LMFDB - Embedded newform 304.5.r.d.145.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.10
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93870 + 1.11931i) q^{3} +(-15.6195 - 27.0538i) q^{5} +6.74912 q^{7} +(-37.9943 + 65.8080i) q^{9} +O(q^{10})$	\(q+(-1.93870 + 1.11931i) q^{3} +(-15.6195 - 27.0538i) q^{5} +6.74912 q^{7} +(-37.9943 + 65.8080i) q^{9} +124.903 q^{11} +(134.659 + 77.7455i) q^{13} +(60.5631 + 34.9661i) q^{15} +(127.427 + 220.710i) q^{17} +(-161.629 - 322.796i) q^{19} +(-13.0845 + 7.55435i) q^{21} +(193.260 - 334.736i) q^{23} +(-175.438 + 303.867i) q^{25} -351.438i q^{27} +(-985.611 - 569.043i) q^{29} -593.148i q^{31} +(-242.149 + 139.805i) q^{33} +(-105.418 - 182.589i) q^{35} -360.278i q^{37} -348.085 q^{39} +(-1647.63 + 951.257i) q^{41} +(-794.184 - 1375.57i) q^{43} +2373.81 q^{45} +(1347.57 - 2334.06i) q^{47} -2355.45 q^{49} +(-494.085 - 285.260i) q^{51} +(-1.97124 - 1.13810i) q^{53} +(-1950.92 - 3379.09i) q^{55} +(674.659 + 444.891i) q^{57} +(3490.96 - 2015.51i) q^{59} +(3481.53 - 6030.18i) q^{61} +(-256.428 + 444.146i) q^{63} -4857.38i q^{65} +(4546.94 + 2625.18i) q^{67} +865.270i q^{69} +(-2217.11 + 1280.05i) q^{71} +(110.303 + 191.050i) q^{73} -785.477i q^{75} +842.982 q^{77} +(-2249.78 + 1298.91i) q^{79} +(-2684.17 - 4649.12i) q^{81} -7437.65 q^{83} +(3980.68 - 6894.75i) q^{85} +2547.74 q^{87} +(-8825.30 - 5095.29i) q^{89} +(908.830 + 524.713i) q^{91} +(663.917 + 1149.94i) q^{93} +(-6208.27 + 9414.59i) q^{95} +(8257.62 - 4767.54i) q^{97} +(-4745.58 + 8219.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.93870	+	1.11931i	−0.215411	+	0.124368i	−0.603824	−	0.797118i	$-0.706357\pi$
$3$	−1.93870	+	1.11931i	−0.215411	+	0.124368i	0.388412	+	0.921486i	$0.373024\pi$
$4$		0			0
$5$	−15.6195	−	27.0538i	−0.624780	−	1.08215i	−0.988583	−	0.150675i	$-0.951855\pi$
$5$	−15.6195	−	27.0538i	−0.624780	−	1.08215i	0.363803	−	0.931476i	$-0.381478\pi$
$6$		0			0
$7$	6.74912			0.137737			0.0688685	−	0.997626i	$-0.478061\pi$
$7$	6.74912			0.137737			0.0688685	+	0.997626i	$0.478061\pi$
$8$		0			0
$9$	−37.9943	+	65.8080i	−0.469065	+	0.812445i
$10$		0			0
$11$	124.903			1.03225			0.516126	−	0.856513i	$-0.327374\pi$
$11$	124.903			1.03225			0.516126	+	0.856513i	$0.327374\pi$
$12$		0			0
$13$	134.659	+	77.7455i	0.796800	+	0.460032i	0.842351	−	0.538930i	$-0.181171\pi$
$13$	134.659	+	77.7455i	0.796800	+	0.460032i	−0.0455512	+	0.998962i	$0.514504\pi$
$14$		0			0
$15$	60.5631	+	34.9661i	0.269169	+	0.155405i
$16$		0			0
$17$	127.427	+	220.710i	0.440923	+	0.763701i	0.997758	−	0.0669221i	$-0.0213179\pi$
$17$	127.427	+	220.710i	0.440923	+	0.763701i	−0.556835	+	0.830623i	$0.687985\pi$
$18$		0			0
$19$	−161.629	−	322.796i	−0.447726	−	0.894171i
$19$	−161.629	−	322.796i	−0.447726	−	0.894171i
$20$		0			0
$21$	−13.0845	+	7.55435i	−0.0296701	+	0.0171300i
$22$		0			0
$23$	193.260	−	334.736i	0.365331	−	0.632771i	−0.623499	−	0.781824i	$-0.714289\pi$
$23$	193.260	−	334.736i	0.365331	−	0.632771i	0.988829	+	0.149053i	$0.0476226\pi$
$24$		0			0
$25$	−175.438	+	303.867i	−0.280700	+	0.486187i
$26$		0			0
$27$		−	351.438i		−	0.482082i
$28$		0			0
$29$	−985.611	−	569.043i	−1.17195	−	0.676626i	−0.217812	−	0.975991i	$-0.569892\pi$
$29$	−985.611	−	569.043i	−1.17195	−	0.676626i	−0.954139	+	0.299364i	$0.903225\pi$
$30$		0			0
$31$		−	593.148i		−	0.617220i	−0.951189	−	0.308610i	$-0.900136\pi$
$31$		−	593.148i		−	0.617220i	0.951189	−	0.308610i	$-0.0998638\pi$
$32$		0			0
$33$	−242.149	+	139.805i	−0.222359	+	0.128379i
$34$		0			0
$35$	−105.418	−	182.589i	−0.0860554	−	0.149052i
$36$		0			0
$37$		−	360.278i		−	0.263169i	−0.991305	−	0.131585i	$-0.957994\pi$
$37$		−	360.278i		−	0.263169i	0.991305	−	0.131585i	$-0.0420065\pi$
$38$		0			0
$39$	−348.085			−0.228853
$40$		0			0
$41$	−1647.63	+	951.257i	−0.980146	+	0.565888i	−0.902314	−	0.431079i	$-0.858133\pi$
$41$	−1647.63	+	951.257i	−0.980146	+	0.565888i	−0.0778321	+	0.996966i	$0.524800\pi$
$42$		0			0
$43$	−794.184	−	1375.57i	−0.429521	−	0.743952i	0.567310	−	0.823504i	$-0.307984\pi$
$43$	−794.184	−	1375.57i	−0.429521	−	0.743952i	−0.996831	+	0.0795528i	$0.974651\pi$
$44$		0			0
$45$	2373.81			1.17225
$46$		0			0
$47$	1347.57	−	2334.06i	0.610035	−	1.05661i	−0.381198	−	0.924493i	$-0.624489\pi$
$47$	1347.57	−	2334.06i	0.610035	−	1.05661i	0.991234	−	0.132119i	$-0.0421781\pi$
$48$		0			0
$49$	−2355.45			−0.981028
$50$		0			0
$51$	−494.085	−	285.260i	−0.189959	−	0.109673i
$52$		0			0
$53$	−1.97124	−	1.13810i	−0.000701759	−	0.000405161i	0.499649	−	0.866228i	$-0.333462\pi$
$53$	−1.97124	−	1.13810i	−0.000701759	−	0.000405161i	−0.500351	+	0.865823i	$0.666796\pi$
$54$		0			0
$55$	−1950.92	−	3379.09i	−0.644931	−	1.11705i
$56$		0			0
$57$	674.659	+	444.891i	0.207651	+	0.136932i
$58$		0			0
$59$	3490.96	−	2015.51i	1.00286	−	0.579002i	0.0937680	−	0.995594i	$-0.470109\pi$
$59$	3490.96	−	2015.51i	1.00286	−	0.579002i	0.909094	+	0.416592i	$0.136775\pi$
$60$		0			0
$61$	3481.53	−	6030.18i	0.935643	−	1.62058i	0.162161	−	0.986764i	$-0.448154\pi$
$61$	3481.53	−	6030.18i	0.935643	−	1.62058i	0.773483	−	0.633817i	$-0.218513\pi$
$62$		0			0
$63$	−256.428	+	444.146i	−0.0646077	+	0.111904i
$64$		0			0
$65$		−	4857.38i		−	1.14968i
$66$		0			0
$67$	4546.94	+	2625.18i	1.01291	+	0.584802i	0.912041	−	0.410098i	$-0.134505\pi$
$67$	4546.94	+	2625.18i	1.01291	+	0.584802i	0.100866	+	0.994900i	$0.467839\pi$
$68$		0			0
$69$			865.270i			0.181741i
$70$		0			0
$71$	−2217.11	+	1280.05i	−0.439816	+	0.253928i	−0.703519	−	0.710676i	$-0.748389\pi$
$71$	−2217.11	+	1280.05i	−0.439816	+	0.253928i	0.263704	+	0.964604i	$0.415056\pi$
$72$		0			0
$73$	110.303	+	191.050i	0.0206986	+	0.0358511i	0.876189	−	0.481967i	$-0.160078\pi$
$73$	110.303	+	191.050i	0.0206986	+	0.0358511i	−0.855491	+	0.517818i	$0.826744\pi$
$74$		0			0
$75$		−	785.477i		−	0.139640i
$76$		0			0
$77$	842.982			0.142179
$78$		0			0
$79$	−2249.78	+	1298.91i	−0.360485	+	0.208126i	−0.669293	−	0.742998i	$-0.733403\pi$
$79$	−2249.78	+	1298.91i	−0.360485	+	0.208126i	0.308809	+	0.951124i	$0.400070\pi$
$80$		0			0
$81$	−2684.17	−	4649.12i	−0.409110	−	0.708599i
$82$		0			0
$83$	−7437.65			−1.07964			−0.539821	−	0.841780i	$-0.681508\pi$
$83$	−7437.65			−1.07964			−0.539821	+	0.841780i	$0.681508\pi$
$84$		0			0
