LMFDB - Embedded newform 300.5.f.a.199.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(199,300)]

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, 1]))

N = Newforms(chi, 5, names="a")

//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);

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: 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:	$8$
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			199.8
Root			$1.12824 - 0.651388i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.5.f.a.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.98852 + 0.302776i) q^{2} -5.19615 q^{3} +(15.8167 + 2.41526i) q^{4} +(-20.7250 - 1.57327i) q^{6} -43.0318 q^{7} +(62.3538 + 14.4222i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(3.98852 + 0.302776i) q^{2} -5.19615 q^{3} +(15.8167 + 2.41526i) q^{4} +(-20.7250 - 1.57327i) q^{6} -43.0318 q^{7} +(62.3538 + 14.4222i) q^{8} +27.0000 q^{9} +65.2790i q^{11} +(-82.1857 - 12.5500i) q^{12} -99.0665i q^{13} +(-171.633 - 13.0290i) q^{14} +(244.333 + 76.4025i) q^{16} +207.689i q^{17} +(107.690 + 8.17494i) q^{18} +569.960i q^{19} +223.600 q^{21} +(-19.7649 + 260.367i) q^{22} -371.198 q^{23} +(-324.000 - 74.9400i) q^{24} +(29.9949 - 395.129i) q^{26} -140.296 q^{27} +(-680.619 - 103.933i) q^{28} -423.911 q^{29} +1174.18i q^{31} +(951.396 + 378.711i) q^{32} -339.199i q^{33} +(-62.8831 + 828.372i) q^{34} +(427.050 + 65.2119i) q^{36} +1448.13i q^{37} +(-172.570 + 2273.30i) q^{38} +514.764i q^{39} -265.822 q^{41} +(891.833 + 67.7005i) q^{42} -699.900 q^{43} +(-157.665 + 1032.49i) q^{44} +(-1480.53 - 112.390i) q^{46} +1250.00 q^{47} +(-1269.59 - 396.999i) q^{48} -549.266 q^{49} -1079.18i q^{51} +(239.271 - 1566.90i) q^{52} +787.645i q^{53} +(-559.574 - 42.4782i) q^{54} +(-2683.20 - 620.613i) q^{56} -2961.60i q^{57} +(-1690.78 - 128.350i) q^{58} +3012.53i q^{59} +4519.33 q^{61} +(-355.512 + 4683.23i) q^{62} -1161.86 q^{63} +(3680.00 + 1798.56i) q^{64} +(102.701 - 1352.91i) q^{66} -5215.70 q^{67} +(-501.622 + 3284.94i) q^{68} +1928.80 q^{69} +4693.16i q^{71} +(1683.55 + 389.400i) q^{72} -5404.92i q^{73} +(-438.459 + 5775.91i) q^{74} +(-1376.60 + 9014.86i) q^{76} -2809.07i q^{77} +(-155.858 + 2053.15i) q^{78} +7453.44i q^{79} +729.000 q^{81} +(-1060.24 - 80.4843i) q^{82} -8950.92 q^{83} +(3536.60 + 540.051i) q^{84} +(-2791.57 - 211.913i) q^{86} +2202.71 q^{87} +(-941.466 + 4070.39i) q^{88} +616.496 q^{89} +4263.01i q^{91} +(-5871.11 - 896.538i) q^{92} -6101.20i q^{93} +(4985.66 + 378.470i) q^{94} +(-4943.60 - 1967.84i) q^{96} -13723.1i q^{97} +(-2190.76 - 166.304i) q^{98} +1762.53i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9}+O(q^{10}) $ 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9	$ 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}+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

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 $

$2$	3.98852	+	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	$0.0869403\pi$
$11$			65.2790i			0.539495i	−0.962931	+	0.269748i	$0.913060\pi$
$12$	−82.1857	−	12.5500i	−0.570734	−	0.0871530i
$13$		−	99.0665i		−	0.586192i	−0.956083	−	0.293096i	$-0.905314\pi$
$13$		−	99.0665i		−	0.586192i	0.956083	−	0.293096i	$-0.0946856\pi$
