LMFDB - Embedded newform 300.5.f.a.199.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [300,5,Mod(199,300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("300.199"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(300, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.592240896.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.7
Root			$1.12824 + 0.651388i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.5.f.a.199.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.98852 - 0.302776i) q^{2} -5.19615 q^{3} +(15.8167 - 2.41526i) q^{4} +(-20.7250 + 1.57327i) q^{6} -43.0318 q^{7} +(62.3538 - 14.4222i) q^{8} +27.0000 q^{9} -65.2790i q^{11} +(-82.1857 + 12.5500i) q^{12} +99.0665i q^{13} +(-171.633 + 13.0290i) q^{14} +(244.333 - 76.4025i) q^{16} -207.689i q^{17} +(107.690 - 8.17494i) q^{18} -569.960i q^{19} +223.600 q^{21} +(-19.7649 - 260.367i) q^{22} -371.198 q^{23} +(-324.000 + 74.9400i) q^{24} +(29.9949 + 395.129i) q^{26} -140.296 q^{27} +(-680.619 + 103.933i) q^{28} -423.911 q^{29} -1174.18i q^{31} +(951.396 - 378.711i) q^{32} +339.199i q^{33} +(-62.8831 - 828.372i) q^{34} +(427.050 - 65.2119i) q^{36} -1448.13i q^{37} +(-172.570 - 2273.30i) q^{38} -514.764i q^{39} -265.822 q^{41} +(891.833 - 67.7005i) q^{42} -699.900 q^{43} +(-157.665 - 1032.49i) q^{44} +(-1480.53 + 112.390i) q^{46} +1250.00 q^{47} +(-1269.59 + 396.999i) q^{48} -549.266 q^{49} +1079.18i q^{51} +(239.271 + 1566.90i) q^{52} -787.645i q^{53} +(-559.574 + 42.4782i) q^{54} +(-2683.20 + 620.613i) q^{56} +2961.60i q^{57} +(-1690.78 + 128.350i) q^{58} -3012.53i q^{59} +4519.33 q^{61} +(-355.512 - 4683.23i) q^{62} -1161.86 q^{63} +(3680.00 - 1798.56i) q^{64} +(102.701 + 1352.91i) q^{66} -5215.70 q^{67} +(-501.622 - 3284.94i) q^{68} +1928.80 q^{69} -4693.16i q^{71} +(1683.55 - 389.400i) q^{72} +5404.92i q^{73} +(-438.459 - 5775.91i) q^{74} +(-1376.60 - 9014.86i) q^{76} +2809.07i q^{77} +(-155.858 - 2053.15i) q^{78} -7453.44i q^{79} +729.000 q^{81} +(-1060.24 + 80.4843i) q^{82} -8950.92 q^{83} +(3536.60 - 540.051i) q^{84} +(-2791.57 + 211.913i) q^{86} +2202.71 q^{87} +(-941.466 - 4070.39i) q^{88} +616.496 q^{89} -4263.01i q^{91} +(-5871.11 + 896.538i) q^{92} +6101.20i q^{93} +(4985.66 - 378.470i) q^{94} +(-4943.60 + 1967.84i) q^{96} +13723.1i q^{97} +(-2190.76 + 166.304i) q^{98} -1762.53i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9} - 1200 q^{14} + 224 q^{16} - 288 q^{21} - 2592 q^{24} + 3384 q^{26} - 1776 q^{29} + 968 q^{34} + 1080 q^{36} + 1104 q^{41} + 7392 q^{44} - 768 q^{46} + 1144 q^{49}+ \cdots - 16704 q^{96}+O(q^{100}) $ 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9 - 1200 * q^14 + 224 * q^16 - 288 * q^21 - 2592 * q^24 + 3384 * q^26 - 1776 * q^29 + 968 * q^34 + 1080 * q^36 + 1104 * q^41 + 7392 * q^44 - 768 * q^46 + 1144 * q^49 - 972 * q^54 + 3456 * q^56 + 8464 * q^61 + 29440 * q^64 + 9648 * q^66 + 19584 * q^69 + 8232 * q^74 - 3744 * q^76 + 5832 * q^81 + 21024 * q^84 - 39120 * q^86 + 50160 * q^89 + 10464 * q^94 - 16704 * q^96

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 $

$2$	3.98852	−	0.302776i	0.997131	−	0.0756939i
$2$	3.98852	−	0.302776i	0.997131	−	0.0756939i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	15.8167	−	2.41526i	0.988541	−	0.150954i
$5$		0			0
$5$		0			0
$6$	−20.7250	+	1.57327i	−0.575694	+	0.0437019i
$7$	−43.0318			−0.878200			−0.439100	−	0.898438i	$-0.644703\pi$
$7$	−43.0318			−0.878200			−0.439100	+	0.898438i	$0.644703\pi$
$8$	62.3538	−	14.4222i	0.974279	−	0.225347i
$9$	27.0000			0.333333
$10$		0			0
$11$		−	65.2790i		−	0.539495i	−0.962931	−	0.269748i	$-0.913060\pi$
$11$		−	65.2790i		−	0.539495i	0.962931	−	0.269748i	$-0.0869403\pi$
$12$	−82.1857	+	12.5500i	−0.570734	+	0.0871530i
$13$			99.0665i			0.586192i	0.956083	+	0.293096i	$0.0946856\pi$
$13$			99.0665i			0.586192i	−0.956083	+	0.293096i	$0.905314\pi$
$14$	−171.633	+	13.0290i	−0.875680	+	0.0664744i
$15$		0			0
$16$	244.333	−	76.4025i	0.954426	−	0.298447i
$17$		−	207.689i		−	0.718646i	−0.933213	−	0.359323i	$-0.883008\pi$
$17$		−	207.689i		−	0.718646i	0.933213	−	0.359323i	$-0.116992\pi$
$18$	107.690	−	8.17494i	0.332377	−	0.0252313i
$19$		−	569.960i		−	1.57884i	−0.613856	−	0.789418i	$-0.710382\pi$
$19$		−	569.960i		−	1.57884i	0.613856	−	0.789418i	$-0.289618\pi$
$20$		0			0
$21$	223.600			0.507029
$22$	−19.7649	−	260.367i	−0.0408365	−	0.537948i
$23$	−371.198			−0.701697			−0.350849	−	0.936432i	$-0.614107\pi$
$23$	−371.198			−0.701697			−0.350849	+	0.936432i	$0.614107\pi$
$24$	−324.000	+	74.9400i	−0.562500	+	0.130104i
$25$		0			0
$26$	29.9949	+	395.129i	0.0443712	+	0.584510i
$27$	−140.296			−0.192450
$28$	−680.619	+	103.933i	−0.868136	+	0.132567i
$29$	−423.911			−0.504056			−0.252028	−	0.967720i	$-0.581097\pi$
$29$	−423.911			−0.504056			−0.252028	+	0.967720i	$0.581097\pi$
$30$		0			0
$31$		−	1174.18i		−	1.22183i	−0.791697	−	0.610914i	$-0.790802\pi$
$31$		−	1174.18i		−	1.22183i	0.791697	−	0.610914i	$-0.209198\pi$
$32$	951.396	−	378.711i	0.929097	−	0.369835i
$33$			339.199i			0.311478i
$34$	−62.8831	−	828.372i	−0.0543972	−	0.716585i
$35$		0			0
$36$	427.050	−	65.2119i	0.329514	−	0.0503178i
$37$		−	1448.13i		−	1.05780i	−0.848683	−	0.528902i	$-0.822604\pi$
$37$		−	1448.13i		−	1.05780i	0.848683	−	0.528902i	$-0.177396\pi$
$38$	−172.570	−	2273.30i	−0.119508	−	1.57431i
$39$		−	514.764i		−	0.338438i
$40$		0			0
$41$	−265.822			−0.158133			−0.0790666	−	0.996869i	$-0.525194\pi$
$41$	−265.822			−0.158133			−0.0790666	+	0.996869i	$0.525194\pi$
$42$	891.833	−	67.7005i	0.505574	−	0.0383790i
$43$	−699.900			−0.378529			−0.189265	−	0.981926i	$-0.560610\pi$
$43$	−699.900			−0.378529			−0.189265	+	0.981926i	$0.560610\pi$
$44$	−157.665	−	1032.49i	−0.0814387	−	0.533313i
$45$		0			0
$46$	−1480.53	+	112.390i	−0.699684	+	0.0531142i
$47$	1250.00			0.565868			0.282934	−	0.959139i	$-0.408692\pi$
$47$	1250.00			0.565868			0.282934	+	0.959139i	$0.408692\pi$
$48$	−1269.59	+	396.999i	−0.551038	+	0.172309i
$49$	−549.266			−0.228765
$50$		0			0
$51$			1079.18i			0.414911i
$52$	239.271	+	1566.90i	0.0884877	+	0.579475i
$53$		−	787.645i		−	0.280401i	−0.990123	−	0.140200i	$-0.955225\pi$
$53$		−	787.645i		−	0.280401i	0.990123	−	0.140200i	$-0.0447746\pi$
$54$	−559.574	+	42.4782i	−0.191898	+	0.0145673i
$55$		0			0
$56$	−2683.20	+	620.613i	−0.855611	+	0.197900i
$57$			2961.60i			0.911541i
$58$	−1690.78	+	128.350i	−0.502610	+	0.0381539i
$59$		−	3012.53i		−	0.865422i	−0.901533	−	0.432711i	$-0.857557\pi$
$59$		−	3012.53i		−	0.865422i	0.901533	−	0.432711i	$-0.142443\pi$
$60$		0			0
$61$	4519.33			1.21455			0.607273	−	0.794493i	$-0.292263\pi$
$61$	4519.33			1.21455			0.607273	+	0.794493i	$0.292263\pi$
$62$	−355.512	−	4683.23i	−0.0924849	−	1.21832i
$63$	−1161.86			−0.292733
$64$	3680.00	−	1798.56i	0.898438	−	0.439101i
$65$		0			0
$66$	102.701	+	1352.91i	0.0235770	+	0.310584i
$67$	−5215.70			−1.16189			−0.580943	−	0.813945i	$-0.697316\pi$
$67$	−5215.70			−1.16189			−0.580943	+	0.813945i	$0.697316\pi$
$68$	−501.622	−	3284.94i	−0.108482	−	0.710411i
$69$	1928.80			0.405125
$70$		0			0
$71$		−	4693.16i		−	0.930998i	−0.885048	−	0.465499i	$-0.845875\pi$
$71$		−	4693.16i		−	0.930998i	0.885048	−	0.465499i	$-0.154125\pi$