$85$	3980.68	−	6894.75i	0.550960	−	0.954290i
$86$		0			0
$87$	2547.74			0.336602
$88$		0			0
$89$	−8825.30	−	5095.29i	−1.11417	−	0.643263i	−0.174260	−	0.984700i	$-0.555753\pi$
$89$	−8825.30	−	5095.29i	−1.11417	−	0.643263i	−0.939905	+	0.341436i	$0.889087\pi$
$90$		0			0
$91$	908.830	+	524.713i	0.109749	+	0.0633635i
$92$		0			0
$93$	663.917	+	1149.94i	0.0767622	+	0.132956i
$94$		0			0
$95$	−6208.27	+	9414.59i	−0.687897	+	1.04317i
$96$		0			0
$97$	8257.62	−	4767.54i	0.877630	−	0.506700i	0.00775402	−	0.999970i	$-0.497532\pi$
$97$	8257.62	−	4767.54i	0.877630	−	0.506700i	0.869876	+	0.493270i	$0.164198\pi$
$98$		0			0
$99$	−4745.58	+	8219.59i	−0.484194	+	0.838648i
$100$		0			0
$101$	−2086.44	+	3613.82i	−0.204533	+	0.354262i	−0.949984	−	0.312299i	$-0.898901\pi$
$101$	−2086.44	+	3613.82i	−0.204533	+	0.354262i	0.745451	+	0.666561i	$0.232234\pi$
$102$		0			0
$103$		−	18149.7i		−	1.71079i	−0.517978	−	0.855394i	$-0.673315\pi$
$103$		−	18149.7i		−	1.71079i	0.517978	−	0.855394i	$-0.326685\pi$
$104$		0			0
$105$	408.747	+	235.990i	0.0370746	+	0.0214050i
$106$		0			0
$107$		−	7747.72i		−	0.676715i	−0.941018	−	0.338358i	$-0.890129\pi$
$107$		−	7747.72i		−	0.676715i	0.941018	−	0.338358i	$-0.109871\pi$
$108$		0			0
$109$	5236.87	−	3023.51i	0.440777	−	0.254482i	−0.263150	−	0.964755i	$-0.584762\pi$
$109$	5236.87	−	3023.51i	0.440777	−	0.254482i	0.703927	+	0.710272i	$0.251428\pi$
$110$		0			0
$111$	403.263	+	698.472i	0.0327297	+	0.0566896i
$112$		0			0
$113$		−	9479.00i		−	0.742345i	−0.928564	−	0.371172i	$-0.878956\pi$
$113$		−	9479.00i		−	0.742345i	0.928564	−	0.371172i	$-0.121044\pi$
$114$		0			0
$115$	−12074.5			−0.913005
$116$		0			0
$117$	−10232.6	+	5907.77i	−0.747502	+	0.431571i
$118$		0			0
$119$	860.018	+	1489.59i	0.0607314	+	0.105190i
$120$		0			0
$121$	959.647			0.0655452
$122$		0			0
$123$	2129.50	−	3688.41i	0.140756	−	0.243797i
$124$		0			0
$125$	−8563.37			−0.548056
$126$		0			0
$127$	17568.6	+	10143.2i	1.08926	+	0.628882i	0.933378	−	0.358895i	$-0.116846\pi$
$127$	17568.6	+	10143.2i	1.08926	+	0.628882i	0.155877	+	0.987776i	$0.450180\pi$
$128$		0			0
$129$	3079.37	+	1777.87i	0.185047	+	0.106837i
$130$		0			0
$131$	11345.0	+	19650.1i	0.661091	+	1.14504i	0.980329	+	0.197369i	$0.0632395\pi$
$131$	11345.0	+	19650.1i	0.661091	+	1.14504i	−0.319239	+	0.947674i	$0.603427\pi$
$132$		0			0
$133$	−1090.85	−	2178.59i	−0.0616685	−	0.123160i
$134$		0			0
$135$	−9507.71	+	5489.28i	−0.521685	+	0.301195i
$136$		0			0
$137$	1696.68	−	2938.74i	0.0903980	−	0.156574i	−0.817281	−	0.576240i	$-0.804519\pi$
$137$	1696.68	−	2938.74i	0.0903980	−	0.156574i	0.907679	+	0.419666i	$0.137853\pi$
$138$		0			0
$139$	6450.95	−	11173.4i	0.333883	−	0.578302i	−0.649387	−	0.760458i	$-0.724974\pi$
$139$	6450.95	−	11173.4i	0.333883	−	0.578302i	0.983270	+	0.182156i	$0.0583077\pi$
$140$		0			0
$141$			6033.38i			0.303475i
$142$		0			0
$143$	16819.3	+	9710.61i	0.822498	+	0.474870i
$144$		0			0
$145$			35552.7i			1.69097i
$146$		0			0
$147$	4566.51	−	2636.48i	0.211325	−	0.122008i
$148$		0			0
$149$	17701.7	+	30660.2i	0.797336	+	1.38103i	0.921345	+	0.388745i	$0.127091\pi$
$149$	17701.7	+	30660.2i	0.797336	+	1.38103i	−0.124010	+	0.992281i	$0.539575\pi$
$150$		0			0
$151$		−	17092.2i		−	0.749626i	−0.927100	−	0.374813i	$-0.877707\pi$
$151$		−	17092.2i		−	0.749626i	0.927100	−	0.374813i	$-0.122293\pi$
$152$		0			0
$153$	−19366.0			−0.827287
$154$		0			0
$155$	−16046.9	+	9264.68i	−0.667925	+	0.385627i
$156$		0			0
$157$	17919.8	+	31038.0i	0.726999	+	1.25920i	0.958146	+	0.286280i	$0.0924187\pi$
$157$	17919.8	+	31038.0i	0.726999	+	1.25920i	−0.231147	+	0.972919i	$0.574248\pi$
$158$		0			0
$159$	5.09553			0.000201556
$160$		0			0
$161$	1304.33	−	2259.17i	0.0503196	−	0.0871560i
$162$		0			0
$163$	6266.05			0.235841			0.117920	−	0.993023i	$-0.462377\pi$
$163$	6266.05			0.235841			0.117920	+	0.993023i	$0.462377\pi$
$164$		0			0
$165$	7564.48	+	4367.36i	0.277851	+	0.160417i
$166$		0			0
$167$	−20148.4	−	11632.7i	−0.722448	−	0.417106i	0.0932050	−	0.995647i	$-0.470289\pi$
$167$	−20148.4	−	11632.7i	−0.722448	−	0.417106i	−0.815653	+	0.578541i	$0.803622\pi$
$168$		0			0
$169$	−2191.78	−	3796.27i	−0.0767402	−	0.132918i
$170$		0			0
$171$	27383.5	+	1627.89i	0.936477	+	0.0556714i
$172$		0			0
$173$	7165.62	−	4137.07i	0.239421	−	0.138230i	−0.375490	−	0.926827i	$-0.622525\pi$
$173$	7165.62	−	4137.07i	0.239421	−	0.138230i	0.614910	+	0.788597i	$0.289192\pi$
$174$		0			0
$175$	−1184.05	+	2050.84i	−0.0386629	+	0.0669660i
$176$		0			0
$177$	−4511.95	+	7814.93i	−0.144018	+	0.249447i
$178$		0			0
$179$		−	43730.2i		−	1.36482i	−0.730969	−	0.682410i	$-0.760932\pi$
$179$		−	43730.2i		−	1.36482i	0.730969	−	0.682410i	$-0.239068\pi$
$180$		0			0
$181$	7670.94	+	4428.82i	0.234149	+	0.135186i	0.612484	−	0.790483i	$-0.290170\pi$
$181$	7670.94	+	4428.82i	0.234149	+	0.135186i	−0.378336	+	0.925668i	$0.623504\pi$
$182$		0			0
$183$			15587.6i			0.465455i
$184$		0			0
$185$	−9746.89	+	5627.37i	−0.284789	+	0.164423i
$186$		0			0
$187$	15915.9	+	27567.2i	0.455144	+	0.788332i
$188$		0			0
$189$		−	2371.89i		−	0.0664005i
$190$		0			0
$191$	−7936.99			−0.217565			−0.108783	−	0.994066i	$-0.534695\pi$
$191$	−7936.99			−0.217565			−0.108783	+	0.994066i	$0.534695\pi$
$192$		0			0
$193$	−43557.3	+	25147.8i	−1.16936	+	0.675128i	−0.953528	−	0.301304i	$-0.902578\pi$
$193$	−43557.3	+	25147.8i	−1.16936	+	0.675128i	−0.215827	+	0.976432i	$0.569245\pi$
$194$		0			0
$195$	5436.92	+	9417.01i	0.142983	+	0.247653i
$196$		0			0
$197$	−19563.5			−0.504096			−0.252048	−	0.967715i	$-0.581104\pi$
$197$	−19563.5			−0.504096			−0.252048	+	0.967715i	$0.581104\pi$
$198$		0			0
$199$	12415.8	−	21504.9i	0.313523	−	0.543038i	−0.665599	−	0.746309i	$-0.731824\pi$
$199$	12415.8	−	21504.9i	0.313523	−	0.543038i	0.979122	+	0.203271i	$0.0651573\pi$
$200$		0			0
$201$	−11753.5			−0.290922
$202$		0			0
$203$	−6652.00	−	3840.54i	−0.161421	−	0.0931965i
$204$		0			0
$205$	51470.2	+	29716.3i	1.22475	+	0.707111i
$206$		0			0
$207$	14685.5	+	25436.1i	0.342728	+	0.593622i
$208$		0			0
$209$	−20187.9	−	40318.0i	−0.462167	−	0.923010i
$210$		0			0
$211$	−18973.0	+	10954.1i	−0.426158	+	0.246043i	−0.697709	−	0.716382i	$-0.745797\pi$
$211$	−18973.0	+	10954.1i	−0.426158	+	0.246043i	0.271550	+	0.962424i	$0.412464\pi$
