LMFDB - Embedded newform 300.3.c.d.151.8

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

$q$-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	$0.346130\pi$
$7$			12.3959i			1.77084i	−0.464789	+	0.885422i	$0.653870\pi$
$8$	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	$-0.832659\pi$
$11$		−	11.0403i		−	1.00366i	0.864965	−	0.501832i	$-0.167341\pi$
$12$	−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	$0.263594\pi$
$19$			27.9928i			1.47330i	−0.676273	+	0.736651i	$0.736406\pi$
$20$		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	$-0.945032\pi$
$23$		−	7.90421i		−	0.343661i	0.985126	−	0.171831i	$-0.0549682\pi$
$24$	−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	$-0.800609\pi$
$31$		−	36.3467i		−	1.17247i	0.810140	−	0.586236i	$-0.199391\pi$
$32$	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	$-0.822162\pi$
$43$		−	45.5870i		−	1.06016i	0.847947	−	0.530081i	$-0.177838\pi$
$44$	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	$0.0398064\pi$
$47$			11.7246i			0.249460i	−0.992191	+	0.124730i	$0.960194\pi$
$48$	−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	$-0.971094\pi$
$59$		−	10.7008i		−	0.181370i	0.995880	−	0.0906848i	$-0.0289056\pi$
$60$		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	$-0.961493\pi$
$67$		−	16.1709i		−	0.241357i	0.992692	−	0.120679i	$-0.0385071\pi$
$68$	−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	$-0.845721\pi$
$71$		−	66.1617i		−	0.931855i	0.884823	−	0.465928i	$-0.154279\pi$
$72$	−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	$-0.715809\pi$
$79$		−	123.057i		−	1.55768i	0.627223	−	0.778840i	$-0.284191\pi$
$80$		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	$-0.794999\pi$
$83$		−	99.6700i		−	1.20084i	0.799684	−	0.600422i	$-0.205001\pi$
$84$	−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	$-0.950594\pi$
$103$		−	31.8455i		−	0.309180i	0.987979	−	0.154590i	$-0.0494056\pi$
$104$	−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	$0.0504732\pi$
$107$			33.7912i			0.315805i	−0.987455	+	0.157903i	$0.949527\pi$
$108$	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	$0.0209251\pi$
$127$			16.6855i			0.131382i	−0.997840	+	0.0656909i	$0.979075\pi$
$128$	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	$0.269796\pi$
$131$			196.418i			1.49937i	−0.661794	+	0.749686i	$0.730204\pi$
$132$	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	$0.235218\pi$
$139$			187.238i			1.34704i	−0.739170	+	0.673519i	$0.764782\pi$
$140$		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	$0.249425\pi$
$151$			213.160i			1.41166i	−0.708382	+	0.705829i	$0.750575\pi$
$152$	−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	$0.230404\pi$
$163$			215.898i			1.32452i	−0.749272	+	0.662262i	$0.769596\pi$
$164$	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	$-0.723450\pi$
$167$		−	255.029i		−	1.52712i	0.645737	−	0.763560i	$-0.276550\pi$
$168$	−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	$0.0925869\pi$
$179$			102.669i			0.573572i	−0.957995	+	0.286786i	$0.907413\pi$
$180$		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	$-0.863815\pi$
$191$		−	158.493i		−	0.829808i	0.909865	−	0.414904i	$-0.136185\pi$
$192$	−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	$0.0112253\pi$
$199$			14.0326i			0.0705157i	−0.999378	+	0.0352579i	$0.988775\pi$
$200$		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	$-0.943514\pi$
$211$		−	74.4941i		−	0.353052i	0.984296	−	0.176526i	$-0.0564860\pi$
$212$	−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	$0.116792\pi$
$223$			159.996i			0.717471i	−0.933439	+	0.358736i	$0.883208\pi$
$224$	−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	$0.126702\pi$
$227$			175.978i			0.775236i	−0.921820	+	0.387618i	$0.873298\pi$
$228$	−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	$0.0946780\pi$
$239$			140.089i			0.586147i	−0.956090	+	0.293073i	$0.905322\pi$
$240$		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	$0.108540\pi$
$251$			167.879i			0.668839i	−0.942424	+	0.334420i	$0.891460\pi$
$252$	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	$-0.633328\pi$
$263$		−	480.528i		−	1.82710i	0.406722	−	0.913552i	$-0.366672\pi$
$264$	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	$0.104069\pi$
$271$			174.063i			0.642299i	−0.947029	+	0.321150i	$0.895931\pi$
$272$	−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	$0.0662392\pi$
