LMFDB - Embedded newform 15.3.c.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,3,Mod(11,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, 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("15.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	15.c (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:	$0.408720396540$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-5}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 5 $ x^2 + 5
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			11.1
Root			$-2.23607i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.3.c.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607i q^{2} +(-2.00000 + 2.23607i) q^{3} -1.00000 q^{4} +2.23607i q^{5} +(5.00000 + 4.47214i) q^{6} -6.00000 q^{7} -6.70820i q^{8} +(-1.00000 - 8.94427i) q^{9} +O(q^{10})$	\(q-2.23607i q^{2} +(-2.00000 + 2.23607i) q^{3} -1.00000 q^{4} +2.23607i q^{5} +(5.00000 + 4.47214i) q^{6} -6.00000 q^{7} -6.70820i q^{8} +(-1.00000 - 8.94427i) q^{9} +5.00000 q^{10} +4.47214i q^{11} +(2.00000 - 2.23607i) q^{12} +16.0000 q^{13} +13.4164i q^{14} +(-5.00000 - 4.47214i) q^{15} -19.0000 q^{16} +4.47214i q^{17} +(-20.0000 + 2.23607i) q^{18} -2.00000 q^{19} -2.23607i q^{20} +(12.0000 - 13.4164i) q^{21} +10.0000 q^{22} +13.4164i q^{23} +(15.0000 + 13.4164i) q^{24} -5.00000 q^{25} -35.7771i q^{26} +(22.0000 + 15.6525i) q^{27} +6.00000 q^{28} -31.3050i q^{29} +(-10.0000 + 11.1803i) q^{30} -18.0000 q^{31} +15.6525i q^{32} +(-10.0000 - 8.94427i) q^{33} +10.0000 q^{34} -13.4164i q^{35} +(1.00000 + 8.94427i) q^{36} -16.0000 q^{37} +4.47214i q^{38} +(-32.0000 + 35.7771i) q^{39} +15.0000 q^{40} +62.6099i q^{41} +(-30.0000 - 26.8328i) q^{42} +16.0000 q^{43} -4.47214i q^{44} +(20.0000 - 2.23607i) q^{45} +30.0000 q^{46} -49.1935i q^{47} +(38.0000 - 42.4853i) q^{48} -13.0000 q^{49} +11.1803i q^{50} +(-10.0000 - 8.94427i) q^{51} -16.0000 q^{52} +4.47214i q^{53} +(35.0000 - 49.1935i) q^{54} -10.0000 q^{55} +40.2492i q^{56} +(4.00000 - 4.47214i) q^{57} -70.0000 q^{58} +4.47214i q^{59} +(5.00000 + 4.47214i) q^{60} +82.0000 q^{61} +40.2492i q^{62} +(6.00000 + 53.6656i) q^{63} -41.0000 q^{64} +35.7771i q^{65} +(-20.0000 + 22.3607i) q^{66} +24.0000 q^{67} -4.47214i q^{68} +(-30.0000 - 26.8328i) q^{69} -30.0000 q^{70} -125.220i q^{71} +(-60.0000 + 6.70820i) q^{72} -74.0000 q^{73} +35.7771i q^{74} +(10.0000 - 11.1803i) q^{75} +2.00000 q^{76} -26.8328i q^{77} +(80.0000 + 71.5542i) q^{78} +138.000 q^{79} -42.4853i q^{80} +(-79.0000 + 17.8885i) q^{81} +140.000 q^{82} -93.9149i q^{83} +(-12.0000 + 13.4164i) q^{84} -10.0000 q^{85} -35.7771i q^{86} +(70.0000 + 62.6099i) q^{87} +30.0000 q^{88} +107.331i q^{89} +(-5.00000 - 44.7214i) q^{90} -96.0000 q^{91} -13.4164i q^{92} +(36.0000 - 40.2492i) q^{93} -110.000 q^{94} -4.47214i q^{95} +(-35.0000 - 31.3050i) q^{96} -166.000 q^{97} +29.0689i q^{98} +(40.0000 - 4.47214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} - 2 q^{4} + 10 q^{6} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 2 * q - 4 * q^3 - 2 * q^4 + 10 * q^6 - 12 * q^7 - 2 * q^9	$ 2 q - 4 q^{3} - 2 q^{4} + 10 q^{6} - 12 q^{7} - 2 q^{9} + 10 q^{10} + 4 q^{12} + 32 q^{13} - 10 q^{15} - 38 q^{16} - 40 q^{18} - 4 q^{19} + 24 q^{21} + 20 q^{22} + 30 q^{24} - 10 q^{25} + 44 q^{27} + 12 q^{28} - 20 q^{30} - 36 q^{31} - 20 q^{33} + 20 q^{34} + 2 q^{36} - 32 q^{37} - 64 q^{39} + 30 q^{40} - 60 q^{42} + 32 q^{43} + 40 q^{45} + 60 q^{46} + 76 q^{48} - 26 q^{49} - 20 q^{51} - 32 q^{52} + 70 q^{54} - 20 q^{55} + 8 q^{57} - 140 q^{58} + 10 q^{60} + 164 q^{61} + 12 q^{63} - 82 q^{64} - 40 q^{66} + 48 q^{67} - 60 q^{69} - 60 q^{70} - 120 q^{72} - 148 q^{73} + 20 q^{75} + 4 q^{76} + 160 q^{78} + 276 q^{79} - 158 q^{81} + 280 q^{82} - 24 q^{84} - 20 q^{85} + 140 q^{87} + 60 q^{88} - 10 q^{90} - 192 q^{91} + 72 q^{93} - 220 q^{94} - 70 q^{96} - 332 q^{97} + 80 q^{99}+O(q^{100}) $ 2 * q - 4 * q^3 - 2 * q^4 + 10 * q^6 - 12 * q^7 - 2 * q^9 + 10 * q^10 + 4 * q^12 + 32 * q^13 - 10 * q^15 - 38 * q^16 - 40 * q^18 - 4 * q^19 + 24 * q^21 + 20 * q^22 + 30 * q^24 - 10 * q^25 + 44 * q^27 + 12 * q^28 - 20 * q^30 - 36 * q^31 - 20 * q^33 + 20 * q^34 + 2 * q^36 - 32 * q^37 - 64 * q^39 + 30 * q^40 - 60 * q^42 + 32 * q^43 + 40 * q^45 + 60 * q^46 + 76 * q^48 - 26 * q^49 - 20 * q^51 - 32 * q^52 + 70 * q^54 - 20 * q^55 + 8 * q^57 - 140 * q^58 + 10 * q^60 + 164 * q^61 + 12 * q^63 - 82 * q^64 - 40 * q^66 + 48 * q^67 - 60 * q^69 - 60 * q^70 - 120 * q^72 - 148 * q^73 + 20 * q^75 + 4 * q^76 + 160 * q^78 + 276 * q^79 - 158 * q^81 + 280 * q^82 - 24 * q^84 - 20 * q^85 + 140 * q^87 + 60 * q^88 - 10 * q^90 - 192 * q^91 + 72 * q^93 - 220 * q^94 - 70 * q^96 - 332 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.23607i		−	1.11803i	−0.829156	−	0.559017i	$-0.811179\pi$
$2$		−	2.23607i		−	1.11803i	0.829156	−	0.559017i	$-0.188821\pi$
$3$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$3$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$4$	−1.00000			−0.250000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	5.00000	+	4.47214i	0.833333	+	0.745356i
$7$	−6.00000			−0.857143			−0.428571	−	0.903508i	$-0.640983\pi$
$7$	−6.00000			−0.857143			−0.428571	+	0.903508i	$0.640983\pi$
$8$		−	6.70820i		−	0.838525i
$9$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$10$	5.00000			0.500000
$11$			4.47214i			0.406558i	0.979121	+	0.203279i	$0.0651598\pi$
$11$			4.47214i			0.406558i	−0.979121	+	0.203279i	$0.934840\pi$
$12$	2.00000	−	2.23607i	0.166667	−	0.186339i
$13$	16.0000			1.23077			0.615385	−	0.788227i	$-0.289001\pi$
$13$	16.0000			1.23077			0.615385	+	0.788227i	$0.289001\pi$
$14$			13.4164i			0.958315i
$15$	−5.00000	−	4.47214i	−0.333333	−	0.298142i
$16$	−19.0000			−1.18750
$17$			4.47214i			0.263067i	0.991312	+	0.131533i	$0.0419901\pi$
$17$			4.47214i			0.263067i	−0.991312	+	0.131533i	$0.958010\pi$
$18$	−20.0000	+	2.23607i	−1.11111	+	0.124226i
$19$	−2.00000			−0.105263			−0.0526316	−	0.998614i	$-0.516761\pi$
$19$	−2.00000			−0.105263			−0.0526316	+	0.998614i	$0.516761\pi$
$20$		−	2.23607i		−	0.111803i
$21$	12.0000	−	13.4164i	0.571429	−	0.638877i
$22$	10.0000			0.454545
$23$			13.4164i			0.583322i	0.956522	+	0.291661i	$0.0942079\pi$
$23$			13.4164i			0.583322i	−0.956522	+	0.291661i	$0.905792\pi$
$24$	15.0000	+	13.4164i	0.625000	+	0.559017i
$25$	−5.00000			−0.200000
$26$		−	35.7771i		−	1.37604i
$27$	22.0000	+	15.6525i	0.814815	+	0.579721i
$28$	6.00000			0.214286
$29$		−	31.3050i		−	1.07948i	−0.841831	−	0.539741i	$-0.818522\pi$
$29$		−	31.3050i		−	1.07948i	0.841831	−	0.539741i	$-0.181478\pi$
$30$	−10.0000	+	11.1803i	−0.333333	+	0.372678i
$31$	−18.0000			−0.580645			−0.290323	−	0.956929i	$-0.593763\pi$
$31$	−18.0000			−0.580645			−0.290323	+	0.956929i	$0.593763\pi$
$32$			15.6525i			0.489140i
$33$	−10.0000	−	8.94427i	−0.303030	−	0.271039i
$34$	10.0000			0.294118
$35$		−	13.4164i		−	0.383326i
$36$	1.00000	+	8.94427i	0.0277778	+	0.248452i
$37$	−16.0000			−0.432432			−0.216216	−	0.976346i	$-0.569372\pi$
$37$	−16.0000			−0.432432			−0.216216	+	0.976346i	$0.569372\pi$
$38$			4.47214i			0.117688i
$39$	−32.0000	+	35.7771i	−0.820513	+	0.917361i
$40$	15.0000			0.375000
$41$			62.6099i			1.52707i	0.645766	+	0.763535i	$0.276538\pi$
$41$			62.6099i			1.52707i	−0.645766	+	0.763535i	$0.723462\pi$
$42$	−30.0000	−	26.8328i	−0.714286	−	0.638877i
$43$	16.0000			0.372093			0.186047	−	0.982541i	$-0.440432\pi$
$43$	16.0000			0.372093			0.186047	+	0.982541i	$0.440432\pi$
$44$		−	4.47214i		−	0.101639i
$45$	20.0000	−	2.23607i	0.444444	−	0.0496904i
$46$	30.0000			0.652174
$47$		−	49.1935i		−	1.04667i	−0.852127	−	0.523335i	$-0.824688\pi$
$47$		−	49.1935i		−	1.04667i	0.852127	−	0.523335i	$-0.175312\pi$
$48$	38.0000	−	42.4853i	0.791667	−	0.885110i
$49$	−13.0000			−0.265306
$50$			11.1803i			0.223607i