$72$	1683.55	−	389.400i	0.324760	−	0.0751157i
$73$			5404.92i			1.01425i	0.861873	+	0.507124i	$0.169291\pi$
$73$			5404.92i			1.01425i	−0.861873	+	0.507124i	$0.830709\pi$
$74$	−438.459	−	5775.91i	−0.0800693	−	1.05477i
$75$		0			0
$76$	−1376.60	−	9014.86i	−0.238331	−	1.56074i
$77$			2809.07i			0.473785i
$78$	−155.858	−	2053.15i	−0.0256177	−	0.337467i
$79$		−	7453.44i		−	1.19427i	−0.802141	−	0.597135i	$-0.796306\pi$
$79$		−	7453.44i		−	1.19427i	0.802141	−	0.597135i	$-0.203694\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−1060.24	+	80.4843i	−0.157679	+	0.0119697i
$83$	−8950.92			−1.29931			−0.649653	−	0.760231i	$-0.725086\pi$
$83$	−8950.92			−1.29931			−0.649653	+	0.760231i	$0.725086\pi$
$84$	3536.60	−	540.051i	0.501219	−	0.0765378i
$85$		0			0
$86$	−2791.57	+	211.913i	−0.377443	+	0.0286523i
$87$	2202.71			0.291017
$88$	−941.466	−	4070.39i	−0.121574	−	0.525619i
$89$	616.496			0.0778305			0.0389153	−	0.999243i	$-0.487610\pi$
$89$	616.496			0.0778305			0.0389153	+	0.999243i	$0.487610\pi$
$90$		0			0
$91$		−	4263.01i		−	0.514794i
$92$	−5871.11	+	896.538i	−0.693656	+	0.105924i
$93$			6101.20i			0.705422i
$94$	4985.66	−	378.470i	0.564244	−	0.0428327i
$95$		0			0
$96$	−4943.60	+	1967.84i	−0.536415	+	0.213525i
$97$			13723.1i			1.45850i	0.684246	+	0.729252i	$0.260132\pi$
$97$			13723.1i			1.45850i	−0.684246	+	0.729252i	$0.739868\pi$
$98$	−2190.76	+	166.304i	−0.228109	+	0.0173162i
$99$		−	1762.53i		−	0.179832i
$100$		0			0
$101$	14758.8			1.44680			0.723401	−	0.690428i	$-0.242578\pi$
$101$	14758.8			1.44680			0.723401	+	0.690428i	$0.242578\pi$
$102$	326.750	+	4304.35i	0.0314062	+	0.413720i
$103$	−1859.14			−0.175242			−0.0876210	−	0.996154i	$-0.527926\pi$
$103$	−1859.14			−0.175242			−0.0876210	+	0.996154i	$0.527926\pi$
$104$	1428.76	+	6177.17i	0.132097	+	0.571114i
$105$		0			0
$106$	−238.480	−	3141.54i	−0.0212246	−	0.279596i
$107$	10664.4			0.931466			0.465733	−	0.884925i	$-0.345791\pi$
$107$	10664.4			0.931466			0.465733	+	0.884925i	$0.345791\pi$
$108$	−2219.02	+	338.851i	−0.190245	+	0.0290510i
$109$	4479.34			0.377017			0.188508	−	0.982072i	$-0.439635\pi$
$109$	4479.34			0.377017			0.188508	+	0.982072i	$0.439635\pi$
$110$		0			0
$111$			7524.72i			0.610723i
$112$	−10514.1	+	3287.74i	−0.838177	+	0.262096i
$113$			21225.5i			1.66227i	0.556070	+	0.831135i	$0.312309\pi$
$113$			21225.5i			1.66227i	−0.556070	+	0.831135i	$0.687691\pi$
$114$	896.700	+	11812.4i	0.0689981	+	0.908926i
$115$		0			0
$116$	−6704.85	+	1023.85i	−0.498280	+	0.0760890i
$117$			2674.79i			0.195397i
$118$	−912.122	−	12015.6i	−0.0655072	−	0.862939i
$119$			8937.22i			0.631115i
$120$		0			0
$121$	10379.7			0.708945
$122$	18025.5	−	1368.34i	1.21106	−	0.0919338i
$123$	1381.25			0.0912982
$124$	−2835.94	−	18571.5i	−0.184439	−	1.20783i
$125$		0			0
$126$	−4634.10	+	351.782i	−0.291893	+	0.0221581i
$127$	−4676.78			−0.289961			−0.144980	−	0.989435i	$-0.546312\pi$
$127$	−4676.78			−0.289961			−0.144980	+	0.989435i	$0.546312\pi$
$128$	14133.2	−	8287.81i	0.862623	−	0.505848i
$129$	3636.79			0.218544
$130$		0			0
$131$			29922.6i			1.74364i	0.489828	+	0.871819i	$0.337060\pi$
$131$			29922.6i			1.74364i	−0.489828	+	0.871819i	$0.662940\pi$
$132$	819.253	+	5365.00i	0.0470187	+	0.307909i
$133$			24526.4i			1.38653i
$134$	−20803.0	+	1579.19i	−1.15855	+	0.0879476i
$135$		0			0
$136$	−2995.33	−	12950.2i	−0.161945	−	0.700162i
$137$		−	19273.3i		−	1.02687i	−0.858129	−	0.513434i	$-0.828373\pi$
$137$		−	19273.3i		−	1.02687i	0.858129	−	0.513434i	$-0.171627\pi$
$138$	7693.07	−	583.994i	0.403963	−	0.0306655i
$139$			24086.9i			1.24667i	0.781955	+	0.623335i	$0.214222\pi$
$139$			24086.9i			1.24667i	−0.781955	+	0.623335i	$0.785778\pi$
$140$		0			0
$141$	−6495.20			−0.326704
$142$	−1420.98	−	18718.8i	−0.0704709	−	0.928327i
$143$	6466.95			0.316248
$144$	6596.99	−	2062.87i	0.318142	−	0.0994825i
$145$		0			0
$146$	1636.48	+	21557.7i	0.0767723	+	1.01134i
$147$	2854.07			0.132078
$148$	−3497.61	−	22904.6i	−0.159679	−	1.04568i
$149$	−43993.2			−1.98159			−0.990794	−	0.135378i	$-0.956775\pi$
$149$	−43993.2			−1.98159			−0.990794	+	0.135378i	$0.956775\pi$
$150$		0			0
$151$			1388.00i			0.0608746i	0.999537	+	0.0304373i	$0.00969000\pi$
$151$			1388.00i			0.0608746i	−0.999537	+	0.0304373i	$0.990310\pi$
$152$	−8220.08	−	35539.2i	−0.355786	−	1.53823i
$153$		−	5607.60i		−	0.239549i
$154$	850.518	+	11204.0i	0.0358626	+	0.472425i
$155$		0			0
$156$	−1243.29	−	8141.85i	−0.0510884	−	0.334560i
$157$			7464.93i			0.302849i	0.988469	+	0.151425i	$0.0483861\pi$
$157$			7464.93i			0.302849i	−0.988469	+	0.151425i	$0.951614\pi$
$158$	−2256.72	−	29728.2i	−0.0903989	−	1.19084i
$159$			4092.72i			0.161889i
$160$		0			0
$161$	15973.3			0.616230
$162$	2907.63	−	220.723i	0.110792	−	0.00841043i
$163$	47291.0			1.77993			0.889965	−	0.456029i	$-0.150729\pi$
$163$	47291.0			1.77993			0.889965	+	0.456029i	$0.150729\pi$
$164$	−4204.41	+	642.028i	−0.156321	+	0.0238707i
$165$		0			0
$166$	−35701.0	+	2710.12i	−1.29558	+	0.0983496i
$167$	−90.1917			−0.00323395			−0.00161698	−	0.999999i	$-0.500515\pi$
$167$	−90.1917			−0.00323395			−0.00161698	+	0.999999i	$0.500515\pi$
$168$	13942.3	−	3224.80i	0.493987	−	0.114257i
$169$	18746.8			0.656379
$170$		0			0
$171$		−	15388.9i		−	0.526279i
$172$	−11070.1	+	1690.44i	−0.374191	+	0.0571403i
$173$			1212.10i			0.0404993i	0.999795	+	0.0202497i	$0.00644611\pi$
$173$			1212.10i			0.0404993i	−0.999795	+	0.0202497i	$0.993554\pi$
$174$	8785.54	−	666.926i	0.290182	−	0.0220282i
$175$		0			0
$176$	−4987.48	−	15949.8i	−0.161011	−	0.514909i
$177$			15653.6i			0.499652i
$178$	2458.91	−	186.660i	0.0776072	−	0.00589130i
$179$		−	20697.3i		−	0.645964i	−0.946405	−	0.322982i	$-0.895315\pi$
$179$		−	20697.3i		−	0.645964i	0.946405	−	0.322982i	$-0.104685\pi$
$180$		0			0
$181$	18722.8			0.571496			0.285748	−	0.958305i	$-0.407758\pi$
$181$	18722.8			0.571496			0.285748	+	0.958305i	$0.407758\pi$
$182$	−1290.73	−	17003.1i	−0.0389667	−	0.513317i
$183$	−23483.1			−0.701219
$184$	−23145.6	+	5353.49i	−0.683649	+	0.158125i
$185$		0			0
$186$	1847.29	+	24334.8i	0.0533962	+	0.703399i
$187$	−13557.7			−0.387706
$188$	19770.8	−	3019.07i	0.559383	−	0.0854197i
$189$	6037.19			0.169010
$190$		0			0
$191$		−	37058.2i		−	1.01582i	−0.861410	−	0.507910i	$-0.830418\pi$
$191$		−	37058.2i		−	1.01582i	0.861410	−	0.507910i	$-0.169582\pi$
$192$	−19121.8	+	9345.59i	−0.518713	+	0.253515i
$193$			23019.8i			0.617999i	0.951062	+	0.308999i	$0.0999941\pi$
$193$			23019.8i			0.617999i	−0.951062	+	0.308999i	$0.900006\pi$
$194$	4155.01	+	54734.7i	0.110400	+	1.45432i
$195$		0			0
$196$	−8687.55	+	1326.62i	−0.226144	+	0.0345329i
$197$		−	42137.6i		−	1.08577i	−0.839807	−	0.542885i	$-0.817332\pi$
$197$		−	42137.6i		−	1.08577i	0.839807	−	0.542885i	$-0.182668\pi$
$198$	−533.652	−	7029.90i	−0.0136122	−	0.179316i
$199$			68550.6i			1.73103i	0.500881	+	0.865516i	$0.333009\pi$
$199$			68550.6i			1.73103i	−0.500881	+	0.865516i	$0.666991\pi$
$200$		0			0
$201$	27101.6			0.670815
$202$	58866.0	−	4468.62i	1.44265	−	0.109514i
$203$	18241.6			0.442662
$204$	2606.50	+	17069.1i	0.0626322	+	0.410156i
$205$		0			0
$206$	−7415.23	+	562.903i	−0.174739	+	0.0132647i