$283$			116.934i			0.413196i	−0.978426	+	0.206598i	$0.933761\pi$
$284$	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	$-0.794456\pi$
$307$		−	369.497i		−	1.20357i	0.798657	−	0.601786i	$-0.205544\pi$
$308$	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	$0.162221\pi$
$311$			303.446i			0.975712i	−0.872924	+	0.487856i	$0.837779\pi$
$312$	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	$-0.746361\pi$
$331$		−	473.426i		−	1.43029i	0.698976	−	0.715145i	$-0.253639\pi$
$332$	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	$0.145445\pi$
$347$			306.190i			0.882391i	−0.897411	+	0.441195i	$0.854555\pi$
$348$	−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	$-0.750019\pi$
$359$		−	507.672i		−	1.41413i	0.707149	−	0.707065i	$-0.249981\pi$
$360$		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	$-0.972747\pi$
$367$		−	62.7671i		−	0.171028i	0.996337	−	0.0855138i	$-0.0272532\pi$
$368$	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	$-0.834385\pi$
$379$		−	376.828i		−	0.994270i	0.867673	−	0.497135i	$-0.165615\pi$
$380$		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	$-0.819132\pi$
$383$		−	412.206i		−	1.07625i	0.842864	−	0.538127i	$-0.180868\pi$
$384$	−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	$0.0920647\pi$
$419$			239.009i			0.570428i	−0.958464	+	0.285214i	$0.907935\pi$
$420$		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	$-0.869669\pi$
$431$		−	343.164i		−	0.796205i	0.917341	−	0.398103i	$-0.130331\pi$
$432$	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	$0.140256\pi$
$439$			374.473i			0.853013i	−0.904484	+	0.426507i	$0.859744\pi$
$440$		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	$0.0390992\pi$
$443$			108.557i			0.245050i	−0.992465	+	0.122525i	$0.960901\pi$
$444$	−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	$-0.704802\pi$
$463$		−	740.855i		−	1.60012i	0.599921	−	0.800059i	$-0.295198\pi$
$464$	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	$-0.913966\pi$
$467$		−	249.381i		−	0.534007i	0.963696	−	0.267004i	$-0.0860336\pi$
$468$	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	$-0.929341\pi$
$479$		−	210.915i		−	0.440324i	0.975463	−	0.220162i	$-0.0706587\pi$
$480$		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	$0.260251\pi$
$487$			710.541i			1.45902i	−0.683972	+	0.729508i	$0.739749\pi$
$488$	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	$-0.748393\pi$
$491$		−	697.876i		−	1.42134i	0.703528	−	0.710668i	$-0.251607\pi$
$492$	−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	$0.340695\pi$
$499$			875.602i			1.75471i	−0.479838	+	0.877357i	$0.659305\pi$
$500$		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	$0.0453524\pi$
$503$			142.849i			0.283995i	−0.989867	+	0.141997i	$0.954648\pi$
$504$	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	$0.115189\pi$
$523$			370.317i			0.708063i	−0.935233	+	0.354032i	$0.884811\pi$
$524$	−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	$-0.884685\pi$
$547$		−	387.716i		−	0.708804i	0.935093	−	0.354402i	$-0.115315\pi$
$548$	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	$-0.895921\pi$
$563$		−	361.646i		−	0.642355i	0.947019	−	0.321178i	$-0.104079\pi$
$564$	−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	$0.128241\pi$
$571$			447.745i			0.784142i	−0.919935	+	0.392071i	$0.871759\pi$
$572$	−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	$-0.964779\pi$
$587$		−	129.637i		−	0.220847i	0.993885	−	0.110424i	$-0.0352208\pi$
$588$	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	$-0.670286\pi$
$599$		−	1030.62i		−	1.72057i	0.509816	−	0.860284i	$-0.329714\pi$
$600$		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	$-0.755788\pi$
$607$		−	842.678i		−	1.38827i	0.719847	−	0.694133i	$-0.244212\pi$
$608$	−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	$-0.812135\pi$
$619$		−	688.974i		−	1.11304i	0.830833	−	0.556522i	$-0.187865\pi$
$620$		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	$-0.892281\pi$
$631$		−	418.968i		−	0.663975i	0.943284	−	0.331987i	$-0.107719\pi$
$632$	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	$0.186435\pi$
$643$			710.880i			1.10557i	−0.833325	+	0.552784i	$0.813565\pi$
$644$	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	$0.117845\pi$
$647$			468.195i			0.723641i	−0.932248	+	0.361820i	$0.882155\pi$
