LMFDB - Embedded newform 300.5.f.b.199.3

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:	$32$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	300.199
Dual form			300.5.f.b.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.78966 - 1.28004i) q^{2} -5.19615 q^{3} +(12.7230 + 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} -89.0673 q^{7} +(-35.7972 - 53.0524i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(-3.78966 - 1.28004i) q^{2} -5.19615 q^{3} +(12.7230 + 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} -89.0673 q^{7} +(-35.7972 - 53.0524i) q^{8} +27.0000 q^{9} -174.486i q^{11} +(-66.1107 - 50.4120i) q^{12} -22.9919i q^{13} +(337.534 + 114.009i) q^{14} +(67.7503 + 246.872i) q^{16} -69.2339i q^{17} +(-102.321 - 34.5610i) q^{18} -341.023i q^{19} +462.807 q^{21} +(-223.348 + 661.242i) q^{22} +319.580 q^{23} +(186.008 + 275.668i) q^{24} +(-29.4305 + 87.1316i) q^{26} -140.296 q^{27} +(-1133.20 - 864.112i) q^{28} -679.276 q^{29} +72.5397i q^{31} +(59.2548 - 1022.28i) q^{32} +906.656i q^{33} +(-88.6218 + 262.373i) q^{34} +(343.521 + 261.948i) q^{36} -2373.44i q^{37} +(-436.521 + 1292.36i) q^{38} +119.470i q^{39} -762.724 q^{41} +(-1753.88 - 592.410i) q^{42} -3111.55 q^{43} +(1692.83 - 2219.99i) q^{44} +(-1211.10 - 409.073i) q^{46} +315.636 q^{47} +(-352.041 - 1282.79i) q^{48} +5531.98 q^{49} +359.750i q^{51} +(223.063 - 292.527i) q^{52} +3385.94i q^{53} +(531.674 + 179.584i) q^{54} +(3188.36 + 4725.23i) q^{56} +1772.01i q^{57} +(2574.22 + 869.498i) q^{58} +6683.46i q^{59} -5316.04 q^{61} +(92.8534 - 274.901i) q^{62} -2404.82 q^{63} +(-1533.12 + 3798.26i) q^{64} +(1160.55 - 3435.92i) q^{66} +4015.09 q^{67} +(671.693 - 880.863i) q^{68} -1660.58 q^{69} +2954.05i q^{71} +(-966.525 - 1432.41i) q^{72} +5741.92i q^{73} +(-3038.09 + 8994.54i) q^{74} +(3308.53 - 4338.84i) q^{76} +15541.0i q^{77} +(152.925 - 452.749i) q^{78} -414.704i q^{79} +729.000 q^{81} +(2890.46 + 976.314i) q^{82} +9738.88 q^{83} +(5888.30 + 4490.06i) q^{84} +(11791.7 + 3982.90i) q^{86} +3529.62 q^{87} +(-9256.90 + 6246.12i) q^{88} +8192.42 q^{89} +2047.83i q^{91} +(4066.02 + 3100.50i) q^{92} -376.927i q^{93} +(-1196.15 - 404.025i) q^{94} +(-307.897 + 5311.94i) q^{96} -9564.24i q^{97} +(-20964.3 - 7081.13i) q^{98} -4711.12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 52 q^{4} + 36 q^{6} + 864 q^{9}+O(q^{10}) $ 32 * q - 52 * q^4 + 36 * q^6 + 864 * q^9	$ 32 q - 52 q^{4} + 36 q^{6} + 864 q^{9} + 1608 q^{14} - 380 q^{16} + 576 q^{21} + 3996 q^{24} - 1704 q^{26} + 6912 q^{29} - 9544 q^{34} - 1404 q^{36} + 2496 q^{41} + 12840 q^{44} - 2224 q^{46} + 7904 q^{49} + 972 q^{54} - 5208 q^{56} - 7616 q^{61} + 23804 q^{64} - 5832 q^{66} - 19584 q^{69} - 61032 q^{74} - 10320 q^{76} + 23328 q^{81} + 4104 q^{84} + 79536 q^{86} - 15168 q^{89} - 99552 q^{94} + 37764 q^{96}+O(q^{100}) $ 32 * q - 52 * q^4 + 36 * q^6 + 864 * q^9 + 1608 * q^14 - 380 * q^16 + 576 * q^21 + 3996 * q^24 - 1704 * q^26 + 6912 * q^29 - 9544 * q^34 - 1404 * q^36 + 2496 * q^41 + 12840 * q^44 - 2224 * q^46 + 7904 * q^49 + 972 * q^54 - 5208 * q^56 - 7616 * q^61 + 23804 * q^64 - 5832 * q^66 - 19584 * q^69 - 61032 * q^74 - 10320 * q^76 + 23328 * q^81 + 4104 * q^84 + 79536 * q^86 - 15168 * q^89 - 99552 * q^94 + 37764 * 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 $

$2$	−3.78966	−	1.28004i	−0.947415	−	0.320009i
$2$	−3.78966	−	1.28004i	−0.947415	−	0.320009i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	12.7230	+	9.70180i	0.795189	+	0.606362i
$5$		0			0
$5$		0			0
$6$	19.6916	+	6.65126i	0.546990	+	0.184757i
$7$	−89.0673			−1.81770			−0.908850	−	0.417124i	$-0.863038\pi$
$7$	−89.0673			−1.81770			−0.908850	+	0.417124i	$0.863038\pi$
$8$	−35.7972	−	53.0524i	−0.559332	−	0.828944i
$9$	27.0000			0.333333
$10$		0			0
$11$		−	174.486i		−	1.44203i	−0.692918	−	0.721017i	$-0.743675\pi$
$11$		−	174.486i		−	1.44203i	0.692918	−	0.721017i	$-0.256325\pi$
$12$	−66.1107	−	50.4120i	−0.459102	−	0.350083i
$13$		−	22.9919i		−	0.136047i	−0.997684	−	0.0680235i	$-0.978331\pi$
$13$		−	22.9919i		−	0.136047i	0.997684	−	0.0680235i	$-0.0216693\pi$
$14$	337.534	+	114.009i	1.72211	+	0.581680i
$15$		0			0
$16$	67.7503	+	246.872i	0.264650	+	0.964345i
$17$		−	69.2339i		−	0.239563i	−0.992800	−	0.119782i	$-0.961781\pi$
$17$		−	69.2339i		−	0.239563i	0.992800	−	0.119782i	$-0.0382195\pi$
$18$	−102.321	−	34.5610i	−0.315805	−	0.106670i
$19$		−	341.023i		−	0.944662i	−0.881421	−	0.472331i	$-0.843413\pi$
$19$		−	341.023i		−	0.944662i	0.881421	−	0.472331i	$-0.156587\pi$
$20$		0			0
$21$	462.807			1.04945
$22$	−223.348	+	661.242i	−0.461464	+	1.36620i
$23$	319.580			0.604120			0.302060	−	0.953289i	$-0.402326\pi$
$23$	319.580			0.604120			0.302060	+	0.953289i	$0.402326\pi$
$24$	186.008	+	275.668i	0.322930	+	0.478591i
$25$		0			0
$26$	−29.4305	+	87.1316i	−0.0435362	+	0.128893i
$27$	−140.296			−0.192450
$28$	−1133.20	−	864.112i	−1.44541	−	1.10218i
$29$	−679.276			−0.807701			−0.403850	−	0.914825i	$-0.632328\pi$
$29$	−679.276			−0.807701			−0.403850	+	0.914825i	$0.632328\pi$
$30$		0			0
$31$			72.5397i			0.0754835i	0.999288	+	0.0377418i	$0.0120164\pi$
$31$			72.5397i			0.0754835i	−0.999288	+	0.0377418i	$0.987984\pi$
$32$	59.2548	−	1022.28i	0.0578660	−	0.998324i
$33$			906.656i			0.832558i
$34$	−88.6218	+	262.373i	−0.0766625	+	0.226966i
$35$		0			0
$36$	343.521	+	261.948i	0.265063	+	0.202121i
$37$		−	2373.44i		−	1.73371i	−0.498564	−	0.866853i	$-0.666139\pi$
$37$		−	2373.44i		−	1.73371i	0.498564	−	0.866853i	$-0.333861\pi$
$38$	−436.521	+	1292.36i	−0.302300	+	0.894986i
$39$			119.470i			0.0785467i
$40$		0			0
$41$	−762.724			−0.453732			−0.226866	−	0.973926i	$-0.572848\pi$
$41$	−762.724			−0.453732			−0.226866	+	0.973926i	$0.572848\pi$
$42$	−1753.88	−	592.410i	−0.994263	−	0.335833i
$43$	−3111.55			−1.68283			−0.841415	−	0.540390i	$-0.818277\pi$
$43$	−3111.55			−1.68283			−0.841415	+	0.540390i	$0.818277\pi$
$44$	1692.83	−	2219.99i	0.874395	−	1.14669i
$45$		0			0
$46$	−1211.10	−	409.073i	−0.572352	−	0.193324i
$47$	315.636			0.142886			0.0714432	−	0.997445i	$-0.477240\pi$
$47$	315.636			0.142886			0.0714432	+	0.997445i	$0.477240\pi$
$48$	−352.041	−	1282.79i	−0.152796	−	0.556765i
$49$	5531.98			2.30403
$50$		0			0
$51$			359.750i			0.138312i
$52$	223.063	−	292.527i	0.0824937	−	0.108183i
$53$			3385.94i			1.20539i	0.797972	+	0.602695i	$0.205906\pi$
$53$			3385.94i			1.20539i	−0.797972	+	0.602695i	$0.794094\pi$
$54$	531.674	+	179.584i	0.182330	+	0.0615858i
$55$		0			0
$56$	3188.36	+	4725.23i	1.01670	+	1.50677i
$57$			1772.01i			0.545401i
$58$	2574.22	+	869.498i	0.765227	+	0.258471i
$59$			6683.46i			1.91998i	0.280032	+	0.959991i	$0.409655\pi$
$59$			6683.46i			1.91998i	−0.280032	+	0.959991i	$0.590345\pi$
$60$		0			0
$61$	−5316.04			−1.42866			−0.714330	−	0.699809i	$-0.753268\pi$
$61$	−5316.04			−1.42866			−0.714330	+	0.699809i	$0.753268\pi$
$62$	92.8534	−	274.901i	0.0241554	−	0.0715142i
$63$	−2404.82			−0.605900
$64$	−1533.12	+	3798.26i	−0.374296	+	0.927309i
$65$		0			0
$66$	1160.55	−	3435.92i	0.266426	−	0.788778i
$67$	4015.09			0.894429			0.447215	−	0.894427i	$-0.352416\pi$
$67$	4015.09			0.894429			0.447215	+	0.894427i	$0.352416\pi$
$68$	671.693	−	880.863i	0.145262	−	0.190498i