$207$	−10022.3			−0.233899
$208$	7568.93	+	24205.2i	0.174948	+	0.559477i
$209$	−37206.4			−0.851775
$210$		0			0
$211$			37678.5i			0.846308i	0.906058	+	0.423154i	$0.139077\pi$
$211$			37678.5i			0.846308i	−0.906058	+	0.423154i	$0.860923\pi$
$212$	−1902.36	−	12457.9i	−0.0423274	−	0.277187i
$213$			24386.4i			0.537512i
$214$	42535.0	−	3228.91i	0.928794	−	0.0705063i
$215$		0			0
$216$	−8748.00	+	2023.38i	−0.187500	+	0.0433680i
$217$			50526.9i			1.07301i
$218$	17866.0	−	1356.23i	0.375935	−	0.0285379i
$219$		−	28084.8i		−	0.585576i
$220$		0			0
$221$	20575.0			0.421265
$222$	2278.30	+	30012.5i	0.0462280	+	0.608971i
$223$	−9238.47			−0.185776			−0.0928882	−	0.995677i	$-0.529610\pi$
$223$	−9238.47			−0.185776			−0.0928882	+	0.995677i	$0.529610\pi$
$224$	−40940.2	+	16296.6i	−0.815933	+	0.324789i
$225$		0			0
$226$	6426.57	+	84658.6i	0.125824	+	1.65750i
$227$	−48884.8			−0.948685			−0.474342	−	0.880340i	$-0.657314\pi$
$227$	−48884.8			−0.948685			−0.474342	+	0.880340i	$0.657314\pi$
$228$	7153.02	+	46842.6i	0.137600	+	0.901096i
$229$	−17654.5			−0.336654			−0.168327	−	0.985731i	$-0.553836\pi$
$229$	−17654.5			−0.336654			−0.168327	+	0.985731i	$0.553836\pi$
$230$		0			0
$231$		−	14596.4i		−	0.273540i
$232$	−26432.5	+	6113.73i	−0.491091	+	0.113587i
$233$		−	52029.9i		−	0.958387i	−0.877709	−	0.479193i	$-0.840929\pi$
$233$		−	52029.9i		−	0.958387i	0.877709	−	0.479193i	$-0.159071\pi$
$234$	809.863	+	10668.5i	0.0147904	+	0.194837i
$235$		0			0
$236$	−7276.04	−	47648.2i	−0.130638	−	0.855505i
$237$			38729.2i			0.689512i
$238$	2705.97	+	35646.3i	0.0477716	+	0.629304i
$239$		−	53899.3i		−	0.943598i	−0.881706	−	0.471799i	$-0.843605\pi$
$239$		−	53899.3i		−	0.943598i	0.881706	−	0.471799i	$-0.156395\pi$
$240$		0			0
$241$	−56311.0			−0.969526			−0.484763	−	0.874646i	$-0.661094\pi$
$241$	−56311.0			−0.969526			−0.484763	+	0.874646i	$0.661094\pi$
$242$	41399.5	−	3142.71i	0.706911	−	0.0536628i
$243$	−3788.00			−0.0641500
$244$	71480.7	−	10915.3i	1.20063	−	0.183340i
$245$		0			0
$246$	5509.15	−	418.209i	0.0910363	−	0.00691072i
$247$	56463.9			0.925501
$248$	−16934.2	−	73214.4i	−0.275335	−	1.19040i
$249$	46510.3			0.750155
$250$		0			0
$251$		−	11951.6i		−	0.189705i	−0.995491	−	0.0948525i	$-0.969762\pi$
$251$		−	11951.6i		−	0.189705i	0.995491	−	0.0948525i	$-0.0302379\pi$
$252$	−18376.7	+	2806.18i	−0.289379	+	0.0441891i
$253$			24231.4i			0.378562i
$254$	−18653.5	+	1416.02i	−0.289129	+	0.0219483i
$255$		0			0
$256$	53861.3	−	37335.3i	0.821858	−	0.569692i
$257$		−	15483.1i		−	0.234418i	−0.993107	−	0.117209i	$-0.962605\pi$
$257$		−	15483.1i		−	0.234418i	0.993107	−	0.117209i	$-0.0373948\pi$
$258$	14505.4	−	1101.13i	0.217917	−	0.0165424i
$259$			62315.7i			0.928963i
$260$		0			0
$261$	−11445.6			−0.168019
$262$	9059.83	+	119347.i	0.131983	+	1.73864i
$263$	−16337.3			−0.236194			−0.118097	−	0.993002i	$-0.537679\pi$
$263$	−16337.3			−0.236194			−0.118097	+	0.993002i	$0.537679\pi$
$264$	4892.00	+	21150.4i	0.0701906	+	0.303466i
$265$		0			0
$266$	7425.99	+	97824.1i	0.104952	+	1.38256i
$267$	−3203.41			−0.0449355
$268$	−82495.0	+	12597.3i	−1.14857	+	0.175391i
$269$	82062.5			1.13407			0.567035	−	0.823694i	$-0.308090\pi$
$269$	82062.5			1.13407			0.567035	+	0.823694i	$0.308090\pi$
$270$		0			0
$271$			75123.6i			1.02291i	0.859310	+	0.511456i	$0.170894\pi$
$271$			75123.6i			1.02291i	−0.859310	+	0.511456i	$0.829106\pi$
$272$	−15868.0	−	50745.2i	−0.214478	−	0.685895i
$273$			22151.2i			0.297216i
$274$	−5835.48	−	76872.0i	−0.0777277	−	1.02392i
$275$		0			0
$276$	30507.2	−	4658.55i	0.400483	−	0.0611551i
$277$			9651.88i			0.125792i	0.998020	+	0.0628959i	$0.0200336\pi$
$277$			9651.88i			0.125792i	−0.998020	+	0.0628959i	$0.979966\pi$
$278$	7292.92	+	96071.2i	0.0943653	+	1.24309i
$279$		−	31702.8i		−	0.407276i
$280$		0			0
$281$	−90483.6			−1.14593			−0.572964	−	0.819581i	$-0.694206\pi$
$281$	−90483.6			−1.14593			−0.572964	+	0.819581i	$0.694206\pi$
$282$	−25906.3	+	1966.59i	−0.325767	+	0.0247295i
$283$	44901.3			0.560643			0.280321	−	0.959906i	$-0.409559\pi$
$283$	44901.3			0.560643			0.280321	+	0.959906i	$0.409559\pi$
$284$	−11335.2	−	74230.1i	−0.140537	−	0.920330i
$285$		0			0
$286$	25793.6	−	1958.04i	0.315341	−	0.0239380i
$287$	11438.8			0.138872
$288$	25687.7	−	10225.2i	0.309699	−	0.123278i
$289$	40386.4			0.483547
$290$		0			0
$291$		−	71307.1i		−	0.842067i
$292$	13054.3	+	85487.8i	0.153104	+	1.00262i
$293$		−	30326.7i		−	0.353257i	−0.984278	−	0.176628i	$-0.943481\pi$
$293$		−	30326.7i		−	0.353257i	0.984278	−	0.176628i	$-0.0565191\pi$
$294$	11383.5	−	864.143i	0.131699	−	0.00999748i
$295$		0			0
$296$	−20885.3	−	90296.6i	−0.238373	−	1.03060i
$297$			9158.38i			0.103826i
$298$	−175468.	+	13320.1i	−1.97590	+	0.149994i
$299$		−	36773.3i		−	0.411329i
$300$		0			0
$301$	30118.0			0.332424
$302$	420.253	+	5536.08i	0.00460784	+	0.0607000i
$303$	−76689.2			−0.835312
$304$	−43546.4	−	139260.i	−0.471200	−	1.50688i
$305$		0			0
$306$	−1697.84	−	22366.0i	−0.0181324	−	0.238862i
$307$	−35547.6			−0.377167			−0.188583	−	0.982057i	$-0.560390\pi$
$307$	−35547.6			−0.377167			−0.188583	+	0.982057i	$0.560390\pi$
$308$	6784.62	+	44430.1i	0.0715195	+	0.468356i
$309$	9660.38			0.101176
$310$		0			0
$311$		−	72202.2i		−	0.746500i	−0.927731	−	0.373250i	$-0.878243\pi$
$311$		−	72202.2i		−	0.746500i	0.927731	−	0.373250i	$-0.121757\pi$
$312$	−7424.04	−	32097.5i	−0.0762660	−	0.329733i
$313$		−	162750.i		−	1.66124i	−0.556842	−	0.830618i	$-0.687987\pi$
$313$		−	162750.i		−	1.66124i	0.556842	−	0.830618i	$-0.312013\pi$
$314$	2260.20	+	29774.1i	0.0229238	+	0.301980i
$315$		0			0
$316$	−18002.0	−	117888.i	−0.180279	−	1.18058i
$317$		−	64556.9i		−	0.642428i	−0.947007	−	0.321214i	$-0.895909\pi$
$317$		−	64556.9i		−	0.642428i	0.947007	−	0.321214i	$-0.104091\pi$
$318$	1239.18	+	16323.9i	0.0122540	+	0.161425i
$319$			27672.5i			0.271936i
$320$		0			0
$321$	−55413.6			−0.537782
$322$	63709.9	−	4836.33i	0.614462	−	0.0466449i
$323$	−118374.			−1.13462
$324$	11530.3	−	1760.72i	0.109838	−	0.0167726i
$325$		0			0
$326$	188621.	−	14318.6i	1.77482	−	0.134730i
$327$	−23275.3			−0.217671
$328$	−16575.0	+	3833.74i	−0.154066	+	0.0356348i
$329$	−53789.8			−0.496945
$330$		0			0
$331$			11544.1i			0.105367i	0.998611	+	0.0526833i	$0.0167774\pi$
$331$			11544.1i			0.105367i	−0.998611	+	0.0526833i	$0.983223\pi$
$332$	−141574.	+	21618.8i	−1.28442	+	0.196135i
$333$		−	39099.6i		−	0.352601i
$334$	−359.732	+	27.3078i	−0.00322467	+	0.000244790i
$335$		0			0
$336$	54632.8	−	17083.6i	0.483921	−	0.151321i
$337$		−	209011.i		−	1.84039i	−0.391461	−	0.920195i	$-0.628030\pi$
$337$		−	209011.i		−	1.84039i	0.391461	−	0.920195i	$-0.371970\pi$
$338$	74772.2	−	5676.09i	0.654496	−	0.0496839i
$339$		−	110291.i		−	0.959712i
$340$		0			0
$341$	−76649.0			−0.659170
$342$	−4659.39	−	61379.1i	−0.0398361	−	0.524769i
$343$	126955.			1.07910
$344$	−43641.5	+	10094.1i	−0.368793	+	0.0853004i
$345$		0			0
$346$	366.996	+	4834.51i	0.00306555	+	0.0403831i
$347$	161304.			1.33964			0.669819	−	0.742525i	$-0.266372\pi$
$347$	161304.			1.33964			0.669819	+	0.742525i	$0.266372\pi$
$348$	34839.4	−	5320.10i	0.287682	−	0.0439300i
