LMFDB - Embedded newform 300.5.c.d.151.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,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, 5, names="a")

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
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:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.10
Root			$2.70166 + 0.837276i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.d.151.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.08838 + 2.54203i) q^{2} +5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +(-13.2088 + 16.0477i) q^{6} +86.5709i q^{7} +(-30.4132 + 56.3120i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(3.08838 + 2.54203i) q^{2} +5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +(-13.2088 + 16.0477i) q^{6} +86.5709i q^{7} +(-30.4132 + 56.3120i) q^{8} -27.0000 q^{9} +97.6947i q^{11} +(-81.5874 + 15.9844i) q^{12} +297.644 q^{13} +(-220.066 + 267.364i) q^{14} +(-237.074 + 96.6018i) q^{16} +58.8402 q^{17} +(-83.3863 - 68.6347i) q^{18} -497.315i q^{19} -449.835 q^{21} +(-248.343 + 301.718i) q^{22} +120.919i q^{23} +(-292.606 - 158.031i) q^{24} +(919.237 + 756.618i) q^{26} -140.296i q^{27} +(-1359.29 + 266.309i) q^{28} -947.079 q^{29} -559.454i q^{31} +(-977.739 - 304.306i) q^{32} -507.636 q^{33} +(181.721 + 149.573i) q^{34} +(-83.0573 - 423.940i) q^{36} -1163.36 q^{37} +(1264.19 - 1535.90i) q^{38} +1546.60i q^{39} +3178.56 q^{41} +(-1389.26 - 1143.49i) q^{42} +1166.21i q^{43} +(-1533.95 + 300.528i) q^{44} +(-307.380 + 373.445i) q^{46} +1060.01i q^{47} +(-501.958 - 1231.87i) q^{48} -5093.52 q^{49} +305.743i q^{51} +(915.610 + 4673.45i) q^{52} -1440.77 q^{53} +(356.637 - 433.288i) q^{54} +(-4874.98 - 2632.89i) q^{56} +2584.13 q^{57} +(-2924.94 - 2407.50i) q^{58} +2004.76i q^{59} +3522.56 q^{61} +(1422.15 - 1727.81i) q^{62} -2337.41i q^{63} +(-2246.08 - 3425.25i) q^{64} +(-1567.77 - 1290.43i) q^{66} -6169.67i q^{67} +(181.004 + 923.879i) q^{68} -628.315 q^{69} -882.122i q^{71} +(821.156 - 1520.42i) q^{72} -1659.75 q^{73} +(-3592.90 - 2957.30i) q^{74} +(7808.59 - 1529.84i) q^{76} -8457.51 q^{77} +(-3931.50 + 4776.50i) q^{78} -7276.52i q^{79} +729.000 q^{81} +(9816.61 + 8079.99i) q^{82} +5346.39i q^{83} +(-1383.78 - 7063.09i) q^{84} +(-2964.55 + 3601.72i) q^{86} -4921.17i q^{87} +(-5501.38 - 2971.20i) q^{88} +9009.81 q^{89} +25767.3i q^{91} +(-1898.61 + 371.971i) q^{92} +2907.01 q^{93} +(-2694.57 + 3273.71i) q^{94} +(1581.22 - 5080.48i) q^{96} +9798.06 q^{97} +(-15730.7 - 12947.9i) q^{98} -2637.76i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	$ 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) $ 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 + 352 * q^13 - 804 * q^14 - 190 * q^16 - 324 * q^18 + 288 * q^21 - 436 * q^22 - 1998 * q^24 - 852 * q^26 + 1156 * q^28 - 3456 * q^29 - 7668 * q^32 + 4772 * q^34 - 702 * q^36 - 9376 * q^37 + 1320 * q^38 + 1248 * q^41 + 324 * q^42 - 6420 * q^44 - 1112 * q^46 + 4176 * q^48 - 3952 * q^49 - 12704 * q^52 + 5184 * q^53 - 486 * q^54 - 2604 * q^56 + 11232 * q^57 - 12708 * q^58 - 3808 * q^61 + 16152 * q^62 - 11902 * q^64 - 2916 * q^66 + 12312 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 + 30516 * q^74 - 5160 * q^76 + 27456 * q^77 + 3600 * q^78 + 11664 * q^81 + 54040 * q^82 - 2052 * q^84 + 39768 * q^86 + 7220 * q^88 + 7584 * q^89 - 28848 * q^92 - 19872 * q^93 + 49776 * q^94 + 18882 * q^96 + 14496 * q^97 - 23940 * 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 $

$2$	3.08838	+	2.54203i	0.772095	+	0.635507i
$2$	3.08838	+	2.54203i	0.772095	+	0.635507i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	3.07620	+	15.7015i	0.192262	+	0.981344i
$5$		0			0
$5$		0			0
$6$	−13.2088	+	16.0477i	−0.366910	+	0.445769i
$7$			86.5709i			1.76675i	0.468665	+	0.883376i	$0.344735\pi$
$7$			86.5709i			1.76675i	−0.468665	+	0.883376i	$0.655265\pi$
$8$	−30.4132	+	56.3120i	−0.475206	+	0.879875i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			97.6947i			0.807394i	0.914893	+	0.403697i	$0.132275\pi$
$11$			97.6947i			0.807394i	−0.914893	+	0.403697i	$0.867725\pi$
$12$	−81.5874	+	15.9844i	−0.566579	+	0.111003i
$13$	297.644			1.76121			0.880603	−	0.473856i	$-0.157138\pi$
$13$	297.644			1.76121			0.880603	+	0.473856i	$0.157138\pi$
$14$	−220.066	+	267.364i	−1.12278	+	1.36410i
$15$		0			0
$16$	−237.074	+	96.6018i	−0.926070	+	0.377351i
$17$	58.8402			0.203599			0.101800	−	0.994805i	$-0.467540\pi$
$17$	58.8402			0.203599			0.101800	+	0.994805i	$0.467540\pi$
$18$	−83.3863	−	68.6347i	−0.257365	−	0.211836i
$19$		−	497.315i		−	1.37760i	−0.724949	−	0.688802i	$-0.758137\pi$
$19$		−	497.315i		−	1.37760i	0.724949	−	0.688802i	$-0.241863\pi$
$20$		0			0
$21$	−449.835			−1.02004
$22$	−248.343	+	301.718i	−0.513104	+	0.623385i
$23$			120.919i			0.228581i	0.993447	+	0.114290i	$0.0364594\pi$
$23$			120.919i			0.228581i	−0.993447	+	0.114290i	$0.963541\pi$
$24$	−292.606	−	158.031i	−0.507996	−	0.274360i
$25$		0			0
$26$	919.237	+	756.618i	1.35982	+	1.11926i
$27$		−	140.296i		−	0.192450i
$28$	−1359.29	+	266.309i	−1.73379	+	0.339680i
$29$	−947.079			−1.12613			−0.563067	−	0.826411i	$-0.690379\pi$
$29$	−947.079			−1.12613			−0.563067	+	0.826411i	$0.690379\pi$
$30$		0			0
$31$		−	559.454i		−	0.582158i	−0.956699	−	0.291079i	$-0.905986\pi$
$31$		−	559.454i		−	0.582158i	0.956699	−	0.291079i	$-0.0940142\pi$
$32$	−977.739	−	304.306i	−0.954824	−	0.297173i
$33$	−507.636			−0.466149
$34$	181.721	+	149.573i	0.157198	+	0.129389i
$35$		0			0
$36$	−83.0573	−	423.940i	−0.0640874	−	0.327115i
$37$	−1163.36			−0.849789			−0.424894	−	0.905243i	$-0.639689\pi$
$37$	−1163.36			−0.849789			−0.424894	+	0.905243i	$0.639689\pi$
$38$	1264.19	−	1535.90i	0.875477	−	1.06364i
$39$			1546.60i			1.01683i
$40$		0			0
$41$	3178.56			1.89088			0.945438	−	0.325802i	$-0.105634\pi$
$41$	3178.56			1.89088			0.945438	+	0.325802i	$0.105634\pi$
$42$	−1389.26	−	1143.49i	−0.787564	−	0.648239i
$43$			1166.21i			0.630727i	0.948971	+	0.315364i	$0.102126\pi$
$43$			1166.21i			0.630727i	−0.948971	+	0.315364i	$0.897874\pi$
$44$	−1533.95	+	300.528i	−0.792331	+	0.155231i
$45$		0			0
$46$	−307.380	+	373.445i	−0.145265	+	0.176486i
$47$			1060.01i			0.479859i	0.970790	+	0.239930i	$0.0771244\pi$
$47$			1060.01i			0.479859i	−0.970790	+	0.239930i	$0.922876\pi$
$48$	−501.958	−	1231.87i	−0.217863	−	0.534667i
$49$	−5093.52			−2.12141
$50$		0			0
$51$			305.743i			0.117548i
$52$	915.610	+	4673.45i	0.338613	+	1.72835i
$53$	−1440.77			−0.512911			−0.256455	−	0.966556i	$-0.582555\pi$
$53$	−1440.77			−0.512911			−0.256455	+	0.966556i	$0.582555\pi$
$54$	356.637	−	433.288i	0.122303	−	0.148590i
$55$		0			0
$56$	−4874.98	−	2632.89i	−1.55452	−	0.839571i
$57$	2584.13			0.795360
$58$	−2924.94	−	2407.50i	−0.869483	−	0.715666i
$59$			2004.76i			0.575914i	0.957643	+	0.287957i	$0.0929760\pi$
$59$			2004.76i			0.575914i	−0.957643	+	0.287957i	$0.907024\pi$
$60$		0			0
$61$	3522.56			0.946671			0.473335	−	0.880882i	$-0.343050\pi$
$61$	3522.56			0.946671			0.473335	+	0.880882i	$0.343050\pi$
$62$	1422.15	−	1727.81i	0.369965	−	0.449481i
$63$		−	2337.41i		−	0.588917i
$64$	−2246.08	−	3425.25i	−0.548359	−	0.836243i
$65$		0			0
$66$	−1567.77	−	1290.43i	−0.359912	−	0.296241i