$69$	−1660.58			−0.348789
$70$		0			0
$71$			2954.05i			0.586005i	0.956112	+	0.293002i	$0.0946544\pi$
$71$			2954.05i			0.586005i	−0.956112	+	0.293002i	$0.905346\pi$
$72$	−966.525	−	1432.41i	−0.186444	−	0.276315i
$73$			5741.92i			1.07749i	0.842470	+	0.538743i	$0.181101\pi$
$73$			5741.92i			1.07749i	−0.842470	+	0.538743i	$0.818899\pi$
$74$	−3038.09	+	8994.54i	−0.554801	+	1.64254i
$75$		0			0
$76$	3308.53	−	4338.84i	0.572807	−	0.751184i
$77$			15541.0i			2.62118i
$78$	152.925	−	452.749i	0.0251357	−	0.0744163i
$79$		−	414.704i		−	0.0664484i	−0.999448	−	0.0332242i	$-0.989422\pi$
$79$		−	414.704i		−	0.0664484i	0.999448	−	0.0332242i	$-0.0105775\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	2890.46	+	976.314i	0.429873	+	0.145198i
$83$	9738.88			1.41368			0.706842	−	0.707371i	$-0.250119\pi$
$83$	9738.88			1.41368			0.706842	+	0.707371i	$0.250119\pi$
$84$	5888.30	+	4490.06i	0.834510	+	0.636346i
$85$		0			0
$86$	11791.7	+	3982.90i	1.59434	+	0.538521i
$87$	3529.62			0.466326
$88$	−9256.90	+	6246.12i	−1.19536	+	0.806575i
$89$	8192.42			1.03427			0.517133	−	0.855905i	$-0.326999\pi$
$89$	8192.42			1.03427			0.517133	+	0.855905i	$0.326999\pi$
$90$		0			0
$91$			2047.83i			0.247292i
$92$	4066.02	+	3100.50i	0.480389	+	0.366316i
$93$		−	376.927i		−	0.0435804i
$94$	−1196.15	−	404.025i	−0.135373	−	0.0457249i
$95$		0			0
$96$	−307.897	+	5311.94i	−0.0334089	+	0.576383i
$97$		−	9564.24i		−	1.01650i	−0.861210	−	0.508250i	$-0.830293\pi$
$97$		−	9564.24i		−	1.01650i	0.861210	−	0.508250i	$-0.169707\pi$
$98$	−20964.3	−	7081.13i	−2.18287	−	0.737310i
$99$		−	4711.12i		−	0.480678i
$100$		0			0
$101$	−1386.95			−0.135962			−0.0679809	−	0.997687i	$-0.521656\pi$
$101$	−1386.95			−0.135962			−0.0679809	+	0.997687i	$0.521656\pi$
$102$	460.492	−	1363.33i	0.0442611	−	0.131039i
$103$	−627.330			−0.0591318			−0.0295659	−	0.999563i	$-0.509412\pi$
$103$	−627.330			−0.0591318			−0.0295659	+	0.999563i	$0.509412\pi$
$104$	−1219.78	+	823.048i	−0.112775	+	0.0760954i
$105$		0			0
$106$	4334.12	−	12831.5i	0.385735	−	1.14200i
$107$	−2988.95			−0.261067			−0.130533	−	0.991444i	$-0.541669\pi$
$107$	−2988.95			−0.261067			−0.130533	+	0.991444i	$0.541669\pi$
$108$	−1784.99	−	1361.12i	−0.153034	−	0.116694i
$109$	−15704.4			−1.32181			−0.660905	−	0.750469i	$-0.729827\pi$
$109$	−15704.4			−1.32181			−0.660905	+	0.750469i	$0.729827\pi$
$110$		0			0
$111$			12332.8i			1.00096i
$112$	−6034.33	−	21988.2i	−0.481053	−	1.75289i
$113$			19067.1i			1.49323i	0.665255	+	0.746616i	$0.268323\pi$
$113$			19067.1i			1.49323i	−0.665255	+	0.746616i	$0.731677\pi$
$114$	2268.23	−	6715.30i	0.174533	−	0.516720i
$115$		0			0
$116$	−8642.44	−	6590.20i	−0.642274	−	0.489759i
$117$		−	620.782i		−	0.0453490i
$118$	8555.06	−	25328.0i	0.614411	−	1.81902i
$119$			6166.47i			0.435454i
$120$		0			0
$121$	−15804.4			−1.07946
$122$	20146.0	+	6804.72i	1.35353	+	0.457184i
$123$	3963.23			0.261962
$124$	−703.765	+	922.924i	−0.0457704	+	0.0600237i
$125$		0			0
$126$	9113.43	+	3078.25i	0.574038	+	0.193893i
$127$	375.889			0.0233052			0.0116526	−	0.999932i	$-0.496291\pi$
$127$	375.889			0.0233052			0.0116526	+	0.999932i	$0.496291\pi$
$128$	10671.9	−	12431.7i	0.651361	−	0.758768i
$129$	16168.1			0.971582
$130$		0			0
$131$		−	11766.3i		−	0.685639i	−0.939401	−	0.342820i	$-0.888618\pi$
$131$		−	11766.3i		−	0.685639i	0.939401	−	0.342820i	$-0.111382\pi$
$132$	−8796.19	+	11535.4i	−0.504832	+	0.662041i
$133$			30374.0i			1.71711i
$134$	−15215.8	−	5139.46i	−0.847395	−	0.286225i
$135$		0			0
$136$	−3673.02	+	2478.38i	−0.198585	+	0.133995i
$137$		−	1889.31i		−	0.100661i	−0.998733	−	0.0503306i	$-0.983973\pi$
$137$		−	1889.31i		−	0.100661i	0.998733	−	0.0503306i	$-0.0160275\pi$
$138$	6293.04	+	2125.61i	0.330448	+	0.111616i
$139$			15093.1i			0.781174i	0.920566	+	0.390587i	$0.127728\pi$
$139$			15093.1i			0.781174i	−0.920566	+	0.390587i	$0.872272\pi$
$140$		0			0
$141$	−1640.09			−0.0824955
$142$	3781.29	−	11194.8i	0.187527	−	0.555189i
$143$	−4011.77			−0.196184
$144$	1829.26	+	6665.55i	0.0882166	+	0.321448i
$145$		0			0
$146$	7349.87	−	21759.9i	0.344805	−	1.02083i
$147$	−28745.0			−1.33023
$148$	23026.7	−	30197.3i	1.05125	−	1.37862i
$149$	−29887.1			−1.34621			−0.673103	−	0.739549i	$-0.735039\pi$
$149$	−29887.1			−1.34621			−0.673103	+	0.739549i	$0.735039\pi$
$150$		0			0
$151$			15818.0i			0.693741i	0.937913	+	0.346871i	$0.112756\pi$
$151$			15818.0i			0.693741i	−0.937913	+	0.346871i	$0.887244\pi$
$152$	−18092.1	+	12207.7i	−0.783071	+	0.528379i
$153$		−	1869.31i		−	0.0798545i
$154$	19893.0	−	58895.0i	0.838802	−	2.48335i
$155$		0			0
$156$	−1159.07	+	1520.01i	−0.0476278	+	0.0624595i
$157$			32589.5i			1.32214i	0.750324	+	0.661071i	$0.229898\pi$
$157$			32589.5i			1.32214i	−0.750324	+	0.661071i	$0.770102\pi$
$158$	−530.836	+	1571.59i	−0.0212641	+	0.0629541i
$159$		−	17593.9i		−	0.695932i
$160$		0			0
$161$	−28464.1			−1.09811
$162$	−2762.66	−	933.146i	−0.105268	−	0.0355565i
$163$	19528.4			0.735008			0.367504	−	0.930022i	$-0.380212\pi$
$163$	19528.4			0.735008			0.367504	+	0.930022i	$0.380212\pi$
$164$	−9704.15	−	7399.79i	−0.360803	−	0.275126i
$165$		0			0
$166$	−36907.0	−	12466.1i	−1.33935	−	0.452392i
$167$	20882.0			0.748755			0.374377	−	0.927276i	$-0.377856\pi$
$167$	20882.0			0.748755			0.374377	+	0.927276i	$0.377856\pi$
$168$	−16567.2	−	24553.0i	−0.586990	−	0.869934i
$169$	28032.4			0.981491
$170$		0			0
$171$		−	9207.62i		−	0.314887i
$172$	−39588.3	−	30187.6i	−1.33817	−	1.02040i
$173$		−	5278.82i		−	0.176378i	−0.996104	−	0.0881891i	$-0.971892\pi$
$173$		−	5278.82i		−	0.176378i	0.996104	−	0.0881891i	$-0.0281080\pi$
$174$	−13376.1	−	4518.04i	−0.441804	−	0.149229i
$175$		0			0
$176$	43075.8	−	11821.5i	1.39062	−	0.381634i
$177$		−	34728.3i		−	1.10850i
$178$	−31046.5	−	10486.6i	−0.979878	−	0.330974i
$179$		−	47041.6i		−	1.46817i	−0.679058	−	0.734084i	$-0.737612\pi$
$179$		−	47041.6i		−	1.46817i	0.679058	−	0.734084i	$-0.262388\pi$
$180$		0			0
$181$	−16396.0			−0.500472			−0.250236	−	0.968185i	$-0.580508\pi$
$181$	−16396.0			−0.500472			−0.250236	+	0.968185i	$0.580508\pi$
$182$	2621.29	−	7760.57i	0.0791358	−	0.234288i
$183$	27623.0			0.824837
$184$	−11440.1	−	16954.5i	−0.337904	−	0.500782i
$185$		0			0
$186$	−482.480	+	1428.43i	−0.0139461	+	0.0412887i
$187$	−12080.3			−0.345459
$188$	4015.84	+	3062.23i	0.113622	+	0.0866409i
$189$	12495.8			0.349816
$190$		0			0
$191$			32485.2i			0.890469i	0.895414	+	0.445235i	$0.146880\pi$
$191$			32485.2i			0.890469i	−0.895414	+	0.445235i	$0.853120\pi$
$192$	7966.30	−	19736.3i	0.216100	−	0.535382i
$193$		−	10400.5i		−	0.279215i	−0.990207	−	0.139607i	$-0.955416\pi$
$193$		−	10400.5i		−	0.279215i	0.990207	−	0.139607i	$-0.0445840\pi$
$194$	−12242.6	+	36245.2i	−0.325289	+	0.963046i
$195$		0			0
$196$	70383.4	+	53670.1i	1.83214	+	1.39708i
$197$			47175.4i			1.21558i	0.794098	+	0.607790i	$0.207944\pi$
$197$			47175.4i			1.21558i	−0.794098	+	0.607790i	$0.792056\pi$
$198$	−6030.41	+	17853.5i	−0.153821	+	0.455401i
$199$		−	57145.1i		−	1.44302i	−0.692403	−	0.721511i	$-0.743448\pi$
$199$		−	57145.1i		−	1.44302i	0.692403	−	0.721511i	$-0.256552\pi$
$200$		0			0
$201$	−20863.0			−0.516399
$202$	5256.05	+	1775.34i	0.128812	+	0.0435090i
