LMFDB - Embedded newform 300.5.c.e.151.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.17
Character	$\chi$	$=$	300.151
Dual form			300.5.c.e.151.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03548 - 3.44337i) q^{2} -5.19615i q^{3} +(-7.71364 - 14.0178i) q^{4} +(-17.8923 - 10.5767i) q^{6} +51.0440i q^{7} +(-63.9696 - 1.97210i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(2.03548 - 3.44337i) q^{2} -5.19615i q^{3} +(-7.71364 - 14.0178i) q^{4} +(-17.8923 - 10.5767i) q^{6} +51.0440i q^{7} +(-63.9696 - 1.97210i) q^{8} -27.0000 q^{9} -37.8608i q^{11} +(-72.8388 + 40.0812i) q^{12} -201.199 q^{13} +(175.763 + 103.899i) q^{14} +(-137.000 + 216.257i) q^{16} +370.875 q^{17} +(-54.9580 + 92.9711i) q^{18} +474.940i q^{19} +265.232 q^{21} +(-130.369 - 77.0650i) q^{22} +386.396i q^{23} +(-10.2473 + 332.396i) q^{24} +(-409.538 + 692.805i) q^{26} +140.296i q^{27} +(715.526 - 393.735i) q^{28} -1164.83 q^{29} +1459.12i q^{31} +(465.794 + 911.928i) q^{32} -196.731 q^{33} +(754.909 - 1277.06i) q^{34} +(208.268 + 378.482i) q^{36} +609.708 q^{37} +(1635.40 + 966.731i) q^{38} +1045.46i q^{39} +731.186 q^{41} +(539.875 - 913.293i) q^{42} -1825.96i q^{43} +(-530.727 + 292.045i) q^{44} +(1330.50 + 786.501i) q^{46} -1394.19i q^{47} +(1123.70 + 711.871i) q^{48} -204.486 q^{49} -1927.12i q^{51} +(1551.98 + 2820.38i) q^{52} +3052.05 q^{53} +(483.092 + 285.570i) q^{54} +(100.664 - 3265.26i) q^{56} +2467.86 q^{57} +(-2370.99 + 4010.95i) q^{58} -2232.89i q^{59} -5509.38 q^{61} +(5024.28 + 2970.00i) q^{62} -1378.19i q^{63} +(4088.22 + 252.309i) q^{64} +(-400.442 + 677.417i) q^{66} +5332.45i q^{67} +(-2860.80 - 5198.86i) q^{68} +2007.77 q^{69} +5691.93i q^{71} +(1727.18 + 53.2467i) q^{72} -4464.89 q^{73} +(1241.05 - 2099.45i) q^{74} +(6657.63 - 3663.52i) q^{76} +1932.57 q^{77} +(3599.92 + 2128.02i) q^{78} +3141.04i q^{79} +729.000 q^{81} +(1488.31 - 2517.75i) q^{82} +6107.15i q^{83} +(-2045.91 - 3717.98i) q^{84} +(-6287.46 - 3716.71i) q^{86} +6052.64i q^{87} +(-74.6654 + 2421.94i) q^{88} -9513.18 q^{89} -10270.0i q^{91} +(5416.43 - 2980.52i) q^{92} +7581.79 q^{93} +(-4800.72 - 2837.85i) q^{94} +(4738.52 - 2420.34i) q^{96} +3487.02 q^{97} +(-416.227 + 704.121i) q^{98} +1022.24i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 14 q^{4} - 18 q^{6} - 648 q^{9}+O(q^{10}) $ 24 * q - 14 * q^4 - 18 * q^6 - 648 * q^9	$ 24 q - 14 q^{4} - 18 q^{6} - 648 q^{9} + 36 q^{14} + 594 q^{16} + 594 q^{24} - 2868 q^{26} + 1680 q^{29} - 3076 q^{34} + 378 q^{36} - 4848 q^{41} + 3828 q^{44} - 15280 q^{46} - 5416 q^{49} + 486 q^{54} + 32172 q^{56} + 2896 q^{61} + 18298 q^{64} - 15588 q^{66} - 9792 q^{69} - 31836 q^{74} + 50136 q^{76} + 17496 q^{81} + 4284 q^{84} - 58152 q^{86} + 38544 q^{89} - 4808 q^{94} + 21978 q^{96}+O(q^{100}) $ 24 * q - 14 * q^4 - 18 * q^6 - 648 * q^9 + 36 * q^14 + 594 * q^16 + 594 * q^24 - 2868 * q^26 + 1680 * q^29 - 3076 * q^34 + 378 * q^36 - 4848 * q^41 + 3828 * q^44 - 15280 * q^46 - 5416 * q^49 + 486 * q^54 + 32172 * q^56 + 2896 * q^61 + 18298 * q^64 - 15588 * q^66 - 9792 * q^69 - 31836 * q^74 + 50136 * q^76 + 17496 * q^81 + 4284 * q^84 - 58152 * q^86 + 38544 * q^89 - 4808 * q^94 + 21978 * 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 $

$2$	2.03548	−	3.44337i	0.508870	−	0.860843i
$2$	2.03548	−	3.44337i	0.508870	−	0.860843i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−7.71364	−	14.0178i	−0.482102	−	0.876115i
$5$		0			0
$5$		0			0
$6$	−17.8923	−	10.5767i	−0.497008	−	0.293796i
$7$			51.0440i			1.04171i	0.853644	+	0.520857i	$0.174387\pi$
$7$			51.0440i			1.04171i	−0.853644	+	0.520857i	$0.825613\pi$
$8$	−63.9696	−	1.97210i	−0.999525	−	0.0308141i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	37.8608i		−	0.312900i	−0.987686	−	0.156450i	$-0.949995\pi$
$11$		−	37.8608i		−	0.312900i	0.987686	−	0.156450i	$-0.0500049\pi$
$12$	−72.8388	+	40.0812i	−0.505825	+	0.278342i
$13$	−201.199			−1.19053			−0.595265	−	0.803530i	$-0.702953\pi$
$13$	−201.199			−1.19053			−0.595265	+	0.803530i	$0.702953\pi$
$14$	175.763	+	103.899i	0.896752	+	0.530097i
$15$		0			0
$16$	−137.000	+	216.257i	−0.535155	+	0.844754i
$17$	370.875			1.28330			0.641652	−	0.766996i	$-0.278249\pi$
$17$	370.875			1.28330			0.641652	+	0.766996i	$0.278249\pi$
$18$	−54.9580	+	92.9711i	−0.169623	+	0.286948i
$19$			474.940i			1.31562i	0.753183	+	0.657812i	$0.228518\pi$
$19$			474.940i			1.31562i	−0.753183	+	0.657812i	$0.771482\pi$
$20$		0			0
$21$	265.232			0.601434
$22$	−130.369	−	77.0650i	−0.269357	−	0.159225i
$23$			386.396i			0.730426i	0.930924	+	0.365213i	$0.119004\pi$
$23$			386.396i			0.730426i	−0.930924	+	0.365213i	$0.880996\pi$
$24$	−10.2473	+	332.396i	−0.0177905	+	0.577076i
$25$		0			0
$26$	−409.538	+	692.805i	−0.605825	+	1.02486i
$27$			140.296i			0.192450i
$28$	715.526	−	393.735i	0.912661	−	0.502213i
$29$	−1164.83			−1.38505			−0.692527	−	0.721392i	$-0.743503\pi$
$29$	−1164.83			−1.38505			−0.692527	+	0.721392i	$0.743503\pi$
$30$		0			0
$31$			1459.12i			1.51833i	0.650898	+	0.759166i	$0.274393\pi$
$31$			1459.12i			1.51833i	−0.650898	+	0.759166i	$0.725607\pi$
$32$	465.794	+	911.928i	0.454877	+	0.890554i
$33$	−196.731			−0.180653
$34$	754.909	−	1277.06i	0.653035	−	1.10472i
$35$		0			0
$36$	208.268	+	378.482i	0.160701	+	0.292038i
$37$	609.708			0.445368			0.222684	−	0.974891i	$-0.428518\pi$
$37$	609.708			0.445368			0.222684	+	0.974891i	$0.428518\pi$
$38$	1635.40	+	966.731i	1.13255	+	0.669481i
$39$			1045.46i			0.687353i
$40$		0			0
$41$	731.186			0.434971			0.217485	−	0.976064i	$-0.430215\pi$
$41$	731.186			0.434971			0.217485	+	0.976064i	$0.430215\pi$
$42$	539.875	−	913.293i	0.306052	−	0.517740i
$43$		−	1825.96i		−	0.987539i	−0.869593	−	0.493770i	$-0.835619\pi$
$43$		−	1825.96i		−	0.987539i	0.869593	−	0.493770i	$-0.164381\pi$
$44$	−530.727	+	292.045i	−0.274136	+	0.150850i
$45$		0			0
$46$	1330.50	+	786.501i	0.628783	+	0.371692i
$47$		−	1394.19i		−	0.631141i	−0.948902	−	0.315570i	$-0.897804\pi$
$47$		−	1394.19i		−	0.631141i	0.948902	−	0.315570i	$-0.102196\pi$
$48$	1123.70	+	711.871i	0.487719	+	0.308972i
$49$	−204.486			−0.0851670
$50$		0			0
$51$		−	1927.12i		−	0.740916i
$52$	1551.98	+	2820.38i	0.573957	+	1.04304i
$53$	3052.05			1.08653			0.543263	−	0.839562i	$-0.317189\pi$
$53$	3052.05			1.08653			0.543263	+	0.839562i	$0.317189\pi$
$54$	483.092	+	285.570i	0.165669	+	0.0979321i
$55$		0			0
$56$	100.664	−	3265.26i	0.0320994	−	1.04122i
$57$	2467.86			0.759575
$58$	−2370.99	+	4010.95i	−0.704813	+	1.19231i
$59$		−	2232.89i		−	0.641451i	−0.947172	−	0.320725i	$-0.896073\pi$
$59$		−	2232.89i		−	0.641451i	0.947172	−	0.320725i	$-0.103927\pi$
$60$		0			0
$61$	−5509.38			−1.48062			−0.740309	−	0.672267i	$-0.765321\pi$
$61$	−5509.38			−1.48062			−0.740309	+	0.672267i	$0.765321\pi$
$62$	5024.28	+	2970.00i	1.30705	+	0.772633i
$63$		−	1378.19i		−	0.347238i
$64$	4088.22	+	252.309i	0.998101	+	0.0615989i
$65$		0			0
$66$	−400.442	+	677.417i	−0.0919287	+	0.155514i
$67$			5332.45i			1.18789i	0.804505	+	0.593946i	$0.202431\pi$
$67$			5332.45i			1.18789i	−0.804505	+	0.593946i	$0.797569\pi$
$68$	−2860.80	−	5198.86i	−0.618684	−	1.12432i
$69$	2007.77			0.421712
$70$		0			0
$71$			5691.93i			1.12913i	0.825390	+	0.564563i	$0.190955\pi$