$67$		−	6169.67i		−	1.37440i	−0.726470	−	0.687199i	$-0.758840\pi$
$67$		−	6169.67i		−	1.37440i	0.726470	−	0.687199i	$-0.241160\pi$
$68$	181.004	+	923.879i	0.0391445	+	0.199801i
$69$	−628.315			−0.131971
$70$		0			0
$71$		−	882.122i		−	0.174990i	−0.996165	−	0.0874948i	$-0.972114\pi$
$71$		−	882.122i		−	0.174990i	0.996165	−	0.0874948i	$-0.0278861\pi$
$72$	821.156	−	1520.42i	0.158402	−	0.293292i
$73$	−1659.75			−0.311457			−0.155728	−	0.987800i	$-0.549772\pi$
$73$	−1659.75			−0.311457			−0.155728	+	0.987800i	$0.549772\pi$
$74$	−3592.90	−	2957.30i	−0.656118	−	0.540047i
$75$		0			0
$76$	7808.59	−	1529.84i	1.35190	−	0.264861i
$77$	−8457.51			−1.42647
$78$	−3931.50	+	4776.50i	−0.646204	+	0.785091i
$79$		−	7276.52i		−	1.16592i	−0.812500	−	0.582961i	$-0.801894\pi$
$79$		−	7276.52i		−	1.16592i	0.812500	−	0.582961i	$-0.198106\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	9816.61	+	8079.99i	1.45994	+	1.20166i
$83$			5346.39i			0.776076i	0.921643	+	0.388038i	$0.126847\pi$
$83$			5346.39i			0.776076i	−0.921643	+	0.388038i	$0.873153\pi$
$84$	−1383.78	−	7063.09i	−0.196114	−	1.00100i
$85$		0			0
$86$	−2964.55	+	3601.72i	−0.400831	+	0.486982i
$87$		−	4921.17i		−	0.650174i
$88$	−5501.38	−	2971.20i	−0.710406	−	0.383678i
$89$	9009.81			1.13746			0.568730	−	0.822525i	$-0.307435\pi$
$89$	9009.81			1.13746			0.568730	+	0.822525i	$0.307435\pi$
$90$		0			0
$91$			25767.3i			3.11161i
$92$	−1898.61	+	371.971i	−0.224316	+	0.0439475i
$93$	2907.01			0.336109
$94$	−2694.57	+	3273.71i	−0.304954	+	0.370497i
$95$		0			0
$96$	1581.22	−	5080.48i	0.171573	−	0.551268i
$97$	9798.06			1.04135			0.520675	−	0.853755i	$-0.325680\pi$
$97$	9798.06			1.04135			0.520675	+	0.853755i	$0.325680\pi$
$98$	−15730.7	−	12947.9i	−1.63793	−	1.34817i
$99$		−	2637.76i		−	0.269131i
$100$		0			0
$101$	5404.90			0.529841			0.264920	−	0.964270i	$-0.414654\pi$
$101$	5404.90			0.529841			0.264920	+	0.964270i	$0.414654\pi$
$102$	−777.206	+	944.250i	−0.0747026	+	0.0907584i
$103$			8294.77i			0.781862i	0.920420	+	0.390931i	$0.127847\pi$
$103$			8294.77i			0.781862i	−0.920420	+	0.390931i	$0.872153\pi$
$104$	−9052.29	+	16760.9i	−0.836935	+	1.54964i
$105$		0			0
$106$	−4449.64	−	3662.47i	−0.396016	−	0.325958i
$107$			5744.62i			0.501758i	0.968018	+	0.250879i	$0.0807196\pi$
$107$			5744.62i			0.501758i	−0.968018	+	0.250879i	$0.919280\pi$
$108$	2202.86	−	431.578i	0.188860	−	0.0370009i
$109$	4709.84			0.396418			0.198209	−	0.980160i	$-0.436488\pi$
$109$	4709.84			0.396418			0.198209	+	0.980160i	$0.436488\pi$
$110$		0			0
$111$		−	6045.00i		−	0.490626i
$112$	−8362.90	−	20523.7i	−0.666685	−	1.63614i
$113$	−241.555			−0.0189173			−0.00945864	−	0.999955i	$-0.503011\pi$
$113$	−241.555			−0.0189173			−0.00945864	+	0.999955i	$0.503011\pi$
$114$	7980.76	+	6568.92i	0.614094	+	0.505457i
$115$		0			0
$116$	−2913.40	−	14870.6i	−0.216513	−	1.10513i
$117$	−8036.38			−0.587068
$118$	−5096.14	+	6191.45i	−0.365997	+	0.444660i
$119$			5093.85i			0.359710i
$120$		0			0
$121$	5096.75			0.348115
$122$	10879.0	+	8954.45i	0.730920	+	0.601616i
$123$			16516.3i			1.09170i
$124$	8784.26	−	1720.99i	0.571297	−	0.111927i
$125$		0			0
$126$	5941.77	−	7218.82i	0.374261	−	0.454700i
$127$			6882.74i			0.426731i	0.976972	+	0.213365i	$0.0684425\pi$
$127$			6882.74i			0.426731i	−0.976972	+	0.213365i	$0.931558\pi$
$128$	1770.34	−	16288.1i	0.108053	−	0.994145i
$129$	−6059.83			−0.364151
$130$		0			0
$131$			1247.82i			0.0727126i	0.999339	+	0.0363563i	$0.0115751\pi$
$131$			1247.82i			0.0727126i	−0.999339	+	0.0363563i	$0.988425\pi$
$132$	−1561.59	−	7970.65i	−0.0896229	−	0.457452i
$133$	43053.0			2.43389
$134$	15683.5	−	19054.3i	0.873439	−	1.06117i
$135$		0			0
$136$	−1789.52	+	3313.41i	−0.0967516	+	0.179142i
$137$	−1712.53			−0.0912422			−0.0456211	−	0.998959i	$-0.514527\pi$
$137$	−1712.53			−0.0912422			−0.0456211	+	0.998959i	$0.514527\pi$
$138$	−1940.48	−	1597.19i	−0.101894	−	0.0838686i
$139$			6748.58i			0.349287i	0.984632	+	0.174644i	$0.0558773\pi$
$139$			6748.58i			0.349287i	−0.984632	+	0.174644i	$0.944123\pi$
$140$		0			0
$141$	−5507.97			−0.277047
$142$	2242.38	−	2724.33i	0.111207	−	0.135109i
$143$			29078.2i			1.42199i
$144$	6401.00	−	2608.25i	0.308690	−	0.125784i
$145$		0			0
$146$	−5125.95	−	4219.14i	−0.240474	−	0.197933i
$147$		−	26466.7i		−	1.22480i
$148$	−3578.73	−	18266.5i	−0.163382	−	0.833935i
$149$	−38109.7			−1.71657			−0.858287	−	0.513170i	$-0.828471\pi$
$149$	−38109.7			−1.71657			−0.858287	+	0.513170i	$0.828471\pi$
$150$		0			0
$151$		−	4383.99i		−	0.192272i	−0.995368	−	0.0961360i	$-0.969352\pi$
$151$		−	4383.99i		−	0.192272i	0.995368	−	0.0961360i	$-0.0306484\pi$
$152$	28004.8	+	15124.9i	1.21212	+	0.654645i
$153$	−1588.69			−0.0678665
$154$	−26120.0	−	21499.2i	−1.10137	−	0.906528i
$155$		0			0
$156$	−24284.0	+	4757.65i	−0.997862	+	0.195498i
$157$	−18910.0			−0.767173			−0.383586	−	0.923505i	$-0.625311\pi$
$157$	−18910.0			−0.767173			−0.383586	+	0.923505i	$0.625311\pi$
$158$	18497.1	−	22472.7i	0.740951	−	0.900202i
$159$		−	7486.44i		−	0.296129i
$160$		0			0
$161$	−10468.1			−0.403846
$162$	2251.43	+	1853.14i	0.0857884	+	0.0706119i
$163$			2243.95i			0.0844575i	0.999108	+	0.0422288i	$0.0134458\pi$
$163$			2243.95i			0.0844575i	−0.999108	+	0.0422288i	$0.986554\pi$
$164$	9777.88	+	49908.2i	0.363544	+	1.85560i
$165$		0			0
$166$	−13590.7	+	16511.7i	−0.493201	+	0.599204i
$167$			24011.7i			0.860972i	0.902597	+	0.430486i	$0.141658\pi$
$167$			24011.7i			0.860972i	−0.902597	+	0.430486i	$0.858342\pi$
$168$	13680.9	−	25331.1i	0.484726	−	0.897503i
$169$	60030.7			2.10184
$170$		0			0
$171$			13427.5i			0.459201i
$172$	−18311.3	+	3587.51i	−0.618960	+	0.121265i
$173$	38810.8			1.29676			0.648381	−	0.761316i	$-0.275446\pi$
$173$	38810.8			1.29676			0.648381	+	0.761316i	$0.275446\pi$
$174$	12509.7	−	15198.4i	0.413190	−	0.501996i
$175$		0			0
$176$	−9437.48	−	23160.9i	−0.304671	−	0.747704i
$177$	−10417.0			−0.332504
$178$	27825.7	+	22903.2i	0.878227	+	0.722863i
$179$			56139.5i			1.75211i	0.482207	+	0.876057i	$0.339835\pi$
$179$			56139.5i			1.75211i	−0.482207	+	0.876057i	$0.660165\pi$
$180$		0			0
$181$	19958.6			0.609217			0.304609	−	0.952478i	$-0.401474\pi$
$181$	19958.6			0.609217			0.304609	+	0.952478i	$0.401474\pi$
$182$	−65501.1	+	79579.2i	−1.97745	+	2.40246i
$183$			18303.8i			0.546561i
$184$	−6809.20	−	3677.54i	−0.201122	−	0.108623i
$185$		0			0
$186$	8977.95	+	7389.69i	0.259508	+	0.213600i
$187$			5748.38i			0.164385i
$188$	−16643.7	+	3260.80i	−0.470907	+	0.0922588i
$189$	12145.6			0.340012
$190$		0			0
$191$			57207.0i			1.56813i	0.620677	+	0.784066i	$0.286858\pi$
$191$			57207.0i			1.56813i	−0.620677	+	0.784066i	$0.713142\pi$
$192$	17798.1	−	11671.0i	0.482805	−	0.316595i
$193$	4603.04			0.123575			0.0617874	−	0.998089i	$-0.480320\pi$
$193$	4603.04			0.123575			0.0617874	+	0.998089i	$0.480320\pi$
$194$	30260.1	+	24906.9i	0.804021	+	0.661785i
$195$		0			0
$196$	−15668.7	−	79975.8i	−0.407868	−	2.08184i
$197$	−30077.6			−0.775017			−0.387509	−	0.921866i	$-0.626664\pi$
$197$	−30077.6			−0.775017			−0.387509	+	0.921866i	$0.626664\pi$
$198$	6705.25	−	8146.40i	0.171035	−	0.207795i
$199$		−	42243.9i		−	1.06674i	−0.845883	−	0.533369i	$-0.820926\pi$
