.797572i	$-0.293883\pi$
$384$	−32.0000	−	11.3137i	−0.0833333	−	0.0294628i
$385$		0			0
$386$			35.3553i			0.0915941i
$387$	−287.000	−	231.931i	−0.741602	−	0.599305i
$388$	98.0000			0.252577
$389$		−	347.897i		−	0.894336i	−0.894450	−	0.447168i	$-0.852433\pi$
$389$		−	347.897i		−	0.894336i	0.894450	−	0.447168i	$-0.147567\pi$
$390$		0			0
$391$	648.000			1.65729
$392$		0			0
$393$	552.000	+	195.161i	1.40458	+	0.496594i
$394$	192.000			0.487310
$395$		0			0
$396$	96.0000	−	118.794i	0.242424	−	0.299985i
$397$	239.000			0.602015			0.301008	−	0.953622i	$-0.402677\pi$
$397$	239.000			0.602015			0.301008	+	0.953622i	$0.402677\pi$
$398$			145.664i			0.365990i
$399$	−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	$-0.0371296\pi$
$402$	68.0000	+	24.0416i	0.169154	+	0.0598051i
$403$	175.000			0.434243
$404$		−	118.794i		−	0.294044i
$405$		0			0
$406$	−420.000			−1.03448
$407$		−	16.9706i		−	0.0416967i
$408$	72.0000	−	203.647i	0.176471	−	0.499134i
$409$	455.000			1.11247			0.556235	−	0.831025i	$-0.312246\pi$
$409$	455.000			1.11247			0.556235	+	0.831025i	$0.312246\pi$
$410$		0			0
$411$	336.000	+	118.794i	0.817518	+	0.289036i
$412$	308.000			0.747573
$413$			237.588i			0.575273i
$414$	252.000	+	203.647i	0.608696	+	0.491900i
$415$		0			0
$416$			141.421i			0.339955i
$417$	154.000	−	435.578i	0.369305	−	1.04455i
$418$	84.0000			0.200957
$419$		−	296.985i		−	0.708794i	−0.935095	−	0.354397i	$-0.884686\pi$
$419$		−	296.985i		−	0.708794i	0.935095	−	0.354397i	$-0.115314\pi$
$420$		0			0
$421$	−526.000			−1.24941			−0.624703	−	0.780862i	$-0.714780\pi$
$421$	−526.000			−1.24941			−0.624703	+	0.780862i	$0.714780\pi$
$422$			9.89949i			0.0234585i
$423$		0			0
$424$	168.000			0.396226
$425$		0			0
$426$	−60.0000	+	169.706i	−0.140845	+	0.398370i
$427$	7.00000			0.0163934
$428$			356.382i			0.832668i
$429$	−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	$0.894689\pi$
$432$	92.0000	−	56.5685i	0.212963	−	0.130946i
$433$	119.000			0.274827			0.137413	−	0.990514i	$-0.456121\pi$
$433$	119.000			0.274827			0.137413	+	0.990514i	$0.456121\pi$
$434$		−	69.2965i		−	0.159669i
$435$		0			0
$436$	50.0000			0.114679
$437$			178.191i			0.407760i
$438$	−280.000	−	98.9949i	−0.639269	−	0.226016i
$439$	−727.000			−1.65604			−0.828018	−	0.560701i	$-0.810532\pi$
$439$	−727.000			−1.65604			−0.828018	+	0.560701i	$0.810532\pi$
$440$		0			0
$441$		0			0
$442$	−900.000			−2.03620
$443$			526.087i			1.18756i	0.804629	+	0.593778i	$0.202364\pi$
$443$			526.087i			1.18756i	−0.804629	+	0.593778i	$0.797636\pi$
$444$	4.00000	−	11.3137i	0.00900901	−	0.0254813i
$445$		0			0
$446$		−	227.688i		−	0.510512i
$447$	432.000	+	152.735i	0.966443	+	0.341689i
$448$	56.0000			0.125000
$449$		−	254.558i		−	0.566945i	−0.958980	−	0.283473i	$-0.908513\pi$
$449$		−	254.558i		−	0.566945i	0.958980	−	0.283473i	$-0.0914865\pi$
$450$		0			0
$451$	72.0000			0.159645
$452$		−	33.9411i		−	0.0750910i
$453$	199.000	−	562.857i	0.439294	−	1.24251i
$454$	−84.0000			−0.185022
$455$		0			0
$456$	56.0000	+	19.7990i	0.122807	+	0.0434188i
$457$	−310.000			−0.678337			−0.339168	−	0.940726i	$-0.610146\pi$
$457$	−310.000			−0.678337			−0.339168	+	0.940726i	$0.610146\pi$
$458$			137.179i			0.299517i
$459$	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	$-0.285936\pi$
$462$	−84.0000	+	237.588i	−0.181818	+	0.514259i
$463$	−730.000			−1.57667			−0.788337	−	0.615244i	$-0.789058\pi$
$463$	−730.000			−1.57667			−0.788337	+	0.615244i	$0.789058\pi$
$464$			169.706i			0.365745i
$465$		0			0
$466$	372.000			0.798283
$467$			195.161i			0.417905i	0.977926	+	0.208952i	$0.0670053\pi$
