LMFDB - Embedded newform 300.3.c.d.151.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.7
Root			$-1.34966 - 0.422403i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.d.151.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 - 0.675358i) q^{4} +(-0.293494 - 3.45165i) q^{6} -12.3959i q^{7} +(7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 - 0.675358i) q^{4} +(-0.293494 - 3.45165i) q^{6} -12.3959i q^{7} +(7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +11.0403i q^{11} +(-1.16975 - 6.82874i) q^{12} -2.82009 q^{13} +(-2.10047 - 24.7027i) q^{14} +(15.0878 - 5.32529i) q^{16} -6.52606 q^{17} +(-5.97843 + 0.508346i) q^{18} -27.9928i q^{19} -21.4703 q^{21} +(1.87077 + 22.0012i) q^{22} +7.90421i q^{23} +(-3.48822 - 13.4102i) q^{24} +(-5.61989 + 0.477860i) q^{26} +5.19615i q^{27} +(-8.37167 - 48.8718i) q^{28} +50.7169 q^{29} +36.3467i q^{31} +(29.1647 - 13.1689i) q^{32} +19.1224 q^{33} +(-13.0052 + 1.10583i) q^{34} +(-11.8277 + 2.02607i) q^{36} +18.9279 q^{37} +(-4.74333 - 55.7842i) q^{38} +4.88453i q^{39} +5.30410 q^{41} +(-42.7863 + 3.63812i) q^{42} +45.5870i q^{43} +(7.45616 + 43.5273i) q^{44} +(1.33936 + 15.7516i) q^{46} -11.7246i q^{47} +(-9.22368 - 26.1328i) q^{48} -104.658 q^{49} +11.3035i q^{51} +(-11.1184 + 1.90457i) q^{52} -41.1680 q^{53} +(0.880481 + 10.3549i) q^{54} +(-24.9644 - 95.9735i) q^{56} -48.4849 q^{57} +(101.069 - 8.59391i) q^{58} +10.7008i q^{59} +56.1297 q^{61} +(6.15889 + 72.4319i) q^{62} +37.1877i q^{63} +(55.8882 - 31.1850i) q^{64} +(38.1073 - 3.24026i) q^{66} +16.1709i q^{67} +(-25.7295 + 4.40743i) q^{68} +13.6905 q^{69} +66.1617i q^{71} +(-23.2271 + 6.04177i) q^{72} -15.6330 q^{73} +(37.7198 - 3.20731i) q^{74} +(-18.9051 - 110.363i) q^{76} +136.855 q^{77} +(0.827677 + 9.73394i) q^{78} +123.057i q^{79} +9.00000 q^{81} +(10.5701 - 0.898773i) q^{82} +99.6700i q^{83} +(-84.6484 + 14.5002i) q^{84} +(7.72465 + 90.8461i) q^{86} -87.8443i q^{87} +(22.2343 + 85.4781i) q^{88} +101.083 q^{89} +34.9575i q^{91} +(5.33817 + 31.1629i) q^{92} +62.9543 q^{93} +(-1.98672 - 23.3649i) q^{94} +(-22.8092 - 50.5148i) q^{96} -127.293 q^{97} +(-208.564 + 17.7342i) q^{98} -33.1209i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.99281	−	0.169449i	0.996404	−	0.0847243i
$2$	1.99281	−	0.169449i	0.996404	−	0.0847243i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.94257	−	0.675358i	0.985644	−	0.168839i
$5$		0			0
$5$		0			0
$6$	−0.293494	−	3.45165i	−0.0489156	−	0.575274i
$7$		−	12.3959i		−	1.77084i	−0.464789	−	0.885422i	$-0.653870\pi$
$7$		−	12.3959i		−	1.77084i	0.464789	−	0.885422i	$-0.346130\pi$
$8$	7.74236	−	2.01392i	0.967795	−	0.251740i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			11.0403i			1.00366i	0.864965	+	0.501832i	$0.167341\pi$
$11$			11.0403i			1.00366i	−0.864965	+	0.501832i	$0.832659\pi$
$12$	−1.16975	−	6.82874i	−0.0974795	−	0.569062i
$13$	−2.82009			−0.216930			−0.108465	−	0.994100i	$-0.534593\pi$
$13$	−2.82009			−0.216930			−0.108465	+	0.994100i	$0.534593\pi$
$14$	−2.10047	−	24.7027i	−0.150034	−	1.76448i
$15$		0			0
$16$	15.0878	−	5.32529i	0.942987	−	0.332831i
$17$	−6.52606			−0.383886			−0.191943	−	0.981406i	$-0.561479\pi$
$17$	−6.52606			−0.383886			−0.191943	+	0.981406i	$0.561479\pi$
$18$	−5.97843	+	0.508346i	−0.332135	+	0.0282414i
$19$		−	27.9928i		−	1.47330i	−0.676273	−	0.736651i	$-0.736406\pi$
$19$		−	27.9928i		−	1.47330i	0.676273	−	0.736651i	$-0.263594\pi$
$20$		0			0
$21$	−21.4703			−1.02240
$22$	1.87077	+	22.0012i	0.0850348	+	1.00006i
$23$			7.90421i			0.343661i	0.985126	+	0.171831i	$0.0549682\pi$
$23$			7.90421i			0.343661i	−0.985126	+	0.171831i	$0.945032\pi$
$24$	−3.48822	−	13.4102i	−0.145342	−	0.558757i
$25$		0			0
$26$	−5.61989	+	0.477860i	−0.216150	+	0.0183792i
$27$			5.19615i			0.192450i
$28$	−8.37167	−	48.8718i	−0.298988	−	1.74542i
$29$	50.7169			1.74886			0.874429	−	0.485153i	$-0.161236\pi$
$29$	50.7169			1.74886			0.874429	+	0.485153i	$0.161236\pi$
$30$		0			0
$31$			36.3467i			1.17247i	0.810140	+	0.586236i	$0.199391\pi$
$31$			36.3467i			1.17247i	−0.810140	+	0.586236i	$0.800609\pi$
$32$	29.1647	−	13.1689i	0.911397	−	0.411528i
$33$	19.1224			0.579466
$34$	−13.0052	+	1.10583i	−0.382506	+	0.0325245i
$35$		0			0
$36$	−11.8277	+	2.02607i	−0.328548	+	0.0562798i
$37$	18.9279			0.511566			0.255783	−	0.966734i	$-0.417667\pi$
$37$	18.9279			0.511566			0.255783	+	0.966734i	$0.417667\pi$
$38$	−4.74333	−	55.7842i	−0.124825	−	1.46801i
$39$			4.88453i			0.125244i
$40$		0			0
$41$	5.30410			0.129368			0.0646842	−	0.997906i	$-0.479396\pi$
$41$	5.30410			0.129368			0.0646842	+	0.997906i	$0.479396\pi$
$42$	−42.7863	+	3.63812i	−1.01872	+	0.0866219i
$43$			45.5870i			1.06016i	0.847947	+	0.530081i	$0.177838\pi$
$43$			45.5870i			1.06016i	−0.847947	+	0.530081i	$0.822162\pi$
$44$	7.45616	+	43.5273i	0.169458	+	0.989256i
$45$		0			0
$46$	1.33936	+	15.7516i	0.0291165	+	0.342426i
$47$		−	11.7246i		−	0.249460i	−0.992191	−	0.124730i	$-0.960194\pi$
$47$		−	11.7246i		−	0.249460i	0.992191	−	0.124730i	$-0.0398064\pi$
$48$	−9.22368	−	26.1328i	−0.192160	−	0.544434i
$49$	−104.658			−2.13589
$50$		0			0
$51$			11.3035i			0.221637i
$52$	−11.1184	+	1.90457i	−0.213815	+	0.0366263i
$53$	−41.1680			−0.776755			−0.388378	−	0.921500i	$-0.626964\pi$
$53$	−41.1680			−0.776755			−0.388378	+	0.921500i	$0.626964\pi$
$54$	0.880481	+	10.3549i	0.0163052	+	0.191758i
$55$		0			0
$56$	−24.9644	−	95.9735i	−0.445793	−	1.71381i
$57$	−48.4849			−0.850612
$58$	101.069	−	8.59391i	1.74257	−	0.148171i
$59$			10.7008i			0.181370i	0.995880	+	0.0906848i	$0.0289056\pi$
$59$			10.7008i			0.181370i	−0.995880	+	0.0906848i	$0.971094\pi$
$60$		0			0
$61$	56.1297			0.920159			0.460080	−	0.887878i	$-0.347821\pi$
$61$	56.1297			0.920159			0.460080	+	0.887878i	$0.347821\pi$
$62$	6.15889	+	72.4319i	0.0993370	+	1.16826i
$63$			37.1877i			0.590281i
$64$	55.8882	−	31.1850i	0.873254	−	0.487266i
$65$		0			0
$66$	38.1073	−	3.24026i	0.577383	−	0.0490949i
$67$			16.1709i			0.241357i	0.992692	+	0.120679i	$0.0385071\pi$
$67$			16.1709i			0.241357i	−0.992692	+	0.120679i	$0.961493\pi$
$68$	−25.7295	+	4.40743i	−0.378375	+	0.0648151i
$69$	13.6905			0.198413
$70$		0			0
$71$			66.1617i			0.931855i	0.884823	+	0.465928i	$0.154279\pi$
$71$			66.1617i			0.931855i	−0.884823	+	0.465928i	$0.845721\pi$
$72$	−23.2271	+	6.04177i	−0.322598	+	0.0839134i
$73$	−15.6330			−0.214150			−0.107075	−	0.994251i	$-0.534149\pi$
$73$	−15.6330			−0.214150			−0.107075	+	0.994251i	$0.534149\pi$
$74$	37.7198	−	3.20731i	0.509727	−	0.0433421i
$75$		0			0
$76$	−18.9051	−	110.363i	−0.248752	−	1.45215i
$77$	136.855			1.77733
$78$	0.827677	+	9.73394i	0.0106112	+	0.124794i
$79$			123.057i			1.55768i	0.627223	+	0.778840i	$0.284191\pi$
$79$			123.057i			1.55768i	−0.627223	+	0.778840i	$0.715809\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	10.5701	−	0.898773i	0.128903	−	0.0109606i
$83$			99.6700i			1.20084i	0.799684	+	0.600422i	$0.205001\pi$
$83$			99.6700i			1.20084i	−0.799684	+	0.600422i	$0.794999\pi$