$199$		−	42243.9i		−	1.06674i	0.845883	−	0.533369i	$-0.179074\pi$
$200$		0			0
$201$	32058.5			0.793509
$202$	16692.4	+	13739.4i	0.409087	+	0.336717i
$203$		−	81989.5i		−	1.98960i
$204$	−4800.62	+	940.525i	−0.115355	+	0.0226001i
$205$		0			0
$206$	−21085.5	+	25617.4i	−0.496878	+	0.603672i
$207$		−	3264.82i		−	0.0761936i
$208$	−70563.6	+	28752.9i	−1.63100	+	0.664592i
$209$	48585.0			1.11227
$210$		0			0
$211$			3093.80i			0.0694908i	0.999396	+	0.0347454i	$0.0110620\pi$
$211$			3093.80i			0.0694908i	−0.999396	+	0.0347454i	$0.988938\pi$
$212$	−4432.08	−	22622.2i	−0.0986134	−	0.503342i
$213$	4583.64			0.101030
$214$	−14603.0	+	17741.6i	−0.318870	+	0.387405i
$215$		0			0
$216$	7900.35	+	4266.85i	0.169332	+	0.0914534i
$217$	48432.4			1.02853
$218$	14545.8	+	11972.5i	0.306072	+	0.251926i
$219$		−	8624.33i		−	0.179820i
$220$		0			0
$221$	17513.4			0.358580
$222$	15366.6	−	18669.3i	0.311796	−	0.378810i
$223$			43059.5i			0.865884i	0.901422	+	0.432942i	$0.142525\pi$
$223$			43059.5i			0.865884i	−0.901422	+	0.432942i	$0.857475\pi$
$224$	26344.0	−	84643.7i	0.525032	−	1.68694i
$225$		0			0
$226$	−746.013	−	614.039i	−0.0146059	−	0.0120221i
$227$		−	43385.8i		−	0.841968i	−0.907068	−	0.420984i	$-0.861685\pi$
$227$		−	43385.8i		−	0.841968i	0.907068	−	0.420984i	$-0.138315\pi$
$228$	7949.28	+	40574.6i	0.152918	+	0.780522i
$229$	56036.8			1.06857			0.534285	−	0.845305i	$-0.320581\pi$
$229$	56036.8			1.06857			0.534285	+	0.845305i	$0.320581\pi$
$230$		0			0
$231$		−	43946.5i		−	0.823570i
$232$	28803.7	−	53331.9i	0.535146	−	0.990857i
$233$	41638.3			0.766974			0.383487	−	0.923546i	$-0.374723\pi$
$233$	41638.3			0.766974			0.383487	+	0.923546i	$0.374723\pi$
$234$	−24819.4	−	20428.7i	−0.453273	−	0.373086i
$235$		0			0
$236$	−31477.7	+	6167.02i	−0.565169	+	0.110726i
$237$	37809.9			0.673145
$238$	−12948.7	+	15731.7i	−0.228598	+	0.277730i
$239$			71028.3i			1.24347i	0.783227	+	0.621736i	$0.213572\pi$
$239$			71028.3i			1.24347i	−0.783227	+	0.621736i	$0.786428\pi$
$240$		0			0
$241$	−58695.9			−1.01059			−0.505294	−	0.862947i	$-0.668616\pi$
$241$	−58695.9			−1.01059			−0.505294	+	0.862947i	$0.668616\pi$
$242$	15740.7	+	12956.1i	0.268778	+	0.221229i
$243$			3788.00i			0.0641500i
$244$	10836.1	+	55309.5i	0.182009	+	0.929009i
$245$		0			0
$246$	−41984.9	+	51008.6i	−0.693781	+	0.842895i
$247$		−	148023.i		−	2.42624i
$248$	31504.0	+	17014.8i	0.512226	+	0.276645i
$249$	−27780.6			−0.448068
$250$		0			0
$251$		−	40236.7i		−	0.638668i	−0.947642	−	0.319334i	$-0.896541\pi$
$251$		−	40236.7i		−	0.638668i	0.947642	−	0.319334i	$-0.103459\pi$
$252$	36700.9	−	7190.34i	0.577930	−	0.113227i
$253$	−11813.2			−0.184555
$254$	−17496.1	+	21256.5i	−0.271190	+	0.329477i
$255$		0			0
$256$	46872.2	−	45803.5i	0.715213	−	0.698907i
$257$	85304.1			1.29153			0.645763	−	0.763538i	$-0.276539\pi$
$257$	85304.1			1.29153			0.645763	+	0.763538i	$0.276539\pi$
$258$	−18715.1	−	15404.3i	−0.281159	−	0.231420i
$259$		−	100713.i		−	1.50137i
$260$		0			0
$261$	25571.1			0.375378
$262$	−3172.00	+	3853.75i	−0.0462094	+	0.0561411i
$263$			87162.9i			1.26014i	0.776537	+	0.630072i	$0.216975\pi$
$263$			87162.9i			1.26014i	−0.776537	+	0.630072i	$0.783025\pi$
$264$	15438.8	−	28586.0i	0.221517	−	0.410153i
$265$		0			0
$266$	132964.	+	109442.i	1.87919	+	1.54675i
$267$			46816.4i			0.656712i
$268$	96873.0	−	18979.1i	1.34876	−	0.264245i
$269$	−125878.			−1.73958			−0.869789	−	0.493424i	$-0.835745\pi$
$269$	−125878.			−1.73958			−0.869789	+	0.493424i	$0.835745\pi$
$270$		0			0
$271$		−	94283.5i		−	1.28380i	−0.766789	−	0.641899i	$-0.778147\pi$
$271$		−	94283.5i		−	1.28380i	0.766789	−	0.641899i	$-0.221853\pi$
$272$	−13949.5	+	5684.07i	−0.188547	+	0.0768283i
$273$	−133891.			−1.79649
$274$	−5288.93	−	4353.29i	−0.0704477	−	0.0579850i
$275$		0			0
$276$	−1932.82	−	9865.48i	−0.0253731	−	0.129509i
$277$	−65798.3			−0.857541			−0.428771	−	0.903413i	$-0.641053\pi$
$277$	−65798.3			−0.857541			−0.428771	+	0.903413i	$0.641053\pi$
$278$	−17155.1	+	20842.2i	−0.221974	+	0.269683i
$279$			15105.3i			0.194053i
$280$		0			0
$281$	16122.0			0.204177			0.102088	−	0.994775i	$-0.467448\pi$
$281$	16122.0			0.204177			0.102088	+	0.994775i	$0.467448\pi$
$282$	−17010.7	−	14001.4i	−0.213907	−	0.176065i
$283$		−	128462.i		−	1.60399i	−0.597329	−	0.801997i	$-0.703771\pi$
$283$		−	128462.i		−	1.60399i	0.597329	−	0.801997i	$-0.296229\pi$
$284$	13850.6	−	2713.58i	0.171725	−	0.0336439i
$285$		0			0
$286$	−73917.6	+	89804.6i	−0.903682	+	1.09791i
$287$			275171.i			3.34071i
$288$	26399.0	+	8216.25i	0.318275	+	0.0990578i
$289$	−80058.8			−0.958547
$290$		0			0
$291$			50912.2i			0.601224i
$292$	−5105.73	−	26060.6i	−0.0598814	−	0.305646i
$293$	−161599.			−1.88236			−0.941180	−	0.337906i	$-0.890282\pi$
$293$	−161599.			−1.88236			−0.941180	+	0.337906i	$0.890282\pi$
$294$	67279.0	−	81739.2i	0.778368	−	0.945662i
$295$		0			0
$296$	35381.5	−	65511.2i	0.403825	−	0.747708i
$297$	13706.2			0.155383
$298$	−117697.	−	96875.8i	−1.32536	−	1.09089i
$299$			35990.8i			0.402578i
$300$		0			0
$301$	−100960.			−1.11434
$302$	11144.2	−	13539.4i	0.122190	−	0.148452i
$303$			28084.7i			0.305904i
$304$	48041.5	+	117901.i	0.519840	+	1.27576i
$305$		0			0
$306$	−4906.47	−	4038.48i	−0.0523994	−	0.0431296i
$307$		−	39700.0i		−	0.421224i	−0.977570	−	0.210612i	$-0.932454\pi$
$307$		−	39700.0i		−	0.421224i	0.977570	−	0.210612i	$-0.0675457\pi$
$308$	−26017.0	−	132796.i	−0.274255	−	1.39985i
$309$	−43100.9			−0.451408
$310$		0			0
$311$		−	16610.8i		−	0.171739i	−0.996306	−	0.0858696i	$-0.972633\pi$
$311$		−	16610.8i		−	0.171739i	0.996306	−	0.0858696i	$-0.0273669\pi$
$312$	−87092.2	−	47037.1i	−0.894685	−	0.483205i
$313$	34354.3			0.350665			0.175332	−	0.984509i	$-0.443900\pi$
$313$	34354.3			0.350665			0.175332	+	0.984509i	$0.443900\pi$
$314$	−58401.4	−	48069.8i	−0.592331	−	0.487544i
$315$		0			0
$316$	114252.	−	22384.0i	1.14417	−	0.224163i
$317$	51349.0			0.510991			0.255495	−	0.966810i	$-0.417761\pi$
$317$	51349.0			0.510991			0.255495	+	0.966810i	$0.417761\pi$
$318$	19030.7	−	23121.0i	0.188192	−	0.228640i
$319$		−	92524.6i		−	0.909234i
$320$		0			0
$321$	−29849.9			−0.289690
$322$	−32329.4	−	26610.2i	−0.311807	−	0.256647i
$323$		−	29262.1i		−	0.280479i
$324$	2242.55	+	11446.4i	0.0213625	+	0.109038i
$325$		0			0
$326$	−5704.19	+	6930.18i	−0.0536733	+	0.0652092i
$327$			24473.0i			0.228872i
$328$	−96670.1	+	178991.i	−0.898555	+	1.66373i
$329$	−91765.9			−0.847792
$330$		0			0
$331$			28680.3i			0.261775i	0.991397	+	0.130887i	$0.0417826\pi$
$331$			28680.3i			0.261775i	−0.991397	+	0.130887i	$0.958217\pi$
$332$	−83946.3	+	16446.5i	−0.761597	+	0.149210i
$333$	31410.7			0.283263
$334$	−61038.3	+	74157.2i	−0.547154	+	0.664753i
$335$		0			0
$336$	106644.	−	43454.9i	0.944624	−	0.384911i
$337$	−99523.5			−0.876326			−0.438163	−	0.898895i	$-0.644371\pi$
$337$	−99523.5			−0.876326			−0.438163	+	0.898895i	$0.644371\pi$
$338$	185398.	+	152600.i	1.62282	+	1.33574i
$339$		−	1255.16i		−	0.0109219i
$340$		0			0
$341$	54655.7			0.470031
$342$	−34133.1	+	41469.3i	−0.291826	+	0.354547i
$343$		−	233093.i		−	1.98126i
$344$	−65671.9	−	35468.3i	−0.554961	−	0.299725i
$345$		0			0
$346$	119863.	+	98658.1i	1.00122	+	0.824102i