$51$	−10.0000	−	8.94427i	−0.196078	−	0.175378i
$52$	−16.0000			−0.307692
$53$			4.47214i			0.0843799i	0.999110	+	0.0421900i	$0.0134335\pi$
$53$			4.47214i			0.0843799i	−0.999110	+	0.0421900i	$0.986567\pi$
$54$	35.0000	−	49.1935i	0.648148	−	0.910991i
$55$	−10.0000			−0.181818
$56$			40.2492i			0.718736i
$57$	4.00000	−	4.47214i	0.0701754	−	0.0784585i
$58$	−70.0000			−1.20690
$59$			4.47214i			0.0757989i	0.999282	+	0.0378995i	$0.0120667\pi$
$59$			4.47214i			0.0757989i	−0.999282	+	0.0378995i	$0.987933\pi$
$60$	5.00000	+	4.47214i	0.0833333	+	0.0745356i
$61$	82.0000			1.34426			0.672131	−	0.740432i	$-0.265379\pi$
$61$	82.0000			1.34426			0.672131	+	0.740432i	$0.265379\pi$
$62$			40.2492i			0.649181i
$63$	6.00000	+	53.6656i	0.0952381	+	0.851835i
$64$	−41.0000			−0.640625
$65$			35.7771i			0.550417i
$66$	−20.0000	+	22.3607i	−0.303030	+	0.338798i
$67$	24.0000			0.358209			0.179104	−	0.983830i	$-0.442680\pi$
$67$	24.0000			0.358209			0.179104	+	0.983830i	$0.442680\pi$
$68$		−	4.47214i		−	0.0657667i
$69$	−30.0000	−	26.8328i	−0.434783	−	0.388881i
$70$	−30.0000			−0.428571
$71$		−	125.220i		−	1.76366i	−0.471568	−	0.881830i	$-0.656312\pi$
$71$		−	125.220i		−	1.76366i	0.471568	−	0.881830i	$-0.343688\pi$
$72$	−60.0000	+	6.70820i	−0.833333	+	0.0931695i
$73$	−74.0000			−1.01370			−0.506849	−	0.862035i	$-0.669190\pi$
$73$	−74.0000			−1.01370			−0.506849	+	0.862035i	$0.669190\pi$
$74$			35.7771i			0.483474i
$75$	10.0000	−	11.1803i	0.133333	−	0.149071i
$76$	2.00000			0.0263158
$77$		−	26.8328i		−	0.348478i
$78$	80.0000	+	71.5542i	1.02564	+	0.917361i
$79$	138.000			1.74684			0.873418	−	0.486972i	$-0.161899\pi$
$79$	138.000			1.74684			0.873418	+	0.486972i	$0.161899\pi$
$80$		−	42.4853i		−	0.531066i
$81$	−79.0000	+	17.8885i	−0.975309	+	0.220846i
$82$	140.000			1.70732
$83$		−	93.9149i		−	1.13150i	−0.824575	−	0.565752i	$-0.808586\pi$
$83$		−	93.9149i		−	1.13150i	0.824575	−	0.565752i	$-0.191414\pi$
$84$	−12.0000	+	13.4164i	−0.142857	+	0.159719i
$85$	−10.0000			−0.117647
$86$		−	35.7771i		−	0.416013i
$87$	70.0000	+	62.6099i	0.804598	+	0.719654i
$88$	30.0000			0.340909
$89$			107.331i			1.20597i	0.797753	+	0.602985i	$0.206022\pi$
$89$			107.331i			1.20597i	−0.797753	+	0.602985i	$0.793978\pi$
$90$	−5.00000	−	44.7214i	−0.0555556	−	0.496904i
$91$	−96.0000			−1.05495
$92$		−	13.4164i		−	0.145831i
$93$	36.0000	−	40.2492i	0.387097	−	0.432787i
$94$	−110.000			−1.17021
$95$		−	4.47214i		−	0.0470751i
$96$	−35.0000	−	31.3050i	−0.364583	−	0.326093i
$97$	−166.000			−1.71134			−0.855670	−	0.517522i	$-0.826855\pi$
$97$	−166.000			−1.71134			−0.855670	+	0.517522i	$0.826855\pi$
$98$			29.0689i			0.296621i
$99$	40.0000	−	4.47214i	0.404040	−	0.0451731i
$100$	5.00000			0.0500000
$101$			67.0820i			0.664179i	0.943248	+	0.332089i	$0.107754\pi$
$101$			67.0820i			0.664179i	−0.943248	+	0.332089i	$0.892246\pi$
$102$	−20.0000	+	22.3607i	−0.196078	+	0.219222i
$103$	26.0000			0.252427			0.126214	−	0.992003i	$-0.459718\pi$
$103$	26.0000			0.252427			0.126214	+	0.992003i	$0.459718\pi$
$104$		−	107.331i		−	1.03203i
$105$	30.0000	+	26.8328i	0.285714	+	0.255551i
$106$	10.0000			0.0943396
$107$			201.246i			1.88080i	0.340064	+	0.940402i	$0.389551\pi$
$107$			201.246i			1.88080i	−0.340064	+	0.940402i	$0.610449\pi$
$108$	−22.0000	−	15.6525i	−0.203704	−	0.144930i
$109$	38.0000			0.348624			0.174312	−	0.984690i	$-0.444230\pi$
$109$	38.0000			0.348624			0.174312	+	0.984690i	$0.444230\pi$
$110$			22.3607i			0.203279i
$111$	32.0000	−	35.7771i	0.288288	−	0.322316i
$112$	114.000			1.01786
$113$			31.3050i			0.277035i	0.990360	+	0.138517i	$0.0442337\pi$
$113$			31.3050i			0.277035i	−0.990360	+	0.138517i	$0.955766\pi$
$114$	−10.0000	−	8.94427i	−0.0877193	−	0.0784585i
$115$	−30.0000			−0.260870
$116$			31.3050i			0.269870i
$117$	−16.0000	−	143.108i	−0.136752	−	1.22315i
$118$	10.0000			0.0847458
$119$		−	26.8328i		−	0.225486i
$120$	−30.0000	+	33.5410i	−0.250000	+	0.279508i
$121$	101.000			0.834711
$122$		−	183.358i		−	1.50293i
$123$	−140.000	−	125.220i	−1.13821	−	1.01805i
$124$	18.0000			0.145161
$125$		−	11.1803i		−	0.0894427i
$126$	120.000	−	13.4164i	0.952381	−	0.106479i
$127$	−26.0000			−0.204724			−0.102362	−	0.994747i	$-0.532640\pi$
$127$	−26.0000			−0.204724			−0.102362	+	0.994747i	$0.532640\pi$
$128$			154.289i			1.20538i
$129$	−32.0000	+	35.7771i	−0.248062	+	0.277342i
$130$	80.0000			0.615385
$131$			13.4164i			0.102415i	0.998688	+	0.0512077i	$0.0163070\pi$
$131$			13.4164i			0.102415i	−0.998688	+	0.0512077i	$0.983693\pi$
$132$	10.0000	+	8.94427i	0.0757576	+	0.0677596i
$133$	12.0000			0.0902256
$134$		−	53.6656i		−	0.400490i
$135$	−35.0000	+	49.1935i	−0.259259	+	0.364396i
$136$	30.0000			0.220588
$137$		−	120.748i		−	0.881370i	−0.897662	−	0.440685i	$-0.854736\pi$
$137$		−	120.748i		−	0.881370i	0.897662	−	0.440685i	$-0.145264\pi$
$138$	−60.0000	+	67.0820i	−0.434783	+	0.486102i
$139$	−82.0000			−0.589928			−0.294964	−	0.955508i	$-0.595308\pi$
$139$	−82.0000			−0.589928			−0.294964	+	0.955508i	$0.595308\pi$
$140$			13.4164i			0.0958315i
$141$	110.000	+	98.3870i	0.780142	+	0.697780i
$142$	−280.000			−1.97183
$143$			71.5542i			0.500379i
$144$	19.0000	+	169.941i	0.131944	+	1.18015i
$145$	70.0000			0.482759
$146$			165.469i			1.13335i
$147$	26.0000	−	29.0689i	0.176871	−	0.197748i
$148$	16.0000			0.108108
$149$		−	111.803i		−	0.750358i	−0.926952	−	0.375179i	$-0.877581\pi$
$149$		−	111.803i		−	0.750358i	0.926952	−	0.375179i	$-0.122419\pi$
$150$	−25.0000	−	22.3607i	−0.166667	−	0.149071i
$151$	−158.000			−1.04636			−0.523179	−	0.852223i	$-0.675254\pi$
$151$	−158.000			−1.04636			−0.523179	+	0.852223i	$0.675254\pi$
$152$			13.4164i			0.0882658i
$153$	40.0000	−	4.47214i	0.261438	−	0.0292296i
$154$	−60.0000			−0.389610
$155$		−	40.2492i		−	0.259672i
$156$	32.0000	−	35.7771i	0.205128	−	0.229340i
$157$	164.000			1.04459			0.522293	−	0.852766i	$-0.325077\pi$
$157$	164.000			1.04459			0.522293	+	0.852766i	$0.325077\pi$
$158$		−	308.577i		−	1.95302i
$159$	−10.0000	−	8.94427i	−0.0628931	−	0.0562533i
$160$	−35.0000			−0.218750
$161$		−	80.4984i		−	0.499990i
$162$	40.0000	+	176.649i	0.246914	+	1.09043i
$163$	236.000			1.44785			0.723926	−	0.689877i	$-0.242336\pi$
$163$	236.000			1.44785			0.723926	+	0.689877i	$0.242336\pi$
$164$		−	62.6099i		−	0.381768i
$165$	20.0000	−	22.3607i	0.121212	−	0.135519i
$166$	−210.000			−1.26506
$167$			93.9149i			0.562364i	0.959654	+	0.281182i	$0.0907265\pi$
$167$			93.9149i			0.562364i	−0.959654	+	0.281182i	$0.909273\pi$
$168$	−90.0000	−	80.4984i	−0.535714	−	0.479157i
$169$	87.0000			0.514793
$170$			22.3607i			0.131533i
$171$	2.00000	+	17.8885i	0.0116959	+	0.104611i
$172$	−16.0000			−0.0930233
$173$			13.4164i			0.0775515i	0.999248	+	0.0387757i	$0.0123458\pi$
$173$			13.4164i			0.0775515i	−0.999248	+	0.0387757i	$0.987654\pi$
$174$	140.000	−	156.525i	0.804598	−	0.899568i
$175$	30.0000			0.171429
$176$		−	84.9706i		−	0.482787i
$177$	−10.0000	−	8.94427i	−0.0564972	−	0.0505326i
$178$	240.000			1.34831
$179$			192.302i			1.07431i	0.843483	+	0.537156i	$0.180501\pi$
$179$			192.302i			1.07431i	−0.843483	+	0.537156i	$0.819499\pi$
$180$	−20.0000	+	2.23607i	−0.111111	+	0.0124226i
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$			214.663i			1.17946i
$183$	−164.000	+	183.358i	−0.896175	+	1.00195i
$184$	90.0000			0.489130
$185$		−	35.7771i		−	0.193390i
$186$	−90.0000	−	80.4984i	−0.483871	−	0.432787i
$187$	−20.0000			−0.106952
$188$			49.1935i			0.261668i
$189$	−132.000	−	93.9149i	−0.698413	−	0.496904i
$190$	−10.0000			−0.0526316
$191$		−	205.718i		−	1.07706i	−0.842607	−	0.538529i	$-0.818980\pi$
$191$		−	205.718i		−	1.07706i	0.842607	−	0.538529i	$-0.181020\pi$
$192$	82.0000	−	91.6788i	0.427083	−	0.477494i
$193$	−214.000			−1.10881			−0.554404	−	0.832248i	$-0.687054\pi$
$193$	−214.000			−1.10881			−0.554404	+	0.832248i	$0.687054\pi$