$84$	−84.6484	+	14.5002i	−1.00772	+	0.172621i
$85$		0			0
$86$	7.72465	+	90.8461i	0.0898215	+	1.05635i
$87$		−	87.8443i		−	1.00970i
$88$	22.2343	+	85.4781i	0.252663	+	0.971342i
$89$	101.083			1.13576			0.567881	−	0.823110i	$-0.307763\pi$
$89$	101.083			1.13576			0.567881	+	0.823110i	$0.307763\pi$
$90$		0			0
$91$			34.9575i			0.384148i
$92$	5.33817	+	31.1629i	0.0580236	+	0.338728i
$93$	62.9543			0.676927
$94$	−1.98672	−	23.3649i	−0.0211353	−	0.248563i
$95$		0			0
$96$	−22.8092	−	50.5148i	−0.237596	−	0.526195i
$97$	−127.293			−1.31230			−0.656151	−	0.754630i	$-0.727817\pi$
$97$	−127.293			−1.31230			−0.656151	+	0.754630i	$0.727817\pi$
$98$	−208.564	+	17.7342i	−2.12821	+	0.180962i
$99$		−	33.1209i		−	0.334555i
$100$		0			0
$101$	−94.3535			−0.934193			−0.467096	−	0.884206i	$-0.654700\pi$
$101$	−94.3535			−0.934193			−0.467096	+	0.884206i	$0.654700\pi$
$102$	1.91536	+	22.5257i	0.0187780	+	0.220840i
$103$			31.8455i			0.309180i	0.987979	+	0.154590i	$0.0494056\pi$
$103$			31.8455i			0.309180i	−0.987979	+	0.154590i	$0.950594\pi$
$104$	−21.8341	+	5.67943i	−0.209943	+	0.0546099i
$105$		0			0
$106$	−82.0400	+	6.97587i	−0.773962	+	0.0658101i
$107$		−	33.7912i		−	0.315805i	−0.987455	−	0.157903i	$-0.949527\pi$
$107$		−	33.7912i		−	0.315805i	0.987455	−	0.157903i	$-0.0504732\pi$
$108$	3.50926	+	20.4862i	0.0324932	+	0.189687i
$109$	−83.4266			−0.765382			−0.382691	−	0.923876i	$-0.625003\pi$
$109$	−83.4266			−0.765382			−0.382691	+	0.923876i	$0.625003\pi$
$110$		0			0
$111$		−	32.7842i		−	0.295353i
$112$	−66.0118	−	187.027i	−0.589391	−	1.66988i
$113$	111.796			0.989342			0.494671	−	0.869080i	$-0.335289\pi$
$113$	111.796			0.989342			0.494671	+	0.869080i	$0.335289\pi$
$114$	−96.6211	+	8.21569i	−0.847553	+	0.0720675i
$115$		0			0
$116$	199.955	−	34.2520i	1.72375	−	0.295276i
$117$	8.46026			0.0723099
$118$	1.81324	+	21.3247i	0.0153664	+	0.180717i
$119$			80.8964i			0.679802i
$120$		0			0
$121$	−0.888544			−0.00734334
$122$	111.856	−	9.51110i	0.916851	−	0.0779599i
$123$		−	9.18697i		−	0.0746908i
$124$	24.5470	+	143.299i	0.197960	+	1.15564i
$125$		0			0
$126$	6.30141	+	74.1080i	0.0500112	+	0.588159i
$127$		−	16.6855i		−	0.131382i	−0.997840	−	0.0656909i	$-0.979075\pi$
$127$		−	16.6855i		−	0.131382i	0.997840	−	0.0656909i	$-0.0209251\pi$
$128$	106.090	−	71.6160i	0.828831	−	0.559500i
$129$	78.9589			0.612085
$130$		0			0
$131$		−	196.418i		−	1.49937i	−0.661794	−	0.749686i	$-0.730204\pi$
$131$		−	196.418i		−	1.49937i	0.661794	−	0.749686i	$-0.269796\pi$
$132$	75.3914	−	12.9144i	0.571147	−	0.0978367i
$133$	−346.995			−2.60899
$134$	2.74015	+	32.2256i	0.0204488	+	0.240490i
$135$		0			0
$136$	−50.5271	+	13.1430i	−0.371523	+	0.0966396i
$137$	117.127			0.854942			0.427471	−	0.904029i	$-0.359405\pi$
$137$	117.127			0.854942			0.427471	+	0.904029i	$0.359405\pi$
$138$	27.2825	−	2.31984i	0.197700	−	0.0168104i
$139$		−	187.238i		−	1.34704i	−0.739170	−	0.673519i	$-0.764782\pi$
$139$		−	187.238i		−	1.34704i	0.739170	−	0.673519i	$-0.235218\pi$
$140$		0			0
$141$	−20.3076			−0.144026
$142$	11.2110	+	131.848i	0.0789508	+	0.928505i
$143$		−	31.1346i		−	0.217725i
$144$	−45.2634	+	15.9759i	−0.314329	+	0.110944i
$145$		0			0
$146$	−31.1535	+	2.64899i	−0.213380	+	0.0181437i
$147$			181.274i			1.23315i
$148$	74.6248	−	12.7831i	0.504222	−	0.0863725i
$149$	−50.2274			−0.337096			−0.168548	−	0.985693i	$-0.553908\pi$
$149$	−50.2274			−0.337096			−0.168548	+	0.985693i	$0.553908\pi$
$150$		0			0
$151$		−	213.160i		−	1.41166i	−0.708382	−	0.705829i	$-0.750575\pi$
$151$		−	213.160i		−	1.41166i	0.708382	−	0.705829i	$-0.249425\pi$
$152$	−56.3752	−	216.730i	−0.370890	−	1.42585i
$153$	19.5782			0.127962
$154$	272.725	−	23.1898i	1.77094	−	0.150583i
$155$		0			0
$156$	3.29880	+	19.2576i	0.0211462	+	0.123446i
$157$	−203.918			−1.29884			−0.649419	−	0.760431i	$-0.724988\pi$
$157$	−203.918			−1.29884			−0.649419	+	0.760431i	$0.724988\pi$
$158$	20.8518	+	245.228i	0.131973	+	1.55208i
$159$			71.3051i			0.448460i
$160$		0			0
$161$	97.9798			0.608570
$162$	17.9353	−	1.52504i	0.110712	−	0.00941381i
$163$		−	215.898i		−	1.32452i	−0.749272	−	0.662262i	$-0.769596\pi$
$163$		−	215.898i		−	1.32452i	0.749272	−	0.662262i	$-0.230404\pi$
$164$	20.9118	−	3.58216i	0.127511	−	0.0218425i
$165$		0			0
$166$	16.8889	+	198.623i	0.101741	+	1.19653i
$167$			255.029i			1.52712i	0.645737	+	0.763560i	$0.276550\pi$
$167$			255.029i			1.52712i	−0.645737	+	0.763560i	$0.723450\pi$
$168$	−166.231	+	43.2396i	−0.989470	+	0.257378i
$169$	−161.047			−0.952942
$170$		0			0
$171$			83.9783i			0.491101i
$172$	30.7875	+	179.730i	0.178997	+	1.04494i
$173$	235.426			1.36084			0.680421	−	0.732822i	$-0.261797\pi$
$173$	235.426			1.36084			0.680421	+	0.732822i	$0.261797\pi$
$174$	−14.8851	−	175.057i	−0.0855465	−	1.00607i
$175$		0			0
$176$	58.7929	+	166.574i	0.334051	+	0.946443i
$177$	18.5343			0.104714
$178$	201.439	−	17.1284i	1.13168	−	0.0962267i
$179$		−	102.669i		−	0.573572i	−0.957995	−	0.286786i	$-0.907413\pi$
$179$		−	102.669i		−	0.573572i	0.957995	−	0.286786i	$-0.0925869\pi$
$180$		0			0
$181$	−56.8222			−0.313935			−0.156967	−	0.987604i	$-0.550172\pi$
$181$	−56.8222			−0.313935			−0.156967	+	0.987604i	$0.550172\pi$
$182$	5.92350	+	69.6636i	0.0325467	+	0.382767i
$183$		−	97.2195i		−	0.531254i
$184$	15.9185	+	61.1972i	0.0865134	+	0.332594i
$185$		0			0
$186$	125.456	−	10.6675i	0.674493	−	0.0573522i
$187$		−	72.0498i		−	0.385293i
$188$	−7.91830	−	46.2251i	−0.0421186	−	0.245878i
$189$	64.4110			0.340799
$190$		0			0
$191$			158.493i			0.829808i	0.909865	+	0.414904i	$0.136185\pi$
$191$			158.493i			0.829808i	−0.909865	+	0.414904i	$0.863815\pi$
$192$	−54.0140	−	96.8013i	−0.281323	−	0.504173i
$193$	156.732			0.812084			0.406042	−	0.913854i	$-0.366909\pi$
$193$	156.732			0.812084			0.406042	+	0.913854i	$0.366909\pi$
$194$	−253.671	+	21.5697i	−1.30758	+	0.111184i
$195$		0			0
$196$	−412.624	+	70.6819i	−2.10522	+	0.360622i
$197$	−260.127			−1.32044			−0.660221	−	0.751072i	$-0.729537\pi$
$197$	−260.127			−1.32044			−0.660221	+	0.751072i	$0.729537\pi$
$198$	−5.61230	−	66.0037i	−0.0283449	−	0.333352i
$199$		−	14.0326i		−	0.0705157i	−0.999378	−	0.0352579i	$-0.988775\pi$
$199$		−	14.0326i		−	0.0705157i	0.999378	−	0.0352579i	$-0.0112253\pi$
$200$		0			0
$201$	28.0089			0.139348
$202$	−188.028	+	15.9881i	−0.930834	+	0.0791489i
$203$		−	628.682i		−	3.09696i
$204$	7.63389	+	44.5648i	0.0374210	+	0.218455i
$205$		0			0
$206$	5.39618	+	63.4620i	0.0261950	+	0.308068i
$207$		−	23.7126i		−	0.114554i
$208$	−42.5488	+	15.0178i	−0.204562	+	0.0722009i
$209$	309.049			1.47870
$210$		0			0
$211$			74.4941i			0.353052i	0.984296	+	0.176526i	$0.0564860\pi$
$211$			74.4941i			0.353052i	−0.984296	+	0.176526i	$0.943514\pi$
$212$	−162.308	+	27.8031i	−0.765604	+	0.131147i
$213$	114.595			0.538007
$214$	−5.72587	−	67.3393i	−0.0267564	−	0.314670i
$215$		0			0
$216$	10.4646	+	40.2305i	0.0484474	+	0.186252i
$217$	450.550			2.07627
$218$	−166.253	+	14.1365i	−0.762630	+	0.0648465i
$219$			27.0771i			0.123640i
$220$		0			0