$71$			5691.93i			1.12913i	−0.825390	+	0.564563i	$0.809045\pi$
$72$	1727.18	+	53.2467i	0.333175	+	0.0102714i
$73$	−4464.89			−0.837848			−0.418924	−	0.908021i	$-0.637593\pi$
$73$	−4464.89			−0.837848			−0.418924	+	0.908021i	$0.637593\pi$
$74$	1241.05	−	2099.45i	0.226634	−	0.383392i
$75$		0			0
$76$	6657.63	−	3663.52i	1.15264	−	0.634265i
$77$	1932.57			0.325952
$78$	3599.92	+	2128.02i	0.591703	+	0.349773i
$79$			3141.04i			0.503292i	0.967819	+	0.251646i	$0.0809718\pi$
$79$			3141.04i			0.503292i	−0.967819	+	0.251646i	$0.919028\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	1488.31	−	2517.75i	0.221344	−	0.374442i
$83$			6107.15i			0.886507i	0.896396	+	0.443254i	$0.146176\pi$
$83$			6107.15i			0.886507i	−0.896396	+	0.443254i	$0.853824\pi$
$84$	−2045.91	−	3717.98i	−0.289953	−	0.526925i
$85$		0			0
$86$	−6287.46	−	3716.71i	−0.850117	−	0.502529i
$87$			6052.64i			0.799661i
$88$	−74.6654	+	2421.94i	−0.00964171	+	0.312751i
$89$	−9513.18			−1.20101			−0.600504	−	0.799622i	$-0.705033\pi$
$89$	−9513.18			−1.20101			−0.600504	+	0.799622i	$0.705033\pi$
$90$		0			0
$91$		−	10270.0i		−	1.24019i
$92$	5416.43	−	2980.52i	0.639937	−	0.352140i
$93$	7581.79			0.876609
$94$	−4800.72	−	2837.85i	−0.543313	−	0.321169i
$95$		0			0
$96$	4738.52	−	2420.34i	0.514162	−	0.262623i
$97$	3487.02			0.370605			0.185302	−	0.982682i	$-0.440674\pi$
$97$	3487.02			0.370605			0.185302	+	0.982682i	$0.440674\pi$
$98$	−416.227	+	704.121i	−0.0433389	+	0.0733154i
$99$			1022.24i			0.104300i
$100$		0			0
$101$	−9548.01			−0.935987			−0.467994	−	0.883732i	$-0.655023\pi$
$101$	−9548.01			−0.935987			−0.467994	+	0.883732i	$0.655023\pi$
$102$	−6635.80	−	3922.62i	−0.637813	−	0.377030i
$103$			5516.29i			0.519963i	0.965614	+	0.259981i	$0.0837164\pi$
$103$			5516.29i			0.519963i	−0.965614	+	0.259981i	$0.916284\pi$
$104$	12870.7	+	396.786i	1.18996	+	0.0366851i
$105$		0			0
$106$	6212.39	−	10509.4i	0.552901	−	0.935329i
$107$			2923.03i			0.255309i	0.991819	+	0.127654i	$0.0407448\pi$
$107$			2923.03i			0.255309i	−0.991819	+	0.127654i	$0.959255\pi$
$108$	1966.65	−	1082.19i	0.168608	−	0.0927806i
$109$	−21658.4			−1.82294			−0.911471	−	0.411364i	$-0.865053\pi$
$109$	−21658.4			−1.82294			−0.911471	+	0.411364i	$0.865053\pi$
$110$		0			0
$111$		−	3168.14i		−	0.257133i
$112$	−11038.6	−	6993.00i	−0.879992	−	0.557478i
$113$	14588.6			1.14250			0.571252	−	0.820775i	$-0.306458\pi$
$113$	14588.6			1.14250			0.571252	+	0.820775i	$0.306458\pi$
$114$	5023.28	−	8497.76i	0.386525	−	0.653875i
$115$		0			0
$116$	8985.08	+	16328.4i	0.667738	+	1.21347i
$117$	5432.39			0.396843
$118$	−7688.67	−	4545.00i	−0.552189	−	0.326415i
$119$			18930.9i			1.33684i
$120$		0			0
$121$	13207.6			0.902094
$122$	−11214.2	+	18970.9i	−0.753442	+	1.27458i
$123$		−	3799.35i		−	0.251131i
$124$	20453.7	−	11255.1i	1.33023	−	0.731991i
$125$		0			0
$126$	−4745.61	−	2805.27i	−0.298917	−	0.176699i
$127$		−	22165.2i		−	1.37425i	−0.726541	−	0.687123i	$-0.758873\pi$
$127$		−	22165.2i		−	1.37425i	0.726541	−	0.687123i	$-0.241127\pi$
$128$	9190.29	−	13563.7i	0.560931	−	0.827863i
$129$	−9487.97			−0.570156
$130$		0			0
$131$			25664.9i			1.49553i	0.663961	+	0.747767i	$0.268874\pi$
$131$			25664.9i			1.49553i	−0.663961	+	0.747767i	$0.731126\pi$
$132$	1517.51	+	2757.74i	0.0870931	+	0.158272i
$133$	−24242.8			−1.37050
$134$	18361.6	+	10854.1i	1.02259	+	0.604483i
$135$		0			0
$136$	−23724.7	−	731.403i	−1.28269	−	0.0395438i
$137$	530.885			0.0282852			0.0141426	−	0.999900i	$-0.495498\pi$
$137$	530.885			0.0282852			0.0141426	+	0.999900i	$0.495498\pi$
$138$	4086.78	−	6913.50i	0.214597	−	0.363028i
$139$			20974.6i			1.08558i	0.839867	+	0.542792i	$0.182633\pi$
$139$			20974.6i			1.08558i	−0.839867	+	0.542792i	$0.817367\pi$
$140$		0			0
$141$	−7244.43			−0.364389
$142$	19599.4	+	11585.8i	0.972001	+	0.574579i
$143$			7617.58i			0.372516i
$144$	3698.99	−	5838.94i	0.178385	−	0.281585i
$145$		0			0
$146$	−9088.20	+	15374.3i	−0.426356	+	0.721256i
$147$			1062.54i			0.0491712i
$148$	−4703.07	−	8546.79i	−0.214713	−	0.390193i
$149$	−31793.5			−1.43207			−0.716037	−	0.698062i	$-0.754046\pi$
$149$	−31793.5			−1.43207			−0.716037	+	0.698062i	$0.754046\pi$
$150$		0			0
$151$		−	1630.74i		−	0.0715203i	−0.999360	−	0.0357602i	$-0.988615\pi$
$151$		−	1630.74i		−	0.0715203i	0.999360	−	0.0357602i	$-0.0113852\pi$
$152$	936.629	−	30381.7i	0.0405397	−	1.31500i
$153$	−10013.6			−0.427768
$154$	3933.70	−	6654.55i	0.165867	−	0.280593i
$155$		0			0
$156$	14655.1	−	8064.32i	0.602200	−	0.331374i
$157$	−33255.4			−1.34916			−0.674578	−	0.738203i	$-0.735675\pi$
$157$	−33255.4			−1.34916			−0.674578	+	0.738203i	$0.735675\pi$
$158$	10815.8	+	6393.53i	0.433255	+	0.256110i
$159$		−	15858.9i		−	0.627306i
$160$		0			0
$161$	−19723.2			−0.760895
$162$	1483.87	−	2510.22i	0.0565411	−	0.0956493i
$163$		−	22085.6i		−	0.831255i	−0.909535	−	0.415628i	$-0.863562\pi$
$163$		−	22085.6i		−	0.831255i	0.909535	−	0.415628i	$-0.136438\pi$
$164$	−5640.10	−	10249.6i	−0.209700	−	0.381084i
$165$		0			0
$166$	21029.2	+	12431.0i	0.763144	+	0.451117i
$167$		−	4028.51i		−	0.144448i	−0.997388	−	0.0722240i	$-0.976990\pi$
$167$		−	4028.51i		−	0.144448i	0.997388	−	0.0722240i	$-0.0230096\pi$
$168$	−16966.8	−	523.065i	−0.601148	−	0.0185326i
$169$	11920.2			0.417360
$170$		0			0
$171$		−	12823.4i		−	0.438541i
$172$	−25596.0	+	14084.8i	−0.865198	+	0.476095i
$173$	−23111.2			−0.772201			−0.386100	−	0.922457i	$-0.626178\pi$
$173$	−23111.2			−0.772201			−0.386100	+	0.922457i	$0.626178\pi$
$174$	20841.5	+	12320.0i	0.688383	+	0.406924i
$175$		0			0
$176$	8187.68	+	5186.92i	0.264323	+	0.167450i
$177$	−11602.4			−0.370342
$178$	−19363.9	+	32757.4i	−0.611157	+	1.03388i
$179$			47662.6i			1.48755i	0.668429	+	0.743776i	$0.266967\pi$
$179$			47662.6i			1.48755i	−0.668429	+	0.743776i	$0.733033\pi$
$180$		0			0
$181$	−2398.35			−0.0732073			−0.0366037	−	0.999330i	$-0.511654\pi$
$181$	−2398.35			−0.0732073			−0.0366037	+	0.999330i	$0.511654\pi$
$182$	−35363.5	−	20904.4i	−1.06761	−	0.631096i
$183$			28627.6i			0.854835i
$184$	762.011	−	24717.6i	0.0225074	−	0.730079i
$185$		0			0
$186$	15432.6	−	26106.9i	0.446080	−	0.754623i
$187$		−	14041.6i		−	0.401545i
$188$	−19543.5	+	10754.3i	−0.552952	+	0.304275i
$189$	−7161.27			−0.200478
$190$		0			0
$191$			53842.6i			1.47591i	0.674851	+	0.737954i	$0.264208\pi$
$191$			53842.6i			1.47591i	−0.674851	+	0.737954i	$0.735792\pi$
$192$	1311.04	−	21243.0i	0.0355641	−	0.576254i
$193$	34598.0			0.928831			0.464415	−	0.885618i	$-0.346264\pi$
$193$	34598.0			0.928831			0.464415	+	0.885618i	$0.346264\pi$
$194$	7097.76	−	12007.1i	0.188590	−	0.319032i
$195$		0			0
$196$	1577.33	+	2866.45i	0.0410592	+	0.0746160i
$197$	−14197.5			−0.365831			−0.182915	−	0.983129i	$-0.558553\pi$
$197$	−14197.5			−0.365831			−0.182915	+	0.983129i	$0.558553\pi$
$198$	3519.96	+	2080.76i	0.0897858	+	0.0530751i
$199$		−	64774.5i		−	1.63568i	−0.575447	−	0.817839i	$-0.695172\pi$
$199$		−	64774.5i		−	1.63568i	0.575447	−	0.817839i	$-0.304828\pi$
$200$		0			0
$201$	27708.2			0.685830
$202$	−19434.8	+	32877.4i	−0.476296	+	0.805738i
$203$		−	59457.6i		−	1.44283i
$204$	−27014.1	+	14865.1i	−0.649128	+	0.357197i
$205$		0			0
$206$	18994.6	+	11228.3i	0.447607	+	0.264594i