$467$			195.161i			0.417905i	−0.977926	+	0.208952i	$0.932995\pi$
$468$	−350.000	−	282.843i	−0.747863	−	0.604365i
$469$	−119.000			−0.253731
$470$		0			0
$471$	145.000	−	410.122i	0.307856	−	0.870747i
$472$	96.0000			0.203390
$473$		−	347.897i		−	0.735511i
$474$	−232.000	−	82.0244i	−0.489451	−	0.173047i
$475$		0			0
$476$			356.382i			0.748701i
$477$	−336.000	+	415.779i	−0.704403	+	0.871654i
$478$	84.0000			0.175732
$479$			390.323i			0.814870i	0.913234	+	0.407435i	$0.133577\pi$
$479$			390.323i			0.814870i	−0.913234	+	0.407435i	$0.866423\pi$
$480$		0			0
$481$	−50.0000			−0.103950
$482$		−	168.291i		−	0.349152i
$483$	−504.000	−	178.191i	−1.04348	−	0.368925i
$484$	−98.0000			−0.202479
$485$		0			0
$486$	−44.0000	+	340.825i	−0.0905350	+	0.701287i
$487$	473.000			0.971253			0.485626	−	0.874167i	$-0.338592\pi$
$487$	473.000			0.971253			0.485626	+	0.874167i	$0.338592\pi$
$488$		−	2.82843i		−	0.00579596i
$489$	−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	$-0.311385\pi$
$492$	48.0000	+	16.9706i	0.0975610	+	0.0344930i
$493$	−1080.00			−2.19067
$494$		−	247.487i		−	0.500987i
$495$		0			0
$496$	−28.0000			−0.0564516
$497$		−	296.985i		−	0.597555i
$498$	−168.000	+	475.176i	−0.337349	+	0.954168i
$499$	−175.000			−0.350701			−0.175351	−	0.984506i	$-0.556106\pi$
$499$	−175.000			−0.350701			−0.175351	+	0.984506i	$0.556106\pi$
$500$		0			0
$501$	−312.000	−	110.309i	−0.622754	−	0.220177i
$502$	408.000			0.812749
$503$			347.897i			0.691643i	0.938300	+	0.345822i	$0.112400\pi$
$503$			347.897i			0.691643i	−0.938300	+	0.345822i	$0.887600\pi$
$504$	−112.000	+	138.593i	−0.222222	+	0.274986i
$505$		0			0
$506$			305.470i			0.603696i
$507$	−456.000	+	1289.76i	−0.899408	+	2.54391i
$508$	68.0000			0.133858
$509$		−	729.734i		−	1.43366i	−0.697247	−	0.716831i	$-0.745592\pi$
$509$		−	729.734i		−	1.43366i	0.697247	−	0.716831i	$-0.254408\pi$
$510$		0			0
$511$	490.000			0.958904
$512$		−	22.6274i		−	0.0441942i
$513$	−161.000	+	98.9949i	−0.313840	+	0.192973i
$514$	168.000			0.326848
$515$		0			0
$516$	82.0000	−	231.931i	0.158915	−	0.449479i
$517$		0			0
$518$			19.7990i			0.0382220i
$519$	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	$0.816302\pi$
$522$	−420.000	−	339.411i	−0.804598	−	0.650213i
$523$	−175.000			−0.334608			−0.167304	−	0.985905i	$-0.553506\pi$
$523$	−175.000			−0.334608			−0.167304	+	0.985905i	$0.553506\pi$
$524$			390.323i			0.744891i
$525$		0			0
$526$	−12.0000			−0.0228137
$527$		−	178.191i		−	0.338123i
$528$	96.0000	+	33.9411i	0.181818	+	0.0642824i
$529$	−119.000			−0.224953
$530$		0			0
$531$	−192.000	+	237.588i	−0.361582	+	0.447435i
$532$	−98.0000			−0.184211
$533$		−	212.132i		−	0.397996i
$534$	−192.000	+	543.058i	−0.359551	+	1.01696i
$535$		0			0
$536$			48.0833i			0.0897076i
$537$	336.000	+	118.794i	0.625698	+	0.221218i
$538$	84.0000			0.156134
$539$		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	$0.206104\pi$
$542$		−	664.680i		−	1.22635i
$543$	217.000	−	613.769i	0.399632	−	1.13033i
$544$	144.000			0.264706
$545$		0			0
$546$	700.000	+	247.487i	1.28205	+	0.453274i
$547$	−778.000			−1.42230			−0.711152	−	0.703039i	$-0.751826\pi$
$547$	−778.000			−1.42230			−0.711152	+	0.703039i	$0.751826\pi$
$548$			237.588i			0.433555i
$549$	7.00000	+	5.65685i	0.0127505	+	0.0103039i
$550$		0			0
$551$		−	296.985i		−	0.538992i
$552$	−72.0000	+	203.647i	−0.130435	+	0.368925i
$553$	406.000			0.734177
$554$			306.884i			0.553943i
$555$		0			0
$556$	308.000			0.553957
$557$			424.264i			0.761695i	0.924638	+	0.380847i	$0.124368\pi$
$557$			424.264i			0.761695i	−0.924638	+	0.380847i	$0.875632\pi$