$349$	−88041.4			−0.722830			−0.361415	−	0.932405i	$-0.617706\pi$
$349$	−88041.4			−0.722830			−0.361415	+	0.932405i	$0.617706\pi$
$350$		0			0
$351$		−	13898.6i		−	0.112813i
$352$	−24721.9	−	62106.1i	−0.199525	−	0.501244i
$353$		−	186762.i		−	1.49878i	−0.662128	−	0.749391i	$-0.730347\pi$
$353$		−	186762.i		−	1.49878i	0.662128	−	0.749391i	$-0.269653\pi$
$354$	4739.52	+	62434.7i	0.0378206	+	0.498218i
$355$		0			0
$356$	9750.90	−	1488.99i	0.0769387	−	0.0117488i
$357$		−	46439.2i		−	0.364374i
$358$	−6266.65	−	82551.8i	−0.0488955	−	0.644111i
$359$		−	226517.i		−	1.75756i	−0.477224	−	0.878782i	$-0.658357\pi$
$359$		−	226517.i		−	1.75756i	0.477224	−	0.878782i	$-0.341643\pi$
$360$		0			0
$361$	−194533.			−1.49272
$362$	74676.3	−	5668.80i	0.569857	−	0.0432588i
$363$	−53934.3			−0.409309
$364$	−10296.3	−	67426.5i	−0.0777099	−	0.508895i
$365$		0			0
$366$	−93663.0	+	7110.12i	−0.699207	+	0.0530780i
$367$	106652.			0.791839			0.395920	−	0.918285i	$-0.370426\pi$
$367$	106652.			0.791839			0.395920	+	0.918285i	$0.370426\pi$
$368$	−90695.9	+	28360.5i	−0.669718	+	0.209420i
$369$	−7177.19			−0.0527110
$370$		0			0
$371$			33893.8i			0.246248i
$372$	14736.0	+	96500.5i	0.106486	+	0.697339i
$373$		−	129184.i		−	0.928518i	−0.885699	−	0.464259i	$-0.846321\pi$
$373$		−	129184.i		−	0.928518i	0.885699	−	0.464259i	$-0.153679\pi$
$374$	−54075.3	+	4104.94i	−0.386594	+	0.0293470i
$375$		0			0
$376$	77942.4	−	18027.8i	0.551313	−	0.127517i
$377$		−	41995.3i		−	0.295473i
$378$	24079.5	−	1827.91i	0.168525	−	0.0127930i
$379$			156156.i			1.08713i	0.839368	+	0.543563i	$0.182925\pi$
$379$			156156.i			1.08713i	−0.839368	+	0.543563i	$0.817075\pi$
$380$		0			0
$381$	24301.3			0.167409
$382$	−11220.3	−	147807.i	−0.0768915	−	1.01291i
$383$	−261403.			−1.78202			−0.891012	−	0.453980i	$-0.850004\pi$
$383$	−261403.			−1.78202			−0.891012	+	0.453980i	$0.850004\pi$
$384$	−73438.3	+	43064.7i	−0.498035	+	0.292051i
$385$		0			0
$386$	6969.85	+	91815.2i	0.0467787	+	0.616226i
$387$	−18897.3			−0.126176
$388$	33144.7	+	217053.i	0.220166	+	1.44179i
$389$	1046.60			0.00691644			0.00345822	−	0.999994i	$-0.498899\pi$
$389$	1046.60			0.00691644			0.00345822	+	0.999994i	$0.498899\pi$
$390$		0			0
$391$			77093.6i			0.504272i
$392$	−34248.8	+	7921.62i	−0.222881	+	0.0515516i
$393$		−	155482.i		−	1.00669i
$394$	−12758.3	−	168067.i	−0.0821862	−	1.08265i
$395$		0			0
$396$	−4256.97	−	27877.4i	−0.0271462	−	0.177771i
$397$			181472.i			1.15140i	0.817659	+	0.575702i	$0.195271\pi$
$397$			181472.i			1.15140i	−0.817659	+	0.575702i	$0.804729\pi$
$398$	20755.5	+	273416.i	0.131029	+	1.72607i
$399$		−	127443.i		−	0.800515i
$400$		0			0
$401$	144404.			0.898029			0.449015	−	0.893524i	$-0.351775\pi$
$401$	144404.			0.898029			0.449015	+	0.893524i	$0.351775\pi$
$402$	108095.	−	8205.70i	0.668890	−	0.0507766i
$403$	116321.			0.716226
$404$	233435.	−	35646.4i	1.43022	−	0.218400i
$405$		0			0
$406$	72757.2	−	5523.12i	0.441392	−	0.0335068i
$407$	−94532.6			−0.570680
$408$	15564.2	+	67291.2i	0.0934989	+	0.404239i
$409$	−1867.96			−0.0111666			−0.00558330	−	0.999984i	$-0.501777\pi$
$409$	−1867.96			−0.0111666			−0.00558330	+	0.999984i	$0.501777\pi$
$410$		0			0
$411$			100147.i			0.592863i
$412$	−29405.4	+	4490.30i	−0.173234	+	0.0264534i
$413$			129635.i			0.760013i
$414$	−39974.4	+	3034.52i	−0.233228	+	0.0177047i
$415$		0			0
$416$	37517.6	+	94251.4i	0.216795	+	0.544629i
$417$		−	125159.i		−	0.719765i
$418$	−148399.	+	11265.2i	−0.849331	+	0.0644742i
$419$			112803.i			0.642531i	0.946989	+	0.321266i	$0.104108\pi$
$419$			112803.i			0.642531i	−0.946989	+	0.321266i	$0.895892\pi$
$420$		0			0
$421$	−77595.0			−0.437794			−0.218897	−	0.975748i	$-0.570246\pi$
$421$	−77595.0			−0.437794			−0.218897	+	0.975748i	$0.570246\pi$
$422$	11408.1	+	150282.i	0.0640604	+	0.843881i
$423$	33750.0			0.188623
$424$	−11359.6	−	49112.7i	−0.0631874	−	0.273188i
$425$		0			0
$426$	7383.60	+	97265.7i	0.0406864	+	0.535970i
$427$	−194475.			−1.06661
$428$	168674.	−	25757.2i	0.920792	−	0.140608i
$429$	−33603.3			−0.182586
$430$		0			0
$431$		−	156726.i		−	0.843699i	−0.906666	−	0.421850i	$-0.861381\pi$
$431$		−	156726.i		−	0.843699i	0.906666	−	0.421850i	$-0.138619\pi$
$432$	−34279.0	+	10719.0i	−0.183679	+	0.0574362i
$433$			41267.2i			0.220105i	0.993926	+	0.110052i	$0.0351019\pi$
$433$			41267.2i			0.220105i	−0.993926	+	0.110052i	$0.964898\pi$
$434$	15298.3	+	201528.i	0.0812202	+	1.06993i
$435$		0			0
$436$	70848.1	−	10818.7i	0.372697	−	0.0569120i
$437$			211568.i			1.10786i
$438$	−8503.40	−	112017.i	−0.0443245	−	0.583896i
$439$			154804.i			0.803252i	0.915804	+	0.401626i	$0.131555\pi$
$439$			154804.i			0.803252i	−0.915804	+	0.401626i	$0.868445\pi$
$440$		0			0
$441$	−14830.2			−0.0762551
$442$	82063.9	−	6229.61i	0.420056	−	0.0318872i
$443$	251131.			1.27966			0.639828	−	0.768518i	$-0.279006\pi$
$443$	251131.			1.27966			0.639828	+	0.768518i	$0.279006\pi$
$444$	18174.1	+	119016.i	0.0921908	+	0.603725i
$445$		0			0
$446$	−36847.9	+	2797.18i	−0.185243	+	0.0140621i
$447$	228596.			1.14407
$448$	−158357.	+	77395.2i	−0.789007	+	0.385619i
$449$	31888.6			0.158177			0.0790884	−	0.996868i	$-0.474799\pi$
$449$	31888.6			0.158177			0.0790884	+	0.996868i	$0.474799\pi$
$450$		0			0
$451$			17352.6i			0.0853121i
$452$	51265.1	+	335717.i	0.250926	+	1.64322i
$453$		−	7212.27i		−	0.0351460i
$454$	−194978.	+	14801.1i	−0.945963	+	0.0718096i
$455$		0			0
$456$	42712.8	+	184667.i	0.205413	+	0.888095i
$457$		−	166922.i		−	0.799247i	−0.916679	−	0.399624i	$-0.869141\pi$
$457$		−	166922.i		−	0.799247i	0.916679	−	0.399624i	$-0.130859\pi$
$458$	−70415.3	+	5345.35i	−0.335688	+	0.0254827i
$459$			29137.9i			0.138304i
$460$		0			0
$461$	−130544.			−0.614266			−0.307133	−	0.951667i	$-0.599370\pi$
$461$	−130544.			−0.614266			−0.307133	+	0.951667i	$0.599370\pi$
$462$	−4419.42	−	58217.9i	−0.0207053	−	0.272755i
$463$	273167.			1.27428			0.637142	−	0.770746i	$-0.280116\pi$
$463$	273167.			1.27428			0.637142	+	0.770746i	$0.280116\pi$
$464$	−103575.	+	32387.9i	−0.481084	+	0.150434i
$465$		0			0
$466$	−15753.4	−	207522.i	−0.0725440	−	0.955637i
$467$	56070.3			0.257098			0.128549	−	0.991703i	$-0.458968\pi$
$467$	56070.3			0.257098			0.128549	+	0.991703i	$0.458968\pi$
$468$	6460.31	+	42306.3i	0.0294959	+	0.193158i
$469$	224441.			1.02037
$470$		0			0
$471$		−	38788.9i		−	0.174850i
$472$	−43447.4	−	187843.i	−0.195020	−	0.843162i
$473$			45688.8i			0.204215i
$474$	11726.3	+	154472.i	0.0521918	+	0.687534i
$475$		0			0
$476$	21585.7	+	141357.i	0.0952690	+	0.623883i
$477$		−	21266.4i		−	0.0934668i
$478$	−16319.4	−	214978.i	−0.0714246	−	0.940891i
$479$			160400.i			0.699091i	0.936919	+	0.349546i	$0.113664\pi$
$479$			160400.i			0.699091i	−0.936919	+	0.349546i	$0.886336\pi$
$480$		0			0
$481$	143461.			0.620076
$482$	−224598.	+	17049.6i	−0.966745	+	0.0733872i
$483$	−82999.7			−0.355781
$484$	164171.	−	25069.5i	0.700821	−	0.107018i
$485$		0			0
$486$	−15108.5	+	1146.91i	−0.0639660	+	0.00485577i
$487$	−314133.			−1.32451			−0.662256	−	0.749278i	$-0.730401\pi$
$487$	−314133.			−1.32451			−0.662256	+	0.749278i	$0.730401\pi$
$488$	281797.	−	65178.7i	1.18331	−	0.273694i
$489$	−245731.			−1.02764
$490$		0			0