$212$		0			0
$213$	2865.54	−	4963.27i	0.0631608	−	0.109398i
$214$		0			0
$215$	−24809.5	+	42971.3i	−0.536712	+	0.929612i
$216$		0			0
$217$		−	4003.23i		−	0.0850141i
$218$		0			0
$219$	−427.689	−	246.926i	−0.00891743	−	0.00514848i
$220$		0			0
$221$			39627.4i			0.811355i
$222$		0			0
$223$	3246.29	−	1874.25i	0.0652796	−	0.0376892i	−0.467005	−	0.884255i	$-0.654667\pi$
$223$	3246.29	−	1874.25i	0.0652796	−	0.0376892i	0.532285	+	0.846565i	$0.321334\pi$
$224$		0			0
$225$	−13331.3	−	23090.4i	−0.263334	−	0.456107i
$226$		0			0
$227$			69169.5i			1.34234i	0.741303	+	0.671170i	$0.234208\pi$
$227$			69169.5i			1.34234i	−0.741303	+	0.671170i	$0.765792\pi$
$228$		0			0
$229$	−4633.97			−0.0883655			−0.0441827	−	0.999023i	$-0.514068\pi$
$229$	−4633.97			−0.0883655			−0.0441827	+	0.999023i	$0.514068\pi$
$230$		0			0
$231$	−1634.29	+	943.558i	−0.0306270	+	0.0176825i
$232$		0			0
$233$	−8090.94	−	14013.9i	−0.149035	−	0.258136i	0.781836	−	0.623484i	$-0.214283\pi$
$233$	−8090.94	−	14013.9i	−0.149035	−	0.258136i	−0.930871	+	0.365348i	$0.880950\pi$
$234$		0			0
$235$	−84193.4			−1.52455
$236$		0			0
$237$	2907.77	−	5036.41i	0.0517683	−	0.0896653i
$238$		0			0
$239$	−9138.88			−0.159992			−0.0799958	−	0.996795i	$-0.525491\pi$
$239$	−9138.88			−0.159992			−0.0799958	+	0.996795i	$0.525491\pi$
$240$		0			0
$241$	33766.2	+	19494.9i	0.581363	+	0.335650i	0.761675	−	0.647959i	$-0.224377\pi$
$241$	33766.2	+	19494.9i	0.581363	+	0.335650i	−0.180312	+	0.983610i	$0.557711\pi$
$242$		0			0
$243$	35060.3	+	20242.1i	0.593749	+	0.342801i
$244$		0			0
$245$	36791.0	+	63723.8i	0.612927	+	1.06162i
$246$		0			0
$247$	3331.05	−	56033.3i	0.0545993	−	0.918443i
$248$		0			0
$249$	14419.4	−	8325.03i	0.232567	−	0.134273i
$250$		0			0
$251$	21264.0	−	36830.3i	0.337519	−	0.584599i	−0.646447	−	0.762959i	$-0.723746\pi$
$251$	21264.0	−	36830.3i	0.337519	−	0.584599i	0.983965	+	0.178360i	$0.0570791\pi$
$252$		0			0
$253$	24138.7	−	41809.4i	0.377113	−	0.653180i
$254$		0			0
$255$			17822.5i			0.274086i
$256$		0			0
$257$	−75878.9	−	43808.7i	−1.14883	−	0.663276i	−0.200226	−	0.979750i	$-0.564168\pi$
$257$	−75878.9	−	43808.7i	−1.14883	−	0.663276i	−0.948601	+	0.316474i	$0.897501\pi$
$258$		0			0
$259$		−	2431.56i		−	0.0362481i
$260$		0			0
$261$	74895.2	−	43240.7i	1.09944	−	0.634764i
$262$		0			0
$263$	30776.8	+	53306.9i	0.444950	+	0.770677i	0.998049	−	0.0624394i	$-0.0198880\pi$
$263$	30776.8	+	53306.9i	0.444950	+	0.770677i	−0.553098	+	0.833116i	$0.686555\pi$
$264$		0			0
$265$			71.1060i			0.00101255i
$266$		0			0
$267$	22812.8			0.320005
$268$		0			0
$269$	67084.3	−	38731.2i	0.927078	−	0.535249i	0.0411921	−	0.999151i	$-0.486884\pi$
$269$	67084.3	−	38731.2i	0.927078	−	0.535249i	0.885886	+	0.463902i	$0.153551\pi$
$270$		0			0
$271$	56026.7	+	97041.1i	0.762880	+	1.32135i	0.941360	+	0.337404i	$0.109549\pi$
$271$	56026.7	+	97041.1i	0.762880	+	1.32135i	−0.178480	+	0.983944i	$0.557118\pi$
$272$		0			0
$273$	−2349.27			−0.0315215
$274$		0			0
$275$	−21912.6	+	37953.8i	−0.289754	+	0.501868i
$276$		0			0
$277$	128472.			1.67436			0.837179	−	0.546929i	$-0.184203\pi$
$277$	128472.			1.67436			0.837179	+	0.546929i	$0.184203\pi$
$278$		0			0
$279$	39033.9	+	22536.3i	0.501457	+	0.289516i
$280$		0			0
$281$	−111706.	−	64493.4i	−1.41470	−	0.816776i	−0.418871	−	0.908046i	$-0.637574\pi$
$281$	−111706.	−	64493.4i	−1.41470	−	0.816776i	−0.995826	+	0.0912700i	$0.970907\pi$
$282$		0			0
$283$	−72402.9	−	125405.i	−0.904030	−	1.56583i	−0.822214	−	0.569179i	$-0.807261\pi$
$283$	−72402.9	−	125405.i	−0.904030	−	1.56583i	−0.0818162	−	0.996647i	$-0.526072\pi$
$284$		0			0
$285$	1498.14	−	25201.0i	0.0184444	−	0.310262i
$286$		0			0
$287$	−11120.0	+	6420.15i	−0.135003	+	0.0779437i
$288$		0			0
$289$	9285.36	−	16082.7i	0.111174	−	0.192559i
$290$		0			0
$291$	−10672.7	+	18485.7i	−0.126034	+	0.218298i
$292$		0			0
$293$		−	142973.i		−	1.66541i	−0.553720	−	0.832703i	$-0.686792\pi$
$293$		−	142973.i		−	1.66541i	0.553720	−	0.832703i	$-0.313208\pi$
$294$		0			0
$295$	−109054.	−	62962.5i	−1.25314	−	0.723499i
$296$		0			0
$297$		−	43895.5i		−	0.497630i
$298$		0			0
$299$	52048.4	−	30050.2i	0.582191	−	0.336128i
$300$		0			0
$301$	−5360.04	−	9283.86i	−0.0591609	−	0.102470i
$302$		0			0
$303$		−	9341.50i		−	0.101749i
$304$		0			0
$305$	−217519.			−2.33829
$306$		0			0
$307$	−93661.1	+	54075.2i	−0.993762	+	0.573749i	−0.906397	−	0.422428i	$-0.861178\pi$
$307$	−93661.1	+	54075.2i	−0.993762	+	0.573749i	−0.0873652	+	0.996176i	$0.527845\pi$
$308$		0			0
$309$	20315.2	+	35186.9i	0.212767	+	0.368523i
$310$		0			0
$311$	115895.			1.19824			0.599121	−	0.800659i	$-0.295517\pi$
$311$	115895.			1.19824			0.599121	+	0.800659i	$0.295517\pi$
$312$		0			0
$313$	−58215.1	+	100831.i	−0.594219	+	1.02922i	0.399437	+	0.916760i	$0.369206\pi$
$313$	−58215.1	+	100831.i	−0.594219	+	1.02922i	−0.993657	+	0.112457i	$0.964128\pi$
$314$		0			0
$315$	16021.1			0.161462
$316$		0			0
$317$	24219.2	+	13983.0i	0.241014	+	0.139149i	0.615643	−	0.788025i	$-0.288896\pi$
$317$	24219.2	+	13983.0i	0.241014	+	0.139149i	−0.374629	+	0.927175i	$0.622230\pi$
$318$		0			0
$319$	−123105.	−	71074.9i	−1.20975	−	0.698449i
$320$		0			0
$321$	8672.09	+	15020.5i	0.0841616	+	0.145772i
$322$		0			0
$323$	50648.2	−	76805.9i	0.485466	−	0.736189i
$324$		0			0
$325$	−47248.6	+	27279.0i	−0.447324	+	0.258263i
$326$		0			0
$327$	−6768.48	+	11723.3i	−0.0632988	+	0.109637i
$328$		0			0
$329$	9094.89	−	15752.8i	0.0840245	−	0.145535i
$330$		0			0
$331$		−	101916.i		−	0.930224i	−0.885252	−	0.465112i	$-0.846014\pi$
$331$		−	101916.i		−	0.930224i	0.885252	−	0.465112i	$-0.153986\pi$
$332$		0			0
$333$	23709.2	+	13688.5i	0.213810	+	0.123443i
$334$		0			0
$335$		−	164016.i		−	1.46149i
$336$		0			0
$337$	−7232.06	+	4175.43i	−0.0636799	+	0.0367656i	−0.531502	−	0.847057i	$-0.678372\pi$
$337$	−7232.06	+	4175.43i	−0.0636799	+	0.0367656i	0.467822	+	0.883823i	$0.345039\pi$
$338$		0			0
$339$	10609.9	+	18376.9i	0.0923237	+	0.159909i
$340$		0			0
$341$		−	74085.7i		−	0.637127i
$342$		0			0
$343$	−32101.8			−0.272861
$344$		0			0
$345$	23408.8	−	13515.1i	0.196672	−	0.113548i
$346$		0			0
$347$	−45577.0	−	78941.6i	−0.378518	−	0.655612i	0.612329	−	0.790603i	$-0.290233\pi$