$207$		−	10432.7i		−	0.243475i
$208$	27564.2	−	43510.8i	0.637117	−	1.00570i
$209$	17981.6			0.411658
$210$		0			0
$211$			16618.2i			0.373267i	0.982430	+	0.186633i	$0.0597576\pi$
$211$			16618.2i			0.373267i	−0.982430	+	0.186633i	$0.940242\pi$
$212$	−23542.4	−	42783.2i	−0.523817	−	0.951922i
$213$	29576.1			0.651902
$214$	10065.1	+	5949.77i	0.219781	+	0.129919i
$215$		0			0
$216$	276.678	−	8974.69i	0.00593017	−	0.192359i
$217$	−74479.1			−1.58167
$218$	−44085.2	+	74577.9i	−0.927641	+	1.56927i
$219$			23200.3i			0.483732i
$220$		0			0
$221$	−74619.8			−1.52781
$222$	−10909.1	−	6448.68i	−0.221351	−	0.130847i
$223$			3438.26i			0.0691400i	0.999402	+	0.0345700i	$0.0110062\pi$
$223$			3438.26i			0.0691400i	−0.999402	+	0.0345700i	$0.988994\pi$
$224$	−46548.4	+	23776.0i	−0.927702	+	0.473851i
$225$		0			0
$226$	29694.9	−	50234.1i	0.581386	−	0.983517i
$227$			69197.7i			1.34289i	0.741055	+	0.671444i	$0.234326\pi$
$227$			69197.7i			1.34289i	−0.741055	+	0.671444i	$0.765674\pi$
$228$	−19036.2	−	34594.1i	−0.366193	−	0.665475i
$229$	−27160.9			−0.517933			−0.258966	−	0.965886i	$-0.583382\pi$
$229$	−27160.9			−0.517933			−0.258966	+	0.965886i	$0.583382\pi$
$230$		0			0
$231$		−	10041.9i		−	0.188188i
$232$	74513.7	+	2297.16i	1.38440	+	0.0426792i
$233$	−61634.9			−1.13531			−0.567655	−	0.823266i	$-0.692149\pi$
$233$	−61634.9			−1.13531			−0.567655	+	0.823266i	$0.692149\pi$
$234$	11057.5	−	18705.7i	0.201942	−	0.341620i
$235$		0			0
$236$	−31300.3	+	17223.7i	−0.561985	+	0.309245i
$237$	16321.3			0.290576
$238$	65186.2	+	38533.5i	1.15081	+	0.680276i
$239$		−	8898.70i		−	0.155787i	−0.996962	−	0.0778934i	$-0.975181\pi$
$239$		−	8898.70i		−	0.155787i	0.996962	−	0.0778934i	$-0.0248194\pi$
$240$		0			0
$241$	−13180.6			−0.226935			−0.113468	−	0.993542i	$-0.536196\pi$
$241$	−13180.6			−0.226935			−0.113468	+	0.993542i	$0.536196\pi$
$242$	26883.7	−	45478.5i	0.459049	−	0.776561i
$243$		−	3788.00i		−	0.0641500i
$244$	42497.4	+	77229.6i	0.713810	+	1.29719i
$245$		0			0
$246$	−13082.6	−	7733.51i	−0.216184	−	0.127793i
$247$		−	95557.7i		−	1.56629i
$248$	2877.52	−	93339.1i	0.0467860	−	1.51761i
$249$	31733.7			0.511825
$250$		0			0
$251$		−	104252.i		−	1.65476i	−0.561640	−	0.827382i	$-0.689829\pi$
$251$		−	104252.i		−	1.65476i	0.561640	−	0.827382i	$-0.310171\pi$
$252$	−19319.2	+	10630.8i	−0.304220	+	0.167404i
$253$	14629.3			0.228550
$254$	−76323.1	−	45116.9i	−1.18301	−	0.699313i
$255$		0			0
$256$	−27998.2	−	59254.2i	−0.427219	−	0.904148i
$257$	75052.8			1.13632			0.568160	−	0.822918i	$-0.307656\pi$
$257$	75052.8			1.13632			0.568160	+	0.822918i	$0.307656\pi$
$258$	−19312.6	+	32670.6i	−0.290135	+	0.490815i
$259$			31121.9i			0.463945i
$260$		0			0
$261$	31450.4			0.461685
$262$	88373.7	+	52240.3i	1.28742	+	0.761033i
$263$			10228.9i			0.147882i	0.997263	+	0.0739411i	$0.0235577\pi$
$263$			10228.9i			0.147882i	−0.997263	+	0.0739411i	$0.976442\pi$
$264$	12584.8	+	387.973i	0.180567	+	0.00556664i
$265$		0			0
$266$	−49345.8	+	83477.1i	−0.697408	+	1.17979i
$267$			49431.9i			0.693402i
$268$	74749.4	−	41132.6i	1.04073	−	0.572686i
$269$	−8355.99			−0.115476			−0.0577382	−	0.998332i	$-0.518389\pi$
$269$	−8355.99			−0.115476			−0.0577382	+	0.998332i	$0.518389\pi$
$270$		0			0
$271$		−	66166.8i		−	0.900952i	−0.892788	−	0.450476i	$-0.851254\pi$
$271$		−	66166.8i		−	0.900952i	0.892788	−	0.450476i	$-0.148746\pi$
$272$	−50809.7	+	80204.3i	−0.686766	+	1.08408i
$273$	−53364.6			−0.716024
$274$	1080.61	−	1828.04i	0.0143935	−	0.0243491i
$275$		0			0
$276$	−15487.2	−	28144.6i	−0.203308	−	0.369468i
$277$	117613.			1.53283			0.766417	−	0.642343i	$-0.222038\pi$
$277$	117613.			1.53283			0.766417	+	0.642343i	$0.222038\pi$
$278$	72223.3	+	42693.3i	0.934518	+	0.552421i
$279$		−	39396.1i		−	0.506110i
$280$		0			0
$281$	84024.3			1.06412			0.532062	−	0.846705i	$-0.321417\pi$
$281$	84024.3			1.06412			0.532062	+	0.846705i	$0.321417\pi$
$282$	−14745.9	+	24945.3i	−0.185427	+	0.313682i
$283$		−	61114.9i		−	0.763087i	−0.924351	−	0.381544i	$-0.875393\pi$
$283$		−	61114.9i		−	0.763087i	0.924351	−	0.381544i	$-0.124607\pi$
$284$	79788.5	−	43905.5i	0.989245	−	0.544355i
$285$		0			0
$286$	26230.2	+	15505.4i	0.320678	+	0.189562i
$287$			37322.6i			0.453115i
$288$	−12576.4	−	24622.0i	−0.151626	−	0.296851i
$289$	54027.2			0.646870
$290$		0			0
$291$		−	18119.1i		−	0.213969i
$292$	34440.6	+	62588.1i	0.403929	+	0.734051i
$293$	64656.8			0.753146			0.376573	−	0.926387i	$-0.377102\pi$
$293$	64656.8			0.753146			0.376573	+	0.926387i	$0.377102\pi$
$294$	3658.72	+	2162.78i	0.0423287	+	0.0250217i
$295$		0			0
$296$	−39002.8	−	1202.41i	−0.445156	−	0.0137236i
$297$	5311.73			0.0602175
$298$	−64715.0	+	109477.i	−0.728740	+	1.23279i
$299$		−	77742.6i		−	0.869594i
$300$		0			0
$301$	93204.2			1.02873
$302$	−5615.23	−	3319.33i	−0.0615678	−	0.0363946i
$303$			49612.9i			0.540393i
$304$	−102709.	−	65066.6i	−1.11138	−	0.704062i
$305$		0			0
$306$	−20382.5	+	34480.6i	−0.217678	+	0.368241i
$307$		−	144462.i		−	1.53277i	−0.642381	−	0.766386i	$-0.722053\pi$
$307$		−	144462.i		−	1.53277i	0.642381	−	0.766386i	$-0.277947\pi$
$308$	−14907.1	−	27090.4i	−0.157142	−	0.285571i
$309$	28663.5			0.300201
$310$		0			0
$311$			109152.i			1.12852i	0.825597	+	0.564260i	$0.190839\pi$
$311$			109152.i			1.12852i	−0.825597	+	0.564260i	$0.809161\pi$
$312$	2061.76	−	66877.9i	0.0211801	−	0.687026i
$313$	37361.4			0.381360			0.190680	−	0.981652i	$-0.438931\pi$
$313$	37361.4			0.381360			0.190680	+	0.981652i	$0.438931\pi$
$314$	−67690.7	+	114511.i	−0.686546	+	1.16141i
$315$		0			0
$316$	44030.6	−	24228.9i	0.440941	−	0.242638i
$317$	−31439.8			−0.312868			−0.156434	−	0.987688i	$-0.550000\pi$
$317$	−31439.8			−0.312868			−0.156434	+	0.987688i	$0.550000\pi$
$318$	−54608.2	−	32280.5i	−0.540012	−	0.319217i
$319$			44101.5i			0.433383i
$320$		0			0
$321$	15188.5			0.147403
$322$	−40146.1	+	67914.2i	−0.387197	+	0.655011i
$323$			176143.i			1.68834i
$324$	−5623.24	−	10219.0i	−0.0535669	−	0.0973461i
$325$		0			0
$326$	−76049.1	−	44954.9i	−0.715581	−	0.423001i
$327$			112540.i			1.05248i
$328$	−46773.7	−	1441.97i	−0.434764	−	0.0134032i
$329$	71165.0			0.657468
$330$		0			0
$331$		−	60318.3i		−	0.550545i	−0.961366	−	0.275273i	$-0.911232\pi$
$331$		−	60318.3i		−	0.550545i	0.961366	−	0.275273i	$-0.0887681\pi$
$332$	85609.0	−	47108.3i	0.776682	−	0.427387i
$333$	−16462.1			−0.148456
$334$	−13871.7	−	8199.95i	−0.124347	−	0.0735052i
$335$		0			0
$336$	−36336.7	+	57358.3i	−0.321860	+	0.508063i
$337$	−35916.7			−0.316254			−0.158127	−	0.987419i	$-0.550546\pi$
$337$	−35916.7			−0.316254			−0.158127	+	0.987419i	$0.550546\pi$
$338$	24263.4	−	41045.8i	0.212382	−	0.359282i
$339$		−	75804.7i		−	0.659625i
$340$		0			0
$341$	55243.4			0.475085
$342$	−44155.7	−	26101.7i	−0.377515	−	0.223160i
$343$			112119.i			0.952994i
$344$	−3600.98	+	116806.i	−0.0304301	+	0.987070i
$345$		0			0
$346$	−47042.4	+	79580.5i	−0.392950	+	0.664744i
$347$			98807.1i			0.820596i	0.911952	+	0.410298i	$0.134575\pi$
$347$			98807.1i			0.820596i	−0.911952	+	0.410298i	$0.865425\pi$
$348$	84844.9	−	46687.8i	0.700595	−	0.385519i
$349$	73220.1			0.601145			0.300573	−	0.953759i	$-0.402822\pi$
$349$	73220.1			0.601145			0.300573	+	0.953759i	$0.402822\pi$