$221$	18.4041			0.0832763
$222$	−5.55523	−	65.3326i	−0.0250236	−	0.294291i
$223$		−	159.996i		−	0.717471i	−0.933439	−	0.358736i	$-0.883208\pi$
$223$		−	159.996i		−	0.717471i	0.933439	−	0.358736i	$-0.116792\pi$
$224$	−163.240	−	361.523i	−0.728752	−	1.61394i
$225$		0			0
$226$	222.787	−	18.9436i	0.985784	−	0.0838213i
$227$		−	175.978i		−	0.775236i	−0.921820	−	0.387618i	$-0.873298\pi$
$227$		−	175.978i		−	0.775236i	0.921820	−	0.387618i	$-0.126702\pi$
$228$	−191.155	+	32.7446i	−0.838400	+	0.143617i
$229$	−114.170			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$229$	−114.170			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$230$		0			0
$231$		−	237.039i		−	1.02614i
$232$	392.668	−	102.140i	1.69254	−	0.440258i
$233$	−260.062			−1.11615			−0.558073	−	0.829792i	$-0.688459\pi$
$233$	−260.062			−1.11615			−0.558073	+	0.829792i	$0.688459\pi$
$234$	16.8597	−	1.43358i	0.0720499	−	0.00612641i
$235$		0			0
$236$	7.22687	+	42.1887i	0.0306223	+	0.178766i
$237$	213.140			0.899327
$238$	13.7078	+	161.211i	0.0575958	+	0.677358i
$239$		−	140.089i		−	0.586147i	−0.956090	−	0.293073i	$-0.905322\pi$
$239$		−	140.089i		−	0.586147i	0.956090	−	0.293073i	$-0.0946780\pi$
$240$		0			0
$241$	105.920			0.439503			0.219752	−	0.975556i	$-0.429475\pi$
$241$	105.920			0.439503			0.219752	+	0.975556i	$0.429475\pi$
$242$	−1.77070	+	0.150563i	−0.00731693	+	0.000622159i
$243$		−	15.5885i		−	0.0641500i
$244$	221.296	−	37.9076i	0.906949	−	0.155359i
$245$		0			0
$246$	−1.55672	−	18.3079i	−0.00632813	−	0.0744223i
$247$			78.9419i			0.319603i
$248$	73.1993	+	281.409i	0.295159	+	1.13471i
$249$	172.633			0.693307
$250$		0			0
$251$		−	167.879i		−	0.668839i	−0.942424	−	0.334420i	$-0.891460\pi$
$251$		−	167.879i		−	0.668839i	0.942424	−	0.334420i	$-0.108540\pi$
$252$	25.1150	+	146.615i	0.0996627	+	0.581807i
$253$	−87.2650			−0.344921
$254$	−2.82733	−	33.2510i	−0.0111312	−	0.130909i
$255$		0			0
$256$	199.282	−	160.694i	0.778447	−	0.627710i
$257$	−198.849			−0.773732			−0.386866	−	0.922136i	$-0.626442\pi$
$257$	−198.849			−0.773732			−0.386866	+	0.922136i	$0.626442\pi$
$258$	157.350	−	13.3795i	0.609884	−	0.0518585i
$259$		−	234.629i		−	0.905903i
$260$		0			0
$261$	−152.151			−0.582953
$262$	−33.2827	−	391.423i	−0.127033	−	1.49398i
$263$			480.528i			1.82710i	0.406722	+	0.913552i	$0.366672\pi$
$263$			480.528i			1.82710i	−0.406722	+	0.913552i	$0.633328\pi$
$264$	148.052	−	38.5110i	0.560804	−	0.145875i
$265$		0			0
$266$	−691.496	+	58.7979i	−2.59961	+	0.221045i
$267$		−	175.081i		−	0.655733i
$268$	10.9212	+	63.7552i	0.0407506	+	0.237892i
$269$	−291.496			−1.08363			−0.541815	−	0.840498i	$-0.682263\pi$
$269$	−291.496			−1.08363			−0.541815	+	0.840498i	$0.682263\pi$
$270$		0			0
$271$		−	174.063i		−	0.642299i	−0.947029	−	0.321150i	$-0.895931\pi$
$271$		−	174.063i		−	0.642299i	0.947029	−	0.321150i	$-0.104069\pi$
$272$	−98.4638	+	34.7532i	−0.361999	+	0.127769i
$273$	60.5482			0.221788
$274$	233.412	−	19.8470i	0.851868	−	0.0724344i
$275$		0			0
$276$	53.9758	−	9.24598i	0.195564	−	0.0334999i
$277$	50.5203			0.182384			0.0911918	−	0.995833i	$-0.470932\pi$
$277$	50.5203			0.182384			0.0911918	+	0.995833i	$0.470932\pi$
$278$	−31.7273	−	373.130i	−0.114127	−	1.34219i
$279$		−	109.040i		−	0.390824i
$280$		0			0
$281$	−66.0514			−0.235058			−0.117529	−	0.993069i	$-0.537497\pi$
$281$	−66.0514			−0.235058			−0.117529	+	0.993069i	$0.537497\pi$
$282$	−40.4692	+	3.44110i	−0.143508	+	0.0122025i
$283$		−	116.934i		−	0.413196i	−0.978426	−	0.206598i	$-0.933761\pi$
$283$		−	116.934i		−	0.413196i	0.978426	−	0.206598i	$-0.0662392\pi$
$284$	44.6828	+	260.848i	0.157334	+	0.918477i
$285$		0			0
$286$	−5.27572	−	62.0454i	−0.0184466	−	0.216942i
$287$		−	65.7491i		−	0.229091i
$288$	−87.4941	+	39.5067i	−0.303799	+	0.137176i
$289$	−246.411			−0.852631
$290$		0			0
$291$			220.478i			0.757658i
$292$	−61.6341	+	10.5578i	−0.211076	+	0.0361570i
$293$	68.3732			0.233356			0.116678	−	0.993170i	$-0.462776\pi$
$293$	68.3732			0.233356			0.116678	+	0.993170i	$0.462776\pi$
$294$	30.7166	+	361.244i	0.104478	+	1.22872i
$295$		0			0
$296$	146.547	−	38.1194i	0.495091	−	0.128782i
$297$	−57.3672			−0.193155
$298$	−100.094	+	8.51096i	−0.335884	+	0.0285603i
$299$		−	22.2905i		−	0.0745503i
$300$		0			0
$301$	565.092			1.87738
$302$	−36.1197	−	424.788i	−0.119602	−	1.40658i
$303$			163.425i			0.539356i
$304$	−149.070	−	422.349i	−0.490361	−	1.38930i
$305$		0			0
$306$	39.0156	−	3.31750i	0.127502	−	0.0108415i
$307$			369.497i			1.20357i	0.798657	+	0.601786i	$0.205544\pi$
$307$			369.497i			1.20357i	−0.798657	+	0.601786i	$0.794456\pi$
$308$	539.560	−	92.4258i	1.75182	−	0.300084i
$309$	55.1580			0.178505
$310$		0			0
$311$		−	303.446i		−	0.975712i	−0.872924	−	0.487856i	$-0.837779\pi$
$311$		−	303.446i		−	0.975712i	0.872924	−	0.487856i	$-0.162221\pi$
$312$	9.83707	+	37.8178i	0.0315291	+	0.121211i
$313$	−297.693			−0.951097			−0.475549	−	0.879689i	$-0.657750\pi$
$313$	−297.693			−0.951097			−0.475549	+	0.879689i	$0.657750\pi$
$314$	−406.369	+	34.5536i	−1.29417	+	0.110043i
$315$		0			0
$316$	83.1072	+	485.160i	0.262998	+	1.53532i
$317$	−264.678			−0.834948			−0.417474	−	0.908689i	$-0.637084\pi$
$317$	−264.678			−0.834948			−0.417474	+	0.908689i	$0.637084\pi$
$318$	12.0826	+	142.097i	0.0379955	+	0.446847i
$319$			559.931i			1.75527i
$320$		0			0
$321$	−58.5280			−0.182330
$322$	195.255	−	16.6026i	0.606382	−	0.0515607i
$323$			182.682i			0.565580i
$324$	35.4832	−	6.07822i	0.109516	−	0.0187599i
$325$		0			0
$326$	−36.5835	−	430.243i	−0.112219	−	1.31976i
$327$			144.499i			0.441893i
$328$	41.0663	−	10.6820i	0.125202	−	0.0325672i
$329$	−145.337			−0.441754
$330$		0			0
$331$			473.426i			1.43029i	0.698976	+	0.715145i	$0.253639\pi$
$331$			473.426i			1.43029i	−0.698976	+	0.715145i	$0.746361\pi$
$332$	67.3129	+	392.956i	0.202750	+	1.18360i
$333$	−56.7838			−0.170522
$334$	43.2143	+	508.224i	0.129384	+	1.52163i
$335$		0			0
$336$	−323.940	+	114.336i	−0.964107	+	0.340285i
$337$	−29.7588			−0.0883051			−0.0441526	−	0.999025i	$-0.514059\pi$
$337$	−29.7588			−0.0883051			−0.0441526	+	0.999025i	$0.514059\pi$
$338$	−320.936	+	27.2892i	−0.949515	+	0.0807373i
$339$		−	193.636i		−	0.571197i
$340$		0			0
$341$	−401.278			−1.17677
$342$	14.2300	+	167.353i	0.0416082	+	0.489335i
$343$			689.937i			2.01148i
$344$	91.8086	+	352.951i	0.266885	+	1.02602i
$345$		0			0
$346$	469.158	−	39.8925i	1.35595	−	0.115296i
$347$		−	306.190i		−	0.882391i	−0.897411	−	0.441195i	$-0.854555\pi$
$347$		−	306.190i		−	0.882391i	0.897411	−	0.441195i	$-0.145445\pi$
$348$	−59.3263	−	346.333i	−0.170478	−	0.995208i
$349$	649.149			1.86002			0.930012	−	0.367528i	$-0.119796\pi$
$349$	649.149			1.86002			0.930012	+	0.367528i	$0.119796\pi$
$350$		0			0
$351$		−	14.6536i		−	0.0417481i
$352$	145.389	+	321.988i	0.413036	+	0.914737i
$353$	275.547			0.780587			0.390293	−	0.920691i	$-0.372374\pi$
$353$	275.547			0.780587			0.390293	+	0.920691i	$0.372374\pi$
$354$	36.9354	−	3.14062i	0.104337	−	0.00887181i
$355$		0			0