$347$	−45577.0	−	78941.6i	−0.378518	−	0.655612i	−0.990847	+	0.134991i	$0.956899\pi$
$348$		0			0
$349$	−29079.9			−0.238750			−0.119375	−	0.992849i	$-0.538089\pi$
$349$	−29079.9			−0.238750			−0.119375	+	0.992849i	$0.538089\pi$
$350$		0			0
$351$	27322.7	−	47324.3i	0.221773	−	0.384123i
$352$		0			0
$353$	134292.			1.07771			0.538854	−	0.842399i	$-0.318857\pi$
$353$	134292.			1.07771			0.538854	+	0.842399i	$0.318857\pi$
$354$		0			0
$355$	69260.4	+	39987.5i	0.549576	+	0.317298i
$356$		0			0
$357$	−3334.63	−	1925.25i	−0.0261645	−	0.0151061i
$358$		0			0
$359$	−69994.3	−	121234.i	−0.543093	−	0.940664i	−0.998724	−	0.0504957i	$-0.983920\pi$
$359$	−69994.3	−	121234.i	−0.543093	−	0.940664i	0.455632	−	0.890168i	$-0.349413\pi$
$360$		0			0
$361$	−78073.0	+	104346.i	−0.599082	+	0.800688i
$362$		0			0
$363$	−1860.47	+	1074.14i	−0.0141192	+	0.00815170i
$364$		0			0
$365$	3445.76	−	5968.22i	0.0258642	−	0.0447981i
$366$		0			0
$367$	84019.8	−	145527.i	0.623806	−	1.08046i	−0.364965	−	0.931021i	$-0.618919\pi$
$367$	84019.8	−	145527.i	0.623806	−	1.08046i	0.988770	−	0.149442i	$-0.0477478\pi$
$368$		0			0
$369$		−	144569.i		−	1.06175i
$370$		0			0
$371$	−13.3041	−	7.68115i	−9.66582e−5	−	5.58057e-5i
$372$		0			0
$373$			88343.1i			0.634973i	0.948263	+	0.317486i	$0.102839\pi$
$373$			88343.1i			0.634973i	−0.948263	+	0.317486i	$0.897161\pi$
$374$		0			0
$375$	16601.8	−	9585.07i	0.118057	−	0.0681605i
$376$		0			0
$377$	−88481.0	−	153254.i	−0.622540	−	1.07827i
$378$		0			0
$379$		−	2419.75i		−	0.0168458i	−0.999965	−	0.00842292i	$-0.997319\pi$
$379$		−	2419.75i		−	0.0168458i	0.999965	−	0.00842292i	$-0.00268113\pi$
$380$		0			0
$381$	−45413.7			−0.312850
$382$		0			0
$383$	−104816.	+	60515.8i	−0.714549	+	0.412545i	−0.812743	−	0.582622i	$-0.802027\pi$
$383$	−104816.	+	60515.8i	−0.714549	+	0.412545i	0.0981944	+	0.995167i	$0.468693\pi$
$384$		0			0
$385$	−13167.0	−	22805.8i	−0.0888309	−	0.153860i
$386$		0			0
$387$	120698.			0.805893
$388$		0			0
$389$	−101360.	+	175561.i	−0.669834	+	1.16019i	0.308116	+	0.951349i	$0.400301\pi$
$389$	−101360.	+	175561.i	−0.669834	+	1.16019i	−0.977950	+	0.208838i	$0.933032\pi$
$390$		0			0
$391$	98505.9			0.644330
$392$		0			0
$393$	−43989.0	−	25397.1i	−0.284813	−	0.164437i
$394$		0			0
$395$	70281.0	+	40576.8i	0.450447	+	0.260066i
$396$		0			0
$397$	57516.2	+	99621.1i	0.364930	+	0.632077i	0.988765	−	0.149479i	$-0.0477596\pi$
$397$	57516.2	+	99621.1i	0.364930	+	0.632077i	−0.623835	+	0.781556i	$0.714426\pi$
$398$		0			0
$399$	4553.35	+	3002.62i	0.0286013	+	0.0188606i
$400$		0			0
$401$	129215.	−	74602.5i	0.803573	−	0.463943i	−0.0411460	−	0.999153i	$-0.513101\pi$
$401$	129215.	−	74602.5i	0.803573	−	0.463943i	0.844719	+	0.535210i	$0.179768\pi$
$402$		0			0
$403$	46114.6	−	79872.8i	0.283941	−	0.491801i
$404$		0			0
$405$	−83850.8	+	145234.i	−0.511208	+	0.885437i
$406$		0			0
$407$		−	44999.7i		−	0.271657i
$408$		0			0
$409$	146230.	+	84426.2i	0.874160	+	0.504697i	0.868729	−	0.495288i	$-0.164938\pi$
$409$	146230.	+	84426.2i	0.874160	+	0.504697i	0.00543191	+	0.999985i	$0.498271\pi$
$410$		0			0
$411$			7596.44i			0.0449704i
$412$		0			0
$413$	23560.9	−	13602.9i	0.138131	−	0.0797501i
$414$		0			0
$415$	116172.	+	201216.i	0.674538	+	1.16833i
$416$		0			0
$417$			28882.4i			0.166097i
$418$		0			0
$419$	61370.4			0.349567			0.174784	−	0.984607i	$-0.444077\pi$
$419$	61370.4			0.349567			0.174784	+	0.984607i	$0.444077\pi$
$420$		0			0
$421$	203447.	−	117460.i	1.14786	−	0.662716i	0.199493	−	0.979899i	$-0.436070\pi$
$421$	203447.	−	117460.i	1.14786	−	0.662716i	0.948364	+	0.317183i	$0.102737\pi$
$422$		0			0
$423$	102400.	+	177362.i	0.572293	+	0.991240i
$424$		0			0
$425$	−89421.9			−0.495069
$426$		0			0
$427$	23497.2	−	40698.4i	0.128873	−	0.223214i
$428$		0			0
$429$	−43476.7			−0.236234
$430$		0			0
$431$	−199518.	−	115192.i	−1.07406	−	0.620106i	−0.144769	−	0.989466i	$-0.546244\pi$
$431$	−199518.	−	115192.i	−1.07406	−	0.620106i	−0.929287	+	0.369359i	$0.879577\pi$
$432$		0			0
$433$	144263.	+	83290.1i	0.769447	+	0.444240i	0.832677	−	0.553759i	$-0.186807\pi$
$433$	144263.	+	83290.1i	0.769447	+	0.444240i	−0.0632306	+	0.997999i	$0.520140\pi$
$434$		0			0
$435$	−39794.4	−	68926.0i	−0.210302	−	0.364254i
$436$		0			0
$437$	−139288.	−	8280.33i	−0.729373	−	0.0433595i
$438$		0			0
$439$	−226379.	+	130700.i	−1.17465	+	0.678183i	−0.954770	−	0.297345i	$-0.903899\pi$
$439$	−226379.	+	130700.i	−1.17465	+	0.678183i	−0.219877	+	0.975528i	$0.570566\pi$
$440$		0			0
$441$	89493.6	−	155008.i	0.460166	−	0.797032i
$442$		0			0
$443$	−104145.	+	180384.i	−0.530676	+	0.919157i	0.468684	+	0.883366i	$0.344728\pi$
$443$	−104145.	+	180384.i	−0.530676	+	0.919157i	−0.999359	+	0.0357911i	$0.988605\pi$
$444$		0			0
$445$			318344.i			1.60759i
$446$		0			0
$447$	−68636.4	−	39627.3i	−0.343510	−	0.198326i
$448$		0			0
$449$			110756.i			0.549381i	0.961533	+	0.274691i	$0.0885754\pi$
$449$			110756.i			0.549381i	−0.961533	+	0.274691i	$0.911425\pi$
$450$		0			0
$451$	−205793.	+	118814.i	−1.01176	+	0.584139i
$452$		0			0
$453$	19131.5	+	33136.7i	0.0932293	+	0.161478i
$454$		0			0
$455$		−	32783.1i		−	0.158353i
$456$		0			0
$457$	−128375.			−0.614680			−0.307340	−	0.951600i	$-0.599439\pi$
$457$	−128375.			−0.614680			−0.307340	+	0.951600i	$0.599439\pi$
$458$		0			0
$459$	77565.6	−	44782.5i	0.368166	−	0.212561i
$460$		0			0
$461$	−1280.81	−	2218.42i	−0.00602674	−	0.0104386i	0.862996	−	0.505210i	$-0.168585\pi$
$461$	−1280.81	−	2218.42i	−0.00602674	−	0.0104386i	−0.869023	+	0.494772i	$0.835252\pi$
$462$		0			0
$463$	318274.			1.48470			0.742350	−	0.670012i	$-0.233711\pi$
$463$	318274.			1.48470			0.742350	+	0.670012i	$0.233711\pi$
$464$		0			0
$465$	20740.1	−	35922.9i	0.0959190	−	0.166137i
$466$		0			0
$467$	−262467.			−1.20349			−0.601743	−	0.798690i	$-0.705527\pi$
$467$	−262467.			−1.20349			−0.601743	+	0.798690i	$0.705527\pi$
$468$		0			0
$469$	30687.8	+	17717.6i	0.139515	+	0.0805489i
$470$		0			0
$471$	−69482.2	−	40115.6i	−0.313207	−	0.180830i
$472$		0			0
$473$	−99195.6	−	171812.i	−0.443374	−	0.767946i
$474$		0			0
$475$	126443.	+	7516.73i	0.560412	+	0.0333151i
$476$		0			0
$477$	149.792	−	86.4824i	0.000658342	−	0.000380094i
$478$		0			0
$479$	−102699.	+	177879.i	−0.447604	+	0.775273i	−0.998230	−	0.0594795i	$-0.981056\pi$