$558$	56.0000	−	69.2965i	0.100358	−	0.124187i
$559$	−1025.00			−1.83363
$560$		0			0
$561$	−216.000	+	610.940i	−0.385027	+	1.08902i
$562$	732.000			1.30249
$563$			381.838i			0.678220i	0.940747	+	0.339110i	$0.110126\pi$
$563$			381.838i			0.678220i	−0.940747	+	0.339110i	$0.889874\pi$
$564$		0			0
$565$		0			0
$566$		−	91.9239i		−	0.162410i
$567$	−119.000	−	554.372i	−0.209877	−	0.977728i
$568$	−120.000			−0.211268
$569$		−	381.838i		−	0.671068i	−0.942028	−	0.335534i	$-0.891083\pi$
$569$		−	381.838i		−	0.671068i	0.942028	−	0.335534i	$-0.108917\pi$
$570$		0			0
$571$	−535.000			−0.936953			−0.468476	−	0.883476i	$-0.655197\pi$
$571$	−535.000			−0.936953			−0.468476	+	0.883476i	$0.655197\pi$
$572$		−	424.264i		−	0.741720i
$573$	168.000	+	59.3970i	0.293194	+	0.103660i
$574$	−84.0000			−0.146341
$575$		0			0
$576$	56.0000	+	45.2548i	0.0972222	+	0.0785674i
$577$	−49.0000			−0.0849220			−0.0424610	−	0.999098i	$-0.513520\pi$
$577$	−49.0000			−0.0849220			−0.0424610	+	0.999098i	$0.513520\pi$
$578$			507.703i			0.878378i
$579$	25.0000	−	70.7107i	0.0431779	−	0.122126i
$580$		0			0
$581$		−	831.558i		−	1.43125i
$582$	−196.000	−	69.2965i	−0.336770	−	0.119066i
$583$	−504.000			−0.864494
$584$		−	197.990i		−	0.339024i
$585$		0			0
$586$	−240.000			−0.409556
$587$		−	415.779i		−	0.708311i	−0.935186	−	0.354156i	$-0.884768\pi$
$587$		−	415.779i		−	0.708311i	0.935186	−	0.354156i	$-0.115232\pi$
$588$		0			0
$589$	49.0000			0.0831919
$590$		0			0
$591$	−384.000	−	135.765i	−0.649746	−	0.229720i
$592$	8.00000			0.0135135
$593$			772.161i			1.30213i	0.759024	+	0.651063i	$0.225677\pi$
$593$			772.161i			1.30213i	−0.759024	+	0.651063i	$0.774323\pi$
$594$	−276.000	+	169.706i	−0.464646	+	0.285700i
$595$		0			0
$596$			305.470i			0.512534i
$597$	103.000	−	291.328i	0.172529	−	0.487987i
$598$	900.000			1.50502
$599$		−	644.881i		−	1.07660i	−0.842754	−	0.538298i	$-0.819067\pi$
$599$		−	644.881i		−	1.07660i	0.842754	−	0.538298i	$-0.180933\pi$
$600$		0			0
$601$	455.000			0.757072			0.378536	−	0.925587i	$-0.376428\pi$
$601$	455.000			0.757072			0.378536	+	0.925587i	$0.376428\pi$
$602$			405.879i			0.674218i
$603$	−119.000	−	96.1665i	−0.197347	−	0.159480i
$604$	398.000			0.658940
$605$		0			0
$606$	−84.0000	+	237.588i	−0.138614	+	0.392059i
$607$	566.000			0.932455			0.466227	−	0.884665i	$-0.345613\pi$
$607$	566.000			0.932455			0.466227	+	0.884665i	$0.345613\pi$
$608$			39.5980i			0.0651283i
$609$	840.000	+	296.985i	1.37931	+	0.487660i
$610$		0			0
$611$		0			0
$612$	−288.000	+	356.382i	−0.470588	+	0.582323i
$613$	578.000			0.942904			0.471452	−	0.881892i	$-0.343730\pi$
$613$	578.000			0.942904			0.471452	+	0.881892i	$0.343730\pi$
$614$		−	736.805i		−	1.20001i
$615$		0			0
$616$	−168.000			−0.272727
$617$			636.396i			1.03144i	0.856758	+	0.515718i	$0.172475\pi$
$617$			636.396i			1.03144i	−0.856758	+	0.515718i	$0.827525\pi$
$618$	−616.000	−	217.789i	−0.996764	−	0.352409i
$619$	593.000			0.957997			0.478998	−	0.877816i	$-0.341000\pi$
$619$	593.000			0.957997			0.478998	+	0.877816i	$0.341000\pi$
$620$		0			0
$621$	−360.000	−	585.484i	−0.579710	−	0.942809i
$622$	−48.0000			−0.0771704
$623$		−	950.352i		−	1.52544i
$624$	100.000	−	282.843i	0.160256	−	0.453274i
$625$		0			0
$626$		−	168.291i		−	0.268836i
$627$	−168.000	−	59.3970i	−0.267943	−	0.0947320i
$628$	290.000			0.461783
$629$			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	$0.646067\pi$
$632$		−	164.049i		−	0.259571i
$633$	7.00000	−	19.7990i	0.0110585	−	0.0312780i
$634$	216.000			0.340694
$635$		0			0
$636$	−336.000	−	118.794i	−0.528302	−	0.186783i
$637$		0			0
$638$		−	509.117i		−	0.797989i