$194$			371.187i			1.91334i
$195$	−80.0000	−	71.5542i	−0.410256	−	0.366944i
$196$	13.0000			0.0663265
$197$		−	93.9149i		−	0.476725i	−0.971176	−	0.238363i	$-0.923389\pi$
$197$		−	93.9149i		−	0.476725i	0.971176	−	0.238363i	$-0.0766107\pi$
$198$	−10.0000	−	89.4427i	−0.0505051	−	0.451731i
$199$	−242.000			−1.21608			−0.608040	−	0.793906i	$-0.708044\pi$
$199$	−242.000			−1.21608			−0.608040	+	0.793906i	$0.708044\pi$
$200$			33.5410i			0.167705i
$201$	−48.0000	+	53.6656i	−0.238806	+	0.266993i
$202$	150.000			0.742574
$203$			187.830i			0.925270i
$204$	10.0000	+	8.94427i	0.0490196	+	0.0438445i
$205$	−140.000			−0.682927
$206$		−	58.1378i		−	0.282222i
$207$	120.000	−	13.4164i	0.579710	−	0.0648136i
$208$	−304.000			−1.46154
$209$		−	8.94427i		−	0.0427956i
$210$	60.0000	−	67.0820i	0.285714	−	0.319438i
$211$	2.00000			0.00947867			0.00473934	−	0.999989i	$-0.498491\pi$
$211$	2.00000			0.00947867			0.00473934	+	0.999989i	$0.498491\pi$
$212$		−	4.47214i		−	0.0210950i
$213$	280.000	+	250.440i	1.31455	+	1.17577i
$214$	450.000			2.10280
$215$			35.7771i			0.166405i
$216$	105.000	−	147.580i	0.486111	−	0.683243i
$217$	108.000			0.497696
$218$		−	84.9706i		−	0.389773i
$219$	148.000	−	165.469i	0.675799	−	0.755566i
$220$	10.0000			0.0454545
$221$			71.5542i			0.323775i
$222$	−80.0000	−	71.5542i	−0.360360	−	0.322316i
$223$	86.0000			0.385650			0.192825	−	0.981233i	$-0.438235\pi$
$223$	86.0000			0.385650			0.192825	+	0.981233i	$0.438235\pi$
$224$		−	93.9149i		−	0.419263i
$225$	5.00000	+	44.7214i	0.0222222	+	0.198762i
$226$	70.0000			0.309735
$227$		−	58.1378i		−	0.256114i	−0.991767	−	0.128057i	$-0.959126\pi$
$227$		−	58.1378i		−	0.256114i	0.991767	−	0.128057i	$-0.0408740\pi$
$228$	−4.00000	+	4.47214i	−0.0175439	+	0.0196146i
$229$	−282.000			−1.23144			−0.615721	−	0.787965i	$-0.711135\pi$
$229$	−282.000			−1.23144			−0.615721	+	0.787965i	$0.711135\pi$
$230$			67.0820i			0.291661i
$231$	60.0000	+	53.6656i	0.259740	+	0.232319i
$232$	−210.000			−0.905172
$233$		−	362.243i		−	1.55469i	−0.629074	−	0.777346i	$-0.716566\pi$
$233$		−	362.243i		−	1.55469i	0.629074	−	0.777346i	$-0.283434\pi$
$234$	−320.000	+	35.7771i	−1.36752	+	0.152894i
$235$	110.000			0.468085
$236$		−	4.47214i		−	0.0189497i
$237$	−276.000	+	308.577i	−1.16456	+	1.30201i
$238$	−60.0000			−0.252101
$239$		−	250.440i		−	1.04786i	−0.851760	−	0.523932i	$-0.824464\pi$
$239$		−	250.440i		−	1.04786i	0.851760	−	0.523932i	$-0.175536\pi$
$240$	95.0000	+	84.9706i	0.395833	+	0.354044i
$241$	262.000			1.08714			0.543568	−	0.839365i	$-0.317073\pi$
$241$	262.000			1.08714			0.543568	+	0.839365i	$0.317073\pi$
$242$		−	225.843i		−	0.933235i
$243$	118.000	−	212.426i	0.485597	−	0.874183i
$244$	−82.0000			−0.336066
$245$		−	29.0689i		−	0.118649i
$246$	−280.000	+	313.050i	−1.13821	+	1.27256i
$247$	−32.0000			−0.129555
$248$			120.748i			0.486886i
$249$	210.000	+	187.830i	0.843373	+	0.754336i
$250$	−25.0000			−0.100000
$251$			469.574i			1.87081i	0.353573	+	0.935407i	$0.384967\pi$
$251$			469.574i			1.87081i	−0.353573	+	0.935407i	$0.615033\pi$
$252$	−6.00000	−	53.6656i	−0.0238095	−	0.212959i
$253$	−60.0000			−0.237154
$254$			58.1378i			0.228889i
$255$	20.0000	−	22.3607i	0.0784314	−	0.0876889i
$256$	181.000			0.707031
$257$			201.246i			0.783059i	0.920166	+	0.391529i	$0.128054\pi$
$257$			201.246i			0.783059i	−0.920166	+	0.391529i	$0.871946\pi$
$258$	80.0000	+	71.5542i	0.310078	+	0.277342i
$259$	96.0000			0.370656
$260$		−	35.7771i		−	0.137604i
$261$	−280.000	+	31.3050i	−1.07280	+	0.119942i
$262$	30.0000			0.114504
$263$		−	58.1378i		−	0.221056i	−0.993873	−	0.110528i	$-0.964746\pi$
$263$		−	58.1378i		−	0.221056i	0.993873	−	0.110528i	$-0.0352542\pi$
$264$	−60.0000	+	67.0820i	−0.227273	+	0.254099i
$265$	−10.0000			−0.0377358
$266$		−	26.8328i		−	0.100875i
$267$	−240.000	−	214.663i	−0.898876	−	0.803979i
$268$	−24.0000			−0.0895522
$269$		−	371.187i		−	1.37988i	−0.723867	−	0.689939i	$-0.757637\pi$
$269$		−	371.187i		−	1.37988i	0.723867	−	0.689939i	$-0.242363\pi$
$270$	110.000	+	78.2624i	0.407407	+	0.289861i
$271$	82.0000			0.302583			0.151292	−	0.988489i	$-0.451657\pi$
$271$	82.0000			0.302583			0.151292	+	0.988489i	$0.451657\pi$
$272$		−	84.9706i		−	0.312392i
$273$	192.000	−	214.663i	0.703297	−	0.786310i
$274$	−270.000			−0.985401
$275$		−	22.3607i		−	0.0813116i
$276$	30.0000	+	26.8328i	0.108696	+	0.0972203i
$277$	24.0000			0.0866426			0.0433213	−	0.999061i	$-0.486206\pi$
$277$	24.0000			0.0866426			0.0433213	+	0.999061i	$0.486206\pi$
$278$			183.358i			0.659560i
$279$	18.0000	+	160.997i	0.0645161	+	0.577050i
$280$	−90.0000			−0.321429
$281$		−	187.830i		−	0.668433i	−0.942496	−	0.334217i	$-0.891528\pi$
$281$		−	187.830i		−	0.668433i	0.942496	−	0.334217i	$-0.108472\pi$
$282$	220.000	−	245.967i	0.780142	−	0.872225i
$283$	−144.000			−0.508834			−0.254417	−	0.967095i	$-0.581884\pi$
$283$	−144.000			−0.508834			−0.254417	+	0.967095i	$0.581884\pi$
$284$			125.220i			0.440915i
$285$	10.0000	+	8.94427i	0.0350877	+	0.0313834i
$286$	160.000			0.559441
$287$		−	375.659i		−	1.30892i
$288$	140.000	−	15.6525i	0.486111	−	0.0543489i
$289$	269.000			0.930796
$290$		−	156.525i		−	0.539741i
$291$	332.000	−	371.187i	1.14089	−	1.27556i
$292$	74.0000			0.253425
$293$			469.574i			1.60264i	0.598234	+	0.801321i	$0.295869\pi$
$293$			469.574i			1.60264i	−0.598234	+	0.801321i	$0.704131\pi$
$294$	−65.0000	−	58.1378i	−0.221088	−	0.197748i
$295$	−10.0000			−0.0338983
$296$			107.331i			0.362606i
$297$	−70.0000	+	98.3870i	−0.235690	+	0.331269i
$298$	−250.000			−0.838926
$299$			214.663i			0.717935i
$300$	−10.0000	+	11.1803i	−0.0333333	+	0.0372678i
$301$	−96.0000			−0.318937
$302$			353.299i			1.16986i
$303$	−150.000	−	134.164i	−0.495050	−	0.442786i
$304$	38.0000			0.125000
$305$			183.358i			0.601172i
$306$	−10.0000	−	89.4427i	−0.0326797	−	0.292296i
$307$	184.000			0.599349			0.299674	−	0.954042i	$-0.403122\pi$
$307$	184.000			0.599349			0.299674	+	0.954042i	$0.403122\pi$
$308$			26.8328i			0.0871195i
$309$	−52.0000	+	58.1378i	−0.168285	+	0.188148i
$310$	−90.0000			−0.290323
$311$			160.997i			0.517675i	0.965921	+	0.258837i	$0.0833394\pi$
$311$			160.997i			0.517675i	−0.965921	+	0.258837i	$0.916661\pi$
$312$	240.000	+	214.663i	0.769231	+	0.688021i
$313$	−394.000			−1.25879			−0.629393	−	0.777087i	$-0.716696\pi$
$313$	−394.000			−1.25879			−0.629393	+	0.777087i	$0.716696\pi$
$314$		−	366.715i		−	1.16788i
$315$	−120.000	+	13.4164i	−0.380952	+	0.0425918i
$316$	−138.000			−0.436709
$317$			451.686i			1.42488i	0.701735	+	0.712438i	$0.252409\pi$
$317$			451.686i			1.42488i	−0.701735	+	0.712438i	$0.747591\pi$
$318$	−20.0000	+	22.3607i	−0.0628931	+	0.0703166i
$319$	140.000			0.438871
$320$		−	91.6788i		−	0.286496i
$321$	−450.000	−	402.492i	−1.40187	−	1.25387i
$322$	−180.000			−0.559006
$323$		−	8.94427i		−	0.0276912i
$324$	79.0000	−	17.8885i	0.243827	−	0.0552116i
$325$	−80.0000			−0.246154
$326$		−	527.712i		−	1.61875i
$327$	−76.0000	+	84.9706i	−0.232416	+	0.259849i
$328$	420.000			1.28049
$329$			295.161i			0.897146i
$330$	−50.0000	−	44.7214i	−0.151515	−	0.135519i
$331$	−198.000			−0.598187			−0.299094	−	0.954224i	$-0.596684\pi$
$331$	−198.000			−0.598187			−0.299094	+	0.954224i	$0.596684\pi$
$332$			93.9149i			0.282876i
$333$	16.0000	+	143.108i	0.0480480	+	0.429755i
$334$	210.000			0.628743
$335$			53.6656i			0.160196i
$336$	−228.000	+	254.912i	−0.678571	+	0.758666i
$337$	394.000			1.16914			0.584570	−	0.811343i	$-0.301263\pi$
$337$	394.000			1.16914			0.584570	+	0.811343i	$0.301263\pi$
$338$		−	194.538i		−	0.575556i
$339$	−70.0000	−	62.6099i	−0.206490	−	0.184690i
$340$	10.0000			0.0294118
$341$		−	80.4984i		−	0.236066i
$342$	40.0000	−	4.47214i	0.116959	−	0.0130764i
$343$	372.000			1.08455
$344$		−	107.331i		−	0.312009i
$345$	60.0000	−	67.0820i	0.173913	−	0.194441i