$648$	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	$0.0383136\pi$
$659$			158.259i			0.240151i	−0.992765	+	0.120075i	$0.961686\pi$
$660$		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	$0.206928\pi$
$683$			826.776i			1.21051i	−0.796033	+	0.605254i	$0.793072\pi$
$684$	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	$0.246182\pi$
$691$			965.432i			1.39715i	−0.715536	+	0.698576i	$0.753818\pi$
$692$	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	$0.0423641\pi$
$719$			190.820i			0.265396i	−0.991157	+	0.132698i	$0.957636\pi$
$720$		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	$-0.955605\pi$
$727$		−	202.134i		−	0.278039i	0.990290	−	0.139019i	$-0.0443951\pi$
$728$	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	$0.217215\pi$
$739$			932.112i			1.26132i	−0.776061	+	0.630658i	$0.782785\pi$
$740$		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	$-0.717054\pi$
$743$		−	1153.70i		−	1.55276i	0.630266	−	0.776379i	$-0.282946\pi$
$744$	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	$0.0434434\pi$
$751$			204.359i			0.272116i	−0.990701	+	0.136058i	$0.956557\pi$
$752$	−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	$0.0906665\pi$
$787$			442.296i			0.562002i	−0.959707	+	0.281001i	$0.909334\pi$
$788$	−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	$0.194539\pi$
$811$			930.734i			1.14764i	−0.818982	+	0.573819i	$0.805461\pi$
$812$	−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	$-0.988159\pi$
$823$		−	61.2187i		−	0.0743849i	0.999308	−	0.0371924i	$-0.0118414\pi$
$824$	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	$-0.991107\pi$
$827$		−	46.2063i		−	0.0558721i	0.999610	−	0.0279361i	$-0.00889348\pi$
$828$	−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	$-0.930826\pi$
$839$		−	361.794i		−	0.431220i	0.976480	−	0.215610i	$-0.0691740\pi$
$840$		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	$0.247558\pi$
$859$			1205.45i			1.40332i	−0.712512	+	0.701660i	$0.752442\pi$
$860$		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	$-0.952079\pi$
$863$		−	258.868i		−	0.299963i	0.988689	−	0.149981i	$-0.0479214\pi$
$864$	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	$-0.973025\pi$
$883$		−	149.478i		−	0.169284i	0.996411	−	0.0846420i	$-0.0269747\pi$
$884$	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	$0.331812\pi$
$887$			1532.07i			1.72725i	−0.504134	+	0.863626i	$0.668188\pi$
$888$	−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	$0.240784\pi$
$907$			1245.02i			1.37268i	−0.727280	+	0.686341i	$0.759216\pi$
$908$	−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	$-0.969611\pi$
$911$		−	173.681i		−	0.190649i	0.995446	−	0.0953245i	$-0.0303889\pi$
$912$	−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	$0.157823\pi$
$919$			874.426i			0.951498i	−0.879581	+	0.475749i	$0.842177\pi$
$920$		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	$-0.820337\pi$
$947$		−	1013.16i		−	1.06986i	0.844895	−	0.534932i	$-0.179663\pi$
$948$	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	$-0.949763\pi$
$967$		−	303.965i		−	0.314338i	0.987572	−	0.157169i	$-0.0502367\pi$
$968$	−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	$-0.941290\pi$
$971$		−	356.162i		−	0.366799i	0.983038	−	0.183399i	$-0.0587101\pi$
$972$	−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	$0.0470340\pi$
$983$			289.444i			0.294449i	−0.989103	+	0.147225i	$0.952966\pi$
$984$	−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	$-0.928416\pi$
$991$		−	441.980i		−	0.445994i	0.974819	−	0.222997i	$-0.0715840\pi$
$992$	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.151.8		8
3.2	odd	2		900.3.c.u.451.1		8
4.3	odd	2	inner	300.3.c.d.151.7		8
5.2	odd	4		300.3.f.b.199.8		16
5.3	odd	4		300.3.f.b.199.9		16
5.4	even	2		60.3.c.a.31.1	✓	8
12.11	even	2		900.3.c.u.451.2		8
15.2	even	4		900.3.f.f.199.9		16
15.8	even	4		900.3.f.f.199.8		16
15.14	odd	2		180.3.c.b.91.8		8
20.3	even	4		300.3.f.b.199.7		16
20.7	even	4		300.3.f.b.199.10		16
20.19	odd	2		60.3.c.a.31.2	yes	8
40.19	odd	2		960.3.e.c.511.4		8
40.29	even	2		960.3.e.c.511.7		8
60.23	odd	4		900.3.f.f.199.10		16
60.47	odd	4		900.3.f.f.199.7		16
60.59	even	2		180.3.c.b.91.7		8
120.29	odd	2		2880.3.e.j.2431.1		8
120.59	even	2		2880.3.e.j.2431.4		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
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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