$639$	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	$0.860765\pi$
$642$	252.000	−	712.764i	0.392523	−	1.11022i
$643$	854.000			1.32815			0.664075	−	0.747666i	$-0.268826\pi$
$643$	854.000			1.32815			0.664075	+	0.747666i	$0.268826\pi$
$644$		−	356.382i		−	0.553388i
$645$		0			0
$646$	−252.000			−0.390093
$647$		−	322.441i		−	0.498363i	−0.968457	−	0.249181i	$-0.919838\pi$
$647$		−	322.441i		−	0.498363i	0.968457	−	0.249181i	$-0.0801615\pi$
$648$	−224.000	+	48.0833i	−0.345679	+	0.0742026i
$649$	−288.000			−0.443760
$650$		0			0
$651$	−49.0000	+	138.593i	−0.0752688	+	0.212892i
$652$	−322.000			−0.493865
$653$		−	356.382i		−	0.545761i	−0.962048	−	0.272880i	$-0.912024\pi$
$653$		−	356.382i		−	0.545761i	0.962048	−	0.272880i	$-0.0879763\pi$
$654$	−100.000	−	35.3553i	−0.152905	−	0.0540602i
$655$		0			0
$656$			33.9411i			0.0517395i
$657$	490.000	+	395.980i	0.745814	+	0.602709i
$658$		0			0
$659$		−	890.955i		−	1.35198i	−0.736911	−	0.675990i	$-0.763716\pi$
$659$		−	890.955i		−	1.35198i	0.736911	−	0.675990i	$-0.236284\pi$
$660$		0			0
$661$	−910.000			−1.37670			−0.688351	−	0.725378i	$-0.741665\pi$
$661$	−910.000			−1.37670			−0.688351	+	0.725378i	$0.741665\pi$
$662$			591.141i			0.892963i
$663$	1800.00	+	636.396i	2.71493	+	0.959873i
$664$	−336.000			−0.506024
$665$		0			0
$666$	−16.0000	+	19.7990i	−0.0240240	+	0.0297282i
$667$	1080.00			1.61919
$668$		−	220.617i		−	0.330265i
$669$	−161.000	+	455.377i	−0.240658	+	0.680683i
$670$		0			0
$671$			8.48528i			0.0126457i
$672$	−112.000	−	39.5980i	−0.166667	−	0.0589256i
$673$	−742.000			−1.10253			−0.551263	−	0.834332i	$-0.685854\pi$
$673$	−742.000			−1.10253			−0.551263	+	0.834332i	$0.685854\pi$
$674$			782.060i			1.16033i
$675$		0			0
$676$	−912.000			−1.34911
$677$		−	432.749i		−	0.639216i	−0.947550	−	0.319608i	$-0.896449\pi$
$677$		−	432.749i		−	0.639216i	0.947550	−	0.319608i	$-0.103551\pi$
$678$	−24.0000	+	67.8823i	−0.0353982	+	0.100121i
$679$	343.000			0.505155
$680$		0			0
$681$	168.000	+	59.3970i	0.246696	+	0.0872202i
$682$	84.0000			0.123167
$683$		−	661.852i		−	0.969037i	−0.874781	−	0.484518i	$-0.838995\pi$
$683$		−	661.852i		−	0.969037i	0.874781	−	0.484518i	$-0.161005\pi$
$684$	−98.0000	−	79.1960i	−0.143275	−	0.115784i
$685$		0			0
$686$		−	485.075i		−	0.707107i
$687$	97.0000	−	274.357i	0.141194	−	0.399356i
$688$	164.000			0.238372
$689$			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	$0.429876\pi$
$692$			356.382i			0.515003i
$693$	336.000	−	415.779i	0.484848	−	0.599969i
$694$	912.000			1.31412
$695$		0			0
$696$	120.000	−	339.411i	0.172414	−	0.487660i
$697$	−216.000			−0.309900
$698$		−	376.181i		−	0.538941i
$699$	−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	$0.959434\pi$
$702$	500.000	+	813.173i	0.712251	+	1.15837i
$703$	−14.0000			−0.0199147
$704$			67.8823i			0.0964237i
$705$		0			0
$706$	588.000			0.832861
$707$		−	415.779i		−	0.588089i
$708$	−192.000	−	67.8823i	−0.271186	−	0.0958789i
$709$	95.0000			0.133992			0.0669958	−	0.997753i	$-0.478659\pi$
$709$	95.0000			0.133992			0.0669958	+	0.997753i	$0.478659\pi$
$710$		0			0
$711$	406.000	+	328.098i	0.571027	+	0.461459i
$712$	−384.000			−0.539326
$713$			178.191i			0.249917i
$714$	252.000	−	712.764i	0.352941	−	0.998268i
$715$		0			0
$716$			237.588i			0.331827i
$717$	−168.000	−	59.3970i	−0.234310	−	0.0828410i
$718$	468.000			0.651811
$719$			873.984i			1.21555i	0.794107	+	0.607777i	$0.207939\pi$
$719$			873.984i			1.21555i	−0.794107	+	0.607777i	$0.792061\pi$
$720$		0			0
$721$	1078.00			1.49515
$722$			441.235i			0.611128i
$723$	−119.000	+	336.583i	−0.164592	+	0.465536i