$203$	60501.3			1.46816
$204$	−3490.22	+	4577.10i	−0.0838672	+	0.109984i
$205$		0			0
$206$	2377.36	+	803.004i	0.0560224	+	0.0189227i
$207$	8628.65			0.201373
$208$	5676.07	−	1557.71i	0.131196	−	0.0360048i
$209$	−59503.7			−1.36223
$210$		0			0
$211$		−	24560.7i		−	0.551666i	−0.961206	−	0.275833i	$-0.911046\pi$
$211$		−	24560.7i		−	0.551666i	0.961206	−	0.275833i	$-0.0889536\pi$
$212$	−32849.7	+	43079.3i	−0.730902	+	0.958512i
$213$		−	15349.7i		−	0.338330i
$214$	11327.1	+	3825.96i	0.247338	+	0.0835436i
$215$		0			0
$216$	5022.21	+	7443.05i	0.107643	+	0.159530i
$217$		−	6460.91i		−	0.137206i
$218$	59514.4	+	20102.2i	1.25230	+	0.422991i
$219$		−	29835.9i		−	0.622087i
$220$		0			0
$221$	−1591.82			−0.0325919
$222$	15786.4	−	46737.0i	0.320315	−	0.948319i
$223$	−71260.5			−1.43298			−0.716489	−	0.697599i	$-0.754252\pi$
$223$	−71260.5			−1.43298			−0.716489	+	0.697599i	$0.754252\pi$
$224$	−5277.66	+	91052.0i	−0.105183	+	1.81465i
$225$		0			0
$226$	24406.6	−	72257.7i	0.477848	−	1.41471i
$227$	73287.1			1.42225			0.711125	−	0.703066i	$-0.248186\pi$
$227$	73287.1			1.42225			0.711125	+	0.703066i	$0.248186\pi$
$228$	−17191.6	+	22545.3i	−0.330710	+	0.433696i
$229$	37103.1			0.707520			0.353760	−	0.935336i	$-0.384903\pi$
$229$	37103.1			0.707520			0.353760	+	0.935336i	$0.384903\pi$
$230$		0			0
$231$		−	80753.4i		−	1.51334i
$232$	24316.2	+	36037.2i	0.451773	+	0.669538i
$233$			21001.4i			0.386844i	0.981116	+	0.193422i	$0.0619586\pi$
$233$			21001.4i			0.386844i	−0.981116	+	0.193422i	$0.938041\pi$
$234$	−794.623	+	2352.55i	−0.0145121	+	0.0429643i
$235$		0			0
$236$	−64841.5	+	85033.7i	−1.16420	+	1.52675i
$237$			2154.87i			0.0383640i
$238$	7893.30	−	23368.8i	0.139349	−	0.412556i
$239$			8886.00i			0.155565i	0.996970	+	0.0777823i	$0.0247839\pi$
$239$			8886.00i			0.155565i	−0.996970	+	0.0777823i	$0.975216\pi$
$240$		0			0
$241$	−11033.8			−0.189973			−0.0949864	−	0.995479i	$-0.530281\pi$
$241$	−11033.8			−0.189973			−0.0949864	+	0.995479i	$0.530281\pi$
$242$	59893.2	+	20230.2i	1.02270	+	0.345437i
$243$	−3788.00			−0.0641500
$244$	−67636.1	−	51575.1i	−1.13605	−	0.866285i
$245$		0			0
$246$	−15019.3	−	5073.08i	−0.248187	−	0.0838303i
$247$	−7840.77			−0.128518
$248$	3848.41	−	2596.72i	0.0625716	−	0.0422204i
$249$	−50604.7			−0.816191
$250$		0			0
$251$		−	51472.3i		−	0.817008i	−0.912756	−	0.408504i	$-0.866051\pi$
$251$		−	51472.3i		−	0.817008i	0.912756	−	0.408504i	$-0.133949\pi$
$252$	−30596.5	−	23331.0i	−0.481804	−	0.367395i
$253$		−	55762.2i		−	0.871161i
$254$	−1424.49	−	481.152i	−0.0220797	−	0.00745787i
$255$		0			0
$256$	−56355.8	+	33451.3i	−0.859921	+	0.510427i
$257$			42550.6i			0.644227i	0.946701	+	0.322114i	$0.104393\pi$
$257$			42550.6i			0.644227i	−0.946701	+	0.322114i	$0.895607\pi$
$258$	−61271.6	−	20695.7i	−0.920491	−	0.310915i
$259$			211396.i			3.15135i
$260$		0			0
$261$	−18340.5			−0.269234
$262$	−15061.2	+	44590.1i	−0.219411	+	0.649585i
$263$	−5761.02			−0.0832891			−0.0416445	−	0.999132i	$-0.513260\pi$
$263$	−5761.02			−0.0832891			−0.0416445	+	0.999132i	$0.513260\pi$
$264$	48100.3	−	32455.8i	0.690144	−	0.465676i
$265$		0			0
$266$	38879.8	−	115107.i	0.549491	−	1.62682i
$267$	−42569.0			−0.597133
$268$	51084.1	+	38953.6i	0.711240	+	0.542348i
$269$	−19772.4			−0.273247			−0.136623	−	0.990623i	$-0.543625\pi$
$269$	−19772.4			−0.273247			−0.136623	+	0.990623i	$0.543625\pi$
$270$		0			0
$271$			60381.3i			0.822174i	0.911596	+	0.411087i	$0.134851\pi$
$271$			60381.3i			0.822174i	−0.911596	+	0.411087i	$0.865149\pi$
$272$	17091.9	−	4690.62i	0.231022	−	0.0634004i
$273$		−	10640.8i		−	0.142774i
$274$	−2418.38	+	7159.84i	−0.0322125	+	0.0953679i
$275$		0			0
$276$	−21127.6	−	16110.6i	−0.277353	−	0.211492i
$277$		−	137089.i		−	1.78666i	−0.449398	−	0.893332i	$-0.648362\pi$
$277$		−	137089.i		−	1.78666i	0.449398	−	0.893332i	$-0.351638\pi$
$278$	19319.6	−	57197.5i	0.249983	−	0.740095i
$279$			1958.57i			0.0251612i
$280$		0			0
$281$	68276.4			0.864685			0.432343	−	0.901709i	$-0.357687\pi$
$281$	68276.4			0.864685			0.432343	+	0.901709i	$0.357687\pi$
$282$	6215.39	+	2099.38i	0.0781574	+	0.0263993i
$283$	−46455.4			−0.580047			−0.290024	−	0.957019i	$-0.593663\pi$
$283$	−46455.4			−0.580047			−0.290024	+	0.957019i	$0.593663\pi$
$284$	−28659.6	+	37584.4i	−0.355331	+	0.465984i
$285$		0			0
$286$	15203.2	+	5135.21i	0.185868	+	0.0627807i
$287$	67933.7			0.824749
$288$	1599.88	−	27601.7i	0.0192887	−	0.332775i
$289$	78727.7			0.942609
$290$		0			0
$291$			49697.3i			0.586876i
$292$	−55707.0	+	73054.6i	−0.653347	+	0.856805i
$293$			75824.8i			0.883234i	0.897204	+	0.441617i	$0.145595\pi$
$293$			75824.8i			0.883234i	−0.897204	+	0.441617i	$0.854405\pi$
$294$	108934.	+	36794.6i	1.26028	+	0.425686i
$295$		0			0
$296$	−125917.	+	84962.7i	−1.43714	+	0.969717i
$297$			24479.7i			0.277519i
$298$	113262.	+	38256.6i	1.27542	+	0.430798i
$299$		−	7347.75i		−	0.0821887i
$300$		0			0
$301$	277137.			3.05888
$302$	20247.6	−	59944.8i	0.222003	−	0.657261i
$303$	7206.79			0.0784976
$304$	84189.1	−	23104.4i	0.910979	−	0.250004i
$305$		0			0
$306$	−2392.79	+	7084.06i	−0.0255542	+	0.0756553i
$307$	−115095.			−1.22118			−0.610590	−	0.791947i	$-0.709068\pi$
$307$	−115095.			−1.22118			−0.610590	+	0.791947i	$0.709068\pi$
$308$	−150776.	+	197728.i	−1.58939	+	2.08433i
$309$	3259.70			0.0341398
$310$		0			0
$311$			45164.1i			0.466953i	0.972362	+	0.233476i	$0.0750102\pi$
$311$			45164.1i			0.466953i	−0.972362	+	0.233476i	$0.924990\pi$
$312$	6338.15	−	4276.68i	0.0651108	−	0.0439337i
$313$			27892.1i			0.284704i	0.989816	+	0.142352i	$0.0454664\pi$
$313$			27892.1i			0.284704i	−0.989816	+	0.142352i	$0.954534\pi$
$314$	41715.7	−	123503.i	0.423097	−	1.25262i
$315$		0			0
$316$	4023.38	−	5276.29i	0.0402918	−	0.0528390i
$317$		−	90168.8i		−	0.897300i	−0.893708	−	0.448650i	$-0.851905\pi$
$317$		−	90168.8i		−	0.897300i	0.893708	−	0.448650i	$-0.148095\pi$
$318$	−22520.8	+	66674.7i	−0.222704	+	0.659336i
$319$			118524.i			1.16473i
$320$		0			0
$321$	15531.0			0.150727
$322$	107869.	+	36435.0i	1.04036	+	0.351405i
$323$	−23610.3			−0.226306
$324$	9275.08	+	7072.61i	0.0883543	+	0.0673736i
$325$		0			0
$326$	−74006.1	−	24997.1i	−0.696357	−	0.235209i
$327$	81602.6			0.763148
$328$	27303.4	+	40464.3i	0.253787	+	0.376119i
$329$	−28112.8			−0.259724
$330$		0			0
$331$			135944.i			1.24081i	0.784283	+	0.620403i	$0.213031\pi$
$331$			135944.i			1.24081i	−0.784283	+	0.620403i	$0.786969\pi$
$332$	123908.	+	94484.6i	1.12415	+	0.857205i
$333$		−	64082.9i		−	0.577902i
$334$	−79135.7	−	26729.7i	−0.709381	−	0.239608i
$335$		0			0
$336$	31355.3	+	114254.i	0.277736	+	1.01203i
$337$			83154.4i			0.732193i	0.930577	+	0.366096i	$0.119306\pi$
$337$			83154.4i			0.732193i	−0.930577	+	0.366096i	$0.880694\pi$
$338$	−106233.	−	35882.4i	−0.929879	−	0.314086i
$339$		−	99075.5i		−	0.862118i
$340$		0			0
$341$	12657.2			0.108850
$342$	−11786.1	+	34893.7i	−0.100767	+	0.298329i
$343$	−278867.			−2.37033
$344$	111385.	+	165075.i	0.941260	+	1.39497i
$345$		0			0
$346$	−6757.08	+	20004.9i	−0.0564426	+	0.167103i
$347$	−119011.			−0.988391			−0.494195	−	0.869351i	$-0.664537\pi$
$347$	−119011.			−0.988391			−0.494195	+	0.869351i	$0.664537\pi$