$14$	−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	$0.116992\pi$
$17$			207.689i			0.718646i	−0.933213	+	0.359323i	$0.883008\pi$
$18$	107.690	+	8.17494i	0.332377	+	0.0252313i
$19$			569.960i			1.57884i	0.613856	+	0.789418i	$0.289618\pi$
$19$			569.960i			1.57884i	−0.613856	+	0.789418i	$0.710382\pi$
$20$		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	$0.209198\pi$
$31$			1174.18i			1.22183i	−0.791697	+	0.610914i	$0.790802\pi$
$32$	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	$0.177396\pi$
$37$			1448.13i			1.05780i	−0.848683	+	0.528902i	$0.822604\pi$
$38$	−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	$0.0447746\pi$
$53$			787.645i			0.280401i	−0.990123	+	0.140200i	$0.955225\pi$
$54$	−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	$0.142443\pi$
$59$			3012.53i			0.865422i	−0.901533	+	0.432711i	$0.857557\pi$
$60$		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	$0.154125\pi$
$71$			4693.16i			0.930998i	−0.885048	+	0.465499i	$0.845875\pi$
$72$	1683.55	+	389.400i	0.324760	+	0.0751157i
$73$		−	5404.92i		−	1.01425i	−0.861873	−	0.507124i	$-0.830709\pi$
$73$		−	5404.92i		−	1.01425i	0.861873	−	0.507124i	$-0.169291\pi$
$74$	−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	$0.203694\pi$
$79$			7453.44i			1.19427i	−0.802141	+	0.597135i	$0.796306\pi$
$80$		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	$-0.739868\pi$
$97$		−	13723.1i		−	1.45850i	0.684246	−	0.729252i	$-0.260132\pi$
$98$	−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	$-0.687691\pi$
$113$		−	21225.5i		−	1.66227i	0.556070	−	0.831135i	$-0.312309\pi$
$114$	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	$-0.662940\pi$
$131$		−	29922.6i		−	1.74364i	0.489828	−	0.871819i	$-0.337060\pi$
$132$	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	$0.171627\pi$
$137$			19273.3i			1.02687i	−0.858129	+	0.513434i	$0.828373\pi$
$138$	7693.07	+	583.994i	0.403963	+	0.0306655i
$139$		−	24086.9i		−	1.24667i	−0.781955	−	0.623335i	$-0.785778\pi$
$139$		−	24086.9i		−	1.24667i	0.781955	−	0.623335i	$-0.214222\pi$
$140$		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	$-0.990310\pi$
$151$		−	1388.00i		−	0.0608746i	0.999537	−	0.0304373i	$-0.00969000\pi$
$152$	−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	$-0.951614\pi$
$157$		−	7464.93i		−	0.302849i	0.988469	−	0.151425i	$-0.0483861\pi$
$158$	−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	$-0.993554\pi$
$173$		−	1212.10i		−	0.0404993i	0.999795	−	0.0202497i	$-0.00644611\pi$
$174$	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	$0.104685\pi$
$179$			20697.3i			0.645964i	−0.946405	+	0.322982i	$0.895315\pi$
$180$		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	$0.169582\pi$
$191$			37058.2i			1.01582i	−0.861410	+	0.507910i	$0.830418\pi$
$192$	−19121.8	−	9345.59i	−0.518713	−	0.253515i
$193$		−	23019.8i		−	0.617999i	−0.951062	−	0.308999i	$-0.900006\pi$
$193$		−	23019.8i		−	0.617999i	0.951062	−	0.308999i	$-0.0999941\pi$
$194$	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	$0.182668\pi$
$197$			42137.6i			1.08577i	−0.839807	+	0.542885i	$0.817332\pi$
$198$	−533.652	+	7029.90i	−0.0136122	+	0.179316i
$199$		−	68550.6i		−	1.73103i	−0.500881	−	0.865516i	$-0.666991\pi$