$724$	434.000			0.599448
$725$		0			0
$726$	196.000	+	69.2965i	0.269972	+	0.0954497i
$727$	−871.000			−1.19807			−0.599037	−	0.800721i	$-0.704450\pi$
$727$	−871.000			−1.19807			−0.599037	+	0.800721i	$0.704450\pi$
$728$			494.975i			0.679910i
$729$	329.000	−	650.538i	0.451303	−	0.892371i
$730$		0			0
$731$			1043.69i			1.42776i
$732$	−2.00000	+	5.65685i	−0.00273224	+	0.00772794i
$733$	−406.000			−0.553888			−0.276944	−	0.960886i	$-0.589322\pi$
$733$	−406.000			−0.553888			−0.276944	+	0.960886i	$0.589322\pi$
$734$			145.664i			0.198452i
$735$		0			0
$736$	−144.000			−0.195652
$737$		−	144.250i		−	0.195726i
$738$	−84.0000	−	67.8823i	−0.113821	−	0.0919814i
$739$	830.000			1.12314			0.561570	−	0.827429i	$-0.310198\pi$
$739$	830.000			1.12314			0.561570	+	0.827429i	$0.310198\pi$
$740$		0			0
$741$	−175.000	+	494.975i	−0.236167	+	0.667982i
$742$	588.000			0.792453
$743$			1306.73i			1.75873i	0.476152	+	0.879363i	$0.342031\pi$
$743$			1306.73i			1.75873i	−0.476152	+	0.879363i	$0.657969\pi$
$744$	56.0000	+	19.7990i	0.0752688	+	0.0266115i
$745$		0			0
$746$		−	507.703i		−	0.680567i
$747$	672.000	−	831.558i	0.899598	−	1.11320i
$748$	−432.000			−0.577540
$749$			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
$753$	−816.000	−	288.500i	−1.08367	−	0.383134i
$754$	−1500.00			−1.98939
$755$		0			0
$756$	322.000	−	197.990i	0.425926	−	0.261891i
$757$	−265.000			−0.350066			−0.175033	−	0.984563i	$-0.556003\pi$
$757$	−265.000			−0.350066			−0.175033	+	0.984563i	$0.556003\pi$
$758$		−	533.159i		−	0.703375i
$759$	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	$0.752085\pi$
$762$	−136.000	−	48.0833i	−0.178478	−	0.0631014i
$763$	175.000			0.229358
$764$			118.794i			0.155489i
$765$		0			0
$766$	−864.000			−1.12794
$767$			848.528i			1.10629i
$768$	−16.0000	+	45.2548i	−0.0208333	+	0.0589256i
$769$	−529.000			−0.687906			−0.343953	−	0.938987i	$-0.611766\pi$
$769$	−529.000			−0.687906			−0.343953	+	0.938987i	$0.611766\pi$
$770$		0			0
$771$	−336.000	−	118.794i	−0.435798	−	0.154078i
$772$	50.0000			0.0647668
$773$		−	1009.75i		−	1.30627i	−0.757240	−	0.653136i	$-0.773453\pi$
$773$		−	1009.75i		−	1.30627i	0.757240	−	0.653136i	$-0.226547\pi$
$774$	−328.000	+	405.879i	−0.423773	+	0.524392i
$775$		0			0
$776$		−	138.593i		−	0.178599i
$777$	14.0000	−	39.5980i	0.0180180	−	0.0509627i
$778$	−492.000			−0.632391
$779$		−	59.3970i		−	0.0762477i
$780$		0			0
$781$	360.000			0.460948
$782$		−	916.410i		−	1.17188i
$783$	600.000	+	975.807i	0.766284	+	1.24624i
$784$		0			0
$785$		0			0
$786$	276.000	−	780.646i	0.351145	−	0.993188i
$787$	−1519.00			−1.93011			−0.965057	−	0.262039i	$-0.915605\pi$
$787$	−1519.00			−1.93011			−0.965057	+	0.262039i	$0.915605\pi$
$788$		−	271.529i		−	0.344580i
$789$	24.0000	+	8.48528i	0.0304183	+	0.0107545i
$790$		0			0
$791$		−	118.794i		−	0.150182i
$792$	−168.000	−	135.765i	−0.212121	−	0.171420i
$793$	25.0000			0.0315259
$794$		−	337.997i		−	0.425689i
$795$		0			0
$796$	206.000			0.258794
$797$			526.087i			0.660085i	0.943966	+	0.330042i	$0.107063\pi$
$797$			526.087i			0.660085i	−0.943966	+	0.330042i	$0.892937\pi$
$798$	196.000	+	69.2965i	0.245614	+	0.0868377i
$799$		0			0
$800$		0			0
$801$	768.000	−	950.352i	0.958801	−	1.18646i
$802$	−132.000			−0.164589
$803$			593.970i			0.739688i
$804$	34.0000	−	96.1665i	0.0422886	−	0.119610i
$805$		0			0
$806$		−	247.487i		−	0.307056i
$807$	−168.000	−	59.3970i	−0.208178	−	0.0736022i
$808$	−168.000			−0.207921
$809$			823.072i			1.01739i	0.860945	+	0.508697i	$0.169873\pi$
$809$			823.072i			1.01739i	−0.860945	+	0.508697i	$0.830127\pi$
$810$		0			0