$356$	398.527	−	68.2671i	1.11946	−	0.191761i
$357$	140.117			0.392484
$358$	−17.3972	−	204.600i	−0.0485955	−	0.571510i
$359$			507.672i			1.41413i	0.707149	+	0.707065i	$0.249981\pi$
$359$			507.672i			1.41413i	−0.707149	+	0.707065i	$0.750019\pi$
$360$		0			0
$361$	−422.594			−1.17062
$362$	−113.236	+	9.62845i	−0.312806	+	0.0265979i
$363$			1.53900i			0.00423968i
$364$	23.6088	+	137.823i	0.0648594	+	0.378633i
$365$		0			0
$366$	−16.4737	−	193.740i	−0.0450102	−	0.529344i
$367$			62.7671i			0.171028i	0.996337	+	0.0855138i	$0.0272532\pi$
$367$			62.7671i			0.171028i	−0.996337	+	0.0855138i	$0.972747\pi$
$368$	42.0923	+	119.257i	0.114381	+	0.324068i
$369$	−15.9123			−0.0431228
$370$		0			0
$371$			510.315i			1.37551i
$372$	248.202	−	42.5166i	0.667209	−	0.114292i
$373$	272.776			0.731302			0.365651	−	0.930752i	$-0.380846\pi$
$373$	272.776			0.731302			0.365651	+	0.930752i	$0.380846\pi$
$374$	−12.2087	−	143.581i	−0.0326437	−	0.383908i
$375$		0			0
$376$	−23.6124	−	90.7761i	−0.0627990	−	0.241426i
$377$	−143.026			−0.379379
$378$	128.359	−	10.9144i	0.339574	−	0.0288740i
$379$			376.828i			0.994270i	0.867673	+	0.497135i	$0.165615\pi$
$379$			376.828i			0.994270i	−0.867673	+	0.497135i	$0.834385\pi$
$380$		0			0
$381$	−28.9001			−0.0758533
$382$	26.8565	+	315.847i	0.0703049	+	0.826825i
$383$			412.206i			1.07625i	0.842864	+	0.538127i	$0.180868\pi$
$383$			412.206i			1.07625i	−0.842864	+	0.538127i	$0.819132\pi$
$384$	−124.042	−	183.754i	−0.323027	−	0.478526i
$385$		0			0
$386$	312.337	−	26.5581i	0.809164	−	0.0688032i
$387$		−	136.761i		−	0.353387i
$388$	−501.863	+	85.9685i	−1.29346	+	0.221568i
$389$	−161.289			−0.414623			−0.207312	−	0.978275i	$-0.566471\pi$
$389$	−161.289			−0.414623			−0.207312	+	0.978275i	$0.566471\pi$
$390$		0			0
$391$		−	51.5834i		−	0.131927i
$392$	−810.303	+	210.774i	−2.06710	+	0.537689i
$393$	−340.206			−0.865663
$394$	−518.383	+	44.0782i	−1.31569	+	0.111874i
$395$		0			0
$396$	−22.3685	−	130.582i	−0.0564861	−	0.329752i
$397$	186.505			0.469785			0.234893	−	0.972021i	$-0.424526\pi$
$397$	186.505			0.469785			0.234893	+	0.972021i	$0.424526\pi$
$398$	−2.37781	−	27.9643i	−0.00597440	−	0.0702622i
$399$			601.014i			1.50630i
$400$		0			0
$401$	239.061			0.596162			0.298081	−	0.954541i	$-0.403653\pi$
$401$	239.061			0.596162			0.298081	+	0.954541i	$0.403653\pi$
$402$	55.8164	−	4.74607i	0.138847	−	0.0118061i
$403$		−	102.501i		−	0.254344i
$404$	−371.996	+	63.7223i	−0.920781	+	0.157729i
$405$		0			0
$406$	−106.529	−	1252.84i	−0.262387	−	3.08582i
$407$			208.970i			0.513441i
$408$	22.7643	+	87.5155i	0.0557949	+	0.214499i
$409$	47.8016			0.116874			0.0584372	−	0.998291i	$-0.481388\pi$
$409$	47.8016			0.116874			0.0584372	+	0.998291i	$0.481388\pi$
$410$		0			0
$411$		−	202.870i		−	0.493601i
$412$	21.5071	+	125.553i	0.0522017	+	0.304741i
$413$	132.646			0.321177
$414$	−4.01807	−	47.2547i	−0.00970549	−	0.114142i
$415$		0			0
$416$	−82.2470	+	37.1374i	−0.197709	+	0.0892726i
$417$	−324.306			−0.777713
$418$	615.875	−	52.3679i	1.47339	−	0.125282i
$419$		−	239.009i		−	0.570428i	−0.958464	−	0.285214i	$-0.907935\pi$
$419$		−	239.009i		−	0.570428i	0.958464	−	0.285214i	$-0.0920647\pi$
$420$		0			0
$421$	−257.592			−0.611857			−0.305929	−	0.952054i	$-0.598967\pi$
$421$	−257.592			−0.611857			−0.305929	+	0.952054i	$0.598967\pi$
$422$	12.6229	+	148.452i	0.0299121	+	0.351783i
$423$			35.1738i			0.0831532i
$424$	−318.738	+	82.9092i	−0.751740	+	0.195541i
$425$		0			0
$426$	228.367	−	19.4181i	0.536073	−	0.0455823i
$427$		−	695.779i		−	1.62946i
$428$	−22.8211	−	133.224i	−0.0533204	−	0.311271i
$429$	−53.9268			−0.125703
$430$		0			0
$431$			343.164i			0.796205i	0.917341	+	0.398103i	$0.130331\pi$
$431$			343.164i			0.796205i	−0.917341	+	0.398103i	$0.869669\pi$
$432$	27.6710	+	78.3984i	0.0640533	+	0.181478i
$433$	234.760			0.542171			0.271085	−	0.962555i	$-0.412617\pi$
$433$	234.760			0.542171			0.271085	+	0.962555i	$0.412617\pi$
$434$	897.859	−	76.3450i	2.06880	−	0.175910i
$435$		0			0
$436$	−328.916	+	56.3428i	−0.754394	+	0.129227i
$437$	221.261			0.506317
$438$	4.58818	+	53.9595i	0.0104753	+	0.123195i
$439$		−	374.473i		−	0.853013i	−0.904484	−	0.426507i	$-0.859744\pi$
$439$		−	374.473i		−	0.853013i	0.904484	−	0.426507i	$-0.140256\pi$
$440$		0			0
$441$	313.975			0.711962
$442$	36.6758	−	3.11854i	0.0829768	−	0.00705553i
$443$		−	108.557i		−	0.245050i	−0.992465	−	0.122525i	$-0.960901\pi$
$443$		−	108.557i		−	0.245050i	0.992465	−	0.122525i	$-0.0390992\pi$
$444$	−22.1410	−	129.254i	−0.0498672	−	0.291113i
$445$		0			0
$446$	−27.1111	−	318.842i	−0.0607873	−	0.714891i
$447$			86.9963i			0.194623i
$448$	−386.566	−	692.785i	−0.862872	−	1.54640i
$449$	−431.511			−0.961050			−0.480525	−	0.876981i	$-0.659554\pi$
$449$	−431.511			−0.961050			−0.480525	+	0.876981i	$0.659554\pi$
$450$		0			0
$451$			58.5589i			0.129842i
$452$	440.762	−	75.5020i	0.975138	−	0.167040i
$453$	−369.205			−0.815021
$454$	−29.8193	−	350.692i	−0.0656813	−	0.772448i
$455$		0			0
$456$	−375.387	+	97.6448i	−0.823218	+	0.214133i
$457$	−219.747			−0.480847			−0.240424	−	0.970668i	$-0.577286\pi$
$457$	−219.747			−0.480847			−0.240424	+	0.970668i	$0.577286\pi$
$458$	−227.520	+	19.3460i	−0.496768	+	0.0422402i
$459$		−	33.9104i		−	0.0738789i
$460$		0			0
$461$	223.434			0.484673			0.242337	−	0.970192i	$-0.422086\pi$
$461$	223.434			0.484673			0.242337	+	0.970192i	$0.422086\pi$
$462$	−40.1660	−	472.374i	−0.0869394	−	1.02245i
$463$			740.855i			1.60012i	0.599921	+	0.800059i	$0.295198\pi$
$463$			740.855i			1.60012i	−0.599921	+	0.800059i	$0.704802\pi$
$464$	765.206	−	270.082i	1.64915	−	0.582074i
$465$		0			0
$466$	−518.254	+	44.0672i	−1.11213	+	0.0945648i
$467$			249.381i			0.534007i	0.963696	+	0.267004i	$0.0860336\pi$
$467$			249.381i			0.534007i	−0.963696	+	0.267004i	$0.913966\pi$
$468$	33.3552	−	5.71370i	0.0712718	−	0.0122088i
$469$	200.454			0.427406
$470$		0			0
$471$			353.196i			0.749885i
$472$	21.5506	+	82.8495i	0.0456580	+	0.175529i
$473$	−503.294			−1.06405
$474$	424.748	−	36.1164i	0.896093	−	0.0761948i
$475$		0			0
$476$	54.6340	+	318.940i	0.114777	+	0.670043i
$477$	123.504			0.258918
$478$	−23.7379	−	279.171i	−0.0496609	−	0.584039i
$479$			210.915i			0.440324i	0.975463	+	0.220162i	$0.0706587\pi$
$479$			210.915i			0.440324i	−0.975463	+	0.220162i	$0.929341\pi$
$480$		0			0
$481$	−53.3784			−0.110974
$482$	211.079	−	17.9480i	0.437923	−	0.0372366i
$483$		−	169.706i		−	0.351358i
$484$	−3.50315	+	0.600085i	−0.00723791	+	0.00123984i
$485$		0			0
$486$	−2.64144	−	31.0648i	−0.00543507	−	0.0639194i
$487$		−	710.541i		−	1.45902i	−0.683972	−	0.729508i	$-0.739749\pi$
$487$		−	710.541i		−	1.45902i	0.683972	−	0.729508i	$-0.260251\pi$
$488$	434.576	−	113.041i	0.890525	−	0.231641i
$489$	−373.946			−0.764715
$490$		0			0
$491$			697.876i			1.42134i	0.703528	+	0.710668i	$0.251607\pi$
$491$			697.876i			1.42134i	−0.703528	+	0.710668i	$0.748393\pi$
$492$	−6.20449	−	36.2203i	−0.0126108	−	0.0736185i
$493$	−330.982			−0.671363
$494$	13.3766	+	157.316i	0.0270781	+	0.318454i