$350$		0			0
$351$		−	28227.5i		−	0.229118i
$352$	34526.4	−	17635.3i	0.278654	−	0.142331i
$353$	78557.6			0.630433			0.315216	−	0.949020i	$-0.397923\pi$
$353$	78557.6			0.630433			0.315216	+	0.949020i	$0.397923\pi$
$354$	−23616.5	+	39951.5i	−0.188456	+	0.318806i
$355$		0			0
$356$	73381.2	+	133354.i	0.579009	+	1.05222i
$357$	98368.0			0.771822
$358$	164120.	+	97016.3i	1.28055	+	0.756970i
$359$		−	50142.5i		−	0.389060i	−0.980897	−	0.194530i	$-0.937682\pi$
$359$		−	50142.5i		−	0.389060i	0.980897	−	0.194530i	$-0.0623182\pi$
$360$		0			0
$361$	−95247.0			−0.730864
$362$	−4881.78	+	8258.40i	−0.0372530	+	0.0630200i
$363$		−	68628.5i		−	0.520824i
$364$	−143963.	+	79219.2i	−1.08655	+	0.597899i
$365$		0			0
$366$	98575.4	+	58270.9i	0.735879	+	0.435000i
$367$			165475.i			1.22857i	0.789085	+	0.614284i	$0.210555\pi$
$367$			165475.i			1.22857i	−0.789085	+	0.614284i	$0.789445\pi$
$368$	−83560.8	−	52936.0i	−0.617031	−	0.390891i
$369$	−19742.0			−0.144990
$370$		0			0
$371$			155789.i			1.13185i
$372$	−58483.2	−	106280.i	−0.422615	−	0.768010i
$373$	−56871.4			−0.408767			−0.204384	−	0.978891i	$-0.565519\pi$
$373$	−56871.4			−0.408767			−0.204384	+	0.978891i	$0.565519\pi$
$374$	−48350.6	−	28581.5i	−0.345668	−	0.204334i
$375$		0			0
$376$	−2749.48	+	89185.8i	−0.0194480	+	0.630841i
$377$	234363.			1.64895
$378$	−14576.6	+	24658.9i	−0.102017	+	0.172580i
$379$		−	166749.i		−	1.16088i	−0.814305	−	0.580438i	$-0.802882\pi$
$379$		−	166749.i		−	1.16088i	0.814305	−	0.580438i	$-0.197118\pi$
$380$		0			0
$381$	−115174.			−0.793421
$382$	185400.	+	109596.i	1.27053	+	0.751046i
$383$		−	10594.7i		−	0.0722257i	−0.999348	−	0.0361128i	$-0.988502\pi$
$383$		−	10594.7i		−	0.0722257i	0.999348	−	0.0361128i	$-0.0114976\pi$
$384$	−70479.1	−	47754.1i	−0.477967	−	0.323854i
$385$		0			0
$386$	70423.6	−	119134.i	0.472654	−	0.799578i
$387$			49300.9i			0.329180i
$388$	−26897.6	−	48880.5i	−0.178669	−	0.324692i
$389$	251272.			1.66052			0.830262	−	0.557373i	$-0.188191\pi$
$389$	251272.			1.66052			0.830262	+	0.557373i	$0.188191\pi$
$390$		0			0
$391$			143304.i			0.937359i
$392$	13080.9	+	403.267i	0.0851265	+	0.00262434i
$393$	133359.			0.863447
$394$	−28898.8	+	48887.4i	−0.186160	+	0.314923i
$395$		0			0
$396$	14329.6	−	7885.21i	0.0913786	−	0.0502832i
$397$	−145938.			−0.925952			−0.462976	−	0.886371i	$-0.653218\pi$
$397$	−145938.			−0.925952			−0.462976	+	0.886371i	$0.653218\pi$
$398$	−223043.	−	131847.i	−1.40806	−	0.832348i
$399$			125969.i			0.791260i
$400$		0			0
$401$	−636.947			−0.00396109			−0.00198054	−	0.999998i	$-0.500630\pi$
$401$	−636.947			−0.00396109			−0.00198054	+	0.999998i	$0.500630\pi$
$402$	56399.5	−	95409.8i	0.348998	−	0.590392i
$403$		−	293573.i		−	1.80762i
$404$	73649.9	+	133842.i	0.451242	+	0.820032i
$405$		0			0
$406$	−204735.	−	121025.i	−1.24205	−	0.734213i
$407$		−	23084.1i		−	0.139355i
$408$	−3800.48	+	123277.i	−0.0228306	+	0.740564i
$409$	280113.			1.67450			0.837252	−	0.546816i	$-0.184160\pi$
$409$	280113.			1.67450			0.837252	+	0.546816i	$0.184160\pi$
$410$		0			0
$411$		−	2758.56i		−	0.0163305i
$412$	77326.4	−	42550.6i	0.455547	−	0.250675i
$413$	113976.			0.668208
$414$	−35923.6	−	21235.5i	−0.209594	−	0.123897i
$415$		0			0
$416$	−93717.5	−	183479.i	−0.541544	−	1.06023i
$417$	108987.			0.626762
$418$	36601.3	−	61917.5i	0.209480	−	0.354373i
$419$			7136.79i			0.0406513i	0.999793	+	0.0203257i	$0.00647031\pi$
$419$			7136.79i			0.0406513i	−0.999793	+	0.0203257i	$0.993530\pi$
$420$		0			0
$421$	127649.			0.720200			0.360100	−	0.932914i	$-0.382743\pi$
$421$	127649.			0.720200			0.360100	+	0.932914i	$0.382743\pi$
$422$	57222.7	+	33826.0i	0.321324	+	0.189944i
$423$			37643.1i			0.210380i
$424$	−195239.	−	6018.95i	−1.08601	−	0.0334803i
$425$		0			0
$426$	60201.6	−	101842.i	0.331733	−	0.561185i
$427$		−	281221.i		−	1.54238i
$428$	40974.6	−	22547.2i	0.223680	−	0.123085i
$429$	39582.1			0.215072
$430$		0			0
$431$		−	295330.i		−	1.58984i	−0.606717	−	0.794918i	$-0.707514\pi$
$431$		−	295330.i		−	1.58984i	0.606717	−	0.794918i	$-0.292486\pi$
$432$	−30340.0	−	19220.5i	−0.162573	−	0.102991i
$433$	−103955.			−0.554457			−0.277228	−	0.960804i	$-0.589416\pi$
$433$	−103955.			−0.554457			−0.277228	+	0.960804i	$0.589416\pi$
$434$	−151601.	+	256459.i	−0.804863	+	1.36157i
$435$		0			0
$436$	167065.	+	303604.i	0.878845	+	1.59711i
$437$	−183515.			−0.960966
$438$	79887.2	+	47223.7i	0.416417	+	0.246157i
$439$		−	45639.3i		−	0.236815i	−0.992965	−	0.118408i	$-0.962221\pi$
$439$		−	45639.3i		−	0.236815i	0.992965	−	0.118408i	$-0.0377790\pi$
$440$		0			0
$441$	5521.12			0.0283890
$442$	−151887.	+	256944.i	−0.777458	+	1.31521i
$443$			126637.i			0.645290i	0.946520	+	0.322645i	$0.104572\pi$
$443$			126637.i			0.645290i	−0.946520	+	0.322645i	$0.895428\pi$
$444$	−44410.4	+	24437.9i	−0.225278	+	0.123964i
$445$		0			0
$446$	11839.2	+	6998.52i	0.0595187	+	0.0351833i
$447$			165204.i			0.826808i
$448$	−12878.9	+	208679.i	−0.0641684	+	1.03974i
$449$	−98148.3			−0.486844			−0.243422	−	0.969920i	$-0.578270\pi$
$449$	−98148.3			−0.486844			−0.243422	+	0.969920i	$0.578270\pi$
$450$		0			0
$451$		−	27683.3i		−	0.136102i
$452$	−112531.	−	204501.i	−0.550804	−	1.00096i
$453$	−8473.55			−0.0412923
$454$	238274.	+	140851.i	1.15602	+	0.683356i
$455$		0			0
$456$	−157868.	−	4866.87i	−0.759215	−	0.0234056i
$457$	−323140.			−1.54724			−0.773622	−	0.633648i	$-0.781557\pi$
$457$	−323140.			−1.54724			−0.773622	+	0.633648i	$0.781557\pi$
$458$	−55285.5	+	93525.1i	−0.263560	+	0.445859i
$459$			52032.3i			0.246972i
$460$		0			0
$461$	101678.			0.478437			0.239218	−	0.970966i	$-0.423109\pi$
$461$	101678.			0.478437			0.239218	+	0.970966i	$0.423109\pi$
$462$	−34578.1	−	20440.1i	−0.162001	−	0.0957634i
$463$		−	155652.i		−	0.726094i	−0.931771	−	0.363047i	$-0.881736\pi$
$463$		−	155652.i		−	0.726094i	0.931771	−	0.363047i	$-0.118264\pi$
$464$	159581.	−	251903.i	0.741218	−	1.17003i
$465$		0			0
$466$	−125457.	+	212232.i	−0.577726	+	0.977325i
$467$		−	299837.i		−	1.37484i	−0.726262	−	0.687418i	$-0.758744\pi$
$467$		−	299837.i		−	1.37484i	0.726262	−	0.687418i	$-0.241256\pi$
$468$	−41903.5	−	76150.3i	−0.191319	−	0.347680i
$469$	−272189.			−1.23744
$470$		0			0
$471$			172800.i			0.778936i
$472$	−4403.48	+	142837.i	−0.0197657	+	0.641146i
$473$	−69132.4			−0.309001
$474$	33221.8	−	56200.5i	0.147865	−	0.250140i
$475$		0			0
$476$	265371.	−	146026.i	1.17122	−	0.644492i
$477$	−82405.4			−0.362175
$478$	−30641.5	−	18113.1i	−0.134108	−	0.0792753i
$479$		−	178034.i		−	0.775948i	−0.921670	−	0.387974i	$-0.873175\pi$
$479$		−	178034.i		−	0.775948i	0.921670	−	0.387974i	$-0.126825\pi$
$480$		0			0
$481$	−122673.			−0.530223
$482$	−26828.9	+	45385.8i	−0.115481	+	0.195356i
$483$			102485.i			0.439303i
$484$	−101878.	−	185141.i	−0.434902	−	0.790338i
$485$		0			0
$486$	−13043.5	−	7710.39i	−0.0552231	−	0.0326440i
$487$		−	318199.i		−	1.34165i	−0.741614	−	0.670827i	$-0.765939\pi$
$487$		−	318199.i		−	1.34165i	0.741614	−	0.670827i	$-0.234061\pi$
$488$	352433.	+	10865.1i	1.47992	+	0.0456239i
$489$	−114760.			−0.479926
$490$		0			0
$491$		−	167000.i		−	0.692712i	−0.938103	−	0.346356i	$-0.887419\pi$
$491$		−	167000.i		−	0.692712i	0.938103	−	0.346356i	$-0.112581\pi$