$479$	−102699.	+	177879.i	−0.447604	+	0.775273i	0.550626	+	0.834752i	$0.314389\pi$
$480$		0			0
$481$	28010.0	−	48514.8i	0.121066	−	0.209693i
$482$		0			0
$483$			5839.81i			0.0250325i
$484$		0			0
$485$	−257960.	−	148933.i	−1.09665	−	0.633152i
$486$		0			0
$487$			24740.3i			0.104315i	0.998639	+	0.0521576i	$0.0166098\pi$
$487$			24740.3i			0.104315i	−0.998639	+	0.0521576i	$0.983390\pi$
$488$		0			0
$489$	−12148.0	+	7013.65i	−0.0508028	+	0.0293310i
$490$		0			0
$491$	162868.	+	282096.i	0.675574	+	1.17013i	0.976301	+	0.216418i	$0.0694374\pi$
$491$	162868.	+	282096.i	0.675574	+	1.17013i	−0.300727	+	0.953710i	$0.597229\pi$
$492$		0			0
$493$		−	290045.i		−	1.19336i
$494$		0			0
$495$	296495.			1.21006
$496$		0			0
$497$	−14963.5	+	8639.21i	−0.0605789	+	0.0349753i
$498$		0			0
$499$	−42795.3	−	74123.6i	−0.171868	−	0.297684i	0.767205	−	0.641402i	$-0.221647\pi$
$499$	−42795.3	−	74123.6i	−0.171868	−	0.297684i	−0.939073	+	0.343718i	$0.888314\pi$
$500$		0			0
$501$	52082.2			0.207498
$502$		0			0
$503$	−102109.	+	176858.i	−0.403578	+	0.699017i	−0.994155	−	0.107964i	$-0.965567\pi$
$503$	−102109.	+	176858.i	−0.403578	+	0.699017i	0.590577	+	0.806981i	$0.298900\pi$
$504$		0			0
$505$	130357.			0.511153
$506$		0			0
$507$	8498.40	+	4906.56i	0.0330614	+	0.0190880i
$508$		0			0
$509$	309500.	+	178690.i	1.19461	+	0.689707i	0.959348	−	0.282226i	$-0.0910728\pi$
$509$	309500.	+	178690.i	1.19461	+	0.689707i	0.235259	+	0.971933i	$0.424406\pi$
$510$		0			0
$511$	744.448	+	1289.42i	0.00285097	+	0.00493802i
$512$		0			0
$513$	−113443.	+	56802.6i	−0.431063	+	0.215841i
$514$		0			0
$515$	−491019.	+	283490.i	−1.85133	+	1.06887i
$516$		0			0
$517$	168315.	−	291530.i	0.629711	−	1.09069i
$518$		0			0
$519$	−9261.33	+	16041.1i	−0.0343826	+	0.0595524i
$520$		0			0
$521$			279875.i			1.03107i	0.856868	+	0.515536i	$0.172407\pi$
$521$			279875.i			1.03107i	−0.856868	+	0.515536i	$0.827593\pi$
$522$		0			0
$523$	472250.	+	272654.i	1.72651	+	0.996800i	0.903221	+	0.429176i	$0.141196\pi$
$523$	472250.	+	272654.i	1.72651	+	0.996800i	0.823288	+	0.567625i	$0.192137\pi$
$524$		0			0
$525$		−	5301.27i		−	0.0192336i
$526$		0			0
$527$	130914.	−	75583.0i	0.471371	−	0.272146i
$528$		0			0
$529$	65221.7	+	112967.i	0.233067	+	0.403684i
$530$		0			0
$531$			306311.i			1.08636i
$532$		0			0
$533$	−295824.			−1.04131
$534$		0			0
$535$	−209605.	+	121015.i	−0.732308	+	0.422798i
$536$		0			0
$537$	48947.7	+	84779.8i	0.169740	+	0.293998i
$538$		0			0
$539$	−294202.			−1.01267
$540$		0			0
$541$	111400.	−	192950.i	0.380618	−	0.659249i	−0.610533	−	0.791991i	$-0.709045\pi$
$541$	111400.	−	192950.i	0.380618	−	0.659249i	0.991151	+	0.132742i	$0.0423780\pi$
$542$		0			0
$543$	−19828.9			−0.0672510
$544$		0			0
$545$	−163594.	−	94451.3i	−0.550777	−	0.317991i
$546$		0			0
$547$	28990.1	+	16737.5i	0.0968893	+	0.0559390i	0.547662	−	0.836700i	$-0.315518\pi$
$547$	28990.1	+	16737.5i	0.0968893	+	0.0559390i	−0.450772	+	0.892639i	$0.648851\pi$
$548$		0			0
$549$	264556.	+	458225.i	0.877756	+	1.52032i
$550$		0			0
$551$	−24381.0	+	410125.i	−0.0803059	+	1.35087i
$552$		0			0
$553$	−15184.1	+	8766.52i	−0.0496521	+	0.0286667i
$554$		0			0
$555$	12597.5	−	21819.6i	0.0408978	−	0.0708370i
$556$		0			0
$557$	175167.	−	303398.i	0.564601	−	0.977918i	−0.432485	−	0.901641i	$-0.642363\pi$
$557$	175167.	−	303398.i	0.564601	−	0.977918i	0.997087	−	0.0762774i	$-0.0243034\pi$
$558$		0			0
$559$		−	246977.i		−	0.790374i
$560$		0			0
$561$	−61712.4	−	35629.7i	−0.196086	−	0.113210i
$562$		0			0
$563$		−	510897.i		−	1.61182i	−0.592038	−	0.805910i	$-0.701676\pi$
$563$		−	510897.i		−	1.61182i	0.592038	−	0.805910i	$-0.298324\pi$
$564$		0			0
$565$	−256443.	+	148057.i	−0.803329	+	0.463802i
$566$		0			0
$567$	−18115.8	−	31377.4i	−0.0563496	−	0.0976004i
$568$		0			0
$569$			298435.i			0.921775i	0.887459	+	0.460887i	$0.152469\pi$
$569$			298435.i			0.921775i	−0.887459	+	0.460887i	$0.847531\pi$
$570$		0			0
$571$	411772.			1.26294			0.631472	−	0.775399i	$-0.282451\pi$
$571$	411772.			1.26294			0.631472	+	0.775399i	$0.282451\pi$
$572$		0			0
$573$	15387.4	−	8883.95i	0.0468659	−	0.0270581i
$574$		0			0
$575$	67810.2	+	117451.i	0.205097	+	0.355238i
$576$		0			0
$577$	454898.			1.36635			0.683176	−	0.730254i	$-0.260598\pi$
$577$	454898.			1.36635			0.683176	+	0.730254i	$0.260598\pi$
$578$		0			0
$579$	56296.4	−	97508.3i	0.167928	−	0.290860i
$580$		0			0
$581$	−50197.6			−0.148707
$582$		0			0
$583$	−246.213	−	142.151i	−0.000724393	−	0.000418228i
$584$		0			0
$585$	319655.	+	184553.i	0.934049	+	0.539273i
$586$		0			0
$587$	−18802.2	−	32566.4i	−0.0545673	−	0.0945133i	0.837451	−	0.546512i	$-0.184045\pi$
$587$	−18802.2	−	32566.4i	−0.0545673	−	0.0945133i	−0.892019	+	0.451998i	$0.850711\pi$
$588$		0			0
$589$	−191466.	+	95870.1i	−0.551900	+	0.276346i
$590$		0			0
$591$	37927.7	−	21897.6i	0.108588	−	0.0626933i
$592$		0			0
$593$	123237.	−	213453.i	0.350454	−	0.607004i	−0.635875	−	0.771792i	$-0.719361\pi$
$593$	123237.	−	213453.i	0.350454	−	0.607004i	0.986329	+	0.164788i	$0.0526939\pi$
$594$		0			0
$595$	26866.1	−	46533.5i	0.0758876	−	0.131441i
$596$		0			0
$597$			55588.6i			0.155969i
$598$		0			0
$599$	−70920.3	−	40945.9i	−0.197659	−	0.114119i	0.397904	−	0.917427i	$-0.369738\pi$
$599$	−70920.3	−	40945.9i	−0.197659	−	0.114119i	−0.595563	+	0.803308i	$0.703071\pi$
$600$		0			0
$601$			552301.i			1.52907i	0.644583	+	0.764534i	$0.277031\pi$
$601$			552301.i			1.52907i	−0.644583	+	0.764534i	$0.722969\pi$
$602$		0			0
$603$	−345516.	+	199483.i	−0.950239	+	0.548621i
$604$		0			0
$605$	−14989.2	−	25962.1i	−0.0409513	−	0.0709298i
$606$		0			0
$607$		−	123618.i		−	0.335509i	−0.985829	−	0.167755i	$-0.946348\pi$
$607$		−	123618.i		−	0.335509i	0.985829	−	0.167755i	$-0.0536516\pi$
$608$		0			0
$609$	17195.0			0.0463626
$610$		0			0
$611$	362925.	−	209535.i	0.972152	−	0.561272i
$612$		0			0
$613$	−333223.	−	577160.i	−0.886777	−	1.53594i	−0.843663	−	0.536873i	$-0.819606\pi$
$613$	−333223.	−	577160.i	−0.886777	−	1.53594i	−0.0431137	−	0.999070i	$-0.513728\pi$
$614$		0			0
$615$	−133047.			−0.351767
$616$		0			0
$617$	−29382.7	+	50892.4i	−0.0771831	+	0.133685i	−0.902034	−	0.431666i	$-0.857926\pi$
$617$	−29382.7	+	50892.4i	−0.0771831	+	0.133685i	0.824850	+	0.565351i	$0.191259\pi$