$491$			57822.1i			0.239845i	0.992783	+	0.119923i	$0.0382646\pi$
$491$			57822.1i			0.239845i	−0.992783	+	0.119923i	$0.961735\pi$
$492$	21846.8	−	3336.07i	0.0902520	−	0.0137818i
$493$			88041.5i			0.362238i
$494$	225208.	−	17095.9i	0.922846	−	0.0700548i
$495$		0			0
$496$	−89710.0	−	286890.i	−0.364651	−	1.16614i
$497$			201955.i			0.817602i
$498$	185508.	−	14082.2i	0.748003	−	0.0567821i
$499$			276054.i			1.10865i	0.832301	+	0.554324i	$0.187023\pi$
$499$			276054.i			1.10865i	−0.832301	+	0.554324i	$0.812977\pi$
$500$		0			0
$501$	468.650			0.00186712
$502$	−3618.66	−	47669.3i	−0.0143595	−	0.189161i
$503$	−124228.			−0.491002			−0.245501	−	0.969396i	$-0.578952\pi$
$503$	−124228.			−0.491002			−0.245501	+	0.969396i	$0.578952\pi$
$504$	−72446.3	+	16756.6i	−0.285204	+	0.0659665i
$505$		0			0
$506$	7336.68	+	96647.6i	0.0286549	+	0.377476i
$507$	−97411.4			−0.378961
$508$	−73971.0	+	11295.6i	−0.286638	+	0.0437706i
$509$	335116.			1.29348			0.646739	−	0.762711i	$-0.276132\pi$
$509$	335116.			1.29348			0.646739	+	0.762711i	$0.276132\pi$
$510$		0			0
$511$		−	232584.i		−	0.890712i
$512$	203523.	−	165221.i	0.776378	−	0.630267i
$513$			79963.2i			0.303847i
$514$	−4687.91	−	61754.7i	−0.0177440	−	0.233746i
$515$		0			0
$516$	57521.8	−	8783.77i	0.216040	−	0.0329900i
$517$		−	81598.8i		−	0.305283i
$518$	18867.7	+	248548.i	0.0703168	+	0.926297i
$519$		−	6298.28i		−	0.0233823i
$520$		0			0
$521$	−320361.			−1.18022			−0.590111	−	0.807322i	$-0.700916\pi$
$521$	−320361.			−1.18022			−0.590111	+	0.807322i	$0.700916\pi$
$522$	−45651.0	+	3465.45i	−0.167537	+	0.0127180i
$523$	202708.			0.741085			0.370542	−	0.928816i	$-0.379172\pi$
$523$	202708.			0.741085			0.370542	+	0.928816i	$0.379172\pi$
$524$	72270.7	+	473275.i	0.263208	+	1.72366i
$525$		0			0
$526$	−65161.7	+	4946.53i	−0.235516	+	0.0178784i
$527$	−243863.			−0.878062
$528$	25915.7	+	82877.6i	0.0929598	+	0.297283i
$529$	−142053.			−0.507621
$530$		0			0
$531$		−	81338.4i		−	0.288474i
$532$	59237.5	+	387925.i	0.209302	+	1.37064i
$533$		−	26334.0i		−	0.0926964i
$534$	−12776.9	+	969.913i	−0.0448066	+	0.00340134i
$535$		0			0
$536$	−325219.	+	75221.9i	−1.13200	+	0.261827i
$537$			107546.i			0.372947i
$538$	327308.	−	24846.5i	1.13082	−	0.0858422i
$539$			35855.5i			0.123418i
$540$		0			0
$541$	195927.			0.669421			0.334710	−	0.942321i	$-0.391361\pi$
$541$	195927.			0.669421			0.334710	+	0.942321i	$0.391361\pi$
$542$	22745.6	+	299632.i	0.0774282	+	1.01998i
$543$	−97286.5			−0.329954
$544$	−78654.1	−	197594.i	−0.265781	−	0.667692i
$545$		0			0
$546$	6706.85	+	88350.7i	0.0224975	+	0.296364i
$547$	71049.9			0.237459			0.118730	−	0.992927i	$-0.462118\pi$
$547$	71049.9			0.237459			0.118730	+	0.992927i	$0.462118\pi$
$548$	−46549.9	−	304839.i	−0.155009	−	1.01510i
$549$	122022.			0.404849
$550$		0			0
$551$			241612.i			0.795821i
$552$	120268.	−	27817.6i	0.394705	−	0.0912937i
$553$			320735.i			1.04881i
$554$	2922.35	+	38496.7i	0.00952167	+	0.125431i
$555$		0			0
$556$	58176.0	+	380974.i	0.188189	+	1.23238i
$557$			152777.i			0.492432i	0.969215	+	0.246216i	$0.0791873\pi$
$557$			152777.i			0.492432i	−0.969215	+	0.246216i	$0.920813\pi$
$558$	−9598.82	−	126447.i	−0.0308283	−	0.406107i
$559$		−	69336.6i		−	0.221891i
$560$		0			0
$561$	70447.9			0.223842
$562$	−360896.	+	27396.2i	−1.14264	+	0.0867398i
$563$	128620.			0.405782			0.202891	−	0.979201i	$-0.434966\pi$
$563$	128620.			0.405782			0.202891	+	0.979201i	$0.434966\pi$
$564$	−102732.	+	15687.6i	−0.322960	+	0.0493171i
$565$		0			0
$566$	179090.	−	13595.0i	0.559034	−	0.0424372i
$567$	−31370.2			−0.0975777
$568$	−67685.7	−	292637.i	−0.209798	−	0.907052i
$569$	353147.			1.09076			0.545382	−	0.838188i	$-0.316385\pi$
$569$	353147.			1.09076			0.545382	+	0.838188i	$0.316385\pi$
$570$		0			0
$571$			9607.19i			0.0294662i	0.999891	+	0.0147331i	$0.00468986\pi$
$571$			9607.19i			0.0294662i	−0.999891	+	0.0147331i	$0.995310\pi$
$572$	102286.	−	15619.4i	0.312624	−	0.0477387i
$573$			192560.i			0.586484i
$574$	45623.9	−	3463.38i	0.138474	−	0.0105118i
$575$		0			0
$576$	99360.0	−	48561.1i	0.299479	−	0.146367i
$577$		−	35488.3i		−	0.106594i	−0.998579	−	0.0532971i	$-0.983027\pi$
$577$		−	35488.3i		−	0.106594i	0.998579	−	0.0532971i	$-0.0169730\pi$
$578$	161082.	−	12228.0i	0.482160	−	0.0366016i
$579$		−	119615.i		−	0.356802i
$580$		0			0
$581$	385174.			1.14105
$582$	−21590.1	−	284410.i	−0.0637394	−	0.839651i
$583$	−51416.6			−0.151275
$584$	77950.9	+	337018.i	0.228558	+	0.988159i
$585$		0			0
$586$	−9182.20	−	120959.i	−0.0267394	−	0.352243i
$587$	396523.			1.15078			0.575390	−	0.817879i	$-0.304850\pi$
$587$	396523.			1.15078			0.575390	+	0.817879i	$0.304850\pi$
$588$	45141.8	−	6893.31i	0.130564	−	0.0199376i
$589$	−669233.			−1.92907
$590$		0			0
$591$			218954.i			0.626869i
$592$	−110641.	−	353827.i	−0.315699	−	1.00960i
$593$			199308.i			0.566780i	0.959005	+	0.283390i	$0.0914591\pi$
$593$			199308.i			0.566780i	−0.959005	+	0.283390i	$0.908541\pi$
$594$	2772.94	+	36528.4i	0.00785899	+	0.103528i
$595$		0			0
$596$	−695826.	+	106255.i	−1.95888	+	0.299128i
$597$		−	356199.i		−	0.999412i
$598$	−11134.0	−	146671.i	−0.0311351	−	0.410149i
$599$		−	596802.i		−	1.66332i	−0.555284	−	0.831661i	$-0.687390\pi$
$599$		−	596802.i		−	1.66332i	0.555284	−	0.831661i	$-0.312610\pi$
$600$		0			0
$601$	171774.			0.475563			0.237782	−	0.971319i	$-0.423580\pi$
$601$	171774.			0.475563			0.237782	+	0.971319i	$0.423580\pi$
$602$	120126.	−	9118.98i	0.331470	−	0.0251625i
$603$	−140824.			−0.387295
$604$	3352.38	+	21953.6i	0.00918924	+	0.0601771i
$605$		0			0
$606$	−305877.	+	23219.6i	−0.832916	+	0.0632280i
$607$	204299.			0.554485			0.277243	−	0.960800i	$-0.410579\pi$
$607$	204299.			0.554485			0.277243	+	0.960800i	$0.410579\pi$
$608$	−215850.	−	542257.i	−0.583910	−	1.46689i
$609$	−94786.3			−0.255571
$610$		0			0
$611$			123833.i			0.331707i
$612$	−13543.8	−	88693.4i	−0.0361607	−	0.236804i
$613$		−	72753.9i		−	0.193613i	−0.995303	−	0.0968066i	$-0.969137\pi$
$613$		−	72753.9i		−	0.193613i	0.995303	−	0.0968066i	$-0.0308628\pi$
$614$	−141782.	+	10762.9i	−0.376085	+	0.0285492i
$615$		0			0
$616$	40513.0	+	175156.i	0.106766	+	0.461598i
$617$			387966.i			1.01911i	0.860437	+	0.509557i	$0.170191\pi$
$617$			387966.i			1.01911i	−0.860437	+	0.509557i	$0.829809\pi$
$618$	38530.7	−	2924.93i	0.100886	−	0.00765841i
$619$			676575.i			1.76577i	0.469587	+	0.882886i	$0.344403\pi$
$619$			676575.i			1.76577i	−0.469587	+	0.882886i	$0.655597\pi$
$620$		0			0
$621$	52077.6			0.135042
$622$	−21861.1	−	287980.i	−0.0565055	−	0.744358i
$623$	−26528.9			−0.0683507
$624$	−39329.3	−	125774.i	−0.101006	−	0.323014i
$625$		0			0
$626$	−49276.6	−	649131.i	−0.125745	−	1.65647i
$627$	193330.			0.491772
$628$	18029.7	+	118070.i	0.0457162	+	0.299379i
$629$	−300761.			−0.760187
$630$		0			0
$631$			383055.i			0.962059i	0.876704	+	0.481030i	$0.159737\pi$
$631$			383055.i			0.962059i	−0.876704	+	0.481030i	$0.840263\pi$
$632$	−107495.	−	464750.i	−0.269125	−	1.16355i
$633$		−	195783.i		−	0.488616i
$634$	−19546.3	−	257487.i	−0.0486279	−	0.640585i
$635$		0			0
$636$	9884.98	+	64733.2i	0.0244378	+	0.160034i
$637$		−	54413.8i		−	0.134100i
$638$	8378.55	+	110372.i	0.0205839	+	0.271156i