$346$	30.0000			0.0867052
$347$		−	183.358i		−	0.528408i	−0.964467	−	0.264204i	$-0.914891\pi$
$347$		−	183.358i		−	0.528408i	0.964467	−	0.264204i	$-0.0851092\pi$
$348$	−70.0000	−	62.6099i	−0.201149	−	0.179914i
$349$	−362.000			−1.03725			−0.518625	−	0.855002i	$-0.673556\pi$
$349$	−362.000			−1.03725			−0.518625	+	0.855002i	$0.673556\pi$
$350$		−	67.0820i		−	0.191663i
$351$	352.000	+	250.440i	1.00285	+	0.713503i
$352$	−70.0000			−0.198864
$353$		−	308.577i		−	0.874157i	−0.899423	−	0.437078i	$-0.856013\pi$
$353$		−	308.577i		−	0.874157i	0.899423	−	0.437078i	$-0.143987\pi$
$354$	−20.0000	+	22.3607i	−0.0564972	+	0.0631658i
$355$	280.000			0.788732
$356$		−	107.331i		−	0.301492i
$357$	60.0000	+	53.6656i	0.168067	+	0.150324i
$358$	430.000			1.20112
$359$			295.161i			0.822175i	0.911596	+	0.411088i	$0.134851\pi$
$359$			295.161i			0.822175i	−0.911596	+	0.411088i	$0.865149\pi$
$360$	−15.0000	−	134.164i	−0.0416667	−	0.372678i
$361$	−357.000			−0.988920
$362$		−	4.47214i		−	0.0123540i
$363$	−202.000	+	225.843i	−0.556474	+	0.622157i
$364$	96.0000			0.263736
$365$		−	165.469i		−	0.453340i
$366$	410.000	+	366.715i	1.12022	+	1.00195i
$367$	−186.000			−0.506812			−0.253406	−	0.967360i	$-0.581551\pi$
$367$	−186.000			−0.506812			−0.253406	+	0.967360i	$0.581551\pi$
$368$		−	254.912i		−	0.692695i
$369$	560.000	−	62.6099i	1.51762	−	0.169675i
$370$	−80.0000			−0.216216
$371$		−	26.8328i		−	0.0723256i
$372$	−36.0000	+	40.2492i	−0.0967742	+	0.108197i
$373$	−44.0000			−0.117962			−0.0589812	−	0.998259i	$-0.518785\pi$
$373$	−44.0000			−0.117962			−0.0589812	+	0.998259i	$0.518785\pi$
$374$			44.7214i			0.119576i
$375$	25.0000	+	22.3607i	0.0666667	+	0.0596285i
$376$	−330.000			−0.877660
$377$		−	500.879i		−	1.32859i
$378$	−210.000	+	295.161i	−0.555556	+	0.780849i
$379$	−362.000			−0.955145			−0.477573	−	0.878592i	$-0.658483\pi$
$379$	−362.000			−0.955145			−0.477573	+	0.878592i	$0.658483\pi$
$380$			4.47214i			0.0117688i
$381$	52.0000	−	58.1378i	0.136483	−	0.152593i
$382$	−460.000			−1.20419
$383$		−	362.243i		−	0.945804i	−0.881115	−	0.472902i	$-0.843206\pi$
$383$		−	362.243i		−	0.945804i	0.881115	−	0.472902i	$-0.156794\pi$
$384$	−345.000	−	308.577i	−0.898438	−	0.803587i
$385$	60.0000			0.155844
$386$			478.519i			1.23969i
$387$	−16.0000	−	143.108i	−0.0413437	−	0.369789i
$388$	166.000			0.427835
$389$			442.741i			1.13815i	0.822285	+	0.569076i	$0.192699\pi$
$389$			442.741i			1.13815i	−0.822285	+	0.569076i	$0.807301\pi$
$390$	−160.000	+	178.885i	−0.410256	+	0.458681i
$391$	−60.0000			−0.153453
$392$			87.2067i			0.222466i
$393$	−30.0000	−	26.8328i	−0.0763359	−	0.0682769i
$394$	−210.000			−0.532995
$395$			308.577i			0.781209i
$396$	−40.0000	+	4.47214i	−0.101010	+	0.0112933i
$397$	124.000			0.312343			0.156171	−	0.987730i	$-0.450085\pi$
$397$	124.000			0.312343			0.156171	+	0.987730i	$0.450085\pi$
$398$			541.128i			1.35962i
$399$	−24.0000	+	26.8328i	−0.0601504	+	0.0672502i
$400$	95.0000			0.237500
$401$		−	268.328i		−	0.669148i	−0.942370	−	0.334574i	$-0.891408\pi$
$401$		−	268.328i		−	0.669148i	0.942370	−	0.334574i	$-0.108592\pi$
$402$	120.000	+	107.331i	0.298507	+	0.266993i
$403$	−288.000			−0.714640
$404$		−	67.0820i		−	0.166045i
$405$	−40.0000	−	176.649i	−0.0987654	−	0.436171i
$406$	420.000			1.03448
$407$		−	71.5542i		−	0.175809i
$408$	−60.0000	+	67.0820i	−0.147059	+	0.164417i
$409$	458.000			1.11980			0.559902	−	0.828559i	$-0.310839\pi$
$409$	458.000			1.11980			0.559902	+	0.828559i	$0.310839\pi$
$410$			313.050i			0.763535i
$411$	270.000	+	241.495i	0.656934	+	0.587580i
$412$	−26.0000			−0.0631068
$413$		−	26.8328i		−	0.0649705i
$414$	−30.0000	−	268.328i	−0.0724638	−	0.648136i
$415$	210.000			0.506024
$416$			250.440i			0.602018i
$417$	164.000	−	183.358i	0.393285	−	0.439706i
$418$	−20.0000			−0.0478469
$419$		−	594.794i		−	1.41956i	−0.704425	−	0.709778i	$-0.748795\pi$
$419$		−	594.794i		−	1.41956i	0.704425	−	0.709778i	$-0.251205\pi$
$420$	−30.0000	−	26.8328i	−0.0714286	−	0.0638877i
$421$	562.000			1.33492			0.667458	−	0.744647i	$-0.267382\pi$
$421$	562.000			1.33492			0.667458	+	0.744647i	$0.267382\pi$
$422$		−	4.47214i		−	0.0105975i
$423$	−440.000	+	49.1935i	−1.04019	+	0.116297i
$424$	30.0000			0.0707547
$425$		−	22.3607i		−	0.0526134i
$426$	560.000	−	626.099i	1.31455	−	1.46972i
$427$	−492.000			−1.15222
$428$		−	201.246i		−	0.470201i
$429$	−160.000	−	143.108i	−0.372960	−	0.333586i
$430$	80.0000			0.186047
$431$			348.827i			0.809342i	0.914462	+	0.404671i	$0.132614\pi$
$431$			348.827i			0.809342i	−0.914462	+	0.404671i	$0.867386\pi$
$432$	−418.000	−	297.397i	−0.967593	−	0.688419i
$433$	226.000			0.521940			0.260970	−	0.965347i	$-0.415958\pi$
$433$	226.000			0.521940			0.260970	+	0.965347i	$0.415958\pi$
$434$		−	241.495i		−	0.556441i
$435$	−140.000	+	156.525i	−0.321839	+	0.359827i
$436$	−38.0000			−0.0871560
$437$		−	26.8328i		−	0.0614023i
$438$	−370.000	−	330.938i	−0.844749	−	0.755566i
$439$	−2.00000			−0.00455581			−0.00227790	−	0.999997i	$-0.500725\pi$
$439$	−2.00000			−0.00455581			−0.00227790	+	0.999997i	$0.500725\pi$
$440$			67.0820i			0.152459i
$441$	13.0000	+	116.276i	0.0294785	+	0.263663i
$442$	160.000			0.361991
$443$			201.246i			0.454280i	0.973862	+	0.227140i	$0.0729375\pi$
$443$			201.246i			0.454280i	−0.973862	+	0.227140i	$0.927062\pi$
$444$	−32.0000	+	35.7771i	−0.0720721	+	0.0805790i
$445$	−240.000			−0.539326
$446$		−	192.302i		−	0.431170i
$447$	250.000	+	223.607i	0.559284	+	0.500239i
$448$	246.000			0.549107
$449$			313.050i			0.697215i	0.937269	+	0.348607i	$0.113345\pi$
$449$			313.050i			0.697215i	−0.937269	+	0.348607i	$0.886655\pi$
$450$	100.000	−	11.1803i	0.222222	−	0.0248452i
$451$	−280.000			−0.620843
$452$		−	31.3050i		−	0.0692587i
$453$	316.000	−	353.299i	0.697572	−	0.779909i
$454$	−130.000			−0.286344
$455$		−	214.663i		−	0.471786i
$456$	−30.0000	−	26.8328i	−0.0657895	−	0.0588439i
$457$	334.000			0.730853			0.365427	−	0.930840i	$-0.380923\pi$
$457$	334.000			0.730853			0.365427	+	0.930840i	$0.380923\pi$
$458$			630.571i			1.37679i
$459$	−70.0000	+	98.3870i	−0.152505	+	0.214351i
$460$	30.0000			0.0652174
$461$			93.9149i			0.203720i	0.994799	+	0.101860i	$0.0324794\pi$
$461$			93.9149i			0.203720i	−0.994799	+	0.101860i	$0.967521\pi$
$462$	120.000	−	134.164i	0.259740	−	0.290398i
$463$	366.000			0.790497			0.395248	−	0.918574i	$-0.370659\pi$
$463$	366.000			0.790497			0.395248	+	0.918574i	$0.370659\pi$
$464$			594.794i			1.28188i
$465$	90.0000	+	80.4984i	0.193548	+	0.173115i
$466$	−810.000			−1.73820
$467$			451.686i			0.967207i	0.875287	+	0.483604i	$0.160672\pi$
$467$			451.686i			0.967207i	−0.875287	+	0.483604i	$0.839328\pi$
$468$	16.0000	+	143.108i	0.0341880	+	0.305787i
$469$	−144.000			−0.307036
$470$		−	245.967i		−	0.523335i
$471$	−328.000	+	366.715i	−0.696391	+	0.778588i
$472$	30.0000			0.0635593
$473$			71.5542i			0.151277i
$474$	690.000	+	617.155i	1.45570	+	1.30201i
$475$	10.0000			0.0210526
$476$			26.8328i			0.0563715i
$477$	40.0000	−	4.47214i	0.0838574	−	0.00937555i
$478$	−560.000			−1.17155
$479$		−	590.322i		−	1.23240i	−0.787588	−	0.616202i	$-0.788670\pi$
$479$		−	590.322i		−	1.23240i	0.787588	−	0.616202i	$-0.211330\pi$
$480$	70.0000	−	78.2624i	0.145833	−	0.163047i
$481$	−256.000			−0.532225
$482$		−	585.850i		−	1.21546i
$483$	180.000	+	160.997i	0.372671	+	0.333327i
$484$	−101.000			−0.208678
$485$		−	371.187i		−	0.765335i
$486$	−475.000	−	263.856i	−0.977366	−	0.542914i
$487$	−886.000			−1.81930			−0.909651	−	0.415374i	$-0.863651\pi$
$487$	−886.000			−1.81930			−0.909651	+	0.415374i	$0.863651\pi$
$488$		−	550.073i		−	1.12720i
$489$	−472.000	+	527.712i	−0.965235	+	1.07917i
$490$	−65.0000			−0.132653
$491$		−	406.964i		−	0.828848i	−0.910084	−	0.414424i	$-0.863983\pi$
$491$		−	406.964i		−	0.828848i	0.910084	−	0.414424i	$-0.136017\pi$