$199$		−	68550.6i		−	1.73103i	0.500881	−	0.865516i	$-0.333009\pi$
$200$		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	$-0.860923\pi$
$211$		−	37678.5i		−	0.846308i	0.906058	−	0.423154i	$-0.139077\pi$
$212$	−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	$0.159071\pi$
$233$			52029.9i			0.958387i	−0.877709	+	0.479193i	$0.840929\pi$
$234$	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	$0.156395\pi$
$239$			53899.3i			0.943598i	−0.881706	+	0.471799i	$0.843605\pi$
$240$		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	$0.0302379\pi$
$251$			11951.6i			0.189705i	−0.995491	+	0.0948525i	$0.969762\pi$
$252$	−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	$0.0373948\pi$
$257$			15483.1i			0.234418i	−0.993107	+	0.117209i	$0.962605\pi$
$258$	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	$-0.829106\pi$
$271$		−	75123.6i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$272$	−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	$-0.979966\pi$
$277$		−	9651.88i		−	0.125792i	0.998020	−	0.0628959i	$-0.0200336\pi$
$278$	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	$0.0565191\pi$
$293$			30326.7i			0.353257i	−0.984278	+	0.176628i	$0.943481\pi$
$294$	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	$0.121757\pi$
$311$			72202.2i			0.746500i	−0.927731	+	0.373250i	$0.878243\pi$
$312$	−7424.04	+	32097.5i	−0.0762660	+	0.329733i
$313$			162750.i			1.66124i	0.556842	+	0.830618i	$0.312013\pi$
$313$			162750.i			1.66124i	−0.556842	+	0.830618i	$0.687987\pi$
$314$	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	$0.104091\pi$
$317$			64556.9i			0.642428i	−0.947007	+	0.321214i	$0.895909\pi$
$318$	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	$-0.983223\pi$
$331$		−	11544.1i		−	0.105367i	0.998611	−	0.0526833i	$-0.0167774\pi$
$332$	−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	$0.371970\pi$
$337$			209011.i			1.84039i	−0.391461	+	0.920195i	$0.628030\pi$
$338$	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	$0.269653\pi$
$353$			186762.i			1.49878i	−0.662128	+	0.749391i	$0.730347\pi$
$354$	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	$0.341643\pi$
$359$			226517.i			1.75756i	−0.477224	+	0.878782i	$0.658357\pi$
$360$		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	$0.153679\pi$
$373$			129184.i			0.928518i	−0.885699	+	0.464259i	$0.846321\pi$
$374$	−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	$-0.817075\pi$
$379$		−	156156.i		−	1.08713i	0.839368	−	0.543563i	$-0.182925\pi$
$380$		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	$-0.804729\pi$
$397$		−	181472.i		−	1.15140i	0.817659	−	0.575702i	$-0.195271\pi$
$398$	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	$-0.895892\pi$
$419$		−	112803.i		−	0.642531i	0.946989	−	0.321266i	$-0.104108\pi$
$420$		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	$0.138619\pi$
$431$			156726.i			0.843699i	−0.906666	+	0.421850i	$0.861381\pi$
$432$	−34279.0	−	10719.0i	−0.183679	−	0.0574362i
$433$		−	41267.2i		−	0.220105i	−0.993926	−	0.110052i	$-0.964898\pi$
$433$		−	41267.2i		−	0.220105i	0.993926	−	0.110052i	$-0.0351019\pi$
$434$	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	$-0.868445\pi$