$495$		0			0
$496$	193.557	+	548.390i	0.390235	+	1.10563i
$497$	820.135			1.65017
$498$	344.025	−	29.2525i	0.690814	−	0.0587400i
$499$		−	875.602i		−	1.75471i	−0.479838	−	0.877357i	$-0.659305\pi$
$499$		−	875.602i		−	1.75471i	0.479838	−	0.877357i	$-0.340695\pi$
$500$		0			0
$501$	441.723			0.881683
$502$	−28.4468	−	334.550i	−0.0566670	−	0.666434i
$503$		−	142.849i		−	0.283995i	−0.989867	−	0.141997i	$-0.954648\pi$
$503$		−	142.849i		−	0.283995i	0.989867	−	0.141997i	$-0.0453524\pi$
$504$	74.8932	+	287.921i	0.148598	+	0.571271i
$505$		0			0
$506$	−173.902	+	14.7869i	−0.343681	+	0.0292232i
$507$			278.942i			0.550181i
$508$	−11.2687	−	65.7837i	−0.0221824	−	0.129496i
$509$	−147.662			−0.290102			−0.145051	−	0.989424i	$-0.546335\pi$
$509$	−147.662			−0.290102			−0.145051	+	0.989424i	$0.546335\pi$
$510$		0			0
$511$			193.785i			0.379227i
$512$	369.903	−	354.000i	0.722466	−	0.691407i
$513$	145.455			0.283537
$514$	−396.268	+	33.6947i	−0.770950	+	0.0655539i
$515$		0			0
$516$	311.301	−	53.3255i	0.603297	−	0.103344i
$517$	129.443			0.250374
$518$	−39.7576	−	467.571i	−0.0767520	−	0.902646i
$519$		−	407.769i		−	0.785682i
$520$		0			0
$521$	−348.592			−0.669082			−0.334541	−	0.942381i	$-0.608581\pi$
$521$	−348.592			−0.669082			−0.334541	+	0.942381i	$0.608581\pi$
$522$	−303.207	+	25.7817i	−0.580857	+	0.0493903i
$523$		−	370.317i		−	0.708063i	−0.935233	−	0.354032i	$-0.884811\pi$
$523$		−	370.317i		−	0.708063i	0.935233	−	0.354032i	$-0.115189\pi$
$524$	−132.652	−	774.392i	−0.253153	−	1.47785i
$525$		0			0
$526$	81.4249	+	957.601i	0.154800	+	1.82053i
$527$		−	237.201i		−	0.450096i
$528$	288.514	−	101.832i	0.546429	−	0.192864i
$529$	466.523			0.881897
$530$		0			0
$531$		−	32.1024i		−	0.0604565i
$532$	−1368.06	+	234.346i	−2.57153	+	0.440500i
$533$	−14.9580			−0.0280638
$534$	−29.6672	−	348.902i	−0.0555565	−	0.653375i
$535$		0			0
$536$	32.5670	+	125.201i	0.0607594	+	0.233584i
$537$	−177.829			−0.331152
$538$	−580.897	+	49.3937i	−1.07973	+	0.0918098i
$539$		−	1155.46i		−	2.14371i
$540$		0			0
$541$	−279.719			−0.517041			−0.258520	−	0.966006i	$-0.583235\pi$
$541$	−279.719			−0.517041			−0.258520	+	0.966006i	$0.583235\pi$
$542$	−29.4947	−	346.874i	−0.0544183	−	0.639990i
$543$			98.4190i			0.181250i
$544$	−190.331	+	85.9411i	−0.349873	+	0.157980i
$545$		0			0
$546$	120.661	−	10.2598i	0.220991	−	0.0187909i
$547$			387.716i			0.708804i	0.935093	+	0.354402i	$0.115315\pi$
$547$			387.716i			0.708804i	−0.935093	+	0.354402i	$0.884685\pi$
$548$	461.782	−	79.1026i	0.842668	−	0.144348i
$549$	−168.389			−0.306720
$550$		0			0
$551$		−	1419.71i		−	2.57660i
$552$	105.997	−	27.5716i	0.192023	−	0.0499485i
$553$	1525.40			2.75841
$554$	100.677	−	8.56059i	0.181728	−	0.0154523i
$555$		0			0
$556$	−126.453	−	738.201i	−0.227433	−	1.32770i
$557$	−43.5564			−0.0781983			−0.0390991	−	0.999235i	$-0.512449\pi$
$557$	−43.5564			−0.0781983			−0.0390991	+	0.999235i	$0.512449\pi$
$558$	−18.4767	−	217.296i	−0.0331123	−	0.389419i
$559$		−	128.559i		−	0.229981i
$560$		0			0
$561$	−124.794			−0.222449
$562$	−131.628	+	11.1923i	−0.234213	+	0.0199152i
$563$			361.646i			0.642355i	0.947019	+	0.321178i	$0.104079\pi$
$563$			361.646i			0.642355i	−0.947019	+	0.321178i	$0.895921\pi$
$564$	−80.0642	+	13.7149i	−0.141958	+	0.0243172i
$565$		0			0
$566$	−19.8144	−	233.028i	−0.0350078	−	0.411710i
$567$		−	111.563i		−	0.196760i
$568$	133.245	+	512.248i	0.234586	+	0.901845i
$569$	888.559			1.56161			0.780807	−	0.624772i	$-0.214808\pi$
$569$	888.559			1.56161			0.780807	+	0.624772i	$0.214808\pi$
$570$		0			0
$571$		−	447.745i		−	0.784142i	−0.919935	−	0.392071i	$-0.871759\pi$
$571$		−	447.745i		−	0.784142i	0.919935	−	0.392071i	$-0.128241\pi$
$572$	−21.0270	−	122.751i	−0.0367605	−	0.214599i
$573$	274.519			0.479090
$574$	−11.1411	−	131.025i	−0.0194096	−	0.228267i
$575$		0			0
$576$	−167.665	+	93.5551i	−0.291085	+	0.162422i
$577$	−1069.90			−1.85425			−0.927124	−	0.374756i	$-0.877727\pi$
$577$	−1069.90			−1.85425			−0.927124	+	0.374756i	$0.877727\pi$
$578$	−491.049	+	41.7539i	−0.849566	+	0.0722386i
$579$		−	271.468i		−	0.468857i
$580$		0			0
$581$	1235.50			2.12651
$582$	37.3598	+	439.371i	0.0641921	+	0.754934i
$583$		−	454.508i		−	0.779602i
$584$	−121.036	+	31.4836i	−0.207253	+	0.0539102i
$585$		0			0
$586$	136.255	−	11.5857i	0.232517	−	0.0197709i
$587$			129.637i			0.220847i	0.993885	+	0.110424i	$0.0352208\pi$
$587$			129.637i			0.220847i	−0.993885	+	0.110424i	$0.964779\pi$
$588$	122.425	+	714.685i	0.208205	+	1.21545i
$589$	1017.44			1.72741
$590$		0			0
$591$			450.553i			0.762357i
$592$	285.581	−	100.797i	0.482400	−	0.170265i
$593$	−892.757			−1.50549			−0.752746	−	0.658311i	$-0.771271\pi$
$593$	−892.757			−1.50549			−0.752746	+	0.658311i	$0.771271\pi$
$594$	−114.322	+	9.72079i	−0.192461	+	0.0163650i
$595$		0			0
$596$	−198.025	+	33.9214i	−0.332257	+	0.0569151i
$597$	−24.3052			−0.0407123
$598$	−3.77710	−	44.4208i	−0.00631623	−	0.0742823i
$599$			1030.62i			1.72057i	0.509816	+	0.860284i	$0.329714\pi$
$599$			1030.62i			1.72057i	−0.509816	+	0.860284i	$0.670286\pi$
$600$		0			0
$601$	−815.961			−1.35767			−0.678836	−	0.734289i	$-0.737515\pi$
$601$	−815.961			−1.35767			−0.678836	+	0.734289i	$0.737515\pi$
$602$	1126.12	−	95.7540i	1.87063	−	0.159060i
$603$		−	48.5128i		−	0.0804525i
$604$	−143.959	−	840.401i	−0.238343	−	1.39139i
$605$		0			0
$606$	27.6921	+	325.675i	0.0456966	+	0.537417i
$607$			842.678i			1.38827i	0.719847	+	0.694133i	$0.244212\pi$
$607$			842.678i			1.38827i	−0.719847	+	0.694133i	$0.755788\pi$
$608$	−368.634	−	816.400i	−0.606305	−	1.34276i
$609$	−1088.91			−1.78803
$610$		0			0
$611$			33.0644i			0.0541152i
$612$	77.1885	−	13.2223i	0.126125	−	0.0216050i
$613$	731.088			1.19264			0.596320	−	0.802747i	$-0.296629\pi$
$613$	731.088			1.19264			0.596320	+	0.802747i	$0.296629\pi$
$614$	62.6107	+	736.336i	0.101972	+	1.19924i
$615$		0			0
$616$	1059.58	−	275.615i	1.72009	−	0.447426i
$617$	919.609			1.49045			0.745226	−	0.666812i	$-0.232342\pi$
$617$	919.609			1.49045			0.745226	+	0.666812i	$0.232342\pi$
$618$	109.919	−	9.34645i	0.177863	−	0.0151237i
$619$			688.974i			1.11304i	0.830833	+	0.556522i	$0.187865\pi$
$619$			688.974i			1.11304i	−0.830833	+	0.556522i	$0.812135\pi$
$620$		0			0
$621$	−41.0715			−0.0661377
$622$	−51.4186	−	604.711i	−0.0826665	−	0.972203i
$623$		−	1253.01i		−	2.01126i
$624$	26.0116	+	73.6968i	0.0416852	+	0.118104i
$625$		0			0
$626$	−593.246	+	50.4438i	−0.947678	+	0.0805811i
$627$		−	535.288i		−	0.853729i
$628$	−803.960	+	137.717i	−1.28019	+	0.219295i
$629$	−123.525			−0.196383
$630$		0			0
$631$			418.968i			0.663975i	0.943284	+	0.331987i	$0.107719\pi$
$631$			418.968i			0.663975i	−0.943284	+	0.331987i	$0.892281\pi$
$632$	247.827	+	952.749i	0.392131	+	1.50751i
$633$	129.027			0.203835
$634$	−527.454	+	44.8494i	−0.831946	+	0.0707404i
$635$		0			0
$636$	48.1565	+	281.126i	0.0757177	+	0.442022i
$637$	295.146			0.463337
$638$	94.8795	+	1115.83i	0.148714	+	1.74896i
$639$		−	198.485i		−	0.310618i