$492$	−53258.7	+	29306.8i	−0.220019	+	0.121071i
$493$	−432006.			−1.77745
$494$	−329041.	−	194506.i	−1.34833	−	0.797037i
$495$		0			0
$496$	−315544.	−	199898.i	−1.28262	−	0.812542i
$497$	−290539.			−1.17623
$498$	64593.3	−	109271.i	0.260453	−	0.440601i
$499$		−	26900.7i		−	0.108034i	−0.998540	−	0.0540172i	$-0.982797\pi$
$499$		−	26900.7i		−	0.108034i	0.998540	−	0.0540172i	$-0.0172026\pi$
$500$		0			0
$501$	−20932.7			−0.0833971
$502$	−358978.	−	212202.i	−1.42449	−	0.842060i
$503$		−	217917.i		−	0.861301i	−0.902519	−	0.430650i	$-0.858284\pi$
$503$		−	217917.i		−	0.861301i	0.902519	−	0.430650i	$-0.141716\pi$
$504$	−2717.92	+	88162.1i	−0.0106998	+	0.347073i
$505$		0			0
$506$	29777.6	−	50374.0i	0.116302	−	0.196746i
$507$		−	61939.3i		−	0.240963i
$508$	−310708.	+	170974.i	−1.20400	+	0.662527i
$509$	−294895.			−1.13823			−0.569117	−	0.822256i	$-0.692715\pi$
$509$	−294895.			−1.13823			−0.569117	+	0.822256i	$0.692715\pi$
$510$		0			0
$511$		−	227906.i		−	0.872798i
$512$	−261024.	−	24202.5i	−0.995729	−	0.0923252i
$513$	−66632.2			−0.253192
$514$	152768.	−	258435.i	0.578239	−	0.978193i
$515$		0			0
$516$	73186.7	+	133001.i	0.274874	+	0.499522i
$517$	−52785.2			−0.197484
$518$	107164.	+	63348.1i	0.399384	+	0.236088i
$519$			120089.i			0.445830i
$520$		0			0
$521$	247783.			0.912842			0.456421	−	0.889764i	$-0.349131\pi$
$521$	247783.			0.912842			0.456421	+	0.889764i	$0.349131\pi$
$522$	64016.7	−	108296.i	0.234938	−	0.397438i
$523$			90277.4i			0.330047i	0.986290	+	0.165023i	$0.0527700\pi$
$523$			90277.4i			0.330047i	−0.986290	+	0.165023i	$0.947230\pi$
$524$	359766.	−	197970.i	1.31026	−	0.721001i
$525$		0			0
$526$	35221.8	+	20820.6i	0.127303	+	0.0752528i
$527$			541150.i			1.94848i
$528$	26952.0	−	42544.4i	0.0966771	−	0.152607i
$529$	130540.			0.466477
$530$		0			0
$531$			60288.0i			0.213817i
$532$	187000.	+	339832.i	0.660722	+	1.20072i
$533$	−147114.			−0.517846
$534$	170213.	+	100618.i	0.596911	+	0.352852i
$535$		0			0
$536$	10516.1	−	341115.i	0.0366038	−	1.18733i
$537$	247662.			0.858838
$538$	−17008.5	+	28772.8i	−0.0587625	+	0.0994071i
$539$			7742.01i			0.0266487i
$540$		0			0
$541$	153234.			0.523553			0.261777	−	0.965128i	$-0.415692\pi$
$541$	153234.			0.523553			0.261777	+	0.965128i	$0.415692\pi$
$542$	−227837.	−	134681.i	−0.775579	−	0.458468i
$543$			12462.2i			0.0422663i
$544$	172751.	+	338211.i	0.583745	+	1.14285i
$545$		0			0
$546$	−108623.	+	183754.i	−0.364363	+	0.616385i
$547$		−	432810.i		−	1.44652i	−0.690578	−	0.723258i	$-0.742644\pi$
$547$		−	432810.i		−	1.44652i	0.690578	−	0.723258i	$-0.257356\pi$
$548$	−4095.06	−	7441.86i	−0.0136364	−	0.0247811i
$549$	148753.			0.493539
$550$		0			0
$551$		−	553224.i		−	1.82221i
$552$	−128436.	−	3959.52i	−0.421512	−	0.0129947i
$553$	−160331.			−0.524286
$554$	239399.	−	404985.i	0.780013	−	1.31953i
$555$		0			0
$556$	294018.	−	161790.i	0.951097	−	0.523363i
$557$	590478.			1.90324			0.951619	−	0.307281i	$-0.0994191\pi$
$557$	590478.			1.90324			0.951619	+	0.307281i	$0.0994191\pi$
$558$	−135656.	−	80190.1i	−0.435682	−	0.257544i
$559$			367382.i			1.17569i
$560$		0			0
$561$	−72962.5			−0.231832
$562$	171030.	−	289327.i	0.541501	−	0.916044i
$563$			200378.i			0.632169i	0.948731	+	0.316084i	$0.102368\pi$
$563$			200378.i			0.632169i	−0.948731	+	0.316084i	$0.897632\pi$
$564$	55880.9	+	101551.i	0.175673	+	0.319247i
$565$		0			0
$566$	−210441.	−	124398.i	−0.656898	−	0.388312i
$567$			37211.0i			0.115746i
$568$	11225.1	−	364110.i	0.0347930	−	1.12859i
$569$	102871.			0.317738			0.158869	−	0.987300i	$-0.449215\pi$
$569$	102871.			0.317738			0.158869	+	0.987300i	$0.449215\pi$
$570$		0			0
$571$			478647.i			1.46806i	0.679118	+	0.734029i	$0.262362\pi$
$571$			478647.i			1.46806i	−0.679118	+	0.734029i	$0.737638\pi$
$572$	106782.	−	58759.3i	0.326367	−	0.179591i
$573$	279775.			0.852116
$574$	128516.	+	75969.5i	0.390061	+	0.230577i
$575$		0			0
$576$	−110382.	−	6812.34i	−0.332700	−	0.0205330i
$577$	−299722.			−0.900257			−0.450128	−	0.892964i	$-0.648622\pi$
$577$	−299722.			−0.900257			−0.450128	+	0.892964i	$0.648622\pi$
$578$	109971.	−	186036.i	0.329173	−	0.556854i
$579$		−	179777.i		−	0.536261i
$580$		0			0
$581$	−311733.			−0.923487
$582$	−62390.7	−	36881.0i	−0.184193	−	0.108882i
$583$		−	115553.i		−	0.339974i
$584$	285617.	+	8805.22i	0.837450	+	0.0258175i
$585$		0			0
$586$	131608.	−	222638.i	0.383253	−	0.648341i
$587$			77803.7i			0.225800i	0.993606	+	0.112900i	$0.0360140\pi$
$587$			77803.7i			0.225800i	−0.993606	+	0.112900i	$0.963986\pi$
$588$	14894.5	−	8196.05i	0.0430796	−	0.0237055i
$589$	−692993.			−1.99755
$590$		0			0
$591$			73772.5i			0.211213i
$592$	−83529.8	+	131854.i	−0.238340	+	0.376226i
$593$	219310.			0.623662			0.311831	−	0.950138i	$-0.399058\pi$
$593$	219310.			0.623662			0.311831	+	0.950138i	$0.399058\pi$
$594$	10811.9	−	18290.3i	0.0306429	−	0.0518379i
$595$		0			0
$596$	245243.	+	445676.i	0.690406	+	1.25466i
$597$	−336578.			−0.944360
$598$	−267697.	−	158243.i	−0.748584	−	0.442510i
$599$			81343.8i			0.226710i	0.993555	+	0.113355i	$0.0361598\pi$
$599$			81343.8i			0.226710i	−0.993555	+	0.113355i	$0.963840\pi$
$600$		0			0
$601$	−442777.			−1.22585			−0.612924	−	0.790142i	$-0.710007\pi$
$601$	−442777.			−1.22585			−0.612924	+	0.790142i	$0.710007\pi$
$602$	189715.	−	320937.i	0.523491	−	0.885578i
$603$		−	143976.i		−	0.395964i
$604$	−22859.4	+	12578.9i	−0.0626600	+	0.0344801i
$605$		0			0
$606$	170836.	+	100986.i	0.465193	+	0.274990i
$607$			325514.i			0.883472i	0.897145	+	0.441736i	$0.145637\pi$
$607$			325514.i			0.883472i	−0.897145	+	0.441736i	$0.854363\pi$
$608$	−433111.	+	221224.i	−1.17163	+	0.598446i
$609$	−308950.			−0.833018
$610$		0			0
$611$			280510.i			0.751392i
$612$	77241.5	+	140369.i	0.206228	+	0.374774i
$613$	370093.			0.984896			0.492448	−	0.870342i	$-0.336102\pi$
$613$	370093.			0.984896			0.492448	+	0.870342i	$0.336102\pi$
$614$	−497437.	−	294050.i	−1.31948	−	0.779982i
$615$		0			0
$616$	−123626.	−	3811.22i	−0.325797	−	0.0100439i
$617$	64817.4			0.170263			0.0851317	−	0.996370i	$-0.472869\pi$
$617$	64817.4			0.170263			0.0851317	+	0.996370i	$0.472869\pi$
$618$	58343.9	−	98699.0i	0.152763	−	0.258426i
$619$			499198.i			1.30284i	0.758716	+	0.651421i	$0.225827\pi$
$619$			499198.i			1.30284i	−0.758716	+	0.651421i	$0.774173\pi$
$620$		0			0
$621$	−54209.8			−0.140571
$622$	375850.	+	222176.i	0.971480	+	0.574271i
$623$		−	485590.i		−	1.25111i
$624$	−226089.	−	143228.i	−0.580644	−	0.367840i
$625$		0			0
$626$	76048.5	−	128649.i	0.194063	−	0.328291i
$627$		−	93435.3i		−	0.237671i
$628$	256520.	+	466168.i	0.650432	+	1.18202i
$629$	226125.			0.571542
$630$		0			0
$631$			541326.i			1.35956i	0.733414	+	0.679782i	$0.237926\pi$
$631$			541326.i			1.35956i	−0.733414	+	0.679782i	$0.762074\pi$
$632$	6194.45	−	200931.i	0.0155085	−	0.503053i
$633$	86350.7			0.215506
$634$	−63995.1	+	108259.i	−0.159209	+	0.269330i
$635$		0			0
$636$	−222308.	+	122330.i	−0.549592	+	0.302426i
$637$	41142.5			0.101394
$638$	151858.	+	89767.7i	0.373075	+	0.220536i
$639$		−	153682.i		−	0.376376i
$640$		0			0
$641$	−38288.9			−0.0931873			−0.0465936	−	0.998914i	$-0.514837\pi$
$641$	−38288.9			−0.0931873			−0.0465936	+	0.998914i	$0.514837\pi$