$347$		−	47129.6i		−	0.391413i	−0.980663	−	0.195706i	$-0.937300\pi$
$347$		−	47129.6i		−	0.391413i	0.980663	−	0.195706i	$-0.0626999\pi$
$348$	77269.7	−	15138.5i	0.638044	−	0.125004i
$349$	171932.			1.41158			0.705792	−	0.708419i	$-0.250591\pi$
$349$	171932.			1.41158			0.705792	+	0.708419i	$0.250591\pi$
$350$		0			0
$351$		−	41758.2i		−	0.338944i
$352$	29729.0	−	95519.9i	0.239936	−	0.770919i
$353$	−210420.			−1.68864			−0.844321	−	0.535837i	$-0.819996\pi$
$353$	−210420.			−1.68864			−0.844321	+	0.535837i	$0.819996\pi$
$354$	−32171.7	−	26480.3i	−0.256725	−	0.211308i
$355$		0			0
$356$	27716.0	+	141468.i	0.218690	+	1.11624i
$357$	−26468.4			−0.207678
$358$	−142708.	+	173380.i	−1.11348	+	1.35280i
$359$		−	123067.i		−	0.954888i	−0.878662	−	0.477444i	$-0.841563\pi$
$359$		−	123067.i		−	0.954888i	0.878662	−	0.477444i	$-0.158437\pi$
$360$		0			0
$361$	−117001.			−0.897794
$362$	61639.6	+	50735.2i	0.470374	+	0.387162i
$363$			26483.5i			0.200984i
$364$	−404585.	+	79265.2i	−3.05356	+	0.598246i
$365$		0			0
$366$	−46528.7	+	56529.0i	−0.347343	+	0.421997i
$367$			113887.i			0.845553i	0.906234	+	0.422777i	$0.138944\pi$
$367$			113887.i			0.845553i	−0.906234	+	0.422777i	$0.861056\pi$
$368$	−11681.0	−	28666.8i	−0.0862551	−	0.211682i
$369$	−85821.2			−0.630292
$370$		0			0
$371$		−	124728.i		−	0.906187i
$372$	8942.52	+	45644.4i	0.0646211	+	0.329838i
$373$	69712.3			0.501062			0.250531	−	0.968109i	$-0.419395\pi$
$373$	69712.3			0.501062			0.250531	+	0.968109i	$0.419395\pi$
$374$	−14612.5	+	17753.2i	−0.104468	+	0.126921i
$375$		0			0
$376$	−59691.2	−	32238.2i	−0.422216	−	0.228032i
$377$	−281892.			−1.98335
$378$	37510.1	+	30874.3i	0.262521	+	0.216080i
$379$			35367.5i			0.246222i	0.992393	+	0.123111i	$0.0392871\pi$
$379$			35367.5i			0.246222i	−0.992393	+	0.123111i	$0.960713\pi$
$380$		0			0
$381$	−35763.8			−0.246373
$382$	−145422.	+	176677.i	−0.996559	+	1.21075i
$383$		−	256391.i		−	1.74785i	−0.486058	−	0.873926i	$-0.661566\pi$
$383$		−	256391.i		−	1.74785i	0.486058	−	0.873926i	$-0.338434\pi$
$384$	84635.3	+	9198.93i	0.573970	+	0.0623843i
$385$		0			0
$386$	14215.9	+	11701.1i	0.0954116	+	0.0785327i
$387$		−	31487.8i		−	0.210242i
$388$	30140.8	+	153844.i	0.200212	+	1.02192i
$389$	55802.7			0.368770			0.184385	−	0.982854i	$-0.440971\pi$
$389$	55802.7			0.368770			0.184385	+	0.982854i	$0.440971\pi$
$390$		0			0
$391$			7114.91i			0.0465389i
$392$	154910.	−	286826.i	1.00811	−	1.86658i
$393$	−6483.87			−0.0419806
$394$	−92891.2	−	76458.2i	−0.598387	−	0.492529i
$395$		0			0
$396$	41416.7	−	8114.25i	0.264110	−	0.0517438i
$397$	264607.			1.67888			0.839442	−	0.543449i	$-0.182882\pi$
$397$	264607.			1.67888			0.839442	+	0.543449i	$0.182882\pi$
$398$	107385.	−	130465.i	0.677919	−	0.823623i
$399$			223710.i			1.40520i
$400$		0			0
$401$	−232397.			−1.44525			−0.722623	−	0.691243i	$-0.757063\pi$
$401$	−232397.			−1.44525			−0.722623	+	0.691243i	$0.757063\pi$
$402$	99009.0	+	81493.7i	0.612664	+	0.504280i
$403$		−	166518.i		−	1.02530i
$404$	16626.5	+	84865.1i	0.101868	+	0.519956i
$405$		0			0
$406$	208419.	−	253215.i	1.26441	−	1.53616i
$407$		−	113654.i		−	0.686114i
$408$	−17217.0	−	9298.60i	−0.103428	−	0.0558596i
$409$	−72108.2			−0.431060			−0.215530	−	0.976497i	$-0.569148\pi$
$409$	−72108.2			−0.431060			−0.215530	+	0.976497i	$0.569148\pi$
$410$		0			0
$411$		−	8898.54i		−	0.0526787i
$412$	−130240.	+	25516.3i	−0.767275	+	0.150322i
$413$	−173553.			−1.01750
$414$	8299.26	−	10083.0i	0.0484216	−	0.0588287i
$415$		0			0
$416$	−291018.	−	90574.6i	−1.68164	−	0.523383i
$417$	−35066.6			−0.201661
$418$	150049.	+	123504.i	0.858778	+	0.706855i
$419$		−	36120.5i		−	0.205743i	−0.994695	−	0.102872i	$-0.967197\pi$
$419$		−	36120.5i		−	0.205743i	0.994695	−	0.102872i	$-0.0328031\pi$
$420$		0			0
$421$	218504.			1.23281			0.616405	−	0.787429i	$-0.288589\pi$
$421$	218504.			1.23281			0.616405	+	0.787429i	$0.288589\pi$
$422$	−7864.53	+	9554.84i	−0.0441619	+	0.0536535i
$423$		−	28620.2i		−	0.159953i
$424$	43818.3	−	81132.4i	0.243738	−	0.451297i
$425$		0			0
$426$	14156.0	+	11651.7i	0.0780050	+	0.0642054i
$427$			304951.i			1.67253i
$428$	−90199.2	+	17671.6i	−0.492397	+	0.0964691i
$429$	−151095.			−0.820984
$430$		0			0
$431$		−	84359.7i		−	0.454130i	−0.973880	−	0.227065i	$-0.927087\pi$
$431$		−	84359.7i		−	0.454130i	0.973880	−	0.227065i	$-0.0729130\pi$
$432$	13552.9	+	33260.6i	0.0726212	+	0.178222i
$433$	80951.5			0.431767			0.215883	−	0.976419i	$-0.430737\pi$
$433$	80951.5			0.431767			0.215883	+	0.976419i	$0.430737\pi$
$434$	149578.	+	123116.i	0.794122	+	0.653637i
$435$		0			0
$436$	14488.4	+	73951.5i	0.0762161	+	0.389022i
$437$	60135.0			0.314894
$438$	21923.3	−	26635.2i	0.114277	−	0.138838i
$439$			31983.1i			0.165955i	0.996551	+	0.0829777i	$0.0264430\pi$
$439$			31983.1i			0.165955i	−0.996551	+	0.0829777i	$0.973557\pi$
$440$		0			0
$441$	137525.			0.707138
$442$	54088.1	+	44519.6i	0.276858	+	0.227880i
$443$			376981.i			1.92093i	0.278394	+	0.960467i	$0.410198\pi$
$443$			376981.i			1.92093i	−0.278394	+	0.960467i	$0.589802\pi$
$444$	94915.6	−	18595.6i	0.481473	−	0.0943288i
$445$		0			0
$446$	−109459.	+	132984.i	−0.550275	+	0.668545i
$447$		−	198024.i		−	0.991064i
$448$	296527.	−	194445.i	1.47743	−	0.968815i
$449$	−105390.			−0.522767			−0.261384	−	0.965235i	$-0.584179\pi$
$449$	−105390.			−0.522767			−0.261384	+	0.965235i	$0.584179\pi$
$450$		0			0
$451$			310529.i			1.52668i
$452$	−743.070	−	3792.77i	−0.00363708	−	0.0185644i
$453$	22779.9			0.111008
$454$	110288.	−	133992.i	0.535076	−	0.650080i
$455$		0			0
$456$	−78591.4	+	145517.i	−0.377960	+	0.699817i
$457$	260309.			1.24640			0.623200	−	0.782063i	$-0.285832\pi$
$457$	260309.			1.24640			0.623200	+	0.782063i	$0.285832\pi$
$458$	173063.	+	142447.i	0.825037	+	0.679083i
$459$		−	8255.05i		−	0.0391827i
$460$		0			0
$461$	112820.			0.530865			0.265433	−	0.964129i	$-0.414485\pi$
$461$	112820.			0.530865			0.265433	+	0.964129i	$0.414485\pi$
$462$	111713.	−	135724.i	0.523384	−	0.635875i
$463$			188351.i			0.878628i	0.898334	+	0.439314i	$0.144778\pi$
$463$			188351.i			0.878628i	−0.898334	+	0.439314i	$0.855222\pi$
$464$	224528.	−	91489.5i	1.04288	−	0.424948i
$465$		0			0
$466$	128595.	+	105846.i	0.592177	+	0.487417i
$467$		−	373875.i		−	1.71432i	−0.515048	−	0.857161i	$-0.672226\pi$
$467$		−	373875.i		−	1.71432i	0.515048	−	0.857161i	$-0.327774\pi$
$468$	−24721.5	−	126183.i	−0.112871	−	0.576116i
$469$	534114.			2.42822
$470$		0			0
$471$		−	98259.5i		−	0.442927i
$472$	−112892.	−	60971.0i	−0.506732	−	0.273677i
$473$	−113933.			−0.509245
$474$	116771.	+	96113.7i	0.519732	+	0.427788i
$475$		0			0
$476$	−79981.0	+	15669.7i	−0.352999	+	0.0691586i
$477$	38900.7			0.170970
$478$	−180556.	+	219363.i	−0.790235	+	0.960079i
$479$			169326.i			0.737993i	0.929431	+	0.368997i	$0.120299\pi$
$479$			169326.i			0.737993i	−0.929431	+	0.368997i	$0.879701\pi$
$480$		0			0
$481$	−346267.			−1.49665
$482$	−181275.	−	149207.i	−0.780270	−	0.642235i
$483$		−	54393.8i		−	0.233160i
$484$	15678.6	+	80026.6i	0.0669294	+	0.341620i
$485$		0			0
$486$	−9629.19	+	11698.8i	−0.0407678	+	0.0495299i
$487$			27221.0i			0.114774i	0.998352	+	0.0573872i	$0.0182770\pi$