$640$		0			0
$641$	−47.2426			−0.0737014			−0.0368507	−	0.999321i	$-0.511733\pi$
$641$	−47.2426			−0.0737014			−0.0368507	+	0.999321i	$0.511733\pi$
$642$	−116.635	+	9.91749i	−0.181675	+	0.0154478i
$643$		−	710.880i		−	1.10557i	−0.833325	−	0.552784i	$-0.813565\pi$
$643$		−	710.880i		−	1.10557i	0.833325	−	0.552784i	$-0.186435\pi$
$644$	386.293	−	66.1714i	0.599834	−	0.102751i
$645$		0			0
$646$	30.9553	+	364.051i	0.0479184	+	0.563547i
$647$		−	468.195i		−	0.723641i	−0.932248	−	0.361820i	$-0.882155\pi$
$647$		−	468.195i		−	0.723641i	0.932248	−	0.361820i	$-0.117845\pi$
$648$	69.6812	−	18.1253i	0.107533	−	0.0279711i
$649$	−118.140			−0.182034
$650$		0			0
$651$		−	780.375i		−	1.19873i
$652$	−145.808	−	851.192i	−0.223632	−	1.30551i
$653$	−551.066			−0.843900			−0.421950	−	0.906619i	$-0.638654\pi$
$653$	−551.066			−0.843900			−0.421950	+	0.906619i	$0.638654\pi$
$654$	24.4852	+	287.959i	0.0374391	+	0.440304i
$655$		0			0
$656$	80.0271	−	28.2459i	0.121993	−	0.0430578i
$657$	46.8989			0.0713834
$658$	−289.629	+	24.6272i	−0.440165	+	0.0374273i
$659$		−	158.259i		−	0.240151i	−0.992765	−	0.120075i	$-0.961686\pi$
$659$		−	158.259i		−	0.240151i	0.992765	−	0.120075i	$-0.0383136\pi$
$660$		0			0
$661$	92.4953			0.139932			0.0699662	−	0.997549i	$-0.477711\pi$
$661$	92.4953			0.139932			0.0699662	+	0.997549i	$0.477711\pi$
$662$	80.2214	+	943.447i	0.121180	+	1.42515i
$663$		−	31.8768i		−	0.0480796i
$664$	200.728	+	771.681i	0.302301	+	1.16217i
$665$		0			0
$666$	−113.159	+	9.62194i	−0.169909	+	0.0144474i
$667$			400.877i			0.601015i
$668$	172.236	+	1005.47i	0.257838	+	1.50520i
$669$	−277.121			−0.414232
$670$		0			0
$671$			619.690i			0.923532i
$672$	−626.176	+	282.741i	−0.931810	+	0.420745i
$673$	−956.062			−1.42060			−0.710299	−	0.703900i	$-0.751440\pi$
$673$	−956.062			−1.42060			−0.710299	+	0.703900i	$0.751440\pi$
$674$	−59.3037	+	5.04259i	−0.0879876	+	0.00748159i
$675$		0			0
$676$	−634.940	+	108.764i	−0.939261	+	0.160894i
$677$	−1116.67			−1.64944			−0.824719	−	0.565543i	$-0.808667\pi$
$677$	−1116.67			−1.64944			−0.824719	+	0.565543i	$0.808667\pi$
$678$	−32.8113	−	385.879i	−0.0483942	−	0.569143i
$679$			1577.92i			2.32388i
$680$		0			0
$681$	−304.804			−0.447583
$682$	−799.671	+	67.9961i	−1.17254	+	0.0997010i
$683$		−	826.776i		−	1.21051i	−0.796033	−	0.605254i	$-0.793072\pi$
$683$		−	826.776i		−	1.21051i	0.796033	−	0.605254i	$-0.206928\pi$
$684$	56.7153	+	331.090i	0.0829172	+	0.484050i
$685$		0			0
$686$	116.909	+	1374.91i	0.170421	+	2.00424i
$687$			197.749i			0.287844i
$688$	242.764	+	687.806i	0.352855	+	0.999718i
$689$	116.097			0.168501
$690$		0			0
$691$		−	965.432i		−	1.39715i	−0.715536	−	0.698576i	$-0.753818\pi$
$691$		−	965.432i		−	1.39715i	0.715536	−	0.698576i	$-0.246182\pi$
$692$	928.183	−	158.996i	1.34130	−	0.229764i
$693$	−410.564			−0.592444
$694$	−51.8834	−	610.177i	−0.0747600	−	0.879218i
$695$		0			0
$696$	−176.912	−	680.122i	−0.254183	−	0.977186i
$697$	−34.6149			−0.0496627
$698$	1293.63	−	109.997i	1.85334	−	0.157589i
$699$			450.441i			0.644408i
$700$		0			0
$701$	−1109.94			−1.58337			−0.791686	−	0.610928i	$-0.790797\pi$
$701$	−1109.94			−1.58337			−0.791686	+	0.610928i	$0.790797\pi$
$702$	−2.48303	−	29.2018i	−0.00353708	−	0.0415980i
$703$		−	529.845i		−	0.753691i
$704$	344.292	+	617.024i	0.489052	+	0.876454i
$705$		0			0
$706$	549.113	−	46.6911i	0.777780	−	0.0661347i
$707$			1169.60i			1.65431i
$708$	73.0730	−	12.5173i	0.103210	−	0.0176798i
$709$	−964.244			−1.36001			−0.680003	−	0.733210i	$-0.738021\pi$
$709$	−964.244			−1.36001			−0.680003	+	0.733210i	$0.738021\pi$
$710$		0			0
$711$		−	369.170i		−	0.519226i
$712$	782.620	−	203.573i	1.09919	−	0.285917i
$713$	−287.292			−0.402934
$714$	279.226	−	23.7426i	0.391073	−	0.0332529i
$715$		0			0
$716$	−69.3385	−	404.782i	−0.0968415	−	0.565338i
$717$	−242.641			−0.338412
$718$	86.0244	+	1011.69i	0.119811	+	1.40904i
$719$		−	190.820i		−	0.265396i	−0.991157	−	0.132698i	$-0.957636\pi$
$719$		−	190.820i		−	0.265396i	0.991157	−	0.132698i	$-0.0423641\pi$
$720$		0			0
$721$	394.754			0.547509
$722$	−842.149	+	71.6080i	−1.16641	+	0.0991801i
$723$		−	183.459i		−	0.253747i
$724$	−224.026	+	38.3753i	−0.309428	+	0.0530046i
$725$		0			0
$726$	0.260782	+	3.06694i	0.000359204	+	0.00422443i
$727$			202.134i			0.278039i	0.990290	+	0.139019i	$0.0443951\pi$
$727$			202.134i			0.278039i	−0.990290	+	0.139019i	$0.955605\pi$
$728$	70.4017	+	270.654i	0.0967056	+	0.371777i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	297.503i		−	0.406981i
$732$	−65.6579	−	383.295i	−0.0896966	−	0.523627i
$733$	962.435			1.31301			0.656504	−	0.754322i	$-0.272034\pi$
$733$	962.435			1.31301			0.656504	+	0.754322i	$0.272034\pi$
$734$	10.6358	+	125.083i	0.0144902	+	0.170413i
$735$		0			0
$736$	104.090	+	230.524i	0.141426	+	0.313212i
$737$	−178.532			−0.242242
$738$	−31.7102	+	2.69632i	−0.0429677	+	0.00365355i
$739$		−	932.112i		−	1.26132i	−0.776061	−	0.630658i	$-0.782785\pi$
$739$		−	932.112i		−	1.26132i	0.776061	−	0.630658i	$-0.217215\pi$
$740$		0			0
$741$	136.731			0.184523
$742$	86.4722	+	1016.96i	0.116539	+	1.37057i
$743$			1153.70i			1.55276i	0.630266	+	0.776379i	$0.282946\pi$
$743$			1153.70i			1.55276i	−0.630266	+	0.776379i	$0.717054\pi$
$744$	487.414	−	126.785i	0.655127	−	0.170410i
$745$		0			0
$746$	543.590	−	46.2215i	0.728672	−	0.0619591i
$747$		−	299.010i		−	0.400281i
$748$	−48.6594	−	284.062i	−0.0650526	−	0.379762i
$749$	−418.872			−0.559242
$750$		0			0
$751$		−	204.359i		−	0.272116i	−0.990701	−	0.136058i	$-0.956557\pi$
$751$		−	204.359i		−	0.272116i	0.990701	−	0.136058i	$-0.0434434\pi$
$752$	−62.4369	−	176.898i	−0.0830279	−	0.235237i
$753$	−290.774			−0.386155
$754$	−285.023	+	24.2356i	−0.378015	+	0.0321427i
$755$		0			0
$756$	253.945	−	43.5005i	0.335906	−	0.0575403i
$757$	216.739			0.286314			0.143157	−	0.989700i	$-0.454275\pi$
$757$	216.739			0.286314			0.143157	+	0.989700i	$0.454275\pi$
$758$	63.8530	+	750.947i	0.0842388	+	0.990695i
$759$			151.147i			0.199140i
$760$		0			0
$761$	1324.78			1.74085			0.870424	−	0.492303i	$-0.163845\pi$
$761$	1324.78			1.74085			0.870424	+	0.492303i	$0.163845\pi$
$762$	−57.5924	+	4.89708i	−0.0755805	+	0.00642662i
$763$			1034.15i			1.35537i
$764$	107.040	+	624.872i	0.140104	+	0.817895i
$765$		0			0
$766$	69.8477	+	821.447i	0.0911849	+	1.07238i
$767$		−	30.1772i		−	0.0393444i
$768$	−278.330	−	345.167i	−0.362409	−	0.449437i
$769$	444.088			0.577488			0.288744	−	0.957406i	$-0.406762\pi$
$769$	444.088			0.577488			0.288744	+	0.957406i	$0.406762\pi$
$770$		0			0
$771$			344.417i			0.446714i
$772$	617.928	−	105.850i	0.800425	−	0.137112i
$773$	751.987			0.972817			0.486408	−	0.873732i	$-0.338307\pi$
$773$	751.987			0.972817			0.486408	+	0.873732i	$0.338307\pi$
$774$	−23.1739	−	272.538i	−0.0299405	−	0.352117i
$775$		0			0
$776$	−985.550	+	256.359i	−1.27004	+	0.330359i
$777$	−406.389			−0.523023
$778$	−321.417	+	27.3301i	−0.413133	+	0.0351287i
$779$		−	148.476i		−	0.190599i
$780$		0			0
$781$	−730.446			−0.935271