$811$	−319.000			−0.393342			−0.196671	−	0.980470i	$-0.563013\pi$
$811$	−319.000			−0.393342			−0.196671	+	0.980470i	$0.563013\pi$
$812$			593.970i			0.731490i
$813$	−470.000	+	1329.36i	−0.578106	+	1.63513i
$814$	−24.0000			−0.0294840
$815$		0			0
$816$	−288.000	−	101.823i	−0.352941	−	0.124784i
$817$	−287.000			−0.351285
$818$		−	643.467i		−	0.786635i
$819$	−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	$0.976951\pi$
$822$	168.000	−	475.176i	0.204380	−	0.578073i
$823$	−1375.00			−1.67072			−0.835358	−	0.549706i	$-0.814740\pi$
$823$	−1375.00			−1.67072			−0.835358	+	0.549706i	$0.814740\pi$
$824$		−	435.578i		−	0.528614i
$825$		0			0
$826$	336.000			0.406780
$827$			280.014i			0.338590i	0.985565	+	0.169295i	$0.0541491\pi$
$827$			280.014i			0.338590i	−0.985565	+	0.169295i	$0.945851\pi$
$828$	288.000	−	356.382i	0.347826	−	0.430413i
$829$	−142.000			−0.171291			−0.0856454	−	0.996326i	$-0.527295\pi$
$829$	−142.000			−0.171291			−0.0856454	+	0.996326i	$0.527295\pi$
$830$		0			0
$831$	217.000	−	613.769i	0.261131	−	0.738590i
$832$	200.000			0.240385
$833$		0			0
$834$	−616.000	−	217.789i	−0.738609	−	0.261138i
$835$		0			0
$836$		−	118.794i		−	0.142098i
$837$	−161.000	+	98.9949i	−0.192354	+	0.118274i
$838$	−420.000			−0.501193
$839$		−	1247.34i		−	1.48669i	−0.668906	−	0.743347i	$-0.733237\pi$
$839$		−	1247.34i		−	1.48669i	0.668906	−	0.743347i	$-0.266763\pi$
$840$		0			0
$841$	−959.000			−1.14031
$842$			743.876i			0.883464i
$843$	−1464.00	−	517.602i	−1.73665	−	0.614000i
$844$	14.0000			0.0165877
$845$		0			0
$846$		0			0
$847$	−343.000			−0.404959
$848$		−	237.588i		−	0.280174i
$849$	−65.0000	+	183.848i	−0.0765607	+	0.216546i
$850$		0			0
$851$		−	50.9117i		−	0.0598257i
$852$	240.000	+	84.8528i	0.281690	+	0.0995925i
$853$	−1057.00			−1.23916			−0.619578	−	0.784935i	$-0.712696\pi$
$853$	−1057.00			−1.23916			−0.619578	+	0.784935i	$0.712696\pi$
$854$		−	9.89949i		−	0.0115919i
$855$		0			0
$856$	504.000			0.588785
$857$			627.911i			0.732685i	0.930480	+	0.366342i	$0.119390\pi$
$857$			627.911i			0.732685i	−0.930480	+	0.366342i	$0.880610\pi$
$858$	−300.000	+	848.528i	−0.349650	+	0.988961i
$859$	−946.000			−1.10128			−0.550640	−	0.834743i	$-0.685616\pi$
$859$	−946.000			−1.10128			−0.550640	+	0.834743i	$0.685616\pi$
$860$		0			0
$861$	168.000	+	59.3970i	0.195122	+	0.0689860i
$862$	396.000			0.459397
$863$			390.323i			0.452286i	0.974094	+	0.226143i	$0.0726117\pi$
$863$			390.323i			0.452286i	−0.974094	+	0.226143i	$0.927388\pi$
$864$	−80.0000	−	130.108i	−0.0925926	−	0.150588i
$865$		0			0
$866$		−	168.291i		−	0.194332i
$867$	359.000	−	1015.41i	0.414072	−	1.17117i
$868$	−98.0000			−0.112903
$869$			492.146i			0.566336i
$870$		0			0
$871$	−425.000			−0.487945
$872$		−	70.7107i		−	0.0810902i
$873$	343.000	+	277.186i	0.392898	+	0.317510i
$874$	252.000			0.288330
$875$		0			0
$876$	−140.000	+	395.980i	−0.159817	+	0.452032i
$877$	1463.00			1.66819			0.834094	−	0.551623i	$-0.185991\pi$
$877$	1463.00			1.66819			0.834094	+	0.551623i	$0.185991\pi$
$878$			1028.13i			1.17099i
$879$	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
$883$	1289.00			1.45980			0.729898	−	0.683556i	$-0.239568\pi$
$883$	1289.00			1.45980			0.729898	+	0.683556i	$0.239568\pi$
$884$			1272.79i			1.43981i
$885$		0			0
$886$	744.000			0.839729
$887$		−	1289.76i		−	1.45407i	−0.686599	−	0.727037i	$-0.740897\pi$
$887$		−	1289.76i		−	1.45407i	0.686599	−	0.727037i	$-0.259103\pi$
$888$	−16.0000	−	5.65685i	−0.0180180	−	0.00637033i
$889$	238.000			0.267717
$890$		0			0
$891$	672.000	−	144.250i	0.754209	−	0.161897i
$892$	−322.000			−0.360987
$893$		0			0