$639$		−	126715.i		−	0.310333i
$640$		0			0
$641$	218038.			0.530660			0.265330	−	0.964158i	$-0.414519\pi$
$641$	218038.			0.530660			0.265330	+	0.964158i	$0.414519\pi$
$642$	−221019.	+	16777.9i	−0.536239	+	0.0407068i
$643$	329758.			0.797579			0.398789	−	0.917043i	$-0.369430\pi$
$643$	329758.			0.797579			0.398789	+	0.917043i	$0.369430\pi$
$644$	252644.	−	38579.6i	0.609169	−	0.0930221i
$645$		0			0
$646$	−472139.	+	35840.8i	−1.13137	+	0.0858842i
$647$	−166751.			−0.398346			−0.199173	−	0.979964i	$-0.563826\pi$
$647$	−166751.			−0.398346			−0.199173	+	0.979964i	$0.563826\pi$
$648$	45455.9	−	10513.8i	0.108253	−	0.0250386i
$649$	−196655.			−0.466891
$650$		0			0
$651$		−	262545.i		−	0.619502i
$652$	747985.	−	114220.i	1.75953	−	0.268687i
$653$			684629.i			1.60557i	0.596269	+	0.802785i	$0.296649\pi$
$653$			684629.i			1.60557i	−0.596269	+	0.802785i	$0.703351\pi$
$654$	−92834.2	+	7047.20i	−0.217046	+	0.0164764i
$655$		0			0
$656$	−64949.0	+	20309.5i	−0.150926	+	0.0471944i
$657$			145933.i			0.338082i
$658$	−214542.	+	16286.2i	−0.495519	+	0.0376157i
$659$			580631.i			1.33699i	0.743714	+	0.668497i	$0.233062\pi$
$659$			580631.i			1.33699i	−0.743714	+	0.668497i	$0.766938\pi$
$660$		0			0
$661$	324617.			0.742964			0.371482	−	0.928440i	$-0.378850\pi$
$661$	324617.			0.742964			0.371482	+	0.928440i	$0.378850\pi$
$662$	3495.26	+	46043.8i	0.00797561	+	0.105064i
$663$	−106911.			−0.243217
$664$	−558124.	+	129092.i	−1.26589	+	0.292795i
$665$		0			0
$666$	−11838.4	−	155950.i	−0.0266898	−	0.351590i
$667$	157355.			0.353695
$668$	−1426.53	+	217.836i	−0.00319689	+	0.000488176i
$669$	48004.5			0.107258
$670$		0			0
$671$		−	295017.i		−	0.655243i
$672$	212732.	−	84679.8i	0.471079	−	0.187517i
$673$		−	46209.4i		−	0.102024i	−0.998698	−	0.0510118i	$-0.983755\pi$
$673$		−	46209.4i		−	0.102024i	0.998698	−	0.0510118i	$-0.0162446\pi$
$674$	−63283.5	−	833646.i	−0.139306	−	1.83511i
$675$		0			0
$676$	296512.	−	45278.4i	0.648857	−	0.0990827i
$677$		−	98225.8i		−	0.214313i	−0.994242	−	0.107156i	$-0.965825\pi$
$677$		−	98225.8i		−	0.214313i	0.994242	−	0.107156i	$-0.0341746\pi$
$678$	−33393.5	−	439899.i	−0.0726444	−	0.956959i
$679$		−	590528.i		−	1.28086i
$680$		0			0
$681$	254013.			0.547723
$682$	−305716.	+	23207.4i	−0.657279	+	0.0498952i
$683$	−454709.			−0.974747			−0.487373	−	0.873194i	$-0.662045\pi$
$683$	−454709.			−0.974747			−0.487373	+	0.873194i	$0.662045\pi$
$684$	−37168.2	−	243401.i	−0.0794436	−	0.520248i
$685$		0			0
$686$	506364.	−	38438.9i	1.07601	−	0.0816814i
$687$	91735.4			0.194367
$688$	−171009.	+	53474.2i	−0.361278	+	0.112971i
$689$	78029.2			0.164369
$690$		0			0
$691$			190359.i			0.398673i	0.979931	+	0.199337i	$0.0638787\pi$
$691$			190359.i			0.398673i	−0.979931	+	0.199337i	$0.936121\pi$
$692$	2927.54	+	19171.4i	0.00611352	+	0.0400352i
$693$			75844.9i			0.157928i
$694$	643366.	−	48839.0i	1.33579	−	0.101402i
$695$		0			0
$696$	137347.	−	31767.9i	0.283531	−	0.0655797i
$697$			55208.2i			0.113642i
$698$	−351155.	+	26656.8i	−0.720756	+	0.0547138i
$699$			270355.i			0.553325i
$700$		0			0
$701$	504089.			1.02582			0.512910	−	0.858442i	$-0.328567\pi$
$701$	504089.			1.02582			0.512910	+	0.858442i	$0.328567\pi$
$702$	−4208.17	−	55435.1i	−0.00853924	−	0.112489i
$703$	−825378.			−1.67010
$704$	−117408.	−	240227.i	−0.236893	−	0.484703i
$705$		0			0
$706$	−56546.9	−	744903.i	−0.113449	−	1.49448i
$707$	−635099.			−1.27058
$708$	37807.4	+	247587.i	0.0754241	+	0.493926i
$709$	160106.			0.318504			0.159252	−	0.987238i	$-0.449092\pi$
$709$	160106.			0.318504			0.159252	+	0.987238i	$0.449092\pi$
$710$		0			0
$711$		−	201243.i		−	0.398090i
$712$	38440.9	−	8891.23i	0.0758286	−	0.0175389i
$713$			435852.i			0.857353i
$714$	−14060.6	−	185224.i	−0.0275809	−	0.363329i
$715$		0			0
$716$	−49989.3	−	327362.i	−0.0975105	−	0.638562i
$717$			280069.i			0.544786i
$718$	−68583.7	−	903467.i	−0.133037	−	1.75252i
$719$		−	918988.i		−	1.77767i	−0.458224	−	0.888836i	$-0.651514\pi$
$719$		−	918988.i		−	1.77767i	0.458224	−	0.888836i	$-0.348486\pi$
$720$		0			0
$721$	80002.2			0.153897
$722$	−775900.	+	58899.9i	−1.48844	+	0.112990i
$723$	292601.			0.559756
$724$	296132.	−	45220.3i	0.564947	−	0.0862694i
$725$		0			0
$726$	−215118.	+	16330.0i	−0.408135	+	0.0309822i
$727$	339605.			0.642548			0.321274	−	0.946986i	$-0.395889\pi$
$727$	339605.			0.642548			0.321274	+	0.946986i	$0.395889\pi$
$728$	−61482.0	−	265815.i	−0.116007	−	0.501552i
$729$	19683.0			0.0370370
$730$		0			0
$731$			145361.i			0.272029i
$732$	−371424.	+	56717.8i	−0.693184	+	0.105851i
$733$			310186.i			0.577317i	0.957432	+	0.288659i	$0.0932092\pi$
$733$			310186.i			0.577317i	−0.957432	+	0.288659i	$0.906791\pi$
$734$	425384.	−	32291.6i	0.789567	−	0.0599374i
$735$		0			0
$736$	−353156.	+	140577.i	−0.651945	+	0.259513i
$737$			340476.i			0.626832i
$738$	−28626.4	+	2173.08i	−0.0525598	+	0.00398990i
$739$		−	561855.i		−	1.02881i	−0.857547	−	0.514405i	$-0.828013\pi$
$739$		−	561855.i		−	1.02881i	0.857547	−	0.514405i	$-0.171987\pi$
$740$		0			0
$741$	−293395.			−0.534338
$742$	10262.2	+	135186.i	0.0186394	+	0.245541i
$743$	89658.6			0.162411			0.0812053	−	0.996697i	$-0.474123\pi$
$743$	89658.6			0.162411			0.0812053	+	0.996697i	$0.474123\pi$
$744$	87992.7	+	380433.i	0.158965	+	0.687278i
$745$		0			0
$746$	−39113.7	−	515253.i	−0.0702832	−	0.925854i
$747$	−241675.			−0.433102
$748$	−214438.	+	32745.3i	−0.383264	+	0.0585257i
$749$	−458906.			−0.818013
$750$		0			0
$751$		−	58229.8i		−	0.103244i	−0.998667	−	0.0516221i	$-0.983561\pi$
$751$		−	58229.8i		−	0.103244i	0.998667	−	0.0516221i	$-0.0164391\pi$
$752$	305417.	−	95503.3i	0.540079	−	0.168882i
$753$			62102.4i			0.109526i
$754$	−12715.2	−	167499.i	−0.0223655	−	0.294626i
$755$		0			0
$756$	95488.2	−	14581.4i	0.167073	−	0.0255126i
$757$		−	77925.2i		−	0.135983i	−0.997686	−	0.0679917i	$-0.978341\pi$
$757$		−	77925.2i		−	0.135983i	0.997686	−	0.0679917i	$-0.0216592\pi$
$758$	47280.2	+	622832.i	0.0822889	+	1.08401i
$759$		−	125910.i		−	0.218563i
$760$		0			0
$761$	241107.			0.416332			0.208166	−	0.978094i	$-0.433251\pi$
$761$	241107.			0.416332			0.208166	+	0.978094i	$0.433251\pi$
$762$	96926.2	−	7357.83i	0.166929	−	0.0126718i
$763$	−192754.			−0.331096
$764$	−89505.0	−	586136.i	−0.153342	−	1.00418i
$765$		0			0
$766$	−1.04261e6	+	79146.5i	−1.77691	+	0.134888i
$767$	298441.			0.507303
$768$	−279872.	+	194000.i	−0.474500	+	0.328912i
$769$	805186.			1.36158			0.680791	−	0.732478i	$-0.261636\pi$
$769$	805186.			1.36158			0.680791	+	0.732478i	$0.261636\pi$
$770$		0			0
$771$			80452.5i			0.135342i
$772$	55598.8	+	364097.i	0.0932891	+	0.610917i
$773$		−	431024.i		−	0.721344i	−0.932693	−	0.360672i	$-0.882547\pi$
$773$		−	431024.i		−	0.721344i	0.932693	−	0.360672i	$-0.117453\pi$
$774$	−75372.4	+	5721.64i	−0.125814	+	0.00955078i
$775$		0			0
$776$	197917.	+	855685.i	0.328669	+	1.42099i
$777$		−	323802.i		−	0.536337i
$778$	4174.40	−	316.886i	0.00689660	−	0.000523532i
$779$			151508.i			0.249666i
$780$		0			0
$781$	−306365.			−0.502269
$782$	23342.1	+	307490.i	0.0381703	+	0.502826i
$783$	59473.0			0.0970056
$784$	−134204.	+	41965.3i	−0.218340	+	0.0682745i
$785$		0			0