$492$	140.000	+	125.220i	0.284553	+	0.254512i
$493$	140.000			0.283976
$494$			71.5542i			0.144847i
$495$	10.0000	+	89.4427i	0.0202020	+	0.180692i
$496$	342.000			0.689516
$497$			751.319i			1.51171i
$498$	420.000	−	469.574i	0.843373	−	0.942920i
$499$	−2.00000			−0.00400802			−0.00200401	−	0.999998i	$-0.500638\pi$
$499$	−2.00000			−0.00400802			−0.00200401	+	0.999998i	$0.500638\pi$
$500$			11.1803i			0.0223607i
$501$	−210.000	−	187.830i	−0.419162	−	0.374910i
$502$	1050.00			2.09163
$503$		−	219.135i		−	0.435655i	−0.975987	−	0.217828i	$-0.930103\pi$
$503$		−	219.135i		−	0.435655i	0.975987	−	0.217828i	$-0.0698971\pi$
$504$	360.000	−	40.2492i	0.714286	−	0.0798596i
$505$	−150.000			−0.297030
$506$			134.164i			0.265146i
$507$	−174.000	+	194.538i	−0.343195	+	0.383704i
$508$	26.0000			0.0511811
$509$		−	800.512i		−	1.57272i	−0.617771	−	0.786358i	$-0.711964\pi$
$509$		−	800.512i		−	1.57272i	0.617771	−	0.786358i	$-0.288036\pi$
$510$	−50.0000	−	44.7214i	−0.0980392	−	0.0876889i
$511$	444.000			0.868885
$512$			212.426i			0.414895i
$513$	−44.0000	−	31.3050i	−0.0857700	−	0.0610233i
$514$	450.000			0.875486
$515$			58.1378i			0.112889i
$516$	32.0000	−	35.7771i	0.0620155	−	0.0693354i
$517$	220.000			0.425532
$518$		−	214.663i		−	0.414406i
$519$	−30.0000	−	26.8328i	−0.0578035	−	0.0517010i
$520$	240.000			0.461538
$521$		−	527.712i		−	1.01288i	−0.862274	−	0.506441i	$-0.830961\pi$
$521$		−	527.712i		−	1.01288i	0.862274	−	0.506441i	$-0.169039\pi$
$522$	70.0000	+	626.099i	0.134100	+	1.19942i
$523$	376.000			0.718929			0.359465	−	0.933159i	$-0.382959\pi$
$523$	376.000			0.718929			0.359465	+	0.933159i	$0.382959\pi$
$524$		−	13.4164i		−	0.0256038i
$525$	−60.0000	+	67.0820i	−0.114286	+	0.127775i
$526$	−130.000			−0.247148
$527$		−	80.4984i		−	0.152748i
$528$	190.000	+	169.941i	0.359848	+	0.321858i
$529$	349.000			0.659735
$530$			22.3607i			0.0421900i
$531$	40.0000	−	4.47214i	0.0753296	−	0.00842210i
$532$	−12.0000			−0.0225564
$533$			1001.76i			1.87947i
$534$	−480.000	+	536.656i	−0.898876	+	1.00497i
$535$	−450.000			−0.841121
$536$		−	160.997i		−	0.300367i
$537$	−430.000	−	384.604i	−0.800745	−	0.716208i
$538$	−830.000			−1.54275
$539$		−	58.1378i		−	0.107862i
$540$	35.0000	−	49.1935i	0.0648148	−	0.0910991i
$541$	−198.000			−0.365989			−0.182994	−	0.983114i	$-0.558579\pi$
$541$	−198.000			−0.365989			−0.182994	+	0.983114i	$0.558579\pi$
$542$		−	183.358i		−	0.338298i
$543$	−4.00000	+	4.47214i	−0.00736648	+	0.00823598i
$544$	−70.0000			−0.128676
$545$			84.9706i			0.155909i
$546$	−480.000	−	429.325i	−0.879121	−	0.786310i
$547$	1024.00			1.87203			0.936015	−	0.351961i	$-0.114485\pi$
$547$	1024.00			1.87203			0.936015	+	0.351961i	$0.114485\pi$
$548$			120.748i			0.220342i
$549$	−82.0000	−	733.430i	−0.149362	−	1.33594i
$550$	−50.0000			−0.0909091
$551$			62.6099i			0.113630i
$552$	−180.000	+	201.246i	−0.326087	+	0.364576i
$553$	−828.000			−1.49729
$554$		−	53.6656i		−	0.0968694i
$555$	80.0000	+	71.5542i	0.144144	+	0.128926i
$556$	82.0000			0.147482
$557$			67.0820i			0.120435i	0.998185	+	0.0602173i	$0.0191794\pi$
$557$			67.0820i			0.120435i	−0.998185	+	0.0602173i	$0.980821\pi$
$558$	360.000	−	40.2492i	0.645161	−	0.0721312i
$559$	256.000			0.457961
$560$			254.912i			0.455200i
$561$	40.0000	−	44.7214i	0.0713012	−	0.0797172i
$562$	−420.000			−0.747331
$563$			254.912i			0.452774i	0.974037	+	0.226387i	$0.0726914\pi$
$563$			254.912i			0.452774i	−0.974037	+	0.226387i	$0.927309\pi$
$564$	−110.000	−	98.3870i	−0.195035	−	0.174445i
$565$	−70.0000			−0.123894
$566$			321.994i			0.568894i
$567$	474.000	−	107.331i	0.835979	−	0.189297i
$568$	−840.000			−1.47887
$569$			858.650i			1.50905i	0.656271	+	0.754526i	$0.272133\pi$
$569$			858.650i			1.50905i	−0.656271	+	0.754526i	$0.727867\pi$
$570$	20.0000	−	22.3607i	0.0350877	−	0.0392293i
$571$	962.000			1.68476			0.842382	−	0.538881i	$-0.181153\pi$
$571$	962.000			1.68476			0.842382	+	0.538881i	$0.181153\pi$
$572$		−	71.5542i		−	0.125095i
$573$	460.000	+	411.437i	0.802792	+	0.718039i
$574$	−840.000			−1.46341
$575$		−	67.0820i		−	0.116664i
$576$	41.0000	+	366.715i	0.0711806	+	0.636658i
$577$	−886.000			−1.53553			−0.767764	−	0.640732i	$-0.778631\pi$
$577$	−886.000			−1.53553			−0.767764	+	0.640732i	$0.778631\pi$
$578$		−	601.502i		−	1.04066i
$579$	428.000	−	478.519i	0.739206	−	0.826457i
$580$	−70.0000			−0.120690
$581$			563.489i			0.969861i
$582$	−830.000	−	742.375i	−1.42612	−	1.27556i
$583$	−20.0000			−0.0343053
$584$			496.407i			0.850012i
$585$	320.000	−	35.7771i	0.547009	−	0.0611574i
$586$	1050.00			1.79181
$587$		−	657.404i		−	1.11994i	−0.828513	−	0.559969i	$-0.810813\pi$
$587$		−	657.404i		−	1.11994i	0.828513	−	0.559969i	$-0.189187\pi$
$588$	−26.0000	+	29.0689i	−0.0442177	+	0.0494369i
$589$	36.0000			0.0611205
$590$			22.3607i			0.0378995i
$591$	210.000	+	187.830i	0.355330	+	0.317817i
$592$	304.000			0.513514
$593$		−	111.803i		−	0.188539i	−0.995547	−	0.0942693i	$-0.969949\pi$
$593$		−	111.803i		−	0.188539i	0.995547	−	0.0942693i	$-0.0300515\pi$
$594$	220.000	+	156.525i	0.370370	+	0.263510i
$595$	60.0000			0.100840
$596$			111.803i			0.187590i
$597$	484.000	−	541.128i	0.810720	−	0.906413i
$598$	480.000			0.802676
$599$			223.607i			0.373300i	0.982426	+	0.186650i	$0.0597631\pi$
$599$			223.607i			0.373300i	−0.982426	+	0.186650i	$0.940237\pi$
$600$	−75.0000	−	67.0820i	−0.125000	−	0.111803i
$601$	2.00000			0.00332779			0.00166389	−	0.999999i	$-0.499470\pi$
$601$	2.00000			0.00332779			0.00166389	+	0.999999i	$0.499470\pi$
$602$			214.663i			0.356582i
$603$	−24.0000	−	214.663i	−0.0398010	−	0.355991i
$604$	158.000			0.261589
$605$			225.843i			0.373294i
$606$	−300.000	+	335.410i	−0.495050	+	0.553482i
$607$	−506.000			−0.833608			−0.416804	−	0.908996i	$-0.636850\pi$
$607$	−506.000			−0.833608			−0.416804	+	0.908996i	$0.636850\pi$
$608$		−	31.3050i		−	0.0514884i
$609$	−420.000	−	375.659i	−0.689655	−	0.616846i
$610$	410.000			0.672131
$611$		−	787.096i		−	1.28821i
$612$	−40.0000	+	4.47214i	−0.0653595	+	0.00730741i
$613$	556.000			0.907015			0.453507	−	0.891253i	$-0.350173\pi$
$613$	556.000			0.907015			0.453507	+	0.891253i	$0.350173\pi$
$614$		−	411.437i		−	0.670092i
$615$	280.000	−	313.050i	0.455285	−	0.509024i
$616$	−180.000			−0.292208
$617$			93.9149i			0.152212i	0.997100	+	0.0761060i	$0.0242488\pi$
$617$			93.9149i			0.152212i	−0.997100	+	0.0761060i	$0.975751\pi$
$618$	130.000	+	116.276i	0.210356	+	0.188148i
$619$	−802.000			−1.29564			−0.647819	−	0.761794i	$-0.724319\pi$
$619$	−802.000			−1.29564			−0.647819	+	0.761794i	$0.724319\pi$
$620$			40.2492i			0.0649181i
$621$	−210.000	+	295.161i	−0.338164	+	0.475299i
$622$	360.000			0.578778
$623$		−	643.988i		−	1.03369i
$624$	608.000	−	679.765i	0.974359	−	1.08937i
$625$	25.0000			0.0400000
$626$			881.011i			1.40737i
$627$	20.0000	+	17.8885i	0.0318979	+	0.0285304i
$628$	−164.000			−0.261146
$629$		−	71.5542i		−	0.113759i
$630$	30.0000	+	268.328i	0.0476190	+	0.425918i
$631$	−698.000			−1.10618			−0.553090	−	0.833121i	$-0.686552\pi$
$631$	−698.000			−1.10618			−0.553090	+	0.833121i	$0.686552\pi$
$632$		−	925.732i		−	1.46477i
$633$	−4.00000	+	4.47214i	−0.00631912	+	0.00706499i
$634$	1010.00			1.59306
$635$		−	58.1378i		−	0.0915555i
$636$	10.0000	+	8.94427i	0.0157233	+	0.0140633i
$637$	−208.000			−0.326531
$638$		−	313.050i		−	0.490673i
$639$	−1120.00	+	125.220i	−1.75274	+	0.195962i
$640$	−345.000			−0.539062
$641$			912.316i			1.42327i	0.702550	+	0.711635i	$0.252045\pi$
$641$			912.316i			1.42327i	−0.702550	+	0.711635i	$0.747955\pi$
$642$	−900.000	+	1006.23i	−1.40187	+	1.56734i
$643$	156.000			0.242613			0.121306	−	0.992615i	$-0.461292\pi$
$643$	156.000			0.242613			0.121306	+	0.992615i	$0.461292\pi$
$644$			80.4984i			0.124998i
$645$	−80.0000	−	71.5542i	−0.124031	−	0.110937i