$782$	−8.74073	−	102.796i	−0.0111774	−	0.131452i
$783$			263.533i			0.336568i
$784$	−1579.06	+	557.337i	−2.01411	+	0.710889i
$785$		0			0
$786$	−677.965	+	57.6474i	−0.862550	+	0.0733427i
$787$		−	442.296i		−	0.562002i	−0.959707	−	0.281001i	$-0.909334\pi$
$787$		−	442.296i		−	0.562002i	0.959707	−	0.281001i	$-0.0906665\pi$
$788$	−1025.57	+	175.679i	−1.30148	+	0.222943i
$789$	832.299			1.05488
$790$		0			0
$791$		−	1385.81i		−	1.75197i
$792$	−66.7030	−	256.434i	−0.0842210	−	0.323781i
$793$	−158.291			−0.199610
$794$	371.668	−	31.6030i	0.468096	−	0.0398022i
$795$		0			0
$796$	−9.47704	−	55.3247i	−0.0119058	−	0.0695034i
$797$	56.2072			0.0705235			0.0352618	−	0.999378i	$-0.488774\pi$
$797$	56.2072			0.0705235			0.0352618	+	0.999378i	$0.488774\pi$
$798$	101.841	+	1197.71i	0.127620	+	1.50088i
$799$			76.5155i			0.0957641i
$800$		0			0
$801$	−303.249			−0.378588
$802$	476.403	−	40.5086i	0.594019	−	0.0505094i
$803$		−	172.593i		−	0.214935i
$804$	110.427	−	18.9160i	0.137347	−	0.0235274i
$805$		0			0
$806$	−17.3686	−	204.264i	−0.0215491	−	0.253430i
$807$			504.887i			0.625634i
$808$	−730.518	+	190.021i	−0.904107	+	0.235174i
$809$	1522.16			1.88153			0.940765	−	0.339060i	$-0.110109\pi$
$809$	1522.16			1.88153			0.940765	+	0.339060i	$0.110109\pi$
$810$		0			0
$811$		−	930.734i		−	1.14764i	−0.818982	−	0.573819i	$-0.805461\pi$
$811$		−	930.734i		−	1.14764i	0.818982	−	0.573819i	$-0.194539\pi$
$812$	−424.585	−	2478.63i	−0.522888	−	3.05249i
$813$	−301.486			−0.370832
$814$	35.4098	+	416.438i	0.0435009	+	0.511595i
$815$		0			0
$816$	60.1943	+	170.544i	0.0737676	+	0.209000i
$817$	1276.10			1.56194
$818$	95.2595	−	8.09992i	0.116454	−	0.00990210i
$819$		−	104.873i		−	0.128049i
$820$		0			0
$821$	349.814			0.426083			0.213041	−	0.977043i	$-0.431663\pi$
$821$	349.814			0.426083			0.213041	+	0.977043i	$0.431663\pi$
$822$	−34.3761	−	404.281i	−0.0418200	−	0.491826i
$823$			61.2187i			0.0743849i	0.999308	+	0.0371924i	$0.0118414\pi$
$823$			61.2187i			0.0743849i	−0.999308	+	0.0371924i	$0.988159\pi$
$824$	64.1344	+	246.559i	0.0778330	+	0.299222i
$825$		0			0
$826$	264.338	−	22.4767i	0.320022	−	0.0272115i
$827$			46.2063i			0.0558721i	0.999610	+	0.0279361i	$0.00889348\pi$
$827$			46.2063i			0.0558721i	−0.999610	+	0.0279361i	$0.991107\pi$
$828$	−16.0145	−	93.4888i	−0.0193412	−	0.112909i
$829$	223.832			0.270002			0.135001	−	0.990845i	$-0.456896\pi$
$829$	223.832			0.270002			0.135001	+	0.990845i	$0.456896\pi$
$830$		0			0
$831$		−	87.5037i		−	0.105299i
$832$	−157.610	+	87.9444i	−0.189435	+	0.105702i
$833$	683.007			0.819937
$834$	−646.280	+	54.9532i	−0.774916	+	0.0658912i
$835$		0			0
$836$	1218.45	−	208.718i	1.45747	−	0.249663i
$837$	−188.863			−0.225642
$838$	−40.4998	−	476.300i	−0.0483291	−	0.568377i
$839$			361.794i			0.431220i	0.976480	+	0.215610i	$0.0691740\pi$
$839$			361.794i			0.431220i	−0.976480	+	0.215610i	$0.930826\pi$
$840$		0			0
$841$	1731.20			2.05851
$842$	−513.332	+	43.6486i	−0.609657	+	0.0518392i
$843$			114.404i			0.135711i
$844$	50.3101	+	293.698i	0.0596092	+	0.347984i
$845$		0			0
$846$	5.96015	+	70.0947i	0.00704510	+	0.0828542i
$847$			11.0143i			0.0130039i
$848$	−621.134	+	219.232i	−0.732470	+	0.258528i
$849$	−202.536			−0.238559
$850$		0			0
$851$			149.610i			0.175805i
$852$	451.801	−	77.3929i	0.530283	−	0.0908368i
$853$	844.503			0.990039			0.495019	−	0.868882i	$-0.335161\pi$
$853$	844.503			0.990039			0.495019	+	0.868882i	$0.335161\pi$
$854$	−117.899	−	1386.55i	−0.138055	−	1.62360i
$855$		0			0
$856$	−68.0528	−	261.623i	−0.0795009	−	0.305635i
$857$	1389.51			1.62137			0.810685	−	0.585482i	$-0.199095\pi$
$857$	1389.51			1.62137			0.810685	+	0.585482i	$0.199095\pi$
$858$	−107.466	+	9.13782i	−0.125251	+	0.0106501i
$859$		−	1205.45i		−	1.40332i	−0.712512	−	0.701660i	$-0.752442\pi$
$859$		−	1205.45i		−	1.40332i	0.712512	−	0.701660i	$-0.247558\pi$
$860$		0			0
$861$	−113.881			−0.132266
$862$	58.1487	+	683.861i	0.0674579	+	0.793342i
$863$			258.868i			0.299963i	0.988689	+	0.149981i	$0.0479214\pi$
$863$			258.868i			0.299963i	−0.988689	+	0.149981i	$0.952079\pi$
$864$	68.4276	+	151.544i	0.0791986	+	0.175398i
$865$		0			0
$866$	467.832	−	39.7798i	0.540222	−	0.0459351i
$867$			426.796i			0.492267i
$868$	1776.33	−	304.282i	2.04646	−	0.350555i
$869$	−1358.58			−1.56339
$870$		0			0
$871$		−	45.6035i		−	0.0523576i
$872$	−645.919	+	168.015i	−0.740732	+	0.192677i
$873$	381.880			0.437434
$874$	440.930	−	37.4923i	0.504497	−	0.0428974i
$875$		0			0
$876$	18.2867	+	106.753i	0.0208752	+	0.121865i
$877$	156.268			0.178185			0.0890926	−	0.996023i	$-0.471603\pi$
$877$	156.268			0.178185			0.0890926	+	0.996023i	$0.471603\pi$
$878$	−63.4539	−	746.253i	−0.0722710	−	0.849946i
$879$		−	118.426i		−	0.134728i
$880$		0			0
$881$	−1343.58			−1.52507			−0.762533	−	0.646950i	$-0.776044\pi$
$881$	−1343.58			−1.52507			−0.762533	+	0.646950i	$0.776044\pi$
$882$	625.693	−	53.2027i	0.709402	−	0.0603205i
$883$			149.478i			0.169284i	0.996411	+	0.0846420i	$0.0269747\pi$
$883$			149.478i			0.169284i	−0.996411	+	0.0846420i	$0.973025\pi$
$884$	72.5594	−	12.4293i	0.0820807	−	0.0140603i
$885$		0			0
$886$	−18.3949	−	216.334i	−0.0207617	−	0.244169i
$887$		−	1532.07i		−	1.72725i	−0.504134	−	0.863626i	$-0.668188\pi$
$887$		−	1532.07i		−	1.72725i	0.504134	−	0.863626i	$-0.331812\pi$
$888$	−66.0247	−	253.827i	−0.0743522	−	0.285841i
$889$	−206.832			−0.232656
$890$		0			0
$891$			99.3628i			0.111518i
$892$	−108.055	−	630.796i	−0.121137	−	0.707171i
$893$	−328.204			−0.367529
$894$	14.7414	+	173.367i	0.0164893	+	0.193923i
$895$		0			0
$896$	−887.745	−	1315.09i	−0.990786	−	1.46773i
$897$	−38.6084			−0.0430417
$898$	−859.919	+	73.1190i	−0.957594	+	0.0814243i
$899$			1843.39i			2.05049i
$900$		0			0
$901$	268.665			0.298186
$902$	9.92273	+	116.697i	0.0110008	+	0.129376i
$903$		−	978.767i		−	1.08391i
$904$	865.562	−	225.148i	0.957480	−	0.249057i
$905$		0			0
$906$	−735.754	+	62.5612i	−0.812091	+	0.0690521i
$907$		−	1245.02i		−	1.37268i	−0.727280	−	0.686341i	$-0.759216\pi$
$907$		−	1245.02i		−	1.37268i	0.727280	−	0.686341i	$-0.240784\pi$
$908$	−118.848	−	693.808i	−0.130890	−	0.764106i
$909$	283.060			0.311398
$910$		0			0
$911$			173.681i			0.190649i	0.995446	+	0.0953245i	$0.0303889\pi$
$911$			173.681i			0.190649i	−0.995446	+	0.0953245i	$0.969611\pi$
$912$	−731.529	+	258.196i	−0.802115	+	0.283110i
$913$	−1100.39			−1.20524
$914$	−437.914	+	37.2359i	−0.479118	+	0.0407395i
$915$		0			0
$916$	−450.125	+	77.1058i	−0.491403	+	0.0841766i
$917$	−2434.78			−2.65515
$918$	−5.74607	−	67.5770i	−0.00625934	−	0.0736133i
$919$		−	874.426i		−	0.951498i	−0.879581	−	0.475749i	$-0.842177\pi$
$919$		−	874.426i		−	0.951498i	0.879581	−	0.475749i	$-0.157823\pi$
$920$		0			0
$921$	639.987			0.694882
$922$	445.262	−	37.8607i	0.482931	−	0.0410636i
$923$		−	186.582i		−	0.202147i
$924$	−160.086	−	934.545i	−0.173254	−	1.01141i
$925$		0			0
$926$	125.537	+	1476.38i	0.135569	+	1.59436i
$927$		−	95.5365i		−	0.103060i
$928$	1479.14	−	667.886i	1.59390	−	0.719705i