$786$	−47076.2	−	620145.i	−0.0762003	−	1.00380i
$787$	347948.			0.561778			0.280889	−	0.959740i	$-0.409371\pi$
$787$	347948.			0.561778			0.280889	+	0.959740i	$0.409371\pi$
$788$	−101773.	−	666476.i	−0.163901	−	1.07333i
$789$	84891.0			0.136367
$790$		0			0
$791$		−	913373.i		−	1.45981i
$792$	−25419.6	−	109901.i	−0.0405246	−	0.175206i
$793$			447714.i			0.711958i
$794$	54945.2	+	723804.i	0.0871543	+	1.14810i
$795$		0			0
$796$	165567.	+	1.08424e6i	0.261305	+	1.71120i
$797$		−	460443.i		−	0.724868i	−0.932009	−	0.362434i	$-0.881946\pi$
$797$		−	460443.i		−	0.724868i	0.932009	−	0.362434i	$-0.118054\pi$
$798$	−38586.6	−	508309.i	−0.0605941	−	0.798219i
$799$		−	259611.i		−	0.406659i
$800$		0			0
$801$	16645.4			0.0259435
$802$	575959.	−	43722.0i	0.895453	−	0.0679753i
$803$	352828.			0.547182
$804$	428656.	−	65457.3i	0.663128	−	0.101262i
$805$		0			0
$806$	463951.	−	35219.3i	0.714171	−	0.0542139i
$807$	−426409.			−0.654756
$808$	920270.	−	212855.i	1.40959	−	0.326033i
$809$	621711.			0.949930			0.474965	−	0.880005i	$-0.342461\pi$
$809$	621711.			0.949930			0.474965	+	0.880005i	$0.342461\pi$
$810$		0			0
$811$			25991.9i			0.0395181i	0.999805	+	0.0197591i	$0.00628991\pi$
$811$			25991.9i			0.0395181i	−0.999805	+	0.0197591i	$0.993710\pi$
$812$	288522.	−	44058.2i	0.437589	−	0.0668213i
$813$		−	390354.i		−	0.590578i
$814$	−377046.	+	28622.2i	−0.569043	+	0.0431970i
$815$		0			0
$816$	82452.3	+	263680.i	0.123829	+	0.396002i
$817$			398915.i			0.597635i
$818$	−7450.41	+	565.573i	−0.0111346	+	0.000845244i
$819$		−	115101.i		−	0.171598i
$820$		0			0
$821$	−917945.			−1.36185			−0.680927	−	0.732352i	$-0.738423\pi$
$821$	−917945.			−1.36185			−0.680927	+	0.732352i	$0.738423\pi$
$822$	30322.1	+	399439.i	0.0448761	+	0.591162i
$823$	−1.22951e6			−1.81523			−0.907613	−	0.419807i	$-0.862098\pi$
$823$	−1.22951e6			−1.81523			−0.907613	+	0.419807i	$0.862098\pi$
$824$	−115925.	+	26812.9i	−0.170734	+	0.0394902i
$825$		0			0
$826$	39250.2	+	517051.i	0.0575284	+	0.757833i
$827$	−254347.			−0.371891			−0.185946	−	0.982560i	$-0.559535\pi$
$827$	−254347.			−0.371891			−0.185946	+	0.982560i	$0.559535\pi$
$828$	−158520.	+	24206.5i	−0.231219	+	0.0353079i
$829$	456708.			0.664552			0.332276	−	0.943182i	$-0.392183\pi$
$829$	456708.			0.664552			0.332276	+	0.943182i	$0.392183\pi$
$830$		0			0
$831$		−	50152.6i		−	0.0726259i
$832$	178177.	+	364565.i	0.257398	+	0.526657i
$833$			114076.i			0.164401i
$834$	−37895.1	−	499200.i	−0.0544818	−	0.717700i
$835$		0			0
$836$	−588480.	+	89862.9i	−0.842014	+	0.128578i
$837$			164732.i			0.235141i
$838$	34154.1	+	449919.i	0.0486357	+	0.640688i
$839$			397834.i			0.565168i	0.959243	+	0.282584i	$0.0911916\pi$
$839$			397834.i			0.565168i	−0.959243	+	0.282584i	$0.908808\pi$
$840$		0			0
$841$	−527581.			−0.745928
$842$	−309490.	+	23493.9i	−0.436538	+	0.0331383i
$843$	470167.			0.661602
$844$	91003.2	+	595948.i	0.127753	+	0.836611i
$845$		0			0
$846$	134613.	−	10218.7i	0.188081	−	0.0142776i
$847$	−446655.			−0.622595
$848$	−60178.1	−	192448.i	−0.0836848	−	0.267622i
$849$	−233314.			−0.323687
$850$		0			0
$851$			537544.i			0.742258i
$852$	58899.4	+	385711.i	0.0811393	+	0.531353i
$853$		−	683508.i		−	0.939389i	−0.882829	−	0.469694i	$-0.844364\pi$
$853$		−	683508.i		−	0.939389i	0.882829	−	0.469694i	$-0.155636\pi$
$854$	−775667.	+	58882.2i	−1.06355	+	0.0807362i
$855$		0			0
$856$	664964.	−	153804.i	0.907508	−	0.209903i
$857$		−	116155.i		−	0.158152i	−0.996869	−	0.0790760i	$-0.974803\pi$
$857$		−	116155.i		−	0.158152i	0.996869	−	0.0790760i	$-0.0251970\pi$
$858$	−134028.	+	10174.3i	−0.182062	+	0.0138206i
$859$			169632.i			0.229890i	0.993372	+	0.114945i	$0.0366692\pi$
$859$			169632.i			0.229890i	−0.993372	+	0.114945i	$0.963331\pi$
$860$		0			0
$861$	−59437.7			−0.0801780
$862$	−47452.9	−	625107.i	−0.0638629	−	0.841279i
$863$	−651371.			−0.874595			−0.437298	−	0.899317i	$-0.644064\pi$
$863$	−651371.			−0.874595			−0.437298	+	0.899317i	$0.644064\pi$
$864$	−133477.	+	53131.8i	−0.178805	+	0.0711749i
$865$		0			0
$866$	12494.7	+	164595.i	0.0166606	+	0.219473i
$867$	−209854.			−0.279176
$868$	122035.	+	799166.i	0.161974	+	1.06071i
$869$	−486552.			−0.644303
$870$		0			0
$871$		−	516701.i		−	0.681088i
$872$	279304.	−	64601.9i	0.367320	−	0.0849596i
$873$			370523.i			0.486168i
$874$	64057.6	+	843844.i	0.0838586	+	1.10469i
$875$		0			0
$876$	−67832.0	−	444208.i	−0.0883947	−	0.578866i
$877$			1.36009e6i			1.76836i	0.467151	+	0.884178i	$0.345280\pi$
$877$			1.36009e6i			1.76836i	−0.467151	+	0.884178i	$0.654720\pi$
$878$	46870.7	+	617438.i	0.0608013	+	0.800947i
$879$			157582.i			0.203953i
$880$		0			0
$881$	976763.			1.25845			0.629227	−	0.777222i	$-0.283372\pi$
$881$	976763.			1.25845			0.629227	+	0.777222i	$0.283372\pi$
$882$	−59150.5	+	4490.22i	−0.0760364	+	0.00577205i
$883$	1.29155e6			1.65650			0.828248	−	0.560362i	$-0.189338\pi$
$883$	1.29155e6			1.65650			0.828248	+	0.560362i	$0.189338\pi$
$884$	325428.	−	49693.9i	0.416438	−	0.0635914i
$885$		0			0
$886$	1.00164e6	−	76036.4i	1.27598	−	0.0968621i
$887$	1.40632e6			1.78747			0.893733	−	0.448599i	$-0.148077\pi$
$887$	1.40632e6			1.78747			0.893733	+	0.448599i	$0.148077\pi$
$888$	108523.	+	469195.i	0.137625	+	0.595014i
$889$	201250.			0.254644
$890$		0			0
$891$		−	47588.4i		−	0.0599439i
$892$	−146122.	+	22313.3i	−0.183648	+	0.0280436i
$893$		−	712451.i		−	0.893412i
$894$	911759.	−	69213.2i	1.14079	−	0.0865992i
$895$		0			0
$896$	−608177.	+	356639.i	−0.757555	+	0.444235i
$897$			191079.i			0.237481i
$898$	127188.	−	9655.09i	0.157723	−	0.0119730i
$899$			497746.i			0.615869i
$900$		0			0
$901$	−163585.			−0.201509
$902$	5253.93	+	69211.1i	0.00645761	+	0.0850673i
$903$	−156497.			−0.191925
$904$	306119.	+	1.32349e6i	0.374588	+	1.61951i
$905$		0			0
$906$	−2183.70	−	28766.3i	−0.00266034	−	0.0350452i
$907$	−373379.			−0.453874			−0.226937	−	0.973909i	$-0.572871\pi$
$907$	−373379.			−0.453874			−0.226937	+	0.973909i	$0.572871\pi$
$908$	−773193.	+	118069.i	−0.937813	+	0.143207i
$909$	398489.			0.482268
$910$		0			0
$911$			62632.1i			0.0754675i	0.999288	+	0.0377338i	$0.0120139\pi$
$911$			62632.1i			0.0754675i	−0.999288	+	0.0377338i	$0.987986\pi$
$912$	226274.	+	723616.i	0.272047	+	0.869999i
$913$			584307.i			0.700970i
$914$	−50539.9	−	665772.i	−0.0604981	−	0.796954i
$915$		0			0
$916$	−279235.	+	42640.1i	−0.332796	+	0.0508191i
$917$		−	1.28762e6i		−	1.53126i
$918$	8822.26	+	116217.i	0.0104687	+	0.137907i
$919$		−	829993.i		−	0.982751i	−0.870948	−	0.491375i	$-0.836494\pi$
$919$		−	829993.i		−	0.982751i	0.870948	−	0.491375i	$-0.163506\pi$
$920$		0			0
$921$	184711.			0.217757
$922$	−520679.	+	39525.7i	−0.612503	+	0.0464962i
$923$	464935.			0.545744
$924$	−35253.9	−	230865.i	−0.0412918	−	0.270405i
$925$		0			0
$926$	1.08953e6	−	82708.3i	1.27063	−	0.0964556i
$927$	−50196.8			−0.0584140
$928$	−403307.	+	160540.i	−0.468317	+	0.186418i
$929$	−1.22106e6			−1.41483			−0.707416	−	0.706798i	$-0.750139\pi$
$929$	−1.22106e6			−1.41483			−0.707416	+	0.706798i	$0.750139\pi$
$930$		0			0
$931$			313059.i			0.361183i
$932$	−125665.	−	822938.i	−0.144672	−	0.947404i
$933$			375174.i			0.430992i
$934$	223638.	−	16976.7i	0.256361	−	0.0194608i