$348$	44907.5	+	34243.7i	0.370817	+	0.282763i
$349$	101177.			0.830673			0.415337	−	0.909668i	$-0.363664\pi$
$349$	101177.			0.830673			0.415337	+	0.909668i	$0.363664\pi$
$350$		0			0
$351$			3225.68i			0.0261822i
$352$	−178374.	−	10339.1i	−1.43962	−	0.0834447i
$353$		−	204510.i		−	1.64121i	−0.571495	−	0.820606i	$-0.693636\pi$
$353$		−	204510.i		−	1.64121i	0.571495	−	0.820606i	$-0.306364\pi$
$354$	−44453.4	+	131608.i	−0.354730	+	1.05021i
$355$		0			0
$356$	104232.	+	79481.2i	0.822436	+	0.627140i
$357$		−	32041.9i		−	0.251410i
$358$	−60214.9	+	178272.i	−0.469827	+	1.39096i
$359$			45291.4i			0.351420i	0.984442	+	0.175710i	$0.0562222\pi$
$359$			45291.4i			0.351420i	−0.984442	+	0.175710i	$0.943778\pi$
$360$		0			0
$361$	14024.4			0.107615
$362$	62135.1	+	20987.4i	0.474154	+	0.160155i
$363$	82122.0			0.623227
$364$	−19867.6	+	26054.6i	−0.149949	+	0.196644i
$365$		0			0
$366$	−104682.	−	35358.4i	−0.781462	−	0.263955i
$367$	−17522.8			−0.130098			−0.0650490	−	0.997882i	$-0.520720\pi$
$367$	−17522.8			−0.130098			−0.0650490	+	0.997882i	$0.520720\pi$
$368$	21651.6	+	78895.3i	0.159880	+	0.582580i
$369$	−20593.5			−0.151244
$370$		0			0
$371$		−	301576.i		−	2.19103i
$372$	3656.87	−	4795.65i	0.0264255	−	0.0346547i
$373$		−	16535.7i		−	0.118852i	−0.998233	−	0.0594258i	$-0.981073\pi$
$373$		−	16535.7i		−	0.118852i	0.998233	−	0.0594258i	$-0.0189270\pi$
$374$	45780.4	+	15463.3i	0.327292	+	0.110550i
$375$		0			0
$376$	−11298.9	−	16745.2i	−0.0799209	−	0.118445i
$377$			15617.9i			0.109885i
$378$	−47354.8	−	15995.1i	−0.331421	−	0.111944i
$379$		−	63835.5i		−	0.444410i	−0.975000	−	0.222205i	$-0.928675\pi$
$379$		−	63835.5i		−	0.444410i	0.975000	−	0.222205i	$-0.0713255\pi$
$380$		0			0
$381$	−1953.18			−0.0134553
$382$	41582.2	−	123108.i	0.284958	−	0.843643i
$383$	79806.3			0.544051			0.272025	−	0.962290i	$-0.412307\pi$
$383$	79806.3			0.544051			0.272025	+	0.962290i	$0.412307\pi$
$384$	−55452.8	+	64596.8i	−0.376063	+	0.438075i
$385$		0			0
$386$	−13313.0	+	39414.2i	−0.0893512	+	0.264532i
$387$	−84011.9			−0.560943
$388$	92790.3	−	121686.i	0.616367	−	0.808309i
$389$	159539.			1.05431			0.527153	−	0.849770i	$-0.323259\pi$
$389$	159539.			1.05431			0.527153	+	0.849770i	$0.323259\pi$
$390$		0			0
$391$		−	22125.7i		−	0.144725i
$392$	−198029.	−	293485.i	−1.28872	−	1.90991i
$393$			61139.3i			0.395854i
$394$	60386.2	−	178779.i	0.388996	−	1.15166i
$395$		0			0
$396$	45706.4	−	59939.7i	0.291465	−	0.382229i
$397$		−	147558.i		−	0.936231i	−0.883667	−	0.468115i	$-0.844933\pi$
$397$		−	147558.i		−	0.936231i	0.883667	−	0.468115i	$-0.155067\pi$
$398$	−73147.8	+	216561.i	−0.461780	+	1.36714i
$399$		−	157828.i		−	0.991374i
$400$		0			0
$401$	−47897.3			−0.297867			−0.148934	−	0.988847i	$-0.547584\pi$
$401$	−47897.3			−0.297867			−0.148934	+	0.988847i	$0.547584\pi$
$402$	79063.8	+	26705.4i	0.489244	+	0.165252i
$403$	1667.83			0.0102693
$404$	−17646.2	−	13455.9i	−0.108115	−	0.0824421i
$405$		0			0
$406$	−229279.	−	77443.8i	−1.39095	−	0.469823i
$407$	−414133.			−2.50006
$408$	19085.6	−	12878.0i	0.114653	−	0.0773623i
$409$	−25189.0			−0.150579			−0.0752894	−	0.997162i	$-0.523988\pi$
$409$	−25189.0			−0.150579			−0.0752894	+	0.997162i	$0.523988\pi$
$410$		0			0
$411$			9817.14i			0.0581168i
$412$	−7981.53	−	6086.22i	−0.0470210	−	0.0358553i
$413$		−	595277.i		−	3.48995i
$414$	−32699.6	−	11045.0i	−0.190784	−	0.0644413i
$415$		0			0
$416$	−23504.3	−	1362.38i	−0.135819	−	0.00787249i
$417$		−	78425.8i		−	0.451011i
$418$	225499.	+	76166.9i	1.29060	+	0.435927i
$419$		−	180642.i		−	1.02894i	−0.857508	−	0.514470i	$-0.827989\pi$
$419$		−	180642.i		−	1.02894i	0.857508	−	0.514470i	$-0.172011\pi$
$420$		0			0
$421$	−139551.			−0.787354			−0.393677	−	0.919249i	$-0.628797\pi$
$421$	−139551.			−0.787354			−0.393677	+	0.919249i	$0.628797\pi$
$422$	−31438.6	+	93076.7i	−0.176538	+	0.522656i
$423$	8522.17			0.0476288
$424$	179632.	−	121207.i	0.999200	−	0.674213i
$425$		0			0
$426$	−19648.2	+	58170.1i	−0.108269	+	0.320539i
$427$	473485.			2.59687
$428$	−38028.5	−	28998.2i	−0.207597	−	0.158301i
$429$	20845.8			0.113267
$430$		0			0
$431$			165053.i			0.888523i	0.895897	+	0.444261i	$0.146534\pi$
$431$			165053.i			0.888523i	−0.895897	+	0.444261i	$0.853466\pi$
$432$	−9505.11	−	34635.2i	−0.0509319	−	0.185588i
$433$			26213.4i			0.139813i	0.997554	+	0.0699065i	$0.0222701\pi$
$433$			26213.4i			0.139813i	−0.997554	+	0.0699065i	$0.977730\pi$
$434$	−8270.20	+	24484.6i	−0.0439073	+	0.129991i
$435$		0			0
$436$	−199808.	−	152361.i	−1.05109	−	0.801496i
$437$		−	108984.i		−	0.570689i
$438$	−38191.0	+	113068.i	−0.199073	+	0.589374i
$439$			355921.i			1.84682i	0.383813	+	0.923411i	$0.374611\pi$
$439$			355921.i			1.84682i	−0.383813	+	0.923411i	$0.625389\pi$
$440$		0			0
$441$	149363.			0.768010
$442$	6032.45	+	2037.59i	0.0308780	+	0.0104297i
$443$	−114260.			−0.582220			−0.291110	−	0.956690i	$-0.594025\pi$
$443$	−114260.			−0.582220			−0.291110	+	0.956690i	$0.594025\pi$
$444$	−119650.	+	156910.i	−0.606941	+	0.795948i
$445$		0			0
$446$	270053.	+	91216.0i	1.35762	+	0.458566i
$447$	155298.			0.777232
$448$	136550.	−	338301.i	0.680357	−	1.68557i
$449$	−85579.1			−0.424497			−0.212249	−	0.977216i	$-0.568079\pi$
$449$	−85579.1			−0.424497			−0.212249	+	0.977216i	$0.568079\pi$
$450$		0			0
$451$			133085.i			0.654297i
$452$	−184985.	+	242591.i	−0.905440	+	1.18740i
$453$		−	82192.7i		−	0.400532i
$454$	−277733.	−	93810.1i	−1.34746	−	0.455133i
$455$		0			0
$456$	94009.2	−	63432.9i	0.452106	−	0.305060i
$457$			388386.i			1.85965i	0.368000	+	0.929826i	$0.380042\pi$
$457$			388386.i			1.85965i	−0.368000	+	0.929826i	$0.619958\pi$
$458$	−140608.	−	47493.3i	−0.670315	−	0.226413i
$459$			9713.24i			0.0461040i
$460$		0			0
$461$	322691.			1.51840			0.759198	−	0.650860i	$-0.225591\pi$
$461$	322691.			1.51840			0.759198	+	0.650860i	$0.225591\pi$
$462$	−103367.	+	306028.i	−0.484283	+	1.43376i
$463$	−186325.			−0.869181			−0.434591	−	0.900628i	$-0.643107\pi$
$463$	−186325.			−0.869181			−0.434591	+	0.900628i	$0.643107\pi$
$464$	−46021.2	−	167694.i	−0.213758	−	0.778902i
$465$		0			0
$466$	26882.5	−	79588.0i	0.123793	−	0.366501i
$467$	119419.			0.547572			0.273786	−	0.961791i	$-0.411724\pi$
$467$	119419.			0.547572			0.273786	+	0.961791i	$0.411724\pi$
$468$	6022.70	−	7898.22i	0.0274979	−	0.0360610i
$469$	−357613.			−1.62580
$470$		0			0
$471$		−	169340.i		−	0.763339i
$472$	354573.	−	239249.i	1.59156	−	1.07391i
$473$			542922.i			2.42670i
$474$	2758.31	−	8166.21i	0.0122768	−	0.0363466i
$475$		0			0
$476$	−59825.8	+	78456.1i	−0.264043	+	0.346268i
$477$			91420.3i			0.401796i
$478$	11374.4	−	33674.9i	0.0497820	−	0.147384i
$479$			91602.7i			0.399243i	0.979873	+	0.199622i	$0.0639713\pi$
$479$			91602.7i			0.399243i	−0.979873	+	0.199622i	$0.936029\pi$
$480$		0			0
$481$	−54570.0			−0.235865
$482$	41814.4	+	14123.7i	0.179983	+	0.0607930i
$483$	147904.			0.633993
$484$	−201079.	−	153331.i	−0.858375	−	0.654544i
$485$		0			0
$486$	14355.2	+	4848.77i	0.0607767	+	0.0205286i
$487$	204150.			0.860778			0.430389	−	0.902644i	$-0.358376\pi$
$487$	204150.			0.860778			0.430389	+	0.902644i	$0.358376\pi$
$488$	190300.	+	282029.i	0.799095	+	1.18428i
$489$	−101473.			−0.424357
$490$		0			0