$618$		0			0
$619$	466387.			1.21721			0.608605	−	0.793473i	$-0.291729\pi$
$619$	466387.			1.21721			0.608605	+	0.793473i	$0.291729\pi$
$620$		0			0
$621$	−117639.	−	67918.8i	−0.305047	−	0.176119i
$622$		0			0
$623$	−59563.0	−	34388.7i	−0.153462	−	0.0886012i
$624$		0			0
$625$	243404.	+	421589.i	0.623115	+	1.07927i
$626$		0			0
$627$	84266.6	+	55568.0i	0.214348	+	0.141348i
$628$		0			0
$629$	79516.9	−	45909.1i	0.200982	−	0.116037i
$630$		0			0
$631$	−332333.	+	575618.i	−0.834671	+	1.44569i	0.0596278	+	0.998221i	$0.481009\pi$
$631$	−332333.	+	575618.i	−0.834671	+	1.44569i	−0.894298	+	0.447471i	$0.852325\pi$
$632$		0			0
$633$	24522.0	−	42473.3i	0.0611995	−	0.106001i
$634$		0			0
$635$		−	633729.i		−	1.57165i
$636$		0			0
$637$	−317183.	−	183126.i	−0.781683	−	0.451305i
$638$		0			0
$639$		−	194538.i		−	0.476435i
$640$		0			0
$641$	−643227.	+	371367.i	−1.56548	+	0.903831i	−0.568796	+	0.822478i	$0.692591\pi$
$641$	−643227.	+	371367.i	−1.56548	+	0.903831i	−0.996685	+	0.0813527i	$0.974076\pi$
$642$		0			0
$643$	93473.9	+	161902.i	0.226083	+	0.391588i	0.956644	−	0.291260i	$-0.0940745\pi$
$643$	93473.9	+	161902.i	0.226083	+	0.391588i	−0.730561	+	0.682848i	$0.760741\pi$
$644$		0			0
$645$		−	111078.i		−	0.266999i
$646$		0			0
$647$	476329.			1.13789			0.568943	−	0.822377i	$-0.307353\pi$
$647$	476329.			1.13789			0.568943	+	0.822377i	$0.307353\pi$
$648$		0			0
$649$	436030.	−	251742.i	1.03521	−	0.597677i
$650$		0			0
$651$	4480.85	+	7761.06i	0.0105730	+	0.0183130i
$652$		0			0
$653$	−740783.			−1.73726			−0.868630	−	0.495462i	$-0.834999\pi$
$653$	−740783.			−1.73726			−0.868630	+	0.495462i	$0.834999\pi$
$654$		0			0
$655$	354406.	−	613849.i	0.826073	−	1.43080i
$656$		0			0
$657$	−16763.5			−0.0388360
$658$		0			0
$659$	−686805.	−	396527.i	−1.58148	−	0.913066i	−0.994644	−	0.103358i	$-0.967041\pi$
$659$	−686805.	−	396527.i	−1.58148	−	0.913066i	−0.586833	−	0.809708i	$-0.699625\pi$
$660$		0			0
$661$	279193.	+	161192.i	0.639001	+	0.368927i	0.784230	−	0.620471i	$-0.213058\pi$
$661$	279193.	+	161192.i	0.639001	+	0.368927i	−0.145229	+	0.989398i	$0.546392\pi$
$662$		0			0
$663$	−44355.3	−	76825.7i	−0.100906	−	0.174775i
$664$		0			0
$665$	−41900.3	+	63540.1i	−0.0947489	+	0.143683i
$666$		0			0
$667$	−380958.	+	219946.i	−0.856299	+	0.494385i
$668$		0			0
$669$	−4195.72	+	7267.21i	−0.00937464	+	0.0162374i
$670$		0			0
$671$	434852.	−	753185.i	0.965820	−	1.67285i
$672$		0			0
$673$			66308.4i			0.146399i	0.997317	+	0.0731996i	$0.0233210\pi$
$673$			66308.4i			0.146399i	−0.997317	+	0.0731996i	$0.976679\pi$
$674$		0			0
$675$	106790.	+	61655.4i	0.234382	+	0.135321i
$676$		0			0
$677$			614850.i			1.34150i	0.741682	+	0.670752i	$0.234028\pi$
$677$			614850.i			1.34150i	−0.741682	+	0.670752i	$0.765972\pi$
$678$		0			0
$679$	55731.7	−	32176.7i	0.120882	−	0.0697914i
$680$		0			0
$681$	−77422.0	−	134099.i	−0.166944	−	0.289155i
$682$		0			0
$683$			386557.i			0.828652i	0.910129	+	0.414326i	$0.135983\pi$
$683$			386557.i			0.828652i	−0.910129	+	0.414326i	$0.864017\pi$
$684$		0			0
$685$	−106005.			−0.225915
$686$		0			0
$687$	8983.89	−	5186.85i	0.0190349	−	0.0109898i
$688$		0			0
$689$	−176.964	−	306.510i	−0.000372774	−	0.000645664i
$690$		0			0
$691$	−267742.			−0.560739			−0.280369	−	0.959892i	$-0.590457\pi$
$691$	−267742.			−0.560739			−0.280369	+	0.959892i	$0.590457\pi$
$692$		0			0
$693$	−32028.5	+	55475.0i	−0.0666914	+	0.115513i
$694$		0			0
$695$	−403042.			−0.834413
$696$		0			0
$697$	−419903.	−	242431.i	−0.864338	−	0.499026i
$698$		0			0
$699$	31371.8	+	18112.5i	0.0642075	+	0.0370702i
$700$		0			0
$701$	−187934.	−	325511.i	−0.382445	−	0.662415i	0.608966	−	0.793196i	$-0.291585\pi$
$701$	−187934.	−	325511.i	−0.382445	−	0.662415i	−0.991411	+	0.130782i	$0.958251\pi$
$702$		0			0
$703$	−116296.	+	58231.5i	−0.235318	+	0.117828i
$704$		0			0
$705$	163226.	−	94238.4i	0.328406	−	0.189605i
$706$		0			0
$707$	−14081.6	+	24390.1i	−0.0281718	+	0.0487950i
$708$		0			0
$709$	37666.3	−	65239.9i	0.0749308	−	0.129784i	−0.826125	−	0.563486i	$-0.809460\pi$
$709$	37666.3	−	65239.9i	0.0749308	−	0.129784i	0.901056	+	0.433702i	$0.142793\pi$
$710$		0			0
$711$		−	197405.i		−	0.390499i
$712$		0			0
$713$	−198548.	−	114632.i	−0.390559	−	0.225489i
$714$		0			0
$715$		−	606700.i		−	1.18676i
$716$		0			0
$717$	17717.6	−	10229.2i	0.0344640	−	0.0198978i
$718$		0			0
$719$	−347929.	−	602631.i	−0.673028	−	1.16572i	−0.977041	−	0.213051i	$-0.931660\pi$
$719$	−347929.	−	602631.i	−0.673028	−	1.16572i	0.304013	−	0.952668i	$-0.401673\pi$
$720$		0			0
$721$		−	122495.i		−	0.235639i
$722$		0			0
$723$	−87283.3			−0.166976
$724$		0			0
$725$	345827.	−	199663.i	0.657934	−	0.379859i
$726$		0			0
$727$	341985.	+	592336.i	0.647051	+	1.12072i	0.983824	+	0.179139i	$0.0573311\pi$
$727$	341985.	+	592336.i	0.647051	+	1.12072i	−0.336773	+	0.941586i	$0.609336\pi$
$728$		0			0
$729$	344207.			0.647686
$730$		0			0
$731$	202400.	−	350568.i	0.378771	−	0.656051i
$732$		0			0
$733$	−408184.			−0.759709			−0.379855	−	0.925046i	$-0.624026\pi$
$733$	−408184.			−0.759709			−0.379855	+	0.925046i	$0.624026\pi$
$734$		0			0
$735$	−142653.	−	82360.9i	−0.264063	−	0.152457i
$736$		0			0
$737$	567924.	+	327891.i	1.04558	+	0.603663i
$738$		0			0
$739$	−522561.	−	905102.i	−0.956859	−	1.65733i	−0.730056	−	0.683387i	$-0.760506\pi$
$739$	−522561.	−	905102.i	−0.956859	−	1.65733i	−0.226802	−	0.973941i	$-0.572827\pi$
$740$		0			0
$741$	56260.7	+	112360.i	0.102463	+	0.204633i
$742$		0			0
$743$	−680267.	+	392752.i	−1.23226	+	0.711444i	−0.967500	−	0.252870i	$-0.918625\pi$
$743$	−680267.	+	392752.i	−1.23226	+	0.711444i	−0.264758	+	0.964315i	$0.585292\pi$
$744$		0			0
$745$	552982.	−	957793.i	0.996319	−	1.72568i
$746$		0			0
$747$	282588.	−	489457.i	0.506422	−	0.877149i
$748$		0			0
$749$		−	52290.2i		−	0.0932088i
$750$		0			0
$751$	411795.	+	237750.i	0.730132	+	0.421542i	0.818470	−	0.574549i	$-0.194822\pi$
$751$	411795.	+	237750.i	0.730132	+	0.421542i	−0.0883387	+	0.996090i	$0.528156\pi$
$752$		0			0
$753$			95204.0i			0.167906i
$754$		0			0
$755$	−462409.	+	266972.i	−0.811209	+	0.468352i
$756$		0			0
$757$	−496513.	−	859985.i	−0.866440	−	1.50072i	−0.865610	−	0.500718i	$-0.833069\pi$
$757$	−496513.	−	859985.i	−0.866440	−	1.50072i	−0.000829615	−	1.00000i	$-0.500264\pi$