$646$	−20.0000			−0.0309598
$647$			755.791i			1.16815i	0.811701	+	0.584073i	$0.198542\pi$
$647$			755.791i			1.16815i	−0.811701	+	0.584073i	$0.801458\pi$
$648$	120.000	+	529.948i	0.185185	+	0.817821i
$649$	−20.0000			−0.0308166
$650$			178.885i			0.275208i
$651$	−216.000	+	241.495i	−0.331797	+	0.370961i
$652$	−236.000			−0.361963
$653$		−	487.463i		−	0.746497i	−0.927731	−	0.373249i	$-0.878244\pi$
$653$		−	487.463i		−	0.746497i	0.927731	−	0.373249i	$-0.121756\pi$
$654$	190.000	+	169.941i	0.290520	+	0.259849i
$655$	−30.0000			−0.0458015
$656$		−	1189.59i		−	1.81340i
$657$	74.0000	+	661.876i	0.112633	+	1.00742i
$658$	660.000			1.00304
$659$			406.964i			0.617548i	0.951135	+	0.308774i	$0.0999187\pi$
$659$			406.964i			0.617548i	−0.951135	+	0.308774i	$0.900081\pi$
$660$	−20.0000	+	22.3607i	−0.0303030	+	0.0338798i
$661$	682.000			1.03177			0.515885	−	0.856658i	$-0.327463\pi$
$661$	682.000			1.03177			0.515885	+	0.856658i	$0.327463\pi$
$662$			442.741i			0.668794i
$663$	−160.000	−	143.108i	−0.241327	−	0.215850i
$664$	−630.000			−0.948795
$665$			26.8328i			0.0403501i
$666$	320.000	−	35.7771i	0.480480	−	0.0537194i
$667$	420.000			0.629685
$668$		−	93.9149i		−	0.140591i
$669$	−172.000	+	192.302i	−0.257100	+	0.287447i
$670$	120.000			0.179104
$671$			366.715i			0.546520i
$672$	210.000	+	187.830i	0.312500	+	0.279508i
$673$	−894.000			−1.32838			−0.664190	−	0.747564i	$-0.731223\pi$
$673$	−894.000			−1.32838			−0.664190	+	0.747564i	$0.731223\pi$
$674$		−	881.011i		−	1.30714i
$675$	−110.000	−	78.2624i	−0.162963	−	0.115944i
$676$	−87.0000			−0.128698
$677$		−	550.073i		−	0.812515i	−0.913759	−	0.406258i	$-0.866834\pi$
$677$		−	550.073i		−	0.812515i	0.913759	−	0.406258i	$-0.133166\pi$
$678$	−140.000	+	156.525i	−0.206490	+	0.230862i
$679$	996.000			1.46686
$680$			67.0820i			0.0986501i
$681$	130.000	+	116.276i	0.190896	+	0.170742i
$682$	−180.000			−0.263930
$683$			442.741i			0.648231i	0.946018	+	0.324115i	$0.105067\pi$
$683$			442.741i			0.648231i	−0.946018	+	0.324115i	$0.894933\pi$
$684$	−2.00000	−	17.8885i	−0.00292398	−	0.0261528i
$685$	270.000			0.394161
$686$		−	831.817i		−	1.21256i
$687$	564.000	−	630.571i	0.820961	−	0.917862i
$688$	−304.000			−0.441860
$689$			71.5542i			0.103852i
$690$	−150.000	−	134.164i	−0.217391	−	0.194441i
$691$	−758.000			−1.09696			−0.548480	−	0.836163i	$-0.684793\pi$
$691$	−758.000			−1.09696			−0.548480	+	0.836163i	$0.684793\pi$
$692$		−	13.4164i		−	0.0193879i
$693$	−240.000	+	26.8328i	−0.346320	+	0.0387198i
$694$	−410.000			−0.590778
$695$		−	183.358i		−	0.263824i
$696$	420.000	−	469.574i	0.603448	−	0.674676i
$697$	−280.000			−0.401722
$698$			809.457i			1.15968i
$699$	810.000	+	724.486i	1.15880	+	1.03646i
$700$	−30.0000			−0.0428571
$701$		−	782.624i		−	1.11644i	−0.829693	−	0.558220i	$-0.811485\pi$
$701$		−	782.624i		−	1.11644i	0.829693	−	0.558220i	$-0.188515\pi$
$702$	560.000	−	787.096i	0.797721	−	1.12122i
$703$	32.0000			0.0455192
$704$		−	183.358i		−	0.260451i
$705$	−220.000	+	245.967i	−0.312057	+	0.348890i
$706$	−690.000			−0.977337
$707$		−	402.492i		−	0.569296i
$708$	10.0000	+	8.94427i	0.0141243	+	0.0126332i
$709$	−2.00000			−0.00282087			−0.00141044	−	0.999999i	$-0.500449\pi$
$709$	−2.00000			−0.00282087			−0.00141044	+	0.999999i	$0.500449\pi$
$710$		−	626.099i		−	0.881830i
$711$	−138.000	−	1234.31i	−0.194093	−	1.73602i
$712$	720.000			1.01124
$713$		−	241.495i		−	0.338703i
$714$	120.000	−	134.164i	0.168067	−	0.187905i
$715$	−160.000			−0.223776
$716$		−	192.302i		−	0.268578i
$717$	560.000	+	500.879i	0.781032	+	0.698576i
$718$	660.000			0.919220
$719$			858.650i			1.19423i	0.802156	+	0.597114i	$0.203686\pi$
$719$			858.650i			1.19423i	−0.802156	+	0.597114i	$0.796314\pi$
$720$	−380.000	+	42.4853i	−0.527778	+	0.0590073i
$721$	−156.000			−0.216366
$722$			798.276i			1.10565i
$723$	−524.000	+	585.850i	−0.724758	+	0.810304i
$724$	−2.00000			−0.00276243
$725$			156.525i			0.215896i
$726$	505.000	+	451.686i	0.695592	+	0.622157i
$727$	674.000			0.927098			0.463549	−	0.886071i	$-0.346576\pi$
$727$	674.000			0.927098			0.463549	+	0.886071i	$0.346576\pi$
$728$			643.988i			0.884598i
$729$	239.000	+	688.709i	0.327846	+	0.944731i
$730$	−370.000			−0.506849
$731$			71.5542i			0.0978853i
$732$	164.000	−	183.358i	0.224044	−	0.250488i
$733$	656.000			0.894952			0.447476	−	0.894296i	$-0.352323\pi$
$733$	656.000			0.894952			0.447476	+	0.894296i	$0.352323\pi$
$734$			415.909i			0.566633i
$735$	65.0000	+	58.1378i	0.0884354	+	0.0790990i
$736$	−210.000			−0.285326
$737$			107.331i			0.145633i
$738$	−140.000	−	1252.20i	−0.189702	−	1.69675i
$739$	598.000			0.809202			0.404601	−	0.914493i	$-0.367410\pi$
$739$	598.000			0.809202			0.404601	+	0.914493i	$0.367410\pi$
$740$			35.7771i			0.0483474i
$741$	64.0000	−	71.5542i	0.0863698	−	0.0965643i
$742$	−60.0000			−0.0808625
$743$			782.624i			1.05333i	0.850073	+	0.526665i	$0.176558\pi$
$743$			782.624i			1.05333i	−0.850073	+	0.526665i	$0.823442\pi$
$744$	−270.000	−	241.495i	−0.362903	−	0.324591i
$745$	250.000			0.335570
$746$			98.3870i			0.131886i
$747$	−840.000	+	93.9149i	−1.12450	+	0.125723i
$748$	20.0000			0.0267380
$749$		−	1207.48i		−	1.61212i
$750$	50.0000	−	55.9017i	0.0666667	−	0.0745356i
$751$	−338.000			−0.450067			−0.225033	−	0.974351i	$-0.572249\pi$
$751$	−338.000			−0.450067			−0.225033	+	0.974351i	$0.572249\pi$
$752$			934.676i			1.24292i
$753$	−1050.00	−	939.149i	−1.39442	−	1.24721i
$754$	−1120.00			−1.48541
$755$		−	353.299i		−	0.467945i
$756$	132.000	+	93.9149i	0.174603	+	0.124226i
$757$	−656.000			−0.866579			−0.433289	−	0.901255i	$-0.642647\pi$
$757$	−656.000			−0.866579			−0.433289	+	0.901255i	$0.642647\pi$
$758$			809.457i			1.06788i
$759$	120.000	−	134.164i	0.158103	−	0.176764i
$760$	−30.0000			−0.0394737
$761$			295.161i			0.387859i	0.981015	+	0.193930i	$0.0621234\pi$
$761$			295.161i			0.387859i	−0.981015	+	0.193930i	$0.937877\pi$
$762$	−130.000	−	116.276i	−0.170604	−	0.152593i
$763$	−228.000			−0.298820
$764$			205.718i			0.269265i
$765$	10.0000	+	89.4427i	0.0130719	+	0.116919i
$766$	−810.000			−1.05744
$767$			71.5542i			0.0932910i
$768$	−362.000	+	404.728i	−0.471354	+	0.526990i
$769$	−82.0000			−0.106632			−0.0533160	−	0.998578i	$-0.516979\pi$
$769$	−82.0000			−0.106632			−0.0533160	+	0.998578i	$0.516979\pi$
$770$		−	134.164i		−	0.174239i
$771$	−450.000	−	402.492i	−0.583658	−	0.522039i
$772$	214.000			0.277202
$773$		−	1059.90i		−	1.37115i	−0.728004	−	0.685573i	$-0.759552\pi$
$773$		−	1059.90i		−	1.37115i	0.728004	−	0.685573i	$-0.240448\pi$
$774$	−320.000	+	35.7771i	−0.413437	+	0.0462236i
$775$	90.0000			0.116129
$776$			1113.56i			1.43500i
$777$	−192.000	+	214.663i	−0.247104	+	0.276271i
$778$	990.000			1.27249
$779$		−	125.220i		−	0.160744i
$780$	80.0000	+	71.5542i	0.102564	+	0.0917361i
$781$	560.000			0.717029
$782$			134.164i			0.171565i
$783$	490.000	−	688.709i	0.625798	−	0.879577i
$784$	247.000			0.315051
$785$			366.715i			0.467153i
$786$	−60.0000	+	67.0820i	−0.0763359	+	0.0853461i
$787$	−536.000			−0.681067			−0.340534	−	0.940232i	$-0.610608\pi$
$787$	−536.000			−0.681067			−0.340534	+	0.940232i	$0.610608\pi$
$788$			93.9149i			0.119181i
$789$	130.000	+	116.276i	0.164766	+	0.147371i
$790$	690.000			0.873418
$791$		−	187.830i		−	0.237459i
$792$	−30.0000	−	268.328i	−0.0378788	−	0.338798i
$793$	1312.00			1.65448
$794$		−	277.272i		−	0.349210i
$795$	20.0000	−	22.3607i	0.0251572	−	0.0281266i
$796$	242.000			0.304020
$797$		−	406.964i		−	0.510620i	−0.966859	−	0.255310i	$-0.917822\pi$
$797$		−	406.964i		−	0.510620i	0.966859	−	0.255310i	$-0.0821776\pi$
$798$	60.0000	+	53.6656i	0.0751880	+	0.0672502i
$799$	220.000			0.275344
$800$		−	78.2624i		−	0.0978280i
$801$	960.000	−	107.331i	1.19850	−	0.133997i
$802$	−600.000			−0.748130
$803$		−	330.938i		−	0.412127i