$487$			27221.0i			0.114774i	−0.998352	+	0.0573872i	$0.981723\pi$
$488$	−107132.	+	198362.i	−0.449863	+	0.832952i
$489$	−11659.9			−0.0487616
$490$		0			0
$491$		−	437686.i		−	1.81552i	−0.419495	−	0.907758i	$-0.637793\pi$
$491$		−	437686.i		−	1.81552i	0.419495	−	0.907758i	$-0.362207\pi$
$492$	−259331.	+	50807.4i	−1.07133	+	0.209892i
$493$	−55726.3			−0.229280
$494$	376278.	−	457151.i	1.54189	−	1.87329i
$495$		0			0
$496$	54044.2	+	132632.i	0.219678	+	0.539119i
$497$	76366.1			0.309163
$498$	−85797.2	−	70619.1i	−0.345951	−	0.284750i
$499$		−	347647.i		−	1.39617i	−0.716016	−	0.698084i	$-0.754036\pi$
$499$		−	347647.i		−	1.39617i	0.716016	−	0.698084i	$-0.245964\pi$
$500$		0			0
$501$	−124768.			−0.497083
$502$	102283.	−	124266.i	0.405878	−	0.493112i
$503$			262758.i			1.03853i	0.854612	+	0.519267i	$0.173795\pi$
$503$			262758.i			1.03853i	−0.854612	+	0.519267i	$0.826205\pi$
$504$	131624.	+	71088.1i	0.518174	+	0.279857i
$505$		0			0
$506$	−36483.6	−	30029.4i	−0.142494	−	0.117286i
$507$			311929.i			1.21350i
$508$	−108069.	+	21172.7i	−0.418769	+	0.0820442i
$509$	192747.			0.743963			0.371981	−	0.928240i	$-0.378679\pi$
$509$	192747.			0.743963			0.371981	+	0.928240i	$0.378679\pi$
$510$		0			0
$511$		−	143686.i		−	0.550267i
$512$	261193.	−	22308.4i	0.996372	−	0.0850998i
$513$	−69771.4			−0.265120
$514$	263451.	+	216845.i	0.997182	+	0.820774i
$515$		0			0
$516$	−18641.2	−	95148.4i	−0.0700124	−	0.357357i
$517$	−103557.			−0.387435
$518$	256016.	−	311041.i	0.954129	−	1.15920i
$519$			201667.i			0.748686i
$520$		0			0
$521$	377715.			1.39152			0.695760	−	0.718275i	$-0.255068\pi$
$521$	377715.			1.39152			0.695760	+	0.718275i	$0.255068\pi$
$522$	78973.4	+	65002.5i	0.289828	+	0.238555i
$523$		−	234085.i		−	0.855798i	−0.903827	−	0.427899i	$-0.859254\pi$
$523$		−	234085.i		−	0.855798i	0.903827	−	0.427899i	$-0.140746\pi$
$524$	−19592.7	+	3838.54i	−0.0713561	+	0.0139799i
$525$		0			0
$526$	−221570.	+	269192.i	−0.800830	+	0.972951i
$527$		−	32918.4i		−	0.118527i
$528$	120347.	−	49038.6i	0.431687	−	0.175902i
$529$	265220.			0.947751
$530$		0			0
$531$		−	54128.4i		−	0.191971i
$532$	132439.	+	675997.i	0.467944	+	2.38848i
$533$	946079.			3.33022
$534$	−119008.	+	144587.i	−0.417345	+	0.507044i
$535$		0			0
$536$	347426.	+	187639.i	1.20930	+	0.653121i
$537$	−291709.			−1.01158
$538$	−388758.	−	319984.i	−1.34312	−	1.10551i
$539$		−	497609.i		−	1.71282i
$540$		0			0
$541$	−27230.3			−0.0930374			−0.0465187	−	0.998917i	$-0.514813\pi$
$541$	−27230.3			−0.0930374			−0.0465187	+	0.998917i	$0.514813\pi$
$542$	239671.	−	291183.i	0.815863	−	0.991215i
$543$			103708.i			0.351732i
$544$	−57530.4	−	17905.4i	−0.194401	−	0.0605043i
$545$		0			0
$546$	−413505.	−	340354.i	−1.38706	−	1.14168i
$547$			219088.i			0.732225i	0.930571	+	0.366112i	$0.119311\pi$
$547$			219088.i			0.732225i	−0.930571	+	0.366112i	$0.880689\pi$
$548$	−5268.06	−	26889.2i	−0.0175424	−	0.0895400i
$549$	−95109.2			−0.315557
$550$		0			0
$551$			470997.i			1.55137i
$552$	19109.0	−	35381.7i	0.0627135	−	0.116118i
$553$	629934.			2.05989
$554$	−203210.	−	167261.i	−0.662104	−	0.544973i
$555$		0			0
$556$	−105963.	+	20759.9i	−0.342771	+	0.0671547i
$557$	507368.			1.63536			0.817678	−	0.575675i	$-0.195261\pi$
$557$	507368.			1.63536			0.817678	+	0.575675i	$0.195261\pi$
$558$	−38398.0	+	46650.8i	−0.123322	+	0.149827i
$559$			347116.i			1.11084i
$560$		0			0
$561$	−29869.4			−0.0949077
$562$	49790.9	+	40982.6i	0.157644	+	0.129756i
$563$		−	165410.i		−	0.521850i	−0.965359	−	0.260925i	$-0.915972\pi$
$563$		−	165410.i		−	0.521850i	0.965359	−	0.260925i	$-0.0840276\pi$
$564$	−16943.6	−	86483.3i	−0.0532656	−	0.271878i
$565$		0			0
$566$	326554.	−	396740.i	1.01935	−	1.23844i
$567$			63110.2i			0.196306i
$568$	49674.1	+	26828.1i	0.153969	+	0.0831561i
$569$	59830.4			0.184798			0.0923990	−	0.995722i	$-0.470546\pi$
$569$	59830.4			0.184798			0.0923990	+	0.995722i	$0.470546\pi$
$570$		0			0
$571$			149969.i			0.459969i	0.973194	+	0.229984i	$0.0738675\pi$
$571$			149969.i			0.459969i	−0.973194	+	0.229984i	$0.926132\pi$
$572$	−456571.	+	89450.2i	−1.39546	+	0.273394i
$573$	−297256.			−0.905361
$574$	−699492.	+	849833.i	−2.12304	+	2.57935i
$575$		0			0
$576$	60644.1	+	92481.8i	0.182786	+	0.278748i
$577$	195679.			0.587750			0.293875	−	0.955844i	$-0.405055\pi$
$577$	195679.			0.587750			0.293875	+	0.955844i	$0.405055\pi$
$578$	−247252.	−	203512.i	−0.740090	−	0.609163i
$579$			23918.1i			0.0713460i
$580$		0			0
$581$	−462841.			−1.37113
$582$	−129420.	+	157236.i	−0.382082	+	0.464202i
$583$		−	140755.i		−	0.414121i
$584$	50478.4	−	93464.0i	0.148006	−	0.274043i
$585$		0			0
$586$	−499078.	−	410788.i	−1.45336	−	1.19625i
$587$		−	273284.i		−	0.793119i	−0.918009	−	0.396559i	$-0.870204\pi$
$587$		−	273284.i		−	0.793119i	0.918009	−	0.396559i	$-0.129796\pi$
$588$	415567.	−	81416.7i	1.20195	−	0.235483i
$589$	−278225.			−0.801983
$590$		0			0
$591$		−	156288.i		−	0.447456i
$592$	275803.	−	112383.i	0.786964	−	0.320668i
$593$	−151488.			−0.430794			−0.215397	−	0.976527i	$-0.569105\pi$
$593$	−151488.			−0.430794			−0.215397	+	0.976527i	$0.569105\pi$
$594$	42329.9	+	34841.5i	0.119971	+	0.0987470i
$595$		0			0
$596$	−117233.	−	598379.i	−0.330032	−	1.68455i
$597$	219506.			0.615881
$598$	−91489.7	+	111153.i	−0.255841	+	0.310828i
$599$			371626.i			1.03575i	0.855458	+	0.517873i	$0.173276\pi$
$599$			371626.i			1.03575i	−0.855458	+	0.517873i	$0.826724\pi$
$600$		0			0
$601$	368841.			1.02115			0.510575	−	0.859833i	$-0.329433\pi$
$601$	368841.			1.02115			0.510575	+	0.859833i	$0.329433\pi$
$602$	−311804.	−	256644.i	−0.860376	−	0.708170i
$603$			166581.i			0.458132i
$604$	68835.2	−	13486.0i	0.188685	−	0.0369666i
$605$		0			0
$606$	−71392.1	+	86736.3i	−0.194404	+	0.236187i
$607$		−	511656.i		−	1.38868i	−0.719649	−	0.694338i	$-0.755697\pi$
$607$		−	511656.i		−	1.38868i	0.719649	−	0.694338i	$-0.244303\pi$
$608$	−151336.	+	486245.i	−0.409387	+	1.31537i
$609$	426030.			1.14870
$610$		0			0
$611$			315505.i			0.845130i
$612$	−4887.11	−	24944.7i	−0.0130482	−	0.0666003i
$613$	384682.			1.02372			0.511859	−	0.859069i	$-0.328957\pi$
$613$	384682.			1.02372			0.511859	+	0.859069i	$0.328957\pi$
$614$	100918.	−	122609.i	0.267691	−	0.325225i
$615$		0			0
$616$	257220.	−	476259.i	0.677864	−	1.25511i
$617$	−326231.			−0.856949			−0.428475	−	0.903554i	$-0.640949\pi$
$617$	−326231.			−0.856949			−0.428475	+	0.903554i	$0.640949\pi$
$618$	−133112.	−	109564.i	−0.348530	−	0.286873i
$619$		−	752595.i		−	1.96417i	−0.188428	−	0.982087i	$-0.560339\pi$
$619$		−	752595.i		−	1.96417i	0.188428	−	0.982087i	$-0.439661\pi$
$620$		0			0
$621$	16964.5			0.0439904
$622$	42225.1	−	51300.5i	0.109141	−	0.132599i
$623$			779987.i			2.00961i
$624$	−149404.	−	366659.i	−0.383702	−	0.941658i
$625$		0			0
$626$	106099.	+	87329.5i	0.270746	+	0.222850i
$627$			252455.i			0.642169i
$628$	−58171.0	−	296916.i	−0.147498	−	0.752860i
$629$	−68452.4			−0.173016
$630$		0			0
$631$			514641.i			1.29255i	0.763106	+	0.646273i	$0.223673\pi$
$631$			514641.i			1.29255i	−0.763106	+	0.646273i	$0.776327\pi$
$632$	409755.	+	221302.i	1.02586	+	0.554053i
$633$	−16075.9			−0.0401206
$634$	158585.	+	130530.i	0.394534	+	0.324738i