$929$	−1564.05			−1.68358			−0.841792	−	0.539803i	$-0.818499\pi$
$929$	−1564.05			−1.68358			−0.841792	+	0.539803i	$0.818499\pi$
$930$		0			0
$931$			2929.68i			3.14681i
$932$	−1025.31	+	175.635i	−1.10012	+	0.188450i
$933$	−525.584			−0.563327
$934$	42.2573	+	496.970i	0.0452434	+	0.532087i
$935$		0			0
$936$	65.5023	−	17.0383i	0.0699811	−	0.0182033i
$937$	−958.621			−1.02308			−0.511538	−	0.859261i	$-0.670924\pi$
$937$	−958.621			−1.02308			−0.511538	+	0.859261i	$0.670924\pi$
$938$	399.466	−	33.9666i	0.425869	−	0.0362117i
$939$			515.620i			0.549116i
$940$		0			0
$941$	−752.357			−0.799529			−0.399765	−	0.916618i	$-0.630908\pi$
$941$	−752.357			−0.799529			−0.399765	+	0.916618i	$0.630908\pi$
$942$	59.8485	+	703.852i	0.0635335	+	0.747188i
$943$			41.9247i			0.0444589i
$944$	56.9849	+	161.451i	0.0603654	+	0.171029i
$945$		0			0
$946$	−1002.97	+	85.2825i	−1.06022	+	0.0901507i
$947$			1013.16i			1.06986i	0.844895	+	0.534932i	$0.179663\pi$
$947$			1013.16i			1.06986i	−0.844895	+	0.534932i	$0.820337\pi$
$948$	840.322	−	143.946i	0.886415	−	0.151842i
$949$	44.0863			0.0464555
$950$		0			0
$951$			458.436i			0.482057i
$952$	162.919	+	626.329i	0.171134	+	0.657909i
$953$	21.5482			0.0226109			0.0113054	−	0.999936i	$-0.496401\pi$
$953$	21.5482			0.0226109			0.0113054	+	0.999936i	$0.496401\pi$
$954$	246.120	−	20.9276i	0.257987	−	0.0219367i
$955$		0			0
$956$	−94.6102	−	552.312i	−0.0989646	−	0.577732i
$957$	969.828			1.01340
$958$	35.7393	+	420.314i	0.0373062	+	0.438741i
$959$		−	1451.90i		−	1.51397i
$960$		0			0
$961$	−360.079			−0.374692
$962$	−106.373	+	9.04490i	−0.110575	+	0.00940218i
$963$			101.373i			0.105268i
$964$	417.599	−	71.5340i	0.433193	−	0.0742054i
$965$		0			0
$966$	−28.7565	−	338.192i	−0.0297686	−	0.350095i
$967$			303.965i			0.314338i	0.987572	+	0.157169i	$0.0502367\pi$
$967$			303.965i			0.314338i	−0.987572	+	0.157169i	$0.949763\pi$
$968$	−6.87942	+	1.78946i	−0.00710684	+	0.00184861i
$969$	316.415			0.326538
$970$		0			0
$971$			356.162i			0.366799i	0.983038	+	0.183399i	$0.0587101\pi$
$971$			356.162i			0.366799i	−0.983038	+	0.183399i	$0.941290\pi$
$972$	−10.5278	−	61.4587i	−0.0108311	−	0.0632291i
$973$	−2320.99			−2.38539
$974$	−120.400	−	1415.97i	−0.123614	−	1.45377i
$975$		0			0
$976$	846.873	−	298.907i	0.867698	−	0.306257i
$977$	1845.09			1.88852			0.944262	−	0.329194i	$-0.106777\pi$
$977$	1845.09			1.88852			0.944262	+	0.329194i	$0.106777\pi$
$978$	−745.202	+	63.3646i	−0.761965	+	0.0647899i
$979$			1115.99i			1.13993i
$980$		0			0
$981$	250.280			0.255127
$982$	118.254	+	1390.73i	0.120422	+	1.41623i
$983$		−	289.444i		−	0.294449i	−0.989103	−	0.147225i	$-0.952966\pi$
$983$		−	289.444i		−	0.294449i	0.989103	−	0.147225i	$-0.0470340\pi$
$984$	−18.5019	−	71.1288i	−0.0188027	−	0.0722854i
$985$		0			0
$986$	−659.583	+	56.0844i	−0.668949	+	0.0568807i
$987$			251.731i			0.255047i
$988$	53.3140	+	311.234i	0.0539616	+	0.315015i
$989$	−360.329			−0.364337
$990$		0			0
$991$			441.980i			0.445994i	0.974819	+	0.222997i	$0.0715840\pi$
$991$			441.980i			0.445994i	−0.974819	+	0.222997i	$0.928416\pi$
$992$	478.645	+	1060.04i	0.482505	+	1.06859i
$993$	819.998			0.825778
$994$	1634.37	−	138.971i	1.64424	−	0.139810i
$995$		0			0
$996$	680.620	−	116.589i	0.683354	−	0.117058i
$997$	1045.42			1.04856			0.524282	−	0.851545i	$-0.324334\pi$
$997$	1045.42			1.04856			0.524282	+	0.851545i	$0.324334\pi$
$998$	−148.370	−	1744.91i	−0.148667	−	1.74841i
$999$			98.3525i			0.0984509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.d.151.7		8
3.2	odd	2		900.3.c.u.451.2		8
4.3	odd	2	inner	300.3.c.d.151.8		8
5.2	odd	4		300.3.f.b.199.10		16
5.3	odd	4		300.3.f.b.199.7		16
5.4	even	2		60.3.c.a.31.2	yes	8
12.11	even	2		900.3.c.u.451.1		8
15.2	even	4		900.3.f.f.199.7		16
15.8	even	4		900.3.f.f.199.10		16
15.14	odd	2		180.3.c.b.91.7		8
20.3	even	4		300.3.f.b.199.9		16
20.7	even	4		300.3.f.b.199.8		16
20.19	odd	2		60.3.c.a.31.1	✓	8
40.19	odd	2		960.3.e.c.511.7		8
40.29	even	2		960.3.e.c.511.4		8
60.23	odd	4		900.3.f.f.199.8		16
60.47	odd	4		900.3.f.f.199.9		16
60.59	even	2		180.3.c.b.91.8		8
120.29	odd	2		2880.3.e.j.2431.4		8
120.59	even	2		2880.3.e.j.2431.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.1	✓	8	20.19	odd	2
60.3.c.a.31.2	yes	8	5.4	even	2
180.3.c.b.91.7		8	15.14	odd	2
180.3.c.b.91.8		8	60.59	even	2
300.3.c.d.151.7		8	1.1	even	1	trivial
300.3.c.d.151.8		8	4.3	odd	2	inner
300.3.f.b.199.7		16	5.3	odd	4
300.3.f.b.199.8		16	20.7	even	4
300.3.f.b.199.9		16	20.3	even	4
300.3.f.b.199.10		16	5.2	odd	4
900.3.c.u.451.1		8	12.11	even	2
900.3.c.u.451.2		8	3.2	odd	2
900.3.f.f.199.7		16	15.2	even	4
900.3.f.f.199.8		16	60.23	odd	4
900.3.f.f.199.9		16	60.47	odd	4
900.3.f.f.199.10		16	15.8	even	4
960.3.e.c.511.4		8	40.29	even	2
960.3.e.c.511.7		8	40.19	odd	2
2880.3.e.j.2431.1		8	120.59	even	2
2880.3.e.j.2431.4		8	120.29	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 - 0.675358i) q^{4} +(-0.293494 - 3.45165i) q^{6} -12.3959i q^{7} +(7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.99281 - 0.169449i) q^{2} -1.73205i q^{3} +(3.94257 - 0.675358i) q^{4} +(-0.293494 - 3.45165i) q^{6} -12.3959i q^{7} +(7.74236 - 2.01392i) q^{8} -3.00000 q^{9} +11.0403i q^{11} +(-1.16975 - 6.82874i) q^{12} -2.82009 q^{13} +(-2.10047 - 24.7027i) q^{14} +(15.0878 - 5.32529i) q^{16} -6.52606 q^{17} +(-5.97843 + 0.508346i) q^{18} -27.9928i q^{19} -21.4703 q^{21} +(1.87077 + 22.0012i) q^{22} +7.90421i q^{23} +(-3.48822 - 13.4102i) q^{24} +(-5.61989 + 0.477860i) q^{26} +5.19615i q^{27} +(-8.37167 - 48.8718i) q^{28} +50.7169 q^{29} +36.3467i q^{31} +(29.1647 - 13.1689i) q^{32} +19.1224 q^{33} +(-13.0052 + 1.10583i) q^{34} +(-11.8277 + 2.02607i) q^{36} +18.9279 q^{37} +(-4.74333 - 55.7842i) q^{38} +4.88453i q^{39} +5.30410 q^{41} +(-42.7863 + 3.63812i) q^{42} +45.5870i q^{43} +(7.45616 + 43.5273i) q^{44} +(1.33936 + 15.7516i) q^{46} -11.7246i q^{47} +(-9.22368 - 26.1328i) q^{48} -104.658 q^{49} +11.3035i q^{51} +(-11.1184 + 1.90457i) q^{52} -41.1680 q^{53} +(0.880481 + 10.3549i) q^{54} +(-24.9644 - 95.9735i) q^{56} -48.4849 q^{57} +(101.069 - 8.59391i) q^{58} +10.7008i q^{59} +56.1297 q^{61} +(6.15889 + 72.4319i) q^{62} +37.1877i q^{63} +(55.8882 - 31.1850i) q^{64} +(38.1073 - 3.24026i) q^{66} +16.1709i q^{67} +(-25.7295 + 4.40743i) q^{68} +13.6905 q^{69} +66.1617i q^{71} +(-23.2271 + 6.04177i) q^{72} -15.6330 q^{73} +(37.7198 - 3.20731i) q^{74} +(-18.9051 - 110.363i) q^{76} +136.855 q^{77} +(0.827677 + 9.73394i) q^{78} +123.057i q^{79} +9.00000 q^{81} +(10.5701 - 0.898773i) q^{82} +99.6700i q^{83} +(-84.6484 + 14.5002i) q^{84} +(7.72465 + 90.8461i) q^{86} -87.8443i q^{87} +(22.2343 + 85.4781i) q^{88} +101.083 q^{89} +34.9575i q^{91} +(5.33817 + 31.1629i) q^{92} +62.9543 q^{93} +(-1.98672 - 23.3649i) q^{94} +(-22.8092 - 50.5148i) q^{96} -127.293 q^{97} +(-208.564 + 17.7342i) q^{98} -33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

Introduction

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