$804$	48.0000	−	53.6656i	0.0597015	−	0.0667483i
$805$	180.000			0.223602
$806$			643.988i			0.798992i
$807$	830.000	+	742.375i	1.02850	+	0.919919i
$808$	450.000			0.556931
$809$		−	1091.20i		−	1.34883i	−0.738354	−	0.674414i	$-0.764397\pi$
$809$		−	1091.20i		−	1.34883i	0.738354	−	0.674414i	$-0.235603\pi$
$810$	−395.000	+	89.4427i	−0.487654	+	0.110423i
$811$	−558.000			−0.688039			−0.344020	−	0.938962i	$-0.611789\pi$
$811$	−558.000			−0.688039			−0.344020	+	0.938962i	$0.611789\pi$
$812$		−	187.830i		−	0.231317i
$813$	−164.000	+	183.358i	−0.201722	+	0.225532i
$814$	−160.000			−0.196560
$815$			527.712i			0.647499i
$816$	190.000	+	169.941i	0.232843	+	0.208261i
$817$	−32.0000			−0.0391677
$818$		−	1024.12i		−	1.25198i
$819$	96.0000	+	858.650i	0.117216	+	1.04841i
$820$	140.000			0.170732
$821$			389.076i			0.473905i	0.971521	+	0.236952i	$0.0761485\pi$
$821$			389.076i			0.473905i	−0.971521	+	0.236952i	$0.923851\pi$
$822$	540.000	−	603.738i	0.656934	−	0.734475i
$823$	−214.000			−0.260024			−0.130012	−	0.991512i	$-0.541502\pi$
$823$	−214.000			−0.260024			−0.130012	+	0.991512i	$0.541502\pi$
$824$		−	174.413i		−	0.211667i
$825$	50.0000	+	44.7214i	0.0606061	+	0.0542077i
$826$	−60.0000			−0.0726392
$827$			31.3050i			0.0378536i	0.999821	+	0.0189268i	$0.00602495\pi$
$827$			31.3050i			0.0378536i	−0.999821	+	0.0189268i	$0.993975\pi$
$828$	−120.000	+	13.4164i	−0.144928	+	0.0162034i
$829$	318.000			0.383595			0.191797	−	0.981435i	$-0.438568\pi$
$829$	318.000			0.383595			0.191797	+	0.981435i	$0.438568\pi$
$830$		−	469.574i		−	0.565752i
$831$	−48.0000	+	53.6656i	−0.0577617	+	0.0645796i
$832$	−656.000			−0.788462
$833$		−	58.1378i		−	0.0697932i
$834$	−410.000	−	366.715i	−0.491607	−	0.439706i
$835$	−210.000			−0.251497
$836$			8.94427i			0.0106989i
$837$	−396.000	−	281.745i	−0.473118	−	0.336612i
$838$	−1330.00			−1.58711
$839$			62.6099i			0.0746244i	0.999304	+	0.0373122i	$0.0118796\pi$
$839$			62.6099i			0.0746244i	−0.999304	+	0.0373122i	$0.988120\pi$
$840$	180.000	−	201.246i	0.214286	−	0.239579i
$841$	−139.000			−0.165279
$842$		−	1256.67i		−	1.49248i
$843$	420.000	+	375.659i	0.498221	+	0.445622i
$844$	−2.00000			−0.00236967
$845$			194.538i			0.230222i
$846$	110.000	+	983.870i	0.130024	+	1.16297i
$847$	−606.000			−0.715466
$848$		−	84.9706i		−	0.100201i
$849$	288.000	−	321.994i	0.339223	−	0.379262i
$850$	−50.0000			−0.0588235
$851$		−	214.663i		−	0.252247i
$852$	−280.000	−	250.440i	−0.328638	−	0.293943i
$853$	−684.000			−0.801876			−0.400938	−	0.916105i	$-0.631316\pi$
$853$	−684.000			−0.801876			−0.400938	+	0.916105i	$0.631316\pi$
$854$			1100.15i			1.28823i
$855$	−40.0000	+	4.47214i	−0.0467836	+	0.00523057i
$856$	1350.00			1.57710
$857$		−	1498.17i		−	1.74815i	−0.485790	−	0.874076i	$-0.661468\pi$
$857$		−	1498.17i		−	1.74815i	0.485790	−	0.874076i	$-0.338532\pi$
$858$	−320.000	+	357.771i	−0.372960	+	0.416982i
$859$	−842.000			−0.980210			−0.490105	−	0.871664i	$-0.663041\pi$
$859$	−842.000			−0.980210			−0.490105	+	0.871664i	$0.663041\pi$
$860$		−	35.7771i		−	0.0416013i
$861$	840.000	+	751.319i	0.975610	+	0.872612i
$862$	780.000			0.904872
$863$			1015.17i			1.17633i	0.808740	+	0.588166i	$0.200150\pi$
$863$			1015.17i			1.17633i	−0.808740	+	0.588166i	$0.799850\pi$
$864$	−245.000	+	344.354i	−0.283565	+	0.398558i
$865$	−30.0000			−0.0346821
$866$		−	505.351i		−	0.583547i
$867$	−538.000	+	601.502i	−0.620531	+	0.693774i
$868$	−108.000			−0.124424
$869$			617.155i			0.710190i
$870$	350.000	+	313.050i	0.402299	+	0.359827i
$871$	384.000			0.440873
$872$		−	254.912i		−	0.292330i
$873$	166.000	+	1484.75i	0.190149	+	1.70074i
$874$	−60.0000			−0.0686499
$875$			67.0820i			0.0766652i
$876$	−148.000	+	165.469i	−0.168950	+	0.188892i
$877$	−156.000			−0.177879			−0.0889396	−	0.996037i	$-0.528348\pi$
$877$	−156.000			−0.177879			−0.0889396	+	0.996037i	$0.528348\pi$
$878$			4.47214i			0.00509355i
$879$	−1050.00	−	939.149i	−1.19454	−	1.06843i
$880$	190.000			0.215909
$881$			125.220i			0.142134i	0.997472	+	0.0710669i	$0.0226404\pi$
$881$			125.220i			0.142134i	−0.997472	+	0.0710669i	$0.977360\pi$
$882$	260.000	−	29.0689i	0.294785	−	0.0329579i
$883$	−964.000			−1.09173			−0.545866	−	0.837872i	$-0.683799\pi$
$883$	−964.000			−1.09173			−0.545866	+	0.837872i	$0.683799\pi$
$884$		−	71.5542i		−	0.0809436i
$885$	20.0000	−	22.3607i	0.0225989	−	0.0252663i
$886$	450.000			0.507901
$887$			952.565i			1.07392i	0.843608	+	0.536959i	$0.180427\pi$
$887$			952.565i			1.07392i	−0.843608	+	0.536959i	$0.819573\pi$
$888$	−240.000	−	214.663i	−0.270270	−	0.241737i
$889$	156.000			0.175478
$890$			536.656i			0.602985i
$891$	−80.0000	−	353.299i	−0.0897868	−	0.396519i
$892$	−86.0000			−0.0964126
$893$			98.3870i			0.110176i
$894$	500.000	−	559.017i	0.559284	−	0.625299i
$895$	−430.000			−0.480447
$896$		−	925.732i		−	1.03318i
$897$	−480.000	−	429.325i	−0.535117	−	0.478623i
$898$	700.000			0.779510
$899$			563.489i			0.626795i
$900$	−5.00000	−	44.7214i	−0.00555556	−	0.0496904i
$901$	−20.0000			−0.0221976
$902$			626.099i			0.694123i
$903$	192.000	−	214.663i	0.212625	−	0.237722i
$904$	210.000			0.232301
$905$			4.47214i			0.00494159i
$906$	−790.000	−	706.597i	−0.871965	−	0.779909i
$907$	1284.00			1.41566			0.707828	−	0.706385i	$-0.249675\pi$
$907$	1284.00			1.41566			0.707828	+	0.706385i	$0.249675\pi$
$908$			58.1378i			0.0640284i
$909$	600.000	−	67.0820i	0.660066	−	0.0737976i
$910$	−480.000			−0.527473
$911$		−	62.6099i		−	0.0687266i	−0.999409	−	0.0343633i	$-0.989060\pi$
$911$		−	62.6099i		−	0.0687266i	0.999409	−	0.0343633i	$-0.0109403\pi$
$912$	−76.0000	+	84.9706i	−0.0833333	+	0.0931695i
$913$	420.000			0.460022
$914$		−	746.847i		−	0.817119i
$915$	−410.000	−	366.715i	−0.448087	−	0.400782i
$916$	282.000			0.307860
$917$		−	80.4984i		−	0.0877846i
$918$	220.000	+	156.525i	0.239651	+	0.170506i
$919$	418.000			0.454842			0.227421	−	0.973797i	$-0.426971\pi$
$919$	418.000			0.454842			0.227421	+	0.973797i	$0.426971\pi$
$920$			201.246i			0.218746i
$921$	−368.000	+	411.437i	−0.399566	+	0.446728i
$922$	210.000			0.227766
$923$		−	2003.52i		−	2.17066i
$924$	−60.0000	−	53.6656i	−0.0649351	−	0.0580797i
$925$	80.0000			0.0864865
$926$		−	818.401i		−	0.883802i
$927$	−26.0000	−	232.551i	−0.0280475	−	0.250864i
$928$	490.000			0.528017
$929$			169.941i			0.182929i	0.995808	+	0.0914646i	$0.0291548\pi$
$929$			169.941i			0.182929i	−0.995808	+	0.0914646i	$0.970845\pi$
$930$	180.000	−	201.246i	0.193548	−	0.216394i
$931$	26.0000			0.0279270
$932$			362.243i			0.388673i
$933$	−360.000	−	321.994i	−0.385852	−	0.345117i
$934$	1010.00			1.08137
$935$		−	44.7214i		−	0.0478303i
$936$	−960.000	+	107.331i	−1.02564	+	0.114670i
$937$	534.000			0.569904			0.284952	−	0.958542i	$-0.408022\pi$
$937$	534.000			0.569904			0.284952	+	0.958542i	$0.408022\pi$
$938$			321.994i			0.343277i
$939$	788.000	−	881.011i	0.839191	−	0.938244i
$940$	−110.000			−0.117021
$941$			129.692i			0.137824i	0.997623	+	0.0689118i	$0.0219527\pi$
$941$			129.692i			0.137824i	−0.997623	+	0.0689118i	$0.978047\pi$
$942$	820.000	+	733.430i	0.870488	+	0.778588i
$943$	−840.000			−0.890774
$944$		−	84.9706i		−	0.0900112i
$945$	210.000	−	295.161i	0.222222	−	0.312340i
$946$	160.000			0.169133
$947$			1516.05i			1.60090i	0.599398	+	0.800451i	$0.295407\pi$
$947$			1516.05i			1.60090i	−0.599398	+	0.800451i	$0.704593\pi$
$948$	276.000	−	308.577i	0.291139	−	0.325504i
$949$	−1184.00			−1.24763
$950$		−	22.3607i		−	0.0235376i
$951$	−1010.00	−	903.371i	−1.06204	−	0.949917i
$952$	−180.000			−0.189076
$953$			406.964i			0.427035i	0.976939	+	0.213518i	$0.0684920\pi$
$953$			406.964i			0.427035i	−0.976939	+	0.213518i	$0.931508\pi$
$954$	−10.0000	−	89.4427i	−0.0104822	−	0.0937555i
$955$	460.000			0.481675
$956$			250.440i			0.261966i
$957$	−280.000	+	313.050i	−0.292581	+	0.327115i