$491$		−	191987.i		−	0.796360i	−0.917307	−	0.398180i	$-0.869642\pi$
$491$		−	191987.i		−	0.796360i	0.917307	−	0.398180i	$-0.130358\pi$
$492$	50424.2	+	38450.5i	0.208310	+	0.158844i
$493$			47028.9i			0.193496i
$494$	29713.9	+	10036.5i	0.121760	+	0.0411270i
$495$		0			0
$496$	−17908.0	+	4914.59i	−0.0727922	+	0.0199767i
$497$		−	263109.i		−	1.06518i
$498$	191774.	+	64775.8i	0.773272	+	0.261189i
$499$			86859.0i			0.348830i	0.984672	+	0.174415i	$0.0558034\pi$
$499$			86859.0i			0.348830i	−0.984672	+	0.174415i	$0.944197\pi$
$500$		0			0
$501$	−108506.			−0.432294
$502$	−65886.4	+	195063.i	−0.261450	+	0.774046i
$503$	351571.			1.38956			0.694780	−	0.719222i	$-0.255502\pi$
$503$	351571.			1.38956			0.694780	+	0.719222i	$0.255502\pi$
$504$	86085.8	+	127581.i	0.338899	+	0.502257i
$505$		0			0
$506$	−71377.6	+	211320.i	−0.278779	+	0.825351i
$507$	−145660.			−0.566664
$508$	4782.45	+	3646.80i	0.0185320	+	0.0141314i
$509$	50040.2			0.193145			0.0965725	−	0.995326i	$-0.469212\pi$
$509$	50040.2			0.193145			0.0965725	+	0.995326i	$0.469212\pi$
$510$		0			0
$511$		−	511417.i		−	1.95855i
$512$	256388.	−	54631.7i	0.978043	−	0.208403i
$513$			47844.2i			0.181800i
$514$	54466.3	−	161252.i	0.206159	−	0.610350i
$515$		0			0
$516$	205707.	+	156860.i	0.772591	+	0.589131i
$517$		−	55074.1i		−	0.206047i
$518$	270594.	−	801119.i	1.00846	−	2.98564i
$519$			27429.6i			0.101832i
$520$		0			0
$521$	−149074.			−0.549195			−0.274598	−	0.961559i	$-0.588545\pi$
$521$	−149074.			−0.549195			−0.274598	+	0.961559i	$0.588545\pi$
$522$	69504.1	+	23476.4i	0.255076	+	0.0861571i
$523$	−109372.			−0.399854			−0.199927	−	0.979811i	$-0.564070\pi$
$523$	−109372.			−0.399854			−0.199927	+	0.979811i	$0.564070\pi$
$524$	114154.	−	149702.i	0.415746	−	0.545213i
$525$		0			0
$526$	21832.3	+	7374.31i	0.0789093	+	0.0266532i
$527$	5022.20			0.0180831
$528$	−223828.	+	61426.2i	−0.802873	+	0.220336i
$529$	−177710.			−0.635039
$530$		0			0
$531$			180453.i			0.639994i
$532$	−294682.	+	386448.i	−1.04119	+	1.36543i
$533$			17536.5i			0.0617289i
$534$	161322.	+	54489.9i	0.565733	+	0.191088i
$535$		0			0
$536$	−143729.	−	213010.i	−0.500283	−	0.741432i
$537$			244435.i			0.847648i
$538$	74930.7	+	25309.4i	0.258878	+	0.0874414i
$539$		−	965252.i		−	3.32249i
$540$		0			0
$541$	102538.			0.350340			0.175170	−	0.984538i	$-0.443953\pi$
$541$	102538.			0.350340			0.175170	+	0.984538i	$0.443953\pi$
$542$	77290.2	−	228825.i	0.263103	−	0.778940i
$543$	85195.9			0.288947
$544$	−70776.7	−	4102.43i	−0.239162	−	0.0138626i
$545$		0			0
$546$	−13620.6	+	40325.1i	−0.0456891	+	0.135266i
$547$	−388547.			−1.29858			−0.649290	−	0.760541i	$-0.724934\pi$
$547$	−388547.			−1.29858			−0.649290	+	0.760541i	$0.724934\pi$
$548$	18329.7	−	24037.7i	0.0610371	−	0.0800446i
$549$	−143533.			−0.476220
$550$		0			0
$551$			231649.i			0.763004i
$552$	59444.3	+	88098.0i	0.195089	+	0.289126i
$553$			36936.6i			0.120783i
$554$	−175479.	+	519520.i	−0.571748	+	1.69271i
$555$		0			0
$556$	−146430.	+	192029.i	−0.473674	+	0.621180i
$557$			24464.5i			0.0788544i	0.999222	+	0.0394272i	$0.0125533\pi$
$557$			24464.5i			0.0788544i	−0.999222	+	0.0394272i	$0.987447\pi$
$558$	2507.04	−	7422.32i	0.00805180	−	0.0238381i
$559$			71540.6i			0.228944i
$560$		0			0
$561$	62771.3			0.199451
$562$	−258744.	−	87396.3i	−0.819216	−	0.276707i
$563$	534256.			1.68551			0.842757	−	0.538294i	$-0.180931\pi$
$563$	534256.			1.68551			0.842757	+	0.538294i	$0.180931\pi$
$564$	−20866.9	−	15911.8i	−0.0655994	−	0.0500221i
$565$		0			0
$566$	176050.	+	59464.6i	0.549545	+	0.185620i
$567$	−64930.0			−0.201967
$568$	156719.	−	105747.i	0.485765	−	0.327771i
$569$	264769.			0.817792			0.408896	−	0.912581i	$-0.365914\pi$
$569$	264769.			0.817792			0.408896	+	0.912581i	$0.365914\pi$
$570$		0			0
$571$			159329.i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$571$			159329.i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$572$	−51041.8	−	38921.4i	−0.156003	−	0.118959i
$573$		−	168798.i		−	0.514113i
$574$	−257446.	−	86957.6i	−0.781379	−	0.263927i
$575$		0			0
$576$	−41394.1	+	102553.i	−0.124765	+	0.309103i
$577$		−	244978.i		−	0.735827i	−0.929860	−	0.367913i	$-0.880072\pi$
$577$		−	244978.i		−	0.735827i	0.929860	−	0.367913i	$-0.119928\pi$
$578$	−298351.	−	100774.i	−0.893042	−	0.301643i
$579$			54042.4i			0.161205i
$580$		0			0
$581$	−867415.			−2.56965
$582$	63614.3	−	188336.i	0.187806	−	0.556015i
$583$	590799.			1.73821
$584$	304623.	−	205545.i	0.893176	−	0.602672i
$585$		0			0
$586$	97058.4	−	287350.i	0.282643	−	0.836789i
$587$	415608.			1.20617			0.603084	−	0.797678i	$-0.293938\pi$
$587$	415608.			1.20617			0.603084	+	0.797678i	$0.293938\pi$
$588$	−365723.	−	278878.i	−1.05779	−	0.806603i
$589$	24737.7			0.0713064
$590$		0			0
$591$		−	245131.i		−	0.701815i
$592$	585937.	−	160801.i	1.67189	−	0.458825i
$593$		−	149847.i		−	0.426128i	−0.977038	−	0.213064i	$-0.931656\pi$
$593$		−	149847.i		−	0.426128i	0.977038	−	0.213064i	$-0.0683442\pi$
$594$	31334.9	−	92769.7i	0.0888087	−	0.262926i
$595$		0			0
$596$	−380254.	−	289959.i	−1.07049	−	0.816289i
$597$			296935.i			0.833129i
$598$	−9405.38	+	27845.5i	−0.0263011	+	0.0778668i
$599$		−	34050.6i		−	0.0949011i	−0.998874	−	0.0474505i	$-0.984890\pi$
$599$		−	34050.6i		−	0.0949011i	0.998874	−	0.0474505i	$-0.0151096\pi$
$600$		0			0
$601$	−618647.			−1.71275			−0.856375	−	0.516355i	$-0.827288\pi$
$601$	−618647.			−1.71275			−0.856375	+	0.516355i	$0.827288\pi$
$602$	−1.05026e6	−	354746.i	−2.89803	−	0.978868i
$603$	108408.			0.298143
$604$	−153463.	+	201253.i	−0.420659	+	0.551655i
$605$		0			0
$606$	−27311.3	−	9224.95i	−0.0743698	−	0.0251199i
$607$	−35350.6			−0.0959444			−0.0479722	−	0.998849i	$-0.515276\pi$
$607$	−35350.6			−0.0959444			−0.0479722	+	0.998849i	$0.515276\pi$
$608$	−348622.	−	20207.2i	−0.943079	−	0.0546638i
$609$	−314374.			−0.847641
$610$		0			0
$611$		−	7257.08i		−	0.0194392i
$612$	18135.7	−	23783.3i	0.0484208	−	0.0634994i
$613$			690354.i			1.83718i	0.395215	+	0.918588i	$0.370670\pi$
$613$			690354.i			1.83718i	−0.395215	+	0.918588i	$0.629330\pi$
$614$	436171.	+	147326.i	1.15696	+	0.390789i
$615$		0			0
$616$	824487.	−	556325.i	2.17281	−	1.46611i
$617$			94309.0i			0.247732i	0.992299	+	0.123866i	$0.0395294\pi$
$617$			94309.0i			0.247732i	−0.992299	+	0.123866i	$0.960471\pi$
$618$	−12353.2	−	4172.53i	−0.0323445	−	0.0109250i
$619$		−	107669.i		−	0.281002i	−0.990081	−	0.140501i	$-0.955129\pi$
$619$		−	107669.i		−	0.281002i	0.990081	−	0.140501i	$-0.0448713\pi$
$620$		0			0
$621$	−44835.8			−0.116263
$622$	57811.7	−	171157.i	0.149429	−	0.442398i
$623$	−729676.			−1.87998
$624$	−29493.7	+	8094.10i	−0.0757461	+	0.0207874i
$625$		0			0
$626$	35702.9	−	105702.i	0.0911077	−	0.269732i
$627$	309190.			0.786486
$628$	−316176.	+	414636.i	−0.801697	+	1.05135i
$629$	−164323.			−0.415332
$630$		0			0
$631$			489941.i			1.23051i	0.788329	+	0.615254i	$0.210947\pi$
$631$			489941.i			1.23051i	−0.788329	+	0.615254i	$0.789053\pi$
$632$	−22001.1	+	14845.3i	−0.0550820	+	0.0371667i
$633$			127621.i			0.318504i
$634$	−115419.	+	341709.i	−0.287144	+	0.850115i
$635$		0			0
$636$	170692.	−	223847.i	0.421987	−	0.553397i
$637$		−	127191.i		−	0.313456i
$638$	151715.	−	449166.i	0.372724	−	1.10348i