$758$		0			0
$759$			108074.i			0.187603i
$760$		0			0
$761$	−81817.3			−0.141278			−0.0706392	−	0.997502i	$-0.522504\pi$
$761$	−81817.3			−0.141278			−0.0706392	+	0.997502i	$0.522504\pi$
$762$		0			0
$763$	35344.2	−	20406.0i	0.0607113	−	0.0350517i
$764$		0			0
$765$	302487.	+	523922.i	0.516872	+	0.895249i
$766$		0			0
$767$	626787.			1.06544
$768$		0			0
$769$	−98144.6	+	169991.i	−0.165964	+	0.287458i	−0.936997	−	0.349337i	$-0.886407\pi$
$769$	−98144.6	+	169991.i	−0.165964	+	0.287458i	0.771033	+	0.636795i	$0.219740\pi$
$770$		0			0
$771$	196142.			0.329960
$772$		0			0
$773$	−821675.	−	474394.i	−1.37512	−	0.793927i	−0.383554	−	0.923518i	$-0.625300\pi$
$773$	−821675.	−	474394.i	−1.37512	−	0.793927i	−0.991567	+	0.129592i	$0.958633\pi$
$774$		0			0
$775$	180238.	+	104061.i	0.300085	+	0.173254i
$776$		0			0
$777$	2721.67	+	4714.07i	0.00450810	+	0.00780826i
$778$		0			0
$779$	573366.	+	378095.i	0.944838	+	0.623055i
$780$		0			0
$781$	−276923.	+	159881.i	−0.454001	+	0.262118i
$782$		0			0
$783$	−199983.	+	346381.i	−0.326189	+	0.564976i
$784$		0			0
$785$	559797.	−	969596.i	0.908429	−	1.57344i
$786$		0			0
$787$			994511.i			1.60568i	0.596192	+	0.802842i	$0.296680\pi$
$787$			994511.i			1.60568i	−0.596192	+	0.802842i	$0.703320\pi$
$788$		0			0
$789$	−119334.	−	68897.5i	−0.191695	−	0.110675i
$790$		0			0
$791$		−	63974.9i		−	0.102248i
$792$		0			0
$793$	937639.	−	541346.i	1.49104	−	0.860853i
$794$		0			0
$795$	−79.5896	−	137.853i	−0.000125928	−	0.000218114i
$796$		0			0
$797$			272658.i			0.429242i	0.976697	+	0.214621i	$0.0688516\pi$
$797$			272658.i			0.429242i	−0.976697	+	0.214621i	$0.931148\pi$
$798$		0			0
$799$	686865.			1.07591
$800$		0			0
$801$	670622.	−	387184.i	1.04523	−	0.603465i
$802$		0			0
$803$	13777.1	+	23862.7i	0.0213662	+	0.0370074i
$804$		0			0
$805$	−81492.2			−0.125755
$806$		0			0
$807$	−86704.3	+	150176.i	−0.133135	+	0.230597i
$808$		0			0
$809$	588970.			0.899903			0.449952	−	0.893053i	$-0.351441\pi$
$809$	588970.			0.899903			0.449952	+	0.893053i	$0.351441\pi$
$810$		0			0
$811$	699080.	+	403614.i	1.06288	+	0.613655i	0.926228	−	0.376964i	$-0.123032\pi$
$811$	699080.	+	403614.i	1.06288	+	0.613655i	0.136654	+	0.990619i	$0.456365\pi$
$812$		0			0
$813$	−217238.	−	125422.i	−0.328666	−	0.189755i
$814$		0			0
$815$	−97872.7	−	169520.i	−0.147349	−	0.255215i
$816$		0			0
$817$	−315663.	+	478691.i	−0.472912	+	0.717151i
$818$		0			0
$819$	−69060.7	+	39872.2i	−0.102959	+	0.0594433i
$820$		0			0
$821$	225213.	−	390081.i	0.334124	−	0.578719i	−0.649192	−	0.760624i	$-0.724893\pi$
$821$	225213.	−	390081.i	0.334124	−	0.578719i	0.983316	+	0.181905i	$0.0582263\pi$
$822$		0			0
$823$	212992.	−	368912.i	0.314458	−	0.544657i	−0.664864	−	0.746964i	$-0.731511\pi$
$823$	212992.	−	368912.i	0.314458	−	0.544657i	0.979322	+	0.202307i	$0.0648439\pi$
$824$		0			0
$825$		−	98108.0i		−	0.144144i
$826$		0			0
$827$	−1.00410e6	−	579720.i	−1.46814	−	0.847632i	−0.468778	−	0.883316i	$-0.655306\pi$
$827$	−1.00410e6	−	579720.i	−1.46814	−	0.847632i	−0.999363	+	0.0356845i	$0.988639\pi$
$828$		0			0
$829$		−	119777.i		−	0.174287i	−0.996196	−	0.0871436i	$-0.972226\pi$
$829$		−	119777.i		−	0.174287i	0.996196	−	0.0871436i	$-0.0277739\pi$
$830$		0			0
$831$	−249068.	+	143800.i	−0.360675	+	0.208236i
$832$		0			0
$833$	−300147.	−	519870.i	−0.432558	−	0.749212i
$834$		0			0
$835$			726785.i			1.04240i
$836$		0			0
$837$	−208455.			−0.297550
$838$		0			0
$839$	−1.17823e6	+	680253.i	−1.67381	+	0.966377i	−0.708342	+	0.705869i	$0.750557\pi$
$839$	−1.17823e6	+	680253.i	−1.67381	+	0.966377i	−0.965472	+	0.260508i	$0.916110\pi$
$840$		0			0
$841$	293979.	+	509186.i	0.415646	+	0.719920i
$842$		0			0
$843$	288752.			0.406322
$844$		0			0
$845$	−68469.0	+	118592.i	−0.0958915	+	0.166089i
$846$		0			0
$847$	6476.77			0.00902800
$848$		0			0
$849$	280735.	+	162082.i	0.389476	+	0.224864i
$850$		0			0
$851$	−120598.	−	69627.4i	−0.166526	−	0.0961437i
$852$		0			0
$853$	−406987.	−	704922.i	−0.559349	−	0.968820i	−0.997551	−	0.0699438i	$-0.977718\pi$
$853$	−406987.	−	704922.i	−0.559349	−	0.968820i	0.438202	−	0.898876i	$-0.355615\pi$
$854$		0			0
$855$	−383677.	−	766255.i	−0.524848	−	1.04819i
$856$		0			0
$857$	201512.	−	116343.i	0.274372	−	0.158409i	−0.356501	−	0.934295i	$-0.616030\pi$
$857$	201512.	−	116343.i	0.274372	−	0.158409i	0.630873	+	0.775886i	$0.282697\pi$
$858$		0			0
$859$	522786.	−	905492.i	0.708497	−	1.22715i	−0.256918	−	0.966433i	$-0.582707\pi$
$859$	522786.	−	905492.i	0.708497	−	1.22715i	0.965415	−	0.260719i	$-0.0839597\pi$
$860$		0			0
$861$	14372.3	−	24893.5i	0.0193874	−	0.0335799i
$862$		0			0
$863$		−	1.15469e6i		−	1.55040i	−0.631715	−	0.775200i	$-0.717649\pi$
$863$		−	1.15469e6i		−	1.55040i	0.631715	−	0.775200i	$-0.282351\pi$
$864$		0			0
$865$	−223847.	−	129238.i	−0.299171	−	0.172726i
$866$		0			0
$867$			41572.8i			0.0553058i
$868$		0			0
$869$	−281004.	+	162238.i	−0.372111	+	0.214838i
$870$		0			0
$871$	408191.	+	707008.i	0.538056	+	0.931940i
$872$		0			0
$873$			724558.i			0.950702i
$874$		0			0
$875$	−57795.2			−0.0754876
$876$		0			0
$877$	108941.	−	62897.4i	0.141643	−	0.0817774i	−0.427504	−	0.904013i	$-0.640607\pi$
$877$	108941.	−	62897.4i	0.141643	−	0.0817774i	0.569147	+	0.822236i	$0.307274\pi$
$878$		0			0
$879$	160032.	+	277183.i	0.207123	+	0.358747i
$880$		0			0
$881$	−170516.			−0.219692			−0.109846	−	0.993949i	$-0.535036\pi$
$881$	−170516.			−0.219692			−0.109846	+	0.993949i	$0.535036\pi$
$882$		0			0
$883$	−418950.	+	725643.i	−0.537330	+	0.930683i	0.461717	+	0.887028i	$0.347234\pi$
$883$	−418950.	+	725643.i	−0.537330	+	0.930683i	−0.999047	+	0.0436555i	$0.986100\pi$
$884$		0			0
$885$	281898.			0.359919
$886$		0			0
$887$	−1.16240e6	−	671114.i	−1.47744	−	0.853000i	−0.477764	−	0.878488i	$-0.658553\pi$
$887$	−1.16240e6	−	671114.i	−1.47744	−	0.853000i	−0.999675	+	0.0254881i	$0.991886\pi$
$888$		0			0
$889$	118573.	+	68457.9i	0.150031	+	0.0866203i
$890$		0			0
$891$	−335260.	−	580687.i	−0.422305	−	0.731453i
$892$		0			0
$893$	−971230.	−	57737.3i	−1.21792	−	0.0724025i
$894$		0			0
$895$	−1.18307e6	+	683044.i	−1.47694	+	0.852713i
$896$		0			0
$897$	−67270.9	+	116517.i	−0.0836069	+	0.144811i
$898$		0			0