$642$	30915.9	−	52299.7i	0.0750088	−	0.126891i
$643$			570529.i			1.37993i	0.723845	+	0.689963i	$0.242373\pi$
$643$			570529.i			1.37993i	−0.723845	+	0.689963i	$0.757627\pi$
$644$	152137.	+	276476.i	0.366829	+	0.666631i
$645$		0			0
$646$	606527.	+	358536.i	1.45340	+	0.859148i
$647$			415706.i			0.993066i	0.868018	+	0.496533i	$0.165394\pi$
$647$			415706.i			0.993066i	−0.868018	+	0.496533i	$0.834606\pi$
$648$	−46633.8	−	1437.66i	−0.111058	−	0.00342379i
$649$	−84539.1			−0.200710
$650$		0			0
$651$			387005.i			0.913175i
$652$	−309593.	+	170361.i	−0.728275	+	0.400750i
$653$	91144.2			0.213748			0.106874	−	0.994273i	$-0.465916\pi$
$653$	91144.2			0.213748			0.106874	+	0.994273i	$0.465916\pi$
$654$	387518.	+	229073.i	0.906017	+	0.535574i
$655$		0			0
$656$	−100172.	+	158124.i	−0.232777	+	0.367443i
$657$	120552.			0.279283
$658$	144855.	−	245048.i	0.334566	−	0.565977i
$659$			25068.2i			0.0577235i	0.999583	+	0.0288618i	$0.00918826\pi$
$659$			25068.2i			0.0577235i	−0.999583	+	0.0288618i	$0.990812\pi$
$660$		0			0
$661$	−183147.			−0.419177			−0.209589	−	0.977790i	$-0.567212\pi$
$661$	−183147.			−0.419177			−0.209589	+	0.977790i	$0.567212\pi$
$662$	−207698.	−	122777.i	−0.473933	−	0.280156i
$663$			387736.i			0.882082i
$664$	12043.9	−	390672.i	0.0273169	−	0.886086i
$665$		0			0
$666$	−33508.3	+	56685.2i	−0.0755447	+	0.127797i
$667$		−	450085.i		−	1.01168i
$668$	−56471.0	+	31074.5i	−0.126553	+	0.0696387i
$669$	17865.7			0.0399180
$670$		0			0
$671$			208590.i			0.463285i
$672$	123544.	+	241873.i	0.273578	+	0.535609i
$673$	292902.			0.646684			0.323342	−	0.946282i	$-0.395194\pi$
$673$	292902.			0.646684			0.323342	+	0.946282i	$0.395194\pi$
$674$	−73107.7	+	123675.i	−0.160932	+	0.272246i
$675$		0			0
$676$	−91948.4	−	167096.i	−0.201210	−	0.365656i
$677$	−264707.			−0.577548			−0.288774	−	0.957397i	$-0.593248\pi$
$677$	−264707.			−0.577548			−0.288774	+	0.957397i	$0.593248\pi$
$678$	−261024.	−	154299.i	−0.567834	−	0.335663i
$679$			177991.i			0.386064i
$680$		0			0
$681$	359562.			0.775317
$682$	112447.	−	190224.i	0.241757	−	0.408974i
$683$		−	202073.i		−	0.433178i	−0.976263	−	0.216589i	$-0.930507\pi$
$683$		−	202073.i		−	0.433178i	0.976263	−	0.216589i	$-0.0694932\pi$
$684$	−179756.	+	98914.9i	−0.384212	+	0.211422i
$685$		0			0
$686$	386067.	+	228216.i	0.820378	+	0.484950i
$687$			141132.i			0.299029i
$688$	394877.	+	250156.i	0.834228	+	0.528486i
$689$	−614071.			−1.29354
$690$		0			0
$691$			105012.i			0.219928i	0.993936	+	0.109964i	$0.0350736\pi$
$691$			105012.i			0.219928i	−0.993936	+	0.109964i	$0.964926\pi$
$692$	178271.	+	323969.i	0.372280	+	0.676537i
$693$	−52179.3			−0.108651
$694$	340230.	+	201120.i	0.706404	+	0.417577i
$695$		0			0
$696$	11936.4	−	387185.i	0.0246408	−	0.799281i
$697$	271179.			0.558200
$698$	149038.	−	252124.i	0.305905	−	0.517492i
$699$			320264.i			0.655472i
$700$		0			0
$701$	−240544.			−0.489506			−0.244753	−	0.969585i	$-0.578707\pi$
$701$	−240544.			−0.489506			−0.244753	+	0.969585i	$0.578707\pi$
$702$	−97197.8	−	57456.5i	−0.197234	−	0.116591i
$703$			289575.i			0.585936i
$704$	9552.63	−	154784.i	0.0192743	−	0.312305i
$705$		0			0
$706$	159902.	−	270503.i	0.320808	−	0.542704i
$707$		−	487368.i		−	0.975031i
$708$	89497.0	+	162641.i	0.178543	+	0.324462i
$709$	−65769.2			−0.130837			−0.0654184	−	0.997858i	$-0.520838\pi$
$709$	−65769.2			−0.130837			−0.0654184	+	0.997858i	$0.520838\pi$
$710$		0			0
$711$		−	84808.2i		−	0.167764i
$712$	608555.	+	18761.0i	1.20044	+	0.0370079i
$713$	−563796.			−1.10903
$714$	200226.	−	338718.i	0.392757	−	0.664418i
$715$		0			0
$716$	668127.	−	367652.i	1.30327	−	0.717152i
$717$	−46239.0			−0.0899436
$718$	−172659.	−	102064.i	−0.334920	−	0.197981i
$719$			793740.i			1.53540i	0.640812	+	0.767698i	$0.278598\pi$
$719$			793740.i			1.53540i	−0.640812	+	0.767698i	$0.721402\pi$
$720$		0			0
$721$	−281573.			−0.541652
$722$	−193873.	+	327971.i	−0.371915	+	0.629160i
$723$			68488.5i			0.131021i
$724$	18500.0	+	33619.6i	0.0352934	+	0.0641380i
$725$		0			0
$726$	−236313.	−	139692.i	−0.448348	−	0.265032i
$727$			1.00277e6i			1.89728i	0.316362	+	0.948639i	$0.397539\pi$
$727$			1.00277e6i			1.89728i	−0.316362	+	0.948639i	$0.602461\pi$
$728$	−20253.5	+	656969.i	−0.0382153	+	1.23960i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	677203.i		−	1.26731i
$732$	401297.	−	220823.i	0.748934	−	0.412118i
$733$	323556.			0.602201			0.301100	−	0.953592i	$-0.402646\pi$
$733$	323556.			0.602201			0.301100	+	0.953592i	$0.402646\pi$
$734$	569791.	+	336820.i	1.05760	+	0.625181i
$735$		0			0
$736$	−352365.	+	179981.i	−0.650484	+	0.332254i
$737$	201891.			0.371691
$738$	−40184.5	+	67979.1i	−0.0737812	+	0.124814i
$739$		−	954629.i		−	1.74802i	−0.485911	−	0.874008i	$-0.661512\pi$
$739$		−	954629.i		−	1.74802i	0.485911	−	0.874008i	$-0.338488\pi$
$740$		0			0
$741$	−496532.			−0.904297
$742$	536439.	+	317105.i	0.974345	+	0.575964i
$743$			796623.i			1.44303i	0.692399	+	0.721515i	$0.256554\pi$
$743$			796623.i			1.44303i	−0.692399	+	0.721515i	$0.743446\pi$
$744$	−485004.	−	14952.1i	−0.876193	−	0.0270119i
$745$		0			0
$746$	−115761.	+	195830.i	−0.208010	+	0.351885i
$747$		−	164893.i		−	0.295502i
$748$	−196833.	+	108312.i	−0.351800	+	0.193586i
$749$	−149203.			−0.265959
$750$		0			0
$751$		−	294285.i		−	0.521782i	−0.965368	−	0.260891i	$-0.915984\pi$
$751$		−	294285.i		−	0.521782i	0.965368	−	0.260891i	$-0.0840163\pi$
$752$	301504.	+	191003.i	0.533159	+	0.337758i
$753$	−541708.			−0.955378
$754$	477042.	−	807000.i	0.839100	−	1.41949i
$755$		0			0
$756$	55239.4	+	100386.i	0.0966509	+	0.175642i
$757$	859620.			1.50008			0.750041	−	0.661391i	$-0.230034\pi$
$757$	859620.			1.50008			0.750041	+	0.661391i	$0.230034\pi$
$758$	−574180.	−	339415.i	−0.999332	−	0.590735i
$759$		−	76015.9i		−	0.131953i
$760$		0			0
$761$	682493.			1.17850			0.589249	−	0.807951i	$-0.299424\pi$
$761$	682493.			1.17850			0.589249	+	0.807951i	$0.299424\pi$
$762$	−234434.	+	396586.i	−0.403748	+	0.683011i
$763$		−	1.10553e6i		−	1.89898i
$764$	754757.	−	415323.i	1.29307	−	0.711539i
$765$		0			0
$766$	−36481.5	−	21565.3i	−0.0621750	−	0.0367535i
$767$			449256.i			0.763666i
$768$	−307894.	+	145483.i	−0.522010	+	0.246655i
$769$	−452888.			−0.765840			−0.382920	−	0.923781i	$-0.625082\pi$
$769$	−452888.			−0.765840			−0.382920	+	0.923781i	$0.625082\pi$
$770$		0			0
$771$		−	389986.i		−	0.656055i
$772$	−266877.	−	484989.i	−0.447792	−	0.813762i
$773$	30549.1			0.0511257			0.0255628	−	0.999673i	$-0.491862\pi$
$773$	30549.1			0.0511257			0.0255628	+	0.999673i	$0.491862\pi$
$774$	169761.	+	100351.i	0.283372	+	0.167510i
$775$		0			0
$776$	−223063.	−	6876.75i	−0.370429	−	0.0114198i
$777$	161714.			0.267859
$778$	511460.	−	865224.i	0.844991	−	1.42945i
$779$			347269.i			0.572258i
$780$		0			0
$781$	215501.			0.353303
$782$	493451.	+	291693.i	0.806919	+	0.476994i
$783$		−	163421.i		−	0.266554i
$784$	28014.5	−	44221.5i	0.0455775	−	0.0719451i
$785$		0			0
$786$	271449.	−	459203.i	0.439383	−	0.743293i
$787$		−	171230.i		−	0.276459i	−0.990400	−	0.138229i	$-0.955859\pi$
$787$		−	171230.i		−	0.276459i	0.990400	−	0.138229i	$-0.0441411\pi$
$788$	109515.	+	199019.i	0.176368	+	0.320510i
$789$	53150.7			0.0853798
$790$		0			0