$639$			79759.3i			0.195335i
$640$		0			0
$641$	593431.			1.44429			0.722145	−	0.691742i	$-0.243156\pi$
$641$	593431.			1.44429			0.722145	+	0.691742i	$0.243156\pi$
$642$	−58857.3	−	19880.3i	−0.142801	−	0.0482339i
$643$	−263108.			−0.636372			−0.318186	−	0.948028i	$-0.603074\pi$
$643$	−263108.			−0.636372			−0.318186	+	0.948028i	$0.603074\pi$
$644$	−362149.	−	276153.i	−0.873203	−	0.665851i
$645$		0			0
$646$	89475.1	+	30222.1i	0.214406	+	0.0724201i
$647$	−640998.			−1.53126			−0.765629	−	0.643282i	$-0.777572\pi$
$647$	−640998.			−1.53126			−0.765629	+	0.643282i	$0.777572\pi$
$648$	−26096.2	−	38675.2i	−0.0621480	−	0.0921049i
$649$	1.16617e6			2.76868
$650$		0			0
$651$			33571.9i			0.0792161i
$652$	248461.	+	189461.i	0.584470	+	0.445681i
$653$			453024.i			1.06242i	0.847241	+	0.531208i	$0.178262\pi$
$653$			453024.i			1.06242i	−0.847241	+	0.531208i	$0.821738\pi$
$654$	−309246.	−	104454.i	−0.723017	−	0.244214i
$655$		0			0
$656$	−51674.8	−	188295.i	−0.120080	−	0.437554i
$657$			155032.i			0.359162i
$658$	106538.	+	35985.4i	0.246067	+	0.0831141i
$659$		−	16332.5i		−	0.0376081i	−0.999823	−	0.0188040i	$-0.994014\pi$
$659$		−	16332.5i		−	0.0376081i	0.999823	−	0.0188040i	$-0.00598586\pi$
$660$		0			0
$661$	143631.			0.328735			0.164367	−	0.986399i	$-0.447442\pi$
$661$	143631.			0.328735			0.164367	+	0.986399i	$0.447442\pi$
$662$	174013.	−	515181.i	0.397069	−	1.17556i
$663$	8271.34			0.0188169
$664$	−348625.	−	516671.i	−0.790719	−	1.17187i
$665$		0			0
$666$	−82028.5	+	242852.i	−0.184934	+	0.547513i
$667$	−217083.			−0.487948
$668$	265682.	+	202593.i	0.595401	+	0.454017i
$669$	370281.			0.827330
$670$		0			0
$671$			927575.i			2.06017i
$672$	27423.5	−	473120.i	0.0607274	−	1.04769i
$673$		−	331571.i		−	0.732058i	−0.930603	−	0.366029i	$-0.880717\pi$
$673$		−	331571.i		−	0.732058i	0.930603	−	0.366029i	$-0.119283\pi$
$674$	106441.	−	315127.i	0.234308	−	0.693690i
$675$		0			0
$676$	356656.	+	271964.i	0.780471	+	0.595139i
$677$			495629.i			1.08138i	0.841221	+	0.540691i	$0.181837\pi$
$677$			495629.i			1.08138i	−0.841221	+	0.540691i	$0.818163\pi$
$678$	−126820.	+	375462.i	−0.275886	+	0.816783i
$679$			851861.i			1.84769i
$680$		0			0
$681$	−380811.			−0.821136
$682$	−47966.3	−	16201.6i	−0.103126	−	0.0348329i
$683$	−490413.			−1.05128			−0.525642	−	0.850706i	$-0.676175\pi$
$683$	−490413.			−1.05128			−0.525642	+	0.850706i	$0.676175\pi$
$684$	89330.4	−	117149.i	0.190936	−	0.250395i
$685$		0			0
$686$	1.05681e6	+	356960.i	2.24569	+	0.758528i
$687$	−192793.			−0.408487
$688$	−210809.	−	768156.i	−0.445360	−	1.62283i
$689$	77849.3			0.163990
$690$		0			0
$691$		−	157915.i		−	0.330725i	−0.986233	−	0.165363i	$-0.947121\pi$
$691$		−	157915.i		−	0.330725i	0.986233	−	0.165363i	$-0.0528794\pi$
$692$	51214.1	−	67162.6i	0.106949	−	0.140254i
$693$			419607.i			0.873728i
$694$	451012.	+	152339.i	0.936416	+	0.316294i
$695$		0			0
$696$	−126351.	−	187255.i	−0.260831	−	0.386558i
$697$			52806.3i			0.108698i
$698$	−383425.	−	129510.i	−0.786992	−	0.265823i
$699$		−	109126.i		−	0.223344i
$700$		0			0
$701$	−125021.			−0.254418			−0.127209	−	0.991876i	$-0.540602\pi$
$701$	−125021.			−0.254418			−0.127209	+	0.991876i	$0.540602\pi$
$702$	4128.98	−	12224.2i	0.00837855	−	0.0248054i
$703$	−809398.			−1.63776
$704$	662743.	+	267507.i	1.33721	+	0.539747i
$705$		0			0
$706$	−261780.	+	775022.i	−0.525202	+	1.55491i
$707$	123532.			0.247138
$708$	336926.	−	441848.i	0.672154	−	0.881468i
$709$	223380.			0.444377			0.222189	−	0.975004i	$-0.428680\pi$
$709$	223380.			0.444377			0.222189	+	0.975004i	$0.428680\pi$
$710$		0			0
$711$		−	11197.0i		−	0.0221495i
$712$	−293266.	−	434627.i	−0.578498	−	0.857348i
$713$			23182.2i			0.0456011i
$714$	−41014.8	+	121428.i	−0.0804533	+	0.238189i
$715$		0			0
$716$	456388.	−	598511.i	0.890242	−	1.16747i
$717$		−	46173.0i		−	0.0898152i
$718$	57974.6	−	171639.i	0.112458	−	0.332941i
$719$			839679.i			1.62426i	0.583477	+	0.812130i	$0.301692\pi$
$719$			839679.i			1.62426i	−0.583477	+	0.812130i	$0.698308\pi$
$720$		0			0
$721$	55874.5			0.107484
$722$	−53147.8	−	17951.8i	−0.101956	−	0.0344376i
$723$	57333.4			0.109681
$724$	−208606.	−	159070.i	−0.397969	−	0.303467i
$725$		0			0
$726$	−311214.	−	105119.i	−0.590454	−	0.199438i
$727$	244897.			0.463355			0.231678	−	0.972793i	$-0.425579\pi$
$727$	244897.			0.463355			0.231678	+	0.972793i	$0.425579\pi$
$728$	108642.	−	73306.6i	0.204991	−	0.138319i
$729$	19683.0			0.0370370
$730$		0			0
$731$			215425.i			0.403145i
$732$	351447.	+	267992.i	0.655901	+	0.500150i
$733$			370157.i			0.688935i	0.938798	+	0.344467i	$0.111940\pi$
$733$			370157.i			0.688935i	−0.938798	+	0.344467i	$0.888060\pi$
$734$	66405.3	+	22429.8i	0.123257	+	0.0416325i
$735$		0			0
$736$	18936.6	−	326701.i	0.0349580	−	0.603108i
$737$		−	700578.i		−	1.28980i
$738$	78042.5	+	26360.5i	0.143291	+	0.0483995i
$739$		−	555878.i		−	1.01787i	−0.860806	−	0.508933i	$-0.830040\pi$
$739$		−	555878.i		−	1.01787i	0.860806	−	0.508933i	$-0.169960\pi$
$740$		0			0
$741$	40741.9			0.0742001
$742$	−386028.	+	1.14287e6i	−0.701151	+	2.07582i
$743$	−282516.			−0.511759			−0.255880	−	0.966709i	$-0.582365\pi$
$743$	−282516.			−0.511759			−0.255880	+	0.966709i	$0.582365\pi$
$744$	−19996.9	+	13493.0i	−0.0361257	+	0.0243759i
$745$		0			0
$746$	−21166.3	+	62664.7i	−0.0380336	+	0.112602i
$747$	262950.			0.471228
$748$	−153698.	−	117201.i	−0.274705	−	0.209473i
$749$	266218.			0.474540
$750$		0			0
$751$			406925.i			0.721498i	0.932663	+	0.360749i	$0.117479\pi$
$751$			406925.i			0.721498i	−0.932663	+	0.360749i	$0.882521\pi$
$752$	21384.4	+	77921.7i	0.0378148	+	0.137792i
$753$			267458.i			0.471700i
$754$	19991.4	−	59186.4i	0.0351642	−	0.104107i
$755$		0			0
$756$	158984.	+	121232.i	0.278170	+	0.212115i
$757$			973008.i			1.69795i	0.528434	+	0.848974i	$0.322779\pi$
$757$			973008.i			1.69795i	−0.528434	+	0.848974i	$0.677221\pi$
$758$	−81711.8	+	241915.i	−0.142215	+	0.421041i
$759$			289749.i			0.502965i
$760$		0			0
$761$	−457654.			−0.790255			−0.395128	−	0.918626i	$-0.629300\pi$
$761$	−457654.			−0.790255			−0.395128	+	0.918626i	$0.629300\pi$
$762$	7401.88	+	2500.14i	0.0127477	+	0.00430580i
$763$	1.39875e6			2.40265
$764$	−315165.	+	413310.i	−0.539947	+	0.708091i
$765$		0			0
$766$	−302439.	−	102155.i	−0.515442	−	0.174101i
$767$	153666.			0.261208
$768$	292833.	−	173818.i	0.496476	−	0.294695i
$769$	−449424.			−0.759982			−0.379991	−	0.924990i	$-0.624073\pi$
$769$	−449424.			−0.759982			−0.379991	+	0.924990i	$0.624073\pi$
$770$		0			0
$771$		−	221099.i		−	0.371945i
$772$	100903.	−	132325.i	0.169305	−	0.222028i
$773$			842657.i			1.41024i	0.709090	+	0.705118i	$0.249106\pi$
$773$			842657.i			1.41024i	−0.709090	+	0.705118i	$0.750894\pi$
$774$	318376.	+	107538.i	0.531446	+	0.179507i
$775$		0			0
$776$	−507406.	+	342373.i	−0.842621	+	0.568560i
$777$		−	1.09845e6i		−	1.81944i
$778$	−604597.	−	204215.i	−0.998865	−	0.337387i
$779$			260106.i			0.428623i
$780$		0			0
$781$	515440.			0.845038
$782$	−28321.7	+	83848.9i	−0.0463133	+	0.137115i
$783$	95299.8			0.155442
$784$	374793.	+	1.36569e6i	0.609761	+	2.22188i
$785$		0			0
$786$	78260.4	−	231697.i	0.126677	−	0.375038i
$787$	−370408.			−0.598041			−0.299021	−	0.954247i	$-0.596660\pi$