$635$		0			0
$636$	117548.	−	23029.8i	0.290605	−	0.0569345i
$637$	−1.51605e6			−3.73625
$638$	235200.	−	285751.i	0.577825	−	0.702016i
$639$			23817.3i			0.0583299i
$640$		0			0
$641$	417472.			1.01604			0.508021	−	0.861345i	$-0.330377\pi$
$641$	417472.			1.01604			0.508021	+	0.861345i	$0.330377\pi$
$642$	−92188.0	−	75879.4i	−0.223668	−	0.184100i
$643$			347739.i			0.841070i	0.907276	+	0.420535i	$0.138158\pi$
$643$			347739.i			0.841070i	−0.907276	+	0.420535i	$0.861842\pi$
$644$	−32201.9	−	164365.i	−0.0776443	−	0.396311i
$645$		0			0
$646$	74385.1	−	90372.6i	0.178247	−	0.216557i
$647$		−	451372.i		−	1.07827i	−0.842221	−	0.539133i	$-0.818752\pi$
$647$		−	451372.i		−	1.07827i	0.842221	−	0.539133i	$-0.181248\pi$
$648$	−22171.2	+	41051.4i	−0.0528006	+	0.0977639i
$649$	−195854.			−0.464989
$650$		0			0
$651$			251662.i			0.593821i
$652$	−35233.4	+	6902.83i	−0.0828818	+	0.0162380i
$653$	−378215.			−0.886977			−0.443489	−	0.896280i	$-0.646259\pi$
$653$	−378215.			−0.886977			−0.443489	+	0.896280i	$0.646259\pi$
$654$	−62211.1	+	75582.1i	−0.145450	+	0.176711i
$655$		0			0
$656$	−753555.	+	307055.i	−1.75108	+	0.713523i
$657$	44813.4			0.103819
$658$	−283408.	−	233271.i	−0.654576	−	0.538778i
$659$			625044.i			1.43926i	0.694357	+	0.719631i	$0.255689\pi$
$659$			625044.i			1.43926i	−0.694357	+	0.719631i	$0.744311\pi$
$660$		0			0
$661$	576980.			1.32056			0.660280	−	0.751020i	$-0.270438\pi$
$661$	576980.			1.32056			0.660280	+	0.751020i	$0.270438\pi$
$662$	−72906.1	+	88575.7i	−0.166360	+	0.202115i
$663$			91002.4i			0.207026i
$664$	−301066.	−	162601.i	−0.682849	−	0.368796i
$665$		0			0
$666$	97008.4	+	79847.0i	0.218706	+	0.180016i
$667$		−	114520.i		−	0.257413i
$668$	−377019.	+	73864.6i	−0.844910	+	0.165532i
$669$	−223744.			−0.499918
$670$		0			0
$671$			344136.i			0.764336i
$672$	439822.	+	136887.i	0.973953	+	0.303127i
$673$	−411758.			−0.909101			−0.454550	−	0.890721i	$-0.650200\pi$
$673$	−411758.			−0.909101			−0.454550	+	0.890721i	$0.650200\pi$
$674$	−307367.	−	252991.i	−0.676607	−	0.556911i
$675$		0			0
$676$	184666.	+	942573.i	0.404105	+	2.06263i
$677$	−628737.			−1.37180			−0.685902	−	0.727694i	$-0.740592\pi$
$677$	−628737.			−1.37180			−0.685902	+	0.727694i	$0.740592\pi$
$678$	3190.64	−	3876.40i	0.00694094	−	0.00843275i
$679$			848227.i			1.83981i
$680$		0			0
$681$	225439.			0.486110
$682$	168797.	+	138936.i	0.362909	+	0.298708i
$683$		−	531547.i		−	1.13946i	−0.821831	−	0.569731i	$-0.807047\pi$
$683$		−	531547.i		−	1.13946i	0.821831	−	0.569731i	$-0.192953\pi$
$684$	−210832.	+	41305.7i	−0.450634	+	0.0882871i
$685$		0			0
$686$	592530.	−	719881.i	1.25911	−	1.52972i
$687$			291176.i			0.616939i
$688$	−112658.	−	276479.i	−0.238005	−	0.584098i
$689$	−428835.			−0.903341
$690$		0			0
$691$		−	157186.i		−	0.329198i	−0.986361	−	0.164599i	$-0.947367\pi$
$691$		−	157186.i		−	0.329198i	0.986361	−	0.164599i	$-0.0526330\pi$
$692$	119390.	+	609388.i	0.249319	+	1.27257i
$693$	228353.			0.475488
$694$	119805.	−	145554.i	0.248745	−	0.302208i
$695$		0			0
$696$	277121.	+	149668.i	0.572072	+	0.308967i
$697$	187027.			0.384981
$698$	530993.	+	437057.i	1.08988	+	0.897071i
$699$			216359.i			0.442813i
$700$		0			0
$701$	−194246.			−0.395290			−0.197645	−	0.980274i	$-0.563329\pi$
$701$	−194246.			−0.395290			−0.197645	+	0.980274i	$0.563329\pi$
$702$	106151.	−	128965.i	0.215401	−	0.261697i
$703$			578557.i			1.17067i
$704$	334629.	−	219430.i	0.675178	−	0.442742i
$705$		0			0
$706$	−649857.	−	534893.i	−1.30379	−	1.07314i
$707$			467907.i			0.936097i
$708$	−32044.8	−	163563.i	−0.0639279	−	0.326301i
$709$	−455572.			−0.906285			−0.453142	−	0.891438i	$-0.649697\pi$
$709$	−455572.			−0.906285			−0.453142	+	0.891438i	$0.649697\pi$
$710$		0			0
$711$			196466.i			0.388640i
$712$	−274017.	+	507360.i	−0.540527	+	1.00082i
$713$	67648.7			0.133070
$714$	−81744.5	−	67283.4i	−0.160348	−	0.131981i
$715$		0			0
$716$	−881474.	+	172696.i	−1.71943	+	0.336865i
$717$	−369074.			−0.717919
$718$	312839.	−	380077.i	0.606838	−	0.737264i
$719$		−	561316.i		−	1.08580i	−0.839797	−	0.542900i	$-0.817326\pi$
$719$		−	561316.i		−	1.08580i	0.839797	−	0.542900i	$-0.182674\pi$
$720$		0			0
$721$	−718086.			−1.38136
$722$	−361345.	−	297421.i	−0.693182	−	0.570554i
$723$		−	304993.i		−	0.583463i
$724$	61396.4	+	313379.i	0.117129	+	0.597851i
$725$		0			0
$726$	−67321.8	+	81791.1i	−0.127727	+	0.155179i
$727$			155857.i			0.294889i	0.989070	+	0.147444i	$0.0471047\pi$
$727$			155857.i			0.294889i	−0.989070	+	0.147444i	$0.952895\pi$
$728$	−1.45101e6	−	783664.i	−2.73783	−	1.47866i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			68620.3i			0.128416i
$732$	−287397.	+	56306.0i	−0.536364	+	0.105083i
$733$	−744418.			−1.38551			−0.692754	−	0.721174i	$-0.743603\pi$
$733$	−744418.			−1.38551			−0.692754	+	0.721174i	$0.743603\pi$
$734$	−289503.	+	351726.i	−0.537355	+	0.652848i
$735$		0			0
$736$	36796.4	−	118227.i	0.0679281	−	0.218254i
$737$	602744.			1.10968
$738$	−265049.	−	218160.i	−0.486645	−	0.400555i
$739$		−	200689.i		−	0.367480i	−0.982975	−	0.183740i	$-0.941180\pi$
$739$		−	200689.i		−	0.367480i	0.982975	−	0.183740i	$-0.0588205\pi$
$740$		0			0
$741$	769149.			1.40079
$742$	317063.	−	385209.i	0.575888	−	0.699662i
$743$			20434.2i			0.0370152i	0.999829	+	0.0185076i	$0.00589149\pi$
$743$			20434.2i			0.0370152i	−0.999829	+	0.0185076i	$0.994109\pi$
$744$	−88411.3	+	163699.i	−0.159721	+	0.295734i
$745$		0			0
$746$	215298.	+	177210.i	0.386868	+	0.318428i
$747$		−	144352.i		−	0.258692i
$748$	−90258.1	+	17683.1i	−0.161318	+	0.0316050i
$749$	−497317.			−0.886482
$750$		0			0
$751$		−	60228.7i		−	0.106788i	−0.998574	−	0.0533941i	$-0.982996\pi$
$751$		−	60228.7i		−	0.106788i	0.998574	−	0.0533941i	$-0.0170040\pi$
$752$	−102399.	−	251301.i	−0.181075	−	0.444383i
$753$	209076.			0.368735
$754$	−870590.	−	716578.i	−1.53134	−	1.26044i
$755$		0			0
$756$	37362.1	+	190703.i	0.0653714	+	0.333668i
$757$	554160.			0.967037			0.483519	−	0.875334i	$-0.339359\pi$
$757$	554160.			0.967037			0.483519	+	0.875334i	$0.339359\pi$
$758$	−89905.2	+	109228.i	−0.156475	+	0.190107i
$759$		−	61383.0i		−	0.106553i
$760$		0			0
$761$	62269.4			0.107524			0.0537620	−	0.998554i	$-0.482879\pi$
$761$	62269.4			0.107524			0.0537620	+	0.998554i	$0.482879\pi$
$762$	−110452.	−	90912.5i	−0.190224	−	0.156572i
$763$			407735.i			0.700372i
$764$	−898236.	+	175980.i	−1.53888	+	0.301493i
$765$		0			0
$766$	651752.	−	791833.i	1.11077	−	1.34951i
$767$			596703.i			1.01430i
$768$	238002.	+	243555.i	0.403514	+	0.412928i
$769$	547774.			0.926295			0.463147	−	0.886281i	$-0.346720\pi$
$769$	547774.			0.926295			0.463147	+	0.886281i	$0.346720\pi$
$770$		0			0
$771$			443253.i			0.745663i
$772$	14159.9	+	72274.6i	0.0237588	+	0.121269i
$773$	23192.7			0.0388144			0.0194072	−	0.999812i	$-0.493822\pi$
$773$	23192.7			0.0388144			0.0194072	+	0.999812i	$0.493822\pi$
$774$	80042.8	−	97246.3i	0.133610	−	0.162327i
$775$		0			0
$776$	−297990.	+	551748.i	−0.494855	+	0.916257i
$777$	523321.			0.866814
$778$	172340.	+	141852.i	0.284726	+	0.234356i
$779$		−	1.58075e6i		−	2.60488i
$780$		0			0
$781$	86178.7			0.141286
$782$	−18086.3	+	21973.6i	−0.0295758	+	0.0359325i