$935$		0			0
$936$	38576.4	+	166784.i	0.0440322	+	0.190371i
$937$		−	238403.i		−	0.271539i	−0.990740	−	0.135770i	$-0.956649\pi$
$937$		−	238403.i		−	0.271539i	0.990740	−	0.135770i	$-0.0433507\pi$
$938$	895188.	−	67955.3i	1.01744	−	0.0772356i
$939$			845672.i			0.959115i
$940$		0			0
$941$	−1.17958e6			−1.33214			−0.666070	−	0.745889i	$-0.732025\pi$
$941$	−1.17958e6			−1.33214			−0.666070	+	0.745889i	$0.732025\pi$
$942$	−11744.3	−	154711.i	−0.0132351	−	0.174348i
$943$	98672.5			0.110962
$944$	−230165.	−	736062.i	−0.258283	−	0.825981i
$945$		0			0
$946$	13833.4	+	182231.i	0.0154578	+	0.203629i
$947$	−886731.			−0.988762			−0.494381	−	0.869245i	$-0.664605\pi$
$947$	−886731.			−0.988762			−0.494381	+	0.869245i	$0.664605\pi$
$948$	93540.9	+	612566.i	0.104084	+	0.681611i
$949$	−535447.			−0.594544
$950$		0			0
$951$			335448.i			0.370906i
$952$	128894.	+	557270.i	0.142220	+	0.614882i
$953$		−	1.72385e6i		−	1.89807i	−0.315166	−	0.949037i	$-0.602060\pi$
$953$		−	1.72385e6i		−	1.89807i	0.315166	−	0.949037i	$-0.397940\pi$
$954$	−6438.95	−	84821.6i	−0.00707487	−	0.0931987i
$955$		0			0
$956$	−130181.	−	852506.i	−0.142439	−	0.932785i
$957$		−	143790.i		−	0.157002i
$958$	48565.3	+	639760.i	0.0529169	+	0.697086i
$959$			829364.i			0.901796i
$960$		0			0
$961$	−455168.			−0.492862
$962$	572199.	−	43436.6i	0.618297	−	0.0469360i
$963$	287938.			0.310489
$964$	−890652.	+	136006.i	−0.958416	+	0.146353i
$965$		0			0
$966$	−331046.	+	25130.3i	−0.354760	+	0.0269304i
$967$	−652513.			−0.697808			−0.348904	−	0.937158i	$-0.613446\pi$
$967$	−652513.			−0.697808			−0.348904	+	0.937158i	$0.613446\pi$
$968$	647211.	−	149698.i	0.690710	−	0.159759i
$969$	615091.			0.655076
$970$		0			0
$971$		−	399968.i		−	0.424216i	−0.977246	−	0.212108i	$-0.931967\pi$
$971$		−	399968.i		−	0.424216i	0.977246	−	0.212108i	$-0.0680328\pi$
$972$	−59913.4	+	9148.98i	−0.0634149	+	0.00968367i
$973$		−	1.03650e6i		−	1.09482i
$974$	−1.25293e6	+	95111.8i	−1.32071	+	0.100257i
$975$		0			0
$976$	1.10422e6	−	345288.i	1.15920	−	0.362478i
$977$		−	1.43718e6i		−	1.50564i	−0.658227	−	0.752820i	$-0.728693\pi$
$977$		−	1.43718e6i		−	1.50564i	0.658227	−	0.752820i	$-0.271307\pi$
$978$	−980104.	+	74401.4i	−1.02470	+	0.0777863i
$979$		−	40244.2i		−	0.0419892i
$980$		0			0
$981$	120942.			0.125672
$982$	17507.1	+	230625.i	0.0181548	+	0.239157i
$983$	1.64352e6			1.70086			0.850428	−	0.526092i	$-0.176343\pi$
$983$	1.64352e6			1.70086			0.850428	+	0.526092i	$0.176343\pi$
$984$	86126.2	−	19920.7i	0.0889499	−	0.0205738i
$985$		0			0
$986$	26656.8	+	351156.i	0.0274192	+	0.361199i
$987$	279500.			0.286911
$988$	893070.	−	136375.i	0.914896	−	0.139708i
$989$	259801.			0.265613
$990$		0			0
$991$		−	713551.i		−	0.726570i	−0.931678	−	0.363285i	$-0.881655\pi$
$991$		−	713551.i		−	0.726570i	0.931678	−	0.363285i	$-0.118345\pi$
$992$	−444674.	−	1.11711e6i	−0.451875	−	1.13520i
$993$		−	59984.8i		−	0.0608334i
$994$	61147.1	+	805503.i	0.0618875	+	0.815257i
$995$		0			0
$996$	735638.	−	112334.i	0.741559	−	0.113238i
$997$		−	1.13252e6i		−	1.13935i	−0.821871	−	0.569673i	$-0.807070\pi$
$997$		−	1.13252e6i		−	1.13935i	0.821871	−	0.569673i	$-0.192930\pi$
$998$	83582.5	+	1.10105e6i	0.0839179	+	1.10547i
$999$			203167.i			0.203574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.f.a.199.7		8
4.3	odd	2	inner	300.5.f.a.199.1		8
5.2	odd	4		300.5.c.a.151.4		4
5.3	odd	4		12.5.d.a.7.1	✓	4
5.4	even	2	inner	300.5.f.a.199.2		8
15.8	even	4		36.5.d.b.19.4		4
20.3	even	4		12.5.d.a.7.2	yes	4
20.7	even	4		300.5.c.a.151.3		4
20.19	odd	2	inner	300.5.f.a.199.8		8
40.3	even	4		192.5.g.d.127.1		4
40.13	odd	4		192.5.g.d.127.3		4
60.23	odd	4		36.5.d.b.19.3		4
80.3	even	4		768.5.b.g.127.1		8
80.13	odd	4		768.5.b.g.127.5		8
80.43	even	4		768.5.b.g.127.8		8
80.53	odd	4		768.5.b.g.127.4		8
120.53	even	4		576.5.g.m.127.4		4
120.83	odd	4		576.5.g.m.127.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.1	✓	4	5.3	odd	4
12.5.d.a.7.2	yes	4	20.3	even	4
36.5.d.b.19.3		4	60.23	odd	4
36.5.d.b.19.4		4	15.8	even	4
192.5.g.d.127.1		4	40.3	even	4
192.5.g.d.127.3		4	40.13	odd	4
300.5.c.a.151.3		4	20.7	even	4
300.5.c.a.151.4		4	5.2	odd	4
300.5.f.a.199.1		8	4.3	odd	2	inner
300.5.f.a.199.2		8	5.4	even	2	inner
300.5.f.a.199.7		8	1.1	even	1	trivial
300.5.f.a.199.8		8	20.19	odd	2	inner
576.5.g.m.127.3		4	120.83	odd	4
576.5.g.m.127.4		4	120.53	even	4
768.5.b.g.127.1		8	80.3	even	4
768.5.b.g.127.4		8	80.53	odd	4
768.5.b.g.127.5		8	80.13	odd	4
768.5.b.g.127.8		8	80.43	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.98852 - 0.302776i) q^{2} -5.19615 q^{3} +(15.8167 - 2.41526i) q^{4} +(-20.7250 + 1.57327i) q^{6} -43.0318 q^{7} +(62.3538 - 14.4222i) q^{8} +27.0000 q^{9} -65.2790i q^{11} +(-82.1857 + 12.5500i) q^{12} +99.0665i q^{13} +(-171.633 + 13.0290i) q^{14} +(244.333 - 76.4025i) q^{16} -207.689i q^{17} +(107.690 - 8.17494i) q^{18} -569.960i q^{19} +223.600 q^{21} +(-19.7649 - 260.367i) q^{22} -371.198 q^{23} +(-324.000 + 74.9400i) q^{24} +(29.9949 + 395.129i) q^{26} -140.296 q^{27} +(-680.619 + 103.933i) q^{28} -423.911 q^{29} -1174.18i q^{31} +(951.396 - 378.711i) q^{32} +339.199i q^{33} +(-62.8831 - 828.372i) q^{34} +(427.050 - 65.2119i) q^{36} -1448.13i q^{37} +(-172.570 - 2273.30i) q^{38} -514.764i q^{39} -265.822 q^{41} +(891.833 - 67.7005i) q^{42} -699.900 q^{43} +(-157.665 - 1032.49i) q^{44} +(-1480.53 + 112.390i) q^{46} +1250.00 q^{47} +(-1269.59 + 396.999i) q^{48} -549.266 q^{49} +1079.18i q^{51} +(239.271 + 1566.90i) q^{52} -787.645i q^{53} +(-559.574 + 42.4782i) q^{54} +(-2683.20 + 620.613i) q^{56} +2961.60i q^{57} +(-1690.78 + 128.350i) q^{58} -3012.53i q^{59} +4519.33 q^{61} +(-355.512 - 4683.23i) q^{62} -1161.86 q^{63} +(3680.00 - 1798.56i) q^{64} +(102.701 + 1352.91i) q^{66} -5215.70 q^{67} +(-501.622 - 3284.94i) q^{68} +1928.80 q^{69} -4693.16i q^{71} +(1683.55 - 389.400i) q^{72} +5404.92i q^{73} +(-438.459 - 5775.91i) q^{74} +(-1376.60 - 9014.86i) q^{76} +2809.07i q^{77} +(-155.858 - 2053.15i) q^{78} -7453.44i q^{79} +729.000 q^{81} +(-1060.24 + 80.4843i) q^{82} -8950.92 q^{83} +(3536.60 - 540.051i) q^{84} +(-2791.57 + 211.913i) q^{86} +2202.71 q^{87} +(-941.466 - 4070.39i) q^{88} +616.496 q^{89} -4263.01i q^{91} +(-5871.11 + 896.538i) q^{92} +6101.20i q^{93} +(4985.66 - 378.470i) q^{94} +(-4943.60 + 1967.84i) q^{96} +13723.1i q^{97} +(-2190.76 + 166.304i) q^{98} -1762.53i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9} - 1200 q^{14} + 224 q^{16} - 288 q^{21} - 2592 q^{24} + 3384 q^{26} - 1776 q^{29} + 968 q^{34} + 1080 q^{36} + 1104 q^{41} + 7392 q^{44} - 768 q^{46} + 1144 q^{49}+ \cdots - 16704 q^{96}+O(q^{100}) \) 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9 - 1200 * q^14 + 224 * q^16 - 288 * q^21 - 2592 * q^24 + 3384 * q^26 - 1776 * q^29 + 968 * q^34 + 1080 * q^36 + 1104 * q^41 + 7392 * q^44 - 768 * q^46 + 1144 * q^49 - 972 * q^54 + 3456 * q^56 + 8464 * q^61 + 29440 * q^64 + 9648 * q^66 + 19584 * q^69 + 8232 * q^74 - 3744 * q^76 + 5832 * q^81 + 21024 * q^84 - 39120 * q^86 + 50160 * q^89 + 10464 * q^94 - 16704 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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