$958$	−1320.00			−1.37787
$959$			724.486i			0.755460i
$960$	205.000	+	183.358i	0.213542	+	0.190997i
$961$	−637.000			−0.662851
$962$			572.433i			0.595045i
$963$	1800.00	−	201.246i	1.86916	−	0.208978i
$964$	−262.000			−0.271784
$965$		−	478.519i		−	0.495874i
$966$	360.000	−	402.492i	0.372671	−	0.416659i
$967$	674.000			0.697001			0.348501	−	0.937309i	$-0.386691\pi$
$967$	674.000			0.697001			0.348501	+	0.937309i	$0.386691\pi$
$968$		−	677.529i		−	0.699926i
$969$	20.0000	+	17.8885i	0.0206398	+	0.0184608i
$970$	−830.000			−0.855670
$971$			1328.22i			1.36789i	0.729532	+	0.683947i	$0.239738\pi$
$971$			1328.22i			1.36789i	−0.729532	+	0.683947i	$0.760262\pi$
$972$	−118.000	+	212.426i	−0.121399	+	0.218546i
$973$	492.000			0.505653
$974$			1981.16i			2.03404i
$975$	160.000	−	178.885i	0.164103	−	0.183472i
$976$	−1558.00			−1.59631
$977$		−	371.187i		−	0.379926i	−0.981791	−	0.189963i	$-0.939163\pi$
$977$		−	371.187i		−	0.379926i	0.981791	−	0.189963i	$-0.0608367\pi$
$978$	1180.00	+	1055.42i	1.20654	+	1.07917i
$979$	−480.000			−0.490296
$980$			29.0689i			0.0296621i
$981$	−38.0000	−	339.882i	−0.0387360	−	0.346465i
$982$	−910.000			−0.926680
$983$			442.741i			0.450398i	0.974313	+	0.225199i	$0.0723033\pi$
$983$			442.741i			0.450398i	−0.974313	+	0.225199i	$0.927697\pi$
$984$	−840.000	+	939.149i	−0.853659	+	0.954419i
$985$	210.000			0.213198
$986$		−	313.050i		−	0.317494i
$987$	−660.000	−	590.322i	−0.668693	−	0.598097i
$988$	32.0000			0.0323887
$989$			214.663i			0.217050i
$990$	200.000	−	22.3607i	0.202020	−	0.0225865i
$991$	962.000			0.970737			0.485368	−	0.874310i	$-0.338686\pi$
$991$	962.000			0.970737			0.485368	+	0.874310i	$0.338686\pi$
$992$		−	281.745i		−	0.284017i
$993$	396.000	−	442.741i	0.398792	−	0.445862i
$994$	1680.00			1.69014
$995$		−	541.128i		−	0.543848i
$996$	−210.000	−	187.830i	−0.210843	−	0.188584i
$997$	24.0000			0.0240722			0.0120361	−	0.999928i	$-0.496169\pi$
$997$	24.0000			0.0240722			0.0120361	+	0.999928i	$0.496169\pi$
$998$			4.47214i			0.00448110i
$999$	−352.000	−	250.440i	−0.352352	−	0.250690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.3.c.a.11.1	✓	2
3.2	odd	2	inner	15.3.c.a.11.2	yes	2
4.3	odd	2		240.3.l.b.161.1		2
5.2	odd	4		75.3.d.b.74.4		4
5.3	odd	4		75.3.d.b.74.1		4
5.4	even	2		75.3.c.e.26.2		2
8.3	odd	2		960.3.l.b.641.2		2
8.5	even	2		960.3.l.c.641.1		2
9.2	odd	6		405.3.i.b.296.2		4
9.4	even	3		405.3.i.b.26.2		4
9.5	odd	6		405.3.i.b.26.1		4
9.7	even	3		405.3.i.b.296.1		4
12.11	even	2		240.3.l.b.161.2		2
15.2	even	4		75.3.d.b.74.2		4
15.8	even	4		75.3.d.b.74.3		4
15.14	odd	2		75.3.c.e.26.1		2
20.3	even	4		1200.3.c.f.449.4		4
20.7	even	4		1200.3.c.f.449.1		4
20.19	odd	2		1200.3.l.g.401.2		2
24.5	odd	2		960.3.l.c.641.2		2
24.11	even	2		960.3.l.b.641.1		2
60.23	odd	4		1200.3.c.f.449.2		4
60.47	odd	4		1200.3.c.f.449.3		4
60.59	even	2		1200.3.l.g.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.c.a.11.1	✓	2	1.1	even	1	trivial
15.3.c.a.11.2	yes	2	3.2	odd	2	inner
75.3.c.e.26.1		2	15.14	odd	2
75.3.c.e.26.2		2	5.4	even	2
75.3.d.b.74.1		4	5.3	odd	4
75.3.d.b.74.2		4	15.2	even	4
75.3.d.b.74.3		4	15.8	even	4
75.3.d.b.74.4		4	5.2	odd	4
240.3.l.b.161.1		2	4.3	odd	2
240.3.l.b.161.2		2	12.11	even	2
405.3.i.b.26.1		4	9.5	odd	6
405.3.i.b.26.2		4	9.4	even	3
405.3.i.b.296.1		4	9.7	even	3
405.3.i.b.296.2		4	9.2	odd	6
960.3.l.b.641.1		2	24.11	even	2
960.3.l.b.641.2		2	8.3	odd	2
960.3.l.c.641.1		2	8.5	even	2
960.3.l.c.641.2		2	24.5	odd	2
1200.3.c.f.449.1		4	20.7	even	4
1200.3.c.f.449.2		4	60.23	odd	4
1200.3.c.f.449.3		4	60.47	odd	4
1200.3.c.f.449.4		4	20.3	even	4
1200.3.l.g.401.1		2	60.59	even	2
1200.3.l.g.401.2		2	20.19	odd	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.23607i q^{2} +(-2.00000 + 2.23607i) q^{3} -1.00000 q^{4} +2.23607i q^{5} +(5.00000 + 4.47214i) q^{6} -6.00000 q^{7} -6.70820i q^{8} +(-1.00000 - 8.94427i) q^{9} +O(q^{10})\)	\(q-2.23607i q^{2} +(-2.00000 + 2.23607i) q^{3} -1.00000 q^{4} +2.23607i q^{5} +(5.00000 + 4.47214i) q^{6} -6.00000 q^{7} -6.70820i q^{8} +(-1.00000 - 8.94427i) q^{9} +5.00000 q^{10} +4.47214i q^{11} +(2.00000 - 2.23607i) q^{12} +16.0000 q^{13} +13.4164i q^{14} +(-5.00000 - 4.47214i) q^{15} -19.0000 q^{16} +4.47214i q^{17} +(-20.0000 + 2.23607i) q^{18} -2.00000 q^{19} -2.23607i q^{20} +(12.0000 - 13.4164i) q^{21} +10.0000 q^{22} +13.4164i q^{23} +(15.0000 + 13.4164i) q^{24} -5.00000 q^{25} -35.7771i q^{26} +(22.0000 + 15.6525i) q^{27} +6.00000 q^{28} -31.3050i q^{29} +(-10.0000 + 11.1803i) q^{30} -18.0000 q^{31} +15.6525i q^{32} +(-10.0000 - 8.94427i) q^{33} +10.0000 q^{34} -13.4164i q^{35} +(1.00000 + 8.94427i) q^{36} -16.0000 q^{37} +4.47214i q^{38} +(-32.0000 + 35.7771i) q^{39} +15.0000 q^{40} +62.6099i q^{41} +(-30.0000 - 26.8328i) q^{42} +16.0000 q^{43} -4.47214i q^{44} +(20.0000 - 2.23607i) q^{45} +30.0000 q^{46} -49.1935i q^{47} +(38.0000 - 42.4853i) q^{48} -13.0000 q^{49} +11.1803i q^{50} +(-10.0000 - 8.94427i) q^{51} -16.0000 q^{52} +4.47214i q^{53} +(35.0000 - 49.1935i) q^{54} -10.0000 q^{55} +40.2492i q^{56} +(4.00000 - 4.47214i) q^{57} -70.0000 q^{58} +4.47214i q^{59} +(5.00000 + 4.47214i) q^{60} +82.0000 q^{61} +40.2492i q^{62} +(6.00000 + 53.6656i) q^{63} -41.0000 q^{64} +35.7771i q^{65} +(-20.0000 + 22.3607i) q^{66} +24.0000 q^{67} -4.47214i q^{68} +(-30.0000 - 26.8328i) q^{69} -30.0000 q^{70} -125.220i q^{71} +(-60.0000 + 6.70820i) q^{72} -74.0000 q^{73} +35.7771i q^{74} +(10.0000 - 11.1803i) q^{75} +2.00000 q^{76} -26.8328i q^{77} +(80.0000 + 71.5542i) q^{78} +138.000 q^{79} -42.4853i q^{80} +(-79.0000 + 17.8885i) q^{81} +140.000 q^{82} -93.9149i q^{83} +(-12.0000 + 13.4164i) q^{84} -10.0000 q^{85} -35.7771i q^{86} +(70.0000 + 62.6099i) q^{87} +30.0000 q^{88} +107.331i q^{89} +(-5.00000 - 44.7214i) q^{90} -96.0000 q^{91} -13.4164i q^{92} +(36.0000 - 40.2492i) q^{93} -110.000 q^{94} -4.47214i q^{95} +(-35.0000 - 31.3050i) q^{96} -166.000 q^{97} +29.0689i q^{98} +(40.0000 - 4.47214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} - 2 q^{4} + 10 q^{6} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 2 * q - 4 * q^3 - 2 * q^4 + 10 * q^6 - 12 * q^7 - 2 * q^9	\( 2 q - 4 q^{3} - 2 q^{4} + 10 q^{6} - 12 q^{7} - 2 q^{9} + 10 q^{10} + 4 q^{12} + 32 q^{13} - 10 q^{15} - 38 q^{16} - 40 q^{18} - 4 q^{19} + 24 q^{21} + 20 q^{22} + 30 q^{24} - 10 q^{25} + 44 q^{27} + 12 q^{28} - 20 q^{30} - 36 q^{31} - 20 q^{33} + 20 q^{34} + 2 q^{36} - 32 q^{37} - 64 q^{39} + 30 q^{40} - 60 q^{42} + 32 q^{43} + 40 q^{45} + 60 q^{46} + 76 q^{48} - 26 q^{49} - 20 q^{51} - 32 q^{52} + 70 q^{54} - 20 q^{55} + 8 q^{57} - 140 q^{58} + 10 q^{60} + 164 q^{61} + 12 q^{63} - 82 q^{64} - 40 q^{66} + 48 q^{67} - 60 q^{69} - 60 q^{70} - 120 q^{72} - 148 q^{73} + 20 q^{75} + 4 q^{76} + 160 q^{78} + 276 q^{79} - 158 q^{81} + 280 q^{82} - 24 q^{84} - 20 q^{85} + 140 q^{87} + 60 q^{88} - 10 q^{90} - 192 q^{91} + 72 q^{93} - 220 q^{94} - 70 q^{96} - 332 q^{97} + 80 q^{99}+O(q^{100}) \) 2 * q - 4 * q^3 - 2 * q^4 + 10 * q^6 - 12 * q^7 - 2 * q^9 + 10 * q^10 + 4 * q^12 + 32 * q^13 - 10 * q^15 - 38 * q^16 - 40 * q^18 - 4 * q^19 + 24 * q^21 + 20 * q^22 + 30 * q^24 - 10 * q^25 + 44 * q^27 + 12 * q^28 - 20 * q^30 - 36 * q^31 - 20 * q^33 + 20 * q^34 + 2 * q^36 - 32 * q^37 - 64 * q^39 + 30 * q^40 - 60 * q^42 + 32 * q^43 + 40 * q^45 + 60 * q^46 + 76 * q^48 - 26 * q^49 - 20 * q^51 - 32 * q^52 + 70 * q^54 - 20 * q^55 + 8 * q^57 - 140 * q^58 + 10 * q^60 + 164 * q^61 + 12 * q^63 - 82 * q^64 - 40 * q^66 + 48 * q^67 - 60 * q^69 - 60 * q^70 - 120 * q^72 - 148 * q^73 + 20 * q^75 + 4 * q^76 + 160 * q^78 + 276 * q^79 - 158 * q^81 + 280 * q^82 - 24 * q^84 - 20 * q^85 + 140 * q^87 + 60 * q^88 - 10 * q^90 - 192 * q^91 + 72 * q^93 - 220 * q^94 - 70 * q^96 - 332 * q^97 + 80 * q^99

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