$783$			132872.i			0.216725i
$784$	1.20754e6	−	492043.i	1.96458	−	0.800517i
$785$		0			0
$786$	−20024.7	−	16482.2i	−0.0324131	−	0.0266790i
$787$		−	642178.i		−	1.03683i	−0.855130	−	0.518413i	$-0.826523\pi$
$787$		−	642178.i		−	1.03683i	0.855130	−	0.518413i	$-0.173477\pi$
$788$	−92524.7	−	472264.i	−0.149007	−	0.760558i
$789$	−452912.			−0.727544
$790$		0			0
$791$		−	20911.6i		−	0.0334222i
$792$	148537.	+	80222.5i	0.236802	+	0.127893i
$793$	1.04847e6			1.66728
$794$	817208.	+	672639.i	1.29626	+	1.06694i
$795$		0			0
$796$	663292.	−	129950.i	1.04684	−	0.205093i
$797$	385649.			0.607122			0.303561	−	0.952812i	$-0.401824\pi$
$797$	385649.			0.607122			0.303561	+	0.952812i	$0.401824\pi$
$798$	−568677.	+	690902.i	−0.893017	+	1.08495i
$799$			62371.1i			0.0976990i
$800$		0			0
$801$	−243265.			−0.379153
$802$	−717730.	−	590759.i	−1.11587	−	0.918463i
$803$		−	162149.i		−	0.251468i
$804$	98618.4	+	503367.i	0.152562	+	0.778705i
$805$		0			0
$806$	423293.	−	514271.i	0.651585	−	0.791629i
$807$		−	654079.i		−	1.00435i
$808$	−164380.	+	304361.i	−0.251783	+	0.466193i
$809$	404473.			0.618006			0.309003	−	0.951061i	$-0.400005\pi$
$809$	404473.			0.618006			0.309003	+	0.951061i	$0.400005\pi$
$810$		0			0
$811$		−	740872.i		−	1.12642i	−0.826313	−	0.563212i	$-0.809566\pi$
$811$		−	740872.i		−	1.12642i	0.826313	−	0.563212i	$-0.190434\pi$
$812$	1.28736e6	−	252216.i	1.95248	−	0.382525i
$813$	489911.			0.741202
$814$	288912.	−	351007.i	0.436030	−	0.529746i
$815$		0			0
$816$	−29535.3	−	72483.7i	−0.0443569	−	0.108858i
$817$	579976.			0.868893
$818$	−222698.	−	183301.i	−0.332820	−	0.273942i
$819$		−	695716.i		−	1.03720i
$820$		0			0
$821$	326364.			0.484190			0.242095	−	0.970253i	$-0.422165\pi$
$821$	326364.			0.484190			0.242095	+	0.970253i	$0.422165\pi$
$822$	22620.3	−	27482.1i	0.0334777	−	0.0406730i
$823$		−	6015.58i		−	0.00888132i	−0.999990	−	0.00444066i	$-0.998586\pi$
$823$		−	6015.58i		−	0.00888132i	0.999990	−	0.00444066i	$-0.00141351\pi$
$824$	−467095.	−	252270.i	−0.687940	−	0.371545i
$825$		0			0
$826$	−535999.	−	441177.i	−0.785604	−	0.646626i
$827$		−	489341.i		−	0.715485i	−0.933820	−	0.357742i	$-0.883547\pi$
$827$		−	489341.i		−	0.715485i	0.933820	−	0.357742i	$-0.116453\pi$
$828$	51262.6	−	10043.2i	0.0747721	−	0.0146492i
$829$	−92567.3			−0.134694			−0.0673470	−	0.997730i	$-0.521453\pi$
$829$	−92567.3			−0.134694			−0.0673470	+	0.997730i	$0.521453\pi$
$830$		0			0
$831$		−	341898.i		−	0.495102i
$832$	−668531.	−	1.01950e6i	−0.965773	−	1.47280i
$833$	−299704.			−0.431919
$834$	−108299.	−	89140.4i	−0.155702	−	0.128157i
$835$		0			0
$836$	149457.	+	762858.i	0.213847	+	1.09152i
$837$	−78489.2			−0.112036
$838$	91819.2	−	111554.i	0.130751	−	0.158853i
$839$			1.34655e6i			1.91293i	0.291847	+	0.956465i	$0.405730\pi$
$839$			1.34655e6i			1.91293i	−0.291847	+	0.956465i	$0.594270\pi$
$840$		0			0
$841$	189678.			0.268179
$842$	674825.	+	555444.i	0.951846	+	0.783459i
$843$			83772.5i			0.117882i
$844$	−48577.3	+	9517.14i	−0.0681944	+	0.0133605i
$845$		0			0
$846$	72753.4	−	88390.2i	0.101651	−	0.123499i
$847$			441230.i			0.615033i
$848$	341568.	−	139181.i	0.474992	−	0.193547i
$849$	667509.			0.926066
$850$		0			0
$851$		−	140673.i		−	0.194245i
$852$	14100.2	+	71970.1i	0.0194243	+	0.0991454i
$853$	−1.23563e6			−1.69820			−0.849101	−	0.528230i	$-0.822856\pi$
$853$	−1.23563e6			−1.69820			−0.849101	+	0.528230i	$0.822856\pi$
$854$	−775194.	+	941806.i	−1.06291	+	1.29135i
$855$		0			0
$856$	−323491.	−	174712.i	−0.441484	−	0.238438i
$857$	−496036.			−0.675385			−0.337693	−	0.941256i	$-0.609646\pi$
$857$	−496036.			−0.675385			−0.337693	+	0.941256i	$0.609646\pi$
$858$	−466638.	−	384087.i	−0.633878	−	0.521741i
$859$			74255.5i			0.100633i	0.998733	+	0.0503167i	$0.0160231\pi$
$859$			74255.5i			0.100633i	−0.998733	+	0.0503167i	$0.983977\pi$
$860$		0			0
$861$	−1.42983e6			−1.92876
$862$	214445.	−	260535.i	0.288603	−	0.350632i
$863$			28282.1i			0.0379743i	0.999820	+	0.0189872i	$0.00604417\pi$
$863$			28282.1i			0.0379743i	−0.999820	+	0.0189872i	$0.993956\pi$
$864$	−42692.9	+	137173.i	−0.0571910	+	0.183756i
$865$		0			0
$866$	250009.	+	205781.i	0.333365	+	0.274391i
$867$		−	415998.i		−	0.553418i
$868$	148988.	+	760461.i	0.197747	+	1.00934i
$869$	710877.			0.941358
$870$		0			0
$871$		−	1.83636e6i		−	2.42060i
$872$	−143241.	+	265220.i	−0.188380	+	0.348798i
$873$	−264548.			−0.347117
$874$	185720.	+	152865.i	0.243128	+	0.200117i
$875$		0			0
$876$	135415.	−	26530.1i	0.176465	−	0.0345725i
$877$	345796.			0.449594			0.224797	−	0.974406i	$-0.427828\pi$
$877$	345796.			0.449594			0.224797	+	0.974406i	$0.427828\pi$
$878$	−81301.9	+	98776.0i	−0.105466	+	0.128133i
$879$		−	839692.i		−	1.08678i
$880$		0			0
$881$	756432.			0.974581			0.487290	−	0.873240i	$-0.337985\pi$
$881$	756432.			0.974581			0.487290	+	0.873240i	$0.337985\pi$
$882$	424729.	+	349592.i	0.545978	+	0.449391i
$883$		−	1.37291e6i		−	1.76084i	−0.474195	−	0.880420i	$-0.657261\pi$
$883$		−	1.37291e6i		−	1.76084i	0.474195	−	0.880420i	$-0.342739\pi$
$884$	53874.7	+	274987.i	0.0689414	+	0.351890i
$885$		0			0
$886$	−958297.	+	1.16426e6i	−1.22077	+	1.48314i
$887$			240951.i			0.306254i	0.988207	+	0.153127i	$0.0489344\pi$
$887$			240951.i			0.306254i	−0.988207	+	0.153127i	$0.951066\pi$
$888$	340406.	+	183848.i	0.431689	+	0.233148i
$889$	−595845.			−0.753928
$890$		0			0
$891$			71219.4i			0.0897104i
$892$	−676099.	+	132460.i	−0.849730	+	0.166477i
$893$	527158.			0.661056
$894$	503381.	−	611572.i	0.629828	−	0.765196i
$895$		0			0
$896$	1.41007e6	+	153259.i	1.75641	+	0.190902i
$897$	−187014.			−0.232428
$898$	−325486.	−	267905.i	−0.403626	−	0.332222i
$899$			529847.i			0.655588i
$900$		0			0
$901$	−84775.0			−0.104428
$902$	−789372.	+	959031.i	−0.970217	+	1.17874i
$903$		−	524605.i		−	0.643364i
$904$	7346.45	−	13602.4i	0.00898960	−	0.0166448i
$905$		0			0
$906$	70353.0	+	57907.1i	0.0857089	+	0.0705465i
$907$		−	125297.i		−	0.152310i	−0.997096	−	0.0761549i	$-0.975736\pi$
$907$		−	125297.i		−	0.152310i	0.997096	−	0.0761549i	$-0.0242643\pi$
$908$	681222.	−	133463.i	0.826260	−	0.161879i
$909$	−145932.			−0.176614
$910$		0			0
$911$		−	1.15679e6i		−	1.39386i	−0.717140	−	0.696929i	$-0.754549\pi$
$911$		−	1.15679e6i		−	1.39386i	0.717140	−	0.696929i	$-0.245451\pi$
$912$	−612629.	+	249631.i	−0.736560	+	0.300130i
$913$	−522313.			−0.626599
$914$	803934.	+	661713.i	0.962339	+	0.792095i
$915$		0			0
$916$	172380.	+	879862.i	0.205445	+	1.04863i
$917$	−108025.			−0.128465
$918$	20984.6	−	25494.8i	0.0249009	−	0.0302528i
$919$			1.27592e6i			1.51076i	0.655290	+	0.755378i	$0.272547\pi$
$919$			1.27592e6i			1.51076i	−0.655290	+	0.755378i	$0.727453\pi$
$920$		0			0
$921$	206287.			0.243194
$922$	348431.	+	286792.i	0.409879	+	0.337369i
$923$		−	262558.i		−	0.308193i
$924$	690026.	−	135188.i	0.808205	−	0.158341i
$925$		0			0
$926$	−478792.	+	581698.i	−0.558374	+	0.678384i
$927$		−	223959.i		−	0.260621i
$928$	925997.	+	288202.i	1.07526	+	0.334657i
$929$	829467.			0.961098			0.480549	−	0.876968i	$-0.340437\pi$
$929$	829467.			0.961098			0.480549	+	0.876968i	$0.340437\pi$
$930$		0			0
$931$			2.53308e6i			2.92247i
$932$	128087.	+	653783.i	0.147460	+	0.752665i
$933$	86312.2			0.0991537