$894$	216.000	−	610.940i	0.241611	−	0.683378i
$895$		0			0
$896$		−	79.1960i		−	0.0883883i
$897$	−1800.00	−	636.396i	−2.00669	−	0.709472i
$898$	−360.000			−0.400891
$899$		−	296.985i		−	0.330350i
$900$		0			0
$901$	1512.00			1.67814
$902$		−	101.823i		−	0.112886i
$903$	287.000	−	811.759i	0.317829	−	0.898957i
$904$	−48.0000			−0.0530973
$905$		0			0
$906$	−796.000	−	281.428i	−0.878587	−	0.310627i
$907$	14.0000			0.0154355			0.00771775	−	0.999970i	$-0.497543\pi$
$907$	14.0000			0.0154355			0.00771775	+	0.999970i	$0.497543\pi$
$908$			118.794i			0.130830i
$909$	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	$-0.124725\pi$
$912$	28.0000	−	79.1960i	0.0307018	−	0.0868377i
$913$	1008.00			1.10405
$914$			438.406i			0.479657i
$915$		0			0
$916$	194.000			0.211790
$917$			1366.13i			1.48978i
$918$	828.000	−	509.117i	0.901961	−	0.554594i
$919$	−1423.00			−1.54842			−0.774211	−	0.632927i	$-0.781853\pi$
$919$	−1423.00			−1.54842			−0.774211	+	0.632927i	$0.781853\pi$
$920$		0			0
$921$	−521.000	+	1473.61i	−0.565689	+	1.60001i
$922$	−1020.00			−1.10629
$923$		−	1060.66i		−	1.14914i
$924$	336.000	+	118.794i	0.363636	+	0.128565i
$925$		0			0
$926$			1032.38i			1.11488i
$927$	1078.00	+	871.156i	1.16289	+	0.939758i
$928$	240.000			0.258621
$929$			415.779i			0.447555i	0.974640	+	0.223778i	$0.0718389\pi$
$929$			415.779i			0.447555i	−0.974640	+	0.223778i	$0.928161\pi$
$930$		0			0
$931$		0			0
$932$		−	526.087i		−	0.564472i
$933$	96.0000	+	33.9411i	0.102894	+	0.0363785i
$934$	276.000			0.295503
$935$		0			0
$936$	−400.000	+	494.975i	−0.427350	+	0.528819i
$937$	1655.00			1.76628			0.883138	−	0.469114i	$-0.155427\pi$
$937$	1655.00			1.76628			0.883138	+	0.469114i	$0.155427\pi$
$938$			168.291i			0.179415i
$939$	−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	$0.655048\pi$
$942$	−580.000	−	205.061i	−0.615711	−	0.217687i
$943$	216.000			0.229056
$944$		−	135.765i		−	0.143818i
$945$		0			0
$946$	−492.000			−0.520085
$947$		−	415.779i		−	0.439048i	−0.975607	−	0.219524i	$-0.929550\pi$
$947$		−	415.779i		−	0.439048i	0.975607	−	0.219524i	$-0.0704505\pi$
$948$	−116.000	+	328.098i	−0.122363	+	0.346094i
$949$	1750.00			1.84405
$950$		0			0
$951$	−432.000	−	152.735i	−0.454259	−	0.160605i
$952$	504.000			0.529412
$953$		−	1680.09i		−	1.76294i	−0.472236	−	0.881472i	$-0.656553\pi$
$953$		−	1680.09i		−	1.76294i	0.472236	−	0.881472i	$-0.343447\pi$
$954$	588.000	+	475.176i	0.616352	+	0.498088i
$955$		0			0
$956$		−	118.794i		−	0.124261i
$957$	−360.000	+	1018.23i	−0.376176	+	1.06399i
$958$	552.000			0.576200
$959$			831.558i			0.867109i
$960$		0			0
$961$	−912.000			−0.949011
$962$			70.7107i			0.0735038i
$963$	−1008.00	+	1247.34i	−1.04673	+	1.29526i
$964$	−238.000			−0.246888
$965$		0			0
$966$	−252.000	+	712.764i	−0.260870	+	0.737851i
$967$	−1162.00			−1.20165			−0.600827	−	0.799379i	$-0.705162\pi$
$967$	−1162.00			−1.20165			−0.600827	+	0.799379i	$0.705162\pi$
$968$			138.593i			0.143175i
$969$	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	$-0.119624\pi$
$972$	482.000	+	62.2254i	0.495885	+	0.0640179i
$973$	1078.00			1.10791
$974$		−	668.923i		−	0.686779i
$975$		0			0
$976$	−4.00000			−0.00409836
$977$		−	899.440i		−	0.920614i	−0.887760	−	0.460307i	$-0.847739\pi$
$977$		−	899.440i		−	0.920614i	0.887760	−	0.460307i	$-0.152261\pi$
$978$	644.000	+	227.688i	0.658487	+	0.232810i
$979$	1152.00			1.17671
$980$		0			0
$981$	175.000	+	141.421i	0.178389	+	0.144160i
$982$	−1152.00			−1.17312
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	24.0000	−	67.8823i	0.0243902	−	0.0689860i
$985$		0			0
$986$			1527.35i			1.54904i
$987$		0			0