$791$			744661.i			1.19016i
$792$	2015.97	−	65392.5i	0.00321390	−	0.104250i
$793$	1.10848e6			1.76272
$794$	−297055.	+	502520.i	−0.471189	+	0.797099i
$795$		0			0
$796$	−907999.	+	499647.i	−1.43304	+	0.788565i
$797$	681307.			1.07257			0.536286	−	0.844036i	$-0.319827\pi$
$797$	681307.			1.07257			0.536286	+	0.844036i	$0.319827\pi$
$798$	433760.	+	256408.i	0.681151	+	0.402649i
$799$		−	517070.i		−	0.809946i
$800$		0			0
$801$	256856.			0.400336
$802$	−1296.49	+	2193.25i	−0.00201568	+	0.00340988i
$803$			169045.i			0.262162i
$804$	−213731.	−	388409.i	−0.330640	−	0.600866i
$805$		0			0
$806$	−1.01088e6	−	597563.i	−1.55608	−	0.919843i
$807$			43419.0i			0.0666703i
$808$	610782.	+	18829.6i	0.935543	+	0.0288416i
$809$	67654.6			0.103371			0.0516857	−	0.998663i	$-0.483541\pi$
$809$	67654.6			0.103371			0.0516857	+	0.998663i	$0.483541\pi$
$810$		0			0
$811$		−	617988.i		−	0.939590i	−0.882776	−	0.469795i	$-0.844328\pi$
$811$		−	617988.i		−	0.939590i	0.882776	−	0.469795i	$-0.155672\pi$
$812$	−833466.	+	458634.i	−1.26408	+	0.695591i
$813$	−343813.			−0.520165
$814$	−79487.1	−	46987.2i	−0.119963	−	0.0709137i
$815$		0			0
$816$	416754.	+	264015.i	0.625892	+	0.396505i
$817$	867221.			1.29923
$818$	570164.	−	964533.i	0.852106	−	1.44149i
$819$			277290.i			0.413397i
$820$		0			0
$821$	−539888.			−0.800972			−0.400486	−	0.916303i	$-0.631159\pi$
$821$	−539888.			−0.800972			−0.400486	+	0.916303i	$0.631159\pi$
$822$	−9498.75	−	5615.00i	−0.0140580	−	0.00831009i
$823$			258227.i			0.381242i	0.981664	+	0.190621i	$0.0610502\pi$
$823$			258227.i			0.381242i	−0.981664	+	0.190621i	$0.938950\pi$
$824$	10878.7	−	352875.i	0.0160222	−	0.519716i
$825$		0			0
$826$	231995.	−	392460.i	0.340031	−	0.575222i
$827$		−	475190.i		−	0.694794i	−0.937718	−	0.347397i	$-0.887066\pi$
$827$		−	475190.i		−	0.694794i	0.937718	−	0.347397i	$-0.112934\pi$
$828$	−146244.	+	80473.9i	−0.213312	+	0.117380i
$829$	267309.			0.388959			0.194480	−	0.980907i	$-0.437698\pi$
$829$	267309.			0.388959			0.194480	+	0.980907i	$0.437698\pi$
$830$		0			0
$831$		−	611134.i		−	0.884982i
$832$	−822548.	−	50764.4i	−1.18827	−	0.0733353i
$833$	−75838.7			−0.109295
$834$	221841.	−	375283.i	0.318941	−	0.539544i
$835$		0			0
$836$	−138704.	−	252064.i	−0.198461	−	0.360660i
$837$	−204708.			−0.292203
$838$	24574.6	+	14526.8i	0.0349944	+	0.0206862i
$839$		−	266377.i		−	0.378419i	−0.981937	−	0.189209i	$-0.939408\pi$
$839$		−	266377.i		−	0.378419i	0.981937	−	0.189209i	$-0.0605925\pi$
$840$		0			0
$841$	649549.			0.918374
$842$	259827.	−	439543.i	0.366488	−	0.619979i
$843$		−	436603.i		−	0.614372i
$844$	232951.	−	128187.i	0.327024	−	0.179953i
$845$		0			0
$846$	129619.	+	76621.9i	0.181104	+	0.107056i
$847$			674166.i			0.939723i
$848$	−418130.	+	660028.i	−0.581460	+	0.917848i
$849$	−317562.			−0.440569
$850$		0			0
$851$			235588.i			0.325308i
$852$	−228140.	−	414593.i	−0.314283	−	0.571141i
$853$	−1.15218e6			−1.58351			−0.791755	−	0.610839i	$-0.790832\pi$
$853$	−1.15218e6			−1.58351			−0.791755	+	0.610839i	$0.790832\pi$
$854$	−968347.	−	572419.i	−1.32775	−	0.784871i
$855$		0			0
$856$	5764.51	−	186985.i	0.00786710	−	0.255187i
$857$	−854725.			−1.16376			−0.581882	−	0.813273i	$-0.697683\pi$
$857$	−854725.			−1.16376			−0.581882	+	0.813273i	$0.697683\pi$
$858$	80568.6	−	136296.i	0.109444	−	0.185144i
$859$			972193.i			1.31755i	0.752341	+	0.658774i	$0.228925\pi$
$859$			972193.i			1.31755i	−0.752341	+	0.658774i	$0.771075\pi$
$860$		0			0
$861$	193934.			0.261606
$862$	−1.01693e6	−	601137.i	−1.36860	−	0.809020i
$863$			121346.i			0.162931i	0.996676	+	0.0814653i	$0.0259600\pi$
$863$			121346.i			0.162931i	−0.996676	+	0.0814653i	$0.974040\pi$
$864$	−127940.	+	65349.1i	−0.171387	+	0.0875411i
$865$		0			0
$866$	−211597.	+	357954.i	−0.282147	+	0.477300i
$867$		−	280734.i		−	0.373471i
$868$	574505.	+	1.04404e6i	0.762525	+	1.38572i
$869$	118923.			0.157480
$870$		0			0
$871$		−	1.07289e6i		−	1.41422i
$872$	1.38548e6	+	42712.5i	1.82208	+	0.0561723i
$873$	−94149.5			−0.123535
$874$	−373541.	+	631910.i	−0.489007	+	0.827241i
$875$		0			0
$876$	325217.	−	178958.i	0.423805	−	0.233208i
$877$	−691356.			−0.898882			−0.449441	−	0.893310i	$-0.648377\pi$
$877$	−691356.			−0.898882			−0.449441	+	0.893310i	$0.648377\pi$
$878$	−157153.	−	92897.9i	−0.203861	−	0.120508i
$879$		−	335967.i		−	0.434829i
$880$		0			0
$881$	31766.7			0.0409280			0.0204640	−	0.999791i	$-0.493486\pi$
$881$	31766.7			0.0409280			0.0204640	+	0.999791i	$0.493486\pi$
$882$	11238.1	−	19011.3i	0.0144463	−	0.0244385i
$883$			393237.i			0.504351i	0.967682	+	0.252175i	$0.0811460\pi$
$883$			393237.i			0.504351i	−0.967682	+	0.252175i	$0.918854\pi$
$884$	575590.	+	1.04601e6i	0.736562	+	1.33854i
$885$		0			0
$886$	436060.	+	257768.i	0.555493	+	0.328369i
$887$		−	1.29403e6i		−	1.64474i	−0.568957	−	0.822368i	$-0.692653\pi$
$887$		−	1.29403e6i		−	1.64474i	0.568957	−	0.822368i	$-0.307347\pi$
$888$	−6247.88	+	202664.i	−0.00792332	+	0.257011i
$889$	1.13140e6			1.43157
$890$		0			0
$891$		−	27600.6i		−	0.0347666i
$892$	48197.0	−	26521.5i	0.0605746	−	0.0333326i
$893$	662157.			0.830344
$894$	568858.	+	336269.i	0.711752	+	0.420738i
$895$		0			0
$896$	692345.	+	469109.i	0.862396	+	0.584329i
$897$	−403962.			−0.502060
$898$	−199779.	+	337961.i	−0.247740	+	0.419096i
$899$		−	1.69962e6i		−	2.10297i
$900$		0			0
$901$	1.13193e6			1.39434
$902$	−95324.0	−	56348.9i	−0.117163	−	0.0692583i
$903$		−	484303.i		−	0.593939i
$904$	−933229.	−	28770.2i	−1.14196	−	0.0352052i
$905$		0			0
$906$	−17247.7	+	29177.6i	−0.0210124	+	0.0355462i
$907$			1.05297e6i			1.27997i	0.768386	+	0.639987i	$0.221060\pi$
$907$			1.05297e6i			1.27997i	−0.768386	+	0.639987i	$0.778940\pi$
$908$	970002.	−	533766.i	1.17652	−	0.647410i
$909$	257796.			0.311996
$910$		0			0
$911$			1.11267e6i			1.34069i	0.742048	+	0.670347i	$0.233855\pi$
$911$			1.11267e6i			1.34069i	−0.742048	+	0.670347i	$0.766145\pi$
$912$	−338096.	+	533692.i	−0.406490	+	0.641654i
$913$	231222.			0.277388
$914$	−657746.	+	1.11269e6i	−0.787346	+	1.33193i
$915$		0			0
$916$	209509.	+	380737.i	0.249697	+	0.453769i
$917$	−1.31004e6			−1.55792
$918$	179167.	+	105911.i	0.212604	+	0.125677i
$919$		−	265960.i		−	0.314909i	−0.987526	−	0.157455i	$-0.949671\pi$
$919$		−	265960.i		−	0.314909i	0.987526	−	0.157455i	$-0.0503288\pi$
$920$		0			0
$921$	−750648.			−0.884946
$922$	206963.	−	350115.i	0.243462	−	0.411859i
$923$		−	1.14521e6i		−	1.34426i
$924$	−140766.	+	77459.7i	−0.164875	+	0.0907260i
$925$		0			0
$926$	−535968.	−	316827.i	−0.625053	−	0.369487i
$927$		−	148940.i		−	0.173321i
$928$	−542571.	−	1.06224e6i	−0.630029	−	1.23347i
$929$	−345791.			−0.400666			−0.200333	−	0.979728i	$-0.564202\pi$
$929$	−345791.			−0.400666			−0.200333	+	0.979728i	$0.564202\pi$
$930$		0			0
$931$		−	97118.5i		−	0.112048i
$932$	475429.	+	863988.i	0.547336	+	0.994663i
$933$	567169.			0.651552
$934$	−1.03245e6	−	610311.i	−1.18352	−	0.699613i
$935$		0			0
$936$	−347508.	−	10713.2i	−0.396655	−	0.0122284i
$937$	−865910.			−0.986264			−0.493132	−	0.869954i	$-0.664148\pi$
$937$	−865910.			−0.986264			−0.493132	+	0.869954i	$0.664148\pi$
$938$	−554036.	+	937250.i	−0.629698	+	1.06525i
$939$		−	194136.i		−	0.220178i
$940$		0			0