$439$		−	154804.i		−	0.803252i	0.915804	−	0.401626i	$-0.131555\pi$
$440$		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	$0.130859\pi$
$457$			166922.i			0.799247i	−0.916679	+	0.399624i	$0.869141\pi$
$458$	−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	$-0.886336\pi$
$479$		−	160400.i		−	0.699091i	0.936919	−	0.349546i	$-0.113664\pi$
$480$		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	$-0.961735\pi$
$491$		−	57822.1i		−	0.239845i	0.992783	−	0.119923i	$-0.0382646\pi$
$492$	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	$-0.812977\pi$
$499$		−	276054.i		−	1.10865i	0.832301	−	0.554324i	$-0.187023\pi$
$500$		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	$-0.920813\pi$
$557$		−	152777.i		−	0.492432i	0.969215	−	0.246216i	$-0.0791873\pi$
$558$	−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	$-0.995310\pi$
$571$		−	9607.19i		−	0.0294662i	0.999891	−	0.0147331i	$-0.00468986\pi$
$572$	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	$0.0169730\pi$
$577$			35488.3i			0.106594i	−0.998579	+	0.0532971i	$0.983027\pi$
$578$	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	$-0.908541\pi$
$593$		−	199308.i		−	0.566780i	0.959005	−	0.283390i	$-0.0914591\pi$
$594$	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	$0.312610\pi$
$599$			596802.i			1.66332i	−0.555284	+	0.831661i	$0.687390\pi$
$600$		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	$0.0308628\pi$
$613$			72753.9i			0.193613i	−0.995303	+	0.0968066i	$0.969137\pi$
$614$	−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	$-0.829809\pi$
$617$		−	387966.i		−	1.01911i	0.860437	−	0.509557i	$-0.170191\pi$
$618$	38530.7	+	2924.93i	0.100886	+	0.00765841i
$619$		−	676575.i		−	1.76577i	−0.469587	−	0.882886i	$-0.655597\pi$
$619$		−	676575.i		−	1.76577i	0.469587	−	0.882886i	$-0.344403\pi$
$620$		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	$-0.840263\pi$
$631$		−	383055.i		−	0.962059i	0.876704	−	0.481030i	$-0.159737\pi$
$632$	−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	$-0.703351\pi$
$653$		−	684629.i		−	1.60557i	0.596269	−	0.802785i	$-0.296649\pi$
$654$	−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	$-0.766938\pi$
$659$		−	580631.i		−	1.33699i	0.743714	−	0.668497i	$-0.233062\pi$
$660$		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	$0.0162446\pi$
$673$			46209.4i			0.102024i	−0.998698	+	0.0510118i	$0.983755\pi$
$674$	−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	$0.0341746\pi$
$677$			98225.8i			0.214313i	−0.994242	+	0.107156i	$0.965825\pi$
$678$	−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	$-0.936121\pi$
$691$		−	190359.i		−	0.398673i	0.979931	−	0.199337i	$-0.0638787\pi$
$692$	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	$0.348486\pi$
$719$			918988.i			1.77767i	−0.458224	+	0.888836i	$0.651514\pi$
$720$		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	$-0.906791\pi$
$733$		−	310186.i		−	0.577317i	0.957432	−	0.288659i	$-0.0932092\pi$
$734$	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	$0.171987\pi$
$739$			561855.i			1.02881i	−0.857547	+	0.514405i	$0.828013\pi$
$740$		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	$0.0164391\pi$
$751$			58229.8i			0.103244i	−0.998667	+	0.0516221i	$0.983561\pi$