$787$	−370408.			−0.598041			−0.299021	+	0.954247i	$0.596660\pi$
$788$	−457686.	+	600214.i	−0.737081	+	0.966615i
$789$	29935.1			0.0480870
$790$		0			0
$791$		−	1.69825e6i		−	2.71425i
$792$	−249936.	+	168645.i	−0.398455	+	0.268858i
$793$			122226.i			0.194365i
$794$	−188880.	+	559196.i	−0.299602	+	0.886999i
$795$		0			0
$796$	554410.	−	727058.i	0.874994	−	1.14747i
$797$			321175.i			0.505621i	0.967516	+	0.252810i	$0.0813549\pi$
$797$			321175.i			0.505621i	−0.967516	+	0.252810i	$0.918645\pi$
$798$	−202025.	+	598113.i	−0.317249	+	0.939242i
$799$		−	21852.7i		−	0.0342303i
$800$		0			0
$801$	221195.			0.344755
$802$	181514.	+	61310.3i	0.282204	+	0.0953201i
$803$	1.00189e6			1.55377
$804$	−265441.	−	202409.i	−0.410635	−	0.313125i
$805$		0			0
$806$	−6320.50	−	2134.88i	−0.00972929	−	0.00328627i
$807$	102740.			0.157759
$808$	49648.9	+	73580.9i	0.0760478	+	0.112705i
$809$	−596798.			−0.911864			−0.455932	−	0.890015i	$-0.650694\pi$
$809$	−596798.			−0.911864			−0.455932	+	0.890015i	$0.650694\pi$
$810$		0			0
$811$			479347.i			0.728800i	0.931243	+	0.364400i	$0.118726\pi$
$811$			479347.i			0.728800i	−0.931243	+	0.364400i	$0.881274\pi$
$812$	769759.	+	586971.i	1.16746	+	0.890235i
$813$		−	313750.i		−	0.474683i
$814$	1.56942e6	+	530105.i	2.36859	+	0.800042i
$815$		0			0
$816$	−88812.2	+	24373.2i	−0.133380	+	0.0366042i
$817$			1.06111e6i			1.58970i
$818$	95457.7	+	32242.8i	0.142661	+	0.0481866i
$819$			55291.4i			0.0824308i
$820$		0			0
$821$	84958.2			0.126043			0.0630215	−	0.998012i	$-0.479926\pi$
$821$	84958.2			0.126043			0.0630215	+	0.998012i	$0.479926\pi$
$822$	12566.3	−	37203.6i	0.0185979	−	0.0550607i
$823$	67392.6			0.0994975			0.0497488	−	0.998762i	$-0.484158\pi$
$823$	67392.6			0.0994975			0.0497488	+	0.998762i	$0.484158\pi$
$824$	22456.7	+	33281.3i	0.0330743	+	0.0490170i
$825$		0			0
$826$	−761976.	+	2.25590e6i	−1.11681	+	3.30643i
$827$	433061.			0.633196			0.316598	−	0.948560i	$-0.397459\pi$
$827$	433061.			0.633196			0.316598	+	0.948560i	$0.397459\pi$
$828$	109782.	+	83713.4i	0.160130	+	0.122105i
$829$	−1.14798e6			−1.67043			−0.835213	−	0.549927i	$-0.814655\pi$
$829$	−1.14798e6			−1.67043			−0.835213	+	0.549927i	$0.814655\pi$
$830$		0			0
$831$			712335.i			1.03153i
$832$	87329.3	+	35249.3i	0.126158	+	0.0509218i
$833$		−	383000.i		−	0.551961i
$834$	−100388.	+	297207.i	−0.144327	+	0.427294i
$835$		0			0
$836$	−757067.	−	577293.i	−1.08323	−	0.826007i
$837$		−	10177.0i		−	0.0145268i
$838$	−231228.	+	684570.i	−0.329270	+	0.974832i
$839$			499869.i			0.710121i	0.934843	+	0.355060i	$0.115540\pi$
$839$			499869.i			0.710121i	−0.934843	+	0.355060i	$0.884460\pi$
$840$		0			0
$841$	−245865.			−0.347620
$842$	528852.	+	178631.i	0.745950	+	0.251960i
$843$	−354775.			−0.499226
$844$	238283.	−	312486.i	0.334509	−	0.438678i
$845$		0			0
$846$	−32296.1	−	10908.7i	−0.0451242	−	0.0152416i
$847$	1.40765e6			1.96213
$848$	−835894.	+	229398.i	−1.16241	+	0.319006i
$849$	241389.			0.334890
$850$		0			0
$851$		−	758504.i		−	1.04737i
$852$	148920.	−	195294.i	0.205151	−	0.269036i
$853$			490741.i			0.674457i	0.941423	+	0.337228i	$0.109489\pi$
$853$			490741.i			0.674457i	−0.941423	+	0.337228i	$0.890511\pi$
$854$	−1.79435e6	−	606078.i	−2.46031	−	0.831022i
$855$		0			0
$856$	106996.	+	158571.i	0.146023	+	0.216410i
$857$		−	920396.i		−	1.25318i	−0.779349	−	0.626590i	$-0.784450\pi$
$857$		−	920396.i		−	1.25318i	0.779349	−	0.626590i	$-0.215550\pi$
$858$	−78998.4	−	26683.3i	−0.107311	−	0.0362465i
$859$		−	1.31521e6i		−	1.78242i	−0.453595	−	0.891208i	$-0.649859\pi$
$859$		−	1.31521e6i		−	1.78242i	0.453595	−	0.891208i	$-0.350141\pi$
$860$		0			0
$861$	−352994.			−0.476169
$862$	211274.	−	625494.i	0.284335	−	0.841799i
$863$	68287.4			0.0916894			0.0458447	−	0.998949i	$-0.485402\pi$
$863$	68287.4			0.0916894			0.0458447	+	0.998949i	$0.485402\pi$
$864$	−8313.21	+	143422.i	−0.0111363	+	0.192128i
$865$		0			0
$866$	33554.1	−	99339.8i	0.0447414	−	0.132461i
$867$	−409081.			−0.544216
$868$	62682.4	−	82202.3i	0.0831968	−	0.109105i
$869$	−72360.1			−0.0958208
$870$		0			0
$871$		−	92314.8i		−	0.121684i
$872$	562175.	+	833158.i	0.739331	+	1.09571i
$873$		−	258235.i		−	0.338833i
$874$	−139503.	+	413012.i	−0.182626	+	0.540679i
$875$		0			0
$876$	289462.	−	379603.i	0.377210	−	0.494676i
$877$		−	1.14924e6i		−	1.49421i	−0.664707	−	0.747104i	$-0.731444\pi$
$877$		−	1.14924e6i		−	1.49421i	0.664707	−	0.747104i	$-0.268556\pi$
$878$	455592.	−	1.34882e6i	0.591000	−	1.74971i
$879$		−	393997.i		−	0.509935i
$880$		0			0
$881$	−79533.6			−0.102470			−0.0512352	−	0.998687i	$-0.516316\pi$
$881$	−79533.6			−0.102470			−0.0512352	+	0.998687i	$0.516316\pi$
$882$	−566036.	−	191190.i	−0.727624	−	0.245770i
$883$	−226846.			−0.290945			−0.145472	−	0.989362i	$-0.546470\pi$
$883$	−226846.			−0.290945			−0.145472	+	0.989362i	$0.546470\pi$
$884$	−20252.8	−	15443.5i	−0.0259167	−	0.0197625i
$885$		0			0
$886$	433007.	+	146257.i	0.551604	+	0.186316i
$887$	421203.			0.535358			0.267679	−	0.963508i	$-0.413743\pi$
$887$	421203.			0.535358			0.267679	+	0.963508i	$0.413743\pi$
$888$	654283.	−	441479.i	0.829736	−	0.559866i
$889$	−33479.4			−0.0423618
$890$		0			0
$891$		−	127200.i		−	0.160226i
$892$	−906649.	−	691355.i	−1.13949	−	0.868904i
$893$		−	107639.i		−	0.134979i
$894$	−588526.	−	198787.i	−0.736361	−	0.248721i
$895$		0			0
$896$	−950516.	+	1.10725e6i	−1.18398	+	1.37921i
$897$			38180.0i			0.0474517i
$898$	324316.	+	109544.i	0.402175	+	0.135843i
$899$		−	49274.5i		−	0.0609681i
$900$		0			0
$901$	234422.			0.288767
$902$	170353.	−	504346.i	0.209381	−	0.619891i
$903$	−1.44005e6			−1.76604
$904$	1.01155e6	−	682549.i	1.23781	−	0.835213i
$905$		0			0
$906$	−105210.	+	311482.i	−0.128174	+	0.379470i
$907$	−743335.			−0.903587			−0.451793	−	0.892123i	$-0.649216\pi$
$907$	−743335.			−0.903587			−0.451793	+	0.892123i	$0.649216\pi$
$908$	932433.	+	711016.i	1.13096	+	0.862398i
$909$	−37447.6			−0.0453206
$910$		0			0
$911$			460545.i			0.554927i	0.960736	+	0.277463i	$0.0894937\pi$
$911$			460545.i			0.554927i	−0.960736	+	0.277463i	$0.910506\pi$
$912$	−437459.	+	120054.i	−0.525954	+	0.144340i
$913$		−	1.69930e6i		−	2.03858i
$914$	497148.	−	1.47185e6i	0.595105	−	1.76186i
$915$		0			0
$916$	472063.	+	359966.i	0.562612	+	0.429014i
$917$			1.04799e6i			1.24629i
$918$	12433.3	−	36809.9i	0.0147537	−	0.0436796i
$919$			398036.i			0.471293i	0.971839	+	0.235647i	$0.0757208\pi$
$919$			398036.i			0.471293i	−0.971839	+	0.235647i	$0.924279\pi$
$920$		0			0
$921$	598052.			0.705049
$922$	−1.22289e6	−	413056.i	−1.43855	−	0.485900i
$923$	67919.3			0.0797241
$924$	783453.	−	1.02743e6i	0.917633	−	1.20339i
$925$		0			0
$926$	706110.	+	238503.i	0.823475	+	0.278146i
$927$	−16937.9			−0.0197106
$928$	−40250.3	+	694413.i	−0.0467384	+	0.806347i
$929$	1.29517e6			1.50070			0.750352	−	0.661039i	$-0.229884\pi$
$929$	1.29517e6			1.50070			0.750352	+	0.661039i	$0.229884\pi$
$930$		0			0
$931$		−	1.88653e6i		−	2.17653i
$932$	−203751.	+	267201.i	−0.234567	+	0.307614i
$933$		−	234680.i		−	0.269595i
$934$	−452559.	−	152861.i	−0.518778	−	0.175228i
$935$		0			0
$936$	−32934.0	+	22222.3i	−0.0375918	+	0.0253651i
$937$		−	567776.i		−	0.646693i	−0.946281	−	0.323347i	$-0.895192\pi$