$941$	−459940.			−0.519424			−0.259712	−	0.965686i	$-0.583628\pi$
$941$	−459940.			−0.519424			−0.259712	+	0.965686i	$0.583628\pi$
$942$	595015.	+	351731.i	0.670542	+	0.396377i
$943$			282527.i			0.317714i
$944$	482878.	+	305905.i	0.541868	+	0.343275i
$945$		0			0
$946$	−140718.	+	238049.i	−0.157241	+	0.266001i
$947$		−	1.52574e6i		−	1.70130i	−0.525730	−	0.850651i	$-0.676208\pi$
$947$		−	1.52574e6i		−	1.70130i	0.525730	−	0.850651i	$-0.323792\pi$
$948$	−125897.	−	228790.i	−0.140087	−	0.254578i
$949$	898334.			0.997483
$950$		0			0
$951$			163366.i			0.180634i
$952$	37333.7	−	1.21100e6i	0.0411933	−	1.33620i
$953$	−426620.			−0.469737			−0.234869	−	0.972027i	$-0.575466\pi$
$953$	−426620.			−0.469737			−0.234869	+	0.972027i	$0.575466\pi$
$954$	−167735.	+	283753.i	−0.184300	+	0.311776i
$955$		0			0
$956$	−124741.	+	68641.4i	−0.136487	+	0.0751052i
$957$	229158.			0.250214
$958$	−613039.	−	362385.i	−0.667970	−	0.394857i
$959$			27098.5i			0.0294651i
$960$		0			0
$961$	−1.20550e6			−1.30533
$962$	−249698.	+	422409.i	−0.269815	+	0.456439i
$963$		−	78921.8i		−	0.0851029i
$964$	101671.	+	184764.i	0.109406	+	0.198821i
$965$		0			0
$966$	352892.	+	208605.i	0.378171	+	0.223548i
$967$			178041.i			0.190400i	0.995458	+	0.0951999i	$0.0303490\pi$
$967$			178041.i			0.190400i	−0.995458	+	0.0951999i	$0.969651\pi$
$968$	−844882.	−	26046.6i	−0.901666	−	0.0277972i
$969$	915268.			0.974766
$970$		0			0
$971$			1.24791e6i			1.32356i	0.749696	+	0.661782i	$0.230200\pi$
$971$			1.24791e6i			1.32356i	−0.749696	+	0.661782i	$0.769800\pi$
$972$	−53099.5	+	29219.2i	−0.0562028	+	0.0309269i
$973$	−1.07063e6			−1.13087
$974$	−1.09568e6	−	647687.i	−1.15495	−	0.682727i
$975$		0			0
$976$	754783.	−	1.19144e6i	0.792360	−	1.25076i
$977$	−106345.			−0.111411			−0.0557055	−	0.998447i	$-0.517741\pi$
$977$	−106345.			−0.111411			−0.0557055	+	0.998447i	$0.517741\pi$
$978$	−233592.	+	395162.i	−0.244220	+	0.413141i
$979$			360177.i			0.375795i
$980$		0			0
$981$	584776.			0.607648
$982$	−575042.	−	339925.i	−0.596316	−	0.352500i
$983$			1.12950e6i			1.16891i	0.811427	+	0.584454i	$0.198691\pi$
$983$			1.12950e6i			1.16891i	−0.811427	+	0.584454i	$0.801309\pi$
$984$	−7492.71	+	243043.i	−0.00773835	+	0.251011i
$985$		0			0
$986$	−879341.	+	1.48756e6i	−0.904489	+	1.53010i
$987$		−	369784.i		−	0.379589i
$988$	−1.33951e6	+	737097.i	−1.37225	+	0.755111i
$989$	705543.			0.721325
$990$		0			0
$991$			1.25503e6i			1.27793i	0.769234	+	0.638967i	$0.220638\pi$
$991$			1.25503e6i			1.27793i	−0.769234	+	0.638967i	$0.779362\pi$
$992$	−1.33061e6	+	679647.i	−1.35216	+	0.690654i
$993$	−313423.			−0.317857
$994$	−591385.	+	1.00043e6i	−0.598546	+	1.01255i
$995$		0			0
$996$	−244782.	−	444838.i	−0.246752	−	0.448418i
$997$	1.24545e6			1.25295			0.626477	−	0.779440i	$-0.284496\pi$
$997$	1.24545e6			1.25295			0.626477	+	0.779440i	$0.284496\pi$
$998$	−92629.1	−	54755.8i	−0.0930007	−	0.0549755i
$999$			85539.7i			0.0857110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.e.151.17		24
4.3	odd	2	inner	300.5.c.e.151.18		24
5.2	odd	4		60.5.f.a.19.20	yes	24
5.3	odd	4		60.5.f.a.19.5	✓	24
5.4	even	2	inner	300.5.c.e.151.8		24
15.2	even	4		180.5.f.i.19.5		24
15.8	even	4		180.5.f.i.19.20		24
20.3	even	4		60.5.f.a.19.19	yes	24
20.7	even	4		60.5.f.a.19.6	yes	24
20.19	odd	2	inner	300.5.c.e.151.7		24
40.3	even	4		960.5.j.d.319.21		24
40.13	odd	4		960.5.j.d.319.4		24
40.27	even	4		960.5.j.d.319.9		24
40.37	odd	4		960.5.j.d.319.16		24
60.23	odd	4		180.5.f.i.19.6		24
60.47	odd	4		180.5.f.i.19.19		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.5	✓	24	5.3	odd	4
60.5.f.a.19.6	yes	24	20.7	even	4
60.5.f.a.19.19	yes	24	20.3	even	4
60.5.f.a.19.20	yes	24	5.2	odd	4
180.5.f.i.19.5		24	15.2	even	4
180.5.f.i.19.6		24	60.23	odd	4
180.5.f.i.19.19		24	60.47	odd	4
180.5.f.i.19.20		24	15.8	even	4
300.5.c.e.151.7		24	20.19	odd	2	inner
300.5.c.e.151.8		24	5.4	even	2	inner
300.5.c.e.151.17		24	1.1	even	1	trivial
300.5.c.e.151.18		24	4.3	odd	2	inner
960.5.j.d.319.4		24	40.13	odd	4
960.5.j.d.319.9		24	40.27	even	4
960.5.j.d.319.16		24	40.37	odd	4
960.5.j.d.319.21		24	40.3	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03548 - 3.44337i) q^{2} -5.19615i q^{3} +(-7.71364 - 14.0178i) q^{4} +(-17.8923 - 10.5767i) q^{6} +51.0440i q^{7} +(-63.9696 - 1.97210i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(2.03548 - 3.44337i) q^{2} -5.19615i q^{3} +(-7.71364 - 14.0178i) q^{4} +(-17.8923 - 10.5767i) q^{6} +51.0440i q^{7} +(-63.9696 - 1.97210i) q^{8} -27.0000 q^{9} -37.8608i q^{11} +(-72.8388 + 40.0812i) q^{12} -201.199 q^{13} +(175.763 + 103.899i) q^{14} +(-137.000 + 216.257i) q^{16} +370.875 q^{17} +(-54.9580 + 92.9711i) q^{18} +474.940i q^{19} +265.232 q^{21} +(-130.369 - 77.0650i) q^{22} +386.396i q^{23} +(-10.2473 + 332.396i) q^{24} +(-409.538 + 692.805i) q^{26} +140.296i q^{27} +(715.526 - 393.735i) q^{28} -1164.83 q^{29} +1459.12i q^{31} +(465.794 + 911.928i) q^{32} -196.731 q^{33} +(754.909 - 1277.06i) q^{34} +(208.268 + 378.482i) q^{36} +609.708 q^{37} +(1635.40 + 966.731i) q^{38} +1045.46i q^{39} +731.186 q^{41} +(539.875 - 913.293i) q^{42} -1825.96i q^{43} +(-530.727 + 292.045i) q^{44} +(1330.50 + 786.501i) q^{46} -1394.19i q^{47} +(1123.70 + 711.871i) q^{48} -204.486 q^{49} -1927.12i q^{51} +(1551.98 + 2820.38i) q^{52} +3052.05 q^{53} +(483.092 + 285.570i) q^{54} +(100.664 - 3265.26i) q^{56} +2467.86 q^{57} +(-2370.99 + 4010.95i) q^{58} -2232.89i q^{59} -5509.38 q^{61} +(5024.28 + 2970.00i) q^{62} -1378.19i q^{63} +(4088.22 + 252.309i) q^{64} +(-400.442 + 677.417i) q^{66} +5332.45i q^{67} +(-2860.80 - 5198.86i) q^{68} +2007.77 q^{69} +5691.93i q^{71} +(1727.18 + 53.2467i) q^{72} -4464.89 q^{73} +(1241.05 - 2099.45i) q^{74} +(6657.63 - 3663.52i) q^{76} +1932.57 q^{77} +(3599.92 + 2128.02i) q^{78} +3141.04i q^{79} +729.000 q^{81} +(1488.31 - 2517.75i) q^{82} +6107.15i q^{83} +(-2045.91 - 3717.98i) q^{84} +(-6287.46 - 3716.71i) q^{86} +6052.64i q^{87} +(-74.6654 + 2421.94i) q^{88} -9513.18 q^{89} -10270.0i q^{91} +(5416.43 - 2980.52i) q^{92} +7581.79 q^{93} +(-4800.72 - 2837.85i) q^{94} +(4738.52 - 2420.34i) q^{96} +3487.02 q^{97} +(-416.227 + 704.121i) q^{98} +1022.24i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 14 q^{4} - 18 q^{6} - 648 q^{9}+O(q^{10}) \) 24 * q - 14 * q^4 - 18 * q^6 - 648 * q^9	\( 24 q - 14 q^{4} - 18 q^{6} - 648 q^{9} + 36 q^{14} + 594 q^{16} + 594 q^{24} - 2868 q^{26} + 1680 q^{29} - 3076 q^{34} + 378 q^{36} - 4848 q^{41} + 3828 q^{44} - 15280 q^{46} - 5416 q^{49} + 486 q^{54} + 32172 q^{56} + 2896 q^{61} + 18298 q^{64} - 15588 q^{66} - 9792 q^{69} - 31836 q^{74} + 50136 q^{76} + 17496 q^{81} + 4284 q^{84} - 58152 q^{86} + 38544 q^{89} - 4808 q^{94} + 21978 q^{96}+O(q^{100}) \) 24 * q - 14 * q^4 - 18 * q^6 - 648 * q^9 + 36 * q^14 + 594 * q^16 + 594 * q^24 - 2868 * q^26 + 1680 * q^29 - 3076 * q^34 + 378 * q^36 - 4848 * q^41 + 3828 * q^44 - 15280 * q^46 - 5416 * q^49 + 486 * q^54 + 32172 * q^56 + 2896 * q^61 + 18298 * q^64 - 15588 * q^66 - 9792 * q^69 - 31836 * q^74 + 50136 * q^76 + 17496 * q^81 + 4284 * q^84 - 58152 * q^86 + 38544 * q^89 - 4808 * q^94 + 21978 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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