$988$	−350.000			−0.354251
$989$		−	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	$0.587000\pi$
$992$			39.5980i			0.0399173i
$993$	418.000	−	1182.28i	0.420947	−	1.19062i
$994$	−420.000			−0.422535
$995$		0			0
$996$	672.000	+	237.588i	0.674699	+	0.238542i
$997$	1274.00			1.27783			0.638917	−	0.769276i	$-0.279383\pi$
$997$	1274.00			1.27783			0.638917	+	0.769276i	$0.279383\pi$
$998$			247.487i			0.247983i
$999$	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.d.a.101.1	✓	2
3.2	odd	2	inner	150.3.d.a.101.2	yes	2
4.3	odd	2		1200.3.l.p.401.1		2
5.2	odd	4		150.3.b.a.149.4		4
5.3	odd	4		150.3.b.a.149.1		4
5.4	even	2		150.3.d.b.101.2	yes	2
12.11	even	2		1200.3.l.p.401.2		2
15.2	even	4		150.3.b.a.149.2		4
15.8	even	4		150.3.b.a.149.3		4
15.14	odd	2		150.3.d.b.101.1	yes	2
20.3	even	4		1200.3.c.h.449.4		4
20.7	even	4		1200.3.c.h.449.1		4
20.19	odd	2		1200.3.l.i.401.2		2
60.23	odd	4		1200.3.c.h.449.2		4
60.47	odd	4		1200.3.c.h.449.3		4
60.59	even	2		1200.3.l.i.401.1		2

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.00000 + 2.82843i) q^{3} -2.00000 q^{4} +(4.00000 + 1.41421i) q^{6} -7.00000 q^{7} +2.82843i q^{8} +(-7.00000 - 5.65685i) q^{9} -8.48528i q^{11} +(2.00000 - 5.65685i) q^{12} -25.0000 q^{13} +9.89949i q^{14} +4.00000 q^{16} +25.4558i q^{17} +(-8.00000 + 9.89949i) q^{18} -7.00000 q^{19} +(7.00000 - 19.7990i) q^{21} -12.0000 q^{22} -25.4558i q^{23} +(-8.00000 - 2.82843i) q^{24} +35.3553i q^{26} +(23.0000 - 14.1421i) q^{27} +14.0000 q^{28} +42.4264i q^{29} -7.00000 q^{31} -5.65685i q^{32} +(24.0000 + 8.48528i) q^{33} +36.0000 q^{34} +(14.0000 + 11.3137i) q^{36} +2.00000 q^{37} +9.89949i q^{38} +(25.0000 - 70.7107i) q^{39} +8.48528i q^{41} +(-28.0000 - 9.89949i) q^{42} +41.0000 q^{43} +16.9706i q^{44} -36.0000 q^{46} +(-4.00000 + 11.3137i) q^{48} +(-72.0000 - 25.4558i) q^{51} +50.0000 q^{52} -59.3970i q^{53} +(-20.0000 - 32.5269i) q^{54} -19.7990i q^{56} +(7.00000 - 19.7990i) q^{57} +60.0000 q^{58} -33.9411i q^{59} -1.00000 q^{61} +9.89949i q^{62} +(49.0000 + 39.5980i) q^{63} -8.00000 q^{64} +(12.0000 - 33.9411i) q^{66} +17.0000 q^{67} -50.9117i q^{68} +(72.0000 + 25.4558i) q^{69} +42.4264i q^{71} +(16.0000 - 19.7990i) q^{72} -70.0000 q^{73} -2.82843i q^{74} +14.0000 q^{76} +59.3970i q^{77} +(-100.000 - 35.3553i) q^{78} -58.0000 q^{79} +(17.0000 + 79.1960i) q^{81} +12.0000 q^{82} +118.794i q^{83} +(-14.0000 + 39.5980i) q^{84} -57.9828i q^{86} +(-120.000 - 42.4264i) q^{87} +24.0000 q^{88} +135.765i q^{89} +175.000 q^{91} +50.9117i q^{92} +(7.00000 - 19.7990i) q^{93} +(16.0000 + 5.65685i) q^{96} -49.0000 q^{97} +(-48.0000 + 59.3970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{4} + 8 q^{6} - 14 q^{7} - 14 q^{9} + 4 q^{12} - 50 q^{13} + 8 q^{16} - 16 q^{18} - 14 q^{19} + 14 q^{21} - 24 q^{22} - 16 q^{24} + 46 q^{27} + 28 q^{28} - 14 q^{31} + 48 q^{33} + 72 q^{34}+ \cdots - 96 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^4 + 8 * q^6 - 14 * q^7 - 14 * q^9 + 4 * q^12 - 50 * q^13 + 8 * q^16 - 16 * q^18 - 14 * q^19 + 14 * q^21 - 24 * q^22 - 16 * q^24 + 46 * q^27 + 28 * q^28 - 14 * q^31 + 48 * q^33 + 72 * q^34 + 28 * q^36 + 4 * q^37 + 50 * q^39 - 56 * q^42 + 82 * q^43 - 72 * q^46 - 8 * q^48 - 144 * q^51 + 100 * q^52 - 40 * q^54 + 14 * q^57 + 120 * q^58 - 2 * q^61 + 98 * q^63 - 16 * q^64 + 24 * q^66 + 34 * q^67 + 144 * q^69 + 32 * q^72 - 140 * q^73 + 28 * q^76 - 200 * q^78 - 116 * q^79 + 34 * q^81 + 24 * q^82 - 28 * q^84 - 240 * q^87 + 48 * q^88 + 350 * q^91 + 14 * q^93 + 32 * q^96 - 98 * q^97 - 96 * q^99

Introduction

L-functions

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