$937$		−	567776.i		−	0.646693i	0.946281	−	0.323347i	$-0.104808\pi$
$938$	1.35523e6	+	457758.i	1.54031	+	0.520272i
$939$		−	144932.i		−	0.164374i
$940$		0			0
$941$	595092.			0.672055			0.336027	−	0.941852i	$-0.390917\pi$
$941$	595092.			0.672055			0.336027	+	0.941852i	$0.390917\pi$
$942$	−216761.	+	641740.i	−0.244275	+	0.723198i
$943$	−243751.			−0.274109
$944$	−1.64996e6	+	452806.i	−1.85152	+	0.508122i
$945$		0			0
$946$	694960.	−	2.05749e6i	0.776565	−	2.29909i
$947$	−847579.			−0.945105			−0.472552	−	0.881303i	$-0.656667\pi$
$947$	−847579.			−0.945105			−0.472552	+	0.881303i	$0.656667\pi$
$948$	−20906.1	+	27416.4i	−0.0232625	+	0.0305066i
$949$	132018.			0.146589
$950$		0			0
$951$			468531.i			0.518056i
$952$	327146.	−	220743.i	0.360967	−	0.243563i
$953$		−	705705.i		−	0.777030i	−0.921442	−	0.388515i	$-0.872988\pi$
$953$		−	705705.i		−	0.777030i	0.921442	−	0.388515i	$-0.127012\pi$
$954$	117021.	−	346452.i	0.128578	−	0.380668i
$955$		0			0
$956$	−86210.2	+	113057.i	−0.0943285	+	0.123703i
$957$		−	615870.i		−	0.672458i
$958$	117255.	−	347143.i	0.127761	−	0.378249i
$959$			168276.i			0.182972i
$960$		0			0
$961$	918259.			0.994302
$962$	206802.	+	69851.6i	0.223462	+	0.0754790i
$963$	−80701.7			−0.0870222
$964$	−140383.	−	107048.i	−0.151064	−	0.115192i
$965$		0			0
$966$	−560504.	−	189322.i	−0.600654	−	0.202883i
$967$	−1.51802e6			−1.62339			−0.811697	−	0.584079i	$-0.801456\pi$
$967$	−1.51802e6			−1.62339			−0.811697	+	0.584079i	$0.801456\pi$
$968$	565753.	+	838460.i	0.603777	+	0.894812i
$969$	122683.			0.130658
$970$		0			0
$971$			697559.i			0.739848i	0.929062	+	0.369924i	$0.120616\pi$
$971$			697559.i			0.739848i	−0.929062	+	0.369924i	$0.879384\pi$
$972$	−48194.7	−	36750.4i	−0.0510114	−	0.0388982i
$973$		−	1.34430e6i		−	1.41994i
$974$	−773658.	−	261319.i	−0.815513	−	0.275457i
$975$		0			0
$976$	−360163.	−	1.31238e6i	−0.378094	−	1.37772i
$977$			1.31716e6i			1.37990i	0.723856	+	0.689952i	$0.242368\pi$
$977$			1.31716e6i			1.37990i	−0.723856	+	0.689952i	$0.757632\pi$
$978$	384547.	+	129889.i	0.402042	+	0.135798i
$979$		−	1.42946e6i		−	1.49145i
$980$		0			0
$981$	−424020.			−0.440603
$982$	−245751.	+	727566.i	−0.254842	+	0.754483i
$983$	−1.38061e6			−1.42878			−0.714389	−	0.699749i	$-0.753295\pi$
$983$	−1.38061e6			−1.42878			−0.714389	+	0.699749i	$0.753295\pi$
$984$	−141873.	−	210259.i	−0.146524	−	0.217152i
$985$		0			0
$986$	60198.7	−	178223.i	0.0619203	−	0.183321i
$987$	146078.			0.149952
$988$	−99758.3	−	76069.6i	−0.102196	−	0.0779287i
$989$	−994388.			−1.01663
$990$		0			0
$991$		−	183725.i		−	0.187077i	−0.995616	−	0.0935385i	$-0.970182\pi$
$991$		−	183725.i		−	0.187077i	0.995616	−	0.0935385i	$-0.0298178\pi$
$992$	74156.2	+	4298.32i	0.0753571	+	0.00436793i
$993$		−	706385.i		−	0.716379i
$994$	−336789.	+	997093.i	−0.340867	+	1.00917i
$995$		0			0
$996$	−643844.	−	490956.i	−0.649026	−	0.494908i
$997$		−	547047.i		−	0.550344i	−0.961395	−	0.275172i	$-0.911265\pi$
$997$		−	547047.i		−	0.550344i	0.961395	−	0.275172i	$-0.0887348\pi$
$998$	111183.	−	329166.i	0.111629	−	0.330486i
$999$			332985.i			0.333652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.f.b.199.3		32
4.3	odd	2	inner	300.5.f.b.199.29		32
5.2	odd	4		60.5.c.a.31.11	✓	16
5.3	odd	4		300.5.c.d.151.6		16
5.4	even	2	inner	300.5.f.b.199.30		32
15.2	even	4		180.5.c.c.91.6		16
20.3	even	4		300.5.c.d.151.5		16
20.7	even	4		60.5.c.a.31.12	yes	16
20.19	odd	2	inner	300.5.f.b.199.4		32
40.27	even	4		960.5.e.f.511.12		16
40.37	odd	4		960.5.e.f.511.1		16
60.47	odd	4		180.5.c.c.91.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.11	✓	16	5.2	odd	4
60.5.c.a.31.12	yes	16	20.7	even	4
180.5.c.c.91.5		16	60.47	odd	4
180.5.c.c.91.6		16	15.2	even	4
300.5.c.d.151.5		16	20.3	even	4
300.5.c.d.151.6		16	5.3	odd	4
300.5.f.b.199.3		32	1.1	even	1	trivial
300.5.f.b.199.4		32	20.19	odd	2	inner
300.5.f.b.199.29		32	4.3	odd	2	inner
300.5.f.b.199.30		32	5.4	even	2	inner
960.5.e.f.511.1		16	40.37	odd	4
960.5.e.f.511.12		16	40.27	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-3.78966 - 1.28004i) q^{2} -5.19615 q^{3} +(12.7230 + 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} -89.0673 q^{7} +(-35.7972 - 53.0524i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(-3.78966 - 1.28004i) q^{2} -5.19615 q^{3} +(12.7230 + 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} -89.0673 q^{7} +(-35.7972 - 53.0524i) q^{8} +27.0000 q^{9} -174.486i q^{11} +(-66.1107 - 50.4120i) q^{12} -22.9919i q^{13} +(337.534 + 114.009i) q^{14} +(67.7503 + 246.872i) q^{16} -69.2339i q^{17} +(-102.321 - 34.5610i) q^{18} -341.023i q^{19} +462.807 q^{21} +(-223.348 + 661.242i) q^{22} +319.580 q^{23} +(186.008 + 275.668i) q^{24} +(-29.4305 + 87.1316i) q^{26} -140.296 q^{27} +(-1133.20 - 864.112i) q^{28} -679.276 q^{29} +72.5397i q^{31} +(59.2548 - 1022.28i) q^{32} +906.656i q^{33} +(-88.6218 + 262.373i) q^{34} +(343.521 + 261.948i) q^{36} -2373.44i q^{37} +(-436.521 + 1292.36i) q^{38} +119.470i q^{39} -762.724 q^{41} +(-1753.88 - 592.410i) q^{42} -3111.55 q^{43} +(1692.83 - 2219.99i) q^{44} +(-1211.10 - 409.073i) q^{46} +315.636 q^{47} +(-352.041 - 1282.79i) q^{48} +5531.98 q^{49} +359.750i q^{51} +(223.063 - 292.527i) q^{52} +3385.94i q^{53} +(531.674 + 179.584i) q^{54} +(3188.36 + 4725.23i) q^{56} +1772.01i q^{57} +(2574.22 + 869.498i) q^{58} +6683.46i q^{59} -5316.04 q^{61} +(92.8534 - 274.901i) q^{62} -2404.82 q^{63} +(-1533.12 + 3798.26i) q^{64} +(1160.55 - 3435.92i) q^{66} +4015.09 q^{67} +(671.693 - 880.863i) q^{68} -1660.58 q^{69} +2954.05i q^{71} +(-966.525 - 1432.41i) q^{72} +5741.92i q^{73} +(-3038.09 + 8994.54i) q^{74} +(3308.53 - 4338.84i) q^{76} +15541.0i q^{77} +(152.925 - 452.749i) q^{78} -414.704i q^{79} +729.000 q^{81} +(2890.46 + 976.314i) q^{82} +9738.88 q^{83} +(5888.30 + 4490.06i) q^{84} +(11791.7 + 3982.90i) q^{86} +3529.62 q^{87} +(-9256.90 + 6246.12i) q^{88} +8192.42 q^{89} +2047.83i q^{91} +(4066.02 + 3100.50i) q^{92} -376.927i q^{93} +(-1196.15 - 404.025i) q^{94} +(-307.897 + 5311.94i) q^{96} -9564.24i q^{97} +(-20964.3 - 7081.13i) q^{98} -4711.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 52 q^{4} + 36 q^{6} + 864 q^{9}+O(q^{10}) \) 32 * q - 52 * q^4 + 36 * q^6 + 864 * q^9	\( 32 q - 52 q^{4} + 36 q^{6} + 864 q^{9} + 1608 q^{14} - 380 q^{16} + 576 q^{21} + 3996 q^{24} - 1704 q^{26} + 6912 q^{29} - 9544 q^{34} - 1404 q^{36} + 2496 q^{41} + 12840 q^{44} - 2224 q^{46} + 7904 q^{49} + 972 q^{54} - 5208 q^{56} - 7616 q^{61} + 23804 q^{64} - 5832 q^{66} - 19584 q^{69} - 61032 q^{74} - 10320 q^{76} + 23328 q^{81} + 4104 q^{84} + 79536 q^{86} - 15168 q^{89} - 99552 q^{94} + 37764 q^{96}+O(q^{100}) \) 32 * q - 52 * q^4 + 36 * q^6 + 864 * q^9 + 1608 * q^14 - 380 * q^16 + 576 * q^21 + 3996 * q^24 - 1704 * q^26 + 6912 * q^29 - 9544 * q^34 - 1404 * q^36 + 2496 * q^41 + 12840 * q^44 - 2224 * q^46 + 7904 * q^49 + 972 * q^54 - 5208 * q^56 - 7616 * q^61 + 23804 * q^64 - 5832 * q^66 - 19584 * q^69 - 61032 * q^74 - 10320 * q^76 + 23328 * q^81 + 4104 * q^84 + 79536 * q^86 - 15168 * q^89 - 99552 * q^94 + 37764 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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