$752$	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	$0.0216592\pi$
$757$			77925.2i			0.135983i	−0.997686	+	0.0679917i	$0.978341\pi$
$758$	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	$0.117453\pi$
$773$			431024.i			0.721344i	−0.932693	+	0.360672i	$0.882547\pi$
$774$	−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	$0.118054\pi$
$797$			460443.i			0.724868i	−0.932009	+	0.362434i	$0.881946\pi$
$798$	−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	$-0.993710\pi$
$811$		−	25991.9i		−	0.0395181i	0.999805	−	0.0197591i	$-0.00628991\pi$
$812$	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	$-0.908808\pi$
$839$		−	397834.i		−	0.565168i	0.959243	−	0.282584i	$-0.0911916\pi$
$840$		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	$0.155636\pi$
$853$			683508.i			0.939389i	−0.882829	+	0.469694i	$0.844364\pi$
$854$	−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	$0.0251970\pi$
$857$			116155.i			0.158152i	−0.996869	+	0.0790760i	$0.974803\pi$
$858$	−134028.	−	10174.3i	−0.182062	−	0.0138206i
$859$		−	169632.i		−	0.229890i	−0.993372	−	0.114945i	$-0.963331\pi$
$859$		−	169632.i		−	0.229890i	0.993372	−	0.114945i	$-0.0366692\pi$
$860$		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	$-0.654720\pi$
$877$		−	1.36009e6i		−	1.76836i	0.467151	−	0.884178i	$-0.345280\pi$
$878$	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	$-0.987986\pi$
$911$		−	62632.1i		−	0.0754675i	0.999288	−	0.0377338i	$-0.0120139\pi$
$912$	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	$0.163506\pi$
$919$			829993.i			0.982751i	−0.870948	+	0.491375i	$0.836494\pi$
$920$		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	$0.0433507\pi$
$937$			238403.i			0.271539i	−0.990740	+	0.135770i	$0.956649\pi$
$938$	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	$0.397940\pi$
$953$			1.72385e6i			1.89807i	−0.315166	+	0.949037i	$0.602060\pi$
$954$	−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	$0.0680328\pi$
$971$			399968.i			0.424216i	−0.977246	+	0.212108i	$0.931967\pi$
$972$	−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	$0.271307\pi$
$977$			1.43718e6i			1.50564i	−0.658227	+	0.752820i	$0.728693\pi$
$978$	−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	$0.118345\pi$
$991$			713551.i			0.726570i	−0.931678	+	0.363285i	$0.881655\pi$
$992$	−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	$0.192930\pi$
$997$			1.13252e6i			1.13935i	−0.821871	+	0.569673i	$0.807070\pi$
$998$	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.199.8		8
4.3	odd	2	inner	300.5.f.a.199.2		8
5.2	odd	4		12.5.d.a.7.2	yes	4
5.3	odd	4		300.5.c.a.151.3		4
5.4	even	2	inner	300.5.f.a.199.1		8
15.2	even	4		36.5.d.b.19.3		4
20.3	even	4		300.5.c.a.151.4		4
20.7	even	4		12.5.d.a.7.1	✓	4
20.19	odd	2	inner	300.5.f.a.199.7		8
40.27	even	4		192.5.g.d.127.3		4
40.37	odd	4		192.5.g.d.127.1		4
60.47	odd	4		36.5.d.b.19.4		4
80.27	even	4		768.5.b.g.127.4		8
80.37	odd	4		768.5.b.g.127.8		8
80.67	even	4		768.5.b.g.127.5		8
80.77	odd	4		768.5.b.g.127.1		8
120.77	even	4		576.5.g.m.127.3		4
120.107	odd	4		576.5.g.m.127.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.1	✓	4	20.7	even	4
12.5.d.a.7.2	yes	4	5.2	odd	4
36.5.d.b.19.3		4	15.2	even	4