$934$	950400.	−	1.15467e6i	1.08946	−	1.32362i
$935$		0			0
$936$	244412.	−	452544.i	0.278978	−	0.516547i
$937$	−448946.			−0.511346			−0.255673	−	0.966763i	$-0.582297\pi$
$937$	−448946.			−0.511346			−0.255673	+	0.966763i	$0.582297\pi$
$938$	1.64955e6	+	1.35773e6i	1.87482	+	1.54315i
$939$			178510.i			0.202456i
$940$		0			0
$941$	37415.5			0.0422544			0.0211272	−	0.999777i	$-0.493275\pi$
$941$	37415.5			0.0422544			0.0211272	+	0.999777i	$0.493275\pi$
$942$	249778.	−	303463.i	0.281483	−	0.341982i
$943$			384349.i			0.432218i
$944$	−193663.	−	475275.i	−0.217321	−	0.533337i
$945$		0			0
$946$	−351868.	−	289621.i	−0.393186	−	0.323629i
$947$			1.58481e6i			1.76717i	0.468275	+	0.883583i	$0.344876\pi$
$947$			1.58481e6i			1.76717i	−0.468275	+	0.883583i	$0.655124\pi$
$948$	116311.	+	593672.i	0.129420	+	0.660587i
$949$	−494015.			−0.548539
$950$		0			0
$951$			266817.i			0.295021i
$952$	−286845.	−	154920.i	−0.316499	−	0.170936i
$953$	166901.			0.183769			0.0918846	−	0.995770i	$-0.470711\pi$
$953$	166901.			0.183769			0.0918846	+	0.995770i	$0.470711\pi$
$954$	120140.	+	98886.6i	0.132005	+	0.108653i
$955$		0			0
$956$	−1.11525e6	+	218497.i	−1.22027	+	0.239073i
$957$	480772.			0.524947
$958$	−430431.	+	522943.i	−0.469000	+	0.569801i
$959$		−	148255.i		−	0.161202i
$960$		0			0
$961$	610532.			0.661092
$962$	−1.06940e6	−	880220.i	−1.15556	−	0.951133i
$963$		−	155105.i		−	0.167253i
$964$	−180560.	−	921614.i	−0.194298	−	0.991734i
$965$		0			0
$966$	138270.	−	167989.i	0.148175	−	0.180022i
$967$			873454.i			0.934087i	0.884234	+	0.467043i	$0.154681\pi$
$967$			873454.i			0.934087i	−0.884234	+	0.467043i	$0.845319\pi$
$968$	−155008.	+	287008.i	−0.165426	+	0.306298i
$969$	152050.			0.161935
$970$		0			0
$971$			1.16584e6i			1.23651i	0.785976	+	0.618257i	$0.212161\pi$
$971$			1.16584e6i			1.23651i	−0.785976	+	0.618257i	$0.787839\pi$
$972$	−59477.2	+	11652.6i	−0.0629532	+	0.0123336i
$973$	−584230.			−0.617104
$974$	−69196.4	+	84068.7i	−0.0729400	+	0.0886168i
$975$		0			0
$976$	−835108.	+	340286.i	−0.876684	+	0.357227i
$977$	−885391.			−0.927569			−0.463784	−	0.885948i	$-0.653509\pi$
$977$	−885391.			−0.927569			−0.463784	+	0.885948i	$0.653509\pi$
$978$	−36010.3	−	29639.8i	−0.0376486	−	0.0309883i
$979$			880211.i			0.918378i
$980$		0			0
$981$	−127166.			−0.132139
$982$	1.11261e6	−	1.35174e6i	1.15377	−	1.40175i
$983$			671668.i			0.695101i	0.937661	+	0.347550i	$0.112986\pi$
$983$			671668.i			0.695101i	−0.937661	+	0.347550i	$0.887014\pi$
$984$	−930065.	−	502313.i	−0.960557	−	0.518781i
$985$		0			0
$986$	−172104.	−	141658.i	−0.177026	−	0.145709i
$987$		−	476830.i		−	0.489473i
$988$	2.32418e6	−	455347.i	2.38098	−	0.466475i
$989$	−141018.			−0.144172
$990$		0			0
$991$		−	417477.i		−	0.425094i	−0.977151	−	0.212547i	$-0.931824\pi$
$991$		−	417477.i		−	0.425094i	0.977151	−	0.212547i	$-0.0681759\pi$
$992$	−170245.	+	547000.i	−0.173002	+	0.555858i
$993$	−149027.			−0.151136
$994$	235848.	+	194125.i	0.238703	+	0.196475i
$995$		0			0
$996$	−85458.7	−	436198.i	−0.0861465	−	0.439708i
$997$	129166.			0.129945			0.0649724	−	0.997887i	$-0.479304\pi$
$997$	129166.			0.129945			0.0649724	+	0.997887i	$0.479304\pi$
$998$	883729.	−	1.07367e6i	0.887274	−	1.07798i
$999$			163215.i			0.163542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.d.151.10		16
4.3	odd	2	inner	300.5.c.d.151.9		16
5.2	odd	4		300.5.f.b.199.8		32
5.3	odd	4		300.5.f.b.199.25		32
5.4	even	2		60.5.c.a.31.7	✓	16
15.14	odd	2		180.5.c.c.91.10		16
20.3	even	4		300.5.f.b.199.7		32
20.7	even	4		300.5.f.b.199.26		32
20.19	odd	2		60.5.c.a.31.8	yes	16
40.19	odd	2		960.5.e.f.511.4		16
40.29	even	2		960.5.e.f.511.9		16
60.59	even	2		180.5.c.c.91.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.7	✓	16	5.4	even	2
60.5.c.a.31.8	yes	16	20.19	odd	2
180.5.c.c.91.9		16	60.59	even	2
180.5.c.c.91.10		16	15.14	odd	2
300.5.c.d.151.9		16	4.3	odd	2	inner
300.5.c.d.151.10		16	1.1	even	1	trivial
300.5.f.b.199.7		32	20.3	even	4
300.5.f.b.199.8		32	5.2	odd	4
300.5.f.b.199.25		32	5.3	odd	4
300.5.f.b.199.26		32	20.7	even	4
960.5.e.f.511.4		16	40.19	odd	2
960.5.e.f.511.9		16	40.29	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.08838 + 2.54203i) q^{2} +5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +(-13.2088 + 16.0477i) q^{6} +86.5709i q^{7} +(-30.4132 + 56.3120i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(3.08838 + 2.54203i) q^{2} +5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +(-13.2088 + 16.0477i) q^{6} +86.5709i q^{7} +(-30.4132 + 56.3120i) q^{8} -27.0000 q^{9} +97.6947i q^{11} +(-81.5874 + 15.9844i) q^{12} +297.644 q^{13} +(-220.066 + 267.364i) q^{14} +(-237.074 + 96.6018i) q^{16} +58.8402 q^{17} +(-83.3863 - 68.6347i) q^{18} -497.315i q^{19} -449.835 q^{21} +(-248.343 + 301.718i) q^{22} +120.919i q^{23} +(-292.606 - 158.031i) q^{24} +(919.237 + 756.618i) q^{26} -140.296i q^{27} +(-1359.29 + 266.309i) q^{28} -947.079 q^{29} -559.454i q^{31} +(-977.739 - 304.306i) q^{32} -507.636 q^{33} +(181.721 + 149.573i) q^{34} +(-83.0573 - 423.940i) q^{36} -1163.36 q^{37} +(1264.19 - 1535.90i) q^{38} +1546.60i q^{39} +3178.56 q^{41} +(-1389.26 - 1143.49i) q^{42} +1166.21i q^{43} +(-1533.95 + 300.528i) q^{44} +(-307.380 + 373.445i) q^{46} +1060.01i q^{47} +(-501.958 - 1231.87i) q^{48} -5093.52 q^{49} +305.743i q^{51} +(915.610 + 4673.45i) q^{52} -1440.77 q^{53} +(356.637 - 433.288i) q^{54} +(-4874.98 - 2632.89i) q^{56} +2584.13 q^{57} +(-2924.94 - 2407.50i) q^{58} +2004.76i q^{59} +3522.56 q^{61} +(1422.15 - 1727.81i) q^{62} -2337.41i q^{63} +(-2246.08 - 3425.25i) q^{64} +(-1567.77 - 1290.43i) q^{66} -6169.67i q^{67} +(181.004 + 923.879i) q^{68} -628.315 q^{69} -882.122i q^{71} +(821.156 - 1520.42i) q^{72} -1659.75 q^{73} +(-3592.90 - 2957.30i) q^{74} +(7808.59 - 1529.84i) q^{76} -8457.51 q^{77} +(-3931.50 + 4776.50i) q^{78} -7276.52i q^{79} +729.000 q^{81} +(9816.61 + 8079.99i) q^{82} +5346.39i q^{83} +(-1383.78 - 7063.09i) q^{84} +(-2964.55 + 3601.72i) q^{86} -4921.17i q^{87} +(-5501.38 - 2971.20i) q^{88} +9009.81 q^{89} +25767.3i q^{91} +(-1898.61 + 371.971i) q^{92} +2907.01 q^{93} +(-2694.57 + 3273.71i) q^{94} +(1581.22 - 5080.48i) q^{96} +9798.06 q^{97} +(-15730.7 - 12947.9i) q^{98} -2637.76i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) \) 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 + 352 * q^13 - 804 * q^14 - 190 * q^16 - 324 * q^18 + 288 * q^21 - 436 * q^22 - 1998 * q^24 - 852 * q^26 + 1156 * q^28 - 3456 * q^29 - 7668 * q^32 + 4772 * q^34 - 702 * q^36 - 9376 * q^37 + 1320 * q^38 + 1248 * q^41 + 324 * q^42 - 6420 * q^44 - 1112 * q^46 + 4176 * q^48 - 3952 * q^49 - 12704 * q^52 + 5184 * q^53 - 486 * q^54 - 2604 * q^56 + 11232 * q^57 - 12708 * q^58 - 3808 * q^61 + 16152 * q^62 - 11902 * q^64 - 2916 * q^66 + 12312 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 + 30516 * q^74 - 5160 * q^76 + 27456 * q^77 + 3600 * q^78 + 11664 * q^81 + 54040 * q^82 - 2052 * q^84 + 39768 * q^86 + 7220 * q^88 + 7584 * q^89 - 28848 * q^92 - 19872 * q^93 + 49776 * q^94 + 18882 * q^96 + 14496 * q^97 - 23940 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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