$899$	−337527.	+	584613.i	−0.417627	+	0.723352i
$900$		0			0
$901$		−	580.096i		−	0.000714579i
$902$		0			0
$903$	20783.0	+	11999.1i	0.0254878	+	0.0147154i
$904$		0			0
$905$		−	276704.i		−	0.337846i
$906$		0			0
$907$	72775.9	−	42017.2i	0.0884653	−	0.0510755i	−0.455115	−	0.890433i	$-0.650402\pi$
$907$	72775.9	−	42017.2i	0.0884653	−	0.0510755i	0.543580	+	0.839357i	$0.317068\pi$
$908$		0			0
$909$	−158546.	−	274609.i	−0.191879	−	0.332344i
$910$		0			0
$911$			429356.i			0.517345i	0.965965	+	0.258673i	$0.0832851\pi$
$911$			429356.i			0.517345i	−0.965965	+	0.258673i	$0.916715\pi$
$912$		0			0
$913$	−928981.			−1.11446
$914$		0			0
$915$	421704.	−	243471.i	0.503693	−	0.290807i
$916$		0			0
$917$	76568.6	+	132621.i	0.0910567	+	0.157715i
$918$		0			0
$919$	826582.			0.978711			0.489356	−	0.872084i	$-0.337232\pi$
$919$	826582.			0.978711			0.489356	+	0.872084i	$0.337232\pi$
$920$		0			0
$921$	121054.	−	209671.i	0.142712	−	0.247184i
$922$		0			0
$923$	−398072.			−0.467260
$924$		0			0
$925$	109477.	+	63206.5i	0.127950	+	0.0738717i
$926$		0			0
$927$	1.19440e6	+	689587.i	1.38992	+	0.802471i
$928$		0			0
$929$	755950.	+	1.30934e6i	0.875915	+	1.51713i	0.855785	+	0.517332i	$0.173075\pi$
$929$	755950.	+	1.30934e6i	0.875915	+	1.51713i	0.0201297	+	0.999797i	$0.493592\pi$
$930$		0			0
$931$	380709.	+	760329.i	0.439232	+	0.877207i
$932$		0			0
$933$	−224686.	+	129722.i	−0.258115	+	0.149023i
$934$		0			0
$935$	497198.	−	861172.i	0.568730	−	0.985069i
$936$		0			0
$937$	−278250.	+	481942.i	−0.316924	+	0.548929i	−0.979845	−	0.199761i	$-0.935983\pi$
$937$	−278250.	+	481942.i	−0.316924	+	0.548929i	0.662920	+	0.748690i	$0.269317\pi$
$938$		0			0
$939$		−	260643.i		−	0.295607i
$940$		0			0
$941$	127927.	+	73858.6i	0.144471	+	0.0834107i	0.570493	−	0.821302i	$-0.306752\pi$
$941$	127927.	+	73858.6i	0.144471	+	0.0834107i	−0.426022	+	0.904713i	$0.640085\pi$
$942$		0			0
$943$			735360.i			0.826945i
$944$		0			0
$945$	−64168.7	+	37047.8i	−0.0718554	+	0.0414857i
$946$		0			0
$947$	805825.	+	1.39573e6i	0.898547	+	1.55633i	0.829353	+	0.558725i	$0.188709\pi$
$947$	805825.	+	1.39573e6i	0.898547	+	1.55633i	0.0691937	+	0.997603i	$0.477957\pi$
$948$		0			0
$949$			34302.2i			0.0380882i
$950$		0			0
$951$	−62605.2			−0.0692228
$952$		0			0
$953$	−468828.	+	270678.i	−0.516211	+	0.298035i	−0.735383	−	0.677651i	$-0.762998\pi$
$953$	−468828.	+	270678.i	−0.516211	+	0.298035i	0.219172	+	0.975686i	$0.429664\pi$
$954$		0			0
$955$	123972.	+	214726.i	0.135930	+	0.235438i
$956$		0			0
$957$	318219.			0.347458
$958$		0			0
$959$	11451.1	−	19833.9i	0.0124512	−	0.0215660i
$960$		0			0
$961$	571696.			0.619040
$962$		0			0
$963$	509862.	+	294369.i	0.549794	+	0.317424i
$964$		0			0
$965$	1.36069e6	+	785593.i	1.46118	+	0.843613i
$966$		0			0
$967$	−300748.	−	520910.i	−0.321624	−	0.557070i	0.659199	−	0.751969i	$-0.270896\pi$
$967$	−300748.	−	520910.i	−0.321624	−	0.557070i	−0.980823	+	0.194899i	$0.937562\pi$
$968$		0			0
$969$	−12222.1	+	205595.i	−0.0130166	+	0.218960i
$970$		0			0
$971$	330430.	−	190774.i	0.350463	−	0.202340i	−0.314426	−	0.949282i	$-0.601812\pi$
$971$	330430.	−	190774.i	0.350463	−	0.202340i	0.664889	+	0.746942i	$0.268479\pi$
$972$		0			0
$973$	43538.2	−	75410.4i	0.0459880	−	0.0796536i
$974$		0			0
$975$	61067.3	−	105772.i	0.0642391	−	0.111265i
$976$		0			0
$977$			445014.i			0.466213i	0.972451	+	0.233106i	$0.0748890\pi$
$977$			445014.i			0.466213i	−0.972451	+	0.233106i	$0.925111\pi$
$978$		0			0
$979$	−1.10230e6	−	636415.i	−1.15010	−	0.664010i
$980$		0			0
$981$			459504.i			0.477476i
$982$		0			0
$983$	470900.	−	271874.i	0.487329	−	0.281359i	−0.236137	−	0.971720i	$-0.575881\pi$
$983$	470900.	−	271874.i	0.487329	−	0.281359i	0.723466	+	0.690360i	$0.242548\pi$
$984$		0			0
$985$	305572.	+	529266.i	0.314949	+	0.545508i
$986$		0			0
$987$			40720.0i			0.0417997i
$988$		0			0
$989$	−613935.			−0.627668
$990$		0			0
$991$	527372.	−	304478.i	0.536994	−	0.310034i	−0.206866	−	0.978369i	$-0.566326\pi$
$991$	527372.	−	304478.i	0.536994	−	0.310034i	0.743860	+	0.668336i	$0.232993\pi$
$992$		0			0
$993$	114076.	+	197585.i	0.115690	+	0.200381i
$994$		0			0
$995$	−775717.			−0.783532
$996$		0			0
$997$	−563173.	+	975445.i	−0.566568	+	0.981324i	0.430334	+	0.902670i	$0.358396\pi$
$997$	−563173.	+	975445.i	−0.566568	+	0.981324i	−0.996902	+	0.0786545i	$0.974938\pi$
$998$		0			0
$999$	−126615.			−0.126869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.10		40
4.3	odd	2		152.5.n.a.145.11	yes	40
19.8	odd	6	inner	304.5.r.d.65.10		40
76.27	even	6		152.5.n.a.65.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.11	✓	40	76.27	even	6
152.5.n.a.145.11	yes	40	4.3	odd	2
304.5.r.d.65.10		40	19.8	odd	6	inner
304.5.r.d.145.10		40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93870 + 1.11931i) q^{3} +(-15.6195 - 27.0538i) q^{5} +6.74912 q^{7} +(-37.9943 + 65.8080i) q^{9} +O(q^{10})\)	\(q+(-1.93870 + 1.11931i) q^{3} +(-15.6195 - 27.0538i) q^{5} +6.74912 q^{7} +(-37.9943 + 65.8080i) q^{9} +124.903 q^{11} +(134.659 + 77.7455i) q^{13} +(60.5631 + 34.9661i) q^{15} +(127.427 + 220.710i) q^{17} +(-161.629 - 322.796i) q^{19} +(-13.0845 + 7.55435i) q^{21} +(193.260 - 334.736i) q^{23} +(-175.438 + 303.867i) q^{25} -351.438i q^{27} +(-985.611 - 569.043i) q^{29} -593.148i q^{31} +(-242.149 + 139.805i) q^{33} +(-105.418 - 182.589i) q^{35} -360.278i q^{37} -348.085 q^{39} +(-1647.63 + 951.257i) q^{41} +(-794.184 - 1375.57i) q^{43} +2373.81 q^{45} +(1347.57 - 2334.06i) q^{47} -2355.45 q^{49} +(-494.085 - 285.260i) q^{51} +(-1.97124 - 1.13810i) q^{53} +(-1950.92 - 3379.09i) q^{55} +(674.659 + 444.891i) q^{57} +(3490.96 - 2015.51i) q^{59} +(3481.53 - 6030.18i) q^{61} +(-256.428 + 444.146i) q^{63} -4857.38i q^{65} +(4546.94 + 2625.18i) q^{67} +865.270i q^{69} +(-2217.11 + 1280.05i) q^{71} +(110.303 + 191.050i) q^{73} -785.477i q^{75} +842.982 q^{77} +(-2249.78 + 1298.91i) q^{79} +(-2684.17 - 4649.12i) q^{81} -7437.65 q^{83} +(3980.68 - 6894.75i) q^{85} +2547.74 q^{87} +(-8825.30 - 5095.29i) q^{89} +(908.830 + 524.713i) q^{91} +(663.917 + 1149.94i) q^{93} +(-6208.27 + 9414.59i) q^{95} +(8257.62 - 4767.54i) q^{97} +(-4745.58 + 8219.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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