36.5.d.b.19.4		4	60.47	odd	4
192.5.g.d.127.1		4	40.37	odd	4
192.5.g.d.127.3		4	40.27	even	4
300.5.c.a.151.3		4	5.3	odd	4
300.5.c.a.151.4		4	20.3	even	4
300.5.f.a.199.1		8	5.4	even	2	inner
300.5.f.a.199.2		8	4.3	odd	2	inner
300.5.f.a.199.7		8	20.19	odd	2	inner
300.5.f.a.199.8		8	1.1	even	1	trivial
576.5.g.m.127.3		4	120.77	even	4
576.5.g.m.127.4		4	120.107	odd	4
768.5.b.g.127.1		8	80.77	odd	4
768.5.b.g.127.4		8	80.27	even	4
768.5.b.g.127.5		8	80.67	even	4
768.5.b.g.127.8		8	80.37	odd	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(3.98852 + 0.302776i) q^{2} -5.19615 q^{3} +(15.8167 + 2.41526i) q^{4} +(-20.7250 - 1.57327i) q^{6} -43.0318 q^{7} +(62.3538 + 14.4222i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(3.98852 + 0.302776i) q^{2} -5.19615 q^{3} +(15.8167 + 2.41526i) q^{4} +(-20.7250 - 1.57327i) q^{6} -43.0318 q^{7} +(62.3538 + 14.4222i) q^{8} +27.0000 q^{9} +65.2790i q^{11} +(-82.1857 - 12.5500i) q^{12} -99.0665i q^{13} +(-171.633 - 13.0290i) q^{14} +(244.333 + 76.4025i) q^{16} +207.689i q^{17} +(107.690 + 8.17494i) q^{18} +569.960i q^{19} +223.600 q^{21} +(-19.7649 + 260.367i) q^{22} -371.198 q^{23} +(-324.000 - 74.9400i) q^{24} +(29.9949 - 395.129i) q^{26} -140.296 q^{27} +(-680.619 - 103.933i) q^{28} -423.911 q^{29} +1174.18i q^{31} +(951.396 + 378.711i) q^{32} -339.199i q^{33} +(-62.8831 + 828.372i) q^{34} +(427.050 + 65.2119i) q^{36} +1448.13i q^{37} +(-172.570 + 2273.30i) q^{38} +514.764i q^{39} -265.822 q^{41} +(891.833 + 67.7005i) q^{42} -699.900 q^{43} +(-157.665 + 1032.49i) q^{44} +(-1480.53 - 112.390i) q^{46} +1250.00 q^{47} +(-1269.59 - 396.999i) q^{48} -549.266 q^{49} -1079.18i q^{51} +(239.271 - 1566.90i) q^{52} +787.645i q^{53} +(-559.574 - 42.4782i) q^{54} +(-2683.20 - 620.613i) q^{56} -2961.60i q^{57} +(-1690.78 - 128.350i) q^{58} +3012.53i q^{59} +4519.33 q^{61} +(-355.512 + 4683.23i) q^{62} -1161.86 q^{63} +(3680.00 + 1798.56i) q^{64} +(102.701 - 1352.91i) q^{66} -5215.70 q^{67} +(-501.622 + 3284.94i) q^{68} +1928.80 q^{69} +4693.16i q^{71} +(1683.55 + 389.400i) q^{72} -5404.92i q^{73} +(-438.459 + 5775.91i) q^{74} +(-1376.60 + 9014.86i) q^{76} -2809.07i q^{77} +(-155.858 + 2053.15i) q^{78} +7453.44i q^{79} +729.000 q^{81} +(-1060.24 - 80.4843i) q^{82} -8950.92 q^{83} +(3536.60 + 540.051i) q^{84} +(-2791.57 - 211.913i) q^{86} +2202.71 q^{87} +(-941.466 + 4070.39i) q^{88} +616.496 q^{89} +4263.01i q^{91} +(-5871.11 - 896.538i) q^{92} -6101.20i q^{93} +(4985.66 + 378.470i) q^{94} +(-4943.60 - 1967.84i) q^{96} -13723.1i q^{97} +(-2190.76 - 166.304i) q^{98} +1762.53i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9}+O(q^{10}) \) 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9	\( 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9} - 1200 q^{14} + 224 q^{16} - 288 q^{21} - 2592 q^{24} + 3384 q^{26} - 1776 q^{29} + 968 q^{34} + 1080 q^{36} + 1104 q^{41} + 7392 q^{44} - 768 q^{46} + 1144 q^{49} - 972 q^{54} + 3456 q^{56} + 8464 q^{61} + 29440 q^{64} + 9648 q^{66} + 19584 q^{69} + 8232 q^{74} - 3744 q^{76} + 5832 q^{81} + 21024 q^{84} - 39120 q^{86} + 50160 q^{89} + 10464 q^{94} - 16704 q^{96}+O(q^{100}) \) 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

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